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comparison bn_mp_toom_mul.c @ 1:22d5cf7d4b1a libtommath

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Renaming branch
author Matt Johnston <matt@ucc.asn.au>
date Mon, 31 May 2004 18:23:46 +0000
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children d29b64170cf0
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-1:000000000000 1:22d5cf7d4b1a
1 /* LibTomMath, multiple-precision integer library -- Tom St Denis
2 *
3 * LibTomMath is a library that provides multiple-precision
4 * integer arithmetic as well as number theoretic functionality.
5 *
6 * The library was designed directly after the MPI library by
7 * Michael Fromberger but has been written from scratch with
8 * additional optimizations in place.
9 *
10 * The library is free for all purposes without any express
11 * guarantee it works.
12 *
13 * Tom St Denis, [email protected], http://math.libtomcrypt.org
14 */
15 #include <tommath.h>
16
17 /* multiplication using the Toom-Cook 3-way algorithm */
18 int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
19 {
20 mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
21 int res, B;
22
23 /* init temps */
24 if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
25 &a0, &a1, &a2, &b0, &b1,
26 &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
27 return res;
28 }
29
30 /* B */
31 B = MIN(a->used, b->used) / 3;
32
33 /* a = a2 * B**2 + a1 * B + a0 */
34 if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
35 goto ERR;
36 }
37
38 if ((res = mp_copy(a, &a1)) != MP_OKAY) {
39 goto ERR;
40 }
41 mp_rshd(&a1, B);
42 mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
43
44 if ((res = mp_copy(a, &a2)) != MP_OKAY) {
45 goto ERR;
46 }
47 mp_rshd(&a2, B*2);
48
49 /* b = b2 * B**2 + b1 * B + b0 */
50 if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
51 goto ERR;
52 }
53
54 if ((res = mp_copy(b, &b1)) != MP_OKAY) {
55 goto ERR;
56 }
57 mp_rshd(&b1, B);
58 mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
59
60 if ((res = mp_copy(b, &b2)) != MP_OKAY) {
61 goto ERR;
62 }
63 mp_rshd(&b2, B*2);
64
65 /* w0 = a0*b0 */
66 if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
67 goto ERR;
68 }
69
70 /* w4 = a2 * b2 */
71 if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
72 goto ERR;
73 }
74
75 /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
76 if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
77 goto ERR;
78 }
79 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
80 goto ERR;
81 }
82 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
83 goto ERR;
84 }
85 if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
86 goto ERR;
87 }
88
89 if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
90 goto ERR;
91 }
92 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
93 goto ERR;
94 }
95 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
96 goto ERR;
97 }
98 if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
99 goto ERR;
100 }
101
102 if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
103 goto ERR;
104 }
105
106 /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
107 if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
108 goto ERR;
109 }
110 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
111 goto ERR;
112 }
113 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
114 goto ERR;
115 }
116 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
117 goto ERR;
118 }
119
120 if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
121 goto ERR;
122 }
123 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
124 goto ERR;
125 }
126 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
127 goto ERR;
128 }
129 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
130 goto ERR;
131 }
132
133 if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
134 goto ERR;
135 }
136
137
138 /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
139 if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
140 goto ERR;
141 }
142 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
143 goto ERR;
144 }
145 if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) {
146 goto ERR;
147 }
148 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
149 goto ERR;
150 }
151 if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
152 goto ERR;
153 }
154
155 /* now solve the matrix
156
157 0 0 0 0 1
158 1 2 4 8 16
159 1 1 1 1 1
160 16 8 4 2 1
161 1 0 0 0 0
162
163 using 12 subtractions, 4 shifts,
164 2 small divisions and 1 small multiplication
165 */
166
167 /* r1 - r4 */
168 if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
169 goto ERR;
170 }
171 /* r3 - r0 */
172 if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
173 goto ERR;
174 }
175 /* r1/2 */
176 if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
177 goto ERR;
178 }
179 /* r3/2 */
180 if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
181 goto ERR;
182 }
183 /* r2 - r0 - r4 */
184 if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
185 goto ERR;
186 }
187 if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
188 goto ERR;
189 }
190 /* r1 - r2 */
191 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
192 goto ERR;
193 }
194 /* r3 - r2 */
195 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
196 goto ERR;
197 }
198 /* r1 - 8r0 */
199 if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
200 goto ERR;
201 }
202 if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
203 goto ERR;
204 }
205 /* r3 - 8r4 */
206 if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
207 goto ERR;
208 }
209 if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
210 goto ERR;
211 }
212 /* 3r2 - r1 - r3 */
213 if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
214 goto ERR;
215 }
216 if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
217 goto ERR;
218 }
219 if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
220 goto ERR;
221 }
222 /* r1 - r2 */
223 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
224 goto ERR;
225 }
226 /* r3 - r2 */
227 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
228 goto ERR;
229 }
230 /* r1/3 */
231 if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
232 goto ERR;
233 }
234 /* r3/3 */
235 if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
236 goto ERR;
237 }
238
239 /* at this point shift W[n] by B*n */
240 if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
241 goto ERR;
242 }
243 if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
244 goto ERR;
245 }
246 if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
247 goto ERR;
248 }
249 if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
250 goto ERR;
251 }
252
253 if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
254 goto ERR;
255 }
256 if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
257 goto ERR;
258 }
259 if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
260 goto ERR;
261 }
262 if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
263 goto ERR;
264 }
265
266 ERR:
267 mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
268 &a0, &a1, &a2, &b0, &b1,
269 &b2, &tmp1, &tmp2, NULL);
270 return res;
271 }
272