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authorkennykb <kennykb@noemail.net>2005-01-19 22:41:25 (GMT)
committerkennykb <kennykb@noemail.net>2005-01-19 22:41:25 (GMT)
commitb3ce7426a67ecb023356a28d94171635385dc616 (patch)
tree47f8ad0d7291237c7f9af988c5e05275ed9286ee /libtommath/mtest
parentccd3f20006ac278b5ded38d34df7f6d6e5b6b886 (diff)
downloadtcl-b3ce7426a67ecb023356a28d94171635385dc616.zip
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Import of libtommath 0.33
FossilOrigin-Name: bd185c2b4e79e51a5759271085f1702fafff39a3
Diffstat (limited to 'libtommath/mtest')
-rw-r--r--libtommath/mtest/logtab.h20
-rw-r--r--libtommath/mtest/mpi-config.h86
-rw-r--r--libtommath/mtest/mpi-types.h16
-rw-r--r--libtommath/mtest/mpi.c3981
-rw-r--r--libtommath/mtest/mpi.h227
-rw-r--r--libtommath/mtest/mtest.c304
6 files changed, 4634 insertions, 0 deletions
diff --git a/libtommath/mtest/logtab.h b/libtommath/mtest/logtab.h
new file mode 100644
index 0000000..68462bd
--- /dev/null
+++ b/libtommath/mtest/logtab.h
@@ -0,0 +1,20 @@
+const float s_logv_2[] = {
+ 0.000000000, 0.000000000, 1.000000000, 0.630929754, /* 0 1 2 3 */
+ 0.500000000, 0.430676558, 0.386852807, 0.356207187, /* 4 5 6 7 */
+ 0.333333333, 0.315464877, 0.301029996, 0.289064826, /* 8 9 10 11 */
+ 0.278942946, 0.270238154, 0.262649535, 0.255958025, /* 12 13 14 15 */
+ 0.250000000, 0.244650542, 0.239812467, 0.235408913, /* 16 17 18 19 */
+ 0.231378213, 0.227670249, 0.224243824, 0.221064729, /* 20 21 22 23 */
+ 0.218104292, 0.215338279, 0.212746054, 0.210309918, /* 24 25 26 27 */
+ 0.208014598, 0.205846832, 0.203795047, 0.201849087, /* 28 29 30 31 */
+ 0.200000000, 0.198239863, 0.196561632, 0.194959022, /* 32 33 34 35 */
+ 0.193426404, 0.191958720, 0.190551412, 0.189200360, /* 36 37 38 39 */
+ 0.187901825, 0.186652411, 0.185449023, 0.184288833, /* 40 41 42 43 */
+ 0.183169251, 0.182087900, 0.181042597, 0.180031327, /* 44 45 46 47 */
+ 0.179052232, 0.178103594, 0.177183820, 0.176291434, /* 48 49 50 51 */
+ 0.175425064, 0.174583430, 0.173765343, 0.172969690, /* 52 53 54 55 */
+ 0.172195434, 0.171441601, 0.170707280, 0.169991616, /* 56 57 58 59 */
+ 0.169293808, 0.168613099, 0.167948779, 0.167300179, /* 60 61 62 63 */
+ 0.166666667
+};
+
diff --git a/libtommath/mtest/mpi-config.h b/libtommath/mtest/mpi-config.h
new file mode 100644
index 0000000..dcdbd35
--- /dev/null
+++ b/libtommath/mtest/mpi-config.h
@@ -0,0 +1,86 @@
+/* Default configuration for MPI library */
+/* $Id: mpi-config.h,v 1.1.1.1 2005/01/19 22:41:29 kennykb Exp $ */
+
+#ifndef MPI_CONFIG_H_
+#define MPI_CONFIG_H_
+
+/*
+ For boolean options,
+ 0 = no
+ 1 = yes
+
+ Other options are documented individually.
+
+ */
+
+#ifndef MP_IOFUNC
+#define MP_IOFUNC 0 /* include mp_print() ? */
+#endif
+
+#ifndef MP_MODARITH
+#define MP_MODARITH 1 /* include modular arithmetic ? */
+#endif
+
+#ifndef MP_NUMTH
+#define MP_NUMTH 1 /* include number theoretic functions? */
+#endif
+
+#ifndef MP_LOGTAB
+#define MP_LOGTAB 1 /* use table of logs instead of log()? */
+#endif
+
+#ifndef MP_MEMSET
+#define MP_MEMSET 1 /* use memset() to zero buffers? */
+#endif
+
+#ifndef MP_MEMCPY
+#define MP_MEMCPY 1 /* use memcpy() to copy buffers? */
+#endif
+
+#ifndef MP_CRYPTO
+#define MP_CRYPTO 1 /* erase memory on free? */
+#endif
+
+#ifndef MP_ARGCHK
+/*
+ 0 = no parameter checks
+ 1 = runtime checks, continue execution and return an error to caller
+ 2 = assertions; dump core on parameter errors
+ */
+#define MP_ARGCHK 2 /* how to check input arguments */
+#endif
+
+#ifndef MP_DEBUG
+#define MP_DEBUG 0 /* print diagnostic output? */
+#endif
+
+#ifndef MP_DEFPREC
+#define MP_DEFPREC 64 /* default precision, in digits */
+#endif
+
+#ifndef MP_MACRO
+#define MP_MACRO 1 /* use macros for frequent calls? */
+#endif
+
+#ifndef MP_SQUARE
+#define MP_SQUARE 1 /* use separate squaring code? */
+#endif
+
+#ifndef MP_PTAB_SIZE
+/*
+ When building mpprime.c, we build in a table of small prime
+ values to use for primality testing. The more you include,
+ the more space they take up. See primes.c for the possible
+ values (currently 16, 32, 64, 128, 256, and 6542)
+ */
+#define MP_PTAB_SIZE 128 /* how many built-in primes? */
+#endif
+
+#ifndef MP_COMPAT_MACROS
+#define MP_COMPAT_MACROS 1 /* define compatibility macros? */
+#endif
+
+#endif /* ifndef MPI_CONFIG_H_ */
+
+
+/* crc==3287762869, version==2, Sat Feb 02 06:43:53 2002 */
diff --git a/libtommath/mtest/mpi-types.h b/libtommath/mtest/mpi-types.h
new file mode 100644
index 0000000..e097188
--- /dev/null
+++ b/libtommath/mtest/mpi-types.h
@@ -0,0 +1,16 @@
+/* Type definitions generated by 'types.pl' */
+typedef char mp_sign;
+typedef unsigned short mp_digit; /* 2 byte type */
+typedef unsigned int mp_word; /* 4 byte type */
+typedef unsigned int mp_size;
+typedef int mp_err;
+
+#define MP_DIGIT_BIT (CHAR_BIT*sizeof(mp_digit))
+#define MP_DIGIT_MAX USHRT_MAX
+#define MP_WORD_BIT (CHAR_BIT*sizeof(mp_word))
+#define MP_WORD_MAX UINT_MAX
+
+#define MP_DIGIT_SIZE 2
+#define DIGIT_FMT "%04X"
+#define RADIX (MP_DIGIT_MAX+1)
+
diff --git a/libtommath/mtest/mpi.c b/libtommath/mtest/mpi.c
new file mode 100644
index 0000000..0517602
--- /dev/null
+++ b/libtommath/mtest/mpi.c
@@ -0,0 +1,3981 @@
+/*
+ mpi.c
+
+ by Michael J. Fromberger <sting@linguist.dartmouth.edu>
+ Copyright (C) 1998 Michael J. Fromberger, All Rights Reserved
+
+ Arbitrary precision integer arithmetic library
+
+ $Id: mpi.c,v 1.1.1.1 2005/01/19 22:41:29 kennykb Exp $
+ */
+
+#include "mpi.h"
+#include <stdlib.h>
+#include <string.h>
+#include <ctype.h>
+
+#if MP_DEBUG
+#include <stdio.h>
+
+#define DIAG(T,V) {fprintf(stderr,T);mp_print(V,stderr);fputc('\n',stderr);}
+#else
+#define DIAG(T,V)
+#endif
+
+/*
+ If MP_LOGTAB is not defined, use the math library to compute the
+ logarithms on the fly. Otherwise, use the static table below.
+ Pick which works best for your system.
+ */
+#if MP_LOGTAB
+
+/* {{{ s_logv_2[] - log table for 2 in various bases */
+
+/*
+ A table of the logs of 2 for various bases (the 0 and 1 entries of
+ this table are meaningless and should not be referenced).
+
+ This table is used to compute output lengths for the mp_toradix()
+ function. Since a number n in radix r takes up about log_r(n)
+ digits, we estimate the output size by taking the least integer
+ greater than log_r(n), where:
+
+ log_r(n) = log_2(n) * log_r(2)
+
+ This table, therefore, is a table of log_r(2) for 2 <= r <= 36,
+ which are the output bases supported.
+ */
+
+#include "logtab.h"
+
+/* }}} */
+#define LOG_V_2(R) s_logv_2[(R)]
+
+#else
+
+#include <math.h>
+#define LOG_V_2(R) (log(2.0)/log(R))
+
+#endif
+
+/* Default precision for newly created mp_int's */
+static unsigned int s_mp_defprec = MP_DEFPREC;
+
+/* {{{ Digit arithmetic macros */
+
+/*
+ When adding and multiplying digits, the results can be larger than
+ can be contained in an mp_digit. Thus, an mp_word is used. These
+ macros mask off the upper and lower digits of the mp_word (the
+ mp_word may be more than 2 mp_digits wide, but we only concern
+ ourselves with the low-order 2 mp_digits)
+
+ If your mp_word DOES have more than 2 mp_digits, you need to
+ uncomment the first line, and comment out the second.
+ */
+
+/* #define CARRYOUT(W) (((W)>>DIGIT_BIT)&MP_DIGIT_MAX) */
+#define CARRYOUT(W) ((W)>>DIGIT_BIT)
+#define ACCUM(W) ((W)&MP_DIGIT_MAX)
+
+/* }}} */
+
+/* {{{ Comparison constants */
+
+#define MP_LT -1
+#define MP_EQ 0
+#define MP_GT 1
+
+/* }}} */
+
+/* {{{ Constant strings */
+
+/* Constant strings returned by mp_strerror() */
+static const char *mp_err_string[] = {
+ "unknown result code", /* say what? */
+ "boolean true", /* MP_OKAY, MP_YES */
+ "boolean false", /* MP_NO */
+ "out of memory", /* MP_MEM */
+ "argument out of range", /* MP_RANGE */
+ "invalid input parameter", /* MP_BADARG */
+ "result is undefined" /* MP_UNDEF */
+};
+
+/* Value to digit maps for radix conversion */
+
+/* s_dmap_1 - standard digits and letters */
+static const char *s_dmap_1 =
+ "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
+
+#if 0
+/* s_dmap_2 - base64 ordering for digits */
+static const char *s_dmap_2 =
+ "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
+#endif
+
+/* }}} */
+
+/* {{{ Static function declarations */
+
+/*
+ If MP_MACRO is false, these will be defined as actual functions;
+ otherwise, suitable macro definitions will be used. This works
+ around the fact that ANSI C89 doesn't support an 'inline' keyword
+ (although I hear C9x will ... about bloody time). At present, the
+ macro definitions are identical to the function bodies, but they'll
+ expand in place, instead of generating a function call.
+
+ I chose these particular functions to be made into macros because
+ some profiling showed they are called a lot on a typical workload,
+ and yet they are primarily housekeeping.
+ */
+#if MP_MACRO == 0
+ void s_mp_setz(mp_digit *dp, mp_size count); /* zero digits */
+ void s_mp_copy(mp_digit *sp, mp_digit *dp, mp_size count); /* copy */
+ void *s_mp_alloc(size_t nb, size_t ni); /* general allocator */
+ void s_mp_free(void *ptr); /* general free function */
+#else
+
+ /* Even if these are defined as macros, we need to respect the settings
+ of the MP_MEMSET and MP_MEMCPY configuration options...
+ */
+ #if MP_MEMSET == 0
+ #define s_mp_setz(dp, count) \
+ {int ix;for(ix=0;ix<(count);ix++)(dp)[ix]=0;}
+ #else
+ #define s_mp_setz(dp, count) memset(dp, 0, (count) * sizeof(mp_digit))
+ #endif /* MP_MEMSET */
+
+ #if MP_MEMCPY == 0
+ #define s_mp_copy(sp, dp, count) \
+ {int ix;for(ix=0;ix<(count);ix++)(dp)[ix]=(sp)[ix];}
+ #else
+ #define s_mp_copy(sp, dp, count) memcpy(dp, sp, (count) * sizeof(mp_digit))
+ #endif /* MP_MEMCPY */
+
+ #define s_mp_alloc(nb, ni) calloc(nb, ni)
+ #define s_mp_free(ptr) {if(ptr) free(ptr);}
+#endif /* MP_MACRO */
+
+mp_err s_mp_grow(mp_int *mp, mp_size min); /* increase allocated size */
+mp_err s_mp_pad(mp_int *mp, mp_size min); /* left pad with zeroes */
+
+void s_mp_clamp(mp_int *mp); /* clip leading zeroes */
+
+void s_mp_exch(mp_int *a, mp_int *b); /* swap a and b in place */
+
+mp_err s_mp_lshd(mp_int *mp, mp_size p); /* left-shift by p digits */
+void s_mp_rshd(mp_int *mp, mp_size p); /* right-shift by p digits */
+void s_mp_div_2d(mp_int *mp, mp_digit d); /* divide by 2^d in place */
+void s_mp_mod_2d(mp_int *mp, mp_digit d); /* modulo 2^d in place */
+mp_err s_mp_mul_2d(mp_int *mp, mp_digit d); /* multiply by 2^d in place*/
+void s_mp_div_2(mp_int *mp); /* divide by 2 in place */
+mp_err s_mp_mul_2(mp_int *mp); /* multiply by 2 in place */
+mp_digit s_mp_norm(mp_int *a, mp_int *b); /* normalize for division */
+mp_err s_mp_add_d(mp_int *mp, mp_digit d); /* unsigned digit addition */
+mp_err s_mp_sub_d(mp_int *mp, mp_digit d); /* unsigned digit subtract */
+mp_err s_mp_mul_d(mp_int *mp, mp_digit d); /* unsigned digit multiply */
+mp_err s_mp_div_d(mp_int *mp, mp_digit d, mp_digit *r);
+ /* unsigned digit divide */
+mp_err s_mp_reduce(mp_int *x, mp_int *m, mp_int *mu);
+ /* Barrett reduction */
+mp_err s_mp_add(mp_int *a, mp_int *b); /* magnitude addition */
+mp_err s_mp_sub(mp_int *a, mp_int *b); /* magnitude subtract */
+mp_err s_mp_mul(mp_int *a, mp_int *b); /* magnitude multiply */
+#if 0
+void s_mp_kmul(mp_digit *a, mp_digit *b, mp_digit *out, mp_size len);
+ /* multiply buffers in place */
+#endif
+#if MP_SQUARE
+mp_err s_mp_sqr(mp_int *a); /* magnitude square */
+#else
+#define s_mp_sqr(a) s_mp_mul(a, a)
+#endif
+mp_err s_mp_div(mp_int *a, mp_int *b); /* magnitude divide */
+mp_err s_mp_2expt(mp_int *a, mp_digit k); /* a = 2^k */
+int s_mp_cmp(mp_int *a, mp_int *b); /* magnitude comparison */
+int s_mp_cmp_d(mp_int *a, mp_digit d); /* magnitude digit compare */
+int s_mp_ispow2(mp_int *v); /* is v a power of 2? */
+int s_mp_ispow2d(mp_digit d); /* is d a power of 2? */
+
+int s_mp_tovalue(char ch, int r); /* convert ch to value */
+char s_mp_todigit(int val, int r, int low); /* convert val to digit */
+int s_mp_outlen(int bits, int r); /* output length in bytes */
+
+/* }}} */
+
+/* {{{ Default precision manipulation */
+
+unsigned int mp_get_prec(void)
+{
+ return s_mp_defprec;
+
+} /* end mp_get_prec() */
+
+void mp_set_prec(unsigned int prec)
+{
+ if(prec == 0)
+ s_mp_defprec = MP_DEFPREC;
+ else
+ s_mp_defprec = prec;
+
+} /* end mp_set_prec() */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* {{{ mp_init(mp) */
+
+/*
+ mp_init(mp)
+
+ Initialize a new zero-valued mp_int. Returns MP_OKAY if successful,
+ MP_MEM if memory could not be allocated for the structure.
+ */
+
+mp_err mp_init(mp_int *mp)
+{
+ return mp_init_size(mp, s_mp_defprec);
+
+} /* end mp_init() */
+
+/* }}} */
+
+/* {{{ mp_init_array(mp[], count) */
+
+mp_err mp_init_array(mp_int mp[], int count)
+{
+ mp_err res;
+ int pos;
+
+ ARGCHK(mp !=NULL && count > 0, MP_BADARG);
+
+ for(pos = 0; pos < count; ++pos) {
+ if((res = mp_init(&mp[pos])) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ return MP_OKAY;
+
+ CLEANUP:
+ while(--pos >= 0)
+ mp_clear(&mp[pos]);
+
+ return res;
+
+} /* end mp_init_array() */
+
+/* }}} */
+
+/* {{{ mp_init_size(mp, prec) */
+
+/*
+ mp_init_size(mp, prec)
+
+ Initialize a new zero-valued mp_int with at least the given
+ precision; returns MP_OKAY if successful, or MP_MEM if memory could
+ not be allocated for the structure.
+ */
+
+mp_err mp_init_size(mp_int *mp, mp_size prec)
+{
+ ARGCHK(mp != NULL && prec > 0, MP_BADARG);
+
+ if((DIGITS(mp) = s_mp_alloc(prec, sizeof(mp_digit))) == NULL)
+ return MP_MEM;
+
+ SIGN(mp) = MP_ZPOS;
+ USED(mp) = 1;
+ ALLOC(mp) = prec;
+
+ return MP_OKAY;
+
+} /* end mp_init_size() */
+
+/* }}} */
+
+/* {{{ mp_init_copy(mp, from) */
+
+/*
+ mp_init_copy(mp, from)
+
+ Initialize mp as an exact copy of from. Returns MP_OKAY if
+ successful, MP_MEM if memory could not be allocated for the new
+ structure.
+ */
+
+mp_err mp_init_copy(mp_int *mp, mp_int *from)
+{
+ ARGCHK(mp != NULL && from != NULL, MP_BADARG);
+
+ if(mp == from)
+ return MP_OKAY;
+
+ if((DIGITS(mp) = s_mp_alloc(USED(from), sizeof(mp_digit))) == NULL)
+ return MP_MEM;
+
+ s_mp_copy(DIGITS(from), DIGITS(mp), USED(from));
+ USED(mp) = USED(from);
+ ALLOC(mp) = USED(from);
+ SIGN(mp) = SIGN(from);
+
+ return MP_OKAY;
+
+} /* end mp_init_copy() */
+
+/* }}} */
+
+/* {{{ mp_copy(from, to) */
+
+/*
+ mp_copy(from, to)
+
+ Copies the mp_int 'from' to the mp_int 'to'. It is presumed that
+ 'to' has already been initialized (if not, use mp_init_copy()
+ instead). If 'from' and 'to' are identical, nothing happens.
+ */
+
+mp_err mp_copy(mp_int *from, mp_int *to)
+{
+ ARGCHK(from != NULL && to != NULL, MP_BADARG);
+
+ if(from == to)
+ return MP_OKAY;
+
+ { /* copy */
+ mp_digit *tmp;
+
+ /*
+ If the allocated buffer in 'to' already has enough space to hold
+ all the used digits of 'from', we'll re-use it to avoid hitting
+ the memory allocater more than necessary; otherwise, we'd have
+ to grow anyway, so we just allocate a hunk and make the copy as
+ usual
+ */
+ if(ALLOC(to) >= USED(from)) {
+ s_mp_setz(DIGITS(to) + USED(from), ALLOC(to) - USED(from));
+ s_mp_copy(DIGITS(from), DIGITS(to), USED(from));
+
+ } else {
+ if((tmp = s_mp_alloc(USED(from), sizeof(mp_digit))) == NULL)
+ return MP_MEM;
+
+ s_mp_copy(DIGITS(from), tmp, USED(from));
+
+ if(DIGITS(to) != NULL) {
+#if MP_CRYPTO
+ s_mp_setz(DIGITS(to), ALLOC(to));
+#endif
+ s_mp_free(DIGITS(to));
+ }
+
+ DIGITS(to) = tmp;
+ ALLOC(to) = USED(from);
+ }
+
+ /* Copy the precision and sign from the original */
+ USED(to) = USED(from);
+ SIGN(to) = SIGN(from);
+ } /* end copy */
+
+ return MP_OKAY;
+
+} /* end mp_copy() */
+
+/* }}} */
+
+/* {{{ mp_exch(mp1, mp2) */
+
+/*
+ mp_exch(mp1, mp2)
+
+ Exchange mp1 and mp2 without allocating any intermediate memory
+ (well, unless you count the stack space needed for this call and the
+ locals it creates...). This cannot fail.
+ */
+
+void mp_exch(mp_int *mp1, mp_int *mp2)
+{
+#if MP_ARGCHK == 2
+ assert(mp1 != NULL && mp2 != NULL);
+#else
+ if(mp1 == NULL || mp2 == NULL)
+ return;
+#endif
+
+ s_mp_exch(mp1, mp2);
+
+} /* end mp_exch() */
+
+/* }}} */
+
+/* {{{ mp_clear(mp) */
+
+/*
+ mp_clear(mp)
+
+ Release the storage used by an mp_int, and void its fields so that
+ if someone calls mp_clear() again for the same int later, we won't
+ get tollchocked.
+ */
+
+void mp_clear(mp_int *mp)
+{
+ if(mp == NULL)
+ return;
+
+ if(DIGITS(mp) != NULL) {
+#if MP_CRYPTO
+ s_mp_setz(DIGITS(mp), ALLOC(mp));
+#endif
+ s_mp_free(DIGITS(mp));
+ DIGITS(mp) = NULL;
+ }
+
+ USED(mp) = 0;
+ ALLOC(mp) = 0;
+
+} /* end mp_clear() */
+
+/* }}} */
+
+/* {{{ mp_clear_array(mp[], count) */
+
+void mp_clear_array(mp_int mp[], int count)
+{
+ ARGCHK(mp != NULL && count > 0, MP_BADARG);
+
+ while(--count >= 0)
+ mp_clear(&mp[count]);
+
+} /* end mp_clear_array() */
+
+/* }}} */
+
+/* {{{ mp_zero(mp) */
+
+/*
+ mp_zero(mp)
+
+ Set mp to zero. Does not change the allocated size of the structure,
+ and therefore cannot fail (except on a bad argument, which we ignore)
+ */
+void mp_zero(mp_int *mp)
+{
+ if(mp == NULL)
+ return;
+
+ s_mp_setz(DIGITS(mp), ALLOC(mp));
+ USED(mp) = 1;
+ SIGN(mp) = MP_ZPOS;
+
+} /* end mp_zero() */
+
+/* }}} */
+
+/* {{{ mp_set(mp, d) */
+
+void mp_set(mp_int *mp, mp_digit d)
+{
+ if(mp == NULL)
+ return;
+
+ mp_zero(mp);
+ DIGIT(mp, 0) = d;
+
+} /* end mp_set() */
+
+/* }}} */
+
+/* {{{ mp_set_int(mp, z) */
+
+mp_err mp_set_int(mp_int *mp, long z)
+{
+ int ix;
+ unsigned long v = abs(z);
+ mp_err res;
+
+ ARGCHK(mp != NULL, MP_BADARG);
+
+ mp_zero(mp);
+ if(z == 0)
+ return MP_OKAY; /* shortcut for zero */
+
+ for(ix = sizeof(long) - 1; ix >= 0; ix--) {
+
+ if((res = s_mp_mul_2d(mp, CHAR_BIT)) != MP_OKAY)
+ return res;
+
+ res = s_mp_add_d(mp,
+ (mp_digit)((v >> (ix * CHAR_BIT)) & UCHAR_MAX));
+ if(res != MP_OKAY)
+ return res;
+
+ }
+
+ if(z < 0)
+ SIGN(mp) = MP_NEG;
+
+ return MP_OKAY;
+
+} /* end mp_set_int() */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* {{{ Digit arithmetic */
+
+/* {{{ mp_add_d(a, d, b) */
+
+/*
+ mp_add_d(a, d, b)
+
+ Compute the sum b = a + d, for a single digit d. Respects the sign of
+ its primary addend (single digits are unsigned anyway).
+ */
+
+mp_err mp_add_d(mp_int *a, mp_digit d, mp_int *b)
+{
+ mp_err res = MP_OKAY;
+
+ ARGCHK(a != NULL && b != NULL, MP_BADARG);
+
+ if((res = mp_copy(a, b)) != MP_OKAY)
+ return res;
+
+ if(SIGN(b) == MP_ZPOS) {
+ res = s_mp_add_d(b, d);
+ } else if(s_mp_cmp_d(b, d) >= 0) {
+ res = s_mp_sub_d(b, d);
+ } else {
+ SIGN(b) = MP_ZPOS;
+
+ DIGIT(b, 0) = d - DIGIT(b, 0);
+ }
+
+ return res;
+
+} /* end mp_add_d() */
+
+/* }}} */
+
+/* {{{ mp_sub_d(a, d, b) */
+
+/*
+ mp_sub_d(a, d, b)
+
+ Compute the difference b = a - d, for a single digit d. Respects the
+ sign of its subtrahend (single digits are unsigned anyway).
+ */
+
+mp_err mp_sub_d(mp_int *a, mp_digit d, mp_int *b)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL, MP_BADARG);
+
+ if((res = mp_copy(a, b)) != MP_OKAY)
+ return res;
+
+ if(SIGN(b) == MP_NEG) {
+ if((res = s_mp_add_d(b, d)) != MP_OKAY)
+ return res;
+
+ } else if(s_mp_cmp_d(b, d) >= 0) {
+ if((res = s_mp_sub_d(b, d)) != MP_OKAY)
+ return res;
+
+ } else {
+ mp_neg(b, b);
+
+ DIGIT(b, 0) = d - DIGIT(b, 0);
+ SIGN(b) = MP_NEG;
+ }
+
+ if(s_mp_cmp_d(b, 0) == 0)
+ SIGN(b) = MP_ZPOS;
+
+ return MP_OKAY;
+
+} /* end mp_sub_d() */
+
+/* }}} */
+
+/* {{{ mp_mul_d(a, d, b) */
+
+/*
+ mp_mul_d(a, d, b)
+
+ Compute the product b = a * d, for a single digit d. Respects the sign
+ of its multiplicand (single digits are unsigned anyway)
+ */
+
+mp_err mp_mul_d(mp_int *a, mp_digit d, mp_int *b)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL, MP_BADARG);
+
+ if(d == 0) {
+ mp_zero(b);
+ return MP_OKAY;
+ }
+
+ if((res = mp_copy(a, b)) != MP_OKAY)
+ return res;
+
+ res = s_mp_mul_d(b, d);
+
+ return res;
+
+} /* end mp_mul_d() */
+
+/* }}} */
+
+/* {{{ mp_mul_2(a, c) */
+
+mp_err mp_mul_2(mp_int *a, mp_int *c)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && c != NULL, MP_BADARG);
+
+ if((res = mp_copy(a, c)) != MP_OKAY)
+ return res;
+
+ return s_mp_mul_2(c);
+
+} /* end mp_mul_2() */
+
+/* }}} */
+
+/* {{{ mp_div_d(a, d, q, r) */
+
+/*
+ mp_div_d(a, d, q, r)
+
+ Compute the quotient q = a / d and remainder r = a mod d, for a
+ single digit d. Respects the sign of its divisor (single digits are
+ unsigned anyway).
+ */
+
+mp_err mp_div_d(mp_int *a, mp_digit d, mp_int *q, mp_digit *r)
+{
+ mp_err res;
+ mp_digit rem;
+ int pow;
+
+ ARGCHK(a != NULL, MP_BADARG);
+
+ if(d == 0)
+ return MP_RANGE;
+
+ /* Shortcut for powers of two ... */
+ if((pow = s_mp_ispow2d(d)) >= 0) {
+ mp_digit mask;
+
+ mask = (1 << pow) - 1;
+ rem = DIGIT(a, 0) & mask;
+
+ if(q) {
+ mp_copy(a, q);
+ s_mp_div_2d(q, pow);
+ }
+
+ if(r)
+ *r = rem;
+
+ return MP_OKAY;
+ }
+
+ /*
+ If the quotient is actually going to be returned, we'll try to
+ avoid hitting the memory allocator by copying the dividend into it
+ and doing the division there. This can't be any _worse_ than
+ always copying, and will sometimes be better (since it won't make
+ another copy)
+
+ If it's not going to be returned, we need to allocate a temporary
+ to hold the quotient, which will just be discarded.
+ */
+ if(q) {
+ if((res = mp_copy(a, q)) != MP_OKAY)
+ return res;
+
+ res = s_mp_div_d(q, d, &rem);
+ if(s_mp_cmp_d(q, 0) == MP_EQ)
+ SIGN(q) = MP_ZPOS;
+
+ } else {
+ mp_int qp;
+
+ if((res = mp_init_copy(&qp, a)) != MP_OKAY)
+ return res;
+
+ res = s_mp_div_d(&qp, d, &rem);
+ if(s_mp_cmp_d(&qp, 0) == 0)
+ SIGN(&qp) = MP_ZPOS;
+
+ mp_clear(&qp);
+ }
+
+ if(r)
+ *r = rem;
+
+ return res;
+
+} /* end mp_div_d() */
+
+/* }}} */
+
+/* {{{ mp_div_2(a, c) */
+
+/*
+ mp_div_2(a, c)
+
+ Compute c = a / 2, disregarding the remainder.
+ */
+
+mp_err mp_div_2(mp_int *a, mp_int *c)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && c != NULL, MP_BADARG);
+
+ if((res = mp_copy(a, c)) != MP_OKAY)
+ return res;
+
+ s_mp_div_2(c);
+
+ return MP_OKAY;
+
+} /* end mp_div_2() */
+
+/* }}} */
+
+/* {{{ mp_expt_d(a, d, b) */
+
+mp_err mp_expt_d(mp_int *a, mp_digit d, mp_int *c)
+{
+ mp_int s, x;
+ mp_err res;
+
+ ARGCHK(a != NULL && c != NULL, MP_BADARG);
+
+ if((res = mp_init(&s)) != MP_OKAY)
+ return res;
+ if((res = mp_init_copy(&x, a)) != MP_OKAY)
+ goto X;
+
+ DIGIT(&s, 0) = 1;
+
+ while(d != 0) {
+ if(d & 1) {
+ if((res = s_mp_mul(&s, &x)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ d >>= 1;
+
+ if((res = s_mp_sqr(&x)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ s_mp_exch(&s, c);
+
+CLEANUP:
+ mp_clear(&x);
+X:
+ mp_clear(&s);
+
+ return res;
+
+} /* end mp_expt_d() */
+
+/* }}} */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* {{{ Full arithmetic */
+
+/* {{{ mp_abs(a, b) */
+
+/*
+ mp_abs(a, b)
+
+ Compute b = |a|. 'a' and 'b' may be identical.
+ */
+
+mp_err mp_abs(mp_int *a, mp_int *b)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL, MP_BADARG);
+
+ if((res = mp_copy(a, b)) != MP_OKAY)
+ return res;
+
+ SIGN(b) = MP_ZPOS;
+
+ return MP_OKAY;
+
+} /* end mp_abs() */
+
+/* }}} */
+
+/* {{{ mp_neg(a, b) */
+
+/*
+ mp_neg(a, b)
+
+ Compute b = -a. 'a' and 'b' may be identical.
+ */
+
+mp_err mp_neg(mp_int *a, mp_int *b)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL, MP_BADARG);
+
+ if((res = mp_copy(a, b)) != MP_OKAY)
+ return res;
+
+ if(s_mp_cmp_d(b, 0) == MP_EQ)
+ SIGN(b) = MP_ZPOS;
+ else
+ SIGN(b) = (SIGN(b) == MP_NEG) ? MP_ZPOS : MP_NEG;
+
+ return MP_OKAY;
+
+} /* end mp_neg() */
+
+/* }}} */
+
+/* {{{ mp_add(a, b, c) */
+
+/*
+ mp_add(a, b, c)
+
+ Compute c = a + b. All parameters may be identical.
+ */
+
+mp_err mp_add(mp_int *a, mp_int *b, mp_int *c)
+{
+ mp_err res;
+ int cmp;
+
+ ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
+
+ if(SIGN(a) == SIGN(b)) { /* same sign: add values, keep sign */
+
+ /* Commutativity of addition lets us do this in either order,
+ so we avoid having to use a temporary even if the result
+ is supposed to replace the output
+ */
+ if(c == b) {
+ if((res = s_mp_add(c, a)) != MP_OKAY)
+ return res;
+ } else {
+ if(c != a && (res = mp_copy(a, c)) != MP_OKAY)
+ return res;
+
+ if((res = s_mp_add(c, b)) != MP_OKAY)
+ return res;
+ }
+
+ } else if((cmp = s_mp_cmp(a, b)) > 0) { /* different sign: a > b */
+
+ /* If the output is going to be clobbered, we will use a temporary
+ variable; otherwise, we'll do it without touching the memory
+ allocator at all, if possible
+ */
+ if(c == b) {
+ mp_int tmp;
+
+ if((res = mp_init_copy(&tmp, a)) != MP_OKAY)
+ return res;
+ if((res = s_mp_sub(&tmp, b)) != MP_OKAY) {
+ mp_clear(&tmp);
+ return res;
+ }
+
+ s_mp_exch(&tmp, c);
+ mp_clear(&tmp);
+
+ } else {
+
+ if(c != a && (res = mp_copy(a, c)) != MP_OKAY)
+ return res;
+ if((res = s_mp_sub(c, b)) != MP_OKAY)
+ return res;
+
+ }
+
+ } else if(cmp == 0) { /* different sign, a == b */
+
+ mp_zero(c);
+ return MP_OKAY;
+
+ } else { /* different sign: a < b */
+
+ /* See above... */
+ if(c == a) {
+ mp_int tmp;
+
+ if((res = mp_init_copy(&tmp, b)) != MP_OKAY)
+ return res;
+ if((res = s_mp_sub(&tmp, a)) != MP_OKAY) {
+ mp_clear(&tmp);
+ return res;
+ }
+
+ s_mp_exch(&tmp, c);
+ mp_clear(&tmp);
+
+ } else {
+
+ if(c != b && (res = mp_copy(b, c)) != MP_OKAY)
+ return res;
+ if((res = s_mp_sub(c, a)) != MP_OKAY)
+ return res;
+
+ }
+ }
+
+ if(USED(c) == 1 && DIGIT(c, 0) == 0)
+ SIGN(c) = MP_ZPOS;
+
+ return MP_OKAY;
+
+} /* end mp_add() */
+
+/* }}} */
+
+/* {{{ mp_sub(a, b, c) */
+
+/*
+ mp_sub(a, b, c)
+
+ Compute c = a - b. All parameters may be identical.
