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boringssl/boringssl.git/044abb0aaa18012c65ea0e7c46988eff283ed200/./crypto/bn/generic.c
blob: 8b3b0f8700ced3f128bdf5889cf3733a53bfe972 [file]
/* 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.] */
#include <openssl/bn.h>
#include <assert.h>
#include "internal.h"
/* Generic implementations of most operations are needed for:
* - Configurations without inline assembly.
* - Architectures other than x86 or x86_64.
* - Windows x84_64; x86_64-gcc.c does not build on MSVC. */
#if defined(OPENSSL_NO_ASM) || \
(!defined(OPENSSL_X86_64) && !defined(OPENSSL_X86)) || \
(defined(OPENSSL_X86_64) && defined(OPENSSL_WINDOWS))
#if defined(OPENSSL_WINDOWS)
#define alloca _alloca
#else
#include <alloca.h>
#endif
#ifdef BN_LLONG
#define mul_add(r, a, w, c) \
{ \
BN_ULLONG t; \
t = (BN_ULLONG)w * (a) + (r) + (c); \
(r) = Lw(t); \
(c) = Hw(t); \
}
#define mul(r, a, w, c) \
{ \
BN_ULLONG t; \
t = (BN_ULLONG)w * (a) + (c); \
(r) = Lw(t); \
(c) = Hw(t); \
}
#define sqr(r0, r1, a) \
{ \
BN_ULLONG t; \
t = (BN_ULLONG)(a) * (a); \
(r0) = Lw(t); \
(r1) = Hw(t); \
}
#elif defined(BN_UMULT_LOHI)
#define mul_add(r, a, w, c) \
{ \
BN_ULONG high, low, ret, tmp = (a); \
ret = (r); \
BN_UMULT_LOHI(low, high, w, tmp); \
ret += (c); \
(c) = (ret < (c)) ? 1 : 0; \
(c) += high; \
ret += low; \
(c) += (ret < low) ? 1 : 0; \
(r) = ret; \
}
#define mul(r, a, w, c) \
{ \
BN_ULONG high, low, ret, ta = (a); \
BN_UMULT_LOHI(low, high, w, ta); \
ret = low + (c); \
(c) = high; \
(c) += (ret < low) ? 1 : 0; \
(r) = ret; \
}
#define sqr(r0, r1, a) \
{ \
BN_ULONG tmp = (a); \
BN_UMULT_LOHI(r0, r1, tmp, tmp); \
}
#elif defined(BN_UMULT_HIGH)
#define mul_add(r, a, w, c) \
{ \
BN_ULONG high, low, ret, tmp = (a); \
ret = (r); \
high = BN_UMULT_HIGH(w, tmp); \
ret += (c); \
low = (w) * tmp; \
(c) = (ret < (c)) ? 1 : 0; \
(c) += high; \
ret += low; \
(c) += (ret < low) ? 1 : 0; \
(r) = ret; \
}
#define mul(r, a, w, c) \
{ \
BN_ULONG high, low, ret, ta = (a); \
low = (w) * ta; \
high = BN_UMULT_HIGH(w, ta); \
ret = low + (c); \
(c) = high; \
(c) += (ret < low) ? 1 : 0; \
(r) = ret; \
}
#define sqr(r0, r1, a) \
{ \
BN_ULONG tmp = (a); \
(r0) = tmp * tmp; \
(r1) = BN_UMULT_HIGH(tmp, tmp); \
}
#else
/*************************************************************
* No long long type
*/
#define LBITS(a) ((a) & BN_MASK2l)
#define HBITS(a) (((a) >> BN_BITS4) & BN_MASK2l)
#define L2HBITS(a) (((a) << BN_BITS4) & BN_MASK2)
#define LLBITS(a) ((a) & BN_MASKl)
#define LHBITS(a) (((a) >> BN_BITS2) & BN_MASKl)
#define LL2HBITS(a) ((BN_ULLONG)((a) & BN_MASKl) << BN_BITS2)
#define mul64(l, h, bl, bh) \
{ \
BN_ULONG m, m1, lt, ht; \
\
lt = l; \
ht = h; \
m = (bh) * (lt); \
lt = (bl) * (lt); \
m1 = (bl) * (ht); \
