d3409d5e |
1 | /* -*-c-*- |
2 | * |
c9110b35 |
3 | * $Id: mp-gcd.c,v 1.4 2000/06/17 11:34:46 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 $ |
c9110b35 |
33 | * Revision 1.4 2000/06/17 11:34:46 mdw |
34 | * More hacking for the signs of the outputs. |
35 | * |
ef5f4810 |
36 | * Revision 1.3 1999/12/10 23:18:39 mdw |
37 | * Change interface for suggested destinations. |
38 | * |
da83a561 |
39 | * Revision 1.2 1999/11/22 20:49:56 mdw |
40 | * Fix bug which failed to favour `x' when `y' wasn't wanted and the two |
41 | * arguments needed swapping. |
42 | * |
d3409d5e |
43 | * Revision 1.1 1999/11/17 18:02:16 mdw |
44 | * New multiprecision integer arithmetic suite. |
45 | * |
46 | */ |
47 | |
48 | /*----- Header files ------------------------------------------------------*/ |
49 | |
50 | #include "mp.h" |
51 | |
52 | /*----- Main code ---------------------------------------------------------*/ |
53 | |
54 | /* --- @mp_gcd@ --- * |
55 | * |
56 | * Arguments: @mp **gcd, **xx, **yy@ = where to write the results |
57 | * @mp *a, *b@ = sources (must be nonzero) |
58 | * |
59 | * Returns: --- |
60 | * |
61 | * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that |
62 | * @ax + by = gcd(a, b)@. This is useful for computing modular |
ef5f4810 |
63 | * inverses. |
d3409d5e |
64 | */ |
65 | |
66 | void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b) |
67 | { |
68 | mp *X = MP_ONE, *Y = MP_ZERO; |
69 | mp *x = MP_ZERO, *y = MP_ONE; |
70 | mp *u, *v; |
71 | size_t shift = 0; |
ef5f4810 |
72 | unsigned f = 0; |
73 | |
74 | enum { |
75 | f_swap = 1u, |
76 | f_aneg = 2u, |
77 | f_bneg = 4u, |
78 | f_ext = 8u |
79 | }; |
80 | |
81 | /* --- Sort out some initial flags --- */ |
d3409d5e |
82 | |
ef5f4810 |
83 | if (xx || yy) |
84 | f |= f_ext; |
d3409d5e |
85 | |
ef5f4810 |
86 | if (a->f & MP_NEG) |
87 | f |= f_aneg; |
88 | if (b->f & MP_NEG) |
89 | f |= f_bneg; |
90 | |
91 | /* --- Ensure that @a@ is larger than @b@ --- * |
92 | * |
93 | * Use absolute values here! |
94 | */ |
95 | |
96 | if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { |
d3409d5e |
97 | { mp *t = a; a = b; b = t; } |
ef5f4810 |
98 | f |= f_swap; |
99 | } |
100 | |
101 | /* --- Check for zeroness --- */ |
102 | |
103 | if (MP_CMP(b, ==, MP_ZERO)) { |
104 | |
105 | /* --- Store %$|a|$% as the GCD --- */ |
106 | |
107 | if (gcd) { |
108 | if (*gcd) MP_DROP(*gcd); |
109 | a = MP_COPY(a); |
110 | if (a->f & MP_NEG) { |
111 | MP_SPLIT(a); |
112 | a->f &= ~MP_NEG; |
113 | f |= f_aneg; |
114 | } |
115 | *gcd = a; |
116 | } |
117 | |
118 | /* --- Store %$1$% and %$0$% in the appropriate bins --- */ |
119 | |
120 | if (f & f_ext) { |
121 | if (f & f_swap) { |
122 | mp **t = xx; xx = yy; yy = t; |
123 | } |
124 | if (xx) { |
125 | if (*xx) MP_DROP(*xx); |
126 | if (MP_CMP(a, ==, MP_ZERO)) |
