Pollard's rho algorithm for computing discrete logs.

[u/mdw/catacomb] / mpx-kmul.c

/* -*-c-*-
 *
 * $Id: mpx-kmul.c,v 1.4 2000/06/17 11:42:11 mdw Exp $
 *
 * Karatsuba's multiplication algorithm
 *
 * (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: mpx-kmul.c,v $
 * Revision 1.4  2000/06/17 11:42:11  mdw
 * Moved the Karatsuba macros into a separate file for better sharing.
 * Fixed some comments.
 *
 * Revision 1.3  1999/12/13 15:35:01  mdw
 * Simplify and improve.
 *
 * Revision 1.2  1999/12/11 10:58:02  mdw
 * Remove tweakable comments.
 *
 * Revision 1.1  1999/12/10 23:23:51  mdw
 * Karatsuba-Ofman multiplication algorithm.
 *
 */

/*----- Header files ------------------------------------------------------*/

#include <assert.h>
#include <stdio.h>

#include "mpx.h"
#include "mpx-kmac.h"

/*----- Tweakables --------------------------------------------------------*/

#ifdef TEST_RIG
#  undef KARATSUBA_CUTOFF
#  define KARATSUBA_CUTOFF 2
#endif

/*----- Main code ---------------------------------------------------------*/

/* --- @mpx_kmul@ --- *
 *
 * Arguments:	@mpw *dv, *dvl@ = pointer to destination buffer
 *		@const mpw *av, *avl@ = pointer to first argument
 *		@const mpw *bv, *bvl@ = pointer to second argument
 *		@mpw *sv, *svl@ = pointer to scratch workspace
 *
 * Returns:	---
 *
 * Use:		Multiplies two multiprecision integers using Karatsuba's
 *		algorithm.  This is rather faster than traditional long
 *		multiplication (e.g., @mpx_umul@) on large numbers, although
 *		more expensive on small ones.
 *
 *		The destination must be twice as large as the larger
 *		argument.  The scratch space must be twice as large as the
 *		larger argument, plus the magic number @KARATSUBA_SLOP@.
 */

void mpx_kmul(mpw *dv, mpw *dvl,
	      const mpw *av, const mpw *avl,
	      const mpw *bv, const mpw *bvl,
	      mpw *sv, mpw *svl)
{
  const mpw *avm, *bvm;
  size_t m;

  /* --- Dispose of easy cases to @mpx_umul@ --- *
   *
   * Karatsuba is only a win on large numbers, because of all the
   * recursiveness and bookkeeping.  The recursive calls make a quick check
   * to see whether to bottom out to @mpx_umul@ which should help quite a
   * lot, but sometimes the only way to know is to make sure...
   */

  MPX_SHRINK(av, avl);
  MPX_SHRINK(bv, bvl);

  if (avl - av <= KARATSUBA_CUTOFF || bvl - bv <= KARATSUBA_CUTOFF) {
    mpx_umul(dv, dvl, av, avl, bv, bvl);
    return;
  }

  /* --- How the algorithm works --- *
   *
   * Let %$A = xb + y$% and %$B = ub + v$%.  Then, simply by expanding,
   * %$AB = x u b^2 + b(x v + y u) + y v$%.  That's not helped any, because
   * I've got four multiplications, each four times easier than the one I
   * started with.  However, note that I can rewrite the coefficient of %$b$%
   * as %$xv + yu = (x + y)(u + v) - xu - yv$%.  The terms %$xu$% and %$yv$%
   * I've already calculated, and that leaves only one more multiplication to
   * do.  So now I have three multiplications, each four times easier, and
   * that's a win.
   */

  /* --- First things --- *
   *
   * Sort out where to break the factors in half.  I'll choose the midpoint
   * of the largest one, since this minimizes the amount of work I have to do
   * most effectively.
   */

  if (avl - av > bvl - bv) {
    m = (avl - av + 1) >> 1;
    avm = av + m;
    if (bvl - bv > m)
      bvm = bv + m;
    else
      bvm = bvl;
  } else {
    m = (bvl - bv + 1) >> 1;
    bvm = bv + m;
    if (avl - av > m)
      avm = av + m;
    else
      avm = avl;
  }

  assert(((void)"Destination too small for Karatsuba multiply",
	  dvl - dv >= 4 * m));
  assert(((void)"Not enough workspace for Karatsuba multiply",
	  svl - sv >= 4 * m));

