From 293d30f0a2a4756db591e83e93eae24681e0ec7a Mon Sep 17 00:00:00 2001
From: dkf <donal.k.fellows@manchester.ac.uk>
Date: Sat, 11 Feb 2017 21:36:36 +0000
Subject: Proposed implementation of [regsub -command].

---
 generic/tclCmdMZ.c    | 82 +++++++++++++++++++++++++++++++++++++++++++++++----
 tests/regexp.test     | 22 +++++++++++++-
 tests/regexpComp.test |  2 +-
 3 files changed, 98 insertions(+), 8 deletions(-)

diff --git a/generic/tclCmdMZ.c b/generic/tclCmdMZ.c
index ba1fc41..ffae8b2 100644
--- a/generic/tclCmdMZ.c
+++ b/generic/tclCmdMZ.c
@@ -487,26 +487,28 @@ Tcl_RegsubObjCmd(
     Tcl_Obj *const objv[])	/* Argument objects. */
 {
     int idx, result, cflags, all, wlen, wsublen, numMatches, offset;
-    int start, end, subStart, subEnd, match;
+    int start, end, subStart, subEnd, match, command;
     Tcl_RegExp regExpr;
     Tcl_RegExpInfo info;
     Tcl_Obj *resultPtr, *subPtr, *objPtr, *startIndex = NULL;
+    Tcl_Obj **args = NULL, *parts[2], *cmdObj;
     Tcl_UniChar ch, *wsrc, *wfirstChar, *wstring, *wsubspec, *wend;
 
     static const char *const options[] = {
-	"-all",		"-nocase",	"-expanded",
-	"-line",	"-linestop",	"-lineanchor",	"-start",
+	"-all",		"-command",	"-expanded",	"-line",
+	"-linestop",	"-lineanchor",	"-nocase",	"-start",
 	"--",		NULL
     };
     enum options {
-	REGSUB_ALL,	REGSUB_NOCASE,	REGSUB_EXPANDED,
-	REGSUB_LINE,	REGSUB_LINESTOP, REGSUB_LINEANCHOR,	REGSUB_START,
+	REGSUB_ALL, REGSUB_COMMAND, REGSUB_EXPANDED, REGSUB_LINE,
+	REGSUB_LINESTOP, REGSUB_LINEANCHOR, REGSUB_NOCASE, REGSUB_START,
 	REGSUB_LAST
     };
 
     cflags = TCL_REG_ADVANCED;
     all = 0;
     offset = 0;
+    command = 0;
     resultPtr = NULL;
 
     for (idx = 1; idx < objc; idx++) {
@@ -528,6 +530,9 @@ Tcl_RegsubObjCmd(
 	case REGSUB_NOCASE:
 	    cflags |= TCL_REG_NOCASE;
 	    break;
+	case REGSUB_COMMAND:
+	    command = 1;
+	    break;
 	case REGSUB_EXPANDED:
 	    cflags |= TCL_REG_EXPANDED;
 	    break;
@@ -585,7 +590,7 @@ Tcl_RegsubObjCmd(
 	}
     }
 
-    if (all && (offset == 0)
+    if (all && (offset == 0) && (command == 0)
 	    && (strpbrk(TclGetString(objv[2]), "&\\") == NULL)
 	    && (strpbrk(TclGetString(objv[0]), "*+?{}()[].\\|^$") == NULL)) {
 	/*
@@ -737,6 +742,68 @@ Tcl_RegsubObjCmd(
 	Tcl_AppendUnicodeToObj(resultPtr, wstring + offset, start);
 
 	/*
+	 * In -command mode, the substitutions are added as quoted arguments
+	 * to the subSpec to form a command, that is then executed and the
+	 * result used as the string to substitute in.
+	 */
+
+	if (command) {
+	    if (args == NULL) {
+		args = ckalloc(sizeof(Tcl_Obj*) * (info.nsubs + 1));
+	    }
+
+	    for (idx = 0 ; idx <= info.nsubs ; idx++) {
+		subStart = info.matches[idx].start;
+		subEnd = info.matches[idx].end;
+		if ((subStart >= 0) && (subEnd >= 0)) {
+		    args[idx] = Tcl_NewUnicodeObj(
+			    wstring + offset + subStart, subEnd - subStart);
+		} else {
+		    args[idx] = Tcl_NewObj();
+		}
+	    }
+	    parts[0] = subPtr;
+	    parts[1] = Tcl_NewListObj(info.nsubs+1, args);
+	    cmdObj = Tcl_ConcatObj(2, parts);
+	    Tcl_IncrRefCount(cmdObj);
+	    Tcl_DecrRefCount(parts[1]);
+
+	    result = Tcl_EvalObjEx(interp, cmdObj, TCL_EVAL_DIRECT);
+	    Tcl_DecrRefCount(cmdObj);
+	    if (result != TCL_OK) {
+		if (result == TCL_ERROR) {
+		    Tcl_AppendObjToErrorInfo(interp, Tcl_ObjPrintf(
+			    "\n    (%s substitution computation script)",
+			    options[REGSUB_COMMAND]));
+		}
+		goto done;
+	    }
+
+	    Tcl_AppendObjToObj(resultPtr, Tcl_GetObjResult(interp));
+	    Tcl_ResetResult(interp);
+
+	    offset += end;
+	    if (end == 0 || start == end) {
+		/*
+		 * Always consume at least one character of the input string
+		 * in order to prevent infinite loops, even when we
+		 * technically matched the empty string; we must not match
+		 * again at the same spot.
+		 */
+
+		if (offset < wlen) {
+		    Tcl_AppendUnicodeToObj(resultPtr, wstring + offset, 1);
+		}
+		offset++;
+	    }
+	    if (all) {
+		continue;
+	    } else {
+		break;
+	    }
+	}
+
+	/*
 	 * Append the subSpec argument to the variable, making appropriate
 	 * substitutions. This code is a bit hairy because of the backslash
 	 * conventions and because the code saves up ranges of characters in
@@ -864,6 +931,9 @@ Tcl_RegsubObjCmd(
     if (subPtr && (objv[2] == objv[0])) {
 	Tcl_DecrRefCount(subPtr);
     }
+    if (args) {
+	ckfree(args);
+    }
     if (resultPtr) {
 	Tcl_DecrRefCount(resultPtr);
     }
diff --git a/tests/regexp.test b/tests/regexp.test
index 4ffdbdb..6c77b41 100644
--- a/tests/regexp.test
+++ b/tests/regexp.test
@@ -453,7 +453,7 @@ test regexp-11.4 {regsub errors} {
 } {1 {wrong # args: should be "regsub ?-option ...? exp string subSpec ?varName?"}}
 test regexp-11.5 {regsub errors} {
     list [catch {regsub -gorp a b c} msg] $msg
-} {1 {bad option "-gorp": must be -all, -nocase, -expanded, -line, -linestop, -lineanchor, -start, or --}}
+} {1 {bad option "-gorp": must be -all, -command, -expanded, -line, -linestop, -lineanchor, -nocase, -start, or --}}
 test regexp-11.6 {regsub errors} {
     list [catch {regsub -nocase a( b c d} msg] $msg
 } {1 {couldn't compile regular expression pattern: parentheses () not balanced}}
@@ -1123,6 +1123,26 @@ test regexp-26.12 {regexp with -line option} {
 test regexp-26.13 {regexp without -line option} {
     regexp -all -inline -- {a*} "b\n"
 } {{} {}}
+
+test regexp-27.1 {regsub -command} {
+    regsub -command {.x.} {abcxdef} {string length}
+} ab3ef
+test regexp-27.2 {regsub -command} {
+    regsub -command {.x.} {abcxdefxghi} {string length}
+} ab3efxghi
+test regexp-27.3 {regsub -command} {
+    set x 0
+    regsub -all -command {(?=.)} abcde "incr x;#"
+} 1a2b3c4d5e
+test regexp-27.4 {regsub -command} -body {
+    regsub -command {.x.} {abcxdef} error
+} -returnCodes error -result cxd
+test regexp-27.5 {regsub -command} {
+    regsub -command {(.)(.)} {abcdef} {list ,}
+} {, ab a bcdef}
+test regexp-27.6 {regsub -command} {
+    regsub -command -all {(.)(.)} {abcdef} {list ,}
+} {, ab a b, cd c d, ef e f}
 
 # cleanup
 ::tcltest::cleanupTests
diff --git a/tests/regexpComp.test b/tests/regexpComp.test
index b8e64b6..fbf8012 100644
--- a/tests/regexpComp.test
+++ b/tests/regexpComp.test
@@ -587,7 +587,7 @@ test regexpComp-11.5 {regsub errors} {
     evalInProc {
 	list [catch {regsub -gorp a b c} msg] $msg
     }
-} {1 {bad option "-gorp": must be -all, -nocase, -expanded, -line, -linestop, -lineanchor, -start, or --}}
+} {1 {bad option "-gorp": must be -all, -command, -expanded, -line, -linestop, -lineanchor, -nocase, -start, or --}}
 test regexpComp-11.6 {regsub errors} {
     evalInProc {
 	list [catch {regsub -nocase a( b c d} msg] $msg
-- 
cgit v0.12


From 203058f02d4fbfde79ae5a95f9648f61681a36fa Mon Sep 17 00:00:00 2001
From: dkf <donal.k.fellows@manchester.ac.uk>
Date: Fri, 17 Feb 2017 06:08:18 +0000
Subject: Switch to using command prefixes properly. This is quite a bit
 faster.

---
 generic/tclCmdMZ.c | 63 +++++++++++++++++++++++++++++++++++++++---------------
 tests/regexp.test  |  2 +-
 2 files changed, 47 insertions(+), 18 deletions(-)

diff --git a/generic/tclCmdMZ.c b/generic/tclCmdMZ.c
index ffae8b2..d6d0152 100644
--- a/generic/tclCmdMZ.c
+++ b/generic/tclCmdMZ.c
@@ -487,11 +487,11 @@ Tcl_RegsubObjCmd(
     Tcl_Obj *const objv[])	/* Argument objects. */
 {
     int idx, result, cflags, all, wlen, wsublen, numMatches, offset;
-    int start, end, subStart, subEnd, match, command;
+    int start, end, subStart, subEnd, match, command, numParts, numArgs;
     Tcl_RegExp regExpr;
     Tcl_RegExpInfo info;
     Tcl_Obj *resultPtr, *subPtr, *objPtr, *startIndex = NULL;
-    Tcl_Obj **args = NULL, *parts[2], *cmdObj;
+    Tcl_Obj **args = NULL, **parts;
     Tcl_UniChar ch, *wsrc, *wfirstChar, *wstring, *wsubspec, *wend;
 
     static const char *const options[] = {
@@ -666,6 +666,20 @@ Tcl_RegsubObjCmd(
 	return TCL_ERROR;
     }
 
+    if (command) {
+	/*
+	 * In command-prefix mode, we require that the third non-option
+	 * argument be a list, so we enforce that here. Afterwards, we fetch
+	 * the RE compilation again in case objv[0] and objv[2] are the same
+	 * object. (If they aren't, that's cheap to do.)
+	 */
+
+	if (Tcl_ListObjLength(interp, objv[2], &numParts) != TCL_OK) {
+	    return TCL_ERROR;
+	}
+	regExpr = Tcl_GetRegExpFromObj(interp, objv[0], cflags);
+    }
+
     /*
      * Make sure to avoid problems where the objects are shared. This can
      * cause RegExpObj <> UnicodeObj shimmering that causes data corruption.
@@ -683,7 +697,9 @@ Tcl_RegsubObjCmd(
     } else {
 	subPtr = objv[2];
     }
-    wsubspec = Tcl_GetUnicodeFromObj(subPtr, &wsublen);
+    if (!command) {
+	wsubspec = Tcl_GetUnicodeFromObj(subPtr, &wsublen);
+    }
 
     result = TCL_OK;
 
@@ -742,34 +758,47 @@ Tcl_RegsubObjCmd(
 	Tcl_AppendUnicodeToObj(resultPtr, wstring + offset, start);
 
 	/*
-	 * In -command mode, the substitutions are added as quoted arguments
-	 * to the subSpec to form a command, that is then executed and the
-	 * result used as the string to substitute in.
+	 * In command-prefix mode, the substitutions are added as quoted
+	 * arguments to the subSpec to form a command, that is then executed
+	 * and the result used as the string to substitute in. Actually,
+	 * everything is passed through Tcl_EvalObjv, as that's much faster.
 	 */
 
 	if (command) {
 	    if (args == NULL) {
-		args = ckalloc(sizeof(Tcl_Obj*) * (info.nsubs + 1));
+		Tcl_ListObjGetElements(interp, subPtr, &numParts, &parts);
+		numArgs = numParts + info.nsubs + 1;
+		args = ckalloc(sizeof(Tcl_Obj*) * numArgs);
+		memcpy(args, parts, sizeof(Tcl_Obj*) * numParts);
 	    }
 
 	    for (idx = 0 ; idx <= info.nsubs ; idx++) {
 		subStart = info.matches[idx].start;
 		subEnd = info.matches[idx].end;
 		if ((subStart >= 0) && (subEnd >= 0)) {
-		    args[idx] = Tcl_NewUnicodeObj(
+		    args[idx + numParts] = Tcl_NewUnicodeObj(
 			    wstring + offset + subStart, subEnd - subStart);
 		} else {
-		    args[idx] = Tcl_NewObj();
+		    args[idx + numParts] = Tcl_NewObj();
 		}
+		Tcl_IncrRefCount(args[idx + numParts]);
+	    }
+
+	    /*
+	     * At this point, we're locally holding the references to the
+	     * argument words we added for this time round the loop, and the
+	     * subPtr is holding the references to the words that the user
+	     * supplied directly. None are zero-refcount, which is important
+	     * because Tcl_EvalObjv is "hairy monster" in terms of refcount
+	     * handling, being able to optionally add references to any of its
+	     * argument words. We'll drop the local refs immediately
+	     * afterwarsds; subPtr is handled in the main exit stanza.
+	     */
+
+	    result = Tcl_EvalObjv(interp, numArgs, args, 0);
+	    for (idx = 0 ; idx <= info.nsubs ; idx++) {
+		TclDecrRefCount(args[idx + numParts]);
 	    }
-	    parts[0] = subPtr;
-	    parts[1] = Tcl_NewListObj(info.nsubs+1, args);
-	    cmdObj = Tcl_ConcatObj(2, parts);
-	    Tcl_IncrRefCount(cmdObj);
-	    Tcl_DecrRefCount(parts[1]);
-
-	    result = Tcl_EvalObjEx(interp, cmdObj, TCL_EVAL_DIRECT);
-	    Tcl_DecrRefCount(cmdObj);
 	    if (result != TCL_OK) {
 		if (result == TCL_ERROR) {
 		    Tcl_AppendObjToErrorInfo(interp, Tcl_ObjPrintf(
diff --git a/tests/regexp.test b/tests/regexp.test
index 6c77b41..6c3d774 100644
--- a/tests/regexp.test
+++ b/tests/regexp.test
@@ -1132,7 +1132,7 @@ test regexp-27.2 {regsub -command} {
 } ab3efxghi
 test regexp-27.3 {regsub -command} {
     set x 0
-    regsub -all -command {(?=.)} abcde "incr x;#"
+    regsub -all -command {(?=.)} abcde {apply {args {incr ::x}}}
 } 1a2b3c4d5e
 test regexp-27.4 {regsub -command} -body {
     regsub -command {.x.} {abcxdef} error
-- 
cgit v0.12


From 4d7b9162e578238f275688adcef5d56242b8ae7e Mon Sep 17 00:00:00 2001
From: dkf <donal.k.fellows@manchester.ac.uk>
Date: Fri, 17 Feb 2017 09:20:49 +0000
Subject: Stop problems with representation smashes.

---
 generic/tclCmdMZ.c | 7 +++++++
 tests/regexp.test  | 6 ++++++
 2 files changed, 13 insertions(+)

diff --git a/generic/tclCmdMZ.c b/generic/tclCmdMZ.c
index d6d0152..110de4c 100644
--- a/generic/tclCmdMZ.c
+++ b/generic/tclCmdMZ.c
@@ -811,6 +811,13 @@ Tcl_RegsubObjCmd(
 	    Tcl_AppendObjToObj(resultPtr, Tcl_GetObjResult(interp));
 	    Tcl_ResetResult(interp);
 
+	    /*
+	     * Refetch the unicode, in case the representation was smashed by
+	     * the user code.
+	     */
+
+	    wstring = Tcl_GetUnicodeFromObj(objPtr, &wlen);
+
 	    offset += end;
 	    if (end == 0 || start == end) {
 		/*
diff --git a/tests/regexp.test b/tests/regexp.test
index 6c3d774..ad770fa 100644
--- a/tests/regexp.test
+++ b/tests/regexp.test
@@ -1143,6 +1143,12 @@ test regexp-27.5 {regsub -command} {
 test regexp-27.6 {regsub -command} {
     regsub -command -all {(.)(.)} {abcdef} {list ,}
 } {, ab a b, cd c d, ef e f}
+test regexp-27.7 {regsub -command representation smash} {
+    set ::s {123=456 789}
+    regsub -command -all {\d+} $::s {apply {n {
+	expr {[llength $::s] + $n}
+    }}}
+} {125=458 791}
 
 # cleanup
 ::tcltest::cleanupTests
-- 
cgit v0.12


From 768fa857c25a31f96cfdfeeb34e8628f68ddb7ba Mon Sep 17 00:00:00 2001
From: dkf <donal.k.fellows@manchester.ac.uk>
Date: Sat, 18 Feb 2017 14:26:34 +0000
Subject: Add more representation smashing testing and a memleak test.

---
 tests/regexp.test | 29 +++++++++++++++++++++++++++++
 1 file changed, 29 insertions(+)

diff --git a/tests/regexp.test b/tests/regexp.test
index ad770fa..f1be6eb 100644
--- a/tests/regexp.test
+++ b/tests/regexp.test
@@ -19,6 +19,20 @@ if {"::tcltest" ni [namespace children]} {
 unset -nocomplain foo
 
 testConstraint exec [llength [info commands exec]]
+
+# Used for constraining memory leak tests
+testConstraint memory [llength [info commands memory]]
+if {[testConstraint memory]} {
+    proc memtest script {
+	set end [lindex [split [memory info] \n] 3 3]
+	for {set i 0} {$i < 5} {incr i} {
+	    uplevel 1 $script
+	    set tmp $end
+	    set end [lindex [split [memory info] \n] 3 3]
+	}
+	expr {$end - $tmp}
+    }
+}
 
 test regexp-1.1 {basic regexp operation} {
     regexp ab*c abbbc
@@ -1149,6 +1163,21 @@ test regexp-27.7 {regsub -command representation smash} {
 	expr {[llength $::s] + $n}
     }}}
 } {125=458 791}
+test regexp-27.8 {regsub -command representation smash} {
+    set ::t {apply {n {
+	expr {[llength [lindex $::t 1 1 1]] + $n}
+    }}}
+    regsub -command -all {\d+} "123=456 789" $::t
+} {131=464 797}
+test regexp-27.9 {regsub -command memory leak testing} memory {
+    set ::s "123=456 789"
+    set ::t {apply {n {
+	expr {[llength [lindex $::t 1 1 1]] + [llength $::s] + $n}
+    }}}
+    memtest {
+	regsub -command -all {\d+} $::s $::t
+    }
+} 0
 
 # cleanup
 ::tcltest::cleanupTests
-- 
cgit v0.12


From fcf8e64d6b12e1682af90b9e25b364e22d04c7bf Mon Sep 17 00:00:00 2001
From: dkf <donal.k.fellows@manchester.ac.uk>
Date: Sat, 18 Feb 2017 16:24:09 +0000
Subject: Testing for some error cases.

---
 generic/tclCmdMZ.c | 8 ++++++++
 tests/regexp.test  | 6 ++++++
 2 files changed, 14 insertions(+)

diff --git a/generic/tclCmdMZ.c b/generic/tclCmdMZ.c
index 110de4c..d5a6b01 100644
--- a/generic/tclCmdMZ.c
+++ b/generic/tclCmdMZ.c
@@ -677,6 +677,14 @@ Tcl_RegsubObjCmd(
 	if (Tcl_ListObjLength(interp, objv[2], &numParts) != TCL_OK) {
 	    return TCL_ERROR;
 	}
+	if (numParts < 1) {
+	    Tcl_SetObjResult(interp, Tcl_NewStringObj(
+		    "command prefix must be a list of at least one element",
+		    -1));
+	    Tcl_SetErrorCode(interp, "TCL", "OPERATION", "REGSUB",
+		    "CMDEMPTY", NULL);
+	    return TCL_ERROR;
+	}
 	regExpr = Tcl_GetRegExpFromObj(interp, objv[0], cflags);
     }
 
diff --git a/tests/regexp.test b/tests/regexp.test
index f1be6eb..2686526 100644
--- a/tests/regexp.test
+++ b/tests/regexp.test
@@ -1178,6 +1178,12 @@ test regexp-27.9 {regsub -command memory leak testing} memory {
 	regsub -command -all {\d+} $::s $::t
     }
 } 0
+test regexp-27.10 {regsub -command error cases} -returnCodes error -body {
+    regsub -command . abc "def \{ghi"
+} -result {unmatched open brace in list}
+test regexp-27.11 {regsub -command error cases} -returnCodes error -body {
+    regsub -command . abc {}
+} -result {command prefix must be a list of at least one element}
 
 # cleanup
 ::tcltest::cleanupTests
-- 
cgit v0.12


From 6aa0cc7188b6df1dac97b03bc0b9240aa780799b Mon Sep 17 00:00:00 2001
From: dkf <donal.k.fellows@manchester.ac.uk>
Date: Sat, 18 Feb 2017 18:38:52 +0000
Subject: Add documentation of [regsub -command].

---
 doc/regsub.n       | 72 ++++++++++++++++++++++++++++++++++++++++++++++++++++++
 generic/tclCmdMZ.c |  4 +--
 2 files changed, 74 insertions(+), 2 deletions(-)

diff --git a/doc/regsub.n b/doc/regsub.n
index a5b79de..23bbff9 100644
--- a/doc/regsub.n
+++ b/doc/regsub.n
@@ -68,6 +68,31 @@ and
 sequences are handled for each substitution using the information
 from the corresponding match.
 .TP
+\fB\-command\fR
+.VS 8.7
+Changes the handling of the substitution string so that it no longer treats
+.QW &
+and
+.QW \e
+as special characters, but instead uses them as a non-empty list of words.
+Each time a substitution is processed, another complete Tcl word is appended
+to that list for each substitution value (the first such argument represents
+the overall matched substring, the subsequent arguments will be one per
+capturing sub-RE, much as are returned from \fBregexp\fR \fB\-inline\fR) and
+the overall list is then evaluated as a Tcl command call. If the command
+finishes successfully, the result of command call is substituted into the
+resulting string.
+.RS
+.PP
+If \fB\-all\fR is not also given, the command callback will be invoked at most
+once (exactly when the regular expression matches). If \fB\-all\fR is given,
+the command callback will be invoked for each matched location, in sequence.
+The exact location indices that matched are not made available to the script.
+.PP
+See \fBEXAMPLES\fR below for illustrative cases.
+.RE
+.VE 8.7
+.TP
 \fB\-expanded\fR
 .
 Enables use of the expanded regular expression syntax where
@@ -183,6 +208,53 @@ set substitution {[format \e\e\e\eu%04x [scan "\e\e&" %c]]}
 set quoted [subst [string map {\en {\e\eu000a}} \e
         [\fBregsub\fR -all $RE $string $substitution]]]
 .CE
+.PP
+.VS 8.7
+The above operation can be done using \fBregsub \-command\fR instead, which is
+often faster. (A full pre-computed \fBstring map\fR would be faster still, but
+the cost of computing the map for a transformation as complex as this can be
+quite large.)
+.PP
+.CS
+# This RE is just a character class for everything "bad"
+set RE {[][{};#\e\e\e$\es\eu0080-\euffff]}
+
+# This encodes what the RE described above matches
+proc encodeChar {ch} {
+    # newline is handled specially since backslash-newline is a
+    # special sequence.
+    if {$ch eq "\en"} {
+        return "\e\eu000a"
+    }
+    # No point in writing this as a one-liner
+    scan $ch %c charNumber
+    format "\e\eu%04x" $charNumber
+}
+
+set quoted [\fBregsub\fR -all -command $RE $string encodeChar]
+.CE
+.PP
+Decoding a URL-encoded string using \fBregsub \-command\fR, a lambda term and
+the \fBapply\fR command.
+.PP
+.CS
+# Match one of the sequences in a URL-encoded string that needs
+# fixing, converting + to space and %XX to the right character
+# (e.g., %7e becomes ~)
+set RE {(\e+)|%([0-9A-Fa-f]{2})}
+
+# Note that -command uses a command prefix, not a command name
+set decoded [\fBregsub\fR -all -command $RE $string {apply {{- p h} {
+    # + is a special case; handle directly
+    if {$p eq "+"} {
+        return " "
+    }
+    # convert hex to a char
+    scan $h %x charNumber
+    format %c $charNumber
+}}}]
+.CE
+.VE 8.7
 .SH "SEE ALSO"
 regexp(n), re_syntax(n), subst(n), string(n)
 .SH KEYWORDS
diff --git a/generic/tclCmdMZ.c b/generic/tclCmdMZ.c
index d5a6b01..4178ba8 100644
--- a/generic/tclCmdMZ.c
+++ b/generic/tclCmdMZ.c
@@ -500,8 +500,8 @@ Tcl_RegsubObjCmd(
 	"--",		NULL
     };
     enum options {
-	REGSUB_ALL, REGSUB_COMMAND, REGSUB_EXPANDED, REGSUB_LINE,
-	REGSUB_LINESTOP, REGSUB_LINEANCHOR, REGSUB_NOCASE, REGSUB_START,
+	REGSUB_ALL,	 REGSUB_COMMAND,    REGSUB_EXPANDED, REGSUB_LINE,
+	REGSUB_LINESTOP, REGSUB_LINEANCHOR, REGSUB_NOCASE,   REGSUB_START,
 	REGSUB_LAST
     };
 
-- 
cgit v0.12


From 623bbf71b6f3c7bb603c35225cbd667fd138ff8e Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Fri, 10 Mar 2017 15:22:08 +0000
Subject: Start RC branch for Tcl 8.6.7

---
 README            | 2 +-
 generic/tcl.h     | 4 ++--
 library/init.tcl  | 2 +-
 unix/configure    | 2 +-
 unix/configure.in | 2 +-
 unix/tcl.spec     | 2 +-
 win/configure     | 2 +-
 win/configure.in  | 2 +-
 8 files changed, 9 insertions(+), 9 deletions(-)

diff --git a/README b/README
index 401b6e6..57985d3 100644
--- a/README
+++ b/README
@@ -1,5 +1,5 @@
 README:  Tcl
-    This is the Tcl 8.6.6 source distribution.
+    This is the Tcl 8.6.7 source distribution.
 	http://sourceforge.net/projects/tcl/files/Tcl/
     You can get any source release of Tcl from the URL above.
 
diff --git a/generic/tcl.h b/generic/tcl.h
index 64c7d14..3790b58 100644
--- a/generic/tcl.h
+++ b/generic/tcl.h
@@ -55,10 +55,10 @@ extern "C" {
 #define TCL_MAJOR_VERSION   8
 #define TCL_MINOR_VERSION   6
 #define TCL_RELEASE_LEVEL   TCL_FINAL_RELEASE
-#define TCL_RELEASE_SERIAL  6
+#define TCL_RELEASE_SERIAL  7
 
 #define TCL_VERSION	    "8.6"
-#define TCL_PATCH_LEVEL	    "8.6.6"
+#define TCL_PATCH_LEVEL	    "8.6.7"
 
 /*
  *----------------------------------------------------------------------------
diff --git a/library/init.tcl b/library/init.tcl
index 9ca4514..0437412 100644
--- a/library/init.tcl
+++ b/library/init.tcl
@@ -16,7 +16,7 @@
 if {[info commands package] == ""} {
     error "version mismatch: library\nscripts expect Tcl version 7.5b1 or later but the loaded version is\nonly [info patchlevel]"
 }
-package require -exact Tcl 8.6.6
+package require -exact Tcl 8.6.7
 
 # Compute the auto path to use in this interpreter.
 # The values on the path come from several locations:
diff --git a/unix/configure b/unix/configure
index 38c3f9a..a333fc1 100755
--- a/unix/configure
+++ b/unix/configure
@@ -1335,7 +1335,7 @@ ac_compiler_gnu=$ac_cv_c_compiler_gnu
 TCL_VERSION=8.6
 TCL_MAJOR_VERSION=8
 TCL_MINOR_VERSION=6
-TCL_PATCH_LEVEL=".6"
+TCL_PATCH_LEVEL=".7"
 VERSION=${TCL_VERSION}
 
 EXTRA_INSTALL_BINARIES=${EXTRA_INSTALL_BINARIES:-"@:"}
diff --git a/unix/configure.in b/unix/configure.in
index 1d86213..220a4aa 100644
--- a/unix/configure.in
+++ b/unix/configure.in
@@ -25,7 +25,7 @@ m4_ifdef([SC_USE_CONFIG_HEADERS], [
 TCL_VERSION=8.6
 TCL_MAJOR_VERSION=8
 TCL_MINOR_VERSION=6
-TCL_PATCH_LEVEL=".6"
+TCL_PATCH_LEVEL=".7"
 VERSION=${TCL_VERSION}
 
 EXTRA_INSTALL_BINARIES=${EXTRA_INSTALL_BINARIES:-"@:"}
diff --git a/unix/tcl.spec b/unix/tcl.spec
index 8bf77f3..141511d 100644
--- a/unix/tcl.spec
+++ b/unix/tcl.spec
@@ -4,7 +4,7 @@
 
 Name:          tcl
 Summary:       Tcl scripting language development environment
-Version:       8.6.6
+Version:       8.6.7
 Release:       2
 License:       BSD
 Group:         Development/Languages
diff --git a/win/configure b/win/configure
index e8e4b87..835afb8 100755
--- a/win/configure
+++ b/win/configure
@@ -1311,7 +1311,7 @@ SHELL=/bin/sh
 TCL_VERSION=8.6
 TCL_MAJOR_VERSION=8
 TCL_MINOR_VERSION=6
-TCL_PATCH_LEVEL=".6"
+TCL_PATCH_LEVEL=".7"
 VER=$TCL_MAJOR_VERSION$TCL_MINOR_VERSION
 
 TCL_DDE_VERSION=1.4
diff --git a/win/configure.in b/win/configure.in
index 8bb9c48..8d712eb 100644
--- a/win/configure.in
+++ b/win/configure.in
@@ -14,7 +14,7 @@ SHELL=/bin/sh
 TCL_VERSION=8.6
 TCL_MAJOR_VERSION=8
 TCL_MINOR_VERSION=6
-TCL_PATCH_LEVEL=".6"
+TCL_PATCH_LEVEL=".7"
 VER=$TCL_MAJOR_VERSION$TCL_MINOR_VERSION
 
 TCL_DDE_VERSION=1.4
-- 
cgit v0.12


From 70498dad4bb1b36989e3c7863e3fd1b3e79864fc Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Fri, 10 Mar 2017 15:28:46 +0000
Subject: Dup test name

---
 tests/link.test | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tests/link.test b/tests/link.test
index dda7d6b..6bff356 100644
--- a/tests/link.test
+++ b/tests/link.test
@@ -152,7 +152,7 @@ test link-2.8 {writing C variables from Tcl} -constraints {testlink} -setup {
     set uwide "0O"
     concat [testlink get] | $int $real $bool $string $wide $char $uchar $short $ushort $uint $long $ulong $float $uwide
 } -result {0 0.0 0 0 0 0 0 0 0 0 0 0 0.0 0 | 0x 0b 0 0 0O 0X 0B 0O 0x 0b 0o 0X 0B 0O}
-test link-2.8 {writing C variables from Tcl} -constraints {testlink} -setup {
+test link-2.9 {writing C variables from Tcl} -constraints {testlink} -setup {
     testlink delete
 } -body {
     testlink set 43 1.21 4 - 56785678 64 250 30000 60000 0xbaadbeef 12321 32123 3.25 1231231234
-- 
cgit v0.12


From 99447d298b4baa4001b027b1aa9c9c60fea2098d Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Fri, 10 Mar 2017 16:41:32 +0000
Subject: Silence valgrind complaints from [representation].

---
 generic/tclInt.h | 2 ++
 generic/tclObj.c | 1 +
 2 files changed, 3 insertions(+)

diff --git a/generic/tclInt.h b/generic/tclInt.h
index 4d3c0b1..65ef1c6 100644
--- a/generic/tclInt.h
+++ b/generic/tclInt.h
@@ -4521,6 +4521,7 @@ MODULE_SCOPE Tcl_PackageInitProc Procbodytest_SafeInit;
     do {							\
 	TclInvalidateStringRep(objPtr);				\
 	TclFreeIntRep(objPtr);					\
+	(objPtr)->internalRep.twoPtrValue.ptr2 = NULL;		\
 	(objPtr)->internalRep.doubleValue = (double)(d);	\
 	(objPtr)->typePtr = &tclDoubleType;			\
     } while (0)
@@ -4570,6 +4571,7 @@ MODULE_SCOPE Tcl_PackageInitProc Procbodytest_SafeInit;
 	TclAllocObjStorage(objPtr);				\
 	(objPtr)->refCount = 0;					\
 	(objPtr)->bytes = NULL;					\
+	(objPtr)->internalRep.twoPtrValue.ptr2 = NULL;		\
 	(objPtr)->internalRep.doubleValue = (double)(d);	\
 	(objPtr)->typePtr = &tclDoubleType;			\
 	TCL_DTRACE_OBJ_CREATE(objPtr);				\
diff --git a/generic/tclObj.c b/generic/tclObj.c
index a346987..d549fdc 100644
--- a/generic/tclObj.c
+++ b/generic/tclObj.c
@@ -2203,6 +2203,7 @@ Tcl_DbNewDoubleObj(
     TclDbNewObj(objPtr, file, line);
     objPtr->bytes = NULL;
 
+    objPtr->internalRep.twoPtrValue.ptr2 = NULL; /* valgrind */
     objPtr->internalRep.doubleValue = dblValue;
     objPtr->typePtr = &tclDoubleType;
     return objPtr;
-- 
cgit v0.12


From ba078102bb35ae671db5adb952ee48ecef4003ed Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Mon, 13 Mar 2017 17:03:50 +0000
Subject: Different solution to silencing the non-useful valgrind alerts.

---
 generic/tclInt.h |  2 --
 generic/tclObj.c | 19 ++++++++++++++++++-
 2 files changed, 18 insertions(+), 3 deletions(-)

diff --git a/generic/tclInt.h b/generic/tclInt.h
index 65ef1c6..4d3c0b1 100644
--- a/generic/tclInt.h
+++ b/generic/tclInt.h
@@ -4521,7 +4521,6 @@ MODULE_SCOPE Tcl_PackageInitProc Procbodytest_SafeInit;
     do {							\
 	TclInvalidateStringRep(objPtr);				\
 	TclFreeIntRep(objPtr);					\
-	(objPtr)->internalRep.twoPtrValue.ptr2 = NULL;		\
 	(objPtr)->internalRep.doubleValue = (double)(d);	\
 	(objPtr)->typePtr = &tclDoubleType;			\
     } while (0)
@@ -4571,7 +4570,6 @@ MODULE_SCOPE Tcl_PackageInitProc Procbodytest_SafeInit;
 	TclAllocObjStorage(objPtr);				\
 	(objPtr)->refCount = 0;					\
 	(objPtr)->bytes = NULL;					\
-	(objPtr)->internalRep.twoPtrValue.ptr2 = NULL;		\
 	(objPtr)->internalRep.doubleValue = (double)(d);	\
 	(objPtr)->typePtr = &tclDoubleType;			\
 	TCL_DTRACE_OBJ_CREATE(objPtr);				\
diff --git a/generic/tclObj.c b/generic/tclObj.c
index d549fdc..3bf5b8e 100644
--- a/generic/tclObj.c
+++ b/generic/tclObj.c
@@ -2203,7 +2203,6 @@ Tcl_DbNewDoubleObj(
     TclDbNewObj(objPtr, file, line);
     objPtr->bytes = NULL;
 
-    objPtr->internalRep.twoPtrValue.ptr2 = NULL; /* valgrind */
     objPtr->internalRep.doubleValue = dblValue;
     objPtr->typePtr = &tclDoubleType;
     return objPtr;
@@ -4489,6 +4488,24 @@ Tcl_RepresentationCmd(
             objv[1]->typePtr ? objv[1]->typePtr->name : "pure string",
 	    objv[1]->refCount, ptrBuffer);
 
+    /*
+     * This is a workaround to silence reports from `make valgrind`
+     * on 64-bit systems.  The problem is that the test suite
+     * includes calling the [represenation] command on values of
+     * &tclDoubleType.  When these values are created, the "doubleValue"
+     * is set, but when the "twoPtrValue" is examined, its "ptr2"
+     * field has never been initialized.  Since [representation]
+     * presents the value of the ptr2 value in its output, valgrind
+     * alerts about the read of uninitialized memory.
+     *
+     * The general problem with [representation], that it can read
+     * and report uninitialized fields, is still present.  This is
+     * just the minimal workaround to silence one particular test.
+     */
+
+    if ((sizeof(void *) > 4) && objv[1]->typePtr == &tclDoubleType) {
+	objv[1]->internalRep.twoPtrValue.ptr2 = NULL;
+    }
     if (objv[1]->typePtr) {
 	sprintf(ptrBuffer, "%p:%p",
 		(void *) objv[1]->internalRep.twoPtrValue.ptr1,
-- 
cgit v0.12


From f325616ca0b76bfb644bb17a91bc9ac2146b8644 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Tue, 11 Apr 2017 19:11:27 +0000
Subject: More changes work

---
 changes | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/changes b/changes
index 68b2fb5..c3a4be3 100644
--- a/changes
+++ b/changes
@@ -8704,6 +8704,15 @@ improvements to regexp engine from Postgres (lane,porter,fellows,seltenreich)
 2016-09-07 (bug)[4dbdd9] Memleak in test var-8.3 (mr_calvin,porter)
 
 2016-10-03 (bug)[2bf561] Allow empty command as alias target (yorick,nijtmans)
+        *** POTENTIAL INCOMPATIBILITY ***
+
+2016-10-04 (bug)[4d5ae7] Crash in async connects host no address (gahr,fellows)
+
+2016-10-08 (bug)[838e99] treat application/xml as text (gahr,fellows)
+=> http 2.8.10
+
+2016-10-11 (bug)[3cc1d9] Thread finalization crash in zippy (neumann)
+
 
 
 
-- 
cgit v0.12


From d8f3d43759697e3be6d3613094aebedc9f83063d Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Wed, 12 Apr 2017 20:23:56 +0000
Subject: Bump msgcat and tcl tests and continue updates to changes.

---
 changes                      | 12 ++++++++++++
 library/msgcat/msgcat.tcl    |  2 +-
 library/msgcat/pkgIndex.tcl  |  2 +-
 library/tcltest/pkgIndex.tcl |  2 +-
 library/tcltest/tcltest.tcl  |  2 +-
 unix/Makefile.in             |  8 ++++----
 win/Makefile.in              |  8 ++++----
 7 files changed, 24 insertions(+), 12 deletions(-)

diff --git a/changes b/changes
index c3a4be3..bf25784 100644
--- a/changes
+++ b/changes
@@ -8713,6 +8713,18 @@ improvements to regexp engine from Postgres (lane,porter,fellows,seltenreich)
 
 2016-10-11 (bug)[3cc1d9] Thread finalization crash in zippy (neumann)
 
+2016-10-12 (bug)[be003d] Fix [scan 0x1 %b], [scan 0x1 %o] (porter)
+
+2016-10-14 (bug)[eb6b68] Fix stringComp-14.5 (porter)
+
+2016-10-30 (bug)[b26e38] Fix zlib-7.8 (fellows)
+
+2016-10-30 (bug)[1ae129] Fix memleak in [history] destruction (fellows)
+
+2016-11-04 (feature) Provision Tcl 9 support in msgcat and tcltest (nijtmans)
+=> msgcat 1.6.1
+=> tcltest 2.4.1
+
 
 
 
diff --git a/library/msgcat/msgcat.tcl b/library/msgcat/msgcat.tcl
index 928474d..646bc17 100644
--- a/library/msgcat/msgcat.tcl
+++ b/library/msgcat/msgcat.tcl
@@ -14,7 +14,7 @@
 package require Tcl 8.5-
 # When the version number changes, be sure to update the pkgIndex.tcl file,
 # and the installation directory in the Makefiles.
-package provide msgcat 1.6.0
+package provide msgcat 1.6.1
 
 namespace eval msgcat {
     namespace export mc mcexists mcload mclocale mcmax mcmset mcpreferences mcset\
diff --git a/library/msgcat/pkgIndex.tcl b/library/msgcat/pkgIndex.tcl
index 7399c92..7cdb703 100644
--- a/library/msgcat/pkgIndex.tcl
+++ b/library/msgcat/pkgIndex.tcl
@@ -1,2 +1,2 @@
 if {![package vsatisfies [package provide Tcl] 8.5]} {return}
-package ifneeded msgcat 1.6.0 [list source [file join $dir msgcat.tcl]]
+package ifneeded msgcat 1.6.1 [list source [file join $dir msgcat.tcl]]
diff --git a/library/tcltest/pkgIndex.tcl b/library/tcltest/pkgIndex.tcl
index 5ac8823..c9d3759 100644
--- a/library/tcltest/pkgIndex.tcl
+++ b/library/tcltest/pkgIndex.tcl
@@ -9,4 +9,4 @@
 # full path name of this file's directory.
 
 if {![package vsatisfies [package provide Tcl] 8.5]} {return}
-package ifneeded tcltest 2.4.0 [list source [file join $dir tcltest.tcl]]
+package ifneeded tcltest 2.4.1 [list source [file join $dir tcltest.tcl]]
diff --git a/library/tcltest/tcltest.tcl b/library/tcltest/tcltest.tcl
index 75975d2..f1b6082 100644
--- a/library/tcltest/tcltest.tcl
+++ b/library/tcltest/tcltest.tcl
@@ -22,7 +22,7 @@ namespace eval tcltest {
     # When the version number changes, be sure to update the pkgIndex.tcl file,
     # and the install directory in the Makefiles.  When the minor version
     # changes (new feature) be sure to update the man page as well.
-    variable Version 2.4.0
+    variable Version 2.4.1
 
     # Compatibility support for dumb variables defined in tcltest 1
     # Do not use these.  Call [package provide Tcl] and [info patchlevel]
diff --git a/unix/Makefile.in b/unix/Makefile.in
index 9ad106c..e03e874 100644
--- a/unix/Makefile.in
+++ b/unix/Makefile.in
@@ -847,10 +847,10 @@ install-libraries: libraries
 	    do \
 	    $(INSTALL_DATA) $$i "$(SCRIPT_INSTALL_DIR)"/opt0.4; \
 	    done;
-	@echo "Installing package msgcat 1.6.0 as a Tcl Module";
-	@$(INSTALL_DATA) $(TOP_DIR)/library/msgcat/msgcat.tcl "$(SCRIPT_INSTALL_DIR)"/../tcl8/8.5/msgcat-1.6.0.tm;
-	@echo "Installing package tcltest 2.4.0 as a Tcl Module";
-	@$(INSTALL_DATA) $(TOP_DIR)/library/tcltest/tcltest.tcl "$(SCRIPT_INSTALL_DIR)"/../tcl8/8.5/tcltest-2.4.0.tm;
+	@echo "Installing package msgcat 1.6.1 as a Tcl Module";
+	@$(INSTALL_DATA) $(TOP_DIR)/library/msgcat/msgcat.tcl "$(SCRIPT_INSTALL_DIR)"/../tcl8/8.5/msgcat-1.6.1.tm;
+	@echo "Installing package tcltest 2.4.1 as a Tcl Module";
+	@$(INSTALL_DATA) $(TOP_DIR)/library/tcltest/tcltest.tcl "$(SCRIPT_INSTALL_DIR)"/../tcl8/8.5/tcltest-2.4.1.tm;
 
 	@echo "Installing package platform 1.0.14 as a Tcl Module";
 	@$(INSTALL_DATA) $(TOP_DIR)/library/platform/platform.tcl "$(SCRIPT_INSTALL_DIR)"/../tcl8/8.4/platform-1.0.14.tm;
diff --git a/win/Makefile.in b/win/Makefile.in
index 0ab4204..255c9b4 100644
--- a/win/Makefile.in
+++ b/win/Makefile.in
@@ -658,10 +658,10 @@ install-libraries: libraries install-tzdata install-msgs
 	    do \
 	    $(COPY) "$$j" "$(SCRIPT_INSTALL_DIR)/opt0.4"; \
 	    done;
-	@echo "Installing package msgcat 1.6.0 as a Tcl Module";
-	@$(COPY) $(ROOT_DIR)/library/msgcat/msgcat.tcl $(SCRIPT_INSTALL_DIR)/../tcl8/8.5/msgcat-1.6.0.tm;
-	@echo "Installing package tcltest 2.4.0 as a Tcl Module";
-	@$(COPY) $(ROOT_DIR)/library/tcltest/tcltest.tcl $(SCRIPT_INSTALL_DIR)/../tcl8/8.5/tcltest-2.4.0.tm;
+	@echo "Installing package msgcat 1.6.1 as a Tcl Module";
+	@$(COPY) $(ROOT_DIR)/library/msgcat/msgcat.tcl $(SCRIPT_INSTALL_DIR)/../tcl8/8.5/msgcat-1.6.1.tm;
+	@echo "Installing package tcltest 2.4.1 as a Tcl Module";
+	@$(COPY) $(ROOT_DIR)/library/tcltest/tcltest.tcl $(SCRIPT_INSTALL_DIR)/../tcl8/8.5/tcltest-2.4.1.tm;
 	@echo "Installing package platform 1.0.14 as a Tcl Module";
 	@$(COPY) $(ROOT_DIR)/library/platform/platform.tcl $(SCRIPT_INSTALL_DIR)/../tcl8/8.4/platform-1.0.14.tm;
 	@echo "Installing package platform::shell 1.1.4 as a Tcl Module";
-- 
cgit v0.12


From 23217a1cc40da71bb99cc988804ea9013254955b Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Thu, 13 Apr 2017 16:39:15 +0000
Subject: Bump TclOO 1.0.6; finish changes.

---
 changes             | 29 +++++++++++++++++++++++++++--
 generic/tclOO.h     |  2 +-
 unix/tclooConfig.sh |  2 +-
 win/tclooConfig.sh  |  2 +-
 4 files changed, 30 insertions(+), 5 deletions(-)

diff --git a/changes b/changes
index bf25784..74ab4ee 100644
--- a/changes
+++ b/changes
@@ -8721,19 +8721,44 @@ improvements to regexp engine from Postgres (lane,porter,fellows,seltenreich)
 
 2016-10-30 (bug)[1ae129] Fix memleak in [history] destruction (fellows)
 
-2016-11-04 (feature) Provision Tcl 9 support in msgcat and tcltest (nijtmans)
+2016-11-04 (feature) Provisional Tcl 9 support in msgcat and tcltest (nijtmans)
 => msgcat 1.6.1
 => tcltest 2.4.1
 
+2016-11-04 (bug)[824752] Crash in Tcl_ListObjReplace() (gahr,porter)
 
+2016-11-11 (bug)[79614f] invalidate VFS mounts on sytem encoding change (yorick)
 
+2016-11-14 OSX: End panic() as legacy support macro; system conflicts (nijtmans)
+        *** POTENTIAL INCOMPATIBILITY ***
+
+2016-11-15 (bug) TclOO fix stops crash mixing Itcl and snit (fellows)
 
+2016-11-17 (update) Reconcile libtommath updates; purge unused files (nijtmans)
+        *** POTENTIAL INCOMPATIBILITY ***
 
+2017-01-09 (bug)[b87ad7] Repair drifts in timer clock (sebres)
 
+2017-01-17 (update) => zlib 1.2.11 (nijtmans)
+
+2017-01-31 (bug)[39f630] Revise Tcl_LinkVar to tolerate some prefixes (nijtmans)
+        *** POTENTIAL INCOMPATIBILITY ***
+
+2017-02-01 (bug)[d0f7ba] Improper NAN optimization. expr-22.1[01] (aspect)
+
+2017-02-26 (bug)[25842c] zlib stream finalization (aspect)
+
+2017-03-07 (deprecate) Remove unmaintained makefile.bc file (nijtmans)
+        *** POTENTIAL INCOMPATIBILITY ***
 
+2017-03-14 (enhancement) [clock] and [encoding] are now ensembles (kenny)
 
+2017-03-15 (enhancement) several [clock] subcommands bytecoded (kenny)
 
+2017-03-23 tzdata updated to Olson's tzdata2017b (jima)
 
+2017-03-29 (bug)[900cb0] Fix OO unexport introspection (napier)
 
+2017-04-12 (bug)[42202b] Nesting imbalance in coro injection (nadkarni,sebres)
 
---- Released 8.6.7, March 31, 2016 --- http://core.tcl.tk/tcl/ for details
+--- Released 8.6.7, April 30, 2016 --- http://core.tcl.tk/tcl/ for details
diff --git a/generic/tclOO.h b/generic/tclOO.h
index 46f01fb..823d773 100644
--- a/generic/tclOO.h
+++ b/generic/tclOO.h
@@ -24,7 +24,7 @@
  * win/tclooConfig.sh
  */
 
-#define TCLOO_VERSION "1.0.5"
+#define TCLOO_VERSION "1.0.6"
 #define TCLOO_PATCHLEVEL TCLOO_VERSION
 
 #include "tcl.h"
diff --git a/unix/tclooConfig.sh b/unix/tclooConfig.sh
index ee10b81..e5d42bb 100644
--- a/unix/tclooConfig.sh
+++ b/unix/tclooConfig.sh
@@ -16,4 +16,4 @@ TCLOO_STUB_LIB_SPEC=""
 TCLOO_INCLUDE_SPEC=""
 TCLOO_PRIVATE_INCLUDE_SPEC=""
 TCLOO_CFLAGS=""
-TCLOO_VERSION=1.0.4
+TCLOO_VERSION=1.0.6
diff --git a/win/tclooConfig.sh b/win/tclooConfig.sh
index ee10b81..e5d42bb 100644
--- a/win/tclooConfig.sh
+++ b/win/tclooConfig.sh
@@ -16,4 +16,4 @@ TCLOO_STUB_LIB_SPEC=""
 TCLOO_INCLUDE_SPEC=""
 TCLOO_PRIVATE_INCLUDE_SPEC=""
 TCLOO_CFLAGS=""
-TCLOO_VERSION=1.0.4
+TCLOO_VERSION=1.0.6
-- 
cgit v0.12


From 728c64fc037b7b9cbad80e040b2c58317d78271a Mon Sep 17 00:00:00 2001
From: dkf <donal.k.fellows@manchester.ac.uk>
Date: Thu, 27 Apr 2017 12:38:21 +0000
Subject: Start of implementation of TIP #470.

---
 generic/tclOO.c           |  1 +
 generic/tclOODefineCmds.c | 43 ++++++++++++++++++++++++++++++++++++++-----
 generic/tclOOInt.h        |  3 +++
 3 files changed, 42 insertions(+), 5 deletions(-)

diff --git a/generic/tclOO.c b/generic/tclOO.c
index ef0c987..73acce8 100644
--- a/generic/tclOO.c
+++ b/generic/tclOO.c
@@ -41,6 +41,7 @@ static const struct {
     {"forward", TclOODefineForwardObjCmd, 1},
     {"method", TclOODefineMethodObjCmd, 1},
     {"renamemethod", TclOODefineRenameMethodObjCmd, 1},
+    {"self", TclOODefineObjSelfObjCmd, 0},
     {"unexport", TclOODefineUnexportObjCmd, 1},
     {NULL, NULL, 0}
 };
diff --git a/generic/tclOODefineCmds.c b/generic/tclOODefineCmds.c
index 5b0dfc3..d3ab1eb 100644
--- a/generic/tclOODefineCmds.c
+++ b/generic/tclOODefineCmds.c
@@ -1028,16 +1028,16 @@ TclOODefineSelfObjCmd(
     int result;
     Object *oPtr;
 
-    if (objc < 2) {
-	Tcl_WrongNumArgs(interp, 1, objv, "arg ?arg ...?");
-	return TCL_ERROR;
-    }
-
     oPtr = (Object *) TclOOGetDefineCmdContext(interp);
     if (oPtr == NULL) {
 	return TCL_ERROR;
     }
 
+    if (objc < 2) {
+	Tcl_SetObjResult(interp, TclOOObjectName(interp, oPtr));
+	return TCL_OK;
+    }
+
     /*
      * Make the oo::objdefine namespace the current namespace and evaluate the
      * command(s).
@@ -1113,6 +1113,39 @@ TclOODefineSelfObjCmd(
 /*
  * ----------------------------------------------------------------------
  *
+ * TclOODefineObjSelfObjCmd --
+ *	Implementation of the "self" subcommand of the "oo::objdefine"
+ *	command.
+ *
+ * ----------------------------------------------------------------------
+ */
+
+int
+TclOODefineObjSelfObjCmd(
+    ClientData clientData,
+    Tcl_Interp *interp,
+    int objc,
+    Tcl_Obj *const *objv)
+{
+    Object *oPtr;
+
+    if (objc != 1) {
+	Tcl_WrongNumArgs(interp, 1, objv, NULL);
+	return TCL_ERROR;
+    }
+
+    oPtr = (Object *) TclOOGetDefineCmdContext(interp);
+    if (oPtr == NULL) {
+	return TCL_ERROR;
+    }
+
+    Tcl_SetObjResult(interp, TclOOObjectName(interp, oPtr));
+    return TCL_OK;
+}
+
+/*
+ * ----------------------------------------------------------------------
+ *
  * TclOODefineClassObjCmd --
  *	Implementation of the "class" subcommand of the "oo::objdefine"
  *	command.
diff --git a/generic/tclOOInt.h b/generic/tclOOInt.h
index ae24dee..476446d 100644
--- a/generic/tclOOInt.h
+++ b/generic/tclOOInt.h
@@ -431,6 +431,9 @@ MODULE_SCOPE int	TclOODefineClassObjCmd(ClientData clientData,
 MODULE_SCOPE int	TclOODefineSelfObjCmd(ClientData clientData,
 			    Tcl_Interp *interp, int objc,
 			    Tcl_Obj *const *objv);
+MODULE_SCOPE int	TclOODefineObjSelfObjCmd(ClientData clientData,
+			    Tcl_Interp *interp, int objc,
+			    Tcl_Obj *const *objv);
 MODULE_SCOPE int	TclOOUnknownDefinition(ClientData clientData,
 			    Tcl_Interp *interp, int objc,
 			    Tcl_Obj *const *objv);
-- 
cgit v0.12


From 7aab6826d8c0c63f62a1d8a8c42d514d5559e420 Mon Sep 17 00:00:00 2001
From: griffin <brian_griffin@mentor.com>
Date: Sat, 27 May 2017 22:17:21 +0000
Subject: Implement proposed 0d decimal radix prefix to compliment 0x,0b,0o.

---
 doc/GetInt.3        |  7 +++++--
 doc/expr.n          |  2 +-
 generic/tclStrToD.c | 16 +++++++++++++++-
 tests/cmdIL.test    |  4 ++--
 tests/util.test     | 18 ++++++++++++++++++
 5 files changed, 41 insertions(+), 6 deletions(-)

diff --git a/doc/GetInt.3 b/doc/GetInt.3
index 5a3304a..8d7a4d0 100644
--- a/doc/GetInt.3
+++ b/doc/GetInt.3
@@ -56,6 +56,9 @@ followed by white space.  If the first two characters of \fIsrc\fR
 after the optional white space and sign are
 .QW \fB0x\fR
 then \fIsrc\fR is expected to be in hexadecimal form;  otherwise,
+if the first such characters are 
+.QW \fB0d\fR 
+then \fIsrc\fR is expected to be in decimal form; otherwise, 
 if the first such characters are
 .QW \fB0o\fR
 then \fIsrc\fR is expected to be in octal form;  otherwise,
@@ -65,8 +68,8 @@ then \fIsrc\fR is expected to be in binary form;  otherwise,
 if the first such character is
 .QW \fB0\fR
 then \fIsrc\fR
-is expected to be in octal form;  otherwise, \fIsrc\fR is
-expected to be in decimal form.
+is expected to be in octal form;  otherwise, \fIsrc\fR 
+is expected to be in decimal form.
 .PP
 \fBTcl_GetDouble\fR expects \fIsrc\fR to consist of a floating-point
 number, which is:  white space;  a sign; a sequence of digits;  a
diff --git a/doc/expr.n b/doc/expr.n
index cbb2395..3cd6d16 100644
--- a/doc/expr.n
+++ b/doc/expr.n
@@ -46,7 +46,7 @@ value is the form produced by the \fB%g\fR format specifier of Tcl's
 An expression consists of a combination of operands, operators, parentheses and
 commas, possibly with whitespace between any of these elements, which is
 ignored.
-An integer operand may be specified in decimal, binary
+An integer operand may be specified in decimal (the optional first two characters are \fB0d\fR), binary
 (the first two characters are \fB0b\fR), octal
 (the first two characters are \fB0o\fR), or hexadecimal
 (the first two characters are \fB0x\fR) form.  For
diff --git a/generic/tclStrToD.c b/generic/tclStrToD.c
index c7fdc5a..cbdc3a0 100644
--- a/generic/tclStrToD.c
+++ b/generic/tclStrToD.c
@@ -482,7 +482,7 @@ TclParseNumber(
 {
     enum State {
 	INITIAL, SIGNUM, ZERO, ZERO_X,
-	ZERO_O, ZERO_B, BINARY,
+	ZERO_O, ZERO_B, ZERO_D, BINARY,
 	HEXADECIMAL, OCTAL, BAD_OCTAL, DECIMAL,
 	LEADING_RADIX_POINT, FRACTION,
 	EXPONENT_START, EXPONENT_SIGNUM, EXPONENT,
@@ -664,6 +664,10 @@ TclParseNumber(
 		state = ZERO_O;
 		break;
 	    }
+	    if (c == 'd' || c == 'D') {
+		state = ZERO_D;
+		break;
+	    }
 #ifdef TCL_NO_DEPRECATED
 	    goto decimal;
 #endif
@@ -880,6 +884,16 @@ TclParseNumber(
 	    state = BINARY;
 	    break;
 
+	case ZERO_D:
+	    if (c == '0') {
+		numTrailZeros++;
+	    } else if ( ! isdigit(UCHAR(c))) {
+		goto endgame;
+	    }		
+	    state = DECIMAL;
+	    flags |= TCL_PARSE_INTEGER_ONLY;
+	    /* FALLTHROUGH */
+
 	case DECIMAL:
 	    /*
 	     * Scanned an optional + or - followed by a string of decimal
diff --git a/tests/cmdIL.test b/tests/cmdIL.test
index 23a5f96..70ac6bb 100644
--- a/tests/cmdIL.test
+++ b/tests/cmdIL.test
@@ -219,8 +219,8 @@ test cmdIL-3.10 {SortCompare procedure, -integer option} -body {
     lsort -integer {3 q}
 } -returnCodes error -result {expected integer but got "q"}
 test cmdIL-3.11 {SortCompare procedure, -integer option} {
-    lsort -integer {35 21 0x20 30 0o23 100 8}
-} {8 0o23 21 30 0x20 35 100}
+    lsort -integer {35 21 0x20 0d30 0o23 100 8}
+} {8 0o23 21 0d30 0x20 35 100}
 test cmdIL-3.12 {SortCompare procedure, -real option} -body {
     lsort -real {6...4 3}
 } -returnCodes error -result {expected floating-point number but got "6...4"}
diff --git a/tests/util.test b/tests/util.test
index 22d120b..35fc642 100644
--- a/tests/util.test
+++ b/tests/util.test
@@ -553,6 +553,12 @@ test util-9.0.6 {TclGetIntForIndex} {
 test util-9.0.7 {TclGetIntForIndex} {
     string index abcd { 01 }
 } b
+test util-9.0.8 {TclGetIntForIndex} {
+    string index abcd { 0d0 }
+} a
+test util-9.0.9 {TclGetIntForIndex} {
+    string index abcd { -0d0 }
+} a
 test util-9.1.0 {TclGetIntForIndex} {
     string index abcd 3
 } d
@@ -565,6 +571,12 @@ test util-9.1.2 {TclGetIntForIndex} {
 test util-9.1.3 {TclGetIntForIndex} {
     string index abcdefghijk { 0xa }
 } k
+test util-9.1.4 {TclGetIntForIndex} {
+    string index abcdefghijk 0d10
+} k
+test util-9.1.5 {TclGetIntForIndex} {
+    string index abcdefghijk { 0d10 }
+} k
 test util-9.2.0 {TclGetIntForIndex} {
     string index abcd end
 } d
@@ -672,12 +684,18 @@ test util-9.30 {TclGetIntForIndex} -body {
 test util-9.31 {TclGetIntForIndex} -body {
     string index a 0x
 } -returnCodes error -match glob -result *
+test util-9.31.1 {TclGetIntForIndex} -body {
+    string index a 0d
+} -returnCodes error -match glob -result *
 test util-9.32 {TclGetIntForIndex} -body {
     string index a 0x1FFFFFFFF+0
 } -returnCodes error -match glob -result *
 test util-9.33 {TclGetIntForIndex} -body {
     string index a 100000000000+0
 } -returnCodes error -match glob -result *
+test util-9.33.1 {TclGetIntForIndex} -body {
+    string index a 0d100000000000+0
+} -returnCodes error -match glob -result *
 test util-9.34 {TclGetIntForIndex} -body {
     string index a 1.0
 } -returnCodes error -match glob -result *
-- 
cgit v0.12


From 7ad256b22a418232031230af7c60a0e21e979df6 Mon Sep 17 00:00:00 2001
From: griffin <brian_griffin@mentor.com>
Date: Sun, 28 May 2017 16:06:29 +0000
Subject: 0d in LinkVar

---
 generic/tclLink.c |  4 ++--
 tests/link.test   | 21 +++++++++++++++++++++
 2 files changed, 23 insertions(+), 2 deletions(-)

diff --git a/generic/tclLink.c b/generic/tclLink.c
index a39dfcd..7366acc 100644
--- a/generic/tclLink.c
+++ b/generic/tclLink.c
@@ -692,7 +692,7 @@ SetInvalidRealFromAny(Tcl_Interp *interp, Tcl_Obj *objPtr) {
 /*
  * This function checks for integer representations, which are valid
  * when linking with C variables, but which are invalid in other
- * contexts in Tcl. Handled are "+", "-", "", "0x", "0b" and "0o"
+ * contexts in Tcl. Handled are "+", "-", "", "0x", "0b", "0d" and "0o"
  * (upperand lowercase). See bug [39f6304c2e].
  */
 int
@@ -701,7 +701,7 @@ GetInvalidIntFromObj(Tcl_Obj *objPtr, int *intPtr)
     const char *str = TclGetString(objPtr);
 
     if ((objPtr->length == 0) ||
-	    ((objPtr->length == 2) && (str[0] == '0') && strchr("xXbBoO", str[1]))) {
+	    ((objPtr->length == 2) && (str[0] == '0') && strchr("xXbBoOdD", str[1]))) {
 	*intPtr = 0;
 	return TCL_OK;
     } else if ((objPtr->length == 1) && strchr("+-", str[0])) {
diff --git a/tests/link.test b/tests/link.test
index 6bff356..a12759d 100644
--- a/tests/link.test
+++ b/tests/link.test
@@ -173,6 +173,27 @@ test link-2.9 {writing C variables from Tcl} -constraints {testlink} -setup {
     set uwide 0
     concat [testlink get] | $int $real $bool $string $wide $char $uchar $short $ushort $uint $long $ulong $float $uwide
 } -result {0 5000.0 0 0 0 0 0 0 0 0 0 0 -60.0 0 | 0 5000e 0 0 0 0 0 0 0 0 0 0 -60.00e+ 0}
+test link-2.10 {writing C variables from Tcl} -constraints {testlink} -setup {
+    testlink delete
+} -body {
+    testlink set 43 1.21 4 - 56785678 64 250 30000 60000 0xbaadbeef 12321 32123 3.25 1231231234
+    testlink create 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+    set int "0x"
+    set real "0b"
+    set bool 0
+    set string "0"
+    set wide "0D"
+    set char "0X"
+    set uchar "0B"
+    set short "0D"
+    set ushort "0x"
+    set uint "0b"
+    set long "0d"
+    set ulong "0X"
+    set float "0B"
+    set uwide "0D"
+    concat [testlink get] | $int $real $bool $string $wide $char $uchar $short $ushort $uint $long $ulong $float $uwide
+} -result {0 0.0 0 0 0 0 0 0 0 0 0 0 0.0 0 | 0x 0b 0 0 0D 0X 0B 0D 0x 0b 0d 0X 0B 0D}
 
 test link-3.1 {read-only variables} -constraints {testlink} -setup {
     testlink delete
-- 
cgit v0.12


From 2ab08afabdfc1091ae69439fb7c8bf81e8729e3e Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Thu, 8 Jun 2017 08:26:58 +0000
Subject: Better UTF-8 surrogate handling, only functional when TCL_UTF_MAX>3

---
 generic/tclBinary.c    |  6 ++---
 generic/tclCmdIL.c     |  2 +-
 generic/tclCmdMZ.c     | 10 ++++----
 generic/tclCompExpr.c  |  2 +-
 generic/tclEncoding.c  | 20 +++++++--------
 generic/tclLoad.c      |  2 +-
 generic/tclParse.c     |  2 +-
 generic/tclScan.c      |  2 +-
 generic/tclStringObj.c |  4 +--
 generic/tclUtf.c       | 68 ++++++++++++++++++++++++++++++++++++--------------
 generic/tclUtil.c      |  2 +-
 win/tclWinPipe.c       |  2 +-
 12 files changed, 76 insertions(+), 46 deletions(-)

diff --git a/generic/tclBinary.c b/generic/tclBinary.c
index d0d9d5e..bb918f2 100644
--- a/generic/tclBinary.c
+++ b/generic/tclBinary.c
@@ -454,7 +454,7 @@ SetByteArrayFromAny(
     const char *src, *srcEnd;
     unsigned char *dst;
     ByteArray *byteArrayPtr;
-    Tcl_UniChar ch;
+    Tcl_UniChar ch = 0;
 
     if (objPtr->typePtr != &tclByteArrayType) {
 	src = TclGetStringFromObj(objPtr, &length);
@@ -1210,7 +1210,7 @@ BinaryFormatCmd(
 
  badField:
     {
-	Tcl_UniChar ch;
+	Tcl_UniChar ch = 0;
 	char buf[TCL_UTF_MAX + 1];
 
 	TclUtfToUniChar(errorString, &ch);
@@ -1580,7 +1580,7 @@ BinaryScanCmd(
 
  badField:
     {
-	Tcl_UniChar ch;
+	Tcl_UniChar ch = 0;
 	char buf[TCL_UTF_MAX + 1];
 
 	TclUtfToUniChar(errorString, &ch);
diff --git a/generic/tclCmdIL.c b/generic/tclCmdIL.c
index ba9e1cf..e3c5f10 100644
--- a/generic/tclCmdIL.c
+++ b/generic/tclCmdIL.c
@@ -4345,7 +4345,7 @@ static int
 DictionaryCompare(
     const char *left, const char *right)	/* The strings to compare. */
 {
-    Tcl_UniChar uniLeft, uniRight, uniLeftLower, uniRightLower;
+    Tcl_UniChar uniLeft = 0, uniRight = 0, uniLeftLower, uniRightLower;
     int diff, zeros;
     int secondaryDiff = 0;
 
diff --git a/generic/tclCmdMZ.c b/generic/tclCmdMZ.c
index 3f79ca4..7010495 100644
--- a/generic/tclCmdMZ.c
+++ b/generic/tclCmdMZ.c
@@ -1037,7 +1037,7 @@ Tcl_SplitObjCmd(
     int objc,			/* Number of arguments. */
     Tcl_Obj *const objv[])	/* Argument objects. */
 {
-    Tcl_UniChar ch;
+    Tcl_UniChar ch = 0;
     int len;
     const char *splitChars;
     const char *stringPtr;
@@ -1122,7 +1122,7 @@ Tcl_SplitObjCmd(
     } else {
 	const char *element, *p, *splitEnd;
 	int splitLen;
-	Tcl_UniChar splitChar;
+	Tcl_UniChar splitChar = 0;
 
 	/*
 	 * Normal case: split on any of a given set of characters. Discard
@@ -1451,7 +1451,7 @@ StringIsCmd(
     Tcl_Obj *const objv[])	/* Argument objects. */
 {
     const char *string1, *end, *stop;
-    Tcl_UniChar ch;
+    Tcl_UniChar ch = 0;
     int (*chcomp)(int) = NULL;	/* The UniChar comparison function. */
     int i, failat = 0, result = 1, strict = 0, index, length1, length2;
     Tcl_Obj *objPtr, *failVarObj = NULL;
@@ -2436,7 +2436,7 @@ StringStartCmd(
     int objc,			/* Number of arguments. */
     Tcl_Obj *const objv[])	/* Argument objects. */
 {
-    Tcl_UniChar ch;
+    Tcl_UniChar ch = 0;
     const char *p, *string;
     int cur, index, length, numChars;
 
@@ -2497,7 +2497,7 @@ StringEndCmd(
     int objc,			/* Number of arguments. */
     Tcl_Obj *const objv[])	/* Argument objects. */
 {
-    Tcl_UniChar ch;
+    Tcl_UniChar ch = 0;
     const char *p, *end, *string;
     int cur, index, length, numChars;
 
diff --git a/generic/tclCompExpr.c b/generic/tclCompExpr.c
index 59eecf9..9c7ab8d 100644
--- a/generic/tclCompExpr.c
+++ b/generic/tclCompExpr.c
@@ -1885,7 +1885,7 @@ ParseLexeme(
 {
     const char *end;
     int scanned;
-    Tcl_UniChar ch;
+    Tcl_UniChar ch = 0;
     Tcl_Obj *literal = NULL;
     unsigned char byte;
 
diff --git a/generic/tclEncoding.c b/generic/tclEncoding.c
index b4acb5f..8450128 100644
--- a/generic/tclEncoding.c
+++ b/generic/tclEncoding.c
@@ -2296,7 +2296,7 @@ UtfToUtfProc(
     const char *srcStart, *srcEnd, *srcClose;
     const char *dstStart, *dstEnd;
     int result, numChars, charLimit = INT_MAX;
-    Tcl_UniChar ch;
+    Tcl_UniChar ch = 0;
 
     result = TCL_OK;
 
@@ -2345,8 +2345,8 @@ UtfToUtfProc(
 	} else if (!Tcl_UtfCharComplete(src, srcEnd - src)) {
 	    /*
 	     * Always check before using TclUtfToUniChar. Not doing can so
-	     * cause it run beyond the endof the buffer! If we happen such an
-	     * incomplete char its byts are made to represent themselves.
+	     * cause it run beyond the end of the buffer! If we happen such an
+	     * incomplete char its bytes are made to represent themselves.
 	     */
 
 	    ch = (unsigned char) *src;
@@ -2410,7 +2410,7 @@ UnicodeToUtfProc(
     const char *srcStart, *srcEnd;
     const char *dstEnd, *dstStart;
     int result, numChars, charLimit = INT_MAX;
-    Tcl_UniChar ch;
+    Tcl_UniChar ch = 0;
 
     if (flags & TCL_ENCODING_CHAR_LIMIT) {
 	charLimit = *dstCharsPtr;
@@ -2500,7 +2500,7 @@ UtfToUnicodeProc(
 {
     const char *srcStart, *srcEnd, *srcClose, *dstStart, *dstEnd;
     int result, numChars;
-    Tcl_UniChar ch;
+    Tcl_UniChar ch = 0;
 
     srcStart = src;
     srcEnd = src + srcLen;
@@ -2610,7 +2610,7 @@ TableToUtfProc(
     const char *srcStart, *srcEnd;
     const char *dstEnd, *dstStart, *prefixBytes;
     int result, byte, numChars, charLimit = INT_MAX;
-    Tcl_UniChar ch;
+    Tcl_UniChar ch = 0;
     const unsigned short *const *toUnicode;
     const unsigned short *pageZero;
     TableEncodingData *dataPtr = clientData;
@@ -2722,7 +2722,7 @@ TableFromUtfProc(
 {
     const char *srcStart, *srcEnd, *srcClose;
     const char *dstStart, *dstEnd, *prefixBytes;
-    Tcl_UniChar ch;
+    Tcl_UniChar ch = 0;
     int result, len, word, numChars;
     TableEncodingData *dataPtr = clientData;
     const unsigned short *const *fromUnicode;
@@ -2856,7 +2856,7 @@ Iso88591ToUtfProc(
 
     result = TCL_OK;
     for (numChars = 0; src < srcEnd && numChars <= charLimit; numChars++) {
-	Tcl_UniChar ch;
+	Tcl_UniChar ch = 0;
 
 	if (dst > dstEnd) {
 	    result = TCL_CONVERT_NOSPACE;
@@ -2942,7 +2942,7 @@ Iso88591FromUtfProc(
     dstEnd = dst + dstLen - 1;
 
     for (numChars = 0; src < srcEnd; numChars++) {
-	Tcl_UniChar ch;
+	Tcl_UniChar ch = 0;
 	int len;
 
 	if ((src > srcClose) && (!Tcl_UtfCharComplete(src, srcEnd - src))) {
@@ -3329,7 +3329,7 @@ EscapeFromUtfProc(
     for (numChars = 0; src < srcEnd; numChars++) {
 	unsigned len;
 	int word;
-	Tcl_UniChar ch;
+	Tcl_UniChar ch = 0;
 
 	if ((src > srcClose) && (!Tcl_UtfCharComplete(src, srcEnd - src))) {
 	    /*
diff --git a/generic/tclLoad.c b/generic/tclLoad.c
index 942e6b4..f1bd248 100644
--- a/generic/tclLoad.c
+++ b/generic/tclLoad.c
@@ -130,7 +130,7 @@ Tcl_LoadObjCmd(
     Tcl_PackageInitProc *initProc;
     const char *p, *fullFileName, *packageName;
     Tcl_LoadHandle loadHandle;
-    Tcl_UniChar ch;
+    Tcl_UniChar ch = 0;
     unsigned len;
     int index, flags = 0;
     Tcl_Obj *const *savedobjv = objv;
diff --git a/generic/tclParse.c b/generic/tclParse.c
index 3ecf4a5..f2cf322 100644
--- a/generic/tclParse.c
+++ b/generic/tclParse.c
@@ -841,7 +841,7 @@ TclParseBackslash(
 				 * written there. */
 {
     register const char *p = src+1;
-    Tcl_UniChar unichar;
+    Tcl_UniChar unichar = 0;
     int result;
     int count;
     char buf[TCL_UTF_MAX];
diff --git a/generic/tclScan.c b/generic/tclScan.c
index 17069eb..7a6a8a2 100644
--- a/generic/tclScan.c
+++ b/generic/tclScan.c
@@ -257,7 +257,7 @@ ValidateFormat(
 {
     int gotXpg, gotSequential, value, i, flags;
     char *end;
-    Tcl_UniChar ch;
+    Tcl_UniChar ch = 0;
     int objIndex, xpgSize, nspace = numVars;
     int *nassign = TclStackAlloc(interp, nspace * sizeof(int));
     char buf[TCL_UTF_MAX+1];
diff --git a/generic/tclStringObj.c b/generic/tclStringObj.c
index 4a3b6f1..0cafffb 100644
--- a/generic/tclStringObj.c
+++ b/generic/tclStringObj.c
@@ -1709,7 +1709,7 @@ Tcl_AppendFormatToObj(
 #endif
 	int newXpg, numChars, allocSegment = 0, segmentLimit, segmentNumBytes;
 	Tcl_Obj *segment;
-	Tcl_UniChar ch;
+	Tcl_UniChar ch = 0;
 	int step = TclUtfToUniChar(format, &ch);
 
 	format += step;
@@ -2693,7 +2693,7 @@ TclStringObjReverse(
     Tcl_Obj *objPtr)
 {
     String *stringPtr;
-    Tcl_UniChar ch;
+    Tcl_UniChar ch = 0;
 
     if (TclIsPureByteArray(objPtr)) {
 	int numBytes;
diff --git a/generic/tclUtf.c b/generic/tclUtf.c
index 52b4291..db941e2 100644
--- a/generic/tclUtf.c
+++ b/generic/tclUtf.c
@@ -134,7 +134,7 @@ UtfCount(
  *---------------------------------------------------------------------------
  */
 
-INLINE int
+int
 Tcl_UniCharToUtf(
     int ch,			/* The Tcl_UniChar to be stored in the
 				 * buffer. */
@@ -259,6 +259,15 @@ Tcl_UniCharToUtfDString(
  *	Tcl_UtfCharComplete() before calling this routine to ensure that
  *	enough bytes remain in the string.
  *
+ *	If TCL_UTF_MAX == 4, special handling of Surrogate pairs is done:
+ *	For any UTF-8 string containing a character outside of the BMP, the
+ *	first call to this function will fill *chPtr with the high surrogate
+ *	and generate a return value of 0. Calling Tcl_UtfToUniChar again
+ *	will produce the low surrogate and a return value of 4. Because *chPtr
+ *	is used to remember whether the high surrogate is already produced, it
+ *	is recommended to initialize the variable it points to as 0 before
+ *	the first call to Tcl_UtfToUniChar is done.
+ *
  * Results:
  *	*chPtr is filled with the Tcl_UniChar, and the return value is the
  *	number of bytes from the UTF-8 string that were consumed.
@@ -278,7 +287,7 @@ Tcl_UtfToUniChar(
     register int byte;
 
     /*
-     * Unroll 1 to 3 byte UTF-8 sequences, use loop to handle longer ones.
+     * Unroll 1 to 3 (or 4) byte UTF-8 sequences.
      */
 
     byte = *((unsigned char *) src);
@@ -331,12 +340,30 @@ Tcl_UtfToUniChar(
 	    /*
 	     * Four-byte-character lead byte followed by three trail bytes.
 	     */
-
+#if TCL_UTF_MAX == 4
+	    Tcl_UniChar surrogate;
+
+	    byte = (((byte & 0x07) << 18) | ((src[1] & 0x3F) << 12)
+		    | ((src[2] & 0x3F) << 6) | (src[3] & 0x3F)) - 0x10000;
+	    surrogate = (Tcl_UniChar) (0xD800 + (byte >> 10));
+	    if (byte & 0x100000) {
+		/* out of range, < 0x10000 or > 0x10ffff */
+	    } else if (*chPtr != surrogate) {
+		/* produce high surrogate, but don't advance source pointer */
+		*chPtr = surrogate;
+		return 0;
+	    } else {
+		/* produce low surrogate, and advance source pointer */
+		*chPtr = (Tcl_UniChar) (0xDC00 | (byte & 0x3FF));
+		return 4;
+	    }
+#else
 	    *chPtr = (Tcl_UniChar) (((byte & 0x07) << 18) | ((src[1] & 0x3F) << 12)
 		    | ((src[2] & 0x3F) << 6) | (src[3] & 0x3F));
 	    if ((unsigned)(*chPtr - 0x10000) <= 0xFFFFF) {
 		return 4;
 	    }
+#endif
 	}
 
 	/*
@@ -377,7 +404,7 @@ Tcl_UtfToUniCharDString(
 				 * appended to this previously initialized
 				 * DString. */
 {
-    Tcl_UniChar *w, *wString;
+    Tcl_UniChar ch, *w, *wString;
     const char *p, *end;
     int oldLength;
 
@@ -399,8 +426,8 @@ Tcl_UtfToUniCharDString(
     w = wString;
     end = src + length;
     for (p = src; p < end; ) {
-	p += TclUtfToUniChar(p, w);
-	w++;
+	p += TclUtfToUniChar(p, &ch);
+	*w++ = ch;
     }
     *w = '\0';
     Tcl_DStringSetLength(dsPtr,
@@ -434,9 +461,8 @@ Tcl_UtfCharComplete(
 				 * a complete UTF-8 character. */
     int length)			/* Length of above string in bytes. */
 {
-    int ch;
+    int ch = *((unsigned char *) src);
 
-    ch = *((unsigned char *) src);
     return length >= totalBytes[ch];
 }
 
@@ -464,8 +490,7 @@ Tcl_NumUtfChars(
     int length)			/* The length of the string in bytes, or -1
 				 * for strlen(string). */
 {
-    Tcl_UniChar ch;
-    register Tcl_UniChar *chPtr = &ch;
+    Tcl_UniChar ch = 0;
     register int i;
 
     /*
@@ -478,7 +503,7 @@ Tcl_NumUtfChars(
     i = 0;
     if (length < 0) {
 	while (*src != '\0') {
-	    src += TclUtfToUniChar(src, chPtr);
+	    src += TclUtfToUniChar(src, &ch);
 	    i++;
 	}
     } else {
@@ -489,7 +514,7 @@ Tcl_NumUtfChars(
 		length--;
 		src++;
 	    } else {
-		n = Tcl_UtfToUniChar(src, chPtr);
+		n = Tcl_UtfToUniChar(src, &ch);
 		length -= n;
 		src += n;
 	    }
@@ -524,7 +549,7 @@ Tcl_UtfFindFirst(
     int ch)			/* The Tcl_UniChar to search for. */
 {
     int len;
-    Tcl_UniChar find;
+    Tcl_UniChar find = 0;
 
     while (1) {
 	len = TclUtfToUniChar(src, &find);
@@ -563,7 +588,7 @@ Tcl_UtfFindLast(
     int ch)			/* The Tcl_UniChar to search for. */
 {
     int len;
-    Tcl_UniChar find;
+    Tcl_UniChar find = 0;
     const char *last;
 
     last = NULL;
@@ -603,9 +628,15 @@ const char *
 Tcl_UtfNext(
     const char *src)		/* The current location in the string. */
 {
-    Tcl_UniChar ch;
+    Tcl_UniChar ch = 0;
+    int len = TclUtfToUniChar(src, &ch);
 
-    return src + TclUtfToUniChar(src, &ch);
+#if TCL_UTF_MAX == 4
+    if (len == 0) {
+      len = TclUtfToUniChar(src, &ch);
+    }
+#endif
+    return src + len;
 }
 
 /*
@@ -638,8 +669,7 @@ Tcl_UtfPrev(
     const char *look;
     int i, byte;
 
-    src--;
-    look = src;
+    look = --src;
     for (i = 0; i < TCL_UTF_MAX; i++) {
 	if (look < start) {
 	    if (src < start) {
@@ -712,7 +742,7 @@ Tcl_UtfAtIndex(
     register const char *src,	/* The UTF-8 string. */
     register int index)		/* The position of the desired character. */
 {
-    Tcl_UniChar ch;
+    Tcl_UniChar ch = 0;
 
     while (index > 0) {
 	index--;
diff --git a/generic/tclUtil.c b/generic/tclUtil.c
index 553593c..0eddb00 100644
--- a/generic/tclUtil.c
+++ b/generic/tclUtil.c
@@ -1646,7 +1646,7 @@ Tcl_Backslash(
 				 * src, unless NULL. */
 {
     char buf[TCL_UTF_MAX];
-    Tcl_UniChar ch;
+    Tcl_UniChar ch = 0;
 
     Tcl_UtfBackslash(src, readPtr, buf);
     TclUtfToUniChar(buf, &ch);
diff --git a/win/tclWinPipe.c b/win/tclWinPipe.c
index fe0ed2d..4b372a5 100644
--- a/win/tclWinPipe.c
+++ b/win/tclWinPipe.c
@@ -1479,7 +1479,7 @@ BuildCommandLine(
 	    quote = 1;
 	} else {
 	    int count;
-	    Tcl_UniChar ch;
+	    Tcl_UniChar ch = 0;
 
 	    for (start = arg; *start != '\0'; start += count) {
 		count = TclUtfToUniChar(start, &ch);
-- 
cgit v0.12


From 78e17f7f0cce0233cc1009b3f7c3aa2ea32763d7 Mon Sep 17 00:00:00 2001
From: griffin <brian_griffin@mentor.com>
Date: Mon, 12 Jun 2017 14:04:29 +0000
Subject: Add support of 0d in the format %# conversion flag.  Add tests for
 same.

---
 doc/format.n           | 16 +++++++++-------
 generic/tclStringObj.c |  4 ++++
 tests/format.test      | 19 +++++++++++++++++++
 3 files changed, 32 insertions(+), 7 deletions(-)

diff --git a/doc/format.n b/doc/format.n
index ba044f2..a386464 100644
--- a/doc/format.n
+++ b/doc/format.n
@@ -83,14 +83,16 @@ Specifies that the number should be padded on the left with
 zeroes instead of spaces.
 .TP 10
 \fB#\fR
-Requests an alternate output form. For \fBo\fR and \fBO\fR
-conversions it guarantees that the first digit is always \fB0\fR.
-For \fBx\fR or \fBX\fR conversions, \fB0x\fR or \fB0X\fR (respectively)
-will be added to the beginning of the result unless it is zero.
+Requests an alternate output form. For \fBo\fR and \fBO\fR 
+conversions it guarantees that the first digit is always \fB0\fR. 
+For \fBx\fR or \fBX\fR conversions, \fB0x\fR or \fB0X\fR (respectively) 
+will be added to the beginning of the result unless it is zero. 
 For \fBb\fR conversions, \fB0b\fR
-will be added to the beginning of the result unless it is zero.
-For all floating-point conversions (\fBe\fR, \fBE\fR, \fBf\fR,
-\fBg\fR, and \fBG\fR) it guarantees that the result always
+will be added to the beginning of the result unless it is zero. 
+For \fBd\fR conversions, \fB0d\fR will be added to the beginning 
+of the result unless it is zero. 
+For all floating-point conversions (\fBe\fR, \fBE\fR, \fBf\fR, 
+\fBg\fR, and \fBG\fR) it guarantees that the result always 
 has a decimal point.
 For \fBg\fR and \fBG\fR conversions it specifies that
 trailing zeroes should not be removed.
diff --git a/generic/tclStringObj.c b/generic/tclStringObj.c
index 7c898b7..3a6e60e 100644
--- a/generic/tclStringObj.c
+++ b/generic/tclStringObj.c
@@ -2039,6 +2039,10 @@ Tcl_AppendFormatToObj(
 		    Tcl_AppendToObj(segment, "0b", 2);
 		    segmentLimit -= 2;
 		    break;
+		case 'd':
+		    Tcl_AppendToObj(segment, "0d", 2);
+		    segmentLimit -= 2;
+		    break;
 		}
 	    }
 
diff --git a/tests/format.test b/tests/format.test
index 722ad21..577365b 100644
--- a/tests/format.test
+++ b/tests/format.test
@@ -79,6 +79,25 @@ test format-1.11.1 {integer formatting} longIs64bit {
 test format-1.12 {integer formatting} {
     format "%b %#b %#b %llb" 5 0 5 [expr {2**100}]
 } {101 0b0 0b101 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}
+test format-1.13 {integer formatting} longIs32bit {
+    format "%#d %#d %#d %#d %#d" 0 6 34 16923 -12 -1
+} {0d0 0d6 0d34 0d16923 -0d12}
+test format-1.13.1 {integer formatting} longIs64bit {
+    format "%#d %#d %#d %#d %#d" 0 6 34 16923 -12 -1
+} {0d0 0d6 0d34 0d16923 -0d12}
+test format-1.14 {integer formatting} longIs32bit {
+    format "%#5d %#20d %#20d %#20d %#20d" 0 6 34 16923 -12 -1
+} {  0d0                  0d6                 0d34              0d16923                -0d12}
+test format-1.14.1 {integer formatting} longIs64bit {
+    format "%#5d %#20d %#20d %#20d %#20d" 0 6 34 16923 -12 -1
+} {  0d0                  0d6                 0d34              0d16923           -0d12}
+test format-1.15 {integer formatting} longIs32bit {
+    format "%-#5d %-#20d %-#20d %-#20d %-#20d" 0 6 34 16923 -12 -1
+} {0d0   0d6                  0d34                 0d16923              -0d12               }
+test format-1.15.1 {integer formatting} longIs64bit {
+    format "%-#5d %-#20d %-#20d %-#20d %-#20d" 0 6 34 16923 -12 -1
+} {0d0   0d6                  0d34                 0d16923              -0d12      }
+
 
 test format-2.1 {string formatting} {
     format "%s %s %c %s" abcd {This is a very long test string.} 120 x
-- 
cgit v0.12


From 84481c3d32d19d3c3d8bdc97d6b378fb9665ced7 Mon Sep 17 00:00:00 2001
From: dkf <donal.k.fellows@manchester.ac.uk>
Date: Tue, 13 Jun 2017 11:10:11 +0000
Subject: Add tests and docs.

---
 doc/define.n  |  15 ++++++++
 tests/oo.test | 107 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 122 insertions(+)

diff --git a/doc/define.n b/doc/define.n
index 7599ec0..1692c94 100644
--- a/doc/define.n
+++ b/doc/define.n
@@ -142,6 +142,8 @@ be afterwards.
 \fBself\fI subcommand arg ...\fR
 .TP
 \fBself\fI script\fR
+.TP
+\fBself\fR
 .
 This command is equivalent to calling \fBoo::objdefine\fR on the class being
 defined (see \fBCONFIGURING OBJECTS\fR below for a description of the
@@ -151,6 +153,13 @@ and
 .QW "\fBoo::define \fIcls \fBself \fIsubcommand ...\fR"
 operates identically to
 .QW "\fBoo::objdefine \fIcls subcommand ...\fR" .
+.RS
+.PP
+.VS TIP470
+If no arguments at all are used, this gives the name of the class currently
+being configured.
+.VE TIP470
+.RE
 .TP
 \fBsuperclass\fR ?\fI\-slotOperation\fR? ?\fIclassName ...\fR?
 .VS
@@ -265,6 +274,12 @@ not previously refer to a method in that object. Does not affect the classes
 that the object is an instance of. Does not change the export status of the
 method; if it was exported before, it will be afterwards.
 .TP
+\fBself \fR
+.
+.VS TIP470
+This gives the name of the object currently being configured.
+.VE TIP470
+.TP
 \fBunexport\fI name \fR?\fIname ...\fR?
 .
 This arranges for each of the named methods, \fIname\fR, to be not exported
diff --git a/tests/oo.test b/tests/oo.test
index e03911b..ae36f87 100644
--- a/tests/oo.test
+++ b/tests/oo.test
@@ -3766,6 +3766,113 @@ test oo-35.4 {Bug 593baa032c: mixins list teardown} {
     namespace eval [info object namespace D] [list [namespace which B] destroy]
 } {}
 
+test oo-36.1 {TIP #470: introspection within oo::define} {
+    oo::define oo::object self
+} ::oo::object
+test oo-36.2 {TIP #470: introspection within oo::define} -setup {
+    oo::class create Cls
+} -body {
+    oo::define Cls self
+} -cleanup {
+    Cls destroy
+} -result ::Cls
+test oo-36.3 {TIP #470: introspection within oo::define} -setup {
+    oo::class create Super
+    set result uncalled
+} -body {
+    oo::class create Sub {
+	superclass Super
+	::set ::result [self]
+    }
+    return $result
+} -cleanup {
+    Super destroy
+} -result ::Sub
+test oo-36.4 {TIP #470: introspection within oo::define} -setup {
+    oo::class create Super
+    set result uncalled
+} -body {
+    oo::class create Sub {
+	superclass Super
+	::set ::result [self {}]
+    }
+    return $result
+} -cleanup {
+    Super destroy
+} -result {}
+test oo-36.5 {TIP #470: introspection within oo::define} -setup {
+    oo::class create Super
+    set result uncalled
+} -body {
+    oo::class create Sub {
+	superclass Super
+	::set ::result [self self]
+    }
+} -cleanup {
+    Super destroy
+} -result ::Sub
+test oo-36.6 {TIP #470: introspection within oo::objdefine} -setup {
+    oo::class create Cls
+    set result uncalled
+} -body {
+    Cls create obj
+    oo::objdefine obj {
+	::set ::result [self]
+    }
+} -cleanup {
+    Cls destroy
+} -result ::obj
+test oo-36.7 {TIP #470: introspection within oo::objdefine} -setup {
+    oo::class create Cls
+} -body {
+    Cls create obj
+    oo::objdefine obj {
+	self
+    }
+} -cleanup {
+    Cls destroy
+} -result ::obj
+test oo-36.8 {TIP #470: introspection within oo::objdefine} -setup {
+    oo::class create Cls
+} -body {
+    Cls create obj
+    oo::objdefine obj {
+	self anything
+    }
+} -returnCodes error -cleanup {
+    Cls destroy
+} -result {wrong # args: should be "self"}
+test oo-36.9 {TIP #470: introspection within oo::define} -setup {
+    oo::class create Cls
+    set result uncalled
+} -body {
+    proc oo::define::testself {} {
+	global result
+	set result [list [catch {self} msg] $msg \
+			[catch {uplevel 1 self} msg] $msg]
+	return
+    }
+    list [oo::define Cls testself] $result
+} -cleanup {
+    Cls destroy
+    catch {rename oo::define::testself {}}
+} -result {{} {1 {this command may only be called from within the context of an ::oo::define or ::oo::objdefine command} 0 ::Cls}}
+test oo-36.10 {TIP #470: introspection within oo::define} -setup {
+    oo::class create Cls
+    set result uncalled
+} -body {
+    proc oo::objdefine::testself {} {
+	global result
+	set result [list [catch {self} msg] $msg \
+			[catch {uplevel 1 self} msg] $msg]
+	return
+    }
+    Cls create obj
+    list [oo::objdefine obj testself] $result
+} -cleanup {
+    Cls destroy
+    catch {rename oo::objdefine::testself {}}
+} -result {{} {1 {this command may only be called from within the context of an ::oo::define or ::oo::objdefine command} 0 ::obj}}
 
 cleanupTests
 return
-- 
cgit v0.12


From 865f11be2c3ee4294408debefcd72de0fc6b2772 Mon Sep 17 00:00:00 2001
From: dkf <donal.k.fellows@manchester.ac.uk>
Date: Wed, 14 Jun 2017 21:42:38 +0000
Subject: [f2336c116b] Move pragmas to make gcc happy; it is pickier than
 clang.

---
 unix/tclUnixSock.c | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/unix/tclUnixSock.c b/unix/tclUnixSock.c
index 2353f94..c0df035 100644
--- a/unix/tclUnixSock.c
+++ b/unix/tclUnixSock.c
@@ -730,6 +730,8 @@ TcpClose2Proc(
  */
 
 #ifndef NEED_FAKE_RFC2553
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wstrict-aliasing"
 static inline int
 IPv6AddressNeedsNumericRendering(
     struct in6_addr addr)
@@ -743,16 +745,14 @@ IPv6AddressNeedsNumericRendering(
      * at least some versions of OSX.
      */
 
-#pragma GCC diagnostic push
-#pragma GCC diagnostic ignored "-Wstrict-aliasing"
     if (!IN6_IS_ADDR_V4MAPPED(&addr)) {
-#pragma GCC diagnostic pop
         return 0;
     }
 
     return (addr.s6_addr[12] == 0 && addr.s6_addr[13] == 0
             && addr.s6_addr[14] == 0 && addr.s6_addr[15] == 0);
 }
+#pragma GCC diagnostic pop
 #endif /* NEED_FAKE_RFC2553 */
 
 static void
-- 
cgit v0.12


From affb7e28db4184bd802837ba53146b985adee9ba Mon Sep 17 00:00:00 2001
From: dkf <donal.k.fellows@manchester.ac.uk>
Date: Wed, 14 Jun 2017 21:49:08 +0000
Subject: [9c058c5803e30d02] Correction to cross linking in dict(n)'s SEE ALSO
 section.

---
 doc/dict.n | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/doc/dict.n b/doc/dict.n
index fecad85..cd7e94c 100644
--- a/doc/dict.n
+++ b/doc/dict.n
@@ -437,7 +437,7 @@ puts $foo
 #    prints: \fIa b foo {a b} bar 2 baz 3\fR
 .CE
 .SH "SEE ALSO"
-append(n), array(n), foreach(n), mapeach(n), incr(n), list(n), lappend(n), set(n)
+append(n), array(n), foreach(n), incr(n), list(n), lappend(n), lmap(n), set(n)
 .SH KEYWORDS
 dictionary, create, update, lookup, iterate, filter, map
 '\" Local Variables:
-- 
cgit v0.12


From f7860f65a494888a46e377831ba0419de5f364d9 Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Thu, 15 Jun 2017 09:13:51 +0000
Subject: Make panic in TclParseNumber() work when IEEE_FLOATING_POINT is not
 defined.

---
 generic/tclStrToD.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/generic/tclStrToD.c b/generic/tclStrToD.c
index 67b6482..2091928 100644
--- a/generic/tclStrToD.c
+++ b/generic/tclStrToD.c
@@ -1183,9 +1183,9 @@ TclParseNumber(
 	case sNA:
 	case sNANPAREN:
 	case sNANHEX:
+#endif
 	    Tcl_Panic("TclParseNumber: bad acceptState %d parsing '%s'",
 		    acceptState, bytes);
-#endif
 	case BINARY:
 	    shift = numTrailZeros;
 	    if (!significandOverflow && significandWide != 0 &&
-- 
cgit v0.12


From bcc916d762591d6fae72ea0ba0ac0c747bcc0173 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Fri, 16 Jun 2017 11:47:46 +0000
Subject: Better define the meaning of "first" and "last".

---
 generic/tclStringObj.c | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/generic/tclStringObj.c b/generic/tclStringObj.c
index aa99545..0a38836 100644
--- a/generic/tclStringObj.c
+++ b/generic/tclStringObj.c
@@ -2848,8 +2848,10 @@ TclStringCatObjv(
     Tcl_Obj **objPtrPtr)
 {
     Tcl_Obj *objPtr, *objResultPtr, * const *ov;
-    int oc, length = 0, binary = 1, first = 0, last = 0;
+    int oc, length = 0, binary = 1;
     int allowUniChar = 1, requestUniChar = 0;
+    int first = objc - 1;	/* Index of first value possibly not empty */
+    int last = 0;		/* Index of last value possibly not empty */
 
     /* assert ( objc >= 0 ) */
 
@@ -2981,9 +2983,9 @@ TclStringCatObjv(
 	} while (--oc);
     }
 
-    if (last == first /*|| length == 0 */) {
+    if (last <= first /*|| length == 0 */) {
 	/* Only one non-empty value or zero length; return first */
-	/* NOTE: (length == 0) implies (last == first) */
+	/* NOTE: (length == 0) implies (last <= first) */
 	*objPtrPtr = objv[first];
 	return TCL_OK;
     }
-- 
cgit v0.12


From fdf4b7c6eef91298ad2b24e4f622229eb10cc9b5 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Fri, 16 Jun 2017 12:56:03 +0000
Subject: Extend cases where string rep generation can be prevented.

---
 generic/tclStringObj.c | 16 ++++++++++++++++
 tests/string.test      | 15 +++++++++++++++
 2 files changed, 31 insertions(+)

diff --git a/generic/tclStringObj.c b/generic/tclStringObj.c
index 0a38836..261e01f 100644
--- a/generic/tclStringObj.c
+++ b/generic/tclStringObj.c
@@ -2966,9 +2966,25 @@ TclStringCatObjv(
 
 		Tcl_GetStringFromObj(objPtr, &numBytes); /* PANIC? */
 		if (numBytes == 0) {
+		    if (pendingPtr && pendingPtr->bytes) {
+			/*
+			 * Generating string rep of objPtr also 
+			 * generated string rep of pendingPtr.
+			 */
+			if (pendingPtr->length) {
+			    /* Can this happen? */
+			    goto foo;
+			} else {
+			    /* string-29.14 */
+			    first = objc - 1;
+			    last = 0;
+			    pendingPtr = NULL;
+			}
+		    }
 		    continue;
 		}
 		last = objc - oc;
+foo:
 		if (pendingPtr) {
 		    Tcl_GetStringFromObj(pendingPtr, &length); /* PANIC? */
 		    pendingPtr = NULL;
diff --git a/tests/string.test b/tests/string.test
index 9c43f29..7b02928 100644
--- a/tests/string.test
+++ b/tests/string.test
@@ -2024,6 +2024,21 @@ test string-29.13 {string cat, efficiency} -body {
     tcl::unsupported::representation [string cat \
 	[encoding convertto utf-8 {}] [encoding convertto utf-8 {}] [list x]]
 } -match glob -result {*, string representation "x"}
+test string-29.14 {string cat, efficiency} -setup {
+    set e [encoding convertto utf-8 {}]
+} -cleanup {
+    unset e
+} -body {
+    tcl::unsupported::representation [string cat $e $e [list x]]
+} -match glob -result {*no string representation}
+test string-29.15 {string cat, efficiency} -setup {
+    set e [encoding convertto utf-8 {}]
+    set f [encoding convertto utf-8 {}]
+} -cleanup {
+    unset e f
+} -body {
+    tcl::unsupported::representation [string cat $e $f $e $f [list x]]
+} -match glob -result {*no string representation}
 
 
 
-- 
cgit v0.12


From b146fea6c309eba008fed11685a34076a44d1ce0 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Fri, 16 Jun 2017 14:43:16 +0000
Subject: Rework the logic. Equivalent function.

---
 generic/tclStringObj.c | 28 +++++++++-------------------
 1 file changed, 9 insertions(+), 19 deletions(-)

diff --git a/generic/tclStringObj.c b/generic/tclStringObj.c
index 261e01f..587ba76 100644
--- a/generic/tclStringObj.c
+++ b/generic/tclStringObj.c
@@ -2965,32 +2965,22 @@ TclStringCatObjv(
 	    } else {
 
 		Tcl_GetStringFromObj(objPtr, &numBytes); /* PANIC? */
-		if (numBytes == 0) {
-		    if (pendingPtr && pendingPtr->bytes) {
-			/*
-			 * Generating string rep of objPtr also 
-			 * generated string rep of pendingPtr.
-			 */
-			if (pendingPtr->length) {
-			    /* Can this happen? */
-			    goto foo;
-			} else {
-			    /* string-29.14 */
-			    first = objc - 1;
-			    last = 0;
-			    pendingPtr = NULL;
-			}
-		    }
+		if (numBytes) {
+		    last = objc - oc;
+		} else if (pendingPtr == NULL || pendingPtr->bytes == NULL) {
 		    continue;
 		}
-		last = objc - oc;
-foo:
 		if (pendingPtr) {
 		    Tcl_GetStringFromObj(pendingPtr, &length); /* PANIC? */
 		    pendingPtr = NULL;
 		}
 		if (length == 0) {
-		    first = last;
+		    if (numBytes) {
+			first = last;
+		    } else {
+			first = objc - 1;
+			last = 0;
+		    }
 		} else if (numBytes > INT_MAX - length) {
 		    goto overflow;
 		}
-- 
cgit v0.12


From 214ae82fc9c08209d8d3ed426f86a72b10410c4e Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Fri, 16 Jun 2017 14:46:56 +0000
Subject: Use local variables.

---
 generic/tclStringObj.c | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/generic/tclStringObj.c b/generic/tclStringObj.c
index 587ba76..8155711 100644
--- a/generic/tclStringObj.c
+++ b/generic/tclStringObj.c
@@ -2847,7 +2847,7 @@ TclStringCatObjv(
     Tcl_Obj * const objv[],
     Tcl_Obj **objPtrPtr)
 {
-    Tcl_Obj *objPtr, *objResultPtr, * const *ov;
+    Tcl_Obj *objResultPtr, * const *ov;
     int oc, length = 0, binary = 1;
     int allowUniChar = 1, requestUniChar = 0;
     int first = objc - 1;	/* Index of first value possibly not empty */
@@ -2872,7 +2872,7 @@ TclStringCatObjv(
 
     ov = objv, oc = objc;
     do {
-	objPtr = *ov++;
+	Tcl_Obj *objPtr = *ov++;
 
 	if (objPtr->bytes) {
 	    /* Value has a string rep. */
@@ -2908,7 +2908,7 @@ TclStringCatObjv(
 	/* Result will be pure byte array. Pre-size it */
 	ov = objv; oc = objc;
 	do {
-	    objPtr = *ov++;
+	    Tcl_Obj *objPtr = *ov++;
 
 	    if (objPtr->bytes == NULL) {
 		int numBytes;
@@ -2929,7 +2929,7 @@ TclStringCatObjv(
 	/* Result will be pure Tcl_UniChar array. Pre-size it. */
 	ov = objv; oc = objc;
 	do {
-	    objPtr = *ov++;
+	    Tcl_Obj *objPtr = *ov++;
 
 	    if ((objPtr->bytes == NULL) || (objPtr->length)) {
 		int numChars;
@@ -2954,7 +2954,7 @@ TclStringCatObjv(
 	do {
 	    int numBytes;
 
-	    objPtr = *ov++;
+	    Tcl_Obj *objPtr = *ov++;
 
 	    if ((length == 0) && (objPtr->bytes == NULL) && !pendingPtr) {
 		/* No string rep; Take the chance we can avoid making it */
-- 
cgit v0.12


From 44fb1d2c660ae623debe25e06b4ce34c30791141 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Fri, 16 Jun 2017 15:51:12 +0000
Subject: Factor out and simplify loop scanning leading known empty values.

---
 generic/tclStringObj.c | 21 +++++++++++++++++++++
 1 file changed, 21 insertions(+)

diff --git a/generic/tclStringObj.c b/generic/tclStringObj.c
index 8155711..870696e 100644
--- a/generic/tclStringObj.c
+++ b/generic/tclStringObj.c
@@ -2952,6 +2952,26 @@ TclStringCatObjv(
 	/* Result will be concat of string reps. Pre-size it. */
 	ov = objv; oc = objc;
 	do {
+	    /* assert ( pendingPtr == NULL ) */
+	    /* assert ( length == 0 ) */
+
+	    Tcl_Obj *objPtr = *ov++;
+
+	    if (objPtr->bytes == NULL) {
+		/* No string rep; Take the chance we can avoid making it */
+		pendingPtr = objPtr;
+	    } else {
+		Tcl_GetStringFromObj(objPtr, &length); /* PANIC? */
+	    }
+	} while (--oc && (length == 0) && (pendingPtr == NULL));
+
+      if (oc) {
+
+	/* assert ( length > 0 || pendingPtr != NULL )  */
+
+	first = last = objc - oc - 1;
+
+	do {
 	    int numBytes;
 
 	    Tcl_Obj *objPtr = *ov++;
@@ -2987,6 +3007,7 @@ TclStringCatObjv(
 		length += numBytes;
 	    }
 	} while (--oc);
+      }
     }
 
     if (last <= first /*|| length == 0 */) {
-- 
cgit v0.12


From 58311abbb709a5255f685e5d45ae837b0e9c7251 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Fri, 16 Jun 2017 16:07:48 +0000
Subject: Split loop into two cases for further simplification.

---
 generic/tclStringObj.c | 45 +++++++++++++++++++++++++++++++++++++++++++--
 1 file changed, 43 insertions(+), 2 deletions(-)

diff --git a/generic/tclStringObj.c b/generic/tclStringObj.c
index 870696e..be686cf 100644
--- a/generic/tclStringObj.c
+++ b/generic/tclStringObj.c
@@ -2965,11 +2965,52 @@ TclStringCatObjv(
 	    }
 	} while (--oc && (length == 0) && (pendingPtr == NULL));
 
+	first = last = objc - oc - 1;
+
+	while (oc && (length == 0)) {
+	    int numBytes;
+	    Tcl_Obj *objPtr = *ov++;
+
+	    /* assert ( pendingPtr != NULL ) <-- aiming for */
+
+	    if ((length == 0) && (objPtr->bytes == NULL) && !pendingPtr) {
+		/* No string rep; Take the chance we can avoid making it */
+
+		last = objc - oc;
+		first = last;
+		pendingPtr = objPtr;
+	    } else {
+
+		Tcl_GetStringFromObj(objPtr, &numBytes); /* PANIC? */
+		if (numBytes) {
+		    last = objc - oc;
+		} else if (pendingPtr == NULL || pendingPtr->bytes == NULL) {
+		    --oc;
+		    continue;
+		}
+		if (pendingPtr) {
+		    Tcl_GetStringFromObj(pendingPtr, &length); /* PANIC? */
+		    pendingPtr = NULL;
+		}
+		if (length == 0) {
+		    if (numBytes) {
+			first = last;
+		    } else {
+			first = objc - 1;
+			last = 0;
+		    }
+		} else if (numBytes > INT_MAX - length) {
+		    goto overflow;
+		}
+		length += numBytes;
+	    }
+	    --oc;
+	}
+
       if (oc) {
 
-	/* assert ( length > 0 || pendingPtr != NULL )  */
+	/* assert ( length > 0 )  */
 
-	first = last = objc - oc - 1;
 
 	do {
 	    int numBytes;
-- 
cgit v0.12


From 5425edf173bf9efcf17955623e5be64196eae2fa Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Fri, 16 Jun 2017 16:23:22 +0000
Subject: Simplify the final loop when we know we're generating strings for
 all.

---
 generic/tclStringObj.c | 40 +++++++---------------------------------
 1 file changed, 7 insertions(+), 33 deletions(-)

diff --git a/generic/tclStringObj.c b/generic/tclStringObj.c
index be686cf..51d6c13 100644
--- a/generic/tclStringObj.c
+++ b/generic/tclStringObj.c
@@ -3007,48 +3007,22 @@ TclStringCatObjv(
 	    --oc;
 	}
 
-      if (oc) {
-
-	/* assert ( length > 0 )  */
-
-
-	do {
+	while (oc) {
 	    int numBytes;
-
 	    Tcl_Obj *objPtr = *ov++;
 
-	    if ((length == 0) && (objPtr->bytes == NULL) && !pendingPtr) {
-		/* No string rep; Take the chance we can avoid making it */
+	    /* assert ( length > 0 && pendingPtr == NULL )  */
 
+	    Tcl_GetStringFromObj(objPtr, &numBytes); /* PANIC? */
+	    if (numBytes) {
 		last = objc - oc;
-		first = last;
-		pendingPtr = objPtr;
-	    } else {
-
-		Tcl_GetStringFromObj(objPtr, &numBytes); /* PANIC? */
-		if (numBytes) {
-		    last = objc - oc;
-		} else if (pendingPtr == NULL || pendingPtr->bytes == NULL) {
-		    continue;
-		}
-		if (pendingPtr) {
-		    Tcl_GetStringFromObj(pendingPtr, &length); /* PANIC? */
-		    pendingPtr = NULL;
-		}
-		if (length == 0) {
-		    if (numBytes) {
-			first = last;
-		    } else {
-			first = objc - 1;
-			last = 0;
-		    }
-		} else if (numBytes > INT_MAX - length) {
+		if (numBytes > INT_MAX - length) {
 		    goto overflow;
 		}
 		length += numBytes;
 	    }
-	} while (--oc);
-      }
+	    --oc;
+	}
     }
 
     if (last <= first /*|| length == 0 */) {
-- 
cgit v0.12


From b4133af5ee0c655f627443f04d50f492eedc58fa Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Fri, 16 Jun 2017 19:54:57 +0000
Subject: Another reworking, now with comments.

---
 generic/tclStringObj.c | 79 +++++++++++++++++++++++++++-----------------------
 1 file changed, 43 insertions(+), 36 deletions(-)

diff --git a/generic/tclStringObj.c b/generic/tclStringObj.c
index 51d6c13..41dad65 100644
--- a/generic/tclStringObj.c
+++ b/generic/tclStringObj.c
@@ -2947,65 +2947,72 @@ TclStringCatObjv(
 	    }
 	} while (--oc);
     } else {
-	Tcl_Obj *pendingPtr = NULL;
-
 	/* Result will be concat of string reps. Pre-size it. */
 	ov = objv; oc = objc;
 	do {
-	    /* assert ( pendingPtr == NULL ) */
-	    /* assert ( length == 0 ) */
+	    Tcl_Obj *pendingPtr = NULL;
 
-	    Tcl_Obj *objPtr = *ov++;
+	    /*
+	     * Loop until a possibly non-empty value is reached.
+	     * Keep string rep generation pending when possible.
+	     */
 
-	    if (objPtr->bytes == NULL) {
-		/* No string rep; Take the chance we can avoid making it */
-		pendingPtr = objPtr;
-	    } else {
-		Tcl_GetStringFromObj(objPtr, &length); /* PANIC? */
-	    }
-	} while (--oc && (length == 0) && (pendingPtr == NULL));
+	    do {
+		/* assert ( pendingPtr == NULL ) */
+		/* assert ( length == 0 ) */
 
-	first = last = objc - oc - 1;
+		Tcl_Obj *objPtr = *ov++;
 
-	while (oc && (length == 0)) {
-	    int numBytes;
-	    Tcl_Obj *objPtr = *ov++;
+		if (objPtr->bytes == NULL) {
+		    /* No string rep; Take the chance we can avoid making it */
+		    pendingPtr = objPtr;
+		} else {
+		    Tcl_GetStringFromObj(objPtr, &length); /* PANIC? */
+		}
+	    } while (--oc && (length == 0) && (pendingPtr == NULL));
+
+	    /*
+ 	     * Either we found a possibly non-empty value, and we
+ 	     * remember this index as the first and last such value so
+ 	     * far seen, or (oc == 0) and all values are known empty,
+ 	     * so first = last = objc - 1 signals the right quick return.
+ 	     */
 
-	    /* assert ( pendingPtr != NULL ) <-- aiming for */
+	    first = last = objc - oc - 1;
 
-	    if ((length == 0) && (objPtr->bytes == NULL) && !pendingPtr) {
-		/* No string rep; Take the chance we can avoid making it */
+	    if (oc && (length == 0)) {
+		int numBytes;
 
-		last = objc - oc;
-		first = last;
-		pendingPtr = objPtr;
-	    } else {
+		/* assert ( pendingPtr != NULL ) */
+
+		/*
+		 * There's a pending value followed by more values.
+		 * Loop over remaining values generating strings until
+		 * a non-empty value is found, or the pending value gets
+		 * its string generated.
+		 */
+
+		do {
+		    Tcl_Obj *objPtr = *ov++;
+		    Tcl_GetStringFromObj(objPtr, &numBytes); /* PANIC? */
+		} while (--oc && numBytes == 0 && pendingPtr->bytes == NULL);
 
-		Tcl_GetStringFromObj(objPtr, &numBytes); /* PANIC? */
 		if (numBytes) {
-		    last = objc - oc;
-		} else if (pendingPtr == NULL || pendingPtr->bytes == NULL) {
-		    --oc;
-		    continue;
+		    last = objc -oc -1;
 		}
-		if (pendingPtr) {
-		    Tcl_GetStringFromObj(pendingPtr, &length); /* PANIC? */
-		    pendingPtr = NULL;
+		if (oc || numBytes) {
+		    Tcl_GetStringFromObj(pendingPtr, &length);
 		}
 		if (length == 0) {
 		    if (numBytes) {
 			first = last;
-		    } else {
-			first = objc - 1;
-			last = 0;
 		    }
 		} else if (numBytes > INT_MAX - length) {
 		    goto overflow;
 		}
 		length += numBytes;
 	    }
-	    --oc;
-	}
+	} while (oc && (length == 0));
 
 	while (oc) {
 	    int numBytes;
-- 
cgit v0.12


From 0e24bd44bfdeacaed97aa9b1292be5689fca79f1 Mon Sep 17 00:00:00 2001
From: dkf <donal.k.fellows@manchester.ac.uk>
Date: Sun, 18 Jun 2017 14:01:00 +0000
Subject: Factor out chunk of non-obvious code in the guts of [oo::define] into
 one place.

---
 generic/tclOODefineCmds.c | 200 +++++++++++++++++-----------------------------
 1 file changed, 74 insertions(+), 126 deletions(-)

diff --git a/generic/tclOODefineCmds.c b/generic/tclOODefineCmds.c
index 8747ff5..e953dc0 100644
--- a/generic/tclOODefineCmds.c
+++ b/generic/tclOODefineCmds.c
@@ -47,8 +47,11 @@ struct DeclaredSlot {
 static inline void	BumpGlobalEpoch(Tcl_Interp *interp, Class *classPtr);
 static Tcl_Command	FindCommand(Tcl_Interp *interp, Tcl_Obj *stringObj,
 			    Tcl_Namespace *const namespacePtr);
-static void		GenerateErrorInfo(Tcl_Interp *interp, Object *oPtr,
+static inline void	GenerateErrorInfo(Tcl_Interp *interp, Object *oPtr,
 			    Tcl_Obj *savedNameObj, const char *typeOfSubject);
+static inline int	MagicDefinitionInvoke(Tcl_Interp *interp,
+			    Tcl_Namespace *nsPtr, int cmdIndex,
+			    int objc, Tcl_Obj *const *objv);
 static inline Class *	GetClassInOuterContext(Tcl_Interp *interp,
 			    Tcl_Obj *className, const char *errMsg);
 static inline int	InitDefineContext(Tcl_Interp *interp,
@@ -755,7 +758,7 @@ GetClassInOuterContext(
  * ----------------------------------------------------------------------
  */
 
-static void
+static inline void
 GenerateErrorInfo(
     Tcl_Interp *interp,		/* Where to store the error info trace. */
     Object *oPtr,		/* What object (or class) was being configured
@@ -787,6 +790,69 @@ GenerateErrorInfo(
 /*
  * ----------------------------------------------------------------------
  *
+ * MagicDefinitionInvoke --
+ *	Part of the implementation of the "oo::define" and "oo::objdefine"
+ *	commands that is used to implement the more-than-one-argument case,
+ *	applying ensemble-like tricks with dispatch so that error messages are
+ *	clearer. Doesn't handle the management of the stack frame.
+ *
+ * ----------------------------------------------------------------------
+ */
+
+static inline int
+MagicDefinitionInvoke(
+    Tcl_Interp *interp,
+    Tcl_Namespace *nsPtr,
+    int cmdIndex,
+    int objc,
+    Tcl_Obj *const *objv)
+{
+    Tcl_Obj *objPtr, *obj2Ptr, **objs;
+    Tcl_Command cmd;
+    int isRoot, dummy, result, offset = cmdIndex + 1;
+
+    /*
+     * More than one argument: fire them through the ensemble processing
+     * engine so that everything appears to be good and proper in error
+     * messages. Note that we cannot just concatenate and send through
+     * Tcl_EvalObjEx, as that doesn't do ensemble processing, and we cannot go
+     * through Tcl_EvalObjv without the extra work to pre-find the command, as
+     * that finds command names in the wrong namespace at the moment. Ugly!
+     */
+
+    isRoot = TclInitRewriteEnsemble(interp, offset, 1, objv);
+
+    /*
+     * Build the list of arguments using a Tcl_Obj as a workspace. See
+     * comments above for why these contortions are necessary.
+     */
+
+    objPtr = Tcl_NewObj();
+    obj2Ptr = Tcl_NewObj();
+    cmd = FindCommand(interp, objv[cmdIndex], nsPtr);
+    if (cmd == NULL) {
+	/* punt this case! */
+	Tcl_AppendObjToObj(obj2Ptr, objv[cmdIndex]);
+    } else {
+	Tcl_GetCommandFullName(interp, cmd, obj2Ptr);
+    }
+    Tcl_ListObjAppendElement(NULL, objPtr, obj2Ptr);
+    /* TODO: overflow? */
+    Tcl_ListObjReplace(NULL, objPtr, 1, 0, objc-offset, objv+offset);
+    Tcl_ListObjGetElements(NULL, objPtr, &dummy, &objs);
+
+    result = Tcl_EvalObjv(interp, objc-cmdIndex, objs, TCL_EVAL_INVOKE);
+    if (isRoot) {
+	TclResetRewriteEnsemble(interp, 1);
+    }
+    Tcl_DecrRefCount(objPtr);
+
+    return result;
+}
+
+/*
+ * ----------------------------------------------------------------------
+ *
  * TclOODefineObjCmd --
  *	Implementation of the "oo::define" command. Works by effectively doing
  *	the same as 'namespace eval', but with extra magic applied so that the
@@ -805,8 +871,8 @@ TclOODefineObjCmd(
     Tcl_Obj *const *objv)
 {
     Foundation *fPtr = TclOOGetFoundation(interp);
-    int result;
     Object *oPtr;
+    int result;
 
     if (objc < 3) {
 	Tcl_WrongNumArgs(interp, 1, objv, "className arg ?arg ...?");
@@ -846,46 +912,7 @@ TclOODefineObjCmd(
 	}
 	TclDecrRefCount(objNameObj);
     } else {
-	Tcl_Obj *objPtr, *obj2Ptr, **objs;
-	Tcl_Command cmd;
-	int isRoot, dummy;
-
-	/*
-	 * More than one argument: fire them through the ensemble processing
-	 * engine so that everything appears to be good and proper in error
-	 * messages. Note that we cannot just concatenate and send through
-	 * Tcl_EvalObjEx, as that doesn't do ensemble processing, and we
-	 * cannot go through Tcl_EvalObjv without the extra work to pre-find
-	 * the command, as that finds command names in the wrong namespace at
-	 * the moment. Ugly!
-	 */
-
-	isRoot = TclInitRewriteEnsemble(interp, 3, 1, objv);
-
-	/*
-	 * Build the list of arguments using a Tcl_Obj as a workspace. See
-	 * comments above for why these contortions are necessary.
-	 */
-
-	objPtr = Tcl_NewObj();
-	obj2Ptr = Tcl_NewObj();
-	cmd = FindCommand(interp, objv[2], fPtr->defineNs);
-	if (cmd == NULL) {
-	    /* punt this case! */
-	    Tcl_AppendObjToObj(obj2Ptr, objv[2]);
-	} else {
-	    Tcl_GetCommandFullName(interp, cmd, obj2Ptr);
-	}
-	Tcl_ListObjAppendElement(NULL, objPtr, obj2Ptr);
-	/* TODO: overflow? */
-	Tcl_ListObjReplace(NULL, objPtr, 1, 0, objc-3, objv+3);
-	Tcl_ListObjGetElements(NULL, objPtr, &dummy, &objs);
-
-	result = Tcl_EvalObjv(interp, objc-2, objs, TCL_EVAL_INVOKE);
-	if (isRoot) {
-	    TclResetRewriteEnsemble(interp, 1);
-	}
-	Tcl_DecrRefCount(objPtr);
+	result = MagicDefinitionInvoke(interp, fPtr->defineNs, 2, objc, objv);
     }
     DelRef(oPtr);
 
@@ -918,8 +945,8 @@ TclOOObjDefObjCmd(
     Tcl_Obj *const *objv)
 {
     Foundation *fPtr = TclOOGetFoundation(interp);
-    int isRoot, result;
     Object *oPtr;
+    int result;
 
     if (objc < 3) {
 	Tcl_WrongNumArgs(interp, 1, objv, "objectName arg ?arg ...?");
@@ -952,47 +979,7 @@ TclOOObjDefObjCmd(
 	}
 	TclDecrRefCount(objNameObj);
     } else {
-	Tcl_Obj *objPtr, *obj2Ptr, **objs;
-	Tcl_Command cmd;
-	int dummy;
-
-	/*
-	 * More than one argument: fire them through the ensemble processing
-	 * engine so that everything appears to be good and proper in error
-	 * messages. Note that we cannot just concatenate and send through
-	 * Tcl_EvalObjEx, as that doesn't do ensemble processing, and we
-	 * cannot go through Tcl_EvalObjv without the extra work to pre-find
-	 * the command, as that finds command names in the wrong namespace at
-	 * the moment. Ugly!
-	 */
-
-	isRoot = TclInitRewriteEnsemble(interp, 3, 1, objv);
-
-	/*
-	 * Build the list of arguments using a Tcl_Obj as a workspace. See
-	 * comments above for why these contortions are necessary.
-	 */
-
-	objPtr = Tcl_NewObj();
-	obj2Ptr = Tcl_NewObj();
-	cmd = FindCommand(interp, objv[2], fPtr->objdefNs);
-	if (cmd == NULL) {
-	    /* punt this case! */
-	    Tcl_AppendObjToObj(obj2Ptr, objv[2]);
-	} else {
-	    Tcl_GetCommandFullName(interp, cmd, obj2Ptr);
-	}
-	Tcl_ListObjAppendElement(NULL, objPtr, obj2Ptr);
-	/* TODO: overflow? */
-	Tcl_ListObjReplace(NULL, objPtr, 1, 0, objc-3, objv+3);
-	Tcl_ListObjGetElements(NULL, objPtr, &dummy, &objs);
-
-	result = Tcl_EvalObjv(interp, objc-2, objs, TCL_EVAL_INVOKE);
-
-	if (isRoot) {
-	    TclResetRewriteEnsemble(interp, 1);
-	}
-	Tcl_DecrRefCount(objPtr);
+	result = MagicDefinitionInvoke(interp, fPtr->objdefNs, 2, objc, objv);
     }
     DelRef(oPtr);
 
@@ -1025,8 +1012,8 @@ TclOODefineSelfObjCmd(
     Tcl_Obj *const *objv)
 {
     Foundation *fPtr = TclOOGetFoundation(interp);
-    int result;
     Object *oPtr;
+    int result;
 
     if (objc < 2) {
 	Tcl_WrongNumArgs(interp, 1, objv, "arg ?arg ...?");
@@ -1059,46 +1046,7 @@ TclOODefineSelfObjCmd(
 	}
 	TclDecrRefCount(objNameObj);
     } else {
-	Tcl_Obj *objPtr, *obj2Ptr, **objs;
-	Tcl_Command cmd;
-	int isRoot, dummy;
-
-	/*
-	 * More than one argument: fire them through the ensemble processing
-	 * engine so that everything appears to be good and proper in error
-	 * messages. Note that we cannot just concatenate and send through
-	 * Tcl_EvalObjEx, as that doesn't do ensemble processing, and we
-	 * cannot go through Tcl_EvalObjv without the extra work to pre-find
-	 * the command, as that finds command names in the wrong namespace at
-	 * the moment. Ugly!
-	 */
-
-	isRoot = TclInitRewriteEnsemble(interp, 2, 1, objv);
-
-	/*
-	 * Build the list of arguments using a Tcl_Obj as a workspace. See
-	 * comments above for why these contortions are necessary.
-	 */
-
-	objPtr = Tcl_NewObj();
-	obj2Ptr = Tcl_NewObj();
-	cmd = FindCommand(interp, objv[1], fPtr->objdefNs);
-	if (cmd == NULL) {
-	    /* punt this case! */
-	    Tcl_AppendObjToObj(obj2Ptr, objv[1]);
-	} else {
-	    Tcl_GetCommandFullName(interp, cmd, obj2Ptr);
-	}
-	Tcl_ListObjAppendElement(NULL, objPtr, obj2Ptr);
-	/* TODO: overflow? */
-	Tcl_ListObjReplace(NULL, objPtr, 1, 0, objc-2, objv+2);
-	Tcl_ListObjGetElements(NULL, objPtr, &dummy, &objs);
-
-	result = Tcl_EvalObjv(interp, objc-1, objs, TCL_EVAL_INVOKE);
-	if (isRoot) {
-	    TclResetRewriteEnsemble(interp, 1);
-	}
-	Tcl_DecrRefCount(objPtr);
+	result = MagicDefinitionInvoke(interp, fPtr->objdefNs, 1, objc, objv);
     }
     DelRef(oPtr);
 
-- 
cgit v0.12


From 1a87cddf6f7c4d151340598b7e26b3562049e101 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Mon, 19 Jun 2017 18:04:23 +0000
Subject: Silence compiler warning

---
 generic/tclDictObj.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/generic/tclDictObj.c b/generic/tclDictObj.c
index 729f4b8..d6211cd 100644
--- a/generic/tclDictObj.c
+++ b/generic/tclDictObj.c
@@ -530,7 +530,7 @@ UpdateStringOfDict(
 	elem = TclGetString(keyPtr);
 	length = keyPtr->length;
 	bytesNeeded += TclScanElement(elem, length, flagPtr+i);
-	if (bytesNeeded < 0) {
+	if (bytesNeeded > INT_MAX) {
 	    Tcl_Panic("max size for a Tcl value (%d bytes) exceeded", INT_MAX);
 	}
 
-- 
cgit v0.12


From 0d73e7f26411020d1345814bcdb9fe78272335ff Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Thu, 22 Jun 2017 08:15:13 +0000
Subject: Add test-cases, testing the legacy behavior of "format %#d"

---
 doc/GetInt.3      |  2 +-
 tests/format.test | 19 +++++++++++++++++++
 tests/util.test   |  6 +++---
 3 files changed, 23 insertions(+), 4 deletions(-)

diff --git a/doc/GetInt.3 b/doc/GetInt.3
index 3e7204c..5a3304a 100644
--- a/doc/GetInt.3
+++ b/doc/GetInt.3
@@ -4,7 +4,7 @@
 '\"
 '\" See the file "license.terms" for information on usage and redistribution
 '\" of this file, and for a DISCLAIMER OF ALL WARRANTIES.
-'\" 
+'\"
 .TH Tcl_GetInt 3 "" Tcl "Tcl Library Procedures"
 .so man.macros
 .BS
diff --git a/tests/format.test b/tests/format.test
index 9afedd9..2795ac2 100644
--- a/tests/format.test
+++ b/tests/format.test
@@ -78,6 +78,25 @@ test format-1.11.1 {integer formatting} longIs64bit {
 test format-1.12 {integer formatting} {
     format "%b %#b %#b %llb" 5 0 5 [expr {2**100}]
 } {101 0b0 0b101 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}
+test format-1.13 {integer formatting} longIs32bit {
+    format "%#d %#d %#d %#d %#d" 0 6 34 16923 -12 -1
+} {0 6 34 16923 -12}
+test format-1.13.1 {integer formatting} longIs64bit {
+    format "%#d %#d %#d %#d %#d" 0 6 34 16923 -12 -1
+} {0 6 34 16923 -12}
+test format-1.14 {integer formatting} longIs32bit {
+    format "%#5d %#20d %#20d %#20d %#20d" 0 6 34 16923 -12 -1
+} {    0                    6                   34                16923                  -12}
+test format-1.14.1 {integer formatting} longIs64bit {
+    format "%#5d %#20d %#20d %#20d %#20d" 0 6 34 16923 -12 -1
+} {    0                    6                   34                16923                  -12}
+test format-1.15 {integer formatting} longIs32bit {
+    format "%-#5d %-#20d %-#20d %-#20d %-#20d" 0 6 34 16923 -12 -1
+} {0     6                    34                   16923                -12                 }
+test format-1.15.1 {integer formatting} longIs64bit {
+    format "%-#5d %-#20d %-#20d %-#20d %-#20d" 0 6 34 16923 -12 -1
+} {0     6                    34                   16923                -12                 }
+
 
 test format-2.1 {string formatting} {
     format "%s %s %c %s" abcd {This is a very long test string.} 120 x
diff --git a/tests/util.test b/tests/util.test
index 7782f35..2ac11bf 100644
--- a/tests/util.test
+++ b/tests/util.test
@@ -208,7 +208,7 @@ test util-4.6 {Tcl_ConcatObj - utf-8 sequence with "whitespace" char} {
 } \xe0
 test util-4.7 {Tcl_ConcatObj - refCount safety} testconcatobj {
     # Check for Bug #1447328 (actually, bugs in its original "fix"). One of the
-    # symptoms was Bug #2055782. 
+    # symptoms was Bug #2055782.
     testconcatobj
 } {}
 
@@ -566,7 +566,7 @@ test util-9.1.3 {TclGetIntForIndex} {
 } k
 test util-9.2.0 {TclGetIntForIndex} {
     string index abcd end
-} d 
+} d
 test util-9.2.1 {TclGetIntForIndex} -body {
     string index abcd { end}
 } -returnCodes error -match glob -result *
@@ -4007,7 +4007,7 @@ test util-17.1 {bankers' rounding [Bug 3349507]} {ieeeFloatingPoint} {
     }
     set r
 } [list {*}{
-    0x43fffffffffffffc 0xc3fffffffffffffc 
+    0x43fffffffffffffc 0xc3fffffffffffffc
     0x43fffffffffffffc 0xc3fffffffffffffc
     0x43fffffffffffffd 0xc3fffffffffffffd
     0x43fffffffffffffe 0xc3fffffffffffffe
-- 
cgit v0.12


From c0468b3264ddb516b6086f5f0c57aaee4824f25c Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Thu, 22 Jun 2017 08:58:14 +0000
Subject: Upgrade all internal character tables to Unicode 10

---
 generic/regc_locale.c |  411 +++++++++--------
 generic/tclUniData.c  | 1232 +++++++++++++++++++++++++------------------------
 2 files changed, 836 insertions(+), 807 deletions(-)

diff --git a/generic/regc_locale.c b/generic/regc_locale.c
index 6444b55..32adee8 100644
--- a/generic/regc_locale.c
+++ b/generic/regc_locale.c
@@ -140,73 +140,73 @@ static const crange alphaRangeTable[] = {
     {0x3f7, 0x481}, {0x48a, 0x52f}, {0x531, 0x556}, {0x561, 0x587},
     {0x5d0, 0x5ea}, {0x5f0, 0x5f2}, {0x620, 0x64a}, {0x671, 0x6d3},
     {0x6fa, 0x6fc}, {0x712, 0x72f}, {0x74d, 0x7a5}, {0x7ca, 0x7ea},
-    {0x800, 0x815}, {0x840, 0x858}, {0x8a0, 0x8b4}, {0x8b6, 0x8bd},
-    {0x904, 0x939}, {0x958, 0x961}, {0x971, 0x980}, {0x985, 0x98c},
-    {0x993, 0x9a8}, {0x9aa, 0x9b0}, {0x9b6, 0x9b9}, {0x9df, 0x9e1},
-    {0xa05, 0xa0a}, {0xa13, 0xa28}, {0xa2a, 0xa30}, {0xa59, 0xa5c},
-    {0xa72, 0xa74}, {0xa85, 0xa8d}, {0xa8f, 0xa91}, {0xa93, 0xaa8},
-    {0xaaa, 0xab0}, {0xab5, 0xab9}, {0xb05, 0xb0c}, {0xb13, 0xb28},
-    {0xb2a, 0xb30}, {0xb35, 0xb39}, {0xb5f, 0xb61}, {0xb85, 0xb8a},
-    {0xb8e, 0xb90}, {0xb92, 0xb95}, {0xba8, 0xbaa}, {0xbae, 0xbb9},
-    {0xc05, 0xc0c}, {0xc0e, 0xc10}, {0xc12, 0xc28}, {0xc2a, 0xc39},
-    {0xc58, 0xc5a}, {0xc85, 0xc8c}, {0xc8e, 0xc90}, {0xc92, 0xca8},
-    {0xcaa, 0xcb3}, {0xcb5, 0xcb9}, {0xd05, 0xd0c}, {0xd0e, 0xd10},
-    {0xd12, 0xd3a}, {0xd54, 0xd56}, {0xd5f, 0xd61}, {0xd7a, 0xd7f},
-    {0xd85, 0xd96}, {0xd9a, 0xdb1}, {0xdb3, 0xdbb}, {0xdc0, 0xdc6},
-    {0xe01, 0xe30}, {0xe40, 0xe46}, {0xe94, 0xe97}, {0xe99, 0xe9f},
-    {0xea1, 0xea3}, {0xead, 0xeb0}, {0xec0, 0xec4}, {0xedc, 0xedf},
-    {0xf40, 0xf47}, {0xf49, 0xf6c}, {0xf88, 0xf8c}, {0x1000, 0x102a},
-    {0x1050, 0x1055}, {0x105a, 0x105d}, {0x106e, 0x1070}, {0x1075, 0x1081},
-    {0x10a0, 0x10c5}, {0x10d0, 0x10fa}, {0x10fc, 0x1248}, {0x124a, 0x124d},
-    {0x1250, 0x1256}, {0x125a, 0x125d}, {0x1260, 0x1288}, {0x128a, 0x128d},
-    {0x1290, 0x12b0}, {0x12b2, 0x12b5}, {0x12b8, 0x12be}, {0x12c2, 0x12c5},
-    {0x12c8, 0x12d6}, {0x12d8, 0x1310}, {0x1312, 0x1315}, {0x1318, 0x135a},
-    {0x1380, 0x138f}, {0x13a0, 0x13f5}, {0x13f8, 0x13fd}, {0x1401, 0x166c},
-    {0x166f, 0x167f}, {0x1681, 0x169a}, {0x16a0, 0x16ea}, {0x16f1, 0x16f8},
-    {0x1700, 0x170c}, {0x170e, 0x1711}, {0x1720, 0x1731}, {0x1740, 0x1751},
-    {0x1760, 0x176c}, {0x176e, 0x1770}, {0x1780, 0x17b3}, {0x1820, 0x1877},
-    {0x1880, 0x1884}, {0x1887, 0x18a8}, {0x18b0, 0x18f5}, {0x1900, 0x191e},
-    {0x1950, 0x196d}, {0x1970, 0x1974}, {0x1980, 0x19ab}, {0x19b0, 0x19c9},
-    {0x1a00, 0x1a16}, {0x1a20, 0x1a54}, {0x1b05, 0x1b33}, {0x1b45, 0x1b4b},
-    {0x1b83, 0x1ba0}, {0x1bba, 0x1be5}, {0x1c00, 0x1c23}, {0x1c4d, 0x1c4f},
-    {0x1c5a, 0x1c7d}, {0x1c80, 0x1c88}, {0x1ce9, 0x1cec}, {0x1cee, 0x1cf1},
-    {0x1d00, 0x1dbf}, {0x1e00, 0x1f15}, {0x1f18, 0x1f1d}, {0x1f20, 0x1f45},
-    {0x1f48, 0x1f4d}, {0x1f50, 0x1f57}, {0x1f5f, 0x1f7d}, {0x1f80, 0x1fb4},
-    {0x1fb6, 0x1fbc}, {0x1fc2, 0x1fc4}, {0x1fc6, 0x1fcc}, {0x1fd0, 0x1fd3},
-    {0x1fd6, 0x1fdb}, {0x1fe0, 0x1fec}, {0x1ff2, 0x1ff4}, {0x1ff6, 0x1ffc},
-    {0x2090, 0x209c}, {0x210a, 0x2113}, {0x2119, 0x211d}, {0x212a, 0x212d},
-    {0x212f, 0x2139}, {0x213c, 0x213f}, {0x2145, 0x2149}, {0x2c00, 0x2c2e},
-    {0x2c30, 0x2c5e}, {0x2c60, 0x2ce4}, {0x2ceb, 0x2cee}, {0x2d00, 0x2d25},
-    {0x2d30, 0x2d67}, {0x2d80, 0x2d96}, {0x2da0, 0x2da6}, {0x2da8, 0x2dae},
-    {0x2db0, 0x2db6}, {0x2db8, 0x2dbe}, {0x2dc0, 0x2dc6}, {0x2dc8, 0x2dce},
-    {0x2dd0, 0x2dd6}, {0x2dd8, 0x2dde}, {0x3031, 0x3035}, {0x3041, 0x3096},
-    {0x309d, 0x309f}, {0x30a1, 0x30fa}, {0x30fc, 0x30ff}, {0x3105, 0x312d},
-    {0x3131, 0x318e}, {0x31a0, 0x31ba}, {0x31f0, 0x31ff}, {0x3400, 0x4db5},
-    {0x4e00, 0x9fd5}, {0xa000, 0xa48c}, {0xa4d0, 0xa4fd}, {0xa500, 0xa60c},
-    {0xa610, 0xa61f}, {0xa640, 0xa66e}, {0xa67f, 0xa69d}, {0xa6a0, 0xa6e5},
-    {0xa717, 0xa71f}, {0xa722, 0xa788}, {0xa78b, 0xa7ae}, {0xa7b0, 0xa7b7},
-    {0xa7f7, 0xa801}, {0xa803, 0xa805}, {0xa807, 0xa80a}, {0xa80c, 0xa822},
-    {0xa840, 0xa873}, {0xa882, 0xa8b3}, {0xa8f2, 0xa8f7}, {0xa90a, 0xa925},
-    {0xa930, 0xa946}, {0xa960, 0xa97c}, {0xa984, 0xa9b2}, {0xa9e0, 0xa9e4},
-    {0xa9e6, 0xa9ef}, {0xa9fa, 0xa9fe}, {0xaa00, 0xaa28}, {0xaa40, 0xaa42},
-    {0xaa44, 0xaa4b}, {0xaa60, 0xaa76}, {0xaa7e, 0xaaaf}, {0xaab9, 0xaabd},
-    {0xaadb, 0xaadd}, {0xaae0, 0xaaea}, {0xaaf2, 0xaaf4}, {0xab01, 0xab06},
-    {0xab09, 0xab0e}, {0xab11, 0xab16}, {0xab20, 0xab26}, {0xab28, 0xab2e},
-    {0xab30, 0xab5a}, {0xab5c, 0xab65}, {0xab70, 0xabe2}, {0xac00, 0xd7a3},
-    {0xd7b0, 0xd7c6}, {0xd7cb, 0xd7fb}, {0xdc00, 0xdc3e}, {0xdc40, 0xdc7e},
-    {0xdc80, 0xdcbe}, {0xdcc0, 0xdcfe}, {0xdd00, 0xdd3e}, {0xdd40, 0xdd7e},
-    {0xdd80, 0xddbe}, {0xddc0, 0xddfe}, {0xde00, 0xde3e}, {0xde40, 0xde7e},
-    {0xde80, 0xdebe}, {0xdec0, 0xdefe}, {0xdf00, 0xdf3e}, {0xdf40, 0xdf7e},
-    {0xdf80, 0xdfbe}, {0xdfc0, 0xdffe}, {0xf900, 0xfa6d}, {0xfa70, 0xfad9},
-    {0xfb00, 0xfb06}, {0xfb13, 0xfb17}, {0xfb1f, 0xfb28}, {0xfb2a, 0xfb36},
-    {0xfb38, 0xfb3c}, {0xfb46, 0xfbb1}, {0xfbd3, 0xfd3d}, {0xfd50, 0xfd8f},
-    {0xfd92, 0xfdc7}, {0xfdf0, 0xfdfb}, {0xfe70, 0xfe74}, {0xfe76, 0xfefc},
-    {0xff21, 0xff3a}, {0xff41, 0xff5a}, {0xff66, 0xffbe}, {0xffc2, 0xffc7},
-    {0xffca, 0xffcf}, {0xffd2, 0xffd7}, {0xffda, 0xffdc}
+    {0x800, 0x815}, {0x840, 0x858}, {0x860, 0x86a}, {0x8a0, 0x8b4},
+    {0x8b6, 0x8bd}, {0x904, 0x939}, {0x958, 0x961}, {0x971, 0x980},
+    {0x985, 0x98c}, {0x993, 0x9a8}, {0x9aa, 0x9b0}, {0x9b6, 0x9b9},
+    {0x9df, 0x9e1}, {0xa05, 0xa0a}, {0xa13, 0xa28}, {0xa2a, 0xa30},
+    {0xa59, 0xa5c}, {0xa72, 0xa74}, {0xa85, 0xa8d}, {0xa8f, 0xa91},
+    {0xa93, 0xaa8}, {0xaaa, 0xab0}, {0xab5, 0xab9}, {0xb05, 0xb0c},
+    {0xb13, 0xb28}, {0xb2a, 0xb30}, {0xb35, 0xb39}, {0xb5f, 0xb61},
+    {0xb85, 0xb8a}, {0xb8e, 0xb90}, {0xb92, 0xb95}, {0xba8, 0xbaa},
+    {0xbae, 0xbb9}, {0xc05, 0xc0c}, {0xc0e, 0xc10}, {0xc12, 0xc28},
+    {0xc2a, 0xc39}, {0xc58, 0xc5a}, {0xc85, 0xc8c}, {0xc8e, 0xc90},
+    {0xc92, 0xca8}, {0xcaa, 0xcb3}, {0xcb5, 0xcb9}, {0xd05, 0xd0c},
+    {0xd0e, 0xd10}, {0xd12, 0xd3a}, {0xd54, 0xd56}, {0xd5f, 0xd61},
+    {0xd7a, 0xd7f}, {0xd85, 0xd96}, {0xd9a, 0xdb1}, {0xdb3, 0xdbb},
+    {0xdc0, 0xdc6}, {0xe01, 0xe30}, {0xe40, 0xe46}, {0xe94, 0xe97},
+    {0xe99, 0xe9f}, {0xea1, 0xea3}, {0xead, 0xeb0}, {0xec0, 0xec4},
+    {0xedc, 0xedf}, {0xf40, 0xf47}, {0xf49, 0xf6c}, {0xf88, 0xf8c},
+    {0x1000, 0x102a}, {0x1050, 0x1055}, {0x105a, 0x105d}, {0x106e, 0x1070},
+    {0x1075, 0x1081}, {0x10a0, 0x10c5}, {0x10d0, 0x10fa}, {0x10fc, 0x1248},
+    {0x124a, 0x124d}, {0x1250, 0x1256}, {0x125a, 0x125d}, {0x1260, 0x1288},
+    {0x128a, 0x128d}, {0x1290, 0x12b0}, {0x12b2, 0x12b5}, {0x12b8, 0x12be},
+    {0x12c2, 0x12c5}, {0x12c8, 0x12d6}, {0x12d8, 0x1310}, {0x1312, 0x1315},
+    {0x1318, 0x135a}, {0x1380, 0x138f}, {0x13a0, 0x13f5}, {0x13f8, 0x13fd},
+    {0x1401, 0x166c}, {0x166f, 0x167f}, {0x1681, 0x169a}, {0x16a0, 0x16ea},
+    {0x16f1, 0x16f8}, {0x1700, 0x170c}, {0x170e, 0x1711}, {0x1720, 0x1731},
+    {0x1740, 0x1751}, {0x1760, 0x176c}, {0x176e, 0x1770}, {0x1780, 0x17b3},
+    {0x1820, 0x1877}, {0x1880, 0x1884}, {0x1887, 0x18a8}, {0x18b0, 0x18f5},
+    {0x1900, 0x191e}, {0x1950, 0x196d}, {0x1970, 0x1974}, {0x1980, 0x19ab},
+    {0x19b0, 0x19c9}, {0x1a00, 0x1a16}, {0x1a20, 0x1a54}, {0x1b05, 0x1b33},
+    {0x1b45, 0x1b4b}, {0x1b83, 0x1ba0}, {0x1bba, 0x1be5}, {0x1c00, 0x1c23},
+    {0x1c4d, 0x1c4f}, {0x1c5a, 0x1c7d}, {0x1c80, 0x1c88}, {0x1ce9, 0x1cec},
+    {0x1cee, 0x1cf1}, {0x1d00, 0x1dbf}, {0x1e00, 0x1f15}, {0x1f18, 0x1f1d},
+    {0x1f20, 0x1f45}, {0x1f48, 0x1f4d}, {0x1f50, 0x1f57}, {0x1f5f, 0x1f7d},
+    {0x1f80, 0x1fb4}, {0x1fb6, 0x1fbc}, {0x1fc2, 0x1fc4}, {0x1fc6, 0x1fcc},
+    {0x1fd0, 0x1fd3}, {0x1fd6, 0x1fdb}, {0x1fe0, 0x1fec}, {0x1ff2, 0x1ff4},
+    {0x1ff6, 0x1ffc}, {0x2090, 0x209c}, {0x210a, 0x2113}, {0x2119, 0x211d},
+    {0x212a, 0x212d}, {0x212f, 0x2139}, {0x213c, 0x213f}, {0x2145, 0x2149},
+    {0x2c00, 0x2c2e}, {0x2c30, 0x2c5e}, {0x2c60, 0x2ce4}, {0x2ceb, 0x2cee},
+    {0x2d00, 0x2d25}, {0x2d30, 0x2d67}, {0x2d80, 0x2d96}, {0x2da0, 0x2da6},
+    {0x2da8, 0x2dae}, {0x2db0, 0x2db6}, {0x2db8, 0x2dbe}, {0x2dc0, 0x2dc6},
+    {0x2dc8, 0x2dce}, {0x2dd0, 0x2dd6}, {0x2dd8, 0x2dde}, {0x3031, 0x3035},
+    {0x3041, 0x3096}, {0x309d, 0x309f}, {0x30a1, 0x30fa}, {0x30fc, 0x30ff},
+    {0x3105, 0x312e}, {0x3131, 0x318e}, {0x31a0, 0x31ba}, {0x31f0, 0x31ff},
+    {0x3400, 0x4db5}, {0x4e00, 0x9fea}, {0xa000, 0xa48c}, {0xa4d0, 0xa4fd},
+    {0xa500, 0xa60c}, {0xa610, 0xa61f}, {0xa640, 0xa66e}, {0xa67f, 0xa69d},
+    {0xa6a0, 0xa6e5}, {0xa717, 0xa71f}, {0xa722, 0xa788}, {0xa78b, 0xa7ae},
+    {0xa7b0, 0xa7b7}, {0xa7f7, 0xa801}, {0xa803, 0xa805}, {0xa807, 0xa80a},
+    {0xa80c, 0xa822}, {0xa840, 0xa873}, {0xa882, 0xa8b3}, {0xa8f2, 0xa8f7},
+    {0xa90a, 0xa925}, {0xa930, 0xa946}, {0xa960, 0xa97c}, {0xa984, 0xa9b2},
+    {0xa9e0, 0xa9e4}, {0xa9e6, 0xa9ef}, {0xa9fa, 0xa9fe}, {0xaa00, 0xaa28},
+    {0xaa40, 0xaa42}, {0xaa44, 0xaa4b}, {0xaa60, 0xaa76}, {0xaa7e, 0xaaaf},
+    {0xaab9, 0xaabd}, {0xaadb, 0xaadd}, {0xaae0, 0xaaea}, {0xaaf2, 0xaaf4},
+    {0xab01, 0xab06}, {0xab09, 0xab0e}, {0xab11, 0xab16}, {0xab20, 0xab26},
+    {0xab28, 0xab2e}, {0xab30, 0xab5a}, {0xab5c, 0xab65}, {0xab70, 0xabe2},
+    {0xac00, 0xd7a3}, {0xd7b0, 0xd7c6}, {0xd7cb, 0xd7fb}, {0xdc00, 0xdc3e},
+    {0xdc40, 0xdc7e}, {0xdc80, 0xdcbe}, {0xdcc0, 0xdcfe}, {0xdd00, 0xdd3e},
+    {0xdd40, 0xdd7e}, {0xdd80, 0xddbe}, {0xddc0, 0xddfe}, {0xde00, 0xde3e},
+    {0xde40, 0xde7e}, {0xde80, 0xdebe}, {0xdec0, 0xdefe}, {0xdf00, 0xdf3e},
+    {0xdf40, 0xdf7e}, {0xdf80, 0xdfbe}, {0xdfc0, 0xdffe}, {0xf900, 0xfa6d},
+    {0xfa70, 0xfad9}, {0xfb00, 0xfb06}, {0xfb13, 0xfb17}, {0xfb1f, 0xfb28},
+    {0xfb2a, 0xfb36}, {0xfb38, 0xfb3c}, {0xfb46, 0xfbb1}, {0xfbd3, 0xfd3d},
+    {0xfd50, 0xfd8f}, {0xfd92, 0xfdc7}, {0xfdf0, 0xfdfb}, {0xfe70, 0xfe74},
+    {0xfe76, 0xfefc}, {0xff21, 0xff3a}, {0xff41, 0xff5a}, {0xff66, 0xffbe},
+    {0xffc2, 0xffc7}, {0xffca, 0xffcf}, {0xffd2, 0xffd7}, {0xffda, 0xffdc}
 #if TCL_UTF_MAX > 4
     ,{0x10000, 0x1000b}, {0x1000d, 0x10026}, {0x10028, 0x1003a}, {0x1003f, 0x1004d},
     {0x10050, 0x1005d}, {0x10080, 0x100fa}, {0x10280, 0x1029c}, {0x102a0, 0x102d0},
-    {0x10300, 0x1031f}, {0x10330, 0x10340}, {0x10342, 0x10349}, {0x10350, 0x10375},
+    {0x10300, 0x1031f}, {0x1032d, 0x10340}, {0x10342, 0x10349}, {0x10350, 0x10375},
     {0x10380, 0x1039d}, {0x103a0, 0x103c3}, {0x103c8, 0x103cf}, {0x10400, 0x1049d},
     {0x104b0, 0x104d3}, {0x104d8, 0x104fb}, {0x10500, 0x10527}, {0x10530, 0x10563},
     {0x10600, 0x10736}, {0x10740, 0x10755}, {0x10760, 0x10767}, {0x10800, 0x10805},
@@ -222,24 +222,26 @@ static const crange alphaRangeTable[] = {
     {0x11305, 0x1130c}, {0x11313, 0x11328}, {0x1132a, 0x11330}, {0x11335, 0x11339},
     {0x1135d, 0x11361}, {0x11400, 0x11434}, {0x11447, 0x1144a}, {0x11480, 0x114af},
     {0x11580, 0x115ae}, {0x115d8, 0x115db}, {0x11600, 0x1162f}, {0x11680, 0x116aa},
-    {0x11700, 0x11719}, {0x118a0, 0x118df}, {0x11ac0, 0x11af8}, {0x11c00, 0x11c08},
-    {0x11c0a, 0x11c2e}, {0x11c72, 0x11c8f}, {0x12000, 0x12399}, {0x12480, 0x12543},
-    {0x13000, 0x1342e}, {0x14400, 0x14646}, {0x16800, 0x16a38}, {0x16a40, 0x16a5e},
-    {0x16ad0, 0x16aed}, {0x16b00, 0x16b2f}, {0x16b40, 0x16b43}, {0x16b63, 0x16b77},
-    {0x16b7d, 0x16b8f}, {0x16f00, 0x16f44}, {0x16f93, 0x16f9f}, {0x17000, 0x187ec},
-    {0x18800, 0x18af2}, {0x1bc00, 0x1bc6a}, {0x1bc70, 0x1bc7c}, {0x1bc80, 0x1bc88},
-    {0x1bc90, 0x1bc99}, {0x1d400, 0x1d454}, {0x1d456, 0x1d49c}, {0x1d4a9, 0x1d4ac},
-    {0x1d4ae, 0x1d4b9}, {0x1d4bd, 0x1d4c3}, {0x1d4c5, 0x1d505}, {0x1d507, 0x1d50a},
-    {0x1d50d, 0x1d514}, {0x1d516, 0x1d51c}, {0x1d51e, 0x1d539}, {0x1d53b, 0x1d53e},
-    {0x1d540, 0x1d544}, {0x1d54a, 0x1d550}, {0x1d552, 0x1d6a5}, {0x1d6a8, 0x1d6c0},
-    {0x1d6c2, 0x1d6da}, {0x1d6dc, 0x1d6fa}, {0x1d6fc, 0x1d714}, {0x1d716, 0x1d734},
-    {0x1d736, 0x1d74e}, {0x1d750, 0x1d76e}, {0x1d770, 0x1d788}, {0x1d78a, 0x1d7a8},
-    {0x1d7aa, 0x1d7c2}, {0x1d7c4, 0x1d7cb}, {0x1e800, 0x1e8c4}, {0x1e900, 0x1e943},
-    {0x1ee00, 0x1ee03}, {0x1ee05, 0x1ee1f}, {0x1ee29, 0x1ee32}, {0x1ee34, 0x1ee37},
-    {0x1ee4d, 0x1ee4f}, {0x1ee67, 0x1ee6a}, {0x1ee6c, 0x1ee72}, {0x1ee74, 0x1ee77},
-    {0x1ee79, 0x1ee7c}, {0x1ee80, 0x1ee89}, {0x1ee8b, 0x1ee9b}, {0x1eea1, 0x1eea3},
-    {0x1eea5, 0x1eea9}, {0x1eeab, 0x1eebb}, {0x20000, 0x2a6d6}, {0x2a700, 0x2b734},
-    {0x2b740, 0x2b81d}, {0x2b820, 0x2cea1}, {0x2f800, 0x2fa1d}
+    {0x11700, 0x11719}, {0x118a0, 0x118df}, {0x11a0b, 0x11a32}, {0x11a5c, 0x11a83},
+    {0x11a86, 0x11a89}, {0x11ac0, 0x11af8}, {0x11c00, 0x11c08}, {0x11c0a, 0x11c2e},
+    {0x11c72, 0x11c8f}, {0x11d00, 0x11d06}, {0x11d0b, 0x11d30}, {0x12000, 0x12399},
+    {0x12480, 0x12543}, {0x13000, 0x1342e}, {0x14400, 0x14646}, {0x16800, 0x16a38},
+    {0x16a40, 0x16a5e}, {0x16ad0, 0x16aed}, {0x16b00, 0x16b2f}, {0x16b40, 0x16b43},
+    {0x16b63, 0x16b77}, {0x16b7d, 0x16b8f}, {0x16f00, 0x16f44}, {0x16f93, 0x16f9f},
+    {0x17000, 0x187ec}, {0x18800, 0x18af2}, {0x1b000, 0x1b11e}, {0x1b170, 0x1b2fb},
+    {0x1bc00, 0x1bc6a}, {0x1bc70, 0x1bc7c}, {0x1bc80, 0x1bc88}, {0x1bc90, 0x1bc99},
+    {0x1d400, 0x1d454}, {0x1d456, 0x1d49c}, {0x1d4a9, 0x1d4ac}, {0x1d4ae, 0x1d4b9},
+    {0x1d4bd, 0x1d4c3}, {0x1d4c5, 0x1d505}, {0x1d507, 0x1d50a}, {0x1d50d, 0x1d514},
+    {0x1d516, 0x1d51c}, {0x1d51e, 0x1d539}, {0x1d53b, 0x1d53e}, {0x1d540, 0x1d544},
+    {0x1d54a, 0x1d550}, {0x1d552, 0x1d6a5}, {0x1d6a8, 0x1d6c0}, {0x1d6c2, 0x1d6da},
+    {0x1d6dc, 0x1d6fa}, {0x1d6fc, 0x1d714}, {0x1d716, 0x1d734}, {0x1d736, 0x1d74e},
+    {0x1d750, 0x1d76e}, {0x1d770, 0x1d788}, {0x1d78a, 0x1d7a8}, {0x1d7aa, 0x1d7c2},
+    {0x1d7c4, 0x1d7cb}, {0x1e800, 0x1e8c4}, {0x1e900, 0x1e943}, {0x1ee00, 0x1ee03},
+    {0x1ee05, 0x1ee1f}, {0x1ee29, 0x1ee32}, {0x1ee34, 0x1ee37}, {0x1ee4d, 0x1ee4f},
+    {0x1ee67, 0x1ee6a}, {0x1ee6c, 0x1ee72}, {0x1ee74, 0x1ee77}, {0x1ee79, 0x1ee7c},
+    {0x1ee80, 0x1ee89}, {0x1ee8b, 0x1ee9b}, {0x1eea1, 0x1eea3}, {0x1eea5, 0x1eea9},
+    {0x1eeab, 0x1eebb}, {0x20000, 0x2a6d6}, {0x2a700, 0x2b734}, {0x2b740, 0x2b81d},
+    {0x2b820, 0x2cea1}, {0x2ceb0, 0x2ebe0}, {0x2f800, 0x2fa1d}
 #endif
 };
 
@@ -250,28 +252,29 @@ static const chr alphaCharTable[] = {
     0x38c, 0x559, 0x66e, 0x66f, 0x6d5, 0x6e5, 0x6e6, 0x6ee, 0x6ef,
     0x6ff, 0x710, 0x7b1, 0x7f4, 0x7f5, 0x7fa, 0x81a, 0x824, 0x828,
     0x93d, 0x950, 0x98f, 0x990, 0x9b2, 0x9bd, 0x9ce, 0x9dc, 0x9dd,
-    0x9f0, 0x9f1, 0xa0f, 0xa10, 0xa32, 0xa33, 0xa35, 0xa36, 0xa38,
-    0xa39, 0xa5e, 0xab2, 0xab3, 0xabd, 0xad0, 0xae0, 0xae1, 0xaf9,
-    0xb0f, 0xb10, 0xb32, 0xb33, 0xb3d, 0xb5c, 0xb5d, 0xb71, 0xb83,
-    0xb99, 0xb9a, 0xb9c, 0xb9e, 0xb9f, 0xba3, 0xba4, 0xbd0, 0xc3d,
-    0xc60, 0xc61, 0xc80, 0xcbd, 0xcde, 0xce0, 0xce1, 0xcf1, 0xcf2,
-    0xd3d, 0xd4e, 0xdbd, 0xe32, 0xe33, 0xe81, 0xe82, 0xe84, 0xe87,
-    0xe88, 0xe8a, 0xe8d, 0xea5, 0xea7, 0xeaa, 0xeab, 0xeb2, 0xeb3,
-    0xebd, 0xec6, 0xf00, 0x103f, 0x1061, 0x1065, 0x1066, 0x108e, 0x10c7,
-    0x10cd, 0x1258, 0x12c0, 0x17d7, 0x17dc, 0x18aa, 0x1aa7, 0x1bae, 0x1baf,
-    0x1cf5, 0x1cf6, 0x1f59, 0x1f5b, 0x1f5d, 0x1fbe, 0x2071, 0x207f, 0x2102,
-    0x2107, 0x2115, 0x2124, 0x2126, 0x2128, 0x214e, 0x2183, 0x2184, 0x2cf2,
-    0x2cf3, 0x2d27, 0x2d2d, 0x2d6f, 0x2e2f, 0x3005, 0x3006, 0x303b, 0x303c,
-    0xa62a, 0xa62b, 0xa8fb, 0xa8fd, 0xa9cf, 0xaa7a, 0xaab1, 0xaab5, 0xaab6,
-    0xaac0, 0xaac2, 0xfb1d, 0xfb3e, 0xfb40, 0xfb41, 0xfb43, 0xfb44
+    0x9f0, 0x9f1, 0x9fc, 0xa0f, 0xa10, 0xa32, 0xa33, 0xa35, 0xa36,
+    0xa38, 0xa39, 0xa5e, 0xab2, 0xab3, 0xabd, 0xad0, 0xae0, 0xae1,
+    0xaf9, 0xb0f, 0xb10, 0xb32, 0xb33, 0xb3d, 0xb5c, 0xb5d, 0xb71,
+    0xb83, 0xb99, 0xb9a, 0xb9c, 0xb9e, 0xb9f, 0xba3, 0xba4, 0xbd0,
+    0xc3d, 0xc60, 0xc61, 0xc80, 0xcbd, 0xcde, 0xce0, 0xce1, 0xcf1,
+    0xcf2, 0xd3d, 0xd4e, 0xdbd, 0xe32, 0xe33, 0xe81, 0xe82, 0xe84,
+    0xe87, 0xe88, 0xe8a, 0xe8d, 0xea5, 0xea7, 0xeaa, 0xeab, 0xeb2,
+    0xeb3, 0xebd, 0xec6, 0xf00, 0x103f, 0x1061, 0x1065, 0x1066, 0x108e,
+    0x10c7, 0x10cd, 0x1258, 0x12c0, 0x17d7, 0x17dc, 0x18aa, 0x1aa7, 0x1bae,
+    0x1baf, 0x1cf5, 0x1cf6, 0x1f59, 0x1f5b, 0x1f5d, 0x1fbe, 0x2071, 0x207f,
+    0x2102, 0x2107, 0x2115, 0x2124, 0x2126, 0x2128, 0x214e, 0x2183, 0x2184,
+    0x2cf2, 0x2cf3, 0x2d27, 0x2d2d, 0x2d6f, 0x2e2f, 0x3005, 0x3006, 0x303b,
+    0x303c, 0xa62a, 0xa62b, 0xa8fb, 0xa8fd, 0xa9cf, 0xaa7a, 0xaab1, 0xaab5,
+    0xaab6, 0xaac0, 0xaac2, 0xfb1d, 0xfb3e, 0xfb40, 0xfb41, 0xfb43, 0xfb44
 #if TCL_UTF_MAX > 4
     ,0x1003c, 0x1003d, 0x10808, 0x10837, 0x10838, 0x1083c, 0x108f4, 0x108f5, 0x109be,
     0x109bf, 0x10a00, 0x11176, 0x111da, 0x111dc, 0x11288, 0x1130f, 0x11310, 0x11332,
-    0x11333, 0x1133d, 0x11350, 0x114c4, 0x114c5, 0x114c7, 0x11644, 0x118ff, 0x11c40,
-    0x16f50, 0x16fe0, 0x1b000, 0x1b001, 0x1d49e, 0x1d49f, 0x1d4a2, 0x1d4a5, 0x1d4a6,
-    0x1d4bb, 0x1d546, 0x1ee21, 0x1ee22, 0x1ee24, 0x1ee27, 0x1ee39, 0x1ee3b, 0x1ee42,
-    0x1ee47, 0x1ee49, 0x1ee4b, 0x1ee51, 0x1ee52, 0x1ee54, 0x1ee57, 0x1ee59, 0x1ee5b,
-    0x1ee5d, 0x1ee5f, 0x1ee61, 0x1ee62, 0x1ee64, 0x1ee7e
+    0x11333, 0x1133d, 0x11350, 0x114c4, 0x114c5, 0x114c7, 0x11644, 0x118ff, 0x11a00,
+    0x11a3a, 0x11a50, 0x11c40, 0x11d08, 0x11d09, 0x11d46, 0x16f50, 0x16fe0, 0x16fe1,
+    0x1d49e, 0x1d49f, 0x1d4a2, 0x1d4a5, 0x1d4a6, 0x1d4bb, 0x1d546, 0x1ee21, 0x1ee22,
+    0x1ee24, 0x1ee27, 0x1ee39, 0x1ee3b, 0x1ee42, 0x1ee47, 0x1ee49, 0x1ee4b, 0x1ee51,
+    0x1ee52, 0x1ee54, 0x1ee57, 0x1ee59, 0x1ee5b, 0x1ee5d, 0x1ee5f, 0x1ee61, 0x1ee62,
+    0x1ee64, 0x1ee7e
 #endif
 };
 
@@ -321,8 +324,8 @@ static const crange digitRangeTable[] = {
     ,{0x104a0, 0x104a9}, {0x11066, 0x1106f}, {0x110f0, 0x110f9}, {0x11136, 0x1113f},
     {0x111d0, 0x111d9}, {0x112f0, 0x112f9}, {0x11450, 0x11459}, {0x114d0, 0x114d9},
     {0x11650, 0x11659}, {0x116c0, 0x116c9}, {0x11730, 0x11739}, {0x118e0, 0x118e9},
-    {0x11c50, 0x11c59}, {0x16a60, 0x16a69}, {0x16b50, 0x16b59}, {0x1d7ce, 0x1d7ff},
-    {0x1e950, 0x1e959}
+    {0x11c50, 0x11c59}, {0x11d50, 0x11d59}, {0x16a60, 0x16a69}, {0x16b50, 0x16b59},
+    {0x1d7ce, 0x1d7ff}, {0x1e950, 0x1e959}
 #endif
 };
 
@@ -345,7 +348,7 @@ static const crange punctRangeTable[] = {
     {0x1b5a, 0x1b60}, {0x1bfc, 0x1bff}, {0x1c3b, 0x1c3f}, {0x1cc0, 0x1cc7},
     {0x2010, 0x2027}, {0x2030, 0x2043}, {0x2045, 0x2051}, {0x2053, 0x205e},
     {0x2308, 0x230b}, {0x2768, 0x2775}, {0x27e6, 0x27ef}, {0x2983, 0x2998},
-    {0x29d8, 0x29db}, {0x2cf9, 0x2cfc}, {0x2e00, 0x2e2e}, {0x2e30, 0x2e44},
+    {0x29d8, 0x29db}, {0x2cf9, 0x2cfc}, {0x2e00, 0x2e2e}, {0x2e30, 0x2e49},
     {0x3001, 0x3003}, {0x3008, 0x3011}, {0x3014, 0x301f}, {0xa60d, 0xa60f},
     {0xa6f2, 0xa6f7}, {0xa874, 0xa877}, {0xa8f8, 0xa8fa}, {0xa9c1, 0xa9cd},
     {0xaa5c, 0xaa5f}, {0xfe10, 0xfe19}, {0xfe30, 0xfe52}, {0xfe54, 0xfe61},
@@ -356,7 +359,8 @@ static const crange punctRangeTable[] = {
     {0x10b99, 0x10b9c}, {0x11047, 0x1104d}, {0x110be, 0x110c1}, {0x11140, 0x11143},
     {0x111c5, 0x111c9}, {0x111dd, 0x111df}, {0x11238, 0x1123d}, {0x1144b, 0x1144f},
     {0x115c1, 0x115d7}, {0x11641, 0x11643}, {0x11660, 0x1166c}, {0x1173c, 0x1173e},
-    {0x11c41, 0x11c45}, {0x12470, 0x12474}, {0x16b37, 0x16b3b}, {0x1da87, 0x1da8b}
+    {0x11a3f, 0x11a46}, {0x11a9a, 0x11a9c}, {0x11a9e, 0x11aa2}, {0x11c41, 0x11c45},
+    {0x12470, 0x12474}, {0x16b37, 0x16b3b}, {0x1da87, 0x1da8b}
 #endif
 };
 
@@ -367,14 +371,14 @@ static const chr punctCharTable[] = {
     0xab, 0xb6, 0xb7, 0xbb, 0xbf, 0x37e, 0x387, 0x589, 0x58a,
     0x5be, 0x5c0, 0x5c3, 0x5c6, 0x5f3, 0x5f4, 0x609, 0x60a, 0x60c,
     0x60d, 0x61b, 0x61e, 0x61f, 0x6d4, 0x85e, 0x964, 0x965, 0x970,
-    0xaf0, 0xdf4, 0xe4f, 0xe5a, 0xe5b, 0xf14, 0xf85, 0xfd9, 0xfda,
-    0x10fb, 0x1400, 0x166d, 0x166e, 0x169b, 0x169c, 0x1735, 0x1736, 0x1944,
-    0x1945, 0x1a1e, 0x1a1f, 0x1c7e, 0x1c7f, 0x1cd3, 0x207d, 0x207e, 0x208d,
-    0x208e, 0x2329, 0x232a, 0x27c5, 0x27c6, 0x29fc, 0x29fd, 0x2cfe, 0x2cff,
-    0x2d70, 0x3030, 0x303d, 0x30a0, 0x30fb, 0xa4fe, 0xa4ff, 0xa673, 0xa67e,
-    0xa8ce, 0xa8cf, 0xa8fc, 0xa92e, 0xa92f, 0xa95f, 0xa9de, 0xa9df, 0xaade,
-    0xaadf, 0xaaf0, 0xaaf1, 0xabeb, 0xfd3e, 0xfd3f, 0xfe63, 0xfe68, 0xfe6a,
-    0xfe6b, 0xff1a, 0xff1b, 0xff1f, 0xff20, 0xff3f, 0xff5b, 0xff5d
+    0x9fd, 0xaf0, 0xdf4, 0xe4f, 0xe5a, 0xe5b, 0xf14, 0xf85, 0xfd9,
+    0xfda, 0x10fb, 0x1400, 0x166d, 0x166e, 0x169b, 0x169c, 0x1735, 0x1736,
+    0x1944, 0x1945, 0x1a1e, 0x1a1f, 0x1c7e, 0x1c7f, 0x1cd3, 0x207d, 0x207e,
+    0x208d, 0x208e, 0x2329, 0x232a, 0x27c5, 0x27c6, 0x29fc, 0x29fd, 0x2cfe,
+    0x2cff, 0x2d70, 0x3030, 0x303d, 0x30a0, 0x30fb, 0xa4fe, 0xa4ff, 0xa673,
+    0xa67e, 0xa8ce, 0xa8cf, 0xa8fc, 0xa92e, 0xa92f, 0xa95f, 0xa9de, 0xa9df,
+    0xaade, 0xaadf, 0xaaf0, 0xaaf1, 0xabeb, 0xfd3e, 0xfd3f, 0xfe63, 0xfe68,
+    0xfe6a, 0xfe6b, 0xff1a, 0xff1b, 0xff1f, 0xff20, 0xff3f, 0xff5b, 0xff5d
 #if TCL_UTF_MAX > 4
     ,0x1039f, 0x103d0, 0x1056f, 0x10857, 0x1091f, 0x1093f, 0x10a7f, 0x110bb, 0x110bc,
     0x11174, 0x11175, 0x111cd, 0x111db, 0x112a9, 0x1145b, 0x1145d, 0x114c6, 0x11c70,
@@ -615,63 +619,63 @@ static const crange graphRangeTable[] = {
     {0x559, 0x55f}, {0x561, 0x587}, {0x58d, 0x58f}, {0x591, 0x5c7},
     {0x5d0, 0x5ea}, {0x5f0, 0x5f4}, {0x606, 0x61b}, {0x61e, 0x6dc},
     {0x6de, 0x70d}, {0x710, 0x74a}, {0x74d, 0x7b1}, {0x7c0, 0x7fa},
-    {0x800, 0x82d}, {0x830, 0x83e}, {0x840, 0x85b}, {0x8a0, 0x8b4},
-    {0x8b6, 0x8bd}, {0x8d4, 0x8e1}, {0x8e3, 0x983}, {0x985, 0x98c},
-    {0x993, 0x9a8}, {0x9aa, 0x9b0}, {0x9b6, 0x9b9}, {0x9bc, 0x9c4},
-    {0x9cb, 0x9ce}, {0x9df, 0x9e3}, {0x9e6, 0x9fb}, {0xa01, 0xa03},
-    {0xa05, 0xa0a}, {0xa13, 0xa28}, {0xa2a, 0xa30}, {0xa3e, 0xa42},
-    {0xa4b, 0xa4d}, {0xa59, 0xa5c}, {0xa66, 0xa75}, {0xa81, 0xa83},
-    {0xa85, 0xa8d}, {0xa8f, 0xa91}, {0xa93, 0xaa8}, {0xaaa, 0xab0},
-    {0xab5, 0xab9}, {0xabc, 0xac5}, {0xac7, 0xac9}, {0xacb, 0xacd},
-    {0xae0, 0xae3}, {0xae6, 0xaf1}, {0xb01, 0xb03}, {0xb05, 0xb0c},
-    {0xb13, 0xb28}, {0xb2a, 0xb30}, {0xb35, 0xb39}, {0xb3c, 0xb44},
-    {0xb4b, 0xb4d}, {0xb5f, 0xb63}, {0xb66, 0xb77}, {0xb85, 0xb8a},
-    {0xb8e, 0xb90}, {0xb92, 0xb95}, {0xba8, 0xbaa}, {0xbae, 0xbb9},
-    {0xbbe, 0xbc2}, {0xbc6, 0xbc8}, {0xbca, 0xbcd}, {0xbe6, 0xbfa},
-    {0xc00, 0xc03}, {0xc05, 0xc0c}, {0xc0e, 0xc10}, {0xc12, 0xc28},
-    {0xc2a, 0xc39}, {0xc3d, 0xc44}, {0xc46, 0xc48}, {0xc4a, 0xc4d},
-    {0xc58, 0xc5a}, {0xc60, 0xc63}, {0xc66, 0xc6f}, {0xc78, 0xc83},
-    {0xc85, 0xc8c}, {0xc8e, 0xc90}, {0xc92, 0xca8}, {0xcaa, 0xcb3},
-    {0xcb5, 0xcb9}, {0xcbc, 0xcc4}, {0xcc6, 0xcc8}, {0xcca, 0xccd},
-    {0xce0, 0xce3}, {0xce6, 0xcef}, {0xd01, 0xd03}, {0xd05, 0xd0c},
-    {0xd0e, 0xd10}, {0xd12, 0xd3a}, {0xd3d, 0xd44}, {0xd46, 0xd48},
-    {0xd4a, 0xd4f}, {0xd54, 0xd63}, {0xd66, 0xd7f}, {0xd85, 0xd96},
-    {0xd9a, 0xdb1}, {0xdb3, 0xdbb}, {0xdc0, 0xdc6}, {0xdcf, 0xdd4},
-    {0xdd8, 0xddf}, {0xde6, 0xdef}, {0xdf2, 0xdf4}, {0xe01, 0xe3a},
-    {0xe3f, 0xe5b}, {0xe94, 0xe97}, {0xe99, 0xe9f}, {0xea1, 0xea3},
-    {0xead, 0xeb9}, {0xebb, 0xebd}, {0xec0, 0xec4}, {0xec8, 0xecd},
-    {0xed0, 0xed9}, {0xedc, 0xedf}, {0xf00, 0xf47}, {0xf49, 0xf6c},
-    {0xf71, 0xf97}, {0xf99, 0xfbc}, {0xfbe, 0xfcc}, {0xfce, 0xfda},
-    {0x1000, 0x10c5}, {0x10d0, 0x1248}, {0x124a, 0x124d}, {0x1250, 0x1256},
-    {0x125a, 0x125d}, {0x1260, 0x1288}, {0x128a, 0x128d}, {0x1290, 0x12b0},
-    {0x12b2, 0x12b5}, {0x12b8, 0x12be}, {0x12c2, 0x12c5}, {0x12c8, 0x12d6},
-    {0x12d8, 0x1310}, {0x1312, 0x1315}, {0x1318, 0x135a}, {0x135d, 0x137c},
-    {0x1380, 0x1399}, {0x13a0, 0x13f5}, {0x13f8, 0x13fd}, {0x1400, 0x167f},
-    {0x1681, 0x169c}, {0x16a0, 0x16f8}, {0x1700, 0x170c}, {0x170e, 0x1714},
-    {0x1720, 0x1736}, {0x1740, 0x1753}, {0x1760, 0x176c}, {0x176e, 0x1770},
-    {0x1780, 0x17dd}, {0x17e0, 0x17e9}, {0x17f0, 0x17f9}, {0x1800, 0x180d},
-    {0x1810, 0x1819}, {0x1820, 0x1877}, {0x1880, 0x18aa}, {0x18b0, 0x18f5},
-    {0x1900, 0x191e}, {0x1920, 0x192b}, {0x1930, 0x193b}, {0x1944, 0x196d},
-    {0x1970, 0x1974}, {0x1980, 0x19ab}, {0x19b0, 0x19c9}, {0x19d0, 0x19da},
-    {0x19de, 0x1a1b}, {0x1a1e, 0x1a5e}, {0x1a60, 0x1a7c}, {0x1a7f, 0x1a89},
-    {0x1a90, 0x1a99}, {0x1aa0, 0x1aad}, {0x1ab0, 0x1abe}, {0x1b00, 0x1b4b},
-    {0x1b50, 0x1b7c}, {0x1b80, 0x1bf3}, {0x1bfc, 0x1c37}, {0x1c3b, 0x1c49},
-    {0x1c4d, 0x1c88}, {0x1cc0, 0x1cc7}, {0x1cd0, 0x1cf6}, {0x1d00, 0x1df5},
-    {0x1dfb, 0x1f15}, {0x1f18, 0x1f1d}, {0x1f20, 0x1f45}, {0x1f48, 0x1f4d},
-    {0x1f50, 0x1f57}, {0x1f5f, 0x1f7d}, {0x1f80, 0x1fb4}, {0x1fb6, 0x1fc4},
-    {0x1fc6, 0x1fd3}, {0x1fd6, 0x1fdb}, {0x1fdd, 0x1fef}, {0x1ff2, 0x1ff4},
-    {0x1ff6, 0x1ffe}, {0x2010, 0x2027}, {0x2030, 0x205e}, {0x2074, 0x208e},
-    {0x2090, 0x209c}, {0x20a0, 0x20be}, {0x20d0, 0x20f0}, {0x2100, 0x218b},
-    {0x2190, 0x23fe}, {0x2400, 0x2426}, {0x2440, 0x244a}, {0x2460, 0x2b73},
-    {0x2b76, 0x2b95}, {0x2b98, 0x2bb9}, {0x2bbd, 0x2bc8}, {0x2bca, 0x2bd1},
+    {0x800, 0x82d}, {0x830, 0x83e}, {0x840, 0x85b}, {0x860, 0x86a},
+    {0x8a0, 0x8b4}, {0x8b6, 0x8bd}, {0x8d4, 0x8e1}, {0x8e3, 0x983},
+    {0x985, 0x98c}, {0x993, 0x9a8}, {0x9aa, 0x9b0}, {0x9b6, 0x9b9},
+    {0x9bc, 0x9c4}, {0x9cb, 0x9ce}, {0x9df, 0x9e3}, {0x9e6, 0x9fd},
+    {0xa01, 0xa03}, {0xa05, 0xa0a}, {0xa13, 0xa28}, {0xa2a, 0xa30},
+    {0xa3e, 0xa42}, {0xa4b, 0xa4d}, {0xa59, 0xa5c}, {0xa66, 0xa75},
+    {0xa81, 0xa83}, {0xa85, 0xa8d}, {0xa8f, 0xa91}, {0xa93, 0xaa8},
+    {0xaaa, 0xab0}, {0xab5, 0xab9}, {0xabc, 0xac5}, {0xac7, 0xac9},
+    {0xacb, 0xacd}, {0xae0, 0xae3}, {0xae6, 0xaf1}, {0xaf9, 0xaff},
+    {0xb01, 0xb03}, {0xb05, 0xb0c}, {0xb13, 0xb28}, {0xb2a, 0xb30},
+    {0xb35, 0xb39}, {0xb3c, 0xb44}, {0xb4b, 0xb4d}, {0xb5f, 0xb63},
+    {0xb66, 0xb77}, {0xb85, 0xb8a}, {0xb8e, 0xb90}, {0xb92, 0xb95},
+    {0xba8, 0xbaa}, {0xbae, 0xbb9}, {0xbbe, 0xbc2}, {0xbc6, 0xbc8},
+    {0xbca, 0xbcd}, {0xbe6, 0xbfa}, {0xc00, 0xc03}, {0xc05, 0xc0c},
+    {0xc0e, 0xc10}, {0xc12, 0xc28}, {0xc2a, 0xc39}, {0xc3d, 0xc44},
+    {0xc46, 0xc48}, {0xc4a, 0xc4d}, {0xc58, 0xc5a}, {0xc60, 0xc63},
+    {0xc66, 0xc6f}, {0xc78, 0xc83}, {0xc85, 0xc8c}, {0xc8e, 0xc90},
+    {0xc92, 0xca8}, {0xcaa, 0xcb3}, {0xcb5, 0xcb9}, {0xcbc, 0xcc4},
+    {0xcc6, 0xcc8}, {0xcca, 0xccd}, {0xce0, 0xce3}, {0xce6, 0xcef},
+    {0xd00, 0xd03}, {0xd05, 0xd0c}, {0xd0e, 0xd10}, {0xd12, 0xd44},
+    {0xd46, 0xd48}, {0xd4a, 0xd4f}, {0xd54, 0xd63}, {0xd66, 0xd7f},
+    {0xd85, 0xd96}, {0xd9a, 0xdb1}, {0xdb3, 0xdbb}, {0xdc0, 0xdc6},
+    {0xdcf, 0xdd4}, {0xdd8, 0xddf}, {0xde6, 0xdef}, {0xdf2, 0xdf4},
+    {0xe01, 0xe3a}, {0xe3f, 0xe5b}, {0xe94, 0xe97}, {0xe99, 0xe9f},
+    {0xea1, 0xea3}, {0xead, 0xeb9}, {0xebb, 0xebd}, {0xec0, 0xec4},
+    {0xec8, 0xecd}, {0xed0, 0xed9}, {0xedc, 0xedf}, {0xf00, 0xf47},
+    {0xf49, 0xf6c}, {0xf71, 0xf97}, {0xf99, 0xfbc}, {0xfbe, 0xfcc},
+    {0xfce, 0xfda}, {0x1000, 0x10c5}, {0x10d0, 0x1248}, {0x124a, 0x124d},
+    {0x1250, 0x1256}, {0x125a, 0x125d}, {0x1260, 0x1288}, {0x128a, 0x128d},
+    {0x1290, 0x12b0}, {0x12b2, 0x12b5}, {0x12b8, 0x12be}, {0x12c2, 0x12c5},
+    {0x12c8, 0x12d6}, {0x12d8, 0x1310}, {0x1312, 0x1315}, {0x1318, 0x135a},
+    {0x135d, 0x137c}, {0x1380, 0x1399}, {0x13a0, 0x13f5}, {0x13f8, 0x13fd},
+    {0x1400, 0x167f}, {0x1681, 0x169c}, {0x16a0, 0x16f8}, {0x1700, 0x170c},
+    {0x170e, 0x1714}, {0x1720, 0x1736}, {0x1740, 0x1753}, {0x1760, 0x176c},
+    {0x176e, 0x1770}, {0x1780, 0x17dd}, {0x17e0, 0x17e9}, {0x17f0, 0x17f9},
+    {0x1800, 0x180d}, {0x1810, 0x1819}, {0x1820, 0x1877}, {0x1880, 0x18aa},
+    {0x18b0, 0x18f5}, {0x1900, 0x191e}, {0x1920, 0x192b}, {0x1930, 0x193b},
+    {0x1944, 0x196d}, {0x1970, 0x1974}, {0x1980, 0x19ab}, {0x19b0, 0x19c9},
+    {0x19d0, 0x19da}, {0x19de, 0x1a1b}, {0x1a1e, 0x1a5e}, {0x1a60, 0x1a7c},
+    {0x1a7f, 0x1a89}, {0x1a90, 0x1a99}, {0x1aa0, 0x1aad}, {0x1ab0, 0x1abe},
+    {0x1b00, 0x1b4b}, {0x1b50, 0x1b7c}, {0x1b80, 0x1bf3}, {0x1bfc, 0x1c37},
+    {0x1c3b, 0x1c49}, {0x1c4d, 0x1c88}, {0x1cc0, 0x1cc7}, {0x1cd0, 0x1cf9},
+    {0x1d00, 0x1df9}, {0x1dfb, 0x1f15}, {0x1f18, 0x1f1d}, {0x1f20, 0x1f45},
+    {0x1f48, 0x1f4d}, {0x1f50, 0x1f57}, {0x1f5f, 0x1f7d}, {0x1f80, 0x1fb4},
+    {0x1fb6, 0x1fc4}, {0x1fc6, 0x1fd3}, {0x1fd6, 0x1fdb}, {0x1fdd, 0x1fef},
+    {0x1ff2, 0x1ff4}, {0x1ff6, 0x1ffe}, {0x2010, 0x2027}, {0x2030, 0x205e},
+    {0x2074, 0x208e}, {0x2090, 0x209c}, {0x20a0, 0x20bf}, {0x20d0, 0x20f0},
+    {0x2100, 0x218b}, {0x2190, 0x2426}, {0x2440, 0x244a}, {0x2460, 0x2b73},
+    {0x2b76, 0x2b95}, {0x2b98, 0x2bb9}, {0x2bbd, 0x2bc8}, {0x2bca, 0x2bd2},
     {0x2bec, 0x2bef}, {0x2c00, 0x2c2e}, {0x2c30, 0x2c5e}, {0x2c60, 0x2cf3},
     {0x2cf9, 0x2d25}, {0x2d30, 0x2d67}, {0x2d7f, 0x2d96}, {0x2da0, 0x2da6},
     {0x2da8, 0x2dae}, {0x2db0, 0x2db6}, {0x2db8, 0x2dbe}, {0x2dc0, 0x2dc6},
-    {0x2dc8, 0x2dce}, {0x2dd0, 0x2dd6}, {0x2dd8, 0x2dde}, {0x2de0, 0x2e44},
+    {0x2dc8, 0x2dce}, {0x2dd0, 0x2dd6}, {0x2dd8, 0x2dde}, {0x2de0, 0x2e49},
     {0x2e80, 0x2e99}, {0x2e9b, 0x2ef3}, {0x2f00, 0x2fd5}, {0x2ff0, 0x2ffb},
-    {0x3001, 0x303f}, {0x3041, 0x3096}, {0x3099, 0x30ff}, {0x3105, 0x312d},
+    {0x3001, 0x303f}, {0x3041, 0x3096}, {0x3099, 0x30ff}, {0x3105, 0x312e},
     {0x3131, 0x318e}, {0x3190, 0x31ba}, {0x31c0, 0x31e3}, {0x31f0, 0x321e},
-    {0x3220, 0x32fe}, {0x3300, 0x4db5}, {0x4dc0, 0x9fd5}, {0xa000, 0xa48c},
+    {0x3220, 0x32fe}, {0x3300, 0x4db5}, {0x4dc0, 0x9fea}, {0xa000, 0xa48c},
     {0xa490, 0xa4c6}, {0xa4d0, 0xa62b}, {0xa640, 0xa6f7}, {0xa700, 0xa7ae},
     {0xa7b0, 0xa7b7}, {0xa7f7, 0xa82b}, {0xa830, 0xa839}, {0xa840, 0xa877},
     {0xa880, 0xa8c5}, {0xa8ce, 0xa8d9}, {0xa8e0, 0xa8fd}, {0xa900, 0xa953},
@@ -694,7 +698,7 @@ static const crange graphRangeTable[] = {
     ,{0x10000, 0x1000b}, {0x1000d, 0x10026}, {0x10028, 0x1003a}, {0x1003f, 0x1004d},
     {0x10050, 0x1005d}, {0x10080, 0x100fa}, {0x10100, 0x10102}, {0x10107, 0x10133},
     {0x10137, 0x1018e}, {0x10190, 0x1019b}, {0x101d0, 0x101fd}, {0x10280, 0x1029c},
-    {0x102a0, 0x102d0}, {0x102e0, 0x102fb}, {0x10300, 0x10323}, {0x10330, 0x1034a},
+    {0x102a0, 0x102d0}, {0x102e0, 0x102fb}, {0x10300, 0x10323}, {0x1032d, 0x1034a},
     {0x10350, 0x1037a}, {0x10380, 0x1039d}, {0x1039f, 0x103c3}, {0x103c8, 0x103d5},
     {0x10400, 0x1049d}, {0x104a0, 0x104a9}, {0x104b0, 0x104d3}, {0x104d8, 0x104fb},
     {0x10500, 0x10527}, {0x10530, 0x10563}, {0x10600, 0x10736}, {0x10740, 0x10755},
@@ -717,35 +721,38 @@ static const crange graphRangeTable[] = {
     {0x114d0, 0x114d9}, {0x11580, 0x115b5}, {0x115b8, 0x115dd}, {0x11600, 0x11644},
     {0x11650, 0x11659}, {0x11660, 0x1166c}, {0x11680, 0x116b7}, {0x116c0, 0x116c9},
     {0x11700, 0x11719}, {0x1171d, 0x1172b}, {0x11730, 0x1173f}, {0x118a0, 0x118f2},
+    {0x11a00, 0x11a47}, {0x11a50, 0x11a83}, {0x11a86, 0x11a9c}, {0x11a9e, 0x11aa2},
     {0x11ac0, 0x11af8}, {0x11c00, 0x11c08}, {0x11c0a, 0x11c36}, {0x11c38, 0x11c45},
     {0x11c50, 0x11c6c}, {0x11c70, 0x11c8f}, {0x11c92, 0x11ca7}, {0x11ca9, 0x11cb6},
+    {0x11d00, 0x11d06}, {0x11d0b, 0x11d36}, {0x11d3f, 0x11d47}, {0x11d50, 0x11d59},
     {0x12000, 0x12399}, {0x12400, 0x1246e}, {0x12470, 0x12474}, {0x12480, 0x12543},
     {0x13000, 0x1342e}, {0x14400, 0x14646}, {0x16800, 0x16a38}, {0x16a40, 0x16a5e},
     {0x16a60, 0x16a69}, {0x16ad0, 0x16aed}, {0x16af0, 0x16af5}, {0x16b00, 0x16b45},
     {0x16b50, 0x16b59}, {0x16b5b, 0x16b61}, {0x16b63, 0x16b77}, {0x16b7d, 0x16b8f},
     {0x16f00, 0x16f44}, {0x16f50, 0x16f7e}, {0x16f8f, 0x16f9f}, {0x17000, 0x187ec},
-    {0x18800, 0x18af2}, {0x1bc00, 0x1bc6a}, {0x1bc70, 0x1bc7c}, {0x1bc80, 0x1bc88},
-    {0x1bc90, 0x1bc99}, {0x1bc9c, 0x1bc9f}, {0x1d000, 0x1d0f5}, {0x1d100, 0x1d126},
-    {0x1d129, 0x1d172}, {0x1d17b, 0x1d1e8}, {0x1d200, 0x1d245}, {0x1d300, 0x1d356},
-    {0x1d360, 0x1d371}, {0x1d400, 0x1d454}, {0x1d456, 0x1d49c}, {0x1d4a9, 0x1d4ac},
-    {0x1d4ae, 0x1d4b9}, {0x1d4bd, 0x1d4c3}, {0x1d4c5, 0x1d505}, {0x1d507, 0x1d50a},
-    {0x1d50d, 0x1d514}, {0x1d516, 0x1d51c}, {0x1d51e, 0x1d539}, {0x1d53b, 0x1d53e},
-    {0x1d540, 0x1d544}, {0x1d54a, 0x1d550}, {0x1d552, 0x1d6a5}, {0x1d6a8, 0x1d7cb},
-    {0x1d7ce, 0x1da8b}, {0x1da9b, 0x1da9f}, {0x1daa1, 0x1daaf}, {0x1e000, 0x1e006},
-    {0x1e008, 0x1e018}, {0x1e01b, 0x1e021}, {0x1e026, 0x1e02a}, {0x1e800, 0x1e8c4},
-    {0x1e8c7, 0x1e8d6}, {0x1e900, 0x1e94a}, {0x1e950, 0x1e959}, {0x1ee00, 0x1ee03},
-    {0x1ee05, 0x1ee1f}, {0x1ee29, 0x1ee32}, {0x1ee34, 0x1ee37}, {0x1ee4d, 0x1ee4f},
-    {0x1ee67, 0x1ee6a}, {0x1ee6c, 0x1ee72}, {0x1ee74, 0x1ee77}, {0x1ee79, 0x1ee7c},
-    {0x1ee80, 0x1ee89}, {0x1ee8b, 0x1ee9b}, {0x1eea1, 0x1eea3}, {0x1eea5, 0x1eea9},
-    {0x1eeab, 0x1eebb}, {0x1f000, 0x1f02b}, {0x1f030, 0x1f093}, {0x1f0a0, 0x1f0ae},
-    {0x1f0b1, 0x1f0bf}, {0x1f0c1, 0x1f0cf}, {0x1f0d1, 0x1f0f5}, {0x1f100, 0x1f10c},
-    {0x1f110, 0x1f12e}, {0x1f130, 0x1f16b}, {0x1f170, 0x1f1ac}, {0x1f1e6, 0x1f202},
-    {0x1f210, 0x1f23b}, {0x1f240, 0x1f248}, {0x1f300, 0x1f6d2}, {0x1f6e0, 0x1f6ec},
-    {0x1f6f0, 0x1f6f6}, {0x1f700, 0x1f773}, {0x1f780, 0x1f7d4}, {0x1f800, 0x1f80b},
-    {0x1f810, 0x1f847}, {0x1f850, 0x1f859}, {0x1f860, 0x1f887}, {0x1f890, 0x1f8ad},
-    {0x1f910, 0x1f91e}, {0x1f920, 0x1f927}, {0x1f933, 0x1f93e}, {0x1f940, 0x1f94b},
-    {0x1f950, 0x1f95e}, {0x1f980, 0x1f991}, {0x20000, 0x2a6d6}, {0x2a700, 0x2b734},
-    {0x2b740, 0x2b81d}, {0x2b820, 0x2cea1}, {0x2f800, 0x2fa1d}, {0xe0100, 0xe01ef}
+    {0x18800, 0x18af2}, {0x1b000, 0x1b11e}, {0x1b170, 0x1b2fb}, {0x1bc00, 0x1bc6a},
+    {0x1bc70, 0x1bc7c}, {0x1bc80, 0x1bc88}, {0x1bc90, 0x1bc99}, {0x1bc9c, 0x1bc9f},
+    {0x1d000, 0x1d0f5}, {0x1d100, 0x1d126}, {0x1d129, 0x1d172}, {0x1d17b, 0x1d1e8},
+    {0x1d200, 0x1d245}, {0x1d300, 0x1d356}, {0x1d360, 0x1d371}, {0x1d400, 0x1d454},
+    {0x1d456, 0x1d49c}, {0x1d4a9, 0x1d4ac}, {0x1d4ae, 0x1d4b9}, {0x1d4bd, 0x1d4c3},
+    {0x1d4c5, 0x1d505}, {0x1d507, 0x1d50a}, {0x1d50d, 0x1d514}, {0x1d516, 0x1d51c},
+    {0x1d51e, 0x1d539}, {0x1d53b, 0x1d53e}, {0x1d540, 0x1d544}, {0x1d54a, 0x1d550},
+    {0x1d552, 0x1d6a5}, {0x1d6a8, 0x1d7cb}, {0x1d7ce, 0x1da8b}, {0x1da9b, 0x1da9f},
+    {0x1daa1, 0x1daaf}, {0x1e000, 0x1e006}, {0x1e008, 0x1e018}, {0x1e01b, 0x1e021},
+    {0x1e026, 0x1e02a}, {0x1e800, 0x1e8c4}, {0x1e8c7, 0x1e8d6}, {0x1e900, 0x1e94a},
+    {0x1e950, 0x1e959}, {0x1ee00, 0x1ee03}, {0x1ee05, 0x1ee1f}, {0x1ee29, 0x1ee32},
+    {0x1ee34, 0x1ee37}, {0x1ee4d, 0x1ee4f}, {0x1ee67, 0x1ee6a}, {0x1ee6c, 0x1ee72},
+    {0x1ee74, 0x1ee77}, {0x1ee79, 0x1ee7c}, {0x1ee80, 0x1ee89}, {0x1ee8b, 0x1ee9b},
+    {0x1eea1, 0x1eea3}, {0x1eea5, 0x1eea9}, {0x1eeab, 0x1eebb}, {0x1f000, 0x1f02b},
+    {0x1f030, 0x1f093}, {0x1f0a0, 0x1f0ae}, {0x1f0b1, 0x1f0bf}, {0x1f0c1, 0x1f0cf},
+    {0x1f0d1, 0x1f0f5}, {0x1f100, 0x1f10c}, {0x1f110, 0x1f12e}, {0x1f130, 0x1f16b},
+    {0x1f170, 0x1f1ac}, {0x1f1e6, 0x1f202}, {0x1f210, 0x1f23b}, {0x1f240, 0x1f248},
+    {0x1f260, 0x1f265}, {0x1f300, 0x1f6d4}, {0x1f6e0, 0x1f6ec}, {0x1f6f0, 0x1f6f8},
+    {0x1f700, 0x1f773}, {0x1f780, 0x1f7d4}, {0x1f800, 0x1f80b}, {0x1f810, 0x1f847},
+    {0x1f850, 0x1f859}, {0x1f860, 0x1f887}, {0x1f890, 0x1f8ad}, {0x1f900, 0x1f90b},
+    {0x1f910, 0x1f93e}, {0x1f940, 0x1f94c}, {0x1f950, 0x1f96b}, {0x1f980, 0x1f997},
+    {0x1f9d0, 0x1f9e6}, {0x20000, 0x2a6d6}, {0x2a700, 0x2b734}, {0x2b740, 0x2b81d},
+    {0x2b820, 0x2cea1}, {0x2ceb0, 0x2ebe0}, {0x2f800, 0x2fa1d}, {0xe0100, 0xe01ef}
 #endif
 };
 
@@ -755,23 +762,23 @@ static const chr graphCharTable[] = {
     0x38c, 0x589, 0x58a, 0x85e, 0x98f, 0x990, 0x9b2, 0x9c7, 0x9c8,
     0x9d7, 0x9dc, 0x9dd, 0xa0f, 0xa10, 0xa32, 0xa33, 0xa35, 0xa36,
     0xa38, 0xa39, 0xa3c, 0xa47, 0xa48, 0xa51, 0xa5e, 0xab2, 0xab3,
-    0xad0, 0xaf9, 0xb0f, 0xb10, 0xb32, 0xb33, 0xb47, 0xb48, 0xb56,
-    0xb57, 0xb5c, 0xb5d, 0xb82, 0xb83, 0xb99, 0xb9a, 0xb9c, 0xb9e,
-    0xb9f, 0xba3, 0xba4, 0xbd0, 0xbd7, 0xc55, 0xc56, 0xcd5, 0xcd6,
-    0xcde, 0xcf1, 0xcf2, 0xd82, 0xd83, 0xdbd, 0xdca, 0xdd6, 0xe81,
-    0xe82, 0xe84, 0xe87, 0xe88, 0xe8a, 0xe8d, 0xea5, 0xea7, 0xeaa,
-    0xeab, 0xec6, 0x10c7, 0x10cd, 0x1258, 0x12c0, 0x1772, 0x1773, 0x1940,
-    0x1cf8, 0x1cf9, 0x1f59, 0x1f5b, 0x1f5d, 0x2070, 0x2071, 0x2d27, 0x2d2d,
-    0x2d6f, 0x2d70, 0xfb3e, 0xfb40, 0xfb41, 0xfb43, 0xfb44, 0xfffc, 0xfffd
+    0xad0, 0xb0f, 0xb10, 0xb32, 0xb33, 0xb47, 0xb48, 0xb56, 0xb57,
+    0xb5c, 0xb5d, 0xb82, 0xb83, 0xb99, 0xb9a, 0xb9c, 0xb9e, 0xb9f,
+    0xba3, 0xba4, 0xbd0, 0xbd7, 0xc55, 0xc56, 0xcd5, 0xcd6, 0xcde,
+    0xcf1, 0xcf2, 0xd82, 0xd83, 0xdbd, 0xdca, 0xdd6, 0xe81, 0xe82,
+    0xe84, 0xe87, 0xe88, 0xe8a, 0xe8d, 0xea5, 0xea7, 0xeaa, 0xeab,
+    0xec6, 0x10c7, 0x10cd, 0x1258, 0x12c0, 0x1772, 0x1773, 0x1940, 0x1f59,
+    0x1f5b, 0x1f5d, 0x2070, 0x2071, 0x2d27, 0x2d2d, 0x2d6f, 0x2d70, 0xfb3e,
+    0xfb40, 0xfb41, 0xfb43, 0xfb44, 0xfffc, 0xfffd
 #if TCL_UTF_MAX > 4
     ,0x1003c, 0x1003d, 0x101a0, 0x1056f, 0x10808, 0x10837, 0x10838, 0x1083c, 0x108f4,
     0x108f5, 0x1093f, 0x10a05, 0x10a06, 0x11288, 0x1130f, 0x11310, 0x11332, 0x11333,
-    0x11347, 0x11348, 0x11350, 0x11357, 0x1145b, 0x1145d, 0x118ff, 0x16a6e, 0x16a6f,
-    0x16fe0, 0x1b000, 0x1b001, 0x1d49e, 0x1d49f, 0x1d4a2, 0x1d4a5, 0x1d4a6, 0x1d4bb,
-    0x1d546, 0x1e023, 0x1e024, 0x1e95e, 0x1e95f, 0x1ee21, 0x1ee22, 0x1ee24, 0x1ee27,
-    0x1ee39, 0x1ee3b, 0x1ee42, 0x1ee47, 0x1ee49, 0x1ee4b, 0x1ee51, 0x1ee52, 0x1ee54,
-    0x1ee57, 0x1ee59, 0x1ee5b, 0x1ee5d, 0x1ee5f, 0x1ee61, 0x1ee62, 0x1ee64, 0x1ee7e,
-    0x1eef0, 0x1eef1, 0x1f250, 0x1f251, 0x1f930, 0x1f9c0
+    0x11347, 0x11348, 0x11350, 0x11357, 0x1145b, 0x1145d, 0x118ff, 0x11d08, 0x11d09,
+    0x11d3a, 0x11d3c, 0x11d3d, 0x16a6e, 0x16a6f, 0x16fe0, 0x16fe1, 0x1d49e, 0x1d49f,
+    0x1d4a2, 0x1d4a5, 0x1d4a6, 0x1d4bb, 0x1d546, 0x1e023, 0x1e024, 0x1e95e, 0x1e95f,
+    0x1ee21, 0x1ee22, 0x1ee24, 0x1ee27, 0x1ee39, 0x1ee3b, 0x1ee42, 0x1ee47, 0x1ee49,
+    0x1ee4b, 0x1ee51, 0x1ee52, 0x1ee54, 0x1ee57, 0x1ee59, 0x1ee5b, 0x1ee5d, 0x1ee5f,
+    0x1ee61, 0x1ee62, 0x1ee64, 0x1ee7e, 0x1eef0, 0x1eef1, 0x1f250, 0x1f251, 0x1f9c0
 #endif
 };
 
diff --git a/generic/tclUniData.c b/generic/tclUniData.c
index 20fab8c..9f05230 100644
--- a/generic/tclUniData.c
+++ b/generic/tclUniData.c
@@ -29,36 +29,36 @@ static const unsigned short pageMap[] = {
     832, 864, 896, 928, 960, 992, 224, 1024, 224, 1056, 224, 224, 1088,
     1120, 1152, 1184, 1216, 1248, 1280, 1312, 1344, 1376, 1408, 1344, 1344,
     1440, 1472, 1504, 1536, 1568, 1344, 1344, 1600, 1632, 1664, 1696, 1728,
-    1760, 1792, 1792, 1824, 1856, 1888, 1920, 1952, 1984, 2016, 2048, 2080,
-    2112, 2144, 2176, 2208, 2240, 2272, 2304, 2336, 2368, 2400, 2432, 2464,
-    2496, 2528, 2560, 2592, 2624, 2656, 2688, 2720, 2752, 2784, 2816, 2848,
-    2880, 2912, 2944, 2976, 3008, 3040, 3072, 3104, 3136, 3168, 3200, 3232,
-    3264, 1792, 3296, 3328, 3360, 1792, 3392, 3424, 3456, 3488, 3520, 3552,
-    3584, 1792, 1344, 3616, 3648, 3680, 3712, 3744, 3776, 3808, 1344, 1344,
-    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 3840, 1344, 3872, 3904,
-    3936, 1344, 3968, 1344, 4000, 4032, 4064, 4096, 4096, 4128, 4160, 1344,
+    1760, 1792, 1824, 1856, 1888, 1920, 1952, 1984, 2016, 2048, 2080, 2112,
+    2144, 2176, 2208, 2240, 2272, 2304, 2336, 2368, 2400, 2432, 2464, 2496,
+    2528, 2560, 2592, 2624, 2656, 2688, 2720, 2752, 2784, 2816, 2848, 2880,
+    2912, 2944, 2976, 3008, 3040, 3072, 3104, 3136, 3168, 3200, 3232, 3264,
+    3296, 1824, 3328, 3360, 3392, 1824, 3424, 3456, 3488, 3520, 3552, 3584,
+    3616, 1824, 1344, 3648, 3680, 3712, 3744, 3776, 3808, 3840, 1344, 1344,
+    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 3872, 1344, 3904, 3936,
+    3968, 1344, 4000, 1344, 4032, 4064, 4096, 4128, 4128, 4160, 4192, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
-    1344, 1344, 1344, 1344, 1344, 4192, 4224, 1344, 1344, 4256, 4288, 4320,
-    4352, 4384, 1344, 4416, 4448, 4480, 4512, 1344, 4544, 4576, 4608, 4640,
-    1344, 4672, 4704, 4736, 4768, 4800, 1344, 4832, 4864, 4896, 4928, 1344,
-    4960, 4992, 5024, 5056, 1792, 1792, 5088, 5120, 5152, 5184, 5216, 5248,
-    1344, 5280, 1344, 5312, 5344, 5376, 5408, 1792, 5440, 5472, 5504, 5536,
-    5568, 5600, 5632, 5568, 704, 5664, 224, 224, 224, 224, 5696, 224, 224,
-    224, 5728, 5760, 5792, 5824, 5856, 5888, 5920, 5952, 5984, 6016, 6048,
-    6080, 6112, 6144, 6176, 6208, 6240, 6272, 6304, 6336, 6368, 6400, 6432,
-    6464, 6496, 6496, 6496, 6496, 6496, 6496, 6496, 6496, 6528, 6560, 4896,
-    6592, 6624, 6656, 6688, 6720, 4896, 6752, 6784, 6816, 6848, 6880, 6912,
-    6944, 4896, 4896, 4896, 4896, 4896, 6976, 7008, 7040, 4896, 4896, 4896,
-    7072, 4896, 4896, 4896, 4896, 4896, 4896, 4896, 7104, 7136, 4896, 7168,
-    7200, 4896, 4896, 4896, 4896, 4896, 4896, 4896, 4896, 6496, 6496, 6496,
-    6496, 7232, 6496, 7264, 7296, 6496, 6496, 6496, 6496, 6496, 6496, 6496,
-    6496, 4896, 7328, 7360, 7392, 7424, 7456, 7488, 7520, 7552, 7584, 7616,
-    7648, 224, 224, 224, 7680, 7712, 7744, 1344, 7776, 7808, 7840, 7840,
-    704, 7872, 7904, 7936, 1792, 7968, 4896, 4896, 8000, 4896, 4896, 4896,
-    4896, 4896, 4896, 8032, 8064, 8096, 8128, 3200, 1344, 8160, 4160, 1344,
-    8192, 8224, 8256, 1344, 1344, 8288, 8320, 4896, 8352, 8384, 8416, 8448,
-    4896, 8416, 8480, 4896, 8384, 4896, 4896, 4896, 4896, 4896, 4896, 4896,
-    4896, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 1344, 4224, 4256, 1344, 1344, 4288, 4320, 4352,
+    4384, 4416, 1344, 4448, 4480, 4512, 4544, 1344, 4576, 4608, 4640, 4672,
+    1344, 4704, 4736, 4768, 4800, 4832, 1344, 4864, 4896, 4928, 4960, 1344,
+    4992, 5024, 5056, 5088, 1824, 1824, 5120, 5152, 5184, 5216, 5248, 5280,
+    1344, 5312, 1344, 5344, 5376, 5408, 5440, 1824, 5472, 5504, 5536, 5568,
+    5600, 5632, 5664, 5600, 704, 5696, 224, 224, 224, 224, 5728, 224, 224,
+    224, 5760, 5792, 5824, 5856, 5888, 5920, 5952, 5984, 6016, 6048, 6080,
+    6112, 6144, 6176, 6208, 6240, 6272, 6304, 6336, 6368, 6400, 6432, 6464,
+    6496, 6528, 6528, 6528, 6528, 6528, 6528, 6528, 6528, 6560, 6592, 4928,
+    6624, 6656, 6688, 6720, 6752, 4928, 6784, 6816, 6848, 6880, 6912, 6944,
+    6976, 4928, 4928, 4928, 4928, 4928, 7008, 7040, 7072, 4928, 4928, 4928,
+    7104, 4928, 4928, 4928, 4928, 4928, 4928, 4928, 7136, 7168, 4928, 7200,
+    7232, 4928, 4928, 4928, 4928, 4928, 4928, 4928, 4928, 6528, 6528, 6528,
+    6528, 7264, 6528, 7296, 7328, 6528, 6528, 6528, 6528, 6528, 6528, 6528,
+    6528, 4928, 7360, 7392, 7424, 7456, 7488, 7520, 7552, 7584, 7616, 7648,
+    7680, 224, 224, 224, 7712, 7744, 7776, 1344, 7808, 7840, 7872, 7872,
+    704, 7904, 7936, 7968, 1824, 8000, 4928, 4928, 8032, 4928, 4928, 4928,
+    4928, 4928, 4928, 8064, 8096, 8128, 8160, 3232, 1344, 8192, 4192, 1344,
+    8224, 8256, 8288, 1344, 1344, 8320, 8352, 4928, 8384, 8416, 8448, 8480,
+    4928, 8448, 8512, 4928, 8416, 4928, 4928, 4928, 4928, 4928, 4928, 4928,
+    4928, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
@@ -75,7 +75,7 @@ static const unsigned short pageMap[] = {
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
-    1344, 1344, 4672, 4896, 4896, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 4704, 4928, 4928, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
@@ -129,17 +129,16 @@ static const unsigned short pageMap[] = {
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
-    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 4672,
-    1792, 8512, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1792, 8544, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
-    1344, 8544, 4896, 8576, 5376, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
-    1344, 8608, 8640, 224, 8672, 8704, 1344, 1344, 8736, 8768, 8800, 224,
-    8832, 8864, 8896, 1792, 8928, 8960, 8992, 1344, 9024, 9056, 9088, 9120,
-    9152, 1632, 9184, 9216, 9248, 1920, 9280, 9312, 9344, 1344, 9376, 9408,
-    9440, 1344, 9472, 9504, 9536, 9568, 9600, 9632, 9664, 9696, 9696, 1344,
-    9728, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 8576, 4928, 8608, 5408, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 8640, 8672, 224, 8704, 8736, 1344, 1344, 8768, 8800, 8832, 224,
+    8864, 8896, 8928, 1824, 8960, 8992, 9024, 1344, 9056, 9088, 9120, 9152,
+    9184, 1632, 9216, 9248, 9280, 1952, 9312, 9344, 9376, 1344, 9408, 9440,
+    9472, 1344, 9504, 9536, 9568, 9600, 9632, 9664, 9696, 9728, 9728, 1344,
+    9760, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
@@ -167,211 +166,217 @@ static const unsigned short pageMap[] = {
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
-    1344, 1344, 9760, 9792, 9824, 9856, 9856, 9856, 9856, 9856, 9856, 9856,
-    9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856,
-    9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856,
-    9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856,
-    9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856,
-    9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856, 9856, 9888, 9888, 9888,
-    9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888,
-    9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888,
-    9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888,
-    9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888,
-    9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888,
-    9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888,
-    9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888,
-    9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888,
-    9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888,
-    9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888,
-    9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888,
-    9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888,
+    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 9792, 9824, 9856, 9888, 9888, 9888, 9888, 9888, 9888, 9888,
     9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888,
     9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888,
     9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888,
     9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888,
-    9888, 9888, 9888, 9888, 9888, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
-    1344, 1344, 1344, 1344, 9920, 1344, 1344, 9952, 1792, 9984, 10016,
-    10048, 1344, 1344, 10080, 10112, 1344, 1344, 1344, 1344, 1344, 1344,
-    1344, 1344, 1344, 1344, 10144, 10176, 1344, 10208, 1344, 10240, 10272,
-    10304, 10336, 10368, 10400, 1344, 1344, 1344, 10432, 10464, 64, 10496,
-    10528, 10560, 4704, 10592, 10624
+    9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9888, 9920, 9920, 9920,
+    9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920,
+    9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920,
+    9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920,
+    9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920,
+    9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920,
+    9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920,
+    9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920,
+    9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920,
+    9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920,
+    9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920,
+    9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920,
+    9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920,
+    9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920,
+    9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920,
+    9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920,
+    9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920, 9920,
+    9920, 9920, 9920, 9920, 9920, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 9952, 1344, 1344, 9984, 1824, 10016, 10048,
+    10080, 1344, 1344, 10112, 10144, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 10176, 10208, 1344, 10240, 1344, 10272, 10304,
+    10336, 10368, 10400, 10432, 1344, 1344, 1344, 10464, 10496, 64, 10528,
+    10560, 10592, 4736, 10624, 10656
 #if TCL_UTF_MAX > 3
-    ,10656, 10688, 10720, 1792, 1344, 1344, 1344, 8320, 10752, 10784, 10816,
-    10848, 10880, 10912, 10944, 10976, 1792, 1792, 1792, 1792, 9248, 1344,
-    11008, 11040, 1344, 11072, 11104, 11136, 11168, 1344, 11200, 1792,
-    11232, 11264, 11296, 1344, 11328, 11360, 11392, 11424, 1344, 11456,
-    1344, 11488, 1792, 1792, 1792, 1792, 1344, 1344, 1344, 1344, 1344,
-    1344, 1344, 1344, 1344, 7808, 4672, 10240, 1792, 1792, 1792, 1792,
-    11520, 11552, 11584, 11616, 4704, 11648, 1792, 11680, 11712, 11744,
-    1792, 1792, 1344, 11776, 11808, 6816, 11840, 11872, 11904, 11936, 11968,
-    1792, 12000, 12032, 1344, 12064, 12096, 12128, 12160, 12192, 1792,
-    1792, 1344, 1344, 12224, 1792, 12256, 12288, 12320, 12352, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 12384, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 12416,
-    12448, 12480, 12512, 5216, 12544, 12576, 12608, 12640, 12672, 12704,
-    12736, 5216, 12768, 12800, 12832, 12864, 12896, 1792, 1792, 12928,
-    12960, 12992, 13024, 13056, 2336, 13088, 13120, 1792, 1792, 1792, 1792,
-    1344, 13152, 13184, 1792, 1344, 13216, 13248, 1792, 1792, 1792, 1792,
-    1792, 1344, 13280, 13312, 1792, 1344, 13344, 13376, 13408, 1344, 13440,
-    13472, 1792, 13504, 13536, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 13568, 13600, 13632, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1344, 13664,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 13696, 13728, 13760,
-    13792, 13824, 13856, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1344, 1344, 1344, 1344, 1344, 1344,
-    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
-    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 9952, 1792,
-    1792, 1792, 10816, 10816, 10816, 13888, 1344, 1344, 1344, 1344, 1344,
-    1344, 13920, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
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-    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
-    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
-    1344, 13952, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
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-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1344, 1344, 1344,
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     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
-    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 16896, 1344, 1344,
-    1344, 1344, 1344, 1344, 11328, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
@@ -505,40 +509,36 @@ static const unsigned short pageMap[] = {
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 17184, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
     1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
-    1344, 1344, 1344, 1344, 1344, 1344, 14400, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792, 1792,
-    1792, 1792, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
-    1344, 1344, 1344, 1344, 1344, 1344, 11328
+    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 17216, 1824, 1824, 1824, 1824, 1824, 1824,
+    1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824,
+    1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824,
+    1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824,
+    1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824,
+    1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824,
+    1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824,
+    1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824, 1824,
+    1824, 1824, 1824, 1824, 1824, 1824, 1344, 1344, 1344, 1344, 1344, 1344,
+    1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 11360
 #endif /* TCL_UTF_MAX > 3 */
 };
 
@@ -652,72 +652,74 @@ static const unsigned char groupMap[] = {
     92, 92, 91, 92, 92, 92, 91, 92, 92, 92, 92, 92, 0, 0, 3, 3, 3, 3, 3,
     3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15,
     15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 92,
-    92, 92, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0,
-    15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92,
-    92, 92, 92, 92, 17, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92,
+    92, 92, 0, 0, 3, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 0, 15, 15, 15, 15, 15, 15, 15, 15,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92,
+    92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 17, 92, 92, 92,
     92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92,
-    92, 92, 92, 124, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 124, 15, 15, 15, 15,
     15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
     15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 92, 124, 92, 15, 124, 124, 124, 92, 92,
-    92, 92, 92, 92, 92, 92, 124, 124, 124, 124, 92, 124, 124, 15, 92, 92,
-    92, 92, 92, 92, 92, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 92, 92,
-    3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3, 91, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 92, 124, 124, 0, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 92,
+    124, 92, 15, 124, 124, 124, 92, 92, 92, 92, 92, 92, 92, 92, 124, 124,
+    124, 124, 92, 124, 124, 15, 92, 92, 92, 92, 92, 92, 92, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 92, 92, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9,
+    9, 3, 91, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    92, 124, 124, 0, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 15, 15, 0, 0,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 0, 15, 15, 15, 15, 15, 15, 15, 0, 15, 0, 0, 0,
+    15, 15, 15, 15, 0, 0, 92, 15, 124, 124, 124, 92, 92, 92, 92, 0, 0,
+    124, 124, 0, 0, 124, 124, 92, 15, 0, 0, 0, 0, 0, 0, 0, 0, 124, 0, 0,
+    0, 0, 15, 15, 0, 15, 15, 15, 92, 92, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9,
+    9, 9, 15, 15, 4, 4, 18, 18, 18, 18, 18, 18, 14, 4, 15, 3, 0, 0, 0,
+    92, 92, 124, 0, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 15, 15, 0, 0, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 0, 15, 15, 15, 15, 15, 15, 15, 0, 15, 15, 0, 15, 15,
+    0, 15, 15, 0, 0, 92, 0, 124, 124, 124, 92, 92, 0, 0, 0, 0, 92, 92,
+    0, 0, 92, 92, 92, 0, 0, 0, 92, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15,
+    0, 15, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 92, 92, 15,
+    15, 15, 92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 92, 124, 0, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 0, 15, 15, 15, 0, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0,
+    15, 15, 15, 15, 15, 15, 15, 0, 15, 15, 0, 15, 15, 15, 15, 15, 0, 0,
+    92, 15, 124, 124, 124, 92, 92, 92, 92, 92, 0, 92, 92, 124, 0, 124,
+    124, 92, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15,
+    15, 92, 92, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 3, 4, 0, 0, 0, 0, 0,
+    0, 0, 15, 92, 92, 92, 92, 92, 92, 0, 92, 124, 124, 0, 15, 15, 15, 15,
     15, 15, 15, 15, 0, 0, 15, 15, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15,
     15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 15, 15,
-    15, 15, 15, 15, 15, 0, 15, 0, 0, 0, 15, 15, 15, 15, 0, 0, 92, 15, 124,
-    124, 124, 92, 92, 92, 92, 0, 0, 124, 124, 0, 0, 124, 124, 92, 15, 0,
-    0, 0, 0, 0, 0, 0, 0, 124, 0, 0, 0, 0, 15, 15, 0, 15, 15, 15, 92, 92,
-    0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 15, 15, 4, 4, 18, 18, 18, 18, 18,
-    18, 14, 4, 0, 0, 0, 0, 0, 92, 92, 124, 0, 15, 15, 15, 15, 15, 15, 0,
-    0, 0, 0, 15, 15, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 15, 15, 15, 15, 15,
-    15, 15, 0, 15, 15, 0, 15, 15, 0, 15, 15, 0, 0, 92, 0, 124, 124, 124,
-    92, 92, 0, 0, 0, 0, 92, 92, 0, 0, 92, 92, 92, 0, 0, 0, 92, 0, 0, 0,
-    0, 0, 0, 0, 15, 15, 15, 15, 0, 15, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9, 9,
-    9, 9, 9, 9, 9, 9, 92, 92, 15, 15, 15, 92, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 92, 92, 124, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 15, 15,
-    15, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 0, 15, 15, 15, 15, 15, 15, 15, 0, 15, 15,
-    0, 15, 15, 15, 15, 15, 0, 0, 92, 15, 124, 124, 124, 92, 92, 92, 92,
-    92, 0, 92, 92, 124, 0, 124, 124, 92, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 0, 0, 15, 15, 92, 92, 0, 0, 9, 9, 9, 9, 9, 9, 9,
-    9, 9, 9, 3, 4, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 92, 124,
-    124, 0, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 15, 15, 0, 0, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 0, 15, 15, 15, 15, 15, 15, 15, 0, 15, 15, 0, 15, 15, 15,
-    15, 15, 0, 0, 92, 15, 124, 92, 124, 92, 92, 92, 92, 0, 0, 124, 124,
-    0, 0, 124, 124, 92, 0, 0, 0, 0, 0, 0, 0, 0, 92, 124, 0, 0, 0, 0, 15,
-    15, 0, 15, 15, 15, 92, 92, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 14,
-    15, 18, 18, 18, 18, 18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 15, 0,
-    15, 15, 15, 15, 15, 15, 0, 0, 0, 15, 15, 15, 0, 15, 15, 15, 15, 0,
-    0, 0, 15, 15, 0, 15, 0, 15, 15, 0, 0, 0, 15, 15, 0, 0, 0, 15, 15, 15,
-    0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0,
-    124, 124, 92, 124, 124, 0, 0, 0, 124, 124, 124, 0, 124, 124, 124, 92,
-    0, 0, 15, 0, 0, 0, 0, 0, 0, 124, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 18, 18, 18, 14, 14, 14, 14, 14,
-    14, 4, 14, 0, 0, 0, 0, 0, 92, 124, 124, 124, 0, 15, 15, 15, 15, 15,
-    15, 15, 15, 0, 15, 15, 15, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 15, 92,
-    92, 92, 124, 124, 124, 124, 0, 92, 92, 92, 0, 92, 92, 92, 92, 0, 0,
-    0, 0, 0, 0, 0, 92, 92, 0, 15, 15, 15, 0, 0, 0, 0, 0, 15, 15, 92, 92,
-    0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 18, 18,
-    18, 18, 18, 18, 18, 14, 15, 92, 124, 124, 0, 15, 15, 15, 15, 15, 15,
-    15, 15, 0, 15, 15, 15, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 0, 15, 15, 15, 15, 15, 0, 0, 92, 15, 124, 92,
-    124, 124, 124, 124, 124, 0, 92, 124, 124, 0, 124, 124, 92, 92, 0, 0,
-    0, 0, 0, 0, 0, 124, 124, 0, 0, 0, 0, 0, 0, 0, 15, 0, 15, 15, 92, 92,
-    0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 0, 92, 124, 124, 0, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 0, 15, 15, 0, 15, 15, 15, 15, 15, 0, 0, 92, 15,
+    124, 92, 124, 92, 92, 92, 92, 0, 0, 124, 124, 0, 0, 124, 124, 92, 0,
+    0, 0, 0, 0, 0, 0, 0, 92, 124, 0, 0, 0, 0, 15, 15, 0, 15, 15, 15, 92,
+    92, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 14, 15, 18, 18, 18, 18, 18,
+    18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 15, 0, 15, 15, 15, 15, 15, 15,
+    0, 0, 0, 15, 15, 15, 0, 15, 15, 15, 15, 0, 0, 0, 15, 15, 0, 15, 0,
+    15, 15, 0, 0, 0, 15, 15, 0, 0, 0, 15, 15, 15, 0, 0, 0, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 124, 124, 92, 124,
+    124, 0, 0, 0, 124, 124, 124, 0, 124, 124, 124, 92, 0, 0, 15, 0, 0,
+    0, 0, 0, 0, 124, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 9,
+    9, 9, 9, 9, 9, 9, 9, 18, 18, 18, 14, 14, 14, 14, 14, 14, 4, 14, 0,
+    0, 0, 0, 0, 92, 124, 124, 124, 0, 15, 15, 15, 15, 15, 15, 15, 15, 0,
+    15, 15, 15, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 15, 92, 92, 92, 124,
+    124, 124, 124, 0, 92, 92, 92, 0, 92, 92, 92, 92, 0, 0, 0, 0, 0, 0,
+    0, 92, 92, 0, 15, 15, 15, 0, 0, 0, 0, 0, 15, 15, 92, 92, 0, 0, 9, 9,
+    9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 18, 18, 18, 18, 18,
+    18, 18, 14, 15, 92, 124, 124, 0, 15, 15, 15, 15, 15, 15, 15, 15, 0,
+    15, 15, 15, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 0, 15, 15, 15, 15, 15, 0, 0, 92, 15, 124, 92, 124,
+    124, 124, 124, 124, 0, 92, 124, 124, 0, 124, 124, 92, 92, 0, 0, 0,
+    0, 0, 0, 0, 124, 124, 0, 0, 0, 0, 0, 0, 0, 15, 0, 15, 15, 92, 92, 0,
+    0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 92, 92, 124, 124, 0, 15, 15, 15, 15, 15, 15, 15, 15,
     0, 15, 15, 15, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
     15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 15, 124, 124, 124,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 92, 92, 15, 124, 124, 124,
     92, 92, 92, 92, 0, 124, 124, 124, 0, 124, 124, 124, 92, 15, 14, 0,
     0, 0, 0, 15, 15, 15, 124, 18, 18, 18, 18, 18, 18, 18, 15, 15, 15, 92,
     92, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 18, 18, 18, 18, 18, 18, 18,
@@ -857,7 +859,7 @@ static const unsigned char groupMap[] = {
     0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0,
     92, 92, 92, 3, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92,
     124, 92, 92, 92, 92, 92, 92, 92, 15, 15, 15, 15, 92, 15, 15, 15, 15,
-    124, 124, 92, 15, 15, 0, 92, 92, 0, 0, 0, 0, 0, 0, 21, 21, 21, 21,
+    124, 124, 92, 15, 15, 124, 92, 92, 0, 0, 0, 0, 0, 0, 21, 21, 21, 21,
     21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
     21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
     21, 21, 21, 21, 21, 21, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91,
@@ -868,9 +870,9 @@ static const unsigned char groupMap[] = {
     21, 21, 137, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
     21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 91, 91,
     91, 91, 91, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92,
-    92, 92, 92, 92, 92, 92, 92, 92, 0, 0, 0, 0, 0, 92, 92, 92, 92, 92,
-    23, 24, 23, 24, 23, 24, 23, 24, 23, 24, 23, 24, 23, 24, 23, 24, 23,
-    24, 23, 24, 23, 24, 21, 21, 21, 21, 21, 138, 21, 21, 139, 21, 140,
+    92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 0, 92, 92, 92, 92,
+    92, 23, 24, 23, 24, 23, 24, 23, 24, 23, 24, 23, 24, 23, 24, 23, 24,
+    23, 24, 23, 24, 23, 24, 21, 21, 21, 21, 21, 138, 21, 21, 139, 21, 140,
     140, 140, 140, 140, 140, 140, 140, 141, 141, 141, 141, 141, 141, 141,
     141, 140, 140, 140, 140, 140, 140, 0, 0, 141, 141, 141, 141, 141, 141,
     0, 0, 140, 140, 140, 140, 140, 140, 140, 140, 141, 141, 141, 141, 141,
@@ -897,7 +899,7 @@ static const unsigned char groupMap[] = {
     18, 18, 7, 7, 7, 5, 6, 91, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18,
     7, 7, 7, 5, 6, 0, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91,
     0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
-    4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
     0, 0, 0, 0, 0, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92,
     119, 119, 119, 119, 92, 119, 119, 119, 92, 92, 92, 92, 92, 92, 92,
     92, 92, 92, 92, 92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14,
@@ -930,7 +932,7 @@ static const unsigned char groupMap[] = {
     14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
     14, 14, 14, 14, 7, 7, 7, 7, 7, 7, 14, 14, 14, 14, 14, 14, 14, 14, 14,
     14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
-    14, 14, 14, 0, 14, 14, 14, 14, 14, 14, 14, 0, 0, 0, 0, 0, 0, 0, 0,
+    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 0, 0, 0, 0, 0, 0, 0,
     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14,
     14, 14, 14, 14, 14, 14, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
     0, 0, 0, 0, 0, 0, 0, 0, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18,
@@ -971,9 +973,9 @@ static const unsigned char groupMap[] = {
     14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
     14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 0, 0, 14,
     14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 14, 14, 14, 14, 14,
-    14, 14, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 122, 122, 122, 122, 122, 122, 122, 122, 122, 122,
+    14, 14, 14, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 122, 122, 122, 122, 122, 122, 122, 122, 122, 122,
     122, 122, 122, 122, 122, 122, 122, 122, 122, 122, 122, 122, 122, 122,
     122, 122, 122, 122, 122, 122, 122, 122, 122, 122, 122, 122, 122, 122,
     122, 122, 122, 122, 122, 122, 122, 122, 122, 0, 123, 123, 123, 123,
@@ -996,7 +998,7 @@ static const unsigned char groupMap[] = {
     0, 3, 3, 16, 20, 16, 20, 3, 3, 3, 16, 20, 3, 16, 20, 3, 3, 3, 3, 3,
     3, 3, 3, 3, 8, 3, 3, 8, 3, 16, 20, 3, 3, 16, 20, 5, 6, 5, 6, 5, 6,
     5, 6, 3, 3, 3, 3, 3, 91, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 8, 8, 3, 3,
-    3, 3, 8, 3, 5, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    3, 3, 8, 3, 5, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14,
     14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
     0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
@@ -1014,7 +1016,7 @@ static const unsigned char groupMap[] = {
     15, 15, 15, 15, 15, 3, 91, 91, 91, 15, 0, 0, 0, 0, 0, 15, 15, 15, 15,
     15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
     15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
     15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
     15, 0, 14, 14, 18, 18, 18, 18, 14, 14, 14, 14, 14, 14, 14, 14, 14,
     14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
@@ -1173,245 +1175,269 @@ static const unsigned char groupMap[] = {
     15, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92,
     18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18,
     18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 0, 0, 0, 0, 18, 18, 18, 18,
-    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 127, 15, 15, 15, 15, 15, 15, 15,
-    15, 127, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 127, 15, 15, 15, 15, 15, 15,
+    15, 15, 127, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
     15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 92, 92, 92, 92, 92, 0, 0, 0,
-    0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 3, 15, 15,
-    15, 15, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 3, 127, 127, 127,
-    127, 127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 194, 194, 194, 194, 194, 194,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 92, 92, 92, 92, 92, 0,
+    0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0,
+    3, 15, 15, 15, 15, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 3, 127,
+    127, 127, 127, 127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 194, 194, 194, 194,
     194, 194, 194, 194, 194, 194, 194, 194, 194, 194, 194, 194, 194, 194,
     194, 194, 194, 194, 194, 194, 194, 194, 194, 194, 194, 194, 194, 194,
-    194, 194, 194, 194, 194, 194, 195, 195, 195, 195, 195, 195, 195, 195,
+    194, 194, 194, 194, 194, 194, 194, 194, 195, 195, 195, 195, 195, 195,
     195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 195,
     195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 195,
-    195, 195, 195, 195, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    195, 195, 195, 195, 195, 195, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
     15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
     15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 194, 194, 194,
+    15, 15, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 0, 0, 194,
     194, 194, 194, 194, 194, 194, 194, 194, 194, 194, 194, 194, 194, 194,
     194, 194, 194, 194, 194, 194, 194, 194, 194, 194, 194, 194, 194, 194,
-    194, 194, 194, 194, 194, 0, 0, 0, 0, 195, 195, 195, 195, 195, 195,
+    194, 194, 194, 194, 194, 194, 194, 0, 0, 0, 0, 195, 195, 195, 195,
     195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 195,
     195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 195, 195,
-    195, 195, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 0,
-    0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 0, 0, 15,
-    0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 15, 15, 0, 0, 0, 15,
-    0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 0, 3, 18, 18, 18, 18, 18, 18, 18, 18, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 14, 14, 18, 18, 18, 18, 18, 18, 18, 0, 0, 0, 0,
-    0, 0, 0, 18, 18, 18, 18, 18, 18, 18, 18, 18, 0, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 0, 15, 15, 0, 0, 0, 0, 0, 18, 18, 18,
-    18, 18, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 18, 18, 18, 18, 18, 18, 0, 0, 0, 3, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 0, 3, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 0, 0, 0, 0, 18, 18, 15, 15, 18, 18, 18, 18, 18, 18, 18, 18,
-    18, 18, 18, 18, 18, 18, 18, 18, 0, 0, 18, 18, 18, 18, 18, 18, 18, 18,
-    18, 18, 18, 18, 18, 18, 15, 92, 92, 92, 0, 92, 92, 0, 0, 0, 0, 0, 92,
-    92, 92, 92, 15, 15, 15, 15, 0, 15, 15, 15, 0, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 0, 0, 0, 0, 92, 92, 92, 0, 0, 0, 0, 92, 18, 18, 18,
-    18, 18, 18, 18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 3,
-    3, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 18, 18, 3, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 18,
-    18, 18, 15, 15, 15, 15, 15, 15, 15, 15, 14, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 92, 92, 0, 0, 0, 0, 18, 18, 18, 18, 18, 3, 3, 3,
-    3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0,
-    3, 3, 3, 3, 3, 3, 3, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 18, 18, 18, 18, 18, 18,
-    18, 18, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 0, 0, 0, 0, 0, 18, 18, 18, 18, 18, 18, 18, 18, 15,
+    195, 195, 195, 195, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 0,
+    0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15,
+    15, 0, 0, 15, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
     15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-    18, 18, 18, 18, 18, 18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 97, 97, 97, 97, 97, 97,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 15, 15,
+    0, 0, 0, 15, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 3, 18, 18, 18, 18, 18,
+    18, 18, 18, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 14, 14, 18, 18, 18, 18, 18, 18,
+    18, 0, 0, 0, 0, 0, 0, 0, 18, 18, 18, 18, 18, 18, 18, 18, 18, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 15, 15, 0, 0, 0,
+    0, 0, 18, 18, 18, 18, 18, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 18, 18, 18, 18, 18, 18,
+    0, 0, 0, 3, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 0, 3, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 18, 18, 15, 15, 18, 18, 18, 18,
+    18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 0, 0, 18, 18, 18, 18,
+    18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 15, 92, 92, 92, 0, 92, 92,
+    0, 0, 0, 0, 0, 92, 92, 92, 92, 15, 15, 15, 15, 0, 15, 15, 15, 0, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 92, 92, 92, 0, 0, 0,
+    0, 92, 18, 18, 18, 18, 18, 18, 18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3,
+    3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 18, 18, 3, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 18, 18, 18, 15, 15, 15, 15, 15, 15, 15, 15, 14, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 92, 92, 0, 0, 0, 0, 18, 18, 18,
+    18, 18, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 0, 0, 0, 3, 3, 3, 3, 3, 3, 3, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 18, 18,
+    18, 18, 18, 18, 18, 18, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 0, 18, 18, 18, 18, 18,
+    18, 18, 18, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 18, 18, 18, 18, 18, 18, 18, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 97,
     97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97,
     97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97,
-    97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 0, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102,
+    97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 97, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 102, 102, 102, 102, 102, 102, 102,
     102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102,
     102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102,
-    102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 0, 0, 0,
-    0, 0, 0, 0, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18,
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+    124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124,
     124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124,
     124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124,
-    124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 124, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 92, 92, 92, 91, 91, 91,
-    91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 92, 92, 92, 91,
+    91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 91, 0, 0, 0, 0,
     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0,
-    14, 92, 92, 3, 17, 17, 17, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 14,
-    14, 14, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
-    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 124, 124, 92,
-    92, 92, 14, 14, 14, 124, 124, 124, 124, 124, 124, 17, 17, 17, 17, 17,
-    17, 17, 17, 92, 92, 92, 92, 92, 92, 92, 92, 14, 14, 92, 92, 92, 92,
-    92, 92, 92, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
-    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 92,
-    92, 92, 92, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
-    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 92, 92,
-    92, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
-    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-    18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18,
-    18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 107, 107, 107, 107, 107,
+    0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 0, 0, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0,
+    0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 14, 92, 92, 3, 17,
+    17, 17, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 0, 0, 14, 14,
+    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
+    14, 14, 14, 14, 14, 14, 14, 14, 14, 124, 124, 92, 92, 92, 14, 14, 14,
+    124, 124, 124, 124, 124, 124, 17, 17, 17, 17, 17, 17, 17, 17, 92, 92,
+    92, 92, 92, 92, 92, 92, 14, 14, 92, 92, 92, 92, 92, 92, 92, 14, 14,
+    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
+    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 92, 92, 92, 92, 14, 14,
+    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
+    14, 14, 14, 14, 14, 14, 14, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 92, 92, 92, 14, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14,
+    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
+    14, 14, 14, 14, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 18, 18, 18, 18,
+    18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 107, 107, 107, 107, 107, 107, 107, 107,
+    107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107,
+    107, 107, 107, 107, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
+    21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 107, 107, 107,
+    107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107,
+    107, 107, 107, 107, 107, 107, 107, 107, 107, 21, 21, 21, 21, 21, 21,
+    21, 0, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
+    21, 21, 21, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107,
+    107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107,
+    107, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
+    21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 107, 0, 107, 107, 0, 0, 107,
+    0, 0, 107, 107, 0, 0, 107, 107, 107, 107, 0, 107, 107, 107, 107, 107,
+    107, 107, 107, 21, 21, 21, 21, 0, 21, 0, 21, 21, 21, 21, 21, 21, 21,
+    0, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 107, 107, 107, 107,
+    107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107,
+    107, 107, 107, 107, 107, 107, 107, 107, 21, 21, 21, 21, 21, 21, 21,
+    21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
+    21, 21, 107, 107, 0, 107, 107, 107, 107, 0, 0, 107, 107, 107, 107,
+    107, 107, 107, 107, 0, 107, 107, 107, 107, 107, 107, 107, 0, 21, 21,
+    21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
+    21, 21, 21, 21, 21, 21, 21, 107, 107, 0, 107, 107, 107, 107, 0, 107,
+    107, 107, 107, 107, 0, 107, 0, 0, 0, 107, 107, 107, 107, 107, 107,
+    107, 0, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
+    21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 107, 107, 107, 107, 107,
     107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107,
     107, 107, 107, 107, 107, 107, 107, 21, 21, 21, 21, 21, 21, 21, 21,
     21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
     21, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107,
-    107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 21,
-    21, 21, 21, 21, 21, 21, 0, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
-    21, 21, 21, 21, 21, 21, 21, 21, 107, 107, 107, 107, 107, 107, 107,
+    107, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
+    21, 21, 107, 107, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
+    21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 107, 107, 107,
     107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107,
-    107, 107, 107, 107, 107, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
-    21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 107, 0,
-    107, 107, 0, 0, 107, 0, 0, 107, 107, 0, 0, 107, 107, 107, 107, 0, 107,
-    107, 107, 107, 107, 107, 107, 107, 21, 21, 21, 21, 0, 21, 0, 21, 21,
-    21, 21, 21, 21, 21, 0, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
-    107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107,
-    107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 21, 21,
+    107, 107, 107, 107, 107, 107, 107, 107, 107, 21, 21, 21, 21, 21, 21,
     21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
-    21, 21, 21, 21, 21, 21, 21, 107, 107, 0, 107, 107, 107, 107, 0, 0,
-    107, 107, 107, 107, 107, 107, 107, 107, 0, 107, 107, 107, 107, 107,
-    107, 107, 0, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
-    21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 107, 107, 0, 107, 107,
-    107, 107, 0, 107, 107, 107, 107, 107, 0, 107, 0, 0, 0, 107, 107, 107,
-    107, 107, 107, 107, 0, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
-    21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 107, 107,
+    21, 21, 21, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107,
+    107, 107, 107, 107, 107, 21, 21, 21, 21, 21, 21, 0, 0, 107, 107, 107,
     107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107,
-    107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 21, 21, 21, 21, 21,
+    107, 107, 107, 107, 107, 107, 107, 107, 7, 21, 21, 21, 21, 21, 21,
     21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
+    21, 21, 7, 21, 21, 21, 21, 21, 21, 107, 107, 107, 107, 107, 107, 107,
+    107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107,
+    107, 107, 107, 107, 7, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
+    21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 7, 21, 21,
     21, 21, 21, 21, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107,
-    107, 107, 107, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
-    21, 21, 21, 21, 21, 107, 107, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
-    21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 107,
     107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107,
-    107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 21, 21, 21,
-    21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
-    21, 21, 21, 21, 21, 21, 107, 107, 107, 107, 107, 107, 107, 107, 107,
-    107, 107, 107, 107, 107, 107, 107, 21, 21, 21, 21, 21, 21, 0, 0, 107,
+    7, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
+    21, 21, 21, 21, 21, 21, 21, 21, 21, 7, 21, 21, 21, 21, 21, 21, 107,
     107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107,
     107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 7, 21, 21, 21, 21,
     21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
@@ -1419,89 +1445,81 @@ static const unsigned char groupMap[] = {
     107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107,
     107, 107, 107, 107, 107, 107, 7, 21, 21, 21, 21, 21, 21, 21, 21, 21,
     21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 7,
-    21, 21, 21, 21, 21, 21, 107, 107, 107, 107, 107, 107, 107, 107, 107,
-    107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107,
-    107, 107, 7, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
-    21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 7, 21, 21, 21, 21, 21,
-    21, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107,
-    107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 7, 21,
-    21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
-    21, 21, 21, 21, 21, 21, 21, 7, 21, 21, 21, 21, 21, 21, 107, 107, 107,
-    107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107, 107,
-    107, 107, 107, 107, 107, 107, 107, 107, 7, 21, 21, 21, 21, 21, 21,
-    21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
-    21, 21, 7, 21, 21, 21, 21, 21, 21, 107, 21, 0, 0, 9, 9, 9, 9, 9, 9,
+    21, 21, 21, 21, 21, 21, 107, 21, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
     9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
-    9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 92,
+    9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 92, 92, 92, 92,
     92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92,
-    92, 92, 92, 92, 92, 14, 14, 14, 14, 92, 92, 92, 92, 92, 92, 92, 92,
-    92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 14, 14, 14, 14, 14, 14, 14,
-    14, 92, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 92,
-    14, 14, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-    92, 92, 92, 92, 92, 0, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92,
-    92, 92, 92, 92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92,
-    92, 92, 92, 92, 92, 92, 0, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92,
-    92, 92, 92, 92, 92, 92, 92, 0, 0, 92, 92, 92, 92, 92, 92, 92, 0, 92,
-    92, 0, 92, 92, 92, 92, 92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 0, 0, 18, 18, 18, 18, 18,
-    18, 18, 18, 18, 92, 92, 92, 92, 92, 92, 92, 0, 0, 0, 0, 0, 0, 0, 0,
-    0, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196,
+    92, 92, 14, 14, 14, 14, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92,
+    92, 92, 92, 92, 92, 92, 92, 14, 14, 14, 14, 14, 14, 14, 14, 92, 14,
+    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 92, 14, 14, 3,
+    3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 92, 92,
+    92, 92, 0, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92,
+    92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 92, 92, 92,
+    92, 92, 92, 0, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92, 92,
+    92, 92, 92, 92, 0, 0, 92, 92, 92, 92, 92, 92, 92, 0, 92, 92, 0, 92,
+    92, 92, 92, 92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 15, 15, 15, 15, 15, 0, 0, 18, 18, 18, 18, 18, 18, 18, 18,
+    18, 92, 92, 92, 92, 92, 92, 92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196, 196,
     196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196,
-    196, 196, 196, 196, 196, 196, 196, 197, 197, 197, 197, 197, 197, 197,
+    196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196, 196,
+    196, 196, 196, 196, 197, 197, 197, 197, 197, 197, 197, 197, 197, 197,
     197, 197, 197, 197, 197, 197, 197, 197, 197, 197, 197, 197, 197, 197,
-    197, 197, 197, 197, 197, 197, 197, 197, 197, 197, 197, 197, 197, 92,
-    92, 92, 92, 92, 92, 92, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
-    0, 0, 0, 0, 3, 3, 15, 15, 15, 15, 0, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 0, 15, 15, 0, 15, 0, 0, 15, 0, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 0, 15, 15, 15, 15, 0, 15, 0, 15, 0, 0, 0, 0, 0, 0, 15,
-    0, 0, 0, 0, 15, 0, 15, 0, 15, 0, 15, 15, 15, 0, 15, 15, 0, 15, 0, 0,
-    15, 0, 15, 0, 15, 0, 15, 0, 15, 0, 15, 15, 0, 15, 0, 0, 15, 15, 15,
-    15, 0, 15, 15, 15, 15, 15, 15, 15, 0, 15, 15, 15, 15, 0, 15, 15, 15,
-    15, 0, 15, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0,
-    0, 15, 15, 15, 0, 15, 15, 15, 15, 15, 0, 15, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 0, 0,
-    0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
-    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 0, 14,
-    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 14, 14,
-    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 14, 14, 14,
-    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 18, 18, 18, 18, 18,
-    18, 18, 18, 18, 18, 18, 18, 18, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14,
-    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
-    14, 14, 14, 14, 14, 14, 14, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14,
+    197, 197, 197, 197, 197, 197, 197, 197, 197, 197, 92, 92, 92, 92, 92,
+    92, 92, 0, 0, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 0, 0, 0, 3,
+    3, 15, 15, 15, 15, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 15,
+    15, 0, 15, 0, 0, 15, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0,
+    15, 15, 15, 15, 0, 15, 0, 15, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 15,
+    0, 15, 0, 15, 0, 15, 15, 15, 0, 15, 15, 0, 15, 0, 0, 15, 0, 15, 0,
+    15, 0, 15, 0, 15, 0, 15, 15, 0, 15, 0, 0, 15, 15, 15, 15, 0, 15, 15,
+    15, 15, 15, 15, 15, 0, 15, 15, 15, 15, 0, 15, 15, 15, 15, 0, 15, 0,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 0, 15, 15,
+    15, 0, 15, 15, 15, 15, 15, 0, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 0, 0, 0, 14, 14,
     14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
-    14, 14, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
-    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0,
-    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14,
+    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 0, 14, 14, 14, 14,
+    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 14, 14, 14, 14, 14,
+    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 14, 14, 14, 14, 14, 14,
+    14, 14, 14, 14, 14, 14, 14, 14, 14, 18, 18, 18, 18, 18, 18, 18, 18,
+    18, 18, 18, 18, 18, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
     14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
+    14, 14, 14, 14, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
     14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
-    14, 14, 0, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 0, 0, 0,
-    0, 0, 0, 14, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
+    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
     14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
-    14, 14, 14, 14, 14, 14, 14, 14, 11, 11, 11, 11, 11, 14, 14, 14, 14,
-    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
-    14, 14, 14, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 0, 0, 0, 0, 0, 0,
+    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0,
+    0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 0, 0, 0, 0, 0, 0, 14,
+    14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 14, 14,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
     0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
-    14, 14, 14, 14, 14, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 14,
-    14, 14, 14, 14, 14, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 14, 14,
-    14, 14, 14, 14, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 0,
-    0, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
+    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 11, 11, 11, 11, 11,
     14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
-    14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14,
-    14, 14, 14, 14, 14, 14, 14, 14, 0, 14, 14, 14, 14, 14, 14, 14, 14,
-    0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14,
-    14, 14, 14, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 0,
-    0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0,
+    14, 14, 14, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 14,
+    14, 14, 14, 14, 14, 14, 14, 14, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14,
+    14, 14, 0, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 0, 0,
+    0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 0, 0,
+    0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 0, 0, 0, 0, 0, 0, 0, 0, 14,
     14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
-    14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15, 15,
-    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0,
-    0, 0, 0, 0, 0, 0, 0, 0
+    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14,
+    14, 14, 14, 14, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
+    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 14,
+    14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
+    14, 14, 14, 14, 14, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
+    14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 15, 15, 15, 15,
+    15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0
 #endif /* TCL_UTF_MAX > 3 */
 };
 
@@ -1607,4 +1625,8 @@ enum {
  * Unicode character tables.
  */
 
-#define GetUniCharInfo(ch) (groups[groupMap[pageMap[((ch) & 0xffff) >> OFFSET_BITS] | ((ch) & ((1 << OFFSET_BITS)-1))]])
+#if TCL_UTF_MAX > 3
+#   define GetUniCharInfo(ch) (groups[groupMap[pageMap[((ch) & 0x1fffff) >> OFFSET_BITS] | ((ch) & ((1 << OFFSET_BITS)-1))]])
+#else
+#   define GetUniCharInfo(ch) (groups[groupMap[pageMap[((ch) & 0xffff) >> OFFSET_BITS] | ((ch) & ((1 << OFFSET_BITS)-1))]])
+#endif
-- 
cgit v0.12


From 7dc2f698a1f0fa20b7989be0d73fd3c20b0e66fb Mon Sep 17 00:00:00 2001
From: dkf <donal.k.fellows@manchester.ac.uk>
Date: Thu, 22 Jun 2017 21:55:45 +0000
Subject: Rebase for final implementation work

---
 doc/copy.n           | 21 +++++++++++++++------
 generic/tclOOBasic.c | 32 +++++++++++++++++++++++++++-----
 tests/oo.test        | 35 +++++++++++++++++++++++++++++++++++
 3 files changed, 77 insertions(+), 11 deletions(-)

diff --git a/doc/copy.n b/doc/copy.n
index 100d564..8149397 100644
--- a/doc/copy.n
+++ b/doc/copy.n
@@ -14,7 +14,7 @@ oo::copy \- create copies of objects and classes
 .nf
 package require TclOO
 
-\fBoo::copy\fI sourceObject \fR?\fItargetObject\fR?
+\fBoo::copy\fI sourceObject \fR?\fItargetObject\fR? ?\fItargetNamespace\fR?
 .fi
 .BE
 .SH DESCRIPTION
@@ -22,11 +22,20 @@ package require TclOO
 The \fBoo::copy\fR command creates a copy of an object or class. It takes the
 name of the object or class to be copied, \fIsourceObject\fR, and optionally
 the name of the object or class to create, \fItargetObject\fR, which will be
-resolved relative to the current namespace if not an absolute qualified name.
-If \fItargetObject\fR is omitted, a new name is chosen. The copied object will
-be of the same class as the source object, and will have all its per-object
-methods copied. If it is a class, it will also have all the class methods in
-the class copied, but it will not have any of its instances copied.
+resolved relative to the current namespace if not an absolute qualified name
+and
+.VS TIP473
+\fItargetNamespace\fR which is the name of the namespace where the object is
+going to be created in.
+If either \fItargetObject\fR or \fItargetNamespace\fR is omitted or is given
+as the empty string, a new name is chosen. Names, unless specified, are
+chosen with the same algorithm used by the \fBnew\fR method of
+\fBoo::class\fR.
+.VE TIP473
+The copied object will be of the same class as the source object, and will have 
+all its per-object methods copied. If it is a class, it will also have all the 
+class methods in the class copied, but it will not have any of its instances 
+copied.
 .PP
 .VS
 After the \fItargetObject\fR has been created and all definitions of its
diff --git a/generic/tclOOBasic.c b/generic/tclOOBasic.c
index 8cb80e5..b2c06a7 100644
--- a/generic/tclOOBasic.c
+++ b/generic/tclOOBasic.c
@@ -1183,8 +1183,9 @@ TclOOCopyObjectCmd(
 {
     Tcl_Object oPtr, o2Ptr;
 
-    if (objc < 2 || objc > 3) {
-	Tcl_WrongNumArgs(interp, 1, objv, "sourceName ?targetName?");
+    if (objc < 2 || objc > 4) {
+	Tcl_WrongNumArgs(interp, 1, objv,
+			 "sourceName ?targetName? ?targetNamespace?");
 	return TCL_ERROR;
     }
 
@@ -1204,12 +1205,14 @@ TclOOCopyObjectCmd(
     if (objc == 2) {
 	o2Ptr = Tcl_CopyObjectInstance(interp, oPtr, NULL, NULL);
     } else {
-	const char *name;
+	const char *name, *namespaceName;
 	Tcl_DString buffer;
 
 	name = TclGetString(objv[2]);
 	Tcl_DStringInit(&buffer);
-	if (name[0]!=':' || name[1]!=':') {
+	if (name[0] == '\0') {
+	    name = NULL;
+	} else if (name[0]!=':' || name[1]!=':') {
 	    Interp *iPtr = (Interp *) interp;
 
 	    if (iPtr->varFramePtr != NULL) {
@@ -1220,7 +1223,26 @@ TclOOCopyObjectCmd(
 	    Tcl_DStringAppend(&buffer, name, -1);
 	    name = Tcl_DStringValue(&buffer);
 	}
-	o2Ptr = Tcl_CopyObjectInstance(interp, oPtr, name, NULL);
+
+	/*
+	 * Choose a unique namespace name if the user didn't supply one.
+	 */
+
+	namespaceName = NULL;
+	if (objc == 4) {
+	    namespaceName = TclGetString(objv[3]);
+
+	    if (namespaceName[0] == '\0') {
+		namespaceName = NULL;
+	    } else if (Tcl_FindNamespace(interp, namespaceName, NULL,
+		    0) != NULL) {
+		Tcl_SetObjResult(interp, Tcl_ObjPrintf(
+			"%s refers to an existing namespace", namespaceName));
+		return TCL_ERROR;
+	    }
+	}
+
+	o2Ptr = Tcl_CopyObjectInstance(interp, oPtr, name, namespaceName);
 	Tcl_DStringFree(&buffer);
     }
 
diff --git a/tests/oo.test b/tests/oo.test
index cb37a76..5eaa8bf 100644
--- a/tests/oo.test
+++ b/tests/oo.test
@@ -2013,6 +2013,41 @@ test oo-15.10 {variable binding must not bleed through oo::copy} -setup {
 } -cleanup {
     FooClass destroy
 } -result {foo bar grill bar}
+test oo-15.11 {OO: object cloning} -returnCodes error -body {
+    oo::copy
+} -result {wrong # args: should be "oo::copy sourceName ?targetName? ?targetNamespace?"}
+test oo-15.12 {OO: object cloning with target NS} -setup {
+    oo::class create Super
+    oo::class create Cls {superclass Super}
+} -body {
+    namespace eval ::existing {}
+    oo::copy Cls {} ::existing
+} -returnCodes error -cleanup {
+    Super destroy
+    catch {namespace delete ::existing}
+} -result {::existing refers to an existing namespace}
+test oo-15.13 {OO: object cloning with target NS} -setup {
+    oo::class create Super
+    oo::class create Cls {superclass Super}
+} -body {
+    list [namespace exist ::dupens] [oo::copy Cls Cls2 ::dupens] [namespace exist ::dupens]
+} -cleanup {
+    Super destroy
+} -result {0 ::Cls2 1}
+test oo-15.14 {OO: object cloning with target NS} -setup {
+    oo::class create Cls {export eval}
+    set result {}
+} -body {
+    Cls create obj
+    obj eval {
+	proc test-15.14 {} {}
+    }
+    lappend result [info commands ::dupens::t*]
+    oo::copy obj obj2 ::dupens
+    lappend result [info commands ::dupens::t*]
+} -cleanup {
+    Cls destroy
+} -result {{} ::dupens::test-15.14}
 
 test oo-16.1 {OO: object introspection} -body {
     info object
-- 
cgit v0.12


From 78b1275a4aa81d3b173e4834b73373aa8ebe4ec3 Mon Sep 17 00:00:00 2001
From: dkf <donal.k.fellows@manchester.ac.uk>
Date: Thu, 22 Jun 2017 22:00:39 +0000
Subject: Documentation correction; issue pointed out by DGP.

---
 doc/copy.n | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/doc/copy.n b/doc/copy.n
index 8149397..789a76c 100644
--- a/doc/copy.n
+++ b/doc/copy.n
@@ -25,8 +25,9 @@ the name of the object or class to create, \fItargetObject\fR, which will be
 resolved relative to the current namespace if not an absolute qualified name
 and
 .VS TIP473
-\fItargetNamespace\fR which is the name of the namespace where the object is
-going to be created in.
+\fItargetNamespace\fR which is the name of the namespace that will hold the
+internal state of the object (\fBmy\fR command, etc.); it \fImust not\fR
+refer to an existing namespace.
 If either \fItargetObject\fR or \fItargetNamespace\fR is omitted or is given
 as the empty string, a new name is chosen. Names, unless specified, are
 chosen with the same algorithm used by the \fBnew\fR method of
-- 
cgit v0.12


From ab4e3e7729712e4c16038e99e657401788e364b5 Mon Sep 17 00:00:00 2001
From: dkf <donal.k.fellows@manchester.ac.uk>
Date: Thu, 22 Jun 2017 22:54:32 +0000
Subject: Add [regsub -command] case that wasn't actively tested for.

---
 tests/regexp.test | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/tests/regexp.test b/tests/regexp.test
index 2686526..7367af7 100644
--- a/tests/regexp.test
+++ b/tests/regexp.test
@@ -1184,6 +1184,10 @@ test regexp-27.10 {regsub -command error cases} -returnCodes error -body {
 test regexp-27.11 {regsub -command error cases} -returnCodes error -body {
     regsub -command . abc {}
 } -result {command prefix must be a list of at least one element}
+test regexp-27.12 {regsub -command representation smash} {
+    set s {list (.+)}
+    regsub -command $s {list list} $s
+} {(.+) {list list} list}
 
 # cleanup
 ::tcltest::cleanupTests
-- 
cgit v0.12


From 40fe644b9d30b5b9d2e4c428b86165e3eb6a1b03 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Fri, 23 Jun 2017 12:28:57 +0000
Subject: Repair compiler warning about uninitialized value.

---
 generic/tclCmdMZ.c | 20 +++++++++-----------
 1 file changed, 9 insertions(+), 11 deletions(-)

diff --git a/generic/tclCmdMZ.c b/generic/tclCmdMZ.c
index 2c6b7bb..ad3ee8e 100644
--- a/generic/tclCmdMZ.c
+++ b/generic/tclCmdMZ.c
@@ -487,11 +487,10 @@ Tcl_RegsubObjCmd(
     Tcl_Obj *const objv[])	/* Argument objects. */
 {
     int idx, result, cflags, all, wlen, wsublen, numMatches, offset;
-    int start, end, subStart, subEnd, match, command, numParts, numArgs;
+    int start, end, subStart, subEnd, match, command, numParts;
     Tcl_RegExp regExpr;
     Tcl_RegExpInfo info;
     Tcl_Obj *resultPtr, *subPtr, *objPtr, *startIndex = NULL;
-    Tcl_Obj **args = NULL, **parts;
     Tcl_UniChar ch, *wsrc, *wfirstChar, *wstring, *wsubspec, *wend;
 
     static const char *const options[] = {
@@ -773,12 +772,13 @@ Tcl_RegsubObjCmd(
 	 */
 
 	if (command) {
-	    if (args == NULL) {
-		Tcl_ListObjGetElements(interp, subPtr, &numParts, &parts);
-		numArgs = numParts + info.nsubs + 1;
-		args = ckalloc(sizeof(Tcl_Obj*) * numArgs);
-		memcpy(args, parts, sizeof(Tcl_Obj*) * numParts);
-	    }
+	    Tcl_Obj **args = NULL, **parts;
+	    int numArgs;
+
+	    Tcl_ListObjGetElements(interp, subPtr, &numParts, &parts);
+	    numArgs = numParts + info.nsubs + 1;
+	    args = ckalloc(sizeof(Tcl_Obj*) * numArgs);
+	    memcpy(args, parts, sizeof(Tcl_Obj*) * numParts);
 
 	    for (idx = 0 ; idx <= info.nsubs ; idx++) {
 		subStart = info.matches[idx].start;
@@ -807,6 +807,7 @@ Tcl_RegsubObjCmd(
 	    for (idx = 0 ; idx <= info.nsubs ; idx++) {
 		TclDecrRefCount(args[idx + numParts]);
 	    }
+	    ckfree(args);
 	    if (result != TCL_OK) {
 		if (result == TCL_ERROR) {
 		    Tcl_AppendObjToErrorInfo(interp, Tcl_ObjPrintf(
@@ -975,9 +976,6 @@ Tcl_RegsubObjCmd(
     if (subPtr && (objv[2] == objv[0])) {
 	Tcl_DecrRefCount(subPtr);
     }
-    if (args) {
-	ckfree(args);
-    }
     if (resultPtr) {
 	Tcl_DecrRefCount(resultPtr);
     }
-- 
cgit v0.12


From ad64b08c4f3fc6ee6c6f3247c8a56d8b45136eca Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Fri, 23 Jun 2017 12:39:13 +0000
Subject: repair broken tests

---
 tests/format.test | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/tests/format.test b/tests/format.test
index 577365b..1c20d0f 100644
--- a/tests/format.test
+++ b/tests/format.test
@@ -90,13 +90,13 @@ test format-1.14 {integer formatting} longIs32bit {
 } {  0d0                  0d6                 0d34              0d16923                -0d12}
 test format-1.14.1 {integer formatting} longIs64bit {
     format "%#5d %#20d %#20d %#20d %#20d" 0 6 34 16923 -12 -1
-} {  0d0                  0d6                 0d34              0d16923           -0d12}
+} {  0d0                  0d6                 0d34              0d16923                -0d12}
 test format-1.15 {integer formatting} longIs32bit {
     format "%-#5d %-#20d %-#20d %-#20d %-#20d" 0 6 34 16923 -12 -1
 } {0d0   0d6                  0d34                 0d16923              -0d12               }
 test format-1.15.1 {integer formatting} longIs64bit {
     format "%-#5d %-#20d %-#20d %-#20d %-#20d" 0 6 34 16923 -12 -1
-} {0d0   0d6                  0d34                 0d16923              -0d12      }
+} {0d0   0d6                  0d34                 0d16923              -0d12               }
 
 
 test format-2.1 {string formatting} {
-- 
cgit v0.12


From 5bf26c2a0b6c22fc86b985d78527fba48650f1b6 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Fri, 23 Jun 2017 13:09:23 +0000
Subject: Rewrite the documentation of [regsub -command] so it's not quite such
 a mess.

---
 doc/regsub.n | 22 ++++++++++++----------
 1 file changed, 12 insertions(+), 10 deletions(-)

diff --git a/doc/regsub.n b/doc/regsub.n
index 23bbff9..29c118a 100644
--- a/doc/regsub.n
+++ b/doc/regsub.n
@@ -70,18 +70,20 @@ from the corresponding match.
 .TP
 \fB\-command\fR
 .VS 8.7
-Changes the handling of the substitution string so that it no longer treats
+Changes the handling of \fIsubSpec\fR so that it is not treated
+as a template for a substitution string and the substrings
 .QW &
 and
-.QW \e
-as special characters, but instead uses them as a non-empty list of words.
-Each time a substitution is processed, another complete Tcl word is appended
-to that list for each substitution value (the first such argument represents
-the overall matched substring, the subsequent arguments will be one per
-capturing sub-RE, much as are returned from \fBregexp\fR \fB\-inline\fR) and
-the overall list is then evaluated as a Tcl command call. If the command
-finishes successfully, the result of command call is substituted into the
-resulting string.
+.QW \e\fIn\fR
+no longer have special meaning. Instead \fIsubSpec\fR must be a
+command prefix, that is, a non-empty list.  The substring of \fIstring\fR
+that matches \fIexp\fR, and then each substring that matches each
+capturing sub-RE within \fIexp\fR are appended as additional elements
+to that list. (The items appended to the list are much like what
+\fBregexp\fR \fB-inline\fR would return).  The completed list is then
+evaluated as a Tcl command, and the result of that command is the
+substitution string.  Any error or exception from command evaluation
+becomes an error or exception from the \fBregsub\fR command.
 .RS
 .PP
 If \fB\-all\fR is not also given, the command callback will be invoked at most
-- 
cgit v0.12


From 2f3481e35d9efa4888b2c192cc8c8e43a98f8ca5 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Fri, 23 Jun 2017 13:11:37 +0000
Subject: typo fix

---
 generic/tclCmdMZ.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/generic/tclCmdMZ.c b/generic/tclCmdMZ.c
index ad3ee8e..83382a7 100644
--- a/generic/tclCmdMZ.c
+++ b/generic/tclCmdMZ.c
@@ -800,7 +800,7 @@ Tcl_RegsubObjCmd(
 	     * because Tcl_EvalObjv is "hairy monster" in terms of refcount
 	     * handling, being able to optionally add references to any of its
 	     * argument words. We'll drop the local refs immediately
-	     * afterwarsds; subPtr is handled in the main exit stanza.
+	     * afterwards; subPtr is handled in the main exit stanza.
 	     */
 
 	    result = Tcl_EvalObjv(interp, numArgs, args, 0);
-- 
cgit v0.12


From 66abf13830abd7dba19fa8275307fcabbc7b71f3 Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Fri, 23 Jun 2017 15:04:44 +0000
Subject: No longer split tests for longIs32bit/longIs64bit, since the results
 should be identical

---
 tests/format.test | 15 +++------------
 1 file changed, 3 insertions(+), 12 deletions(-)

diff --git a/tests/format.test b/tests/format.test
index 1c20d0f..094b7b3 100644
--- a/tests/format.test
+++ b/tests/format.test
@@ -79,22 +79,13 @@ test format-1.11.1 {integer formatting} longIs64bit {
 test format-1.12 {integer formatting} {
     format "%b %#b %#b %llb" 5 0 5 [expr {2**100}]
 } {101 0b0 0b101 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}
-test format-1.13 {integer formatting} longIs32bit {
+test format-1.13 {integer formatting} {
     format "%#d %#d %#d %#d %#d" 0 6 34 16923 -12 -1
 } {0d0 0d6 0d34 0d16923 -0d12}
-test format-1.13.1 {integer formatting} longIs64bit {
-    format "%#d %#d %#d %#d %#d" 0 6 34 16923 -12 -1
-} {0d0 0d6 0d34 0d16923 -0d12}
-test format-1.14 {integer formatting} longIs32bit {
-    format "%#5d %#20d %#20d %#20d %#20d" 0 6 34 16923 -12 -1
-} {  0d0                  0d6                 0d34              0d16923                -0d12}
-test format-1.14.1 {integer formatting} longIs64bit {
+test format-1.14 {integer formatting} {
     format "%#5d %#20d %#20d %#20d %#20d" 0 6 34 16923 -12 -1
 } {  0d0                  0d6                 0d34              0d16923                -0d12}
-test format-1.15 {integer formatting} longIs32bit {
-    format "%-#5d %-#20d %-#20d %-#20d %-#20d" 0 6 34 16923 -12 -1
-} {0d0   0d6                  0d34                 0d16923              -0d12               }
-test format-1.15.1 {integer formatting} longIs64bit {
+test format-1.15 {integer formatting} {
     format "%-#5d %-#20d %-#20d %-#20d %-#20d" 0 6 34 16923 -12 -1
 } {0d0   0d6                  0d34                 0d16923              -0d12               }
 
-- 
cgit v0.12


From c4c7df6e176c32ac510fc6e454147a478ffc4cf1 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Mon, 26 Jun 2017 17:30:15 +0000
Subject: Test demonstrating autoloader fragility.

---
 tests/init.test | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/tests/init.test b/tests/init.test
index 41b8624..3a5197a 100644
--- a/tests/init.test
+++ b/tests/init.test
@@ -168,6 +168,16 @@ foreach arg [subst -nocommands -novariables {
     incr count
 }
 
+test init-4.$count {[Bug 46f801ed5a]} -setup {
+    auto_reset
+    array set auto_index {demo {proc demo {} {tailcall error foo}}}
+} -body {
+    demo
+} -cleanup {
+    array unset auto_index demo
+    rename demo {}
+} -match glob -result *
+
 test init-5.0 {return options passed through ::unknown} -setup {
     catch {rename xxx {}}
     set ::auto_index(::xxx) {proc ::xxx {} {
-- 
cgit v0.12


From 45b7c8a7643c1ccb4268653e962709300c237d85 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Mon, 26 Jun 2017 19:17:12 +0000
Subject: Try to make good stack trace. Fallback to making not-so-good stack
 trace. Stop failing altogether. Test in test suite, not program fragility.

---
 library/init.tcl | 50 ++++++++++++++++++++++++++++----------------------
 tests/init.test  |  2 +-
 2 files changed, 29 insertions(+), 23 deletions(-)

diff --git a/library/init.tcl b/library/init.tcl
index a202054..6173b86 100644
--- a/library/init.tcl
+++ b/library/init.tcl
@@ -284,14 +284,9 @@ proc unknown args {
 		    }
 		    append cinfo ...
 		}
-		append cinfo "\"\n    (\"uplevel\" body line 1)"
-		append cinfo "\n    invoked from within"
-		append cinfo "\n\"uplevel 1 \$args\""
-		#
-		# Try each possible form of the stack trace
-		# and trim the extra contribution from the matching case
-		#
-		set expect "$msg\n    while executing\n\"$cinfo"
+		set tail "\n    (\"uplevel\" body line 1)\n    invoked\
+			from within\n\"uplevel 1 \$args\""
+		set expect "$msg\n    while executing\n\"$cinfo\"$tail"
 		if {$errInfo eq $expect} {
 		    #
 		    # The stack has only the eval from the expanded command
@@ -305,21 +300,32 @@ proc unknown args {
 		# Stack trace is nested, trim off just the contribution
 		# from the extra "eval" of $args due to the "catch" above.
 		#
-		set expect "\n    invoked from within\n\"$cinfo"
-		set exlen [string length $expect]
-		set eilen [string length $errInfo]
-		set i [expr {$eilen - $exlen - 1}]
-		set einfo [string range $errInfo 0 $i]
-		#
-		# For now verify that $errInfo consists of what we are about
-		# to return plus what we expected to trim off.
-		#
-		if {$errInfo ne "$einfo$expect"} {
-		    error "Tcl bug: unexpected stack trace in \"unknown\"" {} \
-			[list CORE UNKNOWN BADTRACE $einfo $expect $errInfo]
+		set last [string last $tail $errInfo]
+		if {$last + [string length $tail] != [string length $errInfo]} {
+		    # Very likely cannot happen
+		    return -options $opts $msg
 		}
-		return -code error -errorcode $errCode \
-			-errorinfo $einfo $msg
+		set errInfo [string range $errInfo 0 $last-1]
+		set tail "\"$cinfo\""
+		set last [string last $tail $errInfo]
+		if {$last + [string length $tail] != [string length $errInfo]} {
+		    return -code error -errorcode $errCode \
+			    -errorinfo $errInfo $msg
+		}
+		set errInfo [string range $errInfo 0 $last-1]
+		set tail "\n    invoked from within\n"
+		set last [string last $tail $errInfo]
+		if {$last + [string length $tail] == [string length $errInfo]} {
+		    return -code error -errorcode $errCode \
+			    -errorinfo [string range $errInfo 0 $last-1] $msg
+		}
+		set tail "\n    while executing\n"
+		set last [string last $tail $errInfo]
+		if {$last + [string length $tail] == [string length $errInfo]} {
+		    return -code error -errorcode $errCode \
+			    -errorinfo [string range $errInfo 0 $last-1] $msg
+		}
+		return -options $opts $msg
 	    } else {
 		dict incr opts -level
 		return -options $opts $msg
diff --git a/tests/init.test b/tests/init.test
index 3a5197a..639389f 100644
--- a/tests/init.test
+++ b/tests/init.test
@@ -176,7 +176,7 @@ test init-4.$count {[Bug 46f801ed5a]} -setup {
 } -cleanup {
     array unset auto_index demo
     rename demo {}
-} -match glob -result *
+} -returnCodes error -result foo
 
 test init-5.0 {return options passed through ::unknown} -setup {
     catch {rename xxx {}}
-- 
cgit v0.12


From 2223757a3583e4541ae5814fc6e7059e6048e480 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Mon, 26 Jun 2017 19:37:34 +0000
Subject: Bump to TclOO 1.1.0

---
 generic/tclOO.h     | 2 +-
 unix/tclooConfig.sh | 2 +-
 win/tclooConfig.sh  | 2 +-
 3 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/generic/tclOO.h b/generic/tclOO.h
index 46f01fb..32afbf1 100644
--- a/generic/tclOO.h
+++ b/generic/tclOO.h
@@ -24,7 +24,7 @@
  * win/tclooConfig.sh
  */
 
-#define TCLOO_VERSION "1.0.5"
+#define TCLOO_VERSION "1.1.0"
 #define TCLOO_PATCHLEVEL TCLOO_VERSION
 
 #include "tcl.h"
diff --git a/unix/tclooConfig.sh b/unix/tclooConfig.sh
index ee10b81..2279542 100644
--- a/unix/tclooConfig.sh
+++ b/unix/tclooConfig.sh
@@ -16,4 +16,4 @@ TCLOO_STUB_LIB_SPEC=""
 TCLOO_INCLUDE_SPEC=""
 TCLOO_PRIVATE_INCLUDE_SPEC=""
 TCLOO_CFLAGS=""
-TCLOO_VERSION=1.0.4
+TCLOO_VERSION=1.1.0
diff --git a/win/tclooConfig.sh b/win/tclooConfig.sh
index ee10b81..2279542 100644
--- a/win/tclooConfig.sh
+++ b/win/tclooConfig.sh
@@ -16,4 +16,4 @@ TCLOO_STUB_LIB_SPEC=""
 TCLOO_INCLUDE_SPEC=""
 TCLOO_PRIVATE_INCLUDE_SPEC=""
 TCLOO_CFLAGS=""
-TCLOO_VERSION=1.0.4
+TCLOO_VERSION=1.1.0
-- 
cgit v0.12


From 9bbcda6793ebf1d466c034f4b63342abaafcd2dc Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Mon, 26 Jun 2017 19:56:37 +0000
Subject: update changes

---
 changes | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/changes b/changes
index 359f8b8..f662059 100644
--- a/changes
+++ b/changes
@@ -8783,4 +8783,11 @@ improvements to regexp engine from Postgres (lane,porter,fellows,seltenreich)
 
 2017-06-08 (bug)[2738427] Tcl_NumUtfChars() corner case utf-4.9 (nijtmans)
 
+2017-06-22 (update) Update Unicode data to 10.0 (nijtmans)
+        *** POTENTIAL INCOMPATIBILITY ***
+
+2017-06-22 (TIP 473) Let [oo::copy] specify target namespace (fellows)
+
+2017-06-26 (bug)[46f801] Repair autoloader fragility (porter)
+
 --- Released 8.6.7, ????, 2017 --- http://core.tcl.tk/tcl/ for details
-- 
cgit v0.12


From 073ff3c5fe40eeac93ae5508b647a7019006f431 Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Wed, 28 Jun 2017 13:32:16 +0000
Subject: Eliminate use of (expensive)  Tcl_UtfToUpper() from "format": Just
 generate the expected uppercase characters right away from the start. No
 change in functionality, just code optimization.