ht = (bh) * (ht); \
m = (m + m1) & BN_MASK2; \
if (m < m1) \
ht += L2HBITS((BN_ULONG)1); \
ht += HBITS(m); \
m1 = L2HBITS(m); \
lt = (lt + m1) & BN_MASK2; \
if (lt < m1) \
ht++; \
(l) = lt; \
(h) = ht; \
}
#define sqr64(lo, ho, in) \
{ \
BN_ULONG l, h, m; \
\
h = (in); \
l = LBITS(h); \
h = HBITS(h); \
m = (l) * (h); \
l *= l; \
h *= h; \
h += (m & BN_MASK2h1) >> (BN_BITS4 - 1); \
m = (m & BN_MASK2l) << (BN_BITS4 + 1); \
l = (l + m) & BN_MASK2; \
if (l < m) \
h++; \
(lo) = l; \
(ho) = h; \
}
#define mul_add(r, a, bl, bh, c) \
{ \
BN_ULONG l, h; \
\
h = (a); \
l = LBITS(h); \
h = HBITS(h); \
mul64(l, h, (bl), (bh)); \
\
/* non-multiply part */ \
l = (l + (c)) & BN_MASK2; \
if (l < (c)) \
h++; \
(c) = (r); \
l = (l + (c)) & BN_MASK2; \
if (l < (c)) \
h++; \
(c) = h & BN_MASK2; \
(r) = l; \
}
#define mul(r, a, bl, bh, c) \
{ \
BN_ULONG l, h; \
\
h = (a); \
l = LBITS(h); \
h = HBITS(h); \
mul64(l, h, (bl), (bh)); \
\
/* non-multiply part */ \
l += (c); \
if ((l & BN_MASK2) < (c)) \
h++; \
(c) = h & BN_MASK2; \
(r) = l & BN_MASK2; \
}
#endif /* !BN_LLONG */
#if defined(BN_LLONG) || defined(BN_UMULT_HIGH)
BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
BN_ULONG w) {
BN_ULONG c1 = 0;
assert(num >= 0);
if (num <= 0) {
return c1;
}
while (num & ~3) {
mul_add(rp[0], ap[0], w, c1);
mul_add(rp[1], ap[1], w, c1);
mul_add(rp[2], ap[2], w, c1);
mul_add(rp[3], ap[3], w, c1);
ap += 4;
rp += 4;
num -= 4;
}
while (num) {
mul_add(rp[0], ap[0], w, c1);
ap++;
rp++;
num--;
}
return c1;
}
BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w) {
BN_ULONG c1 = 0;
assert(num >= 0);
if (num <= 0) {
return c1;
}
while (num & ~3) {
mul(rp[0], ap[0], w, c1);
mul(rp[1], ap[1], w, c1);
mul(rp[2], ap[2], w, c1);
mul(rp[3], ap[3], w, c1);
ap += 4;
rp += 4;
num -= 4;
}
while (num) {
mul(rp[0], ap[0], w, c1);
ap++;
rp++;
num--;
}
return c1;
}
void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n) {
assert(n >= 0);
if (n <= 0) {
return;
}
while (n & ~3) {
sqr(r[0], r[1], a[0]);
sqr(r[2], r[3], a[1]);
sqr(r[4], r[5], a[2]);
sqr(r[6], r[7], a[3]);
a += 4;
r += 8;
n -= 4;
}
while (n) {
sqr(r[0], r[1], a[0]);
a++;
r += 2;
n--;
}
}
#else /* !(defined(BN_LLONG) || defined(BN_UMULT_HIGH)) */
BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
BN_ULONG w) {
BN_ULONG c = 0;
BN_ULONG bl, bh;
assert(num >= 0);
if (num <= 0) {
return (BN_ULONG)0;
}
bl = LBITS(w);
bh = HBITS(w);
while (num & ~3) {
mul_add(rp[0], ap[0], bl, bh, c);
mul_add(rp[1], ap[1], bl, bh, c);
mul_add(rp[2], ap[2], bl, bh, c);
mul_add(rp[3], ap[3], bl, bh, c);
ap += 4;
rp += 4;
num -= 4;
}
while (num) {
mul_add(rp[0], ap[0], bl, bh, c);
ap++;
rp++;
num--;
}
return c;
}
BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w) {
BN_ULONG carry = 0;
BN_ULONG bl, bh;
assert(num >= 0);
