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 the GNU Lesser General Public License as published by 19 the Free Software Foundation; either version 3 of the License, or (at your 20 option) any later version. 21 22 The GNU MP Library is distributed in the hope that it will be useful, but 23 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 24 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 25 License for more details. 26 27 You should have received a copy of the GNU Lesser General Public License 28 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ 29 30 31 #include "gmp.h" 32 #include "gmp-impl.h" 33 34 /* Evaluate in: -2, -1, 0, +1, +2, +inf 35 36 <-s-><--n--><--n--><--n--><--n--> 37 ___ ______ ______ ______ ______ 38 |a4_|___a3_|___a2_|___a1_|___a0_| 39 |b1|___b0_| 40 <t-><--n--> 41 42 v0 = a0 * b0 # A(0)*B(0) 43 v1 = (a0+ a1+ a2+ a3+ a4)*(b0+ b1) # A(1)*B(1) ah <= 4 bh <= 1 44 vm1 = (a0- a1+ a2- a3+ a4)*(b0- b1) # A(-1)*B(-1) |ah| <= 2 bh = 0 45 v2 = (a0+2a1+4a2+8a3+16a4)*(b0+2b1) # A(2)*B(2) ah <= 30 bh <= 2 46 vm2 = (a0-2a1+4a2-8a3+16a4)*(b0-2b1) # A(-2)*B(-2) |ah| <= 20 |bh|<= 1 47 vinf= a4 * b1 # A(inf)*B(inf) 48 49 Some slight optimization in evaluation are taken from the paper: 50 "Towards Optimal Toom-Cook Multiplication for Univariate and 51 Multivariate Polynomials in Characteristic 2 and 0." 52 */ 53 54 void 55 mpn_toom52_mul (mp_ptr pp, 56 mp_srcptr ap, mp_size_t an, 57 mp_srcptr bp, mp_size_t bn, mp_ptr scratch) 58 { 59 mp_size_t n, s, t; 60 enum toom6_flags flags; 61 62 #define a0 ap 63 #define a1 (ap + n) 64 #define a2 (ap + 2 * n) 65 #define a3 (ap + 3 * n) 66 #define a4 (ap + 4 * n) 67 #define b0 bp 68 #define b1 (bp + n) 69 70 n = 1 + (2 * an >= 5 * bn ? (an - 1) / (size_t) 5 : (bn - 1) >> 1); 71 72 s = an - 4 * n; 73 t = bn - n; 74 75 ASSERT (0 < s && s <= n); 76 ASSERT (0 < t && t <= n); 77 78 /* Ensures that 5 values of n+1 limbs each fits in the product area. 79 Borderline cases are an = 32, bn = 8, n = 7, and an = 36, bn = 9, 80 n = 8. */ 81 ASSERT (s+t >= 5); 82 83 #define v0 pp /* 2n */ 84 #define vm1 (scratch) /* 2n+1 */ 85 #define v1 (pp + 2 * n) /* 2n+1 */ 86 #define vm2 (scratch + 2 * n + 1) /* 2n+1 */ 87 #define v2 (scratch + 4 * n + 2) /* 2n+1 */ 88 #define vinf (pp + 5 * n) /* s+t */ 89 #define bs1 pp /* n+1 */ 90 #define bsm1 (scratch + 2 * n + 2) /* n */ 91 #define asm1 (scratch + 3 * n + 3) /* n+1 */ 92 #define asm2 (scratch + 4 * n + 4) /* n+1 */ 93 #define bsm2 (pp + n + 1) /* n+1 */ 94 #define bs2 (pp + 2 * n + 2) /* n+1 */ 95 #define as2 (pp + 3 * n + 3) /* n+1 */ 96 #define as1 (pp + 4 * n + 4) /* n+1 */ 97 98 /* Scratch need is 6 * n + 3 + 1. We need one extra limb, because 99 products will overwrite 2n+2 limbs. */ 100 101 #define a0a2 scratch 102 #define a1a3 asm1 103 104 /* Compute as2 and asm2. */ 105 flags = toom6_vm2_neg & mpn_toom_eval_pm2 (as2, asm2, 