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openssl1.0/crypto/bn/bn_mul.c

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Imported Upstream version 1.0.2s
2019-08-09 10:00:55 +02:00
/* crypto/bn/bn_mul.c */
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
* All rights reserved.
*
* This package is an SSL implementation written
* by Eric Young (eay@cryptsoft.com).
* The implementation was written so as to conform with Netscapes SSL.
*
* This library is free for commercial and non-commercial use as long as
* the following conditions are aheared to. The following conditions
* apply to all code found in this distribution, be it the RC4, RSA,
* lhash, DES, etc., code; not just the SSL code. The SSL documentation
* included with this distribution is covered by the same copyright terms
* except that the holder is Tim Hudson (tjh@cryptsoft.com).
*
* Copyright remains Eric Young's, and as such any Copyright notices in
* the code are not to be removed.
* If this package is used in a product, Eric Young should be given attribution
* as the author of the parts of the library used.
* This can be in the form of a textual message at program startup or
* in documentation (online or textual) provided with the package.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* "This product includes cryptographic software written by
* Eric Young (eay@cryptsoft.com)"
* The word 'cryptographic' can be left out if the rouines from the library
* being used are not cryptographic related :-).
* 4. If you include any Windows specific code (or a derivative thereof) from
* the apps directory (application code) you must include an acknowledgement:
* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
*
* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* The licence and distribution terms for any publically available version or
* derivative of this code cannot be changed. i.e. this code cannot simply be
* copied and put under another distribution licence
* [including the GNU Public Licence.]
*/
#ifndef BN_DEBUG
# undef NDEBUG /* avoid conflicting definitions */
# define NDEBUG
#endif
#include <stdio.h>
#include <assert.h>
#include "cryptlib.h"
#include "bn_lcl.h"
#if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS)
/*
* Here follows specialised variants of bn_add_words() and bn_sub_words().
* They have the property performing operations on arrays of different sizes.
* The sizes of those arrays is expressed through cl, which is the common
* length ( basicall, min(len(a),len(b)) ), and dl, which is the delta
* between the two lengths, calculated as len(a)-len(b). All lengths are the
* number of BN_ULONGs... For the operations that require a result array as
* parameter, it must have the length cl+abs(dl). These functions should
* probably end up in bn_asm.c as soon as there are assembler counterparts
* for the systems that use assembler files.
*/
BN_ULONG bn_sub_part_words(BN_ULONG *r,
const BN_ULONG *a, const BN_ULONG *b,
int cl, int dl)
{
BN_ULONG c, t;
assert(cl >= 0);
c = bn_sub_words(r, a, b, cl);
if (dl == 0)
return c;
r += cl;
a += cl;
b += cl;
if (dl < 0) {
# ifdef BN_COUNT
fprintf(stderr, " bn_sub_part_words %d + %d (dl < 0, c = %d)\n", cl,
dl, c);
# endif
for (;;) {
t = b[0];
r[0] = (0 - t - c) & BN_MASK2;
if (t != 0)
c = 1;
if (++dl >= 0)
break;
t = b[1];
r[1] = (0 - t - c) & BN_MASK2;
if (t != 0)
c = 1;
if (++dl >= 0)
break;
t = b[2];
r[2] = (0 - t - c) & BN_MASK2;
if (t != 0)
c = 1;
if (++dl >= 0)
break;
t = b[3];
r[3] = (0 - t - c) & BN_MASK2;
if (t != 0)
c = 1;
if (++dl >= 0)
break;
b += 4;
r += 4;
}
} else {
int save_dl = dl;
