+++ /dev/null
-/* -*-c-*-
- *
- * $Id$
- *
- * Euclidian algorithm on binary polynomials
- *
- * (c) 2004 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Library General Public License as
- * published by the Free Software Foundation; either version 2 of the
- * License, or (at your option) any later version.
- *
- * Catacomb is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-/*----- Header files ------------------------------------------------------*/
-
-#include "gf.h"
-
-/*----- Main code ---------------------------------------------------------*/
-
-/* --- @gf_gcd@ --- *
- *
- * Arguments: @mp **gcd, **xx, **yy@ = where to write the results
- * @mp *a, *b@ = sources (must be nonzero)
- *
- *
- * Returns: ---
- *
- * Use: Calculates @gcd(a, b)@, and two numbers @x@ and @y@ such that
- * @ax + by = gcd(a, b)@. This is useful for computing modular
- * inverses.
- */
-
-void gf_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b)
-{
- mp *x = MP_ONE, *X = MP_ZERO;
- mp *y = MP_ZERO, *Y = MP_ONE;
- mp *u, *v;
- mp *q = MP_NEW, *t, *spare = MP_NEW;
- unsigned f = 0;
-
-#define f_swap 1u
-#define f_ext 2u
-
- /* --- Sort out some initial flags --- */
-
- if (xx || yy)
- f |= f_ext;
-
- /* --- Ensure that @a@ is larger than @b@ --- *
- *
- * If they're the same length we don't care which order they're in, so this
- * unsigned comparison is fine.
- */
-
- if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
- t = a; a = b; b = t;
- f |= f_swap;
- }
-
- /* --- Check for zeroness --- */
-
- if (MP_EQ(b, MP_ZERO)) {
-
- /* --- Store %$|a|$% as the GCD --- */
-
- if (gcd) {
- if (*gcd) MP_DROP(*gcd);
- a = MP_COPY(a);
- *gcd = a;
- }
-
- /* --- Store %$1$% and %$0$% in the appropriate bins --- */
-
- if (f & f_ext) {
- if (f & f_swap) {
- mp **t = xx; xx = yy; yy = t;
- }
- if (xx) {
- if (*xx) MP_DROP(*xx);
- if (MP_EQ(a, MP_ZERO))
- *xx = MP_ZERO;
- else
- *xx = MP_ONE;
- }
- if (yy) {
- if (*yy) MP_DROP(*yy);
- *yy = MP_ZERO;
- }
- }
- return;
- }
-
- /* --- Main extended Euclidean algorithm --- */
-
- u = MP_COPY(a);
- v = MP_COPY(b);
-
- while (!MP_ZEROP(v)) {
- gf_div(&q, &u, u, v);
- if (f & f_ext) {
- t = gf_mul(spare, X, q);
- t = gf_add(t, t, x);
- spare = x; x = X; X = t;
- t = gf_mul(spare, Y, q);
- t = gf_add(t, t, y);
- spare = y; y = Y; Y = t;
- }
- t = u; u = v; v = t;
- }
-
- MP_DROP(q); if (spare) MP_DROP(spare);
- if (!gcd)
- MP_DROP(u);
- else {
- if (*gcd) MP_DROP(*gcd);
- u->f &= ~MP_NEG;
- *gcd = u;
- }
-
- /* --- Perform a little normalization --- */
-
- if (f & f_ext) {
-
- /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */
-
- if (f & f_swap) {
- t = x; x = y; y = t;
- t = a; a = b; b = t;
- }
-
- /* --- Store the results --- */
-
- if (!xx)
- MP_DROP(x);
- else {
- if (*xx) MP_DROP(*xx);
- *xx = x;
- }
-
- if (!yy)
- MP_DROP(y);
- else {
- if (*yy) MP_DROP(*yy);
- *yy = y;
- }
- }
-
- MP_DROP(v);
- MP_DROP(X); MP_DROP(Y);
-}
-
-/* -- @gf_modinv@ --- *
- *
- * Arguments: @mp *d@ = destination
- * @mp *x@ = argument
- * @mp *p@ = modulus
- *
- * Returns: The inverse %$x^{-1} \bmod p$%.
- *
- * Use: Computes a modular inverse, the catch being that the
- * arguments and results are binary polynomials. An assertion
- * fails if %$p$% has no inverse.
- */
-
-mp *gf_modinv(mp *d, mp *x, mp *p)
-{
- mp *g = MP_NEW;
- gf_gcd(&g, 0, &d, p, x);
- assert(MP_EQ(g, MP_ONE));
- mp_drop(g);
- return (d);
-}
-
-/*----- Test rig ----------------------------------------------------------*/
-
-#ifdef TEST_RIG
-
-static int gcd(dstr *v)
-{
- int ok = 1;
- mp *a = *(mp **)v[0].buf;
- mp *b = *(mp **)v[1].buf;
- mp *g = *(mp **)v[2].buf;
- mp *x = *(mp **)v[3].buf;
- mp *y = *(mp **)v[4].buf;
-
- mp *gg = MP_NEW, *xx = MP_NEW, *yy = MP_NEW;
- gf_gcd(&gg, &xx, &yy, a, b);
- if (!MP_EQ(x, xx)) {
- fputs("\n*** gf_gcd(x) failed", stderr);
- fputs("\na = ", stderr); mp_writefile(a, stderr, 16);
- fputs("\nb = ", stderr); mp_writefile(b, stderr, 16);
- fputs("\nexpect = ", stderr); mp_writefile(x, stderr, 16);
- fputs("\nresult = ", stderr); mp_writefile(xx, stderr, 16);
- fputc('\n', stderr);
- ok = 0;
- }
- if (!MP_EQ(y, yy)) {
- fputs("\n*** gf_gcd(y) failed", stderr);
- fputs("\na = ", stderr); mp_writefile(a, stderr, 16);
- fputs("\nb = ", stderr); mp_writefile(b, stderr, 16);
- fputs("\nexpect = ", stderr); mp_writefile(y, stderr, 16);
- fputs("\nresult = ", stderr); mp_writefile(yy, stderr, 16);
- fputc('\n', stderr);
- ok = 0;
- }
-
- if (!ok) {
- mp *ax = gf_mul(MP_NEW, a, xx);
- mp *by = gf_mul(MP_NEW, b, yy);
- ax = gf_add(ax, ax, by);
- if (MP_EQ(ax, gg))
- fputs("\n*** (Alternative result found.)\n", stderr);
- MP_DROP(ax);
- MP_DROP(by);
- }
-
- if (!MP_EQ(g, gg)) {
- fputs("\n*** gf_gcd(gcd) failed", stderr);
- fputs("\na = ", stderr); mp_writefile(a, stderr, 16);
- fputs("\nb = ", stderr); mp_writefile(b, stderr, 16);
- fputs("\nexpect = ", stderr); mp_writefile(g, stderr, 16);
- fputs("\nresult = ", stderr); mp_writefile(gg, stderr, 16);
- fputc('\n', stderr);
- ok = 0;
- }
- MP_DROP(a); MP_DROP(b); MP_DROP(g); MP_DROP(x); MP_DROP(y);
- MP_DROP(gg); MP_DROP(xx); MP_DROP(yy);
- assert(mparena_count(MPARENA_GLOBAL) == 0);
- return (ok);
-}
-
-static test_chunk tests[] = {
- { "gcd", gcd, { &type_mp, &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
- { 0, 0, { 0 } }
-};
-
-int main(int argc, char *argv[])
-{
- sub_init();
- test_run(argc, argv, tests, SRCDIR "/tests/gf");
- return (0);
-}
-
-#endif
-
-/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff