d3409d5e |
1 | /* -*-c-*- |
2 | * |
b817bfc6 |
3 | * $Id: mp-gcd.c,v 1.7 2004/04/08 01:36:15 mdw Exp $ |
d3409d5e |
4 | * |
5 | * Extended GCD calculation |
6 | * |
7 | * (c) 1999 Straylight/Edgeware |
8 | */ |
9 | |
10 | /*----- Licensing notice --------------------------------------------------* |
11 | * |
12 | * This file is part of Catacomb. |
13 | * |
14 | * Catacomb is free software; you can redistribute it and/or modify |
15 | * it under the terms of the GNU Library General Public License as |
16 | * published by the Free Software Foundation; either version 2 of the |
17 | * License, or (at your option) any later version. |
18 | * |
19 | * Catacomb is distributed in the hope that it will be useful, |
20 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
21 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
22 | * GNU Library General Public License for more details. |
23 | * |
24 | * You should have received a copy of the GNU Library General Public |
25 | * License along with Catacomb; if not, write to the Free |
26 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
27 | * MA 02111-1307, USA. |
28 | */ |
29 | |
d3409d5e |
30 | /*----- Header files ------------------------------------------------------*/ |
31 | |
32 | #include "mp.h" |
33 | |
34 | /*----- Main code ---------------------------------------------------------*/ |
35 | |
36 | /* --- @mp_gcd@ --- * |
37 | * |
38 | * Arguments: @mp **gcd, **xx, **yy@ = where to write the results |
39 | * @mp *a, *b@ = sources (must be nonzero) |
40 | * |
41 | * Returns: --- |
42 | * |
43 | * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that |
44 | * @ax + by = gcd(a, b)@. This is useful for computing modular |
ef5f4810 |
45 | * inverses. |
d3409d5e |
46 | */ |
47 | |
48 | void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b) |
49 | { |
b2253c70 |
50 | mp *x = MP_ONE, *X = MP_ZERO; |
51 | mp *y = MP_ZERO, *Y = MP_ONE; |
d3409d5e |
52 | mp *u, *v; |
b2253c70 |
53 | mp *q = MP_NEW; |
ef5f4810 |
54 | unsigned f = 0; |
55 | |
ceb3f0c0 |
56 | #define f_swap 1u |
57 | #define f_aneg 2u |
58 | #define f_bneg 4u |
59 | #define f_ext 8u |
ef5f4810 |
60 | |
61 | /* --- Sort out some initial flags --- */ |
d3409d5e |
62 | |
ef5f4810 |
63 | if (xx || yy) |
64 | f |= f_ext; |
d3409d5e |
65 | |
ef5f4810 |
66 | if (a->f & MP_NEG) |
67 | f |= f_aneg; |
68 | if (b->f & MP_NEG) |
69 | f |= f_bneg; |
70 | |
71 | /* --- Ensure that @a@ is larger than @b@ --- * |
72 | * |
73 | * Use absolute values here! |
74 | */ |
75 | |
76 | if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { |
d3409d5e |
77 | { mp *t = a; a = b; b = t; } |
ef5f4810 |
78 | f |= f_swap; |
79 | } |
80 | |
81 | /* --- Check for zeroness --- */ |
82 | |
b2253c70 |
83 | if (MP_EQ(b, MP_ZERO)) { |
ef5f4810 |
84 | |
85 | /* --- Store %$|a|$% as the GCD --- */ |
86 | |
87 | if (gcd) { |
88 | if (*gcd) MP_DROP(*gcd); |
89 | a = MP_COPY(a); |
90 | if (a->f & MP_NEG) { |
91 | MP_SPLIT(a); |
92 | a->f &= ~MP_NEG; |
93 | f |= f_aneg; |
94 | } |
95 | *gcd = a; |
96 | } |
97 | |
98 | /* --- Store %$1$% and %$0$% in the appropriate bins --- */ |
99 | |
100 | if (f & f_ext) { |
101 | if (f & f_swap) { |
102 | mp **t = xx; xx = yy; yy = t; |
103 | } |
104 | if (xx) { |
105 | if (*xx) MP_DROP(*xx); |
