contrib/mpfr/factorial.c

   1 /* mpfr_fac_ui -- factorial of a non-negative integer
   2
   3 Copyright 2001, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
   4 Contributed by the Arenaire and Cacao projects, INRIA.
   5
   6 This file is part of the GNU MPFR Library.
   7
   8 The GNU MPFR Library is free software; you can redistribute it and/or modify
   9 it under the terms of the GNU Lesser General Public License as published by
  10 the Free Software Foundation; either version 2.1 of the License, or (at your
  11 option) any later version.
  12
  13 The GNU MPFR Library is distributed in the hope that it will be useful, but
  14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  15 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  16 License for more details.
  17
  18 You should have received a copy of the GNU Lesser General Public License
  19 along with the GNU MPFR Library; see the file COPYING.LIB.  If not, write to
  20 the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
  21 MA 02110-1301, USA. */
  22
  23 #define MPFR_NEED_LONGLONG_H
  24 #include "mpfr-impl.h"
  25
  26  /* The computation of n! is done by
  27
  28     n!=prod^{n}_{i=1}i
  29  */
  30
  31 /* FIXME: efficient problems with large arguments; see comments in gamma.c. */
  32
  33 int
  34 mpfr_fac_ui (mpfr_ptr y, unsigned long int x, mp_rnd_t rnd_mode)
  35 {
  36   mpfr_t t;       /* Variable of Intermediary Calculation*/
  37   unsigned long i;
  38   int round, inexact;
  39
  40   mp_prec_t Ny;   /* Precision of output variable */
  41   mp_prec_t Nt;   /* Precision of Intermediary Calculation variable */
  42   mp_prec_t err;  /* Precision of error */
  43
  44   mp_rnd_t rnd;
  45   MPFR_SAVE_EXPO_DECL (expo);
  46   MPFR_ZIV_DECL (loop);
  47
  48   /***** test x = 0  and x == 1******/
  49   if (MPFR_UNLIKELY (x <= 1))
  50     return mpfr_set_ui (y, 1, rnd_mode); /* 0! = 1 and 1! = 1 */
  51
  52   MPFR_SAVE_EXPO_MARK (expo);
  53
  54   /* Initialisation of the Precision */
  55   Ny = MPFR_PREC (y);
  56
  57   /* compute the size of intermediary variable */
  58   Nt = Ny + 2 * MPFR_INT_CEIL_LOG2 (x) + 7;
  59
  60   mpfr_init2 (t, Nt); /* initialise of intermediary variable */
  61
  62   rnd = GMP_RNDZ;
  63   MPFR_ZIV_INIT (loop, Nt);
  64   for (;;)
  65     {
  66       /* compute factorial */
  67       inexact = mpfr_set_ui (t, 1, rnd);
  68       for (i = 2 ; i <= x ; i++)
  69         {
  70           round = mpfr_mul_ui (t, t, i, rnd);
  71           /* assume the first inexact product gives the sign
  72              of difference: is that always correct? */
  73           if (inexact == 0)
  74             inexact = round;
  75         }
  76
  77       err = Nt - 1 - MPFR_INT_CEIL_LOG2 (Nt);
  78
  79       round = !inexact || mpfr_can_round (t, err, rnd, GMP_RNDZ,
  80                                           Ny + (rnd_mode == GMP_RNDN));
  81
  82       if (MPFR_LIKELY (round))
  83         {
  84           /* If inexact = 0, then t is exactly x!, so round is the
  85              correct inexact flag.
  86              Otherwise, t != x! since we rounded to zero or away. */
  87           round = mpfr_set (y, t, rnd_mode);
  88           if (inexact == 0)
  89             {
  90               inexact = round;
  91               break;
  92             }
  93           else if ((inexact < 0 && round <= 0)
  94                    || (inexact > 0 && round >= 0))
  95             break;
  96           else /* inexact and round have opposite signs: we cannot
  97                   compute the inexact flag. Restart using the
  98                   symmetric rounding. */
  99             rnd = (rnd == GMP_RNDZ) ? GMP_RNDU : GMP_RNDZ;
 100         }
 101       MPFR_ZIV_NEXT (loop, Nt);
 102       mpfr_set_prec (t, Nt);
 103     }
 104   MPFR_ZIV_FREE (loop);
 105
 106   mpfr_clear (t);
 107   MPFR_SAVE_EXPO_FREE (expo);
 108   return mpfr_check_range (y, inexact, rnd_mode);
 109 }
 110
 111
 112
 113