toom52_mul.c
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- /* mpn_toom52_mul -- Multiply {ap,an} and {bp,bn} where an is nominally 4/3
- times as large as bn. Or more accurately, bn < an < 2 bn.
- Contributed to the GNU project by Marco Bodrato.
- The idea of applying toom to unbalanced multiplication is due to Marco
- Bodrato and Alberto Zanoni.
- THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY
- SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
- GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
- Copyright 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 "gmp.h"
- #include "gmp-impl.h"
- /* Evaluate in: -2, -1, 0, +1, +2, +inf
- <-s-><--n--><--n--><--n--><--n-->
- ___ ______ ______ ______ ______
- |a4_|___a3_|___a2_|___a1_|___a0_|
- |b1|___b0_|
- <t-><--n-->
- v0 = a0 * b0 # A(0)*B(0)
- v1 = (a0+ a1+ a2+ a3+ a4)*(b0+ b1) # A(1)*B(1) ah <= 4 bh <= 1
- vm1 = (a0- a1+ a2- a3+ a4)*(b0- b1) # A(-1)*B(-1) |ah| <= 2 bh = 0
- v2 = (a0+2a1+4a2+8a3+16a4)*(b0+2b1) # A(2)*B(2) ah <= 30 bh <= 2
- vm2 = (a0-2a1+4a2-8a3+16a4)*(b0-2b1) # A(-2)*B(-2) |ah| <= 20 |bh|<= 1
- vinf= a4 * b1 # A(inf)*B(inf)
- Some slight optimization in evaluation are taken from the paper:
- "Towards Optimal Toom-Cook Multiplication for Univariate and
- Multivariate Polynomials in Characteristic 2 and 0."
- */
- void
- mpn_toom52_mul (mp_ptr pp,
- mp_srcptr ap, mp_size_t an,
- mp_srcptr bp, mp_size_t bn, mp_ptr scratch)
- {
- mp_size_t n, s, t;
- enum toom6_flags flags;
- #define a0 ap
- #define a1 (ap + n)
- #define a2 (ap + 2 * n)
- #define a3 (ap + 3 * n)
- #define a4 (ap + 4 * n)
- #define b0 bp
- #define b1 (bp + n)
- n = 1 + (2 * an >= 5 * bn ? (an - 1) / (size_t) 5 : (bn - 1) >> 1);
- s = an - 4 * n;
- t = bn - n;
- ASSERT (0 < s && s <= n);
- ASSERT (0 < t && t <= n);
- /* Ensures that 5 values of n+1 limbs each fits in the product area.
- Borderline cases are an = 32, bn = 8, n = 7, and an = 36, bn = 9,
- n = 8. */
- ASSERT (s+t >= 5);
- #define v0 pp /* 2n */
- #define vm1 (scratch) /* 2n+1 */
- #define v1 (pp + 2 * n) /* 2n+1 */
- #define vm2 (scratch + 2 * n + 1) /* 2n+1 */
- #define v2 (scratch + 4 * n + 2) /* 2n+1 */
- #define vinf (pp + 5 * n) /* s+t */
- #define bs1 pp /* n+1 */
- #define bsm1 (scratch + 2 * n + 2) /* n */
- #define asm1 (scratch + 3 * n + 3) /* n+1 */
- #define asm2 (scratch + 4 * n + 4) /* n+1 */
- #define bsm2 (pp + n + 1) /* n+1 */
- #define bs2 (pp + 2 * n + 2) /* n+1 */
- #define as2 (pp + 3 * n + 3) /* n+1 */
- #define as1 (pp + 4 * n + 4) /* n+1 */
- /* Scratch need is 6 * n + 3 + 1. We need one extra limb, because
- products will overwrite 2n+2 limbs. */
- #define a0a2 scratch
