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1 | /* -*-c-*- |
2 | * |
da83a561 |
3 | * $Id: mp-gcd.c,v 1.2 1999/11/22 20:49:56 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 | |
30 | /*----- Revision history --------------------------------------------------* |
31 | * |
32 | * $Log: mp-gcd.c,v $ |
da83a561 |
33 | * Revision 1.2 1999/11/22 20:49:56 mdw |
34 | * Fix bug which failed to favour `x' when `y' wasn't wanted and the two |
35 | * arguments needed swapping. |
36 | * |
d3409d5e |
37 | * Revision 1.1 1999/11/17 18:02:16 mdw |
38 | * New multiprecision integer arithmetic suite. |
39 | * |
40 | */ |
41 | |
42 | /*----- Header files ------------------------------------------------------*/ |
43 | |
44 | #include "mp.h" |
45 | |
46 | /*----- Main code ---------------------------------------------------------*/ |
47 | |
48 | /* --- @mp_gcd@ --- * |
49 | * |
50 | * Arguments: @mp **gcd, **xx, **yy@ = where to write the results |
51 | * @mp *a, *b@ = sources (must be nonzero) |
52 | * |
53 | * Returns: --- |
54 | * |
55 | * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that |
56 | * @ax + by = gcd(a, b)@. This is useful for computing modular |
57 | * inverses. Neither @a@ nor @b@ may be zero. Note that, |
58 | * unlike @mp_div@ for example, it is not possible to specify |
59 | * explicit destinations -- new MPs are always allocated. |
60 | */ |
61 | |
62 | void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b) |
63 | { |
64 | mp *X = MP_ONE, *Y = MP_ZERO; |
65 | mp *x = MP_ZERO, *y = MP_ONE; |
66 | mp *u, *v; |
67 | size_t shift = 0; |
68 | int ext = xx || yy; |
69 | int swap = 0; |
70 | |
71 | /* --- Ensure that @a@ is larger than @b@ --- */ |
72 | |
73 | if (MP_CMP(a, <, b)) { |
74 | { mp *t = a; a = b; b = t; } |
75 | swap = 1; |
76 | } |
77 | |
78 | /* --- Take a reference to the arguments --- */ |
79 | |
80 | a = MP_COPY(a); |
81 | b = MP_COPY(b); |
82 | |
83 | /* --- Make sure @a@ and @b@ are not both even --- */ |
84 | |
85 | if (((a->v[0] | b->v[0]) & 1) == 0) { |
86 | mpscan asc, bsc; |
87 | |
88 | /* --- Break off my copies --- */ |
89 | |
90 | MP_SPLIT(a); |
91 | MP_SPLIT(b); |
92 | MP_SCAN(&asc, a); |
93 | MP_SCAN(&bsc, b); |
94 | |
95 | /* --- Start scanning --- */ |
96 | |
97 | for (;;) { |
98 | if (!MP_STEP(&asc) || !MP_STEP(&bsc)) |
99 | assert(((void)"zero argument passed to mp_gcd", 0)); |
100 | if (MP_BIT(&asc) || MP_BIT(&bsc)) |
101 | break; |
102 | shift++; |
103 | } |
104 | |
105 | /* --- Shift @a@ and @b@ down --- */ |
106 | |
107 | a = mp_lsr(a, a, shift); |
108 | b = mp_lsr(b, b, shift); |
109 | } |
110 | |
111 | /* --- Set up @u@ and @v@ --- */ |
112 | |
113 | u = MP_COPY(a); |
114 | v = MP_COPY(b); |
115 | |
116 | /* --- Start the main loop --- */ |
117 | |
118 | for (;;) { |
119 | |
120 | /* --- While @u@ is even --- */ |
121 | |
122 | { |
123 | mpscan sc, xsc, ysc; |
124 | size_t n = 0, nn = 0; |
125 | |
126 | MP_SCAN(&sc, u); |
127 | MP_SCAN(&xsc, X); MP_SCAN(&ysc, Y); |
128 | for (;;) { |
129 | MP_STEP(&sc); |
130 | MP_STEP(&xsc); MP_STEP(&ysc); |
131 | if (MP_BIT(&sc)) |
132 | break; |
133 | if (ext && (MP_BIT(&xsc) | MP_BIT(&ysc))) { |
134 | if (n) { |
135 | X = mp_lsr(X, X, n); |
136 | Y = mp_lsr(Y, Y, n); |
137 | n = 0; |
138 | } |
139 | X = mp_add(X, X, b); |
140 | Y = mp_sub(Y, Y, a); |
141 | MP_SCAN(&xsc, X); |
142 | MP_SCAN(&ysc, Y); |
143 | MP_STEP(&xsc); MP_STEP(&ysc); |
144 | } |
145 | n++; nn++; |
146 | } |
147 | |
148 | if (nn) { |
149 | u = mp_lsr(u, u, nn); |
150 | if (ext && n) { |
151 | X = mp_lsr(X, X, n); |
152 | Y = mp_lsr(Y, Y, n); |
153 | } |
154 | } |
155 | } |
156 | |
157 | /* --- While @v@ is even --- */ |
158 | |
159 | { |
160 | mpscan sc, xsc, ysc; |
161 | size_t n = 0, nn = 0; |
162 | |
163 | MP_SCAN(&sc, v); |
164 | MP_SCAN(&xsc, x); MP_SCAN(&ysc, y); |
165 | for (;;) { |
166 | MP_STEP(&sc); |
167 | MP_STEP(&xsc); MP_STEP(&ysc); |
168 | if (MP_BIT(&sc)) |
169 | break; |
170 | if (ext && (MP_BIT(&xsc) | MP_BIT(&ysc))) { |
171 | if (n) { |
172 | x = mp_lsr(x, x, n); |
173 | y = mp_lsr(y, y, n); |
174 | n = 0; |
175 | } |
176 | x = mp_add(x, x, b); |
