X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/71ec78ce88339bda7c265d6dafa4982077acc901..d3409d5ecf2492cff862616de72a580d1a8e8dc0:/mp-gcd.c

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+/* -*-c-*-
+ *
+ * $Id: mp-gcd.c,v 1.1 1999/11/17 18:02:16 mdw Exp $
+ *
+ * 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.
+ */
+
+/*----- Revision history --------------------------------------------------* 
+ *
+ * $Log: mp-gcd.c,v $
+ * Revision 1.1  1999/11/17 18:02:16  mdw
+ * New multiprecision integer arithmetic suite.
+ *
+ */
+
+/*----- 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.  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.
+ */
+
+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 *u, *v;
+  size_t shift = 0;
+  int ext = xx || yy;
+  int swap = 0;
+
+  /* --- Ensure that @a@ is larger than @b@ --- */
+
+  if (MP_CMP(a, <, b)) {
+    { mp *t = a; a = b; b = t; }
+    swap = 1;
+  }
+
+  /* --- Take a reference to the arguments --- */
+
+  a = MP_COPY(a);
+  b = MP_COPY(b);
+
+  /* --- Make sure @a@ and @b@ are not both even --- */
+
+  if (((a->v[0] | b->v[0]) & 1) == 0) {
+    mpscan asc, bsc;
+
+    /* --- Break off my copies --- */
+
+    MP_SPLIT(a);
+    MP_SPLIT(b);
+    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 (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 (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 (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 (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 (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);
+      }
+    }
+
+    if (MP_CMP(u, ==, MP_ZERO))
+      break;
+  }
+
+  /* --- Write the results out --- */
+
+  if (gcd)
+    *gcd = mp_lsl(v, v, shift);
+  else
+    MP_DROP(v);
+
+  /* --- Perform a little normalization --- *
+   *
+   * Ensure that the coefficient returned is positive, if there is only one.
+   * If there are two, favour @y@.
+   */
+
+  if (ext) {
+    if (swap) {
+      mp *t = x; x = y; y = t;
+    }
+    if (yy) {
+      if (y->f & MP_NEG) {
+	y = mp_add(y, y, a);
+	x = mp_sub(x, x, b);
+      }
+    } else if (x->f & MP_NEG)
+      x = mp_add(x, x, b);
+
+    if (xx) *xx = x; else MP_DROP(x);
+    if (yy) *yy = y; else MP_DROP(y);
+  }
+
+  MP_DROP(u);
+  MP_DROP(X); MP_DROP(Y);
+  MP_DROP(a); MP_DROP(b);
+}
+
+/*----- Test rig ----------------------------------------------------------*/
+
+#ifdef TEST_RIG
+
+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, *xx, *yy;
+  mp_gcd(&gg, &xx, &yy, a, b);
+  if (MP_CMP(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_CMP(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_CMP(ax, ==, gg))
+      fputs("\n*** (Alternative result found.)\n", stderr);
+    MP_DROP(ax);
+    MP_DROP(by);
+  }
+
+  if (MP_CMP(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);
+  return (ok);
+}
+
+static test_chunk tests[] = {
+  { "gcd", gcd, { &type_mp, &type_mp, &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 -------------------------------------------------*/