bn_mp_toom_mul.c 6.76 KB
Newer Older
1
#include "tommath_private.h"
2 3 4 5 6 7 8 9 10 11
#ifdef BN_MP_TOOM_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
 *
 * LibTomMath is a library that provides multiple-precision
 * integer arithmetic as well as number theoretic functionality.
 *
 * The library was designed directly after the MPI library by
 * Michael Fromberger but has been written from scratch with
 * additional optimizations in place.
 *
12
 * SPDX-License-Identifier: Unlicense
13 14
 */

15
/* multiplication using the Toom-Cook 3-way algorithm
16
 *
17 18 19
 * Much more complicated than Karatsuba but has a lower
 * asymptotic running time of O(N**1.464).  This algorithm is
 * only particularly useful on VERY large inputs
20 21
 * (we're talking 1000s of digits here...).
*/
22
int mp_toom_mul(const mp_int *a, const mp_int *b, mp_int *c)
23
{
24 25
   mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
   int res, B;
26

27 28 29 30 31 32
   /* init temps */
   if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
                            &a0, &a1, &a2, &b0, &b1,
                            &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
      return res;
   }
33

34 35
   /* B */
   B = MIN(a->used, b->used) / 3;
36

37 38 39 40
   /* a = a2 * B**2 + a1 * B + a0 */
   if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
      goto LBL_ERR;
   }
41

42 43 44 45 46 47 48
   if ((res = mp_copy(a, &a1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   mp_rshd(&a1, B);
   if ((res = mp_mod_2d(&a1, DIGIT_BIT * B, &a1)) != MP_OKAY) {
      goto LBL_ERR;
   }
49

50 51 52 53
   if ((res = mp_copy(a, &a2)) != MP_OKAY) {
      goto LBL_ERR;
   }
   mp_rshd(&a2, B*2);
54

55 56 57 58
   /* b = b2 * B**2 + b1 * B + b0 */
   if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
      goto LBL_ERR;
   }
59

60 61 62 63 64
   if ((res = mp_copy(b, &b1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   mp_rshd(&b1, B);
   (void)mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
65

66 67 68 69
   if ((res = mp_copy(b, &b2)) != MP_OKAY) {
      goto LBL_ERR;
   }
   mp_rshd(&b2, B*2);
70

71 72 73 74
   /* w0 = a0*b0 */
   if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
      goto LBL_ERR;
   }
75

76 77 78 79
   /* w4 = a2 * b2 */
   if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
      goto LBL_ERR;
   }
80

81 82 83 84 85 86 87 88 89 90 91 92 93
   /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
   if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
      goto LBL_ERR;
   }
94

95 96 97 98 99 100 101 102 103 104 105 106
   if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
      goto LBL_ERR;
   }
107

108 109 110
   if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
      goto LBL_ERR;
   }
111

112 113 114 115 116 117 118 119 120 121 122 123 124
   /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
   if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
      goto LBL_ERR;
   }
125

126 127 128 129 130 131 132 133 134 135 136 137
   if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
      goto LBL_ERR;
   }
138

139 140 141
   if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
      goto LBL_ERR;
   }
142

143

144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159
   /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
   if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
      goto LBL_ERR;
   }
160

161
   /* now solve the matrix
162

163 164 165 166 167
      0  0  0  0  1
      1  2  4  8  16
      1  1  1  1  1
      16 8  4  2  1
      1  0  0  0  0
168

169 170 171
      using 12 subtractions, 4 shifts,
             2 small divisions and 1 small multiplication
    */
172

173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243
   /* r1 - r4 */
   if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   /* r3 - r0 */
   if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
      goto LBL_ERR;
   }
   /* r1/2 */
   if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   /* r3/2 */
   if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
      goto LBL_ERR;
   }
   /* r2 - r0 - r4 */
   if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
      goto LBL_ERR;
   }
   /* r1 - r2 */
   if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   /* r3 - r2 */
   if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
      goto LBL_ERR;
   }
   /* r1 - 8r0 */
   if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   /* r3 - 8r4 */
   if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
      goto LBL_ERR;
   }
   /* 3r2 - r1 - r3 */
   if ((res = mp_mul_d(&w2, 3uL, &w2)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
      goto LBL_ERR;
   }
   /* r1 - r2 */
   if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   /* r3 - r2 */
   if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
      goto LBL_ERR;
   }
   /* r1/3 */
   if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
      goto LBL_ERR;
   }
   /* r3/3 */
   if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
      goto LBL_ERR;
   }
244

245 246 247 248 249 250 251 252 253 254 255 256 257
   /* at this point shift W[n] by B*n */
   if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
      goto LBL_ERR;
   }
258

259 260 261 262 263 264 265 266 267 268 269 270
   if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
      goto LBL_ERR;
   }
271

272 273 274 275 276
LBL_ERR:
   mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
                  &a0, &a1, &a2, &b0, &b1,
                  &b2, &tmp1, &tmp2, NULL);
   return res;
277 278
}

279 280
#endif

281 282 283
/* ref:         HEAD -> master, tag: v1.1.0 */
/* git commit:  08549ad6bc8b0cede0b357a9c341c5c6473a9c55 */
/* commit time: 2019-01-28 20:32:32 +0100 */