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/* mpfr_fac_ui -- factorial of a non-negative integer
Copyright 2001, 2004 Free Software Foundation, Inc.
This file is part of the MPFR Library.
The 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 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 MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"
/* The computation of n! is done by
n!=prod^{n}_{i=1}i
*/
int
mpfr_fac_ui (mpfr_ptr y, unsigned long int x, mp_rnd_t rnd_mode)
{
/****** Declaration ******/
mpfr_t t; /* Variable of Intermediary Calculation*/
unsigned long i;
int round, inexact = 0;
int loop = 1;
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;
/***** test x = 0 ******/
if (x == 0)
{
return mpfr_set_ui (y, 1, GMP_RNDN); /* 0! = 1 */
}
else
{
/* 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;
while (loop)
{
inexact = mpfr_set_ui (t, 1, rnd);
for (i=2; i<=x; i++) /* compute factorial */
{
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 (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;
loop = 0;
}
else if ((inexact < 0 && round <= 0) ||
(inexact > 0 && round >= 0))
{
loop = 0;
}
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;
Nt = Nt + 10;
/*initialise of intermediary variable */
mpfr_set_prec (t, Nt);
}
}
else
{
Nt = Nt + 10;
/*initialise of intermediary variable */
mpfr_set_prec (t, Nt);
}
}
mpfr_clear (t);
return inexact;
}
}
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