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/toom44_mul.c | 239 +++++++++++++++++++++++++++++++++++++ 1 file changed, 239 insertions(+) create mode 100644 gmp-6.3.0/mpn/generic/toom44_mul.c (limited to 'gmp-6.3.0/mpn/generic/toom44_mul.c') diff --git a/gmp-6.3.0/mpn/generic/toom44_mul.c b/gmp-6.3.0/mpn/generic/toom44_mul.c new file mode 100644 index 0000000..a361899 --- /dev/null +++ b/gmp-6.3.0/mpn/generic/toom44_mul.c @@ -0,0 +1,239 @@ +/* mpn_toom44_mul -- Multiply {ap,an} and {bp,bn} where an and bn are close in + size. Or more accurately, bn <= an < (4/3)bn. + + Contributed to the GNU project by Torbjorn Granlund and 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, 2013 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--> + ____ ______ ______ ______ + |_a3_|___a2_|___a1_|___a0_| + |b3_|___b2_|___b1_|___b0_| + <-t-><--n--><--n--><--n--> + + v0 = a0 * b0 # A(0)*B(0) + v1 = ( a0+ a1+ a2+ a3)*( b0+ b1+ b2+ b3) # A(1)*B(1) ah <= 3 bh <= 3 + vm1 = ( a0- a1+ a2- a3)*( b0- b1+ b2- b3) # A(-1)*B(-1) |ah| <= 1 |bh| <= 1 + v2 = ( a0+2a1+4a2+8a3)*( b0+2b1+4b2+8b3) # A(2)*B(2) ah <= 14 bh <= 14 + vm2 = ( a0-2a1+4a2-8a3)*( b0-2b1+4b2-8b3) # A(-2)*B(-2) |ah| <= 9 |bh| <= 9 + vh = (8a0+4a1+2a2+ a3)*(8b0+4b1+2b2+ b3) # A(1/2)*B(1/2) ah <= 14 bh <= 14 + vinf= a3 * b2 # A(inf)*B(inf) +*/ + +#if TUNE_PROGRAM_BUILD +#define MAYBE_mul_basecase 1 +#define MAYBE_mul_toom22 1 +#define MAYBE_mul_toom44 1 +#else +#define MAYBE_mul_basecase \ + (MUL_TOOM44_THRESHOLD < 4 * MUL_TOOM22_THRESHOLD) +#define MAYBE_mul_toom22 \ + (MUL_TOOM44_THRESHOLD < 4 * MUL_TOOM33_THRESHOLD) +#define MAYBE_mul_toom44 \ + (MUL_TOOM6H_THRESHOLD >= 4 * MUL_TOOM44_THRESHOLD) +#endif + +#define TOOM44_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_toom22 \ + && BELOW_THRESHOLD (n, MUL_TOOM33_THRESHOLD)) \ + mpn_toom22_mul (p, a, n, b, n, ws); \ + else if (! MAYBE_mul_toom44 \ + || BELOW_THRESHOLD (n, MUL_TOOM44_THRESHOLD)) \ + mpn_toom33_mul (p, a, n, b, n, ws); \ + else \ + mpn_toom44_mul (p, a, n, b, n, ws); \ + } while (0) + +/* Use of scratch space. In the product area, we store + + ___________________ + |vinf|____|_v1_|_v0_| + s+t 2n-1 2n+1 2n + + The other recursive products, vm1, v2, vm2, vh are stored in the + scratch area. When computing them, we use the product area for + intermediate values. + + Next, we compute v1. We can store the intermediate factors at v0 + and at vh + 2n + 2. + + Finally, for v0 and vinf, factors are parts of the input operands, + and we need scratch space only for the recursive multiplication. + + In all, if S(an) is the scratch need, the needed space is bounded by + + S(an) <= 4 (2*ceil(an/4) + 1) + 1 + S(ceil(an/4) + 1) + + which should give S(n) = 8 n/3 + c log(n) for some constant c. +*/ + +void +mpn_toom44_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; + enum toom7_flags flags; + +#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) +#define b3 (bp + 3*n) + + ASSERT (an >= bn); + + n = (an + 3) >> 2; + + s = an - 3 * n; + t = bn - 3 * n; + + ASSERT (0 < s && s <= n); + ASSERT (0 < t && t <= n); + ASSERT (s >= t); + + /* NOTE: The multiplications to v2, vm2, vh and vm1 overwrites the + * following limb, so these must be computed in order, and we need a + * one