/* mpfr_acosh -- Inverse Hyperbolic Cosine of Unsigned Integer Number
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-1)*sqrt(x+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))
{
MPFR_SET_NAN(y);
MPFR_RET_NAN;
}
comp=mpfr_cmp_ui(x,1);
if(comp < 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 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 */
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_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 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-_mpfr_ceil_log2(0.5+pow(2,2-MPFR_EXP(t))+pow(2,1+MPFR_EXP(te)-MPFR_EXP(ti)-MPFR_EXP(t)));*/
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);
}
return inexact;
}