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