efee5258bc
The MPFR library is a C library for multiple-precision floating-point computations with exact rounding (also called correct rounding). It is based on the GMP multiple-precision library and should replace the MPF class in further releases of GMP. GCC >= 4.2 requires MPFR.
114 lines
3.5 KiB
C
114 lines
3.5 KiB
C
/* mpfr_fac_ui -- factorial of a non-negative integer
|
|
|
|
Copyright 2001, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011 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 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);
|
|
}
|
|
|
|
|
|
|
|
|