1 /* mpn_toom52_mul -- Multiply {ap,an} and {bp,bn} where an is nominally 4/3 2 times as large as bn. Or more accurately, bn < an < 2 bn. 3 4 Contributed to the GNU project by Marco Bodrato. 5 6 The idea of applying toom to unbalanced multiplication is due to Marco 7 Bodrato and Alberto Zanoni. 8 9 THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY 10 SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST 11 GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE. 12 13 Copyright 2009 Free Software Foundation, Inc. 14 15 This file is part of the GNU MP Library. 16 17 The GNU MP Library is free software; you can redistribute it and/or modify 18 it under the terms of either: 19 20 * the GNU Lesser General Public License as published by the Free 21 Software Foundation; either version 3 of the License, or (at your 22 option) any later version. 23 24 or 25 26 * the GNU General Public License as published by the Free Software 27 Foundation; either version 2 of the License, or (at your option) any 28 later version. 29 30 or both in parallel, as here. 31 32 The GNU MP Library is distributed in the hope that it will be useful, but 33 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 34 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 35 for more details. 36 37 You should have received copies of the GNU General Public License and the 38 GNU Lesser General Public License along with the GNU MP Library. If not, 39 see https://www.gnu.org/licenses/. */ 40 41 42 #include "gmp-impl.h" 43 44 /* Evaluate in: -2, -1, 0, +1, +2, +inf 45 46 <-s-><--n--><--n--><--n--><--n--> 47 ___ ______ ______ ______ ______ 48 |a4_|___a3_|___a2_|___a1_|___a0_| 49 |b1|___b0_| 50 <t-><--n--> 51 52 v0 = a0 * b0 # A(0)*B(0) 53 v1 = (a0+ a1+ a2+ a3+ a4)*(b0+ b1) # A(1)*B(1) ah <= 4 bh <= 1 54 vm1 = (a0- a1+ a2- a3+ a4)*(b0- b1) # A(-1)*B(-1) |ah| <= 2 bh = 0 55 v2 = (a0+2a1+4a2+8a3+16a4)*(b0+2b1) # A(2)*B(2) ah <= 30 bh <= 2 56 vm2 = (a0-2a1+4a2-8a3+16a4)*(b0-2b1) # A(-2)*B(-2) |ah| <= 20 |bh|<= 1 57 vinf= a4 * b1 # A(inf)*B(inf) 58 59 Some slight optimization in evaluation are taken from the paper: 60 "Towards Optimal Toom-Cook Multiplication for Univariate and 61 Multivariate Polynomials in Characteristic 2 and 0." 62 */ 63 64 void 65 mpn_toom52_mul (mp_ptr pp, 66 mp_srcptr ap, mp_size_t an, 67 mp_srcptr bp, mp_size_t bn, mp_ptr scratch) 68 { 69 mp_size_t n, s, t; 70 enum toom6_flags flags; 71 72 #define a0 ap 73 #define a1 (ap + n) 74 #define a2 (ap + 2 * n) 75 #define a3 (ap + 3 * n) 76 #define a4 (ap + 4 * n) 77 #define b0 bp 78 #define b1 (bp + n) 79 80 n = 1 + (2 * an >= 5 * bn ? (an - 1) / (size_t) 5 : (bn - 1) >> 1); 81 82 s = an - 4 * n; 83 t = bn - n; 84 85 ASSERT (0 < s && s <= n); 86 ASSERT (0 < t && t <= n); 87 88 /* Ensures that 5 values of n+1 limbs each fits in the product area. 89 Borderline cases are an = 32, bn = 8, n = 7, and an = 36, bn = 9, 90 n = 8. */ 91 ASSERT (s+t >= 5); 92 93 #define v0 pp /* 2n */ 94 #define vm1 (scratch) /* 2n+1 */ 95 #define v1 (pp + 2 * n) /* 2n+1 */ 96 #define vm2 (scratch + 2 * n + 1) /* 2n+1 */ 97 #define v2 (scratch + 4 * n + 2) /* 2n+1 */ 98 #define vinf (pp + 5 * n) /* s+t */ 99 #define bs1 pp /* n+1 */ 100 #define bsm1 (scratch + 2 * n + 2) /* n */ 101 #define asm1 (scratch + 3 * n + 3) /* n+1 */ 102 #define asm2 (scratch + 4 * n + 4) /* n+1 */ 103 #define bsm2 (pp + n + 1) /* n+1 */ 104 #define bs2 (pp + 2 * n + 2) /* n+1 */ 105 #define as2 (pp + 3 * n + 3) /* n+1 */ 106 #define as1 (pp + 4 * n + 4) /* n+1 */ 107 108 /* Scratch need is 6 * n + 3 + 1. We need one extra limb, because 109 products will overwrite 2n+2 limbs. */ 110 111 #define a0a2 scratch 112 #define a1a3 asm1 113 114 /* Compute as2 and asm2. */ 115 flags = (enum toom6_flags) (toom6_vm2_neg & mpn_toom_eval_pm2 (as2, asm2, 4, ap, n, s, a1a3)); 116 117 /* Compute bs1 and bsm1. */ 118 if (t == n) 119 { 120 #if HAVE_NATIVE_mpn_add_n_sub_n 121 mp_limb_t cy; 122 123 if (mpn_cmp (b0, b1, n) < 0) 124 { 125 cy = mpn_add_n_sub_n (bs1, bsm1, b1, b0, n); 126 flags = (enum toom6_flags) (flags ^ toom6_vm1_neg); 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 if (mpn_cmp (b0, b1, n) < 0) 136 { 137 mpn_sub_n (bsm1, b1, b0, n); 138 flags = (enum toom6_flags) (flags ^ toom6_vm1_neg); 139 } 140 else 141 { 142 mpn_sub_n (bsm1, b0, b1, n); 143 } 144 #endif 145 } 146 else 147 { 148 bs1[n] = mpn_add (bs1, b0, n, b1, t); 149 if (mpn_zero_p (b0 + t, n - t) && mpn_cmp (b0, b1, t) < 0) 150 { 151 mpn_sub_n (bsm1, b1, b0, t); 152 MPN_ZERO (bsm1 + t, n - t); 153 flags = (enum toom6_flags) (flags ^ toom6_vm1_neg); 154 } 155 else 156 { 157 mpn_sub (bsm1, b0, n, b1, t); 158 } 159 } 160 161 /* Compute bs2 and bsm2, recycling bs1 and bsm1. bs2=bs1+b1; bsm2=bsm1-b1 */ 162 mpn_add (bs2, bs1, n+1, b1, t); 163 if (flags & toom6_vm1_neg) 164 { 165 bsm2[n] = mpn_add (bsm2, bsm1, n, b1, t); 166 flags = (enum toom6_flags) (flags ^ toom6_vm2_neg); 167 } 168 else 169 { 170 bsm2[n] = 0; 171 if (t == n) 172 { 173 if (mpn_cmp (bsm1, b1, n) < 0) 174 { 175 mpn_sub_n (bsm2, b1, bsm1, n); 176 flags = (enum toom6_flags) (flags ^ toom6_vm2_neg); 177 } 178 else 179 { 180 mpn_sub_n (bsm2, bsm1, b1, n); 181 } 182 } 183 else 184 { 185 if (mpn_zero_p (bsm1 + t, n - t) && mpn_cmp (bsm1, b1, t) < 0) 186 { 187 mpn_sub_n (bsm2, b1, bsm1, t); 188 MPN_ZERO (bsm2 + t, n - t); 189 flags = (enum toom6_flags) (flags ^ toom6_vm2_neg); 190 } 191 else 192 { 193 mpn_sub (bsm2, bsm1, n, b1, t); 194 } 195 } 196 } 197 198 /* Compute as1 and asm1. */ 199 flags = (enum toom6_flags) (flags ^ (toom6_vm1_neg & mpn_toom_eval_pm1 (as1, asm1, 4, ap, n, s, a0a2))); 200 201 ASSERT (as1[n] <= 4); 202 ASSERT (bs1[n] <= 1); 203 ASSERT (asm1[n] <= 2); 204 /* ASSERT (bsm1[n] <= 1); */ 205 ASSERT (as2[n] <=30); 206 ASSERT (bs2[n] <= 2); 207 ASSERT (asm2[n] <= 20); 208 ASSERT (bsm2[n] <= 1); 209 210 /* vm1, 2n+1 limbs */ 211 mpn_mul (vm1, asm1, n+1, bsm1, n); /* W4 */ 212 213 /* vm2, 2n+1 limbs */ 214 mpn_mul_n (vm2, asm2, bsm2, n+1); /* W2 */ 215 216 /* v2, 2n+1 limbs */ 217 mpn_mul_n (v2, as2, bs2, n+1); /* W1 */ 218 219 /* v1, 2n+1 limbs */ 220 mpn_mul_n (v1, as1, bs1, n+1); /* W3 */ 221 222 /* vinf, s+t limbs */ /* W0 */ 223 if (s > t) mpn_mul (vinf, a4, s, b1, t); 224 else mpn_mul (vinf, b1, t, a4, s); 225 226 /* v0, 2n limbs */ 227 mpn_mul_n (v0, ap, bp, n); /* W5 */ 228 229 mpn_toom_interpolate_6pts (pp, n, flags, vm1, vm2, v2, t + s); 230 231 #undef v0 232 #undef vm1 233 #undef v1 234 #undef vm2 235 #undef v2 236 #undef vinf 237 #undef bs1 238 #undef bs2 239 #undef bsm1 240 #undef bsm2 241 #undef asm1 242 #undef asm2 243 #undef as1 244 #undef as2 245 #undef a0a2 246 #undef b0b2 247 #undef a1a3 248 #undef a0 249 #undef a1 250 #undef a2 251 #undef a3 252 #undef b0 253 #undef b1 254 #undef b2 255 256 } 257