---
 generic/tclStringObj.c | 19 +++++++++----------
 1 file changed, 9 insertions(+), 10 deletions(-)

diff --git a/generic/tclStringObj.c b/generic/tclStringObj.c
index 4a3b6f1..c84b500 100644
--- a/generic/tclStringObj.c
+++ b/generic/tclStringObj.c
@@ -2027,8 +2027,11 @@ Tcl_AppendFormatToObj(
 		    segmentLimit -= 1;
 		    precision--;
 		    break;
-		case 'x':
 		case 'X':
+		    Tcl_AppendToObj(segment, "0X", 2);
+		    segmentLimit -= 2;
+		    break;
+		case 'x':
 		    Tcl_AppendToObj(segment, "0x", 2);
 		    segmentLimit -= 2;
 		    break;
@@ -2192,7 +2195,11 @@ Tcl_AppendFormatToObj(
 		    }
 		    digitOffset = (int) (bits % base);
 		    if (digitOffset > 9) {
-			bytes[numDigits] = 'a' + digitOffset - 10;
+			if (ch == 'X') {
+			    bytes[numDigits] = 'A' + digitOffset - 10;
+			} else {
+			    bytes[numDigits] = 'a' + digitOffset - 10;
+			}
 		    } else {
 			bytes[numDigits] = '0' + digitOffset;
 		    }
@@ -2314,14 +2321,6 @@ Tcl_AppendFormatToObj(
 	    goto error;
 	}
 
-	switch (ch) {
-	case 'E':
-	case 'G':
-	case 'X': {
-	    Tcl_SetObjLength(segment, Tcl_UtfToUpper(TclGetString(segment)));
-	}
-	}
-
 	if (width>0 && numChars<0) {
 	    numChars = Tcl_GetCharLength(segment);
 	}
-- 
cgit v0.12


From 41de3a7f8d82c4026e4586675ca4e24a585627b7 Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Mon, 3 Jul 2017 08:27:42 +0000
Subject: 'inline static' -> 'static inline' and 'INLINE' -> 'inline', for
 consistancy.

---
 generic/tclStrToD.c | 52 ++++++++++++++++++++++++++--------------------------
 generic/tclUtf.c    |  4 ++--
 2 files changed, 28 insertions(+), 28 deletions(-)

diff --git a/generic/tclStrToD.c b/generic/tclStrToD.c
index 2091928..5d601e4 100644
--- a/generic/tclStrToD.c
+++ b/generic/tclStrToD.c
@@ -1973,7 +1973,7 @@ RefineApproximation(
  *----------------------------------------------------------------------
  */
 
-inline static void
+static inline void
 MulPow5(
     mp_int *base, 		/* Number to multiply. */
     unsigned n,			/* Power of 5 to multiply by. */
@@ -2018,7 +2018,7 @@ MulPow5(
  *----------------------------------------------------------------------
  */
 
-inline static int
+static inline int
 NormalizeRightward(
     Tcl_WideUInt *wPtr)		/* INOUT: Number to shift. */
 {
@@ -2109,7 +2109,7 @@ RequiredPrecision(
  *----------------------------------------------------------------------
  */
 
-inline static void
+static inline void
 DoubleToExpAndSig(
     double dv,			/* Number to convert. */
     Tcl_WideUInt *significand,	/* OUTPUT: Significand of the number. */
@@ -2157,7 +2157,7 @@ DoubleToExpAndSig(
  *----------------------------------------------------------------------
  */
 
-inline static void
+static inline void
 TakeAbsoluteValue(
     Double *d,			/* Number to replace with absolute value. */
     int *sign)			/* Place to put the signum. */
@@ -2188,7 +2188,7 @@ TakeAbsoluteValue(
  *----------------------------------------------------------------------
  */
 
-inline static char *
+static inline char *
 FormatInfAndNaN(
     Double *d,			/* Exceptional number to format. */
     int *decpt,			/* Decimal point to set to a bogus value. */
@@ -2230,7 +2230,7 @@ FormatInfAndNaN(
  *----------------------------------------------------------------------
  */
 
-inline static char *
+static inline char *
 FormatZero(
     int *decpt,			/* Location of the decimal point. */
     char **endPtr)		/* Pointer to the end of the formatted data */
@@ -2260,7 +2260,7 @@ FormatZero(
  *----------------------------------------------------------------------
  */
 
-inline static int
+static inline int
 ApproximateLog10(
     Tcl_WideUInt bw,		/* Integer significand of the number. */
     int be,			/* Power of two to scale bw. */
@@ -2308,7 +2308,7 @@ ApproximateLog10(
  *----------------------------------------------------------------------
  */
 
-inline static int
+static inline int
 BetterLog10(
     double d,			/* Original number to format. */
     int k,			/* Characteristic(Log base 10) of the
@@ -2351,7 +2351,7 @@ BetterLog10(
  *----------------------------------------------------------------------
  */
 
-inline static void
+static inline void
 ComputeScale(
     int be,			/* Exponent part of number: d = bw * 2**be. */
     int k,			/* Characteristic of log10(number). */
@@ -2414,7 +2414,7 @@ ComputeScale(
  *----------------------------------------------------------------------
  */
 
-inline static void
+static inline void
 SetPrecisionLimits(
     int convType,		/* Type of conversion: TCL_DD_SHORTEST,
 				 * TCL_DD_STEELE0, TCL_DD_E_FMT,
@@ -2475,7 +2475,7 @@ SetPrecisionLimits(
  *----------------------------------------------------------------------
  */
 
-inline static char *
+static inline char *
 BumpUp(
     char *s,		    	/* Cursor pointing one past the end of the
 				 * string. */
@@ -2509,7 +2509,7 @@ BumpUp(
  *----------------------------------------------------------------------
  */
 
-inline static int
+static inline int
 AdjustRange(
     double *dPtr,		/* INOUT: Number to adjust. */
     int k)			/* IN: floor(log10(d)) */
@@ -2582,7 +2582,7 @@ AdjustRange(
  *----------------------------------------------------------------------
  */
 
-inline static char *
+static inline char *
 ShorteningQuickFormat(
     double d,			/* Number to convert. */
     int k,			/* floor(log10(d)) */
@@ -2657,7 +2657,7 @@ ShorteningQuickFormat(
  *----------------------------------------------------------------------
  */
 
-inline static char *
+static inline char *
 StrictQuickFormat(
     double d,			/* Number to convert. */
     int k,			/* floor(log10(d)) */
@@ -2731,7 +2731,7 @@ StrictQuickFormat(
  *----------------------------------------------------------------------
  */
 
-inline static char *
+static inline char *
 QuickConversion(
     double e,			/* Number to format. */
     int k,			/* floor(log10(d)), approximately. */
@@ -2836,7 +2836,7 @@ QuickConversion(
  *----------------------------------------------------------------------
  */
 
-inline static void
+static inline void
 CastOutPowersOf2(
     int *b2,			/* Power of 2 to multiply the significand. */
     int *m2,			/* Power of 2 to multiply 1/2 ulp. */
@@ -2880,7 +2880,7 @@ CastOutPowersOf2(
  *----------------------------------------------------------------------
  */
 
-inline static char *
+static inline char *
 ShorteningInt64Conversion(
     Double *dPtr,		/* Original number to convert. */
     int convType,		/* Type of conversion (shortest, Steele,
@@ -3049,7 +3049,7 @@ ShorteningInt64Conversion(
  *----------------------------------------------------------------------
  */
 
-inline static char *
+static inline char *
 StrictInt64Conversion(
     Double *dPtr,		/* Original number to convert. */
     int convType,		/* Type of conversion (shortest, Steele,
@@ -3155,7 +3155,7 @@ StrictInt64Conversion(
  *----------------------------------------------------------------------
  */
 
-inline static int
+static inline int
 ShouldBankerRoundUpPowD(
     mp_int *b,			/* Numerator of the fraction. */
     int sd,			/* Denominator is 2**(sd*DIGIT_BIT). */
@@ -3193,7 +3193,7 @@ ShouldBankerRoundUpPowD(
  *----------------------------------------------------------------------
  */
 
-inline static int
+static inline int
 ShouldBankerRoundUpToNextPowD(
     mp_int *b,			/* Numerator of the fraction. */
     mp_int *m,			/* Numerator of the rounding tolerance. */
@@ -3256,7 +3256,7 @@ ShouldBankerRoundUpToNextPowD(
  *----------------------------------------------------------------------
  */
 
-inline static char *
+static inline char *
 ShorteningBignumConversionPowD(
     Double *dPtr,		/* Original number to convert. */
     int convType,		/* Type of conversion (shortest, Steele,
@@ -3449,7 +3449,7 @@ ShorteningBignumConversionPowD(
  *----------------------------------------------------------------------
  */
 
-inline static char *
+static inline char *
 StrictBignumConversionPowD(
     Double *dPtr,		/* Original number to convert. */
     int convType,		/* Type of conversion (shortest, Steele,
@@ -3565,7 +3565,7 @@ StrictBignumConversionPowD(
  *----------------------------------------------------------------------
  */
 
-inline static int
+static inline int
 ShouldBankerRoundUp(
     mp_int *twor,		/* 2x the remainder from thd division that
 				 * produced the last digit. */
@@ -3600,7 +3600,7 @@ ShouldBankerRoundUp(
  *----------------------------------------------------------------------
  */
 
-inline static int
+static inline int
 ShouldBankerRoundUpToNext(
     mp_int *b,			/* Remainder from the division that produced
 				 * the last digit. */
@@ -3654,7 +3654,7 @@ ShouldBankerRoundUpToNext(
  *----------------------------------------------------------------------
  */
 
-inline static char *
+static inline char *
 ShorteningBignumConversion(
     Double *dPtr,		/* Original number being converted. */
     int convType,		/* Conversion type. */
@@ -3870,7 +3870,7 @@ ShorteningBignumConversion(
  *----------------------------------------------------------------------
  */
 
-inline static char *
+static inline char *
 StrictBignumConversion(
     Double *dPtr,		/* Original number being converted. */
     int convType,		/* Conversion type. */
diff --git a/generic/tclUtf.c b/generic/tclUtf.c
index b13ad75..b8b867c 100644
--- a/generic/tclUtf.c
+++ b/generic/tclUtf.c
@@ -98,7 +98,7 @@ static int		UtfCount(int ch);
  *---------------------------------------------------------------------------
  */
 
-INLINE static int
+static inline int
 UtfCount(
     int ch)			/* The Tcl_UniChar whose size is returned. */
 {
@@ -134,7 +134,7 @@ UtfCount(
  *---------------------------------------------------------------------------
  */
 
-INLINE int
+int
 Tcl_UniCharToUtf(
     int ch,			/* The Tcl_UniChar to be stored in the
 				 * buffer. */
-- 
cgit v0.12


From 636bacdfbd8be8be7fd289266dcc8637d3b846c2 Mon Sep 17 00:00:00 2001
From: sebres <sebres@users.sourceforge.net>
Date: Mon, 3 Jul 2017 09:15:23 +0000
Subject: tclPathObj: fixed TclJoinPath (backported from 8.6) - usage of
 released object and object leakage. closes
 [adb198c256df8c4192838cc3c1112fb2821314e9]

---
 generic/tclPathObj.c | 154 +++++++++++++++++++++++----------------------------
 1 file changed, 70 insertions(+), 84 deletions(-)

diff --git a/generic/tclPathObj.c b/generic/tclPathObj.c
index 88e49b5..a306853 100644
--- a/generic/tclPathObj.c
+++ b/generic/tclPathObj.c
@@ -821,50 +821,47 @@ GetExtension(
  *---------------------------------------------------------------------------
  */
 
+Tcl_Obj * TclJoinPath(int elements, Tcl_Obj * const objv[]);
+
 Tcl_Obj *
 Tcl_FSJoinPath(
     Tcl_Obj *listObj,		/* Path elements to join, may have a zero
 				 * reference count. */
     int elements)		/* Number of elements to use (-1 = all) */
 {
-    Tcl_Obj *res;
-    int i;
-    Tcl_Filesystem *fsPtr = NULL;
+    Tcl_Obj *copy, *res;
+    int objc;
+    Tcl_Obj **objv;
 
-    if (elements < 0) {
-	if (Tcl_ListObjLength(NULL, listObj, &elements) != TCL_OK) {
-	    return NULL;
-	}
-    } else {
-	/*
-	 * Just make sure it is a valid list.
-	 */
-
-	int listTest;
-
-	if (Tcl_ListObjLength(NULL, listObj, &listTest) != TCL_OK) {
-	    return NULL;
-	}
-
-	/*
-	 * Correct this if it is too large, otherwise we will waste our time
-	 * joining null elements to the path.
-	 */
-
-	if (elements > listTest) {
-	    elements = listTest;
-	}
+    if (Tcl_ListObjLength(NULL, listObj, &objc) != TCL_OK) {
+	return NULL;
     }
 
-    res = NULL;
+    elements = ((elements >= 0) && (elements <= objc)) ? elements : objc;
+    copy = TclListObjCopy(NULL, listObj);
+    Tcl_ListObjGetElements(NULL, listObj, &objc, &objv);
+    res = TclJoinPath(elements, objv);
+    Tcl_DecrRefCount(copy);
+    return res;
+}
+
+Tcl_Obj *
+TclJoinPath(
+    int elements,
+    Tcl_Obj * const objv[])
+{
+    Tcl_Obj *res = NULL;	/* Resulting path object (container of join) */
+    Tcl_Obj *elt;		/* Path part (result if returns part of path) */
+    int i;
+    Tcl_Filesystem *fsPtr = NULL;
 
     for (i = 0; i < elements; i++) {
-	Tcl_Obj *elt, *driveName = NULL;
 	int driveNameLength, strEltLen, length;
 	Tcl_PathType type;
 	char *strElt, *ptr;
-
-	Tcl_ListObjIndex(NULL, listObj, i, &elt);
+	Tcl_Obj *driveName = NULL;
+	
+	elt = objv[i];
 
 	/*
 	 * This is a special case where we can be much more efficient, where
@@ -873,19 +870,23 @@ Tcl_FSJoinPath(
 	 * object which can be normalized more efficiently. Currently we only
 	 * use the special case when we have exactly two elements, but we
 	 * could expand that in the future.
+         *
+         * Bugfix [a47641a0]. TclNewFSPathObj requires first argument
+         * to be an absolute path. Added a check for that elt is absolute.
 	 */
 
-	if ((i == (elements-2)) && (i == 0) && (elt->typePtr == &tclFsPathType)
-		&& !(elt->bytes != NULL && (elt->bytes[0] == '\0'))) {
-	    Tcl_Obj *tail;
+	if ((i == (elements-2)) && (i == 0)
+                && (elt->typePtr == &tclFsPathType)
+		&& !((elt->bytes != NULL) && (elt->bytes[0] == '\0'))
+                && TclGetPathType(elt, NULL, NULL, NULL) == TCL_PATH_ABSOLUTE) {
+            Tcl_Obj *tailObj = objv[i+1];
 
-	    Tcl_ListObjIndex(NULL, listObj, i+1, &tail);
-	    type = TclGetPathType(tail, NULL, NULL, NULL);
+	    type = TclGetPathType(tailObj, NULL, NULL, NULL);
 	    if (type == TCL_PATH_RELATIVE) {
 		const char *str;
 		int len;
 
-		str = Tcl_GetStringFromObj(tail, &len);
+		str = Tcl_GetStringFromObj(tailObj, &len);
 		if (len == 0) {
 		    /*
 		     * This happens if we try to handle the root volume '/'.
@@ -893,10 +894,7 @@ Tcl_FSJoinPath(
 		     * the base itself is just fine!
 		     */
 
-		    if (res != NULL) {
-			TclDecrRefCount(res);
-		    }
-		    return elt;
+		    goto partReturn; /* return elt; */
 		}
 
 		/*
@@ -917,20 +915,20 @@ Tcl_FSJoinPath(
 		     */
 
 		    if ((tclPlatform != TCL_PLATFORM_WINDOWS)
-			    || (strchr(Tcl_GetString(elt), '\\') == NULL)) {
-			if (res != NULL) {
-			    TclDecrRefCount(res);
-			}
-
+			    || (strchr(Tcl_GetString(elt), '\\') == NULL)
+		    ) {
 			if (PATHFLAGS(elt)) {
-			    return TclNewFSPathObj(elt, str, len);
+			    elt = TclNewFSPathObj(elt, str, len);
+			    goto partReturn; /* return elt; */
 			}
 			if (TCL_PATH_ABSOLUTE != Tcl_FSGetPathType(elt)) {
-			    return TclNewFSPathObj(elt, str, len);
+			    elt = TclNewFSPathObj(elt, str, len);
+			    goto partReturn; /* return elt; */
 			}
 			(void) Tcl_FSGetNormalizedPath(NULL, elt);
 			if (elt == PATHOBJ(elt)->normPathPtr) {
-			    return TclNewFSPathObj(elt, str, len);
+			    elt = TclNewFSPathObj(elt, str, len);
+			    goto partReturn; /* return elt; */
 			}
 		    }
 		}
@@ -940,19 +938,15 @@ Tcl_FSJoinPath(
 		 * more general code below handle things.
 		 */
 	    } else if (tclPlatform == TCL_PLATFORM_UNIX) {
-		if (res != NULL) {
-		    TclDecrRefCount(res);
-		}
-		return tail;
+		elt = tailObj;
+		goto partReturn; /* return elt; */
 	    } else {
-		const char *str = TclGetString(tail);
+		const char *str = TclGetString(tailObj);
 
 		if (tclPlatform == TCL_PLATFORM_WINDOWS) {
 		    if (strchr(str, '\\') == NULL) {
-			if (res != NULL) {
-			    TclDecrRefCount(res);
-			}
-			return tail;
+			elt = tailObj;
+			goto partReturn; /* return elt; */
 		    }
 		}
 	    }
@@ -1031,16 +1025,12 @@ Tcl_FSJoinPath(
 		}
 		ptr++;
 	    }
-	    if (res != NULL) {
-		TclDecrRefCount(res);
-	    }
-
 	    /*
-	     * This element is just what we want to return already - no
-	     * further manipulation is requred.
+	     * This element is just what we want to return already; no further
+	     * manipulation is requred.
 	     */
 
-	    return elt;
+	    goto partReturn; /* return elt; */
 	}
 
 	/*
@@ -1051,10 +1041,8 @@ Tcl_FSJoinPath(
     noQuickReturn:
 	if (res == NULL) {
 	    res = Tcl_NewObj();
-	    ptr = Tcl_GetStringFromObj(res, &length);
-	} else {
-	    ptr = Tcl_GetStringFromObj(res, &length);
 	}
+	ptr = Tcl_GetStringFromObj(res, &length);
 
 	/*
 	 * Strip off any './' before a tilde, unless this is the beginning of
@@ -1083,10 +1071,11 @@ Tcl_FSJoinPath(
 	    int needsSep = 0;
 
 	    if (fsPtr->filesystemSeparatorProc != NULL) {
-		Tcl_Obj *sep = (*fsPtr->filesystemSeparatorProc)(res);
+		Tcl_Obj *sep = fsPtr->filesystemSeparatorProc(res);
 
 		if (sep != NULL) {
 		    separator = TclGetString(sep)[0];
+		    TclDecrRefCount(sep);
 		}
 		/* Safety check in case the VFS driver caused sharing */
 		if (Tcl_IsShared(res)) {
@@ -1126,6 +1115,12 @@ Tcl_FSJoinPath(
 	res = Tcl_NewObj();
     }
     return res;
+
+partReturn:
+    if (res != NULL) {
+	TclDecrRefCount(res);
+    }
+    return elt;
 }
 
 /*
@@ -2516,27 +2511,18 @@ SetFsPathFromAny(
 		}
 		TclDecrRefCount(parts);
 	    } else {
-		/*
-		 * Simple case. "rest" is relative path. Just join it. The
-		 * "rest" object will be freed when Tcl_FSJoinToPath returns
-		 * (unless something else claims a refCount on it).
-		 */
-
-		Tcl_Obj *joined;
-		Tcl_Obj *rest = Tcl_NewStringObj(name+split+1, -1);
+		Tcl_Obj *pair[2];
 
-		Tcl_IncrRefCount(transPtr);
-		joined = Tcl_FSJoinToPath(transPtr, 1, &rest);
-		TclDecrRefCount(transPtr);
-		transPtr = joined;
+		pair[0] = transPtr;
+		pair[1] = Tcl_NewStringObj(name+split+1, -1);
+		transPtr = TclJoinPath(2, pair);
+		TclDecrRefCount(pair[0]);
+		TclDecrRefCount(pair[1]);
 	    }
 	}
 	Tcl_DStringFree(&temp);
     } else {
-	/* Bug 3479689: protect 0-refcount pathPth from getting freed */
-	pathPtr->refCount++;
-	transPtr = Tcl_FSJoinToPath(pathPtr, 0, NULL);
-	pathPtr->refCount--;
+	transPtr = TclJoinPath(1, &pathPtr);
     }
 
     /*
-- 
cgit v0.12


From 8f25f4915310d084a6d0e973b8aa85ba18d7bee7 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Thu, 6 Jul 2017 15:46:58 +0000
Subject: Alternative fix for memleaks in fs path join machinery.

---
 generic/tclPathObj.c | 33 ++++++++++++++++-----------------
 1 file changed, 16 insertions(+), 17 deletions(-)

diff --git a/generic/tclPathObj.c b/generic/tclPathObj.c
index 31ed68e..f8015b2 100644
--- a/generic/tclPathObj.c
+++ b/generic/tclPathObj.c
@@ -13,6 +13,7 @@
 
 #include "tclInt.h"
 #include "tclFileSystem.h"
+#include <assert.h>
 
 /*
  * Prototypes for functions defined later in this file.
@@ -849,11 +850,17 @@ TclJoinPath(
     int elements,
     Tcl_Obj * const objv[])
 {
-    Tcl_Obj *res;
+    Tcl_Obj *res = NULL;
     int i;
     const Tcl_Filesystem *fsPtr = NULL;
 
-    res = NULL;
+    assert ( elements >= 0 );
+
+    if (elements == 0) {
+	return Tcl_NewObj();
+    }
+
+    assert ( elements > 0 );
 
     for (i = 0; i < elements; i++) {
 	int driveNameLength, strEltLen, length;
@@ -893,9 +900,7 @@ TclJoinPath(
 		     * the base itself is just fine!
 		     */
 
-		    if (res != NULL) {
-			TclDecrRefCount(res);
-		    }
+		    assert ( res == NULL );
 		    return elt;
 		}
 
@@ -918,9 +923,8 @@ TclJoinPath(
 
 		    if ((tclPlatform != TCL_PLATFORM_WINDOWS)
 			    || (strchr(Tcl_GetString(elt), '\\') == NULL)) {
-			if (res != NULL) {
-			    TclDecrRefCount(res);
-			}
+
+			assert ( res == NULL );
 
 			if (PATHFLAGS(elt)) {
 			    return TclNewFSPathObj(elt, str, len);
@@ -940,18 +944,14 @@ TclJoinPath(
 		 * more general code below handle things.
 		 */
 	    } else if (tclPlatform == TCL_PLATFORM_UNIX) {
-		if (res != NULL) {
-		    TclDecrRefCount(res);
-		}
+		assert ( res == NULL );
 		return tailObj;
 	    } else {
 		const char *str = TclGetString(tailObj);
 
 		if (tclPlatform == TCL_PLATFORM_WINDOWS) {
 		    if (strchr(str, '\\') == NULL) {
-			if (res != NULL) {
-			    TclDecrRefCount(res);
-			}
+			assert ( res == NULL );
 			return tailObj;
 		    }
 		}
@@ -1087,6 +1087,7 @@ TclJoinPath(
 
 		if (sep != NULL) {
 		    separator = TclGetString(sep)[0];
+		    Tcl_DecrRefCount(sep);
 		}
 		/* Safety check in case the VFS driver caused sharing */
 		if (Tcl_IsShared(res)) {
@@ -1122,9 +1123,7 @@ TclJoinPath(
 	    Tcl_SetObjLength(res, length);
 	}
     }
-    if (res == NULL) {
-	res = Tcl_NewObj();
-    }
+    assert ( res != NULL );
     return res;
 }
 
-- 
cgit v0.12


From 5ef31506293557a4127815e05758bedf889f9b5b Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Thu, 6 Jul 2017 16:00:46 +0000
Subject: Pull out of the loop a block of code that can only run in first
 iteration.

---
 generic/tclPathObj.c | 37 +++++++++++++++++++------------------
 1 file changed, 19 insertions(+), 18 deletions(-)

diff --git a/generic/tclPathObj.c b/generic/tclPathObj.c
index f8015b2..8ee4869 100644
--- a/generic/tclPathObj.c
+++ b/generic/tclPathObj.c
@@ -862,12 +862,8 @@ TclJoinPath(
 
     assert ( elements > 0 );
 
-    for (i = 0; i < elements; i++) {
-	int driveNameLength, strEltLen, length;
-	Tcl_PathType type;
-	char *strElt, *ptr;
-	Tcl_Obj *driveName = NULL;
-	Tcl_Obj *elt = objv[i];
+    if (elements == 2) {
+	Tcl_Obj *elt = objv[0];
 
 	/*
 	 * This is a special case where we can be much more efficient, where
@@ -876,18 +872,17 @@ TclJoinPath(
 	 * object which can be normalized more efficiently. Currently we only
 	 * use the special case when we have exactly two elements, but we
 	 * could expand that in the future.
-         *
-         * Bugfix [a47641a0]. TclNewFSPathObj requires first argument
-         * to be an absolute path. Added a check for that elt is absolute.
+	 *
+	 * Bugfix [a47641a0]. TclNewFSPathObj requires first argument
+	 * to be an absolute path. Added a check for that elt is absolute.
 	 */
 
-	if ((i == (elements-2)) && (i == 0)
-                && (elt->typePtr == &tclFsPathType)
+	if ((elt->typePtr == &tclFsPathType)
 		&& !((elt->bytes != NULL) && (elt->bytes[0] == '\0'))
                 && TclGetPathType(elt, NULL, NULL, NULL) == TCL_PATH_ABSOLUTE) {
-            Tcl_Obj *tailObj = objv[i+1];
+            Tcl_Obj *tailObj = objv[1];
+	    Tcl_PathType type = TclGetPathType(tailObj, NULL, NULL, NULL);
 
-	    type = TclGetPathType(tailObj, NULL, NULL, NULL);
 	    if (type == TCL_PATH_RELATIVE) {
 		const char *str;
 		int len;
@@ -900,7 +895,6 @@ TclJoinPath(
 		     * the base itself is just fine!
 		     */
 
-		    assert ( res == NULL );
 		    return elt;
 		}
 
@@ -924,8 +918,6 @@ TclJoinPath(
 		    if ((tclPlatform != TCL_PLATFORM_WINDOWS)
 			    || (strchr(Tcl_GetString(elt), '\\') == NULL)) {
 
-			assert ( res == NULL );
-
 			if (PATHFLAGS(elt)) {
 			    return TclNewFSPathObj(elt, str, len);
 			}
@@ -944,19 +936,28 @@ TclJoinPath(
 		 * more general code below handle things.
 		 */
 	    } else if (tclPlatform == TCL_PLATFORM_UNIX) {
-		assert ( res == NULL );
 		return tailObj;
 	    } else {
 		const char *str = TclGetString(tailObj);
 
 		if (tclPlatform == TCL_PLATFORM_WINDOWS) {
 		    if (strchr(str, '\\') == NULL) {
-			assert ( res == NULL );
 			return tailObj;
 		    }
 		}
 	    }
 	}
+    }
+
+    assert ( res == NULL );
+
+    for (i = 0; i < elements; i++) {
+	int driveNameLength, strEltLen, length;
+	Tcl_PathType type;
+	char *strElt, *ptr;
+	Tcl_Obj *driveName = NULL;
+	Tcl_Obj *elt = objv[i];
+
 	strElt = Tcl_GetStringFromObj(elt, &strEltLen);
 	driveNameLength = 0;
 	type = TclGetPathType(elt, &fsPtr, &driveNameLength, &driveName);
-- 
cgit v0.12


From ba36e5644b01038e11624290850803281b18ece1 Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Thu, 13 Jul 2017 15:03:27 +0000
Subject: Fix [293344d4f3]: Regression in SQLite test-suite. Long-standing bug
 in implementation of TclUtfToUniChar() macro.

---
 generic/tclInt.h | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/generic/tclInt.h b/generic/tclInt.h
index 6113f23..25bec6a 100644
--- a/generic/tclInt.h
+++ b/generic/tclInt.h
@@ -3670,7 +3670,7 @@ MODULE_SCOPE void	TclDbInitNewObj(Tcl_Obj *objPtr, CONST char *file,
 
 #define TclUtfToUniChar(str, chPtr) \
 	((((unsigned char) *(str)) < 0xC0) ?		\
-	    ((*(chPtr) = (Tcl_UniChar) *(str)), 1)	\
+	    ((*(chPtr) = (unsigned char) *(str)), 1)	\
 	    : Tcl_UtfToUniChar(str, chPtr))
 
 /*
-- 
cgit v0.12


From 94e285cad09f37ba982d10d920ead9ed582bab4f Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Mon, 17 Jul 2017 08:01:11 +0000
Subject: Fix [fb2208172c671f29d60e9ac928d9ded45d01d8b8|fb2208172c]: tclIndex
 varies across builds from auto_mkindex

---
 library/auto.tcl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/library/auto.tcl b/library/auto.tcl
index ec680de..6cb09b6 100644
--- a/library/auto.tcl
+++ b/library/auto.tcl
@@ -211,7 +211,7 @@ proc auto_mkindex {dir args} {
     }
 
     auto_mkindex_parser::init
-    foreach file [glob -- {*}$args] {
+    foreach file [lsort [glob -- {*}$args]] {
         if {[catch {auto_mkindex_parser::mkindex $file} msg opts] == 0} {
             append index $msg
         } else {
@@ -244,7 +244,7 @@ proc auto_mkindex_old {dir args} {
     if {[llength $args] == 0} {
 	set args *.tcl
     }
-    foreach file [glob -- {*}$args] {
+    foreach file [lsort [glob -- {*}$args]] {
 	set f ""
 	set error [catch {
 	    set f [open $file]
-- 
cgit v0.12


From e0f9bcfae392844b48282ffca922a2e4b28aa314 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Tue, 1 Aug 2017 16:05:13 +0000
Subject: update changes

---
 changes | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/changes b/changes
index f662059..ba780e8 100644
--- a/changes
+++ b/changes
@@ -8790,4 +8790,8 @@ improvements to regexp engine from Postgres (lane,porter,fellows,seltenreich)
 
 2017-06-26 (bug)[46f801] Repair autoloader fragility (porter)
 
---- Released 8.6.7, ????, 2017 --- http://core.tcl.tk/tcl/ for details
+2017-07-06 (bug)[adb198] Plug memleak in TclJoinPath (sebres,porter)
+
+2017-07-17 (bug)[fb2208] Repeatable tclIndex generation (wiedemann,nijtmans)
+
+--- Released 8.6.7, August 4, 2017 --- http://core.tcl.tk/tcl/ for details
-- 
cgit v0.12


From 07fa017898edeacecf2cf454f053948cc7263d0d Mon Sep 17 00:00:00 2001
From: dkf <donal.k.fellows@manchester.ac.uk>
Date: Wed, 2 Aug 2017 23:38:20 +0000
Subject: Fix weird hangs in macOS Sierra on some networks. Name resolution
 timeouts not what we want to test in the http package.

---
 tests/http.test    | 29 ++++++++++++++++++-----------
 tests/httpd        |  9 ++++++++-
 tests/httpold.test | 17 ++++++++++++-----
 3 files changed, 38 insertions(+), 17 deletions(-)

diff --git a/tests/http.test b/tests/http.test
index e8f78e3..c2d2fe8 100644
--- a/tests/http.test
+++ b/tests/http.test
@@ -36,6 +36,13 @@ proc bgerror {args} {
     puts stderr $errorInfo
 }
 
+if {$::tcl_platform(os) eq "Darwin"} {
+    # Name resolution often a problem on OSX; not focus of HTTP package anyway
+    set HOST localhost
+} else {
+    set HOST [info hostname]
+}
+
 set port 8010
 set bindata "This is binary data\x0d\x0amore\x0dmore\x0amore\x00null"
 catch {unset data}
@@ -118,8 +125,8 @@ test http-3.1 {http::geturl} -returnCodes error -body {
 test http-3.2 {http::geturl} -returnCodes error -body {
     http::geturl http:junk
 } -result {Unsupported URL: http:junk}
-set url //[info hostname]:$port
-set badurl //[info hostname]:[expr $port+1]
+set url //${::HOST}:$port
+set badurl //${::HOST}:[expr $port+1]
 test http-3.3 {http::geturl} -body {
     set token [http::geturl $url]
     http::data $token
@@ -130,13 +137,13 @@ test http-3.3 {http::geturl} -body {
 <h2>GET /</h2>
 </body></html>"
 set tail /a/b/c
-set url //[info hostname]:$port/a/b/c
-set fullurl HTTP://user:pass@[info hostname]:$port/a/b/c
-set binurl //[info hostname]:$port/binary
-set xmlurl //[info hostname]:$port/xml
-set posturl //[info hostname]:$port/post
-set badposturl //[info hostname]:$port/droppost
-set authorityurl //[info hostname]:$port
+set url //${::HOST}:$port/a/b/c
+set fullurl HTTP://user:pass@${::HOST}:$port/a/b/c
+set binurl //${::HOST}:$port/binary
+set xmlurl //${::HOST}:$port/xml
+set posturl //${::HOST}:$port/post
+set badposturl //${::HOST}:$port/droppost
+set authorityurl //${::HOST}:$port
 set ipv6url http://\[::1\]:$port/
 test http-3.4 {http::geturl} -body {
     set token [http::geturl $url]
@@ -149,7 +156,7 @@ test http-3.4 {http::geturl} -body {
 </body></html>"
 proc selfproxy {host} {
     global port
-    return [list [info hostname] $port]
+    return [list ${::HOST} $port]
 }
 test http-3.5 {http::geturl} -body {
     http::config -proxyfilter selfproxy
@@ -620,7 +627,7 @@ test http-5.5 {http::formatQuery} {
 } {name1=~bwelch&name2=%A1%A2%A2}
 
 test http-6.1 {http::ProxyRequired} -body {
-    http::config -proxyhost [info hostname] -proxyport $port
+    http::config -proxyhost ${::HOST} -proxyport $port
     set token [http::geturl $url]
     http::wait $token
     upvar #0 $token data
diff --git a/tests/httpd b/tests/httpd
index 8753912..16e0382 100644
--- a/tests/httpd
+++ b/tests/httpd
@@ -10,6 +10,13 @@
 
 #set httpLog 1
 
+if {$::tcl_platform(os) eq "Darwin"} {
+    # Name resolution often a problem on OSX; not focus of HTTP package anyway
+    set HOST localhost
+} else {
+    set HOST [info hostname]
+}
+
 proc httpd_init {{port 8015}} {
     socket -server httpdAccept $port
 }
@@ -168,7 +175,7 @@ proc httpdRespond { sock } {
 
     switch -glob -- $data(url) {
 	*binary* {
-	    set html "$bindata[info hostname]:$port$data(url)"
+	    set html "$bindata${::HOST}:$port$data(url)"
 	    set type application/octet-stream
 	}
 	*xml* {
diff --git a/tests/httpold.test b/tests/httpold.test
index 5995bed..e63bcda 100644
--- a/tests/httpold.test
+++ b/tests/httpold.test
@@ -33,6 +33,13 @@ if {[catch {package require http 1.0}]} {
     }
 }
 
+if {$::tcl_platform(os) eq "Darwin"} {
+    # Name resolution often a problem on OSX; not focus of HTTP package anyway
+    set HOST localhost
+} else {
+    set HOST [info hostname]
+}
+
 set bindata "This is binary data\x0d\x0amore\x0dmore\x0amore\x00null"
 catch {unset data}
 
@@ -85,7 +92,7 @@ test httpold-3.2 {http_get} {
     set err
 } {Unsupported URL: http:junk}
 
-set url [info hostname]:$port
+set url ${::HOST}:$port
 test httpold-3.3 {http_get} {
     set token [http_get $url]
     http_data $token
@@ -95,8 +102,8 @@ test httpold-3.3 {http_get} {
 </body></html>"
 
 set tail /a/b/c
-set url [info hostname]:$port/a/b/c
-set binurl [info hostname]:$port/binary
+set url ${::HOST}:$port/a/b/c
+set binurl ${::HOST}:$port/binary
 
 test httpold-3.4 {http_get} {
     set token [http_get $url]
@@ -108,7 +115,7 @@ test httpold-3.4 {http_get} {
 
 proc selfproxy {host} {
     global port
-    return [list [info hostname] $port]
+    return [list ${::HOST} $port]
 }
 test httpold-3.5 {http_get} {
     http_config -proxyfilter selfproxy
@@ -273,7 +280,7 @@ test httpold-5.3 {http_formatQuery} {
 
 test httpold-6.1 {httpProxyRequired} {
     update
-    http_config -proxyhost [info hostname] -proxyport $port
+    http_config -proxyhost ${::HOST} -proxyport $port
     set token [http_get $url]
     http_wait $token
     http_config -proxyhost {} -proxyport {}
-- 
cgit v0.12


From c5d2a041f09785727fad67a457ca2b28aecefe82 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Thu, 3 Aug 2017 14:39:59 +0000
Subject: Improved test http-4.16.

---
 tests/http.test | 14 ++++++++++----
 1 file changed, 10 insertions(+), 4 deletions(-)

diff --git a/tests/http.test b/tests/http.test
index c2d2fe8..5a00cd5 100644
--- a/tests/http.test
+++ b/tests/http.test
@@ -599,14 +599,20 @@ test http-4.15 {http::Event} -body {
 } -cleanup {
     catch {http::cleanup $token}
 } -returnCodes 1 -match glob -result "couldn't open socket*"
-test http-4.16 {Leak with Close vs Keepalive (bug [6ca52aec14]} -body {
+test http-4.16 {Leak with Close vs Keepalive (bug [6ca52aec14]} -setup {
+    proc list-difference {l1 l2} {
+	lmap item $l2 {if {$item in $l1} continue; set item}
+    }
+} -body {
     set before [chan names]
     set token [http::geturl $url -headers {X-Connection keep-alive}]
     http::cleanup $token
     update
-    set after [chan names]
-    expr {$before eq $after}
-} -result 1
+    # Compute what channels have been unexpectedly leaked past cleanup
+    list-difference $before [chan names]
+} -cleanup {
+    rename list-difference {}
+} -result {}
 
 test http-5.1 {http::formatQuery} {
     http::formatQuery name1 value1 name2 "value two"
-- 
cgit v0.12


From 94c0fba63c4bc7a61f181cf02da9042ebf0884a9 Mon Sep 17 00:00:00 2001
From: andy <andrew.m.goth@gmail.com>
Date: Mon, 7 Aug 2017 01:16:39 +0000
Subject: [5bfe3de008]: Modify [source] to set input EOF character but not
 output EOF character.  This avoids having ^Z being appended to the sourced
 file when it is an always-writable [tcl::chan::variable] in a custom VFS. 
 Tested by adding this same change as a patch to Tcl 8.6.6 in KitCreator
 because that seems to be the easiest way to get custom VFS capability exposed
 as script commands.  Original problem introduced by [03cdfc3a86] 2000-05-11
 00:16:52.

---
 generic/tclIOUtil.c | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/generic/tclIOUtil.c b/generic/tclIOUtil.c
index ea407ab..2c389c6 100644
--- a/generic/tclIOUtil.c
+++ b/generic/tclIOUtil.c
@@ -1764,7 +1764,7 @@ Tcl_FSEvalFileEx(
      * this cross-platform to allow for scripted documents. [Bug: 2040]
      */
 
-    Tcl_SetChannelOption(interp, chan, "-eofchar", "\32");
+    Tcl_SetChannelOption(interp, chan, "-eofchar", "\32 {}");
 
     /*
      * If the encoding is specified, set it for the channel. Else don't touch
@@ -1899,7 +1899,7 @@ TclNREvalFile(
      * this cross-platform to allow for scripted documents. [Bug: 2040]
      */
 
-    Tcl_SetChannelOption(interp, chan, "-eofchar", "\32");
+    Tcl_SetChannelOption(interp, chan, "-eofchar", "\32 {}");
 
     /*
      * If the encoding is specified, set it for the channel. Else don't touch
-- 
cgit v0.12


From af03c7e562cc37087f276fcd7aed692c5537056a Mon Sep 17 00:00:00 2001
From: andy <andrew.m.goth@gmail.com>
Date: Tue, 8 Aug 2017 16:42:05 +0000
Subject: Cherrypick [527d354828]

---
 generic/tclIOUtil.c | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/generic/tclIOUtil.c b/generic/tclIOUtil.c
index e00b9ac..41e218f 100644
--- a/generic/tclIOUtil.c
+++ b/generic/tclIOUtil.c
@@ -1762,7 +1762,7 @@ Tcl_FSEvalFileEx(
      * this cross-platform to allow for scripted documents. [Bug: 2040]
      */
 
-    Tcl_SetChannelOption(interp, chan, "-eofchar", "\32");
+    Tcl_SetChannelOption(interp, chan, "-eofchar", "\32 {}");
 
     /*
      * If the encoding is specified, set it for the channel. Else don't touch
@@ -1896,7 +1896,7 @@ TclNREvalFile(
      * this cross-platform to allow for scripted documents. [Bug: 2040]
      */
 
-    Tcl_SetChannelOption(interp, chan, "-eofchar", "\32");
+    Tcl_SetChannelOption(interp, chan, "-eofchar", "\32 {}");
 
     /*
      * If the encoding is specified, set it for the channel. Else don't touch
-- 
cgit v0.12


From 0364abb28794dfc51a043615b44ead2175bf91f4 Mon Sep 17 00:00:00 2001
From: andy <andrew.m.goth@gmail.com>
Date: Tue, 8 Aug 2017 16:45:47 +0000
Subject: Cherrypick [527d354828]

---
 generic/tclIOUtil.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/generic/tclIOUtil.c b/generic/tclIOUtil.c
index e1c5709..6465931 100644
--- a/generic/tclIOUtil.c
+++ b/generic/tclIOUtil.c
@@ -1805,7 +1805,7 @@ Tcl_FSEvalFileEx(
      * this cross-platform to allow for scripted documents. [Bug: 2040]
      */
 
-    Tcl_SetChannelOption(interp, chan, "-eofchar", "\32");
+    Tcl_SetChannelOption(interp, chan, "-eofchar", "\32 {}");
 
     /*
      * If the encoding is specified, set it for the channel. Else don't touch
-- 
cgit v0.12


From 443f0a7ceffa45b9f450afea22b701c44f84b87b Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Wed, 9 Aug 2017 14:41:19 +0000
Subject: bump release date

---
 changes | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/changes b/changes
index ba780e8..f98eafc 100644
--- a/changes
+++ b/changes
@@ -8794,4 +8794,4 @@ improvements to regexp engine from Postgres (lane,porter,fellows,seltenreich)
 
 2017-07-17 (bug)[fb2208] Repeatable tclIndex generation (wiedemann,nijtmans)
 
---- Released 8.6.7, August 4, 2017 --- http://core.tcl.tk/tcl/ for details
+--- Released 8.6.7, August 9, 2017 --- http://core.tcl.tk/tcl/ for details
-- 
cgit v0.12


From d6e5a5012c055c7737f8f12ba124248812b4422a Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Thu, 10 Aug 2017 13:28:48 +0000
Subject: Silence compiler warning in --disable-threads build

---
 generic/tclIORChan.c | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/generic/tclIORChan.c b/generic/tclIORChan.c
index f476a1a..e862761 100644
--- a/generic/tclIORChan.c
+++ b/generic/tclIORChan.c
@@ -41,6 +41,8 @@ static void		ReflectWatch(ClientData clientData, int mask);
 static int		ReflectBlock(ClientData clientData, int mode);
 #ifdef TCL_THREADS
 static void		ReflectThread(ClientData clientData, int action);
+static int		ReflectEventRun(Tcl_Event *ev, int flags);
+static int		ReflectEventDelete(Tcl_Event *ev, ClientData cd);
 #endif
 static Tcl_WideInt	ReflectSeekWide(ClientData clientData,
 			    Tcl_WideInt offset, int mode, int *errorCodePtr);
@@ -748,6 +750,7 @@ TclChanCreateObjCmd(
  *----------------------------------------------------------------------
  */
 
+#ifdef TCL_THREADS
 typedef struct ReflectEvent {
     Tcl_Event header;
     ReflectedChannel *rcPtr;
@@ -791,6 +794,7 @@ ReflectEventDelete(
     }
     return 1;
 }
+#endif
 
 int
 TclChanPostEventObjCmd(
-- 
cgit v0.12


From dcce727d32aec1f557bcb717e8219ee45cfc4582 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Thu, 10 Aug 2017 14:29:11 +0000
Subject: Release candidate branch for Tcl 8.7a1.

---
 README            | 2 +-
 generic/tcl.h     | 4 ++--
 library/init.tcl  | 2 +-
 unix/configure    | 2 +-
 unix/configure.ac | 2 +-
 win/configure     | 2 +-
 win/configure.ac  | 2 +-
 7 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/README b/README
index aab0db5..59de34d 100644
--- a/README
+++ b/README
@@ -1,5 +1,5 @@
 README:  Tcl
-    This is the Tcl 8.7a0 source distribution.
+    This is the Tcl 8.7a1 source distribution.
 	http://sourceforge.net/projects/tcl/files/Tcl/
     You can get any source release of Tcl from the URL above.
 
diff --git a/generic/tcl.h b/generic/tcl.h
index 6fa26f9..2e9d60a 100644
--- a/generic/tcl.h
+++ b/generic/tcl.h
@@ -55,10 +55,10 @@ extern "C" {
 #define TCL_MAJOR_VERSION   8
 #define TCL_MINOR_VERSION   7
 #define TCL_RELEASE_LEVEL   TCL_ALPHA_RELEASE
-#define TCL_RELEASE_SERIAL  0
+#define TCL_RELEASE_SERIAL  1
 
 #define TCL_VERSION	    "8.7"
-#define TCL_PATCH_LEVEL	    "8.7a0"
+#define TCL_PATCH_LEVEL	    "8.7a1"
 
 #if !defined(TCL_NO_DEPRECATED) || defined(RC_INVOKED)
 /*
diff --git a/library/init.tcl b/library/init.tcl
index ece1e44..b6e6e8b 100644
--- a/library/init.tcl
+++ b/library/init.tcl
@@ -16,7 +16,7 @@
 if {[info commands package] == ""} {
     error "version mismatch: library\nscripts expect Tcl version 7.5b1 or later but the loaded version is\nonly [info patchlevel]"
 }
-package require -exact Tcl 8.7a0
+package require -exact Tcl 8.7a1
 
 # Compute the auto path to use in this interpreter.
 # The values on the path come from several locations:
diff --git a/unix/configure b/unix/configure
index a9132b57..0b22a43 100755
--- a/unix/configure
+++ b/unix/configure
@@ -2325,7 +2325,7 @@ ac_compiler_gnu=$ac_cv_c_compiler_gnu
 TCL_VERSION=8.7
 TCL_MAJOR_VERSION=8
 TCL_MINOR_VERSION=7
-TCL_PATCH_LEVEL="a0"
+TCL_PATCH_LEVEL="a1"
 VERSION=${TCL_VERSION}
 
 EXTRA_INSTALL_BINARIES=${EXTRA_INSTALL_BINARIES:-"@:"}
diff --git a/unix/configure.ac b/unix/configure.ac
index b43da6d..d7aa50f 100644
--- a/unix/configure.ac
+++ b/unix/configure.ac
@@ -25,7 +25,7 @@ m4_ifdef([SC_USE_CONFIG_HEADERS], [
 TCL_VERSION=8.7
 TCL_MAJOR_VERSION=8
 TCL_MINOR_VERSION=7
-TCL_PATCH_LEVEL="a0"
+TCL_PATCH_LEVEL="a1"
 VERSION=${TCL_VERSION}
 
 EXTRA_INSTALL_BINARIES=${EXTRA_INSTALL_BINARIES:-"@:"}
diff --git a/win/configure b/win/configure
index d0431cb..a47ff23 100755
--- a/win/configure
+++ b/win/configure
@@ -2102,7 +2102,7 @@ SHELL=/bin/sh
 TCL_VERSION=8.7
 TCL_MAJOR_VERSION=8
 TCL_MINOR_VERSION=7
-TCL_PATCH_LEVEL="a0"
+TCL_PATCH_LEVEL="a1"
 VER=$TCL_MAJOR_VERSION$TCL_MINOR_VERSION
 
 TCL_DDE_VERSION=1.4
diff --git a/win/configure.ac b/win/configure.ac
index 2821bc3..e32dadc 100644
--- a/win/configure.ac
+++ b/win/configure.ac
@@ -14,7 +14,7 @@ SHELL=/bin/sh
 TCL_VERSION=8.7
 TCL_MAJOR_VERSION=8
 TCL_MINOR_VERSION=7
-TCL_PATCH_LEVEL="a0"
+TCL_PATCH_LEVEL="a1"
 VER=$TCL_MAJOR_VERSION$TCL_MINOR_VERSION
 
 TCL_DDE_VERSION=1.4
-- 
cgit v0.12


From e339740a29aa9b5c81844f173a01b4a4dcfdfd9b Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Thu, 10 Aug 2017 14:56:23 +0000
Subject: Bring changes up to the 8.6.7 release.

---
 changes | 171 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 171 insertions(+)

diff --git a/changes b/changes
index 1e24269..f98eafc 100644
--- a/changes
+++ b/changes
@@ -8624,3 +8624,174 @@ improvements to regexp engine from Postgres (lane,porter,fellows,seltenreich)
 2016-02-22 (bug)[9b4702] [info exists env(missing)] kills trace (nijtmans)
 
 --- Released 8.6.5, February 29, 2016 --- http://core.tcl.tk/tcl/ for details
+
+2016-03-01 (bug)[803042] mem leak due to reference cycle (porter)
+
+2016-03-08 (bug)[bbc304] reflected watch race condition (porter)
+
+2016-03-17 (bug)[fadc99] compile-5.3 (rodriguez,porter)
+
+2016-03-17 (enhancement)[1a25fd] compile [variable ${ns}::v] (porter)
+
+2016-03-20 (bug)[1af8de] crash in compiled [string replace] (harder,fellows)
+
+2016-03-21 (bug)[d30718] segv in notifier finalize (hirofumi,nijtmans)
+
+2016-03-23 (enhancement)[7d0db7] parallel make (yarda,nijtmans)
+
+2016-03-23 [f12535] enable test bindings customization (vogel,nijtmans)
+
+2016-04-04 (bug)[47ac84] compiled [lreplace] fixes (aspect,ferrieux,fellows)
+        *** POTENTIAL INCOMPATIBILITY ***
+
+2016-04-08 (bug)[866368] RE \w includes 'Punctuation Connector' (nijtmans)
+
+2016-04-08 (bug)[2538f3] Win crash Tcl_OpenTcpServer() (griffin)
+
+2016-04-10 [07d13d] Restore TclBlend support lost in 8.6.1 (buratti)
+
+2016-05-13 (bug)[3154ea] Mem corruption in assembler exceptions (tkob,kenny)
+
+2016-05-13 (bug) registry package support any Unicode env (nijtmans)
+=> registry 1.3.2
+
+2016-05-21 (bug)[f7d4e] [namespace delete] performance (fellows)
+
+2016-06-02 (TIP 447) execution time verbosity option (cerutti)
+=> tcltest 2.4.0
+
+2016-06-16 (bug)[16828b] crash due to [vwait] trace undo fail (dah,porter)
+
+2016-06-16 (enhancement)[4b61af] good [info frame] from more cases (beric)
+
+2016-06-21 (bug)[c383eb] crash in [glob -path a] (oehlmann,porter)
+
+2016-06-21 (update) Update Unicode data to 9.0 (nijtmans)
+        *** POTENTIAL INCOMPATIBILITY ***
+
+2016-06-22 (bug)[16896d] Tcl_DString tolerate append to self. (dah,porter)
+
+2016-06-23 (bug)[d55322] crash in [dict update] (yorick,fellows)
+
+2016-06-27 (bug)[dd260a] crash in [chan configure -dictionary] (madden,aspect)
+
+2016-07-02 (bug)[f961d7] usage message with parameters with spaces (porter)
+        *** POTENTIAL INCOMPATIBILITY ***
+
+2016-07-02 (enhancement)[09fabc] Sort order of -relateddir (lanam)
+
+2016-07-07 (bug)[5d7ca0] Win: [file executable] for .cmd and .ps1 (nadkarni)
+        *** POTENTIAL INCOMPATIBILITY ***
+
+2016-07-08 (bug)[a47641] [file normalize] & Windows junctions (nadkarni)
+
+2016-07-09 [ae61a6] [file] handling of Win hardcoded names (CON) (nadkarni)
+        *** POTENTIAL INCOMPATIBILITY ***
+
+2016-07-09 [3613671] [file owned] (more) useful on Win (nadkarni)
+
+2016-07-09 (bug)[1493a4] [namespace upvar] use of resolvers (beric,fellows)
+        *** POTENTIAL INCOMPATIBILITY ***
+
+2016-07-10 (bug)[da340d] integer division in clock math (nadkarni)
+
+2016-07-20 tzdata updated to Olson's tzdata2016f (venkat)
+
+--- Released 8.6.6, July 27, 2016 --- http://core.tcl.tk/tcl/ for details
+
+2016-09-07 (bug)[c09edf] Bad caching with  custom resolver (neumann,nijtmans)
+
+2016-09-07 (bug)[4dbdd9] Memleak in test var-8.3 (mr_calvin,porter)
+
+2016-10-03 (bug)[2bf561] Allow empty command as alias target (yorick,nijtmans)
+        *** POTENTIAL INCOMPATIBILITY ***
+
+2016-10-04 (bug)[4d5ae7] Crash in async connects host no address (gahr,fellows)
+
+2016-10-08 (bug)[838e99] treat application/xml as text (gahr,fellows)
+=> http 2.8.10
+
+2016-10-11 (bug)[3cc1d9] Thread finalization crash in zippy (neumann)
+
+2016-10-12 (bug)[be003d] Fix [scan 0x1 %b], [scan 0x1 %o] (porter)
+
+2016-10-14 (bug)[eb6b68] Fix stringComp-14.5 (porter)
+
+2016-10-30 (bug)[b26e38] Fix zlib-7.8 (fellows)
+
+2016-10-30 (bug)[1ae129] Fix memleak in [history] destruction (fellows)
+
+2016-11-04 (feature) Provisional Tcl 9 support in msgcat and tcltest (nijtmans)
+=> msgcat 1.6.1
+=> tcltest 2.4.1
+
+2016-11-04 (bug)[824752] Crash in Tcl_ListObjReplace() (gahr,porter)
+
+2016-11-11 (bug)[79614f] invalidate VFS mounts on sytem encoding change (yorick)
+
+2016-11-14 OSX: End panic() as legacy support macro; system conflicts (nijtmans)
+        *** POTENTIAL INCOMPATIBILITY ***
+
+2016-11-15 (bug) TclOO fix stops crash mixing Itcl and snit (fellows)
+
+2016-11-17 (update) Reconcile libtommath updates; purge unused files (nijtmans)
+        *** POTENTIAL INCOMPATIBILITY ***
+
+2017-01-09 (bug)[b87ad7] Repair drifts in timer clock (sebres)
+
+2017-01-17 (update) => zlib 1.2.11 (nijtmans)
+
+2017-01-31 (bug)[39f630] Revise Tcl_LinkVar to tolerate some prefixes (nijtmans)
+        *** POTENTIAL INCOMPATIBILITY ***
+
+2017-02-01 (bug)[d0f7ba] Improper NAN optimization. expr-22.1[01] (aspect)
+
+2017-02-26 (bug)[25842c] zlib stream finalization (aspect)
+
+2017-03-07 (deprecate) Remove unmaintained makefile.bc file (nijtmans)
+        *** POTENTIAL INCOMPATIBILITY ***
+
+2017-03-14 (enhancement) [clock] and [encoding] are now ensembles (kenny)
+
+2017-03-15 (enhancement) several [clock] subcommands bytecoded (kenny)
+
+2017-03-23 tzdata updated to Olson's tzdata2017b (jima)
+
+2017-03-29 (bug)[900cb0] Fix OO unexport introspection (napier)
+
+2017-04-12 (bug)[42202b] Nesting imbalance in coro injection (nadkarni,sebres)
+
+2017-04-18 (bug)[bc4322] http package support for safe interps (nash,nijtmans)
+
+2017-04-28 (bug)[f34cf8] [file join a //b] => /b (neumann,porter)
+
+2017-05-01 (bug)[8bd13f] Windows threads and pipes (sebres,nijtmans)
+
+2017-05-01 (bug)[f9fe90] [file join //a b] EIAS violation (aspect,porter)
+
+2017-05-04 (bug) Make test filesystem-1.52 pass on Windows (nijtmans)
+
+2017-05-05 (bug)[601522] [binary] field spec overflow -> segfault (porter)
+
+2017-05-08 (bug)[6ca52a] http memleak handling keep-alive (aspect,nijtmans)
+=> http 2.8.11
+
+2017-05-29 (bug)[a3fb33] crash in [lsort] on long lists (sebres)
+
+2017-06-05 (bug)[67aa9a] Tcl_UtfToUniChar() revised handling invalid UTF-8 (nijtmans)
+        *** POTENTIAL INCOMPATIBILITY ***
+
+2017-06-08 (bug)[2738427] Tcl_NumUtfChars() corner case utf-4.9 (nijtmans)
+
+2017-06-22 (update) Update Unicode data to 10.0 (nijtmans)
+        *** POTENTIAL INCOMPATIBILITY ***
+
+2017-06-22 (TIP 473) Let [oo::copy] specify target namespace (fellows)
+
+2017-06-26 (bug)[46f801] Repair autoloader fragility (porter)
+
+2017-07-06 (bug)[adb198] Plug memleak in TclJoinPath (sebres,porter)
+
+2017-07-17 (bug)[fb2208] Repeatable tclIndex generation (wiedemann,nijtmans)
+
+--- Released 8.6.7, August 9, 2017 --- http://core.tcl.tk/tcl/ for details
-- 
cgit v0.12


From ed3d8a5c300d7029bc85bc0c012386ae933e230f Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Thu, 10 Aug 2017 17:03:53 +0000
Subject: Backport [array names -regexp] should support backrefs

---
 generic/tclRegexp.c | 15 +++++++++++----
 tests/set-old.test  |  7 +++++++
 2 files changed, 18 insertions(+), 4 deletions(-)

diff --git a/generic/tclRegexp.c b/generic/tclRegexp.c
index ea25d4b..cfe6388 100644
--- a/generic/tclRegexp.c
+++ b/generic/tclRegexp.c
@@ -502,10 +502,17 @@ Tcl_RegExpMatchObj(
 {
     Tcl_RegExp re;
 
-    re = Tcl_GetRegExpFromObj(interp, patternObj,
-	    TCL_REG_ADVANCED | TCL_REG_NOSUB);
-    if (re == NULL) {
-	return -1;
+    /*
+     * For performance reasons, first try compiling the RE without support for
+     * subexpressions. On failure, try again without TCL_REG_NOSUB in case the
+     * RE has backreferences in it. Closely related to [Bug 1366683]. If this
+     * still fails, an error message will be left in the interpreter.
+     */
+
+    if (!(re = Tcl_GetRegExpFromObj(interp, patternObj,
+            TCL_REG_ADVANCED | TCL_REG_NOSUB))
+     && !(re = Tcl_GetRegExpFromObj(interp, patternObj, TCL_REG_ADVANCED))) {
+        return -1;
     }
     return Tcl_RegExpExecObj(interp, re, textObj, 0 /* offset */,
 	    0 /* nmatches */, 0 /* flags */);
diff --git a/tests/set-old.test b/tests/set-old.test
index 1c68f91..6138ed8 100644
--- a/tests/set-old.test
+++ b/tests/set-old.test
@@ -652,6 +652,13 @@ test set-old-8.52 {array command, array names -regexp on regexp pattern} {
     set a(11) 1
     list [catch {lsort [array names a -regexp ^1]} msg] $msg
 } {0 {1*2 11 12}}
+test set-old-8.52.1 {array command, array names -regexp, backrefs} {
+    catch {unset a}
+    set a(1*2) 1
+    set a(12) 1
+    set a(11) 1
+    list [catch {lsort [array names a -regexp {^(.)\1}]} msg] $msg
+} {0 11}
 test set-old-8.53 {array command, array names -regexp} {
     catch {unset a}
     set a(-glob) 1
-- 
cgit v0.12


From 0ec3676ad3de0d927622af230e5febc9ca673e20 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Thu, 10 Aug 2017 17:34:31 +0000
Subject: Update outdated comment.

---
 generic/tclPkg.c | 17 +++++------------
 1 file changed, 5 insertions(+), 12 deletions(-)

diff --git a/generic/tclPkg.c b/generic/tclPkg.c
index 3b0554a..eb4dc9b 100644
--- a/generic/tclPkg.c
+++ b/generic/tclPkg.c
@@ -331,8 +331,8 @@ Tcl_PkgRequireEx(
 	 *
 	 * Second, how does this work? If we reach this point, then the global
 	 * variable tclEmptyStringRep has the value NULL. Compare that with
-	 * the definition of tclEmptyStringRep near the top of the file
-	 * generic/tclObj.c. It clearly should not have the value NULL; it
+	 * the definition of tclEmptyStringRep near the top of this file.
+	 * It clearly should not have the value NULL; it
 	 * should point to the char tclEmptyString. If we see it having the
 	 * value NULL, then somehow we are seeing a Tcl library that isn't
 	 * completely initialized, and that's an indicator for the error
@@ -348,18 +348,11 @@ Tcl_PkgRequireEx(
 	 * After all, two Tcl libraries can't be a good thing!)
 	 *
 	 * Trouble is that's going to be tricky. We're now using a Tcl library
-	 * that's not fully initialized. In particular, it doesn't have a
-	 * proper value for tclEmptyStringRep. The Tcl_Obj system heavily
-	 * depends on the value of tclEmptyStringRep and all of Tcl depends
-	 * (increasingly) on the Tcl_Obj system, we need to correct that flaw
-	 * before making the calls to set the interpreter result to the error
-	 * message. That's the only flaw corrected; other problems with
-	 * initialization of the Tcl library are not remedied, so be very
-	 * careful about adding any other calls here without checking how they
-	 * behave when initialization is incomplete.
+	 * that's not fully initialized. Functions in it may not work
+	 * reliably, so be very careful about adding any other calls here
+	 * without checking how they behave when initialization is incomplete.
 	 */
 
-	tclEmptyStringRep = &tclEmptyString;
 	Tcl_SetObjResult(interp, Tcl_ObjPrintf(
 		"Cannot load package \"%s\" in standalone executable:"
 		" This package is not compiled with stub support", name));
-- 
cgit v0.12


From 38b319739dd65940f0c634509f00ad6dc5cb98de Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Thu, 10 Aug 2017 19:14:15 +0000
Subject: Add 8.7 -only changes to the changes file.

---
 changes | 41 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 41 insertions(+)

diff --git a/changes b/changes
index f98eafc..7b035fb 100644
--- a/changes
+++ b/changes
@@ -8795,3 +8795,44 @@ improvements to regexp engine from Postgres (lane,porter,fellows,seltenreich)
 2017-07-17 (bug)[fb2208] Repeatable tclIndex generation (wiedemann,nijtmans)
 
 --- Released 8.6.7, August 9, 2017 --- http://core.tcl.tk/tcl/ for details
+
+2016-03-17 (bug)[0b8c38] socket accept callbacks always in global ns (porter)
+        *** POTENTIAL INCOMPATIBILITY ***
+
+2016-07-01 Hack accommodations for legacy Itcl 3 disabled (porter)
+
+2016-07-12 Make TCL_HASH_TYPE build-time configurable (nijtmans)
+
+2016-07-19 (bug)[0363f0] Partial array search ID reform (porter)
+
+2016-07-19 (feature removed) Tcl_ObjType "array search" unregistered (porter)
+	*** POTENTIAL INCOMPATIBILITY for Tcl_GetObjType("array search") ***
+
+2016-10-04 Server socket on port 0 chooses port supporting IPv4 * IPv6 (max)
+
+2016-11-25 [array named -regexp] supports backrefs (goth)
+
+2017-01-04 (TIP 456) New routine Tcl_OpenTcpServerEx() (limeboy)
+
+2017-01-04 (TIP 459) New subcommand [package files] (nijtmans)
+
+2017-01-16 threaded allocator initialization repair (vasiljevic,nijtmans)
+
+2017-01-30 Add to Win shell builtins: assoc ftype move (ashok)
+
+2017-03-31 TCL_MEM_DEBUG facilities better support 64-bit memory (nijtmans)
+
+2017-04-13 \u escaped content in msg files converted to true utf-8 (nijtmans)
+
+2017-05-18 (TIP 458) New epoll or kqueue notifiers are default (alborboz)
+
+2017-05-31 Purge build support for SunOS-4.* (stu)
+
+2017-06-22 (TIP 463) New option [regsub ... -command ...] (fellows)
+
+2017-06-22 (TIP 470) Tcl_GetDefineContextObject();[oo::define [self]] (fellows)
+=> TclOO 1.2.0
+
+2017-06-23 (TIP 472) Support 0d as prefix of decimal numbers (iyer,griffin)
+
+--- Released 8.7a1, August ??, 2017 --- http://core.tcl.tk/tcl/ for details
-- 
cgit v0.12


From 4fd67d5ca799fac826a08aea189b58801f644502 Mon Sep 17 00:00:00 2001
From: andy <andrew.m.goth@gmail.com>
Date: Sat, 12 Aug 2017 19:45:04 +0000
Subject: Correct longstanding typo in continue man page

---
 doc/continue.n | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/doc/continue.n b/doc/continue.n
index 92ff3b4..5eca861 100644
--- a/doc/continue.n
+++ b/doc/continue.n
@@ -23,7 +23,7 @@ exception to occur.
 The exception causes the current script to be aborted
 out to the innermost containing loop command, which then
 continues with the next iteration of the loop.
-Catch exceptions are also handled in a few other situations, such
+Continue exceptions are also handled in a few other situations, such
 as the \fBcatch\fR command and the outermost scripts of procedure
 bodies.
 .SH EXAMPLE
-- 
cgit v0.12


From 9b1b7036b0de2150a62088d4681e966d721fc012 Mon Sep 17 00:00:00 2001
From: Joe Mistachkin <joe@mistachkin.com>
Date: Sun, 13 Aug 2017 22:05:25 +0000
Subject: Support cross-compiling Tcl for 'Win32 on ARM' using Visual Studio.

---
 generic/tclPanic.c |  2 +-
 win/makefile.vc    | 11 +++++++++--
 win/tclWin32Dll.c  |  4 ++--
 win/tclWinFile.c   |  2 +-
 win/tclWinSock.c   |  3 +--
 5 files changed, 14 insertions(+), 8 deletions(-)

diff --git a/generic/tclPanic.c b/generic/tclPanic.c
index b032449..b03ad41 100644
--- a/generic/tclPanic.c
+++ b/generic/tclPanic.c
@@ -111,7 +111,7 @@ Tcl_PanicVA(
 	__builtin_trap();
 #   elif defined(_WIN64)
 	__debugbreak();
-#   elif defined(_MSC_VER)
+#   elif defined(_MSC_VER) && defined (_M_IX86)
 	_asm {int 3}
 #   else
 	DebugBreak();
diff --git a/win/makefile.vc b/win/makefile.vc
index ada08cc..40de392 100644
--- a/win/makefile.vc
+++ b/win/makefile.vc
@@ -121,7 +121,7 @@ the build instructions.
 #		nodep	 = Turns off compatibility macros to ensure the core
 #			    isn't being built with deprecated functions.
 #
-#	MACHINE=(ALPHA|AMD64|IA64|IX86)
+#	MACHINE=(ARM|AMD64|IA64|IX86)
 #		Set the machine type used for the compiler, linker, and
 #		resource compiler.  This hook is needed to tell the tools
 #		when alternate platforms are requested.  IX86 is the default
@@ -484,9 +484,16 @@ cdebug	= -Zi -Od $(DEBUGFLAGS)
 cdebug	= -Zi -WX $(DEBUGFLAGS)
 !endif
 
+### Common compiler options that are architecture specific
+!if "$(MACHINE)" == "ARM"
+carch = -D_ARM_WINAPI_PARTITION_DESKTOP_SDK_AVAILABLE
+!else
+carch =
+!endif
+
 ### Declarations common to all compiler options
 cwarn = $(WARNINGS) -D _CRT_SECURE_NO_DEPRECATE -D _CRT_NONSTDC_NO_DEPRECATE
-cflags = -nologo -c $(COMPILERFLAGS) $(cwarn) -Fp$(TMP_DIR)^\
+cflags = -nologo -c $(COMPILERFLAGS) $(carch) $(cwarn) -Fp$(TMP_DIR)^\
 
 !if $(MSVCRT)
 !if $(DEBUG) && !$(UNCHECKED)
diff --git a/win/tclWin32Dll.c b/win/tclWin32Dll.c
index 688fa8d..84c7a97 100644
--- a/win/tclWin32Dll.c
+++ b/win/tclWin32Dll.c
@@ -29,7 +29,7 @@ static int platformId;		/* Running under NT, or 95/98? */
  * VC++ 5.x has no 'cpuid' assembler instruction, so we must emulate it
  */
 
-#if defined(_MSC_VER) && (_MSC_VER <= 1100)
+#if defined(_MSC_VER) && (_MSC_VER <= 1100) && defined (_M_IX86)
 #define cpuid	__asm __emit 0fh __asm __emit 0a2h
 #endif
 
@@ -735,7 +735,7 @@ TclWinCPUID(
     __cpuid(regsPtr, index);
     status = TCL_OK;
 
-#   else
+#   elif defined (_M_IX86)
     /*
      * Define a structure in the stack frame to hold the registers.
      */
diff --git a/win/tclWinFile.c b/win/tclWinFile.c
index 6662327..7586af1 100644
--- a/win/tclWinFile.c
+++ b/win/tclWinFile.c
@@ -828,7 +828,7 @@ tclWinDebugPanic(
     __builtin_trap();
 #elif defined(_WIN64)
     __debugbreak();
-#elif defined(_MSC_VER)
+#elif defined(_MSC_VER) && defined (_M_IX86)
     _asm {int 3}
 #else
     DebugBreak();
diff --git a/win/tclWinSock.c b/win/tclWinSock.c
index da2e60a..3799d98 100644
--- a/win/tclWinSock.c
+++ b/win/tclWinSock.c
@@ -1426,8 +1426,7 @@ TcpGetOptionProc(
 			    flags |= NI_NUMERICHOST;
 			}
 		    } else if (sockname.sa.sa_family == AF_INET6) {
-			if ((IN6_ARE_ADDR_EQUAL(&sockname.sa6.sin6_addr,
-				    &in6addr_any)) ||
+			if (IN6_IS_ADDR_UNSPECIFIED(&sockname.sa6.sin6_addr) ||
 				(IN6_IS_ADDR_V4MAPPED(&sockname.sa6.sin6_addr)
 				&& sockname.sa6.sin6_addr.s6_addr[12] == 0
 				&& sockname.sa6.sin6_addr.s6_addr[13] == 0
-- 
cgit v0.12


From 8e69db979dd54dd5edf2a4ee6c7283748660ca8a Mon Sep 17 00:00:00 2001
From: Joe Mistachkin <joe@mistachkin.com>
Date: Sun, 13 Aug 2017 22:15:30 +0000
Subject: Always define '_USING_V110_SDK71_', in case targeting the pre-Windows
 8.x SDKs.

---
 win/rules.vc | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/win/rules.vc b/win/rules.vc
index 4a3ae26..979fb14 100644
--- a/win/rules.vc
+++ b/win/rules.vc
@@ -159,7 +159,7 @@ DEBUGFLAGS     = $(DEBUGFLAGS) -RTC1
 DEBUGFLAGS     = $(DEBUGFLAGS) -GZ
 !endif
 
-COMPILERFLAGS  =-W3 /DUNICODE /D_UNICODE /D_ATL_XP_TARGETING
+COMPILERFLAGS  =-W3 -DUNICODE -D_UNICODE -D_USING_V110_SDK71_ -D_ATL_XP_TARGETING
 
 # In v13 -GL and -YX are incompatible.
 !if [nmakehlp -c -YX]
-- 
cgit v0.12


From a18c3eca9bb851589fcb45fbcef0d8be43396a15 Mon Sep 17 00:00:00 2001
From: Joe Mistachkin <joe@mistachkin.com>
Date: Sun, 13 Aug 2017 22:31:19 +0000
Subject: The 'clean' target should delete the generated 'nmhlp-out.txt' file
 as well.

---
 win/makefile.vc | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/win/makefile.vc b/win/makefile.vc
index 40de392..e0d8d9d 100644
--- a/win/makefile.vc
+++ b/win/makefile.vc
@@ -1229,6 +1229,8 @@ clean: clean-pkgs
 	@if exist $(WINDIR)\nmakehlp.obj del $(WINDIR)\nmakehlp.obj
 	@echo Cleaning $(WINDIR)\nmakehlp.exe ...
 	@if exist $(WINDIR)\nmakehlp.exe del $(WINDIR)\nmakehlp.exe
+	@echo Cleaning $(WINDIR)\nmhlp-out.txt ...
+	@if exist $(WINDIR)\nmhlp-out.txt del $(WINDIR)\nmhlp-out.txt
 	@echo Cleaning $(WINDIR)\_junk.pch ...
 	@if exist $(WINDIR)\_junk.pch del $(WINDIR)\_junk.pch
 	@echo Cleaning $(WINDIR)\vercl.x ...
-- 
cgit v0.12


From 580c27ad7379a995540d3b372c59d3611c498031 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Mon, 14 Aug 2017 15:33:03 +0000
Subject: [f2336c116b] Move pragmas to make gcc happy; it is pickier than
 clang.

---
 unix/tclUnixSock.c | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/unix/tclUnixSock.c b/unix/tclUnixSock.c
index b9b6b53..2f1a78e 100644
--- a/unix/tclUnixSock.c
+++ b/unix/tclUnixSock.c
@@ -700,6 +700,8 @@ TcpClose2Proc(
  */
 
 #ifndef NEED_FAKE_RFC2553
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wstrict-aliasing"
 static inline int
 IPv6AddressNeedsNumericRendering(
     struct in6_addr addr)
@@ -713,16 +715,14 @@ IPv6AddressNeedsNumericRendering(
      * at least some versions of OSX.
      */
 
-#pragma GCC diagnostic push
-#pragma GCC diagnostic ignored "-Wstrict-aliasing"
     if (!IN6_IS_ADDR_V4MAPPED(&addr)) {
-#pragma GCC diagnostic pop
         return 0;
     }
 
     return (addr.s6_addr[12] == 0 && addr.s6_addr[13] == 0
             && addr.s6_addr[14] == 0 && addr.s6_addr[15] == 0);
 }
+#pragma GCC diagnostic pop
 #endif /* NEED_FAKE_RFC2553 */
 
 static void
-- 
cgit v0.12


From 3fa2df99d2930a900ec7494cb122eb01b975c6c6 Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Thu, 17 Aug 2017 21:52:42 +0000
Subject: '#if' -> '#ifdef' in tclUnixPort.h. Suggested by Gustaf Neumann.
 Reduces the number of gcc warnings, when compiling Tcl with -Wundef.
 Harmless.

---
 unix/tclUnixPort.h | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/unix/tclUnixPort.h b/unix/tclUnixPort.h
index 2728957..ba56089 100644
--- a/unix/tclUnixPort.h
+++ b/unix/tclUnixPort.h
@@ -125,11 +125,11 @@ typedef off_t		Tcl_SeekOffset;
 #   include <sys/select.h>
 #endif
 #include <sys/stat.h>
-#if TIME_WITH_SYS_TIME
+#ifdef TIME_WITH_SYS_TIME
 #   include <sys/time.h>
 #   include <time.h>
 #else
-#if HAVE_SYS_TIME_H
+#ifdef HAVE_SYS_TIME_H
 #   include <sys/time.h>
 #else
 #   include <time.h>
@@ -138,11 +138,11 @@ typedef off_t		Tcl_SeekOffset;
 #ifndef NO_SYS_WAIT_H
 #   include <sys/wait.h>
 #endif
-#if HAVE_INTTYPES_H
+#ifdef HAVE_INTTYPES_H
 #   include <inttypes.h>
 #endif
 #include <limits.h>
-#if HAVE_STDINT_H
+#ifdef HAVE_STDINT_H
 #   include <stdint.h>
 #endif
 #ifdef HAVE_UNISTD_H
-- 
cgit v0.12


From 3728831c291bc29f51ee826731bd206f28687d0d Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Tue, 22 Aug 2017 12:12:11 +0000
Subject: Fix [d2612a2fa193196787aab33bb57f69b1eef9e30c|d2612a2fa1]: Build
 breaks because of gcc error. Only use "#pragma GCC diagnostic" if the
 compiler supports this. Also re-format tclUnixSock.c without further
 functional changes.

---
 unix/tclLoadDyld.c |   2 +
 unix/tclUnixSock.c | 293 +++++++++++++++++++++++++++++++----------------------
 2 files changed, 172 insertions(+), 123 deletions(-)

diff --git a/unix/tclLoadDyld.c b/unix/tclLoadDyld.c
index 8b7dc58..e998bf9 100644
--- a/unix/tclLoadDyld.c
+++ b/unix/tclLoadDyld.c
@@ -48,7 +48,9 @@
 #endif /* TCL_DYLD_USE_DLFCN */
 
 #if TCL_DYLD_USE_NSMODULE || defined(TCL_LOAD_FROM_MEMORY)
+#if defined (__clang__) || ((__GNUC__)  && ((__GNUC__ > 4) || ((__GNUC__ == 4) && (__GNUC_MINOR__ > 5))))
 #pragma GCC diagnostic ignored "-Wdeprecated-declarations"
+#endif
 #include <mach-o/dyld.h>
 #include <mach-o/fat.h>
 #include <mach-o/swap.h>
diff --git a/unix/tclUnixSock.c b/unix/tclUnixSock.c
index 2f1a78e..e418ff0 100644
--- a/unix/tclUnixSock.c
+++ b/unix/tclUnixSock.c
@@ -19,6 +19,7 @@
 
 #define SET_BITS(var, bits)	((var) |= (bits))
 #define CLEAR_BITS(var, bits)	((var) &= ~(bits))
+#define GOT_BITS(var, bits)     (((var) & (bits)) != 0)
 
 /* "sock" + a pointer in hex + \0 */
 #define SOCK_CHAN_LENGTH        (4 + sizeof(void *) * 2 + 1)
@@ -117,8 +118,7 @@ struct TcpState {
  * Static routines for this file:
  */
 
-static int		TcpConnect(Tcl_Interp *interp,
-                                           TcpState *state);
+static int		TcpConnect(Tcl_Interp *interp, TcpState *state);
 static void		TcpAccept(ClientData data, int mask);
 static int		TcpBlockModeProc(ClientData data, int mode);
 static int		TcpCloseProc(ClientData instanceData,
@@ -173,21 +173,24 @@ static ProcessGlobalValue hostName =
 
 #if 0
 /* printf debugging */
-void printaddrinfo(struct addrinfo *addrlist, char *prefix)
+void
+printaddrinfo(
+    struct addrinfo *addrlist,
+    char *prefix)
 {
     char host[NI_MAXHOST], port[NI_MAXSERV];
     struct addrinfo *ai;
+
     for (ai = addrlist; ai != NULL; ai = ai->ai_next) {
 	getnameinfo(ai->ai_addr, ai->ai_addrlen,
-		    host, sizeof(host),
-		    port, sizeof(port),
-		    NI_NUMERICHOST|NI_NUMERICSERV);
+		host, sizeof(host), port, sizeof(port),
+		NI_NUMERICHOST|NI_NUMERICSERV);
 	fprintf(stderr,"%s: %s:%s\n", prefix, host, port);
     }
 }
 #endif
 /*
- *----------------------------------------------------------------------
+ * ----------------------------------------------------------------------
  *
  * InitializeHostName --
  *
@@ -197,7 +200,7 @@ void printaddrinfo(struct addrinfo *addrlist, char *prefix)
  * Results:
  *	None.
  *
- *----------------------------------------------------------------------
+ * ----------------------------------------------------------------------
  */
 
 static void
@@ -271,12 +274,12 @@ InitializeHostName(
 
     *encodingPtr = Tcl_GetEncoding(NULL, NULL);
     *lengthPtr = strlen(native);
-    *valuePtr = ckalloc((*lengthPtr) + 1);
-    memcpy(*valuePtr, native, (size_t)(*lengthPtr)+1);
+    *valuePtr = ckalloc(*lengthPtr + 1);
+    memcpy(*valuePtr, native, (size_t)(*lengthPtr) + 1);
 }
 
 /*
- *----------------------------------------------------------------------
+ * ----------------------------------------------------------------------
  *
  * Tcl_GetHostName --
  *
@@ -290,7 +293,7 @@ InitializeHostName(
  * Side effects:
  *	Caches the name to return for future calls.
  *
- *----------------------------------------------------------------------
+ * ----------------------------------------------------------------------
  */
 
 const char *
@@ -300,7 +303,7 @@ Tcl_GetHostName(void)
 }
 
 /*
- *----------------------------------------------------------------------
+ * ----------------------------------------------------------------------
  *
  * TclpHasSockets --
  *
@@ -312,7 +315,7 @@ Tcl_GetHostName(void)
  * Side effects:
  *	None.
  *
- *----------------------------------------------------------------------
+ * ----------------------------------------------------------------------
  */
 
 int
@@ -323,7 +326,7 @@ TclpHasSockets(
 }
 
 /*
- *----------------------------------------------------------------------
+ * ----------------------------------------------------------------------
  *
  * TclpFinalizeSockets --
  *
@@ -335,7 +338,7 @@ TclpHasSockets(
  * Side effects:
  *	None.
  *
- *----------------------------------------------------------------------
+ * ----------------------------------------------------------------------
  */
 
 void
@@ -345,7 +348,7 @@ TclpFinalizeSockets(void)
 }
 
 /*
- *----------------------------------------------------------------------
+ * ----------------------------------------------------------------------
  *
  * TcpBlockModeProc --
  *
@@ -358,7 +361,7 @@ TclpFinalizeSockets(void)
  * Side effects:
  *	Sets the device into blocking or nonblocking mode.
  *
- *----------------------------------------------------------------------
+ * ----------------------------------------------------------------------
  */
 
 	/* ARGSUSED */
@@ -376,7 +379,7 @@ TcpBlockModeProc(
     } else {
 	SET_BITS(statePtr->flags, TCP_NONBLOCKING);
     }
-    if (statePtr->flags & TCP_ASYNC_CONNECT) {
+    if (GOT_BITS(statePtr->flags, TCP_ASYNC_CONNECT)) {
         statePtr->cachedBlocking = mode;
         return 0;
     }
@@ -387,33 +390,32 @@ TcpBlockModeProc(
 }
 
 /*
- *----------------------------------------------------------------------
+ * ----------------------------------------------------------------------
  *
  * WaitForConnect --
  *
- *	Check the state of an async connect process. If a connection
- *	attempt terminated, process it, which may finalize it or may
- *	start the next attempt. If a connect error occures, it is saved
- *	in statePtr->connectError to be reported by 'fconfigure -error'.
+ *	Check the state of an async connect process. If a connection attempt
+ *	terminated, process it, which may finalize it or may start the next
+ *	attempt. If a connect error occures, it is saved in
+ *	statePtr->connectError to be reported by 'fconfigure -error'.
  *
  *	There are two modes of operation, defined by errorCodePtr:
- *	 *  non-NULL: Called by explicite read/write command. block if
+ *	 *  non-NULL: Called by explicite read/write command. Blocks if the
  *	    socket is blocking.
  *	    May return two error codes:
  *	     *	EWOULDBLOCK: if connect is still in progress
- *	     *	ENOTCONN: if connect failed. This would be the error
- *		message of a rect or sendto syscall so this is
- *		emulated here.
- *	 *  NULL: Called by a backround operation. Do not block and
- *	    don't return any error code.
+ *	     *	ENOTCONN: if connect failed. This would be the error message
+ *		of a rect or sendto syscall so this is emulated here.
+ *	 *  NULL: Called by a backround operation. Do not block and do not
+ *	    return any error code.
  *
  * Results:
- * 	0 if the connection has completed, -1 if still in progress
- * 	or there is an error.
+ * 	0 if the connection has completed, -1 if still in progress or there is
+ * 	an error.
  *
  * Side effects:
- *	Processes socket events off the system queue.
- *	May process asynchroneous connect.
+ *	Processes socket events off the system queue. May process
+ *	asynchroneous connects.
  *
  *----------------------------------------------------------------------
  */
@@ -426,11 +428,11 @@ WaitForConnect(
     int timeout;
 
     /*
-     * Check if an async connect failed already and error reporting is demanded,
-     * return the error ENOTCONN
+     * Check if an async connect failed already and error reporting is
+     * demanded, return the error ENOTCONN
      */
 
-    if (errorCodePtr != NULL && (statePtr->flags & TCP_ASYNC_FAILED)) {
+    if (errorCodePtr != NULL && GOT_BITS(statePtr->flags, TCP_ASYNC_FAILED)) {
 	*errorCodePtr = ENOTCONN;
 	return -1;
     }
@@ -439,26 +441,29 @@ WaitForConnect(
      * Check if an async connect is running. If not return ok
      */
 
-    if (!(statePtr->flags & TCP_ASYNC_PENDING)) {
+    if (!GOT_BITS(statePtr->flags, TCP_ASYNC_PENDING)) {
 	return 0;
     }
 
-    if (errorCodePtr == NULL || (statePtr->flags & TCP_NONBLOCKING)) {
+    if (errorCodePtr == NULL || GOT_BITS(statePtr->flags, TCP_NONBLOCKING)) {
         timeout = 0;
     } else {
         timeout = -1;
     }
     do {
         if (TclUnixWaitForFile(statePtr->fds.fd,
-                                TCL_WRITABLE | TCL_EXCEPTION, timeout) != 0) {
+                TCL_WRITABLE | TCL_EXCEPTION, timeout) != 0) {
             TcpConnect(NULL, statePtr);
         }
-        /* Do this only once in the nonblocking case and repeat it until the
-         * socket is final when blocking */
-    } while (timeout == -1 && statePtr->flags & TCP_ASYNC_CONNECT);
+
+        /*
+         * Do this only once in the nonblocking case and repeat it until the
+         * socket is final when blocking.
+         */
+    } while (timeout == -1 && GOT_BITS(statePtr->flags, TCP_ASYNC_CONNECT));
 
     if (errorCodePtr != NULL) {
-        if (statePtr->flags & TCP_ASYNC_PENDING) {
+        if (GOT_BITS(statePtr->flags, TCP_ASYNC_PENDING)) {
             *errorCodePtr = EAGAIN;
             return -1;
         } else if (statePtr->connectError != 0) {
@@ -615,7 +620,8 @@ TcpCloseProc(
     fds = statePtr->fds.next;
     while (fds != NULL) {
 	TcpFdList *next = fds->next;
-        ckfree(fds);
+
+	ckfree(fds);
 	fds = next;
     }
     if (statePtr->addrlist != NULL) {
@@ -685,10 +691,9 @@ TcpClose2Proc(
  *
  * TcpHostPortList --
  *
- *	This function is called by the -gethostname and -getpeername
- *	switches of TcpGetOptionProc() to add three list elements
- *	with the textual representation of the given address to the
- *	given DString.
+ *	This function is called by the -gethostname and -getpeername switches
+ *	of TcpGetOptionProc() to add three list elements with the textual
+ *	representation of the given address to the given DString.
  *
  * Results:
  *	None.
@@ -700,8 +705,10 @@ TcpClose2Proc(
  */
 
 #ifndef NEED_FAKE_RFC2553
+#if defined (__clang__) || ((__GNUC__)  && ((__GNUC__ > 4) || ((__GNUC__ == 4) && (__GNUC_MINOR__ > 5))))
 #pragma GCC diagnostic push
 #pragma GCC diagnostic ignored "-Wstrict-aliasing"
+#endif
 static inline int
 IPv6AddressNeedsNumericRendering(
     struct in6_addr addr)
@@ -722,7 +729,9 @@ IPv6AddressNeedsNumericRendering(
     return (addr.s6_addr[12] == 0 && addr.s6_addr[13] == 0
             && addr.s6_addr[14] == 0 && addr.s6_addr[15] == 0);
 }
+#if defined (__clang__) || ((__GNUC__)  && ((__GNUC__ > 4) || ((__GNUC__ == 4) && (__GNUC_MINOR__ > 5))))
 #pragma GCC diagnostic pop
+#endif
 #endif /* NEED_FAKE_RFC2553 */
 
 static void
@@ -736,14 +745,15 @@ TcpHostPortList(
     char host[NI_MAXHOST], nhost[NI_MAXHOST], nport[NI_MAXSERV];
     int flags = 0;
 
-    getnameinfo(&addr.sa, salen,
-                nhost, sizeof(nhost), nport, sizeof(nport),
-                NI_NUMERICHOST | NI_NUMERICSERV);
+    getnameinfo(&addr.sa, salen, nhost, sizeof(nhost), nport, sizeof(nport),
+            NI_NUMERICHOST | NI_NUMERICSERV);
     Tcl_DStringAppendElement(dsPtr, nhost);
+
     /*
-     * We don't want to resolve INADDR_ANY and sin6addr_any; they
-     * can sometimes cause problems (and never have a name).
+     * We don't want to resolve INADDR_ANY and sin6addr_any; they can
+     * sometimes cause problems (and never have a name).
      */
+
     if (addr.sa.sa_family == AF_INET) {
         if (addr.sa4.sin_addr.s_addr == INADDR_ANY) {
             flags |= NI_NUMERICHOST;
@@ -755,15 +765,27 @@ TcpHostPortList(
         }
 #endif /* NEED_FAKE_RFC2553 */
     }
-    /* Check if reverse DNS has been switched off globally */
-    if (interp != NULL && Tcl_GetVar(interp, SUPPRESS_RDNS_VAR, 0) != NULL) {
+
+    /*
+     * Check if reverse DNS has been switched off globally.
+     */
+
+    if (interp != NULL &&
+            Tcl_GetVar2(interp, SUPPRESS_RDNS_VAR, NULL, 0) != NULL) {
         flags |= NI_NUMERICHOST;
     }
-    if (getnameinfo(&addr.sa, salen, host, sizeof(host), NULL, 0, flags) == 0) {
-        /* Reverse mapping worked */
+    if (getnameinfo(&addr.sa, salen, host, sizeof(host), NULL, 0,
+            flags) == 0) {
+        /*
+         * Reverse mapping worked.
+         */
+
         Tcl_DStringAppendElement(dsPtr, host);
     } else {
-        /* Reverse mappong failed - use the numeric rep once more */
+        /*
+         * Reverse mapping failed - use the numeric rep once more.
+         */
+
         Tcl_DStringAppendElement(dsPtr, nhost);
     }
     Tcl_DStringAppendElement(dsPtr, nport);
@@ -813,16 +835,20 @@ TcpGetOptionProc(
 	    (strncmp(optionName, "-error", len) == 0)) {
 	socklen_t optlen = sizeof(int);
 
-        if (statePtr->flags & TCP_ASYNC_CONNECT) {
-            /* Suppress errors as long as we are not done */
+        if (GOT_BITS(statePtr->flags, TCP_ASYNC_CONNECT)) {
+            /*
+             * Suppress errors as long as we are not done.
+             */
+
             errno = 0;
         } else if (statePtr->connectError != 0) {
             errno = statePtr->connectError;
             statePtr->connectError = 0;
         } else {
             int err;
-            getsockopt(statePtr->fds.fd, SOL_SOCKET, SO_ERROR,
-                    (char *) &err, &optlen);
+
+            getsockopt(statePtr->fds.fd, SOL_SOCKET, SO_ERROR, (char *) &err,
+                    &optlen);
             errno = err;
         }
         if (errno != 0) {
@@ -833,9 +859,8 @@ TcpGetOptionProc(
 
     if ((len > 1) && (optionName[1] == 'c') &&
 	    (strncmp(optionName, "-connecting", len) == 0)) {
-
         Tcl_DStringAppend(dsPtr,
-                        (statePtr->flags & TCP_ASYNC_CONNECT) ? "1" : "0", -1);
+                GOT_BITS(statePtr->flags, TCP_ASYNC_CONNECT) ? "1" : "0", -1);
         return TCL_OK;
     }
 
@@ -844,10 +869,11 @@ TcpGetOptionProc(
         address peername;
         socklen_t size = sizeof(peername);
 
-	if ( (statePtr->flags & TCP_ASYNC_CONNECT) ) {
+	if (GOT_BITS(statePtr->flags, TCP_ASYNC_CONNECT)) {
 	    /*
 	     * In async connect output an empty string
 	     */
+
 	    if (len == 0) {
 		Tcl_DStringAppendElement(dsPtr, "-peername");
 		Tcl_DStringAppendElement(dsPtr, "");
@@ -858,6 +884,7 @@ TcpGetOptionProc(
 	    /*
 	     * Peername fetch succeeded - output list
 	     */
+
 	    if (len == 0) {
 		Tcl_DStringAppendElement(dsPtr, "-peername");
 		Tcl_DStringStartSublist(dsPtr);
@@ -897,11 +924,12 @@ TcpGetOptionProc(
 	    Tcl_DStringAppendElement(dsPtr, "-sockname");
 	    Tcl_DStringStartSublist(dsPtr);
 	}
-	if ( (statePtr->flags & TCP_ASYNC_CONNECT) ) {
+	if (GOT_BITS(statePtr->flags, TCP_ASYNC_CONNECT)) {
 	    /*
 	     * In async connect output an empty string
 	     */
-	     found = 1;
+
+            found = 1;
 	} else {
 	    for (fds = &statePtr->fds; fds != NULL; fds = fds->next) {
 		size = sizeof(sockname);
@@ -926,14 +954,15 @@ TcpGetOptionProc(
     }
 
     if (len > 0) {
-	return Tcl_BadChannelOption(interp, optionName, "connecting peername sockname");
+	return Tcl_BadChannelOption(interp, optionName,
+                "connecting peername sockname");
     }
 
     return TCL_OK;
 }
 
 /*
- *----------------------------------------------------------------------
+ * ----------------------------------------------------------------------
  *
  * TcpWatchProc --
  *
@@ -946,7 +975,7 @@ TcpGetOptionProc(
  *	Sets up the notifier so that a future event on the channel will be
  *	seen by Tcl.
  *
- *----------------------------------------------------------------------
+ * ----------------------------------------------------------------------
  */
 
 static void
@@ -959,17 +988,17 @@ WrapNotify(
 
     if (newmask == 0) {
 	/*
-	 * There was no overlap between the states the channel is
-	 * interested in notifications for, and the states that are
-	 * reported present on the file descriptor by select().  The
-	 * only way that can happen is when the channel is interested
-	 * in a writable condition, and only a readable state is reported
-	 * present (see TcpWatchProc() below).  In that case, signal back
-	 * to the caller the writable state, which is really an error
-	 * condition.  As an extra check on that assumption, check for
-	 * a non-zero value of errno before reporting an artificial
+	 * There was no overlap between the states the channel is interested
+	 * in notifications for, and the states that are reported present on
+	 * the file descriptor by select().  The only way that can happen is
+	 * when the channel is interested in a writable condition, and only a
+	 * readable state is reported present (see TcpWatchProc() below).  In
+	 * that case, signal back to the caller the writable state, which is
+	 * really an error condition.  As an extra check on that assumption,
+	 * check for a non-zero value of errno before reporting an artificial
 	 * writable state.
 	 */
+
 	if (errno == 0) {
 	    return;
 	}
@@ -993,33 +1022,36 @@ TcpWatchProc(
          * be readable or writable at the Tcl level. This keeps Tcl scripts
          * from interfering with the -accept behavior (bug #3394732).
          */
+
     	return;
     }
 
-    if (statePtr->flags & TCP_ASYNC_PENDING) {
-        /* Async sockets use a FileHandler internally while connecting, so we
-         * need to cache this request until the connection has succeeded. */
+    if (GOT_BITS(statePtr->flags, TCP_ASYNC_PENDING)) {
+        /*
+         * Async sockets use a FileHandler internally while connecting, so we
+         * need to cache this request until the connection has succeeded.
+         */
+
         statePtr->filehandlers = mask;
     } else if (mask) {
 
 	/*
-	 * Whether it is a bug or feature or otherwise, it is a fact
-	 * of life that on at least some Linux kernels select() fails
-	 * to report that a socket file descriptor is writable when
-	 * the other end of the socket is closed.  This is in contrast
-	 * to the guarantees Tcl makes that its channels become
-	 * writable and fire writable events on an error conditon.
-	 * This has caused a leak of file descriptors in a state of
+	 * Whether it is a bug or feature or otherwise, it is a fact of life
+	 * that on at least some Linux kernels select() fails to report that a
+	 * socket file descriptor is writable when the other end of the socket
+	 * is closed.  This is in contrast to the guarantees Tcl makes that
+	 * its channels become writable and fire writable events on an error
+	 * conditon.  This has caused a leak of file descriptors in a state of
 	 * background flushing.  See Tcl ticket 1758a0b603.
 	 *
-	 * As a workaround, when our caller indicates an interest in
-	 * writable notifications, we must tell the notifier built
-	 * around select() that we are interested in the readable state
-	 * of the file descriptor as well, as that is the only reliable
-	 * means to get notified of error conditions.  Then it is the
-	 * task of WrapNotify() above to untangle the meaning of these
-	 * channel states and report the chan events as best it can.
-	 * We save a copy of the mask passed in to assist with that.
+	 * As a workaround, when our caller indicates an interest in writable
+	 * notifications, we must tell the notifier built around select() that
+	 * we are interested in the readable state of the file descriptor as
+	 * well, as that is the only reliable means to get notified of error
+	 * conditions.  Then it is the task of WrapNotify() above to untangle
+	 * the meaning of these channel states and report the chan events as
+	 * best it can.  We save a copy of the mask passed in to assist with
+	 * that.
 	 */
 
 	statePtr->interest = mask;
@@ -1031,7 +1063,7 @@ TcpWatchProc(
 }
 
 /*
- *----------------------------------------------------------------------
+ * ----------------------------------------------------------------------
  *
  * TcpGetHandleProc --
  *
@@ -1045,7 +1077,7 @@ TcpWatchProc(
  * Side effects:
  *	None.
  *
- *----------------------------------------------------------------------
+ * ----------------------------------------------------------------------
  */
 
 	/* ARGSUSED */
@@ -1062,16 +1094,17 @@ TcpGetHandleProc(
 }
 
 /*
- *----------------------------------------------------------------------
+ * ----------------------------------------------------------------------
  *
  * TcpAsyncCallback --
  *
- *	Called by the event handler that TcpConnect sets up
- *	internally for [socket -async] to get notified when the
- *	asyncronous connection attempt has succeeded or failed.
+ *	Called by the event handler that TcpConnect sets up internally for
+ *	[socket -async] to get notified when the asyncronous connection
+ *	attempt has succeeded or failed.
  *
- *----------------------------------------------------------------------
+ * ----------------------------------------------------------------------
  */
+
 static void
 TcpAsyncCallback(
     ClientData clientData,	/* The socket state. */
@@ -1083,7 +1116,7 @@ TcpAsyncCallback(
 }
 
 /*
- *----------------------------------------------------------------------
+ * ----------------------------------------------------------------------
  *
  * TcpConnect --
  *
@@ -1109,7 +1142,7 @@ TcpAsyncCallback(
  *	return and the loops resume as if they had never been interrupted.
  *	For syncronously connecting sockets, the loops work the usual way.
  *
- *----------------------------------------------------------------------
+ * ----------------------------------------------------------------------
  */
 
 static int
@@ -1118,9 +1151,9 @@ TcpConnect(
     TcpState *statePtr)
 {
     socklen_t optlen;
-    int async_callback = statePtr->flags & TCP_ASYNC_PENDING;
+    int async_callback = GOT_BITS(statePtr->flags, TCP_ASYNC_PENDING);
     int ret = -1, error = EHOSTUNREACH;
-    int async = statePtr->flags & TCP_ASYNC_CONNECT;
+    int async = GOT_BITS(statePtr->flags, TCP_ASYNC_CONNECT);
 
     if (async_callback) {
         goto reenter;
@@ -1128,8 +1161,8 @@ TcpConnect(
 
     for (statePtr->addr = statePtr->addrlist; statePtr->addr != NULL;
             statePtr->addr = statePtr->addr->ai_next) {
-
-        for (statePtr->myaddr = statePtr->myaddrlist; statePtr->myaddr != NULL;
+        for (statePtr->myaddr = statePtr->myaddrlist;
+                statePtr->myaddr != NULL;
                 statePtr->myaddr = statePtr->myaddr->ai_next) {
             int reuseaddr = 1;
 
@@ -1153,7 +1186,8 @@ TcpConnect(
                 errno = 0;
 	    }
 
-	    statePtr->fds.fd = socket(statePtr->addr->ai_family, SOCK_STREAM, 0);
+	    statePtr->fds.fd = socket(statePtr->addr->ai_family, SOCK_STREAM,
+                    0);
 	    if (statePtr->fds.fd < 0) {
 		continue;
 	    }
@@ -1172,14 +1206,18 @@ TcpConnect(
 	    TclSockMinimumBuffers(INT2PTR(statePtr->fds.fd), SOCKET_BUFSIZE);
 
 	    if (async) {
-                ret = TclUnixSetBlockingMode(statePtr->fds.fd,TCL_MODE_NONBLOCKING);
+                ret = TclUnixSetBlockingMode(statePtr->fds.fd,
+                        TCL_MODE_NONBLOCKING);
                 if (ret < 0) {
                     continue;
                 }
             }
 
-            /* Gotta reset the error variable here, before we use it for the
-             * first time in this iteration. */
+            /*
+             * Must reset the error variable here, before we use it for the
+             * first time in this iteration.
+             */
+
             error = 0;
 
             (void) setsockopt(statePtr->fds.fd, SOL_SOCKET, SO_REUSEADDR,
@@ -1200,10 +1238,13 @@ TcpConnect(
 
 	    ret = connect(statePtr->fds.fd, statePtr->addr->ai_addr,
                         statePtr->addr->ai_addrlen);
-            if (ret < 0) error = errno;
+            if (ret < 0) {
+                error = errno;
+            }
 	    if (ret < 0 && errno == EINPROGRESS) {
                 Tcl_CreateFileHandler(statePtr->fds.fd,
-                        TCL_WRITABLE|TCL_EXCEPTION, TcpAsyncCallback, statePtr);
+                        TCL_WRITABLE | TCL_EXCEPTION, TcpAsyncCallback,
+                        statePtr);
                 errno = EWOULDBLOCK;
                 SET_BITS(statePtr->flags, TCP_ASYNC_PENDING);
                 return TCL_OK;
@@ -1231,7 +1272,7 @@ TcpConnect(
 	}
     }
 
-out:
+  out:
     statePtr->connectError = error;
     CLEAR_BITS(statePtr->flags, TCP_ASYNC_CONNECT);
     if (async_callback) {
@@ -1329,6 +1370,7 @@ Tcl_OpenTcpClient(
     /*
      * Allocate a new TcpState for this socket.
      */
+
     statePtr = ckalloc(sizeof(TcpState));
     memset(statePtr, 0, sizeof(TcpState));
     statePtr->flags = async ? TCP_ASYNC_CONNECT : 0;
@@ -1340,6 +1382,7 @@ Tcl_OpenTcpClient(
     /*
      * Create a new client socket and wrap it in a channel.
      */
+
     if (TcpConnect(interp, statePtr) != TCL_OK) {
         TcpCloseProc(statePtr, NULL);
         return NULL;
@@ -1347,8 +1390,8 @@ Tcl_OpenTcpClient(
 
     sprintf(channelName, SOCK_TEMPLATE, (long) statePtr);
 
-    statePtr->channel = Tcl_CreateChannel(&tcpChannelType, channelName, statePtr,
-            (TCL_READABLE | TCL_WRITABLE));
+    statePtr->channel = Tcl_CreateChannel(&tcpChannelType, channelName,
+            statePtr, TCL_READABLE | TCL_WRITABLE);
     if (Tcl_SetChannelOption(interp, statePtr->channel, "-translation",
 	    "auto crlf") == TCL_ERROR) {
 	Tcl_Close(NULL, statePtr->channel);
@@ -1377,7 +1420,8 @@ Tcl_Channel
 Tcl_MakeTcpClientChannel(
     ClientData sock)		/* The socket to wrap up into a channel. */
 {
-    return (Tcl_Channel) TclpMakeTcpClientChannelMode(sock, (TCL_READABLE | TCL_WRITABLE));
+    return (Tcl_Channel) TclpMakeTcpClientChannelMode(sock,
+            TCL_READABLE | TCL_WRITABLE);
 }
 
 /*
@@ -1516,7 +1560,10 @@ Tcl_OpenTcpServer(
 	}
 
 #ifdef IPV6_V6ONLY
-	/* Missing on: Solaris 2.8 */
+	/*
+         * Missing on: Solaris 2.8
+         */
+
         if (addrPtr->ai_family == AF_INET6) {
             int v6only = 1;
 
@@ -1662,7 +1709,7 @@ TcpAccept(
 
     sprintf(channelName, SOCK_TEMPLATE, (long) newSockState);
     newSockState->channel = Tcl_CreateChannel(&tcpChannelType, channelName,
-	    newSockState, (TCL_READABLE | TCL_WRITABLE));
+	    newSockState, TCL_READABLE | TCL_WRITABLE);
 
     Tcl_SetChannelOption(NULL, newSockState->channel, "-translation",
 	    "auto crlf");
-- 
cgit v0.12


From 1dac20d62e354430a8f82e46bf0805c70cdde4e3 Mon Sep 17 00:00:00 2001
From: ferrieux <ferrieux@users.sourceforge.net>
Date: Thu, 24 Aug 2017 16:56:51 +0000
Subject: Fix [b50fb214] : add to 2>> the same O_APPEND that was added to >>
 back in 2005.

---
 generic/tclPipe.c | 8 +++++++-
 tests/exec.test   | 8 ++++++--
 2 files changed, 13 insertions(+), 3 deletions(-)

diff --git a/generic/tclPipe.c b/generic/tclPipe.c
index d6cd188..b679ec4 100644
--- a/generic/tclPipe.c
+++ b/generic/tclPipe.c
@@ -668,7 +668,13 @@ TclCreatePipeline(
 	    if (*p == '>') {
 		p++;
 		atOK = 0;
-		flags = O_WRONLY | O_CREAT;
+
+		/*
+		 * Note that the O_APPEND flag only has an effect on POSIX
+		 * platforms. On Windows, we just have to carry on regardless.
+		 */
+
+		flags = O_WRONLY | O_CREAT | O_APPEND;
 	    }
 	    if (errorClose != 0) {
 		errorClose = 0;
diff --git a/tests/exec.test b/tests/exec.test
index 2a4b31e..dffd960 100644
--- a/tests/exec.test
+++ b/tests/exec.test
@@ -671,8 +671,12 @@ test exec-19.1 {exec >> uses O_APPEND} -constraints {exec unix} -setup {
     exec /bin/sh -c \
 	    {for a in 1 2 3; do sleep 1; echo $a; done} >>$tmpfile &
     exec /bin/sh -c \
+	    {for a in 4 5 6; do sleep 1; echo $a >&2; done} 2>>$tmpfile &
+    exec /bin/sh -c \
 	    {for a in a b c; do sleep 1; echo $a; done} >>$tmpfile &
-    # The above two shell invokations take about 3 seconds to finish, so allow
+    exec /bin/sh -c \
+	    {for a in d e f; do sleep 1; echo $a >&2; done} 2>>$tmpfile &
+    # The above four shell invokations take about 3 seconds to finish, so allow
     # 5s (in case the machine is busy)
     after 5000
     # Check that no bytes have got lost through mixups with overlapping
@@ -681,7 +685,7 @@ test exec-19.1 {exec >> uses O_APPEND} -constraints {exec unix} -setup {
     file size $tmpfile
 } -cleanup {
     removeFile $tmpfile
-} -result 14
+} -result 26
 
 # Tests to ensure batch files and .CMD (Bug 9ece99d58b)
 # can be executed on Windows
-- 
cgit v0.12


From 908e496e8fd9227aa05156e3e9f1f2801ce14e16 Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Tue, 29 Aug 2017 09:24:29 +0000
Subject: (cherry-pick): Fix
 [b50fb21410dababca95baa122964b2e312cb9d8a|b50fb214] : exec redirection to
 append stdout and stderr to the same file

---
 generic/tclPipe.c | 8 +++++++-
 tests/exec.test   | 8 ++++++--
 2 files changed, 13 insertions(+), 3 deletions(-)

diff --git a/generic/tclPipe.c b/generic/tclPipe.c
index 83fb818..2ecc5a6 100644
--- a/generic/tclPipe.c
+++ b/generic/tclPipe.c
@@ -668,7 +668,13 @@ TclCreatePipeline(
 	    if (*p == '>') {
 		p++;
 		atOK = 0;
-		flags = O_WRONLY | O_CREAT;
+
+		/*
+		 * Note that the O_APPEND flag only has an effect on POSIX
+		 * platforms. On Windows, we just have to carry on regardless.
+		 */
+
+		flags = O_WRONLY | O_CREAT | O_APPEND;
 	    }
 	    if (errorClose != 0) {
 		errorClose = 0;
diff --git a/tests/exec.test b/tests/exec.test
index 38927d3..5f3a0cb 100644
--- a/tests/exec.test
+++ b/tests/exec.test
@@ -671,8 +671,12 @@ test exec-19.1 {exec >> uses O_APPEND} -constraints {exec unix} -setup {
     exec /bin/sh -c \
 	    {for a in 1 2 3; do sleep 1; echo $a; done} >>$tmpfile &
     exec /bin/sh -c \
+	    {for a in 4 5 6; do sleep 1; echo $a >&2; done} 2>>$tmpfile &
+    exec /bin/sh -c \
 	    {for a in a b c; do sleep 1; echo $a; done} >>$tmpfile &
-    # The above two shell invokations take about 3 seconds to finish, so allow
+    exec /bin/sh -c \
+	    {for a in d e f; do sleep 1; echo $a >&2; done} 2>>$tmpfile &
+    # The above four shell invokations take about 3 seconds to finish, so allow
     # 5s (in case the machine is busy)
     after 5000
     # Check that no bytes have got lost through mixups with overlapping
@@ -681,7 +685,7 @@ test exec-19.1 {exec >> uses O_APPEND} -constraints {exec unix} -setup {
     file size $tmpfile
 } -cleanup {
     removeFile $tmpfile
-} -result 14
+} -result 26
 
 # Tests to ensure batch files and .CMD (Bug 9ece99d58b)
 # can be executed on Windows
-- 
cgit v0.12


From ff1658cbdd0982b1fe292259ef37bc9abb41a932 Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Tue, 29 Aug 2017 19:52:35 +0000
Subject: libtommath 1.0.1 rc 2

---
 libtommath/bn_error.c                            |  6 ++--
 libtommath/bn_fast_mp_invmod.c                   |  6 ++--
 libtommath/bn_fast_mp_montgomery_reduce.c        |  6 ++--
 libtommath/bn_fast_s_mp_mul_digs.c               |  6 ++--
 libtommath/bn_fast_s_mp_mul_high_digs.c          |  6 ++--
 libtommath/bn_fast_s_mp_sqr.c                    |  6 ++--
 libtommath/bn_mp_2expt.c                         |  6 ++--
 libtommath/bn_mp_abs.c                           |  6 ++--
 libtommath/bn_mp_add.c                           |  6 ++--
 libtommath/bn_mp_add_d.c                         | 12 +++----
 libtommath/bn_mp_addmod.c                        |  6 ++--
 libtommath/bn_mp_and.c                           |  6 ++--
 libtommath/bn_mp_clamp.c                         |  6 ++--
 libtommath/bn_mp_clear.c                         |  6 ++--
 libtommath/bn_mp_clear_multi.c                   |  6 ++--
 libtommath/bn_mp_cmp.c                           |  6 ++--
 libtommath/bn_mp_cmp_d.c                         |  6 ++--
 libtommath/bn_mp_cmp_mag.c                       |  6 ++--
 libtommath/bn_mp_cnt_lsb.c                       |  6 ++--
 libtommath/bn_mp_copy.c                          |  6 ++--
 libtommath/bn_mp_count_bits.c                    |  6 ++--
 libtommath/bn_mp_div.c                           |  6 ++--
 libtommath/bn_mp_div_2.c                         |  6 ++--
 libtommath/bn_mp_div_2d.c                        | 25 ++++---------
 libtommath/bn_mp_div_3.c                         |  6 ++--
 libtommath/bn_mp_div_d.c                         |  6 ++--
 libtommath/bn_mp_dr_is_modulus.c                 |  6 ++--
 libtommath/bn_mp_dr_reduce.c                     |  6 ++--
 libtommath/bn_mp_dr_setup.c                      |  6 ++--
 libtommath/bn_mp_exch.c                          |  6 ++--
 libtommath/bn_mp_export.c                        | 16 ++++-----
 libtommath/bn_mp_expt_d.c                        |  6 ++--
 libtommath/bn_mp_expt_d_ex.c                     |  6 ++--
 libtommath/bn_mp_exptmod.c                       |  6 ++--
 libtommath/bn_mp_exptmod_fast.c                  | 20 +++++------
 libtommath/bn_mp_exteuclid.c                     | 45 ++++++++++++------------
 libtommath/bn_mp_fread.c                         |  8 +++--
 libtommath/bn_mp_fwrite.c                        |  8 +++--
 libtommath/bn_mp_gcd.c                           |  6 ++--
 libtommath/bn_mp_get_int.c                       |  6 ++--
 libtommath/bn_mp_grow.c                          |  6 ++--
 libtommath/bn_mp_import.c                        | 16 ++++-----
 libtommath/bn_mp_init.c                          |  6 ++--
 libtommath/bn_mp_init_copy.c                     | 13 ++++---
 libtommath/bn_mp_init_multi.c                    |  9 ++---
 libtommath/bn_mp_init_set.c                      |  6 ++--
 libtommath/bn_mp_init_set_int.c                  |  6 ++--
 libtommath/bn_mp_init_size.c                     |  6 ++--
 libtommath/bn_mp_invmod.c                        |  8 ++---
 libtommath/bn_mp_invmod_slow.c                   |  6 ++--
 libtommath/bn_mp_is_square.c                     |  6 ++--
 libtommath/bn_mp_jacobi.c                        |  6 ++--
 libtommath/bn_mp_karatsuba_mul.c                 |  6 ++--
 libtommath/bn_mp_karatsuba_sqr.c                 |  6 ++--
 libtommath/bn_mp_lcm.c                           |  6 ++--
 libtommath/bn_mp_lshd.c                          |  6 ++--
 libtommath/bn_mp_mod.c                           |  8 ++---
 libtommath/bn_mp_mod_2d.c                        |  6 ++--
 libtommath/bn_mp_mod_d.c                         |  6 ++--
 libtommath/bn_mp_montgomery_calc_normalization.c |  6 ++--
 libtommath/bn_mp_montgomery_reduce.c             |  6 ++--
 libtommath/bn_mp_montgomery_setup.c              |  6 ++--
 libtommath/bn_mp_mul.c                           |  6 ++--
 libtommath/bn_mp_mul_2.c                         |  6 ++--
 libtommath/bn_mp_mul_2d.c                        |  6 ++--
 libtommath/bn_mp_mul_d.c                         |  6 ++--
 libtommath/bn_mp_mulmod.c                        |  8 ++---
 libtommath/bn_mp_n_root.c                        |  6 ++--
 libtommath/bn_mp_n_root_ex.c                     |  6 ++--
 libtommath/bn_mp_neg.c                           |  6 ++--
 libtommath/bn_mp_or.c                            |  6 ++--
 libtommath/bn_mp_prime_fermat.c                  |  6 ++--
 libtommath/bn_mp_prime_is_divisible.c            |  6 ++--
 libtommath/bn_mp_prime_is_prime.c                |  6 ++--
 libtommath/bn_mp_prime_miller_rabin.c            |  6 ++--
 libtommath/bn_mp_prime_next_prime.c              |  6 ++--
 libtommath/bn_mp_prime_rabin_miller_trials.c     |  6 ++--
 libtommath/bn_mp_prime_random_ex.c               |  6 ++--
 libtommath/bn_mp_radix_size.c                    |  6 ++--
 libtommath/bn_mp_radix_smap.c                    |  6 ++--
 libtommath/bn_mp_rand.c                          | 35 +++++++++++++++---
 libtommath/bn_mp_read_radix.c                    |  6 ++--
 libtommath/bn_mp_read_signed_bin.c               |  6 ++--
 libtommath/bn_mp_read_unsigned_bin.c             |  6 ++--
 libtommath/bn_mp_reduce.c                        |  6 ++--
 libtommath/bn_mp_reduce_2k.c                     |  6 ++--
 libtommath/bn_mp_reduce_2k_l.c                   |  6 ++--
 libtommath/bn_mp_reduce_2k_setup.c               |  6 ++--
 libtommath/bn_mp_reduce_2k_setup_l.c             |  6 ++--
 libtommath/bn_mp_reduce_is_2k.c                  |  6 ++--
 libtommath/bn_mp_reduce_is_2k_l.c                |  6 ++--
 libtommath/bn_mp_reduce_setup.c                  |  6 ++--
 libtommath/bn_mp_rshd.c                          |  6 ++--
 libtommath/bn_mp_set.c                           |  6 ++--
 libtommath/bn_mp_set_int.c                       |  6 ++--
 libtommath/bn_mp_set_long.c                      |  6 ++--
 libtommath/bn_mp_set_long_long.c                 |  6 ++--
 libtommath/bn_mp_shrink.c                        |  6 ++--
 libtommath/bn_mp_signed_bin_size.c               |  6 ++--
 libtommath/bn_mp_sqr.c                           |  6 ++--
 libtommath/bn_mp_sqrmod.c                        |  6 ++--
 libtommath/bn_mp_sqrt.c                          |  6 ++--
 libtommath/bn_mp_sub.c                           |  6 ++--
 libtommath/bn_mp_sub_d.c                         |  6 ++--
 libtommath/bn_mp_submod.c                        |  6 ++--
 libtommath/bn_mp_to_signed_bin.c                 |  6 ++--
 libtommath/bn_mp_to_signed_bin_n.c               |  6 ++--
 libtommath/bn_mp_to_unsigned_bin.c               |  6 ++--
 libtommath/bn_mp_to_unsigned_bin_n.c             |  6 ++--
 libtommath/bn_mp_toom_mul.c                      |  6 ++--
 libtommath/bn_mp_toom_sqr.c                      |  6 ++--
 libtommath/bn_mp_toradix.c                       |  6 ++--
 libtommath/bn_mp_toradix_n.c                     |  6 ++--
 libtommath/bn_mp_unsigned_bin_size.c             |  6 ++--
 libtommath/bn_mp_xor.c                           |  6 ++--
 libtommath/bn_mp_zero.c                          |  6 ++--
 libtommath/bn_prime_tab.c                        |  6 ++--
 libtommath/bn_reverse.c                          |  6 ++--
 libtommath/bn_s_mp_add.c                         |  6 ++--
 libtommath/bn_s_mp_exptmod.c                     |  6 ++--
 libtommath/bn_s_mp_mul_digs.c                    |  6 ++--
 libtommath/bn_s_mp_mul_high_digs.c               |  6 ++--
 libtommath/bn_s_mp_sqr.c                         |  6 ++--
 libtommath/bn_s_mp_sub.c                         |  6 ++--
 libtommath/bncore.c                              |  6 ++--
 libtommath/tommath.h                             | 35 ++++++++----------
 libtommath/tommath_class.h                       | 12 +++----
 libtommath/tommath_private.h                     | 14 +++++---
 libtommath/tommath_superclass.h                  |  6 ++--
 129 files changed, 492 insertions(+), 472 deletions(-)

diff --git a/libtommath/bn_error.c b/libtommath/bn_error.c
index 3abf1a7..397f834 100644
--- a/libtommath/bn_error.c
+++ b/libtommath/bn_error.c
@@ -42,6 +42,6 @@ const char *mp_error_to_string(int code)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_fast_mp_invmod.c b/libtommath/bn_fast_mp_invmod.c
index aa41098..fa31853 100644
--- a/libtommath/bn_fast_mp_invmod.c
+++ b/libtommath/bn_fast_mp_invmod.c
@@ -143,6 +143,6 @@ LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_fast_mp_montgomery_reduce.c b/libtommath/bn_fast_mp_montgomery_reduce.c
index a63839d..d13452d 100644
--- a/libtommath/bn_fast_mp_montgomery_reduce.c
+++ b/libtommath/bn_fast_mp_montgomery_reduce.c
@@ -167,6 +167,6 @@ int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_fast_s_mp_mul_digs.c b/libtommath/bn_fast_s_mp_mul_digs.c
index acd13b4..18bea3f 100644
--- a/libtommath/bn_fast_s_mp_mul_digs.c
+++ b/libtommath/bn_fast_s_mp_mul_digs.c
@@ -102,6 +102,6 @@ int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_fast_s_mp_mul_high_digs.c b/libtommath/bn_fast_s_mp_mul_high_digs.c
index b96cf60..8fd5117 100644
--- a/libtommath/bn_fast_s_mp_mul_high_digs.c
+++ b/libtommath/bn_fast_s_mp_mul_high_digs.c
@@ -93,6 +93,6 @@ int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_fast_s_mp_sqr.c b/libtommath/bn_fast_s_mp_sqr.c
index 775c76f..293c54a 100644
--- a/libtommath/bn_fast_s_mp_sqr.c
+++ b/libtommath/bn_fast_s_mp_sqr.c
@@ -109,6 +109,6 @@ int fast_s_mp_sqr (mp_int * a, mp_int * b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_2expt.c b/libtommath/bn_mp_2expt.c
index 2845814..eb5e664 100644
--- a/libtommath/bn_mp_2expt.c
+++ b/libtommath/bn_mp_2expt.c
@@ -43,6 +43,6 @@ mp_2expt (mp_int * a, int b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_abs.c b/libtommath/bn_mp_abs.c
index cc9c3db..16662c0 100644
--- a/libtommath/bn_mp_abs.c
+++ b/libtommath/bn_mp_abs.c
@@ -38,6 +38,6 @@ mp_abs (mp_int * a, mp_int * b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_add.c b/libtommath/bn_mp_add.c
index 236fc75..0d91d24 100644
--- a/libtommath/bn_mp_add.c
+++ b/libtommath/bn_mp_add.c
@@ -48,6 +48,6 @@ int mp_add (mp_int * a, mp_int * b, mp_int * c)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_add_d.c b/libtommath/bn_mp_add_d.c
index 4d4e1df..6b9dbef 100644
--- a/libtommath/bn_mp_add_d.c
+++ b/libtommath/bn_mp_add_d.c
@@ -49,9 +49,6 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c)
   /* old number of used digits in c */
   oldused = c->used;
 
-  /* sign always positive */
-  c->sign = MP_ZPOS;
-
   /* source alias */
   tmpa    = a->dp;
 
@@ -96,6 +93,9 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c)
      ix       = 1;
   }
 
+  /* sign always positive */
+  c->sign = MP_ZPOS;
+
   /* now zero to oldused */
   while (ix++ < oldused) {
      *tmpc++ = 0;
@@ -107,6 +107,6 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_addmod.c b/libtommath/bn_mp_addmod.c
index 825c928..800e10a 100644
--- a/libtommath/bn_mp_addmod.c
+++ b/libtommath/bn_mp_addmod.c
@@ -36,6 +36,6 @@ mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_and.c b/libtommath/bn_mp_and.c
index 3b6b03e..6a18639 100644
--- a/libtommath/bn_mp_and.c
+++ b/libtommath/bn_mp_and.c
@@ -52,6 +52,6 @@ mp_and (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_clamp.c b/libtommath/bn_mp_clamp.c
index d4fb70d..b392c10 100644
--- a/libtommath/bn_mp_clamp.c
+++ b/libtommath/bn_mp_clamp.c
@@ -39,6 +39,6 @@ mp_clamp (mp_int * a)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_clear.c b/libtommath/bn_mp_clear.c
index 17ef9d5..bf0873a 100644
--- a/libtommath/bn_mp_clear.c
+++ b/libtommath/bn_mp_clear.c
@@ -39,6 +39,6 @@ mp_clear (mp_int * a)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_clear_multi.c b/libtommath/bn_mp_clear_multi.c
index 441a200..e659cf8 100644
--- a/libtommath/bn_mp_clear_multi.c
+++ b/libtommath/bn_mp_clear_multi.c
@@ -29,6 +29,6 @@ void mp_clear_multi(mp_int *mp, ...)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_cmp.c b/libtommath/bn_mp_cmp.c
index 74a98fe..6266a7e 100644
--- a/libtommath/bn_mp_cmp.c
+++ b/libtommath/bn_mp_cmp.c
@@ -38,6 +38,6 @@ mp_cmp (mp_int * a, mp_int * b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_cmp_d.c b/libtommath/bn_mp_cmp_d.c
index 28a53ce..a1cdaa1 100644
--- a/libtommath/bn_mp_cmp_d.c
+++ b/libtommath/bn_mp_cmp_d.c
@@ -39,6 +39,6 @@ int mp_cmp_d(mp_int * a, mp_digit b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_cmp_mag.c b/libtommath/bn_mp_cmp_mag.c
index f72830f..b3839f0 100644
--- a/libtommath/bn_mp_cmp_mag.c
+++ b/libtommath/bn_mp_cmp_mag.c
@@ -50,6 +50,6 @@ int mp_cmp_mag (mp_int * a, mp_int * b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_cnt_lsb.c b/libtommath/bn_mp_cnt_lsb.c
index 9d7eef8..42d2219 100644
--- a/libtommath/bn_mp_cnt_lsb.c
+++ b/libtommath/bn_mp_cnt_lsb.c
@@ -48,6 +48,6 @@ int mp_cnt_lsb(mp_int *a)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_copy.c b/libtommath/bn_mp_copy.c
index 69e9464..6f2ee59 100644
--- a/libtommath/bn_mp_copy.c
+++ b/libtommath/bn_mp_copy.c
@@ -63,6 +63,6 @@ mp_copy (mp_int * a, mp_int * b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_count_bits.c b/libtommath/bn_mp_count_bits.c
index 74b59b6..e2db126 100644
--- a/libtommath/bn_mp_count_bits.c
+++ b/libtommath/bn_mp_count_bits.c
@@ -40,6 +40,6 @@ mp_count_bits (mp_int * a)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_div.c b/libtommath/bn_mp_div.c
index 3ca5d7f..81d30eb 100644
--- a/libtommath/bn_mp_div.c
+++ b/libtommath/bn_mp_div.c
@@ -290,6 +290,6 @@ LBL_Q:mp_clear (&q);
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_div_2.c b/libtommath/bn_mp_div_2.c
index d2a213f..2004da7 100644
--- a/libtommath/bn_mp_div_2.c
+++ b/libtommath/bn_mp_div_2.c
@@ -63,6 +63,6 @@ int mp_div_2(mp_int * a, mp_int * b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_div_2d.c b/libtommath/bn_mp_div_2d.c
index 5b9fb48..a5b8494 100644
--- a/libtommath/bn_mp_div_2d.c
+++ b/libtommath/bn_mp_div_2d.c
@@ -20,8 +20,6 @@ int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
 {
   mp_digit D, r, rr;
   int     x, res;
-  mp_int  t;
-
 
   /* if the shift count is <= 0 then we do no work */
   if (b <= 0) {
@@ -32,24 +30,19 @@ int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
     return res;
   }
 
-  if ((res = mp_init (&t)) != MP_OKAY) {
+  /* copy */
+  if ((res = mp_copy (a, c)) != MP_OKAY) {
     return res;
   }
+  /* 'a' should not be used after here - it might be the same as d */
 
   /* get the remainder */
   if (d != NULL) {
-    if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) {
-      mp_clear (&t);
+    if ((res = mp_mod_2d (a, b, d)) != MP_OKAY) {
       return res;
     }
   }
 
-  /* copy */
-  if ((res = mp_copy (a, c)) != MP_OKAY) {
-    mp_clear (&t);
-    return res;
-  }
-
   /* shift by as many digits in the bit count */
   if (b >= (int)DIGIT_BIT) {
     mp_rshd (c, b / DIGIT_BIT);
@@ -84,14 +77,10 @@ int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
     }
   }
   mp_clamp (c);
-  if (d != NULL) {
-    mp_exch (&t, d);
-  }
-  mp_clear (&t);
   return MP_OKAY;
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_div_3.c b/libtommath/bn_mp_div_3.c
index c2b76fb..6c79332 100644
--- a/libtommath/bn_mp_div_3.c
+++ b/libtommath/bn_mp_div_3.c
@@ -74,6 +74,6 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_div_d.c b/libtommath/bn_mp_div_d.c
index 4df1d36..aab298a 100644
--- a/libtommath/bn_mp_div_d.c
+++ b/libtommath/bn_mp_div_d.c
@@ -110,6 +110,6 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_dr_is_modulus.c b/libtommath/bn_mp_dr_is_modulus.c
index 599d929..d4dbec6 100644
--- a/libtommath/bn_mp_dr_is_modulus.c
+++ b/libtommath/bn_mp_dr_is_modulus.c
@@ -38,6 +38,6 @@ int mp_dr_is_modulus(mp_int *a)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_dr_reduce.c b/libtommath/bn_mp_dr_reduce.c
index 2273c79..2005f3c 100644
--- a/libtommath/bn_mp_dr_reduce.c
+++ b/libtommath/bn_mp_dr_reduce.c
@@ -91,6 +91,6 @@ top:
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_dr_setup.c b/libtommath/bn_mp_dr_setup.c
index 1bccb2b..7f60c67 100644
--- a/libtommath/bn_mp_dr_setup.c
+++ b/libtommath/bn_mp_dr_setup.c
@@ -27,6 +27,6 @@ void mp_dr_setup(mp_int *a, mp_digit *d)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_exch.c b/libtommath/bn_mp_exch.c
index 634193b..8dd5180 100644
--- a/libtommath/bn_mp_exch.c
+++ b/libtommath/bn_mp_exch.c
@@ -29,6 +29,6 @@ mp_exch (mp_int * a, mp_int * b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_export.c b/libtommath/bn_mp_export.c
index ac4c2f9..6477dd9 100644
--- a/libtommath/bn_mp_export.c
+++ b/libtommath/bn_mp_export.c
@@ -31,12 +31,12 @@ int mp_export(void* rop, size_t* countp, int order, size_t size,
 	}
 
 	if (endian == 0) {
-		union {
-			unsigned int i;
-			char c[4];
+		union {
+			unsigned int i;
+			char c[4];
 		} lint;
-		lint.i = 0x01020304;
-
+		lint.i = 0x01020304;
+
 		endian = (lint.c[0] == 4) ? -1 : 1;
 	}
 
@@ -83,6 +83,6 @@ int mp_export(void* rop, size_t* countp, int order, size_t size,
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_expt_d.c b/libtommath/bn_mp_expt_d.c
index 61c5a1d..0a4b90b 100644
--- a/libtommath/bn_mp_expt_d.c
+++ b/libtommath/bn_mp_expt_d.c
@@ -23,6 +23,6 @@ int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_expt_d_ex.c b/libtommath/bn_mp_expt_d_ex.c
index 649d224..3bef24a 100644
--- a/libtommath/bn_mp_expt_d_ex.c
+++ b/libtommath/bn_mp_expt_d_ex.c
@@ -78,6 +78,6 @@ int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_exptmod.c b/libtommath/bn_mp_exptmod.c
index 0973e44..697ef52 100644
--- a/libtommath/bn_mp_exptmod.c
+++ b/libtommath/bn_mp_exptmod.c
@@ -107,6 +107,6 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_exptmod_fast.c b/libtommath/bn_mp_exptmod_fast.c
index 8d280bd..312305e 100644
--- a/libtommath/bn_mp_exptmod_fast.c
+++ b/libtommath/bn_mp_exptmod_fast.c
@@ -67,13 +67,13 @@ int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode
 
   /* init M array */
   /* init first cell */
-  if ((err = mp_init(&M[1])) != MP_OKAY) {
+  if ((err = mp_init_size(&M[1], P->alloc)) != MP_OKAY) {
      return err;
   }
 
   /* now init the second half of the array */
   for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
-    if ((err = mp_init(&M[x])) != MP_OKAY) {
+    if ((err = mp_init_size(&M[x], P->alloc)) != MP_OKAY) {
       for (y = 1<<(winsize-1); y < x; y++) {
         mp_clear (&M[y]);
       }
@@ -133,7 +133,7 @@ int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode
   }
 
   /* setup result */
-  if ((err = mp_init (&res)) != MP_OKAY) {
+  if ((err = mp_init_size (&res, P->alloc)) != MP_OKAY) {
     goto LBL_M;
   }
 
@@ -150,15 +150,15 @@ int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode
      if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
        goto LBL_RES;
      }
-#else 
-     err = MP_VAL;
-     goto LBL_RES;
-#endif
 
      /* now set M[1] to G * R mod m */
      if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
        goto LBL_RES;
      }
+#else
+     err = MP_VAL;
+     goto LBL_RES;
+#endif
   } else {
      mp_set(&res, 1);
      if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
@@ -316,6 +316,6 @@ LBL_M:
 #endif
 
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_exteuclid.c b/libtommath/bn_mp_exteuclid.c
index fbbd92c..f941385 100644
--- a/libtommath/bn_mp_exteuclid.c
+++ b/libtommath/bn_mp_exteuclid.c
@@ -29,41 +29,41 @@ int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
 
    /* initialize, (u1,u2,u3) = (1,0,a) */
    mp_set(&u1, 1);
-   if ((err = mp_copy(a, &u3)) != MP_OKAY)                                        { goto _ERR; }
+   if ((err = mp_copy(a, &u3)) != MP_OKAY)                                        { goto LBL_ERR; }
 
    /* initialize, (v1,v2,v3) = (0,1,b) */
    mp_set(&v2, 1);
-   if ((err = mp_copy(b, &v3)) != MP_OKAY)                                        { goto _ERR; }
+   if ((err = mp_copy(b, &v3)) != MP_OKAY)                                        { goto LBL_ERR; }
 
    /* loop while v3 != 0 */
    while (mp_iszero(&v3) == MP_NO) {
        /* q = u3/v3 */
-       if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY)                         { goto _ERR; }
+       if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY)                         { goto LBL_ERR; }
 
        /* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */
-       if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY)                              { goto _ERR; }
-       if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY)                             { goto _ERR; }
-       if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY)                              { goto _ERR; }
-       if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY)                             { goto _ERR; }
-       if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY)                              { goto _ERR; }
-       if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY)                             { goto _ERR; }
+       if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY)                              { goto LBL_ERR; }
+       if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY)                             { goto LBL_ERR; }
+       if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY)                              { goto LBL_ERR; }
+       if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY)                             { goto LBL_ERR; }
+       if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY)                              { goto LBL_ERR; }
+       if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY)                             { goto LBL_ERR; }
 
        /* (u1,u2,u3) = (v1,v2,v3) */
-       if ((err = mp_copy(&v1, &u1)) != MP_OKAY)                                  { goto _ERR; }
-       if ((err = mp_copy(&v2, &u2)) != MP_OKAY)                                  { goto _ERR; }
-       if ((err = mp_copy(&v3, &u3)) != MP_OKAY)                                  { goto _ERR; }
+       if ((err = mp_copy(&v1, &u1)) != MP_OKAY)                                  { goto LBL_ERR; }
+       if ((err = mp_copy(&v2, &u2)) != MP_OKAY)                                  { goto LBL_ERR; }
+       if ((err = mp_copy(&v3, &u3)) != MP_OKAY)                                  { goto LBL_ERR; }
 
        /* (v1,v2,v3) = (t1,t2,t3) */
-       if ((err = mp_copy(&t1, &v1)) != MP_OKAY)                                  { goto _ERR; }
-       if ((err = mp_copy(&t2, &v2)) != MP_OKAY)                                  { goto _ERR; }
-       if ((err = mp_copy(&t3, &v3)) != MP_OKAY)                                  { goto _ERR; }
+       if ((err = mp_copy(&t1, &v1)) != MP_OKAY)                                  { goto LBL_ERR; }
+       if ((err = mp_copy(&t2, &v2)) != MP_OKAY)                                  { goto LBL_ERR; }
+       if ((err = mp_copy(&t3, &v3)) != MP_OKAY)                                  { goto LBL_ERR; }
    }
 
    /* make sure U3 >= 0 */
    if (u3.sign == MP_NEG) {
-       if ((err = mp_neg(&u1, &u1)) != MP_OKAY)                                   { goto _ERR; }
-       if ((err = mp_neg(&u2, &u2)) != MP_OKAY)                                   { goto _ERR; }
-       if ((err = mp_neg(&u3, &u3)) != MP_OKAY)                                   { goto _ERR; }
+       if ((err = mp_neg(&u1, &u1)) != MP_OKAY)                                   { goto LBL_ERR; }
+       if ((err = mp_neg(&u2, &u2)) != MP_OKAY)                                   { goto LBL_ERR; }
+       if ((err = mp_neg(&u3, &u3)) != MP_OKAY)                                   { goto LBL_ERR; }
    }
 
    /* copy result out */
@@ -72,11 +72,12 @@ int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
    if (U3 != NULL) { mp_exch(U3, &u3); }
 
    err = MP_OKAY;
-_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
+LBL_ERR:
+   mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
    return err;
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_fread.c b/libtommath/bn_mp_fread.c
index a4fa8c9..6792437 100644
--- a/libtommath/bn_mp_fread.c
+++ b/libtommath/bn_mp_fread.c
@@ -15,6 +15,7 @@
  * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
+#ifndef LTM_NO_FILE
 /* read a bigint from a file stream in ASCII */
 int mp_fread(mp_int *a, int radix, FILE *stream)
 {
@@ -59,9 +60,10 @@ int mp_fread(mp_int *a, int radix, FILE *stream)
    
    return MP_OKAY;
 }
+#endif
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_fwrite.c b/libtommath/bn_mp_fwrite.c
index 90f1fc5..44812d5 100644
--- a/libtommath/bn_mp_fwrite.c
+++ b/libtommath/bn_mp_fwrite.c
@@ -15,6 +15,7 @@
  * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
+#ifndef LTM_NO_FILE
 int mp_fwrite(mp_int *a, int radix, FILE *stream)
 {
    char *buf;
@@ -44,9 +45,10 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream)
    XFREE (buf);
    return MP_OKAY;
 }
+#endif
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_gcd.c b/libtommath/bn_mp_gcd.c
index 16acfd9..fdefc1b 100644
--- a/libtommath/bn_mp_gcd.c
+++ b/libtommath/bn_mp_gcd.c
@@ -100,6 +100,6 @@ LBL_U:mp_clear (&v);
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_get_int.c b/libtommath/bn_mp_get_int.c
index 99fb850..4d8ecd2 100644
--- a/libtommath/bn_mp_get_int.c
+++ b/libtommath/bn_mp_get_int.c
@@ -40,6 +40,6 @@ unsigned long mp_get_int(mp_int * a)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_grow.c b/libtommath/bn_mp_grow.c
index cbdcfed..7fbc5a2 100644
--- a/libtommath/bn_mp_grow.c
+++ b/libtommath/bn_mp_grow.c
@@ -52,6 +52,6 @@ int mp_grow (mp_int * a, int size)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_import.c b/libtommath/bn_mp_import.c
index dd4b8e6..c615a84 100644
--- a/libtommath/bn_mp_import.c
+++ b/libtommath/bn_mp_import.c
@@ -27,12 +27,12 @@ int mp_import(mp_int* rop, size_t count, int order, size_t size,
 	mp_zero(rop);
 
 	if (endian == 0) {
-		union {
-			unsigned int i;
-			char c[4];
+		union {
+			unsigned int i;
+			char c[4];
 		} lint;
-		lint.i = 0x01020304;
-
+		lint.i = 0x01020304;
+
 		endian = (lint.c[0] == 4) ? -1 : 1;
 	}
 
@@ -68,6 +68,6 @@ int mp_import(mp_int* rop, size_t count, int order, size_t size,
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_init.c b/libtommath/bn_mp_init.c
index 7a57730..8a26f09 100644
--- a/libtommath/bn_mp_init.c
+++ b/libtommath/bn_mp_init.c
@@ -41,6 +41,6 @@ int mp_init (mp_int * a)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_init_copy.c b/libtommath/bn_mp_init_copy.c
index 9e15f36..ab0e130 100644
--- a/libtommath/bn_mp_init_copy.c
+++ b/libtommath/bn_mp_init_copy.c
@@ -23,10 +23,15 @@ int mp_init_copy (mp_int * a, mp_int * b)
   if ((res = mp_init_size (a, b->used)) != MP_OKAY) {
     return res;
   }
-  return mp_copy (b, a);
+
+  if((res = mp_copy (b, a)) != MP_OKAY) {
+    mp_clear(a);
+  }
+
+  return res;
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_init_multi.c b/libtommath/bn_mp_init_multi.c
index 52220a3..78ed62d 100644
--- a/libtommath/bn_mp_init_multi.c
+++ b/libtommath/bn_mp_init_multi.c
@@ -31,9 +31,6 @@ int mp_init_multi(mp_int *mp, ...)
             */
             va_list clean_args;
             
-            /* end the current list */
-            va_end(args);
-            
             /* now start cleaning up */            
             cur_arg = mp;
             va_start(clean_args, mp);
@@ -54,6 +51,6 @@ int mp_init_multi(mp_int *mp, ...)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_init_set.c b/libtommath/bn_mp_init_set.c
index c337e50..0b5cf36 100644
--- a/libtommath/bn_mp_init_set.c
+++ b/libtommath/bn_mp_init_set.c
@@ -27,6 +27,6 @@ int mp_init_set (mp_int * a, mp_digit b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_init_set_int.c b/libtommath/bn_mp_init_set_int.c
index c88f14e..a9bf232 100644
--- a/libtommath/bn_mp_init_set_int.c
+++ b/libtommath/bn_mp_init_set_int.c
@@ -26,6 +26,6 @@ int mp_init_set_int (mp_int * a, unsigned long b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_init_size.c b/libtommath/bn_mp_init_size.c
index e1d1b51..44b875f 100644
--- a/libtommath/bn_mp_init_size.c
+++ b/libtommath/bn_mp_init_size.c
@@ -43,6 +43,6 @@ int mp_init_size (mp_int * a, int size)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_invmod.c b/libtommath/bn_mp_invmod.c
index 44951e5..c374fd2 100644
--- a/libtommath/bn_mp_invmod.c
+++ b/libtommath/bn_mp_invmod.c
@@ -25,7 +25,7 @@ int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
 
 #ifdef BN_FAST_MP_INVMOD_C
   /* if the modulus is odd we can use a faster routine instead */
-  if (mp_isodd (b) == MP_YES) {
+  if ((mp_isodd(b) == MP_YES) && (mp_cmp_d(b, 1) != MP_EQ)) {
     return fast_mp_invmod (a, b, c);
   }
 #endif
@@ -38,6 +38,6 @@ int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_invmod_slow.c b/libtommath/bn_mp_invmod_slow.c
index a21f947..879e971 100644
--- a/libtommath/bn_mp_invmod_slow.c
+++ b/libtommath/bn_mp_invmod_slow.c
@@ -170,6 +170,6 @@ LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_is_square.c b/libtommath/bn_mp_is_square.c
index 9f065ef..15e632e 100644
--- a/libtommath/bn_mp_is_square.c
+++ b/libtommath/bn_mp_is_square.c
@@ -104,6 +104,6 @@ ERR:mp_clear(&t);
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_jacobi.c b/libtommath/bn_mp_jacobi.c
index 3c114e3..4e6c474 100644
--- a/libtommath/bn_mp_jacobi.c
+++ b/libtommath/bn_mp_jacobi.c
@@ -112,6 +112,6 @@ LBL_A1:mp_clear (&a1);
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_karatsuba_mul.c b/libtommath/bn_mp_karatsuba_mul.c
index d65e37e..307a0d9 100644
--- a/libtommath/bn_mp_karatsuba_mul.c
+++ b/libtommath/bn_mp_karatsuba_mul.c
@@ -162,6 +162,6 @@ ERR:
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_karatsuba_sqr.c b/libtommath/bn_mp_karatsuba_sqr.c
index 739840d..3993cd9 100644
--- a/libtommath/bn_mp_karatsuba_sqr.c
+++ b/libtommath/bn_mp_karatsuba_sqr.c
@@ -116,6 +116,6 @@ ERR:
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_lcm.c b/libtommath/bn_mp_lcm.c
index 3bff571..b6a0ec1 100644
--- a/libtommath/bn_mp_lcm.c
+++ b/libtommath/bn_mp_lcm.c
@@ -55,6 +55,6 @@ LBL_T:
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_lshd.c b/libtommath/bn_mp_lshd.c
index f6f800f..b6cb111 100644
--- a/libtommath/bn_mp_lshd.c
+++ b/libtommath/bn_mp_lshd.c
@@ -62,6 +62,6 @@ int mp_lshd (mp_int * a, int b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_mod.c b/libtommath/bn_mp_mod.c
index b67467d..0c9bc3e 100644
--- a/libtommath/bn_mp_mod.c
+++ b/libtommath/bn_mp_mod.c
@@ -22,7 +22,7 @@ mp_mod (mp_int * a, mp_int * b, mp_int * c)
   mp_int  t;
   int     res;
 
-  if ((res = mp_init (&t)) != MP_OKAY) {
+  if ((res = mp_init_size (&t, b->used)) != MP_OKAY) {
     return res;
   }
 
@@ -43,6 +43,6 @@ mp_mod (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_mod_2d.c b/libtommath/bn_mp_mod_2d.c
index 926f810..1f2c47c 100644
--- a/libtommath/bn_mp_mod_2d.c
+++ b/libtommath/bn_mp_mod_2d.c
@@ -50,6 +50,6 @@ mp_mod_2d (mp_int * a, int b, mp_int * c)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_mod_d.c b/libtommath/bn_mp_mod_d.c
index d8722f0..4553cba 100644
--- a/libtommath/bn_mp_mod_d.c
+++ b/libtommath/bn_mp_mod_d.c
@@ -22,6 +22,6 @@ mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_montgomery_calc_normalization.c b/libtommath/bn_mp_montgomery_calc_normalization.c
index ea87cbd..2b11749 100644
--- a/libtommath/bn_mp_montgomery_calc_normalization.c
+++ b/libtommath/bn_mp_montgomery_calc_normalization.c
@@ -54,6 +54,6 @@ int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_montgomery_reduce.c b/libtommath/bn_mp_montgomery_reduce.c
index af2cc58..d3746a6 100644
--- a/libtommath/bn_mp_montgomery_reduce.c
+++ b/libtommath/bn_mp_montgomery_reduce.c
@@ -113,6 +113,6 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_montgomery_setup.c b/libtommath/bn_mp_montgomery_setup.c
index 264a2bd..c71d362 100644
--- a/libtommath/bn_mp_montgomery_setup.c
+++ b/libtommath/bn_mp_montgomery_setup.c
@@ -54,6 +54,6 @@ mp_montgomery_setup (mp_int * n, mp_digit * rho)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_mul.c b/libtommath/bn_mp_mul.c
index ea53d5e..d81f68b 100644
--- a/libtommath/bn_mp_mul.c
+++ b/libtommath/bn_mp_mul.c
@@ -62,6 +62,6 @@ int mp_mul (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_mul_2.c b/libtommath/bn_mp_mul_2.c
index 9c72c7f..20fb9d6 100644
--- a/libtommath/bn_mp_mul_2.c
+++ b/libtommath/bn_mp_mul_2.c
@@ -77,6 +77,6 @@ int mp_mul_2(mp_int * a, mp_int * b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_mul_2d.c b/libtommath/bn_mp_mul_2d.c
index 9967e46..b5d3cae 100644
--- a/libtommath/bn_mp_mul_2d.c
+++ b/libtommath/bn_mp_mul_2d.c
@@ -80,6 +80,6 @@ int mp_mul_2d (mp_int * a, int b, mp_int * c)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_mul_d.c b/libtommath/bn_mp_mul_d.c
index e77da5d..c0c24cd 100644
--- a/libtommath/bn_mp_mul_d.c
+++ b/libtommath/bn_mp_mul_d.c
@@ -74,6 +74,6 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_mulmod.c b/libtommath/bn_mp_mulmod.c
index 5ea88ef..375674f 100644
--- a/libtommath/bn_mp_mulmod.c
+++ b/libtommath/bn_mp_mulmod.c
@@ -21,7 +21,7 @@ int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
   int     res;
   mp_int  t;
 
-  if ((res = mp_init (&t)) != MP_OKAY) {
+  if ((res = mp_init_size (&t, c->used)) != MP_OKAY) {
     return res;
   }
 
@@ -35,6 +35,6 @@ int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_n_root.c b/libtommath/bn_mp_n_root.c
index a14ee67..b7a4817 100644
--- a/libtommath/bn_mp_n_root.c
+++ b/libtommath/bn_mp_n_root.c
@@ -25,6 +25,6 @@ int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_n_root_ex.c b/libtommath/bn_mp_n_root_ex.c
index 79d1dfb..c163c1d 100644
--- a/libtommath/bn_mp_n_root_ex.c
+++ b/libtommath/bn_mp_n_root_ex.c
@@ -127,6 +127,6 @@ LBL_T1:mp_clear (&t1);
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_neg.c b/libtommath/bn_mp_neg.c
index ea32e46..b8a014a 100644
--- a/libtommath/bn_mp_neg.c
+++ b/libtommath/bn_mp_neg.c
@@ -35,6 +35,6 @@ int mp_neg (mp_int * a, mp_int * b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_or.c b/libtommath/bn_mp_or.c
index b7f2e4f..fc303d2 100644
--- a/libtommath/bn_mp_or.c
+++ b/libtommath/bn_mp_or.c
@@ -45,6 +45,6 @@ int mp_or (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_prime_fermat.c b/libtommath/bn_mp_prime_fermat.c
index 9dc9e85..1b1300c 100644
--- a/libtommath/bn_mp_prime_fermat.c
+++ b/libtommath/bn_mp_prime_fermat.c
@@ -57,6 +57,6 @@ LBL_T:mp_clear (&t);
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_prime_is_divisible.c b/libtommath/bn_mp_prime_is_divisible.c
index 5854f08..b97390e 100644
--- a/libtommath/bn_mp_prime_is_divisible.c
+++ b/libtommath/bn_mp_prime_is_divisible.c
@@ -45,6 +45,6 @@ int mp_prime_is_divisible (mp_int * a, int *result)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_prime_is_prime.c b/libtommath/bn_mp_prime_is_prime.c
index be5ebe4..4a36047 100644
--- a/libtommath/bn_mp_prime_is_prime.c
+++ b/libtommath/bn_mp_prime_is_prime.c
@@ -78,6 +78,6 @@ LBL_B:mp_clear (&b);
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_prime_miller_rabin.c b/libtommath/bn_mp_prime_miller_rabin.c
index 7b5c8d2..569d78a 100644
--- a/libtommath/bn_mp_prime_miller_rabin.c
+++ b/libtommath/bn_mp_prime_miller_rabin.c
@@ -98,6 +98,6 @@ LBL_N1:mp_clear (&n1);
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_prime_next_prime.c b/libtommath/bn_mp_prime_next_prime.c
index 9951dc3..c0b7895 100644
--- a/libtommath/bn_mp_prime_next_prime.c
+++ b/libtommath/bn_mp_prime_next_prime.c
@@ -165,6 +165,6 @@ LBL_ERR:
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_prime_rabin_miller_trials.c b/libtommath/bn_mp_prime_rabin_miller_trials.c
index bca4229..ad954cc 100644
--- a/libtommath/bn_mp_prime_rabin_miller_trials.c
+++ b/libtommath/bn_mp_prime_rabin_miller_trials.c
@@ -47,6 +47,6 @@ int mp_prime_rabin_miller_trials(int size)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_prime_random_ex.c b/libtommath/bn_mp_prime_random_ex.c
index 1efc4fc..655e8ae 100644
--- a/libtommath/bn_mp_prime_random_ex.c
+++ b/libtommath/bn_mp_prime_random_ex.c
@@ -119,6 +119,6 @@ error:
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_radix_size.c b/libtommath/bn_mp_radix_size.c
index e5d7772..e9cb55a 100644
--- a/libtommath/bn_mp_radix_size.c
+++ b/libtommath/bn_mp_radix_size.c
@@ -73,6 +73,6 @@ int mp_radix_size (mp_int * a, int radix, int *size)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_radix_smap.c b/libtommath/bn_mp_radix_smap.c
index d1c75ad..425e0e6 100644
--- a/libtommath/bn_mp_radix_smap.c
+++ b/libtommath/bn_mp_radix_smap.c
@@ -19,6 +19,6 @@
 const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_rand.c b/libtommath/bn_mp_rand.c
index 4c9610d..7c8f106 100644
--- a/libtommath/bn_mp_rand.c
+++ b/libtommath/bn_mp_rand.c
@@ -15,7 +15,32 @@
  * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
+#if MP_GEN_RANDOM_MAX == 0xffffffff
+  #define MP_GEN_RANDOM_SHIFT  32
+#elif MP_GEN_RANDOM_MAX == 32767
+  /* SHRT_MAX */
+  #define MP_GEN_RANDOM_SHIFT  15
+#elif MP_GEN_RANDOM_MAX == 2147483647
+  /* INT_MAX */
+  #define MP_GEN_RANDOM_SHIFT  31
+#elif !defined(MP_GEN_RANDOM_SHIFT)
+#error Thou shalt define their own valid MP_GEN_RANDOM_SHIFT
+#endif
+
 /* makes a pseudo-random int of a given size */
+static mp_digit s_gen_random(void)
+{
+  mp_digit d = 0, msk = 0;
+  do {
+    d <<= MP_GEN_RANDOM_SHIFT;
+    d |= ((mp_digit) MP_GEN_RANDOM());
+    msk <<= MP_GEN_RANDOM_SHIFT;
+    msk |= (MP_MASK & MP_GEN_RANDOM_MAX);
+  } while ((MP_MASK & msk) != MP_MASK);
+  d &= MP_MASK;
+  return d;
+}
+
 int
 mp_rand (mp_int * a, int digits)
 {
@@ -29,7 +54,7 @@ mp_rand (mp_int * a, int digits)
 
   /* first place a random non-zero digit */
   do {
-    d = ((mp_digit) abs (MP_GEN_RANDOM())) & MP_MASK;
+    d = s_gen_random();
   } while (d == 0);
 
   if ((res = mp_add_d (a, d, a)) != MP_OKAY) {
@@ -41,7 +66,7 @@ mp_rand (mp_int * a, int digits)
       return res;
     }
 
-    if ((res = mp_add_d (a, ((mp_digit) abs (MP_GEN_RANDOM())), a)) != MP_OKAY) {
+    if ((res = mp_add_d (a, s_gen_random(), a)) != MP_OKAY) {
       return res;
     }
   }
@@ -50,6 +75,6 @@ mp_rand (mp_int * a, int digits)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_read_radix.c b/libtommath/bn_mp_read_radix.c
index 5c9eb5e..6f2cc04 100644
--- a/libtommath/bn_mp_read_radix.c
+++ b/libtommath/bn_mp_read_radix.c
@@ -80,6 +80,6 @@ int mp_read_radix (mp_int * a, const char *str, int radix)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_read_signed_bin.c b/libtommath/bn_mp_read_signed_bin.c
index a4d4760..1448d21 100644
--- a/libtommath/bn_mp_read_signed_bin.c
+++ b/libtommath/bn_mp_read_signed_bin.c
@@ -36,6 +36,6 @@ int mp_read_signed_bin (mp_int * a, const unsigned char *b, int c)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_read_unsigned_bin.c b/libtommath/bn_mp_read_unsigned_bin.c
index e8e5df8..b2e399d 100644
--- a/libtommath/bn_mp_read_unsigned_bin.c
+++ b/libtommath/bn_mp_read_unsigned_bin.c
@@ -50,6 +50,6 @@ int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_reduce.c b/libtommath/bn_mp_reduce.c
index e2c3a58..c15b54e 100644
--- a/libtommath/bn_mp_reduce.c
+++ b/libtommath/bn_mp_reduce.c
@@ -95,6 +95,6 @@ CLEANUP:
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_reduce_2k.c b/libtommath/bn_mp_reduce_2k.c
index 2876a75..daea5e7 100644
--- a/libtommath/bn_mp_reduce_2k.c
+++ b/libtommath/bn_mp_reduce_2k.c
@@ -58,6 +58,6 @@ ERR:
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_reduce_2k_l.c b/libtommath/bn_mp_reduce_2k_l.c
index 3225214..d6c2aa4 100644
--- a/libtommath/bn_mp_reduce_2k_l.c
+++ b/libtommath/bn_mp_reduce_2k_l.c
@@ -59,6 +59,6 @@ ERR:
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_reduce_2k_setup.c b/libtommath/bn_mp_reduce_2k_setup.c
index 545051e..f4650b4 100644
--- a/libtommath/bn_mp_reduce_2k_setup.c
+++ b/libtommath/bn_mp_reduce_2k_setup.c
@@ -42,6 +42,6 @@ int mp_reduce_2k_setup(mp_int *a, mp_digit *d)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_reduce_2k_setup_l.c b/libtommath/bn_mp_reduce_2k_setup_l.c
index 59132dd..7945d6a 100644
--- a/libtommath/bn_mp_reduce_2k_setup_l.c
+++ b/libtommath/bn_mp_reduce_2k_setup_l.c
@@ -39,6 +39,6 @@ ERR:
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_reduce_is_2k.c b/libtommath/bn_mp_reduce_is_2k.c
index 784947b..e68d704 100644
--- a/libtommath/bn_mp_reduce_is_2k.c
+++ b/libtommath/bn_mp_reduce_is_2k.c
@@ -47,6 +47,6 @@ int mp_reduce_is_2k(mp_int *a)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_reduce_is_2k_l.c b/libtommath/bn_mp_reduce_is_2k_l.c
index c193f39..5426352 100644
--- a/libtommath/bn_mp_reduce_is_2k_l.c
+++ b/libtommath/bn_mp_reduce_is_2k_l.c
@@ -39,6 +39,6 @@ int mp_reduce_is_2k_l(mp_int *a)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_reduce_setup.c b/libtommath/bn_mp_reduce_setup.c
index f97eed5..d3ed42f 100644
--- a/libtommath/bn_mp_reduce_setup.c
+++ b/libtommath/bn_mp_reduce_setup.c
@@ -29,6 +29,6 @@ int mp_reduce_setup (mp_int * a, mp_int * b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_rshd.c b/libtommath/bn_mp_rshd.c
index 77b0f6c..6ea4f2f 100644
--- a/libtommath/bn_mp_rshd.c
+++ b/libtommath/bn_mp_rshd.c
@@ -67,6 +67,6 @@ void mp_rshd (mp_int * a, int b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_set.c b/libtommath/bn_mp_set.c
index cac48ea..c10850d 100644
--- a/libtommath/bn_mp_set.c
+++ b/libtommath/bn_mp_set.c
@@ -24,6 +24,6 @@ void mp_set (mp_int * a, mp_digit b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_set_int.c b/libtommath/bn_mp_set_int.c
index 5aa59d5..3e9ae87 100644
--- a/libtommath/bn_mp_set_int.c
+++ b/libtommath/bn_mp_set_int.c
@@ -43,6 +43,6 @@ int mp_set_int (mp_int * a, unsigned long b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_set_long.c b/libtommath/bn_mp_set_long.c
index 281fce7..680781b 100644
--- a/libtommath/bn_mp_set_long.c
+++ b/libtommath/bn_mp_set_long.c
@@ -19,6 +19,6 @@
 MP_SET_XLONG(mp_set_long, unsigned long)
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_set_long_long.c b/libtommath/bn_mp_set_long_long.c
index 3c4b01a..7fde01a 100644
--- a/libtommath/bn_mp_set_long_long.c
+++ b/libtommath/bn_mp_set_long_long.c
@@ -19,6 +19,6 @@
 MP_SET_XLONG(mp_set_long_long, unsigned long long)
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_shrink.c b/libtommath/bn_mp_shrink.c
index 1ad2ede..ef71874 100644
--- a/libtommath/bn_mp_shrink.c
+++ b/libtommath/bn_mp_shrink.c
@@ -36,6 +36,6 @@ int mp_shrink (mp_int * a)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_signed_bin_size.c b/libtommath/bn_mp_signed_bin_size.c
index 0e760a6..261f036 100644
--- a/libtommath/bn_mp_signed_bin_size.c
+++ b/libtommath/bn_mp_signed_bin_size.c
@@ -22,6 +22,6 @@ int mp_signed_bin_size (mp_int * a)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_sqr.c b/libtommath/bn_mp_sqr.c
index ad2099b..e0c2e85 100644
--- a/libtommath/bn_mp_sqr.c
+++ b/libtommath/bn_mp_sqr.c
@@ -55,6 +55,6 @@ mp_sqr (mp_int * a, mp_int * b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_sqrmod.c b/libtommath/bn_mp_sqrmod.c
index 2f9463d..25ca55e 100644
--- a/libtommath/bn_mp_sqrmod.c
+++ b/libtommath/bn_mp_sqrmod.c
@@ -36,6 +36,6 @@ mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_sqrt.c b/libtommath/bn_mp_sqrt.c
index 4a52f5e..77078e8 100644
--- a/libtommath/bn_mp_sqrt.c
+++ b/libtommath/bn_mp_sqrt.c
@@ -76,6 +76,6 @@ E2: mp_clear(&t1);
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_sub.c b/libtommath/bn_mp_sub.c
index 0d616c2..cf7d58e 100644
--- a/libtommath/bn_mp_sub.c
+++ b/libtommath/bn_mp_sub.c
@@ -54,6 +54,6 @@ mp_sub (mp_int * a, mp_int * b, mp_int * c)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_sub_d.c b/libtommath/bn_mp_sub_d.c
index f5a932f..482de39 100644
--- a/libtommath/bn_mp_sub_d.c
+++ b/libtommath/bn_mp_sub_d.c
@@ -88,6 +88,6 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_submod.c b/libtommath/bn_mp_submod.c
index 87e0889..f6098b3 100644
--- a/libtommath/bn_mp_submod.c
+++ b/libtommath/bn_mp_submod.c
@@ -37,6 +37,6 @@ mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_to_signed_bin.c b/libtommath/bn_mp_to_signed_bin.c
index e9289ea..077b0bf 100644
--- a/libtommath/bn_mp_to_signed_bin.c
+++ b/libtommath/bn_mp_to_signed_bin.c
@@ -28,6 +28,6 @@ int mp_to_signed_bin (mp_int * a, unsigned char *b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_to_signed_bin_n.c b/libtommath/bn_mp_to_signed_bin_n.c
index d4fe6e6..2edb8e0 100644
--- a/libtommath/bn_mp_to_signed_bin_n.c
+++ b/libtommath/bn_mp_to_signed_bin_n.c
@@ -26,6 +26,6 @@ int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_to_unsigned_bin.c b/libtommath/bn_mp_to_unsigned_bin.c
index d3ef46f..203bf75 100644
--- a/libtommath/bn_mp_to_unsigned_bin.c
+++ b/libtommath/bn_mp_to_unsigned_bin.c
@@ -43,6 +43,6 @@ int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_to_unsigned_bin_n.c b/libtommath/bn_mp_to_unsigned_bin_n.c
index 2da13cc..d28d7f4 100644
--- a/libtommath/bn_mp_to_unsigned_bin_n.c
+++ b/libtommath/bn_mp_to_unsigned_bin_n.c
@@ -26,6 +26,6 @@ int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_toom_mul.c b/libtommath/bn_mp_toom_mul.c
index 4731f8f..dc4f0a9 100644
--- a/libtommath/bn_mp_toom_mul.c
+++ b/libtommath/bn_mp_toom_mul.c
@@ -281,6 +281,6 @@ ERR:
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_toom_sqr.c b/libtommath/bn_mp_toom_sqr.c
index 69b69d4..06a568e 100644
--- a/libtommath/bn_mp_toom_sqr.c
+++ b/libtommath/bn_mp_toom_sqr.c
@@ -223,6 +223,6 @@ ERR:
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_toradix.c b/libtommath/bn_mp_toradix.c
index f04352d..5bd9165 100644
--- a/libtommath/bn_mp_toradix.c
+++ b/libtommath/bn_mp_toradix.c
@@ -70,6 +70,6 @@ int mp_toradix (mp_int * a, char *str, int radix)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_toradix_n.c b/libtommath/bn_mp_toradix_n.c
index 19b61d7..d1587a3 100644
--- a/libtommath/bn_mp_toradix_n.c
+++ b/libtommath/bn_mp_toradix_n.c
@@ -83,6 +83,6 @@ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_unsigned_bin_size.c b/libtommath/bn_mp_unsigned_bin_size.c
index 0312625..e81cd82 100644
--- a/libtommath/bn_mp_unsigned_bin_size.c
+++ b/libtommath/bn_mp_unsigned_bin_size.c
@@ -23,6 +23,6 @@ int mp_unsigned_bin_size (mp_int * a)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_xor.c b/libtommath/bn_mp_xor.c
index 3c2ba9e..1fc8bdf 100644
--- a/libtommath/bn_mp_xor.c
+++ b/libtommath/bn_mp_xor.c
@@ -46,6 +46,6 @@ mp_xor (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_mp_zero.c b/libtommath/bn_mp_zero.c
index 21365ed..f607ce6 100644
--- a/libtommath/bn_mp_zero.c
+++ b/libtommath/bn_mp_zero.c
@@ -31,6 +31,6 @@ void mp_zero (mp_int * a)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_prime_tab.c b/libtommath/bn_prime_tab.c
index ae727a4..4354a48 100644
--- a/libtommath/bn_prime_tab.c
+++ b/libtommath/bn_prime_tab.c
@@ -56,6 +56,6 @@ const mp_digit ltm_prime_tab[] = {
 };
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_reverse.c b/libtommath/bn_reverse.c
index fc6eb2d..9811a81 100644
--- a/libtommath/bn_reverse.c
+++ b/libtommath/bn_reverse.c
@@ -34,6 +34,6 @@ bn_reverse (unsigned char *s, int len)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_s_mp_add.c b/libtommath/bn_s_mp_add.c
index c2ad649..5d886e7 100644
--- a/libtommath/bn_s_mp_add.c
+++ b/libtommath/bn_s_mp_add.c
@@ -104,6 +104,6 @@ s_mp_add (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_s_mp_exptmod.c b/libtommath/bn_s_mp_exptmod.c
index 63e1b1e..617b56c 100644
--- a/libtommath/bn_s_mp_exptmod.c
+++ b/libtommath/bn_s_mp_exptmod.c
@@ -247,6 +247,6 @@ LBL_M:
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_s_mp_mul_digs.c b/libtommath/bn_s_mp_mul_digs.c
index bd8553d..cf2f50c 100644
--- a/libtommath/bn_s_mp_mul_digs.c
+++ b/libtommath/bn_s_mp_mul_digs.c
@@ -85,6 +85,6 @@ int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_s_mp_mul_high_digs.c b/libtommath/bn_s_mp_mul_high_digs.c
index 153cea44..1d5b2f0 100644
--- a/libtommath/bn_s_mp_mul_high_digs.c
+++ b/libtommath/bn_s_mp_mul_high_digs.c
@@ -76,6 +76,6 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_s_mp_sqr.c b/libtommath/bn_s_mp_sqr.c
index 68c95bc..b85f1b8 100644
--- a/libtommath/bn_s_mp_sqr.c
+++ b/libtommath/bn_s_mp_sqr.c
@@ -79,6 +79,6 @@ int s_mp_sqr (mp_int * a, mp_int * b)
 }
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bn_s_mp_sub.c b/libtommath/bn_s_mp_sub.c
index c0ea556..ac3f785 100644
--- a/libtommath/bn_s_mp_sub.c
+++ b/libtommath/bn_s_mp_sub.c
@@ -84,6 +84,6 @@ s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/bncore.c b/libtommath/bncore.c
index 9552714..8bd4681 100644
--- a/libtommath/bncore.c
+++ b/libtommath/bncore.c
@@ -31,6 +31,6 @@ int     KARATSUBA_MUL_CUTOFF = 80,      /* Min. number of digits before Karatsub
         TOOM_SQR_CUTOFF      = 400; 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/tommath.h b/libtommath/tommath.h
index 4c66e15..0a065f6 100644
--- a/libtommath/tommath.h
+++ b/libtommath/tommath.h
@@ -27,7 +27,12 @@ extern "C" {
 #endif
 
 /* detect 64-bit mode if possible */
-#if defined(__x86_64__)
+#if defined(__x86_64__) || defined(_M_X64) || defined(_M_AMD64) || \
+    defined(__powerpc64__) || defined(__ppc64__) || defined(__PPC64__) || \
+    defined(__s390x__) || defined(__arch64__) || defined(__aarch64__) || \
+    defined(__sparcv9) || defined(__sparc_v9__) || defined(__sparc64__) || \
+    defined(__ia64) || defined(__ia64__) || defined(__itanium__) || defined(_M_IA64) || \
+    defined(__LP64__) || defined(_LP64) || defined(__64BIT__)
    #if !(defined(MP_32BIT) || defined(MP_16BIT) || defined(MP_8BIT))
       #define MP_64BIT
    #endif
@@ -57,11 +62,6 @@ extern "C" {
 #endif
 #elif defined(MP_64BIT)
    /* for GCC only on supported platforms */
-#ifndef CRYPT
-   typedef unsigned long long   ulong64;
-   typedef signed long long     long64;
-#endif
-
    typedef uint64_t mp_digit;
 #if defined(_WIN32)
    typedef unsigned __int128    mp_word;
@@ -78,11 +78,6 @@ extern "C" {
    /* this is the default case, 28-bit digits */
 
    /* this is to make porting into LibTomCrypt easier :-) */
-#ifndef CRYPT
-   typedef unsigned long long   ulong64;
-   typedef signed long long     long64;
-#endif
-
    typedef uint32_t             mp_digit;
    typedef uint64_t             mp_word;
 
@@ -104,16 +99,16 @@ extern "C" {
    typedef mp_digit mp_min_u32;
 #endif
 
-/* platforms that can use a better rand function */
+/* use arc4random on platforms that support it */
 #if defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__DragonFly__)
-    #define MP_USE_ALT_RAND 1
+    #define MP_GEN_RANDOM()    arc4random()
+    #define MP_GEN_RANDOM_MAX  0xffffffff
 #endif
 
-/* use arc4random on platforms that support it */
-#ifdef MP_USE_ALT_RAND
-    #define MP_GEN_RANDOM()    arc4random()
-#else
+/* use rand() as fall-back if there's no better rand function */
+#ifndef MP_GEN_RANDOM
     #define MP_GEN_RANDOM()    rand()
+    #define MP_GEN_RANDOM_MAX  RAND_MAX
 #endif
 
 #define MP_DIGIT_BIT     DIGIT_BIT
@@ -570,6 +565,6 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream);
 #endif
 
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/tommath_class.h b/libtommath/tommath_class.h
index 2085521..e860613 100644
--- a/libtommath/tommath_class.h
+++ b/libtommath/tommath_class.h
@@ -282,12 +282,9 @@
 #if defined(BN_MP_DIV_2D_C)
    #define BN_MP_COPY_C
    #define BN_MP_ZERO_C
-   #define BN_MP_INIT_C
    #define BN_MP_MOD_2D_C
-   #define BN_MP_CLEAR_C
    #define BN_MP_RSHD_C
    #define BN_MP_CLAMP_C
-   #define BN_MP_EXCH_C
 #endif
 
 #if defined(BN_MP_DIV_3_C)
@@ -359,7 +356,7 @@
 
 #if defined(BN_MP_EXPTMOD_FAST_C)
    #define BN_MP_COUNT_BITS_C
-   #define BN_MP_INIT_C
+   #define BN_MP_INIT_SIZE_C
    #define BN_MP_CLEAR_C
    #define BN_MP_MONTGOMERY_SETUP_C
    #define BN_FAST_MP_MONTGOMERY_REDUCE_C
@@ -441,6 +438,7 @@
 #if defined(BN_MP_INIT_COPY_C)
    #define BN_MP_INIT_SIZE_C
    #define BN_MP_COPY_C
+   #define BN_MP_CLEAR_C
 #endif
 
 #if defined(BN_MP_INIT_MULTI_C)
@@ -466,6 +464,7 @@
 #if defined(BN_MP_INVMOD_C)
    #define BN_MP_ISZERO_C
    #define BN_MP_ISODD_C
+   #define BN_MP_CMP_D_C
    #define BN_FAST_MP_INVMOD_C
    #define BN_MP_INVMOD_SLOW_C
 #endif
@@ -500,6 +499,7 @@
 #endif
 
 #if defined(BN_MP_JACOBI_C)
+   #define BN_MP_ISNEG_C
    #define BN_MP_CMP_D_C
    #define BN_MP_ISZERO_C
    #define BN_MP_INIT_COPY_C
@@ -546,7 +546,7 @@
 #endif
 
 #if defined(BN_MP_MOD_C)
-   #define BN_MP_INIT_C
+   #define BN_MP_INIT_SIZE_C
    #define BN_MP_DIV_C
    #define BN_MP_CLEAR_C
    #define BN_MP_ISZERO_C
@@ -610,7 +610,7 @@
 #endif
 
 #if defined(BN_MP_MULMOD_C)
-   #define BN_MP_INIT_C
+   #define BN_MP_INIT_SIZE_C
    #define BN_MP_MUL_C
    #define BN_MP_CLEAR_C
    #define BN_MP_MOD_C
diff --git a/libtommath/tommath_private.h b/libtommath/tommath_private.h
index bc7cd35..407ebd5 100644
--- a/libtommath/tommath_private.h
+++ b/libtommath/tommath_private.h
@@ -18,9 +18,13 @@
 #include <tommath.h>
 #include <ctype.h>
 
-#define MIN(x,y) (((x) < (y)) ? (x) : (y))
+#ifndef MIN
+  #define MIN(x,y) (((x) < (y)) ? (x) : (y))
+#endif
 
-#define MAX(x,y) (((x) > (y)) ? (x) : (y))
+#ifndef MAX
+  #define MAX(x,y) (((x) > (y)) ? (x) : (y))
+#endif
 
 #ifdef __cplusplus
 extern "C" {
@@ -114,6 +118,6 @@ int func_name (mp_int * a, type b)                       \
 #endif
 
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
diff --git a/libtommath/tommath_superclass.h b/libtommath/tommath_superclass.h
index 1b26841..8f6ef03 100644
--- a/libtommath/tommath_superclass.h
+++ b/libtommath/tommath_superclass.h
@@ -71,6 +71,6 @@
 
 #endif
 
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
+/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
+/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
+/* commit time: 2017-08-29 10:48:46 +0200 */
-- 
cgit v0.12


From d2f4a7137d403a7acf2b9cffe545c8350245ae54 Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Tue, 29 Aug 2017 19:55:52 +0000
Subject: Fix eol-style (fossil warning: mixed line endings)

---
 libtommath/bn_mp_export.c | 10 +++++-----
 libtommath/bn_mp_import.c | 10 +++++-----
 2 files changed, 10 insertions(+), 10 deletions(-)

diff --git a/libtommath/bn_mp_export.c b/libtommath/bn_mp_export.c
index 6477dd9..58d71d5 100644
--- a/libtommath/bn_mp_export.c
+++ b/libtommath/bn_mp_export.c
@@ -31,12 +31,12 @@ int mp_export(void* rop, size_t* countp, int order, size_t size,
 	}
 
 	if (endian == 0) {
-		union {
-			unsigned int i;
-			char c[4];
+		union {
+			unsigned int i;
+			char c[4];
 		} lint;
-		lint.i = 0x01020304;
-
+		lint.i = 0x01020304;
+
 		endian = (lint.c[0] == 4) ? -1 : 1;
 	}
 
diff --git a/libtommath/bn_mp_import.c b/libtommath/bn_mp_import.c
index c615a84..d9248fd 100644
--- a/libtommath/bn_mp_import.c
+++ b/libtommath/bn_mp_import.c
@@ -27,12 +27,12 @@ int mp_import(mp_int* rop, size_t count, int order, size_t size,
 	mp_zero(rop);
 
 	if (endian == 0) {
-		union {
-			unsigned int i;
-			char c[4];
+		union {
+			unsigned int i;
+			char c[4];
 		} lint;
-		lint.i = 0x01020304;
-
+		lint.i = 0x01020304;
+
 		endian = (lint.c[0] == 4) ? -1 : 1;
 	}
 
-- 
cgit v0.12


From 1e2b7a8725e0220f97dcfc07c240b682bdea7b3a Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Tue, 29 Aug 2017 20:39:15 +0000
Subject: libtommath 1.0.1

---
 libtommath/bn_error.c                            | 6 +++---
 libtommath/bn_fast_mp_invmod.c                   | 6 +++---
 libtommath/bn_fast_mp_montgomery_reduce.c        | 6 +++---
 libtommath/bn_fast_s_mp_mul_digs.c               | 6 +++---
 libtommath/bn_fast_s_mp_mul_high_digs.c          | 6 +++---
 libtommath/bn_fast_s_mp_sqr.c                    | 6 +++---
 libtommath/bn_mp_2expt.c                         | 6 +++---
 libtommath/bn_mp_abs.c                           | 6 +++---
 libtommath/bn_mp_add.c                           | 6 +++---
 libtommath/bn_mp_add_d.c                         | 6 +++---
 libtommath/bn_mp_addmod.c                        | 6 +++---
 libtommath/bn_mp_and.c                           | 6 +++---
 libtommath/bn_mp_clamp.c                         | 6 +++---
 libtommath/bn_mp_clear.c                         | 6 +++---
 libtommath/bn_mp_clear_multi.c                   | 6 +++---
 libtommath/bn_mp_cmp.c                           | 6 +++---
 libtommath/bn_mp_cmp_d.c                         | 6 +++---
 libtommath/bn_mp_cmp_mag.c                       | 6 +++---
 libtommath/bn_mp_cnt_lsb.c                       | 6 +++---
 libtommath/bn_mp_copy.c                          | 6 +++---
 libtommath/bn_mp_count_bits.c                    | 6 +++---
 libtommath/bn_mp_div.c                           | 6 +++---
 libtommath/bn_mp_div_2.c                         | 6 +++---
 libtommath/bn_mp_div_2d.c                        | 6 +++---
 libtommath/bn_mp_div_3.c                         | 6 +++---
 libtommath/bn_mp_div_d.c                         | 6 +++---
 libtommath/bn_mp_dr_is_modulus.c                 | 6 +++---
 libtommath/bn_mp_dr_reduce.c                     | 6 +++---
 libtommath/bn_mp_dr_setup.c                      | 6 +++---
 libtommath/bn_mp_exch.c                          | 6 +++---
 libtommath/bn_mp_export.c                        | 6 +++---
 libtommath/bn_mp_expt_d.c                        | 6 +++---
 libtommath/bn_mp_expt_d_ex.c                     | 6 +++---
 libtommath/bn_mp_exptmod.c                       | 6 +++---
 libtommath/bn_mp_exptmod_fast.c                  | 6 +++---
 libtommath/bn_mp_exteuclid.c                     | 6 +++---
 libtommath/bn_mp_fread.c                         | 6 +++---
 libtommath/bn_mp_fwrite.c                        | 6 +++---
 libtommath/bn_mp_gcd.c                           | 6 +++---
 libtommath/bn_mp_get_int.c                       | 6 +++---
 libtommath/bn_mp_grow.c                          | 6 +++---
 libtommath/bn_mp_import.c                        | 6 +++---
 libtommath/bn_mp_init.c                          | 6 +++---
 libtommath/bn_mp_init_copy.c                     | 6 +++---
 libtommath/bn_mp_init_multi.c                    | 6 +++---
 libtommath/bn_mp_init_set.c                      | 6 +++---
 libtommath/bn_mp_init_set_int.c                  | 6 +++---
 libtommath/bn_mp_init_size.c                     | 6 +++---
 libtommath/bn_mp_invmod.c                        | 6 +++---
 libtommath/bn_mp_invmod_slow.c                   | 6 +++---
 libtommath/bn_mp_is_square.c                     | 6 +++---
 libtommath/bn_mp_jacobi.c                        | 6 +++---
 libtommath/bn_mp_karatsuba_mul.c                 | 6 +++---
 libtommath/bn_mp_karatsuba_sqr.c                 | 6 +++---
 libtommath/bn_mp_lcm.c                           | 6 +++---
 libtommath/bn_mp_lshd.c                          | 6 +++---
 libtommath/bn_mp_mod.c                           | 6 +++---
 libtommath/bn_mp_mod_2d.c                        | 6 +++---
 libtommath/bn_mp_mod_d.c                         | 6 +++---
 libtommath/bn_mp_montgomery_calc_normalization.c | 6 +++---
 libtommath/bn_mp_montgomery_reduce.c             | 6 +++---
 libtommath/bn_mp_montgomery_setup.c              | 6 +++---
 libtommath/bn_mp_mul.c                           | 6 +++---
 libtommath/bn_mp_mul_2.c                         | 6 +++---
 libtommath/bn_mp_mul_2d.c                        | 6 +++---
 libtommath/bn_mp_mul_d.c                         | 6 +++---
 libtommath/bn_mp_mulmod.c                        | 6 +++---
 libtommath/bn_mp_n_root.c                        | 6 +++---
 libtommath/bn_mp_n_root_ex.c                     | 6 +++---
 libtommath/bn_mp_neg.c                           | 6 +++---
 libtommath/bn_mp_or.c                            | 6 +++---
 libtommath/bn_mp_prime_fermat.c                  | 6 +++---
 libtommath/bn_mp_prime_is_divisible.c            | 6 +++---
 libtommath/bn_mp_prime_is_prime.c                | 6 +++---
 libtommath/bn_mp_prime_miller_rabin.c            | 6 +++---
 libtommath/bn_mp_prime_next_prime.c              | 6 +++---
 libtommath/bn_mp_prime_rabin_miller_trials.c     | 6 +++---
 libtommath/bn_mp_prime_random_ex.c               | 6 +++---
 libtommath/bn_mp_radix_size.c                    | 6 +++---
 libtommath/bn_mp_radix_smap.c                    | 6 +++---
 libtommath/bn_mp_rand.c                          | 6 +++---
 libtommath/bn_mp_read_radix.c                    | 6 +++---
 libtommath/bn_mp_read_signed_bin.c               | 6 +++---
 libtommath/bn_mp_read_unsigned_bin.c             | 6 +++---
 libtommath/bn_mp_reduce.c                        | 6 +++---
 libtommath/bn_mp_reduce_2k.c                     | 6 +++---
 libtommath/bn_mp_reduce_2k_l.c                   | 6 +++---
 libtommath/bn_mp_reduce_2k_setup.c               | 6 +++---
 libtommath/bn_mp_reduce_2k_setup_l.c             | 6 +++---
 libtommath/bn_mp_reduce_is_2k.c                  | 6 +++---
 libtommath/bn_mp_reduce_is_2k_l.c                | 6 +++---
 libtommath/bn_mp_reduce_setup.c                  | 6 +++---
 libtommath/bn_mp_rshd.c                          | 6 +++---
 libtommath/bn_mp_set.c                           | 6 +++---
 libtommath/bn_mp_set_int.c                       | 6 +++---
 libtommath/bn_mp_set_long.c                      | 6 +++---
 libtommath/bn_mp_set_long_long.c                 | 6 +++---
 libtommath/bn_mp_shrink.c                        | 6 +++---
 libtommath/bn_mp_signed_bin_size.c               | 6 +++---
 libtommath/bn_mp_sqr.c                           | 6 +++---
 libtommath/bn_mp_sqrmod.c                        | 6 +++---
 libtommath/bn_mp_sqrt.c                          | 6 +++---
 libtommath/bn_mp_sub.c                           | 6 +++---
 libtommath/bn_mp_sub_d.c                         | 6 +++---
 libtommath/bn_mp_submod.c                        | 6 +++---
 libtommath/bn_mp_to_signed_bin.c                 | 6 +++---
 libtommath/bn_mp_to_signed_bin_n.c               | 6 +++---
 libtommath/bn_mp_to_unsigned_bin.c               | 6 +++---
 libtommath/bn_mp_to_unsigned_bin_n.c             | 6 +++---
 libtommath/bn_mp_toom_mul.c                      | 6 +++---
 libtommath/bn_mp_toom_sqr.c                      | 6 +++---
 libtommath/bn_mp_toradix.c                       | 6 +++---
 libtommath/bn_mp_toradix_n.c                     | 6 +++---
 libtommath/bn_mp_unsigned_bin_size.c             | 6 +++---
 libtommath/bn_mp_xor.c                           | 6 +++---
 libtommath/bn_mp_zero.c                          | 6 +++---
 libtommath/bn_prime_tab.c                        | 6 +++---
 libtommath/bn_reverse.c                          | 6 +++---
 libtommath/bn_s_mp_add.c                         | 6 +++---
 libtommath/bn_s_mp_exptmod.c                     | 6 +++---
 libtommath/bn_s_mp_mul_digs.c                    | 6 +++---
 libtommath/bn_s_mp_mul_high_digs.c               | 6 +++---
 libtommath/bn_s_mp_sqr.c                         | 6 +++---
 libtommath/bn_s_mp_sub.c                         | 6 +++---
 libtommath/bncore.c                              | 6 +++---
 libtommath/tommath.h                             | 6 +++---
 libtommath/tommath_private.h                     | 6 +++---
 libtommath/tommath_superclass.h                  | 6 +++---
 128 files changed, 384 insertions(+), 384 deletions(-)

diff --git a/libtommath/bn_error.c b/libtommath/bn_error.c
index 397f834..380f46a 100644
--- a/libtommath/bn_error.c
+++ b/libtommath/bn_error.c
@@ -42,6 +42,6 @@ const char *mp_error_to_string(int code)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_fast_mp_invmod.c b/libtommath/bn_fast_mp_invmod.c
index fa31853..c1d6271 100644
--- a/libtommath/bn_fast_mp_invmod.c
+++ b/libtommath/bn_fast_mp_invmod.c
@@ -143,6 +143,6 @@ LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_fast_mp_montgomery_reduce.c b/libtommath/bn_fast_mp_montgomery_reduce.c
index d13452d..4d74630 100644
--- a/libtommath/bn_fast_mp_montgomery_reduce.c
+++ b/libtommath/bn_fast_mp_montgomery_reduce.c
@@ -167,6 +167,6 @@ int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_fast_s_mp_mul_digs.c b/libtommath/bn_fast_s_mp_mul_digs.c
index 18bea3f..59cfa38 100644
--- a/libtommath/bn_fast_s_mp_mul_digs.c
+++ b/libtommath/bn_fast_s_mp_mul_digs.c
@@ -102,6 +102,6 @@ int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_fast_s_mp_mul_high_digs.c b/libtommath/bn_fast_s_mp_mul_high_digs.c
index 8fd5117..16f056c 100644
--- a/libtommath/bn_fast_s_mp_mul_high_digs.c
+++ b/libtommath/bn_fast_s_mp_mul_high_digs.c
@@ -93,6 +93,6 @@ int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_fast_s_mp_sqr.c b/libtommath/bn_fast_s_mp_sqr.c
index 293c54a..8fa8958 100644
--- a/libtommath/bn_fast_s_mp_sqr.c
+++ b/libtommath/bn_fast_s_mp_sqr.c
@@ -109,6 +109,6 @@ int fast_s_mp_sqr (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_2expt.c b/libtommath/bn_mp_2expt.c
index eb5e664..36915bb 100644
--- a/libtommath/bn_mp_2expt.c
+++ b/libtommath/bn_mp_2expt.c
@@ -43,6 +43,6 @@ mp_2expt (mp_int * a, int b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_abs.c b/libtommath/bn_mp_abs.c
index 16662c0..f3ec518 100644
--- a/libtommath/bn_mp_abs.c
+++ b/libtommath/bn_mp_abs.c
@@ -38,6 +38,6 @@ mp_abs (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_add.c b/libtommath/bn_mp_add.c
index 0d91d24..2487aba 100644
--- a/libtommath/bn_mp_add.c
+++ b/libtommath/bn_mp_add.c
@@ -48,6 +48,6 @@ int mp_add (mp_int * a, mp_int * b, mp_int * c)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_add_d.c b/libtommath/bn_mp_add_d.c
index 6b9dbef..b7c8ea8 100644
--- a/libtommath/bn_mp_add_d.c
+++ b/libtommath/bn_mp_add_d.c
@@ -107,6 +107,6 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_addmod.c b/libtommath/bn_mp_addmod.c
index 800e10a..706e739 100644
--- a/libtommath/bn_mp_addmod.c
+++ b/libtommath/bn_mp_addmod.c
@@ -36,6 +36,6 @@ mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_and.c b/libtommath/bn_mp_and.c
index 6a18639..46c41a2 100644
--- a/libtommath/bn_mp_and.c
+++ b/libtommath/bn_mp_and.c
@@ -52,6 +52,6 @@ mp_and (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_clamp.c b/libtommath/bn_mp_clamp.c
index b392c10..149f1a8 100644
--- a/libtommath/bn_mp_clamp.c
+++ b/libtommath/bn_mp_clamp.c
@@ -39,6 +39,6 @@ mp_clamp (mp_int * a)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_clear.c b/libtommath/bn_mp_clear.c
index bf0873a..37ce1e1 100644
--- a/libtommath/bn_mp_clear.c
+++ b/libtommath/bn_mp_clear.c
@@ -39,6 +39,6 @@ mp_clear (mp_int * a)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_clear_multi.c b/libtommath/bn_mp_clear_multi.c
index e659cf8..583b1da 100644
--- a/libtommath/bn_mp_clear_multi.c
+++ b/libtommath/bn_mp_clear_multi.c
@@ -29,6 +29,6 @@ void mp_clear_multi(mp_int *mp, ...)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_cmp.c b/libtommath/bn_mp_cmp.c
index 6266a7e..538ba34 100644
--- a/libtommath/bn_mp_cmp.c
+++ b/libtommath/bn_mp_cmp.c
@@ -38,6 +38,6 @@ mp_cmp (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_cmp_d.c b/libtommath/bn_mp_cmp_d.c
index a1cdaa1..e66b1e4 100644
--- a/libtommath/bn_mp_cmp_d.c
+++ b/libtommath/bn_mp_cmp_d.c
@@ -39,6 +39,6 @@ int mp_cmp_d(mp_int * a, mp_digit b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_cmp_mag.c b/libtommath/bn_mp_cmp_mag.c
index b3839f0..d46a1be 100644
--- a/libtommath/bn_mp_cmp_mag.c
+++ b/libtommath/bn_mp_cmp_mag.c
@@ -50,6 +50,6 @@ int mp_cmp_mag (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_cnt_lsb.c b/libtommath/bn_mp_cnt_lsb.c
index 42d2219..1cf6159 100644
--- a/libtommath/bn_mp_cnt_lsb.c
+++ b/libtommath/bn_mp_cnt_lsb.c
@@ -48,6 +48,6 @@ int mp_cnt_lsb(mp_int *a)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_copy.c b/libtommath/bn_mp_copy.c
index 6f2ee59..1ba7381 100644
--- a/libtommath/bn_mp_copy.c
+++ b/libtommath/bn_mp_copy.c
@@ -63,6 +63,6 @@ mp_copy (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_count_bits.c b/libtommath/bn_mp_count_bits.c
index e2db126..bd12a87 100644
--- a/libtommath/bn_mp_count_bits.c
+++ b/libtommath/bn_mp_count_bits.c
@@ -40,6 +40,6 @@ mp_count_bits (mp_int * a)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_div.c b/libtommath/bn_mp_div.c
index 81d30eb..73f8779 100644
--- a/libtommath/bn_mp_div.c
+++ b/libtommath/bn_mp_div.c
@@ -290,6 +290,6 @@ LBL_Q:mp_clear (&q);
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_div_2.c b/libtommath/bn_mp_div_2.c
index 2004da7..a428869 100644
--- a/libtommath/bn_mp_div_2.c
+++ b/libtommath/bn_mp_div_2.c
@@ -63,6 +63,6 @@ int mp_div_2(mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_div_2d.c b/libtommath/bn_mp_div_2d.c
index a5b8494..b8e27ba 100644
--- a/libtommath/bn_mp_div_2d.c
+++ b/libtommath/bn_mp_div_2d.c
@@ -81,6 +81,6 @@ int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_div_3.c b/libtommath/bn_mp_div_3.c
index 6c79332..b716b22 100644
--- a/libtommath/bn_mp_div_3.c
+++ b/libtommath/bn_mp_div_3.c
@@ -74,6 +74,6 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_div_d.c b/libtommath/bn_mp_div_d.c
index aab298a..a2022ad 100644
--- a/libtommath/bn_mp_div_d.c
+++ b/libtommath/bn_mp_div_d.c
@@ -110,6 +110,6 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_dr_is_modulus.c b/libtommath/bn_mp_dr_is_modulus.c
index d4dbec6..f6d39c1 100644
--- a/libtommath/bn_mp_dr_is_modulus.c
+++ b/libtommath/bn_mp_dr_is_modulus.c
@@ -38,6 +38,6 @@ int mp_dr_is_modulus(mp_int *a)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_dr_reduce.c b/libtommath/bn_mp_dr_reduce.c
index 2005f3c..920b52e 100644
--- a/libtommath/bn_mp_dr_reduce.c
+++ b/libtommath/bn_mp_dr_reduce.c
@@ -91,6 +91,6 @@ top:
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_dr_setup.c b/libtommath/bn_mp_dr_setup.c
index 7f60c67..3aac30f 100644
--- a/libtommath/bn_mp_dr_setup.c
+++ b/libtommath/bn_mp_dr_setup.c
@@ -27,6 +27,6 @@ void mp_dr_setup(mp_int *a, mp_digit *d)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_exch.c b/libtommath/bn_mp_exch.c
index 8dd5180..5b5b359 100644
--- a/libtommath/bn_mp_exch.c
+++ b/libtommath/bn_mp_exch.c
@@ -29,6 +29,6 @@ mp_exch (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_export.c b/libtommath/bn_mp_export.c
index 58d71d5..2e71a27 100644
--- a/libtommath/bn_mp_export.c
+++ b/libtommath/bn_mp_export.c
@@ -83,6 +83,6 @@ int mp_export(void* rop, size_t* countp, int order, size_t size,
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_expt_d.c b/libtommath/bn_mp_expt_d.c
index 0a4b90b..d5ca456 100644
--- a/libtommath/bn_mp_expt_d.c
+++ b/libtommath/bn_mp_expt_d.c
@@ -23,6 +23,6 @@ int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_expt_d_ex.c b/libtommath/bn_mp_expt_d_ex.c
index 3bef24a..dced5a1 100644
--- a/libtommath/bn_mp_expt_d_ex.c
+++ b/libtommath/bn_mp_expt_d_ex.c
@@ -78,6 +78,6 @@ int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_exptmod.c b/libtommath/bn_mp_exptmod.c
index 697ef52..0998ce7 100644
--- a/libtommath/bn_mp_exptmod.c
+++ b/libtommath/bn_mp_exptmod.c
@@ -107,6 +107,6 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_exptmod_fast.c b/libtommath/bn_mp_exptmod_fast.c
index 312305e..3322544 100644
--- a/libtommath/bn_mp_exptmod_fast.c
+++ b/libtommath/bn_mp_exptmod_fast.c
@@ -316,6 +316,6 @@ LBL_M:
 #endif
 
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_exteuclid.c b/libtommath/bn_mp_exteuclid.c
index f941385..d9951ec 100644
--- a/libtommath/bn_mp_exteuclid.c
+++ b/libtommath/bn_mp_exteuclid.c
@@ -78,6 +78,6 @@ LBL_ERR:
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_fread.c b/libtommath/bn_mp_fread.c
index 6792437..4e38c6f 100644
--- a/libtommath/bn_mp_fread.c
+++ b/libtommath/bn_mp_fread.c
@@ -64,6 +64,6 @@ int mp_fread(mp_int *a, int radix, FILE *stream)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_fwrite.c b/libtommath/bn_mp_fwrite.c
index 44812d5..daa15db 100644
--- a/libtommath/bn_mp_fwrite.c
+++ b/libtommath/bn_mp_fwrite.c
@@ -49,6 +49,6 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_gcd.c b/libtommath/bn_mp_gcd.c
index fdefc1b..40e7034 100644
--- a/libtommath/bn_mp_gcd.c
+++ b/libtommath/bn_mp_gcd.c
@@ -100,6 +100,6 @@ LBL_U:mp_clear (&v);
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_get_int.c b/libtommath/bn_mp_get_int.c
index 4d8ecd2..f99ffb2 100644
--- a/libtommath/bn_mp_get_int.c
+++ b/libtommath/bn_mp_get_int.c
@@ -40,6 +40,6 @@ unsigned long mp_get_int(mp_int * a)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_grow.c b/libtommath/bn_mp_grow.c
index 7fbc5a2..3d47822 100644
--- a/libtommath/bn_mp_grow.c
+++ b/libtommath/bn_mp_grow.c
@@ -52,6 +52,6 @@ int mp_grow (mp_int * a, int size)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_import.c b/libtommath/bn_mp_import.c
index d9248fd..22e2342 100644
--- a/libtommath/bn_mp_import.c
+++ b/libtommath/bn_mp_import.c
@@ -68,6 +68,6 @@ int mp_import(mp_int* rop, size_t count, int order, size_t size,
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_init.c b/libtommath/bn_mp_init.c
index 8a26f09..0f628df 100644
--- a/libtommath/bn_mp_init.c
+++ b/libtommath/bn_mp_init.c
@@ -41,6 +41,6 @@ int mp_init (mp_int * a)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_init_copy.c b/libtommath/bn_mp_init_copy.c
index ab0e130..c918d46 100644
--- a/libtommath/bn_mp_init_copy.c
+++ b/libtommath/bn_mp_init_copy.c
@@ -32,6 +32,6 @@ int mp_init_copy (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_init_multi.c b/libtommath/bn_mp_init_multi.c
index 78ed62d..c121188 100644
--- a/libtommath/bn_mp_init_multi.c
+++ b/libtommath/bn_mp_init_multi.c
@@ -51,6 +51,6 @@ int mp_init_multi(mp_int *mp, ...)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_init_set.c b/libtommath/bn_mp_init_set.c
index 0b5cf36..24dc8bb 100644
--- a/libtommath/bn_mp_init_set.c
+++ b/libtommath/bn_mp_init_set.c
@@ -27,6 +27,6 @@ int mp_init_set (mp_int * a, mp_digit b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_init_set_int.c b/libtommath/bn_mp_init_set_int.c
index a9bf232..5a75e3e 100644
--- a/libtommath/bn_mp_init_set_int.c
+++ b/libtommath/bn_mp_init_set_int.c
@@ -26,6 +26,6 @@ int mp_init_set_int (mp_int * a, unsigned long b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_init_size.c b/libtommath/bn_mp_init_size.c
index 44b875f..4e30a2b 100644
--- a/libtommath/bn_mp_init_size.c
+++ b/libtommath/bn_mp_init_size.c
@@ -43,6 +43,6 @@ int mp_init_size (mp_int * a, int size)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_invmod.c b/libtommath/bn_mp_invmod.c
index c374fd2..75763ab 100644
--- a/libtommath/bn_mp_invmod.c
+++ b/libtommath/bn_mp_invmod.c
@@ -38,6 +38,6 @@ int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_invmod_slow.c b/libtommath/bn_mp_invmod_slow.c
index 879e971..cb7233d 100644
--- a/libtommath/bn_mp_invmod_slow.c
+++ b/libtommath/bn_mp_invmod_slow.c
@@ -170,6 +170,6 @@ LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_is_square.c b/libtommath/bn_mp_is_square.c
index 15e632e..56d19c0 100644
--- a/libtommath/bn_mp_is_square.c
+++ b/libtommath/bn_mp_is_square.c
@@ -104,6 +104,6 @@ ERR:mp_clear(&t);
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_jacobi.c b/libtommath/bn_mp_jacobi.c
index 4e6c474..8d147e0 100644
--- a/libtommath/bn_mp_jacobi.c
+++ b/libtommath/bn_mp_jacobi.c
@@ -112,6 +112,6 @@ LBL_A1:mp_clear (&a1);
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_karatsuba_mul.c b/libtommath/bn_mp_karatsuba_mul.c
index 307a0d9..31ed2e3 100644
--- a/libtommath/bn_mp_karatsuba_mul.c
+++ b/libtommath/bn_mp_karatsuba_mul.c
@@ -162,6 +162,6 @@ ERR:
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_karatsuba_sqr.c b/libtommath/bn_mp_karatsuba_sqr.c
index 3993cd9..33a2bee 100644
--- a/libtommath/bn_mp_karatsuba_sqr.c
+++ b/libtommath/bn_mp_karatsuba_sqr.c
@@ -116,6 +116,6 @@ ERR:
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_lcm.c b/libtommath/bn_mp_lcm.c
index b6a0ec1..d4bb1b6 100644
--- a/libtommath/bn_mp_lcm.c
+++ b/libtommath/bn_mp_lcm.c
@@ -55,6 +55,6 @@ LBL_T:
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_lshd.c b/libtommath/bn_mp_lshd.c
index b6cb111..e4f9abc 100644
--- a/libtommath/bn_mp_lshd.c
+++ b/libtommath/bn_mp_lshd.c
@@ -62,6 +62,6 @@ int mp_lshd (mp_int * a, int b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_mod.c b/libtommath/bn_mp_mod.c
index 0c9bc3e..0bc9530 100644
--- a/libtommath/bn_mp_mod.c
+++ b/libtommath/bn_mp_mod.c
@@ -43,6 +43,6 @@ mp_mod (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_mod_2d.c b/libtommath/bn_mp_mod_2d.c
index 1f2c47c..472aa58 100644
--- a/libtommath/bn_mp_mod_2d.c
+++ b/libtommath/bn_mp_mod_2d.c
@@ -50,6 +50,6 @@ mp_mod_2d (mp_int * a, int b, mp_int * c)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_mod_d.c b/libtommath/bn_mp_mod_d.c
index 4553cba..6fbc2c3 100644
--- a/libtommath/bn_mp_mod_d.c
+++ b/libtommath/bn_mp_mod_d.c
@@ -22,6 +22,6 @@ mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_montgomery_calc_normalization.c b/libtommath/bn_mp_montgomery_calc_normalization.c
index 2b11749..3e66d3f 100644
--- a/libtommath/bn_mp_montgomery_calc_normalization.c
+++ b/libtommath/bn_mp_montgomery_calc_normalization.c
@@ -54,6 +54,6 @@ int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_montgomery_reduce.c b/libtommath/bn_mp_montgomery_reduce.c
index d3746a6..b64c80a 100644
--- a/libtommath/bn_mp_montgomery_reduce.c
+++ b/libtommath/bn_mp_montgomery_reduce.c
@@ -113,6 +113,6 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_montgomery_setup.c b/libtommath/bn_mp_montgomery_setup.c
index c71d362..b15bafd 100644
--- a/libtommath/bn_mp_montgomery_setup.c
+++ b/libtommath/bn_mp_montgomery_setup.c
@@ -54,6 +54,6 @@ mp_montgomery_setup (mp_int * n, mp_digit * rho)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_mul.c b/libtommath/bn_mp_mul.c
index d81f68b..3819c0a 100644
--- a/libtommath/bn_mp_mul.c
+++ b/libtommath/bn_mp_mul.c
@@ -62,6 +62,6 @@ int mp_mul (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_mul_2.c b/libtommath/bn_mp_mul_2.c
index 20fb9d6..eba1450 100644
--- a/libtommath/bn_mp_mul_2.c
+++ b/libtommath/bn_mp_mul_2.c
@@ -77,6 +77,6 @@ int mp_mul_2(mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_mul_2d.c b/libtommath/bn_mp_mul_2d.c
index b5d3cae..798a1da 100644
--- a/libtommath/bn_mp_mul_2d.c
+++ b/libtommath/bn_mp_mul_2d.c
@@ -80,6 +80,6 @@ int mp_mul_2d (mp_int * a, int b, mp_int * c)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_mul_d.c b/libtommath/bn_mp_mul_d.c
index c0c24cd..fa918da 100644
--- a/libtommath/bn_mp_mul_d.c
+++ b/libtommath/bn_mp_mul_d.c
@@ -74,6 +74,6 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_mulmod.c b/libtommath/bn_mp_mulmod.c
index 375674f..3c7e41b 100644
--- a/libtommath/bn_mp_mulmod.c
+++ b/libtommath/bn_mp_mulmod.c
@@ -35,6 +35,6 @@ int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_n_root.c b/libtommath/bn_mp_n_root.c
index b7a4817..f8f9d13 100644
--- a/libtommath/bn_mp_n_root.c
+++ b/libtommath/bn_mp_n_root.c
@@ -25,6 +25,6 @@ int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_n_root_ex.c b/libtommath/bn_mp_n_root_ex.c
index c163c1d..28d6b18 100644
--- a/libtommath/bn_mp_n_root_ex.c
+++ b/libtommath/bn_mp_n_root_ex.c
@@ -127,6 +127,6 @@ LBL_T1:mp_clear (&t1);
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_neg.c b/libtommath/bn_mp_neg.c
index b8a014a..f488b57 100644
--- a/libtommath/bn_mp_neg.c
+++ b/libtommath/bn_mp_neg.c
@@ -35,6 +35,6 @@ int mp_neg (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_or.c b/libtommath/bn_mp_or.c
index fc303d2..aee9734 100644
--- a/libtommath/bn_mp_or.c
+++ b/libtommath/bn_mp_or.c
@@ -45,6 +45,6 @@ int mp_or (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_prime_fermat.c b/libtommath/bn_mp_prime_fermat.c
index 1b1300c..5b992b5 100644
--- a/libtommath/bn_mp_prime_fermat.c
+++ b/libtommath/bn_mp_prime_fermat.c
@@ -57,6 +57,6 @@ LBL_T:mp_clear (&t);
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_prime_is_divisible.c b/libtommath/bn_mp_prime_is_divisible.c
index b97390e..f97498f 100644
--- a/libtommath/bn_mp_prime_is_divisible.c
+++ b/libtommath/bn_mp_prime_is_divisible.c
@@ -45,6 +45,6 @@ int mp_prime_is_divisible (mp_int * a, int *result)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_prime_is_prime.c b/libtommath/bn_mp_prime_is_prime.c
index 4a36047..29571ba 100644
--- a/libtommath/bn_mp_prime_is_prime.c
+++ b/libtommath/bn_mp_prime_is_prime.c
@@ -78,6 +78,6 @@ LBL_B:mp_clear (&b);
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_prime_miller_rabin.c b/libtommath/bn_mp_prime_miller_rabin.c
index 569d78a..b168f01 100644
--- a/libtommath/bn_mp_prime_miller_rabin.c
+++ b/libtommath/bn_mp_prime_miller_rabin.c
@@ -98,6 +98,6 @@ LBL_N1:mp_clear (&n1);
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_prime_next_prime.c b/libtommath/bn_mp_prime_next_prime.c
index c0b7895..6515b1c 100644
--- a/libtommath/bn_mp_prime_next_prime.c
+++ b/libtommath/bn_mp_prime_next_prime.c
@@ -165,6 +165,6 @@ LBL_ERR:
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_prime_rabin_miller_trials.c b/libtommath/bn_mp_prime_rabin_miller_trials.c
index ad954cc..c98de6e 100644
--- a/libtommath/bn_mp_prime_rabin_miller_trials.c
+++ b/libtommath/bn_mp_prime_rabin_miller_trials.c
@@ -47,6 +47,6 @@ int mp_prime_rabin_miller_trials(int size)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_prime_random_ex.c b/libtommath/bn_mp_prime_random_ex.c
index 655e8ae..04a7cf7 100644
--- a/libtommath/bn_mp_prime_random_ex.c
+++ b/libtommath/bn_mp_prime_random_ex.c
@@ -119,6 +119,6 @@ error:
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_radix_size.c b/libtommath/bn_mp_radix_size.c
index e9cb55a..4a58e41 100644
--- a/libtommath/bn_mp_radix_size.c
+++ b/libtommath/bn_mp_radix_size.c
@@ -73,6 +73,6 @@ int mp_radix_size (mp_int * a, int radix, int *size)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_radix_smap.c b/libtommath/bn_mp_radix_smap.c
index 425e0e6..e351146 100644
--- a/libtommath/bn_mp_radix_smap.c
+++ b/libtommath/bn_mp_radix_smap.c
@@ -19,6 +19,6 @@
 const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_rand.c b/libtommath/bn_mp_rand.c
index 7c8f106..d5967c2 100644
--- a/libtommath/bn_mp_rand.c
+++ b/libtommath/bn_mp_rand.c
@@ -75,6 +75,6 @@ mp_rand (mp_int * a, int digits)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_read_radix.c b/libtommath/bn_mp_read_radix.c
index 6f2cc04..03384e3 100644
--- a/libtommath/bn_mp_read_radix.c
+++ b/libtommath/bn_mp_read_radix.c
@@ -80,6 +80,6 @@ int mp_read_radix (mp_int * a, const char *str, int radix)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_read_signed_bin.c b/libtommath/bn_mp_read_signed_bin.c
index 1448d21..a034fbd 100644
--- a/libtommath/bn_mp_read_signed_bin.c
+++ b/libtommath/bn_mp_read_signed_bin.c
@@ -36,6 +36,6 @@ int mp_read_signed_bin (mp_int * a, const unsigned char *b, int c)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_read_unsigned_bin.c b/libtommath/bn_mp_read_unsigned_bin.c
index b2e399d..27af256 100644
--- a/libtommath/bn_mp_read_unsigned_bin.c
+++ b/libtommath/bn_mp_read_unsigned_bin.c
@@ -50,6 +50,6 @@ int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_reduce.c b/libtommath/bn_mp_reduce.c
index c15b54e..a87fc30 100644
--- a/libtommath/bn_mp_reduce.c
+++ b/libtommath/bn_mp_reduce.c
@@ -95,6 +95,6 @@ CLEANUP:
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_reduce_2k.c b/libtommath/bn_mp_reduce_2k.c
index daea5e7..4f13b07 100644
--- a/libtommath/bn_mp_reduce_2k.c
+++ b/libtommath/bn_mp_reduce_2k.c
@@ -58,6 +58,6 @@ ERR:
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_reduce_2k_l.c b/libtommath/bn_mp_reduce_2k_l.c
index d6c2aa4..b41677a 100644
--- a/libtommath/bn_mp_reduce_2k_l.c
+++ b/libtommath/bn_mp_reduce_2k_l.c
@@ -59,6 +59,6 @@ ERR:
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_reduce_2k_setup.c b/libtommath/bn_mp_reduce_2k_setup.c
index f4650b4..a0c507f 100644
--- a/libtommath/bn_mp_reduce_2k_setup.c
+++ b/libtommath/bn_mp_reduce_2k_setup.c
@@ -42,6 +42,6 @@ int mp_reduce_2k_setup(mp_int *a, mp_digit *d)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_reduce_2k_setup_l.c b/libtommath/bn_mp_reduce_2k_setup_l.c
index 7945d6a..7083533 100644
--- a/libtommath/bn_mp_reduce_2k_setup_l.c
+++ b/libtommath/bn_mp_reduce_2k_setup_l.c
@@ -39,6 +39,6 @@ ERR:
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_reduce_is_2k.c b/libtommath/bn_mp_reduce_is_2k.c
index e68d704..2e61839 100644
--- a/libtommath/bn_mp_reduce_is_2k.c
+++ b/libtommath/bn_mp_reduce_is_2k.c
@@ -47,6 +47,6 @@ int mp_reduce_is_2k(mp_int *a)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_reduce_is_2k_l.c b/libtommath/bn_mp_reduce_is_2k_l.c
index 5426352..65ae46e 100644
--- a/libtommath/bn_mp_reduce_is_2k_l.c
+++ b/libtommath/bn_mp_reduce_is_2k_l.c
@@ -39,6 +39,6 @@ int mp_reduce_is_2k_l(mp_int *a)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_reduce_setup.c b/libtommath/bn_mp_reduce_setup.c
index d3ed42f..ffddbce 100644
--- a/libtommath/bn_mp_reduce_setup.c
+++ b/libtommath/bn_mp_reduce_setup.c
@@ -29,6 +29,6 @@ int mp_reduce_setup (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_rshd.c b/libtommath/bn_mp_rshd.c
index 6ea4f2f..f412d93 100644
--- a/libtommath/bn_mp_rshd.c
+++ b/libtommath/bn_mp_rshd.c
@@ -67,6 +67,6 @@ void mp_rshd (mp_int * a, int b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_set.c b/libtommath/bn_mp_set.c
index c10850d..8eec001 100644
--- a/libtommath/bn_mp_set.c
+++ b/libtommath/bn_mp_set.c
@@ -24,6 +24,6 @@ void mp_set (mp_int * a, mp_digit b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_set_int.c b/libtommath/bn_mp_set_int.c
index 3e9ae87..f456a3a 100644
--- a/libtommath/bn_mp_set_int.c
+++ b/libtommath/bn_mp_set_int.c
@@ -43,6 +43,6 @@ int mp_set_int (mp_int * a, unsigned long b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_set_long.c b/libtommath/bn_mp_set_long.c
index 680781b..fbf9f82 100644
--- a/libtommath/bn_mp_set_long.c
+++ b/libtommath/bn_mp_set_long.c
@@ -19,6 +19,6 @@
 MP_SET_XLONG(mp_set_long, unsigned long)
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_set_long_long.c b/libtommath/bn_mp_set_long_long.c
index 7fde01a..0a688c8 100644
--- a/libtommath/bn_mp_set_long_long.c
+++ b/libtommath/bn_mp_set_long_long.c
@@ -19,6 +19,6 @@
 MP_SET_XLONG(mp_set_long_long, unsigned long long)
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_shrink.c b/libtommath/bn_mp_shrink.c
index ef71874..9422a54 100644
--- a/libtommath/bn_mp_shrink.c
+++ b/libtommath/bn_mp_shrink.c
@@ -36,6 +36,6 @@ int mp_shrink (mp_int * a)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_signed_bin_size.c b/libtommath/bn_mp_signed_bin_size.c
index 261f036..bb63407 100644
--- a/libtommath/bn_mp_signed_bin_size.c
+++ b/libtommath/bn_mp_signed_bin_size.c
@@ -22,6 +22,6 @@ int mp_signed_bin_size (mp_int * a)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_sqr.c b/libtommath/bn_mp_sqr.c
index e0c2e85..299308d 100644
--- a/libtommath/bn_mp_sqr.c
+++ b/libtommath/bn_mp_sqr.c
@@ -55,6 +55,6 @@ mp_sqr (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_sqrmod.c b/libtommath/bn_mp_sqrmod.c
index 25ca55e..05ea9e0 100644
--- a/libtommath/bn_mp_sqrmod.c
+++ b/libtommath/bn_mp_sqrmod.c
@@ -36,6 +36,6 @@ mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_sqrt.c b/libtommath/bn_mp_sqrt.c
index 77078e8..72d98f0 100644
--- a/libtommath/bn_mp_sqrt.c
+++ b/libtommath/bn_mp_sqrt.c
@@ -76,6 +76,6 @@ E2: mp_clear(&t1);
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_sub.c b/libtommath/bn_mp_sub.c
index cf7d58e..67da8da 100644
--- a/libtommath/bn_mp_sub.c
+++ b/libtommath/bn_mp_sub.c
@@ -54,6 +54,6 @@ mp_sub (mp_int * a, mp_int * b, mp_int * c)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_sub_d.c b/libtommath/bn_mp_sub_d.c
index 482de39..a4e1b1c 100644
--- a/libtommath/bn_mp_sub_d.c
+++ b/libtommath/bn_mp_sub_d.c
@@ -88,6 +88,6 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_submod.c b/libtommath/bn_mp_submod.c
index f6098b3..ec7885c 100644
--- a/libtommath/bn_mp_submod.c
+++ b/libtommath/bn_mp_submod.c
@@ -37,6 +37,6 @@ mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_to_signed_bin.c b/libtommath/bn_mp_to_signed_bin.c
index 077b0bf..109d8f7 100644
--- a/libtommath/bn_mp_to_signed_bin.c
+++ b/libtommath/bn_mp_to_signed_bin.c
@@ -28,6 +28,6 @@ int mp_to_signed_bin (mp_int * a, unsigned char *b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_to_signed_bin_n.c b/libtommath/bn_mp_to_signed_bin_n.c
index 2edb8e0..bcbdf79 100644
--- a/libtommath/bn_mp_to_signed_bin_n.c
+++ b/libtommath/bn_mp_to_signed_bin_n.c
@@ -26,6 +26,6 @@ int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_to_unsigned_bin.c b/libtommath/bn_mp_to_unsigned_bin.c
index 203bf75..0ac9887 100644
--- a/libtommath/bn_mp_to_unsigned_bin.c
+++ b/libtommath/bn_mp_to_unsigned_bin.c
@@ -43,6 +43,6 @@ int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_to_unsigned_bin_n.c b/libtommath/bn_mp_to_unsigned_bin_n.c
index d28d7f4..19fe1e4 100644
--- a/libtommath/bn_mp_to_unsigned_bin_n.c
+++ b/libtommath/bn_mp_to_unsigned_bin_n.c
@@ -26,6 +26,6 @@ int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_toom_mul.c b/libtommath/bn_mp_toom_mul.c
index dc4f0a9..9a347fa 100644
--- a/libtommath/bn_mp_toom_mul.c
+++ b/libtommath/bn_mp_toom_mul.c
@@ -281,6 +281,6 @@ ERR:
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_toom_sqr.c b/libtommath/bn_mp_toom_sqr.c
index 06a568e..327a85f 100644
--- a/libtommath/bn_mp_toom_sqr.c
+++ b/libtommath/bn_mp_toom_sqr.c
@@ -223,6 +223,6 @@ ERR:
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_toradix.c b/libtommath/bn_mp_toradix.c
index 5bd9165..baf0e3b 100644
--- a/libtommath/bn_mp_toradix.c
+++ b/libtommath/bn_mp_toradix.c
@@ -70,6 +70,6 @@ int mp_toradix (mp_int * a, char *str, int radix)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_toradix_n.c b/libtommath/bn_mp_toradix_n.c
index d1587a3..881cb52 100644
--- a/libtommath/bn_mp_toradix_n.c
+++ b/libtommath/bn_mp_toradix_n.c
@@ -83,6 +83,6 @@ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_unsigned_bin_size.c b/libtommath/bn_mp_unsigned_bin_size.c
index e81cd82..74f6ed0 100644
--- a/libtommath/bn_mp_unsigned_bin_size.c
+++ b/libtommath/bn_mp_unsigned_bin_size.c
@@ -23,6 +23,6 @@ int mp_unsigned_bin_size (mp_int * a)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_xor.c b/libtommath/bn_mp_xor.c
index 1fc8bdf..9c83126 100644
--- a/libtommath/bn_mp_xor.c
+++ b/libtommath/bn_mp_xor.c
@@ -46,6 +46,6 @@ mp_xor (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_mp_zero.c b/libtommath/bn_mp_zero.c
index f607ce6..a76c2a9 100644
--- a/libtommath/bn_mp_zero.c
+++ b/libtommath/bn_mp_zero.c
@@ -31,6 +31,6 @@ void mp_zero (mp_int * a)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_prime_tab.c b/libtommath/bn_prime_tab.c
index 4354a48..77535c7 100644
--- a/libtommath/bn_prime_tab.c
+++ b/libtommath/bn_prime_tab.c
@@ -56,6 +56,6 @@ const mp_digit ltm_prime_tab[] = {
 };
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_reverse.c b/libtommath/bn_reverse.c
index 9811a81..9c00f2b 100644
--- a/libtommath/bn_reverse.c
+++ b/libtommath/bn_reverse.c
@@ -34,6 +34,6 @@ bn_reverse (unsigned char *s, int len)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_s_mp_add.c b/libtommath/bn_s_mp_add.c
index 5d886e7..2069d88 100644
--- a/libtommath/bn_s_mp_add.c
+++ b/libtommath/bn_s_mp_add.c
@@ -104,6 +104,6 @@ s_mp_add (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_s_mp_exptmod.c b/libtommath/bn_s_mp_exptmod.c
index 617b56c..8b10003 100644
--- a/libtommath/bn_s_mp_exptmod.c
+++ b/libtommath/bn_s_mp_exptmod.c
@@ -247,6 +247,6 @@ LBL_M:
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_s_mp_mul_digs.c b/libtommath/bn_s_mp_mul_digs.c
index cf2f50c..41bca7b 100644
--- a/libtommath/bn_s_mp_mul_digs.c
+++ b/libtommath/bn_s_mp_mul_digs.c
@@ -85,6 +85,6 @@ int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_s_mp_mul_high_digs.c b/libtommath/bn_s_mp_mul_high_digs.c
index 1d5b2f0..7e18680 100644
--- a/libtommath/bn_s_mp_mul_high_digs.c
+++ b/libtommath/bn_s_mp_mul_high_digs.c
@@ -76,6 +76,6 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_s_mp_sqr.c b/libtommath/bn_s_mp_sqr.c
index b85f1b8..3bcc7c9 100644
--- a/libtommath/bn_s_mp_sqr.c
+++ b/libtommath/bn_s_mp_sqr.c
@@ -79,6 +79,6 @@ int s_mp_sqr (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bn_s_mp_sub.c b/libtommath/bn_s_mp_sub.c
index ac3f785..260a95f 100644
--- a/libtommath/bn_s_mp_sub.c
+++ b/libtommath/bn_s_mp_sub.c
@@ -84,6 +84,6 @@ s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/bncore.c b/libtommath/bncore.c
index 8bd4681..b07c629 100644
--- a/libtommath/bncore.c
+++ b/libtommath/bncore.c
@@ -31,6 +31,6 @@ int     KARATSUBA_MUL_CUTOFF = 80,      /* Min. number of digits before Karatsub
         TOOM_SQR_CUTOFF      = 400; 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/tommath.h b/libtommath/tommath.h
index 0a065f6..4547488 100644
--- a/libtommath/tommath.h
+++ b/libtommath/tommath.h
@@ -565,6 +565,6 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream);
 #endif
 
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/tommath_private.h b/libtommath/tommath_private.h
index 407ebd5..4c5389c 100644
--- a/libtommath/tommath_private.h
+++ b/libtommath/tommath_private.h
@@ -118,6 +118,6 @@ int func_name (mp_int * a, type b)                       \
 #endif
 
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
diff --git a/libtommath/tommath_superclass.h b/libtommath/tommath_superclass.h
index 8f6ef03..2489a07 100644
--- a/libtommath/tommath_superclass.h
+++ b/libtommath/tommath_superclass.h
@@ -71,6 +71,6 @@
 
 #endif
 
-/* ref:         HEAD -> release/1.0.1, tag: v1.0.1-rc2 */
-/* git commit:  e8c27ba7df0efb90708029115c94d681dfa7812f */
-/* commit time: 2017-08-29 10:48:46 +0200 */
+/* ref:         tag: v1.0.1, master */
+/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
+/* commit time: 2017-08-29 22:27:36 +0200 */
-- 
cgit v0.12


From 3a2a78a48a0eeea16928dca431306167ed6cddaa Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Tue, 29 Aug 2017 21:16:54 +0000
Subject: Forgot a few files from libtommath 1.0.1

---
 libtommath/callgraph.txt   | 21404 +++++++++++++++++++++----------------------
 libtommath/changes.txt     |    18 +-
 libtommath/makefile        |   124 +-
 libtommath/makefile.shared |    25 +-
 4 files changed, 10698 insertions(+), 10873 deletions(-)

diff --git a/libtommath/callgraph.txt b/libtommath/callgraph.txt
index e98a910..52007c0 100644
--- a/libtommath/callgraph.txt
+++ b/libtommath/callgraph.txt
@@ -1,139 +1,156 @@
-BN_MP_KARATSUBA_MUL_C
-+--->BN_MP_MUL_C
-|   +--->BN_MP_TOOM_MUL_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MUL_2_C
+BNCORE_C
+
+
+BN_ERROR_C
+
+
+BN_FAST_MP_INVMOD_C
++--->BN_MP_INIT_MULTI_C
+|   +--->BN_MP_INIT_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_MOD_C
+|   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_INIT_C
+|   +--->BN_MP_DIV_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_SET_C
+|   |   +--->BN_MP_COUNT_BITS_C
+|   |   +--->BN_MP_ABS_C
+|   |   +--->BN_MP_MUL_2D_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_C
+|   |   +--->BN_MP_SUB_C
 |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SUB_C
+|   |   +--->BN_MP_ADD_C
 |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2_C
-|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_2D_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_INIT_COPY_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_LSHD_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_RSHD_C
 |   |   +--->BN_MP_MUL_D_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_3_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_ADD_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_MP_CLAMP_C
++--->BN_MP_SET_C
+|   +--->BN_MP_ZERO_C
++--->BN_MP_DIV_2_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_SUB_C
+|   +--->BN_S_MP_ADD_C
 |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_MUL_DIGS_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-+--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_INIT_C
-+--->BN_MP_CLAMP_C
-+--->BN_S_MP_ADD_C
-|   +--->BN_MP_GROW_C
++--->BN_MP_CMP_C
+|   +--->BN_MP_CMP_MAG_C
++--->BN_MP_CMP_D_C
 +--->BN_MP_ADD_C
+|   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
 |   +--->BN_MP_CMP_MAG_C
 |   +--->BN_S_MP_SUB_C
 |   |   +--->BN_MP_GROW_C
-+--->BN_S_MP_SUB_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_LSHD_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_ZERO_C
-+--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_MULTI_C
+|   +--->BN_MP_CLEAR_C
 
 
-BN_MP_ZERO_C
+BN_FAST_MP_MONTGOMERY_REDUCE_C
++--->BN_MP_GROW_C
++--->BN_MP_RSHD_C
+|   +--->BN_MP_ZERO_C
++--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
 
 
-BN_MP_SET_C
-+--->BN_MP_ZERO_C
+BN_FAST_S_MP_MUL_DIGS_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
 
 
-BN_MP_TO_SIGNED_BIN_C
-+--->BN_MP_TO_UNSIGNED_BIN_C
-|   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_DIV_2D_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CLEAR_C
+BN_FAST_S_MP_MUL_HIGH_DIGS_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
 
 
-BN_S_MP_SUB_C
+BN_FAST_S_MP_SQR_C
 +--->BN_MP_GROW_C
 +--->BN_MP_CLAMP_C
 
 
-BN_MP_JACOBI_C
-+--->BN_MP_CMP_D_C
-+--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_COPY_C
+BN_MP_2EXPT_C
++--->BN_MP_ZERO_C
++--->BN_MP_GROW_C
+
+
+BN_MP_ABS_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
+
+
+BN_MP_ADDMOD_C
++--->BN_MP_INIT_C
++--->BN_MP_ADD_C
+|   +--->BN_S_MP_ADD_C
 |   |   +--->BN_MP_GROW_C
-+--->BN_MP_CNT_LSB_C
-+--->BN_MP_DIV_2D_C
-|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
 |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_MOD_2D_C
 |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_RSHD_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
 +--->BN_MP_MOD_C
+|   +--->BN_MP_INIT_SIZE_C
 |   +--->BN_MP_DIV_C
 |   |   +--->BN_MP_CMP_MAG_C
 |   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_ZERO_C
 |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
 |   |   +--->BN_MP_SET_C
 |   |   +--->BN_MP_COUNT_BITS_C
 |   |   +--->BN_MP_ABS_C
@@ -150,17 +167,14 @@ BN_MP_JACOBI_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_EXCH_C
 |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_INIT_COPY_C
 |   |   +--->BN_MP_LSHD_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_RSHD_C
@@ -169,701 +183,934 @@ BN_MP_JACOBI_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_CLEAR_C
 |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_ADD_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_CLEAR_C
 
 
-BN_MP_INIT_COPY_C
-+--->BN_MP_INIT_SIZE_C
-+--->BN_MP_COPY_C
+BN_MP_ADD_C
++--->BN_S_MP_ADD_C
 |   +--->BN_MP_GROW_C
-
-
-BN_MP_ABS_C
-+--->BN_MP_COPY_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
 |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
 
 
-BN_MP_RADIX_SMAP_C
-
-
-BN_MP_EXCH_C
+BN_MP_ADD_D_C
++--->BN_MP_GROW_C
++--->BN_MP_SUB_D_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_CLAMP_C
 
 
-BN_MP_EXPORT_C
+BN_MP_AND_C
 +--->BN_MP_INIT_COPY_C
 |   +--->BN_MP_INIT_SIZE_C
 |   +--->BN_MP_COPY_C
 |   |   +--->BN_MP_GROW_C
-+--->BN_MP_COUNT_BITS_C
-+--->BN_MP_DIV_2D_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_MOD_2D_C
-|   |   +--->BN_MP_CLAMP_C
 |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_RSHD_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
 +--->BN_MP_CLEAR_C
 
 
-BN_MP_TO_UNSIGNED_BIN_N_C
-+--->BN_MP_UNSIGNED_BIN_SIZE_C
-|   +--->BN_MP_COUNT_BITS_C
-+--->BN_MP_TO_UNSIGNED_BIN_C
-|   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_DIV_2D_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CLEAR_C
+BN_MP_CLAMP_C
 
 
-BN_MP_TO_SIGNED_BIN_N_C
-+--->BN_MP_SIGNED_BIN_SIZE_C
-|   +--->BN_MP_UNSIGNED_BIN_SIZE_C
-|   |   +--->BN_MP_COUNT_BITS_C
-+--->BN_MP_TO_SIGNED_BIN_C
-|   +--->BN_MP_TO_UNSIGNED_BIN_C
-|   |   +--->BN_MP_INIT_COPY_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
+BN_MP_CLEAR_C
 
 
-BN_MP_LCM_C
+BN_MP_CLEAR_MULTI_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_CMP_C
++--->BN_MP_CMP_MAG_C
+
+
+BN_MP_CMP_D_C
+
+
+BN_MP_CMP_MAG_C
+
+
+BN_MP_CNT_LSB_C
+
+
+BN_MP_COPY_C
++--->BN_MP_GROW_C
+
+
+BN_MP_COUNT_BITS_C
+
+
+BN_MP_DIV_2D_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_ZERO_C
++--->BN_MP_MOD_2D_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_RSHD_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_DIV_2_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_DIV_3_C
++--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_DIV_C
++--->BN_MP_CMP_MAG_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_ZERO_C
 +--->BN_MP_INIT_MULTI_C
 |   +--->BN_MP_INIT_C
 |   +--->BN_MP_CLEAR_C
-+--->BN_MP_GCD_C
-|   +--->BN_MP_ABS_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_CNT_LSB_C
-|   +--->BN_MP_DIV_2D_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
++--->BN_MP_SET_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_ABS_C
++--->BN_MP_MUL_2D_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_LSHD_C
 |   |   +--->BN_MP_RSHD_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_C
++--->BN_MP_SUB_C
+|   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_MP_EXCH_C
 |   +--->BN_S_MP_SUB_C
 |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_MUL_2D_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
++--->BN_MP_ADD_C
+|   +--->BN_S_MP_ADD_C
 |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
 |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_CMP_MAG_C
-+--->BN_MP_DIV_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_SET_C
-|   +--->BN_MP_COUNT_BITS_C
-|   +--->BN_MP_ABS_C
-|   +--->BN_MP_MUL_2D_C
+|   +--->BN_S_MP_SUB_C
 |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_RSHD_C
 |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_C
-|   +--->BN_MP_SUB_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_ADD_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_DIV_2D_C
-|   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_RSHD_C
++--->BN_MP_DIV_2D_C
+|   +--->BN_MP_MOD_2D_C
 |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CLEAR_MULTI_C
-|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_RSHD_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_MULTI_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_INIT_C
++--->BN_MP_INIT_C
++--->BN_MP_INIT_COPY_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_LSHD_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_RSHD_C
++--->BN_MP_RSHD_C
++--->BN_MP_MUL_D_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_DIV_D_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_DIV_2D_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_MOD_2D_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_RSHD_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_3_C
 |   +--->BN_MP_INIT_SIZE_C
 |   |   +--->BN_MP_INIT_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_SIZE_C
 |   +--->BN_MP_INIT_C
-|   +--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_LSHD_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_DR_IS_MODULUS_C
+
+
+BN_MP_DR_REDUCE_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+
+
+BN_MP_DR_SETUP_C
+
+
+BN_MP_EXCH_C
+
+
+BN_MP_EXPORT_C
++--->BN_MP_INIT_COPY_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_COPY_C
 |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_RSHD_C
-|   +--->BN_MP_RSHD_C
-|   +--->BN_MP_MUL_D_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_DIV_2D_C
+|   +--->BN_MP_COPY_C
 |   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_MOD_2D_C
 |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_RSHD_C
 |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_MUL_C
-|   +--->BN_MP_TOOM_MUL_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MUL_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_EXPTMOD_C
++--->BN_MP_INIT_C
++--->BN_MP_INVMOD_C
+|   +--->BN_MP_CMP_D_C
+|   +--->BN_FAST_MP_INVMOD_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_MOD_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_DIV_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   +--->BN_MP_ABS_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_DIV_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SUB_C
+|   |   +--->BN_MP_CMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_MP_ADD_C
 |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_3_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_INVMOD_SLOW_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_MOD_C
 |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_INIT_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_DIV_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   +--->BN_MP_ABS_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_KARATSUBA_MUL_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_DIV_2_C
 |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_MUL_DIGS_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_MP_CMP_MAG_C
 |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-+--->BN_MP_CLEAR_MULTI_C
-|   +--->BN_MP_CLEAR_C
-
-
-BN_MP_CMP_MAG_C
-
-
-BN_MP_PRIME_RABIN_MILLER_TRIALS_C
-
-
-BN_MP_MUL_2D_C
-+--->BN_MP_COPY_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_GROW_C
-+--->BN_MP_LSHD_C
-|   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_ZERO_C
-+--->BN_MP_CLAMP_C
-
-
-BN_MP_MUL_C
-+--->BN_MP_TOOM_MUL_C
-|   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_MOD_2D_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
++--->BN_MP_ABS_C
 |   +--->BN_MP_COPY_C
 |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_ZERO_C
-|   +--->BN_MP_MUL_2_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_ADD_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_SUB_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
++--->BN_MP_CLEAR_MULTI_C
++--->BN_MP_REDUCE_IS_2K_L_C
++--->BN_S_MP_EXPTMOD_C
+|   +--->BN_MP_COUNT_BITS_C
+|   +--->BN_MP_REDUCE_SETUP_C
+|   |   +--->BN_MP_2EXPT_C
+|   |   |   +--->BN_MP_ZERO_C
 |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_DIV_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_DIV_2_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_MUL_2D_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_MUL_D_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_DIV_3_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_LSHD_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLEAR_MULTI_C
-|   |   +--->BN_MP_CLEAR_C
-+--->BN_MP_KARATSUBA_MUL_C
-|   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_ADD_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_LSHD_C
-|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_REDUCE_C
+|   |   +--->BN_MP_INIT_COPY_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_RSHD_C
 |   |   |   +--->BN_MP_ZERO_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_FAST_S_MP_MUL_DIGS_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_S_MP_MUL_DIGS_C
-|   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CLEAR_C
-
-
-BN_MP_SQR_C
-+--->BN_MP_TOOM_SQR_C
-|   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_MOD_2D_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_ZERO_C
-|   +--->BN_MP_MUL_2_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_ADD_C
-|   |   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_MUL_C
+|   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_S_MP_MUL_HIGH_DIGS_C
+|   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_D_C
+|   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
 |   |   +--->BN_S_MP_SUB_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_SUB_C
-|   |   +--->BN_S_MP_ADD_C
+|   +--->BN_MP_REDUCE_2K_SETUP_L_C
+|   |   +--->BN_MP_2EXPT_C
+|   |   |   +--->BN_MP_ZERO_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
 |   |   +--->BN_S_MP_SUB_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_DIV_2_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_MUL_2D_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_MUL_D_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_DIV_3_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_LSHD_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLEAR_MULTI_C
-|   |   +--->BN_MP_CLEAR_C
-+--->BN_MP_KARATSUBA_SQR_C
-|   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_LSHD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_RSHD_C
+|   +--->BN_MP_REDUCE_2K_L_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_ZERO_C
-|   +--->BN_MP_ADD_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_FAST_S_MP_SQR_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_S_MP_SQR_C
-|   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CLEAR_C
-
-
-BN_MP_INIT_C
-
-
-BN_MP_2EXPT_C
-+--->BN_MP_ZERO_C
-+--->BN_MP_GROW_C
-
-
-BN_MP_SIGNED_BIN_SIZE_C
-+--->BN_MP_UNSIGNED_BIN_SIZE_C
-|   +--->BN_MP_COUNT_BITS_C
-
-
-BN_MP_OR_C
-+--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-+--->BN_MP_CLAMP_C
-+--->BN_MP_EXCH_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_MOD_C
-+--->BN_MP_INIT_C
-+--->BN_MP_DIV_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_SET_C
-|   +--->BN_MP_COUNT_BITS_C
-|   +--->BN_MP_ABS_C
-|   +--->BN_MP_MUL_2D_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_C
-|   +--->BN_MP_SUB_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_ADD_C
+|   |   +--->BN_MP_MUL_C
+|   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
 |   |   +--->BN_S_MP_ADD_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_MAG_C
 |   |   +--->BN_S_MP_SUB_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_DIV_2D_C
-|   |   +--->BN_MP_MOD_2D_C
+|   +--->BN_MP_MOD_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_DIV_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CLEAR_MULTI_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_LSHD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_RSHD_C
-|   +--->BN_MP_RSHD_C
-|   +--->BN_MP_MUL_D_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_CLEAR_C
-+--->BN_MP_EXCH_C
-+--->BN_MP_ADD_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-
-
-BN_MP_DIV_C
-+--->BN_MP_CMP_MAG_C
-+--->BN_MP_COPY_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_ZERO_C
-+--->BN_MP_INIT_MULTI_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_SET_C
-+--->BN_MP_COUNT_BITS_C
-+--->BN_MP_ABS_C
-+--->BN_MP_MUL_2D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_LSHD_C
-|   |   +--->BN_MP_RSHD_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_CMP_C
-+--->BN_MP_SUB_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_ADD_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_COPY_C
 |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_DIV_2D_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_MOD_2D_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_RSHD_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-+--->BN_MP_EXCH_C
-+--->BN_MP_CLEAR_MULTI_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_INIT_C
-+--->BN_MP_INIT_C
-+--->BN_MP_INIT_COPY_C
-+--->BN_MP_LSHD_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_RSHD_C
-+--->BN_MP_RSHD_C
-+--->BN_MP_MUL_D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_CLAMP_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_INIT_SET_C
-+--->BN_MP_INIT_C
-+--->BN_MP_SET_C
-|   +--->BN_MP_ZERO_C
-
-
-BN_MP_PRIME_IS_PRIME_C
-+--->BN_MP_CMP_D_C
-+--->BN_MP_PRIME_IS_DIVISIBLE_C
-|   +--->BN_MP_MOD_D_C
-|   |   +--->BN_MP_DIV_D_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_DIV_2D_C
+|   +--->BN_MP_SQR_C
+|   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_INIT_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_SQR_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   +--->BN_MP_MUL_C
+|   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_DIV_3_C
 |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_INIT_C
 |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_MUL_DIGS_C
 |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_INIT_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_C
-+--->BN_MP_INIT_C
-+--->BN_MP_SET_C
-|   +--->BN_MP_ZERO_C
-+--->BN_MP_PRIME_MILLER_RABIN_C
-|   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_COPY_C
+|   +--->BN_MP_SET_C
+|   |   +--->BN_MP_ZERO_C
+|   +--->BN_MP_EXCH_C
++--->BN_MP_DR_IS_MODULUS_C
++--->BN_MP_REDUCE_IS_2K_C
+|   +--->BN_MP_REDUCE_2K_C
+|   |   +--->BN_MP_COUNT_BITS_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_D_C
 |   |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_SUB_D_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_D_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CNT_LSB_C
-|   +--->BN_MP_DIV_2D_C
-|   |   +--->BN_MP_COPY_C
+|   |   +--->BN_S_MP_ADD_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MOD_2D_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_COUNT_BITS_C
++--->BN_MP_EXPTMOD_FAST_C
+|   +--->BN_MP_COUNT_BITS_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_MONTGOMERY_SETUP_C
+|   +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+|   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_ZERO_C
 |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_EXPTMOD_C
-|   |   +--->BN_MP_INVMOD_C
-|   |   |   +--->BN_FAST_MP_INVMOD_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_MOD_C
-|   |   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   |   |   +--->BN_MP_ABS_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   +--->BN_MP_MONTGOMERY_REDUCE_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   +--->BN_MP_DR_SETUP_C
+|   +--->BN_MP_DR_REDUCE_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   +--->BN_MP_REDUCE_2K_SETUP_C
+|   |   +--->BN_MP_2EXPT_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_REDUCE_2K_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+|   |   +--->BN_MP_2EXPT_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MUL_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_MULMOD_C
+|   |   +--->BN_MP_MUL_C
+|   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -871,9 +1118,7 @@ BN_MP_PRIME_IS_PRIME_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -881,326 +1126,159 @@ BN_MP_PRIME_IS_PRIME_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_INVMOD_SLOW_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_MOD_C
-|   |   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   |   |   +--->BN_MP_ABS_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_MOD_C
+|   |   |   +--->BN_MP_DIV_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_ABS_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   +--->BN_MP_REDUCE_IS_2K_L_C
-|   |   +--->BN_S_MP_EXPTMOD_C
-|   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   +--->BN_MP_REDUCE_SETUP_C
-|   |   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_REDUCE_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MUL_C
-|   |   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_S_MP_MUL_HIGH_DIGS_C
-|   |   |   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+|   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_SET_C
+|   |   +--->BN_MP_ZERO_C
+|   +--->BN_MP_MOD_C
+|   |   +--->BN_MP_DIV_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_REDUCE_2K_SETUP_L_C
-|   |   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_REDUCE_2K_L_C
-|   |   |   |   +--->BN_MP_MUL_C
-|   |   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_SQR_C
+|   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
 |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -1208,188 +1286,7 @@ BN_MP_PRIME_IS_PRIME_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MOD_C
-|   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_SQR_C
-|   |   |   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_FAST_S_MP_SQR_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SQR_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_MUL_C
-|   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_DR_IS_MODULUS_C
-|   |   +--->BN_MP_REDUCE_IS_2K_C
-|   |   |   +--->BN_MP_REDUCE_2K_C
-|   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SUB_C
 |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -1397,41 +1294,58 @@ BN_MP_PRIME_IS_PRIME_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   +--->BN_MP_EXPTMOD_FAST_C
-|   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   +--->BN_MP_MONTGOMERY_SETUP_C
-|   |   |   +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+|   |   |   +--->BN_MP_DIV_2_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_MONTGOMERY_REDUCE_C
+|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_ADD_C
 |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_DR_SETUP_C
-|   |   |   +--->BN_MP_DR_REDUCE_C
-|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_SQR_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   +--->BN_MP_MUL_C
+|   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_REDUCE_2K_SETUP_C
-|   |   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_REDUCE_2K_C
-|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SUB_C
 |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -1439,423 +1353,453 @@ BN_MP_PRIME_IS_PRIME_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
-|   |   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
 |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MULMOD_C
-|   |   |   |   +--->BN_MP_MUL_C
-|   |   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_MOD_C
-|   |   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MOD_C
-|   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   +--->BN_MP_EXCH_C
+
+
+BN_MP_EXPTMOD_FAST_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_INIT_C
++--->BN_MP_CLEAR_C
++--->BN_MP_MONTGOMERY_SETUP_C
++--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_ZERO_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
++--->BN_MP_MONTGOMERY_REDUCE_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_ZERO_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
++--->BN_MP_DR_SETUP_C
++--->BN_MP_DR_REDUCE_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
++--->BN_MP_REDUCE_2K_SETUP_C
+|   +--->BN_MP_INIT_C
+|   +--->BN_MP_2EXPT_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
++--->BN_MP_REDUCE_2K_C
+|   +--->BN_MP_INIT_C
+|   +--->BN_MP_DIV_2D_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_MUL_D_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
++--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+|   +--->BN_MP_2EXPT_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_SET_C
+|   |   +--->BN_MP_ZERO_C
+|   +--->BN_MP_MUL_2_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
++--->BN_MP_MULMOD_C
+|   +--->BN_MP_MUL_C
+|   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_INIT_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_SQR_C
-|   |   |   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SQR_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_MUL_C
-|   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   +--->BN_MP_SQRMOD_C
-|   |   +--->BN_MP_SQR_C
-|   |   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   +--->BN_MP_MOD_C
+|   |   +--->BN_MP_DIV_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_INIT_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_ABS_C
+|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SQR_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
++--->BN_MP_SET_C
+|   +--->BN_MP_ZERO_C
++--->BN_MP_MOD_C
+|   +--->BN_MP_DIV_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_ABS_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_ADD_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_SQR_C
+|   +--->BN_MP_TOOM_SQR_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MUL_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_3_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   +--->BN_MP_KARATSUBA_SQR_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   +--->BN_FAST_S_MP_SQR_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_S_MP_SQR_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
++--->BN_MP_MUL_C
+|   +--->BN_MP_TOOM_MUL_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MUL_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_3_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   +--->BN_MP_KARATSUBA_MUL_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_S_MP_MUL_DIGS_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
++--->BN_MP_EXCH_C
+
+
+BN_MP_EXPT_D_C
++--->BN_MP_EXPT_D_EX_C
+|   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_MOD_C
-|   |   |   +--->BN_MP_DIV_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   +--->BN_MP_SET_C
+|   |   +--->BN_MP_ZERO_C
+|   +--->BN_MP_MUL_C
+|   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   +--->BN_MP_ABS_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_MP_SUB_C
 |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -1863,316 +1807,224 @@ BN_MP_PRIME_IS_PRIME_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_CLEAR_C
-
-
-BN_FAST_S_MP_SQR_C
-+--->BN_MP_GROW_C
-+--->BN_MP_CLAMP_C
-
-
-BN_MP_UNSIGNED_BIN_SIZE_C
-+--->BN_MP_COUNT_BITS_C
-
-
-BN_MP_INIT_SIZE_C
-+--->BN_MP_INIT_C
-
-
-BN_FAST_S_MP_MUL_DIGS_C
-+--->BN_MP_GROW_C
-+--->BN_MP_CLAMP_C
-
-
-BN_MP_REDUCE_IS_2K_L_C
+|   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_SQR_C
+|   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_SQR_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
 
 
-BN_MP_REDUCE_IS_2K_C
-+--->BN_MP_REDUCE_2K_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_COUNT_BITS_C
-|   +--->BN_MP_DIV_2D_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ZERO_C
+BN_MP_EXPT_D_EX_C
++--->BN_MP_INIT_COPY_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_SET_C
+|   +--->BN_MP_ZERO_C
++--->BN_MP_MUL_C
+|   +--->BN_MP_TOOM_MUL_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
 |   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MUL_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_3_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_KARATSUBA_MUL_C
+|   |   +--->BN_MP_INIT_SIZE_C
 |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_MUL_D_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_ADD_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_FAST_S_MP_MUL_DIGS_C
 |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
+|   +--->BN_S_MP_MUL_DIGS_C
+|   |   +--->BN_MP_INIT_SIZE_C
 |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_COUNT_BITS_C
-
-
-BN_MP_SUB_C
-+--->BN_S_MP_ADD_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_CMP_MAG_C
-+--->BN_S_MP_SUB_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-
-
-BN_MP_REDUCE_2K_SETUP_C
-+--->BN_MP_INIT_C
-+--->BN_MP_COUNT_BITS_C
-+--->BN_MP_2EXPT_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_CLEAR_C
-+--->BN_S_MP_SUB_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-
-
-BN_MP_DIV_2D_C
-+--->BN_MP_COPY_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_ZERO_C
-+--->BN_MP_INIT_C
-+--->BN_MP_MOD_2D_C
-|   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
 +--->BN_MP_CLEAR_C
-+--->BN_MP_RSHD_C
-+--->BN_MP_CLAMP_C
-+--->BN_MP_EXCH_C
-
-
-BN_MP_DR_REDUCE_C
-+--->BN_MP_GROW_C
-+--->BN_MP_CLAMP_C
-+--->BN_MP_CMP_MAG_C
-+--->BN_S_MP_SUB_C
-
-
-BN_MP_SQRT_C
-+--->BN_MP_N_ROOT_C
-|   +--->BN_MP_N_ROOT_EX_C
-|   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_SET_C
++--->BN_MP_SQR_C
+|   +--->BN_MP_TOOM_SQR_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   +--->BN_MP_MOD_2D_C
 |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_EXPT_D_EX_C
-|   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_MUL_C
-|   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_SQR_C
-|   |   |   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_FAST_S_MP_SQR_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SQR_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_MUL_C
-|   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MUL_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_CLEAR_C
 |   |   +--->BN_MP_SUB_C
 |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
@@ -2181,74 +2033,62 @@ BN_MP_SQRT_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_MUL_D_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   +--->BN_MP_ABS_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_DIV_3_C
 |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_RSHD_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_CMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_MP_SUB_D_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_LSHD_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-+--->BN_MP_ZERO_C
-+--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   +--->BN_MP_KARATSUBA_SQR_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   +--->BN_FAST_S_MP_SQR_C
 |   |   +--->BN_MP_GROW_C
-+--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_S_MP_SQR_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+
+
+BN_MP_EXTEUCLID_C
++--->BN_MP_INIT_MULTI_C
+|   +--->BN_MP_INIT_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_SET_C
+|   +--->BN_MP_ZERO_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
 +--->BN_MP_DIV_C
 |   +--->BN_MP_CMP_MAG_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_SET_C
+|   +--->BN_MP_ZERO_C
 |   +--->BN_MP_COUNT_BITS_C
 |   +--->BN_MP_ABS_C
 |   +--->BN_MP_MUL_2D_C
 |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_RSHD_C
 |   |   +--->BN_MP_CLAMP_C
 |   +--->BN_MP_CMP_C
 |   +--->BN_MP_SUB_C
@@ -2268,49 +2108,30 @@ BN_MP_SQRT_C
 |   +--->BN_MP_DIV_2D_C
 |   |   +--->BN_MP_MOD_2D_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_RSHD_C
 |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
 |   +--->BN_MP_EXCH_C
 |   +--->BN_MP_CLEAR_MULTI_C
 |   |   +--->BN_MP_CLEAR_C
 |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_INIT_C
+|   +--->BN_MP_INIT_C
+|   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_CLEAR_C
 |   +--->BN_MP_LSHD_C
 |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_RSHD_C
+|   +--->BN_MP_RSHD_C
 |   +--->BN_MP_MUL_D_C
 |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_CLAMP_C
 |   +--->BN_MP_CLAMP_C
 |   +--->BN_MP_CLEAR_C
-+--->BN_MP_ADD_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_DIV_2_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_CMP_MAG_C
-+--->BN_MP_EXCH_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_MULMOD_C
-+--->BN_MP_INIT_C
 +--->BN_MP_MUL_C
 |   +--->BN_MP_TOOM_MUL_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
 |   |   +--->BN_MP_MOD_2D_C
 |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_RSHD_C
 |   |   |   +--->BN_MP_ZERO_C
 |   |   +--->BN_MP_MUL_2_C
@@ -2343,6 +2164,7 @@ BN_MP_MULMOD_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_DIV_3_C
 |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_INIT_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_CLEAR_C
@@ -2352,6 +2174,7 @@ BN_MP_MULMOD_C
 |   |   |   +--->BN_MP_CLEAR_C
 |   +--->BN_MP_KARATSUBA_MUL_C
 |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
 |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_S_MP_ADD_C
 |   |   |   +--->BN_MP_GROW_C
@@ -2371,84 +2194,205 @@ BN_MP_MULMOD_C
 |   |   +--->BN_MP_CLAMP_C
 |   +--->BN_S_MP_MUL_DIGS_C
 |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
 |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_EXCH_C
 |   |   +--->BN_MP_CLEAR_C
-+--->BN_MP_CLEAR_C
-+--->BN_MP_MOD_C
-|   +--->BN_MP_DIV_C
-|   |   +--->BN_MP_CMP_MAG_C
++--->BN_MP_SUB_C
+|   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
++--->BN_MP_NEG_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_MULTI_C
+|   +--->BN_MP_CLEAR_C
+
+
+BN_MP_FREAD_C
++--->BN_MP_ZERO_C
++--->BN_MP_MUL_D_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_ADD_D_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_SUB_D_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_D_C
+
+
+BN_MP_FWRITE_C
++--->BN_MP_RADIX_SIZE_C
+|   +--->BN_MP_COUNT_BITS_C
+|   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_INIT_SIZE_C
 |   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_SET_C
-|   |   +--->BN_MP_COUNT_BITS_C
-|   |   +--->BN_MP_ABS_C
-|   |   +--->BN_MP_MUL_2D_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_DIV_D_C
+|   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_ZERO_C
 |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_RSHD_C
 |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_3_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_TORADIX_C
+|   +--->BN_MP_INIT_COPY_C
 |   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_MUL_D_C
+|   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_ADD_C
-|   |   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_DIV_D_C
+|   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_DIV_3_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_CLEAR_C
 
 
-BN_MP_INVMOD_C
-+--->BN_FAST_MP_INVMOD_C
-|   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_CLEAR_C
+BN_MP_GCD_C
++--->BN_MP_ABS_C
 |   +--->BN_MP_COPY_C
 |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_MOD_C
-|   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_DIV_C
-|   |   |   +--->BN_MP_CMP_MAG_C
++--->BN_MP_INIT_COPY_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_CNT_LSB_C
++--->BN_MP_DIV_2D_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_MOD_2D_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_RSHD_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_MP_EXCH_C
++--->BN_S_MP_SUB_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_2D_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_RSHD_C
 |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_SET_C
-|   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   +--->BN_MP_ABS_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_GET_INT_C
+
+
+BN_MP_GET_LONG_C
+
+
+BN_MP_GET_LONG_LONG_C
+
+
+BN_MP_GROW_C
+
+
+BN_MP_IMPORT_C
++--->BN_MP_ZERO_C
++--->BN_MP_MUL_2D_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_RSHD_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_INIT_C
+
+
+BN_MP_INIT_COPY_C
++--->BN_MP_INIT_SIZE_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_INIT_MULTI_C
++--->BN_MP_INIT_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_INIT_SET_C
++--->BN_MP_INIT_C
++--->BN_MP_SET_C
+|   +--->BN_MP_ZERO_C
+
+
+BN_MP_INIT_SET_INT_C
++--->BN_MP_INIT_C
++--->BN_MP_SET_INT_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_MUL_2D_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLAMP_C
+
+
+BN_MP_INIT_SIZE_C
++--->BN_MP_INIT_C
+
+
+BN_MP_INVMOD_C
++--->BN_MP_CMP_D_C
++--->BN_FAST_MP_INVMOD_C
+|   +--->BN_MP_INIT_MULTI_C
+|   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_MOD_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_DIV_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   +--->BN_MP_ABS_C
 |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_LSHD_C
@@ -2472,15 +2416,14 @@ BN_MP_INVMOD_C
 |   |   |   +--->BN_MP_DIV_2D_C
 |   |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_CLEAR_MULTI_C
 |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
 |   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_RSHD_C
@@ -2515,7 +2458,6 @@ BN_MP_INVMOD_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   +--->BN_MP_CMP_C
 |   |   +--->BN_MP_CMP_MAG_C
-|   +--->BN_MP_CMP_D_C
 |   +--->BN_MP_ADD_C
 |   |   +--->BN_S_MP_ADD_C
 |   |   |   +--->BN_MP_GROW_C
@@ -2532,7 +2474,8 @@ BN_MP_INVMOD_C
 |   |   +--->BN_MP_INIT_C
 |   |   +--->BN_MP_CLEAR_C
 |   +--->BN_MP_MOD_C
-|   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
 |   |   +--->BN_MP_DIV_C
 |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   +--->BN_MP_COPY_C
@@ -2564,15 +2507,14 @@ BN_MP_INVMOD_C
 |   |   |   +--->BN_MP_DIV_2D_C
 |   |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_CLEAR_MULTI_C
 |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
 |   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_RSHD_C
@@ -2617,264 +2559,363 @@ BN_MP_INVMOD_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   +--->BN_MP_CMP_C
 |   |   +--->BN_MP_CMP_MAG_C
-|   +--->BN_MP_CMP_D_C
 |   +--->BN_MP_CMP_MAG_C
 |   +--->BN_MP_EXCH_C
 |   +--->BN_MP_CLEAR_MULTI_C
 |   |   +--->BN_MP_CLEAR_C
 
 
-BN_MP_PRIME_MILLER_RABIN_C
-+--->BN_MP_CMP_D_C
-+--->BN_MP_INIT_COPY_C
+BN_MP_INVMOD_SLOW_C
++--->BN_MP_INIT_MULTI_C
+|   +--->BN_MP_INIT_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_MOD_C
 |   +--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-+--->BN_MP_SUB_D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_ADD_D_C
+|   |   +--->BN_MP_INIT_C
+|   +--->BN_MP_DIV_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_SET_C
+|   |   +--->BN_MP_COUNT_BITS_C
+|   |   +--->BN_MP_ABS_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_INIT_COPY_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_ADD_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_SET_C
+|   +--->BN_MP_ZERO_C
++--->BN_MP_DIV_2_C
+|   +--->BN_MP_GROW_C
 |   +--->BN_MP_CLAMP_C
-+--->BN_MP_CNT_LSB_C
-+--->BN_MP_DIV_2D_C
-|   +--->BN_MP_COPY_C
++--->BN_MP_ADD_C
+|   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
++--->BN_MP_SUB_C
+|   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
 |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_MOD_2D_C
 |   |   +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_C
+|   +--->BN_MP_CMP_MAG_C
++--->BN_MP_CMP_D_C
++--->BN_MP_CMP_MAG_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_MULTI_C
 |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_RSHD_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-+--->BN_MP_EXPTMOD_C
-|   +--->BN_MP_INVMOD_C
-|   |   +--->BN_FAST_MP_INVMOD_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
+
+
+BN_MP_IS_SQUARE_C
++--->BN_MP_MOD_D_C
+|   +--->BN_MP_DIV_D_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_3_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_INIT_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_SET_INT_C
+|   +--->BN_MP_INIT_C
+|   +--->BN_MP_SET_INT_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MUL_2D_C
 |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_MOD_C
-|   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_SET_C
-|   |   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   |   +--->BN_MP_ABS_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CLAMP_C
++--->BN_MP_MOD_C
+|   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_INIT_C
+|   +--->BN_MP_DIV_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_SET_C
+|   |   +--->BN_MP_COUNT_BITS_C
+|   |   +--->BN_MP_ABS_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_INIT_COPY_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_ADD_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
++--->BN_MP_GET_INT_C
++--->BN_MP_SQRT_C
+|   +--->BN_MP_N_ROOT_C
+|   |   +--->BN_MP_N_ROOT_EX_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_EXPT_D_EX_C
+|   |   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_MUL_C
+|   |   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_2_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SET_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_INVMOD_SLOW_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_MOD_C
-|   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_SET_C
-|   |   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   |   +--->BN_MP_ABS_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_SQR_C
+|   |   |   |   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_2_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_SET_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_ABS_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLEAR_MULTI_C
-|   +--->BN_MP_REDUCE_IS_2K_L_C
-|   +--->BN_S_MP_EXPTMOD_C
-|   |   +--->BN_MP_COUNT_BITS_C
-|   |   +--->BN_MP_REDUCE_SETUP_C
-|   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_DIV_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_SET_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_S_MP_SQR_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_REDUCE_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_MUL_C
 |   |   |   |   +--->BN_MP_TOOM_MUL_C
 |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   |   +--->BN_MP_MUL_2_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_ADD_C
@@ -2907,8 +2948,11 @@ BN_MP_PRIME_MILLER_RABIN_C
 |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
 |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -2922,6 +2966,9 @@ BN_MP_PRIME_MILLER_RABIN_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -2929,28 +2976,7 @@ BN_MP_PRIME_MILLER_RABIN_C
 |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_S_MP_MUL_HIGH_DIGS_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
@@ -2959,333 +2985,144 @@ BN_MP_PRIME_MILLER_RABIN_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SET_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_REDUCE_2K_SETUP_L_C
-|   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_REDUCE_2K_L_C
-|   |   |   +--->BN_MP_MUL_C
-|   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MOD_C
 |   |   |   +--->BN_MP_DIV_C
 |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   +--->BN_MP_ABS_C
 |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_CMP_C
 |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_SQR_C
-|   |   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   +--->BN_MP_SUB_D_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SQR_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_MUL_C
-|   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_ADD_D_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_RSHD_C
+|   +--->BN_MP_DIV_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_SET_C
+|   |   +--->BN_MP_COUNT_BITS_C
+|   |   +--->BN_MP_ABS_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_SET_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_DR_IS_MODULUS_C
-|   +--->BN_MP_REDUCE_IS_2K_C
-|   |   +--->BN_MP_REDUCE_2K_C
-|   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_ADD_C
 |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_COUNT_BITS_C
-|   +--->BN_MP_EXPTMOD_FAST_C
-|   |   +--->BN_MP_COUNT_BITS_C
-|   |   +--->BN_MP_MONTGOMERY_SETUP_C
-|   |   +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_MUL_D_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_MONTGOMERY_REDUCE_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_ADD_C
+|   |   +--->BN_S_MP_ADD_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_DR_SETUP_C
-|   |   +--->BN_MP_DR_REDUCE_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_REDUCE_2K_SETUP_C
-|   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   +--->BN_MP_ZERO_C
+|   +--->BN_MP_DIV_2_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_SQR_C
+|   +--->BN_MP_TOOM_SQR_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MUL_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_REDUCE_2K_C
-|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_SUB_C
 |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
@@ -3293,734 +3130,575 @@ BN_MP_PRIME_MILLER_RABIN_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
-|   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_SET_C
+|   |   +--->BN_MP_DIV_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_3_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_INIT_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_KARATSUBA_SQR_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
 |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_FAST_S_MP_SQR_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_S_MP_SQR_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
++--->BN_MP_CMP_MAG_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_JACOBI_C
++--->BN_MP_CMP_D_C
++--->BN_MP_INIT_COPY_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_CNT_LSB_C
++--->BN_MP_DIV_2D_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_MOD_2D_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_RSHD_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_MOD_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_DIV_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_SET_C
+|   |   +--->BN_MP_COUNT_BITS_C
+|   |   +--->BN_MP_ABS_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MULMOD_C
-|   |   |   +--->BN_MP_MUL_C
-|   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_MOD_C
-|   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_SET_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SET_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MOD_C
-|   |   |   +--->BN_MP_DIV_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_SQR_C
-|   |   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_FAST_S_MP_SQR_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SQR_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_MUL_C
-|   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
 |   |   +--->BN_MP_EXCH_C
-+--->BN_MP_CMP_C
-|   +--->BN_MP_CMP_MAG_C
-+--->BN_MP_SQRMOD_C
-|   +--->BN_MP_SQR_C
-|   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_2_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_ADD_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_KARATSUBA_MUL_C
++--->BN_MP_MUL_C
+|   +--->BN_MP_TOOM_MUL_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MUL_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_SUB_C
 |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_D_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_SQR_C
+|   |   +--->BN_MP_DIV_3_C
 |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_INIT_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_MOD_C
-|   |   +--->BN_MP_DIV_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_SET_C
-|   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   +--->BN_MP_ABS_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_S_MP_MUL_DIGS_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_S_MP_ADD_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_ADD_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
++--->BN_S_MP_SUB_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_LSHD_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_ZERO_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_KARATSUBA_SQR_C
++--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_SQR_C
+|   +--->BN_MP_TOOM_SQR_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MUL_2_C
+|   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_ADD_C
 |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_DIV_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_DIV_3_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   +--->BN_FAST_S_MP_SQR_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_S_MP_SQR_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
++--->BN_S_MP_ADD_C
+|   +--->BN_MP_GROW_C
++--->BN_S_MP_SUB_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_LSHD_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_ZERO_C
++--->BN_MP_ADD_C
+|   +--->BN_MP_CMP_MAG_C
 +--->BN_MP_CLEAR_C
 
 
-BN_MP_READ_UNSIGNED_BIN_C
-+--->BN_MP_GROW_C
-+--->BN_MP_ZERO_C
-+--->BN_MP_MUL_2D_C
-|   +--->BN_MP_COPY_C
-|   +--->BN_MP_LSHD_C
-|   |   +--->BN_MP_RSHD_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_CLAMP_C
-
-
-BN_MP_N_ROOT_C
-+--->BN_MP_N_ROOT_EX_C
+BN_MP_LCM_C
++--->BN_MP_INIT_MULTI_C
 |   +--->BN_MP_INIT_C
-|   +--->BN_MP_SET_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_GCD_C
+|   +--->BN_MP_ABS_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_CNT_LSB_C
+|   +--->BN_MP_DIV_2D_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_MUL_2D_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_CMP_MAG_C
++--->BN_MP_DIV_C
 |   +--->BN_MP_COPY_C
 |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_EXPT_D_EX_C
-|   |   +--->BN_MP_INIT_COPY_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_MUL_C
-|   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_SQR_C
-|   |   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_FAST_S_MP_SQR_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SQR_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_MUL_C
-|   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_MUL_DIGS_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_SET_C
+|   +--->BN_MP_COUNT_BITS_C
+|   +--->BN_MP_ABS_C
+|   +--->BN_MP_MUL_2D_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_C
+|   +--->BN_MP_SUB_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_ADD_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_DIV_2D_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_INIT_C
+|   +--->BN_MP_INIT_C
+|   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_RSHD_C
+|   +--->BN_MP_RSHD_C
+|   +--->BN_MP_MUL_D_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_MUL_C
+|   +--->BN_MP_TOOM_MUL_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MUL_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_3_C
 |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_INIT_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_SUB_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_LSHD_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_MUL_D_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_DIV_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_INIT_MULTI_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
 |   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_COUNT_BITS_C
-|   |   +--->BN_MP_ABS_C
-|   |   +--->BN_MP_MUL_2D_C
+|   +--->BN_MP_KARATSUBA_MUL_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_ADD_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_C
 |   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_LSHD_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_ZERO_C
 |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_CMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   +--->BN_MP_SUB_D_C
+|   +--->BN_FAST_S_MP_MUL_DIGS_C
 |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_D_C
-|   |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
+|   +--->BN_S_MP_MUL_DIGS_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_MULTI_C
 |   +--->BN_MP_CLEAR_C
 
 
-BN_MP_EXPT_D_EX_C
-+--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_INIT_SIZE_C
+BN_MP_LSHD_C
++--->BN_MP_GROW_C
++--->BN_MP_RSHD_C
+|   +--->BN_MP_ZERO_C
+
+
+BN_MP_MOD_2D_C
++--->BN_MP_ZERO_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_MOD_C
++--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_INIT_C
++--->BN_MP_DIV_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_INIT_MULTI_C
+|   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_SET_C
+|   +--->BN_MP_COUNT_BITS_C
+|   +--->BN_MP_ABS_C
+|   +--->BN_MP_MUL_2D_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_C
+|   +--->BN_MP_SUB_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_ADD_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_DIV_2D_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_INIT_C
+|   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_RSHD_C
+|   +--->BN_MP_RSHD_C
+|   +--->BN_MP_MUL_D_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
++--->BN_MP_EXCH_C
++--->BN_MP_ADD_C
+|   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+
+
+BN_MP_MOD_D_C
++--->BN_MP_DIV_D_C
 |   +--->BN_MP_COPY_C
 |   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_DIV_2D_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_DIV_3_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_INIT_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLEAR_C
+
+
+BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_2EXPT_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_GROW_C
 +--->BN_MP_SET_C
 |   +--->BN_MP_ZERO_C
++--->BN_MP_MUL_2_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
+
+
+BN_MP_MONTGOMERY_REDUCE_C
++--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_ZERO_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
++--->BN_MP_RSHD_C
+|   +--->BN_MP_ZERO_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+
+
+BN_MP_MONTGOMERY_SETUP_C
+
+
+BN_MP_MULMOD_C
++--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_INIT_C
 +--->BN_MP_MUL_C
 |   +--->BN_MP_TOOM_MUL_C
 |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_INIT_C
 |   |   |   +--->BN_MP_CLEAR_C
 |   |   +--->BN_MP_MOD_2D_C
 |   |   |   +--->BN_MP_ZERO_C
@@ -4060,7 +3738,6 @@ BN_MP_EXPT_D_EX_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_DIV_3_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_CLEAR_C
@@ -4069,7 +3746,6 @@ BN_MP_EXPT_D_EX_C
 |   |   +--->BN_MP_CLEAR_MULTI_C
 |   |   |   +--->BN_MP_CLEAR_C
 |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   +--->BN_MP_INIT_SIZE_C
 |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_S_MP_ADD_C
 |   |   |   +--->BN_MP_GROW_C
@@ -4088,99 +3764,325 @@ BN_MP_EXPT_D_EX_C
 |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_CLAMP_C
 |   +--->BN_S_MP_MUL_DIGS_C
-|   |   +--->BN_MP_INIT_SIZE_C
 |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_EXCH_C
 |   |   +--->BN_MP_CLEAR_C
 +--->BN_MP_CLEAR_C
-+--->BN_MP_SQR_C
-|   +--->BN_MP_TOOM_SQR_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
++--->BN_MP_MOD_C
+|   +--->BN_MP_DIV_C
+|   |   +--->BN_MP_CMP_MAG_C
 |   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MUL_2_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_SET_C
+|   |   +--->BN_MP_COUNT_BITS_C
+|   |   +--->BN_MP_ABS_C
+|   |   +--->BN_MP_MUL_2D_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_C
+|   |   +--->BN_MP_SUB_C
 |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SUB_C
+|   |   +--->BN_MP_ADD_C
 |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2_C
-|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_2D_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_LSHD_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_RSHD_C
 |   |   +--->BN_MP_MUL_D_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_3_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   +--->BN_MP_KARATSUBA_SQR_C
-|   |   +--->BN_MP_INIT_SIZE_C
 |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_ADD_C
 |   |   +--->BN_S_MP_ADD_C
 |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_MAG_C
 |   |   +--->BN_S_MP_SUB_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   +--->BN_FAST_S_MP_SQR_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_SQR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLAMP_C
 
 
-BN_MP_EXPT_D_C
-+--->BN_MP_EXPT_D_EX_C
-|   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_INIT_SIZE_C
+BN_MP_MUL_2D_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_GROW_C
++--->BN_MP_LSHD_C
+|   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_ZERO_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_MUL_2_C
++--->BN_MP_GROW_C
+
+
+BN_MP_MUL_C
++--->BN_MP_TOOM_MUL_C
+|   +--->BN_MP_INIT_MULTI_C
+|   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_MOD_2D_C
+|   |   +--->BN_MP_ZERO_C
 |   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_SET_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_RSHD_C
 |   |   +--->BN_MP_ZERO_C
-|   +--->BN_MP_MUL_C
-|   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_MUL_2_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_ADD_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_SUB_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_DIV_2_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_MUL_2D_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_MUL_D_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_DIV_3_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_CLEAR_C
++--->BN_MP_KARATSUBA_MUL_C
+|   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_INIT_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_ADD_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_ZERO_C
+|   +--->BN_MP_CLEAR_C
++--->BN_FAST_S_MP_MUL_DIGS_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_S_MP_MUL_DIGS_C
+|   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_INIT_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLEAR_C
+
+
+BN_MP_MUL_D_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_NEG_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
+
+
+BN_MP_N_ROOT_C
++--->BN_MP_N_ROOT_EX_C
+|   +--->BN_MP_INIT_C
+|   +--->BN_MP_SET_C
+|   |   +--->BN_MP_ZERO_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_EXPT_D_EX_C
+|   |   +--->BN_MP_INIT_COPY_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_MUL_C
+|   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_SQR_C
+|   |   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_SQR_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   +--->BN_MP_MUL_C
+|   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   +--->BN_MP_MUL_2_C
@@ -4244,34 +4146,169 @@ BN_MP_EXPT_D_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_SQR_C
-|   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   +--->BN_MP_SUB_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_MUL_D_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_DIV_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_COUNT_BITS_C
+|   |   +--->BN_MP_ABS_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_INIT_COPY_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_CMP_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   +--->BN_MP_SUB_D_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_D_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLEAR_C
+
+
+BN_MP_N_ROOT_EX_C
++--->BN_MP_INIT_C
++--->BN_MP_SET_C
+|   +--->BN_MP_ZERO_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_EXPT_D_EX_C
+|   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_MUL_C
+|   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_SQR_C
+|   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -4312,451 +4349,534 @@ BN_MP_EXPT_D_C
 |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_EXCH_C
-
-
-BN_MP_XOR_C
-+--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-+--->BN_MP_CLAMP_C
-+--->BN_MP_EXCH_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_REDUCE_SETUP_C
-+--->BN_MP_2EXPT_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_DIV_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_SET_C
-|   +--->BN_MP_COUNT_BITS_C
-|   +--->BN_MP_ABS_C
-|   +--->BN_MP_MUL_2D_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_C
-|   +--->BN_MP_SUB_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
++--->BN_MP_MUL_C
+|   +--->BN_MP_TOOM_MUL_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_ZERO_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MUL_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_2_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_ADD_C
-|   |   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_MUL_2D_C
 |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_MUL_D_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_DIV_2D_C
-|   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_MOD_2D_C
+|   |   +--->BN_MP_DIV_3_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_KARATSUBA_MUL_C
+|   |   +--->BN_MP_INIT_SIZE_C
 |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CLEAR_MULTI_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_S_MP_MUL_DIGS_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
++--->BN_MP_SUB_C
+|   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_D_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_INIT_MULTI_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_COUNT_BITS_C
+|   +--->BN_MP_ABS_C
+|   +--->BN_MP_MUL_2D_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_C
+|   +--->BN_MP_ADD_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_DIV_2D_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_CLEAR_C
 |   +--->BN_MP_LSHD_C
 |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_RSHD_C
 |   +--->BN_MP_RSHD_C
-|   +--->BN_MP_MUL_D_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
 |   +--->BN_MP_CLAMP_C
 |   +--->BN_MP_CLEAR_C
-
-
-BN_MP_RSHD_C
-+--->BN_MP_ZERO_C
-
-
-BN_MP_NEG_C
-+--->BN_MP_COPY_C
++--->BN_MP_CMP_C
+|   +--->BN_MP_CMP_MAG_C
++--->BN_MP_SUB_D_C
 |   +--->BN_MP_GROW_C
+|   +--->BN_MP_ADD_D_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
 
 
-BN_MP_SHRINK_C
+BN_MP_OR_C
++--->BN_MP_INIT_COPY_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
 
