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/* mpfr_sinh -- hyperbolic sine
Copyright (C) 2001-2002 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. */
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* The computation of cosh is done by
cosh= 1/2[e^(x)-e^(-x)]
*/
int
mpfr_sinh (mpfr_ptr y, mpfr_srcptr xt, mp_rnd_t rnd_mode)
{
/****** Declaration ******/
mpfr_t x;
mp_prec_t Nxt = MPFR_PREC(xt);
int flag_neg=0, inexact =0;
if (MPFR_IS_NAN(xt))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
MPFR_CLEAR_NAN(y);
if (MPFR_IS_INF(xt))
{
MPFR_SET_INF(y);
MPFR_SET_SAME_SIGN(y,xt);
MPFR_RET(0);
}
MPFR_CLEAR_INF(y);
if (MPFR_IS_ZERO(xt))
{
MPFR_SET_ZERO(y); /* sinh(0) = 0 */
MPFR_SET_SAME_SIGN(y,xt);
MPFR_RET(0);
}
mpfr_init2(x,Nxt);
mpfr_set(x,xt,GMP_RNDN);
if(MPFR_SIGN(x)<0)
{
MPFR_CHANGE_SIGN(x);
flag_neg=1;
}
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t, te,ti;
int d;
/* Declaration of the size variable */
mp_prec_t Nx = Nxt; /* 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+_mpfr_ceil_log2(5)+_mpfr_ceil_log2(Nt);
/* initialise of intermediary variable */
mpfr_init(t);
mpfr_init(te);
mpfr_init(ti);
/* First computation of cosh */
do {
/* reactualisation of the precision */
mpfr_set_prec(t,Nt);
mpfr_set_prec(te,Nt);
mpfr_set_prec(ti,Nt);
/* compute sinh */
mpfr_exp(te,x,GMP_RNDD); /* exp(x) */
mpfr_ui_div(ti,1,te,GMP_RNDU); /* 1/exp(x) */
mpfr_sub(t,te,ti,GMP_RNDN); /* exp(x) - 1/exp(x)*/
mpfr_div_2ui(t,t,1,GMP_RNDN); /* 1/2(exp(x) - 1/exp(x))*/
/* calculation of the error*/
d = MPFR_EXP(te)-MPFR_EXP(t)+2;
/* estimation of the error */
/* err = Nt-(_mpfr_ceil_log2(1+pow(2,d)));*/
err = Nt-(MAX(d,0)+1);
/* actualisation of the precision */
Nt += 10;
} while ((err < 0) || !mpfr_can_round(t,err,GMP_RNDN,rnd_mode,Ny));
if (flag_neg==1)
MPFR_CHANGE_SIGN(t);
inexact = mpfr_set(y,t,rnd_mode);
mpfr_clear(t);
mpfr_clear(ti);
mpfr_clear(te);
}
mpfr_clear(x);
return inexact;
}
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