Pollard's rho algorithm for computing discrete logs.

[u/mdw/catacomb] / mp-gcd.c

/* -*-c-*-
 *
 * $Id: mp-gcd.c,v 1.4 2000/06/17 11:34:46 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 1.4  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"

/*----- 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.
 */

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;
  unsigned f = 0;

  enum {
    f_swap = 1u,
    f_aneg = 2u,
    f_bneg = 4u,
    f_ext = 8u
  };

  /* --- Sort out some initial flags --- */

  if (xx || yy)
    f |= f_ext;

  if (a->f & MP_NEG)
    f |= f_aneg;
  if (b->f & MP_NEG)
    f |= f_bneg;

  /* --- Ensure that @a@ is larger than @b@ --- *
   *
   * Use absolute values here!
   */

  if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
    { mp *t = a; a = b; b = t; }
    f |= f_swap;
  }

  /* --- Check for zeroness --- */

  if (MP_CMP(b, ==, MP_ZERO)) {

    /* --- Store %$|a|$% as the GCD --- */

    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;
    }

    /* --- Store %$1$% and %$0$% in the appropriate bins --- */

    if (f & f_ext) {
      if (f & f_swap) {
	mp **t = xx; xx = yy; yy = t;
      }
      if (xx) {
	if (*xx) MP_DROP(*xx);
	if (MP_CMP(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;
  }

  /* --- Take a reference to the arguments --- */

  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 --- */

    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);
      }
    }

    if (MP_CMP(u, ==, MP_ZERO))
      break;
  }

  /* --- Write the results out --- */

  if (!gcd)
    MP_DROP(v);
  else {
    if (*gcd) MP_DROP(*gcd);
    *gcd = mp_lsl(v, v, shift);
  }

  /* --- Perform a little normalization --- *
   *
   * Ensure that the coefficient returned is positive, if there is only one.
   * 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 (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) {
	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);
      }
    }

    /* --- Twiddle the signs --- */

    if (f & f_aneg)
      x->f ^= MP_NEG;
    if (f & f_bneg)
      y->f ^= MP_NEG;

    /* --- Store the results --- */

    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(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 = MP_NEW, *xx = MP_NEW, *yy = MP_NEW;
  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);
  assert(mparena_count(MPARENA_GLOBAL) == 0);
  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 -------------------------------------------------*/