Fix [e6f27aa56fa51bfc1752ce768bf0d301c60bfd2c|e6f27aa56f]: Update libtommath to 1.0

161 files changed, 9439 insertions, 15484 deletions

diff --git a/.fossil-settings/ignore-glob b/.fossil-settings/ignore-glob
index 2b3ab8b..2f93505 100644
--- a/.fossil-settings/ignore-glob
+++ b/.fossil-settings/ignore-glob
@@ -19,7 +19,11 @@
 */versions.vc
 libtommath/bn.ilg
 libtommath/bn.ind
+libtommath/pretty.build
+libtommath/tommath.src
 libtommath/*.pdf
+libtommath/*.pl
+libtommath/*.sh
 libtommath/tombc/*
 libtommath/pre_gen/*
 libtommath/pics/*
diff --git a/generic/tclExecute.c b/generic/tclExecute.c
index 1cfc030..1f78ead 100644
--- a/generic/tclExecute.c
+++ b/generic/tclExecute.c
@@ -8935,7 +8935,7 @@ ExecuteExtendedBinaryMathOp(
 	}
 	Tcl_TakeBignumFromObj(NULL, valuePtr, &big1);
 	mp_init(&bigResult);
-	mp_expt_d(&big1, big2.dp[0], &bigResult);
+	mp_expt_d_ex(&big1, big2.dp[0], &bigResult, 1);
 	mp_clear(&big1);
 	mp_clear(&big2);
 	BIG_RESULT(&bigResult);
diff --git a/generic/tclStubInit.c b/generic/tclStubInit.c
index 5b7a1cd..2f1bb8b 100644
--- a/generic/tclStubInit.c
+++ b/generic/tclStubInit.c
@@ -749,6 +749,7 @@ const TclTomMathStubs tclTomMathStubs = {
     TclBNInitBignumFromLong, /* 64 */
     TclBNInitBignumFromWideInt, /* 65 */
     TclBNInitBignumFromWideUInt, /* 66 */
+    TclBN_mp_expt_d_ex, /* 67 */
 };
 
 static const TclStubHooks tclStubHooks = {
diff --git a/generic/tclTomMath.decls b/generic/tclTomMath.decls
index 610a031..74ccefc 100644
--- a/generic/tclTomMath.decls
+++ b/generic/tclTomMath.decls
@@ -90,7 +90,7 @@ declare 21 {
     int TclBN_mp_init(mp_int *a)
 }
 declare 22 {
-    int TclBN_mp_init_copy(mp_int *a, mp_int *b)
+    int TclBN_mp_init_copy(mp_int *a, const mp_int *b)
 }
 declare 23 {
     int TclBN_mp_init_multi(mp_int *a, ...)
@@ -129,7 +129,7 @@ declare 34 {
     int TclBN_mp_or(mp_int *a, mp_int *b, mp_int *c)
 }
 declare 35 {
-    int TclBN_mp_radix_size(mp_int *a, int radix, int *size)
+    int TclBN_mp_radix_size(const mp_int *a, int radix, int *size)
 }
 declare 36 {
     int TclBN_mp_read_radix(mp_int *a, const char *str, int radix)
@@ -233,6 +233,11 @@ declare 66 {
     void TclBNInitBignumFromWideUInt(mp_int *bignum, Tcl_WideUInt initVal)
 }
 
+# Added in libtommath 1.0
+declare 67 {
+    int TclBN_mp_expt_d_ex(mp_int *a, mp_digit b, mp_int *c, int fast)
+}
+
 # Local Variables:
 # mode: tcl
 # End:
diff --git a/generic/tclTomMath.h b/generic/tclTomMath.h
index dd9edaf..690cd80 100644
--- a/generic/tclTomMath.h
+++ b/generic/tclTomMath.h
@@ -10,11 +10,12 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://math.libtomcrypt.com
  */
 #ifndef BN_H_
 #define BN_H_
 
+#include "tclInt.h"
 #include "tclTomMathDecls.h"
 #ifndef MODULE_SCOPE
 #define MODULE_SCOPE extern
@@ -22,33 +23,15 @@
 
 
 
-#ifndef MIN
-#   define MIN(x,y) ((x)<(y)?(x):(y))
-#endif
-
-#ifndef MAX
-#   define MAX(x,y) ((x)>(y)?(x):(y))
-#endif
-
 #ifdef __cplusplus
 extern "C" {
-
-/* C++ compilers don't like assigning void * to mp_digit * */
-#define  OPT_CAST(x)  (x *)
-
-#else
-
-/* C on the other hand doesn't care */
-#define  OPT_CAST(x)
-
 #endif
 
-
 /* detect 64-bit mode if possible */
-#if defined(NEVER)  /* 128-bit ints fail in too many places */
-#   if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT))
-#	define MP_64BIT
-#   endif
+#if defined(NEVER) /* 128-bit ints fail in too many places */
+   #if !(defined(MP_32BIT) || defined(MP_16BIT) || defined(MP_8BIT))
+      #define MP_64BIT
+   #endif
 #endif
 
 /* some default configurations.
@@ -61,83 +44,89 @@ extern "C" {
  */
 #ifdef MP_8BIT
 #ifndef MP_DIGIT_DECLARED
-   typedef unsigned char      mp_digit;
+   typedef uint8_t              mp_digit;
 #define MP_DIGIT_DECLARED
 #endif
-   typedef unsigned short     mp_word;
+   typedef uint16_t             mp_word;
+#define MP_SIZEOF_MP_DIGIT      1
+#ifdef DIGIT_BIT
+#error You must not define DIGIT_BIT when using MP_8BIT
+#endif
 #elif defined(MP_16BIT)
 #ifndef MP_DIGIT_DECLARED
-   typedef unsigned short     mp_digit;
+   typedef uint16_t             mp_digit;
 #define MP_DIGIT_DECLARED
 #endif
-   typedef unsigned long      mp_word;
+   typedef uint32_t             mp_word;
+#define MP_SIZEOF_MP_DIGIT      2
+#ifdef DIGIT_BIT
+#error You must not define DIGIT_BIT when using MP_16BIT
+#endif
 #elif defined(MP_64BIT)
    /* for GCC only on supported platforms */
 #ifndef CRYPT
-   typedef unsigned long long ulong64;
-   typedef signed long long   long64;
+   typedef unsigned long long   ulong64;
+   typedef signed long long     long64;
 #endif
 
 #ifndef MP_DIGIT_DECLARED
-   typedef unsigned long      mp_digit;
+   typedef ulong64 mp_digit;
 #define MP_DIGIT_DECLARED
 #endif
-   typedef unsigned long      mp_word __attribute__ ((mode(TI)));
+#if defined(_WIN32)
+   typedef unsigned __int128    mp_word;
+#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 */
+   typedef uint128_t            mp_word;
+#endif
 
-#  define DIGIT_BIT          60
+   #define DIGIT_BIT            60
 #else
    /* this is the default case, 28-bit digits */
-   
+
    /* this is to make porting into LibTomCrypt easier :-) */
 #ifndef CRYPT
-#  if defined(_MSC_VER) || defined(__BORLANDC__)
-      typedef unsigned __int64   ulong64;
-      typedef signed __int64     long64;
-#  else
-      typedef unsigned long long ulong64;
-      typedef signed long long   long64;
-#  endif
+   typedef unsigned long long   ulong64;
+   typedef signed long long     long64;
 #endif
 
 #ifndef MP_DIGIT_DECLARED
-   typedef unsigned int      mp_digit;
+   typedef uint32_t             mp_digit;
 #define MP_DIGIT_DECLARED
 #endif
-   typedef ulong64            mp_word;
+   typedef ulong64              mp_word;
 
-#ifdef MP_31BIT   
+#ifdef MP_31BIT
    /* this is an extension that uses 31-bit digits */
-#  define DIGIT_BIT          31
+   #define DIGIT_BIT            31
 #else
    /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */
-#  define DIGIT_BIT          28
-#  define MP_28BIT
-#endif   
-#endif
-
-/* define heap macros */
-#if 0 /* these are macros in tclTomMathDecls.h */
-#ifndef CRYPT
-   /* default to libc stuff */
-#  ifndef XMALLOC
-#     define XMALLOC  malloc
-#     define XFREE    free
-#     define XREALLOC realloc
-#     define XCALLOC  calloc
-#  else
-      /* prototypes for our heap functions */
-      extern void *XMALLOC(size_t n);
-      extern void *XREALLOC(void *p, size_t n);
-      extern void *XCALLOC(size_t n, size_t s);
-      extern void XFREE(void *p);
-#  endif
+   #define DIGIT_BIT            28
+   #define MP_28BIT
 #endif
 #endif
 
-
 /* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
 #ifndef DIGIT_BIT
-#   define DIGIT_BIT     ((int)((CHAR_BIT * sizeof(mp_digit) - 1)))  /* bits per digit */
+   #define DIGIT_BIT     (((CHAR_BIT * MP_SIZEOF_MP_DIGIT) - 1))  /* bits per digit */
+   typedef uint_least32_t mp_min_u32;
+#else
+   typedef mp_digit mp_min_u32;
+#endif
+
+/* platforms that can use a better rand function */
+#if defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__DragonFly__)
+    #define MP_USE_ALT_RAND 1
+#endif
+
+/* use arc4random on platforms that support it */
+#ifdef MP_USE_ALT_RAND
+    #define MP_GEN_RANDOM()    arc4random()
+#else
+    #define MP_GEN_RANDOM()    rand()
 #endif
 
 #define MP_DIGIT_BIT     DIGIT_BIT
@@ -180,15 +169,15 @@ MODULE_SCOPE int KARATSUBA_MUL_CUTOFF,
 
 /* default precision */
 #ifndef MP_PREC
-#  ifndef MP_LOW_MEM
-#     define MP_PREC                 32     /* default digits of precision */
-#  else
-#     define MP_PREC                 8      /* default digits of precision */
-#  endif
+   #ifndef MP_LOW_MEM
+      #define MP_PREC                 32     /* default digits of precision */
+   #else
+      #define MP_PREC                 8      /* default digits of precision */
+   #endif
 #endif
 
 /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
-#define MP_WARRAY               (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
+#define MP_WARRAY               (1 << (((sizeof(mp_word) * CHAR_BIT) - (2 * DIGIT_BIT)) + 1))
 
 /* the infamous mp_int structure */
 #ifndef MP_INT_DECLARED
@@ -209,9 +198,7 @@ typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
 #define SIGN(m)    ((m)->sign)
 
 /* error code to char* string */
-/*
-char *mp_error_to_string(int code);
-*/
+const char *mp_error_to_string(int code);
 
 /* ---> init and deinit bignum functions <--- */
 /* init a bignum */
@@ -256,8 +243,9 @@ 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] & 1) == 0)) ? MP_YES : MP_NO)
-#define mp_isodd(a)  (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? 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)
 
 /* set to zero */
 /*
@@ -274,9 +262,25 @@ void mp_set(mp_int *a, mp_digit b);
 int mp_set_int(mp_int *a, unsigned long b);
 */
 
+/* set a platform dependent unsigned long value */
+/*
+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);
+*/
+
 /* get a 32-bit value */
 unsigned long mp_get_int(mp_int * a);
 
+/* get a platform dependent unsigned long value */
+unsigned long mp_get_long(mp_int * a);
+
+/* get a platform dependent unsigned long long value */
+unsigned long long mp_get_long_long(mp_int * a);
+
 /* initialize and set a digit */
 /*
 int mp_init_set (mp_int * a, mp_digit b);
@@ -294,7 +298,7 @@ int mp_copy(const mp_int *a, mp_int *b);
 
 /* inits and copies, a = b */
 /*
-int mp_init_copy(mp_int *a, mp_int *b);
+int mp_init_copy(mp_int *a, const mp_int *b);
 */
 
 /* trim unused digits */
@@ -302,6 +306,16 @@ int mp_init_copy(mp_int *a, mp_int *b);
 void mp_clamp(mp_int *a);
 */
 
+/* import binary data */
+/*
+int mp_import(mp_int* rop, size_t count, int order, size_t size, int endian, size_t nails, const void* op);
+*/
+
+/* export binary data */
+/*
+int mp_export(void* rop, size_t* countp, int order, size_t size, int endian, size_t nails, mp_int* op);
+*/
+
 /* ---> digit manipulation <--- */
 
 /* right shift by "b" digits */
@@ -314,7 +328,7 @@ void mp_rshd(mp_int *a, int b);
 int mp_lshd(mp_int *a, int b);
 */
 
-/* c = a / 2**b */
+/* c = a / 2**b, implemented as c = a >> b */
 /*
 int mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d);
 */
@@ -324,7 +338,7 @@ int mp_div_2d(const mp_int *a, int b, mp_int *c, mp_int *d);
 int mp_div_2(mp_int *a, mp_int *b);
 */
 
-/* c = a * 2**b */
+/* c = a * 2**b, implemented as c = a << b */
 /*
 int mp_mul_2d(const mp_int *a, int b, mp_int *c);
 */
@@ -334,7 +348,7 @@ int mp_mul_2d(const mp_int *a, int b, mp_int *c);
 int mp_mul_2(mp_int *a, mp_int *b);
 */
 
-/* c = a mod 2**d */
+/* c = a mod 2**b */
 /*
 int mp_mod_2d(const mp_int *a, int b, mp_int *c);
 */
@@ -460,6 +474,9 @@ int mp_div_3(mp_int *a, mp_int *c, mp_digit *d);
 /*
 int mp_expt_d(mp_int *a, mp_digit b, mp_int *c);
 */
+/*
+int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast);
+*/
 
 /* c = a mod b, 0 <= c < b  */
 /*
@@ -515,12 +532,20 @@ int mp_lcm(mp_int *a, mp_int *b, mp_int *c);
 /*
 int mp_n_root(mp_int *a, mp_digit b, mp_int *c);
 */
+/*
+int mp_n_root_ex (mp_int * a, mp_digit b, mp_int * c, int fast);
+*/
 
 /* special sqrt algo */
 /*
 int mp_sqrt(mp_int *arg, mp_int *ret);
 */
 
+/* special sqrt (mod prime) */
+/*
+int mp_sqrtmod_prime(mp_int *arg, mp_int *prime, mp_int *ret);
+*/
+
 /* is number a square? */
 /*
 int mp_is_square(mp_int *arg, int *ret);
@@ -623,7 +648,7 @@ int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
 
 /* table of first PRIME_SIZE primes */
 #if defined(BUILD_tcl) || !defined(_WIN32)
-MODULE_SCOPE const mp_digit ltm_prime_tab[];
+MODULE_SCOPE const mp_digit ltm_prime_tab[PRIME_SIZE];
 #endif
 
 /* result=1 if a is divisible by one of the first PRIME_SIZE primes */
@@ -646,7 +671,7 @@ int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result);
 */
 
 /* This gives [for a given bit size] the number of trials required
- * such that Miller-Rabin gives a prob of failure lower than 2^-96 
+ * such that Miller-Rabin gives a prob of failure lower than 2^-96
  */
 /*
 int mp_prime_rabin_miller_trials(int size);
@@ -673,7 +698,7 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style);
 */
 
 /* makes a truly random prime of a given size (bytes),
- * call with bbs = 1 if you want it to be congruent to 3 mod 4 
+ * call with bbs = 1 if you want it to be congruent to 3 mod 4
  *
  * 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
@@ -686,10 +711,9 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style);
 /* 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
@@ -742,15 +766,17 @@ int mp_toradix(mp_int *a, char *str, int radix);
 int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen);
 */
 /*
-int mp_radix_size(mp_int *a, int radix, int *size);
+int mp_radix_size(const mp_int *a, int radix, int *size);
 */
 
+#ifndef LTM_NO_FILE
 /*
 int mp_fread(mp_int *a, int radix, FILE *stream);
 */
 /*
 int mp_fwrite(mp_int *a, int radix, FILE *stream);
 */
+#endif
 
 #define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
 #define mp_raw_size(mp)           mp_signed_bin_size(mp)
@@ -764,69 +790,14 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream);
 #define mp_todecimal(M, S) mp_toradix((M), (S), 10)
 #define mp_tohex(M, S)     mp_toradix((M), (S), 16)
 
-/* lowlevel functions, do not call! */
-/*
-int s_mp_add(mp_int *a, mp_int *b, mp_int *c);
-*/
-/*
-int s_mp_sub(mp_int *a, mp_int *b, mp_int *c);
-*/
-#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
-/*
-int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
-*/
-/*
-int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
-*/
-/*
-int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
-*/
-/*
-int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
-*/
-/*
-int fast_s_mp_sqr(mp_int *a, mp_int *b);
-*/
-/*
-int s_mp_sqr(mp_int *a, mp_int *b);
-*/
-/*
-int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c);
-*/
-/*
-int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c);
-*/
-/*
-int mp_karatsuba_sqr(mp_int *a, mp_int *b);
-*/
-/*
-int mp_toom_sqr(mp_int *a, mp_int *b);
-*/
-/*
-int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c);
-*/
-/*
-int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c);
-*/
-/*
-int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
-*/
-/*
-int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode);
-*/
-/*
-int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode);
-*/
-/*
-void bn_reverse(unsigned char *s, int len);
-*/
-
-#if defined(BUILD_tcl) || !defined(_WIN32)
-MODULE_SCOPE const char *mp_s_rmap;
-#endif
-
 #ifdef __cplusplus
-}
+   }
 #endif
 
 #endif
+
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
+
diff --git a/generic/tclTomMathDecls.h b/generic/tclTomMathDecls.h
index 2ce9d5a..209c486 100644
--- a/generic/tclTomMathDecls.h
+++ b/generic/tclTomMathDecls.h
@@ -73,6 +73,7 @@
 #define mp_div_d TclBN_mp_div_d
 #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_grow TclBN_mp_grow
 #define mp_init TclBN_mp_init
 #define mp_init_copy TclBN_mp_init_copy
@@ -190,7 +191,7 @@ EXTERN int		TclBN_mp_grow(mp_int *a, int size);
 /* 21 */
 EXTERN int		TclBN_mp_init(mp_int *a);
 /* 22 */
-EXTERN int		TclBN_mp_init_copy(mp_int *a, mp_int *b);
+EXTERN int		TclBN_mp_init_copy(mp_int *a, const mp_int *b);
 /* 23 */
 EXTERN int		TclBN_mp_init_multi(mp_int *a, ...);
 /* 24 */
@@ -216,7 +217,8 @@ EXTERN int		TclBN_mp_neg(const mp_int *a, mp_int *b);
 /* 34 */
 EXTERN int		TclBN_mp_or(mp_int *a, mp_int *b, mp_int *c);
 /* 35 */
-EXTERN int		TclBN_mp_radix_size(mp_int *a, int radix, int *size);
+EXTERN int		TclBN_mp_radix_size(const mp_int *a, int radix,
+				int *size);
 /* 36 */
 EXTERN int		TclBN_mp_read_radix(mp_int *a, const char *str,
 				int radix);
@@ -287,6 +289,9 @@ EXTERN void		TclBNInitBignumFromWideInt(mp_int *bignum,
 /* 66 */
 EXTERN void		TclBNInitBignumFromWideUInt(mp_int *bignum,
 				Tcl_WideUInt initVal);
+/* 67 */
+EXTERN int		TclBN_mp_expt_d_ex(mp_int *a, mp_digit b, mp_int *c,
+				int fast);
 
 typedef struct TclTomMathStubs {
     int magic;
@@ -314,7 +319,7 @@ typedef struct TclTomMathStubs {
     int (*tclBN_mp_expt_d) (mp_int *a, mp_digit b, mp_int *c); /* 19 */
     int (*tclBN_mp_grow) (mp_int *a, int size); /* 20 */
     int (*tclBN_mp_init) (mp_int *a); /* 21 */
-    int (*tclBN_mp_init_copy) (mp_int *a, mp_int *b); /* 22 */
+    int (*tclBN_mp_init_copy) (mp_int *a, const mp_int *b); /* 22 */
     int (*tclBN_mp_init_multi) (mp_int *a, ...); /* 23 */
     int (*tclBN_mp_init_set) (mp_int *a, mp_digit b); /* 24 */
     int (*tclBN_mp_init_size) (mp_int *a, int size); /* 25 */
@@ -327,7 +332,7 @@ typedef struct TclTomMathStubs {
     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 */
-    int (*tclBN_mp_radix_size) (mp_int *a, int radix, int *size); /* 35 */
+    int (*tclBN_mp_radix_size) (const mp_int *a, int radix, int *size); /* 35 */
     int (*tclBN_mp_read_radix) (mp_int *a, const char *str, int radix); /* 36 */
     void (*tclBN_mp_rshd) (mp_int *a, int shift); /* 37 */
     int (*tclBN_mp_shrink) (mp_int *a); /* 38 */
@@ -359,6 +364,7 @@ typedef struct TclTomMathStubs {
     void (*tclBNInitBignumFromLong) (mp_int *bignum, long initVal); /* 64 */
     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 */
 } TclTomMathStubs;
 
 extern const TclTomMathStubs *tclTomMathStubsPtr;
@@ -507,6 +513,8 @@ extern const TclTomMathStubs *tclTomMathStubsPtr;
 	(tclTomMathStubsPtr->tclBNInitBignumFromWideInt) /* 65 */
 #define TclBNInitBignumFromWideUInt \
 	(tclTomMathStubsPtr->tclBNInitBignumFromWideUInt) /* 66 */
+#define TclBN_mp_expt_d_ex \
+	(tclTomMathStubsPtr->tclBN_mp_expt_d_ex) /* 67 */
 
 #endif /* defined(USE_TCL_STUBS) */
 
diff --git a/libtommath/LICENSE b/libtommath/LICENSE
index 5baa792..a75014d 100644
--- a/libtommath/LICENSE
+++ b/libtommath/LICENSE
@@ -1,4 +1,29 @@
-LibTomMath is hereby released into the Public Domain.  
+LibTomMath is licensed under DUAL licensing terms.
 
--- Tom St Denis
+Choose and use the license of your needs.
 
+[LICENSE #1]
+
+LibTomMath is public domain.  As should all quality software be.
+
+Tom St Denis
+
+[/LICENSE #1]
+
+[LICENSE #2]
+
+            DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
+                    Version 2, December 2004
+
+ Copyright (C) 2004 Sam Hocevar <sam@hocevar.net>
+
+ Everyone is permitted to copy and distribute verbatim or modified
+ copies of this license document, and changing it is allowed as long
+ as the name is changed.
+
+            DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE
+   TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
+
+  0. You just DO WHAT THE FUCK YOU WANT TO.
+
+[/LICENSE #2]
diff --git a/libtommath/bn.tex b/libtommath/bn.tex
deleted file mode 100644
index e8eb994..0000000
--- a/libtommath/bn.tex
+++ /dev/null
@@ -1,1835 +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{LibTomMath User Manual \\ v0.39}
-\author{Tom St Denis \\ tomstdenis@iahu.ca}
-\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{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.  
-
-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.
-
-\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}
-\begin{alltt}
-int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
-\end{alltt}
-This computes $c = a^b$ using a simple binary left-to-right algorithm.  It is faster than repeated multiplications by 
-$a$ for all values of $b$ greater than three.  
-
-\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 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_error.c b/libtommath/bn_error.c
index 6393bb0..3abf1a7 100644
--- a/libtommath/bn_error.c
+++ b/libtommath/bn_error.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_ERROR_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,12 +12,12 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 static const struct {
      int code;
-     char *msg;
+     const char *msg;
 } msgs[] = {
      { MP_OKAY, "Successful" },
      { MP_MEM,  "Out of heap" },
@@ -25,7 +25,7 @@ static const struct {
 };
 
 /* return a char * string for a given code */
-char *mp_error_to_string(int code)
+const char *mp_error_to_string(int code)
 {
    int x;
 
@@ -41,3 +41,7 @@ char *mp_error_to_string(int code)
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_fast_mp_invmod.c b/libtommath/bn_fast_mp_invmod.c
index fafd9dc..aa41098 100644
--- a/libtommath/bn_fast_mp_invmod.c
+++ b/libtommath/bn_fast_mp_invmod.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_FAST_MP_INVMOD_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* computes the modular inverse via binary extended euclidean algorithm, 
@@ -27,7 +27,7 @@ int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
   int     res, neg;
 
   /* 2. [modified] b must be odd   */
-  if (mp_iseven (b) == 1) {
+  if (mp_iseven (b) == MP_YES) {
     return MP_VAL;
   }
 
@@ -57,13 +57,13 @@ int fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
 
 top:
   /* 4.  while u is even do */
-  while (mp_iseven (&u) == 1) {
+  while (mp_iseven (&u) == MP_YES) {
     /* 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 (mp_isodd (&B) == MP_YES) {
       if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
         goto LBL_ERR;
       }
@@ -75,13 +75,13 @@ top:
   }
 
   /* 5.  while v is even do */
-  while (mp_iseven (&v) == 1) {
+  while (mp_iseven (&v) == MP_YES) {
     /* 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) {
+    if (mp_isodd (&D) == MP_YES) {
       /* D = (D-x)/2 */
       if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
         goto LBL_ERR;
@@ -115,7 +115,7 @@ top:
   }
 
   /* if not zero goto step 4 */
-  if (mp_iszero (&u) == 0) {
+  if (mp_iszero (&u) == MP_NO) {
     goto top;
   }
 
@@ -142,3 +142,7 @@ LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
   return res;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_fast_mp_montgomery_reduce.c b/libtommath/bn_fast_mp_montgomery_reduce.c
index e941dc2..a63839d 100644
--- a/libtommath/bn_fast_mp_montgomery_reduce.c
+++ b/libtommath/bn_fast_mp_montgomery_reduce.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* computes xR**-1 == x (mod N) via Montgomery Reduction
@@ -32,7 +32,7 @@ int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
   olduse = x->used;
 
   /* grow a as required */
-  if (x->alloc < n->used + 1) {
+  if (x->alloc < (n->used + 1)) {
     if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
       return res;
     }
@@ -42,8 +42,8 @@ int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
    * an array of double precision words W[...]
    */
   {
-    register mp_word *_W;
-    register mp_digit *tmpx;
+    mp_word *_W;
+    mp_digit *tmpx;
 
     /* alias for the W[] array */
     _W   = W;
@@ -57,7 +57,7 @@ int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
     }
 
     /* zero the high words of W[a->used..m->used*2] */
-    for (; ix < n->used * 2 + 1; ix++) {
+    for (; ix < ((n->used * 2) + 1); ix++) {
       *_W++ = 0;
     }
   }
@@ -72,7 +72,7 @@ int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
      * 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;
+    mp_digit mu;
     mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
 
     /* a = a + mu * m * b**i
@@ -90,9 +90,9 @@ int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
      * first m->used words of W[] have the carries fixed
      */
     {
-      register int iy;
-      register mp_digit *tmpn;
-      register mp_word *_W;
+      int iy;
+      mp_digit *tmpn;
+      mp_word *_W;
 
       /* alias for the digits of the modulus */
       tmpn = n->dp;
@@ -115,8 +115,8 @@ int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
    * significant digits we zeroed].
    */
   {
-    register mp_digit *tmpx;
-    register mp_word *_W, *_W1;
+    mp_digit *tmpx;
+    mp_word *_W, *_W1;
 
     /* nox fix rest of carries */
 
@@ -126,7 +126,7 @@ int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
     /* alias for next word, where the carry goes */
     _W = W + ++ix;
 
-    for (; ix <= n->used * 2 + 1; ix++) {
+    for (; ix <= ((n->used * 2) + 1); ix++) {
       *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
     }
 
@@ -143,7 +143,7 @@ int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
     /* alias for shifted double precision result */
     _W = W + n->used;
 
-    for (ix = 0; ix < n->used + 1; ix++) {
+    for (ix = 0; ix < (n->used + 1); ix++) {
       *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
     }
 
@@ -166,3 +166,7 @@ int fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_fast_s_mp_mul_digs.c b/libtommath/bn_fast_s_mp_mul_digs.c
index ab157b9..acd13b4 100644
--- a/libtommath/bn_fast_s_mp_mul_digs.c
+++ b/libtommath/bn_fast_s_mp_mul_digs.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_FAST_S_MP_MUL_DIGS_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* Fast (comba) multiplier
@@ -35,7 +35,7 @@ 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;
+  mp_word  _W;
 
   /* grow the destination as required */
   if (c->alloc < digs) {
@@ -78,16 +78,16 @@ int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
 
       /* make next carry */
       _W = _W >> ((mp_word)DIGIT_BIT);
- }
+  }
 
   /* setup dest */
   olduse  = c->used;
   c->used = pa;
 
   {
-    register mp_digit *tmpc;
+    mp_digit *tmpc;
     tmpc = c->dp;
-    for (ix = 0; ix < pa+1; ix++) {
+    for (ix = 0; ix < (pa + 1); ix++) {
       /* now extract the previous digit [below the carry] */
       *tmpc++ = W[ix];
     }
@@ -101,3 +101,7 @@ int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_fast_s_mp_mul_high_digs.c b/libtommath/bn_fast_s_mp_mul_high_digs.c
index ec9f58a..b96cf60 100644
--- a/libtommath/bn_fast_s_mp_mul_high_digs.c
+++ b/libtommath/bn_fast_s_mp_mul_high_digs.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* this is a modified version of fast_s_mul_digs that only produces
@@ -75,7 +75,7 @@ int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
   c->used = pa;
 
   {
-    register mp_digit *tmpc;
+    mp_digit *tmpc;
 
     tmpc = c->dp + digs;
     for (ix = digs; ix < pa; ix++) {
@@ -92,3 +92,7 @@ int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_fast_s_mp_sqr.c b/libtommath/bn_fast_s_mp_sqr.c
index 1abf24b..775c76f 100644
--- a/libtommath/bn_fast_s_mp_sqr.c
+++ b/libtommath/bn_fast_s_mp_sqr.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_FAST_S_MP_SQR_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* the jist of squaring...
@@ -66,7 +66,7 @@ int fast_s_mp_sqr (mp_int * a, mp_int * b)
        * 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);
+      iy = MIN(iy, ((ty-tx)+1)>>1);
 
       /* execute loop */
       for (iz = 0; iz < iy; iz++) {
@@ -108,3 +108,7 @@ int fast_s_mp_sqr (mp_int * a, mp_int * b)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_2expt.c b/libtommath/bn_mp_2expt.c
index a32572d..2845814 100644
--- a/libtommath/bn_mp_2expt.c
+++ b/libtommath/bn_mp_2expt.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_2EXPT_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* computes a = 2**b 
@@ -29,12 +29,12 @@ mp_2expt (mp_int * a, int b)
   mp_zero (a);
 
   /* grow a to accomodate the single bit */
-  if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
+  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;
+  a->used = (b / DIGIT_BIT) + 1;
 
   /* put the single bit in its place */
   a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
@@ -42,3 +42,7 @@ mp_2expt (mp_int * a, int b)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_abs.c b/libtommath/bn_mp_abs.c
index dc51884..cc9c3db 100644
--- a/libtommath/bn_mp_abs.c
+++ b/libtommath/bn_mp_abs.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_ABS_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* b = |a| 
@@ -37,3 +37,7 @@ mp_abs (mp_int * a, mp_int * b)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_add.c b/libtommath/bn_mp_add.c
index d9b8fa5..236fc75 100644
--- a/libtommath/bn_mp_add.c
+++ b/libtommath/bn_mp_add.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_ADD_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* high level addition (handles signs) */
@@ -47,3 +47,7 @@ int mp_add (mp_int * a, mp_int * b, mp_int * c)
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_add_d.c b/libtommath/bn_mp_add_d.c
index aec8fc8..4d4e1df 100644
--- a/libtommath/bn_mp_add_d.c
+++ b/libtommath/bn_mp_add_d.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_ADD_D_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* single digit addition */
@@ -23,14 +23,14 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c)
   mp_digit *tmpa, *tmpc, mu;
 
   /* grow c as required */
-  if (c->alloc < a->used + 1) {
+  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)) {
+  if ((a->sign == MP_NEG) && ((a->used > 1) || (a->dp[0] >= b))) {
      /* temporarily fix sign of a */
      a->sign = MP_ZPOS;
 
@@ -108,5 +108,5 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c)
 #endif
 
 /* $Source$ */
-/* $Revision: 0.41 $ */
-/* $Date: 2007-04-18 09:58:18 +0000 $ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_addmod.c b/libtommath/bn_mp_addmod.c
index bff193f..825c928 100644
--- a/libtommath/bn_mp_addmod.c
+++ b/libtommath/bn_mp_addmod.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_ADDMOD_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* d = a + b (mod c) */
@@ -35,3 +35,7 @@ mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
   return res;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_and.c b/libtommath/bn_mp_and.c
index 02bef18..3b6b03e 100644
--- a/libtommath/bn_mp_and.c
+++ b/libtommath/bn_mp_and.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_AND_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* AND two ints together */
@@ -51,3 +51,7 @@ mp_and (mp_int * a, mp_int * b, mp_int * c)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_clamp.c b/libtommath/bn_mp_clamp.c
index 74887bb..d4fb70d 100644
--- a/libtommath/bn_mp_clamp.c
+++ b/libtommath/bn_mp_clamp.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_CLAMP_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* trim unused digits 
@@ -28,7 +28,7 @@ mp_clamp (mp_int * a)
   /* decrease used while the most significant digit is
    * zero.
    */
-  while (a->used > 0 && a->dp[a->used - 1] == 0) {
+  while ((a->used > 0) && (a->dp[a->used - 1] == 0)) {
     --(a->used);
   }
 
@@ -38,3 +38,7 @@ mp_clamp (mp_int * a)
   }
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_clear.c b/libtommath/bn_mp_clear.c
index bd07e76..17ef9d5 100644
--- a/libtommath/bn_mp_clear.c
+++ b/libtommath/bn_mp_clear.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_CLEAR_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* clear one (frees)  */
@@ -38,3 +38,7 @@ mp_clear (mp_int * a)
   }
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_clear_multi.c b/libtommath/bn_mp_clear_multi.c
index c3ad7a8..441a200 100644
--- a/libtommath/bn_mp_clear_multi.c
+++ b/libtommath/bn_mp_clear_multi.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_CLEAR_MULTI_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 #include <stdarg.h>
 
