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 13Copyright 2009 Free Software Foundation, Inc. 14 15This file is part of the GNU MP Library. 16 17The GNU MP Library is free software; you can redistribute it and/or modify 18it under the terms of the GNU Lesser General Public License as published by 19the Free Software Foundation; either version 3 of the License, or (at your 20option) any later version. 21 22The GNU MP Library is distributed in the hope that it will be useful, but 23WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 24or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 25License for more details. 26 27You should have received a copy of the GNU Lesser General Public License 28along 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 54void 55mpn_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