/* -*-c-*-
*
- * $Id: mp-gcd.c,v 1.4 2000/06/17 11:34:46 mdw Exp $
+ * $Id: mp-gcd.c,v 1.5 2000/10/08 12:02:41 mdw Exp $
*
* Extended GCD calculation
*
/*----- Revision history --------------------------------------------------*
*
* $Log: mp-gcd.c,v $
+ * Revision 1.5 2000/10/08 12:02:41 mdw
+ * Use Euclid's algorithm rather than the binary one.
+ *
* Revision 1.4 2000/06/17 11:34:46 mdw
* More hacking for the signs of the outputs.
*
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;
unsigned f = 0;
enum {
/* --- Check for zeroness --- */
- if (MP_CMP(b, ==, MP_ZERO)) {
+ if (MP_EQ(b, MP_ZERO)) {
/* --- Store %$|a|$% as the GCD --- */
}
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;
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 --- */
-
- 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_LEN(v)) {
+ mp *t;
+ mp_div(&q, &u, u, v);
+ if (f & f_ext) {
+ t = mp_mul(MP_NEW, X, q);
+ t = mp_sub(t, x, t);
+ MP_DROP(x); x = X; X = t;
+ t = mp_mul(MP_NEW, Y, q);
+ t = mp_sub(t, y, t);
+ MP_DROP(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 (!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 --- *
}
}
- MP_DROP(u);
+ MP_DROP(v);
MP_DROP(X); MP_DROP(Y);
MP_DROP(a); MP_DROP(b);
}
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);
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);
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);