@@ -28,3 +28,7 @@ void mp_clear_multi(mp_int *mp, ...)
     va_end(args);
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_cmp.c b/libtommath/bn_mp_cmp.c
index 943249d..15179ca 100644
--- a/libtommath/bn_mp_cmp.c
+++ b/libtommath/bn_mp_cmp.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_CMP_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* compare two ints (signed)*/
@@ -37,3 +37,7 @@ mp_cmp (const mp_int * a, const mp_int * b)
   }
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_cmp_d.c b/libtommath/bn_mp_cmp_d.c
index ecec091..0c9fc86 100644
--- a/libtommath/bn_mp_cmp_d.c
+++ b/libtommath/bn_mp_cmp_d.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_CMP_D_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* compare a digit */
@@ -38,3 +38,7 @@ int mp_cmp_d(const mp_int * a, mp_digit b)
   }
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_cmp_mag.c b/libtommath/bn_mp_cmp_mag.c
index b23a191..a537608 100644
--- a/libtommath/bn_mp_cmp_mag.c
+++ b/libtommath/bn_mp_cmp_mag.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_CMP_MAG_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* compare maginitude of two ints (unsigned) */
@@ -49,3 +49,7 @@ int mp_cmp_mag (const mp_int * a, const mp_int * b)
   return MP_EQ;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_cnt_lsb.c b/libtommath/bn_mp_cnt_lsb.c
index f205e8c..b638dc4 100644
--- a/libtommath/bn_mp_cnt_lsb.c
+++ b/libtommath/bn_mp_cnt_lsb.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_CNT_LSB_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 static const int lnz[16] = { 
@@ -26,12 +26,12 @@ int mp_cnt_lsb(const mp_int *a)
    mp_digit q, qq;
 
    /* easy out */
-   if (mp_iszero(a) == 1) {
+   if (mp_iszero(a) == MP_YES) {
       return 0;
    }
 
    /* scan lower digits until non-zero */
-   for (x = 0; x < a->used && a->dp[x] == 0; x++);
+   for (x = 0; (x < a->used) && (a->dp[x] == 0); x++) {}
    q = a->dp[x];
    x *= DIGIT_BIT;
 
@@ -47,3 +47,7 @@ int mp_cnt_lsb(const mp_int *a)
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_copy.c b/libtommath/bn_mp_copy.c
index ffbc0d4..c15f961 100644
--- a/libtommath/bn_mp_copy.c
+++ b/libtommath/bn_mp_copy.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_COPY_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* copy, b = a */
@@ -35,7 +35,7 @@ mp_copy (const mp_int * a, mp_int * b)
 
   /* zero b and copy the parameters over */
   {
-    register mp_digit *tmpa, *tmpb;
+    mp_digit *tmpa, *tmpb;
 
     /* pointer aliases */
 
@@ -62,3 +62,7 @@ mp_copy (const mp_int * a, mp_int * b)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_count_bits.c b/libtommath/bn_mp_count_bits.c
index 00d364e..47aa569 100644
--- a/libtommath/bn_mp_count_bits.c
+++ b/libtommath/bn_mp_count_bits.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_COUNT_BITS_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* returns the number of bits in an int */
@@ -39,3 +39,7 @@ mp_count_bits (const mp_int * a)
   return r;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_div.c b/libtommath/bn_mp_div.c
index de4ca04..3ca5d7f 100644
--- a/libtommath/bn_mp_div.c
+++ b/libtommath/bn_mp_div.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_DIV_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 #ifdef BN_MP_DIV_SMALL
@@ -24,7 +24,7 @@ int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
    int    res, n, n2;
 
   /* is divisor zero ? */
-  if (mp_iszero (b) == 1) {
+  if (mp_iszero (b) == MP_YES) {
     return MP_VAL;
   }
 
@@ -40,9 +40,9 @@ int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
     }
     return res;
   }
-	
+
   /* init our temps */
-  if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
+  if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL)) != MP_OKAY) {
      return res;
   }
 
@@ -50,7 +50,7 @@ int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
   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_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;
@@ -71,7 +71,7 @@ int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
 
   /* now q == quotient and ta == remainder */
   n  = a->sign;
-  n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
+  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;
@@ -87,17 +87,17 @@ LBL_ERR:
 
 #else
 
-/* integer signed division. 
+/* 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 
+ * 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 
+ * 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)
@@ -106,7 +106,7 @@ int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
   int     res, n, t, i, norm, neg;
 
   /* is divisor zero ? */
-  if (mp_iszero (b) == 1) {
+  if (mp_iszero (b) == MP_YES) {
     return MP_VAL;
   }
 
@@ -187,51 +187,52 @@ int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
       continue;
     }
 
-    /* step 3.1 if xi == yt then set q{i-t-1} to b-1, 
+    /* 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);
+      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)
+      if (tmp > (mp_word) MP_MASK) {
         tmp = MP_MASK;
-      q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (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; 
+    /* 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;
+    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;
+      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[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) {
+      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[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) {
+    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) {
+    if ((res = mp_lshd (&t1, (i - t) - 1)) != MP_OKAY) {
       goto LBL_Y;
     }
 
@@ -244,23 +245,23 @@ int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
       if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
         goto LBL_Y;
       }
-      if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
+      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;
+      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] 
+  /* 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;
+  x.sign = (x.used == 0) ? MP_ZPOS : a->sign;
 
   if (c != NULL) {
     mp_clamp (&q);
@@ -269,7 +270,9 @@ int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
   }
 
   if (d != NULL) {
-    mp_div_2d (&x, norm, &x, NULL);
+    if ((res = mp_div_2d (&x, norm, &x, NULL)) != MP_OKAY) {
+      goto LBL_Y;
+    }
     mp_exch (&x, d);
   }
 
@@ -286,3 +289,7 @@ LBL_Q:mp_clear (&q);
 #endif
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_div_2.c b/libtommath/bn_mp_div_2.c
index 186a959..d2a213f 100644
--- a/libtommath/bn_mp_div_2.c
+++ b/libtommath/bn_mp_div_2.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_DIV_2_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* b = a/2 */
@@ -30,7 +30,7 @@ int mp_div_2(mp_int * a, mp_int * b)
   oldused = b->used;
   b->used = a->used;
   {
-    register mp_digit r, rr, *tmpa, *tmpb;
+    mp_digit r, rr, *tmpa, *tmpb;
 
     /* source alias */
     tmpa = a->dp + b->used - 1;
@@ -62,3 +62,7 @@ int mp_div_2(mp_int * a, mp_int * b)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_div_2d.c b/libtommath/bn_mp_div_2d.c
index d7b7e05..49d7479 100644
--- a/libtommath/bn_mp_div_2d.c
+++ b/libtommath/bn_mp_div_2d.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_DIV_2D_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* shift right by a certain bit count (store quotient in c, optional remainder in d) */
@@ -58,7 +58,7 @@ int mp_div_2d (const mp_int * a, int b, mp_int * c, mp_int * d)
   /* shift any bit count < DIGIT_BIT */
   D = (mp_digit) (b % DIGIT_BIT);
   if (D != 0) {
-    register mp_digit *tmpc, mask, shift;
+    mp_digit *tmpc, mask, shift;
 
     /* mask */
     mask = (((mp_digit)1) << D) - 1;
@@ -91,3 +91,7 @@ int mp_div_2d (const mp_int * a, int b, mp_int * c, mp_int * d)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_div_3.c b/libtommath/bn_mp_div_3.c
index 79a9816..c2b76fb 100644
--- a/libtommath/bn_mp_div_3.c
+++ b/libtommath/bn_mp_div_3.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_DIV_3_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* divide by three (based on routine from MPI and the GMP manual) */
@@ -73,3 +73,7 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_div_d.c b/libtommath/bn_mp_div_d.c
index af18d0a..7dc0904 100644
--- a/libtommath/bn_mp_div_d.c
+++ b/libtommath/bn_mp_div_d.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_DIV_D_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 static int s_is_power_of_two(mp_digit b, int *p)
@@ -20,7 +20,7 @@ static int s_is_power_of_two(mp_digit b, int *p)
    int x;
 
    /* quick out - if (b & (b-1)) isn't zero, b isn't a power of two */
-   if ((b==0) || (b & (b-1))) {
+   if ((b == 0) || ((b & (b-1)) != 0)) {
        return 0;
    }
    for (x = 1; x < DIGIT_BIT; x++) {
@@ -46,7 +46,7 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
   }
 
   /* quick outs */
-  if (b == 1 || mp_iszero(a) == 1) {
+  if ((b == 1) || (mp_iszero(a) == MP_YES)) {
      if (d != NULL) {
         *d = 0;
      }
@@ -108,3 +108,7 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_dr_is_modulus.c b/libtommath/bn_mp_dr_is_modulus.c
index 8ad31dc..599d929 100644
--- a/libtommath/bn_mp_dr_is_modulus.c
+++ b/libtommath/bn_mp_dr_is_modulus.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_DR_IS_MODULUS_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* determines if a number is a valid DR modulus */
@@ -37,3 +37,7 @@ int mp_dr_is_modulus(mp_int *a)
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_dr_reduce.c b/libtommath/bn_mp_dr_reduce.c
index 8337591..2273c79 100644
--- a/libtommath/bn_mp_dr_reduce.c
+++ b/libtommath/bn_mp_dr_reduce.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_DR_REDUCE_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
@@ -40,7 +40,7 @@ mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k)
   m = n->used;
 
   /* ensure that "x" has at least 2m digits */
-  if (x->alloc < m + m) {
+  if (x->alloc < (m + m)) {
     if ((err = mp_grow (x, m + m)) != MP_OKAY) {
       return err;
     }
@@ -62,7 +62,7 @@ top:
 
   /* 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;
+      r         = (((mp_word)*tmpx2++) * (mp_word)k) + *tmpx1 + mu;
       *tmpx1++  = (mp_digit)(r & MP_MASK);
       mu        = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
   }
@@ -82,9 +82,15 @@ top:
    * Each successive "recursion" makes the input smaller and smaller.
    */
   if (mp_cmp_mag (x, n) != MP_LT) {
-    s_mp_sub(x, n, x);
+    if ((err = s_mp_sub(x, n, x)) != MP_OKAY) {
+      return err;
+    }
     goto top;
   }
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_dr_setup.c b/libtommath/bn_mp_dr_setup.c
index de00e2d..1bccb2b 100644
--- a/libtommath/bn_mp_dr_setup.c
+++ b/libtommath/bn_mp_dr_setup.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_DR_SETUP_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* determines the setup value */
@@ -26,3 +26,7 @@ void mp_dr_setup(mp_int *a, mp_digit *d)
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_exch.c b/libtommath/bn_mp_exch.c
index b7bd186..634193b 100644
--- a/libtommath/bn_mp_exch.c
+++ b/libtommath/bn_mp_exch.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_EXCH_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* swap the elements of two integers, for cases where you can't simply swap the 
@@ -28,3 +28,7 @@ mp_exch (mp_int * a, mp_int * b)
   *b = t;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_export.c b/libtommath/bn_mp_export.c
new file mode 100644
index 0000000..ac4c2f9
--- /dev/null
+++ b/libtommath/bn_mp_export.c
@@ -0,0 +1,88 @@
+#include <tommath_private.h>
+#ifdef BN_MP_EXPORT_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, tstdenis82@gmail.com, http://libtom.org
+ */
+
+/* based on gmp's mpz_export.
+ * see http://gmplib.org/manual/Integer-Import-and-Export.html
+ */
+int mp_export(void* rop, size_t* countp, int order, size_t size, 
+                                int endian, size_t nails, mp_int* op) {
+	int result;
+	size_t odd_nails, nail_bytes, i, j, bits, count;
+	unsigned char odd_nail_mask;
+
+	mp_int t;
+
+	if ((result = mp_init_copy(&t, op)) != MP_OKAY) {
+		return result;
+	}
+
+	if (endian == 0) {
+		union {
+			unsigned int i;
+			char c[4];
+		} lint;
+		lint.i = 0x01020304;
+
+		endian = (lint.c[0] == 4) ? -1 : 1;
+	}
+
+	odd_nails = (nails % 8);
+	odd_nail_mask = 0xff;
+	for (i = 0; i < odd_nails; ++i) {
+		odd_nail_mask ^= (1 << (7 - i));
+	}
+	nail_bytes = nails / 8;
+
+	bits = mp_count_bits(&t);
+	count = (bits / ((size * 8) - nails)) + (((bits % ((size * 8) - nails)) != 0) ? 1 : 0);
+
+	for (i = 0; i < count; ++i) {
+		for (j = 0; j < size; ++j) {
+			unsigned char* byte = (
+				(unsigned char*)rop + 
+				(((order == -1) ? i : ((count - 1) - i)) * size) +
+				((endian == -1) ? j : ((size - 1) - j))
+			);
+
+			if (j >= (size - nail_bytes)) {
+				*byte = 0;
+				continue;
+			}
+
+			*byte = (unsigned char)((j == ((size - nail_bytes) - 1)) ? (t.dp[0] & odd_nail_mask) : (t.dp[0] & 0xFF));
+
+			if ((result = mp_div_2d(&t, ((j == ((size - nail_bytes) - 1)) ? (8 - odd_nails) : 8), &t, NULL)) != MP_OKAY) {
+				mp_clear(&t);
+				return result;
+			}
+		}
+	}
+
+	mp_clear(&t);
+
+	if (countp != NULL) {
+		*countp = count;
+	}
+
+	return MP_OKAY;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_expt_d.c b/libtommath/bn_mp_expt_d.c
index 132f480..61c5a1d 100644
--- a/libtommath/bn_mp_expt_d.c
+++ b/libtommath/bn_mp_expt_d.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_EXPT_D_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,42 +12,17 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
-/* calculate c = a**b  using a square-multiply algorithm */
+/* wrapper function for mp_expt_d_ex() */
 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;
+  return mp_expt_d_ex(a, b, c, 0);
 }
+
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_expt_d_ex.c b/libtommath/bn_mp_expt_d_ex.c
new file mode 100644
index 0000000..649d224
--- /dev/null
+++ b/libtommath/bn_mp_expt_d_ex.c
@@ -0,0 +1,83 @@
+#include <tommath_private.h>
+#ifdef BN_MP_EXPT_D_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, tstdenis82@gmail.com, http://libtom.org
+ */
+
+/* calculate c = a**b  using a square-multiply algorithm */
+int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
+{
+  int     res;
+  unsigned int x;
+
+  mp_int  g;
+
+  if ((res = mp_init_copy (&g, a)) != MP_OKAY) {
+    return res;
+  }
+
+  /* set initial result */
+  mp_set (c, 1);
+
+  if (fast != 0) {
+    while (b > 0) {
+      /* if the bit is set multiply */
+      if ((b & 1) != 0) {
+        if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
+          mp_clear (&g);
+          return res;
+        }
+      }
+
+      /* square */
+      if (b > 1) {
+        if ((res = mp_sqr (&g, &g)) != MP_OKAY) {
+          mp_clear (&g);
+          return res;
+        }
+      }
+
+      /* shift to next bit */
+      b >>= 1;
+    }
+  }
+  else {
+    for (x = 0; x < 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;
+    }
+  } /* if ... else */
+
+  mp_clear (&g);
+  return MP_OKAY;
+}
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_exptmod.c b/libtommath/bn_mp_exptmod.c
index b7d9fb7..0973e44 100644
--- a/libtommath/bn_mp_exptmod.c
+++ b/libtommath/bn_mp_exptmod.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_EXPTMOD_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 
@@ -89,7 +89,7 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
     
   /* 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) {
+  if ((mp_isodd (P) == MP_YES) || (dr !=  0)) {
     return mp_exptmod_fast (G, X, P, Y, dr);
   } else {
 #endif
@@ -106,3 +106,7 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_exptmod_fast.c b/libtommath/bn_mp_exptmod_fast.c
index 1902e79..8d280bd 100644
--- a/libtommath/bn_mp_exptmod_fast.c
+++ b/libtommath/bn_mp_exptmod_fast.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_EXPTMOD_FAST_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
@@ -96,8 +96,8 @@ int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode
 
      /* 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)))) {
+     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
@@ -219,12 +219,12 @@ int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode
      * in the exponent.  Technically this opt is not required but it
      * does lower the # of trivial squaring/reductions used
      */
-    if (mode == 0 && y == 0) {
+    if ((mode == 0) && (y == 0)) {
       continue;
     }
 
     /* if the bit is zero and mode == 1 then we square */
-    if (mode == 1 && y == 0) {
+    if ((mode == 1) && (y == 0)) {
       if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
         goto LBL_RES;
       }
@@ -266,7 +266,7 @@ int mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode
   }
 
   /* if bits remain then square/multiply */
-  if (mode == 2 && bitcpy > 0) {
+  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) {
@@ -314,3 +314,8 @@ LBL_M:
   return err;
 }
 #endif
+
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_exteuclid.c b/libtommath/bn_mp_exteuclid.c
index 2e69ce1..fbbd92c 100644
--- a/libtommath/bn_mp_exteuclid.c
+++ b/libtommath/bn_mp_exteuclid.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_EXTEUCLID_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,10 +12,10 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
-/* Extended euclidean algorithm of (a, b) produces 
+/* 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)
@@ -61,9 +61,9 @@ int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
 
    /* make sure U3 >= 0 */
    if (u3.sign == MP_NEG) {
-      mp_neg(&u1, &u1);
-      mp_neg(&u2, &u2);
-      mp_neg(&u3, &u3);
+       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; }
    }
 
    /* copy result out */
@@ -76,3 +76,7 @@ _ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL
    return err;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_fread.c b/libtommath/bn_mp_fread.c
index 44e1ea8..a4fa8c9 100644
--- a/libtommath/bn_mp_fread.c
+++ b/libtommath/bn_mp_fread.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_FREAD_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* read a bigint from a file stream in ASCII */
@@ -61,3 +61,7 @@ int mp_fread(mp_int *a, int radix, FILE *stream)
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_fwrite.c b/libtommath/bn_mp_fwrite.c
index b0ec29e..90f1fc5 100644
--- a/libtommath/bn_mp_fwrite.c
+++ b/libtommath/bn_mp_fwrite.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_FWRITE_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 int mp_fwrite(mp_int *a, int radix, FILE *stream)
@@ -46,3 +46,7 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream)
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_gcd.c b/libtommath/bn_mp_gcd.c
index 68cfa03..16acfd9 100644
--- a/libtommath/bn_mp_gcd.c
+++ b/libtommath/bn_mp_gcd.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_GCD_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* Greatest Common Divisor using the binary method */
@@ -70,7 +70,7 @@ int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
      }
   }
 
-  while (mp_iszero(&v) == 0) {
+  while (mp_iszero(&v) == MP_NO) {
      /* make sure v is the largest */
      if (mp_cmp_mag(&u, &v) == MP_GT) {
         /* swap u and v to make sure v is >= u */
@@ -99,3 +99,7 @@ LBL_U:mp_clear (&v);
   return res;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_get_int.c b/libtommath/bn_mp_get_int.c
index 762cb23..99fb850 100644
--- a/libtommath/bn_mp_get_int.c
+++ b/libtommath/bn_mp_get_int.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_GET_INT_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,25 +12,25 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* get the lower 32-bits of an mp_int */
-unsigned long mp_get_int(mp_int * a) 
+unsigned long mp_get_int(mp_int * a)
 {
   int i;
-  unsigned long res;
+  mp_min_u32 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;
+  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);
   }
@@ -39,3 +39,7 @@ unsigned long mp_get_int(mp_int * a)
   return res & 0xFFFFFFFFUL;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_get_long.c b/libtommath/bn_mp_get_long.c
new file mode 100644
index 0000000..7c3d0fe
--- /dev/null
+++ b/libtommath/bn_mp_get_long.c
@@ -0,0 +1,41 @@
+#include <tommath_private.h>
+#ifdef BN_MP_GET_LONG_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, tstdenis82@gmail.com, http://libtom.org
+ */
+
+/* get the lower unsigned long of an mp_int, platform dependent */
+unsigned long mp_get_long(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);
+
+#if (ULONG_MAX != 0xffffffffuL) || (DIGIT_BIT < 32)
+  while (--i >= 0) {
+    res = (res << DIGIT_BIT) | DIGIT(a,i);
+  }
+#endif
+  return res;
+}
+#endif
diff --git a/libtommath/bn_mp_get_long_long.c b/libtommath/bn_mp_get_long_long.c
new file mode 100644
index 0000000..4b959e6
--- /dev/null
+++ b/libtommath/bn_mp_get_long_long.c
@@ -0,0 +1,41 @@
+#include <tommath_private.h>
+#ifdef BN_MP_GET_LONG_LONG_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, tstdenis82@gmail.com, http://libtom.org
+ */
+
+/* get the lower unsigned long long of an mp_int, platform dependent */
+unsigned long long mp_get_long_long (mp_int * a)
+{
+  int i;
+  unsigned long 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 long) * CHAR_BIT) + DIGIT_BIT - 1) / DIGIT_BIT)) - 1;
+
+  /* get most significant digit of result */
+  res = DIGIT(a,i);
+
+#if DIGIT_BIT < 64
+  while (--i >= 0) {
+    res = (res << DIGIT_BIT) | DIGIT(a,i);
+  }
+#endif
+  return res;
+}
+#endif
diff --git a/libtommath/bn_mp_grow.c b/libtommath/bn_mp_grow.c
index b5b2407..cbdcfed 100644
--- a/libtommath/bn_mp_grow.c
+++ b/libtommath/bn_mp_grow.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_GROW_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* grow as required */
@@ -51,3 +51,7 @@ int mp_grow (mp_int * a, int size)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_import.c b/libtommath/bn_mp_import.c
new file mode 100644
index 0000000..dd4b8e6
--- /dev/null
+++ b/libtommath/bn_mp_import.c
@@ -0,0 +1,73 @@
+#include <tommath_private.h>
+#ifdef BN_MP_IMPORT_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, tstdenis82@gmail.com, http://libtom.org
+ */
+
+/* based on gmp's mpz_import.
+ * see http://gmplib.org/manual/Integer-Import-and-Export.html
+ */
+int mp_import(mp_int* rop, size_t count, int order, size_t size, 
+                            int endian, size_t nails, const void* op) {
+	int result;
+	size_t odd_nails, nail_bytes, i, j;
+	unsigned char odd_nail_mask;
+
+	mp_zero(rop);
+
+	if (endian == 0) {
+		union {
+			unsigned int i;
+			char c[4];
+		} lint;
+		lint.i = 0x01020304;
+
+		endian = (lint.c[0] == 4) ? -1 : 1;
+	}
+
+	odd_nails = (nails % 8);
+	odd_nail_mask = 0xff;
+	for (i = 0; i < odd_nails; ++i) {
+		odd_nail_mask ^= (1 << (7 - i));
+	}
+	nail_bytes = nails / 8;
+
+	for (i = 0; i < count; ++i) {
+		for (j = 0; j < (size - nail_bytes); ++j) {
+			unsigned char byte = *(
+					(unsigned char*)op + 
+					(((order == 1) ? i : ((count - 1) - i)) * size) +
+					((endian == 1) ? (j + nail_bytes) : (((size - 1) - j) - nail_bytes))
+				);
+
+			if (
+				(result = mp_mul_2d(rop, ((j == 0) ? (8 - odd_nails) : 8), rop)) != MP_OKAY) {
+				return result;
+			}
+
+			rop->dp[0] |= (j == 0) ? (byte & odd_nail_mask) : byte;
+			rop->used  += 1;
+		}
+	}
+
+	mp_clamp(rop);
+
+	return MP_OKAY;
+}
+
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_init.c b/libtommath/bn_mp_init.c
index ddb2d07..7a57730 100644
--- a/libtommath/bn_mp_init.c
+++ b/libtommath/bn_mp_init.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_INIT_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* init a new mp_int */
@@ -40,3 +40,7 @@ int mp_init (mp_int * a)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_init_copy.c b/libtommath/bn_mp_init_copy.c
index 2410a9f..33b0e82 100644
--- a/libtommath/bn_mp_init_copy.c
+++ b/libtommath/bn_mp_init_copy.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_INIT_COPY_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,17 +12,21 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* creates "a" then copies b into it */
-int mp_init_copy (mp_int * a, mp_int * b)
+int mp_init_copy (mp_int * a, const mp_int * b)
 {
   int     res;
 
-  if ((res = mp_init (a)) != MP_OKAY) {
+  if ((res = mp_init_size (a, b->used)) != MP_OKAY) {
     return res;
   }
   return mp_copy (b, a);
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_init_multi.c b/libtommath/bn_mp_init_multi.c
index 44e3fe6..52220a3 100644
--- a/libtommath/bn_mp_init_multi.c
+++ b/libtommath/bn_mp_init_multi.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_INIT_MULTI_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 #include <stdarg.h>
 
@@ -37,7 +37,7 @@ int mp_init_multi(mp_int *mp, ...)
             /* now start cleaning up */            
             cur_arg = mp;
             va_start(clean_args, mp);
-            while (n--) {
+            while (n-- != 0) {
                 mp_clear(cur_arg);
                 cur_arg = va_arg(clean_args, mp_int*);
             }
@@ -53,3 +53,7 @@ int mp_init_multi(mp_int *mp, ...)
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_init_set.c b/libtommath/bn_mp_init_set.c
index dc08867..c337e50 100644
--- a/libtommath/bn_mp_init_set.c
+++ b/libtommath/bn_mp_init_set.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_INIT_SET_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* initialize and set a digit */
@@ -26,3 +26,7 @@ int mp_init_set (mp_int * a, mp_digit b)
   return err;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_init_set_int.c b/libtommath/bn_mp_init_set_int.c
index 56b27e0..c88f14e 100644
--- a/libtommath/bn_mp_init_set_int.c
+++ b/libtommath/bn_mp_init_set_int.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_INIT_SET_INT_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* initialize and set a digit */
@@ -25,3 +25,7 @@ int mp_init_set_int (mp_int * a, unsigned long b)
   return mp_set_int(a, b);
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_init_size.c b/libtommath/bn_mp_init_size.c
index 8ed2c2a..e1d1b51 100644
--- a/libtommath/bn_mp_init_size.c
+++ b/libtommath/bn_mp_init_size.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_INIT_SIZE_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* init an mp_init for a given size */
@@ -42,3 +42,7 @@ int mp_init_size (mp_int * a, int size)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_invmod.c b/libtommath/bn_mp_invmod.c
index fdb6c88..44951e5 100644
--- a/libtommath/bn_mp_invmod.c
+++ b/libtommath/bn_mp_invmod.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_INVMOD_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,28 +12,32 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@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) {
+  if ((b->sign == MP_NEG) || (mp_iszero(b) == MP_YES)) {
     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) {
+  if (mp_isodd (b) == MP_YES) {
     return fast_mp_invmod (a, b, c);
   }
 #endif
 
 #ifdef BN_MP_INVMOD_SLOW_C
   return mp_invmod_slow(a, b, c);
-#endif
-
+#else
   return MP_VAL;
+#endif
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_invmod_slow.c b/libtommath/bn_mp_invmod_slow.c
index e079819..a21f947 100644
--- a/libtommath/bn_mp_invmod_slow.c
+++ b/libtommath/bn_mp_invmod_slow.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_INVMOD_SLOW_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* hac 14.61, pp608 */
@@ -22,7 +22,7 @@ int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
   int     res;
 
   /* b cannot be negative */
-  if (b->sign == MP_NEG || mp_iszero(b) == 1) {
+  if ((b->sign == MP_NEG) || (mp_iszero(b) == MP_YES)) {
     return MP_VAL;
   }
 
@@ -41,7 +41,7 @@ int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
   }
 
   /* 2. [modified] if x,y are both even then return an error! */
-  if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
+  if ((mp_iseven (&x) == MP_YES) && (mp_iseven (&y) == MP_YES)) {
     res = MP_VAL;
     goto LBL_ERR;
   }
@@ -58,13 +58,13 @@ int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
 
 top:
   /* 4.  while u is even do */
-  while (mp_iseven (&u) == 1) {
+  while (mp_iseven (&u) == MP_YES) {
     /* 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) {
+    if ((mp_isodd (&A) == MP_YES) || (mp_isodd (&B) == MP_YES)) {
       /* A = (A+y)/2, B = (B-x)/2 */
       if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
          goto LBL_ERR;
@@ -83,13 +83,13 @@ top:
   }
 
   /* 5.  while v is even do */
-  while (mp_iseven (&v) == 1) {
+  while (mp_iseven (&v) == MP_YES) {
     /* 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) {
+    if ((mp_isodd (&C) == MP_YES) || (mp_isodd (&D) == MP_YES)) {
       /* C = (C+y)/2, D = (D-x)/2 */
       if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
          goto LBL_ERR;
@@ -137,7 +137,7 @@ top:
   }
 
   /* if not zero goto step 4 */
-  if (mp_iszero (&u) == 0)
+  if (mp_iszero (&u) == MP_NO)
     goto top;
 
   /* now a = C, b = D, gcd == g*v */
@@ -169,3 +169,7 @@ LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
   return res;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_is_square.c b/libtommath/bn_mp_is_square.c
index 926b449..9f065ef 100644
--- a/libtommath/bn_mp_is_square.c
+++ b/libtommath/bn_mp_is_square.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_IS_SQUARE_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* Check if remainders are possible squares - fast exclude non-squares */
@@ -82,13 +82,13 @@ int mp_is_square(mp_int *arg,int *ret)
    * 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;
+  if (((1L<<(r%11)) & 0x5C4L) != 0L)       goto ERR;
+  if (((1L<<(r%13)) & 0x9E4L) != 0L)       goto ERR;
+  if (((1L<<(r%17)) & 0x5CE8L) != 0L)      goto ERR;
+  if (((1L<<(r%19)) & 0x4F50CL) != 0L)     goto ERR;
+  if (((1L<<(r%23)) & 0x7ACCA0L) != 0L)    goto ERR;
+  if (((1L<<(r%29)) & 0xC2EDD0CL) != 0L)   goto ERR;
+  if (((1L<<(r%31)) & 0x6DE2B848L) != 0L)  goto ERR;
 
   /* Final check - is sqr(sqrt(arg)) == arg ? */
   if ((res = mp_sqrt(arg,&t)) != MP_OKAY) {
@@ -103,3 +103,7 @@ ERR:mp_clear(&t);
   return res;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_jacobi.c b/libtommath/bn_mp_jacobi.c
index 1644698..3c114e3 100644
--- a/libtommath/bn_mp_jacobi.c
+++ b/libtommath/bn_mp_jacobi.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_JACOBI_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,27 +12,39 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* computes the jacobi c = (a | n) (or Legendre if n is prime)
  * HAC pp. 73 Algorithm 2.149
+ * HAC is wrong here, as the special case of (0 | 1) is not
+ * handled correctly.
  */
-int mp_jacobi (mp_int * a, mp_int * p, int *c)
+int mp_jacobi (mp_int * a, mp_int * n, 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) {
+  /* if a < 0 return MP_VAL */
+  if (mp_isneg(a) == MP_YES) {
      return MP_VAL;
   }
 
-  /* step 1.  if a == 0, return 0 */
-  if (mp_iszero (a) == 1) {
-    *c = 0;
-    return MP_OKAY;
+  /* if n <= 0 return MP_VAL */
+  if (mp_cmp_d(n, 0) != MP_GT) {
+     return MP_VAL;
+  }
+
+  /* step 1. handle case of a == 0 */
+  if (mp_iszero (a) == MP_YES) {
+     /* special case of a == 0 and n == 1 */
+     if (mp_cmp_d (n, 1) == MP_EQ) {
+       *c = 1;
+     } else {
+       *c = 0;
+     }
+     return MP_OKAY;
   }
 
   /* step 2.  if a == 1, return 1 */
@@ -64,17 +76,17 @@ int mp_jacobi (mp_int * a, mp_int * p, int *c)
     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;
+    residue = n->dp[0] & 7;
 
-    if (residue == 1 || residue == 7) {
+    if ((residue == 1) || (residue == 7)) {
       s = 1;
-    } else if (residue == 3 || residue == 5) {
+    } 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)) {
+  if ( ((n->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
     s = -s;
   }
 
@@ -83,7 +95,7 @@ int mp_jacobi (mp_int * a, mp_int * p, int *c)
     *c = s;
   } else {
     /* n1 = n mod a1 */
-    if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) {
+    if ((res = mp_mod (n, &a1, &p1)) != MP_OKAY) {
       goto LBL_P1;
     }
     if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
@@ -99,3 +111,7 @@ LBL_A1:mp_clear (&a1);
   return res;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_karatsuba_mul.c b/libtommath/bn_mp_karatsuba_mul.c
index 0d62b9b..d65e37e 100644
--- a/libtommath/bn_mp_karatsuba_mul.c
+++ b/libtommath/bn_mp_karatsuba_mul.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_KARATSUBA_MUL_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* c = |a| * |b| using Karatsuba Multiplication using 
@@ -82,8 +82,8 @@ int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
   y1.used = b->used - B;
 
   {
-    register int x;
-    register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
+    int x;
+    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
@@ -161,3 +161,7 @@ ERR:
   return err;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_karatsuba_sqr.c b/libtommath/bn_mp_karatsuba_sqr.c
index 829405a..739840d 100644
--- a/libtommath/bn_mp_karatsuba_sqr.c
+++ b/libtommath/bn_mp_karatsuba_sqr.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_KARATSUBA_SQR_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* Karatsuba squaring, computes b = a*a using three 
@@ -52,8 +52,8 @@ int mp_karatsuba_sqr (mp_int * a, mp_int * b)
     goto X0X0;
 
   {
-    register int x;
-    register mp_digit *dst, *src;
+    int x;
+    mp_digit *dst, *src;
 
     src = a->dp;
 
@@ -115,3 +115,7 @@ ERR:
   return err;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_lcm.c b/libtommath/bn_mp_lcm.c
index 1d53921..3bff571 100644
--- a/libtommath/bn_mp_lcm.c
+++ b/libtommath/bn_mp_lcm.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_LCM_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* computes least common multiple as |a*b|/(a, b) */
@@ -54,3 +54,7 @@ LBL_T:
   return res;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_lshd.c b/libtommath/bn_mp_lshd.c
index ce1e63b..f6f800f 100644
--- a/libtommath/bn_mp_lshd.c
+++ b/libtommath/bn_mp_lshd.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_LSHD_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* shift left a certain amount of digits */
@@ -26,14 +26,14 @@ int mp_lshd (mp_int * a, int b)
   }
 
   /* grow to fit the new digits */
-  if (a->alloc < a->used + b) {
+  if (a->alloc < (a->used + b)) {
      if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
        return res;
      }
   }
 
   {
-    register mp_digit *top, *bottom;
+    mp_digit *top, *bottom;
 
     /* increment the used by the shift amount then copy upwards */
     a->used += b;
@@ -42,7 +42,7 @@ int mp_lshd (mp_int * a, int b)
     top = a->dp + a->used - 1;
 