# ifdef BN_COUNT
fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, c = %d)\n", cl,
dl, c);
# endif
while (c) {
t = a[0];
r[0] = (t - c) & BN_MASK2;
if (t != 0)
c = 0;
if (--dl <= 0)
break;
t = a[1];
r[1] = (t - c) & BN_MASK2;
if (t != 0)
c = 0;
if (--dl <= 0)
break;
t = a[2];
r[2] = (t - c) & BN_MASK2;
if (t != 0)
c = 0;
if (--dl <= 0)
break;
t = a[3];
r[3] = (t - c) & BN_MASK2;
if (t != 0)
c = 0;
if (--dl <= 0)
break;
save_dl = dl;
a += 4;
r += 4;
}
if (dl > 0) {
# ifdef BN_COUNT
fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, c == 0)\n",
cl, dl);
# endif
if (save_dl > dl) {
switch (save_dl - dl) {
case 1:
r[1] = a[1];
if (--dl <= 0)
break;
case 2:
r[2] = a[2];
if (--dl <= 0)
break;
case 3:
r[3] = a[3];
if (--dl <= 0)
break;
}
a += 4;
r += 4;
}
}
if (dl > 0) {
# ifdef BN_COUNT
fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, copy)\n",
cl, dl);
# endif
for (;;) {
r[0] = a[0];
if (--dl <= 0)
break;
r[1] = a[1];
if (--dl <= 0)
break;
r[2] = a[2];
if (--dl <= 0)
break;
r[3] = a[3];
if (--dl <= 0)
break;
a += 4;
r += 4;
}
}
}
return c;
}
#endif
BN_ULONG bn_add_part_words(BN_ULONG *r,
const BN_ULONG *a, const BN_ULONG *b,
int cl, int dl)
{
BN_ULONG c, l, t;
assert(cl >= 0);
c = bn_add_words(r, a, b, cl);
if (dl == 0)
return c;
r += cl;
a += cl;
b += cl;
if (dl < 0) {
int save_dl = dl;
#ifdef BN_COUNT
fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, c = %d)\n", cl,
dl, c);
#endif
while (c) {
l = (c + b[0]) & BN_MASK2;
c = (l < c);
r[0] = l;
if (++dl >= 0)
break;
l = (c + b[1]) & BN_MASK2;
c = (l < c);
r[1] = l;
if (++dl >= 0)
break;
l = (c + b[2]) & BN_MASK2;
c = (l < c);
r[2] = l;
if (++dl >= 0)
break;
l = (c + b[3]) & BN_MASK2;
c = (l < c);
r[3] = l;
if (++dl >= 0)
break;
save_dl = dl;
b += 4;
r += 4;
}
if (dl < 0) {
#ifdef BN_COUNT
fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, c == 0)\n",
cl, dl);
#endif
if (save_dl < dl) {
switch (dl - save_dl) {
case 1:
r[1] = b[1];
if (++dl >= 0)
break;
case 2:
r[2] = b[2];
if (++dl >= 0)
break;
case 3:
r[3] = b[3];
if (++dl >= 0)
break;
}
b += 4;
r += 4;
}
}
if (dl < 0) {
#ifdef BN_COUNT
fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, copy)\n",
cl, dl);
#endif
for (;;) {
r[0] = b[0];
if (++dl >= 0)
break;
r[1] = b[1];
if (++dl >= 0)
break;
r[2] = b[2];
if (++dl >= 0)
break;
r[3] = b[3];
if (++dl >= 0)
break;
b += 4;
r += 4;
}
}
} else {
int save_dl = dl;
#ifdef BN_COUNT
fprintf(stderr, " bn_add_part_words %d + %d (dl > 0)\n", cl, dl);
#endif
while (c) {
t = (a[0] + c) & BN_MASK2;
c = (t < c);
r[0] = t;
if (--dl <= 0)
break;
t = (a[1] + c) & BN_MASK2;
c = (t < c);
r[1] = t;
if (--dl <= 0)
break;
t = (a[2] + c) & BN_MASK2;
c = (t < c);
r[2] = t;
if (--dl <= 0)
break;
t = (a[3] + c) & BN_MASK2;
c = (t < c);
r[3] = t;
if (--dl <= 0)
break;
save_dl = dl;
a += 4;
r += 4;
}
#ifdef BN_COUNT
fprintf(stderr, " bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl,
dl);
#endif
if (dl > 0) {
if (save_dl > dl) {
switch (save_dl - dl) {
case 1:
r[1] = a[1];
if (--dl <= 0)
break;
case 2:
r[2] = a[2];
if (--dl <= 0)
break;
case 3:
r[3] = a[3];
if (--dl <= 0)
break;
}
a += 4;
r += 4;
}
}
if (dl > 0) {
#ifdef BN_COUNT
fprintf(stderr, " bn_add_part_words %d + %d (dl > 0, copy)\n",
cl, dl);
#endif
for (;;) {
r[0] = a[0];
if (--dl <= 0)
break;
r[1] = a[1];
if (--dl <= 0)
break;
r[2] = a[2];
if (--dl <= 0)
break;
r[3] = a[3];
if (--dl <= 0)
break;
a += 4;
r += 4;
}
}
}
return c;
}
#ifdef BN_RECURSION
/*
* Karatsuba recursive multiplication algorithm (cf. Knuth, The Art of
* Computer Programming, Vol. 2)
*/
/*-
* r is 2*n2 words in size,
* a and b are both n2 words in size.
