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/toom53_mul.c | 331 +++++++++++++++++++++++++++++++++++++ 1 file changed, 331 insertions(+) create mode 100644 gmp-6.3.0/mpn/generic/toom53_mul.c (limited to 'gmp-6.3.0/mpn/generic/toom53_mul.c') diff --git a/gmp-6.3.0/mpn/generic/toom53_mul.c b/gmp-6.3.0/mpn/generic/toom53_mul.c new file mode 100644 index 0000000..c934297 --- /dev/null +++ b/gmp-6.3.0/mpn/generic/toom53_mul.c @@ -0,0 +1,331 @@ +/* mpn_toom53_mul -- Multiply {ap,an} and {bp,bn} where an is nominally 5/3 + times as large as bn. Or more accurately, (4/3)bn < an < (5/2)bn. + + Contributed to the GNU project by Torbjorn Granlund and 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 2006-2008, 2012, 2014, 2015 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: 0, +1, -1, +2, -2, 1/2, +inf + + <-s-><--n--><--n--><--n--><--n--> + ___ ______ ______ ______ ______ + |a4_|___a3_|___a2_|___a1_|___a0_| + |__b2|___b1_|___b0_| + <-t--><--n--><--n--> + + v0 = a0 * b0 # A(0)*B(0) + v1 = ( a0+ a1+ a2+ a3+ a4)*( b0+ b1+ b2) # A(1)*B(1) ah <= 4 bh <= 2 + vm1 = ( a0- a1+ a2- a3+ a4)*( b0- b1+ b2) # A(-1)*B(-1) |ah| <= 2 bh <= 1 + v2 = ( a0+2a1+4a2+8a3+16a4)*( b0+2b1+4b2) # A(2)*B(2) ah <= 30 bh <= 6 + vm2 = ( a0-2a1+4a2-8a3+16a4)*( b0-2b1+4b2) # A(2)*B(2) -9<=ah<=20 -1<=bh<=4 + vh = (16a0+8a1+4a2+2a3+ a4)*(4b0+2b1+ b2) # A(1/2)*B(1/2) ah <= 30 bh <= 6 + vinf= a4 * b2 # A(inf)*B(inf) +*/ + +void +mpn_toom53_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; + mp_limb_t cy; + mp_ptr gp; + mp_ptr as1, asm1, as2, asm2, ash; + mp_ptr bs1, bsm1, bs2, bsm2, bsh; + mp_ptr tmp; + enum toom7_flags flags; + TMP_DECL; + +#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) +#define b2 (bp + 2*n) + + n = 1 + (3 * an >= 5 * bn ? (an - 1) / (size_t) 5 : (bn - 1) / (size_t) 3); + + s = an - 4 * n; + t = bn - 2 * n; + + ASSERT (0 < s && s <= n); + ASSERT (0 < t && t <= n); + + TMP_MARK; + + tmp = TMP_ALLOC_LIMBS (10 * (n + 1)); + as1 = tmp; tmp += n + 1; + asm1 = tmp; tmp += n + 1; + as2 = tmp; tmp += n + 1; + asm2 = tmp; tmp += n + 1; + ash = tmp; tmp += n + 1; + bs1 = tmp; tmp += n + 1; + bsm1 = tmp; tmp += n + 1; + bs2 = tmp; tmp += n + 1; + bsm2 = tmp; tmp += n + 1; + bsh = tmp; tmp += n + 1; + + gp = pp; + + /* Compute as1 and asm1. */ + flags = (enum toom7_flags) (toom7_w3_neg & mpn_toom_eval_pm1 (as1, asm1, 4, ap, n, s, gp)); + + /* Compute as2 and asm2. */ + flags = (enum toom7_flags) (flags | (toom7_w1_neg & mpn_toom_eval_pm2 (as2, asm2, 4, ap, n, s, gp))); + + /* Compute ash = 16 a0 + 8 a1 + 4 a2 + 2 a3 + a4 + = 2*(2*(2*(2*a0 + a1) + a2) + a3) + a4 */ +#if HAVE_NATIVE_mpn_addlsh1_n + cy = mpn_addlsh1_n (ash, a1, a0, n); + cy = 2*cy + mpn_addlsh1_n (ash, a2, ash, n); + cy = 2*cy + mpn_addlsh1_n (ash, a3, ash, n); + if (s < n) + { + mp_limb_t cy2; + cy2 = mpn_addlsh1_n (ash, a4, ash, s); + ash[n] = 2*cy + mpn_lshift (ash + s, ash + s, n - s, 1); + MPN_INCR_U (ash + s, n+1-s, cy2); + } + else + ash[n] = 2*cy + mpn_addlsh1_n (ash, a4, ash, n); +#else + cy = mpn_lshift (ash, a0, n, 1); + cy += mpn_add_n (ash, ash, a1, n); + cy = 2*cy + mpn_lshift (ash, ash, n, 1); + cy += mpn_add_n (ash, ash, a2, n); + cy = 2*cy + mpn_lshift (ash, ash, n, 1); + cy += mpn_add_n (ash, ash, a3, n); + cy = 2*cy + mpn_lshift (ash, ash, n, 1); + ash[n] = cy + mpn_add (ash, ash, n, a4, s); +#endif + + /* Compute bs1 and bsm1. */ + bs1[n] = mpn_add (bs1, b0, n, b2, t); /* b0 + b2 */ +#if HAVE_NATIVE_mpn_add_n_sub_n + if (bs1[n] == 0 && mpn_cmp (bs1, b1, n) < 0) + { + bs1[n] = mpn_add_n_sub_n (bs1, bsm1, b1, bs1, n) >> 1; + bsm1[n] = 0; + flags = (enum toom7_flags) (flags ^ toom7_w3_neg); + } + else + { + cy = mpn_add_n_sub_n (bs1, bsm1, bs1, b1, n); + bsm1[n] = bs1[n] - (cy & 1); + bs1[n] += (cy >> 1); + } +#else + if (bs1[n] == 0 && mpn_cmp (bs1, b1, n) < 0) + { + mpn_sub_n (bsm1, b1, bs1, n); + bsm1[n] = 0; + flags = (enum toom7_flags) (flags ^ toom7_w3_neg); + } + else + { + bsm1[n] = bs1[n] - mpn_sub_n (bsm1, bs1, b1, n); + } + bs1[n] += mpn_add_n (bs1, bs1, b1, n); /* b0+b1+b2 */ +#endif + + /* Compute bs2 and bsm2. */ +#if HAVE_NATIVE_mpn_addlsh_n || HAVE_NATIVE_mpn_addlsh2_n +#if HAVE_NATIVE_mpn_addlsh2_n + cy = mpn_addlsh2_n (bs2, b0, b2, t); +#else /* HAVE_NATIVE_mpn_addlsh_n */ + cy = mpn_addlsh_n (bs2, b0, b2, t, 2); +#endif + if (t < n) + cy = mpn_add_1 (bs2 + t, b0 + t, n - t, cy); + bs2[n] = cy; +#else + cy = mpn_lshift (gp, b2, t, 2); + bs2[n] = mpn_add (bs2, b0, n, gp, t); + MPN_INCR_U (bs2 + t, n+1-t, cy); +#endif + + gp[n] = mpn_lshift (gp, b1, n, 1); + +#if HAVE_NATIVE_mpn_add_n_sub_n + if (mpn_cmp (bs2, gp, n+1) < 0) + { + ASSERT_NOCARRY (mpn_add_n_sub_n (bs2, bsm2, gp, bs2, n+1)); + flags = (enum toom7_flags) (flags ^ toom7_w1_neg); + } + else + { + ASSERT_NOCARRY (mpn_add_n_sub_n (bs2, bsm2, bs2, gp, n+1)); + } +#else + if (mpn_cmp (bs2, gp, n+1) < 0) + { + ASSERT_NOCARRY (mpn_sub_n (bsm2, gp, bs2, n+1)); + flags = (enum toom7_flags) (flags ^ toom7_w1_neg); + } + else + { + ASSERT_NOCARRY (mpn_sub_n (bsm2, bs2, gp, n+1)); + } + mpn_add_n (bs2, bs2, gp, n+1); +#endif + + /* Compute bsh = 4 b0 + 2 b1 + b2 = 2*(2*b0 + b1)+b2. */ +#if HAVE_NATIVE_mpn_addlsh1_n + cy = mpn_addlsh1_n (bsh, b1, b0, n); + if (t < n) + { + mp_limb_t cy2; + cy2 = mpn_addlsh1_n (bsh, b2, bsh, t); + bsh[n] = 2*cy + mpn_lshift (bsh + t, bsh + t, n - t, 1); + MPN_INCR_U (bsh + t, n+1-t, cy2); + } + else + bsh[n] = 2*cy + mpn_addlsh1_n (bsh, b2, bsh, n); +#else + cy = mpn_lshift (bsh, b0, n, 1); + cy += mpn_add_n (bsh, bsh, b1, n); + cy = 2*cy + mpn_lshift (bsh, bsh, n, 1); + bsh[n] = cy + mpn_add (bsh, bsh, n, b2, t); +#endif + + ASSERT (as1[n] <= 4); + ASSERT (bs1[n] <= 2); + ASSERT (asm1[n] <= 2); + ASSERT (bsm1[n] <= 1); + ASSERT (as2[n] <= 30); + ASSERT (bs2[n] <= 6); + ASSERT (asm2[n] <= 20); + ASSERT (bsm2[n] <= 4); + ASSERT (ash[n] <= 30); + ASSERT (bsh[n] <= 6); + +#define v0 pp /* 2n */ +#define v1 (pp + 2 * n) /* 2n+1 */ +#define vinf (pp + 6 * n) /* s+t */ +#define v2 scratch /* 2n+1 */ +#define vm2 (scratch + 2 * n + 1) /* 2n+1 */ +#define vh (scratch + 4 * n + 2) /* 2n+1 */ +#define vm1 (scratch + 6 * n + 3) /* 2n+1 */ +#define scratch_out (scratch + 8 * n + 4) /* 2n+1 */ + /* Total scratch need: 10*n+5 */ + + /* Must be in allocation order, as they overwrite one limb beyond + * 2n+1. */ + mpn_mul_n (v2, as2, bs2, n + 1); /* v2, 2n+1 limbs */ + mpn_mul_n (vm2, asm2, bsm2, n + 1); /* vm2, 2n+1 limbs */ + mpn_mul_n (vh, ash, bsh, n + 1); /* vh, 2n+1 limbs */ + + /* vm1, 2n+1 limbs */ +#ifdef SMALLER_RECURSION + mpn_mul_n (vm1, asm1, bsm1, n); + if (asm1[n] == 1) + { + cy = bsm1[n] + mpn_add_n (vm1 + n, vm1 + n, bsm1, n); + } + else if (asm1[n] == 2) + { +#if HAVE_NATIVE_mpn_addlsh1_n_ip1 + cy = 2 * bsm1[n] + mpn_addlsh1_n_ip1 (vm1 + n, bsm1, n); +#else + cy = 2 * bsm1[n] + mpn_addmul_1 (vm1 + n, bsm1, n, CNST_LIMB(2)); +#endif + } + else + cy = 0; + if (bsm1[n] != 0) + cy += mpn_add_n (vm1 + n, vm1 + n, asm1, n); + vm1[2 * n] = cy; +#else /* SMALLER_RECURSION */ + vm1[2 * n] = 0; + mpn_mul_n (vm1, asm1, bsm1, n + ((asm1[n] | bsm1[n]) != 0)); +#endif /* SMALLER_RECURSION */ + + /* v1, 2n+1 limbs */ +#ifdef SMALLER_RECURSION + mpn_mul_n (v1, as1, bs1, n); + if (as1[n] == 1) + { + cy = bs1[n] + mpn_add_n (v1 + n, v1 + n, bs1, n); + } + else if (as1[n] == 2) + { +#if HAVE_NATIVE_mpn_addlsh1_n_ip1 + cy = 2 * bs1[n] + mpn_addlsh1_n_ip1 (v1 + n, bs1, n); +#else + cy = 2 * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, CNST_LIMB(2)); +#endif + } + else if (as1[n] != 0) + { + cy = as1[n] * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, as1[n]); + } + else + cy = 0; + if (bs1[n] == 1) + { + cy += mpn_add_n (v1 + n, v1 + n, as1, n); + } + else if (bs1[n] == 2) + { +#if HAVE_NATIVE_mpn_addlsh1_n_ip1 + cy += mpn_addlsh1_n_ip1 (v1 + n, as1, n); +#else + cy += mpn_addmul_1 (v1 + n, as1, n, CNST_LIMB(2)); +#endif + } + v1[2 * n] = cy; +#else /* SMALLER_RECURSION */ + v1[2 * n] = 0; + mpn_mul_n (v1, as1, bs1, n + ((as1[n] | bs1[n]) != 0)); +#endif /* SMALLER_RECURSION */ + + mpn_mul_n (v0, a0, b0, n); /* v0, 2n limbs */ + + /* vinf, s+t limbs */ + if (s > t) mpn_mul (vinf, a4, s, b2, t); + else mpn_mul (vinf, b2, t, a4, s); + + mpn_toom_interpolate_7pts (pp, n, flags, vm2, vm1, v2, vh, s + t, + scratch_out); + + TMP_FREE; +} -- cgit v1.2.3