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/* mpfr_expm1 -- Compute exp(x)-1
Copyright 2001, 2002, 2003, 2004, 2005 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. */
#define MPFR_NEED_LONGLONG_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;
MPFR_SAVE_EXPO_DECL (expo);
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN (x))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
/* check for inf or -inf (expm1(-inf)=-1) */
else if (MPFR_IS_INF (x))
{
if (MPFR_IS_POS (x))
{
MPFR_SET_INF (y);
MPFR_SET_POS (y);
MPFR_RET (0);
}
else
return mpfr_set_si (y, -1, rnd_mode);
}
else
{
MPFR_ASSERTD (MPFR_IS_ZERO (x));
MPFR_SET_ZERO (y); /* expm1(+/- 0) = +/- 0 */
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0);
}
}
MPFR_SAVE_EXPO_MARK (expo);
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t 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 */
mp_exp_t err, exp_te; /* Precision of error */
MPFR_ZIV_DECL (loop);
/* compute the precision of intermediary variable */
Nt = MAX (Nx, Ny);
/* the optimal number of bits : see algorithms.ps */
Nt = Nt + 5 + MPFR_INT_CEIL_LOG2 (Nt);
/* initialise of intermediary variable */
mpfr_init2 (t, Nt);
/* First computation of cosh */
MPFR_ZIV_INIT (loop, Nt);
for (;;)
{
/* compute expm1 */
mpfr_exp (t, x, GMP_RNDN); /* exp(x)*/
exp_te = MPFR_GET_EXP (t); /* FIXME: exp(x) may overflow! */
mpfr_sub_ui (t, t, 1, GMP_RNDN); /* exp(x)-1 */
/* error estimate */
/*err=Nt-(__gmpfr_ceil_log2(1+pow(2,MPFR_EXP(te)-MPFR_EXP(t))));*/
err = Nt - (MAX (exp_te - MPFR_GET_EXP (t), 0) + 1);
if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
break;
/* actualisation of the precision */
MPFR_ZIV_NEXT (loop, Nt);
mpfr_set_prec (t, Nt);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (y, t, rnd_mode);
mpfr_clear (t);
}
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inexact, rnd_mode);
}
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