* n2 must be a power of 2.
* We multiply and return the result.
* t must be 2*n2 words in size
* We calculate
* a[0]*b[0]
* a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
* a[1]*b[1]
*/
/* dnX may not be positive, but n2/2+dnX has to be */
void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
int dna, int dnb, BN_ULONG *t)
{
int n = n2 / 2, c1, c2;
int tna = n + dna, tnb = n + dnb;
unsigned int neg, zero;
BN_ULONG ln, lo, *p;
# ifdef BN_COUNT
fprintf(stderr, " bn_mul_recursive %d%+d * %d%+d\n", n2, dna, n2, dnb);
# endif
# ifdef BN_MUL_COMBA
# if 0
if (n2 == 4) {
bn_mul_comba4(r, a, b);
return;
}
# endif
/*
* Only call bn_mul_comba 8 if n2 == 8 and the two arrays are complete
* [steve]
*/
if (n2 == 8 && dna == 0 && dnb == 0) {
bn_mul_comba8(r, a, b);
return;
}
# endif /* BN_MUL_COMBA */
/* Else do normal multiply */
if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) {
bn_mul_normal(r, a, n2 + dna, b, n2 + dnb);
if ((dna + dnb) < 0)
memset(&r[2 * n2 + dna + dnb], 0,
sizeof(BN_ULONG) * -(dna + dnb));
return;
}
/* r=(a[0]-a[1])*(b[1]-b[0]) */
c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
zero = neg = 0;
switch (c1 * 3 + c2) {
case -4:
bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
break;
case -3:
zero = 1;
break;
case -2:
bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
neg = 1;
break;
case -1:
case 0:
case 1:
zero = 1;
break;
case 2:
bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
neg = 1;
break;
case 3:
zero = 1;
break;
case 4:
bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
break;
}
# ifdef BN_MUL_COMBA
if (n == 4 && dna == 0 && dnb == 0) { /* XXX: bn_mul_comba4 could take
* extra args to do this well */
if (!zero)
bn_mul_comba4(&(t[n2]), t, &(t[n]));
else
memset(&(t[n2]), 0, 8 * sizeof(BN_ULONG));
bn_mul_comba4(r, a, b);
bn_mul_comba4(&(r[n2]), &(a[n]), &(b[n]));
} else if (n == 8 && dna == 0 && dnb == 0) { /* XXX: bn_mul_comba8 could
* take extra args to do
* this well */
if (!zero)
bn_mul_comba8(&(t[n2]), t, &(t[n]));
else
memset(&(t[n2]), 0, 16 * sizeof(BN_ULONG));
bn_mul_comba8(r, a, b);
bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n]));
} else
# endif /* BN_MUL_COMBA */
{
p = &(t[n2 * 2]);
if (!zero)
bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
else
memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG));
bn_mul_recursive(r, a, b, n, 0, 0, p);
bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), n, dna, dnb, p);
}
/*-
* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
* r[10] holds (a[0]*b[0])
* r[32] holds (b[1]*b[1])
*/
c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
if (neg) { /* if t[32] is negative */
c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
} else {
/* Might have a carry */
c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
}
/*-
* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
* r[10] holds (a[0]*b[0])
* r[32] holds (b[1]*b[1])
* c1 holds the carry bits
*/
c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
if (c1) {
p = &(r[n + n2]);
lo = *p;
ln = (lo + c1) & BN_MASK2;
*p = ln;
/*
* The overflow will stop before we over write words we should not
* overwrite
*/
if (ln < (BN_ULONG)c1) {
do {
p++;
lo = *p;
ln = (lo + 1) & BN_MASK2;
*p = ln;
} while (ln == 0);
}
}
}
/*
* n+tn is the word length t needs to be n*4 is size, as does r
*/
/* tnX may not be negative but less than n */
void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
int tna, int tnb, BN_ULONG *t)
{
int i, j, n2 = n * 2;
int c1, c2, neg;
BN_ULONG ln, lo, *p;
# ifdef BN_COUNT
fprintf(stderr, " bn_mul_part_recursive (%d%+d) * (%d%+d)\n",
n, tna, n, tnb);
# endif
if (n < 8) {
bn_mul_normal(r, a, n + tna, b, n + tnb);
return;
}
/* r=(a[0]-a[1])*(b[1]-b[0]) */
c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
neg = 0;
switch (c1 * 3 + c2) {
case -4:
bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
break;
case -3:
/* break; */
case -2:
bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
neg = 1;
break;
case -1:
case 0:
case 1:
/* break; */
case 2:
bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
neg = 1;
break;
case 3:
/* break; */
case 4:
bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
break;
}
/*
* The zero case isn't yet implemented here. The speedup would probably
* be negligible.
