dist/tests/turandom.c

/* Test file for mpfr_urandom

Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2006, 2007, 2008, 2009, 2010, 2011 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao 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-test.h"

static void
test_urandom (long nbtests, mpfr_prec_t prec, mpfr_rnd_t rnd, long bit_index,
              int verbose)
{
  mpfr_t x;
  int *tab, size_tab, k, sh, xn;
  double d, av = 0, var = 0, chi2 = 0, th;
  mpfr_exp_t emin;
  mp_size_t limb_index = 0;
  mp_limb_t limb_mask = 0;
  long count = 0;
  int i;
  int inex = 1;

  size_tab = (nbtests >= 1000 ? nbtests / 50 : 20);
  tab = (int *) calloc (size_tab, sizeof(int));
  if (tab == NULL)
    {
      fprintf (stderr, "trandom: can't allocate memory in test_urandom\n");
      exit (1);
    }

  mpfr_init2 (x, prec);
  xn = 1 + (prec - 1) / mp_bits_per_limb;
  sh = xn * mp_bits_per_limb - prec;
  if (bit_index >= 0 && bit_index < prec)
    {
      /* compute the limb index and limb mask to fetch the bit #bit_index */
      limb_index = (prec - bit_index) / mp_bits_per_limb;
      i = 1 + bit_index - (bit_index / mp_bits_per_limb) * mp_bits_per_limb;
      limb_mask = MPFR_LIMB_ONE << (mp_bits_per_limb - i);
    }

  for (k = 0; k < nbtests; k++)
    {
      i = mpfr_urandom (x, RANDS, rnd);
      inex = (i != 0) && inex;
      /* check that lower bits are zero */
      if (MPFR_MANT(x)[0] & MPFR_LIMB_MASK(sh) && !MPFR_IS_ZERO (x))
        {
          printf ("Error: mpfr_urandom() returns invalid numbers:\n");
          mpfr_print_binary (x); puts ("");
          exit (1);
        }
      /* check that the value is in [0,1] */
      if (mpfr_cmp_ui (x, 0) < 0 || mpfr_cmp_ui (x, 1) > 0)
        {
          printf ("Error: mpfr_urandom() returns number outside [0, 1]:\n");
          mpfr_print_binary (x); puts ("");
          exit (1);
        }

      d = mpfr_get_d1 (x); av += d; var += d*d;
      i = (int)(size_tab * d);
      if (d == 1.0) i --;
      tab[i]++;

      if (limb_mask && (MPFR_MANT (x)[limb_index] & limb_mask))
        count ++;
    }

  if (inex == 0)
    {
      /* one call in the loop pretended to return an exact number! */
      printf ("Error: mpfr_urandom() returns a zero ternary value.\n");
      exit (1);
    }

  /* coverage test */
  emin = mpfr_get_emin ();
  for (k = 0; k < 5; k++)
    {
      set_emin (k+1);
      inex = mpfr_urandom (x, RANDS, rnd);
      if ((   (rnd == MPFR_RNDZ || rnd == MPFR_RNDD)
              && (!MPFR_IS_ZERO (x) || inex != -1))
          || ((rnd == MPFR_RNDU || rnd == MPFR_RNDA)
              && (mpfr_cmp_ui (x, 1 << k) != 0 || inex != +1))
          || (rnd == MPFR_RNDN
              && (k > 0 || mpfr_cmp_ui (x, 1 << k) != 0 || inex != +1)
              && (!MPFR_IS_ZERO (x) || inex != -1)))
        {
          printf ("Error: mpfr_urandom() do not handle correctly a restricted"
                  " exponent range.\nrounding mode: %s\nternary value: %d\n"
                  "random value: ", mpfr_print_rnd_mode (rnd), inex);
          mpfr_print_binary (x); puts ("");
          exit (1);
        }
    }
  set_emin (emin);

  mpfr_clear (x);
  if (!verbose)
    {
      free(tab);
      return;
    }

  av /= nbtests;
  var = (var / nbtests) - av * av;

  th = (double)nbtests / size_tab;
  printf ("Average = %.5f\nVariance = %.5f\n", av, var);
  printf ("Repartition for urandom with rounding mode %s. "
          "Each integer should be close to %d.\n",
         mpfr_print_rnd_mode (rnd), (int)th);

  for (k = 0; k < size_tab; k++)
    {
      chi2 += (tab[k] - th) * (tab[k] - th) / th;
      printf("%d ", tab[k]);
      if (((k+1) & 7) == 0)
        printf("\n");
    }

  printf("\nChi2 statistics value (with %d degrees of freedom) : %.5f\n",
         size_tab - 1, chi2);

  if (limb_mask)
    printf ("Bit #%ld is set %ld/%ld = %.1f %% of time\n",
            bit_index, count, nbtests, count * 100.0 / nbtests);

  puts ("");

  free(tab);
  return;
}


int
main (int argc, char *argv[])
{
  long nbtests;
  mpfr_prec_t prec;
  int verbose = 0;
  int rnd;
  long bit_index;

  tests_start_mpfr ();

  if (argc > 1)
    verbose = 1;

  nbtests = 10000;
  if (argc > 1)
    {
      long a = atol(argv[1]);
      if (a != 0)
        nbtests = a;
    }

  if (argc <= 2)
    prec = 1000;
  else
    prec = atol(argv[2]);

  if (argc <= 3)
    bit_index = -1;
  else
    {
      bit_index = atol(argv[3]);
      if (bit_index >= prec)
        {
          printf ("Warning. Cannot compute the bit frequency: the given bit "
                  "index (= %ld) is not less than the precision (= %ld).\n",
                  bit_index, prec);
          bit_index = -1;
        }
    }

  RND_LOOP(rnd)
    {
      test_urandom (nbtests, prec, (mpfr_rnd_t) rnd, bit_index, verbose);

      if (argc == 1)  /* check also small precision */
        {
          test_urandom (nbtests, 2, (mpfr_rnd_t) rnd, -1, 0);
        }
    }

  tests_end_mpfr ();
  return 0;
}