if (num <= 0) {
return (BN_ULONG)0;
}
bl = LBITS(w);
bh = HBITS(w);
while (num & ~3) {
mul(rp[0], ap[0], bl, bh, carry);
mul(rp[1], ap[1], bl, bh, carry);
mul(rp[2], ap[2], bl, bh, carry);
mul(rp[3], ap[3], bl, bh, carry);
ap += 4;
rp += 4;
num -= 4;
}
while (num) {
mul(rp[0], ap[0], bl, bh, carry);
ap++;
rp++;
num--;
}
return carry;
}
void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n) {
assert(n >= 0);
if (n <= 0) {
return;
}
while (n & ~3) {
sqr64(r[0], r[1], a[0]);
sqr64(r[2], r[3], a[1]);
sqr64(r[4], r[5], a[2]);
sqr64(r[6], r[7], a[3]);
a += 4;
r += 8;
n -= 4;
}
while (n) {
sqr64(r[0], r[1], a[0]);
a++;
r += 2;
n--;
}
}
#endif /* !(defined(BN_LLONG) || defined(BN_UMULT_HIGH)) */
#if defined(BN_LLONG) && defined(BN_DIV2W)
BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d) {
return (BN_ULONG)(((((BN_ULLONG)h) << BN_BITS2) | l) / (BN_ULLONG)d);
}
#else
/* Divide h,l by d and return the result. */
BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d) {
BN_ULONG dh, dl, q, ret = 0, th, tl, t;
int i, count = 2;
if (d == 0) {
return BN_MASK2;
}
i = BN_num_bits_word(d);
assert((i == BN_BITS2) || (h <= (BN_ULONG)1 << i));
i = BN_BITS2 - i;
if (h >= d) {
h -= d;
}
if (i) {
d <<= i;
h = (h << i) | (l >> (BN_BITS2 - i));
l <<= i;
}
dh = (d & BN_MASK2h) >> BN_BITS4;
dl = (d & BN_MASK2l);
for (;;) {
if ((h >> BN_BITS4) == dh) {
q = BN_MASK2l;
} else {
q = h / dh;
}
th = q * dh;
tl = dl * q;
for (;;) {
t = h - th;
if ((t & BN_MASK2h) ||
((tl) <= ((t << BN_BITS4) | ((l & BN_MASK2h) >> BN_BITS4)))) {
break;
}
q--;
th -= dh;
tl -= dl;
}
t = (tl >> BN_BITS4);
tl = (tl << BN_BITS4) & BN_MASK2h;
th += t;
if (l < tl) {
th++;
}
l -= tl;
if (h < th) {
h += d;
q--;
}
h -= th;
if (--count == 0) {
break;
}
ret = q << BN_BITS4;
h = ((h << BN_BITS4) | (l >> BN_BITS4)) & BN_MASK2;
l = (l & BN_MASK2l) << BN_BITS4;
}
ret |= q;
return ret;
}
#endif /* !defined(BN_LLONG) && defined(BN_DIV2W) */
#ifdef BN_LLONG
BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
int n) {
BN_ULLONG ll = 0;
assert(n >= 0);
if (n <= 0) {
return (BN_ULONG)0;
}
while (n & ~3) {
ll += (BN_ULLONG)a[0] + b[0];
r[0] = (BN_ULONG)ll & BN_MASK2;
ll >>= BN_BITS2;
ll += (BN_ULLONG)a[1] + b[1];
r[1] = (BN_ULONG)ll & BN_MASK2;
ll >>= BN_BITS2;
ll += (BN_ULLONG)a[2] + b[2];
r[2] = (BN_ULONG)ll & BN_MASK2;
ll >>= BN_BITS2;
ll += (BN_ULLONG)a[3] + b[3];
r[3] = (BN_ULONG)ll & BN_MASK2;
ll >>= BN_BITS2;
a += 4;
b += 4;
r += 4;
n -= 4;
}
while (n) {
ll += (BN_ULLONG)a[0] + b[0];
r[0] = (BN_ULONG)ll & BN_MASK2;
ll >>= BN_BITS2;
a++;
b++;
r++;
n--;
}
return (BN_ULONG)ll;
}
#else /* !BN_LLONG */
BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
int n) {
BN_ULONG c, l, t;
assert(n >= 0);
if (n <= 0) {
return (BN_ULONG)0;
}
c = 0;
while (n & ~3) {