+ */
+
+mp_err mp_sub(mp_int *a, mp_int *b, mp_int *c)
+{
+ mp_err res;
+ int cmp;
+
+ ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
+
+ if(SIGN(a) != SIGN(b)) {
+ if(c == a) {
+ if((res = s_mp_add(c, b)) != MP_OKAY)
+ return res;
+ } else {
+ if(c != b && ((res = mp_copy(b, c)) != MP_OKAY))
+ return res;
+ if((res = s_mp_add(c, a)) != MP_OKAY)
+ return res;
+ SIGN(c) = SIGN(a);
+ }
+
+ } else if((cmp = s_mp_cmp(a, b)) > 0) { /* Same sign, a > b */
+ if(c == b) {
+ mp_int tmp;
+
+ if((res = mp_init_copy(&tmp, a)) != MP_OKAY)
+ return res;
+ if((res = s_mp_sub(&tmp, b)) != MP_OKAY) {
+ mp_clear(&tmp);
+ return res;
+ }
+ s_mp_exch(&tmp, c);
+ mp_clear(&tmp);
+
+ } else {
+ if(c != a && ((res = mp_copy(a, c)) != MP_OKAY))
+ return res;
+
+ if((res = s_mp_sub(c, b)) != MP_OKAY)
+ return res;
+ }
+
+ } else if(cmp == 0) { /* Same sign, equal magnitude */
+ mp_zero(c);
+ return MP_OKAY;
+
+ } else { /* Same sign, b > a */
+ if(c == a) {
+ mp_int tmp;
+
+ if((res = mp_init_copy(&tmp, b)) != MP_OKAY)
+ return res;
+
+ if((res = s_mp_sub(&tmp, a)) != MP_OKAY) {
+ mp_clear(&tmp);
+ return res;
+ }
+ s_mp_exch(&tmp, c);
+ mp_clear(&tmp);
+
+ } else {
+ if(c != b && ((res = mp_copy(b, c)) != MP_OKAY))
+ return res;
+
+ if((res = s_mp_sub(c, a)) != MP_OKAY)
+ return res;
+ }
+
+ SIGN(c) = !SIGN(b);
+ }
+
+ if(USED(c) == 1 && DIGIT(c, 0) == 0)
+ SIGN(c) = MP_ZPOS;
+
+ return MP_OKAY;
+
+} /* end mp_sub() */
+
+/* }}} */
+
+/* {{{ mp_mul(a, b, c) */
+
+/*
+ mp_mul(a, b, c)
+
+ Compute c = a * b. All parameters may be identical.
+ */
+
+mp_err mp_mul(mp_int *a, mp_int *b, mp_int *c)
+{
+ mp_err res;
+ mp_sign sgn;
+
+ ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
+
+ sgn = (SIGN(a) == SIGN(b)) ? MP_ZPOS : MP_NEG;
+
+ if(c == b) {
+ if((res = s_mp_mul(c, a)) != MP_OKAY)
+ return res;
+
+ } else {
+ if((res = mp_copy(a, c)) != MP_OKAY)
+ return res;
+
+ if((res = s_mp_mul(c, b)) != MP_OKAY)
+ return res;
+ }
+
+ if(sgn == MP_ZPOS || s_mp_cmp_d(c, 0) == MP_EQ)
+ SIGN(c) = MP_ZPOS;
+ else
+ SIGN(c) = sgn;
+
+ return MP_OKAY;
+
+} /* end mp_mul() */
+
+/* }}} */
+
+/* {{{ mp_mul_2d(a, d, c) */
+
+/*
+ mp_mul_2d(a, d, c)
+
+ Compute c = a * 2^d. a may be the same as c.
+ */
+
+mp_err mp_mul_2d(mp_int *a, mp_digit d, mp_int *c)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && c != NULL, MP_BADARG);
+
+ if((res = mp_copy(a, c)) != MP_OKAY)
+ return res;
+
+ if(d == 0)
+ return MP_OKAY;
+
+ return s_mp_mul_2d(c, d);
+
+} /* end mp_mul() */
+
+/* }}} */
+
+/* {{{ mp_sqr(a, b) */
+
+#if MP_SQUARE
+mp_err mp_sqr(mp_int *a, mp_int *b)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL, MP_BADARG);
+
+ if((res = mp_copy(a, b)) != MP_OKAY)
+ return res;
+
+ if((res = s_mp_sqr(b)) != MP_OKAY)
+ return res;
+
+ SIGN(b) = MP_ZPOS;
+
+ return MP_OKAY;
+
+} /* end mp_sqr() */
+#endif
+
+/* }}} */
+
+/* {{{ mp_div(a, b, q, r) */
+
+/*
+ mp_div(a, b, q, r)
+
+ Compute q = a / b and r = a mod b. Input parameters may be re-used
+ as output parameters. If q or r is NULL, that portion of the
+ computation will be discarded (although it will still be computed)
+
+ Pay no attention to the hacker behind the curtain.
+ */
+
+mp_err mp_div(mp_int *a, mp_int *b, mp_int *q, mp_int *r)
+{
+ mp_err res;
+ mp_int qtmp, rtmp;
+ int cmp;
+
+ ARGCHK(a != NULL && b != NULL, MP_BADARG);
+
+ if(mp_cmp_z(b) == MP_EQ)
+ return MP_RANGE;
+
+ /* If a <= b, we can compute the solution without division, and
+ avoid any memory allocation
+ */
+ if((cmp = s_mp_cmp(a, b)) < 0) {
+ if(r) {
+ if((res = mp_copy(a, r)) != MP_OKAY)
+ return res;
+ }
+
+ if(q)
+ mp_zero(q);
+
+ return MP_OKAY;
+
+ } else if(cmp == 0) {
+
+ /* Set quotient to 1, with appropriate sign */
+ if(q) {
+ int qneg = (SIGN(a) != SIGN(b));
+
+ mp_set(q, 1);
+ if(qneg)
+ SIGN(q) = MP_NEG;
+ }
+
+ if(r)
+ mp_zero(r);
+
+ return MP_OKAY;
+ }
+
+ /* If we get here, it means we actually have to do some division */
+
+ /* Set up some temporaries... */
+ if((res = mp_init_copy(&qtmp, a)) != MP_OKAY)
+ return res;
+ if((res = mp_init_copy(&rtmp, b)) != MP_OKAY)
+ goto CLEANUP;
+
+ if((res = s_mp_div(&qtmp, &rtmp)) != MP_OKAY)
+ goto CLEANUP;
+
+ /* Compute the signs for the output */
+ SIGN(&rtmp) = SIGN(a); /* Sr = Sa */
+ if(SIGN(a) == SIGN(b))
+ SIGN(&qtmp) = MP_ZPOS; /* Sq = MP_ZPOS if Sa = Sb */
+ else
+ SIGN(&qtmp) = MP_NEG; /* Sq = MP_NEG if Sa != Sb */
+
+ if(s_mp_cmp_d(&qtmp, 0) == MP_EQ)
+ SIGN(&qtmp) = MP_ZPOS;
+ if(s_mp_cmp_d(&rtmp, 0) == MP_EQ)
+ SIGN(&rtmp) = MP_ZPOS;
+
+ /* Copy output, if it is needed */
+ if(q)
+ s_mp_exch(&qtmp, q);
+
+ if(r)
+ s_mp_exch(&rtmp, r);
+
+CLEANUP:
+ mp_clear(&rtmp);
+ mp_clear(&qtmp);
+
+ return res;
+
+} /* end mp_div() */
+
+/* }}} */
+
+/* {{{ mp_div_2d(a, d, q, r) */
+
+mp_err mp_div_2d(mp_int *a, mp_digit d, mp_int *q, mp_int *r)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL, MP_BADARG);
+
+ if(q) {
+ if((res = mp_copy(a, q)) != MP_OKAY)
+ return res;
+
+ s_mp_div_2d(q, d);
+ }
+
+ if(r) {
+ if((res = mp_copy(a, r)) != MP_OKAY)
+ return res;
+
+ s_mp_mod_2d(r, d);
+ }
+
+ return MP_OKAY;
+
+} /* end mp_div_2d() */
+
+/* }}} */
+
+/* {{{ mp_expt(a, b, c) */
+
+/*
+ mp_expt(a, b, c)
+
+ Compute c = a ** b, that is, raise a to the b power. Uses a
+ standard iterative square-and-multiply technique.
+ */
+
+mp_err mp_expt(mp_int *a, mp_int *b, mp_int *c)
+{
+ mp_int s, x;
+ mp_err res;
+ mp_digit d;
+ int dig, bit;
+
+ ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
+
+ if(mp_cmp_z(b) < 0)
+ return MP_RANGE;
+
+ if((res = mp_init(&s)) != MP_OKAY)
+ return res;
+
+ mp_set(&s, 1);
+
+ if((res = mp_init_copy(&x, a)) != MP_OKAY)
+ goto X;
+
+ /* Loop over low-order digits in ascending order */
+ for(dig = 0; dig < (USED(b) - 1); dig++) {
+ d = DIGIT(b, dig);
+
+ /* Loop over bits of each non-maximal digit */
+ for(bit = 0; bit < DIGIT_BIT; bit++) {
+ if(d & 1) {
+ if((res = s_mp_mul(&s, &x)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ d >>= 1;
+
+ if((res = s_mp_sqr(&x)) != MP_OKAY)
+ goto CLEANUP;
+ }
+ }
+
+ /* Consider now the last digit... */
+ d = DIGIT(b, dig);
+
+ while(d) {
+ if(d & 1) {
+ if((res = s_mp_mul(&s, &x)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ d >>= 1;
+
+ if((res = s_mp_sqr(&x)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ if(mp_iseven(b))
+ SIGN(&s) = SIGN(a);
+
+ res = mp_copy(&s, c);
+
+CLEANUP:
+ mp_clear(&x);
+X:
+ mp_clear(&s);
+
+ return res;
+
+} /* end mp_expt() */
+
+/* }}} */
+
+/* {{{ mp_2expt(a, k) */
+
+/* Compute a = 2^k */
+
+mp_err mp_2expt(mp_int *a, mp_digit k)
+{
+ ARGCHK(a != NULL, MP_BADARG);
+
+ return s_mp_2expt(a, k);
+
+} /* end mp_2expt() */
+
+/* }}} */
+
+/* {{{ mp_mod(a, m, c) */
+
+/*
+ mp_mod(a, m, c)
+
+ Compute c = a (mod m). Result will always be 0 <= c < m.
+ */
+
+mp_err mp_mod(mp_int *a, mp_int *m, mp_int *c)
+{
+ mp_err res;
+ int mag;
+
+ ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG);
+
+ if(SIGN(m) == MP_NEG)
+ return MP_RANGE;
+
+ /*
+ If |a| > m, we need to divide to get the remainder and take the
+ absolute value.
+
+ If |a| < m, we don't need to do any division, just copy and adjust
+ the sign (if a is negative).
+
+ If |a| == m, we can simply set the result to zero.
+
+ This order is intended to minimize the average path length of the
+ comparison chain on common workloads -- the most frequent cases are
+ that |a| != m, so we do those first.
+ */
+ if((mag = s_mp_cmp(a, m)) > 0) {
+ if((res = mp_div(a, m, NULL, c)) != MP_OKAY)
+ return res;
+
+ if(SIGN(c) == MP_NEG) {
+ if((res = mp_add(c, m, c)) != MP_OKAY)
+ return res;
+ }
+
+ } else if(mag < 0) {
+ if((res = mp_copy(a, c)) != MP_OKAY)
+ return res;
+
+ if(mp_cmp_z(a) < 0) {
+ if((res = mp_add(c, m, c)) != MP_OKAY)
+ return res;
+
+ }
+
+ } else {
+ mp_zero(c);
+
+ }
+
+ return MP_OKAY;
+
+} /* end mp_mod() */
+
+/* }}} */
+
+/* {{{ mp_mod_d(a, d, c) */
+
+/*
+ mp_mod_d(a, d, c)
+
+ Compute c = a (mod d). Result will always be 0 <= c < d
+ */
+mp_err mp_mod_d(mp_int *a, mp_digit d, mp_digit *c)
+{
+ mp_err res;
+ mp_digit rem;
+
+ ARGCHK(a != NULL && c != NULL, MP_BADARG);
+
+ if(s_mp_cmp_d(a, d) > 0) {
+ if((res = mp_div_d(a, d, NULL, &rem)) != MP_OKAY)
+ return res;
+
+ } else {
+ if(SIGN(a) == MP_NEG)
+ rem = d - DIGIT(a, 0);
+ else
+ rem = DIGIT(a, 0);
+ }
+
+ if(c)
+ *c = rem;
+
+ return MP_OKAY;
+
+} /* end mp_mod_d() */
+
+/* }}} */
+
+/* {{{ mp_sqrt(a, b) */
+
+/*
+ mp_sqrt(a, b)
+
+ Compute the integer square root of a, and store the result in b.
+ Uses an integer-arithmetic version of Newton's iterative linear
+ approximation technique to determine this value; the result has the
+ following two properties:
+
+ b^2 <= a
+ (b+1)^2 >= a
+
+ It is a range error to pass a negative value.