  /* --- Sort out the middle term --- */

  {
    mpw *bsv = sv + m + 1, *ssv = bsv + m + 1;
    mpw *rdv = dv + m, *rdvl = rdv + 2 * (m + 2);

    UADD2(sv, bsv, av, avm, avm, avl);
    UADD2(bsv, ssv, bv, bvm, bvm, bvl);
    if (m > KARATSUBA_CUTOFF)
      mpx_kmul(rdv, rdvl, sv, bsv, bsv, ssv, ssv, svl);
    else
      mpx_umul(rdv, rdvl, sv, bsv, bsv, ssv);
  }

  /* --- Sort out the other two terms --- */

  {
    mpw *svm = sv + m, *svn = svm + m, *ssv = svn + 4;
    mpw *tdv = dv + m;
    mpw *rdv = tdv + m;

    if (avl == avm || bvl == bvm)
      MPX_ZERO(rdv + m + 1, dvl);
    else {
      if (m > KARATSUBA_CUTOFF)
	mpx_kmul(sv, ssv, avm, avl, bvm, bvl, ssv, svl);
      else
	mpx_umul(sv, ssv, avm, avl, bvm, bvl);
      MPX_COPY(rdv + m + 1, dvl, svm + 1, svn);
      UADD(rdv, sv, svm + 1);
      USUB(tdv, sv, svn);
    }

    if (m > KARATSUBA_CUTOFF)
      mpx_kmul(sv, ssv, av, avm, bv, bvm, ssv, svl);
    else
      mpx_umul(sv, ssv, av, avm, bv, bvm);
    MPX_COPY(dv, tdv, sv, svm);
    USUB(tdv, sv, svn);
    UADD(tdv, svm, svn);
  }
}

/*----- Test rig ----------------------------------------------------------*/

#ifdef TEST_RIG

#include <mLib/alloc.h>
#include <mLib/testrig.h>

#include "mpscan.h"

#define ALLOC(v, vl, sz) do {                                           \
  size_t _sz = (sz);                                                    \
  mpw *_vv = xmalloc(MPWS(_sz));                                        \
  mpw *_vvl = _vv + _sz;                                                \
  (v) = _vv;                                                            \
  (vl) = _vvl;                                                          \
} while (0)

#define LOAD(v, vl, d) do {                                             \
  const dstr *_d = (d);                                                 \
  mpw *_v, *_vl;                                                        \
  ALLOC(_v, _vl, MPW_RQ(_d->len));                                      \
  mpx_loadb(_v, _vl, _d->buf, _d->len);                                 \
  (v) = _v;                                                             \
  (vl) = _vl;                                                           \
} while (0)

#define MAX(x, y) ((x) > (y) ? (x) : (y))

static void dumpmp(const char *msg, const mpw *v, const mpw *vl)
{
  fputs(msg, stderr);
  MPX_SHRINK(v, vl);
  while (v < vl)
    fprintf(stderr, " %08lx", (unsigned long)*--vl);
  fputc('\n', stderr);
}

static int umul(dstr *v)
{
  mpw *a, *al;
  mpw *b, *bl;
  mpw *c, *cl;
  mpw *d, *dl;
  mpw *s, *sl;
  size_t m;
  int ok = 1;

  LOAD(a, al, &v[0]);
  LOAD(b, bl, &v[1]);
  LOAD(c, cl, &v[2]);
  m = MAX(al - a, bl - b) + 1;
  ALLOC(d, dl, 2 * m);
  ALLOC(s, sl, 2 * m + 32);

  mpx_kmul(d, dl, a, al, b, bl, s, sl);
  if (MPX_UCMP(d, dl, !=, c, cl)) {
    fprintf(stderr, "\n*** umul failed\n");
    dumpmp("       a", a, al);
    dumpmp("       b", b, bl);
    dumpmp("expected", c, cl);
    dumpmp("  result", d, dl);
    ok = 0;
  }

  free(a); free(b); free(c); free(d); free(s);
  return (ok);
}

static test_chunk defs[] = {
  { "umul", umul, { &type_hex, &type_hex, &type_hex, 0 } },
  { 0, 0, { 0 } }
};

int main(int argc, char *argv[])
{
  test_run(argc, argv, defs, SRCDIR"/tests/mpx");
  return (0);
}

#endif

/*----- That's all, folks -------------------------------------------------*/