diff options
Diffstat (limited to 'vendor/gmp-6.3.0/mpn/generic/toom43_mul.c')
-rw-r--r-- | vendor/gmp-6.3.0/mpn/generic/toom43_mul.c | 238 |
1 files changed, 238 insertions, 0 deletions
diff --git a/vendor/gmp-6.3.0/mpn/generic/toom43_mul.c b/vendor/gmp-6.3.0/mpn/generic/toom43_mul.c new file mode 100644 index 0000000..34acd25 --- /dev/null +++ b/vendor/gmp-6.3.0/mpn/generic/toom43_mul.c @@ -0,0 +1,238 @@ +/* mpn_toom43_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, 2020 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--> + ___ ______ ______ ______ + |a3_|___a2_|___a1_|___a0_| + |_b2_|___b1_|___b0_| + <-t--><--n--><--n--> + + v0 = a0 * b0 # A(0)*B(0) + v1 = (a0+ a1+ a2+ a3)*(b0+ b1+ b2) # A(1)*B(1) ah <= 3 bh <= 2 + vm1 = (a0- a1+ a2- a3)*(b0- b1+ b2) # A(-1)*B(-1) |ah| <= 1 |bh|<= 1 + v2 = (a0+2a1+4a2+8a3)*(b0+2b1+4b2) # A(2)*B(2) ah <= 14 bh <= 6 + vm2 = (a0-2a1+4a2-8a3)*(b0-2b1+4b2) # A(-2)*B(-2) |ah| <= 9 |bh|<= 4 + vinf= a3 * b2 # A(inf)*B(inf) +*/ + +void +mpn_toom43_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; + mp_limb_t cy; + +#define a0 ap +#define a1 (ap + n) +#define a2 (ap + 2 * n) +#define a3 (ap + 3 * n) +#define b0 bp +#define b1 (bp + n) +#define b2 (bp + 2 * n) + + n = 1 + (3 * an >= 4 * bn ? (an - 1) >> 2 : (bn - 1) / (size_t) 3); + + s = an - 3 * n; + t = bn - 2 * n; + + ASSERT (0 < s && s <= n); + ASSERT (0 < t && t <= n); + + /* This is true whenever an >= 25 or bn >= 19, I think. It + guarantees that we can fit 5 values of size n+1 in the product + area. */ + 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+1 */ +#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 */ + + /* Total sccratch need is 6 * n + 3 + 1; we allocate one extra + limb, because products will overwrite 2n+2 limbs. */ + +#define a0a2 scratch +#define b0b2 scratch +#define a1a3 asm1 +#define b1d bsm1 + + /* Compute as2 and asm2. */ + flags = (enum toom6_flags) (toom6_vm2_neg & mpn_toom_eval_dgr3_pm2 (as2, asm2, ap, n, s, a1a3)); + + /* Compute bs2 and bsm2. */ + b1d[n] = mpn_lshift (b1d, b1, n, 1); /* 2b1 */ +#if HAVE_NATIVE_mpn_addlsh2_n + cy = mpn_addlsh2_n (b0b2, b0, b2, t); /* 4b2 + b0 */ +#else + cy = mpn_lshift (b0b2, b2, t, 2); /* 4b2 */ + cy += mpn_add_n (b0b2, b0b2, b0, t); /* 4b2 + b0 */ +#endif + if (t != n) + cy = mpn_add_1 (b0b2 + t, b0 + t, n - t, cy); + b0b2[n] = cy; + +#if HAVE_NATIVE_mpn_add_n_sub_n + if (mpn_cmp (b0b2, b1d, n+1) < 0) + { + mpn_add_n_sub_n (bs2, bsm2, b1d, b0b2, n+1); + flags = (enum toom6_flags) (flags ^ toom6_vm2_neg); + } + else + { + mpn_add_n_sub_n (bs2, bsm2, b0b2, b1d, n+1); + } +#else + mpn_add_n (bs2, b0b2, b1d, n+1); + if (mpn_cmp (b0b2, b1d, n+1) < 0) + { + mpn_sub_n (bsm2, b1d, b0b2, n+1); + flags = (enum toom6_flags) (flags ^ toom6_vm2_neg); + } + else + { + mpn_sub_n (bsm2, b0b2, b1d, n+1); + } +#endif + + /* Compute as1 and asm1. */ + flags = (enum toom6_flags) (flags ^ (toom6_vm1_neg & mpn_toom_eval_dgr3_pm1 (as1, asm1, ap, n, s, a0a2))); + + /* Compute bs1 and bsm1. */ + bsm1[n] = mpn_add (bsm1, b0, n, b2, t); +#if HAVE_NATIVE_mpn_add_n_sub_n + if (bsm1[n] == 0 && mpn_cmp (bsm1, b1, n) < 0) + { + cy = mpn_add_n_sub_n (bs1, bsm1, b1, bsm1, n); + bs1[n] = cy >> 1; + flags = (enum toom6_flags) (flags ^ toom6_vm1_neg); + } + else + { + cy = mpn_add_n_sub_n (bs1, bsm1, bsm1, b1, n); + bs1[n] = bsm1[n] + (cy >> 1); + bsm1[n]-= cy & 1; + } +#else + bs1[n] = bsm1[n] + mpn_add_n (bs1, bsm1, b1, n); + if (bsm1[n] == 0 && mpn_cmp (bsm1, b1, n) < 0) + { + mpn_sub_n (bsm1, b1, bsm1, n); + flags = (enum toom6_flags) (flags ^ toom6_vm1_neg); + } + else + { + bsm1[n] -= mpn_sub_n (bsm1, bsm1, b1, n); + } +#endif + + ASSERT (as1[n] <= 3); + ASSERT (bs1[n] <= 2); + ASSERT (asm1[n] <= 1); + ASSERT (bsm1[n] <= 1); + ASSERT (as2[n] <=14); + ASSERT (bs2[n] <= 6); + ASSERT (asm2[n] <= 9); + ASSERT (bsm2[n] <= 4); + + /* vm1, 2n+1 limbs */ + vm1[2*n] = 0; + mpn_mul_n (vm1, asm1, bsm1, n + (asm1[n] | 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, a3, s, b2, t); + else mpn_mul (vinf, b2, t, a3, 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 b1d +#undef a0 +#undef a1 +#undef a2 +#undef a3 +#undef b0 +#undef b1 +#undef b2 +} |