 
-BN_MP_PRIME_RANDOM_EX_C
-+--->BN_MP_READ_UNSIGNED_BIN_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_MUL_2D_C
-|   |   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_PRIME_IS_PRIME_C
-|   +--->BN_MP_CMP_D_C
-|   +--->BN_MP_PRIME_IS_DIVISIBLE_C
-|   |   +--->BN_MP_MOD_D_C
-|   |   |   +--->BN_MP_DIV_D_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_INIT_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_INIT_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_INIT_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
+BN_MP_PRIME_FERMAT_C
++--->BN_MP_CMP_D_C
++--->BN_MP_INIT_C
++--->BN_MP_EXPTMOD_C
+|   +--->BN_MP_INVMOD_C
+|   |   +--->BN_FAST_MP_INVMOD_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
 |   |   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_SET_C
-|   |   +--->BN_MP_ZERO_C
-|   +--->BN_MP_PRIME_MILLER_RABIN_C
-|   |   +--->BN_MP_INIT_COPY_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_SUB_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CNT_LSB_C
-|   |   +--->BN_MP_DIV_2D_C
 |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_EXPTMOD_C
-|   |   |   +--->BN_MP_INVMOD_C
-|   |   |   |   +--->BN_FAST_MP_INVMOD_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_MOD_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   |   +--->BN_MP_ABS_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_MOD_C
-|   |   |   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   |   |   |   +--->BN_MP_ABS_C
-|   |   |   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_C
 |   |   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
 |   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_INVMOD_SLOW_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_INIT_COPY_C
 |   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_MOD_C
-|   |   |   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   |   |   |   +--->BN_MP_ABS_C
-|   |   |   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_INVMOD_SLOW_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_MOD_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   |   +--->BN_MP_ABS_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
 |   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_ABS_C
-|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_REDUCE_IS_2K_L_C
-|   |   |   +--->BN_S_MP_EXPTMOD_C
-|   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   +--->BN_MP_REDUCE_SETUP_C
-|   |   |   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_ABS_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLEAR_MULTI_C
+|   +--->BN_MP_REDUCE_IS_2K_L_C
+|   +--->BN_S_MP_EXPTMOD_C
+|   |   +--->BN_MP_COUNT_BITS_C
+|   |   +--->BN_MP_REDUCE_SETUP_C
+|   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_DIV_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_REDUCE_C
+|   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MUL_C
+|   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_REDUCE_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_MUL_C
-|   |   |   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_S_MP_MUL_HIGH_DIGS_C
-|   |   |   |   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_3_C
 |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_S_MP_MUL_HIGH_DIGS_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_REDUCE_2K_SETUP_L_C
+|   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_REDUCE_2K_L_C
+|   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_C
+|   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
 |   |   |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -4764,9 +4884,7 @@ BN_MP_PRIME_RANDOM_EX_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -4774,318 +4892,179 @@ BN_MP_PRIME_RANDOM_EX_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_DIV_2_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_REDUCE_2K_SETUP_L_C
-|   |   |   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_REDUCE_2K_L_C
-|   |   |   |   |   +--->BN_MP_MUL_C
-|   |   |   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MOD_C
-|   |   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_DIV_3_C
 |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_SQR_C
-|   |   |   |   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SQR_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_MUL_C
-|   |   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MOD_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_DIV_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_DR_IS_MODULUS_C
-|   |   |   +--->BN_MP_REDUCE_IS_2K_C
-|   |   |   |   +--->BN_MP_REDUCE_2K_C
-|   |   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   +--->BN_MP_EXPTMOD_FAST_C
-|   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   +--->BN_MP_MONTGOMERY_SETUP_C
-|   |   |   |   +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+|   |   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_MONTGOMERY_REDUCE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_DR_SETUP_C
-|   |   |   |   +--->BN_MP_DR_REDUCE_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_SQR_C
+|   |   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_REDUCE_2K_SETUP_C
-|   |   |   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_REDUCE_2K_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_SQR_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_MUL_C
+|   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -5093,423 +5072,332 @@ BN_MP_PRIME_RANDOM_EX_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
-|   |   |   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_EXCH_C
+|   +--->BN_MP_DR_IS_MODULUS_C
+|   +--->BN_MP_REDUCE_IS_2K_C
+|   |   +--->BN_MP_REDUCE_2K_C
+|   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_COUNT_BITS_C
+|   +--->BN_MP_EXPTMOD_FAST_C
+|   |   +--->BN_MP_COUNT_BITS_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_MONTGOMERY_SETUP_C
+|   |   +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_MONTGOMERY_REDUCE_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_DR_SETUP_C
+|   |   +--->BN_MP_DR_REDUCE_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_REDUCE_2K_SETUP_C
+|   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_REDUCE_2K_C
+|   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+|   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MULMOD_C
+|   |   |   +--->BN_MP_MUL_C
+|   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MULMOD_C
-|   |   |   |   |   +--->BN_MP_MUL_C
-|   |   |   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_MOD_C
-|   |   |   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MOD_C
-|   |   |   |   |   +--->BN_MP_DIV_C
 |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_SQR_C
-|   |   |   |   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_MOD_C
+|   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SQR_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_MUL_C
-|   |   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_MP_SQRMOD_C
-|   |   |   +--->BN_MP_SQR_C
-|   |   |   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MOD_C
+|   |   |   +--->BN_MP_DIV_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SQR_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_MOD_C
-|   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_SQR_C
+|   |   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   |   +--->BN_MP_ABS_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -5517,2686 +5405,941 @@ BN_MP_PRIME_RANDOM_EX_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_SUB_D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_ADD_D_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_DIV_2_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_MUL_2_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_ADD_D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-
-
-BN_MP_CMP_D_C
-
-
-BN_MP_DR_IS_MODULUS_C
-
-
-BN_MP_IMPORT_C
-+--->BN_MP_ZERO_C
-+--->BN_MP_MUL_2D_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_LSHD_C
-|   |   +--->BN_MP_RSHD_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_CLAMP_C
-
-
-BN_MP_COUNT_BITS_C
-
-
-BN_MP_FREAD_C
-+--->BN_MP_ZERO_C
-+--->BN_MP_MUL_D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_ADD_D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_SUB_D_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_CMP_D_C
-
-
-BN_MP_REDUCE_2K_L_C
-+--->BN_MP_INIT_C
-+--->BN_MP_COUNT_BITS_C
-+--->BN_MP_DIV_2D_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_MOD_2D_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_RSHD_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-+--->BN_MP_MUL_C
-|   +--->BN_MP_TOOM_MUL_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MUL_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_KARATSUBA_SQR_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_S_MP_SQR_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_MUL_C
+|   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_EXCH_C
++--->BN_MP_CMP_C
+|   +--->BN_MP_CMP_MAG_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_PRIME_IS_DIVISIBLE_C
++--->BN_MP_MOD_D_C
+|   +--->BN_MP_DIV_D_C
+|   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_DIV_3_C
 |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_INIT_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_KARATSUBA_MUL_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_MUL_DIGS_C
 |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
 |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_EXCH_C
 |   |   +--->BN_MP_CLEAR_C
-+--->BN_S_MP_ADD_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_CMP_MAG_C
-+--->BN_S_MP_SUB_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_CLEAR_C
 
 
-BN_MP_AND_C
-+--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-+--->BN_MP_CLAMP_C
-+--->BN_MP_EXCH_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_SQRMOD_C
-+--->BN_MP_INIT_C
-+--->BN_MP_SQR_C
-|   +--->BN_MP_TOOM_SQR_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_ZERO_C
+BN_MP_PRIME_IS_PRIME_C
++--->BN_MP_CMP_D_C
++--->BN_MP_PRIME_IS_DIVISIBLE_C
+|   +--->BN_MP_MOD_D_C
+|   |   +--->BN_MP_DIV_D_C
 |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_INIT_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_INIT_C
 |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_C
++--->BN_MP_SET_C
+|   +--->BN_MP_ZERO_C
++--->BN_MP_PRIME_MILLER_RABIN_C
+|   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_INIT_SIZE_C
 |   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MUL_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_3_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_KARATSUBA_SQR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_MP_CMP_MAG_C
 |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_FAST_S_MP_SQR_C
+|   +--->BN_MP_SUB_D_C
 |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_SQR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-+--->BN_MP_CLEAR_C
-+--->BN_MP_MOD_C
-|   +--->BN_MP_DIV_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_SET_C
-|   |   +--->BN_MP_COUNT_BITS_C
-|   |   +--->BN_MP_ABS_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_ADD_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_D_C
 |   |   |   +--->BN_MP_CLAMP_C
-
-
-BN_MP_DIV_D_C
-+--->BN_MP_COPY_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_DIV_2D_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_MOD_2D_C
 |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_RSHD_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-+--->BN_MP_DIV_3_C
-|   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_INIT_C
-+--->BN_MP_CLAMP_C
-+--->BN_MP_EXCH_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_INIT_MULTI_C
-+--->BN_MP_INIT_C
-+--->BN_MP_CLEAR_C
-
-
-BN_S_MP_EXPTMOD_C
-+--->BN_MP_COUNT_BITS_C
-+--->BN_MP_INIT_C
-+--->BN_MP_CLEAR_C
-+--->BN_MP_REDUCE_SETUP_C
-|   +--->BN_MP_2EXPT_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_DIV_C
-|   |   +--->BN_MP_CMP_MAG_C
+|   +--->BN_MP_CNT_LSB_C
+|   +--->BN_MP_DIV_2D_C
 |   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_SET_C
-|   |   +--->BN_MP_ABS_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_MOD_2D_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
 |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_REDUCE_C
-|   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_ZERO_C
-|   +--->BN_MP_MUL_C
-|   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_ZERO_C
+|   +--->BN_MP_EXPTMOD_C
+|   |   +--->BN_MP_INVMOD_C
+|   |   |   +--->BN_FAST_MP_INVMOD_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_MOD_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   |   |   +--->BN_MP_ABS_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   +--->BN_S_MP_MUL_HIGH_DIGS_C
-|   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_MOD_2D_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_MUL_DIGS_C
-|   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_SUB_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_D_C
-|   +--->BN_MP_SET_C
-|   |   +--->BN_MP_ZERO_C
-|   +--->BN_MP_LSHD_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_ADD_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_REDUCE_2K_SETUP_L_C
-|   +--->BN_MP_2EXPT_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_REDUCE_2K_L_C
-|   +--->BN_MP_DIV_2D_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_MUL_C
-|   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_INVMOD_SLOW_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_MOD_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   |   |   +--->BN_MP_ABS_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_DIV_2_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_ABS_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_REDUCE_IS_2K_L_C
+|   |   +--->BN_S_MP_EXPTMOD_C
+|   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   +--->BN_MP_REDUCE_SETUP_C
+|   |   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_REDUCE_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MUL_C
+|   |   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_S_MP_MUL_HIGH_DIGS_C
+|   |   |   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_MP_REDUCE_2K_SETUP_L_C
+|   |   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_REDUCE_2K_L_C
+|   |   |   |   +--->BN_MP_MUL_C
+|   |   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_MOD_C
-|   +--->BN_MP_DIV_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_SET_C
-|   |   +--->BN_MP_ABS_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MOD_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_SQR_C
+|   |   |   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_SQR_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_MUL_C
+|   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_DR_IS_MODULUS_C
+|   |   +--->BN_MP_REDUCE_IS_2K_C
+|   |   |   +--->BN_MP_REDUCE_2K_C
+|   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   +--->BN_MP_EXPTMOD_FAST_C
+|   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_MONTGOMERY_SETUP_C
+|   |   |   +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
 |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_MONTGOMERY_REDUCE_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_DR_SETUP_C
+|   |   |   +--->BN_MP_DR_REDUCE_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_ADD_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_COPY_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_SQR_C
-|   +--->BN_MP_TOOM_SQR_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MUL_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_3_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   +--->BN_MP_KARATSUBA_SQR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   +--->BN_FAST_S_MP_SQR_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_SQR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-+--->BN_MP_MUL_C
-|   +--->BN_MP_TOOM_MUL_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MUL_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_3_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   +--->BN_MP_KARATSUBA_MUL_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_MUL_DIGS_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-+--->BN_MP_SET_C
-|   +--->BN_MP_ZERO_C
-+--->BN_MP_EXCH_C
-
-
-BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
-+--->BN_MP_COUNT_BITS_C
-+--->BN_MP_2EXPT_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_SET_C
-|   +--->BN_MP_ZERO_C
-+--->BN_MP_MUL_2_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_CMP_MAG_C
-+--->BN_S_MP_SUB_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-
-
-BN_MP_MONTGOMERY_SETUP_C
-
-
-BN_FAST_MP_INVMOD_C
-+--->BN_MP_INIT_MULTI_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_COPY_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_MOD_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_DIV_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_SET_C
-|   |   +--->BN_MP_COUNT_BITS_C
-|   |   +--->BN_MP_ABS_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_ADD_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_SET_C
-|   +--->BN_MP_ZERO_C
-+--->BN_MP_DIV_2_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_SUB_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_CMP_C
-|   +--->BN_MP_CMP_MAG_C
-+--->BN_MP_CMP_D_C
-+--->BN_MP_ADD_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_EXCH_C
-+--->BN_MP_CLEAR_MULTI_C
-|   +--->BN_MP_CLEAR_C
-
-
-BN_MP_TO_UNSIGNED_BIN_C
-+--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-+--->BN_MP_DIV_2D_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_MOD_2D_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_RSHD_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_CLEAR_MULTI_C
-+--->BN_MP_CLEAR_C
-
-
-BNCORE_C
-
-
-BN_MP_TORADIX_C
-+--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-+--->BN_MP_DIV_D_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_DIV_2D_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_DIV_3_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_EXPTMOD_FAST_C
-+--->BN_MP_COUNT_BITS_C
-+--->BN_MP_INIT_C
-+--->BN_MP_CLEAR_C
-+--->BN_MP_MONTGOMERY_SETUP_C
-+--->BN_FAST_MP_MONTGOMERY_REDUCE_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_ZERO_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-+--->BN_MP_MONTGOMERY_REDUCE_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_ZERO_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-+--->BN_MP_DR_SETUP_C
-+--->BN_MP_DR_REDUCE_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-+--->BN_MP_REDUCE_2K_SETUP_C
-|   +--->BN_MP_2EXPT_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_REDUCE_2K_C
-|   +--->BN_MP_DIV_2D_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_MUL_D_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
-|   +--->BN_MP_2EXPT_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_SET_C
-|   |   +--->BN_MP_ZERO_C
-|   +--->BN_MP_MUL_2_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_MULMOD_C
-|   +--->BN_MP_MUL_C
-|   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_MOD_C
-|   |   +--->BN_MP_DIV_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_SET_C
-|   |   |   +--->BN_MP_ABS_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_SET_C
-|   +--->BN_MP_ZERO_C
-+--->BN_MP_MOD_C
-|   +--->BN_MP_DIV_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_ABS_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_ADD_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_COPY_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_SQR_C
-|   +--->BN_MP_TOOM_SQR_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MUL_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_3_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   +--->BN_MP_KARATSUBA_SQR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   +--->BN_FAST_S_MP_SQR_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_SQR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-+--->BN_MP_MUL_C
-|   +--->BN_MP_TOOM_MUL_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MUL_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_3_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   +--->BN_MP_KARATSUBA_MUL_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_MUL_DIGS_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-+--->BN_MP_EXCH_C
-
-
-BN_MP_MUL_D_C
-+--->BN_MP_GROW_C
-+--->BN_MP_CLAMP_C
-
-
-BN_MP_SET_LONG_LONG_C
-
-
-BN_MP_DIV_2_C
-+--->BN_MP_GROW_C
-+--->BN_MP_CLAMP_C
-
-
-BN_ERROR_C
-
-
-BN_MP_RAND_C
-+--->BN_MP_ZERO_C
-+--->BN_MP_ADD_D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_SUB_D_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_LSHD_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_RSHD_C
-
-
-BN_S_MP_SQR_C
-+--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_INIT_C
-+--->BN_MP_CLAMP_C
-+--->BN_MP_EXCH_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_CMP_C
-+--->BN_MP_CMP_MAG_C
-
-
-BN_MP_N_ROOT_EX_C
-+--->BN_MP_INIT_C
-+--->BN_MP_SET_C
-|   +--->BN_MP_ZERO_C
-+--->BN_MP_COPY_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_EXPT_D_EX_C
-|   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_MUL_C
-|   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_SQR_C
-|   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_FAST_S_MP_SQR_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_SQR_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-+--->BN_MP_MUL_C
-|   +--->BN_MP_TOOM_MUL_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MUL_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_3_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_KARATSUBA_MUL_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_MUL_DIGS_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-+--->BN_MP_SUB_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_MUL_D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_DIV_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_COUNT_BITS_C
-|   +--->BN_MP_ABS_C
-|   +--->BN_MP_MUL_2D_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_C
-|   +--->BN_MP_ADD_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_DIV_2D_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CLEAR_MULTI_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_LSHD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_RSHD_C
-|   +--->BN_MP_RSHD_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_CMP_C
-|   +--->BN_MP_CMP_MAG_C
-+--->BN_MP_SUB_D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_ADD_D_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_EXCH_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_PRIME_IS_DIVISIBLE_C
-+--->BN_MP_MOD_D_C
-|   +--->BN_MP_DIV_D_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_DIV_3_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_INIT_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-
-
-BN_MP_INIT_SET_INT_C
-+--->BN_MP_INIT_C
-+--->BN_MP_SET_INT_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_MUL_2D_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLAMP_C
-
-
-BN_MP_DIV_3_C
-+--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_INIT_C
-+--->BN_MP_CLAMP_C
-+--->BN_MP_EXCH_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_MONTGOMERY_REDUCE_C
-+--->BN_FAST_MP_MONTGOMERY_REDUCE_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_ZERO_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-+--->BN_MP_GROW_C
-+--->BN_MP_CLAMP_C
-+--->BN_MP_RSHD_C
-|   +--->BN_MP_ZERO_C
-+--->BN_MP_CMP_MAG_C
-+--->BN_S_MP_SUB_C
-
-
-BN_MP_INVMOD_SLOW_C
-+--->BN_MP_INIT_MULTI_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_MOD_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_DIV_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_SET_C
-|   |   +--->BN_MP_COUNT_BITS_C
-|   |   +--->BN_MP_ABS_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_ADD_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_COPY_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_SET_C
-|   +--->BN_MP_ZERO_C
-+--->BN_MP_DIV_2_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_ADD_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_SUB_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_CMP_C
-|   +--->BN_MP_CMP_MAG_C
-+--->BN_MP_CMP_D_C
-+--->BN_MP_CMP_MAG_C
-+--->BN_MP_EXCH_C
-+--->BN_MP_CLEAR_MULTI_C
-|   +--->BN_MP_CLEAR_C
-
-
-BN_S_MP_ADD_C
-+--->BN_MP_GROW_C
-+--->BN_MP_CLAMP_C
-
-
-BN_MP_READ_SIGNED_BIN_C
-+--->BN_MP_READ_UNSIGNED_BIN_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_MUL_2D_C
-|   |   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLAMP_C
-
-
-BN_MP_MOD_D_C
-+--->BN_MP_DIV_D_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_DIV_2D_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_DIV_3_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CLEAR_C
-
-
-BN_MP_SQRTMOD_PRIME_C
-+--->BN_MP_CMP_D_C
-+--->BN_MP_ZERO_C
-+--->BN_MP_JACOBI_C
-|   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_CNT_LSB_C
-|   +--->BN_MP_DIV_2D_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_MOD_C
-|   |   +--->BN_MP_DIV_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_SET_C
-|   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   +--->BN_MP_ABS_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_INIT_MULTI_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_MOD_D_C
-|   +--->BN_MP_DIV_D_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_DIV_3_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_INIT_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-+--->BN_MP_ADD_D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_SUB_D_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_DIV_2_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_EXPTMOD_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_INVMOD_C
-|   |   +--->BN_FAST_MP_INVMOD_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_MOD_C
-|   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_MP_SET_C
-|   |   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   |   +--->BN_MP_ABS_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SET_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_INVMOD_SLOW_C
-|   |   |   +--->BN_MP_MOD_C
-|   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_SET_C
-|   |   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   |   +--->BN_MP_ABS_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_SET_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_ABS_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLEAR_MULTI_C
-|   +--->BN_MP_REDUCE_IS_2K_L_C
-|   +--->BN_S_MP_EXPTMOD_C
-|   |   +--->BN_MP_COUNT_BITS_C
-|   |   +--->BN_MP_REDUCE_SETUP_C
-|   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_DIV_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_SET_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_REDUCE_C
-|   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_MUL_C
-|   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_S_MP_MUL_HIGH_DIGS_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SET_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_REDUCE_2K_SETUP_L_C
-|   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_REDUCE_2K_L_C
-|   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_MUL_C
-|   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MOD_C
-|   |   |   +--->BN_MP_DIV_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_SET_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_REDUCE_2K_SETUP_C
+|   |   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_SQR_C
-|   |   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_FAST_S_MP_SQR_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SQR_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_MUL_C
-|   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_SET_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_DR_IS_MODULUS_C
-|   +--->BN_MP_REDUCE_IS_2K_C
-|   |   +--->BN_MP_REDUCE_2K_C
-|   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_COUNT_BITS_C
-|   +--->BN_MP_EXPTMOD_FAST_C
-|   |   +--->BN_MP_COUNT_BITS_C
-|   |   +--->BN_MP_MONTGOMERY_SETUP_C
-|   |   +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_MONTGOMERY_REDUCE_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_DR_SETUP_C
-|   |   +--->BN_MP_DR_REDUCE_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_REDUCE_2K_SETUP_C
-|   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_REDUCE_2K_C
-|   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_REDUCE_2K_C
+|   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
-|   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_SET_C
-|   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MULMOD_C
-|   |   |   +--->BN_MP_MUL_C
-|   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+|   |   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MULMOD_C
+|   |   |   |   +--->BN_MP_MUL_C
+|   |   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_2_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_MP_MOD_C
+|   |   |   |   |   +--->BN_MP_DIV_C
 |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_MOD_C
 |   |   |   |   +--->BN_MP_DIV_C
 |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
 |   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_LSHD_C
@@ -8217,15 +6360,7 @@ BN_MP_SQRTMOD_PRIME_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_INIT_COPY_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_RSHD_C
@@ -8243,545 +6378,328 @@ BN_MP_SQRTMOD_PRIME_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SET_C
-|   |   +--->BN_MP_MOD_C
-|   |   |   +--->BN_MP_DIV_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_SQR_C
+|   |   |   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
 |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_SQR_C
-|   |   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_MUL_2_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_2_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_KARATSUBA_SQR_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_S_MP_SQR_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_MUL_C
+|   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_FAST_S_MP_SQR_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SQR_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_MUL_C
-|   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_MUL_2_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_2_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_EXCH_C
-+--->BN_MP_COPY_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_SUB_D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_SET_INT_C
-|   +--->BN_MP_MUL_2D_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_SQRMOD_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_SQR_C
-|   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_FAST_S_MP_SQR_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_SQR_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_MOD_C
-|   |   +--->BN_MP_DIV_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_SET_C
-|   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   +--->BN_MP_ABS_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CMP_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   +--->BN_MP_SQRMOD_C
+|   |   +--->BN_MP_SQR_C
+|   |   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MUL_2_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_MULMOD_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_MUL_C
-|   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_3_C
+|   |   |   +--->BN_S_MP_SQR_C
 |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_MOD_C
 |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_MP_DIV_C
 |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_MOD_C
-|   |   +--->BN_MP_DIV_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_SET_C
-|   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   +--->BN_MP_ABS_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   +--->BN_MP_ABS_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_SET_C
-+--->BN_MP_CLEAR_MULTI_C
 |   +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
 
 
-BN_FAST_S_MP_MUL_HIGH_DIGS_C
-+--->BN_MP_GROW_C
-+--->BN_MP_CLAMP_C
-
-
-BN_REVERSE_C
-
-
-BN_MP_PRIME_NEXT_PRIME_C
+BN_MP_PRIME_MILLER_RABIN_C
 +--->BN_MP_CMP_D_C
-+--->BN_MP_SET_C
-|   +--->BN_MP_ZERO_C
-+--->BN_MP_SUB_D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_ADD_D_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_MOD_D_C
-|   +--->BN_MP_DIV_D_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_DIV_3_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_INIT_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-+--->BN_MP_INIT_C
-+--->BN_MP_ADD_D_C
++--->BN_MP_INIT_COPY_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_SUB_D_C
 |   +--->BN_MP_GROW_C
+|   +--->BN_MP_ADD_D_C
+|   |   +--->BN_MP_CLAMP_C
 |   +--->BN_MP_CLAMP_C
-+--->BN_MP_PRIME_MILLER_RABIN_C
-|   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_CNT_LSB_C
-|   +--->BN_MP_DIV_2D_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_RSHD_C
++--->BN_MP_CNT_LSB_C
++--->BN_MP_DIV_2D_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_MOD_2D_C
 |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_EXPTMOD_C
-|   |   +--->BN_MP_INVMOD_C
-|   |   |   +--->BN_FAST_MP_INVMOD_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_MOD_C
-|   |   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   |   |   +--->BN_MP_ABS_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_RSHD_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_EXPTMOD_C
+|   +--->BN_MP_INVMOD_C
+|   |   +--->BN_FAST_MP_INVMOD_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_MOD_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   |   +--->BN_MP_ABS_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -8789,237 +6707,429 @@ BN_MP_PRIME_NEXT_PRIME_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_INVMOD_SLOW_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_MOD_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_DIV_C
 |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   |   +--->BN_MP_ABS_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_INVMOD_SLOW_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_MOD_C
-|   |   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   |   |   +--->BN_MP_ABS_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_ABS_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLEAR_MULTI_C
+|   +--->BN_MP_REDUCE_IS_2K_L_C
+|   +--->BN_S_MP_EXPTMOD_C
+|   |   +--->BN_MP_COUNT_BITS_C
+|   |   +--->BN_MP_REDUCE_SETUP_C
+|   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_DIV_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_ABS_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   +--->BN_MP_REDUCE_IS_2K_L_C
-|   |   +--->BN_S_MP_EXPTMOD_C
-|   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   +--->BN_MP_REDUCE_SETUP_C
-|   |   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_REDUCE_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MUL_C
+|   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_MUL_2_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_DIV_2_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_REDUCE_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MUL_C
-|   |   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_S_MP_MUL_HIGH_DIGS_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_REDUCE_2K_SETUP_L_C
+|   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_REDUCE_2K_L_C
+|   |   |   +--->BN_MP_MUL_C
+|   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_3_C
 |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MOD_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_DIV_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_S_MP_MUL_HIGH_DIGS_C
-|   |   |   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_SQR_C
+|   |   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
 |   |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
@@ -9028,8 +7138,52 @@ BN_MP_PRIME_NEXT_PRIME_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_SQR_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_MUL_C
+|   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
@@ -9038,94 +7192,190 @@ BN_MP_PRIME_NEXT_PRIME_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_REDUCE_2K_SETUP_L_C
-|   |   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_REDUCE_2K_L_C
-|   |   |   |   +--->BN_MP_MUL_C
-|   |   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_EXCH_C
+|   +--->BN_MP_DR_IS_MODULUS_C
+|   +--->BN_MP_REDUCE_IS_2K_C
+|   |   +--->BN_MP_REDUCE_2K_C
+|   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_COUNT_BITS_C
+|   +--->BN_MP_EXPTMOD_FAST_C
+|   |   +--->BN_MP_COUNT_BITS_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_MONTGOMERY_SETUP_C
+|   |   +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_MONTGOMERY_REDUCE_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_DR_SETUP_C
+|   |   +--->BN_MP_DR_REDUCE_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_REDUCE_2K_SETUP_C
+|   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_REDUCE_2K_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+|   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MULMOD_C
+|   |   |   +--->BN_MP_MUL_C
+|   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_DIV_3_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_MOD_C
 |   |   |   |   +--->BN_MP_DIV_C
 |   |   |   |   |   +--->BN_MP_CMP_MAG_C
@@ -9133,6 +7383,7 @@ BN_MP_PRIME_NEXT_PRIME_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_SET_C
 |   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_LSHD_C
@@ -9154,7 +7405,6 @@ BN_MP_PRIME_NEXT_PRIME_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_RSHD_C
@@ -9172,142 +7422,203 @@ BN_MP_PRIME_NEXT_PRIME_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_SQR_C
-|   |   |   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MOD_C
+|   |   |   +--->BN_MP_DIV_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_SQR_C
+|   |   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SQR_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_DIV_3_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_MUL_C
-|   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_SQR_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_MUL_C
+|   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_DIV_3_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_DR_IS_MODULUS_C
-|   |   +--->BN_MP_REDUCE_IS_2K_C
-|   |   |   +--->BN_MP_REDUCE_2K_C
-|   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_EXCH_C
++--->BN_MP_CMP_C
+|   +--->BN_MP_CMP_MAG_C
++--->BN_MP_SQRMOD_C
+|   +--->BN_MP_SQR_C
+|   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SUB_C
 |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -9315,134 +7626,241 @@ BN_MP_PRIME_NEXT_PRIME_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   +--->BN_MP_EXPTMOD_FAST_C
-|   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   +--->BN_MP_MONTGOMERY_SETUP_C
-|   |   |   +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+|   |   |   +--->BN_MP_DIV_2_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_MONTGOMERY_REDUCE_C
+|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_ADD_C
 |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_DR_SETUP_C
-|   |   |   +--->BN_MP_DR_REDUCE_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_SQR_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_MOD_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_DIV_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   +--->BN_MP_ABS_C
+|   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_REDUCE_2K_SETUP_C
-|   |   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_REDUCE_2K_C
-|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_ADD_C
 |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
-|   |   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_PRIME_NEXT_PRIME_C
++--->BN_MP_CMP_D_C
++--->BN_MP_SET_C
+|   +--->BN_MP_ZERO_C
++--->BN_MP_SUB_D_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_ADD_D_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_MOD_D_C
+|   +--->BN_MP_DIV_D_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_3_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_INIT_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_C
++--->BN_MP_ADD_D_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_PRIME_MILLER_RABIN_C
+|   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_CNT_LSB_C
+|   +--->BN_MP_DIV_2D_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXPTMOD_C
+|   |   +--->BN_MP_INVMOD_C
+|   |   |   +--->BN_FAST_MP_INVMOD_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MULMOD_C
-|   |   |   |   +--->BN_MP_MUL_C
-|   |   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   +--->BN_MP_MOD_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   |   |   +--->BN_MP_ABS_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_INVMOD_SLOW_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   |   +--->BN_MP_MOD_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   +--->BN_MP_DIV_C
 |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   |   |   +--->BN_MP_ABS_C
 |   |   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_LSHD_C
@@ -9464,7 +7882,8 @@ BN_MP_PRIME_NEXT_PRIME_C
 |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
@@ -9473,6 +7892,8 @@ BN_MP_PRIME_NEXT_PRIME_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   |   +--->BN_S_MP_ADD_C
@@ -9482,45 +7903,20 @@ BN_MP_PRIME_NEXT_PRIME_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MOD_C
-|   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -9528,154 +7924,150 @@ BN_MP_PRIME_NEXT_PRIME_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_ABS_C
 |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_SQR_C
-|   |   |   |   +--->BN_MP_TOOM_SQR_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_REDUCE_IS_2K_L_C
+|   |   +--->BN_S_MP_EXPTMOD_C
+|   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   +--->BN_MP_REDUCE_SETUP_C
+|   |   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_FAST_S_MP_SQR_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SQR_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_MUL_C
-|   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_REDUCE_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MUL_C
+|   |   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_2_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
 |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_S_MP_MUL_HIGH_DIGS_C
+|   |   |   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   +--->BN_MP_SQRMOD_C
-|   |   +--->BN_MP_SQR_C
-|   |   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -9683,7 +8075,9 @@ BN_MP_PRIME_NEXT_PRIME_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -9691,519 +8085,699 @@ BN_MP_PRIME_NEXT_PRIME_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_REDUCE_2K_SETUP_L_C
+|   |   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_REDUCE_2K_L_C
+|   |   |   |   +--->BN_MP_MUL_C
+|   |   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_FAST_S_MP_SQR_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SQR_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MOD_C
 |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_MOD_C
-|   |   |   +--->BN_MP_DIV_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   +--->BN_MP_ABS_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_SQR_C
+|   |   |   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_2_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_TOOM_MUL_C
-+--->BN_MP_INIT_MULTI_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_MOD_2D_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_COPY_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_RSHD_C
-|   +--->BN_MP_ZERO_C
-+--->BN_MP_MUL_C
-|   +--->BN_MP_KARATSUBA_MUL_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_MUL_DIGS_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-+--->BN_MP_MUL_2_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_ADD_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_SUB_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_DIV_2_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_MUL_2D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_LSHD_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_MUL_D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_DIV_3_C
-|   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_LSHD_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_CLEAR_MULTI_C
-|   +--->BN_MP_CLEAR_C
-
-
-BN_MP_CNT_LSB_C
-
-
-BN_MP_CLAMP_C
-
-
-BN_MP_SUB_D_C
-+--->BN_MP_GROW_C
-+--->BN_MP_ADD_D_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_CLAMP_C
-
-
-BN_MP_ADD_C
-+--->BN_S_MP_ADD_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_CMP_MAG_C
-+--->BN_S_MP_SUB_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-
-
-BN_MP_REDUCE_2K_C
-+--->BN_MP_INIT_C
-+--->BN_MP_COUNT_BITS_C
-+--->BN_MP_DIV_2D_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_MOD_2D_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_RSHD_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-+--->BN_MP_MUL_D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_S_MP_ADD_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_CMP_MAG_C
-+--->BN_S_MP_SUB_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_REDUCE_C
-+--->BN_MP_REDUCE_SETUP_C
-|   +--->BN_MP_2EXPT_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_DIV_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_SET_C
-|   |   +--->BN_MP_COUNT_BITS_C
-|   |   +--->BN_MP_ABS_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_SQR_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_MUL_C
+|   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_DR_IS_MODULUS_C
+|   |   +--->BN_MP_REDUCE_IS_2K_C
+|   |   |   +--->BN_MP_REDUCE_2K_C
+|   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   +--->BN_MP_EXPTMOD_FAST_C
+|   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_MONTGOMERY_SETUP_C
+|   |   |   +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
 |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_MONTGOMERY_REDUCE_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_DR_SETUP_C
+|   |   |   +--->BN_MP_DR_REDUCE_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
-+--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-+--->BN_MP_RSHD_C
-|   +--->BN_MP_ZERO_C
-+--->BN_MP_MUL_C
-|   +--->BN_MP_TOOM_MUL_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_REDUCE_2K_SETUP_C
+|   |   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_REDUCE_2K_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+|   |   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MULMOD_C
+|   |   |   |   +--->BN_MP_MUL_C
+|   |   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_MOD_C
+|   |   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MOD_C
+|   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_MUL_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_3_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_KARATSUBA_MUL_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_MUL_DIGS_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-+--->BN_S_MP_MUL_HIGH_DIGS_C
-|   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_MOD_2D_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_S_MP_MUL_DIGS_C
-|   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_SUB_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_CMP_D_C
-+--->BN_MP_SET_C
-|   +--->BN_MP_ZERO_C
-+--->BN_MP_LSHD_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_ADD_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_CMP_C
-|   +--->BN_MP_CMP_MAG_C
-+--->BN_S_MP_SUB_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_EXPTMOD_C
-+--->BN_MP_INIT_C
-+--->BN_MP_INVMOD_C
-|   +--->BN_FAST_MP_INVMOD_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_MOD_C
-|   |   |   +--->BN_MP_DIV_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_SET_C
-|   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   +--->BN_MP_ABS_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_SQR_C
+|   |   |   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_SQR_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_MUL_C
+|   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CMP_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   +--->BN_MP_SQRMOD_C
+|   |   +--->BN_MP_SQR_C
+|   |   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_ADD_C
 |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SET_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_DIV_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_MP_CMP_D_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_S_MP_SQR_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_INVMOD_SLOW_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_CLEAR_C
 |   |   +--->BN_MP_MOD_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   +--->BN_MP_DIV_C
 |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
 |   |   |   |   +--->BN_MP_COUNT_BITS_C
 |   |   |   |   +--->BN_MP_ABS_C
 |   |   |   |   +--->BN_MP_MUL_2D_C
@@ -10211,7 +8785,6 @@ BN_MP_EXPTMOD_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_C
 |   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
@@ -10226,18 +8799,8 @@ BN_MP_EXPTMOD_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_INIT_COPY_C
 |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_RSHD_C
@@ -10246,755 +8809,1273 @@ BN_MP_EXPTMOD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_SET_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_DIV_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_MP_CMP_D_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-+--->BN_MP_CLEAR_C
-+--->BN_MP_ABS_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-+--->BN_MP_CLEAR_MULTI_C
-+--->BN_MP_REDUCE_IS_2K_L_C
-+--->BN_S_MP_EXPTMOD_C
-|   +--->BN_MP_COUNT_BITS_C
-|   +--->BN_MP_REDUCE_SETUP_C
-|   |   +--->BN_MP_2EXPT_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_DIV_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_SET_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_PRIME_RABIN_MILLER_TRIALS_C
+
+
+BN_MP_PRIME_RANDOM_EX_C
++--->BN_MP_READ_UNSIGNED_BIN_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_MUL_2D_C
+|   |   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_PRIME_IS_PRIME_C
+|   +--->BN_MP_CMP_D_C
+|   +--->BN_MP_PRIME_IS_DIVISIBLE_C
+|   |   +--->BN_MP_MOD_D_C
+|   |   |   +--->BN_MP_DIV_D_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_INIT_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_INIT_C
 |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_INIT_C
+|   +--->BN_MP_SET_C
+|   |   +--->BN_MP_ZERO_C
+|   +--->BN_MP_PRIME_MILLER_RABIN_C
+|   |   +--->BN_MP_INIT_COPY_C
 |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_SUB_D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_D_C
 |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_REDUCE_C
-|   |   +--->BN_MP_INIT_COPY_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_CNT_LSB_C
+|   |   +--->BN_MP_DIV_2D_C
 |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_RSHD_C
 |   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MUL_C
-|   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXPTMOD_C
+|   |   |   +--->BN_MP_INVMOD_C
+|   |   |   |   +--->BN_FAST_MP_INVMOD_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MOD_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   |   |   |   +--->BN_MP_ABS_C
+|   |   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_INVMOD_SLOW_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_MP_MOD_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   |   |   |   +--->BN_MP_ABS_C
+|   |   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_ABS_C
 |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_REDUCE_IS_2K_L_C
+|   |   |   +--->BN_S_MP_EXPTMOD_C
+|   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   +--->BN_MP_REDUCE_SETUP_C
+|   |   |   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_REDUCE_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_MUL_C
+|   |   |   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_S_MP_MUL_HIGH_DIGS_C
+|   |   |   |   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_S_MP_MUL_HIGH_DIGS_C
-|   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_D_C
-|   |   +--->BN_MP_SET_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_REDUCE_2K_SETUP_L_C
-|   |   +--->BN_MP_2EXPT_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_REDUCE_2K_L_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_MUL_C
-|   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_REDUCE_2K_SETUP_L_C
+|   |   |   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_MOD_C
-|   |   +--->BN_MP_DIV_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_SET_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_SQR_C
-|   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_FAST_S_MP_SQR_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_SQR_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_MUL_C
-|   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_REDUCE_2K_L_C
+|   |   |   |   |   +--->BN_MP_MUL_C
+|   |   |   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MOD_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_SET_C
-|   |   +--->BN_MP_ZERO_C
-|   +--->BN_MP_EXCH_C
-+--->BN_MP_DR_IS_MODULUS_C
-+--->BN_MP_REDUCE_IS_2K_C
-|   +--->BN_MP_REDUCE_2K_C
-|   |   +--->BN_MP_COUNT_BITS_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_COUNT_BITS_C
-+--->BN_MP_EXPTMOD_FAST_C
-|   +--->BN_MP_COUNT_BITS_C
-|   +--->BN_MP_MONTGOMERY_SETUP_C
-|   +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   +--->BN_MP_MONTGOMERY_REDUCE_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   +--->BN_MP_DR_SETUP_C
-|   +--->BN_MP_DR_REDUCE_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   +--->BN_MP_REDUCE_2K_SETUP_C
-|   |   +--->BN_MP_2EXPT_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_REDUCE_2K_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
-|   |   +--->BN_MP_2EXPT_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_SET_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MUL_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_MULMOD_C
-|   |   +--->BN_MP_MUL_C
-|   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_SQR_C
+|   |   |   |   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_SQR_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_MUL_C
+|   |   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_DR_IS_MODULUS_C
+|   |   |   +--->BN_MP_REDUCE_IS_2K_C
+|   |   |   |   +--->BN_MP_REDUCE_2K_C
+|   |   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   +--->BN_MP_EXPTMOD_FAST_C
+|   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_MONTGOMERY_SETUP_C
+|   |   |   |   +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_MONTGOMERY_REDUCE_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_DR_SETUP_C
+|   |   |   |   +--->BN_MP_DR_REDUCE_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_REDUCE_2K_SETUP_C
+|   |   |   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_REDUCE_2K_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+|   |   |   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MULMOD_C
+|   |   |   |   |   +--->BN_MP_MUL_C
+|   |   |   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_MOD_C
+|   |   |   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MOD_C
+|   |   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_SQR_C
+|   |   |   |   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_SQR_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_MUL_C
+|   |   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_MP_SQRMOD_C
+|   |   |   +--->BN_MP_SQR_C
+|   |   |   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_2_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_KARATSUBA_SQR_C
 |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_MOD_C
-|   |   |   +--->BN_MP_DIV_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_SET_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_SQR_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_MOD_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   |   +--->BN_MP_ABS_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_SET_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_SUB_D_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_ADD_D_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_2_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_2_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_ADD_D_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
+
+
+BN_MP_RADIX_SIZE_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_INIT_COPY_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_DIV_D_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_DIV_2D_C
 |   |   +--->BN_MP_ZERO_C
-|   +--->BN_MP_MOD_C
-|   |   +--->BN_MP_DIV_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_DIV_3_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_RADIX_SMAP_C
+
+
+BN_MP_RAND_C
++--->BN_MP_ZERO_C
++--->BN_MP_ADD_D_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_SUB_D_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_LSHD_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_RSHD_C
+
+
+BN_MP_READ_RADIX_C
++--->BN_MP_ZERO_C
++--->BN_MP_MUL_D_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_ADD_D_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_SUB_D_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLAMP_C
+
+
+BN_MP_READ_SIGNED_BIN_C
++--->BN_MP_READ_UNSIGNED_BIN_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_MUL_2D_C
+|   |   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_LSHD_C
 |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_MUL_D_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLAMP_C
+
+
+BN_MP_READ_UNSIGNED_BIN_C
++--->BN_MP_GROW_C
++--->BN_MP_ZERO_C
++--->BN_MP_MUL_2D_C
+|   +--->BN_MP_COPY_C
+|   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_RSHD_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_REDUCE_2K_C
++--->BN_MP_INIT_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_DIV_2D_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_MOD_2D_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_RSHD_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_D_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_S_MP_ADD_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_REDUCE_2K_L_C
++--->BN_MP_INIT_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_DIV_2D_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_MOD_2D_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_RSHD_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_C
+|   +--->BN_MP_TOOM_MUL_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MUL_2_C
+|   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_ADD_C
 |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
@@ -11003,223 +10084,167 @@ BN_MP_EXPTMOD_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_SQR_C
-|   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_2D_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_DIV_2_C
+|   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_D_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_SQR_C
+|   |   +--->BN_MP_DIV_3_C
 |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_MUL_C
-|   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_KARATSUBA_MUL_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   +--->BN_S_MP_SUB_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_S_MP_MUL_DIGS_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
++--->BN_S_MP_ADD_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
 
 
-BN_MP_LSHD_C
-+--->BN_MP_GROW_C
-+--->BN_MP_RSHD_C
+BN_MP_REDUCE_2K_SETUP_C
++--->BN_MP_INIT_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_2EXPT_C
 |   +--->BN_MP_ZERO_C
-
-
-BN_MP_ADD_D_C
-+--->BN_MP_GROW_C
-+--->BN_MP_SUB_D_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_CLEAR_C
++--->BN_S_MP_SUB_C
+|   +--->BN_MP_GROW_C
 |   +--->BN_MP_CLAMP_C
-+--->BN_MP_CLAMP_C
-
-
-BN_MP_GET_LONG_C
-
-
-BN_MP_GET_LONG_LONG_C
 
 
-BN_MP_CLEAR_C
-
-
-BN_MP_EXTEUCLID_C
-+--->BN_MP_INIT_MULTI_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_SET_C
+BN_MP_REDUCE_2K_SETUP_L_C
++--->BN_MP_INIT_C
++--->BN_MP_2EXPT_C
 |   +--->BN_MP_ZERO_C
-+--->BN_MP_COPY_C
 |   +--->BN_MP_GROW_C
-+--->BN_MP_DIV_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_COUNT_BITS_C
-|   +--->BN_MP_ABS_C
-|   +--->BN_MP_MUL_2D_C
++--->BN_MP_COUNT_BITS_C
++--->BN_S_MP_SUB_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_REDUCE_C
++--->BN_MP_REDUCE_SETUP_C
+|   +--->BN_MP_2EXPT_C
+|   |   +--->BN_MP_ZERO_C
 |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_C
-|   +--->BN_MP_SUB_C
-|   |   +--->BN_S_MP_ADD_C
+|   +--->BN_MP_DIV_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_SET_C
+|   |   +--->BN_MP_COUNT_BITS_C
+|   |   +--->BN_MP_ABS_C
+|   |   +--->BN_MP_MUL_2D_C
 |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_ADD_C
-|   |   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_INIT_COPY_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_LSHD_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_MUL_D_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_DIV_2D_C
-|   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_RSHD_C
 |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CLEAR_MULTI_C
 |   |   +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_COPY_C
 |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_LSHD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_RSHD_C
-|   +--->BN_MP_RSHD_C
-|   +--->BN_MP_MUL_D_C
+|   +--->BN_MP_COPY_C
 |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLAMP_C
 |   +--->BN_MP_CLEAR_C
++--->BN_MP_RSHD_C
+|   +--->BN_MP_ZERO_C
 +--->BN_MP_MUL_C
 |   +--->BN_MP_TOOM_MUL_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
 |   |   +--->BN_MP_MOD_2D_C
 |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_MUL_2_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_ADD_C
@@ -11250,7 +10275,6 @@ BN_MP_EXTEUCLID_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_DIV_3_C
 |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_INIT_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_CLEAR_C
@@ -11260,7 +10284,6 @@ BN_MP_EXTEUCLID_C
 |   |   |   +--->BN_MP_CLEAR_C
 |   +--->BN_MP_KARATSUBA_MUL_C
 |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
 |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_S_MP_ADD_C
 |   |   |   +--->BN_MP_GROW_C
@@ -11272,18 +10295,39 @@ BN_MP_EXTEUCLID_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_LSHD_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
 |   |   +--->BN_MP_CLEAR_C
 |   +--->BN_FAST_S_MP_MUL_DIGS_C
 |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_CLAMP_C
 |   +--->BN_S_MP_MUL_DIGS_C
 |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
 |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_EXCH_C
 |   |   +--->BN_MP_CLEAR_C
++--->BN_S_MP_MUL_HIGH_DIGS_C
+|   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLEAR_C
++--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_MOD_2D_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_S_MP_MUL_DIGS_C
+|   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLEAR_C
 +--->BN_MP_SUB_C
 |   +--->BN_S_MP_ADD_C
 |   |   +--->BN_MP_GROW_C
@@ -11292,230 +10336,232 @@ BN_MP_EXTEUCLID_C
 |   +--->BN_S_MP_SUB_C
 |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_NEG_C
-+--->BN_MP_EXCH_C
-+--->BN_MP_CLEAR_MULTI_C
-|   +--->BN_MP_CLEAR_C
-
-
-BN_MP_TORADIX_N_C
-+--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-+--->BN_MP_DIV_D_C
-|   +--->BN_MP_COPY_C
++--->BN_MP_CMP_D_C
++--->BN_MP_SET_C
+|   +--->BN_MP_ZERO_C
++--->BN_MP_LSHD_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_ADD_C
+|   +--->BN_S_MP_ADD_C
 |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_DIV_2D_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_RSHD_C
 |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_DIV_3_C
-|   |   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_INIT_SIZE_C
++--->BN_MP_CMP_C
+|   +--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+|   +--->BN_MP_GROW_C
 |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CLEAR_C
 +--->BN_MP_CLEAR_C
 
 
-BN_MP_RADIX_SIZE_C
-+--->BN_MP_COUNT_BITS_C
-+--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-+--->BN_MP_DIV_D_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
+BN_MP_REDUCE_IS_2K_C
++--->BN_MP_REDUCE_2K_C
+|   +--->BN_MP_INIT_C
+|   +--->BN_MP_COUNT_BITS_C
 |   +--->BN_MP_DIV_2D_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_ZERO_C
 |   |   +--->BN_MP_MOD_2D_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
 |   |   +--->BN_MP_RSHD_C
 |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_DIV_3_C
-|   |   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_MUL_D_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
 |   +--->BN_MP_CLEAR_C
-+--->BN_MP_CLEAR_C
++--->BN_MP_COUNT_BITS_C
 
 
-BN_S_MP_MUL_HIGH_DIGS_C
-+--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_INIT_C
-+--->BN_MP_CLAMP_C
-+--->BN_MP_EXCH_C
-+--->BN_MP_CLEAR_C
+BN_MP_REDUCE_IS_2K_L_C
 
 
-BN_MP_SET_INT_C
-+--->BN_MP_ZERO_C
-+--->BN_MP_MUL_2D_C
+BN_MP_REDUCE_SETUP_C
++--->BN_MP_2EXPT_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_DIV_C
+|   +--->BN_MP_CMP_MAG_C
 |   +--->BN_MP_COPY_C
 |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_LSHD_C
-|   |   +--->BN_MP_RSHD_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_CLAMP_C
-
-
-BN_MP_DR_SETUP_C
-
-
-BN_MP_MUL_2_C
-+--->BN_MP_GROW_C
-
-
-BN_MP_FWRITE_C
-+--->BN_MP_RADIX_SIZE_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_INIT_MULTI_C
+|   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_SET_C
 |   +--->BN_MP_COUNT_BITS_C
-|   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_DIV_D_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_ABS_C
+|   +--->BN_MP_MUL_2D_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
 |   |   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_C
+|   +--->BN_MP_SUB_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_DIV_3_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_TORADIX_C
-|   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_COPY_C
+|   +--->BN_MP_ADD_C
+|   |   +--->BN_S_MP_ADD_C
 |   |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_DIV_D_C
-|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_SUB_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_RSHD_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_DIV_3_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_DIV_2D_C
+|   |   +--->BN_MP_MOD_2D_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_RSHD_C
 |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_INIT_C
+|   +--->BN_MP_INIT_C
+|   +--->BN_MP_INIT_COPY_C
 |   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_RSHD_C
+|   +--->BN_MP_RSHD_C
+|   +--->BN_MP_MUL_D_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLAMP_C
 |   +--->BN_MP_CLEAR_C
 
 
-BN_MP_GROW_C
+BN_MP_RSHD_C
++--->BN_MP_ZERO_C
 
 
-BN_MP_READ_RADIX_C
+BN_MP_SET_C
 +--->BN_MP_ZERO_C
-+--->BN_MP_MUL_D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_ADD_D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_SUB_D_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLAMP_C
 
 
-BN_S_MP_MUL_DIGS_C
-+--->BN_FAST_S_MP_MUL_DIGS_C
+BN_MP_SET_INT_C
++--->BN_MP_ZERO_C
++--->BN_MP_MUL_2D_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
 |   +--->BN_MP_GROW_C
+|   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_RSHD_C
 |   +--->BN_MP_CLAMP_C
-+--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_INIT_C
 +--->BN_MP_CLAMP_C
-+--->BN_MP_EXCH_C
-+--->BN_MP_CLEAR_C
 
 
-BN_PRIME_TAB_C
+BN_MP_SET_LONG_C
 
 
-BN_MP_IS_SQUARE_C
-+--->BN_MP_MOD_D_C
-|   +--->BN_MP_DIV_D_C
+BN_MP_SET_LONG_LONG_C
+
+
+BN_MP_SHRINK_C
+
+
+BN_MP_SIGNED_BIN_SIZE_C
++--->BN_MP_UNSIGNED_BIN_SIZE_C
+|   +--->BN_MP_COUNT_BITS_C
+
+
+BN_MP_SQRMOD_C
++--->BN_MP_INIT_C
++--->BN_MP_SQR_C
+|   +--->BN_MP_TOOM_SQR_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_DIV_2D_C
+|   |   +--->BN_MP_RSHD_C
 |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   |   +--->BN_MP_MOD_2D_C
+|   |   +--->BN_MP_MUL_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
 |   |   +--->BN_MP_DIV_3_C
 |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_INIT_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_KARATSUBA_SQR_C
 |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
 |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-+--->BN_MP_INIT_SET_INT_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_SET_INT_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_S_MP_ADD_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_FAST_S_MP_SQR_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_S_MP_SQR_C
+|   |   +--->BN_MP_INIT_SIZE_C
 |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
 +--->BN_MP_MOD_C
-|   +--->BN_MP_INIT_C
+|   +--->BN_MP_INIT_SIZE_C
 |   +--->BN_MP_DIV_C
 |   |   +--->BN_MP_CMP_MAG_C
 |   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_ZERO_C
 |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
 |   |   +--->BN_MP_SET_C
 |   |   +--->BN_MP_COUNT_BITS_C
 |   |   +--->BN_MP_ABS_C
@@ -11542,14 +10588,10 @@ BN_MP_IS_SQUARE_C
 |   |   +--->BN_MP_DIV_2D_C
 |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLEAR_C
 |   |   |   +--->BN_MP_RSHD_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
 |   |   +--->BN_MP_EXCH_C
 |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_INIT_SIZE_C
 |   |   +--->BN_MP_INIT_COPY_C
 |   |   +--->BN_MP_LSHD_C
 |   |   |   +--->BN_MP_GROW_C
@@ -11559,8 +10601,6 @@ BN_MP_IS_SQUARE_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_CLEAR_C
 |   +--->BN_MP_EXCH_C
 |   +--->BN_MP_ADD_C
 |   |   +--->BN_S_MP_ADD_C
@@ -11570,161 +10610,463 @@ BN_MP_IS_SQUARE_C
 |   |   +--->BN_S_MP_SUB_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_GET_INT_C
-+--->BN_MP_SQRT_C
-|   +--->BN_MP_N_ROOT_C
-|   |   +--->BN_MP_N_ROOT_EX_C
-|   |   |   +--->BN_MP_INIT_C
+
+
+BN_MP_SQRTMOD_PRIME_C
++--->BN_MP_CMP_D_C
++--->BN_MP_ZERO_C
++--->BN_MP_JACOBI_C
+|   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_CNT_LSB_C
+|   +--->BN_MP_DIV_2D_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_MOD_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_DIV_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   +--->BN_MP_SET_C
-|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   +--->BN_MP_ABS_C
+|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_MULTI_C
+|   +--->BN_MP_INIT_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_MOD_D_C
+|   +--->BN_MP_DIV_D_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_3_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_INIT_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
++--->BN_MP_ADD_D_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_SUB_D_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_2_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_EXPTMOD_C
+|   +--->BN_MP_INIT_C
+|   +--->BN_MP_INVMOD_C
+|   |   +--->BN_FAST_MP_INVMOD_C
 |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_EXPT_D_EX_C
-|   |   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_MUL_C
-|   |   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   +--->BN_MP_MOD_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   |   +--->BN_MP_ABS_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_INVMOD_SLOW_C
+|   |   |   +--->BN_MP_MOD_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   |   |   +--->BN_MP_ABS_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
 |   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
 |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_SQR_C
-|   |   |   |   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_ABS_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLEAR_MULTI_C
+|   +--->BN_MP_REDUCE_IS_2K_L_C
+|   +--->BN_S_MP_EXPTMOD_C
+|   |   +--->BN_MP_COUNT_BITS_C
+|   |   +--->BN_MP_REDUCE_SETUP_C
+|   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_DIV_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_REDUCE_C
+|   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_MUL_C
+|   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SQR_C
+|   |   |   |   |   +--->BN_MP_DIV_3_C
 |   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_S_MP_MUL_HIGH_DIGS_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_REDUCE_2K_SETUP_L_C
+|   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_REDUCE_2K_L_C
+|   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_MUL_C
 |   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   |   +--->BN_MP_MUL_2_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_ADD_C
@@ -11743,829 +11085,898 @@ BN_MP_IS_SQUARE_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MOD_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_DIV_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_SQR_C
+|   |   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_DIV_3_C
 |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_DIV_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   +--->BN_MP_ABS_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_S_MP_SQR_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_MUL_C
+|   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_KARATSUBA_MUL_C
 |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_SUB_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_D_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_RSHD_C
-|   +--->BN_MP_DIV_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_SET_C
-|   |   +--->BN_MP_COUNT_BITS_C
-|   |   +--->BN_MP_ABS_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_SET_C
 |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_ADD_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_DIV_2_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_SQR_C
-|   +--->BN_MP_TOOM_SQR_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MUL_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_DR_IS_MODULUS_C
+|   +--->BN_MP_REDUCE_IS_2K_C
+|   |   +--->BN_MP_REDUCE_2K_C
+|   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SUB_C
 |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_3_C
-|   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_INIT_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_COUNT_BITS_C
+|   +--->BN_MP_EXPTMOD_FAST_C
+|   |   +--->BN_MP_COUNT_BITS_C
 |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_MONTGOMERY_SETUP_C
+|   |   +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_FAST_S_MP_SQR_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_SQR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-+--->BN_MP_CMP_MAG_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_COPY_C
-+--->BN_MP_GROW_C
-
-
-BN_MP_TOOM_SQR_C
-+--->BN_MP_INIT_MULTI_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_MOD_2D_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_COPY_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_RSHD_C
-|   +--->BN_MP_ZERO_C
-+--->BN_MP_SQR_C
-|   +--->BN_MP_KARATSUBA_SQR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_MONTGOMERY_REDUCE_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_DR_SETUP_C
+|   |   +--->BN_MP_DR_REDUCE_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_MP_CLEAR_C
-|   +--->BN_FAST_S_MP_SQR_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_SQR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-+--->BN_MP_MUL_2_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_ADD_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_SUB_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_DIV_2_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_MUL_2D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_LSHD_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_MUL_D_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_DIV_3_C
-|   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_LSHD_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_CLEAR_MULTI_C
-|   +--->BN_MP_CLEAR_C
-
-
-BN_MP_KARATSUBA_SQR_C
-+--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_INIT_C
-+--->BN_MP_CLAMP_C
-+--->BN_MP_SQR_C
-|   +--->BN_MP_TOOM_SQR_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_REDUCE_2K_SETUP_C
+|   |   |   +--->BN_MP_2EXPT_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MUL_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_REDUCE_2K_C
+|   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+|   |   |   +--->BN_MP_2EXPT_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_MUL_2_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_DIV_2_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_DIV_3_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MULMOD_C
+|   |   |   +--->BN_MP_MUL_C
+|   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_MOD_C
+|   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_SET_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_SET_C
+|   |   +--->BN_MP_MOD_C
+|   |   |   +--->BN_MP_DIV_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_FAST_S_MP_SQR_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_S_MP_SQR_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_C
-+--->BN_S_MP_ADD_C
-|   +--->BN_MP_GROW_C
-+--->BN_S_MP_SUB_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_LSHD_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_ZERO_C
-+--->BN_MP_ADD_C
-|   +--->BN_MP_CMP_MAG_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_GCD_C
-+--->BN_MP_ABS_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-+--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-+--->BN_MP_CNT_LSB_C
-+--->BN_MP_DIV_2D_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_MOD_2D_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_RSHD_C
-|   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-+--->BN_MP_CMP_MAG_C
-+--->BN_MP_EXCH_C
-+--->BN_S_MP_SUB_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_MUL_2D_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_LSHD_C
-|   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_ZERO_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_MOD_2D_C
-+--->BN_MP_ZERO_C
-+--->BN_MP_COPY_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_CLAMP_C
-
-
-BN_FAST_MP_MONTGOMERY_REDUCE_C
-+--->BN_MP_GROW_C
-+--->BN_MP_RSHD_C
-|   +--->BN_MP_ZERO_C
-+--->BN_MP_CLAMP_C
-+--->BN_MP_CMP_MAG_C
-+--->BN_S_MP_SUB_C
-
-
-BN_MP_SUBMOD_C
-+--->BN_MP_INIT_C
-+--->BN_MP_SUB_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_CLEAR_C
-+--->BN_MP_MOD_C
-|   +--->BN_MP_DIV_C
-|   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_SET_C
-|   |   +--->BN_MP_COUNT_BITS_C
-|   |   +--->BN_MP_ABS_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_SQR_C
+|   |   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_S_MP_SQR_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_MUL_C
+|   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_S_MP_MUL_DIGS_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_EXCH_C
 |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_COPY_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_SUB_D_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_SET_INT_C
+|   +--->BN_MP_MUL_2D_C
+|   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-|   +--->BN_MP_ADD_C
-|   |   +--->BN_S_MP_ADD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_S_MP_SUB_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-
-
-BN_MP_GET_INT_C
-
-
-BN_MP_SET_LONG_C
-
-
-BN_MP_ADDMOD_C
-+--->BN_MP_INIT_C
-+--->BN_MP_ADD_C
-|   +--->BN_S_MP_ADD_C
-|   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_CLEAR_C
-+--->BN_MP_MOD_C
-|   +--->BN_MP_DIV_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_SET_C
-|   |   +--->BN_MP_COUNT_BITS_C
-|   |   +--->BN_MP_ABS_C
-|   |   +--->BN_MP_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_SQRMOD_C
+|   +--->BN_MP_INIT_C
+|   +--->BN_MP_SQR_C
+|   |   +--->BN_MP_TOOM_SQR_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CMP_C
-|   |   +--->BN_MP_SUB_C
 |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2D_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_SQR_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_MOD_C
 |   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_MUL_D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_EXCH_C
-
-
-BN_MP_PRIME_FERMAT_C
-+--->BN_MP_CMP_D_C
-+--->BN_MP_INIT_C
-+--->BN_MP_EXPTMOD_C
-|   +--->BN_MP_INVMOD_C
-|   |   +--->BN_FAST_MP_INVMOD_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_DIV_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   +--->BN_MP_ABS_C
+|   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_MOD_C
-|   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_SET_C
-|   |   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   |   +--->BN_MP_ABS_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
++--->BN_MP_MULMOD_C
+|   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_INIT_C
+|   +--->BN_MP_MUL_C
+|   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_MOD_C
+|   |   +--->BN_MP_DIV_C
+|   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   +--->BN_MP_SET_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_DIV_2_C
+|   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   +--->BN_MP_ABS_C
+|   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_C
 |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
++--->BN_MP_SET_C
++--->BN_MP_CLEAR_MULTI_C
+|   +--->BN_MP_CLEAR_C
+
+
+BN_MP_SQRT_C
++--->BN_MP_N_ROOT_C
+|   +--->BN_MP_N_ROOT_EX_C
+|   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_EXPT_D_EX_C
+|   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_INVMOD_SLOW_C
-|   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_MP_MOD_C
-|   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_SET_C
-|   |   |   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   |   |   +--->BN_MP_ABS_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_MUL_C
+|   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_SUB_C
 |   |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_DIV_2_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_SET_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SUB_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_CLEAR_MULTI_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_ABS_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLEAR_MULTI_C
-|   +--->BN_MP_REDUCE_IS_2K_L_C
-|   +--->BN_S_MP_EXPTMOD_C
-|   |   +--->BN_MP_COUNT_BITS_C
-|   |   +--->BN_MP_REDUCE_SETUP_C
-|   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_DIV_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_SET_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_REDUCE_C
-|   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MUL_C
-|   |   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_SQR_C
+|   |   |   |   +--->BN_MP_TOOM_SQR_C
 |   |   |   |   |   +--->BN_MP_INIT_MULTI_C
 |   |   |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   |   +--->BN_MP_MUL_2_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_ADD_C
@@ -12600,606 +12011,763 @@ BN_MP_PRIME_FERMAT_C
 |   |   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   +--->BN_MP_KARATSUBA_SQR_C
 |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_S_MP_SQR_C
 |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_S_MP_MUL_HIGH_DIGS_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+|   |   +--->BN_MP_MUL_C
+|   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_MUL_D_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_KARATSUBA_MUL_C
 |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   +--->BN_MP_ABS_C
+|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_C
+|   |   |   +--->BN_MP_ADD_C
 |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_SET_C
-|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_DIV_2D_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_COPY_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_CMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_MP_SUB_D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
++--->BN_MP_ZERO_C
++--->BN_MP_INIT_COPY_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_RSHD_C
++--->BN_MP_DIV_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_INIT_MULTI_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_SET_C
+|   +--->BN_MP_COUNT_BITS_C
+|   +--->BN_MP_ABS_C
+|   +--->BN_MP_MUL_2D_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_C
+|   +--->BN_MP_SUB_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_ADD_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_DIV_2D_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_MUL_D_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_ADD_C
+|   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_2_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_SQR_C
++--->BN_MP_TOOM_SQR_C
+|   +--->BN_MP_INIT_MULTI_C
+|   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_MOD_2D_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_ZERO_C
+|   +--->BN_MP_MUL_2_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_ADD_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_SUB_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_DIV_2_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_MUL_2D_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_MUL_D_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_DIV_3_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_CLEAR_C
++--->BN_MP_KARATSUBA_SQR_C
+|   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_INIT_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_ZERO_C
+|   +--->BN_MP_ADD_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   +--->BN_MP_CLEAR_C
++--->BN_FAST_S_MP_SQR_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_S_MP_SQR_C
+|   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_INIT_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLEAR_C
+
+
+BN_MP_SUBMOD_C
++--->BN_MP_INIT_C
++--->BN_MP_SUB_C
+|   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
++--->BN_MP_MOD_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_DIV_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   +--->BN_MP_SET_C
+|   |   +--->BN_MP_COUNT_BITS_C
+|   |   +--->BN_MP_ABS_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_REDUCE_2K_SETUP_L_C
-|   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_REDUCE_2K_L_C
-|   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_MUL_C
-|   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_ADD_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+
+
+BN_MP_SUB_C
++--->BN_S_MP_ADD_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
+
+
+BN_MP_SUB_D_C
++--->BN_MP_GROW_C
++--->BN_MP_ADD_D_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_TOOM_MUL_C
++--->BN_MP_INIT_MULTI_C
+|   +--->BN_MP_INIT_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_MOD_2D_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_RSHD_C
+|   +--->BN_MP_ZERO_C
++--->BN_MP_MUL_C
+|   +--->BN_MP_KARATSUBA_MUL_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
 |   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MOD_C
-|   |   |   +--->BN_MP_DIV_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_SET_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_ADD_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_S_MP_MUL_DIGS_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
++--->BN_MP_MUL_2_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_ADD_C
+|   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
++--->BN_MP_SUB_C
+|   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_2_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_2D_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_LSHD_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_D_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_3_C
+|   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_INIT_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_LSHD_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_CLEAR_MULTI_C
+|   +--->BN_MP_CLEAR_C
+
+
+BN_MP_TOOM_SQR_C
++--->BN_MP_INIT_MULTI_C
+|   +--->BN_MP_INIT_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_MOD_2D_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_RSHD_C
+|   +--->BN_MP_ZERO_C
++--->BN_MP_SQR_C
+|   +--->BN_MP_KARATSUBA_SQR_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_FAST_S_MP_SQR_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_S_MP_SQR_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
++--->BN_MP_MUL_2_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_ADD_C
+|   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
++--->BN_MP_SUB_C
+|   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_2_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_2D_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_LSHD_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_D_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_3_C
+|   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_INIT_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_LSHD_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_CLEAR_MULTI_C
+|   +--->BN_MP_CLEAR_C
+
+
+BN_MP_TORADIX_C
++--->BN_MP_INIT_COPY_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_DIV_D_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_DIV_2D_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_DIV_3_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_TORADIX_N_C
++--->BN_MP_INIT_COPY_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_DIV_D_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_DIV_2D_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_DIV_3_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_TO_SIGNED_BIN_C
++--->BN_MP_TO_UNSIGNED_BIN_C
+|   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_INIT_SIZE_C
 |   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_SQR_C
-|   |   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_KARATSUBA_SQR_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_FAST_S_MP_SQR_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_DIV_2D_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLEAR_C
+
+
+BN_MP_TO_SIGNED_BIN_N_C
++--->BN_MP_SIGNED_BIN_SIZE_C
+|   +--->BN_MP_UNSIGNED_BIN_SIZE_C
+|   |   +--->BN_MP_COUNT_BITS_C
++--->BN_MP_TO_SIGNED_BIN_C
+|   +--->BN_MP_TO_UNSIGNED_BIN_C
+|   |   +--->BN_MP_INIT_COPY_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SQR_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_MUL_C
-|   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_SET_C
 |   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_EXCH_C
-|   +--->BN_MP_DR_IS_MODULUS_C
-|   +--->BN_MP_REDUCE_IS_2K_C
-|   |   +--->BN_MP_REDUCE_2K_C
-|   |   |   +--->BN_MP_COUNT_BITS_C
-|   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CLEAR_C
+
+
+BN_MP_TO_UNSIGNED_BIN_C
++--->BN_MP_INIT_COPY_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_DIV_2D_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_MOD_2D_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_RSHD_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_TO_UNSIGNED_BIN_N_C
++--->BN_MP_UNSIGNED_BIN_SIZE_C
+|   +--->BN_MP_COUNT_BITS_C
++--->BN_MP_TO_UNSIGNED_BIN_C
+|   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_DIV_2D_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLEAR_C
+
+
+BN_MP_UNSIGNED_BIN_SIZE_C
++--->BN_MP_COUNT_BITS_C
+
+
+BN_MP_XOR_C
++--->BN_MP_INIT_COPY_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_COPY_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLEAR_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_ZERO_C
+
+
+BN_PRIME_TAB_C
+
+
+BN_REVERSE_C
+
+
+BN_S_MP_ADD_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_S_MP_EXPTMOD_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_INIT_C
++--->BN_MP_CLEAR_C
++--->BN_MP_REDUCE_SETUP_C
+|   +--->BN_MP_2EXPT_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_DIV_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   +--->BN_MP_SET_C
+|   |   +--->BN_MP_ABS_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_ADD_C
 |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_COUNT_BITS_C
-|   +--->BN_MP_EXPTMOD_FAST_C
-|   |   +--->BN_MP_COUNT_BITS_C
-|   |   +--->BN_MP_MONTGOMERY_SETUP_C
-|   |   +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
-|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_MONTGOMERY_REDUCE_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_LSHD_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CLAMP_C
 |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_DR_SETUP_C
-|   |   +--->BN_MP_DR_REDUCE_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_MUL_D_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_REDUCE_2K_SETUP_C
-|   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_REDUCE_2K_C
-|   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
-|   |   |   +--->BN_MP_2EXPT_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_SET_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MULMOD_C
-|   |   |   +--->BN_MP_MUL_C
-|   |   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   +--->BN_MP_MOD_C
-|   |   |   |   +--->BN_MP_DIV_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   |   +--->BN_MP_SET_C
-|   |   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SET_C
-|   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_MOD_C
-|   |   |   +--->BN_MP_DIV_C
-|   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_CMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2D_C
-|   |   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   +--->BN_MP_CLAMP_C
++--->BN_MP_REDUCE_C
+|   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_ZERO_C
+|   +--->BN_MP_MUL_C
+|   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_ADD_C
 |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
@@ -13208,149 +12776,413 @@ BN_MP_PRIME_FERMAT_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   +--->BN_S_MP_MUL_HIGH_DIGS_C
+|   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_MOD_2D_C
+|   |   +--->BN_MP_ZERO_C
 |   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_SQR_C
-|   |   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MUL_2_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_S_MP_MUL_DIGS_C
+|   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   +--->BN_MP_SUB_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_D_C
+|   +--->BN_MP_SET_C
+|   |   +--->BN_MP_ZERO_C
+|   +--->BN_MP_LSHD_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_MP_ADD_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
++--->BN_MP_REDUCE_2K_SETUP_L_C
+|   +--->BN_MP_2EXPT_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_GROW_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
++--->BN_MP_REDUCE_2K_L_C
+|   +--->BN_MP_DIV_2D_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_MUL_C
+|   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_COPY_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_MUL_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_SUB_C
+|   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_DIV_2_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_2D_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_KARATSUBA_SQR_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_MUL_D_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_DIV_3_C
 |   |   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   |   +--->BN_MP_EXCH_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_MUL_DIGS_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   +--->BN_S_MP_ADD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CMP_MAG_C
+|   +--->BN_S_MP_SUB_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
++--->BN_MP_MOD_C
+|   +--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_DIV_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   +--->BN_MP_SET_C
+|   |   +--->BN_MP_ABS_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_2D_C
+|   |   |   +--->BN_MP_MOD_2D_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_INIT_COPY_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_ADD_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CMP_MAG_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_SQR_C
+|   +--->BN_MP_TOOM_SQR_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MUL_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_SQR_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_MUL_C
-|   |   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   |   +--->BN_MP_INIT_MULTI_C
-|   |   |   |   +--->BN_MP_MOD_2D_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   +--->BN_MP_MUL_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_C
-|   |   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_2_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_2D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_MUL_D_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_DIV_3_C
-|   |   |   |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_KARATSUBA_MUL_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_ADD_C
-|   |   |   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   +--->BN_MP_DIV_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_3_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   +--->BN_MP_KARATSUBA_SQR_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   +--->BN_FAST_S_MP_SQR_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_S_MP_SQR_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_EXCH_C
++--->BN_MP_MUL_C
+|   +--->BN_MP_TOOM_MUL_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   +--->BN_MP_MOD_2D_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_RSHD_C
+|   |   |   +--->BN_MP_ZERO_C
+|   |   +--->BN_MP_MUL_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_S_MP_MUL_DIGS_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_SUB_C
+|   |   |   +--->BN_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_2_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_MUL_D_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_DIV_3_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   +--->BN_MP_KARATSUBA_MUL_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_C
+|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_S_MP_SUB_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_LSHD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_CLAMP_C
+|   +--->BN_S_MP_MUL_DIGS_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_EXCH_C
-+--->BN_MP_CMP_C
-|   +--->BN_MP_CMP_MAG_C
-+--->BN_MP_CLEAR_C
++--->BN_MP_SET_C
+|   +--->BN_MP_ZERO_C
++--->BN_MP_EXCH_C
 
 
-BN_MP_REDUCE_2K_SETUP_L_C
-+--->BN_MP_INIT_C
-+--->BN_MP_2EXPT_C
-|   +--->BN_MP_ZERO_C
+BN_S_MP_MUL_DIGS_C
++--->BN_FAST_S_MP_MUL_DIGS_C
 |   +--->BN_MP_GROW_C
-+--->BN_MP_COUNT_BITS_C
-+--->BN_S_MP_SUB_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_S_MP_MUL_HIGH_DIGS_C
++--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
 |   +--->BN_MP_GROW_C
 |   +--->BN_MP_CLAMP_C
++--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_S_MP_SQR_C
++--->BN_MP_INIT_SIZE_C
+|   +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
 +--->BN_MP_CLEAR_C
 
 
+BN_S_MP_SUB_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
diff --git a/libtommath/changes.txt b/libtommath/changes.txt
index d70d589..3379f71 100644
--- a/libtommath/changes.txt
+++ b/libtommath/changes.txt
@@ -1,6 +1,20 @@
+XXX, 2017
+v1.0.1
+       -- Dmitry Kovalenko provided fixes to mp_add_d() and mp_init_copy()
+       -- Matt Johnston contributed some improvements to mp_div_2d(),
+          mp_exptmod_fast(), mp_mod() and mp_mulmod()
+       -- Julien Nabet provided a fix to the error handling in mp_init_multi()
+       -- Ben Gardner provided a fix regarding usage of reserved keywords
+       -- Fixed mp_rand() to fill the correct number of bits
+       -- Fixed mp_invmod()
+       -- Use the same 64-bit detection code as in libtomcrypt
+       -- Correct usage of DESTDIR, PREFIX, etc. when installing the library
+       -- Francois Perrad updated all the perl scripts to an actual perl version
+
+
 Feb 5th, 2016
-v1.0.0
-       -- Bump to 1.0.0
+v1.0
+       -- Bump to 1.0
        -- Dirkjan Bussink provided a faster version of mp_expt_d()
        -- Moritz Lenz contributed a fix to mp_mod()
           and provided mp_get_long() and mp_set_long()
diff --git a/libtommath/makefile b/libtommath/makefile
index f90971c..fdd2435 100644
--- a/libtommath/makefile
+++ b/libtommath/makefile
@@ -8,12 +8,6 @@ else
 silent=@
 endif
 
-%.o: %.c
-ifneq ($V,1)
-	@echo "   * ${CC} $@"
-endif
-	${silent} ${CC} -c ${CFLAGS} $^ -o $@
-
 #default files to install
 ifndef LIBNAME
    LIBNAME=libtommath.a
@@ -21,7 +15,13 @@ endif
 
 coverage: LIBNAME:=-Wl,--whole-archive $(LIBNAME)  -Wl,--no-whole-archive
 
-include makefile.include
+include makefile_include.mk
+
+%.o: %.c
+ifneq ($V,1)
+	@echo "   * ${CC} $@"
+endif
+	${silent} ${CC} -c ${CFLAGS} $< -o $@
 
 LCOV_ARGS=--directory .
 
@@ -53,6 +53,8 @@ bn_s_mp_sqr.o bn_s_mp_sub.o
 
 #END_INS
 
+$(OBJECTS): $(HEADERS)
+
 $(LIBNAME):  $(OBJECTS)
 	$(AR) $(ARFLAGS) $@ $(OBJECTS)
 	$(RANLIB) $@
@@ -86,6 +88,10 @@ install: $(LIBNAME)
 	install -m 644 $(LIBNAME) $(DESTDIR)$(LIBPATH)
 	install -m 644 $(HEADERS_PUB) $(DESTDIR)$(INCPATH)
 
+uninstall:
+	rm $(DESTDIR)$(LIBPATH)/$(LIBNAME)
+	rm $(HEADERS_PUB:%=$(DESTDIR)$(INCPATH)/%)
+
 test: $(LIBNAME) demo/demo.o
 	$(CC) $(CFLAGS) demo/demo.o $(LIBNAME) $(LFLAGS) -o test
 
@@ -96,94 +102,50 @@ test_standalone: $(LIBNAME) demo/demo.o
 mtest:
 	cd mtest ; $(CC) $(CFLAGS) -O0 mtest.c $(LFLAGS) -o mtest
 
+travis_mtest: test mtest
+	@ for i in `seq 1 10` ; do sleep 500 && echo alive; done &
+	./mtest/mtest 666666 | ./test > test.log
+
 timing: $(LIBNAME)
 	$(CC) $(CFLAGS) -DTIMER demo/timing.c $(LIBNAME) $(LFLAGS) -o ltmtest
 
-coveralls: coverage
-	cpp-coveralls
-
-# makes the LTM book DVI file, requires tetex, perl and makeindex [part of tetex I think]
-docdvi: tommath.src
-	cd pics ; MAKE=${MAKE} ${MAKE}
-	echo "hello" > tommath.ind
-	perl booker.pl
-	latex tommath > /dev/null
-	latex tommath > /dev/null
-	makeindex tommath
-	latex tommath > /dev/null
-
-# poster, makes the single page PDF poster
-poster: poster.tex
-	cp poster.tex poster.bak
-	touch --reference=poster.tex poster.bak
-	(printf "%s" "\def\fixedpdfdate{"; date +'D:%Y%m%d%H%M%S%:z' -d @$$(stat --format=%Y poster.tex) | sed "s/:\([0-9][0-9]\)$$/'\1'}/g") > poster-deterministic.tex
-	printf "%s\n" "\pdfinfo{" >> poster-deterministic.tex
-	printf "%s\n" "  /CreationDate (\fixedpdfdate)" >> poster-deterministic.tex
-	printf "%s\n}\n" "  /ModDate (\fixedpdfdate)" >> poster-deterministic.tex
-	cat poster.tex >> poster-deterministic.tex
-	mv poster-deterministic.tex poster.tex
-	touch --reference=poster.bak poster.tex
-	pdflatex poster
-	sed -b -i 's,^/ID \[.*\]$$,/ID [<0> <0>],g' poster.pdf
-	mv poster.bak poster.tex
-	rm -f poster.aux poster.log poster.out
-
-# makes the LTM book PDF file, requires tetex, cleans up the LaTeX temp files
-docs:   docdvi
-	dvipdf tommath
-	rm -f tommath.log tommath.aux tommath.dvi tommath.idx tommath.toc tommath.lof tommath.ind tommath.ilg
-	cd pics ; MAKE=${MAKE} ${MAKE} clean
-
-#LTM user manual
-mandvi: bn.tex
-	cp bn.tex bn.bak
-	touch --reference=bn.tex bn.bak
-	(printf "%s" "\def\fixedpdfdate{"; date +'D:%Y%m%d%H%M%S%:z' -d @$$(stat --format=%Y bn.tex) | sed "s/:\([0-9][0-9]\)$$/'\1'}/g") > bn-deterministic.tex
-	printf "%s\n" "\pdfinfo{" >> bn-deterministic.tex
-	printf "%s\n" "  /CreationDate (\fixedpdfdate)" >> bn-deterministic.tex
-	printf "%s\n}\n" "  /ModDate (\fixedpdfdate)" >> bn-deterministic.tex
-	cat bn.tex >> bn-deterministic.tex
-	mv bn-deterministic.tex bn.tex
-	touch --reference=bn.bak bn.tex
-	echo "hello" > bn.ind
-	latex bn > /dev/null
-	latex bn > /dev/null
-	makeindex bn
-	latex bn > /dev/null
-
-#LTM user manual [pdf]
-manual:	mandvi
-	pdflatex bn >/dev/null
-	sed -b -i 's,^/ID \[.*\]$$,/ID [<0> <0>],g' bn.pdf
-	mv bn.bak bn.tex
-	rm -f bn.aux bn.dvi bn.log bn.idx bn.lof bn.out bn.toc
+# You have to create a file .coveralls.yml with the content "repo_token: <the token>"
+# in the base folder to be able to submit to coveralls
+coveralls: lcov
+	coveralls-lcov
+
+docdvi poster docs mandvi manual:
+	$(MAKE) -C doc/ $@ V=$(V)
 
 pretty:
 	perl pretty.build
 
-#\zipup the project (take that!)
-no_oops: clean
-	cd .. ; cvs commit
-	echo Scanning for scratch/dirty files
-	find . -type f | grep -v CVS | xargs -n 1 bash mess.sh
-
 .PHONY: pre_gen
 pre_gen:
 	perl gen.pl
 	sed -e 's/[[:blank:]]*$$//' mpi.c > pre_gen/mpi.c
 	rm mpi.c
 
-zipup:
-	rm -rf ../libtommath-$(VERSION) \
-		&& rm -f ../ltm-$(VERSION).zip ../ltm-$(VERSION).zip.asc ../ltm-$(VERSION).tar.xz ../ltm-$(VERSION).tar.xz.asc
-	git archive HEAD --prefix=libtommath-$(VERSION)/ > ../libtommath-$(VERSION).tar
-	cd .. ; tar xf libtommath-$(VERSION).tar
-	MAKE=${MAKE} ${MAKE} -C ../libtommath-$(VERSION) clean manual poster docs
-	tar -c ../libtommath-$(VERSION)/* | xz -9 > ../ltm-$(VERSION).tar.xz
-	find ../libtommath-$(VERSION)/ -type f -exec unix2dos -q {} \;
-	cd .. ; zip -9r ltm-$(VERSION).zip libtommath-$(VERSION)
-	gpg -b -a ../ltm-$(VERSION).tar.xz && gpg -b -a ../ltm-$(VERSION).zip
+zipup: clean pre_gen new_file manual poster docs
+	@# Update the index, so diff-index won't fail in case the pdf has been created.
+	@#   As the pdf creation modifies the tex files, git sometimes detects the
+	@#   modified files, but misses that it's put back to its original version.
+	@git update-index --refresh
+	@git diff-index --quiet HEAD -- || ( echo "FAILURE: uncommited changes or not a git" && exit 1 )
+	rm -rf libtommath-$(VERSION) ltm-$(VERSION).*
+	@# files/dirs excluded from "git archive" are defined in .gitattributes
+	git archive --format=tar --prefix=libtommath-$(VERSION)/ HEAD | tar x
+	mkdir -p libtommath-$(VERSION)/doc
+	cp doc/bn.pdf doc/tommath.pdf doc/poster.pdf libtommath-$(VERSION)/doc/
+	tar -c libtommath-$(VERSION)/ | xz -6e -c - > ltm-$(VERSION).tar.xz
+	zip -9rq ltm-$(VERSION).zip libtommath-$(VERSION)
+	rm -rf libtommath-$(VERSION)
+	gpg -b -a ltm-$(VERSION).tar.xz
+	gpg -b -a ltm-$(VERSION).zip
 
 new_file:
 	bash updatemakes.sh
 	perl dep.pl
+
+perlcritic:
+	perlcritic *.pl
diff --git a/libtommath/makefile.shared b/libtommath/makefile.shared
index 559720e..67213a2 100644
--- a/libtommath/makefile.shared
+++ b/libtommath/makefile.shared
@@ -7,9 +7,16 @@ ifndef LIBNAME
    LIBNAME=libtommath.la
 endif
 
-include makefile.include
+include makefile_include.mk
 
-LT	?= libtool
+
+ifndef LT
+  ifeq ($(PLATFORM), Darwin)
+    LT:=glibtool
+  else
+    LT:=libtool
+  endif
+endif
 LTCOMPILE = $(LT) --mode=compile --tag=CC $(CC)
 
 LCOV_ARGS=--directory .libs --directory .
@@ -47,14 +54,24 @@ objs: $(OBJECTS)
 .c.o:
 	$(LTCOMPILE) $(CFLAGS) $(LDFLAGS) -o $@ -c $<
 
+LOBJECTS = $(OBJECTS:.o=.lo)
+
 $(LIBNAME):  $(OBJECTS)
-	$(LT) --mode=link --tag=CC $(CC) $(LDFLAGS) *.lo -o $(LIBNAME) -rpath $(LIBPATH) -version-info $(VERSION_SO)
+	$(LT) --mode=link --tag=CC $(CC) $(LDFLAGS) $(LOBJECTS) -o $(LIBNAME) -rpath $(LIBPATH) -version-info $(VERSION_SO)
 
 install: $(LIBNAME)
 	install -d $(DESTDIR)$(LIBPATH)
 	install -d $(DESTDIR)$(INCPATH)
-	$(LT) --mode=install install -c $(LIBNAME) $(DESTDIR)$(LIBPATH)/$(LIBNAME)
+	$(LT) --mode=install install -m 644 $(LIBNAME) $(DESTDIR)$(LIBPATH)/$(LIBNAME)
 	install -m 644 $(HEADERS_PUB) $(DESTDIR)$(INCPATH)
+	sed -e 's,^prefix=.*,prefix=$(PREFIX),' -e 's,^Version:.*,Version: $(VERSION_PC),' libtommath.pc.in > libtommath.pc
+	install -d $(DESTDIR)$(LIBPATH)/pkgconfig
+	install -m 644 libtommath.pc $(DESTDIR)$(LIBPATH)/pkgconfig/
+
+uninstall:
+	$(LT) --mode=uninstall rm $(DESTDIR)$(LIBPATH)/$(LIBNAME)
+	rm $(HEADERS_PUB:%=$(DESTDIR)$(INCPATH)/%)
+	rm $(DESTDIR)$(LIBPATH)/pkgconfig/libtommath.pc
 
 test: $(LIBNAME) demo/demo.o
 	$(CC) $(CFLAGS) -c demo/demo.c -o demo/demo.o
-- 
cgit v0.12


From d1a565fde90f8805d8e50073455049f92bef1d43 Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Wed, 30 Aug 2017 11:20:19 +0000
Subject: Cherry-pick
 [https://github.com/libtom/libtommath/commit/a0a86c696a7182f8be4b10bb79a1c5c971dc9561]:
 Merge branch 'tcl-fixes' into develop Remove many files, which are not used
 in Tcl. Modify "changelog.txt", with real release-date of 1.0.1 version

---
 libtommath/bn.ilg                   |     6 -
 libtommath/bn.ind                   |    88 -
 libtommath/bn.pdf                   |   Bin 383770 -> 0 bytes
 libtommath/bn.tex                   |  1913 ------
 libtommath/bn_mp_read_radix.c       |     8 +-
 libtommath/booker.pl                |   267 -
 libtommath/changes.txt              |     2 +-
 libtommath/demo/demo.c              |   986 ----
 libtommath/demo/timing.c            |   339 --
 libtommath/dep.pl                   |   123 -
 libtommath/etc/2kprime.1            |     2 -
 libtommath/etc/2kprime.c            |    84 -
 libtommath/etc/drprime.c            |    64 -
 libtommath/etc/drprimes.28          |    25 -
 libtommath/etc/drprimes.txt         |     9 -
 libtommath/etc/makefile             |    50 -
 libtommath/etc/makefile.icc         |    67 -
 libtommath/etc/makefile.msvc        |    23 -
 libtommath/etc/mersenne.c           |   144 -
 libtommath/etc/mont.c               |    50 -
 libtommath/etc/pprime.c             |   400 --
 libtommath/etc/prime.1024           |   414 --
 libtommath/etc/prime.512            |   205 -
 libtommath/etc/timer.asm            |    37 -
 libtommath/etc/tune.c               |   145 -
 libtommath/filter.pl                |    34 -
 libtommath/gen.pl                   |    19 -
 libtommath/genlist.sh               |     8 -
 libtommath/libtommath.dsp           |   572 --
 libtommath/libtommath_VS2005.sln    |    20 -
 libtommath/libtommath_VS2005.vcproj |  2847 ---------
 libtommath/libtommath_VS2008.sln    |    20 -
 libtommath/libtommath_VS2008.vcproj |  2813 ---------
 libtommath/logs/README              |    13 -
 libtommath/logs/add.log             |    16 -
 libtommath/logs/addsub.png          |   Bin 6254 -> 0 bytes
 libtommath/logs/expt.log            |     7 -
 libtommath/logs/expt.png            |   Bin 6605 -> 0 bytes
 libtommath/logs/expt_2k.log         |     5 -
 libtommath/logs/expt_2kl.log        |     4 -
 libtommath/logs/expt_dr.log         |     7 -
 libtommath/logs/graphs.dem          |    17 -
 libtommath/logs/index.html          |    27 -
 libtommath/logs/invmod.log          |     0
 libtommath/logs/invmod.png          |   Bin 4918 -> 0 bytes
 libtommath/logs/mult.log            |    84 -
 libtommath/logs/mult.png            |   Bin 6770 -> 0 bytes
 libtommath/logs/mult_kara.log       |    84 -
 libtommath/logs/sqr.log             |    84 -
 libtommath/logs/sqr_kara.log        |    84 -
 libtommath/logs/sub.log             |    16 -
 libtommath/makefile_include.mk      |   117 +
 libtommath/mess.sh                  |     4 -
 libtommath/mtest/logtab.h           |    24 -
 libtommath/mtest/mpi-config.h       |    90 -
 libtommath/mtest/mpi-types.h        |    20 -
 libtommath/mtest/mpi.c              |  3985 -------------
 libtommath/mtest/mpi.h              |   231 -
 libtommath/mtest/mtest.c            |   374 --
 libtommath/parsenames.pl            |    25 -
 libtommath/pics/design_process.sxd  |   Bin 6950 -> 0 bytes
 libtommath/pics/design_process.tif  |   Bin 79042 -> 0 bytes
 libtommath/pics/expt_state.sxd      |   Bin 6869 -> 0 bytes
 libtommath/pics/expt_state.tif      |   Bin 87542 -> 0 bytes
 libtommath/pics/makefile            |    35 -
 libtommath/pics/primality.tif       |   Bin 85514 -> 0 bytes
 libtommath/pics/radix.sxd           |   Bin 6181 -> 0 bytes
 libtommath/pics/sliding_window.sxd  |   Bin 6787 -> 0 bytes
 libtommath/pics/sliding_window.tif  |   Bin 53880 -> 0 bytes
 libtommath/poster.out               |     0
 libtommath/poster.pdf               |   Bin 73388 -> 0 bytes
 libtommath/poster.tex               |    35 -
 libtommath/pre_gen/mpi.c            |  9524 ------------------------------
 libtommath/pretty.build             |    66 -
 libtommath/testme.sh                |   174 -
 libtommath/tombc/grammar.txt        |    35 -
 libtommath/tommath.h                |     2 +-
 libtommath/tommath.out              |   139 -
 libtommath/tommath.pdf              |   Bin 1526291 -> 0 bytes
 libtommath/tommath.src              |  6339 --------------------
 libtommath/tommath.tex              | 10816 ----------------------------------
 81 files changed, 126 insertions(+), 44141 deletions(-)
 delete mode 100644 libtommath/bn.ilg
 delete mode 100644 libtommath/bn.ind
 delete mode 100644 libtommath/bn.pdf
 delete mode 100644 libtommath/bn.tex
 delete mode 100644 libtommath/booker.pl
 delete mode 100644 libtommath/demo/demo.c
 delete mode 100644 libtommath/demo/timing.c
 delete mode 100644 libtommath/dep.pl
 delete mode 100644 libtommath/etc/2kprime.1
 delete mode 100644 libtommath/etc/2kprime.c
 delete mode 100644 libtommath/etc/drprime.c
 delete mode 100644 libtommath/etc/drprimes.28
 delete mode 100644 libtommath/etc/drprimes.txt
 delete mode 100644 libtommath/etc/makefile
 delete mode 100644 libtommath/etc/makefile.icc
 delete mode 100644 libtommath/etc/makefile.msvc
 delete mode 100644 libtommath/etc/mersenne.c
 delete mode 100644 libtommath/etc/mont.c
 delete mode 100644 libtommath/etc/pprime.c
 delete mode 100644 libtommath/etc/prime.1024
 delete mode 100644 libtommath/etc/prime.512
 delete mode 100644 libtommath/etc/timer.asm
 delete mode 100644 libtommath/etc/tune.c
 delete mode 100755 libtommath/filter.pl
 delete mode 100644 libtommath/gen.pl
 delete mode 100755 libtommath/genlist.sh
 delete mode 100644 libtommath/libtommath.dsp
 delete mode 100644 libtommath/libtommath_VS2005.sln
 delete mode 100644 libtommath/libtommath_VS2005.vcproj
 delete mode 100644 libtommath/libtommath_VS2008.sln
 delete mode 100644 libtommath/libtommath_VS2008.vcproj
 delete mode 100644 libtommath/logs/README
 delete mode 100644 libtommath/logs/add.log
 delete mode 100644 libtommath/logs/addsub.png
 delete mode 100644 libtommath/logs/expt.log
 delete mode 100644 libtommath/logs/expt.png
 delete mode 100644 libtommath/logs/expt_2k.log
 delete mode 100644 libtommath/logs/expt_2kl.log
 delete mode 100644 libtommath/logs/expt_dr.log
 delete mode 100644 libtommath/logs/graphs.dem
 delete mode 100644 libtommath/logs/index.html
 delete mode 100644 libtommath/logs/invmod.log
 delete mode 100644 libtommath/logs/invmod.png
 delete mode 100644 libtommath/logs/mult.log
 delete mode 100644 libtommath/logs/mult.png
 delete mode 100644 libtommath/logs/mult_kara.log
 delete mode 100644 libtommath/logs/sqr.log
 delete mode 100644 libtommath/logs/sqr_kara.log
 delete mode 100644 libtommath/logs/sub.log
 create mode 100644 libtommath/makefile_include.mk
 delete mode 100644 libtommath/mess.sh
 delete mode 100644 libtommath/mtest/logtab.h
 delete mode 100644 libtommath/mtest/mpi-config.h
 delete mode 100644 libtommath/mtest/mpi-types.h
 delete mode 100644 libtommath/mtest/mpi.c
 delete mode 100644 libtommath/mtest/mpi.h
 delete mode 100644 libtommath/mtest/mtest.c
 delete mode 100755 libtommath/parsenames.pl
 delete mode 100644 libtommath/pics/design_process.sxd
 delete mode 100644 libtommath/pics/design_process.tif
 delete mode 100644 libtommath/pics/expt_state.sxd
 delete mode 100644 libtommath/pics/expt_state.tif
 delete mode 100644 libtommath/pics/makefile
 delete mode 100644 libtommath/pics/primality.tif
 delete mode 100644 libtommath/pics/radix.sxd
 delete mode 100644 libtommath/pics/sliding_window.sxd
 delete mode 100644 libtommath/pics/sliding_window.tif
 delete mode 100644 libtommath/poster.out
 delete mode 100644 libtommath/poster.pdf
 delete mode 100644 libtommath/poster.tex
 delete mode 100644 libtommath/pre_gen/mpi.c
 delete mode 100644 libtommath/pretty.build
 delete mode 100755 libtommath/testme.sh
 delete mode 100644 libtommath/tombc/grammar.txt
 delete mode 100644 libtommath/tommath.out
 delete mode 100644 libtommath/tommath.pdf
 delete mode 100644 libtommath/tommath.src
 delete mode 100644 libtommath/tommath.tex

diff --git a/libtommath/bn.ilg b/libtommath/bn.ilg
deleted file mode 100644
index 2a14624..0000000
--- a/libtommath/bn.ilg
+++ /dev/null
@@ -1,6 +0,0 @@
-This is makeindex, version 2.15 [TeX Live 2013] (kpathsea + Thai support).
-Scanning input file bn.idx....done (85 entries accepted, 0 rejected).
-Sorting entries....done (554 comparisons).
-Generating output file bn.ind....done (88 lines written, 0 warnings).
-Output written in bn.ind.
-Transcript written in bn.ilg.
diff --git a/libtommath/bn.ind b/libtommath/bn.ind
deleted file mode 100644
index 01cff1a..0000000
--- a/libtommath/bn.ind
+++ /dev/null
@@ -1,88 +0,0 @@
-\begin{theindex}
-
-  \item mp\_add, \hyperpage{24}
-  \item mp\_add\_d, \hyperpage{44}
-  \item mp\_and, \hyperpage{24}
-  \item mp\_clear, \hyperpage{9}
-  \item mp\_clear\_multi, \hyperpage{10}
-  \item mp\_cmp, \hyperpage{19}
-  \item mp\_cmp\_d, \hyperpage{20}
-  \item mp\_cmp\_mag, \hyperpage{18}
-  \item mp\_div, \hyperpage{24}
-  \item mp\_div\_2, \hyperpage{22}
-  \item mp\_div\_2d, \hyperpage{23}
-  \item mp\_div\_d, \hyperpage{44}
-  \item mp\_dr\_reduce, \hyperpage{33}
-  \item mp\_dr\_setup, \hyperpage{33}
-  \item MP\_EQ, \hyperpage{18}
-  \item mp\_error\_to\_string, \hyperpage{7}
-  \item mp\_expt\_d, \hyperpage{35}
-  \item mp\_expt\_d\_ex, \hyperpage{35}
-  \item mp\_exptmod, \hyperpage{35}
-  \item mp\_exteuclid, \hyperpage{43}
-  \item mp\_gcd, \hyperpage{43}
-  \item mp\_get\_int, \hyperpage{16}
-  \item mp\_get\_long, \hyperpage{17}
-  \item mp\_get\_long\_long, \hyperpage{17}
-  \item mp\_grow, \hyperpage{13}
-  \item MP\_GT, \hyperpage{18}
-  \item mp\_init, \hyperpage{8}
-  \item mp\_init\_copy, \hyperpage{10}
-  \item mp\_init\_multi, \hyperpage{10}
-  \item mp\_init\_set, \hyperpage{17}
-  \item mp\_init\_set\_int, \hyperpage{17}
-  \item mp\_init\_size, \hyperpage{11}
-  \item mp\_int, \hyperpage{8}
-  \item mp\_invmod, \hyperpage{44}
-  \item mp\_jacobi, \hyperpage{43}
-  \item mp\_lcm, \hyperpage{43}
-  \item mp\_lshd, \hyperpage{23}
-  \item MP\_LT, \hyperpage{18}
-  \item MP\_MEM, \hyperpage{7}
-  \item mp\_mod, \hyperpage{29}
-  \item mp\_mod\_d, \hyperpage{44}
-  \item mp\_montgomery\_calc\_normalization, \hyperpage{31}
-  \item mp\_montgomery\_reduce, \hyperpage{31}
-  \item mp\_montgomery\_setup, \hyperpage{31}
-  \item mp\_mul, \hyperpage{25}
-  \item mp\_mul\_2, \hyperpage{22}
-  \item mp\_mul\_2d, \hyperpage{23}
-  \item mp\_mul\_d, \hyperpage{44}
-  \item mp\_n\_root, \hyperpage{36}
-  \item mp\_neg, \hyperpage{24}
-  \item MP\_NO, \hyperpage{7}
-  \item MP\_OKAY, \hyperpage{7}
-  \item mp\_or, \hyperpage{24}
-  \item mp\_prime\_fermat, \hyperpage{37}
-  \item mp\_prime\_is\_divisible, \hyperpage{37}
-  \item mp\_prime\_is\_prime, \hyperpage{38}
-  \item mp\_prime\_miller\_rabin, \hyperpage{37}
-  \item mp\_prime\_next\_prime, \hyperpage{38}
-  \item mp\_prime\_rabin\_miller\_trials, \hyperpage{38}
-  \item mp\_prime\_random, \hyperpage{38}
-  \item mp\_prime\_random\_ex, \hyperpage{39}
-  \item mp\_radix\_size, \hyperpage{41}
-  \item mp\_read\_radix, \hyperpage{41}
-  \item mp\_read\_unsigned\_bin, \hyperpage{42}
-  \item mp\_reduce, \hyperpage{30}
-  \item mp\_reduce\_2k, \hyperpage{34}
-  \item mp\_reduce\_2k\_setup, \hyperpage{34}
-  \item mp\_reduce\_setup, \hyperpage{29}
-  \item mp\_rshd, \hyperpage{23}
-  \item mp\_set, \hyperpage{15}
-  \item mp\_set\_int, \hyperpage{16}
-  \item mp\_set\_long, \hyperpage{17}
-  \item mp\_set\_long\_long, \hyperpage{17}
-  \item mp\_shrink, \hyperpage{12}
-  \item mp\_sqr, \hyperpage{26}
-  \item mp\_sqrtmod\_prime, \hyperpage{44}
-  \item mp\_sub, \hyperpage{24}
-  \item mp\_sub\_d, \hyperpage{44}
-  \item mp\_to\_unsigned\_bin, \hyperpage{42}
-  \item mp\_toradix, \hyperpage{41}
-  \item mp\_unsigned\_bin\_size, \hyperpage{41}
-  \item MP\_VAL, \hyperpage{7}
-  \item mp\_xor, \hyperpage{24}
-  \item MP\_YES, \hyperpage{7}
-
-\end{theindex}
diff --git a/libtommath/bn.pdf b/libtommath/bn.pdf
deleted file mode 100644
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diff --git a/libtommath/bn.tex b/libtommath/bn.tex
deleted file mode 100644
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--- a/libtommath/bn.tex
+++ /dev/null
@@ -1,1913 +0,0 @@
-\documentclass[synpaper]{book}
-\usepackage{hyperref}
-\usepackage{makeidx}
-\usepackage{amssymb}
-\usepackage{color}
-\usepackage{alltt}
-\usepackage{graphicx}
-\usepackage{layout}
-\def\union{\cup}
-\def\intersect{\cap}
-\def\getsrandom{\stackrel{\rm R}{\gets}}
-\def\cross{\times}
-\def\cat{\hspace{0.5em} \| \hspace{0.5em}}
-\def\catn{$\|$}
-\def\divides{\hspace{0.3em} | \hspace{0.3em}}
-\def\nequiv{\not\equiv}
-\def\approx{\raisebox{0.2ex}{\mbox{\small $\sim$}}}
-\def\lcm{{\rm lcm}}
-\def\gcd{{\rm gcd}}
-\def\log{{\rm log}}
-\def\ord{{\rm ord}}
-\def\abs{{\mathit abs}}
-\def\rep{{\mathit rep}}
-\def\mod{{\mathit\ mod\ }}
-\renewcommand{\pmod}[1]{\ ({\rm mod\ }{#1})}
-\newcommand{\floor}[1]{\left\lfloor{#1}\right\rfloor}
-\newcommand{\ceil}[1]{\left\lceil{#1}\right\rceil}
-\def\Or{{\rm\ or\ }}
-\def\And{{\rm\ and\ }}
-\def\iff{\hspace{1em}\Longleftrightarrow\hspace{1em}}
-\def\implies{\Rightarrow}
-\def\undefined{{\rm ``undefined"}}
-\def\Proof{\vspace{1ex}\noindent {\bf Proof:}\hspace{1em}}
-\let\oldphi\phi
-\def\phi{\varphi}
-\def\Pr{{\rm Pr}}
-\newcommand{\str}[1]{{\mathbf{#1}}}
-\def\F{{\mathbb F}}
-\def\N{{\mathbb N}}
-\def\Z{{\mathbb Z}}
-\def\R{{\mathbb R}}
-\def\C{{\mathbb C}}
-\def\Q{{\mathbb Q}}
-\definecolor{DGray}{gray}{0.5}
-\newcommand{\emailaddr}[1]{\mbox{$<${#1}$>$}}
-\def\twiddle{\raisebox{0.3ex}{\mbox{\tiny $\sim$}}}
-\def\gap{\vspace{0.5ex}}
-\makeindex
-\begin{document}
-\frontmatter
-\pagestyle{empty}
-\title{LibTomMath User Manual \\ v1.0.0}
-\author{Tom St Denis \\ tstdenis82@gmail.com}
-\maketitle
-This text, the library and the accompanying textbook are all hereby placed in the public domain.  This book has been
-formatted for B5 [176x250] paper using the \LaTeX{} {\em book} macro package.
-
-\vspace{10cm}
-
-\begin{flushright}Open Source.  Open Academia.  Open Minds.
-
-\mbox{ }
-
-Tom St Denis,
-
-Ontario, Canada
-\end{flushright}
-
-\tableofcontents
-\listoffigures
-\mainmatter
-\pagestyle{headings}
-\chapter{Introduction}
-\section{What is LibTomMath?}
-LibTomMath is a library of source code which provides a series of efficient and carefully written functions for manipulating
-large integer numbers.  It was written in portable ISO C source code so that it will build on any platform with a conforming
-C compiler.
-
-In a nutshell the library was written from scratch with verbose comments to help instruct computer science students how
-to implement ``bignum'' math.  However, the resulting code has proven to be very useful.  It has been used by numerous
-universities, commercial and open source software developers.  It has been used on a variety of platforms ranging from
-Linux and Windows based x86 to ARM based Gameboys and PPC based MacOS machines.
-
-\section{License}
-As of the v0.25 the library source code has been placed in the public domain with every new release.  As of the v0.28
-release the textbook ``Implementing Multiple Precision Arithmetic'' has been placed in the public domain with every new
-release as well.  This textbook is meant to compliment the project by providing a more solid walkthrough of the development
-algorithms used in the library.
-
-Since both\footnote{Note that the MPI files under mtest/ are copyrighted by Michael Fromberger.  They are not required to use LibTomMath.} are in the
-public domain everyone is entitled to do with them as they see fit.
-
-\section{Building LibTomMath}
-
-LibTomMath is meant to be very ``GCC friendly'' as it comes with a makefile well suited for GCC.  However, the library will
-also build in MSVC, Borland C out of the box.  For any other ISO C compiler a makefile will have to be made by the end
-developer.
-
-\subsection{Static Libraries}
-To build as a static library for GCC issue the following
-\begin{alltt}
-make
-\end{alltt}
-
-command.  This will build the library and archive the object files in ``libtommath.a''.  Now you link against
-that and include ``tommath.h'' within your programs.  Alternatively to build with MSVC issue the following
-\begin{alltt}
-nmake -f makefile.msvc
-\end{alltt}
-
-This will build the library and archive the object files in ``tommath.lib''.  This has been tested with MSVC
-version 6.00 with service pack 5.
-
-\subsection{Shared Libraries}
-To build as a shared library for GCC issue the following
-\begin{alltt}
-make -f makefile.shared
-\end{alltt}
-This requires the ``libtool'' package (common on most Linux/BSD systems).  It will build LibTomMath as both shared
-and static then install (by default) into /usr/lib as well as install the header files in /usr/include.  The shared
-library (resource) will be called ``libtommath.la'' while the static library called ``libtommath.a''.  Generally
-you use libtool to link your application against the shared object.
-
-There is limited support for making a ``DLL'' in windows via the ``makefile.cygwin\_dll'' makefile.  It requires
-Cygwin to work with since it requires the auto-export/import functionality.  The resulting DLL and import library
-``libtommath.dll.a'' can be used to link LibTomMath dynamically to any Windows program using Cygwin.
-
-\subsection{Testing}
-To build the library and the test harness type
-
-\begin{alltt}
-make test
-\end{alltt}
-
-This will build the library, ``test'' and ``mtest/mtest''.  The ``test'' program will accept test vectors and verify the
-results.  ``mtest/mtest'' will generate test vectors using the MPI library by Michael Fromberger\footnote{A copy of MPI
-is included in the package}.  Simply pipe mtest into test using
-
-\begin{alltt}
-mtest/mtest | test
-\end{alltt}
-
-If you do not have a ``/dev/urandom'' style RNG source you will have to write your own PRNG and simply pipe that into
-mtest.  For example, if your PRNG program is called ``myprng'' simply invoke
-
-\begin{alltt}
-myprng | mtest/mtest | test
-\end{alltt}
-
-This will output a row of numbers that are increasing.  Each column is a different test (such as addition, multiplication, etc)
-that is being performed.  The numbers represent how many times the test was invoked.  If an error is detected the program
-will exit with a dump of the relevent numbers it was working with.
-
-\section{Build Configuration}
-LibTomMath can configured at build time in three phases we shall call ``depends'', ``tweaks'' and ``trims''.
-Each phase changes how the library is built and they are applied one after another respectively.
-
-To make the system more powerful you can tweak the build process.  Classes are defined in the file
-``tommath\_superclass.h''.  By default, the symbol ``LTM\_ALL'' shall be defined which simply
-instructs the system to build all of the functions.  This is how LibTomMath used to be packaged.  This will give you
-access to every function LibTomMath offers.
-
-However, there are cases where such a build is not optional.  For instance, you want to perform RSA operations.  You
-don't need the vast majority of the library to perform these operations.  Aside from LTM\_ALL there is
-another pre--defined class ``SC\_RSA\_1'' which works in conjunction with the RSA from LibTomCrypt.  Additional
-classes can be defined base on the need of the user.
-
-\subsection{Build Depends}
-In the file tommath\_class.h you will see a large list of C ``defines'' followed by a series of ``ifdefs''
-which further define symbols.  All of the symbols (technically they're macros $\ldots$) represent a given C source
-file.  For instance, BN\_MP\_ADD\_C represents the file ``bn\_mp\_add.c''.  When a define has been enabled the
-function in the respective file will be compiled and linked into the library.  Accordingly when the define
-is absent the file will not be compiled and not contribute any size to the library.
-
-You will also note that the header tommath\_class.h is actually recursively included (it includes itself twice).
-This is to help resolve as many dependencies as possible.  In the last pass the symbol LTM\_LAST will be defined.
-This is useful for ``trims''.
-
-\subsection{Build Tweaks}
-A tweak is an algorithm ``alternative''.  For example, to provide tradeoffs (usually between size and space).
-They can be enabled at any pass of the configuration phase.
-
-\begin{small}
-\begin{center}
-\begin{tabular}{|l|l|}
-\hline \textbf{Define} & \textbf{Purpose} \\
-\hline BN\_MP\_DIV\_SMALL & Enables a slower, smaller and equally \\
-                          & functional mp\_div() function \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-
-\subsection{Build Trims}
-A trim is a manner of removing functionality from a function that is not required.  For instance, to perform
-RSA cryptography you only require exponentiation with odd moduli so even moduli support can be safely removed.
-Build trims are meant to be defined on the last pass of the configuration which means they are to be defined
-only if LTM\_LAST has been defined.
-
-\subsubsection{Moduli Related}
-\begin{small}
-\begin{center}
-\begin{tabular}{|l|l|}
-\hline \textbf{Restriction} & \textbf{Undefine} \\
-\hline Exponentiation with odd moduli only & BN\_S\_MP\_EXPTMOD\_C \\
-                                           & BN\_MP\_REDUCE\_C \\
-                                           & BN\_MP\_REDUCE\_SETUP\_C \\
-                                           & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
-                                           & BN\_FAST\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
-\hline Exponentiation with random odd moduli & (The above plus the following) \\
-                                           & BN\_MP\_REDUCE\_2K\_C \\
-                                           & BN\_MP\_REDUCE\_2K\_SETUP\_C \\
-                                           & BN\_MP\_REDUCE\_IS\_2K\_C \\
-                                           & BN\_MP\_DR\_IS\_MODULUS\_C \\
-                                           & BN\_MP\_DR\_REDUCE\_C \\
-                                           & BN\_MP\_DR\_SETUP\_C \\
-\hline Modular inverse odd moduli only     & BN\_MP\_INVMOD\_SLOW\_C \\
-\hline Modular inverse (both, smaller/slower) & BN\_FAST\_MP\_INVMOD\_C \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-
-\subsubsection{Operand Size Related}
-\begin{small}
-\begin{center}
-\begin{tabular}{|l|l|}
-\hline \textbf{Restriction} & \textbf{Undefine} \\
-\hline Moduli $\le 2560$ bits              & BN\_MP\_MONTGOMERY\_REDUCE\_C \\
-                                           & BN\_S\_MP\_MUL\_DIGS\_C \\
-                                           & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
-                                           & BN\_S\_MP\_SQR\_C \\
-\hline Polynomial Schmolynomial            & BN\_MP\_KARATSUBA\_MUL\_C \\
-                                           & BN\_MP\_KARATSUBA\_SQR\_C \\
-                                           & BN\_MP\_TOOM\_MUL\_C \\
-                                           & BN\_MP\_TOOM\_SQR\_C \\
-
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-
-
-\section{Purpose of LibTomMath}
-Unlike  GNU MP (GMP) Library, LIP, OpenSSL or various other commercial kits (Miracl), LibTomMath was not written with
-bleeding edge performance in mind.  First and foremost LibTomMath was written to be entirely open.  Not only is the
-source code public domain (unlike various other GPL/etc licensed code), not only is the code freely downloadable but the
-source code is also accessible for computer science students attempting to learn ``BigNum'' or multiple precision
-arithmetic techniques.
-
-LibTomMath was written to be an instructive collection of source code.  This is why there are many comments, only one
-function per source file and often I use a ``middle-road'' approach where I don't cut corners for an extra 2\% speed
-increase.
-
-Source code alone cannot really teach how the algorithms work which is why I also wrote a textbook that accompanies
-the library (beat that!).
-
-So you may be thinking ``should I use LibTomMath?'' and the answer is a definite maybe.  Let me tabulate what I think
-are the pros and cons of LibTomMath by comparing it to the math routines from GnuPG\footnote{GnuPG v1.2.3 versus LibTomMath v0.28}.
-
-\newpage\begin{figure}[here]
-\begin{small}
-\begin{center}
-\begin{tabular}{|l|c|c|l|}
-\hline \textbf{Criteria} & \textbf{Pro} & \textbf{Con} & \textbf{Notes} \\
-\hline Few lines of code per file & X & & GnuPG $ = 300.9$, LibTomMath  $ = 71.97$ \\
-\hline Commented function prototypes & X && GnuPG function names are cryptic. \\
-\hline Speed && X & LibTomMath is slower.  \\
-\hline Totally free & X & & GPL has unfavourable restrictions.\\
-\hline Large function base & X & & GnuPG is barebones. \\
-\hline Five modular reduction algorithms & X & & Faster modular exponentiation for a variety of moduli. \\
-\hline Portable & X & & GnuPG requires configuration to build. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{LibTomMath Valuation}
-\end{figure}
-
-It may seem odd to compare LibTomMath to GnuPG since the math in GnuPG is only a small portion of the entire application.
-However, LibTomMath was written with cryptography in mind.  It provides essentially all of the functions a cryptosystem
-would require when working with large integers.
-
-So it may feel tempting to just rip the math code out of GnuPG (or GnuMP where it was taken from originally) in your
-own application but I think there are reasons not to.  While LibTomMath is slower than libraries such as GnuMP it is
-not normally significantly slower.  On x86 machines the difference is normally a factor of two when performing modular
-exponentiations.  It depends largely on the processor, compiler and the moduli being used.
-
-Essentially the only time you wouldn't use LibTomMath is when blazing speed is the primary concern.  However,
-on the other side of the coin LibTomMath offers you a totally free (public domain) well structured math library
-that is very flexible, complete and performs well in resource contrained environments.  Fast RSA for example can
-be performed with as little as 8KB of ram for data (again depending on build options).
-
-\chapter{Getting Started with LibTomMath}
-\section{Building Programs}
-In order to use LibTomMath you must include ``tommath.h'' and link against the appropriate library file (typically
-libtommath.a).  There is no library initialization required and the entire library is thread safe.
-
-\section{Return Codes}
-There are three possible return codes a function may return.
-
-\index{MP\_OKAY}\index{MP\_YES}\index{MP\_NO}\index{MP\_VAL}\index{MP\_MEM}
-\begin{figure}[here!]
-\begin{center}
-\begin{small}
-\begin{tabular}{|l|l|}
-\hline \textbf{Code} & \textbf{Meaning} \\
-\hline MP\_OKAY & The function succeeded. \\
-\hline MP\_VAL  & The function input was invalid. \\
-\hline MP\_MEM  & Heap memory exhausted. \\
-\hline &\\
-\hline MP\_YES  & Response is yes. \\
-\hline MP\_NO   & Response is no. \\
-\hline
-\end{tabular}
-\end{small}
-\end{center}
-\caption{Return Codes}
-\end{figure}
-
-The last two codes listed are not actually ``return'ed'' by a function.  They are placed in an integer (the caller must
-provide the address of an integer it can store to) which the caller can access.  To convert one of the three return codes
-to a string use the following function.
-
-\index{mp\_error\_to\_string}
-\begin{alltt}
-char *mp_error_to_string(int code);
-\end{alltt}
-
-This will return a pointer to a string which describes the given error code.  It will not work for the return codes
-MP\_YES and MP\_NO.
-
-\section{Data Types}
-The basic ``multiple precision integer'' type is known as the ``mp\_int'' within LibTomMath.  This data type is used to
-organize all of the data required to manipulate the integer it represents.  Within LibTomMath it has been prototyped
-as the following.
-
-\index{mp\_int}
-\begin{alltt}
-typedef struct  \{
-    int used, alloc, sign;
-    mp_digit *dp;
-\} mp_int;
-\end{alltt}
-
-Where ``mp\_digit'' is a data type that represents individual digits of the integer.  By default, an mp\_digit is the
-ISO C ``unsigned long'' data type and each digit is $28-$bits long.  The mp\_digit type can be configured to suit other
-platforms by defining the appropriate macros.
-
-All LTM functions that use the mp\_int type will expect a pointer to mp\_int structure.  You must allocate memory to
-hold the structure itself by yourself (whether off stack or heap it doesn't matter).  The very first thing that must be
-done to use an mp\_int is that it must be initialized.
-
-\section{Function Organization}
-
-The arithmetic functions of the library are all organized to have the same style prototype.  That is source operands
-are passed on the left and the destination is on the right.  For instance,
-
-\begin{alltt}
-mp_add(&a, &b, &c);       /* c = a + b */
-mp_mul(&a, &a, &c);       /* c = a * a */
-mp_div(&a, &b, &c, &d);   /* c = [a/b], d = a mod b */
-\end{alltt}
-
-Another feature of the way the functions have been implemented is that source operands can be destination operands as well.
-For instance,
-
-\begin{alltt}
-mp_add(&a, &b, &b);       /* b = a + b */
-mp_div(&a, &b, &a, &c);   /* a = [a/b], c = a mod b */
-\end{alltt}
-
-This allows operands to be re-used which can make programming simpler.
-
-\section{Initialization}
-\subsection{Single Initialization}
-A single mp\_int can be initialized with the ``mp\_init'' function.
-
-\index{mp\_init}
-\begin{alltt}
-int mp_init (mp_int * a);
-\end{alltt}
-
-This function expects a pointer to an mp\_int structure and will initialize the members of the structure so the mp\_int
-represents the default integer which is zero.  If the functions returns MP\_OKAY then the mp\_int is ready to be used
-by the other LibTomMath functions.
-
-\begin{small} \begin{alltt}
-int main(void)
-\{
-   mp_int number;
-   int result;
-
-   if ((result = mp_init(&number)) != MP_OKAY) \{
-      printf("Error initializing the number.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* use the number */
-
-   return EXIT_SUCCESS;
-\}
-\end{alltt} \end{small}
-
-\subsection{Single Free}
-When you are finished with an mp\_int it is ideal to return the heap it used back to the system.  The following function
-provides this functionality.
-
-\index{mp\_clear}
-\begin{alltt}
-void mp_clear (mp_int * a);
-\end{alltt}
-
-The function expects a pointer to a previously initialized mp\_int structure and frees the heap it uses.  It sets the
-pointer\footnote{The ``dp'' member.} within the mp\_int to \textbf{NULL} which is used to prevent double free situations.
-Is is legal to call mp\_clear() twice on the same mp\_int in a row.
-
-\begin{small} \begin{alltt}
-int main(void)
-\{
-   mp_int number;
-   int result;
-
-   if ((result = mp_init(&number)) != MP_OKAY) \{
-      printf("Error initializing the number.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* use the number */
-
-   /* We're done with it. */
-   mp_clear(&number);
-
-   return EXIT_SUCCESS;
-\}
-\end{alltt} \end{small}
-
-\subsection{Multiple Initializations}
-Certain algorithms require more than one large integer.  In these instances it is ideal to initialize all of the mp\_int
-variables in an ``all or nothing'' fashion.  That is, they are either all initialized successfully or they are all
-not initialized.
-
-The  mp\_init\_multi() function provides this functionality.
-
-\index{mp\_init\_multi} \index{mp\_clear\_multi}
-\begin{alltt}
-int mp_init_multi(mp_int *mp, ...);
-\end{alltt}
-
-It accepts a \textbf{NULL} terminated list of pointers to mp\_int structures.  It will attempt to initialize them all
-at once.  If the function returns MP\_OKAY then all of the mp\_int variables are ready to use, otherwise none of them
-are available for use.  A complementary mp\_clear\_multi() function allows multiple mp\_int variables to be free'd
-from the heap at the same time.
-
-\begin{small} \begin{alltt}
-int main(void)
-\{
-   mp_int num1, num2, num3;
-   int result;
-
-   if ((result = mp_init_multi(&num1,
-                               &num2,
-                               &num3, NULL)) != MP\_OKAY) \{
-      printf("Error initializing the numbers.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* use the numbers */
-
-   /* We're done with them. */
-   mp_clear_multi(&num1, &num2, &num3, NULL);
-
-   return EXIT_SUCCESS;
-\}
-\end{alltt} \end{small}
-
-\subsection{Other Initializers}
-To initialized and make a copy of an mp\_int the mp\_init\_copy() function has been provided.
-
-\index{mp\_init\_copy}
-\begin{alltt}
-int mp_init_copy (mp_int * a, mp_int * b);
-\end{alltt}
-
-This function will initialize $a$ and make it a copy of $b$ if all goes well.
-
-\begin{small} \begin{alltt}
-int main(void)
-\{
-   mp_int num1, num2;
-   int result;
-
-   /* initialize and do work on num1 ... */
-
-   /* We want a copy of num1 in num2 now */
-   if ((result = mp_init_copy(&num2, &num1)) != MP_OKAY) \{
-     printf("Error initializing the copy.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* now num2 is ready and contains a copy of num1 */
-
-   /* We're done with them. */
-   mp_clear_multi(&num1, &num2, NULL);
-
-   return EXIT_SUCCESS;
-\}
-\end{alltt} \end{small}
-
-Another less common initializer is mp\_init\_size() which allows the user to initialize an mp\_int with a given
-default number of digits.  By default, all initializers allocate \textbf{MP\_PREC} digits.  This function lets
-you override this behaviour.
-
-\index{mp\_init\_size}
-\begin{alltt}
-int mp_init_size (mp_int * a, int size);
-\end{alltt}
-
-The $size$ parameter must be greater than zero.  If the function succeeds the mp\_int $a$ will be initialized
-to have $size$ digits (which are all initially zero).
-
-\begin{small} \begin{alltt}
-int main(void)
-\{
-   mp_int number;
-   int result;
-
-   /* we need a 60-digit number */
-   if ((result = mp_init_size(&number, 60)) != MP_OKAY) \{
-      printf("Error initializing the number.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* use the number */
-
-   return EXIT_SUCCESS;
-\}
-\end{alltt} \end{small}
-
-\section{Maintenance Functions}
-
-\subsection{Reducing Memory Usage}
-When an mp\_int is in a state where it won't be changed again\footnote{A Diffie-Hellman modulus for instance.} excess
-digits can be removed to return memory to the heap with the mp\_shrink() function.
-
-\index{mp\_shrink}
-\begin{alltt}
-int mp_shrink (mp_int * a);
-\end{alltt}
-
-This will remove excess digits of the mp\_int $a$.  If the operation fails the mp\_int should be intact without the
-excess digits being removed.  Note that you can use a shrunk mp\_int in further computations, however, such operations
-will require heap operations which can be slow.  It is not ideal to shrink mp\_int variables that you will further
-modify in the system (unless you are seriously low on memory).
-
-\begin{small} \begin{alltt}
-int main(void)
-\{
-   mp_int number;
-   int result;
-
-   if ((result = mp_init(&number)) != MP_OKAY) \{
-      printf("Error initializing the number.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* use the number [e.g. pre-computation]  */
-
-   /* We're done with it for now. */
-   if ((result = mp_shrink(&number)) != MP_OKAY) \{
-      printf("Error shrinking the number.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* use it .... */
-
-
-   /* we're done with it. */
-   mp_clear(&number);
-
-   return EXIT_SUCCESS;
-\}
-\end{alltt} \end{small}
-
-\subsection{Adding additional digits}
-
-Within the mp\_int structure are two parameters which control the limitations of the array of digits that represent
-the integer the mp\_int is meant to equal.   The \textit{used} parameter dictates how many digits are significant, that is,
-contribute to the value of the mp\_int.  The \textit{alloc} parameter dictates how many digits are currently available in
-the array.  If you need to perform an operation that requires more digits you will have to mp\_grow() the mp\_int to
-your desired size.
-
-\index{mp\_grow}
-\begin{alltt}
-int mp_grow (mp_int * a, int size);
-\end{alltt}
-
-This will grow the array of digits of $a$ to $size$.  If the \textit{alloc} parameter is already bigger than
-$size$ the function will not do anything.
-
-\begin{small} \begin{alltt}
-int main(void)
-\{
-   mp_int number;
-   int result;
-
-   if ((result = mp_init(&number)) != MP_OKAY) \{
-      printf("Error initializing the number.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* use the number */
-
-   /* We need to add 20 digits to the number  */
-   if ((result = mp_grow(&number, number.alloc + 20)) != MP_OKAY) \{
-      printf("Error growing the number.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-
-   /* use the number */
-
-   /* we're done with it. */
-   mp_clear(&number);
-
-   return EXIT_SUCCESS;
-\}
-\end{alltt} \end{small}
-
-\chapter{Basic Operations}
-\section{Small Constants}
-Setting mp\_ints to small constants is a relatively common operation.  To accomodate these instances there are two
-small constant assignment functions.  The first function is used to set a single digit constant while the second sets
-an ISO C style ``unsigned long'' constant.  The reason for both functions is efficiency.  Setting a single digit is quick but the
-domain of a digit can change (it's always at least $0 \ldots 127$).
-
-\subsection{Single Digit}
-
-Setting a single digit can be accomplished with the following function.
-
-\index{mp\_set}
-\begin{alltt}
-void mp_set (mp_int * a, mp_digit b);
-\end{alltt}
-
-This will zero the contents of $a$ and make it represent an integer equal to the value of $b$.  Note that this
-function has a return type of \textbf{void}.  It cannot cause an error so it is safe to assume the function
-succeeded.
-
-\begin{small} \begin{alltt}
-int main(void)
-\{
-   mp_int number;
-   int result;
-
-   if ((result = mp_init(&number)) != MP_OKAY) \{
-      printf("Error initializing the number.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* set the number to 5 */
-   mp_set(&number, 5);
-
-   /* we're done with it. */
-   mp_clear(&number);
-
-   return EXIT_SUCCESS;
-\}
-\end{alltt} \end{small}
-
-\subsection{Long Constants}
-
-To set a constant that is the size of an ISO C ``unsigned long'' and larger than a single digit the following function
-can be used.
-
-\index{mp\_set\_int}
-\begin{alltt}
-int mp_set_int (mp_int * a, unsigned long b);
-\end{alltt}
-
-This will assign the value of the 32-bit variable $b$ to the mp\_int $a$.  Unlike mp\_set() this function will always
-accept a 32-bit input regardless of the size of a single digit.  However, since the value may span several digits
-this function can fail if it runs out of heap memory.
-
-To get the ``unsigned long'' copy of an mp\_int the following function can be used.
-
-\index{mp\_get\_int}
-\begin{alltt}
-unsigned long mp_get_int (mp_int * a);
-\end{alltt}
-
-This will return the 32 least significant bits of the mp\_int $a$.
-
-\begin{small} \begin{alltt}
-int main(void)
-\{
-   mp_int number;
-   int result;
-
-   if ((result = mp_init(&number)) != MP_OKAY) \{
-      printf("Error initializing the number.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* set the number to 654321 (note this is bigger than 127) */
-   if ((result = mp_set_int(&number, 654321)) != MP_OKAY) \{
-      printf("Error setting the value of the number.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   printf("number == \%lu", mp_get_int(&number));
-
-   /* we're done with it. */
-   mp_clear(&number);
-
-   return EXIT_SUCCESS;
-\}
-\end{alltt} \end{small}
-
-This should output the following if the program succeeds.
-
-\begin{alltt}
-number == 654321
-\end{alltt}
-
-\subsection{Long Constants - platform dependant}
-
-\index{mp\_set\_long}
-\begin{alltt}
-int mp_set_long (mp_int * a, unsigned long b);
-\end{alltt}
-
-This will assign the value of the platform-dependant sized variable $b$ to the mp\_int $a$.
-
-To get the ``unsigned long'' copy of an mp\_int the following function can be used.
-
-\index{mp\_get\_long}
-\begin{alltt}
-unsigned long mp_get_long (mp_int * a);
-\end{alltt}
-
-This will return the least significant bits of the mp\_int $a$ that fit into an ``unsigned long''.
-
-\subsection{Long Long Constants}
-
-\index{mp\_set\_long\_long}
-\begin{alltt}
-int mp_set_long_long (mp_int * a, unsigned long long b);
-\end{alltt}
-
-This will assign the value of the 64-bit variable $b$ to the mp\_int $a$.
-
-To get the ``unsigned long long'' copy of an mp\_int the following function can be used.
-
-\index{mp\_get\_long\_long}
-\begin{alltt}
-unsigned long long mp_get_long_long (mp_int * a);
-\end{alltt}
-
-This will return the 64 least significant bits of the mp\_int $a$.
-
-\subsection{Initialize and Setting Constants}
-To both initialize and set small constants the following two functions are available.
-\index{mp\_init\_set} \index{mp\_init\_set\_int}
-\begin{alltt}
-int mp_init_set (mp_int * a, mp_digit b);
-int mp_init_set_int (mp_int * a, unsigned long b);
-\end{alltt}
-
-Both functions work like the previous counterparts except they first mp\_init $a$ before setting the values.
-
-\begin{alltt}
-int main(void)
-\{
-   mp_int number1, number2;
-   int    result;
-
-   /* initialize and set a single digit */
-   if ((result = mp_init_set(&number1, 100)) != MP_OKAY) \{
-      printf("Error setting number1: \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* initialize and set a long */
-   if ((result = mp_init_set_int(&number2, 1023)) != MP_OKAY) \{
-      printf("Error setting number2: \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* display */
-   printf("Number1, Number2 == \%lu, \%lu",
-          mp_get_int(&number1), mp_get_int(&number2));
-
-   /* clear */
-   mp_clear_multi(&number1, &number2, NULL);
-
-   return EXIT_SUCCESS;
-\}
-\end{alltt}
-
-If this program succeeds it shall output.
-\begin{alltt}
-Number1, Number2 == 100, 1023
-\end{alltt}
-
-\section{Comparisons}
-
-Comparisons in LibTomMath are always performed in a ``left to right'' fashion.  There are three possible return codes
-for any comparison.
-
-\index{MP\_GT} \index{MP\_EQ} \index{MP\_LT}
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{|c|c|}
-\hline \textbf{Result Code} & \textbf{Meaning} \\
-\hline MP\_GT & $a > b$ \\
-\hline MP\_EQ & $a = b$ \\
-\hline MP\_LT & $a < b$ \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Comparison Codes for $a, b$}
-\label{fig:CMP}
-\end{figure}
-
-In figure \ref{fig:CMP} two integers $a$ and $b$ are being compared.  In this case $a$ is said to be ``to the left'' of
-$b$.
-
-\subsection{Unsigned comparison}
-
-An unsigned comparison considers only the digits themselves and not the associated \textit{sign} flag of the
-mp\_int structures.  This is analogous to an absolute comparison.  The function mp\_cmp\_mag() will compare two
-mp\_int variables based on their digits only.
-
-\index{mp\_cmp\_mag}
-\begin{alltt}
-int mp_cmp_mag(mp_int * a, mp_int * b);
-\end{alltt}
-This will compare $a$ to $b$ placing $a$ to the left of $b$.  This function cannot fail and will return one of the
-three compare codes listed in figure \ref{fig:CMP}.
-
-\begin{small} \begin{alltt}
-int main(void)
-\{
-   mp_int number1, number2;
-   int result;
-
-   if ((result = mp_init_multi(&number1, &number2, NULL)) != MP_OKAY) \{
-      printf("Error initializing the numbers.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* set the number1 to 5 */
-   mp_set(&number1, 5);
-
-   /* set the number2 to -6 */
-   mp_set(&number2, 6);
-   if ((result = mp_neg(&number2, &number2)) != MP_OKAY) \{
-      printf("Error negating number2.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   switch(mp_cmp_mag(&number1, &number2)) \{
-       case MP_GT:  printf("|number1| > |number2|"); break;
-       case MP_EQ:  printf("|number1| = |number2|"); break;
-       case MP_LT:  printf("|number1| < |number2|"); break;
-   \}
-
-   /* we're done with it. */
-   mp_clear_multi(&number1, &number2, NULL);
-
-   return EXIT_SUCCESS;
-\}
-\end{alltt} \end{small}
-
-If this program\footnote{This function uses the mp\_neg() function which is discussed in section \ref{sec:NEG}.} completes
-successfully it should print the following.
-
-\begin{alltt}
-|number1| < |number2|
-\end{alltt}
-
-This is because $\vert -6 \vert = 6$ and obviously $5 < 6$.
-
-\subsection{Signed comparison}
-
-To compare two mp\_int variables based on their signed value the mp\_cmp() function is provided.
-
-\index{mp\_cmp}
-\begin{alltt}
-int mp_cmp(mp_int * a, mp_int * b);
-\end{alltt}
-
-This will compare $a$ to the left of $b$.  It will first compare the signs of the two mp\_int variables.  If they
-differ it will return immediately based on their signs.  If the signs are equal then it will compare the digits
-individually.  This function will return one of the compare conditions codes listed in figure \ref{fig:CMP}.
-
-\begin{small} \begin{alltt}
-int main(void)
-\{
-   mp_int number1, number2;
-   int result;
-
-   if ((result = mp_init_multi(&number1, &number2, NULL)) != MP_OKAY) \{
-      printf("Error initializing the numbers.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* set the number1 to 5 */
-   mp_set(&number1, 5);
-
-   /* set the number2 to -6 */
-   mp_set(&number2, 6);
-   if ((result = mp_neg(&number2, &number2)) != MP_OKAY) \{
-      printf("Error negating number2.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   switch(mp_cmp(&number1, &number2)) \{
-       case MP_GT:  printf("number1 > number2"); break;
-       case MP_EQ:  printf("number1 = number2"); break;
-       case MP_LT:  printf("number1 < number2"); break;
-   \}
-
-   /* we're done with it. */
-   mp_clear_multi(&number1, &number2, NULL);
-
-   return EXIT_SUCCESS;
-\}
-\end{alltt} \end{small}
-
-If this program\footnote{This function uses the mp\_neg() function which is discussed in section \ref{sec:NEG}.} completes
-successfully it should print the following.
-
-\begin{alltt}
-number1 > number2
-\end{alltt}
-
-\subsection{Single Digit}
-
-To compare a single digit against an mp\_int the following function has been provided.
-
-\index{mp\_cmp\_d}
-\begin{alltt}
-int mp_cmp_d(mp_int * a, mp_digit b);
-\end{alltt}
-
-This will compare $a$ to the left of $b$ using a signed comparison.  Note that it will always treat $b$ as
-positive.  This function is rather handy when you have to compare against small values such as $1$ (which often
-comes up in cryptography).  The function cannot fail and will return one of the tree compare condition codes
-listed in figure \ref{fig:CMP}.
-
-
-\begin{small} \begin{alltt}
-int main(void)
-\{
-   mp_int number;
-   int result;
-
-   if ((result = mp_init(&number)) != MP_OKAY) \{
-      printf("Error initializing the number.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* set the number to 5 */
-   mp_set(&number, 5);
-
-   switch(mp_cmp_d(&number, 7)) \{
-       case MP_GT:  printf("number > 7"); break;
-       case MP_EQ:  printf("number = 7"); break;
-       case MP_LT:  printf("number < 7"); break;
-   \}
-
-   /* we're done with it. */
-   mp_clear(&number);
-
-   return EXIT_SUCCESS;
-\}
-\end{alltt} \end{small}
-
-If this program functions properly it will print out the following.
-
-\begin{alltt}
-number < 7
-\end{alltt}
-
-\section{Logical Operations}
-
-Logical operations are operations that can be performed either with simple shifts or boolean operators such as
-AND, XOR and OR directly.  These operations are very quick.
-
-\subsection{Multiplication by two}
-
-Multiplications and divisions by any power of two can be performed with quick logical shifts either left or
-right depending on the operation.
-
-When multiplying or dividing by two a special case routine can be used which are as follows.
-\index{mp\_mul\_2} \index{mp\_div\_2}
-\begin{alltt}
-int mp_mul_2(mp_int * a, mp_int * b);
-int mp_div_2(mp_int * a, mp_int * b);
-\end{alltt}
-
-The former will assign twice $a$ to $b$ while the latter will assign half $a$ to $b$.  These functions are fast
-since the shift counts and maskes are hardcoded into the routines.
-
-\begin{small} \begin{alltt}
-int main(void)
-\{
-   mp_int number;
-   int result;
-
-   if ((result = mp_init(&number)) != MP_OKAY) \{
-      printf("Error initializing the number.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* set the number to 5 */
-   mp_set(&number, 5);
-
-   /* multiply by two */
-   if ((result = mp\_mul\_2(&number, &number)) != MP_OKAY) \{
-      printf("Error multiplying the number.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-   switch(mp_cmp_d(&number, 7)) \{
-       case MP_GT:  printf("2*number > 7"); break;
-       case MP_EQ:  printf("2*number = 7"); break;
-       case MP_LT:  printf("2*number < 7"); break;
-   \}
-
-   /* now divide by two */
-   if ((result = mp\_div\_2(&number, &number)) != MP_OKAY) \{
-      printf("Error dividing the number.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-   switch(mp_cmp_d(&number, 7)) \{
-       case MP_GT:  printf("2*number/2 > 7"); break;
-       case MP_EQ:  printf("2*number/2 = 7"); break;
-       case MP_LT:  printf("2*number/2 < 7"); break;
-   \}
-
-   /* we're done with it. */
-   mp_clear(&number);
-
-   return EXIT_SUCCESS;
-\}
-\end{alltt} \end{small}
-
-If this program is successful it will print out the following text.
-
-\begin{alltt}
-2*number > 7
-2*number/2 < 7
-\end{alltt}
-
-Since $10 > 7$ and $5 < 7$.
-
-To multiply by a power of two the following function can be used.
-
-\index{mp\_mul\_2d}
-\begin{alltt}
-int mp_mul_2d(mp_int * a, int b, mp_int * c);
-\end{alltt}
-
-This will multiply $a$ by $2^b$ and store the result in ``c''.  If the value of $b$ is less than or equal to
-zero the function will copy $a$ to ``c'' without performing any further actions.  The multiplication itself
-is implemented as a right-shift operation of $a$ by $b$ bits.
-
-To divide by a power of two use the following.
-
-\index{mp\_div\_2d}
-\begin{alltt}
-int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d);
-\end{alltt}
-Which will divide $a$ by $2^b$, store the quotient in ``c'' and the remainder in ``d'.  If $b \le 0$ then the
-function simply copies $a$ over to ``c'' and zeroes $d$.  The variable $d$ may be passed as a \textbf{NULL}
-value to signal that the remainder is not desired.  The division itself is implemented as a left-shift
-operation of $a$ by $b$ bits.
-
-\subsection{Polynomial Basis Operations}
-
-Strictly speaking the organization of the integers within the mp\_int structures is what is known as a
-``polynomial basis''.  This simply means a field element is stored by divisions of a radix.  For example, if
-$f(x) = \sum_{i=0}^{k} y_ix^k$ for any vector $\vec y$ then the array of digits in $\vec y$ are said to be
-the polynomial basis representation of $z$ if $f(\beta) = z$ for a given radix $\beta$.
-
-To multiply by the polynomial $g(x) = x$ all you have todo is shift the digits of the basis left one place.  The
-following function provides this operation.
-
-\index{mp\_lshd}
-\begin{alltt}
-int mp_lshd (mp_int * a, int b);
-\end{alltt}
-
-This will multiply $a$ in place by $x^b$ which is equivalent to shifting the digits left $b$ places and inserting zeroes
-in the least significant digits.  Similarly to divide by a power of $x$ the following function is provided.
-
-\index{mp\_rshd}
-\begin{alltt}
-void mp_rshd (mp_int * a, int b)
-\end{alltt}
-This will divide $a$ in place by $x^b$ and discard the remainder.  This function cannot fail as it performs the operations
-in place and no new digits are required to complete it.
-
-\subsection{AND, OR and XOR Operations}
-
-While AND, OR and XOR operations are not typical ``bignum functions'' they can be useful in several instances.  The
-three functions are prototyped as follows.
-
-\index{mp\_or} \index{mp\_and} \index{mp\_xor}
-\begin{alltt}
-int mp_or  (mp_int * a, mp_int * b, mp_int * c);
-int mp_and (mp_int * a, mp_int * b, mp_int * c);
-int mp_xor (mp_int * a, mp_int * b, mp_int * c);
-\end{alltt}
-
-Which compute $c = a \odot b$ where $\odot$ is one of OR, AND or XOR.
-
-\section{Addition and Subtraction}
-
-To compute an addition or subtraction the following two functions can be used.
-
-\index{mp\_add} \index{mp\_sub}
-\begin{alltt}
-int mp_add (mp_int * a, mp_int * b, mp_int * c);
-int mp_sub (mp_int * a, mp_int * b, mp_int * c)
-\end{alltt}
-
-Which perform $c = a \odot b$ where $\odot$ is one of signed addition or subtraction.  The operations are fully sign
-aware.
-
-\section{Sign Manipulation}
-\subsection{Negation}
-\label{sec:NEG}
-Simple integer negation can be performed with the following.
-
-\index{mp\_neg}
-\begin{alltt}
-int mp_neg (mp_int * a, mp_int * b);
-\end{alltt}
-
-Which assigns $-a$ to $b$.
-
-\subsection{Absolute}
-Simple integer absolutes can be performed with the following.
-
-\index{mp\_neg}
-\begin{alltt}
-int mp_abs (mp_int * a, mp_int * b);
-\end{alltt}
-
-Which assigns $\vert a \vert$ to $b$.
-
-\section{Integer Division and Remainder}
-To perform a complete and general integer division with remainder use the following function.
-
-\index{mp\_div}
-\begin{alltt}
-int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d);
-\end{alltt}
-
-This divides $a$ by $b$ and stores the quotient in $c$ and $d$.  The signed quotient is computed such that
-$bc + d = a$.  Note that either of $c$ or $d$ can be set to \textbf{NULL} if their value is not required.  If
-$b$ is zero the function returns \textbf{MP\_VAL}.
-
-
-\chapter{Multiplication and Squaring}
-\section{Multiplication}
-A full signed integer multiplication can be performed with the following.
-\index{mp\_mul}
-\begin{alltt}
-int mp_mul (mp_int * a, mp_int * b, mp_int * c);
-\end{alltt}
-Which assigns the full signed product $ab$ to $c$.  This function actually breaks into one of four cases which are
-specific multiplication routines optimized for given parameters.  First there are the Toom-Cook multiplications which
-should only be used with very large inputs.  This is followed by the Karatsuba multiplications which are for moderate
-sized inputs.  Then followed by the Comba and baseline multipliers.
-
-Fortunately for the developer you don't really need to know this unless you really want to fine tune the system.  mp\_mul()
-will determine on its own\footnote{Some tweaking may be required.} what routine to use automatically when it is called.
-
-\begin{alltt}
-int main(void)
-\{
-   mp_int number1, number2;
-   int result;
-
-   /* Initialize the numbers */
-   if ((result = mp_init_multi(&number1,
-                               &number2, NULL)) != MP_OKAY) \{
-      printf("Error initializing the numbers.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* set the terms */
-   if ((result = mp_set_int(&number, 257)) != MP_OKAY) \{
-      printf("Error setting number1.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   if ((result = mp_set_int(&number2, 1023)) != MP_OKAY) \{
-      printf("Error setting number2.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* multiply them */
-   if ((result = mp_mul(&number1, &number2,
-                        &number1)) != MP_OKAY) \{
-      printf("Error multiplying terms.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* display */
-   printf("number1 * number2 == \%lu", mp_get_int(&number1));
-
-   /* free terms and return */
-   mp_clear_multi(&number1, &number2, NULL);
-
-   return EXIT_SUCCESS;
-\}
-\end{alltt}
-
-If this program succeeds it shall output the following.
-
-\begin{alltt}
-number1 * number2 == 262911
-\end{alltt}
-
-\section{Squaring}
-Since squaring can be performed faster than multiplication it is performed it's own function instead of just using
-mp\_mul().
-
-\index{mp\_sqr}
-\begin{alltt}
-int mp_sqr (mp_int * a, mp_int * b);
-\end{alltt}
-
-Will square $a$ and store it in $b$.  Like the case of multiplication there are four different squaring
-algorithms all which can be called from mp\_sqr().  It is ideal to use mp\_sqr over mp\_mul when squaring terms because
-of the speed difference.
-
-\section{Tuning Polynomial Basis Routines}
-
-Both of the Toom-Cook and Karatsuba multiplication algorithms are faster than the traditional $O(n^2)$ approach that
-the Comba and baseline algorithms use.  At $O(n^{1.464973})$ and $O(n^{1.584962})$ running times respectively they require
-considerably less work.  For example, a 10000-digit multiplication would take roughly 724,000 single precision
-multiplications with Toom-Cook or 100,000,000 single precision multiplications with the standard Comba (a factor
-of 138).
-
-So why not always use Karatsuba or Toom-Cook?   The simple answer is that they have so much overhead that they're not
-actually faster than Comba until you hit distinct  ``cutoff'' points.  For Karatsuba with the default configuration,
-GCC 3.3.1 and an Athlon XP processor the cutoff point is roughly 110 digits (about 70 for the Intel P4).  That is, at
-110 digits Karatsuba and Comba multiplications just about break even and for 110+ digits Karatsuba is faster.
-
-Toom-Cook has incredible overhead and is probably only useful for very large inputs.  So far no known cutoff points
-exist and for the most part I just set the cutoff points very high to make sure they're not called.
-
-A demo program in the ``etc/'' directory of the project called ``tune.c'' can be used to find the cutoff points.  This
-can be built with GCC as follows
-
-\begin{alltt}
-make XXX
-\end{alltt}
-Where ``XXX'' is one of the following entries from the table \ref{fig:tuning}.
-
-\begin{figure}[here]
-\begin{center}
-\begin{small}
-\begin{tabular}{|l|l|}
-\hline \textbf{Value of XXX} & \textbf{Meaning} \\
-\hline tune & Builds portable tuning application \\
-\hline tune86 & Builds x86 (pentium and up) program for COFF \\
-\hline tune86c & Builds x86 program for Cygwin \\
-\hline tune86l & Builds x86 program for Linux (ELF format) \\
-\hline
-\end{tabular}
-\end{small}
-\end{center}
-\caption{Build Names for Tuning Programs}
-\label{fig:tuning}
-\end{figure}
-
-When the program is running it will output a series of measurements for different cutoff points.  It will first find
-good Karatsuba squaring and multiplication points.  Then it proceeds to find Toom-Cook points.  Note that the Toom-Cook
-tuning takes a very long time as the cutoff points are likely to be very high.
-
-\chapter{Modular Reduction}
-
-Modular reduction is process of taking the remainder of one quantity divided by another.  Expressed
-as (\ref{eqn:mod}) the modular reduction is equivalent to the remainder of $b$ divided by $c$.
-
-\begin{equation}
-a \equiv b \mbox{ (mod }c\mbox{)}
-\label{eqn:mod}
-\end{equation}
-
-Of particular interest to cryptography are reductions where $b$ is limited to the range $0 \le b < c^2$ since particularly
-fast reduction algorithms can be written for the limited range.
-
-Note that one of the four optimized reduction algorithms are automatically chosen in the modular exponentiation
-algorithm mp\_exptmod when an appropriate modulus is detected.
-
-\section{Straight Division}
-In order to effect an arbitrary modular reduction the following algorithm is provided.
-
-\index{mp\_mod}
-\begin{alltt}
-int mp_mod(mp_int *a, mp_int *b, mp_int *c);
-\end{alltt}
-
-This reduces $a$ modulo $b$ and stores the result in $c$.  The sign of $c$ shall agree with the sign
-of $b$.  This algorithm accepts an input $a$ of any range and is not limited by $0 \le a < b^2$.
-
-\section{Barrett Reduction}
-
-Barrett reduction is a generic optimized reduction algorithm that requires pre--computation to achieve
-a decent speedup over straight division.  First a $\mu$ value must be precomputed with the following function.
-
-\index{mp\_reduce\_setup}
-\begin{alltt}
-int mp_reduce_setup(mp_int *a, mp_int *b);
-\end{alltt}
-
-Given a modulus in $b$ this produces the required $\mu$ value in $a$.  For any given modulus this only has to
-be computed once.  Modular reduction can now be performed with the following.
-
-\index{mp\_reduce}
-\begin{alltt}
-int mp_reduce(mp_int *a, mp_int *b, mp_int *c);
-\end{alltt}
-
-This will reduce $a$ in place modulo $b$ with the precomputed $\mu$ value in $c$.  $a$ must be in the range
-$0 \le a < b^2$.
-
-\begin{alltt}
-int main(void)
-\{
-   mp_int   a, b, c, mu;
-   int      result;
-
-   /* initialize a,b to desired values, mp_init mu,
-    * c and set c to 1...we want to compute a^3 mod b
-    */
-
-   /* get mu value */
-   if ((result = mp_reduce_setup(&mu, b)) != MP_OKAY) \{
-      printf("Error getting mu.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* square a to get c = a^2 */
-   if ((result = mp_sqr(&a, &c)) != MP_OKAY) \{
-      printf("Error squaring.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* now reduce `c' modulo b */
-   if ((result = mp_reduce(&c, &b, &mu)) != MP_OKAY) \{
-      printf("Error reducing.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* multiply a to get c = a^3 */
-   if ((result = mp_mul(&a, &c, &c)) != MP_OKAY) \{
-      printf("Error reducing.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* now reduce `c' modulo b  */
-   if ((result = mp_reduce(&c, &b, &mu)) != MP_OKAY) \{
-      printf("Error reducing.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* c now equals a^3 mod b */
-
-   return EXIT_SUCCESS;
-\}
-\end{alltt}
-
-This program will calculate $a^3 \mbox{ mod }b$ if all the functions succeed.
-
-\section{Montgomery Reduction}
-
-Montgomery is a specialized reduction algorithm for any odd moduli.  Like Barrett reduction a pre--computation
-step is required.  This is accomplished with the following.
-
-\index{mp\_montgomery\_setup}
-\begin{alltt}
-int mp_montgomery_setup(mp_int *a, mp_digit *mp);
-\end{alltt}
-
-For the given odd moduli $a$ the precomputation value is placed in $mp$.  The reduction is computed with the
-following.
-
-\index{mp\_montgomery\_reduce}
-\begin{alltt}
-int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
-\end{alltt}
-This reduces $a$ in place modulo $m$ with the pre--computed value $mp$.   $a$ must be in the range
-$0 \le a < b^2$.
-
-Montgomery reduction is faster than Barrett reduction for moduli smaller than the ``comba'' limit.  With the default
-setup for instance, the limit is $127$ digits ($3556$--bits).   Note that this function is not limited to
-$127$ digits just that it falls back to a baseline algorithm after that point.
-
-An important observation is that this reduction does not return $a \mbox{ mod }m$ but $aR^{-1} \mbox{ mod }m$
-where $R = \beta^n$, $n$ is the n number of digits in $m$ and $\beta$ is radix used (default is $2^{28}$).
-
-To quickly calculate $R$ the following function was provided.
-
-\index{mp\_montgomery\_calc\_normalization}
-\begin{alltt}
-int mp_montgomery_calc_normalization(mp_int *a, mp_int *b);
-\end{alltt}
-Which calculates $a = R$ for the odd moduli $b$ without using multiplication or division.
-
-The normal modus operandi for Montgomery reductions is to normalize the integers before entering the system.  For
-example, to calculate $a^3 \mbox { mod }b$ using Montgomery reduction the value of $a$ can be normalized by
-multiplying it by $R$.  Consider the following code snippet.
-
-\begin{alltt}
-int main(void)
-\{
-   mp_int   a, b, c, R;
-   mp_digit mp;
-   int      result;
-
-   /* initialize a,b to desired values,
-    * mp_init R, c and set c to 1....
-    */
-
-   /* get normalization */
-   if ((result = mp_montgomery_calc_normalization(&R, b)) != MP_OKAY) \{
-      printf("Error getting norm.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* get mp value */
-   if ((result = mp_montgomery_setup(&c, &mp)) != MP_OKAY) \{
-      printf("Error setting up montgomery.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* normalize `a' so now a is equal to aR */
-   if ((result = mp_mulmod(&a, &R, &b, &a)) != MP_OKAY) \{
-      printf("Error computing aR.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* square a to get c = a^2R^2 */
-   if ((result = mp_sqr(&a, &c)) != MP_OKAY) \{
-      printf("Error squaring.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* now reduce `c' back down to c = a^2R^2 * R^-1 == a^2R */
-   if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
-      printf("Error reducing.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* multiply a to get c = a^3R^2 */
-   if ((result = mp_mul(&a, &c, &c)) != MP_OKAY) \{
-      printf("Error reducing.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* now reduce `c' back down to c = a^3R^2 * R^-1 == a^3R */
-   if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
-      printf("Error reducing.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* now reduce (again) `c' back down to c = a^3R * R^-1 == a^3 */
-   if ((result = mp_montgomery_reduce(&c, &b, mp)) != MP_OKAY) \{
-      printf("Error reducing.  \%s",
-             mp_error_to_string(result));
-      return EXIT_FAILURE;
-   \}
-
-   /* c now equals a^3 mod b */
-
-   return EXIT_SUCCESS;
-\}
-\end{alltt}
-
-This particular example does not look too efficient but it demonstrates the point of the algorithm.  By
-normalizing the inputs the reduced results are always of the form $aR$ for some variable $a$.  This allows
-a single final reduction to correct for the normalization and the fast reduction used within the algorithm.
-
-For more details consider examining the file \textit{bn\_mp\_exptmod\_fast.c}.
-
-\section{Restricted Dimminished Radix}
-
-``Dimminished Radix'' reduction refers to reduction with respect to moduli that are ameniable to simple
-digit shifting and small multiplications.  In this case the ``restricted'' variant refers to moduli of the
-form $\beta^k - p$ for some $k \ge 0$ and $0 < p < \beta$ where $\beta$ is the radix (default to $2^{28}$).
-
-As in the case of Montgomery reduction there is a pre--computation phase required for a given modulus.
-
-\index{mp\_dr\_setup}
-\begin{alltt}
-void mp_dr_setup(mp_int *a, mp_digit *d);
-\end{alltt}
-
-This computes the value required for the modulus $a$ and stores it in $d$.  This function cannot fail
-and does not return any error codes.  After the pre--computation a reduction can be performed with the
-following.
-
-\index{mp\_dr\_reduce}
-\begin{alltt}
-int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp);
-\end{alltt}
-
-This reduces $a$ in place modulo $b$ with the pre--computed value $mp$.  $b$ must be of a restricted
-dimminished radix form and $a$ must be in the range $0 \le a < b^2$.  Dimminished radix reductions are
-much faster than both Barrett and Montgomery reductions as they have a much lower asymtotic running time.
-
-Since the moduli are restricted this algorithm is not particularly useful for something like Rabin, RSA or
-BBS cryptographic purposes.  This reduction algorithm is useful for Diffie-Hellman and ECC where fixed
-primes are acceptable.
-
-Note that unlike Montgomery reduction there is no normalization process.  The result of this function is
-equal to the correct residue.
-
-\section{Unrestricted Dimminshed Radix}
-
-Unrestricted reductions work much like the restricted counterparts except in this case the moduli is of the
-form $2^k - p$ for $0 < p < \beta$.  In this sense the unrestricted reductions are more flexible as they
-can be applied to a wider range of numbers.
-
-\index{mp\_reduce\_2k\_setup}
-\begin{alltt}
-int mp_reduce_2k_setup(mp_int *a, mp_digit *d);
-\end{alltt}
-
-This will compute the required $d$ value for the given moduli $a$.
-
-\index{mp\_reduce\_2k}
-\begin{alltt}
-int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);
-\end{alltt}
-
-This will reduce $a$ in place modulo $n$ with the pre--computed value $d$.  From my experience this routine is
-slower than mp\_dr\_reduce but faster for most moduli sizes than the Montgomery reduction.
-
-\chapter{Exponentiation}
-\section{Single Digit Exponentiation}
-\index{mp\_expt\_d\_ex}
-\begin{alltt}
-int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
-\end{alltt}
-This function computes $c = a^b$.
-
-With parameter \textit{fast} set to $0$ the old version of the algorithm is used,
-when \textit{fast} is $1$, a faster but not statically timed version of the algorithm is used.
-
-The old version uses a simple binary left-to-right algorithm.
-It is faster than repeated multiplications by $a$ for all values of $b$ greater than three.
-
-The new version uses a binary right-to-left algorithm.
-
-The difference between the old and the new version is that the old version always
-executes $DIGIT\_BIT$ iterations. The new algorithm executes only $n$ iterations
-where $n$ is equal to the position of the highest bit that is set in $b$.
-
-\index{mp\_expt\_d}
-\begin{alltt}
-int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
-\end{alltt}
-mp\_expt\_d(a, b, c) is a wrapper function to mp\_expt\_d\_ex(a, b, c, 0).
-
-\section{Modular Exponentiation}
-\index{mp\_exptmod}
-\begin{alltt}
-int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
-\end{alltt}
-This computes $Y \equiv G^X \mbox{ (mod }P\mbox{)}$ using a variable width sliding window algorithm.  This function
-will automatically detect the fastest modular reduction technique to use during the operation.  For negative values of
-$X$ the operation is performed as $Y \equiv (G^{-1} \mbox{ mod }P)^{\vert X \vert} \mbox{ (mod }P\mbox{)}$ provided that
-$gcd(G, P) = 1$.
-
-This function is actually a shell around the two internal exponentiation functions.  This routine will automatically
-detect when Barrett, Montgomery, Restricted and Unrestricted Dimminished Radix based exponentiation can be used.  Generally
-moduli of the a ``restricted dimminished radix'' form lead to the fastest modular exponentiations.  Followed by Montgomery
-and the other two algorithms.
-
-\section{Root Finding}
-\index{mp\_n\_root}
-\begin{alltt}
-int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
-\end{alltt}
-This computes $c = a^{1/b}$ such that $c^b \le a$ and $(c+1)^b > a$.  The implementation of this function is not
-ideal for values of $b$ greater than three.  It will work but become very slow.  So unless you are working with very small
-numbers (less than 1000 bits) I'd avoid $b > 3$ situations.  Will return a positive root only for even roots and return
-a root with the sign of the input for odd roots.  For example, performing $4^{1/2}$ will return $2$ whereas $(-8)^{1/3}$
-will return $-2$.
-
-This algorithm uses the ``Newton Approximation'' method and will converge on the correct root fairly quickly.  Since
-the algorithm requires raising $a$ to the power of $b$ it is not ideal to attempt to find roots for large
-values of $b$.  If particularly large roots are required then a factor method could be used instead.  For example,
-$a^{1/16}$ is equivalent to $\left (a^{1/4} \right)^{1/4}$ or simply
-$\left ( \left ( \left ( a^{1/2} \right )^{1/2} \right )^{1/2} \right )^{1/2}$
-
-\chapter{Prime Numbers}
-\section{Trial Division}
-\index{mp\_prime\_is\_divisible}
-\begin{alltt}
-int mp_prime_is_divisible (mp_int * a, int *result)
-\end{alltt}
-This will attempt to evenly divide $a$ by a list of primes\footnote{Default is the first 256 primes.} and store the
-outcome in ``result''.  That is if $result = 0$ then $a$ is not divisible by the primes, otherwise it is.  Note that
-if the function does not return \textbf{MP\_OKAY} the value in ``result'' should be considered undefined\footnote{Currently
-the default is to set it to zero first.}.
-
-\section{Fermat Test}
-\index{mp\_prime\_fermat}
-\begin{alltt}
-int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
-\end{alltt}
-Performs a Fermat primality test to the base $b$.  That is it computes $b^a \mbox{ mod }a$ and tests whether the value is
-equal to $b$ or not.  If the values are equal then $a$ is probably prime and $result$ is set to one.  Otherwise $result$
-is set to zero.
-
-\section{Miller-Rabin Test}
-\index{mp\_prime\_miller\_rabin}
-\begin{alltt}
-int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
-\end{alltt}
-Performs a Miller-Rabin test to the base $b$ of $a$.  This test is much stronger than the Fermat test and is very hard to
-fool (besides with Carmichael numbers).  If $a$ passes the test (therefore is probably prime) $result$ is set to one.
-Otherwise $result$ is set to zero.
-
-Note that is suggested that you use the Miller-Rabin test instead of the Fermat test since all of the failures of
-Miller-Rabin are a subset of the failures of the Fermat test.
-
-\subsection{Required Number of Tests}
-Generally to ensure a number is very likely to be prime you have to perform the Miller-Rabin with at least a half-dozen
-or so unique bases.  However, it has been proven that the probability of failure goes down as the size of the input goes up.
-This is why a simple function has been provided to help out.
-
-\index{mp\_prime\_rabin\_miller\_trials}
-\begin{alltt}
-int mp_prime_rabin_miller_trials(int size)
-\end{alltt}
-This returns the number of trials required for a $2^{-96}$ (or lower) probability of failure for a given ``size'' expressed
-in bits.  This comes in handy specially since larger numbers are slower to test.  For example, a 512-bit number would
-require ten tests whereas a 1024-bit number would only require four tests.
-
-You should always still perform a trial division before a Miller-Rabin test though.
-
-\section{Primality Testing}
-\index{mp\_prime\_is\_prime}
-\begin{alltt}
-int mp_prime_is_prime (mp_int * a, int t, int *result)
-\end{alltt}
-This will perform a trial division followed by $t$ rounds of Miller-Rabin tests on $a$ and store the result in $result$.
-If $a$ passes all of the tests $result$ is set to one, otherwise it is set to zero.  Note that $t$ is bounded by
-$1 \le t < PRIME\_SIZE$ where $PRIME\_SIZE$ is the number of primes in the prime number table (by default this is $256$).
-
-\section{Next Prime}
-\index{mp\_prime\_next\_prime}
-\begin{alltt}
-int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
-\end{alltt}
-This finds the next prime after $a$ that passes mp\_prime\_is\_prime() with $t$ tests.  Set $bbs\_style$ to one if you
-want only the next prime congruent to $3 \mbox{ mod } 4$, otherwise set it to zero to find any next prime.
-
-\section{Random Primes}
-\index{mp\_prime\_random}
-\begin{alltt}
-int mp_prime_random(mp_int *a, int t, int size, int bbs,
-                    ltm_prime_callback cb, void *dat)
-\end{alltt}
-This will find a prime greater than $256^{size}$ which can be ``bbs\_style'' or not depending on $bbs$ and must pass
-$t$ rounds of tests.  The ``ltm\_prime\_callback'' is a typedef for
-
-\begin{alltt}
-typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
-\end{alltt}
-
-Which is a function that must read $len$ bytes (and return the amount stored) into $dst$.  The $dat$ variable is simply
-copied from the original input.  It can be used to pass RNG context data to the callback.  The function
-mp\_prime\_random() is more suitable for generating primes which must be secret (as in the case of RSA) since there
-is no skew on the least significant bits.
-
-\textit{Note:}  As of v0.30 of the LibTomMath library this function has been deprecated.  It is still available
-but users are encouraged to use the new mp\_prime\_random\_ex() function instead.
-
-\subsection{Extended Generation}
-\index{mp\_prime\_random\_ex}
-\begin{alltt}
-int mp_prime_random_ex(mp_int *a,    int t,
-                       int     size, int flags,
-                       ltm_prime_callback cb, void *dat);
-\end{alltt}
-This will generate a prime in $a$ using $t$ tests of the primality testing algorithms.  The variable $size$
-specifies the bit length of the prime desired.  The variable $flags$ specifies one of several options available
-(see fig. \ref{fig:primeopts}) which can be OR'ed together.  The callback parameters are used as in
-mp\_prime\_random().
-
-\begin{figure}[here]
-\begin{center}
-\begin{small}
-\begin{tabular}{|r|l|}
-\hline \textbf{Flag}         & \textbf{Meaning} \\
-\hline LTM\_PRIME\_BBS       & Make the prime congruent to $3$ modulo $4$ \\
-\hline LTM\_PRIME\_SAFE      & Make a prime $p$ such that $(p - 1)/2$ is also prime. \\
-                             & This option implies LTM\_PRIME\_BBS as well. \\
-\hline LTM\_PRIME\_2MSB\_OFF & Makes sure that the bit adjacent to the most significant bit \\
-                             & Is forced to zero.  \\
-\hline LTM\_PRIME\_2MSB\_ON  & Makes sure that the bit adjacent to the most significant bit \\
-                             & Is forced to one. \\
-\hline
-\end{tabular}
-\end{small}
-\end{center}
-\caption{Primality Generation Options}
-\label{fig:primeopts}
-\end{figure}
-
-\chapter{Input and Output}
-\section{ASCII Conversions}
-\subsection{To ASCII}
-\index{mp\_toradix}
-\begin{alltt}
-int mp_toradix (mp_int * a, char *str, int radix);
-\end{alltt}
-This still store $a$ in ``str'' as a base-``radix'' string of ASCII chars.  This function appends a NUL character
-to terminate the string.  Valid values of ``radix'' line in the range $[2, 64]$.  To determine the size (exact) required
-by the conversion before storing any data use the following function.
-
-\index{mp\_radix\_size}
-\begin{alltt}
-int mp_radix_size (mp_int * a, int radix, int *size)
-\end{alltt}
-This stores in ``size'' the number of characters (including space for the NUL terminator) required.  Upon error this
-function returns an error code and ``size'' will be zero.
-
-\subsection{From ASCII}
-\index{mp\_read\_radix}
-\begin{alltt}
-int mp_read_radix (mp_int * a, char *str, int radix);
-\end{alltt}
-This will read the base-``radix'' NUL terminated string from ``str'' into $a$.  It will stop reading when it reads a
-character it does not recognize (which happens to include th NUL char... imagine that...).  A single leading $-$ sign
-can be used to denote a negative number.
-
-\section{Binary Conversions}
-
-Converting an mp\_int to and from binary is another keen idea.
-
-\index{mp\_unsigned\_bin\_size}
-\begin{alltt}
-int mp_unsigned_bin_size(mp_int *a);
-\end{alltt}
-
-This will return the number of bytes (octets) required to store the unsigned copy of the integer $a$.
-
-\index{mp\_to\_unsigned\_bin}
-\begin{alltt}
-int mp_to_unsigned_bin(mp_int *a, unsigned char *b);
-\end{alltt}
-This will store $a$ into the buffer $b$ in big--endian format.  Fortunately this is exactly what DER (or is it ASN?)
-requires.  It does not store the sign of the integer.
-
-\index{mp\_read\_unsigned\_bin}
-\begin{alltt}
-int mp_read_unsigned_bin(mp_int *a, unsigned char *b, int c);
-\end{alltt}
-This will read in an unsigned big--endian array of bytes (octets) from $b$ of length $c$ into $a$.  The resulting
-integer $a$ will always be positive.
-
-For those who acknowledge the existence of negative numbers (heretic!) there are ``signed'' versions of the
-previous functions.
-
-\begin{alltt}
-int mp_signed_bin_size(mp_int *a);
-int mp_read_signed_bin(mp_int *a, unsigned char *b, int c);
-int mp_to_signed_bin(mp_int *a, unsigned char *b);
-\end{alltt}
-They operate essentially the same as the unsigned copies except they prefix the data with zero or non--zero
-byte depending on the sign.  If the sign is zpos (e.g. not negative) the prefix is zero, otherwise the prefix
-is non--zero.
-
-\chapter{Algebraic Functions}
-\section{Extended Euclidean Algorithm}
-\index{mp\_exteuclid}
-\begin{alltt}
-int mp_exteuclid(mp_int *a, mp_int *b,
-                 mp_int *U1, mp_int *U2, mp_int *U3);
-\end{alltt}
-
-This finds the triple U1/U2/U3 using the Extended Euclidean algorithm such that the following equation holds.
-
-\begin{equation}
-a \cdot U1 + b \cdot U2 = U3
-\end{equation}
-
-Any of the U1/U2/U3 paramters can be set to \textbf{NULL} if they are not desired.
-
-\section{Greatest Common Divisor}
-\index{mp\_gcd}
-\begin{alltt}
-int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
-\end{alltt}
-This will compute the greatest common divisor of $a$ and $b$ and store it in $c$.
-
-\section{Least Common Multiple}
-\index{mp\_lcm}
-\begin{alltt}
-int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
-\end{alltt}
-This will compute the least common multiple of $a$ and $b$ and store it in $c$.
-
-\section{Jacobi Symbol}
-\index{mp\_jacobi}
-\begin{alltt}
-int mp_jacobi (mp_int * a, mp_int * p, int *c)
-\end{alltt}
-This will compute the Jacobi symbol for $a$ with respect to $p$.  If $p$ is prime this essentially computes the Legendre
-symbol.  The result is stored in $c$ and can take on one of three values $\lbrace -1, 0, 1 \rbrace$.  If $p$ is prime
-then the result will be $-1$ when $a$ is not a quadratic residue modulo $p$.  The result will be $0$ if $a$ divides $p$
-and the result will be $1$ if $a$ is a quadratic residue modulo $p$.
-
-\section{Modular square root}
-\index{mp\_sqrtmod\_prime}
-\begin{alltt}
-int mp_sqrtmod_prime(mp_int *n, mp_int *p, mp_int *r)
-\end{alltt}
-
-This will solve the modular equatioon $r^2 = n \mod p$ where $p$ is a prime number greater than 2 (odd prime).
-The result is returned in the third argument $r$, the function returns \textbf{MP\_OKAY} on success,
-other return values indicate failure.
-
-The implementation is split for two different cases:
-
-1. if $p \mod 4 == 3$ we apply \href{http://cacr.uwaterloo.ca/hac/}{Handbook of Applied Cryptography algorithm 3.36} and compute $r$ directly as
-$r = n^{(p+1)/4} \mod p$
-
-2. otherwise we use \href{https://en.wikipedia.org/wiki/Tonelli-Shanks_algorithm}{Tonelli-Shanks algorithm}
-
-The function does not check the primality of parameter $p$ thus it is up to the caller to assure that this parameter
-is a prime number. When $p$ is a composite the function behaviour is undefined, it may even return a false-positive
-\textbf{MP\_OKAY}.
-
-\section{Modular Inverse}
-\index{mp\_invmod}
-\begin{alltt}
-int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
-\end{alltt}
-Computes the multiplicative inverse of $a$ modulo $b$ and stores the result in $c$ such that $ac \equiv 1 \mbox{ (mod }b\mbox{)}$.
-
-\section{Single Digit Functions}
-
-For those using small numbers (\textit{snicker snicker}) there are several ``helper'' functions
-
-\index{mp\_add\_d} \index{mp\_sub\_d} \index{mp\_mul\_d} \index{mp\_div\_d} \index{mp\_mod\_d}
-\begin{alltt}
-int mp_add_d(mp_int *a, mp_digit b, mp_int *c);
-int mp_sub_d(mp_int *a, mp_digit b, mp_int *c);
-int mp_mul_d(mp_int *a, mp_digit b, mp_int *c);
-int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d);
-int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
-\end{alltt}
-
-These work like the full mp\_int capable variants except the second parameter $b$ is a mp\_digit.  These
-functions fairly handy if you have to work with relatively small numbers since you will not have to allocate
-an entire mp\_int to store a number like $1$ or $2$.
-
-\input{bn.ind}
-
-\end{document}
diff --git a/libtommath/bn_mp_read_radix.c b/libtommath/bn_mp_read_radix.c
index 03384e3..a4d1c8a 100644
--- a/libtommath/bn_mp_read_radix.c
+++ b/libtommath/bn_mp_read_radix.c
@@ -71,7 +71,13 @@ int mp_read_radix (mp_int * a, const char *str, int radix)
     }
     ++str;
   }
-  
+
+  /* if an illegal character was found, fail. */
+  if (!(*str == '\0' || *str == '\r' || *str == '\n')) {
+      mp_zero(a);
+      return MP_VAL;
+  }
+
   /* set the sign only if a != 0 */
   if (mp_iszero(a) != MP_YES) {
      a->sign = neg;
diff --git a/libtommath/booker.pl b/libtommath/booker.pl
deleted file mode 100644
index c2abae6..0000000
--- a/libtommath/booker.pl
+++ /dev/null
@@ -1,267 +0,0 @@
-#!/bin/perl
-#
-#Used to prepare the book "tommath.src" for LaTeX by pre-processing it into a .tex file
-#
-#Essentially you write the "tommath.src" as normal LaTex except where you want code snippets you put
-#
-#EXAM,file
-#
-#This preprocessor will then open "file" and insert it as a verbatim copy.
-#
-#Tom St Denis
-
-#get graphics type
-if (shift =~ /PDF/) {
-   $graph = "";
-} else {
-   $graph = ".ps";
-}
-
-open(IN,"<tommath.src") or die "Can't open source file";
-open(OUT,">tommath.tex") or die "Can't open destination file";
-
-print "Scanning for sections\n";
-$chapter = $section = $subsection = 0;
-$x = 0;
-while (<IN>) {
-   print ".";
-   if (!(++$x % 80)) { print "\n"; }
-   #update the headings
-   if (~($_ =~ /\*/)) {
-      if ($_ =~ /\\chapter\{.+}/) {
-          ++$chapter;
-          $section = $subsection = 0;
-      } elsif ($_ =~ /\\section\{.+}/) {
-          ++$section;
-          $subsection = 0;
-      } elsif ($_ =~ /\\subsection\{.+}/) {
-          ++$subsection;
-      }
-   }
-
-   if ($_ =~ m/MARK/) {
-      @m = split(",",$_);
-      chomp(@m[1]);
-      $index1{@m[1]} = $chapter;
-      $index2{@m[1]} = $section;
-      $index3{@m[1]} = $subsection;
-   }
-}
-close(IN);
-
-open(IN,"<tommath.src") or die "Can't open source file";
-$readline = $wroteline = 0;
-$srcline = 0;
-
-while (<IN>) {
-   ++$readline;
-   ++$srcline;
-
-   if ($_ =~ m/MARK/) {
-   } elsif ($_ =~ m/EXAM/ || $_ =~ m/LIST/) {
-      if ($_ =~ m/EXAM/) {
-         $skipheader = 1;
-      } else {
-         $skipheader = 0;
-      }
-
-      # EXAM,file
-      chomp($_);
-      @m = split(",",$_);
-      open(SRC,"<$m[1]") or die "Error:$srcline:Can't open source file $m[1]";
-
-      print "$srcline:Inserting $m[1]:";
-
-      $line = 0;
-      $tmp = $m[1];
-      $tmp =~ s/_/"\\_"/ge;
-      print OUT "\\vspace{+3mm}\\begin{small}\n\\hspace{-5.1mm}{\\bf File}: $tmp\n\\vspace{-3mm}\n\\begin{alltt}\n";
-      $wroteline += 5;
-
-      if ($skipheader == 1) {
-         # scan till next end of comment, e.g. skip license
-         while (<SRC>) {
-            $text[$line++] = $_;
-            last if ($_ =~ /libtom\.org/);
-         }
-         <SRC>;
-      }
-
-      $inline = 0;
-      while (<SRC>) {
-      next if ($_ =~ /\$Source/);
-      next if ($_ =~ /\$Revision/);
-      next if ($_ =~ /\$Date/);
-         $text[$line++] = $_;
-         ++$inline;
-         chomp($_);
-         $_ =~ s/\t/"    "/ge;
-         $_ =~ s/{/"^{"/ge;
-         $_ =~ s/}/"^}"/ge;
-         $_ =~ s/\\/'\symbol{92}'/ge;
-         $_ =~ s/\^/"\\"/ge;
-
-         printf OUT ("%03d   ", $line);
-         for ($x = 0; $x < length($_); $x++) {
-             print OUT chr(vec($_, $x, 8));
-             if ($x == 75) {
-                 print OUT "\n      ";
-                 ++$wroteline;
-             }
-         }
-         print OUT "\n";
-         ++$wroteline;
-      }
-      $totlines = $line;
-      print OUT "\\end{alltt}\n\\end{small}\n";
-      close(SRC);
-      print "$inline lines\n";
-      $wroteline += 2;
-   } elsif ($_ =~ m/@\d+,.+@/) {
-     # line contains [number,text]
-     # e.g. @14,for (ix = 0)@
-     $txt = $_;
-     while ($txt =~ m/@\d+,.+@/) {
-        @m = split("@",$txt);      # splits into text, one, two
-        @parms = split(",",$m[1]);  # splits one,two into two elements
-
-        # now search from $parms[0] down for $parms[1]
-        $found1 = 0;
-        $found2 = 0;
-        for ($i = $parms[0]; $i < $totlines && $found1 == 0; $i++) {
-           if ($text[$i] =~ m/\Q$parms[1]\E/) {
-              $foundline1 = $i + 1;
-              $found1 = 1;
-           }
-        }
-
-        # now search backwards
-        for ($i = $parms[0] - 1; $i >= 0 && $found2 == 0; $i--) {
-           if ($text[$i] =~ m/\Q$parms[1]\E/) {
-              $foundline2 = $i + 1;
-              $found2 = 1;
-           }
-        }
-
-        # now use the closest match or the first if tied
-        if ($found1 == 1 && $found2 == 0) {
-           $found = 1;
-           $foundline = $foundline1;
-        } elsif ($found1 == 0 && $found2 == 1) {
-           $found = 1;
-           $foundline = $foundline2;
-        } elsif ($found1 == 1 && $found2 == 1) {
-           $found = 1;
-           if (($foundline1 - $parms[0]) <= ($parms[0] - $foundline2)) {
-              $foundline = $foundline1;
-           } else {
-              $foundline = $foundline2;
-           }
-        } else {
-           $found = 0;
-        }
-
-        # if found replace
-        if ($found == 1) {
-           $delta = $parms[0] - $foundline;
-           print "Found replacement tag for \"$parms[1]\" on line $srcline which refers to line $foundline (delta $delta)\n";
-           $_ =~ s/@\Q$m[1]\E@/$foundline/;
-        } else {
-           print "ERROR:  The tag \"$parms[1]\" on line $srcline was not found in the most recently parsed source!\n";
-        }
-
-        # remake the rest of the line
-        $cnt = @m;
-        $txt = "";
-        for ($i = 2; $i < $cnt; $i++) {
-            $txt = $txt . $m[$i] . "@";
-        }
-     }
-     print OUT $_;
-     ++$wroteline;
-   } elsif ($_ =~ /~.+~/) {
-      # line contains a ~text~ pair used to refer to indexing :-)
-      $txt = $_;
-      while ($txt =~ /~.+~/) {
-         @m = split("~", $txt);
-
-         # word is the second position
-         $word = @m[1];
-         $a = $index1{$word};
-         $b = $index2{$word};
-         $c = $index3{$word};
-
-         # if chapter (a) is zero it wasn't found
-         if ($a == 0) {
-            print "ERROR: the tag \"$word\" on line $srcline was not found previously marked.\n";
-         } else {
-            # format the tag as x, x.y or x.y.z depending on the values
-            $str = $a;
-            $str = $str . ".$b" if ($b != 0);
-            $str = $str . ".$c" if ($c != 0);
-
-            if ($b == 0 && $c == 0) {
-               # its a chapter
-               if ($a <= 10) {
-                  if ($a == 1) {
-                     $str = "chapter one";
-                  } elsif ($a == 2) {
-                     $str = "chapter two";
-                  } elsif ($a == 3) {
-                     $str = "chapter three";
-                  } elsif ($a == 4) {
-                     $str = "chapter four";
-                  } elsif ($a == 5) {
-                     $str = "chapter five";
-                  } elsif ($a == 6) {
-                     $str = "chapter six";
-                  } elsif ($a == 7) {
-                     $str = "chapter seven";
-                  } elsif ($a == 8) {
-                     $str = "chapter eight";
-                  } elsif ($a == 9) {
-                     $str = "chapter nine";
-                  } elsif ($a == 10) {
-                     $str = "chapter ten";
-                  }
-               } else {
-                  $str = "chapter " . $str;
-               }
-            } else {
-               $str = "section " . $str     if ($b != 0 && $c == 0);
-               $str = "sub-section " . $str if ($b != 0 && $c != 0);
-            }
-
-            #substitute
-            $_ =~ s/~\Q$word\E~/$str/;
-
-            print "Found replacement tag for marker \"$word\" on line $srcline which refers to $str\n";
-         }
-
-         # remake rest of the line
-         $cnt = @m;
-         $txt = "";
-         for ($i = 2; $i < $cnt; $i++) {
-             $txt = $txt . $m[$i] . "~";
-         }
-      }
-      print OUT $_;
-      ++$wroteline;
-   } elsif ($_ =~ m/FIGU/) {
-      # FIGU,file,caption
-      chomp($_);
-      @m = split(",", $_);
-      print OUT "\\begin{center}\n\\begin{figure}[here]\n\\includegraphics{pics/$m[1]$graph}\n";
-      print OUT "\\caption{$m[2]}\n\\label{pic:$m[1]}\n\\end{figure}\n\\end{center}\n";
-      $wroteline += 4;
-   } else {
-      print OUT $_;
-      ++$wroteline;
-   }
-}
-print "Read $readline lines, wrote $wroteline lines\n";
-
-close (OUT);
-close (IN);
-
-system('perl -pli -e "s/\s*$//" tommath.tex');
diff --git a/libtommath/changes.txt b/libtommath/changes.txt
index 3379f71..51da801 100644
--- a/libtommath/changes.txt
+++ b/libtommath/changes.txt
@@ -1,4 +1,4 @@
-XXX, 2017
+Aug 29th, 2017
 v1.0.1
        -- Dmitry Kovalenko provided fixes to mp_add_d() and mp_init_copy()
        -- Matt Johnston contributed some improvements to mp_div_2d(),
diff --git a/libtommath/demo/demo.c b/libtommath/demo/demo.c
deleted file mode 100644
index b46b7f8..0000000
--- a/libtommath/demo/demo.c
+++ /dev/null
@@ -1,986 +0,0 @@
-#include <string.h>
-#include <time.h>
-
-#ifdef IOWNANATHLON
-#include <unistd.h>
-#define SLEEP sleep(4)
-#else
-#define SLEEP
-#endif
-
-/*
- * Configuration
- */
-#ifndef LTM_DEMO_TEST_VS_MTEST
-#define LTM_DEMO_TEST_VS_MTEST 1
-#endif
-
-#ifndef LTM_DEMO_TEST_REDUCE_2K_L
-/* This test takes a moment so we disable it by default, but it can be:
- * 0 to disable testing
- * 1 to make the test with P = 2^1024 - 0x2A434 B9FDEC95 D8F9D550 FFFFFFFF FFFFFFFF
- * 2 to make the test with P = 2^2048 - 0x1 00000000 00000000 00000000 00000000 4945DDBF 8EA2A91D 5776399B B83E188F
- */
-#define LTM_DEMO_TEST_REDUCE_2K_L 0
-#endif
-
-#ifdef LTM_DEMO_REAL_RAND
-#define LTM_DEMO_RAND_SEED  time(NULL)
-#else
-#define LTM_DEMO_RAND_SEED  23
-#endif
-
-#include "tommath.h"
-
-void ndraw(mp_int * a, char *name)
-{
-   char buf[16000];
-
-   printf("%s: ", name);
-   mp_toradix(a, buf, 10);
-   printf("%s\n", buf);
-   mp_toradix(a, buf, 16);
-   printf("0x%s\n", buf);
-}
-
-#if LTM_DEMO_TEST_VS_MTEST
-static void draw(mp_int * a)
-{
-   ndraw(a, "");
-}
-#endif
-
-
-unsigned long lfsr = 0xAAAAAAAAUL;
-
-int lbit(void)
-{
-   if (lfsr & 0x80000000UL) {
-      lfsr = ((lfsr << 1) ^ 0x8000001BUL) & 0xFFFFFFFFUL;
-      return 1;
-   } else {
-      lfsr <<= 1;
-      return 0;
-   }
-}
-
-#if defined(LTM_DEMO_REAL_RAND) && !defined(_WIN32)
-static FILE* fd_urandom;
-#endif
-int myrng(unsigned char *dst, int len, void *dat)
-{
-   int x;
-   (void)dat;
-#if defined(LTM_DEMO_REAL_RAND)
-   if (!fd_urandom) {
-#if !defined(_WIN32)
-      fprintf(stderr, "\nno /dev/urandom\n");
-#endif
-   }
-   else {
-      return fread(dst, 1, len, fd_urandom);
-   }
-#endif
-   for (x = 0; x < len; ) {
-      unsigned int r = (unsigned int)rand();
-      do {
-         dst[x++] = r & 0xFF;
-         r >>= 8;
-      } while((r != 0) && (x < len));
-   }
-   return len;
-}
-
-#if LTM_DEMO_TEST_VS_MTEST != 0
-static void _panic(int l)
-{
-  fprintf(stderr, "\n%d: fgets failed\n", l);
-  exit(EXIT_FAILURE);
-}
-#endif
-
-mp_int a, b, c, d, e, f;
-
-static void _cleanup(void)
-{
-  mp_clear_multi(&a, &b, &c, &d, &e, &f, NULL);
-  printf("\n");
-
-#ifdef LTM_DEMO_REAL_RAND
-  if(fd_urandom)
-     fclose(fd_urandom);
-#endif
-}
-struct mp_sqrtmod_prime_st {
-   unsigned long p;
-   unsigned long n;
-   mp_digit r;
-};
-struct mp_sqrtmod_prime_st sqrtmod_prime[] = {
-      { 5, 14, 3 },
-      { 7, 9, 4 },
-      { 113, 2, 62 }
-};
-struct mp_jacobi_st {
-   unsigned long n;
-   int c[16];
-};
-struct mp_jacobi_st jacobi[] = {
-      { 3, {  1, -1,  0,  1, -1,  0,  1, -1,  0,  1, -1,  0,  1, -1,  0,  1 } },
-      { 5, {  0,  1, -1, -1,  1,  0,  1, -1, -1,  1,  0,  1, -1, -1,  1,  0 } },
-      { 7, {  1, -1,  1, -1, -1,  0,  1,  1, -1,  1, -1, -1,  0,  1,  1, -1 } },
-      { 9, { -1,  1,  0,  1,  1,  0,  1,  1,  0,  1,  1,  0,  1,  1,  0,  1 } },
-};
-
-char cmd[4096], buf[4096];
-int main(void)
-{
-   unsigned rr;
-   int cnt, ix;
-#if LTM_DEMO_TEST_VS_MTEST
-   unsigned long expt_n, add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n,
-      gcd_n, lcm_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n;
-   char* ret;
-#else
-   unsigned long s, t;
-   unsigned long long q, r;
-   mp_digit mp;
-   int i, n, err, should;
-#endif
-
-   if (mp_init_multi(&a, &b, &c, &d, &e, &f, NULL)!= MP_OKAY)
-     return EXIT_FAILURE;
-
-   atexit(_cleanup);
-
-#if defined(LTM_DEMO_REAL_RAND)
-   if (!fd_urandom) {
-      fd_urandom = fopen("/dev/urandom", "r");
-      if (!fd_urandom) {
-#if !defined(_WIN32)
-         fprintf(stderr, "\ncould not open /dev/urandom\n");
-#endif
-      }
-   }
-#endif
-   srand(LTM_DEMO_RAND_SEED);
-
-#ifdef MP_8BIT
-   printf("Digit size 8 Bit \n");
-#endif
-#ifdef MP_16BIT
-   printf("Digit size 16 Bit \n");
-#endif
-#ifdef MP_32BIT
-   printf("Digit size 32 Bit \n");
-#endif
-#ifdef MP_64BIT
-   printf("Digit size 64 Bit \n");
-#endif
-   printf("Size of mp_digit: %u\n", (unsigned int)sizeof(mp_digit));
-   printf("Size of mp_word: %u\n", (unsigned int)sizeof(mp_word));
-   printf("DIGIT_BIT: %d\n", DIGIT_BIT);
-   printf("MP_PREC: %d\n", MP_PREC);
-
-#if LTM_DEMO_TEST_VS_MTEST == 0
-   // trivial stuff
-   mp_set_int(&a, 5);
-   mp_neg(&a, &b);
-   if (mp_cmp(&a, &b) != MP_GT) {
-      return EXIT_FAILURE;
-   }
-   if (mp_cmp(&b, &a) != MP_LT) {
-      return EXIT_FAILURE;
-   }
-   mp_neg(&a, &a);
-   if (mp_cmp(&b, &a) != MP_EQ) {
-      return EXIT_FAILURE;
-   }
-   mp_abs(&a, &b);
-   if (mp_isneg(&b) != MP_NO) {
-      return EXIT_FAILURE;
-   }
-   mp_add_d(&a, 1, &b);
-   mp_add_d(&a, 6, &b);
-
-
-   mp_set_int(&a, 0);
-   mp_set_int(&b, 1);
-   if ((err = mp_jacobi(&a, &b, &i)) != MP_OKAY) {
-      printf("Failed executing mp_jacobi(0 | 1) %s.\n", mp_error_to_string(err));
-      return EXIT_FAILURE;
-   }
-   if (i != 1) {
-      printf("Failed trivial mp_jacobi(0 | 1) %d != 1\n", i);
-      return EXIT_FAILURE;
-   }
-   for (cnt = 0; cnt < (int)(sizeof(jacobi)/sizeof(jacobi[0])); ++cnt) {
-      mp_set_int(&b, jacobi[cnt].n);
-      /* only test positive values of a */
-      for (n = -5; n <= 10; ++n) {
-         mp_set_int(&a, abs(n));
-         should = MP_OKAY;
-         if (n < 0) {
-            mp_neg(&a, &a);
-            /* Until #44 is fixed the negative a's must fail */
-            should = MP_VAL;
-         }
-         if ((err = mp_jacobi(&a, &b, &i)) != should) {
-            printf("Failed executing mp_jacobi(%d | %lu) %s.\n", n, jacobi[cnt].n, mp_error_to_string(err));
-            return EXIT_FAILURE;
-         }
-         if (err == MP_OKAY && i != jacobi[cnt].c[n + 5]) {
-            printf("Failed trivial mp_jacobi(%d | %lu) %d != %d\n", n, jacobi[cnt].n, i, jacobi[cnt].c[n + 5]);
-            return EXIT_FAILURE;
-         }
-      }
-   }
-
-   // test mp_get_int
-   printf("\n\nTesting: mp_get_int");
-   for (i = 0; i < 1000; ++i) {
-      t = ((unsigned long) rand () * rand () + 1) & 0xFFFFFFFF;
-      mp_set_int (&a, t);
-      if (t != mp_get_int (&a)) {
-         printf ("\nmp_get_int() bad result!");
-         return EXIT_FAILURE;
-      }
-   }
-   mp_set_int(&a, 0);
-   if (mp_get_int(&a) != 0) {
-      printf("\nmp_get_int() bad result!");
-      return EXIT_FAILURE;
-   }
-   mp_set_int(&a, 0xffffffff);
-   if (mp_get_int(&a) != 0xffffffff) {
-      printf("\nmp_get_int() bad result!");
-      return EXIT_FAILURE;
-   }
-
-   printf("\n\nTesting: mp_get_long\n");
-   for (i = 0; i < (int)(sizeof(unsigned long)*CHAR_BIT) - 1; ++i) {
-      t = (1ULL << (i+1)) - 1;
-      if (!t)
-         t = -1;
-      printf(" t = 0x%lx i = %d\r", t, i);
-      do {
-         if (mp_set_long(&a, t) != MP_OKAY) {
-            printf("\nmp_set_long() error!");
-            return EXIT_FAILURE;
-         }
-         s = mp_get_long(&a);
-         if (s != t) {
-            printf("\nmp_get_long() bad result! 0x%lx != 0x%lx", s, t);
-            return EXIT_FAILURE;
-         }
-         t <<= 1;
-      } while(t);
-   }
-
-   printf("\n\nTesting: mp_get_long_long\n");
-   for (i = 0; i < (int)(sizeof(unsigned long long)*CHAR_BIT) - 1; ++i) {
-      r = (1ULL << (i+1)) - 1;
-      if (!r)
-         r = -1;
-      printf(" r = 0x%llx i = %d\r", r, i);
-      do {
-         if (mp_set_long_long(&a, r) != MP_OKAY) {
-            printf("\nmp_set_long_long() error!");
-            return EXIT_FAILURE;
-         }
-         q = mp_get_long_long(&a);
-         if (q != r) {
-            printf("\nmp_get_long_long() bad result! 0x%llx != 0x%llx", q, r);
-            return EXIT_FAILURE;
-         }
-         r <<= 1;
-      } while(r);
-   }
-
-   // test mp_sqrt
-   printf("\n\nTesting: mp_sqrt\n");
-   for (i = 0; i < 1000; ++i) {
-      printf ("%6d\r", i);
-      fflush (stdout);
-      n = (rand () & 15) + 1;
-      mp_rand (&a, n);
-      if (mp_sqrt (&a, &b) != MP_OKAY) {
-         printf ("\nmp_sqrt() error!");
-         return EXIT_FAILURE;
-      }
-      mp_n_root_ex (&a, 2, &c, 0);
-      mp_n_root_ex (&a, 2, &d, 1);
-      if (mp_cmp_mag (&c, &d) != MP_EQ) {
-         printf ("\nmp_n_root_ex() bad result!");
-         return EXIT_FAILURE;
-      }
-      if (mp_cmp_mag (&b, &c) != MP_EQ) {
-         printf ("mp_sqrt() bad result!\n");
-         return EXIT_FAILURE;
-      }
-   }
-
-   printf("\n\nTesting: mp_is_square\n");
-   for (i = 0; i < 1000; ++i) {
-      printf ("%6d\r", i);
-      fflush (stdout);
-
-      /* test mp_is_square false negatives */
-      n = (rand () & 7) + 1;
-      mp_rand (&a, n);
-      mp_sqr (&a, &a);
-      if (mp_is_square (&a, &n) != MP_OKAY) {
-         printf ("\nfn:mp_is_square() error!");
-         return EXIT_FAILURE;
-      }
-      if (n == 0) {
-         printf ("\nfn:mp_is_square() bad result!");
-         return EXIT_FAILURE;
-      }
-
-      /* test for false positives */
-      mp_add_d (&a, 1, &a);
-      if (mp_is_square (&a, &n) != MP_OKAY) {
-         printf ("\nfp:mp_is_square() error!");
-         return EXIT_FAILURE;
-      }
-      if (n == 1) {
-         printf ("\nfp:mp_is_square() bad result!");
-         return EXIT_FAILURE;
-      }
-
-   }
-   printf("\n\n");
-
-   // r^2 = n (mod p)
-   for (i = 0; i < (int)(sizeof(sqrtmod_prime)/sizeof(sqrtmod_prime[0])); ++i) {
-      mp_set_int(&a, sqrtmod_prime[i].p);
-      mp_set_int(&b, sqrtmod_prime[i].n);
-      if (mp_sqrtmod_prime(&b, &a, &c) != MP_OKAY) {
-         printf("Failed executing %d. mp_sqrtmod_prime\n", (i+1));
-         return EXIT_FAILURE;
-      }
-      if (mp_cmp_d(&c, sqrtmod_prime[i].r) != MP_EQ) {
-         printf("Failed %d. trivial mp_sqrtmod_prime\n", (i+1));
-         ndraw(&c, "r");
-         return EXIT_FAILURE;
-      }
-   }
-
-   /* test for size */
-   for (ix = 10; ix < 128; ix++) {
-      printf ("Testing (not safe-prime): %9d bits    \r", ix);
-      fflush (stdout);
-      err = mp_prime_random_ex (&a, 8, ix,
-                                (rand () & 1) ? 0 : LTM_PRIME_2MSB_ON, myrng,
-                                NULL);
-      if (err != MP_OKAY) {
-         printf ("failed with err code %d\n", err);
-         return EXIT_FAILURE;
-      }
-      if (mp_count_bits (&a) != ix) {
-         printf ("Prime is %d not %d bits!!!\n", mp_count_bits (&a), ix);
-         return EXIT_FAILURE;
-      }
-   }
-   printf("\n");
-
-   for (ix = 16; ix < 128; ix++) {
-      printf ("Testing (    safe-prime): %9d bits    \r", ix);
-      fflush (stdout);
-      err = mp_prime_random_ex (
-            &a, 8, ix, ((rand () & 1) ? 0 : LTM_PRIME_2MSB_ON) | LTM_PRIME_SAFE,
-            myrng, NULL);
-      if (err != MP_OKAY) {
-         printf ("failed with err code %d\n", err);
-         return EXIT_FAILURE;
-      }
-      if (mp_count_bits (&a) != ix) {
-         printf ("Prime is %d not %d bits!!!\n", mp_count_bits (&a), ix);
-         return EXIT_FAILURE;
-      }
-      /* let's see if it's really a safe prime */
-      mp_sub_d (&a, 1, &a);
-      mp_div_2 (&a, &a);
-      mp_prime_is_prime (&a, 8, &cnt);
-      if (cnt != MP_YES) {
-         printf ("sub is not prime!\n");
-         return EXIT_FAILURE;
-      }
-   }
-
-   printf("\n\n");
-
-   // test montgomery
-   printf("Testing: montgomery...\n");
-   for (i = 1; i <= 10; i++) {
-      if (i == 10)
-         i = 1000;
-      printf(" digit size: %2d\r", i);
-      fflush(stdout);
-      for (n = 0; n < 1000; n++) {
-         mp_rand(&a, i);
-         a.dp[0] |= 1;
-
-         // let's see if R is right
-         mp_montgomery_calc_normalization(&b, &a);
-         mp_montgomery_setup(&a, &mp);
-
-         // now test a random reduction
-         for (ix = 0; ix < 100; ix++) {
-             mp_rand(&c, 1 + abs(rand()) % (2*i));
-             mp_copy(&c, &d);
-             mp_copy(&c, &e);
-
-             mp_mod(&d, &a, &d);
-             mp_montgomery_reduce(&c, &a, mp);
-             mp_mulmod(&c, &b, &a, &c);
-
-             if (mp_cmp(&c, &d) != MP_EQ) {
-printf("d = e mod a, c = e MOD a\n");
-mp_todecimal(&a, buf); printf("a = %s\n", buf);
-mp_todecimal(&e, buf); printf("e = %s\n", buf);
-mp_todecimal(&d, buf); printf("d = %s\n", buf);
-mp_todecimal(&c, buf); printf("c = %s\n", buf);
-printf("compare no compare!\n"); return EXIT_FAILURE; }
-             /* only one big montgomery reduction */
-             if (i > 10)
-             {
-                n = 1000;
-                ix = 100;
-             }
-         }
-      }
-   }
-
-   printf("\n\n");
-
-   mp_read_radix(&a, "123456", 10);
-   mp_toradix_n(&a, buf, 10, 3);
-   printf("a == %s\n", buf);
-   mp_toradix_n(&a, buf, 10, 4);
-   printf("a == %s\n", buf);
-   mp_toradix_n(&a, buf, 10, 30);
-   printf("a == %s\n", buf);
-
-
-#if 0
-   for (;;) {
-      fgets(buf, sizeof(buf), stdin);
-      mp_read_radix(&a, buf, 10);
-      mp_prime_next_prime(&a, 5, 1);
-      mp_toradix(&a, buf, 10);
-      printf("%s, %lu\n", buf, a.dp[0] & 3);
-   }
-#endif
-
-   /* test mp_cnt_lsb */
-   printf("\n\nTesting: mp_cnt_lsb");
-   mp_set(&a, 1);
-   for (ix = 0; ix < 1024; ix++) {
-      if (mp_cnt_lsb (&a) != ix) {
-         printf ("Failed at %d, %d\n", ix, mp_cnt_lsb (&a));
-         return EXIT_FAILURE;
-      }
-      mp_mul_2 (&a, &a);
-   }
-
-/* test mp_reduce_2k */
-   printf("\n\nTesting: mp_reduce_2k\n");
-   for (cnt = 3; cnt <= 128; ++cnt) {
-      mp_digit tmp;
-
-      mp_2expt (&a, cnt);
-      mp_sub_d (&a, 2, &a); /* a = 2**cnt - 2 */
-
-      printf ("\r %4d bits", cnt);
-      printf ("(%d)", mp_reduce_is_2k (&a));
-      mp_reduce_2k_setup (&a, &tmp);
-      printf ("(%lu)", (unsigned long) tmp);
-      for (ix = 0; ix < 1000; ix++) {
-         if (!(ix & 127)) {
-            printf (".");
-            fflush (stdout);
-         }
-         mp_rand (&b, (cnt / DIGIT_BIT + 1) * 2);
-         mp_copy (&c, &b);
-         mp_mod (&c, &a, &c);
-         mp_reduce_2k (&b, &a, 2);
-         if (mp_cmp (&c, &b)) {
-            printf ("FAILED\n");
-            return EXIT_FAILURE;
-         }
-      }
-   }
-
-/* test mp_div_3  */
-   printf("\n\nTesting: mp_div_3...\n");
-   mp_set(&d, 3);
-   for (cnt = 0; cnt < 10000;) {
-      mp_digit r2;
-
-      if (!(++cnt & 127))
-      {
-        printf("%9d\r", cnt);
-        fflush(stdout);
-      }
-      mp_rand(&a, abs(rand()) % 128 + 1);
-      mp_div(&a, &d, &b, &e);
-      mp_div_3(&a, &c, &r2);
-
-      if (mp_cmp(&b, &c) || mp_cmp_d(&e, r2)) {
-	 printf("\nmp_div_3 => Failure\n");
-      }
-   }
-   printf("\nPassed div_3 testing");
-
-/* test the DR reduction */
-   printf("\n\nTesting: mp_dr_reduce...\n");
-   for (cnt = 2; cnt < 32; cnt++) {
-      printf ("\r%d digit modulus", cnt);
-      mp_grow (&a, cnt);
-      mp_zero (&a);
-      for (ix = 1; ix < cnt; ix++) {
-         a.dp[ix] = MP_MASK;
-      }
-      a.used = cnt;
-      a.dp[0] = 3;
-
-      mp_rand (&b, cnt - 1);
-      mp_copy (&b, &c);
-
-      rr = 0;
-      do {
-         if (!(rr & 127)) {
-            printf (".");
-            fflush (stdout);
-         }
-         mp_sqr (&b, &b);
-         mp_add_d (&b, 1, &b);
-         mp_copy (&b, &c);
-
-         mp_mod (&b, &a, &b);
-         mp_dr_setup(&a, &mp),
-         mp_dr_reduce (&c, &a, mp);
-
-         if (mp_cmp (&b, &c) != MP_EQ) {
-            printf ("Failed on trial %u\n", rr);
-            return EXIT_FAILURE;
-         }
-      } while (++rr < 500);
-      printf (" passed");
-      fflush (stdout);
-   }
-
-#if LTM_DEMO_TEST_REDUCE_2K_L
-/* test the mp_reduce_2k_l code */
-#if LTM_DEMO_TEST_REDUCE_2K_L == 1
-/* first load P with 2^1024 - 0x2A434 B9FDEC95 D8F9D550 FFFFFFFF FFFFFFFF */
-   mp_2expt(&a, 1024);
-   mp_read_radix(&b, "2A434B9FDEC95D8F9D550FFFFFFFFFFFFFFFF", 16);
-   mp_sub(&a, &b, &a);
-#elif LTM_DEMO_TEST_REDUCE_2K_L == 2
-/*  p = 2^2048 - 0x1 00000000 00000000 00000000 00000000 4945DDBF 8EA2A91D 5776399B B83E188F  */
-   mp_2expt(&a, 2048);
-   mp_read_radix(&b,
-		 "1000000000000000000000000000000004945DDBF8EA2A91D5776399BB83E188F",
-		 16);
-   mp_sub(&a, &b, &a);
-#else
-#error oops
-#endif
-
-   mp_todecimal(&a, buf);
-   printf("\n\np==%s\n", buf);
-/* now mp_reduce_is_2k_l() should return */
-   if (mp_reduce_is_2k_l(&a) != 1) {
-      printf("mp_reduce_is_2k_l() return 0, should be 1\n");
-      return EXIT_FAILURE;
-   }
-   mp_reduce_2k_setup_l(&a, &d);
-   /* now do a million square+1 to see if it varies */
-   mp_rand(&b, 64);
-   mp_mod(&b, &a, &b);
-   mp_copy(&b, &c);
-   printf("Testing: mp_reduce_2k_l...");
-   fflush(stdout);
-   for (cnt = 0; cnt < (int)(1UL << 20); cnt++) {
-      mp_sqr(&b, &b);
-      mp_add_d(&b, 1, &b);
-      mp_reduce_2k_l(&b, &a, &d);
-      mp_sqr(&c, &c);
-      mp_add_d(&c, 1, &c);
-      mp_mod(&c, &a, &c);
-      if (mp_cmp(&b, &c) != MP_EQ) {
-	 printf("mp_reduce_2k_l() failed at step %d\n", cnt);
-	 mp_tohex(&b, buf);
-	 printf("b == %s\n", buf);
-	 mp_tohex(&c, buf);
-	 printf("c == %s\n", buf);
-	 return EXIT_FAILURE;
-      }
-   }
-   printf("...Passed\n");
-#endif /* LTM_DEMO_TEST_REDUCE_2K_L */
-
-#else
-
-   div2_n = mul2_n = inv_n = expt_n = lcm_n = gcd_n = add_n =
-      sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = cnt = add_d_n =
-      sub_d_n = 0;
-
-   /* force KARA and TOOM to enable despite cutoffs */
-   KARATSUBA_SQR_CUTOFF = KARATSUBA_MUL_CUTOFF = 8;
-   TOOM_SQR_CUTOFF = TOOM_MUL_CUTOFF = 16;
-
-   for (;;) {
-      /* randomly clear and re-init one variable, this has the affect of triming the alloc space */
-      switch (abs(rand()) % 7) {
-      case 0:
-	 mp_clear(&a);
-	 mp_init(&a);
-	 break;
-      case 1:
-	 mp_clear(&b);
-	 mp_init(&b);
-	 break;
-      case 2:
-	 mp_clear(&c);
-	 mp_init(&c);
-	 break;
-      case 3:
-	 mp_clear(&d);
-	 mp_init(&d);
-	 break;
-      case 4:
-	 mp_clear(&e);
-	 mp_init(&e);
-	 break;
-      case 5:
-	 mp_clear(&f);
-	 mp_init(&f);
-	 break;
-      case 6:
-	 break;			/* don't clear any */
-      }
-
-
-      printf
-	 ("%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu/%4lu ",
-	  add_n, sub_n, mul_n, div_n, sqr_n, mul2d_n, div2d_n, gcd_n, lcm_n,
-	  expt_n, inv_n, div2_n, mul2_n, add_d_n, sub_d_n);
-      ret=fgets(cmd, 4095, stdin); if(!ret){_panic(__LINE__);}
-      cmd[strlen(cmd) - 1] = 0;
-      printf("%-6s ]\r", cmd);
-      fflush(stdout);
-      if (!strcmp(cmd, "mul2d")) {
-	 ++mul2d_n;
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&a, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 sscanf(buf, "%d", &rr);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&b, buf, 64);
-
-	 mp_mul_2d(&a, rr, &a);
-	 a.sign = b.sign;
-	 if (mp_cmp(&a, &b) != MP_EQ) {
-	    printf("mul2d failed, rr == %d\n", rr);
-	    draw(&a);
-	    draw(&b);
-	    return EXIT_FAILURE;
-	 }
-      } else if (!strcmp(cmd, "div2d")) {
-	 ++div2d_n;
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&a, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 sscanf(buf, "%d", &rr);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&b, buf, 64);
-
-	 mp_div_2d(&a, rr, &a, &e);
-	 a.sign = b.sign;
-	 if (a.used == b.used && a.used == 0) {
-	    a.sign = b.sign = MP_ZPOS;
-	 }
-	 if (mp_cmp(&a, &b) != MP_EQ) {
-	    printf("div2d failed, rr == %d\n", rr);
-	    draw(&a);
-	    draw(&b);
-	    return EXIT_FAILURE;
-	 }
-      } else if (!strcmp(cmd, "add")) {
-	 ++add_n;
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&a, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&b, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&c, buf, 64);
-	 mp_copy(&a, &d);
-	 mp_add(&d, &b, &d);
-	 if (mp_cmp(&c, &d) != MP_EQ) {
-	    printf("add %lu failure!\n", add_n);
-	    draw(&a);
-	    draw(&b);
-	    draw(&c);
-	    draw(&d);
-	    return EXIT_FAILURE;
-	 }
-
-	 /* test the sign/unsigned storage functions */
-
-	 rr = mp_signed_bin_size(&c);
-	 mp_to_signed_bin(&c, (unsigned char *) cmd);
-	 memset(cmd + rr, rand() & 255, sizeof(cmd) - rr);
-	 mp_read_signed_bin(&d, (unsigned char *) cmd, rr);
-	 if (mp_cmp(&c, &d) != MP_EQ) {
-	    printf("mp_signed_bin failure!\n");
-	    draw(&c);
-	    draw(&d);
-	    return EXIT_FAILURE;
-	 }
-
-
-	 rr = mp_unsigned_bin_size(&c);
-	 mp_to_unsigned_bin(&c, (unsigned char *) cmd);
-	 memset(cmd + rr, rand() & 255, sizeof(cmd) - rr);
-	 mp_read_unsigned_bin(&d, (unsigned char *) cmd, rr);
-	 if (mp_cmp_mag(&c, &d) != MP_EQ) {
-	    printf("mp_unsigned_bin failure!\n");
-	    draw(&c);
-	    draw(&d);
-	    return EXIT_FAILURE;
-	 }
-
-      } else if (!strcmp(cmd, "sub")) {
-	 ++sub_n;
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&a, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&b, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&c, buf, 64);
-	 mp_copy(&a, &d);
-	 mp_sub(&d, &b, &d);
-	 if (mp_cmp(&c, &d) != MP_EQ) {
-	    printf("sub %lu failure!\n", sub_n);
-	    draw(&a);
-	    draw(&b);
-	    draw(&c);
-	    draw(&d);
-	    return EXIT_FAILURE;
-	 }
-      } else if (!strcmp(cmd, "mul")) {
-	 ++mul_n;
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&a, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&b, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&c, buf, 64);
-	 mp_copy(&a, &d);
-	 mp_mul(&d, &b, &d);
-	 if (mp_cmp(&c, &d) != MP_EQ) {
-	    printf("mul %lu failure!\n", mul_n);
-	    draw(&a);
-	    draw(&b);
-	    draw(&c);
-	    draw(&d);
-	    return EXIT_FAILURE;
-	 }
-      } else if (!strcmp(cmd, "div")) {
-	 ++div_n;
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&a, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&b, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&c, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&d, buf, 64);
-
-	 mp_div(&a, &b, &e, &f);
-	 if (mp_cmp(&c, &e) != MP_EQ || mp_cmp(&d, &f) != MP_EQ) {
-	    printf("div %lu %d, %d, failure!\n", div_n, mp_cmp(&c, &e),
-		   mp_cmp(&d, &f));
-	    draw(&a);
-	    draw(&b);
-	    draw(&c);
-	    draw(&d);
-	    draw(&e);
-	    draw(&f);
-	    return EXIT_FAILURE;
-	 }
-
-      } else if (!strcmp(cmd, "sqr")) {
-	 ++sqr_n;
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&a, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&b, buf, 64);
-	 mp_copy(&a, &c);
-	 mp_sqr(&c, &c);
-	 if (mp_cmp(&b, &c) != MP_EQ) {
-	    printf("sqr %lu failure!\n", sqr_n);
-	    draw(&a);
-	    draw(&b);
-	    draw(&c);
-	    return EXIT_FAILURE;
-	 }
-      } else if (!strcmp(cmd, "gcd")) {
-	 ++gcd_n;
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&a, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&b, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&c, buf, 64);
-	 mp_copy(&a, &d);
-	 mp_gcd(&d, &b, &d);
-	 d.sign = c.sign;
-	 if (mp_cmp(&c, &d) != MP_EQ) {
-	    printf("gcd %lu failure!\n", gcd_n);
-	    draw(&a);
-	    draw(&b);
-	    draw(&c);
-	    draw(&d);
-	    return EXIT_FAILURE;
-	 }
-      } else if (!strcmp(cmd, "lcm")) {
-	 ++lcm_n;
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&a, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&b, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&c, buf, 64);
-	 mp_copy(&a, &d);
-	 mp_lcm(&d, &b, &d);
-	 d.sign = c.sign;
-	 if (mp_cmp(&c, &d) != MP_EQ) {
-	    printf("lcm %lu failure!\n", lcm_n);
-	    draw(&a);
-	    draw(&b);
-	    draw(&c);
-	    draw(&d);
-	    return EXIT_FAILURE;
-	 }
-      } else if (!strcmp(cmd, "expt")) {
-	 ++expt_n;
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&a, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&b, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&c, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&d, buf, 64);
-	 mp_copy(&a, &e);
-	 mp_exptmod(&e, &b, &c, &e);
-	 if (mp_cmp(&d, &e) != MP_EQ) {
-	    printf("expt %lu failure!\n", expt_n);
-	    draw(&a);
-	    draw(&b);
-	    draw(&c);
-	    draw(&d);
-	    draw(&e);
-	    return EXIT_FAILURE;
-	 }
-      } else if (!strcmp(cmd, "invmod")) {
-	 ++inv_n;
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&a, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&b, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&c, buf, 64);
-	 mp_invmod(&a, &b, &d);
-	 mp_mulmod(&d, &a, &b, &e);
-	 if (mp_cmp_d(&e, 1) != MP_EQ) {
-	    printf("inv [wrong value from MPI?!] failure\n");
-	    draw(&a);
-	    draw(&b);
-	    draw(&c);
-	    draw(&d);
-	    draw(&e);
-	    mp_gcd(&a, &b, &e);
-	    draw(&e);
-	    return EXIT_FAILURE;
-	 }
-
-      } else if (!strcmp(cmd, "div2")) {
-	 ++div2_n;
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&a, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&b, buf, 64);
-	 mp_div_2(&a, &c);
-	 if (mp_cmp(&c, &b) != MP_EQ) {
-	    printf("div_2 %lu failure\n", div2_n);
-	    draw(&a);
-	    draw(&b);
-	    draw(&c);
-	    return EXIT_FAILURE;
-	 }
-      } else if (!strcmp(cmd, "mul2")) {
-	 ++mul2_n;
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&a, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&b, buf, 64);
-	 mp_mul_2(&a, &c);
-	 if (mp_cmp(&c, &b) != MP_EQ) {
-	    printf("mul_2 %lu failure\n", mul2_n);
-	    draw(&a);
-	    draw(&b);
-	    draw(&c);
-	    return EXIT_FAILURE;
-	 }
-      } else if (!strcmp(cmd, "add_d")) {
-	 ++add_d_n;
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&a, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 sscanf(buf, "%d", &ix);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&b, buf, 64);
-	 mp_add_d(&a, ix, &c);
-	 if (mp_cmp(&b, &c) != MP_EQ) {
-	    printf("add_d %lu failure\n", add_d_n);
-	    draw(&a);
-	    draw(&b);
-	    draw(&c);
-	    printf("d == %d\n", ix);
-	    return EXIT_FAILURE;
-	 }
-      } else if (!strcmp(cmd, "sub_d")) {
-	 ++sub_d_n;
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&a, buf, 64);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 sscanf(buf, "%d", &ix);
-	 ret=fgets(buf, 4095, stdin); if(!ret){_panic(__LINE__);}
-	 mp_read_radix(&b, buf, 64);
-	 mp_sub_d(&a, ix, &c);
-	 if (mp_cmp(&b, &c) != MP_EQ) {
-	    printf("sub_d %lu failure\n", sub_d_n);
-	    draw(&a);
-	    draw(&b);
-	    draw(&c);
-	    printf("d == %d\n", ix);
-	    return EXIT_FAILURE;
-	 }
-      } else if (!strcmp(cmd, "exit")) {
-         printf("\nokay, exiting now\n");
-         break;
-      }
-   }
-#endif
-   return 0;
-}
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
diff --git a/libtommath/demo/timing.c b/libtommath/demo/timing.c
deleted file mode 100644
index 1bd8489..0000000
--- a/libtommath/demo/timing.c
+++ /dev/null
@@ -1,339 +0,0 @@
-#include <tommath.h>
-#include <time.h>
-#include <unistd.h>
-
-ulong64 _tt;
-
-#ifdef IOWNANATHLON
-#include <unistd.h>
-#define SLEEP sleep(4)
-#else
-#define SLEEP
-#endif
-
-#ifdef LTM_TIMING_REAL_RAND
-#define LTM_TIMING_RAND_SEED  time(NULL)
-#else
-#define LTM_TIMING_RAND_SEED  23
-#endif
-
-
-void ndraw(mp_int * a, char *name)
-{
-   char buf[4096];
-
-   printf("%s: ", name);
-   mp_toradix(a, buf, 64);
-   printf("%s\n", buf);
-}
-
-static void draw(mp_int * a)
-{
-   ndraw(a, "");
-}
-
-
-unsigned long lfsr = 0xAAAAAAAAUL;
-
-int lbit(void)
-{
-   if (lfsr & 0x80000000UL) {
-      lfsr = ((lfsr << 1) ^ 0x8000001BUL) & 0xFFFFFFFFUL;
-      return 1;
-   } else {
-      lfsr <<= 1;
-      return 0;
-   }
-}
-
-/* RDTSC from Scott Duplichan */
-static ulong64 TIMFUNC(void)
-{
-#if defined __GNUC__
-#if defined(__i386__) || defined(__x86_64__)
-  /* version from http://www.mcs.anl.gov/~kazutomo/rdtsc.html
-   * the old code always got a warning issued by gcc, clang did not complain...
-   */
-  unsigned hi, lo;
-  __asm__ __volatile__ ("rdtsc" : "=a"(lo), "=d"(hi));
-  return ((ulong64)lo)|( ((ulong64)hi)<<32);
-#else /* gcc-IA64 version */
-   unsigned long result;
-   __asm__ __volatile__("mov %0=ar.itc":"=r"(result)::"memory");
-
-   while (__builtin_expect((int) result == -1, 0))
-      __asm__ __volatile__("mov %0=ar.itc":"=r"(result)::"memory");
-
-   return result;
-#endif
-
-   // Microsoft and Intel Windows compilers
-#elif defined _M_IX86
-   __asm rdtsc
-#elif defined _M_AMD64
-   return __rdtsc();
-#elif defined _M_IA64
-#if defined __INTEL_COMPILER
-#include <ia64intrin.h>
-#endif
-   return __getReg(3116);
-#else
-#error need rdtsc function for this build
-#endif
-}
-
-#define DO(x) x; x;
-//#define DO4(x) DO2(x); DO2(x);
-//#define DO8(x) DO4(x); DO4(x);
-//#define DO(x)  DO8(x); DO8(x);
-
-#ifdef TIMING_NO_LOGS
-#define FOPEN(a, b)     NULL
-#define FPRINTF(a,b,c,d)
-#define FFLUSH(a)
-#define FCLOSE(a)       (void)(a)
-#else
-#define FOPEN(a,b)       fopen(a,b)
-#define FPRINTF(a,b,c,d) fprintf(a,b,c,d)
-#define FFLUSH(a)        fflush(a)
-#define FCLOSE(a)        fclose(a)
-#endif
-
-int main(void)
-{
-   ulong64 tt, gg, CLK_PER_SEC;
-   FILE *log, *logb, *logc, *logd;
-   mp_int a, b, c, d, e, f;
-   int n, cnt, ix, old_kara_m, old_kara_s, old_toom_m, old_toom_s;
-   unsigned rr;
-
-   mp_init(&a);
-   mp_init(&b);
-   mp_init(&c);
-   mp_init(&d);
-   mp_init(&e);
-   mp_init(&f);
-
-   srand(LTM_TIMING_RAND_SEED);
-
-
-   CLK_PER_SEC = TIMFUNC();
-   sleep(1);
-   CLK_PER_SEC = TIMFUNC() - CLK_PER_SEC;
-
-   printf("CLK_PER_SEC == %llu\n", CLK_PER_SEC);
-   log = FOPEN("logs/add.log", "w");
-   for (cnt = 8; cnt <= 128; cnt += 8) {
-      SLEEP;
-      mp_rand(&a, cnt);
-      mp_rand(&b, cnt);
-      rr = 0;
-      tt = -1;
-      do {
-	 gg = TIMFUNC();
-	 DO(mp_add(&a, &b, &c));
-	 gg = (TIMFUNC() - gg) >> 1;
-	 if (tt > gg)
-	    tt = gg;
-      } while (++rr < 100000);
-      printf("Adding\t\t%4d-bit => %9llu/sec, %9llu cycles\n",
-	     mp_count_bits(&a), CLK_PER_SEC / tt, tt);
-      FPRINTF(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
-      FFLUSH(log);
-   }
-   FCLOSE(log);
-
-   log = FOPEN("logs/sub.log", "w");
-   for (cnt = 8; cnt <= 128; cnt += 8) {
-      SLEEP;
-      mp_rand(&a, cnt);
-      mp_rand(&b, cnt);
-      rr = 0;
-      tt = -1;
-      do {
-	 gg = TIMFUNC();
-	 DO(mp_sub(&a, &b, &c));
-	 gg = (TIMFUNC() - gg) >> 1;
-	 if (tt > gg)
-	    tt = gg;
-      } while (++rr < 100000);
-
-      printf("Subtracting\t\t%4d-bit => %9llu/sec, %9llu cycles\n",
-	     mp_count_bits(&a), CLK_PER_SEC / tt, tt);
-      FPRINTF(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
-      FFLUSH(log);
-   }
-   FCLOSE(log);
-
-   /* do mult/square twice, first without karatsuba and second with */
-   old_kara_m = KARATSUBA_MUL_CUTOFF;
-   old_kara_s = KARATSUBA_SQR_CUTOFF;
-   /* currently toom-cook cut-off is too high to kick in, so we just use the karatsuba values */
-   old_toom_m = old_kara_m;
-   old_toom_s = old_kara_m;
-   for (ix = 0; ix < 3; ix++) {
-      printf("With%s Karatsuba, With%s Toom\n", (ix == 0) ? "out" : "", (ix == 1) ? "out" : "");
-
-      KARATSUBA_MUL_CUTOFF = (ix == 1) ? old_kara_m : 9999;
-      KARATSUBA_SQR_CUTOFF = (ix == 1) ? old_kara_s : 9999;
-      TOOM_MUL_CUTOFF = (ix == 2) ? old_toom_m : 9999;
-      TOOM_SQR_CUTOFF = (ix == 2) ? old_toom_s : 9999;
-
-      log = FOPEN((ix == 0) ? "logs/mult.log" : (ix == 1) ? "logs/mult_kara.log" : "logs/mult_toom.log", "w");
-      for (cnt = 4; cnt <= 10240 / DIGIT_BIT; cnt += 2) {
-	 SLEEP;
-	 mp_rand(&a, cnt);
-	 mp_rand(&b, cnt);
-	 rr = 0;
-	 tt = -1;
-	 do {
-	    gg = TIMFUNC();
-	    DO(mp_mul(&a, &b, &c));
-	    gg = (TIMFUNC() - gg) >> 1;
-	    if (tt > gg)
-	       tt = gg;
-	 } while (++rr < 100);
-	 printf("Multiplying\t%4d-bit => %9llu/sec, %9llu cycles\n",
-		mp_count_bits(&a), CLK_PER_SEC / tt, tt);
-	 FPRINTF(log, "%d %9llu\n", mp_count_bits(&a), tt);
-	 FFLUSH(log);
-      }
-      FCLOSE(log);
-
-      log = FOPEN((ix == 0) ? "logs/sqr.log" : (ix == 1) ? "logs/sqr_kara.log" : "logs/sqr_toom.log", "w");
-      for (cnt = 4; cnt <= 10240 / DIGIT_BIT; cnt += 2) {
-	 SLEEP;
-	 mp_rand(&a, cnt);
-	 rr = 0;
-	 tt = -1;
-	 do {
-	    gg = TIMFUNC();
-	    DO(mp_sqr(&a, &b));
-	    gg = (TIMFUNC() - gg) >> 1;
-	    if (tt > gg)
-	       tt = gg;
-	 } while (++rr < 100);
-	 printf("Squaring\t%4d-bit => %9llu/sec, %9llu cycles\n",
-		mp_count_bits(&a), CLK_PER_SEC / tt, tt);
-	 FPRINTF(log, "%d %9llu\n", mp_count_bits(&a), tt);
-	 FFLUSH(log);
-      }
-      FCLOSE(log);
-
-   }
-
-   {
-      char *primes[] = {
-	 /* 2K large moduli */
-	 "179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586239334100047359817950870678242457666208137217",
-	 "32317006071311007300714876688669951960444102669715484032130345427524655138867890893197201411522913463688717960921898019494119559150490921095088152386448283120630877367300996091750197750389652106796057638384067568276792218642619756161838094338476170470581645852036305042887575891541065808607552399123930385521914333389668342420684974786564569494856176035326322058077805659331026192708460314150258592864177116725943603718461857357598351152301645904403697613233287231227125684710820209725157101726931323469678542580656697935045997268352998638099733077152121140120031150424541696791951097529546801429027668869927491725169",
-	 "1044388881413152506691752710716624382579964249047383780384233483283953907971557456848826811934997558340890106714439262837987573438185793607263236087851365277945956976543709998340361590134383718314428070011855946226376318839397712745672334684344586617496807908705803704071284048740118609114467977783598029006686938976881787785946905630190260940599579453432823469303026696443059025015972399867714215541693835559885291486318237914434496734087811872639496475100189041349008417061675093668333850551032972088269550769983616369411933015213796825837188091833656751221318492846368125550225998300412344784862595674492194617023806505913245610825731835380087608622102834270197698202313169017678006675195485079921636419370285375124784014907159135459982790513399611551794271106831134090584272884279791554849782954323534517065223269061394905987693002122963395687782878948440616007412945674919823050571642377154816321380631045902916136926708342856440730447899971901781465763473223850267253059899795996090799469201774624817718449867455659250178329070473119433165550807568221846571746373296884912819520317457002440926616910874148385078411929804522981857338977648103126085902995208257421855249796721729039744118165938433694823325696642096892124547425283",
-	 /* 2K moduli mersenne primes */
-	 "6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151",
-	 "531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127",
-	 "10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087",
-	 "1475979915214180235084898622737381736312066145333169775147771216478570297878078949377407337049389289382748507531496480477281264838760259191814463365330269540496961201113430156902396093989090226259326935025281409614983499388222831448598601834318536230923772641390209490231836446899608210795482963763094236630945410832793769905399982457186322944729636418890623372171723742105636440368218459649632948538696905872650486914434637457507280441823676813517852099348660847172579408422316678097670224011990280170474894487426924742108823536808485072502240519452587542875349976558572670229633962575212637477897785501552646522609988869914013540483809865681250419497686697771007",
-	 "259117086013202627776246767922441530941818887553125427303974923161874019266586362086201209516800483406550695241733194177441689509238807017410377709597512042313066624082916353517952311186154862265604547691127595848775610568757931191017711408826252153849035830401185072116424747461823031471398340229288074545677907941037288235820705892351068433882986888616658650280927692080339605869308790500409503709875902119018371991620994002568935113136548829739112656797303241986517250116412703509705427773477972349821676443446668383119322540099648994051790241624056519054483690809616061625743042361721863339415852426431208737266591962061753535748892894599629195183082621860853400937932839420261866586142503251450773096274235376822938649407127700846077124211823080804139298087057504713825264571448379371125032081826126566649084251699453951887789613650248405739378594599444335231188280123660406262468609212150349937584782292237144339628858485938215738821232393687046160677362909315071",
-	 "190797007524439073807468042969529173669356994749940177394741882673528979787005053706368049835514900244303495954950709725762186311224148828811920216904542206960744666169364221195289538436845390250168663932838805192055137154390912666527533007309292687539092257043362517857366624699975402375462954490293259233303137330643531556539739921926201438606439020075174723029056838272505051571967594608350063404495977660656269020823960825567012344189908927956646011998057988548630107637380993519826582389781888135705408653045219655801758081251164080554609057468028203308718724654081055323215860189611391296030471108443146745671967766308925858547271507311563765171008318248647110097614890313562856541784154881743146033909602737947385055355960331855614540900081456378659068370317267696980001187750995491090350108417050917991562167972281070161305972518044872048331306383715094854938415738549894606070722584737978176686422134354526989443028353644037187375385397838259511833166416134323695660367676897722287918773420968982326089026150031515424165462111337527431154890666327374921446276833564519776797633875503548665093914556482031482248883127023777039667707976559857333357013727342079099064400455741830654320379350833236245819348824064783585692924881021978332974949906122664421376034687815350484991",
-
-	 /* DR moduli */
-	 "14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368612079",
-	 "101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039",
-	 "736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821797602431",
-	 "38564998830736521417281865696453025806593491967131023221754800625044118265468851210705360385717536794615180260494208076605798671660719333199513807806252394423283413430106003596332513246682903994829528690198205120921557533726473585751382193953592127439965050261476810842071573684505878854588706623484573925925903505747545471088867712185004135201289273405614415899438276535626346098904241020877974002916168099951885406379295536200413493190419727789712076165162175783",
-	 "542189391331696172661670440619180536749994166415993334151601745392193484590296600979602378676624808129613777993466242203025054573692562689251250471628358318743978285860720148446448885701001277560572526947619392551574490839286458454994488665744991822837769918095117129546414124448777033941223565831420390846864429504774477949153794689948747680362212954278693335653935890352619041936727463717926744868338358149568368643403037768649616778526013610493696186055899318268339432671541328195724261329606699831016666359440874843103020666106568222401047720269951530296879490444224546654729111504346660859907296364097126834834235287147",
-	 "1487259134814709264092032648525971038895865645148901180585340454985524155135260217788758027400478312256339496385275012465661575576202252063145698732079880294664220579764848767704076761853197216563262660046602703973050798218246170835962005598561669706844469447435461092542265792444947706769615695252256130901271870341005768912974433684521436211263358097522726462083917939091760026658925757076733484173202927141441492573799914240222628795405623953109131594523623353044898339481494120112723445689647986475279242446083151413667587008191682564376412347964146113898565886683139407005941383669325997475076910488086663256335689181157957571445067490187939553165903773554290260531009121879044170766615232300936675369451260747671432073394867530820527479172464106442450727640226503746586340279816318821395210726268291535648506190714616083163403189943334431056876038286530365757187367147446004855912033137386225053275419626102417236133948503",
-	 "1095121115716677802856811290392395128588168592409109494900178008967955253005183831872715423151551999734857184538199864469605657805519106717529655044054833197687459782636297255219742994736751541815269727940751860670268774903340296040006114013971309257028332849679096824800250742691718610670812374272414086863715763724622797509437062518082383056050144624962776302147890521249477060215148275163688301275847155316042279405557632639366066847442861422164832655874655824221577849928863023018366835675399949740429332468186340518172487073360822220449055340582568461568645259954873303616953776393853174845132081121976327462740354930744487429617202585015510744298530101547706821590188733515880733527449780963163909830077616357506845523215289297624086914545378511082534229620116563260168494523906566709418166011112754529766183554579321224940951177394088465596712620076240067370589036924024728375076210477267488679008016579588696191194060127319035195370137160936882402244399699172017835144537488486396906144217720028992863941288217185353914991583400421682751000603596655790990815525126154394344641336397793791497068253936771017031980867706707490224041075826337383538651825493679503771934836094655802776331664261631740148281763487765852746577808019633679",
-
-	 /* generic unrestricted moduli */
-	 "17933601194860113372237070562165128350027320072176844226673287945873370751245439587792371960615073855669274087805055507977323024886880985062002853331424203",
-	 "2893527720709661239493896562339544088620375736490408468011883030469939904368086092336458298221245707898933583190713188177399401852627749210994595974791782790253946539043962213027074922559572312141181787434278708783207966459019479487",
-	 "347743159439876626079252796797422223177535447388206607607181663903045907591201940478223621722118173270898487582987137708656414344685816179420855160986340457973820182883508387588163122354089264395604796675278966117567294812714812796820596564876450716066283126720010859041484786529056457896367683122960411136319",
-	 "47266428956356393164697365098120418976400602706072312735924071745438532218237979333351774907308168340693326687317443721193266215155735814510792148768576498491199122744351399489453533553203833318691678263241941706256996197460424029012419012634671862283532342656309677173602509498417976091509154360039893165037637034737020327399910409885798185771003505320583967737293415979917317338985837385734747478364242020380416892056650841470869294527543597349250299539682430605173321029026555546832473048600327036845781970289288898317888427517364945316709081173840186150794397479045034008257793436817683392375274635794835245695887",
-	 "436463808505957768574894870394349739623346440601945961161254440072143298152040105676491048248110146278752857839930515766167441407021501229924721335644557342265864606569000117714935185566842453630868849121480179691838399545644365571106757731317371758557990781880691336695584799313313687287468894148823761785582982549586183756806449017542622267874275103877481475534991201849912222670102069951687572917937634467778042874315463238062009202992087620963771759666448266532858079402669920025224220613419441069718482837399612644978839925207109870840278194042158748845445131729137117098529028886770063736487420613144045836803985635654192482395882603511950547826439092832800532152534003936926017612446606135655146445620623395788978726744728503058670046885876251527122350275750995227",
-	 "11424167473351836398078306042624362277956429440521137061889702611766348760692206243140413411077394583180726863277012016602279290144126785129569474909173584789822341986742719230331946072730319555984484911716797058875905400999504305877245849119687509023232790273637466821052576859232452982061831009770786031785669030271542286603956118755585683996118896215213488875253101894663403069677745948305893849505434201763745232895780711972432011344857521691017896316861403206449421332243658855453435784006517202894181640562433575390821384210960117518650374602256601091379644034244332285065935413233557998331562749140202965844219336298970011513882564935538704289446968322281451907487362046511461221329799897350993370560697505809686438782036235372137015731304779072430260986460269894522159103008260495503005267165927542949439526272736586626709581721032189532726389643625590680105784844246152702670169304203783072275089194754889511973916207",
-	 "1214855636816562637502584060163403830270705000634713483015101384881871978446801224798536155406895823305035467591632531067547890948695117172076954220727075688048751022421198712032848890056357845974246560748347918630050853933697792254955890439720297560693579400297062396904306270145886830719309296352765295712183040773146419022875165382778007040109957609739589875590885701126197906063620133954893216612678838507540777138437797705602453719559017633986486649523611975865005712371194067612263330335590526176087004421363598470302731349138773205901447704682181517904064735636518462452242791676541725292378925568296858010151852326316777511935037531017413910506921922450666933202278489024521263798482237150056835746454842662048692127173834433089016107854491097456725016327709663199738238442164843147132789153725513257167915555162094970853584447993125488607696008169807374736711297007473812256272245489405898470297178738029484459690836250560495461579533254473316340608217876781986188705928270735695752830825527963838355419762516246028680280988020401914551825487349990306976304093109384451438813251211051597392127491464898797406789175453067960072008590614886532333015881171367104445044718144312416815712216611576221546455968770801413440778423979",
-	 NULL
-      };
-      log = FOPEN("logs/expt.log", "w");
-      logb = FOPEN("logs/expt_dr.log", "w");
-      logc = FOPEN("logs/expt_2k.log", "w");
-      logd = FOPEN("logs/expt_2kl.log", "w");
-      for (n = 0; primes[n]; n++) {
-	 SLEEP;
-	 mp_read_radix(&a, primes[n], 10);
-	 mp_zero(&b);
-	 for (rr = 0; rr < (unsigned) mp_count_bits(&a); rr++) {
-	    mp_mul_2(&b, &b);
-	    b.dp[0] |= lbit();
-	    b.used += 1;
-	 }
-	 mp_sub_d(&a, 1, &c);
-	 mp_mod(&b, &c, &b);
-	 mp_set(&c, 3);
-	 rr = 0;
-	 tt = -1;
-	 do {
-	    gg = TIMFUNC();
-	    DO(mp_exptmod(&c, &b, &a, &d));
-	    gg = (TIMFUNC() - gg) >> 1;
-	    if (tt > gg)
-	       tt = gg;
-	 } while (++rr < 10);
-	 mp_sub_d(&a, 1, &e);
-	 mp_sub(&e, &b, &b);
-	 mp_exptmod(&c, &b, &a, &e);	/* c^(p-1-b) mod a */
-	 mp_mulmod(&e, &d, &a, &d);	/* c^b * c^(p-1-b) == c^p-1 == 1 */
-	 if (mp_cmp_d(&d, 1)) {
-	    printf("Different (%d)!!!\n", mp_count_bits(&a));
-	    draw(&d);
-	    exit(0);
-	 }
-	 printf("Exponentiating\t%4d-bit => %9llu/sec, %9llu cycles\n",
-		mp_count_bits(&a), CLK_PER_SEC / tt, tt);
-	 FPRINTF(n < 4 ? logd : (n < 9) ? logc : (n < 16) ? logb : log,
-		 "%d %9llu\n", mp_count_bits(&a), tt);
-      }
-   }
-   FCLOSE(log);
-   FCLOSE(logb);
-   FCLOSE(logc);
-   FCLOSE(logd);
-
-   log = FOPEN("logs/invmod.log", "w");
-   for (cnt = 4; cnt <= 32; cnt += 4) {
-      SLEEP;
-      mp_rand(&a, cnt);
-      mp_rand(&b, cnt);
-
-      do {
-	 mp_add_d(&b, 1, &b);
-	 mp_gcd(&a, &b, &c);
-      } while (mp_cmp_d(&c, 1) != MP_EQ);
-
-      rr = 0;
-      tt = -1;
-      do {
-	 gg = TIMFUNC();
-	 DO(mp_invmod(&b, &a, &c));
-	 gg = (TIMFUNC() - gg) >> 1;
-	 if (tt > gg)
-	    tt = gg;
-      } while (++rr < 1000);
-      mp_mulmod(&b, &c, &a, &d);
-      if (mp_cmp_d(&d, 1) != MP_EQ) {
-	 printf("Failed to invert\n");
-	 return 0;
-      }
-      printf("Inverting mod\t%4d-bit => %9llu/sec, %9llu cycles\n",
-	     mp_count_bits(&a), CLK_PER_SEC / tt, tt);
-      FPRINTF(log, "%d %9llu\n", cnt * DIGIT_BIT, tt);
-   }
-   FCLOSE(log);
-
-   return 0;
-}
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
diff --git a/libtommath/dep.pl b/libtommath/dep.pl
deleted file mode 100644
index 0a5d19a..0000000
--- a/libtommath/dep.pl
+++ /dev/null
@@ -1,123 +0,0 @@
-#!/usr/bin/perl 
-#
-# Walk through source, add labels and make classes
-#
-#use strict;
-
-my %deplist;
-
-#open class file and write preamble 
-open(CLASS, ">tommath_class.h") or die "Couldn't open tommath_class.h for writing\n";
-print CLASS "#if !(defined(LTM1) && defined(LTM2) && defined(LTM3))\n#if defined(LTM2)\n#define LTM3\n#endif\n#if defined(LTM1)\n#define LTM2\n#endif\n#define LTM1\n\n#if defined(LTM_ALL)\n";
-
-foreach my $filename (glob "bn*.c") {
-   my $define = $filename;
-
-print "Processing $filename\n";
-
-   # convert filename to upper case so we can use it as a define 
-   $define =~ tr/[a-z]/[A-Z]/;
-   $define =~ tr/\./_/;
-   print CLASS "#define $define\n";
-
-   # now copy text and apply #ifdef as required 
-   my $apply = 0;
-   open(SRC, "<$filename");
-   open(OUT, ">tmp");
-
-   # first line will be the #ifdef
-   my $line = <SRC>;
-   if ($line =~ /include/) {
-      print OUT $line;
-   } else {
-      print OUT "#include <tommath.h>\n#ifdef $define\n$line";
-      $apply = 1;
-   }
-   while (<SRC>) {
-      if (!($_ =~ /tommath\.h/)) {
-         print OUT $_;
-      }
-   }
-   if ($apply == 1) {
-      print OUT "#endif\n";
-   }
-   close SRC;
-   close OUT;
-
-   unlink($filename);
-   rename("tmp", $filename);
-}
-print CLASS "#endif\n\n";
-
-# now do classes 
-
-foreach my $filename (glob "bn*.c") {
-   open(SRC, "<$filename") or die "Can't open source file!\n"; 
-
-   # convert filename to upper case so we can use it as a define 
-   $filename =~ tr/[a-z]/[A-Z]/;
-   $filename =~ tr/\./_/;
-
-   print CLASS "#if defined($filename)\n";
-   my $list = $filename;
-
-   # scan for mp_* and make classes
-   while (<SRC>) {
-      my $line = $_;
-      while ($line =~ m/(fast_)*(s_)*mp\_[a-z_0-9]*/) {
-          $line = $';
-          # now $& is the match, we want to skip over LTM keywords like
-          # mp_int, mp_word, mp_digit
-          if (!($& eq "mp_digit") && !($& eq "mp_word") && !($& eq "mp_int") && !($& eq "mp_min_u32")) {
-             my $a = $&;
-             $a =~ tr/[a-z]/[A-Z]/;
-             $a = "BN_" . $a . "_C";
-             if (!($list =~ /$a/)) {
-                print CLASS "   #define $a\n";
-             }
-             $list = $list . "," . $a;
-          }
-      }
-   }
-   @deplist{$filename} = $list;
-
-   print CLASS "#endif\n\n";
-   close SRC;
-}
-
-print CLASS "#ifdef LTM3\n#define LTM_LAST\n#endif\n#include <tommath_superclass.h>\n#include <tommath_class.h>\n#else\n#define LTM_LAST\n#endif\n";
-close CLASS;
-
-#now let's make a cool call graph... 
-
-open(OUT,">callgraph.txt");
-$indent = 0;
-foreach (keys %deplist) {
-   $list = "";
-   draw_func(@deplist{$_});
-   print OUT "\n\n";
-}
-close(OUT);
-
-sub draw_func()
-{
-   my @funcs = split(",", $_[0]);
-   if ($list =~ /@funcs[0]/) {
-      return;
-   } else {
-      $list = $list . @funcs[0];
-   }
-   if ($indent == 0) { }
-   elsif ($indent >= 1) { print OUT "|   " x ($indent - 1) . "+--->"; }
-   print OUT @funcs[0] . "\n";   
-   shift @funcs;
-      my $temp = $list;
-   foreach my $i (@funcs) {
-      ++$indent;
-      draw_func(@deplist{$i});
-      --$indent;
-   }
-      $list = $temp;
-}
-
-
diff --git a/libtommath/etc/2kprime.1 b/libtommath/etc/2kprime.1
deleted file mode 100644
index c41ded1..0000000
--- a/libtommath/etc/2kprime.1
+++ /dev/null
@@ -1,2 +0,0 @@
-256-bits (k = 36113) = 115792089237316195423570985008687907853269984665640564039457584007913129603823
-512-bits (k = 38117) = 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006045979
diff --git a/libtommath/etc/2kprime.c b/libtommath/etc/2kprime.c
deleted file mode 100644
index 9450283..0000000
--- a/libtommath/etc/2kprime.c
+++ /dev/null
@@ -1,84 +0,0 @@
-/* Makes safe primes of a 2k nature */
-#include <tommath.h>
-#include <time.h>
-
-int sizes[] = {256, 512, 768, 1024, 1536, 2048, 3072, 4096};
-
-int main(void)
-{
-   char buf[2000];
-   int x, y;
-   mp_int q, p;
-   FILE *out;
-   clock_t t1;
-   mp_digit z;
-   
-   mp_init_multi(&q, &p, NULL);
-   
-   out = fopen("2kprime.1", "w");
-   for (x = 0; x < (int)(sizeof(sizes) / sizeof(sizes[0])); x++) {
-   top:
-       mp_2expt(&q, sizes[x]);
-       mp_add_d(&q, 3, &q);
-       z = -3;
-       
-       t1 = clock();
-       for(;;) {
-         mp_sub_d(&q, 4, &q);
-         z += 4;
-
-         if (z > MP_MASK) {
-            printf("No primes of size %d found\n", sizes[x]);
-            break;
-         }
-         
-         if (clock() - t1 > CLOCKS_PER_SEC) { 
-            printf("."); fflush(stdout);
-//            sleep((clock() - t1 + CLOCKS_PER_SEC/2)/CLOCKS_PER_SEC);
-            t1 = clock();
-         }
-         
-         /* quick test on q */
-         mp_prime_is_prime(&q, 1, &y);
-         if (y == 0) {
-            continue;
-         }
-
-         /* find (q-1)/2 */
-         mp_sub_d(&q, 1, &p);
-         mp_div_2(&p, &p);
-         mp_prime_is_prime(&p, 3, &y);
-         if (y == 0) {
-            continue;
-         }
-
-         /* test on q */
-         mp_prime_is_prime(&q, 3, &y);
-         if (y == 0) {
-            continue;
-         }
-
-         break;
-       }
-       
-       if (y == 0) {
-          ++sizes[x];
-          goto top;
-       }
-       
-       mp_toradix(&q, buf, 10);
-       printf("\n\n%d-bits (k = %lu) = %s\n", sizes[x], z, buf);
-       fprintf(out, "%d-bits (k = %lu) = %s\n", sizes[x], z, buf); fflush(out);
-   }
-   
-   return 0;
-}   
-       
-         
-            
-            
-          
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
diff --git a/libtommath/etc/drprime.c b/libtommath/etc/drprime.c
deleted file mode 100644
index c7d253f..0000000
--- a/libtommath/etc/drprime.c
+++ /dev/null
@@ -1,64 +0,0 @@
-/* Makes safe primes of a DR nature */
-#include <tommath.h>
-
-int sizes[] = { 1+256/DIGIT_BIT, 1+512/DIGIT_BIT, 1+768/DIGIT_BIT, 1+1024/DIGIT_BIT, 1+2048/DIGIT_BIT, 1+4096/DIGIT_BIT };
-int main(void)
-{
-   int res, x, y;
-   char buf[4096];
-   FILE *out;
-   mp_int a, b;
-   
-   mp_init(&a);
-   mp_init(&b);
-   
-   out = fopen("drprimes.txt", "w");
-   for (x = 0; x < (int)(sizeof(sizes)/sizeof(sizes[0])); x++) {
-   top:
-       printf("Seeking a %d-bit safe prime\n", sizes[x] * DIGIT_BIT);
-       mp_grow(&a, sizes[x]);
-       mp_zero(&a);
-       for (y = 1; y < sizes[x]; y++) {
-           a.dp[y] = MP_MASK;
-       }
-       
-       /* make a DR modulus */
-       a.dp[0] = -1;
-       a.used = sizes[x];
-       
-       /* now loop */
-       res = 0;
-       for (;;) { 
-          a.dp[0] += 4;
-          if (a.dp[0] >= MP_MASK) break;
-          mp_prime_is_prime(&a, 1, &res);
-          if (res == 0) continue;
-          printf("."); fflush(stdout);
-          mp_sub_d(&a, 1, &b);
-          mp_div_2(&b, &b);
-          mp_prime_is_prime(&b, 3, &res);  
-          if (res == 0) continue;
-          mp_prime_is_prime(&a, 3, &res);
-          if (res == 1) break;
-	}
-        
-        if (res != 1) {
-           printf("Error not DR modulus\n"); sizes[x] += 1; goto top;
-        } else {
-           mp_toradix(&a, buf, 10);
-           printf("\n\np == %s\n\n", buf);
-           fprintf(out, "%d-bit prime:\np == %s\n\n", mp_count_bits(&a), buf); fflush(out);
-        }           
-   }
-   fclose(out);
-   
-   mp_clear(&a);
-   mp_clear(&b);
-   
-   return 0;
-}
-
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
diff --git a/libtommath/etc/drprimes.28 b/libtommath/etc/drprimes.28
deleted file mode 100644
index 9d438ad..0000000
--- a/libtommath/etc/drprimes.28
+++ /dev/null
@@ -1,25 +0,0 @@
-DR safe primes for 28-bit digits.
-
-224-bit prime:
-p == 26959946667150639794667015087019630673637144422540572481103341844143
-
-532-bit prime:
-p == 14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368691747
-
-784-bit prime:
-p == 101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039
-
-1036-bit prime:
-p == 736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821798437127
-
-1540-bit prime:
-p == 38564998830736521417281865696453025806593491967131023221754800625044118265468851210705360385717536794615180260494208076605798671660719333199513807806252394423283413430106003596332513246682903994829528690198205120921557533726473585751382193953592127439965050261476810842071573684505878854588706623484573925925903505747545471088867712185004135201289273405614415899438276535626346098904241020877974002916168099951885406379295536200413493190419727789712076165162175783
-
-2072-bit prime:
-p == 542189391331696172661670440619180536749994166415993334151601745392193484590296600979602378676624808129613777993466242203025054573692562689251250471628358318743978285860720148446448885701001277560572526947619392551574490839286458454994488665744991822837769918095117129546414124448777033941223565831420390846864429504774477949153794689948747680362212954278693335653935890352619041936727463717926744868338358149568368643403037768649616778526013610493696186055899318268339432671541328195724261329606699831016666359440874843103020666106568222401047720269951530296879490444224546654729111504346660859907296364097126834834235287147
-
-3080-bit prime:
-p == 1487259134814709264092032648525971038895865645148901180585340454985524155135260217788758027400478312256339496385275012465661575576202252063145698732079880294664220579764848767704076761853197216563262660046602703973050798218246170835962005598561669706844469447435461092542265792444947706769615695252256130901271870341005768912974433684521436211263358097522726462083917939091760026658925757076733484173202927141441492573799914240222628795405623953109131594523623353044898339481494120112723445689647986475279242446083151413667587008191682564376412347964146113898565886683139407005941383669325997475076910488086663256335689181157957571445067490187939553165903773554290260531009121879044170766615232300936675369451260747671432073394867530820527479172464106442450727640226503746586340279816318821395210726268291535648506190714616083163403189943334431056876038286530365757187367147446004855912033137386225053275419626102417236133948503
-
-4116-bit prime:
-p == 1095121115716677802856811290392395128588168592409109494900178008967955253005183831872715423151551999734857184538199864469605657805519106717529655044054833197687459782636297255219742994736751541815269727940751860670268774903340296040006114013971309257028332849679096824800250742691718610670812374272414086863715763724622797509437062518082383056050144624962776302147890521249477060215148275163688301275847155316042279405557632639366066847442861422164832655874655824221577849928863023018366835675399949740429332468186340518172487073360822220449055340582568461568645259954873303616953776393853174845132081121976327462740354930744487429617202585015510744298530101547706821590188733515880733527449780963163909830077616357506845523215289297624086914545378511082534229620116563260168494523906566709418166011112754529766183554579321224940951177394088465596712620076240067370589036924024728375076210477267488679008016579588696191194060127319035195370137160936882402244399699172017835144537488486396906144217720028992863941288217185353914991583400421682751000603596655790990815525126154394344641336397793791497068253936771017031980867706707490224041075826337383538651825493679503771934836094655802776331664261631740148281763487765852746577808019633679
diff --git a/libtommath/etc/drprimes.txt b/libtommath/etc/drprimes.txt
deleted file mode 100644
index 7c97f67..0000000
--- a/libtommath/etc/drprimes.txt
+++ /dev/null
@@ -1,9 +0,0 @@
-300-bit prime:
-p == 2037035976334486086268445688409378161051468393665936250636140449354381298610415201576637819
-
-540-bit prime:
-p == 3599131035634557106248430806148785487095757694641533306480604458089470064537190296255232548883112685719936728506816716098566612844395439751206810991770626477344739
-
-780-bit prime:
-p == 6359114106063703798370219984742410466332205126109989319225557147754704702203399726411277962562135973685197744935448875852478791860694279747355800678568677946181447581781401213133886609947027230004277244697462656003655947791725966271167
-
diff --git a/libtommath/etc/makefile b/libtommath/etc/makefile
deleted file mode 100644
index 99154d8..0000000
--- a/libtommath/etc/makefile
+++ /dev/null
@@ -1,50 +0,0 @@
-CFLAGS += -Wall -W -Wshadow -O3 -fomit-frame-pointer -funroll-loops -I../
-
-# default lib name (requires install with root)
-# LIBNAME=-ltommath
-
-# libname when you can't install the lib with install
-LIBNAME=../libtommath.a
-
-#provable primes
-pprime: pprime.o
-	$(CC) pprime.o $(LIBNAME) -o pprime
-
-# portable [well requires clock()] tuning app
-tune: tune.o
-	$(CC) tune.o $(LIBNAME) -o tune
-	
-# same app but using RDTSC for higher precision [requires 80586+], coff based gcc installs [e.g. ming, cygwin, djgpp]
-tune86: tune.c
-	nasm -f coff timer.asm
-	$(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o  $(LIBNAME) -o tune86
-	
-# for cygwin
-tune86c: tune.c
-	nasm -f gnuwin32 timer.asm
-	$(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o  $(LIBNAME) -o tune86
-
-#make tune86 for linux or any ELF format
-tune86l: tune.c
-	nasm -f elf -DUSE_ELF timer.asm
-	$(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86l
-        
-# spits out mersenne primes
-mersenne: mersenne.o
-	$(CC) mersenne.o $(LIBNAME) -o mersenne
-
-# fines DR safe primes for the given config
-drprime: drprime.o
-	$(CC) drprime.o $(LIBNAME) -o drprime
-	
-# fines 2k safe primes for the given config
-2kprime: 2kprime.o
-	$(CC) 2kprime.o $(LIBNAME) -o 2kprime
-
-mont: mont.o
-	$(CC) mont.o $(LIBNAME) -o mont
-
-        
-clean:
-	rm -f *.log *.o *.obj *.exe pprime tune mersenne drprime tune86 tune86l mont 2kprime pprime.dat \
-         *.da *.dyn *.dpi *~
diff --git a/libtommath/etc/makefile.icc b/libtommath/etc/makefile.icc
deleted file mode 100644
index 8a1ffff..0000000
--- a/libtommath/etc/makefile.icc
+++ /dev/null
@@ -1,67 +0,0 @@
-CC = icc
-
-CFLAGS += -I../
-
-# optimize for SPEED
-#
-# -mcpu= can be pentium, pentiumpro (covers PII through PIII) or pentium4
-# -ax?   specifies make code specifically for ? but compatible with IA-32
-# -x?    specifies compile solely for ? [not specifically IA-32 compatible]
-#
-# where ? is 
-#   K - PIII
-#   W - first P4 [Williamette]
-#   N - P4 Northwood
-#   P - P4 Prescott
-#   B - Blend of P4 and PM [mobile]
-#
-# Default to just generic max opts
-CFLAGS += -O3 -xP -ip
-
-# default lib name (requires install with root)
-# LIBNAME=-ltommath
-
-# libname when you can't install the lib with install
-LIBNAME=../libtommath.a
-
-#provable primes
-pprime: pprime.o
-	$(CC) pprime.o $(LIBNAME) -o pprime
-
-# portable [well requires clock()] tuning app
-tune: tune.o
-	$(CC) tune.o $(LIBNAME) -o tune
-	
-# same app but using RDTSC for higher precision [requires 80586+], coff based gcc installs [e.g. ming, cygwin, djgpp]
-tune86: tune.c
-	nasm -f coff timer.asm
-	$(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o  $(LIBNAME) -o tune86
-	
-# for cygwin
-tune86c: tune.c
-	nasm -f gnuwin32 timer.asm
-	$(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o  $(LIBNAME) -o tune86
-
-#make tune86 for linux or any ELF format
-tune86l: tune.c
-	nasm -f elf -DUSE_ELF timer.asm
-	$(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86l
-        
-# spits out mersenne primes
-mersenne: mersenne.o
-	$(CC) mersenne.o $(LIBNAME) -o mersenne
-
-# fines DR safe primes for the given config
-drprime: drprime.o
-	$(CC) drprime.o $(LIBNAME) -o drprime
-	
-# fines 2k safe primes for the given config
-2kprime: 2kprime.o
-	$(CC) 2kprime.o $(LIBNAME) -o 2kprime
-
-mont: mont.o
-	$(CC) mont.o $(LIBNAME) -o mont
-
-        
-clean:
-	rm -f *.log *.o *.obj *.exe pprime tune mersenne drprime tune86 tune86l mont 2kprime pprime.dat *.il
diff --git a/libtommath/etc/makefile.msvc b/libtommath/etc/makefile.msvc
deleted file mode 100644
index 2833372..0000000
--- a/libtommath/etc/makefile.msvc
+++ /dev/null
@@ -1,23 +0,0 @@
-#MSVC Makefile
-#
-#Tom St Denis
-
-CFLAGS = /I../ /Ox /DWIN32 /W3
-
-pprime: pprime.obj
-	cl pprime.obj ../tommath.lib 
-
-mersenne: mersenne.obj
-	cl mersenne.obj ../tommath.lib
-	
-tune: tune.obj
-	cl tune.obj ../tommath.lib
-
-mont: mont.obj
-	cl mont.obj ../tommath.lib
-	
-drprime: drprime.obj
-	cl drprime.obj ../tommath.lib
-
-2kprime: 2kprime.obj
-	cl 2kprime.obj ../tommath.lib
diff --git a/libtommath/etc/mersenne.c b/libtommath/etc/mersenne.c
deleted file mode 100644
index ae6725a..0000000
--- a/libtommath/etc/mersenne.c
+++ /dev/null
@@ -1,144 +0,0 @@
-/* Finds Mersenne primes using the Lucas-Lehmer test 
- *
- * Tom St Denis, tomstdenis@gmail.com
- */
-#include <time.h>
-#include <tommath.h>
-
-int
-is_mersenne (long s, int *pp)
-{
-  mp_int  n, u;
-  int     res, k;
-  
-  *pp = 0;
-
-  if ((res = mp_init (&n)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_init (&u)) != MP_OKAY) {
-    goto LBL_N;
-  }
-
-  /* n = 2^s - 1 */
-  if ((res = mp_2expt(&n, s)) != MP_OKAY) {
-     goto LBL_MU;
-  }
-  if ((res = mp_sub_d (&n, 1, &n)) != MP_OKAY) {
-    goto LBL_MU;
-  }
-
-  /* set u=4 */
-  mp_set (&u, 4);
-
-  /* for k=1 to s-2 do */
-  for (k = 1; k <= s - 2; k++) {
-    /* u = u^2 - 2 mod n */
-    if ((res = mp_sqr (&u, &u)) != MP_OKAY) {
-      goto LBL_MU;
-    }
-    if ((res = mp_sub_d (&u, 2, &u)) != MP_OKAY) {
-      goto LBL_MU;
-    }
-
-    /* make sure u is positive */
-    while (u.sign == MP_NEG) {
-      if ((res = mp_add (&u, &n, &u)) != MP_OKAY) {
-         goto LBL_MU;
-      }
-    }
-
-    /* reduce */
-    if ((res = mp_reduce_2k (&u, &n, 1)) != MP_OKAY) {
-      goto LBL_MU;
-    }
-  }
-
-  /* if u == 0 then its prime */
-  if (mp_iszero (&u) == 1) {
-    mp_prime_is_prime(&n, 8, pp);
-  if (*pp != 1) printf("FAILURE\n");
-  }
-
-  res = MP_OKAY;
-LBL_MU:mp_clear (&u);
-LBL_N:mp_clear (&n);
-  return res;
-}
-
-/* square root of a long < 65536 */
-long
-i_sqrt (long x)
-{
-  long    x1, x2;
-
-  x2 = 16;
-  do {
-    x1 = x2;
-    x2 = x1 - ((x1 * x1) - x) / (2 * x1);
-  } while (x1 != x2);
-
-  if (x1 * x1 > x) {
-    --x1;
-  }
-
-  return x1;
-}
-
-/* is the long prime by brute force */
-int
-isprime (long k)
-{
-  long    y, z;
-
-  y = i_sqrt (k);
-  for (z = 2; z <= y; z++) {
-    if ((k % z) == 0)
-      return 0;
-  }
-  return 1;
-}
-
-
-int
-main (void)
-{
-  int     pp;
-  long    k;
-  clock_t tt;
-
-  k = 3;
-
-  for (;;) {
-    /* start time */
-    tt = clock ();
-
-    /* test if 2^k - 1 is prime */
-    if (is_mersenne (k, &pp) != MP_OKAY) {
-      printf ("Whoa error\n");
-      return -1;
-    }
-
-    if (pp == 1) {
-      /* count time */
-      tt = clock () - tt;
-
-      /* display if prime */
-      printf ("2^%-5ld - 1 is prime, test took %ld ticks\n", k, tt);
-    }
-
-    /* goto next odd exponent */
-    k += 2;
-
-    /* but make sure its prime */
-    while (isprime (k) == 0) {
-      k += 2;
-    }
-  }
-  return 0;
-}
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
diff --git a/libtommath/etc/mont.c b/libtommath/etc/mont.c
deleted file mode 100644
index 45cf3fd..0000000
--- a/libtommath/etc/mont.c
+++ /dev/null
@@ -1,50 +0,0 @@
-/* tests the montgomery routines */
-#include <tommath.h>
-
-int main(void)
-{
-   mp_int modulus, R, p, pp;
-   mp_digit mp;
-   long x, y;
-
-   srand(time(NULL));
-   mp_init_multi(&modulus, &R, &p, &pp, NULL);
-
-   /* loop through various sizes */
-   for (x = 4; x < 256; x++) {
-       printf("DIGITS == %3ld...", x); fflush(stdout);
-       
-       /* make up the odd modulus */
-       mp_rand(&modulus, x);
-       modulus.dp[0] |= 1;
-       
-       /* now find the R value */
-       mp_montgomery_calc_normalization(&R, &modulus);
-       mp_montgomery_setup(&modulus, &mp);
-       
-       /* now run through a bunch tests */
-       for (y = 0; y < 1000; y++) {
-           mp_rand(&p, x/2);        /* p = random */
-           mp_mul(&p, &R, &pp);     /* pp = R * p */
-           mp_montgomery_reduce(&pp, &modulus, mp);
-           
-           /* should be equal to p */
-           if (mp_cmp(&pp, &p) != MP_EQ) {
-              printf("FAILURE!\n");
-              exit(-1);
-           }
-       }
-       printf("PASSED\n");
-    }
-    
-    return 0;
-}
-
-
-
-
-
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
diff --git a/libtommath/etc/pprime.c b/libtommath/etc/pprime.c
deleted file mode 100644
index 9f94423..0000000
--- a/libtommath/etc/pprime.c
+++ /dev/null
@@ -1,400 +0,0 @@
-/* Generates provable primes
- *
- * See http://gmail.com:8080/papers/pp.pdf for more info.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://tom.gmail.com
- */
-#include <time.h>
-#include "tommath.h"
-
-int   n_prime;
-FILE *primes;
-
-/* fast square root */
-static  mp_digit
-i_sqrt (mp_word x)
-{
-  mp_word x1, x2;
-
-  x2 = x;
-  do {
-    x1 = x2;
-    x2 = x1 - ((x1 * x1) - x) / (2 * x1);
-  } while (x1 != x2);
-
-  if (x1 * x1 > x) {
-    --x1;
-  }
-
-  return x1;
-}
-
-
-/* generates a prime digit */
-static void gen_prime (void)
-{
-  mp_digit r, x, y, next;
-  FILE *out;
-
-  out = fopen("pprime.dat", "wb");
-
-  /* write first set of primes */
-  r = 3; fwrite(&r, 1, sizeof(mp_digit), out);
-  r = 5; fwrite(&r, 1, sizeof(mp_digit), out);
-  r = 7; fwrite(&r, 1, sizeof(mp_digit), out);
-  r = 11; fwrite(&r, 1, sizeof(mp_digit), out);
-  r = 13; fwrite(&r, 1, sizeof(mp_digit), out);
-  r = 17; fwrite(&r, 1, sizeof(mp_digit), out);
-  r = 19; fwrite(&r, 1, sizeof(mp_digit), out);
-  r = 23; fwrite(&r, 1, sizeof(mp_digit), out);
-  r = 29; fwrite(&r, 1, sizeof(mp_digit), out);
-  r = 31; fwrite(&r, 1, sizeof(mp_digit), out);
-
-  /* get square root, since if 'r' is composite its factors must be < than this */
-  y = i_sqrt (r);
-  next = (y + 1) * (y + 1);
-
-  for (;;) {
-  do {
-    r += 2;			/* next candidate */
-    r &= MP_MASK;
-    if (r < 31) break;
-
-    /* update sqrt ? */
-    if (next <= r) {
-      ++y;
-      next = (y + 1) * (y + 1);
-    }
-
-    /* loop if divisible by 3,5,7,11,13,17,19,23,29  */
-    if ((r % 3) == 0) {
-      x = 0;
-      continue;
-    }
-    if ((r % 5) == 0) {
-      x = 0;
-      continue;
-    }
-    if ((r % 7) == 0) {
-      x = 0;
-      continue;
-    }
-    if ((r % 11) == 0) {
-      x = 0;
-      continue;
-    }
-    if ((r % 13) == 0) {
-      x = 0;
-      continue;
-    }
-    if ((r % 17) == 0) {
-      x = 0;
-      continue;
-    }
-    if ((r % 19) == 0) {
-      x = 0;
-      continue;
-    }
-    if ((r % 23) == 0) {
-      x = 0;
-      continue;
-    }
-    if ((r % 29) == 0) {
-      x = 0;
-      continue;
-    }
-
-    /* now check if r is divisible by x + k={1,7,11,13,17,19,23,29} */
-    for (x = 30; x <= y; x += 30) {
-      if ((r % (x + 1)) == 0) {
-	x = 0;
-	break;
-      }
-      if ((r % (x + 7)) == 0) {
-	x = 0;
-	break;
-      }
-      if ((r % (x + 11)) == 0) {
-	x = 0;
-	break;
-      }
-      if ((r % (x + 13)) == 0) {
-	x = 0;
-	break;
-      }
-      if ((r % (x + 17)) == 0) {
-	x = 0;
-	break;
-      }
-      if ((r % (x + 19)) == 0) {
-	x = 0;
-	break;
-      }
-      if ((r % (x + 23)) == 0) {
-	x = 0;
-	break;
-      }
-      if ((r % (x + 29)) == 0) {
-	x = 0;
-	break;
-      }
-    }
-  } while (x == 0);
-  if (r > 31) { fwrite(&r, 1, sizeof(mp_digit), out); printf("%9d\r", r); fflush(stdout); }
-  if (r < 31) break;
-  }
-
-  fclose(out);
-}
-
-void load_tab(void)
-{
-   primes = fopen("pprime.dat", "rb");
-   if (primes == NULL) {
-      gen_prime();
-      primes = fopen("pprime.dat", "rb");
-   }
-   fseek(primes, 0, SEEK_END);
-   n_prime = ftell(primes) / sizeof(mp_digit);
-}
-
-mp_digit prime_digit(void)
-{
-   int n;
-   mp_digit d;
-
-   n = abs(rand()) % n_prime;
-   fseek(primes, n * sizeof(mp_digit), SEEK_SET);
-   fread(&d, 1, sizeof(mp_digit), primes);
-   return d;
-}
-
-
-/* makes a prime of at least k bits */
-int
-pprime (int k, int li, mp_int * p, mp_int * q)
-{
-  mp_int  a, b, c, n, x, y, z, v;
-  int     res, ii;
-  static const mp_digit bases[] = { 2, 3, 5, 7, 11, 13, 17, 19 };
-
-  /* single digit ? */
-  if (k <= (int) DIGIT_BIT) {
-    mp_set (p, prime_digit ());
-    return MP_OKAY;
-  }
-
-  if ((res = mp_init (&c)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_init (&v)) != MP_OKAY) {
-    goto LBL_C;
-  }
-
-  /* product of first 50 primes */
-  if ((res =
-       mp_read_radix (&v,
-		      "19078266889580195013601891820992757757219839668357012055907516904309700014933909014729740190",
-		      10)) != MP_OKAY) {
-    goto LBL_V;
-  }
-
-  if ((res = mp_init (&a)) != MP_OKAY) {
-    goto LBL_V;
-  }
-
-  /* set the prime */
-  mp_set (&a, prime_digit ());
-
-  if ((res = mp_init (&b)) != MP_OKAY) {
-    goto LBL_A;
-  }
-
-  if ((res = mp_init (&n)) != MP_OKAY) {
-    goto LBL_B;
-  }
-
-  if ((res = mp_init (&x)) != MP_OKAY) {
-    goto LBL_N;
-  }
-
-  if ((res = mp_init (&y)) != MP_OKAY) {
-    goto LBL_X;
-  }
-
-  if ((res = mp_init (&z)) != MP_OKAY) {
-    goto LBL_Y;
-  }
-
-  /* now loop making the single digit */
-  while (mp_count_bits (&a) < k) {
-    fprintf (stderr, "prime has %4d bits left\r", k - mp_count_bits (&a));
-    fflush (stderr);
-  top:
-    mp_set (&b, prime_digit ());
-
-    /* now compute z = a * b * 2 */
-    if ((res = mp_mul (&a, &b, &z)) != MP_OKAY) {	/* z = a * b */
-      goto LBL_Z;
-    }
-
-    if ((res = mp_copy (&z, &c)) != MP_OKAY) {	/* c = a * b */
-      goto LBL_Z;
-    }
-
-    if ((res = mp_mul_2 (&z, &z)) != MP_OKAY) {	/* z = 2 * a * b */
-      goto LBL_Z;
-    }
-
-    /* n = z + 1 */
-    if ((res = mp_add_d (&z, 1, &n)) != MP_OKAY) {	/* n = z + 1 */
-      goto LBL_Z;
-    }
-
-    /* check (n, v) == 1 */
-    if ((res = mp_gcd (&n, &v, &y)) != MP_OKAY) {	/* y = (n, v) */
-      goto LBL_Z;
-    }
-
-    if (mp_cmp_d (&y, 1) != MP_EQ)
-      goto top;
-
-    /* now try base x=bases[ii]  */
-    for (ii = 0; ii < li; ii++) {
-      mp_set (&x, bases[ii]);
-
-      /* compute x^a mod n */
-      if ((res = mp_exptmod (&x, &a, &n, &y)) != MP_OKAY) {	/* y = x^a mod n */
-	goto LBL_Z;
-      }
-
-      /* if y == 1 loop */
-      if (mp_cmp_d (&y, 1) == MP_EQ)
-	continue;
-
-      /* now x^2a mod n */
-      if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) {	/* y = x^2a mod n */
-	goto LBL_Z;
-      }
-
-      if (mp_cmp_d (&y, 1) == MP_EQ)
-	continue;
-
-      /* compute x^b mod n */
-      if ((res = mp_exptmod (&x, &b, &n, &y)) != MP_OKAY) {	/* y = x^b mod n */
-	goto LBL_Z;
-      }
-
-      /* if y == 1 loop */
-      if (mp_cmp_d (&y, 1) == MP_EQ)
-	continue;
-
-      /* now x^2b mod n */
-      if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) {	/* y = x^2b mod n */
-	goto LBL_Z;
-      }
-
-      if (mp_cmp_d (&y, 1) == MP_EQ)
-	continue;
-
-      /* compute x^c mod n == x^ab mod n */
-      if ((res = mp_exptmod (&x, &c, &n, &y)) != MP_OKAY) {	/* y = x^ab mod n */
-	goto LBL_Z;
-      }
-
-      /* if y == 1 loop */
-      if (mp_cmp_d (&y, 1) == MP_EQ)
-	continue;
-
-      /* now compute (x^c mod n)^2 */
-      if ((res = mp_sqrmod (&y, &n, &y)) != MP_OKAY) {	/* y = x^2ab mod n */
-	goto LBL_Z;
-      }
-
-      /* y should be 1 */
-      if (mp_cmp_d (&y, 1) != MP_EQ)
-	continue;
-      break;
-    }
-
-    /* no bases worked? */
-    if (ii == li)
-      goto top;
-
-{
-   char buf[4096];
-
-   mp_toradix(&n, buf, 10);
-   printf("Certificate of primality for:\n%s\n\n", buf);
-   mp_toradix(&a, buf, 10);
-   printf("A == \n%s\n\n", buf);
-   mp_toradix(&b, buf, 10);
-   printf("B == \n%s\n\nG == %d\n", buf, bases[ii]);
-   printf("----------------------------------------------------------------\n");
-}
-
-    /* a = n */
-    mp_copy (&n, &a);
-  }
-
-  /* get q to be the order of the large prime subgroup */
-  mp_sub_d (&n, 1, q);
-  mp_div_2 (q, q);
-  mp_div (q, &b, q, NULL);
-
-  mp_exch (&n, p);
-
-  res = MP_OKAY;
-LBL_Z:mp_clear (&z);
-LBL_Y:mp_clear (&y);
-LBL_X:mp_clear (&x);
-LBL_N:mp_clear (&n);
-LBL_B:mp_clear (&b);
-LBL_A:mp_clear (&a);
-LBL_V:mp_clear (&v);
-LBL_C:mp_clear (&c);
-  return res;
-}
-
-
-int
-main (void)
-{
-  mp_int  p, q;
-  char    buf[4096];
-  int     k, li;
-  clock_t t1;
-
-  srand (time (NULL));
-  load_tab();
-
-  printf ("Enter # of bits: \n");
-  fgets (buf, sizeof (buf), stdin);
-  sscanf (buf, "%d", &k);
-
-  printf ("Enter number of bases to try (1 to 8):\n");
-  fgets (buf, sizeof (buf), stdin);
-  sscanf (buf, "%d", &li);
-
-
-  mp_init (&p);
-  mp_init (&q);
-
-  t1 = clock ();
-  pprime (k, li, &p, &q);
-  t1 = clock () - t1;
-
-  printf ("\n\nTook %ld ticks, %d bits\n", t1, mp_count_bits (&p));
-
-  mp_toradix (&p, buf, 10);
-  printf ("P == %s\n", buf);
-  mp_toradix (&q, buf, 10);
-  printf ("Q == %s\n", buf);
-
-  return 0;
-}
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
diff --git a/libtommath/etc/prime.1024 b/libtommath/etc/prime.1024
deleted file mode 100644
index 5636e2d..0000000
--- a/libtommath/etc/prime.1024
+++ /dev/null
@@ -1,414 +0,0 @@
-Enter # of bits: 
-Enter number of bases to try (1 to 8):
-Certificate of primality for:
-36360080703173363
-
-A == 
-89963569
-
-B == 
-202082249
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-4851595597739856136987139
-
-A == 
-36360080703173363
-
-B == 
-66715963
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-19550639734462621430325731591027
-
-A == 
-4851595597739856136987139
-
-B == 
-2014867
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-10409036141344317165691858509923818734539
-
-A == 
-19550639734462621430325731591027
-
-B == 
-266207047
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-1049829549988285012736475602118094726647504414203
-
-A == 
-10409036141344317165691858509923818734539
-
-B == 
-50428759
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-77194737385528288387712399596835459931920358844586615003
-
-A == 
-1049829549988285012736475602118094726647504414203
-
-B == 
-36765367
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-35663756695365208574443215955488689578374232732893628896541201763
-
-A == 
-77194737385528288387712399596835459931920358844586615003
-
-B == 
-230998627
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-16711831463502165169495622246023119698415848120292671294127567620396469803
-
-A == 
-35663756695365208574443215955488689578374232732893628896541201763
-
-B == 
-234297127
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-6163534781560285962890718925972249753147470953579266394395432475622345597103528739
-
-A == 
-16711831463502165169495622246023119698415848120292671294127567620396469803
-
-B == 
-184406323
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-814258256205243497704094951432575867360065658372158511036259934640748088306764553488803787
-
-A == 
-6163534781560285962890718925972249753147470953579266394395432475622345597103528739
-
-B == 
-66054487
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-176469695533271657902814176811660357049007467856432383037590673407330246967781451723764079581998187
-
-A == 
-814258256205243497704094951432575867360065658372158511036259934640748088306764553488803787
-
-B == 
-108362239
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-44924492859445516541759485198544012102424796403707253610035148063863073596051272171194806669756971406400419
-
-A == 
-176469695533271657902814176811660357049007467856432383037590673407330246967781451723764079581998187
-
-B == 
-127286707
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-20600996927219343383225424320134474929609459588323857796871086845924186191561749519858600696159932468024710985371059
-
-A == 
-44924492859445516541759485198544012102424796403707253610035148063863073596051272171194806669756971406400419
-
-B == 
-229284691
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-6295696427695493110141186605837397185848992307978456138112526915330347715236378041486547994708748840844217371233735072572979
-
-A == 
-20600996927219343383225424320134474929609459588323857796871086845924186191561749519858600696159932468024710985371059
-
-B == 
-152800771
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-3104984078042317488749073016454213579257792635142218294052134804187631661145261015102617582090263808696699966840735333252107678792123
-
-A == 
-6295696427695493110141186605837397185848992307978456138112526915330347715236378041486547994708748840844217371233735072572979
-
-B == 
-246595759
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-26405175827665701256325699315126705508919255051121452292124404943796947287968603975320562847910946802396632302209435206627913466015741799499
-
-A == 
-3104984078042317488749073016454213579257792635142218294052134804187631661145261015102617582090263808696699966840735333252107678792123
-
-B == 
-4252063
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-11122146237908413610034600609460545703591095894418599759742741406628055069007082998134905595800236452010905900391505454890446585211975124558601770163
-
-A == 
-26405175827665701256325699315126705508919255051121452292124404943796947287968603975320562847910946802396632302209435206627913466015741799499
-
-B == 
-210605419
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-1649861642047798890580354082088712649911849362201343649289384923147797960364736011515757482030049342943790127685185806092659832129486307035500638595572396187
-
-A == 
-11122146237908413610034600609460545703591095894418599759742741406628055069007082998134905595800236452010905900391505454890446585211975124558601770163
-
-B == 
-74170111
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-857983367126266717607389719637086684134462613006415859877666235955788392464081914127715967940968197765042399904117392707518175220864852816390004264107201177394565363
-
-A == 
-1649861642047798890580354082088712649911849362201343649289384923147797960364736011515757482030049342943790127685185806092659832129486307035500638595572396187
-
-B == 
-260016763
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-175995909353623703257072120479340610010337144085688850745292031336724691277374210929188442230237711063783727092685448718515661641054886101716698390145283196296702450566161283
-
-A == 
-857983367126266717607389719637086684134462613006415859877666235955788392464081914127715967940968197765042399904117392707518175220864852816390004264107201177394565363
-
-B == 
-102563707
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-48486002551155667224487059713350447239190772068092630563272168418880661006593537218144160068395218642353495339720640699721703003648144463556291315694787862009052641640656933232794283
-
-A == 
-175995909353623703257072120479340610010337144085688850745292031336724691277374210929188442230237711063783727092685448718515661641054886101716698390145283196296702450566161283
-
-B == 
-137747527
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-13156468011529105025061495011938518171328604045212410096476697450506055664012861932372156505805788068791146986282263016790631108386790291275939575123375304599622623328517354163964228279867403
-
-A == 
-48486002551155667224487059713350447239190772068092630563272168418880661006593537218144160068395218642353495339720640699721703003648144463556291315694787862009052641640656933232794283
-
-B == 
-135672847
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-6355194692790533601105154341731997464407930009404822926832136060319955058388106456084549316415200519472481147942263916585428906582726749131479465958107142228236909665306781538860053107680830113869123
-
-A == 
-13156468011529105025061495011938518171328604045212410096476697450506055664012861932372156505805788068791146986282263016790631108386790291275939575123375304599622623328517354163964228279867403
-
-B == 
-241523587
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-3157116676535430302794438027544146642863331358530722860333745617571010460905857862561870488000265751138954271040017454405707755458702044884023184574412221802502351503929935224995314581932097706874819348858083
-
-A == 
-6355194692790533601105154341731997464407930009404822926832136060319955058388106456084549316415200519472481147942263916585428906582726749131479465958107142228236909665306781538860053107680830113869123
-
-B == 
-248388667
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-390533129219992506725320633489467713907837370444962163378727819939092929448752905310115311180032249230394348337568973177802874166228132778126338883671958897238722734394783244237133367055422297736215754829839364158067
-
-A == 
-3157116676535430302794438027544146642863331358530722860333745617571010460905857862561870488000265751138954271040017454405707755458702044884023184574412221802502351503929935224995314581932097706874819348858083
-
-B == 
-61849651
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-48583654555070224891047847050732516652910250240135992225139515777200432486685999462997073444468380434359929499498804723793106565291183220444221080449740542884172281158126259373095216435009661050109711341419005972852770440739
-
-A == 
-390533129219992506725320633489467713907837370444962163378727819939092929448752905310115311180032249230394348337568973177802874166228132778126338883671958897238722734394783244237133367055422297736215754829839364158067
-
-B == 
-62201707
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-25733035251905120039135866524384525138869748427727001128764704499071378939227862068500633813538831598776578372709963673670934388213622433800015759585470542686333039614931682098922935087822950084908715298627996115185849260703525317419
-
-A == 
-48583654555070224891047847050732516652910250240135992225139515777200432486685999462997073444468380434359929499498804723793106565291183220444221080449740542884172281158126259373095216435009661050109711341419005972852770440739
-
-B == 
-264832231
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-2804594464939948901906623499531073917980499195397462605359913717827014360538186518540781517129548650937632008683280555602633122170458773895504894807182664540529077836857897972175530148107545939211339044386106111633510166695386323426241809387
-
-A == 
-25733035251905120039135866524384525138869748427727001128764704499071378939227862068500633813538831598776578372709963673670934388213622433800015759585470542686333039614931682098922935087822950084908715298627996115185849260703525317419
-
-B == 
-54494047
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-738136612083433720096707308165797114449914259256979340471077690416567237592465306112484843530074782721390528773594351482384711900456440808251196845265132086486672447136822046628407467459921823150600138073268385534588238548865012638209515923513516547
-
-A == 
-2804594464939948901906623499531073917980499195397462605359913717827014360538186518540781517129548650937632008683280555602633122170458773895504894807182664540529077836857897972175530148107545939211339044386106111633510166695386323426241809387
-
-B == 
-131594179
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-392847529056126766528615419937165193421166694172790666626558750047057558168124866940509180171236517681470100877687445134633784815352076138790217228749332398026714192707447855731679485746120589851992221508292976900578299504461333767437280988393026452846013683
-
-A == 
-738136612083433720096707308165797114449914259256979340471077690416567237592465306112484843530074782721390528773594351482384711900456440808251196845265132086486672447136822046628407467459921823150600138073268385534588238548865012638209515923513516547
-
-B == 
-266107603
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-168459393231883505975876919268398655632763956627405508859662408056221544310200546265681845397346956580604208064328814319465940958080244889692368602591598503944015835190587740756859842792554282496742843600573336023639256008687581291233481455395123454655488735304365627
-
-A == 
-392847529056126766528615419937165193421166694172790666626558750047057558168124866940509180171236517681470100877687445134633784815352076138790217228749332398026714192707447855731679485746120589851992221508292976900578299504461333767437280988393026452846013683
-
-B == 
-214408111
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-14865774288636941404884923981945833072113667565310054952177860608355263252462409554658728941191929400198053290113492910272458441655458514080123870132092365833472436407455910185221474386718838138135065780840839893113912689594815485706154461164071775481134379794909690501684643
-
-A == 
-168459393231883505975876919268398655632763956627405508859662408056221544310200546265681845397346956580604208064328814319465940958080244889692368602591598503944015835190587740756859842792554282496742843600573336023639256008687581291233481455395123454655488735304365627
-
-B == 
-44122723
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-1213301773203241614897109856134894783021668292000023984098824423682568173639394290886185366993108292039068940333907505157813934962357206131450244004178619265868614859794316361031904412926604138893775068853175215502104744339658944443630407632290152772487455298652998368296998719996019
-
-A == 
-14865774288636941404884923981945833072113667565310054952177860608355263252462409554658728941191929400198053290113492910272458441655458514080123870132092365833472436407455910185221474386718838138135065780840839893113912689594815485706154461164071775481134379794909690501684643
-
-B == 
-40808563
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-186935245989515158127969129347464851990429060640910951266513740972248428651109062997368144722015290092846666943896556191257222521203647606911446635194198213436423080005867489516421559330500722264446765608763224572386410155413161172707802334865729654109050873820610813855041667633843601286843
-
-A == 
-1213301773203241614897109856134894783021668292000023984098824423682568173639394290886185366993108292039068940333907505157813934962357206131450244004178619265868614859794316361031904412926604138893775068853175215502104744339658944443630407632290152772487455298652998368296998719996019
-
-B == 
-77035759
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-83142661079751490510739960019112406284111408348732592580459037404394946037094409915127399165633756159385609671956087845517678367844901424617866988187132480585966721962585586730693443536100138246516868613250009028187662080828012497191775172228832247706080044971423654632146928165751885302331924491683
-
-A == 
-186935245989515158127969129347464851990429060640910951266513740972248428651109062997368144722015290092846666943896556191257222521203647606911446635194198213436423080005867489516421559330500722264446765608763224572386410155413161172707802334865729654109050873820610813855041667633843601286843
-
-B == 
-222383587
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-3892354773803809855317742245039794448230625839512638747643814927766738642436392673485997449586432241626440927010641564064764336402368634186618250134234189066179771240232458249806850838490410473462391401438160528157981942499581634732706904411807195259620779379274017704050790865030808501633772117217899534443
-
-A == 
-83142661079751490510739960019112406284111408348732592580459037404394946037094409915127399165633756159385609671956087845517678367844901424617866988187132480585966721962585586730693443536100138246516868613250009028187662080828012497191775172228832247706080044971423654632146928165751885302331924491683
-
-B == 
-23407687
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-1663606652988091811284014366560171522582683318514519379924950390627250155440313691226744227787921928894551755219495501365555370027257568506349958010457682898612082048959464465369892842603765280317696116552850664773291371490339084156052244256635115997453399761029567033971998617303988376172539172702246575225837054723
-
-A == 
-3892354773803809855317742245039794448230625839512638747643814927766738642436392673485997449586432241626440927010641564064764336402368634186618250134234189066179771240232458249806850838490410473462391401438160528157981942499581634732706904411807195259620779379274017704050790865030808501633772117217899534443
-
-B == 
-213701827
-
-G == 2
-----------------------------------------------------------------
-
-
-Took 33057 ticks, 1048 bits
-P == 1663606652988091811284014366560171522582683318514519379924950390627250155440313691226744227787921928894551755219495501365555370027257568506349958010457682898612082048959464465369892842603765280317696116552850664773291371490339084156052244256635115997453399761029567033971998617303988376172539172702246575225837054723
-Q == 3892354773803809855317742245039794448230625839512638747643814927766738642436392673485997449586432241626440927010641564064764336402368634186618250134234189066179771240232458249806850838490410473462391401438160528157981942499581634732706904411807195259620779379274017704050790865030808501633772117217899534443
diff --git a/libtommath/etc/prime.512 b/libtommath/etc/prime.512
deleted file mode 100644
index cb6ec30..0000000
--- a/libtommath/etc/prime.512
+++ /dev/null
@@ -1,205 +0,0 @@
-Enter # of bits: 
-Enter number of bases to try (1 to 8):
-Certificate of primality for:
-85933926807634727
-
-A == 
-253758023
-
-B == 
-169322581
-
-G == 5
-----------------------------------------------------------------
-Certificate of primality for:
-23930198825086241462113799
-
-A == 
-85933926807634727
-
-B == 
-139236037
-
-G == 11
-----------------------------------------------------------------
-Certificate of primality for:
-6401844647261612602378676572510019
-
-A == 
-23930198825086241462113799
-
-B == 
-133760791
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-269731366027728777712034888684015329354259
-
-A == 
-6401844647261612602378676572510019
-
-B == 
-21066691
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-37942338209025571690075025099189467992329684223707
-
-A == 
-269731366027728777712034888684015329354259
-
-B == 
-70333567
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-15306904714258982484473490774101705363308327436988160248323
-
-A == 
-37942338209025571690075025099189467992329684223707
-
-B == 
-201712723
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-1616744757018513392810355191503853040357155275733333124624513530099
-
-A == 
-15306904714258982484473490774101705363308327436988160248323
-
-B == 
-52810963
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-464222094814208047161771036072622485188658077940154689939306386289983787983
-
-A == 
-1616744757018513392810355191503853040357155275733333124624513530099
-
-B == 
-143566909
-
-G == 5
-----------------------------------------------------------------
-Certificate of primality for:
-187429931674053784626487560729643601208757374994177258429930699354770049369025096447
-
-A == 
-464222094814208047161771036072622485188658077940154689939306386289983787983
-
-B == 
-201875281
-
-G == 5
-----------------------------------------------------------------
-Certificate of primality for:
-100579220846502621074093727119851331775052664444339632682598589456666938521976625305832917563
-
-A == 
-187429931674053784626487560729643601208757374994177258429930699354770049369025096447
-
-B == 
-268311523
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-1173616081309758475197022137833792133815753368965945885089720153370737965497134878651384030219765163
-
-A == 
-100579220846502621074093727119851331775052664444339632682598589456666938521976625305832917563
-
-B == 
-5834287
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-191456913489905913185935197655672585713573070349044195411728114905691721186574907738081340754373032735283623
-
-A == 
-1173616081309758475197022137833792133815753368965945885089720153370737965497134878651384030219765163
-
-B == 
-81567097
-
-G == 5
-----------------------------------------------------------------
-Certificate of primality for:
-57856530489201750164178576399448868489243874083056587683743345599898489554401618943240901541005080049321706789987519
-
-A == 
-191456913489905913185935197655672585713573070349044195411728114905691721186574907738081340754373032735283623
-
-B == 
-151095433
-
-G == 7
-----------------------------------------------------------------
-Certificate of primality for:
-13790529750452576698109671710773784949185621244122040804792403407272729038377767162233653248852099545134831722512085881814803
-
-A == 
-57856530489201750164178576399448868489243874083056587683743345599898489554401618943240901541005080049321706789987519
-
-B == 
-119178679
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-7075985989000817742677547821106534174334812111605018857703825637170140040509067704269696198231266351631132464035671858077052876058979
-
-A == 
-13790529750452576698109671710773784949185621244122040804792403407272729038377767162233653248852099545134831722512085881814803
-
-B == 
-256552363
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-1227273006232588072907488910282307435921226646895131225407452056677899411162892829564455154080310937471747140942360789623819327234258162420463
-
-A == 
-7075985989000817742677547821106534174334812111605018857703825637170140040509067704269696198231266351631132464035671858077052876058979
-
-B == 
-86720989
-
-G == 5
-----------------------------------------------------------------
-Certificate of primality for:
-446764896913554613686067036908702877942872355053329937790398156069936255759889884246832779737114032666318220500106499161852193765380831330106375235763
-
-A == 
-1227273006232588072907488910282307435921226646895131225407452056677899411162892829564455154080310937471747140942360789623819327234258162420463
-
-B == 
-182015287
-
-G == 2
-----------------------------------------------------------------
-Certificate of primality for:
-5290203010849586596974953717018896543907195901082056939587768479377028575911127944611236020459652034082251335583308070846379514569838984811187823420951275243
-
-A == 
-446764896913554613686067036908702877942872355053329937790398156069936255759889884246832779737114032666318220500106499161852193765380831330106375235763
-
-B == 
-5920567
-
-G == 2
-----------------------------------------------------------------
-
-
-Took 3454 ticks, 521 bits
-P == 5290203010849586596974953717018896543907195901082056939587768479377028575911127944611236020459652034082251335583308070846379514569838984811187823420951275243
-Q == 446764896913554613686067036908702877942872355053329937790398156069936255759889884246832779737114032666318220500106499161852193765380831330106375235763
diff --git a/libtommath/etc/timer.asm b/libtommath/etc/timer.asm
deleted file mode 100644
index 326a947..0000000
--- a/libtommath/etc/timer.asm
+++ /dev/null
@@ -1,37 +0,0 @@
-; x86 timer in NASM
-;
-; Tom St Denis, tomstdenis@iahu.ca
-[bits 32]
-[section .data]
-time dd 0, 0
-
-[section .text]
-
-%ifdef USE_ELF
-[global t_start]
-t_start:
-%else
-[global _t_start]
-_t_start:
-%endif
-   push edx
-   push eax
-   rdtsc
-   mov [time+0],edx
-   mov [time+4],eax
-   pop eax
-   pop edx
-   ret
-   
-%ifdef USE_ELF
-[global t_read]
-t_read:
-%else
-[global _t_read]
-_t_read:
-%endif
-   rdtsc
-   sub eax,[time+4]
-   sbb edx,[time+0]
-   ret
-   
\ No newline at end of file
diff --git a/libtommath/etc/tune.c b/libtommath/etc/tune.c
deleted file mode 100644
index c2ac998..0000000
--- a/libtommath/etc/tune.c
+++ /dev/null
@@ -1,145 +0,0 @@
-/* Tune the Karatsuba parameters
- *
- * Tom St Denis, tomstdenis@gmail.com
- */
-#include <tommath.h>
-#include <time.h>
-
-/* how many times todo each size mult.  Depends on your computer.  For slow computers
- * this can be low like 5 or 10.  For fast [re: Athlon] should be 25 - 50 or so
- */
-#define TIMES (1UL<<14UL)
-
-#ifndef X86_TIMER
-
-/* RDTSC from Scott Duplichan */
-static ulong64 TIMFUNC (void)
-   {
-   #if defined __GNUC__
-      #if defined(__i386__) || defined(__x86_64__)
-        /* version from http://www.mcs.anl.gov/~kazutomo/rdtsc.html
-         * the old code always got a warning issued by gcc, clang did not complain...
-         */
-        unsigned hi, lo;
-        __asm__ __volatile__ ("rdtsc" : "=a"(lo), "=d"(hi));
-        return ((ulong64)lo)|( ((ulong64)hi)<<32);
-      #else /* gcc-IA64 version */
-         unsigned long result;
-         __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory");
-         while (__builtin_expect ((int) result == -1, 0))
-         __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory");
-         return result;
-      #endif
-
-   // Microsoft and Intel Windows compilers
-   #elif defined _M_IX86
-     __asm rdtsc
-   #elif defined _M_AMD64
-     return __rdtsc ();
-   #elif defined _M_IA64
-     #if defined __INTEL_COMPILER
-       #include <ia64intrin.h>
-     #endif
-      return __getReg (3116);
-   #else
-     #error need rdtsc function for this build
-   #endif
-   }
-
-
-/* generic ISO C timer */
-ulong64 LBL_T;
-void t_start(void) { LBL_T = TIMFUNC(); }
-ulong64 t_read(void) { return TIMFUNC() - LBL_T; }
-
-#else
-extern void t_start(void);
-extern ulong64 t_read(void);
-#endif
-
-ulong64 time_mult(int size, int s)
-{
-  unsigned long     x;
-  mp_int  a, b, c;
-  ulong64 t1;
-
-  mp_init (&a);
-  mp_init (&b);
-  mp_init (&c);
-
-  mp_rand (&a, size);
-  mp_rand (&b, size);
-
-  if (s == 1) {
-      KARATSUBA_MUL_CUTOFF = size;
-  } else {
-      KARATSUBA_MUL_CUTOFF = 100000;
-  }
-
-  t_start();
-  for (x = 0; x < TIMES; x++) {
-      mp_mul(&a,&b,&c);
-  }
-  t1 = t_read();
-  mp_clear (&a);
-  mp_clear (&b);
-  mp_clear (&c);
-  return t1;
-}
-
-ulong64 time_sqr(int size, int s)
-{
-  unsigned long     x;
-  mp_int  a, b;
-  ulong64 t1;
-
-  mp_init (&a);
-  mp_init (&b);
-
-  mp_rand (&a, size);
-
-  if (s == 1) {
-      KARATSUBA_SQR_CUTOFF = size;
-  } else {
-      KARATSUBA_SQR_CUTOFF = 100000;
-  }
-
-  t_start();
-  for (x = 0; x < TIMES; x++) {
-      mp_sqr(&a,&b);
-  }
-  t1 = t_read();
-  mp_clear (&a);
-  mp_clear (&b);
-  return t1;
-}
-
-int
-main (void)
-{
-  ulong64 t1, t2;
-  int x, y;
-
-  for (x = 8; ; x += 2) {
-     t1 = time_mult(x, 0);
-     t2 = time_mult(x, 1);
-     printf("%d: %9llu %9llu, %9llu\n", x, t1, t2, t2 - t1);
-     if (t2 < t1) break;
-  }
-  y = x;
-
-  for (x = 8; ; x += 2) {
-     t1 = time_sqr(x, 0);
-     t2 = time_sqr(x, 1);
-     printf("%d: %9llu %9llu, %9llu\n", x, t1, t2, t2 - t1);
-     if (t2 < t1) break;
-  }
-  printf("KARATSUBA_MUL_CUTOFF = %d\n", y);
-  printf("KARATSUBA_SQR_CUTOFF = %d\n", x);
-
-  return 0;
-}
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
diff --git a/libtommath/filter.pl b/libtommath/filter.pl
deleted file mode 100755
index a8a50c7..0000000
--- a/libtommath/filter.pl
+++ /dev/null
@@ -1,34 +0,0 @@
-#!/usr/bin/perl
-
-# we want to filter every between START_INS and END_INS out and then insert crap from another file (this is fun)
-
-$dst = shift;
-$ins = shift;
-
-open(SRC,"<$dst");
-open(INS,"<$ins");
-open(TMP,">tmp.delme");
-
-$l = 0;
-while (<SRC>) {
-   if ($_ =~ /START_INS/) {
-      print TMP $_;
-      $l = 1;
-      while (<INS>) {
-         print TMP $_;
-      }
-      close INS;
-   } elsif ($_ =~ /END_INS/) {
-      print TMP $_;
-      $l = 0;
-   } elsif ($l == 0) {
-      print TMP $_;
-   }
-}
-
-close TMP;
-close SRC;
-
-# $Source$
-# $Revision$
-# $Date$
diff --git a/libtommath/gen.pl b/libtommath/gen.pl
deleted file mode 100644
index 57f65ac..0000000
--- a/libtommath/gen.pl
+++ /dev/null
@@ -1,19 +0,0 @@
-#!/usr/bin/perl -w
-#
-# Generates a "single file" you can use to quickly
-# add the whole source without any makefile troubles
-#
-use strict;
-
-open( OUT, ">mpi.c" ) or die "Couldn't open mpi.c for writing: $!";
-foreach my $filename (glob "bn*.c") {
-   open( SRC, "<$filename" ) or die "Couldn't open $filename for reading: $!";
-   print OUT "/* Start: $filename */\n";
-   print OUT while <SRC>;
-   print OUT "\n/* End: $filename */\n\n";
-   close SRC or die "Error closing $filename after reading: $!";
-}
-print OUT "\n/* EOF */\n";
-close OUT or die "Error closing mpi.c after writing: $!";
-
-system('perl -pli -e "s/\s*$//" mpi.c');
diff --git a/libtommath/genlist.sh b/libtommath/genlist.sh
deleted file mode 100755
index 1f53b66..0000000
--- a/libtommath/genlist.sh
+++ /dev/null
@@ -1,8 +0,0 @@
-#!/bin/bash
-
-export a=`find . -maxdepth 1 -type f -name '*.c' | sort | sed -e 'sE\./EE' | sed -e 's/\.c/\.o/' | xargs`
-perl ./parsenames.pl OBJECTS "$a"
-
-# $Source$
-# $Revision$
-# $Date$
diff --git a/libtommath/libtommath.dsp b/libtommath/libtommath.dsp
deleted file mode 100644
index 71ac243..0000000
--- a/libtommath/libtommath.dsp
+++ /dev/null
@@ -1,572 +0,0 @@
-# Microsoft Developer Studio Project File - Name="libtommath" - Package Owner=<4>
-# Microsoft Developer Studio Generated Build File, Format Version 6.00
-# ** DO NOT EDIT **
-
-# TARGTYPE "Win32 (x86) Static Library" 0x0104
-
-CFG=libtommath - Win32 Debug
-!MESSAGE This is not a valid makefile. To build this project using NMAKE,
-!MESSAGE use the Export Makefile command and run
-!MESSAGE 
-!MESSAGE NMAKE /f "libtommath.mak".
-!MESSAGE 
-!MESSAGE You can specify a configuration when running NMAKE
-!MESSAGE by defining the macro CFG on the command line. For example:
-!MESSAGE 
-!MESSAGE NMAKE /f "libtommath.mak" CFG="libtommath - Win32 Debug"
-!MESSAGE 
-!MESSAGE Possible choices for configuration are:
-!MESSAGE 
-!MESSAGE "libtommath - Win32 Release" (based on "Win32 (x86) Static Library")
-!MESSAGE "libtommath - Win32 Debug" (based on "Win32 (x86) Static Library")
-!MESSAGE 
-
-# Begin Project
-# PROP AllowPerConfigDependencies 0
-# PROP Scc_ProjName "libtommath"
-# PROP Scc_LocalPath "."
-CPP=cl.exe
-RSC=rc.exe
-
-!IF  "$(CFG)" == "libtommath - Win32 Release"
-
-# PROP BASE Use_MFC 0
-# PROP BASE Use_Debug_Libraries 0
-# PROP BASE Output_Dir "Release"
-# PROP BASE Intermediate_Dir "Release"
-# PROP BASE Target_Dir ""
-# PROP Use_MFC 0
-# PROP Use_Debug_Libraries 0
-# PROP Output_Dir "Release"
-# PROP Intermediate_Dir "Release"
-# PROP Target_Dir ""
-# ADD BASE CPP /nologo /W3 /GX /O2 /D "WIN32" /D "NDEBUG" /D "_MBCS" /D "_LIB" /YX /FD /c
-# ADD CPP /nologo /W3 /GX /O2 /I "." /D "WIN32" /D "NDEBUG" /D "_MBCS" /D "_LIB" /YX /FD /c
-# ADD BASE RSC /l 0x409 /d "NDEBUG"
-# ADD RSC /l 0x409 /d "NDEBUG"
-BSC32=bscmake.exe
-# ADD BASE BSC32 /nologo
-# ADD BSC32 /nologo
-LIB32=link.exe -lib
-# ADD BASE LIB32 /nologo
-# ADD LIB32 /nologo /out:"Release\tommath.lib"
-
-!ELSEIF  "$(CFG)" == "libtommath - Win32 Debug"
-
-# PROP BASE Use_MFC 0
-# PROP BASE Use_Debug_Libraries 1
-# PROP BASE Output_Dir "Debug"
-# PROP BASE Intermediate_Dir "Debug"
-# PROP BASE Target_Dir ""
-# PROP Use_MFC 0
-# PROP Use_Debug_Libraries 1
-# PROP Output_Dir "Debug"
-# PROP Intermediate_Dir "Debug"
-# PROP Target_Dir ""
-# ADD BASE CPP /nologo /W3 /Gm /GX /ZI /Od /D "WIN32" /D "_DEBUG" /D "_MBCS" /D "_LIB" /YX /FD /GZ /c
-# ADD CPP /nologo /W3 /Gm /GX /ZI /Od /I "." /D "WIN32" /D "_DEBUG" /D "_MBCS" /D "_LIB" /YX /FD /GZ /c
-# ADD BASE RSC /l 0x409 /d "_DEBUG"
-# ADD RSC /l 0x409 /d "_DEBUG"
-BSC32=bscmake.exe
-# ADD BASE BSC32 /nologo
-# ADD BSC32 /nologo
-LIB32=link.exe -lib
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diff --git a/libtommath/logs/README b/libtommath/logs/README
deleted file mode 100644
index 965e7c8..0000000
--- a/libtommath/logs/README
+++ /dev/null
@@ -1,13 +0,0 @@
-To use the pretty graphs you have to first build/run the ltmtest from the root directory of the package.  
-Todo this type 
-
-make timing ; ltmtest
-
-in the root.  It will run for a while [about ten minutes on most PCs] and produce a series of .log files in logs/.
-
-After doing that run "gnuplot graphs.dem" to make the PNGs.  If you managed todo that all so far just open index.html to view
-them all :-)
-
-Have fun
-
-Tom
\ No newline at end of file
diff --git a/libtommath/logs/add.log b/libtommath/logs/add.log
deleted file mode 100644
index 43503ac..0000000
--- a/libtommath/logs/add.log
+++ /dev/null
@@ -1,16 +0,0 @@
-480        87
-960       111
-1440       135
-1920       159
-2400       200
-2880       224
-3360       248
-3840       272
-4320       296
-4800       320
-5280       344
-5760       368
-6240       392
-6720       416
-7200       440
-7680       464
diff --git a/libtommath/logs/addsub.png b/libtommath/logs/addsub.png
deleted file mode 100644
index a5679ac..0000000
Binary files a/libtommath/logs/addsub.png and /dev/null differ
diff --git a/libtommath/logs/expt.log b/libtommath/logs/expt.log
deleted file mode 100644
index 70932ab..0000000
--- a/libtommath/logs/expt.log
+++ /dev/null
@@ -1,7 +0,0 @@
-513   1435869
-769   3544970
-1025   7791638
-2049  46902238
-2561  85334899
-3073 141451412
-4097 308770310
diff --git a/libtommath/logs/expt.png b/libtommath/logs/expt.png
deleted file mode 100644
index 9ee8bb7..0000000
Binary files a/libtommath/logs/expt.png and /dev/null differ
diff --git a/libtommath/logs/expt_2k.log b/libtommath/logs/expt_2k.log
deleted file mode 100644
index 97d325f..0000000
--- a/libtommath/logs/expt_2k.log
+++ /dev/null
@@ -1,5 +0,0 @@
-607   2109225
-1279  10148314
-2203  34126877
-3217  82716424
-4253 161569606
diff --git a/libtommath/logs/expt_2kl.log b/libtommath/logs/expt_2kl.log
deleted file mode 100644
index d9ad4be..0000000
--- a/libtommath/logs/expt_2kl.log
+++ /dev/null
@@ -1,4 +0,0 @@
-1024   7705271
-2048  34286851
-4096 165207491
-521   1618631
diff --git a/libtommath/logs/expt_dr.log b/libtommath/logs/expt_dr.log
deleted file mode 100644
index c6bbe07..0000000
--- a/libtommath/logs/expt_dr.log
+++ /dev/null
@@ -1,7 +0,0 @@
-532   1928550
-784   3763908
-1036   7564221
-1540  16566059
-2072  32283784
-3080  79851565
-4116 157843530
diff --git a/libtommath/logs/graphs.dem b/libtommath/logs/graphs.dem
deleted file mode 100644
index dfaf613..0000000
--- a/libtommath/logs/graphs.dem
+++ /dev/null
@@ -1,17 +0,0 @@
-set terminal png
-set size 1.75
-set ylabel "Cycles per Operation"
-set xlabel "Operand size (bits)"
-
-set output "addsub.png"
-plot 'add.log' smooth bezier title "Addition", 'sub.log' smooth bezier title "Subtraction"
-
-set output "mult.png"
-plot 'sqr.log' smooth bezier title "Squaring (without Karatsuba)", 'sqr_kara.log' smooth bezier title "Squaring (Karatsuba)", 'mult.log' smooth bezier title "Multiplication (without Karatsuba)", 'mult_kara.log' smooth bezier title "Multiplication (Karatsuba)"
-
-set output "expt.png"
-plot 'expt.log' smooth bezier title "Exptmod (Montgomery)", 'expt_dr.log' smooth bezier title "Exptmod (Dimminished Radix)", 'expt_2k.log' smooth bezier title "Exptmod (2k Reduction)"
-
-set output "invmod.png"
-plot 'invmod.log' smooth bezier title "Modular Inverse"
-
diff --git a/libtommath/logs/index.html b/libtommath/logs/index.html
deleted file mode 100644
index 4b68c25..0000000
--- a/libtommath/logs/index.html
+++ /dev/null
@@ -1,27 +0,0 @@
-<html>
-<head>
-<title>LibTomMath Log Plots</title>
-</head>
-<body>
-
-<h1>Addition and Subtraction</h1>
-<center><img src=addsub.png></center>
-<hr>
-
-<h1>Multipliers</h1>
-<center><img src=mult.png></center>
-<hr>
-
-<h1>Exptmod</h1>
-<center><img src=expt.png></center>
-<hr>
-
-<h1>Modular Inverse</h1>
-<center><img src=invmod.png></center>
-<hr>
-
-</body>
-</html>
-/* $Source: /cvs/libtom/libtommath/logs/index.html,v $ */
-/* $Revision: 1.2 $ */
-/* $Date: 2005/05/05 14:38:47 $ */
diff --git a/libtommath/logs/invmod.log b/libtommath/logs/invmod.log
deleted file mode 100644
index e69de29..0000000
diff --git a/libtommath/logs/invmod.png b/libtommath/logs/invmod.png
deleted file mode 100644
index 0a8a4ad..0000000
Binary files a/libtommath/logs/invmod.png and /dev/null differ
diff --git a/libtommath/logs/mult.log b/libtommath/logs/mult.log
deleted file mode 100644
index 33563fc..0000000
--- a/libtommath/logs/mult.log
+++ /dev/null
@@ -1,84 +0,0 @@
-271       555
-390       855
-508      1161
-631      1605
-749      2117
-871      2687
-991      3329
-1108      4084
-1231      4786
-1351      5624
-1470      6392
-1586      7364
-1710      8218
-1830      9255
-1951     10217
-2067     11461
-2191     12463
-2308     13677
-2430     14800
-2551     16232
-2671     17460
-2791     18899
-2902     20247
-3028     21902
-3151     23240
-3267     24927
-3391     26441
-3511     28277
-3631     29838
-3749     31751
-3869     33673
-3989     35431
-4111     37518
-4231     39426
-4349     41504
-4471     43567
-4591     45786
-4711     47876
-4831     50299
-4951     52427
-5071     54785
-5189     57241
-5307     59730
-5431     62194
-5551     64761
-5670     67322
-5789     70073
-5907     72663
-6030     75437
-6151     78242
-6268     81202
-6389     83948
-6509     86985
-6631     89903
-6747     93184
-6869     96044
-6991     99286
-7109    102395
-7229    105917
-7351    108940
-7470    112490
-7589    115702
-7711    119508
-7831    122632
-7951    126410
-8071    129808
-8190    133895
-8311    137146
-8431    141218
-8549    144732
-8667    149131
-8790    152462
-8911    156754
-9030    160479
-9149    165138
-9271    168601
-9391    173185
-9511    176988
-9627    181976
-9751    185539
-9870    190388
-9991    194335
-10110    199605
-10228    203298
diff --git a/libtommath/logs/mult.png b/libtommath/logs/mult.png
deleted file mode 100644
index 4f7a4ee..0000000
Binary files a/libtommath/logs/mult.png and /dev/null differ
diff --git a/libtommath/logs/mult_kara.log b/libtommath/logs/mult_kara.log
deleted file mode 100644
index 7136c79..0000000
--- a/libtommath/logs/mult_kara.log
+++ /dev/null
@@ -1,84 +0,0 @@
-271       560
-391       870
-511      1159
-631      1605
-750      2111
-871      2737
-991      3361
-1111      4054
-1231      4778
-1351      5600
-1471      6404
-1591      7323
-1710      8255
-1831      9239
-1948     10257
-2070     11397
-2190     12531
-2308     13665
-2429     14870
-2550     16175
-2671     17539
-2787     18879
-2911     20350
-3031     21807
-3150     23415
-3270     24897
-3388     26567
-3511     28205
-3627     30076
-3751     31744
-3869     33657
-3991     35425
-4111     37522
-4229     39363
-4351     41503
-4470     43491
-4590     45827
-4711     47795
-4828     50166
-4951     52318
-5070     54911
-5191     57036
-5308     58237
-5431     60248
-5551     62678
-5671     64786
-5791     67294
-5908     69343
-6031     71607
-6151     74166
-6271     76590
-6391     78734
-6511     81175
-6631     83742
-6750     86403
-6868     88873
-6990     91150
-7110     94211
-7228     96922
-7351     99445
-7469    102216
-7589    104968
-7711    108113
-7827    110758
-7950    113714
-8071    116511
-8186    119643
-8310    122679
-8425    125581
-8551    128715
-8669    131778
-8788    135116
-8910    138138
-9031    141628
-9148    144754
-9268    148367
-9391    151551
-9511    155033
-9631    158652
-9751    162125
-9871    165248
-9988    168627
-10111    172427
-10231    176412
diff --git a/libtommath/logs/sqr.log b/libtommath/logs/sqr.log
deleted file mode 100644
index cd29fc5..0000000
--- a/libtommath/logs/sqr.log
+++ /dev/null
@@ -1,84 +0,0 @@
-265       562
-389       882
-509      1207
-631      1572
-750      1990
-859      2433
-991      2894
-1109      3555
-1230      4228
-1350      5018
-1471      5805
-1591      6579
-1709      7415
-1829      8329
-1949      9225
-2071     10139
-2188     11239
-2309     12178
-2431     13212
-2551     14294
-2671     15551
-2791     16512
-2911     17718
-3030     18876
-3150     20259
-3270     21374
-3391     22650
-3511     23948
-3631     25493
-3750     26756
-3870     28225
-3989     29705
-4110     31409
-4230     32834
-4351     34327
-4471     35818
-4591     37636
-4711     39228
-4830     40868
-4949     42393
-5070     44541
-5191     46269
-5310     48162
-5429     49728
-5548     51985
-5671     53948
-5791     55885
-5910     57584
-6031     60082
-6150     62239
-6270     64309
-6390     66014
-6511     68766
-6631     71012
-6750     73172
-6871     74952
-6991     77909
-7111     80371
-7231     82666
-7351     84531
-7469     87698
-7589     90318
-7711    225384
-7830    232428
-7950    240009
-8070    246522
-8190    253662
-8310    260961
-8431    269253
-8549    275743
-8671    283769
-8789    290811
-8911    300034
-9030    306873
-9149    315085
-9270    323944
-9390    332390
-9508    337519
-9631    348986
-9749    356904
-9871    367013
-9989    373831
-10108    381033
-10230    393475
diff --git a/libtommath/logs/sqr_kara.log b/libtommath/logs/sqr_kara.log
deleted file mode 100644
index 06355a7..0000000
--- a/libtommath/logs/sqr_kara.log
+++ /dev/null
@@ -1,84 +0,0 @@
-271       560
-388       878
-511      1179
-629      1625
-751      1988
-871      2423
-989      2896
-1111      3561
-1231      4209
-1350      5015
-1470      5804
-1591      6556
-1709      7420
-1831      8263
-1951      9173
-2070     10153
-2191     11229
-2310     12167
-2431     13211
-2550     14309
-2671     15524
-2788     16525
-2910     17712
-3028     18822
-3148     20220
-3271     21343
-3391     22652
-3511     23944
-3630     25485
-3750     26778
-3868     28201
-3990     29653
-4111     31393
-4225     32841
-4350     34328
-4471     35786
-4590     37652
-4711     39245
-4830     40876
-4951     42433
-5068     44547
-5191     46321
-5311     48140
-5430     49727
-5550     52034
-5671     53954
-5791     55921
-5908     57597
-6031     60084
-6148     62226
-6270     64295
-6390     66045
-6511     68779
-6629     71003
-6751     73169
-6871     74992
-6991     77895
-7110     80376
-7231     82628
-7351     84468
-7470     87664
-7591     90284
-7711     91352
-7828     93995
-7950     96276
-8071     98691
-8190    101256
-8308    103631
-8431    105222
-8550    108343
-8671    110281
-8787    112764
-8911    115397
-9031    117690
-9151    120266
-9271    122715
-9391    124624
-9510    127937
-9630    130313
-9750    132914
-9871    136129
-9991    138517
-10108    141525
-10231    144225
diff --git a/libtommath/logs/sub.log b/libtommath/logs/sub.log
deleted file mode 100644
index 9f84fa2..0000000
--- a/libtommath/logs/sub.log
+++ /dev/null
@@ -1,16 +0,0 @@
-480        94
-960       116
-1440       140
-1920       164
-2400       205
-2880       229
-3360       253
-3840       277
-4320       299
-4800       321
-5280       345
-5760       371
-6240       395
-6720       419
-7200       441
-7680       465
diff --git a/libtommath/makefile_include.mk b/libtommath/makefile_include.mk
new file mode 100644
index 0000000..3a599e8
--- /dev/null
+++ b/libtommath/makefile_include.mk
@@ -0,0 +1,117 @@
+#
+# Include makefile for libtommath
+#
+
+#version of library
+VERSION=1.0.1
+VERSION_PC=1.0.1
+VERSION_SO=1:1
+
+PLATFORM := $(shell uname | sed -e 's/_.*//')
+
+# default make target
+default: ${LIBNAME}
+
+# Compiler and Linker Names
+ifndef CROSS_COMPILE
+  CROSS_COMPILE=
+endif
+
+ifeq ($(CC),cc)
+  CC = $(CROSS_COMPILE)gcc
+endif
+LD=$(CROSS_COMPILE)ld
+AR=$(CROSS_COMPILE)ar
+RANLIB=$(CROSS_COMPILE)ranlib
+
+ifndef MAKE
+   MAKE=make
+endif
+
+CFLAGS += -I./ -Wall -Wsign-compare -Wextra -Wshadow
+
+ifndef NO_ADDTL_WARNINGS
+# additional warnings
+CFLAGS += -Wsystem-headers -Wdeclaration-after-statement -Wbad-function-cast -Wcast-align
+CFLAGS += -Wstrict-prototypes -Wpointer-arith
+endif
+
+ifdef COMPILE_DEBUG
+#debug
+CFLAGS += -g3
+else
+
+ifdef COMPILE_SIZE
+#for size
+CFLAGS += -Os
+else
+
+ifndef IGNORE_SPEED
+#for speed
+CFLAGS += -O3 -funroll-loops
+
+#x86 optimizations [should be valid for any GCC install though]
+CFLAGS  += -fomit-frame-pointer
+endif
+
+endif # COMPILE_SIZE
+endif # COMPILE_DEBUG
+
+ifneq ($(findstring clang,$(CC)),)
+CFLAGS += -Wno-typedef-redefinition -Wno-tautological-compare -Wno-builtin-requires-header
+endif
+ifeq ($(PLATFORM), Darwin)
+CFLAGS += -Wno-nullability-completeness
+endif
+
+# adjust coverage set
+ifneq ($(filter $(shell arch), i386 i686 x86_64 amd64 ia64),)
+   COVERAGE = test_standalone timing
+   COVERAGE_APP = ./test && ./ltmtest
+else
+   COVERAGE = test_standalone
+   COVERAGE_APP = ./test
+endif
+
+HEADERS_PUB=tommath.h tommath_class.h tommath_superclass.h
+HEADERS=tommath_private.h $(HEADERS_PUB)
+
+test_standalone: CFLAGS+=-DLTM_DEMO_TEST_VS_MTEST=0
+
+#LIBPATH  The directory for libtommath to be installed to.
+#INCPATH  The directory to install the header files for libtommath.
+#DATAPATH The directory to install the pdf docs.
+DESTDIR  ?=
+PREFIX   ?= /usr/local
+LIBPATH  ?= $(PREFIX)/lib
+INCPATH  ?= $(PREFIX)/include
+DATAPATH ?= $(PREFIX)/share/doc/libtommath/pdf
+
+#make the code coverage of the library
+#
+coverage: CFLAGS += -fprofile-arcs -ftest-coverage -DTIMING_NO_LOGS
+coverage: LFLAGS += -lgcov
+coverage: LDFLAGS += -lgcov
+
+coverage: $(COVERAGE)
+	$(COVERAGE_APP)
+
+lcov: coverage
+	rm -f coverage.info
+	lcov --capture --no-external --no-recursion $(LCOV_ARGS) --output-file coverage.info -q
+	genhtml coverage.info --output-directory coverage -q
+
+# target that removes all coverage output
+cleancov-clean:
+	rm -f `find . -type f -name "*.info" | xargs`
+	rm -rf coverage/
+
+# cleans everything - coverage output and standard 'clean'
+cleancov: cleancov-clean clean
+
+clean:
+	rm -f *.gcda *.gcno *.gcov *.bat *.o *.a *.obj *.lib *.exe *.dll etclib/*.o demo/demo.o test ltmtest mpitest mtest/mtest mtest/mtest.exe \
+        *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.da *.dyn *.dpi tommath.tex `find . -type f | grep [~] | xargs` *.lo *.la
+	rm -rf .libs/
+	${MAKE} -C etc/ clean MAKE=${MAKE}
+	${MAKE} -C doc/ clean MAKE=${MAKE}
diff --git a/libtommath/mess.sh b/libtommath/mess.sh
deleted file mode 100644
index bf639ce..0000000
--- a/libtommath/mess.sh
+++ /dev/null
@@ -1,4 +0,0 @@
-#!/bin/bash
-if cvs log $1 >/dev/null 2>/dev/null; then exit 0; else echo "$1 shouldn't be here" ; exit 1; fi
-
-
diff --git a/libtommath/mtest/logtab.h b/libtommath/mtest/logtab.h
deleted file mode 100644
index 751111e..0000000
--- a/libtommath/mtest/logtab.h
+++ /dev/null
@@ -1,24 +0,0 @@
-const float s_logv_2[] = {
-   0.000000000, 0.000000000, 1.000000000, 0.630929754, 	/*  0  1  2  3 */
-   0.500000000, 0.430676558, 0.386852807, 0.356207187, 	/*  4  5  6  7 */
-   0.333333333, 0.315464877, 0.301029996, 0.289064826, 	/*  8  9 10 11 */
-   0.278942946, 0.270238154, 0.262649535, 0.255958025, 	/* 12 13 14 15 */
-   0.250000000, 0.244650542, 0.239812467, 0.235408913, 	/* 16 17 18 19 */
-   0.231378213, 0.227670249, 0.224243824, 0.221064729, 	/* 20 21 22 23 */
-   0.218104292, 0.215338279, 0.212746054, 0.210309918, 	/* 24 25 26 27 */
-   0.208014598, 0.205846832, 0.203795047, 0.201849087, 	/* 28 29 30 31 */
-   0.200000000, 0.198239863, 0.196561632, 0.194959022, 	/* 32 33 34 35 */
-   0.193426404, 0.191958720, 0.190551412, 0.189200360, 	/* 36 37 38 39 */
-   0.187901825, 0.186652411, 0.185449023, 0.184288833, 	/* 40 41 42 43 */
-   0.183169251, 0.182087900, 0.181042597, 0.180031327, 	/* 44 45 46 47 */
-   0.179052232, 0.178103594, 0.177183820, 0.176291434, 	/* 48 49 50 51 */
-   0.175425064, 0.174583430, 0.173765343, 0.172969690, 	/* 52 53 54 55 */
-   0.172195434, 0.171441601, 0.170707280, 0.169991616, 	/* 56 57 58 59 */
-   0.169293808, 0.168613099, 0.167948779, 0.167300179, 	/* 60 61 62 63 */
-   0.166666667
-};
-
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
diff --git a/libtommath/mtest/mpi-config.h b/libtommath/mtest/mpi-config.h
deleted file mode 100644
index fc2a885..0000000
--- a/libtommath/mtest/mpi-config.h
+++ /dev/null
@@ -1,90 +0,0 @@
-/* Default configuration for MPI library */
-/* $Id$ */
-
-#ifndef MPI_CONFIG_H_
-#define MPI_CONFIG_H_
-
-/*
-  For boolean options, 
-  0 = no
-  1 = yes
-
-  Other options are documented individually.
-
- */
-
-#ifndef MP_IOFUNC
-#define MP_IOFUNC     0  /* include mp_print() ?                */
-#endif
-
-#ifndef MP_MODARITH
-#define MP_MODARITH   1  /* include modular arithmetic ?        */
-#endif
-
-#ifndef MP_NUMTH
-#define MP_NUMTH      1  /* include number theoretic functions? */
-#endif
-
-#ifndef MP_LOGTAB
-#define MP_LOGTAB     1  /* use table of logs instead of log()? */
-#endif
-
-#ifndef MP_MEMSET
-#define MP_MEMSET     1  /* use memset() to zero buffers?       */
-#endif
-
-#ifndef MP_MEMCPY
-#define MP_MEMCPY     1  /* use memcpy() to copy buffers?       */
-#endif
-
-#ifndef MP_CRYPTO
-#define MP_CRYPTO     1  /* erase memory on free?               */
-#endif
-
-#ifndef MP_ARGCHK
-/*
-  0 = no parameter checks
-  1 = runtime checks, continue execution and return an error to caller
-  2 = assertions; dump core on parameter errors
- */
-#define MP_ARGCHK     2  /* how to check input arguments        */
-#endif
-
-#ifndef MP_DEBUG
-#define MP_DEBUG      0  /* print diagnostic output?            */
-#endif
-
-#ifndef MP_DEFPREC
-#define MP_DEFPREC    64 /* default precision, in digits        */
-#endif
-
-#ifndef MP_MACRO
-#define MP_MACRO      1  /* use macros for frequent calls?      */
-#endif
-
-#ifndef MP_SQUARE
-#define MP_SQUARE     1  /* use separate squaring code?         */
-#endif
-
-#ifndef MP_PTAB_SIZE
-/*
-  When building mpprime.c, we build in a table of small prime
-  values to use for primality testing.  The more you include,
-  the more space they take up.  See primes.c for the possible
-  values (currently 16, 32, 64, 128, 256, and 6542)
- */
-#define MP_PTAB_SIZE  128  /* how many built-in primes?         */
-#endif
-
-#ifndef MP_COMPAT_MACROS
-#define MP_COMPAT_MACROS 1   /* define compatibility macros?    */
-#endif
-
-#endif /* ifndef MPI_CONFIG_H_ */
-
-
-/* crc==3287762869, version==2, Sat Feb 02 06:43:53 2002 */
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
diff --git a/libtommath/mtest/mpi-types.h b/libtommath/mtest/mpi-types.h
deleted file mode 100644
index f99d7ee..0000000
--- a/libtommath/mtest/mpi-types.h
+++ /dev/null
@@ -1,20 +0,0 @@
-/* Type definitions generated by 'types.pl' */
-typedef char               mp_sign;
-typedef unsigned short     mp_digit;  /* 2 byte type */
-typedef unsigned int       mp_word;   /* 4 byte type */
-typedef unsigned int       mp_size;
-typedef int                mp_err;
-
-#define MP_DIGIT_BIT       (CHAR_BIT*sizeof(mp_digit))
-#define MP_DIGIT_MAX       USHRT_MAX
-#define MP_WORD_BIT        (CHAR_BIT*sizeof(mp_word))
-#define MP_WORD_MAX        UINT_MAX
-
-#define MP_DIGIT_SIZE      2
-#define DIGIT_FMT          "%04X"
-#define RADIX              (MP_DIGIT_MAX+1)
-
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
diff --git a/libtommath/mtest/mpi.c b/libtommath/mtest/mpi.c
deleted file mode 100644
index 48dbe27..0000000
--- a/libtommath/mtest/mpi.c
+++ /dev/null
@@ -1,3985 +0,0 @@
-/*
-    mpi.c
-
-    by Michael J. Fromberger <sting@linguist.dartmouth.edu>
-    Copyright (C) 1998 Michael J. Fromberger, All Rights Reserved
-
-    Arbitrary precision integer arithmetic library
-
-    $Id$
- */
-
-#include "mpi.h"
-#include <stdlib.h>
-#include <string.h>
-#include <ctype.h>
-
-#if MP_DEBUG
-#include <stdio.h>
-
-#define DIAG(T,V) {fprintf(stderr,T);mp_print(V,stderr);fputc('\n',stderr);}
-#else
-#define DIAG(T,V)
-#endif
-
-/*
-   If MP_LOGTAB is not defined, use the math library to compute the
-   logarithms on the fly.  Otherwise, use the static table below.
-   Pick which works best for your system.
- */
-#if MP_LOGTAB
-
-/* {{{ s_logv_2[] - log table for 2 in various bases */
-
-/*
-  A table of the logs of 2 for various bases (the 0 and 1 entries of
-  this table are meaningless and should not be referenced).
-
-  This table is used to compute output lengths for the mp_toradix()
-  function.  Since a number n in radix r takes up about log_r(n)
-  digits, we estimate the output size by taking the least integer
-  greater than log_r(n), where:
-
-  log_r(n) = log_2(n) * log_r(2)
-
-  This table, therefore, is a table of log_r(2) for 2 <= r <= 36,
-  which are the output bases supported.
- */
-
-#include "logtab.h"
-
-/* }}} */
-#define LOG_V_2(R)  s_logv_2[(R)]
-
-#else
-
-#include <math.h>
-#define LOG_V_2(R)  (log(2.0)/log(R))
-
-#endif
-
-/* Default precision for newly created mp_int's      */
-static unsigned int s_mp_defprec = MP_DEFPREC;
-
-/* {{{ Digit arithmetic macros */
-
-/*
-  When adding and multiplying digits, the results can be larger than
-  can be contained in an mp_digit.  Thus, an mp_word is used.  These
-  macros mask off the upper and lower digits of the mp_word (the
-  mp_word may be more than 2 mp_digits wide, but we only concern
-  ourselves with the low-order 2 mp_digits)
-
-  If your mp_word DOES have more than 2 mp_digits, you need to
-  uncomment the first line, and comment out the second.
- */
-
-/* #define  CARRYOUT(W)  (((W)>>DIGIT_BIT)&MP_DIGIT_MAX) */
-#define  CARRYOUT(W)  ((W)>>DIGIT_BIT)
-#define  ACCUM(W)     ((W)&MP_DIGIT_MAX)
-
-/* }}} */
-
-/* {{{ Comparison constants */
-
-#define  MP_LT       -1
-#define  MP_EQ        0
-#define  MP_GT        1
-
-/* }}} */
-
-/* {{{ Constant strings */
-
-/* Constant strings returned by mp_strerror() */
-static const char *mp_err_string[] = {
-  "unknown result code",     /* say what?            */
-  "boolean true",            /* MP_OKAY, MP_YES      */
-  "boolean false",           /* MP_NO                */
-  "out of memory",           /* MP_MEM               */
-  "argument out of range",   /* MP_RANGE             */
-  "invalid input parameter", /* MP_BADARG            */
-  "result is undefined"      /* MP_UNDEF             */
-};
-
-/* Value to digit maps for radix conversion   */
-
-/* s_dmap_1 - standard digits and letters */
-static const char *s_dmap_1 =
-  "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
-
-#if 0
-/* s_dmap_2 - base64 ordering for digits  */
-static const char *s_dmap_2 =
-  "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
-#endif
-
-/* }}} */
-
-/* {{{ Static function declarations */
-
-/*
-   If MP_MACRO is false, these will be defined as actual functions;
-   otherwise, suitable macro definitions will be used.  This works
-   around the fact that ANSI C89 doesn't support an 'inline' keyword
-   (although I hear C9x will ... about bloody time).  At present, the
-   macro definitions are identical to the function bodies, but they'll
-   expand in place, instead of generating a function call.
-
-   I chose these particular functions to be made into macros because
-   some profiling showed they are called a lot on a typical workload,
-   and yet they are primarily housekeeping.
- */
-#if MP_MACRO == 0
- void     s_mp_setz(mp_digit *dp, mp_size count); /* zero digits           */
- void     s_mp_copy(mp_digit *sp, mp_digit *dp, mp_size count); /* copy    */
- void    *s_mp_alloc(size_t nb, size_t ni);       /* general allocator     */
- void     s_mp_free(void *ptr);                   /* general free function */
-#else
-
- /* Even if these are defined as macros, we need to respect the settings
-    of the MP_MEMSET and MP_MEMCPY configuration options...
-  */
- #if MP_MEMSET == 0
-  #define  s_mp_setz(dp, count) \
-       {int ix;for(ix=0;ix<(count);ix++)(dp)[ix]=0;}
- #else
-  #define  s_mp_setz(dp, count) memset(dp, 0, (count) * sizeof(mp_digit))
- #endif /* MP_MEMSET */
-
- #if MP_MEMCPY == 0
-  #define  s_mp_copy(sp, dp, count) \
-       {int ix;for(ix=0;ix<(count);ix++)(dp)[ix]=(sp)[ix];}
- #else
-  #define  s_mp_copy(sp, dp, count) memcpy(dp, sp, (count) * sizeof(mp_digit))
- #endif /* MP_MEMCPY */
-
- #define  s_mp_alloc(nb, ni)  calloc(nb, ni)
- #define  s_mp_free(ptr) {if(ptr) free(ptr);}
-#endif /* MP_MACRO */
-
-mp_err   s_mp_grow(mp_int *mp, mp_size min);   /* increase allocated size */
-mp_err   s_mp_pad(mp_int *mp, mp_size min);    /* left pad with zeroes    */
-
-void     s_mp_clamp(mp_int *mp);               /* clip leading zeroes     */
-
-void     s_mp_exch(mp_int *a, mp_int *b);      /* swap a and b in place   */
-
-mp_err   s_mp_lshd(mp_int *mp, mp_size p);     /* left-shift by p digits  */
-void     s_mp_rshd(mp_int *mp, mp_size p);     /* right-shift by p digits */
-void     s_mp_div_2d(mp_int *mp, mp_digit d);  /* divide by 2^d in place  */
-void     s_mp_mod_2d(mp_int *mp, mp_digit d);  /* modulo 2^d in place     */
-mp_err   s_mp_mul_2d(mp_int *mp, mp_digit d);  /* multiply by 2^d in place*/
-void     s_mp_div_2(mp_int *mp);               /* divide by 2 in place    */
-mp_err   s_mp_mul_2(mp_int *mp);               /* multiply by 2 in place  */
-mp_digit s_mp_norm(mp_int *a, mp_int *b);      /* normalize for division  */
-mp_err   s_mp_add_d(mp_int *mp, mp_digit d);   /* unsigned digit addition */
-mp_err   s_mp_sub_d(mp_int *mp, mp_digit d);   /* unsigned digit subtract */
-mp_err   s_mp_mul_d(mp_int *mp, mp_digit d);   /* unsigned digit multiply */
-mp_err   s_mp_div_d(mp_int *mp, mp_digit d, mp_digit *r);
-		                               /* unsigned digit divide   */
-mp_err   s_mp_reduce(mp_int *x, mp_int *m, mp_int *mu);
-                                               /* Barrett reduction       */
-mp_err   s_mp_add(mp_int *a, mp_int *b);       /* magnitude addition      */
-mp_err   s_mp_sub(mp_int *a, mp_int *b);       /* magnitude subtract      */
-mp_err   s_mp_mul(mp_int *a, mp_int *b);       /* magnitude multiply      */
-#if 0
-void     s_mp_kmul(mp_digit *a, mp_digit *b, mp_digit *out, mp_size len);
-                                               /* multiply buffers in place */
-#endif
-#if MP_SQUARE
-mp_err   s_mp_sqr(mp_int *a);                  /* magnitude square        */
-#else
-#define  s_mp_sqr(a) s_mp_mul(a, a)
-#endif
-mp_err   s_mp_div(mp_int *a, mp_int *b);       /* magnitude divide        */
-mp_err   s_mp_2expt(mp_int *a, mp_digit k);    /* a = 2^k                 */
-int      s_mp_cmp(mp_int *a, mp_int *b);       /* magnitude comparison    */
-int      s_mp_cmp_d(mp_int *a, mp_digit d);    /* magnitude digit compare */
-int      s_mp_ispow2(mp_int *v);               /* is v a power of 2?      */
-int      s_mp_ispow2d(mp_digit d);             /* is d a power of 2?      */
-
-int      s_mp_tovalue(char ch, int r);          /* convert ch to value    */
-char     s_mp_todigit(int val, int r, int low); /* convert val to digit   */
-int      s_mp_outlen(int bits, int r);          /* output length in bytes */
-
-/* }}} */
-
-/* {{{ Default precision manipulation */
-
-unsigned int mp_get_prec(void)
-{
-  return s_mp_defprec;
-
-} /* end mp_get_prec() */
-
-void         mp_set_prec(unsigned int prec)
-{
-  if(prec == 0)
-    s_mp_defprec = MP_DEFPREC;
-  else
-    s_mp_defprec = prec;
-
-} /* end mp_set_prec() */
-
-/* }}} */
-
-/*------------------------------------------------------------------------*/
-/* {{{ mp_init(mp) */
-
-/*
-  mp_init(mp)
-
-  Initialize a new zero-valued mp_int.  Returns MP_OKAY if successful,
-  MP_MEM if memory could not be allocated for the structure.
- */
-
-mp_err mp_init(mp_int *mp)
-{
-  return mp_init_size(mp, s_mp_defprec);
-
-} /* end mp_init() */
-
-/* }}} */
-
-/* {{{ mp_init_array(mp[], count) */
-
-mp_err mp_init_array(mp_int mp[], int count)
-{
-  mp_err  res;
-  int     pos;
-
-  ARGCHK(mp !=NULL && count > 0, MP_BADARG);
-
-  for(pos = 0; pos < count; ++pos) {
-    if((res = mp_init(&mp[pos])) != MP_OKAY)
-      goto CLEANUP;
-  }
-
-  return MP_OKAY;
-
- CLEANUP:
-  while(--pos >= 0)
-    mp_clear(&mp[pos]);
-
-  return res;
-
-} /* end mp_init_array() */
-
-/* }}} */
-
-/* {{{ mp_init_size(mp, prec) */
-
-/*
-  mp_init_size(mp, prec)
-
-  Initialize a new zero-valued mp_int with at least the given
-  precision; returns MP_OKAY if successful, or MP_MEM if memory could
-  not be allocated for the structure.
- */
-
-mp_err mp_init_size(mp_int *mp, mp_size prec)
-{
-  ARGCHK(mp != NULL && prec > 0, MP_BADARG);
-
-  if((DIGITS(mp) = s_mp_alloc(prec, sizeof(mp_digit))) == NULL)
-    return MP_MEM;
-
-  SIGN(mp) = MP_ZPOS;
-  USED(mp) = 1;
-  ALLOC(mp) = prec;
-
-  return MP_OKAY;
-
-} /* end mp_init_size() */
-
-/* }}} */
-
-/* {{{ mp_init_copy(mp, from) */
-
-/*
-  mp_init_copy(mp, from)
-
-  Initialize mp as an exact copy of from.  Returns MP_OKAY if
-  successful, MP_MEM if memory could not be allocated for the new
-  structure.
- */
-
-mp_err mp_init_copy(mp_int *mp, mp_int *from)
-{
-  ARGCHK(mp != NULL && from != NULL, MP_BADARG);
-
-  if(mp == from)
-    return MP_OKAY;
-
-  if((DIGITS(mp) = s_mp_alloc(USED(from), sizeof(mp_digit))) == NULL)
-    return MP_MEM;
-
-  s_mp_copy(DIGITS(from), DIGITS(mp), USED(from));
-  USED(mp) = USED(from);
-  ALLOC(mp) = USED(from);
-  SIGN(mp) = SIGN(from);
-
-  return MP_OKAY;
-
-} /* end mp_init_copy() */
-
-/* }}} */
-
-/* {{{ mp_copy(from, to) */
-
-/*
-  mp_copy(from, to)
-
-  Copies the mp_int 'from' to the mp_int 'to'.  It is presumed that
-  'to' has already been initialized (if not, use mp_init_copy()
-  instead). If 'from' and 'to' are identical, nothing happens.
- */
-
-mp_err mp_copy(mp_int *from, mp_int *to)
-{
-  ARGCHK(from != NULL && to != NULL, MP_BADARG);
-
-  if(from == to)
-    return MP_OKAY;
-
-  { /* copy */
-    mp_digit   *tmp;
-
-    /*
-      If the allocated buffer in 'to' already has enough space to hold
-      all the used digits of 'from', we'll re-use it to avoid hitting
-      the memory allocater more than necessary; otherwise, we'd have
-      to grow anyway, so we just allocate a hunk and make the copy as
-      usual
-     */
-    if(ALLOC(to) >= USED(from)) {
-      s_mp_setz(DIGITS(to) + USED(from), ALLOC(to) - USED(from));
-      s_mp_copy(DIGITS(from), DIGITS(to), USED(from));
-
-    } else {
-      if((tmp = s_mp_alloc(USED(from), sizeof(mp_digit))) == NULL)
-	return MP_MEM;
-
-      s_mp_copy(DIGITS(from), tmp, USED(from));
-
-      if(DIGITS(to) != NULL) {
-#if MP_CRYPTO
-	s_mp_setz(DIGITS(to), ALLOC(to));
-#endif
-	s_mp_free(DIGITS(to));
-      }
-
-      DIGITS(to) = tmp;
-      ALLOC(to) = USED(from);
-    }
-
-    /* Copy the precision and sign from the original */
-    USED(to) = USED(from);
-    SIGN(to) = SIGN(from);
-  } /* end copy */
-
-  return MP_OKAY;
-
-} /* end mp_copy() */
-
-/* }}} */
-
-/* {{{ mp_exch(mp1, mp2) */
-
-/*
-  mp_exch(mp1, mp2)
-
-  Exchange mp1 and mp2 without allocating any intermediate memory
-  (well, unless you count the stack space needed for this call and the
-  locals it creates...).  This cannot fail.
- */
-
-void mp_exch(mp_int *mp1, mp_int *mp2)
-{
-#if MP_ARGCHK == 2
-  assert(mp1 != NULL && mp2 != NULL);
-#else
-  if(mp1 == NULL || mp2 == NULL)
-    return;
-#endif
-
-  s_mp_exch(mp1, mp2);
-
-} /* end mp_exch() */
-
-/* }}} */
-
-/* {{{ mp_clear(mp) */
-
-/*
-  mp_clear(mp)
-
-  Release the storage used by an mp_int, and void its fields so that
-  if someone calls mp_clear() again for the same int later, we won't
-  get tollchocked.
- */
-
-void   mp_clear(mp_int *mp)
-{
-  if(mp == NULL)
-    return;
-
-  if(DIGITS(mp) != NULL) {
-#if MP_CRYPTO
-    s_mp_setz(DIGITS(mp), ALLOC(mp));
-#endif
-    s_mp_free(DIGITS(mp));
-    DIGITS(mp) = NULL;
-  }
-
-  USED(mp) = 0;
-  ALLOC(mp) = 0;
-
-} /* end mp_clear() */
-
-/* }}} */
-
-/* {{{ mp_clear_array(mp[], count) */
-
-void   mp_clear_array(mp_int mp[], int count)
-{
-  ARGCHK(mp != NULL && count > 0, MP_BADARG);
-
-  while(--count >= 0)
-    mp_clear(&mp[count]);
-
-} /* end mp_clear_array() */
-
-/* }}} */
-
-/* {{{ mp_zero(mp) */
-
-/*
-  mp_zero(mp)
-
-  Set mp to zero.  Does not change the allocated size of the structure,
-  and therefore cannot fail (except on a bad argument, which we ignore)
- */
-void   mp_zero(mp_int *mp)
-{
-  if(mp == NULL)
-    return;
-
-  s_mp_setz(DIGITS(mp), ALLOC(mp));
-  USED(mp) = 1;
-  SIGN(mp) = MP_ZPOS;
-
-} /* end mp_zero() */
-
-/* }}} */
-
-/* {{{ mp_set(mp, d) */
-
-void   mp_set(mp_int *mp, mp_digit d)
-{
-  if(mp == NULL)
-    return;
-
-  mp_zero(mp);
-  DIGIT(mp, 0) = d;
-
-} /* end mp_set() */
-
-/* }}} */
-
-/* {{{ mp_set_int(mp, z) */
-
-mp_err mp_set_int(mp_int *mp, long z)
-{
-  int            ix;
-  unsigned long  v = abs(z);
-  mp_err         res;
-
-  ARGCHK(mp != NULL, MP_BADARG);
-
-  mp_zero(mp);
-  if(z == 0)
-    return MP_OKAY;  /* shortcut for zero */
-
-  for(ix = sizeof(long) - 1; ix >= 0; ix--) {
-
-    if((res = s_mp_mul_2d(mp, CHAR_BIT)) != MP_OKAY)
-      return res;
-
-    res = s_mp_add_d(mp,
-		     (mp_digit)((v >> (ix * CHAR_BIT)) & UCHAR_MAX));
-    if(res != MP_OKAY)
-      return res;
-
-  }
-
-  if(z < 0)
-    SIGN(mp) = MP_NEG;
-
-  return MP_OKAY;
-
-} /* end mp_set_int() */
-
-/* }}} */
-
-/*------------------------------------------------------------------------*/
-/* {{{ Digit arithmetic */
-
-/* {{{ mp_add_d(a, d, b) */
-
-/*
-  mp_add_d(a, d, b)
-
-  Compute the sum b = a + d, for a single digit d.  Respects the sign of
-  its primary addend (single digits are unsigned anyway).
- */
-
-mp_err mp_add_d(mp_int *a, mp_digit d, mp_int *b)
-{
-  mp_err   res = MP_OKAY;
-
-  ARGCHK(a != NULL && b != NULL, MP_BADARG);
-
-  if((res = mp_copy(a, b)) != MP_OKAY)
-    return res;
-
-  if(SIGN(b) == MP_ZPOS) {
-    res = s_mp_add_d(b, d);
-  } else if(s_mp_cmp_d(b, d) >= 0) {
-    res = s_mp_sub_d(b, d);
-  } else {
-    SIGN(b) = MP_ZPOS;
-
-    DIGIT(b, 0) = d - DIGIT(b, 0);
-  }
-
-  return res;
-
-} /* end mp_add_d() */
-
-/* }}} */
-
-/* {{{ mp_sub_d(a, d, b) */
-
-/*
-  mp_sub_d(a, d, b)
-
-  Compute the difference b = a - d, for a single digit d.  Respects the
-  sign of its subtrahend (single digits are unsigned anyway).
- */
-
-mp_err mp_sub_d(mp_int *a, mp_digit d, mp_int *b)
-{
-  mp_err   res;
-
-  ARGCHK(a != NULL && b != NULL, MP_BADARG);
-
-  if((res = mp_copy(a, b)) != MP_OKAY)
-    return res;
-
-  if(SIGN(b) == MP_NEG) {
-    if((res = s_mp_add_d(b, d)) != MP_OKAY)
-      return res;
-
-  } else if(s_mp_cmp_d(b, d) >= 0) {
-    if((res = s_mp_sub_d(b, d)) != MP_OKAY)
-      return res;
-
-  } else {
-    mp_neg(b, b);
-
-    DIGIT(b, 0) = d - DIGIT(b, 0);
-    SIGN(b) = MP_NEG;
-  }
-
-  if(s_mp_cmp_d(b, 0) == 0)
-    SIGN(b) = MP_ZPOS;
-
-  return MP_OKAY;
-
-} /* end mp_sub_d() */
-
-/* }}} */
-
-/* {{{ mp_mul_d(a, d, b) */
-
-/*
-  mp_mul_d(a, d, b)
-
-  Compute the product b = a * d, for a single digit d.  Respects the sign
-  of its multiplicand (single digits are unsigned anyway)
- */
-
-mp_err mp_mul_d(mp_int *a, mp_digit d, mp_int *b)
-{
-  mp_err  res;
-
-  ARGCHK(a != NULL && b != NULL, MP_BADARG);
-
-  if(d == 0) {
-    mp_zero(b);
-    return MP_OKAY;
-  }
-
-  if((res = mp_copy(a, b)) != MP_OKAY)
-    return res;
-
-  res = s_mp_mul_d(b, d);
-
-  return res;
-
-} /* end mp_mul_d() */
-
-/* }}} */
-
-/* {{{ mp_mul_2(a, c) */
-
-mp_err mp_mul_2(mp_int *a, mp_int *c)
-{
-  mp_err  res;
-
-  ARGCHK(a != NULL && c != NULL, MP_BADARG);
-
-  if((res = mp_copy(a, c)) != MP_OKAY)
-    return res;
-
-  return s_mp_mul_2(c);
-
-} /* end mp_mul_2() */
-
-/* }}} */
-
-/* {{{ mp_div_d(a, d, q, r) */
-
-/*
-  mp_div_d(a, d, q, r)
-
-  Compute the quotient q = a / d and remainder r = a mod d, for a
-  single digit d.  Respects the sign of its divisor (single digits are
-  unsigned anyway).
- */
-
-mp_err mp_div_d(mp_int *a, mp_digit d, mp_int *q, mp_digit *r)
-{
-  mp_err   res;
-  mp_digit rem;
-  int      pow;
-
-  ARGCHK(a != NULL, MP_BADARG);
-
-  if(d == 0)
-    return MP_RANGE;
-
-  /* Shortcut for powers of two ... */
-  if((pow = s_mp_ispow2d(d)) >= 0) {
-    mp_digit  mask;
-
-    mask = (1 << pow) - 1;
-    rem = DIGIT(a, 0) & mask;
-
-    if(q) {
-      mp_copy(a, q);
-      s_mp_div_2d(q, pow);
-    }
-
-    if(r)
-      *r = rem;
-
-    return MP_OKAY;
-  }
-
-  /*
-    If the quotient is actually going to be returned, we'll try to
-    avoid hitting the memory allocator by copying the dividend into it
-    and doing the division there.  This can't be any _worse_ than
-    always copying, and will sometimes be better (since it won't make
-    another copy)
-
-    If it's not going to be returned, we need to allocate a temporary
-    to hold the quotient, which will just be discarded.
-   */
-  if(q) {
-    if((res = mp_copy(a, q)) != MP_OKAY)
-      return res;
-
-    res = s_mp_div_d(q, d, &rem);
-    if(s_mp_cmp_d(q, 0) == MP_EQ)
-      SIGN(q) = MP_ZPOS;
-
-  } else {
-    mp_int  qp;
-
-    if((res = mp_init_copy(&qp, a)) != MP_OKAY)
-      return res;
-
-    res = s_mp_div_d(&qp, d, &rem);
-    if(s_mp_cmp_d(&qp, 0) == 0)
-      SIGN(&qp) = MP_ZPOS;
-
-    mp_clear(&qp);
-  }
-
-  if(r)
-    *r = rem;
-
-  return res;
-
-} /* end mp_div_d() */
-
-/* }}} */
-
-/* {{{ mp_div_2(a, c) */
-
-/*
-  mp_div_2(a, c)
-
-  Compute c = a / 2, disregarding the remainder.
- */
-
-mp_err mp_div_2(mp_int *a, mp_int *c)
-{
-  mp_err  res;
-
-  ARGCHK(a != NULL && c != NULL, MP_BADARG);
-
-  if((res = mp_copy(a, c)) != MP_OKAY)
-    return res;
-
-  s_mp_div_2(c);
-
-  return MP_OKAY;
-
-} /* end mp_div_2() */
-
-/* }}} */
-
-/* {{{ mp_expt_d(a, d, b) */
-
-mp_err mp_expt_d(mp_int *a, mp_digit d, mp_int *c)
-{
-  mp_int   s, x;
-  mp_err   res;
-
-  ARGCHK(a != NULL && c != NULL, MP_BADARG);
-
-  if((res = mp_init(&s)) != MP_OKAY)
-    return res;
-  if((res = mp_init_copy(&x, a)) != MP_OKAY)
-    goto X;
-
-  DIGIT(&s, 0) = 1;
-
-  while(d != 0) {
-    if(d & 1) {
-      if((res = s_mp_mul(&s, &x)) != MP_OKAY)
-	goto CLEANUP;
-    }
-
-    d >>= 1;
-
-    if((res = s_mp_sqr(&x)) != MP_OKAY)
-      goto CLEANUP;
-  }
-
-  s_mp_exch(&s, c);
-
-CLEANUP:
-  mp_clear(&x);
-X:
-  mp_clear(&s);
-
-  return res;
-
-} /* end mp_expt_d() */
-
-/* }}} */
-
-/* }}} */
-
-/*------------------------------------------------------------------------*/
-/* {{{ Full arithmetic */
-
-/* {{{ mp_abs(a, b) */
-
-/*
-  mp_abs(a, b)
-
-  Compute b = |a|.  'a' and 'b' may be identical.
- */
-
-mp_err mp_abs(mp_int *a, mp_int *b)
-{
-  mp_err   res;
-
-  ARGCHK(a != NULL && b != NULL, MP_BADARG);
-
-  if((res = mp_copy(a, b)) != MP_OKAY)
-    return res;
-
-  SIGN(b) = MP_ZPOS;
-
-  return MP_OKAY;
-
-} /* end mp_abs() */
-
-/* }}} */
-
-/* {{{ mp_neg(a, b) */
-
-/*
-  mp_neg(a, b)
-
-  Compute b = -a.  'a' and 'b' may be identical.
- */
-
-mp_err mp_neg(mp_int *a, mp_int *b)
-{
-  mp_err   res;
-
-  ARGCHK(a != NULL && b != NULL, MP_BADARG);
-
-  if((res = mp_copy(a, b)) != MP_OKAY)
-    return res;
-
-  if(s_mp_cmp_d(b, 0) == MP_EQ)
-    SIGN(b) = MP_ZPOS;
-  else
-    SIGN(b) = (SIGN(b) == MP_NEG) ? MP_ZPOS : MP_NEG;
-
-  return MP_OKAY;
-
-} /* end mp_neg() */
-
-/* }}} */
-
-/* {{{ mp_add(a, b, c) */
-
-/*
-  mp_add(a, b, c)
-
-  Compute c = a + b.  All parameters may be identical.
- */
-
-mp_err mp_add(mp_int *a, mp_int *b, mp_int *c)
-{
-  mp_err  res;
-  int     cmp;
-
-  ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
-
-  if(SIGN(a) == SIGN(b)) { /* same sign:  add values, keep sign */
-
-    /* Commutativity of addition lets us do this in either order,
-       so we avoid having to use a temporary even if the result
-       is supposed to replace the output
-     */
-    if(c == b) {
-      if((res = s_mp_add(c, a)) != MP_OKAY)
-	return res;
-    } else {
-      if(c != a && (res = mp_copy(a, c)) != MP_OKAY)
-	return res;
-
-      if((res = s_mp_add(c, b)) != MP_OKAY)
-	return res;
-    }
-
-  } else if((cmp = s_mp_cmp(a, b)) > 0) {  /* different sign: a > b   */
-
-    /* If the output is going to be clobbered, we will use a temporary
-       variable; otherwise, we'll do it without touching the memory
-       allocator at all, if possible
-     */
-    if(c == b) {
-      mp_int  tmp;
-
-      if((res = mp_init_copy(&tmp, a)) != MP_OKAY)
-	return res;
-      if((res = s_mp_sub(&tmp, b)) != MP_OKAY) {
-	mp_clear(&tmp);
-	return res;
-      }
-
-      s_mp_exch(&tmp, c);
-      mp_clear(&tmp);
-
-    } else {
-
-      if(c != a && (res = mp_copy(a, c)) != MP_OKAY)
-	return res;
-      if((res = s_mp_sub(c, b)) != MP_OKAY)
-	return res;
-
-    }
-
-  } else if(cmp == 0) {             /* different sign, a == b   */
-
-    mp_zero(c);
-    return MP_OKAY;
-
-  } else {                          /* different sign: a < b    */
-
-    /* See above... */
-    if(c == a) {
-      mp_int  tmp;
-
-      if((res = mp_init_copy(&tmp, b)) != MP_OKAY)
-	return res;
-      if((res = s_mp_sub(&tmp, a)) != MP_OKAY) {
-	mp_clear(&tmp);
-	return res;
-      }
-
-      s_mp_exch(&tmp, c);
-      mp_clear(&tmp);
-
-    } else {
-
-      if(c != b && (res = mp_copy(b, c)) != MP_OKAY)
-	return res;
-      if((res = s_mp_sub(c, a)) != MP_OKAY)
-	return res;
-
-    }
-  }
-
-  if(USED(c) == 1 && DIGIT(c, 0) == 0)
-    SIGN(c) = MP_ZPOS;
-
-  return MP_OKAY;
-
-} /* end mp_add() */
-
-/* }}} */
-
-/* {{{ mp_sub(a, b, c) */
-
-/*
-  mp_sub(a, b, c)
-
-  Compute c = a - b.  All parameters may be identical.
- */
-
-mp_err mp_sub(mp_int *a, mp_int *b, mp_int *c)
-{
-  mp_err  res;
-  int     cmp;
-
-  ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
-
-  if(SIGN(a) != SIGN(b)) {
-    if(c == a) {
-      if((res = s_mp_add(c, b)) != MP_OKAY)
-	return res;
-    } else {
-      if(c != b && ((res = mp_copy(b, c)) != MP_OKAY))
-	return res;
-      if((res = s_mp_add(c, a)) != MP_OKAY)
-	return res;
-      SIGN(c) = SIGN(a);
-    }
-
-  } else if((cmp = s_mp_cmp(a, b)) > 0) { /* Same sign, a > b */
-    if(c == b) {
-      mp_int  tmp;
-
-      if((res = mp_init_copy(&tmp, a)) != MP_OKAY)
-	return res;
-      if((res = s_mp_sub(&tmp, b)) != MP_OKAY) {
-	mp_clear(&tmp);
-	return res;
-      }
-      s_mp_exch(&tmp, c);
-      mp_clear(&tmp);
-
-    } else {
-      if(c != a && ((res = mp_copy(a, c)) != MP_OKAY))
-	return res;
-
-      if((res = s_mp_sub(c, b)) != MP_OKAY)
-	return res;
-    }
-
-  } else if(cmp == 0) {  /* Same sign, equal magnitude */
-    mp_zero(c);
-    return MP_OKAY;
-
-  } else {               /* Same sign, b > a */
-    if(c == a) {
-      mp_int  tmp;
-
-      if((res = mp_init_copy(&tmp, b)) != MP_OKAY)
-	return res;
-
-      if((res = s_mp_sub(&tmp, a)) != MP_OKAY) {
-	mp_clear(&tmp);
-	return res;
-      }
-      s_mp_exch(&tmp, c);
-      mp_clear(&tmp);
-
-    } else {
-      if(c != b && ((res = mp_copy(b, c)) != MP_OKAY))
-	return res;
-
-      if((res = s_mp_sub(c, a)) != MP_OKAY)
-	return res;
-    }
-
-    SIGN(c) = !SIGN(b);
-  }
-
-  if(USED(c) == 1 && DIGIT(c, 0) == 0)
-    SIGN(c) = MP_ZPOS;
-
-  return MP_OKAY;
-
-} /* end mp_sub() */
-
-/* }}} */
-
-/* {{{ mp_mul(a, b, c) */
-
-/*
-  mp_mul(a, b, c)
-
-  Compute c = a * b.  All parameters may be identical.
- */
-
-mp_err mp_mul(mp_int *a, mp_int *b, mp_int *c)
-{
-  mp_err   res;
-  mp_sign  sgn;
-
-  ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
-
-  sgn = (SIGN(a) == SIGN(b)) ? MP_ZPOS : MP_NEG;
-
-  if(c == b) {
-    if((res = s_mp_mul(c, a)) != MP_OKAY)
-      return res;
-
-  } else {
-    if((res = mp_copy(a, c)) != MP_OKAY)
-      return res;
-
-    if((res = s_mp_mul(c, b)) != MP_OKAY)
-      return res;
-  }
-
-  if(sgn == MP_ZPOS || s_mp_cmp_d(c, 0) == MP_EQ)
-    SIGN(c) = MP_ZPOS;
-  else
-    SIGN(c) = sgn;
-
-  return MP_OKAY;
-
-} /* end mp_mul() */
-
-/* }}} */
-
-/* {{{ mp_mul_2d(a, d, c) */
-
-/*
-  mp_mul_2d(a, d, c)
-
-  Compute c = a * 2^d.  a may be the same as c.
- */
-
-mp_err mp_mul_2d(mp_int *a, mp_digit d, mp_int *c)
-{
-  mp_err   res;
-
-  ARGCHK(a != NULL && c != NULL, MP_BADARG);
-
-  if((res = mp_copy(a, c)) != MP_OKAY)
-    return res;
-
-  if(d == 0)
-    return MP_OKAY;
-
-  return s_mp_mul_2d(c, d);
-
-} /* end mp_mul() */
-
-/* }}} */
-
-/* {{{ mp_sqr(a, b) */
-
-#if MP_SQUARE
-mp_err mp_sqr(mp_int *a, mp_int *b)
-{
-  mp_err   res;
-
-  ARGCHK(a != NULL && b != NULL, MP_BADARG);
-
-  if((res = mp_copy(a, b)) != MP_OKAY)
-    return res;
-
-  if((res = s_mp_sqr(b)) != MP_OKAY)
-    return res;
-
-  SIGN(b) = MP_ZPOS;
-
-  return MP_OKAY;
-
-} /* end mp_sqr() */
-#endif
-
-/* }}} */
-
-/* {{{ mp_div(a, b, q, r) */
-
-/*
-  mp_div(a, b, q, r)
-
-  Compute q = a / b and r = a mod b.  Input parameters may be re-used
-  as output parameters.  If q or r is NULL, that portion of the
-  computation will be discarded (although it will still be computed)
-
-  Pay no attention to the hacker behind the curtain.
- */
-
-mp_err mp_div(mp_int *a, mp_int *b, mp_int *q, mp_int *r)
-{
-  mp_err   res;
-  mp_int   qtmp, rtmp;
-  int      cmp;
-
-  ARGCHK(a != NULL && b != NULL, MP_BADARG);
-
-  if(mp_cmp_z(b) == MP_EQ)
-    return MP_RANGE;
-
-  /* If a <= b, we can compute the solution without division, and
-     avoid any memory allocation
-   */
-  if((cmp = s_mp_cmp(a, b)) < 0) {
-    if(r) {
-      if((res = mp_copy(a, r)) != MP_OKAY)
-	return res;
-    }
-
-    if(q)
-      mp_zero(q);
-
-    return MP_OKAY;
-
-  } else if(cmp == 0) {
-
-    /* Set quotient to 1, with appropriate sign */
-    if(q) {
-      int qneg = (SIGN(a) != SIGN(b));
-
-      mp_set(q, 1);
-      if(qneg)
-	SIGN(q) = MP_NEG;
-    }
-
-    if(r)
-      mp_zero(r);
-
-    return MP_OKAY;
-  }
-
-  /* If we get here, it means we actually have to do some division */
-
-  /* Set up some temporaries... */
-  if((res = mp_init_copy(&qtmp, a)) != MP_OKAY)
-    return res;
-  if((res = mp_init_copy(&rtmp, b)) != MP_OKAY)
-    goto CLEANUP;
-
-  if((res = s_mp_div(&qtmp, &rtmp)) != MP_OKAY)
-    goto CLEANUP;
-
-  /* Compute the signs for the output  */
-  SIGN(&rtmp) = SIGN(a); /* Sr = Sa              */
-  if(SIGN(a) == SIGN(b))
-    SIGN(&qtmp) = MP_ZPOS;  /* Sq = MP_ZPOS if Sa = Sb */
-  else
-    SIGN(&qtmp) = MP_NEG;   /* Sq = MP_NEG if Sa != Sb */
-
-  if(s_mp_cmp_d(&qtmp, 0) == MP_EQ)
-    SIGN(&qtmp) = MP_ZPOS;
-  if(s_mp_cmp_d(&rtmp, 0) == MP_EQ)
-    SIGN(&rtmp) = MP_ZPOS;
-
-  /* Copy output, if it is needed      */
-  if(q)
-    s_mp_exch(&qtmp, q);
-
-  if(r)
-    s_mp_exch(&rtmp, r);
-
-CLEANUP:
-  mp_clear(&rtmp);
-  mp_clear(&qtmp);
-
-  return res;
-
-} /* end mp_div() */
-
-/* }}} */
-
-/* {{{ mp_div_2d(a, d, q, r) */
-
-mp_err mp_div_2d(mp_int *a, mp_digit d, mp_int *q, mp_int *r)
-{
-  mp_err  res;
-
-  ARGCHK(a != NULL, MP_BADARG);
-
-  if(q) {
-    if((res = mp_copy(a, q)) != MP_OKAY)
-      return res;
-
-    s_mp_div_2d(q, d);
-  }
-
-  if(r) {
-    if((res = mp_copy(a, r)) != MP_OKAY)
-      return res;
-
-    s_mp_mod_2d(r, d);
-  }
-
-  return MP_OKAY;
-
-} /* end mp_div_2d() */
-
-/* }}} */
-
-/* {{{ mp_expt(a, b, c) */
-
-/*
-  mp_expt(a, b, c)
-
-  Compute c = a ** b, that is, raise a to the b power.  Uses a
-  standard iterative square-and-multiply technique.
- */
-
-mp_err mp_expt(mp_int *a, mp_int *b, mp_int *c)
-{
-  mp_int   s, x;
-  mp_err   res;
-  mp_digit d;
-  unsigned int bit, dig;
-
-  ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
-
-  if(mp_cmp_z(b) < 0)
-    return MP_RANGE;
-
-  if((res = mp_init(&s)) != MP_OKAY)
-    return res;
-
-  mp_set(&s, 1);
-
-  if((res = mp_init_copy(&x, a)) != MP_OKAY)
-    goto X;
-
-  /* Loop over low-order digits in ascending order */
-  for(dig = 0; dig < (USED(b) - 1); dig++) {
-    d = DIGIT(b, dig);
-
-    /* Loop over bits of each non-maximal digit */
-    for(bit = 0; bit < DIGIT_BIT; bit++) {
-      if(d & 1) {
-	if((res = s_mp_mul(&s, &x)) != MP_OKAY)
-	  goto CLEANUP;
-      }
-
-      d >>= 1;
-
-      if((res = s_mp_sqr(&x)) != MP_OKAY)
-	goto CLEANUP;
-    }
-  }
-
-  /* Consider now the last digit... */
-  d = DIGIT(b, dig);
-
-  while(d) {
-    if(d & 1) {
-      if((res = s_mp_mul(&s, &x)) != MP_OKAY)
-	goto CLEANUP;
-    }
-
-    d >>= 1;
-
-    if((res = s_mp_sqr(&x)) != MP_OKAY)
-      goto CLEANUP;
-  }
-
-  if(mp_iseven(b))
-    SIGN(&s) = SIGN(a);
-
-  res = mp_copy(&s, c);
-
-CLEANUP:
-  mp_clear(&x);
-X:
-  mp_clear(&s);
-
-  return res;
-
-} /* end mp_expt() */
-
-/* }}} */
-
-/* {{{ mp_2expt(a, k) */
-
-/* Compute a = 2^k */
-
-mp_err mp_2expt(mp_int *a, mp_digit k)
-{
-  ARGCHK(a != NULL, MP_BADARG);
-
-  return s_mp_2expt(a, k);
-
-} /* end mp_2expt() */
-
-/* }}} */
-
-/* {{{ mp_mod(a, m, c) */
-
-/*
-  mp_mod(a, m, c)
-
-  Compute c = a (mod m).  Result will always be 0 <= c < m.
- */
-
-mp_err mp_mod(mp_int *a, mp_int *m, mp_int *c)
-{
-  mp_err  res;
-  int     mag;
-
-  ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG);
-
-  if(SIGN(m) == MP_NEG)
-    return MP_RANGE;
-
-  /*
-     If |a| > m, we need to divide to get the remainder and take the
-     absolute value.
-
-     If |a| < m, we don't need to do any division, just copy and adjust
-     the sign (if a is negative).
-
-     If |a| == m, we can simply set the result to zero.
-
-     This order is intended to minimize the average path length of the
-     comparison chain on common workloads -- the most frequent cases are
-     that |a| != m, so we do those first.
-   */
-  if((mag = s_mp_cmp(a, m)) > 0) {
-    if((res = mp_div(a, m, NULL, c)) != MP_OKAY)
-      return res;
-
-    if(SIGN(c) == MP_NEG) {
-      if((res = mp_add(c, m, c)) != MP_OKAY)
-	return res;
-    }
-
-  } else if(mag < 0) {
-    if((res = mp_copy(a, c)) != MP_OKAY)
-      return res;
-
-    if(mp_cmp_z(a) < 0) {
-      if((res = mp_add(c, m, c)) != MP_OKAY)
-	return res;
-
-    }
-
-  } else {
-    mp_zero(c);
-
-  }
-
-  return MP_OKAY;
-
-} /* end mp_mod() */
-
-/* }}} */
-
-/* {{{ mp_mod_d(a, d, c) */
-
-/*
-  mp_mod_d(a, d, c)
-
-  Compute c = a (mod d).  Result will always be 0 <= c < d
- */
-mp_err mp_mod_d(mp_int *a, mp_digit d, mp_digit *c)
-{
-  mp_err   res;
-  mp_digit rem;
-
-  ARGCHK(a != NULL && c != NULL, MP_BADARG);
-
-  if(s_mp_cmp_d(a, d) > 0) {
-    if((res = mp_div_d(a, d, NULL, &rem)) != MP_OKAY)
-      return res;
-
-  } else {
-    if(SIGN(a) == MP_NEG)
-      rem = d - DIGIT(a, 0);
-    else
-      rem = DIGIT(a, 0);
-  }
-
-  if(c)
-    *c = rem;
-
-  return MP_OKAY;
-
-} /* end mp_mod_d() */
-
-/* }}} */
-
-/* {{{ mp_sqrt(a, b) */
-
-/*
-  mp_sqrt(a, b)
-
-  Compute the integer square root of a, and store the result in b.
-  Uses an integer-arithmetic version of Newton's iterative linear
-  approximation technique to determine this value; the result has the
-  following two properties:
-
-     b^2 <= a
-     (b+1)^2 >= a
-
-  It is a range error to pass a negative value.
- */
-mp_err mp_sqrt(mp_int *a, mp_int *b)
-{
-  mp_int   x, t;
-  mp_err   res;
-
-  ARGCHK(a != NULL && b != NULL, MP_BADARG);
-
-  /* Cannot take square root of a negative value */
-  if(SIGN(a) == MP_NEG)
-    return MP_RANGE;
-
-  /* Special cases for zero and one, trivial     */
-  if(mp_cmp_d(a, 0) == MP_EQ || mp_cmp_d(a, 1) == MP_EQ)
-    return mp_copy(a, b);
-
-  /* Initialize the temporaries we'll use below  */
-  if((res = mp_init_size(&t, USED(a))) != MP_OKAY)
-    return res;
-
-  /* Compute an initial guess for the iteration as a itself */
-  if((res = mp_init_copy(&x, a)) != MP_OKAY)
-    goto X;
-
-s_mp_rshd(&x, (USED(&x)/2)+1);
-mp_add_d(&x, 1, &x);
-
-  for(;;) {
-    /* t = (x * x) - a */
-    mp_copy(&x, &t);      /* can't fail, t is big enough for original x */
-    if((res = mp_sqr(&t, &t)) != MP_OKAY ||
-       (res = mp_sub(&t, a, &t)) != MP_OKAY)
-      goto CLEANUP;
-
-    /* t = t / 2x       */
-    s_mp_mul_2(&x);
-    if((res = mp_div(&t, &x, &t, NULL)) != MP_OKAY)
-      goto CLEANUP;
-    s_mp_div_2(&x);
-
-    /* Terminate the loop, if the quotient is zero */
-    if(mp_cmp_z(&t) == MP_EQ)
-      break;
-
-    /* x = x - t       */
-    if((res = mp_sub(&x, &t, &x)) != MP_OKAY)
-      goto CLEANUP;
-
-  }
-
-  /* Copy result to output parameter */
-  mp_sub_d(&x, 1, &x);
-  s_mp_exch(&x, b);
-
- CLEANUP:
-  mp_clear(&x);
- X:
-  mp_clear(&t);
-
-  return res;
-
-} /* end mp_sqrt() */
-
-/* }}} */
-
-/* }}} */
-
-/*------------------------------------------------------------------------*/
-/* {{{ Modular arithmetic */
-
-#if MP_MODARITH
-/* {{{ mp_addmod(a, b, m, c) */
-
-/*
-  mp_addmod(a, b, m, c)
-
-  Compute c = (a + b) mod m
- */
-
-mp_err mp_addmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
-{
-  mp_err  res;
-
-  ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG);
-
-  if((res = mp_add(a, b, c)) != MP_OKAY)
-    return res;
-  if((res = mp_mod(c, m, c)) != MP_OKAY)
-    return res;
-
-  return MP_OKAY;
-
-}
-
-/* }}} */
-
-/* {{{ mp_submod(a, b, m, c) */
-
-/*
-  mp_submod(a, b, m, c)
-
-  Compute c = (a - b) mod m
- */
-
-mp_err mp_submod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
-{
-  mp_err  res;
-
-  ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG);
-
-  if((res = mp_sub(a, b, c)) != MP_OKAY)
-    return res;
-  if((res = mp_mod(c, m, c)) != MP_OKAY)
-    return res;
-
-  return MP_OKAY;
-
-}
-
-/* }}} */
-
-/* {{{ mp_mulmod(a, b, m, c) */
-
-/*
-  mp_mulmod(a, b, m, c)
-
-  Compute c = (a * b) mod m
- */
-
-mp_err mp_mulmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
-{
-  mp_err  res;
-
-  ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG);
-
-  if((res = mp_mul(a, b, c)) != MP_OKAY)
-    return res;
-  if((res = mp_mod(c, m, c)) != MP_OKAY)
-    return res;
-
-  return MP_OKAY;
-
-}
-
-/* }}} */
-
-/* {{{ mp_sqrmod(a, m, c) */
-
-#if MP_SQUARE
-mp_err mp_sqrmod(mp_int *a, mp_int *m, mp_int *c)
-{
-  mp_err  res;
-
-  ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG);
-
-  if((res = mp_sqr(a, c)) != MP_OKAY)
-    return res;
-  if((res = mp_mod(c, m, c)) != MP_OKAY)
-    return res;
-
-  return MP_OKAY;
-
-} /* end mp_sqrmod() */
-#endif
-
-/* }}} */
-
-/* {{{ mp_exptmod(a, b, m, c) */
-
-/*
-  mp_exptmod(a, b, m, c)
-
-  Compute c = (a ** b) mod m.  Uses a standard square-and-multiply
-  method with modular reductions at each step. (This is basically the
-  same code as mp_expt(), except for the addition of the reductions)
-
-  The modular reductions are done using Barrett's algorithm (see
-  s_mp_reduce() below for details)
- */
-
-mp_err mp_exptmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
-{
-  mp_int   s, x, mu;
-  mp_err   res;
-  mp_digit d, *db = DIGITS(b);
-  mp_size  ub = USED(b);
-  unsigned int bit, dig;
-
-  ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
-
-  if(mp_cmp_z(b) < 0 || mp_cmp_z(m) <= 0)
-    return MP_RANGE;
-
-  if((res = mp_init(&s)) != MP_OKAY)
-    return res;
-  if((res = mp_init_copy(&x, a)) != MP_OKAY)
-    goto X;
-  if((res = mp_mod(&x, m, &x)) != MP_OKAY ||
-     (res = mp_init(&mu)) != MP_OKAY)
-    goto MU;
-
-  mp_set(&s, 1);
-
-  /* mu = b^2k / m */
-  s_mp_add_d(&mu, 1);
-  s_mp_lshd(&mu, 2 * USED(m));
-  if((res = mp_div(&mu, m, &mu, NULL)) != MP_OKAY)
-    goto CLEANUP;
-
-  /* Loop over digits of b in ascending order, except highest order */
-  for(dig = 0; dig < (ub - 1); dig++) {
-    d = *db++;
-
-    /* Loop over the bits of the lower-order digits */
-    for(bit = 0; bit < DIGIT_BIT; bit++) {
-      if(d & 1) {
-	if((res = s_mp_mul(&s, &x)) != MP_OKAY)
-	  goto CLEANUP;
-	if((res = s_mp_reduce(&s, m, &mu)) != MP_OKAY)
-	  goto CLEANUP;
-      }
-
-      d >>= 1;
-
-      if((res = s_mp_sqr(&x)) != MP_OKAY)
-	goto CLEANUP;
-      if((res = s_mp_reduce(&x, m, &mu)) != MP_OKAY)
-	goto CLEANUP;
-    }
-  }
-
-  /* Now do the last digit... */
-  d = *db;
-
-  while(d) {
-    if(d & 1) {
-      if((res = s_mp_mul(&s, &x)) != MP_OKAY)
-	goto CLEANUP;
-      if((res = s_mp_reduce(&s, m, &mu)) != MP_OKAY)
-	goto CLEANUP;
-    }
-
-    d >>= 1;
-
-    if((res = s_mp_sqr(&x)) != MP_OKAY)
-      goto CLEANUP;
-    if((res = s_mp_reduce(&x, m, &mu)) != MP_OKAY)
-      goto CLEANUP;
-  }
-
-  s_mp_exch(&s, c);
-
- CLEANUP:
-  mp_clear(&mu);
- MU:
-  mp_clear(&x);
- X:
-  mp_clear(&s);
-
-  return res;
-
-} /* end mp_exptmod() */
-
-/* }}} */
-
-/* {{{ mp_exptmod_d(a, d, m, c) */
-
-mp_err mp_exptmod_d(mp_int *a, mp_digit d, mp_int *m, mp_int *c)
-{
-  mp_int   s, x;
-  mp_err   res;
-
-  ARGCHK(a != NULL && c != NULL, MP_BADARG);
-
-  if((res = mp_init(&s)) != MP_OKAY)
-    return res;
-  if((res = mp_init_copy(&x, a)) != MP_OKAY)
-    goto X;
-
-  mp_set(&s, 1);
-
-  while(d != 0) {
-    if(d & 1) {
-      if((res = s_mp_mul(&s, &x)) != MP_OKAY ||
-	 (res = mp_mod(&s, m, &s)) != MP_OKAY)
-	goto CLEANUP;
-    }
-
-    d /= 2;
-
-    if((res = s_mp_sqr(&x)) != MP_OKAY ||
-       (res = mp_mod(&x, m, &x)) != MP_OKAY)
-      goto CLEANUP;
-  }
-
-  s_mp_exch(&s, c);
-
-CLEANUP:
-  mp_clear(&x);
-X:
-  mp_clear(&s);
-
-  return res;
-
-} /* end mp_exptmod_d() */
-
-/* }}} */
-#endif /* if MP_MODARITH */
-
-/* }}} */
-
-/*------------------------------------------------------------------------*/
-/* {{{ Comparison functions */
-
-/* {{{ mp_cmp_z(a) */
-
-/*
-  mp_cmp_z(a)
-
-  Compare a <=> 0.  Returns <0 if a<0, 0 if a=0, >0 if a>0.
- */
-
-int    mp_cmp_z(mp_int *a)
-{
-  if(SIGN(a) == MP_NEG)
-    return MP_LT;
-  else if(USED(a) == 1 && DIGIT(a, 0) == 0)
-    return MP_EQ;
-  else
-    return MP_GT;
-
-} /* end mp_cmp_z() */
-
-/* }}} */
-
-/* {{{ mp_cmp_d(a, d) */
-
-/*
-  mp_cmp_d(a, d)
-
-  Compare a <=> d.  Returns <0 if a<d, 0 if a=d, >0 if a>d
- */
-
-int    mp_cmp_d(mp_int *a, mp_digit d)
-{
-  ARGCHK(a != NULL, MP_EQ);
-
-  if(SIGN(a) == MP_NEG)
-    return MP_LT;
-
-  return s_mp_cmp_d(a, d);
-
-} /* end mp_cmp_d() */
-
-/* }}} */
-
-/* {{{ mp_cmp(a, b) */
-
-int    mp_cmp(mp_int *a, mp_int *b)
-{
-  ARGCHK(a != NULL && b != NULL, MP_EQ);
-
-  if(SIGN(a) == SIGN(b)) {
-    int  mag;
-
-    if((mag = s_mp_cmp(a, b)) == MP_EQ)
-      return MP_EQ;
-
-    if(SIGN(a) == MP_ZPOS)
-      return mag;
-    else
-      return -mag;
-
-  } else if(SIGN(a) == MP_ZPOS) {
-    return MP_GT;
-  } else {
-    return MP_LT;
-  }
-
-} /* end mp_cmp() */
-
-/* }}} */
-
-/* {{{ mp_cmp_mag(a, b) */
-
-/*
-  mp_cmp_mag(a, b)
-
-  Compares |a| <=> |b|, and returns an appropriate comparison result
- */
-
-int    mp_cmp_mag(mp_int *a, mp_int *b)
-{
-  ARGCHK(a != NULL && b != NULL, MP_EQ);
-
-  return s_mp_cmp(a, b);
-
-} /* end mp_cmp_mag() */
-
-/* }}} */
-
-/* {{{ mp_cmp_int(a, z) */
-
-/*
-  This just converts z to an mp_int, and uses the existing comparison
-  routines.  This is sort of inefficient, but it's not clear to me how
-  frequently this wil get used anyway.  For small positive constants,
-  you can always use mp_cmp_d(), and for zero, there is mp_cmp_z().
- */
-int    mp_cmp_int(mp_int *a, long z)
-{
-  mp_int  tmp;
-  int     out;
-
-  ARGCHK(a != NULL, MP_EQ);
-
-  mp_init(&tmp); mp_set_int(&tmp, z);
-  out = mp_cmp(a, &tmp);
-  mp_clear(&tmp);
-
-  return out;
-
-} /* end mp_cmp_int() */
-
-/* }}} */
-
-/* {{{ mp_isodd(a) */
-
-/*
-  mp_isodd(a)
-
-  Returns a true (non-zero) value if a is odd, false (zero) otherwise.
- */
-int    mp_isodd(mp_int *a)
-{
-  ARGCHK(a != NULL, 0);
-
-  return (DIGIT(a, 0) & 1);
-
-} /* end mp_isodd() */
-
-/* }}} */
-
-/* {{{ mp_iseven(a) */
-
-int    mp_iseven(mp_int *a)
-{
-  return !mp_isodd(a);
-
-} /* end mp_iseven() */
-
-/* }}} */
-
-/* }}} */
-
-/*------------------------------------------------------------------------*/
-/* {{{ Number theoretic functions */
-
-#if MP_NUMTH
-/* {{{ mp_gcd(a, b, c) */
-
-/*
-  Like the old mp_gcd() function, except computes the GCD using the
-  binary algorithm due to Josef Stein in 1961 (via Knuth).
- */
-mp_err mp_gcd(mp_int *a, mp_int *b, mp_int *c)
-{
-  mp_err   res;
-  mp_int   u, v, t;
-  mp_size  k = 0;
-
-  ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
-
-  if(mp_cmp_z(a) == MP_EQ && mp_cmp_z(b) == MP_EQ)
-      return MP_RANGE;
-  if(mp_cmp_z(a) == MP_EQ) {
-    return mp_copy(b, c);
-  } else if(mp_cmp_z(b) == MP_EQ) {
-    return mp_copy(a, c);
-  }
-
-  if((res = mp_init(&t)) != MP_OKAY)
-    return res;
-  if((res = mp_init_copy(&u, a)) != MP_OKAY)
-    goto U;
-  if((res = mp_init_copy(&v, b)) != MP_OKAY)
-    goto V;
-
-  SIGN(&u) = MP_ZPOS;
-  SIGN(&v) = MP_ZPOS;
-
-  /* Divide out common factors of 2 until at least 1 of a, b is even */
-  while(mp_iseven(&u) && mp_iseven(&v)) {
-    s_mp_div_2(&u);
-    s_mp_div_2(&v);
-    ++k;
-  }
-
-  /* Initialize t */
-  if(mp_isodd(&u)) {
-    if((res = mp_copy(&v, &t)) != MP_OKAY)
-      goto CLEANUP;
-
-    /* t = -v */
-    if(SIGN(&v) == MP_ZPOS)
-      SIGN(&t) = MP_NEG;
-    else
-      SIGN(&t) = MP_ZPOS;
-
-  } else {
-    if((res = mp_copy(&u, &t)) != MP_OKAY)
-      goto CLEANUP;
-
-  }
-
-  for(;;) {
-    while(mp_iseven(&t)) {
-      s_mp_div_2(&t);
-    }
-
-    if(mp_cmp_z(&t) == MP_GT) {
-      if((res = mp_copy(&t, &u)) != MP_OKAY)
-	goto CLEANUP;
-
-    } else {
-      if((res = mp_copy(&t, &v)) != MP_OKAY)
-	goto CLEANUP;
-
-      /* v = -t */
-      if(SIGN(&t) == MP_ZPOS)
-	SIGN(&v) = MP_NEG;
-      else
-	SIGN(&v) = MP_ZPOS;
-    }
-
-    if((res = mp_sub(&u, &v, &t)) != MP_OKAY)
-      goto CLEANUP;
-
-    if(s_mp_cmp_d(&t, 0) == MP_EQ)
-      break;
-  }
-
-  s_mp_2expt(&v, k);       /* v = 2^k   */
-  res = mp_mul(&u, &v, c); /* c = u * v */
-
- CLEANUP:
-  mp_clear(&v);
- V:
-  mp_clear(&u);
- U:
-  mp_clear(&t);
-
-  return res;
-
-} /* end mp_bgcd() */
-
-/* }}} */
-
-/* {{{ mp_lcm(a, b, c) */
-
-/* We compute the least common multiple using the rule:
-
-   ab = [a, b](a, b)
-
-   ... by computing the product, and dividing out the gcd.
- */
-
-mp_err mp_lcm(mp_int *a, mp_int *b, mp_int *c)
-{
-  mp_int  gcd, prod;
-  mp_err  res;
-
-  ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
-
-  /* Set up temporaries */
-  if((res = mp_init(&gcd)) != MP_OKAY)
-    return res;
-  if((res = mp_init(&prod)) != MP_OKAY)
-    goto GCD;
-
-  if((res = mp_mul(a, b, &prod)) != MP_OKAY)
-    goto CLEANUP;
-  if((res = mp_gcd(a, b, &gcd)) != MP_OKAY)
-    goto CLEANUP;
-
-  res = mp_div(&prod, &gcd, c, NULL);
-
- CLEANUP:
-  mp_clear(&prod);
- GCD:
-  mp_clear(&gcd);
-
-  return res;
-
-} /* end mp_lcm() */
-
-/* }}} */
-
-/* {{{ mp_xgcd(a, b, g, x, y) */
-
-/*
-  mp_xgcd(a, b, g, x, y)
-
-  Compute g = (a, b) and values x and y satisfying Bezout's identity
-  (that is, ax + by = g).  This uses the extended binary GCD algorithm
-  based on the Stein algorithm used for mp_gcd()
- */
-
-mp_err mp_xgcd(mp_int *a, mp_int *b, mp_int *g, mp_int *x, mp_int *y)
-{
-  mp_int   gx, xc, yc, u, v, A, B, C, D;
-  mp_int  *clean[9];
-  mp_err   res;
-  int      last = -1;
-
-  if(mp_cmp_z(b) == 0)
-    return MP_RANGE;
-
-  /* Initialize all these variables we need */
-  if((res = mp_init(&u)) != MP_OKAY) goto CLEANUP;
-  clean[++last] = &u;
-  if((res = mp_init(&v)) != MP_OKAY) goto CLEANUP;
-  clean[++last] = &v;
-  if((res = mp_init(&gx)) != MP_OKAY) goto CLEANUP;
-  clean[++last] = &gx;
-  if((res = mp_init(&A)) != MP_OKAY) goto CLEANUP;
-  clean[++last] = &A;
-  if((res = mp_init(&B)) != MP_OKAY) goto CLEANUP;
-  clean[++last] = &B;
-  if((res = mp_init(&C)) != MP_OKAY) goto CLEANUP;
-  clean[++last] = &C;
-  if((res = mp_init(&D)) != MP_OKAY) goto CLEANUP;
-  clean[++last] = &D;
-  if((res = mp_init_copy(&xc, a)) != MP_OKAY) goto CLEANUP;
-  clean[++last] = &xc;
-  mp_abs(&xc, &xc);
-  if((res = mp_init_copy(&yc, b)) != MP_OKAY) goto CLEANUP;
-  clean[++last] = &yc;
-  mp_abs(&yc, &yc);
-
-  mp_set(&gx, 1);
-
-  /* Divide by two until at least one of them is even */
-  while(mp_iseven(&xc) && mp_iseven(&yc)) {
-    s_mp_div_2(&xc);
-    s_mp_div_2(&yc);
-    if((res = s_mp_mul_2(&gx)) != MP_OKAY)
-      goto CLEANUP;
-  }
-
-  mp_copy(&xc, &u);
-  mp_copy(&yc, &v);
-  mp_set(&A, 1); mp_set(&D, 1);
-
-  /* Loop through binary GCD algorithm */
-  for(;;) {
-    while(mp_iseven(&u)) {
-      s_mp_div_2(&u);
-
-      if(mp_iseven(&A) && mp_iseven(&B)) {
-	s_mp_div_2(&A); s_mp_div_2(&B);
-      } else {
-	if((res = mp_add(&A, &yc, &A)) != MP_OKAY) goto CLEANUP;
-	s_mp_div_2(&A);
-	if((res = mp_sub(&B, &xc, &B)) != MP_OKAY) goto CLEANUP;
-	s_mp_div_2(&B);
-      }
-    }
-
-    while(mp_iseven(&v)) {
-      s_mp_div_2(&v);
-
-      if(mp_iseven(&C) && mp_iseven(&D)) {
-	s_mp_div_2(&C); s_mp_div_2(&D);
-      } else {
-	if((res = mp_add(&C, &yc, &C)) != MP_OKAY) goto CLEANUP;
-	s_mp_div_2(&C);
-	if((res = mp_sub(&D, &xc, &D)) != MP_OKAY) goto CLEANUP;
-	s_mp_div_2(&D);
-      }
-    }
-
-    if(mp_cmp(&u, &v) >= 0) {
-      if((res = mp_sub(&u, &v, &u)) != MP_OKAY) goto CLEANUP;
-      if((res = mp_sub(&A, &C, &A)) != MP_OKAY) goto CLEANUP;
-      if((res = mp_sub(&B, &D, &B)) != MP_OKAY) goto CLEANUP;
-
-    } else {
-      if((res = mp_sub(&v, &u, &v)) != MP_OKAY) goto CLEANUP;
-      if((res = mp_sub(&C, &A, &C)) != MP_OKAY) goto CLEANUP;
-      if((res = mp_sub(&D, &B, &D)) != MP_OKAY) goto CLEANUP;
-
-    }
-
-    /* If we're done, copy results to output */
-    if(mp_cmp_z(&u) == 0) {
-      if(x)
-	if((res = mp_copy(&C, x)) != MP_OKAY) goto CLEANUP;
-
-      if(y)
-	if((res = mp_copy(&D, y)) != MP_OKAY) goto CLEANUP;
-
-      if(g)
-	if((res = mp_mul(&gx, &v, g)) != MP_OKAY) goto CLEANUP;
-
-      break;
-    }
-  }
-
- CLEANUP:
-  while(last >= 0)
-    mp_clear(clean[last--]);
-
-  return res;
-
-} /* end mp_xgcd() */
-
-/* }}} */
-
-/* {{{ mp_invmod(a, m, c) */
-
-/*
-  mp_invmod(a, m, c)
-
-  Compute c = a^-1 (mod m), if there is an inverse for a (mod m).
-  This is equivalent to the question of whether (a, m) = 1.  If not,
-  MP_UNDEF is returned, and there is no inverse.
- */
-
-mp_err mp_invmod(mp_int *a, mp_int *m, mp_int *c)
-{
-  mp_int  g, x;
-  mp_err  res;
-
-  ARGCHK(a && m && c, MP_BADARG);
-
-  if(mp_cmp_z(a) == 0 || mp_cmp_z(m) == 0)
-    return MP_RANGE;
-
-  if((res = mp_init(&g)) != MP_OKAY)
-    return res;
-  if((res = mp_init(&x)) != MP_OKAY)
-    goto X;
-
-  if((res = mp_xgcd(a, m, &g, &x, NULL)) != MP_OKAY)
-    goto CLEANUP;
-
-  if(mp_cmp_d(&g, 1) != MP_EQ) {
-    res = MP_UNDEF;
-    goto CLEANUP;
-  }
-
-  res = mp_mod(&x, m, c);
-  SIGN(c) = SIGN(a);
-
-CLEANUP:
-  mp_clear(&x);
-X:
-  mp_clear(&g);
-
-  return res;
-
-} /* end mp_invmod() */
-
-/* }}} */
-#endif /* if MP_NUMTH */
-
-/* }}} */
-
-/*------------------------------------------------------------------------*/
-/* {{{ mp_print(mp, ofp) */
-
-#if MP_IOFUNC
-/*
-  mp_print(mp, ofp)
-
-  Print a textual representation of the given mp_int on the output
-  stream 'ofp'.  Output is generated using the internal radix.
- */
-
-void   mp_print(mp_int *mp, FILE *ofp)
-{
-  int   ix;
-
-  if(mp == NULL || ofp == NULL)
-    return;
-
-  fputc((SIGN(mp) == MP_NEG) ? '-' : '+', ofp);
-
-  for(ix = USED(mp) - 1; ix >= 0; ix--) {
-    fprintf(ofp, DIGIT_FMT, DIGIT(mp, ix));
-  }
-
-} /* end mp_print() */
-
-#endif /* if MP_IOFUNC */
-
-/* }}} */
-
-/*------------------------------------------------------------------------*/
-/* {{{ More I/O Functions */
-
-/* {{{ mp_read_signed_bin(mp, str, len) */
-
-/*
-   mp_read_signed_bin(mp, str, len)
-
-   Read in a raw value (base 256) into the given mp_int
- */
-
-mp_err  mp_read_signed_bin(mp_int *mp, unsigned char *str, int len)
-{
-  mp_err         res;
-
-  ARGCHK(mp != NULL && str != NULL && len > 0, MP_BADARG);
-
-  if((res = mp_read_unsigned_bin(mp, str + 1, len - 1)) == MP_OKAY) {
-    /* Get sign from first byte */
-    if(str[0])
-      SIGN(mp) = MP_NEG;
-    else
-      SIGN(mp) = MP_ZPOS;
-  }
-
-  return res;
-
-} /* end mp_read_signed_bin() */
-
-/* }}} */
-
-/* {{{ mp_signed_bin_size(mp) */
-
-int    mp_signed_bin_size(mp_int *mp)
-{
-  ARGCHK(mp != NULL, 0);
-
-  return mp_unsigned_bin_size(mp) + 1;
-
-} /* end mp_signed_bin_size() */
-
-/* }}} */
-
-/* {{{ mp_to_signed_bin(mp, str) */
-
-mp_err mp_to_signed_bin(mp_int *mp, unsigned char *str)
-{
-  ARGCHK(mp != NULL && str != NULL, MP_BADARG);
-
-  /* Caller responsible for allocating enough memory (use mp_raw_size(mp)) */
-  str[0] = (char)SIGN(mp);
-
-  return mp_to_unsigned_bin(mp, str + 1);
-
-} /* end mp_to_signed_bin() */
-
-/* }}} */
-
-/* {{{ mp_read_unsigned_bin(mp, str, len) */
-
-/*
-  mp_read_unsigned_bin(mp, str, len)
-
-  Read in an unsigned value (base 256) into the given mp_int
- */
-
-mp_err  mp_read_unsigned_bin(mp_int *mp, unsigned char *str, int len)
-{
-  int     ix;
-  mp_err  res;
-
-  ARGCHK(mp != NULL && str != NULL && len > 0, MP_BADARG);
-
-  mp_zero(mp);
-
-  for(ix = 0; ix < len; ix++) {
-    if((res = s_mp_mul_2d(mp, CHAR_BIT)) != MP_OKAY)
-      return res;
-
-    if((res = mp_add_d(mp, str[ix], mp)) != MP_OKAY)
-      return res;
-  }
-
-  return MP_OKAY;
-
-} /* end mp_read_unsigned_bin() */
-
-/* }}} */
-
-/* {{{ mp_unsigned_bin_size(mp) */
-
-int     mp_unsigned_bin_size(mp_int *mp)
-{
-  mp_digit   topdig;
-  int        count;
-
-  ARGCHK(mp != NULL, 0);
-
-  /* Special case for the value zero */
-  if(USED(mp) == 1 && DIGIT(mp, 0) == 0)
-    return 1;
-
-  count = (USED(mp) - 1) * sizeof(mp_digit);
-  topdig = DIGIT(mp, USED(mp) - 1);
-
-  while(topdig != 0) {
-    ++count;
-    topdig >>= CHAR_BIT;
-  }
-
-  return count;
-
-} /* end mp_unsigned_bin_size() */
-
-/* }}} */
-
-/* {{{ mp_to_unsigned_bin(mp, str) */
-
-mp_err mp_to_unsigned_bin(mp_int *mp, unsigned char *str)
-{
-  mp_digit      *dp, *end, d;
-  unsigned char *spos;
-
-  ARGCHK(mp != NULL && str != NULL, MP_BADARG);
-
-  dp = DIGITS(mp);
-  end = dp + USED(mp) - 1;
-  spos = str;
-
-  /* Special case for zero, quick test */
-  if(dp == end && *dp == 0) {
-    *str = '\0';
-    return MP_OKAY;
-  }
-
-  /* Generate digits in reverse order */
-  while(dp < end) {
-    unsigned int ix;
-
-    d = *dp;
-    for(ix = 0; ix < sizeof(mp_digit); ++ix) {
-      *spos = d & UCHAR_MAX;
-      d >>= CHAR_BIT;
-      ++spos;
-    }
-
-    ++dp;
-  }
-
-  /* Now handle last digit specially, high order zeroes are not written */
-  d = *end;
-  while(d != 0) {
-    *spos = d & UCHAR_MAX;
-    d >>= CHAR_BIT;
-    ++spos;
-  }
-
-  /* Reverse everything to get digits in the correct order */
-  while(--spos > str) {
-    unsigned char t = *str;
-    *str = *spos;
-    *spos = t;
-
-    ++str;
-  }
-
-  return MP_OKAY;
-
-} /* end mp_to_unsigned_bin() */
-
-/* }}} */
-
-/* {{{ mp_count_bits(mp) */
-
-int    mp_count_bits(mp_int *mp)
-{
-  int      len;
-  mp_digit d;
-
-  ARGCHK(mp != NULL, MP_BADARG);
-
-  len = DIGIT_BIT * (USED(mp) - 1);
-  d = DIGIT(mp, USED(mp) - 1);
-
-  while(d != 0) {
-    ++len;
-    d >>= 1;
-  }
-
-  return len;
-
-} /* end mp_count_bits() */
-
-/* }}} */
-
-/* {{{ mp_read_radix(mp, str, radix) */
-
-/*
-  mp_read_radix(mp, str, radix)
-
-  Read an integer from the given string, and set mp to the resulting
-  value.  The input is presumed to be in base 10.  Leading non-digit
-  characters are ignored, and the function reads until a non-digit
-  character or the end of the string.
- */
-
-mp_err  mp_read_radix(mp_int *mp, unsigned char *str, int radix)
-{
-  int     ix = 0, val = 0;
-  mp_err  res;
-  mp_sign sig = MP_ZPOS;
-
-  ARGCHK(mp != NULL && str != NULL && radix >= 2 && radix <= MAX_RADIX,
-	 MP_BADARG);
-
-  mp_zero(mp);
-
-  /* Skip leading non-digit characters until a digit or '-' or '+' */
-  while(str[ix] &&
-	(s_mp_tovalue(str[ix], radix) < 0) &&
-	str[ix] != '-' &&
-	str[ix] != '+') {
-    ++ix;
-  }
-
-  if(str[ix] == '-') {
-    sig = MP_NEG;
-    ++ix;
-  } else if(str[ix] == '+') {
-    sig = MP_ZPOS; /* this is the default anyway... */
-    ++ix;
-  }
-
-  while((val = s_mp_tovalue(str[ix], radix)) >= 0) {
-    if((res = s_mp_mul_d(mp, radix)) != MP_OKAY)
-      return res;
-    if((res = s_mp_add_d(mp, val)) != MP_OKAY)
-      return res;
-    ++ix;
-  }
-
-  if(s_mp_cmp_d(mp, 0) == MP_EQ)
-    SIGN(mp) = MP_ZPOS;
-  else
-    SIGN(mp) = sig;
-
-  return MP_OKAY;
-
-} /* end mp_read_radix() */
-
-/* }}} */
-
-/* {{{ mp_radix_size(mp, radix) */
-
-int    mp_radix_size(mp_int *mp, int radix)
-{
-  int  len;
-  ARGCHK(mp != NULL, 0);
-
-  len = s_mp_outlen(mp_count_bits(mp), radix) + 1; /* for NUL terminator */
-
-  if(mp_cmp_z(mp) < 0)
-    ++len; /* for sign */
-
-  return len;
-
-} /* end mp_radix_size() */
-
-/* }}} */
-
-/* {{{ mp_value_radix_size(num, qty, radix) */
-
-/* num = number of digits
-   qty = number of bits per digit
-   radix = target base
-
-   Return the number of digits in the specified radix that would be
-   needed to express 'num' digits of 'qty' bits each.
- */
-int    mp_value_radix_size(int num, int qty, int radix)
-{
-  ARGCHK(num >= 0 && qty > 0 && radix >= 2 && radix <= MAX_RADIX, 0);
-
-  return s_mp_outlen(num * qty, radix);
-
-} /* end mp_value_radix_size() */
-
-/* }}} */
-
-/* {{{ mp_toradix(mp, str, radix) */
-
-mp_err mp_toradix(mp_int *mp, char *str, int radix)
-{
-  int  ix, pos = 0;
-
-  ARGCHK(mp != NULL && str != NULL, MP_BADARG);
-  ARGCHK(radix > 1 && radix <= MAX_RADIX, MP_RANGE);
-
-  if(mp_cmp_z(mp) == MP_EQ) {
-    str[0] = '0';
-    str[1] = '\0';
-  } else {
-    mp_err   res;
-    mp_int   tmp;
-    mp_sign  sgn;
-    mp_digit rem, rdx = (mp_digit)radix;
-    char     ch;
-
-    if((res = mp_init_copy(&tmp, mp)) != MP_OKAY)
-      return res;
-
-    /* Save sign for later, and take absolute value */
-    sgn = SIGN(&tmp); SIGN(&tmp) = MP_ZPOS;
-
-    /* Generate output digits in reverse order      */
-    while(mp_cmp_z(&tmp) != 0) {
-      if((res = s_mp_div_d(&tmp, rdx, &rem)) != MP_OKAY) {
-	mp_clear(&tmp);
-	return res;
-      }
-
-      /* Generate digits, use capital letters */
-      ch = s_mp_todigit(rem, radix, 0);
-
-      str[pos++] = ch;
-    }
-
-    /* Add - sign if original value was negative */
-    if(sgn == MP_NEG)
-      str[pos++] = '-';
-
-    /* Add trailing NUL to end the string        */
-    str[pos--] = '\0';
-
-    /* Reverse the digits and sign indicator     */
-    ix = 0;
-    while(ix < pos) {
-      char _tmp = str[ix];
-
-      str[ix] = str[pos];
-      str[pos] = _tmp;
-      ++ix;
-      --pos;
-    }
-
-    mp_clear(&tmp);
-  }
-
-  return MP_OKAY;
-
-} /* end mp_toradix() */
-
-/* }}} */
-
-/* {{{ mp_char2value(ch, r) */
-
-int    mp_char2value(char ch, int r)
-{
-  return s_mp_tovalue(ch, r);
-
-} /* end mp_tovalue() */
-
-/* }}} */
-
-/* }}} */
-
-/* {{{ mp_strerror(ec) */
-
-/*
-  mp_strerror(ec)
-
-  Return a string describing the meaning of error code 'ec'.  The
-  string returned is allocated in static memory, so the caller should
-  not attempt to modify or free the memory associated with this
-  string.
- */
-const char  *mp_strerror(mp_err ec)
-{
-  int   aec = (ec < 0) ? -ec : ec;
-
-  /* Code values are negative, so the senses of these comparisons
-     are accurate */
-  if(ec < MP_LAST_CODE || ec > MP_OKAY) {
-    return mp_err_string[0];  /* unknown error code */
-  } else {
-    return mp_err_string[aec + 1];
-  }
-
-} /* end mp_strerror() */
-
-/* }}} */
-
-/*========================================================================*/
-/*------------------------------------------------------------------------*/
-/* Static function definitions (internal use only)                        */
-
-/* {{{ Memory management */
-
-/* {{{ s_mp_grow(mp, min) */
-
-/* Make sure there are at least 'min' digits allocated to mp              */
-mp_err   s_mp_grow(mp_int *mp, mp_size min)
-{
-  if(min > ALLOC(mp)) {
-    mp_digit   *tmp;
-
-    /* Set min to next nearest default precision block size */
-    min = ((min + (s_mp_defprec - 1)) / s_mp_defprec) * s_mp_defprec;
-
-    if((tmp = s_mp_alloc(min, sizeof(mp_digit))) == NULL)
-      return MP_MEM;
-
-    s_mp_copy(DIGITS(mp), tmp, USED(mp));
-
-#if MP_CRYPTO
-    s_mp_setz(DIGITS(mp), ALLOC(mp));
-#endif
-    s_mp_free(DIGITS(mp));
-    DIGITS(mp) = tmp;
-    ALLOC(mp) = min;
-  }
-
-  return MP_OKAY;
-
-} /* end s_mp_grow() */
-
-/* }}} */
-
-/* {{{ s_mp_pad(mp, min) */
-
-/* Make sure the used size of mp is at least 'min', growing if needed     */
-mp_err   s_mp_pad(mp_int *mp, mp_size min)
-{
-  if(min > USED(mp)) {
-    mp_err  res;
-
-    /* Make sure there is room to increase precision  */
-    if(min > ALLOC(mp) && (res = s_mp_grow(mp, min)) != MP_OKAY)
-      return res;
-
-    /* Increase precision; should already be 0-filled */
-    USED(mp) = min;
-  }
-
-  return MP_OKAY;
-
-} /* end s_mp_pad() */
-
-/* }}} */
-
-/* {{{ s_mp_setz(dp, count) */
-
-#if MP_MACRO == 0
-/* Set 'count' digits pointed to by dp to be zeroes                       */
-void s_mp_setz(mp_digit *dp, mp_size count)
-{
-#if MP_MEMSET == 0
-  int  ix;
-
-  for(ix = 0; ix < count; ix++)
-    dp[ix] = 0;
-#else
-  memset(dp, 0, count * sizeof(mp_digit));
-#endif
-
-} /* end s_mp_setz() */
-#endif
-
-/* }}} */
-
-/* {{{ s_mp_copy(sp, dp, count) */
-
-#if MP_MACRO == 0
-/* Copy 'count' digits from sp to dp                                      */
-void s_mp_copy(mp_digit *sp, mp_digit *dp, mp_size count)
-{
-#if MP_MEMCPY == 0
-  int  ix;
-
-  for(ix = 0; ix < count; ix++)
-    dp[ix] = sp[ix];
-#else
-  memcpy(dp, sp, count * sizeof(mp_digit));
-#endif
-
-} /* end s_mp_copy() */
-#endif
-
-/* }}} */
-
-/* {{{ s_mp_alloc(nb, ni) */
-
-#if MP_MACRO == 0
-/* Allocate ni records of nb bytes each, and return a pointer to that     */
-void    *s_mp_alloc(size_t nb, size_t ni)
-{
-  return calloc(nb, ni);
-
-} /* end s_mp_alloc() */
-#endif
-
-/* }}} */
-
-/* {{{ s_mp_free(ptr) */
-
-#if MP_MACRO == 0
-/* Free the memory pointed to by ptr                                      */
-void     s_mp_free(void *ptr)
-{
-  if(ptr)
-    free(ptr);
-
-} /* end s_mp_free() */
-#endif
-
-/* }}} */
-
-/* {{{ s_mp_clamp(mp) */
-
-/* Remove leading zeroes from the given value                             */
-void     s_mp_clamp(mp_int *mp)
-{
-  mp_size   du = USED(mp);
-  mp_digit *zp = DIGITS(mp) + du - 1;
-
-  while(du > 1 && !*zp--)
-    --du;
-
-  USED(mp) = du;
-
-} /* end s_mp_clamp() */
-
-
-/* }}} */
-
-/* {{{ s_mp_exch(a, b) */
-
-/* Exchange the data for a and b; (b, a) = (a, b)                         */
-void     s_mp_exch(mp_int *a, mp_int *b)
-{
-  mp_int   tmp;
-
-  tmp = *a;
-  *a = *b;
-  *b = tmp;
-
-} /* end s_mp_exch() */
-
-/* }}} */
-
-/* }}} */
-
-/* {{{ Arithmetic helpers */
-
-/* {{{ s_mp_lshd(mp, p) */
-
-/*
-   Shift mp leftward by p digits, growing if needed, and zero-filling
-   the in-shifted digits at the right end.  This is a convenient
-   alternative to multiplication by powers of the radix
- */
-
-mp_err   s_mp_lshd(mp_int *mp, mp_size p)
-{
-  mp_err   res;
-  mp_size  pos;
-  mp_digit *dp;
-  int ix;
-
-  if(p == 0)
-    return MP_OKAY;
-
-  if((res = s_mp_pad(mp, USED(mp) + p)) != MP_OKAY)
-    return res;
-
-  pos = USED(mp) - 1;
-  dp = DIGITS(mp);
-
-  /* Shift all the significant figures over as needed */
-  for(ix = pos - p; ix >= 0; ix--)
-    dp[ix + p] = dp[ix];
-
-  /* Fill the bottom digits with zeroes */
-  for(ix = 0; (unsigned)ix < p; ix++)
-    dp[ix] = 0;
-
-  return MP_OKAY;
-
-} /* end s_mp_lshd() */
-
-/* }}} */
-
-/* {{{ s_mp_rshd(mp, p) */
-
-/*
-   Shift mp rightward by p digits.  Maintains the invariant that
-   digits above the precision are all zero.  Digits shifted off the
-   end are lost.  Cannot fail.
- */
-
-void     s_mp_rshd(mp_int *mp, mp_size p)
-{
-  mp_size  ix;
-  mp_digit *dp;
-
-  if(p == 0)
-    return;
-
-  /* Shortcut when all digits are to be shifted off */
-  if(p >= USED(mp)) {
-    s_mp_setz(DIGITS(mp), ALLOC(mp));
-    USED(mp) = 1;
-    SIGN(mp) = MP_ZPOS;
-    return;
-  }
-
-  /* Shift all the significant figures over as needed */
-  dp = DIGITS(mp);
-  for(ix = p; ix < USED(mp); ix++)
-    dp[ix - p] = dp[ix];
-
-  /* Fill the top digits with zeroes */
-  ix -= p;
-  while(ix < USED(mp))
-    dp[ix++] = 0;
-
-  /* Strip off any leading zeroes    */
-  s_mp_clamp(mp);
-
-} /* end s_mp_rshd() */
-
-/* }}} */
-
-/* {{{ s_mp_div_2(mp) */
-
-/* Divide by two -- take advantage of radix properties to do it fast      */
-void     s_mp_div_2(mp_int *mp)
-{
-  s_mp_div_2d(mp, 1);
-
-} /* end s_mp_div_2() */
-
-/* }}} */
-
-/* {{{ s_mp_mul_2(mp) */
-
-mp_err s_mp_mul_2(mp_int *mp)
-{
-  unsigned int ix;
-  mp_digit kin = 0, kout, *dp = DIGITS(mp);
-  mp_err   res;
-
-  /* Shift digits leftward by 1 bit */
-  for(ix = 0; ix < USED(mp); ix++) {
-    kout = (dp[ix] >> (DIGIT_BIT - 1)) & 1;
-    dp[ix] = (dp[ix] << 1) | kin;
-
-    kin = kout;
-  }
-
-  /* Deal with rollover from last digit */
-  if(kin) {
-    if(ix >= ALLOC(mp)) {
-      if((res = s_mp_grow(mp, ALLOC(mp) + 1)) != MP_OKAY)
-	return res;
-      dp = DIGITS(mp);
-    }
-
-    dp[ix] = kin;
-    USED(mp) += 1;
-  }
-
-  return MP_OKAY;
-
-} /* end s_mp_mul_2() */
-
-/* }}} */
-
-/* {{{ s_mp_mod_2d(mp, d) */
-
-/*
-  Remainder the integer by 2^d, where d is a number of bits.  This
-  amounts to a bitwise AND of the value, and does not require the full
-  division code
- */
-void     s_mp_mod_2d(mp_int *mp, mp_digit d)
-{
-  unsigned int  ndig = (d / DIGIT_BIT), nbit = (d % DIGIT_BIT);
-  unsigned int  ix;
-  mp_digit      dmask, *dp = DIGITS(mp);
-
-  if(ndig >= USED(mp))
-    return;
-
-  /* Flush all the bits above 2^d in its digit */
-  dmask = (1 << nbit) - 1;
-  dp[ndig] &= dmask;
-
-  /* Flush all digits above the one with 2^d in it */
-  for(ix = ndig + 1; ix < USED(mp); ix++)
-    dp[ix] = 0;
-
-  s_mp_clamp(mp);
-
-} /* end s_mp_mod_2d() */
-
-/* }}} */
-
-/* {{{ s_mp_mul_2d(mp, d) */
-
-/*
-  Multiply by the integer 2^d, where d is a number of bits.  This
-  amounts to a bitwise shift of the value, and does not require the
-  full multiplication code.
- */
-mp_err    s_mp_mul_2d(mp_int *mp, mp_digit d)
-{
-  mp_err   res;
-  mp_digit save, next, mask, *dp;
-  mp_size  used;
-  unsigned int ix;
-
-  if((res = s_mp_lshd(mp, d / DIGIT_BIT)) != MP_OKAY)
-    return res;
-
-  dp = DIGITS(mp); used = USED(mp);
-  d %= DIGIT_BIT;
-
-  mask = (1 << d) - 1;
-
-  /* If the shift requires another digit, make sure we've got one to
-     work with */
-  if((dp[used - 1] >> (DIGIT_BIT - d)) & mask) {
-    if((res = s_mp_grow(mp, used + 1)) != MP_OKAY)
-      return res;
-    dp = DIGITS(mp);
-  }
-
-  /* Do the shifting... */
-  save = 0;
-  for(ix = 0; ix < used; ix++) {
-    next = (dp[ix] >> (DIGIT_BIT - d)) & mask;
-    dp[ix] = (dp[ix] << d) | save;
-    save = next;
-  }
-
-  /* If, at this point, we have a nonzero carryout into the next
-     digit, we'll increase the size by one digit, and store it...
-   */
-  if(save) {
-    dp[used] = save;
-    USED(mp) += 1;
-  }
-
-  s_mp_clamp(mp);
-  return MP_OKAY;
-
-} /* end s_mp_mul_2d() */
-
-/* }}} */
-
-/* {{{ s_mp_div_2d(mp, d) */
-
-/*
-  Divide the integer by 2^d, where d is a number of bits.  This
-  amounts to a bitwise shift of the value, and does not require the
-  full division code (used in Barrett reduction, see below)
- */
-void     s_mp_div_2d(mp_int *mp, mp_digit d)
-{
-  int       ix;
-  mp_digit  save, next, mask, *dp = DIGITS(mp);
-
-  s_mp_rshd(mp, d / DIGIT_BIT);
-  d %= DIGIT_BIT;
-
-  mask = (1 << d) - 1;
-
-  save = 0;
-  for(ix = USED(mp) - 1; ix >= 0; ix--) {
-    next = dp[ix] & mask;
-    dp[ix] = (dp[ix] >> d) | (save << (DIGIT_BIT - d));
-    save = next;
-  }
-
-  s_mp_clamp(mp);
-
-} /* end s_mp_div_2d() */
-
-/* }}} */
-
-/* {{{ s_mp_norm(a, b) */
-
-/*
-  s_mp_norm(a, b)
-
-  Normalize a and b for division, where b is the divisor.  In order
-  that we might make good guesses for quotient digits, we want the
-  leading digit of b to be at least half the radix, which we
-  accomplish by multiplying a and b by a constant.  This constant is
-  returned (so that it can be divided back out of the remainder at the
-  end of the division process).
-
-  We multiply by the smallest power of 2 that gives us a leading digit
-  at least half the radix.  By choosing a power of 2, we simplify the
-  multiplication and division steps to simple shifts.
- */
-mp_digit s_mp_norm(mp_int *a, mp_int *b)
-{
-  mp_digit  t, d = 0;
-
-  t = DIGIT(b, USED(b) - 1);
-  while(t < (RADIX / 2)) {
-    t <<= 1;
-    ++d;
-  }
-
-  if(d != 0) {
-    s_mp_mul_2d(a, d);
-    s_mp_mul_2d(b, d);
-  }
-
-  return d;
-
-} /* end s_mp_norm() */
-
-/* }}} */
-
-/* }}} */
-
-/* {{{ Primitive digit arithmetic */
-
-/* {{{ s_mp_add_d(mp, d) */
-
-/* Add d to |mp| in place                                                 */
-mp_err   s_mp_add_d(mp_int *mp, mp_digit d)    /* unsigned digit addition */
-{
-  mp_word   w, k = 0;
-  mp_size   ix = 1, used = USED(mp);
-  mp_digit *dp = DIGITS(mp);
-
-  w = dp[0] + d;
-  dp[0] = ACCUM(w);
-  k = CARRYOUT(w);
-
-  while(ix < used && k) {
-    w = dp[ix] + k;
-    dp[ix] = ACCUM(w);
-    k = CARRYOUT(w);
-    ++ix;
-  }
-
-  if(k != 0) {
-    mp_err  res;
-
-    if((res = s_mp_pad(mp, USED(mp) + 1)) != MP_OKAY)
-      return res;
-
-    DIGIT(mp, ix) = k;
-  }
-
-  return MP_OKAY;
-
-} /* end s_mp_add_d() */
-
-/* }}} */
-
-/* {{{ s_mp_sub_d(mp, d) */
-
-/* Subtract d from |mp| in place, assumes |mp| > d                        */
-mp_err   s_mp_sub_d(mp_int *mp, mp_digit d)    /* unsigned digit subtract */
-{
-  mp_word   w, b = 0;
-  mp_size   ix = 1, used = USED(mp);
-  mp_digit *dp = DIGITS(mp);
-
-  /* Compute initial subtraction    */
-  w = (RADIX + dp[0]) - d;
-  b = CARRYOUT(w) ? 0 : 1;
-  dp[0] = ACCUM(w);
-
-  /* Propagate borrows leftward     */
-  while(b && ix < used) {
-    w = (RADIX + dp[ix]) - b;
-    b = CARRYOUT(w) ? 0 : 1;
-    dp[ix] = ACCUM(w);
-    ++ix;
-  }
-
-  /* Remove leading zeroes          */
-  s_mp_clamp(mp);
-
-  /* If we have a borrow out, it's a violation of the input invariant */
-  if(b)
-    return MP_RANGE;
-  else
-    return MP_OKAY;
-
-} /* end s_mp_sub_d() */
-
-/* }}} */
-
-/* {{{ s_mp_mul_d(a, d) */
-
-/* Compute a = a * d, single digit multiplication                         */
-mp_err   s_mp_mul_d(mp_int *a, mp_digit d)
-{
-  mp_word w, k = 0;
-  mp_size ix, max;
-  mp_err  res;
-  mp_digit *dp = DIGITS(a);
-
-  /*
-    Single-digit multiplication will increase the precision of the
-    output by at most one digit.  However, we can detect when this
-    will happen -- if the high-order digit of a, times d, gives a
-    two-digit result, then the precision of the result will increase;
-    otherwise it won't.  We use this fact to avoid calling s_mp_pad()
-    unless absolutely necessary.
-   */
-  max = USED(a);
-  w = dp[max - 1] * d;
-  if(CARRYOUT(w) != 0) {
-    if((res = s_mp_pad(a, max + 1)) != MP_OKAY)
-      return res;
-    dp = DIGITS(a);
-  }
-
-  for(ix = 0; ix < max; ix++) {
-    w = (dp[ix] * d) + k;
-    dp[ix] = ACCUM(w);
-    k = CARRYOUT(w);
-  }
-
-  /* If there is a precision increase, take care of it here; the above
-     test guarantees we have enough storage to do this safely.
-   */
-  if(k) {
-    dp[max] = k;
-    USED(a) = max + 1;
-  }
-
-  s_mp_clamp(a);
-
-  return MP_OKAY;
-
-} /* end s_mp_mul_d() */
-
-/* }}} */
-
-/* {{{ s_mp_div_d(mp, d, r) */
-
-/*
-  s_mp_div_d(mp, d, r)
-
-  Compute the quotient mp = mp / d and remainder r = mp mod d, for a
-  single digit d.  If r is null, the remainder will be discarded.
- */
-
-mp_err   s_mp_div_d(mp_int *mp, mp_digit d, mp_digit *r)
-{
-  mp_word   w = 0, t;
-  mp_int    quot;
-  mp_err    res;
-  mp_digit *dp = DIGITS(mp), *qp;
-  int       ix;
-
-  if(d == 0)
-    return MP_RANGE;
-
-  /* Make room for the quotient */
-  if((res = mp_init_size(&quot, USED(mp))) != MP_OKAY)
-    return res;
-
-  USED(&quot) = USED(mp); /* so clamping will work below */
-  qp = DIGITS(&quot);
-
-  /* Divide without subtraction */
-  for(ix = USED(mp) - 1; ix >= 0; ix--) {
-    w = (w << DIGIT_BIT) | dp[ix];
-
-    if(w >= d) {
-      t = w / d;
-      w = w % d;
-    } else {
-      t = 0;
-    }
-
-    qp[ix] = t;
-  }
-
-  /* Deliver the remainder, if desired */
-  if(r)
-    *r = w;
-
-  s_mp_clamp(&quot);
-  mp_exch(&quot, mp);
-  mp_clear(&quot);
-
-  return MP_OKAY;
-
-} /* end s_mp_div_d() */
-
-/* }}} */
-
-/* }}} */
-
-/* {{{ Primitive full arithmetic */
-
-/* {{{ s_mp_add(a, b) */
-
-/* Compute a = |a| + |b|                                                  */
-mp_err   s_mp_add(mp_int *a, mp_int *b)        /* magnitude addition      */
-{
-  mp_word   w = 0;
-  mp_digit *pa, *pb;
-  mp_size   ix, used = USED(b);
-  mp_err    res;
-
-  /* Make sure a has enough precision for the output value */
-  if((used > USED(a)) && (res = s_mp_pad(a, used)) != MP_OKAY)
-    return res;
-
-  /*
-    Add up all digits up to the precision of b.  If b had initially
-    the same precision as a, or greater, we took care of it by the
-    padding step above, so there is no problem.  If b had initially
-    less precision, we'll have to make sure the carry out is duly
-    propagated upward among the higher-order digits of the sum.
-   */
-  pa = DIGITS(a);
-  pb = DIGITS(b);
-  for(ix = 0; ix < used; ++ix) {
-    w += *pa + *pb++;
-    *pa++ = ACCUM(w);
-    w = CARRYOUT(w);
-  }
-
-  /* If we run out of 'b' digits before we're actually done, make
-     sure the carries get propagated upward...
-   */
-  used = USED(a);
-  while(w && ix < used) {
-    w += *pa;
-    *pa++ = ACCUM(w);
-    w = CARRYOUT(w);
-    ++ix;
-  }
-
-  /* If there's an overall carry out, increase precision and include
-     it.  We could have done this initially, but why touch the memory
-     allocator unless we're sure we have to?
-   */
-  if(w) {
-    if((res = s_mp_pad(a, used + 1)) != MP_OKAY)
-      return res;
-
-    DIGIT(a, ix) = w;  /* pa may not be valid after s_mp_pad() call */
-  }
-
-  return MP_OKAY;
-
-} /* end s_mp_add() */
-
-/* }}} */
-
-/* {{{ s_mp_sub(a, b) */
-
-/* Compute a = |a| - |b|, assumes |a| >= |b|                              */
-mp_err   s_mp_sub(mp_int *a, mp_int *b)        /* magnitude subtract      */
-{
-  mp_word   w = 0;
-  mp_digit *pa, *pb;
-  mp_size   ix, used = USED(b);
-
-  /*
-    Subtract and propagate borrow.  Up to the precision of b, this
-    accounts for the digits of b; after that, we just make sure the
-    carries get to the right place.  This saves having to pad b out to
-    the precision of a just to make the loops work right...
-   */
-  pa = DIGITS(a);
-  pb = DIGITS(b);
-
-  for(ix = 0; ix < used; ++ix) {
-    w = (RADIX + *pa) - w - *pb++;
-    *pa++ = ACCUM(w);
-    w = CARRYOUT(w) ? 0 : 1;
-  }
-
-  used = USED(a);
-  while(ix < used) {
-    w = RADIX + *pa - w;
-    *pa++ = ACCUM(w);
-    w = CARRYOUT(w) ? 0 : 1;
-    ++ix;
-  }
-
-  /* Clobber any leading zeroes we created    */
-  s_mp_clamp(a);
-
-  /*
-     If there was a borrow out, then |b| > |a| in violation
-     of our input invariant.  We've already done the work,
-     but we'll at least complain about it...
-   */
-  if(w)
-    return MP_RANGE;
-  else
-    return MP_OKAY;
-
-} /* end s_mp_sub() */
-
-/* }}} */
-
-mp_err   s_mp_reduce(mp_int *x, mp_int *m, mp_int *mu)
-{
-  mp_int   q;
-  mp_err   res;
-  mp_size  um = USED(m);
-
-  if((res = mp_init_copy(&q, x)) != MP_OKAY)
-    return res;
-
-  s_mp_rshd(&q, um - 1);       /* q1 = x / b^(k-1)  */
-  s_mp_mul(&q, mu);            /* q2 = q1 * mu      */
-  s_mp_rshd(&q, um + 1);       /* q3 = q2 / b^(k+1) */
-
-  /* x = x mod b^(k+1), quick (no division) */
-  s_mp_mod_2d(x, (mp_digit)(DIGIT_BIT * (um + 1)));
-
-  /* q = q * m mod b^(k+1), quick (no division), uses the short multiplier */
-#ifndef SHRT_MUL
-  s_mp_mul(&q, m);
-  s_mp_mod_2d(&q, (mp_digit)(DIGIT_BIT * (um + 1)));
-#else
-  s_mp_mul_dig(&q, m, um + 1);
-#endif
-
-  /* x = x - q */
-  if((res = mp_sub(x, &q, x)) != MP_OKAY)
-    goto CLEANUP;
-
-  /* If x < 0, add b^(k+1) to it */
-  if(mp_cmp_z(x) < 0) {
-    mp_set(&q, 1);
-    if((res = s_mp_lshd(&q, um + 1)) != MP_OKAY)
-      goto CLEANUP;
-    if((res = mp_add(x, &q, x)) != MP_OKAY)
-      goto CLEANUP;
-  }
-
-  /* Back off if it's too big */
-  while(mp_cmp(x, m) >= 0) {
-    if((res = s_mp_sub(x, m)) != MP_OKAY)
-      break;
-  }
-
- CLEANUP:
-  mp_clear(&q);
-
-  return res;
-
-} /* end s_mp_reduce() */
-
-
-
-/* {{{ s_mp_mul(a, b) */
-
-/* Compute a = |a| * |b|                                                  */
-mp_err   s_mp_mul(mp_int *a, mp_int *b)
-{
-  mp_word   w, k = 0;
-  mp_int    tmp;
-  mp_err    res;
-  mp_size   ix, jx, ua = USED(a), ub = USED(b);
-  mp_digit *pa, *pb, *pt, *pbt;
-
-  if((res = mp_init_size(&tmp, ua + ub)) != MP_OKAY)
-    return res;
-
-  /* This has the effect of left-padding with zeroes... */
-  USED(&tmp) = ua + ub;
-
-  /* We're going to need the base value each iteration */
-  pbt = DIGITS(&tmp);
-
-  /* Outer loop:  Digits of b */
-
-  pb = DIGITS(b);
-  for(ix = 0; ix < ub; ++ix, ++pb) {
-    if(*pb == 0)
-      continue;
-
-    /* Inner product:  Digits of a */
-    pa = DIGITS(a);
-    for(jx = 0; jx < ua; ++jx, ++pa) {
-      pt = pbt + ix + jx;
-      w = *pb * *pa + k + *pt;
-      *pt = ACCUM(w);
-      k = CARRYOUT(w);
-    }
-
-    pbt[ix + jx] = k;
-    k = 0;
-  }
-
-  s_mp_clamp(&tmp);
-  s_mp_exch(&tmp, a);
-
-  mp_clear(&tmp);
-
-  return MP_OKAY;
-
-} /* end s_mp_mul() */
-
-/* }}} */
-
-/* {{{ s_mp_kmul(a, b, out, len) */
-
-#if 0
-void   s_mp_kmul(mp_digit *a, mp_digit *b, mp_digit *out, mp_size len)
-{
-  mp_word   w, k = 0;
-  mp_size   ix, jx;
-  mp_digit *pa, *pt;
-
-  for(ix = 0; ix < len; ++ix, ++b) {
-    if(*b == 0)
-      continue;
-
-    pa = a;
-    for(jx = 0; jx < len; ++jx, ++pa) {
-      pt = out + ix + jx;
-      w = *b * *pa + k + *pt;
-      *pt = ACCUM(w);
-      k = CARRYOUT(w);
-    }
-
-    out[ix + jx] = k;
-    k = 0;
-  }
-
-} /* end s_mp_kmul() */
-#endif
-
-/* }}} */
-
-/* {{{ s_mp_sqr(a) */
-
-/*
-  Computes the square of a, in place.  This can be done more
-  efficiently than a general multiplication, because many of the
-  computation steps are redundant when squaring.  The inner product
-  step is a bit more complicated, but we save a fair number of
-  iterations of the multiplication loop.
- */
-#if MP_SQUARE
-mp_err   s_mp_sqr(mp_int *a)
-{
-  mp_word  w, k = 0;
-  mp_int   tmp;
-  mp_err   res;
-  mp_size  ix, jx, kx, used = USED(a);
-  mp_digit *pa1, *pa2, *pt, *pbt;
-
-  if((res = mp_init_size(&tmp, 2 * used)) != MP_OKAY)
-    return res;
-
-  /* Left-pad with zeroes */
-  USED(&tmp) = 2 * used;
-
-  /* We need the base value each time through the loop */
-  pbt = DIGITS(&tmp);
-
-  pa1 = DIGITS(a);
-  for(ix = 0; ix < used; ++ix, ++pa1) {
-    if(*pa1 == 0)
-      continue;
-
-    w = DIGIT(&tmp, ix + ix) + (*pa1 * *pa1);
-
-    pbt[ix + ix] = ACCUM(w);
-    k = CARRYOUT(w);
-
-    /*
-      The inner product is computed as:
-
-         (C, S) = t[i,j] + 2 a[i] a[j] + C
-
-      This can overflow what can be represented in an mp_word, and
-      since C arithmetic does not provide any way to check for
-      overflow, we have to check explicitly for overflow conditions
-      before they happen.
-     */
-    for(jx = ix + 1, pa2 = DIGITS(a) + jx; jx < used; ++jx, ++pa2) {
-      mp_word  u = 0, v;
-
-      /* Store this in a temporary to avoid indirections later */
-      pt = pbt + ix + jx;
-
-      /* Compute the multiplicative step */
-      w = *pa1 * *pa2;
-
-      /* If w is more than half MP_WORD_MAX, the doubling will
-	 overflow, and we need to record a carry out into the next
-	 word */
-      u = (w >> (MP_WORD_BIT - 1)) & 1;
-
-      /* Double what we've got, overflow will be ignored as defined
-	 for C arithmetic (we've already noted if it is to occur)
-       */
-      w *= 2;
-
-      /* Compute the additive step */
-      v = *pt + k;
-
-      /* If we do not already have an overflow carry, check to see
-	 if the addition will cause one, and set the carry out if so
-       */
-      u |= ((MP_WORD_MAX - v) < w);
-
-      /* Add in the rest, again ignoring overflow */
-      w += v;
-
-      /* Set the i,j digit of the output */
-      *pt = ACCUM(w);
-
-      /* Save carry information for the next iteration of the loop.
-	 This is why k must be an mp_word, instead of an mp_digit */
-      k = CARRYOUT(w) | (u << DIGIT_BIT);
-
-    } /* for(jx ...) */
-
-    /* Set the last digit in the cycle and reset the carry */
-    k = DIGIT(&tmp, ix + jx) + k;
-    pbt[ix + jx] = ACCUM(k);
-    k = CARRYOUT(k);
-
-    /* If we are carrying out, propagate the carry to the next digit
-       in the output.  This may cascade, so we have to be somewhat
-       circumspect -- but we will have enough precision in the output
-       that we won't overflow
-     */
-    kx = 1;
-    while(k) {
-      k = pbt[ix + jx + kx] + 1;
-      pbt[ix + jx + kx] = ACCUM(k);
-      k = CARRYOUT(k);
-      ++kx;
-    }
-  } /* for(ix ...) */
-
-  s_mp_clamp(&tmp);
-  s_mp_exch(&tmp, a);
-
-  mp_clear(&tmp);
-
-  return MP_OKAY;
-
-} /* end s_mp_sqr() */
-#endif
-
-/* }}} */
-
-/* {{{ s_mp_div(a, b) */
-
-/*
-  s_mp_div(a, b)
-
-  Compute a = a / b and b = a mod b.  Assumes b > a.
- */
-
-mp_err   s_mp_div(mp_int *a, mp_int *b)
-{
-  mp_int   quot, rem, t;
-  mp_word  q;
-  mp_err   res;
-  mp_digit d;
-  int      ix;
-
-  if(mp_cmp_z(b) == 0)
-    return MP_RANGE;
-
-  /* Shortcut if b is power of two */
-  if((ix = s_mp_ispow2(b)) >= 0) {
-    mp_copy(a, b);  /* need this for remainder */
-    s_mp_div_2d(a, (mp_digit)ix);
-    s_mp_mod_2d(b, (mp_digit)ix);
-
-    return MP_OKAY;
-  }
-
-  /* Allocate space to store the quotient */
-  if((res = mp_init_size(&quot, USED(a))) != MP_OKAY)
-    return res;
-
-  /* A working temporary for division     */
-  if((res = mp_init_size(&t, USED(a))) != MP_OKAY)
-    goto T;
-
-  /* Allocate space for the remainder     */
-  if((res = mp_init_size(&rem, USED(a))) != MP_OKAY)
-    goto REM;
-
-  /* Normalize to optimize guessing       */
-  d = s_mp_norm(a, b);
-
-  /* Perform the division itself...woo!   */
-  ix = USED(a) - 1;
-
-  while(ix >= 0) {
-    /* Find a partial substring of a which is at least b */
-    while(s_mp_cmp(&rem, b) < 0 && ix >= 0) {
-      if((res = s_mp_lshd(&rem, 1)) != MP_OKAY)
-	goto CLEANUP;
-
-      if((res = s_mp_lshd(&quot, 1)) != MP_OKAY)
-	goto CLEANUP;
-
-      DIGIT(&rem, 0) = DIGIT(a, ix);
-      s_mp_clamp(&rem);
-      --ix;
-    }
-
-    /* If we didn't find one, we're finished dividing    */
-    if(s_mp_cmp(&rem, b) < 0)
-      break;
-
-    /* Compute a guess for the next quotient digit       */
-    q = DIGIT(&rem, USED(&rem) - 1);
-    if(q <= DIGIT(b, USED(b) - 1) && USED(&rem) > 1)
-      q = (q << DIGIT_BIT) | DIGIT(&rem, USED(&rem) - 2);
-
-    q /= DIGIT(b, USED(b) - 1);
-
-    /* The guess can be as much as RADIX + 1 */
-    if(q >= RADIX)
-      q = RADIX - 1;
-
-    /* See what that multiplies out to                   */
-    mp_copy(b, &t);
-    if((res = s_mp_mul_d(&t, q)) != MP_OKAY)
-      goto CLEANUP;
-
-    /*
-       If it's too big, back it off.  We should not have to do this
-       more than once, or, in rare cases, twice.  Knuth describes a
-       method by which this could be reduced to a maximum of once, but
-       I didn't implement that here.
-     */
-    while(s_mp_cmp(&t, &rem) > 0) {
-      --q;
-      s_mp_sub(&t, b);
-    }
-
-    /* At this point, q should be the right next digit   */
-    if((res = s_mp_sub(&rem, &t)) != MP_OKAY)
-      goto CLEANUP;
-
-    /*
-      Include the digit in the quotient.  We allocated enough memory
-      for any quotient we could ever possibly get, so we should not
-      have to check for failures here
-     */
-    DIGIT(&quot, 0) = q;
-  }
-
-  /* Denormalize remainder                */
-  if(d != 0)
-    s_mp_div_2d(&rem, d);
-
-  s_mp_clamp(&quot);
-  s_mp_clamp(&rem);
-
-  /* Copy quotient back to output         */
-  s_mp_exch(&quot, a);
-
-  /* Copy remainder back to output        */
-  s_mp_exch(&rem, b);
-
-CLEANUP:
-  mp_clear(&rem);
-REM:
-  mp_clear(&t);
-T:
-  mp_clear(&quot);
-
-  return res;
-
-} /* end s_mp_div() */
-
-/* }}} */
-
-/* {{{ s_mp_2expt(a, k) */
-
-mp_err   s_mp_2expt(mp_int *a, mp_digit k)
-{
-  mp_err    res;
-  mp_size   dig, bit;
-
-  dig = k / DIGIT_BIT;
-  bit = k % DIGIT_BIT;
-
-  mp_zero(a);
-  if((res = s_mp_pad(a, dig + 1)) != MP_OKAY)
-    return res;
-
-  DIGIT(a, dig) |= (1 << bit);
-
-  return MP_OKAY;
-
-} /* end s_mp_2expt() */
-
-/* }}} */
-
-
-/* }}} */
-
-/* }}} */
-
-/* {{{ Primitive comparisons */
-
-/* {{{ s_mp_cmp(a, b) */
-
-/* Compare |a| <=> |b|, return 0 if equal, <0 if a<b, >0 if a>b           */
-int      s_mp_cmp(mp_int *a, mp_int *b)
-{
-  mp_size   ua = USED(a), ub = USED(b);
-
-  if(ua > ub)
-    return MP_GT;
-  else if(ua < ub)
-    return MP_LT;
-  else {
-    int      ix = ua - 1;
-    mp_digit *ap = DIGITS(a) + ix, *bp = DIGITS(b) + ix;
-
-    while(ix >= 0) {
-      if(*ap > *bp)
-	return MP_GT;
-      else if(*ap < *bp)
-	return MP_LT;
-
-      --ap; --bp; --ix;
-    }
-
-    return MP_EQ;
-  }
-
-} /* end s_mp_cmp() */
-
-/* }}} */
-
-/* {{{ s_mp_cmp_d(a, d) */
-
-/* Compare |a| <=> d, return 0 if equal, <0 if a<d, >0 if a>d             */
-int      s_mp_cmp_d(mp_int *a, mp_digit d)
-{
-  mp_size  ua = USED(a);
-  mp_digit *ap = DIGITS(a);
-
-  if(ua > 1)
-    return MP_GT;
-
-  if(*ap < d)
-    return MP_LT;
-  else if(*ap > d)
-    return MP_GT;
-  else
-    return MP_EQ;
-
-} /* end s_mp_cmp_d() */
-
-/* }}} */
-
-/* {{{ s_mp_ispow2(v) */
-
-/*
-  Returns -1 if the value is not a power of two; otherwise, it returns
-  k such that v = 2^k, i.e. lg(v).
- */
-int      s_mp_ispow2(mp_int *v)
-{
-  mp_digit d, *dp;
-  mp_size  uv = USED(v);
-  int      extra = 0, ix;
-
-  d = DIGIT(v, uv - 1); /* most significant digit of v */
-
-  while(d && ((d & 1) == 0)) {
-    d >>= 1;
-    ++extra;
-  }
-
-  if(d == 1) {
-    ix = uv - 2;
-    dp = DIGITS(v) + ix;
-
-    while(ix >= 0) {
-      if(*dp)
-	return -1; /* not a power of two */
-
-      --dp; --ix;
-    }
-
-    return ((uv - 1) * DIGIT_BIT) + extra;
-  }
-
-  return -1;
-
-} /* end s_mp_ispow2() */
-
-/* }}} */
-
-/* {{{ s_mp_ispow2d(d) */
-
-int      s_mp_ispow2d(mp_digit d)
-{
-  int   pow = 0;
-
-  while((d & 1) == 0) {
-    ++pow; d >>= 1;
-  }
-
-  if(d == 1)
-    return pow;
-
-  return -1;
-
-} /* end s_mp_ispow2d() */
-
-/* }}} */
-
-/* }}} */
-
-/* {{{ Primitive I/O helpers */
-
-/* {{{ s_mp_tovalue(ch, r) */
-
-/*
-  Convert the given character to its digit value, in the given radix.
-  If the given character is not understood in the given radix, -1 is
-  returned.  Otherwise the digit's numeric value is returned.
-
-  The results will be odd if you use a radix < 2 or > 62, you are
-  expected to know what you're up to.
- */
-int      s_mp_tovalue(char ch, int r)
-{
-  int    val, xch;
-
-  if(r > 36)
-    xch = ch;
-  else
-    xch = toupper(ch);
-
-  if(isdigit(xch))
-    val = xch - '0';
-  else if(isupper(xch))
-    val = xch - 'A' + 10;
-  else if(islower(xch))
-    val = xch - 'a' + 36;
-  else if(xch == '+')
-    val = 62;
-  else if(xch == '/')
-    val = 63;
-  else
-    return -1;
-
-  if(val < 0 || val >= r)
-    return -1;
-
-  return val;
-
-} /* end s_mp_tovalue() */
-
-/* }}} */
-
-/* {{{ s_mp_todigit(val, r, low) */
-
-/*
-  Convert val to a radix-r digit, if possible.  If val is out of range
-  for r, returns zero.  Otherwise, returns an ASCII character denoting
-  the value in the given radix.
-
-  The results may be odd if you use a radix < 2 or > 64, you are
-  expected to know what you're doing.
- */
-
-char     s_mp_todigit(int val, int r, int low)
-{
-  char   ch;
-
-  if(val < 0 || val >= r)
-    return 0;
-
-  ch = s_dmap_1[val];
-
-  if(r <= 36 && low)
-    ch = tolower(ch);
-
-  return ch;
-
-} /* end s_mp_todigit() */
-
-/* }}} */
-
-/* {{{ s_mp_outlen(bits, radix) */
-
-/*
-   Return an estimate for how long a string is needed to hold a radix
-   r representation of a number with 'bits' significant bits.
-
-   Does not include space for a sign or a NUL terminator.
- */
-int      s_mp_outlen(int bits, int r)
-{
-  return (int)((double)bits * LOG_V_2(r));
-
-} /* end s_mp_outlen() */
-
-/* }}} */
-
-/* }}} */
-
-/*------------------------------------------------------------------------*/
-/* HERE THERE BE DRAGONS                                                  */
-/* crc==4242132123, version==2, Sat Feb 02 06:43:52 2002 */
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
diff --git a/libtommath/mtest/mpi.h b/libtommath/mtest/mpi.h
deleted file mode 100644
index 5accb52..0000000
--- a/libtommath/mtest/mpi.h
+++ /dev/null
@@ -1,231 +0,0 @@
-/*
-    mpi.h
-
-    by Michael J. Fromberger <sting@linguist.dartmouth.edu>
-    Copyright (C) 1998 Michael J. Fromberger, All Rights Reserved
-
-    Arbitrary precision integer arithmetic library
-
-    $Id$
- */
-
-#ifndef _H_MPI_
-#define _H_MPI_
-
-#include "mpi-config.h"
-
-#define  MP_LT       -1
-#define  MP_EQ        0
-#define  MP_GT        1
-
-#if MP_DEBUG
-#undef MP_IOFUNC
-#define MP_IOFUNC 1
-#endif
-
-#if MP_IOFUNC
-#include <stdio.h>
-#include <ctype.h>
-#endif
-
-#include <limits.h>
-
-#define  MP_NEG  1
-#define  MP_ZPOS 0
-
-/* Included for compatibility... */
-#define  NEG     MP_NEG
-#define  ZPOS    MP_ZPOS
-
-#define  MP_OKAY          0 /* no error, all is well */
-#define  MP_YES           0 /* yes (boolean result)  */
-#define  MP_NO           -1 /* no (boolean result)   */
-#define  MP_MEM          -2 /* out of memory         */
-#define  MP_RANGE        -3 /* argument out of range */
-#define  MP_BADARG       -4 /* invalid parameter     */
-#define  MP_UNDEF        -5 /* answer is undefined   */
-#define  MP_LAST_CODE    MP_UNDEF
-
-#include "mpi-types.h"
-
-/* Included for compatibility... */
-#define DIGIT_BIT         MP_DIGIT_BIT
-#define DIGIT_MAX         MP_DIGIT_MAX
-
-/* Macros for accessing the mp_int internals           */
-#define  SIGN(MP)     ((MP)->sign)
-#define  USED(MP)     ((MP)->used)
-#define  ALLOC(MP)    ((MP)->alloc)
-#define  DIGITS(MP)   ((MP)->dp)
-#define  DIGIT(MP,N)  (MP)->dp[(N)]
-
-#if MP_ARGCHK == 1
-#define  ARGCHK(X,Y)  {if(!(X)){return (Y);}}
-#elif MP_ARGCHK == 2
-#include <assert.h>
-#define  ARGCHK(X,Y)  assert(X)
-#else
-#define  ARGCHK(X,Y)  /*  */
-#endif
-
-/* This defines the maximum I/O base (minimum is 2)   */
-#define MAX_RADIX         64
-
-typedef struct {
-  mp_sign       sign;    /* sign of this quantity      */
-  mp_size       alloc;   /* how many digits allocated  */
-  mp_size       used;    /* how many digits used       */
-  mp_digit     *dp;      /* the digits themselves      */
-} mp_int;
-
-/*------------------------------------------------------------------------*/
-/* Default precision                                                      */
-
-unsigned int mp_get_prec(void);
-void         mp_set_prec(unsigned int prec);
-
-/*------------------------------------------------------------------------*/
-/* Memory management                                                      */
-
-mp_err mp_init(mp_int *mp);
-mp_err mp_init_array(mp_int mp[], int count);
-mp_err mp_init_size(mp_int *mp, mp_size prec);
-mp_err mp_init_copy(mp_int *mp, mp_int *from);
-mp_err mp_copy(mp_int *from, mp_int *to);
-void   mp_exch(mp_int *mp1, mp_int *mp2);
-void   mp_clear(mp_int *mp);
-void   mp_clear_array(mp_int mp[], int count);
-void   mp_zero(mp_int *mp);
-void   mp_set(mp_int *mp, mp_digit d);
-mp_err mp_set_int(mp_int *mp, long z);
-mp_err mp_shrink(mp_int *a);
-
-
-/*------------------------------------------------------------------------*/
-/* Single digit arithmetic                                                */
-
-mp_err mp_add_d(mp_int *a, mp_digit d, mp_int *b);
-mp_err mp_sub_d(mp_int *a, mp_digit d, mp_int *b);
-mp_err mp_mul_d(mp_int *a, mp_digit d, mp_int *b);
-mp_err mp_mul_2(mp_int *a, mp_int *c);
-mp_err mp_div_d(mp_int *a, mp_digit d, mp_int *q, mp_digit *r);
-mp_err mp_div_2(mp_int *a, mp_int *c);
-mp_err mp_expt_d(mp_int *a, mp_digit d, mp_int *c);
-
-/*------------------------------------------------------------------------*/
-/* Sign manipulations                                                     */
-
-mp_err mp_abs(mp_int *a, mp_int *b);
-mp_err mp_neg(mp_int *a, mp_int *b);
-
-/*------------------------------------------------------------------------*/
-/* Full arithmetic                                                        */
-
-mp_err mp_add(mp_int *a, mp_int *b, mp_int *c);
-mp_err mp_sub(mp_int *a, mp_int *b, mp_int *c);
-mp_err mp_mul(mp_int *a, mp_int *b, mp_int *c);
-mp_err mp_mul_2d(mp_int *a, mp_digit d, mp_int *c);
-#if MP_SQUARE
-mp_err mp_sqr(mp_int *a, mp_int *b);
-#else
-#define mp_sqr(a, b) mp_mul(a, a, b)
-#endif
-mp_err mp_div(mp_int *a, mp_int *b, mp_int *q, mp_int *r);
-mp_err mp_div_2d(mp_int *a, mp_digit d, mp_int *q, mp_int *r);
-mp_err mp_expt(mp_int *a, mp_int *b, mp_int *c);
-mp_err mp_2expt(mp_int *a, mp_digit k);
-mp_err mp_sqrt(mp_int *a, mp_int *b);
-
-/*------------------------------------------------------------------------*/
-/* Modular arithmetic                                                     */
-
-#if MP_MODARITH
-mp_err mp_mod(mp_int *a, mp_int *m, mp_int *c);
-mp_err mp_mod_d(mp_int *a, mp_digit d, mp_digit *c);
-mp_err mp_addmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c);
-mp_err mp_submod(mp_int *a, mp_int *b, mp_int *m, mp_int *c);
-mp_err mp_mulmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c);
-#if MP_SQUARE
-mp_err mp_sqrmod(mp_int *a, mp_int *m, mp_int *c);
-#else
-#define mp_sqrmod(a, m, c) mp_mulmod(a, a, m, c)
-#endif
-mp_err mp_exptmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c);
-mp_err mp_exptmod_d(mp_int *a, mp_digit d, mp_int *m, mp_int *c);
-#endif /* MP_MODARITH */
-
-/*------------------------------------------------------------------------*/
-/* Comparisons                                                            */
-
-int    mp_cmp_z(mp_int *a);
-int    mp_cmp_d(mp_int *a, mp_digit d);
-int    mp_cmp(mp_int *a, mp_int *b);
-int    mp_cmp_mag(mp_int *a, mp_int *b);
-int    mp_cmp_int(mp_int *a, long z);
-int    mp_isodd(mp_int *a);
-int    mp_iseven(mp_int *a);
-
-/*------------------------------------------------------------------------*/
-/* Number theoretic                                                       */
-
-#if MP_NUMTH
-mp_err mp_gcd(mp_int *a, mp_int *b, mp_int *c);
-mp_err mp_lcm(mp_int *a, mp_int *b, mp_int *c);
-mp_err mp_xgcd(mp_int *a, mp_int *b, mp_int *g, mp_int *x, mp_int *y);
-mp_err mp_invmod(mp_int *a, mp_int *m, mp_int *c);
-#endif /* end MP_NUMTH */
-
-/*------------------------------------------------------------------------*/
-/* Input and output                                                       */
-
-#if MP_IOFUNC
-void   mp_print(mp_int *mp, FILE *ofp);
-#endif /* end MP_IOFUNC */
-
-/*------------------------------------------------------------------------*/
-/* Base conversion                                                        */
-
-#define BITS     1
-#define BYTES    CHAR_BIT
-
-mp_err mp_read_signed_bin(mp_int *mp, unsigned char *str, int len);
-int    mp_signed_bin_size(mp_int *mp);
-mp_err mp_to_signed_bin(mp_int *mp, unsigned char *str);
-
-mp_err mp_read_unsigned_bin(mp_int *mp, unsigned char *str, int len);
-int    mp_unsigned_bin_size(mp_int *mp);
-mp_err mp_to_unsigned_bin(mp_int *mp, unsigned char *str);
-
-int    mp_count_bits(mp_int *mp);
-
-#if MP_COMPAT_MACROS
-#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
-#define mp_raw_size(mp)           mp_signed_bin_size(mp)
-#define mp_toraw(mp, str)         mp_to_signed_bin((mp), (str))
-#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
-#define mp_mag_size(mp)           mp_unsigned_bin_size(mp)
-#define mp_tomag(mp, str)         mp_to_unsigned_bin((mp), (str))
-#endif
-
-mp_err mp_read_radix(mp_int *mp, unsigned char *str, int radix);
-int    mp_radix_size(mp_int *mp, int radix);
-int    mp_value_radix_size(int num, int qty, int radix);
-mp_err mp_toradix(mp_int *mp, char *str, int radix);
-
-int    mp_char2value(char ch, int r);
-
-#define mp_tobinary(M, S)  mp_toradix((M), (S), 2)
-#define mp_tooctal(M, S)   mp_toradix((M), (S), 8)
-#define mp_todecimal(M, S) mp_toradix((M), (S), 10)
-#define mp_tohex(M, S)     mp_toradix((M), (S), 16)
-
-/*------------------------------------------------------------------------*/
-/* Error strings                                                          */
-
-const  char  *mp_strerror(mp_err ec);
-
-#endif /* end _H_MPI_ */
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
diff --git a/libtommath/mtest/mtest.c b/libtommath/mtest/mtest.c
deleted file mode 100644
index 56b5a90..0000000
--- a/libtommath/mtest/mtest.c
+++ /dev/null
@@ -1,374 +0,0 @@
-/* makes a bignum test harness with NUM tests per operation
- *
- * the output is made in the following format [one parameter per line]
-
-operation
-operand1
-operand2
-[... operandN]
-result1
-result2
-[... resultN]
-
-So for example "a * b mod n" would be
-
-mulmod
-a
-b
-n
-a*b mod n
-
-e.g. if a=3, b=4 n=11 then
-
-mulmod
-3
-4
-11
-1
-
- */
-
-#ifdef MP_8BIT
-#define THE_MASK 127
-#else
-#define THE_MASK 32767
-#endif
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <time.h>
-#include "mpi.c"
-
-#ifdef LTM_MTEST_REAL_RAND
-#define getRandChar() fgetc(rng)
-FILE *rng;
-#else
-#define getRandChar() (rand()&0xFF)
-#endif
-
-void rand_num(mp_int *a)
-{
-   int size;
-   unsigned char buf[2048];
-   size_t sz;
-
-   size = 1 + ((getRandChar()<<8) + getRandChar()) % 101;
-   buf[0] = (getRandChar()&1)?1:0;
-#ifdef LTM_MTEST_REAL_RAND
-   sz = fread(buf+1, 1, size, rng);
-#else
-   sz = 1;
-   while (sz < (unsigned)size) {
-       buf[sz] = getRandChar();
-       ++sz;
-   }
-#endif
-   if (sz != (unsigned)size) {
-       fprintf(stderr, "\nWarning: fread failed\n\n");
-   }
-   while (buf[1] == 0) buf[1] = getRandChar();
-   mp_read_raw(a, buf, 1+size);
-}
-
-void rand_num2(mp_int *a)
-{
-   int size;
-   unsigned char buf[2048];
-   size_t sz;
-
-   size = 10 + ((getRandChar()<<8) + getRandChar()) % 101;
-   buf[0] = (getRandChar()&1)?1:0;
-#ifdef LTM_MTEST_REAL_RAND
-   sz = fread(buf+1, 1, size, rng);
-#else
-   sz = 1;
-   while (sz < (unsigned)size) {
-       buf[sz] = getRandChar();
-       ++sz;
-   }
-#endif
-   if (sz != (unsigned)size) {
-       fprintf(stderr, "\nWarning: fread failed\n\n");
-   }
-   while (buf[1] == 0) buf[1] = getRandChar();
-   mp_read_raw(a, buf, 1+size);
-}
-
-#define mp_to64(a, b) mp_toradix(a, b, 64)
-
-int main(int argc, char *argv[])
-{
-   int n, tmp;
-   long long max;
-   mp_int a, b, c, d, e;
-#ifdef MTEST_NO_FULLSPEED
-   clock_t t1;
-#endif
-   char buf[4096];
-
-   mp_init(&a);
-   mp_init(&b);
-   mp_init(&c);
-   mp_init(&d);
-   mp_init(&e);
-
-   if (argc > 1) {
-       max = strtol(argv[1], NULL, 0);
-       if (max < 0) {
-           if (max > -64) {
-               max = (1 << -(max)) + 1;
-           } else {
-               max = 1;
-           }
-       } else if (max == 0) {
-           max = 1;
-       }
-   }
-   else {
-       max = 0;
-   }
-
-
-   /* initial (2^n - 1)^2 testing, makes sure the comba multiplier works [it has the new carry code] */
-/*
-   mp_set(&a, 1);
-   for (n = 1; n < 8192; n++) {
-       mp_mul(&a, &a, &c);
-       printf("mul\n");
-       mp_to64(&a, buf);
-       printf("%s\n%s\n", buf, buf);
-       mp_to64(&c, buf);
-       printf("%s\n", buf);
-
-       mp_add_d(&a, 1, &a);
-       mp_mul_2(&a, &a);
-       mp_sub_d(&a, 1, &a);
-   }
-*/
-
-#ifdef LTM_MTEST_REAL_RAND
-   rng = fopen("/dev/urandom", "rb");
-   if (rng == NULL) {
-      rng = fopen("/dev/random", "rb");
-      if (rng == NULL) {
-         fprintf(stderr, "\nWarning:  stdin used as random source\n\n");
-         rng = stdin;
-      }
-   }
-#else
-   srand(23);
-#endif
-
-#ifdef MTEST_NO_FULLSPEED
-   t1 = clock();
-#endif
-   for (;;) {
-#ifdef MTEST_NO_FULLSPEED
-      if (clock() - t1 > CLOCKS_PER_SEC) {
-         sleep(2);
-         t1 = clock();
-      }
-#endif
-       n = getRandChar() % 15;
-
-       if (max != 0) {
-           --max;
-           if (max == 0)
-             n = 255;
-       }
-
-   if (n == 0) {
-       /* add tests */
-       rand_num(&a);
-       rand_num(&b);
-       mp_add(&a, &b, &c);
-       printf("add\n");
-       mp_to64(&a, buf);
-       printf("%s\n", buf);
-       mp_to64(&b, buf);
-       printf("%s\n", buf);
-       mp_to64(&c, buf);
-       printf("%s\n", buf);
-   } else if (n == 1) {
-      /* sub tests */
-       rand_num(&a);
-       rand_num(&b);
-       mp_sub(&a, &b, &c);
-       printf("sub\n");
-       mp_to64(&a, buf);
-       printf("%s\n", buf);
-       mp_to64(&b, buf);
-       printf("%s\n", buf);
-       mp_to64(&c, buf);
-       printf("%s\n", buf);
-   } else if (n == 2) {
-       /* mul tests */
-       rand_num(&a);
-       rand_num(&b);
-       mp_mul(&a, &b, &c);
-       printf("mul\n");
-       mp_to64(&a, buf);
-       printf("%s\n", buf);
-       mp_to64(&b, buf);
-       printf("%s\n", buf);
-       mp_to64(&c, buf);
-       printf("%s\n", buf);
-   } else if (n == 3) {
-      /* div tests */
-       rand_num(&a);
-       rand_num(&b);
-       mp_div(&a, &b, &c, &d);
-       printf("div\n");
-       mp_to64(&a, buf);
-       printf("%s\n", buf);
-       mp_to64(&b, buf);
-       printf("%s\n", buf);
-       mp_to64(&c, buf);
-       printf("%s\n", buf);
-       mp_to64(&d, buf);
-       printf("%s\n", buf);
-   } else if (n == 4) {
-      /* sqr tests */
-       rand_num(&a);
-       mp_sqr(&a, &b);
-       printf("sqr\n");
-       mp_to64(&a, buf);
-       printf("%s\n", buf);
-       mp_to64(&b, buf);
-       printf("%s\n", buf);
-   } else if (n == 5) {
-      /* mul_2d test */
-      rand_num(&a);
-      mp_copy(&a, &b);
-      n = getRandChar() & 63;
-      mp_mul_2d(&b, n, &b);
-      mp_to64(&a, buf);
-      printf("mul2d\n");
-      printf("%s\n", buf);
-      printf("%d\n", n);
-      mp_to64(&b, buf);
-      printf("%s\n", buf);
-   } else if (n == 6) {
-      /* div_2d test */
-      rand_num(&a);
-      mp_copy(&a, &b);
-      n = getRandChar() & 63;
-      mp_div_2d(&b, n, &b, NULL);
-      mp_to64(&a, buf);
-      printf("div2d\n");
-      printf("%s\n", buf);
-      printf("%d\n", n);
-      mp_to64(&b, buf);
-      printf("%s\n", buf);
-   } else if (n == 7) {
-      /* gcd test */
-      rand_num(&a);
-      rand_num(&b);
-      a.sign = MP_ZPOS;
-      b.sign = MP_ZPOS;
-      mp_gcd(&a, &b, &c);
-      printf("gcd\n");
-      mp_to64(&a, buf);
-      printf("%s\n", buf);
-      mp_to64(&b, buf);
-      printf("%s\n", buf);
-      mp_to64(&c, buf);
-      printf("%s\n", buf);
-   } else if (n == 8) {
-      /* lcm test */
-      rand_num(&a);
-      rand_num(&b);
-      a.sign = MP_ZPOS;
-      b.sign = MP_ZPOS;
-      mp_lcm(&a, &b, &c);
-      printf("lcm\n");
-      mp_to64(&a, buf);
-      printf("%s\n", buf);
-      mp_to64(&b, buf);
-      printf("%s\n", buf);
-      mp_to64(&c, buf);
-      printf("%s\n", buf);
-   } else if (n == 9) {
-      /* exptmod test */
-      rand_num2(&a);
-      rand_num2(&b);
-      rand_num2(&c);
-//      if (c.dp[0]&1) mp_add_d(&c, 1, &c);
-      a.sign = b.sign = c.sign = 0;
-      mp_exptmod(&a, &b, &c, &d);
-      printf("expt\n");
-      mp_to64(&a, buf);
-      printf("%s\n", buf);
-      mp_to64(&b, buf);
-      printf("%s\n", buf);
-      mp_to64(&c, buf);
-      printf("%s\n", buf);
-      mp_to64(&d, buf);
-      printf("%s\n", buf);
-   } else if (n == 10) {
-      /* invmod test */
-      rand_num2(&a);
-      rand_num2(&b);
-      b.sign = MP_ZPOS;
-      a.sign = MP_ZPOS;
-      mp_gcd(&a, &b, &c);
-      if (mp_cmp_d(&c, 1) != 0) continue;
-      if (mp_cmp_d(&b, 1) == 0) continue;
-      mp_invmod(&a, &b, &c);
-      printf("invmod\n");
-      mp_to64(&a, buf);
-      printf("%s\n", buf);
-      mp_to64(&b, buf);
-      printf("%s\n", buf);
-      mp_to64(&c, buf);
-      printf("%s\n", buf);
-   } else if (n == 11) {
-      rand_num(&a);
-      mp_mul_2(&a, &a);
-      mp_div_2(&a, &b);
-      printf("div2\n");
-      mp_to64(&a, buf);
-      printf("%s\n", buf);
-      mp_to64(&b, buf);
-      printf("%s\n", buf);
-   } else if (n == 12) {
-      rand_num2(&a);
-      mp_mul_2(&a, &b);
-      printf("mul2\n");
-      mp_to64(&a, buf);
-      printf("%s\n", buf);
-      mp_to64(&b, buf);
-      printf("%s\n", buf);
-   } else if (n == 13) {
-      rand_num2(&a);
-      tmp = abs(rand()) & THE_MASK;
-      mp_add_d(&a, tmp, &b);
-      printf("add_d\n");
-      mp_to64(&a, buf);
-      printf("%s\n%d\n", buf, tmp);
-      mp_to64(&b, buf);
-      printf("%s\n", buf);
-   } else if (n == 14) {
-      rand_num2(&a);
-      tmp = abs(rand()) & THE_MASK;
-      mp_sub_d(&a, tmp, &b);
-      printf("sub_d\n");
-      mp_to64(&a, buf);
-      printf("%s\n%d\n", buf, tmp);
-      mp_to64(&b, buf);
-      printf("%s\n", buf);
-   } else if (n == 255) {
-      printf("exit\n");
-      break;
-   }
-
-   }
-#ifdef LTM_MTEST_REAL_RAND
-   fclose(rng);
-#endif
-   return 0;
-}
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
diff --git a/libtommath/parsenames.pl b/libtommath/parsenames.pl
deleted file mode 100755
index cc57673..0000000
--- a/libtommath/parsenames.pl
+++ /dev/null
@@ -1,25 +0,0 @@
-#!/usr/bin/perl
-#
-# Splits the list of files and outputs for makefile type files
-# wrapped at 80 chars
-#
-# Tom St Denis
-@a = split(" ", $ARGV[1]);
-$b = "$ARGV[0]=";
-$len = length($b);
-print $b;
-foreach my $obj (@a) {
-   $len = $len + length($obj);
-   $obj =~ s/\*/\$/;
-   if ($len > 100) {
-      printf "\\\n";
-      $len = length($obj);
-   }
-   print "$obj ";
-}
-
-print "\n\n";
-
-# $Source$
-# $Revision$
-# $Date$
diff --git a/libtommath/pics/design_process.sxd b/libtommath/pics/design_process.sxd
deleted file mode 100644
index 7414dbb..0000000
Binary files a/libtommath/pics/design_process.sxd and /dev/null differ
diff --git a/libtommath/pics/design_process.tif b/libtommath/pics/design_process.tif
deleted file mode 100644
index 4a0c012..0000000
Binary files a/libtommath/pics/design_process.tif and /dev/null differ
diff --git a/libtommath/pics/expt_state.sxd b/libtommath/pics/expt_state.sxd
deleted file mode 100644
index 6518404..0000000
Binary files a/libtommath/pics/expt_state.sxd and /dev/null differ
diff --git a/libtommath/pics/expt_state.tif b/libtommath/pics/expt_state.tif
deleted file mode 100644
index cb06e8e..0000000
Binary files a/libtommath/pics/expt_state.tif and /dev/null differ
diff --git a/libtommath/pics/makefile b/libtommath/pics/makefile
deleted file mode 100644
index 3ecb02f..0000000
--- a/libtommath/pics/makefile
+++ /dev/null
@@ -1,35 +0,0 @@
-# makes the images... yeah
-
-default:  pses
-
-design_process.ps: design_process.tif
-	tiff2ps -s -e design_process.tif > design_process.ps
-
-sliding_window.ps: sliding_window.tif
-	tiff2ps -s -e sliding_window.tif > sliding_window.ps
-	
-expt_state.ps: expt_state.tif
-	tiff2ps -s -e expt_state.tif > expt_state.ps
-
-primality.ps: primality.tif
-	tiff2ps -s -e primality.tif > primality.ps
-
-design_process.pdf: design_process.ps
-	epstopdf design_process.ps
-
-sliding_window.pdf: sliding_window.ps
-	epstopdf sliding_window.ps
-	
-expt_state.pdf: expt_state.ps
-	epstopdf expt_state.ps
-
-primality.pdf: primality.ps
-	epstopdf primality.ps
-
-
-pses: sliding_window.ps expt_state.ps primality.ps design_process.ps
-pdfes: sliding_window.pdf expt_state.pdf primality.pdf design_process.pdf
-
-clean:
-	rm -rf *.ps *.pdf .xvpics
-   
\ No newline at end of file
diff --git a/libtommath/pics/primality.tif b/libtommath/pics/primality.tif
deleted file mode 100644
index 76d6be3..0000000
Binary files a/libtommath/pics/primality.tif and /dev/null differ
diff --git a/libtommath/pics/radix.sxd b/libtommath/pics/radix.sxd
deleted file mode 100644
index b9eb9a0..0000000
Binary files a/libtommath/pics/radix.sxd and /dev/null differ
diff --git a/libtommath/pics/sliding_window.sxd b/libtommath/pics/sliding_window.sxd
deleted file mode 100644
index 91e7c0d..0000000
Binary files a/libtommath/pics/sliding_window.sxd and /dev/null differ
diff --git a/libtommath/pics/sliding_window.tif b/libtommath/pics/sliding_window.tif
deleted file mode 100644
index bb4cb96..0000000
Binary files a/libtommath/pics/sliding_window.tif and /dev/null differ
diff --git a/libtommath/poster.out b/libtommath/poster.out
deleted file mode 100644
index e69de29..0000000
diff --git a/libtommath/poster.pdf b/libtommath/poster.pdf
deleted file mode 100644
index f212c3e..0000000
Binary files a/libtommath/poster.pdf and /dev/null differ
diff --git a/libtommath/poster.tex b/libtommath/poster.tex
deleted file mode 100644
index e7388f4..0000000
--- a/libtommath/poster.tex
+++ /dev/null
@@ -1,35 +0,0 @@
-\documentclass[landscape,11pt]{article}
-\usepackage{amsmath, amssymb}
-\usepackage{hyperref}
-\begin{document}
-\hspace*{-3in}
-\begin{tabular}{llllll}
-$c = a + b$  & {\tt mp\_add(\&a, \&b, \&c)} & $b = 2a$  & {\tt mp\_mul\_2(\&a, \&b)} & \\
-$c = a - b$  & {\tt mp\_sub(\&a, \&b, \&c)} & $b = a/2$ & {\tt mp\_div\_2(\&a, \&b)} & \\
-$c = ab $   & {\tt mp\_mul(\&a, \&b, \&c)}  & $c = 2^ba$  & {\tt mp\_mul\_2d(\&a, b, \&c)}  \\
-$b = a^2 $  & {\tt mp\_sqr(\&a, \&b)}       & $c = a/2^b, d = a \mod 2^b$ & {\tt mp\_div\_2d(\&a, b, \&c, \&d)} \\
-$c = \lfloor a/b \rfloor, d = a \mod b$ & {\tt mp\_div(\&a, \&b, \&c, \&d)} & $c = a \mod 2^b $  & {\tt mp\_mod\_2d(\&a, b, \&c)}  \\
- && \\
-$a = b $  & {\tt mp\_set\_int(\&a, b)}  & $c = a \vee b$  & {\tt mp\_or(\&a, \&b, \&c)}  \\
-$b = a $  & {\tt mp\_copy(\&a, \&b)} & $c = a \wedge b$  & {\tt mp\_and(\&a, \&b, \&c)}  \\
- && $c = a \oplus b$  & {\tt mp\_xor(\&a, \&b, \&c)}  \\
- & \\
-$b = -a $  & {\tt mp\_neg(\&a, \&b)}  & $d = a + b \mod c$  & {\tt mp\_addmod(\&a, \&b, \&c, \&d)}  \\
-$b = |a| $  & {\tt mp\_abs(\&a, \&b)} & $d = a - b \mod c$  & {\tt mp\_submod(\&a, \&b, \&c, \&d)}  \\
- && $d = ab \mod c$  & {\tt mp\_mulmod(\&a, \&b, \&c, \&d)}  \\
-Compare $a$ and $b$ & {\tt mp\_cmp(\&a, \&b)} & $c = a^2 \mod b$  & {\tt mp\_sqrmod(\&a, \&b, \&c)}  \\
-Is Zero? & {\tt mp\_iszero(\&a)} & $c = a^{-1} \mod b$  & {\tt mp\_invmod(\&a, \&b, \&c)} \\
-Is Even? & {\tt mp\_iseven(\&a)} & $d = a^b \mod c$ & {\tt mp\_exptmod(\&a, \&b, \&c, \&d)} \\
-Is Odd ? & {\tt mp\_isodd(\&a)} \\
-&\\
-$\vert \vert a \vert \vert$ & {\tt mp\_unsigned\_bin\_size(\&a)} & $res$ = 1 if $a$ prime to $t$ rounds? & {\tt mp\_prime\_is\_prime(\&a, t, \&res)} \\
-$buf \leftarrow a$          & {\tt mp\_to\_unsigned\_bin(\&a, buf)} & Next prime after $a$ to $t$ rounds. & {\tt mp\_prime\_next\_prime(\&a, t, bbs\_style)} \\
-$a \leftarrow buf[0..len-1]$          & {\tt mp\_read\_unsigned\_bin(\&a, buf, len)} \\
-&\\
-$b = \sqrt{a}$ & {\tt mp\_sqrt(\&a, \&b)}  & $c = \mbox{gcd}(a, b)$ & {\tt mp\_gcd(\&a, \&b, \&c)} \\
-$c = a^{1/b}$ & {\tt mp\_n\_root(\&a, b, \&c)} & $c = \mbox{lcm}(a, b)$ & {\tt mp\_lcm(\&a, \&b, \&c)} \\
-&\\
-Greater Than & MP\_GT & Equal To & MP\_EQ \\
-Less Than & MP\_LT & Bits per digit & DIGIT\_BIT \\
-\end{tabular}
-\end{document}
diff --git a/libtommath/pre_gen/mpi.c b/libtommath/pre_gen/mpi.c
deleted file mode 100644
index 0d55d73..0000000
--- a/libtommath/pre_gen/mpi.c
+++ /dev/null
@@ -1,9524 +0,0 @@
-/* Start: bn_error.c */
-#include <tommath.h>
-#ifdef BN_ERROR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-static const struct {
-     int code;
-     char *msg;
-} msgs[] = {
-     { MP_OKAY, "Successful" },
-     { MP_MEM,  "Out of heap" },
-     { MP_VAL,  "Value out of range" }
-};
-
-/* return a char * string for a given code */
-char *mp_error_to_string(int code)
-{
-   int x;
-
-   /* scan the lookup table for the given message */
-   for (x = 0; x < (int)(sizeof(msgs) / sizeof(msgs[0])); x++) {
-       if (msgs[x].code == code) {
-          return msgs[x].msg;
-       }
-   }
-
-   /* generic reply for invalid code */
-   return "Invalid error code";
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_error.c */
-
-/* Start: bn_fast_mp_invmod.c */
-#include <tommath.h>
-#ifdef BN_FAST_MP_INVMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* computes the modular inverse via binary extended euclidean algorithm,
- * that is c = 1/a mod b
- *
- * Based on slow invmod except this is optimized for the case where b is
- * odd as per HAC Note 14.64 on pp. 610
- */
-int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
-{
-  mp_int  x, y, u, v, B, D;
-  int     res, neg;
-
-  /* 2. [modified] b must be odd   */
-  if (mp_iseven (b) == 1) {
-    return MP_VAL;
-  }
-
-  /* init all our temps */
-  if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
-     return res;
-  }
-
-  /* x == modulus, y == value to invert */
-  if ((res = mp_copy (b, &x)) != MP_OKAY) {
-    goto LBL_ERR;
-  }
-
-  /* we need y = |a| */
-  if ((res = mp_mod (a, b, &y)) != MP_OKAY) {
-    goto LBL_ERR;
-  }
-
-  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
-  if ((res = mp_copy (&x, &u)) != MP_OKAY) {
-    goto LBL_ERR;
-  }
-  if ((res = mp_copy (&y, &v)) != MP_OKAY) {
-    goto LBL_ERR;
-  }
-  mp_set (&D, 1);
-
-top:
-  /* 4.  while u is even do */
-  while (mp_iseven (&u) == 1) {
-    /* 4.1 u = u/2 */
-    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-    /* 4.2 if B is odd then */
-    if (mp_isodd (&B) == 1) {
-      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
-        goto LBL_ERR;
-      }
-    }
-    /* B = B/2 */
-    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-  }
-
-  /* 5.  while v is even do */
-  while (mp_iseven (&v) == 1) {
-    /* 5.1 v = v/2 */
-    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-    /* 5.2 if D is odd then */
-    if (mp_isodd (&D) == 1) {
-      /* D = (D-x)/2 */
-      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
-        goto LBL_ERR;
-      }
-    }
-    /* D = D/2 */
-    if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-  }
-
-  /* 6.  if u >= v then */
-  if (mp_cmp (&u, &v) != MP_LT) {
-    /* u = u - v, B = B - D */
-    if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-
-    if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-  } else {
-    /* v - v - u, D = D - B */
-    if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-
-    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-  }
-
-  /* if not zero goto step 4 */
-  if (mp_iszero (&u) == 0) {
-    goto top;
-  }
-
-  /* now a = C, b = D, gcd == g*v */
-
-  /* if v != 1 then there is no inverse */
-  if (mp_cmp_d (&v, 1) != MP_EQ) {
-    res = MP_VAL;
-    goto LBL_ERR;
-  }
-
-  /* b is now the inverse */
-  neg = a->sign;
-  while (D.sign == MP_NEG) {
-    if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-  }
-  mp_exch (&D, c);
-  c->sign = neg;
-  res = MP_OKAY;
-
-LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
-  return res;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_fast_mp_invmod.c */
-
-/* Start: bn_fast_mp_montgomery_reduce.c */
-#include <tommath.h>
-#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* computes xR**-1 == x (mod N) via Montgomery Reduction
- *
- * This is an optimized implementation of montgomery_reduce
- * which uses the comba method to quickly calculate the columns of the
- * reduction.
- *
- * Based on Algorithm 14.32 on pp.601 of HAC.
-*/
-int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
-{
-  int     ix, res, olduse;
-  mp_word W[MP_WARRAY];
-
-  /* get old used count */
-  olduse = x->used;
-
-  /* grow a as required */
-  if (x->alloc < n->used + 1) {
-    if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  /* first we have to get the digits of the input into
-   * an array of double precision words W[...]
-   */
-  {
-    register mp_word *_W;
-    register mp_digit *tmpx;
-
-    /* alias for the W[] array */
-    _W   = W;
-
-    /* alias for the digits of  x*/
-    tmpx = x->dp;
-
-    /* copy the digits of a into W[0..a->used-1] */
-    for (ix = 0; ix < x->used; ix++) {
-      *_W++ = *tmpx++;
-    }
-
-    /* zero the high words of W[a->used..m->used*2] */
-    for (; ix < n->used * 2 + 1; ix++) {
-      *_W++ = 0;
-    }
-  }
-
-  /* now we proceed to zero successive digits
-   * from the least significant upwards
-   */
-  for (ix = 0; ix < n->used; ix++) {
-    /* mu = ai * m' mod b
-     *
-     * We avoid a double precision multiplication (which isn't required)
-     * by casting the value down to a mp_digit.  Note this requires
-     * that W[ix-1] have  the carry cleared (see after the inner loop)
-     */
-    register mp_digit mu;
-    mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
-
-    /* a = a + mu * m * b**i
-     *
-     * This is computed in place and on the fly.  The multiplication
-     * by b**i is handled by offseting which columns the results
-     * are added to.
-     *
-     * Note the comba method normally doesn't handle carries in the
-     * inner loop In this case we fix the carry from the previous
-     * column since the Montgomery reduction requires digits of the
-     * result (so far) [see above] to work.  This is
-     * handled by fixing up one carry after the inner loop.  The
-     * carry fixups are done in order so after these loops the
-     * first m->used words of W[] have the carries fixed
-     */
-    {
-      register int iy;
-      register mp_digit *tmpn;
-      register mp_word *_W;
-
-      /* alias for the digits of the modulus */
-      tmpn = n->dp;
-
-      /* Alias for the columns set by an offset of ix */
-      _W = W + ix;
-
-      /* inner loop */
-      for (iy = 0; iy < n->used; iy++) {
-          *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
-      }
-    }
-
-    /* now fix carry for next digit, W[ix+1] */
-    W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
-  }
-
-  /* now we have to propagate the carries and
-   * shift the words downward [all those least
-   * significant digits we zeroed].
-   */
-  {
-    register mp_digit *tmpx;
-    register mp_word *_W, *_W1;
-
-    /* nox fix rest of carries */
-
-    /* alias for current word */
-    _W1 = W + ix;
-
-    /* alias for next word, where the carry goes */
-    _W = W + ++ix;
-
-    for (; ix <= n->used * 2 + 1; ix++) {
-      *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
-    }
-
-    /* copy out, A = A/b**n
-     *
-     * The result is A/b**n but instead of converting from an
-     * array of mp_word to mp_digit than calling mp_rshd
-     * we just copy them in the right order
-     */
-
-    /* alias for destination word */
-    tmpx = x->dp;
-
-    /* alias for shifted double precision result */
-    _W = W + n->used;
-
-    for (ix = 0; ix < n->used + 1; ix++) {
-      *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
-    }
-
-    /* zero oldused digits, if the input a was larger than
-     * m->used+1 we'll have to clear the digits
-     */
-    for (; ix < olduse; ix++) {
-      *tmpx++ = 0;
-    }
-  }
-
-  /* set the max used and clamp */
-  x->used = n->used + 1;
-  mp_clamp (x);
-
-  /* if A >= m then A = A - m */
-  if (mp_cmp_mag (x, n) != MP_LT) {
-    return s_mp_sub (x, n, x);
-  }
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_fast_mp_montgomery_reduce.c */
-
-/* Start: bn_fast_s_mp_mul_digs.c */
-#include <tommath.h>
-#ifdef BN_FAST_S_MP_MUL_DIGS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* Fast (comba) multiplier
- *
- * This is the fast column-array [comba] multiplier.  It is
- * designed to compute the columns of the product first
- * then handle the carries afterwards.  This has the effect
- * of making the nested loops that compute the columns very
- * simple and schedulable on super-scalar processors.
- *
- * This has been modified to produce a variable number of
- * digits of output so if say only a half-product is required
- * you don't have to compute the upper half (a feature
- * required for fast Barrett reduction).
- *
- * Based on Algorithm 14.12 on pp.595 of HAC.
- *
- */
-int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
-{
-  int     olduse, res, pa, ix, iz;
-  mp_digit W[MP_WARRAY];
-  register mp_word  _W;
-
-  /* grow the destination as required */
-  if (c->alloc < digs) {
-    if ((res = mp_grow (c, digs)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  /* number of output digits to produce */
-  pa = MIN(digs, a->used + b->used);
-
-  /* clear the carry */
-  _W = 0;
-  for (ix = 0; ix < pa; ix++) {
-      int      tx, ty;
-      int      iy;
-      mp_digit *tmpx, *tmpy;
-
-      /* get offsets into the two bignums */
-      ty = MIN(b->used-1, ix);
-      tx = ix - ty;
-
-      /* setup temp aliases */
-      tmpx = a->dp + tx;
-      tmpy = b->dp + ty;
-
-      /* this is the number of times the loop will iterrate, essentially
-         while (tx++ < a->used && ty-- >= 0) { ... }
-       */
-      iy = MIN(a->used-tx, ty+1);
-
-      /* execute loop */
-      for (iz = 0; iz < iy; ++iz) {
-         _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
-
-      }
-
-      /* store term */
-      W[ix] = ((mp_digit)_W) & MP_MASK;
-
-      /* make next carry */
-      _W = _W >> ((mp_word)DIGIT_BIT);
- }
-
-  /* setup dest */
-  olduse  = c->used;
-  c->used = pa;
-
-  {
-    register mp_digit *tmpc;
-    tmpc = c->dp;
-    for (ix = 0; ix < pa+1; ix++) {
-      /* now extract the previous digit [below the carry] */
-      *tmpc++ = W[ix];
-    }
-
-    /* clear unused digits [that existed in the old copy of c] */
-    for (; ix < olduse; ix++) {
-      *tmpc++ = 0;
-    }
-  }
-  mp_clamp (c);
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_fast_s_mp_mul_digs.c */
-
-/* Start: bn_fast_s_mp_mul_high_digs.c */
-#include <tommath.h>
-#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* this is a modified version of fast_s_mul_digs that only produces
- * output digits *above* digs.  See the comments for fast_s_mul_digs
- * to see how it works.
- *
- * This is used in the Barrett reduction since for one of the multiplications
- * only the higher digits were needed.  This essentially halves the work.
- *
- * Based on Algorithm 14.12 on pp.595 of HAC.
- */
-int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
-{
-  int     olduse, res, pa, ix, iz;
-  mp_digit W[MP_WARRAY];
-  mp_word  _W;
-
-  /* grow the destination as required */
-  pa = a->used + b->used;
-  if (c->alloc < pa) {
-    if ((res = mp_grow (c, pa)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  /* number of output digits to produce */
-  pa = a->used + b->used;
-  _W = 0;
-  for (ix = digs; ix < pa; ix++) {
-      int      tx, ty, iy;
-      mp_digit *tmpx, *tmpy;
-
-      /* get offsets into the two bignums */
-      ty = MIN(b->used-1, ix);
-      tx = ix - ty;
-
-      /* setup temp aliases */
-      tmpx = a->dp + tx;
-      tmpy = b->dp + ty;
-
-      /* this is the number of times the loop will iterrate, essentially its
-         while (tx++ < a->used && ty-- >= 0) { ... }
-       */
-      iy = MIN(a->used-tx, ty+1);
-
-      /* execute loop */
-      for (iz = 0; iz < iy; iz++) {
-         _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
-      }
-
-      /* store term */
-      W[ix] = ((mp_digit)_W) & MP_MASK;
-
-      /* make next carry */
-      _W = _W >> ((mp_word)DIGIT_BIT);
-  }
-
-  /* setup dest */
-  olduse  = c->used;
-  c->used = pa;
-
-  {
-    register mp_digit *tmpc;
-
-    tmpc = c->dp + digs;
-    for (ix = digs; ix < pa; ix++) {
-      /* now extract the previous digit [below the carry] */
-      *tmpc++ = W[ix];
-    }
-
-    /* clear unused digits [that existed in the old copy of c] */
-    for (; ix < olduse; ix++) {
-      *tmpc++ = 0;
-    }
-  }
-  mp_clamp (c);
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_fast_s_mp_mul_high_digs.c */
-
-/* Start: bn_fast_s_mp_sqr.c */
-#include <tommath.h>
-#ifdef BN_FAST_S_MP_SQR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* the jist of squaring...
- * you do like mult except the offset of the tmpx [one that
- * starts closer to zero] can't equal the offset of tmpy.
- * So basically you set up iy like before then you min it with
- * (ty-tx) so that it never happens.  You double all those
- * you add in the inner loop
-
-After that loop you do the squares and add them in.
-*/
-
-int fast_s_mp_sqr (mp_int * a, mp_int * b)
-{
-  int       olduse, res, pa, ix, iz;
-  mp_digit   W[MP_WARRAY], *tmpx;
-  mp_word   W1;
-
-  /* grow the destination as required */
-  pa = a->used + a->used;
-  if (b->alloc < pa) {
-    if ((res = mp_grow (b, pa)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  /* number of output digits to produce */
-  W1 = 0;
-  for (ix = 0; ix < pa; ix++) {
-      int      tx, ty, iy;
-      mp_word  _W;
-      mp_digit *tmpy;
-
-      /* clear counter */
-      _W = 0;
-
-      /* get offsets into the two bignums */
-      ty = MIN(a->used-1, ix);
-      tx = ix - ty;
-
-      /* setup temp aliases */
-      tmpx = a->dp + tx;
-      tmpy = a->dp + ty;
-
-      /* this is the number of times the loop will iterrate, essentially
-         while (tx++ < a->used && ty-- >= 0) { ... }
-       */
-      iy = MIN(a->used-tx, ty+1);
-
-      /* now for squaring tx can never equal ty
-       * we halve the distance since they approach at a rate of 2x
-       * and we have to round because odd cases need to be executed
-       */
-      iy = MIN(iy, (ty-tx+1)>>1);
-
-      /* execute loop */
-      for (iz = 0; iz < iy; iz++) {
-         _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
-      }
-
-      /* double the inner product and add carry */
-      _W = _W + _W + W1;
-
-      /* even columns have the square term in them */
-      if ((ix&1) == 0) {
-         _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
-      }
-
-      /* store it */
-      W[ix] = (mp_digit)(_W & MP_MASK);
-
-      /* make next carry */
-      W1 = _W >> ((mp_word)DIGIT_BIT);
-  }
-
-  /* setup dest */
-  olduse  = b->used;
-  b->used = a->used+a->used;
-
-  {
-    mp_digit *tmpb;
-    tmpb = b->dp;
-    for (ix = 0; ix < pa; ix++) {
-      *tmpb++ = W[ix] & MP_MASK;
-    }
-
-    /* clear unused digits [that existed in the old copy of c] */
-    for (; ix < olduse; ix++) {
-      *tmpb++ = 0;
-    }
-  }
-  mp_clamp (b);
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_fast_s_mp_sqr.c */
-
-/* Start: bn_mp_2expt.c */
-#include <tommath.h>
-#ifdef BN_MP_2EXPT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* computes a = 2**b
- *
- * Simple algorithm which zeroes the int, grows it then just sets one bit
- * as required.
- */
-int
-mp_2expt (mp_int * a, int b)
-{
-  int     res;
-
-  /* zero a as per default */
-  mp_zero (a);
-
-  /* grow a to accomodate the single bit */
-  if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
-    return res;
-  }
-
-  /* set the used count of where the bit will go */
-  a->used = b / DIGIT_BIT + 1;
-
-  /* put the single bit in its place */
-  a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
-
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_2expt.c */
-
-/* Start: bn_mp_abs.c */
-#include <tommath.h>
-#ifdef BN_MP_ABS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* b = |a|
- *
- * Simple function copies the input and fixes the sign to positive
- */
-int
-mp_abs (mp_int * a, mp_int * b)
-{
-  int     res;
-
-  /* copy a to b */
-  if (a != b) {
-     if ((res = mp_copy (a, b)) != MP_OKAY) {
-       return res;
-     }
-  }
-
-  /* force the sign of b to positive */
-  b->sign = MP_ZPOS;
-
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_abs.c */
-
-/* Start: bn_mp_add.c */
-#include <tommath.h>
-#ifdef BN_MP_ADD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* high level addition (handles signs) */
-int mp_add (mp_int * a, mp_int * b, mp_int * c)
-{
-  int     sa, sb, res;
-
-  /* get sign of both inputs */
-  sa = a->sign;
-  sb = b->sign;
-
-  /* handle two cases, not four */
-  if (sa == sb) {
-    /* both positive or both negative */
-    /* add their magnitudes, copy the sign */
-    c->sign = sa;
-    res = s_mp_add (a, b, c);
-  } else {
-    /* one positive, the other negative */
-    /* subtract the one with the greater magnitude from */
-    /* the one of the lesser magnitude.  The result gets */
-    /* the sign of the one with the greater magnitude. */
-    if (mp_cmp_mag (a, b) == MP_LT) {
-      c->sign = sb;
-      res = s_mp_sub (b, a, c);
-    } else {
-      c->sign = sa;
-      res = s_mp_sub (a, b, c);
-    }
-  }
-  return res;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_add.c */
-
-/* Start: bn_mp_add_d.c */
-#include <tommath.h>
-#ifdef BN_MP_ADD_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* single digit addition */
-int
-mp_add_d (mp_int * a, mp_digit b, mp_int * c)
-{
-  int     res, ix, oldused;
-  mp_digit *tmpa, *tmpc, mu;
-
-  /* grow c as required */
-  if (c->alloc < a->used + 1) {
-     if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
-        return res;
-     }
-  }
-
-  /* if a is negative and |a| >= b, call c = |a| - b */
-  if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) {
-     /* temporarily fix sign of a */
-     a->sign = MP_ZPOS;
-
-     /* c = |a| - b */
-     res = mp_sub_d(a, b, c);
-
-     /* fix sign  */
-     a->sign = c->sign = MP_NEG;
-
-     /* clamp */
-     mp_clamp(c);
-
-     return res;
-  }
-
-  /* old number of used digits in c */
-  oldused = c->used;
-
-  /* sign always positive */
-  c->sign = MP_ZPOS;
-
-  /* source alias */
-  tmpa    = a->dp;
-
-  /* destination alias */
-  tmpc    = c->dp;
-
-  /* if a is positive */
-  if (a->sign == MP_ZPOS) {
-     /* add digit, after this we're propagating
-      * the carry.
-      */
-     *tmpc   = *tmpa++ + b;
-     mu      = *tmpc >> DIGIT_BIT;
-     *tmpc++ &= MP_MASK;
-
-     /* now handle rest of the digits */
-     for (ix = 1; ix < a->used; ix++) {
-        *tmpc   = *tmpa++ + mu;
-        mu      = *tmpc >> DIGIT_BIT;
-        *tmpc++ &= MP_MASK;
-     }
-     /* set final carry */
-     ix++;
-     *tmpc++  = mu;
-
-     /* setup size */
-     c->used = a->used + 1;
-  } else {
-     /* a was negative and |a| < b */
-     c->used  = 1;
-
-     /* the result is a single digit */
-     if (a->used == 1) {
-        *tmpc++  =  b - a->dp[0];
-     } else {
-        *tmpc++  =  b;
-     }
-
-     /* setup count so the clearing of oldused
-      * can fall through correctly
-      */
-     ix       = 1;
-  }
-
-  /* now zero to oldused */
-  while (ix++ < oldused) {
-     *tmpc++ = 0;
-  }
-  mp_clamp(c);
-
-  return MP_OKAY;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_add_d.c */
-
-/* Start: bn_mp_addmod.c */
-#include <tommath.h>
-#ifdef BN_MP_ADDMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* d = a + b (mod c) */
-int
-mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-{
-  int     res;
-  mp_int  t;
-
-  if ((res = mp_init (&t)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_add (a, b, &t)) != MP_OKAY) {
-    mp_clear (&t);
-    return res;
-  }
-  res = mp_mod (&t, c, d);
-  mp_clear (&t);
-  return res;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_addmod.c */
-
-/* Start: bn_mp_and.c */
-#include <tommath.h>
-#ifdef BN_MP_AND_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* AND two ints together */
-int
-mp_and (mp_int * a, mp_int * b, mp_int * c)
-{
-  int     res, ix, px;
-  mp_int  t, *x;
-
-  if (a->used > b->used) {
-    if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
-      return res;
-    }
-    px = b->used;
-    x = b;
-  } else {
-    if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
-      return res;
-    }
-    px = a->used;
-    x = a;
-  }
-
-  for (ix = 0; ix < px; ix++) {
-    t.dp[ix] &= x->dp[ix];
-  }
-
-  /* zero digits above the last from the smallest mp_int */
-  for (; ix < t.used; ix++) {
-    t.dp[ix] = 0;
-  }
-
-  mp_clamp (&t);
-  mp_exch (c, &t);
-  mp_clear (&t);
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_and.c */
-
-/* Start: bn_mp_clamp.c */
-#include <tommath.h>
-#ifdef BN_MP_CLAMP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* trim unused digits
- *
- * This is used to ensure that leading zero digits are
- * trimed and the leading "used" digit will be non-zero
- * Typically very fast.  Also fixes the sign if there
- * are no more leading digits
- */
-void
-mp_clamp (mp_int * a)
-{
-  /* decrease used while the most significant digit is
-   * zero.
-   */
-  while (a->used > 0 && a->dp[a->used - 1] == 0) {
-    --(a->used);
-  }
-
-  /* reset the sign flag if used == 0 */
-  if (a->used == 0) {
-    a->sign = MP_ZPOS;
-  }
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_clamp.c */
-
-/* Start: bn_mp_clear.c */
-#include <tommath.h>
-#ifdef BN_MP_CLEAR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* clear one (frees)  */
-void
-mp_clear (mp_int * a)
-{
-  int i;
-
-  /* only do anything if a hasn't been freed previously */
-  if (a->dp != NULL) {
-    /* first zero the digits */
-    for (i = 0; i < a->used; i++) {
-        a->dp[i] = 0;
-    }
-
-    /* free ram */
-    XFREE(a->dp);
-
-    /* reset members to make debugging easier */
-    a->dp    = NULL;
-    a->alloc = a->used = 0;
-    a->sign  = MP_ZPOS;
-  }
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_clear.c */
-
-/* Start: bn_mp_clear_multi.c */
-#include <tommath.h>
-#ifdef BN_MP_CLEAR_MULTI_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-#include <stdarg.h>
-
-void mp_clear_multi(mp_int *mp, ...)
-{
-    mp_int* next_mp = mp;
-    va_list args;
-    va_start(args, mp);
-    while (next_mp != NULL) {
-        mp_clear(next_mp);
-        next_mp = va_arg(args, mp_int*);
-    }
-    va_end(args);
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_clear_multi.c */
-
-/* Start: bn_mp_cmp.c */
-#include <tommath.h>
-#ifdef BN_MP_CMP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* compare two ints (signed)*/
-int
-mp_cmp (mp_int * a, mp_int * b)
-{
-  /* compare based on sign */
-  if (a->sign != b->sign) {
-     if (a->sign == MP_NEG) {
-        return MP_LT;
-     } else {
-        return MP_GT;
-     }
-  }
-
-  /* compare digits */
-  if (a->sign == MP_NEG) {
-     /* if negative compare opposite direction */
-     return mp_cmp_mag(b, a);
-  } else {
-     return mp_cmp_mag(a, b);
-  }
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_cmp.c */
-
-/* Start: bn_mp_cmp_d.c */
-#include <tommath.h>
-#ifdef BN_MP_CMP_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* compare a digit */
-int mp_cmp_d(mp_int * a, mp_digit b)
-{
-  /* compare based on sign */
-  if (a->sign == MP_NEG) {
-    return MP_LT;
-  }
-
-  /* compare based on magnitude */
-  if (a->used > 1) {
-    return MP_GT;
-  }
-
-  /* compare the only digit of a to b */
-  if (a->dp[0] > b) {
-    return MP_GT;
-  } else if (a->dp[0] < b) {
-    return MP_LT;
-  } else {
-    return MP_EQ;
-  }
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_cmp_d.c */
-
-/* Start: bn_mp_cmp_mag.c */
-#include <tommath.h>
-#ifdef BN_MP_CMP_MAG_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* compare maginitude of two ints (unsigned) */
-int mp_cmp_mag (mp_int * a, mp_int * b)
-{
-  int     n;
-  mp_digit *tmpa, *tmpb;
-
-  /* compare based on # of non-zero digits */
-  if (a->used > b->used) {
-    return MP_GT;
-  }
-
-  if (a->used < b->used) {
-    return MP_LT;
-  }
-
-  /* alias for a */
-  tmpa = a->dp + (a->used - 1);
-
-  /* alias for b */
-  tmpb = b->dp + (a->used - 1);
-
-  /* compare based on digits  */
-  for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
-    if (*tmpa > *tmpb) {
-      return MP_GT;
-    }
-
-    if (*tmpa < *tmpb) {
-      return MP_LT;
-    }
-  }
-  return MP_EQ;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_cmp_mag.c */
-
-/* Start: bn_mp_cnt_lsb.c */
-#include <tommath.h>
-#ifdef BN_MP_CNT_LSB_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-static const int lnz[16] = {
-   4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
-};
-
-/* Counts the number of lsbs which are zero before the first zero bit */
-int mp_cnt_lsb(mp_int *a)
-{
-   int x;
-   mp_digit q, qq;
-
-   /* easy out */
-   if (mp_iszero(a) == 1) {
-      return 0;
-   }
-
-   /* scan lower digits until non-zero */
-   for (x = 0; x < a->used && a->dp[x] == 0; x++);
-   q = a->dp[x];
-   x *= DIGIT_BIT;
-
-   /* now scan this digit until a 1 is found */
-   if ((q & 1) == 0) {
-      do {
-         qq  = q & 15;
-         x  += lnz[qq];
-         q >>= 4;
-      } while (qq == 0);
-   }
-   return x;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_cnt_lsb.c */
-
-/* Start: bn_mp_copy.c */
-#include <tommath.h>
-#ifdef BN_MP_COPY_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* copy, b = a */
-int
-mp_copy (mp_int * a, mp_int * b)
-{
-  int     res, n;
-
-  /* if dst == src do nothing */
-  if (a == b) {
-    return MP_OKAY;
-  }
-
-  /* grow dest */
-  if (b->alloc < a->used) {
-     if ((res = mp_grow (b, a->used)) != MP_OKAY) {
-        return res;
-     }
-  }
-
-  /* zero b and copy the parameters over */
-  {
-    register mp_digit *tmpa, *tmpb;
-
-    /* pointer aliases */
-
-    /* source */
-    tmpa = a->dp;
-
-    /* destination */
-    tmpb = b->dp;
-
-    /* copy all the digits */
-    for (n = 0; n < a->used; n++) {
-      *tmpb++ = *tmpa++;
-    }
-
-    /* clear high digits */
-    for (; n < b->used; n++) {
-      *tmpb++ = 0;
-    }
-  }
-
-  /* copy used count and sign */
-  b->used = a->used;
-  b->sign = a->sign;
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_copy.c */
-
-/* Start: bn_mp_count_bits.c */
-#include <tommath.h>
-#ifdef BN_MP_COUNT_BITS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* returns the number of bits in an int */
-int
-mp_count_bits (mp_int * a)
-{
-  int     r;
-  mp_digit q;
-
-  /* shortcut */
-  if (a->used == 0) {
-    return 0;
-  }
-
-  /* get number of digits and add that */
-  r = (a->used - 1) * DIGIT_BIT;
-
-  /* take the last digit and count the bits in it */
-  q = a->dp[a->used - 1];
-  while (q > ((mp_digit) 0)) {
-    ++r;
-    q >>= ((mp_digit) 1);
-  }
-  return r;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_count_bits.c */
-
-/* Start: bn_mp_div.c */
-#include <tommath.h>
-#ifdef BN_MP_DIV_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-#ifdef BN_MP_DIV_SMALL
-
-/* slower bit-bang division... also smaller */
-int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-{
-   mp_int ta, tb, tq, q;
-   int    res, n, n2;
-
-  /* is divisor zero ? */
-  if (mp_iszero (b) == 1) {
-    return MP_VAL;
-  }
-
-  /* if a < b then q=0, r = a */
-  if (mp_cmp_mag (a, b) == MP_LT) {
-    if (d != NULL) {
-      res = mp_copy (a, d);
-    } else {
-      res = MP_OKAY;
-    }
-    if (c != NULL) {
-      mp_zero (c);
-    }
-    return res;
-  }
-	
-  /* init our temps */
-  if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
-     return res;
-  }
-
-
-  mp_set(&tq, 1);
-  n = mp_count_bits(a) - mp_count_bits(b);
-  if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
-      ((res = mp_abs(b, &tb)) != MP_OKAY) ||
-      ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
-      ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
-      goto LBL_ERR;
-  }
-
-  while (n-- >= 0) {
-     if (mp_cmp(&tb, &ta) != MP_GT) {
-        if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
-            ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
-           goto LBL_ERR;
-        }
-     }
-     if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
-         ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
-           goto LBL_ERR;
-     }
-  }
-
-  /* now q == quotient and ta == remainder */
-  n  = a->sign;
-  n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
-  if (c != NULL) {
-     mp_exch(c, &q);
-     c->sign  = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
-  }
-  if (d != NULL) {
-     mp_exch(d, &ta);
-     d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
-  }
-LBL_ERR:
-   mp_clear_multi(&ta, &tb, &tq, &q, NULL);
-   return res;
-}
-
-#else
-
-/* integer signed division.
- * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
- * HAC pp.598 Algorithm 14.20
- *
- * Note that the description in HAC is horribly
- * incomplete.  For example, it doesn't consider
- * the case where digits are removed from 'x' in
- * the inner loop.  It also doesn't consider the
- * case that y has fewer than three digits, etc..
- *
- * The overall algorithm is as described as
- * 14.20 from HAC but fixed to treat these cases.
-*/
-int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-{
-  mp_int  q, x, y, t1, t2;
-  int     res, n, t, i, norm, neg;
-
-  /* is divisor zero ? */
-  if (mp_iszero (b) == 1) {
-    return MP_VAL;
-  }
-
-  /* if a < b then q=0, r = a */
-  if (mp_cmp_mag (a, b) == MP_LT) {
-    if (d != NULL) {
-      res = mp_copy (a, d);
-    } else {
-      res = MP_OKAY;
-    }
-    if (c != NULL) {
-      mp_zero (c);
-    }
-    return res;
-  }
-
-  if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) {
-    return res;
-  }
-  q.used = a->used + 2;
-
-  if ((res = mp_init (&t1)) != MP_OKAY) {
-    goto LBL_Q;
-  }
-
-  if ((res = mp_init (&t2)) != MP_OKAY) {
-    goto LBL_T1;
-  }
-
-  if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
-    goto LBL_T2;
-  }
-
-  if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
-    goto LBL_X;
-  }
-
-  /* fix the sign */
-  neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
-  x.sign = y.sign = MP_ZPOS;
-
-  /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
-  norm = mp_count_bits(&y) % DIGIT_BIT;
-  if (norm < (int)(DIGIT_BIT-1)) {
-     norm = (DIGIT_BIT-1) - norm;
-     if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
-       goto LBL_Y;
-     }
-     if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
-       goto LBL_Y;
-     }
-  } else {
-     norm = 0;
-  }
-
-  /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
-  n = x.used - 1;
-  t = y.used - 1;
-
-  /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
-  if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
-    goto LBL_Y;
-  }
-
-  while (mp_cmp (&x, &y) != MP_LT) {
-    ++(q.dp[n - t]);
-    if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
-      goto LBL_Y;
-    }
-  }
-
-  /* reset y by shifting it back down */
-  mp_rshd (&y, n - t);
-
-  /* step 3. for i from n down to (t + 1) */
-  for (i = n; i >= (t + 1); i--) {
-    if (i > x.used) {
-      continue;
-    }
-
-    /* step 3.1 if xi == yt then set q{i-t-1} to b-1,
-     * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
-    if (x.dp[i] == y.dp[t]) {
-      q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
-    } else {
-      mp_word tmp;
-      tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
-      tmp |= ((mp_word) x.dp[i - 1]);
-      tmp /= ((mp_word) y.dp[t]);
-      if (tmp > (mp_word) MP_MASK)
-        tmp = MP_MASK;
-      q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
-    }
-
-    /* while (q{i-t-1} * (yt * b + y{t-1})) >
-             xi * b**2 + xi-1 * b + xi-2
-
-       do q{i-t-1} -= 1;
-    */
-    q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
-    do {
-      q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
-
-      /* find left hand */
-      mp_zero (&t1);
-      t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
-      t1.dp[1] = y.dp[t];
-      t1.used = 2;
-      if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
-        goto LBL_Y;
-      }
-
-      /* find right hand */
-      t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
-      t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
-      t2.dp[2] = x.dp[i];
-      t2.used = 3;
-    } while (mp_cmp_mag(&t1, &t2) == MP_GT);
-
-    /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
-    if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
-      goto LBL_Y;
-    }
-
-    if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
-      goto LBL_Y;
-    }
-
-    if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
-      goto LBL_Y;
-    }
-
-    /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
-    if (x.sign == MP_NEG) {
-      if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
-        goto LBL_Y;
-      }
-      if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
-        goto LBL_Y;
-      }
-      if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
-        goto LBL_Y;
-      }
-
-      q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
-    }
-  }
-
-  /* now q is the quotient and x is the remainder
-   * [which we have to normalize]
-   */
-
-  /* get sign before writing to c */
-  x.sign = x.used == 0 ? MP_ZPOS : a->sign;
-
-  if (c != NULL) {
-    mp_clamp (&q);
-    mp_exch (&q, c);
-    c->sign = neg;
-  }
-
-  if (d != NULL) {
-    mp_div_2d (&x, norm, &x, NULL);
-    mp_exch (&x, d);
-  }
-
-  res = MP_OKAY;
-
-LBL_Y:mp_clear (&y);
-LBL_X:mp_clear (&x);
-LBL_T2:mp_clear (&t2);
-LBL_T1:mp_clear (&t1);
-LBL_Q:mp_clear (&q);
-  return res;
-}
-
-#endif
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_div.c */
-
-/* Start: bn_mp_div_2.c */
-#include <tommath.h>
-#ifdef BN_MP_DIV_2_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* b = a/2 */
-int mp_div_2(mp_int * a, mp_int * b)
-{
-  int     x, res, oldused;
-
-  /* copy */
-  if (b->alloc < a->used) {
-    if ((res = mp_grow (b, a->used)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  oldused = b->used;
-  b->used = a->used;
-  {
-    register mp_digit r, rr, *tmpa, *tmpb;
-
-    /* source alias */
-    tmpa = a->dp + b->used - 1;
-
-    /* dest alias */
-    tmpb = b->dp + b->used - 1;
-
-    /* carry */
-    r = 0;
-    for (x = b->used - 1; x >= 0; x--) {
-      /* get the carry for the next iteration */
-      rr = *tmpa & 1;
-
-      /* shift the current digit, add in carry and store */
-      *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
-
-      /* forward carry to next iteration */
-      r = rr;
-    }
-
-    /* zero excess digits */
-    tmpb = b->dp + b->used;
-    for (x = b->used; x < oldused; x++) {
-      *tmpb++ = 0;
-    }
-  }
-  b->sign = a->sign;
-  mp_clamp (b);
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_div_2.c */
-
-/* Start: bn_mp_div_2d.c */
-#include <tommath.h>
-#ifdef BN_MP_DIV_2D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
-int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
-{
-  mp_digit D, r, rr;
-  int     x, res;
-  mp_int  t;
-
-
-  /* if the shift count is <= 0 then we do no work */
-  if (b <= 0) {
-    res = mp_copy (a, c);
-    if (d != NULL) {
-      mp_zero (d);
-    }
-    return res;
-  }
-
-  if ((res = mp_init (&t)) != MP_OKAY) {
-    return res;
-  }
-
-  /* get the remainder */
-  if (d != NULL) {
-    if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) {
-      mp_clear (&t);
-      return res;
-    }
-  }
-
-  /* copy */
-  if ((res = mp_copy (a, c)) != MP_OKAY) {
-    mp_clear (&t);
-    return res;
-  }
-
-  /* shift by as many digits in the bit count */
-  if (b >= (int)DIGIT_BIT) {
-    mp_rshd (c, b / DIGIT_BIT);
-  }
-
-  /* shift any bit count < DIGIT_BIT */
-  D = (mp_digit) (b % DIGIT_BIT);
-  if (D != 0) {
-    register mp_digit *tmpc, mask, shift;
-
-    /* mask */
-    mask = (((mp_digit)1) << D) - 1;
-
-    /* shift for lsb */
-    shift = DIGIT_BIT - D;
-
-    /* alias */
-    tmpc = c->dp + (c->used - 1);
-
-    /* carry */
-    r = 0;
-    for (x = c->used - 1; x >= 0; x--) {
-      /* get the lower  bits of this word in a temp */
-      rr = *tmpc & mask;
-
-      /* shift the current word and mix in the carry bits from the previous word */
-      *tmpc = (*tmpc >> D) | (r << shift);
-      --tmpc;
-
-      /* set the carry to the carry bits of the current word found above */
-      r = rr;
-    }
-  }
-  mp_clamp (c);
-  if (d != NULL) {
-    mp_exch (&t, d);
-  }
-  mp_clear (&t);
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_div_2d.c */
-
-/* Start: bn_mp_div_3.c */
-#include <tommath.h>
-#ifdef BN_MP_DIV_3_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* divide by three (based on routine from MPI and the GMP manual) */
-int
-mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
-{
-  mp_int   q;
-  mp_word  w, t;
-  mp_digit b;
-  int      res, ix;
-
-  /* b = 2**DIGIT_BIT / 3 */
-  b = (((mp_word)1) << ((mp_word)DIGIT_BIT)) / ((mp_word)3);
-
-  if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
-     return res;
-  }
-
-  q.used = a->used;
-  q.sign = a->sign;
-  w = 0;
-  for (ix = a->used - 1; ix >= 0; ix--) {
-     w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
-
-     if (w >= 3) {
-        /* multiply w by [1/3] */
-        t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT);
-
-        /* now subtract 3 * [w/3] from w, to get the remainder */
-        w -= t+t+t;
-
-        /* fixup the remainder as required since
-         * the optimization is not exact.
-         */
-        while (w >= 3) {
-           t += 1;
-           w -= 3;
-        }
-      } else {
-        t = 0;
-      }
-      q.dp[ix] = (mp_digit)t;
-  }
-
-  /* [optional] store the remainder */
-  if (d != NULL) {
-     *d = (mp_digit)w;
-  }
-
-  /* [optional] store the quotient */
-  if (c != NULL) {
-     mp_clamp(&q);
-     mp_exch(&q, c);
-  }
-  mp_clear(&q);
-
-  return res;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_div_3.c */
-
-/* Start: bn_mp_div_d.c */
-#include <tommath.h>
-#ifdef BN_MP_DIV_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-static int s_is_power_of_two(mp_digit b, int *p)
-{
-   int x;
-
-   /* fast return if no power of two */
-   if ((b==0) || (b & (b-1))) {
-      return 0;
-   }
-
-   for (x = 0; x < DIGIT_BIT; x++) {
-      if (b == (((mp_digit)1)<<x)) {
-         *p = x;
-         return 1;
-      }
-   }
-   return 0;
-}
-
-/* single digit division (based on routine from MPI) */
-int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
-{
-  mp_int  q;
-  mp_word w;
-  mp_digit t;
-  int     res, ix;
-
-  /* cannot divide by zero */
-  if (b == 0) {
-     return MP_VAL;
-  }
-
-  /* quick outs */
-  if (b == 1 || mp_iszero(a) == 1) {
-     if (d != NULL) {
-        *d = 0;
-     }
-     if (c != NULL) {
-        return mp_copy(a, c);
-     }
-     return MP_OKAY;
-  }
-
-  /* power of two ? */
-  if (s_is_power_of_two(b, &ix) == 1) {
-     if (d != NULL) {
-        *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
-     }
-     if (c != NULL) {
-        return mp_div_2d(a, ix, c, NULL);
-     }
-     return MP_OKAY;
-  }
-
-#ifdef BN_MP_DIV_3_C
-  /* three? */
-  if (b == 3) {
-     return mp_div_3(a, c, d);
-  }
-#endif
-
-  /* no easy answer [c'est la vie].  Just division */
-  if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
-     return res;
-  }
-
-  q.used = a->used;
-  q.sign = a->sign;
-  w = 0;
-  for (ix = a->used - 1; ix >= 0; ix--) {
-     w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
-
-     if (w >= b) {
-        t = (mp_digit)(w / b);
-        w -= ((mp_word)t) * ((mp_word)b);
-      } else {
-        t = 0;
-      }
-      q.dp[ix] = (mp_digit)t;
-  }
-
-  if (d != NULL) {
-     *d = (mp_digit)w;
-  }
-
-  if (c != NULL) {
-     mp_clamp(&q);
-     mp_exch(&q, c);
-  }
-  mp_clear(&q);
-
-  return res;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_div_d.c */
-
-/* Start: bn_mp_dr_is_modulus.c */
-#include <tommath.h>
-#ifdef BN_MP_DR_IS_MODULUS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* determines if a number is a valid DR modulus */
-int mp_dr_is_modulus(mp_int *a)
-{
-   int ix;
-
-   /* must be at least two digits */
-   if (a->used < 2) {
-      return 0;
-   }
-
-   /* must be of the form b**k - a [a <= b] so all
-    * but the first digit must be equal to -1 (mod b).
-    */
-   for (ix = 1; ix < a->used; ix++) {
-       if (a->dp[ix] != MP_MASK) {
-          return 0;
-       }
-   }
-   return 1;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_dr_is_modulus.c */
-
-/* Start: bn_mp_dr_reduce.c */
-#include <tommath.h>
-#ifdef BN_MP_DR_REDUCE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
- *
- * Based on algorithm from the paper
- *
- * "Generating Efficient Primes for Discrete Log Cryptosystems"
- *                 Chae Hoon Lim, Pil Joong Lee,
- *          POSTECH Information Research Laboratories
- *
- * The modulus must be of a special format [see manual]
- *
- * Has been modified to use algorithm 7.10 from the LTM book instead
- *
- * Input x must be in the range 0 <= x <= (n-1)**2
- */
-int
-mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k)
-{
-  int      err, i, m;
-  mp_word  r;
-  mp_digit mu, *tmpx1, *tmpx2;
-
-  /* m = digits in modulus */
-  m = n->used;
-
-  /* ensure that "x" has at least 2m digits */
-  if (x->alloc < m + m) {
-    if ((err = mp_grow (x, m + m)) != MP_OKAY) {
-      return err;
-    }
-  }
-
-/* top of loop, this is where the code resumes if
- * another reduction pass is required.
- */
-top:
-  /* aliases for digits */
-  /* alias for lower half of x */
-  tmpx1 = x->dp;
-
-  /* alias for upper half of x, or x/B**m */
-  tmpx2 = x->dp + m;
-
-  /* set carry to zero */
-  mu = 0;
-
-  /* compute (x mod B**m) + k * [x/B**m] inline and inplace */
-  for (i = 0; i < m; i++) {
-      r         = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu;
-      *tmpx1++  = (mp_digit)(r & MP_MASK);
-      mu        = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
-  }
-
-  /* set final carry */
-  *tmpx1++ = mu;
-
-  /* zero words above m */
-  for (i = m + 1; i < x->used; i++) {
-      *tmpx1++ = 0;
-  }
-
-  /* clamp, sub and return */
-  mp_clamp (x);
-
-  /* if x >= n then subtract and reduce again
-   * Each successive "recursion" makes the input smaller and smaller.
-   */
-  if (mp_cmp_mag (x, n) != MP_LT) {
-    s_mp_sub(x, n, x);
-    goto top;
-  }
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_dr_reduce.c */
-
-/* Start: bn_mp_dr_setup.c */
-#include <tommath.h>
-#ifdef BN_MP_DR_SETUP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* determines the setup value */
-void mp_dr_setup(mp_int *a, mp_digit *d)
-{
-   /* the casts are required if DIGIT_BIT is one less than
-    * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
-    */
-   *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) -
-        ((mp_word)a->dp[0]));
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_dr_setup.c */
-
-/* Start: bn_mp_exch.c */
-#include <tommath.h>
-#ifdef BN_MP_EXCH_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* swap the elements of two integers, for cases where you can't simply swap the
- * mp_int pointers around
- */
-void
-mp_exch (mp_int * a, mp_int * b)
-{
-  mp_int  t;
-
-  t  = *a;
-  *a = *b;
-  *b = t;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_exch.c */
-
-/* Start: bn_mp_expt_d.c */
-#include <tommath.h>
-#ifdef BN_MP_EXPT_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* calculate c = a**b  using a square-multiply algorithm */
-int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
-{
-  int     res, x;
-  mp_int  g;
-
-  if ((res = mp_init_copy (&g, a)) != MP_OKAY) {
-    return res;
-  }
-
-  /* set initial result */
-  mp_set (c, 1);
-
-  for (x = 0; x < (int) DIGIT_BIT; x++) {
-    /* square */
-    if ((res = mp_sqr (c, c)) != MP_OKAY) {
-      mp_clear (&g);
-      return res;
-    }
-
-    /* if the bit is set multiply */
-    if ((b & (mp_digit) (((mp_digit)1) << (DIGIT_BIT - 1))) != 0) {
-      if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
-         mp_clear (&g);
-         return res;
-      }
-    }
-
-    /* shift to next bit */
-    b <<= 1;
-  }
-
-  mp_clear (&g);
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_expt_d.c */
-
-/* Start: bn_mp_exptmod.c */
-#include <tommath.h>
-#ifdef BN_MP_EXPTMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-
-/* this is a shell function that calls either the normal or Montgomery
- * exptmod functions.  Originally the call to the montgomery code was
- * embedded in the normal function but that wasted alot of stack space
- * for nothing (since 99% of the time the Montgomery code would be called)
- */
-int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
-{
-  int dr;
-
-  /* modulus P must be positive */
-  if (P->sign == MP_NEG) {
-     return MP_VAL;
-  }
-
-  /* if exponent X is negative we have to recurse */
-  if (X->sign == MP_NEG) {
-#ifdef BN_MP_INVMOD_C
-     mp_int tmpG, tmpX;
-     int err;
-
-     /* first compute 1/G mod P */
-     if ((err = mp_init(&tmpG)) != MP_OKAY) {
-        return err;
-     }
-     if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
-        mp_clear(&tmpG);
-        return err;
-     }
-
-     /* now get |X| */
-     if ((err = mp_init(&tmpX)) != MP_OKAY) {
-        mp_clear(&tmpG);
-        return err;
-     }
-     if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
-        mp_clear_multi(&tmpG, &tmpX, NULL);
-        return err;
-     }
-
-     /* and now compute (1/G)**|X| instead of G**X [X < 0] */
-     err = mp_exptmod(&tmpG, &tmpX, P, Y);
-     mp_clear_multi(&tmpG, &tmpX, NULL);
-     return err;
-#else
-     /* no invmod */
-     return MP_VAL;
-#endif
-  }
-
-/* modified diminished radix reduction */
-#if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && defined(BN_S_MP_EXPTMOD_C)
-  if (mp_reduce_is_2k_l(P) == MP_YES) {
-     return s_mp_exptmod(G, X, P, Y, 1);
-  }
-#endif
-
-#ifdef BN_MP_DR_IS_MODULUS_C
-  /* is it a DR modulus? */
-  dr = mp_dr_is_modulus(P);
-#else
-  /* default to no */
-  dr = 0;
-#endif
-
-#ifdef BN_MP_REDUCE_IS_2K_C
-  /* if not, is it a unrestricted DR modulus? */
-  if (dr == 0) {
-     dr = mp_reduce_is_2k(P) << 1;
-  }
-#endif
-
-  /* if the modulus is odd or dr != 0 use the montgomery method */
-#ifdef BN_MP_EXPTMOD_FAST_C
-  if (mp_isodd (P) == 1 || dr !=  0) {
-    return mp_exptmod_fast (G, X, P, Y, dr);
-  } else {
-#endif
-#ifdef BN_S_MP_EXPTMOD_C
-    /* otherwise use the generic Barrett reduction technique */
-    return s_mp_exptmod (G, X, P, Y, 0);
-#else
-    /* no exptmod for evens */
-    return MP_VAL;
-#endif
-#ifdef BN_MP_EXPTMOD_FAST_C
-  }
-#endif
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_exptmod.c */
-
-/* Start: bn_mp_exptmod_fast.c */
-#include <tommath.h>
-#ifdef BN_MP_EXPTMOD_FAST_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
- *
- * Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
- * The value of k changes based on the size of the exponent.
- *
- * Uses Montgomery or Diminished Radix reduction [whichever appropriate]
- */
-
-#ifdef MP_LOW_MEM
-   #define TAB_SIZE 32
-#else
-   #define TAB_SIZE 256
-#endif
-
-int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
-{
-  mp_int  M[TAB_SIZE], res;
-  mp_digit buf, mp;
-  int     err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
-
-  /* use a pointer to the reduction algorithm.  This allows us to use
-   * one of many reduction algorithms without modding the guts of
-   * the code with if statements everywhere.
-   */
-  int     (*redux)(mp_int*,mp_int*,mp_digit);
-
-  /* find window size */
-  x = mp_count_bits (X);
-  if (x <= 7) {
-    winsize = 2;
-  } else if (x <= 36) {
-    winsize = 3;
-  } else if (x <= 140) {
-    winsize = 4;
-  } else if (x <= 450) {
-    winsize = 5;
-  } else if (x <= 1303) {
-    winsize = 6;
-  } else if (x <= 3529) {
-    winsize = 7;
-  } else {
-    winsize = 8;
-  }
-
-#ifdef MP_LOW_MEM
-  if (winsize > 5) {
-     winsize = 5;
-  }
-#endif
-
-  /* init M array */
-  /* init first cell */
-  if ((err = mp_init(&M[1])) != MP_OKAY) {
-     return err;
-  }
-
-  /* now init the second half of the array */
-  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
-    if ((err = mp_init(&M[x])) != MP_OKAY) {
-      for (y = 1<<(winsize-1); y < x; y++) {
-        mp_clear (&M[y]);
-      }
-      mp_clear(&M[1]);
-      return err;
-    }
-  }
-
-  /* determine and setup reduction code */
-  if (redmode == 0) {
-#ifdef BN_MP_MONTGOMERY_SETUP_C
-     /* now setup montgomery  */
-     if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
-        goto LBL_M;
-     }
-#else
-     err = MP_VAL;
-     goto LBL_M;
-#endif
-
-     /* automatically pick the comba one if available (saves quite a few calls/ifs) */
-#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
-     if (((P->used * 2 + 1) < MP_WARRAY) &&
-          P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
-        redux = fast_mp_montgomery_reduce;
-     } else
-#endif
-     {
-#ifdef BN_MP_MONTGOMERY_REDUCE_C
-        /* use slower baseline Montgomery method */
-        redux = mp_montgomery_reduce;
-#else
-        err = MP_VAL;
-        goto LBL_M;
-#endif
-     }
-  } else if (redmode == 1) {
-#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
-     /* setup DR reduction for moduli of the form B**k - b */
-     mp_dr_setup(P, &mp);
-     redux = mp_dr_reduce;
-#else
-     err = MP_VAL;
-     goto LBL_M;
-#endif
-  } else {
-#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
-     /* setup DR reduction for moduli of the form 2**k - b */
-     if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
-        goto LBL_M;
-     }
-     redux = mp_reduce_2k;
-#else
-     err = MP_VAL;
-     goto LBL_M;
-#endif
-  }
-
-  /* setup result */
-  if ((err = mp_init (&res)) != MP_OKAY) {
-    goto LBL_M;
-  }
-
-  /* create M table
-   *
-
-   *
-   * The first half of the table is not computed though accept for M[0] and M[1]
-   */
-
-  if (redmode == 0) {
-#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
-     /* now we need R mod m */
-     if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
-       goto LBL_RES;
-     }
-#else
-     err = MP_VAL;
-     goto LBL_RES;
-#endif
-
-     /* now set M[1] to G * R mod m */
-     if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
-       goto LBL_RES;
-     }
-  } else {
-     mp_set(&res, 1);
-     if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
-        goto LBL_RES;
-     }
-  }
-
-  /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
-  if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
-    goto LBL_RES;
-  }
-
-  for (x = 0; x < (winsize - 1); x++) {
-    if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
-      goto LBL_RES;
-    }
-    if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
-      goto LBL_RES;
-    }
-  }
-
-  /* create upper table */
-  for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
-    if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
-      goto LBL_RES;
-    }
-    if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
-      goto LBL_RES;
-    }
-  }
-
-  /* set initial mode and bit cnt */
-  mode   = 0;
-  bitcnt = 1;
-  buf    = 0;
-  digidx = X->used - 1;
-  bitcpy = 0;
-  bitbuf = 0;
-
-  for (;;) {
-    /* grab next digit as required */
-    if (--bitcnt == 0) {
-      /* if digidx == -1 we are out of digits so break */
-      if (digidx == -1) {
-        break;
-      }
-      /* read next digit and reset bitcnt */
-      buf    = X->dp[digidx--];
-      bitcnt = (int)DIGIT_BIT;
-    }
-
-    /* grab the next msb from the exponent */
-    y     = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
-    buf <<= (mp_digit)1;
-
-    /* if the bit is zero and mode == 0 then we ignore it
-     * These represent the leading zero bits before the first 1 bit
-     * in the exponent.  Technically this opt is not required but it
-     * does lower the # of trivial squaring/reductions used
-     */
-    if (mode == 0 && y == 0) {
-      continue;
-    }
-
-    /* if the bit is zero and mode == 1 then we square */
-    if (mode == 1 && y == 0) {
-      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
-        goto LBL_RES;
-      }
-      if ((err = redux (&res, P, mp)) != MP_OKAY) {
-        goto LBL_RES;
-      }
-      continue;
-    }
-
-    /* else we add it to the window */
-    bitbuf |= (y << (winsize - ++bitcpy));
-    mode    = 2;
-
-    if (bitcpy == winsize) {
-      /* ok window is filled so square as required and multiply  */
-      /* square first */
-      for (x = 0; x < winsize; x++) {
-        if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
-          goto LBL_RES;
-        }
-        if ((err = redux (&res, P, mp)) != MP_OKAY) {
-          goto LBL_RES;
-        }
-      }
-
-      /* then multiply */
-      if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
-        goto LBL_RES;
-      }
-      if ((err = redux (&res, P, mp)) != MP_OKAY) {
-        goto LBL_RES;
-      }
-
-      /* empty window and reset */
-      bitcpy = 0;
-      bitbuf = 0;
-      mode   = 1;
-    }
-  }
-
-  /* if bits remain then square/multiply */
-  if (mode == 2 && bitcpy > 0) {
-    /* square then multiply if the bit is set */
-    for (x = 0; x < bitcpy; x++) {
-      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
-        goto LBL_RES;
-      }
-      if ((err = redux (&res, P, mp)) != MP_OKAY) {
-        goto LBL_RES;
-      }
-
-      /* get next bit of the window */
-      bitbuf <<= 1;
-      if ((bitbuf & (1 << winsize)) != 0) {
-        /* then multiply */
-        if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
-          goto LBL_RES;
-        }
-        if ((err = redux (&res, P, mp)) != MP_OKAY) {
-          goto LBL_RES;
-        }
-      }
-    }
-  }
-
-  if (redmode == 0) {
-     /* fixup result if Montgomery reduction is used
-      * recall that any value in a Montgomery system is
-      * actually multiplied by R mod n.  So we have
-      * to reduce one more time to cancel out the factor
-      * of R.
-      */
-     if ((err = redux(&res, P, mp)) != MP_OKAY) {
-       goto LBL_RES;
-     }
-  }
-
-  /* swap res with Y */
-  mp_exch (&res, Y);
-  err = MP_OKAY;
-LBL_RES:mp_clear (&res);
-LBL_M:
-  mp_clear(&M[1]);
-  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
-    mp_clear (&M[x]);
-  }
-  return err;
-}
-#endif
-
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_exptmod_fast.c */
-
-/* Start: bn_mp_exteuclid.c */
-#include <tommath.h>
-#ifdef BN_MP_EXTEUCLID_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* Extended euclidean algorithm of (a, b) produces
-   a*u1 + b*u2 = u3
- */
-int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
-{
-   mp_int u1,u2,u3,v1,v2,v3,t1,t2,t3,q,tmp;
-   int err;
-
-   if ((err = mp_init_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL)) != MP_OKAY) {
-      return err;
-   }
-
-   /* initialize, (u1,u2,u3) = (1,0,a) */
-   mp_set(&u1, 1);
-   if ((err = mp_copy(a, &u3)) != MP_OKAY)                                        { goto _ERR; }
-
-   /* initialize, (v1,v2,v3) = (0,1,b) */
-   mp_set(&v2, 1);
-   if ((err = mp_copy(b, &v3)) != MP_OKAY)                                        { goto _ERR; }
-
-   /* loop while v3 != 0 */
-   while (mp_iszero(&v3) == MP_NO) {
-       /* q = u3/v3 */
-       if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY)                         { goto _ERR; }
-
-       /* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */
-       if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY)                              { goto _ERR; }
-       if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY)                             { goto _ERR; }
-       if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY)                              { goto _ERR; }
-       if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY)                             { goto _ERR; }
-       if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY)                              { goto _ERR; }
-       if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY)                             { goto _ERR; }
-
-       /* (u1,u2,u3) = (v1,v2,v3) */
-       if ((err = mp_copy(&v1, &u1)) != MP_OKAY)                                  { goto _ERR; }
-       if ((err = mp_copy(&v2, &u2)) != MP_OKAY)                                  { goto _ERR; }
-       if ((err = mp_copy(&v3, &u3)) != MP_OKAY)                                  { goto _ERR; }
-
-       /* (v1,v2,v3) = (t1,t2,t3) */
-       if ((err = mp_copy(&t1, &v1)) != MP_OKAY)                                  { goto _ERR; }
-       if ((err = mp_copy(&t2, &v2)) != MP_OKAY)                                  { goto _ERR; }
-       if ((err = mp_copy(&t3, &v3)) != MP_OKAY)                                  { goto _ERR; }
-   }
-
-   /* make sure U3 >= 0 */
-   if (u3.sign == MP_NEG) {
-      mp_neg(&u1, &u1);
-      mp_neg(&u2, &u2);
-      mp_neg(&u3, &u3);
-   }
-
-   /* copy result out */
-   if (U1 != NULL) { mp_exch(U1, &u1); }
-   if (U2 != NULL) { mp_exch(U2, &u2); }
-   if (U3 != NULL) { mp_exch(U3, &u3); }
-
-   err = MP_OKAY;
-_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
-   return err;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_exteuclid.c */
-
-/* Start: bn_mp_fread.c */
-#include <tommath.h>
-#ifdef BN_MP_FREAD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* read a bigint from a file stream in ASCII */
-int mp_fread(mp_int *a, int radix, FILE *stream)
-{
-   int err, ch, neg, y;
-
-   /* clear a */
-   mp_zero(a);
-
-   /* if first digit is - then set negative */
-   ch = fgetc(stream);
-   if (ch == '-') {
-      neg = MP_NEG;
-      ch = fgetc(stream);
-   } else {
-      neg = MP_ZPOS;
-   }
-
-   for (;;) {
-      /* find y in the radix map */
-      for (y = 0; y < radix; y++) {
-          if (mp_s_rmap[y] == ch) {
-             break;
-          }
-      }
-      if (y == radix) {
-         break;
-      }
-
-      /* shift up and add */
-      if ((err = mp_mul_d(a, radix, a)) != MP_OKAY) {
-         return err;
-      }
-      if ((err = mp_add_d(a, y, a)) != MP_OKAY) {
-         return err;
-      }
-
-      ch = fgetc(stream);
-   }
-   if (mp_cmp_d(a, 0) != MP_EQ) {
-      a->sign = neg;
-   }
-
-   return MP_OKAY;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_fread.c */
-
-/* Start: bn_mp_fwrite.c */
-#include <tommath.h>
-#ifdef BN_MP_FWRITE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-int mp_fwrite(mp_int *a, int radix, FILE *stream)
-{
-   char *buf;
-   int err, len, x;
-
-   if ((err = mp_radix_size(a, radix, &len)) != MP_OKAY) {
-      return err;
-   }
-
-   buf = OPT_CAST(char) XMALLOC (len);
-   if (buf == NULL) {
-      return MP_MEM;
-   }
-
-   if ((err = mp_toradix(a, buf, radix)) != MP_OKAY) {
-      XFREE (buf);
-      return err;
-   }
-
-   for (x = 0; x < len; x++) {
-       if (fputc(buf[x], stream) == EOF) {
-          XFREE (buf);
-          return MP_VAL;
-       }
-   }
-
-   XFREE (buf);
-   return MP_OKAY;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_fwrite.c */
-
-/* Start: bn_mp_gcd.c */
-#include <tommath.h>
-#ifdef BN_MP_GCD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* Greatest Common Divisor using the binary method */
-int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
-{
-  mp_int  u, v;
-  int     k, u_lsb, v_lsb, res;
-
-  /* either zero than gcd is the largest */
-  if (mp_iszero (a) == MP_YES) {
-    return mp_abs (b, c);
-  }
-  if (mp_iszero (b) == MP_YES) {
-    return mp_abs (a, c);
-  }
-
-  /* get copies of a and b we can modify */
-  if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_init_copy (&v, b)) != MP_OKAY) {
-    goto LBL_U;
-  }
-
-  /* must be positive for the remainder of the algorithm */
-  u.sign = v.sign = MP_ZPOS;
-
-  /* B1.  Find the common power of two for u and v */
-  u_lsb = mp_cnt_lsb(&u);
-  v_lsb = mp_cnt_lsb(&v);
-  k     = MIN(u_lsb, v_lsb);
-
-  if (k > 0) {
-     /* divide the power of two out */
-     if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
-        goto LBL_V;
-     }
-
-     if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
-        goto LBL_V;
-     }
-  }
-
-  /* divide any remaining factors of two out */
-  if (u_lsb != k) {
-     if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
-        goto LBL_V;
-     }
-  }
-
-  if (v_lsb != k) {
-     if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
-        goto LBL_V;
-     }
-  }
-
-  while (mp_iszero(&v) == 0) {
-     /* make sure v is the largest */
-     if (mp_cmp_mag(&u, &v) == MP_GT) {
-        /* swap u and v to make sure v is >= u */
-        mp_exch(&u, &v);
-     }
-
-     /* subtract smallest from largest */
-     if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) {
-        goto LBL_V;
-     }
-
-     /* Divide out all factors of two */
-     if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
-        goto LBL_V;
-     }
-  }
-
-  /* multiply by 2**k which we divided out at the beginning */
-  if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) {
-     goto LBL_V;
-  }
-  c->sign = MP_ZPOS;
-  res = MP_OKAY;
-LBL_V:mp_clear (&u);
-LBL_U:mp_clear (&v);
-  return res;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_gcd.c */
-
-/* Start: bn_mp_get_int.c */
-#include <tommath.h>
-#ifdef BN_MP_GET_INT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* get the lower 32-bits of an mp_int */
-unsigned long mp_get_int(mp_int * a)
-{
-  int i;
-  unsigned long res;
-
-  if (a->used == 0) {
-     return 0;
-  }
-
-  /* get number of digits of the lsb we have to read */
-  i = MIN(a->used,(int)((sizeof(unsigned long)*CHAR_BIT+DIGIT_BIT-1)/DIGIT_BIT))-1;
-
-  /* get most significant digit of result */
-  res = DIGIT(a,i);
-
-  while (--i >= 0) {
-    res = (res << DIGIT_BIT) | DIGIT(a,i);
-  }
-
-  /* force result to 32-bits always so it is consistent on non 32-bit platforms */
-  return res & 0xFFFFFFFFUL;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_get_int.c */
-
-/* Start: bn_mp_grow.c */
-#include <tommath.h>
-#ifdef BN_MP_GROW_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* grow as required */
-int mp_grow (mp_int * a, int size)
-{
-  int     i;
-  mp_digit *tmp;
-
-  /* if the alloc size is smaller alloc more ram */
-  if (a->alloc < size) {
-    /* ensure there are always at least MP_PREC digits extra on top */
-    size += (MP_PREC * 2) - (size % MP_PREC);
-
-    /* reallocate the array a->dp
-     *
-     * We store the return in a temporary variable
-     * in case the operation failed we don't want
-     * to overwrite the dp member of a.
-     */
-    tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size);
-    if (tmp == NULL) {
-      /* reallocation failed but "a" is still valid [can be freed] */
-      return MP_MEM;
-    }
-
-    /* reallocation succeeded so set a->dp */
-    a->dp = tmp;
-
-    /* zero excess digits */
-    i        = a->alloc;
-    a->alloc = size;
-    for (; i < a->alloc; i++) {
-      a->dp[i] = 0;
-    }
-  }
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_grow.c */
-
-/* Start: bn_mp_init.c */
-#include <tommath.h>
-#ifdef BN_MP_INIT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* init a new mp_int */
-int mp_init (mp_int * a)
-{
-  int i;
-
-  /* allocate memory required and clear it */
-  a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
-  if (a->dp == NULL) {
-    return MP_MEM;
-  }
-
-  /* set the digits to zero */
-  for (i = 0; i < MP_PREC; i++) {
-      a->dp[i] = 0;
-  }
-
-  /* set the used to zero, allocated digits to the default precision
-   * and sign to positive */
-  a->used  = 0;
-  a->alloc = MP_PREC;
-  a->sign  = MP_ZPOS;
-
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_init.c */
-
-/* Start: bn_mp_init_copy.c */
-#include <tommath.h>
-#ifdef BN_MP_INIT_COPY_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* creates "a" then copies b into it */
-int mp_init_copy (mp_int * a, mp_int * b)
-{
-  int     res;
-
-  if ((res = mp_init (a)) != MP_OKAY) {
-    return res;
-  }
-  return mp_copy (b, a);
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_init_copy.c */
-
-/* Start: bn_mp_init_multi.c */
-#include <tommath.h>
-#ifdef BN_MP_INIT_MULTI_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-#include <stdarg.h>
-
-int mp_init_multi(mp_int *mp, ...)
-{
-    mp_err res = MP_OKAY;      /* Assume ok until proven otherwise */
-    int n = 0;                 /* Number of ok inits */
-    mp_int* cur_arg = mp;
-    va_list args;
-
-    va_start(args, mp);        /* init args to next argument from caller */
-    while (cur_arg != NULL) {
-        if (mp_init(cur_arg) != MP_OKAY) {
-            /* Oops - error! Back-track and mp_clear what we already
-               succeeded in init-ing, then return error.
-            */
-            va_list clean_args;
-
-            /* end the current list */
-            va_end(args);
-
-            /* now start cleaning up */
-            cur_arg = mp;
-            va_start(clean_args, mp);
-            while (n--) {
-                mp_clear(cur_arg);
-                cur_arg = va_arg(clean_args, mp_int*);
-            }
-            va_end(clean_args);
-            res = MP_MEM;
-            break;
-        }
-        n++;
-        cur_arg = va_arg(args, mp_int*);
-    }
-    va_end(args);
-    return res;                /* Assumed ok, if error flagged above. */
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_init_multi.c */
-
-/* Start: bn_mp_init_set.c */
-#include <tommath.h>
-#ifdef BN_MP_INIT_SET_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* initialize and set a digit */
-int mp_init_set (mp_int * a, mp_digit b)
-{
-  int err;
-  if ((err = mp_init(a)) != MP_OKAY) {
-     return err;
-  }
-  mp_set(a, b);
-  return err;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_init_set.c */
-
-/* Start: bn_mp_init_set_int.c */
-#include <tommath.h>
-#ifdef BN_MP_INIT_SET_INT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* initialize and set a digit */
-int mp_init_set_int (mp_int * a, unsigned long b)
-{
-  int err;
-  if ((err = mp_init(a)) != MP_OKAY) {
-     return err;
-  }
-  return mp_set_int(a, b);
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_init_set_int.c */
-
-/* Start: bn_mp_init_size.c */
-#include <tommath.h>
-#ifdef BN_MP_INIT_SIZE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* init an mp_init for a given size */
-int mp_init_size (mp_int * a, int size)
-{
-  int x;
-
-  /* pad size so there are always extra digits */
-  size += (MP_PREC * 2) - (size % MP_PREC);	
-
-  /* alloc mem */
-  a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
-  if (a->dp == NULL) {
-    return MP_MEM;
-  }
-
-  /* set the members */
-  a->used  = 0;
-  a->alloc = size;
-  a->sign  = MP_ZPOS;
-
-  /* zero the digits */
-  for (x = 0; x < size; x++) {
-      a->dp[x] = 0;
-  }
-
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_init_size.c */
-
-/* Start: bn_mp_invmod.c */
-#include <tommath.h>
-#ifdef BN_MP_INVMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* hac 14.61, pp608 */
-int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
-{
-  /* b cannot be negative */
-  if (b->sign == MP_NEG || mp_iszero(b) == 1) {
-    return MP_VAL;
-  }
-
-#ifdef BN_FAST_MP_INVMOD_C
-  /* if the modulus is odd we can use a faster routine instead */
-  if (mp_isodd (b) == 1) {
-    return fast_mp_invmod (a, b, c);
-  }
-#endif
-
-#ifdef BN_MP_INVMOD_SLOW_C
-  return mp_invmod_slow(a, b, c);
-#endif
-
-  return MP_VAL;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_invmod.c */
-
-/* Start: bn_mp_invmod_slow.c */
-#include <tommath.h>
-#ifdef BN_MP_INVMOD_SLOW_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* hac 14.61, pp608 */
-int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
-{
-  mp_int  x, y, u, v, A, B, C, D;
-  int     res;
-
-  /* b cannot be negative */
-  if (b->sign == MP_NEG || mp_iszero(b) == 1) {
-    return MP_VAL;
-  }
-
-  /* init temps */
-  if ((res = mp_init_multi(&x, &y, &u, &v,
-                           &A, &B, &C, &D, NULL)) != MP_OKAY) {
-     return res;
-  }
-
-  /* x = a, y = b */
-  if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
-      goto LBL_ERR;
-  }
-  if ((res = mp_copy (b, &y)) != MP_OKAY) {
-    goto LBL_ERR;
-  }
-
-  /* 2. [modified] if x,y are both even then return an error! */
-  if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
-    res = MP_VAL;
-    goto LBL_ERR;
-  }
-
-  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
-  if ((res = mp_copy (&x, &u)) != MP_OKAY) {
-    goto LBL_ERR;
-  }
-  if ((res = mp_copy (&y, &v)) != MP_OKAY) {
-    goto LBL_ERR;
-  }
-  mp_set (&A, 1);
-  mp_set (&D, 1);
-
-top:
-  /* 4.  while u is even do */
-  while (mp_iseven (&u) == 1) {
-    /* 4.1 u = u/2 */
-    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-    /* 4.2 if A or B is odd then */
-    if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
-      /* A = (A+y)/2, B = (B-x)/2 */
-      if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
-         goto LBL_ERR;
-      }
-      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
-         goto LBL_ERR;
-      }
-    }
-    /* A = A/2, B = B/2 */
-    if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-  }
-
-  /* 5.  while v is even do */
-  while (mp_iseven (&v) == 1) {
-    /* 5.1 v = v/2 */
-    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-    /* 5.2 if C or D is odd then */
-    if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
-      /* C = (C+y)/2, D = (D-x)/2 */
-      if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
-         goto LBL_ERR;
-      }
-      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
-         goto LBL_ERR;
-      }
-    }
-    /* C = C/2, D = D/2 */
-    if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-    if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-  }
-
-  /* 6.  if u >= v then */
-  if (mp_cmp (&u, &v) != MP_LT) {
-    /* u = u - v, A = A - C, B = B - D */
-    if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-
-    if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-
-    if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-  } else {
-    /* v - v - u, C = C - A, D = D - B */
-    if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-
-    if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-
-    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-  }
-
-  /* if not zero goto step 4 */
-  if (mp_iszero (&u) == 0)
-    goto top;
-
-  /* now a = C, b = D, gcd == g*v */
-
-  /* if v != 1 then there is no inverse */
-  if (mp_cmp_d (&v, 1) != MP_EQ) {
-    res = MP_VAL;
-    goto LBL_ERR;
-  }
-
-  /* if its too low */
-  while (mp_cmp_d(&C, 0) == MP_LT) {
-      if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
-         goto LBL_ERR;
-      }
-  }
-
-  /* too big */
-  while (mp_cmp_mag(&C, b) != MP_LT) {
-      if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
-         goto LBL_ERR;
-      }
-  }
-
-  /* C is now the inverse */
-  mp_exch (&C, c);
-  res = MP_OKAY;
-LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
-  return res;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_invmod_slow.c */
-
-/* Start: bn_mp_is_square.c */
-#include <tommath.h>
-#ifdef BN_MP_IS_SQUARE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* Check if remainders are possible squares - fast exclude non-squares */
-static const char rem_128[128] = {
- 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1
-};
-
-static const char rem_105[105] = {
- 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
- 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1,
- 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1,
- 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
- 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
- 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1,
- 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1
-};
-
-/* Store non-zero to ret if arg is square, and zero if not */
-int mp_is_square(mp_int *arg,int *ret)
-{
-  int           res;
-  mp_digit      c;
-  mp_int        t;
-  unsigned long r;
-
-  /* Default to Non-square :) */
-  *ret = MP_NO;
-
-  if (arg->sign == MP_NEG) {
-    return MP_VAL;
-  }
-
-  /* digits used?  (TSD) */
-  if (arg->used == 0) {
-     return MP_OKAY;
-  }
-
-  /* First check mod 128 (suppose that DIGIT_BIT is at least 7) */
-  if (rem_128[127 & DIGIT(arg,0)] == 1) {
-     return MP_OKAY;
-  }
-
-  /* Next check mod 105 (3*5*7) */
-  if ((res = mp_mod_d(arg,105,&c)) != MP_OKAY) {
-     return res;
-  }
-  if (rem_105[c] == 1) {
-     return MP_OKAY;
-  }
-
-
-  if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) {
-     return res;
-  }
-  if ((res = mp_mod(arg,&t,&t)) != MP_OKAY) {
-     goto ERR;
-  }
-  r = mp_get_int(&t);
-  /* Check for other prime modules, note it's not an ERROR but we must
-   * free "t" so the easiest way is to goto ERR.  We know that res
-   * is already equal to MP_OKAY from the mp_mod call
-   */
-  if ( (1L<<(r%11)) & 0x5C4L )             goto ERR;
-  if ( (1L<<(r%13)) & 0x9E4L )             goto ERR;
-  if ( (1L<<(r%17)) & 0x5CE8L )            goto ERR;
-  if ( (1L<<(r%19)) & 0x4F50CL )           goto ERR;
-  if ( (1L<<(r%23)) & 0x7ACCA0L )          goto ERR;
-  if ( (1L<<(r%29)) & 0xC2EDD0CL )         goto ERR;
-  if ( (1L<<(r%31)) & 0x6DE2B848L )        goto ERR;
-
-  /* Final check - is sqr(sqrt(arg)) == arg ? */
-  if ((res = mp_sqrt(arg,&t)) != MP_OKAY) {
-     goto ERR;
-  }
-  if ((res = mp_sqr(&t,&t)) != MP_OKAY) {
-     goto ERR;
-  }
-
-  *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO;
-ERR:mp_clear(&t);
-  return res;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_is_square.c */
-
-/* Start: bn_mp_jacobi.c */
-#include <tommath.h>
-#ifdef BN_MP_JACOBI_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* computes the jacobi c = (a | n) (or Legendre if n is prime)
- * HAC pp. 73 Algorithm 2.149
- */
-int mp_jacobi (mp_int * a, mp_int * p, int *c)
-{
-  mp_int  a1, p1;
-  int     k, s, r, res;
-  mp_digit residue;
-
-  /* if p <= 0 return MP_VAL */
-  if (mp_cmp_d(p, 0) != MP_GT) {
-     return MP_VAL;
-  }
-
-  /* step 1.  if a == 0, return 0 */
-  if (mp_iszero (a) == 1) {
-    *c = 0;
-    return MP_OKAY;
-  }
-
-  /* step 2.  if a == 1, return 1 */
-  if (mp_cmp_d (a, 1) == MP_EQ) {
-    *c = 1;
-    return MP_OKAY;
-  }
-
-  /* default */
-  s = 0;
-
-  /* step 3.  write a = a1 * 2**k  */
-  if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_init (&p1)) != MP_OKAY) {
-    goto LBL_A1;
-  }
-
-  /* divide out larger power of two */
-  k = mp_cnt_lsb(&a1);
-  if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) {
-     goto LBL_P1;
-  }
-
-  /* step 4.  if e is even set s=1 */
-  if ((k & 1) == 0) {
-    s = 1;
-  } else {
-    /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
-    residue = p->dp[0] & 7;
-
-    if (residue == 1 || residue == 7) {
-      s = 1;
-    } else if (residue == 3 || residue == 5) {
-      s = -1;
-    }
-  }
-
-  /* step 5.  if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
-  if ( ((p->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
-    s = -s;
-  }
-
-  /* if a1 == 1 we're done */
-  if (mp_cmp_d (&a1, 1) == MP_EQ) {
-    *c = s;
-  } else {
-    /* n1 = n mod a1 */
-    if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) {
-      goto LBL_P1;
-    }
-    if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
-      goto LBL_P1;
-    }
-    *c = s * r;
-  }
-
-  /* done */
-  res = MP_OKAY;
-LBL_P1:mp_clear (&p1);
-LBL_A1:mp_clear (&a1);
-  return res;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_jacobi.c */
-
-/* Start: bn_mp_karatsuba_mul.c */
-#include <tommath.h>
-#ifdef BN_MP_KARATSUBA_MUL_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* c = |a| * |b| using Karatsuba Multiplication using
- * three half size multiplications
- *
- * Let B represent the radix [e.g. 2**DIGIT_BIT] and
- * let n represent half of the number of digits in
- * the min(a,b)
- *
- * a = a1 * B**n + a0
- * b = b1 * B**n + b0
- *
- * Then, a * b =>
-   a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
- *
- * Note that a1b1 and a0b0 are used twice and only need to be
- * computed once.  So in total three half size (half # of
- * digit) multiplications are performed, a0b0, a1b1 and
- * (a1+b1)(a0+b0)
- *
- * Note that a multiplication of half the digits requires
- * 1/4th the number of single precision multiplications so in
- * total after one call 25% of the single precision multiplications
- * are saved.  Note also that the call to mp_mul can end up back
- * in this function if the a0, a1, b0, or b1 are above the threshold.
- * This is known as divide-and-conquer and leads to the famous
- * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
- * the standard O(N**2) that the baseline/comba methods use.
- * Generally though the overhead of this method doesn't pay off
- * until a certain size (N ~ 80) is reached.
- */
-int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
-{
-  mp_int  x0, x1, y0, y1, t1, x0y0, x1y1;
-  int     B, err;
-
-  /* default the return code to an error */
-  err = MP_MEM;
-
-  /* min # of digits */
-  B = MIN (a->used, b->used);
-
-  /* now divide in two */
-  B = B >> 1;
-
-  /* init copy all the temps */
-  if (mp_init_size (&x0, B) != MP_OKAY)
-    goto ERR;
-  if (mp_init_size (&x1, a->used - B) != MP_OKAY)
-    goto X0;
-  if (mp_init_size (&y0, B) != MP_OKAY)
-    goto X1;
-  if (mp_init_size (&y1, b->used - B) != MP_OKAY)
-    goto Y0;
-
-  /* init temps */
-  if (mp_init_size (&t1, B * 2) != MP_OKAY)
-    goto Y1;
-  if (mp_init_size (&x0y0, B * 2) != MP_OKAY)
-    goto T1;
-  if (mp_init_size (&x1y1, B * 2) != MP_OKAY)
-    goto X0Y0;
-
-  /* now shift the digits */
-  x0.used = y0.used = B;
-  x1.used = a->used - B;
-  y1.used = b->used - B;
-
-  {
-    register int x;
-    register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
-
-    /* we copy the digits directly instead of using higher level functions
-     * since we also need to shift the digits
-     */
-    tmpa = a->dp;
-    tmpb = b->dp;
-
-    tmpx = x0.dp;
-    tmpy = y0.dp;
-    for (x = 0; x < B; x++) {
-      *tmpx++ = *tmpa++;
-      *tmpy++ = *tmpb++;
-    }
-
-    tmpx = x1.dp;
-    for (x = B; x < a->used; x++) {
-      *tmpx++ = *tmpa++;
-    }
-
-    tmpy = y1.dp;
-    for (x = B; x < b->used; x++) {
-      *tmpy++ = *tmpb++;
-    }
-  }
-
-  /* only need to clamp the lower words since by definition the
-   * upper words x1/y1 must have a known number of digits
-   */
-  mp_clamp (&x0);
-  mp_clamp (&y0);
-
-  /* now calc the products x0y0 and x1y1 */
-  /* after this x0 is no longer required, free temp [x0==t2]! */
-  if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)
-    goto X1Y1;          /* x0y0 = x0*y0 */
-  if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
-    goto X1Y1;          /* x1y1 = x1*y1 */
-
-  /* now calc x1+x0 and y1+y0 */
-  if (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
-    goto X1Y1;          /* t1 = x1 - x0 */
-  if (s_mp_add (&y1, &y0, &x0) != MP_OKAY)
-    goto X1Y1;          /* t2 = y1 - y0 */
-  if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
-    goto X1Y1;          /* t1 = (x1 + x0) * (y1 + y0) */
-
-  /* add x0y0 */
-  if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
-    goto X1Y1;          /* t2 = x0y0 + x1y1 */
-  if (s_mp_sub (&t1, &x0, &t1) != MP_OKAY)
-    goto X1Y1;          /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
-
-  /* shift by B */
-  if (mp_lshd (&t1, B) != MP_OKAY)
-    goto X1Y1;          /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
-  if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
-    goto X1Y1;          /* x1y1 = x1y1 << 2*B */
-
-  if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
-    goto X1Y1;          /* t1 = x0y0 + t1 */
-  if (mp_add (&t1, &x1y1, c) != MP_OKAY)
-    goto X1Y1;          /* t1 = x0y0 + t1 + x1y1 */
-
-  /* Algorithm succeeded set the return code to MP_OKAY */
-  err = MP_OKAY;
-
-X1Y1:mp_clear (&x1y1);
-X0Y0:mp_clear (&x0y0);
-T1:mp_clear (&t1);
-Y1:mp_clear (&y1);
-Y0:mp_clear (&y0);
-X1:mp_clear (&x1);
-X0:mp_clear (&x0);
-ERR:
-  return err;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_karatsuba_mul.c */
-
-/* Start: bn_mp_karatsuba_sqr.c */
-#include <tommath.h>
-#ifdef BN_MP_KARATSUBA_SQR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* Karatsuba squaring, computes b = a*a using three
- * half size squarings
- *
- * See comments of karatsuba_mul for details.  It
- * is essentially the same algorithm but merely
- * tuned to perform recursive squarings.
- */
-int mp_karatsuba_sqr (mp_int * a, mp_int * b)
-{
-  mp_int  x0, x1, t1, t2, x0x0, x1x1;
-  int     B, err;
-
-  err = MP_MEM;
-
-  /* min # of digits */
-  B = a->used;
-
-  /* now divide in two */
-  B = B >> 1;
-
-  /* init copy all the temps */
-  if (mp_init_size (&x0, B) != MP_OKAY)
-    goto ERR;
-  if (mp_init_size (&x1, a->used - B) != MP_OKAY)
-    goto X0;
-
-  /* init temps */
-  if (mp_init_size (&t1, a->used * 2) != MP_OKAY)
-    goto X1;
-  if (mp_init_size (&t2, a->used * 2) != MP_OKAY)
-    goto T1;
-  if (mp_init_size (&x0x0, B * 2) != MP_OKAY)
-    goto T2;
-  if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY)
-    goto X0X0;
-
-  {
-    register int x;
-    register mp_digit *dst, *src;
-
-    src = a->dp;
-
-    /* now shift the digits */
-    dst = x0.dp;
-    for (x = 0; x < B; x++) {
-      *dst++ = *src++;
-    }
-
-    dst = x1.dp;
-    for (x = B; x < a->used; x++) {
-      *dst++ = *src++;
-    }
-  }
-
-  x0.used = B;
-  x1.used = a->used - B;
-
-  mp_clamp (&x0);
-
-  /* now calc the products x0*x0 and x1*x1 */
-  if (mp_sqr (&x0, &x0x0) != MP_OKAY)
-    goto X1X1;           /* x0x0 = x0*x0 */
-  if (mp_sqr (&x1, &x1x1) != MP_OKAY)
-    goto X1X1;           /* x1x1 = x1*x1 */
-
-  /* now calc (x1+x0)**2 */
-  if (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
-    goto X1X1;           /* t1 = x1 - x0 */
-  if (mp_sqr (&t1, &t1) != MP_OKAY)
-    goto X1X1;           /* t1 = (x1 - x0) * (x1 - x0) */
-
-  /* add x0y0 */
-  if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY)
-    goto X1X1;           /* t2 = x0x0 + x1x1 */
-  if (s_mp_sub (&t1, &t2, &t1) != MP_OKAY)
-    goto X1X1;           /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */
-
-  /* shift by B */
-  if (mp_lshd (&t1, B) != MP_OKAY)
-    goto X1X1;           /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */
-  if (mp_lshd (&x1x1, B * 2) != MP_OKAY)
-    goto X1X1;           /* x1x1 = x1x1 << 2*B */
-
-  if (mp_add (&x0x0, &t1, &t1) != MP_OKAY)
-    goto X1X1;           /* t1 = x0x0 + t1 */
-  if (mp_add (&t1, &x1x1, b) != MP_OKAY)
-    goto X1X1;           /* t1 = x0x0 + t1 + x1x1 */
-
-  err = MP_OKAY;
-
-X1X1:mp_clear (&x1x1);
-X0X0:mp_clear (&x0x0);
-T2:mp_clear (&t2);
-T1:mp_clear (&t1);
-X1:mp_clear (&x1);
-X0:mp_clear (&x0);
-ERR:
-  return err;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_karatsuba_sqr.c */
-
-/* Start: bn_mp_lcm.c */
-#include <tommath.h>
-#ifdef BN_MP_LCM_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* computes least common multiple as |a*b|/(a, b) */
-int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
-{
-  int     res;
-  mp_int  t1, t2;
-
-
-  if ((res = mp_init_multi (&t1, &t2, NULL)) != MP_OKAY) {
-    return res;
-  }
-
-  /* t1 = get the GCD of the two inputs */
-  if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) {
-    goto LBL_T;
-  }
-
-  /* divide the smallest by the GCD */
-  if (mp_cmp_mag(a, b) == MP_LT) {
-     /* store quotient in t2 such that t2 * b is the LCM */
-     if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) {
-        goto LBL_T;
-     }
-     res = mp_mul(b, &t2, c);
-  } else {
-     /* store quotient in t2 such that t2 * a is the LCM */
-     if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) {
-        goto LBL_T;
-     }
-     res = mp_mul(a, &t2, c);
-  }
-
-  /* fix the sign to positive */
-  c->sign = MP_ZPOS;
-
-LBL_T:
-  mp_clear_multi (&t1, &t2, NULL);
-  return res;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_lcm.c */
-
-/* Start: bn_mp_lshd.c */
-#include <tommath.h>
-#ifdef BN_MP_LSHD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* shift left a certain amount of digits */
-int mp_lshd (mp_int * a, int b)
-{
-  int     x, res;
-
-  /* if its less than zero return */
-  if (b <= 0) {
-    return MP_OKAY;
-  }
-
-  /* grow to fit the new digits */
-  if (a->alloc < a->used + b) {
-     if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
-       return res;
-     }
-  }
-
-  {
-    register mp_digit *top, *bottom;
-
-    /* increment the used by the shift amount then copy upwards */
-    a->used += b;
-
-    /* top */
-    top = a->dp + a->used - 1;
-
-    /* base */
-    bottom = a->dp + a->used - 1 - b;
-
-    /* much like mp_rshd this is implemented using a sliding window
-     * except the window goes the otherway around.  Copying from
-     * the bottom to the top.  see bn_mp_rshd.c for more info.
-     */
-    for (x = a->used - 1; x >= b; x--) {
-      *top-- = *bottom--;
-    }
-
-    /* zero the lower digits */
-    top = a->dp;
-    for (x = 0; x < b; x++) {
-      *top++ = 0;
-    }
-  }
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_lshd.c */
-
-/* Start: bn_mp_mod.c */
-#include <tommath.h>
-#ifdef BN_MP_MOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* c = a mod b, 0 <= c < b */
-int
-mp_mod (mp_int * a, mp_int * b, mp_int * c)
-{
-  mp_int  t;
-  int     res;
-
-  if ((res = mp_init (&t)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
-    mp_clear (&t);
-    return res;
-  }
-
-  if (t.sign != b->sign) {
-    res = mp_add (b, &t, c);
-  } else {
-    res = MP_OKAY;
-    mp_exch (&t, c);
-  }
-
-  mp_clear (&t);
-  return res;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_mod.c */
-
-/* Start: bn_mp_mod_2d.c */
-#include <tommath.h>
-#ifdef BN_MP_MOD_2D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* calc a value mod 2**b */
-int
-mp_mod_2d (mp_int * a, int b, mp_int * c)
-{
-  int     x, res;
-
-  /* if b is <= 0 then zero the int */
-  if (b <= 0) {
-    mp_zero (c);
-    return MP_OKAY;
-  }
-
-  /* if the modulus is larger than the value than return */
-  if (b >= (int) (a->used * DIGIT_BIT)) {
-    res = mp_copy (a, c);
-    return res;
-  }
-
-  /* copy */
-  if ((res = mp_copy (a, c)) != MP_OKAY) {
-    return res;
-  }
-
-  /* zero digits above the last digit of the modulus */
-  for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
-    c->dp[x] = 0;
-  }
-  /* clear the digit that is not completely outside/inside the modulus */
-  c->dp[b / DIGIT_BIT] &=
-    (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
-  mp_clamp (c);
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_mod_2d.c */
-
-/* Start: bn_mp_mod_d.c */
-#include <tommath.h>
-#ifdef BN_MP_MOD_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-int
-mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
-{
-  return mp_div_d(a, b, NULL, c);
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_mod_d.c */
-
-/* Start: bn_mp_montgomery_calc_normalization.c */
-#include <tommath.h>
-#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/*
- * shifts with subtractions when the result is greater than b.
- *
- * The method is slightly modified to shift B unconditionally upto just under
- * the leading bit of b.  This saves alot of multiple precision shifting.
- */
-int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
-{
-  int     x, bits, res;
-
-  /* how many bits of last digit does b use */
-  bits = mp_count_bits (b) % DIGIT_BIT;
-
-  if (b->used > 1) {
-     if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
-        return res;
-     }
-  } else {
-     mp_set(a, 1);
-     bits = 1;
-  }
-
-
-  /* now compute C = A * B mod b */
-  for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
-    if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
-      return res;
-    }
-    if (mp_cmp_mag (a, b) != MP_LT) {
-      if ((res = s_mp_sub (a, b, a)) != MP_OKAY) {
-        return res;
-      }
-    }
-  }
-
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_montgomery_calc_normalization.c */
-
-/* Start: bn_mp_montgomery_reduce.c */
-#include <tommath.h>
-#ifdef BN_MP_MONTGOMERY_REDUCE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* computes xR**-1 == x (mod N) via Montgomery Reduction */
-int
-mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
-{
-  int     ix, res, digs;
-  mp_digit mu;
-
-  /* can the fast reduction [comba] method be used?
-   *
-   * Note that unlike in mul you're safely allowed *less*
-   * than the available columns [255 per default] since carries
-   * are fixed up in the inner loop.
-   */
-  digs = n->used * 2 + 1;
-  if ((digs < MP_WARRAY) &&
-      n->used <
-      (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
-    return fast_mp_montgomery_reduce (x, n, rho);
-  }
-
-  /* grow the input as required */
-  if (x->alloc < digs) {
-    if ((res = mp_grow (x, digs)) != MP_OKAY) {
-      return res;
-    }
-  }
-  x->used = digs;
-
-  for (ix = 0; ix < n->used; ix++) {
-    /* mu = ai * rho mod b
-     *
-     * The value of rho must be precalculated via
-     * montgomery_setup() such that
-     * it equals -1/n0 mod b this allows the
-     * following inner loop to reduce the
-     * input one digit at a time
-     */
-    mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);
-
-    /* a = a + mu * m * b**i */
-    {
-      register int iy;
-      register mp_digit *tmpn, *tmpx, u;
-      register mp_word r;
-
-      /* alias for digits of the modulus */
-      tmpn = n->dp;
-
-      /* alias for the digits of x [the input] */
-      tmpx = x->dp + ix;
-
-      /* set the carry to zero */
-      u = 0;
-
-      /* Multiply and add in place */
-      for (iy = 0; iy < n->used; iy++) {
-        /* compute product and sum */
-        r       = ((mp_word)mu) * ((mp_word)*tmpn++) +
-                  ((mp_word) u) + ((mp_word) * tmpx);
-
-        /* get carry */
-        u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
-
-        /* fix digit */
-        *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
-      }
-      /* At this point the ix'th digit of x should be zero */
-
-
-      /* propagate carries upwards as required*/
-      while (u) {
-        *tmpx   += u;
-        u        = *tmpx >> DIGIT_BIT;
-        *tmpx++ &= MP_MASK;
-      }
-    }
-  }
-
-  /* at this point the n.used'th least
-   * significant digits of x are all zero
-   * which means we can shift x to the
-   * right by n.used digits and the
-   * residue is unchanged.
-   */
-
-  /* x = x/b**n.used */
-  mp_clamp(x);
-  mp_rshd (x, n->used);
-
-  /* if x >= n then x = x - n */
-  if (mp_cmp_mag (x, n) != MP_LT) {
-    return s_mp_sub (x, n, x);
-  }
-
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_montgomery_reduce.c */
-
-/* Start: bn_mp_montgomery_setup.c */
-#include <tommath.h>
-#ifdef BN_MP_MONTGOMERY_SETUP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* setups the montgomery reduction stuff */
-int
-mp_montgomery_setup (mp_int * n, mp_digit * rho)
-{
-  mp_digit x, b;
-
-/* fast inversion mod 2**k
- *
- * Based on the fact that
- *
- * XA = 1 (mod 2**n)  =>  (X(2-XA)) A = 1 (mod 2**2n)
- *                    =>  2*X*A - X*X*A*A = 1
- *                    =>  2*(1) - (1)     = 1
- */
-  b = n->dp[0];
-
-  if ((b & 1) == 0) {
-    return MP_VAL;
-  }
-
-  x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
-  x *= 2 - b * x;               /* here x*a==1 mod 2**8 */
-#if !defined(MP_8BIT)
-  x *= 2 - b * x;               /* here x*a==1 mod 2**16 */
-#endif
-#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
-  x *= 2 - b * x;               /* here x*a==1 mod 2**32 */
-#endif
-#ifdef MP_64BIT
-  x *= 2 - b * x;               /* here x*a==1 mod 2**64 */
-#endif
-
-  /* rho = -1/m mod b */
-  *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
-
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_montgomery_setup.c */
-
-/* Start: bn_mp_mul.c */
-#include <tommath.h>
-#ifdef BN_MP_MUL_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* high level multiplication (handles sign) */
-int mp_mul (mp_int * a, mp_int * b, mp_int * c)
-{
-  int     res, neg;
-  neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
-
-  /* use Toom-Cook? */
-#ifdef BN_MP_TOOM_MUL_C
-  if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) {
-    res = mp_toom_mul(a, b, c);
-  } else
-#endif
-#ifdef BN_MP_KARATSUBA_MUL_C
-  /* use Karatsuba? */
-  if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
-    res = mp_karatsuba_mul (a, b, c);
-  } else
-#endif
-  {
-    /* can we use the fast multiplier?
-     *
-     * The fast multiplier can be used if the output will
-     * have less than MP_WARRAY digits and the number of
-     * digits won't affect carry propagation
-     */
-    int     digs = a->used + b->used + 1;
-
-#ifdef BN_FAST_S_MP_MUL_DIGS_C
-    if ((digs < MP_WARRAY) &&
-        MIN(a->used, b->used) <=
-        (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
-      res = fast_s_mp_mul_digs (a, b, c, digs);
-    } else
-#endif
-#ifdef BN_S_MP_MUL_DIGS_C
-      res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
-#else
-      res = MP_VAL;
-#endif
-
-  }
-  c->sign = (c->used > 0) ? neg : MP_ZPOS;
-  return res;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_mul.c */
-
-/* Start: bn_mp_mul_2.c */
-#include <tommath.h>
-#ifdef BN_MP_MUL_2_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* b = a*2 */
-int mp_mul_2(mp_int * a, mp_int * b)
-{
-  int     x, res, oldused;
-
-  /* grow to accomodate result */
-  if (b->alloc < a->used + 1) {
-    if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  oldused = b->used;
-  b->used = a->used;
-
-  {
-    register mp_digit r, rr, *tmpa, *tmpb;
-
-    /* alias for source */
-    tmpa = a->dp;
-
-    /* alias for dest */
-    tmpb = b->dp;
-
-    /* carry */
-    r = 0;
-    for (x = 0; x < a->used; x++) {
-
-      /* get what will be the *next* carry bit from the
-       * MSB of the current digit
-       */
-      rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1));
-
-      /* now shift up this digit, add in the carry [from the previous] */
-      *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK;
-
-      /* copy the carry that would be from the source
-       * digit into the next iteration
-       */
-      r = rr;
-    }
-
-    /* new leading digit? */
-    if (r != 0) {
-      /* add a MSB which is always 1 at this point */
-      *tmpb = 1;
-      ++(b->used);
-    }
-
-    /* now zero any excess digits on the destination
-     * that we didn't write to
-     */
-    tmpb = b->dp + b->used;
-    for (x = b->used; x < oldused; x++) {
-      *tmpb++ = 0;
-    }
-  }
-  b->sign = a->sign;
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_mul_2.c */
-
-/* Start: bn_mp_mul_2d.c */
-#include <tommath.h>
-#ifdef BN_MP_MUL_2D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* shift left by a certain bit count */
-int mp_mul_2d (mp_int * a, int b, mp_int * c)
-{
-  mp_digit d;
-  int      res;
-
-  /* copy */
-  if (a != c) {
-     if ((res = mp_copy (a, c)) != MP_OKAY) {
-       return res;
-     }
-  }
-
-  if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) {
-     if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
-       return res;
-     }
-  }
-
-  /* shift by as many digits in the bit count */
-  if (b >= (int)DIGIT_BIT) {
-    if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  /* shift any bit count < DIGIT_BIT */
-  d = (mp_digit) (b % DIGIT_BIT);
-  if (d != 0) {
-    register mp_digit *tmpc, shift, mask, r, rr;
-    register int x;
-
-    /* bitmask for carries */
-    mask = (((mp_digit)1) << d) - 1;
-
-    /* shift for msbs */
-    shift = DIGIT_BIT - d;
-
-    /* alias */
-    tmpc = c->dp;
-
-    /* carry */
-    r    = 0;
-    for (x = 0; x < c->used; x++) {
-      /* get the higher bits of the current word */
-      rr = (*tmpc >> shift) & mask;
-
-      /* shift the current word and OR in the carry */
-      *tmpc = ((*tmpc << d) | r) & MP_MASK;
-      ++tmpc;
-
-      /* set the carry to the carry bits of the current word */
-      r = rr;
-    }
-
-    /* set final carry */
-    if (r != 0) {
-       c->dp[(c->used)++] = r;
-    }
-  }
-  mp_clamp (c);
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_mul_2d.c */
-
-/* Start: bn_mp_mul_d.c */
-#include <tommath.h>
-#ifdef BN_MP_MUL_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* multiply by a digit */
-int
-mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
-{
-  mp_digit u, *tmpa, *tmpc;
-  mp_word  r;
-  int      ix, res, olduse;
-
-  /* make sure c is big enough to hold a*b */
-  if (c->alloc < a->used + 1) {
-    if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  /* get the original destinations used count */
-  olduse = c->used;
-
-  /* set the sign */
-  c->sign = a->sign;
-
-  /* alias for a->dp [source] */
-  tmpa = a->dp;
-
-  /* alias for c->dp [dest] */
-  tmpc = c->dp;
-
-  /* zero carry */
-  u = 0;
-
-  /* compute columns */
-  for (ix = 0; ix < a->used; ix++) {
-    /* compute product and carry sum for this term */
-    r       = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
-
-    /* mask off higher bits to get a single digit */
-    *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
-
-    /* send carry into next iteration */
-    u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
-  }
-
-  /* store final carry [if any] and increment ix offset  */
-  *tmpc++ = u;
-  ++ix;
-
-  /* now zero digits above the top */
-  while (ix++ < olduse) {
-     *tmpc++ = 0;
-  }
-
-  /* set used count */
-  c->used = a->used + 1;
-  mp_clamp(c);
-
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_mul_d.c */
-
-/* Start: bn_mp_mulmod.c */
-#include <tommath.h>
-#ifdef BN_MP_MULMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* d = a * b (mod c) */
-int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-{
-  int     res;
-  mp_int  t;
-
-  if ((res = mp_init (&t)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_mul (a, b, &t)) != MP_OKAY) {
-    mp_clear (&t);
-    return res;
-  }
-  res = mp_mod (&t, c, d);
-  mp_clear (&t);
-  return res;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_mulmod.c */
-
-/* Start: bn_mp_n_root.c */
-#include <tommath.h>
-#ifdef BN_MP_N_ROOT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* find the n'th root of an integer
- *
- * Result found such that (c)**b <= a and (c+1)**b > a
- *
- * This algorithm uses Newton's approximation
- * x[i+1] = x[i] - f(x[i])/f'(x[i])
- * which will find the root in log(N) time where
- * each step involves a fair bit.  This is not meant to
- * find huge roots [square and cube, etc].
- */
-int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
-{
-  mp_int  t1, t2, t3;
-  int     res, neg;
-
-  /* input must be positive if b is even */
-  if ((b & 1) == 0 && a->sign == MP_NEG) {
-    return MP_VAL;
-  }
-
-  if ((res = mp_init (&t1)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_init (&t2)) != MP_OKAY) {
-    goto LBL_T1;
-  }
-
-  if ((res = mp_init (&t3)) != MP_OKAY) {
-    goto LBL_T2;
-  }
-
-  /* if a is negative fudge the sign but keep track */
-  neg     = a->sign;
-  a->sign = MP_ZPOS;
-
-  /* t2 = 2 */
-  mp_set (&t2, 2);
-
-  do {
-    /* t1 = t2 */
-    if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
-      goto LBL_T3;
-    }
-
-    /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
-
-    /* t3 = t1**(b-1) */
-    if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) {
-      goto LBL_T3;
-    }
-
-    /* numerator */
-    /* t2 = t1**b */
-    if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {
-      goto LBL_T3;
-    }
-
-    /* t2 = t1**b - a */
-    if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {
-      goto LBL_T3;
-    }
-
-    /* denominator */
-    /* t3 = t1**(b-1) * b  */
-    if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {
-      goto LBL_T3;
-    }
-
-    /* t3 = (t1**b - a)/(b * t1**(b-1)) */
-    if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {
-      goto LBL_T3;
-    }
-
-    if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
-      goto LBL_T3;
-    }
-  }  while (mp_cmp (&t1, &t2) != MP_EQ);
-
-  /* result can be off by a few so check */
-  for (;;) {
-    if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) {
-      goto LBL_T3;
-    }
-
-    if (mp_cmp (&t2, a) == MP_GT) {
-      if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
-         goto LBL_T3;
-      }
-    } else {
-      break;
-    }
-  }
-
-  /* reset the sign of a first */
-  a->sign = neg;
-
-  /* set the result */
-  mp_exch (&t1, c);
-
-  /* set the sign of the result */
-  c->sign = neg;
-
-  res = MP_OKAY;
-
-LBL_T3:mp_clear (&t3);
-LBL_T2:mp_clear (&t2);
-LBL_T1:mp_clear (&t1);
-  return res;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_n_root.c */
-
-/* Start: bn_mp_neg.c */
-#include <tommath.h>
-#ifdef BN_MP_NEG_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* b = -a */
-int mp_neg (mp_int * a, mp_int * b)
-{
-  int     res;
-  if (a != b) {
-     if ((res = mp_copy (a, b)) != MP_OKAY) {
-        return res;
-     }
-  }
-
-  if (mp_iszero(b) != MP_YES) {
-     b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS;
-  } else {
-     b->sign = MP_ZPOS;
-  }
-
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_neg.c */
-
-/* Start: bn_mp_or.c */
-#include <tommath.h>
-#ifdef BN_MP_OR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* OR two ints together */
-int mp_or (mp_int * a, mp_int * b, mp_int * c)
-{
-  int     res, ix, px;
-  mp_int  t, *x;
-
-  if (a->used > b->used) {
-    if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
-      return res;
-    }
-    px = b->used;
-    x = b;
-  } else {
-    if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
-      return res;
-    }
-    px = a->used;
-    x = a;
-  }
-
-  for (ix = 0; ix < px; ix++) {
-    t.dp[ix] |= x->dp[ix];
-  }
-  mp_clamp (&t);
-  mp_exch (c, &t);
-  mp_clear (&t);
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_or.c */
-
-/* Start: bn_mp_prime_fermat.c */
-#include <tommath.h>
-#ifdef BN_MP_PRIME_FERMAT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* performs one Fermat test.
- *
- * If "a" were prime then b**a == b (mod a) since the order of
- * the multiplicative sub-group would be phi(a) = a-1.  That means
- * it would be the same as b**(a mod (a-1)) == b**1 == b (mod a).
- *
- * Sets result to 1 if the congruence holds, or zero otherwise.
- */
-int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
-{
-  mp_int  t;
-  int     err;
-
-  /* default to composite  */
-  *result = MP_NO;
-
-  /* ensure b > 1 */
-  if (mp_cmp_d(b, 1) != MP_GT) {
-     return MP_VAL;
-  }
-
-  /* init t */
-  if ((err = mp_init (&t)) != MP_OKAY) {
-    return err;
-  }
-
-  /* compute t = b**a mod a */
-  if ((err = mp_exptmod (b, a, a, &t)) != MP_OKAY) {
-    goto LBL_T;
-  }
-
-  /* is it equal to b? */
-  if (mp_cmp (&t, b) == MP_EQ) {
-    *result = MP_YES;
-  }
-
-  err = MP_OKAY;
-LBL_T:mp_clear (&t);
-  return err;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_prime_fermat.c */
-
-/* Start: bn_mp_prime_is_divisible.c */
-#include <tommath.h>
-#ifdef BN_MP_PRIME_IS_DIVISIBLE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* determines if an integers is divisible by one
- * of the first PRIME_SIZE primes or not
- *
- * sets result to 0 if not, 1 if yes
- */
-int mp_prime_is_divisible (mp_int * a, int *result)
-{
-  int     err, ix;
-  mp_digit res;
-
-  /* default to not */
-  *result = MP_NO;
-
-  for (ix = 0; ix < PRIME_SIZE; ix++) {
-    /* what is a mod LBL_prime_tab[ix] */
-    if ((err = mp_mod_d (a, ltm_prime_tab[ix], &res)) != MP_OKAY) {
-      return err;
-    }
-
-    /* is the residue zero? */
-    if (res == 0) {
-      *result = MP_YES;
-      return MP_OKAY;
-    }
-  }
-
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_prime_is_divisible.c */
-
-/* Start: bn_mp_prime_is_prime.c */
-#include <tommath.h>
-#ifdef BN_MP_PRIME_IS_PRIME_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* performs a variable number of rounds of Miller-Rabin
- *
- * Probability of error after t rounds is no more than
-
- *
- * Sets result to 1 if probably prime, 0 otherwise
- */
-int mp_prime_is_prime (mp_int * a, int t, int *result)
-{
-  mp_int  b;
-  int     ix, err, res;
-
-  /* default to no */
-  *result = MP_NO;
-
-  /* valid value of t? */
-  if (t <= 0 || t > PRIME_SIZE) {
-    return MP_VAL;
-  }
-
-  /* is the input equal to one of the primes in the table? */
-  for (ix = 0; ix < PRIME_SIZE; ix++) {
-      if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
-         *result = 1;
-         return MP_OKAY;
-      }
-  }
-
-  /* first perform trial division */
-  if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
-    return err;
-  }
-
-  /* return if it was trivially divisible */
-  if (res == MP_YES) {
-    return MP_OKAY;
-  }
-
-  /* now perform the miller-rabin rounds */
-  if ((err = mp_init (&b)) != MP_OKAY) {
-    return err;
-  }
-
-  for (ix = 0; ix < t; ix++) {
-    /* set the prime */
-    mp_set (&b, ltm_prime_tab[ix]);
-
-    if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
-      goto LBL_B;
-    }
-
-    if (res == MP_NO) {
-      goto LBL_B;
-    }
-  }
-
-  /* passed the test */
-  *result = MP_YES;
-LBL_B:mp_clear (&b);
-  return err;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_prime_is_prime.c */
-
-/* Start: bn_mp_prime_miller_rabin.c */
-#include <tommath.h>
-#ifdef BN_MP_PRIME_MILLER_RABIN_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* Miller-Rabin test of "a" to the base of "b" as described in
- * HAC pp. 139 Algorithm 4.24
- *
- * Sets result to 0 if definitely composite or 1 if probably prime.
- * Randomly the chance of error is no more than 1/4 and often
- * very much lower.
- */
-int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
-{
-  mp_int  n1, y, r;
-  int     s, j, err;
-
-  /* default */
-  *result = MP_NO;
-
-  /* ensure b > 1 */
-  if (mp_cmp_d(b, 1) != MP_GT) {
-     return MP_VAL;
-  }
-
-  /* get n1 = a - 1 */
-  if ((err = mp_init_copy (&n1, a)) != MP_OKAY) {
-    return err;
-  }
-  if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) {
-    goto LBL_N1;
-  }
-
-  /* set 2**s * r = n1 */
-  if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
-    goto LBL_N1;
-  }
-
-  /* count the number of least significant bits
-   * which are zero
-   */
-  s = mp_cnt_lsb(&r);
-
-  /* now divide n - 1 by 2**s */
-  if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) {
-    goto LBL_R;
-  }
-
-  /* compute y = b**r mod a */
-  if ((err = mp_init (&y)) != MP_OKAY) {
-    goto LBL_R;
-  }
-  if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
-    goto LBL_Y;
-  }
-
-  /* if y != 1 and y != n1 do */
-  if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) {
-    j = 1;
-    /* while j <= s-1 and y != n1 */
-    while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) {
-      if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
-         goto LBL_Y;
-      }
-
-      /* if y == 1 then composite */
-      if (mp_cmp_d (&y, 1) == MP_EQ) {
-         goto LBL_Y;
-      }
-
-      ++j;
-    }
-
-    /* if y != n1 then composite */
-    if (mp_cmp (&y, &n1) != MP_EQ) {
-      goto LBL_Y;
-    }
-  }
-
-  /* probably prime now */
-  *result = MP_YES;
-LBL_Y:mp_clear (&y);
-LBL_R:mp_clear (&r);
-LBL_N1:mp_clear (&n1);
-  return err;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_prime_miller_rabin.c */
-
-/* Start: bn_mp_prime_next_prime.c */
-#include <tommath.h>
-#ifdef BN_MP_PRIME_NEXT_PRIME_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* finds the next prime after the number "a" using "t" trials
- * of Miller-Rabin.
- *
- * bbs_style = 1 means the prime must be congruent to 3 mod 4
- */
-int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
-{
-   int      err, res, x, y;
-   mp_digit res_tab[PRIME_SIZE], step, kstep;
-   mp_int   b;
-
-   /* ensure t is valid */
-   if (t <= 0 || t > PRIME_SIZE) {
-      return MP_VAL;
-   }
-
-   /* force positive */
-   a->sign = MP_ZPOS;
-
-   /* simple algo if a is less than the largest prime in the table */
-   if (mp_cmp_d(a, ltm_prime_tab[PRIME_SIZE-1]) == MP_LT) {
-      /* find which prime it is bigger than */
-      for (x = PRIME_SIZE - 2; x >= 0; x--) {
-          if (mp_cmp_d(a, ltm_prime_tab[x]) != MP_LT) {
-             if (bbs_style == 1) {
-                /* ok we found a prime smaller or
-                 * equal [so the next is larger]
-                 *
-                 * however, the prime must be
-                 * congruent to 3 mod 4
-                 */
-                if ((ltm_prime_tab[x + 1] & 3) != 3) {
-                   /* scan upwards for a prime congruent to 3 mod 4 */
-                   for (y = x + 1; y < PRIME_SIZE; y++) {
-                       if ((ltm_prime_tab[y] & 3) == 3) {
-                          mp_set(a, ltm_prime_tab[y]);
-                          return MP_OKAY;
-                       }
-                   }
-                }
-             } else {
-                mp_set(a, ltm_prime_tab[x + 1]);
-                return MP_OKAY;
-             }
-          }
-      }
-      /* at this point a maybe 1 */
-      if (mp_cmp_d(a, 1) == MP_EQ) {
-         mp_set(a, 2);
-         return MP_OKAY;
-      }
-      /* fall through to the sieve */
-   }
-
-   /* generate a prime congruent to 3 mod 4 or 1/3 mod 4? */
-   if (bbs_style == 1) {
-      kstep   = 4;
-   } else {
-      kstep   = 2;
-   }
-
-   /* at this point we will use a combination of a sieve and Miller-Rabin */
-
-   if (bbs_style == 1) {
-      /* if a mod 4 != 3 subtract the correct value to make it so */
-      if ((a->dp[0] & 3) != 3) {
-         if ((err = mp_sub_d(a, (a->dp[0] & 3) + 1, a)) != MP_OKAY) { return err; };
-      }
-   } else {
-      if (mp_iseven(a) == 1) {
-         /* force odd */
-         if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) {
-            return err;
-         }
-      }
-   }
-
-   /* generate the restable */
-   for (x = 1; x < PRIME_SIZE; x++) {
-      if ((err = mp_mod_d(a, ltm_prime_tab[x], res_tab + x)) != MP_OKAY) {
-         return err;
-      }
-   }
-
-   /* init temp used for Miller-Rabin Testing */
-   if ((err = mp_init(&b)) != MP_OKAY) {
-      return err;
-   }
-
-   for (;;) {
-      /* skip to the next non-trivially divisible candidate */
-      step = 0;
-      do {
-         /* y == 1 if any residue was zero [e.g. cannot be prime] */
-         y     =  0;
-
-         /* increase step to next candidate */
-         step += kstep;
-
-         /* compute the new residue without using division */
-         for (x = 1; x < PRIME_SIZE; x++) {
-             /* add the step to each residue */
-             res_tab[x] += kstep;
-
-             /* subtract the modulus [instead of using division] */
-             if (res_tab[x] >= ltm_prime_tab[x]) {
-                res_tab[x]  -= ltm_prime_tab[x];
-             }
-
-             /* set flag if zero */
-             if (res_tab[x] == 0) {
-                y = 1;
-             }
-         }
-      } while (y == 1 && step < ((((mp_digit)1)<<DIGIT_BIT) - kstep));
-
-      /* add the step */
-      if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
-         goto LBL_ERR;
-      }
-
-      /* if didn't pass sieve and step == MAX then skip test */
-      if (y == 1 && step >= ((((mp_digit)1)<<DIGIT_BIT) - kstep)) {
-         continue;
-      }
-
-      /* is this prime? */
-      for (x = 0; x < t; x++) {
-          mp_set(&b, ltm_prime_tab[x]);
-          if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
-             goto LBL_ERR;
-          }
-          if (res == MP_NO) {
-             break;
-          }
-      }
-
-      if (res == MP_YES) {
-         break;
-      }
-   }
-
-   err = MP_OKAY;
-LBL_ERR:
-   mp_clear(&b);
-   return err;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_prime_next_prime.c */
-
-/* Start: bn_mp_prime_rabin_miller_trials.c */
-#include <tommath.h>
-#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-
-static const struct {
-   int k, t;
-} sizes[] = {
-{   128,    28 },
-{   256,    16 },
-{   384,    10 },
-{   512,     7 },
-{   640,     6 },
-{   768,     5 },
-{   896,     4 },
-{  1024,     4 }
-};
-
-/* returns # of RM trials required for a given bit size */
-int mp_prime_rabin_miller_trials(int size)
-{
-   int x;
-
-   for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) {
-       if (sizes[x].k == size) {
-          return sizes[x].t;
-       } else if (sizes[x].k > size) {
-          return (x == 0) ? sizes[0].t : sizes[x - 1].t;
-       }
-   }
-   return sizes[x-1].t + 1;
-}
-
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_prime_rabin_miller_trials.c */
-
-/* Start: bn_mp_prime_random_ex.c */
-#include <tommath.h>
-#ifdef BN_MP_PRIME_RANDOM_EX_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* makes a truly random prime of a given size (bits),
- *
- * Flags are as follows:
- *
- *   LTM_PRIME_BBS      - make prime congruent to 3 mod 4
- *   LTM_PRIME_SAFE     - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
- *   LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero
- *   LTM_PRIME_2MSB_ON  - make the 2nd highest bit one
- *
- * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
- * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
- * so it can be NULL
- *
- */
-
-/* This is possibly the mother of all prime generation functions, muahahahahaha! */
-int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat)
-{
-   unsigned char *tmp, maskAND, maskOR_msb, maskOR_lsb;
-   int res, err, bsize, maskOR_msb_offset;
-
-   /* sanity check the input */
-   if (size <= 1 || t <= 0) {
-      return MP_VAL;
-   }
-
-   /* LTM_PRIME_SAFE implies LTM_PRIME_BBS */
-   if (flags & LTM_PRIME_SAFE) {
-      flags |= LTM_PRIME_BBS;
-   }
-
-   /* calc the byte size */
-   bsize = (size>>3) + ((size&7)?1:0);
-
-   /* we need a buffer of bsize bytes */
-   tmp = OPT_CAST(unsigned char) XMALLOC(bsize);
-   if (tmp == NULL) {
-      return MP_MEM;
-   }
-
-   /* calc the maskAND value for the MSbyte*/
-   maskAND = ((size&7) == 0) ? 0xFF : (0xFF >> (8 - (size & 7)));
-
-   /* calc the maskOR_msb */
-   maskOR_msb        = 0;
-   maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0;
-   if (flags & LTM_PRIME_2MSB_ON) {
-      maskOR_msb       |= 0x80 >> ((9 - size) & 7);
-   }
-
-   /* get the maskOR_lsb */
-   maskOR_lsb         = 1;
-   if (flags & LTM_PRIME_BBS) {
-      maskOR_lsb     |= 3;
-   }
-
-   do {
-      /* read the bytes */
-      if (cb(tmp, bsize, dat) != bsize) {
-         err = MP_VAL;
-         goto error;
-      }
-
-      /* work over the MSbyte */
-      tmp[0]    &= maskAND;
-      tmp[0]    |= 1 << ((size - 1) & 7);
-
-      /* mix in the maskORs */
-      tmp[maskOR_msb_offset]   |= maskOR_msb;
-      tmp[bsize-1]             |= maskOR_lsb;
-
-      /* read it in */
-      if ((err = mp_read_unsigned_bin(a, tmp, bsize)) != MP_OKAY)     { goto error; }
-
-      /* is it prime? */
-      if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY)           { goto error; }
-      if (res == MP_NO) {
-         continue;
-      }
-
-      if (flags & LTM_PRIME_SAFE) {
-         /* see if (a-1)/2 is prime */
-         if ((err = mp_sub_d(a, 1, a)) != MP_OKAY)                    { goto error; }
-         if ((err = mp_div_2(a, a)) != MP_OKAY)                       { goto error; }
-
-         /* is it prime? */
-         if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY)        { goto error; }
-      }
-   } while (res == MP_NO);
-
-   if (flags & LTM_PRIME_SAFE) {
-      /* restore a to the original value */
-      if ((err = mp_mul_2(a, a)) != MP_OKAY)                          { goto error; }
-      if ((err = mp_add_d(a, 1, a)) != MP_OKAY)                       { goto error; }
-   }
-
-   err = MP_OKAY;
-error:
-   XFREE(tmp);
-   return err;
-}
-
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_prime_random_ex.c */
-
-/* Start: bn_mp_radix_size.c */
-#include <tommath.h>
-#ifdef BN_MP_RADIX_SIZE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* returns size of ASCII reprensentation */
-int mp_radix_size (mp_int * a, int radix, int *size)
-{
-  int     res, digs;
-  mp_int  t;
-  mp_digit d;
-
-  *size = 0;
-
-  /* special case for binary */
-  if (radix == 2) {
-    *size = mp_count_bits (a) + (a->sign == MP_NEG ? 1 : 0) + 1;
-    return MP_OKAY;
-  }
-
-  /* make sure the radix is in range */
-  if (radix < 2 || radix > 64) {
-    return MP_VAL;
-  }
-
-  if (mp_iszero(a) == MP_YES) {
-    *size = 2;
-    return MP_OKAY;
-  }
-
-  /* digs is the digit count */
-  digs = 0;
-
-  /* if it's negative add one for the sign */
-  if (a->sign == MP_NEG) {
-    ++digs;
-  }
-
-  /* init a copy of the input */
-  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
-    return res;
-  }
-
-  /* force temp to positive */
-  t.sign = MP_ZPOS;
-
-  /* fetch out all of the digits */
-  while (mp_iszero (&t) == MP_NO) {
-    if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
-      mp_clear (&t);
-      return res;
-    }
-    ++digs;
-  }
-  mp_clear (&t);
-
-  /* return digs + 1, the 1 is for the NULL byte that would be required. */
-  *size = digs + 1;
-  return MP_OKAY;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_radix_size.c */
-
-/* Start: bn_mp_radix_smap.c */
-#include <tommath.h>
-#ifdef BN_MP_RADIX_SMAP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* chars used in radix conversions */
-const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_radix_smap.c */
-
-/* Start: bn_mp_rand.c */
-#include <tommath.h>
-#ifdef BN_MP_RAND_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* makes a pseudo-random int of a given size */
-int
-mp_rand (mp_int * a, int digits)
-{
-  int     res;
-  mp_digit d;
-
-  mp_zero (a);
-  if (digits <= 0) {
-    return MP_OKAY;
-  }
-
-  /* first place a random non-zero digit */
-  do {
-    d = ((mp_digit) abs (rand ())) & MP_MASK;
-  } while (d == 0);
-
-  if ((res = mp_add_d (a, d, a)) != MP_OKAY) {
-    return res;
-  }
-
-  while (--digits > 0) {
-    if ((res = mp_lshd (a, 1)) != MP_OKAY) {
-      return res;
-    }
-
-    if ((res = mp_add_d (a, ((mp_digit) abs (rand ())), a)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_rand.c */
-
-/* Start: bn_mp_read_radix.c */
-#include <tommath.h>
-#ifdef BN_MP_READ_RADIX_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* read a string [ASCII] in a given radix */
-int mp_read_radix (mp_int * a, const char *str, int radix)
-{
-  int     y, res, neg;
-  char    ch;
-
-  /* zero the digit bignum */
-  mp_zero(a);
-
-  /* make sure the radix is ok */
-  if (radix < 2 || radix > 64) {
-    return MP_VAL;
-  }
-
-  /* if the leading digit is a
-   * minus set the sign to negative.
-   */
-  if (*str == '-') {
-    ++str;
-    neg = MP_NEG;
-  } else {
-    neg = MP_ZPOS;
-  }
-
-  /* set the integer to the default of zero */
-  mp_zero (a);
-
-  /* process each digit of the string */
-  while (*str) {
-    /* if the radix < 36 the conversion is case insensitive
-     * this allows numbers like 1AB and 1ab to represent the same  value
-     * [e.g. in hex]
-     */
-    ch = (char) ((radix < 36) ? toupper ((int)*str) : *str);
-    for (y = 0; y < 64; y++) {
-      if (ch == mp_s_rmap[y]) {
-         break;
-      }
-    }
-
-    /* if the char was found in the map
-     * and is less than the given radix add it
-     * to the number, otherwise exit the loop.
-     */
-    if (y < radix) {
-      if ((res = mp_mul_d (a, (mp_digit) radix, a)) != MP_OKAY) {
-         return res;
-      }
-      if ((res = mp_add_d (a, (mp_digit) y, a)) != MP_OKAY) {
-         return res;
-      }
-    } else {
-      break;
-    }
-    ++str;
-  }
-
-  /* set the sign only if a != 0 */
-  if (mp_iszero(a) != 1) {
-     a->sign = neg;
-  }
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_read_radix.c */
-
-/* Start: bn_mp_read_signed_bin.c */
-#include <tommath.h>
-#ifdef BN_MP_READ_SIGNED_BIN_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* read signed bin, big endian, first byte is 0==positive or 1==negative */
-int mp_read_signed_bin (mp_int * a, const unsigned char *b, int c)
-{
-  int     res;
-
-  /* read magnitude */
-  if ((res = mp_read_unsigned_bin (a, b + 1, c - 1)) != MP_OKAY) {
-    return res;
-  }
-
-  /* first byte is 0 for positive, non-zero for negative */
-  if (b[0] == 0) {
-     a->sign = MP_ZPOS;
-  } else {
-     a->sign = MP_NEG;
-  }
-
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_read_signed_bin.c */
-
-/* Start: bn_mp_read_unsigned_bin.c */
-#include <tommath.h>
-#ifdef BN_MP_READ_UNSIGNED_BIN_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* reads a unsigned char array, assumes the msb is stored first [big endian] */
-int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
-{
-  int     res;
-
-  /* make sure there are at least two digits */
-  if (a->alloc < 2) {
-     if ((res = mp_grow(a, 2)) != MP_OKAY) {
-        return res;
-     }
-  }
-
-  /* zero the int */
-  mp_zero (a);
-
-  /* read the bytes in */
-  while (c-- > 0) {
-    if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
-      return res;
-    }
-
-#ifndef MP_8BIT
-      a->dp[0] |= *b++;
-      a->used += 1;
-#else
-      a->dp[0] = (*b & MP_MASK);
-      a->dp[1] |= ((*b++ >> 7U) & 1);
-      a->used += 2;
-#endif
-  }
-  mp_clamp (a);
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_read_unsigned_bin.c */
-
-/* Start: bn_mp_reduce.c */
-#include <tommath.h>
-#ifdef BN_MP_REDUCE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* reduces x mod m, assumes 0 < x < m**2, mu is
- * precomputed via mp_reduce_setup.
- * From HAC pp.604 Algorithm 14.42
- */
-int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
-{
-  mp_int  q;
-  int     res, um = m->used;
-
-  /* q = x */
-  if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
-    return res;
-  }
-
-  /* q1 = x / b**(k-1)  */
-  mp_rshd (&q, um - 1);
-
-  /* according to HAC this optimization is ok */
-  if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
-    if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
-      goto CLEANUP;
-    }
-  } else {
-#ifdef BN_S_MP_MUL_HIGH_DIGS_C
-    if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
-      goto CLEANUP;
-    }
-#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
-    if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
-      goto CLEANUP;
-    }
-#else
-    {
-      res = MP_VAL;
-      goto CLEANUP;
-    }
-#endif
-  }
-
-  /* q3 = q2 / b**(k+1) */
-  mp_rshd (&q, um + 1);
-
-  /* x = x mod b**(k+1), quick (no division) */
-  if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
-    goto CLEANUP;
-  }
-
-  /* q = q * m mod b**(k+1), quick (no division) */
-  if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) {
-    goto CLEANUP;
-  }
-
-  /* x = x - q */
-  if ((res = mp_sub (x, &q, x)) != MP_OKAY) {
-    goto CLEANUP;
-  }
-
-  /* If x < 0, add b**(k+1) to it */
-  if (mp_cmp_d (x, 0) == MP_LT) {
-    mp_set (&q, 1);
-    if ((res = mp_lshd (&q, um + 1)) != MP_OKAY)
-      goto CLEANUP;
-    if ((res = mp_add (x, &q, x)) != MP_OKAY)
-      goto CLEANUP;
-  }
-
-  /* Back off if it's too big */
-  while (mp_cmp (x, m) != MP_LT) {
-    if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
-      goto CLEANUP;
-    }
-  }
-
-CLEANUP:
-  mp_clear (&q);
-
-  return res;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_reduce.c */
-
-/* Start: bn_mp_reduce_2k.c */
-#include <tommath.h>
-#ifdef BN_MP_REDUCE_2K_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* reduces a modulo n where n is of the form 2**p - d */
-int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
-{
-   mp_int q;
-   int    p, res;
-
-   if ((res = mp_init(&q)) != MP_OKAY) {
-      return res;
-   }
-
-   p = mp_count_bits(n);
-top:
-   /* q = a/2**p, a = a mod 2**p */
-   if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
-      goto ERR;
-   }
-
-   if (d != 1) {
-      /* q = q * d */
-      if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) {
-         goto ERR;
-      }
-   }
-
-   /* a = a + q */
-   if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
-      goto ERR;
-   }
-
-   if (mp_cmp_mag(a, n) != MP_LT) {
-      s_mp_sub(a, n, a);
-      goto top;
-   }
-
-ERR:
-   mp_clear(&q);
-   return res;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_reduce_2k.c */
-
-/* Start: bn_mp_reduce_2k_l.c */
-#include <tommath.h>
-#ifdef BN_MP_REDUCE_2K_L_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* reduces a modulo n where n is of the form 2**p - d
-   This differs from reduce_2k since "d" can be larger
-   than a single digit.
-*/
-int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
-{
-   mp_int q;
-   int    p, res;
-
-   if ((res = mp_init(&q)) != MP_OKAY) {
-      return res;
-   }
-
-   p = mp_count_bits(n);
-top:
-   /* q = a/2**p, a = a mod 2**p */
-   if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
-      goto ERR;
-   }
-
-   /* q = q * d */
-   if ((res = mp_mul(&q, d, &q)) != MP_OKAY) {
-      goto ERR;
-   }
-
-   /* a = a + q */
-   if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
-      goto ERR;
-   }
-
-   if (mp_cmp_mag(a, n) != MP_LT) {
-      s_mp_sub(a, n, a);
-      goto top;
-   }
-
-ERR:
-   mp_clear(&q);
-   return res;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_reduce_2k_l.c */
-
-/* Start: bn_mp_reduce_2k_setup.c */
-#include <tommath.h>
-#ifdef BN_MP_REDUCE_2K_SETUP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* determines the setup value */
-int mp_reduce_2k_setup(mp_int *a, mp_digit *d)
-{
-   int res, p;
-   mp_int tmp;
-
-   if ((res = mp_init(&tmp)) != MP_OKAY) {
-      return res;
-   }
-
-   p = mp_count_bits(a);
-   if ((res = mp_2expt(&tmp, p)) != MP_OKAY) {
-      mp_clear(&tmp);
-      return res;
-   }
-
-   if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) {
-      mp_clear(&tmp);
-      return res;
-   }
-
-   *d = tmp.dp[0];
-   mp_clear(&tmp);
-   return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_reduce_2k_setup.c */
-
-/* Start: bn_mp_reduce_2k_setup_l.c */
-#include <tommath.h>
-#ifdef BN_MP_REDUCE_2K_SETUP_L_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* determines the setup value */
-int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
-{
-   int    res;
-   mp_int tmp;
-
-   if ((res = mp_init(&tmp)) != MP_OKAY) {
-      return res;
-   }
-
-   if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
-      goto ERR;
-   }
-
-   if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) {
-      goto ERR;
-   }
-
-ERR:
-   mp_clear(&tmp);
-   return res;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_reduce_2k_setup_l.c */
-
-/* Start: bn_mp_reduce_is_2k.c */
-#include <tommath.h>
-#ifdef BN_MP_REDUCE_IS_2K_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* determines if mp_reduce_2k can be used */
-int mp_reduce_is_2k(mp_int *a)
-{
-   int ix, iy, iw;
-   mp_digit iz;
-
-   if (a->used == 0) {
-      return MP_NO;
-   } else if (a->used == 1) {
-      return MP_YES;
-   } else if (a->used > 1) {
-      iy = mp_count_bits(a);
-      iz = 1;
-      iw = 1;
-
-      /* Test every bit from the second digit up, must be 1 */
-      for (ix = DIGIT_BIT; ix < iy; ix++) {
-          if ((a->dp[iw] & iz) == 0) {
-             return MP_NO;
-          }
-          iz <<= 1;
-          if (iz > (mp_digit)MP_MASK) {
-             ++iw;
-             iz = 1;
-          }
-      }
-   }
-   return MP_YES;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_reduce_is_2k.c */
-
-/* Start: bn_mp_reduce_is_2k_l.c */
-#include <tommath.h>
-#ifdef BN_MP_REDUCE_IS_2K_L_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* determines if reduce_2k_l can be used */
-int mp_reduce_is_2k_l(mp_int *a)
-{
-   int ix, iy;
-
-   if (a->used == 0) {
-      return MP_NO;
-   } else if (a->used == 1) {
-      return MP_YES;
-   } else if (a->used > 1) {
-      /* if more than half of the digits are -1 we're sold */
-      for (iy = ix = 0; ix < a->used; ix++) {
-          if (a->dp[ix] == MP_MASK) {
-              ++iy;
-          }
-      }
-      return (iy >= (a->used/2)) ? MP_YES : MP_NO;
-
-   }
-   return MP_NO;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_reduce_is_2k_l.c */
-
-/* Start: bn_mp_reduce_setup.c */
-#include <tommath.h>
-#ifdef BN_MP_REDUCE_SETUP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* pre-calculate the value required for Barrett reduction
- * For a given modulus "b" it calulates the value required in "a"
- */
-int mp_reduce_setup (mp_int * a, mp_int * b)
-{
-  int     res;
-
-  if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
-    return res;
-  }
-  return mp_div (a, b, a, NULL);
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_reduce_setup.c */
-
-/* Start: bn_mp_rshd.c */
-#include <tommath.h>
-#ifdef BN_MP_RSHD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* shift right a certain amount of digits */
-void mp_rshd (mp_int * a, int b)
-{
-  int     x;
-
-  /* if b <= 0 then ignore it */
-  if (b <= 0) {
-    return;
-  }
-
-  /* if b > used then simply zero it and return */
-  if (a->used <= b) {
-    mp_zero (a);
-    return;
-  }
-
-  {
-    register mp_digit *bottom, *top;
-
-    /* shift the digits down */
-
-    /* bottom */
-    bottom = a->dp;
-
-    /* top [offset into digits] */
-    top = a->dp + b;
-
-    /* this is implemented as a sliding window where
-     * the window is b-digits long and digits from
-     * the top of the window are copied to the bottom
-     *
-     * e.g.
-
-     b-2 | b-1 | b0 | b1 | b2 | ... | bb |   ---->
-                 /\                   |      ---->
-                  \-------------------/      ---->
-     */
-    for (x = 0; x < (a->used - b); x++) {
-      *bottom++ = *top++;
-    }
-
-    /* zero the top digits */
-    for (; x < a->used; x++) {
-      *bottom++ = 0;
-    }
-  }
-
-  /* remove excess digits */
-  a->used -= b;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_rshd.c */
-
-/* Start: bn_mp_set.c */
-#include <tommath.h>
-#ifdef BN_MP_SET_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* set to a digit */
-void mp_set (mp_int * a, mp_digit b)
-{
-  mp_zero (a);
-  a->dp[0] = b & MP_MASK;
-  a->used  = (a->dp[0] != 0) ? 1 : 0;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_set.c */
-
-/* Start: bn_mp_set_int.c */
-#include <tommath.h>
-#ifdef BN_MP_SET_INT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* set a 32-bit const */
-int mp_set_int (mp_int * a, unsigned long b)
-{
-  int     x, res;
-
-  mp_zero (a);
-
-  /* set four bits at a time */
-  for (x = 0; x < 8; x++) {
-    /* shift the number up four bits */
-    if ((res = mp_mul_2d (a, 4, a)) != MP_OKAY) {
-      return res;
-    }
-
-    /* OR in the top four bits of the source */
-    a->dp[0] |= (b >> 28) & 15;
-
-    /* shift the source up to the next four bits */
-    b <<= 4;
-
-    /* ensure that digits are not clamped off */
-    a->used += 1;
-  }
-  mp_clamp (a);
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_set_int.c */
-
-/* Start: bn_mp_shrink.c */
-#include <tommath.h>
-#ifdef BN_MP_SHRINK_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* shrink a bignum */
-int mp_shrink (mp_int * a)
-{
-  mp_digit *tmp;
-  int used = 1;
-
-  if(a->used > 0)
-    used = a->used;
-
-  if (a->alloc != used) {
-    if ((tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * used)) == NULL) {
-      return MP_MEM;
-    }
-    a->dp    = tmp;
-    a->alloc = used;
-  }
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_shrink.c */
-
-/* Start: bn_mp_signed_bin_size.c */
-#include <tommath.h>
-#ifdef BN_MP_SIGNED_BIN_SIZE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* get the size for an signed equivalent */
-int mp_signed_bin_size (mp_int * a)
-{
-  return 1 + mp_unsigned_bin_size (a);
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_signed_bin_size.c */
-
-/* Start: bn_mp_sqr.c */
-#include <tommath.h>
-#ifdef BN_MP_SQR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* computes b = a*a */
-int
-mp_sqr (mp_int * a, mp_int * b)
-{
-  int     res;
-
-#ifdef BN_MP_TOOM_SQR_C
-  /* use Toom-Cook? */
-  if (a->used >= TOOM_SQR_CUTOFF) {
-    res = mp_toom_sqr(a, b);
-  /* Karatsuba? */
-  } else
-#endif
-#ifdef BN_MP_KARATSUBA_SQR_C
-if (a->used >= KARATSUBA_SQR_CUTOFF) {
-    res = mp_karatsuba_sqr (a, b);
-  } else
-#endif
-  {
-#ifdef BN_FAST_S_MP_SQR_C
-    /* can we use the fast comba multiplier? */
-    if ((a->used * 2 + 1) < MP_WARRAY &&
-         a->used <
-         (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
-      res = fast_s_mp_sqr (a, b);
-    } else
-#endif
-#ifdef BN_S_MP_SQR_C
-      res = s_mp_sqr (a, b);
-#else
-      res = MP_VAL;
-#endif
-  }
-  b->sign = MP_ZPOS;
-  return res;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_sqr.c */
-
-/* Start: bn_mp_sqrmod.c */
-#include <tommath.h>
-#ifdef BN_MP_SQRMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* c = a * a (mod b) */
-int
-mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
-{
-  int     res;
-  mp_int  t;
-
-  if ((res = mp_init (&t)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_sqr (a, &t)) != MP_OKAY) {
-    mp_clear (&t);
-    return res;
-  }
-  res = mp_mod (&t, b, c);
-  mp_clear (&t);
-  return res;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_sqrmod.c */
-
-/* Start: bn_mp_sqrt.c */
-#include <tommath.h>
-#ifdef BN_MP_SQRT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* this function is less generic than mp_n_root, simpler and faster */
-int mp_sqrt(mp_int *arg, mp_int *ret)
-{
-  int res;
-  mp_int t1,t2;
-
-  /* must be positive */
-  if (arg->sign == MP_NEG) {
-    return MP_VAL;
-  }
-
-  /* easy out */
-  if (mp_iszero(arg) == MP_YES) {
-    mp_zero(ret);
-    return MP_OKAY;
-  }
-
-  if ((res = mp_init_copy(&t1, arg)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_init(&t2)) != MP_OKAY) {
-    goto E2;
-  }
-
-  /* First approx. (not very bad for large arg) */
-  mp_rshd (&t1,t1.used/2);
-
-  /* t1 > 0  */
-  if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
-    goto E1;
-  }
-  if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
-    goto E1;
-  }
-  if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
-    goto E1;
-  }
-  /* And now t1 > sqrt(arg) */
-  do {
-    if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
-      goto E1;
-    }
-    if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
-      goto E1;
-    }
-    if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
-      goto E1;
-    }
-    /* t1 >= sqrt(arg) >= t2 at this point */
-  } while (mp_cmp_mag(&t1,&t2) == MP_GT);
-
-  mp_exch(&t1,ret);
-
-E1: mp_clear(&t2);
-E2: mp_clear(&t1);
-  return res;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_sqrt.c */
-
-/* Start: bn_mp_sub.c */
-#include <tommath.h>
-#ifdef BN_MP_SUB_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* high level subtraction (handles signs) */
-int
-mp_sub (mp_int * a, mp_int * b, mp_int * c)
-{
-  int     sa, sb, res;
-
-  sa = a->sign;
-  sb = b->sign;
-
-  if (sa != sb) {
-    /* subtract a negative from a positive, OR */
-    /* subtract a positive from a negative. */
-    /* In either case, ADD their magnitudes, */
-    /* and use the sign of the first number. */
-    c->sign = sa;
-    res = s_mp_add (a, b, c);
-  } else {
-    /* subtract a positive from a positive, OR */
-    /* subtract a negative from a negative. */
-    /* First, take the difference between their */
-    /* magnitudes, then... */
-    if (mp_cmp_mag (a, b) != MP_LT) {
-      /* Copy the sign from the first */
-      c->sign = sa;
-      /* The first has a larger or equal magnitude */
-      res = s_mp_sub (a, b, c);
-    } else {
-      /* The result has the *opposite* sign from */
-      /* the first number. */
-      c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
-      /* The second has a larger magnitude */
-      res = s_mp_sub (b, a, c);
-    }
-  }
-  return res;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_sub.c */
-
-/* Start: bn_mp_sub_d.c */
-#include <tommath.h>
-#ifdef BN_MP_SUB_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* single digit subtraction */
-int
-mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
-{
-  mp_digit *tmpa, *tmpc, mu;
-  int       res, ix, oldused;
-
-  /* grow c as required */
-  if (c->alloc < a->used + 1) {
-     if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
-        return res;
-     }
-  }
-
-  /* if a is negative just do an unsigned
-   * addition [with fudged signs]
-   */
-  if (a->sign == MP_NEG) {
-     a->sign = MP_ZPOS;
-     res     = mp_add_d(a, b, c);
-     a->sign = c->sign = MP_NEG;
-
-     /* clamp */
-     mp_clamp(c);
-
-     return res;
-  }
-
-  /* setup regs */
-  oldused = c->used;
-  tmpa    = a->dp;
-  tmpc    = c->dp;
-
-  /* if a <= b simply fix the single digit */
-  if ((a->used == 1 && a->dp[0] <= b) || a->used == 0) {
-     if (a->used == 1) {
-        *tmpc++ = b - *tmpa;
-     } else {
-        *tmpc++ = b;
-     }
-     ix      = 1;
-
-     /* negative/1digit */
-     c->sign = MP_NEG;
-     c->used = 1;
-  } else {
-     /* positive/size */
-     c->sign = MP_ZPOS;
-     c->used = a->used;
-
-     /* subtract first digit */
-     *tmpc    = *tmpa++ - b;
-     mu       = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
-     *tmpc++ &= MP_MASK;
-
-     /* handle rest of the digits */
-     for (ix = 1; ix < a->used; ix++) {
-        *tmpc    = *tmpa++ - mu;
-        mu       = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
-        *tmpc++ &= MP_MASK;
-     }
-  }
-
-  /* zero excess digits */
-  while (ix++ < oldused) {
-     *tmpc++ = 0;
-  }
-  mp_clamp(c);
-  return MP_OKAY;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_sub_d.c */
-
-/* Start: bn_mp_submod.c */
-#include <tommath.h>
-#ifdef BN_MP_SUBMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* d = a - b (mod c) */
-int
-mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-{
-  int     res;
-  mp_int  t;
-
-
-  if ((res = mp_init (&t)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_sub (a, b, &t)) != MP_OKAY) {
-    mp_clear (&t);
-    return res;
-  }
-  res = mp_mod (&t, c, d);
-  mp_clear (&t);
-  return res;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_submod.c */
-
-/* Start: bn_mp_to_signed_bin.c */
-#include <tommath.h>
-#ifdef BN_MP_TO_SIGNED_BIN_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* store in signed [big endian] format */
-int mp_to_signed_bin (mp_int * a, unsigned char *b)
-{
-  int     res;
-
-  if ((res = mp_to_unsigned_bin (a, b + 1)) != MP_OKAY) {
-    return res;
-  }
-  b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1);
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_to_signed_bin.c */
-
-/* Start: bn_mp_to_signed_bin_n.c */
-#include <tommath.h>
-#ifdef BN_MP_TO_SIGNED_BIN_N_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* store in signed [big endian] format */
-int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
-{
-   if (*outlen < (unsigned long)mp_signed_bin_size(a)) {
-      return MP_VAL;
-   }
-   *outlen = mp_signed_bin_size(a);
-   return mp_to_signed_bin(a, b);
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_to_signed_bin_n.c */
-
-/* Start: bn_mp_to_unsigned_bin.c */
-#include <tommath.h>
-#ifdef BN_MP_TO_UNSIGNED_BIN_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* store in unsigned [big endian] format */
-int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
-{
-  int     x, res;
-  mp_int  t;
-
-  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
-    return res;
-  }
-
-  x = 0;
-  while (mp_iszero (&t) == 0) {
-#ifndef MP_8BIT
-      b[x++] = (unsigned char) (t.dp[0] & 255);
-#else
-      b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
-#endif
-    if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
-      mp_clear (&t);
-      return res;
-    }
-  }
-  bn_reverse (b, x);
-  mp_clear (&t);
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_to_unsigned_bin.c */
-
-/* Start: bn_mp_to_unsigned_bin_n.c */
-#include <tommath.h>
-#ifdef BN_MP_TO_UNSIGNED_BIN_N_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* store in unsigned [big endian] format */
-int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
-{
-   if (*outlen < (unsigned long)mp_unsigned_bin_size(a)) {
-      return MP_VAL;
-   }
-   *outlen = mp_unsigned_bin_size(a);
-   return mp_to_unsigned_bin(a, b);
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_to_unsigned_bin_n.c */
-
-/* Start: bn_mp_toom_mul.c */
-#include <tommath.h>
-#ifdef BN_MP_TOOM_MUL_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* multiplication using the Toom-Cook 3-way algorithm
- *
- * Much more complicated than Karatsuba but has a lower
- * asymptotic running time of O(N**1.464).  This algorithm is
- * only particularly useful on VERY large inputs
- * (we're talking 1000s of digits here...).
-*/
-int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
-{
-    mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
-    int res, B;
-
-    /* init temps */
-    if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
-                             &a0, &a1, &a2, &b0, &b1,
-                             &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
-       return res;
-    }
-
-    /* B */
-    B = MIN(a->used, b->used) / 3;
-
-    /* a = a2 * B**2 + a1 * B + a0 */
-    if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    if ((res = mp_copy(a, &a1)) != MP_OKAY) {
-       goto ERR;
-    }
-    mp_rshd(&a1, B);
-    mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
-
-    if ((res = mp_copy(a, &a2)) != MP_OKAY) {
-       goto ERR;
-    }
-    mp_rshd(&a2, B*2);
-
-    /* b = b2 * B**2 + b1 * B + b0 */
-    if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    if ((res = mp_copy(b, &b1)) != MP_OKAY) {
-       goto ERR;
-    }
-    mp_rshd(&b1, B);
-    mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
-
-    if ((res = mp_copy(b, &b2)) != MP_OKAY) {
-       goto ERR;
-    }
-    mp_rshd(&b2, B*2);
-
-    /* w0 = a0*b0 */
-    if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    /* w4 = a2 * b2 */
-    if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
-    if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
-    if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
-       goto ERR;
-    }
-
-
-    /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
-    if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    /* now solve the matrix
-
-       0  0  0  0  1
-       1  2  4  8  16
-       1  1  1  1  1
-       16 8  4  2  1
-       1  0  0  0  0
-
-       using 12 subtractions, 4 shifts,
-              2 small divisions and 1 small multiplication
-     */
-
-     /* r1 - r4 */
-     if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3 - r0 */
-     if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1/2 */
-     if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3/2 */
-     if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r2 - r0 - r4 */
-     if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1 - r2 */
-     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3 - r2 */
-     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1 - 8r0 */
-     if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3 - 8r4 */
-     if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* 3r2 - r1 - r3 */
-     if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1 - r2 */
-     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3 - r2 */
-     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1/3 */
-     if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3/3 */
-     if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
-        goto ERR;
-     }
-
-     /* at this point shift W[n] by B*n */
-     if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
-        goto ERR;
-     }
-
-     if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
-        goto ERR;
-     }
-
-ERR:
-     mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
-                    &a0, &a1, &a2, &b0, &b1,
-                    &b2, &tmp1, &tmp2, NULL);
-     return res;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_toom_mul.c */
-
-/* Start: bn_mp_toom_sqr.c */
-#include <tommath.h>
-#ifdef BN_MP_TOOM_SQR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* squaring using Toom-Cook 3-way algorithm */
-int
-mp_toom_sqr(mp_int *a, mp_int *b)
-{
-    mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2;
-    int res, B;
-
-    /* init temps */
-    if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL)) != MP_OKAY) {
-       return res;
-    }
-
-    /* B */
-    B = a->used / 3;
-
-    /* a = a2 * B**2 + a1 * B + a0 */
-    if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    if ((res = mp_copy(a, &a1)) != MP_OKAY) {
-       goto ERR;
-    }
-    mp_rshd(&a1, B);
-    mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
-
-    if ((res = mp_copy(a, &a2)) != MP_OKAY) {
-       goto ERR;
-    }
-    mp_rshd(&a2, B*2);
-
-    /* w0 = a0*a0 */
-    if ((res = mp_sqr(&a0, &w0)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    /* w4 = a2 * a2 */
-    if ((res = mp_sqr(&a2, &w4)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    /* w1 = (a2 + 2(a1 + 2a0))**2 */
-    if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    if ((res = mp_sqr(&tmp1, &w1)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    /* w3 = (a0 + 2(a1 + 2a2))**2 */
-    if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    if ((res = mp_sqr(&tmp1, &w3)) != MP_OKAY) {
-       goto ERR;
-    }
-
-
-    /* w2 = (a2 + a1 + a0)**2 */
-    if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_sqr(&tmp1, &w2)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    /* now solve the matrix
-
-       0  0  0  0  1
-       1  2  4  8  16
-       1  1  1  1  1
-       16 8  4  2  1
-       1  0  0  0  0
-
-       using 12 subtractions, 4 shifts, 2 small divisions and 1 small multiplication.
-     */
-
-     /* r1 - r4 */
-     if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3 - r0 */
-     if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1/2 */
-     if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3/2 */
-     if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r2 - r0 - r4 */
-     if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1 - r2 */
-     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3 - r2 */
-     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1 - 8r0 */
-     if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3 - 8r4 */
-     if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* 3r2 - r1 - r3 */
-     if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1 - r2 */
-     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3 - r2 */
-     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1/3 */
-     if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3/3 */
-     if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
-        goto ERR;
-     }
-
-     /* at this point shift W[n] by B*n */
-     if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
-        goto ERR;
-     }
-
-     if ((res = mp_add(&w0, &w1, b)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_add(&tmp1, b, b)) != MP_OKAY) {
-        goto ERR;
-     }
-
-ERR:
-     mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL);
-     return res;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_toom_sqr.c */
-
-/* Start: bn_mp_toradix.c */
-#include <tommath.h>
-#ifdef BN_MP_TORADIX_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* stores a bignum as a ASCII string in a given radix (2..64) */
-int mp_toradix (mp_int * a, char *str, int radix)
-{
-  int     res, digs;
-  mp_int  t;
-  mp_digit d;
-  char   *_s = str;
-
-  /* check range of the radix */
-  if (radix < 2 || radix > 64) {
-    return MP_VAL;
-  }
-
-  /* quick out if its zero */
-  if (mp_iszero(a) == 1) {
-     *str++ = '0';
-     *str = '\0';
-     return MP_OKAY;
-  }
-
-  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
-    return res;
-  }
-
-  /* if it is negative output a - */
-  if (t.sign == MP_NEG) {
-    ++_s;
-    *str++ = '-';
-    t.sign = MP_ZPOS;
-  }
-
-  digs = 0;
-  while (mp_iszero (&t) == 0) {
-    if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
-      mp_clear (&t);
-      return res;
-    }
-    *str++ = mp_s_rmap[d];
-    ++digs;
-  }
-
-  /* reverse the digits of the string.  In this case _s points
-   * to the first digit [exluding the sign] of the number]
-   */
-  bn_reverse ((unsigned char *)_s, digs);
-
-  /* append a NULL so the string is properly terminated */
-  *str = '\0';
-
-  mp_clear (&t);
-  return MP_OKAY;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_toradix.c */
-
-/* Start: bn_mp_toradix_n.c */
-#include <tommath.h>
-#ifdef BN_MP_TORADIX_N_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* stores a bignum as a ASCII string in a given radix (2..64)
- *
- * Stores upto maxlen-1 chars and always a NULL byte
- */
-int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
-{
-  int     res, digs;
-  mp_int  t;
-  mp_digit d;
-  char   *_s = str;
-
-  /* check range of the maxlen, radix */
-  if (maxlen < 2 || radix < 2 || radix > 64) {
-    return MP_VAL;
-  }
-
-  /* quick out if its zero */
-  if (mp_iszero(a) == MP_YES) {
-     *str++ = '0';
-     *str = '\0';
-     return MP_OKAY;
-  }
-
-  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
-    return res;
-  }
-
-  /* if it is negative output a - */
-  if (t.sign == MP_NEG) {
-    /* we have to reverse our digits later... but not the - sign!! */
-    ++_s;
-
-    /* store the flag and mark the number as positive */
-    *str++ = '-';
-    t.sign = MP_ZPOS;
-
-    /* subtract a char */
-    --maxlen;
-  }
-
-  digs = 0;
-  while (mp_iszero (&t) == 0) {
-    if (--maxlen < 1) {
-       /* no more room */
-       break;
-    }
-    if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
-      mp_clear (&t);
-      return res;
-    }
-    *str++ = mp_s_rmap[d];
-    ++digs;
-  }
-
-  /* reverse the digits of the string.  In this case _s points
-   * to the first digit [exluding the sign] of the number
-   */
-  bn_reverse ((unsigned char *)_s, digs);
-
-  /* append a NULL so the string is properly terminated */
-  *str = '\0';
-
-  mp_clear (&t);
-  return MP_OKAY;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_toradix_n.c */
-
-/* Start: bn_mp_unsigned_bin_size.c */
-#include <tommath.h>
-#ifdef BN_MP_UNSIGNED_BIN_SIZE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* get the size for an unsigned equivalent */
-int mp_unsigned_bin_size (mp_int * a)
-{
-  int     size = mp_count_bits (a);
-  return (size / 8 + ((size & 7) != 0 ? 1 : 0));
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_unsigned_bin_size.c */
-
-/* Start: bn_mp_xor.c */
-#include <tommath.h>
-#ifdef BN_MP_XOR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* XOR two ints together */
-int
-mp_xor (mp_int * a, mp_int * b, mp_int * c)
-{
-  int     res, ix, px;
-  mp_int  t, *x;
-
-  if (a->used > b->used) {
-    if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
-      return res;
-    }
-    px = b->used;
-    x = b;
-  } else {
-    if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
-      return res;
-    }
-    px = a->used;
-    x = a;
-  }
-
-  for (ix = 0; ix < px; ix++) {
-     t.dp[ix] ^= x->dp[ix];
-  }
-  mp_clamp (&t);
-  mp_exch (c, &t);
-  mp_clear (&t);
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_xor.c */
-
-/* Start: bn_mp_zero.c */
-#include <tommath.h>
-#ifdef BN_MP_ZERO_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* set to zero */
-void mp_zero (mp_int * a)
-{
-  int       n;
-  mp_digit *tmp;
-
-  a->sign = MP_ZPOS;
-  a->used = 0;
-
-  tmp = a->dp;
-  for (n = 0; n < a->alloc; n++) {
-     *tmp++ = 0;
-  }
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_mp_zero.c */
-
-/* Start: bn_prime_tab.c */
-#include <tommath.h>
-#ifdef BN_PRIME_TAB_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-const mp_digit ltm_prime_tab[] = {
-  0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
-  0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
-  0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
-  0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,
-#ifndef MP_8BIT
-  0x0083,
-  0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
-  0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
-  0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
-  0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
-
-  0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
-  0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
-  0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
-  0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
-  0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
-  0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
-  0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
-  0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
-
-  0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
-  0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
-  0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
-  0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
-  0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
-  0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
-  0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
-  0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
-
-  0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
-  0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
-  0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
-  0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
-  0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
-  0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
-  0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
-  0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
-#endif
-};
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_prime_tab.c */
-
-/* Start: bn_reverse.c */
-#include <tommath.h>
-#ifdef BN_REVERSE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* reverse an array, used for radix code */
-void
-bn_reverse (unsigned char *s, int len)
-{
-  int     ix, iy;
-  unsigned char t;
-
-  ix = 0;
-  iy = len - 1;
-  while (ix < iy) {
-    t     = s[ix];
-    s[ix] = s[iy];
-    s[iy] = t;
-    ++ix;
-    --iy;
-  }
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_reverse.c */
-
-/* Start: bn_s_mp_add.c */
-#include <tommath.h>
-#ifdef BN_S_MP_ADD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* low level addition, based on HAC pp.594, Algorithm 14.7 */
-int
-s_mp_add (mp_int * a, mp_int * b, mp_int * c)
-{
-  mp_int *x;
-  int     olduse, res, min, max;
-
-  /* find sizes, we let |a| <= |b| which means we have to sort
-   * them.  "x" will point to the input with the most digits
-   */
-  if (a->used > b->used) {
-    min = b->used;
-    max = a->used;
-    x = a;
-  } else {
-    min = a->used;
-    max = b->used;
-    x = b;
-  }
-
-  /* init result */
-  if (c->alloc < max + 1) {
-    if ((res = mp_grow (c, max + 1)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  /* get old used digit count and set new one */
-  olduse = c->used;
-  c->used = max + 1;
-
-  {
-    register mp_digit u, *tmpa, *tmpb, *tmpc;
-    register int i;
-
-    /* alias for digit pointers */
-
-    /* first input */
-    tmpa = a->dp;
-
-    /* second input */
-    tmpb = b->dp;
-
-    /* destination */
-    tmpc = c->dp;
-
-    /* zero the carry */
-    u = 0;
-    for (i = 0; i < min; i++) {
-      /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
-      *tmpc = *tmpa++ + *tmpb++ + u;
-
-      /* U = carry bit of T[i] */
-      u = *tmpc >> ((mp_digit)DIGIT_BIT);
-
-      /* take away carry bit from T[i] */
-      *tmpc++ &= MP_MASK;
-    }
-
-    /* now copy higher words if any, that is in A+B
-     * if A or B has more digits add those in
-     */
-    if (min != max) {
-      for (; i < max; i++) {
-        /* T[i] = X[i] + U */
-        *tmpc = x->dp[i] + u;
-
-        /* U = carry bit of T[i] */
-        u = *tmpc >> ((mp_digit)DIGIT_BIT);
-
-        /* take away carry bit from T[i] */
-        *tmpc++ &= MP_MASK;
-      }
-    }
-
-    /* add carry */
-    *tmpc++ = u;
-
-    /* clear digits above oldused */
-    for (i = c->used; i < olduse; i++) {
-      *tmpc++ = 0;
-    }
-  }
-
-  mp_clamp (c);
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_s_mp_add.c */
-
-/* Start: bn_s_mp_exptmod.c */
-#include <tommath.h>
-#ifdef BN_S_MP_EXPTMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-#ifdef MP_LOW_MEM
-   #define TAB_SIZE 32
-#else
-   #define TAB_SIZE 256
-#endif
-
-int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
-{
-  mp_int  M[TAB_SIZE], res, mu;
-  mp_digit buf;
-  int     err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
-  int (*redux)(mp_int*,mp_int*,mp_int*);
-
-  /* find window size */
-  x = mp_count_bits (X);
-  if (x <= 7) {
-    winsize = 2;
-  } else if (x <= 36) {
-    winsize = 3;
-  } else if (x <= 140) {
-    winsize = 4;
-  } else if (x <= 450) {
-    winsize = 5;
-  } else if (x <= 1303) {
-    winsize = 6;
-  } else if (x <= 3529) {
-    winsize = 7;
-  } else {
-    winsize = 8;
-  }
-
-#ifdef MP_LOW_MEM
-    if (winsize > 5) {
-       winsize = 5;
-    }
-#endif
-
-  /* init M array */
-  /* init first cell */
-  if ((err = mp_init(&M[1])) != MP_OKAY) {
-     return err;
-  }
-
-  /* now init the second half of the array */
-  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
-    if ((err = mp_init(&M[x])) != MP_OKAY) {
-      for (y = 1<<(winsize-1); y < x; y++) {
-        mp_clear (&M[y]);
-      }
-      mp_clear(&M[1]);
-      return err;
-    }
-  }
-
-  /* create mu, used for Barrett reduction */
-  if ((err = mp_init (&mu)) != MP_OKAY) {
-    goto LBL_M;
-  }
-
-  if (redmode == 0) {
-     if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
-        goto LBL_MU;
-     }
-     redux = mp_reduce;
-  } else {
-     if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) {
-        goto LBL_MU;
-     }
-     redux = mp_reduce_2k_l;
-  }
-
-  /* create M table
-   *
-   * The M table contains powers of the base,
-   * e.g. M[x] = G**x mod P
-   *
-   * The first half of the table is not
-   * computed though accept for M[0] and M[1]
-   */
-  if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
-    goto LBL_MU;
-  }
-
-  /* compute the value at M[1<<(winsize-1)] by squaring
-   * M[1] (winsize-1) times
-   */
-  if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
-    goto LBL_MU;
-  }
-
-  for (x = 0; x < (winsize - 1); x++) {
-    /* square it */
-    if ((err = mp_sqr (&M[1 << (winsize - 1)],
-                       &M[1 << (winsize - 1)])) != MP_OKAY) {
-      goto LBL_MU;
-    }
-
-    /* reduce modulo P */
-    if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
-      goto LBL_MU;
-    }
-  }
-
-  /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
-   * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
-   */
-  for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
-    if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
-      goto LBL_MU;
-    }
-    if ((err = redux (&M[x], P, &mu)) != MP_OKAY) {
-      goto LBL_MU;
-    }
-  }
-
-  /* setup result */
-  if ((err = mp_init (&res)) != MP_OKAY) {
-    goto LBL_MU;
-  }
-  mp_set (&res, 1);
-
-  /* set initial mode and bit cnt */
-  mode   = 0;
-  bitcnt = 1;
-  buf    = 0;
-  digidx = X->used - 1;
-  bitcpy = 0;
-  bitbuf = 0;
-
-  for (;;) {
-    /* grab next digit as required */
-    if (--bitcnt == 0) {
-      /* if digidx == -1 we are out of digits */
-      if (digidx == -1) {
-        break;
-      }
-      /* read next digit and reset the bitcnt */
-      buf    = X->dp[digidx--];
-      bitcnt = (int) DIGIT_BIT;
-    }
-
-    /* grab the next msb from the exponent */
-    y     = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
-    buf <<= (mp_digit)1;
-
-    /* if the bit is zero and mode == 0 then we ignore it
-     * These represent the leading zero bits before the first 1 bit
-     * in the exponent.  Technically this opt is not required but it
-     * does lower the # of trivial squaring/reductions used
-     */
-    if (mode == 0 && y == 0) {
-      continue;
-    }
-
-    /* if the bit is zero and mode == 1 then we square */
-    if (mode == 1 && y == 0) {
-      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
-        goto LBL_RES;
-      }
-      if ((err = redux (&res, P, &mu)) != MP_OKAY) {
-        goto LBL_RES;
-      }
-      continue;
-    }
-
-    /* else we add it to the window */
-    bitbuf |= (y << (winsize - ++bitcpy));
-    mode    = 2;
-
-    if (bitcpy == winsize) {
-      /* ok window is filled so square as required and multiply  */
-      /* square first */
-      for (x = 0; x < winsize; x++) {
-        if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
-          goto LBL_RES;
-        }
-        if ((err = redux (&res, P, &mu)) != MP_OKAY) {
-          goto LBL_RES;
-        }
-      }
-
-      /* then multiply */
-      if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
-        goto LBL_RES;
-      }
-      if ((err = redux (&res, P, &mu)) != MP_OKAY) {
-        goto LBL_RES;
-      }
-
-      /* empty window and reset */
-      bitcpy = 0;
-      bitbuf = 0;
-      mode   = 1;
-    }
-  }
-
-  /* if bits remain then square/multiply */
-  if (mode == 2 && bitcpy > 0) {
-    /* square then multiply if the bit is set */
-    for (x = 0; x < bitcpy; x++) {
-      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
-        goto LBL_RES;
-      }
-      if ((err = redux (&res, P, &mu)) != MP_OKAY) {
-        goto LBL_RES;
-      }
-
-      bitbuf <<= 1;
-      if ((bitbuf & (1 << winsize)) != 0) {
-        /* then multiply */
-        if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
-          goto LBL_RES;
-        }
-        if ((err = redux (&res, P, &mu)) != MP_OKAY) {
-          goto LBL_RES;
-        }
-      }
-    }
-  }
-
-  mp_exch (&res, Y);
-  err = MP_OKAY;
-LBL_RES:mp_clear (&res);
-LBL_MU:mp_clear (&mu);
-LBL_M:
-  mp_clear(&M[1]);
-  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
-    mp_clear (&M[x]);
-  }
-  return err;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_s_mp_exptmod.c */
-
-/* Start: bn_s_mp_mul_digs.c */
-#include <tommath.h>
-#ifdef BN_S_MP_MUL_DIGS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* multiplies |a| * |b| and only computes upto digs digits of result
- * HAC pp. 595, Algorithm 14.12  Modified so you can control how
- * many digits of output are created.
- */
-int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
-{
-  mp_int  t;
-  int     res, pa, pb, ix, iy;
-  mp_digit u;
-  mp_word r;
-  mp_digit tmpx, *tmpt, *tmpy;
-
-  /* can we use the fast multiplier? */
-  if (((digs) < MP_WARRAY) &&
-      MIN (a->used, b->used) <
-          (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
-    return fast_s_mp_mul_digs (a, b, c, digs);
-  }
-
-  if ((res = mp_init_size (&t, digs)) != MP_OKAY) {
-    return res;
-  }
-  t.used = digs;
-
-  /* compute the digits of the product directly */
-  pa = a->used;
-  for (ix = 0; ix < pa; ix++) {
-    /* set the carry to zero */
-    u = 0;
-
-    /* limit ourselves to making digs digits of output */
-    pb = MIN (b->used, digs - ix);
-
-    /* setup some aliases */
-    /* copy of the digit from a used within the nested loop */
-    tmpx = a->dp[ix];
-
-    /* an alias for the destination shifted ix places */
-    tmpt = t.dp + ix;
-
-    /* an alias for the digits of b */
-    tmpy = b->dp;
-
-    /* compute the columns of the output and propagate the carry */
-    for (iy = 0; iy < pb; iy++) {
-      /* compute the column as a mp_word */
-      r       = ((mp_word)*tmpt) +
-                ((mp_word)tmpx) * ((mp_word)*tmpy++) +
-                ((mp_word) u);
-
-      /* the new column is the lower part of the result */
-      *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
-
-      /* get the carry word from the result */
-      u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
-    }
-    /* set carry if it is placed below digs */
-    if (ix + iy < digs) {
-      *tmpt = u;
-    }
-  }
-
-  mp_clamp (&t);
-  mp_exch (&t, c);
-
-  mp_clear (&t);
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_s_mp_mul_digs.c */
-
-/* Start: bn_s_mp_mul_high_digs.c */
-#include <tommath.h>
-#ifdef BN_S_MP_MUL_HIGH_DIGS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* multiplies |a| * |b| and does not compute the lower digs digits
- * [meant to get the higher part of the product]
- */
-int
-s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
-{
-  mp_int  t;
-  int     res, pa, pb, ix, iy;
-  mp_digit u;
-  mp_word r;
-  mp_digit tmpx, *tmpt, *tmpy;
-
-  /* can we use the fast multiplier? */
-#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
-  if (((a->used + b->used + 1) < MP_WARRAY)
-      && MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
-    return fast_s_mp_mul_high_digs (a, b, c, digs);
-  }
-#endif
-
-  if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
-    return res;
-  }
-  t.used = a->used + b->used + 1;
-
-  pa = a->used;
-  pb = b->used;
-  for (ix = 0; ix < pa; ix++) {
-    /* clear the carry */
-    u = 0;
-
-    /* left hand side of A[ix] * B[iy] */
-    tmpx = a->dp[ix];
-
-    /* alias to the address of where the digits will be stored */
-    tmpt = &(t.dp[digs]);
-
-    /* alias for where to read the right hand side from */
-    tmpy = b->dp + (digs - ix);
-
-    for (iy = digs - ix; iy < pb; iy++) {
-      /* calculate the double precision result */
-      r       = ((mp_word)*tmpt) +
-                ((mp_word)tmpx) * ((mp_word)*tmpy++) +
-                ((mp_word) u);
-
-      /* get the lower part */
-      *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
-
-      /* carry the carry */
-      u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
-    }
-    *tmpt = u;
-  }
-  mp_clamp (&t);
-  mp_exch (&t, c);
-  mp_clear (&t);
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_s_mp_mul_high_digs.c */
-
-/* Start: bn_s_mp_sqr.c */
-#include <tommath.h>
-#ifdef BN_S_MP_SQR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
-int s_mp_sqr (mp_int * a, mp_int * b)
-{
-  mp_int  t;
-  int     res, ix, iy, pa;
-  mp_word r;
-  mp_digit u, tmpx, *tmpt;
-
-  pa = a->used;
-  if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) {
-    return res;
-  }
-
-  /* default used is maximum possible size */
-  t.used = 2*pa + 1;
-
-  for (ix = 0; ix < pa; ix++) {
-    /* first calculate the digit at 2*ix */
-    /* calculate double precision result */
-    r = ((mp_word) t.dp[2*ix]) +
-        ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
-
-    /* store lower part in result */
-    t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
-
-    /* get the carry */
-    u           = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
-
-    /* left hand side of A[ix] * A[iy] */
-    tmpx        = a->dp[ix];
-
-    /* alias for where to store the results */
-    tmpt        = t.dp + (2*ix + 1);
-
-    for (iy = ix + 1; iy < pa; iy++) {
-      /* first calculate the product */
-      r       = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
-
-      /* now calculate the double precision result, note we use
-       * addition instead of *2 since it's easier to optimize
-       */
-      r       = ((mp_word) *tmpt) + r + r + ((mp_word) u);
-
-      /* store lower part */
-      *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
-
-      /* get carry */
-      u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
-    }
-    /* propagate upwards */
-    while (u != ((mp_digit) 0)) {
-      r       = ((mp_word) *tmpt) + ((mp_word) u);
-      *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
-      u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
-    }
-  }
-
-  mp_clamp (&t);
-  mp_exch (&t, b);
-  mp_clear (&t);
-  return MP_OKAY;
-}
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_s_mp_sqr.c */
-
-/* Start: bn_s_mp_sub.c */
-#include <tommath.h>
-#ifdef BN_S_MP_SUB_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
-int
-s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
-{
-  int     olduse, res, min, max;
-
-  /* find sizes */
-  min = b->used;
-  max = a->used;
-
-  /* init result */
-  if (c->alloc < max) {
-    if ((res = mp_grow (c, max)) != MP_OKAY) {
-      return res;
-    }
-  }
-  olduse = c->used;
-  c->used = max;
-
-  {
-    register mp_digit u, *tmpa, *tmpb, *tmpc;
-    register int i;
-
-    /* alias for digit pointers */
-    tmpa = a->dp;
-    tmpb = b->dp;
-    tmpc = c->dp;
-
-    /* set carry to zero */
-    u = 0;
-    for (i = 0; i < min; i++) {
-      /* T[i] = A[i] - B[i] - U */
-      *tmpc = *tmpa++ - *tmpb++ - u;
-
-      /* U = carry bit of T[i]
-       * Note this saves performing an AND operation since
-       * if a carry does occur it will propagate all the way to the
-       * MSB.  As a result a single shift is enough to get the carry
-       */
-      u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
-
-      /* Clear carry from T[i] */
-      *tmpc++ &= MP_MASK;
-    }
-
-    /* now copy higher words if any, e.g. if A has more digits than B  */
-    for (; i < max; i++) {
-      /* T[i] = A[i] - U */
-      *tmpc = *tmpa++ - u;
-
-      /* U = carry bit of T[i] */
-      u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
-
-      /* Clear carry from T[i] */
-      *tmpc++ &= MP_MASK;
-    }
-
-    /* clear digits above used (since we may not have grown result above) */
-    for (i = c->used; i < olduse; i++) {
-      *tmpc++ = 0;
-    }
-  }
-
-  mp_clamp (c);
-  return MP_OKAY;
-}
-
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bn_s_mp_sub.c */
-
-/* Start: bncore.c */
-#include <tommath.h>
-#ifdef BNCORE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
- */
-
-/* Known optimal configurations
-
- CPU                    /Compiler     /MUL CUTOFF/SQR CUTOFF
--------------------------------------------------------------
- Intel P4 Northwood     /GCC v3.4.1   /        88/       128/LTM 0.32 ;-)
- AMD Athlon64           /GCC v3.4.4   /        80/       120/LTM 0.35
-
-*/
-
-int     KARATSUBA_MUL_CUTOFF = 80,      /* Min. number of digits before Karatsuba multiplication is used. */
-        KARATSUBA_SQR_CUTOFF = 120,     /* Min. number of digits before Karatsuba squaring is used. */
-
-        TOOM_MUL_CUTOFF      = 350,      /* no optimal values of these are known yet so set em high */
-        TOOM_SQR_CUTOFF      = 400;
-#endif
-
-/* $Source$ */
-/* $Revision$ */
-/* $Date$ */
-
-/* End: bncore.c */
-
-
-/* EOF */
diff --git a/libtommath/pretty.build b/libtommath/pretty.build
deleted file mode 100644
index a708b8a..0000000
--- a/libtommath/pretty.build
+++ /dev/null
@@ -1,66 +0,0 @@
-#!/bin/perl -w
-#
-# Cute little builder for perl 
-# Total waste of development time...
-#
-# This will build all the object files and then the archive .a file
-# requires GCC, GNU make and a sense of humour.
-#
-# Tom St Denis
-use strict;
-
-my $count = 0;
-my $starttime = time;
-my $rate  = 0;
-print "Scanning for source files...\n";
-foreach my $filename (glob "*.c") {
-       ++$count;
-}
-print "Source files to build: $count\nBuilding...\n";
-my $i = 0;
-my $lines = 0;
-my $filesbuilt = 0;
-foreach my $filename (glob "*.c") {
-       printf("Building %3.2f%%, ", (++$i/$count)*100.0);
-       if ($i % 4 == 0) { print "/, "; }
-       if ($i % 4 == 1) { print "-, "; }
-       if ($i % 4 == 2) { print "\\, "; }
-       if ($i % 4 == 3) { print "|, "; }
-       if ($rate > 0) {
-           my $tleft = ($count - $i) / $rate;
-           my $tsec  = $tleft%60;
-           my $tmin  = ($tleft/60)%60;
-           my $thour = ($tleft/3600)%60;
-           printf("%2d:%02d:%02d left, ", $thour, $tmin, $tsec);
-       }
-       my $cnt = ($i/$count)*30.0;
-       my $x   = 0;
-       print "[";
-       for (; $x < $cnt; $x++) { print "#"; }
-       for (; $x < 30; $x++)   { print " "; }
-       print "]\r";
-       my $tmp = $filename;
-       $tmp =~ s/\.c/".o"/ge;
-       if (open(SRC, "<$tmp")) {
-          close SRC;
-       } else {
-          !system("make $tmp > /dev/null 2>/dev/null") or die "\nERROR: Failed to make $tmp!!!\n";
-          open( SRC, "<$filename" ) or die "Couldn't open $filename for reading: $!";
-          ++$lines while (<SRC>);
-          close SRC or die "Error closing $filename after reading: $!";
-          ++$filesbuilt;
-       }      
-
-       # update timer 
-       if (time != $starttime) {
-          my $delay = time - $starttime;
-          $rate = $i/$delay;
-       }
-}
-
-# finish building the library 
-printf("\nFinished building source (%d seconds, %3.2f files per second).\n", time - $starttime, $rate);
-print "Compiled approximately $filesbuilt files and $lines lines of code.\n";
-print "Doing final make (building archive...)\n";
-!system("make > /dev/null 2>/dev/null") or die "\nERROR: Failed to perform last make command!!!\n";
-print "done.\n";
\ No newline at end of file
diff --git a/libtommath/testme.sh b/libtommath/testme.sh
deleted file mode 100755
index 6324525..0000000
--- a/libtommath/testme.sh
+++ /dev/null
@@ -1,174 +0,0 @@
-#!/bin/bash
-#
-# return values of this script are:
-#   0  success
-# 128  a test failed
-#  >0  the number of timed-out tests
-
-set -e
-
-if [ -f /proc/cpuinfo ]
-then
-  MAKE_JOBS=$(( ($(cat /proc/cpuinfo | grep -E '^processor[[:space:]]*:' | tail -n -1 | cut -d':' -f2) + 1) * 2 + 1 ))
-else
-  MAKE_JOBS=8
-fi
-
-ret=0
-TEST_CFLAGS=""
-
-_help()
-{
-  echo "Usage options for $(basename $0) [--with-cc=arg [other options]]"
-  echo
-  echo "Executing this script without any parameter will only run the default configuration"
-  echo "that has automatically been determined for the architecture you're running."
-  echo
-  echo "    --with-cc=*             The compiler(s) to use for the tests"
-  echo "        This is an option that will be iterated."
-  echo
-  echo "To be able to specify options a compiler has to be given."
-  echo "All options will be tested with all MP_xBIT configurations."
-  echo
-  echo "    --with-{m64,m32,mx32}   The architecture(s) to build and test for,"
-  echo "                            e.g. --with-mx32."
-  echo "        This is an option that will be iterated, multiple selections are possible."
-  echo "        The mx32 architecture is not supported by clang and will not be executed."
-  echo
-  echo "    --cflags=*              Give an option to the compiler,"
-  echo "                            e.g. --cflags=-g"
-  echo "        This is an option that will always be passed as parameter to CC."
-  echo
-  echo "    --make-option=*         Give an option to make,"
-  echo "                            e.g. --make-option=\"-f makefile.shared\""
-  echo "        This is an option that will always be passed as parameter to make."
-  echo
-  echo "Godmode:"
-  echo
-  echo "    --all                   Choose all architectures and gcc and clang as compilers"
-  echo
-  echo "    --help                  This message"
-  exit 0
-}
-
-_die()
-{
-  echo "error $2 while $1"
-  if [ "$2" != "124" ]
-  then
-    exit 128
-  else
-    echo "assuming timeout while running test - continue"
-    ret=$(( $ret + 1 ))
-  fi
-}
-
-_runtest()
-{
-  echo -ne " Compile $1 $2"
-  make clean > /dev/null
-  CC="$1" CFLAGS="$2 $TEST_CFLAGS" make -j$MAKE_JOBS test_standalone $MAKE_OPTIONS > /dev/null 2>test_errors.txt
-  echo -e "\rRun test $1 $2"
-  timeout --foreground 90 ./test > test_$(echo ${1}${2}  | tr ' ' '_').txt || _die "running tests" $?
-}
-
-_banner()
-{
-  echo "uname="$(uname -a)
-  [[ "$#" != "0" ]] && (echo $1=$($1 -dumpversion)) || true
-}
-
-_exit()
-{
-  if [ "$ret" == "0" ]
-  then
-    echo "Tests successful"
-  else
-    echo "$ret tests timed out"
-  fi
-
-  exit $ret
-}
-
-ARCHFLAGS=""
-COMPILERS=""
-CFLAGS=""
-
-while [ $# -gt 0 ];
-do
-  case $1 in
-    "--with-m64" | "--with-m32" | "--with-mx32")
-      ARCHFLAGS="$ARCHFLAGS ${1:6}"
-    ;;
-    --with-cc=*)
-      COMPILERS="$COMPILERS ${1#*=}"
-    ;;
-    --cflags=*)
-      CFLAGS="$CFLAGS ${1#*=}"
-    ;;
-    --make-option=*)
-      MAKE_OPTIONS="$MAKE_OPTIONS ${1#*=}"
-    ;;
-    --all)
-      COMPILERS="gcc clang"
-      ARCHFLAGS="-m64 -m32 -mx32"
-    ;;
-    --help)
-      _help
-    ;;
-  esac
-  shift
-done
-
-# default to gcc if nothing is given
-if [[ "$COMPILERS" == "" ]]
-then
-  _banner gcc
-  _runtest "gcc" ""
-  _exit
-fi
-
-archflags=( $ARCHFLAGS )
-compilers=( $COMPILERS )
-
-# choosing a compiler without specifying an architecture will use the default architecture
-if [ "${#archflags[@]}" == "0" ]
-then
-  archflags[0]=" "
-fi
-
-_banner
-
-for i in "${compilers[@]}"
-do
-  if [ -z "$(which $i)" ]
-  then
-    echo "Skipped compiler $i, file not found"
-    continue
-  fi
-  compiler_version=$(echo "$i="$($i -dumpversion))
-  if [ "$compiler_version" == "clang=4.2.1" ]
-  then
-    # one of my versions of clang complains about some stuff in stdio.h and stdarg.h ...
-    TEST_CFLAGS="-Wno-typedef-redefinition"
-  else
-    TEST_CFLAGS=""
-  fi
-  echo $compiler_version
-
-  for a in "${archflags[@]}"
-  do
-    if [[ $(expr "$i" : "clang") && "$a" == "-mx32" ]]
-    then
-      echo "clang -mx32 tests skipped"
-      continue
-    fi
-
-    _runtest "$i $a" ""
-    _runtest "$i $a" "-DMP_8BIT"
-    _runtest "$i $a" "-DMP_16BIT"
-    _runtest "$i $a" "-DMP_32BIT"
-  done
-done
-
-_exit
diff --git a/libtommath/tombc/grammar.txt b/libtommath/tombc/grammar.txt
deleted file mode 100644
index a780e75..0000000
--- a/libtommath/tombc/grammar.txt
+++ /dev/null
@@ -1,35 +0,0 @@
-program       := program statement | statement | empty
-statement     := { statement }                                                                              | 
-                 identifier = numexpression;                                                                | 
-                 identifier[numexpression] = numexpression;                                                 |
-                 function(expressionlist);                                                                  | 
-                 for (identifer = numexpression; numexpression; identifier = numexpression) { statement }   |
-                 while (numexpression) { statement }                                                        | 
-                 if (numexpresion) { statement } elif                                                       | 
-                 break;                                                                                     | 
-                 continue;                                                                                  
-                 
-elif          := else statement | empty
-function      := abs | countbits | exptmod | jacobi | print | isprime | nextprime | issquare | readinteger | exit
-expressionlist := expressionlist, expression | expression
-
-// LR(1) !!!?
-expression    := string | numexpression
-numexpression := cmpexpr && cmpexpr | cmpexpr \|\| cmpexpr | cmpexpr
-cmpexpr       := boolexpr  < boolexpr | boolexpr  > boolexpr | boolexpr == boolexpr | 
-                 boolexpr <= boolexpr | boolexpr >= boolexpr | boolexpr
-boolexpr      := shiftexpr & shiftexpr | shiftexpr ^ shiftexpr | shiftexpr \| shiftexpr | shiftexpr
-shiftexpr     := addsubexpr << addsubexpr | addsubexpr >> addsubexpr | addsubexpr
-addsubexpr    := mulexpr + mulexpr | mulexpr - mulexpr | mulexpr
-mulexpr       := expr * expr       | expr / expr | expr % expr | expr
-expr          := -nexpr | nexpr 
-nexpr         := integer | identifier | ( numexpression ) | identifier[numexpression] 
-
-identifier    := identifer digits | identifier alpha | alpha
-alpha         := a ... z | A ... Z
-integer       := hexnumber | digits 
-hexnumber     := 0xhexdigits
-hexdigits     := hexdigits hexdigit | hexdigit
-hexdigit      := 0 ... 9 | a ... f | A ... F
-digits        := digits digit | digit 
-digit         := 0 ... 9
diff --git a/libtommath/tommath.h b/libtommath/tommath.h
index 4547488..fc6b409 100644
--- a/libtommath/tommath.h
+++ b/libtommath/tommath.h
@@ -203,7 +203,7 @@ int mp_init_size(mp_int *a, int size);
 
