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/* mpfr_cosh -- hyperbolic cosine
Copyright 2001-2002, 2004-2020 Free Software Foundation, Inc.
Contributed by the AriC and Caramba projects, INRIA.
This file is part of the GNU MPFR Library.
The GNU 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 3 of the License, or (at your
option) any later version.
The GNU 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 GNU MPFR Library; see the file COPYING.LESSER. If not, see
https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
#define MPFR_NEED_LONGLONG_H
#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 , mpfr_rnd_t rnd_mode)
{
mpfr_t x;
int inexact;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_LOG_FUNC (
("x[%Pu]=%*.Rg rnd=%d", mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode),
("y[%Pu]=%*.Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y,
inexact));
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_SAVE_EXPO_MARK (expo);
/* cosh(x) = 1+x^2/2 + ... <= 1+x^2 for x <= 2.9828...,
thus the error < 2^(2*EXP(x)). If x >= 1, then EXP(x) >= 1,
thus the following will always fail. */
MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, __gmpfr_one, -2 * MPFR_GET_EXP (xt), 0,
1, rnd_mode, inexact = _inexact; goto end);
MPFR_TMP_INIT_ABS(x, xt);
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t, te;
/* Declaration of the size variable */
mpfr_prec_t Ny = MPFR_PREC(y); /* Precision of output variable */
mpfr_prec_t Nt; /* Precision of the intermediary variable */
long int err; /* Precision of error */
MPFR_ZIV_DECL (loop);
MPFR_GROUP_DECL (group);
/* compute the precision of intermediary variable */
/* The optimal number of bits : see algorithms.tex */
Nt = Ny + 3 + MPFR_INT_CEIL_LOG2 (Ny);
/* initialize of intermediary variables */
MPFR_GROUP_INIT_2 (group, Nt, t, te);
/* First computation of cosh */
MPFR_ZIV_INIT (loop, Nt);
for (;;)
{
MPFR_BLOCK_DECL (flags);
/* Compute cosh */
MPFR_BLOCK (flags, mpfr_exp (te, x, MPFR_RNDD)); /* exp(x) */
/* exp can overflow (but not underflow since x>0) */
if (MPFR_OVERFLOW (flags))
/* cosh(x) > exp(x), cosh(x) underflows too */
{
inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN_POS);
MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
break;
}
mpfr_ui_div (t, 1, te, MPFR_RNDU); /* 1/exp(x) */
mpfr_add (t, te, t, MPFR_RNDU); /* exp(x) + 1/exp(x)*/
mpfr_div_2ui (t, t, 1, MPFR_RNDN); /* 1/2(exp(x) + 1/exp(x))*/
/* Estimation of the error */
err = Nt - 3;
/* Check if we can round */
if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
{
inexact = mpfr_set (y, t, rnd_mode);
break;
}
/* Actualisation of the precision */
MPFR_ZIV_NEXT (loop, Nt);
MPFR_GROUP_REPREC_2 (group, Nt, t, te);
}
MPFR_ZIV_FREE (loop);
MPFR_GROUP_CLEAR (group);
}
end:
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inexact, rnd_mode);
}
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