- #define a1a3 asm1
- /* Compute as2 and asm2. */
- flags = toom6_vm2_neg & mpn_toom_eval_pm2 (as2, asm2, 4, ap, n, s, a1a3);
- /* Compute bs1 and bsm1. */
- if (t == n)
- {
- #if HAVE_NATIVE_mpn_add_n_sub_n
- mp_limb_t cy;
- if (mpn_cmp (b0, b1, n) < 0)
- {
- cy = mpn_add_n_sub_n (bs1, bsm1, b1, b0, n);
- flags ^= toom6_vm1_neg;
- }
- else
- {
- cy = mpn_add_n_sub_n (bs1, bsm1, b0, b1, n);
- }
- bs1[n] = cy >> 1;
- #else
- bs1[n] = mpn_add_n (bs1, b0, b1, n);
- if (mpn_cmp (b0, b1, n) < 0)
- {
- mpn_sub_n (bsm1, b1, b0, n);
- flags ^= toom6_vm1_neg;
- }
- else
- {
- mpn_sub_n (bsm1, b0, b1, n);
- }
- #endif
- }
- else
- {
- bs1[n] = mpn_add (bs1, b0, n, b1, t);
- if (mpn_zero_p (b0 + t, n - t) && mpn_cmp (b0, b1, t) < 0)
- {
- mpn_sub_n (bsm1, b1, b0, t);
- MPN_ZERO (bsm1 + t, n - t);
- flags ^= toom6_vm1_neg;
- }
- else
- {
- mpn_sub (bsm1, b0, n, b1, t);
- }
- }
- /* Compute bs2 and bsm2, recycling bs1 and bsm1. bs2=bs1+b1; bsm2=bsm1-b1 */
- mpn_add (bs2, bs1, n+1, b1, t);
- if (flags & toom6_vm1_neg )
- {
- bsm2[n] = mpn_add (bsm2, bsm1, n, b1, t);
- flags ^= toom6_vm2_neg;
- }
- else
- {
- bsm2[n] = 0;
- if (t == n)
- {
- if (mpn_cmp (bsm1, b1, n) < 0)
- {
- mpn_sub_n (bsm2, b1, bsm1, n);
- flags ^= toom6_vm2_neg;
- }
- else
- {
- mpn_sub_n (bsm2, bsm1, b1, n);
- }
- }
- else
- {
- if (mpn_zero_p (bsm1 + t, n - t) && mpn_cmp (bsm1, b1, t) < 0)
- {
- mpn_sub_n (bsm2, b1, bsm1, t);
- MPN_ZERO (bsm2 + t, n - t);
- flags ^= toom6_vm2_neg;
- }
- else
- {
- mpn_sub (bsm2, bsm1, n, b1, t);
- }
- }
- }
- /* Compute as1 and asm1. */
- flags ^= toom6_vm1_neg & mpn_toom_eval_pm1 (as1, asm1, 4, ap, n, s, a0a2);
- ASSERT (as1[n] <= 4);
- ASSERT (bs1[n] <= 1);
- ASSERT (asm1[n] <= 2);
- /* ASSERT (bsm1[n] <= 1); */
- ASSERT (as2[n] <=30);
- ASSERT (bs2[n] <= 2);
- ASSERT (asm2[n] <= 20);
- ASSERT (bsm2[n] <= 1);
- /* vm1, 2n+1 limbs */
- mpn_mul (vm1, asm1, n+1, bsm1, n); /* W4 */
- /* vm2, 2n+1 limbs */
- mpn_mul_n (vm2, asm2, bsm2, n+1); /* W2 */
- /* v2, 2n+1 limbs */
- mpn_mul_n (v2, as2, bs2, n+1); /* W1 */
- /* v1, 2n+1 limbs */
- mpn_mul_n (v1, as1, bs1, n+1); /* W3 */
- /* vinf, s+t limbs */ /* W0 */
- if (s > t) mpn_mul (vinf, a4, s, b1, t);
- else mpn_mul (vinf, b1, t, a4, s);
- /* v0, 2n limbs */
- mpn_mul_n (v0, ap, bp, n); /* W5 */
- mpn_toom_interpolate_6pts (pp, n, flags, vm1, vm2, v2, t + s);
- #undef v0
- #undef vm1
- #undef v1
- #undef vm2
- #undef v2
- #undef vinf
- #undef bs1
- #undef bs2
- #undef bsm1
- #undef bsm2
- #undef asm1
- #undef asm2
- #undef as1
- #undef as2
- #undef a0a2
- #undef b0b2
- #undef a1a3
- #undef a0
- #undef a1
- #undef a2
- #undef a3
- #undef b0
- #undef b1
- #undef b2
- }