 /* ---> Basic Manipulations <--- */
 #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
-#define mp_iseven(a) ((((a)->used > 0) && (((a)->dp[0] & 1u) == 0u)) ? MP_YES : MP_NO)
+#define mp_iseven(a) ((((a)->used == 0) || (((a)->dp[0] & 1u) == 0u)) ? MP_YES : MP_NO)
 #define mp_isodd(a)  ((((a)->used > 0) && (((a)->dp[0] & 1u) == 1u)) ? MP_YES : MP_NO)
 #define mp_isneg(a)  (((a)->sign != MP_ZPOS) ? MP_YES : MP_NO)
 
diff --git a/libtommath/tommath.out b/libtommath/tommath.out
deleted file mode 100644
index de4aada..0000000
--- a/libtommath/tommath.out
+++ /dev/null
@@ -1,139 +0,0 @@
-\BOOKMARK [0][-]{chapter.1}{Introduction}{}% 1
-\BOOKMARK [1][-]{section.1.1}{Multiple Precision Arithmetic}{chapter.1}% 2
-\BOOKMARK [2][-]{subsection.1.1.1}{What is Multiple Precision Arithmetic?}{section.1.1}% 3
-\BOOKMARK [2][-]{subsection.1.1.2}{The Need for Multiple Precision Arithmetic}{section.1.1}% 4
-\BOOKMARK [2][-]{subsection.1.1.3}{Benefits of Multiple Precision Arithmetic}{section.1.1}% 5
-\BOOKMARK [1][-]{section.1.2}{Purpose of This Text}{chapter.1}% 6
-\BOOKMARK [1][-]{section.1.3}{Discussion and Notation}{chapter.1}% 7
-\BOOKMARK [2][-]{subsection.1.3.1}{Notation}{section.1.3}% 8
-\BOOKMARK [2][-]{subsection.1.3.2}{Precision Notation}{section.1.3}% 9
-\BOOKMARK [2][-]{subsection.1.3.3}{Algorithm Inputs and Outputs}{section.1.3}% 10
-\BOOKMARK [2][-]{subsection.1.3.4}{Mathematical Expressions}{section.1.3}% 11
-\BOOKMARK [2][-]{subsection.1.3.5}{Work Effort}{section.1.3}% 12
-\BOOKMARK [1][-]{section.1.4}{Exercises}{chapter.1}% 13
-\BOOKMARK [1][-]{section.1.5}{Introduction to LibTomMath}{chapter.1}% 14
-\BOOKMARK [2][-]{subsection.1.5.1}{What is LibTomMath?}{section.1.5}% 15
-\BOOKMARK [2][-]{subsection.1.5.2}{Goals of LibTomMath}{section.1.5}% 16
-\BOOKMARK [1][-]{section.1.6}{Choice of LibTomMath}{chapter.1}% 17
-\BOOKMARK [2][-]{subsection.1.6.1}{Code Base}{section.1.6}% 18
-\BOOKMARK [2][-]{subsection.1.6.2}{API Simplicity}{section.1.6}% 19
-\BOOKMARK [2][-]{subsection.1.6.3}{Optimizations}{section.1.6}% 20
-\BOOKMARK [2][-]{subsection.1.6.4}{Portability and Stability}{section.1.6}% 21
-\BOOKMARK [2][-]{subsection.1.6.5}{Choice}{section.1.6}% 22
-\BOOKMARK [0][-]{chapter.2}{Getting Started}{}% 23
-\BOOKMARK [1][-]{section.2.1}{Library Basics}{chapter.2}% 24
-\BOOKMARK [1][-]{section.2.2}{What is a Multiple Precision Integer?}{chapter.2}% 25
-\BOOKMARK [2][-]{subsection.2.2.1}{The mp\137int Structure}{section.2.2}% 26
-\BOOKMARK [1][-]{section.2.3}{Argument Passing}{chapter.2}% 27
-\BOOKMARK [1][-]{section.2.4}{Return Values}{chapter.2}% 28
-\BOOKMARK [1][-]{section.2.5}{Initialization and Clearing}{chapter.2}% 29
-\BOOKMARK [2][-]{subsection.2.5.1}{Initializing an mp\137int}{section.2.5}% 30
-\BOOKMARK [2][-]{subsection.2.5.2}{Clearing an mp\137int}{section.2.5}% 31
-\BOOKMARK [1][-]{section.2.6}{Maintenance Algorithms}{chapter.2}% 32
-\BOOKMARK [2][-]{subsection.2.6.1}{Augmenting an mp\137int's Precision}{section.2.6}% 33
-\BOOKMARK [2][-]{subsection.2.6.2}{Initializing Variable Precision mp\137ints}{section.2.6}% 34
-\BOOKMARK [2][-]{subsection.2.6.3}{Multiple Integer Initializations and Clearings}{section.2.6}% 35
-\BOOKMARK [2][-]{subsection.2.6.4}{Clamping Excess Digits}{section.2.6}% 36
-\BOOKMARK [0][-]{chapter.3}{Basic Operations}{}% 37
-\BOOKMARK [1][-]{section.3.1}{Introduction}{chapter.3}% 38
-\BOOKMARK [1][-]{section.3.2}{Assigning Values to mp\137int Structures}{chapter.3}% 39
-\BOOKMARK [2][-]{subsection.3.2.1}{Copying an mp\137int}{section.3.2}% 40
-\BOOKMARK [2][-]{subsection.3.2.2}{Creating a Clone}{section.3.2}% 41
-\BOOKMARK [1][-]{section.3.3}{Zeroing an Integer}{chapter.3}% 42
-\BOOKMARK [1][-]{section.3.4}{Sign Manipulation}{chapter.3}% 43
-\BOOKMARK [2][-]{subsection.3.4.1}{Absolute Value}{section.3.4}% 44
-\BOOKMARK [2][-]{subsection.3.4.2}{Integer Negation}{section.3.4}% 45
-\BOOKMARK [1][-]{section.3.5}{Small Constants}{chapter.3}% 46
-\BOOKMARK [2][-]{subsection.3.5.1}{Setting Small Constants}{section.3.5}% 47
-\BOOKMARK [2][-]{subsection.3.5.2}{Setting Large Constants}{section.3.5}% 48
-\BOOKMARK [1][-]{section.3.6}{Comparisons}{chapter.3}% 49
-\BOOKMARK [2][-]{subsection.3.6.1}{Unsigned Comparisions}{section.3.6}% 50
-\BOOKMARK [2][-]{subsection.3.6.2}{Signed Comparisons}{section.3.6}% 51
-\BOOKMARK [0][-]{chapter.4}{Basic Arithmetic}{}% 52
-\BOOKMARK [1][-]{section.4.1}{Introduction}{chapter.4}% 53
-\BOOKMARK [1][-]{section.4.2}{Addition and Subtraction}{chapter.4}% 54
-\BOOKMARK [2][-]{subsection.4.2.1}{Low Level Addition}{section.4.2}% 55
-\BOOKMARK [2][-]{subsection.4.2.2}{Low Level Subtraction}{section.4.2}% 56
-\BOOKMARK [2][-]{subsection.4.2.3}{High Level Addition}{section.4.2}% 57
-\BOOKMARK [2][-]{subsection.4.2.4}{High Level Subtraction}{section.4.2}% 58
-\BOOKMARK [1][-]{section.4.3}{Bit and Digit Shifting}{chapter.4}% 59
-\BOOKMARK [2][-]{subsection.4.3.1}{Multiplication by Two}{section.4.3}% 60
-\BOOKMARK [2][-]{subsection.4.3.2}{Division by Two}{section.4.3}% 61
-\BOOKMARK [1][-]{section.4.4}{Polynomial Basis Operations}{chapter.4}% 62
-\BOOKMARK [2][-]{subsection.4.4.1}{Multiplication by x}{section.4.4}% 63
-\BOOKMARK [2][-]{subsection.4.4.2}{Division by x}{section.4.4}% 64
-\BOOKMARK [1][-]{section.4.5}{Powers of Two}{chapter.4}% 65
-\BOOKMARK [2][-]{subsection.4.5.1}{Multiplication by Power of Two}{section.4.5}% 66
-\BOOKMARK [2][-]{subsection.4.5.2}{Division by Power of Two}{section.4.5}% 67
-\BOOKMARK [2][-]{subsection.4.5.3}{Remainder of Division by Power of Two}{section.4.5}% 68
-\BOOKMARK [0][-]{chapter.5}{Multiplication and Squaring}{}% 69
-\BOOKMARK [1][-]{section.5.1}{The Multipliers}{chapter.5}% 70
-\BOOKMARK [1][-]{section.5.2}{Multiplication}{chapter.5}% 71
-\BOOKMARK [2][-]{subsection.5.2.1}{The Baseline Multiplication}{section.5.2}% 72
-\BOOKMARK [2][-]{subsection.5.2.2}{Faster Multiplication by the ``Comba'' Method}{section.5.2}% 73
-\BOOKMARK [2][-]{subsection.5.2.3}{Polynomial Basis Multiplication}{section.5.2}% 74
-\BOOKMARK [2][-]{subsection.5.2.4}{Karatsuba Multiplication}{section.5.2}% 75
-\BOOKMARK [2][-]{subsection.5.2.5}{Toom-Cook 3-Way Multiplication}{section.5.2}% 76
-\BOOKMARK [2][-]{subsection.5.2.6}{Signed Multiplication}{section.5.2}% 77
-\BOOKMARK [1][-]{section.5.3}{Squaring}{chapter.5}% 78
-\BOOKMARK [2][-]{subsection.5.3.1}{The Baseline Squaring Algorithm}{section.5.3}% 79
-\BOOKMARK [2][-]{subsection.5.3.2}{Faster Squaring by the ``Comba'' Method}{section.5.3}% 80
-\BOOKMARK [2][-]{subsection.5.3.3}{Polynomial Basis Squaring}{section.5.3}% 81
-\BOOKMARK [2][-]{subsection.5.3.4}{Karatsuba Squaring}{section.5.3}% 82
-\BOOKMARK [2][-]{subsection.5.3.5}{Toom-Cook Squaring}{section.5.3}% 83
-\BOOKMARK [2][-]{subsection.5.3.6}{High Level Squaring}{section.5.3}% 84
-\BOOKMARK [0][-]{chapter.6}{Modular Reduction}{}% 85
-\BOOKMARK [1][-]{section.6.1}{Basics of Modular Reduction}{chapter.6}% 86
-\BOOKMARK [1][-]{section.6.2}{The Barrett Reduction}{chapter.6}% 87
-\BOOKMARK [2][-]{subsection.6.2.1}{Fixed Point Arithmetic}{section.6.2}% 88
-\BOOKMARK [2][-]{subsection.6.2.2}{Choosing a Radix Point}{section.6.2}% 89
-\BOOKMARK [2][-]{subsection.6.2.3}{Trimming the Quotient}{section.6.2}% 90
-\BOOKMARK [2][-]{subsection.6.2.4}{Trimming the Residue}{section.6.2}% 91
-\BOOKMARK [2][-]{subsection.6.2.5}{The Barrett Algorithm}{section.6.2}% 92
-\BOOKMARK [2][-]{subsection.6.2.6}{The Barrett Setup Algorithm}{section.6.2}% 93
-\BOOKMARK [1][-]{section.6.3}{The Montgomery Reduction}{chapter.6}% 94
-\BOOKMARK [2][-]{subsection.6.3.1}{Digit Based Montgomery Reduction}{section.6.3}% 95
-\BOOKMARK [2][-]{subsection.6.3.2}{Baseline Montgomery Reduction}{section.6.3}% 96
-\BOOKMARK [2][-]{subsection.6.3.3}{Faster ``Comba'' Montgomery Reduction}{section.6.3}% 97
-\BOOKMARK [2][-]{subsection.6.3.4}{Montgomery Setup}{section.6.3}% 98
-\BOOKMARK [1][-]{section.6.4}{The Diminished Radix Algorithm}{chapter.6}% 99
-\BOOKMARK [2][-]{subsection.6.4.1}{Choice of Moduli}{section.6.4}% 100
-\BOOKMARK [2][-]{subsection.6.4.2}{Choice of k}{section.6.4}% 101
-\BOOKMARK [2][-]{subsection.6.4.3}{Restricted Diminished Radix Reduction}{section.6.4}% 102
-\BOOKMARK [2][-]{subsection.6.4.4}{Unrestricted Diminished Radix Reduction}{section.6.4}% 103
-\BOOKMARK [1][-]{section.6.5}{Algorithm Comparison}{chapter.6}% 104
-\BOOKMARK [0][-]{chapter.7}{Exponentiation}{}% 105
-\BOOKMARK [1][-]{section.7.1}{Exponentiation Basics}{chapter.7}% 106
-\BOOKMARK [2][-]{subsection.7.1.1}{Single Digit Exponentiation}{section.7.1}% 107
-\BOOKMARK [1][-]{section.7.2}{k-ary Exponentiation}{chapter.7}% 108
-\BOOKMARK [2][-]{subsection.7.2.1}{Optimal Values of k}{section.7.2}% 109
-\BOOKMARK [2][-]{subsection.7.2.2}{Sliding-Window Exponentiation}{section.7.2}% 110
-\BOOKMARK [1][-]{section.7.3}{Modular Exponentiation}{chapter.7}% 111
-\BOOKMARK [2][-]{subsection.7.3.1}{Barrett Modular Exponentiation}{section.7.3}% 112
-\BOOKMARK [1][-]{section.7.4}{Quick Power of Two}{chapter.7}% 113
-\BOOKMARK [0][-]{chapter.8}{Higher Level Algorithms}{}% 114
-\BOOKMARK [1][-]{section.8.1}{Integer Division with Remainder}{chapter.8}% 115
-\BOOKMARK [2][-]{subsection.8.1.1}{Quotient Estimation}{section.8.1}% 116
-\BOOKMARK [2][-]{subsection.8.1.2}{Normalized Integers}{section.8.1}% 117
-\BOOKMARK [2][-]{subsection.8.1.3}{Radix- Division with Remainder}{section.8.1}% 118
-\BOOKMARK [1][-]{section.8.2}{Single Digit Helpers}{chapter.8}% 119
-\BOOKMARK [2][-]{subsection.8.2.1}{Single Digit Addition and Subtraction}{section.8.2}% 120
-\BOOKMARK [2][-]{subsection.8.2.2}{Single Digit Multiplication}{section.8.2}% 121
-\BOOKMARK [2][-]{subsection.8.2.3}{Single Digit Division}{section.8.2}% 122
-\BOOKMARK [2][-]{subsection.8.2.4}{Single Digit Root Extraction}{section.8.2}% 123
-\BOOKMARK [1][-]{section.8.3}{Random Number Generation}{chapter.8}% 124
-\BOOKMARK [1][-]{section.8.4}{Formatted Representations}{chapter.8}% 125
-\BOOKMARK [2][-]{subsection.8.4.1}{Reading Radix-n Input}{section.8.4}% 126
-\BOOKMARK [2][-]{subsection.8.4.2}{Generating Radix-n Output}{section.8.4}% 127
-\BOOKMARK [0][-]{chapter.9}{Number Theoretic Algorithms}{}% 128
-\BOOKMARK [1][-]{section.9.1}{Greatest Common Divisor}{chapter.9}% 129
-\BOOKMARK [2][-]{subsection.9.1.1}{Complete Greatest Common Divisor}{section.9.1}% 130
-\BOOKMARK [1][-]{section.9.2}{Least Common Multiple}{chapter.9}% 131
-\BOOKMARK [1][-]{section.9.3}{Jacobi Symbol Computation}{chapter.9}% 132
-\BOOKMARK [2][-]{subsection.9.3.1}{Jacobi Symbol}{section.9.3}% 133
-\BOOKMARK [1][-]{section.9.4}{Modular Inverse}{chapter.9}% 134
-\BOOKMARK [2][-]{subsection.9.4.1}{General Case}{section.9.4}% 135
-\BOOKMARK [1][-]{section.9.5}{Primality Tests}{chapter.9}% 136
-\BOOKMARK [2][-]{subsection.9.5.1}{Trial Division}{section.9.5}% 137
-\BOOKMARK [2][-]{subsection.9.5.2}{The Fermat Test}{section.9.5}% 138
-\BOOKMARK [2][-]{subsection.9.5.3}{The Miller-Rabin Test}{section.9.5}% 139
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-\documentclass[b5paper]{book}
-\usepackage{hyperref}
-\usepackage{makeidx}
-\usepackage{amssymb}
-\usepackage{color}
-\usepackage{alltt}
-\usepackage{graphicx}
-\usepackage{layout}
-\def\union{\cup}
-\def\intersect{\cap}
-\def\getsrandom{\stackrel{\rm R}{\gets}}
-\def\cross{\times}
-\def\cat{\hspace{0.5em} \| \hspace{0.5em}}
-\def\catn{$\|$}
-\def\divides{\hspace{0.3em} | \hspace{0.3em}}
-\def\nequiv{\not\equiv}
-\def\approx{\raisebox{0.2ex}{\mbox{\small $\sim$}}}
-\def\lcm{{\rm lcm}}
-\def\gcd{{\rm gcd}}
-\def\log{{\rm log}}
-\def\ord{{\rm ord}}
-\def\abs{{\mathit abs}}
-\def\rep{{\mathit rep}}
-\def\mod{{\mathit\ mod\ }}
-\renewcommand{\pmod}[1]{\ ({\rm mod\ }{#1})}
-\newcommand{\floor}[1]{\left\lfloor{#1}\right\rfloor}
-\newcommand{\ceil}[1]{\left\lceil{#1}\right\rceil}
-\def\Or{{\rm\ or\ }}
-\def\And{{\rm\ and\ }}
-\def\iff{\hspace{1em}\Longleftrightarrow\hspace{1em}}
-\def\implies{\Rightarrow}
-\def\undefined{{\rm ``undefined"}}
-\def\Proof{\vspace{1ex}\noindent {\bf Proof:}\hspace{1em}}
-\let\oldphi\phi
-\def\phi{\varphi}
-\def\Pr{{\rm Pr}}
-\newcommand{\str}[1]{{\mathbf{#1}}}
-\def\F{{\mathbb F}}
-\def\N{{\mathbb N}}
-\def\Z{{\mathbb Z}}
-\def\R{{\mathbb R}}
-\def\C{{\mathbb C}}
-\def\Q{{\mathbb Q}}
-\definecolor{DGray}{gray}{0.5}
-\newcommand{\emailaddr}[1]{\mbox{$<${#1}$>$}}
-\def\twiddle{\raisebox{0.3ex}{\mbox{\tiny $\sim$}}}
-\def\gap{\vspace{0.5ex}}
-\makeindex
-\begin{document}
-\frontmatter
-\pagestyle{empty}
-\title{Multi--Precision Math}
-\author{\mbox{
-%\begin{small}
-\begin{tabular}{c}
-Tom St Denis \\
-Algonquin College \\
-\\
-Mads Rasmussen \\
-Open Communications Security \\
-\\
-Greg Rose \\
-QUALCOMM Australia \\
-\end{tabular}
-%\end{small}
-}
-}
-\maketitle
-This text has been placed in the public domain.  This text corresponds to the v0.39 release of the
-LibTomMath project.
-
-This text is formatted to the international B5 paper size of 176mm wide by 250mm tall using the \LaTeX{}
-{\em book} macro package and the Perl {\em booker} package.
-
-\tableofcontents
-\listoffigures
-\chapter*{Prefaces}
-When I tell people about my LibTom projects and that I release them as public domain they are often puzzled.
-They ask why I did it and especially why I continue to work on them for free.  The best I can explain it is ``Because I can.''
-Which seems odd and perhaps too terse for adult conversation. I often qualify it with ``I am able, I am willing.'' which
-perhaps explains it better.  I am the first to admit there is not anything that special with what I have done.  Perhaps
-others can see that too and then we would have a society to be proud of.  My LibTom projects are what I am doing to give
-back to society in the form of tools and knowledge that can help others in their endeavours.
-
-I started writing this book because it was the most logical task to further my goal of open academia.  The LibTomMath source
-code itself was written to be easy to follow and learn from.  There are times, however, where pure C source code does not
-explain the algorithms properly.  Hence this book.  The book literally starts with the foundation of the library and works
-itself outwards to the more complicated algorithms.  The use of both pseudo--code and verbatim source code provides a duality
-of ``theory'' and ``practice'' that the computer science students of the world shall appreciate.  I never deviate too far
-from relatively straightforward algebra and I hope that this book can be a valuable learning asset.
-
-This book and indeed much of the LibTom projects would not exist in their current form if it was not for a plethora
-of kind people donating their time, resources and kind words to help support my work.  Writing a text of significant
-length (along with the source code) is a tiresome and lengthy process.  Currently the LibTom project is four years old,
-comprises of literally thousands of users and over 100,000 lines of source code, TeX and other material.  People like Mads and Greg
-were there at the beginning to encourage me to work well.  It is amazing how timely validation from others can boost morale to
-continue the project. Definitely my parents were there for me by providing room and board during the many months of work in 2003.
-
-To my many friends whom I have met through the years I thank you for the good times and the words of encouragement.  I hope I
-honour your kind gestures with this project.
-
-Open Source.  Open Academia.  Open Minds.
-
-\begin{flushright} Tom St Denis \end{flushright}
-
-\newpage
-I found the opportunity to work with Tom appealing for several reasons, not only could I broaden my own horizons, but also
-contribute to educate others facing the problem of having to handle big number mathematical calculations.
-
-This book is Tom's child and he has been caring and fostering the project ever since the beginning with a clear mind of
-how he wanted the project to turn out. I have helped by proofreading the text and we have had several discussions about
-the layout and language used.
-
-I hold a masters degree in cryptography from the University of Southern Denmark and have always been interested in the
-practical aspects of cryptography.
-
-Having worked in the security consultancy business for several years in S\~{a}o Paulo, Brazil, I have been in touch with a
-great deal of work in which multiple precision mathematics was needed. Understanding the possibilities for speeding up
-multiple precision calculations is often very important since we deal with outdated machine architecture where modular
-reductions, for example, become painfully slow.
-
-This text is for people who stop and wonder when first examining algorithms such as RSA for the first time and asks
-themselves, ``You tell me this is only secure for large numbers, fine; but how do you implement these numbers?''
-
-\begin{flushright}
-Mads Rasmussen
-
-S\~{a}o Paulo - SP
-
-Brazil
-\end{flushright}
-
-\newpage
-It's all because I broke my leg. That just happened to be at about the same time that Tom asked for someone to review the section of the book about
-Karatsuba multiplication. I was laid up, alone and immobile, and thought ``Why not?'' I vaguely knew what Karatsuba multiplication was, but not
-really, so I thought I could help, learn, and stop myself from watching daytime cable TV, all at once.
-
-At the time of writing this, I've still not met Tom or Mads in meatspace. I've been following Tom's progress since his first splash on the
-sci.crypt Usenet news group. I watched him go from a clueless newbie, to the cryptographic equivalent of a reformed smoker, to a real
-contributor to the field, over a period of about two years. I've been impressed with his obvious intelligence, and astounded by his productivity.
-Of course, he's young enough to be my own child, so he doesn't have my problems with staying awake.
-
-When I reviewed that single section of the book, in its very earliest form, I was very pleasantly surprised. So I decided to collaborate more fully,
-and at least review all of it, and perhaps write some bits too. There's still a long way to go with it, and I have watched a number of close
-friends go through the mill of publication, so I think that the way to go is longer than Tom thinks it is. Nevertheless, it's a good effort,
-and I'm pleased to be involved with it.
-
-\begin{flushright}
-Greg Rose, Sydney, Australia, June 2003.
-\end{flushright}
-
-\mainmatter
-\pagestyle{headings}
-\chapter{Introduction}
-\section{Multiple Precision Arithmetic}
-
-\subsection{What is Multiple Precision Arithmetic?}
-When we think of long-hand arithmetic such as addition or multiplication we rarely consider the fact that we instinctively
-raise or lower the precision of the numbers we are dealing with.  For example, in decimal we almost immediate can
-reason that $7$ times $6$ is $42$.  However, $42$ has two digits of precision as opposed to one digit we started with.
-Further multiplications of say $3$ result in a larger precision result $126$.  In these few examples we have multiple
-precisions for the numbers we are working with.  Despite the various levels of precision a single subset\footnote{With the occasional optimization.}
- of algorithms can be designed to accomodate them.
-
-By way of comparison a fixed or single precision operation would lose precision on various operations.  For example, in
-the decimal system with fixed precision $6 \cdot 7 = 2$.
-
-Essentially at the heart of computer based multiple precision arithmetic are the same long-hand algorithms taught in
-schools to manually add, subtract, multiply and divide.
-
-\subsection{The Need for Multiple Precision Arithmetic}
-The most prevalent need for multiple precision arithmetic, often referred to as ``bignum'' math, is within the implementation
-of public-key cryptography algorithms.   Algorithms such as RSA \cite{RSAREF} and Diffie-Hellman \cite{DHREF} require
-integers of significant magnitude to resist known cryptanalytic attacks.  For example, at the time of this writing a
-typical RSA modulus would be at least greater than $10^{309}$.  However, modern programming languages such as ISO C \cite{ISOC} and
-Java \cite{JAVA} only provide instrinsic support for integers which are relatively small and single precision.
-
-\begin{figure}[!here]
-\begin{center}
-\begin{tabular}{|r|c|}
-\hline \textbf{Data Type} & \textbf{Range} \\
-\hline char  & $-128 \ldots 127$ \\
-\hline short & $-32768 \ldots 32767$ \\
-\hline long  & $-2147483648 \ldots 2147483647$ \\
-\hline long long & $-9223372036854775808 \ldots 9223372036854775807$ \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Typical Data Types for the C Programming Language}
-\label{fig:ISOC}
-\end{figure}
-
-The largest data type guaranteed to be provided by the ISO C programming
-language\footnote{As per the ISO C standard.  However, each compiler vendor is allowed to augment the precision as they
-see fit.}  can only represent values up to $10^{19}$ as shown in figure \ref{fig:ISOC}. On its own the C language is
-insufficient to accomodate the magnitude required for the problem at hand.  An RSA modulus of magnitude $10^{19}$ could be
-trivially factored\footnote{A Pollard-Rho factoring would take only $2^{16}$ time.} on the average desktop computer,
-rendering any protocol based on the algorithm insecure.  Multiple precision algorithms solve this very problem by
-extending the range of representable integers while using single precision data types.
-
-Most advancements in fast multiple precision arithmetic stem from the need for faster and more efficient cryptographic
-primitives.  Faster modular reduction and exponentiation algorithms such as Barrett's algorithm, which have appeared in
-various cryptographic journals, can render algorithms such as RSA and Diffie-Hellman more efficient.  In fact, several
-major companies such as RSA Security, Certicom and Entrust have built entire product lines on the implementation and
-deployment of efficient algorithms.
-
-However, cryptography is not the only field of study that can benefit from fast multiple precision integer routines.
-Another auxiliary use of multiple precision integers is high precision floating point data types.
-The basic IEEE \cite{IEEE} standard floating point type is made up of an integer mantissa $q$, an exponent $e$ and a sign bit $s$.
-Numbers are given in the form $n = q \cdot b^e \cdot -1^s$ where $b = 2$ is the most common base for IEEE.  Since IEEE
-floating point is meant to be implemented in hardware the precision of the mantissa is often fairly small
-(\textit{23, 48 and 64 bits}).  The mantissa is merely an integer and a multiple precision integer could be used to create
-a mantissa of much larger precision than hardware alone can efficiently support.  This approach could be useful where
-scientific applications must minimize the total output error over long calculations.
-
-Yet another use for large integers is within arithmetic on polynomials of large characteristic (i.e. $GF(p)[x]$ for large $p$).
-In fact the library discussed within this text has already been used to form a polynomial basis library\footnote{See \url{http://poly.libtomcrypt.org} for more details.}.
-
-\subsection{Benefits of Multiple Precision Arithmetic}
-\index{precision}
-The benefit of multiple precision representations over single or fixed precision representations is that
-no precision is lost while representing the result of an operation which requires excess precision.  For example,
-the product of two $n$-bit integers requires at least $2n$ bits of precision to be represented faithfully.  A multiple
-precision algorithm would augment the precision of the destination to accomodate the result while a single precision system
-would truncate excess bits to maintain a fixed level of precision.
-
-It is possible to implement algorithms which require large integers with fixed precision algorithms.  For example, elliptic
-curve cryptography (\textit{ECC}) is often implemented on smartcards by fixing the precision of the integers to the maximum
-size the system will ever need.  Such an approach can lead to vastly simpler algorithms which can accomodate the
-integers required even if the host platform cannot natively accomodate them\footnote{For example, the average smartcard
-processor has an 8 bit accumulator.}.  However, as efficient as such an approach may be, the resulting source code is not
-normally very flexible.  It cannot, at runtime, accomodate inputs of higher magnitude than the designer anticipated.
-
-Multiple precision algorithms have the most overhead of any style of arithmetic.  For the the most part the
-overhead can be kept to a minimum with careful planning, but overall, it is not well suited for most memory starved
-platforms.  However, multiple precision algorithms do offer the most flexibility in terms of the magnitude of the
-inputs.  That is, the same algorithms based on multiple precision integers can accomodate any reasonable size input
-without the designer's explicit forethought.  This leads to lower cost of ownership for the code as it only has to
-be written and tested once.
-
-\section{Purpose of This Text}
-The purpose of this text is to instruct the reader regarding how to implement efficient multiple precision algorithms.
-That is to not only explain a limited subset of the core theory behind the algorithms but also the various ``house keeping''
-elements that are neglected by authors of other texts on the subject.  Several well reknowned texts \cite{TAOCPV2,HAC}
-give considerably detailed explanations of the theoretical aspects of algorithms and often very little information
-regarding the practical implementation aspects.
-
-In most cases how an algorithm is explained and how it is actually implemented are two very different concepts.  For
-example, the Handbook of Applied Cryptography (\textit{HAC}), algorithm 14.7 on page 594, gives a relatively simple
-algorithm for performing multiple precision integer addition.  However, the description lacks any discussion concerning
-the fact that the two integer inputs may be of differing magnitudes.  As a result the implementation is not as simple
-as the text would lead people to believe.  Similarly the division routine (\textit{algorithm 14.20, pp. 598}) does not
-discuss how to handle sign or handle the dividend's decreasing magnitude in the main loop (\textit{step \#3}).
-
-Both texts also do not discuss several key optimal algorithms required such as ``Comba'' and Karatsuba multipliers
-and fast modular inversion, which we consider practical oversights.  These optimal algorithms are vital to achieve
-any form of useful performance in non-trivial applications.
-
-To solve this problem the focus of this text is on the practical aspects of implementing a multiple precision integer
-package.  As a case study the ``LibTomMath''\footnote{Available at \url{http://math.libtomcrypt.com}} package is used
-to demonstrate algorithms with real implementations\footnote{In the ISO C programming language.} that have been field
-tested and work very well.  The LibTomMath library is freely available on the Internet for all uses and this text
-discusses a very large portion of the inner workings of the library.
-
-The algorithms that are presented will always include at least one ``pseudo-code'' description followed
-by the actual C source code that implements the algorithm.  The pseudo-code can be used to implement the same
-algorithm in other programming languages as the reader sees fit.
-
-This text shall also serve as a walkthrough of the creation of multiple precision algorithms from scratch.  Showing
-the reader how the algorithms fit together as well as where to start on various taskings.
-
-\section{Discussion and Notation}
-\subsection{Notation}
-A multiple precision integer of $n$-digits shall be denoted as $x = (x_{n-1}, \ldots, x_1, x_0)_{ \beta }$ and represent
-the integer $x \equiv \sum_{i=0}^{n-1} x_i\beta^i$.  The elements of the array $x$ are said to be the radix $\beta$ digits
-of the integer.  For example, $x = (1,2,3)_{10}$ would represent the integer
-$1\cdot 10^2 + 2\cdot10^1 + 3\cdot10^0 = 123$.
-
-\index{mp\_int}
-The term ``mp\_int'' shall refer to a composite structure which contains the digits of the integer it represents, as well
-as auxilary data required to manipulate the data.  These additional members are discussed further in section
-\ref{sec:MPINT}.  For the purposes of this text a ``multiple precision integer'' and an ``mp\_int'' are assumed to be
-synonymous.  When an algorithm is specified to accept an mp\_int variable it is assumed the various auxliary data members
-are present as well.  An expression of the type \textit{variablename.item} implies that it should evaluate to the
-member named ``item'' of the variable.  For example, a string of characters may have a member ``length'' which would
-evaluate to the number of characters in the string.  If the string $a$ equals ``hello'' then it follows that
-$a.length = 5$.
-
-For certain discussions more generic algorithms are presented to help the reader understand the final algorithm used
-to solve a given problem.  When an algorithm is described as accepting an integer input it is assumed the input is
-a plain integer with no additional multiple-precision members.  That is, algorithms that use integers as opposed to
-mp\_ints as inputs do not concern themselves with the housekeeping operations required such as memory management.  These
-algorithms will be used to establish the relevant theory which will subsequently be used to describe a multiple
-precision algorithm to solve the same problem.
-
-\subsection{Precision Notation}
-The variable $\beta$ represents the radix of a single digit of a multiple precision integer and
-must be of the form $q^p$ for $q, p \in \Z^+$.  A single precision variable must be able to represent integers in
-the range $0 \le x < q \beta$ while a double precision variable must be able to represent integers in the range
-$0 \le x < q \beta^2$.  The extra radix-$q$ factor allows additions and subtractions to proceed without truncation of the
-carry.  Since all modern computers are binary, it is assumed that $q$ is two.
-
-\index{mp\_digit} \index{mp\_word}
-Within the source code that will be presented for each algorithm, the data type \textbf{mp\_digit} will represent
-a single precision integer type, while, the data type \textbf{mp\_word} will represent a double precision integer type.  In
-several algorithms (notably the Comba routines) temporary results will be stored in arrays of double precision mp\_words.
-For the purposes of this text $x_j$ will refer to the $j$'th digit of a single precision array and $\hat x_j$ will refer to
-the $j$'th digit of a double precision array.  Whenever an expression is to be assigned to a double precision
-variable it is assumed that all single precision variables are promoted to double precision during the evaluation.
-Expressions that are assigned to a single precision variable are truncated to fit within the precision of a single
-precision data type.
-
-For example, if $\beta = 10^2$ a single precision data type may represent a value in the
-range $0 \le x < 10^3$, while a double precision data type may represent a value in the range $0 \le x < 10^5$.  Let
-$a = 23$ and $b = 49$ represent two single precision variables.  The single precision product shall be written
-as $c \leftarrow a \cdot b$ while the double precision product shall be written as $\hat c \leftarrow a \cdot b$.
-In this particular case, $\hat c = 1127$ and $c = 127$.  The most significant digit of the product would not fit
-in a single precision data type and as a result $c \ne \hat c$.
-
-\subsection{Algorithm Inputs and Outputs}
-Within the algorithm descriptions all variables are assumed to be scalars of either single or double precision
-as indicated.  The only exception to this rule is when variables have been indicated to be of type mp\_int.  This
-distinction is important as scalars are often used as array indicies and various other counters.
-
-\subsection{Mathematical Expressions}
-The $\lfloor \mbox{ } \rfloor$ brackets imply an expression truncated to an integer not greater than the expression
-itself.  For example, $\lfloor 5.7 \rfloor = 5$.  Similarly the $\lceil \mbox{ } \rceil$ brackets imply an expression
-rounded to an integer not less than the expression itself.  For example, $\lceil 5.1 \rceil = 6$.  Typically when
-the $/$ division symbol is used the intention is to perform an integer division with truncation.  For example,
-$5/2 = 2$ which will often be written as $\lfloor 5/2 \rfloor = 2$ for clarity.  When an expression is written as a
-fraction a real value division is implied, for example ${5 \over 2} = 2.5$.
-
-The norm of a multiple precision integer, for example $\vert \vert x \vert \vert$, will be used to represent the number of digits in the representation
-of the integer.  For example, $\vert \vert 123 \vert \vert = 3$ and $\vert \vert 79452 \vert \vert = 5$.
-
-\subsection{Work Effort}
-\index{big-Oh}
-To measure the efficiency of the specified algorithms, a modified big-Oh notation is used.  In this system all
-single precision operations are considered to have the same cost\footnote{Except where explicitly noted.}.
-That is a single precision addition, multiplication and division are assumed to take the same time to
-complete.  While this is generally not true in practice, it will simplify the discussions considerably.
-
-Some algorithms have slight advantages over others which is why some constants will not be removed in
-the notation.  For example, a normal baseline multiplication (section \ref{sec:basemult}) requires $O(n^2)$ work while a
-baseline squaring (section \ref{sec:basesquare}) requires $O({{n^2 + n}\over 2})$ work.  In standard big-Oh notation these
-would both be said to be equivalent to $O(n^2)$.  However,
-in the context of the this text this is not the case as the magnitude of the inputs will typically be rather small.  As a
-result small constant factors in the work effort will make an observable difference in algorithm efficiency.
-
-All of the algorithms presented in this text have a polynomial time work level.  That is, of the form
-$O(n^k)$ for $n, k \in \Z^{+}$.  This will help make useful comparisons in terms of the speed of the algorithms and how
-various optimizations will help pay off in the long run.
-
-\section{Exercises}
-Within the more advanced chapters a section will be set aside to give the reader some challenging exercises related to
-the discussion at hand.  These exercises are not designed to be prize winning problems, but instead to be thought
-provoking.  Wherever possible the problems are forward minded, stating problems that will be answered in subsequent
-chapters.  The reader is encouraged to finish the exercises as they appear to get a better understanding of the
-subject material.
-
-That being said, the problems are designed to affirm knowledge of a particular subject matter.  Students in particular
-are encouraged to verify they can answer the problems correctly before moving on.
-
-Similar to the exercises of \cite[pp. ix]{TAOCPV2} these exercises are given a scoring system based on the difficulty of
-the problem.  However, unlike \cite{TAOCPV2} the problems do not get nearly as hard.  The scoring of these
-exercises ranges from one (the easiest) to five (the hardest).  The following table sumarizes the
-scoring system used.
-
-\begin{figure}[here]
-\begin{center}
-\begin{small}
-\begin{tabular}{|c|l|}
-\hline $\left [ 1 \right ]$ & An easy problem that should only take the reader a manner of \\
-                            & minutes to solve.  Usually does not involve much computer time \\
-                            & to solve. \\
-\hline $\left [ 2 \right ]$ & An easy problem that involves a marginal amount of computer \\
-                     & time usage.  Usually requires a program to be written to \\
-                     & solve the problem. \\
-\hline $\left [ 3 \right ]$ & A moderately hard problem that requires a non-trivial amount \\
-                     & of work.  Usually involves trivial research and development of \\
-                     & new theory from the perspective of a student. \\
-\hline $\left [ 4 \right ]$ & A moderately hard problem that involves a non-trivial amount \\
-                     & of work and research, the solution to which will demonstrate \\
-                     & a higher mastery of the subject matter. \\
-\hline $\left [ 5 \right ]$ & A hard problem that involves concepts that are difficult for a \\
-                     & novice to solve.  Solutions to these problems will demonstrate a \\
-                     & complete mastery of the given subject. \\
-\hline
-\end{tabular}
-\end{small}
-\end{center}
-\caption{Exercise Scoring System}
-\end{figure}
-
-Problems at the first level are meant to be simple questions that the reader can answer quickly without programming a solution or
-devising new theory.  These problems are quick tests to see if the material is understood.  Problems at the second level
-are also designed to be easy but will require a program or algorithm to be implemented to arrive at the answer.  These
-two levels are essentially entry level questions.
-
-Problems at the third level are meant to be a bit more difficult than the first two levels.  The answer is often
-fairly obvious but arriving at an exacting solution requires some thought and skill.  These problems will almost always
-involve devising a new algorithm or implementing a variation of another algorithm previously presented.  Readers who can
-answer these questions will feel comfortable with the concepts behind the topic at hand.
-
-Problems at the fourth level are meant to be similar to those of the level three questions except they will require
-additional research to be completed.  The reader will most likely not know the answer right away, nor will the text provide
-the exact details of the answer until a subsequent chapter.
-
-Problems at the fifth level are meant to be the hardest
-problems relative to all the other problems in the chapter.  People who can correctly answer fifth level problems have a
-mastery of the subject matter at hand.
-
-Often problems will be tied together.  The purpose of this is to start a chain of thought that will be discussed in future chapters.  The reader
-is encouraged to answer the follow-up problems and try to draw the relevance of problems.
-
-\section{Introduction to LibTomMath}
-
-\subsection{What is LibTomMath?}
-LibTomMath is a free and open source multiple precision integer library written entirely in portable ISO C.  By portable it
-is meant that the library does not contain any code that is computer platform dependent or otherwise problematic to use on
-any given platform.
-
-The library has been successfully tested under numerous operating systems including Unix\footnote{All of these
-trademarks belong to their respective rightful owners.}, MacOS, Windows, Linux, PalmOS and on standalone hardware such
-as the Gameboy Advance.  The library is designed to contain enough functionality to be able to develop applications such
-as public key cryptosystems and still maintain a relatively small footprint.
-
-\subsection{Goals of LibTomMath}
-
-Libraries which obtain the most efficiency are rarely written in a high level programming language such as C.  However,
-even though this library is written entirely in ISO C, considerable care has been taken to optimize the algorithm implementations within the
-library.  Specifically the code has been written to work well with the GNU C Compiler (\textit{GCC}) on both x86 and ARM
-processors.  Wherever possible, highly efficient algorithms, such as Karatsuba multiplication, sliding window
-exponentiation and Montgomery reduction have been provided to make the library more efficient.
-
-Even with the nearly optimal and specialized algorithms that have been included the Application Programing Interface
-(\textit{API}) has been kept as simple as possible.  Often generic place holder routines will make use of specialized
-algorithms automatically without the developer's specific attention.  One such example is the generic multiplication
-algorithm \textbf{mp\_mul()} which will automatically use Toom--Cook, Karatsuba, Comba or baseline multiplication
-based on the magnitude of the inputs and the configuration of the library.
-
-Making LibTomMath as efficient as possible is not the only goal of the LibTomMath project.  Ideally the library should
-be source compatible with another popular library which makes it more attractive for developers to use.  In this case the
-MPI library was used as a API template for all the basic functions.  MPI was chosen because it is another library that fits
-in the same niche as LibTomMath.  Even though LibTomMath uses MPI as the template for the function names and argument
-passing conventions, it has been written from scratch by Tom St Denis.
-
-The project is also meant to act as a learning tool for students, the logic being that no easy-to-follow ``bignum''
-library exists which can be used to teach computer science students how to perform fast and reliable multiple precision
-integer arithmetic.  To this end the source code has been given quite a few comments and algorithm discussion points.
-
-\section{Choice of LibTomMath}
-LibTomMath was chosen as the case study of this text not only because the author of both projects is one and the same but
-for more worthy reasons.  Other libraries such as GMP \cite{GMP}, MPI \cite{MPI}, LIP \cite{LIP} and OpenSSL
-\cite{OPENSSL} have multiple precision integer arithmetic routines but would not be ideal for this text for
-reasons that will be explained in the following sub-sections.
-
-\subsection{Code Base}
-The LibTomMath code base is all portable ISO C source code.  This means that there are no platform dependent conditional
-segments of code littered throughout the source.  This clean and uncluttered approach to the library means that a
-developer can more readily discern the true intent of a given section of source code without trying to keep track of
-what conditional code will be used.
-
-The code base of LibTomMath is well organized.  Each function is in its own separate source code file
-which allows the reader to find a given function very quickly.  On average there are $76$ lines of code per source
-file which makes the source very easily to follow.  By comparison MPI and LIP are single file projects making code tracing
-very hard.  GMP has many conditional code segments which also hinder tracing.
-
-When compiled with GCC for the x86 processor and optimized for speed the entire library is approximately $100$KiB\footnote{The notation ``KiB'' means $2^{10}$ octets, similarly ``MiB'' means $2^{20}$ octets.}
- which is fairly small compared to GMP (over $250$KiB).  LibTomMath is slightly larger than MPI (which compiles to about
-$50$KiB) but LibTomMath is also much faster and more complete than MPI.
-
-\subsection{API Simplicity}
-LibTomMath is designed after the MPI library and shares the API design.  Quite often programs that use MPI will build
-with LibTomMath without change. The function names correlate directly to the action they perform.  Almost all of the
-functions share the same parameter passing convention.  The learning curve is fairly shallow with the API provided
-which is an extremely valuable benefit for the student and developer alike.
-
-The LIP library is an example of a library with an API that is awkward to work with.  LIP uses function names that are often ``compressed'' to
-illegible short hand.  LibTomMath does not share this characteristic.
-
-The GMP library also does not return error codes.  Instead it uses a POSIX.1 \cite{POSIX1} signal system where errors
-are signaled to the host application.  This happens to be the fastest approach but definitely not the most versatile.  In
-effect a math error (i.e. invalid input, heap error, etc) can cause a program to stop functioning which is definitely
-undersireable in many situations.
-
-\subsection{Optimizations}
-While LibTomMath is certainly not the fastest library (GMP often beats LibTomMath by a factor of two) it does
-feature a set of optimal algorithms for tasks such as modular reduction, exponentiation, multiplication and squaring.  GMP
-and LIP also feature such optimizations while MPI only uses baseline algorithms with no optimizations.  GMP lacks a few
-of the additional modular reduction optimizations that LibTomMath features\footnote{At the time of this writing GMP
-only had Barrett and Montgomery modular reduction algorithms.}.
-
-LibTomMath is almost always an order of magnitude faster than the MPI library at computationally expensive tasks such as modular
-exponentiation.  In the grand scheme of ``bignum'' libraries LibTomMath is faster than the average library and usually
-slower than the best libraries such as GMP and OpenSSL by only a small factor.
-
-\subsection{Portability and Stability}
-LibTomMath will build ``out of the box'' on any platform equipped with a modern version of the GNU C Compiler
-(\textit{GCC}).  This means that without changes the library will build without configuration or setting up any
-variables.  LIP and MPI will build ``out of the box'' as well but have numerous known bugs.  Most notably the author of
-MPI has recently stopped working on his library and LIP has long since been discontinued.
-
-GMP requires a configuration script to run and will not build out of the box.   GMP and LibTomMath are still in active
-development and are very stable across a variety of platforms.
-
-\subsection{Choice}
-LibTomMath is a relatively compact, well documented, highly optimized and portable library which seems only natural for
-the case study of this text.  Various source files from the LibTomMath project will be included within the text.  However,
-the reader is encouraged to download their own copy of the library to actually be able to work with the library.
-
-\chapter{Getting Started}
-\section{Library Basics}
-The trick to writing any useful library of source code is to build a solid foundation and work outwards from it.  First,
-a problem along with allowable solution parameters should be identified and analyzed.  In this particular case the
-inability to accomodate multiple precision integers is the problem.  Futhermore, the solution must be written
-as portable source code that is reasonably efficient across several different computer platforms.
-
-After a foundation is formed the remainder of the library can be designed and implemented in a hierarchical fashion.
-That is, to implement the lowest level dependencies first and work towards the most abstract functions last.  For example,
-before implementing a modular exponentiation algorithm one would implement a modular reduction algorithm.
-By building outwards from a base foundation instead of using a parallel design methodology the resulting project is
-highly modular.  Being highly modular is a desirable property of any project as it often means the resulting product
-has a small footprint and updates are easy to perform.
-
-Usually when I start a project I will begin with the header files.  I define the data types I think I will need and
-prototype the initial functions that are not dependent on other functions (within the library).  After I
-implement these base functions I prototype more dependent functions and implement them.   The process repeats until
-I implement all of the functions I require.  For example, in the case of LibTomMath I implemented functions such as
-mp\_init() well before I implemented mp\_mul() and even further before I implemented mp\_exptmod().  As an example as to
-why this design works note that the Karatsuba and Toom-Cook multipliers were written \textit{after} the
-dependent function mp\_exptmod() was written.  Adding the new multiplication algorithms did not require changes to the
-mp\_exptmod() function itself and lowered the total cost of ownership (\textit{so to speak}) and of development
-for new algorithms.  This methodology allows new algorithms to be tested in a complete framework with relative ease.
-
-FIGU,design_process,Design Flow of the First Few Original LibTomMath Functions.
-
-Only after the majority of the functions were in place did I pursue a less hierarchical approach to auditing and optimizing
-the source code.  For example, one day I may audit the multipliers and the next day the polynomial basis functions.
-
-It only makes sense to begin the text with the preliminary data types and support algorithms required as well.
-This chapter discusses the core algorithms of the library which are the dependents for every other algorithm.
-
-\section{What is a Multiple Precision Integer?}
-Recall that most programming languages, in particular ISO C \cite{ISOC}, only have fixed precision data types that on their own cannot
-be used to represent values larger than their precision will allow. The purpose of multiple precision algorithms is
-to use fixed precision data types to create and manipulate multiple precision integers which may represent values
-that are very large.
-
-As a well known analogy, school children are taught how to form numbers larger than nine by prepending more radix ten digits.  In the decimal system
-the largest single digit value is $9$.  However, by concatenating digits together larger numbers may be represented.  Newly prepended digits
-(\textit{to the left}) are said to be in a different power of ten column.  That is, the number $123$ can be described as having a $1$ in the hundreds
-column, $2$ in the tens column and $3$ in the ones column.  Or more formally $123 = 1 \cdot 10^2 + 2 \cdot 10^1 + 3 \cdot 10^0$.  Computer based
-multiple precision arithmetic is essentially the same concept.  Larger integers are represented by adjoining fixed
-precision computer words with the exception that a different radix is used.
-
-What most people probably do not think about explicitly are the various other attributes that describe a multiple precision
-integer.  For example, the integer $154_{10}$ has two immediately obvious properties.  First, the integer is positive,
-that is the sign of this particular integer is positive as opposed to negative.  Second, the integer has three digits in
-its representation.  There is an additional property that the integer posesses that does not concern pencil-and-paper
-arithmetic.  The third property is how many digits placeholders are available to hold the integer.
-
-The human analogy of this third property is ensuring there is enough space on the paper to write the integer.  For example,
-if one starts writing a large number too far to the right on a piece of paper they will have to erase it and move left.
-Similarly, computer algorithms must maintain strict control over memory usage to ensure that the digits of an integer
-will not exceed the allowed boundaries.  These three properties make up what is known as a multiple precision
-integer or mp\_int for short.
-
-\subsection{The mp\_int Structure}
-\label{sec:MPINT}
-The mp\_int structure is the ISO C based manifestation of what represents a multiple precision integer.  The ISO C standard does not provide for
-any such data type but it does provide for making composite data types known as structures.  The following is the structure definition
-used within LibTomMath.
-
-\index{mp\_int}
-\begin{figure}[here]
-\begin{center}
-\begin{small}
-%\begin{verbatim}
-\begin{tabular}{|l|}
-\hline
-typedef struct \{ \\
-\hspace{3mm}int used, alloc, sign;\\
-\hspace{3mm}mp\_digit *dp;\\
-\} \textbf{mp\_int}; \\
-\hline
-\end{tabular}
-%\end{verbatim}
-\end{small}
-\caption{The mp\_int Structure}
-\label{fig:mpint}
-\end{center}
-\end{figure}
-
-The mp\_int structure (fig. \ref{fig:mpint}) can be broken down as follows.
-
-\begin{enumerate}
-\item The \textbf{used} parameter denotes how many digits of the array \textbf{dp} contain the digits used to represent
-a given integer.  The \textbf{used} count must be positive (or zero) and may not exceed the \textbf{alloc} count.
-
-\item The \textbf{alloc} parameter denotes how
-many digits are available in the array to use by functions before it has to increase in size.  When the \textbf{used} count
-of a result would exceed the \textbf{alloc} count all of the algorithms will automatically increase the size of the
-array to accommodate the precision of the result.
-
-\item The pointer \textbf{dp} points to a dynamically allocated array of digits that represent the given multiple
-precision integer.  It is padded with $(\textbf{alloc} - \textbf{used})$ zero digits.  The array is maintained in a least
-significant digit order.  As a pencil and paper analogy the array is organized such that the right most digits are stored
-first starting at the location indexed by zero\footnote{In C all arrays begin at zero.} in the array.  For example,
-if \textbf{dp} contains $\lbrace a, b, c, \ldots \rbrace$ where \textbf{dp}$_0 = a$, \textbf{dp}$_1 = b$, \textbf{dp}$_2 = c$, $\ldots$ then
-it would represent the integer $a + b\beta + c\beta^2 + \ldots$
-
-\index{MP\_ZPOS} \index{MP\_NEG}
-\item The \textbf{sign} parameter denotes the sign as either zero/positive (\textbf{MP\_ZPOS}) or negative (\textbf{MP\_NEG}).
-\end{enumerate}
-
-\subsubsection{Valid mp\_int Structures}
-Several rules are placed on the state of an mp\_int structure and are assumed to be followed for reasons of efficiency.
-The only exceptions are when the structure is passed to initialization functions such as mp\_init() and mp\_init\_copy().
-
-\begin{enumerate}
-\item The value of \textbf{alloc} may not be less than one.  That is \textbf{dp} always points to a previously allocated
-array of digits.
-\item The value of \textbf{used} may not exceed \textbf{alloc} and must be greater than or equal to zero.
-\item The value of \textbf{used} implies the digit at index $(used - 1)$ of the \textbf{dp} array is non-zero.  That is,
-leading zero digits in the most significant positions must be trimmed.
-   \begin{enumerate}
-   \item Digits in the \textbf{dp} array at and above the \textbf{used} location must be zero.
-   \end{enumerate}
-\item The value of \textbf{sign} must be \textbf{MP\_ZPOS} if \textbf{used} is zero;
-this represents the mp\_int value of zero.
-\end{enumerate}
-
-\section{Argument Passing}
-A convention of argument passing must be adopted early on in the development of any library.  Making the function
-prototypes consistent will help eliminate many headaches in the future as the library grows to significant complexity.
-In LibTomMath the multiple precision integer functions accept parameters from left to right as pointers to mp\_int
-structures.  That means that the source (input) operands are placed on the left and the destination (output) on the right.
-Consider the following examples.
-
-\begin{verbatim}
-   mp_mul(&a, &b, &c);   /* c = a * b */
-   mp_add(&a, &b, &a);   /* a = a + b */
-   mp_sqr(&a, &b);       /* b = a * a */
-\end{verbatim}
-
-The left to right order is a fairly natural way to implement the functions since it lets the developer read aloud the
-functions and make sense of them.  For example, the first function would read ``multiply a and b and store in c''.
-
-Certain libraries (\textit{LIP by Lenstra for instance}) accept parameters the other way around, to mimic the order
-of assignment expressions.  That is, the destination (output) is on the left and arguments (inputs) are on the right.  In
-truth, it is entirely a matter of preference.  In the case of LibTomMath the convention from the MPI library has been
-adopted.
-
-Another very useful design consideration, provided for in LibTomMath, is whether to allow argument sources to also be a
-destination.  For example, the second example (\textit{mp\_add}) adds $a$ to $b$ and stores in $a$.  This is an important
-feature to implement since it allows the calling functions to cut down on the number of variables it must maintain.
-However, to implement this feature specific care has to be given to ensure the destination is not modified before the
-source is fully read.
-
-\section{Return Values}
-A well implemented application, no matter what its purpose, should trap as many runtime errors as possible and return them
-to the caller.  By catching runtime errors a library can be guaranteed to prevent undefined behaviour.  However, the end
-developer can still manage to cause a library to crash.  For example, by passing an invalid pointer an application may
-fault by dereferencing memory not owned by the application.
-
-In the case of LibTomMath the only errors that are checked for are related to inappropriate inputs (division by zero for
-instance) and memory allocation errors.  It will not check that the mp\_int passed to any function is valid nor
-will it check pointers for validity.  Any function that can cause a runtime error will return an error code as an
-\textbf{int} data type with one of the following values (fig \ref{fig:errcodes}).
-
-\index{MP\_OKAY} \index{MP\_VAL} \index{MP\_MEM}
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{|l|l|}
-\hline \textbf{Value} & \textbf{Meaning} \\
-\hline \textbf{MP\_OKAY} & The function was successful \\
-\hline \textbf{MP\_VAL}  & One of the input value(s) was invalid \\
-\hline \textbf{MP\_MEM}  & The function ran out of heap memory \\
-\hline
-\end{tabular}
-\end{center}
-\caption{LibTomMath Error Codes}
-\label{fig:errcodes}
-\end{figure}
-
-When an error is detected within a function it should free any memory it allocated, often during the initialization of
-temporary mp\_ints, and return as soon as possible.  The goal is to leave the system in the same state it was when the
-function was called.  Error checking with this style of API is fairly simple.
-
-\begin{verbatim}
-   int err;
-   if ((err = mp_add(&a, &b, &c)) != MP_OKAY) {
-      printf("Error: %s\n", mp_error_to_string(err));
-      exit(EXIT_FAILURE);
-   }
-\end{verbatim}
-
-The GMP \cite{GMP} library uses C style \textit{signals} to flag errors which is of questionable use.  Not all errors are fatal
-and it was not deemed ideal by the author of LibTomMath to force developers to have signal handlers for such cases.
-
-\section{Initialization and Clearing}
-The logical starting point when actually writing multiple precision integer functions is the initialization and
-clearing of the mp\_int structures.  These two algorithms will be used by the majority of the higher level algorithms.
-
-Given the basic mp\_int structure an initialization routine must first allocate memory to hold the digits of
-the integer.  Often it is optimal to allocate a sufficiently large pre-set number of digits even though
-the initial integer will represent zero.  If only a single digit were allocated quite a few subsequent re-allocations
-would occur when operations are performed on the integers.  There is a tradeoff between how many default digits to allocate
-and how many re-allocations are tolerable.  Obviously allocating an excessive amount of digits initially will waste
-memory and become unmanageable.
-
-If the memory for the digits has been successfully allocated then the rest of the members of the structure must
-be initialized.  Since the initial state of an mp\_int is to represent the zero integer, the allocated digits must be set
-to zero.  The \textbf{used} count set to zero and \textbf{sign} set to \textbf{MP\_ZPOS}.
-
-\subsection{Initializing an mp\_int}
-An mp\_int is said to be initialized if it is set to a valid, preferably default, state such that all of the members of the
-structure are set to valid values.  The mp\_init algorithm will perform such an action.
-
-\index{mp\_init}
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_init}. \\
-\textbf{Input}.   An mp\_int $a$ \\
-\textbf{Output}.  Allocate memory and initialize $a$ to a known valid mp\_int state.  \\
-\hline \\
-1.  Allocate memory for \textbf{MP\_PREC} digits. \\
-2.  If the allocation failed return(\textit{MP\_MEM}) \\
-3.  for $n$ from $0$ to $MP\_PREC - 1$ do  \\
-\hspace{3mm}3.1  $a_n \leftarrow 0$\\
-4.  $a.sign \leftarrow MP\_ZPOS$\\
-5.  $a.used \leftarrow 0$\\
-6.  $a.alloc \leftarrow MP\_PREC$\\
-7.  Return(\textit{MP\_OKAY})\\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_init}
-\end{figure}
-
-\textbf{Algorithm mp\_init.}
-The purpose of this function is to initialize an mp\_int structure so that the rest of the library can properly
-manipulte it.  It is assumed that the input may not have had any of its members previously initialized which is certainly
-a valid assumption if the input resides on the stack.
-
-Before any of the members such as \textbf{sign}, \textbf{used} or \textbf{alloc} are initialized the memory for
-the digits is allocated.  If this fails the function returns before setting any of the other members.  The \textbf{MP\_PREC}
-name represents a constant\footnote{Defined in the ``tommath.h'' header file within LibTomMath.}
-used to dictate the minimum precision of newly initialized mp\_int integers.  Ideally, it is at least equal to the smallest
-precision number you'll be working with.
-
-Allocating a block of digits at first instead of a single digit has the benefit of lowering the number of usually slow
-heap operations later functions will have to perform in the future.  If \textbf{MP\_PREC} is set correctly the slack
-memory and the number of heap operations will be trivial.
-
-Once the allocation has been made the digits have to be set to zero as well as the \textbf{used}, \textbf{sign} and
-\textbf{alloc} members initialized.  This ensures that the mp\_int will always represent the default state of zero regardless
-of the original condition of the input.
-
-\textbf{Remark.}
-This function introduces the idiosyncrasy that all iterative loops, commonly initiated with the ``for'' keyword, iterate incrementally
-when the ``to'' keyword is placed between two expressions.  For example, ``for $a$ from $b$ to $c$ do'' means that
-a subsequent expression (or body of expressions) are to be evaluated upto $c - b$ times so long as $b \le c$.  In each
-iteration the variable $a$ is substituted for a new integer that lies inclusively between $b$ and $c$.  If $b > c$ occured
-the loop would not iterate.  By contrast if the ``downto'' keyword were used in place of ``to'' the loop would iterate
-decrementally.
-
-EXAM,bn_mp_init.c
-
-One immediate observation of this initializtion function is that it does not return a pointer to a mp\_int structure.  It
-is assumed that the caller has already allocated memory for the mp\_int structure, typically on the application stack.  The
-call to mp\_init() is used only to initialize the members of the structure to a known default state.
-
-Here we see (line @23,XMALLOC@) the memory allocation is performed first.  This allows us to exit cleanly and quickly
-if there is an error.  If the allocation fails the routine will return \textbf{MP\_MEM} to the caller to indicate there
-was a memory error.  The function XMALLOC is what actually allocates the memory.  Technically XMALLOC is not a function
-but a macro defined in ``tommath.h``.  By default, XMALLOC will evaluate to malloc() which is the C library's built--in
-memory allocation routine.
-
-In order to assure the mp\_int is in a known state the digits must be set to zero.  On most platforms this could have been
-accomplished by using calloc() instead of malloc().  However,  to correctly initialize a integer type to a given value in a
-portable fashion you have to actually assign the value.  The for loop (line @28,for@) performs this required
-operation.
-
-After the memory has been successfully initialized the remainder of the members are initialized
-(lines @29,used@ through @31,sign@) to their respective default states.  At this point the algorithm has succeeded and
-a success code is returned to the calling function.  If this function returns \textbf{MP\_OKAY} it is safe to assume the
-mp\_int structure has been properly initialized and is safe to use with other functions within the library.
-
-\subsection{Clearing an mp\_int}
-When an mp\_int is no longer required by the application, the memory that has been allocated for its digits must be
-returned to the application's memory pool with the mp\_clear algorithm.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_clear}. \\
-\textbf{Input}.   An mp\_int $a$ \\
-\textbf{Output}.  The memory for $a$ shall be deallocated.  \\
-\hline \\
-1.  If $a$ has been previously freed then return(\textit{MP\_OKAY}). \\
-2.  for $n$ from 0 to $a.used - 1$ do \\
-\hspace{3mm}2.1  $a_n \leftarrow 0$ \\
-3.  Free the memory allocated for the digits of $a$. \\
-4.  $a.used \leftarrow 0$ \\
-5.  $a.alloc \leftarrow 0$ \\
-6.  $a.sign \leftarrow MP\_ZPOS$ \\
-7.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_clear}
-\end{figure}
-
-\textbf{Algorithm mp\_clear.}
-This algorithm accomplishes two goals.  First, it clears the digits and the other mp\_int members.  This ensures that
-if a developer accidentally re-uses a cleared structure it is less likely to cause problems.  The second goal
-is to free the allocated memory.
-
-The logic behind the algorithm is extended by marking cleared mp\_int structures so that subsequent calls to this
-algorithm will not try to free the memory multiple times.  Cleared mp\_ints are detectable by having a pre-defined invalid
-digit pointer \textbf{dp} setting.
-
-Once an mp\_int has been cleared the mp\_int structure is no longer in a valid state for any other algorithm
-with the exception of algorithms mp\_init, mp\_init\_copy, mp\_init\_size and mp\_clear.
-
-EXAM,bn_mp_clear.c
-
-The algorithm only operates on the mp\_int if it hasn't been previously cleared.  The if statement (line @23,a->dp != NULL@)
-checks to see if the \textbf{dp} member is not \textbf{NULL}.  If the mp\_int is a valid mp\_int then \textbf{dp} cannot be
-\textbf{NULL} in which case the if statement will evaluate to true.
-
-The digits of the mp\_int are cleared by the for loop (line @25,for@) which assigns a zero to every digit.  Similar to mp\_init()
-the digits are assigned zero instead of using block memory operations (such as memset()) since this is more portable.
-
-The digits are deallocated off the heap via the XFREE macro.  Similar to XMALLOC the XFREE macro actually evaluates to
-a standard C library function.  In this case the free() function.  Since free() only deallocates the memory the pointer
-still has to be reset to \textbf{NULL} manually (line @33,NULL@).
-
-Now that the digits have been cleared and deallocated the other members are set to their final values (lines @34,= 0@ and @35,ZPOS@).
-
-\section{Maintenance Algorithms}
-
-The previous sections describes how to initialize and clear an mp\_int structure.  To further support operations
-that are to be performed on mp\_int structures (such as addition and multiplication) the dependent algorithms must be
-able to augment the precision of an mp\_int and
-initialize mp\_ints with differing initial conditions.
-
-These algorithms complete the set of low level algorithms required to work with mp\_int structures in the higher level
-algorithms such as addition, multiplication and modular exponentiation.
-
-\subsection{Augmenting an mp\_int's Precision}
-When storing a value in an mp\_int structure, a sufficient number of digits must be available to accomodate the entire
-result of an operation without loss of precision.  Quite often the size of the array given by the \textbf{alloc} member
-is large enough to simply increase the \textbf{used} digit count.  However, when the size of the array is too small it
-must be re-sized appropriately to accomodate the result.  The mp\_grow algorithm will provide this functionality.
-
-\newpage\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_grow}. \\
-\textbf{Input}.   An mp\_int $a$ and an integer $b$. \\
-\textbf{Output}.  $a$ is expanded to accomodate $b$ digits. \\
-\hline \\
-1.  if $a.alloc \ge b$ then return(\textit{MP\_OKAY}) \\
-2.  $u \leftarrow b\mbox{ (mod }MP\_PREC\mbox{)}$ \\
-3.  $v \leftarrow b + 2 \cdot MP\_PREC - u$ \\
-4.  Re-allocate the array of digits $a$ to size $v$ \\
-5.  If the allocation failed then return(\textit{MP\_MEM}). \\
-6.  for n from a.alloc to $v - 1$ do  \\
-\hspace{+3mm}6.1  $a_n \leftarrow 0$ \\
-7.  $a.alloc \leftarrow v$ \\
-8.  Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_grow}
-\end{figure}
-
-\textbf{Algorithm mp\_grow.}
-It is ideal to prevent re-allocations from being performed if they are not required (step one).  This is useful to
-prevent mp\_ints from growing excessively in code that erroneously calls mp\_grow.
-
-The requested digit count is padded up to next multiple of \textbf{MP\_PREC} plus an additional \textbf{MP\_PREC} (steps two and three).
-This helps prevent many trivial reallocations that would grow an mp\_int by trivially small values.
-
-It is assumed that the reallocation (step four) leaves the lower $a.alloc$ digits of the mp\_int intact.  This is much
-akin to how the \textit{realloc} function from the standard C library works.  Since the newly allocated digits are
-assumed to contain undefined values they are initially set to zero.
-
-EXAM,bn_mp_grow.c
-
-A quick optimization is to first determine if a memory re-allocation is required at all.  The if statement (line @24,alloc@) checks
-if the \textbf{alloc} member of the mp\_int is smaller than the requested digit count.  If the count is not larger than \textbf{alloc}
-the function skips the re-allocation part thus saving time.
-
-When a re-allocation is performed it is turned into an optimal request to save time in the future.  The requested digit count is
-padded upwards to 2nd multiple of \textbf{MP\_PREC} larger than \textbf{alloc} (line @25, size@).  The XREALLOC function is used
-to re-allocate the memory.  As per the other functions XREALLOC is actually a macro which evaluates to realloc by default.  The realloc
-function leaves the base of the allocation intact which means the first \textbf{alloc} digits of the mp\_int are the same as before
-the re-allocation.  All	that is left is to clear the newly allocated digits and return.
-
-Note that the re-allocation result is actually stored in a temporary pointer $tmp$.  This is to allow this function to return
-an error with a valid pointer.  Earlier releases of the library stored the result of XREALLOC into the mp\_int $a$.  That would
-result in a memory leak if XREALLOC ever failed.
-
-\subsection{Initializing Variable Precision mp\_ints}
-Occasionally the number of digits required will be known in advance of an initialization, based on, for example, the size
-of input mp\_ints to a given algorithm.  The purpose of algorithm mp\_init\_size is similar to mp\_init except that it
-will allocate \textit{at least} a specified number of digits.
-
-\begin{figure}[here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_init\_size}. \\
-\textbf{Input}.   An mp\_int $a$ and the requested number of digits $b$. \\
-\textbf{Output}.  $a$ is initialized to hold at least $b$ digits. \\
-\hline \\
-1.  $u \leftarrow b \mbox{ (mod }MP\_PREC\mbox{)}$ \\
-2.  $v \leftarrow b + 2 \cdot MP\_PREC - u$ \\
-3.  Allocate $v$ digits. \\
-4.  for $n$ from $0$ to $v - 1$ do \\
-\hspace{3mm}4.1  $a_n \leftarrow 0$ \\
-5.  $a.sign \leftarrow MP\_ZPOS$\\
-6.  $a.used \leftarrow 0$\\
-7.  $a.alloc \leftarrow v$\\
-8.  Return(\textit{MP\_OKAY})\\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_init\_size}
-\end{figure}
-
-\textbf{Algorithm mp\_init\_size.}
-This algorithm will initialize an mp\_int structure $a$ like algorithm mp\_init with the exception that the number of
-digits allocated can be controlled by the second input argument $b$.  The input size is padded upwards so it is a
-multiple of \textbf{MP\_PREC} plus an additional \textbf{MP\_PREC} digits.  This padding is used to prevent trivial
-allocations from becoming a bottleneck in the rest of the algorithms.
-
-Like algorithm mp\_init, the mp\_int structure is initialized to a default state representing the integer zero.  This
-particular algorithm is useful if it is known ahead of time the approximate size of the input.  If the approximation is
-correct no further memory re-allocations are required to work with the mp\_int.
-
-EXAM,bn_mp_init_size.c
-
-The number of digits $b$ requested is padded (line @22,MP_PREC@) by first augmenting it to the next multiple of
-\textbf{MP\_PREC} and then adding \textbf{MP\_PREC} to the result.  If the memory can be successfully allocated the
-mp\_int is placed in a default state representing the integer zero.  Otherwise, the error code \textbf{MP\_MEM} will be
-returned (line @27,return@).
-
-The digits are allocated with the malloc() function (line @27,XMALLOC@) and set to zero afterwards (line @38,for@).  The
-\textbf{used} count is set to zero, the \textbf{alloc} count set to the padded digit count and the \textbf{sign} flag set
-to \textbf{MP\_ZPOS} to achieve a default valid mp\_int state (lines @29,used@, @30,alloc@ and @31,sign@).  If the function
-returns succesfully then it is correct to assume that the mp\_int structure is in a valid state for the remainder of the
-functions to work with.
-
-\subsection{Multiple Integer Initializations and Clearings}
-Occasionally a function will require a series of mp\_int data types to be made available simultaneously.
-The purpose of algorithm mp\_init\_multi is to initialize a variable length array of mp\_int structures in a single
-statement.  It is essentially a shortcut to multiple initializations.
-
-\newpage\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_init\_multi}. \\
-\textbf{Input}.   Variable length array $V_k$ of mp\_int variables of length $k$. \\
-\textbf{Output}.  The array is initialized such that each mp\_int of $V_k$ is ready to use. \\
-\hline \\
-1.  for $n$ from 0 to $k - 1$ do \\
-\hspace{+3mm}1.1.  Initialize the mp\_int $V_n$ (\textit{mp\_init}) \\
-\hspace{+3mm}1.2.  If initialization failed then do \\
-\hspace{+6mm}1.2.1.  for $j$ from $0$ to $n$ do \\
-\hspace{+9mm}1.2.1.1.  Free the mp\_int $V_j$ (\textit{mp\_clear}) \\
-\hspace{+6mm}1.2.2.   Return(\textit{MP\_MEM}) \\
-2.  Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_init\_multi}
-\end{figure}
-
-\textbf{Algorithm mp\_init\_multi.}
-The algorithm will initialize the array of mp\_int variables one at a time.  If a runtime error has been detected
-(\textit{step 1.2}) all of the previously initialized variables are cleared.  The goal is an ``all or nothing''
-initialization which allows for quick recovery from runtime errors.
-
-EXAM,bn_mp_init_multi.c
-
-This function intializes a variable length list of mp\_int structure pointers.  However, instead of having the mp\_int
-structures in an actual C array they are simply passed as arguments to the function.  This function makes use of the
-``...'' argument syntax of the C programming language.  The list is terminated with a final \textbf{NULL} argument
-appended on the right.
-
-The function uses the ``stdarg.h'' \textit{va} functions to step portably through the arguments to the function.  A count
-$n$ of succesfully initialized mp\_int structures is maintained (line @47,n++@) such that if a failure does occur,
-the algorithm can backtrack and free the previously initialized structures (lines @27,if@ to @46,}@).
-
-
-\subsection{Clamping Excess Digits}
-When a function anticipates a result will be $n$ digits it is simpler to assume this is true within the body of
-the function instead of checking during the computation.  For example, a multiplication of a $i$ digit number by a
-$j$ digit produces a result of at most $i + j$ digits.  It is entirely possible that the result is $i + j - 1$
-though, with no final carry into the last position.  However, suppose the destination had to be first expanded
-(\textit{via mp\_grow}) to accomodate $i + j - 1$ digits than further expanded to accomodate the final carry.
-That would be a considerable waste of time since heap operations are relatively slow.
-
-The ideal solution is to always assume the result is $i + j$ and fix up the \textbf{used} count after the function
-terminates.  This way a single heap operation (\textit{at most}) is required.  However, if the result was not checked
-there would be an excess high order zero digit.
-
-For example, suppose the product of two integers was $x_n = (0x_{n-1}x_{n-2}...x_0)_{\beta}$.  The leading zero digit
-will not contribute to the precision of the result.  In fact, through subsequent operations more leading zero digits would
-accumulate to the point the size of the integer would be prohibitive.  As a result even though the precision is very
-low the representation is excessively large.
-
-The mp\_clamp algorithm is designed to solve this very problem.  It will trim high-order zeros by decrementing the
-\textbf{used} count until a non-zero most significant digit is found.  Also in this system, zero is considered to be a
-positive number which means that if the \textbf{used} count is decremented to zero, the sign must be set to
-\textbf{MP\_ZPOS}.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_clamp}. \\
-\textbf{Input}.   An mp\_int $a$ \\
-\textbf{Output}.  Any excess leading zero digits of $a$ are removed \\
-\hline \\
-1.  while $a.used > 0$ and $a_{a.used - 1} = 0$ do \\
-\hspace{+3mm}1.1  $a.used \leftarrow a.used - 1$ \\
-2.  if $a.used = 0$ then do \\
-\hspace{+3mm}2.1  $a.sign \leftarrow MP\_ZPOS$ \\
-\hline \\
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_clamp}
-\end{figure}
-
-\textbf{Algorithm mp\_clamp.}
-As can be expected this algorithm is very simple.  The loop on step one is expected to iterate only once or twice at
-the most.  For example, this will happen in cases where there is not a carry to fill the last position.  Step two fixes the sign for
-when all of the digits are zero to ensure that the mp\_int is valid at all times.
-
-EXAM,bn_mp_clamp.c
-
-Note on line @27,while@ how to test for the \textbf{used} count is made on the left of the \&\& operator.  In the C programming
-language the terms to \&\& are evaluated left to right with a boolean short-circuit if any condition fails.  This is
-important since if the \textbf{used} is zero the test on the right would fetch below the array.  That is obviously
-undesirable.  The parenthesis on line @28,a->used@ is used to make sure the \textbf{used} count is decremented and not
-the pointer ``a''.
-
-\section*{Exercises}
-\begin{tabular}{cl}
-$\left [ 1 \right ]$ & Discuss the relevance of the \textbf{used} member of the mp\_int structure. \\
-                     & \\
-$\left [ 1 \right ]$ & Discuss the consequences of not using padding when performing allocations.  \\
-                     & \\
-$\left [ 2 \right ]$ & Estimate an ideal value for \textbf{MP\_PREC} when performing 1024-bit RSA \\
-                     & encryption when $\beta = 2^{28}$.  \\
-                     & \\
-$\left [ 1 \right ]$ & Discuss the relevance of the algorithm mp\_clamp.  What does it prevent? \\
-                     & \\
-$\left [ 1 \right ]$ & Give an example of when the algorithm  mp\_init\_copy might be useful. \\
-                     & \\
-\end{tabular}
-
-
-%%%
-% CHAPTER FOUR
-%%%
-
-\chapter{Basic Operations}
-
-\section{Introduction}
-In the previous chapter a series of low level algorithms were established that dealt with initializing and maintaining
-mp\_int structures.  This chapter will discuss another set of seemingly non-algebraic algorithms which will form the low
-level basis of the entire library.  While these algorithm are relatively trivial it is important to understand how they
-work before proceeding since these algorithms will be used almost intrinsically in the following chapters.
-
-The algorithms in this chapter deal primarily with more ``programmer'' related tasks such as creating copies of
-mp\_int structures, assigning small values to mp\_int structures and comparisons of the values mp\_int structures
-represent.
-
-\section{Assigning Values to mp\_int Structures}
-\subsection{Copying an mp\_int}
-Assigning the value that a given mp\_int structure represents to another mp\_int structure shall be known as making
-a copy for the purposes of this text.  The copy of the mp\_int will be a separate entity that represents the same
-value as the mp\_int it was copied from.  The mp\_copy algorithm provides this functionality.
-
-\newpage\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_copy}. \\
-\textbf{Input}.  An mp\_int $a$ and $b$. \\
-\textbf{Output}.  Store a copy of $a$ in $b$. \\
-\hline \\
-1.  If $b.alloc < a.used$ then grow $b$ to $a.used$ digits.  (\textit{mp\_grow}) \\
-2.  for $n$ from 0 to $a.used - 1$ do \\
-\hspace{3mm}2.1  $b_{n} \leftarrow a_{n}$ \\
-3.  for $n$ from $a.used$ to $b.used - 1$ do \\
-\hspace{3mm}3.1  $b_{n} \leftarrow 0$ \\
-4.  $b.used \leftarrow a.used$ \\
-5.  $b.sign \leftarrow a.sign$ \\
-6.  return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_copy}
-\end{figure}
-
-\textbf{Algorithm mp\_copy.}
-This algorithm copies the mp\_int $a$ such that upon succesful termination of the algorithm the mp\_int $b$ will
-represent the same integer as the mp\_int $a$.  The mp\_int $b$ shall be a complete and distinct copy of the
-mp\_int $a$ meaing that the mp\_int $a$ can be modified and it shall not affect the value of the mp\_int $b$.
-
-If $b$ does not have enough room for the digits of $a$ it must first have its precision augmented via the mp\_grow
-algorithm.  The digits of $a$ are copied over the digits of $b$ and any excess digits of $b$ are set to zero (step two
-and three).  The \textbf{used} and \textbf{sign} members of $a$ are finally copied over the respective members of
-$b$.
-
-\textbf{Remark.}  This algorithm also introduces a new idiosyncrasy that will be used throughout the rest of the
-text.  The error return codes of other algorithms are not explicitly checked in the pseudo-code presented.  For example, in
-step one of the mp\_copy algorithm the return of mp\_grow is not explicitly checked to ensure it succeeded.  Text space is
-limited so it is assumed that if a algorithm fails it will clear all temporarily allocated mp\_ints and return
-the error code itself.  However, the C code presented will demonstrate all of the error handling logic required to
-implement the pseudo-code.
-
-EXAM,bn_mp_copy.c
-
-Occasionally a dependent algorithm may copy an mp\_int effectively into itself such as when the input and output
-mp\_int structures passed to a function are one and the same.  For this case it is optimal to return immediately without
-copying digits (line @24,a == b@).
-
-The mp\_int $b$ must have enough digits to accomodate the used digits of the mp\_int $a$.  If $b.alloc$ is less than
-$a.used$ the algorithm mp\_grow is used to augment the precision of $b$ (lines @29,alloc@ to @33,}@).  In order to
-simplify the inner loop that copies the digits from $a$ to $b$, two aliases $tmpa$ and $tmpb$ point directly at the digits
-of the mp\_ints $a$ and $b$ respectively.  These aliases (lines @42,tmpa@ and @45,tmpb@) allow the compiler to access the digits without first dereferencing the
-mp\_int pointers and then subsequently the pointer to the digits.
-
-After the aliases are established the digits from $a$ are copied into $b$ (lines @48,for@ to @50,}@) and then the excess
-digits of $b$ are set to zero (lines @53,for@ to @55,}@).  Both ``for'' loops make use of the pointer aliases and in
-fact the alias for $b$ is carried through into the second ``for'' loop to clear the excess digits.  This optimization
-allows the alias to stay in a machine register fairly easy between the two loops.
-
-\textbf{Remarks.}  The use of pointer aliases is an implementation methodology first introduced in this function that will
-be used considerably in other functions.  Technically, a pointer alias is simply a short hand alias used to lower the
-number of pointer dereferencing operations required to access data.  For example, a for loop may resemble
-
-\begin{alltt}
-for (x = 0; x < 100; x++) \{
-    a->num[4]->dp[x] = 0;
-\}
-\end{alltt}
-
-This could be re-written using aliases as
-
-\begin{alltt}
-mp_digit *tmpa;
-a = a->num[4]->dp;
-for (x = 0; x < 100; x++) \{
-    *a++ = 0;
-\}
-\end{alltt}
-
-In this case an alias is used to access the
-array of digits within an mp\_int structure directly.  It may seem that a pointer alias is strictly not required
-as a compiler may optimize out the redundant pointer operations.  However, there are two dominant reasons to use aliases.
-
-The first reason is that most compilers will not effectively optimize pointer arithmetic.  For example, some optimizations
-may work for the Microsoft Visual C++ compiler (MSVC) and not for the GNU C Compiler (GCC).  Also some optimizations may
-work for GCC and not MSVC.  As such it is ideal to find a common ground for as many compilers as possible.  Pointer
-aliases optimize the code considerably before the compiler even reads the source code which means the end compiled code
-stands a better chance of being faster.
-
-The second reason is that pointer aliases often can make an algorithm simpler to read.  Consider the first ``for''
-loop of the function mp\_copy() re-written to not use pointer aliases.
-
-\begin{alltt}
-    /* copy all the digits */
-    for (n = 0; n < a->used; n++) \{
-      b->dp[n] = a->dp[n];
-    \}
-\end{alltt}
-
-Whether this code is harder to read depends strongly on the individual.  However, it is quantifiably slightly more
-complicated as there are four variables within the statement instead of just two.
-
-\subsubsection{Nested Statements}
-Another commonly used technique in the source routines is that certain sections of code are nested.  This is used in
-particular with the pointer aliases to highlight code phases.  For example, a Comba multiplier (discussed in chapter six)
-will typically have three different phases.  First the temporaries are initialized, then the columns calculated and
-finally the carries are propagated.  In this example the middle column production phase will typically be nested as it
-uses temporary variables and aliases the most.
-
-The nesting also simplies the source code as variables that are nested are only valid for their scope.  As a result
-the various temporary variables required do not propagate into other sections of code.
-
-
-\subsection{Creating a Clone}
-Another common operation is to make a local temporary copy of an mp\_int argument.  To initialize an mp\_int
-and then copy another existing mp\_int into the newly intialized mp\_int will be known as creating a clone.  This is
-useful within functions that need to modify an argument but do not wish to actually modify the original copy.  The
-mp\_init\_copy algorithm has been designed to help perform this task.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_init\_copy}. \\
-\textbf{Input}.   An mp\_int $a$ and $b$\\
-\textbf{Output}.  $a$ is initialized to be a copy of $b$. \\
-\hline \\
-1.  Init $a$.  (\textit{mp\_init}) \\
-2.  Copy $b$ to $a$.  (\textit{mp\_copy}) \\
-3.  Return the status of the copy operation. \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_init\_copy}
-\end{figure}
-
-\textbf{Algorithm mp\_init\_copy.}
-This algorithm will initialize an mp\_int variable and copy another previously initialized mp\_int variable into it.  As
-such this algorithm will perform two operations in one step.
-
-EXAM,bn_mp_init_copy.c
-
-This will initialize \textbf{a} and make it a verbatim copy of the contents of \textbf{b}.  Note that
-\textbf{a} will have its own memory allocated which means that \textbf{b} may be cleared after the call
-and \textbf{a} will be left intact.
-
-\section{Zeroing an Integer}
-Reseting an mp\_int to the default state is a common step in many algorithms.  The mp\_zero algorithm will be the algorithm used to
-perform this task.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_zero}. \\
-\textbf{Input}.   An mp\_int $a$ \\
-\textbf{Output}.  Zero the contents of $a$ \\
-\hline \\
-1.  $a.used \leftarrow 0$ \\
-2.  $a.sign \leftarrow$ MP\_ZPOS \\
-3.  for $n$ from 0 to $a.alloc - 1$ do \\
-\hspace{3mm}3.1  $a_n \leftarrow 0$ \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_zero}
-\end{figure}
-
-\textbf{Algorithm mp\_zero.}
-This algorithm simply resets a mp\_int to the default state.
-
-EXAM,bn_mp_zero.c
-
-After the function is completed, all of the digits are zeroed, the \textbf{used} count is zeroed and the
-\textbf{sign} variable is set to \textbf{MP\_ZPOS}.
-
-\section{Sign Manipulation}
-\subsection{Absolute Value}
-With the mp\_int representation of an integer, calculating the absolute value is trivial.  The mp\_abs algorithm will compute
-the absolute value of an mp\_int.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_abs}. \\
-\textbf{Input}.   An mp\_int $a$ \\
-\textbf{Output}.  Computes $b = \vert a \vert$ \\
-\hline \\
-1.  Copy $a$ to $b$.  (\textit{mp\_copy}) \\
-2.  If the copy failed return(\textit{MP\_MEM}). \\
-3.  $b.sign \leftarrow MP\_ZPOS$ \\
-4.  Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_abs}
-\end{figure}
-
-\textbf{Algorithm mp\_abs.}
-This algorithm computes the absolute of an mp\_int input.  First it copies $a$ over $b$.  This is an example of an
-algorithm where the check in mp\_copy that determines if the source and destination are equal proves useful.  This allows,
-for instance, the developer to pass the same mp\_int as the source and destination to this function without addition
-logic to handle it.
-
-EXAM,bn_mp_abs.c
-
-This fairly trivial algorithm first eliminates non--required duplications (line @27,a != b@) and then sets the
-\textbf{sign} flag to \textbf{MP\_ZPOS}.
-
-\subsection{Integer Negation}
-With the mp\_int representation of an integer, calculating the negation is also trivial.  The mp\_neg algorithm will compute
-the negative of an mp\_int input.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_neg}. \\
-\textbf{Input}.   An mp\_int $a$ \\
-\textbf{Output}.  Computes $b = -a$ \\
-\hline \\
-1.  Copy $a$ to $b$.  (\textit{mp\_copy}) \\
-2.  If the copy failed return(\textit{MP\_MEM}). \\
-3.  If $a.used = 0$ then return(\textit{MP\_OKAY}). \\
-4.  If $a.sign = MP\_ZPOS$ then do \\
-\hspace{3mm}4.1  $b.sign = MP\_NEG$. \\
-5.  else do \\
-\hspace{3mm}5.1  $b.sign = MP\_ZPOS$. \\
-6.  Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_neg}
-\end{figure}
-
-\textbf{Algorithm mp\_neg.}
-This algorithm computes the negation of an input.  First it copies $a$ over $b$.  If $a$ has no used digits then
-the algorithm returns immediately.  Otherwise it flips the sign flag and stores the result in $b$.  Note that if
-$a$ had no digits then it must be positive by definition.  Had step three been omitted then the algorithm would return
-zero as negative.
-
-EXAM,bn_mp_neg.c
-
-Like mp\_abs() this function avoids non--required duplications (line @21,a != b@) and then sets the sign.  We
-have to make sure that only non--zero values get a \textbf{sign} of \textbf{MP\_NEG}.  If the mp\_int is zero
-than the \textbf{sign} is hard--coded to \textbf{MP\_ZPOS}.
-
-\section{Small Constants}
-\subsection{Setting Small Constants}
-Often a mp\_int must be set to a relatively small value such as $1$ or $2$.  For these cases the mp\_set algorithm is useful.
-
-\newpage\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_set}. \\
-\textbf{Input}.   An mp\_int $a$ and a digit $b$ \\
-\textbf{Output}.  Make $a$ equivalent to $b$ \\
-\hline \\
-1.  Zero $a$ (\textit{mp\_zero}). \\
-2.  $a_0 \leftarrow b \mbox{ (mod }\beta\mbox{)}$ \\
-3.  $a.used \leftarrow  \left \lbrace \begin{array}{ll}
-                              1 &  \mbox{if }a_0 > 0 \\
-                              0 &  \mbox{if }a_0 = 0
-                              \end{array} \right .$ \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_set}
-\end{figure}
-
-\textbf{Algorithm mp\_set.}
-This algorithm sets a mp\_int to a small single digit value.  Step number 1 ensures that the integer is reset to the default state.  The
-single digit is set (\textit{modulo $\beta$}) and the \textbf{used} count is adjusted accordingly.
-
-EXAM,bn_mp_set.c
-
-First we zero (line @21,mp_zero@) the mp\_int to make sure that the other members are initialized for a
-small positive constant.  mp\_zero() ensures that the \textbf{sign} is positive and the \textbf{used} count
-is zero.  Next we set the digit and reduce it modulo $\beta$ (line @22,MP_MASK@).  After this step we have to
-check if the resulting digit is zero or not.  If it is not then we set the \textbf{used} count to one, otherwise
-to zero.
-
-We can quickly reduce modulo $\beta$ since it is of the form $2^k$ and a quick binary AND operation with
-$2^k - 1$ will perform the same operation.
-
-One important limitation of this function is that it will only set one digit.  The size of a digit is not fixed, meaning source that uses
-this function should take that into account.  Only trivially small constants can be set using this function.
-
-\subsection{Setting Large Constants}
-To overcome the limitations of the mp\_set algorithm the mp\_set\_int algorithm is ideal.  It accepts a ``long''
-data type as input and will always treat it as a 32-bit integer.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_set\_int}. \\
-\textbf{Input}.   An mp\_int $a$ and a ``long'' integer $b$ \\
-\textbf{Output}.  Make $a$ equivalent to $b$ \\
-\hline \\
-1.  Zero $a$ (\textit{mp\_zero}) \\
-2.  for $n$ from 0 to 7 do \\
-\hspace{3mm}2.1  $a \leftarrow a \cdot 16$ (\textit{mp\_mul2d}) \\
-\hspace{3mm}2.2  $u \leftarrow \lfloor b / 2^{4(7 - n)} \rfloor \mbox{ (mod }16\mbox{)}$\\
-\hspace{3mm}2.3  $a_0 \leftarrow a_0 + u$ \\
-\hspace{3mm}2.4  $a.used \leftarrow a.used + 1$ \\
-3.  Clamp excess used digits (\textit{mp\_clamp}) \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_set\_int}
-\end{figure}
-
-\textbf{Algorithm mp\_set\_int.}
-The algorithm performs eight iterations of a simple loop where in each iteration four bits from the source are added to the
-mp\_int.  Step 2.1 will multiply the current result by sixteen making room for four more bits in the less significant positions.  In step 2.2 the
-next four bits from the source are extracted and are added to the mp\_int. The \textbf{used} digit count is
-incremented to reflect the addition.  The \textbf{used} digit counter is incremented since if any of the leading digits were zero the mp\_int would have
-zero digits used and the newly added four bits would be ignored.
-
-Excess zero digits are trimmed in steps 2.1 and 3 by using higher level algorithms mp\_mul2d and mp\_clamp.
-
-EXAM,bn_mp_set_int.c
-
-This function sets four bits of the number at a time to handle all practical \textbf{DIGIT\_BIT} sizes.  The weird
-addition on line @38,a->used@ ensures that the newly added in bits are added to the number of digits.  While it may not
-seem obvious as to why the digit counter does not grow exceedingly large it is because of the shift on line @27,mp_mul_2d@
-as well as the  call to mp\_clamp() on line @40,mp_clamp@.  Both functions will clamp excess leading digits which keeps
-the number of used digits low.
-
-\section{Comparisons}
-\subsection{Unsigned Comparisions}
-Comparing a multiple precision integer is performed with the exact same algorithm used to compare two decimal numbers.  For example,
-to compare $1,234$ to $1,264$ the digits are extracted by their positions.  That is we compare $1 \cdot 10^3 + 2 \cdot 10^2 + 3 \cdot 10^1 + 4 \cdot 10^0$
-to $1 \cdot 10^3 + 2 \cdot 10^2 + 6 \cdot 10^1 + 4 \cdot 10^0$ by comparing single digits at a time starting with the highest magnitude
-positions.  If any leading digit of one integer is greater than a digit in the same position of another integer then obviously it must be greater.
-
-The first comparision routine that will be developed is the unsigned magnitude compare which will perform a comparison based on the digits of two
-mp\_int variables alone.  It will ignore the sign of the two inputs.  Such a function is useful when an absolute comparison is required or if the
-signs are known to agree in advance.
-
-To facilitate working with the results of the comparison functions three constants are required.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{|r|l|}
-\hline \textbf{Constant} & \textbf{Meaning} \\
-\hline \textbf{MP\_GT} & Greater Than \\
-\hline \textbf{MP\_EQ} & Equal To \\
-\hline \textbf{MP\_LT} & Less Than \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Comparison Return Codes}
-\end{figure}
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_cmp\_mag}. \\
-\textbf{Input}.   Two mp\_ints $a$ and $b$.  \\
-\textbf{Output}.  Unsigned comparison results ($a$ to the left of $b$). \\
-\hline \\
-1.  If $a.used > b.used$ then return(\textit{MP\_GT}) \\
-2.  If $a.used < b.used$ then return(\textit{MP\_LT}) \\
-3.  for n from $a.used - 1$ to 0 do \\
-\hspace{+3mm}3.1  if $a_n > b_n$ then return(\textit{MP\_GT}) \\
-\hspace{+3mm}3.2  if $a_n < b_n$ then return(\textit{MP\_LT}) \\
-4.  Return(\textit{MP\_EQ}) \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_cmp\_mag}
-\end{figure}
-
-\textbf{Algorithm mp\_cmp\_mag.}
-By saying ``$a$ to the left of $b$'' it is meant that the comparison is with respect to $a$, that is if $a$ is greater than $b$ it will return
-\textbf{MP\_GT} and similar with respect to when $a = b$ and $a < b$.  The first two steps compare the number of digits used in both $a$ and $b$.
-Obviously if the digit counts differ there would be an imaginary zero digit in the smaller number where the leading digit of the larger number is.
-If both have the same number of digits than the actual digits themselves must be compared starting at the leading digit.
-
-By step three both inputs must have the same number of digits so its safe to start from either $a.used - 1$ or $b.used - 1$ and count down to
-the zero'th digit.  If after all of the digits have been compared, no difference is found, the algorithm returns \textbf{MP\_EQ}.
-
-EXAM,bn_mp_cmp_mag.c
-
-The two if statements (lines @24,if@ and @28,if@) compare the number of digits in the two inputs.  These two are
-performed before all of the digits are compared since it is a very cheap test to perform and can potentially save
-considerable time.  The implementation given is also not valid without those two statements.  $b.alloc$ may be
-smaller than $a.used$, meaning that undefined values will be read from $b$ past the end of the array of digits.
-
-
-
-\subsection{Signed Comparisons}
-Comparing with sign considerations is also fairly critical in several routines (\textit{division for example}).  Based on an unsigned magnitude
-comparison a trivial signed comparison algorithm can be written.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_cmp}. \\
-\textbf{Input}.   Two mp\_ints $a$ and $b$ \\
-\textbf{Output}.  Signed Comparison Results ($a$ to the left of $b$) \\
-\hline \\
-1.  if $a.sign = MP\_NEG$ and $b.sign = MP\_ZPOS$ then return(\textit{MP\_LT}) \\
-2.  if $a.sign = MP\_ZPOS$ and $b.sign = MP\_NEG$ then return(\textit{MP\_GT}) \\
-3.  if $a.sign = MP\_NEG$ then \\
-\hspace{+3mm}3.1  Return the unsigned comparison of $b$ and $a$ (\textit{mp\_cmp\_mag}) \\
-4   Otherwise \\
-\hspace{+3mm}4.1  Return the unsigned comparison of $a$ and $b$ \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_cmp}
-\end{figure}
-
-\textbf{Algorithm mp\_cmp.}
-The first two steps compare the signs of the two inputs.  If the signs do not agree then it can return right away with the appropriate
-comparison code.  When the signs are equal the digits of the inputs must be compared to determine the correct result.  In step
-three the unsigned comparision flips the order of the arguments since they are both negative.  For instance, if $-a > -b$ then
-$\vert a \vert < \vert b \vert$.  Step number four will compare the two when they are both positive.
-
-EXAM,bn_mp_cmp.c
-
-The two if statements (lines @22,if@ and @26,if@) perform the initial sign comparison.  If the signs are not the equal then which ever
-has the positive sign is larger.   The inputs are compared (line @30,if@) based on magnitudes.  If the signs were both
-negative then the unsigned comparison is performed in the opposite direction (line @31,mp_cmp_mag@).  Otherwise, the signs are assumed to
-be both positive and a forward direction unsigned comparison is performed.
-
-\section*{Exercises}
-\begin{tabular}{cl}
-$\left [ 2 \right ]$ & Modify algorithm mp\_set\_int to accept as input a variable length array of bits. \\
-                     & \\
-$\left [ 3 \right ]$ & Give the probability that algorithm mp\_cmp\_mag will have to compare $k$ digits  \\
-                     & of two random digits (of equal magnitude) before a difference is found. \\
-                     & \\
-$\left [ 1 \right ]$ & Suggest a simple method to speed up the implementation of mp\_cmp\_mag based  \\
-                     & on the observations made in the previous problem. \\
-                     &
-\end{tabular}
-
-\chapter{Basic Arithmetic}
-\section{Introduction}
-At this point algorithms for initialization, clearing, zeroing, copying, comparing and setting small constants have been
-established.  The next logical set of algorithms to develop are addition, subtraction and digit shifting algorithms.  These
-algorithms make use of the lower level algorithms and are the cruicial building block for the multiplication algorithms.  It is very important
-that these algorithms are highly optimized.  On their own they are simple $O(n)$ algorithms but they can be called from higher level algorithms
-which easily places them at $O(n^2)$ or even $O(n^3)$ work levels.
-
-MARK,SHIFTS
-All of the algorithms within this chapter make use of the logical bit shift operations denoted by $<<$ and $>>$ for left and right
-logical shifts respectively.  A logical shift is analogous to sliding the decimal point of radix-10 representations.  For example, the real
-number $0.9345$ is equivalent to $93.45\%$ which is found by sliding the the decimal two places to the right (\textit{multiplying by $\beta^2 = 10^2$}).
-Algebraically a binary logical shift is equivalent to a division or multiplication by a power of two.
-For example, $a << k = a \cdot 2^k$ while $a >> k = \lfloor a/2^k \rfloor$.
-
-One significant difference between a logical shift and the way decimals are shifted is that digits below the zero'th position are removed
-from the number.  For example, consider $1101_2 >> 1$ using decimal notation this would produce $110.1_2$.  However, with a logical shift the
-result is $110_2$.
-
-\section{Addition and Subtraction}
-In common twos complement fixed precision arithmetic negative numbers are easily represented by subtraction from the modulus.  For example, with 32-bit integers
-$a - b\mbox{ (mod }2^{32}\mbox{)}$ is the same as $a + (2^{32} - b) \mbox{ (mod }2^{32}\mbox{)}$  since $2^{32} \equiv 0 \mbox{ (mod }2^{32}\mbox{)}$.
-As a result subtraction can be performed with a trivial series of logical operations and an addition.
-
-However, in multiple precision arithmetic negative numbers are not represented in the same way.  Instead a sign flag is used to keep track of the
-sign of the integer.  As a result signed addition and subtraction are actually implemented as conditional usage of lower level addition or
-subtraction algorithms with the sign fixed up appropriately.
-
-The lower level algorithms will add or subtract integers without regard to the sign flag.  That is they will add or subtract the magnitude of
-the integers respectively.
-
-\subsection{Low Level Addition}
-An unsigned addition of multiple precision integers is performed with the same long-hand algorithm used to add decimal numbers.  That is to add the
-trailing digits first and propagate the resulting carry upwards.  Since this is a lower level algorithm the name will have a ``s\_'' prefix.
-Historically that convention stems from the MPI library where ``s\_'' stood for static functions that were hidden from the developer entirely.
-
-\newpage
-\begin{figure}[!here]
-\begin{center}
-\begin{small}
-\begin{tabular}{l}
-\hline Algorithm \textbf{s\_mp\_add}. \\
-\textbf{Input}.   Two mp\_ints $a$ and $b$ \\
-\textbf{Output}.  The unsigned addition $c = \vert a \vert + \vert b \vert$. \\
-\hline \\
-1.  if $a.used > b.used$ then \\
-\hspace{+3mm}1.1  $min \leftarrow b.used$ \\
-\hspace{+3mm}1.2  $max \leftarrow a.used$ \\
-\hspace{+3mm}1.3  $x   \leftarrow a$ \\
-2.  else  \\
-\hspace{+3mm}2.1  $min \leftarrow a.used$ \\
-\hspace{+3mm}2.2  $max \leftarrow b.used$ \\
-\hspace{+3mm}2.3  $x   \leftarrow b$ \\
-3.  If $c.alloc < max + 1$ then grow $c$ to hold at least $max + 1$ digits (\textit{mp\_grow}) \\
-4.  $oldused \leftarrow c.used$ \\
-5.  $c.used \leftarrow max + 1$ \\
-6.  $u \leftarrow 0$ \\
-7.  for $n$ from $0$ to $min - 1$ do \\
-\hspace{+3mm}7.1  $c_n \leftarrow a_n + b_n + u$ \\
-\hspace{+3mm}7.2  $u \leftarrow c_n >> lg(\beta)$ \\
-\hspace{+3mm}7.3  $c_n \leftarrow c_n \mbox{ (mod }\beta\mbox{)}$ \\
-8.  if $min \ne max$ then do \\
-\hspace{+3mm}8.1  for $n$ from $min$ to $max - 1$ do \\
-\hspace{+6mm}8.1.1  $c_n \leftarrow x_n + u$ \\
-\hspace{+6mm}8.1.2  $u \leftarrow c_n >> lg(\beta)$ \\
-\hspace{+6mm}8.1.3  $c_n \leftarrow c_n \mbox{ (mod }\beta\mbox{)}$ \\
-9.  $c_{max} \leftarrow u$ \\
-10.  if $olduse > max$ then \\
-\hspace{+3mm}10.1  for $n$ from $max + 1$ to $oldused - 1$ do \\
-\hspace{+6mm}10.1.1  $c_n \leftarrow 0$ \\
-11.  Clamp excess digits in $c$.  (\textit{mp\_clamp}) \\
-12.  Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{small}
-\end{center}
-\caption{Algorithm s\_mp\_add}
-\end{figure}
-
-\textbf{Algorithm s\_mp\_add.}
-This algorithm is loosely based on algorithm 14.7 of HAC \cite[pp. 594]{HAC} but has been extended to allow the inputs to have different magnitudes.
-Coincidentally the description of algorithm A in Knuth \cite[pp. 266]{TAOCPV2} shares the same deficiency as the algorithm from \cite{HAC}.  Even the
-MIX pseudo  machine code presented by Knuth \cite[pp. 266-267]{TAOCPV2} is incapable of handling inputs which are of different magnitudes.
-
-The first thing that has to be accomplished is to sort out which of the two inputs is the largest.  The addition logic
-will simply add all of the smallest input to the largest input and store that first part of the result in the
-destination.  Then it will apply a simpler addition loop to excess digits of the larger input.
-
-The first two steps will handle sorting the inputs such that $min$ and $max$ hold the digit counts of the two
-inputs.  The variable $x$ will be an mp\_int alias for the largest input or the second input $b$ if they have the
-same number of digits.  After the inputs are sorted the destination $c$ is grown as required to accomodate the sum
-of the two inputs.  The original \textbf{used} count of $c$ is copied and set to the new used count.
-
-At this point the first addition loop will go through as many digit positions that both inputs have.  The carry
-variable $\mu$ is set to zero outside the loop.  Inside the loop an ``addition'' step requires three statements to produce
-one digit of the summand.  First
-two digits from $a$ and $b$ are added together along with the carry $\mu$.  The carry of this step is extracted and stored
-in $\mu$ and finally the digit of the result $c_n$ is truncated within the range $0 \le c_n < \beta$.
-
-Now all of the digit positions that both inputs have in common have been exhausted.  If $min \ne max$ then $x$ is an alias
-for one of the inputs that has more digits.  A simplified addition loop is then used to essentially copy the remaining digits
-and the carry to the destination.
-
-The final carry is stored in $c_{max}$ and digits above $max$ upto $oldused$ are zeroed which completes the addition.
-
-
-EXAM,bn_s_mp_add.c
-
-We first sort (lines @27,if@ to @35,}@) the inputs based on magnitude and determine the $min$ and $max$ variables.
-Note that $x$ is a pointer to an mp\_int assigned to the largest input, in effect it is a local alias.  Next we
-grow the destination (@37,init@ to @42,}@) ensure that it can accomodate the result of the addition.
-
-Similar to the implementation of mp\_copy this function uses the braced code and local aliases coding style.  The three aliases that are on
-lines @56,tmpa@, @59,tmpb@ and @62,tmpc@ represent the two inputs and destination variables respectively.  These aliases are used to ensure the
-compiler does not have to dereference $a$, $b$ or $c$ (respectively) to access the digits of the respective mp\_int.
-
-The initial carry $u$ will be cleared (line @65,u = 0@), note that $u$ is of type mp\_digit which ensures type
-compatibility within the implementation.  The initial addition (line @66,for@ to @75,}@) adds digits from
-both inputs until the smallest input runs out of digits.  Similarly the conditional addition loop
-(line @81,for@ to @90,}@) adds the remaining digits from the larger of the two inputs.  The addition is finished
-with the final carry being stored in $tmpc$ (line @94,tmpc++@).  Note the ``++'' operator within the same expression.
-After line @94,tmpc++@, $tmpc$ will point to the $c.used$'th digit of the mp\_int $c$.  This is useful
-for the next loop (line @97,for@ to @99,}@) which set any old upper digits to zero.
-
-\subsection{Low Level Subtraction}
-The low level unsigned subtraction algorithm is very similar to the low level unsigned addition algorithm.  The principle difference is that the
-unsigned subtraction algorithm requires the result to be positive.  That is when computing $a - b$ the condition $\vert a \vert \ge \vert b\vert$ must
-be met for this algorithm to function properly.  Keep in mind this low level algorithm is not meant to be used in higher level algorithms directly.
-This algorithm as will be shown can be used to create functional signed addition and subtraction algorithms.
-
-MARK,GAMMA
-
-For this algorithm a new variable is required to make the description simpler.  Recall from section 1.3.1 that a mp\_digit must be able to represent
-the range $0 \le x < 2\beta$ for the algorithms to work correctly.  However, it is allowable that a mp\_digit represent a larger range of values.  For
-this algorithm we will assume that the variable $\gamma$ represents the number of bits available in a
-mp\_digit (\textit{this implies $2^{\gamma} > \beta$}).
-
-For example, the default for LibTomMath is to use a ``unsigned long'' for the mp\_digit ``type'' while $\beta = 2^{28}$.  In ISO C an ``unsigned long''
-data type must be able to represent $0 \le x < 2^{32}$ meaning that in this case $\gamma \ge 32$.
-
-\newpage\begin{figure}[!here]
-\begin{center}
-\begin{small}
-\begin{tabular}{l}
-\hline Algorithm \textbf{s\_mp\_sub}. \\
-\textbf{Input}.   Two mp\_ints $a$ and $b$ ($\vert a \vert \ge \vert b \vert$) \\
-\textbf{Output}.  The unsigned subtraction $c = \vert a \vert - \vert b \vert$. \\
-\hline \\
-1.  $min \leftarrow b.used$ \\
-2.  $max \leftarrow a.used$ \\
-3.  If $c.alloc < max$ then grow $c$ to hold at least $max$ digits.  (\textit{mp\_grow}) \\
-4.  $oldused \leftarrow c.used$ \\
-5.  $c.used \leftarrow max$ \\
-6.  $u \leftarrow 0$ \\
-7.  for $n$ from $0$ to $min - 1$ do \\
-\hspace{3mm}7.1  $c_n \leftarrow a_n - b_n - u$ \\
-\hspace{3mm}7.2  $u   \leftarrow c_n >> (\gamma - 1)$ \\
-\hspace{3mm}7.3  $c_n \leftarrow c_n \mbox{ (mod }\beta\mbox{)}$ \\
-8.  if $min < max$ then do \\
-\hspace{3mm}8.1  for $n$ from $min$ to $max - 1$ do \\
-\hspace{6mm}8.1.1  $c_n \leftarrow a_n - u$ \\
-\hspace{6mm}8.1.2  $u   \leftarrow c_n >> (\gamma - 1)$ \\
-\hspace{6mm}8.1.3  $c_n \leftarrow c_n \mbox{ (mod }\beta\mbox{)}$ \\
-9. if $oldused > max$ then do \\
-\hspace{3mm}9.1  for $n$ from $max$ to $oldused - 1$ do \\
-\hspace{6mm}9.1.1  $c_n \leftarrow 0$ \\
-10. Clamp excess digits of $c$.  (\textit{mp\_clamp}). \\
-11. Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{small}
-\end{center}
-\caption{Algorithm s\_mp\_sub}
-\end{figure}
-
-\textbf{Algorithm s\_mp\_sub.}
-This algorithm performs the unsigned subtraction of two mp\_int variables under the restriction that the result must be positive.  That is when
-passing variables $a$ and $b$ the condition that $\vert a \vert \ge \vert b \vert$ must be met for the algorithm to function correctly.  This
-algorithm is loosely based on algorithm 14.9 \cite[pp. 595]{HAC} and is similar to algorithm S in \cite[pp. 267]{TAOCPV2} as well.  As was the case
-of the algorithm s\_mp\_add both other references lack discussion concerning various practical details such as when the inputs differ in magnitude.
-
-The initial sorting of the inputs is trivial in this algorithm since $a$ is guaranteed to have at least the same magnitude of $b$.  Steps 1 and 2
-set the $min$ and $max$ variables.  Unlike the addition routine there is guaranteed to be no carry which means that the final result can be at
-most $max$ digits in length as opposed to $max + 1$.  Similar to the addition algorithm the \textbf{used} count of $c$ is copied locally and
-set to the maximal count for the operation.
-
-The subtraction loop that begins on step seven is essentially the same as the addition loop of algorithm s\_mp\_add except single precision
-subtraction is used instead.  Note the use of the $\gamma$ variable to extract the carry (\textit{also known as the borrow}) within the subtraction
-loops.  Under the assumption that two's complement single precision arithmetic is used this will successfully extract the desired carry.
-
-For example, consider subtracting $0101_2$ from $0100_2$ where $\gamma = 4$ and $\beta = 2$.  The least significant bit will force a carry upwards to
-the third bit which will be set to zero after the borrow.  After the very first bit has been subtracted $4 - 1 \equiv 0011_2$ will remain,  When the
-third bit of $0101_2$ is subtracted from the result it will cause another carry.  In this case though the carry will be forced to propagate all the
-way to the most significant bit.
-
-Recall that $\beta < 2^{\gamma}$.  This means that if a carry does occur just before the $lg(\beta)$'th bit it will propagate all the way to the most
-significant bit.  Thus, the high order bits of the mp\_digit that are not part of the actual digit will either be all zero, or all one. All that
-is needed is a single zero or one bit for the carry.  Therefore a single logical shift right by $\gamma - 1$ positions is sufficient to extract the
-carry.  This method of carry extraction may seem awkward but the reason for it becomes apparent when the implementation is discussed.
-
-If $b$ has a smaller magnitude than $a$ then step 9 will force the carry and copy operation to propagate through the larger input $a$ into $c$.  Step
-10 will ensure that any leading digits of $c$ above the $max$'th position are zeroed.
-
-EXAM,bn_s_mp_sub.c
-
-Like low level addition we ``sort'' the inputs.  Except in this case the sorting is hardcoded
-(lines @24,min@ and @25,max@).  In reality the $min$ and $max$ variables are only aliases and are only
-used to make the source code easier to read.  Again the pointer alias optimization is used
-within this algorithm.  The aliases $tmpa$, $tmpb$ and $tmpc$ are initialized
-(lines @42,tmpa@, @43,tmpb@ and @44,tmpc@) for $a$, $b$ and $c$ respectively.
-
-The first subtraction loop (lines @47,u = 0@ through @61,}@) subtract digits from both inputs until the smaller of
-the two inputs has been exhausted.  As remarked earlier there is an implementation reason for using the ``awkward''
-method of extracting the carry (line @57, >>@).  The traditional method for extracting the carry would be to shift
-by $lg(\beta)$ positions and logically AND the least significant bit.  The AND operation is required because all of
-the bits above the $\lg(\beta)$'th bit will be set to one after a carry occurs from subtraction.  This carry
-extraction requires two relatively cheap operations to extract the carry.  The other method is to simply shift the
-most significant bit to the least significant bit thus extracting the carry with a single cheap operation.  This
-optimization only works on twos compliment machines which is a safe assumption to make.
-
-If $a$ has a larger magnitude than $b$ an additional loop (lines @64,for@ through @73,}@) is required to propagate
-the carry through $a$ and copy the result to $c$.
-
-\subsection{High Level Addition}
-Now that both lower level addition and subtraction algorithms have been established an effective high level signed addition algorithm can be
-established.  This high level addition algorithm will be what other algorithms and developers will use to perform addition of mp\_int data
-types.
-
-Recall from section 5.2 that an mp\_int represents an integer with an unsigned mantissa (\textit{the array of digits}) and a \textbf{sign}
-flag.  A high level addition is actually performed as a series of eight separate cases which can be optimized down to three unique cases.
-
-\begin{figure}[!here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_add}. \\
-\textbf{Input}.   Two mp\_ints $a$ and $b$  \\
-\textbf{Output}.  The signed addition $c = a + b$. \\
-\hline \\
-1.  if $a.sign = b.sign$ then do \\
-\hspace{3mm}1.1  $c.sign \leftarrow a.sign$  \\
-\hspace{3mm}1.2  $c \leftarrow \vert a \vert + \vert b \vert$ (\textit{s\_mp\_add})\\
-2.  else do \\
-\hspace{3mm}2.1  if $\vert a \vert < \vert b \vert$ then do (\textit{mp\_cmp\_mag})  \\
-\hspace{6mm}2.1.1  $c.sign \leftarrow b.sign$ \\
-\hspace{6mm}2.1.2  $c \leftarrow \vert b \vert - \vert a \vert$ (\textit{s\_mp\_sub}) \\
-\hspace{3mm}2.2  else do \\
-\hspace{6mm}2.2.1  $c.sign \leftarrow a.sign$ \\
-\hspace{6mm}2.2.2  $c \leftarrow \vert a \vert - \vert b \vert$ \\
-3.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_add}
-\end{figure}
-
-\textbf{Algorithm mp\_add.}
-This algorithm performs the signed addition of two mp\_int variables.  There is no reference algorithm to draw upon from
-either \cite{TAOCPV2} or \cite{HAC} since they both only provide unsigned operations.  The algorithm is fairly
-straightforward but restricted since subtraction can only produce positive results.
-
-\begin{figure}[here]
-\begin{small}
-\begin{center}
-\begin{tabular}{|c|c|c|c|c|}
-\hline \textbf{Sign of $a$} & \textbf{Sign of $b$} & \textbf{$\vert a \vert > \vert b \vert $} & \textbf{Unsigned Operation} & \textbf{Result Sign Flag} \\
-\hline $+$ & $+$ & Yes & $c = a + b$ & $a.sign$ \\
-\hline $+$ & $+$ & No  & $c = a + b$ & $a.sign$ \\
-\hline $-$ & $-$ & Yes & $c = a + b$ & $a.sign$ \\
-\hline $-$ & $-$ & No  & $c = a + b$ & $a.sign$ \\
-\hline &&&&\\
-
-\hline $+$ & $-$ & No  & $c = b - a$ & $b.sign$ \\
-\hline $-$ & $+$ & No  & $c = b - a$ & $b.sign$ \\
-
-\hline &&&&\\
-
-\hline $+$ & $-$ & Yes & $c = a - b$ & $a.sign$ \\
-\hline $-$ & $+$ & Yes & $c = a - b$ & $a.sign$ \\
-
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Addition Guide Chart}
-\label{fig:AddChart}
-\end{figure}
-
-Figure~\ref{fig:AddChart} lists all of the eight possible input combinations and is sorted to show that only three
-specific cases need to be handled.  The return code of the unsigned operations at step 1.2, 2.1.2 and 2.2.2 are
-forwarded to step three to check for errors.  This simplifies the description of the algorithm considerably and best
-follows how the implementation actually was achieved.
-
-Also note how the \textbf{sign} is set before the unsigned addition or subtraction is performed.  Recall from the descriptions of algorithms
-s\_mp\_add and s\_mp\_sub that the mp\_clamp function is used at the end to trim excess digits.  The mp\_clamp algorithm will set the \textbf{sign}
-to \textbf{MP\_ZPOS} when the \textbf{used} digit count reaches zero.
-
-For example, consider performing $-a + a$ with algorithm mp\_add.  By the description of the algorithm the sign is set to \textbf{MP\_NEG} which would
-produce a result of $-0$.  However, since the sign is set first then the unsigned addition is performed the subsequent usage of algorithm mp\_clamp
-within algorithm s\_mp\_add will force $-0$ to become $0$.
-
-EXAM,bn_mp_add.c
-
-The source code follows the algorithm fairly closely.  The most notable new source code addition is the usage of the $res$ integer variable which
-is used to pass result of the unsigned operations forward.  Unlike in the algorithm, the variable $res$ is merely returned as is without
-explicitly checking it and returning the constant \textbf{MP\_OKAY}.  The observation is this algorithm will succeed or fail only if the lower
-level functions do so.  Returning their return code is sufficient.
-
-\subsection{High Level Subtraction}
-The high level signed subtraction algorithm is essentially the same as the high level signed addition algorithm.
-
-\newpage\begin{figure}[!here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_sub}. \\
-\textbf{Input}.   Two mp\_ints $a$ and $b$  \\
-\textbf{Output}.  The signed subtraction $c = a - b$. \\
-\hline \\
-1.  if $a.sign \ne b.sign$ then do \\
-\hspace{3mm}1.1  $c.sign \leftarrow a.sign$ \\
-\hspace{3mm}1.2  $c \leftarrow \vert a \vert + \vert b \vert$ (\textit{s\_mp\_add}) \\
-2.  else do \\
-\hspace{3mm}2.1  if $\vert a \vert \ge \vert b \vert$ then do (\textit{mp\_cmp\_mag}) \\
-\hspace{6mm}2.1.1  $c.sign \leftarrow a.sign$ \\
-\hspace{6mm}2.1.2  $c \leftarrow \vert a \vert  - \vert b \vert$ (\textit{s\_mp\_sub}) \\
-\hspace{3mm}2.2  else do \\
-\hspace{6mm}2.2.1  $c.sign \leftarrow  \left \lbrace \begin{array}{ll}
-                              MP\_ZPOS &  \mbox{if }a.sign = MP\_NEG \\
-                              MP\_NEG  &  \mbox{otherwise} \\
-                              \end{array} \right .$ \\
-\hspace{6mm}2.2.2  $c \leftarrow \vert b \vert  - \vert a \vert$ \\
-3.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_sub}
-\end{figure}
-
-\textbf{Algorithm mp\_sub.}
-This algorithm performs the signed subtraction of two inputs.  Similar to algorithm mp\_add there is no reference in either \cite{TAOCPV2} or
-\cite{HAC}.  Also this algorithm is restricted by algorithm s\_mp\_sub.  Chart \ref{fig:SubChart} lists the eight possible inputs and
-the operations required.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{|c|c|c|c|c|}
-\hline \textbf{Sign of $a$} & \textbf{Sign of $b$} & \textbf{$\vert a \vert \ge \vert b \vert $} & \textbf{Unsigned Operation} & \textbf{Result Sign Flag} \\
-\hline $+$ & $-$ & Yes & $c = a + b$ & $a.sign$ \\
-\hline $+$ & $-$ & No  & $c = a + b$ & $a.sign$ \\
-\hline $-$ & $+$ & Yes & $c = a + b$ & $a.sign$ \\
-\hline $-$ & $+$ & No  & $c = a + b$ & $a.sign$ \\
-\hline &&&& \\
-\hline $+$ & $+$ & Yes & $c = a - b$ & $a.sign$ \\
-\hline $-$ & $-$ & Yes & $c = a - b$ & $a.sign$ \\
-\hline &&&& \\
-\hline $+$ & $+$ & No  & $c = b - a$ & $\mbox{opposite of }a.sign$ \\
-\hline $-$ & $-$ & No  & $c = b - a$ & $\mbox{opposite of }a.sign$ \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Subtraction Guide Chart}
-\label{fig:SubChart}
-\end{figure}
-
-Similar to the case of algorithm mp\_add the \textbf{sign} is set first before the unsigned addition or subtraction.  That is to prevent the
-algorithm from producing $-a - -a = -0$ as a result.
-
-EXAM,bn_mp_sub.c
-
-Much like the implementation of algorithm mp\_add the variable $res$ is used to catch the return code of the unsigned addition or subtraction operations
-and forward it to the end of the function.  On line @38, != MP_LT@ the ``not equal to'' \textbf{MP\_LT} expression is used to emulate a
-``greater than or equal to'' comparison.
-
-\section{Bit and Digit Shifting}
-MARK,POLY
-It is quite common to think of a multiple precision integer as a polynomial in $x$, that is $y = f(\beta)$ where $f(x) = \sum_{i=0}^{n-1} a_i x^i$.
-This notation arises within discussion of Montgomery and Diminished Radix Reduction as well as Karatsuba multiplication and squaring.
-
-In order to facilitate operations on polynomials in $x$ as above a series of simple ``digit'' algorithms have to be established.  That is to shift
-the digits left or right as well to shift individual bits of the digits left and right.  It is important to note that not all ``shift'' operations
-are on radix-$\beta$ digits.
-
-\subsection{Multiplication by Two}
-
-In a binary system where the radix is a power of two multiplication by two not only arises often in other algorithms it is a fairly efficient
-operation to perform.  A single precision logical shift left is sufficient to multiply a single digit by two.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_mul\_2}. \\
-\textbf{Input}.   One mp\_int $a$ \\
-\textbf{Output}.  $b = 2a$. \\
-\hline \\
-1.  If $b.alloc < a.used + 1$ then grow $b$ to hold $a.used + 1$ digits.  (\textit{mp\_grow}) \\
-2.  $oldused \leftarrow b.used$ \\
-3.  $b.used \leftarrow a.used$ \\
-4.  $r \leftarrow 0$ \\
-5.  for $n$ from 0 to $a.used - 1$ do \\
-\hspace{3mm}5.1  $rr \leftarrow a_n >> (lg(\beta) - 1)$ \\
-\hspace{3mm}5.2  $b_n \leftarrow (a_n << 1) + r \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{3mm}5.3  $r \leftarrow rr$ \\
-6.  If $r \ne 0$ then do \\
-\hspace{3mm}6.1  $b_{n + 1} \leftarrow r$ \\
-\hspace{3mm}6.2  $b.used \leftarrow b.used + 1$ \\
-7.  If $b.used < oldused - 1$ then do \\
-\hspace{3mm}7.1  for $n$ from $b.used$ to $oldused - 1$ do \\
-\hspace{6mm}7.1.1  $b_n \leftarrow 0$ \\
-8.  $b.sign \leftarrow a.sign$ \\
-9.  Return(\textit{MP\_OKAY}).\\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_mul\_2}
-\end{figure}
-
-\textbf{Algorithm mp\_mul\_2.}
-This algorithm will quickly multiply a mp\_int by two provided $\beta$ is a power of two.  Neither \cite{TAOCPV2} nor \cite{HAC} describe such
-an algorithm despite the fact it arises often in other algorithms.  The algorithm is setup much like the lower level algorithm s\_mp\_add since
-it is for all intents and purposes equivalent to the operation $b = \vert a \vert + \vert a \vert$.
-
-Step 1 and 2 grow the input as required to accomodate the maximum number of \textbf{used} digits in the result.  The initial \textbf{used} count
-is set to $a.used$ at step 4.  Only if there is a final carry will the \textbf{used} count require adjustment.
-
-Step 6 is an optimization implementation of the addition loop for this specific case.  That is since the two values being added together
-are the same there is no need to perform two reads from the digits of $a$.  Step 6.1 performs a single precision shift on the current digit $a_n$ to
-obtain what will be the carry for the next iteration.  Step 6.2 calculates the $n$'th digit of the result as single precision shift of $a_n$ plus
-the previous carry.  Recall from ~SHIFTS~ that $a_n << 1$ is equivalent to $a_n \cdot 2$.  An iteration of the addition loop is finished with
-forwarding the carry to the next iteration.
-
-Step 7 takes care of any final carry by setting the $a.used$'th digit of the result to the carry and augmenting the \textbf{used} count of $b$.
-Step 8 clears any leading digits of $b$ in case it originally had a larger magnitude than $a$.
-
-EXAM,bn_mp_mul_2.c
-
-This implementation is essentially an optimized implementation of s\_mp\_add for the case of doubling an input.  The only noteworthy difference
-is the use of the logical shift operator on line @52,<<@ to perform a single precision doubling.
-
-\subsection{Division by Two}
-A division by two can just as easily be accomplished with a logical shift right as multiplication by two can be with a logical shift left.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_div\_2}. \\
-\textbf{Input}.   One mp\_int $a$ \\
-\textbf{Output}.  $b = a/2$. \\
-\hline \\
-1.  If $b.alloc < a.used$ then grow $b$ to hold $a.used$ digits.  (\textit{mp\_grow}) \\
-2.  If the reallocation failed return(\textit{MP\_MEM}). \\
-3.  $oldused \leftarrow b.used$ \\
-4.  $b.used \leftarrow a.used$ \\
-5.  $r \leftarrow 0$ \\
-6.  for $n$ from $b.used - 1$ to $0$ do \\
-\hspace{3mm}6.1  $rr \leftarrow a_n \mbox{ (mod }2\mbox{)}$\\
-\hspace{3mm}6.2  $b_n \leftarrow (a_n >> 1) + (r << (lg(\beta) - 1)) \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{3mm}6.3  $r \leftarrow rr$ \\
-7.  If $b.used < oldused - 1$ then do \\
-\hspace{3mm}7.1  for $n$ from $b.used$ to $oldused - 1$ do \\
-\hspace{6mm}7.1.1  $b_n \leftarrow 0$ \\
-8.  $b.sign \leftarrow a.sign$ \\
-9.  Clamp excess digits of $b$.  (\textit{mp\_clamp}) \\
-10.  Return(\textit{MP\_OKAY}).\\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_div\_2}
-\end{figure}
-
-\textbf{Algorithm mp\_div\_2.}
-This algorithm will divide an mp\_int by two using logical shifts to the right.  Like mp\_mul\_2 it uses a modified low level addition
-core as the basis of the algorithm.  Unlike mp\_mul\_2 the shift operations work from the leading digit to the trailing digit.  The algorithm
-could be written to work from the trailing digit to the leading digit however, it would have to stop one short of $a.used - 1$ digits to prevent
-reading past the end of the array of digits.
-
-Essentially the loop at step 6 is similar to that of mp\_mul\_2 except the logical shifts go in the opposite direction and the carry is at the
-least significant bit not the most significant bit.
-
-EXAM,bn_mp_div_2.c
-
-\section{Polynomial Basis Operations}
-Recall from ~POLY~ that any integer can be represented as a polynomial in $x$ as $y = f(\beta)$.  Such a representation is also known as
-the polynomial basis \cite[pp. 48]{ROSE}. Given such a notation a multiplication or division by $x$ amounts to shifting whole digits a single
-place.  The need for such operations arises in several other higher level algorithms such as Barrett and Montgomery reduction, integer
-division and Karatsuba multiplication.
-
-Converting from an array of digits to polynomial basis is very simple.  Consider the integer $y \equiv (a_2, a_1, a_0)_{\beta}$ and recall that
-$y = \sum_{i=0}^{2} a_i \beta^i$.  Simply replace $\beta$ with $x$ and the expression is in polynomial basis.  For example, $f(x) = 8x + 9$ is the
-polynomial basis representation for $89$ using radix ten.  That is, $f(10) = 8(10) + 9 = 89$.
-
-\subsection{Multiplication by $x$}
-
-Given a polynomial in $x$ such as $f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_0$ multiplying by $x$ amounts to shifting the coefficients up one
-degree.  In this case $f(x) \cdot x = a_n x^{n+1} + a_{n-1} x^n + ... + a_0 x$.  From a scalar basis point of view multiplying by $x$ is equivalent to
-multiplying by the integer $\beta$.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_lshd}. \\
-\textbf{Input}.   One mp\_int $a$ and an integer $b$ \\
-\textbf{Output}.  $a \leftarrow a \cdot \beta^b$ (equivalent to multiplication by $x^b$). \\
-\hline \\
-1.  If $b \le 0$ then return(\textit{MP\_OKAY}). \\
-2.  If $a.alloc < a.used + b$ then grow $a$ to at least $a.used + b$ digits.  (\textit{mp\_grow}). \\
-3.  If the reallocation failed return(\textit{MP\_MEM}). \\
-4.  $a.used \leftarrow a.used + b$ \\
-5.  $i \leftarrow a.used - 1$ \\
-6.  $j \leftarrow a.used - 1 - b$ \\
-7.  for $n$ from $a.used - 1$ to $b$ do \\
-\hspace{3mm}7.1  $a_{i} \leftarrow a_{j}$ \\
-\hspace{3mm}7.2  $i \leftarrow i - 1$ \\
-\hspace{3mm}7.3  $j \leftarrow j - 1$ \\
-8.  for $n$ from 0 to $b - 1$ do \\
-\hspace{3mm}8.1  $a_n \leftarrow 0$ \\
-9.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_lshd}
-\end{figure}
-
-\textbf{Algorithm mp\_lshd.}
-This algorithm multiplies an mp\_int by the $b$'th power of $x$.  This is equivalent to multiplying by $\beta^b$.  The algorithm differs
-from the other algorithms presented so far as it performs the operation in place instead storing the result in a separate location.  The
-motivation behind this change is due to the way this function is typically used.  Algorithms such as mp\_add store the result in an optionally
-different third mp\_int because the original inputs are often still required.  Algorithm mp\_lshd (\textit{and similarly algorithm mp\_rshd}) is
-typically used on values where the original value is no longer required.  The algorithm will return success immediately if
-$b \le 0$ since the rest of algorithm is only valid when $b > 0$.
-
-First the destination $a$ is grown as required to accomodate the result.  The counters $i$ and $j$ are used to form a \textit{sliding window} over
-the digits of $a$ of length $b$.  The head of the sliding window is at $i$ (\textit{the leading digit}) and the tail at $j$ (\textit{the trailing digit}).
-The loop on step 7 copies the digit from the tail to the head.  In each iteration the window is moved down one digit.   The last loop on
-step 8 sets the lower $b$ digits to zero.
-
-\newpage
-FIGU,sliding_window,Sliding Window Movement
-
-EXAM,bn_mp_lshd.c
-
-The if statement (line @24,if@) ensures that the $b$ variable is greater than zero since we do not interpret negative
-shift counts properly.  The \textbf{used} count is incremented by $b$ before the copy loop begins.  This elminates
-the need for an additional variable in the for loop.  The variable $top$ (line @42,top@) is an alias
-for the leading digit while $bottom$ (line @45,bottom@) is an alias for the trailing edge.  The aliases form a
-window of exactly $b$ digits over the input.
-
-\subsection{Division by $x$}
-
-Division by powers of $x$ is easily achieved by shifting the digits right and removing any that will end up to the right of the zero'th digit.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_rshd}. \\
-\textbf{Input}.   One mp\_int $a$ and an integer $b$ \\
-\textbf{Output}.  $a \leftarrow a / \beta^b$ (Divide by $x^b$). \\
-\hline \\
-1.  If $b \le 0$ then return. \\
-2.  If $a.used \le b$ then do \\
-\hspace{3mm}2.1  Zero $a$.  (\textit{mp\_zero}). \\
-\hspace{3mm}2.2  Return. \\
-3.  $i \leftarrow 0$ \\
-4.  $j \leftarrow b$ \\
-5.  for $n$ from 0 to $a.used - b - 1$ do \\
-\hspace{3mm}5.1  $a_i \leftarrow a_j$ \\
-\hspace{3mm}5.2  $i \leftarrow i + 1$ \\
-\hspace{3mm}5.3  $j \leftarrow j + 1$ \\
-6.  for $n$ from $a.used - b$ to $a.used - 1$ do \\
-\hspace{3mm}6.1  $a_n \leftarrow 0$ \\
-7.  $a.used \leftarrow a.used - b$ \\
-8.  Return. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_rshd}
-\end{figure}
-
-\textbf{Algorithm mp\_rshd.}
-This algorithm divides the input in place by the $b$'th power of $x$.  It is analogous to dividing by a $\beta^b$ but much quicker since
-it does not require single precision division.  This algorithm does not actually return an error code as it cannot fail.
-
-If the input $b$ is less than one the algorithm quickly returns without performing any work.  If the \textbf{used} count is less than or equal
-to the shift count $b$ then it will simply zero the input and return.
-
-After the trivial cases of inputs have been handled the sliding window is setup.  Much like the case of algorithm mp\_lshd a sliding window that
-is $b$ digits wide is used to copy the digits.  Unlike mp\_lshd the window slides in the opposite direction from the trailing to the leading digit.
-Also the digits are copied from the leading to the trailing edge.
-
-Once the window copy is complete the upper digits must be zeroed and the \textbf{used} count decremented.
-
-EXAM,bn_mp_rshd.c
-
-The only noteworthy element of this routine is the lack of a return type since it cannot fail.  Like mp\_lshd() we
-form a sliding window except we copy in the other direction.  After the window (line @59,for (;@) we then zero
-the upper digits of the input to make sure the result is correct.
-
-\section{Powers of Two}
-
-Now that algorithms for moving single bits as well as whole digits exist algorithms for moving the ``in between'' distances are required.  For
-example, to quickly multiply by $2^k$ for any $k$ without using a full multiplier algorithm would prove useful.  Instead of performing single
-shifts $k$ times to achieve a multiplication by $2^{\pm k}$ a mixture of whole digit shifting and partial digit shifting is employed.
-
-\subsection{Multiplication by Power of Two}
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_mul\_2d}. \\
-\textbf{Input}.   One mp\_int $a$ and an integer $b$ \\
-\textbf{Output}.  $c \leftarrow a \cdot 2^b$. \\
-\hline \\
-1.  $c \leftarrow a$.  (\textit{mp\_copy}) \\
-2.  If $c.alloc < c.used + \lfloor b / lg(\beta) \rfloor + 2$ then grow $c$ accordingly. \\
-3.  If the reallocation failed return(\textit{MP\_MEM}). \\
-4.  If $b \ge lg(\beta)$ then \\
-\hspace{3mm}4.1  $c \leftarrow c \cdot \beta^{\lfloor b / lg(\beta) \rfloor}$ (\textit{mp\_lshd}). \\
-\hspace{3mm}4.2  If step 4.1 failed return(\textit{MP\_MEM}). \\
-5.  $d \leftarrow b \mbox{ (mod }lg(\beta)\mbox{)}$ \\
-6.  If $d \ne 0$ then do \\
-\hspace{3mm}6.1  $mask \leftarrow 2^d$ \\
-\hspace{3mm}6.2  $r \leftarrow 0$ \\
-\hspace{3mm}6.3  for $n$ from $0$ to $c.used - 1$ do \\
-\hspace{6mm}6.3.1  $rr \leftarrow c_n >> (lg(\beta) - d) \mbox{ (mod }mask\mbox{)}$ \\
-\hspace{6mm}6.3.2  $c_n \leftarrow (c_n << d) + r \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{6mm}6.3.3  $r \leftarrow rr$ \\
-\hspace{3mm}6.4  If $r > 0$ then do \\
-\hspace{6mm}6.4.1  $c_{c.used} \leftarrow r$ \\
-\hspace{6mm}6.4.2  $c.used \leftarrow c.used + 1$ \\
-7.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_mul\_2d}
-\end{figure}
-
-\textbf{Algorithm mp\_mul\_2d.}
-This algorithm multiplies $a$ by $2^b$ and stores the result in $c$.  The algorithm uses algorithm mp\_lshd and a derivative of algorithm mp\_mul\_2 to
-quickly compute the product.
-
-First the algorithm will multiply $a$ by $x^{\lfloor b / lg(\beta) \rfloor}$ which will ensure that the remainder multiplicand is less than
-$\beta$.  For example, if $b = 37$ and $\beta = 2^{28}$ then this step will multiply by $x$ leaving a multiplication by $2^{37 - 28} = 2^{9}$
-left.
-
-After the digits have been shifted appropriately at most $lg(\beta) - 1$ shifts are left to perform.  Step 5 calculates the number of remaining shifts
-required.  If it is non-zero a modified shift loop is used to calculate the remaining product.
-Essentially the loop is a generic version of algorithm mp\_mul\_2 designed to handle any shift count in the range $1 \le x < lg(\beta)$.  The $mask$
-variable is used to extract the upper $d$ bits to form the carry for the next iteration.
-
-This algorithm is loosely measured as a $O(2n)$ algorithm which means that if the input is $n$-digits that it takes $2n$ ``time'' to
-complete.  It is possible to optimize this algorithm down to a $O(n)$ algorithm at a cost of making the algorithm slightly harder to follow.
-
-EXAM,bn_mp_mul_2d.c
-
-The shifting is performed in--place which means the first step (line @24,a != c@) is to copy the input to the
-destination.  We avoid calling mp\_copy() by making sure the mp\_ints are different.  The destination then
-has to be grown (line @31,grow@) to accomodate the result.
-
-If the shift count $b$ is larger than $lg(\beta)$ then a call to mp\_lshd() is used to handle all of the multiples
-of $lg(\beta)$.  Leaving only a remaining shift of $lg(\beta) - 1$ or fewer bits left.  Inside the actual shift
-loop (lines @45,if@ to @76,}@) we make use of pre--computed values $shift$ and $mask$.   These are used to
-extract the carry bit(s) to pass into the next iteration of the loop.  The $r$ and $rr$ variables form a
-chain between consecutive iterations to propagate the carry.
-
-\subsection{Division by Power of Two}
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_div\_2d}. \\
-\textbf{Input}.   One mp\_int $a$ and an integer $b$ \\
-\textbf{Output}.  $c \leftarrow \lfloor a / 2^b \rfloor, d \leftarrow a \mbox{ (mod }2^b\mbox{)}$. \\
-\hline \\
-1.  If $b \le 0$ then do \\
-\hspace{3mm}1.1  $c \leftarrow a$ (\textit{mp\_copy}) \\
-\hspace{3mm}1.2  $d \leftarrow 0$ (\textit{mp\_zero}) \\
-\hspace{3mm}1.3  Return(\textit{MP\_OKAY}). \\
-2.  $c \leftarrow a$ \\
-3.  $d \leftarrow a \mbox{ (mod }2^b\mbox{)}$ (\textit{mp\_mod\_2d}) \\
-4.  If $b \ge lg(\beta)$ then do \\
-\hspace{3mm}4.1  $c \leftarrow \lfloor c/\beta^{\lfloor b/lg(\beta) \rfloor} \rfloor$ (\textit{mp\_rshd}). \\
-5.  $k \leftarrow b \mbox{ (mod }lg(\beta)\mbox{)}$ \\
-6.  If $k \ne 0$ then do \\
-\hspace{3mm}6.1  $mask \leftarrow 2^k$ \\
-\hspace{3mm}6.2  $r \leftarrow 0$ \\
-\hspace{3mm}6.3  for $n$ from $c.used - 1$ to $0$ do \\
-\hspace{6mm}6.3.1  $rr \leftarrow c_n \mbox{ (mod }mask\mbox{)}$ \\
-\hspace{6mm}6.3.2  $c_n \leftarrow (c_n >> k) + (r << (lg(\beta) - k))$ \\
-\hspace{6mm}6.3.3  $r \leftarrow rr$ \\
-7.  Clamp excess digits of $c$.  (\textit{mp\_clamp}) \\
-8.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_div\_2d}
-\end{figure}
-
-\textbf{Algorithm mp\_div\_2d.}
-This algorithm will divide an input $a$ by $2^b$ and produce the quotient and remainder.  The algorithm is designed much like algorithm
-mp\_mul\_2d by first using whole digit shifts then single precision shifts.  This algorithm will also produce the remainder of the division
-by using algorithm mp\_mod\_2d.
-
-EXAM,bn_mp_div_2d.c
-
-The implementation of algorithm mp\_div\_2d is slightly different than the algorithm specifies.  The remainder $d$ may be optionally
-ignored by passing \textbf{NULL} as the pointer to the mp\_int variable.    The temporary mp\_int variable $t$ is used to hold the
-result of the remainder operation until the end.  This allows $d$ and $a$ to represent the same mp\_int without modifying $a$ before
-the quotient is obtained.
-
-The remainder of the source code is essentially the same as the source code for mp\_mul\_2d.  The only significant difference is
-the direction of the shifts.
-
-\subsection{Remainder of Division by Power of Two}
-
-The last algorithm in the series of polynomial basis power of two algorithms is calculating the remainder of division by $2^b$.  This
-algorithm benefits from the fact that in twos complement arithmetic $a \mbox{ (mod }2^b\mbox{)}$ is the same as $a$ AND $2^b - 1$.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_mod\_2d}. \\
-\textbf{Input}.   One mp\_int $a$ and an integer $b$ \\
-\textbf{Output}.  $c \leftarrow a \mbox{ (mod }2^b\mbox{)}$. \\
-\hline \\
-1.  If $b \le 0$ then do \\
-\hspace{3mm}1.1  $c \leftarrow 0$ (\textit{mp\_zero}) \\
-\hspace{3mm}1.2  Return(\textit{MP\_OKAY}). \\
-2.  If $b > a.used \cdot lg(\beta)$ then do \\
-\hspace{3mm}2.1  $c \leftarrow a$ (\textit{mp\_copy}) \\
-\hspace{3mm}2.2  Return the result of step 2.1. \\
-3.  $c \leftarrow a$ \\
-4.  If step 3 failed return(\textit{MP\_MEM}). \\
-5.  for $n$ from $\lceil b / lg(\beta) \rceil$ to $c.used$ do \\
-\hspace{3mm}5.1  $c_n \leftarrow 0$ \\
-6.  $k \leftarrow b \mbox{ (mod }lg(\beta)\mbox{)}$ \\
-7.  $c_{\lfloor b / lg(\beta) \rfloor} \leftarrow c_{\lfloor b / lg(\beta) \rfloor} \mbox{ (mod }2^{k}\mbox{)}$. \\
-8.  Clamp excess digits of $c$.  (\textit{mp\_clamp}) \\
-9.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_mod\_2d}
-\end{figure}
-
-\textbf{Algorithm mp\_mod\_2d.}
-This algorithm will quickly calculate the value of $a \mbox{ (mod }2^b\mbox{)}$.  First if $b$ is less than or equal to zero the
-result is set to zero.  If $b$ is greater than the number of bits in $a$ then it simply copies $a$ to $c$ and returns.  Otherwise, $a$
-is copied to $b$, leading digits are removed and the remaining leading digit is trimed to the exact bit count.
-
-EXAM,bn_mp_mod_2d.c
-
-We first avoid cases of $b \le 0$ by simply mp\_zero()'ing the destination in such cases.  Next if $2^b$ is larger
-than the input we just mp\_copy() the input and return right away.  After this point we know we must actually
-perform some work to produce the remainder.
-
-Recalling that reducing modulo $2^k$ and a binary ``and'' with $2^k - 1$ are numerically equivalent we can quickly reduce
-the number.  First we zero any digits above the last digit in $2^b$ (line @41,for@).  Next we reduce the
-leading digit of both (line @45,&=@) and then mp\_clamp().
-
-\section*{Exercises}
-\begin{tabular}{cl}
-$\left [ 3 \right ] $ & Devise an algorithm that performs $a \cdot 2^b$ for generic values of $b$ \\
-                      & in $O(n)$ time. \\
-                      &\\
-$\left [ 3 \right ] $ & Devise an efficient algorithm to multiply by small low hamming  \\
-                      & weight values such as $3$, $5$ and $9$.  Extend it to handle all values \\
-                      & upto $64$ with a hamming weight less than three. \\
-                      &\\
-$\left [ 2 \right ] $ & Modify the preceding algorithm to handle values of the form \\
-                      & $2^k - 1$ as well. \\
-                      &\\
-$\left [ 3 \right ] $ & Using only algorithms mp\_mul\_2, mp\_div\_2 and mp\_add create an \\
-                      & algorithm to multiply two integers in roughly $O(2n^2)$ time for \\
-                      & any $n$-bit input.  Note that the time of addition is ignored in the \\
-                      & calculation.  \\
-                      & \\
-$\left [ 5 \right ] $ & Improve the previous algorithm to have a working time of at most \\
-                      & $O \left (2^{(k-1)}n + \left ({2n^2 \over k} \right ) \right )$ for an appropriate choice of $k$.  Again ignore \\
-                      & the cost of addition. \\
-                      & \\
-$\left [ 2 \right ] $ & Devise a chart to find optimal values of $k$ for the previous problem \\
-                      & for $n = 64 \ldots 1024$ in steps of $64$. \\
-                      & \\
-$\left [ 2 \right ] $ & Using only algorithms mp\_abs and mp\_sub devise another method for \\
-                      & calculating the result of a signed comparison. \\
-                      &
-\end{tabular}
-
-\chapter{Multiplication and Squaring}
-\section{The Multipliers}
-For most number theoretic problems including certain public key cryptographic algorithms, the ``multipliers'' form the most important subset of
-algorithms of any multiple precision integer package.  The set of multiplier algorithms include integer multiplication, squaring and modular reduction
-where in each of the algorithms single precision multiplication is the dominant operation performed.  This chapter will discuss integer multiplication
-and squaring, leaving modular reductions for the subsequent chapter.
-
-The importance of the multiplier algorithms is for the most part driven by the fact that certain popular public key algorithms are based on modular
-exponentiation, that is computing $d \equiv a^b \mbox{ (mod }c\mbox{)}$ for some arbitrary choice of $a$, $b$, $c$ and $d$.  During a modular
-exponentiation the majority\footnote{Roughly speaking a modular exponentiation will spend about 40\% of the time performing modular reductions,
-35\% of the time performing squaring and 25\% of the time performing multiplications.} of the processor time is spent performing single precision
-multiplications.
-
-For centuries general purpose multiplication has required a lengthly $O(n^2)$ process, whereby each digit of one multiplicand has to be multiplied
-against every digit of the other multiplicand.  Traditional long-hand multiplication is based on this process;  while the techniques can differ the
-overall algorithm used is essentially the same.  Only ``recently'' have faster algorithms been studied.  First Karatsuba multiplication was discovered in
-1962.  This algorithm can multiply two numbers with considerably fewer single precision multiplications when compared to the long-hand approach.
-This technique led to the discovery of polynomial basis algorithms (\textit{good reference?}) and subquently Fourier Transform based solutions.
-
-\section{Multiplication}
-\subsection{The Baseline Multiplication}
-\label{sec:basemult}
-\index{baseline multiplication}
-Computing the product of two integers in software can be achieved using a trivial adaptation of the standard $O(n^2)$ long-hand multiplication
-algorithm that school children are taught.  The algorithm is considered an $O(n^2)$ algorithm since for two $n$-digit inputs $n^2$ single precision
-multiplications are required.  More specifically for a $m$ and $n$ digit input $m \cdot n$ single precision multiplications are required.  To
-simplify most discussions, it will be assumed that the inputs have comparable number of digits.
-
-The ``baseline multiplication'' algorithm is designed to act as the ``catch-all'' algorithm, only to be used when the faster algorithms cannot be
-used.  This algorithm does not use any particularly interesting optimizations and should ideally be avoided if possible.    One important
-facet of this algorithm, is that it has been modified to only produce a certain amount of output digits as resolution.  The importance of this
-modification will become evident during the discussion of Barrett modular reduction.  Recall that for a $n$ and $m$ digit input the product
-will be at most $n + m$ digits.  Therefore, this algorithm can be reduced to a full multiplier by having it produce $n + m$ digits of the product.
-
-Recall from ~GAMMA~ the definition of $\gamma$ as the number of bits in the type \textbf{mp\_digit}.  We shall now extend the variable set to
-include $\alpha$ which shall represent the number of bits in the type \textbf{mp\_word}.  This implies that $2^{\alpha} > 2 \cdot \beta^2$.  The
-constant $\delta = 2^{\alpha - 2lg(\beta)}$ will represent the maximal weight of any column in a product (\textit{see ~COMBA~ for more information}).
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{s\_mp\_mul\_digs}. \\
-\textbf{Input}.   mp\_int $a$, mp\_int $b$ and an integer $digs$ \\
-\textbf{Output}.  $c \leftarrow \vert a \vert \cdot \vert b \vert \mbox{ (mod }\beta^{digs}\mbox{)}$. \\
-\hline \\
-1.  If min$(a.used, b.used) < \delta$ then do \\
-\hspace{3mm}1.1  Calculate $c = \vert a \vert \cdot \vert b \vert$ by the Comba method (\textit{see algorithm~\ref{fig:COMBAMULT}}).  \\
-\hspace{3mm}1.2  Return the result of step 1.1 \\
-\\
-Allocate and initialize a temporary mp\_int. \\
-2.  Init $t$ to be of size $digs$ \\
-3.  If step 2 failed return(\textit{MP\_MEM}). \\
-4.  $t.used \leftarrow digs$ \\
-\\
-Compute the product. \\
-5.  for $ix$ from $0$ to $a.used - 1$ do \\
-\hspace{3mm}5.1  $u \leftarrow 0$ \\
-\hspace{3mm}5.2  $pb \leftarrow \mbox{min}(b.used, digs - ix)$ \\
-\hspace{3mm}5.3  If $pb < 1$ then goto step 6. \\
-\hspace{3mm}5.4  for $iy$ from $0$ to $pb - 1$ do \\
-\hspace{6mm}5.4.1  $\hat r \leftarrow t_{iy + ix} + a_{ix} \cdot b_{iy} + u$ \\
-\hspace{6mm}5.4.2  $t_{iy + ix} \leftarrow \hat r \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{6mm}5.4.3  $u \leftarrow \lfloor \hat r / \beta \rfloor$ \\
-\hspace{3mm}5.5  if $ix + pb < digs$ then do \\
-\hspace{6mm}5.5.1  $t_{ix + pb} \leftarrow u$ \\
-6.  Clamp excess digits of $t$. \\
-7.  Swap $c$ with $t$ \\
-8.  Clear $t$ \\
-9.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm s\_mp\_mul\_digs}
-\end{figure}
-
-\textbf{Algorithm s\_mp\_mul\_digs.}
-This algorithm computes the unsigned product of two inputs $a$ and $b$, limited to an output precision of $digs$ digits.  While it may seem
-a bit awkward to modify the function from its simple $O(n^2)$ description, the usefulness of partial multipliers will arise in a subsequent
-algorithm.  The algorithm is loosely based on algorithm 14.12 from \cite[pp. 595]{HAC} and is similar to Algorithm M of Knuth \cite[pp. 268]{TAOCPV2}.
-Algorithm s\_mp\_mul\_digs differs from these cited references since it can produce a variable output precision regardless of the precision of the
-inputs.
-
-The first thing this algorithm checks for is whether a Comba multiplier can be used instead.   If the minimum digit count of either
-input is less than $\delta$, then the Comba method may be used instead.    After the Comba method is ruled out, the baseline algorithm begins.  A
-temporary mp\_int variable $t$ is used to hold the intermediate result of the product.  This allows the algorithm to be used to
-compute products when either $a = c$ or $b = c$ without overwriting the inputs.
-
-All of step 5 is the infamous $O(n^2)$ multiplication loop slightly modified to only produce upto $digs$ digits of output.  The $pb$ variable
-is given the count of digits to read from $b$ inside the nested loop.  If $pb \le 1$ then no more output digits can be produced and the algorithm
-will exit the loop.  The best way to think of the loops are as a series of $pb \times 1$ multiplications.    That is, in each pass of the
-innermost loop $a_{ix}$ is multiplied against $b$ and the result is added (\textit{with an appropriate shift}) to $t$.
-
-For example, consider multiplying $576$ by $241$.  That is equivalent to computing $10^0(1)(576) + 10^1(4)(576) + 10^2(2)(576)$ which is best
-visualized in the following table.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{|c|c|c|c|c|c|l|}
-\hline   &&          & 5 & 7 & 6 & \\
-\hline   $\times$&&  & 2 & 4 & 1 & \\
-\hline &&&&&&\\
-  &&          & 5 & 7 & 6 & $10^0(1)(576)$ \\
-  &2 &   3    & 6 & 1 & 6 & $10^1(4)(576) + 10^0(1)(576)$ \\
-  1 & 3 & 8 & 8 & 1 & 6 &   $10^2(2)(576) + 10^1(4)(576) + 10^0(1)(576)$ \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Long-Hand Multiplication Diagram}
-\end{figure}
-
-Each row of the product is added to the result after being shifted to the left (\textit{multiplied by a power of the radix}) by the appropriate
-count.  That is in pass $ix$ of the inner loop the product is added starting at the $ix$'th digit of the reult.
-
-Step 5.4.1 introduces the hat symbol (\textit{e.g. $\hat r$}) which represents a double precision variable.  The multiplication on that step
-is assumed to be a double wide output single precision multiplication.  That is, two single precision variables are multiplied to produce a
-double precision result.  The step is somewhat optimized from a long-hand multiplication algorithm because the carry from the addition in step
-5.4.1 is propagated through the nested loop.  If the carry was not propagated immediately it would overflow the single precision digit
-$t_{ix+iy}$ and the result would be lost.
-
-At step 5.5 the nested loop is finished and any carry that was left over should be forwarded.  The carry does not have to be added to the $ix+pb$'th
-digit since that digit is assumed to be zero at this point.  However, if $ix + pb \ge digs$ the carry is not set as it would make the result
-exceed the precision requested.
-
-EXAM,bn_s_mp_mul_digs.c
-
-First we determine (line @30,if@) if the Comba method can be used first since it's faster.  The conditions for
-sing the Comba routine are that min$(a.used, b.used) < \delta$ and the number of digits of output is less than
-\textbf{MP\_WARRAY}.  This new constant is used to control the stack usage in the Comba routines.  By default it is
-set to $\delta$ but can be reduced when memory is at a premium.
-
-If we cannot use the Comba method we proceed to setup the baseline routine.  We allocate the the destination mp\_int
-$t$ (line @36,init@) to the exact size of the output to avoid further re--allocations.  At this point we now
-begin the $O(n^2)$ loop.
-
-This implementation of multiplication has the caveat that it can be trimmed to only produce a variable number of
-digits as output.  In each iteration of the outer loop the $pb$ variable is set (line @48,MIN@) to the maximum
-number of inner loop iterations.
-
-Inside the inner loop we calculate $\hat r$ as the mp\_word product of the two mp\_digits and the addition of the
-carry from the previous iteration.  A particularly important observation is that most modern optimizing
-C compilers (GCC for instance) can recognize that a $N \times N \rightarrow 2N$ multiplication is all that
-is required for the product.  In x86 terms for example, this means using the MUL instruction.
-
-Each digit of the product is stored in turn (line @68,tmpt@) and the carry propagated (line @71,>>@) to the
-next iteration.
-
-\subsection{Faster Multiplication by the ``Comba'' Method}
-MARK,COMBA
-
-One of the huge drawbacks of the ``baseline'' algorithms is that at the $O(n^2)$ level the carry must be
-computed and propagated upwards.  This makes the nested loop very sequential and hard to unroll and implement
-in parallel.  The ``Comba'' \cite{COMBA} method is named after little known (\textit{in cryptographic venues}) Paul G.
-Comba who described a method of implementing fast multipliers that do not require nested carry fixup operations.  As an
-interesting aside it seems that Paul Barrett describes a similar technique in his 1986 paper \cite{BARRETT} written
-five years before.
-
-At the heart of the Comba technique is once again the long-hand algorithm.  Except in this case a slight
-twist is placed on how the columns of the result are produced.  In the standard long-hand algorithm rows of products
-are produced then added together to form the final result.  In the baseline algorithm the columns are added together
-after each iteration to get the result instantaneously.
-
-In the Comba algorithm the columns of the result are produced entirely independently of each other.  That is at
-the $O(n^2)$ level a simple multiplication and addition step is performed.  The carries of the columns are propagated
-after the nested loop to reduce the amount of work requiored. Succintly the first step of the algorithm is to compute
-the product vector $\vec x$ as follows.
-
-\begin{equation}
-\vec x_n = \sum_{i+j = n} a_ib_j, \forall n \in \lbrace 0, 1, 2, \ldots, i + j \rbrace
-\end{equation}
-
-Where $\vec x_n$ is the $n'th$ column of the output vector.  Consider the following example which computes the vector $\vec x$ for the multiplication
-of $576$ and $241$.
-
-\newpage\begin{figure}[here]
-\begin{small}
-\begin{center}
-\begin{tabular}{|c|c|c|c|c|c|}
-  \hline &          & 5 & 7 & 6 & First Input\\
-  \hline $\times$ & & 2 & 4 & 1 & Second Input\\
-\hline            &                        & $1 \cdot 5 = 5$   & $1 \cdot 7 = 7$   & $1 \cdot 6 = 6$ & First pass \\
-                  &  $4 \cdot 5 = 20$      & $4 \cdot 7+5=33$  & $4 \cdot 6+7=31$  & 6               & Second pass \\
-   $2 \cdot 5 = 10$ &  $2 \cdot 7 + 20 = 34$ & $2 \cdot 6+33=45$ & 31                & 6             & Third pass \\
-\hline 10 & 34 & 45 & 31 & 6 & Final Result \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Comba Multiplication Diagram}
-\end{figure}
-
-At this point the vector $x = \left < 10, 34, 45, 31, 6 \right >$ is the result of the first step of the Comba multipler.
-Now the columns must be fixed by propagating the carry upwards.  The resultant vector will have one extra dimension over the input vector which is
-congruent to adding a leading zero digit.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Comba Fixup}. \\
-\textbf{Input}.   Vector $\vec x$ of dimension $k$ \\
-\textbf{Output}.  Vector $\vec x$ such that the carries have been propagated. \\
-\hline \\
-1.  for $n$ from $0$ to $k - 1$ do \\
-\hspace{3mm}1.1 $\vec x_{n+1} \leftarrow \vec x_{n+1} + \lfloor \vec x_{n}/\beta \rfloor$ \\
-\hspace{3mm}1.2 $\vec x_{n} \leftarrow \vec x_{n} \mbox{ (mod }\beta\mbox{)}$ \\
-2.  Return($\vec x$). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm Comba Fixup}
-\end{figure}
-
-With that algorithm and $k = 5$ and $\beta = 10$ the following vector is produced $\vec x= \left < 1, 3, 8, 8, 1, 6 \right >$.  In this case
-$241 \cdot 576$ is in fact $138816$ and the procedure succeeded.  If the algorithm is correct and as will be demonstrated shortly more
-efficient than the baseline algorithm why not simply always use this algorithm?
-
-\subsubsection{Column Weight.}
-At the nested $O(n^2)$ level the Comba method adds the product of two single precision variables to each column of the output
-independently.  A serious obstacle is if the carry is lost, due to lack of precision before the algorithm has a chance to fix
-the carries.  For example, in the multiplication of two three-digit numbers the third column of output will be the sum of
-three single precision multiplications.  If the precision of the accumulator for the output digits is less then $3 \cdot (\beta - 1)^2$ then
-an overflow can occur and the carry information will be lost.  For any $m$ and $n$ digit inputs the maximum weight of any column is
-min$(m, n)$ which is fairly obvious.
-
-The maximum number of terms in any column of a product is known as the ``column weight'' and strictly governs when the algorithm can be used.  Recall
-from earlier that a double precision type has $\alpha$ bits of resolution and a single precision digit has $lg(\beta)$ bits of precision.  Given these
-two quantities we must not violate the following
-
-\begin{equation}
-k \cdot \left (\beta - 1 \right )^2 < 2^{\alpha}
-\end{equation}
-
-Which reduces to
-
-\begin{equation}
-k \cdot \left ( \beta^2 - 2\beta + 1 \right ) < 2^{\alpha}
-\end{equation}
-
-Let $\rho = lg(\beta)$ represent the number of bits in a single precision digit.  By further re-arrangement of the equation the final solution is
-found.
-
-\begin{equation}
-k  < {{2^{\alpha}} \over {\left (2^{2\rho} - 2^{\rho + 1} + 1 \right )}}
-\end{equation}
-
-The defaults for LibTomMath are $\beta = 2^{28}$ and $\alpha = 2^{64}$ which means that $k$ is bounded by $k < 257$.  In this configuration
-the smaller input may not have more than $256$ digits if the Comba method is to be used.  This is quite satisfactory for most applications since
-$256$ digits would allow for numbers in the range of $0 \le x < 2^{7168}$ which, is much larger than most public key cryptographic algorithms require.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{fast\_s\_mp\_mul\_digs}. \\
-\textbf{Input}.   mp\_int $a$, mp\_int $b$ and an integer $digs$ \\
-\textbf{Output}.  $c \leftarrow \vert a \vert \cdot \vert b \vert \mbox{ (mod }\beta^{digs}\mbox{)}$. \\
-\hline \\
-Place an array of \textbf{MP\_WARRAY} single precision digits named $W$ on the stack. \\
-1.  If $c.alloc < digs$ then grow $c$ to $digs$ digits. (\textit{mp\_grow}) \\
-2.  If step 1 failed return(\textit{MP\_MEM}).\\
-\\
-3.  $pa \leftarrow \mbox{MIN}(digs, a.used + b.used)$ \\
-\\
-4.  $\_ \hat W \leftarrow 0$ \\
-5.  for $ix$ from 0 to $pa - 1$ do \\
-\hspace{3mm}5.1  $ty \leftarrow \mbox{MIN}(b.used - 1, ix)$ \\
-\hspace{3mm}5.2  $tx \leftarrow ix - ty$ \\
-\hspace{3mm}5.3  $iy \leftarrow \mbox{MIN}(a.used - tx, ty + 1)$ \\
-\hspace{3mm}5.4  for $iz$ from 0 to $iy - 1$ do \\
-\hspace{6mm}5.4.1  $\_ \hat W \leftarrow \_ \hat W + a_{tx+iy}b_{ty-iy}$ \\
-\hspace{3mm}5.5  $W_{ix} \leftarrow \_ \hat W (\mbox{mod }\beta)$\\
-\hspace{3mm}5.6  $\_ \hat W \leftarrow \lfloor \_ \hat W / \beta \rfloor$ \\
-\\
-6.  $oldused \leftarrow c.used$ \\
-7.  $c.used \leftarrow digs$ \\
-8.  for $ix$ from $0$ to $pa$ do \\
-\hspace{3mm}8.1  $c_{ix} \leftarrow W_{ix}$ \\
-9.  for $ix$ from $pa + 1$ to $oldused - 1$ do \\
-\hspace{3mm}9.1 $c_{ix} \leftarrow 0$ \\
-\\
-10.  Clamp $c$. \\
-11.  Return MP\_OKAY. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm fast\_s\_mp\_mul\_digs}
-\label{fig:COMBAMULT}
-\end{figure}
-
-\textbf{Algorithm fast\_s\_mp\_mul\_digs.}
-This algorithm performs the unsigned multiplication of $a$ and $b$ using the Comba method limited to $digs$ digits of precision.
-
-The outer loop of this algorithm is more complicated than that of the baseline multiplier.  This is because on the inside of the
-loop we want to produce one column per pass.  This allows the accumulator $\_ \hat W$ to be placed in CPU registers and
-reduce the memory bandwidth to two \textbf{mp\_digit} reads per iteration.
-
-The $ty$ variable is set to the minimum count of $ix$ or the number of digits in $b$.  That way if $a$ has more digits than
-$b$ this will be limited to $b.used - 1$.  The $tx$ variable is set to the to the distance past $b.used$ the variable
-$ix$ is.  This is used for the immediately subsequent statement where we find $iy$.
-
-The variable $iy$ is the minimum digits we can read from either $a$ or $b$ before running out.  Computing one column at a time
-means we have to scan one integer upwards and the other downwards.  $a$ starts at $tx$ and $b$ starts at $ty$.  In each
-pass we are producing the $ix$'th output column and we note that $tx + ty = ix$.  As we move $tx$ upwards we have to
-move $ty$ downards so the equality remains valid.  The $iy$ variable is the number of iterations until
-$tx \ge a.used$ or $ty < 0$ occurs.
-
-After every inner pass we store the lower half of the accumulator into $W_{ix}$ and then propagate the carry of the accumulator
-into the next round by dividing $\_ \hat W$ by $\beta$.
-
-To measure the benefits of the Comba method over the baseline method consider the number of operations that are required.  If the
-cost in terms of time of a multiply and addition is $p$ and the cost of a carry propagation is $q$ then a baseline multiplication would require
-$O \left ((p + q)n^2 \right )$ time to multiply two $n$-digit numbers.  The Comba method requires only $O(pn^2 + qn)$ time, however in practice,
-the speed increase is actually much more.  With $O(n)$ space the algorithm can be reduced to $O(pn + qn)$ time by implementing the $n$ multiply
-and addition operations in the nested loop in parallel.
-
-EXAM,bn_fast_s_mp_mul_digs.c
-
-As per the pseudo--code we first calculate $pa$ (line @47,MIN@) as the number of digits to output.  Next we begin the outer loop
-to produce the individual columns of the product.  We use the two aliases $tmpx$ and $tmpy$ (lines @61,tmpx@, @62,tmpy@) to point
-inside the two multiplicands quickly.
-
-The inner loop (lines @70,for@ to @72,}@) of this implementation is where the tradeoff come into play.  Originally this comba
-implementation was ``row--major'' which means it adds to each of the columns in each pass.  After the outer loop it would then fix
-the carries.  This was very fast except it had an annoying drawback.  You had to read a mp\_word and two mp\_digits and write
-one mp\_word per iteration.  On processors such as the Athlon XP and P4 this did not matter much since the cache bandwidth
-is very high and it can keep the ALU fed with data.  It did, however, matter on older and embedded cpus where cache is often
-slower and also often doesn't exist.  This new algorithm only performs two reads per iteration under the assumption that the
-compiler has aliased $\_ \hat W$ to a CPU register.
-
-After the inner loop we store the current accumulator in $W$ and shift $\_ \hat W$ (lines @75,W[ix]@, @78,>>@) to forward it as
-a carry for the next pass.  After the outer loop we use the final carry (line @82,W[ix]@) as the last digit of the product.
-
-\subsection{Polynomial Basis Multiplication}
-To break the $O(n^2)$ barrier in multiplication requires a completely different look at integer multiplication.  In the following algorithms
-the use of polynomial basis representation for two integers $a$ and $b$ as $f(x) = \sum_{i=0}^{n} a_i x^i$ and
-$g(x) = \sum_{i=0}^{n} b_i x^i$ respectively, is required.  In this system both $f(x)$ and $g(x)$ have $n + 1$ terms and are of the $n$'th degree.
-
-The product $a \cdot b \equiv f(x)g(x)$ is the polynomial $W(x) = \sum_{i=0}^{2n} w_i x^i$.  The coefficients $w_i$ will
-directly yield the desired product when $\beta$ is substituted for $x$.  The direct solution to solve for the $2n + 1$ coefficients
-requires $O(n^2)$ time and would in practice be slower than the Comba technique.
-
-However, numerical analysis theory indicates that only $2n + 1$ distinct points in $W(x)$ are required to determine the values of the $2n + 1$ unknown
-coefficients.   This means by finding $\zeta_y = W(y)$ for $2n + 1$ small values of $y$ the coefficients of $W(x)$ can be found with
-Gaussian elimination.  This technique is also occasionally refered to as the \textit{interpolation technique} (\textit{references please...}) since in
-effect an interpolation based on $2n + 1$ points will yield a polynomial equivalent to $W(x)$.
-
-The coefficients of the polynomial $W(x)$ are unknown which makes finding $W(y)$ for any value of $y$ impossible.  However, since
-$W(x) = f(x)g(x)$ the equivalent $\zeta_y = f(y) g(y)$ can be used in its place.  The benefit of this technique stems from the
-fact that $f(y)$ and $g(y)$ are much smaller than either $a$ or $b$ respectively.  As a result finding the $2n + 1$ relations required
-by multiplying $f(y)g(y)$ involves multiplying integers that are much smaller than either of the inputs.
-
-When picking points to gather relations there are always three obvious points to choose, $y = 0, 1$ and $ \infty$.  The $\zeta_0$ term
-is simply the product $W(0) = w_0 = a_0 \cdot b_0$.  The $\zeta_1$ term is the product
-$W(1) = \left (\sum_{i = 0}^{n} a_i \right ) \left (\sum_{i = 0}^{n} b_i \right )$.  The third point $\zeta_{\infty}$ is less obvious but rather
-simple to explain.  The $2n + 1$'th coefficient of $W(x)$ is numerically equivalent to the most significant column in an integer multiplication.
-The point at $\infty$ is used symbolically to represent the most significant column, that is $W(\infty) = w_{2n} = a_nb_n$.  Note that the
-points at $y = 0$ and $\infty$ yield the coefficients $w_0$ and $w_{2n}$ directly.
-
-If more points are required they should be of small values and powers of two such as $2^q$ and the related \textit{mirror points}
-$\left (2^q \right )^{2n}  \cdot \zeta_{2^{-q}}$ for small values of $q$.  The term ``mirror point'' stems from the fact that
-$\left (2^q \right )^{2n}  \cdot \zeta_{2^{-q}}$ can be calculated in the exact opposite fashion as $\zeta_{2^q}$.  For
-example, when $n = 2$ and $q = 1$ then following two equations are equivalent to the point $\zeta_{2}$ and its mirror.
-
-\begin{eqnarray}
-\zeta_{2}                  = f(2)g(2) = (4a_2 + 2a_1 + a_0)(4b_2 + 2b_1 + b_0) \nonumber \\
-16 \cdot \zeta_{1 \over 2} = 4f({1\over 2}) \cdot 4g({1 \over 2}) = (a_2 + 2a_1 + 4a_0)(b_2 + 2b_1 + 4b_0)
-\end{eqnarray}
-
-Using such points will allow the values of $f(y)$ and $g(y)$ to be independently calculated using only left shifts.  For example, when $n = 2$ the
-polynomial $f(2^q)$ is equal to $2^q((2^qa_2) + a_1) + a_0$.  This technique of polynomial representation is known as Horner's method.
-
-As a general rule of the algorithm when the inputs are split into $n$ parts each there are $2n - 1$ multiplications.  Each multiplication is of
-multiplicands that have $n$ times fewer digits than the inputs.  The asymptotic running time of this algorithm is
-$O \left ( k^{lg_n(2n - 1)} \right )$ for $k$ digit inputs (\textit{assuming they have the same number of digits}).  Figure~\ref{fig:exponent}
-summarizes the exponents for various values of $n$.
-
-\begin{figure}
-\begin{center}
-\begin{tabular}{|c|c|c|}
-\hline \textbf{Split into $n$ Parts} & \textbf{Exponent}  & \textbf{Notes}\\
-\hline $2$ & $1.584962501$ & This is Karatsuba Multiplication. \\
-\hline $3$ & $1.464973520$ & This is Toom-Cook Multiplication. \\
-\hline $4$ & $1.403677461$ &\\
-\hline $5$ & $1.365212389$ &\\
-\hline $10$ & $1.278753601$ &\\
-\hline $100$ & $1.149426538$ &\\
-\hline $1000$ & $1.100270931$ &\\
-\hline $10000$ & $1.075252070$ &\\
-\hline
-\end{tabular}
-\end{center}
-\caption{Asymptotic Running Time of Polynomial Basis Multiplication}
-\label{fig:exponent}
-\end{figure}
-
-At first it may seem like a good idea to choose $n = 1000$ since the exponent is approximately $1.1$.  However, the overhead
-of solving for the 2001 terms of $W(x)$ will certainly consume any savings the algorithm could offer for all but exceedingly large
-numbers.
-
-\subsubsection{Cutoff Point}
-The polynomial basis multiplication algorithms all require fewer single precision multiplications than a straight Comba approach.  However,
-the algorithms incur an overhead (\textit{at the $O(n)$ work level}) since they require a system of equations to be solved.  This makes the
-polynomial basis approach more costly to use with small inputs.
-
-Let $m$ represent the number of digits in the multiplicands (\textit{assume both multiplicands have the same number of digits}).  There exists a
-point $y$ such that when $m < y$ the polynomial basis algorithms are more costly than Comba, when $m = y$ they are roughly the same cost and
-when $m > y$ the Comba methods are slower than the polynomial basis algorithms.
-
-The exact location of $y$ depends on several key architectural elements of the computer platform in question.
-
-\begin{enumerate}
-\item  The ratio of clock cycles for single precision multiplication versus other simpler operations such as addition, shifting, etc.  For example
-on the AMD Athlon the ratio is roughly $17 : 1$ while on the Intel P4 it is $29 : 1$.  The higher the ratio in favour of multiplication the lower
-the cutoff point $y$ will be.
-
-\item  The complexity of the linear system of equations (\textit{for the coefficients of $W(x)$}) is.  Generally speaking as the number of splits
-grows the complexity grows substantially.  Ideally solving the system will only involve addition, subtraction and shifting of integers.  This
-directly reflects on the ratio previous mentioned.
-
-\item  To a lesser extent memory bandwidth and function call overheads.  Provided the values are in the processor cache this is less of an
-influence over the cutoff point.
-
-\end{enumerate}
-
-A clean cutoff point separation occurs when a point $y$ is found such that all of the cutoff point conditions are met.  For example, if the point
-is too low then there will be values of $m$ such that $m > y$ and the Comba method is still faster.  Finding the cutoff points is fairly simple when
-a high resolution timer is available.
-
-\subsection{Karatsuba Multiplication}
-Karatsuba \cite{KARA} multiplication when originally proposed in 1962 was among the first set of algorithms to break the $O(n^2)$ barrier for
-general purpose multiplication.  Given two polynomial basis representations $f(x) = ax + b$ and $g(x) = cx + d$, Karatsuba proved with
-light algebra \cite{KARAP} that the following polynomial is equivalent to multiplication of the two integers the polynomials represent.
-
-\begin{equation}
-f(x) \cdot g(x) = acx^2 + ((a + b)(c + d) - (ac + bd))x + bd
-\end{equation}
-
-Using the observation that $ac$ and $bd$ could be re-used only three half sized multiplications would be required to produce the product.  Applying
-this algorithm recursively, the work factor becomes $O(n^{lg(3)})$ which is substantially better than the work factor $O(n^2)$ of the Comba technique.  It turns
-out what Karatsuba did not know or at least did not publish was that this is simply polynomial basis multiplication with the points
-$\zeta_0$, $\zeta_{\infty}$ and $\zeta_{1}$.  Consider the resultant system of equations.
-
-\begin{center}
-\begin{tabular}{rcrcrcrc}
-$\zeta_{0}$ &      $=$ &  &  &  & & $w_0$ \\
-$\zeta_{1}$ &      $=$ & $w_2$ & $+$ & $w_1$ & $+$ & $w_0$ \\
-$\zeta_{\infty}$ & $=$ & $w_2$ &  & &  & \\
-\end{tabular}
-\end{center}
-
-By adding the first and last equation to the equation in the middle the term $w_1$ can be isolated and all three coefficients solved for.  The simplicity
-of this system of equations has made Karatsuba fairly popular.  In fact the cutoff point is often fairly low\footnote{With LibTomMath 0.18 it is 70 and 109 digits for the Intel P4 and AMD Athlon respectively.}
-making it an ideal algorithm to speed up certain public key cryptosystems such as RSA and Diffie-Hellman.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_karatsuba\_mul}. \\
-\textbf{Input}.   mp\_int $a$ and mp\_int $b$ \\
-\textbf{Output}.  $c \leftarrow \vert a \vert \cdot \vert b \vert$ \\
-\hline \\
-1.  Init the following mp\_int variables: $x0$, $x1$, $y0$, $y1$, $t1$, $x0y0$, $x1y1$.\\
-2.  If step 2 failed then return(\textit{MP\_MEM}). \\
-\\
-Split the input.  e.g. $a = x1 \cdot \beta^B + x0$ \\
-3.  $B \leftarrow \mbox{min}(a.used, b.used)/2$ \\
-4.  $x0 \leftarrow a \mbox{ (mod }\beta^B\mbox{)}$ (\textit{mp\_mod\_2d}) \\
-5.  $y0 \leftarrow b \mbox{ (mod }\beta^B\mbox{)}$ \\
-6.  $x1 \leftarrow \lfloor a / \beta^B \rfloor$ (\textit{mp\_rshd}) \\
-7.  $y1 \leftarrow \lfloor b / \beta^B \rfloor$ \\
-\\
-Calculate the three products. \\
-8.  $x0y0 \leftarrow x0 \cdot y0$ (\textit{mp\_mul}) \\
-9.  $x1y1 \leftarrow x1 \cdot y1$ \\
-10.  $t1 \leftarrow x1 + x0$ (\textit{mp\_add}) \\
-11.  $x0 \leftarrow y1 + y0$ \\
-12.  $t1 \leftarrow t1 \cdot x0$ \\
-\\
-Calculate the middle term. \\
-13.  $x0 \leftarrow x0y0 + x1y1$ \\
-14.  $t1 \leftarrow t1 - x0$ (\textit{s\_mp\_sub}) \\
-\\
-Calculate the final product. \\
-15.  $t1 \leftarrow t1 \cdot \beta^B$ (\textit{mp\_lshd}) \\
-16.  $x1y1 \leftarrow x1y1 \cdot \beta^{2B}$ \\
-17.  $t1 \leftarrow x0y0 + t1$ \\
-18.  $c \leftarrow t1 + x1y1$ \\
-19.  Clear all of the temporary variables. \\
-20.  Return(\textit{MP\_OKAY}).\\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_karatsuba\_mul}
-\end{figure}
-
-\textbf{Algorithm mp\_karatsuba\_mul.}
-This algorithm computes the unsigned product of two inputs using the Karatsuba multiplication algorithm.  It is loosely based on the description
-from Knuth \cite[pp. 294-295]{TAOCPV2}.
-
-\index{radix point}
-In order to split the two inputs into their respective halves, a suitable \textit{radix point} must be chosen.  The radix point chosen must
-be used for both of the inputs meaning that it must be smaller than the smallest input.  Step 3 chooses the radix point $B$ as half of the
-smallest input \textbf{used} count.  After the radix point is chosen the inputs are split into lower and upper halves.  Step 4 and 5
-compute the lower halves.  Step 6 and 7 computer the upper halves.
-
-After the halves have been computed the three intermediate half-size products must be computed.  Step 8 and 9 compute the trivial products
-$x0 \cdot y0$ and $x1 \cdot y1$.  The mp\_int $x0$ is used as a temporary variable after $x1 + x0$ has been computed.  By using $x0$ instead
-of an additional temporary variable, the algorithm can avoid an addition memory allocation operation.
-
-The remaining steps 13 through 18 compute the Karatsuba polynomial through a variety of digit shifting and addition operations.
-
-EXAM,bn_mp_karatsuba_mul.c
-
-The new coding element in this routine, not  seen in previous routines, is the usage of goto statements.  The conventional
-wisdom is that goto statements should be avoided.  This is generally true, however when every single function call can fail, it makes sense
-to handle error recovery with a single piece of code.  Lines @61,if@ to @75,if@ handle initializing all of the temporary variables
-required.  Note how each of the if statements goes to a different label in case of failure.  This allows the routine to correctly free only
-the temporaries that have been successfully allocated so far.
-
-The temporary variables are all initialized using the mp\_init\_size routine since they are expected to be large.  This saves the
-additional reallocation that would have been necessary.  Also $x0$, $x1$, $y0$ and $y1$ have to be able to hold at least their respective
-number of digits for the next section of code.
-
-The first algebraic portion of the algorithm is to split the two inputs into their halves.  However, instead of using mp\_mod\_2d and mp\_rshd
-to extract the halves, the respective code has been placed inline within the body of the function.  To initialize the halves, the \textbf{used} and
-\textbf{sign} members are copied first.  The first for loop on line @98,for@ copies the lower halves.  Since they are both the same magnitude it
-is simpler to calculate both lower halves in a single loop.  The for loop on lines @104,for@ and @109,for@ calculate the upper halves $x1$ and
-$y1$ respectively.
-
-By inlining the calculation of the halves, the Karatsuba multiplier has a slightly lower overhead and can be used for smaller magnitude inputs.
-
-When line @152,err@ is reached, the algorithm has completed succesfully.  The ``error status'' variable $err$ is set to \textbf{MP\_OKAY} so that
-the same code that handles errors can be used to clear the temporary variables and return.
-
-\subsection{Toom-Cook $3$-Way Multiplication}
-Toom-Cook $3$-Way \cite{TOOM} multiplication is essentially the polynomial basis algorithm for $n = 2$ except that the points  are
-chosen such that $\zeta$ is easy to compute and the resulting system of equations easy to reduce.  Here, the points $\zeta_{0}$,
-$16 \cdot \zeta_{1 \over 2}$, $\zeta_1$, $\zeta_2$ and $\zeta_{\infty}$ make up the five required points to solve for the coefficients
-of the $W(x)$.
-
-With the five relations that Toom-Cook specifies, the following system of equations is formed.
-
-\begin{center}
-\begin{tabular}{rcrcrcrcrcr}
-$\zeta_0$                    & $=$ & $0w_4$ & $+$ & $0w_3$ & $+$ & $0w_2$ & $+$ & $0w_1$ & $+$ & $1w_0$  \\
-$16 \cdot \zeta_{1 \over 2}$ & $=$ & $1w_4$ & $+$ & $2w_3$ & $+$ & $4w_2$ & $+$ & $8w_1$ & $+$ & $16w_0$  \\
-$\zeta_1$                    & $=$ & $1w_4$ & $+$ & $1w_3$ & $+$ & $1w_2$ & $+$ & $1w_1$ & $+$ & $1w_0$  \\
-$\zeta_2$                    & $=$ & $16w_4$ & $+$ & $8w_3$ & $+$ & $4w_2$ & $+$ & $2w_1$ & $+$ & $1w_0$  \\
-$\zeta_{\infty}$             & $=$ & $1w_4$ & $+$ & $0w_3$ & $+$ & $0w_2$ & $+$ & $0w_1$ & $+$ & $0w_0$  \\
-\end{tabular}
-\end{center}
-
-A trivial solution to this matrix requires $12$ subtractions, two multiplications by a small power of two, two divisions by a small power
-of two, two divisions by three and one multiplication by three.  All of these $19$ sub-operations require less than quadratic time, meaning that
-the algorithm can be faster than a baseline multiplication.  However, the greater complexity of this algorithm places the cutoff point
-(\textbf{TOOM\_MUL\_CUTOFF}) where Toom-Cook becomes more efficient much higher than the Karatsuba cutoff point.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_toom\_mul}. \\
-\textbf{Input}.   mp\_int $a$ and mp\_int $b$ \\
-\textbf{Output}.  $c \leftarrow  a  \cdot  b $ \\
-\hline \\
-Split $a$ and $b$ into three pieces.  E.g. $a = a_2 \beta^{2k} + a_1 \beta^{k} + a_0$ \\
-1.  $k \leftarrow \lfloor \mbox{min}(a.used, b.used) / 3 \rfloor$ \\
-2.  $a_0 \leftarrow a \mbox{ (mod }\beta^{k}\mbox{)}$ \\
-3.  $a_1 \leftarrow \lfloor a / \beta^k \rfloor$, $a_1 \leftarrow a_1 \mbox{ (mod }\beta^{k}\mbox{)}$ \\
-4.  $a_2 \leftarrow \lfloor a / \beta^{2k} \rfloor$, $a_2 \leftarrow a_2 \mbox{ (mod }\beta^{k}\mbox{)}$ \\
-5.  $b_0 \leftarrow a \mbox{ (mod }\beta^{k}\mbox{)}$ \\
-6.  $b_1 \leftarrow \lfloor a / \beta^k \rfloor$, $b_1 \leftarrow b_1 \mbox{ (mod }\beta^{k}\mbox{)}$ \\
-7.  $b_2 \leftarrow \lfloor a / \beta^{2k} \rfloor$, $b_2 \leftarrow b_2 \mbox{ (mod }\beta^{k}\mbox{)}$ \\
-\\
-Find the five equations for $w_0, w_1, ..., w_4$. \\
-8.  $w_0 \leftarrow a_0 \cdot b_0$ \\
-9.  $w_4 \leftarrow a_2 \cdot b_2$ \\
-10. $tmp_1 \leftarrow 2 \cdot a_0$, $tmp_1 \leftarrow a_1 + tmp_1$, $tmp_1 \leftarrow 2 \cdot tmp_1$, $tmp_1 \leftarrow tmp_1 + a_2$ \\
-11. $tmp_2 \leftarrow 2 \cdot b_0$, $tmp_2 \leftarrow b_1 + tmp_2$, $tmp_2 \leftarrow 2 \cdot tmp_2$, $tmp_2 \leftarrow tmp_2 + b_2$ \\
-12. $w_1 \leftarrow tmp_1 \cdot tmp_2$ \\
-13. $tmp_1 \leftarrow 2 \cdot a_2$, $tmp_1 \leftarrow a_1 + tmp_1$, $tmp_1 \leftarrow 2 \cdot tmp_1$, $tmp_1 \leftarrow tmp_1 + a_0$ \\
-14. $tmp_2 \leftarrow 2 \cdot b_2$, $tmp_2 \leftarrow b_1 + tmp_2$, $tmp_2 \leftarrow 2 \cdot tmp_2$, $tmp_2 \leftarrow tmp_2 + b_0$ \\
-15. $w_3 \leftarrow tmp_1 \cdot tmp_2$ \\
-16. $tmp_1 \leftarrow a_0 + a_1$, $tmp_1 \leftarrow tmp_1 + a_2$, $tmp_2 \leftarrow b_0 + b_1$, $tmp_2 \leftarrow tmp_2 + b_2$ \\
-17. $w_2 \leftarrow tmp_1 \cdot tmp_2$ \\
-\\
-Continued on the next page.\\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_toom\_mul}
-\end{figure}
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_toom\_mul} (continued). \\
-\textbf{Input}.   mp\_int $a$ and mp\_int $b$ \\
-\textbf{Output}.  $c \leftarrow a \cdot  b $ \\
-\hline \\
-Now solve the system of equations. \\
-18. $w_1 \leftarrow w_4 - w_1$, $w_3 \leftarrow w_3 - w_0$ \\
-19. $w_1 \leftarrow \lfloor w_1 / 2 \rfloor$, $w_3 \leftarrow \lfloor w_3 / 2 \rfloor$ \\
-20. $w_2 \leftarrow w_2 - w_0$, $w_2 \leftarrow w_2 - w_4$ \\
-21. $w_1 \leftarrow w_1 - w_2$, $w_3 \leftarrow w_3 - w_2$ \\
-22. $tmp_1 \leftarrow 8 \cdot w_0$, $w_1 \leftarrow w_1 - tmp_1$, $tmp_1 \leftarrow 8 \cdot w_4$, $w_3 \leftarrow w_3 - tmp_1$ \\
-23. $w_2 \leftarrow 3 \cdot w_2$, $w_2 \leftarrow w_2 - w_1$, $w_2 \leftarrow w_2 - w_3$ \\
-24. $w_1 \leftarrow w_1 - w_2$, $w_3 \leftarrow w_3 - w_2$ \\
-25. $w_1 \leftarrow \lfloor w_1 / 3 \rfloor, w_3 \leftarrow \lfloor w_3 / 3 \rfloor$ \\
-\\
-Now substitute $\beta^k$ for $x$ by shifting $w_0, w_1, ..., w_4$. \\
-26. for $n$ from $1$ to $4$ do \\
-\hspace{3mm}26.1  $w_n \leftarrow w_n \cdot \beta^{nk}$ \\
-27. $c \leftarrow w_0 + w_1$, $c \leftarrow c + w_2$, $c \leftarrow c + w_3$, $c \leftarrow c + w_4$ \\
-28. Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_toom\_mul (continued)}
-\end{figure}
-
-\textbf{Algorithm mp\_toom\_mul.}
-This algorithm computes the product of two mp\_int variables $a$ and $b$ using the Toom-Cook approach.  Compared to the Karatsuba multiplication, this
-algorithm has a lower asymptotic running time of approximately $O(n^{1.464})$ but at an obvious cost in overhead.  In this
-description, several statements have been compounded to save space.  The intention is that the statements are executed from left to right across
-any given step.
-
-The two inputs $a$ and $b$ are first split into three $k$-digit integers $a_0, a_1, a_2$ and $b_0, b_1, b_2$ respectively.  From these smaller
-integers the coefficients of the polynomial basis representations $f(x)$ and $g(x)$ are known and can be used to find the relations required.
-
-The first two relations $w_0$ and $w_4$ are the points $\zeta_{0}$ and $\zeta_{\infty}$ respectively.  The relation $w_1, w_2$ and $w_3$ correspond
-to the points $16 \cdot \zeta_{1 \over 2}, \zeta_{2}$ and $\zeta_{1}$ respectively.  These are found using logical shifts to independently find
-$f(y)$ and $g(y)$ which significantly speeds up the algorithm.
-
-After the five relations $w_0, w_1, \ldots, w_4$ have been computed, the system they represent must be solved in order for the unknown coefficients
-$w_1, w_2$ and $w_3$ to be isolated.  The steps 18 through 25 perform the system reduction required as previously described.  Each step of
-the reduction represents the comparable matrix operation that would be performed had this been performed by pencil.  For example, step 18 indicates
-that row $1$ must be subtracted from row $4$ and simultaneously row $0$ subtracted from row $3$.
-
-Once the coeffients have been isolated, the polynomial $W(x) = \sum_{i=0}^{2n} w_i x^i$ is known.  By substituting $\beta^{k}$ for $x$, the integer
-result $a \cdot b$ is produced.
-
-EXAM,bn_mp_toom_mul.c
-
-The first obvious thing to note is that this algorithm is complicated.  The complexity is worth it if you are multiplying very
-large numbers.  For example, a 10,000 digit multiplication takes approximaly 99,282,205 fewer single precision multiplications with
-Toom--Cook than a Comba or baseline approach (this is a savings of more than 99$\%$).  For most ``crypto'' sized numbers this
-algorithm is not practical as Karatsuba has a much lower cutoff point.
-
-First we split $a$ and $b$ into three roughly equal portions.  This has been accomplished (lines @40,mod@ to @69,rshd@) with
-combinations of mp\_rshd() and mp\_mod\_2d() function calls.  At this point $a = a2 \cdot \beta^2 + a1 \cdot \beta + a0$ and similiarly
-for $b$.
-
-Next we compute the five points $w0, w1, w2, w3$ and $w4$.  Recall that $w0$ and $w4$ can be computed directly from the portions so
-we get those out of the way first (lines @72,mul@ and @77,mul@).  Next we compute $w1, w2$ and $w3$ using Horners method.
-
-After this point we solve for the actual values of $w1, w2$ and $w3$ by reducing the $5 \times 5$ system which is relatively
-straight forward.
-
-\subsection{Signed Multiplication}
-Now that algorithms to handle multiplications of every useful dimensions have been developed, a rather simple finishing touch is required.  So far all
-of the multiplication algorithms have been unsigned multiplications which leaves only a signed multiplication algorithm to be established.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_mul}. \\
-\textbf{Input}.   mp\_int $a$ and mp\_int $b$ \\
-\textbf{Output}.  $c \leftarrow a \cdot b$ \\
-\hline \\
-1.  If $a.sign = b.sign$ then \\
-\hspace{3mm}1.1  $sign = MP\_ZPOS$ \\
-2.  else \\
-\hspace{3mm}2.1  $sign = MP\_ZNEG$ \\
-3.  If min$(a.used, b.used) \ge TOOM\_MUL\_CUTOFF$ then  \\
-\hspace{3mm}3.1  $c \leftarrow a \cdot b$ using algorithm mp\_toom\_mul \\
-4.  else if min$(a.used, b.used) \ge KARATSUBA\_MUL\_CUTOFF$ then \\
-\hspace{3mm}4.1  $c \leftarrow a \cdot b$ using algorithm mp\_karatsuba\_mul \\
-5.  else \\
-\hspace{3mm}5.1  $digs \leftarrow a.used + b.used + 1$ \\
-\hspace{3mm}5.2  If $digs < MP\_ARRAY$ and min$(a.used, b.used) \le \delta$ then \\
-\hspace{6mm}5.2.1  $c \leftarrow a \cdot b \mbox{ (mod }\beta^{digs}\mbox{)}$ using algorithm fast\_s\_mp\_mul\_digs.  \\
-\hspace{3mm}5.3  else \\
-\hspace{6mm}5.3.1  $c \leftarrow a \cdot b \mbox{ (mod }\beta^{digs}\mbox{)}$ using algorithm s\_mp\_mul\_digs.  \\
-6.  $c.sign \leftarrow sign$ \\
-7.  Return the result of the unsigned multiplication performed. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_mul}
-\end{figure}
-
-\textbf{Algorithm mp\_mul.}
-This algorithm performs the signed multiplication of two inputs.  It will make use of any of the three unsigned multiplication algorithms
-available when the input is of appropriate size.  The \textbf{sign} of the result is not set until the end of the algorithm since algorithm
-s\_mp\_mul\_digs will clear it.
-
-EXAM,bn_mp_mul.c
-
-The implementation is rather simplistic and is not particularly noteworthy.  Line @22,?@ computes the sign of the result using the ``?''
-operator from the C programming language.  Line @37,<<@ computes $\delta$ using the fact that $1 << k$ is equal to $2^k$.
-
-\section{Squaring}
-\label{sec:basesquare}
-
-Squaring is a special case of multiplication where both multiplicands are equal.  At first it may seem like there is no significant optimization
-available but in fact there is.  Consider the multiplication of $576$ against $241$.  In total there will be nine single precision multiplications
-performed which are $1\cdot 6$, $1 \cdot 7$, $1 \cdot 5$, $4 \cdot 6$, $4 \cdot 7$, $4 \cdot 5$, $2 \cdot  6$, $2 \cdot 7$ and $2 \cdot 5$.  Now consider
-the multiplication of $123$ against $123$.  The nine products are $3 \cdot 3$, $3 \cdot 2$, $3 \cdot 1$, $2 \cdot 3$, $2 \cdot 2$, $2 \cdot 1$,
-$1 \cdot 3$, $1 \cdot 2$ and $1 \cdot 1$.  On closer inspection some of the products are equivalent.  For example, $3 \cdot 2 = 2 \cdot 3$
-and $3 \cdot 1 = 1 \cdot 3$.
-
-For any $n$-digit input, there are ${{\left (n^2 + n \right)}\over 2}$ possible unique single precision multiplications required compared to the $n^2$
-required for multiplication.  The following diagram gives an example of the operations required.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{ccccc|c}
-&&1&2&3&\\
-$\times$ &&1&2&3&\\
-\hline && $3 \cdot 1$ & $3 \cdot 2$ & $3 \cdot 3$ & Row 0\\
-       & $2 \cdot 1$  & $2 \cdot 2$ & $2 \cdot 3$ && Row 1 \\
-         $1 \cdot 1$  & $1 \cdot 2$ & $1 \cdot 3$ &&& Row 2 \\
-\end{tabular}
-\end{center}
-\caption{Squaring Optimization Diagram}
-\end{figure}
-
-MARK,SQUARE
-Starting from zero and numbering the columns from right to left a very simple pattern becomes obvious.  For the purposes of this discussion let $x$
-represent the number being squared.  The first observation is that in row $k$ the $2k$'th column of the product has a $\left (x_k \right)^2$ term in it.
-
-The second observation is that every column $j$ in row $k$ where $j \ne 2k$ is part of a double product.  Every non-square term of a column will
-appear twice hence the name ``double product''.  Every odd column is made up entirely of double products.  In fact every column is made up of double
-products and at most one square (\textit{see the exercise section}).
-
-The third and final observation is that for row $k$ the first unique non-square term, that is, one that hasn't already appeared in an earlier row,
-occurs at column $2k + 1$.  For example, on row $1$ of the previous squaring, column one is part of the double product with column one from row zero.
-Column two of row one is a square and column three is the first unique column.
-
-\subsection{The Baseline Squaring Algorithm}
-The baseline squaring algorithm is meant to be a catch-all squaring algorithm.  It will handle any of the input sizes that the faster routines
-will not handle.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{s\_mp\_sqr}. \\
-\textbf{Input}.   mp\_int $a$ \\
-\textbf{Output}.  $b \leftarrow a^2$ \\
-\hline \\
-1.  Init a temporary mp\_int of at least $2 \cdot a.used +1$ digits.  (\textit{mp\_init\_size}) \\
-2.  If step 1 failed return(\textit{MP\_MEM}) \\
-3.  $t.used \leftarrow 2 \cdot a.used + 1$ \\
-4.  For $ix$ from 0 to $a.used - 1$ do \\
-\hspace{3mm}Calculate the square. \\
-\hspace{3mm}4.1  $\hat r \leftarrow t_{2ix} + \left (a_{ix} \right )^2$ \\
-\hspace{3mm}4.2  $t_{2ix} \leftarrow \hat r \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{3mm}Calculate the double products after the square. \\
-\hspace{3mm}4.3  $u \leftarrow \lfloor \hat r / \beta \rfloor$ \\
-\hspace{3mm}4.4  For $iy$ from $ix + 1$ to $a.used - 1$ do \\
-\hspace{6mm}4.4.1  $\hat r \leftarrow 2 \cdot a_{ix}a_{iy} + t_{ix + iy} + u$ \\
-\hspace{6mm}4.4.2  $t_{ix + iy} \leftarrow \hat r \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{6mm}4.4.3  $u \leftarrow \lfloor \hat r / \beta \rfloor$ \\
-\hspace{3mm}Set the last carry. \\
-\hspace{3mm}4.5  While $u > 0$ do \\
-\hspace{6mm}4.5.1  $iy \leftarrow iy + 1$ \\
-\hspace{6mm}4.5.2  $\hat r \leftarrow t_{ix + iy} + u$ \\
-\hspace{6mm}4.5.3  $t_{ix + iy} \leftarrow \hat r \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{6mm}4.5.4  $u \leftarrow \lfloor \hat r / \beta \rfloor$ \\
-5.  Clamp excess digits of $t$.  (\textit{mp\_clamp}) \\
-6.  Exchange $b$ and $t$. \\
-7.  Clear $t$ (\textit{mp\_clear}) \\
-8.  Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm s\_mp\_sqr}
-\end{figure}
-
-\textbf{Algorithm s\_mp\_sqr.}
-This algorithm computes the square of an input using the three observations on squaring.  It is based fairly faithfully on  algorithm 14.16 of HAC
-\cite[pp.596-597]{HAC}.  Similar to algorithm s\_mp\_mul\_digs, a temporary mp\_int is allocated to hold the result of the squaring.  This allows the
-destination mp\_int to be the same as the source mp\_int.
-
-The outer loop of this algorithm begins on step 4. It is best to think of the outer loop as walking down the rows of the partial results, while
-the inner loop computes the columns of the partial result.  Step 4.1 and 4.2 compute the square term for each row, and step 4.3 and 4.4 propagate
-the carry and compute the double products.
-
-The requirement that a mp\_word be able to represent the range $0 \le x < 2 \beta^2$ arises from this
-very algorithm.  The product $a_{ix}a_{iy}$ will lie in the range $0 \le x \le \beta^2 - 2\beta + 1$ which is obviously less than $\beta^2$ meaning that
-when it is multiplied by two, it can be properly represented by a mp\_word.
-
-Similar to algorithm s\_mp\_mul\_digs, after every pass of the inner loop, the destination is correctly set to the sum of all of the partial
-results calculated so far.  This involves expensive carry propagation which will be eliminated in the next algorithm.
-
-EXAM,bn_s_mp_sqr.c
-
-Inside the outer loop (line @32,for@) the square term is calculated on line @35,r =@.  The carry (line @42,>>@) has been
-extracted from the mp\_word accumulator using a right shift.  Aliases for $a_{ix}$ and $t_{ix+iy}$ are initialized
-(lines @45,tmpx@ and @48,tmpt@) to simplify the inner loop.  The doubling is performed using two
-additions (line @57,r + r@) since it is usually faster than shifting, if not at least as fast.
-
-The important observation is that the inner loop does not begin at $iy = 0$ like for multiplication.  As such the inner loops
-get progressively shorter as the algorithm proceeds.  This is what leads to the savings compared to using a multiplication to
-square a number.
-
-\subsection{Faster Squaring by the ``Comba'' Method}
-A major drawback to the baseline method is the requirement for single precision shifting inside the $O(n^2)$ nested loop.  Squaring has an additional
-drawback that it must double the product inside the inner loop as well.  As for multiplication, the Comba technique can be used to eliminate these
-performance hazards.
-
-The first obvious solution is to make an array of mp\_words which will hold all of the columns.  This will indeed eliminate all of the carry
-propagation operations from the inner loop.  However, the inner product must still be doubled $O(n^2)$ times.  The solution stems from the simple fact
-that $2a + 2b + 2c = 2(a + b + c)$.  That is the sum of all of the double products is equal to double the sum of all the products.  For example,
-$ab + ba + ac + ca = 2ab + 2ac = 2(ab + ac)$.
-
-However, we cannot simply double all of the columns, since the squares appear only once per row.  The most practical solution is to have two
-mp\_word arrays.  One array will hold the squares and the other array will hold the double products.  With both arrays the doubling and
-carry propagation can be moved to a $O(n)$ work level outside the $O(n^2)$ level.  In this case, we have an even simpler solution in mind.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{fast\_s\_mp\_sqr}. \\
-\textbf{Input}.   mp\_int $a$ \\
-\textbf{Output}.  $b \leftarrow a^2$ \\
-\hline \\
-Place an array of \textbf{MP\_WARRAY} mp\_digits named $W$ on the stack. \\
-1.  If $b.alloc < 2a.used + 1$ then grow $b$ to $2a.used + 1$ digits.  (\textit{mp\_grow}). \\
-2.  If step 1 failed return(\textit{MP\_MEM}). \\
-\\
-3.  $pa \leftarrow 2 \cdot a.used$ \\
-4.  $\hat W1 \leftarrow 0$ \\
-5.  for $ix$ from $0$ to $pa - 1$ do \\
-\hspace{3mm}5.1  $\_ \hat W \leftarrow 0$ \\
-\hspace{3mm}5.2  $ty \leftarrow \mbox{MIN}(a.used - 1, ix)$ \\
-\hspace{3mm}5.3  $tx \leftarrow ix - ty$ \\
-\hspace{3mm}5.4  $iy \leftarrow \mbox{MIN}(a.used - tx, ty + 1)$ \\
-\hspace{3mm}5.5  $iy \leftarrow \mbox{MIN}(iy, \lfloor \left (ty - tx + 1 \right )/2 \rfloor)$ \\
-\hspace{3mm}5.6  for $iz$ from $0$ to $iz - 1$ do \\
-\hspace{6mm}5.6.1  $\_ \hat W \leftarrow \_ \hat W + a_{tx + iz}a_{ty - iz}$ \\
-\hspace{3mm}5.7  $\_ \hat W \leftarrow 2 \cdot \_ \hat W  + \hat W1$ \\
-\hspace{3mm}5.8  if $ix$ is even then \\
-\hspace{6mm}5.8.1  $\_ \hat W \leftarrow \_ \hat W + \left ( a_{\lfloor ix/2 \rfloor}\right )^2$ \\
-\hspace{3mm}5.9  $W_{ix} \leftarrow \_ \hat W (\mbox{mod }\beta)$ \\
-\hspace{3mm}5.10  $\hat W1 \leftarrow \lfloor \_ \hat W / \beta \rfloor$ \\
-\\
-6.  $oldused \leftarrow b.used$ \\
-7.  $b.used \leftarrow 2 \cdot a.used$ \\
-8.  for $ix$ from $0$ to $pa - 1$ do \\
-\hspace{3mm}8.1  $b_{ix} \leftarrow W_{ix}$ \\
-9.  for $ix$ from $pa$ to $oldused - 1$ do \\
-\hspace{3mm}9.1  $b_{ix} \leftarrow 0$ \\
-10.  Clamp excess digits from $b$.  (\textit{mp\_clamp}) \\
-11.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm fast\_s\_mp\_sqr}
-\end{figure}
-
-\textbf{Algorithm fast\_s\_mp\_sqr.}
-This algorithm computes the square of an input using the Comba technique.  It is designed to be a replacement for algorithm
-s\_mp\_sqr when the number of input digits is less than \textbf{MP\_WARRAY} and less than $\delta \over 2$.
-This algorithm is very similar to the Comba multiplier except with a few key differences we shall make note of.
-
-First, we have an accumulator and carry variables $\_ \hat W$ and $\hat W1$ respectively.  This is because the inner loop
-products are to be doubled.  If we had added the previous carry in we would be doubling too much.  Next we perform an
-addition MIN condition on $iy$ (step 5.5) to prevent overlapping digits.  For example, $a_3 \cdot a_5$ is equal
-$a_5 \cdot a_3$.  Whereas in the multiplication case we would have $5 < a.used$ and $3 \ge 0$ is maintained since we double the sum
-of the products just outside the inner loop we have to avoid doing this.  This is also a good thing since we perform
-fewer multiplications and the routine ends up being faster.
-
-Finally the last difference is the addition of the ``square'' term outside the inner loop (step 5.8).  We add in the square
-only to even outputs and it is the square of the term at the $\lfloor ix / 2 \rfloor$ position.
-
-EXAM,bn_fast_s_mp_sqr.c
-
-This implementation is essentially a copy of Comba multiplication with the appropriate changes added to make it faster for
-the special case of squaring.
-
-\subsection{Polynomial Basis Squaring}
-The same algorithm that performs optimal polynomial basis multiplication can be used to perform polynomial basis squaring.  The minor exception
-is that $\zeta_y = f(y)g(y)$ is actually equivalent to $\zeta_y = f(y)^2$ since $f(y) = g(y)$.  Instead of performing $2n + 1$
-multiplications to find the $\zeta$ relations, squaring operations are performed instead.
-
-\subsection{Karatsuba Squaring}
-Let $f(x) = ax + b$ represent the polynomial basis representation of a number to square.
-Let $h(x) = \left ( f(x) \right )^2$ represent the square of the polynomial.  The Karatsuba equation can be modified to square a
-number with the following equation.
-
-\begin{equation}
-h(x) = a^2x^2 + \left ((a + b)^2 - (a^2 + b^2) \right )x + b^2
-\end{equation}
-
-Upon closer inspection this equation only requires the calculation of three half-sized squares: $a^2$, $b^2$ and $(a + b)^2$.  As in
-Karatsuba multiplication, this algorithm can be applied recursively on the input and will achieve an asymptotic running time of
-$O \left ( n^{lg(3)} \right )$.
-
-If the asymptotic times of Karatsuba squaring and multiplication are the same, why not simply use the multiplication algorithm
-instead?  The answer to this arises from the cutoff point for squaring.  As in multiplication there exists a cutoff point, at which the
-time required for a Comba based squaring and a Karatsuba based squaring meet.  Due to the overhead inherent in the Karatsuba method, the cutoff
-point is fairly high.  For example, on an AMD Athlon XP processor with $\beta = 2^{28}$, the cutoff point is around 127 digits.
-
-Consider squaring a 200 digit number with this technique.  It will be split into two 100 digit halves which are subsequently squared.
-The 100 digit halves will not be squared using Karatsuba, but instead using the faster Comba based squaring algorithm.  If Karatsuba multiplication
-were used instead, the 100 digit numbers would be squared with a slower Comba based multiplication.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_karatsuba\_sqr}. \\
-\textbf{Input}.   mp\_int $a$ \\
-\textbf{Output}.  $b \leftarrow a^2$ \\
-\hline \\
-1.  Initialize the following temporary mp\_ints:  $x0$, $x1$, $t1$, $t2$, $x0x0$ and $x1x1$. \\
-2.  If any of the initializations on step 1 failed return(\textit{MP\_MEM}). \\
-\\
-Split the input.  e.g. $a = x1\beta^B + x0$ \\
-3.  $B \leftarrow \lfloor a.used / 2 \rfloor$ \\
-4.  $x0 \leftarrow a \mbox{ (mod }\beta^B\mbox{)}$ (\textit{mp\_mod\_2d}) \\
-5.  $x1 \leftarrow \lfloor a / \beta^B \rfloor$ (\textit{mp\_lshd}) \\
-\\
-Calculate the three squares. \\
-6.  $x0x0 \leftarrow x0^2$ (\textit{mp\_sqr}) \\
-7.  $x1x1 \leftarrow x1^2$ \\
-8.  $t1 \leftarrow x1 + x0$ (\textit{s\_mp\_add}) \\
-9.  $t1 \leftarrow t1^2$ \\
-\\
-Compute the middle term. \\
-10.  $t2 \leftarrow x0x0 + x1x1$ (\textit{s\_mp\_add}) \\
-11.  $t1 \leftarrow t1 - t2$ \\
-\\
-Compute final product. \\
-12.  $t1 \leftarrow t1\beta^B$ (\textit{mp\_lshd}) \\
-13.  $x1x1 \leftarrow x1x1\beta^{2B}$ \\
-14.  $t1 \leftarrow t1 + x0x0$ \\
-15.  $b \leftarrow t1 + x1x1$ \\
-16.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_karatsuba\_sqr}
-\end{figure}
-
-\textbf{Algorithm mp\_karatsuba\_sqr.}
-This algorithm computes the square of an input $a$ using the Karatsuba technique.  This algorithm is very similar to the Karatsuba based
-multiplication algorithm with the exception that the three half-size multiplications have been replaced with three half-size squarings.
-
-The radix point for squaring is simply placed exactly in the middle of the digits when the input has an odd number of digits, otherwise it is
-placed just below the middle.  Step 3, 4 and 5 compute the two halves required using $B$
-as the radix point.  The first two squares in steps 6 and 7 are rather straightforward while the last square is of a more compact form.
-
-By expanding $\left (x1 + x0 \right )^2$, the $x1^2$ and $x0^2$ terms in the middle disappear, that is $(x0 - x1)^2 - (x1^2 + x0^2)  = 2 \cdot x0 \cdot x1$.
-Now if $5n$ single precision additions and a squaring of $n$-digits is faster than multiplying two $n$-digit numbers and doubling then
-this method is faster.  Assuming no further recursions occur, the difference can be estimated with the following inequality.
-
-Let $p$ represent the cost of a single precision addition and $q$ the cost of a single precision multiplication both in terms of time\footnote{Or
-machine clock cycles.}.
-
-\begin{equation}
-5pn +{{q(n^2 + n)} \over 2} \le pn + qn^2
-\end{equation}
-
-For example, on an AMD Athlon XP processor $p = {1 \over 3}$ and $q = 6$.  This implies that the following inequality should hold.
-\begin{center}
-\begin{tabular}{rcl}
-${5n \over 3} + 3n^2 + 3n$     & $<$ & ${n \over 3} + 6n^2$ \\
-${5 \over 3} + 3n + 3$     & $<$ & ${1 \over 3} + 6n$ \\
-${13 \over 9}$     & $<$ & $n$ \\
-\end{tabular}
-\end{center}
-
-This results in a cutoff point around $n = 2$.  As a consequence it is actually faster to compute the middle term the ``long way'' on processors
-where multiplication is substantially slower\footnote{On the Athlon there is a 1:17 ratio between clock cycles for addition and multiplication.  On
-the Intel P4 processor this ratio is 1:29 making this method even more beneficial.  The only common exception is the ARMv4 processor which has a
-ratio of 1:7.  } than simpler operations such as addition.
-
-EXAM,bn_mp_karatsuba_sqr.c
-
-This implementation is largely based on the implementation of algorithm mp\_karatsuba\_mul.  It uses the same inline style to copy and
-shift the input into the two halves.  The loop from line @54,{@ to line @70,}@ has been modified since only one input exists.  The \textbf{used}
-count of both $x0$ and $x1$ is fixed up and $x0$ is clamped before the calculations begin.  At this point $x1$ and $x0$ are valid equivalents
-to the respective halves as if mp\_rshd and mp\_mod\_2d had been used.
-
-By inlining the copy and shift operations the cutoff point for Karatsuba multiplication can be lowered.  On the Athlon the cutoff point
-is exactly at the point where Comba squaring can no longer be used (\textit{128 digits}).  On slower processors such as the Intel P4
-it is actually below the Comba limit (\textit{at 110 digits}).
-
-This routine uses the same error trap coding style as mp\_karatsuba\_sqr.  As the temporary variables are initialized errors are
-redirected to the error trap higher up.  If the algorithm completes without error the error code is set to \textbf{MP\_OKAY} and
-mp\_clears are executed normally.
-
-\subsection{Toom-Cook Squaring}
-The Toom-Cook squaring algorithm mp\_toom\_sqr is heavily based on the algorithm mp\_toom\_mul with the exception that squarings are used
-instead of multiplication to find the five relations.  The reader is encouraged to read the description of the latter algorithm and try to
-derive their own Toom-Cook squaring algorithm.
-
-\subsection{High Level Squaring}
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_sqr}. \\
-\textbf{Input}.   mp\_int $a$ \\
-\textbf{Output}.  $b \leftarrow a^2$ \\
-\hline \\
-1.  If $a.used \ge TOOM\_SQR\_CUTOFF$ then  \\
-\hspace{3mm}1.1  $b \leftarrow a^2$ using algorithm mp\_toom\_sqr \\
-2.  else if $a.used \ge KARATSUBA\_SQR\_CUTOFF$ then \\
-\hspace{3mm}2.1  $b \leftarrow a^2$ using algorithm mp\_karatsuba\_sqr \\
-3.  else \\
-\hspace{3mm}3.1  $digs \leftarrow a.used + b.used + 1$ \\
-\hspace{3mm}3.2  If $digs < MP\_ARRAY$ and $a.used \le \delta$ then \\
-\hspace{6mm}3.2.1  $b \leftarrow a^2$ using algorithm fast\_s\_mp\_sqr.  \\
-\hspace{3mm}3.3  else \\
-\hspace{6mm}3.3.1  $b \leftarrow a^2$ using algorithm s\_mp\_sqr.  \\
-4.  $b.sign \leftarrow MP\_ZPOS$ \\
-5.  Return the result of the unsigned squaring performed. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_sqr}
-\end{figure}
-
-\textbf{Algorithm mp\_sqr.}
-This algorithm computes the square of the input using one of four different algorithms.  If the input is very large and has at least
-\textbf{TOOM\_SQR\_CUTOFF} or \textbf{KARATSUBA\_SQR\_CUTOFF} digits then either the Toom-Cook or the Karatsuba Squaring algorithm is used.  If
-neither of the polynomial basis algorithms should be used then either the Comba or baseline algorithm is used.
-
-EXAM,bn_mp_sqr.c
-
-\section*{Exercises}
-\begin{tabular}{cl}
-$\left [ 3 \right ] $ & Devise an efficient algorithm for selection of the radix point to handle inputs \\
-                      & that have different number of digits in Karatsuba multiplication. \\
-                      & \\
-$\left [ 2 \right ] $ & In ~SQUARE~ the fact that every column of a squaring is made up \\
-                      & of double products and at most one square is stated.  Prove this statement. \\
-                      & \\
-$\left [ 3 \right ] $ & Prove the equation for Karatsuba squaring. \\
-                      & \\
-$\left [ 1 \right ] $ & Prove that Karatsuba squaring requires $O \left (n^{lg(3)} \right )$ time. \\
-                      & \\
-$\left [ 2 \right ] $ & Determine the minimal ratio between addition and multiplication clock cycles \\
-                      & required for equation $6.7$ to be true.  \\
-                      & \\
-$\left [ 3 \right ] $ & Implement a threaded version of Comba multiplication (and squaring) where you \\
-                      & compute subsets of the columns in each thread.  Determine a cutoff point where \\
-                      & it is effective and add the logic to mp\_mul() and mp\_sqr(). \\
-                      &\\
-$\left [ 4 \right ] $ & Same as the previous but also modify the Karatsuba and Toom-Cook.  You must \\
-                      & increase the throughput of mp\_exptmod() for random odd moduli in the range \\
-                      & $512 \ldots 4096$ bits significantly ($> 2x$) to complete this challenge. \\
-                      & \\
-\end{tabular}
-
-\chapter{Modular Reduction}
-MARK,REDUCTION
-\section{Basics of Modular Reduction}
-\index{modular residue}
-Modular reduction is an operation that arises quite often within public key cryptography algorithms and various number theoretic algorithms,
-such as factoring.  Modular reduction algorithms are the third class of algorithms of the ``multipliers'' set.  A number $a$ is said to be \textit{reduced}
-modulo another number $b$ by finding the remainder of the division $a/b$.  Full integer division with remainder is a topic to be covered
-in~\ref{sec:division}.
-
-Modular reduction is equivalent to solving for $r$ in the following equation.  $a = bq + r$ where $q = \lfloor a/b \rfloor$.  The result
-$r$ is said to be ``congruent to $a$ modulo $b$'' which is also written as $r \equiv a \mbox{ (mod }b\mbox{)}$.  In other vernacular $r$ is known as the
-``modular residue'' which leads to ``quadratic residue''\footnote{That's fancy talk for $b \equiv a^2 \mbox{ (mod }p\mbox{)}$.} and
-other forms of residues.
-
-Modular reductions are normally used to create either finite groups, rings or fields.  The most common usage for performance driven modular reductions
-is in modular exponentiation algorithms.  That is to compute $d = a^b \mbox{ (mod }c\mbox{)}$ as fast as possible.  This operation is used in the
-RSA and Diffie-Hellman public key algorithms, for example.  Modular multiplication and squaring also appears as a fundamental operation in
-elliptic curve cryptographic algorithms.  As will be discussed in the subsequent chapter there exist fast algorithms for computing modular
-exponentiations without having to perform (\textit{in this example}) $b - 1$ multiplications.  These algorithms will produce partial results in the
-range $0 \le x < c^2$ which can be taken advantage of to create several efficient algorithms.   They have also been used to create redundancy check
-algorithms known as CRCs, error correction codes such as Reed-Solomon and solve a variety of number theoeretic problems.
-
-\section{The Barrett Reduction}
-The Barrett reduction algorithm \cite{BARRETT} was inspired by fast division algorithms which multiply by the reciprocal to emulate
-division.  Barretts observation was that the residue $c$ of $a$ modulo $b$ is equal to
-
-\begin{equation}
-c = a - b \cdot \lfloor a/b \rfloor
-\end{equation}
-
-Since algorithms such as modular exponentiation would be using the same modulus extensively, typical DSP\footnote{It is worth noting that Barrett's paper
-targeted the DSP56K processor.}  intuition would indicate the next step would be to replace $a/b$ by a multiplication by the reciprocal.  However,
-DSP intuition on its own will not work as these numbers are considerably larger than the precision of common DSP floating point data types.
-It would take another common optimization to optimize the algorithm.
-
-\subsection{Fixed Point Arithmetic}
-The trick used to optimize the above equation is based on a technique of emulating floating point data types with fixed precision integers.  Fixed
-point arithmetic would become very popular as it greatly optimize the ``3d-shooter'' genre of games in the mid 1990s when floating point units were
-fairly slow if not unavailable.   The idea behind fixed point arithmetic is to take a normal $k$-bit integer data type and break it into $p$-bit
-integer and a $q$-bit fraction part (\textit{where $p+q = k$}).
-
-In this system a $k$-bit integer $n$ would actually represent $n/2^q$.  For example, with $q = 4$ the integer $n = 37$ would actually represent the
-value $2.3125$.  To multiply two fixed point numbers the integers are multiplied using traditional arithmetic and subsequently normalized by
-moving the implied decimal point back to where it should be.  For example, with $q = 4$ to multiply the integers $9$ and $5$ they must be converted
-to fixed point first by multiplying by $2^q$.  Let $a = 9(2^q)$ represent the fixed point representation of $9$ and $b = 5(2^q)$ represent the
-fixed point representation of $5$.  The product $ab$ is equal to $45(2^{2q})$ which when normalized by dividing by $2^q$ produces $45(2^q)$.
-
-This technique became popular since a normal integer multiplication and logical shift right are the only required operations to perform a multiplication
-of two fixed point numbers.  Using fixed point arithmetic, division can be easily approximated by multiplying by the reciprocal.  If $2^q$ is
-equivalent to one than $2^q/b$ is equivalent to the fixed point approximation of $1/b$ using real arithmetic.  Using this fact dividing an integer
-$a$ by another integer $b$ can be achieved with the following expression.
-
-\begin{equation}
-\lfloor a / b \rfloor \mbox{ }\approx\mbox{ } \lfloor (a \cdot \lfloor 2^q / b \rfloor)/2^q \rfloor
-\end{equation}
-
-The precision of the division is proportional to the value of $q$.  If the divisor $b$ is used frequently as is the case with
-modular exponentiation pre-computing $2^q/b$ will allow a division to be performed with a multiplication and a right shift.  Both operations
-are considerably faster than division on most processors.
-
-Consider dividing $19$ by $5$.  The correct result is $\lfloor 19/5 \rfloor = 3$.  With $q = 3$ the reciprocal is $\lfloor 2^q/5 \rfloor = 1$ which
-leads to a product of $19$ which when divided by $2^q$ produces $2$.  However, with $q = 4$ the reciprocal is $\lfloor 2^q/5 \rfloor = 3$ and
-the result of the emulated division is $\lfloor 3 \cdot 19 / 2^q \rfloor = 3$ which is correct.  The value of $2^q$ must be close to or ideally
-larger than the dividend.  In effect if $a$ is the dividend then $q$ should allow $0 \le \lfloor a/2^q \rfloor \le 1$ in order for this approach
-to work correctly.  Plugging this form of divison into the original equation the following modular residue equation arises.
-
-\begin{equation}
-c = a - b \cdot \lfloor (a \cdot \lfloor 2^q / b \rfloor)/2^q \rfloor
-\end{equation}
-
-Using the notation from \cite{BARRETT} the value of $\lfloor 2^q / b \rfloor$ will be represented by the $\mu$ symbol.  Using the $\mu$
-variable also helps re-inforce the idea that it is meant to be computed once and re-used.
-
-\begin{equation}
-c = a - b \cdot \lfloor (a \cdot \mu)/2^q \rfloor
-\end{equation}
-
-Provided that $2^q \ge a$ this algorithm will produce a quotient that is either exactly correct or off by a value of one.  In the context of Barrett
-reduction the value of $a$ is bound by $0 \le a \le (b - 1)^2$ meaning that $2^q \ge b^2$ is sufficient to ensure the reciprocal will have enough
-precision.
-
-Let $n$ represent the number of digits in $b$.  This algorithm requires approximately $2n^2$ single precision multiplications to produce the quotient and
-another $n^2$ single precision multiplications to find the residue.  In total $3n^2$ single precision multiplications are required to
-reduce the number.
-
-For example, if $b = 1179677$ and $q = 41$ ($2^q > b^2$), then the reciprocal $\mu$ is equal to $\lfloor 2^q / b \rfloor = 1864089$.  Consider reducing
-$a = 180388626447$ modulo $b$ using the above reduction equation.  The quotient using the new formula is $\lfloor (a \cdot \mu) / 2^q \rfloor = 152913$.
-By subtracting $152913b$ from $a$ the correct residue $a \equiv 677346 \mbox{ (mod }b\mbox{)}$ is found.
-
-\subsection{Choosing a Radix Point}
-Using the fixed point representation a modular reduction can be performed with $3n^2$ single precision multiplications.  If that were the best
-that could be achieved a full division\footnote{A division requires approximately $O(2cn^2)$ single precision multiplications for a small value of $c$.
-See~\ref{sec:division} for further details.} might as well be used in its place.  The key to optimizing the reduction is to reduce the precision of
-the initial multiplication that finds the quotient.
-
-Let $a$ represent the number of which the residue is sought.  Let $b$ represent the modulus used to find the residue.  Let $m$ represent
-the number of digits in $b$.  For the purposes of this discussion we will assume that the number of digits in $a$ is $2m$, which is generally true if
-two $m$-digit numbers have been multiplied.  Dividing $a$ by $b$ is the same as dividing a $2m$ digit integer by a $m$ digit integer.  Digits below the
-$m - 1$'th digit of $a$ will contribute at most a value of $1$ to the quotient because $\beta^k < b$ for any $0 \le k \le m - 1$.  Another way to
-express this is by re-writing $a$ as two parts.  If $a' \equiv a \mbox{ (mod }b^m\mbox{)}$ and $a'' = a - a'$ then
-${a \over b} \equiv {{a' + a''} \over b}$ which is equivalent to ${a' \over b} + {a'' \over b}$.  Since $a'$ is bound to be less than $b$ the quotient
-is bound by $0 \le {a' \over b} < 1$.
-
-Since the digits of $a'$ do not contribute much to the quotient the observation is that they might as well be zero.  However, if the digits
-``might as well be zero'' they might as well not be there in the first place.  Let $q_0 = \lfloor a/\beta^{m-1} \rfloor$ represent the input
-with the irrelevant digits trimmed.  Now the modular reduction is trimmed to the almost equivalent equation
-
-\begin{equation}
-c = a - b \cdot \lfloor (q_0 \cdot \mu) / \beta^{m+1} \rfloor
-\end{equation}
-
-Note that the original divisor $2^q$ has been replaced with $\beta^{m+1}$ where in this case $q$ is a multiple of $lg(\beta)$. Also note that the
-exponent on the divisor when added to the amount $q_0$ was shifted by equals $2m$.  If the optimization had not been performed the divisor
-would have the exponent $2m$ so in the end the exponents do ``add up''. Using the above equation the quotient
-$\lfloor (q_0 \cdot \mu) / \beta^{m+1} \rfloor$ can be off from the true quotient by at most two.  The original fixed point quotient can be off
-by as much as one (\textit{provided the radix point is chosen suitably}) and now that the lower irrelevent digits have been trimmed the quotient
-can be off by an additional value of one for a total of at most two.  This implies that
-$0 \le a - b \cdot \lfloor (q_0 \cdot \mu) / \beta^{m+1} \rfloor < 3b$.  By first subtracting $b$ times the quotient and then conditionally subtracting
-$b$ once or twice the residue is found.
-
-The quotient is now found using $(m + 1)(m) = m^2 + m$ single precision multiplications and the residue with an additional $m^2$ single
-precision multiplications, ignoring the subtractions required.  In total $2m^2 + m$ single precision multiplications are required to find the residue.
-This is considerably faster than the original attempt.
-
-For example, let $\beta = 10$ represent the radix of the digits.  Let $b = 9999$ represent the modulus which implies $m = 4$. Let $a = 99929878$
-represent the value of which the residue is desired.  In this case $q = 8$ since $10^7 < 9999^2$ meaning that $\mu = \lfloor \beta^{q}/b \rfloor = 10001$.
-With the new observation the multiplicand for the quotient is equal to $q_0 = \lfloor a / \beta^{m - 1} \rfloor = 99929$.  The quotient is then
-$\lfloor (q_0 \cdot \mu) / \beta^{m+1} \rfloor = 9993$.  Subtracting $9993b$ from $a$ and the correct residue $a \equiv 9871 \mbox{ (mod }b\mbox{)}$
-is found.
-
-\subsection{Trimming the Quotient}
-So far the reduction algorithm has been optimized from $3m^2$ single precision multiplications down to $2m^2 + m$ single precision multiplications.  As
-it stands now the algorithm is already fairly fast compared to a full integer division algorithm.  However, there is still room for
-optimization.
-
-After the first multiplication inside the quotient ($q_0 \cdot \mu$) the value is shifted right by $m + 1$ places effectively nullifying the lower
-half of the product.  It would be nice to be able to remove those digits from the product to effectively cut down the number of single precision
-multiplications.  If the number of digits in the modulus $m$ is far less than $\beta$ a full product is not required for the algorithm to work properly.
-In fact the lower $m - 2$ digits will not affect the upper half of the product at all and do not need to be computed.
-
-The value of $\mu$ is a $m$-digit number and $q_0$ is a $m + 1$ digit number.  Using a full multiplier $(m + 1)(m) = m^2 + m$ single precision
-multiplications would be required.  Using a multiplier that will only produce digits at and above the $m - 1$'th digit reduces the number
-of single precision multiplications to ${m^2 + m} \over 2$ single precision multiplications.
-
-\subsection{Trimming the Residue}
-After the quotient has been calculated it is used to reduce the input.  As previously noted the algorithm is not exact and it can be off by a small
-multiple of the modulus, that is $0 \le a - b \cdot \lfloor (q_0 \cdot \mu) / \beta^{m+1} \rfloor < 3b$.  If $b$ is $m$ digits than the
-result of reduction equation is a value of at most $m + 1$ digits (\textit{provided $3 < \beta$}) implying that the upper $m - 1$ digits are
-implicitly zero.
-
-The next optimization arises from this very fact.  Instead of computing $b \cdot \lfloor (q_0 \cdot \mu) / \beta^{m+1} \rfloor$ using a full
-$O(m^2)$ multiplication algorithm only the lower $m+1$ digits of the product have to be computed.  Similarly the value of $a$ can
-be reduced modulo $\beta^{m+1}$ before the multiple of $b$ is subtracted which simplifes the subtraction as well.  A multiplication that produces
-only the lower $m+1$ digits requires ${m^2 + 3m - 2} \over 2$ single precision multiplications.
-
-With both optimizations in place the algorithm is the algorithm Barrett proposed.  It requires $m^2 + 2m - 1$ single precision multiplications which
-is considerably faster than the straightforward $3m^2$ method.
-
-\subsection{The Barrett Algorithm}
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_reduce}. \\
-\textbf{Input}.   mp\_int $a$, mp\_int $b$ and $\mu = \lfloor \beta^{2m}/b \rfloor, m = \lceil lg_{\beta}(b) \rceil, (0 \le a < b^2, b > 1)$ \\
-\textbf{Output}.  $a \mbox{ (mod }b\mbox{)}$ \\
-\hline \\
-Let $m$ represent the number of digits in $b$.  \\
-1.  Make a copy of $a$ and store it in $q$.  (\textit{mp\_init\_copy}) \\
-2.  $q \leftarrow \lfloor q / \beta^{m - 1} \rfloor$ (\textit{mp\_rshd}) \\
-\\
-Produce the quotient. \\
-3.  $q \leftarrow q \cdot \mu$  (\textit{note: only produce digits at or above $m-1$}) \\
-4.  $q \leftarrow \lfloor q / \beta^{m + 1} \rfloor$ \\
-\\
-Subtract the multiple of modulus from the input. \\
-5.  $a \leftarrow a \mbox{ (mod }\beta^{m+1}\mbox{)}$ (\textit{mp\_mod\_2d}) \\
-6.  $q \leftarrow q \cdot b \mbox{ (mod }\beta^{m+1}\mbox{)}$ (\textit{s\_mp\_mul\_digs}) \\
-7.  $a \leftarrow a - q$ (\textit{mp\_sub}) \\
-\\
-Add $\beta^{m+1}$ if a carry occured. \\
-8.  If $a < 0$ then (\textit{mp\_cmp\_d}) \\
-\hspace{3mm}8.1  $q \leftarrow 1$ (\textit{mp\_set}) \\
-\hspace{3mm}8.2  $q \leftarrow q \cdot \beta^{m+1}$ (\textit{mp\_lshd}) \\
-\hspace{3mm}8.3  $a \leftarrow a + q$ \\
-\\
-Now subtract the modulus if the residue is too large (e.g. quotient too small). \\
-9.  While $a \ge b$ do (\textit{mp\_cmp}) \\
-\hspace{3mm}9.1  $c \leftarrow a - b$ \\
-10.  Clear $q$. \\
-11.  Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_reduce}
-\end{figure}
-
-\textbf{Algorithm mp\_reduce.}
-This algorithm will reduce the input $a$ modulo $b$ in place using the Barrett algorithm.  It is loosely based on algorithm 14.42 of HAC
-\cite[pp.  602]{HAC} which is based on the paper from Paul Barrett \cite{BARRETT}.  The algorithm has several restrictions and assumptions which must
-be adhered to for the algorithm to work.
-
-First the modulus $b$ is assumed to be positive and greater than one.  If the modulus were less than or equal to one than subtracting
-a multiple of it would either accomplish nothing or actually enlarge the input.  The input $a$ must be in the range $0 \le a < b^2$ in order
-for the quotient to have enough precision.  If $a$ is the product of two numbers that were already reduced modulo $b$, this will not be a problem.
-Technically the algorithm will still work if $a \ge b^2$ but it will take much longer to finish.  The value of $\mu$ is passed as an argument to this
-algorithm and is assumed to be calculated and stored before the algorithm is used.
-
-Recall that the multiplication for the quotient on step 3 must only produce digits at or above the $m-1$'th position.  An algorithm called
-$s\_mp\_mul\_high\_digs$ which has not been presented is used to accomplish this task.  The algorithm is based on $s\_mp\_mul\_digs$ except that
-instead of stopping at a given level of precision it starts at a given level of precision.  This optimal algorithm can only be used if the number
-of digits in $b$ is very much smaller than $\beta$.
-
-While it is known that
-$a \ge b \cdot \lfloor (q_0 \cdot \mu) / \beta^{m+1} \rfloor$ only the lower $m+1$ digits are being used to compute the residue, so an implied
-``borrow'' from the higher digits might leave a negative result.  After the multiple of the modulus has been subtracted from $a$ the residue must be
-fixed up in case it is negative.  The invariant $\beta^{m+1}$ must be added to the residue to make it positive again.
-
-The while loop at step 9 will subtract $b$ until the residue is less than $b$.  If the algorithm is performed correctly this step is
-performed at most twice, and on average once. However, if $a \ge b^2$ than it will iterate substantially more times than it should.
-
-EXAM,bn_mp_reduce.c
-
-The first multiplication that determines the quotient can be performed by only producing the digits from $m - 1$ and up.  This essentially halves
-the number of single precision multiplications required.  However, the optimization is only safe if $\beta$ is much larger than the number of digits
-in the modulus.  In the source code this is evaluated on lines @36,if@ to @44,}@ where algorithm s\_mp\_mul\_high\_digs is used when it is
-safe to do so.
-
-\subsection{The Barrett Setup Algorithm}
-In order to use algorithm mp\_reduce the value of $\mu$ must be calculated in advance.  Ideally this value should be computed once and stored for
-future use so that the Barrett algorithm can be used without delay.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_reduce\_setup}. \\
-\textbf{Input}.   mp\_int $a$ ($a > 1$)  \\
-\textbf{Output}.  $\mu \leftarrow \lfloor \beta^{2m}/a \rfloor$ \\
-\hline \\
-1.  $\mu \leftarrow 2^{2 \cdot lg(\beta) \cdot  m}$ (\textit{mp\_2expt}) \\
-2.  $\mu \leftarrow \lfloor \mu / b \rfloor$ (\textit{mp\_div}) \\
-3.  Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_reduce\_setup}
-\end{figure}
-
-\textbf{Algorithm mp\_reduce\_setup.}
-This algorithm computes the reciprocal $\mu$ required for Barrett reduction.  First $\beta^{2m}$ is calculated as $2^{2 \cdot lg(\beta) \cdot  m}$ which
-is equivalent and much faster.  The final value is computed by taking the integer quotient of $\lfloor \mu / b \rfloor$.
-
-EXAM,bn_mp_reduce_setup.c
-
-This simple routine calculates the reciprocal $\mu$ required by Barrett reduction.  Note the extended usage of algorithm mp\_div where the variable
-which would received the remainder is passed as NULL.  As will be discussed in~\ref{sec:division} the division routine allows both the quotient and the
-remainder to be passed as NULL meaning to ignore the value.
-
-\section{The Montgomery Reduction}
-Montgomery reduction\footnote{Thanks to Niels Ferguson for his insightful explanation of the algorithm.} \cite{MONT} is by far the most interesting
-form of reduction in common use.  It computes a modular residue which is not actually equal to the residue of the input yet instead equal to a
-residue times a constant.  However, as perplexing as this may sound the algorithm is relatively simple and very efficient.
-
-Throughout this entire section the variable $n$ will represent the modulus used to form the residue.  As will be discussed shortly the value of
-$n$ must be odd.  The variable $x$ will represent the quantity of which the residue is sought.  Similar to the Barrett algorithm the input
-is restricted to $0 \le x < n^2$.  To begin the description some simple number theory facts must be established.
-
-\textbf{Fact 1.}  Adding $n$ to $x$ does not change the residue since in effect it adds one to the quotient $\lfloor x / n \rfloor$.  Another way
-to explain this is that $n$ is (\textit{or multiples of $n$ are}) congruent to zero modulo $n$.  Adding zero will not change the value of the residue.
-
-\textbf{Fact 2.}  If $x$ is even then performing a division by two in $\Z$ is congruent to $x \cdot 2^{-1} \mbox{ (mod }n\mbox{)}$.  Actually
-this is an application of the fact that if $x$ is evenly divisible by any $k \in \Z$ then division in $\Z$ will be congruent to
-multiplication by $k^{-1}$ modulo $n$.
-
-From these two simple facts the following simple algorithm can be derived.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Montgomery Reduction}. \\
-\textbf{Input}.   Integer $x$, $n$ and $k$ \\
-\textbf{Output}.  $2^{-k}x \mbox{ (mod }n\mbox{)}$ \\
-\hline \\
-1.  for $t$ from $1$ to $k$ do \\
-\hspace{3mm}1.1  If $x$ is odd then \\
-\hspace{6mm}1.1.1  $x \leftarrow x + n$ \\
-\hspace{3mm}1.2  $x \leftarrow x/2$ \\
-2.  Return $x$. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm Montgomery Reduction}
-\end{figure}
-
-The algorithm reduces the input one bit at a time using the two congruencies stated previously.  Inside the loop $n$, which is odd, is
-added to $x$ if $x$ is odd.  This forces $x$ to be even which allows the division by two in $\Z$ to be congruent to a modular division by two.  Since
-$x$ is assumed to be initially much larger than $n$ the addition of $n$ will contribute an insignificant magnitude to $x$.  Let $r$ represent the
-final result of the Montgomery algorithm.  If $k > lg(n)$ and $0 \le x < n^2$ then the final result is limited to
-$0 \le r < \lfloor x/2^k \rfloor + n$.  As a result at most a single subtraction is required to get the residue desired.
-
-\begin{figure}[here]
-\begin{small}
-\begin{center}
-\begin{tabular}{|c|l|}
-\hline \textbf{Step number ($t$)} & \textbf{Result ($x$)} \\
-\hline $1$ & $x + n = 5812$, $x/2 = 2906$ \\
-\hline $2$ & $x/2 = 1453$ \\
-\hline $3$ & $x + n = 1710$, $x/2 = 855$ \\
-\hline $4$ & $x + n = 1112$, $x/2 = 556$ \\
-\hline $5$ & $x/2 = 278$ \\
-\hline $6$ & $x/2 = 139$ \\
-\hline $7$ & $x + n = 396$, $x/2 = 198$ \\
-\hline $8$ & $x/2 = 99$ \\
-\hline $9$ & $x + n = 356$, $x/2 = 178$ \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Example of Montgomery Reduction (I)}
-\label{fig:MONT1}
-\end{figure}
-
-Consider the example in figure~\ref{fig:MONT1} which reduces $x = 5555$ modulo $n = 257$ when $k = 9$ (note $\beta^k = 512$ which is larger than $n$).  The result of
-the algorithm $r = 178$ is congruent to the value of $2^{-9} \cdot 5555 \mbox{ (mod }257\mbox{)}$.  When $r$ is multiplied by $2^9$ modulo $257$ the correct residue
-$r \equiv 158$ is produced.
-
-Let $k = \lfloor lg(n) \rfloor + 1$ represent the number of bits in $n$.  The current algorithm requires $2k^2$ single precision shifts
-and $k^2$ single precision additions.  At this rate the algorithm is most certainly slower than Barrett reduction and not terribly useful.
-Fortunately there exists an alternative representation of the algorithm.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Montgomery Reduction} (modified I). \\
-\textbf{Input}.   Integer $x$, $n$ and $k$ ($2^k > n$) \\
-\textbf{Output}.  $2^{-k}x \mbox{ (mod }n\mbox{)}$ \\
-\hline \\
-1.  for $t$ from $1$ to $k$ do \\
-\hspace{3mm}1.1  If the $t$'th bit of $x$ is one then \\
-\hspace{6mm}1.1.1  $x \leftarrow x + 2^tn$ \\
-2.  Return $x/2^k$. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm Montgomery Reduction (modified I)}
-\end{figure}
-
-This algorithm is equivalent since $2^tn$ is a multiple of $n$ and the lower $k$ bits of $x$ are zero by step 2.  The number of single
-precision shifts has now been reduced from $2k^2$ to $k^2 + k$ which is only a small improvement.
-
-\begin{figure}[here]
-\begin{small}
-\begin{center}
-\begin{tabular}{|c|l|r|}
-\hline \textbf{Step number ($t$)} & \textbf{Result ($x$)} & \textbf{Result ($x$) in Binary} \\
-\hline -- & $5555$ & $1010110110011$ \\
-\hline $1$ & $x + 2^{0}n = 5812$ &  $1011010110100$ \\
-\hline $2$ & $5812$ & $1011010110100$ \\
-\hline $3$ & $x + 2^{2}n = 6840$ & $1101010111000$ \\
-\hline $4$ & $x + 2^{3}n = 8896$ & $10001011000000$ \\
-\hline $5$ & $8896$ & $10001011000000$ \\
-\hline $6$ & $8896$ & $10001011000000$ \\
-\hline $7$ & $x + 2^{6}n = 25344$ & $110001100000000$ \\
-\hline $8$ & $25344$ & $110001100000000$ \\
-\hline $9$ & $x + 2^{7}n = 91136$ & $10110010000000000$ \\
-\hline -- & $x/2^k = 178$ & \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Example of Montgomery Reduction (II)}
-\label{fig:MONT2}
-\end{figure}
-
-Figure~\ref{fig:MONT2} demonstrates the modified algorithm reducing $x = 5555$ modulo $n = 257$ with $k = 9$.
-With this algorithm a single shift right at the end is the only right shift required to reduce the input instead of $k$ right shifts inside the
-loop.  Note that for the iterations $t = 2, 5, 6$ and $8$ where the result $x$ is not changed.  In those iterations the $t$'th bit of $x$ is
-zero and the appropriate multiple of $n$ does not need to be added to force the $t$'th bit of the result to zero.
-
-\subsection{Digit Based Montgomery Reduction}
-Instead of computing the reduction on a bit-by-bit basis it is actually much faster to compute it on digit-by-digit basis.  Consider the
-previous algorithm re-written to compute the Montgomery reduction in this new fashion.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Montgomery Reduction} (modified II). \\
-\textbf{Input}.   Integer $x$, $n$ and $k$ ($\beta^k > n$) \\
-\textbf{Output}.  $\beta^{-k}x \mbox{ (mod }n\mbox{)}$ \\
-\hline \\
-1.  for $t$ from $0$ to $k - 1$ do \\
-\hspace{3mm}1.1  $x \leftarrow x + \mu n \beta^t$ \\
-2.  Return $x/\beta^k$. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm Montgomery Reduction (modified II)}
-\end{figure}
-
-The value $\mu n \beta^t$ is a multiple of the modulus $n$ meaning that it will not change the residue.  If the first digit of
-the value $\mu n \beta^t$ equals the negative (modulo $\beta$) of the $t$'th digit of $x$ then the addition will result in a zero digit.  This
-problem breaks down to solving the following congruency.
-
-\begin{center}
-\begin{tabular}{rcl}
-$x_t + \mu n_0$ & $\equiv$ & $0 \mbox{ (mod }\beta\mbox{)}$ \\
-$\mu n_0$ & $\equiv$ & $-x_t \mbox{ (mod }\beta\mbox{)}$ \\
-$\mu$ & $\equiv$ & $-x_t/n_0 \mbox{ (mod }\beta\mbox{)}$ \\
-\end{tabular}
-\end{center}
-
-In each iteration of the loop on step 1 a new value of $\mu$ must be calculated.  The value of $-1/n_0 \mbox{ (mod }\beta\mbox{)}$ is used
-extensively in this algorithm and should be precomputed.  Let $\rho$ represent the negative of the modular inverse of $n_0$ modulo $\beta$.
-
-For example, let $\beta = 10$ represent the radix.  Let $n = 17$ represent the modulus which implies $k = 2$ and $\rho \equiv 7$.  Let $x = 33$
-represent the value to reduce.
-
-\newpage\begin{figure}
-\begin{center}
-\begin{tabular}{|c|c|c|}
-\hline \textbf{Step ($t$)} & \textbf{Value of $x$} & \textbf{Value of $\mu$} \\
-\hline --                 & $33$ & --\\
-\hline $0$                 & $33 + \mu n = 50$ & $1$ \\
-\hline $1$                 & $50 + \mu n \beta = 900$ & $5$ \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Example of Montgomery Reduction}
-\end{figure}
-
-The final result $900$ is then divided by $\beta^k$ to produce the final result $9$.  The first observation is that $9 \nequiv x \mbox{ (mod }n\mbox{)}$
-which implies the result is not the modular residue of $x$ modulo $n$.  However, recall that the residue is actually multiplied by $\beta^{-k}$ in
-the algorithm.  To get the true residue the value must be multiplied by $\beta^k$.  In this case $\beta^k \equiv 15 \mbox{ (mod }n\mbox{)}$ and
-the correct residue is $9 \cdot 15 \equiv 16 \mbox{ (mod }n\mbox{)}$.
-
-\subsection{Baseline Montgomery Reduction}
-The baseline Montgomery reduction algorithm will produce the residue for any size input.  It is designed to be a catch-all algororithm for
-Montgomery reductions.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_montgomery\_reduce}. \\
-\textbf{Input}.   mp\_int $x$, mp\_int $n$ and a digit $\rho \equiv -1/n_0 \mbox{ (mod }n\mbox{)}$. \\
-\hspace{11.5mm}($0 \le x < n^2, n > 1, (n, \beta) = 1, \beta^k > n$) \\
-\textbf{Output}.  $\beta^{-k}x \mbox{ (mod }n\mbox{)}$ \\
-\hline \\
-1.  $digs \leftarrow 2n.used + 1$ \\
-2.  If $digs < MP\_ARRAY$ and $m.used < \delta$ then \\
-\hspace{3mm}2.1  Use algorithm fast\_mp\_montgomery\_reduce instead. \\
-\\
-Setup $x$ for the reduction. \\
-3.  If $x.alloc < digs$ then grow $x$ to $digs$ digits. \\
-4.  $x.used \leftarrow digs$ \\
-\\
-Eliminate the lower $k$ digits. \\
-5.  For $ix$ from $0$ to $k - 1$ do \\
-\hspace{3mm}5.1  $\mu \leftarrow x_{ix} \cdot \rho \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{3mm}5.2  $u \leftarrow 0$ \\
-\hspace{3mm}5.3  For $iy$ from $0$ to $k - 1$ do \\
-\hspace{6mm}5.3.1  $\hat r \leftarrow \mu n_{iy} + x_{ix + iy} + u$ \\
-\hspace{6mm}5.3.2  $x_{ix + iy} \leftarrow \hat r \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{6mm}5.3.3  $u \leftarrow \lfloor \hat r / \beta \rfloor$ \\
-\hspace{3mm}5.4  While $u > 0$ do \\
-\hspace{6mm}5.4.1  $iy \leftarrow iy + 1$ \\
-\hspace{6mm}5.4.2  $x_{ix + iy} \leftarrow x_{ix + iy} + u$ \\
-\hspace{6mm}5.4.3  $u \leftarrow \lfloor x_{ix+iy} / \beta \rfloor$ \\
-\hspace{6mm}5.4.4  $x_{ix + iy} \leftarrow x_{ix+iy} \mbox{ (mod }\beta\mbox{)}$ \\
-\\
-Divide by $\beta^k$ and fix up as required. \\
-6.  $x \leftarrow \lfloor x / \beta^k \rfloor$ \\
-7.  If $x \ge n$ then \\
-\hspace{3mm}7.1  $x \leftarrow x - n$ \\
-8.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_montgomery\_reduce}
-\end{figure}
-
-\textbf{Algorithm mp\_montgomery\_reduce.}
-This algorithm reduces the input $x$ modulo $n$ in place using the Montgomery reduction algorithm.  The algorithm is loosely based
-on algorithm 14.32 of \cite[pp.601]{HAC} except it merges the multiplication of $\mu n \beta^t$ with the addition in the inner loop.  The
-restrictions on this algorithm are fairly easy to adapt to.  First $0 \le x < n^2$ bounds the input to numbers in the same range as
-for the Barrett algorithm.  Additionally if $n > 1$ and $n$ is odd there will exist a modular inverse $\rho$.  $\rho$ must be calculated in
-advance of this algorithm.  Finally the variable $k$ is fixed and a pseudonym for $n.used$.
-
-Step 2 decides whether a faster Montgomery algorithm can be used.  It is based on the Comba technique meaning that there are limits on
-the size of the input.  This algorithm is discussed in ~COMBARED~.
-
-Step 5 is the main reduction loop of the algorithm.  The value of $\mu$ is calculated once per iteration in the outer loop.  The inner loop
-calculates $x + \mu n \beta^{ix}$ by multiplying $\mu n$ and adding the result to $x$ shifted by $ix$ digits.  Both the addition and
-multiplication are performed in the same loop to save time and memory.  Step 5.4 will handle any additional carries that escape the inner loop.
-
-Using a quick inspection this algorithm requires $n$ single precision multiplications for the outer loop and $n^2$ single precision multiplications
-in the inner loop.  In total $n^2 + n$ single precision multiplications which compares favourably to Barrett at $n^2 + 2n - 1$ single precision
-multiplications.
-
-EXAM,bn_mp_montgomery_reduce.c
-
-This is the baseline implementation of the Montgomery reduction algorithm.  Lines @30,digs@ to @35,}@ determine if the Comba based
-routine can be used instead.  Line @47,mu@ computes the value of $\mu$ for that particular iteration of the outer loop.
-
-The multiplication $\mu n \beta^{ix}$ is performed in one step in the inner loop.  The alias $tmpx$ refers to the $ix$'th digit of $x$ and
-the alias $tmpn$ refers to the modulus $n$.
-
-\subsection{Faster ``Comba'' Montgomery Reduction}
-MARK,COMBARED
-
-The Montgomery reduction requires fewer single precision multiplications than a Barrett reduction, however it is much slower due to the serial
-nature of the inner loop.  The Barrett reduction algorithm requires two slightly modified multipliers which can be implemented with the Comba
-technique.  The Montgomery reduction algorithm cannot directly use the Comba technique to any significant advantage since the inner loop calculates
-a $k \times 1$ product $k$ times.
-
-The biggest obstacle is that at the $ix$'th iteration of the outer loop the value of $x_{ix}$ is required to calculate $\mu$.  This means the
-carries from $0$ to $ix - 1$ must have been propagated upwards to form a valid $ix$'th digit.  The solution as it turns out is very simple.
-Perform a Comba like multiplier and inside the outer loop just after the inner loop fix up the $ix + 1$'th digit by forwarding the carry.
-
-With this change in place the Montgomery reduction algorithm can be performed with a Comba style multiplication loop which substantially increases
-the speed of the algorithm.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{fast\_mp\_montgomery\_reduce}. \\
-\textbf{Input}.   mp\_int $x$, mp\_int $n$ and a digit $\rho \equiv -1/n_0 \mbox{ (mod }n\mbox{)}$. \\
-\hspace{11.5mm}($0 \le x < n^2, n > 1, (n, \beta) = 1, \beta^k > n$) \\
-\textbf{Output}.  $\beta^{-k}x \mbox{ (mod }n\mbox{)}$ \\
-\hline \\
-Place an array of \textbf{MP\_WARRAY} mp\_word variables called $\hat W$ on the stack. \\
-1.  if $x.alloc < n.used + 1$ then grow $x$ to $n.used + 1$ digits. \\
-Copy the digits of $x$ into the array $\hat W$ \\
-2.  For $ix$ from $0$ to $x.used - 1$ do \\
-\hspace{3mm}2.1  $\hat W_{ix} \leftarrow x_{ix}$ \\
-3.  For $ix$ from $x.used$ to $2n.used - 1$ do \\
-\hspace{3mm}3.1  $\hat W_{ix} \leftarrow 0$ \\
-Elimiate the lower $k$ digits. \\
-4.  for $ix$ from $0$ to $n.used - 1$ do \\
-\hspace{3mm}4.1  $\mu \leftarrow \hat W_{ix} \cdot \rho \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{3mm}4.2  For $iy$ from $0$ to $n.used - 1$ do \\
-\hspace{6mm}4.2.1  $\hat W_{iy + ix} \leftarrow \hat W_{iy + ix} + \mu \cdot n_{iy}$ \\
-\hspace{3mm}4.3  $\hat W_{ix + 1} \leftarrow \hat W_{ix + 1} + \lfloor \hat W_{ix} / \beta \rfloor$ \\
-Propagate carries upwards. \\
-5.  for $ix$ from $n.used$ to $2n.used + 1$ do \\
-\hspace{3mm}5.1  $\hat W_{ix + 1} \leftarrow \hat W_{ix + 1} + \lfloor \hat W_{ix} / \beta \rfloor$ \\
-Shift right and reduce modulo $\beta$ simultaneously. \\
-6.  for $ix$ from $0$ to $n.used + 1$ do \\
-\hspace{3mm}6.1  $x_{ix} \leftarrow \hat W_{ix + n.used} \mbox{ (mod }\beta\mbox{)}$ \\
-Zero excess digits and fixup $x$. \\
-7.  if $x.used > n.used + 1$ then do \\
-\hspace{3mm}7.1  for $ix$ from $n.used + 1$ to $x.used - 1$ do \\
-\hspace{6mm}7.1.1  $x_{ix} \leftarrow 0$ \\
-8.  $x.used \leftarrow n.used + 1$ \\
-9.  Clamp excessive digits of $x$. \\
-10.  If $x \ge n$ then \\
-\hspace{3mm}10.1  $x \leftarrow x - n$ \\
-11.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm fast\_mp\_montgomery\_reduce}
-\end{figure}
-
-\textbf{Algorithm fast\_mp\_montgomery\_reduce.}
-This algorithm will compute the Montgomery reduction of $x$ modulo $n$ using the Comba technique.  It is on most computer platforms significantly
-faster than algorithm mp\_montgomery\_reduce and algorithm mp\_reduce (\textit{Barrett reduction}).  The algorithm has the same restrictions
-on the input as the baseline reduction algorithm.  An additional two restrictions are imposed on this algorithm.  The number of digits $k$ in the
-the modulus $n$ must not violate $MP\_WARRAY > 2k +1$ and $n < \delta$.   When $\beta = 2^{28}$ this algorithm can be used to reduce modulo
-a modulus of at most $3,556$ bits in length.
-
-As in the other Comba reduction algorithms there is a $\hat W$ array which stores the columns of the product.  It is initially filled with the
-contents of $x$ with the excess digits zeroed.  The reduction loop is very similar the to the baseline loop at heart.  The multiplication on step
-4.1 can be single precision only since $ab \mbox{ (mod }\beta\mbox{)} \equiv (a \mbox{ mod }\beta)(b \mbox{ mod }\beta)$.  Some multipliers such
-as those on the ARM processors take a variable length time to complete depending on the number of bytes of result it must produce.  By performing
-a single precision multiplication instead half the amount of time is spent.
-
-Also note that digit $\hat W_{ix}$ must have the carry from the $ix - 1$'th digit propagated upwards in order for this to work.  That is what step
-4.3 will do.  In effect over the $n.used$ iterations of the outer loop the $n.used$'th lower columns all have the their carries propagated forwards.  Note
-how the upper bits of those same words are not reduced modulo $\beta$.  This is because those values will be discarded shortly and there is no
-point.
-
-Step 5 will propagate the remainder of the carries upwards.  On step 6 the columns are reduced modulo $\beta$ and shifted simultaneously as they are
-stored in the destination $x$.
-
-EXAM,bn_fast_mp_montgomery_reduce.c
-
-The $\hat W$ array is first filled with digits of $x$ on line @49,for@ then the rest of the digits are zeroed on line @54,for@.  Both loops share
-the same alias variables to make the code easier to read.
-
-The value of $\mu$ is calculated in an interesting fashion.  First the value $\hat W_{ix}$ is reduced modulo $\beta$ and cast to a mp\_digit.  This
-forces the compiler to use a single precision multiplication and prevents any concerns about loss of precision.   Line @101,>>@ fixes the carry
-for the next iteration of the loop by propagating the carry from $\hat W_{ix}$ to $\hat W_{ix+1}$.
-
-The for loop on line @113,for@ propagates the rest of the carries upwards through the columns.  The for loop on line @126,for@ reduces the columns
-modulo $\beta$ and shifts them $k$ places at the same time.  The alias $\_ \hat W$ actually refers to the array $\hat W$ starting at the $n.used$'th
-digit, that is $\_ \hat W_{t} = \hat W_{n.used + t}$.
-
-\subsection{Montgomery Setup}
-To calculate the variable $\rho$ a relatively simple algorithm will be required.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_montgomery\_setup}. \\
-\textbf{Input}.   mp\_int $n$ ($n > 1$ and $(n, 2) = 1$) \\
-\textbf{Output}.  $\rho \equiv -1/n_0 \mbox{ (mod }\beta\mbox{)}$ \\
-\hline \\
-1.  $b \leftarrow n_0$ \\
-2.  If $b$ is even return(\textit{MP\_VAL}) \\
-3.  $x \leftarrow (((b + 2) \mbox{ AND } 4) << 1) + b$ \\
-4.  for $k$ from 0 to $\lceil lg(lg(\beta)) \rceil - 2$ do \\
-\hspace{3mm}4.1  $x \leftarrow x \cdot (2 - bx)$ \\
-5.  $\rho \leftarrow \beta - x \mbox{ (mod }\beta\mbox{)}$ \\
-6.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_montgomery\_setup}
-\end{figure}
-
-\textbf{Algorithm mp\_montgomery\_setup.}
-This algorithm will calculate the value of $\rho$ required within the Montgomery reduction algorithms.  It uses a very interesting trick
-to calculate $1/n_0$ when $\beta$ is a power of two.
-
-EXAM,bn_mp_montgomery_setup.c
-
-This source code computes the value of $\rho$ required to perform Montgomery reduction.  It has been modified to avoid performing excess
-multiplications when $\beta$ is not the default 28-bits.
-
-\section{The Diminished Radix Algorithm}
-The Diminished Radix method of modular reduction \cite{DRMET} is a fairly clever technique which can be more efficient than either the Barrett
-or Montgomery methods for certain forms of moduli.  The technique is based on the following simple congruence.
-
-\begin{equation}
-(x \mbox{ mod } n) + k \lfloor x / n \rfloor \equiv x \mbox{ (mod }(n - k)\mbox{)}
-\end{equation}
-
-This observation was used in the MMB \cite{MMB} block cipher to create a diffusion primitive.  It used the fact that if $n = 2^{31}$ and $k=1$ that
-then a x86 multiplier could produce the 62-bit product and use  the ``shrd'' instruction to perform a double-precision right shift.  The proof
-of the above equation is very simple.  First write $x$ in the product form.
-
-\begin{equation}
-x = qn + r
-\end{equation}
-
-Now reduce both sides modulo $(n - k)$.
-
-\begin{equation}
-x \equiv qk + r  \mbox{ (mod }(n-k)\mbox{)}
-\end{equation}
-
-The variable $n$ reduces modulo $n - k$ to $k$.  By putting $q = \lfloor x/n \rfloor$ and $r = x \mbox{ mod } n$
-into the equation the original congruence is reproduced, thus concluding the proof.  The following algorithm is based on this observation.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Diminished Radix Reduction}. \\
-\textbf{Input}.   Integer $x$, $n$, $k$ \\
-\textbf{Output}.  $x \mbox{ mod } (n - k)$ \\
-\hline \\
-1.  $q \leftarrow \lfloor x / n \rfloor$ \\
-2.  $q \leftarrow k \cdot q$ \\
-3.  $x \leftarrow x \mbox{ (mod }n\mbox{)}$ \\
-4.  $x \leftarrow x + q$ \\
-5.  If $x \ge (n - k)$ then \\
-\hspace{3mm}5.1  $x \leftarrow x - (n - k)$ \\
-\hspace{3mm}5.2  Goto step 1. \\
-6.  Return $x$ \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm Diminished Radix Reduction}
-\label{fig:DR}
-\end{figure}
-
-This algorithm will reduce $x$ modulo $n - k$ and return the residue.  If $0 \le x < (n - k)^2$ then the algorithm will loop almost always
-once or twice and occasionally three times.  For simplicity sake the value of $x$ is bounded by the following simple polynomial.
-
-\begin{equation}
-0 \le x < n^2 + k^2 - 2nk
-\end{equation}
-
-The true bound is  $0 \le x < (n - k - 1)^2$ but this has quite a few more terms.  The value of $q$ after step 1 is bounded by the following.
-
-\begin{equation}
-q < n - 2k - k^2/n
-\end{equation}
-
-Since $k^2$ is going to be considerably smaller than $n$ that term will always be zero.  The value of $x$ after step 3 is bounded trivially as
-$0 \le x < n$.  By step four the sum $x + q$ is bounded by
-
-\begin{equation}
-0 \le q + x < (k + 1)n - 2k^2 - 1
-\end{equation}
-
-With a second pass $q$ will be loosely bounded by $0 \le q < k^2$ after step 2 while $x$ will still be loosely bounded by $0 \le x < n$ after step 3.  After the second pass it is highly unlike that the
-sum in step 4 will exceed $n - k$.  In practice fewer than three passes of the algorithm are required to reduce virtually every input in the
-range $0 \le x < (n - k - 1)^2$.
-
-\begin{figure}
-\begin{small}
-\begin{center}
-\begin{tabular}{|l|}
-\hline
-$x = 123456789, n = 256, k = 3$ \\
-\hline $q \leftarrow \lfloor x/n \rfloor = 482253$ \\
-$q \leftarrow q*k = 1446759$ \\
-$x \leftarrow x \mbox{ mod } n = 21$ \\
-$x \leftarrow x + q = 1446780$ \\
-$x \leftarrow x - (n - k) = 1446527$ \\
-\hline
-$q \leftarrow \lfloor x/n \rfloor = 5650$ \\
-$q \leftarrow q*k = 16950$ \\
-$x \leftarrow x \mbox{ mod } n = 127$ \\
-$x \leftarrow x + q = 17077$ \\
-$x \leftarrow x - (n - k) = 16824$ \\
-\hline
-$q \leftarrow \lfloor x/n \rfloor = 65$ \\
-$q \leftarrow q*k = 195$ \\
-$x \leftarrow x \mbox{ mod } n = 184$ \\
-$x \leftarrow x + q = 379$ \\
-$x \leftarrow x - (n - k) = 126$ \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Example Diminished Radix Reduction}
-\label{fig:EXDR}
-\end{figure}
-
-Figure~\ref{fig:EXDR} demonstrates the reduction of $x = 123456789$ modulo $n - k = 253$ when $n = 256$ and $k = 3$.  Note that even while $x$
-is considerably larger than $(n - k - 1)^2 = 63504$ the algorithm still converges on the modular residue exceedingly fast.  In this case only
-three passes were required to find the residue $x \equiv 126$.
-
-
-\subsection{Choice of Moduli}
-On the surface this algorithm looks like a very expensive algorithm.  It requires a couple of subtractions followed by multiplication and other
-modular reductions.  The usefulness of this algorithm becomes exceedingly clear when an appropriate modulus is chosen.
-
-Division in general is a very expensive operation to perform.  The one exception is when the division is by a power of the radix of representation used.
-Division by ten for example is simple for pencil and paper mathematics since it amounts to shifting the decimal place to the right.  Similarly division
-by two (\textit{or powers of two}) is very simple for binary computers to perform.  It would therefore seem logical to choose $n$ of the form $2^p$
-which would imply that $\lfloor x / n \rfloor$ is a simple shift of $x$ right $p$ bits.
-
-However, there is one operation related to division of power of twos that is even faster than this.  If $n = \beta^p$ then the division may be
-performed by moving whole digits to the right $p$ places.  In practice division by $\beta^p$ is much faster than division by $2^p$ for any $p$.
-Also with the choice of $n = \beta^p$ reducing $x$ modulo $n$ merely requires zeroing the digits above the $p-1$'th digit of $x$.
-
-Throughout the next section the term ``restricted modulus'' will refer to a modulus of the form $\beta^p - k$ whereas the term ``unrestricted
-modulus'' will refer to a modulus of the form $2^p - k$.  The word ``restricted'' in this case refers to the fact that it is based on the
-$2^p$ logic except $p$ must be a multiple of $lg(\beta)$.
-
-\subsection{Choice of $k$}
-Now that division and reduction (\textit{step 1 and 3 of figure~\ref{fig:DR}}) have been optimized to simple digit operations the multiplication by $k$
-in step 2 is the most expensive operation.  Fortunately the choice of $k$ is not terribly limited.  For all intents and purposes it might
-as well be a single digit.  The smaller the value of $k$ is the faster the algorithm will be.
-
-\subsection{Restricted Diminished Radix Reduction}
-The restricted Diminished Radix algorithm can quickly reduce an input modulo a modulus of the form $n = \beta^p - k$.  This algorithm can reduce
-an input $x$ within the range $0 \le x < n^2$ using only a couple passes of the algorithm demonstrated in figure~\ref{fig:DR}.  The implementation
-of this algorithm has been optimized to avoid additional overhead associated with a division by $\beta^p$, the multiplication by $k$ or the addition
-of $x$ and $q$.  The resulting algorithm is very efficient and can lead to substantial improvements over Barrett and Montgomery reduction when modular
-exponentiations are performed.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_dr\_reduce}. \\
-\textbf{Input}.   mp\_int $x$, $n$ and a mp\_digit $k = \beta - n_0$ \\
-\hspace{11.5mm}($0 \le x < n^2$, $n > 1$, $0 < k < \beta$) \\
-\textbf{Output}.  $x \mbox{ mod } n$ \\
-\hline \\
-1.  $m \leftarrow n.used$ \\
-2.  If $x.alloc < 2m$ then grow $x$ to $2m$ digits. \\
-3.  $\mu \leftarrow 0$ \\
-4.  for $i$ from $0$ to $m - 1$ do \\
-\hspace{3mm}4.1  $\hat r \leftarrow k \cdot x_{m+i} + x_{i} + \mu$ \\
-\hspace{3mm}4.2  $x_{i} \leftarrow \hat r \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{3mm}4.3  $\mu \leftarrow \lfloor \hat r / \beta \rfloor$ \\
-5.  $x_{m} \leftarrow \mu$ \\
-6.  for $i$ from $m + 1$ to $x.used - 1$ do \\
-\hspace{3mm}6.1  $x_{i} \leftarrow 0$ \\
-7.  Clamp excess digits of $x$. \\
-8.  If $x \ge n$ then \\
-\hspace{3mm}8.1  $x \leftarrow x - n$ \\
-\hspace{3mm}8.2  Goto step 3. \\
-9.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_dr\_reduce}
-\end{figure}
-
-\textbf{Algorithm mp\_dr\_reduce.}
-This algorithm will perform the Dimished Radix reduction of $x$ modulo $n$.  It has similar restrictions to that of the Barrett reduction
-with the addition that $n$ must be of the form $n = \beta^m - k$ where $0 < k <\beta$.
-
-This algorithm essentially implements the pseudo-code in figure~\ref{fig:DR} except with a slight optimization.  The division by $\beta^m$, multiplication by $k$
-and addition of $x \mbox{ mod }\beta^m$ are all performed simultaneously inside the loop on step 4.  The division by $\beta^m$ is emulated by accessing
-the term at the $m+i$'th position which is subsequently multiplied by $k$ and added to the term at the $i$'th position.  After the loop the $m$'th
-digit is set to the carry and the upper digits are zeroed.  Steps 5 and 6 emulate the reduction modulo $\beta^m$ that should have happend to
-$x$ before the addition of the multiple of the upper half.
-
-At step 8 if $x$ is still larger than $n$ another pass of the algorithm is required.  First $n$ is subtracted from $x$ and then the algorithm resumes
-at step 3.
-
-EXAM,bn_mp_dr_reduce.c
-
-The first step is to grow $x$ as required to $2m$ digits since the reduction is performed in place on $x$.  The label on line @49,top:@ is where
-the algorithm will resume if further reduction passes are required.  In theory it could be placed at the top of the function however, the size of
-the modulus and question of whether $x$ is large enough are invariant after the first pass meaning that it would be a waste of time.
-
-The aliases $tmpx1$ and $tmpx2$ refer to the digits of $x$ where the latter is offset by $m$ digits.  By reading digits from $x$ offset by $m$ digits
-a division by $\beta^m$ can be simulated virtually for free.  The loop on line @61,for@ performs the bulk of the work (\textit{corresponds to step 4 of algorithm 7.11})
-in this algorithm.
-
-By line @68,mu@ the pointer $tmpx1$ points to the $m$'th digit of $x$ which is where the final carry will be placed.  Similarly by line @71,for@ the
-same pointer will point to the $m+1$'th digit where the zeroes will be placed.
-
-Since the algorithm is only valid if both $x$ and $n$ are greater than zero an unsigned comparison suffices to determine if another pass is required.
-With the same logic at line @82,sub@ the value of $x$ is known to be greater than or equal to $n$ meaning that an unsigned subtraction can be used
-as well.  Since the destination of the subtraction is the larger of the inputs the call to algorithm s\_mp\_sub cannot fail and the return code
-does not need to be checked.
-
-\subsubsection{Setup}
-To setup the restricted Diminished Radix algorithm the value $k = \beta - n_0$ is required.  This algorithm is not really complicated but provided for
-completeness.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_dr\_setup}. \\
-\textbf{Input}.   mp\_int $n$ \\
-\textbf{Output}.  $k = \beta - n_0$ \\
-\hline \\
-1.  $k \leftarrow \beta - n_0$ \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_dr\_setup}
-\end{figure}
-
-EXAM,bn_mp_dr_setup.c
-
-\subsubsection{Modulus Detection}
-Another algorithm which will be useful is the ability to detect a restricted Diminished Radix modulus.  An integer is said to be
-of restricted Diminished Radix form if all of the digits are equal to $\beta - 1$ except the trailing digit which may be any value.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_dr\_is\_modulus}. \\
-\textbf{Input}.   mp\_int $n$ \\
-\textbf{Output}.  $1$ if $n$ is in D.R form, $0$ otherwise \\
-\hline
-1.  If $n.used < 2$ then return($0$). \\
-2.  for $ix$ from $1$ to $n.used - 1$ do \\
-\hspace{3mm}2.1  If $n_{ix} \ne \beta - 1$ return($0$). \\
-3.  Return($1$). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_dr\_is\_modulus}
-\end{figure}
-
-\textbf{Algorithm mp\_dr\_is\_modulus.}
-This algorithm determines if a value is in Diminished Radix form.  Step 1 rejects obvious cases where fewer than two digits are
-in the mp\_int.  Step 2 tests all but the first digit to see if they are equal to $\beta - 1$.  If the algorithm manages to get to
-step 3 then $n$ must be of Diminished Radix form.
-
-EXAM,bn_mp_dr_is_modulus.c
-
-\subsection{Unrestricted Diminished Radix Reduction}
-The unrestricted Diminished Radix algorithm allows modular reductions to be performed when the modulus is of the form $2^p - k$.  This algorithm
-is a straightforward adaptation of algorithm~\ref{fig:DR}.
-
-In general the restricted Diminished Radix reduction algorithm is much faster since it has considerably lower overhead.  However, this new
-algorithm is much faster than either Montgomery or Barrett reduction when the moduli are of the appropriate form.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_reduce\_2k}. \\
-\textbf{Input}.   mp\_int $a$ and $n$.  mp\_digit $k$  \\
-\hspace{11.5mm}($a \ge 0$, $n > 1$, $0 < k < \beta$, $n + k$ is a power of two) \\
-\textbf{Output}.  $a \mbox{ (mod }n\mbox{)}$ \\
-\hline
-1.  $p \leftarrow \lceil lg(n) \rceil$  (\textit{mp\_count\_bits}) \\
-2.  While $a \ge n$ do \\
-\hspace{3mm}2.1  $q \leftarrow \lfloor a / 2^p \rfloor$ (\textit{mp\_div\_2d}) \\
-\hspace{3mm}2.2  $a \leftarrow a \mbox{ (mod }2^p\mbox{)}$ (\textit{mp\_mod\_2d}) \\
-\hspace{3mm}2.3  $q \leftarrow q \cdot k$ (\textit{mp\_mul\_d}) \\
-\hspace{3mm}2.4  $a \leftarrow a - q$ (\textit{s\_mp\_sub}) \\
-\hspace{3mm}2.5  If $a \ge n$ then do \\
-\hspace{6mm}2.5.1  $a \leftarrow a - n$ \\
-3.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_reduce\_2k}
-\end{figure}
-
-\textbf{Algorithm mp\_reduce\_2k.}
-This algorithm quickly reduces an input $a$ modulo an unrestricted Diminished Radix modulus $n$.  Division by $2^p$ is emulated with a right
-shift which makes the algorithm fairly inexpensive to use.
-
-EXAM,bn_mp_reduce_2k.c
-
-The algorithm mp\_count\_bits calculates the number of bits in an mp\_int which is used to find the initial value of $p$.  The call to mp\_div\_2d
-on line @31,mp_div_2d@ calculates both the quotient $q$ and the remainder $a$ required.  By doing both in a single function call the code size
-is kept fairly small.  The multiplication by $k$ is only performed if $k > 1$. This allows reductions modulo $2^p - 1$ to be performed without
-any multiplications.
-
-The unsigned s\_mp\_add, mp\_cmp\_mag and s\_mp\_sub are used in place of their full sign counterparts since the inputs are only valid if they are
-positive.  By using the unsigned versions the overhead is kept to a minimum.
-
-\subsubsection{Unrestricted Setup}
-To setup this reduction algorithm the value of $k = 2^p - n$ is required.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_reduce\_2k\_setup}. \\
-\textbf{Input}.   mp\_int $n$   \\
-\textbf{Output}.  $k = 2^p - n$ \\
-\hline
-1.  $p \leftarrow \lceil lg(n) \rceil$  (\textit{mp\_count\_bits}) \\
-2.  $x \leftarrow 2^p$ (\textit{mp\_2expt}) \\
-3.  $x \leftarrow x - n$ (\textit{mp\_sub}) \\
-4.  $k \leftarrow x_0$ \\
-5.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_reduce\_2k\_setup}
-\end{figure}
-
-\textbf{Algorithm mp\_reduce\_2k\_setup.}
-This algorithm computes the value of $k$ required for the algorithm mp\_reduce\_2k.  By making a temporary variable $x$ equal to $2^p$ a subtraction
-is sufficient to solve for $k$.  Alternatively if $n$ has more than one digit the value of $k$ is simply $\beta - n_0$.
-
-EXAM,bn_mp_reduce_2k_setup.c
-
-\subsubsection{Unrestricted Detection}
-An integer $n$ is a valid unrestricted Diminished Radix modulus if either of the following are true.
-
-\begin{enumerate}
-\item  The number has only one digit.
-\item  The number has more than one digit and every bit from the $\beta$'th to the most significant is one.
-\end{enumerate}
-
-If either condition is true than there is a power of two $2^p$ such that $0 < 2^p - n < \beta$.   If the input is only
-one digit than it will always be of the correct form.  Otherwise all of the bits above the first digit must be one.  This arises from the fact
-that there will be value of $k$ that when added to the modulus causes a carry in the first digit which propagates all the way to the most
-significant bit.  The resulting sum will be a power of two.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_reduce\_is\_2k}. \\
-\textbf{Input}.   mp\_int $n$   \\
-\textbf{Output}.  $1$ if of proper form, $0$ otherwise \\
-\hline
-1.  If $n.used = 0$ then return($0$). \\
-2.  If $n.used = 1$ then return($1$). \\
-3.  $p \leftarrow \lceil lg(n) \rceil$  (\textit{mp\_count\_bits}) \\
-4.  for $x$ from $lg(\beta)$ to $p$ do \\
-\hspace{3mm}4.1  If the ($x \mbox{ mod }lg(\beta)$)'th bit of the $\lfloor x / lg(\beta) \rfloor$ of $n$ is zero then return($0$). \\
-5.  Return($1$). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_reduce\_is\_2k}
-\end{figure}
-
-\textbf{Algorithm mp\_reduce\_is\_2k.}
-This algorithm quickly determines if a modulus is of the form required for algorithm mp\_reduce\_2k to function properly.
-
-EXAM,bn_mp_reduce_is_2k.c
-
-
-
-\section{Algorithm Comparison}
-So far three very different algorithms for modular reduction have been discussed.  Each of the algorithms have their own strengths and weaknesses
-that makes having such a selection very useful.  The following table sumarizes the three algorithms along with comparisons of work factors.  Since
-all three algorithms have the restriction that $0 \le x < n^2$ and $n > 1$ those limitations are not included in the table.
-
-\begin{center}
-\begin{small}
-\begin{tabular}{|c|c|c|c|c|c|}
-\hline \textbf{Method} & \textbf{Work Required} & \textbf{Limitations} & \textbf{$m = 8$} & \textbf{$m = 32$} & \textbf{$m = 64$} \\
-\hline Barrett    & $m^2 + 2m - 1$ & None              & $79$ & $1087$ & $4223$ \\
-\hline Montgomery & $m^2 + m$      & $n$ must be odd   & $72$ & $1056$ & $4160$ \\
-\hline D.R.       & $2m$           & $n = \beta^m - k$ & $16$ & $64$   & $128$  \\
-\hline
-\end{tabular}
-\end{small}
-\end{center}
-
-In theory Montgomery and Barrett reductions would require roughly the same amount of time to complete.  However, in practice since Montgomery
-reduction can be written as a single function with the Comba technique it is much faster.  Barrett reduction suffers from the overhead of
-calling the half precision multipliers, addition and division by $\beta$ algorithms.
-
-For almost every cryptographic algorithm Montgomery reduction is the algorithm of choice.  The one set of algorithms where Diminished Radix reduction truly
-shines are based on the discrete logarithm problem such as Diffie-Hellman \cite{DH} and ElGamal \cite{ELGAMAL}.  In these algorithms
-primes of the form $\beta^m - k$ can be found and shared amongst users.  These primes will allow the Diminished Radix algorithm to be used in
-modular exponentiation to greatly speed up the operation.
-
-
-
-\section*{Exercises}
-\begin{tabular}{cl}
-$\left [ 3 \right ]$ & Prove that the ``trick'' in algorithm mp\_montgomery\_setup actually \\
-                     & calculates the correct value of $\rho$. \\
-                     & \\
-$\left [ 2 \right ]$ & Devise an algorithm to reduce modulo $n + k$ for small $k$ quickly.  \\
-                     & \\
-$\left [ 4 \right ]$ & Prove that the pseudo-code algorithm ``Diminished Radix Reduction'' \\
-                     & (\textit{figure~\ref{fig:DR}}) terminates.  Also prove the probability that it will \\
-                     & terminate within $1 \le k \le 10$ iterations. \\
-                     & \\
-\end{tabular}
-
-
-\chapter{Exponentiation}
-Exponentiation is the operation of raising one variable to the power of another, for example, $a^b$.  A variant of exponentiation, computed
-in a finite field or ring, is called modular exponentiation.  This latter style of operation is typically used in public key
-cryptosystems such as RSA and Diffie-Hellman.  The ability to quickly compute modular exponentiations is of great benefit to any
-such cryptosystem and many methods have been sought to speed it up.
-
-\section{Exponentiation Basics}
-A trivial algorithm would simply multiply $a$ against itself $b - 1$ times to compute the exponentiation desired.  However, as $b$ grows in size
-the number of multiplications becomes prohibitive.  Imagine what would happen if $b$ $\approx$ $2^{1024}$ as is the case when computing an RSA signature
-with a $1024$-bit key.  Such a calculation could never be completed as it would take simply far too long.
-
-Fortunately there is a very simple algorithm based on the laws of exponents.  Recall that $lg_a(a^b) = b$ and that $lg_a(a^ba^c) = b + c$ which
-are two trivial relationships between the base and the exponent.  Let $b_i$ represent the $i$'th bit of $b$ starting from the least
-significant bit.  If $b$ is a $k$-bit integer than the following equation is true.
-
-\begin{equation}
-a^b = \prod_{i=0}^{k-1} a^{2^i \cdot b_i}
-\end{equation}
-
-By taking the base $a$ logarithm of both sides of the equation the following equation is the result.
-
-\begin{equation}
-b = \sum_{i=0}^{k-1}2^i \cdot b_i
-\end{equation}
-
-The term $a^{2^i}$ can be found from the $i - 1$'th term by squaring the term since $\left ( a^{2^i} \right )^2$ is equal to
-$a^{2^{i+1}}$.  This observation forms the basis of essentially all fast exponentiation algorithms.  It requires $k$ squarings and on average
-$k \over 2$ multiplications to compute the result.  This is indeed quite an improvement over simply multiplying by $a$ a total of $b-1$ times.
-
-While this current method is a considerable speed up there are further improvements to be made.  For example, the $a^{2^i}$ term does not need to
-be computed in an auxilary variable.  Consider the following equivalent algorithm.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Left to Right Exponentiation}. \\
-\textbf{Input}.   Integer $a$, $b$ and $k$ \\
-\textbf{Output}.  $c = a^b$ \\
-\hline \\
-1.  $c \leftarrow 1$ \\
-2.  for $i$ from $k - 1$ to $0$ do \\
-\hspace{3mm}2.1  $c \leftarrow c^2$ \\
-\hspace{3mm}2.2  $c \leftarrow c \cdot a^{b_i}$ \\
-3.  Return $c$. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Left to Right Exponentiation}
-\label{fig:LTOR}
-\end{figure}
-
-This algorithm starts from the most significant bit and works towards the least significant bit.  When the $i$'th bit of $b$ is set $a$ is
-multiplied against the current product.  In each iteration the product is squared which doubles the exponent of the individual terms of the
-product.
-
-For example, let $b = 101100_2 \equiv 44_{10}$.  The following chart demonstrates the actions of the algorithm.
-
-\newpage\begin{figure}
-\begin{center}
-\begin{tabular}{|c|c|}
-\hline \textbf{Value of $i$} & \textbf{Value of $c$} \\
-\hline - & $1$ \\
-\hline $5$ & $a$ \\
-\hline $4$ & $a^2$ \\
-\hline $3$ & $a^4 \cdot a$ \\
-\hline $2$ & $a^8 \cdot a^2 \cdot a$ \\
-\hline $1$ & $a^{16} \cdot a^4 \cdot a^2$ \\
-\hline $0$ & $a^{32} \cdot a^8 \cdot a^4$ \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Example of Left to Right Exponentiation}
-\end{figure}
-
-When the product $a^{32} \cdot a^8 \cdot a^4$ is simplified it is equal $a^{44}$ which is the desired exponentiation.  This particular algorithm is
-called ``Left to Right'' because it reads the exponent in that order.  All of the exponentiation algorithms that will be presented are of this nature.
-
-\subsection{Single Digit Exponentiation}
-The first algorithm in the series of exponentiation algorithms will be an unbounded algorithm where the exponent is a single digit.  It is intended
-to be used when a small power of an input is required (\textit{e.g. $a^5$}).  It is faster than simply multiplying $b - 1$ times for all values of
-$b$ that are greater than three.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_expt\_d}. \\
-\textbf{Input}.   mp\_int $a$ and mp\_digit $b$ \\
-\textbf{Output}.  $c = a^b$ \\
-\hline \\
-1.  $g \leftarrow a$ (\textit{mp\_init\_copy}) \\
-2.  $c \leftarrow 1$ (\textit{mp\_set}) \\
-3.  for $x$ from 1 to $lg(\beta)$ do \\
-\hspace{3mm}3.1  $c \leftarrow c^2$ (\textit{mp\_sqr}) \\
-\hspace{3mm}3.2  If $b$ AND $2^{lg(\beta) - 1} \ne 0$ then \\
-\hspace{6mm}3.2.1  $c \leftarrow c \cdot g$ (\textit{mp\_mul}) \\
-\hspace{3mm}3.3  $b \leftarrow b << 1$ \\
-4.  Clear $g$. \\
-5.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_expt\_d}
-\end{figure}
-
-\textbf{Algorithm mp\_expt\_d.}
-This algorithm computes the value of $a$ raised to the power of a single digit $b$.  It uses the left to right exponentiation algorithm to
-quickly compute the exponentiation.  It is loosely based on algorithm 14.79 of HAC \cite[pp. 615]{HAC} with the difference that the
-exponent is a fixed width.
-
-A copy of $a$ is made first to allow destination variable $c$ be the same as the source variable $a$.  The result is set to the initial value of
-$1$ in the subsequent step.
-
-Inside the loop the exponent is read from the most significant bit first down to the least significant bit.  First $c$ is invariably squared
-on step 3.1.  In the following step if the most significant bit of $b$ is one the copy of $a$ is multiplied against $c$.  The value
-of $b$ is shifted left one bit to make the next bit down from the most signficant bit the new most significant bit.  In effect each
-iteration of the loop moves the bits of the exponent $b$ upwards to the most significant location.
-
-EXAM,bn_mp_expt_d_ex.c
-
-This describes only the algorithm that is used when the parameter $fast$ is $0$.  Line @31,mp_set@ sets the initial value of the result to $1$.  Next the loop on line @54,for@ steps through each bit of the exponent starting from
-the most significant down towards the least significant. The invariant squaring operation placed on line @333,mp_sqr@ is performed first.  After
-the squaring the result $c$ is multiplied by the base $g$ if and only if the most significant bit of the exponent is set.  The shift on line
-@69,<<@ moves all of the bits of the exponent upwards towards the most significant location.
-
-\section{$k$-ary Exponentiation}
-When calculating an exponentiation the most time consuming bottleneck is the multiplications which are in general a small factor
-slower than squaring.  Recall from the previous algorithm that $b_{i}$ refers to the $i$'th bit of the exponent $b$.  Suppose instead it referred to
-the $i$'th $k$-bit digit of the exponent of $b$.  For $k = 1$ the definitions are synonymous and for $k > 1$ algorithm~\ref{fig:KARY}
-computes the same exponentiation.  A group of $k$ bits from the exponent is called a \textit{window}.  That is it is a small window on only a
-portion of the entire exponent.  Consider the following modification to the basic left to right exponentiation algorithm.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{$k$-ary Exponentiation}. \\
-\textbf{Input}.   Integer $a$, $b$, $k$ and $t$ \\
-\textbf{Output}.  $c = a^b$ \\
-\hline \\
-1.  $c \leftarrow 1$ \\
-2.  for $i$ from $t - 1$ to $0$ do \\
-\hspace{3mm}2.1  $c \leftarrow c^{2^k} $ \\
-\hspace{3mm}2.2  Extract the $i$'th $k$-bit word from $b$ and store it in $g$. \\
-\hspace{3mm}2.3  $c \leftarrow c \cdot a^g$ \\
-3.  Return $c$. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{$k$-ary Exponentiation}
-\label{fig:KARY}
-\end{figure}
-
-The squaring on step 2.1 can be calculated by squaring the value $c$ successively $k$ times.  If the values of $a^g$ for $0 < g < 2^k$ have been
-precomputed this algorithm requires only $t$ multiplications and $tk$ squarings.  The table can be generated with $2^{k - 1} - 1$ squarings and
-$2^{k - 1} + 1$ multiplications.  This algorithm assumes that the number of bits in the exponent is evenly divisible by $k$.
-However, when it is not the remaining $0 < x \le k - 1$ bits can be handled with algorithm~\ref{fig:LTOR}.
-
-Suppose $k = 4$ and $t = 100$.  This modified algorithm will require $109$ multiplications and $408$ squarings to compute the exponentiation.  The
-original algorithm would on average have required $200$ multiplications and $400$ squrings to compute the same value.  The total number of squarings
-has increased slightly but the number of multiplications has nearly halved.
-
-\subsection{Optimal Values of $k$}
-An optimal value of $k$ will minimize $2^{k} + \lceil n / k \rceil + n - 1$ for a fixed number of bits in the exponent $n$.  The simplest
-approach is to brute force search amongst the values $k = 2, 3, \ldots, 8$ for the lowest result.  Table~\ref{fig:OPTK} lists optimal values of $k$
-for various exponent sizes and compares the number of multiplication and squarings required against algorithm~\ref{fig:LTOR}.
-
-\begin{figure}[here]
-\begin{center}
-\begin{small}
-\begin{tabular}{|c|c|c|c|c|c|}
-\hline \textbf{Exponent (bits)} & \textbf{Optimal $k$} & \textbf{Work at $k$} & \textbf{Work with ~\ref{fig:LTOR}} \\
-\hline $16$ & $2$ & $27$ & $24$ \\
-\hline $32$ & $3$ & $49$ & $48$ \\
-\hline $64$ & $3$ & $92$ & $96$ \\
-\hline $128$ & $4$ & $175$ & $192$ \\
-\hline $256$ & $4$ & $335$ & $384$ \\
-\hline $512$ & $5$ & $645$ & $768$ \\
-\hline $1024$ & $6$ & $1257$ & $1536$ \\
-\hline $2048$ & $6$ & $2452$ & $3072$ \\
-\hline $4096$ & $7$ & $4808$ & $6144$ \\
-\hline
-\end{tabular}
-\end{small}
-\end{center}
-\caption{Optimal Values of $k$ for $k$-ary Exponentiation}
-\label{fig:OPTK}
-\end{figure}
-
-\subsection{Sliding-Window Exponentiation}
-A simple modification to the previous algorithm is only generate the upper half of the table in the range $2^{k-1} \le g < 2^k$.  Essentially
-this is a table for all values of $g$ where the most significant bit of $g$ is a one.  However, in order for this to be allowed in the
-algorithm values of $g$ in the range $0 \le g < 2^{k-1}$ must be avoided.
-
-Table~\ref{fig:OPTK2} lists optimal values of $k$ for various exponent sizes and compares the work required against algorithm {\ref{fig:KARY}}.
-
-\begin{figure}[here]
-\begin{center}
-\begin{small}
-\begin{tabular}{|c|c|c|c|c|c|}
-\hline \textbf{Exponent (bits)} & \textbf{Optimal $k$} & \textbf{Work at $k$} & \textbf{Work with ~\ref{fig:KARY}} \\
-\hline $16$ & $3$ & $24$ & $27$ \\
-\hline $32$ & $3$ & $45$ & $49$ \\
-\hline $64$ & $4$ & $87$ & $92$ \\
-\hline $128$ & $4$ & $167$ & $175$ \\
-\hline $256$ & $5$ & $322$ & $335$ \\
-\hline $512$ & $6$ & $628$ & $645$ \\
-\hline $1024$ & $6$ & $1225$ & $1257$ \\
-\hline $2048$ & $7$ & $2403$ & $2452$ \\
-\hline $4096$ & $8$ & $4735$ & $4808$ \\
-\hline
-\end{tabular}
-\end{small}
-\end{center}
-\caption{Optimal Values of $k$ for Sliding Window Exponentiation}
-\label{fig:OPTK2}
-\end{figure}
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Sliding Window $k$-ary Exponentiation}. \\
-\textbf{Input}.   Integer $a$, $b$, $k$ and $t$ \\
-\textbf{Output}.  $c = a^b$ \\
-\hline \\
-1.  $c \leftarrow 1$ \\
-2.  for $i$ from $t - 1$ to $0$ do \\
-\hspace{3mm}2.1  If the $i$'th bit of $b$ is a zero then \\
-\hspace{6mm}2.1.1   $c \leftarrow c^2$ \\
-\hspace{3mm}2.2  else do \\
-\hspace{6mm}2.2.1  $c \leftarrow c^{2^k}$ \\
-\hspace{6mm}2.2.2  Extract the $k$ bits from $(b_{i}b_{i-1}\ldots b_{i-(k-1)})$ and store it in $g$. \\
-\hspace{6mm}2.2.3  $c \leftarrow c \cdot a^g$ \\
-\hspace{6mm}2.2.4  $i \leftarrow i - k$ \\
-3.  Return $c$. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Sliding Window $k$-ary Exponentiation}
-\end{figure}
-
-Similar to the previous algorithm this algorithm must have a special handler when fewer than $k$ bits are left in the exponent.  While this
-algorithm requires the same number of squarings it can potentially have fewer multiplications.  The pre-computed table $a^g$ is also half
-the size as the previous table.
-
-Consider the exponent $b = 111101011001000_2 \equiv 31432_{10}$ with $k = 3$ using both algorithms.  The first algorithm will divide the exponent up as
-the following five $3$-bit words $b \equiv \left ( 111, 101, 011, 001, 000 \right )_{2}$.  The second algorithm will break the
-exponent as $b \equiv \left ( 111, 101, 0, 110, 0, 100, 0 \right )_{2}$.  The single digit $0$ in the second representation are where
-a single squaring took place instead of a squaring and multiplication.  In total the first method requires $10$ multiplications and $18$
-squarings.  The second method requires $8$ multiplications and $18$ squarings.
-
-In general the sliding window method is never slower than the generic $k$-ary method and often it is slightly faster.
-
-\section{Modular Exponentiation}
-
-Modular exponentiation is essentially computing the power of a base within a finite field or ring.  For example, computing
-$d \equiv a^b \mbox{ (mod }c\mbox{)}$ is a modular exponentiation.  Instead of first computing $a^b$ and then reducing it
-modulo $c$ the intermediate result is reduced modulo $c$ after every squaring or multiplication operation.
-
-This guarantees that any intermediate result is bounded by $0 \le d \le c^2 - 2c + 1$ and can be reduced modulo $c$ quickly using
-one of the algorithms presented in ~REDUCTION~.
-
-Before the actual modular exponentiation algorithm can be written a wrapper algorithm must be written first.  This algorithm
-will allow the exponent $b$ to be negative which is computed as $c \equiv \left (1 / a \right )^{\vert b \vert} \mbox{(mod }d\mbox{)}$. The
-value of $(1/a) \mbox{ mod }c$ is computed using the modular inverse (\textit{see \ref{sec;modinv}}).  If no inverse exists the algorithm
