312 lines
8.0 KiB
C
312 lines
8.0 KiB
C
/* matrix22_mul.c.
|
|
|
|
Contributed by Niels Möller and Marco Bodrato.
|
|
|
|
THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
|
|
SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
|
|
GUARANTEED THAT THEY'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
|
|
|
|
Copyright 2003, 2004, 2005, 2008, 2009 Free Software Foundation, Inc.
|
|
|
|
This file is part of the GNU MP Library.
|
|
|
|
The GNU MP Library is free software; you can redistribute it and/or modify
|
|
it under the terms of the GNU Lesser General Public License as published by
|
|
the Free Software Foundation; either version 3 of the License, or (at your
|
|
option) any later version.
|
|
|
|
The GNU MP Library is distributed in the hope that it will be useful, but
|
|
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
|
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
|
|
License for more details.
|
|
|
|
You should have received a copy of the GNU Lesser General Public License
|
|
along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
|
|
|
|
#include "mpir.h"
|
|
#include "gmp-impl.h"
|
|
#include "longlong.h"
|
|
|
|
#define MUL(rp, ap, an, bp, bn) do { \
|
|
if (an >= bn) \
|
|
mpn_mul (rp, ap, an, bp, bn); \
|
|
else \
|
|
mpn_mul (rp, bp, bn, ap, an); \
|
|
} while (0)
|
|
|
|
/* Inputs are unsigned. */
|
|
static int
|
|
abs_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
|
|
{
|
|
int c;
|
|
MPN_CMP (c, ap, bp, n);
|
|
if (c >= 0)
|
|
{
|
|
mpn_sub_n (rp, ap, bp, n);
|
|
return 0;
|
|
}
|
|
else
|
|
{
|
|
mpn_sub_n (rp, bp, ap, n);
|
|
return 1;
|
|
}
|
|
}
|
|
|
|
static int
|
|
add_signed_n (mp_ptr rp,
|
|
mp_srcptr ap, int as, mp_srcptr bp, int bs, mp_size_t n)
|
|
{
|
|
if (as != bs)
|
|
return as ^ abs_sub_n (rp, ap, bp, n);
|
|
else
|
|
{
|
|
ASSERT_NOCARRY (mpn_add_n (rp, ap, bp, n));
|
|
return as;
|
|
}
|
|
}
|
|
|
|
mp_size_t
|
|
mpn_matrix22_mul_itch (mp_size_t rn, mp_size_t mn)
|
|
{
|
|
if (BELOW_THRESHOLD (rn, MATRIX22_STRASSEN_THRESHOLD)
|
|
|| BELOW_THRESHOLD (mn, MATRIX22_STRASSEN_THRESHOLD))
|
|
return 3*rn + 2*mn;
|
|
else
|
|
return 3*(rn + mn) + 5;
|
|
}
|
|
|
|
/* Algorithm:
|
|
|
|
/ s0 \ / 1 0 0 0 \ / r0 \
|
|
| s1 | | 0 1 0 1 | | r1 |
|
|
| s2 | | 0 0 -1 1 | | r2 |
|
|
| s3 | = | 0 1 -1 1 | \ r3 /
|
|
| s4 | | -1 1 -1 1 |
|
|
| s5 | | 0 1 0 0 |
|
|
\ s6 / \ 0 0 1 0 /
|
|
|
|
/ t0 \ / 1 0 0 0 \ / m0 \
|
|
| t1 | | 0 1 0 1 | | m1 |
|
|
| t2 | | 0 0 -1 1 | | m2 |
|
|
| t3 | = | 0 1 -1 1 | \ m3 /
|
|
| t4 | | -1 1 -1 1 |
|
|
| t5 | | 0 1 0 0 |
|
|
\ t6 / \ 0 0 1 0 /
|
|
|
|
Note: the two matrices above are the same, but s_i and t_i are used
|
|
in the same product, only for i<4, see "A Strassen-like Matrix
|
|
Multiplication suited for squaring and higher power computation" by
|
|
M. Bodrato, in Proceedings of ISSAC 2010.
|
|
|
|
/ r0 \ / 1 0 0 0 0 1 0 \ / s0*t0 \
|
|
| r1 | = | 0 0 -1 1 -1 1 0 | | s1*t1 |
|
|
| r2 | | 0 1 0 -1 0 -1 -1 | | s2*t2 |
|
|
\ r3 / \ 0 1 1 -1 0 -1 0 / | s3*t3 |
|
|
| s4*t5 |
|
|
| s5*t6 |
|
|
\ s6*t4 /
|
|
|
|
The scheduling uses two temporaries U0 and U1 to store products, and
|
|
two, S0 and T0, to store combinations of entries of the two
|
|
operands.