+ */
+mp_err mp_sqrt(mp_int *a, mp_int *b)
+{
+ mp_int x, t;
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL, MP_BADARG);
+
+ /* Cannot take square root of a negative value */
+ if(SIGN(a) == MP_NEG)
+ return MP_RANGE;
+
+ /* Special cases for zero and one, trivial */
+ if(mp_cmp_d(a, 0) == MP_EQ || mp_cmp_d(a, 1) == MP_EQ)
+ return mp_copy(a, b);
+
+ /* Initialize the temporaries we'll use below */
+ if((res = mp_init_size(&t, USED(a))) != MP_OKAY)
+ return res;
+
+ /* Compute an initial guess for the iteration as a itself */
+ if((res = mp_init_copy(&x, a)) != MP_OKAY)
+ goto X;
+
+s_mp_rshd(&x, (USED(&x)/2)+1);
+mp_add_d(&x, 1, &x);
+
+ for(;;) {
+ /* t = (x * x) - a */
+ mp_copy(&x, &t); /* can't fail, t is big enough for original x */
+ if((res = mp_sqr(&t, &t)) != MP_OKAY ||
+ (res = mp_sub(&t, a, &t)) != MP_OKAY)
+ goto CLEANUP;
+
+ /* t = t / 2x */
+ s_mp_mul_2(&x);
+ if((res = mp_div(&t, &x, &t, NULL)) != MP_OKAY)
+ goto CLEANUP;
+ s_mp_div_2(&x);
+
+ /* Terminate the loop, if the quotient is zero */
+ if(mp_cmp_z(&t) == MP_EQ)
+ break;
+
+ /* x = x - t */
+ if((res = mp_sub(&x, &t, &x)) != MP_OKAY)
+ goto CLEANUP;
+
+ }
+
+ /* Copy result to output parameter */
+ mp_sub_d(&x, 1, &x);
+ s_mp_exch(&x, b);
+
+ CLEANUP:
+ mp_clear(&x);
+ X:
+ mp_clear(&t);
+
+ return res;
+
+} /* end mp_sqrt() */
+
+/* }}} */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* {{{ Modular arithmetic */
+
+#if MP_MODARITH
+/* {{{ mp_addmod(a, b, m, c) */
+
+/*
+ mp_addmod(a, b, m, c)
+
+ Compute c = (a + b) mod m
+ */
+
+mp_err mp_addmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG);
+
+ if((res = mp_add(a, b, c)) != MP_OKAY)
+ return res;
+ if((res = mp_mod(c, m, c)) != MP_OKAY)
+ return res;
+
+ return MP_OKAY;
+
+}
+
+/* }}} */
+
+/* {{{ mp_submod(a, b, m, c) */
+
+/*
+ mp_submod(a, b, m, c)
+
+ Compute c = (a - b) mod m
+ */
+
+mp_err mp_submod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG);
+
+ if((res = mp_sub(a, b, c)) != MP_OKAY)
+ return res;
+ if((res = mp_mod(c, m, c)) != MP_OKAY)
+ return res;
+
+ return MP_OKAY;
+
+}
+
+/* }}} */
+
+/* {{{ mp_mulmod(a, b, m, c) */
+
+/*
+ mp_mulmod(a, b, m, c)
+
+ Compute c = (a * b) mod m
+ */
+
+mp_err mp_mulmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG);
+
+ if((res = mp_mul(a, b, c)) != MP_OKAY)
+ return res;
+ if((res = mp_mod(c, m, c)) != MP_OKAY)
+ return res;
+
+ return MP_OKAY;
+
+}
+
+/* }}} */
+
+/* {{{ mp_sqrmod(a, m, c) */
+
+#if MP_SQUARE
+mp_err mp_sqrmod(mp_int *a, mp_int *m, mp_int *c)
+{
+ mp_err res;
+
+ ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG);
+
+ if((res = mp_sqr(a, c)) != MP_OKAY)
+ return res;
+ if((res = mp_mod(c, m, c)) != MP_OKAY)
+ return res;
+
+ return MP_OKAY;
+
+} /* end mp_sqrmod() */
+#endif
+
+/* }}} */
+
+/* {{{ mp_exptmod(a, b, m, c) */
+
+/*
+ mp_exptmod(a, b, m, c)
+
+ Compute c = (a ** b) mod m. Uses a standard square-and-multiply
+ method with modular reductions at each step. (This is basically the
+ same code as mp_expt(), except for the addition of the reductions)
+
+ The modular reductions are done using Barrett's algorithm (see
+ s_mp_reduce() below for details)
+ */
+
+mp_err mp_exptmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
+{
+ mp_int s, x, mu;
+ mp_err res;
+ mp_digit d, *db = DIGITS(b);
+ mp_size ub = USED(b);
+ int dig, bit;
+
+ ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
+
+ if(mp_cmp_z(b) < 0 || mp_cmp_z(m) <= 0)
+ return MP_RANGE;
+
+ if((res = mp_init(&s)) != MP_OKAY)
+ return res;
+ if((res = mp_init_copy(&x, a)) != MP_OKAY)
+ goto X;
+ if((res = mp_mod(&x, m, &x)) != MP_OKAY ||
+ (res = mp_init(&mu)) != MP_OKAY)
+ goto MU;
+
+ mp_set(&s, 1);
+
+ /* mu = b^2k / m */
+ s_mp_add_d(&mu, 1);
+ s_mp_lshd(&mu, 2 * USED(m));
+ if((res = mp_div(&mu, m, &mu, NULL)) != MP_OKAY)
+ goto CLEANUP;
+
+ /* Loop over digits of b in ascending order, except highest order */
+ for(dig = 0; dig < (ub - 1); dig++) {
+ d = *db++;
+
+ /* Loop over the bits of the lower-order digits */
+ for(bit = 0; bit < DIGIT_BIT; bit++) {
+ if(d & 1) {
+ if((res = s_mp_mul(&s, &x)) != MP_OKAY)
+ goto CLEANUP;
+ if((res = s_mp_reduce(&s, m, &mu)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ d >>= 1;
+
+ if((res = s_mp_sqr(&x)) != MP_OKAY)
+ goto CLEANUP;
+ if((res = s_mp_reduce(&x, m, &mu)) != MP_OKAY)
+ goto CLEANUP;
+ }
+ }
+
+ /* Now do the last digit... */
+ d = *db;
+
+ while(d) {
+ if(d & 1) {
+ if((res = s_mp_mul(&s, &x)) != MP_OKAY)
+ goto CLEANUP;
+ if((res = s_mp_reduce(&s, m, &mu)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ d >>= 1;
+
+ if((res = s_mp_sqr(&x)) != MP_OKAY)
+ goto CLEANUP;
+ if((res = s_mp_reduce(&x, m, &mu)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ s_mp_exch(&s, c);
+
+ CLEANUP:
+ mp_clear(&mu);
+ MU:
+ mp_clear(&x);
+ X:
+ mp_clear(&s);
+
+ return res;
+
+} /* end mp_exptmod() */
+
+/* }}} */
+
+/* {{{ mp_exptmod_d(a, d, m, c) */
+
+mp_err mp_exptmod_d(mp_int *a, mp_digit d, mp_int *m, mp_int *c)
+{
+ mp_int s, x;
+ mp_err res;
+
+ ARGCHK(a != NULL && c != NULL, MP_BADARG);
+
+ if((res = mp_init(&s)) != MP_OKAY)
+ return res;
+ if((res = mp_init_copy(&x, a)) != MP_OKAY)
+ goto X;
+
+ mp_set(&s, 1);
+
+ while(d != 0) {
+ if(d & 1) {
+ if((res = s_mp_mul(&s, &x)) != MP_OKAY ||
+ (res = mp_mod(&s, m, &s)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ d /= 2;
+
+ if((res = s_mp_sqr(&x)) != MP_OKAY ||
+ (res = mp_mod(&x, m, &x)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ s_mp_exch(&s, c);
+
+CLEANUP:
+ mp_clear(&x);
+X:
+ mp_clear(&s);
+
+ return res;
+
+} /* end mp_exptmod_d() */
+
+/* }}} */
+#endif /* if MP_MODARITH */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* {{{ Comparison functions */
+
+/* {{{ mp_cmp_z(a) */
+
+/*
+ mp_cmp_z(a)
+
+ Compare a <=> 0. Returns <0 if a<0, 0 if a=0, >0 if a>0.
+ */
+
+int mp_cmp_z(mp_int *a)
+{
+ if(SIGN(a) == MP_NEG)
+ return MP_LT;
+ else if(USED(a) == 1 && DIGIT(a, 0) == 0)
+ return MP_EQ;
+ else
+ return MP_GT;
+
+} /* end mp_cmp_z() */
+
+/* }}} */
+
+/* {{{ mp_cmp_d(a, d) */
+
+/*
+ mp_cmp_d(a, d)
+
+ Compare a <=> d. Returns <0 if a<d, 0 if a=d, >0 if a>d
+ */
+
+int mp_cmp_d(mp_int *a, mp_digit d)
+{
+ ARGCHK(a != NULL, MP_EQ);
+
+ if(SIGN(a) == MP_NEG)
+ return MP_LT;
+
+ return s_mp_cmp_d(a, d);
+
+} /* end mp_cmp_d() */
+
+/* }}} */
+
+/* {{{ mp_cmp(a, b) */
+
+int mp_cmp(mp_int *a, mp_int *b)
+{
+ ARGCHK(a != NULL && b != NULL, MP_EQ);
+
+ if(SIGN(a) == SIGN(b)) {
+ int mag;
+
+ if((mag = s_mp_cmp(a, b)) == MP_EQ)
+ return MP_EQ;
+
+ if(SIGN(a) == MP_ZPOS)
+ return mag;
+ else
+ return -mag;
+
+ } else if(SIGN(a) == MP_ZPOS) {
+ return MP_GT;
+ } else {
+ return MP_LT;
+ }
+
+} /* end mp_cmp() */
+
+/* }}} */
+
+/* {{{ mp_cmp_mag(a, b) */
+
+/*
+ mp_cmp_mag(a, b)
+
+ Compares |a| <=> |b|, and returns an appropriate comparison result
+ */
+
+int mp_cmp_mag(mp_int *a, mp_int *b)
+{
+ ARGCHK(a != NULL && b != NULL, MP_EQ);
+
+ return s_mp_cmp(a, b);
+
+} /* end mp_cmp_mag() */
+
+/* }}} */
+
+/* {{{ mp_cmp_int(a, z) */
+
+/*
+ This just converts z to an mp_int, and uses the existing comparison
+ routines. This is sort of inefficient, but it's not clear to me how
+ frequently this wil get used anyway. For small positive constants,
+ you can always use mp_cmp_d(), and for zero, there is mp_cmp_z().
+ */
+int mp_cmp_int(mp_int *a, long z)
+{
+ mp_int tmp;
+ int out;
+
+ ARGCHK(a != NULL, MP_EQ);
+
+ mp_init(&tmp); mp_set_int(&tmp, z);
+ out = mp_cmp(a, &tmp);
+ mp_clear(&tmp);
+
+ return out;
+
+} /* end mp_cmp_int() */
+
+/* }}} */
+
+/* {{{ mp_isodd(a) */
+
+/*
+ mp_isodd(a)
+
+ Returns a true (non-zero) value if a is odd, false (zero) otherwise.
+ */
+int mp_isodd(mp_int *a)
+{
+ ARGCHK(a != NULL, 0);
+
+ return (DIGIT(a, 0) & 1);
+
+} /* end mp_isodd() */
+
+/* }}} */
+
+/* {{{ mp_iseven(a) */
+
+int mp_iseven(mp_int *a)
+{
+ return !mp_isodd(a);
+
+} /* end mp_iseven() */
+
+/* }}} */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* {{{ Number theoretic functions */
+
+#if MP_NUMTH
+/* {{{ mp_gcd(a, b, c) */
+
+/*
+ Like the old mp_gcd() function, except computes the GCD using the
+ binary algorithm due to Josef Stein in 1961 (via Knuth).
+ */
+mp_err mp_gcd(mp_int *a, mp_int *b, mp_int *c)
+{
+ mp_err res;
+ mp_int u, v, t;
+ mp_size k = 0;
+
+ ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
+
+ if(mp_cmp_z(a) == MP_EQ && mp_cmp_z(b) == MP_EQ)
+ return MP_RANGE;
+ if(mp_cmp_z(a) == MP_EQ) {
+ return mp_copy(b, c);
+ } else if(mp_cmp_z(b) == MP_EQ) {
+ return mp_copy(a, c);
+ }
+
+ if((res = mp_init(&t)) != MP_OKAY)
+ return res;
+ if((res = mp_init_copy(&u, a)) != MP_OKAY)
+ goto U;
+ if((res = mp_init_copy(&v, b)) != MP_OKAY)
+ goto V;
+
+ SIGN(&u) = MP_ZPOS;
+ SIGN(&v) = MP_ZPOS;
+
+ /* Divide out common factors of 2 until at least 1 of a, b is even */
+ while(mp_iseven(&u) && mp_iseven(&v)) {
+ s_mp_div_2(&u);
+ s_mp_div_2(&v);
+ ++k;
+ }
+
+ /* Initialize t */
+ if(mp_isodd(&u)) {
+ if((res = mp_copy(&v, &t)) != MP_OKAY)
+ goto CLEANUP;
+
+ /* t = -v */
+ if(SIGN(&v) == MP_ZPOS)
+ SIGN(&t) = MP_NEG;
+ else
+ SIGN(&t) = MP_ZPOS;
+
+ } else {
+ if((res = mp_copy(&u, &t)) != MP_OKAY)
+ goto CLEANUP;
+
+ }
+
+ for(;;) {
+ while(mp_iseven(&t)) {
+ s_mp_div_2(&t);
+ }
+
+ if(mp_cmp_z(&t) == MP_GT) {
+ if((res = mp_copy(&t, &u)) != MP_OKAY)
+ goto CLEANUP;
+
+ } else {
+ if((res = mp_copy(&t, &v)) != MP_OKAY)
+ goto CLEANUP;
+
+ /* v = -t */
+ if(SIGN(&t) == MP_ZPOS)
+ SIGN(&v) = MP_NEG;
+ else
+ SIGN(&v) = MP_ZPOS;
+ }
+
+ if((res = mp_sub(&u, &v, &t)) != MP_OKAY)
+ goto CLEANUP;
+
+ if(s_mp_cmp_d(&t, 0) == MP_EQ)
+ break;
+ }
+
+ s_mp_2expt(&v, k); /* v = 2^k */
+ res = mp_mul(&u, &v, c); /* c = u * v */
+
+ CLEANUP:
+ mp_clear(&v);
+ V:
+ mp_clear(&u);
+ U:
+ mp_clear(&t);
+
+ return res;
+
+} /* end mp_bgcd() */
+
+/* }}} */
+
+/* {{{ mp_lcm(a, b, c) */
+
+/* We compute the least common multiple using the rule:
+
+ ab = [a, b](a, b)
+
+ ... by computing the product, and dividing out the gcd.
+ */
+
+mp_err mp_lcm(mp_int *a, mp_int *b, mp_int *c)
+{
+ mp_int gcd, prod;
+ mp_err res;
+
+ ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
+
+ /* Set up temporaries */
+ if((res = mp_init(&gcd)) != MP_OKAY)
+ return res;
+ if((res = mp_init(&prod)) != MP_OKAY)
+ goto GCD;
+
+ if((res = mp_mul(a, b, &prod)) != MP_OKAY)
+ goto CLEANUP;
+ if((res = mp_gcd(a, b, &gcd)) != MP_OKAY)
+ goto CLEANUP;
+
+ res = mp_div(&prod, &gcd, c, NULL);
+
+ CLEANUP:
+ mp_clear(&prod);
+ GCD:
+ mp_clear(&gcd);
+
+ return res;
+
+} /* end mp_lcm() */
+
+/* }}} */
+
+/* {{{ mp_xgcd(a, b, g, x, y) */
+
+/*
+ mp_xgcd(a, b, g, x, y)
+
+ Compute g = (a, b) and values x and y satisfying Bezout's identity
+ (that is, ax + by = g). This uses the extended binary GCD algorithm
+ based on the Stein algorithm used for mp_gcd()
+ */
+
+mp_err mp_xgcd(mp_int *a, mp_int *b, mp_int *g, mp_int *x, mp_int *y)
+{
+ mp_int gx, xc, yc, u, v, A, B, C, D;
+ mp_int *clean[9];
+ mp_err res;
+ int last = -1;
+
+ if(mp_cmp_z(b) == 0)
+ return MP_RANGE;
+
+ /* Initialize all these variables we need */
+ if((res = mp_init(&u)) != MP_OKAY) goto CLEANUP;
+ clean[++last] = &u;
+ if((res = mp_init(&v)) != MP_OKAY) goto CLEANUP;
+ clean[++last] = &v;
+ if((res = mp_init(&gx)) != MP_OKAY) goto CLEANUP;
+ clean[++last] = &gx;
+ if((res = mp_init(&A)) != MP_OKAY) goto CLEANUP;
+ clean[++last] = &A;
+ if((res = mp_init(&B)) != MP_OKAY) goto CLEANUP;
+ clean[++last] = &B;
+ if((res = mp_init(&C)) != MP_OKAY) goto CLEANUP;
+ clean[++last] = &C;
+ if((res = mp_init(&D)) != MP_OKAY) goto CLEANUP;
+ clean[++last] = &D;
+ if((res = mp_init_copy(&xc, a)) != MP_OKAY) goto CLEANUP;
+ clean[++last] = &xc;
+ mp_abs(&xc, &xc);
+ if((res = mp_init_copy(&yc, b)) != MP_OKAY) goto CLEANUP;
+ clean[++last] = &yc;
+ mp_abs(&yc, &yc);
+
+ mp_set(&gx, 1);
+
+ /* Divide by two until at least one of them is even */
+ while(mp_iseven(&xc) && mp_iseven(&yc)) {
+ s_mp_div_2(&xc);
+ s_mp_div_2(&yc);
+ if((res = s_mp_mul_2(&gx)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ mp_copy(&xc, &u);
+ mp_copy(&yc, &v);
+ mp_set(&A, 1); mp_set(&D, 1);
+
+ /* Loop through binary GCD algorithm */
+ for(;;) {
+ while(mp_iseven(&u)) {
+ s_mp_div_2(&u);
+
+ if(mp_iseven(&A) && mp_iseven(&B)) {
+ s_mp_div_2(&A); s_mp_div_2(&B);
+ } else {
+ if((res = mp_add(&A, &yc, &A)) != MP_OKAY) goto CLEANUP;
+ s_mp_div_2(&A);
+ if((res = mp_sub(&B, &xc, &B)) != MP_OKAY) goto CLEANUP;
+ s_mp_div_2(&B);
+ }
+ }
+
+ while(mp_iseven(&v)) {
+ s_mp_div_2(&v);
+
+ if(mp_iseven(&C) && mp_iseven(&D)) {
+ s_mp_div_2(&C); s_mp_div_2(&D);
+ } else {
+ if((res = mp_add(&C, &yc, &C)) != MP_OKAY) goto CLEANUP;
+ s_mp_div_2(&C);
+ if((res = mp_sub(&D, &xc, &D)) != MP_OKAY) goto CLEANUP;
+ s_mp_div_2(&D);
+ }
+ }
+
+ if(mp_cmp(&u, &v) >= 0) {
+ if((res = mp_sub(&u, &v, &u)) != MP_OKAY) goto CLEANUP;
+ if((res = mp_sub(&A, &C, &A)) != MP_OKAY) goto CLEANUP;
+ if((res = mp_sub(&B, &D, &B)) != MP_OKAY) goto CLEANUP;
+
+ } else {
+ if((res = mp_sub(&v, &u, &v)) != MP_OKAY) goto CLEANUP;
+ if((res = mp_sub(&C, &A, &C)) != MP_OKAY) goto CLEANUP;
+ if((res = mp_sub(&D, &B, &D)) != MP_OKAY) goto CLEANUP;
+
+ }
+
+ /* If we're done, copy results to output */
+ if(mp_cmp_z(&u) == 0) {
+ if(x)
+ if((res = mp_copy(&C, x)) != MP_OKAY) goto CLEANUP;
+
+ if(y)
+ if((res = mp_copy(&D, y)) != MP_OKAY) goto CLEANUP;
+
+ if(g)
+ if((res = mp_mul(&gx, &v, g)) != MP_OKAY) goto CLEANUP;
+
+ break;
+ }
+ }
+
+ CLEANUP:
+ while(last >= 0)
+ mp_clear(clean[last--]);
+
+ return res;
+
+} /* end mp_xgcd() */
+
+/* }}} */
+
+/* {{{ mp_invmod(a, m, c) */
+
+/*
+ mp_invmod(a, m, c)
+
+ Compute c = a^-1 (mod m), if there is an inverse for a (mod m).
