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/* mpfr_sinh -- hyperbolic sine
Copyright 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 sinh is done by
sinh(x) = 1/2 [e^(x)-e^(-x)]
*/
int
mpfr_sinh (mpfr_ptr y, mpfr_srcptr xt, mp_rnd_t rnd_mode)
{
/****** Declarations ******/
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 + __gmpfr_ceil_log2 (5) + __gmpfr_ceil_log2 (Nt);
/* initialise of intermediary variable */
mpfr_init (t);
mpfr_init (te);
mpfr_init (ti);
/* First computation of sinh */
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)) */
/* it may be that t is zero (in fact, it can only occur when te=1,
and thus ti=1 too) */
if (MPFR_IS_ZERO(t))
err = -1;
else
{
/* calculation of the error */
d = MPFR_EXP(te) - MPFR_EXP(t) + 2;
/* estimation of the error */
/* err = Nt-(__gmpfr_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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