2 #ifdef BN_MP_TOOM_MUL_C
3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
5 * LibTomMath is a library that provides multiple-precision
6 * integer arithmetic as well as number theoretic functionality.
8 * The library was designed directly after the MPI library by
9 * Michael Fromberger but has been written from scratch with
10 * additional optimizations in place.
12 * The library is free for all purposes without any express
15 * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
18 /* multiplication using the Toom-Cook 3-way algorithm
20 * Much more complicated than Karatsuba but has a lower
21 * asymptotic running time of O(N**1.464). This algorithm is
22 * only particularly useful on VERY large inputs
23 * (we're talking 1000s of digits here...).
25 int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
27 mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
31 if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
32 &a0, &a1, &a2, &b0, &b1,
33 &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
38 B = MIN(a->used, b->used) / 3;
40 /* a = a2 * B**2 + a1 * B + a0 */
41 if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
45 if ((res = mp_copy(a, &a1)) != MP_OKAY) {
49 mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
51 if ((res = mp_copy(a, &a2)) != MP_OKAY) {
56 /* b = b2 * B**2 + b1 * B + b0 */
57 if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
61 if ((res = mp_copy(b, &b1)) != MP_OKAY) {
65 mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
67 if ((res = mp_copy(b, &b2)) != MP_OKAY) {
73 if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
78 if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
82 /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
83 if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
86 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
89 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
92 if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
96 if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
99 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
102 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
105 if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
109 if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
113 /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
114 if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
117 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
120 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
123 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
127 if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
130 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
133 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
136 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
140 if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
145 /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
146 if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
149 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
152 if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) {
155 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
158 if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
162 /* now solve the matrix
170 using 12 subtractions, 4 shifts,
171 2 small divisions and 1 small multiplication
175 if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
179 if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
183 if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
187 if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
191 if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
194 if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
198 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
202 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
206 if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
209 if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
213 if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
216 if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
220 if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
223 if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
226 if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
230 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
234 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
238 if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
242 if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
246 /* at this point shift W[n] by B*n */
247 if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
250 if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
253 if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
256 if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
260 if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
263 if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
266 if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
269 if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
274 mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
275 &a0, &a1, &a2, &b0, &b1,
276 &b2, &tmp1, &tmp2, NULL);