+ This is equivalent to the question of whether (a, m) = 1. If not,
+ MP_UNDEF is returned, and there is no inverse.
+ */
+
+mp_err mp_invmod(mp_int *a, mp_int *m, mp_int *c)
+{
+ mp_int g, x;
+ mp_err res;
+
+ ARGCHK(a && m && c, MP_BADARG);
+
+ if(mp_cmp_z(a) == 0 || mp_cmp_z(m) == 0)
+ return MP_RANGE;
+
+ if((res = mp_init(&g)) != MP_OKAY)
+ return res;
+ if((res = mp_init(&x)) != MP_OKAY)
+ goto X;
+
+ if((res = mp_xgcd(a, m, &g, &x, NULL)) != MP_OKAY)
+ goto CLEANUP;
+
+ if(mp_cmp_d(&g, 1) != MP_EQ) {
+ res = MP_UNDEF;
+ goto CLEANUP;
+ }
+
+ res = mp_mod(&x, m, c);
+ SIGN(c) = SIGN(a);
+
+CLEANUP:
+ mp_clear(&x);
+X:
+ mp_clear(&g);
+
+ return res;
+
+} /* end mp_invmod() */
+
+/* }}} */
+#endif /* if MP_NUMTH */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* {{{ mp_print(mp, ofp) */
+
+#if MP_IOFUNC
+/*
+ mp_print(mp, ofp)
+
+ Print a textual representation of the given mp_int on the output
+ stream 'ofp'. Output is generated using the internal radix.
+ */
+
+void mp_print(mp_int *mp, FILE *ofp)
+{
+ int ix;
+
+ if(mp == NULL || ofp == NULL)
+ return;
+
+ fputc((SIGN(mp) == MP_NEG) ? '-' : '+', ofp);
+
+ for(ix = USED(mp) - 1; ix >= 0; ix--) {
+ fprintf(ofp, DIGIT_FMT, DIGIT(mp, ix));
+ }
+
+} /* end mp_print() */
+
+#endif /* if MP_IOFUNC */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* {{{ More I/O Functions */
+
+/* {{{ mp_read_signed_bin(mp, str, len) */
+
+/*
+ mp_read_signed_bin(mp, str, len)
+
+ Read in a raw value (base 256) into the given mp_int
+ */
+
+mp_err mp_read_signed_bin(mp_int *mp, unsigned char *str, int len)
+{
+ mp_err res;
+
+ ARGCHK(mp != NULL && str != NULL && len > 0, MP_BADARG);
+
+ if((res = mp_read_unsigned_bin(mp, str + 1, len - 1)) == MP_OKAY) {
+ /* Get sign from first byte */
+ if(str[0])
+ SIGN(mp) = MP_NEG;
+ else
+ SIGN(mp) = MP_ZPOS;
+ }
+
+ return res;
+
+} /* end mp_read_signed_bin() */
+
+/* }}} */
+
+/* {{{ mp_signed_bin_size(mp) */
+
+int mp_signed_bin_size(mp_int *mp)
+{
+ ARGCHK(mp != NULL, 0);
+
+ return mp_unsigned_bin_size(mp) + 1;
+
+} /* end mp_signed_bin_size() */
+
+/* }}} */
+
+/* {{{ mp_to_signed_bin(mp, str) */
+
+mp_err mp_to_signed_bin(mp_int *mp, unsigned char *str)
+{
+ ARGCHK(mp != NULL && str != NULL, MP_BADARG);
+
+ /* Caller responsible for allocating enough memory (use mp_raw_size(mp)) */
+ str[0] = (char)SIGN(mp);
+
+ return mp_to_unsigned_bin(mp, str + 1);
+
+} /* end mp_to_signed_bin() */
+
+/* }}} */
+
+/* {{{ mp_read_unsigned_bin(mp, str, len) */
+
+/*
+ mp_read_unsigned_bin(mp, str, len)
+
+ Read in an unsigned value (base 256) into the given mp_int
+ */
+
+mp_err mp_read_unsigned_bin(mp_int *mp, unsigned char *str, int len)
+{
+ int ix;
+ mp_err res;
+
+ ARGCHK(mp != NULL && str != NULL && len > 0, MP_BADARG);
+
+ mp_zero(mp);
+
+ for(ix = 0; ix < len; ix++) {
+ if((res = s_mp_mul_2d(mp, CHAR_BIT)) != MP_OKAY)
+ return res;
+
+ if((res = mp_add_d(mp, str[ix], mp)) != MP_OKAY)
+ return res;
+ }
+
+ return MP_OKAY;
+
+} /* end mp_read_unsigned_bin() */
+
+/* }}} */
+
+/* {{{ mp_unsigned_bin_size(mp) */
+
+int mp_unsigned_bin_size(mp_int *mp)
+{
+ mp_digit topdig;
+ int count;
+
+ ARGCHK(mp != NULL, 0);
+
+ /* Special case for the value zero */
+ if(USED(mp) == 1 && DIGIT(mp, 0) == 0)
+ return 1;
+
+ count = (USED(mp) - 1) * sizeof(mp_digit);
+ topdig = DIGIT(mp, USED(mp) - 1);
+
+ while(topdig != 0) {
+ ++count;
+ topdig >>= CHAR_BIT;
+ }
+
+ return count;
+
+} /* end mp_unsigned_bin_size() */
+
+/* }}} */
+
+/* {{{ mp_to_unsigned_bin(mp, str) */
+
+mp_err mp_to_unsigned_bin(mp_int *mp, unsigned char *str)
+{
+ mp_digit *dp, *end, d;
+ unsigned char *spos;
+
+ ARGCHK(mp != NULL && str != NULL, MP_BADARG);
+
+ dp = DIGITS(mp);
+ end = dp + USED(mp) - 1;
+ spos = str;
+
+ /* Special case for zero, quick test */
+ if(dp == end && *dp == 0) {
+ *str = '\0';
+ return MP_OKAY;
+ }
+
+ /* Generate digits in reverse order */
+ while(dp < end) {
+ int ix;
+
+ d = *dp;
+ for(ix = 0; ix < sizeof(mp_digit); ++ix) {
+ *spos = d & UCHAR_MAX;
+ d >>= CHAR_BIT;
+ ++spos;
+ }
+
+ ++dp;
+ }
+
+ /* Now handle last digit specially, high order zeroes are not written */
+ d = *end;
+ while(d != 0) {
+ *spos = d & UCHAR_MAX;
+ d >>= CHAR_BIT;
+ ++spos;
+ }
+
+ /* Reverse everything to get digits in the correct order */
+ while(--spos > str) {
+ unsigned char t = *str;
+ *str = *spos;
+ *spos = t;
+
+ ++str;
+ }
+
+ return MP_OKAY;
+
+} /* end mp_to_unsigned_bin() */
+
+/* }}} */
+
+/* {{{ mp_count_bits(mp) */
+
+int mp_count_bits(mp_int *mp)
+{
+ int len;
+ mp_digit d;
+
+ ARGCHK(mp != NULL, MP_BADARG);
+
+ len = DIGIT_BIT * (USED(mp) - 1);
+ d = DIGIT(mp, USED(mp) - 1);
+
+ while(d != 0) {
+ ++len;
+ d >>= 1;
+ }
+
+ return len;
+
+} /* end mp_count_bits() */
+
+/* }}} */
+
+/* {{{ mp_read_radix(mp, str, radix) */
+
+/*
+ mp_read_radix(mp, str, radix)
+
+ Read an integer from the given string, and set mp to the resulting
+ value. The input is presumed to be in base 10. Leading non-digit
+ characters are ignored, and the function reads until a non-digit
+ character or the end of the string.
+ */
+
+mp_err mp_read_radix(mp_int *mp, unsigned char *str, int radix)
+{
+ int ix = 0, val = 0;
+ mp_err res;
+ mp_sign sig = MP_ZPOS;
+
+ ARGCHK(mp != NULL && str != NULL && radix >= 2 && radix <= MAX_RADIX,
+ MP_BADARG);
+
+ mp_zero(mp);
+
+ /* Skip leading non-digit characters until a digit or '-' or '+' */
+ while(str[ix] &&
+ (s_mp_tovalue(str[ix], radix) < 0) &&
+ str[ix] != '-' &&
+ str[ix] != '+') {
+ ++ix;
+ }
+
+ if(str[ix] == '-') {
+ sig = MP_NEG;
+ ++ix;
+ } else if(str[ix] == '+') {
+ sig = MP_ZPOS; /* this is the default anyway... */
+ ++ix;
+ }
+
+ while((val = s_mp_tovalue(str[ix], radix)) >= 0) {
+ if((res = s_mp_mul_d(mp, radix)) != MP_OKAY)
+ return res;
+ if((res = s_mp_add_d(mp, val)) != MP_OKAY)
+ return res;
+ ++ix;
+ }
+
+ if(s_mp_cmp_d(mp, 0) == MP_EQ)
+ SIGN(mp) = MP_ZPOS;
+ else
+ SIGN(mp) = sig;
+
+ return MP_OKAY;
+
+} /* end mp_read_radix() */
+
+/* }}} */
+
+/* {{{ mp_radix_size(mp, radix) */
+
+int mp_radix_size(mp_int *mp, int radix)
+{
+ int len;
+ ARGCHK(mp != NULL, 0);
+
+ len = s_mp_outlen(mp_count_bits(mp), radix) + 1; /* for NUL terminator */
+
+ if(mp_cmp_z(mp) < 0)
+ ++len; /* for sign */
+
+ return len;
+
+} /* end mp_radix_size() */
+
+/* }}} */
+
+/* {{{ mp_value_radix_size(num, qty, radix) */
+
+/* num = number of digits
+ qty = number of bits per digit
+ radix = target base
+
+ Return the number of digits in the specified radix that would be
+ needed to express 'num' digits of 'qty' bits each.
+ */
+int mp_value_radix_size(int num, int qty, int radix)
+{
+ ARGCHK(num >= 0 && qty > 0 && radix >= 2 && radix <= MAX_RADIX, 0);
+
+ return s_mp_outlen(num * qty, radix);
+
+} /* end mp_value_radix_size() */
+
+/* }}} */
+
+/* {{{ mp_toradix(mp, str, radix) */
+
+mp_err mp_toradix(mp_int *mp, unsigned char *str, int radix)
+{
+ int ix, pos = 0;
+
+ ARGCHK(mp != NULL && str != NULL, MP_BADARG);
+ ARGCHK(radix > 1 && radix <= MAX_RADIX, MP_RANGE);
+
+ if(mp_cmp_z(mp) == MP_EQ) {
+ str[0] = '0';
+ str[1] = '\0';
+ } else {
+ mp_err res;
+ mp_int tmp;
+ mp_sign sgn;
+ mp_digit rem, rdx = (mp_digit)radix;
+ char ch;
+
+ if((res = mp_init_copy(&tmp, mp)) != MP_OKAY)
+ return res;
+
+ /* Save sign for later, and take absolute value */
+ sgn = SIGN(&tmp); SIGN(&tmp) = MP_ZPOS;
+
+ /* Generate output digits in reverse order */
+ while(mp_cmp_z(&tmp) != 0) {
+ if((res = s_mp_div_d(&tmp, rdx, &rem)) != MP_OKAY) {
+ mp_clear(&tmp);
+ return res;
+ }
+
+ /* Generate digits, use capital letters */
+ ch = s_mp_todigit(rem, radix, 0);
+
+ str[pos++] = ch;
+ }
+
+ /* Add - sign if original value was negative */
+ if(sgn == MP_NEG)
+ str[pos++] = '-';
+
+ /* Add trailing NUL to end the string */
+ str[pos--] = '\0';
+
+ /* Reverse the digits and sign indicator */
+ ix = 0;
+ while(ix < pos) {
+ char tmp = str[ix];
+
+ str[ix] = str[pos];
+ str[pos] = tmp;
+ ++ix;
+ --pos;
+ }
+
+ mp_clear(&tmp);
+ }
+
+ return MP_OKAY;
+
+} /* end mp_toradix() */
+
+/* }}} */
+
+/* {{{ mp_char2value(ch, r) */
+
+int mp_char2value(char ch, int r)
+{
+ return s_mp_tovalue(ch, r);
+
+} /* end mp_tovalue() */
+
+/* }}} */
+
+/* }}} */
+
+/* {{{ mp_strerror(ec) */
+
+/*
+ mp_strerror(ec)
+
+ Return a string describing the meaning of error code 'ec'. The
+ string returned is allocated in static memory, so the caller should
+ not attempt to modify or free the memory associated with this
+ string.
+ */
+const char *mp_strerror(mp_err ec)
+{
+ int aec = (ec < 0) ? -ec : ec;
+
+ /* Code values are negative, so the senses of these comparisons
+ are accurate */
+ if(ec < MP_LAST_CODE || ec > MP_OKAY) {
+ return mp_err_string[0]; /* unknown error code */
+ } else {
+ return mp_err_string[aec + 1];
+ }
+
+} /* end mp_strerror() */
+
+/* }}} */
+
+/*========================================================================*/
+/*------------------------------------------------------------------------*/
+/* Static function definitions (internal use only) */
+
+/* {{{ Memory management */
+
+/* {{{ s_mp_grow(mp, min) */
+
+/* Make sure there are at least 'min' digits allocated to mp */
+mp_err s_mp_grow(mp_int *mp, mp_size min)
+{
+ if(min > ALLOC(mp)) {
+ mp_digit *tmp;
+
+ /* Set min to next nearest default precision block size */
+ min = ((min + (s_mp_defprec - 1)) / s_mp_defprec) * s_mp_defprec;
+
+ if((tmp = s_mp_alloc(min, sizeof(mp_digit))) == NULL)
+ return MP_MEM;
+
+ s_mp_copy(DIGITS(mp), tmp, USED(mp));
+
+#if MP_CRYPTO
+ s_mp_setz(DIGITS(mp), ALLOC(mp));
+#endif
+ s_mp_free(DIGITS(mp));
+ DIGITS(mp) = tmp;
+ ALLOC(mp) = min;
+ }
+
+ return MP_OKAY;
+
+} /* end s_mp_grow() */
+
+/* }}} */
+
+/* {{{ s_mp_pad(mp, min) */
+
+/* Make sure the used size of mp is at least 'min', growing if needed */
+mp_err s_mp_pad(mp_int *mp, mp_size min)
+{
+ if(min > USED(mp)) {
+ mp_err res;
+
+ /* Make sure there is room to increase precision */
+ if(min > ALLOC(mp) && (res = s_mp_grow(mp, min)) != MP_OKAY)
+ return res;
+
+ /* Increase precision; should already be 0-filled */
+ USED(mp) = min;
+ }
+
+ return MP_OKAY;
+
+} /* end s_mp_pad() */
+
+/* }}} */
+
+/* {{{ s_mp_setz(dp, count) */
+
+#if MP_MACRO == 0
+/* Set 'count' digits pointed to by dp to be zeroes */
+void s_mp_setz(mp_digit *dp, mp_size count)
+{
+#if MP_MEMSET == 0
+ int ix;
+
+ for(ix = 0; ix < count; ix++)
+ dp[ix] = 0;
+#else
+ memset(dp, 0, count * sizeof(mp_digit));
+#endif
+
+} /* end s_mp_setz() */
+#endif
+
+/* }}} */
+
+/* {{{ s_mp_copy(sp, dp, count) */
+
+#if MP_MACRO == 0
+/* Copy 'count' digits from sp to dp */
+void s_mp_copy(mp_digit *sp, mp_digit *dp, mp_size count)
+{
+#if MP_MEMCPY == 0
+ int ix;
+
+ for(ix = 0; ix < count; ix++)
+ dp[ix] = sp[ix];
+#else
+ memcpy(dp, sp, count * sizeof(mp_digit));
+#endif
+
+} /* end s_mp_copy() */
+#endif
+
+/* }}} */
+
+/* {{{ s_mp_alloc(nb, ni) */
+
+#if MP_MACRO == 0
+/* Allocate ni records of nb bytes each, and return a pointer to that */
+void *s_mp_alloc(size_t nb, size_t ni)
+{
+ return calloc(nb, ni);
+
+} /* end s_mp_alloc() */
+#endif
+
+/* }}} */
+
+/* {{{ s_mp_free(ptr) */
+
+#if MP_MACRO == 0
+/* Free the memory pointed to by ptr */
+void s_mp_free(void *ptr)
+{
+ if(ptr)
+ free(ptr);
+
+} /* end s_mp_free() */
+#endif
+
+/* }}} */
+
+/* {{{ s_mp_clamp(mp) */
+
+/* Remove leading zeroes from the given value */
+void s_mp_clamp(mp_int *mp)
+{
+ mp_size du = USED(mp);
+ mp_digit *zp = DIGITS(mp) + du - 1;
+
+ while(du > 1 && !*zp--)
+ --du;
+
+ USED(mp) = du;
+
+} /* end s_mp_clamp() */
+
+
+/* }}} */
+
+/* {{{ s_mp_exch(a, b) */
+
+/* Exchange the data for a and b; (b, a) = (a, b) */
+void s_mp_exch(mp_int *a, mp_int *b)
+{
+ mp_int tmp;
+
+ tmp = *a;
+ *a = *b;
+ *b = tmp;
+
+} /* end s_mp_exch() */
+
+/* }}} */
+
+/* }}} */
+
+/* {{{ Arithmetic helpers */
+
+/* {{{ s_mp_lshd(mp, p) */
+
+/*
+ Shift mp leftward by p digits, growing if needed, and zero-filling
+ the in-shifted digits at the right end. This is a convenient
+ alternative to multiplication by powers of the radix
+ */
+
+mp_err s_mp_lshd(mp_int *mp, mp_size p)
+{
+ mp_err res;
+ mp_size pos;
+ mp_digit *dp;
+ int ix;
+
+ if(p == 0)
+ return MP_OKAY;
+
+ if((res = s_mp_pad(mp, USED(mp) + p)) != MP_OKAY)
+ return res;
+
+ pos = USED(mp) - 1;
+ dp = DIGITS(mp);
+
+ /* Shift all the significant figures over as needed */
+ for(ix = pos - p; ix >= 0; ix--)
+ dp[ix + p] = dp[ix];
+
+ /* Fill the bottom digits with zeroes */
+ for(ix = 0; ix < p; ix++)
+ dp[ix] = 0;
+
+ return MP_OKAY;
+
+} /* end s_mp_lshd() */
+
+/* }}} */
+
+/* {{{ s_mp_rshd(mp, p) */
+
+/*
+ Shift mp rightward by p digits. Maintains the invariant that
+ digits above the precision are all zero. Digits shifted off the
+ end are lost. Cannot fail.
