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

Copyright 2001, 2004, 2005 Free Software Foundation, Inc.

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., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */

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

 /* The computation of n! is done by

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

int
mpfr_fac_ui (mpfr_ptr y, unsigned long int x, mp_rnd_t rnd_mode) 
{
  mpfr_t t;       /* Variable of Intermediary Calculation*/
  unsigned long i;
  int round, inexact;
  
  mp_prec_t Ny;   /* Precision of output variable */
  mp_prec_t Nt;   /* Precision of Intermediary Calculation variable */
  mp_prec_t err;  /* Precision of error */
  
  mp_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, GMP_RNDN); /* 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); /* initialise of intermediary variable */
  
  rnd = GMP_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, rnd, GMP_RNDZ,
					  Ny + (rnd_mode == GMP_RNDN));
      
      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 == GMP_RNDZ) ? GMP_RNDU : GMP_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);
}