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257 lines
6.5 KiB
C
257 lines
6.5 KiB
C
/* mpn_toom52_mul -- Multiply {ap,an} and {bp,bn} where an is nominally 4/3
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times as large as bn. Or more accurately, bn < an < 2 bn.
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Contributed to the GNU project by Marco Bodrato.
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The idea of applying toom to unbalanced multiplication is due to Marco
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Bodrato and Alberto Zanoni.
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THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY
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SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
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GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
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Copyright 2009 Free Software Foundation, Inc.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of either:
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* the GNU Lesser General Public License as published by the Free
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Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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or
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* the GNU General Public License as published by the Free Software
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Foundation; either version 2 of the License, or (at your option) any
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later version.
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or both in parallel, as here.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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You should have received copies of the GNU General Public License and the
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GNU Lesser General Public License along with the GNU MP Library. If not,
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see https://www.gnu.org/licenses/. */
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#include "gmp-impl.h"
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/* Evaluate in: -2, -1, 0, +1, +2, +inf
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<-s-><--n--><--n--><--n--><--n-->
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___ ______ ______ ______ ______
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|a4_|___a3_|___a2_|___a1_|___a0_|
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|b1|___b0_|
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<t-><--n-->
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v0 = a0 * b0 # A(0)*B(0)
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v1 = (a0+ a1+ a2+ a3+ a4)*(b0+ b1) # A(1)*B(1) ah <= 4 bh <= 1
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vm1 = (a0- a1+ a2- a3+ a4)*(b0- b1) # A(-1)*B(-1) |ah| <= 2 bh = 0
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v2 = (a0+2a1+4a2+8a3+16a4)*(b0+2b1) # A(2)*B(2) ah <= 30 bh <= 2
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vm2 = (a0-2a1+4a2-8a3+16a4)*(b0-2b1) # A(-2)*B(-2) |ah| <= 20 |bh|<= 1
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vinf= a4 * b1 # A(inf)*B(inf)
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Some slight optimization in evaluation are taken from the paper:
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"Towards Optimal Toom-Cook Multiplication for Univariate and
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Multivariate Polynomials in Characteristic 2 and 0."
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*/
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void
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mpn_toom52_mul (mp_ptr pp,
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mp_srcptr ap, mp_size_t an,
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mp_srcptr bp, mp_size_t bn, mp_ptr scratch)
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{
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mp_size_t n, s, t;
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enum toom6_flags flags;
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#define a0 ap
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#define a1 (ap + n)
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#define a2 (ap + 2 * n)
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#define a3 (ap + 3 * n)
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#define a4 (ap + 4 * n)
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#define b0 bp
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#define b1 (bp + n)
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n = 1 + (2 * an >= 5 * bn ? (an - 1) / (size_t) 5 : (bn - 1) >> 1);
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s = an - 4 * n;
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t = bn - n;
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ASSERT (0 < s && s <= n);
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ASSERT (0 < t && t <= n);
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/* Ensures that 5 values of n+1 limbs each fits in the product area.
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Borderline cases are an = 32, bn = 8, n = 7, and an = 36, bn = 9,
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n = 8. */
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ASSERT (s+t >= 5);
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#define v0 pp /* 2n */
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#define vm1 (scratch) /* 2n+1 */
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#define v1 (pp + 2 * n) /* 2n+1 */
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#define vm2 (scratch + 2 * n + 1) /* 2n+1 */
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#define v2 (scratch + 4 * n + 2) /* 2n+1 */
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#define vinf (pp + 5 * n) /* s+t */
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#define bs1 pp /* n+1 */
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#define bsm1 (scratch + 2 * n + 2) /* n */
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#define asm1 (scratch + 3 * n + 3) /* n+1 */
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#define asm2 (scratch + 4 * n + 4) /* n+1 */
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#define bsm2 (pp + n + 1) /* n+1 */
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#define bs2 (pp + 2 * n + 2) /* n+1 */
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#define as2 (pp + 3 * n + 3) /* n+1 */
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#define as1 (pp + 4 * n + 4) /* n+1 */
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/* Scratch need is 6 * n + 3 + 1. We need one extra limb, because
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products will overwrite 2n+2 limbs. */
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#define a0a2 scratch
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#define a1a3 asm1
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/* Compute as2 and asm2. */
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flags = (enum toom6_flags) (toom6_vm2_neg & mpn_toom_eval_pm2 (as2, asm2, 4, ap, n, s, a1a3));
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/* Compute bs1 and bsm1. */
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if (t == n)
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{
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#if HAVE_NATIVE_mpn_add_n_sub_n
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mp_limb_t cy;
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if (mpn_cmp (b0, b1, n) < 0)
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{
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cy = mpn_add_n_sub_n (bs1, bsm1, b1, b0, n);
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flags = (enum toom6_flags) (flags ^ toom6_vm1_neg);
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}
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else
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{
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cy = mpn_add_n_sub_n (bs1, bsm1, b0, b1, n);