+ */
+
+void s_mp_rshd(mp_int *mp, mp_size p)
+{
+ mp_size ix;
+ mp_digit *dp;
+
+ if(p == 0)
+ return;
+
+ /* Shortcut when all digits are to be shifted off */
+ if(p >= USED(mp)) {
+ s_mp_setz(DIGITS(mp), ALLOC(mp));
+ USED(mp) = 1;
+ SIGN(mp) = MP_ZPOS;
+ return;
+ }
+
+ /* Shift all the significant figures over as needed */
+ dp = DIGITS(mp);
+ for(ix = p; ix < USED(mp); ix++)
+ dp[ix - p] = dp[ix];
+
+ /* Fill the top digits with zeroes */
+ ix -= p;
+ while(ix < USED(mp))
+ dp[ix++] = 0;
+
+ /* Strip off any leading zeroes */
+ s_mp_clamp(mp);
+
+} /* end s_mp_rshd() */
+
+/* }}} */
+
+/* {{{ s_mp_div_2(mp) */
+
+/* Divide by two -- take advantage of radix properties to do it fast */
+void s_mp_div_2(mp_int *mp)
+{
+ s_mp_div_2d(mp, 1);
+
+} /* end s_mp_div_2() */
+
+/* }}} */
+
+/* {{{ s_mp_mul_2(mp) */
+
+mp_err s_mp_mul_2(mp_int *mp)
+{
+ int ix;
+ mp_digit kin = 0, kout, *dp = DIGITS(mp);
+ mp_err res;
+
+ /* Shift digits leftward by 1 bit */
+ for(ix = 0; ix < USED(mp); ix++) {
+ kout = (dp[ix] >> (DIGIT_BIT - 1)) & 1;
+ dp[ix] = (dp[ix] << 1) | kin;
+
+ kin = kout;
+ }
+
+ /* Deal with rollover from last digit */
+ if(kin) {
+ if(ix >= ALLOC(mp)) {
+ if((res = s_mp_grow(mp, ALLOC(mp) + 1)) != MP_OKAY)
+ return res;
+ dp = DIGITS(mp);
+ }
+
+ dp[ix] = kin;
+ USED(mp) += 1;
+ }
+
+ return MP_OKAY;
+
+} /* end s_mp_mul_2() */
+
+/* }}} */
+
+/* {{{ s_mp_mod_2d(mp, d) */
+
+/*
+ Remainder the integer by 2^d, where d is a number of bits. This
+ amounts to a bitwise AND of the value, and does not require the full
+ division code
+ */
+void s_mp_mod_2d(mp_int *mp, mp_digit d)
+{
+ unsigned int ndig = (d / DIGIT_BIT), nbit = (d % DIGIT_BIT);
+ unsigned int ix;
+ mp_digit dmask, *dp = DIGITS(mp);
+
+ if(ndig >= USED(mp))
+ return;
+
+ /* Flush all the bits above 2^d in its digit */
+ dmask = (1 << nbit) - 1;
+ dp[ndig] &= dmask;
+
+ /* Flush all digits above the one with 2^d in it */
+ for(ix = ndig + 1; ix < USED(mp); ix++)
+ dp[ix] = 0;
+
+ s_mp_clamp(mp);
+
+} /* end s_mp_mod_2d() */
+
+/* }}} */
+
+/* {{{ s_mp_mul_2d(mp, d) */
+
+/*
+ Multiply by the integer 2^d, where d is a number of bits. This
+ amounts to a bitwise shift of the value, and does not require the
+ full multiplication code.
+ */
+mp_err s_mp_mul_2d(mp_int *mp, mp_digit d)
+{
+ mp_err res;
+ mp_digit save, next, mask, *dp;
+ mp_size used;
+ int ix;
+
+ if((res = s_mp_lshd(mp, d / DIGIT_BIT)) != MP_OKAY)
+ return res;
+
+ dp = DIGITS(mp); used = USED(mp);
+ d %= DIGIT_BIT;
+
+ mask = (1 << d) - 1;
+
+ /* If the shift requires another digit, make sure we've got one to
+ work with */
+ if((dp[used - 1] >> (DIGIT_BIT - d)) & mask) {
+ if((res = s_mp_grow(mp, used + 1)) != MP_OKAY)
+ return res;
+ dp = DIGITS(mp);
+ }
+
+ /* Do the shifting... */
+ save = 0;
+ for(ix = 0; ix < used; ix++) {
+ next = (dp[ix] >> (DIGIT_BIT - d)) & mask;
+ dp[ix] = (dp[ix] << d) | save;
+ save = next;
+ }
+
+ /* If, at this point, we have a nonzero carryout into the next
+ digit, we'll increase the size by one digit, and store it...
+ */
+ if(save) {
+ dp[used] = save;
+ USED(mp) += 1;
+ }
+
+ s_mp_clamp(mp);
+ return MP_OKAY;
+
+} /* end s_mp_mul_2d() */
+
+/* }}} */
+
+/* {{{ s_mp_div_2d(mp, d) */
+
+/*
+ Divide the integer by 2^d, where d is a number of bits. This
+ amounts to a bitwise shift of the value, and does not require the
+ full division code (used in Barrett reduction, see below)
+ */
+void s_mp_div_2d(mp_int *mp, mp_digit d)
+{
+ int ix;
+ mp_digit save, next, mask, *dp = DIGITS(mp);
+
+ s_mp_rshd(mp, d / DIGIT_BIT);
+ d %= DIGIT_BIT;
+
+ mask = (1 << d) - 1;
+
+ save = 0;
+ for(ix = USED(mp) - 1; ix >= 0; ix--) {
+ next = dp[ix] & mask;
+ dp[ix] = (dp[ix] >> d) | (save << (DIGIT_BIT - d));
+ save = next;
+ }
+
+ s_mp_clamp(mp);
+
+} /* end s_mp_div_2d() */
+
+/* }}} */
+
+/* {{{ s_mp_norm(a, b) */
+
+/*
+ s_mp_norm(a, b)
+
+ Normalize a and b for division, where b is the divisor. In order
+ that we might make good guesses for quotient digits, we want the
+ leading digit of b to be at least half the radix, which we
+ accomplish by multiplying a and b by a constant. This constant is
+ returned (so that it can be divided back out of the remainder at the
+ end of the division process).
+
+ We multiply by the smallest power of 2 that gives us a leading digit
+ at least half the radix. By choosing a power of 2, we simplify the
+ multiplication and division steps to simple shifts.
+ */
+mp_digit s_mp_norm(mp_int *a, mp_int *b)
+{
+ mp_digit t, d = 0;
+
+ t = DIGIT(b, USED(b) - 1);
+ while(t < (RADIX / 2)) {
+ t <<= 1;
+ ++d;
+ }
+
+ if(d != 0) {
+ s_mp_mul_2d(a, d);
+ s_mp_mul_2d(b, d);
+ }
+
+ return d;
+
+} /* end s_mp_norm() */
+
+/* }}} */
+
+/* }}} */
+
+/* {{{ Primitive digit arithmetic */
+
+/* {{{ s_mp_add_d(mp, d) */
+
+/* Add d to |mp| in place */
+mp_err s_mp_add_d(mp_int *mp, mp_digit d) /* unsigned digit addition */
+{
+ mp_word w, k = 0;
+ mp_size ix = 1, used = USED(mp);
+ mp_digit *dp = DIGITS(mp);
+
+ w = dp[0] + d;
+ dp[0] = ACCUM(w);
+ k = CARRYOUT(w);
+
+ while(ix < used && k) {
+ w = dp[ix] + k;
+ dp[ix] = ACCUM(w);
+ k = CARRYOUT(w);
+ ++ix;
+ }
+
+ if(k != 0) {
+ mp_err res;
+
+ if((res = s_mp_pad(mp, USED(mp) + 1)) != MP_OKAY)
+ return res;
+
+ DIGIT(mp, ix) = k;
+ }
+
+ return MP_OKAY;
+
+} /* end s_mp_add_d() */
+
+/* }}} */
+
+/* {{{ s_mp_sub_d(mp, d) */
+
+/* Subtract d from |mp| in place, assumes |mp| > d */
+mp_err s_mp_sub_d(mp_int *mp, mp_digit d) /* unsigned digit subtract */
+{
+ mp_word w, b = 0;
+ mp_size ix = 1, used = USED(mp);
+ mp_digit *dp = DIGITS(mp);
+
+ /* Compute initial subtraction */
+ w = (RADIX + dp[0]) - d;
+ b = CARRYOUT(w) ? 0 : 1;
+ dp[0] = ACCUM(w);
+
+ /* Propagate borrows leftward */
+ while(b && ix < used) {
+ w = (RADIX + dp[ix]) - b;
+ b = CARRYOUT(w) ? 0 : 1;
+ dp[ix] = ACCUM(w);
+ ++ix;
+ }
+
+ /* Remove leading zeroes */
+ s_mp_clamp(mp);
+
+ /* If we have a borrow out, it's a violation of the input invariant */
+ if(b)
+ return MP_RANGE;
+ else
+ return MP_OKAY;
+
+} /* end s_mp_sub_d() */
+
+/* }}} */
+
+/* {{{ s_mp_mul_d(a, d) */
+
+/* Compute a = a * d, single digit multiplication */
+mp_err s_mp_mul_d(mp_int *a, mp_digit d)
+{
+ mp_word w, k = 0;
+ mp_size ix, max;
+ mp_err res;
+ mp_digit *dp = DIGITS(a);
+
+ /*
+ Single-digit multiplication will increase the precision of the
+ output by at most one digit. However, we can detect when this
+ will happen -- if the high-order digit of a, times d, gives a
+ two-digit result, then the precision of the result will increase;
+ otherwise it won't. We use this fact to avoid calling s_mp_pad()
+ unless absolutely necessary.
+ */
+ max = USED(a);
+ w = dp[max - 1] * d;
+ if(CARRYOUT(w) != 0) {
+ if((res = s_mp_pad(a, max + 1)) != MP_OKAY)
+ return res;
+ dp = DIGITS(a);
+ }
+
+ for(ix = 0; ix < max; ix++) {
+ w = (dp[ix] * d) + k;
+ dp[ix] = ACCUM(w);
+ k = CARRYOUT(w);
+ }
+
+ /* If there is a precision increase, take care of it here; the above
+ test guarantees we have enough storage to do this safely.
+ */
+ if(k) {
+ dp[max] = k;
+ USED(a) = max + 1;
+ }
+
+ s_mp_clamp(a);
+
+ return MP_OKAY;
+
+} /* end s_mp_mul_d() */
+
+/* }}} */
+
+/* {{{ s_mp_div_d(mp, d, r) */
+
+/*
+ s_mp_div_d(mp, d, r)
+
+ Compute the quotient mp = mp / d and remainder r = mp mod d, for a
+ single digit d. If r is null, the remainder will be discarded.
+ */
+
+mp_err s_mp_div_d(mp_int *mp, mp_digit d, mp_digit *r)
+{
+ mp_word w = 0, t;
+ mp_int quot;
+ mp_err res;
+ mp_digit *dp = DIGITS(mp), *qp;
+ int ix;
+
+ if(d == 0)
+ return MP_RANGE;
+
+ /* Make room for the quotient */
+ if((res = mp_init_size(&quot, USED(mp))) != MP_OKAY)
+ return res;
+
+ USED(&quot) = USED(mp); /* so clamping will work below */
+ qp = DIGITS(&quot);
+
+ /* Divide without subtraction */
+ for(ix = USED(mp) - 1; ix >= 0; ix--) {
+ w = (w << DIGIT_BIT) | dp[ix];
+
+ if(w >= d) {
+ t = w / d;
+ w = w % d;
+ } else {
+ t = 0;
+ }
+
+ qp[ix] = t;
+ }
+
+ /* Deliver the remainder, if desired */
+ if(r)
+ *r = w;
+
+ s_mp_clamp(&quot);
+ mp_exch(&quot, mp);
+ mp_clear(&quot);
+
+ return MP_OKAY;
+
+} /* end s_mp_div_d() */
+
+/* }}} */
+
+/* }}} */
+
+/* {{{ Primitive full arithmetic */
+
+/* {{{ s_mp_add(a, b) */
+
+/* Compute a = |a| + |b| */
+mp_err s_mp_add(mp_int *a, mp_int *b) /* magnitude addition */
+{
+ mp_word w = 0;
+ mp_digit *pa, *pb;
+ mp_size ix, used = USED(b);
+ mp_err res;
+
+ /* Make sure a has enough precision for the output value */
+ if((used > USED(a)) && (res = s_mp_pad(a, used)) != MP_OKAY)
+ return res;
+
+ /*
+ Add up all digits up to the precision of b. If b had initially
+ the same precision as a, or greater, we took care of it by the
+ padding step above, so there is no problem. If b had initially
+ less precision, we'll have to make sure the carry out is duly
+ propagated upward among the higher-order digits of the sum.
+ */
+ pa = DIGITS(a);
+ pb = DIGITS(b);
+ for(ix = 0; ix < used; ++ix) {
+ w += *pa + *pb++;
+ *pa++ = ACCUM(w);
+ w = CARRYOUT(w);
+ }
+
+ /* If we run out of 'b' digits before we're actually done, make
+ sure the carries get propagated upward...
+ */
+ used = USED(a);
+ while(w && ix < used) {
+ w += *pa;
+ *pa++ = ACCUM(w);
+ w = CARRYOUT(w);
+ ++ix;
+ }
+
+ /* If there's an overall carry out, increase precision and include
+ it. We could have done this initially, but why touch the memory
+ allocator unless we're sure we have to?
+ */
+ if(w) {
+ if((res = s_mp_pad(a, used + 1)) != MP_OKAY)
+ return res;
+
+ DIGIT(a, ix) = w; /* pa may not be valid after s_mp_pad() call */
+ }
+
+ return MP_OKAY;
+
+} /* end s_mp_add() */
+
+/* }}} */
+
+/* {{{ s_mp_sub(a, b) */
+
+/* Compute a = |a| - |b|, assumes |a| >= |b| */
+mp_err s_mp_sub(mp_int *a, mp_int *b) /* magnitude subtract */
+{
+ mp_word w = 0;
+ mp_digit *pa, *pb;
+ mp_size ix, used = USED(b);
+
+ /*
+ Subtract and propagate borrow. Up to the precision of b, this
+ accounts for the digits of b; after that, we just make sure the
+ carries get to the right place. This saves having to pad b out to
+ the precision of a just to make the loops work right...
+ */
+ pa = DIGITS(a);
+ pb = DIGITS(b);
+
+ for(ix = 0; ix < used; ++ix) {
+ w = (RADIX + *pa) - w - *pb++;
+ *pa++ = ACCUM(w);
+ w = CARRYOUT(w) ? 0 : 1;
+ }
+
+ used = USED(a);
+ while(ix < used) {
+ w = RADIX + *pa - w;
+ *pa++ = ACCUM(w);
+ w = CARRYOUT(w) ? 0 : 1;
+ ++ix;
+ }
+
+ /* Clobber any leading zeroes we created */
+ s_mp_clamp(a);
+
+ /*
+ If there was a borrow out, then |b| > |a| in violation
+ of our input invariant. We've already done the work,
+ but we'll at least complain about it...
