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/* mpfr_acosh -- Inverse Hyperbolic Cosine of Unsigned Integer Number
Copyright (C) 1999 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
acosh= ln(x+sqrt(x-1)*sqrt(x+1))
*/
int mpfr_acosh _PROTO((mpfr_ptr, mpfr_srcptr, mp_rnd_t));
int
#if __STDC__
mpfr_acosh (mpfr_ptr y, mpfr_srcptr x , mp_rnd_t rnd_mode)
#else
mpfr_acosh (y, x, rnd_mode)
mpfr_ptr y;
mpfr_srcptr x;
mp_rnd_t rnd_mode;
#endif
{
/****** Declaration ******/
/* Variable of Intermediary Calculation*/
mpfr_t t;
/* Variable of Intermediary Calculation*/
mpfr_t ta,tb;
int round;
int boucle;
int comp;
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 */
if (MPFR_IS_NAN(x)) { MPFR_SET_NAN(y); return 1; }
MPFR_CLEAR_NAN(y);
if (MPFR_IS_INF(x)){
MPFR_SET_INF(y);
if (MPFR_SIGN(y) < 0) MPFR_CHANGE_SIGN(y);
return 1;
}
MPFR_CLEAR_INF(y);
comp=mpfr_cmp_ui(x,1);
if(comp <= 0){
if(comp == 0){
MPFR_SET_ZERO(y); /* acosh(1) = 0 */
return(0);
}
else{
/*fprintf(stderr,"Function acosh of MPFR is only defined for x=[1,+Inf]");
exit(-1);*/
/*An other strategy if output is not define for input return NaN*/
MPFR_SET_NAN(y); return(-1);
}
}
else{
/* Initialisation of the Precision */
Nx=MPFR_PREC(x);
Ny=MPFR_PREC(y);
/* compute the size of intermediary variable */
if(Ny>=Nx)
Nt=Ny+2*CHAR_BIT;
else
Nt=Nx+2*CHAR_BIT;
boucle=1;
/* initialise of intermediary variable */
mpfr_init2(t,Nt);
mpfr_init2(ta,Nt);
mpfr_init2(tb,Nt);
while(boucle==1){
/* compute acosh */
mpfr_add_ui(ta,x,1,GMP_RNDN); /* (x+1) */
mpfr_sub_ui(tb,x,1,GMP_RNDN); /* (x-1) */
mpfr_sqrt(ta,ta,GMP_RNDN); /* sqrt(x+1) */
mpfr_sqrt(tb,tb,GMP_RNDN); /* sqrt(x-1) */
mpfr_mul(t,ta,tb,GMP_RNDN); /* sqrt(x+1)*sqrt(x-1) */
mpfr_add(t,t,x,GMP_RNDN); /* sqrt(x+1)*sqrt(x-1)+x */
mpfr_log(t,t,GMP_RNDN); /* ln(sqrt(x+1)*sqrt(x-1)+x)*/
err=Nt-1-MAX(0,-MPFR_EXP(t));
round=mpfr_can_round(t,err,GMP_RNDN,rnd_mode,Ny);
if(round == 1){
mpfr_set(y,t,rnd_mode);
boucle=0;
}
else{
Nt=Nt+10;
/* initialise of intermediary variable */
mpfr_set_prec(t,Nt);
mpfr_set_prec(ta,Nt);
mpfr_set_prec(tb,Nt);
boucle=1;
}
}
mpfr_clear(t);
mpfr_clear(ta);
mpfr_clear(tb);
return(1);
}
}
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