New function and example program computes Fibonacci numbers fairly fast.

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

/* -*-c-*-
 *
 * $Id$
 *
 * Compute integer square roots
 *
 * (c) 2000 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.
 */

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

#include "mp.h"

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

/* --- @mp_sqrt@ --- *
 *
 * Arguments:	@mp *d@ = pointer to destination integer
 *		@mp *a@ = (nonnegative) integer to take square root of
 *
 * Returns:	The largest integer %$x$% such that %$x^2 \le a$%.
 *
 * Use:		Computes integer square roots.
 *
 *		The current implementation isn't very good: it uses the
 *		Newton-Raphson method to find an approximation to %$a$%.  If
 *		there's any demand for a better version, I'll write one.
 */

mp *mp_sqrt(mp *d, mp *a)
{
  unsigned long z;
  mp *q = MP_NEW, *r = MP_NEW;

  /* --- Sanity preservation --- */

  assert(!MP_NEGP(a));

  /* --- Deal with trivial cases --- */

  MP_SHRINK(a);
  if (MP_ZEROP(a)) {
    mp_drop(d);
    return (MP_ZERO);
  }

  /* --- Find an initial guess of about the right size --- */

  z = mp_bits(a);
  z >>= 1;
  mp_copy(a);
  d = mp_lsr(d, a, z);

  /* --- Main approximation --- *
   *
   * We use the Newton-Raphson recurrence relation
   *
   *   %$x_{i+1} = x_i - \frac{x_i^2 - a}{2 x_i}$%
   *
   * We inspect the term %$q = x^2 - a$% to see when to stop.  Increasing
   * %$x$% is pointless when %$-q < 2 x + 1$%.
   */

  for (;;) {
    q = mp_sqr(q, d);
    q = mp_sub(q, q, a);
    if (MP_ZEROP(q))
      break;
    if (MP_NEGP(q)) {
      r = mp_lsl(r, d, 1);
      r->f |= MP_NEG;
      if (MP_CMP(q, >=, r))
	break;
    }
    mp_div(&r, &q, q, d);
    r = mp_lsr(r, r, 1);
    if (r->v == r->vl)
      d = mp_sub(d, d, MP_ONE);
    else
      d = mp_sub(d, d, r);
  }

  /* --- Finished, at last --- */

  mp_drop(a);
  mp_drop(q);
  mp_drop(r);
  return (d);
}

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

#ifdef TEST_RIG

#include <mLib/testrig.h>

static int verify(dstr *v)
{
  mp *a = *(mp **)v[0].buf;
  mp *qq = *(mp **)v[1].buf;
  mp *q = mp_sqrt(MP_NEW, a);
  int ok = 1;

  if (!MP_EQ(q, qq)) {
    ok = 0;
    fputs("\n*** sqrt failed", stderr);
    fputs("\n*** a	= ", stderr); mp_writefile(a, stderr, 10);
    fputs("\n*** result = ", stderr); mp_writefile(q, stderr, 10);
    fputs("\n*** expect = ", stderr); mp_writefile(qq, stderr, 10);
    fputc('\n', stderr);
  }

  mp_drop(a);
  mp_drop(q);
  mp_drop(qq);
  assert(mparena_count(MPARENA_GLOBAL) == 0);

  return (ok);
}

static test_chunk tests[] = {
  { "sqrt", verify, { &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 -------------------------------------------------*/