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/* mpfr_tanh -- hyperbolic tangent
Copyright 2001, 2002, 2003 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 "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* The computation of cosh is done by
tanh= [e^(x)^2-1]/+[e^(x)^2+1]
*/
int
#if __STDC__
mpfr_tanh (mpfr_ptr y, mpfr_srcptr xt , mp_rnd_t rnd_mode)
#else
mpfr_tanh (y, xt, rnd_mode)
mpfr_ptr y;
mpfr_srcptr xt;
mp_rnd_t rnd_mode;
#endif
{
/****** Declaration ******/
mpfr_t x;
mp_prec_t Nxt = MPFR_PREC(xt);
int flag_neg=0, inexact=0;
/* Special value checking */
if (MPFR_IS_NAN(xt))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
MPFR_CLEAR_NAN(y);
if (MPFR_IS_INF(xt))
{
if (MPFR_SIGN(xt) > 0)
return mpfr_set_si(y,1,rnd_mode); /* tanh(inf) = 1 */
else
return mpfr_set_si(y,-1,rnd_mode); /* tanh(-inf) = -1 */
}
MPFR_CLEAR_INF(y);
/* tanh(0) = 0 */
if (MPFR_IS_ZERO(xt))
{
MPFR_SET_ZERO(y);
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, ta,tb;
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+__gmpfr_ceil_log2(9)+__gmpfr_ceil_log2(Nt);
/* initialise of intermediary variable */
mpfr_init(t);
mpfr_init(te);
mpfr_init(ta);
mpfr_init(tb);
/* First computation of cosh */
do {
/* reactualisation of the precision */
mpfr_set_prec(t,Nt);
mpfr_set_prec(te,Nt);
mpfr_set_prec(ta,Nt);
mpfr_set_prec(tb,Nt);
/* compute tanh */
mpfr_mul_2ui(te,x,1,GMP_RNDN); /* 2x */
mpfr_exp(te,te,GMP_RNDN); /* exp(2x) */
mpfr_add_ui(ta,te,1,GMP_RNDD); /* exp(2x) + 1*/
mpfr_sub_ui(tb,te,1,GMP_RNDU); /* exp(2x) - 1*/
mpfr_div(t,tb,ta,GMP_RNDN); /* (exp(2x)-1)/(exp(2x)+1)*/
/* calculation of the error*/
d = MPFR_GET_EXP (te) - MPFR_GET_EXP (t);
/* estimation of the error */
/*err = Nt-(__gmpfr_ceil_log2(7+pow(2,d+1)));*/
err = Nt-(MAX(d+1,3)+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(te);
mpfr_clear(ta);
mpfr_clear(tb);
}
mpfr_clear(x);
return inexact;
}
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