     /* base */
-    bottom = a->dp + a->used - 1 - b;
+    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
@@ -61,3 +61,7 @@ int mp_lshd (mp_int * a, int b)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_mod.c b/libtommath/bn_mp_mod.c
index 98e155e..b67467d 100644
--- a/libtommath/bn_mp_mod.c
+++ b/libtommath/bn_mp_mod.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_MOD_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,10 +12,10 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
-/* c = a mod b, 0 <= c < b */
+/* c = a mod b, 0 <= c < b if b > 0, b < c <= 0 if b < 0 */
 int
 mp_mod (mp_int * a, mp_int * b, mp_int * c)
 {
@@ -31,14 +31,18 @@ mp_mod (mp_int * a, mp_int * b, mp_int * c)
     return res;
   }
 
-  if (t.sign != b->sign) {
-    res = mp_add (b, &t, c);
-  } else {
+  if ((mp_iszero(&t) != MP_NO) || (t.sign == b->sign)) {
     res = MP_OKAY;
     mp_exch (&t, c);
+  } else {
+    res = mp_add (b, &t, c);
   }
 
   mp_clear (&t);
   return res;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_mod_2d.c b/libtommath/bn_mp_mod_2d.c
index 0170f65..954d64f 100644
--- a/libtommath/bn_mp_mod_2d.c
+++ b/libtommath/bn_mp_mod_2d.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_MOD_2D_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* calc a value mod 2**b */
@@ -39,7 +39,7 @@ mp_mod_2d (const mp_int * a, int b, mp_int * c)
   }
 
   /* zero digits above the last digit of the modulus */
-  for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
+  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 */
@@ -49,3 +49,7 @@ mp_mod_2d (const mp_int * a, int b, mp_int * c)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_mod_d.c b/libtommath/bn_mp_mod_d.c
index f642ee8..d8722f0 100644
--- a/libtommath/bn_mp_mod_d.c
+++ b/libtommath/bn_mp_mod_d.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_MOD_D_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 int
@@ -21,3 +21,7 @@ mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
   return mp_div_d(a, b, NULL, c);
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_montgomery_calc_normalization.c b/libtommath/bn_mp_montgomery_calc_normalization.c
index 0748762..ea87cbd 100644
--- a/libtommath/bn_mp_montgomery_calc_normalization.c
+++ b/libtommath/bn_mp_montgomery_calc_normalization.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /*
@@ -29,7 +29,7 @@ int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
   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) {
+     if ((res = mp_2expt (a, ((b->used - 1) * DIGIT_BIT) + bits - 1)) != MP_OKAY) {
         return res;
      }
   } else {
@@ -53,3 +53,7 @@ int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_montgomery_reduce.c b/libtommath/bn_mp_montgomery_reduce.c
index bc6abb8..af2cc58 100644
--- a/libtommath/bn_mp_montgomery_reduce.c
+++ b/libtommath/bn_mp_montgomery_reduce.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_MONTGOMERY_REDUCE_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* computes xR**-1 == x (mod N) via Montgomery Reduction */
@@ -28,10 +28,10 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
    * than the available columns [255 per default] since carries
    * are fixed up in the inner loop.
    */
-  digs = n->used * 2 + 1;
+  digs = (n->used * 2) + 1;
   if ((digs < MP_WARRAY) &&
-      n->used <
-      (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+      (n->used <
+      (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
     return fast_mp_montgomery_reduce (x, n, rho);
   }
 
@@ -52,13 +52,13 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
      * 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);
+    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;
+      int iy;
+      mp_digit *tmpn, *tmpx, u;
+      mp_word r;
 
       /* alias for digits of the modulus */
       tmpn = n->dp;
@@ -72,8 +72,8 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
       /* 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);
+        r       = ((mp_word)mu * (mp_word)*tmpn++) +
+                   (mp_word) u + (mp_word) *tmpx;
 
         /* get carry */
         u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
@@ -85,7 +85,7 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
 
 
       /* propagate carries upwards as required*/
-      while (u) {
+      while (u != 0) {
         *tmpx   += u;
         u        = *tmpx >> DIGIT_BIT;
         *tmpx++ &= MP_MASK;
@@ -112,3 +112,7 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_montgomery_setup.c b/libtommath/bn_mp_montgomery_setup.c
index b8e1887..264a2bd 100644
--- a/libtommath/bn_mp_montgomery_setup.c
+++ b/libtommath/bn_mp_montgomery_setup.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_MONTGOMERY_SETUP_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* setups the montgomery reduction stuff */
@@ -36,20 +36,24 @@ mp_montgomery_setup (mp_int * n, mp_digit * rho)
   }
 
   x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
-  x *= 2 - b * x;               /* here x*a==1 mod 2**8 */
+  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 */
+  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 */
+  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 */
+  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;
+  *rho = (mp_digit)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
 
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_mul.c b/libtommath/bn_mp_mul.c
index fc024be..ea53d5e 100644
--- a/libtommath/bn_mp_mul.c
+++ b/libtommath/bn_mp_mul.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_MUL_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* high level multiplication (handles sign) */
@@ -44,19 +44,24 @@ int mp_mul (mp_int * a, mp_int * b, mp_int * c)
 
 #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)))) {
+        (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
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_mul_2.c b/libtommath/bn_mp_mul_2.c
index 2ca6022..9c72c7f 100644
--- a/libtommath/bn_mp_mul_2.c
+++ b/libtommath/bn_mp_mul_2.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_MUL_2_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* b = a*2 */
@@ -21,7 +21,7 @@ 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 (b->alloc < (a->used + 1)) {
     if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
       return res;
     }
@@ -31,7 +31,7 @@ int mp_mul_2(mp_int * a, mp_int * b)
   b->used = a->used;
 
   {
-    register mp_digit r, rr, *tmpa, *tmpb;
+    mp_digit r, rr, *tmpa, *tmpb;
 
     /* alias for source */
     tmpa = a->dp;
@@ -76,3 +76,7 @@ int mp_mul_2(mp_int * a, mp_int * b)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_mul_2d.c b/libtommath/bn_mp_mul_2d.c
index 4ac2e4e..e9b284e 100644
--- a/libtommath/bn_mp_mul_2d.c
+++ b/libtommath/bn_mp_mul_2d.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_MUL_2D_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* shift left by a certain bit count */
@@ -28,8 +28,8 @@ int mp_mul_2d (const mp_int * a, int b, mp_int * c)
      }
   }
 
-  if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) {
-     if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
+  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;
      }
   }
@@ -44,8 +44,8 @@ int mp_mul_2d (const mp_int * a, int b, mp_int * c)
   /* 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;
+    mp_digit *tmpc, shift, mask, r, rr;
+    int x;
 
     /* bitmask for carries */
     mask = (((mp_digit)1) << d) - 1;
@@ -79,3 +79,7 @@ int mp_mul_2d (const mp_int * a, int b, mp_int * c)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_mul_d.c b/libtommath/bn_mp_mul_d.c
index ba45a0c..e77da5d 100644
--- a/libtommath/bn_mp_mul_d.c
+++ b/libtommath/bn_mp_mul_d.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_MUL_D_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* multiply by a digit */
@@ -24,7 +24,7 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
   int      ix, res, olduse;
 
   /* make sure c is big enough to hold a*b */
-  if (c->alloc < a->used + 1) {
+  if (c->alloc < (a->used + 1)) {
     if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
       return res;
     }
@@ -48,7 +48,7 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
   /* 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);
+    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));
@@ -73,3 +73,7 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_mulmod.c b/libtommath/bn_mp_mulmod.c
index 649b717..5ea88ef 100644
--- a/libtommath/bn_mp_mulmod.c
+++ b/libtommath/bn_mp_mulmod.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_MULMOD_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* d = a * b (mod c) */
@@ -34,3 +34,7 @@ int mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
   return res;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_n_root.c b/libtommath/bn_mp_n_root.c
index b2700a8..a14ee67 100644
--- a/libtommath/bn_mp_n_root.c
+++ b/libtommath/bn_mp_n_root.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_N_ROOT_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,117 +12,19 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@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].
+/* wrapper function for mp_n_root_ex()
+ * computes c = (a)**(1/b) such that (c)**b <= a and (c+1)**b > a
  */
 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;
+  return mp_n_root_ex(a, b, c, 0);
 }
+
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_n_root_ex.c b/libtommath/bn_mp_n_root_ex.c
new file mode 100644
index 0000000..79d1dfb
--- /dev/null
+++ b/libtommath/bn_mp_n_root_ex.c
@@ -0,0 +1,132 @@
+#include <tommath_private.h>
+#ifdef BN_MP_N_ROOT_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, tstdenis82@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_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
+{
+  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_ex (&t1, b - 1, &t3, fast)) != 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_ex (&t1, b, &t2, fast)) != 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
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_neg.c b/libtommath/bn_mp_neg.c
index 07fb148..952a991 100644
--- a/libtommath/bn_mp_neg.c
+++ b/libtommath/bn_mp_neg.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_NEG_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* b = -a */
@@ -34,3 +34,7 @@ int mp_neg (const mp_int * a, mp_int * b)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_or.c b/libtommath/bn_mp_or.c
index aa5b1bd..b7f2e4f 100644
--- a/libtommath/bn_mp_or.c
+++ b/libtommath/bn_mp_or.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_OR_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* OR two ints together */
@@ -44,3 +44,7 @@ int mp_or (mp_int * a, mp_int * b, mp_int * c)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_prime_fermat.c b/libtommath/bn_mp_prime_fermat.c
index 7b9b12e..9dc9e85 100644
--- a/libtommath/bn_mp_prime_fermat.c
+++ b/libtommath/bn_mp_prime_fermat.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_PRIME_FERMAT_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* performs one Fermat test.
@@ -56,3 +56,7 @@ LBL_T:mp_clear (&t);
   return err;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_prime_is_divisible.c b/libtommath/bn_mp_prime_is_divisible.c
index 710c967..5854f08 100644
--- a/libtommath/bn_mp_prime_is_divisible.c
+++ b/libtommath/bn_mp_prime_is_divisible.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_PRIME_IS_DIVISIBLE_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* determines if an integers is divisible by one 
@@ -44,3 +44,7 @@ int mp_prime_is_divisible (mp_int * a, int *result)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_prime_is_prime.c b/libtommath/bn_mp_prime_is_prime.c
index ce225a3..be5ebe4 100644
--- a/libtommath/bn_mp_prime_is_prime.c
+++ b/libtommath/bn_mp_prime_is_prime.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_PRIME_IS_PRIME_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* performs a variable number of rounds of Miller-Rabin
@@ -31,7 +31,7 @@ int mp_prime_is_prime (mp_int * a, int t, int *result)
   *result = MP_NO;
 
   /* valid value of t? */
-  if (t <= 0 || t > PRIME_SIZE) {
+  if ((t <= 0) || (t > PRIME_SIZE)) {
     return MP_VAL;
   }
 
@@ -77,3 +77,7 @@ LBL_B:mp_clear (&b);
   return err;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_prime_miller_rabin.c b/libtommath/bn_mp_prime_miller_rabin.c
index c5185b8..7b5c8d2 100644
--- a/libtommath/bn_mp_prime_miller_rabin.c
+++ b/libtommath/bn_mp_prime_miller_rabin.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_PRIME_MILLER_RABIN_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* Miller-Rabin test of "a" to the base of "b" as described in 
@@ -67,10 +67,10 @@ int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
   }
 
   /* if y != 1 and y != n1 do */
-  if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) {
+  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) {
+    while ((j <= (s - 1)) && (mp_cmp (&y, &n1) != MP_EQ)) {
       if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
          goto LBL_Y;
       }
@@ -97,3 +97,7 @@ LBL_N1:mp_clear (&n1);
   return err;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_prime_next_prime.c b/libtommath/bn_mp_prime_next_prime.c
index 2433e8c..9951dc3 100644
--- a/libtommath/bn_mp_prime_next_prime.c
+++ b/libtommath/bn_mp_prime_next_prime.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_PRIME_NEXT_PRIME_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* finds the next prime after the number "a" using "t" trials
@@ -22,12 +22,12 @@
  */
 int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
 {
-   int      err, res, x, y;
+   int      err, res = MP_NO, x, y;
    mp_digit res_tab[PRIME_SIZE], step, kstep;
    mp_int   b;
 
    /* ensure t is valid */
-   if (t <= 0 || t > PRIME_SIZE) {
+   if ((t <= 0) || (t > PRIME_SIZE)) {
       return MP_VAL;
    }
 
@@ -84,7 +84,7 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
          if ((err = mp_sub_d(a, (a->dp[0] & 3) + 1, a)) != MP_OKAY) { return err; };
       }
    } else {
-      if (mp_iseven(a) == 1) {
+      if (mp_iseven(a) == MP_YES) {
          /* force odd */
          if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) {
             return err;
@@ -129,7 +129,7 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
                 y = 1;
              }
          }
-      } while (y == 1 && step < ((((mp_digit)1)<<DIGIT_BIT) - kstep));
+      } while ((y == 1) && (step < ((((mp_digit)1) << DIGIT_BIT) - kstep)));
 
       /* add the step */
       if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
@@ -137,7 +137,7 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
       }
 
       /* if didn't pass sieve and step == MAX then skip test */
-      if (y == 1 && step >= ((((mp_digit)1)<<DIGIT_BIT) - kstep)) {
+      if ((y == 1) && (step >= ((((mp_digit)1) << DIGIT_BIT) - kstep))) {
          continue;
       }
 
@@ -164,3 +164,7 @@ LBL_ERR:
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_prime_rabin_miller_trials.c b/libtommath/bn_mp_prime_rabin_miller_trials.c
index e57a43c..bca4229 100644
--- a/libtommath/bn_mp_prime_rabin_miller_trials.c
+++ b/libtommath/bn_mp_prime_rabin_miller_trials.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 
@@ -46,3 +46,7 @@ int mp_prime_rabin_miller_trials(int size)
 
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_prime_random_ex.c b/libtommath/bn_mp_prime_random_ex.c
index a37477e..1efc4fc 100644
--- a/libtommath/bn_mp_prime_random_ex.c
+++ b/libtommath/bn_mp_prime_random_ex.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_PRIME_RANDOM_EX_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* makes a truly random prime of a given size (bits),
@@ -21,7 +21,6 @@
  * 
  *   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
@@ -37,12 +36,12 @@ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback
    int res, err, bsize, maskOR_msb_offset;
 
    /* sanity check the input */
-   if (size <= 1 || t <= 0) {
+   if ((size <= 1) || (t <= 0)) {
       return MP_VAL;
    }
 
    /* LTM_PRIME_SAFE implies LTM_PRIME_BBS */
-   if (flags & LTM_PRIME_SAFE) {
+   if ((flags & LTM_PRIME_SAFE) != 0) {
       flags |= LTM_PRIME_BBS;
    }
 
@@ -61,13 +60,13 @@ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback
    /* calc the maskOR_msb */
    maskOR_msb        = 0;
    maskOR_msb_offset = ((size & 7) == 1) ? 1 : 0;
-   if (flags & LTM_PRIME_2MSB_ON) {
+   if ((flags & LTM_PRIME_2MSB_ON) != 0) {
       maskOR_msb       |= 0x80 >> ((9 - size) & 7);
    }  
 
    /* get the maskOR_lsb */
    maskOR_lsb         = 1;
-   if (flags & LTM_PRIME_BBS) {
+   if ((flags & LTM_PRIME_BBS) != 0) {
       maskOR_lsb     |= 3;
    }
 
@@ -95,7 +94,7 @@ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback
          continue;
       }
 
-      if (flags & LTM_PRIME_SAFE) {
+      if ((flags & LTM_PRIME_SAFE) != 0) {
          /* 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; }
@@ -105,7 +104,7 @@ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback
       }
    } while (res == MP_NO);
 
-   if (flags & LTM_PRIME_SAFE) {
+   if ((flags & LTM_PRIME_SAFE) != 0) {
       /* 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; }
@@ -119,3 +118,7 @@ error:
 
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_radix_size.c b/libtommath/bn_mp_radix_size.c
index 9d95c48..d4a02e8 100644
--- a/libtommath/bn_mp_radix_size.c
+++ b/libtommath/bn_mp_radix_size.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_RADIX_SIZE_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,11 +12,11 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* returns size of ASCII reprensentation */
-int mp_radix_size (mp_int * a, int radix, int *size)
+int mp_radix_size (const mp_int * a, int radix, int *size)
 {
   int     res, digs;
   mp_int  t;
@@ -24,14 +24,8 @@ int mp_radix_size (mp_int * a, int radix, int *size)
 
   *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) {
+  if ((radix < 2) || (radix > 64)) {
     return MP_VAL;
   }
 
@@ -40,6 +34,12 @@ int mp_radix_size (mp_int * a, int radix, int *size)
     return MP_OKAY;
   }
 
+  /* special case for binary */
+  if (radix == 2) {
+    *size = mp_count_bits (a) + ((a->sign == MP_NEG) ? 1 : 0) + 1;
+    return MP_OKAY;
+  }
+
   /* digs is the digit count */
   digs = 0;
 
@@ -74,5 +74,5 @@ int mp_radix_size (mp_int * a, int radix, int *size)
 #endif
 
 /* $Source$ */
-/* $Revision: 0.41 $ */
-/* $Date: 2007-04-18 09:58:18 +0000 $ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_radix_smap.c b/libtommath/bn_mp_radix_smap.c
index 7aeb375..d1c75ad 100644
--- a/libtommath/bn_mp_radix_smap.c
+++ b/libtommath/bn_mp_radix_smap.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_RADIX_SMAP_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,9 +12,13 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* chars used in radix conversions */
 const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_rand.c b/libtommath/bn_mp_rand.c
index 17c1fbe..4c9610d 100644
--- a/libtommath/bn_mp_rand.c
+++ b/libtommath/bn_mp_rand.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_RAND_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* makes a pseudo-random int of a given size */
@@ -29,7 +29,7 @@ mp_rand (mp_int * a, int digits)
 
   /* first place a random non-zero digit */
   do {
-    d = ((mp_digit) abs (rand ())) & MP_MASK;
+    d = ((mp_digit) abs (MP_GEN_RANDOM())) & MP_MASK;
   } while (d == 0);
 
   if ((res = mp_add_d (a, d, a)) != MP_OKAY) {
@@ -41,7 +41,7 @@ mp_rand (mp_int * a, int digits)
       return res;
     }
 
-    if ((res = mp_add_d (a, ((mp_digit) abs (rand ())), a)) != MP_OKAY) {
+    if ((res = mp_add_d (a, ((mp_digit) abs (MP_GEN_RANDOM())), a)) != MP_OKAY) {
       return res;
     }
   }
@@ -49,3 +49,7 @@ mp_rand (mp_int * a, int digits)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_read_radix.c b/libtommath/bn_mp_read_radix.c
index 4b92589..93ccd3b 100644
--- a/libtommath/bn_mp_read_radix.c
+++ b/libtommath/bn_mp_read_radix.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_READ_RADIX_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* read a string [ASCII] in a given radix */
@@ -25,7 +25,7 @@ int mp_read_radix (mp_int * a, const char *str, int radix)
   mp_zero(a);
 
   /* make sure the radix is ok */
-  if (radix < 2 || radix > 64) {
+  if ((radix < 2) || (radix > 64)) {
     return MP_VAL;
   }
 
@@ -43,12 +43,12 @@ int mp_read_radix (mp_int * a, const char *str, int radix)
   mp_zero (a);
   
   /* process each digit of the string */
-  while (*str) {
-    /* if the radix < 36 the conversion is case insensitive
+  while (*str != '\0') {
+    /* 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 ((unsigned char) *str) : *str);
+    ch = (radix <= 36) ? (char)toupper((unsigned char)*str) : *str;
     for (y = 0; y < 64; y++) {
       if (ch == mp_s_rmap[y]) {
          break;
@@ -80,9 +80,13 @@ int mp_read_radix (mp_int * a, const char *str, int radix)
   }
 
   /* set the sign only if a != 0 */
-  if (mp_iszero(a) != 1) {
+  if (mp_iszero(a) != MP_YES) {
      a->sign = neg;
   }
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_read_signed_bin.c b/libtommath/bn_mp_read_signed_bin.c
index 3ee8556..a4d4760 100644
--- a/libtommath/bn_mp_read_signed_bin.c
+++ b/libtommath/bn_mp_read_signed_bin.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_READ_SIGNED_BIN_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* read signed bin, big endian, first byte is 0==positive or 1==negative */
@@ -35,3 +35,7 @@ int mp_read_signed_bin (mp_int * a, const unsigned char *b, int c)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_read_unsigned_bin.c b/libtommath/bn_mp_read_unsigned_bin.c
index caf5be0..e8e5df8 100644
--- a/libtommath/bn_mp_read_unsigned_bin.c
+++ b/libtommath/bn_mp_read_unsigned_bin.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_READ_UNSIGNED_BIN_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* reads a unsigned char array, assumes the msb is stored first [big endian] */
@@ -37,15 +37,19 @@ int mp_read_unsigned_bin (mp_int * a, const unsigned char *b, int c)
     }
 
 #ifndef MP_8BIT
-      a->dp[0] |= *b++;
-      a->used += 1;
+    a->dp[0] |= *b++;
+    a->used += 1;
 #else
-      a->dp[0] = (*b & MP_MASK);
-      a->dp[1] |= ((*b++ >> 7U) & 1);
-      a->used += 2;
+    a->dp[0] = (*b & MP_MASK);
+    a->dp[1] |= ((*b++ >> 7U) & 1);
+    a->used += 2;
 #endif
   }
   mp_clamp (a);
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_reduce.c b/libtommath/bn_mp_reduce.c
index 4375e4e..e2c3a58 100644
--- a/libtommath/bn_mp_reduce.c
+++ b/libtommath/bn_mp_reduce.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_REDUCE_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,10 +12,10 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
-/* reduces x mod m, assumes 0 < x < m**2, mu is 
+/* reduces x mod m, assumes 0 < x < m**2, mu is
  * precomputed via mp_reduce_setup.
  * From HAC pp.604 Algorithm 14.42
  */
@@ -30,10 +30,10 @@ int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
   }
 
   /* q1 = x / b**(k-1)  */
-  mp_rshd (&q, um - 1);         
+  mp_rshd (&q, um - 1);
 
   /* according to HAC this optimization is ok */
-  if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
+  if (((mp_digit) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
     if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
       goto CLEANUP;
     }
@@ -46,8 +46,8 @@ int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
     if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
       goto CLEANUP;
     }
-#else 
-    { 
+#else
+    {
       res = MP_VAL;
       goto CLEANUP;
     }
@@ -55,7 +55,7 @@ int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
   }
 
   /* q3 = q2 / b**(k+1) */
-  mp_rshd (&q, um + 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) {
@@ -87,10 +87,14 @@ int mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
       goto CLEANUP;
     }
   }
-  
+
 CLEANUP:
   mp_clear (&q);
 
   return res;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_reduce_2k.c b/libtommath/bn_mp_reduce_2k.c
index 428f2ff..2876a75 100644
--- a/libtommath/bn_mp_reduce_2k.c
+++ b/libtommath/bn_mp_reduce_2k.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_REDUCE_2K_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* reduces a modulo n where n is of the form 2**p - d */
@@ -20,38 +20,44 @@ 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);    
+
+   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) { 
+      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);
+      if ((res = s_mp_sub(a, n, a)) != MP_OKAY) {
+         goto ERR;
+      }
       goto top;
    }
-   
+
 ERR:
    mp_clear(&q);
    return res;
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_reduce_2k_l.c b/libtommath/bn_mp_reduce_2k_l.c
index 8e52efa..3225214 100644
--- a/libtommath/bn_mp_reduce_2k_l.c
+++ b/libtommath/bn_mp_reduce_2k_l.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_REDUCE_2K_L_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,10 +12,10 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
-/* reduces a modulo n where n is of the form 2**p - d 
+/* 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.
 */
@@ -23,36 +23,42 @@ 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);    
+
+   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) { 
+   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);
+      if ((res = s_mp_sub(a, n, a)) != MP_OKAY) {
+         goto ERR;
+      }
       goto top;
    }
-   
+
 ERR:
    mp_clear(&q);
    return res;
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_reduce_2k_setup.c b/libtommath/bn_mp_reduce_2k_setup.c
index ac043f6..545051e 100644
--- a/libtommath/bn_mp_reduce_2k_setup.c
+++ b/libtommath/bn_mp_reduce_2k_setup.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_REDUCE_2K_SETUP_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* determines the setup value */
@@ -41,3 +41,7 @@ int mp_reduce_2k_setup(mp_int *a, mp_digit *d)
    return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_reduce_2k_setup_l.c b/libtommath/bn_mp_reduce_2k_setup_l.c
index b59a1ed..59132dd 100644
--- a/libtommath/bn_mp_reduce_2k_setup_l.c
+++ b/libtommath/bn_mp_reduce_2k_setup_l.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_REDUCE_2K_SETUP_L_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* determines the setup value */
@@ -38,3 +38,7 @@ ERR:
    return res;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_reduce_is_2k.c b/libtommath/bn_mp_reduce_is_2k.c
index 4655fcf..784947b 100644
--- a/libtommath/bn_mp_reduce_is_2k.c
+++ b/libtommath/bn_mp_reduce_is_2k.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_REDUCE_IS_2K_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* determines if mp_reduce_2k can be used */
@@ -46,3 +46,7 @@ int mp_reduce_is_2k(mp_int *a)
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_reduce_is_2k_l.c b/libtommath/bn_mp_reduce_is_2k_l.c
index 7b57865..c193f39 100644
--- a/libtommath/bn_mp_reduce_is_2k_l.c
+++ b/libtommath/bn_mp_reduce_is_2k_l.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_REDUCE_IS_2K_L_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* determines if reduce_2k_l can be used */
@@ -38,3 +38,7 @@ int mp_reduce_is_2k_l(mp_int *a)
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_reduce_setup.c b/libtommath/bn_mp_reduce_setup.c
index d8cefd9..f97eed5 100644
--- a/libtommath/bn_mp_reduce_setup.c
+++ b/libtommath/bn_mp_reduce_setup.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_REDUCE_SETUP_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* pre-calculate the value required for Barrett reduction
@@ -28,3 +28,7 @@ int mp_reduce_setup (mp_int * a, mp_int * b)
   return mp_div (a, b, a, NULL);
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_rshd.c b/libtommath/bn_mp_rshd.c
index e6095b3..77b0f6c 100644
--- a/libtommath/bn_mp_rshd.c
+++ b/libtommath/bn_mp_rshd.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_RSHD_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* shift right a certain amount of digits */
@@ -32,7 +32,7 @@ void mp_rshd (mp_int * a, int b)
   }
 
   {
-    register mp_digit *bottom, *top;
+    mp_digit *bottom, *top;
 
     /* shift the digits down */
 
@@ -66,3 +66,7 @@ void mp_rshd (mp_int * a, int b)
   a->used -= b;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_set.c b/libtommath/bn_mp_set.c
index c32fc42..cac48ea 100644
--- a/libtommath/bn_mp_set.c
+++ b/libtommath/bn_mp_set.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_SET_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* set to a digit */
@@ -23,3 +23,7 @@ void mp_set (mp_int * a, mp_digit b)
   a->used  = (a->dp[0] != 0) ? 1 : 0;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_set_int.c b/libtommath/bn_mp_set_int.c
index b0fc344..5aa59d5 100644
--- a/libtommath/bn_mp_set_int.c
+++ b/libtommath/bn_mp_set_int.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_SET_INT_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* set a 32-bit const */
@@ -42,3 +42,7 @@ int mp_set_int (mp_int * a, unsigned long b)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_set_long.c b/libtommath/bn_mp_set_long.c
new file mode 100644
index 0000000..281fce7
--- /dev/null
+++ b/libtommath/bn_mp_set_long.c
@@ -0,0 +1,24 @@
+#include <tommath_private.h>
+#ifdef BN_MP_SET_LONG_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, tstdenis82@gmail.com, http://libtom.org
+ */
+
+/* set a platform dependent unsigned long int */
+MP_SET_XLONG(mp_set_long, unsigned long)
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_set_long_long.c b/libtommath/bn_mp_set_long_long.c
new file mode 100644
index 0000000..3c4b01a
--- /dev/null
+++ b/libtommath/bn_mp_set_long_long.c
@@ -0,0 +1,24 @@
+#include <tommath_private.h>
+#ifdef BN_MP_SET_LONG_LONG_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, tstdenis82@gmail.com, http://libtom.org
+ */
+
+/* set a platform dependent unsigned long long int */
+MP_SET_XLONG(mp_set_long_long, unsigned long long)
+#endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_shrink.c b/libtommath/bn_mp_shrink.c
index bfdf93a..1ad2ede 100644
--- a/libtommath/bn_mp_shrink.c
+++ b/libtommath/bn_mp_shrink.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_SHRINK_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* shrink a bignum */
@@ -21,8 +21,9 @@ int mp_shrink (mp_int * a)
   mp_digit *tmp;
   int used = 1;
   
-  if(a->used > 0)
+  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) {
@@ -34,3 +35,7 @@ int mp_shrink (mp_int * a)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_signed_bin_size.c b/libtommath/bn_mp_signed_bin_size.c
index 8f88e76..0e760a6 100644
--- a/libtommath/bn_mp_signed_bin_size.c
+++ b/libtommath/bn_mp_signed_bin_size.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_SIGNED_BIN_SIZE_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* get the size for an signed equivalent */
@@ -21,3 +21,7 @@ int mp_signed_bin_size (mp_int * a)
   return 1 + mp_unsigned_bin_size (a);
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_sqr.c b/libtommath/bn_mp_sqr.c
index 3938537..ad2099b 100644
--- a/libtommath/bn_mp_sqr.c
+++ b/libtommath/bn_mp_sqr.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_SQR_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* computes b = a*a */
@@ -29,26 +29,32 @@ mp_sqr (mp_int * a, mp_int * b)
   } else 
 #endif
 #ifdef BN_MP_KARATSUBA_SQR_C
-if (a->used >= KARATSUBA_SQR_CUTOFF) {
+  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))) {
+    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
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_sqrmod.c b/libtommath/bn_mp_sqrmod.c
index 6f90772..2f9463d 100644
--- a/libtommath/bn_mp_sqrmod.c
+++ b/libtommath/bn_mp_sqrmod.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_SQRMOD_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* c = a * a (mod b) */
@@ -35,3 +35,7 @@ mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
   return res;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_sqrt.c b/libtommath/bn_mp_sqrt.c
index 016b8ba..7c9d25d 100644
--- a/libtommath/bn_mp_sqrt.c
+++ b/libtommath/bn_mp_sqrt.c
@@ -1,5 +1,4 @@
-#include <tommath.h>
-
+#include <tommath_private.h>
 #ifdef BN_MP_SQRT_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -13,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 #ifndef NO_FLOATING_POINT
@@ -140,3 +139,7 @@ E2: mp_clear(&t1);
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_sqrtmod_prime.c b/libtommath/bn_mp_sqrtmod_prime.c
new file mode 100644
index 0000000..968729e
--- /dev/null
+++ b/libtommath/bn_mp_sqrtmod_prime.c
@@ -0,0 +1,124 @@
+#include <tommath_private.h>
+#ifdef BN_MP_SQRTMOD_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 is free for all purposes without any express
+ * guarantee it works.
+ */
+
+/* Tonelli-Shanks algorithm
+ * https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm
+ * https://gmplib.org/list-archives/gmp-discuss/2013-April/005300.html
+ *
+ */
+
+int mp_sqrtmod_prime(mp_int *n, mp_int *prime, mp_int *ret)
+{
+  int res, legendre;
+  mp_int t1, C, Q, S, Z, M, T, R, two;
+  mp_digit i;
+
+  /* first handle the simple cases */
+  if (mp_cmp_d(n, 0) == MP_EQ) {
+    mp_zero(ret);
+    return MP_OKAY;
+  }
+  if (mp_cmp_d(prime, 2) == MP_EQ)                              return MP_VAL; /* prime must be odd */
+  if ((res = mp_jacobi(n, prime, &legendre)) != MP_OKAY)        return res;
+  if (legendre == -1)                                           return MP_VAL; /* quadratic non-residue mod prime */
+
+  if ((res = mp_init_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL)) != MP_OKAY) {
+	return res;
+  }
+
+  /* SPECIAL CASE: if prime mod 4 == 3
+   * compute directly: res = n^(prime+1)/4 mod prime
+   * Handbook of Applied Cryptography algorithm 3.36
+   */
+  if ((res = mp_mod_d(prime, 4, &i)) != MP_OKAY)                goto cleanup;
+  if (i == 3) {
+    if ((res = mp_add_d(prime, 1, &t1)) != MP_OKAY)             goto cleanup;
+    if ((res = mp_div_2(&t1, &t1)) != MP_OKAY)                  goto cleanup;
+    if ((res = mp_div_2(&t1, &t1)) != MP_OKAY)                  goto cleanup;
+    if ((res = mp_exptmod(n, &t1, prime, ret)) != MP_OKAY)      goto cleanup;
+    res = MP_OKAY;
+    goto cleanup;
+  }
+
+  /* NOW: Tonelli-Shanks algorithm */
+
+  /* factor out powers of 2 from prime-1, defining Q and S as: prime-1 = Q*2^S */
+  if ((res = mp_copy(prime, &Q)) != MP_OKAY)                    goto cleanup;
+  if ((res = mp_sub_d(&Q, 1, &Q)) != MP_OKAY)                   goto cleanup;
+  /* Q = prime - 1 */
+  mp_zero(&S);
+  /* S = 0 */
+  while (mp_iseven(&Q) != MP_NO) {
+    if ((res = mp_div_2(&Q, &Q)) != MP_OKAY)                    goto cleanup;
+    /* Q = Q / 2 */
+    if ((res = mp_add_d(&S, 1, &S)) != MP_OKAY)                 goto cleanup;
+    /* S = S + 1 */
+  }
+
+  /* find a Z such that the Legendre symbol (Z|prime) == -1 */
+  if ((res = mp_set_int(&Z, 2)) != MP_OKAY)                     goto cleanup;
+  /* Z = 2 */
+  while(1) {
+    if ((res = mp_jacobi(&Z, prime, &legendre)) != MP_OKAY)     goto cleanup;
+    if (legendre == -1) break;
+    if ((res = mp_add_d(&Z, 1, &Z)) != MP_OKAY)                 goto cleanup;
+    /* Z = Z + 1 */
+  }
+
+  if ((res = mp_exptmod(&Z, &Q, prime, &C)) != MP_OKAY)         goto cleanup;
+  /* C = Z ^ Q mod prime */
+  if ((res = mp_add_d(&Q, 1, &t1)) != MP_OKAY)                  goto cleanup;
+  if ((res = mp_div_2(&t1, &t1)) != MP_OKAY)                    goto cleanup;
+  /* t1 = (Q + 1) / 2 */
+  if ((res = mp_exptmod(n, &t1, prime, &R)) != MP_OKAY)         goto cleanup;
+  /* R = n ^ ((Q + 1) / 2) mod prime */
+  if ((res = mp_exptmod(n, &Q, prime, &T)) != MP_OKAY)          goto cleanup;
+  /* T = n ^ Q mod prime */
+  if ((res = mp_copy(&S, &M)) != MP_OKAY)                       goto cleanup;
+  /* M = S */
+  if ((res = mp_set_int(&two, 2)) != MP_OKAY)                   goto cleanup;
+
+  res = MP_VAL;
+  while (1) {
+    if ((res = mp_copy(&T, &t1)) != MP_OKAY)                    goto cleanup;
+    i = 0;
+    while (1) {
+      if (mp_cmp_d(&t1, 1) == MP_EQ) break;
+      if ((res = mp_exptmod(&t1, &two, prime, &t1)) != MP_OKAY) goto cleanup;
+      i++;
+    }
+    if (i == 0) {
+      if ((res = mp_copy(&R, ret)) != MP_OKAY)                  goto cleanup;
+      res = MP_OKAY;
+      goto cleanup;
+    }
+    if ((res = mp_sub_d(&M, i, &t1)) != MP_OKAY)                goto cleanup;
+    if ((res = mp_sub_d(&t1, 1, &t1)) != MP_OKAY)               goto cleanup;
+    if ((res = mp_exptmod(&two, &t1, prime, &t1)) != MP_OKAY)   goto cleanup;
+    /* t1 = 2 ^ (M - i - 1) */
+    if ((res = mp_exptmod(&C, &t1, prime, &t1)) != MP_OKAY)     goto cleanup;
+    /* t1 = C ^ (2 ^ (M - i - 1)) mod prime */
+    if ((res = mp_sqrmod(&t1, prime, &C)) != MP_OKAY)           goto cleanup;
+    /* C = (t1 * t1) mod prime */
+    if ((res = mp_mulmod(&R, &t1, prime, &R)) != MP_OKAY)       goto cleanup;
+    /* R = (R * t1) mod prime */
+    if ((res = mp_mulmod(&T, &C, prime, &T)) != MP_OKAY)        goto cleanup;
+    /* T = (T * C) mod prime */
+    mp_set(&M, i);
+    /* M = i */
+  }
+
+cleanup:
+  mp_clear_multi(&t1, &C, &Q, &S, &Z, &M, &T, &R, &two, NULL);
+  return res;
+}
+
+#endif
diff --git a/libtommath/bn_mp_sub.c b/libtommath/bn_mp_sub.c
index 13cb43e..0d616c2 100644
--- a/libtommath/bn_mp_sub.c
+++ b/libtommath/bn_mp_sub.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_SUB_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* high level subtraction (handles signs) */
@@ -53,3 +53,7 @@ mp_sub (mp_int * a, mp_int * b, mp_int * c)
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_sub_d.c b/libtommath/bn_mp_sub_d.c
index b1e4e3f..f5a932f 100644
--- a/libtommath/bn_mp_sub_d.c
+++ b/libtommath/bn_mp_sub_d.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_SUB_D_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* single digit subtraction */
@@ -23,7 +23,7 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
   int       res, ix, oldused;
 
