285 lines
6.8 KiB
C
285 lines
6.8 KiB
C
#include <tommath.h>
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#ifdef BN_MP_TOOM_MUL_C
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/* LibTomMath, multiple-precision integer library -- Tom St Denis
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*
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* LibTomMath is a library that provides multiple-precision
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* integer arithmetic as well as number theoretic functionality.
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*
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* The library was designed directly after the MPI library by
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* Michael Fromberger but has been written from scratch with
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* additional optimizations in place.
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*
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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@gmail.com, http://libtom.org
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*/
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/* multiplication using the Toom-Cook 3-way algorithm
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*
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* Much more complicated than Karatsuba but has a lower
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* asymptotic running time of O(N**1.464). This algorithm is
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* only particularly useful on VERY large inputs
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* (we're talking 1000s of digits here...).
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*/
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int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
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{
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mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
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int res, B;
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/* init temps */
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if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
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&a0, &a1, &a2, &b0, &b1,
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&b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
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return res;
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}
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/* B */
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B = MIN(a->used, b->used) / 3;
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/* a = a2 * B**2 + a1 * B + a0 */
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if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_copy(a, &a1)) != MP_OKAY) {
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goto ERR;
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}
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mp_rshd(&a1, B);
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mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
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if ((res = mp_copy(a, &a2)) != MP_OKAY) {
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goto ERR;
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}
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mp_rshd(&a2, B*2);
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/* b = b2 * B**2 + b1 * B + b0 */
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if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_copy(b, &b1)) != MP_OKAY) {
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goto ERR;
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}
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mp_rshd(&b1, B);
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mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
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if ((res = mp_copy(b, &b2)) != MP_OKAY) {
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goto ERR;
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}
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mp_rshd(&b2, B*2);
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/* w0 = a0*b0 */
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if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
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goto ERR;
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}
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/* w4 = a2 * b2 */
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if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
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goto ERR;
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}
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/* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
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if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
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goto ERR;
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}
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/* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
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if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
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goto ERR;
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}
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/* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
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if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
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goto ERR;
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}
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/* now solve the matrix
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0 0 0 0 1
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1 2 4 8 16
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1 1 1 1 1
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16 8 4 2 1
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1 0 0 0 0
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using 12 subtractions, 4 shifts,
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2 small divisions and 1 small multiplication
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*/
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/* r1 - r4 */
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if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
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goto ERR;
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}
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/* r3 - r0 */
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if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
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goto ERR;
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}
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/* r1/2 */
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if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
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goto ERR;
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}
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/* r3/2 */
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if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
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goto ERR;
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}
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/* r2 - r0 - r4 */
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if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
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goto ERR;
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}
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/* r1 - r2 */
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if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
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goto ERR;
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}
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/* r3 - r2 */
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if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
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goto ERR;
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}
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/* r1 - 8r0 */
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if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
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goto ERR;
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}
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/* r3 - 8r4 */
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if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
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goto ERR;
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}
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/* 3r2 - r1 - r3 */
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if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
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goto ERR;
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}
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/* r1 - r2 */
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if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
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goto ERR;
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}
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/* r3 - r2 */
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if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
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goto ERR;
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}
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/* r1/3 */
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if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
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goto ERR;
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}
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/* r3/3 */
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if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
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goto ERR;
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}
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/* at this point shift W[n] by B*n */
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if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
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goto ERR;
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}
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if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
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goto ERR;
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}
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ERR:
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mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
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&a0, &a1, &a2, &b0, &b1,
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&b2, &tmp1, &tmp2, NULL);
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return res;
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}
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#endif
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/* $Source: /cvs/libtom/libtommath/bn_mp_toom_mul.c,v $ */
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/* $Revision: 1.4 $ */
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/* $Date: 2006/12/28 01:25:13 $ */
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