177 | y = mp_sub(y, y, a); |
178 | MP_SCAN(&xsc, x); |
179 | MP_SCAN(&ysc, y); |
180 | MP_STEP(&xsc); MP_STEP(&ysc); |
181 | } |
182 | n++; nn++; |
183 | } |
184 | |
185 | if (nn) { |
186 | v = mp_lsr(v, v, nn); |
187 | if (ext && n) { |
188 | x = mp_lsr(x, x, n); |
189 | y = mp_lsr(y, y, n); |
190 | } |
191 | } |
192 | } |
193 | |
194 | /* --- End-of-loop fiddling --- */ |
195 | |
196 | if (MP_CMP(u, >=, v)) { |
197 | u = mp_sub(u, u, v); |
198 | if (ext) { |
199 | X = mp_sub(X, X, x); |
200 | Y = mp_sub(Y, Y, y); |
201 | } |
202 | } else { |
203 | v = mp_sub(v, v, u); |
204 | if (ext) { |
205 | x = mp_sub(x, x, X); |
206 | y = mp_sub(y, y, Y); |
207 | } |
208 | } |
209 | |
210 | if (MP_CMP(u, ==, MP_ZERO)) |
211 | break; |
212 | } |
213 | |
214 | /* --- Write the results out --- */ |
215 | |
216 | if (gcd) |
217 | *gcd = mp_lsl(v, v, shift); |
218 | else |
219 | MP_DROP(v); |
220 | |
221 | /* --- Perform a little normalization --- * |
222 | * |
223 | * Ensure that the coefficient returned is positive, if there is only one. |
224 | * If there are two, favour @y@. |
225 | */ |
226 | |
227 | if (ext) { |
228 | if (swap) { |
229 | mp *t = x; x = y; y = t; |
da83a561 |
230 | t = a; a = b; b = t; |
d3409d5e |
231 | } |
232 | if (yy) { |
233 | if (y->f & MP_NEG) { |
234 | y = mp_add(y, y, a); |
235 | x = mp_sub(x, x, b); |
236 | } |
237 | } else if (x->f & MP_NEG) |
238 | x = mp_add(x, x, b); |
239 | |
240 | if (xx) *xx = x; else MP_DROP(x); |
241 | if (yy) *yy = y; else MP_DROP(y); |
242 | } |
243 | |
244 | MP_DROP(u); |
245 | MP_DROP(X); MP_DROP(Y); |
246 | MP_DROP(a); MP_DROP(b); |
247 | } |
248 | |
249 | /*----- Test rig ----------------------------------------------------------*/ |
250 | |
251 | #ifdef TEST_RIG |
252 | |
253 | static int gcd(dstr *v) |
254 | { |
255 | int ok = 1; |
256 | mp *a = *(mp **)v[0].buf; |
257 | mp *b = *(mp **)v[1].buf; |
258 | mp *g = *(mp **)v[2].buf; |
259 | mp *x = *(mp **)v[3].buf; |
260 | mp *y = *(mp **)v[4].buf; |
261 | |
262 | mp *gg, *xx, *yy; |
263 | mp_gcd(&gg, &xx, &yy, a, b); |
264 | if (MP_CMP(x, !=, xx)) { |
265 | fputs("\n*** mp_gcd(x) failed", stderr); |
266 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
267 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); |
268 | fputs("\nexpect = ", stderr); mp_writefile(x, stderr, 10); |
269 | fputs("\nresult = ", stderr); mp_writefile(xx, stderr, 10); |
270 | fputc('\n', stderr); |
271 | ok = 0; |
272 | } |
273 | if (MP_CMP(y, !=, yy)) { |
274 | fputs("\n*** mp_gcd(y) failed", stderr); |
275 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
276 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); |
277 | fputs("\nexpect = ", stderr); mp_writefile(y, stderr, 10); |
278 | fputs("\nresult = ", stderr); mp_writefile(yy, stderr, 10); |
279 | fputc('\n', stderr); |
280 | ok = 0; |
281 | } |
282 | |
283 | if (!ok) { |
284 | mp *ax = mp_mul(MP_NEW, a, xx); |
285 | mp *by = mp_mul(MP_NEW, b, yy); |
286 | ax = mp_add(ax, ax, by); |
287 | if (MP_CMP(ax, ==, gg)) |
288 | fputs("\n*** (Alternative result found.)\n", stderr); |
289 | MP_DROP(ax); |
290 | MP_DROP(by); |
291 | } |
292 | |
293 | if (MP_CMP(g, !=, gg)) { |
294 | fputs("\n*** mp_gcd(gcd) failed", stderr); |
295 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
296 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); |
297 | fputs("\nexpect = ", stderr); mp_writefile(g, stderr, 10); |
298 | fputs("\nresult = ", stderr); mp_writefile(gg, stderr, 10); |
299 | fputc('\n', stderr); |
300 | ok = 0; |
301 | } |
302 | MP_DROP(a); MP_DROP(b); MP_DROP(g); MP_DROP(x); MP_DROP(y); |
303 | MP_DROP(gg); MP_DROP(xx); MP_DROP(yy); |
304 | return (ok); |
305 | } |
306 | |
307 | static test_chunk tests[] = { |
308 | { "gcd", gcd, { &type_mp, &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
309 | { 0, 0, { 0 } } |
310 | }; |
311 | |
312 | int main(int argc, char *argv[]) |
313 | { |
314 | sub_init(); |
315 | test_run(argc, argv, tests, SRCDIR "/tests/mp"); |
316 | return (0); |
317 | } |
318 | |
319 | #endif |
320 | |
321 | /*----- That's all, folks -------------------------------------------------*/ |