127 | *xx = MP_ZERO; |
128 | else if (f & f_aneg) |
129 | *xx = MP_MONE; |
130 | else |
131 | *xx = MP_ONE; |
132 | } |
133 | if (yy) { |
134 | if (*yy) MP_DROP(*yy); |
135 | *yy = MP_ZERO; |
136 | } |
137 | } |
138 | return; |
d3409d5e |
139 | } |
140 | |
141 | /* --- Take a reference to the arguments --- */ |
142 | |
143 | a = MP_COPY(a); |
144 | b = MP_COPY(b); |
145 | |
146 | /* --- Make sure @a@ and @b@ are not both even --- */ |
147 | |
ef5f4810 |
148 | MP_SPLIT(a); a->f &= ~MP_NEG; |
149 | MP_SPLIT(b); b->f &= ~MP_NEG; |
150 | |
d3409d5e |
151 | if (((a->v[0] | b->v[0]) & 1) == 0) { |
152 | mpscan asc, bsc; |
153 | |
154 | /* --- Break off my copies --- */ |
155 | |
d3409d5e |
156 | MP_SCAN(&asc, a); |
157 | MP_SCAN(&bsc, b); |
158 | |
159 | /* --- Start scanning --- */ |
160 | |
161 | for (;;) { |
162 | if (!MP_STEP(&asc) || !MP_STEP(&bsc)) |
163 | assert(((void)"zero argument passed to mp_gcd", 0)); |
164 | if (MP_BIT(&asc) || MP_BIT(&bsc)) |
165 | break; |
166 | shift++; |
167 | } |
168 | |
169 | /* --- Shift @a@ and @b@ down --- */ |
170 | |
171 | a = mp_lsr(a, a, shift); |
172 | b = mp_lsr(b, b, shift); |
173 | } |
174 | |
175 | /* --- Set up @u@ and @v@ --- */ |
176 | |
177 | u = MP_COPY(a); |
178 | v = MP_COPY(b); |
179 | |
180 | /* --- Start the main loop --- */ |
181 | |
182 | for (;;) { |
183 | |
184 | /* --- While @u@ is even --- */ |
185 | |
186 | { |
187 | mpscan sc, xsc, ysc; |
188 | size_t n = 0, nn = 0; |
189 | |
190 | MP_SCAN(&sc, u); |
191 | MP_SCAN(&xsc, X); MP_SCAN(&ysc, Y); |
192 | for (;;) { |
193 | MP_STEP(&sc); |
194 | MP_STEP(&xsc); MP_STEP(&ysc); |
195 | if (MP_BIT(&sc)) |
196 | break; |
ef5f4810 |
197 | if ((f & f_ext) && (MP_BIT(&xsc) | MP_BIT(&ysc))) { |
d3409d5e |
198 | if (n) { |
199 | X = mp_lsr(X, X, n); |
200 | Y = mp_lsr(Y, Y, n); |
201 | n = 0; |
202 | } |
203 | X = mp_add(X, X, b); |
204 | Y = mp_sub(Y, Y, a); |
205 | MP_SCAN(&xsc, X); |
206 | MP_SCAN(&ysc, Y); |
207 | MP_STEP(&xsc); MP_STEP(&ysc); |
208 | } |
209 | n++; nn++; |
210 | } |
211 | |
212 | if (nn) { |
213 | u = mp_lsr(u, u, nn); |
ef5f4810 |
214 | if ((f & f_ext) && n) { |
d3409d5e |
215 | X = mp_lsr(X, X, n); |
216 | Y = mp_lsr(Y, Y, n); |
217 | } |
218 | } |
219 | } |
220 | |
221 | /* --- While @v@ is even --- */ |
222 | |
223 | { |
224 | mpscan sc, xsc, ysc; |
225 | size_t n = 0, nn = 0; |
226 | |
227 | MP_SCAN(&sc, v); |
228 | MP_SCAN(&xsc, x); MP_SCAN(&ysc, y); |
229 | for (;;) { |
230 | MP_STEP(&sc); |
231 | MP_STEP(&xsc); MP_STEP(&ysc); |
232 | if (MP_BIT(&sc)) |
233 | break; |
ef5f4810 |
234 | if ((f & f_ext) && (MP_BIT(&xsc) | MP_BIT(&ysc))) { |
d3409d5e |
235 | if (n) { |
236 | x = mp_lsr(x, x, n); |
237 | y = mp_lsr(y, y, n); |
238 | n = 0; |
239 | } |
240 | x = mp_add(x, x, b); |
241 | y = mp_sub(y, y, a); |
242 | MP_SCAN(&xsc, x); |