|
|
*/
|
|
|
|
/* Computes R = R * M. Elements are numbers R = (r0, r1; r2, r3).
|
|
*
|
|
* Resulting elements are of size up to rn + mn + 1.
|
|
*
|
|
* Temporary storage: 3 rn + 3 mn + 5. */
|
|
void
|
|
mpn_matrix22_mul_strassen (mp_ptr r0, mp_ptr r1, mp_ptr r2, mp_ptr r3, mp_size_t rn,
|
|
mp_srcptr m0, mp_srcptr m1, mp_srcptr m2, mp_srcptr m3, mp_size_t mn,
|
|
mp_ptr tp)
|
|
{
|
|
mp_ptr s0, t0, u0, u1;
|
|
int r1s, r3s, s0s, t0s, u1s;
|
|
s0 = tp; tp += rn + 1;
|
|
t0 = tp; tp += mn + 1;
|
|
u0 = tp; tp += rn + mn + 1;
|
|
u1 = tp; /* rn + mn + 2 */
|
|
|
|
MUL (u0, r1, rn, m2, mn); /* u5 = s5 * t6 */
|
|
r3s = abs_sub_n (r3, r3, r2, rn); /* r3 - r2 */
|
|
if (r3s)
|
|
{
|
|
r1s = abs_sub_n (r1, r1, r3, rn);
|
|
r1[rn] = 0;
|
|
}
|
|
else
|
|
{
|
|
r1[rn] = mpn_add_n (r1, r1, r3, rn);
|
|
r1s = 0; /* r1 - r2 + r3 */
|
|
}
|
|
if (r1s)
|
|
{
|
|
s0[rn] = mpn_add_n (s0, r1, r0, rn);
|
|
s0s = 0;
|
|
}
|
|
else if (r1[rn] != 0)
|
|
{
|
|
s0[rn] = r1[rn] - mpn_sub_n (s0, r1, r0, rn);
|
|
s0s = 1; /* s4 = -r0 + r1 - r2 + r3 */
|
|
/* Reverse sign! */
|
|
}
|
|
else
|
|
{
|
|
s0s = abs_sub_n (s0, r0, r1, rn);
|
|
s0[rn] = 0;
|
|
}
|
|
MUL (u1, r0, rn, m0, mn); /* u0 = s0 * t0 */
|
|
r0[rn+mn] = mpn_add_n (r0, u0, u1, rn + mn);
|
|
ASSERT (r0[rn+mn] < 2); /* u0 + u5 */
|
|
|
|
t0s = abs_sub_n (t0, m3, m2, mn);
|
|
u1s = r3s^t0s^1; /* Reverse sign! */
|
|
MUL (u1, r3, rn, t0, mn); /* u2 = s2 * t2 */
|
|
u1[rn+mn] = 0;
|
|
if (t0s)
|
|
{
|
|
t0s = abs_sub_n (t0, m1, t0, mn);
|
|
t0[mn] = 0;
|
|
}
|
|
else
|
|
{
|
|
t0[mn] = mpn_add_n (t0, t0, m1, mn);
|
|
}
|
|
|
|
/* FIXME: Could be simplified if we had space for rn + mn + 2 limbs
|
|
at r3. I'd expect that for matrices of random size, the high
|
|
words t0[mn] and r1[rn] are non-zero with a pretty small
|
|
probability. If that can be confirmed this should be done as an
|
|
unconditional rn x (mn+1) followed by an if (UNLIKELY (r1[rn]))
|
|
add_n. */
|
|
if (t0[mn] != 0)
|
|
{
|
|
MUL (r3, r1, rn, t0, mn + 1); /* u3 = s3 * t3 */
|
|
ASSERT (r1[rn] < 2);
|
|
if (r1[rn] != 0)
|
|
mpn_add_n (r3 + rn, r3 + rn, t0, mn + 1);
|
|
}
|
|
else
|
|
{
|
|
MUL (r3, r1, rn + 1, t0, mn);
|
|
}
|
|
|
|
ASSERT (r3[rn+mn] < 4);
|
|
|
|
u0[rn+mn] = 0;
|
|
if (r1s^t0s)
|
|
{
|
|
r3s = abs_sub_n (r3, u0, r3, rn + mn + 1);
|
|
}
|
|
else
|
|
{
|
|
ASSERT_NOCARRY (mpn_add_n (r3, r3, u0, rn + mn + 1));
|
|
r3s = 0; /* u3 + u5 */
|
|
}
|
|
|
|
if (t0s)
|
|
{
|
|
