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/* mpfr_asinh -- inverse hyperbolic sine
Copyright 2001-2017 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
http://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 asinh is done by *
* asinh = ln(x + sqrt(x^2 + 1)) */
int
mpfr_asinh (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
int inexact;
int signx, neg;
mpfr_prec_t Ny, Nt;
mpfr_t t; /* auxiliary variables */
mpfr_exp_t err;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_ZIV_DECL (loop);
MPFR_LOG_FUNC (
("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode),
("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y,
inexact));
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN (x))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (x))
{
MPFR_SET_INF (y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0);
}
else /* x is necessarily 0 */
{
MPFR_ASSERTD (MPFR_IS_ZERO (x));
MPFR_SET_ZERO (y); /* asinh(0) = 0 */
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0);
}
}
/* asinh(x) = x - x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */
MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -2 * MPFR_GET_EXP (x), 2, 0,
rnd_mode, {});
Ny = MPFR_PREC (y); /* Precision of output variable */
signx = MPFR_SIGN (x);
neg = MPFR_IS_NEG (x);
/* General case */
/* compute the precision of intermediary variable */
/* the optimal number of bits : see algorithms.tex */
Nt = Ny + 4 + MPFR_INT_CEIL_LOG2 (Ny);
MPFR_SAVE_EXPO_MARK (expo);
/* initialize intermediary variables */
mpfr_init2 (t, Nt);
/* First computation of asinh */
MPFR_ZIV_INIT (loop, Nt);
for (;;)
{
/* compute asinh */
mpfr_mul (t, x, x, MPFR_RNDD); /* x^2 */
mpfr_add_ui (t, t, 1, MPFR_RNDD); /* x^2+1 */
mpfr_sqrt (t, t, MPFR_RNDN); /* sqrt(x^2+1) */
(neg ? mpfr_sub : mpfr_add) (t, t, x, MPFR_RNDN); /* sqrt(x^2+1)+x */
mpfr_log (t, t, MPFR_RNDN); /* ln(sqrt(x^2+1)+x)*/
if (MPFR_LIKELY (MPFR_IS_PURE_FP (t)))
{
/* error estimate -- see algorithms.tex */
err = Nt - (MAX (4 - MPFR_GET_EXP (t), 0) + 1);
if (MPFR_LIKELY (MPFR_IS_ZERO (t)
|| MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
break;
}
/* actualization of the precision */
MPFR_ZIV_NEXT (loop, Nt);
mpfr_set_prec (t, Nt);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set4 (y, t, rnd_mode, signx);
mpfr_clear (t);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (y, inexact, rnd_mode);
}
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