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/toom62_mul.c | 310 +++++++++++++++++++++++++++++++++++++ 1 file changed, 310 insertions(+) create mode 100644 gmp-6.3.0/mpn/generic/toom62_mul.c (limited to 'gmp-6.3.0/mpn/generic/toom62_mul.c') diff --git a/gmp-6.3.0/mpn/generic/toom62_mul.c b/gmp-6.3.0/mpn/generic/toom62_mul.c new file mode 100644 index 0000000..d971cc0 --- /dev/null +++ b/gmp-6.3.0/mpn/generic/toom62_mul.c @@ -0,0 +1,310 @@ +/* mpn_toom62_mul -- Multiply {ap,an} and {bp,bn} where an is nominally 3 times + as large as bn. Or more accurately, (5/2)bn < an < 6bn. + + 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 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--><--n--> + ___ ______ ______ ______ ______ ______ + |a5_|___a4_|___a3_|___a2_|___a1_|___a0_| + |_b1_|___b0_| + <-t--><--n--> + + v0 = a0 * b0 # A(0)*B(0) + v1 = ( a0+ a1+ a2+ a3+ a4+ a5)*( b0+ b1) # A(1)*B(1) ah <= 5 bh <= 1 + vm1 = ( a0- a1+ a2- a3+ a4- a5)*( b0- b1) # A(-1)*B(-1) |ah| <= 2 bh = 0 + v2 = ( a0+ 2a1+4a2+8a3+16a4+32a5)*( b0+2b1) # A(2)*B(2) ah <= 62 bh <= 2 + vm2 = ( a0- 2a1+4a2-8a3+16a4-32a5)*( b0-2b1) # A(-2)*B(-2) -41<=ah<=20 -1<=bh<=0 + vh = (32a0+16a1+8a2+4a3+ 2a4+ a5)*(2b0+ b1) # A(1/2)*B(1/2) ah <= 62 bh <= 2 + vinf= a5 * b1 # A(inf)*B(inf) +*/ + +void +mpn_toom62_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 as1, asm1, as2, asm2, ash; + mp_ptr bs1, bsm1, bs2, bsm2, bsh; + mp_ptr gp; + enum toom7_flags aflags, bflags; + 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 a5 (ap + 5*n) +#define b0 bp +#define b1 (bp + n) + + n = 1 + (an >= 3 * bn ? (an - 1) / (size_t) 6 : (bn - 1) >> 1); + + s = an - 5 * n; + t = bn - n; + + ASSERT (0 < s && s <= n); + ASSERT (0 < t && t <= n); + + TMP_MARK; + + as1 = TMP_SALLOC_LIMBS (n + 1); + asm1 = TMP_SALLOC_LIMBS (n + 1); + as2 = TMP_SALLOC_LIMBS (n + 1); + asm2 = TMP_SALLOC_LIMBS (n + 1); + ash = TMP_SALLOC_LIMBS (n + 1); + + bs1 = TMP_SALLOC_LIMBS (n + 1); + bsm1 = TMP_SALLOC_LIMBS (n); + bs2 = TMP_SALLOC_LIMBS (n + 1); + bsm2 = TMP_SALLOC_LIMBS (n + 1); + bsh = TMP_SALLOC_LIMBS (n + 1); + + gp = pp; + + /* Compute as1 and asm1. */ + aflags = (enum toom7_flags) (toom7_w3_neg & mpn_toom_eval_pm1 (as1, asm1, 5, ap, n, s, gp)); + + /* Compute as2 and asm2. */ + aflags = (enum toom7_flags) (aflags | (toom7_w1_neg & mpn_toom_eval_pm2 (as2, asm2, 5, ap, n, s, gp))); + + /* Compute ash = 32 a0 + 16 a1 + 8 a2 + 4 a3 + 2 a4 + a5 + = 2*(2*(2*(2*(2*a0 + a1) + a2) + a3) + a4) + a5 */ + +#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); + cy = 2*cy + mpn_addlsh1_n (ash, a4, ash, n); + if (s < n) + { + mp_limb_t cy2; + cy2 = mpn_addlsh1_n (ash, a5, 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, a5, 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); + cy += mpn_add_n (ash, ash, a4, n); + cy = 2*cy + mpn_lshift (ash, ash, n, 1); + ash[n] = cy + mpn_add (ash, ash, n, a5, s); +#endif + + /* Compute bs1 and bsm1. */ + if (t == n) + { +#if HAVE_NATIVE_mpn_add_n_sub_n + if (mpn_cmp (b0, b1, n) < 0) + { + cy = mpn_add_n_sub_n (bs1, bsm1, b1, b0, n); + bflags = toom7_w3_neg; + } + else + { + cy = mpn_add_n_sub_n (bs1, bsm1, b0, b1, n); + bflags = (enum toom7_flags) 0; + } + 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); + bflags = toom7_w3_neg; + } + else + { + mpn_sub_n (bsm1, b0, b1, n); + bflags = (enum toom7_flags) 0; + } +#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); + bflags = toom7_w3_neg; + } + else + { + mpn_sub (bsm1, b0, n, b1, t); + bflags = (enum toom7_flags) 0; + } + } + + /* Compute bs2 and bsm2. Recycling bs1 and bsm1; bs2=bs1+b1, bsm2 = + bsm1 - b1 */ + mpn_add (bs2, bs1, n + 1, b1, t); + if (bflags & toom7_w3_neg) + { + bsm2[n] = mpn_add (bsm2, bsm1, n, b1, t); + bflags = (enum toom7_flags) (bflags | toom7_w1_neg); + } + else + { + /* FIXME: Simplify this logic? */ + if (t < n) + { + if (mpn_zero_p (bsm1 + t, n - t) && mpn_cmp (bsm1, b1, t) < 0) + { + ASSERT_NOCARRY (mpn_sub_n (bsm2, b1, bsm1, t)); + MPN_ZERO (bsm2 + t, n + 1 - t); + bflags = (enum toom7_flags) (bflags | toom7_w1_neg); + } + else + { + ASSERT_NOCARRY (mpn_sub (bsm2, bsm1, n, b1, t)); + bsm2[n] = 0; + } + } + else + { + if (mpn_cmp (bsm1, b1, n) < 0) + { + ASSERT_NOCARRY (mpn_sub_n (bsm2, b1, bsm1, n)); + bflags = (enum toom7_flags) (bflags | toom7_w1_neg); + } + else + { + ASSERT_NOCARRY (mpn_sub_n (bsm2, bsm1, b1, n)); + } + bsm2[n] = 0; + } + } + + /* Compute bsh, recycling bs1. bsh=bs1+b0; */ + bsh[n] = bs1[n] + mpn_add_n (bsh, bs1, b0, n); + + ASSERT (as1[n] <= 5); + ASSERT (bs1[n] <= 1); + ASSERT (asm1[n] <= 2); + ASSERT (as2[n] <= 62); + ASSERT (bs2[n] <= 2); + ASSERT (asm2[n] <= 41); + ASSERT (bsm2[n] <= 1); + ASSERT (ash[n] <= 62); + ASSERT (bsh[n] <= 2); + +#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 */ + mpn_mul_n (vm1, asm1, bsm1, n); + cy = 0; + if (asm1[n] == 1) + { + cy = mpn_add_n (vm1 + n, vm1 + n, bsm1, n); + } + else if (asm1[n] == 2) + { +#if HAVE_NATIVE_mpn_addlsh1_n + cy = mpn_addlsh1_n (vm1 + n, vm1 + n, bsm1, n); +#else + cy = mpn_addmul_1 (vm1 + n, bsm1, n, CNST_LIMB(2)); +#endif + } + vm1[2 * n] = cy; + + /* v1, 2n+1 limbs */ + 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 + cy = 2 * bs1[n] + mpn_addlsh1_n (v1 + n, 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] != 0) + cy += mpn_add_n (v1 + n, v1 + n, as1, n); + v1[2 * n] = cy; + + mpn_mul_n (v0, a0, b0, n); /* v0, 2n limbs */ + + /* vinf, s+t limbs */ + if (s > t) mpn_mul (vinf, a5, s, b1, t); + else mpn_mul (vinf, b1, t, a5, s); + + mpn_toom_interpolate_7pts (pp, n, (enum toom7_flags) (aflags ^ bflags), + vm2, vm1, v2, vh, s + t, scratch_out); + + TMP_FREE; +} -- cgit v1.2.3