1 /* mpn_toom22_mul -- Multiply {ap,an} and {bp,bn} where an >= bn. Or more 2 accurately, bn <= an < 2bn. 3 4 Contributed to the GNU project by Torbjorn Granlund. 5 6 THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY 7 SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST 8 GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE. 9 10 Copyright 2006, 2007, 2008 Free Software Foundation, Inc. 11 12 This file is part of the GNU MP Library. 13 14 The GNU MP Library is free software; you can redistribute it and/or modify 15 it under the terms of the GNU Lesser General Public License as published by 16 the Free Software Foundation; either version 3 of the License, or (at your 17 option) any later version. 18 19 The GNU MP Library is distributed in the hope that it will be useful, but 20 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 21 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 22 License for more details. 23 24 You should have received a copy of the GNU Lesser General Public License 25 along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ 26 27 28 #include "gmp.h" 29 #include "gmp-impl.h" 30 31 /* Evaluate in: -1, 0, +inf 32 33 <-s--><--n--> 34 ____ ______ 35 |_a1_|___a0_| 36 |b1_|___b0_| 37 <-t-><--n--> 38 39 v0 = a0 * b0 # A(0)*B(0) 40 vm1 = (a0- a1)*(b0- b1) # A(-1)*B(-1) 41 vinf= a1 * b1 # A(inf)*B(inf) 42 */ 43 44 #if TUNE_PROGRAM_BUILD 45 #define MAYBE_mul_toom22 1 46 #else 47 #define MAYBE_mul_toom22 \ 48 (MUL_TOOM33_THRESHOLD >= 2 * MUL_TOOM22_THRESHOLD) 49 #endif 50 51 #define TOOM22_MUL_N_REC(p, a, b, n, ws) \ 52 do { \ 53 if (! MAYBE_mul_toom22 \ 54 || BELOW_THRESHOLD (n, MUL_KARATSUBA_THRESHOLD)) \ 55 mpn_mul_basecase (p, a, n, b, n); \ 56 else \ 57 mpn_toom22_mul (p, a, n, b, n, ws); \ 58 } while (0) 59 60 void 61 mpn_toom22_mul (mp_ptr pp, 62 mp_srcptr ap, mp_size_t an, 63 mp_srcptr bp, mp_size_t bn, 64 mp_ptr scratch) 65 { 66 mp_size_t n, s, t; 67 int vm1_neg; 68 mp_limb_t cy, cy2; 69 mp_ptr asm1; 70 mp_ptr bsm1; 71 72 #define a0 ap 73 #define a1 (ap + n) 74 #define b0 bp 75 #define b1 (bp + n) 76 77 s = an >> 1; 78 n = an - s; 79 t = bn - n; 80 81 ASSERT (an >= bn); 82 83 ASSERT (0 < s && s <= n); 84 ASSERT (0 < t && t <= s); 85 86 asm1 = pp; 87 bsm1 = pp + n; 88 89 vm1_neg = 0; 90 91 /* Compute asm1. */ 92 if (s == n) 93 { 94 if (mpn_cmp (a0, a1, n) < 0) 95 { 96 mpn_sub_n (asm1, a1, a0, n); 97 vm1_neg = 1; 98 } 99 else 100 { 101 mpn_sub_n (asm1, a0, a1, n); 102 } 103 } 104 else 105 { 106 if (mpn_zero_p (a0 + s, n - s) && mpn_cmp (a0, a1, s) < 0) 107 { 108 mpn_sub_n (asm1, a1, a0, s); 109 MPN_ZERO (asm1 + s, n - s); 110 vm1_neg = 1; 111 } 112 else 113 { 114 mpn_sub (asm1, a0, n, a1, s); 115 } 116 } 117 118 /* Compute bsm1. */ 119 if (t == n) 120 { 121 if (mpn_cmp (b0, b1, n) < 0) 122 { 123 mpn_sub_n (bsm1, b1, b0, n); 124 vm1_neg ^= 1; 125 } 126 else 127 { 128 mpn_sub_n (bsm1, b0, b1, n); 129 } 130 } 131 else 132 { 133 if (mpn_zero_p (b0 + t, n - t) && mpn_cmp (b0, b1, t) < 0) 134 { 135 mpn_sub_n (bsm1, b1, b0, t); 136 MPN_ZERO (bsm1 + t, n - t); 137 vm1_neg ^= 1; 138 } 139 else 140 { 141 mpn_sub (bsm1, b0, n, b1, t); 142 } 143 } 144 145 #define v0 pp /* 2n */ 146 #define vinf (pp + 2 * n) /* s+t */ 147 #define vm1 scratch /* 2n */ 148 #define scratch_out scratch + 2 * n 149 150 /* vm1, 2n limbs */ 151 TOOM22_MUL_N_REC (vm1, asm1, bsm1, n, scratch_out); 152 153 /* vinf, s+t limbs */ 154 mpn_mul (vinf, a1, s, b1, t); 155 156 /* v0, 2n limbs */ 157 TOOM22_MUL_N_REC (v0, ap, bp, n, scratch_out); 158 159 /* H(v0) + L(vinf) */ 160 cy = mpn_add_n (pp + 2 * n, v0 + n, vinf, n); 161 162 /* L(v0) + H(v0) */ 163 cy2 = cy + mpn_add_n (pp + n, pp + 2 * n, v0, n); 164 165 /* L(vinf) + H(vinf) */ 166 cy += mpn_add (pp + 2 * n, pp + 2 * n, n, vinf + n, s + t - n); 167 168 if (vm1_neg) 169 cy += mpn_add_n (pp + n, pp + n, vm1, 2 * n); 170 else 171 cy -= mpn_sub_n (pp + n, pp + n, vm1, 2 * n); 172 173 ASSERT (cy + 1 <= 3); 174 ASSERT (cy2 <= 2); 175 176 mpn_incr_u (pp + 2 * n, cy2); 177 if (LIKELY (cy <= 2)) 178 mpn_incr_u (pp + 3 * n, cy); 179 else 180 mpn_decr_u (pp + 3 * n, 1); 181 } 182