1 files changed, 113 insertions, 0 deletions
diff --git a/src/factorial.c b/src/factorial.c
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+/* mpfr_fac_ui -- factorial of a non-negative integer
+
+Copyright 2001, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc.
+Contributed by the Arenaire and Caramel 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
+http://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); /* initialise 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, rnd, MPFR_RNDZ,
+                                          Ny + (rnd_mode == MPFR_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 == 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);
+}
+
+
+
+