*/
# if 0
if (n == 4) {
bn_mul_comba4(&(t[n2]), t, &(t[n]));
bn_mul_comba4(r, a, b);
bn_mul_normal(&(r[n2]), &(a[n]), tn, &(b[n]), tn);
memset(&(r[n2 + tn * 2]), 0, sizeof(BN_ULONG) * (n2 - tn * 2));
} else
# endif
if (n == 8) {
bn_mul_comba8(&(t[n2]), t, &(t[n]));
bn_mul_comba8(r, a, b);
bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb);
memset(&(r[n2 + tna + tnb]), 0, sizeof(BN_ULONG) * (n2 - tna - tnb));
} else {
p = &(t[n2 * 2]);
bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
bn_mul_recursive(r, a, b, n, 0, 0, p);
i = n / 2;
/*
* If there is only a bottom half to the number, just do it
*/
if (tna > tnb)
j = tna - i;
else
j = tnb - i;
if (j == 0) {
bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]),
i, tna - i, tnb - i, p);
memset(&(r[n2 + i * 2]), 0, sizeof(BN_ULONG) * (n2 - i * 2));
} else if (j > 0) { /* eg, n == 16, i == 8 and tn == 11 */
bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]),
i, tna - i, tnb - i, p);
memset(&(r[n2 + tna + tnb]), 0,
sizeof(BN_ULONG) * (n2 - tna - tnb));
} else { /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
memset(&(r[n2]), 0, sizeof(BN_ULONG) * n2);
if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL
&& tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) {
bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb);
} else {
for (;;) {
i /= 2;
/*
* these simplified conditions work exclusively because
* difference between tna and tnb is 1 or 0
*/
if (i < tna || i < tnb) {
bn_mul_part_recursive(&(r[n2]),
&(a[n]), &(b[n]),
i, tna - i, tnb - i, p);
break;
} else if (i == tna || i == tnb) {
bn_mul_recursive(&(r[n2]),
&(a[n]), &(b[n]),
i, tna - i, tnb - i, p);
break;
}
}
}
}
}
/*-
* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
* r[10] holds (a[0]*b[0])
* r[32] holds (b[1]*b[1])
*/
c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
if (neg) { /* if t[32] is negative */
c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
} else {
/* Might have a carry */
c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
}
/*-
* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
* r[10] holds (a[0]*b[0])
* r[32] holds (b[1]*b[1])
* c1 holds the carry bits
*/
c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
if (c1) {
p = &(r[n + n2]);
lo = *p;
ln = (lo + c1) & BN_MASK2;
*p = ln;
/*
* The overflow will stop before we over write words we should not
* overwrite
*/
if (ln < (BN_ULONG)c1) {
do {
p++;
lo = *p;
ln = (lo + 1) & BN_MASK2;
*p = ln;
} while (ln == 0);
}
}
}
/*-
* a and b must be the same size, which is n2.
* r needs to be n2 words and t needs to be n2*2
*/
void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
BN_ULONG *t)
{
int n = n2 / 2;
# ifdef BN_COUNT
fprintf(stderr, " bn_mul_low_recursive %d * %d\n", n2, n2);
# endif
bn_mul_recursive(r, a, b, n, 0, 0, &(t[0]));
if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL) {
bn_mul_low_recursive(&(t[0]), &(a[0]), &(b[n]), n, &(t[n2]));
bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
bn_mul_low_recursive(&(t[0]), &(a[n]), &(b[0]), n, &(t[n2]));
bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
} else {
bn_mul_low_normal(&(t[0]), &(a[0]), &(b[n]), n);
bn_mul_low_normal(&(t[n]), &(a[n]), &(b[0]), n);
bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
bn_add_words(&(r[n]), &(r[n]), &(t[n]), n);
}
}
/*-
* a and b must be the same size, which is n2.
* r needs to be n2 words and t needs to be n2*2
* l is the low words of the output.
