share/doc/mpfr/examples/divworst.c

/* Test of the double rounding effect.
 *
 * This example was presented at the CNC'2 summer school on MPFR and MPC
 * at LORIA, Nancy, France.
 *
 * Arguments: max difference of exponents dmax, significand size n.
 * Optional argument: extended precision p (with double rounding).
 *
 * Return all the couples of positive machine numbers (x,y) such that
 * 1/2 <= y < 1, 0 <= Ex - Ey <= dmax, x - y is exactly representable
 * in precision n and the results of floor(x/y) in the rounding modes
 * toward 0 and to nearest are different.
 */

/*
Copyright 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc.
Contributed by the AriC and Caramel projects, INRIA.

This file is part of the GNU MPFR Library.

The GNU MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

The GNU MPFR Library 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 Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.
*/

#include <stdio.h>
#include <stdlib.h>
#include <mpfr.h>

#define PRECN x, y, z
#define VARS PRECN, t

static unsigned long
eval (mpfr_t x, mpfr_t y, mpfr_t z, mpfr_t t, mpfr_rnd_t rnd)
{
  mpfr_div (t, x, y, rnd);  /* the division x/y in precision p */
  mpfr_set (z, t, rnd);     /* the rounding to the precision n */
  mpfr_rint_floor (z, z, rnd);
  return mpfr_get_ui (z, rnd);
}

int main (int argc, char *argv[])
{
  int dmax, n, p;
  mpfr_t VARS;

  if (argc != 3 && argc != 4)
    {
      fprintf (stderr, "Usage: divworst <dmax> <n> [ <p> ]\n");
      exit (EXIT_FAILURE);
    }

  dmax = atoi (argv[1]);
  n = atoi (argv[2]);
  p = argc == 3 ? n : atoi (argv[3]);
  if (p < n)
    {
      fprintf (stderr, "divworst: p must be greater or equal to n\n");
      exit (EXIT_FAILURE);
    }

  mpfr_inits2 (n, PRECN, (mpfr_ptr) 0);
  mpfr_init2 (t, p);

  for (mpfr_set_ui_2exp (x, 1, -1, MPFR_RNDN);
       mpfr_get_exp (x) <= dmax;
       mpfr_nextabove (x))
    for (mpfr_set_ui_2exp (y, 1, -1, MPFR_RNDN);
         mpfr_get_exp (y) == 0;
         mpfr_nextabove (y))
      {
        unsigned long rz, rn;

        if (mpfr_sub (z, x, y, MPFR_RNDZ) != 0)
          continue;  /* x - y is not representable in precision n */
        rz = eval (x, y, z, t, MPFR_RNDZ);
        rn = eval (x, y, z, t, MPFR_RNDN);
        if (rz == rn)
          continue;
        mpfr_printf ("x = %.*Rb ; y = %.*Rb ; Z: %lu ; N: %lu\n",
                     n - 1, x, n - 1, y, rz, rn);
      }

  mpfr_clears (VARS, (mpfr_ptr) 0);
  return 0;
}