t = a[0];
t = (t + c) & BN_MASK2;
c = (t < c);
l = (t + b[0]) & BN_MASK2;
c += (l < t);
r[0] = l;
t = a[1];
t = (t + c) & BN_MASK2;
c = (t < c);
l = (t + b[1]) & BN_MASK2;
c += (l < t);
r[1] = l;
t = a[2];
t = (t + c) & BN_MASK2;
c = (t < c);
l = (t + b[2]) & BN_MASK2;
c += (l < t);
r[2] = l;
t = a[3];
t = (t + c) & BN_MASK2;
c = (t < c);
l = (t + b[3]) & BN_MASK2;
c += (l < t);
r[3] = l;
a += 4;
b += 4;
r += 4;
n -= 4;
}
while (n) {
t = a[0];
t = (t + c) & BN_MASK2;
c = (t < c);
l = (t + b[0]) & BN_MASK2;
c += (l < t);
r[0] = l;
a++;
b++;
r++;
n--;
}
return (BN_ULONG)c;
}
#endif /* !BN_LLONG */
BN_ULONG bn_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
int n) {
BN_ULONG t1, t2;
int c = 0;
assert(n >= 0);
if (n <= 0) {
return (BN_ULONG)0;
}
while (n & ~3) {
t1 = a[0];
t2 = b[0];
r[0] = (t1 - t2 - c) & BN_MASK2;
if (t1 != t2)
c = (t1 < t2);
t1 = a[1];
t2 = b[1];
r[1] = (t1 - t2 - c) & BN_MASK2;
if (t1 != t2)
c = (t1 < t2);
t1 = a[2];
t2 = b[2];
r[2] = (t1 - t2 - c) & BN_MASK2;
if (t1 != t2)
c = (t1 < t2);
t1 = a[3];
t2 = b[3];
r[3] = (t1 - t2 - c) & BN_MASK2;
if (t1 != t2)
c = (t1 < t2);
a += 4;
b += 4;
r += 4;
n -= 4;
}
while (n) {
t1 = a[0];
t2 = b[0];
r[0] = (t1 - t2 - c) & BN_MASK2;
if (t1 != t2)
c = (t1 < t2);
a++;
b++;
r++;
n--;
}
return c;
}
/* mul_add_c(a,b,c0,c1,c2) -- c+=a*b for three word number c=(c2,c1,c0) */
/* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */
/* sqr_add_c(a,i,c0,c1,c2) -- c+=a[i]^2 for three word number c=(c2,c1,c0) */
/* sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number c=(c2,c1,c0) */
#ifdef BN_LLONG
/* Keep in mind that additions to multiplication result can not overflow,
* because its high half cannot be all-ones. */
#define mul_add_c(a, b, c0, c1, c2) \
do { \
BN_ULONG hi; \
BN_ULLONG t = (BN_ULLONG)(a) * (b); \
t += c0; /* no carry */ \
c0 = (BN_ULONG)Lw(t); \
hi = (BN_ULONG)Hw(t); \
c1 = (c1 + hi) & BN_MASK2; \
if (c1 < hi) \
c2++; \
} while (0)
#define mul_add_c2(a, b, c0, c1, c2) \
do { \
BN_ULONG hi; \
BN_ULLONG t = (BN_ULLONG)(a) * (b); \
BN_ULLONG tt = t + c0; /* no carry */ \
c0 = (BN_ULONG)Lw(tt); \
hi = (BN_ULONG)Hw(tt); \
c1 = (c1 + hi) & BN_MASK2; \
if (c1 < hi) \
c2++; \
t += c0; /* no carry */ \
c0 = (BN_ULONG)Lw(t); \
hi = (BN_ULONG)Hw(t); \
c1 = (c1 + hi) & BN_MASK2; \
if (c1 < hi) \
c2++; \
} while (0)
#define sqr_add_c(a, i, c0, c1, c2) \
do { \
BN_ULONG hi; \
BN_ULLONG t = (BN_ULLONG)a[i] * a[i]; \
t += c0; /* no carry */ \
c0 = (BN_ULONG)Lw(t); \
hi = (BN_ULONG)Hw(t); \
c1 = (c1 + hi) & BN_MASK2; \
if (c1 < hi) \
c2++; \
} while (0)
#define sqr_add_c2(a, i, j, c0, c1, c2) mul_add_c2((a)[i], (a)[j], c0, c1, c2)
#elif defined(BN_UMULT_LOHI)
/* Keep in mind that additions to hi can not overflow, because the high word of
