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/* mpfr_asinh -- inverse hyperbolic sine
Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao projects, INRIA.
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., 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, mp_rnd_t rnd_mode)
{
int inexact;
int signx, neg;
mp_prec_t Ny, Nt;
mpfr_t t; /* auxiliary variables */
mp_exp_t err;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_ZIV_DECL (loop);
MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode),
("y[%#R]=%R inexact=%d", y, 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, GMP_RNDD); /* x^2 */
mpfr_add_ui (t, t, 1, GMP_RNDD); /* x^2+1 */
mpfr_sqrt (t, t, GMP_RNDN); /* sqrt(x^2+1) */
(neg ? mpfr_sub : mpfr_add) (t, t, x, GMP_RNDN); /* sqrt(x^2+1)+x */
mpfr_log (t, t, GMP_RNDN); /* ln(sqrt(x^2+1)+x)*/
/* 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;
/* actualisation 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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