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comparison 3rdparty/libtommath/bn_mp_toom_mul.c @ 0:2cf249471370

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author Takahiro SHIMIZU <anatofuz@cr.ie.u-ryukyu.ac.jp>
date Tue, 08 May 2018 16:09:12 +0900
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-1:000000000000 0:2cf249471370
1 #include <tommath_private.h>
2 #ifdef BN_MP_TOOM_MUL_C
3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
4 *
5 * LibTomMath is a library that provides multiple-precision
6 * integer arithmetic as well as number theoretic functionality.
7 *
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.
11 *
12 * The library is free for all purposes without any express
13 * guarantee it works.
14 *
15 * Tom St Denis, tstdenis82@gmail.com, http://libtom.org
16 */
17
18 /* multiplication using the Toom-Cook 3-way algorithm
19 *
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...).
24 */
25 int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
26 {
27 mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
28 int res, B;
29
30 /* init temps */
31 if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
32 &a0, &a1, &a2, &b0, &b1,
33 &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
34 return res;
35 }
36
37 /* B */
38 B = MIN(a->used, b->used) / 3;
39
40 /* a = a2 * B**2 + a1 * B + a0 */
41 if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
42 goto ERR_;
43 }
44
45 if ((res = mp_copy(a, &a1)) != MP_OKAY) {
46 goto ERR_;
47 }
48 mp_rshd(&a1, B);
49 if ((res = mp_mod_2d(&a1, DIGIT_BIT * B, &a1)) != MP_OKAY) {
50 goto ERR_;
51 }
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 (void)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
275 ERR_:
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 /* $Source$ */
285 /* $Revision$ */
286 /* $Date$ */