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/* mpfr_cosh -- hyperbolic cosine
Copyright 2001, 2002, 2004 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 "mpfr-impl.h"
/* The computation of cosh is done by
cosh= 1/2[e^(x)+e^(-x)]
*/
int
mpfr_cosh (mpfr_ptr y, mpfr_srcptr xt , mp_rnd_t rnd_mode)
{
/****** Declaration ******/
mpfr_t x;
mp_prec_t Nxt = MPFR_PREC(xt);
int inexact =0;
if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(xt)))
{
if (MPFR_IS_NAN(xt))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF(xt))
{
MPFR_SET_INF(y);
MPFR_SET_POS(y);
MPFR_RET(0);
}
else
{
MPFR_ASSERTD(MPFR_IS_ZERO(xt));
return mpfr_set_ui (y, 1, rnd_mode); /* cosh(0) = 1 */
}
}
mpfr_init2 (x, Nxt);
mpfr_abs (x, xt, GMP_RNDN);
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t, te,ti;
/* 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 + 3 + __gmpfr_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 cosh */
mpfr_exp (te, x, GMP_RNDD); /* exp(x) */
mpfr_ui_div (ti, 1, te, GMP_RNDU); /* 1/exp(x) */
mpfr_add (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))*/
/* estimation of the error */
err = Nt - 3;
/* actualisation of the precision */
Nt += 10;
}
while ((err < 0) || !mpfr_can_round (t, err, GMP_RNDN, GMP_RNDZ,
Ny + (rnd_mode == GMP_RNDN)));
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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