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e549ccf added libtommath-0.32
Tom St Denis authored
1 #include <tommath.h>
2 #ifdef BN_MP_TOOM_MUL_C
c1da6aa added libtommath-0.25
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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 *
333aebc added libtommath-0.41
Tom St Denis authored
15 * Tom St Denis, tomstdenis@gmail.com, http://libtom.org
c1da6aa added libtommath-0.25
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16 */
17
e549ccf added libtommath-0.32
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18 /* multiplication using the Toom-Cook 3-way algorithm
19 *
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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...).
e549ccf added libtommath-0.32
Tom St Denis authored
24 */
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25 int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
c1da6aa added libtommath-0.25
Tom St Denis authored
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 mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
50
51 if ((res = mp_copy(a, &a2)) != MP_OKAY) {
52 goto ERR;
53 }
54 mp_rshd(&a2, B*2);
55
56 /* b = b2 * B**2 + b1 * B + b0 */
57 if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
58 goto ERR;
59 }
60
61 if ((res = mp_copy(b, &b1)) != MP_OKAY) {
62 goto ERR;
63 }
64 mp_rshd(&b1, B);
65 mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
66
67 if ((res = mp_copy(b, &b2)) != MP_OKAY) {
68 goto ERR;
69 }
70 mp_rshd(&b2, B*2);
71
72 /* w0 = a0*b0 */
73 if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
74 goto ERR;
75 }
76
77 /* w4 = a2 * b2 */
78 if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
79 goto ERR;
80 }
81
82 /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
83 if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
84 goto ERR;
85 }
86 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
87 goto ERR;
88 }
89 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
90 goto ERR;
91 }
92 if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
93 goto ERR;
94 }
95
96 if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
97 goto ERR;
98 }
99 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
100 goto ERR;
101 }
102 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
103 goto ERR;
104 }
105 if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
106 goto ERR;
107 }
108
109 if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
110 goto ERR;
111 }
112
113 /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
114 if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
115 goto ERR;
116 }
117 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
118 goto ERR;
119 }
120 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
121 goto ERR;
122 }
123 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
124 goto ERR;
125 }
126
127 if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
128 goto ERR;
129 }
130 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
131 goto ERR;
132 }
133 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
134 goto ERR;
135 }
136 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
137 goto ERR;
138 }
139
140 if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
141 goto ERR;
142 }
143
144
145 /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
146 if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
147 goto ERR;
148 }
149 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
150 goto ERR;
151 }
152 if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) {
153 goto ERR;
154 }
155 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
156 goto ERR;
157 }
158 if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
159 goto ERR;
160 }
161
162 /* now solve the matrix
163
164 0 0 0 0 1
165 1 2 4 8 16
166 1 1 1 1 1
167 16 8 4 2 1
168 1 0 0 0 0
169
170 using 12 subtractions, 4 shifts,
171 2 small divisions and 1 small multiplication
172 */
173
174 /* r1 - r4 */
175 if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
176 goto ERR;
177 }
178 /* r3 - r0 */
179 if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
180 goto ERR;
181 }
182 /* r1/2 */
183 if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
184 goto ERR;
185 }
186 /* r3/2 */
187 if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
188 goto ERR;
189 }
190 /* r2 - r0 - r4 */
191 if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
192 goto ERR;
193 }
194 if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
195 goto ERR;
196 }
197 /* r1 - r2 */
198 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
199 goto ERR;
200 }
201 /* r3 - r2 */
202 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
203 goto ERR;
204 }
205 /* r1 - 8r0 */
206 if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
207 goto ERR;
208 }
209 if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
210 goto ERR;
211 }
212 /* r3 - 8r4 */
213 if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
214 goto ERR;
215 }
216 if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
217 goto ERR;
218 }
219 /* 3r2 - r1 - r3 */
220 if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
221 goto ERR;
222 }
223 if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
224 goto ERR;
225 }
226 if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
227 goto ERR;
228 }
229 /* r1 - r2 */
230 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
231 goto ERR;
232 }
233 /* r3 - r2 */
234 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
235 goto ERR;
236 }
237 /* r1/3 */
238 if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
239 goto ERR;
240 }
241 /* r3/3 */
242 if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
243 goto ERR;
244 }
245
246 /* at this point shift W[n] by B*n */
247 if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
248 goto ERR;
249 }
250 if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
251 goto ERR;
252 }
253 if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
254 goto ERR;
255 }
256 if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
257 goto ERR;
258 }
259
260 if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
261 goto ERR;
262 }
263 if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
264 goto ERR;
265 }
266 if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
267 goto ERR;
268 }
269 if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
270 goto ERR;
271 }
272
273 ERR:
274 mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
275 &a0, &a1, &a2, &b0, &b1,
276 &b2, &tmp1, &tmp2, NULL);
277 return res;
278 }
279
e549ccf added libtommath-0.32
Tom St Denis authored
280 #endif
9294e79 added libtommath-0.36
Tom St Denis authored
281
282 /* $Source$ */
283 /* $Revision$ */
284 /* $Date$ */
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