243 | MP_SCAN(&ysc, y); |
244 | MP_STEP(&xsc); MP_STEP(&ysc); |
245 | } |
246 | n++; nn++; |
247 | } |
248 | |
249 | if (nn) { |
250 | v = mp_lsr(v, v, nn); |
ef5f4810 |
251 | if ((f & f_ext) && n) { |
d3409d5e |
252 | x = mp_lsr(x, x, n); |
253 | y = mp_lsr(y, y, n); |
254 | } |
255 | } |
256 | } |
257 | |
258 | /* --- End-of-loop fiddling --- */ |
259 | |
260 | if (MP_CMP(u, >=, v)) { |
261 | u = mp_sub(u, u, v); |
ef5f4810 |
262 | if (f & f_ext) { |
d3409d5e |
263 | X = mp_sub(X, X, x); |
264 | Y = mp_sub(Y, Y, y); |
265 | } |
266 | } else { |
267 | v = mp_sub(v, v, u); |
ef5f4810 |
268 | if (f & f_ext) { |
d3409d5e |
269 | x = mp_sub(x, x, X); |
270 | y = mp_sub(y, y, Y); |
271 | } |
272 | } |
273 | |
274 | if (MP_CMP(u, ==, MP_ZERO)) |
275 | break; |
276 | } |
277 | |
278 | /* --- Write the results out --- */ |
279 | |
ef5f4810 |
280 | if (!gcd) |
d3409d5e |
281 | MP_DROP(v); |
ef5f4810 |
282 | else { |
283 | if (*gcd) MP_DROP(*gcd); |
284 | *gcd = mp_lsl(v, v, shift); |
285 | } |
d3409d5e |
286 | |
287 | /* --- Perform a little normalization --- * |
288 | * |
289 | * Ensure that the coefficient returned is positive, if there is only one. |
ef5f4810 |
290 | * If there are two, favour @y@. Of course, if the original arguments were |
291 | * negative then I'll need to twiddle their signs as well. |
d3409d5e |
292 | */ |
293 | |
ef5f4810 |
294 | if (f & f_ext) { |
295 | |
296 | /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */ |
297 | |
298 | if (f & f_swap) { |
d3409d5e |
299 | mp *t = x; x = y; y = t; |
da83a561 |
300 | t = a; a = b; b = t; |
d3409d5e |
301 | } |
ef5f4810 |
302 | |
303 | /* --- Sort out the signs --- * |
304 | * |
305 | * Note that %$ax + by = a(x - b) + b(y + a)$%. |
c9110b35 |
306 | * |
307 | * This is currently bodgy. It needs sorting out at some time. |
ef5f4810 |
308 | */ |
309 | |
d3409d5e |
310 | if (yy) { |
311 | if (y->f & MP_NEG) { |
c9110b35 |
312 | do { |
313 | y = mp_add(y, y, a); |
314 | x = mp_sub(x, x, b); |
315 | } while (y->f & MP_NEG); |
316 | } else { |
317 | while (MP_CMP(y, >=, a)) { |
318 | y = mp_sub(y, y, a); |
319 | x = mp_add(x, x, b); |
320 | } |
d3409d5e |
321 | } |
c9110b35 |
322 | } else { |
323 | if (x->f & MP_NEG) { |
324 | do |
325 | x = mp_add(x, x, b); |
326 | while (x->f & MP_NEG); |
327 | } else { |
328 | while (MP_CMP(x, >=, b)) |
329 | x = mp_sub(x, x, b); |
330 | } |
331 | } |
d3409d5e |
332 | |
ef5f4810 |
333 | /* --- Twiddle the signs --- */ |
334 | |
335 | if (f & f_aneg) |
336 | x->f ^= MP_NEG; |
337 | if (f & f_bneg) |
338 | y->f ^= MP_NEG; |
339 | |
340 | /* --- Store the results --- */ |
341 | |
342 | if (!xx) |
343 | MP_DROP(x); |
344 | else { |
345 | if (*xx) MP_DROP(*xx); |
346 | *xx = x; |
347 | } |
348 | |
349 | if (!yy) |
350 | MP_DROP(y); |
351 | else { |