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}
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bs1[n] = cy >> 1;
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#else
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bs1[n] = mpn_add_n (bs1, b0, b1, n);
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if (mpn_cmp (b0, b1, n) < 0)
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{
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mpn_sub_n (bsm1, b1, b0, n);
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flags = (enum toom6_flags) (flags ^ toom6_vm1_neg);
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}
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else
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{
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mpn_sub_n (bsm1, b0, b1, n);
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}
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#endif
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}
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else
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{
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bs1[n] = mpn_add (bs1, b0, n, b1, t);
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if (mpn_zero_p (b0 + t, n - t) && mpn_cmp (b0, b1, t) < 0)
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{
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mpn_sub_n (bsm1, b1, b0, t);
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MPN_ZERO (bsm1 + t, n - t);
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flags = (enum toom6_flags) (flags ^ toom6_vm1_neg);
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}
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else
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{
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mpn_sub (bsm1, b0, n, b1, t);
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}
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}
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/* Compute bs2 and bsm2, recycling bs1 and bsm1. bs2=bs1+b1; bsm2=bsm1-b1 */
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mpn_add (bs2, bs1, n+1, b1, t);
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if (flags & toom6_vm1_neg)
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{
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bsm2[n] = mpn_add (bsm2, bsm1, n, b1, t);
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flags = (enum toom6_flags) (flags ^ toom6_vm2_neg);
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}
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else
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{
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bsm2[n] = 0;
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if (t == n)
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{
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if (mpn_cmp (bsm1, b1, n) < 0)
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{
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mpn_sub_n (bsm2, b1, bsm1, n);
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flags = (enum toom6_flags) (flags ^ toom6_vm2_neg);
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}
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else
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{
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mpn_sub_n (bsm2, bsm1, b1, n);
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}
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}
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else
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{
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if (mpn_zero_p (bsm1 + t, n - t) && mpn_cmp (bsm1, b1, t) < 0)
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{
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mpn_sub_n (bsm2, b1, bsm1, t);
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MPN_ZERO (bsm2 + t, n - t);
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flags = (enum toom6_flags) (flags ^ toom6_vm2_neg);
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}
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else
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{
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mpn_sub (bsm2, bsm1, n, b1, t);
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}
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}
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}
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/* Compute as1 and asm1. */
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flags = (enum toom6_flags) (flags ^ (toom6_vm1_neg & mpn_toom_eval_pm1 (as1, asm1, 4, ap, n, s, a0a2)));
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ASSERT (as1[n] <= 4);
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ASSERT (bs1[n] <= 1);
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ASSERT (asm1[n] <= 2);
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/* ASSERT (bsm1[n] <= 1); */
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ASSERT (as2[n] <=30);
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ASSERT (bs2[n] <= 2);
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ASSERT (asm2[n] <= 20);
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ASSERT (bsm2[n] <= 1);
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/* vm1, 2n+1 limbs */
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mpn_mul (vm1, asm1, n+1, bsm1, n); /* W4 */
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/* vm2, 2n+1 limbs */
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mpn_mul_n (vm2, asm2, bsm2, n+1); /* W2 */
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/* v2, 2n+1 limbs */
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mpn_mul_n (v2, as2, bs2, n+1); /* W1 */
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/* v1, 2n+1 limbs */
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mpn_mul_n (v1, as1, bs1, n+1); /* W3 */
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/* vinf, s+t limbs */ /* W0 */
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if (s > t) mpn_mul (vinf, a4, s, b1, t);
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else mpn_mul (vinf, b1, t, a4, s);
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/* v0, 2n limbs */
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mpn_mul_n (v0, ap, bp, n); /* W5 */
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mpn_toom_interpolate_6pts (pp, n, flags, vm1, vm2, v2, t + s);
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#undef v0
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#undef vm1
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#undef v1
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#undef vm2
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#undef v2
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#undef vinf
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#undef bs1
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#undef bs2
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#undef bsm1
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#undef bsm2
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#undef asm1
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#undef asm2
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#undef as1
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#undef as2
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#undef a0a2
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#undef b0b2
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#undef a1a3
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#undef a0
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#undef a1
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#undef a2
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#undef a3
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#undef b0
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#undef b1
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#undef b2
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}
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