* a multiplication result cannot be all-ones. */
#define mul_add_c(a, b, c0, c1, c2) \
do { \
BN_ULONG ta = (a), tb = (b); \
BN_ULONG lo, hi; \
BN_UMULT_LOHI(lo, hi, ta, tb); \
c0 += lo; \
hi += (c0 < lo) ? 1 : 0; \
c1 += hi; \
c2 += (c1 < hi) ? 1 : 0; \
} while (0)
#define mul_add_c2(a, b, c0, c1, c2) \
do { \
BN_ULONG ta = (a), tb = (b); \
BN_ULONG lo, hi, tt; \
BN_UMULT_LOHI(lo, hi, ta, tb); \
c0 += lo; \
tt = hi + ((c0 < lo) ? 1 : 0); \
c1 += tt; \
c2 += (c1 < tt) ? 1 : 0; \
c0 += lo; \
hi += (c0 < lo) ? 1 : 0; \
c1 += hi; \
c2 += (c1 < hi) ? 1 : 0; \
} while (0)
#define sqr_add_c(a, i, c0, c1, c2) \
do { \
BN_ULONG ta = (a)[i]; \
BN_ULONG lo, hi; \
BN_UMULT_LOHI(lo, hi, ta, ta); \
c0 += lo; \
hi += (c0 < lo) ? 1 : 0; \
c1 += hi; \
c2 += (c1 < hi) ? 1 : 0; \
} while (0)
#define sqr_add_c2(a, i, j, c0, c1, c2) mul_add_c2((a)[i], (a)[j], c0, c1, c2)
#elif defined(BN_UMULT_HIGH)
/* Keep in mind that additions to hi can not overflow, because
* the high word of a multiplication result cannot be all-ones. */
#define mul_add_c(a, b, c0, c1, c2) \
do { \
BN_ULONG ta = (a), tb = (b); \
BN_ULONG lo = ta * tb; \
BN_ULONG hi = BN_UMULT_HIGH(ta, tb); \
c0 += lo; \
hi += (c0 < lo) ? 1 : 0; \
c1 += hi; \
c2 += (c1 < hi) ? 1 : 0; \
} while (0)
#define mul_add_c2(a, b, c0, c1, c2) \
do { \
BN_ULONG ta = (a), tb = (b), tt; \
BN_ULONG lo = ta * tb; \
BN_ULONG hi = BN_UMULT_HIGH(ta, tb); \
c0 += lo; \
tt = hi + ((c0 < lo) ? 1 : 0); \
c1 += tt; \
c2 += (c1 < tt) ? 1 : 0; \
c0 += lo; \
hi += (c0 < lo) ? 1 : 0; \
c1 += hi; \
c2 += (c1 < hi) ? 1 : 0; \
} while (0)
#define sqr_add_c(a, i, c0, c1, c2) \
do { \
BN_ULONG ta = (a)[i]; \
BN_ULONG lo = ta * ta; \
BN_ULONG hi = BN_UMULT_HIGH(ta, ta); \
c0 += lo; \
hi += (c0 < lo) ? 1 : 0; \
c1 += hi; \
c2 += (c1 < hi) ? 1 : 0; \
} while (0)
#define sqr_add_c2(a, i, j, c0, c1, c2) mul_add_c2((a)[i], (a)[j], c0, c1, c2)
#else /* !BN_LLONG */
/* Keep in mind that additions to hi can not overflow, because
* the high word of a multiplication result cannot be all-ones. */
#define mul_add_c(a, b, c0, c1, c2) \
do { \
BN_ULONG lo = LBITS(a), hi = HBITS(a); \
BN_ULONG bl = LBITS(b), bh = HBITS(b); \
mul64(lo, hi, bl, bh); \
c0 = (c0 + lo) & BN_MASK2; \
if (c0 < lo) \
hi++; \
c1 = (c1 + hi) & BN_MASK2; \
if (c1 < hi) \
c2++; \
} while (0)
#define mul_add_c2(a, b, c0, c1, c2) \
do { \
BN_ULONG tt; \
BN_ULONG lo = LBITS(a), hi = HBITS(a); \
BN_ULONG bl = LBITS(b), bh = HBITS(b); \
mul64(lo, hi, bl, bh); \
tt = hi; \
c0 = (c0 + lo) & BN_MASK2; \
if (c0 < lo) \
tt++; \
c1 = (c1 + tt) & BN_MASK2; \
if (c1 < tt) \
c2++; \
c0 = (c0 + lo) & BN_MASK2; \
if (c0 < lo) \
hi++; \
c1 = (c1 + hi) & BN_MASK2; \
if (c1 < hi) \
c2++; \
} while (0)
#define sqr_add_c(a, i, c0, c1, c2) \
do { \
BN_ULONG lo, hi; \
