1/* mpn_toom42_mul -- Multiply {ap,an} and {bp,bn} where an is nominally twice 2 as large as bn. Or more accurately, (3/2)bn < an < 4bn. 3 4 Contributed to the GNU project by Torbjorn Granlund. 5 Additional improvements by Marco Bodrato. 6 7 The idea of applying toom to unbalanced multiplication is due to Marco 8 Bodrato and Alberto Zanoni. 9 10 THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY 11 SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST 12 GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE. 13 14Copyright 2006, 2007, 2008 Free Software Foundation, Inc. 15 16This file is part of the GNU MP Library. 17 18The GNU MP Library is free software; you can redistribute it and/or modify 19it under the terms of the GNU Lesser General Public License as published by 20the Free Software Foundation; either version 3 of the License, or (at your 21option) any later version. 22 23The GNU MP Library is distributed in the hope that it will be useful, but 24WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 25or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 26License for more details. 27 28You should have received a copy of the GNU Lesser General Public License 29along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ 30 31 32#include "gmp.h" 33#include "gmp-impl.h" 34 35/* Evaluate in: -1, 0, +1, +2, +inf 36 37 <-s-><--n--><--n--><--n--> 38 ___ ______ ______ ______ 39 |a3_|___a2_|___a1_|___a0_| 40 |_b1_|___b0_| 41 <-t--><--n--> 42 43 v0 = a0 * b0 # A(0)*B(0) 44 v1 = (a0+ a1+ a2+ a3)*(b0+ b1) # A(1)*B(1) ah <= 3 bh <= 1 45 vm1 = (a0- a1+ a2- a3)*(b0- b1) # A(-1)*B(-1) |ah| <= 1 bh = 0 46 v2 = (a0+2a1+4a2+8a3)*(b0+2b1) # A(2)*B(2) ah <= 14 bh <= 2 47 vinf= a3 * b1 # A(inf)*B(inf) 48*/ 49 50#define TOOM42_MUL_N_REC(p, a, b, n, ws) \ 51 do { \ 52 mpn_mul_n (p, a, b, n); \ 53 } while (0) 54 55void 56mpn_toom42_mul (mp_ptr pp, 57 mp_srcptr ap, mp_size_t an, 58 mp_srcptr bp, mp_size_t bn, 59 mp_ptr scratch) 60{ 61 mp_size_t n, s, t; 62 int vm1_neg; 63 mp_limb_t cy, vinf0; 64 mp_ptr a0_a2, a1_a3; 65 mp_ptr as1, asm1, as2; 66 mp_ptr bs1, bsm1, bs2; 67 TMP_DECL; 68 69#define a0 ap 70#define a1 (ap + n) 71#define a2 (ap + 2*n) 72#define a3 (ap + 3*n) 73#define b0 bp 74#define b1 (bp + n) 75 76 n = an >= 2 * bn ? (an + 3) >> 2 : (bn + 1) >> 1; 77 78 s = an - 3 * n; 79 t = bn - n; 80 81 ASSERT (0 < s && s <= n); 82 ASSERT (0 < t && t <= n); 83 84 TMP_MARK; 85 86 as1 = TMP_SALLOC_LIMBS (n + 1); 87 asm1 = TMP_SALLOC_LIMBS (n + 1); 88 as2 = TMP_SALLOC_LIMBS (n + 1); 89 90 bs1 = TMP_SALLOC_LIMBS (n + 1); 91 bsm1 = TMP_SALLOC_LIMBS (n); 92 bs2 = TMP_SALLOC_LIMBS (n + 1); 93 94 a0_a2 = pp; 95 a1_a3 = pp + n + 1; 96 97 /* Compute as1 and asm1. */ 98 vm1_neg = mpn_toom_eval_dgr3_pm1 (as1, asm1, ap, n, s, a0_a2) & 1; 99 100 /* Compute as2. */ 101#if HAVE_NATIVE_mpn_addlsh1_n 102 cy = mpn_addlsh1_n (as2, a2, a3, s); 103 if (s != n) 104 cy = mpn_add_1 (as2 + s, a2 + s, n - s, cy); 105 cy = 2 * cy + mpn_addlsh1_n (as2, a1, as2, n); 106 cy = 2 * cy + mpn_addlsh1_n (as2, a0, as2, n); 107#else 108 cy = mpn_lshift (as2, a3, s, 1); 109 cy += mpn_add_n (as2, a2, as2, s); 110 if (s != n) 111 cy = mpn_add_1 (as2 + s, a2 + s, n - s, cy); 112 cy = 2 * cy + mpn_lshift (as2, as2, n, 1); 113 cy += mpn_add_n (as2, a1, as2, n); 114 cy = 2 * cy + mpn_lshift (as2, as2, n, 1); 115 cy += mpn_add_n (as2, a0, as2, n); 116#endif 117 as2[n] = cy; 118 119 /* Compute bs1 and bsm1. */ 120 if (t == n) 121 { 122#if HAVE_NATIVE_mpn_add_n_sub_n 123 if (mpn_cmp (b0, b1, n) < 0) 124 { 125 cy = mpn_add_n_sub_n (bs1, bsm1, b1, b0, n); 126 vm1_neg ^= 1; 127 } 128 else 129 { 130 cy = mpn_add_n_sub_n (bs1, bsm1, b0, b1, n); 131 } 132 bs1[n] = cy >> 1; 133#else 134 bs1[n] = mpn_add_n (bs1, b0, b1, n); 135 136 if (mpn_cmp (b0, b1, n) < 0) 137 { 138 mpn_sub_n (bsm1, b1, b0, n); 139 vm1_neg ^= 1; 140 } 141 else 142 { 143 mpn_sub_n (bsm1, b0, b1, n); 144 } 145#endif 146 } 147 else 148 { 149 bs1[n] = mpn_add (bs1, b0, n, b1, t); 150 151 if (mpn_zero_p (b0 + t, n - t) && mpn_cmp (b0, b1, t) < 0) 152 { 153 mpn_sub_n (bsm1, b1, b0, t); 154 MPN_ZERO (bsm1 + t, n - t); 155 vm1_neg ^= 1; 156 } 157 else 158 { 159 mpn_sub (bsm1, b0, n, b1, t); 160 } 161 } 162 163 /* Compute bs2, recycling bs1. bs2=bs1+b1 */ 164 mpn_add (bs2, bs1, n + 1, b1, t); 165 166 ASSERT (as1[n] <= 3); 167 ASSERT (bs1[n] <= 1); 168 ASSERT (asm1[n] <= 1); 169/*ASSERT (bsm1[n] == 0);*/ 170 ASSERT (as2[n] <= 14); 171 ASSERT (bs2[n] <= 2); 172 173#define v0 pp /* 2n */ 174#define v1 (pp + 2 * n) /* 2n+1 */ 175#define vinf (pp + 4 * n) /* s+t */ 176#define vm1 scratch /* 2n+1 */ 177#define v2 (scratch + 2 * n + 1) /* 2n+2 */ 178#define scratch_out scratch + 4 * n + 4 /* Currently unused. */ 179 180 /* vm1, 2n+1 limbs */ 181 TOOM42_MUL_N_REC (vm1, asm1, bsm1, n, scratch_out); 182 cy = 0; 183 if (asm1[n] != 0) 184 cy = mpn_add_n (vm1 + n, vm1 + n, bsm1, n); 185 vm1[2 * n] = cy; 186 187 TOOM42_MUL_N_REC (v2, as2, bs2, n + 1, scratch_out); /* v2, 2n+1 limbs */ 188 189 /* vinf, s+t limbs */ 190 if (s > t) mpn_mul (vinf, a3, s, b1, t); 191 else mpn_mul (vinf, b1, t, a3, s); 192 193 vinf0 = vinf[0]; /* v1 overlaps with this */ 194 195 /* v1, 2n+1 limbs */ 196 TOOM42_MUL_N_REC (v1, as1, bs1, n, scratch_out); 197 if (as1[n] == 1) 198 { 199 cy = bs1[n] + mpn_add_n (v1 + n, v1 + n, bs1, n); 200 } 201 else if (as1[n] == 2) 202 { 203#if HAVE_NATIVE_mpn_addlsh1_n 204 cy = 2 * bs1[n] + mpn_addlsh1_n (v1 + n, v1 + n, bs1, n); 205#else 206 cy = 2 * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, CNST_LIMB(2)); 207#endif 208 } 209 else if (as1[n] == 3) 210 { 211 cy = 3 * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, CNST_LIMB(3)); 212 } 213 else 214 cy = 0; 215 if (bs1[n] != 0) 216 cy += mpn_add_n (v1 + n, v1 + n, as1, n); 217 v1[2 * n] = cy; 218 219 TOOM42_MUL_N_REC (v0, ap, bp, n, scratch_out); /* v0, 2n limbs */ 220 221 mpn_toom_interpolate_5pts (pp, v2, vm1, n, s + t, vm1_neg, vinf0); 222 223 TMP_FREE; 224} 225