From 11da511c784eca003deb90c23570f0873954e0de Mon Sep 17 00:00:00 2001 From: Duncan Wilkie Date: Sat, 18 Nov 2023 06:11:09 -0600 Subject: Initial commit. --- gmp-6.3.0/mpn/generic/toom52_mul.c | 256 +++++++++++++++++++++++++++++++++++++ 1 file changed, 256 insertions(+) create mode 100644 gmp-6.3.0/mpn/generic/toom52_mul.c (limited to 'gmp-6.3.0/mpn/generic/toom52_mul.c') diff --git a/gmp-6.3.0/mpn/generic/toom52_mul.c b/gmp-6.3.0/mpn/generic/toom52_mul.c new file mode 100644 index 0000000..974059b --- /dev/null +++ b/gmp-6.3.0/mpn/generic/toom52_mul.c @@ -0,0 +1,256 @@ +/* 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 either: + + * 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. + +or + + * the GNU General Public License as published by the Free Software + Foundation; either version 2 of the License, or (at your option) any + later version. + +or both in parallel, as here. + +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 General Public License +for more details. + +You should have received copies of the GNU General Public License and the +GNU Lesser General Public License along with the GNU MP Library. If not, +see https://www.gnu.org/licenses/. */ + + +#include "gmp-impl.h" + +/* Evaluate in: -2, -1, 0, +1, +2, +inf + + <-s-><--n--><--n--><--n--><--n--> + ___ ______ ______ ______ ______ + |a4_|___a3_|___a2_|___a1_|___a0_| + |b1|___b0_| + <--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 = (enum toom6_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 = (enum toom6_flags) (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 = (enum toom6_flags) (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 = (enum toom6_flags) (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 = (enum toom6_flags) (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 = (enum toom6_flags) (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 = (enum toom6_flags) (flags ^ toom6_vm2_neg); + } + else + { + mpn_sub (bsm2, bsm1, n, b1, t); + } + } + } + + /* Compute as1 and asm1. */ + flags = (enum toom6_flags) (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 + +} -- cgit v1.2.3