4, ap, n, s, a1a3); 106 107 /* Compute bs1 and bsm1. */ 108 if (t == n) 109 { 110 #if HAVE_NATIVE_mpn_add_n_sub_n 111 mp_limb_t cy; 112 113 if (mpn_cmp (b0, b1, n) < 0) 114 { 115 cy = mpn_add_n_sub_n (bs1, bsm1, b1, b0, n); 116 flags ^= toom6_vm1_neg; 117 } 118 else 119 { 120 cy = mpn_add_n_sub_n (bs1, bsm1, b0, b1, n); 121 } 122 bs1[n] = cy >> 1; 123 #else 124 bs1[n] = mpn_add_n (bs1, b0, b1, n); 125 if (mpn_cmp (b0, b1, n) < 0) 126 { 127 mpn_sub_n (bsm1, b1, b0, n); 128 flags ^= toom6_vm1_neg; 129 } 130 else 131 { 132 mpn_sub_n (bsm1, b0, b1, n); 133 } 134 #endif 135 } 136 else 137 { 138 bs1[n] = mpn_add (bs1, b0, n, b1, t); 139 if (mpn_zero_p (b0 + t, n - t) && mpn_cmp (b0, b1, t) < 0) 140 { 141 mpn_sub_n (bsm1, b1, b0, t); 142 MPN_ZERO (bsm1 + t, n - t); 143 flags ^= toom6_vm1_neg; 144 } 145 else 146 { 147 mpn_sub (bsm1, b0, n, b1, t); 148 } 149 } 150 151 /* Compute bs2 and bsm2, recycling bs1 and bsm1. bs2=bs1+b1; bsm2=bsm1-b1 */ 152 mpn_add (bs2, bs1, n+1, b1, t); 153 if (flags & toom6_vm1_neg ) 154 { 155 bsm2[n] = mpn_add (bsm2, bsm1, n, b1, t); 156 flags ^= toom6_vm2_neg; 157 } 158 else 159 { 160 bsm2[n] = 0; 161 if (t == n) 162 { 163 if (mpn_cmp (bsm1, b1, n) < 0) 164 { 165 mpn_sub_n (bsm2, b1, bsm1, n); 166 flags ^= toom6_vm2_neg; 167 } 168 else 169 { 170 mpn_sub_n (bsm2, bsm1, b1, n); 171 } 172 } 173 else 174 { 175 if (mpn_zero_p (bsm1 + t, n - t) && mpn_cmp (bsm1, b1, t) < 0) 176 { 177 mpn_sub_n (bsm2, b1, bsm1, t); 178 MPN_ZERO (bsm2 + t, n - t); 179 flags ^= toom6_vm2_neg; 180 } 181 else 182 { 183 mpn_sub (bsm2, bsm1, n, b1, t); 184 } 185 } 186 } 187 188 /* Compute as1 and asm1. */ 189 flags ^= toom6_vm1_neg & mpn_toom_eval_pm1 (as1, asm1, 4, ap, n, s, a0a2); 190 191 ASSERT (as1[n] <= 4); 192 ASSERT (bs1[n] <= 1); 193 ASSERT (asm1[n] <= 2); 194 /* ASSERT (bsm1[n] <= 1); */ 195 ASSERT (as2[n] <=30); 196 ASSERT (bs2[n] <= 2); 197 ASSERT (asm2[n] <= 20); 198 ASSERT (bsm2[n] <= 1); 199 200 /* vm1, 2n+1 limbs */ 201 mpn_mul (vm1, asm1, n+1, bsm1, n); /* W4 */ 202 203 /* vm2, 2n+1 limbs */ 204 mpn_mul_n (vm2, asm2, bsm2, n+1); /* W2 */ 205 206 /* v2, 2n+1 limbs */ 207 mpn_mul_n (v2, as2, bs2, n+1); /* W1 */ 208 209 /* v1, 2n+1 limbs */ 210 mpn_mul_n (v1, as1, bs1, n+1); /* W3 */ 211 212 /* vinf, s+t limbs */ /* W0 */ 213 if (s > t) mpn_mul (vinf, a4, s, b1, t); 214 else mpn_mul (vinf, b1, t, a4, s); 215 216 /* v0, 2n limbs */ 217 mpn_mul_n (v0, ap, bp, n); /* W5 */ 218 219 mpn_toom_interpolate_6pts (pp, n, flags, vm1, vm2, v2, t + s); 220 221 #undef v0 222 #undef vm1 223 #undef v1 224 #undef vm2 225 #undef v2 226 #undef vinf 227 #undef bs1 228 #undef bs2 229 #undef bsm1 230 #undef bsm2 231 #undef asm1 232 #undef asm2 233 #undef as1 234 #undef as2 235 #undef a0a2 236 #undef b0b2 237 #undef a1a3 238 #undef a0 239 #undef a1 240 #undef a2 241 #undef a3 242 #undef b0 243 #undef b1 244 #undef b2 245 246 } 247