3 * $Id: mp-gcd.c,v 1.4 2000/06/17 11:34:46 mdw Exp $
5 * Extended GCD calculation
7 * (c) 1999 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
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.
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.
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,
30 /*----- Revision history --------------------------------------------------*
33 * Revision 1.4 2000/06/17 11:34:46 mdw
34 * More hacking for the signs of the outputs.
36 * Revision 1.3 1999/12/10 23:18:39 mdw
37 * Change interface for suggested destinations.
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.
43 * Revision 1.1 1999/11/17 18:02:16 mdw
44 * New multiprecision integer arithmetic suite.
48 /*----- Header files ------------------------------------------------------*/
52 /*----- Main code ---------------------------------------------------------*/
56 * Arguments: @mp **gcd, **xx, **yy@ = where to write the results
57 * @mp *a, *b@ = sources (must be nonzero)
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
66 void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b)
68 mp *X = MP_ONE, *Y = MP_ZERO;
69 mp *x = MP_ZERO, *y = MP_ONE;
81 /* --- Sort out some initial flags --- */
91 /* --- Ensure that @a@ is larger than @b@ --- *
93 * Use absolute values here!
96 if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
97 { mp *t = a; a = b; b = t; }
101 /* --- Check for zeroness --- */
103 if (MP_CMP(b, ==, MP_ZERO)) {
105 /* --- Store %$|a|$% as the GCD --- */
108 if (*gcd) MP_DROP(*gcd);
118 /* --- Store %$1$% and %$0$% in the appropriate bins --- */
122 mp **t = xx; xx = yy; yy = t;
125 if (*xx) MP_DROP(*xx);
126 if (MP_CMP(a, ==, MP_ZERO))
134 if (*yy) MP_DROP(*yy);
141 /* --- Take a reference to the arguments --- */
146 /* --- Make sure @a@ and @b@ are not both even --- */
148 MP_SPLIT(a); a->f &= ~MP_NEG;
149 MP_SPLIT(b); b->f &= ~MP_NEG;
151 if (((a->v[0] | b->v[0]) & 1) == 0) {
154 /* --- Break off my copies --- */
159 /* --- Start scanning --- */
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))
169 /* --- Shift @a@ and @b@ down --- */
171 a = mp_lsr(a, a, shift);
172 b = mp_lsr(b, b, shift);
175 /* --- Set up @u@ and @v@ --- */
180 /* --- Start the main loop --- */
184 /* --- While @u@ is even --- */
188 size_t n = 0, nn = 0;
191 MP_SCAN(&xsc, X); MP_SCAN(&ysc, Y);
194 MP_STEP(&xsc); MP_STEP(&ysc);
197 if ((f & f_ext) && (MP_BIT(&xsc) | MP_BIT(&ysc))) {
207 MP_STEP(&xsc); MP_STEP(&ysc);
213 u = mp_lsr(u, u, nn);
214 if ((f & f_ext) && n) {
221 /* --- While @v@ is even --- */
225 size_t n = 0, nn = 0;
228 MP_SCAN(&xsc, x); MP_SCAN(&ysc, y);
231 MP_STEP(&xsc); MP_STEP(&ysc);
234 if ((f & f_ext) && (MP_BIT(&xsc) | MP_BIT(&ysc))) {
244 MP_STEP(&xsc); MP_STEP(&ysc);
250 v = mp_lsr(v, v, nn);
251 if ((f & f_ext) && n) {
258 /* --- End-of-loop fiddling --- */
260 if (MP_CMP(u, >=, v)) {
274 if (MP_CMP(u, ==, MP_ZERO))
278 /* --- Write the results out --- */
283 if (*gcd) MP_DROP(*gcd);
284 *gcd = mp_lsl(v, v, shift);
287 /* --- Perform a little normalization --- *
289 * Ensure that the coefficient returned is positive, if there is only one.
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.
296 /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */
299 mp *t = x; x = y; y = t;
303 /* --- Sort out the signs --- *
305 * Note that %$ax + by = a(x - b) + b(y + a)$%.
307 * This is currently bodgy. It needs sorting out at some time.
315 } while (y->f & MP_NEG);
317 while (MP_CMP(y, >=, a)) {
326 while (x->f & MP_NEG);
328 while (MP_CMP(x, >=, b))
333 /* --- Twiddle the signs --- */
340 /* --- Store the results --- */
345 if (*xx) MP_DROP(*xx);
352 if (*yy) MP_DROP(*yy);
358 MP_DROP(X); MP_DROP(Y);
359 MP_DROP(a); MP_DROP(b);
362 /*----- Test rig ----------------------------------------------------------*/
366 static int gcd(dstr *v)
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;
375 mp *gg = MP_NEW, *xx = MP_NEW, *yy = MP_NEW;
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);
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);
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);
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);
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);
417 assert(mparena_count(MPARENA_GLOBAL) == 0);
421 static test_chunk tests[] = {
422 { "gcd", gcd, { &type_mp, &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
426 int main(int argc, char *argv[])
429 test_run(argc, argv, tests, SRCDIR "/tests/mp");
435 /*----- That's all, folks -------------------------------------------------*/