/* Test file for mpfr_factorial.

Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao projects, INRIA.

This file is part of the MPFR Library.

The 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 2.1 of the License, or (at your
option) any later version.

The 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 MPFR Library; see the file COPYING.LIB.  If not, 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"

#define TEST_FUNCTION mpfr_fac_ui

static void
special (void)
{
  mpfr_t x, y;
  int inex;

  mpfr_init (x);
  mpfr_init (y);

  mpfr_set_prec (x, 21);
  mpfr_set_prec (y, 21);
  mpfr_fac_ui (x, 119, GMP_RNDZ);
  mpfr_set_str_binary (y, "0.101111101110100110110E654");
  if (mpfr_cmp (x, y))
    {
      printf ("Error in mpfr_fac_ui (119)\n");
      exit (1);
    }

  mpfr_set_prec (y, 206);
  inex = mpfr_fac_ui (y, 767, GMP_RNDN);
  mpfr_set_prec (x, 206);
  mpfr_set_str_binary (x, "0.110111100001000001101010010001000111000100000100111000010011100011011111001100011110101000111101101100110001001100110100001001111110000101010000100100011100010011101110000001000010001100010000101001111E6250");
  if (mpfr_cmp (x, y))
    {
      printf ("Error in mpfr_fac_ui (767)\n");
      exit (1);
    }
  if (inex <= 0)
    {
      printf ("Wrong flag for mpfr_fac_ui (767)\n");
      exit (1);
    }

  mpfr_set_prec (y, 202);
  mpfr_fac_ui (y, 69, GMP_RNDU);

  mpfr_clear (x);
  mpfr_clear (y);
}

static void
test_int (void)
{
  unsigned long n0 = 1, n1 = 80, n;
  mpz_t f;
  mpfr_t x, y;
  mp_prec_t prec_f, p;
  int r;
  int inex1, inex2;

  mpz_init (f);
  mpfr_init (x);
  mpfr_init (y);

  mpz_fac_ui (f, n0 - 1);
  for (n = n0; n <= n1; n++)
    {
      mpz_mul_ui (f, f, n); /* f = n! */
      prec_f = mpz_sizeinbase (f, 2) - mpz_scan1 (f, 0);
      for (p = MPFR_PREC_MIN; p <= prec_f; p++)
        {
          mpfr_set_prec (x, p);
          mpfr_set_prec (y, p);
          for (r = 0; r < GMP_RND_MAX; r++)
            {
              inex1 = mpfr_fac_ui (x, n, (mp_rnd_t) r);
              inex2 = mpfr_set_z (y, f, (mp_rnd_t) r);
              if (mpfr_cmp (x, y))
                {
                  printf ("Error for n=%lu prec=%lu rnd=%s\n",
                          n, (unsigned long) p, mpfr_print_rnd_mode ((mp_rnd_t) r));
                  exit (1);
                }
              if ((inex1 < 0 && inex2 >= 0) || (inex1 == 0 && inex2 != 0)
                  || (inex1 > 0 && inex2 <= 0))
                {
                  printf ("Wrong inexact flag for n=%lu prec=%lu rnd=%s\n",
                          n, (unsigned long) p, mpfr_print_rnd_mode ((mp_rnd_t) r));
                  exit (1);
                }
            }
        }
    }

  mpz_clear (f);
  mpfr_clear (x);
  mpfr_clear (y);
}

static void
overflowed_fac0 (void)
{
  mpfr_t x, y;
  int inex, rnd, err = 0;
  mp_exp_t old_emax;

  old_emax = mpfr_get_emax ();

  mpfr_init2 (x, 8);
  mpfr_init2 (y, 8);

