1 /* mpn_toom62_mul -- Multiply {ap,an} and {bp,bn} where an is nominally 3 times 2 as large as bn. Or more accurately, (5/2)bn < an < 6bn. 3 4 Contributed to the GNU project by Torbjorn Granlund and 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 2006, 2007, 2008 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: 35 0, +1, -1, +2, -2, 1/2, +inf 36 37 <-s-><--n--><--n--><--n--><--n--><--n--> 38 ___ ______ ______ ______ ______ ______ 39 |a5_|___a4_|___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+ a4+ a5)*( b0+ b1) # A(1)*B(1) ah <= 5 bh <= 1 45 vm1 = ( a0- a1+ a2- a3+ a4- a5)*( b0- b1) # A(-1)*B(-1) |ah| <= 2 bh = 0 46 v2 = ( a0+ 2a1+4a2+8a3+16a4+32a5)*( b0+2b1) # A(2)*B(2) ah <= 62 bh <= 2 47 vm2 = ( a0- 2a1+4a2-8a3+16a4-32a5)*( b0-2b1) # A(-2)*B(-2) -41<=ah<=20 -1<=bh<=0 48 vh = (32a0+16a1+8a2+4a3+ 2a4+ a5)*(2b0+ b1) # A(1/2)*B(1/2) ah <= 62 bh <= 2 49 vinf= a5 * b1 # A(inf)*B(inf) 50 */ 51 52 void 53 mpn_toom62_mul (mp_ptr pp, 54 mp_srcptr ap, mp_size_t an, 55 mp_srcptr bp, mp_size_t bn, 56 mp_ptr scratch) 57 { 58 mp_size_t n, s, t; 59 mp_limb_t cy; 60 mp_ptr as1, asm1, as2, asm2, ash; 61 mp_ptr bs1, bsm1, bs2, bsm2, bsh; 62 mp_ptr gp; 63 enum toom7_flags aflags, bflags; 64 TMP_DECL; 65 66 #define a0 ap 67 #define a1 (ap + n) 68 #define a2 (ap + 2*n) 69 #define a3 (ap + 3*n) 70 #define a4 (ap + 4*n) 71 #define a5 (ap + 5*n) 72 #define b0 bp 73 #define b1 (bp + n) 74 75 n = 1 + (an >= 3 * bn ? (an - 1) / (size_t) 6 : (bn - 1) >> 1); 76 77 s = an - 5 * n; 78 t = bn - n; 79 80 ASSERT (0 < s && s <= n); 81 ASSERT (0 < t && t <= n); 82 83 TMP_MARK; 84 85 as1 = TMP_SALLOC_LIMBS (n + 1); 86 asm1 = TMP_SALLOC_LIMBS (n + 1); 87 as2 = TMP_SALLOC_LIMBS (n + 1); 88 asm2 = TMP_SALLOC_LIMBS (n + 1); 89 ash = TMP_SALLOC_LIMBS (n + 1); 90 91 bs1 = TMP_SALLOC_LIMBS (n + 1); 92 bsm1 = TMP_SALLOC_LIMBS (n); 93 bs2 = TMP_SALLOC_LIMBS (n + 1); 94 bsm2 = TMP_SALLOC_LIMBS (n + 1); 95 bsh = TMP_SALLOC_LIMBS (n + 1); 96 97 gp = pp; 98 99 /* Compute as1 and asm1. */ 100 aflags = toom7_w3_neg & mpn_toom_eval_pm1 (as1, asm1, 5, ap, n, s, gp); 101 102 /* Compute as2 and asm2. */ 103 aflags |= toom7_w1_neg & mpn_toom_eval_pm2 (as2, asm2, 5, ap, n, s, gp); 104 105 /* Compute ash = 32 a0 + 16 a1 + 8 a2 + 4 a3 + 2 a4 + a5 106 = 2*(2*(2*(2*(2*a0 + a1) + a2) + a3) + a4) + a5 */ 107 108 #if HAVE_NATIVE_mpn_addlsh1_n 109 cy = mpn_addlsh1_n (ash, a1, a0, n); 110 cy = 2*cy + mpn_addlsh1_n (ash, a2, ash, n); 111 cy = 2*cy + mpn_addlsh1_n (ash, a3, ash, n); 112 cy = 2*cy + mpn_addlsh1_n (ash, a4, ash, n); 113 if (s < n) 114 { 115 mp_limb_t cy2; 116 cy2 = mpn_addlsh1_n (ash, a5, ash, s); 117 ash[n] = 2*cy + mpn_lshift (ash + s, ash + s, n - s, 1); 118 MPN_INCR_U (ash + s, n+1-s, cy2); 119 } 120 else 121 ash[n] = 2*cy + mpn_addlsh1_n (ash, a5, ash, n); 122 #else 123 cy = mpn_lshift (ash, a0, n, 1); 124 cy += mpn_add_n (ash, ash, a1, n); 125 cy = 2*cy + mpn_lshift (ash, ash, n, 1); 126 cy += mpn_add_n (ash, ash, a2, n); 127 cy = 2*cy + mpn_lshift (ash, ash, n, 1); 128 cy += mpn_add_n (ash, ash, a3, n); 129 cy = 2*cy + mpn_lshift (ash, ash, n, 1); 130 cy += mpn_add_n (ash, ash, a4, n); 131 cy = 2*cy + mpn_lshift (ash, ash, n, 1); 132 ash[n] = cy + mpn_add (ash, ash, n, a5, s); 133 #endif 134 135 /* Compute bs1 and bsm1. */ 136 if (t == n) 137 { 138 #if HAVE_NATIVE_mpn_add_n_sub_n 139 if (mpn_cmp (b0, b1, n) < 0) 140 { 141 cy = mpn_add_n_sub_n (bs1, bsm1, b1, b0, n); 142 bflags = toom7_w3_neg; 143 } 144 else 145 { 146 cy = mpn_add_n_sub_n (bs1, bsm1, b0, b1, n); 147 bflags = 0; 148 } 149 bs1[n] = cy >> 1; 150 #else 151 bs1[n] = mpn_add_n (bs1, b0, b1, n); 152 if (mpn_cmp (b0, b1, n) < 0) 153 { 154 mpn_sub_n (bsm1, b1, b0, n); 155 bflags = toom7_w3_neg; 156 } 157 else 158 { 159 mpn_sub_n (bsm1, b0, b1, n); 160 bflags = 0; 161 } 162 #endif 163 } 164 else 165 { 166 bs1[n] = mpn_add (bs1, b0, n, b1, t); 167 if (mpn_zero_p (b0 + t, n - t) && mpn_cmp (b0, b1, t) < 0) 168 { 169 mpn_sub_n (bsm1, b1, b0, t); 170 MPN_ZERO (bsm1 + t, n - t); 171 bflags = toom7_w3_neg; 172 } 173 else 174 { 175 mpn_sub (bsm1, b0, n, b1, t); 176 bflags = 0; 177 } 178 } 179 180 /* Compute bs2 and bsm2. Recycling bs1 and bsm1; bs2=bs1+b1, bsm2 = 181 bsm1 - b1 */ 182 mpn_add (bs2, bs1, n + 1, b1, t); 183 if (bflags & toom7_w3_neg) 184 { 185 bsm2[n] = mpn_add (bsm2, bsm1, n, b1, t); 186 bflags |= toom7_w1_neg; 187 } 188 else 189 { 190 /* FIXME: Simplify this logic? */ 191 if (t < n) 192 { 193 if (mpn_zero_p (bsm1 + t, n - t) && mpn_cmp (bsm1, b1, t) < 0) 194 { 195 ASSERT_NOCARRY (mpn_sub_n (bsm2, b1, bsm1, t)); 196 MPN_ZERO (bsm2 + t, n + 1 - t); 197 bflags |= toom7_w1_neg; 198 } 199 else 200 { 201 ASSERT_NOCARRY (mpn_sub (bsm2, bsm1, n, b1, t)); 202 bsm2[n] = 0; 203 } 204 } 205 else 206 { 207 if (mpn_cmp (bsm1, b1, n) < 0) 208 { 209 ASSERT_NOCARRY (mpn_sub_n (bsm2, b1, bsm1, n)); 210 bflags |= toom7_w1_neg; 211 } 212 else 213 { 214 ASSERT_NOCARRY (mpn_sub (bsm2, bsm1, n, b1, n)); 215 } 216 bsm2[n] = 0; 217 } 218 } 219 220 /* Compute bsh, recycling bs1 and bsm1. bsh=bs1+b0; */ 221 mpn_add (bsh, bs1, n + 1, b0, n); 222 223 ASSERT (as1[n] <= 5); 224 ASSERT (bs1[n] <= 1); 225 ASSERT (asm1[n] <= 2); 226 ASSERT (as2[n] <= 62); 227 ASSERT (bs2[n] <= 2); 228 ASSERT (asm2[n] <= 41); 229 ASSERT (bsm2[n] <= 1); 230 ASSERT (ash[n] <= 62); 231 ASSERT (bsh[n] <= 2); 232 233 #define v0 pp /* 2n */ 234 #define v1 (pp + 2 * n) /* 2n+1 */ 235 #define vinf (pp + 6 * n) /* s+t */ 236 #define v2 scratch /* 2n+1 */ 237 #define vm2 (scratch + 2 * n + 1) /* 2n+1 */ 238 #define vh (scratch + 4 * n + 2) /* 2n+1 */ 239 #define vm1 (scratch + 6 * n + 3) /* 2n+1 */ 240 #define scratch_out (scratch + 8 * n + 4) /* 2n+1 */ 241 /* Total scratch need: 10*n+5 */ 242 243 /* Must be in allocation order, as they overwrite one limb beyond 244 * 2n+1. */ 245 mpn_mul_n (v2, as2, bs2, n + 1); /* v2, 2n+1 limbs */ 246 mpn_mul_n (vm2, asm2, bsm2, n + 1); /* vm2, 2n+1 limbs */ 247 mpn_mul_n (vh, ash, bsh, n + 1); /* vh, 2n+1 limbs */ 248 249 /* vm1, 2n+1 limbs */ 250 mpn_mul_n (vm1, asm1, bsm1, n); 251 cy = 0; 252 if (asm1[n] == 1) 253 { 254 cy = mpn_add_n (vm1 + n, vm1 + n, bsm1, n); 255 } 256 else if (asm1[n] == 2) 257 { 258 #if HAVE_NATIVE_mpn_addlsh1_n 259 cy = mpn_addlsh1_n (vm1 + n, vm1 + n, bsm1, n); 260 #else 261 cy = mpn_addmul_1 (vm1 + n, bsm1, n, CNST_LIMB(2)); 262 #endif 263 } 264 vm1[2 * n] = cy; 265 266 /* v1, 2n+1 limbs */ 267 mpn_mul_n (v1, as1, bs1, n); 268 if (as1[n] == 1) 269 { 270 cy = bs1[n] + mpn_add_n (v1 + n, v1 + n, bs1, n); 271 } 272 else if (as1[n] == 2) 273 { 274 #if HAVE_NATIVE_mpn_addlsh1_n 275 cy = 2 * bs1[n] + mpn_addlsh1_n (v1 + n, v1 + n, bs1, n); 276 #else 277 cy = 2 * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, CNST_LIMB(2)); 278 #endif 279 } 280 else if (as1[n] != 0) 281 { 282 cy = as1[n] * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, as1[n]); 283 } 284 else 285 cy = 0; 286 if (bs1[n] != 0) 287 cy += mpn_add_n (v1 + n, v1 + n, as1, n); 288 v1[2 * n] = cy; 289 290 mpn_mul_n (v0, a0, b0, n); /* v0, 2n limbs */ 291 292 /* vinf, s+t limbs */ 293 if (s > t) mpn_mul (vinf, a5, s, b1, t); 294 else mpn_mul (vinf, b1, t, a5, s); 295 296 mpn_toom_interpolate_7pts (pp, n, aflags ^ bflags, 297 vm2, vm1, v2, vh, s + t, scratch_out); 298 299 TMP_FREE; 300 } 301