/* -*-c-*-
*
- * $Id: mp-gcd.c,v 1.4 2000/06/17 11:34:46 mdw Exp $
+ * $Id$
*
* Extended GCD calculation
*
* (c) 1999 Straylight/Edgeware
*/
-/*----- Licensing notice --------------------------------------------------*
+/*----- Licensing notice --------------------------------------------------*
*
* This file is part of Catacomb.
*
* 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.
*/
-/*----- Revision history --------------------------------------------------*
- *
- * $Log: mp-gcd.c,v $
- * Revision 1.4 2000/06/17 11:34:46 mdw
- * More hacking for the signs of the outputs.
- *
- * Revision 1.3 1999/12/10 23:18:39 mdw
- * Change interface for suggested destinations.
- *
- * Revision 1.2 1999/11/22 20:49:56 mdw
- * Fix bug which failed to favour `x' when `y' wasn't wanted and the two
- * arguments needed swapping.
- *
- * Revision 1.1 1999/11/17 18:02:16 mdw
- * New multiprecision integer arithmetic suite.
- *
- */
-
/*----- Header files ------------------------------------------------------*/
#include "mp.h"
void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b)
{
- mp *X = MP_ONE, *Y = MP_ZERO;
- mp *x = MP_ZERO, *y = MP_ONE;
+ mp *x = MP_ONE, *X = MP_ZERO;
+ mp *y = MP_ZERO, *Y = MP_ONE;
mp *u, *v;
- size_t shift = 0;
+ mp *q = MP_NEW, *t, *spare = MP_NEW;
unsigned f = 0;
- enum {
- f_swap = 1u,
- f_aneg = 2u,
- f_bneg = 4u,
- f_ext = 8u
- };
+#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 (a->f & MP_NEG)
+ if (MP_NEGP(a))
f |= f_aneg;
- if (b->f & MP_NEG)
+ if (MP_NEGP(b))
f |= f_bneg;
/* --- Ensure that @a@ is larger than @b@ --- *
*/
if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
- { mp *t = a; a = b; b = t; }
+ t = a; a = b; b = t;
f |= f_swap;
}
/* --- Check for zeroness --- */
- if (MP_CMP(b, ==, MP_ZERO)) {
+ if (MP_ZEROP(b)) {
/* --- Store %$|a|$% as the GCD --- */
if (gcd) {
if (*gcd) MP_DROP(*gcd);
a = MP_COPY(a);
- if (a->f & MP_NEG) {
+ if (MP_NEGP(a)) {
MP_SPLIT(a);
a->f &= ~MP_NEG;
f |= f_aneg;
if (f & f_ext) {
if (f & f_swap) {
- mp **t = xx; xx = yy; yy = t;
+ mp **tt = xx; xx = yy; yy = tt;
}
if (xx) {
if (*xx) MP_DROP(*xx);
- if (MP_CMP(a, ==, MP_ZERO))
+ if (MP_EQ(a, MP_ZERO))
*xx = MP_ZERO;
else if (f & f_aneg)
*xx = MP_MONE;
return;
}
- /* --- Take a reference to the arguments --- */
+ /* --- Force the signs on the arguments and take copies --- */
a = MP_COPY(a);
b = MP_COPY(b);
- /* --- Make sure @a@ and @b@ are not both even --- */
-
MP_SPLIT(a); a->f &= ~MP_NEG;
MP_SPLIT(b); b->f &= ~MP_NEG;
- if (((a->v[0] | b->v[0]) & 1) == 0) {
- mpscan asc, bsc;
-
- /* --- Break off my copies --- */
-
- MP_SCAN(&asc, a);
- MP_SCAN(&bsc, b);
-
- /* --- Start scanning --- */
-
- for (;;) {
- if (!MP_STEP(&asc) || !MP_STEP(&bsc))
- assert(((void)"zero argument passed to mp_gcd", 0));
- if (MP_BIT(&asc) || MP_BIT(&bsc))
- break;
- shift++;
- }
-
- /* --- Shift @a@ and @b@ down --- */
-
- a = mp_lsr(a, a, shift);
- b = mp_lsr(b, b, shift);
- }
-
- /* --- Set up @u@ and @v@ --- */
-
u = MP_COPY(a);
v = MP_COPY(b);
- /* --- Start the main loop --- */
-
- for (;;) {
-
- /* --- While @u@ is even --- */
-
- {
- mpscan sc, xsc, ysc;
- size_t n = 0, nn = 0;
-
- MP_SCAN(&sc, u);
- MP_SCAN(&xsc, X); MP_SCAN(&ysc, Y);
- for (;;) {