t0[mn] = mpn_add_n (t0, t0, m0, mn);
|
|
}
|
|
else if (t0[mn] != 0)
|
|
{
|
|
t0[mn] -= mpn_sub_n (t0, t0, m0, mn);
|
|
}
|
|
else
|
|
{
|
|
t0s = abs_sub_n (t0, t0, m0, mn);
|
|
}
|
|
MUL (u0, r2, rn, t0, mn + 1); /* u6 = s6 * t4 */
|
|
ASSERT (u0[rn+mn] < 2);
|
|
if (r1s)
|
|
{
|
|
ASSERT_NOCARRY (mpn_sub_n (r1, r2, r1, rn));
|
|
}
|
|
else
|
|
{
|
|
r1[rn] += mpn_add_n (r1, r1, r2, rn);
|
|
}
|
|
rn++;
|
|
t0s = add_signed_n (r2, r3, r3s, u0, t0s, rn + mn);
|
|
/* u3 + u5 + u6 */
|
|
ASSERT (r2[rn+mn-1] < 4);
|
|
r3s = add_signed_n (r3, r3, r3s, u1, u1s, rn + mn);
|
|
/* -u2 + u3 + u5 */
|
|
ASSERT (r3[rn+mn-1] < 3);
|
|
MUL (u0, s0, rn, m1, mn); /* u4 = s4 * t5 */
|
|
ASSERT (u0[rn+mn-1] < 2);
|
|
t0[mn] = mpn_add_n (t0, m3, m1, mn);
|
|
MUL (u1, r1, rn, t0, mn + 1); /* u1 = s1 * t1 */
|
|
mn += rn;
|
|
ASSERT (u1[mn-1] < 4);
|
|
ASSERT (u1[mn] == 0);
|
|
ASSERT_NOCARRY (add_signed_n (r1, r3, r3s, u0, s0s, mn));
|
|
/* -u2 + u3 - u4 + u5 */
|
|
ASSERT (r1[mn-1] < 2);
|
|
if (r3s)
|
|
{
|
|
ASSERT_NOCARRY (mpn_add_n (r3, u1, r3, mn));
|
|
}
|
|
else
|
|
{
|
|
ASSERT_NOCARRY (mpn_sub_n (r3, u1, r3, mn));
|
|
/* u1 + u2 - u3 - u5 */
|
|
}
|
|
ASSERT (r3[mn-1] < 2);
|
|
if (t0s)
|
|
{
|
|
ASSERT_NOCARRY (mpn_add_n (r2, u1, r2, mn));
|
|
}
|
|
else
|
|
{
|
|
ASSERT_NOCARRY (mpn_sub_n (r2, u1, r2, mn));
|
|
/* u1 - u3 - u5 - u6 */
|
|
}
|
|
ASSERT (r2[mn-1] < 2);
|
|
}
|
|
|
|
void
|
|
mpn_matrix22_mul (mp_ptr r0, mp_ptr r1, mp_ptr r2, mp_ptr r3, mp_size_t rn,
|
|
mp_srcptr m0, mp_srcptr m1, mp_srcptr m2, mp_srcptr m3, mp_size_t mn,
|
|
mp_ptr tp)
|
|
{
|
|
if (BELOW_THRESHOLD (rn, MATRIX22_STRASSEN_THRESHOLD)
|
|
|| BELOW_THRESHOLD (mn, MATRIX22_STRASSEN_THRESHOLD))
|
|
{
|
|
mp_ptr p0, p1;
|
|
unsigned i;
|
|
|
|
/* Temporary storage: 3 rn + 2 mn */
|
|
p0 = tp + rn;
|
|
p1 = p0 + rn + mn;
|
|
|
|
for (i = 0; i < 2; i++)
|
|
{
|
|
MPN_COPY (tp, r0, rn);
|
|
|
|
if (rn >= mn)
|
|
{
|
|
mpn_mul (p0, r0, rn, m0, mn);
|
|
mpn_mul (p1, r1, rn, m3, mn);
|
|
mpn_mul (r0, r1, rn, m2, mn);
|
|
mpn_mul (r1, tp, rn, m1, mn);
|
|
}
|
|
else
|
|
{
|
|
mpn_mul (p0, m0, mn, r0, rn);
|
|
mpn_mul (p1, m3, mn, r1, rn);
|
|
mpn_mul (r0, m2, mn, r1, rn);
|
|
mpn_mul (r1, m1, mn, tp, rn);
|
|
}
|
|
r0[rn+mn] = mpn_add_n (r0, r0, p0, rn + mn);
|
|
r1[rn+mn] = mpn_add_n (r1, r1, p1, rn + mn);
|
|
|
|
r0 = r2; r1 = r3;
|
|
}
|
|
}
|
|
else
|
|
mpn_matrix22_mul_strassen (r0, r1, r2, r3, rn,
|
|
m0, m1, m2, m3, mn, tp);
|
|
}
|