sqr64(lo, hi, (a)[i]); \
c0 = (c0 + lo) & BN_MASK2; \
if (c0 < lo) \
hi++; \
c1 = (c1 + hi) & BN_MASK2; \
if (c1 < hi) \
c2++; \
} while (0)
#define sqr_add_c2(a, i, j, c0, c1, c2) mul_add_c2((a)[i], (a)[j], c0, c1, c2)
#endif /* !BN_LLONG */
void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b) {
BN_ULONG c1, c2, c3;
c1 = 0;
c2 = 0;
c3 = 0;
mul_add_c(a[0], b[0], c1, c2, c3);
r[0] = c1;
c1 = 0;
mul_add_c(a[0], b[1], c2, c3, c1);
mul_add_c(a[1], b[0], c2, c3, c1);
r[1] = c2;
c2 = 0;
mul_add_c(a[2], b[0], c3, c1, c2);
mul_add_c(a[1], b[1], c3, c1, c2);
mul_add_c(a[0], b[2], c3, c1, c2);
r[2] = c3;
c3 = 0;
mul_add_c(a[0], b[3], c1, c2, c3);
mul_add_c(a[1], b[2], c1, c2, c3);
mul_add_c(a[2], b[1], c1, c2, c3);
mul_add_c(a[3], b[0], c1, c2, c3);
r[3] = c1;
c1 = 0;
mul_add_c(a[4], b[0], c2, c3, c1);
mul_add_c(a[3], b[1], c2, c3, c1);
mul_add_c(a[2], b[2], c2, c3, c1);
mul_add_c(a[1], b[3], c2, c3, c1);
mul_add_c(a[0], b[4], c2, c3, c1);
r[4] = c2;
c2 = 0;
mul_add_c(a[0], b[5], c3, c1, c2);
mul_add_c(a[1], b[4], c3, c1, c2);
mul_add_c(a[2], b[3], c3, c1, c2);
mul_add_c(a[3], b[2], c3, c1, c2);
mul_add_c(a[4], b[1], c3, c1, c2);
mul_add_c(a[5], b[0], c3, c1, c2);
r[5] = c3;
c3 = 0;
mul_add_c(a[6], b[0], c1, c2, c3);
mul_add_c(a[5], b[1], c1, c2, c3);
mul_add_c(a[4], b[2], c1, c2, c3);
mul_add_c(a[3], b[3], c1, c2, c3);
mul_add_c(a[2], b[4], c1, c2, c3);
mul_add_c(a[1], b[5], c1, c2, c3);
mul_add_c(a[0], b[6], c1, c2, c3);
r[6] = c1;
c1 = 0;
mul_add_c(a[0], b[7], c2, c3, c1);
mul_add_c(a[1], b[6], c2, c3, c1);
mul_add_c(a[2], b[5], c2, c3, c1);
mul_add_c(a[3], b[4], c2, c3, c1);
mul_add_c(a[4], b[3], c2, c3, c1);
mul_add_c(a[5], b[2], c2, c3, c1);
mul_add_c(a[6], b[1], c2, c3, c1);
mul_add_c(a[7], b[0], c2, c3, c1);
r[7] = c2;
c2 = 0;
mul_add_c(a[7], b[1], c3, c1, c2);
mul_add_c(a[6], b[2], c3, c1, c2);
mul_add_c(a[5], b[3], c3, c1, c2);
mul_add_c(a[4], b[4], c3, c1, c2);
mul_add_c(a[3], b[5], c3, c1, c2);
mul_add_c(a[2], b[6], c3, c1, c2);
mul_add_c(a[1], b[7], c3, c1, c2);
r[8] = c3;
c3 = 0;
mul_add_c(a[2], b[7], c1, c2, c3);
mul_add_c(a[3], b[6], c1, c2, c3);
mul_add_c(a[4], b[5], c1, c2, c3);
mul_add_c(a[5], b[4], c1, c2, c3);
mul_add_c(a[6], b[3], c1, c2, c3);
mul_add_c(a[7], b[2], c1, c2, c3);
r[9] = c1;
c1 = 0;
mul_add_c(a[7], b[3], c2, c3, c1);
mul_add_c(a[6], b[4], c2, c3, c1);
mul_add_c(a[5], b[5], c2, c3, c1);
mul_add_c(a[4], b[6], c2, c3, c1);
mul_add_c(a[3], b[7], c2, c3, c1);
r[10] = c2;
c2 = 0;
mul_add_c(a[4], b[7], c3, c1, c2);
mul_add_c(a[5], b[6], c3, c1, c2);
mul_add_c(a[6], b[5], c3, c1, c2);
mul_add_c(a[7], b[4], c3, c1, c2);
r[11] = c3;
c3 = 0;
mul_add_c(a[7], b[5], c1, c2, c3);
mul_add_c(a[6], b[6], c1, c2, c3);
mul_add_c(a[5], b[7], c1, c2, c3);
r[12] = c1;
c1 = 0;
