diff options
Diffstat (limited to 'gmp-6.3.0/mpn/generic/toom33_mul.c')
| -rw-r--r-- | gmp-6.3.0/mpn/generic/toom33_mul.c | 316 |
1 files changed, 316 insertions, 0 deletions
diff --git a/gmp-6.3.0/mpn/generic/toom33_mul.c b/gmp-6.3.0/mpn/generic/toom33_mul.c new file mode 100644 index 0000000..54f055f --- /dev/null +++ b/gmp-6.3.0/mpn/generic/toom33_mul.c @@ -0,0 +1,316 @@ +/* mpn_toom33_mul -- Multiply {ap,an} and {p,bn} where an and bn are close in + size. Or more accurately, bn <= an < (3/2)bn. + + Contributed to the GNU project by Torbjorn Granlund. + Additional improvements 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 2006-2008, 2010, 2012, 2015, 2021 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: -1, 0, +1, +2, +inf + + <-s--><--n--><--n--> + ____ ______ ______ + |_a2_|___a1_|___a0_| + |b2_|___b1_|___b0_| + <-t-><--n--><--n--> + + v0 = a0 * b0 # A(0)*B(0) + v1 = (a0+ a1+ a2)*(b0+ b1+ b2) # A(1)*B(1) ah <= 2 bh <= 2 + vm1 = (a0- a1+ a2)*(b0- b1+ b2) # A(-1)*B(-1) |ah| <= 1 bh <= 1 + v2 = (a0+2a1+4a2)*(b0+2b1+4b2) # A(2)*B(2) ah <= 6 bh <= 6 + vinf= a2 * b2 # A(inf)*B(inf) +*/ + +#if TUNE_PROGRAM_BUILD || WANT_FAT_BINARY +#define MAYBE_mul_basecase 1 +#define MAYBE_mul_toom33 1 +#else +#define MAYBE_mul_basecase \ + (MUL_TOOM33_THRESHOLD < 3 * MUL_TOOM22_THRESHOLD) +#define MAYBE_mul_toom33 \ + (MUL_TOOM44_THRESHOLD >= 3 * MUL_TOOM33_THRESHOLD) +#endif + +/* FIXME: TOOM33_MUL_N_REC is not quite right for a balanced + multiplication at the infinity point. We may have + MAYBE_mul_basecase == 0, and still get s just below + MUL_TOOM22_THRESHOLD. If MUL_TOOM33_THRESHOLD == 7, we can even get + s == 1 and mpn_toom22_mul will crash. +*/ + +#define TOOM33_MUL_N_REC(p, a, b, n, ws) \ + do { \ + if (MAYBE_mul_basecase \ + && BELOW_THRESHOLD (n, MUL_TOOM22_THRESHOLD)) \ + mpn_mul_basecase (p, a, n, b, n); \ + else if (! MAYBE_mul_toom33 \ + || BELOW_THRESHOLD (n, MUL_TOOM33_THRESHOLD)) \ + mpn_toom22_mul (p, a, n, b, n, ws); \ + else \ + mpn_toom33_mul (p, a, n, b, n, ws); \ + } while (0) + +void +mpn_toom33_mul (mp_ptr pp, + mp_srcptr ap, mp_size_t an, + mp_srcptr bp, mp_size_t bn, + mp_ptr scratch) +{ + const int __gmpn_cpuvec_initialized = 1; + mp_size_t n, s, t; + int vm1_neg; + mp_limb_t cy, vinf0; + mp_ptr gp; + mp_ptr as1, asm1, as2; + mp_ptr bs1, bsm1, bs2; + +#define a0 ap +#define a1 (ap + n) +#define a2 (ap + 2*n) +#define b0 bp +#define b1 (bp + n) +#define b2 (bp + 2*n) + + n = (an + 2) / (size_t) 3; + + s = an - 2 * n; + t = bn - 2 * n; + + ASSERT (an >= bn); + + ASSERT (0 < s && s <= n); + ASSERT (0 < t && t <= n); + + as1 = scratch + 4 * n + 4; + asm1 = scratch + 2 * n + 2; + as2 = pp + n + 1; + + bs1 = pp; + bsm1 = scratch + 3 * n + 3; /* we need 4n+4 <= 4n+s+t */ + bs2 = pp + 2 * n + 2; + + gp = scratch; + + vm1_neg = 0; + + /* Compute as1 and asm1. */ + cy = mpn_add (gp, a0, n, a2, s); +#if HAVE_NATIVE_mpn_add_n_sub_n + if (cy == 0 && mpn_cmp (gp, a1, n) < 0) + { + cy = mpn_add_n_sub_n (as1, asm1, a1, gp, n); + as1[n] = cy >> 1; + asm1[n] = 0; + vm1_neg = 1; + } + else + { + mp_limb_t cy2; + cy2 = mpn_add_n_sub_n (as1, asm1, gp, a1, n); + as1[n] = cy + (cy2 >> 1); + asm1[n] = cy - (cy2 & 1); + } +#else + as1[n] = cy + mpn_add_n (as1, gp, a1, n); + if (cy == 0 && mpn_cmp (gp, a1, n) < 0) + { + mpn_sub_n (asm1, a1, gp, n); + asm1[n] = 0; + vm1_neg = 1; + } + else + { + cy -= mpn_sub_n (asm1, gp, a1, n); + asm1[n] = cy; + } +#endif + + /* Compute as2. */ +#if HAVE_NATIVE_mpn_rsblsh1_n + cy = mpn_add_n (as2, a2, as1, s); + if (s != n) + cy = mpn_add_1 (as2 + s, as1 + s, n - s, cy); + cy += as1[n]; + cy = 2 * cy + mpn_rsblsh1_n (as2, a0, as2, n); +#else +#if HAVE_NATIVE_mpn_addlsh1_n + cy = mpn_addlsh1_n (as2, a1, a2, s); + if (s != n) + cy = mpn_add_1 (as2 + s, a1 + s, n - s, cy); + cy = 2 * cy + mpn_addlsh1_n (as2, a0, as2, n); +#else + cy = mpn_add_n (as2, a2, as1, s); + if (s != n) + cy = mpn_add_1 (as2 + s, as1 + s, n - s, cy); + cy += as1[n]; + cy = 2 * cy + mpn_lshift (as2, as2, n, 1); + cy -= mpn_sub_n (as2, as2, a0, n); +#endif +#endif + as2[n] = cy; + + /* Compute bs1 and bsm1. */ + cy = mpn_add (gp, b0, n, b2, t); +#if HAVE_NATIVE_mpn_add_n_sub_n + if (cy == 0 && mpn_cmp (gp, b1, n) < 0) + { + cy = mpn_add_n_sub_n (bs1, bsm1, b1, gp, n); + bs1[n] = cy >> 1; + bsm1[n] = 0; + vm1_neg ^= 1; + } + else + { + mp_limb_t cy2; + cy2 = mpn_add_n_sub_n (bs1, bsm1, gp, b1, n); + bs1[n] = cy + (cy2 >> 1); + bsm1[n] = cy - (cy2 & 1); + } +#else + bs1[n] = cy + mpn_add_n (bs1, gp, b1, n); + if (cy == 0 && mpn_cmp (gp, b1, n) < 0) + { + mpn_sub_n (bsm1, b1, gp, n); + bsm1[n] = 0; + vm1_neg ^= 1; + } + else + { + cy -= mpn_sub_n (bsm1, gp, b1, n); + bsm1[n] = cy; + } +#endif + + /* Compute bs2. */ +#if HAVE_NATIVE_mpn_rsblsh1_n + cy = mpn_add_n (bs2, b2, bs1, t); + if (t != n) + cy = mpn_add_1 (bs2 + t, bs1 + t, n - t, cy); + cy += bs1[n]; + cy = 2 * cy + mpn_rsblsh1_n (bs2, b0, bs2, n); +#else +#if HAVE_NATIVE_mpn_addlsh1_n + cy = mpn_addlsh1_n (bs2, b1, b2, t); + if (t != n) + cy = mpn_add_1 (bs2 + t, b1 + t, n - t, cy); + cy = 2 * cy + mpn_addlsh1_n (bs2, b0, bs2, n); +#else + cy = mpn_add_n (bs2, bs1, b2, t); + if (t != n) + cy = mpn_add_1 (bs2 + t, bs1 + t, n - t, cy); + cy += bs1[n]; + cy = 2 * cy + mpn_lshift (bs2, bs2, n, 1); + cy -= mpn_sub_n (bs2, bs2, b0, n); +#endif +#endif + bs2[n] = cy; + + ASSERT (as1[n] <= 2); + ASSERT (bs1[n] <= 2); + ASSERT (asm1[n] <= 1); + ASSERT (bsm1[n] <= 1); + ASSERT (as2[n] <= 6); + ASSERT (bs2[n] <= 6); + +#define v0 pp /* 2n */ +#define v1 (pp + 2 * n) /* 2n+1 */ +#define vinf (pp + 4 * n) /* s+t */ +#define vm1 scratch /* 2n+1 */ +#define v2 (scratch + 2 * n + 1) /* 2n+2 */ +#define scratch_out (scratch + 5 * n + 5) + + /* vm1, 2n+1 limbs */ +#ifdef SMALLER_RECURSION + TOOM33_MUL_N_REC (vm1, asm1, bsm1, n, scratch_out); + cy = 0; + if (asm1[n] != 0) + cy = bsm1[n] + mpn_add_n (vm1 + n, vm1 + n, bsm1, n); + if (bsm1[n] != 0) + cy += mpn_add_n (vm1 + n, vm1 + n, asm1, n); + vm1[2 * n] = cy; +#else + vm1[2 * n] = 0; + TOOM33_MUL_N_REC (vm1, asm1, bsm1, n + (bsm1[n] | asm1[n]), scratch_out); +#endif + + TOOM33_MUL_N_REC (v2, as2, bs2, n + 1, scratch_out); /* v2, 2n+1 limbs */ + + /* vinf, s+t limbs */ + if (s > t) mpn_mul (vinf, a2, s, b2, t); + else TOOM33_MUL_N_REC (vinf, a2, b2, s, scratch_out); + + vinf0 = vinf[0]; /* v1 overlaps with this */ + +#ifdef SMALLER_RECURSION + /* v1, 2n+1 limbs */ + TOOM33_MUL_N_REC (v1, as1, bs1, n, scratch_out); + if (as1[n] == 1) + { + cy = bs1[n] + mpn_add_n (v1 + n, v1 + n, bs1, n); + } + else if (as1[n] != 0) + { +#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 + cy = 0; + if (bs1[n] == 1) + { + cy += mpn_add_n (v1 + n, v1 + n, as1, n); + } + else if (bs1[n] != 0) + { +#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 + cy = vinf[1]; + TOOM33_MUL_N_REC (v1, as1, bs1, n + 1, scratch_out); + vinf[1] = cy; +#endif + + TOOM33_MUL_N_REC (v0, ap, bp, n, scratch_out); /* v0, 2n limbs */ + + mpn_toom_interpolate_5pts (pp, v2, vm1, n, s + t, vm1_neg, vinf0); +} |