* t needs to be n2*3
*/
void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
BN_ULONG *t)
{
int i, n;
int c1, c2;
int neg, oneg, zero;
BN_ULONG ll, lc, *lp, *mp;
# ifdef BN_COUNT
fprintf(stderr, " bn_mul_high %d * %d\n", n2, n2);
# endif
n = n2 / 2;
/* Calculate (al-ah)*(bh-bl) */
neg = zero = 0;
c1 = bn_cmp_words(&(a[0]), &(a[n]), n);
c2 = bn_cmp_words(&(b[n]), &(b[0]), n);
switch (c1 * 3 + c2) {
case -4:
bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n);
bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n);
break;
case -3:
zero = 1;
break;
case -2:
bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n);
bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n);
neg = 1;
break;
case -1:
case 0:
case 1:
zero = 1;
break;
case 2:
bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n);
bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n);
neg = 1;
break;
case 3:
zero = 1;
break;
case 4:
bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n);
bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n);
break;
}
oneg = neg;
/* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
/* r[10] = (a[1]*b[1]) */
# ifdef BN_MUL_COMBA
if (n == 8) {
bn_mul_comba8(&(t[0]), &(r[0]), &(r[n]));
bn_mul_comba8(r, &(a[n]), &(b[n]));
} else
# endif
{
bn_mul_recursive(&(t[0]), &(r[0]), &(r[n]), n, 0, 0, &(t[n2]));
bn_mul_recursive(r, &(a[n]), &(b[n]), n, 0, 0, &(t[n2]));
}
/*-
* s0 == low(al*bl)
* s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
* We know s0 and s1 so the only unknown is high(al*bl)
* high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
* high(al*bl) == s1 - (r[0]+l[0]+t[0])
*/
if (l != NULL) {
lp = &(t[n2 + n]);
c1 = (int)(bn_add_words(lp, &(r[0]), &(l[0]), n));
} else {
c1 = 0;
lp = &(r[0]);
}
if (neg)
neg = (int)(bn_sub_words(&(t[n2]), lp, &(t[0]), n));
else {
bn_add_words(&(t[n2]), lp, &(t[0]), n);
neg = 0;
}
if (l != NULL) {
bn_sub_words(&(t[n2 + n]), &(l[n]), &(t[n2]), n);
} else {
lp = &(t[n2 + n]);
mp = &(t[n2]);
for (i = 0; i < n; i++)
lp[i] = ((~mp[i]) + 1) & BN_MASK2;
}
/*-
* s[0] = low(al*bl)
* t[3] = high(al*bl)
* t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
* r[10] = (a[1]*b[1])
*/
/*-
* R[10] = al*bl
* R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
* R[32] = ah*bh
*/
/*-
* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
* R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
* R[3]=r[1]+(carry/borrow)
*/
if (l != NULL) {
lp = &(t[n2]);
c1 = (int)(bn_add_words(lp, &(t[n2 + n]), &(l[0]), n));
} else {
lp = &(t[n2 + n]);
c1 = 0;
}
c1 += (int)(bn_add_words(&(t[n2]), lp, &(r[0]), n));
if (oneg)
c1 -= (int)(bn_sub_words(&(t[n2]), &(t[n2]), &(t[0]), n));
else
c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), &(t[0]), n));
c2 = (int)(bn_add_words(&(r[0]), &(r[0]), &(t[n2 + n]), n));
c2 += (int)(bn_add_words(&(r[0]), &(r[0]), &(r[n]), n));
if (oneg)
c2 -= (int)(bn_sub_words(&(r[0]), &(r[0]), &(t[n]), n));
else
c2 += (int)(bn_add_words(&(r[0]), &(r[0]), &(t[n]), n));
if (c1 != 0) { /* Add starting at r[0], could be +ve or -ve */
i = 0;
if (c1 > 0) {
lc = c1;
do {
ll = (r[i] + lc) & BN_MASK2;
r[i++] = ll;
lc = (lc > ll);
} while (lc);
} else {
lc = -c1;
do {
ll = r[i];
r[i++] = (ll - lc) & BN_MASK2;
lc = (lc > ll);
} while (lc);
}
}
if (c2 != 0) { /* Add starting at r[1] */
i = n;
if (c2 > 0) {
lc = c2;
do {
ll = (r[i] + lc) & BN_MASK2;
r[i++] = ll;
lc = (lc > ll);
} while (lc);
} else {
lc = -c2;
do {
ll = r[i];
r[i++] = (ll - lc) & BN_MASK2;
lc = (lc > ll);
} while (lc);
}
}
}