-terminates with an error.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_exptmod}. \\
-\textbf{Input}.   mp\_int $a$, $b$ and $c$ \\
-\textbf{Output}.  $y \equiv g^x \mbox{ (mod }p\mbox{)}$ \\
-\hline \\
-1.  If $c.sign = MP\_NEG$ return(\textit{MP\_VAL}). \\
-2.  If $b.sign = MP\_NEG$ then \\
-\hspace{3mm}2.1  $g' \leftarrow g^{-1} \mbox{ (mod }c\mbox{)}$ \\
-\hspace{3mm}2.2  $x' \leftarrow \vert x \vert$ \\
-\hspace{3mm}2.3  Compute $d \equiv g'^{x'} \mbox{ (mod }c\mbox{)}$ via recursion. \\
-3.  if $p$ is odd \textbf{OR} $p$ is a D.R. modulus then \\
-\hspace{3mm}3.1  Compute $y \equiv g^{x} \mbox{ (mod }p\mbox{)}$ via algorithm mp\_exptmod\_fast. \\
-4.  else \\
-\hspace{3mm}4.1  Compute $y \equiv g^{x} \mbox{ (mod }p\mbox{)}$ via algorithm s\_mp\_exptmod. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_exptmod}
-\end{figure}
-
-\textbf{Algorithm mp\_exptmod.}
-The first algorithm which actually performs modular exponentiation is algorithm s\_mp\_exptmod.  It is a sliding window $k$-ary algorithm
-which uses Barrett reduction to reduce the product modulo $p$.  The second algorithm mp\_exptmod\_fast performs the same operation
-except it uses either Montgomery or Diminished Radix reduction.  The two latter reduction algorithms are clumped in the same exponentiation
-algorithm since their arguments are essentially the same (\textit{two mp\_ints and one mp\_digit}).
-
-EXAM,bn_mp_exptmod.c
-
-In order to keep the algorithms in a known state the first step on line @29,if@ is to reject any negative modulus as input.  If the exponent is
-negative the algorithm tries to perform a modular exponentiation with the modular inverse of the base $G$.  The temporary variable $tmpG$ is assigned
-the modular inverse of $G$ and $tmpX$ is assigned the absolute value of $X$.  The algorithm will recuse with these new values with a positive
-exponent.
-
-If the exponent is positive the algorithm resumes the exponentiation.  Line @63,dr_@ determines if the modulus is of the restricted Diminished Radix
-form.  If it is not line @65,reduce@ attempts to determine if it is of a unrestricted Diminished Radix form.  The integer $dr$ will take on one
-of three values.
-
-\begin{enumerate}
-\item $dr = 0$ means that the modulus is not of either restricted or unrestricted Diminished Radix form.
-\item $dr = 1$ means that the modulus is of restricted Diminished Radix form.
-\item $dr = 2$ means that the modulus is of unrestricted Diminished Radix form.
-\end{enumerate}
-
-Line @69,if@ determines if the fast modular exponentiation algorithm can be used.  It is allowed if $dr \ne 0$ or if the modulus is odd.  Otherwise,
-the slower s\_mp\_exptmod algorithm is used which uses Barrett reduction.
-
-\subsection{Barrett Modular Exponentiation}
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{s\_mp\_exptmod}. \\
-\textbf{Input}.   mp\_int $a$, $b$ and $c$ \\
-\textbf{Output}.  $y \equiv g^x \mbox{ (mod }p\mbox{)}$ \\
-\hline \\
-1.  $k \leftarrow lg(x)$ \\
-2.  $winsize \leftarrow  \left \lbrace \begin{array}{ll}
-                              2 &  \mbox{if }k \le 7 \\
-                              3 &  \mbox{if }7 < k \le 36 \\
-                              4 &  \mbox{if }36 < k \le 140 \\
-                              5 &  \mbox{if }140 < k \le 450 \\
-                              6 &  \mbox{if }450 < k \le 1303 \\
-                              7 &  \mbox{if }1303 < k \le 3529 \\
-                              8 &  \mbox{if }3529 < k \\
-                              \end{array} \right .$ \\
-3.  Initialize $2^{winsize}$ mp\_ints in an array named $M$ and one mp\_int named $\mu$ \\
-4.  Calculate the $\mu$ required for Barrett Reduction (\textit{mp\_reduce\_setup}). \\
-5.  $M_1 \leftarrow g \mbox{ (mod }p\mbox{)}$ \\
-\\
-Setup the table of small powers of $g$.  First find $g^{2^{winsize}}$ and then all multiples of it. \\
-6.  $k \leftarrow 2^{winsize - 1}$ \\
-7.  $M_{k} \leftarrow M_1$ \\
-8.  for $ix$ from 0 to $winsize - 2$ do \\
-\hspace{3mm}8.1  $M_k \leftarrow \left ( M_k \right )^2$ (\textit{mp\_sqr})  \\
-\hspace{3mm}8.2  $M_k \leftarrow M_k \mbox{ (mod }p\mbox{)}$ (\textit{mp\_reduce}) \\
-9.  for $ix$ from $2^{winsize - 1} + 1$ to $2^{winsize} - 1$ do \\
-\hspace{3mm}9.1  $M_{ix} \leftarrow M_{ix - 1} \cdot M_{1}$ (\textit{mp\_mul}) \\
-\hspace{3mm}9.2  $M_{ix} \leftarrow M_{ix} \mbox{ (mod }p\mbox{)}$ (\textit{mp\_reduce}) \\
-10.  $res \leftarrow 1$ \\
-\\
-Start Sliding Window. \\
-11.  $mode \leftarrow 0, bitcnt \leftarrow 1, buf \leftarrow 0, digidx \leftarrow x.used - 1, bitcpy \leftarrow 0, bitbuf \leftarrow 0$ \\
-12.  Loop \\
-\hspace{3mm}12.1  $bitcnt \leftarrow bitcnt - 1$ \\
-\hspace{3mm}12.2  If $bitcnt = 0$ then do \\
-\hspace{6mm}12.2.1  If $digidx = -1$ goto step 13. \\
-\hspace{6mm}12.2.2  $buf \leftarrow x_{digidx}$ \\
-\hspace{6mm}12.2.3  $digidx \leftarrow digidx - 1$ \\
-\hspace{6mm}12.2.4  $bitcnt \leftarrow lg(\beta)$ \\
-Continued on next page. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm s\_mp\_exptmod}
-\end{figure}
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{s\_mp\_exptmod} (\textit{continued}). \\
-\textbf{Input}.   mp\_int $a$, $b$ and $c$ \\
-\textbf{Output}.  $y \equiv g^x \mbox{ (mod }p\mbox{)}$ \\
-\hline \\
-\hspace{3mm}12.3  $y \leftarrow (buf >> (lg(\beta) - 1))$ AND $1$ \\
-\hspace{3mm}12.4  $buf \leftarrow buf << 1$ \\
-\hspace{3mm}12.5  if $mode = 0$ and $y = 0$ then goto step 12. \\
-\hspace{3mm}12.6  if $mode = 1$ and $y = 0$ then do \\
-\hspace{6mm}12.6.1  $res \leftarrow res^2$ \\
-\hspace{6mm}12.6.2  $res \leftarrow res \mbox{ (mod }p\mbox{)}$ \\
-\hspace{6mm}12.6.3  Goto step 12. \\
-\hspace{3mm}12.7  $bitcpy \leftarrow bitcpy + 1$ \\
-\hspace{3mm}12.8  $bitbuf \leftarrow bitbuf + (y << (winsize - bitcpy))$ \\
-\hspace{3mm}12.9  $mode \leftarrow 2$ \\
-\hspace{3mm}12.10  If $bitcpy = winsize$ then do \\
-\hspace{6mm}Window is full so perform the squarings and single multiplication. \\
-\hspace{6mm}12.10.1  for $ix$ from $0$ to $winsize -1$ do \\
-\hspace{9mm}12.10.1.1  $res \leftarrow res^2$ \\
-\hspace{9mm}12.10.1.2  $res \leftarrow res \mbox{ (mod }p\mbox{)}$ \\
-\hspace{6mm}12.10.2  $res \leftarrow res \cdot M_{bitbuf}$ \\
-\hspace{6mm}12.10.3  $res \leftarrow res \mbox{ (mod }p\mbox{)}$ \\
-\hspace{6mm}Reset the window. \\
-\hspace{6mm}12.10.4  $bitcpy \leftarrow 0, bitbuf \leftarrow 0, mode \leftarrow 1$ \\
-\\
-No more windows left.  Check for residual bits of exponent. \\
-13.  If $mode = 2$ and $bitcpy > 0$ then do \\
-\hspace{3mm}13.1  for $ix$ form $0$ to $bitcpy - 1$ do \\
-\hspace{6mm}13.1.1  $res \leftarrow res^2$ \\
-\hspace{6mm}13.1.2  $res \leftarrow res \mbox{ (mod }p\mbox{)}$ \\
-\hspace{6mm}13.1.3  $bitbuf \leftarrow bitbuf << 1$ \\
-\hspace{6mm}13.1.4  If $bitbuf$ AND $2^{winsize} \ne 0$ then do \\
-\hspace{9mm}13.1.4.1  $res \leftarrow res \cdot M_{1}$ \\
-\hspace{9mm}13.1.4.2  $res \leftarrow res \mbox{ (mod }p\mbox{)}$ \\
-14.  $y \leftarrow res$ \\
-15.  Clear $res$, $mu$ and the $M$ array. \\
-16.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm s\_mp\_exptmod (continued)}
-\end{figure}
-
-\textbf{Algorithm s\_mp\_exptmod.}
-This algorithm computes the $x$'th power of $g$ modulo $p$ and stores the result in $y$.  It takes advantage of the Barrett reduction
-algorithm to keep the product small throughout the algorithm.
-
-The first two steps determine the optimal window size based on the number of bits in the exponent.  The larger the exponent the
-larger the window size becomes.  After a window size $winsize$ has been chosen an array of $2^{winsize}$ mp\_int variables is allocated.  This
-table will hold the values of $g^x \mbox{ (mod }p\mbox{)}$ for $2^{winsize - 1} \le x < 2^{winsize}$.
-
-After the table is allocated the first power of $g$ is found.  Since $g \ge p$ is allowed it must be first reduced modulo $p$ to make
-the rest of the algorithm more efficient.  The first element of the table at $2^{winsize - 1}$ is found by squaring $M_1$ successively $winsize - 2$
-times.  The rest of the table elements are found by multiplying the previous element by $M_1$ modulo $p$.
-
-Now that the table is available the sliding window may begin.  The following list describes the functions of all the variables in the window.
-\begin{enumerate}
-\item The variable $mode$ dictates how the bits of the exponent are interpreted.
-\begin{enumerate}
-   \item When $mode = 0$ the bits are ignored since no non-zero bit of the exponent has been seen yet.  For example, if the exponent were simply
-         $1$ then there would be $lg(\beta) - 1$ zero bits before the first non-zero bit.  In this case bits are ignored until a non-zero bit is found.
-   \item When $mode = 1$ a non-zero bit has been seen before and a new $winsize$-bit window has not been formed yet.  In this mode leading $0$ bits
-         are read and a single squaring is performed.  If a non-zero bit is read a new window is created.
-   \item When $mode = 2$ the algorithm is in the middle of forming a window and new bits are appended to the window from the most significant bit
-         downwards.
-\end{enumerate}
-\item The variable $bitcnt$ indicates how many bits are left in the current digit of the exponent left to be read.  When it reaches zero a new digit
-      is fetched from the exponent.
-\item The variable $buf$ holds the currently read digit of the exponent.
-\item The variable $digidx$ is an index into the exponents digits.  It starts at the leading digit $x.used - 1$ and moves towards the trailing digit.
-\item The variable $bitcpy$ indicates how many bits are in the currently formed window.  When it reaches $winsize$ the window is flushed and
-      the appropriate operations performed.
-\item The variable $bitbuf$ holds the current bits of the window being formed.
-\end{enumerate}
-
-All of step 12 is the window processing loop.  It will iterate while there are digits available form the exponent to read.  The first step
-inside this loop is to extract a new digit if no more bits are available in the current digit.  If there are no bits left a new digit is
-read and if there are no digits left than the loop terminates.
-
-After a digit is made available step 12.3 will extract the most significant bit of the current digit and move all other bits in the digit
-upwards.  In effect the digit is read from most significant bit to least significant bit and since the digits are read from leading to
-trailing edges the entire exponent is read from most significant bit to least significant bit.
-
-At step 12.5 if the $mode$ and currently extracted bit $y$ are both zero the bit is ignored and the next bit is read.  This prevents the
-algorithm from having to perform trivial squaring and reduction operations before the first non-zero bit is read.  Step 12.6 and 12.7-10 handle
-the two cases of $mode = 1$ and $mode = 2$ respectively.
-
-FIGU,expt_state,Sliding Window State Diagram
-
-By step 13 there are no more digits left in the exponent.  However, there may be partial bits in the window left.  If $mode = 2$ then
-a Left-to-Right algorithm is used to process the remaining few bits.
-
-EXAM,bn_s_mp_exptmod.c
-
-Lines @31,if@ through @45,}@ determine the optimal window size based on the length of the exponent in bits.  The window divisions are sorted
-from smallest to greatest so that in each \textbf{if} statement only one condition must be tested.  For example, by the \textbf{if} statement
-on line @37,if@ the value of $x$ is already known to be greater than $140$.
-
-The conditional piece of code beginning on line @42,ifdef@ allows the window size to be restricted to five bits.  This logic is used to ensure
-the table of precomputed powers of $G$ remains relatively small.
-
-The for loop on line @60,for@ initializes the $M$ array while lines @71,mp_init@ and @75,mp_reduce@ through @85,}@ initialize the reduction
-function that will be used for this modulus.
-
--- More later.
-
-\section{Quick Power of Two}
-Calculating $b = 2^a$ can be performed much quicker than with any of the previous algorithms.  Recall that a logical shift left $m << k$ is
-equivalent to $m \cdot 2^k$.  By this logic when $m = 1$ a quick power of two can be achieved.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_2expt}. \\
-\textbf{Input}.   integer $b$ \\
-\textbf{Output}.  $a \leftarrow 2^b$ \\
-\hline \\
-1.  $a \leftarrow 0$ \\
-2.  If $a.alloc < \lfloor b / lg(\beta) \rfloor + 1$ then grow $a$ appropriately. \\
-3.  $a.used \leftarrow \lfloor b / lg(\beta) \rfloor + 1$ \\
-4.  $a_{\lfloor b / lg(\beta) \rfloor} \leftarrow 1 << (b \mbox{ mod } lg(\beta))$ \\
-5.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_2expt}
-\end{figure}
-
-\textbf{Algorithm mp\_2expt.}
-
-EXAM,bn_mp_2expt.c
-
-\chapter{Higher Level Algorithms}
-
-This chapter discusses the various higher level algorithms that are required to complete a well rounded multiple precision integer package.  These
-routines are less performance oriented than the algorithms of chapters five, six and seven but are no less important.
-
-The first section describes a method of integer division with remainder that is universally well known.  It provides the signed division logic
-for the package.  The subsequent section discusses a set of algorithms which allow a single digit to be the 2nd operand for a variety of operations.
-These algorithms serve mostly to simplify other algorithms where small constants are required.  The last two sections discuss how to manipulate
-various representations of integers.  For example, converting from an mp\_int to a string of character.
-
-\section{Integer Division with Remainder}
-\label{sec:division}
-
-Integer division aside from modular exponentiation is the most intensive algorithm to compute.  Like addition, subtraction and multiplication
-the basis of this algorithm is the long-hand division algorithm taught to school children.  Throughout this discussion several common variables
-will be used.  Let $x$ represent the divisor and $y$ represent the dividend.  Let $q$ represent the integer quotient $\lfloor y / x \rfloor$ and
-let $r$ represent the remainder $r = y - x \lfloor y / x \rfloor$.  The following simple algorithm will be used to start the discussion.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Radix-$\beta$ Integer Division}. \\
-\textbf{Input}.   integer $x$ and $y$ \\
-\textbf{Output}.  $q = \lfloor y/x\rfloor, r = y - xq$ \\
-\hline \\
-1.  $q \leftarrow 0$ \\
-2.  $n \leftarrow \vert \vert y \vert \vert - \vert \vert x \vert \vert$ \\
-3.  for $t$ from $n$ down to $0$ do \\
-\hspace{3mm}3.1  Maximize $k$ such that $kx\beta^t$ is less than or equal to $y$ and $(k + 1)x\beta^t$ is greater. \\
-\hspace{3mm}3.2  $q \leftarrow q + k\beta^t$ \\
-\hspace{3mm}3.3  $y \leftarrow y - kx\beta^t$ \\
-4.  $r \leftarrow y$ \\
-5.  Return($q, r$) \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm Radix-$\beta$ Integer Division}
-\label{fig:raddiv}
-\end{figure}
-
-As children we are taught this very simple algorithm for the case of $\beta = 10$.  Almost instinctively several optimizations are taught for which
-their reason of existing are never explained.  For this example let $y = 5471$ represent the dividend and $x = 23$ represent the divisor.
-
-To find the first digit of the quotient the value of $k$ must be maximized such that $kx\beta^t$ is less than or equal to $y$ and
-simultaneously $(k + 1)x\beta^t$ is greater than $y$.  Implicitly $k$ is the maximum value the $t$'th digit of the quotient may have.  The habitual method
-used to find the maximum is to ``eyeball'' the two numbers, typically only the leading digits and quickly estimate a quotient.  By only using leading
-digits a much simpler division may be used to form an educated guess at what the value must be.  In this case $k = \lfloor 54/23\rfloor = 2$ quickly
-arises as a possible  solution.  Indeed $2x\beta^2 = 4600$ is less than $y = 5471$ and simultaneously $(k + 1)x\beta^2 = 6900$ is larger than $y$.
-As a  result $k\beta^2$ is added to the quotient which now equals $q = 200$ and $4600$ is subtracted from $y$ to give a remainder of $y = 841$.
-
-Again this process is repeated to produce the quotient digit $k = 3$ which makes the quotient $q = 200 + 3\beta = 230$ and the remainder
-$y = 841 - 3x\beta = 181$.  Finally the last iteration of the loop produces $k = 7$ which leads to the quotient $q = 230 + 7 = 237$ and the
-remainder $y = 181 - 7x = 20$.  The final quotient and remainder found are $q = 237$ and $r = y = 20$ which are indeed correct since
-$237 \cdot 23 + 20 = 5471$ is true.
-
-\subsection{Quotient Estimation}
-\label{sec:divest}
-As alluded to earlier the quotient digit $k$ can be estimated from only the leading digits of both the divisor and dividend.  When $p$ leading
-digits are used from both the divisor and dividend to form an estimation the accuracy of the estimation rises as $p$ grows.  Technically
-speaking the estimation is based on assuming the lower $\vert \vert y \vert \vert - p$ and $\vert \vert x \vert \vert - p$ lower digits of the
-dividend and divisor are zero.
-
-The value of the estimation may off by a few values in either direction and in general is fairly correct.  A simplification \cite[pp. 271]{TAOCPV2}
-of the estimation technique is to use $t + 1$ digits of the dividend and $t$ digits of the divisor, in particularly when $t = 1$.  The estimate
-using this technique is never too small.  For the following proof let $t = \vert \vert y \vert \vert - 1$ and $s = \vert \vert x \vert \vert - 1$
-represent the most significant digits of the dividend and divisor respectively.
-
-\textbf{Proof.}\textit{  The quotient $\hat k = \lfloor (y_t\beta + y_{t-1}) / x_s \rfloor$ is greater than or equal to
-$k = \lfloor y / (x \cdot \beta^{\vert \vert y \vert \vert - \vert \vert x \vert \vert - 1}) \rfloor$. }
-The first obvious case is when $\hat k = \beta - 1$ in which case the proof is concluded since the real quotient cannot be larger.  For all other
-cases $\hat k = \lfloor (y_t\beta + y_{t-1}) / x_s \rfloor$ and $\hat k x_s \ge y_t\beta + y_{t-1} - x_s + 1$.  The latter portion of the inequalility
-$-x_s + 1$ arises from the fact that a truncated integer division will give the same quotient for at most $x_s - 1$ values.  Next a series of
-inequalities will prove the hypothesis.
-
-\begin{equation}
-y - \hat k x \le y - \hat k x_s\beta^s
-\end{equation}
-
-This is trivially true since $x \ge x_s\beta^s$.  Next we replace $\hat kx_s\beta^s$ by the previous inequality for $\hat kx_s$.
-
-\begin{equation}
-y - \hat k x \le y_t\beta^t + \ldots + y_0 - (y_t\beta^t + y_{t-1}\beta^{t-1} - x_s\beta^t + \beta^s)
-\end{equation}
-
-By simplifying the previous inequality the following inequality is formed.
-
-\begin{equation}
-y - \hat k x \le y_{t-2}\beta^{t-2} + \ldots + y_0 + x_s\beta^s - \beta^s
-\end{equation}
-
-Subsequently,
-
-\begin{equation}
-y_{t-2}\beta^{t-2} + \ldots +  y_0  + x_s\beta^s - \beta^s < x_s\beta^s \le x
-\end{equation}
-
-Which proves that $y - \hat kx \le x$ and by consequence $\hat k \ge k$ which concludes the proof.  \textbf{QED}
-
-
-\subsection{Normalized Integers}
-For the purposes of division a normalized input is when the divisors leading digit $x_n$ is greater than or equal to $\beta / 2$.  By multiplying both
-$x$ and $y$ by $j = \lfloor (\beta / 2) / x_n \rfloor$ the quotient remains unchanged and the remainder is simply $j$ times the original
-remainder.  The purpose of normalization is to ensure the leading digit of the divisor is sufficiently large such that the estimated quotient will
-lie in the domain of a single digit.  Consider the maximum dividend $(\beta - 1) \cdot \beta + (\beta - 1)$ and the minimum divisor $\beta / 2$.
-
-\begin{equation}
-{{\beta^2 - 1} \over { \beta / 2}} \le 2\beta - {2 \over \beta}
-\end{equation}
-
-At most the quotient approaches $2\beta$, however, in practice this will not occur since that would imply the previous quotient digit was too small.
-
-\subsection{Radix-$\beta$ Division with Remainder}
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_div}. \\
-\textbf{Input}.   mp\_int $a, b$ \\
-\textbf{Output}.  $c = \lfloor a/b \rfloor$, $d = a - bc$ \\
-\hline \\
-1.  If $b = 0$ return(\textit{MP\_VAL}). \\
-2.  If $\vert a \vert < \vert b \vert$ then do \\
-\hspace{3mm}2.1  $d \leftarrow a$ \\
-\hspace{3mm}2.2  $c \leftarrow 0$ \\
-\hspace{3mm}2.3  Return(\textit{MP\_OKAY}). \\
-\\
-Setup the quotient to receive the digits. \\
-3.  Grow $q$ to $a.used + 2$ digits. \\
-4.  $q \leftarrow 0$ \\
-5.  $x \leftarrow \vert a \vert , y \leftarrow \vert b \vert$ \\
-6.  $sign \leftarrow  \left \lbrace \begin{array}{ll}
-                              MP\_ZPOS &  \mbox{if }a.sign = b.sign \\
-                              MP\_NEG  &  \mbox{otherwise} \\
-                              \end{array} \right .$ \\
-\\
-Normalize the inputs such that the leading digit of $y$ is greater than or equal to $\beta / 2$. \\
-7.  $norm \leftarrow (lg(\beta) - 1) - (\lceil lg(y) \rceil \mbox{ (mod }lg(\beta)\mbox{)})$ \\
-8.  $x \leftarrow x \cdot 2^{norm}, y \leftarrow y \cdot 2^{norm}$ \\
-\\
-Find the leading digit of the quotient. \\
-9.  $n \leftarrow x.used - 1, t \leftarrow y.used - 1$ \\
-10.  $y \leftarrow y \cdot \beta^{n - t}$ \\
-11.  While ($x \ge y$) do \\
-\hspace{3mm}11.1  $q_{n - t} \leftarrow q_{n - t} + 1$ \\
-\hspace{3mm}11.2  $x \leftarrow x - y$ \\
-12.  $y \leftarrow \lfloor y / \beta^{n-t} \rfloor$ \\
-\\
-Continued on the next page. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_div}
-\end{figure}
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_div} (continued). \\
-\textbf{Input}.   mp\_int $a, b$ \\
-\textbf{Output}.  $c = \lfloor a/b \rfloor$, $d = a - bc$ \\
-\hline \\
-Now find the remainder fo the digits. \\
-13.  for $i$ from $n$ down to $(t + 1)$ do \\
-\hspace{3mm}13.1  If $i > x.used$ then jump to the next iteration of this loop. \\
-\hspace{3mm}13.2  If $x_{i} = y_{t}$ then \\
-\hspace{6mm}13.2.1  $q_{i - t - 1} \leftarrow \beta - 1$ \\
-\hspace{3mm}13.3  else \\
-\hspace{6mm}13.3.1  $\hat r \leftarrow x_{i} \cdot \beta + x_{i - 1}$ \\
-\hspace{6mm}13.3.2  $\hat r \leftarrow \lfloor \hat r / y_{t} \rfloor$ \\
-\hspace{6mm}13.3.3  $q_{i - t - 1} \leftarrow \hat r$ \\
-\hspace{3mm}13.4  $q_{i - t - 1} \leftarrow q_{i - t - 1} + 1$ \\
-\\
-Fixup quotient estimation. \\
-\hspace{3mm}13.5  Loop \\
-\hspace{6mm}13.5.1  $q_{i - t - 1} \leftarrow q_{i - t - 1} - 1$ \\
-\hspace{6mm}13.5.2  t$1 \leftarrow 0$ \\
-\hspace{6mm}13.5.3  t$1_0 \leftarrow y_{t - 1}, $ t$1_1 \leftarrow y_t,$ t$1.used \leftarrow 2$ \\
-\hspace{6mm}13.5.4  $t1 \leftarrow t1 \cdot q_{i - t - 1}$ \\
-\hspace{6mm}13.5.5  t$2_0 \leftarrow x_{i - 2}, $ t$2_1 \leftarrow x_{i - 1}, $ t$2_2 \leftarrow x_i, $ t$2.used \leftarrow 3$ \\
-\hspace{6mm}13.5.6  If $\vert t1 \vert > \vert t2 \vert$ then goto step 13.5. \\
-\hspace{3mm}13.6  t$1 \leftarrow y \cdot q_{i - t - 1}$ \\
-\hspace{3mm}13.7  t$1 \leftarrow $ t$1 \cdot \beta^{i - t - 1}$ \\
-\hspace{3mm}13.8  $x \leftarrow x - $ t$1$ \\
-\hspace{3mm}13.9  If $x.sign = MP\_NEG$ then \\
-\hspace{6mm}13.10  t$1 \leftarrow y$ \\
-\hspace{6mm}13.11  t$1 \leftarrow $ t$1 \cdot \beta^{i - t - 1}$ \\
-\hspace{6mm}13.12  $x \leftarrow x + $ t$1$ \\
-\hspace{6mm}13.13  $q_{i - t - 1} \leftarrow q_{i - t - 1} - 1$ \\
-\\
-Finalize the result. \\
-14.  Clamp excess digits of $q$ \\
-15.  $c \leftarrow q, c.sign \leftarrow sign$ \\
-16.  $x.sign \leftarrow a.sign$ \\
-17.  $d \leftarrow \lfloor x / 2^{norm} \rfloor$ \\
-18.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_div (continued)}
-\end{figure}
-\textbf{Algorithm mp\_div.}
-This algorithm will calculate quotient and remainder from an integer division given a dividend and divisor.  The algorithm is a signed
-division and will produce a fully qualified quotient and remainder.
-
-First the divisor $b$ must be non-zero which is enforced in step one.  If the divisor is larger than the dividend than the quotient is implicitly
-zero and the remainder is the dividend.
-
-After the first two trivial cases of inputs are handled the variable $q$ is setup to receive the digits of the quotient.  Two unsigned copies of the
-divisor $y$ and dividend $x$ are made as well.  The core of the division algorithm is an unsigned division and will only work if the values are
-positive.  Now the two values $x$ and $y$ must be normalized such that the leading digit of $y$ is greater than or equal to $\beta / 2$.
-This is performed by shifting both to the left by enough bits to get the desired normalization.
-
-At this point the division algorithm can begin producing digits of the quotient.  Recall that maximum value of the estimation used is
-$2\beta - {2 \over \beta}$ which means that a digit of the quotient must be first produced by another means.  In this case $y$ is shifted
-to the left (\textit{step ten}) so that it has the same number of digits as $x$.  The loop on step eleven will subtract multiples of the
-shifted copy of $y$ until $x$ is smaller.  Since the leading digit of $y$ is greater than or equal to $\beta/2$ this loop will iterate at most two
-times to produce the desired leading digit of the quotient.
-
-Now the remainder of the digits can be produced.  The equation $\hat q = \lfloor {{x_i \beta + x_{i-1}}\over y_t} \rfloor$ is used to fairly
-accurately approximate the true quotient digit.  The estimation can in theory produce an estimation as high as $2\beta - {2 \over \beta}$ but by
-induction the upper quotient digit is correct (\textit{as established on step eleven}) and the estimate must be less than $\beta$.
-
-Recall from section~\ref{sec:divest} that the estimation is never too low but may be too high.  The next step of the estimation process is
-to refine the estimation.  The loop on step 13.5 uses $x_i\beta^2 + x_{i-1}\beta + x_{i-2}$ and $q_{i - t - 1}(y_t\beta + y_{t-1})$ as a higher
-order approximation to adjust the quotient digit.
-
-After both phases of estimation the quotient digit may still be off by a value of one\footnote{This is similar to the error introduced
-by optimizing Barrett reduction.}.  Steps 13.6 and 13.7 subtract the multiple of the divisor from the dividend (\textit{Similar to step 3.3 of
-algorithm~\ref{fig:raddiv}} and then subsequently add a multiple of the divisor if the quotient was too large.
-
-Now that the quotient has been determine finializing the result is a matter of clamping the quotient, fixing the sizes and de-normalizing the
-remainder.  An important aspect of this algorithm seemingly overlooked in other descriptions such as that of Algorithm 14.20 HAC \cite[pp. 598]{HAC}
-is that when the estimations are being made (\textit{inside the loop on step 13.5}) that the digits $y_{t-1}$, $x_{i-2}$ and $x_{i-1}$ may lie
-outside their respective boundaries.  For example, if $t = 0$ or $i \le 1$ then the digits would be undefined.  In those cases the digits should
-respectively be replaced with a zero.
-
-EXAM,bn_mp_div.c
-
-The implementation of this algorithm differs slightly from the pseudo code presented previously.  In this algorithm either of the quotient $c$ or
-remainder $d$ may be passed as a \textbf{NULL} pointer which indicates their value is not desired.  For example, the C code to call the division
-algorithm with only the quotient is
-
-\begin{verbatim}
-mp_div(&a, &b, &c, NULL);  /* c = [a/b] */
-\end{verbatim}
-
-Lines @108,if@ and @113,if@ handle the two trivial cases of inputs which are division by zero and dividend smaller than the divisor
-respectively.  After the two trivial cases all of the temporary variables are initialized.  Line @147,neg@ determines the sign of
-the quotient and line @148,sign@ ensures that both $x$ and $y$ are positive.
-
-The number of bits in the leading digit is calculated on line @151,norm@.  Implictly an mp\_int with $r$ digits will require $lg(\beta)(r-1) + k$ bits
-of precision which when reduced modulo $lg(\beta)$ produces the value of $k$.  In this case $k$ is the number of bits in the leading digit which is
-exactly what is required.  For the algorithm to operate $k$ must equal $lg(\beta) - 1$ and when it does not the inputs must be normalized by shifting
-them to the left by $lg(\beta) - 1 - k$ bits.
-
-Throughout the variables $n$ and $t$ will represent the highest digit of $x$ and $y$ respectively.  These are first used to produce the
-leading digit of the quotient.  The loop beginning on line @184,for@ will produce the remainder of the quotient digits.
-
-The conditional ``continue'' on line @186,continue@ is used to prevent the algorithm from reading past the leading edge of $x$ which can occur when the
-algorithm eliminates multiple non-zero digits in a single iteration.  This ensures that $x_i$ is always non-zero since by definition the digits
-above the $i$'th position $x$ must be zero in order for the quotient to be precise\footnote{Precise as far as integer division is concerned.}.
-
-Lines @214,t1@, @216,t1@ and @222,t2@ through @225,t2@ manually construct the high accuracy estimations by setting the digits of the two mp\_int
-variables directly.
-
-\section{Single Digit Helpers}
-
-This section briefly describes a series of single digit helper algorithms which come in handy when working with small constants.  All of
-the helper functions assume the single digit input is positive and will treat them as such.
-
-\subsection{Single Digit Addition and Subtraction}
-
-Both addition and subtraction are performed by ``cheating'' and using mp\_set followed by the higher level addition or subtraction
-algorithms.   As a result these algorithms are subtantially simpler with a slight cost in performance.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_add\_d}. \\
-\textbf{Input}.   mp\_int $a$ and a mp\_digit $b$ \\
-\textbf{Output}.  $c = a + b$ \\
-\hline \\
-1.  $t \leftarrow b$ (\textit{mp\_set}) \\
-2.  $c \leftarrow a + t$ \\
-3.  Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_add\_d}
-\end{figure}
-
-\textbf{Algorithm mp\_add\_d.}
-This algorithm initiates a temporary mp\_int with the value of the single digit and uses algorithm mp\_add to add the two values together.
-
-EXAM,bn_mp_add_d.c
-
-Clever use of the letter 't'.
-
-\subsubsection{Subtraction}
-The single digit subtraction algorithm mp\_sub\_d is essentially the same except it uses mp\_sub to subtract the digit from the mp\_int.
-
-\subsection{Single Digit Multiplication}
-Single digit multiplication arises enough in division and radix conversion that it ought to be implement as a special case of the baseline
-multiplication algorithm.  Essentially this algorithm is a modified version of algorithm s\_mp\_mul\_digs where one of the multiplicands
-only has one digit.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_mul\_d}. \\
-\textbf{Input}.   mp\_int $a$ and a mp\_digit $b$ \\
-\textbf{Output}.  $c = ab$ \\
-\hline \\
-1.  $pa \leftarrow a.used$ \\
-2.  Grow $c$ to at least $pa + 1$ digits. \\
-3.  $oldused \leftarrow c.used$ \\
-4.  $c.used \leftarrow pa + 1$ \\
-5.  $c.sign \leftarrow a.sign$ \\
-6.  $\mu \leftarrow 0$ \\
-7.  for $ix$ from $0$ to $pa - 1$ do \\
-\hspace{3mm}7.1  $\hat r \leftarrow \mu + a_{ix}b$ \\
-\hspace{3mm}7.2  $c_{ix} \leftarrow \hat r \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{3mm}7.3  $\mu \leftarrow \lfloor \hat r / \beta \rfloor$ \\
-8.  $c_{pa} \leftarrow \mu$ \\
-9.  for $ix$ from $pa + 1$ to $oldused$ do \\
-\hspace{3mm}9.1  $c_{ix} \leftarrow 0$ \\
-10.  Clamp excess digits of $c$. \\
-11.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_mul\_d}
-\end{figure}
-\textbf{Algorithm mp\_mul\_d.}
-This algorithm quickly multiplies an mp\_int by a small single digit value.  It is specially tailored to the job and has a minimal of overhead.
-Unlike the full multiplication algorithms this algorithm does not require any significnat temporary storage or memory allocations.
-
-EXAM,bn_mp_mul_d.c
-
-In this implementation the destination $c$ may point to the same mp\_int as the source $a$ since the result is written after the digit is
-read from the source.  This function uses pointer aliases $tmpa$ and $tmpc$ for the digits of $a$ and $c$ respectively.
-
-\subsection{Single Digit Division}
-Like the single digit multiplication algorithm, single digit division is also a fairly common algorithm used in radix conversion.  Since the
-divisor is only a single digit a specialized variant of the division algorithm can be used to compute the quotient.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_div\_d}. \\
-\textbf{Input}.   mp\_int $a$ and a mp\_digit $b$ \\
-\textbf{Output}.  $c = \lfloor a / b \rfloor, d = a - cb$ \\
-\hline \\
-1.  If $b = 0$ then return(\textit{MP\_VAL}).\\
-2.  If $b = 3$ then use algorithm mp\_div\_3 instead. \\
-3.  Init $q$ to $a.used$ digits.  \\
-4.  $q.used \leftarrow a.used$ \\
-5.  $q.sign \leftarrow a.sign$ \\
-6.  $\hat w \leftarrow 0$ \\
-7.  for $ix$ from $a.used - 1$ down to $0$ do \\
-\hspace{3mm}7.1  $\hat w \leftarrow \hat w \beta + a_{ix}$ \\
-\hspace{3mm}7.2  If $\hat w \ge b$ then \\
-\hspace{6mm}7.2.1  $t \leftarrow \lfloor \hat w / b \rfloor$ \\
-\hspace{6mm}7.2.2  $\hat w \leftarrow \hat w \mbox{ (mod }b\mbox{)}$ \\
-\hspace{3mm}7.3  else\\
-\hspace{6mm}7.3.1  $t \leftarrow 0$ \\
-\hspace{3mm}7.4  $q_{ix} \leftarrow t$ \\
-8.  $d \leftarrow \hat w$ \\
-9.  Clamp excess digits of $q$. \\
-10.  $c \leftarrow q$ \\
-11.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_div\_d}
-\end{figure}
-\textbf{Algorithm mp\_div\_d.}
-This algorithm divides the mp\_int $a$ by the single mp\_digit $b$ using an optimized approach.  Essentially in every iteration of the
-algorithm another digit of the dividend is reduced and another digit of quotient produced.  Provided $b < \beta$ the value of $\hat w$
-after step 7.1 will be limited such that $0 \le \lfloor \hat w / b \rfloor < \beta$.
-
-If the divisor $b$ is equal to three a variant of this algorithm is used which is called mp\_div\_3.  It replaces the division by three with
-a multiplication by $\lfloor \beta / 3 \rfloor$ and the appropriate shift and residual fixup.  In essence it is much like the Barrett reduction
-from chapter seven.
-
-EXAM,bn_mp_div_d.c
-
-Like the implementation of algorithm mp\_div this algorithm allows either of the quotient or remainder to be passed as a \textbf{NULL} pointer to
-indicate the respective value is not required.  This allows a trivial single digit modular reduction algorithm, mp\_mod\_d to be created.
-
-The division and remainder on lines @90,/@ and @91,-@ can be replaced often by a single division on most processors.  For example, the 32-bit x86 based
-processors can divide a 64-bit quantity by a 32-bit quantity and produce the quotient and remainder simultaneously.  Unfortunately the GCC
-compiler does not recognize that optimization and will actually produce two function calls to find the quotient and remainder respectively.
-
-\subsection{Single Digit Root Extraction}
-
-Finding the $n$'th root of an integer is fairly easy as far as numerical analysis is concerned.  Algorithms such as the Newton-Raphson approximation
-(\ref{eqn:newton}) series will converge very quickly to a root for any continuous function $f(x)$.
-
-\begin{equation}
-x_{i+1} = x_i - {f(x_i) \over f'(x_i)}
-\label{eqn:newton}
-\end{equation}
-
-In this case the $n$'th root is desired and $f(x) = x^n - a$ where $a$ is the integer of which the root is desired.  The derivative of $f(x)$ is
-simply $f'(x) = nx^{n - 1}$.  Of particular importance is that this algorithm will be used over the integers not over the a more continuous domain
-such as the real numbers.  As a result the root found can be above the true root by few and must be manually adjusted.  Ideally at the end of the
-algorithm the $n$'th root $b$ of an integer $a$ is desired such that $b^n \le a$.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_n\_root}. \\
-\textbf{Input}.   mp\_int $a$ and a mp\_digit $b$ \\
-\textbf{Output}.  $c^b \le a$ \\
-\hline \\
-1.  If $b$ is even and $a.sign = MP\_NEG$ return(\textit{MP\_VAL}). \\
-2.  $sign \leftarrow a.sign$ \\
-3.  $a.sign \leftarrow MP\_ZPOS$ \\
-4.  t$2 \leftarrow 2$ \\
-5.  Loop \\
-\hspace{3mm}5.1  t$1 \leftarrow $ t$2$ \\
-\hspace{3mm}5.2  t$3 \leftarrow $ t$1^{b - 1}$ \\
-\hspace{3mm}5.3  t$2 \leftarrow $ t$3 $ $\cdot$ t$1$ \\
-\hspace{3mm}5.4  t$2 \leftarrow $ t$2 - a$ \\
-\hspace{3mm}5.5  t$3 \leftarrow $ t$3 \cdot b$ \\
-\hspace{3mm}5.6  t$3 \leftarrow \lfloor $t$2 / $t$3 \rfloor$ \\
-\hspace{3mm}5.7  t$2 \leftarrow $ t$1 - $ t$3$ \\
-\hspace{3mm}5.8  If t$1 \ne $ t$2$ then goto step 5.  \\
-6.  Loop \\
-\hspace{3mm}6.1  t$2 \leftarrow $ t$1^b$ \\
-\hspace{3mm}6.2  If t$2 > a$ then \\
-\hspace{6mm}6.2.1  t$1 \leftarrow $ t$1 - 1$ \\
-\hspace{6mm}6.2.2  Goto step 6. \\
-7.  $a.sign \leftarrow sign$ \\
-8.  $c \leftarrow $ t$1$ \\
-9.  $c.sign \leftarrow sign$  \\
-10.  Return(\textit{MP\_OKAY}).  \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_n\_root}
-\end{figure}
-\textbf{Algorithm mp\_n\_root.}
-This algorithm finds the integer $n$'th root of an input using the Newton-Raphson approach.  It is partially optimized based on the observation
-that the numerator of ${f(x) \over f'(x)}$ can be derived from a partial denominator.  That is at first the denominator is calculated by finding
-$x^{b - 1}$.  This value can then be multiplied by $x$ and have $a$ subtracted from it to find the numerator.  This saves a total of $b - 1$
-multiplications by t$1$ inside the loop.
-
-The initial value of the approximation is t$2 = 2$ which allows the algorithm to start with very small values and quickly converge on the
-root.  Ideally this algorithm is meant to find the $n$'th root of an input where $n$ is bounded by $2 \le n \le 5$.
-
-EXAM,bn_mp_n_root.c
-
-\section{Random Number Generation}
-
-Random numbers come up in a variety of activities from public key cryptography to simple simulations and various randomized algorithms.  Pollard-Rho
-factoring for example, can make use of random values as starting points to find factors of a composite integer.  In this case the algorithm presented
-is solely for simulations and not intended for cryptographic use.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_rand}. \\
-\textbf{Input}.   An integer $b$ \\
-\textbf{Output}.  A pseudo-random number of $b$ digits \\
-\hline \\
-1.  $a \leftarrow 0$ \\
-2.  If $b \le 0$ return(\textit{MP\_OKAY}) \\
-3.  Pick a non-zero random digit $d$. \\
-4.  $a \leftarrow a + d$ \\
-5.  for $ix$ from 1 to $d - 1$ do \\
-\hspace{3mm}5.1  $a \leftarrow a \cdot \beta$ \\
-\hspace{3mm}5.2  Pick a random digit $d$. \\
-\hspace{3mm}5.3  $a \leftarrow a + d$ \\
-6.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_rand}
-\end{figure}
-\textbf{Algorithm mp\_rand.}
-This algorithm produces a pseudo-random integer of $b$ digits.  By ensuring that the first digit is non-zero the algorithm also guarantees that the
-final result has at least $b$ digits.  It relies heavily on a third-part random number generator which should ideally generate uniformly all of
-the integers from $0$ to $\beta - 1$.
-
-EXAM,bn_mp_rand.c
-
-\section{Formatted Representations}
-The ability to emit a radix-$n$ textual representation of an integer is useful for interacting with human parties.  For example, the ability to
-be given a string of characters such as ``114585'' and turn it into the radix-$\beta$ equivalent would make it easier to enter numbers
-into a program.
-
-\subsection{Reading Radix-n Input}
-For the purposes of this text we will assume that a simple lower ASCII map (\ref{fig:ASC}) is used for the values of from $0$ to $63$ to
-printable characters.  For example, when the character ``N'' is read it represents the integer $23$.  The first $16$ characters of the
-map are for the common representations up to hexadecimal.  After that they match the ``base64'' encoding scheme which are suitable chosen
-such that they are printable.  While outputting as base64 may not be too helpful for human operators it does allow communication via non binary
-mediums.
-
-\newpage\begin{figure}[here]
-\begin{center}
-\begin{tabular}{cc|cc|cc|cc}
-\hline \textbf{Value} & \textbf{Char} & \textbf{Value} & \textbf{Char} & \textbf{Value} & \textbf{Char} &  \textbf{Value} & \textbf{Char} \\
-\hline
-0 & 0 & 1 & 1 & 2 & 2 & 3 & 3 \\
-4 & 4 & 5 & 5 & 6 & 6 & 7 & 7 \\
-8 & 8 & 9 & 9 & 10 & A & 11 & B \\
-12 & C & 13 & D & 14 & E & 15 & F \\
-16 & G & 17 & H & 18 & I & 19 & J \\
-20 & K & 21 & L & 22 & M & 23 & N \\
-24 & O & 25 & P & 26 & Q & 27 & R \\
-28 & S & 29 & T & 30 & U & 31 & V \\
-32 & W & 33 & X & 34 & Y & 35 & Z \\
-36 & a & 37 & b & 38 & c & 39 & d \\
-40 & e & 41 & f & 42 & g & 43 & h \\
-44 & i & 45 & j & 46 & k & 47 & l \\
-48 & m & 49 & n & 50 & o & 51 & p \\
-52 & q & 53 & r & 54 & s & 55 & t \\
-56 & u & 57 & v & 58 & w & 59 & x \\
-60 & y & 61 & z & 62 & $+$ & 63 & $/$ \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Lower ASCII Map}
-\label{fig:ASC}
-\end{figure}
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_read\_radix}. \\
-\textbf{Input}.   A string $str$ of length $sn$ and radix $r$. \\
-\textbf{Output}.  The radix-$\beta$ equivalent mp\_int. \\
-\hline \\
-1.  If $r < 2$ or $r > 64$ return(\textit{MP\_VAL}). \\
-2.  $ix \leftarrow 0$ \\
-3.  If $str_0 =$ ``-'' then do \\
-\hspace{3mm}3.1  $ix \leftarrow ix + 1$ \\
-\hspace{3mm}3.2  $sign \leftarrow MP\_NEG$ \\
-4.  else \\
-\hspace{3mm}4.1  $sign \leftarrow MP\_ZPOS$ \\
-5.  $a \leftarrow 0$ \\
-6.  for $iy$ from $ix$ to $sn - 1$ do \\
-\hspace{3mm}6.1  Let $y$ denote the position in the map of $str_{iy}$. \\
-\hspace{3mm}6.2  If $str_{iy}$ is not in the map or $y \ge r$ then goto step 7. \\
-\hspace{3mm}6.3  $a \leftarrow a \cdot r$ \\
-\hspace{3mm}6.4  $a \leftarrow a + y$ \\
-7.  If $a \ne 0$ then $a.sign \leftarrow sign$ \\
-8.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_read\_radix}
-\end{figure}
-\textbf{Algorithm mp\_read\_radix.}
-This algorithm will read an ASCII string and produce the radix-$\beta$ mp\_int representation of the same integer.  A minus symbol ``-'' may precede the
-string  to indicate the value is negative, otherwise it is assumed to be positive.  The algorithm will read up to $sn$ characters from the input
-and will stop when it reads a character it cannot map the algorithm stops reading characters from the string.  This allows numbers to be embedded
-as part of larger input without any significant problem.
-
-EXAM,bn_mp_read_radix.c
-
-\subsection{Generating Radix-$n$ Output}
-Generating radix-$n$ output is fairly trivial with a division and remainder algorithm.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_toradix}. \\
-\textbf{Input}.   A mp\_int $a$ and an integer $r$\\
-\textbf{Output}.  The radix-$r$ representation of $a$ \\
-\hline \\
-1.  If $r < 2$ or $r > 64$ return(\textit{MP\_VAL}). \\
-2.  If $a = 0$ then $str = $ ``$0$'' and return(\textit{MP\_OKAY}).  \\
-3.  $t \leftarrow a$ \\
-4.  $str \leftarrow$ ``'' \\
-5.  if $t.sign = MP\_NEG$ then \\
-\hspace{3mm}5.1  $str \leftarrow str + $ ``-'' \\
-\hspace{3mm}5.2  $t.sign = MP\_ZPOS$ \\
-6.  While ($t \ne 0$) do \\
-\hspace{3mm}6.1  $d \leftarrow t \mbox{ (mod }r\mbox{)}$ \\
-\hspace{3mm}6.2  $t \leftarrow \lfloor t / r \rfloor$ \\
-\hspace{3mm}6.3  Look up $d$ in the map and store the equivalent character in $y$. \\
-\hspace{3mm}6.4  $str \leftarrow str + y$ \\
-7.  If $str_0 = $``$-$'' then \\
-\hspace{3mm}7.1  Reverse the digits $str_1, str_2, \ldots str_n$. \\
-8.  Otherwise \\
-\hspace{3mm}8.1  Reverse the digits $str_0, str_1, \ldots str_n$. \\
-9.  Return(\textit{MP\_OKAY}).\\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_toradix}
-\end{figure}
-\textbf{Algorithm mp\_toradix.}
-This algorithm computes the radix-$r$ representation of an mp\_int $a$.  The ``digits'' of the representation are extracted by reducing
-successive powers of $\lfloor a / r^k \rfloor$ the input modulo $r$ until $r^k > a$.  Note that instead of actually dividing by $r^k$ in
-each iteration the quotient $\lfloor a / r \rfloor$ is saved for the next iteration.  As a result a series of trivial $n \times 1$ divisions
-are required instead of a series of $n \times k$ divisions.  One design flaw of this approach is that the digits are produced in the reverse order
-(see~\ref{fig:mpradix}).  To remedy this flaw the digits must be swapped or simply ``reversed''.
-
-\begin{figure}
-\begin{center}
-\begin{tabular}{|c|c|c|}
-\hline \textbf{Value of $a$} & \textbf{Value of $d$} & \textbf{Value of $str$} \\
-\hline $1234$ & -- & -- \\
-\hline $123$  & $4$ & ``4'' \\
-\hline $12$   & $3$ & ``43'' \\
-\hline $1$    & $2$ & ``432'' \\
-\hline $0$    & $1$ & ``4321'' \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Example of Algorithm mp\_toradix.}
-\label{fig:mpradix}
-\end{figure}
-
-EXAM,bn_mp_toradix.c
-
-\chapter{Number Theoretic Algorithms}
-This chapter discusses several fundamental number theoretic algorithms such as the greatest common divisor, least common multiple and Jacobi
-symbol computation.  These algorithms arise as essential components in several key cryptographic algorithms such as the RSA public key algorithm and
-various Sieve based factoring algorithms.
-
-\section{Greatest Common Divisor}
-The greatest common divisor of two integers $a$ and $b$, often denoted as $(a, b)$ is the largest integer $k$ that is a proper divisor of
-both $a$ and $b$.  That is, $k$ is the largest integer such that $0 \equiv a \mbox{ (mod }k\mbox{)}$ and $0 \equiv b \mbox{ (mod }k\mbox{)}$ occur
-simultaneously.
-
-The most common approach (cite) is to reduce one input modulo another.  That is if $a$ and $b$ are divisible by some integer $k$ and if $qa + r = b$ then
-$r$ is also divisible by $k$.  The reduction pattern follows $\left < a , b \right > \rightarrow \left < b, a \mbox{ mod } b \right >$.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Greatest Common Divisor (I)}. \\
-\textbf{Input}.   Two positive integers $a$ and $b$ greater than zero. \\
-\textbf{Output}.  The greatest common divisor $(a, b)$.  \\
-\hline \\
-1.  While ($b > 0$) do \\
-\hspace{3mm}1.1  $r \leftarrow a \mbox{ (mod }b\mbox{)}$ \\
-\hspace{3mm}1.2  $a \leftarrow b$ \\
-\hspace{3mm}1.3  $b \leftarrow r$ \\
-2.  Return($a$). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm Greatest Common Divisor (I)}
-\label{fig:gcd1}
-\end{figure}
-
-This algorithm will quickly converge on the greatest common divisor since the residue $r$ tends diminish rapidly.  However, divisions are
-relatively expensive operations to perform and should ideally be avoided.  There is another approach based on a similar relationship of
-greatest common divisors.  The faster approach is based on the observation that if $k$ divides both $a$ and $b$ it will also divide $a - b$.
-In particular, we would like $a - b$ to decrease in magnitude which implies that $b \ge a$.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Greatest Common Divisor (II)}. \\
-\textbf{Input}.   Two positive integers $a$ and $b$ greater than zero. \\
-\textbf{Output}.  The greatest common divisor $(a, b)$.  \\
-\hline \\
-1.  While ($b > 0$) do \\
-\hspace{3mm}1.1  Swap $a$ and $b$ such that $a$ is the smallest of the two. \\
-\hspace{3mm}1.2  $b \leftarrow b - a$ \\
-2.  Return($a$). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm Greatest Common Divisor (II)}
-\label{fig:gcd2}
-\end{figure}
-
-\textbf{Proof} \textit{Algorithm~\ref{fig:gcd2} will return the greatest common divisor of $a$ and $b$.}
-The algorithm in figure~\ref{fig:gcd2} will eventually terminate since $b \ge a$ the subtraction in step 1.2 will be a value less than $b$.  In other
-words in every iteration that tuple $\left < a, b \right >$ decrease in magnitude until eventually $a = b$.  Since both $a$ and $b$ are always
-divisible by the greatest common divisor (\textit{until the last iteration}) and in the last iteration of the algorithm $b = 0$, therefore, in the
-second to last iteration of the algorithm $b = a$ and clearly $(a, a) = a$ which concludes the proof.  \textbf{QED}.
-
-As a matter of practicality algorithm \ref{fig:gcd1} decreases far too slowly to be useful.  Specially if $b$ is much larger than $a$ such that
-$b - a$ is still very much larger than $a$.  A simple addition to the algorithm is to divide $b - a$ by a power of some integer $p$ which does
-not divide the greatest common divisor but will divide $b - a$.  In this case ${b - a} \over p$ is also an integer and still divisible by
-the greatest common divisor.
-
-However, instead of factoring $b - a$ to find a suitable value of $p$ the powers of $p$ can be removed from $a$ and $b$ that are in common first.
-Then inside the loop whenever $b - a$ is divisible by some power of $p$ it can be safely removed.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Greatest Common Divisor (III)}. \\
-\textbf{Input}.   Two positive integers $a$ and $b$ greater than zero. \\
-\textbf{Output}.  The greatest common divisor $(a, b)$.  \\
-\hline \\
-1.  $k \leftarrow 0$ \\
-2.  While $a$ and $b$ are both divisible by $p$ do \\
-\hspace{3mm}2.1  $a \leftarrow \lfloor a / p \rfloor$ \\
-\hspace{3mm}2.2  $b \leftarrow \lfloor b / p \rfloor$ \\
-\hspace{3mm}2.3  $k \leftarrow k + 1$ \\
-3.  While $a$ is divisible by $p$ do \\
-\hspace{3mm}3.1  $a \leftarrow \lfloor a / p \rfloor$ \\
-4.  While $b$ is divisible by $p$ do \\
-\hspace{3mm}4.1  $b \leftarrow \lfloor b / p \rfloor$ \\
-5.  While ($b > 0$) do \\
-\hspace{3mm}5.1  Swap $a$ and $b$ such that $a$ is the smallest of the two. \\
-\hspace{3mm}5.2  $b \leftarrow b - a$ \\
-\hspace{3mm}5.3  While $b$ is divisible by $p$ do \\
-\hspace{6mm}5.3.1  $b \leftarrow \lfloor b / p \rfloor$ \\
-6.  Return($a \cdot p^k$). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm Greatest Common Divisor (III)}
-\label{fig:gcd3}
-\end{figure}
-
-This algorithm is based on the first except it removes powers of $p$ first and inside the main loop to ensure the tuple $\left < a, b \right >$
-decreases more rapidly.  The first loop on step two removes powers of $p$ that are in common.  A count, $k$, is kept which will present a common
-divisor of $p^k$.  After step two the remaining common divisor of $a$ and $b$ cannot be divisible by $p$.  This means that $p$ can be safely
-divided out of the difference $b - a$ so long as the division leaves no remainder.
-
-In particular the value of $p$ should be chosen such that the division on step 5.3.1 occur often.  It also helps that division by $p$ be easy
-to compute.  The ideal choice of $p$ is two since division by two amounts to a right logical shift.  Another important observation is that by
-step five both $a$ and $b$ are odd.  Therefore, the diffrence $b - a$ must be even which means that each iteration removes one bit from the
-largest of the pair.
-
-\subsection{Complete Greatest Common Divisor}
-The algorithms presented so far cannot handle inputs which are zero or negative.  The following algorithm can handle all input cases properly
-and will produce the greatest common divisor.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_gcd}. \\
-\textbf{Input}.   mp\_int $a$ and $b$ \\
-\textbf{Output}.  The greatest common divisor $c = (a, b)$.  \\
-\hline \\
-1.  If $a = 0$ then \\
-\hspace{3mm}1.1  $c \leftarrow \vert b \vert $ \\
-\hspace{3mm}1.2  Return(\textit{MP\_OKAY}). \\
-2.  If $b = 0$ then \\
-\hspace{3mm}2.1  $c \leftarrow \vert a \vert $ \\
-\hspace{3mm}2.2  Return(\textit{MP\_OKAY}). \\
-3.  $u \leftarrow \vert a \vert, v \leftarrow \vert b \vert$ \\
-4.  $k \leftarrow 0$ \\
-5.  While $u.used > 0$ and $v.used > 0$ and $u_0 \equiv v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\
-\hspace{3mm}5.1  $k \leftarrow k + 1$ \\
-\hspace{3mm}5.2  $u \leftarrow \lfloor u / 2 \rfloor$ \\
-\hspace{3mm}5.3  $v \leftarrow \lfloor v / 2 \rfloor$ \\
-6.  While $u.used > 0$ and $u_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\
-\hspace{3mm}6.1  $u \leftarrow \lfloor u / 2 \rfloor$ \\
-7.  While $v.used > 0$ and $v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\
-\hspace{3mm}7.1  $v \leftarrow \lfloor v / 2 \rfloor$ \\
-8.  While $v.used > 0$ \\
-\hspace{3mm}8.1  If $\vert u \vert > \vert v \vert$ then \\
-\hspace{6mm}8.1.1  Swap $u$ and $v$. \\
-\hspace{3mm}8.2  $v \leftarrow \vert v \vert - \vert u \vert$ \\
-\hspace{3mm}8.3  While $v.used > 0$ and $v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\
-\hspace{6mm}8.3.1  $v \leftarrow \lfloor v / 2 \rfloor$ \\
-9.  $c \leftarrow u \cdot 2^k$ \\
-10.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_gcd}
-\end{figure}
-\textbf{Algorithm mp\_gcd.}
-This algorithm will produce the greatest common divisor of two mp\_ints $a$ and $b$.  The algorithm was originally based on Algorithm B of
-Knuth \cite[pp. 338]{TAOCPV2} but has been modified to be simpler to explain.  In theory it achieves the same asymptotic working time as
-Algorithm B and in practice this appears to be true.
-
-The first two steps handle the cases where either one of or both inputs are zero.  If either input is zero the greatest common divisor is the
-largest input or zero if they are both zero.  If the inputs are not trivial than $u$ and $v$ are assigned the absolute values of
-$a$ and $b$ respectively and the algorithm will proceed to reduce the pair.
-
-Step five will divide out any common factors of two and keep track of the count in the variable $k$.  After this step, two is no longer a
-factor of the remaining greatest common divisor between $u$ and $v$ and can be safely evenly divided out of either whenever they are even.  Step
-six and seven ensure that the $u$ and $v$ respectively have no more factors of two.  At most only one of the while--loops will iterate since
-they cannot both be even.
-
-By step eight both of $u$ and $v$ are odd which is required for the inner logic.  First the pair are swapped such that $v$ is equal to
-or greater than $u$.  This ensures that the subtraction on step 8.2 will always produce a positive and even result.  Step 8.3 removes any
-factors of two from the difference $u$ to ensure that in the next iteration of the loop both are once again odd.
-
-After $v = 0$ occurs the variable $u$ has the greatest common divisor of the pair $\left < u, v \right >$ just after step six.  The result
-must be adjusted by multiplying by the common factors of two ($2^k$) removed earlier.
-
-EXAM,bn_mp_gcd.c
-
-This function makes use of the macros mp\_iszero and mp\_iseven.  The former evaluates to $1$ if the input mp\_int is equivalent to the
-integer zero otherwise it evaluates to $0$.  The latter evaluates to $1$ if the input mp\_int represents a non-zero even integer otherwise
-it evaluates to $0$.  Note that just because mp\_iseven may evaluate to $0$ does not mean the input is odd, it could also be zero.  The three
-trivial cases of inputs are handled on lines @23,zero@ through @29,}@.  After those lines the inputs are assumed to be non-zero.
-
-Lines @32,if@ and @36,if@ make local copies $u$ and $v$ of the inputs $a$ and $b$ respectively.  At this point the common factors of two
-must be divided out of the two inputs.  The block starting at line @43,common@ removes common factors of two by first counting the number of trailing
-zero bits in both.  The local integer $k$ is used to keep track of how many factors of $2$ are pulled out of both values.  It is assumed that
-the number of factors will not exceed the maximum value of a C ``int'' data type\footnote{Strictly speaking no array in C may have more than
-entries than are accessible by an ``int'' so this is not a limitation.}.
-
-At this point there are no more common factors of two in the two values.  The divisions by a power of two on lines @60,div_2d@ and @67,div_2d@ remove
-any independent factors of two such that both $u$ and $v$ are guaranteed to be an odd integer before hitting the main body of the algorithm.  The while loop
-on line @72, while@ performs the reduction of the pair until $v$ is equal to zero.  The unsigned comparison and subtraction algorithms are used in
-place of the full signed routines since both values are guaranteed to be positive and the result of the subtraction is guaranteed to be non-negative.
-
-\section{Least Common Multiple}
-The least common multiple of a pair of integers is their product divided by their greatest common divisor.  For two integers $a$ and $b$ the
-least common multiple is normally denoted as $[ a, b ]$ and numerically equivalent to ${ab} \over {(a, b)}$.  For example, if $a = 2 \cdot 2 \cdot 3 = 12$
-and $b = 2 \cdot 3 \cdot 3 \cdot 7 = 126$ the least common multiple is ${126 \over {(12, 126)}} = {126 \over 6} = 21$.
-
-The least common multiple arises often in coding theory as well as number theory.  If two functions have periods of $a$ and $b$ respectively they will
-collide, that is be in synchronous states, after only $[ a, b ]$ iterations.  This is why, for example, random number generators based on
-Linear Feedback Shift Registers (LFSR) tend to use registers with periods which are co-prime (\textit{e.g. the greatest common divisor is one.}).
-Similarly in number theory if a composite $n$ has two prime factors $p$ and $q$ then maximal order of any unit of $\Z/n\Z$ will be $[ p - 1, q - 1] $.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_lcm}. \\
-\textbf{Input}.   mp\_int $a$ and $b$ \\
-\textbf{Output}.  The least common multiple $c = [a, b]$.  \\
-\hline \\
-1.  $c \leftarrow (a, b)$ \\
-2.  $t \leftarrow a \cdot b$ \\
-3.  $c \leftarrow \lfloor t / c \rfloor$ \\
-4.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_lcm}
-\end{figure}
-\textbf{Algorithm mp\_lcm.}
-This algorithm computes the least common multiple of two mp\_int inputs $a$ and $b$.  It computes the least common multiple directly by
-dividing the product of the two inputs by their greatest common divisor.
-
-EXAM,bn_mp_lcm.c
-
-\section{Jacobi Symbol Computation}
-To explain the Jacobi Symbol we shall first discuss the Legendre function\footnote{Arrg.  What is the name of this?} off which the Jacobi symbol is
-defined.  The Legendre function computes whether or not an integer $a$ is a quadratic residue modulo an odd prime $p$.  Numerically it is
-equivalent to equation \ref{eqn:legendre}.
-
-\textit{-- Tom, don't be an ass, cite your source here...!}
-
-\begin{equation}
-a^{(p-1)/2} \equiv \begin{array}{rl}
-                              -1 &  \mbox{if }a\mbox{ is a quadratic non-residue.} \\
-                              0  &  \mbox{if }a\mbox{ divides }p\mbox{.} \\
-                              1  &  \mbox{if }a\mbox{ is a quadratic residue}.
-                              \end{array} \mbox{ (mod }p\mbox{)}
-\label{eqn:legendre}
-\end{equation}
-
-\textbf{Proof.} \textit{Equation \ref{eqn:legendre} correctly identifies the residue status of an integer $a$ modulo a prime $p$.}
-An integer $a$ is a quadratic residue if the following equation has a solution.
-
-\begin{equation}
-x^2 \equiv a \mbox{ (mod }p\mbox{)}
-\label{eqn:root}
-\end{equation}
-
-Consider the following equation.
-
-\begin{equation}
-0 \equiv x^{p-1} - 1 \equiv \left \lbrace \left (x^2 \right )^{(p-1)/2} - a^{(p-1)/2} \right \rbrace + \left ( a^{(p-1)/2} - 1 \right ) \mbox{ (mod }p\mbox{)}
-\label{eqn:rooti}
-\end{equation}
-
-Whether equation \ref{eqn:root} has a solution or not equation \ref{eqn:rooti} is always true.  If $a^{(p-1)/2} - 1 \equiv 0 \mbox{ (mod }p\mbox{)}$
-then the quantity in the braces must be zero.  By reduction,
-
-\begin{eqnarray}
-\left (x^2 \right )^{(p-1)/2} - a^{(p-1)/2} \equiv 0  \nonumber \\
-\left (x^2 \right )^{(p-1)/2} \equiv a^{(p-1)/2} \nonumber \\
-x^2 \equiv a \mbox{ (mod }p\mbox{)}
-\end{eqnarray}
-
-As a result there must be a solution to the quadratic equation and in turn $a$ must be a quadratic residue.  If $a$ does not divide $p$ and $a$
-is not a quadratic residue then the only other value $a^{(p-1)/2}$ may be congruent to is $-1$ since
-\begin{equation}
-0 \equiv a^{p - 1} - 1 \equiv (a^{(p-1)/2} + 1)(a^{(p-1)/2} - 1) \mbox{ (mod }p\mbox{)}
-\end{equation}
-One of the terms on the right hand side must be zero.  \textbf{QED}
-
-\subsection{Jacobi Symbol}
-The Jacobi symbol is a generalization of the Legendre function for any odd non prime moduli $p$ greater than 2.  If $p = \prod_{i=0}^n p_i$ then
-the Jacobi symbol $\left ( { a \over p } \right )$ is equal to the following equation.
-
-\begin{equation}
-\left ( { a \over p } \right ) = \left ( { a \over p_0} \right ) \left ( { a \over p_1} \right ) \ldots \left ( { a \over p_n} \right )
-\end{equation}
-
-By inspection if $p$ is prime the Jacobi symbol is equivalent to the Legendre function.  The following facts\footnote{See HAC \cite[pp. 72-74]{HAC} for
-further details.} will be used to derive an efficient Jacobi symbol algorithm.  Where $p$ is an odd integer greater than two and $a, b \in \Z$ the
-following are true.
-
-\begin{enumerate}
-\item $\left ( { a \over p} \right )$ equals $-1$, $0$ or $1$.
-\item $\left ( { ab \over p} \right ) = \left ( { a \over p} \right )\left ( { b \over p} \right )$.
-\item If $a \equiv b$ then $\left ( { a \over p} \right ) = \left ( { b \over p} \right )$.
-\item $\left ( { 2 \over p} \right )$ equals $1$ if $p \equiv 1$ or $7 \mbox{ (mod }8\mbox{)}$.  Otherwise, it equals $-1$.
-\item $\left ( { a \over p} \right ) \equiv \left ( { p \over a} \right ) \cdot (-1)^{(p-1)(a-1)/4}$.  More specifically
-$\left ( { a \over p} \right ) = \left ( { p \over a} \right )$ if $p \equiv a \equiv 1 \mbox{ (mod }4\mbox{)}$.
-\end{enumerate}
-
-Using these facts if $a = 2^k \cdot a'$ then
-
-\begin{eqnarray}
-\left ( { a \over p } \right ) = \left ( {{2^k} \over p } \right ) \left ( {a' \over p} \right ) \nonumber \\
-                               = \left ( {2 \over p } \right )^k \left ( {a' \over p} \right )
-\label{eqn:jacobi}
-\end{eqnarray}
-
-By fact five,
-
-\begin{equation}
-\left ( { a \over p } \right ) = \left ( { p \over a } \right ) \cdot (-1)^{(p-1)(a-1)/4}
-\end{equation}
-
-Subsequently by fact three since $p \equiv (p \mbox{ mod }a) \mbox{ (mod }a\mbox{)}$ then
-
-\begin{equation}
-\left ( { a \over p } \right ) = \left ( { {p \mbox{ mod } a} \over a } \right ) \cdot (-1)^{(p-1)(a-1)/4}
-\end{equation}
-
-By putting both observations into equation \ref{eqn:jacobi} the following simplified equation is formed.
-
-\begin{equation}
-\left ( { a \over p } \right ) = \left ( {2 \over p } \right )^k \left ( {{p\mbox{ mod }a'} \over a'} \right )  \cdot (-1)^{(p-1)(a'-1)/4}
-\end{equation}
-
-The value of $\left ( {{p \mbox{ mod }a'} \over a'} \right )$ can be found by using the same equation recursively.  The value of
-$\left ( {2 \over p } \right )^k$ equals $1$ if $k$ is even otherwise it equals $\left ( {2 \over p } \right )$.  Using this approach the
-factors of $p$ do not have to be known.  Furthermore, if $(a, p) = 1$ then the algorithm will terminate when the recursion requests the
-Jacobi symbol computation of $\left ( {1 \over a'} \right )$ which is simply $1$.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_jacobi}. \\
-\textbf{Input}.   mp\_int $a$ and $p$, $a \ge 0$, $p \ge 3$, $p \equiv 1 \mbox{ (mod }2\mbox{)}$ \\
-\textbf{Output}.  The Jacobi symbol $c = \left ( {a \over p } \right )$. \\
-\hline \\
-1.  If $a = 0$ then \\
-\hspace{3mm}1.1  $c \leftarrow 0$ \\
-\hspace{3mm}1.2  Return(\textit{MP\_OKAY}). \\
-2.  If $a = 1$ then \\
-\hspace{3mm}2.1  $c \leftarrow 1$ \\
-\hspace{3mm}2.2  Return(\textit{MP\_OKAY}). \\
-3.  $a' \leftarrow a$ \\
-4.  $k \leftarrow 0$ \\
-5.  While $a'.used > 0$ and $a'_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\
-\hspace{3mm}5.1  $k \leftarrow k + 1$ \\
-\hspace{3mm}5.2  $a' \leftarrow \lfloor a' / 2 \rfloor$ \\
-6.  If $k \equiv 0 \mbox{ (mod }2\mbox{)}$ then \\
-\hspace{3mm}6.1  $s \leftarrow 1$ \\
-7.  else \\
-\hspace{3mm}7.1  $r \leftarrow p_0 \mbox{ (mod }8\mbox{)}$ \\
-\hspace{3mm}7.2  If $r = 1$ or $r = 7$ then \\
-\hspace{6mm}7.2.1  $s \leftarrow 1$ \\
-\hspace{3mm}7.3  else \\
-\hspace{6mm}7.3.1  $s \leftarrow -1$ \\
-8.  If $p_0 \equiv a'_0 \equiv 3 \mbox{ (mod }4\mbox{)}$ then \\
-\hspace{3mm}8.1  $s \leftarrow -s$ \\
-9.  If $a' \ne 1$ then \\
-\hspace{3mm}9.1  $p' \leftarrow p \mbox{ (mod }a'\mbox{)}$ \\
-\hspace{3mm}9.2  $s \leftarrow s \cdot \mbox{mp\_jacobi}(p', a')$ \\
-10.  $c \leftarrow s$ \\
-11.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_jacobi}
-\end{figure}
-\textbf{Algorithm mp\_jacobi.}
-This algorithm computes the Jacobi symbol for an arbitrary positive integer $a$ with respect to an odd integer $p$ greater than three.  The algorithm
-is based on algorithm 2.149 of HAC \cite[pp. 73]{HAC}.
-
-Step numbers one and two handle the trivial cases of $a = 0$ and $a = 1$ respectively.  Step five determines the number of two factors in the
-input $a$.  If $k$ is even than the term $\left ( { 2 \over p } \right )^k$ must always evaluate to one.  If $k$ is odd than the term evaluates to one
-if $p_0$ is congruent to one or seven modulo eight, otherwise it evaluates to $-1$. After the the $\left ( { 2 \over p } \right )^k$ term is handled
-the $(-1)^{(p-1)(a'-1)/4}$ is computed and multiplied against the current product $s$.  The latter term evaluates to one if both $p$ and $a'$
-are congruent to one modulo four, otherwise it evaluates to negative one.
-
-By step nine if $a'$ does not equal one a recursion is required.  Step 9.1 computes $p' \equiv p \mbox{ (mod }a'\mbox{)}$ and will recurse to compute
-$\left ( {p' \over a'} \right )$ which is multiplied against the current Jacobi product.
-
-EXAM,bn_mp_jacobi.c
-
-As a matter of practicality the variable $a'$ as per the pseudo-code is reprensented by the variable $a1$ since the $'$ symbol is not valid for a C
-variable name character.
-
-The two simple cases of $a = 0$ and $a = 1$ are handled at the very beginning to simplify the algorithm.  If the input is non-trivial the algorithm
-has to proceed compute the Jacobi.  The variable $s$ is used to hold the current Jacobi product.  Note that $s$ is merely a C ``int'' data type since
-the values it may obtain are merely $-1$, $0$ and $1$.
-
-After a local copy of $a$ is made all of the factors of two are divided out and the total stored in $k$.  Technically only the least significant
-bit of $k$ is required, however, it makes the algorithm simpler to follow to perform an addition. In practice an exclusive-or and addition have the same
-processor requirements and neither is faster than the other.
-
-Line @59, if@ through @70, }@ determines the value of $\left ( { 2 \over p } \right )^k$.  If the least significant bit of $k$ is zero than
-$k$ is even and the value is one.  Otherwise, the value of $s$ depends on which residue class $p$ belongs to modulo eight.  The value of
-$(-1)^{(p-1)(a'-1)/4}$ is compute and multiplied against $s$ on lines @73, if@ through @75, }@.
-
-Finally, if $a1$ does not equal one the algorithm must recurse and compute $\left ( {p' \over a'} \right )$.
-
-\textit{-- Comment about default $s$ and such...}
-
-\section{Modular Inverse}
-\label{sec:modinv}
-The modular inverse of a number actually refers to the modular multiplicative inverse.  Essentially for any integer $a$ such that $(a, p) = 1$ there
-exist another integer $b$ such that $ab \equiv 1 \mbox{ (mod }p\mbox{)}$.  The integer $b$ is called the multiplicative inverse of $a$ which is
-denoted as $b = a^{-1}$.  Technically speaking modular inversion is a well defined operation for any finite ring or field not just for rings and
-fields of integers.  However, the former will be the matter of discussion.
-
-The simplest approach is to compute the algebraic inverse of the input.  That is to compute $b \equiv a^{\Phi(p) - 1}$.  If $\Phi(p)$ is the
-order of the multiplicative subgroup modulo $p$ then $b$ must be the multiplicative inverse of $a$.  The proof of which is trivial.
-
-\begin{equation}
-ab \equiv a \left (a^{\Phi(p) - 1} \right ) \equiv a^{\Phi(p)} \equiv a^0 \equiv 1 \mbox{ (mod }p\mbox{)}
-\end{equation}
-
-However, as simple as this approach may be it has two serious flaws.  It requires that the value of $\Phi(p)$ be known which if $p$ is composite
-requires all of the prime factors.  This approach also is very slow as the size of $p$ grows.
-
-A simpler approach is based on the observation that solving for the multiplicative inverse is equivalent to solving the linear
-Diophantine\footnote{See LeVeque \cite[pp. 40-43]{LeVeque} for more information.} equation.
-
-\begin{equation}
-ab + pq = 1
-\end{equation}
-
-Where $a$, $b$, $p$ and $q$ are all integers.  If such a pair of integers $ \left < b, q \right >$ exist than $b$ is the multiplicative inverse of
-$a$ modulo $p$.  The extended Euclidean algorithm (Knuth \cite[pp. 342]{TAOCPV2}) can be used to solve such equations provided $(a, p) = 1$.
-However, instead of using that algorithm directly a variant known as the binary Extended Euclidean algorithm will be used in its place.  The
-binary approach is very similar to the binary greatest common divisor algorithm except it will produce a full solution to the Diophantine
-equation.
-
-\subsection{General Case}
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_invmod}. \\
-\textbf{Input}.   mp\_int $a$ and $b$, $(a, b) = 1$, $p \ge 2$, $0 < a < p$.  \\
-\textbf{Output}.  The modular inverse $c \equiv a^{-1} \mbox{ (mod }b\mbox{)}$. \\
-\hline \\
-1.  If $b \le 0$ then return(\textit{MP\_VAL}). \\
-2.  If $b_0 \equiv 1 \mbox{ (mod }2\mbox{)}$ then use algorithm fast\_mp\_invmod. \\
-3.  $x \leftarrow \vert a \vert, y \leftarrow b$ \\
-4.  If $x_0 \equiv y_0  \equiv 0 \mbox{ (mod }2\mbox{)}$ then return(\textit{MP\_VAL}). \\
-5.  $B \leftarrow 0, C \leftarrow 0, A \leftarrow 1, D \leftarrow 1$ \\
-6.  While $u.used > 0$ and $u_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\
-\hspace{3mm}6.1  $u \leftarrow \lfloor u / 2 \rfloor$ \\
-\hspace{3mm}6.2  If ($A.used > 0$ and $A_0 \equiv 1 \mbox{ (mod }2\mbox{)}$) or ($B.used > 0$ and $B_0 \equiv 1 \mbox{ (mod }2\mbox{)}$) then \\
-\hspace{6mm}6.2.1  $A \leftarrow A + y$ \\
-\hspace{6mm}6.2.2  $B \leftarrow B - x$ \\
-\hspace{3mm}6.3  $A \leftarrow \lfloor A / 2 \rfloor$ \\
-\hspace{3mm}6.4  $B \leftarrow \lfloor B / 2 \rfloor$ \\
-7.  While $v.used > 0$ and $v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\
-\hspace{3mm}7.1  $v \leftarrow \lfloor v / 2 \rfloor$ \\
-\hspace{3mm}7.2  If ($C.used > 0$ and $C_0 \equiv 1 \mbox{ (mod }2\mbox{)}$) or ($D.used > 0$ and $D_0 \equiv 1 \mbox{ (mod }2\mbox{)}$) then \\
-\hspace{6mm}7.2.1  $C \leftarrow C + y$ \\
-\hspace{6mm}7.2.2  $D \leftarrow D - x$ \\
-\hspace{3mm}7.3  $C \leftarrow \lfloor C / 2 \rfloor$ \\
-\hspace{3mm}7.4  $D \leftarrow \lfloor D / 2 \rfloor$ \\
-8.  If $u \ge v$ then \\
-\hspace{3mm}8.1  $u \leftarrow u - v$ \\
-\hspace{3mm}8.2  $A \leftarrow A - C$ \\
-\hspace{3mm}8.3  $B \leftarrow B - D$ \\
-9.  else \\
-\hspace{3mm}9.1  $v \leftarrow v - u$ \\
-\hspace{3mm}9.2  $C \leftarrow C - A$ \\
-\hspace{3mm}9.3  $D \leftarrow D - B$ \\
-10.  If $u \ne 0$ goto step 6. \\
-11.  If $v \ne 1$ return(\textit{MP\_VAL}). \\
-12.  While $C \le 0$ do \\
-\hspace{3mm}12.1  $C \leftarrow C + b$ \\
-13.  While $C \ge b$ do \\
-\hspace{3mm}13.1  $C \leftarrow C - b$ \\
-14.  $c \leftarrow C$ \\
-15.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\end{figure}
-\textbf{Algorithm mp\_invmod.}
-This algorithm computes the modular multiplicative inverse of an integer $a$ modulo an integer $b$.  This algorithm is a variation of the
-extended binary Euclidean algorithm from HAC \cite[pp. 608]{HAC}.  It has been modified to only compute the modular inverse and not a complete
-Diophantine solution.
-
-If $b \le 0$ than the modulus is invalid and MP\_VAL is returned.  Similarly if both $a$ and $b$ are even then there cannot be a multiplicative
-inverse for $a$ and the error is reported.
-
-The astute reader will observe that steps seven through nine are very similar to the binary greatest common divisor algorithm mp\_gcd.  In this case
-the other variables to the Diophantine equation are solved.  The algorithm terminates when $u = 0$ in which case the solution is
-
-\begin{equation}
-Ca + Db = v
-\end{equation}
-
-If $v$, the greatest common divisor of $a$ and $b$ is not equal to one then the algorithm will report an error as no inverse exists.  Otherwise, $C$
-is the modular inverse of $a$.  The actual value of $C$ is congruent to, but not necessarily equal to, the ideal modular inverse which should lie
-within $1 \le a^{-1} < b$.  Step numbers twelve and thirteen adjust the inverse until it is in range.  If the original input $a$ is within $0 < a < p$
-then only a couple of additions or subtractions will be required to adjust the inverse.
-
-EXAM,bn_mp_invmod.c
-
-\subsubsection{Odd Moduli}
-
-When the modulus $b$ is odd the variables $A$ and $C$ are fixed and are not required to compute the inverse.  In particular by attempting to solve
-the Diophantine $Cb + Da = 1$ only $B$ and $D$ are required to find the inverse of $a$.
-
-The algorithm fast\_mp\_invmod is a direct adaptation of algorithm mp\_invmod with all all steps involving either $A$ or $C$ removed.  This
-optimization will halve the time required to compute the modular inverse.
-
-\section{Primality Tests}
-
-A non-zero integer $a$ is said to be prime if it is not divisible by any other integer excluding one and itself.  For example, $a = 7$ is prime
-since the integers $2 \ldots 6$ do not evenly divide $a$.  By contrast, $a = 6$ is not prime since $a = 6 = 2 \cdot 3$.
-
-Prime numbers arise in cryptography considerably as they allow finite fields to be formed.  The ability to determine whether an integer is prime or
-not quickly has been a viable subject in cryptography and number theory for considerable time.  The algorithms that will be presented are all
-probablistic algorithms in that when they report an integer is composite it must be composite.  However, when the algorithms report an integer is
-prime the algorithm may be incorrect.
-
-As will be discussed it is possible to limit the probability of error so well that for practical purposes the probablity of error might as
-well be zero.  For the purposes of these discussions let $n$ represent the candidate integer of which the primality is in question.
-
-\subsection{Trial Division}
-
-Trial division means to attempt to evenly divide a candidate integer by small prime integers.  If the candidate can be evenly divided it obviously
-cannot be prime.  By dividing by all primes $1 < p \le \sqrt{n}$ this test can actually prove whether an integer is prime.  However, such a test
-would require a prohibitive amount of time as $n$ grows.
-
-Instead of dividing by every prime, a smaller, more mangeable set of primes may be used instead.  By performing trial division with only a subset
-of the primes less than $\sqrt{n} + 1$ the algorithm cannot prove if a candidate is prime.  However, often it can prove a candidate is not prime.
-
-The benefit of this test is that trial division by small values is fairly efficient.  Specially compared to the other algorithms that will be
-discussed shortly.  The probability that this approach correctly identifies a composite candidate when tested with all primes upto $q$ is given by
-$1 - {1.12 \over ln(q)}$.  The graph (\ref{pic:primality}, will be added later) demonstrates the probability of success for the range
-$3 \le q \le 100$.
-
-At approximately $q = 30$ the gain of performing further tests diminishes fairly quickly.  At $q = 90$ further testing is generally not going to
-be of any practical use.  In the case of LibTomMath the default limit $q = 256$ was chosen since it is not too high and will eliminate
-approximately $80\%$ of all candidate integers.  The constant \textbf{PRIME\_SIZE} is equal to the number of primes in the test base.  The
-array \_\_prime\_tab is an array of the first \textbf{PRIME\_SIZE} prime numbers.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_prime\_is\_divisible}. \\
-\textbf{Input}.   mp\_int $a$ \\
-\textbf{Output}.  $c = 1$ if $n$ is divisible by a small prime, otherwise $c = 0$.  \\
-\hline \\
-1.  for $ix$ from $0$ to $PRIME\_SIZE$ do \\
-\hspace{3mm}1.1  $d \leftarrow n \mbox{ (mod }\_\_prime\_tab_{ix}\mbox{)}$ \\
-\hspace{3mm}1.2  If $d = 0$ then \\
-\hspace{6mm}1.2.1  $c \leftarrow 1$ \\
-\hspace{6mm}1.2.2  Return(\textit{MP\_OKAY}). \\
-2.  $c \leftarrow 0$ \\
-3.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_prime\_is\_divisible}
-\end{figure}
-\textbf{Algorithm mp\_prime\_is\_divisible.}
-This algorithm attempts to determine if a candidate integer $n$ is composite by performing trial divisions.
-
-EXAM,bn_mp_prime_is_divisible.c
-
-The algorithm defaults to a return of $0$ in case an error occurs.  The values in the prime table are all specified to be in the range of a
-mp\_digit.  The table \_\_prime\_tab is defined in the following file.
-
-EXAM,bn_prime_tab.c
-
-Note that there are two possible tables.  When an mp\_digit is 7-bits long only the primes upto $127$ may be included, otherwise the primes
-upto $1619$ are used.  Note that the value of \textbf{PRIME\_SIZE} is a constant dependent on the size of a mp\_digit.
-
-\subsection{The Fermat Test}
-The Fermat test is probably one the oldest tests to have a non-trivial probability of success.  It is based on the fact that if $n$ is in
-fact prime then $a^{n} \equiv a \mbox{ (mod }n\mbox{)}$ for all $0 < a < n$.  The reason being that if $n$ is prime than the order of
-the multiplicative sub group is $n - 1$.  Any base $a$ must have an order which divides $n - 1$ and as such $a^n$ is equivalent to
-$a^1 = a$.
-
-If $n$ is composite then any given base $a$ does not have to have a period which divides $n - 1$.  In which case
-it is possible that $a^n \nequiv a \mbox{ (mod }n\mbox{)}$.  However, this test is not absolute as it is possible that the order
-of a base will divide $n - 1$ which would then be reported as prime.  Such a base yields what is known as a Fermat pseudo-prime.  Several
-integers known as Carmichael numbers will be a pseudo-prime to all valid bases.  Fortunately such numbers are extremely rare as $n$ grows
-in size.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_prime\_fermat}. \\
-\textbf{Input}.   mp\_int $a$ and $b$, $a \ge 2$, $0 < b < a$.  \\
-\textbf{Output}.  $c = 1$ if $b^a \equiv b \mbox{ (mod }a\mbox{)}$, otherwise $c = 0$.  \\
-\hline \\
-1.  $t \leftarrow b^a \mbox{ (mod }a\mbox{)}$ \\
-2.  If $t = b$ then \\
-\hspace{3mm}2.1  $c = 1$ \\
-3.  else \\
-\hspace{3mm}3.1  $c = 0$ \\
-4.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_prime\_fermat}
-\end{figure}
-\textbf{Algorithm mp\_prime\_fermat.}
-This algorithm determines whether an mp\_int $a$ is a Fermat prime to the base $b$ or not.  It uses a single modular exponentiation to
-determine the result.
-
-EXAM,bn_mp_prime_fermat.c
-
-\subsection{The Miller-Rabin Test}
-The Miller-Rabin (citation) test is another primality test which has tighter error bounds than the Fermat test specifically with sequentially chosen
-candidate  integers.  The algorithm is based on the observation that if $n - 1 = 2^kr$ and if $b^r \nequiv \pm 1$ then after upto $k - 1$ squarings the
-value must be equal to $-1$.  The squarings are stopped as soon as $-1$ is observed.  If the value of $1$ is observed first it means that
-some value not congruent to $\pm 1$ when squared equals one which cannot occur if $n$ is prime.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_prime\_miller\_rabin}. \\
-\textbf{Input}.   mp\_int $a$ and $b$, $a \ge 2$, $0 < b < a$.  \\
-\textbf{Output}.  $c = 1$ if $a$ is a Miller-Rabin prime to the base $a$, otherwise $c = 0$.  \\
-\hline
-1.  $a' \leftarrow a - 1$ \\
-2.  $r  \leftarrow n1$    \\
-3.  $c \leftarrow 0, s  \leftarrow 0$ \\
-4.  While $r.used > 0$ and $r_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\
-\hspace{3mm}4.1  $s \leftarrow s + 1$ \\
-\hspace{3mm}4.2  $r \leftarrow \lfloor r / 2 \rfloor$ \\
-5.  $y \leftarrow b^r \mbox{ (mod }a\mbox{)}$ \\
-6.  If $y \nequiv \pm 1$ then \\
-\hspace{3mm}6.1  $j \leftarrow 1$ \\
-\hspace{3mm}6.2  While $j \le (s - 1)$ and $y \nequiv a'$ \\
-\hspace{6mm}6.2.1  $y \leftarrow y^2 \mbox{ (mod }a\mbox{)}$ \\
-\hspace{6mm}6.2.2  If $y = 1$ then goto step 8. \\
-\hspace{6mm}6.2.3  $j \leftarrow j + 1$ \\
-\hspace{3mm}6.3  If $y \nequiv a'$ goto step 8. \\
-7.  $c \leftarrow 1$\\
-8.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_prime\_miller\_rabin}
-\end{figure}
-\textbf{Algorithm mp\_prime\_miller\_rabin.}
-This algorithm performs one trial round of the Miller-Rabin algorithm to the base $b$.  It will set $c = 1$ if the algorithm cannot determine
-if $b$ is composite or $c = 0$ if $b$ is provably composite.  The values of $s$ and $r$ are computed such that $a' = a - 1 = 2^sr$.
-
-If the value $y \equiv b^r$ is congruent to $\pm 1$ then the algorithm cannot prove if $a$ is composite or not.  Otherwise, the algorithm will
-square $y$ upto $s - 1$ times stopping only when $y \equiv -1$.  If $y^2 \equiv 1$ and $y \nequiv \pm 1$ then the algorithm can report that $a$
-is provably composite.  If the algorithm performs $s - 1$ squarings and $y \nequiv -1$ then $a$ is provably composite.  If $a$ is not provably
-composite then it is \textit{probably} prime.
-
-EXAM,bn_mp_prime_miller_rabin.c
-
-
-
-
-\backmatter
-\appendix
-\begin{thebibliography}{ABCDEF}
-\bibitem[1]{TAOCPV2}
-Donald Knuth, \textit{The Art of Computer Programming}, Third Edition, Volume Two, Seminumerical Algorithms, Addison-Wesley, 1998
-
-\bibitem[2]{HAC}
-A. Menezes, P. van Oorschot, S. Vanstone, \textit{Handbook of Applied Cryptography}, CRC Press, 1996
-
-\bibitem[3]{ROSE}
-Michael Rosing, \textit{Implementing Elliptic Curve Cryptography}, Manning Publications, 1999
-
-\bibitem[4]{COMBA}
-Paul G. Comba, \textit{Exponentiation Cryptosystems on the IBM PC}. IBM Systems Journal 29(4): 526-538 (1990)
-
-\bibitem[5]{KARA}
-A. Karatsuba, Doklay Akad. Nauk SSSR 145 (1962), pp.293-294
-
-\bibitem[6]{KARAP}
-Andre Weimerskirch and Christof Paar, \textit{Generalizations of the Karatsuba Algorithm for Polynomial Multiplication}, Submitted to Design, Codes and Cryptography, March 2002
-
-\bibitem[7]{BARRETT}
-Paul Barrett, \textit{Implementing the Rivest Shamir and Adleman Public Key Encryption Algorithm on a Standard Digital Signal Processor}, Advances in Cryptology, Crypto '86, Springer-Verlag.
-
-\bibitem[8]{MONT}
-P.L.Montgomery. \textit{Modular multiplication without trial division}. Mathematics of Computation, 44(170):519-521, April 1985.
-
-\bibitem[9]{DRMET}
-Chae Hoon Lim and Pil Joong Lee, \textit{Generating Efficient Primes for Discrete Log Cryptosystems}, POSTECH Information Research Laboratories
-
-\bibitem[10]{MMB}
-J. Daemen and R. Govaerts and J. Vandewalle, \textit{Block ciphers based on Modular Arithmetic}, State and {P}rogress in the {R}esearch of {C}ryptography, 1993, pp. 80-89
-
-\bibitem[11]{RSAREF}
-R.L. Rivest, A. Shamir, L. Adleman, \textit{A Method for Obtaining Digital Signatures and Public-Key Cryptosystems}
-
-\bibitem[12]{DHREF}
-Whitfield Diffie, Martin E. Hellman, \textit{New Directions in Cryptography}, IEEE Transactions on Information Theory, 1976
-
-\bibitem[13]{IEEE}
-IEEE Standard for Binary Floating-Point Arithmetic (ANSI/IEEE Std 754-1985)
-
-\bibitem[14]{GMP}
-GNU Multiple Precision (GMP), \url{http://www.swox.com/gmp/}
-
-\bibitem[15]{MPI}
-Multiple Precision Integer Library (MPI), Michael Fromberger, \url{http://thayer.dartmouth.edu/~sting/mpi/}
-
-\bibitem[16]{OPENSSL}
-OpenSSL Cryptographic Toolkit, \url{http://openssl.org}
-
-\bibitem[17]{LIP}
-Large Integer Package, \url{http://home.hetnet.nl/~ecstr/LIP.zip}
-
-\bibitem[18]{ISOC}
-JTC1/SC22/WG14, ISO/IEC 9899:1999, ``A draft rationale for the C99 standard.''
-
-\bibitem[19]{JAVA}
-The Sun Java Website, \url{http://java.sun.com/}
-
-\end{thebibliography}
-
-\input{tommath.ind}
-
-\end{document}
diff --git a/libtommath/tommath.tex b/libtommath/tommath.tex
deleted file mode 100644
index d70b64b..0000000
--- a/libtommath/tommath.tex
+++ /dev/null
@@ -1,10816 +0,0 @@
-\documentclass[b5paper]{book}
-\usepackage{hyperref}
-\usepackage{makeidx}
-\usepackage{amssymb}
-\usepackage{color}
-\usepackage{alltt}
-\usepackage{graphicx}
-\usepackage{layout}
-\def\union{\cup}
-\def\intersect{\cap}
-\def\getsrandom{\stackrel{\rm R}{\gets}}
-\def\cross{\times}
-\def\cat{\hspace{0.5em} \| \hspace{0.5em}}
-\def\catn{$\|$}
-\def\divides{\hspace{0.3em} | \hspace{0.3em}}
-\def\nequiv{\not\equiv}
-\def\approx{\raisebox{0.2ex}{\mbox{\small $\sim$}}}
-\def\lcm{{\rm lcm}}
-\def\gcd{{\rm gcd}}
-\def\log{{\rm log}}
-\def\ord{{\rm ord}}
-\def\abs{{\mathit abs}}
-\def\rep{{\mathit rep}}
-\def\mod{{\mathit\ mod\ }}
-\renewcommand{\pmod}[1]{\ ({\rm mod\ }{#1})}
-\newcommand{\floor}[1]{\left\lfloor{#1}\right\rfloor}
-\newcommand{\ceil}[1]{\left\lceil{#1}\right\rceil}
-\def\Or{{\rm\ or\ }}
-\def\And{{\rm\ and\ }}
-\def\iff{\hspace{1em}\Longleftrightarrow\hspace{1em}}
-\def\implies{\Rightarrow}
-\def\undefined{{\rm ``undefined"}}
-\def\Proof{\vspace{1ex}\noindent {\bf Proof:}\hspace{1em}}
-\let\oldphi\phi
-\def\phi{\varphi}
-\def\Pr{{\rm Pr}}
-\newcommand{\str}[1]{{\mathbf{#1}}}
-\def\F{{\mathbb F}}
-\def\N{{\mathbb N}}
-\def\Z{{\mathbb Z}}
-\def\R{{\mathbb R}}
-\def\C{{\mathbb C}}
-\def\Q{{\mathbb Q}}
-\definecolor{DGray}{gray}{0.5}
-\newcommand{\emailaddr}[1]{\mbox{$<${#1}$>$}}
-\def\twiddle{\raisebox{0.3ex}{\mbox{\tiny $\sim$}}}
-\def\gap{\vspace{0.5ex}}
-\makeindex
-\begin{document}
-\frontmatter
-\pagestyle{empty}
-\title{Multi--Precision Math}
-\author{\mbox{
-%\begin{small}
-\begin{tabular}{c}
-Tom St Denis \\
-Algonquin College \\
-\\
-Mads Rasmussen \\
-Open Communications Security \\
-\\
-Greg Rose \\
-QUALCOMM Australia \\
-\end{tabular}
-%\end{small}
-}
-}
-\maketitle
-This text has been placed in the public domain.  This text corresponds to the v0.39 release of the
-LibTomMath project.
-
-This text is formatted to the international B5 paper size of 176mm wide by 250mm tall using the \LaTeX{}
-{\em book} macro package and the Perl {\em booker} package.
-
-\tableofcontents
-\listoffigures
-\chapter*{Prefaces}
-When I tell people about my LibTom projects and that I release them as public domain they are often puzzled.
-They ask why I did it and especially why I continue to work on them for free.  The best I can explain it is ``Because I can.''
-Which seems odd and perhaps too terse for adult conversation. I often qualify it with ``I am able, I am willing.'' which
-perhaps explains it better.  I am the first to admit there is not anything that special with what I have done.  Perhaps
-others can see that too and then we would have a society to be proud of.  My LibTom projects are what I am doing to give
-back to society in the form of tools and knowledge that can help others in their endeavours.
-
-I started writing this book because it was the most logical task to further my goal of open academia.  The LibTomMath source
-code itself was written to be easy to follow and learn from.  There are times, however, where pure C source code does not
-explain the algorithms properly.  Hence this book.  The book literally starts with the foundation of the library and works
-itself outwards to the more complicated algorithms.  The use of both pseudo--code and verbatim source code provides a duality
-of ``theory'' and ``practice'' that the computer science students of the world shall appreciate.  I never deviate too far
-from relatively straightforward algebra and I hope that this book can be a valuable learning asset.
-
-This book and indeed much of the LibTom projects would not exist in their current form if it was not for a plethora
-of kind people donating their time, resources and kind words to help support my work.  Writing a text of significant
-length (along with the source code) is a tiresome and lengthy process.  Currently the LibTom project is four years old,
-comprises of literally thousands of users and over 100,000 lines of source code, TeX and other material.  People like Mads and Greg
-were there at the beginning to encourage me to work well.  It is amazing how timely validation from others can boost morale to
-continue the project. Definitely my parents were there for me by providing room and board during the many months of work in 2003.
-
-To my many friends whom I have met through the years I thank you for the good times and the words of encouragement.  I hope I
-honour your kind gestures with this project.
-
-Open Source.  Open Academia.  Open Minds.
-
-\begin{flushright} Tom St Denis \end{flushright}
-
-\newpage
-I found the opportunity to work with Tom appealing for several reasons, not only could I broaden my own horizons, but also
-contribute to educate others facing the problem of having to handle big number mathematical calculations.
-
-This book is Tom's child and he has been caring and fostering the project ever since the beginning with a clear mind of
-how he wanted the project to turn out. I have helped by proofreading the text and we have had several discussions about
-the layout and language used.
-
-I hold a masters degree in cryptography from the University of Southern Denmark and have always been interested in the
-practical aspects of cryptography.
-
-Having worked in the security consultancy business for several years in S\~{a}o Paulo, Brazil, I have been in touch with a
-great deal of work in which multiple precision mathematics was needed. Understanding the possibilities for speeding up
-multiple precision calculations is often very important since we deal with outdated machine architecture where modular
-reductions, for example, become painfully slow.
-
-This text is for people who stop and wonder when first examining algorithms such as RSA for the first time and asks
-themselves, ``You tell me this is only secure for large numbers, fine; but how do you implement these numbers?''
-
-\begin{flushright}
-Mads Rasmussen
-
-S\~{a}o Paulo - SP
-
-Brazil
-\end{flushright}
-
-\newpage
-It's all because I broke my leg. That just happened to be at about the same time that Tom asked for someone to review the section of the book about
-Karatsuba multiplication. I was laid up, alone and immobile, and thought ``Why not?'' I vaguely knew what Karatsuba multiplication was, but not
-really, so I thought I could help, learn, and stop myself from watching daytime cable TV, all at once.
-
-At the time of writing this, I've still not met Tom or Mads in meatspace. I've been following Tom's progress since his first splash on the
-sci.crypt Usenet news group. I watched him go from a clueless newbie, to the cryptographic equivalent of a reformed smoker, to a real
-contributor to the field, over a period of about two years. I've been impressed with his obvious intelligence, and astounded by his productivity.
-Of course, he's young enough to be my own child, so he doesn't have my problems with staying awake.
-
-When I reviewed that single section of the book, in its very earliest form, I was very pleasantly surprised. So I decided to collaborate more fully,
-and at least review all of it, and perhaps write some bits too. There's still a long way to go with it, and I have watched a number of close
-friends go through the mill of publication, so I think that the way to go is longer than Tom thinks it is. Nevertheless, it's a good effort,
-and I'm pleased to be involved with it.
-
-\begin{flushright}
-Greg Rose, Sydney, Australia, June 2003.
-\end{flushright}
-
-\mainmatter
-\pagestyle{headings}
-\chapter{Introduction}
-\section{Multiple Precision Arithmetic}
-
-\subsection{What is Multiple Precision Arithmetic?}
-When we think of long-hand arithmetic such as addition or multiplication we rarely consider the fact that we instinctively
-raise or lower the precision of the numbers we are dealing with.  For example, in decimal we almost immediate can
-reason that $7$ times $6$ is $42$.  However, $42$ has two digits of precision as opposed to one digit we started with.
-Further multiplications of say $3$ result in a larger precision result $126$.  In these few examples we have multiple
-precisions for the numbers we are working with.  Despite the various levels of precision a single subset\footnote{With the occasional optimization.}
- of algorithms can be designed to accomodate them.
-
-By way of comparison a fixed or single precision operation would lose precision on various operations.  For example, in
-the decimal system with fixed precision $6 \cdot 7 = 2$.
-
-Essentially at the heart of computer based multiple precision arithmetic are the same long-hand algorithms taught in
-schools to manually add, subtract, multiply and divide.
-
-\subsection{The Need for Multiple Precision Arithmetic}
-The most prevalent need for multiple precision arithmetic, often referred to as ``bignum'' math, is within the implementation
-of public-key cryptography algorithms.   Algorithms such as RSA \cite{RSAREF} and Diffie-Hellman \cite{DHREF} require
-integers of significant magnitude to resist known cryptanalytic attacks.  For example, at the time of this writing a
-typical RSA modulus would be at least greater than $10^{309}$.  However, modern programming languages such as ISO C \cite{ISOC} and
-Java \cite{JAVA} only provide instrinsic support for integers which are relatively small and single precision.
-
-\begin{figure}[!here]
-\begin{center}
-\begin{tabular}{|r|c|}
-\hline \textbf{Data Type} & \textbf{Range} \\
-\hline char  & $-128 \ldots 127$ \\
-\hline short & $-32768 \ldots 32767$ \\
-\hline long  & $-2147483648 \ldots 2147483647$ \\
-\hline long long & $-9223372036854775808 \ldots 9223372036854775807$ \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Typical Data Types for the C Programming Language}
-\label{fig:ISOC}
-\end{figure}
-
-The largest data type guaranteed to be provided by the ISO C programming
-language\footnote{As per the ISO C standard.  However, each compiler vendor is allowed to augment the precision as they
-see fit.}  can only represent values up to $10^{19}$ as shown in figure \ref{fig:ISOC}. On its own the C language is
-insufficient to accomodate the magnitude required for the problem at hand.  An RSA modulus of magnitude $10^{19}$ could be
-trivially factored\footnote{A Pollard-Rho factoring would take only $2^{16}$ time.} on the average desktop computer,
-rendering any protocol based on the algorithm insecure.  Multiple precision algorithms solve this very problem by
-extending the range of representable integers while using single precision data types.
-
-Most advancements in fast multiple precision arithmetic stem from the need for faster and more efficient cryptographic
-primitives.  Faster modular reduction and exponentiation algorithms such as Barrett's algorithm, which have appeared in
-various cryptographic journals, can render algorithms such as RSA and Diffie-Hellman more efficient.  In fact, several
-major companies such as RSA Security, Certicom and Entrust have built entire product lines on the implementation and
-deployment of efficient algorithms.
-
-However, cryptography is not the only field of study that can benefit from fast multiple precision integer routines.
-Another auxiliary use of multiple precision integers is high precision floating point data types.
-The basic IEEE \cite{IEEE} standard floating point type is made up of an integer mantissa $q$, an exponent $e$ and a sign bit $s$.
-Numbers are given in the form $n = q \cdot b^e \cdot -1^s$ where $b = 2$ is the most common base for IEEE.  Since IEEE
-floating point is meant to be implemented in hardware the precision of the mantissa is often fairly small
-(\textit{23, 48 and 64 bits}).  The mantissa is merely an integer and a multiple precision integer could be used to create
-a mantissa of much larger precision than hardware alone can efficiently support.  This approach could be useful where
-scientific applications must minimize the total output error over long calculations.
-
-Yet another use for large integers is within arithmetic on polynomials of large characteristic (i.e. $GF(p)[x]$ for large $p$).
-In fact the library discussed within this text has already been used to form a polynomial basis library\footnote{See \url{http://poly.libtomcrypt.org} for more details.}.
-
-\subsection{Benefits of Multiple Precision Arithmetic}
-\index{precision}
-The benefit of multiple precision representations over single or fixed precision representations is that
-no precision is lost while representing the result of an operation which requires excess precision.  For example,
-the product of two $n$-bit integers requires at least $2n$ bits of precision to be represented faithfully.  A multiple
-precision algorithm would augment the precision of the destination to accomodate the result while a single precision system
-would truncate excess bits to maintain a fixed level of precision.
-
-It is possible to implement algorithms which require large integers with fixed precision algorithms.  For example, elliptic
-curve cryptography (\textit{ECC}) is often implemented on smartcards by fixing the precision of the integers to the maximum
-size the system will ever need.  Such an approach can lead to vastly simpler algorithms which can accomodate the
-integers required even if the host platform cannot natively accomodate them\footnote{For example, the average smartcard
-processor has an 8 bit accumulator.}.  However, as efficient as such an approach may be, the resulting source code is not
-normally very flexible.  It cannot, at runtime, accomodate inputs of higher magnitude than the designer anticipated.
-
-Multiple precision algorithms have the most overhead of any style of arithmetic.  For the the most part the
-overhead can be kept to a minimum with careful planning, but overall, it is not well suited for most memory starved
-platforms.  However, multiple precision algorithms do offer the most flexibility in terms of the magnitude of the
-inputs.  That is, the same algorithms based on multiple precision integers can accomodate any reasonable size input
-without the designer's explicit forethought.  This leads to lower cost of ownership for the code as it only has to
-be written and tested once.
-
-\section{Purpose of This Text}
-The purpose of this text is to instruct the reader regarding how to implement efficient multiple precision algorithms.
-That is to not only explain a limited subset of the core theory behind the algorithms but also the various ``house keeping''
-elements that are neglected by authors of other texts on the subject.  Several well reknowned texts \cite{TAOCPV2,HAC}
-give considerably detailed explanations of the theoretical aspects of algorithms and often very little information
-regarding the practical implementation aspects.
-
-In most cases how an algorithm is explained and how it is actually implemented are two very different concepts.  For
-example, the Handbook of Applied Cryptography (\textit{HAC}), algorithm 14.7 on page 594, gives a relatively simple
-algorithm for performing multiple precision integer addition.  However, the description lacks any discussion concerning
-the fact that the two integer inputs may be of differing magnitudes.  As a result the implementation is not as simple
-as the text would lead people to believe.  Similarly the division routine (\textit{algorithm 14.20, pp. 598}) does not
-discuss how to handle sign or handle the dividend's decreasing magnitude in the main loop (\textit{step \#3}).
-
-Both texts also do not discuss several key optimal algorithms required such as ``Comba'' and Karatsuba multipliers
-and fast modular inversion, which we consider practical oversights.  These optimal algorithms are vital to achieve
-any form of useful performance in non-trivial applications.
-
-To solve this problem the focus of this text is on the practical aspects of implementing a multiple precision integer
-package.  As a case study the ``LibTomMath''\footnote{Available at \url{http://math.libtomcrypt.com}} package is used
-to demonstrate algorithms with real implementations\footnote{In the ISO C programming language.} that have been field
-tested and work very well.  The LibTomMath library is freely available on the Internet for all uses and this text
-discusses a very large portion of the inner workings of the library.
-
-The algorithms that are presented will always include at least one ``pseudo-code'' description followed
-by the actual C source code that implements the algorithm.  The pseudo-code can be used to implement the same
-algorithm in other programming languages as the reader sees fit.
-
-This text shall also serve as a walkthrough of the creation of multiple precision algorithms from scratch.  Showing
-the reader how the algorithms fit together as well as where to start on various taskings.
-
-\section{Discussion and Notation}
-\subsection{Notation}
-A multiple precision integer of $n$-digits shall be denoted as $x = (x_{n-1}, \ldots, x_1, x_0)_{ \beta }$ and represent
-the integer $x \equiv \sum_{i=0}^{n-1} x_i\beta^i$.  The elements of the array $x$ are said to be the radix $\beta$ digits
-of the integer.  For example, $x = (1,2,3)_{10}$ would represent the integer
-$1\cdot 10^2 + 2\cdot10^1 + 3\cdot10^0 = 123$.
-
-\index{mp\_int}
-The term ``mp\_int'' shall refer to a composite structure which contains the digits of the integer it represents, as well
-as auxilary data required to manipulate the data.  These additional members are discussed further in section
-\ref{sec:MPINT}.  For the purposes of this text a ``multiple precision integer'' and an ``mp\_int'' are assumed to be
-synonymous.  When an algorithm is specified to accept an mp\_int variable it is assumed the various auxliary data members
-are present as well.  An expression of the type \textit{variablename.item} implies that it should evaluate to the
-member named ``item'' of the variable.  For example, a string of characters may have a member ``length'' which would
-evaluate to the number of characters in the string.  If the string $a$ equals ``hello'' then it follows that
-$a.length = 5$.
-
-For certain discussions more generic algorithms are presented to help the reader understand the final algorithm used
-to solve a given problem.  When an algorithm is described as accepting an integer input it is assumed the input is
-a plain integer with no additional multiple-precision members.  That is, algorithms that use integers as opposed to
-mp\_ints as inputs do not concern themselves with the housekeeping operations required such as memory management.  These
-algorithms will be used to establish the relevant theory which will subsequently be used to describe a multiple
-precision algorithm to solve the same problem.
-
-\subsection{Precision Notation}
-The variable $\beta$ represents the radix of a single digit of a multiple precision integer and
-must be of the form $q^p$ for $q, p \in \Z^+$.  A single precision variable must be able to represent integers in
-the range $0 \le x < q \beta$ while a double precision variable must be able to represent integers in the range
-$0 \le x < q \beta^2$.  The extra radix-$q$ factor allows additions and subtractions to proceed without truncation of the
-carry.  Since all modern computers are binary, it is assumed that $q$ is two.
-
-\index{mp\_digit} \index{mp\_word}
-Within the source code that will be presented for each algorithm, the data type \textbf{mp\_digit} will represent
-a single precision integer type, while, the data type \textbf{mp\_word} will represent a double precision integer type.  In
-several algorithms (notably the Comba routines) temporary results will be stored in arrays of double precision mp\_words.
-For the purposes of this text $x_j$ will refer to the $j$'th digit of a single precision array and $\hat x_j$ will refer to
-the $j$'th digit of a double precision array.  Whenever an expression is to be assigned to a double precision
-variable it is assumed that all single precision variables are promoted to double precision during the evaluation.
-Expressions that are assigned to a single precision variable are truncated to fit within the precision of a single
-precision data type.
-
-For example, if $\beta = 10^2$ a single precision data type may represent a value in the
-range $0 \le x < 10^3$, while a double precision data type may represent a value in the range $0 \le x < 10^5$.  Let
-$a = 23$ and $b = 49$ represent two single precision variables.  The single precision product shall be written
-as $c \leftarrow a \cdot b$ while the double precision product shall be written as $\hat c \leftarrow a \cdot b$.
-In this particular case, $\hat c = 1127$ and $c = 127$.  The most significant digit of the product would not fit
-in a single precision data type and as a result $c \ne \hat c$.
-
-\subsection{Algorithm Inputs and Outputs}
-Within the algorithm descriptions all variables are assumed to be scalars of either single or double precision
-as indicated.  The only exception to this rule is when variables have been indicated to be of type mp\_int.  This
-distinction is important as scalars are often used as array indicies and various other counters.
-
-\subsection{Mathematical Expressions}
-The $\lfloor \mbox{ } \rfloor$ brackets imply an expression truncated to an integer not greater than the expression
-itself.  For example, $\lfloor 5.7 \rfloor = 5$.  Similarly the $\lceil \mbox{ } \rceil$ brackets imply an expression
-rounded to an integer not less than the expression itself.  For example, $\lceil 5.1 \rceil = 6$.  Typically when
-the $/$ division symbol is used the intention is to perform an integer division with truncation.  For example,
-$5/2 = 2$ which will often be written as $\lfloor 5/2 \rfloor = 2$ for clarity.  When an expression is written as a
-fraction a real value division is implied, for example ${5 \over 2} = 2.5$.
-
-The norm of a multiple precision integer, for example $\vert \vert x \vert \vert$, will be used to represent the number of digits in the representation
-of the integer.  For example, $\vert \vert 123 \vert \vert = 3$ and $\vert \vert 79452 \vert \vert = 5$.
-
-\subsection{Work Effort}
-\index{big-Oh}
-To measure the efficiency of the specified algorithms, a modified big-Oh notation is used.  In this system all
-single precision operations are considered to have the same cost\footnote{Except where explicitly noted.}.
-That is a single precision addition, multiplication and division are assumed to take the same time to
-complete.  While this is generally not true in practice, it will simplify the discussions considerably.
-
-Some algorithms have slight advantages over others which is why some constants will not be removed in
-the notation.  For example, a normal baseline multiplication (section \ref{sec:basemult}) requires $O(n^2)$ work while a
-baseline squaring (section \ref{sec:basesquare}) requires $O({{n^2 + n}\over 2})$ work.  In standard big-Oh notation these
-would both be said to be equivalent to $O(n^2)$.  However,
-in the context of the this text this is not the case as the magnitude of the inputs will typically be rather small.  As a
-result small constant factors in the work effort will make an observable difference in algorithm efficiency.
-
-All of the algorithms presented in this text have a polynomial time work level.  That is, of the form
-$O(n^k)$ for $n, k \in \Z^{+}$.  This will help make useful comparisons in terms of the speed of the algorithms and how
-various optimizations will help pay off in the long run.
-
-\section{Exercises}
-Within the more advanced chapters a section will be set aside to give the reader some challenging exercises related to
-the discussion at hand.  These exercises are not designed to be prize winning problems, but instead to be thought
-provoking.  Wherever possible the problems are forward minded, stating problems that will be answered in subsequent
-chapters.  The reader is encouraged to finish the exercises as they appear to get a better understanding of the
-subject material.
-
-That being said, the problems are designed to affirm knowledge of a particular subject matter.  Students in particular
-are encouraged to verify they can answer the problems correctly before moving on.
-
-Similar to the exercises of \cite[pp. ix]{TAOCPV2} these exercises are given a scoring system based on the difficulty of
-the problem.  However, unlike \cite{TAOCPV2} the problems do not get nearly as hard.  The scoring of these
-exercises ranges from one (the easiest) to five (the hardest).  The following table sumarizes the
-scoring system used.
-
-\begin{figure}[here]
-\begin{center}
-\begin{small}
-\begin{tabular}{|c|l|}
-\hline $\left [ 1 \right ]$ & An easy problem that should only take the reader a manner of \\
-                            & minutes to solve.  Usually does not involve much computer time \\
-                            & to solve. \\
-\hline $\left [ 2 \right ]$ & An easy problem that involves a marginal amount of computer \\
-                     & time usage.  Usually requires a program to be written to \\
-                     & solve the problem. \\
-\hline $\left [ 3 \right ]$ & A moderately hard problem that requires a non-trivial amount \\
-                     & of work.  Usually involves trivial research and development of \\
-                     & new theory from the perspective of a student. \\
-\hline $\left [ 4 \right ]$ & A moderately hard problem that involves a non-trivial amount \\
-                     & of work and research, the solution to which will demonstrate \\
-                     & a higher mastery of the subject matter. \\
-\hline $\left [ 5 \right ]$ & A hard problem that involves concepts that are difficult for a \\
-                     & novice to solve.  Solutions to these problems will demonstrate a \\
-                     & complete mastery of the given subject. \\
-\hline
-\end{tabular}
-\end{small}
-\end{center}
-\caption{Exercise Scoring System}
-\end{figure}
-
-Problems at the first level are meant to be simple questions that the reader can answer quickly without programming a solution or
-devising new theory.  These problems are quick tests to see if the material is understood.  Problems at the second level
-are also designed to be easy but will require a program or algorithm to be implemented to arrive at the answer.  These
-two levels are essentially entry level questions.
-
-Problems at the third level are meant to be a bit more difficult than the first two levels.  The answer is often
-fairly obvious but arriving at an exacting solution requires some thought and skill.  These problems will almost always
-involve devising a new algorithm or implementing a variation of another algorithm previously presented.  Readers who can
-answer these questions will feel comfortable with the concepts behind the topic at hand.
-
-Problems at the fourth level are meant to be similar to those of the level three questions except they will require
-additional research to be completed.  The reader will most likely not know the answer right away, nor will the text provide
-the exact details of the answer until a subsequent chapter.
-
-Problems at the fifth level are meant to be the hardest
-problems relative to all the other problems in the chapter.  People who can correctly answer fifth level problems have a
-mastery of the subject matter at hand.
-
-Often problems will be tied together.  The purpose of this is to start a chain of thought that will be discussed in future chapters.  The reader
-is encouraged to answer the follow-up problems and try to draw the relevance of problems.
-
-\section{Introduction to LibTomMath}
-
-\subsection{What is LibTomMath?}
-LibTomMath is a free and open source multiple precision integer library written entirely in portable ISO C.  By portable it
-is meant that the library does not contain any code that is computer platform dependent or otherwise problematic to use on
-any given platform.
-
-The library has been successfully tested under numerous operating systems including Unix\footnote{All of these
-trademarks belong to their respective rightful owners.}, MacOS, Windows, Linux, PalmOS and on standalone hardware such
-as the Gameboy Advance.  The library is designed to contain enough functionality to be able to develop applications such
-as public key cryptosystems and still maintain a relatively small footprint.
-
-\subsection{Goals of LibTomMath}
-
-Libraries which obtain the most efficiency are rarely written in a high level programming language such as C.  However,
-even though this library is written entirely in ISO C, considerable care has been taken to optimize the algorithm implementations within the
-library.  Specifically the code has been written to work well with the GNU C Compiler (\textit{GCC}) on both x86 and ARM
-processors.  Wherever possible, highly efficient algorithms, such as Karatsuba multiplication, sliding window
-exponentiation and Montgomery reduction have been provided to make the library more efficient.
-
-Even with the nearly optimal and specialized algorithms that have been included the Application Programing Interface
-(\textit{API}) has been kept as simple as possible.  Often generic place holder routines will make use of specialized
-algorithms automatically without the developer's specific attention.  One such example is the generic multiplication
-algorithm \textbf{mp\_mul()} which will automatically use Toom--Cook, Karatsuba, Comba or baseline multiplication
-based on the magnitude of the inputs and the configuration of the library.
-
-Making LibTomMath as efficient as possible is not the only goal of the LibTomMath project.  Ideally the library should
-be source compatible with another popular library which makes it more attractive for developers to use.  In this case the
-MPI library was used as a API template for all the basic functions.  MPI was chosen because it is another library that fits
-in the same niche as LibTomMath.  Even though LibTomMath uses MPI as the template for the function names and argument
-passing conventions, it has been written from scratch by Tom St Denis.
-
-The project is also meant to act as a learning tool for students, the logic being that no easy-to-follow ``bignum''
-library exists which can be used to teach computer science students how to perform fast and reliable multiple precision
-integer arithmetic.  To this end the source code has been given quite a few comments and algorithm discussion points.
-
-\section{Choice of LibTomMath}
-LibTomMath was chosen as the case study of this text not only because the author of both projects is one and the same but
-for more worthy reasons.  Other libraries such as GMP \cite{GMP}, MPI \cite{MPI}, LIP \cite{LIP} and OpenSSL
-\cite{OPENSSL} have multiple precision integer arithmetic routines but would not be ideal for this text for
-reasons that will be explained in the following sub-sections.
-
-\subsection{Code Base}
-The LibTomMath code base is all portable ISO C source code.  This means that there are no platform dependent conditional
-segments of code littered throughout the source.  This clean and uncluttered approach to the library means that a
-developer can more readily discern the true intent of a given section of source code without trying to keep track of
-what conditional code will be used.
-
-The code base of LibTomMath is well organized.  Each function is in its own separate source code file
-which allows the reader to find a given function very quickly.  On average there are $76$ lines of code per source
-file which makes the source very easily to follow.  By comparison MPI and LIP are single file projects making code tracing
-very hard.  GMP has many conditional code segments which also hinder tracing.
-
-When compiled with GCC for the x86 processor and optimized for speed the entire library is approximately $100$KiB\footnote{The notation ``KiB'' means $2^{10}$ octets, similarly ``MiB'' means $2^{20}$ octets.}
- which is fairly small compared to GMP (over $250$KiB).  LibTomMath is slightly larger than MPI (which compiles to about
-$50$KiB) but LibTomMath is also much faster and more complete than MPI.
-
-\subsection{API Simplicity}
-LibTomMath is designed after the MPI library and shares the API design.  Quite often programs that use MPI will build
-with LibTomMath without change. The function names correlate directly to the action they perform.  Almost all of the
-functions share the same parameter passing convention.  The learning curve is fairly shallow with the API provided
-which is an extremely valuable benefit for the student and developer alike.
-
-The LIP library is an example of a library with an API that is awkward to work with.  LIP uses function names that are often ``compressed'' to
-illegible short hand.  LibTomMath does not share this characteristic.
-
-The GMP library also does not return error codes.  Instead it uses a POSIX.1 \cite{POSIX1} signal system where errors
-are signaled to the host application.  This happens to be the fastest approach but definitely not the most versatile.  In
-effect a math error (i.e. invalid input, heap error, etc) can cause a program to stop functioning which is definitely
-undersireable in many situations.
-
-\subsection{Optimizations}
-While LibTomMath is certainly not the fastest library (GMP often beats LibTomMath by a factor of two) it does
-feature a set of optimal algorithms for tasks such as modular reduction, exponentiation, multiplication and squaring.  GMP
-and LIP also feature such optimizations while MPI only uses baseline algorithms with no optimizations.  GMP lacks a few
-of the additional modular reduction optimizations that LibTomMath features\footnote{At the time of this writing GMP
-only had Barrett and Montgomery modular reduction algorithms.}.
-
-LibTomMath is almost always an order of magnitude faster than the MPI library at computationally expensive tasks such as modular
-exponentiation.  In the grand scheme of ``bignum'' libraries LibTomMath is faster than the average library and usually
-slower than the best libraries such as GMP and OpenSSL by only a small factor.
-
-\subsection{Portability and Stability}
-LibTomMath will build ``out of the box'' on any platform equipped with a modern version of the GNU C Compiler
-(\textit{GCC}).  This means that without changes the library will build without configuration or setting up any
-variables.  LIP and MPI will build ``out of the box'' as well but have numerous known bugs.  Most notably the author of
-MPI has recently stopped working on his library and LIP has long since been discontinued.
-
-GMP requires a configuration script to run and will not build out of the box.   GMP and LibTomMath are still in active
-development and are very stable across a variety of platforms.
-
-\subsection{Choice}
-LibTomMath is a relatively compact, well documented, highly optimized and portable library which seems only natural for
-the case study of this text.  Various source files from the LibTomMath project will be included within the text.  However,
-the reader is encouraged to download their own copy of the library to actually be able to work with the library.
-
-\chapter{Getting Started}
-\section{Library Basics}
-The trick to writing any useful library of source code is to build a solid foundation and work outwards from it.  First,
-a problem along with allowable solution parameters should be identified and analyzed.  In this particular case the
-inability to accomodate multiple precision integers is the problem.  Futhermore, the solution must be written
-as portable source code that is reasonably efficient across several different computer platforms.
-
-After a foundation is formed the remainder of the library can be designed and implemented in a hierarchical fashion.
-That is, to implement the lowest level dependencies first and work towards the most abstract functions last.  For example,
-before implementing a modular exponentiation algorithm one would implement a modular reduction algorithm.
-By building outwards from a base foundation instead of using a parallel design methodology the resulting project is
-highly modular.  Being highly modular is a desirable property of any project as it often means the resulting product
-has a small footprint and updates are easy to perform.
-
-Usually when I start a project I will begin with the header files.  I define the data types I think I will need and
-prototype the initial functions that are not dependent on other functions (within the library).  After I
-implement these base functions I prototype more dependent functions and implement them.   The process repeats until
-I implement all of the functions I require.  For example, in the case of LibTomMath I implemented functions such as
-mp\_init() well before I implemented mp\_mul() and even further before I implemented mp\_exptmod().  As an example as to
-why this design works note that the Karatsuba and Toom-Cook multipliers were written \textit{after} the
-dependent function mp\_exptmod() was written.  Adding the new multiplication algorithms did not require changes to the
-mp\_exptmod() function itself and lowered the total cost of ownership (\textit{so to speak}) and of development
-for new algorithms.  This methodology allows new algorithms to be tested in a complete framework with relative ease.
-
-\begin{center}
-\begin{figure}[here]
-\includegraphics{pics/design_process.ps}
-\caption{Design Flow of the First Few Original LibTomMath Functions.}
-\label{pic:design_process}
-\end{figure}
-\end{center}
-
-Only after the majority of the functions were in place did I pursue a less hierarchical approach to auditing and optimizing
-the source code.  For example, one day I may audit the multipliers and the next day the polynomial basis functions.
-
-It only makes sense to begin the text with the preliminary data types and support algorithms required as well.
-This chapter discusses the core algorithms of the library which are the dependents for every other algorithm.
-
-\section{What is a Multiple Precision Integer?}
-Recall that most programming languages, in particular ISO C \cite{ISOC}, only have fixed precision data types that on their own cannot
-be used to represent values larger than their precision will allow. The purpose of multiple precision algorithms is
-to use fixed precision data types to create and manipulate multiple precision integers which may represent values
-that are very large.
-
-As a well known analogy, school children are taught how to form numbers larger than nine by prepending more radix ten digits.  In the decimal system
-the largest single digit value is $9$.  However, by concatenating digits together larger numbers may be represented.  Newly prepended digits
-(\textit{to the left}) are said to be in a different power of ten column.  That is, the number $123$ can be described as having a $1$ in the hundreds
-column, $2$ in the tens column and $3$ in the ones column.  Or more formally $123 = 1 \cdot 10^2 + 2 \cdot 10^1 + 3 \cdot 10^0$.  Computer based
-multiple precision arithmetic is essentially the same concept.  Larger integers are represented by adjoining fixed
-precision computer words with the exception that a different radix is used.
-
-What most people probably do not think about explicitly are the various other attributes that describe a multiple precision
-integer.  For example, the integer $154_{10}$ has two immediately obvious properties.  First, the integer is positive,
-that is the sign of this particular integer is positive as opposed to negative.  Second, the integer has three digits in
-its representation.  There is an additional property that the integer posesses that does not concern pencil-and-paper
-arithmetic.  The third property is how many digits placeholders are available to hold the integer.
-
-The human analogy of this third property is ensuring there is enough space on the paper to write the integer.  For example,
-if one starts writing a large number too far to the right on a piece of paper they will have to erase it and move left.
-Similarly, computer algorithms must maintain strict control over memory usage to ensure that the digits of an integer
-will not exceed the allowed boundaries.  These three properties make up what is known as a multiple precision
-integer or mp\_int for short.
-
-\subsection{The mp\_int Structure}
-\label{sec:MPINT}
-The mp\_int structure is the ISO C based manifestation of what represents a multiple precision integer.  The ISO C standard does not provide for
-any such data type but it does provide for making composite data types known as structures.  The following is the structure definition
-used within LibTomMath.
-
-\index{mp\_int}
-\begin{figure}[here]
-\begin{center}
-\begin{small}
-%\begin{verbatim}
-\begin{tabular}{|l|}
-\hline
-typedef struct \{ \\
-\hspace{3mm}int used, alloc, sign;\\
-\hspace{3mm}mp\_digit *dp;\\
-\} \textbf{mp\_int}; \\
-\hline
-\end{tabular}
-%\end{verbatim}
-\end{small}
-\caption{The mp\_int Structure}
-\label{fig:mpint}
-\end{center}
-\end{figure}
-
-The mp\_int structure (fig. \ref{fig:mpint}) can be broken down as follows.
-
-\begin{enumerate}
-\item The \textbf{used} parameter denotes how many digits of the array \textbf{dp} contain the digits used to represent
-a given integer.  The \textbf{used} count must be positive (or zero) and may not exceed the \textbf{alloc} count.
-
-\item The \textbf{alloc} parameter denotes how
-many digits are available in the array to use by functions before it has to increase in size.  When the \textbf{used} count
-of a result would exceed the \textbf{alloc} count all of the algorithms will automatically increase the size of the
-array to accommodate the precision of the result.
-
-\item The pointer \textbf{dp} points to a dynamically allocated array of digits that represent the given multiple
-precision integer.  It is padded with $(\textbf{alloc} - \textbf{used})$ zero digits.  The array is maintained in a least
-significant digit order.  As a pencil and paper analogy the array is organized such that the right most digits are stored
-first starting at the location indexed by zero\footnote{In C all arrays begin at zero.} in the array.  For example,
-if \textbf{dp} contains $\lbrace a, b, c, \ldots \rbrace$ where \textbf{dp}$_0 = a$, \textbf{dp}$_1 = b$, \textbf{dp}$_2 = c$, $\ldots$ then
-it would represent the integer $a + b\beta + c\beta^2 + \ldots$
-
-\index{MP\_ZPOS} \index{MP\_NEG}
-\item The \textbf{sign} parameter denotes the sign as either zero/positive (\textbf{MP\_ZPOS}) or negative (\textbf{MP\_NEG}).
-\end{enumerate}
-
-\subsubsection{Valid mp\_int Structures}
-Several rules are placed on the state of an mp\_int structure and are assumed to be followed for reasons of efficiency.
-The only exceptions are when the structure is passed to initialization functions such as mp\_init() and mp\_init\_copy().
-
-\begin{enumerate}
-\item The value of \textbf{alloc} may not be less than one.  That is \textbf{dp} always points to a previously allocated
-array of digits.
-\item The value of \textbf{used} may not exceed \textbf{alloc} and must be greater than or equal to zero.
-\item The value of \textbf{used} implies the digit at index $(used - 1)$ of the \textbf{dp} array is non-zero.  That is,
-leading zero digits in the most significant positions must be trimmed.
-   \begin{enumerate}
-   \item Digits in the \textbf{dp} array at and above the \textbf{used} location must be zero.
-   \end{enumerate}
-\item The value of \textbf{sign} must be \textbf{MP\_ZPOS} if \textbf{used} is zero;
-this represents the mp\_int value of zero.
-\end{enumerate}
-
-\section{Argument Passing}
-A convention of argument passing must be adopted early on in the development of any library.  Making the function
-prototypes consistent will help eliminate many headaches in the future as the library grows to significant complexity.
-In LibTomMath the multiple precision integer functions accept parameters from left to right as pointers to mp\_int
-structures.  That means that the source (input) operands are placed on the left and the destination (output) on the right.
-Consider the following examples.
-
-\begin{verbatim}
-   mp_mul(&a, &b, &c);   /* c = a * b */
-   mp_add(&a, &b, &a);   /* a = a + b */
-   mp_sqr(&a, &b);       /* b = a * a */
-\end{verbatim}
-
-The left to right order is a fairly natural way to implement the functions since it lets the developer read aloud the
-functions and make sense of them.  For example, the first function would read ``multiply a and b and store in c''.
-
-Certain libraries (\textit{LIP by Lenstra for instance}) accept parameters the other way around, to mimic the order
-of assignment expressions.  That is, the destination (output) is on the left and arguments (inputs) are on the right.  In
-truth, it is entirely a matter of preference.  In the case of LibTomMath the convention from the MPI library has been
-adopted.
-
-Another very useful design consideration, provided for in LibTomMath, is whether to allow argument sources to also be a
-destination.  For example, the second example (\textit{mp\_add}) adds $a$ to $b$ and stores in $a$.  This is an important
-feature to implement since it allows the calling functions to cut down on the number of variables it must maintain.
-However, to implement this feature specific care has to be given to ensure the destination is not modified before the
-source is fully read.
-
-\section{Return Values}
-A well implemented application, no matter what its purpose, should trap as many runtime errors as possible and return them
-to the caller.  By catching runtime errors a library can be guaranteed to prevent undefined behaviour.  However, the end
-developer can still manage to cause a library to crash.  For example, by passing an invalid pointer an application may
-fault by dereferencing memory not owned by the application.
-
-In the case of LibTomMath the only errors that are checked for are related to inappropriate inputs (division by zero for
-instance) and memory allocation errors.  It will not check that the mp\_int passed to any function is valid nor
-will it check pointers for validity.  Any function that can cause a runtime error will return an error code as an
-\textbf{int} data type with one of the following values (fig \ref{fig:errcodes}).
-
-\index{MP\_OKAY} \index{MP\_VAL} \index{MP\_MEM}
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{|l|l|}
-\hline \textbf{Value} & \textbf{Meaning} \\
-\hline \textbf{MP\_OKAY} & The function was successful \\
-\hline \textbf{MP\_VAL}  & One of the input value(s) was invalid \\
-\hline \textbf{MP\_MEM}  & The function ran out of heap memory \\
-\hline
-\end{tabular}
-\end{center}
-\caption{LibTomMath Error Codes}
-\label{fig:errcodes}
-\end{figure}
-
-When an error is detected within a function it should free any memory it allocated, often during the initialization of
-temporary mp\_ints, and return as soon as possible.  The goal is to leave the system in the same state it was when the
-function was called.  Error checking with this style of API is fairly simple.
-
-\begin{verbatim}
-   int err;
-   if ((err = mp_add(&a, &b, &c)) != MP_OKAY) {
-      printf("Error: %s\n", mp_error_to_string(err));
-      exit(EXIT_FAILURE);
-   }
-\end{verbatim}
-
-The GMP \cite{GMP} library uses C style \textit{signals} to flag errors which is of questionable use.  Not all errors are fatal
-and it was not deemed ideal by the author of LibTomMath to force developers to have signal handlers for such cases.
-
-\section{Initialization and Clearing}
-The logical starting point when actually writing multiple precision integer functions is the initialization and
-clearing of the mp\_int structures.  These two algorithms will be used by the majority of the higher level algorithms.
-
-Given the basic mp\_int structure an initialization routine must first allocate memory to hold the digits of
-the integer.  Often it is optimal to allocate a sufficiently large pre-set number of digits even though
-the initial integer will represent zero.  If only a single digit were allocated quite a few subsequent re-allocations
-would occur when operations are performed on the integers.  There is a tradeoff between how many default digits to allocate
-and how many re-allocations are tolerable.  Obviously allocating an excessive amount of digits initially will waste
-memory and become unmanageable.
-
-If the memory for the digits has been successfully allocated then the rest of the members of the structure must
-be initialized.  Since the initial state of an mp\_int is to represent the zero integer, the allocated digits must be set
-to zero.  The \textbf{used} count set to zero and \textbf{sign} set to \textbf{MP\_ZPOS}.
-
-\subsection{Initializing an mp\_int}
-An mp\_int is said to be initialized if it is set to a valid, preferably default, state such that all of the members of the
-structure are set to valid values.  The mp\_init algorithm will perform such an action.
-
-\index{mp\_init}
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_init}. \\
-\textbf{Input}.   An mp\_int $a$ \\
-\textbf{Output}.  Allocate memory and initialize $a$ to a known valid mp\_int state.  \\
-\hline \\
-1.  Allocate memory for \textbf{MP\_PREC} digits. \\
-2.  If the allocation failed return(\textit{MP\_MEM}) \\
-3.  for $n$ from $0$ to $MP\_PREC - 1$ do  \\
-\hspace{3mm}3.1  $a_n \leftarrow 0$\\
-4.  $a.sign \leftarrow MP\_ZPOS$\\
-5.  $a.used \leftarrow 0$\\
-6.  $a.alloc \leftarrow MP\_PREC$\\
-7.  Return(\textit{MP\_OKAY})\\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_init}
-\end{figure}
-
-\textbf{Algorithm mp\_init.}
-The purpose of this function is to initialize an mp\_int structure so that the rest of the library can properly
-manipulte it.  It is assumed that the input may not have had any of its members previously initialized which is certainly
-a valid assumption if the input resides on the stack.
-
-Before any of the members such as \textbf{sign}, \textbf{used} or \textbf{alloc} are initialized the memory for
-the digits is allocated.  If this fails the function returns before setting any of the other members.  The \textbf{MP\_PREC}
-name represents a constant\footnote{Defined in the ``tommath.h'' header file within LibTomMath.}
-used to dictate the minimum precision of newly initialized mp\_int integers.  Ideally, it is at least equal to the smallest
-precision number you'll be working with.
-
-Allocating a block of digits at first instead of a single digit has the benefit of lowering the number of usually slow
-heap operations later functions will have to perform in the future.  If \textbf{MP\_PREC} is set correctly the slack
-memory and the number of heap operations will be trivial.
-
-Once the allocation has been made the digits have to be set to zero as well as the \textbf{used}, \textbf{sign} and
-\textbf{alloc} members initialized.  This ensures that the mp\_int will always represent the default state of zero regardless
-of the original condition of the input.
-
-\textbf{Remark.}
-This function introduces the idiosyncrasy that all iterative loops, commonly initiated with the ``for'' keyword, iterate incrementally
-when the ``to'' keyword is placed between two expressions.  For example, ``for $a$ from $b$ to $c$ do'' means that
-a subsequent expression (or body of expressions) are to be evaluated upto $c - b$ times so long as $b \le c$.  In each
-iteration the variable $a$ is substituted for a new integer that lies inclusively between $b$ and $c$.  If $b > c$ occured
-the loop would not iterate.  By contrast if the ``downto'' keyword were used in place of ``to'' the loop would iterate
-decrementally.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_init.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* init a new mp_int */
-018   int mp_init (mp_int * a)
-019   \{
-020     int i;
-021
-022     /* allocate memory required and clear it */
-023     a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
-024     if (a->dp == NULL) \{
-025       return MP_MEM;
-026     \}
-027
-028     /* set the digits to zero */
-029     for (i = 0; i < MP_PREC; i++) \{
-030         a->dp[i] = 0;
-031     \}
-032
-033     /* set the used to zero, allocated digits to the default precision
-034      * and sign to positive */
-035     a->used  = 0;
-036     a->alloc = MP_PREC;
-037     a->sign  = MP_ZPOS;
-038
-039     return MP_OKAY;
-040   \}
-041   #endif
-042
-\end{alltt}
-\end{small}
-
-One immediate observation of this initializtion function is that it does not return a pointer to a mp\_int structure.  It
-is assumed that the caller has already allocated memory for the mp\_int structure, typically on the application stack.  The
-call to mp\_init() is used only to initialize the members of the structure to a known default state.
-
-Here we see (line 23) the memory allocation is performed first.  This allows us to exit cleanly and quickly
-if there is an error.  If the allocation fails the routine will return \textbf{MP\_MEM} to the caller to indicate there
-was a memory error.  The function XMALLOC is what actually allocates the memory.  Technically XMALLOC is not a function
-but a macro defined in ``tommath.h``.  By default, XMALLOC will evaluate to malloc() which is the C library's built--in
-memory allocation routine.
-
-In order to assure the mp\_int is in a known state the digits must be set to zero.  On most platforms this could have been
-accomplished by using calloc() instead of malloc().  However,  to correctly initialize a integer type to a given value in a
-portable fashion you have to actually assign the value.  The for loop (line 29) performs this required
-operation.
-
-After the memory has been successfully initialized the remainder of the members are initialized
-(lines 33 through 34) to their respective default states.  At this point the algorithm has succeeded and
-a success code is returned to the calling function.  If this function returns \textbf{MP\_OKAY} it is safe to assume the
-mp\_int structure has been properly initialized and is safe to use with other functions within the library.
-
-\subsection{Clearing an mp\_int}
-When an mp\_int is no longer required by the application, the memory that has been allocated for its digits must be
-returned to the application's memory pool with the mp\_clear algorithm.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_clear}. \\
-\textbf{Input}.   An mp\_int $a$ \\
-\textbf{Output}.  The memory for $a$ shall be deallocated.  \\
-\hline \\
-1.  If $a$ has been previously freed then return(\textit{MP\_OKAY}). \\
-2.  for $n$ from 0 to $a.used - 1$ do \\
-\hspace{3mm}2.1  $a_n \leftarrow 0$ \\
-3.  Free the memory allocated for the digits of $a$. \\
-4.  $a.used \leftarrow 0$ \\
-5.  $a.alloc \leftarrow 0$ \\
-6.  $a.sign \leftarrow MP\_ZPOS$ \\
-7.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_clear}
-\end{figure}
-
-\textbf{Algorithm mp\_clear.}
-This algorithm accomplishes two goals.  First, it clears the digits and the other mp\_int members.  This ensures that
-if a developer accidentally re-uses a cleared structure it is less likely to cause problems.  The second goal
-is to free the allocated memory.
-
-The logic behind the algorithm is extended by marking cleared mp\_int structures so that subsequent calls to this
-algorithm will not try to free the memory multiple times.  Cleared mp\_ints are detectable by having a pre-defined invalid
-digit pointer \textbf{dp} setting.
-
-Once an mp\_int has been cleared the mp\_int structure is no longer in a valid state for any other algorithm
-with the exception of algorithms mp\_init, mp\_init\_copy, mp\_init\_size and mp\_clear.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_clear.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* clear one (frees)  */
-018   void
-019   mp_clear (mp_int * a)
-020   \{
-021     int i;
-022
-023     /* only do anything if a hasn't been freed previously */
-024     if (a->dp != NULL) \{
-025       /* first zero the digits */
-026       for (i = 0; i < a->used; i++) \{
-027           a->dp[i] = 0;
-028       \}
-029
-030       /* free ram */
-031       XFREE(a->dp);
-032
-033       /* reset members to make debugging easier */
-034       a->dp    = NULL;
-035       a->alloc = a->used = 0;
-036       a->sign  = MP_ZPOS;
-037     \}
-038   \}
-039   #endif
-040
-\end{alltt}
-\end{small}
-
-The algorithm only operates on the mp\_int if it hasn't been previously cleared.  The if statement (line 24)
-checks to see if the \textbf{dp} member is not \textbf{NULL}.  If the mp\_int is a valid mp\_int then \textbf{dp} cannot be
-\textbf{NULL} in which case the if statement will evaluate to true.
-
-The digits of the mp\_int are cleared by the for loop (line 26) which assigns a zero to every digit.  Similar to mp\_init()
-the digits are assigned zero instead of using block memory operations (such as memset()) since this is more portable.
-
-The digits are deallocated off the heap via the XFREE macro.  Similar to XMALLOC the XFREE macro actually evaluates to
-a standard C library function.  In this case the free() function.  Since free() only deallocates the memory the pointer
-still has to be reset to \textbf{NULL} manually (line 34).
-
-Now that the digits have been cleared and deallocated the other members are set to their final values (lines 35 and 36).
-
-\section{Maintenance Algorithms}
-
-The previous sections describes how to initialize and clear an mp\_int structure.  To further support operations
-that are to be performed on mp\_int structures (such as addition and multiplication) the dependent algorithms must be
-able to augment the precision of an mp\_int and
-initialize mp\_ints with differing initial conditions.
-
-These algorithms complete the set of low level algorithms required to work with mp\_int structures in the higher level
-algorithms such as addition, multiplication and modular exponentiation.
-
-\subsection{Augmenting an mp\_int's Precision}
-When storing a value in an mp\_int structure, a sufficient number of digits must be available to accomodate the entire
-result of an operation without loss of precision.  Quite often the size of the array given by the \textbf{alloc} member
-is large enough to simply increase the \textbf{used} digit count.  However, when the size of the array is too small it
-must be re-sized appropriately to accomodate the result.  The mp\_grow algorithm will provide this functionality.
-
-\newpage\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_grow}. \\
-\textbf{Input}.   An mp\_int $a$ and an integer $b$. \\
-\textbf{Output}.  $a$ is expanded to accomodate $b$ digits. \\
-\hline \\
-1.  if $a.alloc \ge b$ then return(\textit{MP\_OKAY}) \\
-2.  $u \leftarrow b\mbox{ (mod }MP\_PREC\mbox{)}$ \\
-3.  $v \leftarrow b + 2 \cdot MP\_PREC - u$ \\
-4.  Re-allocate the array of digits $a$ to size $v$ \\
-5.  If the allocation failed then return(\textit{MP\_MEM}). \\
-6.  for n from a.alloc to $v - 1$ do  \\
-\hspace{+3mm}6.1  $a_n \leftarrow 0$ \\
-7.  $a.alloc \leftarrow v$ \\
-8.  Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_grow}
-\end{figure}
-
-\textbf{Algorithm mp\_grow.}
-It is ideal to prevent re-allocations from being performed if they are not required (step one).  This is useful to
-prevent mp\_ints from growing excessively in code that erroneously calls mp\_grow.
-
-The requested digit count is padded up to next multiple of \textbf{MP\_PREC} plus an additional \textbf{MP\_PREC} (steps two and three).
-This helps prevent many trivial reallocations that would grow an mp\_int by trivially small values.
-
-It is assumed that the reallocation (step four) leaves the lower $a.alloc$ digits of the mp\_int intact.  This is much
-akin to how the \textit{realloc} function from the standard C library works.  Since the newly allocated digits are
-assumed to contain undefined values they are initially set to zero.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_grow.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* grow as required */
-018   int mp_grow (mp_int * a, int size)
-019   \{
-020     int     i;
-021     mp_digit *tmp;
-022
-023     /* if the alloc size is smaller alloc more ram */
-024     if (a->alloc < size) \{
-025       /* ensure there are always at least MP_PREC digits extra on top */
-026       size += (MP_PREC * 2) - (size % MP_PREC);
-027
-028       /* reallocate the array a->dp
-029        *
-030        * We store the return in a temporary variable
-031        * in case the operation failed we don't want
-032        * to overwrite the dp member of a.
-033        */
-034       tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size);
-035       if (tmp == NULL) \{
-036         /* reallocation failed but "a" is still valid [can be freed] */
-037         return MP_MEM;
-038       \}
-039
-040       /* reallocation succeeded so set a->dp */
-041       a->dp = tmp;
-042
-043       /* zero excess digits */
-044       i        = a->alloc;
-045       a->alloc = size;
-046       for (; i < a->alloc; i++) \{
-047         a->dp[i] = 0;
-048       \}
-049     \}
-050     return MP_OKAY;
-051   \}
-052   #endif
-053
-\end{alltt}
-\end{small}
-
-A quick optimization is to first determine if a memory re-allocation is required at all.  The if statement (line 24) checks
-if the \textbf{alloc} member of the mp\_int is smaller than the requested digit count.  If the count is not larger than \textbf{alloc}
-the function skips the re-allocation part thus saving time.
-
-When a re-allocation is performed it is turned into an optimal request to save time in the future.  The requested digit count is
-padded upwards to 2nd multiple of \textbf{MP\_PREC} larger than \textbf{alloc} (line 26).  The XREALLOC function is used
-to re-allocate the memory.  As per the other functions XREALLOC is actually a macro which evaluates to realloc by default.  The realloc
-function leaves the base of the allocation intact which means the first \textbf{alloc} digits of the mp\_int are the same as before
-the re-allocation.  All	that is left is to clear the newly allocated digits and return.
-
-Note that the re-allocation result is actually stored in a temporary pointer $tmp$.  This is to allow this function to return
-an error with a valid pointer.  Earlier releases of the library stored the result of XREALLOC into the mp\_int $a$.  That would
-result in a memory leak if XREALLOC ever failed.
-
-\subsection{Initializing Variable Precision mp\_ints}
-Occasionally the number of digits required will be known in advance of an initialization, based on, for example, the size
-of input mp\_ints to a given algorithm.  The purpose of algorithm mp\_init\_size is similar to mp\_init except that it
-will allocate \textit{at least} a specified number of digits.
-
-\begin{figure}[here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_init\_size}. \\
-\textbf{Input}.   An mp\_int $a$ and the requested number of digits $b$. \\
-\textbf{Output}.  $a$ is initialized to hold at least $b$ digits. \\
-\hline \\
-1.  $u \leftarrow b \mbox{ (mod }MP\_PREC\mbox{)}$ \\
-2.  $v \leftarrow b + 2 \cdot MP\_PREC - u$ \\
-3.  Allocate $v$ digits. \\
-4.  for $n$ from $0$ to $v - 1$ do \\
-\hspace{3mm}4.1  $a_n \leftarrow 0$ \\
-5.  $a.sign \leftarrow MP\_ZPOS$\\
-6.  $a.used \leftarrow 0$\\
-7.  $a.alloc \leftarrow v$\\
-8.  Return(\textit{MP\_OKAY})\\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_init\_size}
-\end{figure}
-
-\textbf{Algorithm mp\_init\_size.}
-This algorithm will initialize an mp\_int structure $a$ like algorithm mp\_init with the exception that the number of
-digits allocated can be controlled by the second input argument $b$.  The input size is padded upwards so it is a
-multiple of \textbf{MP\_PREC} plus an additional \textbf{MP\_PREC} digits.  This padding is used to prevent trivial
-allocations from becoming a bottleneck in the rest of the algorithms.
-
-Like algorithm mp\_init, the mp\_int structure is initialized to a default state representing the integer zero.  This
-particular algorithm is useful if it is known ahead of time the approximate size of the input.  If the approximation is
-correct no further memory re-allocations are required to work with the mp\_int.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_init\_size.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* init an mp_init for a given size */
-018   int mp_init_size (mp_int * a, int size)
-019   \{
-020     int x;
-021
-022     /* pad size so there are always extra digits */
-023     size += (MP_PREC * 2) - (size % MP_PREC);
-024
-025     /* alloc mem */
-026     a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
-027     if (a->dp == NULL) \{
-028       return MP_MEM;
-029     \}
-030
-031     /* set the members */
-032     a->used  = 0;
-033     a->alloc = size;
-034     a->sign  = MP_ZPOS;
-035
-036     /* zero the digits */
-037     for (x = 0; x < size; x++) \{
-038         a->dp[x] = 0;
-039     \}
-040
-041     return MP_OKAY;
-042   \}
-043   #endif
-044
-\end{alltt}
-\end{small}
-
-The number of digits $b$ requested is padded (line 23) by first augmenting it to the next multiple of
-\textbf{MP\_PREC} and then adding \textbf{MP\_PREC} to the result.  If the memory can be successfully allocated the
-mp\_int is placed in a default state representing the integer zero.  Otherwise, the error code \textbf{MP\_MEM} will be
-returned (line 28).
-
-The digits are allocated with the malloc() function (line 26) and set to zero afterwards (line 37).  The
-\textbf{used} count is set to zero, the \textbf{alloc} count set to the padded digit count and the \textbf{sign} flag set
-to \textbf{MP\_ZPOS} to achieve a default valid mp\_int state (lines 32, 33 and 34).  If the function
-returns succesfully then it is correct to assume that the mp\_int structure is in a valid state for the remainder of the
-functions to work with.
-
-\subsection{Multiple Integer Initializations and Clearings}
-Occasionally a function will require a series of mp\_int data types to be made available simultaneously.
-The purpose of algorithm mp\_init\_multi is to initialize a variable length array of mp\_int structures in a single
-statement.  It is essentially a shortcut to multiple initializations.
-
-\newpage\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_init\_multi}. \\
-\textbf{Input}.   Variable length array $V_k$ of mp\_int variables of length $k$. \\
-\textbf{Output}.  The array is initialized such that each mp\_int of $V_k$ is ready to use. \\
-\hline \\
-1.  for $n$ from 0 to $k - 1$ do \\
-\hspace{+3mm}1.1.  Initialize the mp\_int $V_n$ (\textit{mp\_init}) \\
-\hspace{+3mm}1.2.  If initialization failed then do \\
-\hspace{+6mm}1.2.1.  for $j$ from $0$ to $n$ do \\
-\hspace{+9mm}1.2.1.1.  Free the mp\_int $V_j$ (\textit{mp\_clear}) \\
-\hspace{+6mm}1.2.2.   Return(\textit{MP\_MEM}) \\
-2.  Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_init\_multi}
-\end{figure}
-
-\textbf{Algorithm mp\_init\_multi.}
-The algorithm will initialize the array of mp\_int variables one at a time.  If a runtime error has been detected
-(\textit{step 1.2}) all of the previously initialized variables are cleared.  The goal is an ``all or nothing''
-initialization which allows for quick recovery from runtime errors.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_init\_multi.c
-\vspace{-3mm}
-\begin{alltt}
-016   #include <stdarg.h>
-017
-018   int mp_init_multi(mp_int *mp, ...)
-019   \{
-020       mp_err res = MP_OKAY;      /* Assume ok until proven otherwise */
-021       int n = 0;                 /* Number of ok inits */
-022       mp_int* cur_arg = mp;
-023       va_list args;
-024
-025       va_start(args, mp);        /* init args to next argument from caller */
-026       while (cur_arg != NULL) \{
-027           if (mp_init(cur_arg) != MP_OKAY) \{
-028               /* Oops - error! Back-track and mp_clear what we already
-029                  succeeded in init-ing, then return error.
-030               */
-031               va_list clean_args;
-032
-033               /* end the current list */
-034               va_end(args);
-035
-036               /* now start cleaning up */
-037               cur_arg = mp;
-038               va_start(clean_args, mp);
-039               while (n-- != 0) \{
-040                   mp_clear(cur_arg);
-041                   cur_arg = va_arg(clean_args, mp_int*);
-042               \}
-043               va_end(clean_args);
-044               res = MP_MEM;
-045               break;
-046           \}
-047           n++;
-048           cur_arg = va_arg(args, mp_int*);
-049       \}
-050       va_end(args);
-051       return res;                /* Assumed ok, if error flagged above. */
-052   \}
-053
-054   #endif
-055
-\end{alltt}
-\end{small}
-
-This function intializes a variable length list of mp\_int structure pointers.  However, instead of having the mp\_int
-structures in an actual C array they are simply passed as arguments to the function.  This function makes use of the
-``...'' argument syntax of the C programming language.  The list is terminated with a final \textbf{NULL} argument
-appended on the right.
-
-The function uses the ``stdarg.h'' \textit{va} functions to step portably through the arguments to the function.  A count
-$n$ of succesfully initialized mp\_int structures is maintained (line 47) such that if a failure does occur,
-the algorithm can backtrack and free the previously initialized structures (lines 27 to 46).
-
-
-\subsection{Clamping Excess Digits}
-When a function anticipates a result will be $n$ digits it is simpler to assume this is true within the body of
-the function instead of checking during the computation.  For example, a multiplication of a $i$ digit number by a
-$j$ digit produces a result of at most $i + j$ digits.  It is entirely possible that the result is $i + j - 1$
-though, with no final carry into the last position.  However, suppose the destination had to be first expanded
-(\textit{via mp\_grow}) to accomodate $i + j - 1$ digits than further expanded to accomodate the final carry.
-That would be a considerable waste of time since heap operations are relatively slow.
-
-The ideal solution is to always assume the result is $i + j$ and fix up the \textbf{used} count after the function
-terminates.  This way a single heap operation (\textit{at most}) is required.  However, if the result was not checked
-there would be an excess high order zero digit.
-
-For example, suppose the product of two integers was $x_n = (0x_{n-1}x_{n-2}...x_0)_{\beta}$.  The leading zero digit
-will not contribute to the precision of the result.  In fact, through subsequent operations more leading zero digits would
-accumulate to the point the size of the integer would be prohibitive.  As a result even though the precision is very
-low the representation is excessively large.
-
-The mp\_clamp algorithm is designed to solve this very problem.  It will trim high-order zeros by decrementing the
-\textbf{used} count until a non-zero most significant digit is found.  Also in this system, zero is considered to be a
-positive number which means that if the \textbf{used} count is decremented to zero, the sign must be set to
-\textbf{MP\_ZPOS}.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_clamp}. \\
-\textbf{Input}.   An mp\_int $a$ \\
-\textbf{Output}.  Any excess leading zero digits of $a$ are removed \\
-\hline \\
-1.  while $a.used > 0$ and $a_{a.used - 1} = 0$ do \\
-\hspace{+3mm}1.1  $a.used \leftarrow a.used - 1$ \\
-2.  if $a.used = 0$ then do \\
-\hspace{+3mm}2.1  $a.sign \leftarrow MP\_ZPOS$ \\
-\hline \\
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_clamp}
-\end{figure}
-
-\textbf{Algorithm mp\_clamp.}
-As can be expected this algorithm is very simple.  The loop on step one is expected to iterate only once or twice at
-the most.  For example, this will happen in cases where there is not a carry to fill the last position.  Step two fixes the sign for
-when all of the digits are zero to ensure that the mp\_int is valid at all times.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_clamp.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* trim unused digits
-018    *
-019    * This is used to ensure that leading zero digits are
-020    * trimed and the leading "used" digit will be non-zero
-021    * Typically very fast.  Also fixes the sign if there
-022    * are no more leading digits
-023    */
-024   void
-025   mp_clamp (mp_int * a)
-026   \{
-027     /* decrease used while the most significant digit is
-028      * zero.
-029      */
-030     while ((a->used > 0) && (a->dp[a->used - 1] == 0)) \{
-031       --(a->used);
-032     \}
-033
-034     /* reset the sign flag if used == 0 */
-035     if (a->used == 0) \{
-036       a->sign = MP_ZPOS;
-037     \}
-038   \}
-039   #endif
-040
-\end{alltt}
-\end{small}
-
-Note on line 27 how to test for the \textbf{used} count is made on the left of the \&\& operator.  In the C programming
-language the terms to \&\& are evaluated left to right with a boolean short-circuit if any condition fails.  This is
-important since if the \textbf{used} is zero the test on the right would fetch below the array.  That is obviously
-undesirable.  The parenthesis on line 30 is used to make sure the \textbf{used} count is decremented and not
-the pointer ``a''.
-
-\section*{Exercises}
-\begin{tabular}{cl}
-$\left [ 1 \right ]$ & Discuss the relevance of the \textbf{used} member of the mp\_int structure. \\
-                     & \\
-$\left [ 1 \right ]$ & Discuss the consequences of not using padding when performing allocations.  \\
-                     & \\
-$\left [ 2 \right ]$ & Estimate an ideal value for \textbf{MP\_PREC} when performing 1024-bit RSA \\
-                     & encryption when $\beta = 2^{28}$.  \\
-                     & \\
-$\left [ 1 \right ]$ & Discuss the relevance of the algorithm mp\_clamp.  What does it prevent? \\
-                     & \\
-$\left [ 1 \right ]$ & Give an example of when the algorithm  mp\_init\_copy might be useful. \\
-                     & \\
-\end{tabular}
-
-
-%%%
-% CHAPTER FOUR
-%%%
-
-\chapter{Basic Operations}
-
-\section{Introduction}
-In the previous chapter a series of low level algorithms were established that dealt with initializing and maintaining
-mp\_int structures.  This chapter will discuss another set of seemingly non-algebraic algorithms which will form the low
-level basis of the entire library.  While these algorithm are relatively trivial it is important to understand how they
-work before proceeding since these algorithms will be used almost intrinsically in the following chapters.
-
-The algorithms in this chapter deal primarily with more ``programmer'' related tasks such as creating copies of
-mp\_int structures, assigning small values to mp\_int structures and comparisons of the values mp\_int structures
-represent.
-
-\section{Assigning Values to mp\_int Structures}
-\subsection{Copying an mp\_int}
-Assigning the value that a given mp\_int structure represents to another mp\_int structure shall be known as making
-a copy for the purposes of this text.  The copy of the mp\_int will be a separate entity that represents the same
-value as the mp\_int it was copied from.  The mp\_copy algorithm provides this functionality.
-
-\newpage\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_copy}. \\
-\textbf{Input}.  An mp\_int $a$ and $b$. \\
-\textbf{Output}.  Store a copy of $a$ in $b$. \\
-\hline \\
-1.  If $b.alloc < a.used$ then grow $b$ to $a.used$ digits.  (\textit{mp\_grow}) \\
-2.  for $n$ from 0 to $a.used - 1$ do \\
-\hspace{3mm}2.1  $b_{n} \leftarrow a_{n}$ \\
-3.  for $n$ from $a.used$ to $b.used - 1$ do \\
-\hspace{3mm}3.1  $b_{n} \leftarrow 0$ \\
-4.  $b.used \leftarrow a.used$ \\
-5.  $b.sign \leftarrow a.sign$ \\
-6.  return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_copy}
-\end{figure}
-
-\textbf{Algorithm mp\_copy.}
-This algorithm copies the mp\_int $a$ such that upon succesful termination of the algorithm the mp\_int $b$ will
-represent the same integer as the mp\_int $a$.  The mp\_int $b$ shall be a complete and distinct copy of the
-mp\_int $a$ meaing that the mp\_int $a$ can be modified and it shall not affect the value of the mp\_int $b$.
-
-If $b$ does not have enough room for the digits of $a$ it must first have its precision augmented via the mp\_grow
-algorithm.  The digits of $a$ are copied over the digits of $b$ and any excess digits of $b$ are set to zero (step two
-and three).  The \textbf{used} and \textbf{sign} members of $a$ are finally copied over the respective members of
-$b$.
-
-\textbf{Remark.}  This algorithm also introduces a new idiosyncrasy that will be used throughout the rest of the
-text.  The error return codes of other algorithms are not explicitly checked in the pseudo-code presented.  For example, in
-step one of the mp\_copy algorithm the return of mp\_grow is not explicitly checked to ensure it succeeded.  Text space is
-limited so it is assumed that if a algorithm fails it will clear all temporarily allocated mp\_ints and return
-the error code itself.  However, the C code presented will demonstrate all of the error handling logic required to
-implement the pseudo-code.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_copy.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* copy, b = a */
-018   int
-019   mp_copy (mp_int * a, mp_int * b)
-020   \{
-021     int     res, n;
-022
-023     /* if dst == src do nothing */
-024     if (a == b) \{
-025       return MP_OKAY;
-026     \}
-027
-028     /* grow dest */
-029     if (b->alloc < a->used) \{
-030        if ((res = mp_grow (b, a->used)) != MP_OKAY) \{
-031           return res;
-032        \}
-033     \}
-034
-035     /* zero b and copy the parameters over */
-036     \{
-037       mp_digit *tmpa, *tmpb;
-038
-039       /* pointer aliases */
-040
-041       /* source */
-042       tmpa = a->dp;
-043
-044       /* destination */
-045       tmpb = b->dp;
-046
-047       /* copy all the digits */
-048       for (n = 0; n < a->used; n++) \{
-049         *tmpb++ = *tmpa++;
-050       \}
-051
-052       /* clear high digits */
-053       for (; n < b->used; n++) \{
-054         *tmpb++ = 0;
-055       \}
-056     \}
-057
-058     /* copy used count and sign */
-059     b->used = a->used;
-060     b->sign = a->sign;
-061     return MP_OKAY;
-062   \}
-063   #endif
-064
-\end{alltt}
-\end{small}
-
-Occasionally a dependent algorithm may copy an mp\_int effectively into itself such as when the input and output
-mp\_int structures passed to a function are one and the same.  For this case it is optimal to return immediately without
-copying digits (line 24).
-
-The mp\_int $b$ must have enough digits to accomodate the used digits of the mp\_int $a$.  If $b.alloc$ is less than
-$a.used$ the algorithm mp\_grow is used to augment the precision of $b$ (lines 29 to 33).  In order to
-simplify the inner loop that copies the digits from $a$ to $b$, two aliases $tmpa$ and $tmpb$ point directly at the digits
-of the mp\_ints $a$ and $b$ respectively.  These aliases (lines 42 and 45) allow the compiler to access the digits without first dereferencing the
-mp\_int pointers and then subsequently the pointer to the digits.
-
-After the aliases are established the digits from $a$ are copied into $b$ (lines 48 to 50) and then the excess
-digits of $b$ are set to zero (lines 53 to 55).  Both ``for'' loops make use of the pointer aliases and in
-fact the alias for $b$ is carried through into the second ``for'' loop to clear the excess digits.  This optimization
-allows the alias to stay in a machine register fairly easy between the two loops.
-
-\textbf{Remarks.}  The use of pointer aliases is an implementation methodology first introduced in this function that will
-be used considerably in other functions.  Technically, a pointer alias is simply a short hand alias used to lower the
-number of pointer dereferencing operations required to access data.  For example, a for loop may resemble
-
-\begin{alltt}
-for (x = 0; x < 100; x++) \{
-    a->num[4]->dp[x] = 0;
-\}
-\end{alltt}
-
-This could be re-written using aliases as
-
-\begin{alltt}
-mp_digit *tmpa;
-a = a->num[4]->dp;
-for (x = 0; x < 100; x++) \{
-    *a++ = 0;
-\}
-\end{alltt}
-
-In this case an alias is used to access the
-array of digits within an mp\_int structure directly.  It may seem that a pointer alias is strictly not required
-as a compiler may optimize out the redundant pointer operations.  However, there are two dominant reasons to use aliases.
-
-The first reason is that most compilers will not effectively optimize pointer arithmetic.  For example, some optimizations
-may work for the Microsoft Visual C++ compiler (MSVC) and not for the GNU C Compiler (GCC).  Also some optimizations may
-work for GCC and not MSVC.  As such it is ideal to find a common ground for as many compilers as possible.  Pointer
-aliases optimize the code considerably before the compiler even reads the source code which means the end compiled code
-stands a better chance of being faster.
-
-The second reason is that pointer aliases often can make an algorithm simpler to read.  Consider the first ``for''
-loop of the function mp\_copy() re-written to not use pointer aliases.
-
-\begin{alltt}
-    /* copy all the digits */
-    for (n = 0; n < a->used; n++) \{
-      b->dp[n] = a->dp[n];
-    \}
-\end{alltt}
-
-Whether this code is harder to read depends strongly on the individual.  However, it is quantifiably slightly more
-complicated as there are four variables within the statement instead of just two.
-
-\subsubsection{Nested Statements}
-Another commonly used technique in the source routines is that certain sections of code are nested.  This is used in
-particular with the pointer aliases to highlight code phases.  For example, a Comba multiplier (discussed in chapter six)
-will typically have three different phases.  First the temporaries are initialized, then the columns calculated and
-finally the carries are propagated.  In this example the middle column production phase will typically be nested as it
-uses temporary variables and aliases the most.
-
-The nesting also simplies the source code as variables that are nested are only valid for their scope.  As a result
-the various temporary variables required do not propagate into other sections of code.
-
-
-\subsection{Creating a Clone}
-Another common operation is to make a local temporary copy of an mp\_int argument.  To initialize an mp\_int
-and then copy another existing mp\_int into the newly intialized mp\_int will be known as creating a clone.  This is
-useful within functions that need to modify an argument but do not wish to actually modify the original copy.  The
-mp\_init\_copy algorithm has been designed to help perform this task.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_init\_copy}. \\
-\textbf{Input}.   An mp\_int $a$ and $b$\\
-\textbf{Output}.  $a$ is initialized to be a copy of $b$. \\
-\hline \\
-1.  Init $a$.  (\textit{mp\_init}) \\
-2.  Copy $b$ to $a$.  (\textit{mp\_copy}) \\
-3.  Return the status of the copy operation. \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_init\_copy}
-\end{figure}
-
-\textbf{Algorithm mp\_init\_copy.}
-This algorithm will initialize an mp\_int variable and copy another previously initialized mp\_int variable into it.  As
-such this algorithm will perform two operations in one step.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_init\_copy.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* creates "a" then copies b into it */
-018   int mp_init_copy (mp_int * a, mp_int * b)
-019   \{
-020     int     res;
-021
-022     if ((res = mp_init_size (a, b->used)) != MP_OKAY) \{
-023       return res;
-024     \}
-025     return mp_copy (b, a);
-026   \}
-027   #endif
-028
-\end{alltt}
-\end{small}
-
-This will initialize \textbf{a} and make it a verbatim copy of the contents of \textbf{b}.  Note that
-\textbf{a} will have its own memory allocated which means that \textbf{b} may be cleared after the call
-and \textbf{a} will be left intact.
-
-\section{Zeroing an Integer}
-Reseting an mp\_int to the default state is a common step in many algorithms.  The mp\_zero algorithm will be the algorithm used to
-perform this task.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_zero}. \\
-\textbf{Input}.   An mp\_int $a$ \\
-\textbf{Output}.  Zero the contents of $a$ \\
-\hline \\
-1.  $a.used \leftarrow 0$ \\
-2.  $a.sign \leftarrow$ MP\_ZPOS \\
-3.  for $n$ from 0 to $a.alloc - 1$ do \\
-\hspace{3mm}3.1  $a_n \leftarrow 0$ \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_zero}
-\end{figure}
-
-\textbf{Algorithm mp\_zero.}
-This algorithm simply resets a mp\_int to the default state.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_zero.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* set to zero */
-018   void mp_zero (mp_int * a)
-019   \{
-020     int       n;
-021     mp_digit *tmp;
-022
-023     a->sign = MP_ZPOS;
-024     a->used = 0;
-025
-026     tmp = a->dp;
-027     for (n = 0; n < a->alloc; n++) \{
-028        *tmp++ = 0;
-029     \}
-030   \}
-031   #endif
-032
-\end{alltt}
-\end{small}
-
-After the function is completed, all of the digits are zeroed, the \textbf{used} count is zeroed and the
-\textbf{sign} variable is set to \textbf{MP\_ZPOS}.
-
-\section{Sign Manipulation}
-\subsection{Absolute Value}
-With the mp\_int representation of an integer, calculating the absolute value is trivial.  The mp\_abs algorithm will compute
-the absolute value of an mp\_int.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_abs}. \\
-\textbf{Input}.   An mp\_int $a$ \\
-\textbf{Output}.  Computes $b = \vert a \vert$ \\
-\hline \\
-1.  Copy $a$ to $b$.  (\textit{mp\_copy}) \\
-2.  If the copy failed return(\textit{MP\_MEM}). \\
-3.  $b.sign \leftarrow MP\_ZPOS$ \\
-4.  Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_abs}
-\end{figure}
-
-\textbf{Algorithm mp\_abs.}
-This algorithm computes the absolute of an mp\_int input.  First it copies $a$ over $b$.  This is an example of an
-algorithm where the check in mp\_copy that determines if the source and destination are equal proves useful.  This allows,
-for instance, the developer to pass the same mp\_int as the source and destination to this function without addition
-logic to handle it.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_abs.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* b = |a|
-018    *
-019    * Simple function copies the input and fixes the sign to positive
-020    */
-021   int
-022   mp_abs (mp_int * a, mp_int * b)
-023   \{
-024     int     res;
-025
-026     /* copy a to b */
-027     if (a != b) \{
-028        if ((res = mp_copy (a, b)) != MP_OKAY) \{
-029          return res;
-030        \}
-031     \}
-032
-033     /* force the sign of b to positive */
-034     b->sign = MP_ZPOS;
-035
-036     return MP_OKAY;
-037   \}
-038   #endif
-039
-\end{alltt}
-\end{small}
-
-This fairly trivial algorithm first eliminates non--required duplications (line 27) and then sets the
-\textbf{sign} flag to \textbf{MP\_ZPOS}.
-
-\subsection{Integer Negation}
-With the mp\_int representation of an integer, calculating the negation is also trivial.  The mp\_neg algorithm will compute
-the negative of an mp\_int input.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_neg}. \\
-\textbf{Input}.   An mp\_int $a$ \\
-\textbf{Output}.  Computes $b = -a$ \\
-\hline \\
-1.  Copy $a$ to $b$.  (\textit{mp\_copy}) \\
-2.  If the copy failed return(\textit{MP\_MEM}). \\
-3.  If $a.used = 0$ then return(\textit{MP\_OKAY}). \\
-4.  If $a.sign = MP\_ZPOS$ then do \\
-\hspace{3mm}4.1  $b.sign = MP\_NEG$. \\
-5.  else do \\
-\hspace{3mm}5.1  $b.sign = MP\_ZPOS$. \\
-6.  Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_neg}
-\end{figure}
-
-\textbf{Algorithm mp\_neg.}
-This algorithm computes the negation of an input.  First it copies $a$ over $b$.  If $a$ has no used digits then
-the algorithm returns immediately.  Otherwise it flips the sign flag and stores the result in $b$.  Note that if
-$a$ had no digits then it must be positive by definition.  Had step three been omitted then the algorithm would return
-zero as negative.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_neg.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* b = -a */
-018   int mp_neg (mp_int * a, mp_int * b)
-019   \{
-020     int     res;
-021     if (a != b) \{
-022        if ((res = mp_copy (a, b)) != MP_OKAY) \{
-023           return res;
-024        \}
-025     \}
-026
-027     if (mp_iszero(b) != MP_YES) \{
-028        b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS;
-029     \} else \{
-030        b->sign = MP_ZPOS;
-031     \}
-032
-033     return MP_OKAY;
-034   \}
-035   #endif
-036
-\end{alltt}
-\end{small}
-
-Like mp\_abs() this function avoids non--required duplications (line 21) and then sets the sign.  We
-have to make sure that only non--zero values get a \textbf{sign} of \textbf{MP\_NEG}.  If the mp\_int is zero
-than the \textbf{sign} is hard--coded to \textbf{MP\_ZPOS}.
-
-\section{Small Constants}
-\subsection{Setting Small Constants}
-Often a mp\_int must be set to a relatively small value such as $1$ or $2$.  For these cases the mp\_set algorithm is useful.
-
-\newpage\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_set}. \\
-\textbf{Input}.   An mp\_int $a$ and a digit $b$ \\
-\textbf{Output}.  Make $a$ equivalent to $b$ \\
-\hline \\
-1.  Zero $a$ (\textit{mp\_zero}). \\
-2.  $a_0 \leftarrow b \mbox{ (mod }\beta\mbox{)}$ \\
-3.  $a.used \leftarrow  \left \lbrace \begin{array}{ll}
-                              1 &  \mbox{if }a_0 > 0 \\
-                              0 &  \mbox{if }a_0 = 0
-                              \end{array} \right .$ \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_set}
-\end{figure}
-
-\textbf{Algorithm mp\_set.}
-This algorithm sets a mp\_int to a small single digit value.  Step number 1 ensures that the integer is reset to the default state.  The
-single digit is set (\textit{modulo $\beta$}) and the \textbf{used} count is adjusted accordingly.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_set.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* set to a digit */
-018   void mp_set (mp_int * a, mp_digit b)
-019   \{
-020     mp_zero (a);
-021     a->dp[0] = b & MP_MASK;
-022     a->used  = (a->dp[0] != 0) ? 1 : 0;
-023   \}
-024   #endif
-025
-\end{alltt}
-\end{small}
-
-First we zero (line 20) the mp\_int to make sure that the other members are initialized for a
-small positive constant.  mp\_zero() ensures that the \textbf{sign} is positive and the \textbf{used} count
-is zero.  Next we set the digit and reduce it modulo $\beta$ (line 21).  After this step we have to
-check if the resulting digit is zero or not.  If it is not then we set the \textbf{used} count to one, otherwise
-to zero.
-
-We can quickly reduce modulo $\beta$ since it is of the form $2^k$ and a quick binary AND operation with
-$2^k - 1$ will perform the same operation.
-
-One important limitation of this function is that it will only set one digit.  The size of a digit is not fixed, meaning source that uses
-this function should take that into account.  Only trivially small constants can be set using this function.
-
-\subsection{Setting Large Constants}
-To overcome the limitations of the mp\_set algorithm the mp\_set\_int algorithm is ideal.  It accepts a ``long''
-data type as input and will always treat it as a 32-bit integer.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_set\_int}. \\
-\textbf{Input}.   An mp\_int $a$ and a ``long'' integer $b$ \\
-\textbf{Output}.  Make $a$ equivalent to $b$ \\
-\hline \\
-1.  Zero $a$ (\textit{mp\_zero}) \\
-2.  for $n$ from 0 to 7 do \\
-\hspace{3mm}2.1  $a \leftarrow a \cdot 16$ (\textit{mp\_mul2d}) \\
-\hspace{3mm}2.2  $u \leftarrow \lfloor b / 2^{4(7 - n)} \rfloor \mbox{ (mod }16\mbox{)}$\\
-\hspace{3mm}2.3  $a_0 \leftarrow a_0 + u$ \\
-\hspace{3mm}2.4  $a.used \leftarrow a.used + 1$ \\
-3.  Clamp excess used digits (\textit{mp\_clamp}) \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_set\_int}
-\end{figure}
-
-\textbf{Algorithm mp\_set\_int.}
-The algorithm performs eight iterations of a simple loop where in each iteration four bits from the source are added to the
-mp\_int.  Step 2.1 will multiply the current result by sixteen making room for four more bits in the less significant positions.  In step 2.2 the
-next four bits from the source are extracted and are added to the mp\_int. The \textbf{used} digit count is
-incremented to reflect the addition.  The \textbf{used} digit counter is incremented since if any of the leading digits were zero the mp\_int would have
-zero digits used and the newly added four bits would be ignored.
-
-Excess zero digits are trimmed in steps 2.1 and 3 by using higher level algorithms mp\_mul2d and mp\_clamp.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_set\_int.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* set a 32-bit const */
-018   int mp_set_int (mp_int * a, unsigned long b)
-019   \{
-020     int     x, res;
-021
-022     mp_zero (a);
-023
-024     /* set four bits at a time */
-025     for (x = 0; x < 8; x++) \{
-026       /* shift the number up four bits */
-027       if ((res = mp_mul_2d (a, 4, a)) != MP_OKAY) \{
-028         return res;
-029       \}
-030
-031       /* OR in the top four bits of the source */
-032       a->dp[0] |= (b >> 28) & 15;
-033
-034       /* shift the source up to the next four bits */
-035       b <<= 4;
-036
-037       /* ensure that digits are not clamped off */
-038       a->used += 1;
-039     \}
-040     mp_clamp (a);
-041     return MP_OKAY;
-042   \}
-043   #endif
-044
-\end{alltt}
-\end{small}
-
-This function sets four bits of the number at a time to handle all practical \textbf{DIGIT\_BIT} sizes.  The weird
-addition on line 38 ensures that the newly added in bits are added to the number of digits.  While it may not
-seem obvious as to why the digit counter does not grow exceedingly large it is because of the shift on line 27
-as well as the  call to mp\_clamp() on line 40.  Both functions will clamp excess leading digits which keeps
-the number of used digits low.
-
-\section{Comparisons}
-\subsection{Unsigned Comparisions}
-Comparing a multiple precision integer is performed with the exact same algorithm used to compare two decimal numbers.  For example,
-to compare $1,234$ to $1,264$ the digits are extracted by their positions.  That is we compare $1 \cdot 10^3 + 2 \cdot 10^2 + 3 \cdot 10^1 + 4 \cdot 10^0$
-to $1 \cdot 10^3 + 2 \cdot 10^2 + 6 \cdot 10^1 + 4 \cdot 10^0$ by comparing single digits at a time starting with the highest magnitude
-positions.  If any leading digit of one integer is greater than a digit in the same position of another integer then obviously it must be greater.
-
-The first comparision routine that will be developed is the unsigned magnitude compare which will perform a comparison based on the digits of two
-mp\_int variables alone.  It will ignore the sign of the two inputs.  Such a function is useful when an absolute comparison is required or if the
-signs are known to agree in advance.
-
-To facilitate working with the results of the comparison functions three constants are required.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{|r|l|}
-\hline \textbf{Constant} & \textbf{Meaning} \\
-\hline \textbf{MP\_GT} & Greater Than \\
-\hline \textbf{MP\_EQ} & Equal To \\
-\hline \textbf{MP\_LT} & Less Than \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Comparison Return Codes}
-\end{figure}
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_cmp\_mag}. \\
-\textbf{Input}.   Two mp\_ints $a$ and $b$.  \\
-\textbf{Output}.  Unsigned comparison results ($a$ to the left of $b$). \\
-\hline \\
-1.  If $a.used > b.used$ then return(\textit{MP\_GT}) \\
-2.  If $a.used < b.used$ then return(\textit{MP\_LT}) \\
-3.  for n from $a.used - 1$ to 0 do \\
-\hspace{+3mm}3.1  if $a_n > b_n$ then return(\textit{MP\_GT}) \\
-\hspace{+3mm}3.2  if $a_n < b_n$ then return(\textit{MP\_LT}) \\
-4.  Return(\textit{MP\_EQ}) \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_cmp\_mag}
-\end{figure}
-
-\textbf{Algorithm mp\_cmp\_mag.}
-By saying ``$a$ to the left of $b$'' it is meant that the comparison is with respect to $a$, that is if $a$ is greater than $b$ it will return
-\textbf{MP\_GT} and similar with respect to when $a = b$ and $a < b$.  The first two steps compare the number of digits used in both $a$ and $b$.
-Obviously if the digit counts differ there would be an imaginary zero digit in the smaller number where the leading digit of the larger number is.
-If both have the same number of digits than the actual digits themselves must be compared starting at the leading digit.
-
-By step three both inputs must have the same number of digits so its safe to start from either $a.used - 1$ or $b.used - 1$ and count down to
-the zero'th digit.  If after all of the digits have been compared, no difference is found, the algorithm returns \textbf{MP\_EQ}.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_cmp\_mag.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* compare maginitude of two ints (unsigned) */
-018   int mp_cmp_mag (mp_int * a, mp_int * b)
-019   \{
-020     int     n;
-021     mp_digit *tmpa, *tmpb;
-022
-023     /* compare based on # of non-zero digits */
-024     if (a->used > b->used) \{
-025       return MP_GT;
-026     \}
-027
-028     if (a->used < b->used) \{
-029       return MP_LT;
-030     \}
-031
-032     /* alias for a */
-033     tmpa = a->dp + (a->used - 1);
-034
-035     /* alias for b */
-036     tmpb = b->dp + (a->used - 1);
-037
-038     /* compare based on digits  */
-039     for (n = 0; n < a->used; ++n, --tmpa, --tmpb) \{
-040       if (*tmpa > *tmpb) \{
-041         return MP_GT;
-042       \}
-043
-044       if (*tmpa < *tmpb) \{
-045         return MP_LT;
-046       \}
-047     \}
-048     return MP_EQ;
-049   \}
-050   #endif
-051
-\end{alltt}
-\end{small}
-
-The two if statements (lines 24 and 28) compare the number of digits in the two inputs.  These two are
-performed before all of the digits are compared since it is a very cheap test to perform and can potentially save
-considerable time.  The implementation given is also not valid without those two statements.  $b.alloc$ may be
-smaller than $a.used$, meaning that undefined values will be read from $b$ past the end of the array of digits.
-
-
-
-\subsection{Signed Comparisons}
-Comparing with sign considerations is also fairly critical in several routines (\textit{division for example}).  Based on an unsigned magnitude
-comparison a trivial signed comparison algorithm can be written.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_cmp}. \\
-\textbf{Input}.   Two mp\_ints $a$ and $b$ \\
-\textbf{Output}.  Signed Comparison Results ($a$ to the left of $b$) \\
-\hline \\
-1.  if $a.sign = MP\_NEG$ and $b.sign = MP\_ZPOS$ then return(\textit{MP\_LT}) \\
-2.  if $a.sign = MP\_ZPOS$ and $b.sign = MP\_NEG$ then return(\textit{MP\_GT}) \\
-3.  if $a.sign = MP\_NEG$ then \\
-\hspace{+3mm}3.1  Return the unsigned comparison of $b$ and $a$ (\textit{mp\_cmp\_mag}) \\
-4   Otherwise \\
-\hspace{+3mm}4.1  Return the unsigned comparison of $a$ and $b$ \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_cmp}
-\end{figure}
-
-\textbf{Algorithm mp\_cmp.}
-The first two steps compare the signs of the two inputs.  If the signs do not agree then it can return right away with the appropriate
-comparison code.  When the signs are equal the digits of the inputs must be compared to determine the correct result.  In step
-three the unsigned comparision flips the order of the arguments since they are both negative.  For instance, if $-a > -b$ then
-$\vert a \vert < \vert b \vert$.  Step number four will compare the two when they are both positive.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_cmp.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* compare two ints (signed)*/
-018   int
-019   mp_cmp (mp_int * a, mp_int * b)
-020   \{
-021     /* compare based on sign */
-022     if (a->sign != b->sign) \{
-023        if (a->sign == MP_NEG) \{
-024           return MP_LT;
-025        \} else \{
-026           return MP_GT;
-027        \}
-028     \}
-029
-030     /* compare digits */
-031     if (a->sign == MP_NEG) \{
-032        /* if negative compare opposite direction */
-033        return mp_cmp_mag(b, a);
-034     \} else \{
-035        return mp_cmp_mag(a, b);
-036     \}
-037   \}
-038   #endif
-039
-\end{alltt}
-\end{small}
-
-The two if statements (lines 22 and 23) perform the initial sign comparison.  If the signs are not the equal then which ever
-has the positive sign is larger.   The inputs are compared (line 31) based on magnitudes.  If the signs were both
-negative then the unsigned comparison is performed in the opposite direction (line 33).  Otherwise, the signs are assumed to
-be both positive and a forward direction unsigned comparison is performed.
-
-\section*{Exercises}
-\begin{tabular}{cl}
-$\left [ 2 \right ]$ & Modify algorithm mp\_set\_int to accept as input a variable length array of bits. \\
-                     & \\
-$\left [ 3 \right ]$ & Give the probability that algorithm mp\_cmp\_mag will have to compare $k$ digits  \\
-                     & of two random digits (of equal magnitude) before a difference is found. \\
-                     & \\
-$\left [ 1 \right ]$ & Suggest a simple method to speed up the implementation of mp\_cmp\_mag based  \\
-                     & on the observations made in the previous problem. \\
-                     &
-\end{tabular}
-
-\chapter{Basic Arithmetic}
-\section{Introduction}
-At this point algorithms for initialization, clearing, zeroing, copying, comparing and setting small constants have been
-established.  The next logical set of algorithms to develop are addition, subtraction and digit shifting algorithms.  These
-algorithms make use of the lower level algorithms and are the cruicial building block for the multiplication algorithms.  It is very important
-that these algorithms are highly optimized.  On their own they are simple $O(n)$ algorithms but they can be called from higher level algorithms
-which easily places them at $O(n^2)$ or even $O(n^3)$ work levels.
-
-All of the algorithms within this chapter make use of the logical bit shift operations denoted by $<<$ and $>>$ for left and right
-logical shifts respectively.  A logical shift is analogous to sliding the decimal point of radix-10 representations.  For example, the real
-number $0.9345$ is equivalent to $93.45\%$ which is found by sliding the the decimal two places to the right (\textit{multiplying by $\beta^2 = 10^2$}).
-Algebraically a binary logical shift is equivalent to a division or multiplication by a power of two.
-For example, $a << k = a \cdot 2^k$ while $a >> k = \lfloor a/2^k \rfloor$.
-
-One significant difference between a logical shift and the way decimals are shifted is that digits below the zero'th position are removed
-from the number.  For example, consider $1101_2 >> 1$ using decimal notation this would produce $110.1_2$.  However, with a logical shift the
-result is $110_2$.
-
-\section{Addition and Subtraction}
-In common twos complement fixed precision arithmetic negative numbers are easily represented by subtraction from the modulus.  For example, with 32-bit integers
-$a - b\mbox{ (mod }2^{32}\mbox{)}$ is the same as $a + (2^{32} - b) \mbox{ (mod }2^{32}\mbox{)}$  since $2^{32} \equiv 0 \mbox{ (mod }2^{32}\mbox{)}$.
-As a result subtraction can be performed with a trivial series of logical operations and an addition.
-
-However, in multiple precision arithmetic negative numbers are not represented in the same way.  Instead a sign flag is used to keep track of the
-sign of the integer.  As a result signed addition and subtraction are actually implemented as conditional usage of lower level addition or
-subtraction algorithms with the sign fixed up appropriately.
-
-The lower level algorithms will add or subtract integers without regard to the sign flag.  That is they will add or subtract the magnitude of
-the integers respectively.
-
-\subsection{Low Level Addition}
-An unsigned addition of multiple precision integers is performed with the same long-hand algorithm used to add decimal numbers.  That is to add the
-trailing digits first and propagate the resulting carry upwards.  Since this is a lower level algorithm the name will have a ``s\_'' prefix.
-Historically that convention stems from the MPI library where ``s\_'' stood for static functions that were hidden from the developer entirely.
-
-\newpage
-\begin{figure}[!here]
-\begin{center}
-\begin{small}
-\begin{tabular}{l}
-\hline Algorithm \textbf{s\_mp\_add}. \\
-\textbf{Input}.   Two mp\_ints $a$ and $b$ \\
-\textbf{Output}.  The unsigned addition $c = \vert a \vert + \vert b \vert$. \\
-\hline \\
-1.  if $a.used > b.used$ then \\
-\hspace{+3mm}1.1  $min \leftarrow b.used$ \\
-\hspace{+3mm}1.2  $max \leftarrow a.used$ \\
-\hspace{+3mm}1.3  $x   \leftarrow a$ \\
-2.  else  \\
-\hspace{+3mm}2.1  $min \leftarrow a.used$ \\
-\hspace{+3mm}2.2  $max \leftarrow b.used$ \\
-\hspace{+3mm}2.3  $x   \leftarrow b$ \\
-3.  If $c.alloc < max + 1$ then grow $c$ to hold at least $max + 1$ digits (\textit{mp\_grow}) \\
-4.  $oldused \leftarrow c.used$ \\
-5.  $c.used \leftarrow max + 1$ \\
-6.  $u \leftarrow 0$ \\
-7.  for $n$ from $0$ to $min - 1$ do \\
-\hspace{+3mm}7.1  $c_n \leftarrow a_n + b_n + u$ \\
-\hspace{+3mm}7.2  $u \leftarrow c_n >> lg(\beta)$ \\
-\hspace{+3mm}7.3  $c_n \leftarrow c_n \mbox{ (mod }\beta\mbox{)}$ \\
-8.  if $min \ne max$ then do \\
-\hspace{+3mm}8.1  for $n$ from $min$ to $max - 1$ do \\
-\hspace{+6mm}8.1.1  $c_n \leftarrow x_n + u$ \\
-\hspace{+6mm}8.1.2  $u \leftarrow c_n >> lg(\beta)$ \\
-\hspace{+6mm}8.1.3  $c_n \leftarrow c_n \mbox{ (mod }\beta\mbox{)}$ \\
-9.  $c_{max} \leftarrow u$ \\
-10.  if $olduse > max$ then \\
-\hspace{+3mm}10.1  for $n$ from $max + 1$ to $oldused - 1$ do \\
-\hspace{+6mm}10.1.1  $c_n \leftarrow 0$ \\
-11.  Clamp excess digits in $c$.  (\textit{mp\_clamp}) \\
-12.  Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{small}
-\end{center}
-\caption{Algorithm s\_mp\_add}
-\end{figure}
-
-\textbf{Algorithm s\_mp\_add.}
-This algorithm is loosely based on algorithm 14.7 of HAC \cite[pp. 594]{HAC} but has been extended to allow the inputs to have different magnitudes.
-Coincidentally the description of algorithm A in Knuth \cite[pp. 266]{TAOCPV2} shares the same deficiency as the algorithm from \cite{HAC}.  Even the
-MIX pseudo  machine code presented by Knuth \cite[pp. 266-267]{TAOCPV2} is incapable of handling inputs which are of different magnitudes.
-
-The first thing that has to be accomplished is to sort out which of the two inputs is the largest.  The addition logic
-will simply add all of the smallest input to the largest input and store that first part of the result in the
-destination.  Then it will apply a simpler addition loop to excess digits of the larger input.
-
-The first two steps will handle sorting the inputs such that $min$ and $max$ hold the digit counts of the two
-inputs.  The variable $x$ will be an mp\_int alias for the largest input or the second input $b$ if they have the
-same number of digits.  After the inputs are sorted the destination $c$ is grown as required to accomodate the sum
-of the two inputs.  The original \textbf{used} count of $c$ is copied and set to the new used count.
-
-At this point the first addition loop will go through as many digit positions that both inputs have.  The carry
-variable $\mu$ is set to zero outside the loop.  Inside the loop an ``addition'' step requires three statements to produce
-one digit of the summand.  First
-two digits from $a$ and $b$ are added together along with the carry $\mu$.  The carry of this step is extracted and stored
-in $\mu$ and finally the digit of the result $c_n$ is truncated within the range $0 \le c_n < \beta$.
-
-Now all of the digit positions that both inputs have in common have been exhausted.  If $min \ne max$ then $x$ is an alias
-for one of the inputs that has more digits.  A simplified addition loop is then used to essentially copy the remaining digits
-and the carry to the destination.
-
-The final carry is stored in $c_{max}$ and digits above $max$ upto $oldused$ are zeroed which completes the addition.
-
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_s\_mp\_add.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* low level addition, based on HAC pp.594, Algorithm 14.7 */
-018   int
-019   s_mp_add (mp_int * a, mp_int * b, mp_int * c)
-020   \{
-021     mp_int *x;
-022     int     olduse, res, min, max;
-023
-024     /* find sizes, we let |a| <= |b| which means we have to sort
-025      * them.  "x" will point to the input with the most digits
-026      */
-027     if (a->used > b->used) \{
-028       min = b->used;
-029       max = a->used;
-030       x = a;
-031     \} else \{
-032       min = a->used;
-033       max = b->used;
-034       x = b;
-035     \}
-036
-037     /* init result */
-038     if (c->alloc < (max + 1)) \{
-039       if ((res = mp_grow (c, max + 1)) != MP_OKAY) \{
-040         return res;
-041       \}
-042     \}
-043
-044     /* get old used digit count and set new one */
-045     olduse = c->used;
-046     c->used = max + 1;
-047
-048     \{
-049       mp_digit u, *tmpa, *tmpb, *tmpc;
-050       int i;
-051
-052       /* alias for digit pointers */
-053
-054       /* first input */
-055       tmpa = a->dp;
-056
-057       /* second input */
-058       tmpb = b->dp;
-059
-060       /* destination */
-061       tmpc = c->dp;
-062
-063       /* zero the carry */
-064       u = 0;
-065       for (i = 0; i < min; i++) \{
-066         /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
-067         *tmpc = *tmpa++ + *tmpb++ + u;
-068
-069         /* U = carry bit of T[i] */
-070         u = *tmpc >> ((mp_digit)DIGIT_BIT);
-071
-072         /* take away carry bit from T[i] */
-073         *tmpc++ &= MP_MASK;
-074       \}
-075
-076       /* now copy higher words if any, that is in A+B
-077        * if A or B has more digits add those in
-078        */
-079       if (min != max) \{
-080         for (; i < max; i++) \{
-081           /* T[i] = X[i] + U */
-082           *tmpc = x->dp[i] + u;
-083
-084           /* U = carry bit of T[i] */
-085           u = *tmpc >> ((mp_digit)DIGIT_BIT);
-086
-087           /* take away carry bit from T[i] */
-088           *tmpc++ &= MP_MASK;
-089         \}
-090       \}
-091
-092       /* add carry */
-093       *tmpc++ = u;
-094
-095       /* clear digits above oldused */
-096       for (i = c->used; i < olduse; i++) \{
-097         *tmpc++ = 0;
-098       \}
-099     \}
-100
-101     mp_clamp (c);
-102     return MP_OKAY;
-103   \}
-104   #endif
-105
-\end{alltt}
-\end{small}
-
-We first sort (lines 27 to 35) the inputs based on magnitude and determine the $min$ and $max$ variables.
-Note that $x$ is a pointer to an mp\_int assigned to the largest input, in effect it is a local alias.  Next we
-grow the destination (37 to 42) ensure that it can accomodate the result of the addition.
-
-Similar to the implementation of mp\_copy this function uses the braced code and local aliases coding style.  The three aliases that are on
-lines 55, 58 and 61 represent the two inputs and destination variables respectively.  These aliases are used to ensure the
-compiler does not have to dereference $a$, $b$ or $c$ (respectively) to access the digits of the respective mp\_int.
-
-The initial carry $u$ will be cleared (line 64), note that $u$ is of type mp\_digit which ensures type
-compatibility within the implementation.  The initial addition (line 65 to 74) adds digits from
-both inputs until the smallest input runs out of digits.  Similarly the conditional addition loop
-(line 80 to 90) adds the remaining digits from the larger of the two inputs.  The addition is finished
-with the final carry being stored in $tmpc$ (line 93).  Note the ``++'' operator within the same expression.
-After line 93, $tmpc$ will point to the $c.used$'th digit of the mp\_int $c$.  This is useful
-for the next loop (line 96 to 99) which set any old upper digits to zero.
-
-\subsection{Low Level Subtraction}
-The low level unsigned subtraction algorithm is very similar to the low level unsigned addition algorithm.  The principle difference is that the
-unsigned subtraction algorithm requires the result to be positive.  That is when computing $a - b$ the condition $\vert a \vert \ge \vert b\vert$ must
-be met for this algorithm to function properly.  Keep in mind this low level algorithm is not meant to be used in higher level algorithms directly.
-This algorithm as will be shown can be used to create functional signed addition and subtraction algorithms.
-
-
-For this algorithm a new variable is required to make the description simpler.  Recall from section 1.3.1 that a mp\_digit must be able to represent
-the range $0 \le x < 2\beta$ for the algorithms to work correctly.  However, it is allowable that a mp\_digit represent a larger range of values.  For
-this algorithm we will assume that the variable $\gamma$ represents the number of bits available in a
-mp\_digit (\textit{this implies $2^{\gamma} > \beta$}).
-
-For example, the default for LibTomMath is to use a ``unsigned long'' for the mp\_digit ``type'' while $\beta = 2^{28}$.  In ISO C an ``unsigned long''
-data type must be able to represent $0 \le x < 2^{32}$ meaning that in this case $\gamma \ge 32$.
-
-\newpage\begin{figure}[!here]
-\begin{center}
-\begin{small}
-\begin{tabular}{l}
-\hline Algorithm \textbf{s\_mp\_sub}. \\
-\textbf{Input}.   Two mp\_ints $a$ and $b$ ($\vert a \vert \ge \vert b \vert$) \\
-\textbf{Output}.  The unsigned subtraction $c = \vert a \vert - \vert b \vert$. \\
-\hline \\
-1.  $min \leftarrow b.used$ \\
-2.  $max \leftarrow a.used$ \\
-3.  If $c.alloc < max$ then grow $c$ to hold at least $max$ digits.  (\textit{mp\_grow}) \\
-4.  $oldused \leftarrow c.used$ \\
-5.  $c.used \leftarrow max$ \\
-6.  $u \leftarrow 0$ \\
-7.  for $n$ from $0$ to $min - 1$ do \\
-\hspace{3mm}7.1  $c_n \leftarrow a_n - b_n - u$ \\
-\hspace{3mm}7.2  $u   \leftarrow c_n >> (\gamma - 1)$ \\
-\hspace{3mm}7.3  $c_n \leftarrow c_n \mbox{ (mod }\beta\mbox{)}$ \\
-8.  if $min < max$ then do \\
-\hspace{3mm}8.1  for $n$ from $min$ to $max - 1$ do \\
-\hspace{6mm}8.1.1  $c_n \leftarrow a_n - u$ \\
-\hspace{6mm}8.1.2  $u   \leftarrow c_n >> (\gamma - 1)$ \\
-\hspace{6mm}8.1.3  $c_n \leftarrow c_n \mbox{ (mod }\beta\mbox{)}$ \\
-9. if $oldused > max$ then do \\
-\hspace{3mm}9.1  for $n$ from $max$ to $oldused - 1$ do \\
-\hspace{6mm}9.1.1  $c_n \leftarrow 0$ \\
-10. Clamp excess digits of $c$.  (\textit{mp\_clamp}). \\
-11. Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{small}
-\end{center}
-\caption{Algorithm s\_mp\_sub}
-\end{figure}
-
-\textbf{Algorithm s\_mp\_sub.}
-This algorithm performs the unsigned subtraction of two mp\_int variables under the restriction that the result must be positive.  That is when
-passing variables $a$ and $b$ the condition that $\vert a \vert \ge \vert b \vert$ must be met for the algorithm to function correctly.  This
-algorithm is loosely based on algorithm 14.9 \cite[pp. 595]{HAC} and is similar to algorithm S in \cite[pp. 267]{TAOCPV2} as well.  As was the case
-of the algorithm s\_mp\_add both other references lack discussion concerning various practical details such as when the inputs differ in magnitude.
-
-The initial sorting of the inputs is trivial in this algorithm since $a$ is guaranteed to have at least the same magnitude of $b$.  Steps 1 and 2
-set the $min$ and $max$ variables.  Unlike the addition routine there is guaranteed to be no carry which means that the final result can be at
-most $max$ digits in length as opposed to $max + 1$.  Similar to the addition algorithm the \textbf{used} count of $c$ is copied locally and
-set to the maximal count for the operation.
-
-The subtraction loop that begins on step seven is essentially the same as the addition loop of algorithm s\_mp\_add except single precision
-subtraction is used instead.  Note the use of the $\gamma$ variable to extract the carry (\textit{also known as the borrow}) within the subtraction
-loops.  Under the assumption that two's complement single precision arithmetic is used this will successfully extract the desired carry.
-
-For example, consider subtracting $0101_2$ from $0100_2$ where $\gamma = 4$ and $\beta = 2$.  The least significant bit will force a carry upwards to
-the third bit which will be set to zero after the borrow.  After the very first bit has been subtracted $4 - 1 \equiv 0011_2$ will remain,  When the
-third bit of $0101_2$ is subtracted from the result it will cause another carry.  In this case though the carry will be forced to propagate all the
-way to the most significant bit.
-
-Recall that $\beta < 2^{\gamma}$.  This means that if a carry does occur just before the $lg(\beta)$'th bit it will propagate all the way to the most
-significant bit.  Thus, the high order bits of the mp\_digit that are not part of the actual digit will either be all zero, or all one. All that
-is needed is a single zero or one bit for the carry.  Therefore a single logical shift right by $\gamma - 1$ positions is sufficient to extract the
-carry.  This method of carry extraction may seem awkward but the reason for it becomes apparent when the implementation is discussed.
-
-If $b$ has a smaller magnitude than $a$ then step 9 will force the carry and copy operation to propagate through the larger input $a$ into $c$.  Step
-10 will ensure that any leading digits of $c$ above the $max$'th position are zeroed.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_s\_mp\_sub.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
-018   int
-019   s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
-020   \{
-021     int     olduse, res, min, max;
-022
-023     /* find sizes */
-024     min = b->used;
-025     max = a->used;
-026
-027     /* init result */
-028     if (c->alloc < max) \{
-029       if ((res = mp_grow (c, max)) != MP_OKAY) \{
-030         return res;
-031       \}
-032     \}
-033     olduse = c->used;
-034     c->used = max;
-035
-036     \{
-037       mp_digit u, *tmpa, *tmpb, *tmpc;
-038       int i;
-039
-040       /* alias for digit pointers */
-041       tmpa = a->dp;
-042       tmpb = b->dp;
-043       tmpc = c->dp;
-044
-045       /* set carry to zero */
-046       u = 0;
-047       for (i = 0; i < min; i++) \{
-048         /* T[i] = A[i] - B[i] - U */
-049         *tmpc = (*tmpa++ - *tmpb++) - u;
-050
-051         /* U = carry bit of T[i]
-052          * Note this saves performing an AND operation since
-053          * if a carry does occur it will propagate all the way to the
-054          * MSB.  As a result a single shift is enough to get the carry
-055          */
-056         u = *tmpc >> ((mp_digit)((CHAR_BIT * sizeof(mp_digit)) - 1));
-057
-058         /* Clear carry from T[i] */
-059         *tmpc++ &= MP_MASK;
-060       \}
-061
-062       /* now copy higher words if any, e.g. if A has more digits than B  */
-063       for (; i < max; i++) \{
-064         /* T[i] = A[i] - U */
-065         *tmpc = *tmpa++ - u;
-066
-067         /* U = carry bit of T[i] */
-068         u = *tmpc >> ((mp_digit)((CHAR_BIT * sizeof(mp_digit)) - 1));
-069
-070         /* Clear carry from T[i] */
-071         *tmpc++ &= MP_MASK;
-072       \}
-073
-074       /* clear digits above used (since we may not have grown result above) */
-
-075       for (i = c->used; i < olduse; i++) \{
-076         *tmpc++ = 0;
-077       \}
-078     \}
-079
-080     mp_clamp (c);
-081     return MP_OKAY;
-082   \}
-083
-084   #endif
-085
-\end{alltt}
-\end{small}
-
-Like low level addition we ``sort'' the inputs.  Except in this case the sorting is hardcoded
-(lines 24 and 25).  In reality the $min$ and $max$ variables are only aliases and are only
-used to make the source code easier to read.  Again the pointer alias optimization is used
-within this algorithm.  The aliases $tmpa$, $tmpb$ and $tmpc$ are initialized
-(lines 41, 42 and 43) for $a$, $b$ and $c$ respectively.
-
-The first subtraction loop (lines 46 through 60) subtract digits from both inputs until the smaller of
-the two inputs has been exhausted.  As remarked earlier there is an implementation reason for using the ``awkward''
-method of extracting the carry (line 56).  The traditional method for extracting the carry would be to shift
-by $lg(\beta)$ positions and logically AND the least significant bit.  The AND operation is required because all of
-the bits above the $\lg(\beta)$'th bit will be set to one after a carry occurs from subtraction.  This carry
-extraction requires two relatively cheap operations to extract the carry.  The other method is to simply shift the
-most significant bit to the least significant bit thus extracting the carry with a single cheap operation.  This
-optimization only works on twos compliment machines which is a safe assumption to make.
-
-If $a$ has a larger magnitude than $b$ an additional loop (lines 63 through 72) is required to propagate
-the carry through $a$ and copy the result to $c$.
-
-\subsection{High Level Addition}
-Now that both lower level addition and subtraction algorithms have been established an effective high level signed addition algorithm can be
-established.  This high level addition algorithm will be what other algorithms and developers will use to perform addition of mp\_int data
-types.
-
-Recall from section 5.2 that an mp\_int represents an integer with an unsigned mantissa (\textit{the array of digits}) and a \textbf{sign}
-flag.  A high level addition is actually performed as a series of eight separate cases which can be optimized down to three unique cases.
-
-\begin{figure}[!here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_add}. \\
-\textbf{Input}.   Two mp\_ints $a$ and $b$  \\
-\textbf{Output}.  The signed addition $c = a + b$. \\
-\hline \\
-1.  if $a.sign = b.sign$ then do \\
-\hspace{3mm}1.1  $c.sign \leftarrow a.sign$  \\
-\hspace{3mm}1.2  $c \leftarrow \vert a \vert + \vert b \vert$ (\textit{s\_mp\_add})\\
-2.  else do \\
-\hspace{3mm}2.1  if $\vert a \vert < \vert b \vert$ then do (\textit{mp\_cmp\_mag})  \\
-\hspace{6mm}2.1.1  $c.sign \leftarrow b.sign$ \\
-\hspace{6mm}2.1.2  $c \leftarrow \vert b \vert - \vert a \vert$ (\textit{s\_mp\_sub}) \\
-\hspace{3mm}2.2  else do \\
-\hspace{6mm}2.2.1  $c.sign \leftarrow a.sign$ \\
-\hspace{6mm}2.2.2  $c \leftarrow \vert a \vert - \vert b \vert$ \\
-3.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_add}
-\end{figure}
-
-\textbf{Algorithm mp\_add.}
-This algorithm performs the signed addition of two mp\_int variables.  There is no reference algorithm to draw upon from
-either \cite{TAOCPV2} or \cite{HAC} since they both only provide unsigned operations.  The algorithm is fairly
-straightforward but restricted since subtraction can only produce positive results.
-
-\begin{figure}[here]
-\begin{small}
-\begin{center}
-\begin{tabular}{|c|c|c|c|c|}
-\hline \textbf{Sign of $a$} & \textbf{Sign of $b$} & \textbf{$\vert a \vert > \vert b \vert $} & \textbf{Unsigned Operation} & \textbf{Result Sign Flag} \\
-\hline $+$ & $+$ & Yes & $c = a + b$ & $a.sign$ \\
-\hline $+$ & $+$ & No  & $c = a + b$ & $a.sign$ \\
-\hline $-$ & $-$ & Yes & $c = a + b$ & $a.sign$ \\
-\hline $-$ & $-$ & No  & $c = a + b$ & $a.sign$ \\
-\hline &&&&\\
-
-\hline $+$ & $-$ & No  & $c = b - a$ & $b.sign$ \\
-\hline $-$ & $+$ & No  & $c = b - a$ & $b.sign$ \\
-
-\hline &&&&\\
-
-\hline $+$ & $-$ & Yes & $c = a - b$ & $a.sign$ \\
-\hline $-$ & $+$ & Yes & $c = a - b$ & $a.sign$ \\
-
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Addition Guide Chart}
-\label{fig:AddChart}
-\end{figure}
-
-Figure~\ref{fig:AddChart} lists all of the eight possible input combinations and is sorted to show that only three
-specific cases need to be handled.  The return code of the unsigned operations at step 1.2, 2.1.2 and 2.2.2 are
-forwarded to step three to check for errors.  This simplifies the description of the algorithm considerably and best
-follows how the implementation actually was achieved.
-
-Also note how the \textbf{sign} is set before the unsigned addition or subtraction is performed.  Recall from the descriptions of algorithms
-s\_mp\_add and s\_mp\_sub that the mp\_clamp function is used at the end to trim excess digits.  The mp\_clamp algorithm will set the \textbf{sign}
-to \textbf{MP\_ZPOS} when the \textbf{used} digit count reaches zero.
-
-For example, consider performing $-a + a$ with algorithm mp\_add.  By the description of the algorithm the sign is set to \textbf{MP\_NEG} which would
-produce a result of $-0$.  However, since the sign is set first then the unsigned addition is performed the subsequent usage of algorithm mp\_clamp
-within algorithm s\_mp\_add will force $-0$ to become $0$.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_add.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* high level addition (handles signs) */
-018   int mp_add (mp_int * a, mp_int * b, mp_int * c)
-019   \{
-020     int     sa, sb, res;
-021
-022     /* get sign of both inputs */
-023     sa = a->sign;
-024     sb = b->sign;
-025
-026     /* handle two cases, not four */
-027     if (sa == sb) \{
-028       /* both positive or both negative */
-029       /* add their magnitudes, copy the sign */
-030       c->sign = sa;
-031       res = s_mp_add (a, b, c);
-032     \} else \{
-033       /* one positive, the other negative */
-034       /* subtract the one with the greater magnitude from */
-035       /* the one of the lesser magnitude.  The result gets */
-036       /* the sign of the one with the greater magnitude. */
-037       if (mp_cmp_mag (a, b) == MP_LT) \{
-038         c->sign = sb;
-039         res = s_mp_sub (b, a, c);
-040       \} else \{
-041         c->sign = sa;
-042         res = s_mp_sub (a, b, c);
-043       \}
-044     \}
-045     return res;
-046   \}
-047
-048   #endif
-049
-\end{alltt}
-\end{small}
-
-The source code follows the algorithm fairly closely.  The most notable new source code addition is the usage of the $res$ integer variable which
-is used to pass result of the unsigned operations forward.  Unlike in the algorithm, the variable $res$ is merely returned as is without
-explicitly checking it and returning the constant \textbf{MP\_OKAY}.  The observation is this algorithm will succeed or fail only if the lower
-level functions do so.  Returning their return code is sufficient.
-
-\subsection{High Level Subtraction}
-The high level signed subtraction algorithm is essentially the same as the high level signed addition algorithm.
-
-\newpage\begin{figure}[!here]
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_sub}. \\
-\textbf{Input}.   Two mp\_ints $a$ and $b$  \\
-\textbf{Output}.  The signed subtraction $c = a - b$. \\
-\hline \\
-1.  if $a.sign \ne b.sign$ then do \\
-\hspace{3mm}1.1  $c.sign \leftarrow a.sign$ \\
-\hspace{3mm}1.2  $c \leftarrow \vert a \vert + \vert b \vert$ (\textit{s\_mp\_add}) \\
-2.  else do \\
-\hspace{3mm}2.1  if $\vert a \vert \ge \vert b \vert$ then do (\textit{mp\_cmp\_mag}) \\
-\hspace{6mm}2.1.1  $c.sign \leftarrow a.sign$ \\
-\hspace{6mm}2.1.2  $c \leftarrow \vert a \vert  - \vert b \vert$ (\textit{s\_mp\_sub}) \\
-\hspace{3mm}2.2  else do \\
-\hspace{6mm}2.2.1  $c.sign \leftarrow  \left \lbrace \begin{array}{ll}
-                              MP\_ZPOS &  \mbox{if }a.sign = MP\_NEG \\
-                              MP\_NEG  &  \mbox{otherwise} \\
-                              \end{array} \right .$ \\
-\hspace{6mm}2.2.2  $c \leftarrow \vert b \vert  - \vert a \vert$ \\
-3.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Algorithm mp\_sub}
-\end{figure}
-
-\textbf{Algorithm mp\_sub.}
-This algorithm performs the signed subtraction of two inputs.  Similar to algorithm mp\_add there is no reference in either \cite{TAOCPV2} or
-\cite{HAC}.  Also this algorithm is restricted by algorithm s\_mp\_sub.  Chart \ref{fig:SubChart} lists the eight possible inputs and
-the operations required.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{|c|c|c|c|c|}
-\hline \textbf{Sign of $a$} & \textbf{Sign of $b$} & \textbf{$\vert a \vert \ge \vert b \vert $} & \textbf{Unsigned Operation} & \textbf{Result Sign Flag} \\
-\hline $+$ & $-$ & Yes & $c = a + b$ & $a.sign$ \\
-\hline $+$ & $-$ & No  & $c = a + b$ & $a.sign$ \\
-\hline $-$ & $+$ & Yes & $c = a + b$ & $a.sign$ \\
-\hline $-$ & $+$ & No  & $c = a + b$ & $a.sign$ \\
-\hline &&&& \\
-\hline $+$ & $+$ & Yes & $c = a - b$ & $a.sign$ \\
-\hline $-$ & $-$ & Yes & $c = a - b$ & $a.sign$ \\
-\hline &&&& \\
-\hline $+$ & $+$ & No  & $c = b - a$ & $\mbox{opposite of }a.sign$ \\
-\hline $-$ & $-$ & No  & $c = b - a$ & $\mbox{opposite of }a.sign$ \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Subtraction Guide Chart}
-\label{fig:SubChart}
-\end{figure}
-
-Similar to the case of algorithm mp\_add the \textbf{sign} is set first before the unsigned addition or subtraction.  That is to prevent the
-algorithm from producing $-a - -a = -0$ as a result.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_sub.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* high level subtraction (handles signs) */
-018   int
-019   mp_sub (mp_int * a, mp_int * b, mp_int * c)
-020   \{
-021     int     sa, sb, res;
-022
-023     sa = a->sign;
-024     sb = b->sign;
-025
-026     if (sa != sb) \{
-027       /* subtract a negative from a positive, OR */
-028       /* subtract a positive from a negative. */
-029       /* In either case, ADD their magnitudes, */
-030       /* and use the sign of the first number. */
-031       c->sign = sa;
-032       res = s_mp_add (a, b, c);
-033     \} else \{
-034       /* subtract a positive from a positive, OR */
-035       /* subtract a negative from a negative. */
-036       /* First, take the difference between their */
-037       /* magnitudes, then... */
-038       if (mp_cmp_mag (a, b) != MP_LT) \{
-039         /* Copy the sign from the first */
-040         c->sign = sa;
-041         /* The first has a larger or equal magnitude */
-042         res = s_mp_sub (a, b, c);
-043       \} else \{
-044         /* The result has the *opposite* sign from */
-045         /* the first number. */
-046         c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
-047         /* The second has a larger magnitude */
-048         res = s_mp_sub (b, a, c);
-049       \}
-050     \}
-051     return res;
-052   \}
-053
-054   #endif
-055
-\end{alltt}
-\end{small}
-
-Much like the implementation of algorithm mp\_add the variable $res$ is used to catch the return code of the unsigned addition or subtraction operations
-and forward it to the end of the function.  On line 38 the ``not equal to'' \textbf{MP\_LT} expression is used to emulate a
-``greater than or equal to'' comparison.
-
-\section{Bit and Digit Shifting}
-It is quite common to think of a multiple precision integer as a polynomial in $x$, that is $y = f(\beta)$ where $f(x) = \sum_{i=0}^{n-1} a_i x^i$.
-This notation arises within discussion of Montgomery and Diminished Radix Reduction as well as Karatsuba multiplication and squaring.
-
-In order to facilitate operations on polynomials in $x$ as above a series of simple ``digit'' algorithms have to be established.  That is to shift
-the digits left or right as well to shift individual bits of the digits left and right.  It is important to note that not all ``shift'' operations
-are on radix-$\beta$ digits.
-
-\subsection{Multiplication by Two}
-
-In a binary system where the radix is a power of two multiplication by two not only arises often in other algorithms it is a fairly efficient
-operation to perform.  A single precision logical shift left is sufficient to multiply a single digit by two.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_mul\_2}. \\
-\textbf{Input}.   One mp\_int $a$ \\
-\textbf{Output}.  $b = 2a$. \\
-\hline \\
-1.  If $b.alloc < a.used + 1$ then grow $b$ to hold $a.used + 1$ digits.  (\textit{mp\_grow}) \\
-2.  $oldused \leftarrow b.used$ \\
-3.  $b.used \leftarrow a.used$ \\
-4.  $r \leftarrow 0$ \\
-5.  for $n$ from 0 to $a.used - 1$ do \\
-\hspace{3mm}5.1  $rr \leftarrow a_n >> (lg(\beta) - 1)$ \\
-\hspace{3mm}5.2  $b_n \leftarrow (a_n << 1) + r \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{3mm}5.3  $r \leftarrow rr$ \\
-6.  If $r \ne 0$ then do \\
-\hspace{3mm}6.1  $b_{n + 1} \leftarrow r$ \\
-\hspace{3mm}6.2  $b.used \leftarrow b.used + 1$ \\
-7.  If $b.used < oldused - 1$ then do \\
-\hspace{3mm}7.1  for $n$ from $b.used$ to $oldused - 1$ do \\
-\hspace{6mm}7.1.1  $b_n \leftarrow 0$ \\
-8.  $b.sign \leftarrow a.sign$ \\
-9.  Return(\textit{MP\_OKAY}).\\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_mul\_2}
-\end{figure}
-
-\textbf{Algorithm mp\_mul\_2.}
-This algorithm will quickly multiply a mp\_int by two provided $\beta$ is a power of two.  Neither \cite{TAOCPV2} nor \cite{HAC} describe such
-an algorithm despite the fact it arises often in other algorithms.  The algorithm is setup much like the lower level algorithm s\_mp\_add since
-it is for all intents and purposes equivalent to the operation $b = \vert a \vert + \vert a \vert$.
-
-Step 1 and 2 grow the input as required to accomodate the maximum number of \textbf{used} digits in the result.  The initial \textbf{used} count
-is set to $a.used$ at step 4.  Only if there is a final carry will the \textbf{used} count require adjustment.
-
-Step 6 is an optimization implementation of the addition loop for this specific case.  That is since the two values being added together
-are the same there is no need to perform two reads from the digits of $a$.  Step 6.1 performs a single precision shift on the current digit $a_n$ to
-obtain what will be the carry for the next iteration.  Step 6.2 calculates the $n$'th digit of the result as single precision shift of $a_n$ plus
-the previous carry.  Recall from section 4.1 that $a_n << 1$ is equivalent to $a_n \cdot 2$.  An iteration of the addition loop is finished with
-forwarding the carry to the next iteration.
-
-Step 7 takes care of any final carry by setting the $a.used$'th digit of the result to the carry and augmenting the \textbf{used} count of $b$.
-Step 8 clears any leading digits of $b$ in case it originally had a larger magnitude than $a$.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_mul\_2.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* b = a*2 */
-018   int mp_mul_2(mp_int * a, mp_int * b)
-019   \{
-020     int     x, res, oldused;
-021
-022     /* grow to accomodate result */
-023     if (b->alloc < (a->used + 1)) \{
-024       if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) \{
-025         return res;
-026       \}
-027     \}
-028
-029     oldused = b->used;
-030     b->used = a->used;
-031
-032     \{
-033       mp_digit r, rr, *tmpa, *tmpb;
-034
-035       /* alias for source */
-036       tmpa = a->dp;
-037
-038       /* alias for dest */
-039       tmpb = b->dp;
-040
-041       /* carry */
-042       r = 0;
-043       for (x = 0; x < a->used; x++) \{
-044
-045         /* get what will be the *next* carry bit from the
-046          * MSB of the current digit
-047          */
-048         rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1));
-049
-050         /* now shift up this digit, add in the carry [from the previous] */
-051         *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK;
-052
-053         /* copy the carry that would be from the source
-054          * digit into the next iteration
-055          */
-056         r = rr;
-057       \}
-058
-059       /* new leading digit? */
-060       if (r != 0) \{
-061         /* add a MSB which is always 1 at this point */
-062         *tmpb = 1;
-063         ++(b->used);
-064       \}
-065
-066       /* now zero any excess digits on the destination
-067        * that we didn't write to
-068        */
-069       tmpb = b->dp + b->used;
-070       for (x = b->used; x < oldused; x++) \{
-071         *tmpb++ = 0;
-072       \}
-073     \}
-074     b->sign = a->sign;
-075     return MP_OKAY;
-076   \}
-077   #endif
-078
-\end{alltt}
-\end{small}
-
-This implementation is essentially an optimized implementation of s\_mp\_add for the case of doubling an input.  The only noteworthy difference
-is the use of the logical shift operator on line 51 to perform a single precision doubling.
-
-\subsection{Division by Two}
-A division by two can just as easily be accomplished with a logical shift right as multiplication by two can be with a logical shift left.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_div\_2}. \\
-\textbf{Input}.   One mp\_int $a$ \\
-\textbf{Output}.  $b = a/2$. \\
-\hline \\
-1.  If $b.alloc < a.used$ then grow $b$ to hold $a.used$ digits.  (\textit{mp\_grow}) \\
-2.  If the reallocation failed return(\textit{MP\_MEM}). \\
-3.  $oldused \leftarrow b.used$ \\
-4.  $b.used \leftarrow a.used$ \\
-5.  $r \leftarrow 0$ \\
-6.  for $n$ from $b.used - 1$ to $0$ do \\
-\hspace{3mm}6.1  $rr \leftarrow a_n \mbox{ (mod }2\mbox{)}$\\
-\hspace{3mm}6.2  $b_n \leftarrow (a_n >> 1) + (r << (lg(\beta) - 1)) \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{3mm}6.3  $r \leftarrow rr$ \\
-7.  If $b.used < oldused - 1$ then do \\
-\hspace{3mm}7.1  for $n$ from $b.used$ to $oldused - 1$ do \\
-\hspace{6mm}7.1.1  $b_n \leftarrow 0$ \\
-8.  $b.sign \leftarrow a.sign$ \\
-9.  Clamp excess digits of $b$.  (\textit{mp\_clamp}) \\
-10.  Return(\textit{MP\_OKAY}).\\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_div\_2}
-\end{figure}
-
-\textbf{Algorithm mp\_div\_2.}
-This algorithm will divide an mp\_int by two using logical shifts to the right.  Like mp\_mul\_2 it uses a modified low level addition
-core as the basis of the algorithm.  Unlike mp\_mul\_2 the shift operations work from the leading digit to the trailing digit.  The algorithm
-could be written to work from the trailing digit to the leading digit however, it would have to stop one short of $a.used - 1$ digits to prevent
-reading past the end of the array of digits.
-
-Essentially the loop at step 6 is similar to that of mp\_mul\_2 except the logical shifts go in the opposite direction and the carry is at the
-least significant bit not the most significant bit.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_div\_2.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* b = a/2 */
-018   int mp_div_2(mp_int * a, mp_int * b)
-019   \{
-020     int     x, res, oldused;
-021
-022     /* copy */
-023     if (b->alloc < a->used) \{
-024       if ((res = mp_grow (b, a->used)) != MP_OKAY) \{
-025         return res;
-026       \}
-027     \}
-028
-029     oldused = b->used;
-030     b->used = a->used;
-031     \{
-032       mp_digit r, rr, *tmpa, *tmpb;
-033
-034       /* source alias */
-035       tmpa = a->dp + b->used - 1;
-036
-037       /* dest alias */
-038       tmpb = b->dp + b->used - 1;
-039
-040       /* carry */
-041       r = 0;
-042       for (x = b->used - 1; x >= 0; x--) \{
-043         /* get the carry for the next iteration */
-044         rr = *tmpa & 1;
-045
-046         /* shift the current digit, add in carry and store */
-047         *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
-048
-049         /* forward carry to next iteration */
-050         r = rr;
-051       \}
-052
-053       /* zero excess digits */
-054       tmpb = b->dp + b->used;
-055       for (x = b->used; x < oldused; x++) \{
-056         *tmpb++ = 0;
-057       \}
-058     \}
-059     b->sign = a->sign;
-060     mp_clamp (b);
-061     return MP_OKAY;
-062   \}
-063   #endif
-064
-\end{alltt}
-\end{small}
-
-\section{Polynomial Basis Operations}
-Recall from section 4.3 that any integer can be represented as a polynomial in $x$ as $y = f(\beta)$.  Such a representation is also known as
-the polynomial basis \cite[pp. 48]{ROSE}. Given such a notation a multiplication or division by $x$ amounts to shifting whole digits a single
-place.  The need for such operations arises in several other higher level algorithms such as Barrett and Montgomery reduction, integer
-division and Karatsuba multiplication.
-
-Converting from an array of digits to polynomial basis is very simple.  Consider the integer $y \equiv (a_2, a_1, a_0)_{\beta}$ and recall that
-$y = \sum_{i=0}^{2} a_i \beta^i$.  Simply replace $\beta$ with $x$ and the expression is in polynomial basis.  For example, $f(x) = 8x + 9$ is the
-polynomial basis representation for $89$ using radix ten.  That is, $f(10) = 8(10) + 9 = 89$.
-
-\subsection{Multiplication by $x$}
-
-Given a polynomial in $x$ such as $f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_0$ multiplying by $x$ amounts to shifting the coefficients up one
-degree.  In this case $f(x) \cdot x = a_n x^{n+1} + a_{n-1} x^n + ... + a_0 x$.  From a scalar basis point of view multiplying by $x$ is equivalent to
-multiplying by the integer $\beta$.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_lshd}. \\
-\textbf{Input}.   One mp\_int $a$ and an integer $b$ \\
-\textbf{Output}.  $a \leftarrow a \cdot \beta^b$ (equivalent to multiplication by $x^b$). \\
-\hline \\
-1.  If $b \le 0$ then return(\textit{MP\_OKAY}). \\
-2.  If $a.alloc < a.used + b$ then grow $a$ to at least $a.used + b$ digits.  (\textit{mp\_grow}). \\
-3.  If the reallocation failed return(\textit{MP\_MEM}). \\
-4.  $a.used \leftarrow a.used + b$ \\
-5.  $i \leftarrow a.used - 1$ \\
-6.  $j \leftarrow a.used - 1 - b$ \\
-7.  for $n$ from $a.used - 1$ to $b$ do \\
-\hspace{3mm}7.1  $a_{i} \leftarrow a_{j}$ \\
-\hspace{3mm}7.2  $i \leftarrow i - 1$ \\
-\hspace{3mm}7.3  $j \leftarrow j - 1$ \\
-8.  for $n$ from 0 to $b - 1$ do \\
-\hspace{3mm}8.1  $a_n \leftarrow 0$ \\
-9.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_lshd}
-\end{figure}
-
-\textbf{Algorithm mp\_lshd.}
-This algorithm multiplies an mp\_int by the $b$'th power of $x$.  This is equivalent to multiplying by $\beta^b$.  The algorithm differs
-from the other algorithms presented so far as it performs the operation in place instead storing the result in a separate location.  The
-motivation behind this change is due to the way this function is typically used.  Algorithms such as mp\_add store the result in an optionally
-different third mp\_int because the original inputs are often still required.  Algorithm mp\_lshd (\textit{and similarly algorithm mp\_rshd}) is
-typically used on values where the original value is no longer required.  The algorithm will return success immediately if
-$b \le 0$ since the rest of algorithm is only valid when $b > 0$.
-
-First the destination $a$ is grown as required to accomodate the result.  The counters $i$ and $j$ are used to form a \textit{sliding window} over
-the digits of $a$ of length $b$.  The head of the sliding window is at $i$ (\textit{the leading digit}) and the tail at $j$ (\textit{the trailing digit}).
-The loop on step 7 copies the digit from the tail to the head.  In each iteration the window is moved down one digit.   The last loop on
-step 8 sets the lower $b$ digits to zero.
-
-\newpage
-\begin{center}
-\begin{figure}[here]
-\includegraphics{pics/sliding_window.ps}
-\caption{Sliding Window Movement}
-\label{pic:sliding_window}
-\end{figure}
-\end{center}
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_lshd.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* shift left a certain amount of digits */
-018   int mp_lshd (mp_int * a, int b)
-019   \{
-020     int     x, res;
-021
-022     /* if its less than zero return */
-023     if (b <= 0) \{
-024       return MP_OKAY;
-025     \}
-026
-027     /* grow to fit the new digits */
-028     if (a->alloc < (a->used + b)) \{
-029        if ((res = mp_grow (a, a->used + b)) != MP_OKAY) \{
-030          return res;
-031        \}
-032     \}
-033
-034     \{
-035       mp_digit *top, *bottom;
-036
-037       /* increment the used by the shift amount then copy upwards */
-038       a->used += b;
-039
-040       /* top */
-041       top = a->dp + a->used - 1;
-042
-043       /* base */
-044       bottom = (a->dp + a->used - 1) - b;
-045
-046       /* much like mp_rshd this is implemented using a sliding window
-047        * except the window goes the otherway around.  Copying from
-048        * the bottom to the top.  see bn_mp_rshd.c for more info.
-049        */
-050       for (x = a->used - 1; x >= b; x--) \{
-051         *top-- = *bottom--;
-052       \}
-053
-054       /* zero the lower digits */
-055       top = a->dp;
-056       for (x = 0; x < b; x++) \{
-057         *top++ = 0;
-058       \}
-059     \}
-060     return MP_OKAY;
-061   \}
-062   #endif
-063
-\end{alltt}
-\end{small}
-
-The if statement (line 23) ensures that the $b$ variable is greater than zero since we do not interpret negative
-shift counts properly.  The \textbf{used} count is incremented by $b$ before the copy loop begins.  This elminates
-the need for an additional variable in the for loop.  The variable $top$ (line 41) is an alias
-for the leading digit while $bottom$ (line 44) is an alias for the trailing edge.  The aliases form a
-window of exactly $b$ digits over the input.
-
-\subsection{Division by $x$}
-
-Division by powers of $x$ is easily achieved by shifting the digits right and removing any that will end up to the right of the zero'th digit.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_rshd}. \\
-\textbf{Input}.   One mp\_int $a$ and an integer $b$ \\
-\textbf{Output}.  $a \leftarrow a / \beta^b$ (Divide by $x^b$). \\
-\hline \\
-1.  If $b \le 0$ then return. \\
-2.  If $a.used \le b$ then do \\
-\hspace{3mm}2.1  Zero $a$.  (\textit{mp\_zero}). \\
-\hspace{3mm}2.2  Return. \\
-3.  $i \leftarrow 0$ \\
-4.  $j \leftarrow b$ \\
-5.  for $n$ from 0 to $a.used - b - 1$ do \\
-\hspace{3mm}5.1  $a_i \leftarrow a_j$ \\
-\hspace{3mm}5.2  $i \leftarrow i + 1$ \\
-\hspace{3mm}5.3  $j \leftarrow j + 1$ \\
-6.  for $n$ from $a.used - b$ to $a.used - 1$ do \\
-\hspace{3mm}6.1  $a_n \leftarrow 0$ \\
-7.  $a.used \leftarrow a.used - b$ \\
-8.  Return. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_rshd}
-\end{figure}
-
-\textbf{Algorithm mp\_rshd.}
-This algorithm divides the input in place by the $b$'th power of $x$.  It is analogous to dividing by a $\beta^b$ but much quicker since
-it does not require single precision division.  This algorithm does not actually return an error code as it cannot fail.
-
-If the input $b$ is less than one the algorithm quickly returns without performing any work.  If the \textbf{used} count is less than or equal
-to the shift count $b$ then it will simply zero the input and return.
-
-After the trivial cases of inputs have been handled the sliding window is setup.  Much like the case of algorithm mp\_lshd a sliding window that
-is $b$ digits wide is used to copy the digits.  Unlike mp\_lshd the window slides in the opposite direction from the trailing to the leading digit.
-Also the digits are copied from the leading to the trailing edge.
-
-Once the window copy is complete the upper digits must be zeroed and the \textbf{used} count decremented.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_rshd.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* shift right a certain amount of digits */
-018   void mp_rshd (mp_int * a, int b)
-019   \{
-020     int     x;
-021
-022     /* if b <= 0 then ignore it */
-023     if (b <= 0) \{
-024       return;
-025     \}
-026
-027     /* if b > used then simply zero it and return */
-028     if (a->used <= b) \{
-029       mp_zero (a);
-030       return;
-031     \}
-032
-033     \{
-034       mp_digit *bottom, *top;
-035
-036       /* shift the digits down */
-037
-038       /* bottom */
-039       bottom = a->dp;
-040
-041       /* top [offset into digits] */
-042       top = a->dp + b;
-043
-044       /* this is implemented as a sliding window where
-045        * the window is b-digits long and digits from
-046        * the top of the window are copied to the bottom
-047        *
-048        * e.g.
-049
-050        b-2 | b-1 | b0 | b1 | b2 | ... | bb |   ---->
-051                    /\symbol{92}                   |      ---->
-052                     \symbol{92}-------------------/      ---->
-053        */
-054       for (x = 0; x < (a->used - b); x++) \{
-055         *bottom++ = *top++;
-056       \}
-057
-058       /* zero the top digits */
-059       for (; x < a->used; x++) \{
-060         *bottom++ = 0;
-061       \}
-062     \}
-063
-064     /* remove excess digits */
-065     a->used -= b;
-066   \}
-067   #endif
-068
-\end{alltt}
-\end{small}
-
-The only noteworthy element of this routine is the lack of a return type since it cannot fail.  Like mp\_lshd() we
-form a sliding window except we copy in the other direction.  After the window (line 59) we then zero
-the upper digits of the input to make sure the result is correct.
-
-\section{Powers of Two}
-
-Now that algorithms for moving single bits as well as whole digits exist algorithms for moving the ``in between'' distances are required.  For
-example, to quickly multiply by $2^k$ for any $k$ without using a full multiplier algorithm would prove useful.  Instead of performing single
-shifts $k$ times to achieve a multiplication by $2^{\pm k}$ a mixture of whole digit shifting and partial digit shifting is employed.
-
-\subsection{Multiplication by Power of Two}
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_mul\_2d}. \\
-\textbf{Input}.   One mp\_int $a$ and an integer $b$ \\
-\textbf{Output}.  $c \leftarrow a \cdot 2^b$. \\
-\hline \\
-1.  $c \leftarrow a$.  (\textit{mp\_copy}) \\
-2.  If $c.alloc < c.used + \lfloor b / lg(\beta) \rfloor + 2$ then grow $c$ accordingly. \\
-3.  If the reallocation failed return(\textit{MP\_MEM}). \\
-4.  If $b \ge lg(\beta)$ then \\
-\hspace{3mm}4.1  $c \leftarrow c \cdot \beta^{\lfloor b / lg(\beta) \rfloor}$ (\textit{mp\_lshd}). \\
-\hspace{3mm}4.2  If step 4.1 failed return(\textit{MP\_MEM}). \\
-5.  $d \leftarrow b \mbox{ (mod }lg(\beta)\mbox{)}$ \\
-6.  If $d \ne 0$ then do \\
-\hspace{3mm}6.1  $mask \leftarrow 2^d$ \\
-\hspace{3mm}6.2  $r \leftarrow 0$ \\
-\hspace{3mm}6.3  for $n$ from $0$ to $c.used - 1$ do \\
-\hspace{6mm}6.3.1  $rr \leftarrow c_n >> (lg(\beta) - d) \mbox{ (mod }mask\mbox{)}$ \\
-\hspace{6mm}6.3.2  $c_n \leftarrow (c_n << d) + r \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{6mm}6.3.3  $r \leftarrow rr$ \\
-\hspace{3mm}6.4  If $r > 0$ then do \\
-\hspace{6mm}6.4.1  $c_{c.used} \leftarrow r$ \\
-\hspace{6mm}6.4.2  $c.used \leftarrow c.used + 1$ \\
-7.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_mul\_2d}
-\end{figure}
-
-\textbf{Algorithm mp\_mul\_2d.}
-This algorithm multiplies $a$ by $2^b$ and stores the result in $c$.  The algorithm uses algorithm mp\_lshd and a derivative of algorithm mp\_mul\_2 to
-quickly compute the product.
-
-First the algorithm will multiply $a$ by $x^{\lfloor b / lg(\beta) \rfloor}$ which will ensure that the remainder multiplicand is less than
-$\beta$.  For example, if $b = 37$ and $\beta = 2^{28}$ then this step will multiply by $x$ leaving a multiplication by $2^{37 - 28} = 2^{9}$
-left.
-
-After the digits have been shifted appropriately at most $lg(\beta) - 1$ shifts are left to perform.  Step 5 calculates the number of remaining shifts
-required.  If it is non-zero a modified shift loop is used to calculate the remaining product.
-Essentially the loop is a generic version of algorithm mp\_mul\_2 designed to handle any shift count in the range $1 \le x < lg(\beta)$.  The $mask$
-variable is used to extract the upper $d$ bits to form the carry for the next iteration.
-
-This algorithm is loosely measured as a $O(2n)$ algorithm which means that if the input is $n$-digits that it takes $2n$ ``time'' to
-complete.  It is possible to optimize this algorithm down to a $O(n)$ algorithm at a cost of making the algorithm slightly harder to follow.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_mul\_2d.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* shift left by a certain bit count */
-018   int mp_mul_2d (mp_int * a, int b, mp_int * c)
-019   \{
-020     mp_digit d;
-021     int      res;
-022
-023     /* copy */
-024     if (a != c) \{
-025        if ((res = mp_copy (a, c)) != MP_OKAY) \{
-026          return res;
-027        \}
-028     \}
-029
-030     if (c->alloc < (int)(c->used + (b / DIGIT_BIT) + 1)) \{
-031        if ((res = mp_grow (c, c->used + (b / DIGIT_BIT) + 1)) != MP_OKAY) \{
-032          return res;
-033        \}
-034     \}
-035
-036     /* shift by as many digits in the bit count */
-037     if (b >= (int)DIGIT_BIT) \{
-038       if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) \{
-039         return res;
-040       \}
-041     \}
-042
-043     /* shift any bit count < DIGIT_BIT */
-044     d = (mp_digit) (b % DIGIT_BIT);
-045     if (d != 0) \{
-046       mp_digit *tmpc, shift, mask, r, rr;
-047       int x;
-048
-049       /* bitmask for carries */
-050       mask = (((mp_digit)1) << d) - 1;
-051
-052       /* shift for msbs */
-053       shift = DIGIT_BIT - d;
-054
-055       /* alias */
-056       tmpc = c->dp;
-057
-058       /* carry */
-059       r    = 0;
-060       for (x = 0; x < c->used; x++) \{
-061         /* get the higher bits of the current word */
-062         rr = (*tmpc >> shift) & mask;
-063
-064         /* shift the current word and OR in the carry */
-065         *tmpc = ((*tmpc << d) | r) & MP_MASK;
-066         ++tmpc;
-067
-068         /* set the carry to the carry bits of the current word */
-069         r = rr;
-070       \}
-071
-072       /* set final carry */
-073       if (r != 0) \{
-074          c->dp[(c->used)++] = r;
-075       \}
-076     \}
-077     mp_clamp (c);
-078     return MP_OKAY;
-079   \}
-080   #endif
-081
-\end{alltt}
-\end{small}
-
-The shifting is performed in--place which means the first step (line 24) is to copy the input to the
-destination.  We avoid calling mp\_copy() by making sure the mp\_ints are different.  The destination then
-has to be grown (line 31) to accomodate the result.
-
-If the shift count $b$ is larger than $lg(\beta)$ then a call to mp\_lshd() is used to handle all of the multiples
-of $lg(\beta)$.  Leaving only a remaining shift of $lg(\beta) - 1$ or fewer bits left.  Inside the actual shift
-loop (lines 45 to 76) we make use of pre--computed values $shift$ and $mask$.   These are used to
-extract the carry bit(s) to pass into the next iteration of the loop.  The $r$ and $rr$ variables form a
-chain between consecutive iterations to propagate the carry.
-
-\subsection{Division by Power of Two}
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_div\_2d}. \\
-\textbf{Input}.   One mp\_int $a$ and an integer $b$ \\
-\textbf{Output}.  $c \leftarrow \lfloor a / 2^b \rfloor, d \leftarrow a \mbox{ (mod }2^b\mbox{)}$. \\
-\hline \\
-1.  If $b \le 0$ then do \\
-\hspace{3mm}1.1  $c \leftarrow a$ (\textit{mp\_copy}) \\
-\hspace{3mm}1.2  $d \leftarrow 0$ (\textit{mp\_zero}) \\
-\hspace{3mm}1.3  Return(\textit{MP\_OKAY}). \\
-2.  $c \leftarrow a$ \\
-3.  $d \leftarrow a \mbox{ (mod }2^b\mbox{)}$ (\textit{mp\_mod\_2d}) \\
-4.  If $b \ge lg(\beta)$ then do \\
-\hspace{3mm}4.1  $c \leftarrow \lfloor c/\beta^{\lfloor b/lg(\beta) \rfloor} \rfloor$ (\textit{mp\_rshd}). \\
-5.  $k \leftarrow b \mbox{ (mod }lg(\beta)\mbox{)}$ \\
-6.  If $k \ne 0$ then do \\
-\hspace{3mm}6.1  $mask \leftarrow 2^k$ \\
-\hspace{3mm}6.2  $r \leftarrow 0$ \\
-\hspace{3mm}6.3  for $n$ from $c.used - 1$ to $0$ do \\
-\hspace{6mm}6.3.1  $rr \leftarrow c_n \mbox{ (mod }mask\mbox{)}$ \\
-\hspace{6mm}6.3.2  $c_n \leftarrow (c_n >> k) + (r << (lg(\beta) - k))$ \\
-\hspace{6mm}6.3.3  $r \leftarrow rr$ \\
-7.  Clamp excess digits of $c$.  (\textit{mp\_clamp}) \\
-8.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_div\_2d}
-\end{figure}
-
-\textbf{Algorithm mp\_div\_2d.}
-This algorithm will divide an input $a$ by $2^b$ and produce the quotient and remainder.  The algorithm is designed much like algorithm
-mp\_mul\_2d by first using whole digit shifts then single precision shifts.  This algorithm will also produce the remainder of the division
-by using algorithm mp\_mod\_2d.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_div\_2d.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* shift right by a certain bit count (store quotient in c, optional remaind
-      er in d) */
-018   int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
-019   \{
-020     mp_digit D, r, rr;
-021     int     x, res;
-022     mp_int  t;
-023
-024
-025     /* if the shift count is <= 0 then we do no work */
-026     if (b <= 0) \{
-027       res = mp_copy (a, c);
-028       if (d != NULL) \{
-029         mp_zero (d);
-030       \}
-031       return res;
-032     \}
-033
-034     if ((res = mp_init (&t)) != MP_OKAY) \{
-035       return res;
-036     \}
-037
-038     /* get the remainder */
-039     if (d != NULL) \{
-040       if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) \{
-041         mp_clear (&t);
-042         return res;
-043       \}
-044     \}
-045
-046     /* copy */
-047     if ((res = mp_copy (a, c)) != MP_OKAY) \{
-048       mp_clear (&t);
-049       return res;
-050     \}
-051
-052     /* shift by as many digits in the bit count */
-053     if (b >= (int)DIGIT_BIT) \{
-054       mp_rshd (c, b / DIGIT_BIT);
-055     \}
-056
-057     /* shift any bit count < DIGIT_BIT */
-058     D = (mp_digit) (b % DIGIT_BIT);
-059     if (D != 0) \{
-060       mp_digit *tmpc, mask, shift;
-061
-062       /* mask */
-063       mask = (((mp_digit)1) << D) - 1;
-064
-065       /* shift for lsb */
-066       shift = DIGIT_BIT - D;
-067
-068       /* alias */
-069       tmpc = c->dp + (c->used - 1);
-070
-071       /* carry */
-072       r = 0;
-073       for (x = c->used - 1; x >= 0; x--) \{
-074         /* get the lower  bits of this word in a temp */
-075         rr = *tmpc & mask;
-076
-077         /* shift the current word and mix in the carry bits from the previous
-      word */
-078         *tmpc = (*tmpc >> D) | (r << shift);
-079         --tmpc;
-080
-081         /* set the carry to the carry bits of the current word found above */
-082         r = rr;
-083       \}
-084     \}
-085     mp_clamp (c);
-086     if (d != NULL) \{
-087       mp_exch (&t, d);
-088     \}
-089     mp_clear (&t);
-090     return MP_OKAY;
-091   \}
-092   #endif
-093
-\end{alltt}
-\end{small}
-
-The implementation of algorithm mp\_div\_2d is slightly different than the algorithm specifies.  The remainder $d$ may be optionally
-ignored by passing \textbf{NULL} as the pointer to the mp\_int variable.    The temporary mp\_int variable $t$ is used to hold the
-result of the remainder operation until the end.  This allows $d$ and $a$ to represent the same mp\_int without modifying $a$ before
-the quotient is obtained.
-
-The remainder of the source code is essentially the same as the source code for mp\_mul\_2d.  The only significant difference is
-the direction of the shifts.
-
-\subsection{Remainder of Division by Power of Two}
-
-The last algorithm in the series of polynomial basis power of two algorithms is calculating the remainder of division by $2^b$.  This
-algorithm benefits from the fact that in twos complement arithmetic $a \mbox{ (mod }2^b\mbox{)}$ is the same as $a$ AND $2^b - 1$.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_mod\_2d}. \\
-\textbf{Input}.   One mp\_int $a$ and an integer $b$ \\
-\textbf{Output}.  $c \leftarrow a \mbox{ (mod }2^b\mbox{)}$. \\
-\hline \\
-1.  If $b \le 0$ then do \\
-\hspace{3mm}1.1  $c \leftarrow 0$ (\textit{mp\_zero}) \\
-\hspace{3mm}1.2  Return(\textit{MP\_OKAY}). \\
-2.  If $b > a.used \cdot lg(\beta)$ then do \\
-\hspace{3mm}2.1  $c \leftarrow a$ (\textit{mp\_copy}) \\
-\hspace{3mm}2.2  Return the result of step 2.1. \\
-3.  $c \leftarrow a$ \\
-4.  If step 3 failed return(\textit{MP\_MEM}). \\
-5.  for $n$ from $\lceil b / lg(\beta) \rceil$ to $c.used$ do \\
-\hspace{3mm}5.1  $c_n \leftarrow 0$ \\
-6.  $k \leftarrow b \mbox{ (mod }lg(\beta)\mbox{)}$ \\
-7.  $c_{\lfloor b / lg(\beta) \rfloor} \leftarrow c_{\lfloor b / lg(\beta) \rfloor} \mbox{ (mod }2^{k}\mbox{)}$. \\
-8.  Clamp excess digits of $c$.  (\textit{mp\_clamp}) \\
-9.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_mod\_2d}
-\end{figure}
-
-\textbf{Algorithm mp\_mod\_2d.}
-This algorithm will quickly calculate the value of $a \mbox{ (mod }2^b\mbox{)}$.  First if $b$ is less than or equal to zero the
-result is set to zero.  If $b$ is greater than the number of bits in $a$ then it simply copies $a$ to $c$ and returns.  Otherwise, $a$
-is copied to $b$, leading digits are removed and the remaining leading digit is trimed to the exact bit count.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_mod\_2d.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* calc a value mod 2**b */
-018   int
-019   mp_mod_2d (mp_int * a, int b, mp_int * c)
-020   \{
-021     int     x, res;
-022
-023     /* if b is <= 0 then zero the int */
-024     if (b <= 0) \{
-025       mp_zero (c);
-026       return MP_OKAY;
-027     \}
-028
-029     /* if the modulus is larger than the value than return */
-030     if (b >= (int) (a->used * DIGIT_BIT)) \{
-031       res = mp_copy (a, c);
-032       return res;
-033     \}
-034
-035     /* copy */
-036     if ((res = mp_copy (a, c)) != MP_OKAY) \{
-037       return res;
-038     \}
-039
-040     /* zero digits above the last digit of the modulus */
-041     for (x = (b / DIGIT_BIT) + (((b % DIGIT_BIT) == 0) ? 0 : 1); x < c->used;
-      x++) \{
-042       c->dp[x] = 0;
-043     \}
-044     /* clear the digit that is not completely outside/inside the modulus */
-045     c->dp[b / DIGIT_BIT] &=
-046       (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digi
-      t) 1));
-047     mp_clamp (c);
-048     return MP_OKAY;
-049   \}
-050   #endif
-051
-\end{alltt}
-\end{small}
-
-We first avoid cases of $b \le 0$ by simply mp\_zero()'ing the destination in such cases.  Next if $2^b$ is larger
-than the input we just mp\_copy() the input and return right away.  After this point we know we must actually
-perform some work to produce the remainder.
-
-Recalling that reducing modulo $2^k$ and a binary ``and'' with $2^k - 1$ are numerically equivalent we can quickly reduce
-the number.  First we zero any digits above the last digit in $2^b$ (line 41).  Next we reduce the
-leading digit of both (line 45) and then mp\_clamp().
-
-\section*{Exercises}
-\begin{tabular}{cl}
-$\left [ 3 \right ] $ & Devise an algorithm that performs $a \cdot 2^b$ for generic values of $b$ \\
-                      & in $O(n)$ time. \\
-                      &\\
-$\left [ 3 \right ] $ & Devise an efficient algorithm to multiply by small low hamming  \\
-                      & weight values such as $3$, $5$ and $9$.  Extend it to handle all values \\
-                      & upto $64$ with a hamming weight less than three. \\
-                      &\\
-$\left [ 2 \right ] $ & Modify the preceding algorithm to handle values of the form \\
-                      & $2^k - 1$ as well. \\
-                      &\\
-$\left [ 3 \right ] $ & Using only algorithms mp\_mul\_2, mp\_div\_2 and mp\_add create an \\
-                      & algorithm to multiply two integers in roughly $O(2n^2)$ time for \\
-                      & any $n$-bit input.  Note that the time of addition is ignored in the \\
-                      & calculation.  \\
-                      & \\
-$\left [ 5 \right ] $ & Improve the previous algorithm to have a working time of at most \\
-                      & $O \left (2^{(k-1)}n + \left ({2n^2 \over k} \right ) \right )$ for an appropriate choice of $k$.  Again ignore \\
-                      & the cost of addition. \\
-                      & \\
-$\left [ 2 \right ] $ & Devise a chart to find optimal values of $k$ for the previous problem \\
-                      & for $n = 64 \ldots 1024$ in steps of $64$. \\
-                      & \\
-$\left [ 2 \right ] $ & Using only algorithms mp\_abs and mp\_sub devise another method for \\
-                      & calculating the result of a signed comparison. \\
-                      &
-\end{tabular}
-
-\chapter{Multiplication and Squaring}
-\section{The Multipliers}
-For most number theoretic problems including certain public key cryptographic algorithms, the ``multipliers'' form the most important subset of
-algorithms of any multiple precision integer package.  The set of multiplier algorithms include integer multiplication, squaring and modular reduction
-where in each of the algorithms single precision multiplication is the dominant operation performed.  This chapter will discuss integer multiplication
-and squaring, leaving modular reductions for the subsequent chapter.
-
-The importance of the multiplier algorithms is for the most part driven by the fact that certain popular public key algorithms are based on modular
-exponentiation, that is computing $d \equiv a^b \mbox{ (mod }c\mbox{)}$ for some arbitrary choice of $a$, $b$, $c$ and $d$.  During a modular
-exponentiation the majority\footnote{Roughly speaking a modular exponentiation will spend about 40\% of the time performing modular reductions,
-35\% of the time performing squaring and 25\% of the time performing multiplications.} of the processor time is spent performing single precision
-multiplications.
-
-For centuries general purpose multiplication has required a lengthly $O(n^2)$ process, whereby each digit of one multiplicand has to be multiplied
-against every digit of the other multiplicand.  Traditional long-hand multiplication is based on this process;  while the techniques can differ the
-overall algorithm used is essentially the same.  Only ``recently'' have faster algorithms been studied.  First Karatsuba multiplication was discovered in
-1962.  This algorithm can multiply two numbers with considerably fewer single precision multiplications when compared to the long-hand approach.
-This technique led to the discovery of polynomial basis algorithms (\textit{good reference?}) and subquently Fourier Transform based solutions.
-
-\section{Multiplication}
-\subsection{The Baseline Multiplication}
-\label{sec:basemult}
-\index{baseline multiplication}
-Computing the product of two integers in software can be achieved using a trivial adaptation of the standard $O(n^2)$ long-hand multiplication
-algorithm that school children are taught.  The algorithm is considered an $O(n^2)$ algorithm since for two $n$-digit inputs $n^2$ single precision
-multiplications are required.  More specifically for a $m$ and $n$ digit input $m \cdot n$ single precision multiplications are required.  To
-simplify most discussions, it will be assumed that the inputs have comparable number of digits.
-
-The ``baseline multiplication'' algorithm is designed to act as the ``catch-all'' algorithm, only to be used when the faster algorithms cannot be
-used.  This algorithm does not use any particularly interesting optimizations and should ideally be avoided if possible.    One important
-facet of this algorithm, is that it has been modified to only produce a certain amount of output digits as resolution.  The importance of this
-modification will become evident during the discussion of Barrett modular reduction.  Recall that for a $n$ and $m$ digit input the product
-will be at most $n + m$ digits.  Therefore, this algorithm can be reduced to a full multiplier by having it produce $n + m$ digits of the product.
-
-Recall from sub-section 4.2.2 the definition of $\gamma$ as the number of bits in the type \textbf{mp\_digit}.  We shall now extend the variable set to
-include $\alpha$ which shall represent the number of bits in the type \textbf{mp\_word}.  This implies that $2^{\alpha} > 2 \cdot \beta^2$.  The
-constant $\delta = 2^{\alpha - 2lg(\beta)}$ will represent the maximal weight of any column in a product (\textit{see sub-section 5.2.2 for more information}).
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{s\_mp\_mul\_digs}. \\
-\textbf{Input}.   mp\_int $a$, mp\_int $b$ and an integer $digs$ \\
-\textbf{Output}.  $c \leftarrow \vert a \vert \cdot \vert b \vert \mbox{ (mod }\beta^{digs}\mbox{)}$. \\
-\hline \\
-1.  If min$(a.used, b.used) < \delta$ then do \\
-\hspace{3mm}1.1  Calculate $c = \vert a \vert \cdot \vert b \vert$ by the Comba method (\textit{see algorithm~\ref{fig:COMBAMULT}}).  \\
-\hspace{3mm}1.2  Return the result of step 1.1 \\
-\\
-Allocate and initialize a temporary mp\_int. \\
-2.  Init $t$ to be of size $digs$ \\
-3.  If step 2 failed return(\textit{MP\_MEM}). \\
-4.  $t.used \leftarrow digs$ \\
-\\
-Compute the product. \\
-5.  for $ix$ from $0$ to $a.used - 1$ do \\
-\hspace{3mm}5.1  $u \leftarrow 0$ \\
-\hspace{3mm}5.2  $pb \leftarrow \mbox{min}(b.used, digs - ix)$ \\
-\hspace{3mm}5.3  If $pb < 1$ then goto step 6. \\
-\hspace{3mm}5.4  for $iy$ from $0$ to $pb - 1$ do \\
-\hspace{6mm}5.4.1  $\hat r \leftarrow t_{iy + ix} + a_{ix} \cdot b_{iy} + u$ \\
-\hspace{6mm}5.4.2  $t_{iy + ix} \leftarrow \hat r \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{6mm}5.4.3  $u \leftarrow \lfloor \hat r / \beta \rfloor$ \\
-\hspace{3mm}5.5  if $ix + pb < digs$ then do \\
-\hspace{6mm}5.5.1  $t_{ix + pb} \leftarrow u$ \\
-6.  Clamp excess digits of $t$. \\
-7.  Swap $c$ with $t$ \\
-8.  Clear $t$ \\
-9.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm s\_mp\_mul\_digs}
-\end{figure}
-
-\textbf{Algorithm s\_mp\_mul\_digs.}
-This algorithm computes the unsigned product of two inputs $a$ and $b$, limited to an output precision of $digs$ digits.  While it may seem
-a bit awkward to modify the function from its simple $O(n^2)$ description, the usefulness of partial multipliers will arise in a subsequent
-algorithm.  The algorithm is loosely based on algorithm 14.12 from \cite[pp. 595]{HAC} and is similar to Algorithm M of Knuth \cite[pp. 268]{TAOCPV2}.
-Algorithm s\_mp\_mul\_digs differs from these cited references since it can produce a variable output precision regardless of the precision of the
-inputs.
-
-The first thing this algorithm checks for is whether a Comba multiplier can be used instead.   If the minimum digit count of either
-input is less than $\delta$, then the Comba method may be used instead.    After the Comba method is ruled out, the baseline algorithm begins.  A
-temporary mp\_int variable $t$ is used to hold the intermediate result of the product.  This allows the algorithm to be used to
-compute products when either $a = c$ or $b = c$ without overwriting the inputs.
-
-All of step 5 is the infamous $O(n^2)$ multiplication loop slightly modified to only produce upto $digs$ digits of output.  The $pb$ variable
-is given the count of digits to read from $b$ inside the nested loop.  If $pb \le 1$ then no more output digits can be produced and the algorithm
-will exit the loop.  The best way to think of the loops are as a series of $pb \times 1$ multiplications.    That is, in each pass of the
-innermost loop $a_{ix}$ is multiplied against $b$ and the result is added (\textit{with an appropriate shift}) to $t$.
-
-For example, consider multiplying $576$ by $241$.  That is equivalent to computing $10^0(1)(576) + 10^1(4)(576) + 10^2(2)(576)$ which is best
-visualized in the following table.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{|c|c|c|c|c|c|l|}
-\hline   &&          & 5 & 7 & 6 & \\
-\hline   $\times$&&  & 2 & 4 & 1 & \\
-\hline &&&&&&\\
-  &&          & 5 & 7 & 6 & $10^0(1)(576)$ \\
-  &2 &   3    & 6 & 1 & 6 & $10^1(4)(576) + 10^0(1)(576)$ \\
-  1 & 3 & 8 & 8 & 1 & 6 &   $10^2(2)(576) + 10^1(4)(576) + 10^0(1)(576)$ \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Long-Hand Multiplication Diagram}
-\end{figure}
-
-Each row of the product is added to the result after being shifted to the left (\textit{multiplied by a power of the radix}) by the appropriate
-count.  That is in pass $ix$ of the inner loop the product is added starting at the $ix$'th digit of the reult.
-
-Step 5.4.1 introduces the hat symbol (\textit{e.g. $\hat r$}) which represents a double precision variable.  The multiplication on that step
-is assumed to be a double wide output single precision multiplication.  That is, two single precision variables are multiplied to produce a
-double precision result.  The step is somewhat optimized from a long-hand multiplication algorithm because the carry from the addition in step
-5.4.1 is propagated through the nested loop.  If the carry was not propagated immediately it would overflow the single precision digit
-$t_{ix+iy}$ and the result would be lost.
-
-At step 5.5 the nested loop is finished and any carry that was left over should be forwarded.  The carry does not have to be added to the $ix+pb$'th
-digit since that digit is assumed to be zero at this point.  However, if $ix + pb \ge digs$ the carry is not set as it would make the result
-exceed the precision requested.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_s\_mp\_mul\_digs.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* multiplies |a| * |b| and only computes upto digs digits of result
-018    * HAC pp. 595, Algorithm 14.12  Modified so you can control how
-019    * many digits of output are created.
-020    */
-021   int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
-022   \{
-023     mp_int  t;
-024     int     res, pa, pb, ix, iy;
-025     mp_digit u;
-026     mp_word r;
-027     mp_digit tmpx, *tmpt, *tmpy;
-028
-029     /* can we use the fast multiplier? */
-030     if (((digs) < MP_WARRAY) &&
-031         (MIN (a->used, b->used) <
-032             (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) \{
-033       return fast_s_mp_mul_digs (a, b, c, digs);
-034     \}
-035
-036     if ((res = mp_init_size (&t, digs)) != MP_OKAY) \{
-037       return res;
-038     \}
-039     t.used = digs;
-040
-041     /* compute the digits of the product directly */
-042     pa = a->used;
-043     for (ix = 0; ix < pa; ix++) \{
-044       /* set the carry to zero */
-045       u = 0;
-046
-047       /* limit ourselves to making digs digits of output */
-048       pb = MIN (b->used, digs - ix);
-049
-050       /* setup some aliases */
-051       /* copy of the digit from a used within the nested loop */
-052       tmpx = a->dp[ix];
-053
-054       /* an alias for the destination shifted ix places */
-055       tmpt = t.dp + ix;
-056
-057       /* an alias for the digits of b */
-058       tmpy = b->dp;
-059
-060       /* compute the columns of the output and propagate the carry */
-061       for (iy = 0; iy < pb; iy++) \{
-062         /* compute the column as a mp_word */
-063         r       = (mp_word)*tmpt +
-064                   ((mp_word)tmpx * (mp_word)*tmpy++) +
-065                   (mp_word)u;
-066
-067         /* the new column is the lower part of the result */
-068         *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
-069
-070         /* get the carry word from the result */
-071         u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
-072       \}
-073       /* set carry if it is placed below digs */
-074       if ((ix + iy) < digs) \{
-075         *tmpt = u;
-076       \}
-077     \}
-078
-079     mp_clamp (&t);
-080     mp_exch (&t, c);
-081
-082     mp_clear (&t);
-083     return MP_OKAY;
-084   \}
-085   #endif
-086
-\end{alltt}
-\end{small}
-
-First we determine (line 30) if the Comba method can be used first since it's faster.  The conditions for
-sing the Comba routine are that min$(a.used, b.used) < \delta$ and the number of digits of output is less than
-\textbf{MP\_WARRAY}.  This new constant is used to control the stack usage in the Comba routines.  By default it is
-set to $\delta$ but can be reduced when memory is at a premium.
-
-If we cannot use the Comba method we proceed to setup the baseline routine.  We allocate the the destination mp\_int
-$t$ (line 36) to the exact size of the output to avoid further re--allocations.  At this point we now
-begin the $O(n^2)$ loop.
-
-This implementation of multiplication has the caveat that it can be trimmed to only produce a variable number of
-digits as output.  In each iteration of the outer loop the $pb$ variable is set (line 48) to the maximum
-number of inner loop iterations.
-
-Inside the inner loop we calculate $\hat r$ as the mp\_word product of the two mp\_digits and the addition of the
-carry from the previous iteration.  A particularly important observation is that most modern optimizing
-C compilers (GCC for instance) can recognize that a $N \times N \rightarrow 2N$ multiplication is all that
-is required for the product.  In x86 terms for example, this means using the MUL instruction.
-
-Each digit of the product is stored in turn (line 68) and the carry propagated (line 71) to the
-next iteration.
-
-\subsection{Faster Multiplication by the ``Comba'' Method}
-
-One of the huge drawbacks of the ``baseline'' algorithms is that at the $O(n^2)$ level the carry must be
-computed and propagated upwards.  This makes the nested loop very sequential and hard to unroll and implement
-in parallel.  The ``Comba'' \cite{COMBA} method is named after little known (\textit{in cryptographic venues}) Paul G.
-Comba who described a method of implementing fast multipliers that do not require nested carry fixup operations.  As an
-interesting aside it seems that Paul Barrett describes a similar technique in his 1986 paper \cite{BARRETT} written
-five years before.
-
-At the heart of the Comba technique is once again the long-hand algorithm.  Except in this case a slight
-twist is placed on how the columns of the result are produced.  In the standard long-hand algorithm rows of products
-are produced then added together to form the final result.  In the baseline algorithm the columns are added together
-after each iteration to get the result instantaneously.
-
-In the Comba algorithm the columns of the result are produced entirely independently of each other.  That is at
-the $O(n^2)$ level a simple multiplication and addition step is performed.  The carries of the columns are propagated
-after the nested loop to reduce the amount of work requiored. Succintly the first step of the algorithm is to compute
-the product vector $\vec x$ as follows.
-
-\begin{equation}
-\vec x_n = \sum_{i+j = n} a_ib_j, \forall n \in \lbrace 0, 1, 2, \ldots, i + j \rbrace
-\end{equation}
-
-Where $\vec x_n$ is the $n'th$ column of the output vector.  Consider the following example which computes the vector $\vec x$ for the multiplication
-of $576$ and $241$.
-
-\newpage\begin{figure}[here]
-\begin{small}
-\begin{center}
-\begin{tabular}{|c|c|c|c|c|c|}
-  \hline &          & 5 & 7 & 6 & First Input\\
-  \hline $\times$ & & 2 & 4 & 1 & Second Input\\
-\hline            &                        & $1 \cdot 5 = 5$   & $1 \cdot 7 = 7$   & $1 \cdot 6 = 6$ & First pass \\
-                  &  $4 \cdot 5 = 20$      & $4 \cdot 7+5=33$  & $4 \cdot 6+7=31$  & 6               & Second pass \\
-   $2 \cdot 5 = 10$ &  $2 \cdot 7 + 20 = 34$ & $2 \cdot 6+33=45$ & 31                & 6             & Third pass \\
-\hline 10 & 34 & 45 & 31 & 6 & Final Result \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Comba Multiplication Diagram}
-\end{figure}
-
-At this point the vector $x = \left < 10, 34, 45, 31, 6 \right >$ is the result of the first step of the Comba multipler.
-Now the columns must be fixed by propagating the carry upwards.  The resultant vector will have one extra dimension over the input vector which is
-congruent to adding a leading zero digit.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Comba Fixup}. \\
-\textbf{Input}.   Vector $\vec x$ of dimension $k$ \\
-\textbf{Output}.  Vector $\vec x$ such that the carries have been propagated. \\
-\hline \\
-1.  for $n$ from $0$ to $k - 1$ do \\
-\hspace{3mm}1.1 $\vec x_{n+1} \leftarrow \vec x_{n+1} + \lfloor \vec x_{n}/\beta \rfloor$ \\
-\hspace{3mm}1.2 $\vec x_{n} \leftarrow \vec x_{n} \mbox{ (mod }\beta\mbox{)}$ \\
-2.  Return($\vec x$). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm Comba Fixup}
-\end{figure}
-
-With that algorithm and $k = 5$ and $\beta = 10$ the following vector is produced $\vec x= \left < 1, 3, 8, 8, 1, 6 \right >$.  In this case
-$241 \cdot 576$ is in fact $138816$ and the procedure succeeded.  If the algorithm is correct and as will be demonstrated shortly more
-efficient than the baseline algorithm why not simply always use this algorithm?
-
-\subsubsection{Column Weight.}
-At the nested $O(n^2)$ level the Comba method adds the product of two single precision variables to each column of the output
-independently.  A serious obstacle is if the carry is lost, due to lack of precision before the algorithm has a chance to fix
-the carries.  For example, in the multiplication of two three-digit numbers the third column of output will be the sum of
-three single precision multiplications.  If the precision of the accumulator for the output digits is less then $3 \cdot (\beta - 1)^2$ then
-an overflow can occur and the carry information will be lost.  For any $m$ and $n$ digit inputs the maximum weight of any column is
-min$(m, n)$ which is fairly obvious.
-
-The maximum number of terms in any column of a product is known as the ``column weight'' and strictly governs when the algorithm can be used.  Recall
-from earlier that a double precision type has $\alpha$ bits of resolution and a single precision digit has $lg(\beta)$ bits of precision.  Given these
-two quantities we must not violate the following
-
-\begin{equation}
-k \cdot \left (\beta - 1 \right )^2 < 2^{\alpha}
-\end{equation}
-
-Which reduces to
-
-\begin{equation}
-k \cdot \left ( \beta^2 - 2\beta + 1 \right ) < 2^{\alpha}
-\end{equation}
-
-Let $\rho = lg(\beta)$ represent the number of bits in a single precision digit.  By further re-arrangement of the equation the final solution is
-found.
-
-\begin{equation}
-k  < {{2^{\alpha}} \over {\left (2^{2\rho} - 2^{\rho + 1} + 1 \right )}}
-\end{equation}
-
-The defaults for LibTomMath are $\beta = 2^{28}$ and $\alpha = 2^{64}$ which means that $k$ is bounded by $k < 257$.  In this configuration
-the smaller input may not have more than $256$ digits if the Comba method is to be used.  This is quite satisfactory for most applications since
-$256$ digits would allow for numbers in the range of $0 \le x < 2^{7168}$ which, is much larger than most public key cryptographic algorithms require.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{fast\_s\_mp\_mul\_digs}. \\
-\textbf{Input}.   mp\_int $a$, mp\_int $b$ and an integer $digs$ \\
-\textbf{Output}.  $c \leftarrow \vert a \vert \cdot \vert b \vert \mbox{ (mod }\beta^{digs}\mbox{)}$. \\
-\hline \\
-Place an array of \textbf{MP\_WARRAY} single precision digits named $W$ on the stack. \\
-1.  If $c.alloc < digs$ then grow $c$ to $digs$ digits. (\textit{mp\_grow}) \\
-2.  If step 1 failed return(\textit{MP\_MEM}).\\
-\\
-3.  $pa \leftarrow \mbox{MIN}(digs, a.used + b.used)$ \\
-\\
-4.  $\_ \hat W \leftarrow 0$ \\
-5.  for $ix$ from 0 to $pa - 1$ do \\
-\hspace{3mm}5.1  $ty \leftarrow \mbox{MIN}(b.used - 1, ix)$ \\
-\hspace{3mm}5.2  $tx \leftarrow ix - ty$ \\
-\hspace{3mm}5.3  $iy \leftarrow \mbox{MIN}(a.used - tx, ty + 1)$ \\
-\hspace{3mm}5.4  for $iz$ from 0 to $iy - 1$ do \\
-\hspace{6mm}5.4.1  $\_ \hat W \leftarrow \_ \hat W + a_{tx+iy}b_{ty-iy}$ \\
-\hspace{3mm}5.5  $W_{ix} \leftarrow \_ \hat W (\mbox{mod }\beta)$\\
-\hspace{3mm}5.6  $\_ \hat W \leftarrow \lfloor \_ \hat W / \beta \rfloor$ \\
-\\
-6.  $oldused \leftarrow c.used$ \\
-7.  $c.used \leftarrow digs$ \\
-8.  for $ix$ from $0$ to $pa$ do \\
-\hspace{3mm}8.1  $c_{ix} \leftarrow W_{ix}$ \\
-9.  for $ix$ from $pa + 1$ to $oldused - 1$ do \\
-\hspace{3mm}9.1 $c_{ix} \leftarrow 0$ \\
-\\
-10.  Clamp $c$. \\
-11.  Return MP\_OKAY. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm fast\_s\_mp\_mul\_digs}
-\label{fig:COMBAMULT}
-\end{figure}
-
-\textbf{Algorithm fast\_s\_mp\_mul\_digs.}
-This algorithm performs the unsigned multiplication of $a$ and $b$ using the Comba method limited to $digs$ digits of precision.
-
-The outer loop of this algorithm is more complicated than that of the baseline multiplier.  This is because on the inside of the
-loop we want to produce one column per pass.  This allows the accumulator $\_ \hat W$ to be placed in CPU registers and
-reduce the memory bandwidth to two \textbf{mp\_digit} reads per iteration.
-
-The $ty$ variable is set to the minimum count of $ix$ or the number of digits in $b$.  That way if $a$ has more digits than
-$b$ this will be limited to $b.used - 1$.  The $tx$ variable is set to the to the distance past $b.used$ the variable
-$ix$ is.  This is used for the immediately subsequent statement where we find $iy$.
-
-The variable $iy$ is the minimum digits we can read from either $a$ or $b$ before running out.  Computing one column at a time
-means we have to scan one integer upwards and the other downwards.  $a$ starts at $tx$ and $b$ starts at $ty$.  In each
-pass we are producing the $ix$'th output column and we note that $tx + ty = ix$.  As we move $tx$ upwards we have to
-move $ty$ downards so the equality remains valid.  The $iy$ variable is the number of iterations until
-$tx \ge a.used$ or $ty < 0$ occurs.
-
-After every inner pass we store the lower half of the accumulator into $W_{ix}$ and then propagate the carry of the accumulator
-into the next round by dividing $\_ \hat W$ by $\beta$.
-
-To measure the benefits of the Comba method over the baseline method consider the number of operations that are required.  If the
-cost in terms of time of a multiply and addition is $p$ and the cost of a carry propagation is $q$ then a baseline multiplication would require
-$O \left ((p + q)n^2 \right )$ time to multiply two $n$-digit numbers.  The Comba method requires only $O(pn^2 + qn)$ time, however in practice,
-the speed increase is actually much more.  With $O(n)$ space the algorithm can be reduced to $O(pn + qn)$ time by implementing the $n$ multiply
-and addition operations in the nested loop in parallel.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_fast\_s\_mp\_mul\_digs.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* Fast (comba) multiplier
-018    *
-019    * This is the fast column-array [comba] multiplier.  It is
-020    * designed to compute the columns of the product first
-021    * then handle the carries afterwards.  This has the effect
-022    * of making the nested loops that compute the columns very
-023    * simple and schedulable on super-scalar processors.
-024    *
-025    * This has been modified to produce a variable number of
-026    * digits of output so if say only a half-product is required
-027    * you don't have to compute the upper half (a feature
-028    * required for fast Barrett reduction).
-029    *
-030    * Based on Algorithm 14.12 on pp.595 of HAC.
-031    *
-032    */
-033   int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
-034   \{
-035     int     olduse, res, pa, ix, iz;
-036     mp_digit W[MP_WARRAY];
-037     mp_word  _W;
-038
-039     /* grow the destination as required */
-040     if (c->alloc < digs) \{
-041       if ((res = mp_grow (c, digs)) != MP_OKAY) \{
-042         return res;
-043       \}
-044     \}
-045
-046     /* number of output digits to produce */
-047     pa = MIN(digs, a->used + b->used);
-048
-049     /* clear the carry */
-050     _W = 0;
-051     for (ix = 0; ix < pa; ix++) \{
-052         int      tx, ty;
-053         int      iy;
-054         mp_digit *tmpx, *tmpy;
-055
-056         /* get offsets into the two bignums */
-057         ty = MIN(b->used-1, ix);
-058         tx = ix - ty;
-059
-060         /* setup temp aliases */
-061         tmpx = a->dp + tx;
-062         tmpy = b->dp + ty;
-063
-064         /* this is the number of times the loop will iterrate, essentially
-065            while (tx++ < a->used && ty-- >= 0) \{ ... \}
-066          */
-067         iy = MIN(a->used-tx, ty+1);
-068
-069         /* execute loop */
-070         for (iz = 0; iz < iy; ++iz) \{
-071            _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
-072
-073         \}
-074
-075         /* store term */
-076         W[ix] = ((mp_digit)_W) & MP_MASK;
-077
-078         /* make next carry */
-079         _W = _W >> ((mp_word)DIGIT_BIT);
-080     \}
-081
-082     /* setup dest */
-083     olduse  = c->used;
-084     c->used = pa;
-085
-086     \{
-087       mp_digit *tmpc;
-088       tmpc = c->dp;
-089       for (ix = 0; ix < (pa + 1); ix++) \{
-090         /* now extract the previous digit [below the carry] */
-091         *tmpc++ = W[ix];
-092       \}
-093
-094       /* clear unused digits [that existed in the old copy of c] */
-095       for (; ix < olduse; ix++) \{
-096         *tmpc++ = 0;
-097       \}
-098     \}
-099     mp_clamp (c);
-100     return MP_OKAY;
-101   \}
-102   #endif
-103
-\end{alltt}
-\end{small}
-
-As per the pseudo--code we first calculate $pa$ (line 47) as the number of digits to output.  Next we begin the outer loop
-to produce the individual columns of the product.  We use the two aliases $tmpx$ and $tmpy$ (lines 61, 62) to point
-inside the two multiplicands quickly.
-
-The inner loop (lines 70 to 73) of this implementation is where the tradeoff come into play.  Originally this comba
-implementation was ``row--major'' which means it adds to each of the columns in each pass.  After the outer loop it would then fix
-the carries.  This was very fast except it had an annoying drawback.  You had to read a mp\_word and two mp\_digits and write
-one mp\_word per iteration.  On processors such as the Athlon XP and P4 this did not matter much since the cache bandwidth
-is very high and it can keep the ALU fed with data.  It did, however, matter on older and embedded cpus where cache is often
-slower and also often doesn't exist.  This new algorithm only performs two reads per iteration under the assumption that the
-compiler has aliased $\_ \hat W$ to a CPU register.
-
-After the inner loop we store the current accumulator in $W$ and shift $\_ \hat W$ (lines 76, 79) to forward it as
-a carry for the next pass.  After the outer loop we use the final carry (line 76) as the last digit of the product.
-
-\subsection{Polynomial Basis Multiplication}
-To break the $O(n^2)$ barrier in multiplication requires a completely different look at integer multiplication.  In the following algorithms
-the use of polynomial basis representation for two integers $a$ and $b$ as $f(x) = \sum_{i=0}^{n} a_i x^i$ and
-$g(x) = \sum_{i=0}^{n} b_i x^i$ respectively, is required.  In this system both $f(x)$ and $g(x)$ have $n + 1$ terms and are of the $n$'th degree.
-
-The product $a \cdot b \equiv f(x)g(x)$ is the polynomial $W(x) = \sum_{i=0}^{2n} w_i x^i$.  The coefficients $w_i$ will
-directly yield the desired product when $\beta$ is substituted for $x$.  The direct solution to solve for the $2n + 1$ coefficients
-requires $O(n^2)$ time and would in practice be slower than the Comba technique.
-
-However, numerical analysis theory indicates that only $2n + 1$ distinct points in $W(x)$ are required to determine the values of the $2n + 1$ unknown
-coefficients.   This means by finding $\zeta_y = W(y)$ for $2n + 1$ small values of $y$ the coefficients of $W(x)$ can be found with
-Gaussian elimination.  This technique is also occasionally refered to as the \textit{interpolation technique} (\textit{references please...}) since in
-effect an interpolation based on $2n + 1$ points will yield a polynomial equivalent to $W(x)$.
-
-The coefficients of the polynomial $W(x)$ are unknown which makes finding $W(y)$ for any value of $y$ impossible.  However, since
-$W(x) = f(x)g(x)$ the equivalent $\zeta_y = f(y) g(y)$ can be used in its place.  The benefit of this technique stems from the
-fact that $f(y)$ and $g(y)$ are much smaller than either $a$ or $b$ respectively.  As a result finding the $2n + 1$ relations required
-by multiplying $f(y)g(y)$ involves multiplying integers that are much smaller than either of the inputs.
-
-When picking points to gather relations there are always three obvious points to choose, $y = 0, 1$ and $ \infty$.  The $\zeta_0$ term
-is simply the product $W(0) = w_0 = a_0 \cdot b_0$.  The $\zeta_1$ term is the product
-$W(1) = \left (\sum_{i = 0}^{n} a_i \right ) \left (\sum_{i = 0}^{n} b_i \right )$.  The third point $\zeta_{\infty}$ is less obvious but rather
-simple to explain.  The $2n + 1$'th coefficient of $W(x)$ is numerically equivalent to the most significant column in an integer multiplication.
-The point at $\infty$ is used symbolically to represent the most significant column, that is $W(\infty) = w_{2n} = a_nb_n$.  Note that the
-points at $y = 0$ and $\infty$ yield the coefficients $w_0$ and $w_{2n}$ directly.
-
-If more points are required they should be of small values and powers of two such as $2^q$ and the related \textit{mirror points}
-$\left (2^q \right )^{2n}  \cdot \zeta_{2^{-q}}$ for small values of $q$.  The term ``mirror point'' stems from the fact that
-$\left (2^q \right )^{2n}  \cdot \zeta_{2^{-q}}$ can be calculated in the exact opposite fashion as $\zeta_{2^q}$.  For
-example, when $n = 2$ and $q = 1$ then following two equations are equivalent to the point $\zeta_{2}$ and its mirror.
-
-\begin{eqnarray}
-\zeta_{2}                  = f(2)g(2) = (4a_2 + 2a_1 + a_0)(4b_2 + 2b_1 + b_0) \nonumber \\
-16 \cdot \zeta_{1 \over 2} = 4f({1\over 2}) \cdot 4g({1 \over 2}) = (a_2 + 2a_1 + 4a_0)(b_2 + 2b_1 + 4b_0)
-\end{eqnarray}
-
-Using such points will allow the values of $f(y)$ and $g(y)$ to be independently calculated using only left shifts.  For example, when $n = 2$ the
-polynomial $f(2^q)$ is equal to $2^q((2^qa_2) + a_1) + a_0$.  This technique of polynomial representation is known as Horner's method.
-
-As a general rule of the algorithm when the inputs are split into $n$ parts each there are $2n - 1$ multiplications.  Each multiplication is of
-multiplicands that have $n$ times fewer digits than the inputs.  The asymptotic running time of this algorithm is
-$O \left ( k^{lg_n(2n - 1)} \right )$ for $k$ digit inputs (\textit{assuming they have the same number of digits}).  Figure~\ref{fig:exponent}
-summarizes the exponents for various values of $n$.
-
-\begin{figure}
-\begin{center}
-\begin{tabular}{|c|c|c|}
-\hline \textbf{Split into $n$ Parts} & \textbf{Exponent}  & \textbf{Notes}\\
-\hline $2$ & $1.584962501$ & This is Karatsuba Multiplication. \\
-\hline $3$ & $1.464973520$ & This is Toom-Cook Multiplication. \\
-\hline $4$ & $1.403677461$ &\\
-\hline $5$ & $1.365212389$ &\\
-\hline $10$ & $1.278753601$ &\\
-\hline $100$ & $1.149426538$ &\\
-\hline $1000$ & $1.100270931$ &\\
-\hline $10000$ & $1.075252070$ &\\
-\hline
-\end{tabular}
-\end{center}
-\caption{Asymptotic Running Time of Polynomial Basis Multiplication}
-\label{fig:exponent}
-\end{figure}
-
-At first it may seem like a good idea to choose $n = 1000$ since the exponent is approximately $1.1$.  However, the overhead
-of solving for the 2001 terms of $W(x)$ will certainly consume any savings the algorithm could offer for all but exceedingly large
-numbers.
-
-\subsubsection{Cutoff Point}
-The polynomial basis multiplication algorithms all require fewer single precision multiplications than a straight Comba approach.  However,
-the algorithms incur an overhead (\textit{at the $O(n)$ work level}) since they require a system of equations to be solved.  This makes the
-polynomial basis approach more costly to use with small inputs.
-
-Let $m$ represent the number of digits in the multiplicands (\textit{assume both multiplicands have the same number of digits}).  There exists a
-point $y$ such that when $m < y$ the polynomial basis algorithms are more costly than Comba, when $m = y$ they are roughly the same cost and
-when $m > y$ the Comba methods are slower than the polynomial basis algorithms.
-
-The exact location of $y$ depends on several key architectural elements of the computer platform in question.
-
-\begin{enumerate}
-\item  The ratio of clock cycles for single precision multiplication versus other simpler operations such as addition, shifting, etc.  For example
-on the AMD Athlon the ratio is roughly $17 : 1$ while on the Intel P4 it is $29 : 1$.  The higher the ratio in favour of multiplication the lower
-the cutoff point $y$ will be.
-
-\item  The complexity of the linear system of equations (\textit{for the coefficients of $W(x)$}) is.  Generally speaking as the number of splits
-grows the complexity grows substantially.  Ideally solving the system will only involve addition, subtraction and shifting of integers.  This
-directly reflects on the ratio previous mentioned.
-
-\item  To a lesser extent memory bandwidth and function call overheads.  Provided the values are in the processor cache this is less of an
-influence over the cutoff point.
-
-\end{enumerate}
-
-A clean cutoff point separation occurs when a point $y$ is found such that all of the cutoff point conditions are met.  For example, if the point
-is too low then there will be values of $m$ such that $m > y$ and the Comba method is still faster.  Finding the cutoff points is fairly simple when
-a high resolution timer is available.
-
-\subsection{Karatsuba Multiplication}
-Karatsuba \cite{KARA} multiplication when originally proposed in 1962 was among the first set of algorithms to break the $O(n^2)$ barrier for
-general purpose multiplication.  Given two polynomial basis representations $f(x) = ax + b$ and $g(x) = cx + d$, Karatsuba proved with
-light algebra \cite{KARAP} that the following polynomial is equivalent to multiplication of the two integers the polynomials represent.
-
-\begin{equation}
-f(x) \cdot g(x) = acx^2 + ((a + b)(c + d) - (ac + bd))x + bd
-\end{equation}
-
-Using the observation that $ac$ and $bd$ could be re-used only three half sized multiplications would be required to produce the product.  Applying
-this algorithm recursively, the work factor becomes $O(n^{lg(3)})$ which is substantially better than the work factor $O(n^2)$ of the Comba technique.  It turns
-out what Karatsuba did not know or at least did not publish was that this is simply polynomial basis multiplication with the points
-$\zeta_0$, $\zeta_{\infty}$ and $\zeta_{1}$.  Consider the resultant system of equations.
-
-\begin{center}
-\begin{tabular}{rcrcrcrc}
-$\zeta_{0}$ &      $=$ &  &  &  & & $w_0$ \\
-$\zeta_{1}$ &      $=$ & $w_2$ & $+$ & $w_1$ & $+$ & $w_0$ \\
-$\zeta_{\infty}$ & $=$ & $w_2$ &  & &  & \\
-\end{tabular}
-\end{center}
-
-By adding the first and last equation to the equation in the middle the term $w_1$ can be isolated and all three coefficients solved for.  The simplicity
-of this system of equations has made Karatsuba fairly popular.  In fact the cutoff point is often fairly low\footnote{With LibTomMath 0.18 it is 70 and 109 digits for the Intel P4 and AMD Athlon respectively.}
-making it an ideal algorithm to speed up certain public key cryptosystems such as RSA and Diffie-Hellman.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_karatsuba\_mul}. \\
