3 * $Id: mp-gcd.c,v 1.6 2004/03/21 22:52:06 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 1.6 2004/03/21 22:52:06 mdw
34 * Merge and close elliptic curve branch.
36 * Revision 1.5.4.1 2004/03/21 22:39:46 mdw
37 * Elliptic curves on binary fields work.
39 * Revision 1.5 2000/10/08 12:02:41 mdw
40 * Use Euclid's algorithm rather than the binary one.
42 * Revision 1.4 2000/06/17 11:34:46 mdw
43 * More hacking for the signs of the outputs.
45 * Revision 1.3 1999/12/10 23:18:39 mdw
46 * Change interface for suggested destinations.
48 * Revision 1.2 1999/11/22 20:49:56 mdw
49 * Fix bug which failed to favour `x' when `y' wasn't wanted and the two
50 * arguments needed swapping.
52 * Revision 1.1 1999/11/17 18:02:16 mdw
53 * New multiprecision integer arithmetic suite.
57 /*----- Header files ------------------------------------------------------*/
61 /*----- Main code ---------------------------------------------------------*/
65 * Arguments: @mp **gcd, **xx, **yy@ = where to write the results
66 * @mp *a, *b@ = sources (must be nonzero)
70 * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that
71 * @ax + by = gcd(a, b)@. This is useful for computing modular
75 void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b)
77 mp *x = MP_ONE, *X = MP_ZERO;
78 mp *y = MP_ZERO, *Y = MP_ONE;
88 /* --- Sort out some initial flags --- */
98 /* --- Ensure that @a@ is larger than @b@ --- *
100 * Use absolute values here!
103 if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
104 { mp *t = a; a = b; b = t; }
108 /* --- Check for zeroness --- */
110 if (MP_EQ(b, MP_ZERO)) {
112 /* --- Store %$|a|$% as the GCD --- */
115 if (*gcd) MP_DROP(*gcd);
125 /* --- Store %$1$% and %$0$% in the appropriate bins --- */
129 mp **t = xx; xx = yy; yy = t;
132 if (*xx) MP_DROP(*xx);
133 if (MP_EQ(a, MP_ZERO))
141 if (*yy) MP_DROP(*yy);
148 /* --- Take a reference to the arguments --- */
153 /* --- Make sure @a@ and @b@ are not both even --- */
155 MP_SPLIT(a); a->f &= ~MP_NEG;
156 MP_SPLIT(b); b->f &= ~MP_NEG;
163 mp_div(&q, &u, u, v);
165 t = mp_mul(MP_NEW, X, q);
167 MP_DROP(x); x = X; X = t;
168 t = mp_mul(MP_NEW, Y, q);
170 MP_DROP(y); y = Y; Y = t;
179 if (*gcd) MP_DROP(*gcd);
184 /* --- Perform a little normalization --- *
186 * Ensure that the coefficient returned is positive, if there is only one.
187 * If there are two, favour @y@. Of course, if the original arguments were
188 * negative then I'll need to twiddle their signs as well.
193 /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */
196 mp *t = x; x = y; y = t;
200 /* --- Sort out the signs --- *
202 * Note that %$ax + by = a(x - b) + b(y + a)$%.
204 * This is currently bodgy. It needs sorting out at some time.
212 } while (y->f & MP_NEG);
214 while (MP_CMP(y, >=, a)) {
223 while (x->f & MP_NEG);
225 while (MP_CMP(x, >=, b))
230 /* --- Twiddle the signs --- */
237 /* --- Store the results --- */
242 if (*xx) MP_DROP(*xx);
249 if (*yy) MP_DROP(*yy);
255 MP_DROP(X); MP_DROP(Y);
256 MP_DROP(a); MP_DROP(b);
259 /*----- Test rig ----------------------------------------------------------*/
263 static int gcd(dstr *v)
266 mp *a = *(mp **)v[0].buf;
267 mp *b = *(mp **)v[1].buf;
268 mp *g = *(mp **)v[2].buf;
269 mp *x = *(mp **)v[3].buf;
270 mp *y = *(mp **)v[4].buf;
272 mp *gg = MP_NEW, *xx = MP_NEW, *yy = MP_NEW;
273 mp_gcd(&gg, &xx, &yy, a, b);
275 fputs("\n*** mp_gcd(x) failed", stderr);
276 fputs("\na = ", stderr); mp_writefile(a, stderr, 10);
277 fputs("\nb = ", stderr); mp_writefile(b, stderr, 10);
278 fputs("\nexpect = ", stderr); mp_writefile(x, stderr, 10);
279 fputs("\nresult = ", stderr); mp_writefile(xx, stderr, 10);
284 fputs("\n*** mp_gcd(y) failed", stderr);
285 fputs("\na = ", stderr); mp_writefile(a, stderr, 10);
286 fputs("\nb = ", stderr); mp_writefile(b, stderr, 10);
287 fputs("\nexpect = ", stderr); mp_writefile(y, stderr, 10);
288 fputs("\nresult = ", stderr); mp_writefile(yy, stderr, 10);
294 mp *ax = mp_mul(MP_NEW, a, xx);
295 mp *by = mp_mul(MP_NEW, b, yy);
296 ax = mp_add(ax, ax, by);
298 fputs("\n*** (Alternative result found.)\n", stderr);
304 fputs("\n*** mp_gcd(gcd) failed", stderr);
305 fputs("\na = ", stderr); mp_writefile(a, stderr, 10);
306 fputs("\nb = ", stderr); mp_writefile(b, stderr, 10);
307 fputs("\nexpect = ", stderr); mp_writefile(g, stderr, 10);
308 fputs("\nresult = ", stderr); mp_writefile(gg, stderr, 10);
312 MP_DROP(a); MP_DROP(b); MP_DROP(g); MP_DROP(x); MP_DROP(y);
313 MP_DROP(gg); MP_DROP(xx); MP_DROP(yy);
314 assert(mparena_count(MPARENA_GLOBAL) == 0);
318 static test_chunk tests[] = {
319 { "gcd", gcd, { &type_mp, &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
323 int main(int argc, char *argv[])
326 test_run(argc, argv, tests, SRCDIR "/tests/mp");
332 /*----- That's all, folks -------------------------------------------------*/