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/* mpfr_asinh -- inverse hyperbolic sine
Copyright 2001, 2002, 2003, 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. */
#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 neg = 0;
mp_prec_t Nx, Ny, Nt;
mpfr_t t, te, ti; /* auxiliary variables */
long int err;
MPFR_SAVE_EXPO_DECL (expo);
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);
}
}
MPFR_CLEAR_FLAGS(y);
Nx = MPFR_PREC(x); /* Precision of input variable */
Ny = MPFR_PREC(y); /* Precision of output variable */
neg = MPFR_IS_NEG(x);
/* General case */
/* compute the precision of intermediary variable */
Nt = MAX(Nx, Ny);
/* the optimal number of bits : see algorithms.ps */
Nt = Nt + 4 + MPFR_INT_CEIL_LOG2 (Nt);
MPFR_SAVE_EXPO_MARK (expo);
/* initialize intermediary variables */
mpfr_init2 (t, 2);
mpfr_init2 (te, 2);
mpfr_init2 (ti, 2);
/* First computation of asinh */
do
{
/* reactualisation of the precision */
mpfr_set_prec (t, Nt);
mpfr_set_prec (te, Nt);
mpfr_set_prec (ti, Nt);
/* compute asinh */
mpfr_mul (te, x, x, GMP_RNDD); /* x^2 */
mpfr_add_ui (ti, te, 1, GMP_RNDD); /* x^2+1 */
mpfr_sqrt (t, ti, 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.ps */
err = Nt - (MAX(3 - MPFR_GET_EXP (t), 0) + 1);
/* actualisation of the precision */
Nt += 10;
}
while ((err < 0) || (!mpfr_can_round (t, err, GMP_RNDN, GMP_RNDZ,
Ny + (rnd_mode == GMP_RNDN))
|| MPFR_IS_ZERO(t)));
MPFR_SAVE_EXPO_FREE (expo);
if (neg)
MPFR_CHANGE_SIGN(t);
inexact = mpfr_set (y, t, rnd_mode);
mpfr_clear (t);
mpfr_clear (ti);
mpfr_clear (te);
return mpfr_check_range (y, inexact, rnd_mode);
}
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