/* -*-c-*-
*
- * $Id: mp-gcd.c,v 1.2 1999/11/22 20:49:56 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.
+ *
+ * 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.
*
* 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. Neither @a@ nor @b@ may be zero. Note that,
- * unlike @mp_div@ for example, it is not possible to specify
- * explicit destinations -- new MPs are always allocated.
+ * inverses.
*/
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;
- int ext = xx || yy;
- int swap = 0;
+ mp *q = MP_NEW;
+ unsigned f = 0;
- /* --- Ensure that @a@ is larger than @b@ --- */
+ enum {
+ f_swap = 1u,
+ f_aneg = 2u,
+ f_bneg = 4u,
+ f_ext = 8u
+ };
- if (MP_CMP(a, <, b)) {
- { mp *t = a; a = b; b = t; }
- swap = 1;
- }
+ /* --- Sort out some initial flags --- */
- /* --- Take a reference to the arguments --- */
+ if (xx || yy)
+ f |= f_ext;
- a = MP_COPY(a);
- b = MP_COPY(b);
+ if (a->f & MP_NEG)
+ f |= f_aneg;
+ if (b->f & MP_NEG)
+ f |= f_bneg;
- /* --- Make sure @a@ and @b@ are not both even --- */
+ /* --- Ensure that @a@ is larger than @b@ --- *
+ *
+ * Use absolute values here!
+ */
- if (((a->v[0] | b->v[0]) & 1) == 0) {
- mpscan asc, bsc;
+ if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
+ { mp *t = a; a = b; b = t; }
+ f |= f_swap;
+ }
- /* --- Break off my copies --- */
+ /* --- Check for zeroness --- */
- MP_SPLIT(a);
- MP_SPLIT(b);
- MP_SCAN(&asc, a);
- MP_SCAN(&bsc, b);
+ if (MP_EQ(b, MP_ZERO)) {
- /* --- Start scanning --- */
+ /* --- Store %$|a|$% as the GCD --- */
- 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++;
+ if (gcd) {
+ if (*gcd) MP_DROP(*gcd);
+ a = MP_COPY(a);
+ if (a->f & MP_NEG) {
+ MP_SPLIT(a);
+ a->f &= ~MP_NEG;
+ f |= f_aneg;
+ }
+ *gcd = a;
}
- /* --- Shift @a@ and @b@ down --- */
+ /* --- Store %$1$% and %$0$% in the appropriate bins --- */
- a = mp_lsr(a, a, shift);
- b = mp_lsr(b, b, shift);
+ 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 if (f & f_aneg)
+ *xx = MP_MONE;
+ else
+ *xx = MP_ONE;
+ }
+ if (yy) {
+ if (*yy) MP_DROP(*yy);
+ *yy = MP_ZERO;
+ }
+ }
+ return;
}
- /* --- 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 (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++;
- }
+ /* --- Take a reference to the arguments --- */
- if (nn) {
- u = mp_lsr(u, u, nn);
- if (ext && n) {
- X = mp_lsr(X, X, n);
- Y = mp_lsr(Y, Y, n);
- }
- }
- }
+ a = MP_COPY(a);
+ b = MP_COPY(b);
- /* --- 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 (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++;
- }
+ /* --- Make sure @a@ and @b@ are not both even --- */
- if (nn) {
- v = mp_lsr(v, v, nn);
- if (ext && n) {
- x = mp_lsr(x, x, n);
- y = mp_lsr(y, y, n);
- }
- }
- }
+ MP_SPLIT(a); a->f &= ~MP_NEG;
+ MP_SPLIT(b); b->f &= ~MP_NEG;
- /* --- End-of-loop fiddling --- */
+ u = MP_COPY(a);
+ v = MP_COPY(b);
- if (MP_CMP(u, >=, v)) {
- u = mp_sub(u, u, v);
- if (ext) {
- X = mp_sub(X, X, x);
- Y = mp_sub(Y, Y, y);
- }
- } else {
- v = mp_sub(v, v, u);
- if (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 --- */
-
- if (gcd)
- *gcd = mp_lsl(v, v, shift);
- else
- MP_DROP(v);
+ MP_DROP(q);
+ 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@.
+ * 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 (ext) {
- if (swap) {
+ if (f & f_ext) {
+
+ /* --- If @a@ and @b@ got swapped, swap the coefficients back --- */
+
+ if (f & f_swap) {
mp *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 (y->f & MP_NEG) {
- y = mp_add(y, y, a);
- x = mp_sub(x, x, b);
+ do {
+ y = mp_add(y, y, a);
+ x = mp_sub(x, x, b);
+ } while (y->f & MP_NEG);
+ } else {
+ while (MP_CMP(y, >=, a)) {
+ y = mp_sub(y, y, a);
+ x = mp_add(x, x, b);
+ }
+ }
+ } else {
+ if (x->f & MP_NEG) {
+ do
+ x = mp_add(x, x, b);
+ while (x->f & MP_NEG);
+ } else {
+ while (MP_CMP(x, >=, b))
+ x = mp_sub(x, x, b);
}
- } else if (x->f & MP_NEG)
- x = mp_add(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) *xx = x; else MP_DROP(x);
- if (yy) *yy = y; else MP_DROP(y);
+ 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(u);
+ MP_DROP(v);
MP_DROP(X); MP_DROP(Y);
MP_DROP(a); MP_DROP(b);
}
mp *x = *(mp **)v[3].buf;
mp *y = *(mp **)v[4].buf;
- mp *gg, *xx, *yy;
+ 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);
}
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);
}
projects / u / mdw / catacomb / blobdiff