  mpfr_set_ui (y, 1, GMP_RNDN);
  mpfr_nextbelow (y);
  set_emax (0);  /* 1 is not representable. */
  RND_LOOP (rnd)
    {
      mpfr_clear_flags ();
      inex = mpfr_fac_ui (x, 0, rnd);
      if (! mpfr_overflow_p ())
        {
          printf ("Error in overflowed_fac0 (rnd = %s):\n"
                  "  The overflow flag is not set.\n",
                  mpfr_print_rnd_mode (rnd));
          err = 1;
        }
      if (rnd == GMP_RNDZ || rnd == GMP_RNDD)
        {
          if (inex >= 0)
            {
              printf ("Error in overflowed_fac0 (rnd = %s):\n"
                      "  The inexact value must be negative.\n",
                      mpfr_print_rnd_mode (rnd));
              err = 1;
            }
          if (! mpfr_equal_p (x, y))
            {
              printf ("Error in overflowed_fac0 (rnd = %s):\n"
                      "  Got ", mpfr_print_rnd_mode (rnd));
              mpfr_print_binary (x);
              printf (" instead of 0.11111111E0.\n");
              err = 1;
            }
        }
      else
        {
          if (inex <= 0)
            {
              printf ("Error in overflowed_fac0 (rnd = %s):\n"
                      "  The inexact value must be positive.\n",
                      mpfr_print_rnd_mode (rnd));
              err = 1;
            }
          if (! (mpfr_inf_p (x) && MPFR_SIGN (x) > 0))
            {
              printf ("Error in overflowed_fac0 (rnd = %s):\n"
                      "  Got ", mpfr_print_rnd_mode (rnd));
              mpfr_print_binary (x);
              printf (" instead of +Inf.\n");
              err = 1;
            }
        }
    }
  set_emax (old_emax);

  if (err)
    exit (1);
  mpfr_clear (x);
  mpfr_clear (y);
}

int
main (int argc, char *argv[])
{
  unsigned int prec, err, yprec, n, k, zeros;
  int rnd;
  mpfr_t x, y, z, t;
  int inexact;

  tests_start_mpfr ();

  special ();

  test_int ();

  mpfr_init (x);
  mpfr_init (y);
  mpfr_init (z);
  mpfr_init (t);

  mpfr_fac_ui (y, 0, GMP_RNDN);

  if (mpfr_cmp_ui (y, 1))
    {
      printf ("mpfr_fac_ui(0) does not give 1\n");
      exit (1);
    }

  for (prec = 2; prec <= 100; prec++)
    {
      mpfr_set_prec (x, prec);
      mpfr_set_prec (z, prec);
      mpfr_set_prec (t, prec);
      yprec = prec + 10;
      mpfr_set_prec (y, yprec);

      for (n = 0; n < 50; n++)
        for (rnd = 0; rnd < GMP_RND_MAX; rnd++)
          {
            inexact = mpfr_fac_ui (y, n, (mp_rnd_t) rnd);
            err = (rnd == GMP_RNDN) ? yprec + 1 : yprec;
            if (mpfr_can_round (y, err, (mp_rnd_t) rnd, (mp_rnd_t) rnd, prec))
              {
                mpfr_set (t, y, (mp_rnd_t) rnd);
                inexact = mpfr_fac_ui (z, n, (mp_rnd_t) rnd);
                /* fact(n) ends with floor(n/2)+floor(n/4)+... zeros */
                for (k=n/2, zeros=0; k; k >>= 1)
                  zeros += k;
                if (MPFR_EXP(y) <= (mp_exp_t) (prec + zeros))
                  /* result should be exact */
                  {
                    if (inexact)
                      {
                        printf ("Wrong inexact flag: expected exact\n");
                        exit (1);
                      }
                  }
                else /* result is inexact */
                  {
                    if (!inexact)
                      {
                        printf ("Wrong inexact flag: expected inexact\n");
                        printf ("n=%u prec=%u\n", n, prec);
                        mpfr_print_binary(z); puts ("");
                        exit (1);
                      }
                  }
                if (mpfr_cmp (t, z))
                  {
                    printf ("results differ for x=");
                    mpfr_out_str (stdout, 2, prec, x, GMP_RNDN);
                    printf (" prec=%u rnd_mode=%s\n", prec,
                            mpfr_print_rnd_mode ((mp_rnd_t) rnd));
                    printf ("   got ");
                    mpfr_out_str (stdout, 2, prec, z, GMP_RNDN);
                    puts ("");
                    printf ("   expected ");
                    mpfr_out_str (stdout, 2, prec, t, GMP_RNDN);
                    puts ("");
                    printf ("   approximation was ");
                    mpfr_print_binary (y);
                    puts ("");
                    exit (1);
                  }
              }
          }
    }

  mpfr_clear (x);
  mpfr_clear (y);
  mpfr_clear (z);
  mpfr_clear (t);

  overflowed_fac0 ();

  tests_end_mpfr ();
  return 0;
}