-\textbf{Input}.   mp\_int $a$ and mp\_int $b$ \\
-\textbf{Output}.  $c \leftarrow \vert a \vert \cdot \vert b \vert$ \\
-\hline \\
-1.  Init the following mp\_int variables: $x0$, $x1$, $y0$, $y1$, $t1$, $x0y0$, $x1y1$.\\
-2.  If step 2 failed then return(\textit{MP\_MEM}). \\
-\\
-Split the input.  e.g. $a = x1 \cdot \beta^B + x0$ \\
-3.  $B \leftarrow \mbox{min}(a.used, b.used)/2$ \\
-4.  $x0 \leftarrow a \mbox{ (mod }\beta^B\mbox{)}$ (\textit{mp\_mod\_2d}) \\
-5.  $y0 \leftarrow b \mbox{ (mod }\beta^B\mbox{)}$ \\
-6.  $x1 \leftarrow \lfloor a / \beta^B \rfloor$ (\textit{mp\_rshd}) \\
-7.  $y1 \leftarrow \lfloor b / \beta^B \rfloor$ \\
-\\
-Calculate the three products. \\
-8.  $x0y0 \leftarrow x0 \cdot y0$ (\textit{mp\_mul}) \\
-9.  $x1y1 \leftarrow x1 \cdot y1$ \\
-10.  $t1 \leftarrow x1 + x0$ (\textit{mp\_add}) \\
-11.  $x0 \leftarrow y1 + y0$ \\
-12.  $t1 \leftarrow t1 \cdot x0$ \\
-\\
-Calculate the middle term. \\
-13.  $x0 \leftarrow x0y0 + x1y1$ \\
-14.  $t1 \leftarrow t1 - x0$ (\textit{s\_mp\_sub}) \\
-\\
-Calculate the final product. \\
-15.  $t1 \leftarrow t1 \cdot \beta^B$ (\textit{mp\_lshd}) \\
-16.  $x1y1 \leftarrow x1y1 \cdot \beta^{2B}$ \\
-17.  $t1 \leftarrow x0y0 + t1$ \\
-18.  $c \leftarrow t1 + x1y1$ \\
-19.  Clear all of the temporary variables. \\
-20.  Return(\textit{MP\_OKAY}).\\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_karatsuba\_mul}
-\end{figure}
-
-\textbf{Algorithm mp\_karatsuba\_mul.}
-This algorithm computes the unsigned product of two inputs using the Karatsuba multiplication algorithm.  It is loosely based on the description
-from Knuth \cite[pp. 294-295]{TAOCPV2}.
-
-\index{radix point}
-In order to split the two inputs into their respective halves, a suitable \textit{radix point} must be chosen.  The radix point chosen must
-be used for both of the inputs meaning that it must be smaller than the smallest input.  Step 3 chooses the radix point $B$ as half of the
-smallest input \textbf{used} count.  After the radix point is chosen the inputs are split into lower and upper halves.  Step 4 and 5
-compute the lower halves.  Step 6 and 7 computer the upper halves.
-
-After the halves have been computed the three intermediate half-size products must be computed.  Step 8 and 9 compute the trivial products
-$x0 \cdot y0$ and $x1 \cdot y1$.  The mp\_int $x0$ is used as a temporary variable after $x1 + x0$ has been computed.  By using $x0$ instead
-of an additional temporary variable, the algorithm can avoid an addition memory allocation operation.
-
-The remaining steps 13 through 18 compute the Karatsuba polynomial through a variety of digit shifting and addition operations.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_karatsuba\_mul.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* c = |a| * |b| using Karatsuba Multiplication using
-018    * three half size multiplications
-019    *
-020    * Let B represent the radix [e.g. 2**DIGIT_BIT] and
-021    * let n represent half of the number of digits in
-022    * the min(a,b)
-023    *
-024    * a = a1 * B**n + a0
-025    * b = b1 * B**n + b0
-026    *
-027    * Then, a * b =>
-028      a1b1 * B**2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B + a0b0
-029    *
-030    * Note that a1b1 and a0b0 are used twice and only need to be
-031    * computed once.  So in total three half size (half # of
-032    * digit) multiplications are performed, a0b0, a1b1 and
-033    * (a1+b1)(a0+b0)
-034    *
-035    * Note that a multiplication of half the digits requires
-036    * 1/4th the number of single precision multiplications so in
-037    * total after one call 25% of the single precision multiplications
-038    * are saved.  Note also that the call to mp_mul can end up back
-039    * in this function if the a0, a1, b0, or b1 are above the threshold.
-040    * This is known as divide-and-conquer and leads to the famous
-041    * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than
-042    * the standard O(N**2) that the baseline/comba methods use.
-043    * Generally though the overhead of this method doesn't pay off
-044    * until a certain size (N ~ 80) is reached.
-045    */
-046   int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
-047   \{
-048     mp_int  x0, x1, y0, y1, t1, x0y0, x1y1;
-049     int     B, err;
-050
-051     /* default the return code to an error */
-052     err = MP_MEM;
-053
-054     /* min # of digits */
-055     B = MIN (a->used, b->used);
-056
-057     /* now divide in two */
-058     B = B >> 1;
-059
-060     /* init copy all the temps */
-061     if (mp_init_size (&x0, B) != MP_OKAY)
-062       goto ERR;
-063     if (mp_init_size (&x1, a->used - B) != MP_OKAY)
-064       goto X0;
-065     if (mp_init_size (&y0, B) != MP_OKAY)
-066       goto X1;
-067     if (mp_init_size (&y1, b->used - B) != MP_OKAY)
-068       goto Y0;
-069
-070     /* init temps */
-071     if (mp_init_size (&t1, B * 2) != MP_OKAY)
-072       goto Y1;
-073     if (mp_init_size (&x0y0, B * 2) != MP_OKAY)
-074       goto T1;
-075     if (mp_init_size (&x1y1, B * 2) != MP_OKAY)
-076       goto X0Y0;
-077
-078     /* now shift the digits */
-079     x0.used = y0.used = B;
-080     x1.used = a->used - B;
-081     y1.used = b->used - B;
-082
-083     \{
-084       int x;
-085       mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
-086
-087       /* we copy the digits directly instead of using higher level functions
-088        * since we also need to shift the digits
-089        */
-090       tmpa = a->dp;
-091       tmpb = b->dp;
-092
-093       tmpx = x0.dp;
-094       tmpy = y0.dp;
-095       for (x = 0; x < B; x++) \{
-096         *tmpx++ = *tmpa++;
-097         *tmpy++ = *tmpb++;
-098       \}
-099
-100       tmpx = x1.dp;
-101       for (x = B; x < a->used; x++) \{
-102         *tmpx++ = *tmpa++;
-103       \}
-104
-105       tmpy = y1.dp;
-106       for (x = B; x < b->used; x++) \{
-107         *tmpy++ = *tmpb++;
-108       \}
-109     \}
-110
-111     /* only need to clamp the lower words since by definition the
-112      * upper words x1/y1 must have a known number of digits
-113      */
-114     mp_clamp (&x0);
-115     mp_clamp (&y0);
-116
-117     /* now calc the products x0y0 and x1y1 */
-118     /* after this x0 is no longer required, free temp [x0==t2]! */
-119     if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)
-120       goto X1Y1;          /* x0y0 = x0*y0 */
-121     if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
-122       goto X1Y1;          /* x1y1 = x1*y1 */
-123
-124     /* now calc x1+x0 and y1+y0 */
-125     if (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
-126       goto X1Y1;          /* t1 = x1 - x0 */
-127     if (s_mp_add (&y1, &y0, &x0) != MP_OKAY)
-128       goto X1Y1;          /* t2 = y1 - y0 */
-129     if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
-130       goto X1Y1;          /* t1 = (x1 + x0) * (y1 + y0) */
-131
-132     /* add x0y0 */
-133     if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
-134       goto X1Y1;          /* t2 = x0y0 + x1y1 */
-135     if (s_mp_sub (&t1, &x0, &t1) != MP_OKAY)
-136       goto X1Y1;          /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
-137
-138     /* shift by B */
-139     if (mp_lshd (&t1, B) != MP_OKAY)
-140       goto X1Y1;          /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
-141     if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
-142       goto X1Y1;          /* x1y1 = x1y1 << 2*B */
-143
-144     if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
-145       goto X1Y1;          /* t1 = x0y0 + t1 */
-146     if (mp_add (&t1, &x1y1, c) != MP_OKAY)
-147       goto X1Y1;          /* t1 = x0y0 + t1 + x1y1 */
-148
-149     /* Algorithm succeeded set the return code to MP_OKAY */
-150     err = MP_OKAY;
-151
-152   X1Y1:mp_clear (&x1y1);
-153   X0Y0:mp_clear (&x0y0);
-154   T1:mp_clear (&t1);
-155   Y1:mp_clear (&y1);
-156   Y0:mp_clear (&y0);
-157   X1:mp_clear (&x1);
-158   X0:mp_clear (&x0);
-159   ERR:
-160     return err;
-161   \}
-162   #endif
-163
-\end{alltt}
-\end{small}
-
-The new coding element in this routine, not  seen in previous routines, is the usage of goto statements.  The conventional
-wisdom is that goto statements should be avoided.  This is generally true, however when every single function call can fail, it makes sense
-to handle error recovery with a single piece of code.  Lines 61 to 75 handle initializing all of the temporary variables
-required.  Note how each of the if statements goes to a different label in case of failure.  This allows the routine to correctly free only
-the temporaries that have been successfully allocated so far.
-
-The temporary variables are all initialized using the mp\_init\_size routine since they are expected to be large.  This saves the
-additional reallocation that would have been necessary.  Also $x0$, $x1$, $y0$ and $y1$ have to be able to hold at least their respective
-number of digits for the next section of code.
-
-The first algebraic portion of the algorithm is to split the two inputs into their halves.  However, instead of using mp\_mod\_2d and mp\_rshd
-to extract the halves, the respective code has been placed inline within the body of the function.  To initialize the halves, the \textbf{used} and
-\textbf{sign} members are copied first.  The first for loop on line 101 copies the lower halves.  Since they are both the same magnitude it
-is simpler to calculate both lower halves in a single loop.  The for loop on lines 106 and 106 calculate the upper halves $x1$ and
-$y1$ respectively.
-
-By inlining the calculation of the halves, the Karatsuba multiplier has a slightly lower overhead and can be used for smaller magnitude inputs.
-
-When line 150 is reached, the algorithm has completed succesfully.  The ``error status'' variable $err$ is set to \textbf{MP\_OKAY} so that
-the same code that handles errors can be used to clear the temporary variables and return.
-
-\subsection{Toom-Cook $3$-Way Multiplication}
-Toom-Cook $3$-Way \cite{TOOM} multiplication is essentially the polynomial basis algorithm for $n = 2$ except that the points  are
-chosen such that $\zeta$ is easy to compute and the resulting system of equations easy to reduce.  Here, the points $\zeta_{0}$,
-$16 \cdot \zeta_{1 \over 2}$, $\zeta_1$, $\zeta_2$ and $\zeta_{\infty}$ make up the five required points to solve for the coefficients
-of the $W(x)$.
-
-With the five relations that Toom-Cook specifies, the following system of equations is formed.
-
-\begin{center}
-\begin{tabular}{rcrcrcrcrcr}
-$\zeta_0$                    & $=$ & $0w_4$ & $+$ & $0w_3$ & $+$ & $0w_2$ & $+$ & $0w_1$ & $+$ & $1w_0$  \\
-$16 \cdot \zeta_{1 \over 2}$ & $=$ & $1w_4$ & $+$ & $2w_3$ & $+$ & $4w_2$ & $+$ & $8w_1$ & $+$ & $16w_0$  \\
-$\zeta_1$                    & $=$ & $1w_4$ & $+$ & $1w_3$ & $+$ & $1w_2$ & $+$ & $1w_1$ & $+$ & $1w_0$  \\
-$\zeta_2$                    & $=$ & $16w_4$ & $+$ & $8w_3$ & $+$ & $4w_2$ & $+$ & $2w_1$ & $+$ & $1w_0$  \\
-$\zeta_{\infty}$             & $=$ & $1w_4$ & $+$ & $0w_3$ & $+$ & $0w_2$ & $+$ & $0w_1$ & $+$ & $0w_0$  \\
-\end{tabular}
-\end{center}
-
-A trivial solution to this matrix requires $12$ subtractions, two multiplications by a small power of two, two divisions by a small power
-of two, two divisions by three and one multiplication by three.  All of these $19$ sub-operations require less than quadratic time, meaning that
-the algorithm can be faster than a baseline multiplication.  However, the greater complexity of this algorithm places the cutoff point
-(\textbf{TOOM\_MUL\_CUTOFF}) where Toom-Cook becomes more efficient much higher than the Karatsuba cutoff point.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_toom\_mul}. \\
-\textbf{Input}.   mp\_int $a$ and mp\_int $b$ \\
-\textbf{Output}.  $c \leftarrow  a  \cdot  b $ \\
-\hline \\
-Split $a$ and $b$ into three pieces.  E.g. $a = a_2 \beta^{2k} + a_1 \beta^{k} + a_0$ \\
-1.  $k \leftarrow \lfloor \mbox{min}(a.used, b.used) / 3 \rfloor$ \\
-2.  $a_0 \leftarrow a \mbox{ (mod }\beta^{k}\mbox{)}$ \\
-3.  $a_1 \leftarrow \lfloor a / \beta^k \rfloor$, $a_1 \leftarrow a_1 \mbox{ (mod }\beta^{k}\mbox{)}$ \\
-4.  $a_2 \leftarrow \lfloor a / \beta^{2k} \rfloor$, $a_2 \leftarrow a_2 \mbox{ (mod }\beta^{k}\mbox{)}$ \\
-5.  $b_0 \leftarrow a \mbox{ (mod }\beta^{k}\mbox{)}$ \\
-6.  $b_1 \leftarrow \lfloor a / \beta^k \rfloor$, $b_1 \leftarrow b_1 \mbox{ (mod }\beta^{k}\mbox{)}$ \\
-7.  $b_2 \leftarrow \lfloor a / \beta^{2k} \rfloor$, $b_2 \leftarrow b_2 \mbox{ (mod }\beta^{k}\mbox{)}$ \\
-\\
-Find the five equations for $w_0, w_1, ..., w_4$. \\
-8.  $w_0 \leftarrow a_0 \cdot b_0$ \\
-9.  $w_4 \leftarrow a_2 \cdot b_2$ \\
-10. $tmp_1 \leftarrow 2 \cdot a_0$, $tmp_1 \leftarrow a_1 + tmp_1$, $tmp_1 \leftarrow 2 \cdot tmp_1$, $tmp_1 \leftarrow tmp_1 + a_2$ \\
-11. $tmp_2 \leftarrow 2 \cdot b_0$, $tmp_2 \leftarrow b_1 + tmp_2$, $tmp_2 \leftarrow 2 \cdot tmp_2$, $tmp_2 \leftarrow tmp_2 + b_2$ \\
-12. $w_1 \leftarrow tmp_1 \cdot tmp_2$ \\
-13. $tmp_1 \leftarrow 2 \cdot a_2$, $tmp_1 \leftarrow a_1 + tmp_1$, $tmp_1 \leftarrow 2 \cdot tmp_1$, $tmp_1 \leftarrow tmp_1 + a_0$ \\
-14. $tmp_2 \leftarrow 2 \cdot b_2$, $tmp_2 \leftarrow b_1 + tmp_2$, $tmp_2 \leftarrow 2 \cdot tmp_2$, $tmp_2 \leftarrow tmp_2 + b_0$ \\
-15. $w_3 \leftarrow tmp_1 \cdot tmp_2$ \\
-16. $tmp_1 \leftarrow a_0 + a_1$, $tmp_1 \leftarrow tmp_1 + a_2$, $tmp_2 \leftarrow b_0 + b_1$, $tmp_2 \leftarrow tmp_2 + b_2$ \\
-17. $w_2 \leftarrow tmp_1 \cdot tmp_2$ \\
-\\
-Continued on the next page.\\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_toom\_mul}
-\end{figure}
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_toom\_mul} (continued). \\
-\textbf{Input}.   mp\_int $a$ and mp\_int $b$ \\
-\textbf{Output}.  $c \leftarrow a \cdot  b $ \\
-\hline \\
-Now solve the system of equations. \\
-18. $w_1 \leftarrow w_4 - w_1$, $w_3 \leftarrow w_3 - w_0$ \\
-19. $w_1 \leftarrow \lfloor w_1 / 2 \rfloor$, $w_3 \leftarrow \lfloor w_3 / 2 \rfloor$ \\
-20. $w_2 \leftarrow w_2 - w_0$, $w_2 \leftarrow w_2 - w_4$ \\
-21. $w_1 \leftarrow w_1 - w_2$, $w_3 \leftarrow w_3 - w_2$ \\
-22. $tmp_1 \leftarrow 8 \cdot w_0$, $w_1 \leftarrow w_1 - tmp_1$, $tmp_1 \leftarrow 8 \cdot w_4$, $w_3 \leftarrow w_3 - tmp_1$ \\
-23. $w_2 \leftarrow 3 \cdot w_2$, $w_2 \leftarrow w_2 - w_1$, $w_2 \leftarrow w_2 - w_3$ \\
-24. $w_1 \leftarrow w_1 - w_2$, $w_3 \leftarrow w_3 - w_2$ \\
-25. $w_1 \leftarrow \lfloor w_1 / 3 \rfloor, w_3 \leftarrow \lfloor w_3 / 3 \rfloor$ \\
-\\
-Now substitute $\beta^k$ for $x$ by shifting $w_0, w_1, ..., w_4$. \\
-26. for $n$ from $1$ to $4$ do \\
-\hspace{3mm}26.1  $w_n \leftarrow w_n \cdot \beta^{nk}$ \\
-27. $c \leftarrow w_0 + w_1$, $c \leftarrow c + w_2$, $c \leftarrow c + w_3$, $c \leftarrow c + w_4$ \\
-28. Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_toom\_mul (continued)}
-\end{figure}
-
-\textbf{Algorithm mp\_toom\_mul.}
-This algorithm computes the product of two mp\_int variables $a$ and $b$ using the Toom-Cook approach.  Compared to the Karatsuba multiplication, this
-algorithm has a lower asymptotic running time of approximately $O(n^{1.464})$ but at an obvious cost in overhead.  In this
-description, several statements have been compounded to save space.  The intention is that the statements are executed from left to right across
-any given step.
-
-The two inputs $a$ and $b$ are first split into three $k$-digit integers $a_0, a_1, a_2$ and $b_0, b_1, b_2$ respectively.  From these smaller
-integers the coefficients of the polynomial basis representations $f(x)$ and $g(x)$ are known and can be used to find the relations required.
-
-The first two relations $w_0$ and $w_4$ are the points $\zeta_{0}$ and $\zeta_{\infty}$ respectively.  The relation $w_1, w_2$ and $w_3$ correspond
-to the points $16 \cdot \zeta_{1 \over 2}, \zeta_{2}$ and $\zeta_{1}$ respectively.  These are found using logical shifts to independently find
-$f(y)$ and $g(y)$ which significantly speeds up the algorithm.
-
-After the five relations $w_0, w_1, \ldots, w_4$ have been computed, the system they represent must be solved in order for the unknown coefficients
-$w_1, w_2$ and $w_3$ to be isolated.  The steps 18 through 25 perform the system reduction required as previously described.  Each step of
-the reduction represents the comparable matrix operation that would be performed had this been performed by pencil.  For example, step 18 indicates
-that row $1$ must be subtracted from row $4$ and simultaneously row $0$ subtracted from row $3$.
-
-Once the coeffients have been isolated, the polynomial $W(x) = \sum_{i=0}^{2n} w_i x^i$ is known.  By substituting $\beta^{k}$ for $x$, the integer
-result $a \cdot b$ is produced.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_toom\_mul.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* multiplication using the Toom-Cook 3-way algorithm
-018    *
-019    * Much more complicated than Karatsuba but has a lower
-020    * asymptotic running time of O(N**1.464).  This algorithm is
-021    * only particularly useful on VERY large inputs
-022    * (we're talking 1000s of digits here...).
-023   */
-024   int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
-025   \{
-026       mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
-027       int res, B;
-028
-029       /* init temps */
-030       if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
-031                                &a0, &a1, &a2, &b0, &b1,
-032                                &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) \{
-033          return res;
-034       \}
-035
-036       /* B */
-037       B = MIN(a->used, b->used) / 3;
-038
-039       /* a = a2 * B**2 + a1 * B + a0 */
-040       if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) \{
-041          goto ERR;
-042       \}
-043
-044       if ((res = mp_copy(a, &a1)) != MP_OKAY) \{
-045          goto ERR;
-046       \}
-047       mp_rshd(&a1, B);
-048       if ((res = mp_mod_2d(&a1, DIGIT_BIT * B, &a1)) != MP_OKAY) \{
-049          goto ERR;
-050       \}
-051
-052       if ((res = mp_copy(a, &a2)) != MP_OKAY) \{
-053          goto ERR;
-054       \}
-055       mp_rshd(&a2, B*2);
-056
-057       /* b = b2 * B**2 + b1 * B + b0 */
-058       if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) \{
-059          goto ERR;
-060       \}
-061
-062       if ((res = mp_copy(b, &b1)) != MP_OKAY) \{
-063          goto ERR;
-064       \}
-065       mp_rshd(&b1, B);
-066       (void)mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
-067
-068       if ((res = mp_copy(b, &b2)) != MP_OKAY) \{
-069          goto ERR;
-070       \}
-071       mp_rshd(&b2, B*2);
-072
-073       /* w0 = a0*b0 */
-074       if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) \{
-075          goto ERR;
-076       \}
-077
-078       /* w4 = a2 * b2 */
-079       if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) \{
-080          goto ERR;
-081       \}
-082
-083       /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
-084       if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) \{
-085          goto ERR;
-086       \}
-087       if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) \{
-088          goto ERR;
-089       \}
-090       if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) \{
-091          goto ERR;
-092       \}
-093       if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) \{
-094          goto ERR;
-095       \}
-096
-097       if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) \{
-098          goto ERR;
-099       \}
-100       if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) \{
-101          goto ERR;
-102       \}
-103       if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) \{
-104          goto ERR;
-105       \}
-106       if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) \{
-107          goto ERR;
-108       \}
-109
-110       if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) \{
-111          goto ERR;
-112       \}
-113
-114       /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
-115       if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) \{
-116          goto ERR;
-117       \}
-118       if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) \{
-119          goto ERR;
-120       \}
-121       if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) \{
-122          goto ERR;
-123       \}
-124       if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) \{
-125          goto ERR;
-126       \}
-127
-128       if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) \{
-129          goto ERR;
-130       \}
-131       if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) \{
-132          goto ERR;
-133       \}
-134       if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) \{
-135          goto ERR;
-136       \}
-137       if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) \{
-138          goto ERR;
-139       \}
-140
-141       if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) \{
-142          goto ERR;
-143       \}
-144
-145
-146       /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
-147       if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) \{
-148          goto ERR;
-149       \}
-150       if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) \{
-151          goto ERR;
-152       \}
-153       if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) \{
-154          goto ERR;
-155       \}
-156       if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) \{
-157          goto ERR;
-158       \}
-159       if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) \{
-160          goto ERR;
-161       \}
-162
-163       /* now solve the matrix
-164
-165          0  0  0  0  1
-166          1  2  4  8  16
-167          1  1  1  1  1
-168          16 8  4  2  1
-169          1  0  0  0  0
-170
-171          using 12 subtractions, 4 shifts,
-172                 2 small divisions and 1 small multiplication
-173        */
-174
-175       /* r1 - r4 */
-176       if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) \{
-177          goto ERR;
-178       \}
-179       /* r3 - r0 */
-180       if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) \{
-181          goto ERR;
-182       \}
-183       /* r1/2 */
-184       if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) \{
-185          goto ERR;
-186       \}
-187       /* r3/2 */
-188       if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) \{
-189          goto ERR;
-190       \}
-191       /* r2 - r0 - r4 */
-192       if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) \{
-193          goto ERR;
-194       \}
-195       if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) \{
-196          goto ERR;
-197       \}
-198       /* r1 - r2 */
-199       if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) \{
-200          goto ERR;
-201       \}
-202       /* r3 - r2 */
-203       if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) \{
-204          goto ERR;
-205       \}
-206       /* r1 - 8r0 */
-207       if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) \{
-208          goto ERR;
-209       \}
-210       if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) \{
-211          goto ERR;
-212       \}
-213       /* r3 - 8r4 */
-214       if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) \{
-215          goto ERR;
-216       \}
-217       if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) \{
-218          goto ERR;
-219       \}
-220       /* 3r2 - r1 - r3 */
-221       if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) \{
-222          goto ERR;
-223       \}
-224       if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) \{
-225          goto ERR;
-226       \}
-227       if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) \{
-228          goto ERR;
-229       \}
-230       /* r1 - r2 */
-231       if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) \{
-232          goto ERR;
-233       \}
-234       /* r3 - r2 */
-235       if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) \{
-236          goto ERR;
-237       \}
-238       /* r1/3 */
-239       if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) \{
-240          goto ERR;
-241       \}
-242       /* r3/3 */
-243       if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) \{
-244          goto ERR;
-245       \}
-246
-247       /* at this point shift W[n] by B*n */
-248       if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) \{
-249          goto ERR;
-250       \}
-251       if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) \{
-252          goto ERR;
-253       \}
-254       if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) \{
-255          goto ERR;
-256       \}
-257       if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) \{
-258          goto ERR;
-259       \}
-260
-261       if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) \{
-262          goto ERR;
-263       \}
-264       if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) \{
-265          goto ERR;
-266       \}
-267       if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) \{
-268          goto ERR;
-269       \}
-270       if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) \{
-271          goto ERR;
-272       \}
-273
-274   ERR:
-275       mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
-276                      &a0, &a1, &a2, &b0, &b1,
-277                      &b2, &tmp1, &tmp2, NULL);
-278       return res;
-279   \}
-280
-281   #endif
-282
-\end{alltt}
-\end{small}
-
-The first obvious thing to note is that this algorithm is complicated.  The complexity is worth it if you are multiplying very
-large numbers.  For example, a 10,000 digit multiplication takes approximaly 99,282,205 fewer single precision multiplications with
-Toom--Cook than a Comba or baseline approach (this is a savings of more than 99$\%$).  For most ``crypto'' sized numbers this
-algorithm is not practical as Karatsuba has a much lower cutoff point.
-
-First we split $a$ and $b$ into three roughly equal portions.  This has been accomplished (lines 40 to 71) with
-combinations of mp\_rshd() and mp\_mod\_2d() function calls.  At this point $a = a2 \cdot \beta^2 + a1 \cdot \beta + a0$ and similiarly
-for $b$.
-
-Next we compute the five points $w0, w1, w2, w3$ and $w4$.  Recall that $w0$ and $w4$ can be computed directly from the portions so
-we get those out of the way first (lines 74 and 79).  Next we compute $w1, w2$ and $w3$ using Horners method.
-
-After this point we solve for the actual values of $w1, w2$ and $w3$ by reducing the $5 \times 5$ system which is relatively
-straight forward.
-
-\subsection{Signed Multiplication}
-Now that algorithms to handle multiplications of every useful dimensions have been developed, a rather simple finishing touch is required.  So far all
-of the multiplication algorithms have been unsigned multiplications which leaves only a signed multiplication algorithm to be established.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_mul}. \\
-\textbf{Input}.   mp\_int $a$ and mp\_int $b$ \\
-\textbf{Output}.  $c \leftarrow a \cdot b$ \\
-\hline \\
-1.  If $a.sign = b.sign$ then \\
-\hspace{3mm}1.1  $sign = MP\_ZPOS$ \\
-2.  else \\
-\hspace{3mm}2.1  $sign = MP\_ZNEG$ \\
-3.  If min$(a.used, b.used) \ge TOOM\_MUL\_CUTOFF$ then  \\
-\hspace{3mm}3.1  $c \leftarrow a \cdot b$ using algorithm mp\_toom\_mul \\
-4.  else if min$(a.used, b.used) \ge KARATSUBA\_MUL\_CUTOFF$ then \\
-\hspace{3mm}4.1  $c \leftarrow a \cdot b$ using algorithm mp\_karatsuba\_mul \\
-5.  else \\
-\hspace{3mm}5.1  $digs \leftarrow a.used + b.used + 1$ \\
-\hspace{3mm}5.2  If $digs < MP\_ARRAY$ and min$(a.used, b.used) \le \delta$ then \\
-\hspace{6mm}5.2.1  $c \leftarrow a \cdot b \mbox{ (mod }\beta^{digs}\mbox{)}$ using algorithm fast\_s\_mp\_mul\_digs.  \\
-\hspace{3mm}5.3  else \\
-\hspace{6mm}5.3.1  $c \leftarrow a \cdot b \mbox{ (mod }\beta^{digs}\mbox{)}$ using algorithm s\_mp\_mul\_digs.  \\
-6.  $c.sign \leftarrow sign$ \\
-7.  Return the result of the unsigned multiplication performed. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_mul}
-\end{figure}
-
-\textbf{Algorithm mp\_mul.}
-This algorithm performs the signed multiplication of two inputs.  It will make use of any of the three unsigned multiplication algorithms
-available when the input is of appropriate size.  The \textbf{sign} of the result is not set until the end of the algorithm since algorithm
-s\_mp\_mul\_digs will clear it.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_mul.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* high level multiplication (handles sign) */
-018   int mp_mul (mp_int * a, mp_int * b, mp_int * c)
-019   \{
-020     int     res, neg;
-021     neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
-022
-023     /* use Toom-Cook? */
-024   #ifdef BN_MP_TOOM_MUL_C
-025     if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) \{
-026       res = mp_toom_mul(a, b, c);
-027     \} else
-028   #endif
-029   #ifdef BN_MP_KARATSUBA_MUL_C
-030     /* use Karatsuba? */
-031     if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) \{
-032       res = mp_karatsuba_mul (a, b, c);
-033     \} else
-034   #endif
-035     \{
-036       /* can we use the fast multiplier?
-037        *
-038        * The fast multiplier can be used if the output will
-039        * have less than MP_WARRAY digits and the number of
-040        * digits won't affect carry propagation
-041        */
-042       int     digs = a->used + b->used + 1;
-043
-044   #ifdef BN_FAST_S_MP_MUL_DIGS_C
-045       if ((digs < MP_WARRAY) &&
-046           (MIN(a->used, b->used) <=
-047            (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) \{
-048         res = fast_s_mp_mul_digs (a, b, c, digs);
-049       \} else
-050   #endif
-051       \{
-052   #ifdef BN_S_MP_MUL_DIGS_C
-053         res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
-054   #else
-055         res = MP_VAL;
-056   #endif
-057       \}
-058     \}
-059     c->sign = (c->used > 0) ? neg : MP_ZPOS;
-060     return res;
-061   \}
-062   #endif
-063
-\end{alltt}
-\end{small}
-
-The implementation is rather simplistic and is not particularly noteworthy.  Line 23 computes the sign of the result using the ``?''
-operator from the C programming language.  Line 47 computes $\delta$ using the fact that $1 << k$ is equal to $2^k$.
-
-\section{Squaring}
-\label{sec:basesquare}
-
-Squaring is a special case of multiplication where both multiplicands are equal.  At first it may seem like there is no significant optimization
-available but in fact there is.  Consider the multiplication of $576$ against $241$.  In total there will be nine single precision multiplications
-performed which are $1\cdot 6$, $1 \cdot 7$, $1 \cdot 5$, $4 \cdot 6$, $4 \cdot 7$, $4 \cdot 5$, $2 \cdot  6$, $2 \cdot 7$ and $2 \cdot 5$.  Now consider
-the multiplication of $123$ against $123$.  The nine products are $3 \cdot 3$, $3 \cdot 2$, $3 \cdot 1$, $2 \cdot 3$, $2 \cdot 2$, $2 \cdot 1$,
-$1 \cdot 3$, $1 \cdot 2$ and $1 \cdot 1$.  On closer inspection some of the products are equivalent.  For example, $3 \cdot 2 = 2 \cdot 3$
-and $3 \cdot 1 = 1 \cdot 3$.
-
-For any $n$-digit input, there are ${{\left (n^2 + n \right)}\over 2}$ possible unique single precision multiplications required compared to the $n^2$
-required for multiplication.  The following diagram gives an example of the operations required.
-
-\begin{figure}[here]
-\begin{center}
-\begin{tabular}{ccccc|c}
-&&1&2&3&\\
-$\times$ &&1&2&3&\\
-\hline && $3 \cdot 1$ & $3 \cdot 2$ & $3 \cdot 3$ & Row 0\\
-       & $2 \cdot 1$  & $2 \cdot 2$ & $2 \cdot 3$ && Row 1 \\
-         $1 \cdot 1$  & $1 \cdot 2$ & $1 \cdot 3$ &&& Row 2 \\
-\end{tabular}
-\end{center}
-\caption{Squaring Optimization Diagram}
-\end{figure}
-
-Starting from zero and numbering the columns from right to left a very simple pattern becomes obvious.  For the purposes of this discussion let $x$
-represent the number being squared.  The first observation is that in row $k$ the $2k$'th column of the product has a $\left (x_k \right)^2$ term in it.
-
-The second observation is that every column $j$ in row $k$ where $j \ne 2k$ is part of a double product.  Every non-square term of a column will
-appear twice hence the name ``double product''.  Every odd column is made up entirely of double products.  In fact every column is made up of double
-products and at most one square (\textit{see the exercise section}).
-
-The third and final observation is that for row $k$ the first unique non-square term, that is, one that hasn't already appeared in an earlier row,
-occurs at column $2k + 1$.  For example, on row $1$ of the previous squaring, column one is part of the double product with column one from row zero.
-Column two of row one is a square and column three is the first unique column.
-
-\subsection{The Baseline Squaring Algorithm}
-The baseline squaring algorithm is meant to be a catch-all squaring algorithm.  It will handle any of the input sizes that the faster routines
-will not handle.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{s\_mp\_sqr}. \\
-\textbf{Input}.   mp\_int $a$ \\
-\textbf{Output}.  $b \leftarrow a^2$ \\
-\hline \\
-1.  Init a temporary mp\_int of at least $2 \cdot a.used +1$ digits.  (\textit{mp\_init\_size}) \\
-2.  If step 1 failed return(\textit{MP\_MEM}) \\
-3.  $t.used \leftarrow 2 \cdot a.used + 1$ \\
-4.  For $ix$ from 0 to $a.used - 1$ do \\
-\hspace{3mm}Calculate the square. \\
-\hspace{3mm}4.1  $\hat r \leftarrow t_{2ix} + \left (a_{ix} \right )^2$ \\
-\hspace{3mm}4.2  $t_{2ix} \leftarrow \hat r \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{3mm}Calculate the double products after the square. \\
-\hspace{3mm}4.3  $u \leftarrow \lfloor \hat r / \beta \rfloor$ \\
-\hspace{3mm}4.4  For $iy$ from $ix + 1$ to $a.used - 1$ do \\
-\hspace{6mm}4.4.1  $\hat r \leftarrow 2 \cdot a_{ix}a_{iy} + t_{ix + iy} + u$ \\
-\hspace{6mm}4.4.2  $t_{ix + iy} \leftarrow \hat r \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{6mm}4.4.3  $u \leftarrow \lfloor \hat r / \beta \rfloor$ \\
-\hspace{3mm}Set the last carry. \\
-\hspace{3mm}4.5  While $u > 0$ do \\
-\hspace{6mm}4.5.1  $iy \leftarrow iy + 1$ \\
-\hspace{6mm}4.5.2  $\hat r \leftarrow t_{ix + iy} + u$ \\
-\hspace{6mm}4.5.3  $t_{ix + iy} \leftarrow \hat r \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{6mm}4.5.4  $u \leftarrow \lfloor \hat r / \beta \rfloor$ \\
-5.  Clamp excess digits of $t$.  (\textit{mp\_clamp}) \\
-6.  Exchange $b$ and $t$. \\
-7.  Clear $t$ (\textit{mp\_clear}) \\
-8.  Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm s\_mp\_sqr}
-\end{figure}
-
-\textbf{Algorithm s\_mp\_sqr.}
-This algorithm computes the square of an input using the three observations on squaring.  It is based fairly faithfully on  algorithm 14.16 of HAC
-\cite[pp.596-597]{HAC}.  Similar to algorithm s\_mp\_mul\_digs, a temporary mp\_int is allocated to hold the result of the squaring.  This allows the
-destination mp\_int to be the same as the source mp\_int.
-
-The outer loop of this algorithm begins on step 4. It is best to think of the outer loop as walking down the rows of the partial results, while
-the inner loop computes the columns of the partial result.  Step 4.1 and 4.2 compute the square term for each row, and step 4.3 and 4.4 propagate
-the carry and compute the double products.
-
-The requirement that a mp\_word be able to represent the range $0 \le x < 2 \beta^2$ arises from this
-very algorithm.  The product $a_{ix}a_{iy}$ will lie in the range $0 \le x \le \beta^2 - 2\beta + 1$ which is obviously less than $\beta^2$ meaning that
-when it is multiplied by two, it can be properly represented by a mp\_word.
-
-Similar to algorithm s\_mp\_mul\_digs, after every pass of the inner loop, the destination is correctly set to the sum of all of the partial
-results calculated so far.  This involves expensive carry propagation which will be eliminated in the next algorithm.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_s\_mp\_sqr.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
-018   int s_mp_sqr (mp_int * a, mp_int * b)
-019   \{
-020     mp_int  t;
-021     int     res, ix, iy, pa;
-022     mp_word r;
-023     mp_digit u, tmpx, *tmpt;
-024
-025     pa = a->used;
-026     if ((res = mp_init_size (&t, (2 * pa) + 1)) != MP_OKAY) \{
-027       return res;
-028     \}
-029
-030     /* default used is maximum possible size */
-031     t.used = (2 * pa) + 1;
-032
-033     for (ix = 0; ix < pa; ix++) \{
-034       /* first calculate the digit at 2*ix */
-035       /* calculate double precision result */
-036       r = (mp_word)t.dp[2*ix] +
-037           ((mp_word)a->dp[ix] * (mp_word)a->dp[ix]);
-038
-039       /* store lower part in result */
-040       t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
-041
-042       /* get the carry */
-043       u           = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
-044
-045       /* left hand side of A[ix] * A[iy] */
-046       tmpx        = a->dp[ix];
-047
-048       /* alias for where to store the results */
-049       tmpt        = t.dp + ((2 * ix) + 1);
-050
-051       for (iy = ix + 1; iy < pa; iy++) \{
-052         /* first calculate the product */
-053         r       = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
-054
-055         /* now calculate the double precision result, note we use
-056          * addition instead of *2 since it's easier to optimize
-057          */
-058         r       = ((mp_word) *tmpt) + r + r + ((mp_word) u);
-059
-060         /* store lower part */
-061         *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
-062
-063         /* get carry */
-064         u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
-065       \}
-066       /* propagate upwards */
-067       while (u != ((mp_digit) 0)) \{
-068         r       = ((mp_word) *tmpt) + ((mp_word) u);
-069         *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
-070         u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
-071       \}
-072     \}
-073
-074     mp_clamp (&t);
-075     mp_exch (&t, b);
-076     mp_clear (&t);
-077     return MP_OKAY;
-078   \}
-079   #endif
-080
-\end{alltt}
-\end{small}
-
-Inside the outer loop (line 33) the square term is calculated on line 36.  The carry (line 43) has been
-extracted from the mp\_word accumulator using a right shift.  Aliases for $a_{ix}$ and $t_{ix+iy}$ are initialized
-(lines 46 and 49) to simplify the inner loop.  The doubling is performed using two
-additions (line 58) since it is usually faster than shifting, if not at least as fast.
-
-The important observation is that the inner loop does not begin at $iy = 0$ like for multiplication.  As such the inner loops
-get progressively shorter as the algorithm proceeds.  This is what leads to the savings compared to using a multiplication to
-square a number.
-
-\subsection{Faster Squaring by the ``Comba'' Method}
-A major drawback to the baseline method is the requirement for single precision shifting inside the $O(n^2)$ nested loop.  Squaring has an additional
-drawback that it must double the product inside the inner loop as well.  As for multiplication, the Comba technique can be used to eliminate these
-performance hazards.
-
-The first obvious solution is to make an array of mp\_words which will hold all of the columns.  This will indeed eliminate all of the carry
-propagation operations from the inner loop.  However, the inner product must still be doubled $O(n^2)$ times.  The solution stems from the simple fact
-that $2a + 2b + 2c = 2(a + b + c)$.  That is the sum of all of the double products is equal to double the sum of all the products.  For example,
-$ab + ba + ac + ca = 2ab + 2ac = 2(ab + ac)$.
-
-However, we cannot simply double all of the columns, since the squares appear only once per row.  The most practical solution is to have two
-mp\_word arrays.  One array will hold the squares and the other array will hold the double products.  With both arrays the doubling and
-carry propagation can be moved to a $O(n)$ work level outside the $O(n^2)$ level.  In this case, we have an even simpler solution in mind.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{fast\_s\_mp\_sqr}. \\
-\textbf{Input}.   mp\_int $a$ \\
-\textbf{Output}.  $b \leftarrow a^2$ \\
-\hline \\
-Place an array of \textbf{MP\_WARRAY} mp\_digits named $W$ on the stack. \\
-1.  If $b.alloc < 2a.used + 1$ then grow $b$ to $2a.used + 1$ digits.  (\textit{mp\_grow}). \\
-2.  If step 1 failed return(\textit{MP\_MEM}). \\
-\\
-3.  $pa \leftarrow 2 \cdot a.used$ \\
-4.  $\hat W1 \leftarrow 0$ \\
-5.  for $ix$ from $0$ to $pa - 1$ do \\
-\hspace{3mm}5.1  $\_ \hat W \leftarrow 0$ \\
-\hspace{3mm}5.2  $ty \leftarrow \mbox{MIN}(a.used - 1, ix)$ \\
-\hspace{3mm}5.3  $tx \leftarrow ix - ty$ \\
-\hspace{3mm}5.4  $iy \leftarrow \mbox{MIN}(a.used - tx, ty + 1)$ \\
-\hspace{3mm}5.5  $iy \leftarrow \mbox{MIN}(iy, \lfloor \left (ty - tx + 1 \right )/2 \rfloor)$ \\
-\hspace{3mm}5.6  for $iz$ from $0$ to $iz - 1$ do \\
-\hspace{6mm}5.6.1  $\_ \hat W \leftarrow \_ \hat W + a_{tx + iz}a_{ty - iz}$ \\
-\hspace{3mm}5.7  $\_ \hat W \leftarrow 2 \cdot \_ \hat W  + \hat W1$ \\
-\hspace{3mm}5.8  if $ix$ is even then \\
-\hspace{6mm}5.8.1  $\_ \hat W \leftarrow \_ \hat W + \left ( a_{\lfloor ix/2 \rfloor}\right )^2$ \\
-\hspace{3mm}5.9  $W_{ix} \leftarrow \_ \hat W (\mbox{mod }\beta)$ \\
-\hspace{3mm}5.10  $\hat W1 \leftarrow \lfloor \_ \hat W / \beta \rfloor$ \\
-\\
-6.  $oldused \leftarrow b.used$ \\
-7.  $b.used \leftarrow 2 \cdot a.used$ \\
-8.  for $ix$ from $0$ to $pa - 1$ do \\
-\hspace{3mm}8.1  $b_{ix} \leftarrow W_{ix}$ \\
-9.  for $ix$ from $pa$ to $oldused - 1$ do \\
-\hspace{3mm}9.1  $b_{ix} \leftarrow 0$ \\
-10.  Clamp excess digits from $b$.  (\textit{mp\_clamp}) \\
-11.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm fast\_s\_mp\_sqr}
-\end{figure}
-
-\textbf{Algorithm fast\_s\_mp\_sqr.}
-This algorithm computes the square of an input using the Comba technique.  It is designed to be a replacement for algorithm
-s\_mp\_sqr when the number of input digits is less than \textbf{MP\_WARRAY} and less than $\delta \over 2$.
-This algorithm is very similar to the Comba multiplier except with a few key differences we shall make note of.
-
-First, we have an accumulator and carry variables $\_ \hat W$ and $\hat W1$ respectively.  This is because the inner loop
-products are to be doubled.  If we had added the previous carry in we would be doubling too much.  Next we perform an
-addition MIN condition on $iy$ (step 5.5) to prevent overlapping digits.  For example, $a_3 \cdot a_5$ is equal
-$a_5 \cdot a_3$.  Whereas in the multiplication case we would have $5 < a.used$ and $3 \ge 0$ is maintained since we double the sum
-of the products just outside the inner loop we have to avoid doing this.  This is also a good thing since we perform
-fewer multiplications and the routine ends up being faster.
-
-Finally the last difference is the addition of the ``square'' term outside the inner loop (step 5.8).  We add in the square
-only to even outputs and it is the square of the term at the $\lfloor ix / 2 \rfloor$ position.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_fast\_s\_mp\_sqr.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* the jist of squaring...
-018    * you do like mult except the offset of the tmpx [one that
-019    * starts closer to zero] can't equal the offset of tmpy.
-020    * So basically you set up iy like before then you min it with
-021    * (ty-tx) so that it never happens.  You double all those
-022    * you add in the inner loop
-023
-024   After that loop you do the squares and add them in.
-025   */
-026
-027   int fast_s_mp_sqr (mp_int * a, mp_int * b)
-028   \{
-029     int       olduse, res, pa, ix, iz;
-030     mp_digit   W[MP_WARRAY], *tmpx;
-031     mp_word   W1;
-032
-033     /* grow the destination as required */
-034     pa = a->used + a->used;
-035     if (b->alloc < pa) \{
-036       if ((res = mp_grow (b, pa)) != MP_OKAY) \{
-037         return res;
-038       \}
-039     \}
-040
-041     /* number of output digits to produce */
-042     W1 = 0;
-043     for (ix = 0; ix < pa; ix++) \{
-044         int      tx, ty, iy;
-045         mp_word  _W;
-046         mp_digit *tmpy;
-047
-048         /* clear counter */
-049         _W = 0;
-050
-051         /* get offsets into the two bignums */
-052         ty = MIN(a->used-1, ix);
-053         tx = ix - ty;
-054
-055         /* setup temp aliases */
-056         tmpx = a->dp + tx;
-057         tmpy = a->dp + ty;
-058
-059         /* this is the number of times the loop will iterrate, essentially
-060            while (tx++ < a->used && ty-- >= 0) \{ ... \}
-061          */
-062         iy = MIN(a->used-tx, ty+1);
-063
-064         /* now for squaring tx can never equal ty
-065          * we halve the distance since they approach at a rate of 2x
-066          * and we have to round because odd cases need to be executed
-067          */
-068         iy = MIN(iy, ((ty-tx)+1)>>1);
-069
-070         /* execute loop */
-071         for (iz = 0; iz < iy; iz++) \{
-072            _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
-073         \}
-074
-075         /* double the inner product and add carry */
-076         _W = _W + _W + W1;
-077
-078         /* even columns have the square term in them */
-079         if ((ix&1) == 0) \{
-080            _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
-081         \}
-082
-083         /* store it */
-084         W[ix] = (mp_digit)(_W & MP_MASK);
-085
-086         /* make next carry */
-087         W1 = _W >> ((mp_word)DIGIT_BIT);
-088     \}
-089
-090     /* setup dest */
-091     olduse  = b->used;
-092     b->used = a->used+a->used;
-093
-094     \{
-095       mp_digit *tmpb;
-096       tmpb = b->dp;
-097       for (ix = 0; ix < pa; ix++) \{
-098         *tmpb++ = W[ix] & MP_MASK;
-099       \}
-100
-101       /* clear unused digits [that existed in the old copy of c] */
-102       for (; ix < olduse; ix++) \{
-103         *tmpb++ = 0;
-104       \}
-105     \}
-106     mp_clamp (b);
-107     return MP_OKAY;
-108   \}
-109   #endif
-110
-\end{alltt}
-\end{small}
-
-This implementation is essentially a copy of Comba multiplication with the appropriate changes added to make it faster for
-the special case of squaring.
-
-\subsection{Polynomial Basis Squaring}
-The same algorithm that performs optimal polynomial basis multiplication can be used to perform polynomial basis squaring.  The minor exception
-is that $\zeta_y = f(y)g(y)$ is actually equivalent to $\zeta_y = f(y)^2$ since $f(y) = g(y)$.  Instead of performing $2n + 1$
-multiplications to find the $\zeta$ relations, squaring operations are performed instead.
-
-\subsection{Karatsuba Squaring}
-Let $f(x) = ax + b$ represent the polynomial basis representation of a number to square.
-Let $h(x) = \left ( f(x) \right )^2$ represent the square of the polynomial.  The Karatsuba equation can be modified to square a
-number with the following equation.
-
-\begin{equation}
-h(x) = a^2x^2 + \left ((a + b)^2 - (a^2 + b^2) \right )x + b^2
-\end{equation}
-
-Upon closer inspection this equation only requires the calculation of three half-sized squares: $a^2$, $b^2$ and $(a + b)^2$.  As in
-Karatsuba multiplication, this algorithm can be applied recursively on the input and will achieve an asymptotic running time of
-$O \left ( n^{lg(3)} \right )$.
-
-If the asymptotic times of Karatsuba squaring and multiplication are the same, why not simply use the multiplication algorithm
-instead?  The answer to this arises from the cutoff point for squaring.  As in multiplication there exists a cutoff point, at which the
-time required for a Comba based squaring and a Karatsuba based squaring meet.  Due to the overhead inherent in the Karatsuba method, the cutoff
-point is fairly high.  For example, on an AMD Athlon XP processor with $\beta = 2^{28}$, the cutoff point is around 127 digits.
-
-Consider squaring a 200 digit number with this technique.  It will be split into two 100 digit halves which are subsequently squared.
-The 100 digit halves will not be squared using Karatsuba, but instead using the faster Comba based squaring algorithm.  If Karatsuba multiplication
-were used instead, the 100 digit numbers would be squared with a slower Comba based multiplication.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_karatsuba\_sqr}. \\
-\textbf{Input}.   mp\_int $a$ \\
-\textbf{Output}.  $b \leftarrow a^2$ \\
-\hline \\
-1.  Initialize the following temporary mp\_ints:  $x0$, $x1$, $t1$, $t2$, $x0x0$ and $x1x1$. \\
-2.  If any of the initializations on step 1 failed return(\textit{MP\_MEM}). \\
-\\
-Split the input.  e.g. $a = x1\beta^B + x0$ \\
-3.  $B \leftarrow \lfloor a.used / 2 \rfloor$ \\
-4.  $x0 \leftarrow a \mbox{ (mod }\beta^B\mbox{)}$ (\textit{mp\_mod\_2d}) \\
-5.  $x1 \leftarrow \lfloor a / \beta^B \rfloor$ (\textit{mp\_lshd}) \\
-\\
-Calculate the three squares. \\
-6.  $x0x0 \leftarrow x0^2$ (\textit{mp\_sqr}) \\
-7.  $x1x1 \leftarrow x1^2$ \\
-8.  $t1 \leftarrow x1 + x0$ (\textit{s\_mp\_add}) \\
-9.  $t1 \leftarrow t1^2$ \\
-\\
-Compute the middle term. \\
-10.  $t2 \leftarrow x0x0 + x1x1$ (\textit{s\_mp\_add}) \\
-11.  $t1 \leftarrow t1 - t2$ \\
-\\
-Compute final product. \\
-12.  $t1 \leftarrow t1\beta^B$ (\textit{mp\_lshd}) \\
-13.  $x1x1 \leftarrow x1x1\beta^{2B}$ \\
-14.  $t1 \leftarrow t1 + x0x0$ \\
-15.  $b \leftarrow t1 + x1x1$ \\
-16.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_karatsuba\_sqr}
-\end{figure}
-
-\textbf{Algorithm mp\_karatsuba\_sqr.}
-This algorithm computes the square of an input $a$ using the Karatsuba technique.  This algorithm is very similar to the Karatsuba based
-multiplication algorithm with the exception that the three half-size multiplications have been replaced with three half-size squarings.
-
-The radix point for squaring is simply placed exactly in the middle of the digits when the input has an odd number of digits, otherwise it is
-placed just below the middle.  Step 3, 4 and 5 compute the two halves required using $B$
-as the radix point.  The first two squares in steps 6 and 7 are rather straightforward while the last square is of a more compact form.
-
-By expanding $\left (x1 + x0 \right )^2$, the $x1^2$ and $x0^2$ terms in the middle disappear, that is $(x0 - x1)^2 - (x1^2 + x0^2)  = 2 \cdot x0 \cdot x1$.
-Now if $5n$ single precision additions and a squaring of $n$-digits is faster than multiplying two $n$-digit numbers and doubling then
-this method is faster.  Assuming no further recursions occur, the difference can be estimated with the following inequality.
-
-Let $p$ represent the cost of a single precision addition and $q$ the cost of a single precision multiplication both in terms of time\footnote{Or
-machine clock cycles.}.
-
-\begin{equation}
-5pn +{{q(n^2 + n)} \over 2} \le pn + qn^2
-\end{equation}
-
-For example, on an AMD Athlon XP processor $p = {1 \over 3}$ and $q = 6$.  This implies that the following inequality should hold.
-\begin{center}
-\begin{tabular}{rcl}
-${5n \over 3} + 3n^2 + 3n$     & $<$ & ${n \over 3} + 6n^2$ \\
-${5 \over 3} + 3n + 3$     & $<$ & ${1 \over 3} + 6n$ \\
-${13 \over 9}$     & $<$ & $n$ \\
-\end{tabular}
-\end{center}
-
-This results in a cutoff point around $n = 2$.  As a consequence it is actually faster to compute the middle term the ``long way'' on processors
-where multiplication is substantially slower\footnote{On the Athlon there is a 1:17 ratio between clock cycles for addition and multiplication.  On
-the Intel P4 processor this ratio is 1:29 making this method even more beneficial.  The only common exception is the ARMv4 processor which has a
-ratio of 1:7.  } than simpler operations such as addition.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_karatsuba\_sqr.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* Karatsuba squaring, computes b = a*a using three
-018    * half size squarings
-019    *
-020    * See comments of karatsuba_mul for details.  It
-021    * is essentially the same algorithm but merely
-022    * tuned to perform recursive squarings.
-023    */
-024   int mp_karatsuba_sqr (mp_int * a, mp_int * b)
-025   \{
-026     mp_int  x0, x1, t1, t2, x0x0, x1x1;
-027     int     B, err;
-028
-029     err = MP_MEM;
-030
-031     /* min # of digits */
-032     B = a->used;
-033
-034     /* now divide in two */
-035     B = B >> 1;
-036
-037     /* init copy all the temps */
-038     if (mp_init_size (&x0, B) != MP_OKAY)
-039       goto ERR;
-040     if (mp_init_size (&x1, a->used - B) != MP_OKAY)
-041       goto X0;
-042
-043     /* init temps */
-044     if (mp_init_size (&t1, a->used * 2) != MP_OKAY)
-045       goto X1;
-046     if (mp_init_size (&t2, a->used * 2) != MP_OKAY)
-047       goto T1;
-048     if (mp_init_size (&x0x0, B * 2) != MP_OKAY)
-049       goto T2;
-050     if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY)
-051       goto X0X0;
-052
-053     \{
-054       int x;
-055       mp_digit *dst, *src;
-056
-057       src = a->dp;
-058
-059       /* now shift the digits */
-060       dst = x0.dp;
-061       for (x = 0; x < B; x++) \{
-062         *dst++ = *src++;
-063       \}
-064
-065       dst = x1.dp;
-066       for (x = B; x < a->used; x++) \{
-067         *dst++ = *src++;
-068       \}
-069     \}
-070
-071     x0.used = B;
-072     x1.used = a->used - B;
-073
-074     mp_clamp (&x0);
-075
-076     /* now calc the products x0*x0 and x1*x1 */
-077     if (mp_sqr (&x0, &x0x0) != MP_OKAY)
-078       goto X1X1;           /* x0x0 = x0*x0 */
-079     if (mp_sqr (&x1, &x1x1) != MP_OKAY)
-080       goto X1X1;           /* x1x1 = x1*x1 */
-081
-082     /* now calc (x1+x0)**2 */
-083     if (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
-084       goto X1X1;           /* t1 = x1 - x0 */
-085     if (mp_sqr (&t1, &t1) != MP_OKAY)
-086       goto X1X1;           /* t1 = (x1 - x0) * (x1 - x0) */
-087
-088     /* add x0y0 */
-089     if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY)
-090       goto X1X1;           /* t2 = x0x0 + x1x1 */
-091     if (s_mp_sub (&t1, &t2, &t1) != MP_OKAY)
-092       goto X1X1;           /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */
-093
-094     /* shift by B */
-095     if (mp_lshd (&t1, B) != MP_OKAY)
-096       goto X1X1;           /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */
-097     if (mp_lshd (&x1x1, B * 2) != MP_OKAY)
-098       goto X1X1;           /* x1x1 = x1x1 << 2*B */
-099
-100     if (mp_add (&x0x0, &t1, &t1) != MP_OKAY)
-101       goto X1X1;           /* t1 = x0x0 + t1 */
-102     if (mp_add (&t1, &x1x1, b) != MP_OKAY)
-103       goto X1X1;           /* t1 = x0x0 + t1 + x1x1 */
-104
-105     err = MP_OKAY;
-106
-107   X1X1:mp_clear (&x1x1);
-108   X0X0:mp_clear (&x0x0);
-109   T2:mp_clear (&t2);
-110   T1:mp_clear (&t1);
-111   X1:mp_clear (&x1);
-112   X0:mp_clear (&x0);
-113   ERR:
-114     return err;
-115   \}
-116   #endif
-117
-\end{alltt}
-\end{small}
-
-This implementation is largely based on the implementation of algorithm mp\_karatsuba\_mul.  It uses the same inline style to copy and
-shift the input into the two halves.  The loop from line 53 to line 69 has been modified since only one input exists.  The \textbf{used}
-count of both $x0$ and $x1$ is fixed up and $x0$ is clamped before the calculations begin.  At this point $x1$ and $x0$ are valid equivalents
-to the respective halves as if mp\_rshd and mp\_mod\_2d had been used.
-
-By inlining the copy and shift operations the cutoff point for Karatsuba multiplication can be lowered.  On the Athlon the cutoff point
-is exactly at the point where Comba squaring can no longer be used (\textit{128 digits}).  On slower processors such as the Intel P4
-it is actually below the Comba limit (\textit{at 110 digits}).
-
-This routine uses the same error trap coding style as mp\_karatsuba\_sqr.  As the temporary variables are initialized errors are
-redirected to the error trap higher up.  If the algorithm completes without error the error code is set to \textbf{MP\_OKAY} and
-mp\_clears are executed normally.
-
-\subsection{Toom-Cook Squaring}
-The Toom-Cook squaring algorithm mp\_toom\_sqr is heavily based on the algorithm mp\_toom\_mul with the exception that squarings are used
-instead of multiplication to find the five relations.  The reader is encouraged to read the description of the latter algorithm and try to
-derive their own Toom-Cook squaring algorithm.
-
-\subsection{High Level Squaring}
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_sqr}. \\
-\textbf{Input}.   mp\_int $a$ \\
-\textbf{Output}.  $b \leftarrow a^2$ \\
-\hline \\
-1.  If $a.used \ge TOOM\_SQR\_CUTOFF$ then  \\
-\hspace{3mm}1.1  $b \leftarrow a^2$ using algorithm mp\_toom\_sqr \\
-2.  else if $a.used \ge KARATSUBA\_SQR\_CUTOFF$ then \\
-\hspace{3mm}2.1  $b \leftarrow a^2$ using algorithm mp\_karatsuba\_sqr \\
-3.  else \\
-\hspace{3mm}3.1  $digs \leftarrow a.used + b.used + 1$ \\
-\hspace{3mm}3.2  If $digs < MP\_ARRAY$ and $a.used \le \delta$ then \\
-\hspace{6mm}3.2.1  $b \leftarrow a^2$ using algorithm fast\_s\_mp\_sqr.  \\
-\hspace{3mm}3.3  else \\
-\hspace{6mm}3.3.1  $b \leftarrow a^2$ using algorithm s\_mp\_sqr.  \\
-4.  $b.sign \leftarrow MP\_ZPOS$ \\
-5.  Return the result of the unsigned squaring performed. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_sqr}
-\end{figure}
-
-\textbf{Algorithm mp\_sqr.}
-This algorithm computes the square of the input using one of four different algorithms.  If the input is very large and has at least
-\textbf{TOOM\_SQR\_CUTOFF} or \textbf{KARATSUBA\_SQR\_CUTOFF} digits then either the Toom-Cook or the Karatsuba Squaring algorithm is used.  If
-neither of the polynomial basis algorithms should be used then either the Comba or baseline algorithm is used.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_sqr.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* computes b = a*a */
-018   int
-019   mp_sqr (mp_int * a, mp_int * b)
-020   \{
-021     int     res;
-022
-023   #ifdef BN_MP_TOOM_SQR_C
-024     /* use Toom-Cook? */
-025     if (a->used >= TOOM_SQR_CUTOFF) \{
-026       res = mp_toom_sqr(a, b);
-027     /* Karatsuba? */
-028     \} else
-029   #endif
-030   #ifdef BN_MP_KARATSUBA_SQR_C
-031     if (a->used >= KARATSUBA_SQR_CUTOFF) \{
-032       res = mp_karatsuba_sqr (a, b);
-033     \} else
-034   #endif
-035     \{
-036   #ifdef BN_FAST_S_MP_SQR_C
-037       /* can we use the fast comba multiplier? */
-038       if ((((a->used * 2) + 1) < MP_WARRAY) &&
-039            (a->used <
-040            (1 << (((sizeof(mp_word) * CHAR_BIT) - (2 * DIGIT_BIT)) - 1)))) \{
-041         res = fast_s_mp_sqr (a, b);
-042       \} else
-043   #endif
-044       \{
-045   #ifdef BN_S_MP_SQR_C
-046         res = s_mp_sqr (a, b);
-047   #else
-048         res = MP_VAL;
-049   #endif
-050       \}
-051     \}
-052     b->sign = MP_ZPOS;
-053     return res;
-054   \}
-055   #endif
-056
-\end{alltt}
-\end{small}
-
-\section*{Exercises}
-\begin{tabular}{cl}
-$\left [ 3 \right ] $ & Devise an efficient algorithm for selection of the radix point to handle inputs \\
-                      & that have different number of digits in Karatsuba multiplication. \\
-                      & \\
-$\left [ 2 \right ] $ & In section 5.3 the fact that every column of a squaring is made up \\
-                      & of double products and at most one square is stated.  Prove this statement. \\
-                      & \\
-$\left [ 3 \right ] $ & Prove the equation for Karatsuba squaring. \\
-                      & \\
-$\left [ 1 \right ] $ & Prove that Karatsuba squaring requires $O \left (n^{lg(3)} \right )$ time. \\
-                      & \\
-$\left [ 2 \right ] $ & Determine the minimal ratio between addition and multiplication clock cycles \\
-                      & required for equation $6.7$ to be true.  \\
-                      & \\
-$\left [ 3 \right ] $ & Implement a threaded version of Comba multiplication (and squaring) where you \\
-                      & compute subsets of the columns in each thread.  Determine a cutoff point where \\
-                      & it is effective and add the logic to mp\_mul() and mp\_sqr(). \\
-                      &\\
-$\left [ 4 \right ] $ & Same as the previous but also modify the Karatsuba and Toom-Cook.  You must \\
-                      & increase the throughput of mp\_exptmod() for random odd moduli in the range \\
-                      & $512 \ldots 4096$ bits significantly ($> 2x$) to complete this challenge. \\
-                      & \\
-\end{tabular}
-
-\chapter{Modular Reduction}
-\section{Basics of Modular Reduction}
-\index{modular residue}
-Modular reduction is an operation that arises quite often within public key cryptography algorithms and various number theoretic algorithms,
-such as factoring.  Modular reduction algorithms are the third class of algorithms of the ``multipliers'' set.  A number $a$ is said to be \textit{reduced}
-modulo another number $b$ by finding the remainder of the division $a/b$.  Full integer division with remainder is a topic to be covered
-in~\ref{sec:division}.
-
-Modular reduction is equivalent to solving for $r$ in the following equation.  $a = bq + r$ where $q = \lfloor a/b \rfloor$.  The result
-$r$ is said to be ``congruent to $a$ modulo $b$'' which is also written as $r \equiv a \mbox{ (mod }b\mbox{)}$.  In other vernacular $r$ is known as the
-``modular residue'' which leads to ``quadratic residue''\footnote{That's fancy talk for $b \equiv a^2 \mbox{ (mod }p\mbox{)}$.} and
-other forms of residues.
-
-Modular reductions are normally used to create either finite groups, rings or fields.  The most common usage for performance driven modular reductions
-is in modular exponentiation algorithms.  That is to compute $d = a^b \mbox{ (mod }c\mbox{)}$ as fast as possible.  This operation is used in the
-RSA and Diffie-Hellman public key algorithms, for example.  Modular multiplication and squaring also appears as a fundamental operation in
-elliptic curve cryptographic algorithms.  As will be discussed in the subsequent chapter there exist fast algorithms for computing modular
-exponentiations without having to perform (\textit{in this example}) $b - 1$ multiplications.  These algorithms will produce partial results in the
-range $0 \le x < c^2$ which can be taken advantage of to create several efficient algorithms.   They have also been used to create redundancy check
-algorithms known as CRCs, error correction codes such as Reed-Solomon and solve a variety of number theoeretic problems.
-
-\section{The Barrett Reduction}
-The Barrett reduction algorithm \cite{BARRETT} was inspired by fast division algorithms which multiply by the reciprocal to emulate
-division.  Barretts observation was that the residue $c$ of $a$ modulo $b$ is equal to
-
-\begin{equation}
-c = a - b \cdot \lfloor a/b \rfloor
-\end{equation}
-
-Since algorithms such as modular exponentiation would be using the same modulus extensively, typical DSP\footnote{It is worth noting that Barrett's paper
-targeted the DSP56K processor.}  intuition would indicate the next step would be to replace $a/b$ by a multiplication by the reciprocal.  However,
-DSP intuition on its own will not work as these numbers are considerably larger than the precision of common DSP floating point data types.
-It would take another common optimization to optimize the algorithm.
-
-\subsection{Fixed Point Arithmetic}
-The trick used to optimize the above equation is based on a technique of emulating floating point data types with fixed precision integers.  Fixed
-point arithmetic would become very popular as it greatly optimize the ``3d-shooter'' genre of games in the mid 1990s when floating point units were
-fairly slow if not unavailable.   The idea behind fixed point arithmetic is to take a normal $k$-bit integer data type and break it into $p$-bit
-integer and a $q$-bit fraction part (\textit{where $p+q = k$}).
-
-In this system a $k$-bit integer $n$ would actually represent $n/2^q$.  For example, with $q = 4$ the integer $n = 37$ would actually represent the
-value $2.3125$.  To multiply two fixed point numbers the integers are multiplied using traditional arithmetic and subsequently normalized by
-moving the implied decimal point back to where it should be.  For example, with $q = 4$ to multiply the integers $9$ and $5$ they must be converted
-to fixed point first by multiplying by $2^q$.  Let $a = 9(2^q)$ represent the fixed point representation of $9$ and $b = 5(2^q)$ represent the
-fixed point representation of $5$.  The product $ab$ is equal to $45(2^{2q})$ which when normalized by dividing by $2^q$ produces $45(2^q)$.
-
-This technique became popular since a normal integer multiplication and logical shift right are the only required operations to perform a multiplication
-of two fixed point numbers.  Using fixed point arithmetic, division can be easily approximated by multiplying by the reciprocal.  If $2^q$ is
-equivalent to one than $2^q/b$ is equivalent to the fixed point approximation of $1/b$ using real arithmetic.  Using this fact dividing an integer
-$a$ by another integer $b$ can be achieved with the following expression.
-
-\begin{equation}
-\lfloor a / b \rfloor \mbox{ }\approx\mbox{ } \lfloor (a \cdot \lfloor 2^q / b \rfloor)/2^q \rfloor
-\end{equation}
-
-The precision of the division is proportional to the value of $q$.  If the divisor $b$ is used frequently as is the case with
-modular exponentiation pre-computing $2^q/b$ will allow a division to be performed with a multiplication and a right shift.  Both operations
-are considerably faster than division on most processors.
-
-Consider dividing $19$ by $5$.  The correct result is $\lfloor 19/5 \rfloor = 3$.  With $q = 3$ the reciprocal is $\lfloor 2^q/5 \rfloor = 1$ which
-leads to a product of $19$ which when divided by $2^q$ produces $2$.  However, with $q = 4$ the reciprocal is $\lfloor 2^q/5 \rfloor = 3$ and
-the result of the emulated division is $\lfloor 3 \cdot 19 / 2^q \rfloor = 3$ which is correct.  The value of $2^q$ must be close to or ideally
-larger than the dividend.  In effect if $a$ is the dividend then $q$ should allow $0 \le \lfloor a/2^q \rfloor \le 1$ in order for this approach
-to work correctly.  Plugging this form of divison into the original equation the following modular residue equation arises.
-
-\begin{equation}
-c = a - b \cdot \lfloor (a \cdot \lfloor 2^q / b \rfloor)/2^q \rfloor
-\end{equation}
-
-Using the notation from \cite{BARRETT} the value of $\lfloor 2^q / b \rfloor$ will be represented by the $\mu$ symbol.  Using the $\mu$
-variable also helps re-inforce the idea that it is meant to be computed once and re-used.
-
-\begin{equation}
-c = a - b \cdot \lfloor (a \cdot \mu)/2^q \rfloor
-\end{equation}
-
-Provided that $2^q \ge a$ this algorithm will produce a quotient that is either exactly correct or off by a value of one.  In the context of Barrett
-reduction the value of $a$ is bound by $0 \le a \le (b - 1)^2$ meaning that $2^q \ge b^2$ is sufficient to ensure the reciprocal will have enough
-precision.
-
-Let $n$ represent the number of digits in $b$.  This algorithm requires approximately $2n^2$ single precision multiplications to produce the quotient and
-another $n^2$ single precision multiplications to find the residue.  In total $3n^2$ single precision multiplications are required to
-reduce the number.
-
-For example, if $b = 1179677$ and $q = 41$ ($2^q > b^2$), then the reciprocal $\mu$ is equal to $\lfloor 2^q / b \rfloor = 1864089$.  Consider reducing
-$a = 180388626447$ modulo $b$ using the above reduction equation.  The quotient using the new formula is $\lfloor (a \cdot \mu) / 2^q \rfloor = 152913$.
-By subtracting $152913b$ from $a$ the correct residue $a \equiv 677346 \mbox{ (mod }b\mbox{)}$ is found.
-
-\subsection{Choosing a Radix Point}
-Using the fixed point representation a modular reduction can be performed with $3n^2$ single precision multiplications.  If that were the best
-that could be achieved a full division\footnote{A division requires approximately $O(2cn^2)$ single precision multiplications for a small value of $c$.
-See~\ref{sec:division} for further details.} might as well be used in its place.  The key to optimizing the reduction is to reduce the precision of
-the initial multiplication that finds the quotient.
-
-Let $a$ represent the number of which the residue is sought.  Let $b$ represent the modulus used to find the residue.  Let $m$ represent
-the number of digits in $b$.  For the purposes of this discussion we will assume that the number of digits in $a$ is $2m$, which is generally true if
-two $m$-digit numbers have been multiplied.  Dividing $a$ by $b$ is the same as dividing a $2m$ digit integer by a $m$ digit integer.  Digits below the
-$m - 1$'th digit of $a$ will contribute at most a value of $1$ to the quotient because $\beta^k < b$ for any $0 \le k \le m - 1$.  Another way to
-express this is by re-writing $a$ as two parts.  If $a' \equiv a \mbox{ (mod }b^m\mbox{)}$ and $a'' = a - a'$ then
-${a \over b} \equiv {{a' + a''} \over b}$ which is equivalent to ${a' \over b} + {a'' \over b}$.  Since $a'$ is bound to be less than $b$ the quotient
-is bound by $0 \le {a' \over b} < 1$.
-
-Since the digits of $a'$ do not contribute much to the quotient the observation is that they might as well be zero.  However, if the digits
-``might as well be zero'' they might as well not be there in the first place.  Let $q_0 = \lfloor a/\beta^{m-1} \rfloor$ represent the input
-with the irrelevant digits trimmed.  Now the modular reduction is trimmed to the almost equivalent equation
-
-\begin{equation}
-c = a - b \cdot \lfloor (q_0 \cdot \mu) / \beta^{m+1} \rfloor
-\end{equation}
-
-Note that the original divisor $2^q$ has been replaced with $\beta^{m+1}$ where in this case $q$ is a multiple of $lg(\beta)$. Also note that the
-exponent on the divisor when added to the amount $q_0$ was shifted by equals $2m$.  If the optimization had not been performed the divisor
-would have the exponent $2m$ so in the end the exponents do ``add up''. Using the above equation the quotient
-$\lfloor (q_0 \cdot \mu) / \beta^{m+1} \rfloor$ can be off from the true quotient by at most two.  The original fixed point quotient can be off
-by as much as one (\textit{provided the radix point is chosen suitably}) and now that the lower irrelevent digits have been trimmed the quotient
-can be off by an additional value of one for a total of at most two.  This implies that
-$0 \le a - b \cdot \lfloor (q_0 \cdot \mu) / \beta^{m+1} \rfloor < 3b$.  By first subtracting $b$ times the quotient and then conditionally subtracting
-$b$ once or twice the residue is found.
-
-The quotient is now found using $(m + 1)(m) = m^2 + m$ single precision multiplications and the residue with an additional $m^2$ single
-precision multiplications, ignoring the subtractions required.  In total $2m^2 + m$ single precision multiplications are required to find the residue.
-This is considerably faster than the original attempt.
-
-For example, let $\beta = 10$ represent the radix of the digits.  Let $b = 9999$ represent the modulus which implies $m = 4$. Let $a = 99929878$
-represent the value of which the residue is desired.  In this case $q = 8$ since $10^7 < 9999^2$ meaning that $\mu = \lfloor \beta^{q}/b \rfloor = 10001$.
-With the new observation the multiplicand for the quotient is equal to $q_0 = \lfloor a / \beta^{m - 1} \rfloor = 99929$.  The quotient is then
-$\lfloor (q_0 \cdot \mu) / \beta^{m+1} \rfloor = 9993$.  Subtracting $9993b$ from $a$ and the correct residue $a \equiv 9871 \mbox{ (mod }b\mbox{)}$
-is found.
-
-\subsection{Trimming the Quotient}
-So far the reduction algorithm has been optimized from $3m^2$ single precision multiplications down to $2m^2 + m$ single precision multiplications.  As
-it stands now the algorithm is already fairly fast compared to a full integer division algorithm.  However, there is still room for
-optimization.
-
-After the first multiplication inside the quotient ($q_0 \cdot \mu$) the value is shifted right by $m + 1$ places effectively nullifying the lower
-half of the product.  It would be nice to be able to remove those digits from the product to effectively cut down the number of single precision
-multiplications.  If the number of digits in the modulus $m$ is far less than $\beta$ a full product is not required for the algorithm to work properly.
-In fact the lower $m - 2$ digits will not affect the upper half of the product at all and do not need to be computed.
-
-The value of $\mu$ is a $m$-digit number and $q_0$ is a $m + 1$ digit number.  Using a full multiplier $(m + 1)(m) = m^2 + m$ single precision
-multiplications would be required.  Using a multiplier that will only produce digits at and above the $m - 1$'th digit reduces the number
-of single precision multiplications to ${m^2 + m} \over 2$ single precision multiplications.
-
-\subsection{Trimming the Residue}
-After the quotient has been calculated it is used to reduce the input.  As previously noted the algorithm is not exact and it can be off by a small
-multiple of the modulus, that is $0 \le a - b \cdot \lfloor (q_0 \cdot \mu) / \beta^{m+1} \rfloor < 3b$.  If $b$ is $m$ digits than the
-result of reduction equation is a value of at most $m + 1$ digits (\textit{provided $3 < \beta$}) implying that the upper $m - 1$ digits are
-implicitly zero.
-
-The next optimization arises from this very fact.  Instead of computing $b \cdot \lfloor (q_0 \cdot \mu) / \beta^{m+1} \rfloor$ using a full
-$O(m^2)$ multiplication algorithm only the lower $m+1$ digits of the product have to be computed.  Similarly the value of $a$ can
-be reduced modulo $\beta^{m+1}$ before the multiple of $b$ is subtracted which simplifes the subtraction as well.  A multiplication that produces
-only the lower $m+1$ digits requires ${m^2 + 3m - 2} \over 2$ single precision multiplications.
-
-With both optimizations in place the algorithm is the algorithm Barrett proposed.  It requires $m^2 + 2m - 1$ single precision multiplications which
-is considerably faster than the straightforward $3m^2$ method.
-
-\subsection{The Barrett Algorithm}
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_reduce}. \\
-\textbf{Input}.   mp\_int $a$, mp\_int $b$ and $\mu = \lfloor \beta^{2m}/b \rfloor, m = \lceil lg_{\beta}(b) \rceil, (0 \le a < b^2, b > 1)$ \\
-\textbf{Output}.  $a \mbox{ (mod }b\mbox{)}$ \\
-\hline \\
-Let $m$ represent the number of digits in $b$.  \\
-1.  Make a copy of $a$ and store it in $q$.  (\textit{mp\_init\_copy}) \\
-2.  $q \leftarrow \lfloor q / \beta^{m - 1} \rfloor$ (\textit{mp\_rshd}) \\
-\\
-Produce the quotient. \\
-3.  $q \leftarrow q \cdot \mu$  (\textit{note: only produce digits at or above $m-1$}) \\
-4.  $q \leftarrow \lfloor q / \beta^{m + 1} \rfloor$ \\
-\\
-Subtract the multiple of modulus from the input. \\
-5.  $a \leftarrow a \mbox{ (mod }\beta^{m+1}\mbox{)}$ (\textit{mp\_mod\_2d}) \\
-6.  $q \leftarrow q \cdot b \mbox{ (mod }\beta^{m+1}\mbox{)}$ (\textit{s\_mp\_mul\_digs}) \\
-7.  $a \leftarrow a - q$ (\textit{mp\_sub}) \\
-\\
-Add $\beta^{m+1}$ if a carry occured. \\
-8.  If $a < 0$ then (\textit{mp\_cmp\_d}) \\
-\hspace{3mm}8.1  $q \leftarrow 1$ (\textit{mp\_set}) \\
-\hspace{3mm}8.2  $q \leftarrow q \cdot \beta^{m+1}$ (\textit{mp\_lshd}) \\
-\hspace{3mm}8.3  $a \leftarrow a + q$ \\
-\\
-Now subtract the modulus if the residue is too large (e.g. quotient too small). \\
-9.  While $a \ge b$ do (\textit{mp\_cmp}) \\
-\hspace{3mm}9.1  $c \leftarrow a - b$ \\
-10.  Clear $q$. \\
-11.  Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_reduce}
-\end{figure}
-
-\textbf{Algorithm mp\_reduce.}
-This algorithm will reduce the input $a$ modulo $b$ in place using the Barrett algorithm.  It is loosely based on algorithm 14.42 of HAC
-\cite[pp.  602]{HAC} which is based on the paper from Paul Barrett \cite{BARRETT}.  The algorithm has several restrictions and assumptions which must
-be adhered to for the algorithm to work.
-
-First the modulus $b$ is assumed to be positive and greater than one.  If the modulus were less than or equal to one than subtracting
-a multiple of it would either accomplish nothing or actually enlarge the input.  The input $a$ must be in the range $0 \le a < b^2$ in order
-for the quotient to have enough precision.  If $a$ is the product of two numbers that were already reduced modulo $b$, this will not be a problem.
-Technically the algorithm will still work if $a \ge b^2$ but it will take much longer to finish.  The value of $\mu$ is passed as an argument to this
-algorithm and is assumed to be calculated and stored before the algorithm is used.
-
-Recall that the multiplication for the quotient on step 3 must only produce digits at or above the $m-1$'th position.  An algorithm called
-$s\_mp\_mul\_high\_digs$ which has not been presented is used to accomplish this task.  The algorithm is based on $s\_mp\_mul\_digs$ except that
-instead of stopping at a given level of precision it starts at a given level of precision.  This optimal algorithm can only be used if the number
-of digits in $b$ is very much smaller than $\beta$.
-
-While it is known that
-$a \ge b \cdot \lfloor (q_0 \cdot \mu) / \beta^{m+1} \rfloor$ only the lower $m+1$ digits are being used to compute the residue, so an implied
-``borrow'' from the higher digits might leave a negative result.  After the multiple of the modulus has been subtracted from $a$ the residue must be
-fixed up in case it is negative.  The invariant $\beta^{m+1}$ must be added to the residue to make it positive again.
-
-The while loop at step 9 will subtract $b$ until the residue is less than $b$.  If the algorithm is performed correctly this step is
-performed at most twice, and on average once. However, if $a \ge b^2$ than it will iterate substantially more times than it should.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_reduce.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* reduces x mod m, assumes 0 < x < m**2, mu is
-018    * precomputed via mp_reduce_setup.
-019    * From HAC pp.604 Algorithm 14.42
-020    */
-021   int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
-022   \{
-023     mp_int  q;
-024     int     res, um = m->used;
-025
-026     /* q = x */
-027     if ((res = mp_init_copy (&q, x)) != MP_OKAY) \{
-028       return res;
-029     \}
-030
-031     /* q1 = x / b**(k-1)  */
-032     mp_rshd (&q, um - 1);
-033
-034     /* according to HAC this optimization is ok */
-035     if (((mp_digit) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) \{
-036       if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) \{
-037         goto CLEANUP;
-038       \}
-039     \} else \{
-040   #ifdef BN_S_MP_MUL_HIGH_DIGS_C
-041       if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) \{
-042         goto CLEANUP;
-043       \}
-044   #elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
-045       if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) \{
-046         goto CLEANUP;
-047       \}
-048   #else
-049       \{
-050         res = MP_VAL;
-051         goto CLEANUP;
-052       \}
-053   #endif
-054     \}
-055
-056     /* q3 = q2 / b**(k+1) */
-057     mp_rshd (&q, um + 1);
-058
-059     /* x = x mod b**(k+1), quick (no division) */
-060     if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) \{
-061       goto CLEANUP;
-062     \}
-063
-064     /* q = q * m mod b**(k+1), quick (no division) */
-065     if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) \{
-066       goto CLEANUP;
-067     \}
-068
-069     /* x = x - q */
-070     if ((res = mp_sub (x, &q, x)) != MP_OKAY) \{
-071       goto CLEANUP;
-072     \}
-073
-074     /* If x < 0, add b**(k+1) to it */
-075     if (mp_cmp_d (x, 0) == MP_LT) \{
-076       mp_set (&q, 1);
-077       if ((res = mp_lshd (&q, um + 1)) != MP_OKAY)
-078         goto CLEANUP;
-079       if ((res = mp_add (x, &q, x)) != MP_OKAY)
-080         goto CLEANUP;
-081     \}
-082
-083     /* Back off if it's too big */
-084     while (mp_cmp (x, m) != MP_LT) \{
-085       if ((res = s_mp_sub (x, m, x)) != MP_OKAY) \{
-086         goto CLEANUP;
-087       \}
-088     \}
-089
-090   CLEANUP:
-091     mp_clear (&q);
-092
-093     return res;
-094   \}
-095   #endif
-096
-\end{alltt}
-\end{small}
-
-The first multiplication that determines the quotient can be performed by only producing the digits from $m - 1$ and up.  This essentially halves
-the number of single precision multiplications required.  However, the optimization is only safe if $\beta$ is much larger than the number of digits
-in the modulus.  In the source code this is evaluated on lines 36 to 43 where algorithm s\_mp\_mul\_high\_digs is used when it is
-safe to do so.
-
-\subsection{The Barrett Setup Algorithm}
-In order to use algorithm mp\_reduce the value of $\mu$ must be calculated in advance.  Ideally this value should be computed once and stored for
-future use so that the Barrett algorithm can be used without delay.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_reduce\_setup}. \\
-\textbf{Input}.   mp\_int $a$ ($a > 1$)  \\
-\textbf{Output}.  $\mu \leftarrow \lfloor \beta^{2m}/a \rfloor$ \\
-\hline \\
-1.  $\mu \leftarrow 2^{2 \cdot lg(\beta) \cdot  m}$ (\textit{mp\_2expt}) \\
-2.  $\mu \leftarrow \lfloor \mu / b \rfloor$ (\textit{mp\_div}) \\
-3.  Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_reduce\_setup}
-\end{figure}
-
-\textbf{Algorithm mp\_reduce\_setup.}
-This algorithm computes the reciprocal $\mu$ required for Barrett reduction.  First $\beta^{2m}$ is calculated as $2^{2 \cdot lg(\beta) \cdot  m}$ which
-is equivalent and much faster.  The final value is computed by taking the integer quotient of $\lfloor \mu / b \rfloor$.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_reduce\_setup.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* pre-calculate the value required for Barrett reduction
-018    * For a given modulus "b" it calulates the value required in "a"
-019    */
-020   int mp_reduce_setup (mp_int * a, mp_int * b)
-021   \{
-022     int     res;
-023
-024     if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) \{
-025       return res;
-026     \}
-027     return mp_div (a, b, a, NULL);
-028   \}
-029   #endif
-030
-\end{alltt}
-\end{small}
-
-This simple routine calculates the reciprocal $\mu$ required by Barrett reduction.  Note the extended usage of algorithm mp\_div where the variable
-which would received the remainder is passed as NULL.  As will be discussed in~\ref{sec:division} the division routine allows both the quotient and the
-remainder to be passed as NULL meaning to ignore the value.
-
-\section{The Montgomery Reduction}
-Montgomery reduction\footnote{Thanks to Niels Ferguson for his insightful explanation of the algorithm.} \cite{MONT} is by far the most interesting
-form of reduction in common use.  It computes a modular residue which is not actually equal to the residue of the input yet instead equal to a
-residue times a constant.  However, as perplexing as this may sound the algorithm is relatively simple and very efficient.
-
-Throughout this entire section the variable $n$ will represent the modulus used to form the residue.  As will be discussed shortly the value of
-$n$ must be odd.  The variable $x$ will represent the quantity of which the residue is sought.  Similar to the Barrett algorithm the input
-is restricted to $0 \le x < n^2$.  To begin the description some simple number theory facts must be established.
-
-\textbf{Fact 1.}  Adding $n$ to $x$ does not change the residue since in effect it adds one to the quotient $\lfloor x / n \rfloor$.  Another way
-to explain this is that $n$ is (\textit{or multiples of $n$ are}) congruent to zero modulo $n$.  Adding zero will not change the value of the residue.
-
-\textbf{Fact 2.}  If $x$ is even then performing a division by two in $\Z$ is congruent to $x \cdot 2^{-1} \mbox{ (mod }n\mbox{)}$.  Actually
-this is an application of the fact that if $x$ is evenly divisible by any $k \in \Z$ then division in $\Z$ will be congruent to
-multiplication by $k^{-1}$ modulo $n$.
-
-From these two simple facts the following simple algorithm can be derived.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Montgomery Reduction}. \\
-\textbf{Input}.   Integer $x$, $n$ and $k$ \\
-\textbf{Output}.  $2^{-k}x \mbox{ (mod }n\mbox{)}$ \\
-\hline \\
-1.  for $t$ from $1$ to $k$ do \\
-\hspace{3mm}1.1  If $x$ is odd then \\
-\hspace{6mm}1.1.1  $x \leftarrow x + n$ \\
-\hspace{3mm}1.2  $x \leftarrow x/2$ \\
-2.  Return $x$. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm Montgomery Reduction}
-\end{figure}
-
-The algorithm reduces the input one bit at a time using the two congruencies stated previously.  Inside the loop $n$, which is odd, is
-added to $x$ if $x$ is odd.  This forces $x$ to be even which allows the division by two in $\Z$ to be congruent to a modular division by two.  Since
-$x$ is assumed to be initially much larger than $n$ the addition of $n$ will contribute an insignificant magnitude to $x$.  Let $r$ represent the
-final result of the Montgomery algorithm.  If $k > lg(n)$ and $0 \le x < n^2$ then the final result is limited to
-$0 \le r < \lfloor x/2^k \rfloor + n$.  As a result at most a single subtraction is required to get the residue desired.
-
-\begin{figure}[here]
-\begin{small}
-\begin{center}
-\begin{tabular}{|c|l|}
-\hline \textbf{Step number ($t$)} & \textbf{Result ($x$)} \\
-\hline $1$ & $x + n = 5812$, $x/2 = 2906$ \\
-\hline $2$ & $x/2 = 1453$ \\
-\hline $3$ & $x + n = 1710$, $x/2 = 855$ \\
-\hline $4$ & $x + n = 1112$, $x/2 = 556$ \\
-\hline $5$ & $x/2 = 278$ \\
-\hline $6$ & $x/2 = 139$ \\
-\hline $7$ & $x + n = 396$, $x/2 = 198$ \\
-\hline $8$ & $x/2 = 99$ \\
-\hline $9$ & $x + n = 356$, $x/2 = 178$ \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Example of Montgomery Reduction (I)}
-\label{fig:MONT1}
-\end{figure}
-
-Consider the example in figure~\ref{fig:MONT1} which reduces $x = 5555$ modulo $n = 257$ when $k = 9$ (note $\beta^k = 512$ which is larger than $n$).  The result of
-the algorithm $r = 178$ is congruent to the value of $2^{-9} \cdot 5555 \mbox{ (mod }257\mbox{)}$.  When $r$ is multiplied by $2^9$ modulo $257$ the correct residue
-$r \equiv 158$ is produced.
-
-Let $k = \lfloor lg(n) \rfloor + 1$ represent the number of bits in $n$.  The current algorithm requires $2k^2$ single precision shifts
-and $k^2$ single precision additions.  At this rate the algorithm is most certainly slower than Barrett reduction and not terribly useful.
-Fortunately there exists an alternative representation of the algorithm.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Montgomery Reduction} (modified I). \\
-\textbf{Input}.   Integer $x$, $n$ and $k$ ($2^k > n$) \\
-\textbf{Output}.  $2^{-k}x \mbox{ (mod }n\mbox{)}$ \\
-\hline \\
-1.  for $t$ from $1$ to $k$ do \\
-\hspace{3mm}1.1  If the $t$'th bit of $x$ is one then \\
-\hspace{6mm}1.1.1  $x \leftarrow x + 2^tn$ \\
-2.  Return $x/2^k$. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm Montgomery Reduction (modified I)}
-\end{figure}
-
-This algorithm is equivalent since $2^tn$ is a multiple of $n$ and the lower $k$ bits of $x$ are zero by step 2.  The number of single
-precision shifts has now been reduced from $2k^2$ to $k^2 + k$ which is only a small improvement.
-
-\begin{figure}[here]
-\begin{small}
-\begin{center}
-\begin{tabular}{|c|l|r|}
-\hline \textbf{Step number ($t$)} & \textbf{Result ($x$)} & \textbf{Result ($x$) in Binary} \\
-\hline -- & $5555$ & $1010110110011$ \\
-\hline $1$ & $x + 2^{0}n = 5812$ &  $1011010110100$ \\
-\hline $2$ & $5812$ & $1011010110100$ \\
-\hline $3$ & $x + 2^{2}n = 6840$ & $1101010111000$ \\
-\hline $4$ & $x + 2^{3}n = 8896$ & $10001011000000$ \\
-\hline $5$ & $8896$ & $10001011000000$ \\
-\hline $6$ & $8896$ & $10001011000000$ \\
-\hline $7$ & $x + 2^{6}n = 25344$ & $110001100000000$ \\
-\hline $8$ & $25344$ & $110001100000000$ \\
-\hline $9$ & $x + 2^{7}n = 91136$ & $10110010000000000$ \\
-\hline -- & $x/2^k = 178$ & \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Example of Montgomery Reduction (II)}
-\label{fig:MONT2}
-\end{figure}
-
-Figure~\ref{fig:MONT2} demonstrates the modified algorithm reducing $x = 5555$ modulo $n = 257$ with $k = 9$.
-With this algorithm a single shift right at the end is the only right shift required to reduce the input instead of $k$ right shifts inside the
-loop.  Note that for the iterations $t = 2, 5, 6$ and $8$ where the result $x$ is not changed.  In those iterations the $t$'th bit of $x$ is
-zero and the appropriate multiple of $n$ does not need to be added to force the $t$'th bit of the result to zero.
-
-\subsection{Digit Based Montgomery Reduction}
-Instead of computing the reduction on a bit-by-bit basis it is actually much faster to compute it on digit-by-digit basis.  Consider the
-previous algorithm re-written to compute the Montgomery reduction in this new fashion.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Montgomery Reduction} (modified II). \\
-\textbf{Input}.   Integer $x$, $n$ and $k$ ($\beta^k > n$) \\
-\textbf{Output}.  $\beta^{-k}x \mbox{ (mod }n\mbox{)}$ \\
-\hline \\
-1.  for $t$ from $0$ to $k - 1$ do \\
-\hspace{3mm}1.1  $x \leftarrow x + \mu n \beta^t$ \\
-2.  Return $x/\beta^k$. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm Montgomery Reduction (modified II)}
-\end{figure}
-
-The value $\mu n \beta^t$ is a multiple of the modulus $n$ meaning that it will not change the residue.  If the first digit of
-the value $\mu n \beta^t$ equals the negative (modulo $\beta$) of the $t$'th digit of $x$ then the addition will result in a zero digit.  This
-problem breaks down to solving the following congruency.
-
-\begin{center}
-\begin{tabular}{rcl}
-$x_t + \mu n_0$ & $\equiv$ & $0 \mbox{ (mod }\beta\mbox{)}$ \\
-$\mu n_0$ & $\equiv$ & $-x_t \mbox{ (mod }\beta\mbox{)}$ \\
-$\mu$ & $\equiv$ & $-x_t/n_0 \mbox{ (mod }\beta\mbox{)}$ \\
-\end{tabular}
-\end{center}
-
-In each iteration of the loop on step 1 a new value of $\mu$ must be calculated.  The value of $-1/n_0 \mbox{ (mod }\beta\mbox{)}$ is used
-extensively in this algorithm and should be precomputed.  Let $\rho$ represent the negative of the modular inverse of $n_0$ modulo $\beta$.
-
-For example, let $\beta = 10$ represent the radix.  Let $n = 17$ represent the modulus which implies $k = 2$ and $\rho \equiv 7$.  Let $x = 33$
-represent the value to reduce.
-
-\newpage\begin{figure}
-\begin{center}
-\begin{tabular}{|c|c|c|}
-\hline \textbf{Step ($t$)} & \textbf{Value of $x$} & \textbf{Value of $\mu$} \\
-\hline --                 & $33$ & --\\
-\hline $0$                 & $33 + \mu n = 50$ & $1$ \\
-\hline $1$                 & $50 + \mu n \beta = 900$ & $5$ \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Example of Montgomery Reduction}
-\end{figure}
-
-The final result $900$ is then divided by $\beta^k$ to produce the final result $9$.  The first observation is that $9 \nequiv x \mbox{ (mod }n\mbox{)}$
-which implies the result is not the modular residue of $x$ modulo $n$.  However, recall that the residue is actually multiplied by $\beta^{-k}$ in
-the algorithm.  To get the true residue the value must be multiplied by $\beta^k$.  In this case $\beta^k \equiv 15 \mbox{ (mod }n\mbox{)}$ and
-the correct residue is $9 \cdot 15 \equiv 16 \mbox{ (mod }n\mbox{)}$.
-
-\subsection{Baseline Montgomery Reduction}
-The baseline Montgomery reduction algorithm will produce the residue for any size input.  It is designed to be a catch-all algororithm for
-Montgomery reductions.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_montgomery\_reduce}. \\
-\textbf{Input}.   mp\_int $x$, mp\_int $n$ and a digit $\rho \equiv -1/n_0 \mbox{ (mod }n\mbox{)}$. \\
-\hspace{11.5mm}($0 \le x < n^2, n > 1, (n, \beta) = 1, \beta^k > n$) \\
-\textbf{Output}.  $\beta^{-k}x \mbox{ (mod }n\mbox{)}$ \\
-\hline \\
-1.  $digs \leftarrow 2n.used + 1$ \\
-2.  If $digs < MP\_ARRAY$ and $m.used < \delta$ then \\
-\hspace{3mm}2.1  Use algorithm fast\_mp\_montgomery\_reduce instead. \\
-\\
-Setup $x$ for the reduction. \\
-3.  If $x.alloc < digs$ then grow $x$ to $digs$ digits. \\
-4.  $x.used \leftarrow digs$ \\
-\\
-Eliminate the lower $k$ digits. \\
-5.  For $ix$ from $0$ to $k - 1$ do \\
-\hspace{3mm}5.1  $\mu \leftarrow x_{ix} \cdot \rho \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{3mm}5.2  $u \leftarrow 0$ \\
-\hspace{3mm}5.3  For $iy$ from $0$ to $k - 1$ do \\
-\hspace{6mm}5.3.1  $\hat r \leftarrow \mu n_{iy} + x_{ix + iy} + u$ \\
-\hspace{6mm}5.3.2  $x_{ix + iy} \leftarrow \hat r \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{6mm}5.3.3  $u \leftarrow \lfloor \hat r / \beta \rfloor$ \\
-\hspace{3mm}5.4  While $u > 0$ do \\
-\hspace{6mm}5.4.1  $iy \leftarrow iy + 1$ \\
-\hspace{6mm}5.4.2  $x_{ix + iy} \leftarrow x_{ix + iy} + u$ \\
-\hspace{6mm}5.4.3  $u \leftarrow \lfloor x_{ix+iy} / \beta \rfloor$ \\
-\hspace{6mm}5.4.4  $x_{ix + iy} \leftarrow x_{ix+iy} \mbox{ (mod }\beta\mbox{)}$ \\
-\\
-Divide by $\beta^k$ and fix up as required. \\
-6.  $x \leftarrow \lfloor x / \beta^k \rfloor$ \\
-7.  If $x \ge n$ then \\
-\hspace{3mm}7.1  $x \leftarrow x - n$ \\
-8.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_montgomery\_reduce}
-\end{figure}
-
-\textbf{Algorithm mp\_montgomery\_reduce.}
-This algorithm reduces the input $x$ modulo $n$ in place using the Montgomery reduction algorithm.  The algorithm is loosely based
-on algorithm 14.32 of \cite[pp.601]{HAC} except it merges the multiplication of $\mu n \beta^t$ with the addition in the inner loop.  The
-restrictions on this algorithm are fairly easy to adapt to.  First $0 \le x < n^2$ bounds the input to numbers in the same range as
-for the Barrett algorithm.  Additionally if $n > 1$ and $n$ is odd there will exist a modular inverse $\rho$.  $\rho$ must be calculated in
-advance of this algorithm.  Finally the variable $k$ is fixed and a pseudonym for $n.used$.
-
-Step 2 decides whether a faster Montgomery algorithm can be used.  It is based on the Comba technique meaning that there are limits on
-the size of the input.  This algorithm is discussed in sub-section 6.3.3.
-
-Step 5 is the main reduction loop of the algorithm.  The value of $\mu$ is calculated once per iteration in the outer loop.  The inner loop
-calculates $x + \mu n \beta^{ix}$ by multiplying $\mu n$ and adding the result to $x$ shifted by $ix$ digits.  Both the addition and
-multiplication are performed in the same loop to save time and memory.  Step 5.4 will handle any additional carries that escape the inner loop.
-
-Using a quick inspection this algorithm requires $n$ single precision multiplications for the outer loop and $n^2$ single precision multiplications
-in the inner loop.  In total $n^2 + n$ single precision multiplications which compares favourably to Barrett at $n^2 + 2n - 1$ single precision
-multiplications.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_montgomery\_reduce.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* computes xR**-1 == x (mod N) via Montgomery Reduction */
-018   int
-019   mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
-020   \{
-021     int     ix, res, digs;
-022     mp_digit mu;
-023
-024     /* can the fast reduction [comba] method be used?
-025      *
-026      * Note that unlike in mul you're safely allowed *less*
-027      * than the available columns [255 per default] since carries
-028      * are fixed up in the inner loop.
-029      */
-030     digs = (n->used * 2) + 1;
-031     if ((digs < MP_WARRAY) &&
-032         (n->used <
-033         (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) \{
-034       return fast_mp_montgomery_reduce (x, n, rho);
-035     \}
-036
-037     /* grow the input as required */
-038     if (x->alloc < digs) \{
-039       if ((res = mp_grow (x, digs)) != MP_OKAY) \{
-040         return res;
-041       \}
-042     \}
-043     x->used = digs;
-044
-045     for (ix = 0; ix < n->used; ix++) \{
-046       /* mu = ai * rho mod b
-047        *
-048        * The value of rho must be precalculated via
-049        * montgomery_setup() such that
-050        * it equals -1/n0 mod b this allows the
-051        * following inner loop to reduce the
-052        * input one digit at a time
-053        */
-054       mu = (mp_digit) (((mp_word)x->dp[ix] * (mp_word)rho) & MP_MASK);
-055
-056       /* a = a + mu * m * b**i */
-057       \{
-058         int iy;
-059         mp_digit *tmpn, *tmpx, u;
-060         mp_word r;
-061
-062         /* alias for digits of the modulus */
-063         tmpn = n->dp;
-064
-065         /* alias for the digits of x [the input] */
-066         tmpx = x->dp + ix;
-067
-068         /* set the carry to zero */
-069         u = 0;
-070
-071         /* Multiply and add in place */
-072         for (iy = 0; iy < n->used; iy++) \{
-073           /* compute product and sum */
-074           r       = ((mp_word)mu * (mp_word)*tmpn++) +
-075                      (mp_word) u + (mp_word) *tmpx;
-076
-077           /* get carry */
-078           u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
-079
-080           /* fix digit */
-081           *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
-082         \}
-083         /* At this point the ix'th digit of x should be zero */
-084
-085
-086         /* propagate carries upwards as required*/
-087         while (u != 0) \{
-088           *tmpx   += u;
-089           u        = *tmpx >> DIGIT_BIT;
-090           *tmpx++ &= MP_MASK;
-091         \}
-092       \}
-093     \}
-094
-095     /* at this point the n.used'th least
-096      * significant digits of x are all zero
-097      * which means we can shift x to the
-098      * right by n.used digits and the
-099      * residue is unchanged.
-100      */
-101
-102     /* x = x/b**n.used */
-103     mp_clamp(x);
-104     mp_rshd (x, n->used);
-105
-106     /* if x >= n then x = x - n */
-107     if (mp_cmp_mag (x, n) != MP_LT) \{
-108       return s_mp_sub (x, n, x);
-109     \}
-110
-111     return MP_OKAY;
-112   \}
-113   #endif
-114
-\end{alltt}
-\end{small}
-
-This is the baseline implementation of the Montgomery reduction algorithm.  Lines 30 to 35 determine if the Comba based
-routine can be used instead.  Line 48 computes the value of $\mu$ for that particular iteration of the outer loop.
-
-The multiplication $\mu n \beta^{ix}$ is performed in one step in the inner loop.  The alias $tmpx$ refers to the $ix$'th digit of $x$ and
-the alias $tmpn$ refers to the modulus $n$.
-
-\subsection{Faster ``Comba'' Montgomery Reduction}
-
-The Montgomery reduction requires fewer single precision multiplications than a Barrett reduction, however it is much slower due to the serial
-nature of the inner loop.  The Barrett reduction algorithm requires two slightly modified multipliers which can be implemented with the Comba
-technique.  The Montgomery reduction algorithm cannot directly use the Comba technique to any significant advantage since the inner loop calculates
-a $k \times 1$ product $k$ times.
-
-The biggest obstacle is that at the $ix$'th iteration of the outer loop the value of $x_{ix}$ is required to calculate $\mu$.  This means the
-carries from $0$ to $ix - 1$ must have been propagated upwards to form a valid $ix$'th digit.  The solution as it turns out is very simple.
-Perform a Comba like multiplier and inside the outer loop just after the inner loop fix up the $ix + 1$'th digit by forwarding the carry.
-
-With this change in place the Montgomery reduction algorithm can be performed with a Comba style multiplication loop which substantially increases
-the speed of the algorithm.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{fast\_mp\_montgomery\_reduce}. \\
-\textbf{Input}.   mp\_int $x$, mp\_int $n$ and a digit $\rho \equiv -1/n_0 \mbox{ (mod }n\mbox{)}$. \\
-\hspace{11.5mm}($0 \le x < n^2, n > 1, (n, \beta) = 1, \beta^k > n$) \\
-\textbf{Output}.  $\beta^{-k}x \mbox{ (mod }n\mbox{)}$ \\
-\hline \\
-Place an array of \textbf{MP\_WARRAY} mp\_word variables called $\hat W$ on the stack. \\
-1.  if $x.alloc < n.used + 1$ then grow $x$ to $n.used + 1$ digits. \\
-Copy the digits of $x$ into the array $\hat W$ \\
-2.  For $ix$ from $0$ to $x.used - 1$ do \\
-\hspace{3mm}2.1  $\hat W_{ix} \leftarrow x_{ix}$ \\
-3.  For $ix$ from $x.used$ to $2n.used - 1$ do \\
-\hspace{3mm}3.1  $\hat W_{ix} \leftarrow 0$ \\
-Elimiate the lower $k$ digits. \\
-4.  for $ix$ from $0$ to $n.used - 1$ do \\
-\hspace{3mm}4.1  $\mu \leftarrow \hat W_{ix} \cdot \rho \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{3mm}4.2  For $iy$ from $0$ to $n.used - 1$ do \\
-\hspace{6mm}4.2.1  $\hat W_{iy + ix} \leftarrow \hat W_{iy + ix} + \mu \cdot n_{iy}$ \\
-\hspace{3mm}4.3  $\hat W_{ix + 1} \leftarrow \hat W_{ix + 1} + \lfloor \hat W_{ix} / \beta \rfloor$ \\
-Propagate carries upwards. \\
-5.  for $ix$ from $n.used$ to $2n.used + 1$ do \\
-\hspace{3mm}5.1  $\hat W_{ix + 1} \leftarrow \hat W_{ix + 1} + \lfloor \hat W_{ix} / \beta \rfloor$ \\
-Shift right and reduce modulo $\beta$ simultaneously. \\
-6.  for $ix$ from $0$ to $n.used + 1$ do \\
-\hspace{3mm}6.1  $x_{ix} \leftarrow \hat W_{ix + n.used} \mbox{ (mod }\beta\mbox{)}$ \\
-Zero excess digits and fixup $x$. \\
-7.  if $x.used > n.used + 1$ then do \\
-\hspace{3mm}7.1  for $ix$ from $n.used + 1$ to $x.used - 1$ do \\
-\hspace{6mm}7.1.1  $x_{ix} \leftarrow 0$ \\
-8.  $x.used \leftarrow n.used + 1$ \\
-9.  Clamp excessive digits of $x$. \\
-10.  If $x \ge n$ then \\
-\hspace{3mm}10.1  $x \leftarrow x - n$ \\
-11.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm fast\_mp\_montgomery\_reduce}
-\end{figure}
-
-\textbf{Algorithm fast\_mp\_montgomery\_reduce.}
-This algorithm will compute the Montgomery reduction of $x$ modulo $n$ using the Comba technique.  It is on most computer platforms significantly
-faster than algorithm mp\_montgomery\_reduce and algorithm mp\_reduce (\textit{Barrett reduction}).  The algorithm has the same restrictions
-on the input as the baseline reduction algorithm.  An additional two restrictions are imposed on this algorithm.  The number of digits $k$ in the
-the modulus $n$ must not violate $MP\_WARRAY > 2k +1$ and $n < \delta$.   When $\beta = 2^{28}$ this algorithm can be used to reduce modulo
-a modulus of at most $3,556$ bits in length.
-
-As in the other Comba reduction algorithms there is a $\hat W$ array which stores the columns of the product.  It is initially filled with the
-contents of $x$ with the excess digits zeroed.  The reduction loop is very similar the to the baseline loop at heart.  The multiplication on step
-4.1 can be single precision only since $ab \mbox{ (mod }\beta\mbox{)} \equiv (a \mbox{ mod }\beta)(b \mbox{ mod }\beta)$.  Some multipliers such
-as those on the ARM processors take a variable length time to complete depending on the number of bytes of result it must produce.  By performing
-a single precision multiplication instead half the amount of time is spent.
-
-Also note that digit $\hat W_{ix}$ must have the carry from the $ix - 1$'th digit propagated upwards in order for this to work.  That is what step
-4.3 will do.  In effect over the $n.used$ iterations of the outer loop the $n.used$'th lower columns all have the their carries propagated forwards.  Note
-how the upper bits of those same words are not reduced modulo $\beta$.  This is because those values will be discarded shortly and there is no
-point.
-
-Step 5 will propagate the remainder of the carries upwards.  On step 6 the columns are reduced modulo $\beta$ and shifted simultaneously as they are
-stored in the destination $x$.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_fast\_mp\_montgomery\_reduce.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* computes xR**-1 == x (mod N) via Montgomery Reduction
-018    *
-019    * This is an optimized implementation of montgomery_reduce
-020    * which uses the comba method to quickly calculate the columns of the
-021    * reduction.
-022    *
-023    * Based on Algorithm 14.32 on pp.601 of HAC.
-024   */
-025   int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
-026   \{
-027     int     ix, res, olduse;
-028     mp_word W[MP_WARRAY];
-029
-030     /* get old used count */
-031     olduse = x->used;
-032
-033     /* grow a as required */
-034     if (x->alloc < (n->used + 1)) \{
-035       if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) \{
-036         return res;
-037       \}
-038     \}
-039
-040     /* first we have to get the digits of the input into
-041      * an array of double precision words W[...]
-042      */
-043     \{
-044       mp_word *_W;
-045       mp_digit *tmpx;
-046
-047       /* alias for the W[] array */
-048       _W   = W;
-049
-050       /* alias for the digits of  x*/
-051       tmpx = x->dp;
-052
-053       /* copy the digits of a into W[0..a->used-1] */
-054       for (ix = 0; ix < x->used; ix++) \{
-055         *_W++ = *tmpx++;
-056       \}
-057
-058       /* zero the high words of W[a->used..m->used*2] */
-059       for (; ix < ((n->used * 2) + 1); ix++) \{
-060         *_W++ = 0;
-061       \}
-062     \}
-063
-064     /* now we proceed to zero successive digits
-065      * from the least significant upwards
-066      */
-067     for (ix = 0; ix < n->used; ix++) \{
-068       /* mu = ai * m' mod b
-069        *
-070        * We avoid a double precision multiplication (which isn't required)
-071        * by casting the value down to a mp_digit.  Note this requires
-072        * that W[ix-1] have  the carry cleared (see after the inner loop)
-073        */
-074       mp_digit mu;
-075       mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
-076
-077       /* a = a + mu * m * b**i
-078        *
-079        * This is computed in place and on the fly.  The multiplication
-080        * by b**i is handled by offseting which columns the results
-081        * are added to.
-082        *
-083        * Note the comba method normally doesn't handle carries in the
-084        * inner loop In this case we fix the carry from the previous
-085        * column since the Montgomery reduction requires digits of the
-086        * result (so far) [see above] to work.  This is
-087        * handled by fixing up one carry after the inner loop.  The
-088        * carry fixups are done in order so after these loops the
-089        * first m->used words of W[] have the carries fixed
-090        */
-091       \{
-092         int iy;
-093         mp_digit *tmpn;
-094         mp_word *_W;
-095
-096         /* alias for the digits of the modulus */
-097         tmpn = n->dp;
-098
-099         /* Alias for the columns set by an offset of ix */
-100         _W = W + ix;
-101
-102         /* inner loop */
-103         for (iy = 0; iy < n->used; iy++) \{
-104             *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
-105         \}
-106       \}
-107
-108       /* now fix carry for next digit, W[ix+1] */
-109       W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
-110     \}
-111
-112     /* now we have to propagate the carries and
-113      * shift the words downward [all those least
-114      * significant digits we zeroed].
-115      */
-116     \{
-117       mp_digit *tmpx;
-118       mp_word *_W, *_W1;
-119
-120       /* nox fix rest of carries */
-121
-122       /* alias for current word */
-123       _W1 = W + ix;
-124
-125       /* alias for next word, where the carry goes */
-126       _W = W + ++ix;
-127
-128       for (; ix <= ((n->used * 2) + 1); ix++) \{
-129         *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
-130       \}
-131
-132       /* copy out, A = A/b**n
-133        *
-134        * The result is A/b**n but instead of converting from an
-135        * array of mp_word to mp_digit than calling mp_rshd
-136        * we just copy them in the right order
-137        */
-138
-139       /* alias for destination word */
-140       tmpx = x->dp;
-141
-142       /* alias for shifted double precision result */
-143       _W = W + n->used;
-144
-145       for (ix = 0; ix < (n->used + 1); ix++) \{
-146         *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
-147       \}
-148
-149       /* zero oldused digits, if the input a was larger than
-150        * m->used+1 we'll have to clear the digits
-151        */
-152       for (; ix < olduse; ix++) \{
-153         *tmpx++ = 0;
-154       \}
-155     \}
-156
-157     /* set the max used and clamp */
-158     x->used = n->used + 1;
-159     mp_clamp (x);
-160
-161     /* if A >= m then A = A - m */
-162     if (mp_cmp_mag (x, n) != MP_LT) \{
-163       return s_mp_sub (x, n, x);
-164     \}
-165     return MP_OKAY;
-166   \}
-167   #endif
-168
-\end{alltt}
-\end{small}
-
-The $\hat W$ array is first filled with digits of $x$ on line 50 then the rest of the digits are zeroed on line 54.  Both loops share
-the same alias variables to make the code easier to read.
-
-The value of $\mu$ is calculated in an interesting fashion.  First the value $\hat W_{ix}$ is reduced modulo $\beta$ and cast to a mp\_digit.  This
-forces the compiler to use a single precision multiplication and prevents any concerns about loss of precision.   Line 109 fixes the carry
-for the next iteration of the loop by propagating the carry from $\hat W_{ix}$ to $\hat W_{ix+1}$.
-
-The for loop on line 108 propagates the rest of the carries upwards through the columns.  The for loop on line 125 reduces the columns
-modulo $\beta$ and shifts them $k$ places at the same time.  The alias $\_ \hat W$ actually refers to the array $\hat W$ starting at the $n.used$'th
-digit, that is $\_ \hat W_{t} = \hat W_{n.used + t}$.
-
-\subsection{Montgomery Setup}
-To calculate the variable $\rho$ a relatively simple algorithm will be required.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_montgomery\_setup}. \\
-\textbf{Input}.   mp\_int $n$ ($n > 1$ and $(n, 2) = 1$) \\
-\textbf{Output}.  $\rho \equiv -1/n_0 \mbox{ (mod }\beta\mbox{)}$ \\
-\hline \\
-1.  $b \leftarrow n_0$ \\
-2.  If $b$ is even return(\textit{MP\_VAL}) \\
-3.  $x \leftarrow (((b + 2) \mbox{ AND } 4) << 1) + b$ \\
-4.  for $k$ from 0 to $\lceil lg(lg(\beta)) \rceil - 2$ do \\
-\hspace{3mm}4.1  $x \leftarrow x \cdot (2 - bx)$ \\
-5.  $\rho \leftarrow \beta - x \mbox{ (mod }\beta\mbox{)}$ \\
-6.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_montgomery\_setup}
-\end{figure}
-
-\textbf{Algorithm mp\_montgomery\_setup.}
-This algorithm will calculate the value of $\rho$ required within the Montgomery reduction algorithms.  It uses a very interesting trick
-to calculate $1/n_0$ when $\beta$ is a power of two.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_montgomery\_setup.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* setups the montgomery reduction stuff */
-018   int
-019   mp_montgomery_setup (mp_int * n, mp_digit * rho)
-020   \{
-021     mp_digit x, b;
-022
-023   /* fast inversion mod 2**k
-024    *
-025    * Based on the fact that
-026    *
-027    * XA = 1 (mod 2**n)  =>  (X(2-XA)) A = 1 (mod 2**2n)
-028    *                    =>  2*X*A - X*X*A*A = 1
-029    *                    =>  2*(1) - (1)     = 1
-030    */
-031     b = n->dp[0];
-032
-033     if ((b & 1) == 0) \{
-034       return MP_VAL;
-035     \}
-036
-037     x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
-038     x *= 2 - (b * x);             /* here x*a==1 mod 2**8 */
-039   #if !defined(MP_8BIT)
-040     x *= 2 - (b * x);             /* here x*a==1 mod 2**16 */
-041   #endif
-042   #if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
-043     x *= 2 - (b * x);             /* here x*a==1 mod 2**32 */
-044   #endif
-045   #ifdef MP_64BIT
-046     x *= 2 - (b * x);             /* here x*a==1 mod 2**64 */
-047   #endif
-048
-049     /* rho = -1/m mod b */
-050     *rho = (mp_digit)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
-051
-052     return MP_OKAY;
-053   \}
-054   #endif
-055
-\end{alltt}
-\end{small}
-
-This source code computes the value of $\rho$ required to perform Montgomery reduction.  It has been modified to avoid performing excess
-multiplications when $\beta$ is not the default 28-bits.
-
-\section{The Diminished Radix Algorithm}
-The Diminished Radix method of modular reduction \cite{DRMET} is a fairly clever technique which can be more efficient than either the Barrett
-or Montgomery methods for certain forms of moduli.  The technique is based on the following simple congruence.
-
-\begin{equation}
-(x \mbox{ mod } n) + k \lfloor x / n \rfloor \equiv x \mbox{ (mod }(n - k)\mbox{)}
-\end{equation}
-
-This observation was used in the MMB \cite{MMB} block cipher to create a diffusion primitive.  It used the fact that if $n = 2^{31}$ and $k=1$ that
-then a x86 multiplier could produce the 62-bit product and use  the ``shrd'' instruction to perform a double-precision right shift.  The proof
-of the above equation is very simple.  First write $x$ in the product form.
-
-\begin{equation}
-x = qn + r
-\end{equation}
-
-Now reduce both sides modulo $(n - k)$.
-
-\begin{equation}
-x \equiv qk + r  \mbox{ (mod }(n-k)\mbox{)}
-\end{equation}
-
-The variable $n$ reduces modulo $n - k$ to $k$.  By putting $q = \lfloor x/n \rfloor$ and $r = x \mbox{ mod } n$
-into the equation the original congruence is reproduced, thus concluding the proof.  The following algorithm is based on this observation.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Diminished Radix Reduction}. \\
-\textbf{Input}.   Integer $x$, $n$, $k$ \\
-\textbf{Output}.  $x \mbox{ mod } (n - k)$ \\
-\hline \\
-1.  $q \leftarrow \lfloor x / n \rfloor$ \\
-2.  $q \leftarrow k \cdot q$ \\
-3.  $x \leftarrow x \mbox{ (mod }n\mbox{)}$ \\
-4.  $x \leftarrow x + q$ \\
-5.  If $x \ge (n - k)$ then \\
-\hspace{3mm}5.1  $x \leftarrow x - (n - k)$ \\
-\hspace{3mm}5.2  Goto step 1. \\
-6.  Return $x$ \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm Diminished Radix Reduction}
-\label{fig:DR}
-\end{figure}
-
-This algorithm will reduce $x$ modulo $n - k$ and return the residue.  If $0 \le x < (n - k)^2$ then the algorithm will loop almost always
-once or twice and occasionally three times.  For simplicity sake the value of $x$ is bounded by the following simple polynomial.
-
-\begin{equation}
-0 \le x < n^2 + k^2 - 2nk
-\end{equation}
-
-The true bound is  $0 \le x < (n - k - 1)^2$ but this has quite a few more terms.  The value of $q$ after step 1 is bounded by the following.
-
-\begin{equation}
-q < n - 2k - k^2/n
-\end{equation}
-
-Since $k^2$ is going to be considerably smaller than $n$ that term will always be zero.  The value of $x$ after step 3 is bounded trivially as
-$0 \le x < n$.  By step four the sum $x + q$ is bounded by
-
-\begin{equation}
-0 \le q + x < (k + 1)n - 2k^2 - 1
-\end{equation}
-
-With a second pass $q$ will be loosely bounded by $0 \le q < k^2$ after step 2 while $x$ will still be loosely bounded by $0 \le x < n$ after step 3.  After the second pass it is highly unlike that the
-sum in step 4 will exceed $n - k$.  In practice fewer than three passes of the algorithm are required to reduce virtually every input in the
-range $0 \le x < (n - k - 1)^2$.
-
-\begin{figure}
-\begin{small}
-\begin{center}
-\begin{tabular}{|l|}
-\hline
-$x = 123456789, n = 256, k = 3$ \\
-\hline $q \leftarrow \lfloor x/n \rfloor = 482253$ \\
-$q \leftarrow q*k = 1446759$ \\
-$x \leftarrow x \mbox{ mod } n = 21$ \\
-$x \leftarrow x + q = 1446780$ \\
-$x \leftarrow x - (n - k) = 1446527$ \\
-\hline
-$q \leftarrow \lfloor x/n \rfloor = 5650$ \\
-$q \leftarrow q*k = 16950$ \\
-$x \leftarrow x \mbox{ mod } n = 127$ \\
-$x \leftarrow x + q = 17077$ \\
-$x \leftarrow x - (n - k) = 16824$ \\
-\hline
-$q \leftarrow \lfloor x/n \rfloor = 65$ \\
-$q \leftarrow q*k = 195$ \\
-$x \leftarrow x \mbox{ mod } n = 184$ \\
-$x \leftarrow x + q = 379$ \\
-$x \leftarrow x - (n - k) = 126$ \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Example Diminished Radix Reduction}
-\label{fig:EXDR}
-\end{figure}
-
-Figure~\ref{fig:EXDR} demonstrates the reduction of $x = 123456789$ modulo $n - k = 253$ when $n = 256$ and $k = 3$.  Note that even while $x$
-is considerably larger than $(n - k - 1)^2 = 63504$ the algorithm still converges on the modular residue exceedingly fast.  In this case only
-three passes were required to find the residue $x \equiv 126$.
-
-
-\subsection{Choice of Moduli}
-On the surface this algorithm looks like a very expensive algorithm.  It requires a couple of subtractions followed by multiplication and other
-modular reductions.  The usefulness of this algorithm becomes exceedingly clear when an appropriate modulus is chosen.
-
-Division in general is a very expensive operation to perform.  The one exception is when the division is by a power of the radix of representation used.
-Division by ten for example is simple for pencil and paper mathematics since it amounts to shifting the decimal place to the right.  Similarly division
-by two (\textit{or powers of two}) is very simple for binary computers to perform.  It would therefore seem logical to choose $n$ of the form $2^p$
-which would imply that $\lfloor x / n \rfloor$ is a simple shift of $x$ right $p$ bits.
-
-However, there is one operation related to division of power of twos that is even faster than this.  If $n = \beta^p$ then the division may be
-performed by moving whole digits to the right $p$ places.  In practice division by $\beta^p$ is much faster than division by $2^p$ for any $p$.
-Also with the choice of $n = \beta^p$ reducing $x$ modulo $n$ merely requires zeroing the digits above the $p-1$'th digit of $x$.
-
-Throughout the next section the term ``restricted modulus'' will refer to a modulus of the form $\beta^p - k$ whereas the term ``unrestricted
-modulus'' will refer to a modulus of the form $2^p - k$.  The word ``restricted'' in this case refers to the fact that it is based on the
-$2^p$ logic except $p$ must be a multiple of $lg(\beta)$.
-
-\subsection{Choice of $k$}
-Now that division and reduction (\textit{step 1 and 3 of figure~\ref{fig:DR}}) have been optimized to simple digit operations the multiplication by $k$
-in step 2 is the most expensive operation.  Fortunately the choice of $k$ is not terribly limited.  For all intents and purposes it might
-as well be a single digit.  The smaller the value of $k$ is the faster the algorithm will be.
-
-\subsection{Restricted Diminished Radix Reduction}
-The restricted Diminished Radix algorithm can quickly reduce an input modulo a modulus of the form $n = \beta^p - k$.  This algorithm can reduce
-an input $x$ within the range $0 \le x < n^2$ using only a couple passes of the algorithm demonstrated in figure~\ref{fig:DR}.  The implementation
-of this algorithm has been optimized to avoid additional overhead associated with a division by $\beta^p$, the multiplication by $k$ or the addition
-of $x$ and $q$.  The resulting algorithm is very efficient and can lead to substantial improvements over Barrett and Montgomery reduction when modular
-exponentiations are performed.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_dr\_reduce}. \\
-\textbf{Input}.   mp\_int $x$, $n$ and a mp\_digit $k = \beta - n_0$ \\
-\hspace{11.5mm}($0 \le x < n^2$, $n > 1$, $0 < k < \beta$) \\
-\textbf{Output}.  $x \mbox{ mod } n$ \\
-\hline \\
-1.  $m \leftarrow n.used$ \\
-2.  If $x.alloc < 2m$ then grow $x$ to $2m$ digits. \\
-3.  $\mu \leftarrow 0$ \\
-4.  for $i$ from $0$ to $m - 1$ do \\
-\hspace{3mm}4.1  $\hat r \leftarrow k \cdot x_{m+i} + x_{i} + \mu$ \\
-\hspace{3mm}4.2  $x_{i} \leftarrow \hat r \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{3mm}4.3  $\mu \leftarrow \lfloor \hat r / \beta \rfloor$ \\
-5.  $x_{m} \leftarrow \mu$ \\
-6.  for $i$ from $m + 1$ to $x.used - 1$ do \\
-\hspace{3mm}6.1  $x_{i} \leftarrow 0$ \\
-7.  Clamp excess digits of $x$. \\
-8.  If $x \ge n$ then \\
-\hspace{3mm}8.1  $x \leftarrow x - n$ \\
-\hspace{3mm}8.2  Goto step 3. \\
-9.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_dr\_reduce}
-\end{figure}
-
-\textbf{Algorithm mp\_dr\_reduce.}
-This algorithm will perform the Dimished Radix reduction of $x$ modulo $n$.  It has similar restrictions to that of the Barrett reduction
-with the addition that $n$ must be of the form $n = \beta^m - k$ where $0 < k <\beta$.
-
-This algorithm essentially implements the pseudo-code in figure~\ref{fig:DR} except with a slight optimization.  The division by $\beta^m$, multiplication by $k$
-and addition of $x \mbox{ mod }\beta^m$ are all performed simultaneously inside the loop on step 4.  The division by $\beta^m$ is emulated by accessing
-the term at the $m+i$'th position which is subsequently multiplied by $k$ and added to the term at the $i$'th position.  After the loop the $m$'th
-digit is set to the carry and the upper digits are zeroed.  Steps 5 and 6 emulate the reduction modulo $\beta^m$ that should have happend to
-$x$ before the addition of the multiple of the upper half.
-
-At step 8 if $x$ is still larger than $n$ another pass of the algorithm is required.  First $n$ is subtracted from $x$ and then the algorithm resumes
-at step 3.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_dr\_reduce.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
-018    *
-019    * Based on algorithm from the paper
-020    *
-021    * "Generating Efficient Primes for Discrete Log Cryptosystems"
-022    *                 Chae Hoon Lim, Pil Joong Lee,
-023    *          POSTECH Information Research Laboratories
-024    *
-025    * The modulus must be of a special format [see manual]
-026    *
-027    * Has been modified to use algorithm 7.10 from the LTM book instead
-028    *
-029    * Input x must be in the range 0 <= x <= (n-1)**2
-030    */
-031   int
-032   mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k)
-033   \{
-034     int      err, i, m;
-035     mp_word  r;
-036     mp_digit mu, *tmpx1, *tmpx2;
-037
-038     /* m = digits in modulus */
-039     m = n->used;
-040
-041     /* ensure that "x" has at least 2m digits */
-042     if (x->alloc < (m + m)) \{
-043       if ((err = mp_grow (x, m + m)) != MP_OKAY) \{
-044         return err;
-045       \}
-046     \}
-047
-048   /* top of loop, this is where the code resumes if
-049    * another reduction pass is required.
-050    */
-051   top:
-052     /* aliases for digits */
-053     /* alias for lower half of x */
-054     tmpx1 = x->dp;
-055
-056     /* alias for upper half of x, or x/B**m */
-057     tmpx2 = x->dp + m;
-058
-059     /* set carry to zero */
-060     mu = 0;
-061
-062     /* compute (x mod B**m) + k * [x/B**m] inline and inplace */
-063     for (i = 0; i < m; i++) \{
-064         r         = (((mp_word)*tmpx2++) * (mp_word)k) + *tmpx1 + mu;
-065         *tmpx1++  = (mp_digit)(r & MP_MASK);
-066         mu        = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
-067     \}
-068
-069     /* set final carry */
-070     *tmpx1++ = mu;
-071
-072     /* zero words above m */
-073     for (i = m + 1; i < x->used; i++) \{
-074         *tmpx1++ = 0;
-075     \}
-076
-077     /* clamp, sub and return */
-078     mp_clamp (x);
-079
-080     /* if x >= n then subtract and reduce again
-081      * Each successive "recursion" makes the input smaller and smaller.
-082      */
-083     if (mp_cmp_mag (x, n) != MP_LT) \{
-084       if ((err = s_mp_sub(x, n, x)) != MP_OKAY) \{
-085         return err;
-086       \}
-087       goto top;
-088     \}
-089     return MP_OKAY;
-090   \}
-091   #endif
-092
-\end{alltt}
-\end{small}
-
-The first step is to grow $x$ as required to $2m$ digits since the reduction is performed in place on $x$.  The label on line 51 is where
-the algorithm will resume if further reduction passes are required.  In theory it could be placed at the top of the function however, the size of
-the modulus and question of whether $x$ is large enough are invariant after the first pass meaning that it would be a waste of time.
-
-The aliases $tmpx1$ and $tmpx2$ refer to the digits of $x$ where the latter is offset by $m$ digits.  By reading digits from $x$ offset by $m$ digits
-a division by $\beta^m$ can be simulated virtually for free.  The loop on line 63 performs the bulk of the work (\textit{corresponds to step 4 of algorithm 7.11})
-in this algorithm.
-
-By line 70 the pointer $tmpx1$ points to the $m$'th digit of $x$ which is where the final carry will be placed.  Similarly by line 73 the
-same pointer will point to the $m+1$'th digit where the zeroes will be placed.
-
-Since the algorithm is only valid if both $x$ and $n$ are greater than zero an unsigned comparison suffices to determine if another pass is required.
-With the same logic at line 84 the value of $x$ is known to be greater than or equal to $n$ meaning that an unsigned subtraction can be used
-as well.  Since the destination of the subtraction is the larger of the inputs the call to algorithm s\_mp\_sub cannot fail and the return code
-does not need to be checked.
-
-\subsubsection{Setup}
-To setup the restricted Diminished Radix algorithm the value $k = \beta - n_0$ is required.  This algorithm is not really complicated but provided for
-completeness.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_dr\_setup}. \\
-\textbf{Input}.   mp\_int $n$ \\
-\textbf{Output}.  $k = \beta - n_0$ \\
-\hline \\
-1.  $k \leftarrow \beta - n_0$ \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_dr\_setup}
-\end{figure}
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_dr\_setup.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* determines the setup value */
-018   void mp_dr_setup(mp_int *a, mp_digit *d)
-019   \{
-020      /* the casts are required if DIGIT_BIT is one less than
-021       * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
-022       */
-023      *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) -
-024           ((mp_word)a->dp[0]));
-025   \}
-026
-027   #endif
-028
-\end{alltt}
-\end{small}
-
-\subsubsection{Modulus Detection}
-Another algorithm which will be useful is the ability to detect a restricted Diminished Radix modulus.  An integer is said to be
-of restricted Diminished Radix form if all of the digits are equal to $\beta - 1$ except the trailing digit which may be any value.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_dr\_is\_modulus}. \\
-\textbf{Input}.   mp\_int $n$ \\
-\textbf{Output}.  $1$ if $n$ is in D.R form, $0$ otherwise \\
-\hline
-1.  If $n.used < 2$ then return($0$). \\
-2.  for $ix$ from $1$ to $n.used - 1$ do \\
-\hspace{3mm}2.1  If $n_{ix} \ne \beta - 1$ return($0$). \\
-3.  Return($1$). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_dr\_is\_modulus}
-\end{figure}
-
-\textbf{Algorithm mp\_dr\_is\_modulus.}
-This algorithm determines if a value is in Diminished Radix form.  Step 1 rejects obvious cases where fewer than two digits are
-in the mp\_int.  Step 2 tests all but the first digit to see if they are equal to $\beta - 1$.  If the algorithm manages to get to
-step 3 then $n$ must be of Diminished Radix form.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_dr\_is\_modulus.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* determines if a number is a valid DR modulus */
-018   int mp_dr_is_modulus(mp_int *a)
-019   \{
-020      int ix;
-021
-022      /* must be at least two digits */
-023      if (a->used < 2) \{
-024         return 0;
-025      \}
-026
-027      /* must be of the form b**k - a [a <= b] so all
-028       * but the first digit must be equal to -1 (mod b).
-029       */
-030      for (ix = 1; ix < a->used; ix++) \{
-031          if (a->dp[ix] != MP_MASK) \{
-032             return 0;
-033          \}
-034      \}
-035      return 1;
-036   \}
-037
-038   #endif
-039
-\end{alltt}
-\end{small}
-
-\subsection{Unrestricted Diminished Radix Reduction}
-The unrestricted Diminished Radix algorithm allows modular reductions to be performed when the modulus is of the form $2^p - k$.  This algorithm
-is a straightforward adaptation of algorithm~\ref{fig:DR}.
-
-In general the restricted Diminished Radix reduction algorithm is much faster since it has considerably lower overhead.  However, this new
-algorithm is much faster than either Montgomery or Barrett reduction when the moduli are of the appropriate form.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_reduce\_2k}. \\
-\textbf{Input}.   mp\_int $a$ and $n$.  mp\_digit $k$  \\
-\hspace{11.5mm}($a \ge 0$, $n > 1$, $0 < k < \beta$, $n + k$ is a power of two) \\
-\textbf{Output}.  $a \mbox{ (mod }n\mbox{)}$ \\
-\hline
-1.  $p \leftarrow \lceil lg(n) \rceil$  (\textit{mp\_count\_bits}) \\
-2.  While $a \ge n$ do \\
-\hspace{3mm}2.1  $q \leftarrow \lfloor a / 2^p \rfloor$ (\textit{mp\_div\_2d}) \\
-\hspace{3mm}2.2  $a \leftarrow a \mbox{ (mod }2^p\mbox{)}$ (\textit{mp\_mod\_2d}) \\
-\hspace{3mm}2.3  $q \leftarrow q \cdot k$ (\textit{mp\_mul\_d}) \\
-\hspace{3mm}2.4  $a \leftarrow a - q$ (\textit{s\_mp\_sub}) \\
-\hspace{3mm}2.5  If $a \ge n$ then do \\
-\hspace{6mm}2.5.1  $a \leftarrow a - n$ \\
-3.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_reduce\_2k}
-\end{figure}
-
-\textbf{Algorithm mp\_reduce\_2k.}
-This algorithm quickly reduces an input $a$ modulo an unrestricted Diminished Radix modulus $n$.  Division by $2^p$ is emulated with a right
-shift which makes the algorithm fairly inexpensive to use.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_reduce\_2k.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* reduces a modulo n where n is of the form 2**p - d */
-018   int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
-019   \{
-020      mp_int q;
-021      int    p, res;
-022
-023      if ((res = mp_init(&q)) != MP_OKAY) \{
-024         return res;
-025      \}
-026
-027      p = mp_count_bits(n);
-028   top:
-029      /* q = a/2**p, a = a mod 2**p */
-030      if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) \{
-031         goto ERR;
-032      \}
-033
-034      if (d != 1) \{
-035         /* q = q * d */
-036         if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) \{
-037            goto ERR;
-038         \}
-039      \}
-040
-041      /* a = a + q */
-042      if ((res = s_mp_add(a, &q, a)) != MP_OKAY) \{
-043         goto ERR;
-044      \}
-045
-046      if (mp_cmp_mag(a, n) != MP_LT) \{
-047         if ((res = s_mp_sub(a, n, a)) != MP_OKAY) \{
-048            goto ERR;
-049         \}
-050         goto top;
-051      \}
-052
-053   ERR:
-054      mp_clear(&q);
-055      return res;
-056   \}
-057
-058   #endif
-059
-\end{alltt}
-\end{small}
-
-The algorithm mp\_count\_bits calculates the number of bits in an mp\_int which is used to find the initial value of $p$.  The call to mp\_div\_2d
-on line 30 calculates both the quotient $q$ and the remainder $a$ required.  By doing both in a single function call the code size
-is kept fairly small.  The multiplication by $k$ is only performed if $k > 1$. This allows reductions modulo $2^p - 1$ to be performed without
-any multiplications.
-
-The unsigned s\_mp\_add, mp\_cmp\_mag and s\_mp\_sub are used in place of their full sign counterparts since the inputs are only valid if they are
-positive.  By using the unsigned versions the overhead is kept to a minimum.
-
-\subsubsection{Unrestricted Setup}
-To setup this reduction algorithm the value of $k = 2^p - n$ is required.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_reduce\_2k\_setup}. \\
-\textbf{Input}.   mp\_int $n$   \\
-\textbf{Output}.  $k = 2^p - n$ \\
-\hline
-1.  $p \leftarrow \lceil lg(n) \rceil$  (\textit{mp\_count\_bits}) \\
-2.  $x \leftarrow 2^p$ (\textit{mp\_2expt}) \\
-3.  $x \leftarrow x - n$ (\textit{mp\_sub}) \\
-4.  $k \leftarrow x_0$ \\
-5.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_reduce\_2k\_setup}
-\end{figure}
-
-\textbf{Algorithm mp\_reduce\_2k\_setup.}
-This algorithm computes the value of $k$ required for the algorithm mp\_reduce\_2k.  By making a temporary variable $x$ equal to $2^p$ a subtraction
-is sufficient to solve for $k$.  Alternatively if $n$ has more than one digit the value of $k$ is simply $\beta - n_0$.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_reduce\_2k\_setup.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* determines the setup value */
-018   int mp_reduce_2k_setup(mp_int *a, mp_digit *d)
-019   \{
-020      int res, p;
-021      mp_int tmp;
-022
-023      if ((res = mp_init(&tmp)) != MP_OKAY) \{
-024         return res;
-025      \}
-026
-027      p = mp_count_bits(a);
-028      if ((res = mp_2expt(&tmp, p)) != MP_OKAY) \{
-029         mp_clear(&tmp);
-030         return res;
-031      \}
-032
-033      if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) \{
-034         mp_clear(&tmp);
-035         return res;
-036      \}
-037
-038      *d = tmp.dp[0];
-039      mp_clear(&tmp);
-040      return MP_OKAY;
-041   \}
-042   #endif
-043
-\end{alltt}
-\end{small}
-
-\subsubsection{Unrestricted Detection}
-An integer $n$ is a valid unrestricted Diminished Radix modulus if either of the following are true.
-
-\begin{enumerate}
-\item  The number has only one digit.
-\item  The number has more than one digit and every bit from the $\beta$'th to the most significant is one.
-\end{enumerate}
-
-If either condition is true than there is a power of two $2^p$ such that $0 < 2^p - n < \beta$.   If the input is only
-one digit than it will always be of the correct form.  Otherwise all of the bits above the first digit must be one.  This arises from the fact
-that there will be value of $k$ that when added to the modulus causes a carry in the first digit which propagates all the way to the most
-significant bit.  The resulting sum will be a power of two.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_reduce\_is\_2k}. \\
-\textbf{Input}.   mp\_int $n$   \\
-\textbf{Output}.  $1$ if of proper form, $0$ otherwise \\
-\hline
-1.  If $n.used = 0$ then return($0$). \\
-2.  If $n.used = 1$ then return($1$). \\
-3.  $p \leftarrow \lceil lg(n) \rceil$  (\textit{mp\_count\_bits}) \\
-4.  for $x$ from $lg(\beta)$ to $p$ do \\
-\hspace{3mm}4.1  If the ($x \mbox{ mod }lg(\beta)$)'th bit of the $\lfloor x / lg(\beta) \rfloor$ of $n$ is zero then return($0$). \\
-5.  Return($1$). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_reduce\_is\_2k}
-\end{figure}
-
-\textbf{Algorithm mp\_reduce\_is\_2k.}
-This algorithm quickly determines if a modulus is of the form required for algorithm mp\_reduce\_2k to function properly.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_reduce\_is\_2k.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* determines if mp_reduce_2k can be used */
-018   int mp_reduce_is_2k(mp_int *a)
-019   \{
-020      int ix, iy, iw;
-021      mp_digit iz;
-022
-023      if (a->used == 0) \{
-024         return MP_NO;
-025      \} else if (a->used == 1) \{
-026         return MP_YES;
-027      \} else if (a->used > 1) \{
-028         iy = mp_count_bits(a);
-029         iz = 1;
-030         iw = 1;
-031
-032         /* Test every bit from the second digit up, must be 1 */
-033         for (ix = DIGIT_BIT; ix < iy; ix++) \{
-034             if ((a->dp[iw] & iz) == 0) \{
-035                return MP_NO;
-036             \}
-037             iz <<= 1;
-038             if (iz > (mp_digit)MP_MASK) \{
-039                ++iw;
-040                iz = 1;
-041             \}
-042         \}
-043      \}
-044      return MP_YES;
-045   \}
-046
-047   #endif
-048
-\end{alltt}
-\end{small}
-
-
-
-\section{Algorithm Comparison}
-So far three very different algorithms for modular reduction have been discussed.  Each of the algorithms have their own strengths and weaknesses
-that makes having such a selection very useful.  The following table sumarizes the three algorithms along with comparisons of work factors.  Since
-all three algorithms have the restriction that $0 \le x < n^2$ and $n > 1$ those limitations are not included in the table.
-
-\begin{center}
-\begin{small}
-\begin{tabular}{|c|c|c|c|c|c|}
-\hline \textbf{Method} & \textbf{Work Required} & \textbf{Limitations} & \textbf{$m = 8$} & \textbf{$m = 32$} & \textbf{$m = 64$} \\
-\hline Barrett    & $m^2 + 2m - 1$ & None              & $79$ & $1087$ & $4223$ \\
-\hline Montgomery & $m^2 + m$      & $n$ must be odd   & $72$ & $1056$ & $4160$ \\
-\hline D.R.       & $2m$           & $n = \beta^m - k$ & $16$ & $64$   & $128$  \\
-\hline
-\end{tabular}
-\end{small}
-\end{center}
-
-In theory Montgomery and Barrett reductions would require roughly the same amount of time to complete.  However, in practice since Montgomery
-reduction can be written as a single function with the Comba technique it is much faster.  Barrett reduction suffers from the overhead of
-calling the half precision multipliers, addition and division by $\beta$ algorithms.
-
-For almost every cryptographic algorithm Montgomery reduction is the algorithm of choice.  The one set of algorithms where Diminished Radix reduction truly
-shines are based on the discrete logarithm problem such as Diffie-Hellman \cite{DH} and ElGamal \cite{ELGAMAL}.  In these algorithms
-primes of the form $\beta^m - k$ can be found and shared amongst users.  These primes will allow the Diminished Radix algorithm to be used in
-modular exponentiation to greatly speed up the operation.
-
-
-
-\section*{Exercises}
-\begin{tabular}{cl}
-$\left [ 3 \right ]$ & Prove that the ``trick'' in algorithm mp\_montgomery\_setup actually \\
-                     & calculates the correct value of $\rho$. \\
-                     & \\
-$\left [ 2 \right ]$ & Devise an algorithm to reduce modulo $n + k$ for small $k$ quickly.  \\
-                     & \\
-$\left [ 4 \right ]$ & Prove that the pseudo-code algorithm ``Diminished Radix Reduction'' \\
-                     & (\textit{figure~\ref{fig:DR}}) terminates.  Also prove the probability that it will \\
-                     & terminate within $1 \le k \le 10$ iterations. \\
-                     & \\
-\end{tabular}
-
-
-\chapter{Exponentiation}
-Exponentiation is the operation of raising one variable to the power of another, for example, $a^b$.  A variant of exponentiation, computed
-in a finite field or ring, is called modular exponentiation.  This latter style of operation is typically used in public key
-cryptosystems such as RSA and Diffie-Hellman.  The ability to quickly compute modular exponentiations is of great benefit to any
-such cryptosystem and many methods have been sought to speed it up.
-
-\section{Exponentiation Basics}
-A trivial algorithm would simply multiply $a$ against itself $b - 1$ times to compute the exponentiation desired.  However, as $b$ grows in size
-the number of multiplications becomes prohibitive.  Imagine what would happen if $b$ $\approx$ $2^{1024}$ as is the case when computing an RSA signature
-with a $1024$-bit key.  Such a calculation could never be completed as it would take simply far too long.
-
-Fortunately there is a very simple algorithm based on the laws of exponents.  Recall that $lg_a(a^b) = b$ and that $lg_a(a^ba^c) = b + c$ which
-are two trivial relationships between the base and the exponent.  Let $b_i$ represent the $i$'th bit of $b$ starting from the least
-significant bit.  If $b$ is a $k$-bit integer than the following equation is true.
-
-\begin{equation}
-a^b = \prod_{i=0}^{k-1} a^{2^i \cdot b_i}
-\end{equation}
-
-By taking the base $a$ logarithm of both sides of the equation the following equation is the result.
-
-\begin{equation}
-b = \sum_{i=0}^{k-1}2^i \cdot b_i
-\end{equation}
-
-The term $a^{2^i}$ can be found from the $i - 1$'th term by squaring the term since $\left ( a^{2^i} \right )^2$ is equal to
-$a^{2^{i+1}}$.  This observation forms the basis of essentially all fast exponentiation algorithms.  It requires $k$ squarings and on average
-$k \over 2$ multiplications to compute the result.  This is indeed quite an improvement over simply multiplying by $a$ a total of $b-1$ times.
-
-While this current method is a considerable speed up there are further improvements to be made.  For example, the $a^{2^i}$ term does not need to
-be computed in an auxilary variable.  Consider the following equivalent algorithm.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Left to Right Exponentiation}. \\
-\textbf{Input}.   Integer $a$, $b$ and $k$ \\
-\textbf{Output}.  $c = a^b$ \\
-\hline \\
-1.  $c \leftarrow 1$ \\
-2.  for $i$ from $k - 1$ to $0$ do \\
-\hspace{3mm}2.1  $c \leftarrow c^2$ \\
-\hspace{3mm}2.2  $c \leftarrow c \cdot a^{b_i}$ \\
-3.  Return $c$. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Left to Right Exponentiation}
-\label{fig:LTOR}
-\end{figure}
-
-This algorithm starts from the most significant bit and works towards the least significant bit.  When the $i$'th bit of $b$ is set $a$ is
-multiplied against the current product.  In each iteration the product is squared which doubles the exponent of the individual terms of the
-product.
-
-For example, let $b = 101100_2 \equiv 44_{10}$.  The following chart demonstrates the actions of the algorithm.
-
-\newpage\begin{figure}
-\begin{center}
-\begin{tabular}{|c|c|}
-\hline \textbf{Value of $i$} & \textbf{Value of $c$} \\
-\hline - & $1$ \\
-\hline $5$ & $a$ \\
-\hline $4$ & $a^2$ \\
-\hline $3$ & $a^4 \cdot a$ \\
-\hline $2$ & $a^8 \cdot a^2 \cdot a$ \\
-\hline $1$ & $a^{16} \cdot a^4 \cdot a^2$ \\
-\hline $0$ & $a^{32} \cdot a^8 \cdot a^4$ \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Example of Left to Right Exponentiation}
-\end{figure}
-
-When the product $a^{32} \cdot a^8 \cdot a^4$ is simplified it is equal $a^{44}$ which is the desired exponentiation.  This particular algorithm is
-called ``Left to Right'' because it reads the exponent in that order.  All of the exponentiation algorithms that will be presented are of this nature.
-
-\subsection{Single Digit Exponentiation}
-The first algorithm in the series of exponentiation algorithms will be an unbounded algorithm where the exponent is a single digit.  It is intended
-to be used when a small power of an input is required (\textit{e.g. $a^5$}).  It is faster than simply multiplying $b - 1$ times for all values of
-$b$ that are greater than three.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_expt\_d}. \\
-\textbf{Input}.   mp\_int $a$ and mp\_digit $b$ \\
-\textbf{Output}.  $c = a^b$ \\
-\hline \\
-1.  $g \leftarrow a$ (\textit{mp\_init\_copy}) \\
-2.  $c \leftarrow 1$ (\textit{mp\_set}) \\
-3.  for $x$ from 1 to $lg(\beta)$ do \\
-\hspace{3mm}3.1  $c \leftarrow c^2$ (\textit{mp\_sqr}) \\
-\hspace{3mm}3.2  If $b$ AND $2^{lg(\beta) - 1} \ne 0$ then \\
-\hspace{6mm}3.2.1  $c \leftarrow c \cdot g$ (\textit{mp\_mul}) \\
-\hspace{3mm}3.3  $b \leftarrow b << 1$ \\
-4.  Clear $g$. \\
-5.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_expt\_d}
-\end{figure}
-
-\textbf{Algorithm mp\_expt\_d.}
-This algorithm computes the value of $a$ raised to the power of a single digit $b$.  It uses the left to right exponentiation algorithm to
-quickly compute the exponentiation.  It is loosely based on algorithm 14.79 of HAC \cite[pp. 615]{HAC} with the difference that the
-exponent is a fixed width.
-
-A copy of $a$ is made first to allow destination variable $c$ be the same as the source variable $a$.  The result is set to the initial value of
-$1$ in the subsequent step.
-
-Inside the loop the exponent is read from the most significant bit first down to the least significant bit.  First $c$ is invariably squared
-on step 3.1.  In the following step if the most significant bit of $b$ is one the copy of $a$ is multiplied against $c$.  The value
-of $b$ is shifted left one bit to make the next bit down from the most signficant bit the new most significant bit.  In effect each
-iteration of the loop moves the bits of the exponent $b$ upwards to the most significant location.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_expt\_d\_ex.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* calculate c = a**b  using a square-multiply algorithm */
-018   int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
-019   \{
-020     int     res;
-021     unsigned int x;
-022
-023     mp_int  g;
-024
-025     if ((res = mp_init_copy (&g, a)) != MP_OKAY) \{
-026       return res;
-027     \}
-028
-029     /* set initial result */
-030     mp_set (c, 1);
-031
-032     if (fast != 0) \{
-033       while (b > 0) \{
-034         /* if the bit is set multiply */
-035         if ((b & 1) != 0) \{
-036           if ((res = mp_mul (c, &g, c)) != MP_OKAY) \{
-037             mp_clear (&g);
-038             return res;
-039           \}
-040         \}
-041
-042         /* square */
-043         if (b > 1) \{
-044           if ((res = mp_sqr (&g, &g)) != MP_OKAY) \{
-045             mp_clear (&g);
-046             return res;
-047           \}
-048         \}
-049
-050         /* shift to next bit */
-051         b >>= 1;
-052       \}
-053     \}
-054     else \{
-055       for (x = 0; x < DIGIT_BIT; x++) \{
-056         /* square */
-057         if ((res = mp_sqr (c, c)) != MP_OKAY) \{
-058           mp_clear (&g);
-059           return res;
-060         \}
-061
-062         /* if the bit is set multiply */
-063         if ((b & (mp_digit) (((mp_digit)1) << (DIGIT_BIT - 1))) != 0) \{
-064           if ((res = mp_mul (c, &g, c)) != MP_OKAY) \{
-065              mp_clear (&g);
-066              return res;
-067           \}
-068         \}
-069
-070         /* shift to next bit */
-071         b <<= 1;
-072       \}
-073     \} /* if ... else */
-074
-075     mp_clear (&g);
-076     return MP_OKAY;
-077   \}
-078   #endif
-079
-\end{alltt}
-\end{small}
-
-This describes only the algorithm that is used when the parameter $fast$ is $0$.  Line 30 sets the initial value of the result to $1$.  Next the loop on line 55 steps through each bit of the exponent starting from
-the most significant down towards the least significant. The invariant squaring operation placed on line 57 is performed first.  After
-the squaring the result $c$ is multiplied by the base $g$ if and only if the most significant bit of the exponent is set.  The shift on line
-71 moves all of the bits of the exponent upwards towards the most significant location.
-
-\section{$k$-ary Exponentiation}
-When calculating an exponentiation the most time consuming bottleneck is the multiplications which are in general a small factor
-slower than squaring.  Recall from the previous algorithm that $b_{i}$ refers to the $i$'th bit of the exponent $b$.  Suppose instead it referred to
-the $i$'th $k$-bit digit of the exponent of $b$.  For $k = 1$ the definitions are synonymous and for $k > 1$ algorithm~\ref{fig:KARY}
-computes the same exponentiation.  A group of $k$ bits from the exponent is called a \textit{window}.  That is it is a small window on only a
-portion of the entire exponent.  Consider the following modification to the basic left to right exponentiation algorithm.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{$k$-ary Exponentiation}. \\
-\textbf{Input}.   Integer $a$, $b$, $k$ and $t$ \\
-\textbf{Output}.  $c = a^b$ \\
-\hline \\
-1.  $c \leftarrow 1$ \\
-2.  for $i$ from $t - 1$ to $0$ do \\
-\hspace{3mm}2.1  $c \leftarrow c^{2^k} $ \\
-\hspace{3mm}2.2  Extract the $i$'th $k$-bit word from $b$ and store it in $g$. \\
-\hspace{3mm}2.3  $c \leftarrow c \cdot a^g$ \\
-3.  Return $c$. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{$k$-ary Exponentiation}
-\label{fig:KARY}
-\end{figure}
-
-The squaring on step 2.1 can be calculated by squaring the value $c$ successively $k$ times.  If the values of $a^g$ for $0 < g < 2^k$ have been
-precomputed this algorithm requires only $t$ multiplications and $tk$ squarings.  The table can be generated with $2^{k - 1} - 1$ squarings and
-$2^{k - 1} + 1$ multiplications.  This algorithm assumes that the number of bits in the exponent is evenly divisible by $k$.
-However, when it is not the remaining $0 < x \le k - 1$ bits can be handled with algorithm~\ref{fig:LTOR}.
-
-Suppose $k = 4$ and $t = 100$.  This modified algorithm will require $109$ multiplications and $408$ squarings to compute the exponentiation.  The
-original algorithm would on average have required $200$ multiplications and $400$ squrings to compute the same value.  The total number of squarings
-has increased slightly but the number of multiplications has nearly halved.
-
-\subsection{Optimal Values of $k$}
-An optimal value of $k$ will minimize $2^{k} + \lceil n / k \rceil + n - 1$ for a fixed number of bits in the exponent $n$.  The simplest
-approach is to brute force search amongst the values $k = 2, 3, \ldots, 8$ for the lowest result.  Table~\ref{fig:OPTK} lists optimal values of $k$
-for various exponent sizes and compares the number of multiplication and squarings required against algorithm~\ref{fig:LTOR}.
-
-\begin{figure}[here]
-\begin{center}
-\begin{small}
-\begin{tabular}{|c|c|c|c|c|c|}
-\hline \textbf{Exponent (bits)} & \textbf{Optimal $k$} & \textbf{Work at $k$} & \textbf{Work with ~\ref{fig:LTOR}} \\
-\hline $16$ & $2$ & $27$ & $24$ \\
-\hline $32$ & $3$ & $49$ & $48$ \\
-\hline $64$ & $3$ & $92$ & $96$ \\
-\hline $128$ & $4$ & $175$ & $192$ \\
-\hline $256$ & $4$ & $335$ & $384$ \\
-\hline $512$ & $5$ & $645$ & $768$ \\
-\hline $1024$ & $6$ & $1257$ & $1536$ \\
-\hline $2048$ & $6$ & $2452$ & $3072$ \\
-\hline $4096$ & $7$ & $4808$ & $6144$ \\
-\hline
-\end{tabular}
-\end{small}
-\end{center}
-\caption{Optimal Values of $k$ for $k$-ary Exponentiation}
-\label{fig:OPTK}
-\end{figure}
-
-\subsection{Sliding-Window Exponentiation}
-A simple modification to the previous algorithm is only generate the upper half of the table in the range $2^{k-1} \le g < 2^k$.  Essentially
-this is a table for all values of $g$ where the most significant bit of $g$ is a one.  However, in order for this to be allowed in the
-algorithm values of $g$ in the range $0 \le g < 2^{k-1}$ must be avoided.
-
-Table~\ref{fig:OPTK2} lists optimal values of $k$ for various exponent sizes and compares the work required against algorithm {\ref{fig:KARY}}.
-
-\begin{figure}[here]
-\begin{center}
-\begin{small}
-\begin{tabular}{|c|c|c|c|c|c|}
-\hline \textbf{Exponent (bits)} & \textbf{Optimal $k$} & \textbf{Work at $k$} & \textbf{Work with ~\ref{fig:KARY}} \\
-\hline $16$ & $3$ & $24$ & $27$ \\
-\hline $32$ & $3$ & $45$ & $49$ \\
-\hline $64$ & $4$ & $87$ & $92$ \\
-\hline $128$ & $4$ & $167$ & $175$ \\
-\hline $256$ & $5$ & $322$ & $335$ \\
-\hline $512$ & $6$ & $628$ & $645$ \\
-\hline $1024$ & $6$ & $1225$ & $1257$ \\
-\hline $2048$ & $7$ & $2403$ & $2452$ \\
-\hline $4096$ & $8$ & $4735$ & $4808$ \\
-\hline
-\end{tabular}
-\end{small}
-\end{center}
-\caption{Optimal Values of $k$ for Sliding Window Exponentiation}
-\label{fig:OPTK2}
-\end{figure}
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Sliding Window $k$-ary Exponentiation}. \\
-\textbf{Input}.   Integer $a$, $b$, $k$ and $t$ \\
-\textbf{Output}.  $c = a^b$ \\
-\hline \\
-1.  $c \leftarrow 1$ \\
-2.  for $i$ from $t - 1$ to $0$ do \\
-\hspace{3mm}2.1  If the $i$'th bit of $b$ is a zero then \\
-\hspace{6mm}2.1.1   $c \leftarrow c^2$ \\
-\hspace{3mm}2.2  else do \\
-\hspace{6mm}2.2.1  $c \leftarrow c^{2^k}$ \\
-\hspace{6mm}2.2.2  Extract the $k$ bits from $(b_{i}b_{i-1}\ldots b_{i-(k-1)})$ and store it in $g$. \\
-\hspace{6mm}2.2.3  $c \leftarrow c \cdot a^g$ \\
-\hspace{6mm}2.2.4  $i \leftarrow i - k$ \\
-3.  Return $c$. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Sliding Window $k$-ary Exponentiation}
-\end{figure}
-
-Similar to the previous algorithm this algorithm must have a special handler when fewer than $k$ bits are left in the exponent.  While this
-algorithm requires the same number of squarings it can potentially have fewer multiplications.  The pre-computed table $a^g$ is also half
-the size as the previous table.
-
-Consider the exponent $b = 111101011001000_2 \equiv 31432_{10}$ with $k = 3$ using both algorithms.  The first algorithm will divide the exponent up as
-the following five $3$-bit words $b \equiv \left ( 111, 101, 011, 001, 000 \right )_{2}$.  The second algorithm will break the
-exponent as $b \equiv \left ( 111, 101, 0, 110, 0, 100, 0 \right )_{2}$.  The single digit $0$ in the second representation are where
-a single squaring took place instead of a squaring and multiplication.  In total the first method requires $10$ multiplications and $18$
-squarings.  The second method requires $8$ multiplications and $18$ squarings.
-
-In general the sliding window method is never slower than the generic $k$-ary method and often it is slightly faster.
-
-\section{Modular Exponentiation}
-
-Modular exponentiation is essentially computing the power of a base within a finite field or ring.  For example, computing
-$d \equiv a^b \mbox{ (mod }c\mbox{)}$ is a modular exponentiation.  Instead of first computing $a^b$ and then reducing it
-modulo $c$ the intermediate result is reduced modulo $c$ after every squaring or multiplication operation.
-
-This guarantees that any intermediate result is bounded by $0 \le d \le c^2 - 2c + 1$ and can be reduced modulo $c$ quickly using
-one of the algorithms presented in chapter six.
-
-Before the actual modular exponentiation algorithm can be written a wrapper algorithm must be written first.  This algorithm
-will allow the exponent $b$ to be negative which is computed as $c \equiv \left (1 / a \right )^{\vert b \vert} \mbox{(mod }d\mbox{)}$. The
-value of $(1/a) \mbox{ mod }c$ is computed using the modular inverse (\textit{see \ref{sec;modinv}}).  If no inverse exists the algorithm
-terminates with an error.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_exptmod}. \\
-\textbf{Input}.   mp\_int $a$, $b$ and $c$ \\
-\textbf{Output}.  $y \equiv g^x \mbox{ (mod }p\mbox{)}$ \\
-\hline \\
-1.  If $c.sign = MP\_NEG$ return(\textit{MP\_VAL}). \\
-2.  If $b.sign = MP\_NEG$ then \\
-\hspace{3mm}2.1  $g' \leftarrow g^{-1} \mbox{ (mod }c\mbox{)}$ \\
-\hspace{3mm}2.2  $x' \leftarrow \vert x \vert$ \\
-\hspace{3mm}2.3  Compute $d \equiv g'^{x'} \mbox{ (mod }c\mbox{)}$ via recursion. \\
-3.  if $p$ is odd \textbf{OR} $p$ is a D.R. modulus then \\
-\hspace{3mm}3.1  Compute $y \equiv g^{x} \mbox{ (mod }p\mbox{)}$ via algorithm mp\_exptmod\_fast. \\
-4.  else \\
-\hspace{3mm}4.1  Compute $y \equiv g^{x} \mbox{ (mod }p\mbox{)}$ via algorithm s\_mp\_exptmod. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_exptmod}
-\end{figure}
-
-\textbf{Algorithm mp\_exptmod.}
-The first algorithm which actually performs modular exponentiation is algorithm s\_mp\_exptmod.  It is a sliding window $k$-ary algorithm
-which uses Barrett reduction to reduce the product modulo $p$.  The second algorithm mp\_exptmod\_fast performs the same operation
-except it uses either Montgomery or Diminished Radix reduction.  The two latter reduction algorithms are clumped in the same exponentiation
-algorithm since their arguments are essentially the same (\textit{two mp\_ints and one mp\_digit}).
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_exptmod.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017
-018   /* this is a shell function that calls either the normal or Montgomery
-019    * exptmod functions.  Originally the call to the montgomery code was
-020    * embedded in the normal function but that wasted alot of stack space
-021    * for nothing (since 99% of the time the Montgomery code would be called)
-022    */
-023   int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
-024   \{
-025     int dr;
-026
-027     /* modulus P must be positive */
-028     if (P->sign == MP_NEG) \{
-029        return MP_VAL;
-030     \}
-031
-032     /* if exponent X is negative we have to recurse */
-033     if (X->sign == MP_NEG) \{
-034   #ifdef BN_MP_INVMOD_C
-035        mp_int tmpG, tmpX;
-036        int err;
-037
-038        /* first compute 1/G mod P */
-039        if ((err = mp_init(&tmpG)) != MP_OKAY) \{
-040           return err;
-041        \}
-042        if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) \{
-043           mp_clear(&tmpG);
-044           return err;
-045        \}
-046
-047        /* now get |X| */
-048        if ((err = mp_init(&tmpX)) != MP_OKAY) \{
-049           mp_clear(&tmpG);
-050           return err;
-051        \}
-052        if ((err = mp_abs(X, &tmpX)) != MP_OKAY) \{
-053           mp_clear_multi(&tmpG, &tmpX, NULL);
-054           return err;
-055        \}
-056
-057        /* and now compute (1/G)**|X| instead of G**X [X < 0] */
-058        err = mp_exptmod(&tmpG, &tmpX, P, Y);
-059        mp_clear_multi(&tmpG, &tmpX, NULL);
-060        return err;
-061   #else
-062        /* no invmod */
-063        return MP_VAL;
-064   #endif
-065     \}
-066
-067   /* modified diminished radix reduction */
-068   #if defined(BN_MP_REDUCE_IS_2K_L_C) && defined(BN_MP_REDUCE_2K_L_C) && defin
-      ed(BN_S_MP_EXPTMOD_C)
-069     if (mp_reduce_is_2k_l(P) == MP_YES) \{
-070        return s_mp_exptmod(G, X, P, Y, 1);
-071     \}
-072   #endif
-073
-074   #ifdef BN_MP_DR_IS_MODULUS_C
-075     /* is it a DR modulus? */
-076     dr = mp_dr_is_modulus(P);
-077   #else
-078     /* default to no */
-079     dr = 0;
-080   #endif
-081
-082   #ifdef BN_MP_REDUCE_IS_2K_C
-083     /* if not, is it a unrestricted DR modulus? */
-084     if (dr == 0) \{
-085        dr = mp_reduce_is_2k(P) << 1;
-086     \}
-087   #endif
-088
-089     /* if the modulus is odd or dr != 0 use the montgomery method */
-090   #ifdef BN_MP_EXPTMOD_FAST_C
-091     if ((mp_isodd (P) == MP_YES) || (dr !=  0)) \{
-092       return mp_exptmod_fast (G, X, P, Y, dr);
-093     \} else \{
-094   #endif
-095   #ifdef BN_S_MP_EXPTMOD_C
-096       /* otherwise use the generic Barrett reduction technique */
-097       return s_mp_exptmod (G, X, P, Y, 0);
-098   #else
-099       /* no exptmod for evens */
-100       return MP_VAL;
-101   #endif
-102   #ifdef BN_MP_EXPTMOD_FAST_C
-103     \}
-104   #endif
-105   \}
-106
-107   #endif
-108
-\end{alltt}
-\end{small}
-
-In order to keep the algorithms in a known state the first step on line 28 is to reject any negative modulus as input.  If the exponent is
-negative the algorithm tries to perform a modular exponentiation with the modular inverse of the base $G$.  The temporary variable $tmpG$ is assigned
-the modular inverse of $G$ and $tmpX$ is assigned the absolute value of $X$.  The algorithm will recuse with these new values with a positive
-exponent.
-
-If the exponent is positive the algorithm resumes the exponentiation.  Line 76 determines if the modulus is of the restricted Diminished Radix
-form.  If it is not line 69 attempts to determine if it is of a unrestricted Diminished Radix form.  The integer $dr$ will take on one
-of three values.
-
-\begin{enumerate}
-\item $dr = 0$ means that the modulus is not of either restricted or unrestricted Diminished Radix form.
-\item $dr = 1$ means that the modulus is of restricted Diminished Radix form.
-\item $dr = 2$ means that the modulus is of unrestricted Diminished Radix form.
-\end{enumerate}
-
-Line 69 determines if the fast modular exponentiation algorithm can be used.  It is allowed if $dr \ne 0$ or if the modulus is odd.  Otherwise,
-the slower s\_mp\_exptmod algorithm is used which uses Barrett reduction.
-
-\subsection{Barrett Modular Exponentiation}
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{s\_mp\_exptmod}. \\
-\textbf{Input}.   mp\_int $a$, $b$ and $c$ \\
-\textbf{Output}.  $y \equiv g^x \mbox{ (mod }p\mbox{)}$ \\
-\hline \\
-1.  $k \leftarrow lg(x)$ \\
-2.  $winsize \leftarrow  \left \lbrace \begin{array}{ll}
-                              2 &  \mbox{if }k \le 7 \\
-                              3 &  \mbox{if }7 < k \le 36 \\
-                              4 &  \mbox{if }36 < k \le 140 \\
-                              5 &  \mbox{if }140 < k \le 450 \\
-                              6 &  \mbox{if }450 < k \le 1303 \\
-                              7 &  \mbox{if }1303 < k \le 3529 \\
-                              8 &  \mbox{if }3529 < k \\
-                              \end{array} \right .$ \\
-3.  Initialize $2^{winsize}$ mp\_ints in an array named $M$ and one mp\_int named $\mu$ \\
-4.  Calculate the $\mu$ required for Barrett Reduction (\textit{mp\_reduce\_setup}). \\
-5.  $M_1 \leftarrow g \mbox{ (mod }p\mbox{)}$ \\
-\\
-Setup the table of small powers of $g$.  First find $g^{2^{winsize}}$ and then all multiples of it. \\
-6.  $k \leftarrow 2^{winsize - 1}$ \\
-7.  $M_{k} \leftarrow M_1$ \\
-8.  for $ix$ from 0 to $winsize - 2$ do \\
-\hspace{3mm}8.1  $M_k \leftarrow \left ( M_k \right )^2$ (\textit{mp\_sqr})  \\
-\hspace{3mm}8.2  $M_k \leftarrow M_k \mbox{ (mod }p\mbox{)}$ (\textit{mp\_reduce}) \\
-9.  for $ix$ from $2^{winsize - 1} + 1$ to $2^{winsize} - 1$ do \\
-\hspace{3mm}9.1  $M_{ix} \leftarrow M_{ix - 1} \cdot M_{1}$ (\textit{mp\_mul}) \\
-\hspace{3mm}9.2  $M_{ix} \leftarrow M_{ix} \mbox{ (mod }p\mbox{)}$ (\textit{mp\_reduce}) \\
-10.  $res \leftarrow 1$ \\
-\\
-Start Sliding Window. \\
-11.  $mode \leftarrow 0, bitcnt \leftarrow 1, buf \leftarrow 0, digidx \leftarrow x.used - 1, bitcpy \leftarrow 0, bitbuf \leftarrow 0$ \\
-12.  Loop \\
-\hspace{3mm}12.1  $bitcnt \leftarrow bitcnt - 1$ \\
-\hspace{3mm}12.2  If $bitcnt = 0$ then do \\
-\hspace{6mm}12.2.1  If $digidx = -1$ goto step 13. \\
-\hspace{6mm}12.2.2  $buf \leftarrow x_{digidx}$ \\
-\hspace{6mm}12.2.3  $digidx \leftarrow digidx - 1$ \\
-\hspace{6mm}12.2.4  $bitcnt \leftarrow lg(\beta)$ \\
-Continued on next page. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm s\_mp\_exptmod}
-\end{figure}
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{s\_mp\_exptmod} (\textit{continued}). \\
-\textbf{Input}.   mp\_int $a$, $b$ and $c$ \\
-\textbf{Output}.  $y \equiv g^x \mbox{ (mod }p\mbox{)}$ \\
-\hline \\
-\hspace{3mm}12.3  $y \leftarrow (buf >> (lg(\beta) - 1))$ AND $1$ \\
-\hspace{3mm}12.4  $buf \leftarrow buf << 1$ \\
-\hspace{3mm}12.5  if $mode = 0$ and $y = 0$ then goto step 12. \\
-\hspace{3mm}12.6  if $mode = 1$ and $y = 0$ then do \\
-\hspace{6mm}12.6.1  $res \leftarrow res^2$ \\
-\hspace{6mm}12.6.2  $res \leftarrow res \mbox{ (mod }p\mbox{)}$ \\
-\hspace{6mm}12.6.3  Goto step 12. \\
-\hspace{3mm}12.7  $bitcpy \leftarrow bitcpy + 1$ \\
-\hspace{3mm}12.8  $bitbuf \leftarrow bitbuf + (y << (winsize - bitcpy))$ \\
-\hspace{3mm}12.9  $mode \leftarrow 2$ \\
-\hspace{3mm}12.10  If $bitcpy = winsize$ then do \\
-\hspace{6mm}Window is full so perform the squarings and single multiplication. \\
-\hspace{6mm}12.10.1  for $ix$ from $0$ to $winsize -1$ do \\
-\hspace{9mm}12.10.1.1  $res \leftarrow res^2$ \\
-\hspace{9mm}12.10.1.2  $res \leftarrow res \mbox{ (mod }p\mbox{)}$ \\
-\hspace{6mm}12.10.2  $res \leftarrow res \cdot M_{bitbuf}$ \\
-\hspace{6mm}12.10.3  $res \leftarrow res \mbox{ (mod }p\mbox{)}$ \\
-\hspace{6mm}Reset the window. \\
-\hspace{6mm}12.10.4  $bitcpy \leftarrow 0, bitbuf \leftarrow 0, mode \leftarrow 1$ \\
-\\
-No more windows left.  Check for residual bits of exponent. \\
-13.  If $mode = 2$ and $bitcpy > 0$ then do \\
-\hspace{3mm}13.1  for $ix$ form $0$ to $bitcpy - 1$ do \\
-\hspace{6mm}13.1.1  $res \leftarrow res^2$ \\
-\hspace{6mm}13.1.2  $res \leftarrow res \mbox{ (mod }p\mbox{)}$ \\
-\hspace{6mm}13.1.3  $bitbuf \leftarrow bitbuf << 1$ \\
-\hspace{6mm}13.1.4  If $bitbuf$ AND $2^{winsize} \ne 0$ then do \\
-\hspace{9mm}13.1.4.1  $res \leftarrow res \cdot M_{1}$ \\
-\hspace{9mm}13.1.4.2  $res \leftarrow res \mbox{ (mod }p\mbox{)}$ \\
-14.  $y \leftarrow res$ \\
-15.  Clear $res$, $mu$ and the $M$ array. \\
-16.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm s\_mp\_exptmod (continued)}
-\end{figure}
-
-\textbf{Algorithm s\_mp\_exptmod.}
-This algorithm computes the $x$'th power of $g$ modulo $p$ and stores the result in $y$.  It takes advantage of the Barrett reduction
-algorithm to keep the product small throughout the algorithm.
-
-The first two steps determine the optimal window size based on the number of bits in the exponent.  The larger the exponent the
-larger the window size becomes.  After a window size $winsize$ has been chosen an array of $2^{winsize}$ mp\_int variables is allocated.  This
-table will hold the values of $g^x \mbox{ (mod }p\mbox{)}$ for $2^{winsize - 1} \le x < 2^{winsize}$.
-
-After the table is allocated the first power of $g$ is found.  Since $g \ge p$ is allowed it must be first reduced modulo $p$ to make
-the rest of the algorithm more efficient.  The first element of the table at $2^{winsize - 1}$ is found by squaring $M_1$ successively $winsize - 2$
-times.  The rest of the table elements are found by multiplying the previous element by $M_1$ modulo $p$.
-
-Now that the table is available the sliding window may begin.  The following list describes the functions of all the variables in the window.
-\begin{enumerate}
-\item The variable $mode$ dictates how the bits of the exponent are interpreted.
-\begin{enumerate}
-   \item When $mode = 0$ the bits are ignored since no non-zero bit of the exponent has been seen yet.  For example, if the exponent were simply
-         $1$ then there would be $lg(\beta) - 1$ zero bits before the first non-zero bit.  In this case bits are ignored until a non-zero bit is found.
-   \item When $mode = 1$ a non-zero bit has been seen before and a new $winsize$-bit window has not been formed yet.  In this mode leading $0$ bits
-         are read and a single squaring is performed.  If a non-zero bit is read a new window is created.
-   \item When $mode = 2$ the algorithm is in the middle of forming a window and new bits are appended to the window from the most significant bit
-         downwards.
-\end{enumerate}
-\item The variable $bitcnt$ indicates how many bits are left in the current digit of the exponent left to be read.  When it reaches zero a new digit
-      is fetched from the exponent.
-\item The variable $buf$ holds the currently read digit of the exponent.
-\item The variable $digidx$ is an index into the exponents digits.  It starts at the leading digit $x.used - 1$ and moves towards the trailing digit.
-\item The variable $bitcpy$ indicates how many bits are in the currently formed window.  When it reaches $winsize$ the window is flushed and
-      the appropriate operations performed.
-\item The variable $bitbuf$ holds the current bits of the window being formed.
-\end{enumerate}
-
-All of step 12 is the window processing loop.  It will iterate while there are digits available form the exponent to read.  The first step
-inside this loop is to extract a new digit if no more bits are available in the current digit.  If there are no bits left a new digit is
-read and if there are no digits left than the loop terminates.
-
-After a digit is made available step 12.3 will extract the most significant bit of the current digit and move all other bits in the digit
-upwards.  In effect the digit is read from most significant bit to least significant bit and since the digits are read from leading to
-trailing edges the entire exponent is read from most significant bit to least significant bit.
-
-At step 12.5 if the $mode$ and currently extracted bit $y$ are both zero the bit is ignored and the next bit is read.  This prevents the
-algorithm from having to perform trivial squaring and reduction operations before the first non-zero bit is read.  Step 12.6 and 12.7-10 handle
-the two cases of $mode = 1$ and $mode = 2$ respectively.
-
-\begin{center}
-\begin{figure}[here]
-\includegraphics{pics/expt_state.ps}
-\caption{Sliding Window State Diagram}
-\label{pic:expt_state}
-\end{figure}
-\end{center}
-
-By step 13 there are no more digits left in the exponent.  However, there may be partial bits in the window left.  If $mode = 2$ then
-a Left-to-Right algorithm is used to process the remaining few bits.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_s\_mp\_exptmod.c
-\vspace{-3mm}
-\begin{alltt}
-016   #ifdef MP_LOW_MEM
-017      #define TAB_SIZE 32
-018   #else
-019      #define TAB_SIZE 256
-020   #endif
-021
-022   int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmod
-      e)
-023   \{
-024     mp_int  M[TAB_SIZE], res, mu;
-025     mp_digit buf;
-026     int     err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
-027     int (*redux)(mp_int*,mp_int*,mp_int*);
-028
-029     /* find window size */
-030     x = mp_count_bits (X);
-031     if (x <= 7) \{
-032       winsize = 2;
-033     \} else if (x <= 36) \{
-034       winsize = 3;
-035     \} else if (x <= 140) \{
-036       winsize = 4;
-037     \} else if (x <= 450) \{
-038       winsize = 5;
-039     \} else if (x <= 1303) \{
-040       winsize = 6;
-041     \} else if (x <= 3529) \{
-042       winsize = 7;
-043     \} else \{
-044       winsize = 8;
-045     \}
-046
-047   #ifdef MP_LOW_MEM
-048       if (winsize > 5) \{
-049          winsize = 5;
-050       \}
-051   #endif
-052
-053     /* init M array */
-054     /* init first cell */
-055     if ((err = mp_init(&M[1])) != MP_OKAY) \{
-056        return err;
-057     \}
-058
-059     /* now init the second half of the array */
-060     for (x = 1<<(winsize-1); x < (1 << winsize); x++) \{
-061       if ((err = mp_init(&M[x])) != MP_OKAY) \{
-062         for (y = 1<<(winsize-1); y < x; y++) \{
-063           mp_clear (&M[y]);
-064         \}
-065         mp_clear(&M[1]);
-066         return err;
-067       \}
-068     \}
-069
-070     /* create mu, used for Barrett reduction */
-071     if ((err = mp_init (&mu)) != MP_OKAY) \{
-072       goto LBL_M;
-073     \}
-074
-075     if (redmode == 0) \{
-076        if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) \{
-077           goto LBL_MU;
-078        \}
-079        redux = mp_reduce;
-080     \} else \{
-081        if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) \{
-082           goto LBL_MU;
-083        \}
-084        redux = mp_reduce_2k_l;
-085     \}
-086
-087     /* create M table
-088      *
-089      * The M table contains powers of the base,
-090      * e.g. M[x] = G**x mod P
-091      *
-092      * The first half of the table is not
-093      * computed though accept for M[0] and M[1]
-094      */
-095     if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) \{
-096       goto LBL_MU;
-097     \}
-098
-099     /* compute the value at M[1<<(winsize-1)] by squaring
-100      * M[1] (winsize-1) times
-101      */
-102     if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) \{
-103       goto LBL_MU;
-104     \}
-105
-106     for (x = 0; x < (winsize - 1); x++) \{
-107       /* square it */
-108       if ((err = mp_sqr (&M[1 << (winsize - 1)],
-109                          &M[1 << (winsize - 1)])) != MP_OKAY) \{
-110         goto LBL_MU;
-111       \}
-112
-113       /* reduce modulo P */
-114       if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) \{
-115         goto LBL_MU;
-116       \}
-117     \}
-118
-119     /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
-120      * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
-121      */
-122     for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) \{
-123       if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) \{
-124         goto LBL_MU;
-125       \}
-126       if ((err = redux (&M[x], P, &mu)) != MP_OKAY) \{
-127         goto LBL_MU;
-128       \}
-129     \}
-130
-131     /* setup result */
-132     if ((err = mp_init (&res)) != MP_OKAY) \{
-133       goto LBL_MU;
-134     \}
-135     mp_set (&res, 1);
-136
-137     /* set initial mode and bit cnt */
-138     mode   = 0;
-139     bitcnt = 1;
-140     buf    = 0;
-141     digidx = X->used - 1;
-142     bitcpy = 0;
-143     bitbuf = 0;
-144
-145     for (;;) \{
-146       /* grab next digit as required */
-147       if (--bitcnt == 0) \{
-148         /* if digidx == -1 we are out of digits */
-149         if (digidx == -1) \{
-150           break;
-151         \}
-152         /* read next digit and reset the bitcnt */
-153         buf    = X->dp[digidx--];
-154         bitcnt = (int) DIGIT_BIT;
-155       \}
-156
-157       /* grab the next msb from the exponent */
-158       y     = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
-159       buf <<= (mp_digit)1;
-160
-161       /* if the bit is zero and mode == 0 then we ignore it
-162        * These represent the leading zero bits before the first 1 bit
-163        * in the exponent.  Technically this opt is not required but it
-164        * does lower the # of trivial squaring/reductions used
-165        */
-166       if ((mode == 0) && (y == 0)) \{
-167         continue;
-168       \}
-169
-170       /* if the bit is zero and mode == 1 then we square */
-171       if ((mode == 1) && (y == 0)) \{
-172         if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{
-173           goto LBL_RES;
-174         \}
-175         if ((err = redux (&res, P, &mu)) != MP_OKAY) \{
-176           goto LBL_RES;
-177         \}
-178         continue;
-179       \}
-180
-181       /* else we add it to the window */
-182       bitbuf |= (y << (winsize - ++bitcpy));
-183       mode    = 2;
-184
-185       if (bitcpy == winsize) \{
-186         /* ok window is filled so square as required and multiply  */
-187         /* square first */
-188         for (x = 0; x < winsize; x++) \{
-189           if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{
-190             goto LBL_RES;
-191           \}
-192           if ((err = redux (&res, P, &mu)) != MP_OKAY) \{
-193             goto LBL_RES;
-194           \}
-195         \}
-196
-197         /* then multiply */
-198         if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) \{
-199           goto LBL_RES;
-200         \}
-201         if ((err = redux (&res, P, &mu)) != MP_OKAY) \{
-202           goto LBL_RES;
-203         \}
-204
-205         /* empty window and reset */
-206         bitcpy = 0;
-207         bitbuf = 0;
-208         mode   = 1;
-209       \}
-210     \}
-211
-212     /* if bits remain then square/multiply */
-213     if ((mode == 2) && (bitcpy > 0)) \{
-214       /* square then multiply if the bit is set */
-215       for (x = 0; x < bitcpy; x++) \{
-216         if ((err = mp_sqr (&res, &res)) != MP_OKAY) \{
-217           goto LBL_RES;
-218         \}
-219         if ((err = redux (&res, P, &mu)) != MP_OKAY) \{
-220           goto LBL_RES;
-221         \}
-222
-223         bitbuf <<= 1;
-224         if ((bitbuf & (1 << winsize)) != 0) \{
-225           /* then multiply */
-226           if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) \{
-227             goto LBL_RES;
-228           \}
-229           if ((err = redux (&res, P, &mu)) != MP_OKAY) \{
-230             goto LBL_RES;
-231           \}
-232         \}
-233       \}
-234     \}
-235
-236     mp_exch (&res, Y);
-237     err = MP_OKAY;
-238   LBL_RES:mp_clear (&res);
-239   LBL_MU:mp_clear (&mu);
-240   LBL_M:
-241     mp_clear(&M[1]);
-242     for (x = 1<<(winsize-1); x < (1 << winsize); x++) \{
-243       mp_clear (&M[x]);
-244     \}
-245     return err;
-246   \}
-247   #endif
-248
-\end{alltt}
-\end{small}
-
-Lines 31 through 45 determine the optimal window size based on the length of the exponent in bits.  The window divisions are sorted
-from smallest to greatest so that in each \textbf{if} statement only one condition must be tested.  For example, by the \textbf{if} statement
-on line 37 the value of $x$ is already known to be greater than $140$.
-
-The conditional piece of code beginning on line 47 allows the window size to be restricted to five bits.  This logic is used to ensure
-the table of precomputed powers of $G$ remains relatively small.
-
-The for loop on line 60 initializes the $M$ array while lines 71 and 76 through 85 initialize the reduction
-function that will be used for this modulus.
-
--- More later.
-
-\section{Quick Power of Two}
-Calculating $b = 2^a$ can be performed much quicker than with any of the previous algorithms.  Recall that a logical shift left $m << k$ is
-equivalent to $m \cdot 2^k$.  By this logic when $m = 1$ a quick power of two can be achieved.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_2expt}. \\
-\textbf{Input}.   integer $b$ \\
-\textbf{Output}.  $a \leftarrow 2^b$ \\
-\hline \\
-1.  $a \leftarrow 0$ \\
-2.  If $a.alloc < \lfloor b / lg(\beta) \rfloor + 1$ then grow $a$ appropriately. \\
-3.  $a.used \leftarrow \lfloor b / lg(\beta) \rfloor + 1$ \\
-4.  $a_{\lfloor b / lg(\beta) \rfloor} \leftarrow 1 << (b \mbox{ mod } lg(\beta))$ \\
-5.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_2expt}
-\end{figure}
-
-\textbf{Algorithm mp\_2expt.}
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_2expt.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* computes a = 2**b
-018    *
-019    * Simple algorithm which zeroes the int, grows it then just sets one bit
-020    * as required.
-021    */
-022   int
-023   mp_2expt (mp_int * a, int b)
-024   \{
-025     int     res;
-026
-027     /* zero a as per default */
-028     mp_zero (a);
-029
-030     /* grow a to accomodate the single bit */
-031     if ((res = mp_grow (a, (b / DIGIT_BIT) + 1)) != MP_OKAY) \{
-032       return res;
-033     \}
-034
-035     /* set the used count of where the bit will go */
-036     a->used = (b / DIGIT_BIT) + 1;
-037
-038     /* put the single bit in its place */
-039     a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
-040
-041     return MP_OKAY;
-042   \}
-043   #endif
-044
-\end{alltt}
-\end{small}
-
-\chapter{Higher Level Algorithms}
-
-This chapter discusses the various higher level algorithms that are required to complete a well rounded multiple precision integer package.  These
-routines are less performance oriented than the algorithms of chapters five, six and seven but are no less important.
-
-The first section describes a method of integer division with remainder that is universally well known.  It provides the signed division logic
-for the package.  The subsequent section discusses a set of algorithms which allow a single digit to be the 2nd operand for a variety of operations.
-These algorithms serve mostly to simplify other algorithms where small constants are required.  The last two sections discuss how to manipulate
-various representations of integers.  For example, converting from an mp\_int to a string of character.
-
-\section{Integer Division with Remainder}
-\label{sec:division}
-
-Integer division aside from modular exponentiation is the most intensive algorithm to compute.  Like addition, subtraction and multiplication
-the basis of this algorithm is the long-hand division algorithm taught to school children.  Throughout this discussion several common variables
-will be used.  Let $x$ represent the divisor and $y$ represent the dividend.  Let $q$ represent the integer quotient $\lfloor y / x \rfloor$ and
-let $r$ represent the remainder $r = y - x \lfloor y / x \rfloor$.  The following simple algorithm will be used to start the discussion.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Radix-$\beta$ Integer Division}. \\
-\textbf{Input}.   integer $x$ and $y$ \\
-\textbf{Output}.  $q = \lfloor y/x\rfloor, r = y - xq$ \\
-\hline \\
-1.  $q \leftarrow 0$ \\
-2.  $n \leftarrow \vert \vert y \vert \vert - \vert \vert x \vert \vert$ \\
-3.  for $t$ from $n$ down to $0$ do \\
-\hspace{3mm}3.1  Maximize $k$ such that $kx\beta^t$ is less than or equal to $y$ and $(k + 1)x\beta^t$ is greater. \\
-\hspace{3mm}3.2  $q \leftarrow q + k\beta^t$ \\
-\hspace{3mm}3.3  $y \leftarrow y - kx\beta^t$ \\
-4.  $r \leftarrow y$ \\
-5.  Return($q, r$) \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm Radix-$\beta$ Integer Division}
-\label{fig:raddiv}
-\end{figure}
-
-As children we are taught this very simple algorithm for the case of $\beta = 10$.  Almost instinctively several optimizations are taught for which
-their reason of existing are never explained.  For this example let $y = 5471$ represent the dividend and $x = 23$ represent the divisor.
-
-To find the first digit of the quotient the value of $k$ must be maximized such that $kx\beta^t$ is less than or equal to $y$ and
-simultaneously $(k + 1)x\beta^t$ is greater than $y$.  Implicitly $k$ is the maximum value the $t$'th digit of the quotient may have.  The habitual method
-used to find the maximum is to ``eyeball'' the two numbers, typically only the leading digits and quickly estimate a quotient.  By only using leading
-digits a much simpler division may be used to form an educated guess at what the value must be.  In this case $k = \lfloor 54/23\rfloor = 2$ quickly
-arises as a possible  solution.  Indeed $2x\beta^2 = 4600$ is less than $y = 5471$ and simultaneously $(k + 1)x\beta^2 = 6900$ is larger than $y$.
-As a  result $k\beta^2$ is added to the quotient which now equals $q = 200$ and $4600$ is subtracted from $y$ to give a remainder of $y = 841$.
-
-Again this process is repeated to produce the quotient digit $k = 3$ which makes the quotient $q = 200 + 3\beta = 230$ and the remainder
-$y = 841 - 3x\beta = 181$.  Finally the last iteration of the loop produces $k = 7$ which leads to the quotient $q = 230 + 7 = 237$ and the
-remainder $y = 181 - 7x = 20$.  The final quotient and remainder found are $q = 237$ and $r = y = 20$ which are indeed correct since
-$237 \cdot 23 + 20 = 5471$ is true.
-
-\subsection{Quotient Estimation}
-\label{sec:divest}
-As alluded to earlier the quotient digit $k$ can be estimated from only the leading digits of both the divisor and dividend.  When $p$ leading
-digits are used from both the divisor and dividend to form an estimation the accuracy of the estimation rises as $p$ grows.  Technically
-speaking the estimation is based on assuming the lower $\vert \vert y \vert \vert - p$ and $\vert \vert x \vert \vert - p$ lower digits of the
-dividend and divisor are zero.
-
-The value of the estimation may off by a few values in either direction and in general is fairly correct.  A simplification \cite[pp. 271]{TAOCPV2}
-of the estimation technique is to use $t + 1$ digits of the dividend and $t$ digits of the divisor, in particularly when $t = 1$.  The estimate
-using this technique is never too small.  For the following proof let $t = \vert \vert y \vert \vert - 1$ and $s = \vert \vert x \vert \vert - 1$
-represent the most significant digits of the dividend and divisor respectively.
-
-\textbf{Proof.}\textit{  The quotient $\hat k = \lfloor (y_t\beta + y_{t-1}) / x_s \rfloor$ is greater than or equal to
-$k = \lfloor y / (x \cdot \beta^{\vert \vert y \vert \vert - \vert \vert x \vert \vert - 1}) \rfloor$. }
-The first obvious case is when $\hat k = \beta - 1$ in which case the proof is concluded since the real quotient cannot be larger.  For all other
-cases $\hat k = \lfloor (y_t\beta + y_{t-1}) / x_s \rfloor$ and $\hat k x_s \ge y_t\beta + y_{t-1} - x_s + 1$.  The latter portion of the inequalility
-$-x_s + 1$ arises from the fact that a truncated integer division will give the same quotient for at most $x_s - 1$ values.  Next a series of
-inequalities will prove the hypothesis.
-
-\begin{equation}
-y - \hat k x \le y - \hat k x_s\beta^s
-\end{equation}
-
-This is trivially true since $x \ge x_s\beta^s$.  Next we replace $\hat kx_s\beta^s$ by the previous inequality for $\hat kx_s$.
-
-\begin{equation}
-y - \hat k x \le y_t\beta^t + \ldots + y_0 - (y_t\beta^t + y_{t-1}\beta^{t-1} - x_s\beta^t + \beta^s)
-\end{equation}
-
-By simplifying the previous inequality the following inequality is formed.
-
-\begin{equation}
-y - \hat k x \le y_{t-2}\beta^{t-2} + \ldots + y_0 + x_s\beta^s - \beta^s
-\end{equation}
-
-Subsequently,
-
-\begin{equation}
-y_{t-2}\beta^{t-2} + \ldots +  y_0  + x_s\beta^s - \beta^s < x_s\beta^s \le x
-\end{equation}
-
-Which proves that $y - \hat kx \le x$ and by consequence $\hat k \ge k$ which concludes the proof.  \textbf{QED}
-
-
-\subsection{Normalized Integers}
-For the purposes of division a normalized input is when the divisors leading digit $x_n$ is greater than or equal to $\beta / 2$.  By multiplying both
-$x$ and $y$ by $j = \lfloor (\beta / 2) / x_n \rfloor$ the quotient remains unchanged and the remainder is simply $j$ times the original
-remainder.  The purpose of normalization is to ensure the leading digit of the divisor is sufficiently large such that the estimated quotient will
-lie in the domain of a single digit.  Consider the maximum dividend $(\beta - 1) \cdot \beta + (\beta - 1)$ and the minimum divisor $\beta / 2$.
-
-\begin{equation}
-{{\beta^2 - 1} \over { \beta / 2}} \le 2\beta - {2 \over \beta}
-\end{equation}
-
-At most the quotient approaches $2\beta$, however, in practice this will not occur since that would imply the previous quotient digit was too small.
-
-\subsection{Radix-$\beta$ Division with Remainder}
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_div}. \\
-\textbf{Input}.   mp\_int $a, b$ \\
-\textbf{Output}.  $c = \lfloor a/b \rfloor$, $d = a - bc$ \\
-\hline \\
-1.  If $b = 0$ return(\textit{MP\_VAL}). \\
-2.  If $\vert a \vert < \vert b \vert$ then do \\
-\hspace{3mm}2.1  $d \leftarrow a$ \\
-\hspace{3mm}2.2  $c \leftarrow 0$ \\
-\hspace{3mm}2.3  Return(\textit{MP\_OKAY}). \\
-\\
-Setup the quotient to receive the digits. \\
-3.  Grow $q$ to $a.used + 2$ digits. \\
-4.  $q \leftarrow 0$ \\
-5.  $x \leftarrow \vert a \vert , y \leftarrow \vert b \vert$ \\
-6.  $sign \leftarrow  \left \lbrace \begin{array}{ll}
-                              MP\_ZPOS &  \mbox{if }a.sign = b.sign \\
-                              MP\_NEG  &  \mbox{otherwise} \\
-                              \end{array} \right .$ \\
-\\
-Normalize the inputs such that the leading digit of $y$ is greater than or equal to $\beta / 2$. \\
-7.  $norm \leftarrow (lg(\beta) - 1) - (\lceil lg(y) \rceil \mbox{ (mod }lg(\beta)\mbox{)})$ \\
-8.  $x \leftarrow x \cdot 2^{norm}, y \leftarrow y \cdot 2^{norm}$ \\
-\\
-Find the leading digit of the quotient. \\
-9.  $n \leftarrow x.used - 1, t \leftarrow y.used - 1$ \\
-10.  $y \leftarrow y \cdot \beta^{n - t}$ \\
-11.  While ($x \ge y$) do \\
-\hspace{3mm}11.1  $q_{n - t} \leftarrow q_{n - t} + 1$ \\
-\hspace{3mm}11.2  $x \leftarrow x - y$ \\
-12.  $y \leftarrow \lfloor y / \beta^{n-t} \rfloor$ \\
-\\
-Continued on the next page. \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_div}
-\end{figure}
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_div} (continued). \\
-\textbf{Input}.   mp\_int $a, b$ \\
-\textbf{Output}.  $c = \lfloor a/b \rfloor$, $d = a - bc$ \\
-\hline \\
-Now find the remainder fo the digits. \\
-13.  for $i$ from $n$ down to $(t + 1)$ do \\
-\hspace{3mm}13.1  If $i > x.used$ then jump to the next iteration of this loop. \\
-\hspace{3mm}13.2  If $x_{i} = y_{t}$ then \\
-\hspace{6mm}13.2.1  $q_{i - t - 1} \leftarrow \beta - 1$ \\
-\hspace{3mm}13.3  else \\
-\hspace{6mm}13.3.1  $\hat r \leftarrow x_{i} \cdot \beta + x_{i - 1}$ \\
-\hspace{6mm}13.3.2  $\hat r \leftarrow \lfloor \hat r / y_{t} \rfloor$ \\
-\hspace{6mm}13.3.3  $q_{i - t - 1} \leftarrow \hat r$ \\
-\hspace{3mm}13.4  $q_{i - t - 1} \leftarrow q_{i - t - 1} + 1$ \\
-\\
-Fixup quotient estimation. \\
-\hspace{3mm}13.5  Loop \\
-\hspace{6mm}13.5.1  $q_{i - t - 1} \leftarrow q_{i - t - 1} - 1$ \\
-\hspace{6mm}13.5.2  t$1 \leftarrow 0$ \\
-\hspace{6mm}13.5.3  t$1_0 \leftarrow y_{t - 1}, $ t$1_1 \leftarrow y_t,$ t$1.used \leftarrow 2$ \\
-\hspace{6mm}13.5.4  $t1 \leftarrow t1 \cdot q_{i - t - 1}$ \\
-\hspace{6mm}13.5.5  t$2_0 \leftarrow x_{i - 2}, $ t$2_1 \leftarrow x_{i - 1}, $ t$2_2 \leftarrow x_i, $ t$2.used \leftarrow 3$ \\
-\hspace{6mm}13.5.6  If $\vert t1 \vert > \vert t2 \vert$ then goto step 13.5. \\
-\hspace{3mm}13.6  t$1 \leftarrow y \cdot q_{i - t - 1}$ \\
-\hspace{3mm}13.7  t$1 \leftarrow $ t$1 \cdot \beta^{i - t - 1}$ \\
-\hspace{3mm}13.8  $x \leftarrow x - $ t$1$ \\
-\hspace{3mm}13.9  If $x.sign = MP\_NEG$ then \\
-\hspace{6mm}13.10  t$1 \leftarrow y$ \\
-\hspace{6mm}13.11  t$1 \leftarrow $ t$1 \cdot \beta^{i - t - 1}$ \\
-\hspace{6mm}13.12  $x \leftarrow x + $ t$1$ \\
-\hspace{6mm}13.13  $q_{i - t - 1} \leftarrow q_{i - t - 1} - 1$ \\
-\\
-Finalize the result. \\
-14.  Clamp excess digits of $q$ \\
-15.  $c \leftarrow q, c.sign \leftarrow sign$ \\
-16.  $x.sign \leftarrow a.sign$ \\
-17.  $d \leftarrow \lfloor x / 2^{norm} \rfloor$ \\
-18.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_div (continued)}
-\end{figure}
-\textbf{Algorithm mp\_div.}
-This algorithm will calculate quotient and remainder from an integer division given a dividend and divisor.  The algorithm is a signed
-division and will produce a fully qualified quotient and remainder.
-
-First the divisor $b$ must be non-zero which is enforced in step one.  If the divisor is larger than the dividend than the quotient is implicitly
-zero and the remainder is the dividend.
-
-After the first two trivial cases of inputs are handled the variable $q$ is setup to receive the digits of the quotient.  Two unsigned copies of the
-divisor $y$ and dividend $x$ are made as well.  The core of the division algorithm is an unsigned division and will only work if the values are
-positive.  Now the two values $x$ and $y$ must be normalized such that the leading digit of $y$ is greater than or equal to $\beta / 2$.
-This is performed by shifting both to the left by enough bits to get the desired normalization.
-
-At this point the division algorithm can begin producing digits of the quotient.  Recall that maximum value of the estimation used is
-$2\beta - {2 \over \beta}$ which means that a digit of the quotient must be first produced by another means.  In this case $y$ is shifted
-to the left (\textit{step ten}) so that it has the same number of digits as $x$.  The loop on step eleven will subtract multiples of the
-shifted copy of $y$ until $x$ is smaller.  Since the leading digit of $y$ is greater than or equal to $\beta/2$ this loop will iterate at most two
-times to produce the desired leading digit of the quotient.
-
-Now the remainder of the digits can be produced.  The equation $\hat q = \lfloor {{x_i \beta + x_{i-1}}\over y_t} \rfloor$ is used to fairly
-accurately approximate the true quotient digit.  The estimation can in theory produce an estimation as high as $2\beta - {2 \over \beta}$ but by
-induction the upper quotient digit is correct (\textit{as established on step eleven}) and the estimate must be less than $\beta$.
-
-Recall from section~\ref{sec:divest} that the estimation is never too low but may be too high.  The next step of the estimation process is
-to refine the estimation.  The loop on step 13.5 uses $x_i\beta^2 + x_{i-1}\beta + x_{i-2}$ and $q_{i - t - 1}(y_t\beta + y_{t-1})$ as a higher
-order approximation to adjust the quotient digit.
-
-After both phases of estimation the quotient digit may still be off by a value of one\footnote{This is similar to the error introduced
-by optimizing Barrett reduction.}.  Steps 13.6 and 13.7 subtract the multiple of the divisor from the dividend (\textit{Similar to step 3.3 of
-algorithm~\ref{fig:raddiv}} and then subsequently add a multiple of the divisor if the quotient was too large.
-
-Now that the quotient has been determine finializing the result is a matter of clamping the quotient, fixing the sizes and de-normalizing the
-remainder.  An important aspect of this algorithm seemingly overlooked in other descriptions such as that of Algorithm 14.20 HAC \cite[pp. 598]{HAC}
-is that when the estimations are being made (\textit{inside the loop on step 13.5}) that the digits $y_{t-1}$, $x_{i-2}$ and $x_{i-1}$ may lie
-outside their respective boundaries.  For example, if $t = 0$ or $i \le 1$ then the digits would be undefined.  In those cases the digits should
-respectively be replaced with a zero.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_div.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   #ifdef BN_MP_DIV_SMALL
-018
-019   /* slower bit-bang division... also smaller */
-020   int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-021   \{
-022      mp_int ta, tb, tq, q;
-023      int    res, n, n2;
-024
-025     /* is divisor zero ? */
-026     if (mp_iszero (b) == MP_YES) \{
-027       return MP_VAL;
-028     \}
-029
-030     /* if a < b then q=0, r = a */
-031     if (mp_cmp_mag (a, b) == MP_LT) \{
-032       if (d != NULL) \{
-033         res = mp_copy (a, d);
-034       \} else \{
-035         res = MP_OKAY;
-036       \}
-037       if (c != NULL) \{
-038         mp_zero (c);
-039       \}
-040       return res;
-041     \}
-042
-043     /* init our temps */
-044     if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL)) != MP_OKAY) \{
-045        return res;
-046     \}
-047
-048
-049     mp_set(&tq, 1);
-050     n = mp_count_bits(a) - mp_count_bits(b);
-051     if (((res = mp_abs(a, &ta)) != MP_OKAY) ||
-052         ((res = mp_abs(b, &tb)) != MP_OKAY) ||
-053         ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
-054         ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) \{
-055         goto LBL_ERR;
-056     \}
-057
-058     while (n-- >= 0) \{
-059        if (mp_cmp(&tb, &ta) != MP_GT) \{
-060           if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
-061               ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) \{
-062              goto LBL_ERR;
-063           \}
-064        \}
-065        if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
-066            ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) \{
-067              goto LBL_ERR;
-068        \}
-069     \}
-070
-071     /* now q == quotient and ta == remainder */
-072     n  = a->sign;
-073     n2 = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
-074     if (c != NULL) \{
-075        mp_exch(c, &q);
-076        c->sign  = (mp_iszero(c) == MP_YES) ? MP_ZPOS : n2;
-077     \}
-078     if (d != NULL) \{
-079        mp_exch(d, &ta);
-080        d->sign = (mp_iszero(d) == MP_YES) ? MP_ZPOS : n;
-081     \}
-082   LBL_ERR:
-083      mp_clear_multi(&ta, &tb, &tq, &q, NULL);
-084      return res;
-085   \}
-086
-087   #else
-088
-089   /* integer signed division.
-090    * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
-091    * HAC pp.598 Algorithm 14.20
-092    *
-093    * Note that the description in HAC is horribly
-094    * incomplete.  For example, it doesn't consider
-095    * the case where digits are removed from 'x' in
-096    * the inner loop.  It also doesn't consider the
-097    * case that y has fewer than three digits, etc..
-098    *
-099    * The overall algorithm is as described as
-100    * 14.20 from HAC but fixed to treat these cases.
-101   */
-102   int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-103   \{
-104     mp_int  q, x, y, t1, t2;
-105     int     res, n, t, i, norm, neg;
-106
-107     /* is divisor zero ? */
-108     if (mp_iszero (b) == MP_YES) \{
-109       return MP_VAL;
-110     \}
-111
-112     /* if a < b then q=0, r = a */
-113     if (mp_cmp_mag (a, b) == MP_LT) \{
-114       if (d != NULL) \{
-115         res = mp_copy (a, d);
-116       \} else \{
-117         res = MP_OKAY;
-118       \}
-119       if (c != NULL) \{
-120         mp_zero (c);
-121       \}
-122       return res;
-123     \}
-124
-125     if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) \{
-126       return res;
-127     \}
-128     q.used = a->used + 2;
-129
-130     if ((res = mp_init (&t1)) != MP_OKAY) \{
-131       goto LBL_Q;
-132     \}
-133
-134     if ((res = mp_init (&t2)) != MP_OKAY) \{
-135       goto LBL_T1;
-136     \}
-137
-138     if ((res = mp_init_copy (&x, a)) != MP_OKAY) \{
-139       goto LBL_T2;
-140     \}
-141
-142     if ((res = mp_init_copy (&y, b)) != MP_OKAY) \{
-143       goto LBL_X;
-144     \}
-145
-146     /* fix the sign */
-147     neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
-148     x.sign = y.sign = MP_ZPOS;
-149
-150     /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
-151     norm = mp_count_bits(&y) % DIGIT_BIT;
-152     if (norm < (int)(DIGIT_BIT-1)) \{
-153        norm = (DIGIT_BIT-1) - norm;
-154        if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) \{
-155          goto LBL_Y;
-156        \}
-157        if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) \{
-158          goto LBL_Y;
-159        \}
-160     \} else \{
-161        norm = 0;
-162     \}
-163
-164     /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
-165     n = x.used - 1;
-166     t = y.used - 1;
-167
-168     /* while (x >= y*b**n-t) do \{ q[n-t] += 1; x -= y*b**\{n-t\} \} */
-169     if ((res = mp_lshd (&y, n - t)) != MP_OKAY) \{ /* y = y*b**\{n-t\} */
-170       goto LBL_Y;
-171     \}
-172
-173     while (mp_cmp (&x, &y) != MP_LT) \{
-174       ++(q.dp[n - t]);
-175       if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) \{
-176         goto LBL_Y;
-177       \}
-178     \}
-179
-180     /* reset y by shifting it back down */
-181     mp_rshd (&y, n - t);
-182
-183     /* step 3. for i from n down to (t + 1) */
-184     for (i = n; i >= (t + 1); i--) \{
-185       if (i > x.used) \{
-186         continue;
-187       \}
-188
-189       /* step 3.1 if xi == yt then set q\{i-t-1\} to b-1,
-190        * otherwise set q\{i-t-1\} to (xi*b + x\{i-1\})/yt */
-191       if (x.dp[i] == y.dp[t]) \{
-192         q.dp[(i - t) - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
-193       \} else \{
-194         mp_word tmp;
-195         tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
-196         tmp |= ((mp_word) x.dp[i - 1]);
-197         tmp /= ((mp_word) y.dp[t]);
-198         if (tmp > (mp_word) MP_MASK) \{
-199           tmp = MP_MASK;
-200         \}
-201         q.dp[(i - t) - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
-202       \}
-203
-204       /* while (q\{i-t-1\} * (yt * b + y\{t-1\})) >
-205                xi * b**2 + xi-1 * b + xi-2
-206
-207          do q\{i-t-1\} -= 1;
-208       */
-209       q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] + 1) & MP_MASK;
-210       do \{
-211         q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1) & MP_MASK;
-212
-213         /* find left hand */
-214         mp_zero (&t1);
-215         t1.dp[0] = ((t - 1) < 0) ? 0 : y.dp[t - 1];
-216         t1.dp[1] = y.dp[t];
-217         t1.used = 2;
-218         if ((res = mp_mul_d (&t1, q.dp[(i - t) - 1], &t1)) != MP_OKAY) \{
-219           goto LBL_Y;
-220         \}
-221
-222         /* find right hand */
-223         t2.dp[0] = ((i - 2) < 0) ? 0 : x.dp[i - 2];
-224         t2.dp[1] = ((i - 1) < 0) ? 0 : x.dp[i - 1];
-225         t2.dp[2] = x.dp[i];
-226         t2.used = 3;
-227       \} while (mp_cmp_mag(&t1, &t2) == MP_GT);
-228
-229       /* step 3.3 x = x - q\{i-t-1\} * y * b**\{i-t-1\} */
-230       if ((res = mp_mul_d (&y, q.dp[(i - t) - 1], &t1)) != MP_OKAY) \{
-231         goto LBL_Y;
-232       \}
-233
-234       if ((res = mp_lshd (&t1, (i - t) - 1)) != MP_OKAY) \{
-235         goto LBL_Y;
-236       \}
-237
-238       if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) \{
-239         goto LBL_Y;
-240       \}
-241
-242       /* if x < 0 then \{ x = x + y*b**\{i-t-1\}; q\{i-t-1\} -= 1; \} */
-243       if (x.sign == MP_NEG) \{
-244         if ((res = mp_copy (&y, &t1)) != MP_OKAY) \{
-245           goto LBL_Y;
-246         \}
-247         if ((res = mp_lshd (&t1, (i - t) - 1)) != MP_OKAY) \{
-248           goto LBL_Y;
-249         \}
-250         if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) \{
-251           goto LBL_Y;
-252         \}
-253
-254         q.dp[(i - t) - 1] = (q.dp[(i - t) - 1] - 1UL) & MP_MASK;
-255       \}
-256     \}
-257
-258     /* now q is the quotient and x is the remainder
-259      * [which we have to normalize]
-260      */
-261
-262     /* get sign before writing to c */
-263     x.sign = (x.used == 0) ? MP_ZPOS : a->sign;
-264
-265     if (c != NULL) \{
-266       mp_clamp (&q);
-267       mp_exch (&q, c);
-268       c->sign = neg;
-269     \}
-270
-271     if (d != NULL) \{
-272       if ((res = mp_div_2d (&x, norm, &x, NULL)) != MP_OKAY) \{
-273         goto LBL_Y;
-274       \}
-275       mp_exch (&x, d);
-276     \}
-277
-278     res = MP_OKAY;
-279
-280   LBL_Y:mp_clear (&y);
-281   LBL_X:mp_clear (&x);
-282   LBL_T2:mp_clear (&t2);
-283   LBL_T1:mp_clear (&t1);
-284   LBL_Q:mp_clear (&q);
-285     return res;
-286   \}
-287
-288   #endif
-289
-290   #endif
-291
-\end{alltt}
-\end{small}
-
-The implementation of this algorithm differs slightly from the pseudo code presented previously.  In this algorithm either of the quotient $c$ or
-remainder $d$ may be passed as a \textbf{NULL} pointer which indicates their value is not desired.  For example, the C code to call the division
-algorithm with only the quotient is
-
-\begin{verbatim}
-mp_div(&a, &b, &c, NULL);  /* c = [a/b] */
-\end{verbatim}
-
-Lines 108 and 113 handle the two trivial cases of inputs which are division by zero and dividend smaller than the divisor
-respectively.  After the two trivial cases all of the temporary variables are initialized.  Line 147 determines the sign of
-the quotient and line 148 ensures that both $x$ and $y$ are positive.
-
-The number of bits in the leading digit is calculated on line 151.  Implictly an mp\_int with $r$ digits will require $lg(\beta)(r-1) + k$ bits
-of precision which when reduced modulo $lg(\beta)$ produces the value of $k$.  In this case $k$ is the number of bits in the leading digit which is
-exactly what is required.  For the algorithm to operate $k$ must equal $lg(\beta) - 1$ and when it does not the inputs must be normalized by shifting
-them to the left by $lg(\beta) - 1 - k$ bits.
-
-Throughout the variables $n$ and $t$ will represent the highest digit of $x$ and $y$ respectively.  These are first used to produce the
-leading digit of the quotient.  The loop beginning on line 184 will produce the remainder of the quotient digits.
-
-The conditional ``continue'' on line 186 is used to prevent the algorithm from reading past the leading edge of $x$ which can occur when the
-algorithm eliminates multiple non-zero digits in a single iteration.  This ensures that $x_i$ is always non-zero since by definition the digits
-above the $i$'th position $x$ must be zero in order for the quotient to be precise\footnote{Precise as far as integer division is concerned.}.
-
-Lines 214, 216 and 223 through 225 manually construct the high accuracy estimations by setting the digits of the two mp\_int
-variables directly.
-
-\section{Single Digit Helpers}
-
-This section briefly describes a series of single digit helper algorithms which come in handy when working with small constants.  All of
-the helper functions assume the single digit input is positive and will treat them as such.
-
-\subsection{Single Digit Addition and Subtraction}
-
-Both addition and subtraction are performed by ``cheating'' and using mp\_set followed by the higher level addition or subtraction
-algorithms.   As a result these algorithms are subtantially simpler with a slight cost in performance.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_add\_d}. \\
-\textbf{Input}.   mp\_int $a$ and a mp\_digit $b$ \\
-\textbf{Output}.  $c = a + b$ \\
-\hline \\
-1.  $t \leftarrow b$ (\textit{mp\_set}) \\
-2.  $c \leftarrow a + t$ \\
-3.  Return(\textit{MP\_OKAY}) \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_add\_d}
-\end{figure}
-
-\textbf{Algorithm mp\_add\_d.}
-This algorithm initiates a temporary mp\_int with the value of the single digit and uses algorithm mp\_add to add the two values together.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_add\_d.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* single digit addition */
-018   int
-019   mp_add_d (mp_int * a, mp_digit b, mp_int * c)
-020   \{
-021     int     res, ix, oldused;
-022     mp_digit *tmpa, *tmpc, mu;
-023
-024     /* grow c as required */
-025     if (c->alloc < (a->used + 1)) \{
-026        if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) \{
-027           return res;
-028        \}
-029     \}
-030
-031     /* if a is negative and |a| >= b, call c = |a| - b */
-032     if ((a->sign == MP_NEG) && ((a->used > 1) || (a->dp[0] >= b))) \{
-033        /* temporarily fix sign of a */
-034        a->sign = MP_ZPOS;
-035
-036        /* c = |a| - b */
-037        res = mp_sub_d(a, b, c);
-038
-039        /* fix sign  */
-040        a->sign = c->sign = MP_NEG;
-041
-042        /* clamp */
-043        mp_clamp(c);
-044
-045        return res;
-046     \}
-047
-048     /* old number of used digits in c */
-049     oldused = c->used;
-050
-051     /* sign always positive */
-052     c->sign = MP_ZPOS;
-053
-054     /* source alias */
-055     tmpa    = a->dp;
-056
-057     /* destination alias */
-058     tmpc    = c->dp;
-059
-060     /* if a is positive */
-061     if (a->sign == MP_ZPOS) \{
-062        /* add digit, after this we're propagating
-063         * the carry.
-064         */
-065        *tmpc   = *tmpa++ + b;
-066        mu      = *tmpc >> DIGIT_BIT;
-067        *tmpc++ &= MP_MASK;
-068
-069        /* now handle rest of the digits */
-070        for (ix = 1; ix < a->used; ix++) \{
-071           *tmpc   = *tmpa++ + mu;
-072           mu      = *tmpc >> DIGIT_BIT;
-073           *tmpc++ &= MP_MASK;
-074        \}
-075        /* set final carry */
-076        ix++;
-077        *tmpc++  = mu;
-078
-079        /* setup size */
-080        c->used = a->used + 1;
-081     \} else \{
-082        /* a was negative and |a| < b */
-083        c->used  = 1;
-084
-085        /* the result is a single digit */
-086        if (a->used == 1) \{
-087           *tmpc++  =  b - a->dp[0];
-088        \} else \{
-089           *tmpc++  =  b;
-090        \}
-091
-092        /* setup count so the clearing of oldused
-093         * can fall through correctly
-094         */
-095        ix       = 1;
-096     \}
-097
-098     /* now zero to oldused */
-099     while (ix++ < oldused) \{
-100        *tmpc++ = 0;
-101     \}
-102     mp_clamp(c);
-103
-104     return MP_OKAY;
-105   \}
-106
-107   #endif
-108
-\end{alltt}
-\end{small}
-
-Clever use of the letter 't'.
-
-\subsubsection{Subtraction}
-The single digit subtraction algorithm mp\_sub\_d is essentially the same except it uses mp\_sub to subtract the digit from the mp\_int.
-
-\subsection{Single Digit Multiplication}
-Single digit multiplication arises enough in division and radix conversion that it ought to be implement as a special case of the baseline
-multiplication algorithm.  Essentially this algorithm is a modified version of algorithm s\_mp\_mul\_digs where one of the multiplicands
-only has one digit.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_mul\_d}. \\
-\textbf{Input}.   mp\_int $a$ and a mp\_digit $b$ \\
-\textbf{Output}.  $c = ab$ \\
-\hline \\
-1.  $pa \leftarrow a.used$ \\
-2.  Grow $c$ to at least $pa + 1$ digits. \\
-3.  $oldused \leftarrow c.used$ \\
-4.  $c.used \leftarrow pa + 1$ \\
-5.  $c.sign \leftarrow a.sign$ \\
-6.  $\mu \leftarrow 0$ \\
-7.  for $ix$ from $0$ to $pa - 1$ do \\
-\hspace{3mm}7.1  $\hat r \leftarrow \mu + a_{ix}b$ \\
-\hspace{3mm}7.2  $c_{ix} \leftarrow \hat r \mbox{ (mod }\beta\mbox{)}$ \\
-\hspace{3mm}7.3  $\mu \leftarrow \lfloor \hat r / \beta \rfloor$ \\
-8.  $c_{pa} \leftarrow \mu$ \\
-9.  for $ix$ from $pa + 1$ to $oldused$ do \\
-\hspace{3mm}9.1  $c_{ix} \leftarrow 0$ \\
-10.  Clamp excess digits of $c$. \\
-11.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_mul\_d}
-\end{figure}
-\textbf{Algorithm mp\_mul\_d.}
-This algorithm quickly multiplies an mp\_int by a small single digit value.  It is specially tailored to the job and has a minimal of overhead.
-Unlike the full multiplication algorithms this algorithm does not require any significnat temporary storage or memory allocations.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_mul\_d.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* multiply by a digit */
-018   int
-019   mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
-020   \{
-021     mp_digit u, *tmpa, *tmpc;
-022     mp_word  r;
-023     int      ix, res, olduse;
-024
-025     /* make sure c is big enough to hold a*b */
-026     if (c->alloc < (a->used + 1)) \{
-027       if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) \{
-028         return res;
-029       \}
-030     \}
-031
-032     /* get the original destinations used count */
-033     olduse = c->used;
-034
-035     /* set the sign */
-036     c->sign = a->sign;
-037
-038     /* alias for a->dp [source] */
-039     tmpa = a->dp;
-040
-041     /* alias for c->dp [dest] */
-042     tmpc = c->dp;
-043
-044     /* zero carry */
-045     u = 0;
-046
-047     /* compute columns */
-048     for (ix = 0; ix < a->used; ix++) \{
-049       /* compute product and carry sum for this term */
-050       r       = (mp_word)u + ((mp_word)*tmpa++ * (mp_word)b);
-051
-052       /* mask off higher bits to get a single digit */
-053       *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
-054
-055       /* send carry into next iteration */
-056       u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
-057     \}
-058
-059     /* store final carry [if any] and increment ix offset  */
-060     *tmpc++ = u;
-061     ++ix;
-062
-063     /* now zero digits above the top */
-064     while (ix++ < olduse) \{
-065        *tmpc++ = 0;
-066     \}
-067
-068     /* set used count */
-069     c->used = a->used + 1;
-070     mp_clamp(c);
-071
-072     return MP_OKAY;
-073   \}
-074   #endif
-075
-\end{alltt}
-\end{small}
-
-In this implementation the destination $c$ may point to the same mp\_int as the source $a$ since the result is written after the digit is
-read from the source.  This function uses pointer aliases $tmpa$ and $tmpc$ for the digits of $a$ and $c$ respectively.
-
-\subsection{Single Digit Division}
-Like the single digit multiplication algorithm, single digit division is also a fairly common algorithm used in radix conversion.  Since the
-divisor is only a single digit a specialized variant of the division algorithm can be used to compute the quotient.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_div\_d}. \\
-\textbf{Input}.   mp\_int $a$ and a mp\_digit $b$ \\
-\textbf{Output}.  $c = \lfloor a / b \rfloor, d = a - cb$ \\
-\hline \\
-1.  If $b = 0$ then return(\textit{MP\_VAL}).\\
-2.  If $b = 3$ then use algorithm mp\_div\_3 instead. \\
-3.  Init $q$ to $a.used$ digits.  \\
-4.  $q.used \leftarrow a.used$ \\
-5.  $q.sign \leftarrow a.sign$ \\
-6.  $\hat w \leftarrow 0$ \\
-7.  for $ix$ from $a.used - 1$ down to $0$ do \\
-\hspace{3mm}7.1  $\hat w \leftarrow \hat w \beta + a_{ix}$ \\
-\hspace{3mm}7.2  If $\hat w \ge b$ then \\
-\hspace{6mm}7.2.1  $t \leftarrow \lfloor \hat w / b \rfloor$ \\
-\hspace{6mm}7.2.2  $\hat w \leftarrow \hat w \mbox{ (mod }b\mbox{)}$ \\
-\hspace{3mm}7.3  else\\
-\hspace{6mm}7.3.1  $t \leftarrow 0$ \\
-\hspace{3mm}7.4  $q_{ix} \leftarrow t$ \\
-8.  $d \leftarrow \hat w$ \\
-9.  Clamp excess digits of $q$. \\
-10.  $c \leftarrow q$ \\
-11.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_div\_d}
-\end{figure}
-\textbf{Algorithm mp\_div\_d.}
-This algorithm divides the mp\_int $a$ by the single mp\_digit $b$ using an optimized approach.  Essentially in every iteration of the
-algorithm another digit of the dividend is reduced and another digit of quotient produced.  Provided $b < \beta$ the value of $\hat w$
-after step 7.1 will be limited such that $0 \le \lfloor \hat w / b \rfloor < \beta$.
-
-If the divisor $b$ is equal to three a variant of this algorithm is used which is called mp\_div\_3.  It replaces the division by three with
-a multiplication by $\lfloor \beta / 3 \rfloor$ and the appropriate shift and residual fixup.  In essence it is much like the Barrett reduction
-from chapter seven.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_div\_d.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   static int s_is_power_of_two(mp_digit b, int *p)
-018   \{
-019      int x;
-020
-021      /* fast return if no power of two */
-022      if ((b == 0) || ((b & (b-1)) != 0)) \{
-023         return 0;
-024      \}
-025
-026      for (x = 0; x < DIGIT_BIT; x++) \{
-027         if (b == (((mp_digit)1)<<x)) \{
-028            *p = x;
-029            return 1;
-030         \}
-031      \}
-032      return 0;
-033   \}
-034
-035   /* single digit division (based on routine from MPI) */
-036   int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
-037   \{
-038     mp_int  q;
-039     mp_word w;
-040     mp_digit t;
-041     int     res, ix;
-042
-043     /* cannot divide by zero */
-044     if (b == 0) \{
-045        return MP_VAL;
-046     \}
-047
-048     /* quick outs */
-049     if ((b == 1) || (mp_iszero(a) == MP_YES)) \{
-050        if (d != NULL) \{
-051           *d = 0;
-052        \}
-053        if (c != NULL) \{
-054           return mp_copy(a, c);
-055        \}
-056        return MP_OKAY;
-057     \}
-058
-059     /* power of two ? */
-060     if (s_is_power_of_two(b, &ix) == 1) \{
-061        if (d != NULL) \{
-062           *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
-063        \}
-064        if (c != NULL) \{
-065           return mp_div_2d(a, ix, c, NULL);
-066        \}
-067        return MP_OKAY;
-068     \}
-069
-070   #ifdef BN_MP_DIV_3_C
-071     /* three? */
-072     if (b == 3) \{
-073        return mp_div_3(a, c, d);
-074     \}
-075   #endif
-076
-077     /* no easy answer [c'est la vie].  Just division */
-078     if ((res = mp_init_size(&q, a->used)) != MP_OKAY) \{
-079        return res;
-080     \}
-081
-082     q.used = a->used;
-083     q.sign = a->sign;
-084     w = 0;
-085     for (ix = a->used - 1; ix >= 0; ix--) \{
-086        w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
-087
-088        if (w >= b) \{
-089           t = (mp_digit)(w / b);
-090           w -= ((mp_word)t) * ((mp_word)b);
-091         \} else \{
-092           t = 0;
-093         \}
-094         q.dp[ix] = (mp_digit)t;
-095     \}
-096
-097     if (d != NULL) \{
-098        *d = (mp_digit)w;
-099     \}
-100
-101     if (c != NULL) \{
-102        mp_clamp(&q);
-103        mp_exch(&q, c);
-104     \}
-105     mp_clear(&q);
-106
-107     return res;
-108   \}
-109
-110   #endif
-111
-\end{alltt}
-\end{small}
-
-Like the implementation of algorithm mp\_div this algorithm allows either of the quotient or remainder to be passed as a \textbf{NULL} pointer to
-indicate the respective value is not required.  This allows a trivial single digit modular reduction algorithm, mp\_mod\_d to be created.
-
-The division and remainder on lines 89 and 90 can be replaced often by a single division on most processors.  For example, the 32-bit x86 based
-processors can divide a 64-bit quantity by a 32-bit quantity and produce the quotient and remainder simultaneously.  Unfortunately the GCC
-compiler does not recognize that optimization and will actually produce two function calls to find the quotient and remainder respectively.
-
-\subsection{Single Digit Root Extraction}
-
-Finding the $n$'th root of an integer is fairly easy as far as numerical analysis is concerned.  Algorithms such as the Newton-Raphson approximation
-(\ref{eqn:newton}) series will converge very quickly to a root for any continuous function $f(x)$.
-
-\begin{equation}
-x_{i+1} = x_i - {f(x_i) \over f'(x_i)}
-\label{eqn:newton}
-\end{equation}
-
-In this case the $n$'th root is desired and $f(x) = x^n - a$ where $a$ is the integer of which the root is desired.  The derivative of $f(x)$ is
-simply $f'(x) = nx^{n - 1}$.  Of particular importance is that this algorithm will be used over the integers not over the a more continuous domain
-such as the real numbers.  As a result the root found can be above the true root by few and must be manually adjusted.  Ideally at the end of the
-algorithm the $n$'th root $b$ of an integer $a$ is desired such that $b^n \le a$.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_n\_root}. \\
-\textbf{Input}.   mp\_int $a$ and a mp\_digit $b$ \\
-\textbf{Output}.  $c^b \le a$ \\
-\hline \\
-1.  If $b$ is even and $a.sign = MP\_NEG$ return(\textit{MP\_VAL}). \\
-2.  $sign \leftarrow a.sign$ \\
-3.  $a.sign \leftarrow MP\_ZPOS$ \\
-4.  t$2 \leftarrow 2$ \\
-5.  Loop \\
-\hspace{3mm}5.1  t$1 \leftarrow $ t$2$ \\
-\hspace{3mm}5.2  t$3 \leftarrow $ t$1^{b - 1}$ \\
-\hspace{3mm}5.3  t$2 \leftarrow $ t$3 $ $\cdot$ t$1$ \\
-\hspace{3mm}5.4  t$2 \leftarrow $ t$2 - a$ \\
-\hspace{3mm}5.5  t$3 \leftarrow $ t$3 \cdot b$ \\
-\hspace{3mm}5.6  t$3 \leftarrow \lfloor $t$2 / $t$3 \rfloor$ \\
-\hspace{3mm}5.7  t$2 \leftarrow $ t$1 - $ t$3$ \\
-\hspace{3mm}5.8  If t$1 \ne $ t$2$ then goto step 5.  \\
-6.  Loop \\
-\hspace{3mm}6.1  t$2 \leftarrow $ t$1^b$ \\
-\hspace{3mm}6.2  If t$2 > a$ then \\
-\hspace{6mm}6.2.1  t$1 \leftarrow $ t$1 - 1$ \\
-\hspace{6mm}6.2.2  Goto step 6. \\
-7.  $a.sign \leftarrow sign$ \\
-8.  $c \leftarrow $ t$1$ \\
-9.  $c.sign \leftarrow sign$  \\
-10.  Return(\textit{MP\_OKAY}).  \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_n\_root}
-\end{figure}
-\textbf{Algorithm mp\_n\_root.}
-This algorithm finds the integer $n$'th root of an input using the Newton-Raphson approach.  It is partially optimized based on the observation
-that the numerator of ${f(x) \over f'(x)}$ can be derived from a partial denominator.  That is at first the denominator is calculated by finding
-$x^{b - 1}$.  This value can then be multiplied by $x$ and have $a$ subtracted from it to find the numerator.  This saves a total of $b - 1$
-multiplications by t$1$ inside the loop.
-
-The initial value of the approximation is t$2 = 2$ which allows the algorithm to start with very small values and quickly converge on the
-root.  Ideally this algorithm is meant to find the $n$'th root of an input where $n$ is bounded by $2 \le n \le 5$.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_n\_root.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* wrapper function for mp_n_root_ex()
-018    * computes c = (a)**(1/b) such that (c)**b <= a and (c+1)**b > a
-019    */
-020   int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
-021   \{
-022     return mp_n_root_ex(a, b, c, 0);
-023   \}
-024
-025   #endif
-026
-\end{alltt}
-\end{small}
-
-\section{Random Number Generation}
-
-Random numbers come up in a variety of activities from public key cryptography to simple simulations and various randomized algorithms.  Pollard-Rho
-factoring for example, can make use of random values as starting points to find factors of a composite integer.  In this case the algorithm presented
-is solely for simulations and not intended for cryptographic use.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_rand}. \\
-\textbf{Input}.   An integer $b$ \\
-\textbf{Output}.  A pseudo-random number of $b$ digits \\
-\hline \\
-1.  $a \leftarrow 0$ \\
-2.  If $b \le 0$ return(\textit{MP\_OKAY}) \\
-3.  Pick a non-zero random digit $d$. \\
-4.  $a \leftarrow a + d$ \\
-5.  for $ix$ from 1 to $d - 1$ do \\
-\hspace{3mm}5.1  $a \leftarrow a \cdot \beta$ \\
-\hspace{3mm}5.2  Pick a random digit $d$. \\
-\hspace{3mm}5.3  $a \leftarrow a + d$ \\
-6.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_rand}
-\end{figure}
-\textbf{Algorithm mp\_rand.}
-This algorithm produces a pseudo-random integer of $b$ digits.  By ensuring that the first digit is non-zero the algorithm also guarantees that the
-final result has at least $b$ digits.  It relies heavily on a third-part random number generator which should ideally generate uniformly all of
-the integers from $0$ to $\beta - 1$.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_rand.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* makes a pseudo-random int of a given size */
-018   int
-019   mp_rand (mp_int * a, int digits)
-020   \{
-021     int     res;
-022     mp_digit d;
-023
-024     mp_zero (a);
-025     if (digits <= 0) \{
-026       return MP_OKAY;
-027     \}
-028
-029     /* first place a random non-zero digit */
-030     do \{
-031       d = ((mp_digit) abs (MP_GEN_RANDOM())) & MP_MASK;
-032     \} while (d == 0);
-033
-034     if ((res = mp_add_d (a, d, a)) != MP_OKAY) \{
-035       return res;
-036     \}
-037
-038     while (--digits > 0) \{
-039       if ((res = mp_lshd (a, 1)) != MP_OKAY) \{
-040         return res;
-041       \}
-042
-043       if ((res = mp_add_d (a, ((mp_digit) abs (MP_GEN_RANDOM())), a)) != MP_OK
-      AY) \{
-044         return res;
-045       \}
-046     \}
-047
-048     return MP_OKAY;
-049   \}
-050   #endif
-051
-\end{alltt}
-\end{small}
-
-\section{Formatted Representations}
-The ability to emit a radix-$n$ textual representation of an integer is useful for interacting with human parties.  For example, the ability to
-be given a string of characters such as ``114585'' and turn it into the radix-$\beta$ equivalent would make it easier to enter numbers
-into a program.
-
-\subsection{Reading Radix-n Input}
-For the purposes of this text we will assume that a simple lower ASCII map (\ref{fig:ASC}) is used for the values of from $0$ to $63$ to
-printable characters.  For example, when the character ``N'' is read it represents the integer $23$.  The first $16$ characters of the
-map are for the common representations up to hexadecimal.  After that they match the ``base64'' encoding scheme which are suitable chosen
-such that they are printable.  While outputting as base64 may not be too helpful for human operators it does allow communication via non binary
-mediums.
-
-\newpage\begin{figure}[here]
-\begin{center}
-\begin{tabular}{cc|cc|cc|cc}
-\hline \textbf{Value} & \textbf{Char} & \textbf{Value} & \textbf{Char} & \textbf{Value} & \textbf{Char} &  \textbf{Value} & \textbf{Char} \\
-\hline
-0 & 0 & 1 & 1 & 2 & 2 & 3 & 3 \\
-4 & 4 & 5 & 5 & 6 & 6 & 7 & 7 \\
-8 & 8 & 9 & 9 & 10 & A & 11 & B \\
-12 & C & 13 & D & 14 & E & 15 & F \\
-16 & G & 17 & H & 18 & I & 19 & J \\
-20 & K & 21 & L & 22 & M & 23 & N \\
-24 & O & 25 & P & 26 & Q & 27 & R \\
-28 & S & 29 & T & 30 & U & 31 & V \\
-32 & W & 33 & X & 34 & Y & 35 & Z \\
-36 & a & 37 & b & 38 & c & 39 & d \\
-40 & e & 41 & f & 42 & g & 43 & h \\
-44 & i & 45 & j & 46 & k & 47 & l \\
-48 & m & 49 & n & 50 & o & 51 & p \\
-52 & q & 53 & r & 54 & s & 55 & t \\
-56 & u & 57 & v & 58 & w & 59 & x \\
-60 & y & 61 & z & 62 & $+$ & 63 & $/$ \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Lower ASCII Map}
-\label{fig:ASC}
-\end{figure}
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_read\_radix}. \\
-\textbf{Input}.   A string $str$ of length $sn$ and radix $r$. \\
-\textbf{Output}.  The radix-$\beta$ equivalent mp\_int. \\
-\hline \\
-1.  If $r < 2$ or $r > 64$ return(\textit{MP\_VAL}). \\
-2.  $ix \leftarrow 0$ \\
-3.  If $str_0 =$ ``-'' then do \\
-\hspace{3mm}3.1  $ix \leftarrow ix + 1$ \\
-\hspace{3mm}3.2  $sign \leftarrow MP\_NEG$ \\
-4.  else \\
-\hspace{3mm}4.1  $sign \leftarrow MP\_ZPOS$ \\
-5.  $a \leftarrow 0$ \\
-6.  for $iy$ from $ix$ to $sn - 1$ do \\
-\hspace{3mm}6.1  Let $y$ denote the position in the map of $str_{iy}$. \\
-\hspace{3mm}6.2  If $str_{iy}$ is not in the map or $y \ge r$ then goto step 7. \\
-\hspace{3mm}6.3  $a \leftarrow a \cdot r$ \\
-\hspace{3mm}6.4  $a \leftarrow a + y$ \\
-7.  If $a \ne 0$ then $a.sign \leftarrow sign$ \\
-8.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_read\_radix}
-\end{figure}
-\textbf{Algorithm mp\_read\_radix.}
-This algorithm will read an ASCII string and produce the radix-$\beta$ mp\_int representation of the same integer.  A minus symbol ``-'' may precede the
-string  to indicate the value is negative, otherwise it is assumed to be positive.  The algorithm will read up to $sn$ characters from the input
-and will stop when it reads a character it cannot map the algorithm stops reading characters from the string.  This allows numbers to be embedded
-as part of larger input without any significant problem.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_read\_radix.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* read a string [ASCII] in a given radix */
-018   int mp_read_radix (mp_int * a, const char *str, int radix)
-019   \{
-020     int     y, res, neg;
-021     char    ch;
-022
-023     /* zero the digit bignum */
-024     mp_zero(a);
-025
-026     /* make sure the radix is ok */
-027     if ((radix < 2) || (radix > 64)) \{
-028       return MP_VAL;
-029     \}
-030
-031     /* if the leading digit is a
-032      * minus set the sign to negative.
-033      */
-034     if (*str == '-') \{
-035       ++str;
-036       neg = MP_NEG;
-037     \} else \{
-038       neg = MP_ZPOS;
-039     \}
-040
-041     /* set the integer to the default of zero */
-042     mp_zero (a);
-043
-044     /* process each digit of the string */
-045     while (*str != '\symbol{92}0') \{
-046       /* if the radix <= 36 the conversion is case insensitive
-047        * this allows numbers like 1AB and 1ab to represent the same  value
-048        * [e.g. in hex]
-049        */
-050       ch = (radix <= 36) ? (char)toupper((int)*str) : *str;
-051       for (y = 0; y < 64; y++) \{
-052         if (ch == mp_s_rmap[y]) \{
-053            break;
-054         \}
-055       \}
-056
-057       /* if the char was found in the map
-058        * and is less than the given radix add it
-059        * to the number, otherwise exit the loop.
-060        */
-061       if (y < radix) \{
-062         if ((res = mp_mul_d (a, (mp_digit) radix, a)) != MP_OKAY) \{
-063            return res;
-064         \}
-065         if ((res = mp_add_d (a, (mp_digit) y, a)) != MP_OKAY) \{
-066            return res;
-067         \}
-068       \} else \{
-069         break;
-070       \}
-071       ++str;
-072     \}
-073
-074     /* set the sign only if a != 0 */
-075     if (mp_iszero(a) != MP_YES) \{
-076        a->sign = neg;
-077     \}
-078     return MP_OKAY;
-079   \}
-080   #endif
-081
-\end{alltt}
-\end{small}
-
-\subsection{Generating Radix-$n$ Output}
-Generating radix-$n$ output is fairly trivial with a division and remainder algorithm.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_toradix}. \\
-\textbf{Input}.   A mp\_int $a$ and an integer $r$\\
-\textbf{Output}.  The radix-$r$ representation of $a$ \\
-\hline \\
-1.  If $r < 2$ or $r > 64$ return(\textit{MP\_VAL}). \\
-2.  If $a = 0$ then $str = $ ``$0$'' and return(\textit{MP\_OKAY}).  \\
-3.  $t \leftarrow a$ \\
-4.  $str \leftarrow$ ``'' \\
-5.  if $t.sign = MP\_NEG$ then \\
-\hspace{3mm}5.1  $str \leftarrow str + $ ``-'' \\
-\hspace{3mm}5.2  $t.sign = MP\_ZPOS$ \\
-6.  While ($t \ne 0$) do \\
-\hspace{3mm}6.1  $d \leftarrow t \mbox{ (mod }r\mbox{)}$ \\
-\hspace{3mm}6.2  $t \leftarrow \lfloor t / r \rfloor$ \\
-\hspace{3mm}6.3  Look up $d$ in the map and store the equivalent character in $y$. \\
-\hspace{3mm}6.4  $str \leftarrow str + y$ \\
-7.  If $str_0 = $``$-$'' then \\
-\hspace{3mm}7.1  Reverse the digits $str_1, str_2, \ldots str_n$. \\
-8.  Otherwise \\
-\hspace{3mm}8.1  Reverse the digits $str_0, str_1, \ldots str_n$. \\
-9.  Return(\textit{MP\_OKAY}).\\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_toradix}
-\end{figure}
-\textbf{Algorithm mp\_toradix.}
-This algorithm computes the radix-$r$ representation of an mp\_int $a$.  The ``digits'' of the representation are extracted by reducing
-successive powers of $\lfloor a / r^k \rfloor$ the input modulo $r$ until $r^k > a$.  Note that instead of actually dividing by $r^k$ in
-each iteration the quotient $\lfloor a / r \rfloor$ is saved for the next iteration.  As a result a series of trivial $n \times 1$ divisions
-are required instead of a series of $n \times k$ divisions.  One design flaw of this approach is that the digits are produced in the reverse order
-(see~\ref{fig:mpradix}).  To remedy this flaw the digits must be swapped or simply ``reversed''.
-
-\begin{figure}
-\begin{center}
-\begin{tabular}{|c|c|c|}
-\hline \textbf{Value of $a$} & \textbf{Value of $d$} & \textbf{Value of $str$} \\
-\hline $1234$ & -- & -- \\
-\hline $123$  & $4$ & ``4'' \\
-\hline $12$   & $3$ & ``43'' \\
-\hline $1$    & $2$ & ``432'' \\
-\hline $0$    & $1$ & ``4321'' \\
-\hline
-\end{tabular}
-\end{center}
-\caption{Example of Algorithm mp\_toradix.}
-\label{fig:mpradix}
-\end{figure}
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_toradix.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* stores a bignum as a ASCII string in a given radix (2..64) */
-018   int mp_toradix (mp_int * a, char *str, int radix)
-019   \{
-020     int     res, digs;
-021     mp_int  t;
-022     mp_digit d;
-023     char   *_s = str;
-024
-025     /* check range of the radix */
-026     if ((radix < 2) || (radix > 64)) \{
-027       return MP_VAL;
-028     \}
-029
-030     /* quick out if its zero */
-031     if (mp_iszero(a) == MP_YES) \{
-032        *str++ = '0';
-033        *str = '\symbol{92}0';
-034        return MP_OKAY;
-035     \}
-036
-037     if ((res = mp_init_copy (&t, a)) != MP_OKAY) \{
-038       return res;
-039     \}
-040
-041     /* if it is negative output a - */
-042     if (t.sign == MP_NEG) \{
-043       ++_s;
-044       *str++ = '-';
-045       t.sign = MP_ZPOS;
-046     \}
-047
-048     digs = 0;
-049     while (mp_iszero (&t) == MP_NO) \{
-050       if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) \{
-051         mp_clear (&t);
-052         return res;
-053       \}
-054       *str++ = mp_s_rmap[d];
-055       ++digs;
-056     \}
-057
-058     /* reverse the digits of the string.  In this case _s points
-059      * to the first digit [exluding the sign] of the number]
-060      */
-061     bn_reverse ((unsigned char *)_s, digs);
-062
-063     /* append a NULL so the string is properly terminated */
-064     *str = '\symbol{92}0';
-065
-066     mp_clear (&t);
-067     return MP_OKAY;
-068   \}
-069
-070   #endif
-071
-\end{alltt}
-\end{small}
-
-\chapter{Number Theoretic Algorithms}
-This chapter discusses several fundamental number theoretic algorithms such as the greatest common divisor, least common multiple and Jacobi
-symbol computation.  These algorithms arise as essential components in several key cryptographic algorithms such as the RSA public key algorithm and
-various Sieve based factoring algorithms.
-
-\section{Greatest Common Divisor}
-The greatest common divisor of two integers $a$ and $b$, often denoted as $(a, b)$ is the largest integer $k$ that is a proper divisor of
-both $a$ and $b$.  That is, $k$ is the largest integer such that $0 \equiv a \mbox{ (mod }k\mbox{)}$ and $0 \equiv b \mbox{ (mod }k\mbox{)}$ occur
-simultaneously.
-
-The most common approach (cite) is to reduce one input modulo another.  That is if $a$ and $b$ are divisible by some integer $k$ and if $qa + r = b$ then
-$r$ is also divisible by $k$.  The reduction pattern follows $\left < a , b \right > \rightarrow \left < b, a \mbox{ mod } b \right >$.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Greatest Common Divisor (I)}. \\
-\textbf{Input}.   Two positive integers $a$ and $b$ greater than zero. \\
-\textbf{Output}.  The greatest common divisor $(a, b)$.  \\
-\hline \\
-1.  While ($b > 0$) do \\
-\hspace{3mm}1.1  $r \leftarrow a \mbox{ (mod }b\mbox{)}$ \\
-\hspace{3mm}1.2  $a \leftarrow b$ \\
-\hspace{3mm}1.3  $b \leftarrow r$ \\
-2.  Return($a$). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm Greatest Common Divisor (I)}
-\label{fig:gcd1}
-\end{figure}
-
-This algorithm will quickly converge on the greatest common divisor since the residue $r$ tends diminish rapidly.  However, divisions are
-relatively expensive operations to perform and should ideally be avoided.  There is another approach based on a similar relationship of
-greatest common divisors.  The faster approach is based on the observation that if $k$ divides both $a$ and $b$ it will also divide $a - b$.
-In particular, we would like $a - b$ to decrease in magnitude which implies that $b \ge a$.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Greatest Common Divisor (II)}. \\
-\textbf{Input}.   Two positive integers $a$ and $b$ greater than zero. \\
-\textbf{Output}.  The greatest common divisor $(a, b)$.  \\
-\hline \\
-1.  While ($b > 0$) do \\
-\hspace{3mm}1.1  Swap $a$ and $b$ such that $a$ is the smallest of the two. \\
-\hspace{3mm}1.2  $b \leftarrow b - a$ \\
-2.  Return($a$). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm Greatest Common Divisor (II)}
-\label{fig:gcd2}
-\end{figure}
-
-\textbf{Proof} \textit{Algorithm~\ref{fig:gcd2} will return the greatest common divisor of $a$ and $b$.}
-The algorithm in figure~\ref{fig:gcd2} will eventually terminate since $b \ge a$ the subtraction in step 1.2 will be a value less than $b$.  In other
-words in every iteration that tuple $\left < a, b \right >$ decrease in magnitude until eventually $a = b$.  Since both $a$ and $b$ are always
-divisible by the greatest common divisor (\textit{until the last iteration}) and in the last iteration of the algorithm $b = 0$, therefore, in the
-second to last iteration of the algorithm $b = a$ and clearly $(a, a) = a$ which concludes the proof.  \textbf{QED}.
-
-As a matter of practicality algorithm \ref{fig:gcd1} decreases far too slowly to be useful.  Specially if $b$ is much larger than $a$ such that
-$b - a$ is still very much larger than $a$.  A simple addition to the algorithm is to divide $b - a$ by a power of some integer $p$ which does
-not divide the greatest common divisor but will divide $b - a$.  In this case ${b - a} \over p$ is also an integer and still divisible by
-the greatest common divisor.
-
-However, instead of factoring $b - a$ to find a suitable value of $p$ the powers of $p$ can be removed from $a$ and $b$ that are in common first.
-Then inside the loop whenever $b - a$ is divisible by some power of $p$ it can be safely removed.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{Greatest Common Divisor (III)}. \\
-\textbf{Input}.   Two positive integers $a$ and $b$ greater than zero. \\
-\textbf{Output}.  The greatest common divisor $(a, b)$.  \\
-\hline \\
-1.  $k \leftarrow 0$ \\
-2.  While $a$ and $b$ are both divisible by $p$ do \\
-\hspace{3mm}2.1  $a \leftarrow \lfloor a / p \rfloor$ \\
-\hspace{3mm}2.2  $b \leftarrow \lfloor b / p \rfloor$ \\
-\hspace{3mm}2.3  $k \leftarrow k + 1$ \\
-3.  While $a$ is divisible by $p$ do \\
-\hspace{3mm}3.1  $a \leftarrow \lfloor a / p \rfloor$ \\
-4.  While $b$ is divisible by $p$ do \\
-\hspace{3mm}4.1  $b \leftarrow \lfloor b / p \rfloor$ \\
-5.  While ($b > 0$) do \\
-\hspace{3mm}5.1  Swap $a$ and $b$ such that $a$ is the smallest of the two. \\
-\hspace{3mm}5.2  $b \leftarrow b - a$ \\
-\hspace{3mm}5.3  While $b$ is divisible by $p$ do \\
-\hspace{6mm}5.3.1  $b \leftarrow \lfloor b / p \rfloor$ \\
-6.  Return($a \cdot p^k$). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm Greatest Common Divisor (III)}
-\label{fig:gcd3}
-\end{figure}
-
-This algorithm is based on the first except it removes powers of $p$ first and inside the main loop to ensure the tuple $\left < a, b \right >$
-decreases more rapidly.  The first loop on step two removes powers of $p$ that are in common.  A count, $k$, is kept which will present a common
-divisor of $p^k$.  After step two the remaining common divisor of $a$ and $b$ cannot be divisible by $p$.  This means that $p$ can be safely
-divided out of the difference $b - a$ so long as the division leaves no remainder.
-
-In particular the value of $p$ should be chosen such that the division on step 5.3.1 occur often.  It also helps that division by $p$ be easy
-to compute.  The ideal choice of $p$ is two since division by two amounts to a right logical shift.  Another important observation is that by
-step five both $a$ and $b$ are odd.  Therefore, the diffrence $b - a$ must be even which means that each iteration removes one bit from the
-largest of the pair.
-
-\subsection{Complete Greatest Common Divisor}
-The algorithms presented so far cannot handle inputs which are zero or negative.  The following algorithm can handle all input cases properly
-and will produce the greatest common divisor.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_gcd}. \\
-\textbf{Input}.   mp\_int $a$ and $b$ \\
-\textbf{Output}.  The greatest common divisor $c = (a, b)$.  \\
-\hline \\
-1.  If $a = 0$ then \\
-\hspace{3mm}1.1  $c \leftarrow \vert b \vert $ \\
-\hspace{3mm}1.2  Return(\textit{MP\_OKAY}). \\
-2.  If $b = 0$ then \\
-\hspace{3mm}2.1  $c \leftarrow \vert a \vert $ \\
-\hspace{3mm}2.2  Return(\textit{MP\_OKAY}). \\
-3.  $u \leftarrow \vert a \vert, v \leftarrow \vert b \vert$ \\
-4.  $k \leftarrow 0$ \\
-5.  While $u.used > 0$ and $v.used > 0$ and $u_0 \equiv v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\
-\hspace{3mm}5.1  $k \leftarrow k + 1$ \\
-\hspace{3mm}5.2  $u \leftarrow \lfloor u / 2 \rfloor$ \\
-\hspace{3mm}5.3  $v \leftarrow \lfloor v / 2 \rfloor$ \\
-6.  While $u.used > 0$ and $u_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\
-\hspace{3mm}6.1  $u \leftarrow \lfloor u / 2 \rfloor$ \\
-7.  While $v.used > 0$ and $v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\
-\hspace{3mm}7.1  $v \leftarrow \lfloor v / 2 \rfloor$ \\
-8.  While $v.used > 0$ \\
-\hspace{3mm}8.1  If $\vert u \vert > \vert v \vert$ then \\
-\hspace{6mm}8.1.1  Swap $u$ and $v$. \\
-\hspace{3mm}8.2  $v \leftarrow \vert v \vert - \vert u \vert$ \\
-\hspace{3mm}8.3  While $v.used > 0$ and $v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\
-\hspace{6mm}8.3.1  $v \leftarrow \lfloor v / 2 \rfloor$ \\
-9.  $c \leftarrow u \cdot 2^k$ \\
-10.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_gcd}
-\end{figure}
-\textbf{Algorithm mp\_gcd.}
-This algorithm will produce the greatest common divisor of two mp\_ints $a$ and $b$.  The algorithm was originally based on Algorithm B of
-Knuth \cite[pp. 338]{TAOCPV2} but has been modified to be simpler to explain.  In theory it achieves the same asymptotic working time as
-Algorithm B and in practice this appears to be true.
-
-The first two steps handle the cases where either one of or both inputs are zero.  If either input is zero the greatest common divisor is the
-largest input or zero if they are both zero.  If the inputs are not trivial than $u$ and $v$ are assigned the absolute values of
-$a$ and $b$ respectively and the algorithm will proceed to reduce the pair.
-
-Step five will divide out any common factors of two and keep track of the count in the variable $k$.  After this step, two is no longer a
-factor of the remaining greatest common divisor between $u$ and $v$ and can be safely evenly divided out of either whenever they are even.  Step
-six and seven ensure that the $u$ and $v$ respectively have no more factors of two.  At most only one of the while--loops will iterate since
-they cannot both be even.
-
-By step eight both of $u$ and $v$ are odd which is required for the inner logic.  First the pair are swapped such that $v$ is equal to
-or greater than $u$.  This ensures that the subtraction on step 8.2 will always produce a positive and even result.  Step 8.3 removes any
-factors of two from the difference $u$ to ensure that in the next iteration of the loop both are once again odd.
-
-After $v = 0$ occurs the variable $u$ has the greatest common divisor of the pair $\left < u, v \right >$ just after step six.  The result
-must be adjusted by multiplying by the common factors of two ($2^k$) removed earlier.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_gcd.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* Greatest Common Divisor using the binary method */
-018   int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
-019   \{
-020     mp_int  u, v;
-021     int     k, u_lsb, v_lsb, res;
-022
-023     /* either zero than gcd is the largest */
-024     if (mp_iszero (a) == MP_YES) \{
-025       return mp_abs (b, c);
-026     \}
-027     if (mp_iszero (b) == MP_YES) \{
-028       return mp_abs (a, c);
-029     \}
-030
-031     /* get copies of a and b we can modify */
-032     if ((res = mp_init_copy (&u, a)) != MP_OKAY) \{
-033       return res;
-034     \}
-035
-036     if ((res = mp_init_copy (&v, b)) != MP_OKAY) \{
-037       goto LBL_U;
-038     \}
-039
-040     /* must be positive for the remainder of the algorithm */
-041     u.sign = v.sign = MP_ZPOS;
-042
-043     /* B1.  Find the common power of two for u and v */
-044     u_lsb = mp_cnt_lsb(&u);
-045     v_lsb = mp_cnt_lsb(&v);
-046     k     = MIN(u_lsb, v_lsb);
-047
-048     if (k > 0) \{
-049        /* divide the power of two out */
-050        if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) \{
-051           goto LBL_V;
-052        \}
-053
-054        if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) \{
-055           goto LBL_V;
-056        \}
-057     \}
-058
-059     /* divide any remaining factors of two out */
-060     if (u_lsb != k) \{
-061        if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) \{
-062           goto LBL_V;
-063        \}
-064     \}
-065
-066     if (v_lsb != k) \{
-067        if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) \{
-068           goto LBL_V;
-069        \}
-070     \}
-071
-072     while (mp_iszero(&v) == MP_NO) \{
-073        /* make sure v is the largest */
-074        if (mp_cmp_mag(&u, &v) == MP_GT) \{
-075           /* swap u and v to make sure v is >= u */
-076           mp_exch(&u, &v);
-077        \}
-078
-079        /* subtract smallest from largest */
-080        if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) \{
-081           goto LBL_V;
-082        \}
-083
-084        /* Divide out all factors of two */
-085        if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) \{
-086           goto LBL_V;
-087        \}
-088     \}
-089
-090     /* multiply by 2**k which we divided out at the beginning */
-091     if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) \{
-092        goto LBL_V;
-093     \}
-094     c->sign = MP_ZPOS;
-095     res = MP_OKAY;
-096   LBL_V:mp_clear (&u);
-097   LBL_U:mp_clear (&v);
-098     return res;
-099   \}
-100   #endif
-101
-\end{alltt}
-\end{small}
-
-This function makes use of the macros mp\_iszero and mp\_iseven.  The former evaluates to $1$ if the input mp\_int is equivalent to the
-integer zero otherwise it evaluates to $0$.  The latter evaluates to $1$ if the input mp\_int represents a non-zero even integer otherwise
-it evaluates to $0$.  Note that just because mp\_iseven may evaluate to $0$ does not mean the input is odd, it could also be zero.  The three
-trivial cases of inputs are handled on lines 23 through 29.  After those lines the inputs are assumed to be non-zero.
-
-Lines 32 and 36 make local copies $u$ and $v$ of the inputs $a$ and $b$ respectively.  At this point the common factors of two
-must be divided out of the two inputs.  The block starting at line 43 removes common factors of two by first counting the number of trailing
-zero bits in both.  The local integer $k$ is used to keep track of how many factors of $2$ are pulled out of both values.  It is assumed that
-the number of factors will not exceed the maximum value of a C ``int'' data type\footnote{Strictly speaking no array in C may have more than
-entries than are accessible by an ``int'' so this is not a limitation.}.
-
-At this point there are no more common factors of two in the two values.  The divisions by a power of two on lines 61 and 67 remove
-any independent factors of two such that both $u$ and $v$ are guaranteed to be an odd integer before hitting the main body of the algorithm.  The while loop
-on line 72 performs the reduction of the pair until $v$ is equal to zero.  The unsigned comparison and subtraction algorithms are used in
-place of the full signed routines since both values are guaranteed to be positive and the result of the subtraction is guaranteed to be non-negative.
-
-\section{Least Common Multiple}
-The least common multiple of a pair of integers is their product divided by their greatest common divisor.  For two integers $a$ and $b$ the
-least common multiple is normally denoted as $[ a, b ]$ and numerically equivalent to ${ab} \over {(a, b)}$.  For example, if $a = 2 \cdot 2 \cdot 3 = 12$
-and $b = 2 \cdot 3 \cdot 3 \cdot 7 = 126$ the least common multiple is ${126 \over {(12, 126)}} = {126 \over 6} = 21$.
-
-The least common multiple arises often in coding theory as well as number theory.  If two functions have periods of $a$ and $b$ respectively they will
-collide, that is be in synchronous states, after only $[ a, b ]$ iterations.  This is why, for example, random number generators based on
-Linear Feedback Shift Registers (LFSR) tend to use registers with periods which are co-prime (\textit{e.g. the greatest common divisor is one.}).
-Similarly in number theory if a composite $n$ has two prime factors $p$ and $q$ then maximal order of any unit of $\Z/n\Z$ will be $[ p - 1, q - 1] $.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_lcm}. \\
-\textbf{Input}.   mp\_int $a$ and $b$ \\
-\textbf{Output}.  The least common multiple $c = [a, b]$.  \\
-\hline \\
-1.  $c \leftarrow (a, b)$ \\
-2.  $t \leftarrow a \cdot b$ \\
-3.  $c \leftarrow \lfloor t / c \rfloor$ \\
-4.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_lcm}
-\end{figure}
-\textbf{Algorithm mp\_lcm.}
-This algorithm computes the least common multiple of two mp\_int inputs $a$ and $b$.  It computes the least common multiple directly by
-dividing the product of the two inputs by their greatest common divisor.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_lcm.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* computes least common multiple as |a*b|/(a, b) */
-018   int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
-019   \{
-020     int     res;
-021     mp_int  t1, t2;
-022
-023
-024     if ((res = mp_init_multi (&t1, &t2, NULL)) != MP_OKAY) \{
-025       return res;
-026     \}
-027
-028     /* t1 = get the GCD of the two inputs */
-029     if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) \{
-030       goto LBL_T;
-031     \}
-032
-033     /* divide the smallest by the GCD */
-034     if (mp_cmp_mag(a, b) == MP_LT) \{
-035        /* store quotient in t2 such that t2 * b is the LCM */
-036        if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) \{
-037           goto LBL_T;
-038        \}
-039        res = mp_mul(b, &t2, c);
-040     \} else \{
-041        /* store quotient in t2 such that t2 * a is the LCM */
-042        if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) \{
-043           goto LBL_T;
-044        \}
-045        res = mp_mul(a, &t2, c);
-046     \}
-047
-048     /* fix the sign to positive */
-049     c->sign = MP_ZPOS;
-050
-051   LBL_T:
-052     mp_clear_multi (&t1, &t2, NULL);
-053     return res;
-054   \}
-055   #endif
-056
-\end{alltt}
-\end{small}
-
-\section{Jacobi Symbol Computation}
-To explain the Jacobi Symbol we shall first discuss the Legendre function\footnote{Arrg.  What is the name of this?} off which the Jacobi symbol is
-defined.  The Legendre function computes whether or not an integer $a$ is a quadratic residue modulo an odd prime $p$.  Numerically it is
-equivalent to equation \ref{eqn:legendre}.
-
-\textit{-- Tom, don't be an ass, cite your source here...!}
-
-\begin{equation}
-a^{(p-1)/2} \equiv \begin{array}{rl}
-                              -1 &  \mbox{if }a\mbox{ is a quadratic non-residue.} \\
-                              0  &  \mbox{if }a\mbox{ divides }p\mbox{.} \\
-                              1  &  \mbox{if }a\mbox{ is a quadratic residue}.
-                              \end{array} \mbox{ (mod }p\mbox{)}
-\label{eqn:legendre}
-\end{equation}
-
-\textbf{Proof.} \textit{Equation \ref{eqn:legendre} correctly identifies the residue status of an integer $a$ modulo a prime $p$.}
-An integer $a$ is a quadratic residue if the following equation has a solution.
-
-\begin{equation}
-x^2 \equiv a \mbox{ (mod }p\mbox{)}
-\label{eqn:root}
-\end{equation}
-
-Consider the following equation.
-
-\begin{equation}
-0 \equiv x^{p-1} - 1 \equiv \left \lbrace \left (x^2 \right )^{(p-1)/2} - a^{(p-1)/2} \right \rbrace + \left ( a^{(p-1)/2} - 1 \right ) \mbox{ (mod }p\mbox{)}
-\label{eqn:rooti}
-\end{equation}
-
-Whether equation \ref{eqn:root} has a solution or not equation \ref{eqn:rooti} is always true.  If $a^{(p-1)/2} - 1 \equiv 0 \mbox{ (mod }p\mbox{)}$
-then the quantity in the braces must be zero.  By reduction,
-
-\begin{eqnarray}
-\left (x^2 \right )^{(p-1)/2} - a^{(p-1)/2} \equiv 0  \nonumber \\
-\left (x^2 \right )^{(p-1)/2} \equiv a^{(p-1)/2} \nonumber \\
-x^2 \equiv a \mbox{ (mod }p\mbox{)}
-\end{eqnarray}
-
-As a result there must be a solution to the quadratic equation and in turn $a$ must be a quadratic residue.  If $a$ does not divide $p$ and $a$
-is not a quadratic residue then the only other value $a^{(p-1)/2}$ may be congruent to is $-1$ since
-\begin{equation}
-0 \equiv a^{p - 1} - 1 \equiv (a^{(p-1)/2} + 1)(a^{(p-1)/2} - 1) \mbox{ (mod }p\mbox{)}
-\end{equation}
-One of the terms on the right hand side must be zero.  \textbf{QED}
-
-\subsection{Jacobi Symbol}
-The Jacobi symbol is a generalization of the Legendre function for any odd non prime moduli $p$ greater than 2.  If $p = \prod_{i=0}^n p_i$ then
-the Jacobi symbol $\left ( { a \over p } \right )$ is equal to the following equation.
-
-\begin{equation}
-\left ( { a \over p } \right ) = \left ( { a \over p_0} \right ) \left ( { a \over p_1} \right ) \ldots \left ( { a \over p_n} \right )
-\end{equation}
-
-By inspection if $p$ is prime the Jacobi symbol is equivalent to the Legendre function.  The following facts\footnote{See HAC \cite[pp. 72-74]{HAC} for
-further details.} will be used to derive an efficient Jacobi symbol algorithm.  Where $p$ is an odd integer greater than two and $a, b \in \Z$ the
-following are true.
-
-\begin{enumerate}
-\item $\left ( { a \over p} \right )$ equals $-1$, $0$ or $1$.
-\item $\left ( { ab \over p} \right ) = \left ( { a \over p} \right )\left ( { b \over p} \right )$.
-\item If $a \equiv b$ then $\left ( { a \over p} \right ) = \left ( { b \over p} \right )$.
-\item $\left ( { 2 \over p} \right )$ equals $1$ if $p \equiv 1$ or $7 \mbox{ (mod }8\mbox{)}$.  Otherwise, it equals $-1$.
-\item $\left ( { a \over p} \right ) \equiv \left ( { p \over a} \right ) \cdot (-1)^{(p-1)(a-1)/4}$.  More specifically
-$\left ( { a \over p} \right ) = \left ( { p \over a} \right )$ if $p \equiv a \equiv 1 \mbox{ (mod }4\mbox{)}$.
-\end{enumerate}
-
-Using these facts if $a = 2^k \cdot a'$ then
-
-\begin{eqnarray}
-\left ( { a \over p } \right ) = \left ( {{2^k} \over p } \right ) \left ( {a' \over p} \right ) \nonumber \\
-                               = \left ( {2 \over p } \right )^k \left ( {a' \over p} \right )
-\label{eqn:jacobi}
-\end{eqnarray}
-
-By fact five,
-
-\begin{equation}
-\left ( { a \over p } \right ) = \left ( { p \over a } \right ) \cdot (-1)^{(p-1)(a-1)/4}
-\end{equation}
-
-Subsequently by fact three since $p \equiv (p \mbox{ mod }a) \mbox{ (mod }a\mbox{)}$ then
-
-\begin{equation}
-\left ( { a \over p } \right ) = \left ( { {p \mbox{ mod } a} \over a } \right ) \cdot (-1)^{(p-1)(a-1)/4}
-\end{equation}
-
-By putting both observations into equation \ref{eqn:jacobi} the following simplified equation is formed.
-
-\begin{equation}
-\left ( { a \over p } \right ) = \left ( {2 \over p } \right )^k \left ( {{p\mbox{ mod }a'} \over a'} \right )  \cdot (-1)^{(p-1)(a'-1)/4}
-\end{equation}
-
-The value of $\left ( {{p \mbox{ mod }a'} \over a'} \right )$ can be found by using the same equation recursively.  The value of
-$\left ( {2 \over p } \right )^k$ equals $1$ if $k$ is even otherwise it equals $\left ( {2 \over p } \right )$.  Using this approach the
-factors of $p$ do not have to be known.  Furthermore, if $(a, p) = 1$ then the algorithm will terminate when the recursion requests the
-Jacobi symbol computation of $\left ( {1 \over a'} \right )$ which is simply $1$.
-
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_jacobi}. \\
-\textbf{Input}.   mp\_int $a$ and $p$, $a \ge 0$, $p \ge 3$, $p \equiv 1 \mbox{ (mod }2\mbox{)}$ \\
-\textbf{Output}.  The Jacobi symbol $c = \left ( {a \over p } \right )$. \\
-\hline \\
-1.  If $a = 0$ then \\
-\hspace{3mm}1.1  $c \leftarrow 0$ \\
-\hspace{3mm}1.2  Return(\textit{MP\_OKAY}). \\
-2.  If $a = 1$ then \\
-\hspace{3mm}2.1  $c \leftarrow 1$ \\
-\hspace{3mm}2.2  Return(\textit{MP\_OKAY}). \\
-3.  $a' \leftarrow a$ \\
-4.  $k \leftarrow 0$ \\
-5.  While $a'.used > 0$ and $a'_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\
-\hspace{3mm}5.1  $k \leftarrow k + 1$ \\
-\hspace{3mm}5.2  $a' \leftarrow \lfloor a' / 2 \rfloor$ \\
-6.  If $k \equiv 0 \mbox{ (mod }2\mbox{)}$ then \\
-\hspace{3mm}6.1  $s \leftarrow 1$ \\
-7.  else \\
-\hspace{3mm}7.1  $r \leftarrow p_0 \mbox{ (mod }8\mbox{)}$ \\
-\hspace{3mm}7.2  If $r = 1$ or $r = 7$ then \\
-\hspace{6mm}7.2.1  $s \leftarrow 1$ \\
-\hspace{3mm}7.3  else \\
-\hspace{6mm}7.3.1  $s \leftarrow -1$ \\
-8.  If $p_0 \equiv a'_0 \equiv 3 \mbox{ (mod }4\mbox{)}$ then \\
-\hspace{3mm}8.1  $s \leftarrow -s$ \\
-9.  If $a' \ne 1$ then \\
-\hspace{3mm}9.1  $p' \leftarrow p \mbox{ (mod }a'\mbox{)}$ \\
-\hspace{3mm}9.2  $s \leftarrow s \cdot \mbox{mp\_jacobi}(p', a')$ \\
-10.  $c \leftarrow s$ \\
-11.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_jacobi}
-\end{figure}
-\textbf{Algorithm mp\_jacobi.}
-This algorithm computes the Jacobi symbol for an arbitrary positive integer $a$ with respect to an odd integer $p$ greater than three.  The algorithm
-is based on algorithm 2.149 of HAC \cite[pp. 73]{HAC}.
-
-Step numbers one and two handle the trivial cases of $a = 0$ and $a = 1$ respectively.  Step five determines the number of two factors in the
-input $a$.  If $k$ is even than the term $\left ( { 2 \over p } \right )^k$ must always evaluate to one.  If $k$ is odd than the term evaluates to one
-if $p_0$ is congruent to one or seven modulo eight, otherwise it evaluates to $-1$. After the the $\left ( { 2 \over p } \right )^k$ term is handled
-the $(-1)^{(p-1)(a'-1)/4}$ is computed and multiplied against the current product $s$.  The latter term evaluates to one if both $p$ and $a'$
-are congruent to one modulo four, otherwise it evaluates to negative one.
-
-By step nine if $a'$ does not equal one a recursion is required.  Step 9.1 computes $p' \equiv p \mbox{ (mod }a'\mbox{)}$ and will recurse to compute
-$\left ( {p' \over a'} \right )$ which is multiplied against the current Jacobi product.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_jacobi.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* computes the jacobi c = (a | n) (or Legendre if n is prime)
-018    * HAC pp. 73 Algorithm 2.149
-019    * HAC is wrong here, as the special case of (0 | 1) is not
-020    * handled correctly.
-021    */
-022   int mp_jacobi (mp_int * a, mp_int * n, int *c)
-023   \{
-024     mp_int  a1, p1;
-025     int     k, s, r, res;
-026     mp_digit residue;
-027
-028     /* if a < 0 return MP_VAL */
-029     if (mp_isneg(a) == MP_YES) \{
-030        return MP_VAL;
-031     \}
-032
-033     /* if n <= 0 return MP_VAL */
-034     if (mp_cmp_d(n, 0) != MP_GT) \{
-035        return MP_VAL;
-036     \}
-037
-038     /* step 1. handle case of a == 0 */
-039     if (mp_iszero (a) == MP_YES) \{
-040        /* special case of a == 0 and n == 1 */
-041        if (mp_cmp_d (n, 1) == MP_EQ) \{
-042          *c = 1;
-043        \} else \{
-044          *c = 0;
-045        \}
-046        return MP_OKAY;
-047     \}
-048
-049     /* step 2.  if a == 1, return 1 */
-050     if (mp_cmp_d (a, 1) == MP_EQ) \{
-051       *c = 1;
-052       return MP_OKAY;
-053     \}
-054
-055     /* default */
-056     s = 0;
-057
-058     /* step 3.  write a = a1 * 2**k  */
-059     if ((res = mp_init_copy (&a1, a)) != MP_OKAY) \{
-060       return res;
-061     \}
-062
-063     if ((res = mp_init (&p1)) != MP_OKAY) \{
-064       goto LBL_A1;
-065     \}
-066
-067     /* divide out larger power of two */
-068     k = mp_cnt_lsb(&a1);
-069     if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) \{
-070        goto LBL_P1;
-071     \}
-072
-073     /* step 4.  if e is even set s=1 */
-074     if ((k & 1) == 0) \{
-075       s = 1;
-076     \} else \{
-077       /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
-078       residue = n->dp[0] & 7;
-079
-080       if ((residue == 1) || (residue == 7)) \{
-081         s = 1;
-082       \} else if ((residue == 3) || (residue == 5)) \{
-083         s = -1;
-084       \}
-085     \}
-086
-087     /* step 5.  if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
-088     if ( ((n->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) \{
-089       s = -s;
-090     \}
-091
-092     /* if a1 == 1 we're done */
-093     if (mp_cmp_d (&a1, 1) == MP_EQ) \{
-094       *c = s;
-095     \} else \{
-096       /* n1 = n mod a1 */
-097       if ((res = mp_mod (n, &a1, &p1)) != MP_OKAY) \{
-098         goto LBL_P1;
-099       \}
-100       if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) \{
-101         goto LBL_P1;
-102       \}
-103       *c = s * r;
-104     \}
-105
-106     /* done */
-107     res = MP_OKAY;
-108   LBL_P1:mp_clear (&p1);
-109   LBL_A1:mp_clear (&a1);
-110     return res;
-111   \}
-112   #endif
-113
-\end{alltt}
-\end{small}
-
-As a matter of practicality the variable $a'$ as per the pseudo-code is reprensented by the variable $a1$ since the $'$ symbol is not valid for a C
-variable name character.
-
-The two simple cases of $a = 0$ and $a = 1$ are handled at the very beginning to simplify the algorithm.  If the input is non-trivial the algorithm
-has to proceed compute the Jacobi.  The variable $s$ is used to hold the current Jacobi product.  Note that $s$ is merely a C ``int'' data type since
-the values it may obtain are merely $-1$, $0$ and $1$.
-
-After a local copy of $a$ is made all of the factors of two are divided out and the total stored in $k$.  Technically only the least significant
-bit of $k$ is required, however, it makes the algorithm simpler to follow to perform an addition. In practice an exclusive-or and addition have the same
-processor requirements and neither is faster than the other.
-
-Line 59 through 71 determines the value of $\left ( { 2 \over p } \right )^k$.  If the least significant bit of $k$ is zero than
-$k$ is even and the value is one.  Otherwise, the value of $s$ depends on which residue class $p$ belongs to modulo eight.  The value of
-$(-1)^{(p-1)(a'-1)/4}$ is compute and multiplied against $s$ on lines 73 through 76.
-
-Finally, if $a1$ does not equal one the algorithm must recurse and compute $\left ( {p' \over a'} \right )$.
-
-\textit{-- Comment about default $s$ and such...}
-
-\section{Modular Inverse}
-\label{sec:modinv}
-The modular inverse of a number actually refers to the modular multiplicative inverse.  Essentially for any integer $a$ such that $(a, p) = 1$ there
-exist another integer $b$ such that $ab \equiv 1 \mbox{ (mod }p\mbox{)}$.  The integer $b$ is called the multiplicative inverse of $a$ which is
-denoted as $b = a^{-1}$.  Technically speaking modular inversion is a well defined operation for any finite ring or field not just for rings and
-fields of integers.  However, the former will be the matter of discussion.
-
-The simplest approach is to compute the algebraic inverse of the input.  That is to compute $b \equiv a^{\Phi(p) - 1}$.  If $\Phi(p)$ is the
-order of the multiplicative subgroup modulo $p$ then $b$ must be the multiplicative inverse of $a$.  The proof of which is trivial.
-
-\begin{equation}
-ab \equiv a \left (a^{\Phi(p) - 1} \right ) \equiv a^{\Phi(p)} \equiv a^0 \equiv 1 \mbox{ (mod }p\mbox{)}
-\end{equation}
-
-However, as simple as this approach may be it has two serious flaws.  It requires that the value of $\Phi(p)$ be known which if $p$ is composite
-requires all of the prime factors.  This approach also is very slow as the size of $p$ grows.
-
-A simpler approach is based on the observation that solving for the multiplicative inverse is equivalent to solving the linear
-Diophantine\footnote{See LeVeque \cite[pp. 40-43]{LeVeque} for more information.} equation.
-
-\begin{equation}
-ab + pq = 1
-\end{equation}
-
-Where $a$, $b$, $p$ and $q$ are all integers.  If such a pair of integers $ \left < b, q \right >$ exist than $b$ is the multiplicative inverse of
-$a$ modulo $p$.  The extended Euclidean algorithm (Knuth \cite[pp. 342]{TAOCPV2}) can be used to solve such equations provided $(a, p) = 1$.
-However, instead of using that algorithm directly a variant known as the binary Extended Euclidean algorithm will be used in its place.  The
-binary approach is very similar to the binary greatest common divisor algorithm except it will produce a full solution to the Diophantine
-equation.
-
-\subsection{General Case}
-\newpage\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_invmod}. \\
-\textbf{Input}.   mp\_int $a$ and $b$, $(a, b) = 1$, $p \ge 2$, $0 < a < p$.  \\
-\textbf{Output}.  The modular inverse $c \equiv a^{-1} \mbox{ (mod }b\mbox{)}$. \\
-\hline \\
-1.  If $b \le 0$ then return(\textit{MP\_VAL}). \\
-2.  If $b_0 \equiv 1 \mbox{ (mod }2\mbox{)}$ then use algorithm fast\_mp\_invmod. \\
-3.  $x \leftarrow \vert a \vert, y \leftarrow b$ \\
-4.  If $x_0 \equiv y_0  \equiv 0 \mbox{ (mod }2\mbox{)}$ then return(\textit{MP\_VAL}). \\
-5.  $B \leftarrow 0, C \leftarrow 0, A \leftarrow 1, D \leftarrow 1$ \\
-6.  While $u.used > 0$ and $u_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\
-\hspace{3mm}6.1  $u \leftarrow \lfloor u / 2 \rfloor$ \\
-\hspace{3mm}6.2  If ($A.used > 0$ and $A_0 \equiv 1 \mbox{ (mod }2\mbox{)}$) or ($B.used > 0$ and $B_0 \equiv 1 \mbox{ (mod }2\mbox{)}$) then \\
-\hspace{6mm}6.2.1  $A \leftarrow A + y$ \\
-\hspace{6mm}6.2.2  $B \leftarrow B - x$ \\
-\hspace{3mm}6.3  $A \leftarrow \lfloor A / 2 \rfloor$ \\
-\hspace{3mm}6.4  $B \leftarrow \lfloor B / 2 \rfloor$ \\
-7.  While $v.used > 0$ and $v_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\
-\hspace{3mm}7.1  $v \leftarrow \lfloor v / 2 \rfloor$ \\
-\hspace{3mm}7.2  If ($C.used > 0$ and $C_0 \equiv 1 \mbox{ (mod }2\mbox{)}$) or ($D.used > 0$ and $D_0 \equiv 1 \mbox{ (mod }2\mbox{)}$) then \\
-\hspace{6mm}7.2.1  $C \leftarrow C + y$ \\
-\hspace{6mm}7.2.2  $D \leftarrow D - x$ \\
-\hspace{3mm}7.3  $C \leftarrow \lfloor C / 2 \rfloor$ \\
-\hspace{3mm}7.4  $D \leftarrow \lfloor D / 2 \rfloor$ \\
-8.  If $u \ge v$ then \\
-\hspace{3mm}8.1  $u \leftarrow u - v$ \\
-\hspace{3mm}8.2  $A \leftarrow A - C$ \\
-\hspace{3mm}8.3  $B \leftarrow B - D$ \\
-9.  else \\
-\hspace{3mm}9.1  $v \leftarrow v - u$ \\
-\hspace{3mm}9.2  $C \leftarrow C - A$ \\
-\hspace{3mm}9.3  $D \leftarrow D - B$ \\
-10.  If $u \ne 0$ goto step 6. \\
-11.  If $v \ne 1$ return(\textit{MP\_VAL}). \\
-12.  While $C \le 0$ do \\
-\hspace{3mm}12.1  $C \leftarrow C + b$ \\
-13.  While $C \ge b$ do \\
-\hspace{3mm}13.1  $C \leftarrow C - b$ \\
-14.  $c \leftarrow C$ \\
-15.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\end{figure}
-\textbf{Algorithm mp\_invmod.}
-This algorithm computes the modular multiplicative inverse of an integer $a$ modulo an integer $b$.  This algorithm is a variation of the
-extended binary Euclidean algorithm from HAC \cite[pp. 608]{HAC}.  It has been modified to only compute the modular inverse and not a complete
-Diophantine solution.
-
-If $b \le 0$ than the modulus is invalid and MP\_VAL is returned.  Similarly if both $a$ and $b$ are even then there cannot be a multiplicative
-inverse for $a$ and the error is reported.
-
-The astute reader will observe that steps seven through nine are very similar to the binary greatest common divisor algorithm mp\_gcd.  In this case
-the other variables to the Diophantine equation are solved.  The algorithm terminates when $u = 0$ in which case the solution is
-
-\begin{equation}
-Ca + Db = v
-\end{equation}
-
-If $v$, the greatest common divisor of $a$ and $b$ is not equal to one then the algorithm will report an error as no inverse exists.  Otherwise, $C$
-is the modular inverse of $a$.  The actual value of $C$ is congruent to, but not necessarily equal to, the ideal modular inverse which should lie
-within $1 \le a^{-1} < b$.  Step numbers twelve and thirteen adjust the inverse until it is in range.  If the original input $a$ is within $0 < a < p$
-then only a couple of additions or subtractions will be required to adjust the inverse.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_invmod.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* hac 14.61, pp608 */
-018   int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
-019   \{
-020     /* b cannot be negative */
-021     if ((b->sign == MP_NEG) || (mp_iszero(b) == MP_YES)) \{
-022       return MP_VAL;
-023     \}
-024
-025   #ifdef BN_FAST_MP_INVMOD_C
-026     /* if the modulus is odd we can use a faster routine instead */
-027     if (mp_isodd (b) == MP_YES) \{
-028       return fast_mp_invmod (a, b, c);
-029     \}
-030   #endif
-031
-032   #ifdef BN_MP_INVMOD_SLOW_C
-033     return mp_invmod_slow(a, b, c);
-034   #else
-035     return MP_VAL;
-036   #endif
-037   \}
-038   #endif
-039
-\end{alltt}
-\end{small}
-
-\subsubsection{Odd Moduli}
-
-When the modulus $b$ is odd the variables $A$ and $C$ are fixed and are not required to compute the inverse.  In particular by attempting to solve
-the Diophantine $Cb + Da = 1$ only $B$ and $D$ are required to find the inverse of $a$.
-
-The algorithm fast\_mp\_invmod is a direct adaptation of algorithm mp\_invmod with all all steps involving either $A$ or $C$ removed.  This
-optimization will halve the time required to compute the modular inverse.
-
-\section{Primality Tests}
-
-A non-zero integer $a$ is said to be prime if it is not divisible by any other integer excluding one and itself.  For example, $a = 7$ is prime
-since the integers $2 \ldots 6$ do not evenly divide $a$.  By contrast, $a = 6$ is not prime since $a = 6 = 2 \cdot 3$.
-
-Prime numbers arise in cryptography considerably as they allow finite fields to be formed.  The ability to determine whether an integer is prime or
-not quickly has been a viable subject in cryptography and number theory for considerable time.  The algorithms that will be presented are all
-probablistic algorithms in that when they report an integer is composite it must be composite.  However, when the algorithms report an integer is
-prime the algorithm may be incorrect.
-
-As will be discussed it is possible to limit the probability of error so well that for practical purposes the probablity of error might as
-well be zero.  For the purposes of these discussions let $n$ represent the candidate integer of which the primality is in question.
-
-\subsection{Trial Division}
-
-Trial division means to attempt to evenly divide a candidate integer by small prime integers.  If the candidate can be evenly divided it obviously
-cannot be prime.  By dividing by all primes $1 < p \le \sqrt{n}$ this test can actually prove whether an integer is prime.  However, such a test
-would require a prohibitive amount of time as $n$ grows.
-
-Instead of dividing by every prime, a smaller, more mangeable set of primes may be used instead.  By performing trial division with only a subset
-of the primes less than $\sqrt{n} + 1$ the algorithm cannot prove if a candidate is prime.  However, often it can prove a candidate is not prime.
-
-The benefit of this test is that trial division by small values is fairly efficient.  Specially compared to the other algorithms that will be
-discussed shortly.  The probability that this approach correctly identifies a composite candidate when tested with all primes upto $q$ is given by
-$1 - {1.12 \over ln(q)}$.  The graph (\ref{pic:primality}, will be added later) demonstrates the probability of success for the range
-$3 \le q \le 100$.
-
-At approximately $q = 30$ the gain of performing further tests diminishes fairly quickly.  At $q = 90$ further testing is generally not going to
-be of any practical use.  In the case of LibTomMath the default limit $q = 256$ was chosen since it is not too high and will eliminate
-approximately $80\%$ of all candidate integers.  The constant \textbf{PRIME\_SIZE} is equal to the number of primes in the test base.  The
-array \_\_prime\_tab is an array of the first \textbf{PRIME\_SIZE} prime numbers.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_prime\_is\_divisible}. \\
-\textbf{Input}.   mp\_int $a$ \\
-\textbf{Output}.  $c = 1$ if $n$ is divisible by a small prime, otherwise $c = 0$.  \\
-\hline \\
-1.  for $ix$ from $0$ to $PRIME\_SIZE$ do \\
-\hspace{3mm}1.1  $d \leftarrow n \mbox{ (mod }\_\_prime\_tab_{ix}\mbox{)}$ \\
-\hspace{3mm}1.2  If $d = 0$ then \\
-\hspace{6mm}1.2.1  $c \leftarrow 1$ \\
-\hspace{6mm}1.2.2  Return(\textit{MP\_OKAY}). \\
-2.  $c \leftarrow 0$ \\
-3.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_prime\_is\_divisible}
-\end{figure}
-\textbf{Algorithm mp\_prime\_is\_divisible.}
-This algorithm attempts to determine if a candidate integer $n$ is composite by performing trial divisions.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_prime\_is\_divisible.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* determines if an integers is divisible by one
-018    * of the first PRIME_SIZE primes or not
-019    *
-020    * sets result to 0 if not, 1 if yes
-021    */
-022   int mp_prime_is_divisible (mp_int * a, int *result)
-023   \{
-024     int     err, ix;
-025     mp_digit res;
-026
-027     /* default to not */
-028     *result = MP_NO;
-029
-030     for (ix = 0; ix < PRIME_SIZE; ix++) \{
-031       /* what is a mod LBL_prime_tab[ix] */
-032       if ((err = mp_mod_d (a, ltm_prime_tab[ix], &res)) != MP_OKAY) \{
-033         return err;
-034       \}
-035
-036       /* is the residue zero? */
-037       if (res == 0) \{
-038         *result = MP_YES;
-039         return MP_OKAY;
-040       \}
-041     \}
-042
-043     return MP_OKAY;
-044   \}
-045   #endif
-046
-\end{alltt}
-\end{small}
-
-The algorithm defaults to a return of $0$ in case an error occurs.  The values in the prime table are all specified to be in the range of a
-mp\_digit.  The table \_\_prime\_tab is defined in the following file.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_prime\_tab.c
-\vspace{-3mm}
-\begin{alltt}
-016   const mp_digit ltm_prime_tab[] = \{
-017     0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
-018     0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
-019     0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
-020     0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,
-021   #ifndef MP_8BIT
-022     0x0083,
-023     0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
-024     0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
-025     0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
-026     0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
-027
-028     0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
-029     0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
-030     0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
-031     0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
-032     0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
-033     0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
-034     0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
-035     0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
-036
-037     0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
-038     0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
-039     0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
-040     0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
-041     0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
-042     0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
-043     0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
-044     0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
-045
-046     0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
-047     0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
-048     0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
-049     0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
-050     0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
-051     0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
-052     0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
-053     0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
-054   #endif
-055   \};
-056   #endif
-057
-\end{alltt}
-\end{small}
-
-Note that there are two possible tables.  When an mp\_digit is 7-bits long only the primes upto $127$ may be included, otherwise the primes
-upto $1619$ are used.  Note that the value of \textbf{PRIME\_SIZE} is a constant dependent on the size of a mp\_digit.
-
-\subsection{The Fermat Test}
-The Fermat test is probably one the oldest tests to have a non-trivial probability of success.  It is based on the fact that if $n$ is in
-fact prime then $a^{n} \equiv a \mbox{ (mod }n\mbox{)}$ for all $0 < a < n$.  The reason being that if $n$ is prime than the order of
-the multiplicative sub group is $n - 1$.  Any base $a$ must have an order which divides $n - 1$ and as such $a^n$ is equivalent to
-$a^1 = a$.
-
-If $n$ is composite then any given base $a$ does not have to have a period which divides $n - 1$.  In which case
-it is possible that $a^n \nequiv a \mbox{ (mod }n\mbox{)}$.  However, this test is not absolute as it is possible that the order
-of a base will divide $n - 1$ which would then be reported as prime.  Such a base yields what is known as a Fermat pseudo-prime.  Several
-integers known as Carmichael numbers will be a pseudo-prime to all valid bases.  Fortunately such numbers are extremely rare as $n$ grows
-in size.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_prime\_fermat}. \\
-\textbf{Input}.   mp\_int $a$ and $b$, $a \ge 2$, $0 < b < a$.  \\
-\textbf{Output}.  $c = 1$ if $b^a \equiv b \mbox{ (mod }a\mbox{)}$, otherwise $c = 0$.  \\
-\hline \\
-1.  $t \leftarrow b^a \mbox{ (mod }a\mbox{)}$ \\
-2.  If $t = b$ then \\
-\hspace{3mm}2.1  $c = 1$ \\
-3.  else \\
-\hspace{3mm}3.1  $c = 0$ \\
-4.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_prime\_fermat}
-\end{figure}
-\textbf{Algorithm mp\_prime\_fermat.}
-This algorithm determines whether an mp\_int $a$ is a Fermat prime to the base $b$ or not.  It uses a single modular exponentiation to
-determine the result.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_prime\_fermat.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* performs one Fermat test.
-018    *
-019    * If "a" were prime then b**a == b (mod a) since the order of
-020    * the multiplicative sub-group would be phi(a) = a-1.  That means
-021    * it would be the same as b**(a mod (a-1)) == b**1 == b (mod a).
-022    *
-023    * Sets result to 1 if the congruence holds, or zero otherwise.
-024    */
-025   int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
-026   \{
-027     mp_int  t;
-028     int     err;
-029
-030     /* default to composite  */
-031     *result = MP_NO;
-032
-033     /* ensure b > 1 */
-034     if (mp_cmp_d(b, 1) != MP_GT) \{
-035        return MP_VAL;
-036     \}
-037
-038     /* init t */
-039     if ((err = mp_init (&t)) != MP_OKAY) \{
-040       return err;
-041     \}
-042
-043     /* compute t = b**a mod a */
-044     if ((err = mp_exptmod (b, a, a, &t)) != MP_OKAY) \{
-045       goto LBL_T;
-046     \}
-047
-048     /* is it equal to b? */
-049     if (mp_cmp (&t, b) == MP_EQ) \{
-050       *result = MP_YES;
-051     \}
-052
-053     err = MP_OKAY;
-054   LBL_T:mp_clear (&t);
-055     return err;
-056   \}
-057   #endif
-058
-\end{alltt}
-\end{small}
-
-\subsection{The Miller-Rabin Test}
-The Miller-Rabin (citation) test is another primality test which has tighter error bounds than the Fermat test specifically with sequentially chosen
-candidate  integers.  The algorithm is based on the observation that if $n - 1 = 2^kr$ and if $b^r \nequiv \pm 1$ then after upto $k - 1$ squarings the
-value must be equal to $-1$.  The squarings are stopped as soon as $-1$ is observed.  If the value of $1$ is observed first it means that
-some value not congruent to $\pm 1$ when squared equals one which cannot occur if $n$ is prime.
-
-\begin{figure}[!here]
-\begin{small}
-\begin{center}
-\begin{tabular}{l}
-\hline Algorithm \textbf{mp\_prime\_miller\_rabin}. \\
-\textbf{Input}.   mp\_int $a$ and $b$, $a \ge 2$, $0 < b < a$.  \\
-\textbf{Output}.  $c = 1$ if $a$ is a Miller-Rabin prime to the base $a$, otherwise $c = 0$.  \\
-\hline
-1.  $a' \leftarrow a - 1$ \\
-2.  $r  \leftarrow n1$    \\
-3.  $c \leftarrow 0, s  \leftarrow 0$ \\
-4.  While $r.used > 0$ and $r_0 \equiv 0 \mbox{ (mod }2\mbox{)}$ \\
-\hspace{3mm}4.1  $s \leftarrow s + 1$ \\
-\hspace{3mm}4.2  $r \leftarrow \lfloor r / 2 \rfloor$ \\
-5.  $y \leftarrow b^r \mbox{ (mod }a\mbox{)}$ \\
-6.  If $y \nequiv \pm 1$ then \\
-\hspace{3mm}6.1  $j \leftarrow 1$ \\
-\hspace{3mm}6.2  While $j \le (s - 1)$ and $y \nequiv a'$ \\
-\hspace{6mm}6.2.1  $y \leftarrow y^2 \mbox{ (mod }a\mbox{)}$ \\
-\hspace{6mm}6.2.2  If $y = 1$ then goto step 8. \\
-\hspace{6mm}6.2.3  $j \leftarrow j + 1$ \\
-\hspace{3mm}6.3  If $y \nequiv a'$ goto step 8. \\
-7.  $c \leftarrow 1$\\
-8.  Return(\textit{MP\_OKAY}). \\
-\hline
-\end{tabular}
-\end{center}
-\end{small}
-\caption{Algorithm mp\_prime\_miller\_rabin}
-\end{figure}
-\textbf{Algorithm mp\_prime\_miller\_rabin.}
-This algorithm performs one trial round of the Miller-Rabin algorithm to the base $b$.  It will set $c = 1$ if the algorithm cannot determine
-if $b$ is composite or $c = 0$ if $b$ is provably composite.  The values of $s$ and $r$ are computed such that $a' = a - 1 = 2^sr$.
-
-If the value $y \equiv b^r$ is congruent to $\pm 1$ then the algorithm cannot prove if $a$ is composite or not.  Otherwise, the algorithm will
-square $y$ upto $s - 1$ times stopping only when $y \equiv -1$.  If $y^2 \equiv 1$ and $y \nequiv \pm 1$ then the algorithm can report that $a$
-is provably composite.  If the algorithm performs $s - 1$ squarings and $y \nequiv -1$ then $a$ is provably composite.  If $a$ is not provably
-composite then it is \textit{probably} prime.
-
-\vspace{+3mm}\begin{small}
-\hspace{-5.1mm}{\bf File}: bn\_mp\_prime\_miller\_rabin.c
-\vspace{-3mm}
-\begin{alltt}
-016
-017   /* Miller-Rabin test of "a" to the base of "b" as described in
-018    * HAC pp. 139 Algorithm 4.24
-019    *
-020    * Sets result to 0 if definitely composite or 1 if probably prime.
-021    * Randomly the chance of error is no more than 1/4 and often
-022    * very much lower.
-023    */
-024   int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
-025   \{
-026     mp_int  n1, y, r;
-027     int     s, j, err;
-028
-029     /* default */
-030     *result = MP_NO;
-031
-032     /* ensure b > 1 */
-033     if (mp_cmp_d(b, 1) != MP_GT) \{
-034        return MP_VAL;
-035     \}
-036
-037     /* get n1 = a - 1 */
-038     if ((err = mp_init_copy (&n1, a)) != MP_OKAY) \{
-039       return err;
-040     \}
-041     if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) \{
-042       goto LBL_N1;
-043     \}
-044
-045     /* set 2**s * r = n1 */
-046     if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) \{
-047       goto LBL_N1;
-048     \}
-049
-050     /* count the number of least significant bits
-051      * which are zero
-052      */
-053     s = mp_cnt_lsb(&r);
-054
-055     /* now divide n - 1 by 2**s */
-056     if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) \{
-057       goto LBL_R;
-058     \}
-059
-060     /* compute y = b**r mod a */
-061     if ((err = mp_init (&y)) != MP_OKAY) \{
-062       goto LBL_R;
-063     \}
-064     if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) \{
-065       goto LBL_Y;
-066     \}
-067
-068     /* if y != 1 and y != n1 do */
-069     if ((mp_cmp_d (&y, 1) != MP_EQ) && (mp_cmp (&y, &n1) != MP_EQ)) \{
-070       j = 1;
-071       /* while j <= s-1 and y != n1 */
-072       while ((j <= (s - 1)) && (mp_cmp (&y, &n1) != MP_EQ)) \{
-073         if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) \{
-074            goto LBL_Y;
-075         \}
-076
-077         /* if y == 1 then composite */
-078         if (mp_cmp_d (&y, 1) == MP_EQ) \{
-079            goto LBL_Y;
-080         \}
-081
-082         ++j;
-083       \}
-084
-085       /* if y != n1 then composite */
-086       if (mp_cmp (&y, &n1) != MP_EQ) \{
-087         goto LBL_Y;
-088       \}
-089     \}
-090
-091     /* probably prime now */
-092     *result = MP_YES;
-093   LBL_Y:mp_clear (&y);
-094   LBL_R:mp_clear (&r);
-095   LBL_N1:mp_clear (&n1);
-096     return err;
-097   \}
-098   #endif
-099
-\end{alltt}
-\end{small}
-
-
-
-
-\backmatter
-\appendix
-\begin{thebibliography}{ABCDEF}
-\bibitem[1]{TAOCPV2}
-Donald Knuth, \textit{The Art of Computer Programming}, Third Edition, Volume Two, Seminumerical Algorithms, Addison-Wesley, 1998
-
-\bibitem[2]{HAC}
-A. Menezes, P. van Oorschot, S. Vanstone, \textit{Handbook of Applied Cryptography}, CRC Press, 1996
-
-\bibitem[3]{ROSE}
-Michael Rosing, \textit{Implementing Elliptic Curve Cryptography}, Manning Publications, 1999
-
-\bibitem[4]{COMBA}
-Paul G. Comba, \textit{Exponentiation Cryptosystems on the IBM PC}. IBM Systems Journal 29(4): 526-538 (1990)
-
-\bibitem[5]{KARA}
-A. Karatsuba, Doklay Akad. Nauk SSSR 145 (1962), pp.293-294
-
-\bibitem[6]{KARAP}
-Andre Weimerskirch and Christof Paar, \textit{Generalizations of the Karatsuba Algorithm for Polynomial Multiplication}, Submitted to Design, Codes and Cryptography, March 2002
-
-\bibitem[7]{BARRETT}
-Paul Barrett, \textit{Implementing the Rivest Shamir and Adleman Public Key Encryption Algorithm on a Standard Digital Signal Processor}, Advances in Cryptology, Crypto '86, Springer-Verlag.
-
-\bibitem[8]{MONT}
-P.L.Montgomery. \textit{Modular multiplication without trial division}. Mathematics of Computation, 44(170):519-521, April 1985.
-
-\bibitem[9]{DRMET}
-Chae Hoon Lim and Pil Joong Lee, \textit{Generating Efficient Primes for Discrete Log Cryptosystems}, POSTECH Information Research Laboratories
-
-\bibitem[10]{MMB}
-J. Daemen and R. Govaerts and J. Vandewalle, \textit{Block ciphers based on Modular Arithmetic}, State and {P}rogress in the {R}esearch of {C}ryptography, 1993, pp. 80-89
-
-\bibitem[11]{RSAREF}
-R.L. Rivest, A. Shamir, L. Adleman, \textit{A Method for Obtaining Digital Signatures and Public-Key Cryptosystems}
-
-\bibitem[12]{DHREF}
-Whitfield Diffie, Martin E. Hellman, \textit{New Directions in Cryptography}, IEEE Transactions on Information Theory, 1976
-
-\bibitem[13]{IEEE}
-IEEE Standard for Binary Floating-Point Arithmetic (ANSI/IEEE Std 754-1985)
-
-\bibitem[14]{GMP}
-GNU Multiple Precision (GMP), \url{http://www.swox.com/gmp/}
-
-\bibitem[15]{MPI}
-Multiple Precision Integer Library (MPI), Michael Fromberger, \url{http://thayer.dartmouth.edu/~sting/mpi/}
-
-\bibitem[16]{OPENSSL}
-OpenSSL Cryptographic Toolkit, \url{http://openssl.org}
-
-\bibitem[17]{LIP}
-Large Integer Package, \url{http://home.hetnet.nl/~ecstr/LIP.zip}
-
-\bibitem[18]{ISOC}
-JTC1/SC22/WG14, ISO/IEC 9899:1999, ``A draft rationale for the C99 standard.''
-
-\bibitem[19]{JAVA}
-The Sun Java Website, \url{http://java.sun.com/}
-
-\end{thebibliography}
-
-\input{tommath.ind}
-
-\end{document}
-- 
cgit v0.12


