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/toom8h_mul.c | 305 +++++++++++++++++++++++++++++++++++++ 1 file changed, 305 insertions(+) create mode 100644 gmp-6.3.0/mpn/generic/toom8h_mul.c (limited to 'gmp-6.3.0/mpn/generic/toom8h_mul.c') diff --git a/gmp-6.3.0/mpn/generic/toom8h_mul.c b/gmp-6.3.0/mpn/generic/toom8h_mul.c new file mode 100644 index 0000000..5ba259a --- /dev/null +++ b/gmp-6.3.0/mpn/generic/toom8h_mul.c @@ -0,0 +1,305 @@ +/* Implementation of the multiplication algorithm for Toom-Cook 8.5-way. + + Contributed to the GNU project by Marco Bodrato. + + 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, 2010, 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" + + +#if GMP_NUMB_BITS < 29 +#error Not implemented. +#endif + +#if GMP_NUMB_BITS < 43 +#define BIT_CORRECTION 1 +#define CORRECTION_BITS GMP_NUMB_BITS +#else +#define BIT_CORRECTION 0 +#define CORRECTION_BITS 0 +#endif + + +#if TUNE_PROGRAM_BUILD +#define MAYBE_mul_basecase 1 +#define MAYBE_mul_toom22 1 +#define MAYBE_mul_toom33 1 +#define MAYBE_mul_toom44 1 +#define MAYBE_mul_toom8h 1 +#else +#define MAYBE_mul_basecase \ + (MUL_TOOM8H_THRESHOLD < 8 * MUL_TOOM22_THRESHOLD) +#define MAYBE_mul_toom22 \ + (MUL_TOOM8H_THRESHOLD < 8 * MUL_TOOM33_THRESHOLD) +#define MAYBE_mul_toom33 \ + (MUL_TOOM8H_THRESHOLD < 8 * MUL_TOOM44_THRESHOLD) +#define MAYBE_mul_toom44 \ + (MUL_TOOM8H_THRESHOLD < 8 * MUL_TOOM6H_THRESHOLD) +#define MAYBE_mul_toom8h \ + (MUL_FFT_THRESHOLD >= 8 * MUL_TOOM8H_THRESHOLD) +#endif + +#define TOOM8H_MUL_N_REC(p, a, b, f, p2, a2, b2, n, ws) \ + do { \ + if (MAYBE_mul_basecase \ + && BELOW_THRESHOLD (n, MUL_TOOM22_THRESHOLD)) { \ + mpn_mul_basecase (p, a, n, b, n); \ + if (f) mpn_mul_basecase (p2, a2, n, b2, n); \ + } else if (MAYBE_mul_toom22 \ + && BELOW_THRESHOLD (n, MUL_TOOM33_THRESHOLD)) { \ + mpn_toom22_mul (p, a, n, b, n, ws); \ + if (f) mpn_toom22_mul (p2, a2, n, b2, n, ws); \ + } else if (MAYBE_mul_toom33 \ + && BELOW_THRESHOLD (n, MUL_TOOM44_THRESHOLD)) { \ + mpn_toom33_mul (p, a, n, b, n, ws); \ + if (f) mpn_toom33_mul (p2, a2, n, b2, n, ws); \ + } else if (MAYBE_mul_toom44 \ + && BELOW_THRESHOLD (n, MUL_TOOM6H_THRESHOLD)) { \ + mpn_toom44_mul (p, a, n, b, n, ws); \ + if (f) mpn_toom44_mul (p2, a2, n, b2, n, ws); \ + } else if (! MAYBE_mul_toom8h \ + || BELOW_THRESHOLD (n, MUL_TOOM8H_THRESHOLD)) { \ + mpn_toom6h_mul (p, a, n, b, n, ws); \ + if (f) mpn_toom6h_mul (p2, a2, n, b2, n, ws); \ + } else { \ + mpn_toom8h_mul (p, a, n, b, n, ws); \ + if (f) mpn_toom8h_mul (p2, a2, n, b2, n, ws); \ + } \ + } while (0) + +#define TOOM8H_MUL_REC(p, a, na, b, nb, ws) \ + do { mpn_mul (p, a, na, b, nb); } while (0) + +/* Toom-8.5 , compute the product {pp,an+bn} <- {ap,an} * {bp,bn} + With: an >= bn >= 86, an*5 < bn * 11. + It _may_ work with bn<=?? and bn*?? < an*? < bn*?? + + Evaluate in: infinity, +8,-8,+4,-4,+2,-2,+1,-1,+1/2,-1/2,+1/4,-1/4,+1/8,-1/8,0. +*/ +/* Estimate on needed scratch: + S(n) <= (n+7)\8*13+5+MAX(S((n+7)\8),1+2*(n+7)\8), + since n>80; S(n) <= ceil(log(n/10)/log(8))*(13+5)+n*15\8 < n*15\8 + lg2(n)*6 + */ + +void +mpn_toom8h_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; + int p, q, half; + int sign; + + /***************************** decomposition *******************************/ + + ASSERT (an >= bn); + /* Can not handle too small operands */ + ASSERT (bn >= 86); + /* Can not handle too much unbalancement */ + ASSERT (an <= bn*4); + ASSERT (GMP_NUMB_BITS > 11*3 || an*4 <= bn*11); + ASSERT (GMP_NUMB_BITS > 10*3 || an*1 <= bn* 2); + ASSERT (GMP_NUMB_BITS > 9*3 || an*2 <= bn* 3); + + /* Limit num/den is a rational number between + (16/15)^(log(6)/log(2*6-1)) and (16/15)^(log(8)/log(2*8-1)) */ +#define LIMIT_numerator (21) +#define LIMIT_denominat (20) + + if (LIKELY (an == bn) || an * (LIMIT_denominat>>1) < LIMIT_numerator * (bn>>1) ) /* is 8*... < 8*... */ + { + half = 0; + n = 1 + ((an - 1)>>3); + p = q = 7; + s = an - 7 * n; + t = bn - 7 * n; + } + else + { + if (an * 13 < 16 * bn) /* (an*7*LIMIT_numerator>1) < (LIMIT_numerator/7*9) * (bn>>1)) + { p = 9; q = 7; } + else if (an * 10 < 33 * (bn>>1)) /* (an*3*LIMIT_numerator= p * bn ? (an - 1) / (size_t) p : (bn - 1) / (size_t) q); + p--; q--; + + s = an - p * n; + t = bn - q * n; + + if(half) { /* Recover from badly chosen splitting */ + if (UNLIKELY (s<1)) {p--; s+=n; half=0;} + else if (UNLIKELY (t<1)) {q--; t+=n; half=0;} + } + } +#undef LIMIT_numerator +#undef LIMIT_denominat + + ASSERT (0 < s && s <= n); + ASSERT (0 < t && t <= n); + ASSERT (half || s + t > 3); + ASSERT (n > 2); + +#define r6 (pp + 3 * n) /* 3n+1 */ +#define r4 (pp + 7 * n) /* 3n+1 */ +#define r2 (pp +11 * n) /* 3n+1 */ +#define r0 (pp +15 * n) /* s+t <= 2*n */ +#define r7 (scratch) /* 3n+1 */ +#define r5 (scratch + 3 * n + 1) /* 3n+1 */ +#define r3 (scratch + 6 * n + 2) /* 3n+1 */ +#define r1 (scratch + 9 * n + 3) /* 3n+1 */ +#define v0 (pp +11 * n) /* n+1 */ +#define v1 (pp +12 * n+1) /* n+1 */ +#define v2 (pp +13 * n+2) /* n+1 */ +#define v3 (scratch +12 * n + 4) /* n+1 */ +#define wsi (scratch +12 * n + 4) /* 3n+1 */ +#define wse (scratch +13 * n + 5) /* 2n+1 */ + + /* Alloc also 3n+1 limbs for wsi... toom_interpolate_16pts may + need all of them */ +/* if (scratch == NULL) */ +/* scratch = TMP_SALLOC_LIMBS(mpn_toom8_sqr_itch(n * 8)); */ + ASSERT (15 * n + 6 <= mpn_toom8h_mul_itch (an, bn)); + ASSERT (15 * n + 6 <= mpn_toom8_sqr_itch (n * 8)); + + /********************** evaluation and recursive calls *********************/ + + /* $\pm1/8$ */ + sign = mpn_toom_eval_pm2rexp (v2, v0, p, ap, n, s, 3, pp) ^ + mpn_toom_eval_pm2rexp (v3, v1, q, bp, n, t, 3, pp); + /* A(-1/8)*B(-1/8)*8^. */ /* A(+1/8)*B(+1/8)*8^. */ + TOOM8H_MUL_N_REC(pp, v0, v1, 2, r7, v2, v3, n + 1, wse); + mpn_toom_couple_handling (r7, 2 * n + 1 + BIT_CORRECTION, pp, sign, n, 3*(1+half), 3*(half)); + + /* $\pm1/4$ */ + sign = mpn_toom_eval_pm2rexp (v2, v0, p, ap, n, s, 2, pp) ^ + mpn_toom_eval_pm2rexp (v3, v1, q, bp, n, t, 2, pp); + /* A(-1/4)*B(-1/4)*4^. */ /* A(+1/4)*B(+1/4)*4^. */ + TOOM8H_MUL_N_REC(pp, v0, v1, 2, r5, v2, v3, n + 1, wse); + mpn_toom_couple_handling (r5, 2 * n + 1, pp, sign, n, 2*(1+half), 2*(half)); + + /* $\pm2$ */ + sign = mpn_toom_eval_pm2 (v2, v0, p, ap, n, s, pp) ^ + mpn_toom_eval_pm2 (v3, v1, q, bp, n, t, pp); + /* A(-2)*B(-2) */ /* A(+2)*B(+2) */ + TOOM8H_MUL_N_REC(pp, v0, v1, 2, r3, v2, v3, n + 1, wse); + mpn_toom_couple_handling (r3, 2 * n + 1, pp, sign, n, 1, 2); + + /* $\pm8$ */ + sign = mpn_toom_eval_pm2exp (v2, v0, p, ap, n, s, 3, pp) ^ + mpn_toom_eval_pm2exp (v3, v1, q, bp, n, t, 3, pp); + /* A(-8)*B(-8) */ /* A(+8)*B(+8) */ + TOOM8H_MUL_N_REC(pp, v0, v1, 2, r1, v2, v3, n + 1, wse); + mpn_toom_couple_handling (r1, 2 * n + 1 + BIT_CORRECTION, pp, sign, n, 3, 6); + + /* $\pm1/2$ */ + sign = mpn_toom_eval_pm2rexp (v2, v0, p, ap, n, s, 1, pp) ^ + mpn_toom_eval_pm2rexp (v3, v1, q, bp, n, t, 1, pp); + /* A(-1/2)*B(-1/2)*2^. */ /* A(+1/2)*B(+1/2)*2^. */ + TOOM8H_MUL_N_REC(pp, v0, v1, 2, r6, v2, v3, n + 1, wse); + mpn_toom_couple_handling (r6, 2 * n + 1, pp, sign, n, 1+half, half); + + /* $\pm1$ */ + sign = mpn_toom_eval_pm1 (v2, v0, p, ap, n, s, pp); + if (GMP_NUMB_BITS > 12*3 && UNLIKELY (q == 3)) + sign ^= mpn_toom_eval_dgr3_pm1 (v3, v1, bp, n, t, pp); + else + sign ^= mpn_toom_eval_pm1 (v3, v1, q, bp, n, t, pp); + /* A(-1)*B(-1) */ /* A(1)*B(1) */ + TOOM8H_MUL_N_REC(pp, v0, v1, 2, r4, v2, v3, n + 1, wse); + mpn_toom_couple_handling (r4, 2 * n + 1, pp, sign, n, 0, 0); + + /* $\pm4$ */ + sign = mpn_toom_eval_pm2exp (v2, v0, p, ap, n, s, 2, pp) ^ + mpn_toom_eval_pm2exp (v3, v1, q, bp, n, t, 2, pp); + /* A(-4)*B(-4) */ /* A(+4)*B(+4) */ + TOOM8H_MUL_N_REC(pp, v0, v1, 2, r2, v2, v3, n + 1, wse); + mpn_toom_couple_handling (r2, 2 * n + 1, pp, sign, n, 2, 4); + +#undef v0 +#undef v1 +#undef v2 +#undef v3 +#undef wse + + /* A(0)*B(0) */ + TOOM8H_MUL_N_REC(pp, ap, bp, 0, pp, ap, bp, n, wsi); + + /* Infinity */ + if (UNLIKELY (half != 0)) { + if (s > t) { + TOOM8H_MUL_REC(r0, ap + p * n, s, bp + q * n, t, wsi); + } else { + TOOM8H_MUL_REC(r0, bp + q * n, t, ap + p * n, s, wsi); + }; + }; + + mpn_toom_interpolate_16pts (pp, r1, r3, r5, r7, n, s+t, half, wsi); + +#undef r0 +#undef r1 +#undef r2 +#undef r3 +#undef r4 +#undef r5 +#undef r6 +#undef wsi +} + +#undef TOOM8H_MUL_N_REC +#undef TOOM8H_MUL_REC +#undef MAYBE_mul_basecase +#undef MAYBE_mul_toom22 +#undef MAYBE_mul_toom33 +#undef MAYBE_mul_toom44 +#undef MAYBE_mul_toom8h -- cgit v1.2.3