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/* mpfr_expm1 -- Compute exp(x)-1
Copyright (C) 2001 Free Software Foundation.
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. */
#include <stdio.h>
#include <math.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* The computation of expm1 is done by
expm1(x)=exp(x)-1
*/
int
mpfr_expm1 (mpfr_ptr y, mpfr_srcptr x , mp_rnd_t rnd_mode)
{
int inexact = 0;
if (MPFR_IS_NAN(x))
{
MPFR_SET_NAN(y);
return 1;
}
MPFR_CLEAR_NAN(y);
/* check for inf or -inf (expm1(-inf)=-1) */
if (MPFR_IS_INF(x))
{
if(MPFR_SIGN(x) > 0)
{
MPFR_SET_INF(y);
MPFR_SET_SAME_SIGN(y,x);
return 0;
}
else
return mpfr_set_ui(y,-1,rnd_mode);
}
MPFR_CLEAR_INF(y);
if(!MPFR_NOTZERO(x))
{
MPFR_SET_ZERO(y); /* expm1(+/- 0) = +/- 0 */
MPFR_SET_SAME_SIGN(y,x);
return 0;
}
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t te,t;
/* Declaration of the size variable */
mp_prec_t Nx = MPFR_PREC(x); /* Precision of input variable */
mp_prec_t Ny = MPFR_PREC(y); /* Precision of input variable */
mp_prec_t Nt; /* Precision of the intermediary variable */
long int err; /* Precision of error */
/* compute the precision of intermediary variable */
Nt=MAX(Nx,Ny);
/* the optimal number of bits : see algorithms.ps */
Nt=Nt+5+_mpfr_ceil_log2(Nt);
/* initialise of intermediary variable */
mpfr_init(t);
mpfr_init(te);
/* First computation of cosh */
do {
/* reactualisation of the precision */
mpfr_set_prec(t,Nt);
mpfr_set_prec(te,Nt);
/* compute expm1 */
mpfr_exp(te,x,GMP_RNDN); /* exp(x)*/
mpfr_sub_ui(t,te,1,GMP_RNDN); /* exp(x)-1 */
/* estimation of the error */
err=Nt-(_mpfr_ceil_log2(1+pow(2,MPFR_EXP(te)-MPFR_EXP(t))));
/* actualisation of the precision */
Nt += 10;
} while ((err <0) || !mpfr_can_round(t,err,GMP_RNDN,rnd_mode,Ny));
inexact = mpfr_set(y,t,rnd_mode);
mpfr_clear(t);
mpfr_clear(te);
}
return inexact;
}
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