--- /dev/null
+/* mpfr_fac_ui -- factorial of a non-negative integer
+
+Copyright 2001, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
+Contributed by the Arenaire and Cacao 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 2.1 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.LIB. If not, 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, 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, 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 = 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);
+}
+
+
+
+