X-Git-Url: https://oss.titaniummirror.com/gitweb/?a=blobdiff_plain;f=gmp%2Fmpn%2Fgeneric%2Ftoom62_mul.c;fp=gmp%2Fmpn%2Fgeneric%2Ftoom62_mul.c;h=19ce3a13c004acb2a98c28a0c67cdcf1e98be827;hb=6fed43773c9b0ce596dca5686f37ac3fc0fa11c0;hp=0000000000000000000000000000000000000000;hpb=27b11d56b743098deb193d510b337ba22dc52e5c;p=msp430-gcc.git diff --git a/gmp/mpn/generic/toom62_mul.c b/gmp/mpn/generic/toom62_mul.c new file mode 100644 index 00000000..19ce3a13 --- /dev/null +++ b/gmp/mpn/generic/toom62_mul.c @@ -0,0 +1,356 @@ +/* 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 by 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, 2007, 2008 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 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. + +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 Lesser General Public +License for more details. + +You should have received a copy of the GNU Lesser General Public License +along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ + + +/* + Things to work on: + + 1. Trim allocation. The allocations for as1, asm1, bs1, and bsm1 could be + avoided by instead reusing the pp area and the scratch allocation. +*/ + +#include "gmp.h" +#include "gmp-impl.h" + + +/* Evaluate in: -1, -1/2, 0, +1/2, +1, +2, +inf + + <-s-><--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 + vh = (32a0+16a1+8a2+4a3+ 2a4+ a5)*(2b0+ b1) # A(1/2)*B(1/2) ah <= 62 bh <= 2 + vmh = (32a0-16a1+8a2-4a3+ 2a4- a5)*(2b0- b1) # A(-1/2)*B(-1/2) -20<=ah<=41 0<=bh<=1 + 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; + int vm1_neg, vmh_neg, bsm_neg; + mp_limb_t cy; + mp_ptr a0_a2, a1_a3; + mp_ptr as1, asm1, as2, ash, asmh; + mp_ptr bs1, bsm1, bs2, bsh, bsmh; + enum toom4_flags flags; + 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) / (unsigned long) 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); + ash = TMP_SALLOC_LIMBS (n + 1); + asmh = TMP_SALLOC_LIMBS (n + 1); + + bs1 = TMP_SALLOC_LIMBS (n + 1); + bsm1 = TMP_SALLOC_LIMBS (n); + bs2 = TMP_SALLOC_LIMBS (n + 1); + bsh = TMP_SALLOC_LIMBS (n + 1); + bsmh = TMP_SALLOC_LIMBS (n + 1); + + a0_a2 = pp; + a1_a3 = pp + n + 1; + + /* Compute as1 and asm1. */ + a0_a2[n] = mpn_add_n (a0_a2, a0, a2, n); + a0_a2[n] += mpn_add_n (a0_a2, a0_a2, a4, n); + a1_a3[n] = mpn_add_n (a1_a3, a1, a3, n); + a1_a3[n] += mpn_add (a1_a3, a1_a3, n, a5, s); +#if HAVE_NATIVE_mpn_addsub_n + if (mpn_cmp (a0_a2, a1_a3, n + 1) < 0) + { + mpn_addsub_n (as1, asm1, a1_a3, a0_a2, n + 1); + vm1_neg = 1; + } + else + { + mpn_addsub_n (as1, asm1, a0_a2, a1_a3, n + 1); + vm1_neg = 0; + } +#else + mpn_add_n (as1, a0_a2, a1_a3, n + 1); + if (mpn_cmp (a0_a2, a1_a3, n + 1) < 0) + { + mpn_sub_n (asm1, a1_a3, a0_a2, n + 1); + vm1_neg = 1; + } + else + { + mpn_sub_n (asm1, a0_a2, a1_a3, n + 1); + vm1_neg = 0; + } +#endif + + /* Compute as2. */ +#if HAVE_NATIVE_mpn_addlsh1_n + cy = mpn_addlsh1_n (as2, a4, a5, s); + if (s != n) + cy = mpn_add_1 (as2 + s, a4 + s, n - s, cy); + cy = 2 * cy + mpn_addlsh1_n (as2, a3, as2, n); + cy = 2 * cy + mpn_addlsh1_n (as2, a2, as2, n); + cy = 2 * cy + mpn_addlsh1_n (as2, a1, as2, n); + cy = 2 * cy + mpn_addlsh1_n (as2, a0, as2, n); +#else + cy = mpn_lshift (as2, a5, s, 1); + cy += mpn_add_n (as2, a4, as2, s); + if (s != n) + cy = mpn_add_1 (as2 + s, a4 + s, n - s, cy); + cy = 2 * cy + mpn_lshift (as2, as2, n, 1); + cy += mpn_add_n (as2, a3, as2, n); + cy = 2 * cy + mpn_lshift (as2, as2, n, 1); + cy += mpn_add_n (as2, a2, as2, n); + cy = 2 * cy + mpn_lshift (as2, as2, n, 1); + cy += mpn_add_n (as2, a1, as2, n); + cy = 2 * cy + mpn_lshift (as2, as2, n, 1); + cy += mpn_add_n (as2, a0, as2, n); +#endif + as2[n] = cy; + + /* Compute ash and asmh. */ +#if HAVE_NATIVE_mpn_addlsh_n + cy = mpn_addlsh_n (a0_a2, a2, a0, n, 2); /* 4a0 + a2 */ + cy = 4 * cy + mpn_addlsh_n (a0_a2, a4, a0_a2, n, 2); /* 16a0 + 4a2 + a4 */ + cy = 2 * cy + mpn_lshift (a0_a2, a0_a2, n, 1); /* 32a0 + 8a2 + 2a4 */ + a0_a2[n] = cy; + cy = mpn_addlsh_n (a1_a3, a3, a1, n, 2); /* 4a1 */ + cy = 4 * cy + mpn_addlsh_n (a1_a3, a5, a1_a3, n, 2); /* 16a1 + 4a3 */ + a1_a3[n] = cy; +#else + cy = mpn_lshift (a0_a2, a0, n, 2); /* 4a0 */ + cy += mpn_add_n (a0_a2, a2, a0_a2, n); /* 4a0 + a2 */ + cy = 4 * cy + mpn_lshift (a0_a2, a0_a2, n, 2); /* 16a0 + 4a2 */ + cy += mpn_add_n (a0_a2, a4, a0_a2, n); /* 16a0 + 4a2 + a4 */ + cy = 2 * cy + mpn_lshift (a0_a2, a0_a2, n, 1); /* 32a0 + 8a2 + 2a4 */ + a0_a2[n] = cy; + cy = mpn_lshift (a1_a3, a1, n, 2); /* 4a1 */ + cy += mpn_add_n (a1_a3, a3, a1_a3, n); /* 4a1 + a3 */ + cy = 4 * cy + mpn_lshift (a1_a3, a1_a3, n, 2); /* 16a1 + 4a3 */ + cy += mpn_add (a1_a3, a1_a3, n, a5, s); /* 16a1 + 4a3 + a5 */ + a1_a3[n] = cy; +#endif +#if HAVE_NATIVE_mpn_addsub_n + if (mpn_cmp (a0_a2, a1_a3, n + 1) < 0) + { + mpn_addsub_n (ash, asmh, a1_a3, a0_a2, n + 1); + vmh_neg = 1; + } + else + { + mpn_addsub_n (ash, asmh, a0_a2, a1_a3, n + 1); + vmh_neg = 0; + } +#else + mpn_add_n (ash, a0_a2, a1_a3, n + 1); + if (mpn_cmp (a0_a2, a1_a3, n + 1) < 0) + { + mpn_sub_n (asmh, a1_a3, a0_a2, n + 1); + vmh_neg = 1; + } + else + { + mpn_sub_n (asmh, a0_a2, a1_a3, n + 1); + vmh_neg = 0; + } +#endif + + /* Compute bs1 and bsm1. */ + if (t == n) + { +#if HAVE_NATIVE_mpn_addsub_n + if (mpn_cmp (b0, b1, n) < 0) + { + cy = mpn_addsub_n (bs1, bsm1, b1, b0, n); + bsm_neg = 1; + } + else + { + cy = mpn_addsub_n (bs1, bsm1, b0, b1, n); + bsm_neg = 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); + bsm_neg = 1; + } + else + { + mpn_sub_n (bsm1, b0, b1, n); + bsm_neg = 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); + bsm_neg = 1; + } + else + { + mpn_sub (bsm1, b0, n, b1, t); + bsm_neg = 0; + } + } + + vm1_neg ^= bsm_neg; + + /* Compute bs2, recycling bs1. bs2=bs1+b1 */ + mpn_add (bs2, bs1, n + 1, b1, t); + + /* Compute bsh and bsmh, recycling bs1 and bsm1. bsh=bs1+b0; bsmh=bsmh+b0 */ + if (bsm_neg == 1) + { + bsmh[n] = 0; + if (mpn_cmp (bsm1, b0, n) < 0) + { + bsm_neg = 0; + mpn_sub_n (bsmh, b0, bsm1, n); + } + else + mpn_sub_n (bsmh, bsm1, b0, n); + } + else + bsmh[n] = mpn_add_n (bsmh, bsm1, b0, n); + mpn_add (bsh, bs1, n + 1, b0, n); + vmh_neg ^= bsm_neg; + + + ASSERT (as1[n] <= 5); + ASSERT (bs1[n] <= 1); + ASSERT (asm1[n] <= 2); +/*ASSERT (bsm1[n] == 0);*/ + ASSERT (as2[n] <= 62); + ASSERT (bs2[n] <= 2); + ASSERT (ash[n] <= 62); + ASSERT (bsh[n] <= 2); + ASSERT (asmh[n] <= 41); + ASSERT (bsmh[n] <= 1); + +#define v0 pp /* 2n */ +#define v1 (scratch + 6 * n + 6) /* 2n+1 */ +#define vinf (pp + 6 * n) /* s+t */ +#define vm1 scratch /* 2n+1 */ +#define v2 (scratch + 2 * n + 2) /* 2n+1 */ +#define vh (pp + 2 * n) /* 2n+1 */ +#define vmh (scratch + 4 * n + 4) + + /* 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; + + mpn_mul_n (v2, as2, bs2, n + 1); /* v2, 2n+1 limbs */ + + /* vinf, s+t limbs */ + if (s > t) mpn_mul (vinf, a5, s, b1, t); + else mpn_mul (vinf, b1, t, a5, s); + + /* 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 (vh, ash, bsh, n + 1); + + mpn_mul_n (vmh, asmh, bsmh, n + 1); + + mpn_mul_n (v0, ap, bp, n); /* v0, 2n limbs */ + + flags = vm1_neg ? toom4_w3_neg : 0; + flags |= vmh_neg ? toom4_w1_neg : 0; + + mpn_toom_interpolate_7pts (pp, n, flags, vmh, vm1, v1, v2, s + t, scratch + 8 * n + 8); + + TMP_FREE; +}