- MP_STEP(&sc);
- MP_STEP(&xsc); MP_STEP(&ysc);
- if (MP_BIT(&sc))
- break;
- if ((f & f_ext) && (MP_BIT(&xsc) | MP_BIT(&ysc))) {
- if (n) {
- X = mp_lsr(X, X, n);
- Y = mp_lsr(Y, Y, n);
- n = 0;
- }
- X = mp_add(X, X, b);
- Y = mp_sub(Y, Y, a);
- MP_SCAN(&xsc, X);
- MP_SCAN(&ysc, Y);
- MP_STEP(&xsc); MP_STEP(&ysc);
- }
- n++; nn++;
- }
-
- if (nn) {
- u = mp_lsr(u, u, nn);
- if ((f & f_ext) && n) {
- X = mp_lsr(X, X, n);
- Y = mp_lsr(Y, Y, n);
- }
- }
- }
-
- /* --- While @v@ is even --- */
-
- {
- mpscan sc, xsc, ysc;
- size_t n = 0, nn = 0;
-
- MP_SCAN(&sc, v);
- MP_SCAN(&xsc, x); MP_SCAN(&ysc, y);
- for (;;) {
- MP_STEP(&sc);
- MP_STEP(&xsc); MP_STEP(&ysc);
- if (MP_BIT(&sc))
- break;
- if ((f & f_ext) && (MP_BIT(&xsc) | MP_BIT(&ysc))) {
- if (n) {
- x = mp_lsr(x, x, n);
- y = mp_lsr(y, y, n);
- n = 0;
- }
- x = mp_add(x, x, b);
- y = mp_sub(y, y, a);
- MP_SCAN(&xsc, x);
- MP_SCAN(&ysc, y);
- MP_STEP(&xsc); MP_STEP(&ysc);
- }
- n++; nn++;
- }
-
- if (nn) {
- v = mp_lsr(v, v, nn);
- if ((f & f_ext) && n) {
- x = mp_lsr(x, x, n);
- y = mp_lsr(y, y, n);
- }
- }
- }
-
- /* --- End-of-loop fiddling --- */
+ /* --- Main extended Euclidean algorithm --- */
- if (MP_CMP(u, >=, v)) {
- u = mp_sub(u, u, v);
- if (f & f_ext) {
- X = mp_sub(X, X, x);
- Y = mp_sub(Y, Y, y);
- }
- } else {
- v = mp_sub(v, v, u);
- if (f & f_ext) {
- x = mp_sub(x, x, X);
- y = mp_sub(y, y, Y);
- }
+ 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;
}
-
- if (MP_CMP(u, ==, MP_ZERO))
- break;
+ t = u; u = v; v = t;
}
- /* --- Write the results out --- */
-
+ MP_DROP(q); if (spare) MP_DROP(spare);
if (!gcd)
- MP_DROP(v);
+ MP_DROP(u);
else {
if (*gcd) MP_DROP(*gcd);
- *gcd = mp_lsl(v, v, shift);
+ u->f &= ~MP_NEG;
+ *gcd = u;
}
/* --- Perform a little normalization --- *
/* --- If @a@ and @b@ got swapped, swap the coefficients back --- */
if (f & f_swap) {
- mp *t = x; x = y; y = t;
+ t = x; x = y; y = t;
t = a; a = b; b = t;
}
*/
if (yy) {
- if (y->f & MP_NEG) {
+ if (MP_NEGP(y)) {
do {
y = mp_add(y, y, a);
x = mp_sub(x, x, b);
- } while (y->f & MP_NEG);
+ } while (MP_NEGP(y));
} else {
while (MP_CMP(y, >=, a)) {
y = mp_sub(y, y, a);
}
}
} else {
- if (x->f & MP_NEG) {
+ if (MP_NEGP(x)) {
do
x = mp_add(x, x, b);
- while (x->f & MP_NEG);
+ while (MP_NEGP(x));
} else {
while (MP_CMP(x, >=, b))
x = mp_sub(x, x, b);
}
}
- MP_DROP(u);
+ 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 *gg = MP_NEW, *xx = MP_NEW, *yy = MP_NEW;
mp_gcd(&gg, &xx, &yy, a, b);
- if (MP_CMP(x, !=, xx)) {
+ 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("\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_CMP(y, !=, yy)) {
+ 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("\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);
mp *ax = mp_mul(MP_NEW, a, xx);
mp *by = mp_mul(MP_NEW, b, yy);
ax = mp_add(ax, ax, by);
- if (MP_CMP(ax, ==, gg))
+ if (MP_EQ(ax, gg))
fputs("\n*** (Alternative result found.)\n", stderr);
MP_DROP(ax);
MP_DROP(by);
}
- if (MP_CMP(g, !=, gg)) {
+ 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("\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);
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 } }
};
projects / u / mdw / catacomb / blobdiff