limb gap to tp. */ +#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 tp (scratch + 8*n + 5) + + /* apx and bpx must not overlap with v1 */ +#define apx pp /* n+1 */ +#define amx (pp + n + 1) /* n+1 */ +#define bmx (pp + 2*n + 2) /* n+1 */ +#define bpx (pp + 4*n + 2) /* n+1 */ + + /* Total scratch need: 8*n + 5 + scratch for recursive calls. This + gives roughly 32 n/3 + log term. */ + + /* Compute apx = a0 + 2 a1 + 4 a2 + 8 a3 and amx = a0 - 2 a1 + 4 a2 - 8 a3. */ + flags = (enum toom7_flags) (toom7_w1_neg & mpn_toom_eval_dgr3_pm2 (apx, amx, ap, n, s, tp)); + + /* Compute bpx = b0 + 2 b1 + 4 b2 + 8 b3 and bmx = b0 - 2 b1 + 4 b2 - 8 b3. */ + flags = (enum toom7_flags) (flags ^ (toom7_w1_neg & mpn_toom_eval_dgr3_pm2 (bpx, bmx, bp, n, t, tp))); + + TOOM44_MUL_N_REC (v2, apx, bpx, n + 1, tp); /* v2, 2n+1 limbs */ + TOOM44_MUL_N_REC (vm2, amx, bmx, n + 1, tp); /* vm2, 2n+1 limbs */ + + /* Compute apx = 8 a0 + 4 a1 + 2 a2 + a3 = (((2*a0 + a1) * 2 + a2) * 2 + a3 */ +#if HAVE_NATIVE_mpn_addlsh1_n + cy = mpn_addlsh1_n (apx, a1, a0, n); + cy = 2*cy + mpn_addlsh1_n (apx, a2, apx, n); + if (s < n) + { + mp_limb_t cy2; + cy2 = mpn_addlsh1_n (apx, a3, apx, s); + apx[n] = 2*cy + mpn_lshift (apx + s, apx + s, n - s, 1); + MPN_INCR_U (apx + s, n+1-s, cy2); + } + else + apx[n] = 2*cy + mpn_addlsh1_n (apx, a3, apx, n); +#else + cy = mpn_lshift (apx, a0, n, 1); + cy += mpn_add_n (apx, apx, a1, n); + cy = 2*cy + mpn_lshift (apx, apx, n, 1); + cy += mpn_add_n (apx, apx, a2, n); + cy = 2*cy + mpn_lshift (apx, apx, n, 1); + apx[n] = cy + mpn_add (apx, apx, n, a3, s); +#endif + + /* Compute bpx = 8 b0 + 4 b1 + 2 b2 + b3 = (((2*b0 + b1) * 2 + b2) * 2 + b3 */ +#if HAVE_NATIVE_mpn_addlsh1_n + cy = mpn_addlsh1_n (bpx, b1, b0, n); + cy = 2*cy + mpn_addlsh1_n (bpx, b2, bpx, n); + if (t < n) + { + mp_limb_t cy2; + cy2 = mpn_addlsh1_n (bpx, b3, bpx, t); + bpx[n] = 2*cy + mpn_lshift (bpx + t, bpx + t, n - t, 1); + MPN_INCR_U (bpx + t, n+1-t, cy2); + } + else + bpx[n] = 2*cy + mpn_addlsh1_n (bpx, b3, bpx, n); +#else + cy = mpn_lshift (bpx, b0, n, 1); + cy += mpn_add_n (bpx, bpx, b1, n); + cy = 2*cy + mpn_lshift (bpx, bpx, n, 1); + cy += mpn_add_n (bpx, bpx, b2, n); + cy = 2*cy + mpn_lshift (bpx, bpx, n, 1); + bpx[n] = cy + mpn_add (bpx, bpx, n, b3, t); +#endif + + ASSERT (apx[n] < 15); + ASSERT (bpx[n] < 15); + + TOOM44_MUL_N_REC (vh, apx, bpx, n + 1, tp); /* vh, 2n+1 limbs */ + + /* Compute apx = a0 + a1 + a2 + a3 and amx = a0 - a1 + a2 - a3. */ + flags = (enum toom7_flags) (flags | (toom7_w3_neg & mpn_toom_eval_dgr3_pm1 (apx, amx, ap, n, s, tp))); + + /* Compute bpx = b0 + b1 + b2 + b3 and bmx = b0 - b1 + b2 - b3. */ + flags = (enum toom7_flags) (flags ^ (toom7_w3_neg & mpn_toom_eval_dgr3_pm1 (bpx, bmx, bp, n, t, tp))); + + ASSERT (amx[n] <= 1); + ASSERT (bmx[n] <= 1); + + vm1 [2 * n] = 0; + TOOM44_MUL_N_REC (vm1, amx, bmx, n + (bmx[n] | amx[n]), tp); /* vm1, 2n+1 limbs */ + /* Clobbers amx, bmx. */ + TOOM44_MUL_N_REC (v1, apx, bpx, n + 1, tp); /* v1, 2n+1 limbs */ + + TOOM44_MUL_N_REC (v0, a0, b0, n, tp); + if (s > t) + mpn_mul (vinf, a3, s, b3, t); + else + TOOM44_MUL_N_REC (vinf, a3, b3, s, tp); /* vinf, s+t limbs */ + + mpn_toom_interpolate_7pts (pp, n, flags, vm2, vm1, v2, vh, s + t, tp); +} -- cgit v1.2.3