tommath/bn_mp_toom_mul.c

#include "tommath_private.h"
#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.
 *
 * SPDX-License-Identifier: Unlicense
 */

/* multiplication using the Toom-Cook 3-way algorithm
 *
 * 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
 * (we're talking 1000s of digits here...).
*/
int mp_toom_mul(const mp_int *a, const mp_int *b, mp_int *c)
{
   mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
   int res, B;

   /* 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;
   }

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

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

   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;
   }

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

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

   if ((res = mp_copy(b, &b1)) != MP_OKAY) {
      goto LBL_ERR;
   }
   mp_rshd(&b1, B);
   (void)mp_mod_2d(&b1, DIGIT_BIT * B, &b1);

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

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

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

   /* 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;
   }

   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;
   }

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

   /* 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;
   }

   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;
   }

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


   /* 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;
   }

   /* now solve the matrix

      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

      using 12 subtractions, 4 shifts,
             2 small divisions and 1 small multiplication
    */

   /* 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;
   }

   /* 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;
   }

   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;
   }

LBL_ERR:
   mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
                  &a0, &a1, &a2, &b0, &b1,
                  &b2, &tmp1, &tmp2, NULL);
   return res;
}

#endif

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