b2253c70 |
106 | if (MP_EQ(a, MP_ZERO)) |
ef5f4810 |
107 | *xx = MP_ZERO; |
108 | else if (f & f_aneg) |
109 | *xx = MP_MONE; |
110 | else |
111 | *xx = MP_ONE; |
112 | } |
113 | if (yy) { |
114 | if (*yy) MP_DROP(*yy); |
115 | *yy = MP_ZERO; |
116 | } |
117 | } |
118 | return; |
d3409d5e |
119 | } |
120 | |
121 | /* --- Take a reference to the arguments --- */ |
122 | |
123 | a = MP_COPY(a); |
124 | b = MP_COPY(b); |
125 | |
126 | /* --- Make sure @a@ and @b@ are not both even --- */ |
127 | |
ef5f4810 |
128 | MP_SPLIT(a); a->f &= ~MP_NEG; |
129 | MP_SPLIT(b); b->f &= ~MP_NEG; |
130 | |
d3409d5e |
131 | u = MP_COPY(a); |
132 | v = MP_COPY(b); |
133 | |
b2253c70 |
134 | while (MP_LEN(v)) { |
135 | mp *t; |
136 | mp_div(&q, &u, u, v); |
137 | if (f & f_ext) { |
138 | t = mp_mul(MP_NEW, X, q); |
139 | t = mp_sub(t, x, t); |
140 | MP_DROP(x); x = X; X = t; |
141 | t = mp_mul(MP_NEW, Y, q); |
142 | t = mp_sub(t, y, t); |
143 | MP_DROP(y); y = Y; Y = t; |
d3409d5e |
144 | } |
b2253c70 |
145 | t = u; u = v; v = t; |
d3409d5e |
146 | } |
147 | |
b2253c70 |
148 | MP_DROP(q); |
ef5f4810 |
149 | if (!gcd) |
b2253c70 |
150 | MP_DROP(u); |
ef5f4810 |
151 | else { |
152 | if (*gcd) MP_DROP(*gcd); |
b2253c70 |
153 | u->f &= ~MP_NEG; |
154 | *gcd = u; |
ef5f4810 |
155 | } |
d3409d5e |
156 | |
157 | /* --- Perform a little normalization --- * |
158 | * |
159 | * Ensure that the coefficient returned is positive, if there is only one. |
ef5f4810 |
160 | * If there are two, favour @y@. Of course, if the original arguments were |
161 | * negative then I'll need to twiddle their signs as well. |
d3409d5e |
162 | */ |
163 | |
ef5f4810 |
164 | if (f & f_ext) { |
165 | |
166 | /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */ |
167 | |
168 | if (f & f_swap) { |
d3409d5e |
169 | mp *t = x; x = y; y = t; |
da83a561 |
170 | t = a; a = b; b = t; |
d3409d5e |
171 | } |
ef5f4810 |
172 | |
173 | /* --- Sort out the signs --- * |
174 | * |
175 | * Note that %$ax + by = a(x - b) + b(y + a)$%. |
c9110b35 |
176 | * |
177 | * This is currently bodgy. It needs sorting out at some time. |
ef5f4810 |
178 | */ |
179 | |
d3409d5e |
180 | if (yy) { |
181 | if (y->f & MP_NEG) { |
c9110b35 |
182 | do { |
183 | y = mp_add(y, y, a); |
184 | x = mp_sub(x, x, b); |
185 | } while (y->f & MP_NEG); |
186 | } else { |
187 | while (MP_CMP(y, >=, a)) { |
188 | y = mp_sub(y, y, a); |
189 | x = mp_add(x, x, b); |
190 | } |
d3409d5e |
191 | } |
c9110b35 |
192 | } else { |
193 | if (x->f & MP_NEG) { |
194 | do |
195 | x = mp_add(x, x, b); |
196 | while (x->f & MP_NEG); |
197 | } else { |
198 | while (MP_CMP(x, >=, b)) |
199 | x = mp_sub(x, x, b); |
200 | } |
201 | } |
d3409d5e |
202 | |
ef5f4810 |
203 | /* --- Twiddle the signs --- */ |
204 | |
205 | if (f & f_aneg) |
206 | x->f ^= MP_NEG; |
207 | if (f & f_bneg) |
208 | y->f ^= MP_NEG; |
209 | |
210 | /* --- Store the results --- */ |
211 | |
212 | if (!xx) |
213 | MP_DROP(x); |
214 | else { |
215 | if (*xx) MP_DROP(*xx); |
216 | *xx = x; |
217 | } |
218 | |
219 | if (!yy) |
220 | MP_DROP(y); |
221 | else { |
222 | if (*yy) MP_DROP(*yy); |
223 | *yy = y; |
224 | } |
d3409d5e |
225 | } |
226 | |
b2253c70 |
227 | MP_DROP(v); |
d3409d5e |
228 | MP_DROP(X); MP_DROP(Y); |
229 | MP_DROP(a); MP_DROP(b); |