   /* grow c as required */
-  if (c->alloc < a->used + 1) {
+  if (c->alloc < (a->used + 1)) {
      if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
         return res;
      }
@@ -49,7 +49,7 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
   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) && (a->dp[0] <= b)) || (a->used == 0)) {
      if (a->used == 1) {
         *tmpc++ = b - *tmpa;
      } else {
@@ -67,13 +67,13 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
 
      /* subtract first digit */
      *tmpc    = *tmpa++ - b;
-     mu       = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
+     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);
+        mu       = *tmpc >> ((sizeof(mp_digit) * CHAR_BIT) - 1);
         *tmpc++ &= MP_MASK;
      }
   }
@@ -87,3 +87,7 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_submod.c b/libtommath/bn_mp_submod.c
index 7461678..87e0889 100644
--- a/libtommath/bn_mp_submod.c
+++ b/libtommath/bn_mp_submod.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_SUBMOD_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* d = a - b (mod c) */
@@ -36,3 +36,7 @@ mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
   return res;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_to_signed_bin.c b/libtommath/bn_mp_to_signed_bin.c
index 7871921..e9289ea 100644
--- a/libtommath/bn_mp_to_signed_bin.c
+++ b/libtommath/bn_mp_to_signed_bin.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_TO_SIGNED_BIN_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* store in signed [big endian] format */
@@ -23,7 +23,11 @@ int mp_to_signed_bin (mp_int * a, unsigned char *b)
   if ((res = mp_to_unsigned_bin (a, b + 1)) != MP_OKAY) {
     return res;
   }
-  b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1);
+  b[0] = (a->sign == MP_ZPOS) ? (unsigned char)0 : (unsigned char)1;
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_to_signed_bin_n.c b/libtommath/bn_mp_to_signed_bin_n.c
index 8da9961..d4fe6e6 100644
--- a/libtommath/bn_mp_to_signed_bin_n.c
+++ b/libtommath/bn_mp_to_signed_bin_n.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_TO_SIGNED_BIN_N_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* store in signed [big endian] format */
@@ -25,3 +25,7 @@ int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
    return mp_to_signed_bin(a, b);
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_to_unsigned_bin.c b/libtommath/bn_mp_to_unsigned_bin.c
index 9496398..d3ef46f 100644
--- a/libtommath/bn_mp_to_unsigned_bin.c
+++ b/libtommath/bn_mp_to_unsigned_bin.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_TO_UNSIGNED_BIN_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* store in unsigned [big endian] format */
@@ -26,7 +26,7 @@ int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
   }
 
   x = 0;
-  while (mp_iszero (&t) == 0) {
+  while (mp_iszero (&t) == MP_NO) {
 #ifndef MP_8BIT
       b[x++] = (unsigned char) (t.dp[0] & 255);
 #else
@@ -42,3 +42,7 @@ int mp_to_unsigned_bin (mp_int * a, unsigned char *b)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_to_unsigned_bin_n.c b/libtommath/bn_mp_to_unsigned_bin_n.c
index 4f2a31d..2da13cc 100644
--- a/libtommath/bn_mp_to_unsigned_bin_n.c
+++ b/libtommath/bn_mp_to_unsigned_bin_n.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_TO_UNSIGNED_BIN_N_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* store in unsigned [big endian] format */
@@ -25,3 +25,7 @@ int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen)
    return mp_to_unsigned_bin(a, b);
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_toom_mul.c b/libtommath/bn_mp_toom_mul.c
index 9daefbd..4731f8f 100644
--- a/libtommath/bn_mp_toom_mul.c
+++ b/libtommath/bn_mp_toom_mul.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_TOOM_MUL_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,31 +12,31 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
-/* multiplication using the Toom-Cook 3-way algorithm 
+/* 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 
+ * 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, 
+    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;
@@ -46,13 +46,15 @@ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
        goto ERR;
     }
     mp_rshd(&a1, B);
-    mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
+    if ((res = mp_mod_2d(&a1, DIGIT_BIT * B, &a1)) != MP_OKAY) {
+       goto ERR;
+    }
 
     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;
@@ -62,23 +64,23 @@ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
        goto ERR;
     }
     mp_rshd(&b1, B);
-    mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
+    (void)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;
@@ -92,7 +94,7 @@ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
     if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
        goto ERR;
     }
-    
+
     if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
        goto ERR;
     }
@@ -105,11 +107,11 @@ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
     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;
@@ -123,7 +125,7 @@ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
     if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
        goto ERR;
     }
-    
+
     if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
        goto ERR;
     }
@@ -136,11 +138,11 @@ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
     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) {
@@ -158,123 +160,127 @@ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
     if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
        goto ERR;
     }
-    
-    /* now solve the matrix 
-    
+
+    /* 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 
+
+       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;
-     }     
-     
+
+    /* 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;
-}     
-     
+    mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
+                   &a0, &a1, &a2, &b0, &b1,
+                   &b2, &tmp1, &tmp2, NULL);
+    return res;
+}
+
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_toom_sqr.c b/libtommath/bn_mp_toom_sqr.c
index 9e3f79c..69b69d4 100644
--- a/libtommath/bn_mp_toom_sqr.c
+++ b/libtommath/bn_mp_toom_sqr.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_TOOM_SQR_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* squaring using Toom-Cook 3-way algorithm */
@@ -39,7 +39,9 @@ mp_toom_sqr(mp_int *a, mp_int *b)
        goto ERR;
     }
     mp_rshd(&a1, B);
-    mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
+    if ((res = mp_mod_2d(&a1, DIGIT_BIT * B, &a1)) != MP_OKAY) {
+       goto ERR;
+    }
 
     if ((res = mp_copy(a, &a2)) != MP_OKAY) {
        goto ERR;
@@ -115,108 +117,112 @@ mp_toom_sqr(mp_int *a, mp_int *b)
        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;
-     }
+    /* 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;
+    mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL);
+    return res;
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_toradix.c b/libtommath/bn_mp_toradix.c
index 132743e..f04352d 100644
--- a/libtommath/bn_mp_toradix.c
+++ b/libtommath/bn_mp_toradix.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_TORADIX_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* stores a bignum as a ASCII string in a given radix (2..64) */
@@ -24,12 +24,12 @@ int mp_toradix (mp_int * a, char *str, int radix)
   char   *_s = str;
 
   /* check range of the radix */
-  if (radix < 2 || radix > 64) {
+  if ((radix < 2) || (radix > 64)) {
     return MP_VAL;
   }
 
   /* quick out if its zero */
-  if (mp_iszero(a) == 1) {
+  if (mp_iszero(a) == MP_YES) {
      *str++ = '0';
      *str = '\0';
      return MP_OKAY;
@@ -47,7 +47,7 @@ int mp_toradix (mp_int * a, char *str, int radix)
   }
 
   digs = 0;
-  while (mp_iszero (&t) == 0) {
+  while (mp_iszero (&t) == MP_NO) {
     if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
       mp_clear (&t);
       return res;
@@ -69,3 +69,7 @@ int mp_toradix (mp_int * a, char *str, int radix)
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_toradix_n.c b/libtommath/bn_mp_toradix_n.c
index dedce71..19b61d7 100644
--- a/libtommath/bn_mp_toradix_n.c
+++ b/libtommath/bn_mp_toradix_n.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_TORADIX_N_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* stores a bignum as a ASCII string in a given radix (2..64) 
@@ -27,7 +27,7 @@ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
   char   *_s = str;
 
   /* check range of the maxlen, radix */
-  if (maxlen < 2 || radix < 2 || radix > 64) {
+  if ((maxlen < 2) || (radix < 2) || (radix > 64)) {
     return MP_VAL;
   }
 
@@ -56,7 +56,7 @@ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
   }
 
   digs = 0;
-  while (mp_iszero (&t) == 0) {
+  while (mp_iszero (&t) == MP_NO) {
     if (--maxlen < 1) {
        /* no more room */
        break;
@@ -82,3 +82,7 @@ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_unsigned_bin_size.c b/libtommath/bn_mp_unsigned_bin_size.c
index 58c18fb..0312625 100644
--- a/libtommath/bn_mp_unsigned_bin_size.c
+++ b/libtommath/bn_mp_unsigned_bin_size.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_UNSIGNED_BIN_SIZE_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,13 +12,17 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@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));
+  return (size / 8) + (((size & 7) != 0) ? 1 : 0);
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_xor.c b/libtommath/bn_mp_xor.c
index 432f42e..3c2ba9e 100644
--- a/libtommath/bn_mp_xor.c
+++ b/libtommath/bn_mp_xor.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_XOR_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* XOR two ints together */
@@ -45,3 +45,7 @@ mp_xor (mp_int * a, mp_int * b, mp_int * c)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_mp_zero.c b/libtommath/bn_mp_zero.c
index d697a60..21365ed 100644
--- a/libtommath/bn_mp_zero.c
+++ b/libtommath/bn_mp_zero.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_MP_ZERO_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* set to zero */
@@ -30,3 +30,7 @@ void mp_zero (mp_int * a)
   }
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_prime_tab.c b/libtommath/bn_prime_tab.c
index c47c8bd..ae727a4 100644
--- a/libtommath/bn_prime_tab.c
+++ b/libtommath/bn_prime_tab.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_PRIME_TAB_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 const mp_digit ltm_prime_tab[] = {
   0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
@@ -55,3 +55,7 @@ const mp_digit ltm_prime_tab[] = {
 #endif
 };
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_reverse.c b/libtommath/bn_reverse.c
index 9d7fd29..fc6eb2d 100644
--- a/libtommath/bn_reverse.c
+++ b/libtommath/bn_reverse.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_REVERSE_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* reverse an array, used for radix code */
@@ -33,3 +33,7 @@ bn_reverse (unsigned char *s, int len)
   }
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_s_mp_add.c b/libtommath/bn_s_mp_add.c
index 7527bf8..c2ad649 100644
--- a/libtommath/bn_s_mp_add.c
+++ b/libtommath/bn_s_mp_add.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_S_MP_ADD_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* low level addition, based on HAC pp.594, Algorithm 14.7 */
@@ -36,7 +36,7 @@ s_mp_add (mp_int * a, mp_int * b, mp_int * c)
   }
 
   /* init result */
-  if (c->alloc < max + 1) {
+  if (c->alloc < (max + 1)) {
     if ((res = mp_grow (c, max + 1)) != MP_OKAY) {
       return res;
     }
@@ -47,8 +47,8 @@ s_mp_add (mp_int * a, mp_int * b, mp_int * c)
   c->used = max + 1;
 
   {
-    register mp_digit u, *tmpa, *tmpb, *tmpc;
-    register int i;
+    mp_digit u, *tmpa, *tmpb, *tmpc;
+    int i;
 
     /* alias for digit pointers */
 
@@ -103,3 +103,7 @@ s_mp_add (mp_int * a, mp_int * b, mp_int * c)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_s_mp_exptmod.c b/libtommath/bn_s_mp_exptmod.c
index ff6bd54..63e1b1e 100644
--- a/libtommath/bn_s_mp_exptmod.c
+++ b/libtommath/bn_s_mp_exptmod.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_S_MP_EXPTMOD_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 #ifdef MP_LOW_MEM
    #define TAB_SIZE 32
@@ -164,12 +164,12 @@ int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
      * in the exponent.  Technically this opt is not required but it
      * does lower the # of trivial squaring/reductions used
      */
-    if (mode == 0 && y == 0) {
+    if ((mode == 0) && (y == 0)) {
       continue;
     }
 
     /* if the bit is zero and mode == 1 then we square */
-    if (mode == 1 && y == 0) {
+    if ((mode == 1) && (y == 0)) {
       if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
         goto LBL_RES;
       }
@@ -211,7 +211,7 @@ int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
   }
 
   /* if bits remain then square/multiply */
-  if (mode == 2 && bitcpy > 0) {
+  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) {
@@ -246,3 +246,7 @@ LBL_M:
   return err;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_s_mp_mul_digs.c b/libtommath/bn_s_mp_mul_digs.c
index 401f32e..bd8553d 100644
--- a/libtommath/bn_s_mp_mul_digs.c
+++ b/libtommath/bn_s_mp_mul_digs.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_S_MP_MUL_DIGS_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* multiplies |a| * |b| and only computes upto digs digits of result
@@ -29,8 +29,8 @@ int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
 
   /* can we use the fast multiplier? */
   if (((digs) < MP_WARRAY) &&
-      MIN (a->used, b->used) < 
-          (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+      (MIN (a->used, b->used) < 
+          (1 << ((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))))) {
     return fast_s_mp_mul_digs (a, b, c, digs);
   }
 
@@ -61,9 +61,9 @@ int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
     /* 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);
+      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));
@@ -72,7 +72,7 @@ int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
       u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
     }
     /* set carry if it is placed below digs */
-    if (ix + iy < digs) {
+    if ((ix + iy) < digs) {
       *tmpt = u;
     }
   }
@@ -84,3 +84,7 @@ int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_s_mp_mul_high_digs.c b/libtommath/bn_s_mp_mul_high_digs.c
index f4dca76..153cea44 100644
--- a/libtommath/bn_s_mp_mul_high_digs.c
+++ b/libtommath/bn_s_mp_mul_high_digs.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_S_MP_MUL_HIGH_DIGS_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* multiplies |a| * |b| and does not compute the lower digs digits
@@ -30,7 +30,7 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
   /* 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)))) {
+      && (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
@@ -57,9 +57,9 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
 
     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);
+      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));
@@ -75,3 +75,7 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_s_mp_sqr.c b/libtommath/bn_s_mp_sqr.c
index 464663f..68c95bc 100644
--- a/libtommath/bn_s_mp_sqr.c
+++ b/libtommath/bn_s_mp_sqr.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_S_MP_SQR_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
@@ -24,18 +24,18 @@ int s_mp_sqr (mp_int * a, mp_int * b)
   mp_digit u, tmpx, *tmpt;
 
   pa = a->used;
-  if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) {
+  if ((res = mp_init_size (&t, (2 * pa) + 1)) != MP_OKAY) {
     return res;
   }
 
   /* default used is maximum possible size */
-  t.used = 2*pa + 1;
+  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]);
+    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));
@@ -47,7 +47,7 @@ int s_mp_sqr (mp_int * a, mp_int * b)
     tmpx        = a->dp[ix];
 
     /* alias for where to store the results */
-    tmpt        = t.dp + (2*ix + 1);
+    tmpt        = t.dp + ((2 * ix) + 1);
     
     for (iy = ix + 1; iy < pa; iy++) {
       /* first calculate the product */
@@ -78,3 +78,7 @@ int s_mp_sqr (mp_int * a, mp_int * b)
   return MP_OKAY;
 }
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bn_s_mp_sub.c b/libtommath/bn_s_mp_sub.c
index 328c9e5..c0ea556 100644
--- a/libtommath/bn_s_mp_sub.c
+++ b/libtommath/bn_s_mp_sub.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BN_S_MP_SUB_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
@@ -35,8 +35,8 @@ s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
   c->used = max;
 
   {
-    register mp_digit u, *tmpa, *tmpb, *tmpc;
-    register int i;
+    mp_digit u, *tmpa, *tmpb, *tmpc;
+    int i;
 
     /* alias for digit pointers */
     tmpa = a->dp;
@@ -47,14 +47,14 @@ s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
     u = 0;
     for (i = 0; i < min; i++) {
       /* T[i] = A[i] - B[i] - U */
-      *tmpc = *tmpa++ - *tmpb++ - 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));
+      u = *tmpc >> ((mp_digit)((CHAR_BIT * sizeof(mp_digit)) - 1));
 
       /* Clear carry from T[i] */
       *tmpc++ &= MP_MASK;
@@ -66,7 +66,7 @@ s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
       *tmpc = *tmpa++ - u;
 
       /* U = carry bit of T[i] */
-      u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
+      u = *tmpc >> ((mp_digit)((CHAR_BIT * sizeof(mp_digit)) - 1));
 
       /* Clear carry from T[i] */
       *tmpc++ &= MP_MASK;
@@ -83,3 +83,7 @@ s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
 }
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/bncore.c b/libtommath/bncore.c
index eb95a2e..9552714 100644
--- a/libtommath/bncore.c
+++ b/libtommath/bncore.c
@@ -1,4 +1,4 @@
-#include <tommath.h>
+#include <tommath_private.h>
 #ifdef BNCORE_C
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
@@ -12,7 +12,7 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
  */
 
 /* Known optimal configurations
@@ -30,3 +30,7 @@ int     KARATSUBA_MUL_CUTOFF = 80,      /* Min. number of digits before Karatsub
         TOOM_MUL_CUTOFF      = 350,      /* no optimal values of these are known yet so set em high */
         TOOM_SQR_CUTOFF      = 400; 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/booker.pl b/libtommath/booker.pl
deleted file mode 100644
index df8b30d..0000000
--- a/libtommath/booker.pl
+++ /dev/null
@@ -1,265 +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++] = $_;
-            last if ($_ =~ /math\.libtomcrypt\.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);
diff --git a/libtommath/callgraph.txt b/libtommath/callgraph.txt
index 2efcf24..e98a910 100644
--- a/libtommath/callgraph.txt
+++ b/libtommath/callgraph.txt
@@ -1,249 +1,140 @@
-BN_PRIME_TAB_C
-
-
-BN_MP_SQRT_C
-+--->BN_MP_N_ROOT_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_C
-|   |   +--->BN_MP_INIT_COPY_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_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_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_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_ADD_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_GROW_C
-|   |   |   |   +--->BN_MP_CLEAR_C
-|   |   |   +--->BN_FAST_S_MP_SQR_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_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_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_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_ADD_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_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_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_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_CMP_MAG_C
+|   |   |   +--->BN_S_MP_SUB_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_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_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_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_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_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_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_LSHD_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_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_ZERO_C
+
+
+BN_MP_SET_C
++--->BN_MP_ZERO_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_MUL_D_C
+|   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_RSHD_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
+
+
+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_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_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_CLEAR_C
+|   |   +--->BN_MP_SET_C
 |   |   +--->BN_MP_COUNT_BITS_C
 |   |   +--->BN_MP_ABS_C
 |   |   +--->BN_MP_MUL_2D_C
@@ -252,6 +143,13 @@ BN_MP_SQRT_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
@@ -259,42 +157,481 @@ BN_MP_SQRT_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_COPY_C
++--->BN_MP_INIT_SIZE_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
+
+
+BN_MP_ABS_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
+
+
+BN_MP_RADIX_SMAP_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_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_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_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_LCM_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_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_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_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_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_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_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_COPY_C
+|   |   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_ADD_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_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_CMP_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_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_SUB_D_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_ADD_D_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_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_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_RSHD_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
@@ -303,6 +640,7 @@ BN_MP_SQRT_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
@@ -323,19 +661,25 @@ BN_MP_SQRT_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
@@ -344,134 +688,933 @@ BN_MP_SQRT_C
 |   +--->BN_S_MP_SUB_C
 |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_CLAMP_C
-+--->BN_MP_DIV_2_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_MAG_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_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_CMP_D_C
-
-
-BN_MP_EXCH_C
+BN_MP_INIT_SET_C
++--->BN_MP_INIT_C
++--->BN_MP_SET_C
+|   +--->BN_MP_ZERO_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_INIT_C
-|   |   |   +--->BN_MP_MOD_2D_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_CLEAR_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
-|   |   +--->BN_MP_DIV_3_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_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_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_COPY_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   +--->BN_MP_RSHD_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_C
-|   +--->BN_MP_INIT_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_CLEAR_C
-|   |   +--->BN_MP_SET_C
-|   |   +--->BN_MP_COUNT_BITS_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_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_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_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_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_MUL_2D_C
-|   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_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_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_CLAMP_C
-|   |   +--->BN_MP_CMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_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_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_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_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_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_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_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_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_GET_INT_C
-+--->BN_MP_SQRT_C
-|   +--->BN_MP_N_ROOT_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_C
-|   |   |   +--->BN_MP_INIT_COPY_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_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_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_CLEAR_C
 |   |   |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -509,43 +1652,327 @@ BN_MP_IS_SQUARE_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_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_S_MP_ADD_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_RSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_ZERO_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_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_FAST_S_MP_SQR_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_S_MP_SQR_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_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_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_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_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_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_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_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_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_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_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
@@ -583,32 +2010,96 @@ BN_MP_IS_SQUARE_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_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_ADD_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_FAST_S_MP_MUL_DIGS_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
@@ -661,18 +2152,14 @@ BN_MP_IS_SQUARE_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_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -744,74 +2231,78 @@ BN_MP_IS_SQUARE_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_EXCH_C
 |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_INIT_COPY_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_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_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_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_MUL_D_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_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_CLEAR_C
 |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_MAG_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_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_SQR_C
-|   +--->BN_MP_TOOM_SQR_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_INIT_C
 |   |   |   +--->BN_MP_CLEAR_C
 |   |   +--->BN_MP_MOD_2D_C
 |   |   |   +--->BN_MP_ZERO_C
@@ -852,7 +2343,6 @@ BN_MP_IS_SQUARE_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
@@ -860,498 +2350,81 @@ BN_MP_IS_SQUARE_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_CLEAR_MULTI_C
 |   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_KARATSUBA_SQR_C
+|   +--->BN_MP_KARATSUBA_MUL_C
 |   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
 |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_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_ADD_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_GROW_C
 |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_FAST_S_MP_SQR_C
+|   +--->BN_FAST_S_MP_MUL_DIGS_C
 |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_SQR_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_CMP_MAG_C
 +--->BN_MP_CLEAR_C
-
-
-BN_MP_NEG_C
-+--->BN_MP_COPY_C
-|   +--->BN_MP_GROW_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_MOD_C
+|   +--->BN_MP_DIV_C
+|   |   +--->BN_MP_CMP_MAG_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_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_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_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_INVMOD_SLOW_C
+|   |   +--->BN_MP_ZERO_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_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_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_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_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_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_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_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_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_ADD_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_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_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_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_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_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_ADD_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_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_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
@@ -1359,14 +2432,23 @@ BN_MP_EXPTMOD_C
 |   |   +--->BN_S_MP_SUB_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_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_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_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
@@ -1390,10 +2472,13 @@ BN_MP_EXPTMOD_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
@@ -1404,6 +2489,9 @@ 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
@@ -1412,164 +2500,12 @@ BN_MP_EXPTMOD_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_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_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_S_MP_ADD_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_GROW_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_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_ADD_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_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_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
@@ -1577,50 +2513,10 @@ BN_MP_EXPTMOD_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_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_MP_CMP_D_C
+|   +--->BN_MP_ADD_C
 |   |   +--->BN_S_MP_ADD_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
@@ -1628,154 +2524,23 @@ BN_MP_EXPTMOD_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_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_ADD_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_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_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_SET_C
-|   |   +--->BN_MP_ZERO_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_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_SET_C
+|   |   |   +--->BN_MP_COUNT_BITS_C
+|   |   |   +--->BN_MP_ABS_C
 |   |   |   +--->BN_MP_MUL_2D_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_LSHD_C
@@ -1799,10 +2564,13 @@ BN_MP_EXPTMOD_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
@@ -1813,6 +2581,9 @@ 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
@@ -1821,169 +2592,60 @@ BN_MP_EXPTMOD_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_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_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_S_MP_ADD_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_GROW_C
-|   |   +--->BN_FAST_S_MP_SQR_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_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_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_ADD_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_LSHD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_FAST_S_MP_MUL_DIGS_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_CMP_D_C
+|   +--->BN_MP_CMP_MAG_C
 |   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLEAR_MULTI_C
+|   |   +--->BN_MP_CLEAR_C
 
 
-BN_MP_OR_C
+BN_MP_PRIME_MILLER_RABIN_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_CLAMP_C
-+--->BN_MP_EXCH_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_ZERO_C
-
-
-BN_MP_GROW_C
-
-
-BN_MP_COUNT_BITS_C
-
-
-BN_MP_PRIME_FERMAT_C
-+--->BN_MP_CMP_D_C
-+--->BN_MP_INIT_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
@@ -2018,18 +2680,10 @@ BN_MP_PRIME_FERMAT_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
@@ -2040,6 +2694,7 @@ BN_MP_PRIME_FERMAT_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
@@ -2048,7 +2703,6 @@ BN_MP_PRIME_FERMAT_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_SET_C
 |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   +--->BN_MP_DIV_2_C
@@ -2107,18 +2761,10 @@ BN_MP_PRIME_FERMAT_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
@@ -2129,6 +2775,7 @@ BN_MP_PRIME_FERMAT_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
@@ -2137,7 +2784,6 @@ BN_MP_PRIME_FERMAT_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_SET_C
@@ -2206,15 +2852,8 @@ BN_MP_PRIME_FERMAT_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
@@ -2224,9 +2863,6 @@ BN_MP_PRIME_FERMAT_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_REDUCE_C
-|   |   |   +--->BN_MP_INIT_COPY_C
-|   |   |   |   +--->BN_MP_COPY_C
-|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   +--->BN_MP_MUL_C
@@ -2276,18 +2912,14 @@ BN_MP_PRIME_FERMAT_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_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -2352,15 +2984,6 @@ BN_MP_PRIME_FERMAT_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
@@ -2410,18 +3033,14 @@ BN_MP_PRIME_FERMAT_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_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -2468,15 +3087,8 @@ BN_MP_PRIME_FERMAT_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
@@ -2485,6 +3097,7 @@ BN_MP_PRIME_FERMAT_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
@@ -2493,7 +3106,6 @@ BN_MP_PRIME_FERMAT_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
 |   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_SQR_C
@@ -2541,22 +3153,16 @@ BN_MP_PRIME_FERMAT_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_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_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_GROW_C
 |   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
@@ -2609,18 +3215,14 @@ BN_MP_PRIME_FERMAT_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_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -2639,15 +3241,6 @@ BN_MP_PRIME_FERMAT_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
@@ -2690,15 +3283,6 @@ BN_MP_PRIME_FERMAT_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
@@ -2771,18 +3355,14 @@ BN_MP_PRIME_FERMAT_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_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -2822,15 +3402,8 @@ BN_MP_PRIME_FERMAT_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
@@ -2839,6 +3412,7 @@ BN_MP_PRIME_FERMAT_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
@@ -2847,7 +3421,6 @@ BN_MP_PRIME_FERMAT_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
 |   |   +--->BN_MP_SET_C
 |   |   |   +--->BN_MP_ZERO_C
 |   |   +--->BN_MP_MOD_C
@@ -2877,15 +3450,8 @@ BN_MP_PRIME_FERMAT_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
@@ -2894,6 +3460,7 @@ BN_MP_PRIME_FERMAT_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
@@ -2902,7 +3469,6 @@ BN_MP_PRIME_FERMAT_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
 |   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_SQR_C
@@ -2950,22 +3516,16 @@ BN_MP_PRIME_FERMAT_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_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_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_GROW_C
 |   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
@@ -3018,18 +3578,14 @@ BN_MP_PRIME_FERMAT_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_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -3044,312 +3600,87 @@ BN_MP_PRIME_FERMAT_C
 |   |   +--->BN_MP_EXCH_C
 +--->BN_MP_CMP_C
 |   +--->BN_MP_CMP_MAG_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_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_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_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_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_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_MOD_2D_C
-+--->BN_MP_ZERO_C
-+--->BN_MP_COPY_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_CLAMP_C
-
-
-BN_MP_TORADIX_N_C
-+--->BN_MP_INIT_COPY_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_CMP_C
-+--->BN_MP_CMP_MAG_C
-
-
-BNCORE_C
-
-
-BN_MP_TORADIX_C
-+--->BN_MP_INIT_COPY_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_ADD_D_C
-+--->BN_MP_GROW_C
-+--->BN_MP_SUB_D_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_FAST_S_MP_MUL_DIGS_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_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_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_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_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_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_CMP_MAG_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_S_MP_ADD_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_GROW_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_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_ADD_C
-|   |   +--->BN_S_MP_ADD_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_INVMOD_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_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_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_SET_C
 |   |   |   +--->BN_MP_COUNT_BITS_C
 |   |   |   +--->BN_MP_ABS_C
@@ -3358,7 +3689,6 @@ BN_MP_INVMOD_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
@@ -3373,18 +3703,9 @@ BN_MP_INVMOD_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
@@ -3393,8 +3714,7 @@ BN_MP_INVMOD_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
@@ -3403,114 +3723,234 @@ BN_MP_INVMOD_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_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_INIT_C
 |   +--->BN_MP_SET_C
 |   |   +--->BN_MP_ZERO_C
-|   +--->BN_MP_DIV_2_C
+|   +--->BN_MP_COPY_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_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_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_MP_CMP_C
-|   |   |   +--->BN_MP_SUB_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_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_MUL_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_CLEAR_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_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_EXCH_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_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_EXCH_C
+|   |   |   +--->BN_MP_CLEAR_C
 |   +--->BN_MP_SUB_C
 |   |   +--->BN_S_MP_ADD_C
 |   |   |   +--->BN_MP_GROW_C
@@ -3519,41 +3959,14 @@ BN_MP_INVMOD_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_AND_C
-+--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_COPY_C
+|   +--->BN_MP_MUL_D_C
 |   |   +--->BN_MP_GROW_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_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_CLAMP_C
 |   +--->BN_MP_DIV_C
 |   |   +--->BN_MP_CMP_MAG_C
 |   |   +--->BN_MP_ZERO_C
-|   |   +--->BN_MP_SET_C
+|   |   +--->BN_MP_INIT_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
 |   |   +--->BN_MP_COUNT_BITS_C
 |   |   +--->BN_MP_ABS_C
 |   |   +--->BN_MP_MUL_2D_C
@@ -3562,13 +3975,6 @@ BN_FAST_MP_INVMOD_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
@@ -3592,127 +3998,189 @@ BN_FAST_MP_INVMOD_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_ADD_C
-|   |   +--->BN_S_MP_ADD_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_EXCH_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_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_MULTI_C
+|   +--->BN_MP_EXCH_C
 |   +--->BN_MP_CLEAR_C
 
 
-BN_MP_FWRITE_C
-+--->BN_MP_RADIX_SIZE_C
-|   +--->BN_MP_COUNT_BITS_C
-|   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_DIV_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_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_DIV_2D_C
+|   |   +--->BN_MP_RSHD_C
 |   |   |   +--->BN_MP_ZERO_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_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_TORADIX_C
-|   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_DIV_D_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_DIV_2D_C
+|   |   +--->BN_MP_RSHD_C
 |   |   |   +--->BN_MP_ZERO_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_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_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_CLEAR_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_MP_N_ROOT_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_C
+BN_MP_EXPT_D_C
++--->BN_MP_EXPT_D_EX_C
 |   +--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_SQR_C
-|   |   +--->BN_MP_TOOM_SQR_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   +--->BN_MP_COPY_C
+|   |   |   +--->BN_MP_GROW_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_MUL_2_C
@@ -3752,41 +4220,41 @@ BN_MP_N_ROOT_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLEAR_MULTI_C
 |   |   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_KARATSUBA_SQR_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_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_ADD_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_GROW_C
 |   |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_FAST_S_MP_SQR_C
+|   |   +--->BN_FAST_S_MP_MUL_DIGS_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_S_MP_SQR_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_MUL_C
-|   |   +--->BN_MP_TOOM_MUL_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
@@ -3824,122 +4292,51 @@ BN_MP_N_ROOT_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_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_ADD_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_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_KARATSUBA_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_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_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_INIT_SIZE_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_ADD_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_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_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_MUL_D_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_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
@@ -3948,6 +4345,13 @@ BN_MP_N_ROOT_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
@@ -3956,6 +4360,7 @@ BN_MP_N_ROOT_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
@@ -3966,65 +4371,30 @@ BN_MP_N_ROOT_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_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_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_CLEAR_C
 
