X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/c9110b350af5f22c32dc7523999a2aeae6e51517..5278d9afdf1aff9fd6f64073ea42395d756ee58c:/mp-gcd.c

diff --git a/mp-gcd.c b/mp-gcd.c
index 38f95d4..40531c7 100644
--- a/mp-gcd.c
+++ b/mp-gcd.c
@@ -1,13 +1,13 @@
 /* -*-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.
  *
@@ -15,36 +15,18 @@
  * 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"
@@ -65,27 +47,25 @@
 
 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@ --- *
@@ -94,20 +74,20 @@ void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *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;
@@ -119,11 +99,11 @@ void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b)
 
     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;
@@ -138,150 +118,39 @@ void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b)
     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 --- *
@@ -296,7 +165,7 @@ void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b)
     /* --- 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;
     }
 
@@ -308,11 +177,11 @@ void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b)
      */
 
     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);
@@ -320,10 +189,10 @@ void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *b)
 	}
       }
     } 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);
@@ -354,15 +223,57 @@ void mp_gcd(mp **gcd, mp **xx, mp **yy, mp *a, mp *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;
@@ -374,19 +285,19 @@ static int gcd(dstr *v)
 
   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);
@@ -397,16 +308,16 @@ static int gcd(dstr *v)
     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);
@@ -420,6 +331,7 @@ static int gcd(dstr *v)
 
 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 } }
 };