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/* $OpenBSD: bn_internal.h,v 1.1 2023/01/31 05:48:39 jsing Exp $ */
/*
* Copyright (c) 2023 Joel Sing <jsing@openbsd.org>
*
* Permission to use, copy, modify, and distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/
#include <openssl/bn.h>
#include "bn_arch.h"
#ifndef HEADER_BN_INTERNAL_H
#define HEADER_BN_INTERNAL_H
#ifndef HAVE_BN_UMUL_HILO
#ifdef BN_LLONG
static inline void
bn_umul_hilo(BN_ULONG a, BN_ULONG b, BN_ULONG *out_h, BN_ULONG *out_l)
{
BN_ULLONG r;
r = (BN_ULLONG)a * (BN_ULLONG)b;
*out_h = r >> BN_BITS2;
*out_l = r & BN_MASK2;
}
#else /* !BN_LLONG */
/*
* Multiply two words (a * b) producing a double word result (h:l).
*
* This can be rewritten as:
*
* a * b = (hi32(a) * 2^32 + lo32(a)) * (hi32(b) * 2^32 + lo32(b))
* = hi32(a) * hi32(b) * 2^64 +
* hi32(a) * lo32(b) * 2^32 +
* hi32(b) * lo32(a) * 2^32 +
* lo32(a) * lo32(b)
*
* The multiplication for each part of a and b can be calculated for each of
* these four terms without overflowing a BN_ULONG, as the maximum value of a
* 32 bit x 32 bit multiplication is 32 + 32 = 64 bits. Once these
* multiplications have been performed the result can be partitioned and summed
* into a double word (h:l). The same applies on a 32 bit system, substituting
* 16 for 32 and 32 for 64.
*/
#if 1
static inline void
bn_umul_hilo(BN_ULONG a, BN_ULONG b, BN_ULONG *out_h, BN_ULONG *out_l)
{
BN_ULONG ah, al, bh, bl, h, l, x, c1, c2;
ah = a >> BN_BITS4;
al = a & BN_MASK2l;
bh = b >> BN_BITS4;
bl = b & BN_MASK2l;
h = ah * bh;
l = al * bl;
/* (ah * bl) << BN_BITS4, partition the result across h:l with carry. */
x = ah * bl;
h += x >> BN_BITS4;
x <<= BN_BITS4;
c1 = l | x;
c2 = l & x;
l += x;
h += ((c1 & ~l) | c2) >> (BN_BITS2 - 1); /* carry */
/* (bh * al) << BN_BITS4, partition the result across h:l with carry. */
x = bh * al;
h += x >> BN_BITS4;
x <<= BN_BITS4;
c1 = l | x;
c2 = l & x;
l += x;
h += ((c1 & ~l) | c2) >> (BN_BITS2 - 1); /* carry */
*out_h = h;
*out_l = l;
}
#else
/*
* XXX - this accumulator based version uses fewer instructions, however
* requires more variables/registers. It seems to be slower on at least amd64
* and i386, however may be faster on other architectures that have more
* registers available. Further testing is required and one of the two
* implementations should eventually be removed.
*/
static inline void
bn_umul_hilo(BN_ULONG a, BN_ULONG b, BN_ULONG *out_h, BN_ULONG *out_l)
{
BN_ULONG ah, bh, al, bl, x, h, l;
BN_ULONG acc0, acc1, acc2, acc3;
ah = a >> BN_BITS4;
bh = b >> BN_BITS4;
al = a & BN_MASK2l;
bl = b & BN_MASK2l;
h = ah * bh;
l = al * bl;
acc0 = l & BN_MASK2l;
acc1 = l >> BN_BITS4;
acc2 = h & BN_MASK2l;
acc3 = h >> BN_BITS4;
/* (ah * bl) << BN_BITS4, partition the result across h:l. */
x = ah * bl;
acc1 += x & BN_MASK2l;
acc2 += (acc1 >> BN_BITS4) + (x >> BN_BITS4);
acc3 += acc2 >> BN_BITS4;
/* (bh * al) << BN_BITS4, partition the result across h:l. */
x = bh * al;
acc1 += x & BN_MASK2l;
acc2 += (acc1 >> BN_BITS4) + (x >> BN_BITS4);
acc3 += acc2 >> BN_BITS4;
*out_h = (acc3 << BN_BITS4) | acc2;
*out_l = (acc1 << BN_BITS4) | acc0;
}
#endif
#endif /* !BN_LLONG */
#endif
#ifndef HAVE_BN_UMUL_LO
static inline BN_ULONG
bn_umul_lo(BN_ULONG a, BN_ULONG b)
{
return a * b;
}
#endif
#ifndef HAVE_BN_UMUL_HI
static inline BN_ULONG
bn_umul_hi(BN_ULONG a, BN_ULONG b)
{
BN_ULONG h, l;
bn_umul_hilo(a, b, &h, &l);
return h;
}
#endif
#endif
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