1/* mpfr_fac_ui -- factorial of a non-negative integer
2
3Copyright 2001, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc.
4Contributed by the AriC and Caramel projects, INRIA.
5
6This file is part of the GNU MPFR Library.
7
8The GNU MPFR Library is free software; you can redistribute it and/or modify
9it under the terms of the GNU Lesser General Public License as published by
10the Free Software Foundation; either version 3 of the License, or (at your
11option) any later version.
12
13The GNU MPFR Library is distributed in the hope that it will be useful, but
14WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
15or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
16License for more details.
17
18You should have received a copy of the GNU Lesser General Public License
19along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
20http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
2151 Franklin St, Fifth Floor, Boston, 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
33int
34mpfr_fac_ui (mpfr_ptr y, unsigned long int x, mpfr_rnd_t rnd_mode)
35{
36  mpfr_t t;       /* Variable of Intermediary Calculation*/
37  unsigned long i;
38  int round, inexact;
39
40  mpfr_prec_t Ny;   /* Precision of output variable */
41  mpfr_prec_t Nt;   /* Precision of Intermediary Calculation variable */
42  mpfr_prec_t err;  /* Precision of error */
43
44  mpfr_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 = MPFR_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, MPFR_RNDZ,
80                                          Ny + (rnd_mode == MPFR_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 == MPFR_RNDZ) ? MPFR_RNDU : MPFR_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
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