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openssl/crypto/bn/bn_mul.c
Geoff Thorpe 38d1b3cc02 bn: fix occurances of negative zero 
The BIGNUM behaviour is supposed to be "consistent" when going into and
out of APIs, where "consistent" means 'top' is set minimally and that
'neg' (negative) is not set if the BIGNUM is zero (which is iff 'top' is
zero, due to the previous point).

The BN_DEBUG testing (make test) caught the cases that this patch
corrects.

Note, bn_correct_top() could have been used instead, but that is intended
for where 'top' is expected to (sometimes) require adjustment after direct
word-array manipulation, and so is heavier-weight. Here, we are just
catching the negative-zero case, so we test and correct for that
explicitly, in-place.

Change-Id: Iddefbd3c28a13d935648932beebcc765d5b85ae7
Signed-off-by: Geoff Thorpe <geoff@openssl.org>

Reviewed-by: Richard Levitte <levitte@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/1672)
2017-02-01 02:06:39 +01:00

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/*
* Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
*
* Licensed under the OpenSSL license (the "License"). You may not use
* this file except in compliance with the License. You can obtain a copy
* in the file LICENSE in the source distribution or at
* https://www.openssl.org/source/license.html
*/
#include <assert.h>
#include "internal/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 ( basically, 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) {
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;
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) {
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) {
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;
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) {
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) {
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;
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;
}
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) {
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_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, sizeof(*t) * 8);
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, sizeof(*t) * 16);
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, sizeof(*t) * n2);
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;
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(*r) * (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(*r) * (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(*r) * (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(*r) * 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;
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;
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]);
bn_add_words(lp, &(r[0]), &(l[0]), n);
} else {
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 = 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
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;
#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;
}
# if 0
if (i == 1 && !BN_get_flags(b, BN_FLG_STATIC_DATA)) {
BIGNUM *tmp_bn = (BIGNUM *)b;
if (bn_wexpand(tmp_bn, al) == NULL)
goto err;
tmp_bn->d[bl] = 0;
bl++;
i--;
} else if (i == -1 && !BN_get_flags(a, BN_FLG_STATIC_DATA)) {
BIGNUM *tmp_bn = (BIGNUM *)a;
if (bn_wexpand(tmp_bn, bl) == NULL)
goto err;
tmp_bn->d[al] = 0;
al++;
i++;
}
if (i == 0) {
/* symmetric and > 4 */
/* 16 or larger */
j = BN_num_bits_word((BN_ULONG)al);
j = 1 << (j - 1);
k = j + j;
t = BN_CTX_get(ctx);
if (al == j) { /* exact multiple */
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, al, t->d);
} else {
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, al - j, j, t->d);
}
rr->top = top;
goto end;
}
# endif
}
#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->neg = a->neg ^ b->neg;
bn_correct_top(rr);
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;
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)
{
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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