+ */
+ if(w)
+ return MP_RANGE;
+ else
+ return MP_OKAY;
+
+} /* end s_mp_sub() */
+
+/* }}} */
+
+mp_err s_mp_reduce(mp_int *x, mp_int *m, mp_int *mu)
+{
+ mp_int q;
+ mp_err res;
+ mp_size um = USED(m);
+
+ if((res = mp_init_copy(&q, x)) != MP_OKAY)
+ return res;
+
+ s_mp_rshd(&q, um - 1); /* q1 = x / b^(k-1) */
+ s_mp_mul(&q, mu); /* q2 = q1 * mu */
+ s_mp_rshd(&q, um + 1); /* q3 = q2 / b^(k+1) */
+
+ /* x = x mod b^(k+1), quick (no division) */
+ s_mp_mod_2d(x, (mp_digit)(DIGIT_BIT * (um + 1)));
+
+ /* q = q * m mod b^(k+1), quick (no division), uses the short multiplier */
+#ifndef SHRT_MUL
+ s_mp_mul(&q, m);
+ s_mp_mod_2d(&q, (mp_digit)(DIGIT_BIT * (um + 1)));
+#else
+ s_mp_mul_dig(&q, m, um + 1);
+#endif
+
+ /* x = x - q */
+ if((res = mp_sub(x, &q, x)) != MP_OKAY)
+ goto CLEANUP;
+
+ /* If x < 0, add b^(k+1) to it */
+ if(mp_cmp_z(x) < 0) {
+ mp_set(&q, 1);
+ if((res = s_mp_lshd(&q, um + 1)) != MP_OKAY)
+ goto CLEANUP;
+ if((res = mp_add(x, &q, x)) != MP_OKAY)
+ goto CLEANUP;
+ }
+
+ /* Back off if it's too big */
+ while(mp_cmp(x, m) >= 0) {
+ if((res = s_mp_sub(x, m)) != MP_OKAY)
+ break;
+ }
+
+ CLEANUP:
+ mp_clear(&q);
+
+ return res;
+
+} /* end s_mp_reduce() */
+
+
+
+/* {{{ s_mp_mul(a, b) */
+
+/* Compute a = |a| * |b| */
+mp_err s_mp_mul(mp_int *a, mp_int *b)
+{
+ mp_word w, k = 0;
+ mp_int tmp;
+ mp_err res;
+ mp_size ix, jx, ua = USED(a), ub = USED(b);
+ mp_digit *pa, *pb, *pt, *pbt;
+
+ if((res = mp_init_size(&tmp, ua + ub)) != MP_OKAY)
+ return res;
+
+ /* This has the effect of left-padding with zeroes... */
+ USED(&tmp) = ua + ub;
+
+ /* We're going to need the base value each iteration */
+ pbt = DIGITS(&tmp);
+
+ /* Outer loop: Digits of b */
+
+ pb = DIGITS(b);
+ for(ix = 0; ix < ub; ++ix, ++pb) {
+ if(*pb == 0)
+ continue;
+
+ /* Inner product: Digits of a */
+ pa = DIGITS(a);
+ for(jx = 0; jx < ua; ++jx, ++pa) {
+ pt = pbt + ix + jx;
+ w = *pb * *pa + k + *pt;
+ *pt = ACCUM(w);
+ k = CARRYOUT(w);
+ }
+
+ pbt[ix + jx] = k;
+ k = 0;
+ }
+
+ s_mp_clamp(&tmp);
+ s_mp_exch(&tmp, a);
+
+ mp_clear(&tmp);
+
+ return MP_OKAY;
+
+} /* end s_mp_mul() */
+
+/* }}} */
+
+/* {{{ s_mp_kmul(a, b, out, len) */
+
+#if 0
+void s_mp_kmul(mp_digit *a, mp_digit *b, mp_digit *out, mp_size len)
+{
+ mp_word w, k = 0;
+ mp_size ix, jx;
+ mp_digit *pa, *pt;
+
+ for(ix = 0; ix < len; ++ix, ++b) {
+ if(*b == 0)
+ continue;
+
+ pa = a;
+ for(jx = 0; jx < len; ++jx, ++pa) {
+ pt = out + ix + jx;
+ w = *b * *pa + k + *pt;
+ *pt = ACCUM(w);
+ k = CARRYOUT(w);
+ }
+
+ out[ix + jx] = k;
+ k = 0;
+ }
+
+} /* end s_mp_kmul() */
+#endif
+
+/* }}} */
+
+/* {{{ s_mp_sqr(a) */
+
+/*
+ Computes the square of a, in place. This can be done more
+ efficiently than a general multiplication, because many of the
+ computation steps are redundant when squaring. The inner product
+ step is a bit more complicated, but we save a fair number of
+ iterations of the multiplication loop.
+ */
+#if MP_SQUARE
+mp_err s_mp_sqr(mp_int *a)
+{
+ mp_word w, k = 0;
+ mp_int tmp;
+ mp_err res;
+ mp_size ix, jx, kx, used = USED(a);
+ mp_digit *pa1, *pa2, *pt, *pbt;
+
+ if((res = mp_init_size(&tmp, 2 * used)) != MP_OKAY)
+ return res;
+
+ /* Left-pad with zeroes */
+ USED(&tmp) = 2 * used;
+
+ /* We need the base value each time through the loop */
+ pbt = DIGITS(&tmp);
+
+ pa1 = DIGITS(a);
+ for(ix = 0; ix < used; ++ix, ++pa1) {
+ if(*pa1 == 0)
+ continue;
+
+ w = DIGIT(&tmp, ix + ix) + (*pa1 * *pa1);
+
+ pbt[ix + ix] = ACCUM(w);
+ k = CARRYOUT(w);
+
+ /*
+ The inner product is computed as:
+
+ (C, S) = t[i,j] + 2 a[i] a[j] + C
+
+ This can overflow what can be represented in an mp_word, and
+ since C arithmetic does not provide any way to check for
+ overflow, we have to check explicitly for overflow conditions
+ before they happen.
+ */
+ for(jx = ix + 1, pa2 = DIGITS(a) + jx; jx < used; ++jx, ++pa2) {
+ mp_word u = 0, v;
+
+ /* Store this in a temporary to avoid indirections later */
+ pt = pbt + ix + jx;
+
+ /* Compute the multiplicative step */
+ w = *pa1 * *pa2;
+
+ /* If w is more than half MP_WORD_MAX, the doubling will
+ overflow, and we need to record a carry out into the next
+ word */
+ u = (w >> (MP_WORD_BIT - 1)) & 1;
+
+ /* Double what we've got, overflow will be ignored as defined
+ for C arithmetic (we've already noted if it is to occur)
+ */
+ w *= 2;
+
+ /* Compute the additive step */
+ v = *pt + k;
+
+ /* If we do not already have an overflow carry, check to see
+ if the addition will cause one, and set the carry out if so
+ */
+ u |= ((MP_WORD_MAX - v) < w);
+
+ /* Add in the rest, again ignoring overflow */
+ w += v;
+
+ /* Set the i,j digit of the output */
+ *pt = ACCUM(w);
+
+ /* Save carry information for the next iteration of the loop.
+ This is why k must be an mp_word, instead of an mp_digit */
+ k = CARRYOUT(w) | (u << DIGIT_BIT);
+
+ } /* for(jx ...) */
+
+ /* Set the last digit in the cycle and reset the carry */
+ k = DIGIT(&tmp, ix + jx) + k;
+ pbt[ix + jx] = ACCUM(k);
+ k = CARRYOUT(k);
+
+ /* If we are carrying out, propagate the carry to the next digit
+ in the output. This may cascade, so we have to be somewhat
+ circumspect -- but we will have enough precision in the output
+ that we won't overflow
+ */
+ kx = 1;
+ while(k) {
+ k = pbt[ix + jx + kx] + 1;
+ pbt[ix + jx + kx] = ACCUM(k);
+ k = CARRYOUT(k);
+ ++kx;
+ }
+ } /* for(ix ...) */
+
+ s_mp_clamp(&tmp);
+ s_mp_exch(&tmp, a);
+
+ mp_clear(&tmp);
+
+ return MP_OKAY;
+
+} /* end s_mp_sqr() */
+#endif
+
+/* }}} */
+
+/* {{{ s_mp_div(a, b) */
+
+/*
+ s_mp_div(a, b)
+
+ Compute a = a / b and b = a mod b. Assumes b > a.
+ */
+
+mp_err s_mp_div(mp_int *a, mp_int *b)
+{
+ mp_int quot, rem, t;
+ mp_word q;
+ mp_err res;
+ mp_digit d;
+ int ix;
+
+ if(mp_cmp_z(b) == 0)
+ return MP_RANGE;
+
+ /* Shortcut if b is power of two */
+ if((ix = s_mp_ispow2(b)) >= 0) {
+ mp_copy(a, b); /* need this for remainder */
+ s_mp_div_2d(a, (mp_digit)ix);
+ s_mp_mod_2d(b, (mp_digit)ix);
+
+ return MP_OKAY;
+ }
+
+ /* Allocate space to store the quotient */
+ if((res = mp_init_size(&quot, USED(a))) != MP_OKAY)
+ return res;
+
+ /* A working temporary for division */
+ if((res = mp_init_size(&t, USED(a))) != MP_OKAY)
+ goto T;
+
+ /* Allocate space for the remainder */
+ if((res = mp_init_size(&rem, USED(a))) != MP_OKAY)
+ goto REM;
+
+ /* Normalize to optimize guessing */
+ d = s_mp_norm(a, b);
+
+ /* Perform the division itself...woo! */
+ ix = USED(a) - 1;
+
+ while(ix >= 0) {
+ /* Find a partial substring of a which is at least b */
+ while(s_mp_cmp(&rem, b) < 0 && ix >= 0) {
+ if((res = s_mp_lshd(&rem, 1)) != MP_OKAY)
+ goto CLEANUP;
+
+ if((res = s_mp_lshd(&quot, 1)) != MP_OKAY)
+ goto CLEANUP;
+
+ DIGIT(&rem, 0) = DIGIT(a, ix);
+ s_mp_clamp(&rem);
+ --ix;
+ }
+
+ /* If we didn't find one, we're finished dividing */
+ if(s_mp_cmp(&rem, b) < 0)
+ break;
+
+ /* Compute a guess for the next quotient digit */
+ q = DIGIT(&rem, USED(&rem) - 1);
+ if(q <= DIGIT(b, USED(b) - 1) && USED(&rem) > 1)
+ q = (q << DIGIT_BIT) | DIGIT(&rem, USED(&rem) - 2);
+
+ q /= DIGIT(b, USED(b) - 1);
+
+ /* The guess can be as much as RADIX + 1 */
+ if(q >= RADIX)
+ q = RADIX - 1;
+
+ /* See what that multiplies out to */
+ mp_copy(b, &t);
+ if((res = s_mp_mul_d(&t, q)) != MP_OKAY)
+ goto CLEANUP;
+
+ /*
+ If it's too big, back it off. We should not have to do this
+ more than once, or, in rare cases, twice. Knuth describes a
+ method by which this could be reduced to a maximum of once, but
+ I didn't implement that here.
+ */
+ while(s_mp_cmp(&t, &rem) > 0) {
+ --q;
+ s_mp_sub(&t, b);
+ }
+
+ /* At this point, q should be the right next digit */
+ if((res = s_mp_sub(&rem, &t)) != MP_OKAY)
+ goto CLEANUP;
+
+ /*
+ Include the digit in the quotient. We allocated enough memory
+ for any quotient we could ever possibly get, so we should not
+ have to check for failures here
+ */
+ DIGIT(&quot, 0) = q;
+ }
+
+ /* Denormalize remainder */
+ if(d != 0)
+ s_mp_div_2d(&rem, d);
+
+ s_mp_clamp(&quot);
+ s_mp_clamp(&rem);
+
+ /* Copy quotient back to output */
+ s_mp_exch(&quot, a);
+
+ /* Copy remainder back to output */
+ s_mp_exch(&rem, b);
+
+CLEANUP:
+ mp_clear(&rem);
+REM:
+ mp_clear(&t);
+T:
+ mp_clear(&quot);
+
+ return res;
+
+} /* end s_mp_div() */
+
+/* }}} */
+
+/* {{{ s_mp_2expt(a, k) */
+
+mp_err s_mp_2expt(mp_int *a, mp_digit k)
+{
+ mp_err res;
+ mp_size dig, bit;
+
+ dig = k / DIGIT_BIT;
+ bit = k % DIGIT_BIT;
+
+ mp_zero(a);
+ if((res = s_mp_pad(a, dig + 1)) != MP_OKAY)
+ return res;
+
+ DIGIT(a, dig) |= (1 << bit);
+
+ return MP_OKAY;
+
+} /* end s_mp_2expt() */
+
+/* }}} */
+
+
+/* }}} */
+
+/* }}} */
+
+/* {{{ Primitive comparisons */
+
+/* {{{ s_mp_cmp(a, b) */
+
+/* Compare |a| <=> |b|, return 0 if equal, <0 if a<b, >0 if a>b */
+int s_mp_cmp(mp_int *a, mp_int *b)
+{
+ mp_size ua = USED(a), ub = USED(b);
+
+ if(ua > ub)
+ return MP_GT;
+ else if(ua < ub)
+ return MP_LT;
+ else {
+ int ix = ua - 1;
+ mp_digit *ap = DIGITS(a) + ix, *bp = DIGITS(b) + ix;
+
+ while(ix >= 0) {
+ if(*ap > *bp)
+ return MP_GT;
+ else if(*ap < *bp)
+ return MP_LT;
+
+ --ap; --bp; --ix;
+ }
+
+ return MP_EQ;
+ }
+
+} /* end s_mp_cmp() */
+
+/* }}} */
+
+/* {{{ s_mp_cmp_d(a, d) */
+
+/* Compare |a| <=> d, return 0 if equal, <0 if a<d, >0 if a>d */
+int s_mp_cmp_d(mp_int *a, mp_digit d)
+{
+ mp_size ua = USED(a);
+ mp_digit *ap = DIGITS(a);
+
+ if(ua > 1)
+ return MP_GT;
+
+ if(*ap < d)
+ return MP_LT;
+ else if(*ap > d)
+ return MP_GT;
+ else
+ return MP_EQ;
+
+} /* end s_mp_cmp_d() */
+
+/* }}} */
+
+/* {{{ s_mp_ispow2(v) */
+
+/*
+ Returns -1 if the value is not a power of two; otherwise, it returns
+ k such that v = 2^k, i.e. lg(v).
+ */
+int s_mp_ispow2(mp_int *v)
+{
+ mp_digit d, *dp;
+ mp_size uv = USED(v);
+ int extra = 0, ix;
+
+ d = DIGIT(v, uv - 1); /* most significant digit of v */
+
+ while(d && ((d & 1) == 0)) {
+ d >>= 1;
+ ++extra;
+ }
+
+ if(d == 1) {
+ ix = uv - 2;
+ dp = DIGITS(v) + ix;
+
+ while(ix >= 0) {
+ if(*dp)
+ return -1; /* not a power of two */
+
+ --dp; --ix;
+ }
+
+ return ((uv - 1) * DIGIT_BIT) + extra;
+ }
+
+ return -1;
+
+} /* end s_mp_ispow2() */
+
+/* }}} */
+
+/* {{{ s_mp_ispow2d(d) */
+
+int s_mp_ispow2d(mp_digit d)
+{
+ int pow = 0;
+
+ while((d & 1) == 0) {
+ ++pow; d >>= 1;
+ }
+
+ if(d == 1)
+ return pow;
+
+ return -1;
+
+} /* end s_mp_ispow2d() */
+
+/* }}} */
+
+/* }}} */
+
+/* {{{ Primitive I/O helpers */
+
+/* {{{ s_mp_tovalue(ch, r) */
+
+/*
+ Convert the given character to its digit value, in the given radix.
+ If the given character is not understood in the given radix, -1 is
+ returned. Otherwise the digit's numeric value is returned.
+
+ The results will be odd if you use a radix < 2 or > 62, you are
+ expected to know what you're up to.
+ */
+int s_mp_tovalue(char ch, int r)
+{
+ int val, xch;
+
+ if(r > 36)
+ xch = ch;
+ else
+ xch = toupper(ch);
+
+ if(isdigit(xch))
+ val = xch - '0';
+ else if(isupper(xch))
+ val = xch - 'A' + 10;
+ else if(islower(xch))
+ val = xch - 'a' + 36;
+ else if(xch == '+')
+ val = 62;
+ else if(xch == '/')
+ val = 63;
+ else
+ return -1;
+
+ if(val < 0 || val >= r)
+ return -1;
+
+ return val;
+
+} /* end s_mp_tovalue() */
+
+/* }}} */
+
+/* {{{ s_mp_todigit(val, r, low) */
+
+/*
+ Convert val to a radix-r digit, if possible. If val is out of range
+ for r, returns zero. Otherwise, returns an ASCII character denoting
+ the value in the given radix.
+
+ The results may be odd if you use a radix < 2 or > 64, you are
+ expected to know what you're doing.
+ */
+
+char s_mp_todigit(int val, int r, int low)
+{
+ char ch;
+
+ if(val < 0 || val >= r)
+ return 0;
+
+ ch = s_dmap_1[val];
+
+ if(r <= 36 && low)
+ ch = tolower(ch);
+
+ return ch;
+
+} /* end s_mp_todigit() */
+
+/* }}} */
+
+/* {{{ s_mp_outlen(bits, radix) */
+
+/*
+ Return an estimate for how long a string is needed to hold a radix
+ r representation of a number with 'bits' significant bits.
+
+ Does not include space for a sign or a NUL terminator.