 
-BN_MP_PRIME_RABIN_MILLER_TRIALS_C
+BN_MP_RSHD_C
++--->BN_MP_ZERO_C
 
 
-BN_MP_RADIX_SIZE_C
-+--->BN_MP_COUNT_BITS_C
-+--->BN_MP_INIT_COPY_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_NEG_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_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_SHRINK_C
 
 
 BN_MP_PRIME_RANDOM_EX_C
@@ -4069,6 +4439,7 @@ BN_MP_PRIME_RANDOM_EX_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
@@ -4134,6 +4505,7 @@ BN_MP_PRIME_RANDOM_EX_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
@@ -4142,7 +4514,6 @@ BN_MP_PRIME_RANDOM_EX_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
@@ -4212,6 +4583,7 @@ BN_MP_PRIME_RANDOM_EX_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
@@ -4220,7 +4592,6 @@ BN_MP_PRIME_RANDOM_EX_C
 |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_DIV_2_C
@@ -4346,18 +4717,14 @@ BN_MP_PRIME_RANDOM_EX_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_CMP_MAG_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -4469,18 +4836,14 @@ BN_MP_PRIME_RANDOM_EX_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_CMP_MAG_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -4536,6 +4899,7 @@ BN_MP_PRIME_RANDOM_EX_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
@@ -4544,7 +4908,6 @@ BN_MP_PRIME_RANDOM_EX_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_SQR_C
@@ -4592,22 +4955,16 @@ BN_MP_PRIME_RANDOM_EX_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_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_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_GROW_C
 |   |   |   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -4660,18 +5017,14 @@ BN_MP_PRIME_RANDOM_EX_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_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -4800,18 +5153,14 @@ BN_MP_PRIME_RANDOM_EX_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_CMP_MAG_C
-|   |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -4860,6 +5209,7 @@ BN_MP_PRIME_RANDOM_EX_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
@@ -4868,7 +5218,6 @@ BN_MP_PRIME_RANDOM_EX_C
 |   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   +--->BN_MP_MOD_C
 |   |   |   |   |   +--->BN_MP_DIV_C
 |   |   |   |   |   |   +--->BN_MP_CMP_MAG_C
@@ -4906,6 +5255,7 @@ BN_MP_PRIME_RANDOM_EX_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
@@ -4914,7 +5264,6 @@ BN_MP_PRIME_RANDOM_EX_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_SQR_C
@@ -4962,22 +5311,16 @@ BN_MP_PRIME_RANDOM_EX_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_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_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_GROW_C
 |   |   |   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -5030,18 +5373,14 @@ BN_MP_PRIME_RANDOM_EX_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_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -5110,22 +5449,16 @@ BN_MP_PRIME_RANDOM_EX_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_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_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_GROW_C
 |   |   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   |   +--->BN_MP_GROW_C
@@ -5175,6 +5508,7 @@ BN_MP_PRIME_RANDOM_EX_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
@@ -5183,7 +5517,6 @@ BN_MP_PRIME_RANDOM_EX_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_SUB_D_C
@@ -5201,19 +5534,62 @@ BN_MP_PRIME_RANDOM_EX_C
 |   +--->BN_MP_CLAMP_C
 
 
-BN_MP_KARATSUBA_SQR_C
-+--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_INIT_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_SQR_C
-|   +--->BN_MP_TOOM_SQR_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_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
@@ -5223,106 +5599,793 @@ BN_MP_KARATSUBA_SQR_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_FAST_S_MP_SQR_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_S_MP_SQR_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_CMP_MAG_C
-|   +--->BN_S_MP_SUB_C
-|   |   +--->BN_MP_GROW_C
 +--->BN_S_MP_ADD_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_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_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_INIT_COPY_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_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_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_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_CLAMP_C
+BN_MP_INIT_MULTI_C
++--->BN_MP_INIT_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_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_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_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_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_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_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_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_S_MP_ADD_C
+|   |   +--->BN_MP_GROW_C
+|   |   +--->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_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_RSHD_C
-|   +--->BN_MP_ZERO_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_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_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_S_MP_ADD_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_MP_CLEAR_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_RSHD_C
+|   |   |   |   +--->BN_MP_ZERO_C
+|   +--->BN_FAST_S_MP_MUL_DIGS_C
 |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_S_MP_SQR_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_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_ADD_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
@@ -5330,7 +6393,10 @@ BN_MP_TOOM_SQR_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_CMP_D_C
++--->BN_MP_ADD_C
 |   +--->BN_S_MP_ADD_C
 |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_CLAMP_C
@@ -5338,38 +6404,713 @@ BN_MP_TOOM_SQR_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_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_MUL_2D_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_LSHD_C
+|   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_ZERO_C
 |   +--->BN_MP_CLAMP_C
-+--->BN_MP_MUL_D_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_DIV_3_C
-|   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_INIT_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_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_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_CLEAR_MULTI_C
-|   +--->BN_MP_CLEAR_C
+|   +--->BN_MP_RSHD_C
 
 
-BN_MP_MOD_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_DIV_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_MP_COPY_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_SET_C
 |   +--->BN_MP_COUNT_BITS_C
 |   +--->BN_MP_ABS_C
 |   +--->BN_MP_MUL_2D_C
@@ -5378,13 +7119,6 @@ BN_MP_MOD_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
@@ -5408,70 +7142,156 @@ BN_MP_MOD_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_ADD_C
-|   +--->BN_S_MP_ADD_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_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_INIT_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_TOOM_MUL_C
-+--->BN_MP_INIT_MULTI_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_MOD_2D_C
+BN_MP_INIT_SET_INT_C
++--->BN_MP_INIT_C
++--->BN_MP_SET_INT_C
 |   +--->BN_MP_ZERO_C
-|   +--->BN_MP_COPY_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_COPY_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_MUL_C
-|   +--->BN_MP_KARATSUBA_MUL_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   |   +--->BN_MP_INIT_C
-|   |   +--->BN_MP_CLAMP_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_CMP_MAG_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_CMP_MAG_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_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_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_MUL_2_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
@@ -5488,257 +7308,176 @@ BN_MP_TOOM_MUL_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_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_DIV_3_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_LSHD_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_CLEAR_MULTI_C
-|   +--->BN_MP_CLEAR_C
 
 
-BN_MP_PRIME_IS_PRIME_C
+BN_MP_SQRTMOD_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_CLEAR_C
-+--->BN_MP_INIT_C
-+--->BN_MP_SET_C
-|   +--->BN_MP_ZERO_C
-+--->BN_MP_PRIME_MILLER_RABIN_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_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_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_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_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_DIV_2_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_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_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_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_COPY_C
+|   |   |   +--->BN_MP_ADD_C
+|   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_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_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_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_ABS_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_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_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
@@ -5759,8 +7498,18 @@ BN_MP_PRIME_IS_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_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
@@ -5769,109 +7518,9 @@ BN_MP_PRIME_IS_PRIME_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_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_ADD_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_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_LSHD_C
-|   |   |   |   |   +--->BN_MP_GROW_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
@@ -5880,91 +7529,18 @@ 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_S_MP_SUB_C
+|   |   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_SUB_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_MP_CMP_MAG_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_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_ADD_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_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_ADD_C
 |   |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -5972,13 +7548,18 @@ 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_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
@@ -5999,8 +7580,18 @@ BN_MP_PRIME_IS_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_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
@@ -6009,6 +7600,9 @@ BN_MP_PRIME_IS_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
 |   |   |   |   |   |   +--->BN_MP_GROW_C
@@ -6017,17 +7611,98 @@ 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_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_SQR_C
-|   |   |   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_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_ZERO_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
 |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   +--->BN_MP_ZERO_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
@@ -6046,9 +7721,6 @@ BN_MP_PRIME_IS_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
@@ -6062,40 +7734,95 @@ BN_MP_PRIME_IS_PRIME_C
 |   |   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_KARATSUBA_SQR_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_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_S_MP_ADD_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_GROW_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_FAST_S_MP_MUL_DIGS_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SQR_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_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
@@ -6114,9 +7841,6 @@ BN_MP_PRIME_IS_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
@@ -6133,22 +7857,17 @@ BN_MP_PRIME_IS_PRIME_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_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -6156,56 +7875,58 @@ BN_MP_PRIME_IS_PRIME_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_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_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_MOD_C
+|   |   |   +--->BN_MP_DIV_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_COPY_C
 |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_S_MP_SUB_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_REDUCE_2K_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
@@ -6213,172 +7934,70 @@ 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_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_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_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_ADD_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_LSHD_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   |   +--->BN_MP_RSHD_C
-|   |   |   |   |   |   |   |   +--->BN_MP_ZERO_C
-|   |   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_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_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_SUB_C
+|   |   |   |   |   +--->BN_S_MP_ADD_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_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_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_MUL_2D_C
+|   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_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_MUL_D_C
-|   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   |   +--->BN_MP_CLAMP_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
@@ -6387,17 +8006,139 @@ BN_MP_PRIME_IS_PRIME_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_COPY_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_SQR_C
-|   |   |   |   +--->BN_MP_TOOM_SQR_C
-|   |   |   |   |   +--->BN_MP_INIT_MULTI_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_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_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
@@ -6416,9 +8157,6 @@ BN_MP_PRIME_IS_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
@@ -6432,117 +8170,138 @@ BN_MP_PRIME_IS_PRIME_C
 |   |   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   +--->BN_MP_KARATSUBA_SQR_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_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_ADD_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_GROW_C
-|   |   |   |   +--->BN_FAST_S_MP_SQR_C
+|   |   |   |   +--->BN_FAST_S_MP_MUL_DIGS_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_S_MP_SQR_C
+|   |   |   |   +--->BN_S_MP_MUL_DIGS_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_MOD_C
+|   |   |   |   +--->BN_MP_DIV_C
+|   |   |   |   |   +--->BN_MP_CMP_MAG_C
+|   |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_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_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_EXCH_C
+|   |   |   |   |   +--->BN_MP_INIT_SIZE_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_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_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_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   |   |   +--->BN_MP_ADD_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_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_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_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_CMP_C
-|   |   +--->BN_MP_CMP_MAG_C
-|   +--->BN_MP_SQRMOD_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_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
@@ -6561,9 +8320,6 @@ BN_MP_PRIME_IS_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
@@ -6575,31 +8331,20 @@ BN_MP_PRIME_IS_PRIME_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_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_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_GROW_C
-|   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
@@ -6607,157 +8352,83 @@ BN_MP_PRIME_IS_PRIME_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_LSHD_C
-|   |   |   |   |   |   +--->BN_MP_RSHD_C
+|   |   +--->BN_MP_MUL_C
+|   |   |   +--->BN_MP_TOOM_MUL_C
+|   |   |   |   +--->BN_MP_MOD_2D_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_SUB_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_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_CLEAR_MULTI_C
-|   |   |   |   +--->BN_MP_INIT_SIZE_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_LSHD_C
+|   |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_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_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_EXCH_C
-|   +--->BN_MP_CLEAR_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_COPY_C
-+--->BN_MP_GROW_C
-
-
-BN_S_MP_SUB_C
-+--->BN_MP_GROW_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_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_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_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_SUB_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_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_MULMOD_C
-|   +--->BN_MP_MUL_C
-|   |   +--->BN_MP_TOOM_MUL_C
-|   |   |   +--->BN_MP_INIT_MULTI_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_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
@@ -6776,9 +8447,6 @@ BN_MP_EXPTMOD_FAST_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
@@ -6790,43 +8458,38 @@ BN_MP_EXPTMOD_FAST_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_KARATSUBA_MUL_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_CMP_MAG_C
-|   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_ADD_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_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_FAST_S_MP_MUL_DIGS_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_MUL_DIGS_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
@@ -6866,582 +8529,144 @@ BN_MP_EXPTMOD_FAST_C
 |   |   |   |   +--->BN_MP_GROW_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_EXCH_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_MP_CMP_MAG_C
 |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_DIV_2D_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_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_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_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_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_MUL_2D_C
 |   |   |   |   +--->BN_MP_GROW_C
+|   |   |   |   +--->BN_MP_LSHD_C
 |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_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_GROW_C
+|   |   |   +--->BN_MP_DIV_3_C
+|   |   |   |   +--->BN_MP_INIT_SIZE_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_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_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_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_S_MP_ADD_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_GROW_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_CLEAR_MULTI_C
+|   |   |   |   +--->BN_MP_CLEAR_C
+|   |   +--->BN_MP_KARATSUBA_MUL_C
+|   |   |   +--->BN_MP_INIT_SIZE_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_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_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_RSHD_C
+|   |   |   +--->BN_MP_CLEAR_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_MP_GROW_C
-|   |   +--->BN_MP_CLEAR_MULTI_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_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_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_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_TO_UNSIGNED_BIN_C
-+--->BN_MP_INIT_COPY_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_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_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_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_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_S_MP_ADD_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_GROW_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_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
-|   |   |   +--->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_MOD_C
+|   |   +--->BN_MP_DIV_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_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_GROW_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_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_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_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_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_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_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_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_COPY_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_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_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_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_CLEAR_C
-+--->BN_MP_RSHD_C
-+--->BN_MP_CLAMP_C
-+--->BN_MP_EXCH_C
-
-
-BN_S_MP_ADD_C
-+--->BN_MP_GROW_C
-+--->BN_MP_CLAMP_C
++--->BN_MP_SET_C
++--->BN_MP_CLEAR_MULTI_C
+|   +--->BN_MP_CLEAR_C
 
 
-BN_FAST_S_MP_SQR_C
+BN_FAST_S_MP_MUL_HIGH_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_INIT_C
-+--->BN_MP_CLAMP_C
-+--->BN_MP_EXCH_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_XOR_C
-+--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-+--->BN_MP_CLAMP_C
-+--->BN_MP_EXCH_C
-+--->BN_MP_CLEAR_C
-
-
-BN_MP_RADIX_SMAP_C
-
-
-BN_MP_DR_IS_MODULUS_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_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_INIT_MULTI_C
-+--->BN_MP_INIT_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_REVERSE_C
 
 
 BN_MP_PRIME_NEXT_PRIME_C
@@ -7483,6 +8708,7 @@ BN_MP_PRIME_NEXT_PRIME_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
@@ -7543,6 +8769,7 @@ BN_MP_PRIME_NEXT_PRIME_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
@@ -7551,7 +8778,6 @@ BN_MP_PRIME_NEXT_PRIME_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
@@ -7621,6 +8847,7 @@ BN_MP_PRIME_NEXT_PRIME_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
@@ -7629,7 +8856,6 @@ BN_MP_PRIME_NEXT_PRIME_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_DIV_2_C
@@ -7755,18 +8981,14 @@ BN_MP_PRIME_NEXT_PRIME_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_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -7878,18 +9100,14 @@ BN_MP_PRIME_NEXT_PRIME_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_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -7945,6 +9163,7 @@ BN_MP_PRIME_NEXT_PRIME_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
@@ -7953,7 +9172,6 @@ BN_MP_PRIME_NEXT_PRIME_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_SQR_C
@@ -8001,22 +9219,16 @@ BN_MP_PRIME_NEXT_PRIME_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_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_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_GROW_C
 |   |   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -8069,18 +9281,14 @@ BN_MP_PRIME_NEXT_PRIME_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_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -8209,18 +9417,14 @@ BN_MP_PRIME_NEXT_PRIME_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_CMP_MAG_C
-|   |   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -8269,6 +9473,7 @@ BN_MP_PRIME_NEXT_PRIME_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
@@ -8277,7 +9482,6 @@ BN_MP_PRIME_NEXT_PRIME_C
 |   |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_MOD_C
 |   |   |   |   +--->BN_MP_DIV_C
 |   |   |   |   |   +--->BN_MP_CMP_MAG_C
@@ -8315,6 +9519,7 @@ BN_MP_PRIME_NEXT_PRIME_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
@@ -8323,7 +9528,6 @@ BN_MP_PRIME_NEXT_PRIME_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_SQR_C
@@ -8371,22 +9575,16 @@ BN_MP_PRIME_NEXT_PRIME_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_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_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_GROW_C
 |   |   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
@@ -8439,18 +9637,14 @@ BN_MP_PRIME_NEXT_PRIME_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_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -8519,22 +9713,16 @@ BN_MP_PRIME_NEXT_PRIME_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_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_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_GROW_C
 |   |   |   |   +--->BN_MP_CLEAR_C
 |   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   +--->BN_MP_GROW_C
@@ -8584,6 +9772,7 @@ BN_MP_PRIME_NEXT_PRIME_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
@@ -8592,88 +9781,50 @@ BN_MP_PRIME_NEXT_PRIME_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_SIGNED_BIN_SIZE_C
-+--->BN_MP_UNSIGNED_BIN_SIZE_C
-|   +--->BN_MP_COUNT_BITS_C
-
-
-BN_MP_INVMOD_SLOW_C
+BN_MP_TOOM_MUL_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_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_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_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_S_MP_SUB_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_CLAMP_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_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_EXCH_C
-+--->BN_MP_COPY_C
-|   +--->BN_MP_GROW_C
-+--->BN_MP_SET_C
-|   +--->BN_MP_ZERO_C
-+--->BN_MP_DIV_2_C
++--->BN_MP_MUL_2_C
 |   +--->BN_MP_GROW_C
-|   +--->BN_MP_CLAMP_C
 +--->BN_MP_ADD_C
 |   +--->BN_S_MP_ADD_C
 |   |   +--->BN_MP_GROW_C
@@ -8690,194 +9841,143 @@ BN_MP_INVMOD_SLOW_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_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_LCM_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_ZERO_C
-|   +--->BN_MP_INIT_COPY_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_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_CLAMP_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_MP_DIV_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_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_INIT_C
-|   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_CLEAR_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_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_CLEAR_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_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_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_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_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_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_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_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_CLEAR_C
-|   |   +--->BN_MP_LSHD_C
-|   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_EXCH_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_MP_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
+|   |   +--->BN_MP_INIT_C
+|   |   +--->BN_MP_INIT_COPY_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_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_CLEAR_MULTI_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_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_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
@@ -8889,8 +9989,6 @@ BN_MP_REDUCE_2K_L_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
@@ -8931,22 +10029,16 @@ BN_MP_REDUCE_2K_L_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_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_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_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
@@ -8956,215 +10048,131 @@ BN_MP_REDUCE_2K_L_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_REVERSE_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_SET_C
-+--->BN_MP_ZERO_C
-
-
-BN_MP_GCD_C
-+--->BN_MP_ABS_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-+--->BN_MP_ZERO_C
-+--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-+--->BN_MP_CNT_LSB_C
-+--->BN_MP_DIV_2D_C
-|   +--->BN_MP_COPY_C
++--->BN_S_MP_MUL_HIGH_DIGS_C
+|   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
 |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_MOD_2D_C
 |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_RSHD_C
+|   +--->BN_MP_INIT_SIZE_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_CLEAR_C
++--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
 |   +--->BN_MP_GROW_C
 |   +--->BN_MP_CLAMP_C
-+--->BN_MP_MUL_2D_C
++--->BN_MP_MOD_2D_C
+|   +--->BN_MP_ZERO_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_CLEAR_C
-
-
-BN_MP_REDUCE_2K_SETUP_L_C
-+--->BN_MP_INIT_C
-+--->BN_MP_2EXPT_C
-|   +--->BN_MP_ZERO_C
-|   +--->BN_MP_GROW_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_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_FAST_S_MP_MUL_HIGH_DIGS_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_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_S_MP_MUL_DIGS_C
+|   +--->BN_FAST_S_MP_MUL_DIGS_C
+|   |   +--->BN_MP_GROW_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_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_INIT_SET_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_CMP_D_C
 +--->BN_MP_SET_C
 |   +--->BN_MP_ZERO_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_LSHD_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_ADD_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_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_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_ERROR_C
-
-
-BN_MP_EXPT_D_C
-+--->BN_MP_INIT_COPY_C
-|   +--->BN_MP_COPY_C
-|   |   +--->BN_MP_GROW_C
-+--->BN_MP_SET_C
-|   +--->BN_MP_ZERO_C
-+--->BN_MP_SQR_C
-|   +--->BN_MP_TOOM_SQR_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_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_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_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_MUL_2_C
+|   |   +--->BN_MP_DIV_2_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_C
+|   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_SUB_C
 |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
@@ -9172,7 +10180,10 @@ BN_MP_EXPT_D_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_CMP_D_C
+|   |   +--->BN_MP_ADD_C
 |   |   |   +--->BN_S_MP_ADD_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
@@ -9180,199 +10191,495 @@ BN_MP_EXPT_D_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_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_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_LSHD_C
-|   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_D_C
+|   |   +--->BN_MP_SET_C
+|   |   |   +--->BN_MP_ZERO_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_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_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_ADD_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_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_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_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_C
+|   |   +--->BN_MP_CLEAR_MULTI_C
+|   |   |   +--->BN_MP_CLEAR_C
 +--->BN_MP_CLEAR_C
-+--->BN_MP_MUL_C
-|   +--->BN_MP_TOOM_MUL_C
-|   |   +--->BN_MP_INIT_MULTI_C
-|   |   +--->BN_MP_MOD_2D_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_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_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_MAG_C
-|   |   |   +--->BN_S_MP_SUB_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_SUB_C
-|   |   |   +--->BN_S_MP_ADD_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_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_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_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_DIV_2_C
-|   |   |   +--->BN_MP_GROW_C
+|   |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_2D_C
+|   |   |   +--->BN_MP_EXCH_C
+|   |   +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_MUL_D_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_3_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_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_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_LSHD_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_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_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_CLAMP_C
+|   +--->BN_MP_REDUCE_2K_SETUP_L_C
+|   |   +--->BN_MP_2EXPT_C
+|   |   |   +--->BN_MP_ZERO_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_S_MP_SUB_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_LSHD_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_CLAMP_C
-|   |   +--->BN_MP_CMP_C
-|   |   +--->BN_MP_SUB_C
-|   |   |   +--->BN_S_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_S_MP_SUB_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_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_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_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_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_CLAMP_C
-+--->BN_MP_REDUCE_C
-|   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_ZERO_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_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
@@ -9407,24 +10714,21 @@ BN_S_MP_EXPTMOD_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_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_S_MP_ADD_C
+|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_ADD_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_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
@@ -9432,29 +10736,25 @@ BN_S_MP_EXPTMOD_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_SET_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_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_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
@@ -9462,12 +10762,50 @@ BN_S_MP_EXPTMOD_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_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_ADD_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
@@ -9475,38 +10813,204 @@ BN_S_MP_EXPTMOD_C
 |   |   +--->BN_S_MP_SUB_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_CLAMP_C
-|   +--->BN_MP_CMP_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_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_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_2D_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_GROW_C
+|   |   |   |   +--->BN_MP_CLAMP_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_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_MP_COPY_C
-|   |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_RSHD_C
 |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   +--->BN_MP_MUL_2_C
@@ -9543,22 +11047,79 @@ BN_S_MP_EXPTMOD_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_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_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_ADD_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
@@ -9570,143 +11131,90 @@ BN_S_MP_EXPTMOD_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_EXCH_C
+
+
+BN_MP_LSHD_C
++--->BN_MP_GROW_C
++--->BN_MP_RSHD_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_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_ZERO_C
++--->BN_MP_COPY_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_DIV_C
 |   +--->BN_MP_CMP_MAG_C
-|   +--->BN_S_MP_SUB_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_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_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_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_S_MP_SUB_C
 |   |   |   +--->BN_MP_GROW_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_EXCH_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_DIV_2D_C
+|   |   +--->BN_MP_INIT_C
 |   |   +--->BN_MP_MOD_2D_C
-|   |   |   +--->BN_MP_ZERO_C
 |   |   |   +--->BN_MP_CLAMP_C
+|   |   +--->BN_MP_CLEAR_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_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_S_MP_ADD_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_GROW_C
-|   +--->BN_FAST_S_MP_SQR_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_S_MP_SQR_C
-|   |   +--->BN_MP_INIT_SIZE_C
-|   |   +--->BN_MP_CLAMP_C
-|   |   +--->BN_MP_EXCH_C
+|   +--->BN_MP_CLAMP_C
+|   +--->BN_MP_CLEAR_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
@@ -9742,76 +11250,63 @@ BN_S_MP_EXPTMOD_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_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_S_MP_ADD_C
+|   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_ADD_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_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_SET_C
-|   +--->BN_MP_ZERO_C
-+--->BN_MP_EXCH_C
-
-
-BN_MP_ABS_C
-+--->BN_MP_COPY_C
-|   +--->BN_MP_GROW_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_CLEAR_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_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_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_TO_SIGNED_BIN_C
-+--->BN_MP_TO_UNSIGNED_BIN_C
-|   +--->BN_MP_INIT_COPY_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_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_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
@@ -9819,21 +11314,28 @@ BN_MP_TO_SIGNED_BIN_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_DIV_2_C
-+--->BN_MP_GROW_C
-+--->BN_MP_CLAMP_C
-
-
-BN_MP_REDUCE_IS_2K_C
-+--->BN_MP_REDUCE_2K_C
-|   +--->BN_MP_INIT_C
-|   +--->BN_MP_COUNT_BITS_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_DIV_2D_C
-|   |   +--->BN_MP_COPY_C
-|   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_ZERO_C
 |   |   +--->BN_MP_MOD_2D_C
 |   |   |   +--->BN_MP_CLAMP_C
@@ -9841,185 +11343,85 @@ BN_MP_REDUCE_IS_2K_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_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_COUNT_BITS_C
-
-
-BN_MP_INIT_SIZE_C
-+--->BN_MP_INIT_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_SET_C
-+--->BN_MP_COUNT_BITS_C
-+--->BN_MP_ABS_C
-+--->BN_MP_MUL_2D_C
+BN_S_MP_MUL_HIGH_DIGS_C
++--->BN_FAST_S_MP_MUL_HIGH_DIGS_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_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_EXCH_C
 +--->BN_MP_CLEAR_C
 
 
-BN_MP_CLEAR_C
-
-
-BN_MP_MONTGOMERY_REDUCE_C
-+--->BN_FAST_MP_MONTGOMERY_REDUCE_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_RSHD_C
-|   |   +--->BN_MP_ZERO_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_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_MUL_2_C
-+--->BN_MP_GROW_C
+BN_MP_DR_SETUP_C
 
 
-BN_MP_UNSIGNED_BIN_SIZE_C
-+--->BN_MP_COUNT_BITS_C
+BN_MP_MUL_2_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_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_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_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_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_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_COPY_C
 |   |   |   +--->BN_MP_GROW_C
-|   |   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_RSHD_C
-|   |   +--->BN_MP_MUL_D_C
+|   +--->BN_MP_DIV_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_GROW_C
-|   +--->BN_MP_CLAMP_C
-+--->BN_MP_CMP_MAG_C
-+--->BN_S_MP_SUB_C
-|   +--->BN_MP_GROW_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_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
@@ -10027,71 +11429,92 @@ BN_MP_TO_SIGNED_BIN_N_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_REDUCE_IS_2K_L_C
+BN_MP_GROW_C
 
 
-BN_MP_RAND_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_LSHD_C
-|   +--->BN_MP_GROW_C
-|   +--->BN_MP_RSHD_C
-
 
-BN_MP_CNT_LSB_C
-
-
-BN_MP_2EXPT_C
-+--->BN_MP_ZERO_C
-+--->BN_MP_GROW_C
 
-
-BN_MP_RSHD_C
-+--->BN_MP_ZERO_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_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
 
 
-BN_MP_SHRINK_C
+BN_PRIME_TAB_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_COPY_C
-|   |   |   +--->BN_MP_GROW_C
-|   +--->BN_MP_DIV_2D_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_ZERO_C
-|   |   +--->BN_MP_MOD_2D_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_CLEAR_C
-|   |   +--->BN_MP_RSHD_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_REDUCE_C
-+--->BN_MP_REDUCE_SETUP_C
-|   +--->BN_MP_2EXPT_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_GROW_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_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_INIT_C
 |   |   |   +--->BN_MP_CLEAR_C
 |   |   +--->BN_MP_SET_C
 |   |   +--->BN_MP_COUNT_BITS_C
@@ -10117,7 +11540,6 @@ BN_MP_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
@@ -10128,8 +11550,6 @@ BN_MP_REDUCE_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
@@ -10140,173 +11560,300 @@ BN_MP_REDUCE_C
 |   |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_CLAMP_C
 |   |   +--->BN_MP_CLEAR_C
-+--->BN_MP_INIT_COPY_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_CLEAR_C
+|   +--->BN_MP_EXCH_C
+|   +--->BN_MP_ADD_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_ADD_C
-|   |   |   +--->BN_S_MP_ADD_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_CLAMP_C
-|   |   |   +--->BN_MP_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_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_SUB_C
-|   |   |   +--->BN_S_MP_ADD_C
-|   |   |   |   +--->BN_MP_GROW_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_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_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_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_ZERO_C
+|   +--->BN_MP_INIT_COPY_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_CMP_MAG_C
-|   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   +--->BN_MP_GROW_C
-|   |   +--->BN_MP_ADD_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_LSHD_C
+|   |   +--->BN_MP_COPY_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_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_GET_INT_C
-
-
-BN_MP_JACOBI_C
-+--->BN_MP_CMP_D_C
-+--->BN_MP_INIT_COPY_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_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_CLEAR_C
 |   |   +--->BN_MP_SET_C
@@ -10315,7 +11862,6 @@ BN_MP_JACOBI_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
@@ -10332,20 +11878,23 @@ BN_MP_JACOBI_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_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_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_ADD_C
 |   |   +--->BN_S_MP_ADD_C
 |   |   |   +--->BN_MP_GROW_C
@@ -10354,160 +11903,24 @@ BN_MP_JACOBI_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_MULTI_C
-+--->BN_MP_CLEAR_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
-|   |   +--->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_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_ADD_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_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_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_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_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_MUL_C
-|   +--->BN_MP_TOOM_MUL_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
@@ -10548,137 +11961,120 @@ BN_MP_EXTEUCLID_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_CLEAR_MULTI_C
 |   |   |   +--->BN_MP_CLEAR_C
-|   +--->BN_MP_KARATSUBA_MUL_C
+|   +--->BN_MP_KARATSUBA_SQR_C
 |   |   +--->BN_MP_INIT_SIZE_C
 |   |   |   +--->BN_MP_INIT_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_ADD_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_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_MUL_DIGS_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_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_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_DR_REDUCE_C
-+--->BN_MP_GROW_C
-+--->BN_MP_CLAMP_C
 +--->BN_MP_CMP_MAG_C
-+--->BN_S_MP_SUB_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_COPY_C
++--->BN_MP_GROW_C
 
 
-BN_MP_REDUCE_SETUP_C
-+--->BN_MP_2EXPT_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_GROW_C
-+--->BN_MP_DIV_C
-|   +--->BN_MP_CMP_MAG_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_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_SQR_C
+|   +--->BN_MP_KARATSUBA_SQR_C
+|   |   +--->BN_MP_INIT_SIZE_C
+|   |   |   +--->BN_MP_INIT_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_LSHD_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_ADD_C
+|   |   |   +--->BN_MP_CMP_MAG_C
 |   |   +--->BN_MP_CLEAR_C
-|   |   +--->BN_MP_RSHD_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_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_MUL_2_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_ADD_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_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_MONTGOMERY_SETUP_C
-
-
-BN_MP_KARATSUBA_MUL_C
-+--->BN_MP_MUL_C
-|   +--->BN_MP_TOOM_MUL_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
@@ -10686,7 +12082,6 @@ BN_MP_KARATSUBA_MUL_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
@@ -10696,86 +12091,55 @@ BN_MP_KARATSUBA_MUL_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_FAST_S_MP_MUL_DIGS_C
+|   +--->BN_FAST_S_MP_SQR_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_S_MP_SQR_C
 |   |   +--->BN_MP_EXCH_C
 |   |   +--->BN_MP_CLEAR_C
-+--->BN_MP_INIT_SIZE_C
-|   +--->BN_MP_INIT_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_ADD_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_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_LSHD_C
-+--->BN_MP_GROW_C
-+--->BN_MP_RSHD_C
-|   +--->BN_MP_ZERO_C
-
-
-BN_MP_PRIME_MILLER_RABIN_C
-+--->BN_MP_CMP_D_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_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
@@ -10787,6 +12151,165 @@ BN_MP_PRIME_MILLER_RABIN_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_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_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_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_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_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_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
@@ -10821,10 +12344,18 @@ BN_MP_PRIME_MILLER_RABIN_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
@@ -10835,6 +12366,7 @@ BN_MP_PRIME_MILLER_RABIN_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
@@ -10843,7 +12375,6 @@ BN_MP_PRIME_MILLER_RABIN_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_SET_C
 |   |   |   |   +--->BN_MP_ZERO_C
 |   |   |   +--->BN_MP_DIV_2_C
@@ -10902,10 +12433,18 @@ BN_MP_PRIME_MILLER_RABIN_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
@@ -10916,6 +12455,7 @@ BN_MP_PRIME_MILLER_RABIN_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
@@ -10924,7 +12464,6 @@ BN_MP_PRIME_MILLER_RABIN_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
 |   |   |   +--->BN_MP_COPY_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   +--->BN_MP_SET_C
@@ -10993,8 +12532,15 @@ BN_MP_PRIME_MILLER_RABIN_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
@@ -11004,6 +12550,10 @@ BN_MP_PRIME_MILLER_RABIN_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
@@ -11053,18 +12603,14 @@ BN_MP_PRIME_MILLER_RABIN_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_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -11129,6 +12675,15 @@ BN_MP_PRIME_MILLER_RABIN_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
@@ -11178,18 +12733,14 @@ BN_MP_PRIME_MILLER_RABIN_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_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -11236,8 +12787,15 @@ BN_MP_PRIME_MILLER_RABIN_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
@@ -11246,6 +12804,7 @@ BN_MP_PRIME_MILLER_RABIN_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
@@ -11254,7 +12813,6 @@ BN_MP_PRIME_MILLER_RABIN_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
 |   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_SQR_C
@@ -11302,22 +12860,16 @@ BN_MP_PRIME_MILLER_RABIN_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_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_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_GROW_C
 |   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
@@ -11370,18 +12922,14 @@ BN_MP_PRIME_MILLER_RABIN_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_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -11400,6 +12948,15 @@ BN_MP_PRIME_MILLER_RABIN_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
@@ -11442,6 +12999,15 @@ BN_MP_PRIME_MILLER_RABIN_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
@@ -11514,18 +13080,14 @@ BN_MP_PRIME_MILLER_RABIN_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_CMP_MAG_C
-|   |   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -11565,8 +13127,15 @@ BN_MP_PRIME_MILLER_RABIN_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
@@ -11575,6 +13144,7 @@ BN_MP_PRIME_MILLER_RABIN_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
@@ -11583,7 +13153,6 @@ BN_MP_PRIME_MILLER_RABIN_C
 |   |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   |   +--->BN_MP_EXCH_C
 |   |   +--->BN_MP_SET_C
 |   |   |   +--->BN_MP_ZERO_C
 |   |   +--->BN_MP_MOD_C
@@ -11613,8 +13182,15 @@ BN_MP_PRIME_MILLER_RABIN_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
@@ -11623,6 +13199,7 @@ BN_MP_PRIME_MILLER_RABIN_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
@@ -11631,7 +13208,6 @@ BN_MP_PRIME_MILLER_RABIN_C
 |   |   |   |   +--->BN_S_MP_SUB_C
 |   |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   |   +--->BN_MP_CLAMP_C
-|   |   |   +--->BN_MP_EXCH_C
 |   |   +--->BN_MP_COPY_C
 |   |   |   +--->BN_MP_GROW_C
 |   |   +--->BN_MP_SQR_C
@@ -11679,22 +13255,16 @@ BN_MP_PRIME_MILLER_RABIN_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_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_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_GROW_C
 |   |   |   +--->BN_FAST_S_MP_SQR_C
 |   |   |   |   +--->BN_MP_GROW_C
 |   |   |   |   +--->BN_MP_CLAMP_C
@@ -11747,18 +13317,14 @@ BN_MP_PRIME_MILLER_RABIN_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_CMP_MAG_C
-|   |   |   |   |   +--->BN_S_MP_SUB_C
-|   |   |   |   |   |   +--->BN_MP_GROW_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_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
@@ -11773,141 +13339,18 @@ BN_MP_PRIME_MILLER_RABIN_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_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_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_S_MP_ADD_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_GROW_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_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_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_C
 
 
-BN_MP_DR_SETUP_C
-
-
-BN_MP_CMP_MAG_C
+BN_MP_REDUCE_2K_SETUP_L_C
++--->BN_MP_INIT_C
++--->BN_MP_2EXPT_C
+|   +--->BN_MP_ZERO_C
+|   +--->BN_MP_GROW_C
++--->BN_MP_COUNT_BITS_C
++--->BN_S_MP_SUB_C
+|   +--->BN_MP_GROW_C
+|   +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
 
 
diff --git a/libtommath/changes.txt b/libtommath/changes.txt
index 4fc0913..d70d589 100644
--- a/libtommath/changes.txt
+++ b/libtommath/changes.txt
@@ -1,11 +1,32 @@
+Feb 5th, 2016
+v1.0.0
+       -- Bump to 1.0.0
+       -- 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()
+       -- Fixed bugs in mp_read_radix(), mp_radix_size
+          Thanks to shameister, Gerhard R,
+       -- Christopher Brown provided mp_export() and mp_import()
+       -- Improvements in the code of mp_init_copy()
+          Thanks to ramkumarkoppu,
+       -- lomereiter provided mp_balance_mul()
+       -- Alexander Boström from the heimdal project contributed patches to
+          mp_prime_next_prime() and mp_invmod() and added a mp_isneg() macro
+       -- Fix build issues for Linux x32 ABI
+       -- Added mp_get_long_long() and mp_set_long_long()
+       -- Carlin provided a patch to use arc4random() instead of rand()
+          on platforms where it is supported
+       -- Karel Miko provided mp_sqrtmod_prime()
+
+
 July 23rd, 2010
 v0.42.0
        -- Fix for mp_prime_next_prime() bug when checking generated prime
        -- allow mp_shrink to shrink initialized, but empty MPI's
-       -- Added project and solution files for Visual Studio 2005 and Visual Studio 2008. 
+       -- Added project and solution files for Visual Studio 2005 and Visual Studio 2008.
 
