/* mpfr_fac_ui -- factorial of a non-negative integer

Copyright 2001, 2004-2023 Free Software Foundation, Inc.
Contributed by the AriC and Caramba 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
https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */

#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"

 /* The computation of n! is done by

    n!=prod^{n}_{i=1}i
 */

/* FIXME: efficient problems with large arguments; see comments in gamma.c. */

int
mpfr_fac_ui (mpfr_ptr y, unsigned long int x, mpfr_rnd_t rnd_mode)
{
  mpfr_t t;       /* Variable of Intermediary Calculation*/
  unsigned long i;
  int round, inexact;

  mpfr_prec_t Ny;   /* Precision of output variable */
  mpfr_prec_t Nt;   /* Precision of Intermediary Calculation variable */
  mpfr_prec_t err;  /* Precision of error */

  mpfr_rnd_t rnd;
  MPFR_SAVE_EXPO_DECL (expo);
  MPFR_ZIV_DECL (loop);

  /***** test x = 0  and x == 1******/
  if (MPFR_UNLIKELY (x <= 1))
    return mpfr_set_ui (y, 1, rnd_mode); /* 0! = 1 and 1! = 1 */

  MPFR_SAVE_EXPO_MARK (expo);

  /* Initialisation of the Precision */
  Ny = MPFR_PREC (y);

  /* compute the size of intermediary variable */
  Nt = Ny + 2 * MPFR_INT_CEIL_LOG2 (x) + 7;

  mpfr_init2 (t, Nt); /* initialize of intermediary variable */

  rnd = MPFR_RNDZ;
  MPFR_ZIV_INIT (loop, Nt);
  for (;;)
    {
      /* compute factorial */
      inexact = mpfr_set_ui (t, 1, rnd);
      for (i = 2 ; i <= x ; i++)
        {
          round = mpfr_mul_ui (t, t, i, rnd);
          /* assume the first inexact product gives the sign
             of difference: is that always correct? */
          if (inexact == 0)
            inexact = round;
        }

      err = Nt - 1 - MPFR_INT_CEIL_LOG2 (Nt);

      round = !inexact || MPFR_CAN_ROUND (t, err, Ny, rnd_mode);

      if (MPFR_LIKELY (round))
        {
          /* If inexact = 0, then t is exactly x!, so round is the
             correct inexact flag.
             Otherwise, t != x! since we rounded to zero or away. */
          round = mpfr_set (y, t, rnd_mode);
          if (inexact == 0)
            {
              inexact = round;
              break;
            }
          else if ((inexact < 0 && round <= 0)
                   || (inexact > 0 && round >= 0))
            break;
          else /* inexact and round have opposite signs: we cannot
                  compute the inexact flag. Restart using the
                  symmetric rounding. */
            rnd = (rnd == MPFR_RNDZ) ? MPFR_RNDU : MPFR_RNDZ;
        }
      MPFR_ZIV_NEXT (loop, Nt);
      mpfr_set_prec (t, Nt);
    }
  MPFR_ZIV_FREE (loop);

  mpfr_clear (t);
  MPFR_SAVE_EXPO_FREE (expo);
  return mpfr_check_range (y, inexact, rnd_mode);
}




