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/* mpfr_atanh -- Inverse Hyperbolic Tangente of Unsigned Integer Number
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 acosh is done by
atanh= 1/2*ln(x+1)-1/2*ln(1-x)
*/
int
mpfr_atanh (mpfr_ptr y, mpfr_srcptr xt , mp_rnd_t rnd_mode)
{
int inexact = 0;
mpfr_t x;
mp_prec_t Nx = MPFR_PREC(xt); /* Precision of input variable */
/* Special cases */
if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(xt) ))
{
/* atanh(NaN) = NaN, and atanh(+/-Inf) = NaN since tanh gives a result
between -1 and 1 */
if (MPFR_IS_NAN(xt) || MPFR_IS_INF(xt))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
else /* necessarily xt is 0 */
{
MPFR_ASSERTD(MPFR_IS_ZERO(xt));
MPFR_SET_ZERO(y); /* atanh(0) = 0 */
MPFR_SET_SAME_SIGN(y,xt);
MPFR_RET(0);
}
}
/* Useless due to final mpfr_set
MPFR_CLEAR_FLAGS(y);*/
/* atanh(x) = NaN as soon as |x| > 1, and arctanh(+/-1) = +/-Inf */
if (MPFR_EXP(xt) > 0)
{
if (MPFR_EXP(xt) == 1)
{
if (mpfr_cmp_ui (xt, 1) || mpfr_cmp_si (xt, -1))
{
MPFR_SET_INF(y);
MPFR_SET_SAME_SIGN(y, xt);
MPFR_RET(0);
}
}
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
mpfr_init2 (x, Nx);
mpfr_abs (x, xt, GMP_RNDN);
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t, te,ti;
/* Declaration of the size variable */
mp_prec_t Nx = MPFR_PREC(x); /* Precision of input variable */
mp_prec_t Ny = MPFR_PREC(y); /* Precision of input variable */
mp_prec_t Nt; /* Precision of the intermediary variable */
long 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+MPFR_INT_CEIL_LOG2(Nt);
/* initialise of intermediary variable */
mpfr_init(t);
mpfr_init(te);
mpfr_init(ti);
/* First computation of cosh */
do
{
/* reactualisation of the precision */
mpfr_set_prec(t,Nt);
mpfr_set_prec(te,Nt);
mpfr_set_prec(ti,Nt);
/* compute atanh */
mpfr_ui_sub(te,1,x,GMP_RNDU); /* (1-xt)*/
mpfr_add_ui(ti,x,1,GMP_RNDD); /* (xt+1)*/
mpfr_div(te,ti,te,GMP_RNDN); /* (1+xt)/(1-xt)*/
mpfr_log(te,te,GMP_RNDN); /* ln((1+xt)/(1-xt))*/
mpfr_div_2ui(t,te,1,GMP_RNDN); /* (1/2)*ln((1+xt)/(1-xt))*/
/* error estimate see- algorithms.ps*/
/* err=Nt-__gmpfr_ceil_log2(1+5*pow(2,1-MPFR_EXP(t)));*/
err = Nt - (MAX (4 - 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)));
if (MPFR_IS_NEG(xt))
MPFR_CHANGE_SIGN(t);
inexact = mpfr_set (y, t, rnd_mode);
mpfr_clear(t);
mpfr_clear(ti);
mpfr_clear(te);
}
mpfr_clear(x);
return inexact;
}
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