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/* mpfr_atanh -- Inverse Hyperbolic Tangente of Unsigned Integer Number
Copyright (C) 1999-2001 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 Library General Public License as published by
the Free Software Foundation; either version 2 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 Library General Public
License for more details.
You should have received a copy of the GNU Library 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 <limits.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.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 _PROTO((mpfr_ptr, mpfr_srcptr, mp_rnd_t));
int
#if __STDC__
mpfr_atanh (mpfr_ptr y, mpfr_srcptr x , mp_rnd_t rnd_mode)
#else
mpfr_atanh (y, x, rnd_mode)
mpfr_ptr y;
mpfr_srcptr x;
mp_rnd_t rnd_mode;
#endif
{
/****** Declaration ******/
/* Variable of Intermediary Calculation*/
mpfr_t t,xt;
/* Variable of Intermediary Calculation*/
mpfr_t te,ti;
int round;
int comp;
int boucle;
int flag_neg;
mp_prec_t Nx; /* Precision of input variable */
mp_prec_t Ny; /* Precision of output variable */
mp_prec_t Nt; /* Precision of Intermediary Calculation variable */
mp_prec_t err; /* Precision of error */
Nx=MPFR_PREC(x);
mpfr_init2(xt,Nx);
mpfr_set(xt,x,GMP_RNDN);
if (MPFR_IS_NAN(xt)) { MPFR_SET_NAN(y); return 1; }
MPFR_CLEAR_NAN(y);
comp = mpfr_cmp_ui(xt,0);
if(comp==0){
MPFR_SET_ZERO(y); /* atanh(0) = 0 */
return(0);
}
flag_neg=0;
if(MPFR_SIGN(xt)<0){
MPFR_CHANGE_SIGN(xt);
flag_neg=1;
}
comp=mpfr_cmp_ui(xt,1);
if(comp >= 0){
/*fprintf(stderr,"MPFR atanh function is
only defined for x=[-1,+1]");
exit(-1);*/
/* An other srtategy if output is not define for input return NaN*/
MPFR_SET_NAN(y);return(-1);
}
else{
/* Initialization of the precision */
Nx=MPFR_PREC(xt);
Ny=MPFR_PREC(y);
/* compute the size of temporary variable */
if(Ny>=Nx)
Nt=Ny+2*CHAR_BIT+10;
else
Nt=Nx+2*CHAR_BIT+10;
boucle=1;
/* initialization of a temporary variable */
mpfr_init2(t,Nt);
mpfr_init2(ti,Nt);
mpfr_init2(te,Nt);
while(boucle){
/* compute atanh */
/* Good algorithme near 1 but bad near 0 */
/*
mpfr_ui_sub(te,1,xt,GMP_RNDN); e=1-x
mpfr_ui_div(te,2,te,GMP_RNDN); 2/e
mpfr_sub_ui(te,te,1,GMP_RNDN); (2/e)-1
mpfr_log(te,te,GMP_RNDN); ln((2/e)-1)
mpfr_div_2exp(t,te,1,GMP_RNDN); (1/2)*ln((2/e)-1)
*/
mpfr_ui_sub(te,1,xt,GMP_RNDN); /* (1-xt)*/
mpfr_add_ui(ti,xt,1,GMP_RNDN); /* (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_2exp(t,te,1,GMP_RNDN); /* (1/2)*ln((1+xt)/(1-xt))*/
err = Nt - MAX(0, -MPFR_EXP(t));
round=mpfr_can_round(t,err,GMP_RNDN,rnd_mode,Ny);
if(round == 1){
if(flag_neg==1) MPFR_CHANGE_SIGN(t);
mpfr_set(y,t,rnd_mode);
boucle=0;
}
else{
Nt=Nt+10;
/* initialization of a temporary variable */
mpfr_set_prec(t,Nt);
mpfr_set_prec(te,Nt);
mpfr_set_prec(ti,Nt);
boucle=1;
}
}
mpfr_clear(t);
mpfr_clear(te);
mpfr_clear(ti);
mpfr_clear(xt);
return(1);
}
}
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