 March 10th, 2007
-v0.41  -- Wolfgang Ehrhardt suggested a quick fix to mp_div_d() which makes the detection of powers of two quicker. 
+v0.41  -- Wolfgang Ehrhardt suggested a quick fix to mp_div_d() which makes the detection of powers of two quicker.
        -- [CRI] Added libtommath.dsp for Visual C++ users.
 
 December 24th, 2006
@@ -22,11 +43,11 @@ v0.39  -- Jim Wigginton pointed out my Montgomery examples in figures 6.4 and 6.
 Jan 26th, 2006
 v0.38  -- broken makefile.shared fixed
        -- removed some carry stores that were not required [updated text]
-       
+
 November 18th, 2005
 v0.37  -- [Don Porter] reported on a TCL list [HEY SEND ME BUGREPORTS ALREADY!!!] that mp_add_d() would compute -0 with some inputs.  Fixed.
        -- [rinick@gmail.com] reported the makefile.bcc was messed up.  Fixed.
-       -- [Kevin Kenny] reported some issues with mp_toradix_n().  Now it doesn't require a min of 3 chars of output.  
+       -- [Kevin Kenny] reported some issues with mp_toradix_n().  Now it doesn't require a min of 3 chars of output.
        -- Made the make command renamable.  Wee
 
 August 1st, 2005
@@ -36,8 +57,8 @@ v0.36  -- LTM_PRIME_2MSB_ON was fixed and the "OFF" flag was removed.
        -- Ported LTC patch to fix the prime_random_ex() function to get the bitsize correct [and the maskOR flags]
        -- Kevin Kenny pointed out a stray //
        -- David Hulton pointed out a typo in the textbook [mp_montgomery_setup() pseudo-code]
-       -- Neal Hamilton (Elliptic Semiconductor) pointed out that my Karatsuba notation was backwards and that I could use 
-          unsigned operations in the routine.  
+       -- Neal Hamilton (Elliptic Semiconductor) pointed out that my Karatsuba notation was backwards and that I could use
+          unsigned operations in the routine.
        -- Paul Schmidt pointed out a linking error in mp_exptmod() when BN_S_MP_EXPTMOD_C is undefined (and another for read_radix)
        -- Updated makefiles to be way more flexible
 
@@ -48,7 +69,7 @@ v0.35  -- Stupid XOR function missing line again... oops.
        -- [Wolfgang Ehrhardt] Suggested a fix for mp_reduce() which avoided underruns.  ;-)
        -- mp_rand() would emit one too many digits and it was possible to get a 0 out of it ... oops
        -- Added montgomery to the testing to make sure it handles 1..10 digit moduli correctly
-       -- Fixed bug in comba that would lead to possible erroneous outputs when "pa < digs" 
+       -- Fixed bug in comba that would lead to possible erroneous outputs when "pa < digs"
        -- Fixed bug in mp_toradix_size for "0" [Kevin Kenny]
        -- Updated chapters 1-5 of the textbook ;-) It now talks about the new comba code!
 
@@ -59,7 +80,7 @@ v0.34  -- Fixed two more small errors in mp_prime_random_ex()
        -- Added "large" diminished radix support.  Speeds up things like DSA where the moduli is of the form 2^k - P for some P < 2^(k/2) or so
           Actually is faster than Montgomery on my AMD64 (and probably much faster on a P4)
        -- Updated the manual a bit
-       -- Ok so I haven't done the textbook work yet... My current freelance gig has landed me in France till the 
+       -- Ok so I haven't done the textbook work yet... My current freelance gig has landed me in France till the
           end of Feb/05.  Once I get back I'll have tons of free time and I plan to go to town on the book.
           As of this release the API will freeze.  At least until the book catches up with all the changes.  I welcome
           bug reports but new algorithms will have to wait.
@@ -76,7 +97,7 @@ v0.33  -- Fixed "small" variant for mp_div() which would munge with negative div
 October 29th, 2004
 v0.32  -- Added "makefile.shared" for shared object support
        -- Added more to the build options/configs in the manual
-       -- Started the Depends framework, wrote dep.pl to scan deps and 
+       -- Started the Depends framework, wrote dep.pl to scan deps and
           produce "callgraph.txt" ;-)
        -- Wrote SC_RSA_1 which will enable close to the minimum required to perform
           RSA on 32-bit [or 64-bit] platforms with LibTomCrypt
@@ -84,7 +105,7 @@ v0.32  -- Added "makefile.shared" for shared object support
           you want to use as your mp_div() at build time.  Saves roughly 8KB or so.
        -- Renamed a few files and changed some comments to make depends system work better.
           (No changes to function names)
-       -- Merged in new Combas that perform 2 reads per inner loop instead of the older 
+       -- Merged in new Combas that perform 2 reads per inner loop instead of the older
           3reads/2writes per inner loop of the old code.  Really though if you want speed
           learn to use TomsFastMath ;-)
 
@@ -113,8 +134,8 @@ v0.30  -- Added "mp_toradix_n" which stores upto "n-1" least significant digits
           call.
        -- Removed /etclib directory [um LibTomPoly deprecates this].
        -- Fixed mp_mod() so the sign of the result agrees with the sign of the modulus.
-       ++ N.B.  My semester is almost up so expect updates to the textbook to be posted to the libtomcrypt.org 
-          website.  
+       ++ N.B.  My semester is almost up so expect updates to the textbook to be posted to the libtomcrypt.org
+          website.
 
 Jan 25th, 2004
 v0.29  ++ Note: "Henrik" from the v0.28 changelog refers to Henrik Goldman ;-)
diff --git a/libtommath/dep.pl b/libtommath/dep.pl
deleted file mode 100644
index c39e27e..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")) {
-             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/gen.pl b/libtommath/gen.pl
deleted file mode 100644
index 7236591..0000000
--- a/libtommath/gen.pl
+++ /dev/null
@@ -1,17 +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: $!";
\ No newline at end of file
diff --git a/libtommath/makefile b/libtommath/makefile
index 70de306..f90971c 100644
--- a/libtommath/makefile
+++ b/libtommath/makefile
@@ -2,98 +2,66 @@
 #
 #Tom St Denis
 
-#version of library 
-VERSION=0.42.0
-
-CFLAGS  +=  -I./ -Wall -W -Wshadow -Wsign-compare
-
-ifndef MAKE
-   MAKE=make
-endif
-
-ifndef IGNORE_SPEED
-
-#for speed 
-CFLAGS += -O3 -funroll-loops
-
-#for size 
-#CFLAGS += -Os
-
-#x86 optimizations [should be valid for any GCC install though]
-CFLAGS  += -fomit-frame-pointer
-
-#debug
-#CFLAGS += -g3
-
-endif
-
-#install as this user
-ifndef INSTALL_GROUP
-   GROUP=wheel
+ifeq ($V,1)
+silent=
 else
-   GROUP=$(INSTALL_GROUP)
+silent=@
 endif
 
-ifndef INSTALL_USER
-   USER=root
-else
-   USER=$(INSTALL_USER)
+%.o: %.c
+ifneq ($V,1)
+	@echo "   * ${CC} $@"
 endif
+	${silent} ${CC} -c ${CFLAGS} $^ -o $@
 
 #default files to install
 ifndef LIBNAME
    LIBNAME=libtommath.a
 endif
 
-default: ${LIBNAME}
-
-HEADERS=tommath.h tommath_class.h tommath_superclass.h
-
-#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=
-LIBPATH=/usr/lib
-INCPATH=/usr/include
-DATAPATH=/usr/share/doc/libtommath/pdf
-
-OBJECTS=bncore.o bn_mp_init.o bn_mp_clear.o bn_mp_exch.o bn_mp_grow.o bn_mp_shrink.o \
-bn_mp_clamp.o bn_mp_zero.o  bn_mp_set.o bn_mp_set_int.o bn_mp_init_size.o bn_mp_copy.o \
-bn_mp_init_copy.o bn_mp_abs.o bn_mp_neg.o bn_mp_cmp_mag.o bn_mp_cmp.o bn_mp_cmp_d.o \
-bn_mp_rshd.o bn_mp_lshd.o bn_mp_mod_2d.o bn_mp_div_2d.o bn_mp_mul_2d.o bn_mp_div_2.o \
-bn_mp_mul_2.o bn_s_mp_add.o bn_s_mp_sub.o bn_fast_s_mp_mul_digs.o bn_s_mp_mul_digs.o \
-bn_fast_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_s_mp_sqr.o \
-bn_mp_add.o bn_mp_sub.o bn_mp_karatsuba_mul.o bn_mp_mul.o bn_mp_karatsuba_sqr.o \
-bn_mp_sqr.o bn_mp_div.o bn_mp_mod.o bn_mp_add_d.o bn_mp_sub_d.o bn_mp_mul_d.o \
-bn_mp_div_d.o bn_mp_mod_d.o bn_mp_expt_d.o bn_mp_addmod.o bn_mp_submod.o \
-bn_mp_mulmod.o bn_mp_sqrmod.o bn_mp_gcd.o bn_mp_lcm.o bn_fast_mp_invmod.o bn_mp_invmod.o \
-bn_mp_reduce.o bn_mp_montgomery_setup.o bn_fast_mp_montgomery_reduce.o bn_mp_montgomery_reduce.o \
-bn_mp_exptmod_fast.o bn_mp_exptmod.o bn_mp_2expt.o bn_mp_n_root.o bn_mp_jacobi.o bn_reverse.o \
-bn_mp_count_bits.o bn_mp_read_unsigned_bin.o bn_mp_read_signed_bin.o bn_mp_to_unsigned_bin.o \
-bn_mp_to_signed_bin.o bn_mp_unsigned_bin_size.o bn_mp_signed_bin_size.o  \
-bn_mp_xor.o bn_mp_and.o bn_mp_or.o bn_mp_rand.o bn_mp_montgomery_calc_normalization.o \
-bn_mp_prime_is_divisible.o bn_prime_tab.o bn_mp_prime_fermat.o bn_mp_prime_miller_rabin.o \
-bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \
-bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
-bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
-bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
-bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \
-bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
-bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
-bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
-bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
-bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \
-bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o
+coverage: LIBNAME:=-Wl,--whole-archive $(LIBNAME)  -Wl,--no-whole-archive
+
+include makefile.include
+
+LCOV_ARGS=--directory .
+
+#START_INS
+OBJECTS=bncore.o bn_error.o bn_fast_mp_invmod.o bn_fast_mp_montgomery_reduce.o bn_fast_s_mp_mul_digs.o \
+bn_fast_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_mp_2expt.o bn_mp_abs.o bn_mp_add.o bn_mp_add_d.o \
+bn_mp_addmod.o bn_mp_and.o bn_mp_clamp.o bn_mp_clear.o bn_mp_clear_multi.o bn_mp_cmp.o bn_mp_cmp_d.o \
+bn_mp_cmp_mag.o bn_mp_cnt_lsb.o bn_mp_copy.o bn_mp_count_bits.o bn_mp_div_2.o bn_mp_div_2d.o bn_mp_div_3.o \
+bn_mp_div.o bn_mp_div_d.o bn_mp_dr_is_modulus.o bn_mp_dr_reduce.o bn_mp_dr_setup.o bn_mp_exch.o \
+bn_mp_export.o bn_mp_expt_d.o bn_mp_expt_d_ex.o bn_mp_exptmod.o bn_mp_exptmod_fast.o bn_mp_exteuclid.o \
+bn_mp_fread.o bn_mp_fwrite.o bn_mp_gcd.o bn_mp_get_int.o bn_mp_get_long.o bn_mp_get_long_long.o \
+bn_mp_grow.o bn_mp_import.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_invmod.o bn_mp_invmod_slow.o bn_mp_is_square.o \
+bn_mp_jacobi.o bn_mp_karatsuba_mul.o bn_mp_karatsuba_sqr.o bn_mp_lcm.o bn_mp_lshd.o bn_mp_mod_2d.o \
+bn_mp_mod.o bn_mp_mod_d.o bn_mp_montgomery_calc_normalization.o bn_mp_montgomery_reduce.o \
+bn_mp_montgomery_setup.o bn_mp_mul_2.o bn_mp_mul_2d.o bn_mp_mul.o bn_mp_mul_d.o bn_mp_mulmod.o bn_mp_neg.o \
+bn_mp_n_root.o bn_mp_n_root_ex.o bn_mp_or.o bn_mp_prime_fermat.o bn_mp_prime_is_divisible.o \
+bn_mp_prime_is_prime.o bn_mp_prime_miller_rabin.o bn_mp_prime_next_prime.o \
+bn_mp_prime_rabin_miller_trials.o bn_mp_prime_random_ex.o bn_mp_radix_size.o bn_mp_radix_smap.o \
+bn_mp_rand.o bn_mp_read_radix.o bn_mp_read_signed_bin.o bn_mp_read_unsigned_bin.o bn_mp_reduce_2k.o \
+bn_mp_reduce_2k_l.o bn_mp_reduce_2k_setup.o bn_mp_reduce_2k_setup_l.o bn_mp_reduce.o \
+bn_mp_reduce_is_2k.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_setup.o bn_mp_rshd.o bn_mp_set.o bn_mp_set_int.o \
+bn_mp_set_long.o bn_mp_set_long_long.o bn_mp_shrink.o bn_mp_signed_bin_size.o bn_mp_sqr.o bn_mp_sqrmod.o \
+bn_mp_sqrt.o bn_mp_sqrtmod_prime.o bn_mp_sub.o bn_mp_sub_d.o bn_mp_submod.o bn_mp_toom_mul.o \
+bn_mp_toom_sqr.o bn_mp_toradix.o bn_mp_toradix_n.o bn_mp_to_signed_bin.o bn_mp_to_signed_bin_n.o \
+bn_mp_to_unsigned_bin.o bn_mp_to_unsigned_bin_n.o bn_mp_unsigned_bin_size.o bn_mp_xor.o bn_mp_zero.o \
+bn_prime_tab.o bn_reverse.o bn_s_mp_add.o bn_s_mp_exptmod.o bn_s_mp_mul_digs.o bn_s_mp_mul_high_digs.o \
+bn_s_mp_sqr.o bn_s_mp_sub.o
+
+#END_INS
 
 $(LIBNAME):  $(OBJECTS)
 	$(AR) $(ARFLAGS) $@ $(OBJECTS)
-	ranlib $@
+	$(RANLIB) $@
 
 #make a profiled library (takes a while!!!)
 #
 # This will build the library with profile generation
 # then run the test demo and rebuild the library.
-# 
+#
 # So far I've seen improvements in the MP math
 profiled:
 	make CFLAGS="$(CFLAGS) -fprofile-arcs -DTESTING" timing
@@ -101,35 +69,42 @@ profiled:
 	rm -f *.a *.o ltmtest
 	make CFLAGS="$(CFLAGS) -fbranch-probabilities"
 
-#make a single object profiled library 
+#make a single object profiled library
 profiled_single:
 	perl gen.pl
 	$(CC) $(CFLAGS) -fprofile-arcs -DTESTING -c mpi.c -o mpi.o
-	$(CC) $(CFLAGS) -DTESTING -DTIMER demo/timing.c mpi.o -o ltmtest
+	$(CC) $(CFLAGS) -DTESTING -DTIMER demo/timing.c mpi.o -lgcov -o ltmtest
 	./ltmtest
 	rm -f *.o ltmtest
 	$(CC) $(CFLAGS) -fbranch-probabilities -DTESTING -c mpi.c -o mpi.o
 	$(AR) $(ARFLAGS) $(LIBNAME) mpi.o
-	ranlib $(LIBNAME)	
+	ranlib $(LIBNAME)
 
 install: $(LIBNAME)
-	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(LIBPATH)
-	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH)
-	install -g $(GROUP) -o $(USER) $(LIBNAME) $(DESTDIR)$(LIBPATH)
-	install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH)
+	install -d $(DESTDIR)$(LIBPATH)
+	install -d $(DESTDIR)$(INCPATH)
+	install -m 644 $(LIBNAME) $(DESTDIR)$(LIBPATH)
+	install -m 644 $(HEADERS_PUB) $(DESTDIR)$(INCPATH)
 
 test: $(LIBNAME) demo/demo.o
-	$(CC) $(CFLAGS) demo/demo.o $(LIBNAME) -o test
-	
-mtest: test	
-	cd mtest ; $(CC) $(CFLAGS) mtest.c -o mtest
-        
+	$(CC) $(CFLAGS) demo/demo.o $(LIBNAME) $(LFLAGS) -o test
+
+test_standalone: $(LIBNAME) demo/demo.o
+	$(CC) $(CFLAGS) demo/demo.o $(LIBNAME) $(LFLAGS) -o test
+
+.PHONY: mtest
+mtest:
+	cd mtest ; $(CC) $(CFLAGS) -O0 mtest.c $(LFLAGS) -o mtest
+
 timing: $(LIBNAME)
-	$(CC) $(CFLAGS) -DTIMER demo/timing.c $(LIBNAME) -o ltmtest
+	$(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} ${MAKE} 
+	cd pics ; MAKE=${MAKE} ${MAKE}
 	echo "hello" > tommath.ind
 	perl booker.pl
 	latex tommath > /dev/null
@@ -139,17 +114,37 @@ docdvi: tommath.src
 
 # 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
-	rm -f poster.aux poster.log 
+	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
@@ -159,28 +154,36 @@ mandvi: bn.tex
 #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
 
-pretty: 
+pretty:
 	perl pretty.build
 
-clean:
-	rm -f *.bat *.pdf *.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
-
-#zipup the project (take that!)
+#\zipup the project (take that!)
 no_oops: clean
-	cd .. ; cvs commit 
+	cd .. ; cvs commit
 	echo Scanning for scratch/dirty files
 	find . -type f | grep -v CVS | xargs -n 1 bash mess.sh
 
-zipup: clean manual poster docs
-	perl gen.pl ; mv mpi.c pre_gen/ ; \
-	cd .. ; rm -rf ltm* libtommath-$(VERSION) ; mkdir libtommath-$(VERSION) ; \
-	cp -R ./libtommath/* ./libtommath-$(VERSION)/ ; \
-	tar -c libtommath-$(VERSION)/* | bzip2 -9vvc > ltm-$(VERSION).tar.bz2 ; \
-	zip -9 -r ltm-$(VERSION).zip libtommath-$(VERSION)/* ; \
-	mv -f ltm* ~ ; rm -rf libtommath-$(VERSION)
+.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
+
+new_file:
+	bash updatemakes.sh
+	perl dep.pl
diff --git a/libtommath/makefile.bcc b/libtommath/makefile.bcc
index 67743d9..a0cfd74 100644
--- a/libtommath/makefile.bcc
+++ b/libtommath/makefile.bcc
@@ -7,33 +7,35 @@ LIB = tlib
 CC = bcc32
 CFLAGS = -c -O2 -I.
 
-OBJECTS=bncore.obj bn_mp_init.obj bn_mp_clear.obj bn_mp_exch.obj bn_mp_grow.obj bn_mp_shrink.obj \
-bn_mp_clamp.obj bn_mp_zero.obj  bn_mp_set.obj bn_mp_set_int.obj bn_mp_init_size.obj bn_mp_copy.obj \
-bn_mp_init_copy.obj bn_mp_abs.obj bn_mp_neg.obj bn_mp_cmp_mag.obj bn_mp_cmp.obj bn_mp_cmp_d.obj \
-bn_mp_rshd.obj bn_mp_lshd.obj bn_mp_mod_2d.obj bn_mp_div_2d.obj bn_mp_mul_2d.obj bn_mp_div_2.obj \
-bn_mp_mul_2.obj bn_s_mp_add.obj bn_s_mp_sub.obj bn_fast_s_mp_mul_digs.obj bn_s_mp_mul_digs.obj \
-bn_fast_s_mp_mul_high_digs.obj bn_s_mp_mul_high_digs.obj bn_fast_s_mp_sqr.obj bn_s_mp_sqr.obj \
-bn_mp_add.obj bn_mp_sub.obj bn_mp_karatsuba_mul.obj bn_mp_mul.obj bn_mp_karatsuba_sqr.obj \
-bn_mp_sqr.obj bn_mp_div.obj bn_mp_mod.obj bn_mp_add_d.obj bn_mp_sub_d.obj bn_mp_mul_d.obj \
-bn_mp_div_d.obj bn_mp_mod_d.obj bn_mp_expt_d.obj bn_mp_addmod.obj bn_mp_submod.obj \
-bn_mp_mulmod.obj bn_mp_sqrmod.obj bn_mp_gcd.obj bn_mp_lcm.obj bn_fast_mp_invmod.obj bn_mp_invmod.obj \
-bn_mp_reduce.obj bn_mp_montgomery_setup.obj bn_fast_mp_montgomery_reduce.obj bn_mp_montgomery_reduce.obj \
-bn_mp_exptmod_fast.obj bn_mp_exptmod.obj bn_mp_2expt.obj bn_mp_n_root.obj bn_mp_jacobi.obj bn_reverse.obj \
-bn_mp_count_bits.obj bn_mp_read_unsigned_bin.obj bn_mp_read_signed_bin.obj bn_mp_to_unsigned_bin.obj \
-bn_mp_to_signed_bin.obj bn_mp_unsigned_bin_size.obj bn_mp_signed_bin_size.obj  \
-bn_mp_xor.obj bn_mp_and.obj bn_mp_or.obj bn_mp_rand.obj bn_mp_montgomery_calc_normalization.obj \
-bn_mp_prime_is_divisible.obj bn_prime_tab.obj bn_mp_prime_fermat.obj bn_mp_prime_miller_rabin.obj \
-bn_mp_prime_is_prime.obj bn_mp_prime_next_prime.obj bn_mp_dr_reduce.obj \
-bn_mp_dr_is_modulus.obj bn_mp_dr_setup.obj bn_mp_reduce_setup.obj \
-bn_mp_toom_mul.obj bn_mp_toom_sqr.obj bn_mp_div_3.obj bn_s_mp_exptmod.obj \
-bn_mp_reduce_2k.obj bn_mp_reduce_is_2k.obj bn_mp_reduce_2k_setup.obj \
-bn_mp_reduce_2k_l.obj bn_mp_reduce_is_2k_l.obj bn_mp_reduce_2k_setup_l.obj \
-bn_mp_radix_smap.obj bn_mp_read_radix.obj bn_mp_toradix.obj bn_mp_radix_size.obj \
-bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_cnt_lsb.obj bn_error.obj \
-bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \
-bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj \
-bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj \
-bn_mp_to_signed_bin_n.obj bn_mp_to_unsigned_bin_n.obj
+#START_INS
+OBJECTS=bncore.obj bn_error.obj bn_fast_mp_invmod.obj bn_fast_mp_montgomery_reduce.obj bn_fast_s_mp_mul_digs.obj \
+bn_fast_s_mp_mul_high_digs.obj bn_fast_s_mp_sqr.obj bn_mp_2expt.obj bn_mp_abs.obj bn_mp_add.obj bn_mp_add_d.obj \
+bn_mp_addmod.obj bn_mp_and.obj bn_mp_clamp.obj bn_mp_clear.obj bn_mp_clear_multi.obj bn_mp_cmp.obj bn_mp_cmp_d.obj \
+bn_mp_cmp_mag.obj bn_mp_cnt_lsb.obj bn_mp_copy.obj bn_mp_count_bits.obj bn_mp_div_2.obj bn_mp_div_2d.obj bn_mp_div_3.obj \
+bn_mp_div.obj bn_mp_div_d.obj bn_mp_dr_is_modulus.obj bn_mp_dr_reduce.obj bn_mp_dr_setup.obj bn_mp_exch.obj \
+bn_mp_export.obj bn_mp_expt_d.obj bn_mp_expt_d_ex.obj bn_mp_exptmod.obj bn_mp_exptmod_fast.obj bn_mp_exteuclid.obj \
+bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_gcd.obj bn_mp_get_int.obj bn_mp_get_long.obj bn_mp_get_long_long.obj \
+bn_mp_grow.obj bn_mp_import.obj bn_mp_init.obj bn_mp_init_copy.obj bn_mp_init_multi.obj bn_mp_init_set.obj \
+bn_mp_init_set_int.obj bn_mp_init_size.obj bn_mp_invmod.obj bn_mp_invmod_slow.obj bn_mp_is_square.obj \
+bn_mp_jacobi.obj bn_mp_karatsuba_mul.obj bn_mp_karatsuba_sqr.obj bn_mp_lcm.obj bn_mp_lshd.obj bn_mp_mod_2d.obj \
+bn_mp_mod.obj bn_mp_mod_d.obj bn_mp_montgomery_calc_normalization.obj bn_mp_montgomery_reduce.obj \
+bn_mp_montgomery_setup.obj bn_mp_mul_2.obj bn_mp_mul_2d.obj bn_mp_mul.obj bn_mp_mul_d.obj bn_mp_mulmod.obj bn_mp_neg.obj \
+bn_mp_n_root.obj bn_mp_n_root_ex.obj bn_mp_or.obj bn_mp_prime_fermat.obj bn_mp_prime_is_divisible.obj \
+bn_mp_prime_is_prime.obj bn_mp_prime_miller_rabin.obj bn_mp_prime_next_prime.obj \
+bn_mp_prime_rabin_miller_trials.obj bn_mp_prime_random_ex.obj bn_mp_radix_size.obj bn_mp_radix_smap.obj \
+bn_mp_rand.obj bn_mp_read_radix.obj bn_mp_read_signed_bin.obj bn_mp_read_unsigned_bin.obj bn_mp_reduce_2k.obj \
+bn_mp_reduce_2k_l.obj bn_mp_reduce_2k_setup.obj bn_mp_reduce_2k_setup_l.obj bn_mp_reduce.obj \
+bn_mp_reduce_is_2k.obj bn_mp_reduce_is_2k_l.obj bn_mp_reduce_setup.obj bn_mp_rshd.obj bn_mp_set.obj bn_mp_set_int.obj \
+bn_mp_set_long.obj bn_mp_set_long_long.obj bn_mp_shrink.obj bn_mp_signed_bin_size.obj bn_mp_sqr.obj bn_mp_sqrmod.obj \
+bn_mp_sqrt.obj bn_mp_sqrtmod_prime.obj bn_mp_sub.obj bn_mp_sub_d.obj bn_mp_submod.obj bn_mp_toom_mul.obj \
+bn_mp_toom_sqr.obj bn_mp_toradix.obj bn_mp_toradix_n.obj bn_mp_to_signed_bin.obj bn_mp_to_signed_bin_n.obj \
+bn_mp_to_unsigned_bin.obj bn_mp_to_unsigned_bin_n.obj bn_mp_unsigned_bin_size.obj bn_mp_xor.obj bn_mp_zero.obj \
+bn_prime_tab.obj bn_reverse.obj bn_s_mp_add.obj bn_s_mp_exptmod.obj bn_s_mp_mul_digs.obj bn_s_mp_mul_high_digs.obj \
+bn_s_mp_sqr.obj bn_s_mp_sub.obj
+
+#END_INS
+
+HEADERS=tommath.h tommath_class.h tommath_superclass.h
 
 TARGET = libtommath.lib
 
diff --git a/libtommath/makefile.cygwin_dll b/libtommath/makefile.cygwin_dll
index 85b10c7..59acad3 100644
--- a/libtommath/makefile.cygwin_dll
+++ b/libtommath/makefile.cygwin_dll
@@ -8,37 +8,39 @@
 CFLAGS  +=  -I./ -Wall -W -Wshadow -O3 -funroll-loops -mno-cygwin
 