#endif /* BN_RECURSION */
int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
{
int ret = bn_mul_fixed_top(r, a, b, ctx);
bn_correct_top(r);
bn_check_top(r);
return ret;
}
int bn_mul_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
{
int ret = 0;
int top, al, bl;
BIGNUM *rr;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
int i;
#endif
#ifdef BN_RECURSION
BIGNUM *t = NULL;
int j = 0, k;
#endif
#ifdef BN_COUNT
fprintf(stderr, "BN_mul %d * %d\n", a->top, b->top);
#endif
bn_check_top(a);
bn_check_top(b);
bn_check_top(r);
al = a->top;
bl = b->top;
if ((al == 0) || (bl == 0)) {
BN_zero(r);
return (1);
}
top = al + bl;
BN_CTX_start(ctx);
if ((r == a) || (r == b)) {
if ((rr = BN_CTX_get(ctx)) == NULL)
goto err;
} else
rr = r;
rr->neg = a->neg ^ b->neg;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
i = al - bl;
#endif
#ifdef BN_MUL_COMBA
if (i == 0) {
# if 0
if (al == 4) {
if (bn_wexpand(rr, 8) == NULL)
goto err;
rr->top = 8;
bn_mul_comba4(rr->d, a->d, b->d);
goto end;
}
# endif
if (al == 8) {
if (bn_wexpand(rr, 16) == NULL)
goto err;
rr->top = 16;
bn_mul_comba8(rr->d, a->d, b->d);
goto end;
}
}
#endif /* BN_MUL_COMBA */
#ifdef BN_RECURSION
if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL)) {
if (i >= -1 && i <= 1) {
/*
* Find out the power of two lower or equal to the longest of the
* two numbers
*/
if (i >= 0) {
j = BN_num_bits_word((BN_ULONG)al);
}
if (i == -1) {
j = BN_num_bits_word((BN_ULONG)bl);
}
j = 1 << (j - 1);
assert(j <= al || j <= bl);
k = j + j;
t = BN_CTX_get(ctx);
if (t == NULL)
goto err;
if (al > j || bl > j) {
if (bn_wexpand(t, k * 4) == NULL)
goto err;
if (bn_wexpand(rr, k * 4) == NULL)
goto err;
bn_mul_part_recursive(rr->d, a->d, b->d,
j, al - j, bl - j, t->d);
} else { /* al <= j || bl <= j */
if (bn_wexpand(t, k * 2) == NULL)
goto err;
if (bn_wexpand(rr, k * 2) == NULL)
goto err;
bn_mul_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
}
rr->top = top;
goto end;
}
}
#endif /* BN_RECURSION */
if (bn_wexpand(rr, top) == NULL)
goto err;
rr->top = top;
bn_mul_normal(rr->d, a->d, al, b->d, bl);
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
end:
#endif
rr->flags |= BN_FLG_FIXED_TOP;
if (r != rr && BN_copy(r, rr) == NULL)
goto err;
ret = 1;
err:
bn_check_top(r);
BN_CTX_end(ctx);
return (ret);
}
void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
{
BN_ULONG *rr;
#ifdef BN_COUNT
fprintf(stderr, " bn_mul_normal %d * %d\n", na, nb);
#endif
if (na < nb) {
int itmp;
BN_ULONG *ltmp;
itmp = na;
na = nb;
nb = itmp;
ltmp = a;
a = b;
b = ltmp;
}
rr = &(r[na]);
if (nb <= 0) {
(void)bn_mul_words(r, a, na, 0);
return;
} else
rr[0] = bn_mul_words(r, a, na, b[0]);
for (;;) {
if (--nb <= 0)
return;
rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]);
if (--nb <= 0)
return;
rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]);
if (--nb <= 0)
return;
rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]);
if (--nb <= 0)
return;
rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]);
rr += 4;
r += 4;
b += 4;
}
}
void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
{
#ifdef BN_COUNT
fprintf(stderr, " bn_mul_low_normal %d * %d\n", n, n);
#endif
bn_mul_words(r, a, n, b[0]);
for (;;) {
if (--n <= 0)
return;
bn_mul_add_words(&(r[1]), a, n, b[1]);
if (--n <= 0)
return;
bn_mul_add_words(&(r[2]), a, n, b[2]);
if (--n <= 0)
return;
bn_mul_add_words(&(r[3]), a, n, b[3]);
if (--n <= 0)
return;
bn_mul_add_words(&(r[4]), a, n, b[4]);
r += 4;
b += 4;
}
}
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