1/*	$NetBSD: bn_mp_toom_mul.c,v 1.2 2017/01/28 21:31:47 christos Exp $	*/
2
3#include <tommath.h>
4#ifdef BN_MP_TOOM_MUL_C
5/* LibTomMath, multiple-precision integer library -- Tom St Denis
6 *
7 * LibTomMath is a library that provides multiple-precision
8 * integer arithmetic as well as number theoretic functionality.
9 *
10 * The library was designed directly after the MPI library by
11 * Michael Fromberger but has been written from scratch with
12 * additional optimizations in place.
13 *
14 * The library is free for all purposes without any express
15 * guarantee it works.
16 *
17 * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
18 */
19
20/* multiplication using the Toom-Cook 3-way algorithm
21 *
22 * Much more complicated than Karatsuba but has a lower
23 * asymptotic running time of O(N**1.464).  This algorithm is
24 * only particularly useful on VERY large inputs
25 * (we're talking 1000s of digits here...).
26*/
27int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
28{
29    mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
30    int res, B;
31
32    /* init temps */
33    if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
34                             &a0, &a1, &a2, &b0, &b1,
35                             &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
36       return res;
37    }
38
39    /* B */
40    B = MIN(a->used, b->used) / 3;
41
42    /* a = a2 * B**2 + a1 * B + a0 */
43    if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
44       goto ERR;
45    }
46
47    if ((res = mp_copy(a, &a1)) != MP_OKAY) {
48       goto ERR;
49    }
50    mp_rshd(&a1, B);
51    mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
52
53    if ((res = mp_copy(a, &a2)) != MP_OKAY) {
54       goto ERR;
55    }
56    mp_rshd(&a2, B*2);
57
58    /* b = b2 * B**2 + b1 * B + b0 */
59    if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
60       goto ERR;
61    }
62
63    if ((res = mp_copy(b, &b1)) != MP_OKAY) {
64       goto ERR;
65    }
66    mp_rshd(&b1, B);
67    mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
68
69    if ((res = mp_copy(b, &b2)) != MP_OKAY) {
70       goto ERR;
71    }
72    mp_rshd(&b2, B*2);
73
74    /* w0 = a0*b0 */
75    if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
76       goto ERR;
77    }
78
79    /* w4 = a2 * b2 */
80    if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
81       goto ERR;
82    }
83
84    /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
85    if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
86       goto ERR;
87    }
88    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
89       goto ERR;
90    }
91    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
92       goto ERR;
93    }
94    if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
95       goto ERR;
96    }
97
98    if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
99       goto ERR;
100    }
101    if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
102       goto ERR;
103    }
104    if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
105       goto ERR;
106    }
107    if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
108       goto ERR;
109    }
110
111    if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
112       goto ERR;
113    }
114
115    /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
116    if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
117       goto ERR;
118    }
119    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
120       goto ERR;
121    }
122    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
123       goto ERR;
124    }
125    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
126       goto ERR;
127    }
128
129    if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
130       goto ERR;
131    }
132    if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
133       goto ERR;
134    }
135    if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
136       goto ERR;
137    }
138    if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
139       goto ERR;
140    }
141
142    if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
143       goto ERR;
144    }
145
146
147    /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
148    if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
149       goto ERR;
150    }
151    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
152       goto ERR;
153    }
154    if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) {
155       goto ERR;
156    }
157    if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
158       goto ERR;
159    }
160    if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
161       goto ERR;
162    }
163
164    /* now solve the matrix
165
166       0  0  0  0  1
167       1  2  4  8  16
168       1  1  1  1  1
169       16 8  4  2  1
170       1  0  0  0  0
171
172       using 12 subtractions, 4 shifts,
173              2 small divisions and 1 small multiplication
174     */
175
176     /* r1 - r4 */
177     if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
178        goto ERR;
179     }
180     /* r3 - r0 */
181     if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
182        goto ERR;
183     }
184     /* r1/2 */
185     if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
186        goto ERR;
187     }
188     /* r3/2 */
189     if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
190        goto ERR;
191     }
192     /* r2 - r0 - r4 */
193     if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
194        goto ERR;
195     }
196     if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
197        goto ERR;
198     }
199     /* r1 - r2 */
200     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
201        goto ERR;
202     }
203     /* r3 - r2 */
204     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
205        goto ERR;
206     }
207     /* r1 - 8r0 */
208     if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
209        goto ERR;
210     }
211     if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
212        goto ERR;
213     }
214     /* r3 - 8r4 */
215     if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
216        goto ERR;
217     }
218     if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
219        goto ERR;
220     }
221     /* 3r2 - r1 - r3 */
222     if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
223        goto ERR;
224     }
225     if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
226        goto ERR;
227     }
228     if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
229        goto ERR;
230     }
231     /* r1 - r2 */
232     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
233        goto ERR;
234     }
235     /* r3 - r2 */
236     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
237        goto ERR;
238     }
239     /* r1/3 */
240     if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
241        goto ERR;
242     }
243     /* r3/3 */
244     if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
245        goto ERR;
246     }
247
248     /* at this point shift W[n] by B*n */
249     if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
250        goto ERR;
251     }
252     if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
253        goto ERR;
254     }
255     if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
256        goto ERR;
257     }
258     if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
259        goto ERR;
260     }
261
262     if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
263        goto ERR;
264     }
265     if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
266        goto ERR;
267     }
268     if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
269        goto ERR;
270     }
271     if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
272        goto ERR;
273     }
274
275ERR:
276     mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
277                    &a0, &a1, &a2, &b0, &b1,
278                    &b2, &tmp1, &tmp2, NULL);
279     return res;
280}
281
282#endif
283
284/* Source: /cvs/libtom/libtommath/bn_mp_toom_mul.c,v  */
285/* Revision: 1.4  */
286/* Date: 2006/12/28 01:25:13  */
287