/* 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_grpc/bn.h>
#include <assert.h>
#include "internal.h"
// This file has two other implementations: x86 assembly language in
// asm/bn-586.pl and x86_64 inline assembly in asm/x86_64-gcc.c.
#if defined(OPENSSL_NO_ASM) || \
!(defined(OPENSSL_X86) || \
(defined(OPENSSL_X86_64) && (defined(__GNUC__) || defined(__clang__))))
#ifdef BN_ULLONG
#define mul_add(r, a, w, c) \
do { \
BN_ULLONG t; \
t = (BN_ULLONG)(w) * (a) + (r) + (c); \
(r) = Lw(t); \
(c) = Hw(t); \
} while (0)
#define mul(r, a, w, c) \
do { \
BN_ULLONG t; \
t = (BN_ULLONG)(w) * (a) + (c); \
(r) = Lw(t); \
(c) = Hw(t); \
} while (0)
#define sqr(r0, r1, a) \
do { \
BN_ULLONG t; \
t = (BN_ULLONG)(a) * (a); \
(r0) = Lw(t); \
(r1) = Hw(t); \
} while (0)
#else
#define mul_add(r, a, w, c) \
do { \
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; \
} while (0)
#define mul(r, a, w, c) \
do { \
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; \
} while (0)
#define sqr(r0, r1, a) \
do { \
BN_ULONG tmp = (a); \
BN_UMULT_LOHI(r0, r1, tmp, tmp); \
} while (0)
#endif // !BN_ULLONG
BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num,
BN_ULONG w) {
BN_ULONG c1 = 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, size_t num,
BN_ULONG w) {
BN_ULONG c1 = 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, size_t n) {
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--;
}
}
#ifdef BN_ULLONG
BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
size_t n) {
BN_ULLONG ll = 0;
if (n == 0) {
return 0;
}
while (n & ~3) {
ll += (BN_ULLONG)a[0] + b[0];
r[0] = (BN_ULONG)ll;
ll >>= BN_BITS2;
ll += (BN_ULLONG)a[1] + b[1];
r[1] = (BN_ULONG)ll;
ll >>= BN_BITS2;
ll += (BN_ULLONG)a[2] + b[2];
r[2] = (BN_ULONG)ll;
ll >>= BN_BITS2;
ll += (BN_ULLONG)a[3] + b[3];
r[3] = (BN_ULONG)ll;
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;
ll >>= BN_BITS2;
a++;
b++;
r++;
n--;
}
return (BN_ULONG)ll;
}
#else // !BN_ULLONG
BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
size_t n) {
BN_ULONG c, l, t;
if (n == 0) {
return (BN_ULONG)0;
}
c = 0;
while (n & ~3) {
t = a[0];
t += c;
c = (t < c);
l = t + b[0];
c += (l < t);
r[0] = l;
t = a[1];
t += c;
c = (t < c);
l = t + b[1];
c += (l < t);
r[1] = l;
t = a[2];
t += c;
c = (t < c);
l = t + b[2];
c += (l < t);
r[2] = l;
t = a[3];
t += c;
c = (t < c);
l = t + b[3];
c += (l < t);
r[3] = l;
a += 4;
b += 4;
r += 4;
n -= 4;
}
while (n) {
t = a[0];
t += c;
c = (t < c);
l = t + b[0];
c += (l < t);
r[0] = l;
a++;
b++;
r++;
n--;
}
return (BN_ULONG)c;
}
#endif // !BN_ULLONG
BN_ULONG bn_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
size_t n) {
BN_ULONG t1, t2;
int c = 0;
if (n == 0) {
return (BN_ULONG)0;
}
while (n & ~3) {
t1 = a[0];
t2 = b[0];
r[0] = t1 - t2 - c;
if (t1 != t2) {
c = (t1 < t2);
}
t1 = a[1];
t2 = b[1];
r[1] = t1 - t2 - c;
if (t1 != t2) {
c = (t1 < t2);
}
t1 = a[2];
t2 = b[2];
r[2] = t1 - t2 - c;
if (t1 != t2) {
c = (t1 < t2);
}
t1 = a[3];
t2 = b[3];
r[3] = t1 - t2 - c;
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;
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_ULLONG
// 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) += (hi); \
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) += hi; \
if ((c1) < hi) { \
(c2)++; \
} \
t += (c0); /* no carry */ \
(c0) = (BN_ULONG)Lw(t); \
hi = (BN_ULONG)Hw(t); \
(c1) += hi; \
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) += hi; \
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)
#else
// 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)
#endif // !BN_ULLONG
void bn_mul_comba8(BN_ULONG r[16], const BN_ULONG a[8], const BN_ULONG b[8]) {
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[8], const BN_ULONG a[4], const BN_ULONG b[4]) {
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[16], const BN_ULONG a[8]) {
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[8], const BN_ULONG a[4]) {
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;
}
#undef mul_add
#undef mul
#undef sqr
#undef mul_add_c
#undef mul_add_c2
#undef sqr_add_c
#undef sqr_add_c2
#endif