 #x86 optimizations [should be valid for any GCC install though]
-CFLAGS  += -fomit-frame-pointer 
+CFLAGS  += -fomit-frame-pointer
 
 default: windll
 
-OBJECTS=bncore.o bn_mp_init.o bn_mp_clear.o bn_mp_exch.o bn_mp_grow.o bn_mp_shrink.o \
-bn_mp_clamp.o bn_mp_zero.o  bn_mp_set.o bn_mp_set_int.o bn_mp_init_size.o bn_mp_copy.o \
-bn_mp_init_copy.o bn_mp_abs.o bn_mp_neg.o bn_mp_cmp_mag.o bn_mp_cmp.o bn_mp_cmp_d.o \
-bn_mp_rshd.o bn_mp_lshd.o bn_mp_mod_2d.o bn_mp_div_2d.o bn_mp_mul_2d.o bn_mp_div_2.o \
-bn_mp_mul_2.o bn_s_mp_add.o bn_s_mp_sub.o bn_fast_s_mp_mul_digs.o bn_s_mp_mul_digs.o \
-bn_fast_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_s_mp_sqr.o \
-bn_mp_add.o bn_mp_sub.o bn_mp_karatsuba_mul.o bn_mp_mul.o bn_mp_karatsuba_sqr.o \
-bn_mp_sqr.o bn_mp_div.o bn_mp_mod.o bn_mp_add_d.o bn_mp_sub_d.o bn_mp_mul_d.o \
-bn_mp_div_d.o bn_mp_mod_d.o bn_mp_expt_d.o bn_mp_addmod.o bn_mp_submod.o \
-bn_mp_mulmod.o bn_mp_sqrmod.o bn_mp_gcd.o bn_mp_lcm.o bn_fast_mp_invmod.o bn_mp_invmod.o \
-bn_mp_reduce.o bn_mp_montgomery_setup.o bn_fast_mp_montgomery_reduce.o bn_mp_montgomery_reduce.o \
-bn_mp_exptmod_fast.o bn_mp_exptmod.o bn_mp_2expt.o bn_mp_n_root.o bn_mp_jacobi.o bn_reverse.o \
-bn_mp_count_bits.o bn_mp_read_unsigned_bin.o bn_mp_read_signed_bin.o bn_mp_to_unsigned_bin.o \
-bn_mp_to_signed_bin.o bn_mp_unsigned_bin_size.o bn_mp_signed_bin_size.o  \
-bn_mp_xor.o bn_mp_and.o bn_mp_or.o bn_mp_rand.o bn_mp_montgomery_calc_normalization.o \
-bn_mp_prime_is_divisible.o bn_prime_tab.o bn_mp_prime_fermat.o bn_mp_prime_miller_rabin.o \
-bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \
-bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
-bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
-bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
-bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \
-bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
-bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
-bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
-bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
-bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \
-bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o
+#START_INS
+OBJECTS=bncore.o bn_error.o bn_fast_mp_invmod.o bn_fast_mp_montgomery_reduce.o bn_fast_s_mp_mul_digs.o \
+bn_fast_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_mp_2expt.o bn_mp_abs.o bn_mp_add.o bn_mp_add_d.o \
+bn_mp_addmod.o bn_mp_and.o bn_mp_clamp.o bn_mp_clear.o bn_mp_clear_multi.o bn_mp_cmp.o bn_mp_cmp_d.o \
+bn_mp_cmp_mag.o bn_mp_cnt_lsb.o bn_mp_copy.o bn_mp_count_bits.o bn_mp_div_2.o bn_mp_div_2d.o bn_mp_div_3.o \
+bn_mp_div.o bn_mp_div_d.o bn_mp_dr_is_modulus.o bn_mp_dr_reduce.o bn_mp_dr_setup.o bn_mp_exch.o \
+bn_mp_export.o bn_mp_expt_d.o bn_mp_expt_d_ex.o bn_mp_exptmod.o bn_mp_exptmod_fast.o bn_mp_exteuclid.o \
+bn_mp_fread.o bn_mp_fwrite.o bn_mp_gcd.o bn_mp_get_int.o bn_mp_get_long.o bn_mp_get_long_long.o \
+bn_mp_grow.o bn_mp_import.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_invmod.o bn_mp_invmod_slow.o bn_mp_is_square.o \
+bn_mp_jacobi.o bn_mp_karatsuba_mul.o bn_mp_karatsuba_sqr.o bn_mp_lcm.o bn_mp_lshd.o bn_mp_mod_2d.o \
+bn_mp_mod.o bn_mp_mod_d.o bn_mp_montgomery_calc_normalization.o bn_mp_montgomery_reduce.o \
+bn_mp_montgomery_setup.o bn_mp_mul_2.o bn_mp_mul_2d.o bn_mp_mul.o bn_mp_mul_d.o bn_mp_mulmod.o bn_mp_neg.o \
+bn_mp_n_root.o bn_mp_n_root_ex.o bn_mp_or.o bn_mp_prime_fermat.o bn_mp_prime_is_divisible.o \
+bn_mp_prime_is_prime.o bn_mp_prime_miller_rabin.o bn_mp_prime_next_prime.o \
+bn_mp_prime_rabin_miller_trials.o bn_mp_prime_random_ex.o bn_mp_radix_size.o bn_mp_radix_smap.o \
+bn_mp_rand.o bn_mp_read_radix.o bn_mp_read_signed_bin.o bn_mp_read_unsigned_bin.o bn_mp_reduce_2k.o \
+bn_mp_reduce_2k_l.o bn_mp_reduce_2k_setup.o bn_mp_reduce_2k_setup_l.o bn_mp_reduce.o \
+bn_mp_reduce_is_2k.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_setup.o bn_mp_rshd.o bn_mp_set.o bn_mp_set_int.o \
+bn_mp_set_long.o bn_mp_set_long_long.o bn_mp_shrink.o bn_mp_signed_bin_size.o bn_mp_sqr.o bn_mp_sqrmod.o \
+bn_mp_sqrt.o bn_mp_sqrtmod_prime.o bn_mp_sub.o bn_mp_sub_d.o bn_mp_submod.o bn_mp_toom_mul.o \
+bn_mp_toom_sqr.o bn_mp_toradix.o bn_mp_toradix_n.o bn_mp_to_signed_bin.o bn_mp_to_signed_bin_n.o \
+bn_mp_to_unsigned_bin.o bn_mp_to_unsigned_bin_n.o bn_mp_unsigned_bin_size.o bn_mp_xor.o bn_mp_zero.o \
+bn_prime_tab.o bn_reverse.o bn_s_mp_add.o bn_s_mp_exptmod.o bn_s_mp_mul_digs.o bn_s_mp_mul_high_digs.o \
+bn_s_mp_sqr.o bn_s_mp_sub.o
+
+#END_INS
+
+HEADERS=tommath.h tommath_class.h tommath_superclass.h
 
 # make a Windows DLL via Cygwin
 windll:  $(OBJECTS)
diff --git a/libtommath/makefile.icc b/libtommath/makefile.icc
index cf70ab0..1563802 100644
--- a/libtommath/makefile.icc
+++ b/libtommath/makefile.icc
@@ -11,7 +11,7 @@ CFLAGS  +=  -I./
 # -ax?   specifies make code specifically for ? but compatible with IA-32
 # -x?    specifies compile solely for ? [not specifically IA-32 compatible]
 #
-# where ? is 
+# where ? is
 #   K - PIII
 #   W - first P4 [Williamette]
 #   N - P4 Northwood
@@ -29,7 +29,6 @@ default: libtommath.a
 
 #default files to install
 LIBNAME=libtommath.a
-HEADERS=tommath.h
 
 #LIBPATH-The directory for libtomcrypt to be installed to.
 #INCPATH-The directory to install the header files for libtommath.
@@ -39,33 +38,35 @@ LIBPATH=/usr/lib
 INCPATH=/usr/include
 DATAPATH=/usr/share/doc/libtommath/pdf
 
-OBJECTS=bncore.o bn_mp_init.o bn_mp_clear.o bn_mp_exch.o bn_mp_grow.o bn_mp_shrink.o \
-bn_mp_clamp.o bn_mp_zero.o  bn_mp_set.o bn_mp_set_int.o bn_mp_init_size.o bn_mp_copy.o \
-bn_mp_init_copy.o bn_mp_abs.o bn_mp_neg.o bn_mp_cmp_mag.o bn_mp_cmp.o bn_mp_cmp_d.o \
-bn_mp_rshd.o bn_mp_lshd.o bn_mp_mod_2d.o bn_mp_div_2d.o bn_mp_mul_2d.o bn_mp_div_2.o \
-bn_mp_mul_2.o bn_s_mp_add.o bn_s_mp_sub.o bn_fast_s_mp_mul_digs.o bn_s_mp_mul_digs.o \
-bn_fast_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_s_mp_sqr.o \
-bn_mp_add.o bn_mp_sub.o bn_mp_karatsuba_mul.o bn_mp_mul.o bn_mp_karatsuba_sqr.o \
-bn_mp_sqr.o bn_mp_div.o bn_mp_mod.o bn_mp_add_d.o bn_mp_sub_d.o bn_mp_mul_d.o \
-bn_mp_div_d.o bn_mp_mod_d.o bn_mp_expt_d.o bn_mp_addmod.o bn_mp_submod.o \
-bn_mp_mulmod.o bn_mp_sqrmod.o bn_mp_gcd.o bn_mp_lcm.o bn_fast_mp_invmod.o bn_mp_invmod.o \
-bn_mp_reduce.o bn_mp_montgomery_setup.o bn_fast_mp_montgomery_reduce.o bn_mp_montgomery_reduce.o \
-bn_mp_exptmod_fast.o bn_mp_exptmod.o bn_mp_2expt.o bn_mp_n_root.o bn_mp_jacobi.o bn_reverse.o \
-bn_mp_count_bits.o bn_mp_read_unsigned_bin.o bn_mp_read_signed_bin.o bn_mp_to_unsigned_bin.o \
-bn_mp_to_signed_bin.o bn_mp_unsigned_bin_size.o bn_mp_signed_bin_size.o  \
-bn_mp_xor.o bn_mp_and.o bn_mp_or.o bn_mp_rand.o bn_mp_montgomery_calc_normalization.o \
-bn_mp_prime_is_divisible.o bn_prime_tab.o bn_mp_prime_fermat.o bn_mp_prime_miller_rabin.o \
-bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \
-bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
-bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
-bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
-bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \
-bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
-bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
-bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
-bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
-bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \
-bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o
+#START_INS
+OBJECTS=bncore.o bn_error.o bn_fast_mp_invmod.o bn_fast_mp_montgomery_reduce.o bn_fast_s_mp_mul_digs.o \
+bn_fast_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_mp_2expt.o bn_mp_abs.o bn_mp_add.o bn_mp_add_d.o \
+bn_mp_addmod.o bn_mp_and.o bn_mp_clamp.o bn_mp_clear.o bn_mp_clear_multi.o bn_mp_cmp.o bn_mp_cmp_d.o \
+bn_mp_cmp_mag.o bn_mp_cnt_lsb.o bn_mp_copy.o bn_mp_count_bits.o bn_mp_div_2.o bn_mp_div_2d.o bn_mp_div_3.o \
+bn_mp_div.o bn_mp_div_d.o bn_mp_dr_is_modulus.o bn_mp_dr_reduce.o bn_mp_dr_setup.o bn_mp_exch.o \
+bn_mp_export.o bn_mp_expt_d.o bn_mp_expt_d_ex.o bn_mp_exptmod.o bn_mp_exptmod_fast.o bn_mp_exteuclid.o \
+bn_mp_fread.o bn_mp_fwrite.o bn_mp_gcd.o bn_mp_get_int.o bn_mp_get_long.o bn_mp_get_long_long.o \
+bn_mp_grow.o bn_mp_import.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_invmod.o bn_mp_invmod_slow.o bn_mp_is_square.o \
+bn_mp_jacobi.o bn_mp_karatsuba_mul.o bn_mp_karatsuba_sqr.o bn_mp_lcm.o bn_mp_lshd.o bn_mp_mod_2d.o \
+bn_mp_mod.o bn_mp_mod_d.o bn_mp_montgomery_calc_normalization.o bn_mp_montgomery_reduce.o \
+bn_mp_montgomery_setup.o bn_mp_mul_2.o bn_mp_mul_2d.o bn_mp_mul.o bn_mp_mul_d.o bn_mp_mulmod.o bn_mp_neg.o \
+bn_mp_n_root.o bn_mp_n_root_ex.o bn_mp_or.o bn_mp_prime_fermat.o bn_mp_prime_is_divisible.o \
+bn_mp_prime_is_prime.o bn_mp_prime_miller_rabin.o bn_mp_prime_next_prime.o \
+bn_mp_prime_rabin_miller_trials.o bn_mp_prime_random_ex.o bn_mp_radix_size.o bn_mp_radix_smap.o \
+bn_mp_rand.o bn_mp_read_radix.o bn_mp_read_signed_bin.o bn_mp_read_unsigned_bin.o bn_mp_reduce_2k.o \
+bn_mp_reduce_2k_l.o bn_mp_reduce_2k_setup.o bn_mp_reduce_2k_setup_l.o bn_mp_reduce.o \
+bn_mp_reduce_is_2k.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_setup.o bn_mp_rshd.o bn_mp_set.o bn_mp_set_int.o \
+bn_mp_set_long.o bn_mp_set_long_long.o bn_mp_shrink.o bn_mp_signed_bin_size.o bn_mp_sqr.o bn_mp_sqrmod.o \
+bn_mp_sqrt.o bn_mp_sqrtmod_prime.o bn_mp_sub.o bn_mp_sub_d.o bn_mp_submod.o bn_mp_toom_mul.o \
+bn_mp_toom_sqr.o bn_mp_toradix.o bn_mp_toradix_n.o bn_mp_to_signed_bin.o bn_mp_to_signed_bin_n.o \
+bn_mp_to_unsigned_bin.o bn_mp_to_unsigned_bin_n.o bn_mp_unsigned_bin_size.o bn_mp_xor.o bn_mp_zero.o \
+bn_prime_tab.o bn_reverse.o bn_s_mp_add.o bn_s_mp_exptmod.o bn_s_mp_mul_digs.o bn_s_mp_mul_high_digs.o \
+bn_s_mp_sqr.o bn_s_mp_sub.o
+
+#END_INS
+
+HEADERS=tommath.h tommath_class.h tommath_superclass.h
 
 libtommath.a:  $(OBJECTS)
 	$(AR) $(ARFLAGS) libtommath.a $(OBJECTS)
@@ -75,7 +76,7 @@ libtommath.a:  $(OBJECTS)
 #
 # This will build the library with profile generation
 # then run the test demo and rebuild the library.
-# 
+#
 # So far I've seen improvements in the MP math
 profiled:
 	make -f makefile.icc CFLAGS="$(CFLAGS) -prof_gen -DTESTING" timing
@@ -83,7 +84,7 @@ profiled:
 	rm -f *.a *.o ltmtest
 	make -f makefile.icc CFLAGS="$(CFLAGS) -prof_use"
 
-#make a single object profiled library 
+#make a single object profiled library
 profiled_single:
 	perl gen.pl
 	$(CC) $(CFLAGS) -prof_gen -DTESTING -c mpi.c -o mpi.o
@@ -92,7 +93,7 @@ profiled_single:
 	rm -f *.o ltmtest
 	$(CC) $(CFLAGS) -prof_use -ip -DTESTING -c mpi.c -o mpi.o
 	$(AR) $(ARFLAGS) libtommath.a mpi.o
-	ranlib libtommath.a	
+	ranlib libtommath.a
 
 install: libtommath.a
 	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(LIBPATH)
@@ -102,10 +103,10 @@ install: libtommath.a
 
 test: libtommath.a demo/demo.o
 	$(CC) demo/demo.o libtommath.a -o test
-	
-mtest: test	
+
+mtest: test
 	cd mtest ; $(CC) $(CFLAGS) mtest.c -o mtest
-        
+
 timing: libtommath.a
 	$(CC) $(CFLAGS) -DTIMER demo/timing.c libtommath.a -o ltmtest
 
diff --git a/libtommath/makefile.msvc b/libtommath/makefile.msvc
index 5edebec..a47aadd 100644
--- a/libtommath/makefile.msvc
+++ b/libtommath/makefile.msvc
@@ -6,33 +6,33 @@ CFLAGS = /I. /Ox /DWIN32 /W3 /Fo$@
 
 default: library
 
-OBJECTS=bncore.obj bn_mp_init.obj bn_mp_clear.obj bn_mp_exch.obj bn_mp_grow.obj bn_mp_shrink.obj \
-bn_mp_clamp.obj bn_mp_zero.obj  bn_mp_set.obj bn_mp_set_int.obj bn_mp_init_size.obj bn_mp_copy.obj \
-bn_mp_init_copy.obj bn_mp_abs.obj bn_mp_neg.obj bn_mp_cmp_mag.obj bn_mp_cmp.obj bn_mp_cmp_d.obj \
-bn_mp_rshd.obj bn_mp_lshd.obj bn_mp_mod_2d.obj bn_mp_div_2d.obj bn_mp_mul_2d.obj bn_mp_div_2.obj \
-bn_mp_mul_2.obj bn_s_mp_add.obj bn_s_mp_sub.obj bn_fast_s_mp_mul_digs.obj bn_s_mp_mul_digs.obj \
-bn_fast_s_mp_mul_high_digs.obj bn_s_mp_mul_high_digs.obj bn_fast_s_mp_sqr.obj bn_s_mp_sqr.obj \
-bn_mp_add.obj bn_mp_sub.obj bn_mp_karatsuba_mul.obj bn_mp_mul.obj bn_mp_karatsuba_sqr.obj \
-bn_mp_sqr.obj bn_mp_div.obj bn_mp_mod.obj bn_mp_add_d.obj bn_mp_sub_d.obj bn_mp_mul_d.obj \
-bn_mp_div_d.obj bn_mp_mod_d.obj bn_mp_expt_d.obj bn_mp_addmod.obj bn_mp_submod.obj \
-bn_mp_mulmod.obj bn_mp_sqrmod.obj bn_mp_gcd.obj bn_mp_lcm.obj bn_fast_mp_invmod.obj bn_mp_invmod.obj \
-bn_mp_reduce.obj bn_mp_montgomery_setup.obj bn_fast_mp_montgomery_reduce.obj bn_mp_montgomery_reduce.obj \
-bn_mp_exptmod_fast.obj bn_mp_exptmod.obj bn_mp_2expt.obj bn_mp_n_root.obj bn_mp_jacobi.obj bn_reverse.obj \
-bn_mp_count_bits.obj bn_mp_read_unsigned_bin.obj bn_mp_read_signed_bin.obj bn_mp_to_unsigned_bin.obj \
-bn_mp_to_signed_bin.obj bn_mp_unsigned_bin_size.obj bn_mp_signed_bin_size.obj  \
-bn_mp_xor.obj bn_mp_and.obj bn_mp_or.obj bn_mp_rand.obj bn_mp_montgomery_calc_normalization.obj \
-bn_mp_prime_is_divisible.obj bn_prime_tab.obj bn_mp_prime_fermat.obj bn_mp_prime_miller_rabin.obj \
-bn_mp_prime_is_prime.obj bn_mp_prime_next_prime.obj bn_mp_dr_reduce.obj \
-bn_mp_dr_is_modulus.obj bn_mp_dr_setup.obj bn_mp_reduce_setup.obj \
-bn_mp_toom_mul.obj bn_mp_toom_sqr.obj bn_mp_div_3.obj bn_s_mp_exptmod.obj \
-bn_mp_reduce_2k.obj bn_mp_reduce_is_2k.obj bn_mp_reduce_2k_setup.obj \
-bn_mp_reduce_2k_l.obj bn_mp_reduce_is_2k_l.obj bn_mp_reduce_2k_setup_l.obj \
-bn_mp_radix_smap.obj bn_mp_read_radix.obj bn_mp_toradix.obj bn_mp_radix_size.obj \
-bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_cnt_lsb.obj bn_error.obj \
-bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \
-bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj \
-bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj \
-bn_mp_to_signed_bin_n.obj bn_mp_to_unsigned_bin_n.obj
+#START_INS
+OBJECTS=bncore.obj bn_error.obj bn_fast_mp_invmod.obj bn_fast_mp_montgomery_reduce.obj bn_fast_s_mp_mul_digs.obj \
+bn_fast_s_mp_mul_high_digs.obj bn_fast_s_mp_sqr.obj bn_mp_2expt.obj bn_mp_abs.obj bn_mp_add.obj bn_mp_add_d.obj \
+bn_mp_addmod.obj bn_mp_and.obj bn_mp_clamp.obj bn_mp_clear.obj bn_mp_clear_multi.obj bn_mp_cmp.obj bn_mp_cmp_d.obj \
+bn_mp_cmp_mag.obj bn_mp_cnt_lsb.obj bn_mp_copy.obj bn_mp_count_bits.obj bn_mp_div_2.obj bn_mp_div_2d.obj bn_mp_div_3.obj \
+bn_mp_div.obj bn_mp_div_d.obj bn_mp_dr_is_modulus.obj bn_mp_dr_reduce.obj bn_mp_dr_setup.obj bn_mp_exch.obj \
+bn_mp_export.obj bn_mp_expt_d.obj bn_mp_expt_d_ex.obj bn_mp_exptmod.obj bn_mp_exptmod_fast.obj bn_mp_exteuclid.obj \
+bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_gcd.obj bn_mp_get_int.obj bn_mp_get_long.obj bn_mp_get_long_long.obj \
+bn_mp_grow.obj bn_mp_import.obj bn_mp_init.obj bn_mp_init_copy.obj bn_mp_init_multi.obj bn_mp_init_set.obj \
+bn_mp_init_set_int.obj bn_mp_init_size.obj bn_mp_invmod.obj bn_mp_invmod_slow.obj bn_mp_is_square.obj \
+bn_mp_jacobi.obj bn_mp_karatsuba_mul.obj bn_mp_karatsuba_sqr.obj bn_mp_lcm.obj bn_mp_lshd.obj bn_mp_mod_2d.obj \
+bn_mp_mod.obj bn_mp_mod_d.obj bn_mp_montgomery_calc_normalization.obj bn_mp_montgomery_reduce.obj \
+bn_mp_montgomery_setup.obj bn_mp_mul_2.obj bn_mp_mul_2d.obj bn_mp_mul.obj bn_mp_mul_d.obj bn_mp_mulmod.obj bn_mp_neg.obj \
+bn_mp_n_root.obj bn_mp_n_root_ex.obj bn_mp_or.obj bn_mp_prime_fermat.obj bn_mp_prime_is_divisible.obj \
+bn_mp_prime_is_prime.obj bn_mp_prime_miller_rabin.obj bn_mp_prime_next_prime.obj \
+bn_mp_prime_rabin_miller_trials.obj bn_mp_prime_random_ex.obj bn_mp_radix_size.obj bn_mp_radix_smap.obj \
+bn_mp_rand.obj bn_mp_read_radix.obj bn_mp_read_signed_bin.obj bn_mp_read_unsigned_bin.obj bn_mp_reduce_2k.obj \
+bn_mp_reduce_2k_l.obj bn_mp_reduce_2k_setup.obj bn_mp_reduce_2k_setup_l.obj bn_mp_reduce.obj \
+bn_mp_reduce_is_2k.obj bn_mp_reduce_is_2k_l.obj bn_mp_reduce_setup.obj bn_mp_rshd.obj bn_mp_set.obj bn_mp_set_int.obj \
+bn_mp_set_long.obj bn_mp_set_long_long.obj bn_mp_shrink.obj bn_mp_signed_bin_size.obj bn_mp_sqr.obj bn_mp_sqrmod.obj \
+bn_mp_sqrt.obj bn_mp_sqrtmod_prime.obj bn_mp_sub.obj bn_mp_sub_d.obj bn_mp_submod.obj bn_mp_toom_mul.obj \
+bn_mp_toom_sqr.obj bn_mp_toradix.obj bn_mp_toradix_n.obj bn_mp_to_signed_bin.obj bn_mp_to_signed_bin_n.obj \
+bn_mp_to_unsigned_bin.obj bn_mp_to_unsigned_bin_n.obj bn_mp_unsigned_bin_size.obj bn_mp_xor.obj bn_mp_zero.obj \
+bn_prime_tab.obj bn_reverse.obj bn_s_mp_add.obj bn_s_mp_exptmod.obj bn_s_mp_mul_digs.obj bn_s_mp_mul_high_digs.obj \
+bn_s_mp_sqr.obj bn_s_mp_sub.obj
+
+#END_INS
 
 HEADERS=tommath.h tommath_class.h tommath_superclass.h
 
diff --git a/libtommath/makefile.shared b/libtommath/makefile.shared
index f17bbbd..559720e 100644
--- a/libtommath/makefile.shared
+++ b/libtommath/makefile.shared
@@ -1,102 +1,71 @@
 #Makefile for GCC
 #
 #Tom St Denis
-VERSION=0:41
-
-CC = libtool --mode=compile --tag=CC gcc
-
-CFLAGS  +=  -I./ -Wall -W -Wshadow -Wsign-compare
-
-ifndef IGNORE_SPEED
-
-#for speed 
-CFLAGS += -O3 -funroll-loops
-
-#for size 
-#CFLAGS += -Os
-
-#x86 optimizations [should be valid for any GCC install though]
-CFLAGS  += -fomit-frame-pointer
-
-endif
-
-#install as this user
-ifndef INSTALL_GROUP
-   GROUP=wheel
-else
-   GROUP=$(INSTALL_GROUP)
-endif
-
-ifndef INSTALL_USER
-   USER=root
-else
-   USER=$(INSTALL_USER)
-endif
-
-default: libtommath.la
 
 #default files to install
 ifndef LIBNAME
    LIBNAME=libtommath.la
 endif
-ifndef LIBNAME_S
-   LIBNAME_S=libtommath.a
-endif
-HEADERS=tommath.h tommath_class.h tommath_superclass.h
-
-#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=
-LIBPATH=/usr/lib
-INCPATH=/usr/include
-DATAPATH=/usr/share/doc/libtommath/pdf
 
-OBJECTS=bncore.o bn_mp_init.o bn_mp_clear.o bn_mp_exch.o bn_mp_grow.o bn_mp_shrink.o \
-bn_mp_clamp.o bn_mp_zero.o  bn_mp_set.o bn_mp_set_int.o bn_mp_init_size.o bn_mp_copy.o \
-bn_mp_init_copy.o bn_mp_abs.o bn_mp_neg.o bn_mp_cmp_mag.o bn_mp_cmp.o bn_mp_cmp_d.o \
-bn_mp_rshd.o bn_mp_lshd.o bn_mp_mod_2d.o bn_mp_div_2d.o bn_mp_mul_2d.o bn_mp_div_2.o \
-bn_mp_mul_2.o bn_s_mp_add.o bn_s_mp_sub.o bn_fast_s_mp_mul_digs.o bn_s_mp_mul_digs.o \
-bn_fast_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_s_mp_sqr.o \
-bn_mp_add.o bn_mp_sub.o bn_mp_karatsuba_mul.o bn_mp_mul.o bn_mp_karatsuba_sqr.o \
-bn_mp_sqr.o bn_mp_div.o bn_mp_mod.o bn_mp_add_d.o bn_mp_sub_d.o bn_mp_mul_d.o \
-bn_mp_div_d.o bn_mp_mod_d.o bn_mp_expt_d.o bn_mp_addmod.o bn_mp_submod.o \
-bn_mp_mulmod.o bn_mp_sqrmod.o bn_mp_gcd.o bn_mp_lcm.o bn_fast_mp_invmod.o bn_mp_invmod.o \
-bn_mp_reduce.o bn_mp_montgomery_setup.o bn_fast_mp_montgomery_reduce.o bn_mp_montgomery_reduce.o \
-bn_mp_exptmod_fast.o bn_mp_exptmod.o bn_mp_2expt.o bn_mp_n_root.o bn_mp_jacobi.o bn_reverse.o \
-bn_mp_count_bits.o bn_mp_read_unsigned_bin.o bn_mp_read_signed_bin.o bn_mp_to_unsigned_bin.o \
-bn_mp_to_signed_bin.o bn_mp_unsigned_bin_size.o bn_mp_signed_bin_size.o  \
-bn_mp_xor.o bn_mp_and.o bn_mp_or.o bn_mp_rand.o bn_mp_montgomery_calc_normalization.o \
-bn_mp_prime_is_divisible.o bn_prime_tab.o bn_mp_prime_fermat.o bn_mp_prime_miller_rabin.o \
-bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \
-bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
-bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
-bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
-bn_mp_reduce_2k_l.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_2k_setup_l.o \
-bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
-bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
-bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
-bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
-bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o \
-bn_mp_to_signed_bin_n.o bn_mp_to_unsigned_bin_n.o
+include makefile.include
+
+LT	?= libtool
+LTCOMPILE = $(LT) --mode=compile --tag=CC $(CC)
+
+LCOV_ARGS=--directory .libs --directory .
+
+#START_INS
+OBJECTS=bncore.o bn_error.o bn_fast_mp_invmod.o bn_fast_mp_montgomery_reduce.o bn_fast_s_mp_mul_digs.o \
+bn_fast_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_mp_2expt.o bn_mp_abs.o bn_mp_add.o bn_mp_add_d.o \
+bn_mp_addmod.o bn_mp_and.o bn_mp_clamp.o bn_mp_clear.o bn_mp_clear_multi.o bn_mp_cmp.o bn_mp_cmp_d.o \
+bn_mp_cmp_mag.o bn_mp_cnt_lsb.o bn_mp_copy.o bn_mp_count_bits.o bn_mp_div_2.o bn_mp_div_2d.o bn_mp_div_3.o \
+bn_mp_div.o bn_mp_div_d.o bn_mp_dr_is_modulus.o bn_mp_dr_reduce.o bn_mp_dr_setup.o bn_mp_exch.o \
+bn_mp_export.o bn_mp_expt_d.o bn_mp_expt_d_ex.o bn_mp_exptmod.o bn_mp_exptmod_fast.o bn_mp_exteuclid.o \
+bn_mp_fread.o bn_mp_fwrite.o bn_mp_gcd.o bn_mp_get_int.o bn_mp_get_long.o bn_mp_get_long_long.o \
+bn_mp_grow.o bn_mp_import.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_invmod.o bn_mp_invmod_slow.o bn_mp_is_square.o \
+bn_mp_jacobi.o bn_mp_karatsuba_mul.o bn_mp_karatsuba_sqr.o bn_mp_lcm.o bn_mp_lshd.o bn_mp_mod_2d.o \
+bn_mp_mod.o bn_mp_mod_d.o bn_mp_montgomery_calc_normalization.o bn_mp_montgomery_reduce.o \
+bn_mp_montgomery_setup.o bn_mp_mul_2.o bn_mp_mul_2d.o bn_mp_mul.o bn_mp_mul_d.o bn_mp_mulmod.o bn_mp_neg.o \
+bn_mp_n_root.o bn_mp_n_root_ex.o bn_mp_or.o bn_mp_prime_fermat.o bn_mp_prime_is_divisible.o \
+bn_mp_prime_is_prime.o bn_mp_prime_miller_rabin.o bn_mp_prime_next_prime.o \
+bn_mp_prime_rabin_miller_trials.o bn_mp_prime_random_ex.o bn_mp_radix_size.o bn_mp_radix_smap.o \
+bn_mp_rand.o bn_mp_read_radix.o bn_mp_read_signed_bin.o bn_mp_read_unsigned_bin.o bn_mp_reduce_2k.o \
+bn_mp_reduce_2k_l.o bn_mp_reduce_2k_setup.o bn_mp_reduce_2k_setup_l.o bn_mp_reduce.o \
+bn_mp_reduce_is_2k.o bn_mp_reduce_is_2k_l.o bn_mp_reduce_setup.o bn_mp_rshd.o bn_mp_set.o bn_mp_set_int.o \
+bn_mp_set_long.o bn_mp_set_long_long.o bn_mp_shrink.o bn_mp_signed_bin_size.o bn_mp_sqr.o bn_mp_sqrmod.o \
+bn_mp_sqrt.o bn_mp_sqrtmod_prime.o bn_mp_sub.o bn_mp_sub_d.o bn_mp_submod.o bn_mp_toom_mul.o \
+bn_mp_toom_sqr.o bn_mp_toradix.o bn_mp_toradix_n.o bn_mp_to_signed_bin.o bn_mp_to_signed_bin_n.o \
+bn_mp_to_unsigned_bin.o bn_mp_to_unsigned_bin_n.o bn_mp_unsigned_bin_size.o bn_mp_xor.o bn_mp_zero.o \
+bn_prime_tab.o bn_reverse.o bn_s_mp_add.o bn_s_mp_exptmod.o bn_s_mp_mul_digs.o bn_s_mp_mul_high_digs.o \
+bn_s_mp_sqr.o bn_s_mp_sub.o
+
+#END_INS
 
 objs: $(OBJECTS)
 
+.c.o:
+	$(LTCOMPILE) $(CFLAGS) $(LDFLAGS) -o $@ -c $<
+
 $(LIBNAME):  $(OBJECTS)
-	libtool --mode=link gcc *.lo -o $(LIBNAME) -rpath $(LIBPATH) -version-info $(VERSION)
+	$(LT) --mode=link --tag=CC $(CC) $(LDFLAGS) *.lo -o $(LIBNAME) -rpath $(LIBPATH) -version-info $(VERSION_SO)
 
 install: $(LIBNAME)
-	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(LIBPATH)
-	libtool --mode=install install -c $(LIBNAME) $(DESTDIR)$(LIBPATH)/$(LIBNAME)
-	install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH)
-	install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH)
+	install -d $(DESTDIR)$(LIBPATH)
+	install -d $(DESTDIR)$(INCPATH)
+	$(LT) --mode=install install -c $(LIBNAME) $(DESTDIR)$(LIBPATH)/$(LIBNAME)
+	install -m 644 $(HEADERS_PUB) $(DESTDIR)$(INCPATH)
 
 test: $(LIBNAME) demo/demo.o
-	gcc $(CFLAGS) -c demo/demo.c -o demo/demo.o
-	libtool --mode=link gcc -o test demo/demo.o $(LIBNAME_S)
-	
-mtest: test	
-	cd mtest ; gcc $(CFLAGS) mtest.c -o mtest
-        
+	$(CC) $(CFLAGS) -c demo/demo.c -o demo/demo.o
+	$(LT) --mode=link $(CC) $(LDFLAGS) -o test demo/demo.o $(LIBNAME)
+
+test_standalone: $(LIBNAME) demo/demo.o
+	$(CC) $(CFLAGS) -c demo/demo.c -o demo/demo.o
+	$(LT) --mode=link $(CC) $(LDFLAGS) -o test demo/demo.o $(LIBNAME)
+
+mtest:
+	cd mtest ; $(CC) $(CFLAGS) $(LDFLAGS) mtest.c -o mtest
+
 timing: $(LIBNAME)
-	gcc $(CFLAGS) -DTIMER demo/timing.c $(LIBNAME_S) -o ltmtest
+	$(LT) --mode=link $(CC) $(CFLAGS) $(LDFLAGS) -DTIMER demo/timing.c $(LIBNAME) -o ltmtest
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 "$1 shouldn't be here" ; exit 1; fi
-
-
diff --git a/libtommath/poster.tex b/libtommath/poster.tex
deleted file mode 100644
index e7388f4..0000000
--- a/libtommath/poster.tex
+++ /dev/null
@@ -1,35 +0,0 @@
-\documentclass[landscape,11pt]{article}
-\usepackage{amsmath, amssymb}
-\usepackage{hyperref}
-\begin{document}
-\hspace*{-3in}
-\begin{tabular}{llllll}
-$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/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/tommath.h b/libtommath/tommath.h
index 4b3a76f..1793ed0 100644
--- a/libtommath/tommath.h
+++ b/libtommath/tommath.h
@@ -10,46 +10,27 @@
  * The library is free for all purposes without any express
  * guarantee it works.
  *
- * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ * Tom St Denis, tstdenis82@gmail.com, http://math.libtomcrypt.com
  */
 #ifndef BN_H_
 #define BN_H_
 
 #include <stdio.h>
-#include <string.h>
 #include <stdlib.h>
-#include <ctype.h>
+#include <stdint.h>
 #include <limits.h>
 
 #include <tommath_class.h>
 
-#ifndef MIN
-#   define MIN(x,y) ((x)<(y)?(x):(y))
-#endif
-
-#ifndef MAX
-#   define MAX(x,y) ((x)>(y)?(x):(y))
-#endif
-
 #ifdef __cplusplus
 extern "C" {
-
-/* C++ compilers don't like assigning void * to mp_digit * */
-#define  OPT_CAST(x)  (x *)
-
-#else
-
-/* C on the other hand doesn't care */
-#define  OPT_CAST(x)
-
 #endif
 
-
 /* detect 64-bit mode if possible */
-#if defined(__x86_64__) 
-#   if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT))
-#	define MP_64BIT
-#   endif
+#if defined(__x86_64__)
+   #if !(defined(MP_32BIT) || defined(MP_16BIT) || defined(MP_8BIT))
+      #define MP_64BIT
+   #endif
 #endif
 
