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Initial revision

/* 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;
}