352 | if (*yy) MP_DROP(*yy); |
353 | *yy = y; |
354 | } |
d3409d5e |
355 | } |
356 | |
357 | MP_DROP(u); |
358 | MP_DROP(X); MP_DROP(Y); |
359 | MP_DROP(a); MP_DROP(b); |
360 | } |
361 | |
362 | /*----- Test rig ----------------------------------------------------------*/ |
363 | |
364 | #ifdef TEST_RIG |
365 | |
366 | static int gcd(dstr *v) |
367 | { |
368 | int ok = 1; |
369 | mp *a = *(mp **)v[0].buf; |
370 | mp *b = *(mp **)v[1].buf; |
371 | mp *g = *(mp **)v[2].buf; |
372 | mp *x = *(mp **)v[3].buf; |
373 | mp *y = *(mp **)v[4].buf; |
374 | |
ef5f4810 |
375 | mp *gg = MP_NEW, *xx = MP_NEW, *yy = MP_NEW; |
d3409d5e |
376 | mp_gcd(&gg, &xx, &yy, a, b); |
377 | if (MP_CMP(x, !=, xx)) { |
378 | fputs("\n*** mp_gcd(x) failed", stderr); |
379 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
380 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); |
381 | fputs("\nexpect = ", stderr); mp_writefile(x, stderr, 10); |
382 | fputs("\nresult = ", stderr); mp_writefile(xx, stderr, 10); |
383 | fputc('\n', stderr); |
384 | ok = 0; |
385 | } |
386 | if (MP_CMP(y, !=, yy)) { |
387 | fputs("\n*** mp_gcd(y) failed", stderr); |
388 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
389 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); |
390 | fputs("\nexpect = ", stderr); mp_writefile(y, stderr, 10); |
391 | fputs("\nresult = ", stderr); mp_writefile(yy, stderr, 10); |
392 | fputc('\n', stderr); |
393 | ok = 0; |
394 | } |
395 | |
396 | if (!ok) { |
397 | mp *ax = mp_mul(MP_NEW, a, xx); |
398 | mp *by = mp_mul(MP_NEW, b, yy); |
399 | ax = mp_add(ax, ax, by); |
400 | if (MP_CMP(ax, ==, gg)) |
401 | fputs("\n*** (Alternative result found.)\n", stderr); |
402 | MP_DROP(ax); |
403 | MP_DROP(by); |
404 | } |
405 | |
406 | if (MP_CMP(g, !=, gg)) { |
407 | fputs("\n*** mp_gcd(gcd) failed", stderr); |
408 | fputs("\na = ", stderr); mp_writefile(a, stderr, 10); |
409 | fputs("\nb = ", stderr); mp_writefile(b, stderr, 10); |
410 | fputs("\nexpect = ", stderr); mp_writefile(g, stderr, 10); |
411 | fputs("\nresult = ", stderr); mp_writefile(gg, stderr, 10); |
412 | fputc('\n', stderr); |
413 | ok = 0; |
414 | } |
415 | MP_DROP(a); MP_DROP(b); MP_DROP(g); MP_DROP(x); MP_DROP(y); |
416 | MP_DROP(gg); MP_DROP(xx); MP_DROP(yy); |
ef5f4810 |
417 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
418 | return (ok); |
419 | } |
420 | |
421 | static test_chunk tests[] = { |
422 | { "gcd", gcd, { &type_mp, &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
423 | { 0, 0, { 0 } } |
424 | }; |
425 | |
426 | int main(int argc, char *argv[]) |
427 | { |
428 | sub_init(); |
429 | test_run(argc, argv, tests, SRCDIR "/tests/mp"); |
430 | return (0); |
431 | } |
432 | |
433 | #endif |
434 | |
435 | /*----- That's all, folks -------------------------------------------------*/ |