+ */
+int s_mp_outlen(int bits, int r)
+{
+ return (int)((double)bits * LOG_V_2(r));
+
+} /* end s_mp_outlen() */
+
+/* }}} */
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* HERE THERE BE DRAGONS */
+/* crc==4242132123, version==2, Sat Feb 02 06:43:52 2002 */
diff --git a/libtommath/mtest/mpi.h b/libtommath/mtest/mpi.h
new file mode 100644
index 0000000..b7a8cb5
--- /dev/null
+++ b/libtommath/mtest/mpi.h
@@ -0,0 +1,227 @@
+/*
+ mpi.h
+
+ by Michael J. Fromberger <sting@linguist.dartmouth.edu>
+ Copyright (C) 1998 Michael J. Fromberger, All Rights Reserved
+
+ Arbitrary precision integer arithmetic library
+
+ $Id: mpi.h,v 1.1.1.1 2005/01/19 22:41:29 kennykb Exp $
+ */
+
+#ifndef _H_MPI_
+#define _H_MPI_
+
+#include "mpi-config.h"
+
+#define MP_LT -1
+#define MP_EQ 0
+#define MP_GT 1
+
+#if MP_DEBUG
+#undef MP_IOFUNC
+#define MP_IOFUNC 1
+#endif
+
+#if MP_IOFUNC
+#include <stdio.h>
+#include <ctype.h>
+#endif
+
+#include <limits.h>
+
+#define MP_NEG 1
+#define MP_ZPOS 0
+
+/* Included for compatibility... */
+#define NEG MP_NEG
+#define ZPOS MP_ZPOS
+
+#define MP_OKAY 0 /* no error, all is well */
+#define MP_YES 0 /* yes (boolean result) */
+#define MP_NO -1 /* no (boolean result) */
+#define MP_MEM -2 /* out of memory */
+#define MP_RANGE -3 /* argument out of range */
+#define MP_BADARG -4 /* invalid parameter */
+#define MP_UNDEF -5 /* answer is undefined */
+#define MP_LAST_CODE MP_UNDEF
+
+#include "mpi-types.h"
+
+/* Included for compatibility... */
+#define DIGIT_BIT MP_DIGIT_BIT
+#define DIGIT_MAX MP_DIGIT_MAX
+
+/* Macros for accessing the mp_int internals */
+#define SIGN(MP) ((MP)->sign)
+#define USED(MP) ((MP)->used)
+#define ALLOC(MP) ((MP)->alloc)
+#define DIGITS(MP) ((MP)->dp)
+#define DIGIT(MP,N) (MP)->dp[(N)]
+
+#if MP_ARGCHK == 1
+#define ARGCHK(X,Y) {if(!(X)){return (Y);}}
+#elif MP_ARGCHK == 2
+#include <assert.h>
+#define ARGCHK(X,Y) assert(X)
+#else
+#define ARGCHK(X,Y) /* */
+#endif
+
+/* This defines the maximum I/O base (minimum is 2) */
+#define MAX_RADIX 64
+
+typedef struct {
+ mp_sign sign; /* sign of this quantity */
+ mp_size alloc; /* how many digits allocated */
+ mp_size used; /* how many digits used */
+ mp_digit *dp; /* the digits themselves */
+} mp_int;
+
+/*------------------------------------------------------------------------*/
+/* Default precision */
+
+unsigned int mp_get_prec(void);
+void mp_set_prec(unsigned int prec);
+
+/*------------------------------------------------------------------------*/
+/* Memory management */
+
+mp_err mp_init(mp_int *mp);
+mp_err mp_init_array(mp_int mp[], int count);
+mp_err mp_init_size(mp_int *mp, mp_size prec);
+mp_err mp_init_copy(mp_int *mp, mp_int *from);
+mp_err mp_copy(mp_int *from, mp_int *to);
+void mp_exch(mp_int *mp1, mp_int *mp2);
+void mp_clear(mp_int *mp);
+void mp_clear_array(mp_int mp[], int count);
+void mp_zero(mp_int *mp);
+void mp_set(mp_int *mp, mp_digit d);
+mp_err mp_set_int(mp_int *mp, long z);
+mp_err mp_shrink(mp_int *a);
+
+
+/*------------------------------------------------------------------------*/
+/* Single digit arithmetic */
+
+mp_err mp_add_d(mp_int *a, mp_digit d, mp_int *b);
+mp_err mp_sub_d(mp_int *a, mp_digit d, mp_int *b);
+mp_err mp_mul_d(mp_int *a, mp_digit d, mp_int *b);
+mp_err mp_mul_2(mp_int *a, mp_int *c);
+mp_err mp_div_d(mp_int *a, mp_digit d, mp_int *q, mp_digit *r);
+mp_err mp_div_2(mp_int *a, mp_int *c);
+mp_err mp_expt_d(mp_int *a, mp_digit d, mp_int *c);
+
+/*------------------------------------------------------------------------*/
+/* Sign manipulations */
+
+mp_err mp_abs(mp_int *a, mp_int *b);
+mp_err mp_neg(mp_int *a, mp_int *b);
+
+/*------------------------------------------------------------------------*/
+/* Full arithmetic */
+
+mp_err mp_add(mp_int *a, mp_int *b, mp_int *c);
+mp_err mp_sub(mp_int *a, mp_int *b, mp_int *c);
+mp_err mp_mul(mp_int *a, mp_int *b, mp_int *c);
+mp_err mp_mul_2d(mp_int *a, mp_digit d, mp_int *c);
+#if MP_SQUARE
+mp_err mp_sqr(mp_int *a, mp_int *b);
+#else
+#define mp_sqr(a, b) mp_mul(a, a, b)
+#endif
+mp_err mp_div(mp_int *a, mp_int *b, mp_int *q, mp_int *r);
+mp_err mp_div_2d(mp_int *a, mp_digit d, mp_int *q, mp_int *r);
+mp_err mp_expt(mp_int *a, mp_int *b, mp_int *c);
+mp_err mp_2expt(mp_int *a, mp_digit k);
+mp_err mp_sqrt(mp_int *a, mp_int *b);
+
+/*------------------------------------------------------------------------*/
+/* Modular arithmetic */
+
+#if MP_MODARITH
+mp_err mp_mod(mp_int *a, mp_int *m, mp_int *c);
+mp_err mp_mod_d(mp_int *a, mp_digit d, mp_digit *c);
+mp_err mp_addmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c);
+mp_err mp_submod(mp_int *a, mp_int *b, mp_int *m, mp_int *c);
+mp_err mp_mulmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c);
+#if MP_SQUARE
+mp_err mp_sqrmod(mp_int *a, mp_int *m, mp_int *c);
+#else
+#define mp_sqrmod(a, m, c) mp_mulmod(a, a, m, c)
+#endif
+mp_err mp_exptmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c);
+mp_err mp_exptmod_d(mp_int *a, mp_digit d, mp_int *m, mp_int *c);
+#endif /* MP_MODARITH */
+
+/*------------------------------------------------------------------------*/
+/* Comparisons */
+
+int mp_cmp_z(mp_int *a);
+int mp_cmp_d(mp_int *a, mp_digit d);
+int mp_cmp(mp_int *a, mp_int *b);
+int mp_cmp_mag(mp_int *a, mp_int *b);
+int mp_cmp_int(mp_int *a, long z);
+int mp_isodd(mp_int *a);
+int mp_iseven(mp_int *a);
+
+/*------------------------------------------------------------------------*/
+/* Number theoretic */
+
+#if MP_NUMTH
+mp_err mp_gcd(mp_int *a, mp_int *b, mp_int *c);
+mp_err mp_lcm(mp_int *a, mp_int *b, mp_int *c);
+mp_err mp_xgcd(mp_int *a, mp_int *b, mp_int *g, mp_int *x, mp_int *y);
+mp_err mp_invmod(mp_int *a, mp_int *m, mp_int *c);
+#endif /* end MP_NUMTH */
+
+/*------------------------------------------------------------------------*/
+/* Input and output */
+
+#if MP_IOFUNC
+void mp_print(mp_int *mp, FILE *ofp);
+#endif /* end MP_IOFUNC */
+
+/*------------------------------------------------------------------------*/
+/* Base conversion */
+
+#define BITS 1
+#define BYTES CHAR_BIT
+
+mp_err mp_read_signed_bin(mp_int *mp, unsigned char *str, int len);
+int mp_signed_bin_size(mp_int *mp);
+mp_err mp_to_signed_bin(mp_int *mp, unsigned char *str);
+
+mp_err mp_read_unsigned_bin(mp_int *mp, unsigned char *str, int len);
+int mp_unsigned_bin_size(mp_int *mp);
+mp_err mp_to_unsigned_bin(mp_int *mp, unsigned char *str);
+
+int mp_count_bits(mp_int *mp);
+
+#if MP_COMPAT_MACROS
+#define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
+#define mp_raw_size(mp) mp_signed_bin_size(mp)
+#define mp_toraw(mp, str) mp_to_signed_bin((mp), (str))
+#define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
+#define mp_mag_size(mp) mp_unsigned_bin_size(mp)
+#define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str))
+#endif
+
+mp_err mp_read_radix(mp_int *mp, unsigned char *str, int radix);
+int mp_radix_size(mp_int *mp, int radix);
+int mp_value_radix_size(int num, int qty, int radix);
+mp_err mp_toradix(mp_int *mp, unsigned char *str, int radix);
+
+int mp_char2value(char ch, int r);
+
+#define mp_tobinary(M, S) mp_toradix((M), (S), 2)
+#define mp_tooctal(M, S) mp_toradix((M), (S), 8)
+#define mp_todecimal(M, S) mp_toradix((M), (S), 10)
+#define mp_tohex(M, S) mp_toradix((M), (S), 16)
+
+/*------------------------------------------------------------------------*/
+/* Error strings */
+
+const char *mp_strerror(mp_err ec);
+
+#endif /* end _H_MPI_ */
diff --git a/libtommath/mtest/mtest.c b/libtommath/mtest/mtest.c
new file mode 100644
index 0000000..d46f456
--- /dev/null
+++ b/libtommath/mtest/mtest.c
@@ -0,0 +1,304 @@
+/* makes a bignum test harness with NUM tests per operation
+ *
+ * the output is made in the following format [one parameter per line]
+
+operation
+operand1
+operand2
+[... operandN]
+result1
+result2
+[... resultN]
+
+So for example "a * b mod n" would be
+
+mulmod
+a
+b
+n
+a*b mod n
+
+e.g. if a=3, b=4 n=11 then
+
+mulmod
+3
+4
+11
+1
+
+ */
+
+#ifdef MP_8BIT
+#define THE_MASK 127
+#else
+#define THE_MASK 32767
+#endif
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <time.h>
+#include "mpi.c"
+
+FILE *rng;
+
+void rand_num(mp_int *a)
+{
+ int n, size;
+ unsigned char buf[2048];
+
+ size = 1 + ((fgetc(rng)<<8) + fgetc(rng)) % 101;
+ buf[0] = (fgetc(rng)&1)?1:0;
+ fread(buf+1, 1, size, rng);
+ while (buf[1] == 0) buf[1] = fgetc(rng);
+ mp_read_raw(a, buf, 1+size);
+}
+
+void rand_num2(mp_int *a)
+{
+ int n, size;
+ unsigned char buf[2048];
+
+ size = 10 + ((fgetc(rng)<<8) + fgetc(rng)) % 101;
+ buf[0] = (fgetc(rng)&1)?1:0;
+ fread(buf+1, 1, size, rng);
+ while (buf[1] == 0) buf[1] = fgetc(rng);
+ mp_read_raw(a, buf, 1+size);
+}
+
+#define mp_to64(a, b) mp_toradix(a, b, 64)
+
+int main(void)
+{
+ int n, tmp;
+ mp_int a, b, c, d, e;
+ clock_t t1;
+ char buf[4096];
+
+ mp_init(&a);
+ mp_init(&b);
+ mp_init(&c);
+ mp_init(&d);
+ mp_init(&e);
+
+
+ /* initial (2^n - 1)^2 testing, makes sure the comba multiplier works [it has the new carry code] */
+/*
+ mp_set(&a, 1);
+ for (n = 1; n < 8192; n++) {
+ mp_mul(&a, &a, &c);
+ printf("mul\n");
+ mp_to64(&a, buf);
+ printf("%s\n%s\n", buf, buf);
+ mp_to64(&c, buf);
+ printf("%s\n", buf);
+
+ mp_add_d(&a, 1, &a);
+ mp_mul_2(&a, &a);
+ mp_sub_d(&a, 1, &a);
+ }
+*/
+
+ rng = fopen("/dev/urandom", "rb");
+ if (rng == NULL) {
+ rng = fopen("/dev/random", "rb");
+ if (rng == NULL) {
+ fprintf(stderr, "\nWarning: stdin used as random source\n\n");
+ rng = stdin;
+ }
+ }
+
+ t1 = clock();
+ for (;;) {
+#if 0
+ if (clock() - t1 > CLOCKS_PER_SEC) {
+ sleep(2);
+ t1 = clock();
+ }
+#endif
+ n = fgetc(rng) % 15;
+
+ if (n == 0) {
+ /* add tests */
+ rand_num(&a);
+ rand_num(&b);
+ mp_add(&a, &b, &c);
+ printf("add\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ mp_to64(&c, buf);
+ printf("%s\n", buf);
+ } else if (n == 1) {
+ /* sub tests */
+ rand_num(&a);
+ rand_num(&b);
+ mp_sub(&a, &b, &c);
+ printf("sub\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ mp_to64(&c, buf);
+ printf("%s\n", buf);
+ } else if (n == 2) {
+ /* mul tests */
+ rand_num(&a);
+ rand_num(&b);
+ mp_mul(&a, &b, &c);
+ printf("mul\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ mp_to64(&c, buf);
+ printf("%s\n", buf);
+ } else if (n == 3) {
+ /* div tests */
+ rand_num(&a);
+ rand_num(&b);
+ mp_div(&a, &b, &c, &d);
+ printf("div\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ mp_to64(&c, buf);
+ printf("%s\n", buf);
+ mp_to64(&d, buf);
+ printf("%s\n", buf);
+ } else if (n == 4) {
+ /* sqr tests */
+ rand_num(&a);
+ mp_sqr(&a, &b);
+ printf("sqr\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ } else if (n == 5) {
+ /* mul_2d test */
+ rand_num(&a);
+ mp_copy(&a, &b);
+ n = fgetc(rng) & 63;
+ mp_mul_2d(&b, n, &b);
+ mp_to64(&a, buf);
+ printf("mul2d\n");
+ printf("%s\n", buf);
+ printf("%d\n", n);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ } else if (n == 6) {
+ /* div_2d test */
+ rand_num(&a);
+ mp_copy(&a, &b);
+ n = fgetc(rng) & 63;
+ mp_div_2d(&b, n, &b, NULL);
+ mp_to64(&a, buf);
+ printf("div2d\n");
+ printf("%s\n", buf);
+ printf("%d\n", n);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ } else if (n == 7) {
+ /* gcd test */
+ rand_num(&a);
+ rand_num(&b);
+ a.sign = MP_ZPOS;
+ b.sign = MP_ZPOS;
+ mp_gcd(&a, &b, &c);
+ printf("gcd\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ mp_to64(&c, buf);
+ printf("%s\n", buf);
+ } else if (n == 8) {
+ /* lcm test */
+ rand_num(&a);
+ rand_num(&b);
+ a.sign = MP_ZPOS;
+ b.sign = MP_ZPOS;
+ mp_lcm(&a, &b, &c);
+ printf("lcm\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ mp_to64(&c, buf);
+ printf("%s\n", buf);
+ } else if (n == 9) {
+ /* exptmod test */
+ rand_num2(&a);
+ rand_num2(&b);
+ rand_num2(&c);
+// if (c.dp[0]&1) mp_add_d(&c, 1, &c);
+ a.sign = b.sign = c.sign = 0;
+ mp_exptmod(&a, &b, &c, &d);
+ printf("expt\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ mp_to64(&c, buf);
+ printf("%s\n", buf);
+ mp_to64(&d, buf);
+ printf("%s\n", buf);
+ } else if (n == 10) {
+ /* invmod test */
+ rand_num2(&a);
+ rand_num2(&b);
+ b.sign = MP_ZPOS;
+ a.sign = MP_ZPOS;
+ mp_gcd(&a, &b, &c);
+ if (mp_cmp_d(&c, 1) != 0) continue;
+ if (mp_cmp_d(&b, 1) == 0) continue;
+ mp_invmod(&a, &b, &c);
+ printf("invmod\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ mp_to64(&c, buf);
+ printf("%s\n", buf);
+ } else if (n == 11) {
+ rand_num(&a);
+ mp_mul_2(&a, &a);
+ mp_div_2(&a, &b);
+ printf("div2\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ } else if (n == 12) {
+ rand_num2(&a);
+ mp_mul_2(&a, &b);
+ printf("mul2\n");
+ mp_to64(&a, buf);
+ printf("%s\n", buf);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ } else if (n == 13) {
+ rand_num2(&a);
+ tmp = abs(rand()) & THE_MASK;
+ mp_add_d(&a, tmp, &b);
+ printf("add_d\n");
+ mp_to64(&a, buf);
+ printf("%s\n%d\n", buf, tmp);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ } else if (n == 14) {
+ rand_num2(&a);
+ tmp = abs(rand()) & THE_MASK;
+ mp_sub_d(&a, tmp, &b);
+ printf("sub_d\n");
+ mp_to64(&a, buf);
+ printf("%s\n%d\n", buf, tmp);
+ mp_to64(&b, buf);
+ printf("%s\n", buf);
+ }
+ }
+ fclose(rng);
+ return 0;
+}
generated by cgit v0.12 at 2024-11-14 18:19:53 (GMT)