From b49738ff138e13a39a594458fefc273272acffee Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Wed, 30 Aug 2017 12:37:50 +0000
Subject: Tweak libtommath building, such that it doesn't depend on uint64_t
 any more. (handle mp_word in the same way as mp_digit)

---
 generic/tcl.h           |  2 ++
 generic/tclTomMath.h    | 15 +++++++++++++++
 tools/fix_tommath_h.tcl |  6 ++++++
 3 files changed, 23 insertions(+)

diff --git a/generic/tcl.h b/generic/tcl.h
index 6fa26f9..da9b292 100644
--- a/generic/tcl.h
+++ b/generic/tcl.h
@@ -2263,6 +2263,8 @@ typedef struct mp_int mp_int;
 #define MP_INT_DECLARED
 typedef unsigned int mp_digit;
 #define MP_DIGIT_DECLARED
+typedef unsigned TCL_WIDE_INT_TYPE mp_word;
+#define MP_WORD_DECLARED
 
 /*
  *----------------------------------------------------------------------------
diff --git a/generic/tclTomMath.h b/generic/tclTomMath.h
index 87fe756..39132ed 100644
--- a/generic/tclTomMath.h
+++ b/generic/tclTomMath.h
@@ -46,7 +46,10 @@ extern "C" {
    typedef uint8_t              mp_digit;
 #define MP_DIGIT_DECLARED
 #endif
+#ifndef MP_WORD_DECLARED
    typedef uint16_t             mp_word;
+#define MP_WORD_DECLARED
+#endif
 #define MP_SIZEOF_MP_DIGIT      1
 #ifdef DIGIT_BIT
 #error You must not define DIGIT_BIT when using MP_8BIT
@@ -56,7 +59,10 @@ extern "C" {
    typedef uint16_t             mp_digit;
 #define MP_DIGIT_DECLARED
 #endif
+#ifndef MP_WORD_DECLARED
    typedef uint32_t             mp_word;
+#define MP_WORD_DECLARED
+#endif
 #define MP_SIZEOF_MP_DIGIT      2
 #ifdef DIGIT_BIT
 #error You must not define DIGIT_BIT when using MP_16BIT
@@ -68,13 +74,19 @@ extern "C" {
 #define MP_DIGIT_DECLARED
 #endif
 #if defined(_WIN32)
+#ifndef MP_WORD_DECLARED
    typedef unsigned __int128    mp_word;
+#define MP_WORD_DECLARED
+#endif
 #elif defined(__GNUC__)
    typedef unsigned long        mp_word __attribute__ ((mode(TI)));
 #else
    /* it seems you have a problem
     * but we assume you can somewhere define your own uint128_t */
+#ifndef MP_WORD_DECLARED
    typedef uint128_t            mp_word;
+#define MP_WORD_DECLARED
+#endif
 #endif
 
    #define DIGIT_BIT            60
@@ -86,7 +98,10 @@ extern "C" {
    typedef uint32_t             mp_digit;
 #define MP_DIGIT_DECLARED
 #endif
+#ifndef MP_WORD_DECLARED
    typedef uint64_t             mp_word;
+#define MP_WORD_DECLARED
+#endif
 
 #ifdef MP_31BIT
    /* this is an extension that uses 31-bit digits */
diff --git a/tools/fix_tommath_h.tcl b/tools/fix_tommath_h.tcl
index 61fa4fd..cee29fa 100755
--- a/tools/fix_tommath_h.tcl
+++ b/tools/fix_tommath_h.tcl
@@ -45,6 +45,12 @@ foreach line [split $data \n] {
 		puts "\#define MP_DIGIT_DECLARED"
 		puts "\#endif"
 	    }
+	    {typedef.*mp_word;} {
+		puts "\#ifndef MP_WORD_DECLARED"
+		puts $line
+		puts "\#define MP_WORD_DECLARED"
+		puts "\#endif"
+	    }
 	    {typedef struct} {
 		puts "\#ifndef MP_INT_DECLARED"
 		puts "\#define MP_INT_DECLARED"
-- 
cgit v0.12


From a9ff2a990cea2993e91fa9fc58f7513b7ac41880 Mon Sep 17 00:00:00 2001
From: andy <andrew.m.goth@gmail.com>
Date: Wed, 30 Aug 2017 15:29:16 +0000
Subject: Cherrypick string.test [de104ef5ab]

---
 tests/string.test | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/tests/string.test b/tests/string.test
index 7b02928..549944d 100644
--- a/tests/string.test
+++ b/tests/string.test
@@ -1371,6 +1371,9 @@ test string-14.16 {string replace} {
 test string-14.17 {string replace} {
     string replace abcdefghijklmnop end end-1
 } {abcdefghijklmnop}
+test string-14.18 {string replace} {
+    string replace abcdefghijklmnop 10 9 XXX
+} {abcdefghijklmnop}
 
 test string-15.1 {string tolower too few args} {
     list [catch {string tolower} msg] $msg
-- 
cgit v0.12


From 5a22b3d9674aaf34bb6116f095f12d07a6578e72 Mon Sep 17 00:00:00 2001
From: oehhar <harald.oehlmann@elmicron.de>
Date: Thu, 31 Aug 2017 06:31:05 +0000
Subject: http state 100 continue handling broken [2a94652ee1]

---
 changes                   | 3 +++
 library/http/http.tcl     | 3 ++-
 library/http/pkgIndex.tcl | 2 +-
 unix/Makefile.in          | 4 ++--
 win/Makefile.in           | 4 ++--
 5 files changed, 10 insertions(+), 6 deletions(-)
 mode change 100644 => 100755 changes
 mode change 100644 => 100755 library/http/http.tcl
 mode change 100644 => 100755 library/http/pkgIndex.tcl
 mode change 100644 => 100755 unix/Makefile.in
 mode change 100644 => 100755 win/Makefile.in

diff --git a/changes b/changes
old mode 100644
new mode 100755
index f98eafc..d4be350
--- a/changes
+++ b/changes
@@ -8795,3 +8795,6 @@ improvements to regexp engine from Postgres (lane,porter,fellows,seltenreich)
 2017-07-17 (bug)[fb2208] Repeatable tclIndex generation (wiedemann,nijtmans)
 
 --- Released 8.6.7, August 9, 2017 --- http://core.tcl.tk/tcl/ for details
+
+2017-08-31 (bug)[2a9465] http state 100 continue handling broken (oehlmann)
+=> http 2.8.12
diff --git a/library/http/http.tcl b/library/http/http.tcl
old mode 100644
new mode 100755
index 0350808..9f5310b
--- a/library/http/http.tcl
+++ b/library/http/http.tcl
@@ -11,7 +11,7 @@
 package require Tcl 8.6-
 # Keep this in sync with pkgIndex.tcl and with the install directories in
 # Makefiles
-package provide http 2.8.11
+package provide http 2.8.12
 
 namespace eval http {
     # Allow resourcing to not clobber existing data
@@ -1027,6 +1027,7 @@ proc http::Event {sock token} {
 	    # We have now read all headers
 	    # We ignore HTTP/1.1 100 Continue returns. RFC2616 sec 8.2.3
 	    if {$state(http) == "" || ([regexp {^\S+\s(\d+)} $state(http) {} x] && $x == 100)} {
+		set state(state) "connecting"
 		return
 	    }
 
diff --git a/library/http/pkgIndex.tcl b/library/http/pkgIndex.tcl
old mode 100644
new mode 100755
index a0d28f1..d3fc7af
--- a/library/http/pkgIndex.tcl
+++ b/library/http/pkgIndex.tcl
@@ -1,2 +1,2 @@
 if {![package vsatisfies [package provide Tcl] 8.6-]} {return}
-package ifneeded http 2.8.11 [list tclPkgSetup $dir http 2.8.11 {{http.tcl source {::http::config ::http::formatQuery ::http::geturl ::http::reset ::http::wait ::http::register ::http::unregister ::http::mapReply}}}]
+package ifneeded http 2.8.12 [list tclPkgSetup $dir http 2.8.12 {{http.tcl source {::http::config ::http::formatQuery ::http::geturl ::http::reset ::http::wait ::http::register ::http::unregister ::http::mapReply}}}]
diff --git a/unix/Makefile.in b/unix/Makefile.in
old mode 100644
new mode 100755
index 7f45414..4814ee0
--- a/unix/Makefile.in
+++ b/unix/Makefile.in
@@ -840,8 +840,8 @@ install-libraries: libraries
 	    do \
 	    $(INSTALL_DATA) $$i "$(SCRIPT_INSTALL_DIR)"/http1.0; \
 	    done;
-	@echo "Installing package http 2.8.11 as a Tcl Module";
-	@$(INSTALL_DATA) $(TOP_DIR)/library/http/http.tcl "$(SCRIPT_INSTALL_DIR)"/../tcl8/8.6/http-2.8.11.tm;
+	@echo "Installing package http 2.8.12 as a Tcl Module";
+	@$(INSTALL_DATA) $(TOP_DIR)/library/http/http.tcl "$(SCRIPT_INSTALL_DIR)"/../tcl8/8.6/http-2.8.12.tm;
 	@echo "Installing package opt0.4 files to $(SCRIPT_INSTALL_DIR)/opt0.4/";
 	@for i in $(TOP_DIR)/library/opt/*.tcl ; \
 	    do \
diff --git a/win/Makefile.in b/win/Makefile.in
old mode 100644
new mode 100755
index c62a3c7..633a9f5
--- a/win/Makefile.in
+++ b/win/Makefile.in
@@ -651,8 +651,8 @@ install-libraries: libraries install-tzdata install-msgs
 	    do \
 	    $(COPY) "$$j" "$(SCRIPT_INSTALL_DIR)/http1.0"; \
 	    done;
-	@echo "Installing package http 2.8.11 as a Tcl Module";
-	@$(COPY) $(ROOT_DIR)/library/http/http.tcl $(SCRIPT_INSTALL_DIR)/../tcl8/8.6/http-2.8.11.tm;
+	@echo "Installing package http 2.8.12 as a Tcl Module";
+	@$(COPY) $(ROOT_DIR)/library/http/http.tcl $(SCRIPT_INSTALL_DIR)/../tcl8/8.6/http-2.8.12.tm;
 	@echo "Installing library opt0.4 directory";
 	@for j in $(ROOT_DIR)/library/opt/*.tcl; \
 	    do \
-- 
cgit v0.12


From ad562484f0094b64a85de813c8576165badcc126 Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Thu, 31 Aug 2017 13:32:52 +0000
Subject: Undo tag removal (just get libtommath directly from GitHUB), so we
 don't have useless file changes with every new release

---
 .fossil-settings/crlf-glob                       |  17 ++++
 libtommath/README.md                             |   4 +-
 libtommath/TODO                                  |  16 ----
 libtommath/bn_error.c                            |   6 +-
 libtommath/bn_fast_mp_invmod.c                   |   6 +-
 libtommath/bn_fast_mp_montgomery_reduce.c        |   6 +-
 libtommath/bn_fast_s_mp_mul_digs.c               |   6 +-
 libtommath/bn_fast_s_mp_mul_high_digs.c          |   6 +-
 libtommath/bn_fast_s_mp_sqr.c                    |   6 +-
 libtommath/bn_mp_2expt.c                         |   6 +-
 libtommath/bn_mp_abs.c                           |   6 +-
 libtommath/bn_mp_add.c                           |   6 +-
 libtommath/bn_mp_add_d.c                         |   6 +-
 libtommath/bn_mp_addmod.c                        |   6 +-
 libtommath/bn_mp_and.c                           |   6 +-
 libtommath/bn_mp_clamp.c                         |   6 +-
 libtommath/bn_mp_clear.c                         |   6 +-
 libtommath/bn_mp_clear_multi.c                   |   6 +-
 libtommath/bn_mp_cmp.c                           |   6 +-
 libtommath/bn_mp_cmp_d.c                         |   6 +-
 libtommath/bn_mp_cmp_mag.c                       |   6 +-
 libtommath/bn_mp_cnt_lsb.c                       |   6 +-
 libtommath/bn_mp_copy.c                          |   6 +-
 libtommath/bn_mp_count_bits.c                    |   6 +-
 libtommath/bn_mp_div.c                           |   6 +-
 libtommath/bn_mp_div_2.c                         |   6 +-
 libtommath/bn_mp_div_2d.c                        |   6 +-
 libtommath/bn_mp_div_3.c                         |   6 +-
 libtommath/bn_mp_div_d.c                         |   6 +-
 libtommath/bn_mp_dr_is_modulus.c                 |   6 +-
 libtommath/bn_mp_dr_reduce.c                     |   6 +-
 libtommath/bn_mp_dr_setup.c                      |   6 +-
 libtommath/bn_mp_exch.c                          |   6 +-
 libtommath/bn_mp_export.c                        |   6 +-
 libtommath/bn_mp_expt_d.c                        |   6 +-
 libtommath/bn_mp_expt_d_ex.c                     |   6 +-
 libtommath/bn_mp_exptmod.c                       |   6 +-
 libtommath/bn_mp_exptmod_fast.c                  |   6 +-
 libtommath/bn_mp_exteuclid.c                     |   6 +-
 libtommath/bn_mp_fread.c                         |   6 +-
 libtommath/bn_mp_fwrite.c                        |   6 +-
 libtommath/bn_mp_gcd.c                           |   6 +-
 libtommath/bn_mp_get_int.c                       |   6 +-
 libtommath/bn_mp_grow.c                          |   6 +-
 libtommath/bn_mp_import.c                        |   6 +-
 libtommath/bn_mp_init.c                          |   6 +-
 libtommath/bn_mp_init_copy.c                     |   6 +-
 libtommath/bn_mp_init_multi.c                    |   6 +-
 libtommath/bn_mp_init_set.c                      |   6 +-
 libtommath/bn_mp_init_set_int.c                  |   6 +-
 libtommath/bn_mp_init_size.c                     |   6 +-
 libtommath/bn_mp_invmod.c                        |   6 +-
 libtommath/bn_mp_invmod_slow.c                   |   6 +-
 libtommath/bn_mp_is_square.c                     |   6 +-
 libtommath/bn_mp_jacobi.c                        |   6 +-
 libtommath/bn_mp_karatsuba_mul.c                 |   6 +-
 libtommath/bn_mp_karatsuba_sqr.c                 |   6 +-
 libtommath/bn_mp_lcm.c                           |   6 +-
 libtommath/bn_mp_lshd.c                          |   6 +-
 libtommath/bn_mp_mod.c                           |   6 +-
 libtommath/bn_mp_mod_2d.c                        |   6 +-
 libtommath/bn_mp_mod_d.c                         |   6 +-
 libtommath/bn_mp_montgomery_calc_normalization.c |   6 +-
 libtommath/bn_mp_montgomery_reduce.c             |   6 +-
 libtommath/bn_mp_montgomery_setup.c              |   6 +-
 libtommath/bn_mp_mul.c                           |   6 +-
 libtommath/bn_mp_mul_2.c                         |   6 +-
 libtommath/bn_mp_mul_2d.c                        |   6 +-
 libtommath/bn_mp_mul_d.c                         |   6 +-
 libtommath/bn_mp_mulmod.c                        |   6 +-
 libtommath/bn_mp_n_root.c                        |   6 +-
 libtommath/bn_mp_n_root_ex.c                     |   6 +-
 libtommath/bn_mp_neg.c                           |   6 +-
 libtommath/bn_mp_or.c                            |   6 +-
 libtommath/bn_mp_prime_fermat.c                  |   6 +-
 libtommath/bn_mp_prime_is_divisible.c            |   6 +-
 libtommath/bn_mp_prime_is_prime.c                |   6 +-
 libtommath/bn_mp_prime_miller_rabin.c            |   6 +-
 libtommath/bn_mp_prime_next_prime.c              |   6 +-
 libtommath/bn_mp_prime_rabin_miller_trials.c     |   6 +-
 libtommath/bn_mp_prime_random_ex.c               |   6 +-
 libtommath/bn_mp_radix_size.c                    |   6 +-
 libtommath/bn_mp_radix_smap.c                    |   6 +-
 libtommath/bn_mp_rand.c                          |   6 +-
 libtommath/bn_mp_read_radix.c                    |   6 +-
 libtommath/bn_mp_read_signed_bin.c               |   6 +-
 libtommath/bn_mp_read_unsigned_bin.c             |   6 +-
 libtommath/bn_mp_reduce.c                        |   6 +-
 libtommath/bn_mp_reduce_2k.c                     |   6 +-
 libtommath/bn_mp_reduce_2k_l.c                   |   6 +-
 libtommath/bn_mp_reduce_2k_setup.c               |   6 +-
 libtommath/bn_mp_reduce_2k_setup_l.c             |   6 +-
 libtommath/bn_mp_reduce_is_2k.c                  |   6 +-
 libtommath/bn_mp_reduce_is_2k_l.c                |   6 +-
 libtommath/bn_mp_reduce_setup.c                  |   6 +-
 libtommath/bn_mp_rshd.c                          |   6 +-
 libtommath/bn_mp_set.c                           |   6 +-
 libtommath/bn_mp_set_int.c                       |   6 +-
 libtommath/bn_mp_set_long.c                      |   6 +-
 libtommath/bn_mp_set_long_long.c                 |   6 +-
 libtommath/bn_mp_shrink.c                        |   6 +-
 libtommath/bn_mp_signed_bin_size.c               |   6 +-
 libtommath/bn_mp_sqr.c                           |   6 +-
 libtommath/bn_mp_sqrmod.c                        |   6 +-
 libtommath/bn_mp_sqrt.c                          |   6 +-
 libtommath/bn_mp_sub.c                           |   6 +-
 libtommath/bn_mp_sub_d.c                         |   6 +-
 libtommath/bn_mp_submod.c                        |   6 +-
 libtommath/bn_mp_to_signed_bin.c                 |   6 +-
 libtommath/bn_mp_to_signed_bin_n.c               |   6 +-
 libtommath/bn_mp_to_unsigned_bin.c               |   6 +-
 libtommath/bn_mp_to_unsigned_bin_n.c             |   6 +-
 libtommath/bn_mp_toom_mul.c                      |   6 +-
 libtommath/bn_mp_toom_sqr.c                      |   6 +-
 libtommath/bn_mp_toradix.c                       |   6 +-
 libtommath/bn_mp_toradix_n.c                     |   6 +-
 libtommath/bn_mp_unsigned_bin_size.c             |   6 +-
 libtommath/bn_mp_xor.c                           |   6 +-
 libtommath/bn_mp_zero.c                          |   6 +-
 libtommath/bn_prime_tab.c                        |   6 +-
 libtommath/bn_reverse.c                          |   6 +-
 libtommath/bn_s_mp_add.c                         |   6 +-
 libtommath/bn_s_mp_exptmod.c                     |   6 +-
 libtommath/bn_s_mp_mul_digs.c                    |   6 +-
 libtommath/bn_s_mp_mul_high_digs.c               |   6 +-
 libtommath/bn_s_mp_sqr.c                         |   6 +-
 libtommath/bn_s_mp_sub.c                         |   6 +-
 libtommath/bncore.c                              |   6 +-
 libtommath/makefile.include                      | 105 -----------------------
 libtommath/tommath.h                             |   6 +-
 libtommath/tommath_private.h                     |   6 +-
 libtommath/tommath_superclass.h                  |   6 +-
 libtommath/updatemakes.sh                        |   6 +-
 133 files changed, 407 insertions(+), 509 deletions(-)
 create mode 100644 .fossil-settings/crlf-glob
 delete mode 100644 libtommath/TODO
 delete mode 100644 libtommath/makefile.include

diff --git a/.fossil-settings/crlf-glob b/.fossil-settings/crlf-glob
new file mode 100644
index 0000000..2041cb6
--- /dev/null
+++ b/.fossil-settings/crlf-glob
@@ -0,0 +1,17 @@
+compat/zlib/contrib/dotzlib/DotZLib/UnitTests.cs
+compat/zlib/contrib/vstudio/readme.txt
+compat/zlib/contrib/vstudio/*/zlib.rc
+compat/zlib/win32/*.txt
+compat/zlib/win64/*.txt
+libtommath/*.dsp
+libtommath/*.sln
+libtommath/*.vcproj
+tools/tcl.hpj.in
+tools/tcl.wse.in
+win/buildall.vc.bat
+win/coffbase.txt
+win/makefile.vc
+win/rules.vc
+win/tcl.dsp
+win/tcl.dsw
+win/tcl.hpj.in
\ No newline at end of file
diff --git a/libtommath/README.md b/libtommath/README.md
index 866f024..4c5da71 100644
--- a/libtommath/README.md
+++ b/libtommath/README.md
@@ -1,4 +1,6 @@
-[![Build Status](https://travis-ci.org/libtom/libtommath.png?branch=develop)](https://travis-ci.org/libtom/libtommath)
+[![Build Status - master](https://travis-ci.org/libtom/libtommath.png?branch=master)](https://travis-ci.org/libtom/libtommath)
+
+[![Build Status - develop](https://travis-ci.org/libtom/libtommath.png?branch=develop)](https://travis-ci.org/libtom/libtommath)
 
 This is the git repository for [LibTomMath](http://www.libtom.org/), a free open source portable number theoretic multiple-precision integer (MPI) library written entirely in C.
 
diff --git a/libtommath/TODO b/libtommath/TODO
deleted file mode 100644
index deffba1..0000000
--- a/libtommath/TODO
+++ /dev/null
@@ -1,16 +0,0 @@
-things for book in order of importance...
-
-- Fix up pseudo-code [only] for combas that are not consistent with source
-- Start in chapter 3 [basics] and work up...
-   - re-write to prose [less abrupt]
-   - clean up pseudo code [spacing]
-   - more examples where appropriate and figures
-
-Goal:
-   - Get sync done by mid January [roughly 8-12 hours work]
-   - Finish ch3-6 by end of January [roughly 12-16 hours of work]
-   - Finish ch7-end by mid Feb [roughly 20-24 hours of work].
-
-Goal isn't "first edition" but merely cleaner to read.
-
-
diff --git a/libtommath/bn_error.c b/libtommath/bn_error.c
index 380f46a..0d77411 100644
--- a/libtommath/bn_error.c
+++ b/libtommath/bn_error.c
@@ -42,6 +42,6 @@ const char *mp_error_to_string(int code)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_fast_mp_invmod.c b/libtommath/bn_fast_mp_invmod.c
index c1d6271..12f42de 100644
--- a/libtommath/bn_fast_mp_invmod.c
+++ b/libtommath/bn_fast_mp_invmod.c
@@ -143,6 +143,6 @@ LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_fast_mp_montgomery_reduce.c b/libtommath/bn_fast_mp_montgomery_reduce.c
index 4d74630..16d5ff7 100644
--- a/libtommath/bn_fast_mp_montgomery_reduce.c
+++ b/libtommath/bn_fast_mp_montgomery_reduce.c
@@ -167,6 +167,6 @@ int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_fast_s_mp_mul_digs.c b/libtommath/bn_fast_s_mp_mul_digs.c
index 59cfa38..a1015af 100644
--- a/libtommath/bn_fast_s_mp_mul_digs.c
+++ b/libtommath/bn_fast_s_mp_mul_digs.c
@@ -102,6 +102,6 @@ int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_fast_s_mp_mul_high_digs.c b/libtommath/bn_fast_s_mp_mul_high_digs.c
index 16f056c..08f0355 100644
--- a/libtommath/bn_fast_s_mp_mul_high_digs.c
+++ b/libtommath/bn_fast_s_mp_mul_high_digs.c
@@ -93,6 +93,6 @@ int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_fast_s_mp_sqr.c b/libtommath/bn_fast_s_mp_sqr.c
index 8fa8958..f435af9 100644
--- a/libtommath/bn_fast_s_mp_sqr.c
+++ b/libtommath/bn_fast_s_mp_sqr.c
@@ -109,6 +109,6 @@ int fast_s_mp_sqr (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_2expt.c b/libtommath/bn_mp_2expt.c
index 36915bb..989bb9f 100644
--- a/libtommath/bn_mp_2expt.c
+++ b/libtommath/bn_mp_2expt.c
@@ -43,6 +43,6 @@ mp_2expt (mp_int * a, int b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_abs.c b/libtommath/bn_mp_abs.c
index f3ec518..e7c5e25 100644
--- a/libtommath/bn_mp_abs.c
+++ b/libtommath/bn_mp_abs.c
@@ -38,6 +38,6 @@ mp_abs (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_add.c b/libtommath/bn_mp_add.c
index 2487aba..bdb166f 100644
--- a/libtommath/bn_mp_add.c
+++ b/libtommath/bn_mp_add.c
@@ -48,6 +48,6 @@ int mp_add (mp_int * a, mp_int * b, mp_int * c)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_add_d.c b/libtommath/bn_mp_add_d.c
index b7c8ea8..fd1a186 100644
--- a/libtommath/bn_mp_add_d.c
+++ b/libtommath/bn_mp_add_d.c
@@ -107,6 +107,6 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_addmod.c b/libtommath/bn_mp_addmod.c
index 706e739..dc06788 100644
--- a/libtommath/bn_mp_addmod.c
+++ b/libtommath/bn_mp_addmod.c
@@ -36,6 +36,6 @@ mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_and.c b/libtommath/bn_mp_and.c
index 46c41a2..53008a5 100644
--- a/libtommath/bn_mp_and.c
+++ b/libtommath/bn_mp_and.c
@@ -52,6 +52,6 @@ mp_and (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_clamp.c b/libtommath/bn_mp_clamp.c
index 149f1a8..2c0a1a6 100644
--- a/libtommath/bn_mp_clamp.c
+++ b/libtommath/bn_mp_clamp.c
@@ -39,6 +39,6 @@ mp_clamp (mp_int * a)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_clear.c b/libtommath/bn_mp_clear.c
index 37ce1e1..97f3db0 100644
--- a/libtommath/bn_mp_clear.c
+++ b/libtommath/bn_mp_clear.c
@@ -39,6 +39,6 @@ mp_clear (mp_int * a)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_clear_multi.c b/libtommath/bn_mp_clear_multi.c
index 583b1da..bd4b232 100644
--- a/libtommath/bn_mp_clear_multi.c
+++ b/libtommath/bn_mp_clear_multi.c
@@ -29,6 +29,6 @@ void mp_clear_multi(mp_int *mp, ...)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_cmp.c b/libtommath/bn_mp_cmp.c
index 538ba34..e757ddf 100644
--- a/libtommath/bn_mp_cmp.c
+++ b/libtommath/bn_mp_cmp.c
@@ -38,6 +38,6 @@ mp_cmp (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_cmp_d.c b/libtommath/bn_mp_cmp_d.c
index e66b1e4..3f5ebae 100644
--- a/libtommath/bn_mp_cmp_d.c
+++ b/libtommath/bn_mp_cmp_d.c
@@ -39,6 +39,6 @@ int mp_cmp_d(mp_int * a, mp_digit b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_cmp_mag.c b/libtommath/bn_mp_cmp_mag.c
index d46a1be..7ceda97 100644
--- a/libtommath/bn_mp_cmp_mag.c
+++ b/libtommath/bn_mp_cmp_mag.c
@@ -50,6 +50,6 @@ int mp_cmp_mag (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_cnt_lsb.c b/libtommath/bn_mp_cnt_lsb.c
index 1cf6159..bf201b5 100644
--- a/libtommath/bn_mp_cnt_lsb.c
+++ b/libtommath/bn_mp_cnt_lsb.c
@@ -48,6 +48,6 @@ int mp_cnt_lsb(mp_int *a)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_copy.c b/libtommath/bn_mp_copy.c
index 1ba7381..84e839e 100644
--- a/libtommath/bn_mp_copy.c
+++ b/libtommath/bn_mp_copy.c
@@ -63,6 +63,6 @@ mp_copy (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_count_bits.c b/libtommath/bn_mp_count_bits.c
index bd12a87..ff558eb 100644
--- a/libtommath/bn_mp_count_bits.c
+++ b/libtommath/bn_mp_count_bits.c
@@ -40,6 +40,6 @@ mp_count_bits (mp_int * a)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_div.c b/libtommath/bn_mp_div.c
index 73f8779..0890e65 100644
--- a/libtommath/bn_mp_div.c
+++ b/libtommath/bn_mp_div.c
@@ -290,6 +290,6 @@ LBL_Q:mp_clear (&q);
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_div_2.c b/libtommath/bn_mp_div_2.c
index a428869..2b5bb49 100644
--- a/libtommath/bn_mp_div_2.c
+++ b/libtommath/bn_mp_div_2.c
@@ -63,6 +63,6 @@ int mp_div_2(mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_div_2d.c b/libtommath/bn_mp_div_2d.c
index b8e27ba..635d374 100644
--- a/libtommath/bn_mp_div_2d.c
+++ b/libtommath/bn_mp_div_2d.c
@@ -81,6 +81,6 @@ int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_div_3.c b/libtommath/bn_mp_div_3.c
index b716b22..e8504ea 100644
--- a/libtommath/bn_mp_div_3.c
+++ b/libtommath/bn_mp_div_3.c
@@ -74,6 +74,6 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_div_d.c b/libtommath/bn_mp_div_d.c
index a2022ad..a5dbc59 100644
--- a/libtommath/bn_mp_div_d.c
+++ b/libtommath/bn_mp_div_d.c
@@ -110,6 +110,6 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_dr_is_modulus.c b/libtommath/bn_mp_dr_is_modulus.c
index f6d39c1..ced330c 100644
--- a/libtommath/bn_mp_dr_is_modulus.c
+++ b/libtommath/bn_mp_dr_is_modulus.c
@@ -38,6 +38,6 @@ int mp_dr_is_modulus(mp_int *a)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_dr_reduce.c b/libtommath/bn_mp_dr_reduce.c
index 920b52e..c85ee77 100644
--- a/libtommath/bn_mp_dr_reduce.c
+++ b/libtommath/bn_mp_dr_reduce.c
@@ -91,6 +91,6 @@ top:
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_dr_setup.c b/libtommath/bn_mp_dr_setup.c
index 3aac30f..b0d4a14 100644
--- a/libtommath/bn_mp_dr_setup.c
+++ b/libtommath/bn_mp_dr_setup.c
@@ -27,6 +27,6 @@ void mp_dr_setup(mp_int *a, mp_digit *d)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_exch.c b/libtommath/bn_mp_exch.c
index 5b5b359..fc26bae 100644
--- a/libtommath/bn_mp_exch.c
+++ b/libtommath/bn_mp_exch.c
@@ -29,6 +29,6 @@ mp_exch (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_export.c b/libtommath/bn_mp_export.c
index 2e71a27..4bbc8c5 100644
--- a/libtommath/bn_mp_export.c
+++ b/libtommath/bn_mp_export.c
@@ -83,6 +83,6 @@ int mp_export(void* rop, size_t* countp, int order, size_t size,
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_expt_d.c b/libtommath/bn_mp_expt_d.c
index d5ca456..a311926 100644
--- a/libtommath/bn_mp_expt_d.c
+++ b/libtommath/bn_mp_expt_d.c
@@ -23,6 +23,6 @@ int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_expt_d_ex.c b/libtommath/bn_mp_expt_d_ex.c
index dced5a1..c361b27 100644
--- a/libtommath/bn_mp_expt_d_ex.c
+++ b/libtommath/bn_mp_expt_d_ex.c
@@ -78,6 +78,6 @@ int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_exptmod.c b/libtommath/bn_mp_exptmod.c
index 0998ce7..25c389d 100644
--- a/libtommath/bn_mp_exptmod.c
+++ b/libtommath/bn_mp_exptmod.c
@@ -107,6 +107,6 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_exptmod_fast.c b/libtommath/bn_mp_exptmod_fast.c
index 3322544..5e5c7f2 100644
--- a/libtommath/bn_mp_exptmod_fast.c
+++ b/libtommath/bn_mp_exptmod_fast.c
@@ -316,6 +316,6 @@ LBL_M:
 #endif
 
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_exteuclid.c b/libtommath/bn_mp_exteuclid.c
index d9951ec..3c9612e 100644
--- a/libtommath/bn_mp_exteuclid.c
+++ b/libtommath/bn_mp_exteuclid.c
@@ -78,6 +78,6 @@ LBL_ERR:
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_fread.c b/libtommath/bn_mp_fread.c
index 4e38c6f..140721b 100644
--- a/libtommath/bn_mp_fread.c
+++ b/libtommath/bn_mp_fread.c
@@ -64,6 +64,6 @@ int mp_fread(mp_int *a, int radix, FILE *stream)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_fwrite.c b/libtommath/bn_mp_fwrite.c
index daa15db..23b5f64 100644
--- a/libtommath/bn_mp_fwrite.c
+++ b/libtommath/bn_mp_fwrite.c
@@ -49,6 +49,6 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_gcd.c b/libtommath/bn_mp_gcd.c
index 40e7034..b0be8fb 100644
--- a/libtommath/bn_mp_gcd.c
+++ b/libtommath/bn_mp_gcd.c
@@ -100,6 +100,6 @@ LBL_U:mp_clear (&v);
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_get_int.c b/libtommath/bn_mp_get_int.c
index f99ffb2..5c820f8 100644
--- a/libtommath/bn_mp_get_int.c
+++ b/libtommath/bn_mp_get_int.c
@@ -40,6 +40,6 @@ unsigned long mp_get_int(mp_int * a)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_grow.c b/libtommath/bn_mp_grow.c
index 3d47822..74e07b1 100644
--- a/libtommath/bn_mp_grow.c
+++ b/libtommath/bn_mp_grow.c
@@ -52,6 +52,6 @@ int mp_grow (mp_int * a, int size)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_import.c b/libtommath/bn_mp_import.c
index 22e2342..df29389 100644
--- a/libtommath/bn_mp_import.c
+++ b/libtommath/bn_mp_import.c
@@ -68,6 +68,6 @@ int mp_import(mp_int* rop, size_t count, int order, size_t size,
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_init.c b/libtommath/bn_mp_init.c
index 0f628df..ee374ae 100644
--- a/libtommath/bn_mp_init.c
+++ b/libtommath/bn_mp_init.c
@@ -41,6 +41,6 @@ int mp_init (mp_int * a)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_init_copy.c b/libtommath/bn_mp_init_copy.c
index c918d46..37a57ec 100644
--- a/libtommath/bn_mp_init_copy.c
+++ b/libtommath/bn_mp_init_copy.c
@@ -32,6 +32,6 @@ int mp_init_copy (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_init_multi.c b/libtommath/bn_mp_init_multi.c
index c121188..73d6a0f 100644
--- a/libtommath/bn_mp_init_multi.c
+++ b/libtommath/bn_mp_init_multi.c
@@ -51,6 +51,6 @@ int mp_init_multi(mp_int *mp, ...)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_init_set.c b/libtommath/bn_mp_init_set.c
index 24dc8bb..ed4955c 100644
--- a/libtommath/bn_mp_init_set.c
+++ b/libtommath/bn_mp_init_set.c
@@ -27,6 +27,6 @@ int mp_init_set (mp_int * a, mp_digit b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_init_set_int.c b/libtommath/bn_mp_init_set_int.c
index 5a75e3e..1bc1942 100644
--- a/libtommath/bn_mp_init_set_int.c
+++ b/libtommath/bn_mp_init_set_int.c
@@ -26,6 +26,6 @@ int mp_init_set_int (mp_int * a, unsigned long b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_init_size.c b/libtommath/bn_mp_init_size.c
index 4e30a2b..4446773 100644
--- a/libtommath/bn_mp_init_size.c
+++ b/libtommath/bn_mp_init_size.c
@@ -43,6 +43,6 @@ int mp_init_size (mp_int * a, int size)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_invmod.c b/libtommath/bn_mp_invmod.c
index 75763ab..36011d0 100644
--- a/libtommath/bn_mp_invmod.c
+++ b/libtommath/bn_mp_invmod.c
@@ -38,6 +38,6 @@ int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_invmod_slow.c b/libtommath/bn_mp_invmod_slow.c
index cb7233d..ff0d5ae 100644
--- a/libtommath/bn_mp_invmod_slow.c
+++ b/libtommath/bn_mp_invmod_slow.c
@@ -170,6 +170,6 @@ LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_is_square.c b/libtommath/bn_mp_is_square.c
index 56d19c0..dd08d58 100644
--- a/libtommath/bn_mp_is_square.c
+++ b/libtommath/bn_mp_is_square.c
@@ -104,6 +104,6 @@ ERR:mp_clear(&t);
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_jacobi.c b/libtommath/bn_mp_jacobi.c
index 8d147e0..5fc8593 100644
--- a/libtommath/bn_mp_jacobi.c
+++ b/libtommath/bn_mp_jacobi.c
@@ -112,6 +112,6 @@ LBL_A1:mp_clear (&a1);
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_karatsuba_mul.c b/libtommath/bn_mp_karatsuba_mul.c
index 31ed2e3..4d982c7 100644
--- a/libtommath/bn_mp_karatsuba_mul.c
+++ b/libtommath/bn_mp_karatsuba_mul.c
@@ -162,6 +162,6 @@ ERR:
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_karatsuba_sqr.c b/libtommath/bn_mp_karatsuba_sqr.c
index 33a2bee..764e85a 100644
--- a/libtommath/bn_mp_karatsuba_sqr.c
+++ b/libtommath/bn_mp_karatsuba_sqr.c
@@ -116,6 +116,6 @@ ERR:
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_lcm.c b/libtommath/bn_mp_lcm.c
index d4bb1b6..512e8ec 100644
--- a/libtommath/bn_mp_lcm.c
+++ b/libtommath/bn_mp_lcm.c
@@ -55,6 +55,6 @@ LBL_T:
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_lshd.c b/libtommath/bn_mp_lshd.c
index e4f9abc..0143e94 100644
--- a/libtommath/bn_mp_lshd.c
+++ b/libtommath/bn_mp_lshd.c
@@ -62,6 +62,6 @@ int mp_lshd (mp_int * a, int b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_mod.c b/libtommath/bn_mp_mod.c
index 0bc9530..06240a0 100644
--- a/libtommath/bn_mp_mod.c
+++ b/libtommath/bn_mp_mod.c
@@ -43,6 +43,6 @@ mp_mod (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_mod_2d.c b/libtommath/bn_mp_mod_2d.c
index 472aa58..2bb86da 100644
--- a/libtommath/bn_mp_mod_2d.c
+++ b/libtommath/bn_mp_mod_2d.c
@@ -50,6 +50,6 @@ mp_mod_2d (mp_int * a, int b, mp_int * c)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_mod_d.c b/libtommath/bn_mp_mod_d.c
index 6fbc2c3..bf2ccaa 100644
--- a/libtommath/bn_mp_mod_d.c
+++ b/libtommath/bn_mp_mod_d.c
@@ -22,6 +22,6 @@ mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_montgomery_calc_normalization.c b/libtommath/bn_mp_montgomery_calc_normalization.c
index 3e66d3f..679a871 100644
--- a/libtommath/bn_mp_montgomery_calc_normalization.c
+++ b/libtommath/bn_mp_montgomery_calc_normalization.c
@@ -54,6 +54,6 @@ int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_montgomery_reduce.c b/libtommath/bn_mp_montgomery_reduce.c
index b64c80a..05e8bfa 100644
--- a/libtommath/bn_mp_montgomery_reduce.c
+++ b/libtommath/bn_mp_montgomery_reduce.c
@@ -113,6 +113,6 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_montgomery_setup.c b/libtommath/bn_mp_montgomery_setup.c
index b15bafd..1c17445 100644
--- a/libtommath/bn_mp_montgomery_setup.c
+++ b/libtommath/bn_mp_montgomery_setup.c
@@ -54,6 +54,6 @@ mp_montgomery_setup (mp_int * n, mp_digit * rho)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_mul.c b/libtommath/bn_mp_mul.c
index 3819c0a..cc3b9c8 100644
--- a/libtommath/bn_mp_mul.c
+++ b/libtommath/bn_mp_mul.c
@@ -62,6 +62,6 @@ int mp_mul (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_mul_2.c b/libtommath/bn_mp_mul_2.c
index eba1450..d22fd89 100644
--- a/libtommath/bn_mp_mul_2.c
+++ b/libtommath/bn_mp_mul_2.c
@@ -77,6 +77,6 @@ int mp_mul_2(mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_mul_2d.c b/libtommath/bn_mp_mul_2d.c
index 798a1da..c00fd7e 100644
--- a/libtommath/bn_mp_mul_2d.c
+++ b/libtommath/bn_mp_mul_2d.c
@@ -80,6 +80,6 @@ int mp_mul_2d (mp_int * a, int b, mp_int * c)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_mul_d.c b/libtommath/bn_mp_mul_d.c
index fa918da..6954ed3 100644
--- a/libtommath/bn_mp_mul_d.c
+++ b/libtommath/bn_mp_mul_d.c
@@ -74,6 +74,6 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_mulmod.c b/libtommath/bn_mp_mulmod.c
index 3c7e41b..d7a4d3c 100644
--- a/libtommath/bn_mp_mulmod.c
+++ b/libtommath/bn_mp_mulmod.c
@@ -35,6 +35,6 @@ int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_n_root.c b/libtommath/bn_mp_n_root.c
index f8f9d13..f717f17 100644
--- a/libtommath/bn_mp_n_root.c
+++ b/libtommath/bn_mp_n_root.c
@@ -25,6 +25,6 @@ int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_n_root_ex.c b/libtommath/bn_mp_n_root_ex.c
index 28d6b18..079b4f3 100644
--- a/libtommath/bn_mp_n_root_ex.c
+++ b/libtommath/bn_mp_n_root_ex.c
@@ -127,6 +127,6 @@ LBL_T1:mp_clear (&t1);
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_neg.c b/libtommath/bn_mp_neg.c
index f488b57..d03e92e 100644
--- a/libtommath/bn_mp_neg.c
+++ b/libtommath/bn_mp_neg.c
@@ -35,6 +35,6 @@ int mp_neg (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_or.c b/libtommath/bn_mp_or.c
index aee9734..b9775ce 100644
--- a/libtommath/bn_mp_or.c
+++ b/libtommath/bn_mp_or.c
@@ -45,6 +45,6 @@ int mp_or (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_prime_fermat.c b/libtommath/bn_mp_prime_fermat.c
index 5b992b5..d99feeb 100644
--- a/libtommath/bn_mp_prime_fermat.c
+++ b/libtommath/bn_mp_prime_fermat.c
@@ -57,6 +57,6 @@ LBL_T:mp_clear (&t);
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_prime_is_divisible.c b/libtommath/bn_mp_prime_is_divisible.c
index f97498f..eea4a27 100644
--- a/libtommath/bn_mp_prime_is_divisible.c
+++ b/libtommath/bn_mp_prime_is_divisible.c
@@ -45,6 +45,6 @@ int mp_prime_is_divisible (mp_int * a, int *result)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_prime_is_prime.c b/libtommath/bn_mp_prime_is_prime.c
index 29571ba..3eda4fd 100644
--- a/libtommath/bn_mp_prime_is_prime.c
+++ b/libtommath/bn_mp_prime_is_prime.c
@@ -78,6 +78,6 @@ LBL_B:mp_clear (&b);
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_prime_miller_rabin.c b/libtommath/bn_mp_prime_miller_rabin.c
index b168f01..7de0634 100644
--- a/libtommath/bn_mp_prime_miller_rabin.c
+++ b/libtommath/bn_mp_prime_miller_rabin.c
@@ -98,6 +98,6 @@ LBL_N1:mp_clear (&n1);
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_prime_next_prime.c b/libtommath/bn_mp_prime_next_prime.c
index 6515b1c..7a32d9b 100644
--- a/libtommath/bn_mp_prime_next_prime.c
+++ b/libtommath/bn_mp_prime_next_prime.c
@@ -165,6 +165,6 @@ LBL_ERR:
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_prime_rabin_miller_trials.c b/libtommath/bn_mp_prime_rabin_miller_trials.c
index c98de6e..378ceb2 100644
--- a/libtommath/bn_mp_prime_rabin_miller_trials.c
+++ b/libtommath/bn_mp_prime_rabin_miller_trials.c
@@ -47,6 +47,6 @@ int mp_prime_rabin_miller_trials(int size)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_prime_random_ex.c b/libtommath/bn_mp_prime_random_ex.c
index 04a7cf7..cf5272e 100644
--- a/libtommath/bn_mp_prime_random_ex.c
+++ b/libtommath/bn_mp_prime_random_ex.c
@@ -119,6 +119,6 @@ error:
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_radix_size.c b/libtommath/bn_mp_radix_size.c
index 4a58e41..cb0c134 100644
--- a/libtommath/bn_mp_radix_size.c
+++ b/libtommath/bn_mp_radix_size.c
@@ -73,6 +73,6 @@ int mp_radix_size (mp_int * a, int radix, int *size)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_radix_smap.c b/libtommath/bn_mp_radix_smap.c
index e351146..4c6e57c 100644
--- a/libtommath/bn_mp_radix_smap.c
+++ b/libtommath/bn_mp_radix_smap.c
@@ -19,6 +19,6 @@
 const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_rand.c b/libtommath/bn_mp_rand.c
index d5967c2..93e255a 100644
--- a/libtommath/bn_mp_rand.c
+++ b/libtommath/bn_mp_rand.c
@@ -75,6 +75,6 @@ mp_rand (mp_int * a, int digits)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_read_radix.c b/libtommath/bn_mp_read_radix.c
index a4d1c8a..12aa499 100644
--- a/libtommath/bn_mp_read_radix.c
+++ b/libtommath/bn_mp_read_radix.c
@@ -86,6 +86,6 @@ int mp_read_radix (mp_int * a, const char *str, int radix)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_read_signed_bin.c b/libtommath/bn_mp_read_signed_bin.c
index a034fbd..363e11f 100644
--- a/libtommath/bn_mp_read_signed_bin.c
+++ b/libtommath/bn_mp_read_signed_bin.c
@@ -36,6 +36,6 @@ int mp_read_signed_bin (mp_int * a, const unsigned char *b, int c)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_read_unsigned_bin.c b/libtommath/bn_mp_read_unsigned_bin.c
index 27af256..1a50b58 100644
--- a/libtommath/bn_mp_read_unsigned_bin.c
+++ b/libtommath/bn_mp_read_unsigned_bin.c
@@ -50,6 +50,6 @@ int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_reduce.c b/libtommath/bn_mp_reduce.c
index a87fc30..367383f 100644
--- a/libtommath/bn_mp_reduce.c
+++ b/libtommath/bn_mp_reduce.c
@@ -95,6 +95,6 @@ CLEANUP:
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_reduce_2k.c b/libtommath/bn_mp_reduce_2k.c
index 4f13b07..6bc96d1 100644
--- a/libtommath/bn_mp_reduce_2k.c
+++ b/libtommath/bn_mp_reduce_2k.c
@@ -58,6 +58,6 @@ ERR:
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_reduce_2k_l.c b/libtommath/bn_mp_reduce_2k_l.c
index b41677a..8e6eeb0 100644
--- a/libtommath/bn_mp_reduce_2k_l.c
+++ b/libtommath/bn_mp_reduce_2k_l.c
@@ -59,6 +59,6 @@ ERR:
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_reduce_2k_setup.c b/libtommath/bn_mp_reduce_2k_setup.c
index a0c507f..bf810c0 100644
--- a/libtommath/bn_mp_reduce_2k_setup.c
+++ b/libtommath/bn_mp_reduce_2k_setup.c
@@ -42,6 +42,6 @@ int mp_reduce_2k_setup(mp_int *a, mp_digit *d)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_reduce_2k_setup_l.c b/libtommath/bn_mp_reduce_2k_setup_l.c
index 7083533..56d1ba8 100644
--- a/libtommath/bn_mp_reduce_2k_setup_l.c
+++ b/libtommath/bn_mp_reduce_2k_setup_l.c
@@ -39,6 +39,6 @@ ERR:
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_reduce_is_2k.c b/libtommath/bn_mp_reduce_is_2k.c
index 2e61839..0499e83 100644
--- a/libtommath/bn_mp_reduce_is_2k.c
+++ b/libtommath/bn_mp_reduce_is_2k.c
@@ -47,6 +47,6 @@ int mp_reduce_is_2k(mp_int *a)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_reduce_is_2k_l.c b/libtommath/bn_mp_reduce_is_2k_l.c
index 65ae46e..48b3498 100644
--- a/libtommath/bn_mp_reduce_is_2k_l.c
+++ b/libtommath/bn_mp_reduce_is_2k_l.c
@@ -39,6 +39,6 @@ int mp_reduce_is_2k_l(mp_int *a)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_reduce_setup.c b/libtommath/bn_mp_reduce_setup.c
index ffddbce..8875698 100644
--- a/libtommath/bn_mp_reduce_setup.c
+++ b/libtommath/bn_mp_reduce_setup.c
@@ -29,6 +29,6 @@ int mp_reduce_setup (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_rshd.c b/libtommath/bn_mp_rshd.c
index f412d93..4b598de 100644
--- a/libtommath/bn_mp_rshd.c
+++ b/libtommath/bn_mp_rshd.c
@@ -67,6 +67,6 @@ void mp_rshd (mp_int * a, int b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_set.c b/libtommath/bn_mp_set.c
index 8eec001..dd4de3c 100644
--- a/libtommath/bn_mp_set.c
+++ b/libtommath/bn_mp_set.c
@@ -24,6 +24,6 @@ void mp_set (mp_int * a, mp_digit b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_set_int.c b/libtommath/bn_mp_set_int.c
index f456a3a..3aafec9 100644
--- a/libtommath/bn_mp_set_int.c
+++ b/libtommath/bn_mp_set_int.c
@@ -43,6 +43,6 @@ int mp_set_int (mp_int * a, unsigned long b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_set_long.c b/libtommath/bn_mp_set_long.c
index fbf9f82..8cbb811 100644
--- a/libtommath/bn_mp_set_long.c
+++ b/libtommath/bn_mp_set_long.c
@@ -19,6 +19,6 @@
 MP_SET_XLONG(mp_set_long, unsigned long)
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_set_long_long.c b/libtommath/bn_mp_set_long_long.c
index 0a688c8..3566b45 100644
--- a/libtommath/bn_mp_set_long_long.c
+++ b/libtommath/bn_mp_set_long_long.c
@@ -19,6 +19,6 @@
 MP_SET_XLONG(mp_set_long_long, unsigned long long)
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_shrink.c b/libtommath/bn_mp_shrink.c
index 9422a54..0712c2b 100644
--- a/libtommath/bn_mp_shrink.c
+++ b/libtommath/bn_mp_shrink.c
@@ -36,6 +36,6 @@ int mp_shrink (mp_int * a)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_signed_bin_size.c b/libtommath/bn_mp_signed_bin_size.c
index bb63407..0910333 100644
--- a/libtommath/bn_mp_signed_bin_size.c
+++ b/libtommath/bn_mp_signed_bin_size.c
@@ -22,6 +22,6 @@ int mp_signed_bin_size (mp_int * a)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_sqr.c b/libtommath/bn_mp_sqr.c
index 299308d..ffe94e2 100644
--- a/libtommath/bn_mp_sqr.c
+++ b/libtommath/bn_mp_sqr.c
@@ -55,6 +55,6 @@ mp_sqr (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_sqrmod.c b/libtommath/bn_mp_sqrmod.c
index 05ea9e0..3b29fbc 100644
--- a/libtommath/bn_mp_sqrmod.c
+++ b/libtommath/bn_mp_sqrmod.c
@@ -36,6 +36,6 @@ mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_sqrt.c b/libtommath/bn_mp_sqrt.c
index 72d98f0..d3b5d62 100644
--- a/libtommath/bn_mp_sqrt.c
+++ b/libtommath/bn_mp_sqrt.c
@@ -76,6 +76,6 @@ E2: mp_clear(&t1);
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_sub.c b/libtommath/bn_mp_sub.c
index 67da8da..2f73faa 100644
--- a/libtommath/bn_mp_sub.c
+++ b/libtommath/bn_mp_sub.c
@@ -54,6 +54,6 @@ mp_sub (mp_int * a, mp_int * b, mp_int * c)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_sub_d.c b/libtommath/bn_mp_sub_d.c
index a4e1b1c..5e96030 100644
--- a/libtommath/bn_mp_sub_d.c
+++ b/libtommath/bn_mp_sub_d.c
@@ -88,6 +88,6 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_submod.c b/libtommath/bn_mp_submod.c
index ec7885c..138863c 100644
--- a/libtommath/bn_mp_submod.c
+++ b/libtommath/bn_mp_submod.c
@@ -37,6 +37,6 @@ mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_to_signed_bin.c b/libtommath/bn_mp_to_signed_bin.c
index 109d8f7..c49c87d 100644
--- a/libtommath/bn_mp_to_signed_bin.c
+++ b/libtommath/bn_mp_to_signed_bin.c
@@ -28,6 +28,6 @@ int mp_to_signed_bin (mp_int * a, unsigned char *b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_to_signed_bin_n.c b/libtommath/bn_mp_to_signed_bin_n.c
index bcbdf79..dc5ec26 100644
--- a/libtommath/bn_mp_to_signed_bin_n.c
+++ b/libtommath/bn_mp_to_signed_bin_n.c
@@ -26,6 +26,6 @@ int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_to_unsigned_bin.c b/libtommath/bn_mp_to_unsigned_bin.c
index 0ac9887..d249359 100644
--- a/libtommath/bn_mp_to_unsigned_bin.c
+++ b/libtommath/bn_mp_to_unsigned_bin.c
@@ -43,6 +43,6 @@ int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_to_unsigned_bin_n.c b/libtommath/bn_mp_to_unsigned_bin_n.c
index 19fe1e4..f671621 100644
--- a/libtommath/bn_mp_to_unsigned_bin_n.c
+++ b/libtommath/bn_mp_to_unsigned_bin_n.c
@@ -26,6 +26,6 @@ int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_toom_mul.c b/libtommath/bn_mp_toom_mul.c
index 9a347fa..4a574fc 100644
--- a/libtommath/bn_mp_toom_mul.c
+++ b/libtommath/bn_mp_toom_mul.c
@@ -281,6 +281,6 @@ ERR:
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_toom_sqr.c b/libtommath/bn_mp_toom_sqr.c
index 327a85f..0a38192 100644
--- a/libtommath/bn_mp_toom_sqr.c
+++ b/libtommath/bn_mp_toom_sqr.c
@@ -223,6 +223,6 @@ ERR:
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_toradix.c b/libtommath/bn_mp_toradix.c
index baf0e3b..3337765 100644
--- a/libtommath/bn_mp_toradix.c
+++ b/libtommath/bn_mp_toradix.c
@@ -70,6 +70,6 @@ int mp_toradix (mp_int * a, char *str, int radix)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_toradix_n.c b/libtommath/bn_mp_toradix_n.c
index 881cb52..ae24ada 100644
--- a/libtommath/bn_mp_toradix_n.c
+++ b/libtommath/bn_mp_toradix_n.c
@@ -83,6 +83,6 @@ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_unsigned_bin_size.c b/libtommath/bn_mp_unsigned_bin_size.c
index 74f6ed0..f46d0ba 100644
--- a/libtommath/bn_mp_unsigned_bin_size.c
+++ b/libtommath/bn_mp_unsigned_bin_size.c
@@ -23,6 +23,6 @@ int mp_unsigned_bin_size (mp_int * a)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_xor.c b/libtommath/bn_mp_xor.c
index 9c83126..f51fc8e 100644
--- a/libtommath/bn_mp_xor.c
+++ b/libtommath/bn_mp_xor.c
@@ -46,6 +46,6 @@ mp_xor (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_mp_zero.c b/libtommath/bn_mp_zero.c
index a76c2a9..a7d59e4 100644
--- a/libtommath/bn_mp_zero.c
+++ b/libtommath/bn_mp_zero.c
@@ -31,6 +31,6 @@ void mp_zero (mp_int * a)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_prime_tab.c b/libtommath/bn_prime_tab.c
index 77535c7..5252130 100644
--- a/libtommath/bn_prime_tab.c
+++ b/libtommath/bn_prime_tab.c
@@ -56,6 +56,6 @@ const mp_digit ltm_prime_tab[] = {
 };
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_reverse.c b/libtommath/bn_reverse.c
index 9c00f2b..dc87a4e 100644
--- a/libtommath/bn_reverse.c
+++ b/libtommath/bn_reverse.c
@@ -34,6 +34,6 @@ bn_reverse (unsigned char *s, int len)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_s_mp_add.c b/libtommath/bn_s_mp_add.c
index 2069d88..7a100e8 100644
--- a/libtommath/bn_s_mp_add.c
+++ b/libtommath/bn_s_mp_add.c
@@ -104,6 +104,6 @@ s_mp_add (mp_int * a, mp_int * b, mp_int * c)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_s_mp_exptmod.c b/libtommath/bn_s_mp_exptmod.c
index 8b10003..ab820d4 100644
--- a/libtommath/bn_s_mp_exptmod.c
+++ b/libtommath/bn_s_mp_exptmod.c
@@ -247,6 +247,6 @@ LBL_M:
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_s_mp_mul_digs.c b/libtommath/bn_s_mp_mul_digs.c
index 41bca7b..8f1bf97 100644
--- a/libtommath/bn_s_mp_mul_digs.c
+++ b/libtommath/bn_s_mp_mul_digs.c
@@ -85,6 +85,6 @@ int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_s_mp_mul_high_digs.c b/libtommath/bn_s_mp_mul_high_digs.c
index 7e18680..031f17b 100644
--- a/libtommath/bn_s_mp_mul_high_digs.c
+++ b/libtommath/bn_s_mp_mul_high_digs.c
@@ -76,6 +76,6 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_s_mp_sqr.c b/libtommath/bn_s_mp_sqr.c
index 3bcc7c9..ac0e157 100644
--- a/libtommath/bn_s_mp_sqr.c
+++ b/libtommath/bn_s_mp_sqr.c
@@ -79,6 +79,6 @@ int s_mp_sqr (mp_int * a, mp_int * b)
 }
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bn_s_mp_sub.c b/libtommath/bn_s_mp_sub.c
index 260a95f..8091f4a 100644
--- a/libtommath/bn_s_mp_sub.c
+++ b/libtommath/bn_s_mp_sub.c
@@ -84,6 +84,6 @@ s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/bncore.c b/libtommath/bncore.c
index b07c629..e80ec99 100644
--- a/libtommath/bncore.c
+++ b/libtommath/bncore.c
@@ -31,6 +31,6 @@ int     KARATSUBA_MUL_CUTOFF = 80,      /* Min. number of digits before Karatsub
         TOOM_SQR_CUTOFF      = 400; 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/makefile.include b/libtommath/makefile.include
deleted file mode 100644
index c862f0f..0000000
--- a/libtommath/makefile.include
+++ /dev/null
@@ -1,105 +0,0 @@
-#
-# Include makefile for libtommath
-#
-
-#version of library
-VERSION=1.0
-VERSION_SO=1:0
-
-# default make target
-default: ${LIBNAME}
-
-# Compiler and Linker Names
-ifndef PREFIX
-  PREFIX=
-endif
-
-ifeq ($(CC),cc)
-  CC = $(PREFIX)gcc
-endif
-LD=$(PREFIX)ld
-AR=$(PREFIX)ar
-RANLIB=$(PREFIX)ranlib
-
-ifndef MAKE
-   MAKE=make
-endif
-
-CFLAGS += -I./ -Wall -Wsign-compare -Wextra -Wshadow
-
-ifndef NO_ADDTL_WARNINGS
-# additional warnings
-CFLAGS += -Wsystem-headers -Wdeclaration-after-statement -Wbad-function-cast -Wcast-align
-CFLAGS += -Wstrict-prototypes -Wpointer-arith
-endif
-
-ifdef COMPILE_DEBUG
-#debug
-CFLAGS += -g3
-else
-
-ifdef COMPILE_SIZE
-#for size
-CFLAGS += -Os
-else
-
-ifndef IGNORE_SPEED
-#for speed
-CFLAGS += -O3 -funroll-loops
-
-#x86 optimizations [should be valid for any GCC install though]
-CFLAGS  += -fomit-frame-pointer
-endif
-
-endif # COMPILE_SIZE
-endif # COMPILE_DEBUG
-
-# adjust coverage set
-ifneq ($(filter $(shell arch), i386 i686 x86_64 amd64 ia64),)
-   COVERAGE = test_standalone timing
-   COVERAGE_APP = ./test && ./ltmtest
-else
-   COVERAGE = test_standalone
-   COVERAGE_APP = ./test
-endif
-
-HEADERS_PUB=tommath.h tommath_class.h tommath_superclass.h
-HEADERS=tommath_private.h $(HEADERS_PUB)
-
-test_standalone: CFLAGS+=-DLTM_DEMO_TEST_VS_MTEST=0
-
-#LIBPATH-The directory for libtommath to be installed to.
-#INCPATH-The directory to install the header files for libtommath.
-#DATAPATH-The directory to install the pdf docs.
-LIBPATH?=/usr/lib
-INCPATH?=/usr/include
-DATAPATH?=/usr/share/doc/libtommath/pdf
-
-#make the code coverage of the library
-#
-coverage: CFLAGS += -fprofile-arcs -ftest-coverage -DTIMING_NO_LOGS
-coverage: LFLAGS += -lgcov
-coverage: LDFLAGS += -lgcov
-
-coverage: $(COVERAGE)
-	$(COVERAGE_APP)
-
-lcov: coverage
-	rm -f coverage.info
-	lcov --capture --no-external --no-recursion $(LCOV_ARGS) --output-file coverage.info -q
-	genhtml coverage.info --output-directory coverage -q
-
-# target that removes all coverage output
-cleancov-clean:
-	rm -f `find . -type f -name "*.info" | xargs`
-	rm -rf coverage/
-
-# cleans everything - coverage output and standard 'clean'
-cleancov: cleancov-clean clean
-
-clean:
-	rm -f *.gcda *.gcno *.bat *.o *.a *.obj *.lib *.exe *.dll etclib/*.o demo/demo.o test ltmtest mpitest mtest/mtest mtest/mtest.exe \
-        *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.da *.dyn *.dpi tommath.tex `find . -type f | grep [~] | xargs` *.lo *.la
-	rm -rf .libs/
-	cd etc ; MAKE=${MAKE} ${MAKE} clean
-	cd pics ; MAKE=${MAKE} ${MAKE} clean
diff --git a/libtommath/tommath.h b/libtommath/tommath.h
index fc6b409..80bae69 100644
--- a/libtommath/tommath.h
+++ b/libtommath/tommath.h
@@ -565,6 +565,6 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream);
 #endif
 
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/tommath_private.h b/libtommath/tommath_private.h
index 4c5389c..aeda684 100644
--- a/libtommath/tommath_private.h
+++ b/libtommath/tommath_private.h
@@ -118,6 +118,6 @@ int func_name (mp_int * a, type b)                       \
 #endif
 
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/tommath_superclass.h b/libtommath/tommath_superclass.h
index 2489a07..a2f4d93 100644
--- a/libtommath/tommath_superclass.h
+++ b/libtommath/tommath_superclass.h
@@ -71,6 +71,6 @@
 
 #endif
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
diff --git a/libtommath/updatemakes.sh b/libtommath/updatemakes.sh
index 54c3b84..0f9520e 100755
--- a/libtommath/updatemakes.sh
+++ b/libtommath/updatemakes.sh
@@ -28,6 +28,6 @@ rm -f tmp.delme
 
 rm -f tmplist
 
-# $Source$
-# $Revision$
-# $Date$
+# ref:         $Format:%D$
+# git commit:  $Format:%H$
+# commit time: $Format:%ai$
-- 
cgit v0.12


From 3857cb0131afb184ce494f92185ed6d75f0affa9 Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Thu, 31 Aug 2017 13:43:17 +0000
Subject: Adapt .fossil-settings/crlf-glob, for 5 libtommath-related files
 which have crlf ending

---
 .fossil-settings/crlf-glob | 3 +++
 .fossil-settings/crnl-glob | 3 +++
 2 files changed, 6 insertions(+)

diff --git a/.fossil-settings/crlf-glob b/.fossil-settings/crlf-glob
index f219a75..2041cb6 100644
--- a/.fossil-settings/crlf-glob
+++ b/.fossil-settings/crlf-glob
@@ -3,6 +3,9 @@ compat/zlib/contrib/vstudio/readme.txt
 compat/zlib/contrib/vstudio/*/zlib.rc
 compat/zlib/win32/*.txt
 compat/zlib/win64/*.txt
+libtommath/*.dsp
+libtommath/*.sln
+libtommath/*.vcproj
 tools/tcl.hpj.in
 tools/tcl.wse.in
 win/buildall.vc.bat
diff --git a/.fossil-settings/crnl-glob b/.fossil-settings/crnl-glob
index f219a75..2041cb6 100644
--- a/.fossil-settings/crnl-glob
+++ b/.fossil-settings/crnl-glob
@@ -3,6 +3,9 @@ compat/zlib/contrib/vstudio/readme.txt
 compat/zlib/contrib/vstudio/*/zlib.rc
 compat/zlib/win32/*.txt
 compat/zlib/win64/*.txt
+libtommath/*.dsp
+libtommath/*.sln
+libtommath/*.vcproj
 tools/tcl.hpj.in
 tools/tcl.wse.in
 win/buildall.vc.bat
-- 
cgit v0.12


From 6832ae16ff4f18e496fe00d20334e627e2acf525 Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Fri, 1 Sep 2017 13:48:56 +0000
Subject: Handle Unicode surrogates correctly in Tcl_AppendFormatToObj() and
 BuildCharSet(). Only makes a difference for TCL_UTF_MAX=4, when surrogates
 are used in the format string ... highly unlikely corner-case.

---
 generic/tclScan.c      | 4 ++--
 generic/tclStringObj.c | 2 +-
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/generic/tclScan.c b/generic/tclScan.c
index 7a6a8a2..e1fcad4 100644
--- a/generic/tclScan.c
+++ b/generic/tclScan.c
@@ -72,7 +72,7 @@ BuildCharSet(
     CharSet *cset,
     const char *format)		/* Points to first char of set. */
 {
-    Tcl_UniChar ch, start;
+    Tcl_UniChar ch = 0, start;
     int offset, nranges;
     const char *end;
 
@@ -582,7 +582,7 @@ Tcl_ScanObjCmd(
     char op = 0;
     int width, underflow = 0;
     Tcl_WideInt wideValue;
-    Tcl_UniChar ch, sch;
+    Tcl_UniChar ch = 0, sch = 0;
     Tcl_Obj **objs = NULL, *objPtr = NULL;
     int flags;
     char buf[513];		/* Temporary buffer to hold scanned number
diff --git a/generic/tclStringObj.c b/generic/tclStringObj.c
index 6d97881..01b044e 100644
--- a/generic/tclStringObj.c
+++ b/generic/tclStringObj.c
@@ -1682,6 +1682,7 @@ Tcl_AppendFormatToObj(
     const char *span = format, *msg, *errCode;
     int numBytes = 0, objIndex = 0, gotXpg = 0, gotSequential = 0;
     int originalLength, limit;
+    Tcl_UniChar ch = 0;
     static const char *mixedXPG =
 	    "cannot mix \"%\" and \"%n$\" conversion specifiers";
     static const char *const badIndex[2] = {
@@ -1709,7 +1710,6 @@ Tcl_AppendFormatToObj(
 #endif
 	int newXpg, numChars, allocSegment = 0, segmentLimit, segmentNumBytes;
 	Tcl_Obj *segment;
-	Tcl_UniChar ch = 0;
 	int step = TclUtfToUniChar(format, &ch);
 
 	format += step;
-- 
cgit v0.12


From 5d7ae02a8ce96d7fbec18af96fbe91a775f126d3 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Sat, 2 Sep 2017 19:35:22 +0000
Subject: [Bug 0e4d88b650] First draft fix. Re-resolve namespace after cmd
 deletion.

---
 generic/tclBasic.c | 28 ++++++++++++++++++++--------
 1 file changed, 20 insertions(+), 8 deletions(-)

diff --git a/generic/tclBasic.c b/generic/tclBasic.c
index 44cf543..fddce1a 100644
--- a/generic/tclBasic.c
+++ b/generic/tclBasic.c
@@ -2017,7 +2017,7 @@ Tcl_CreateObjCommand(
     Command *cmdPtr, *refCmdPtr;
     Tcl_HashEntry *hPtr;
     const char *tail;
-    int isNew;
+    int isNew = 0, deleted = 0;
     ImportedCmdData *dataPtr;
 
     if (iPtr->flags & DELETED) {
@@ -2030,6 +2030,14 @@ Tcl_CreateObjCommand(
     }
 
     /*
+     * If the command name we seek to create already exists, we need to
+     * delete that first.  That can be tricky in the presence of traces.
+     * Loop until we no longer find an existing command in the way.
+     */
+
+    while (1) {
+
+    /*
      * Determine where the command should reside. If its name contains
      * namespace qualifiers, we put it in the specified namespace; otherwise,
      * we always put it in the global namespace.
@@ -2047,11 +2055,13 @@ Tcl_CreateObjCommand(
     }
 
     hPtr = Tcl_CreateHashEntry(&nsPtr->cmdTable, tail, &isNew);
-    TclInvalidateNsPath(nsPtr);
-    if (!isNew) {
-	cmdPtr = Tcl_GetHashValue(hPtr);
+
+    if (isNew || deleted) {
+	break;
+    }
 
 	/* Command already exists. */
+	cmdPtr = Tcl_GetHashValue(hPtr);
 
 	/*
 	 * [***] This is wrong.  See Tcl Bug a16752c252.  
@@ -2089,8 +2099,8 @@ Tcl_CreateObjCommand(
 	    cmdPtr->importRefPtr = NULL;
 	}
 	TclCleanupCommandMacro(cmdPtr);
-
-	hPtr = Tcl_CreateHashEntry(&nsPtr->cmdTable, tail, &isNew);
+	deleted = 1;
+    }
 	if (!isNew) {
 	    /*
 	     * If the deletion callback recreated the command, just throw away
@@ -2100,7 +2110,8 @@ Tcl_CreateObjCommand(
 
 	     ckfree(Tcl_GetHashValue(hPtr));
 	}
-    } else {
+
+	if (!deleted) {
 	/*
 	 * The list of command exported from the namespace might have changed.
 	 * However, we do not need to recompute this just yet; next time we
@@ -2108,7 +2119,8 @@ Tcl_CreateObjCommand(
 	 */
 
 	TclInvalidateNsCmdLookup(nsPtr);
-    }
+	TclInvalidateNsPath(nsPtr);
+	}
     cmdPtr = (Command *) ckalloc(sizeof(Command));
     Tcl_SetHashValue(hPtr, cmdPtr);
     cmdPtr->hPtr = hPtr;
-- 
cgit v0.12


From 37007afa53b17d5e10c1553a2af898dba2f886e1 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Sat, 2 Sep 2017 20:17:26 +0000
Subject: Tidy up.

---
 generic/tclBasic.c | 73 ++++++++++++++++++++++++++++++------------------------
 1 file changed, 40 insertions(+), 33 deletions(-)

diff --git a/generic/tclBasic.c b/generic/tclBasic.c
index fddce1a..7c223e9 100644
--- a/generic/tclBasic.c
+++ b/generic/tclBasic.c
@@ -2013,8 +2013,8 @@ Tcl_CreateObjCommand(
 {
     Interp *iPtr = (Interp *) interp;
     ImportRef *oldRefPtr = NULL;
-    Namespace *nsPtr, *dummy1, *dummy2;
-    Command *cmdPtr, *refCmdPtr;
+    Namespace *nsPtr;
+    Command *cmdPtr;
     Tcl_HashEntry *hPtr;
     const char *tail;
     int isNew = 0, deleted = 0;
@@ -2032,35 +2032,41 @@ Tcl_CreateObjCommand(
     /*
      * If the command name we seek to create already exists, we need to
      * delete that first.  That can be tricky in the presence of traces.
-     * Loop until we no longer find an existing command in the way.
+     * Loop until we no longer find an existing command in the way, or
+     * until we've deleted one command and that didn't finish the job.
      */
 
     while (1) {
+        /*
+         * Determine where the command should reside. If its name contains
+         * namespace qualifiers, we put it in the specified namespace;
+	 * otherwise, we always put it in the global namespace.
+         */
 
-    /*
-     * Determine where the command should reside. If its name contains
-     * namespace qualifiers, we put it in the specified namespace; otherwise,
-     * we always put it in the global namespace.
-     */
+        if (strstr(cmdName, "::") != NULL) {
+	    Namespace *dummy1, *dummy2;
 
-    if (strstr(cmdName, "::") != NULL) {
-	TclGetNamespaceForQualName(interp, cmdName, NULL,
+	    TclGetNamespaceForQualName(interp, cmdName, NULL,
 		TCL_CREATE_NS_IF_UNKNOWN, &nsPtr, &dummy1, &dummy2, &tail);
-	if ((nsPtr == NULL) || (tail == NULL)) {
-	    return (Tcl_Command) NULL;
-	}
-    } else {
-	nsPtr = iPtr->globalNsPtr;
-	tail = cmdName;
-    }
+	    if ((nsPtr == NULL) || (tail == NULL)) {
+	        return (Tcl_Command) NULL;
+	    }
+        } else {
+	    nsPtr = iPtr->globalNsPtr;
+	    tail = cmdName;
+        }
 
-    hPtr = Tcl_CreateHashEntry(&nsPtr->cmdTable, tail, &isNew);
+        hPtr = Tcl_CreateHashEntry(&nsPtr->cmdTable, tail, &isNew);
 
-    if (isNew || deleted) {
-	break;
-    }
+        if (isNew || deleted) {
+	    /*
+	     * isNew - No conflict with existing command.
+	     * deleted - We've already deleted a conflicting command
+	     */
+	    break;
+        }
 
-	/* Command already exists. */
+	/* An existing command conflicts. Try to delete it.. */
 	cmdPtr = Tcl_GetHashValue(hPtr);
 
 	/*
@@ -2101,17 +2107,18 @@ Tcl_CreateObjCommand(
 	TclCleanupCommandMacro(cmdPtr);
 	deleted = 1;
     }
-	if (!isNew) {
-	    /*
-	     * If the deletion callback recreated the command, just throw away
-	     * the new command (if we try to delete it again, we could get
-	     * stuck in an infinite loop).
-	     */
 
-	     ckfree(Tcl_GetHashValue(hPtr));
-	}
+    if (!isNew) {
+	/*
+	 * If the deletion callback recreated the command, just throw away
+	 * the new command (if we try to delete it again, we could get
+	 * stuck in an infinite loop).
+	 */
 
-	if (!deleted) {
+	ckfree(Tcl_GetHashValue(hPtr));
+    }
+
+    if (!deleted) {
 	/*
 	 * The list of command exported from the namespace might have changed.
 	 * However, we do not need to recompute this just yet; next time we
@@ -2120,7 +2127,7 @@ Tcl_CreateObjCommand(
 
 	TclInvalidateNsCmdLookup(nsPtr);
 	TclInvalidateNsPath(nsPtr);
-	}
+    }
     cmdPtr = (Command *) ckalloc(sizeof(Command));
     Tcl_SetHashValue(hPtr, cmdPtr);
     cmdPtr->hPtr = hPtr;
@@ -2146,7 +2153,7 @@ Tcl_CreateObjCommand(
     if (oldRefPtr != NULL) {
 	cmdPtr->importRefPtr = oldRefPtr;
 	while (oldRefPtr != NULL) {
-	    refCmdPtr = oldRefPtr->importedCmdPtr;
+	    Command *refCmdPtr = oldRefPtr->importedCmdPtr;
 	    dataPtr = refCmdPtr->objClientData;
 	    dataPtr->realCmdPtr = cmdPtr;
 	    oldRefPtr = oldRefPtr->nextPtr;
-- 
cgit v0.12


From cc912b73a02978ef98876321877d1b923a4a22e5 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Sat, 2 Sep 2017 20:40:44 +0000
Subject: Similar fix to Tcl_CreateCommand().

---
 generic/tclBasic.c | 85 ++++++++++++++++++++++++++++++++++--------------------
 1 file changed, 54 insertions(+), 31 deletions(-)

diff --git a/generic/tclBasic.c b/generic/tclBasic.c
index 7c223e9..7f75892 100644
--- a/generic/tclBasic.c
+++ b/generic/tclBasic.c
@@ -1851,11 +1851,11 @@ Tcl_CreateCommand(
 {
     Interp *iPtr = (Interp *) interp;
     ImportRef *oldRefPtr = NULL;
-    Namespace *nsPtr, *dummy1, *dummy2;
-    Command *cmdPtr, *refCmdPtr;
+    Namespace *nsPtr;
+    Command *cmdPtr;
     Tcl_HashEntry *hPtr;
     const char *tail;
-    int isNew;
+    int isNew = 0, deleted = 0;
     ImportedCmdData *dataPtr;
 
     if (iPtr->flags & DELETED) {
@@ -1868,32 +1868,52 @@ Tcl_CreateCommand(
     }
 
     /*
-     * Determine where the command should reside. If its name contains
-     * namespace qualifiers, we put it in the specified namespace; otherwise,
-     * we always put it in the global namespace.
+     * If the command name we seek to create already exists, we need to
+     * delete that first.  That can be tricky in the presence of traces.
+     * Loop until we no longer find an existing command in the way, or
+     * until we've deleted one command and that didn't finish the job.
      */
 
-    if (strstr(cmdName, "::") != NULL) {
-	TclGetNamespaceForQualName(interp, cmdName, NULL,
-		TCL_CREATE_NS_IF_UNKNOWN, &nsPtr, &dummy1, &dummy2, &tail);
-	if ((nsPtr == NULL) || (tail == NULL)) {
-	    return (Tcl_Command) NULL;
-	}
-    } else {
-	nsPtr = iPtr->globalNsPtr;
-	tail = cmdName;
-    }
+    while (1) {
+        /*
+         * Determine where the command should reside. If its name contains
+         * namespace qualifiers, we put it in the specified namespace;
+	 * otherwise, we always put it in the global namespace.
+         */
 
-    hPtr = Tcl_CreateHashEntry(&nsPtr->cmdTable, tail, &isNew);
-    if (!isNew) {
+        if (strstr(cmdName, "::") != NULL) {
+	    Namespace *dummy1, *dummy2;
+
+	    TclGetNamespaceForQualName(interp, cmdName, NULL,
+		    TCL_CREATE_NS_IF_UNKNOWN, &nsPtr, &dummy1, &dummy2, &tail);
+	    if ((nsPtr == NULL) || (tail == NULL)) {
+	        return (Tcl_Command) NULL;
+	    }
+        } else {
+	    nsPtr = iPtr->globalNsPtr;
+	    tail = cmdName;
+        }
+
+        hPtr = Tcl_CreateHashEntry(&nsPtr->cmdTable, tail, &isNew);
+
+        if (isNew || deleted) {
+	    /*
+	     * isNew - No conflict with existing command.
+	     * deleted - We've already deleted a conflicting command
+	     */
+	    break;
+        }
+
+	/* An existing command conflicts. Try to delete it.. */
+	cmdPtr = Tcl_GetHashValue(hPtr);
+	
 	/*
-	 * Command already exists. Delete the old one. Be careful to preserve
+	 * Be careful to preserve
 	 * any existing import links so we can restore them down below. That
 	 * way, you can redefine a command and its import status will remain
 	 * intact.
 	 */
 
-	cmdPtr = Tcl_GetHashValue(hPtr);
 	cmdPtr->refCount++;
 	if (cmdPtr->importRefPtr) {
 	    cmdPtr->flags |= CMD_REDEF_IN_PROGRESS;
@@ -1906,18 +1926,21 @@ Tcl_CreateCommand(
 	    cmdPtr->importRefPtr = NULL;
 	}
 	TclCleanupCommandMacro(cmdPtr);
+	deleted = 1;
+    }
 
-	hPtr = Tcl_CreateHashEntry(&nsPtr->cmdTable, tail, &isNew);
-	if (!isNew) {
-	    /*
-	     * If the deletion callback recreated the command, just throw away
-	     * the new command (if we try to delete it again, we could get
-	     * stuck in an infinite loop).
-	     */
+    if (!isNew) {
+	/*
+	 * If the deletion callback recreated the command, just throw away
+	 * the new command (if we try to delete it again, we could get
+	 * stuck in an infinite loop).
+	 */
+
+	ckfree((char *) Tcl_GetHashValue(hPtr));
+    }
+
+    if (!deleted) {
 
-	     ckfree((char *) Tcl_GetHashValue(hPtr));
-	}
-    } else {
 	/*
 	 * The list of command exported from the namespace might have changed.
 	 * However, we do not need to recompute this just yet; next time we
@@ -1952,7 +1975,7 @@ Tcl_CreateCommand(
     if (oldRefPtr != NULL) {
 	cmdPtr->importRefPtr = oldRefPtr;
 	while (oldRefPtr != NULL) {
-	    refCmdPtr = oldRefPtr->importedCmdPtr;
+	    Command *refCmdPtr = oldRefPtr->importedCmdPtr;
 	    dataPtr = refCmdPtr->objClientData;
 	    dataPtr->realCmdPtr = cmdPtr;
 	    oldRefPtr = oldRefPtr->nextPtr;
-- 
cgit v0.12


From 39efd5474116799b123d4082bca3a9c30c7b8b82 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Sat, 2 Sep 2017 21:14:55 +0000
Subject: Add test

---
 tests/basic.test | 15 +++++++++++++++
 1 file changed, 15 insertions(+)

diff --git a/tests/basic.test b/tests/basic.test
index 91e4d6c..e4b46fd 100644
--- a/tests/basic.test
+++ b/tests/basic.test
@@ -221,6 +221,21 @@ test basic-15.1 {Tcl_CreateObjCommand, new cmd goes into a namespace specified i
     list [test_ns_basic::cmd] \
          [namespace delete test_ns_basic]
 } {::test_ns_basic {}}
+test basic-15.2 {Tcl_CreateObjCommand, Bug 0e4d88b650} -setup {
+    proc deleter {ns args} {
+        namespace delete $ns
+    }
+    namespace eval n {
+        proc p {} {}
+    }
+    trace add command n::p delete [list [namespace which deleter] [namespace current]::n]
+} -body {
+    proc n::p {} {}
+} -cleanup {
+    namespace delete n
+    rename deleter {}
+}
+
 
 test basic-16.1 {TclInvokeStringCommand} {emptyTest} {
 } {}
-- 
cgit v0.12


From 00deed9129815de66856273e30bc92649e6c111b Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Mon, 4 Sep 2017 12:37:04 +0000
Subject: Typo's (Thanks to Gustaf Neumann), nothing functional.

---
 generic/tclBasic.c    | 2 +-
 generic/tclEncoding.c | 4 ++--
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/generic/tclBasic.c b/generic/tclBasic.c
index 36d2301..acdcf41 100644
--- a/generic/tclBasic.c
+++ b/generic/tclBasic.c
@@ -2097,7 +2097,7 @@ Tcl_CreateCommand(
 
 	/* An existing command conflicts. Try to delete it.. */
 	cmdPtr = Tcl_GetHashValue(hPtr);
-	
+
 	/*
 	 * Be careful to preserve
 	 * any existing import links so we can restore them down below. That
diff --git a/generic/tclEncoding.c b/generic/tclEncoding.c
index 8450128..2548b73 100644
--- a/generic/tclEncoding.c
+++ b/generic/tclEncoding.c
@@ -2329,7 +2329,7 @@ UtfToUtfProc(
 	}
 	if (UCHAR(*src) < 0x80 && !(UCHAR(*src) == 0 && pureNullMode == 0)) {
 	    /*
-	     * Copy 7bit chatacters, but skip null-bytes when we are in input
+	     * Copy 7bit characters, but skip null-bytes when we are in input
 	     * mode, so that they get converted to 0xc080.
 	     */
 
@@ -3374,7 +3374,7 @@ EscapeFromUtfProc(
 
 	    /*
 	     * The state variable has the value of oldState when word is 0.
-	     * In this case, the escape sequense should not be copied to dst
+	     * In this case, the escape sequence should not be copied to dst
 	     * because the current character set is not changed.
 	     */
 
-- 
cgit v0.12


From 0477cb15f93e08f2ef2651122ec92163cbf621c0 Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Mon, 4 Sep 2017 13:59:04 +0000
Subject: Make pkgIndex.tcl from msgcat work for Tcl 9.0 (not really necessary,
 but for consistancy)

---
 library/msgcat/pkgIndex.tcl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/library/msgcat/pkgIndex.tcl b/library/msgcat/pkgIndex.tcl
index 7cdb703..72c5dc0 100644
--- a/library/msgcat/pkgIndex.tcl
+++ b/library/msgcat/pkgIndex.tcl
@@ -1,2 +1,2 @@
-if {![package vsatisfies [package provide Tcl] 8.5]} {return}
+if {![package vsatisfies [package provide Tcl] 8.5-]} {return}
 package ifneeded msgcat 1.6.1 [list source [file join $dir msgcat.tcl]]
-- 
cgit v0.12


From 176661769ec1b78bbe6debfc8f986b7cd7f21734 Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Tue, 5 Sep 2017 15:38:02 +0000
Subject: update changes

---
 changes | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/changes b/changes
index d1e6417..5cc49ea 100644
--- a/changes
+++ b/changes
@@ -8838,4 +8838,6 @@ improvements to regexp engine from Postgres (lane,porter,fellows,seltenreich)
 2017-08-31 (bug)[2a9465] http state 100 continue handling broken (oehlmann)
 => http 2.8.12
 
---- Released 8.7a1, August ??, 2017 --- http://core.tcl.tk/tcl/ for details
+2017-09-02 (bug)[0e4d88] replace command, delete trace kills namespace (porter)
+
+--- Released 8.7a1, September 8, 2017 --- http://core.tcl.tk/tcl/ for details
-- 
cgit v0.12


From 48ce21e3a9c2c9da4e4674bf08275e378629a0e3 Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Wed, 6 Sep 2017 15:02:24 +0000
Subject: Fix use of "long long" (manually) in MSVC

---
 generic/tclTomMath.h | 22 ++++++++++++++--------
 1 file changed, 14 insertions(+), 8 deletions(-)

diff --git a/generic/tclTomMath.h b/generic/tclTomMath.h
index 39132ed..508fadd 100644
--- a/generic/tclTomMath.h
+++ b/generic/tclTomMath.h
@@ -277,13 +277,19 @@ int mp_set_long_long(mp_int *a, unsigned long long b);
 */
 
 /* get a 32-bit value */
-unsigned long mp_get_int(mp_int * a);
+/*
+unsigned long mp_get_int(const mp_int * a);
+*/
 
 /* get a platform dependent unsigned long value */
-unsigned long mp_get_long(mp_int * a);
+/*
+unsigned long mp_get_long(const mp_int * a);
+*/
 
 /* get a platform dependent unsigned long long value */
-unsigned long long mp_get_long_long(mp_int * a);
+/*
+unsigned long long mp_get_long_long(const mp_int * a);
+*/
 
 /* initialize and set a digit */
 /*
@@ -339,7 +345,7 @@ int mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d);
 
 /* b = a/2 */
 /*
-int mp_div_2(mp_int *a, mp_int *b);
+int mp_div_2(const mp_int *a, mp_int *b);
 */
 
 /* c = a * 2**b, implemented as c = a << b */
@@ -349,7 +355,7 @@ int mp_mul_2d(const mp_int *a, int b, mp_int *c);
 
 /* b = a*2 */
 /*
-int mp_mul_2(mp_int *a, mp_int *b);
+int mp_mul_2(const mp_int *a, mp_int *b);
 */
 
 /* c = a mod 2**b */
@@ -801,7 +807,7 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream);
 #endif
 
 
-/* ref:         tag: v1.0.1, master */
-/* git commit:  5953f62e42b24af93748b1ee5e1d062e242c2546 */
-/* commit time: 2017-08-29 22:27:36 +0200 */
+/* ref:         $Format:%D$ */
+/* git commit:  $Format:%H$ */
+/* commit time: $Format:%ai$ */
 
-- 
cgit v0.12


From b9ae4bcae4f10a98c180b3a951f58c8a5ac03f8e Mon Sep 17 00:00:00 2001
From: dgp <dgp@users.sourceforge.net>
Date: Fri, 8 Sep 2017 13:13:15 +0000
Subject: Bump to 8.7a2 to distinguish trunk from 8.7a1 release.

---
 README            | 2 +-
 generic/tcl.h     | 4 ++--
 library/init.tcl  | 2 +-
 unix/configure    | 2 +-
 unix/configure.ac | 2 +-
 win/configure     | 2 +-
 win/configure.ac  | 2 +-
 7 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/README b/README
index 59de34d..322666a 100644
--- a/README
+++ b/README
@@ -1,5 +1,5 @@
 README:  Tcl
-    This is the Tcl 8.7a1 source distribution.
+    This is the Tcl 8.7a2 source distribution.
 	http://sourceforge.net/projects/tcl/files/Tcl/
     You can get any source release of Tcl from the URL above.
 
diff --git a/generic/tcl.h b/generic/tcl.h
index 589a63f..07d841d 100644
--- a/generic/tcl.h
+++ b/generic/tcl.h
@@ -55,10 +55,10 @@ extern "C" {
 #define TCL_MAJOR_VERSION   8
 #define TCL_MINOR_VERSION   7
 #define TCL_RELEASE_LEVEL   TCL_ALPHA_RELEASE
-#define TCL_RELEASE_SERIAL  1
+#define TCL_RELEASE_SERIAL  2
 
 #define TCL_VERSION	    "8.7"
-#define TCL_PATCH_LEVEL	    "8.7a1"
+#define TCL_PATCH_LEVEL	    "8.7a2"
 
 #if !defined(TCL_NO_DEPRECATED) || defined(RC_INVOKED)
 /*
diff --git a/library/init.tcl b/library/init.tcl
index b6e6e8b..e361645 100644
--- a/library/init.tcl
+++ b/library/init.tcl
@@ -16,7 +16,7 @@
 if {[info commands package] == ""} {
     error "version mismatch: library\nscripts expect Tcl version 7.5b1 or later but the loaded version is\nonly [info patchlevel]"
 }
-package require -exact Tcl 8.7a1
+package require -exact Tcl 8.7a2
 
 # Compute the auto path to use in this interpreter.
 # The values on the path come from several locations:
diff --git a/unix/configure b/unix/configure
index 0b22a43..129c283 100755
--- a/unix/configure
+++ b/unix/configure
@@ -2325,7 +2325,7 @@ ac_compiler_gnu=$ac_cv_c_compiler_gnu
 TCL_VERSION=8.7
 TCL_MAJOR_VERSION=8
 TCL_MINOR_VERSION=7
-TCL_PATCH_LEVEL="a1"
+TCL_PATCH_LEVEL="a2"
 VERSION=${TCL_VERSION}
 
 EXTRA_INSTALL_BINARIES=${EXTRA_INSTALL_BINARIES:-"@:"}
diff --git a/unix/configure.ac b/unix/configure.ac
index d7aa50f..e14d85e 100644
--- a/unix/configure.ac
+++ b/unix/configure.ac
@@ -25,7 +25,7 @@ m4_ifdef([SC_USE_CONFIG_HEADERS], [
 TCL_VERSION=8.7
 TCL_MAJOR_VERSION=8
 TCL_MINOR_VERSION=7
-TCL_PATCH_LEVEL="a1"
+TCL_PATCH_LEVEL="a2"
 VERSION=${TCL_VERSION}
 
 EXTRA_INSTALL_BINARIES=${EXTRA_INSTALL_BINARIES:-"@:"}
diff --git a/win/configure b/win/configure
index a47ff23..fdd3adb 100755
--- a/win/configure
+++ b/win/configure
@@ -2102,7 +2102,7 @@ SHELL=/bin/sh
 TCL_VERSION=8.7
 TCL_MAJOR_VERSION=8
 TCL_MINOR_VERSION=7
-TCL_PATCH_LEVEL="a1"
+TCL_PATCH_LEVEL="a2"
 VER=$TCL_MAJOR_VERSION$TCL_MINOR_VERSION
 
 TCL_DDE_VERSION=1.4
diff --git a/win/configure.ac b/win/configure.ac
index e32dadc..d03695c 100644
--- a/win/configure.ac
+++ b/win/configure.ac
@@ -14,7 +14,7 @@ SHELL=/bin/sh
 TCL_VERSION=8.7
 TCL_MAJOR_VERSION=8
 TCL_MINOR_VERSION=7
-TCL_PATCH_LEVEL="a1"
+TCL_PATCH_LEVEL="a2"
 VER=$TCL_MAJOR_VERSION$TCL_MINOR_VERSION
 
 TCL_DDE_VERSION=1.4
-- 
cgit v0.12


From 86eedd9ac8aa6c202c941fe08d1ec6fd255f422f Mon Sep 17 00:00:00 2001
From: gahr <gahr@gahr.ch>
Date: Fri, 8 Sep 2017 13:30:29 +0000
Subject: Be consistent about how I am referred to.

---
 changes | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/changes b/changes
index 5cc49ea..ec8beb1 100644
--- a/changes
+++ b/changes
@@ -8234,7 +8234,7 @@ Dropped support for OS X versions less than 10.4 (Tiger) (fellows)
 
 2013-05-16 (platform support) mingw-4.0 (nijtmans)
 
-2013-05-19 (platform support) FreeBSD updates (cerutti)
+2013-05-19 (platform support) FreeBSD updates (gahr)
 
 2013-05-20 (bug fix)[3613567] access error temp file creation (keene)
 
@@ -8657,7 +8657,7 @@ improvements to regexp engine from Postgres (lane,porter,fellows,seltenreich)
 
 2016-05-21 (bug)[f7d4e] [namespace delete] performance (fellows)
 
-2016-06-02 (TIP 447) execution time verbosity option (cerutti)
+2016-06-02 (TIP 447) execution time verbosity option (gahr)
 => tcltest 2.4.0
 
 2016-06-16 (bug)[16828b] crash due to [vwait] trace undo fail (dah,porter)
-- 
cgit v0.12


From 72cd4c6a0763c30b3f3a4fceb1ed78ad63711cb5 Mon Sep 17 00:00:00 2001
From: "jan.nijtmans" <nijtmans@users.sourceforge.net>
Date: Fri, 8 Sep 2017 14:15:13 +0000
Subject: Add some more functions from libtommath for availability within Tcl
 (mainly the 'long long' variants). Add more 'const' keywords there too.

---
 generic/tclStubInit.c            |  2 ++
 generic/tclTomMath.decls         | 11 +++++++++--
 generic/tclTomMath.h             |  4 ++--
 generic/tclTomMathDecls.h        | 21 +++++++++++++++++----
 libtommath/bn_mp_div_2.c         |  2 +-
 libtommath/bn_mp_get_int.c       |  2 +-
 libtommath/bn_mp_get_long.c      |  2 +-
 libtommath/bn_mp_get_long_long.c |  6 +++---
 libtommath/bn_mp_mul_2.c         |  2 +-
 libtommath/bn_mp_set_long_long.c |  2 +-
 libtommath/tommath.h             | 12 ++++++------
 unix/Makefile.in                 | 16 ++++++++++++++--
 unix/tcl.spec                    |  2 +-
 win/Makefile.in                  |  3 +++
 win/makefile.vc                  |  3 +++
 15 files changed, 65 insertions(+), 25 deletions(-)

diff --git a/generic/tclStubInit.c b/generic/tclStubInit.c
index 8cc21aa..a2f1ed3 100644
--- a/generic/tclStubInit.c
+++ b/generic/tclStubInit.c
@@ -859,6 +859,8 @@ const TclTomMathStubs tclTomMathStubs = {
     TclBNInitBignumFromWideInt, /* 65 */
     TclBNInitBignumFromWideUInt, /* 66 */
     TclBN_mp_expt_d_ex, /* 67 */
+    TclBN_mp_set_long_long, /* 68 */
+    TclBN_mp_get_long_long, /* 69 */
 };
 
 static const TclStubHooks tclStubHooks = {
diff --git a/generic/tclTomMath.decls b/generic/tclTomMath.decls
index 74ccefc..c4299d0 100644
--- a/generic/tclTomMath.decls
+++ b/generic/tclTomMath.decls
@@ -69,7 +69,7 @@ declare 14 {
     int TclBN_mp_div_d(mp_int *a, mp_digit b, mp_int *q, mp_digit *r)
 }
 declare 15 {
-    int TclBN_mp_div_2(mp_int *a, mp_int *q)
+    int TclBN_mp_div_2(const mp_int *a, mp_int *q)
 }
 declare 16 {
     int TclBN_mp_div_2d(const mp_int *a, int b, mp_int *q, mp_int *r)
@@ -117,7 +117,7 @@ declare 30 {
     int TclBN_mp_mul_d(mp_int *a, mp_digit b, mp_int *p)
 }
 declare 31 {
-    int TclBN_mp_mul_2(mp_int *a, mp_int *p)
+    int TclBN_mp_mul_2(const mp_int *a, mp_int *p)
 }
 declare 32 {
     int TclBN_mp_mul_2d(const mp_int *a, int d, mp_int *p)
@@ -237,6 +237,13 @@ declare 66 {
 declare 67 {
     int TclBN_mp_expt_d_ex(mp_int *a, mp_digit b, mp_int *c, int fast)
 }
+# Added in libtommath 1.0.1
+declare 68 {
+    int TclBN_mp_set_long_long(mp_int *a, Tcl_WideUInt i)
+}
+declare 69 {
+    Tcl_WideUInt TclBN_mp_get_long_long(const mp_int *a)
+}
 
 # Local Variables:
 # mode: tcl
diff --git a/generic/tclTomMath.h b/generic/tclTomMath.h
index 508fadd..7e3c29e 100644
--- a/generic/tclTomMath.h
+++ b/generic/tclTomMath.h
@@ -273,7 +273,7 @@ int mp_set_long(mp_int *a, unsigned long b);
 
 /* set a platform dependent unsigned long long value */
 /*
-int mp_set_long_long(mp_int *a, unsigned long long b);
+int mp_set_long_long(mp_int *a, Tcl_WideUInt b);
 */
 
 /* get a 32-bit value */
@@ -288,7 +288,7 @@ unsigned long mp_get_long(const mp_int * a);
 
 /* get a platform dependent unsigned long long value */
 /*
-unsigned long long mp_get_long_long(const mp_int * a);
+Tcl_WideUInt mp_get_long_long(const mp_int * a);
 */
 
 /* initialize and set a digit */
diff --git a/generic/tclTomMathDecls.h b/generic/tclTomMathDecls.h
index 209c486..70de3b1 100644
--- a/generic/tclTomMathDecls.h
+++ b/generic/tclTomMathDecls.h
@@ -74,6 +74,8 @@
 #define mp_exch TclBN_mp_exch
 #define mp_expt_d TclBN_mp_expt_d
 #define mp_expt_d_ex TclBN_mp_expt_d_ex
+#define mp_get_int TclBN_mp_get_int
+#define mp_get_long_long TclBN_mp_get_long_long
 #define mp_grow TclBN_mp_grow
 #define mp_init TclBN_mp_init
 #define mp_init_copy TclBN_mp_init_copy
@@ -98,6 +100,7 @@
 #define mp_s_rmap TclBNMpSRmap
 #define mp_set TclBN_mp_set
 #define mp_set_int TclBN_mp_set_int
+#define mp_set_long_long TclBN_mp_set_long_long
 #define mp_shrink TclBN_mp_shrink
 #define mp_sqr TclBN_mp_sqr
 #define mp_sqrt TclBN_mp_sqrt
@@ -176,7 +179,7 @@ EXTERN int		TclBN_mp_div(mp_int *a, mp_int *b, mp_int *q,
 EXTERN int		TclBN_mp_div_d(mp_int *a, mp_digit b, mp_int *q,
 				mp_digit *r);
 /* 15 */
-EXTERN int		TclBN_mp_div_2(mp_int *a, mp_int *q);
+EXTERN int		TclBN_mp_div_2(const mp_int *a, mp_int *q);
 /* 16 */
 EXTERN int		TclBN_mp_div_2d(const mp_int *a, int b, mp_int *q,
 				mp_int *r);
@@ -209,7 +212,7 @@ EXTERN int		TclBN_mp_mul(mp_int *a, mp_int *b, mp_int *p);
 /* 30 */
 EXTERN int		TclBN_mp_mul_d(mp_int *a, mp_digit b, mp_int *p);
 /* 31 */
-EXTERN int		TclBN_mp_mul_2(mp_int *a, mp_int *p);
+EXTERN int		TclBN_mp_mul_2(const mp_int *a, mp_int *p);
 /* 32 */
 EXTERN int		TclBN_mp_mul_2d(const mp_int *a, int d, mp_int *p);
 /* 33 */
@@ -292,6 +295,10 @@ EXTERN void		TclBNInitBignumFromWideUInt(mp_int *bignum,
 /* 67 */
 EXTERN int		TclBN_mp_expt_d_ex(mp_int *a, mp_digit b, mp_int *c,
 				int fast);
+/* 68 */
+EXTERN int		TclBN_mp_set_long_long(mp_int *a, Tcl_WideUInt i);
+/* 69 */
+EXTERN Tcl_WideUInt	TclBN_mp_get_long_long(const mp_int *a);
 
 typedef struct TclTomMathStubs {
     int magic;
@@ -312,7 +319,7 @@ typedef struct TclTomMathStubs {
     int (*tclBN_mp_count_bits) (const mp_int *a); /* 12 */
     int (*tclBN_mp_div) (mp_int *a, mp_int *b, mp_int *q, mp_int *r); /* 13 */
     int (*tclBN_mp_div_d) (mp_int *a, mp_digit b, mp_int *q, mp_digit *r); /* 14 */
-    int (*tclBN_mp_div_2) (mp_int *a, mp_int *q); /* 15 */
+    int (*tclBN_mp_div_2) (const mp_int *a, mp_int *q); /* 15 */
     int (*tclBN_mp_div_2d) (const mp_int *a, int b, mp_int *q, mp_int *r); /* 16 */
     int (*tclBN_mp_div_3) (mp_int *a, mp_int *q, mp_digit *r); /* 17 */
     void (*tclBN_mp_exch) (mp_int *a, mp_int *b); /* 18 */
@@ -328,7 +335,7 @@ typedef struct TclTomMathStubs {
     int (*tclBN_mp_mod_2d) (const mp_int *a, int b, mp_int *r); /* 28 */
     int (*tclBN_mp_mul) (mp_int *a, mp_int *b, mp_int *p); /* 29 */
     int (*tclBN_mp_mul_d) (mp_int *a, mp_digit b, mp_int *p); /* 30 */
-    int (*tclBN_mp_mul_2) (mp_int *a, mp_int *p); /* 31 */
+    int (*tclBN_mp_mul_2) (const mp_int *a, mp_int *p); /* 31 */
     int (*tclBN_mp_mul_2d) (const mp_int *a, int d, mp_int *p); /* 32 */
     int (*tclBN_mp_neg) (const mp_int *a, mp_int *b); /* 33 */
     int (*tclBN_mp_or) (mp_int *a, mp_int *b, mp_int *c); /* 34 */
@@ -365,6 +372,8 @@ typedef struct TclTomMathStubs {
     void (*tclBNInitBignumFromWideInt) (mp_int *bignum, Tcl_WideInt initVal); /* 65 */
     void (*tclBNInitBignumFromWideUInt) (mp_int *bignum, Tcl_WideUInt initVal); /* 66 */
     int (*tclBN_mp_expt_d_ex) (mp_int *a, mp_digit b, mp_int *c, int fast); /* 67 */
+    int (*tclBN_mp_set_long_long) (mp_int *a, Tcl_WideUInt i); /* 68 */
+    Tcl_WideUInt (*tclBN_mp_get_long_long) (const mp_int *a); /* 69 */
 } TclTomMathStubs;
 
 extern const TclTomMathStubs *tclTomMathStubsPtr;
@@ -515,6 +524,10 @@ extern const TclTomMathStubs *tclTomMathStubsPtr;
 	(tclTomMathStubsPtr->tclBNInitBignumFromWideUInt) /* 66 */
 #define TclBN_mp_expt_d_ex \
 	(tclTomMathStubsPtr->tclBN_mp_expt_d_ex) /* 67 */
+#define TclBN_mp_set_long_long \
+	(tclTomMathStubsPtr->tclBN_mp_set_long_long) /* 68 */
+#define TclBN_mp_get_long_long \
+	(tclTomMathStubsPtr->tclBN_mp_get_long_long) /* 69 */
 
 #endif /* defined(USE_TCL_STUBS) */
 
diff --git a/libtommath/bn_mp_div_2.c b/libtommath/bn_mp_div_2.c
index 2b5bb49..0e981a0 100644
--- a/libtommath/bn_mp_div_2.c
+++ b/libtommath/bn_mp_div_2.c
@@ -16,7 +16,7 @@
  */
 
 /* b = a/2 */
-int mp_div_2(mp_int * a, mp_int * b)
+int mp_div_2(const mp_int * a, mp_int * b)
 {
   int     x, res, oldused;
 
diff --git a/libtommath/bn_mp_get_int.c b/libtommath/bn_mp_get_int.c
index 5c820f8..abb7011 100644
--- a/libtommath/bn_mp_get_int.c
+++ b/libtommath/bn_mp_get_int.c
@@ -16,7 +16,7 @@
  */
 
 /* get the lower 32-bits of an mp_int */
-unsigned long mp_get_int(mp_int * a)
+unsigned long mp_get_int(const mp_int * a)
 {
   int i;
   mp_min_u32 res;
diff --git a/libtommath/bn_mp_get_long.c b/libtommath/bn_mp_get_long.c
index 7c3d0fe..da69080 100644
--- a/libtommath/bn_mp_get_long.c
+++ b/libtommath/bn_mp_get_long.c
@@ -16,7 +16,7 @@
  */
 
 /* get the lower unsigned long of an mp_int, platform dependent */
-unsigned long mp_get_long(mp_int * a)
+unsigned long mp_get_long(const mp_int * a)
 {
   int i;
   unsigned long res;
diff --git a/libtommath/bn_mp_get_long_long.c b/libtommath/bn_mp_get_long_long.c
index 4b959e6..534c48c 100644
--- a/libtommath/bn_mp_get_long_long.c
+++ b/libtommath/bn_mp_get_long_long.c
@@ -16,17 +16,17 @@
  */
 
 /* get the lower unsigned long long of an mp_int, platform dependent */
-unsigned long long mp_get_long_long (mp_int * a)
+Tcl_WideUInt mp_get_long_long (const mp_int * a)
 {
   int i;
-  unsigned long long res;
+  Tcl_WideUInt res;
 
   if (a->used == 0) {
      return 0;
   }
 
   /* get number of digits of the lsb we have to read */
-  i = MIN(a->used,(int)(((sizeof(unsigned long long) * CHAR_BIT) + DIGIT_BIT - 1) / DIGIT_BIT)) - 1;
+  i = MIN(a->used,(int)(((sizeof(Tcl_WideUInt) * CHAR_BIT) + DIGIT_BIT - 1) / DIGIT_BIT)) - 1;
 
   /* get most significant digit of result */
   res = DIGIT(a,i);
diff --git a/libtommath/bn_mp_mul_2.c b/libtommath/bn_mp_mul_2.c
index d22fd89..0c8c2e3 100644
--- a/libtommath/bn_mp_mul_2.c
+++ b/libtommath/bn_mp_mul_2.c
@@ -16,7 +16,7 @@
  */
 
 /* b = a*2 */
-int mp_mul_2(mp_int * a, mp_int * b)
+int mp_mul_2(const mp_int * a, mp_int * b)
 {
   int     x, res, oldused;
 
diff --git a/libtommath/bn_mp_set_long_long.c b/libtommath/bn_mp_set_long_long.c
index 3566b45..0b8be33 100644
--- a/libtommath/bn_mp_set_long_long.c
+++ b/libtommath/bn_mp_set_long_long.c
@@ -16,7 +16,7 @@
  */
 
 /* set a platform dependent unsigned long long int */
-MP_SET_XLONG(mp_set_long_long, unsigned long long)
+MP_SET_XLONG(mp_set_long_long, Tcl_WideUInt)
 #endif
 
 /* ref:         $Format:%D$ */
diff --git a/libtommath/tommath.h b/libtommath/tommath.h
index 7d92d97..a8c9e21 100644
--- a/libtommath/tommath.h
+++ b/libtommath/tommath.h
@@ -220,16 +220,16 @@ int mp_set_int(mp_int *a, unsigned long b);
 int mp_set_long(mp_int *a, unsigned long b);
 
 /* set a platform dependent unsigned long long value */
-int mp_set_long_long(mp_int *a, unsigned long long b);
+int mp_set_long_long(mp_int *a, Tcl_WideUInt b);
 
 /* get a 32-bit value */
-unsigned long mp_get_int(mp_int * a);
+unsigned long mp_get_int(const mp_int * a);
 
 /* get a platform dependent unsigned long value */
-unsigned long mp_get_long(mp_int * a);
+unsigned long mp_get_long(const mp_int * a);
 
 /* get a platform dependent unsigned long long value */
-unsigned long long mp_get_long_long(mp_int * a);
+Tcl_WideUInt mp_get_long_long(const mp_int * a);
 
 /* initialize and set a digit */
 int mp_init_set (mp_int * a, mp_digit b);
@@ -264,13 +264,13 @@ int mp_lshd(mp_int *a, int b);
 int mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d);
 
 /* b = a/2 */
-int mp_div_2(mp_int *a, mp_int *b);
+int mp_div_2(const mp_int *a, mp_int *b);
 
 /* c = a * 2**b, implemented as c = a << b */
 int mp_mul_2d(const mp_int *a, int b, mp_int *c);
 
 /* b = a*2 */
-int mp_mul_2(mp_int *a, mp_int *b);
+int mp_mul_2(const mp_int *a, mp_int *b);
 
 /* c = a mod 2**b */
 int mp_mod_2d(const mp_int *a, int b, mp_int *c);
diff --git a/unix/Makefile.in b/unix/Makefile.in
index fadc147..2f97bf5 100644
--- a/unix/Makefile.in
+++ b/unix/Makefile.in
@@ -320,7 +320,7 @@ TOMMATH_OBJS = bncore.o bn_reverse.o bn_fast_s_mp_mul_digs.o \
 	bn_mp_cnt_lsb.o bn_mp_copy.o \
 	bn_mp_count_bits.o bn_mp_div.o bn_mp_div_d.o bn_mp_div_2.o \
 	bn_mp_div_2d.o bn_mp_div_3.o \
-        bn_mp_exch.o bn_mp_expt_d.o bn_mp_expt_d_ex.o bn_mp_grow.o bn_mp_init.o \
+        bn_mp_exch.o bn_mp_expt_d.o bn_mp_expt_d_ex.o bn_mp_get_int.o bn_mp_get_long_long.o bn_mp_grow.o bn_mp_init.o \
 	bn_mp_init_copy.o bn_mp_init_multi.o bn_mp_init_set.o \
 	bn_mp_init_set_int.o bn_mp_init_size.o bn_mp_karatsuba_mul.o \
 	bn_mp_karatsuba_sqr.o \
@@ -328,7 +328,7 @@ TOMMATH_OBJS = bncore.o bn_reverse.o bn_fast_s_mp_mul_digs.o \
         bn_mp_mul_2d.o bn_mp_mul_d.o bn_mp_neg.o bn_mp_or.o \
 	bn_mp_radix_size.o bn_mp_radix_smap.o \
         bn_mp_read_radix.o bn_mp_rshd.o bn_mp_set.o bn_mp_set_int.o \
-	bn_mp_shrink.o \
+	bn_mp_set_long_long.o bn_mp_shrink.o \
 	bn_mp_sqr.o bn_mp_sqrt.o bn_mp_sub.o bn_mp_sub_d.o \
         bn_mp_to_unsigned_bin.o bn_mp_to_unsigned_bin_n.o \
 	bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_toradix_n.o \
@@ -504,6 +504,8 @@ TOMMATH_SRCS = \
 	$(TOMMATH_DIR)/bn_mp_exch.c \
 	$(TOMMATH_DIR)/bn_mp_expt_d.c \
 	$(TOMMATH_DIR)/bn_mp_expt_d_ex.c \
+	$(TOMMATH_DIR)/bn_mp_get_int.c \
+	$(TOMMATH_DIR)/bn_mp_get_long_long.c \
 	$(TOMMATH_DIR)/bn_mp_grow.c \
 	$(TOMMATH_DIR)/bn_mp_init.c \
 	$(TOMMATH_DIR)/bn_mp_init_copy.c \
@@ -528,6 +530,7 @@ TOMMATH_SRCS = \
 	$(TOMMATH_DIR)/bn_mp_rshd.c \
 	$(TOMMATH_DIR)/bn_mp_set.c \
 	$(TOMMATH_DIR)/bn_mp_set_int.c \
+	$(TOMMATH_DIR)/bn_mp_set_long_long.c \
 	$(TOMMATH_DIR)/bn_mp_shrink.c \
 	$(TOMMATH_DIR)/bn_mp_sqr.c \
 	$(TOMMATH_DIR)/bn_mp_sqrt.c \
@@ -1426,6 +1429,12 @@ bn_mp_expt_d.o: $(TOMMATH_DIR)/bn_mp_expt_d.c $(MATHHDRS)
 bn_mp_expt_d_ex.o: $(TOMMATH_DIR)/bn_mp_expt_d_ex.c $(MATHHDRS)
 	$(CC) -c $(CC_SWITCHES) $(TOMMATH_DIR)/bn_mp_expt_d_ex.c
 
+bn_mp_get_int.o: $(TOMMATH_DIR)/bn_mp_get_int.c $(MATHHDRS)
+	$(CC) -c $(CC_SWITCHES) $(TOMMATH_DIR)/bn_mp_get_int.c
+
+bn_mp_get_long_long.o: $(TOMMATH_DIR)/bn_mp_get_long_long.c $(MATHHDRS)
+	$(CC) -c $(CC_SWITCHES) $(TOMMATH_DIR)/bn_mp_get_long_long.c
+
 bn_mp_grow.o: $(TOMMATH_DIR)/bn_mp_grow.c $(MATHHDRS)
 	$(CC) -c $(CC_SWITCHES) $(TOMMATH_DIR)/bn_mp_grow.c
 
@@ -1498,6 +1507,9 @@ bn_mp_set.o: $(TOMMATH_DIR)/bn_mp_set.c $(MATHHDRS)
 bn_mp_set_int.o: $(TOMMATH_DIR)/bn_mp_set_int.c $(MATHHDRS)
 	$(CC) -c $(CC_SWITCHES) $(TOMMATH_DIR)/bn_mp_set_int.c
 
+bn_mp_set_long_long.o: $(TOMMATH_DIR)/bn_mp_set_long_long.c $(MATHHDRS)
+	$(CC) -c $(CC_SWITCHES) $(TOMMATH_DIR)/bn_mp_set_long_long.c
+
 bn_mp_shrink.o: $(TOMMATH_DIR)/bn_mp_shrink.c $(MATHHDRS)
 	$(CC) -c $(CC_SWITCHES) $(TOMMATH_DIR)/bn_mp_shrink.c
 
diff --git a/unix/tcl.spec b/unix/tcl.spec
index 868a226..265e4df 100644
--- a/unix/tcl.spec
+++ b/unix/tcl.spec
@@ -4,7 +4,7 @@
 
 Name:          tcl
 Summary:       Tcl scripting language development environment
-Version:       8.7a0
+Version:       8.7a2
 Release:       2
 License:       BSD
 Group:         Development/Languages
diff --git a/win/Makefile.in b/win/Makefile.in
index 24cb5b2..4a0f839 100644
--- a/win/Makefile.in
+++ b/win/Makefile.in
@@ -329,6 +329,8 @@ TOMMATH_OBJS = \
 	bn_mp_exch.${OBJEXT} \
 	bn_mp_expt_d.${OBJEXT} \
 	bn_mp_expt_d_ex.${OBJEXT} \
+	bn_mp_get_int.${OBJEXT} \
+	bn_mp_get_long_long.${OBJEXT} \
 	bn_mp_grow.${OBJEXT} \
 	bn_mp_init.${OBJEXT} \
 	bn_mp_init_copy.${OBJEXT} \
@@ -353,6 +355,7 @@ TOMMATH_OBJS = \
 	bn_mp_rshd.${OBJEXT} \
 	bn_mp_set.${OBJEXT} \
 	bn_mp_set_int.${OBJEXT} \
+	bn_mp_set_long_long.${OBJEXT} \
 	bn_mp_shrink.${OBJEXT} \
 	bn_mp_sqr.${OBJEXT} \
 	bn_mp_sqrt.${OBJEXT} \
diff --git a/win/makefile.vc b/win/makefile.vc
index 5566df2..ca8cc08 100644
--- a/win/makefile.vc
+++ b/win/makefile.vc
@@ -384,6 +384,8 @@ TOMMATHOBJS = \
 	$(TMP_DIR)\bn_mp_exch.obj \
 	$(TMP_DIR)\bn_mp_expt_d.obj \
 	$(TMP_DIR)\bn_mp_expt_d_ex.obj \
+	$(TMP_DIR)\bn_mp_get_int.obj \
+	$(TMP_DIR)\bn_mp_get_long_long.obj \
 	$(TMP_DIR)\bn_mp_grow.obj \
 	$(TMP_DIR)\bn_mp_init.obj \
 	$(TMP_DIR)\bn_mp_init_copy.obj \
@@ -408,6 +410,7 @@ TOMMATHOBJS = \
 	$(TMP_DIR)\bn_mp_rshd.obj \
 	$(TMP_DIR)\bn_mp_set.obj \
 	$(TMP_DIR)\bn_mp_set_int.obj \
+	$(TMP_DIR)\bn_mp_set_long_long.obj \
 	$(TMP_DIR)\bn_mp_shrink.obj \
 	$(TMP_DIR)\bn_mp_sqr.obj \
 	$(TMP_DIR)\bn_mp_sqrt.obj \
-- 
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