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/* mpfr_acosh -- inverse hyperbolic cosine
Copyright 2001, 2002 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 "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"
/* The computation of acosh is done by
acosh= ln(x + sqrt(x^2-1))
*/
int
mpfr_acosh (mpfr_ptr y, mpfr_srcptr x , mp_rnd_t rnd_mode)
{
int inexact = 0;
int comp;
if (MPFR_IS_NAN(x) || (comp = mpfr_cmp_ui (x, 1)) < 0)
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
MPFR_CLEAR_NAN(y);
if (comp == 0)
{
MPFR_SET_ZERO(y); /* acosh(1) = 0 */
MPFR_SET_POS(y);
MPFR_RET(0);
}
if (MPFR_IS_INF(x))
{
MPFR_SET_INF(y);
MPFR_SET_POS(y);
MPFR_RET(0);
}
MPFR_CLEAR_INF(y);
/* General case */
{
/* Declaration of the intermediary variables */
mpfr_t t, te, ti;
/* Declaration of the size variables */
mp_prec_t Nx = MPFR_PREC(x); /* Precision of input variable */
mp_prec_t Ny = MPFR_PREC(y); /* Precision of output variable */
mp_prec_t Nt; /* Precision of the intermediary variable */
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 + 4 + __gmpfr_ceil_log2 (Nt);
/* initialization of intermediary variables */
mpfr_init (t);
mpfr_init (te);
mpfr_init (ti);
mpfr_save_emin_emax ();
/* First computation of acosh */
do {
/* reactualisation of the precision */
mpfr_set_prec (t, Nt);
mpfr_set_prec (te, Nt);
mpfr_set_prec (ti, Nt);
/* compute acosh */
mpfr_mul (te, x, x, GMP_RNDD); /* x^2 */
mpfr_sub_ui (ti, te, 1, GMP_RNDD); /* x^2-1 */
mpfr_sqrt (t, ti, GMP_RNDN); /* sqrt(x^2-1) */
mpfr_add (t, t, x, GMP_RNDN); /* sqrt(x^2-1)+x */
mpfr_log (t, t, GMP_RNDN); /* ln(sqrt(x^2-1)+x)*/
/* estimation of the error -- see algorithms.ps */
err = Nt - (-1 + 2 * MAX(2 + MAX(2 - MPFR_EXP(t),
1 + MPFR_EXP(te) - MPFR_EXP(ti) - MPFR_EXP(t)), 0));
/* actualisation of the precision */
Nt += 10;
} while ((err < 0) || !mpfr_can_round (t, err, GMP_RNDN, rnd_mode, Ny));
inexact = mpfr_set (y, t, rnd_mode);
mpfr_clear (t);
mpfr_clear (ti);
mpfr_clear (te);
}
mpfr_restore_emin_emax ();
return mpfr_check_range (y, inexact, rnd_mode);
}
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