+++ /dev/null
-/* -*-c-*-
- *
- * $Id$
- *
- * Extended GCD calculation
- *
- * (c) 1999 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 "mp.h"
-
-/*----- Main code ---------------------------------------------------------*/
-
-/* --- @mp_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 mp_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_aneg 2u
-#define f_bneg 4u
-#define f_ext 8u
-
- /* --- Sort out some initial flags --- */
-
- if (xx || yy)
- f |= f_ext;
-
- if (MP_NEGP(a))
- f |= f_aneg;
- if (MP_NEGP(b))
- f |= f_bneg;
-
- /* --- Ensure that @a@ is larger than @b@ --- *
- *
- * Use absolute values here!
- */
-
- 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_ZEROP(b)) {
-
- /* --- Store %$|a|$% as the GCD --- */
-
- if (gcd) {
- if (*gcd) MP_DROP(*gcd);
- a = MP_COPY(a);
- if (MP_NEGP(a)) {
- MP_SPLIT(a);
- a->f &= ~MP_NEG;
- f |= f_aneg;
- }
- *gcd = a;
- }
-
- /* --- Store %$1$% and %$0$% in the appropriate bins --- */
-
- if (f & f_ext) {
- if (f & f_swap) {
- mp **tt = xx; xx = yy; yy = tt;
- }
- if (xx) {
- if (*xx) MP_DROP(*xx);
- if (MP_EQ(a, MP_ZERO))
- *xx = MP_ZERO;
- else if (f & f_aneg)
- *xx = MP_MONE;
- else
- *xx = MP_ONE;
- }
- if (yy) {
- if (*yy) MP_DROP(*yy);
- *yy = MP_ZERO;
- }
- }
- return;
- }
-
- /* --- Force the signs on the arguments and take copies --- */
-
- a = MP_COPY(a);
- b = MP_COPY(b);
-
- MP_SPLIT(a); a->f &= ~MP_NEG;
- MP_SPLIT(b); b->f &= ~MP_NEG;
-
- u = MP_COPY(a);
- v = MP_COPY(b);
-
- /* --- Main extended Euclidean algorithm --- */
-
- while (!MP_ZEROP(v)) {
- mp_div(&q, &u, u, v);
- if (f & f_ext) {
- t = mp_mul(spare, X, q);
- t = mp_sub(t, x, t);
- spare = x; x = X; X = t;
- t = mp_mul(spare, Y, q);
- t = mp_sub(t, y, t);
- 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 --- *
- *
- * Ensure that the coefficient returned is positive, if there is only one.
- * If there are two, favour @y@. Of course, if the original arguments were
- * negative then I'll need to twiddle their signs as well.
- */
-
- 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;
- }
-
- /* --- Sort out the signs --- *
- *
- * Note that %$ax + by = a(x - b) + b(y + a)$%.
- *
- * This is currently bodgy. It needs sorting out at some time.
- */
-
- if (yy) {
- if (MP_NEGP(y)) {
- do {
- y = mp_add(y, y, a);
- x = mp_sub(x, x, b);
- } while (MP_NEGP(y));
- } else {
- while (MP_CMP(y, >=, a)) {
- y = mp_sub(y, y, a);
- x = mp_add(x, x, b);
- }
- }
- } else {
- if (MP_NEGP(x)) {
- do
- x = mp_add(x, x, b);
- while (MP_NEGP(x));
- } else {
- while (MP_CMP(x, >=, b))
- x = mp_sub(x, x, b);
- }
- }
-
- /* --- Twiddle the signs --- */
-
- if (f & f_aneg)
- x->f ^= MP_NEG;
- if (f & f_bneg)
- y->f ^= MP_NEG;
-
- /* --- 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);
- MP_DROP(a); MP_DROP(b);
-}
-
-/* -- @mp_modinv@ --- *
- *
- * Arguments: @mp *d@ = destination
- * @mp *x@ = argument
- * @mp *p@ = modulus
- *
- * Returns: The inverse %$x^{-1} \bmod p$%.
- *
- * Use: Computes a modular inverse. An assertion fails if %$p$%
- * has no inverse.
- */
-
-mp *mp_modinv(mp *d, mp *x, mp *p)
-{
- mp *g = MP_NEW;
- mp_gcd(&g, 0, &d, p, x);
- assert(MP_EQ(g, MP_ONE));
- mp_drop(g);
- return (d);
-}
-
-/*----- Test rig ----------------------------------------------------------*/
-
-#ifdef TEST_RIG
-
-static int modinv(dstr *v)
-{
- int ok = 1;
- mp *x = *(mp **)v[0].buf;
- mp *m = *(mp **)v[1].buf;
- mp *r = *(mp **)v[2].buf;
-
- mp *y = mp_modinv(MP_NEW, x, m);
- if (!MP_EQ(y, r)) {
- fputs("\n*** mp_modinv failed", stderr);
- fputs("\nx = ", stderr); mp_writefile(x, stderr, 10);
- fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
- fputs("\nexpect = ", stderr); mp_writefile(r, stderr, 10);
- fputs("\nresult = ", stderr); mp_writefile(y, stderr, 10);
- ok = 0;
- }
- MP_DROP(x); MP_DROP(m); MP_DROP(r); MP_DROP(y);
- assert(mparena_count(MPARENA_GLOBAL) == 0);
- return (ok);
-}
-
-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;
- mp_gcd(&gg, &xx, &yy, a, b);
- if (!MP_EQ(x, xx)) {
- fputs("\n*** mp_gcd(x) failed", stderr);
- fputs("\na = ", stderr); mp_writefile(a, stderr, 10);
- fputs("\nb = ", stderr); mp_writefile(b, stderr, 10);
- fputs("\nexpect = ", stderr); mp_writefile(x, stderr, 10);
- fputs("\nresult = ", stderr); mp_writefile(xx, stderr, 10);
- fputc('\n', stderr);
- ok = 0;
- }
- if (!MP_EQ(y, yy)) {
- fputs("\n*** mp_gcd(y) failed", stderr);
- fputs("\na = ", stderr); mp_writefile(a, stderr, 10);
- fputs("\nb = ", stderr); mp_writefile(b, stderr, 10);
- fputs("\nexpect = ", stderr); mp_writefile(y, stderr, 10);
- fputs("\nresult = ", stderr); mp_writefile(yy, stderr, 10);
- fputc('\n', stderr);
- ok = 0;
- }
-
- if (!ok) {
- mp *ax = mp_mul(MP_NEW, a, xx);
- mp *by = mp_mul(MP_NEW, b, yy);
- ax = mp_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*** mp_gcd(gcd) failed", stderr);
- fputs("\na = ", stderr); mp_writefile(a, stderr, 10);
- fputs("\nb = ", stderr); mp_writefile(b, stderr, 10);
- fputs("\nexpect = ", stderr); mp_writefile(g, stderr, 10);
- fputs("\nresult = ", stderr); mp_writefile(gg, stderr, 10);
- 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 } },
- { "modinv", modinv, { &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/mp");
- return (0);
-}
-
-#endif
-
-/*----- That's all, folks -------------------------------------------------*/