mul_add_c(a[6], b[7], c2, c3, c1);
mul_add_c(a[7], b[6], c2, c3, c1);
r[13] = c2;
c2 = 0;
mul_add_c(a[7], b[7], c3, c1, c2);
r[14] = c3;
r[15] = c1;
}
void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b) {
BN_ULONG c1, c2, c3;
c1 = 0;
c2 = 0;
c3 = 0;
mul_add_c(a[0], b[0], c1, c2, c3);
r[0] = c1;
c1 = 0;
mul_add_c(a[0], b[1], c2, c3, c1);
mul_add_c(a[1], b[0], c2, c3, c1);
r[1] = c2;
c2 = 0;
mul_add_c(a[2], b[0], c3, c1, c2);
mul_add_c(a[1], b[1], c3, c1, c2);
mul_add_c(a[0], b[2], c3, c1, c2);
r[2] = c3;
c3 = 0;
mul_add_c(a[0], b[3], c1, c2, c3);
mul_add_c(a[1], b[2], c1, c2, c3);
mul_add_c(a[2], b[1], c1, c2, c3);
mul_add_c(a[3], b[0], c1, c2, c3);
r[3] = c1;
c1 = 0;
mul_add_c(a[3], b[1], c2, c3, c1);
mul_add_c(a[2], b[2], c2, c3, c1);
mul_add_c(a[1], b[3], c2, c3, c1);
r[4] = c2;
c2 = 0;
mul_add_c(a[2], b[3], c3, c1, c2);
mul_add_c(a[3], b[2], c3, c1, c2);
r[5] = c3;
c3 = 0;
mul_add_c(a[3], b[3], c1, c2, c3);
r[6] = c1;
r[7] = c2;
}
void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a) {
BN_ULONG c1, c2, c3;
c1 = 0;
c2 = 0;
c3 = 0;
sqr_add_c(a, 0, c1, c2, c3);
r[0] = c1;
c1 = 0;
sqr_add_c2(a, 1, 0, c2, c3, c1);
r[1] = c2;
c2 = 0;
sqr_add_c(a, 1, c3, c1, c2);
sqr_add_c2(a, 2, 0, c3, c1, c2);
r[2] = c3;
c3 = 0;
sqr_add_c2(a, 3, 0, c1, c2, c3);
sqr_add_c2(a, 2, 1, c1, c2, c3);
r[3] = c1;
c1 = 0;
sqr_add_c(a, 2, c2, c3, c1);
sqr_add_c2(a, 3, 1, c2, c3, c1);
sqr_add_c2(a, 4, 0, c2, c3, c1);
r[4] = c2;
c2 = 0;
sqr_add_c2(a, 5, 0, c3, c1, c2);
sqr_add_c2(a, 4, 1, c3, c1, c2);
sqr_add_c2(a, 3, 2, c3, c1, c2);
r[5] = c3;
c3 = 0;
sqr_add_c(a, 3, c1, c2, c3);
sqr_add_c2(a, 4, 2, c1, c2, c3);
sqr_add_c2(a, 5, 1, c1, c2, c3);
sqr_add_c2(a, 6, 0, c1, c2, c3);
r[6] = c1;
c1 = 0;
sqr_add_c2(a, 7, 0, c2, c3, c1);
sqr_add_c2(a, 6, 1, c2, c3, c1);
sqr_add_c2(a, 5, 2, c2, c3, c1);
sqr_add_c2(a, 4, 3, c2, c3, c1);
r[7] = c2;
c2 = 0;
sqr_add_c(a, 4, c3, c1, c2);
sqr_add_c2(a, 5, 3, c3, c1, c2);
sqr_add_c2(a, 6, 2, c3, c1, c2);
sqr_add_c2(a, 7, 1, c3, c1, c2);
r[8] = c3;
c3 = 0;
sqr_add_c2(a, 7, 2, c1, c2, c3);
sqr_add_c2(a, 6, 3, c1, c2, c3);
sqr_add_c2(a, 5, 4, c1, c2, c3);
r[9] = c1;
c1 = 0;
sqr_add_c(a, 5, c2, c3, c1);
sqr_add_c2(a, 6, 4, c2, c3, c1);
sqr_add_c2(a, 7, 3, c2, c3, c1);
r[10] = c2;
c2 = 0;
sqr_add_c2(a, 7, 4, c3, c1, c2);
sqr_add_c2(a, 6, 5, c3, c1, c2);
r[11] = c3;
c3 = 0;
sqr_add_c(a, 6, c1, c2, c3);
sqr_add_c2(a, 7, 5, c1, c2, c3);
r[12] = c1;
c1 = 0;
sqr_add_c2(a, 7, 6, c2, c3, c1);
r[13] = c2;
c2 = 0;
sqr_add_c(a, 7, c3, c1, c2);
r[14] = c3;
r[15] = c1;
}
void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a) {
BN_ULONG c1, c2, c3;
c1 = 0;
c2 = 0;
c3 = 0;
sqr_add_c(a, 0, c1, c2, c3);
r[0] = c1;
c1 = 0;
sqr_add_c2(a, 1, 0, c2, c3, c1);
r[1] = c2;
c2 = 0;
sqr_add_c(a, 1, c3, c1, c2);
sqr_add_c2(a, 2, 0, c3, c1, c2);
r[2] = c3;
c3 = 0;
sqr_add_c2(a, 3, 0, c1, c2, c3);
sqr_add_c2(a, 2, 1, c1, c2, c3);
r[3] = c1;
c1 = 0;
sqr_add_c(a, 2, c2, c3, c1);
sqr_add_c2(a, 3, 1, c2, c3, c1);
r[4] = c2;
c2 = 0;
sqr_add_c2(a, 3, 2, c3, c1, c2);
r[5] = c3;
c3 = 0;
sqr_add_c(a, 3, c1, c2, c3);
r[6] = c1;
r[7] = c2;
}
#if defined(OPENSSL_NO_ASM) || (!defined(OPENSSL_ARM) && !defined(OPENSSL_X86_64))
/* This is essentially reference implementation, which may or may not
* result in performance improvement. E.g. on IA-32 this routine was
* observed to give 40% faster rsa1024 private key operations and 10%
* faster rsa4096 ones, while on AMD64 it improves rsa1024 sign only
* by 10% and *worsens* rsa4096 sign by 15%. Once again, it's a
* reference implementation, one to be used as starting point for
* platform-specific assembler. Mentioned numbers apply to compiler
* generated code compiled with and without -DOPENSSL_BN_ASM_MONT and
* can vary not only from platform to platform, but even for compiler
* versions. Assembler vs. assembler improvement coefficients can
* [and are known to] differ and are to be documented elsewhere. */
int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
const BN_ULONG *np, const BN_ULONG *n0p, int num) {
BN_ULONG c0, c1, ml, *tp, n0;
#ifdef mul64
BN_ULONG mh;
#endif
volatile BN_ULONG *vp;
int i = 0, j;
#if 0 /* template for platform-specific implementation */
if (ap==bp) return bn_sqr_mont(rp,ap,np,n0p,num);
#endif
vp = tp = alloca((num + 2) * sizeof(BN_ULONG));
n0 = *n0p;
c0 = 0;
ml = bp[0];
#ifdef mul64
mh = HBITS(ml);
ml = LBITS(ml);
for (j = 0; j < num; ++j)
mul(tp[j], ap[j], ml, mh, c0);
#else
for (j = 0; j < num; ++j)
mul(tp[j], ap[j], ml, c0);
#endif
tp[num] = c0;
tp[num + 1] = 0;
goto enter;
for (i = 0; i < num; i++) {
c0 = 0;
ml = bp[i];
#ifdef mul64
mh = HBITS(ml);
ml = LBITS(ml);
for (j = 0; j < num; ++j)
mul_add(tp[j], ap[j], ml, mh, c0);
#else
for (j = 0; j < num; ++j)
mul_add(tp[j], ap[j], ml, c0);
#endif
c1 = (tp[num] + c0) & BN_MASK2;
tp[num] = c1;
tp[num + 1] = (c1 < c0 ? 1 : 0);
enter:
c1 = tp[0];
ml = (c1 * n0) & BN_MASK2;
c0 = 0;
#ifdef mul64
mh = HBITS(ml);
ml = LBITS(ml);
mul_add(c1, np[0], ml, mh, c0);
#else
mul_add(c1, ml, np[0], c0);
#endif
for (j = 1; j < num; j++) {
c1 = tp[j];
#ifdef mul64
mul_add(c1, np[j], ml, mh, c0);
#else
mul_add(c1, ml, np[j], c0);
#endif
tp[j - 1] = c1 & BN_MASK2;
}
c1 = (tp[num] + c0) & BN_MASK2;
tp[num - 1] = c1;
tp[num] = tp[num + 1] + (c1 < c0 ? 1 : 0);
}
if (tp[num] != 0 || tp[num - 1] >= np[num - 1]) {
c0 = bn_sub_words(rp, tp, np, num);
if (tp[num] != 0 || c0 == 0) {
for (i = 0; i < num + 2; i++)
vp[i] = 0;
return 1;
}
}
for (i = 0; i < num; i++)
rp[i] = tp[i], vp[i] = 0;
vp[num] = 0;
vp[num + 1] = 0;
return 1;
}
#endif
#endif