 /* some default configurations.
@@ -61,70 +42,78 @@ extern "C" {
  * [any size beyond that is ok provided it doesn't overflow the data type]
  */
 #ifdef MP_8BIT
-   typedef unsigned char      mp_digit;
-   typedef unsigned short     mp_word;
+   typedef uint8_t              mp_digit;
+   typedef uint16_t             mp_word;
+#define MP_SIZEOF_MP_DIGIT      1
+#ifdef DIGIT_BIT
+#error You must not define DIGIT_BIT when using MP_8BIT
+#endif
 #elif defined(MP_16BIT)
-   typedef unsigned short     mp_digit;
-   typedef unsigned long      mp_word;
+   typedef uint16_t             mp_digit;
+   typedef uint32_t             mp_word;
+#define MP_SIZEOF_MP_DIGIT      2
+#ifdef DIGIT_BIT
+#error You must not define DIGIT_BIT when using MP_16BIT
+#endif
 #elif defined(MP_64BIT)
    /* for GCC only on supported platforms */
 #ifndef CRYPT
-   typedef unsigned long long ulong64;
-   typedef signed long long   long64;
+   typedef unsigned long long   ulong64;
+   typedef signed long long     long64;
 #endif
 
-   typedef unsigned long      mp_digit;
-   typedef unsigned long      mp_word __attribute__ ((mode(TI)));
+   typedef ulong64 mp_digit;
+#if defined(_WIN32)
+   typedef unsigned __int128    mp_word;
+#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 */
+   typedef uint128_t            mp_word;
+#endif
 
-#  define DIGIT_BIT          60
+   #define DIGIT_BIT            60
 #else
    /* this is the default case, 28-bit digits */
-   
+
    /* this is to make porting into LibTomCrypt easier :-) */
 #ifndef CRYPT
-#  if defined(_MSC_VER) || defined(__BORLANDC__)
-      typedef unsigned __int64   ulong64;
-      typedef signed __int64     long64;
-#  else
-      typedef unsigned long long ulong64;
-      typedef signed long long   long64;
-#  endif
+   typedef unsigned long long   ulong64;
+   typedef signed long long     long64;
 #endif
 
-   typedef unsigned long      mp_digit;
-   typedef ulong64            mp_word;
+   typedef uint32_t             mp_digit;
+   typedef ulong64              mp_word;
 
-#ifdef MP_31BIT   
+#ifdef MP_31BIT
    /* this is an extension that uses 31-bit digits */
-#  define DIGIT_BIT          31
+   #define DIGIT_BIT            31
 #else
    /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */
-#  define DIGIT_BIT          28
-#  define MP_28BIT
-#endif   
+   #define DIGIT_BIT            28
+   #define MP_28BIT
 #endif
-
-/* define heap macros */
-#ifndef CRYPT
-   /* default to libc stuff */
-#  ifndef XMALLOC
-#     define XMALLOC  malloc
-#     define XFREE    free
-#     define XREALLOC realloc
-#     define XCALLOC  calloc
-#  else
-      /* prototypes for our heap functions */
-      extern void *XMALLOC(size_t n);
-      extern void *XREALLOC(void *p, size_t n);
-      extern void *XCALLOC(size_t n, size_t s);
-      extern void XFREE(void *p);
-#  endif
 #endif
 
-
 /* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
 #ifndef DIGIT_BIT
-#   define DIGIT_BIT     ((int)((CHAR_BIT * sizeof(mp_digit) - 1)))  /* bits per digit */
+   #define DIGIT_BIT     (((CHAR_BIT * MP_SIZEOF_MP_DIGIT) - 1))  /* bits per digit */
+   typedef uint_least32_t mp_min_u32;
+#else
+   typedef mp_digit mp_min_u32;
+#endif
+
+/* platforms that can use a better rand function */
+#if defined(__FreeBSD__) || defined(__OpenBSD__) || defined(__NetBSD__) || defined(__DragonFly__)
+    #define MP_USE_ALT_RAND 1
+#endif
+
+/* use arc4random on platforms that support it */
+#ifdef MP_USE_ALT_RAND
+    #define MP_GEN_RANDOM()    arc4random()
+#else
+    #define MP_GEN_RANDOM()    rand()
 #endif
 
 #define MP_DIGIT_BIT     DIGIT_BIT
@@ -165,15 +154,15 @@ extern int KARATSUBA_MUL_CUTOFF,
 
 /* default precision */
 #ifndef MP_PREC
-#  ifndef MP_LOW_MEM
-#     define MP_PREC                 32     /* default digits of precision */
-#  else
-#     define MP_PREC                 8      /* default digits of precision */
-#  endif
+   #ifndef MP_LOW_MEM
+      #define MP_PREC                 32     /* default digits of precision */
+   #else
+      #define MP_PREC                 8      /* default digits of precision */
+   #endif
 #endif
 
 /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
-#define MP_WARRAY               (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
+#define MP_WARRAY               (1 << (((sizeof(mp_word) * CHAR_BIT) - (2 * DIGIT_BIT)) + 1))
 
 /* the infamous mp_int structure */
 typedef struct  {
@@ -190,7 +179,7 @@ typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
 #define SIGN(m)    ((m)->sign)
 
 /* error code to char* string */
-char *mp_error_to_string(int code);
+const char *mp_error_to_string(int code);
 
 /* ---> init and deinit bignum functions <--- */
 /* init a bignum */
@@ -219,8 +208,9 @@ 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] & 1) == 0)) ? MP_YES : MP_NO)
-#define mp_isodd(a)  (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? 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)
 
 /* set to zero */
 void mp_zero(mp_int *a);
@@ -231,9 +221,21 @@ void mp_set(mp_int *a, mp_digit b);
 /* set a 32-bit const */
 int mp_set_int(mp_int *a, unsigned long b);
 
+/* set a platform dependent unsigned long value */
+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);
+
 /* get a 32-bit value */
 unsigned long mp_get_int(mp_int * a);
 
+/* get a platform dependent unsigned long value */
+unsigned long mp_get_long(mp_int * a);
+
+/* get a platform dependent unsigned long long value */
+unsigned long long mp_get_long_long(mp_int * a);
+
 /* initialize and set a digit */
 int mp_init_set (mp_int * a, mp_digit b);
 
@@ -244,11 +246,17 @@ int mp_init_set_int (mp_int * a, unsigned long b);
 int mp_copy(const mp_int *a, mp_int *b);
 
 /* inits and copies, a = b */
-int mp_init_copy(mp_int *a, mp_int *b);
+int mp_init_copy(mp_int *a, const mp_int *b);
 
 /* trim unused digits */
 void mp_clamp(mp_int *a);
 
+/* import binary data */
+int mp_import(mp_int* rop, size_t count, int order, size_t size, int endian, size_t nails, const void* op);
+
+/* export binary data */
+int mp_export(void* rop, size_t* countp, int order, size_t size, int endian, size_t nails, mp_int* op);
+
 /* ---> digit manipulation <--- */
 
 /* right shift by "b" digits */
@@ -257,19 +265,19 @@ void mp_rshd(mp_int *a, int b);
 /* left shift by "b" digits */
 int mp_lshd(mp_int *a, int b);
 
-/* c = a / 2**b */
+/* c = a / 2**b, implemented as c = a >> 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);
 
-/* c = a * 2**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);
 
-/* c = a mod 2**d */
+/* c = a mod 2**b */
 int mp_mod_2d(const mp_int *a, int b, mp_int *c);
 
 /* computes a = 2**b */
@@ -347,6 +355,7 @@ int mp_div_3(mp_int *a, mp_int *c, mp_digit *d);
 
 /* c = a**b */
 int mp_expt_d(mp_int *a, mp_digit b, mp_int *c);
+int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast);
 
 /* c = a mod b, 0 <= c < b  */
 int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
@@ -382,10 +391,14 @@ int mp_lcm(mp_int *a, mp_int *b, mp_int *c);
  * returns error if a < 0 and b is even
  */
 int mp_n_root(mp_int *a, mp_digit b, mp_int *c);
+int mp_n_root_ex (mp_int * a, mp_digit b, mp_int * c, int fast);
 
 /* special sqrt algo */
 int mp_sqrt(mp_int *arg, mp_int *ret);
 
+/* special sqrt (mod prime) */
+int mp_sqrtmod_prime(mp_int *arg, mp_int *prime, mp_int *ret);
+
 /* is number a square? */
 int mp_is_square(mp_int *arg, int *ret);
 
@@ -453,7 +466,7 @@ int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
 #endif
 
 /* table of first PRIME_SIZE primes */
-extern const mp_digit ltm_prime_tab[];
+extern const mp_digit ltm_prime_tab[PRIME_SIZE];
 
 /* result=1 if a is divisible by one of the first PRIME_SIZE primes */
 int mp_prime_is_divisible(mp_int *a, int *result);
@@ -469,7 +482,7 @@ int mp_prime_fermat(mp_int *a, mp_int *b, int *result);
 int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result);
 
 /* This gives [for a given bit size] the number of trials required
- * such that Miller-Rabin gives a prob of failure lower than 2^-96 
+ * such that Miller-Rabin gives a prob of failure lower than 2^-96
  */
 int mp_prime_rabin_miller_trials(int size);
 
@@ -490,7 +503,7 @@ int mp_prime_is_prime(mp_int *a, int t, int *result);
 int mp_prime_next_prime(mp_int *a, int t, int bbs_style);
 
 /* makes a truly random prime of a given size (bytes),
- * call with bbs = 1 if you want it to be congruent to 3 mod 4 
+ * call with bbs = 1 if you want it to be congruent to 3 mod 4
  *
  * 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
@@ -503,10 +516,9 @@ int mp_prime_next_prime(mp_int *a, int t, int bbs_style);
 /* 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
@@ -532,10 +544,12 @@ int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen);
 int mp_read_radix(mp_int *a, const char *str, int radix);
 int mp_toradix(mp_int *a, char *str, int radix);
 int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen);
-int mp_radix_size(mp_int *a, int radix, int *size);
+int mp_radix_size(const mp_int *a, int radix, int *size);
 
+#ifndef LTM_NO_FILE
 int mp_fread(mp_int *a, int radix, FILE *stream);
 int mp_fwrite(mp_int *a, int radix, FILE *stream);
+#endif
 
 #define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
 #define mp_raw_size(mp)           mp_signed_bin_size(mp)
@@ -549,31 +563,13 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream);
 #define mp_todecimal(M, S) mp_toradix((M), (S), 10)
 #define mp_tohex(M, S)     mp_toradix((M), (S), 16)
 
-/* lowlevel functions, do not call! */
-int s_mp_add(mp_int *a, mp_int *b, mp_int *c);
-int s_mp_sub(mp_int *a, mp_int *b, mp_int *c);
-#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
-int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
-int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
-int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
-int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
-int fast_s_mp_sqr(mp_int *a, mp_int *b);
-int s_mp_sqr(mp_int *a, mp_int *b);
-int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c);
-int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c);
-int mp_karatsuba_sqr(mp_int *a, mp_int *b);
-int mp_toom_sqr(mp_int *a, mp_int *b);
-int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c);
-int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c);
-int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
-int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode);
-int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode);
-void bn_reverse(unsigned char *s, int len);
-
-extern const char *mp_s_rmap;
-
 #ifdef __cplusplus
-}
+   }
 #endif
 
 #endif
+
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/tommath.src b/libtommath/tommath.src
deleted file mode 100644
index 4065822..0000000
--- a/libtommath/tommath.src
+++ /dev/null
@@ -1,6350 +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.
-
-\begin{alltt}
-Tom St Denis
-111 Banning Rd
-Ottawa, Ontario
-K2L 1C3
-Canada
-
-Phone: 1-613-836-3160
-Email: tomstdenis@gmail.com
-\end{alltt}
-
-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 and set to zero at the same time with the calloc() function (line @25,XCALLOC@).  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.c
-
-Line @29,mp_set@ sets the initial value of the result to $1$.  Next the loop on line @31,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
-@47,<<@ 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 @44,/@ and @45,%@ 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_class.h b/libtommath/tommath_class.h
index b9cc902..2085521 100644
--- a/libtommath/tommath_class.h
+++ b/libtommath/tommath_class.h
@@ -38,7 +38,9 @@
 #define BN_MP_DR_REDUCE_C
 #define BN_MP_DR_SETUP_C
 #define BN_MP_EXCH_C
+#define BN_MP_EXPORT_C
 #define BN_MP_EXPT_D_C
+#define BN_MP_EXPT_D_EX_C
 #define BN_MP_EXPTMOD_C
 #define BN_MP_EXPTMOD_FAST_C
 #define BN_MP_EXTEUCLID_C
@@ -46,7 +48,10 @@
 #define BN_MP_FWRITE_C
 #define BN_MP_GCD_C
 #define BN_MP_GET_INT_C
+#define BN_MP_GET_LONG_C
+#define BN_MP_GET_LONG_LONG_C
 #define BN_MP_GROW_C
+#define BN_MP_IMPORT_C
 #define BN_MP_INIT_C
 #define BN_MP_INIT_COPY_C
 #define BN_MP_INIT_MULTI_C
@@ -73,6 +78,7 @@
 #define BN_MP_MUL_D_C
 #define BN_MP_MULMOD_C
 #define BN_MP_N_ROOT_C
+#define BN_MP_N_ROOT_EX_C
 #define BN_MP_NEG_C
 #define BN_MP_OR_C
 #define BN_MP_PRIME_FERMAT_C
@@ -99,11 +105,14 @@
 #define BN_MP_RSHD_C
 #define BN_MP_SET_C
 #define BN_MP_SET_INT_C
+#define BN_MP_SET_LONG_C
+#define BN_MP_SET_LONG_LONG_C
 #define BN_MP_SHRINK_C
 #define BN_MP_SIGNED_BIN_SIZE_C
 #define BN_MP_SQR_C
 #define BN_MP_SQRMOD_C
 #define BN_MP_SQRT_C
+#define BN_MP_SQRTMOD_PRIME_C
 #define BN_MP_SUB_C
 #define BN_MP_SUB_D_C
 #define BN_MP_SUBMOD_C
@@ -315,12 +324,23 @@
 #if defined(BN_MP_EXCH_C)
 #endif
 
+#if defined(BN_MP_EXPORT_C)
+   #define BN_MP_INIT_COPY_C
+   #define BN_MP_COUNT_BITS_C
+   #define BN_MP_DIV_2D_C
+   #define BN_MP_CLEAR_C
+#endif
+
 #if defined(BN_MP_EXPT_D_C)
+   #define BN_MP_EXPT_D_EX_C
+#endif
+
+#if defined(BN_MP_EXPT_D_EX_C)
    #define BN_MP_INIT_COPY_C
    #define BN_MP_SET_C
-   #define BN_MP_SQR_C
-   #define BN_MP_CLEAR_C
    #define BN_MP_MUL_C
+   #define BN_MP_CLEAR_C
+   #define BN_MP_SQR_C
 #endif
 
 #if defined(BN_MP_EXPTMOD_C)
@@ -387,7 +407,6 @@
 #if defined(BN_MP_GCD_C)
    #define BN_MP_ISZERO_C
    #define BN_MP_ABS_C
-   #define BN_MP_ZERO_C
    #define BN_MP_INIT_COPY_C
    #define BN_MP_CNT_LSB_C
    #define BN_MP_DIV_2D_C
@@ -401,13 +420,26 @@
 #if defined(BN_MP_GET_INT_C)
 #endif
 
+#if defined(BN_MP_GET_LONG_C)
+#endif
+
+#if defined(BN_MP_GET_LONG_LONG_C)
+#endif
+
 #if defined(BN_MP_GROW_C)
 #endif
 
+#if defined(BN_MP_IMPORT_C)
+   #define BN_MP_ZERO_C
+   #define BN_MP_MUL_2D_C
+   #define BN_MP_CLAMP_C
+#endif
+
 #if defined(BN_MP_INIT_C)
 #endif
 
 #if defined(BN_MP_INIT_COPY_C)
+   #define BN_MP_INIT_SIZE_C
    #define BN_MP_COPY_C
 #endif
 
@@ -481,8 +513,9 @@
    #define BN_MP_MUL_C
    #define BN_MP_INIT_SIZE_C
    #define BN_MP_CLAMP_C
-   #define BN_MP_SUB_C
+   #define BN_S_MP_ADD_C
    #define BN_MP_ADD_C
+   #define BN_S_MP_SUB_C
    #define BN_MP_LSHD_C
    #define BN_MP_CLEAR_C
 #endif
@@ -491,8 +524,8 @@
    #define BN_MP_INIT_SIZE_C
    #define BN_MP_CLAMP_C
    #define BN_MP_SQR_C
-   #define BN_MP_SUB_C
    #define BN_S_MP_ADD_C
+   #define BN_S_MP_SUB_C
    #define BN_MP_LSHD_C
    #define BN_MP_ADD_C
    #define BN_MP_CLEAR_C
@@ -516,8 +549,9 @@
    #define BN_MP_INIT_C
    #define BN_MP_DIV_C
    #define BN_MP_CLEAR_C
-   #define BN_MP_ADD_C
+   #define BN_MP_ISZERO_C
    #define BN_MP_EXCH_C
+   #define BN_MP_ADD_C
 #endif
 
 #if defined(BN_MP_MOD_2D_C)
@@ -583,10 +617,14 @@
 #endif
 
 #if defined(BN_MP_N_ROOT_C)
+   #define BN_MP_N_ROOT_EX_C
+#endif
+
+#if defined(BN_MP_N_ROOT_EX_C)
    #define BN_MP_INIT_C
    #define BN_MP_SET_C
    #define BN_MP_COPY_C
-   #define BN_MP_EXPT_D_C
+   #define BN_MP_EXPT_D_EX_C
    #define BN_MP_MUL_C
    #define BN_MP_SUB_C
    #define BN_MP_MUL_D_C
@@ -667,9 +705,9 @@
 #endif
 
 #if defined(BN_MP_RADIX_SIZE_C)
+   #define BN_MP_ISZERO_C
    #define BN_MP_COUNT_BITS_C
    #define BN_MP_INIT_COPY_C
-   #define BN_MP_ISZERO_C
    #define BN_MP_DIV_D_C
    #define BN_MP_CLEAR_C
 #endif
@@ -687,7 +725,6 @@
 #if defined(BN_MP_READ_RADIX_C)
    #define BN_MP_ZERO_C
    #define BN_MP_S_RMAP_C
-   #define BN_MP_RADIX_SMAP_C
    #define BN_MP_MUL_D_C
    #define BN_MP_ADD_D_C
    #define BN_MP_ISZERO_C
@@ -788,6 +825,12 @@
    #define BN_MP_CLAMP_C
 #endif
 
+#if defined(BN_MP_SET_LONG_C)
+#endif
+
+#if defined(BN_MP_SET_LONG_LONG_C)
+#endif
+
 #if defined(BN_MP_SHRINK_C)
 #endif
 
@@ -823,6 +866,25 @@
    #define BN_MP_CLEAR_C
 #endif
 
+#if defined(BN_MP_SQRTMOD_PRIME_C)
+   #define BN_MP_CMP_D_C
+   #define BN_MP_ZERO_C
+   #define BN_MP_JACOBI_C
+   #define BN_MP_INIT_MULTI_C
+   #define BN_MP_MOD_D_C
+   #define BN_MP_ADD_D_C
+   #define BN_MP_DIV_2_C
+   #define BN_MP_EXPTMOD_C
+   #define BN_MP_COPY_C
+   #define BN_MP_SUB_D_C
+   #define BN_MP_ISEVEN_C
+   #define BN_MP_SET_INT_C
+   #define BN_MP_SQRMOD_C
+   #define BN_MP_MULMOD_C
+   #define BN_MP_SET_C
+   #define BN_MP_CLEAR_MULTI_C
+#endif
+
 #if defined(BN_MP_SUB_C)
    #define BN_S_MP_ADD_C
    #define BN_MP_CMP_MAG_C
diff --git a/libtommath/tommath_private.h b/libtommath/tommath_private.h
new file mode 100644
index 0000000..d23c333
--- /dev/null
+++ b/libtommath/tommath_private.h
@@ -0,0 +1,125 @@
+/* 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, tstdenis82@gmail.com, http://math.libtomcrypt.com
+ */
+#ifndef TOMMATH_PRIV_H_
+#define TOMMATH_PRIV_H_
+
+#include <tommath.h>
+#include <ctype.h>
+
+#ifndef MIN
+#define MIN(x,y) (((x) < (y)) ? (x) : (y))
+#endif
+
+#ifndef MAX
+#define MAX(x,y) (((x) > (y)) ? (x) : (y))
+#endif
+
+#ifdef __cplusplus
+extern "C" {
+
+/* C++ compilers don't like assigning void * to mp_digit * */
+#define  OPT_CAST(x)  (x *)
+
+#else
+
+/* C on the other hand doesn't care */
+#define  OPT_CAST(x)
+
+#endif
+
+/* define heap macros */
+#if 0
+#ifndef XMALLOC
+   /* default to libc stuff */
+   #define XMALLOC  malloc
+   #define XFREE    free
+   #define XREALLOC realloc
+   #define XCALLOC  calloc
+#else
+   /* prototypes for our heap functions */
+   extern void *XMALLOC(size_t n);
+   extern void *XREALLOC(void *p, size_t n);
+   extern void *XCALLOC(size_t n, size_t s);
+   extern void XFREE(void *p);
+#endif
+#endif
+
+/* lowlevel functions, do not call! */
+int s_mp_add(mp_int *a, mp_int *b, mp_int *c);
+int s_mp_sub(mp_int *a, mp_int *b, mp_int *c);
+#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
+int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
+int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
+int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
+int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
+int fast_s_mp_sqr(mp_int *a, mp_int *b);
+int s_mp_sqr(mp_int *a, mp_int *b);
+int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c);
+int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c);
+int mp_karatsuba_sqr(mp_int *a, mp_int *b);
+int mp_toom_sqr(mp_int *a, mp_int *b);
+int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c);
+int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c);
+int fast_mp_montgomery_reduce(mp_int *x, mp_int *n, mp_digit rho);
+int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int redmode);
+int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode);
+void bn_reverse(unsigned char *s, int len);
+
+extern const char *mp_s_rmap;
+
+/* Fancy macro to set an MPI from another type.
+ * There are several things assumed:
+ *  x is the counter and unsigned
+ *  a is the pointer to the MPI
+ *  b is the original value that should be set in the MPI.
+ */
+#define MP_SET_XLONG(func_name, type)                    \
+int func_name (mp_int * a, type b)                       \
+{                                                        \
+  unsigned int  x;                                       \
+  int           res;                                     \
+                                                         \
+  mp_zero (a);                                           \
+                                                         \
+  /* set four bits at a time */                          \
+  for (x = 0; x < (sizeof(type) * 2u); 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 >> ((sizeof(type) * 8u) - 4u)) & 15u; \
+                                                         \
+    /* 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;                                        \
+}
+
+#ifdef __cplusplus
+   }
+#endif
+
+#endif
+
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/libtommath/tommath_superclass.h b/libtommath/tommath_superclass.h
index e3926df..0eeaf5f 100644
--- a/libtommath/tommath_superclass.h
+++ b/libtommath/tommath_superclass.h
@@ -60,9 +60,9 @@
    #undef  BN_FAST_MP_INVMOD_C
 
    /* To safely undefine these you have to make sure your RSA key won't exceed the Comba threshold
-    * which is roughly 255 digits [7140 bits for 32-bit machines, 15300 bits for 64-bit machines] 
+    * which is roughly 255 digits [7140 bits for 32-bit machines, 15300 bits for 64-bit machines]
     * which means roughly speaking you can handle upto 2536-bit RSA keys with these defined without
-    * trouble.  
+    * trouble.
     */
    #undef  BN_S_MP_MUL_DIGS_C
    #undef  BN_S_MP_SQR_C
@@ -70,3 +70,7 @@
 #endif
 
 #endif
+
+/* $Source$ */
+/* $Revision$ */
+/* $Date$ */
diff --git a/macosx/Tcl.xcode/project.pbxproj b/macosx/Tcl.xcode/project.pbxproj
index a99afc5..117cd61 100644
--- a/macosx/Tcl.xcode/project.pbxproj
+++ b/macosx/Tcl.xcode/project.pbxproj
@@ -166,6 +166,7 @@
 		F9E61D2A090A4891002B3151 /* bn_mp_sqrt.c in Sources */ = {isa = PBXBuildFile; fileRef = F96D42C008F272B3004A47F5 /* bn_mp_sqrt.c */; };
 		F9E61D2B090A48A4002B3151 /* bn_mp_and.c in Sources */ = {isa = PBXBuildFile; fileRef = F96D426C08F272B3004A47F5 /* bn_mp_and.c */; };
 		F9E61D2C090A48AC002B3151 /* bn_mp_expt_d.c in Sources */ = {isa = PBXBuildFile; fileRef = F96D427F08F272B3004A47F5 /* bn_mp_expt_d.c */; };
+		F9E61D2C090A48AC002B3151 /* bn_mp_expt_d_ex.c in Sources */ = {isa = PBXBuildFile; fileRef = F96D427F08F272B3004A47F5 /* bn_mp_expt_d_ex.c */; };
 		F9E61D2D090A48BB002B3151 /* bn_mp_xor.c in Sources */ = {isa = PBXBuildFile; fileRef = F96D42CD08F272B3004A47F5 /* bn_mp_xor.c */; };
 		F9E61D2E090A48BF002B3151 /* bn_mp_or.c in Sources */ = {isa = PBXBuildFile; fileRef = F96D42A308F272B3004A47F5 /* bn_mp_or.c */; };
 		F9E61D2F090A48C7002B3151 /* bn_mp_shrink.c in Sources */ = {isa = PBXBuildFile; fileRef = F96D42BC08F272B3004A47F5 /* bn_mp_shrink.c */; };
@@ -1442,6 +1443,7 @@
 				F96D427A08F272B3004A47F5 /* bn_mp_div_d.c */,
 				F96D427E08F272B3004A47F5 /* bn_mp_exch.c */,
 				F96D427F08F272B3004A47F5 /* bn_mp_expt_d.c */,
+				F96D427F08F272B3004A47F5 /* bn_mp_expt_d_ex.c */,
 				F96D428708F272B3004A47F5 /* bn_mp_grow.c */,
 				F96D428808F272B3004A47F5 /* bn_mp_init.c */,
 				F96D428908F272B3004A47F5 /* bn_mp_init_copy.c */,
@@ -2075,6 +2077,7 @@
 				F96D48F808F272C3004A47F5 /* bn_mp_div_d.c in Sources */,
 				F96D48FC08F272C3004A47F5 /* bn_mp_exch.c in Sources */,
 				F9E61D2C090A48AC002B3151 /* bn_mp_expt_d.c in Sources */,
+				F9E61D2C090A48AC002B3151 /* bn_mp_expt_d_ex.c in Sources */,
 				F96D490508F272C3004A47F5 /* bn_mp_grow.c in Sources */,
 				F96D490608F272C3004A47F5 /* bn_mp_init.c in Sources */,
 				F96D490708F272C3004A47F5 /* bn_mp_init_copy.c in Sources */,
diff --git a/macosx/Tcl.xcodeproj/project.pbxproj b/macosx/Tcl.xcodeproj/project.pbxproj
index 393fd31..3be274f 100644
--- a/macosx/Tcl.xcodeproj/project.pbxproj
+++ b/macosx/Tcl.xcodeproj/project.pbxproj
@@ -165,7 +165,8 @@
 		F9E61D29090A486C002B3151 /* bn_mp_neg.c in Sources */ = {isa = PBXBuildFile; fileRef = F96D42A208F272B3004A47F5 /* bn_mp_neg.c */; };
 		F9E61D2A090A4891002B3151 /* bn_mp_sqrt.c in Sources */ = {isa = PBXBuildFile; fileRef = F96D42C008F272B3004A47F5 /* bn_mp_sqrt.c */; };
 		F9E61D2B090A48A4002B3151 /* bn_mp_and.c in Sources */ = {isa = PBXBuildFile; fileRef = F96D426C08F272B3004A47F5 /* bn_mp_and.c */; };
-		F9E61D2C090A48AC002B3151 /* bn_mp_expt_d.c in Sources */ = {isa = PBXBuildFile; fileRef = F96D427F08F272B3004A47F5 /* bn_mp_expt_d.c */; };
+		F9E61D2C090A48AC002B3151 /* bn_mp_expt_d.c in Sources */ = {isa = PBXBuildFile; fileRef = F96D427F08F272B3004A47F5 /* bn_mp_expt_d_ex.c */; };
+		F9E61D2C090A48AC002B3151 /* bn_mp_expt_d_ex.c in Sources */ = {isa = PBXBuildFile; fileRef = F96D427F08F272B3004A47F5 /* bn_mp_expt_d.c */; };
 		F9E61D2D090A48BB002B3151 /* bn_mp_xor.c in Sources */ = {isa = PBXBuildFile; fileRef = F96D42CD08F272B3004A47F5 /* bn_mp_xor.c */; };
 		F9E61D2E090A48BF002B3151 /* bn_mp_or.c in Sources */ = {isa = PBXBuildFile; fileRef = F96D42A308F272B3004A47F5 /* bn_mp_or.c */; };
 		F9E61D2F090A48C7002B3151 /* bn_mp_shrink.c in Sources */ = {isa = PBXBuildFile; fileRef = F96D42BC08F272B3004A47F5 /* bn_mp_shrink.c */; };
@@ -579,6 +580,7 @@
 		F96D427A08F272B3004A47F5 /* bn_mp_div_d.c */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.c; path = bn_mp_div_d.c; sourceTree = "<group>"; };
 		F96D427E08F272B3004A47F5 /* bn_mp_exch.c */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.c; path = bn_mp_exch.c; sourceTree = "<group>"; };
 		F96D427F08F272B3004A47F5 /* bn_mp_expt_d.c */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.c; path = bn_mp_expt_d.c; sourceTree = "<group>"; };
+		F96D427F08F272B3004A47F5 /* bn_mp_expt_d_ex.c */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.c; path = bn_mp_expt_d_ex.c; sourceTree = "<group>"; };
 		F96D428708F272B3004A47F5 /* bn_mp_grow.c */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.c; path = bn_mp_grow.c; sourceTree = "<group>"; };
 		F96D428808F272B3004A47F5 /* bn_mp_init.c */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.c; path = bn_mp_init.c; sourceTree = "<group>"; };
 		F96D428908F272B3004A47F5 /* bn_mp_init_copy.c */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.c; path = bn_mp_init_copy.c; sourceTree = "<group>"; };
@@ -1442,6 +1444,7 @@
 				F96D427A08F272B3004A47F5 /* bn_mp_div_d.c */,
 				F96D427E08F272B3004A47F5 /* bn_mp_exch.c */,
 				F96D427F08F272B3004A47F5 /* bn_mp_expt_d.c */,
+				F96D427F08F272B3004A47F5 /* bn_mp_expt_d_ex.c */,
 				F96D428708F272B3004A47F5 /* bn_mp_grow.c */,
 				F96D428808F272B3004A47F5 /* bn_mp_init.c */,
 				F96D428908F272B3004A47F5 /* bn_mp_init_copy.c */,
@@ -2075,6 +2078,7 @@
 				F96D48F808F272C3004A47F5 /* bn_mp_div_d.c in Sources */,
 				F96D48FC08F272C3004A47F5 /* bn_mp_exch.c in Sources */,
 				F9E61D2C090A48AC002B3151 /* bn_mp_expt_d.c in Sources */,
+				F9E61D2C090A48AC002B3151 /* bn_mp_expt_d_ex.c in Sources */,
 				F96D490508F272C3004A47F5 /* bn_mp_grow.c in Sources */,
 				F96D490608F272C3004A47F5 /* bn_mp_init.c in Sources */,
 				F96D490708F272C3004A47F5 /* bn_mp_init_copy.c in Sources */,
diff --git a/unix/Makefile.in b/unix/Makefile.in
index 628c6e9..c4f6136 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_grow.o bn_mp_init.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_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 \
@@ -503,6 +503,7 @@ TOMMATH_SRCS = \
 	$(TOMMATH_DIR)/bn_mp_div_3.c \
 	$(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_grow.c \
 	$(TOMMATH_DIR)/bn_mp_init.c \
 	$(TOMMATH_DIR)/bn_mp_init_copy.c \
@@ -1420,6 +1421,9 @@ bn_mp_exch.o: $(TOMMATH_DIR)/bn_mp_exch.c $(MATHHDRS)
 bn_mp_expt_d.o: $(TOMMATH_DIR)/bn_mp_expt_d.c $(MATHHDRS)
 	$(CC) -c $(CC_SWITCHES) $(TOMMATH_DIR)/bn_mp_expt_d.c
 
+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_grow.o: $(TOMMATH_DIR)/bn_mp_grow.c $(MATHHDRS)
 	$(CC) -c $(CC_SWITCHES) $(TOMMATH_DIR)/bn_mp_grow.c
 
diff --git a/unix/tclUnixNotfy.c b/unix/tclUnixNotfy.c
index 9f9301f..e37962d 100644
--- a/unix/tclUnixNotfy.c
+++ b/unix/tclUnixNotfy.c
@@ -150,8 +150,8 @@ static int triggerPipe = -1;
  * The notifierMutex locks access to all of the global notifier state.
  */
 
-pthread_mutex_t notifierInitMutex = PTHREAD_MUTEX_INITIALIZER;
-pthread_mutex_t notifierMutex     = PTHREAD_MUTEX_INITIALIZER;
+static pthread_mutex_t notifierInitMutex = PTHREAD_MUTEX_INITIALIZER;
+static pthread_mutex_t notifierMutex     = PTHREAD_MUTEX_INITIALIZER;
 /*
  * The following static indicates if the notifier thread is running.
  *
diff --git a/win/Makefile.in b/win/Makefile.in
index 31efb42..e967ef3 100644
--- a/win/Makefile.in
+++ b/win/Makefile.in
@@ -328,6 +328,7 @@ TOMMATH_OBJS = \
 	bn_mp_div_3.${OBJEXT} \
 	bn_mp_exch.${OBJEXT} \
 	bn_mp_expt_d.${OBJEXT} \
+	bn_mp_expt_d_ex.${OBJEXT} \
 	bn_mp_grow.${OBJEXT} \
 	bn_mp_init.${OBJEXT} \
 	bn_mp_init_copy.${OBJEXT} \
diff --git a/win/makefile.vc b/win/makefile.vc
index 6535fde..c10b196 100644
--- a/win/makefile.vc
+++ b/win/makefile.vc
@@ -383,6 +383,7 @@ TOMMATHOBJS = \
 	$(TMP_DIR)\bn_mp_div_3.obj \

 	$(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_grow.obj \

 	$(TMP_DIR)\bn_mp_init.obj \

 	$(TMP_DIR)\bn_mp_init_copy.obj \