230 | } |
231 | |
b817bfc6 |
232 | /* -- @mp_modinv@ --- * |
233 | * |
234 | * Arguments: @mp *d@ = destination |
235 | * @mp *x@ = argument |
236 | * @mp *p@ = modulus |
237 | * |
238 | * Returns: The inverse %$x^{-1} \bmod p$%. |
239 | * |
240 | * Use: Computes a modular inverse. An assertion fails if %$p$% |
241 | * has no inverse. |
242 | */ |
243 | |
244 | mp *mp_modinv(mp *d, mp *x, mp *p) |
245 | { |
246 | mp *g = MP_NEW; |
247 | mp_gcd(&g, 0, &d, p, x); |
248 | assert(MP_EQ(g, MP_ONE)); |
249 | mp_drop(g); |
250 | return (d); |
251 | } |
252 | |
d3409d5e |
253 | /*----- Test rig ----------------------------------------------------------*/ |
254 | |
255 | #ifdef TEST_RIG |
256 | |
257 | static int gcd(dstr *v) |
258 | { |
259 | int ok = 1; |
260 | mp *a = *(mp **)v[0].buf; |
261 | mp *b = *(mp **)v[1].buf; |
262 | mp *g = *(mp **)v[2].buf; |
263 | mp *x = *(mp **)v[3].buf; |
264 | mp *y = *(mp **)v[4].buf; |
265 | |
ef5f4810 |
266 | mp *gg = MP_NEW, *xx = MP_NEW, *yy = MP_NEW; |
d3409d5e |
267 | mp_gcd(&gg, &xx, &yy, a, b); |
b2253c70 |
268 | if (!MP_EQ(x, xx)) { |
d3409d5e |
269 | fputs("\n*** mp_gcd(x) failed", stderr); |
270 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
271 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); |
272 | fputs("\nexpect = ", stderr); mp_writefile(x, stderr, 10); |
273 | fputs("\nresult = ", stderr); mp_writefile(xx, stderr, 10); |
274 | fputc('\n', stderr); |
275 | ok = 0; |
276 | } |
b2253c70 |
277 | if (!MP_EQ(y, yy)) { |
d3409d5e |
278 | fputs("\n*** mp_gcd(y) failed", stderr); |
279 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
280 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); |
281 | fputs("\nexpect = ", stderr); mp_writefile(y, stderr, 10); |
282 | fputs("\nresult = ", stderr); mp_writefile(yy, stderr, 10); |
283 | fputc('\n', stderr); |
284 | ok = 0; |
285 | } |
286 | |
287 | if (!ok) { |
288 | mp *ax = mp_mul(MP_NEW, a, xx); |
289 | mp *by = mp_mul(MP_NEW, b, yy); |
290 | ax = mp_add(ax, ax, by); |
b2253c70 |
291 | if (MP_EQ(ax, gg)) |
d3409d5e |
292 | fputs("\n*** (Alternative result found.)\n", stderr); |
293 | MP_DROP(ax); |
294 | MP_DROP(by); |
295 | } |
296 | |
b2253c70 |
297 | if (!MP_EQ(g, gg)) { |
d3409d5e |
298 | fputs("\n*** mp_gcd(gcd) failed", stderr); |
299 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
300 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); |
301 | fputs("\nexpect = ", stderr); mp_writefile(g, stderr, 10); |
302 | fputs("\nresult = ", stderr); mp_writefile(gg, stderr, 10); |
303 | fputc('\n', stderr); |
304 | ok = 0; |
305 | } |
306 | MP_DROP(a); MP_DROP(b); MP_DROP(g); MP_DROP(x); MP_DROP(y); |
307 | MP_DROP(gg); MP_DROP(xx); MP_DROP(yy); |
ef5f4810 |
308 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
309 | return (ok); |
310 | } |
311 | |
312 | static test_chunk tests[] = { |
313 | { "gcd", gcd, { &type_mp, &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
314 | { 0, 0, { 0 } } |
315 | }; |
316 | |
317 | int main(int argc, char *argv[]) |
318 | { |
319 | sub_init(); |
320 | test_run(argc, argv, tests, SRCDIR "/tests/mp"); |
321 | return (0); |
322 | } |
323 | |
324 | #endif |
325 | |
326 | /*----- That's all, folks -------------------------------------------------*/ |