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bn_asm.c
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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 <openssl/crypto.h>
#include "internal/cryptlib.h"
#include "bn_lcl.h"
#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);
# ifndef OPENSSL_SMALL_FOOTPRINT
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;
}
# endif
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);
# ifndef OPENSSL_SMALL_FOOTPRINT
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;
}
# endif
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;
# ifndef OPENSSL_SMALL_FOOTPRINT
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;
}
# endif
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);
# ifndef OPENSSL_SMALL_FOOTPRINT
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;
}
# endif
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);
# ifndef OPENSSL_SMALL_FOOTPRINT
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;
}
# endif
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;
# ifndef OPENSSL_SMALL_FOOTPRINT
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;
}
# endif
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. */
/* I need to test this some more :-( */
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);
# ifndef OPENSSL_SMALL_FOOTPRINT
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;
}
# endif
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;
# ifndef OPENSSL_SMALL_FOOTPRINT
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;
}
# endif
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);
#ifndef OPENSSL_SMALL_FOOTPRINT
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;
}
#endif
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);
}
#if defined(BN_MUL_COMBA) && !defined(OPENSSL_SMALL_FOOTPRINT)
# undef bn_mul_comba8
# undef bn_mul_comba4
# undef bn_sqr_comba8
# undef bn_sqr_comba4
/* 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;
}
# ifdef OPENSSL_NO_ASM
# ifdef OPENSSL_BN_ASM_MONT
# include <alloca.h>
/*
* 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;
}
# else
/*
* Return value of 0 indicates that multiplication/convolution was not
* performed to signal the caller to fall down to alternative/original
* code-path.
*/
int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
const BN_ULONG *np, const BN_ULONG *n0, int num)
{
return 0;
}
# endif /* OPENSSL_BN_ASM_MONT */
# endif
#else /* !BN_MUL_COMBA */
/* hmm... is it faster just to do a multiply? */
# undef bn_sqr_comba4
# undef bn_sqr_comba8
void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
{
BN_ULONG t[8];
bn_sqr_normal(r, a, 4, t);
}
void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
{
BN_ULONG t[16];
bn_sqr_normal(r, a, 8, t);
}
void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
{
r[4] = bn_mul_words(&(r[0]), a, 4, b[0]);
r[5] = bn_mul_add_words(&(r[1]), a, 4, b[1]);
r[6] = bn_mul_add_words(&(r[2]), a, 4, b[2]);
r[7] = bn_mul_add_words(&(r[3]), a, 4, b[3]);
}
void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
{
r[8] = bn_mul_words(&(r[0]), a, 8, b[0]);
r[9] = bn_mul_add_words(&(r[1]), a, 8, b[1]);
r[10] = bn_mul_add_words(&(r[2]), a, 8, b[2]);
r[11] = bn_mul_add_words(&(r[3]), a, 8, b[3]);
r[12] = bn_mul_add_words(&(r[4]), a, 8, b[4]);
r[13] = bn_mul_add_words(&(r[5]), a, 8, b[5]);
r[14] = bn_mul_add_words(&(r[6]), a, 8, b[6]);
r[15] = bn_mul_add_words(&(r[7]), a, 8, b[7]);
}
# ifdef OPENSSL_NO_ASM
# ifdef OPENSSL_BN_ASM_MONT
# include <alloca.h>
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, *tp, n0 = *n0p;
volatile BN_ULONG *vp;
int i = 0, j;
vp = tp = alloca((num + 2) * sizeof(BN_ULONG));
for (i = 0; i <= num; i++)
tp[i] = 0;