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Initial revision

/* mpfr_cosh -- hyperbolic cosine

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 <stdio.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "mpfr.h"
#include "mpfr-impl.h"

 /* The computation of cosh is done by

    cosh= 1/2[e^(x)+e^(-x)]
 */

int
mpfr_cosh (mpfr_ptr y, mpfr_srcptr xt , mp_rnd_t rnd_mode) 
{
    
  /****** Declaration ******/
    mpfr_t x;
    mp_prec_t Nxt = MPFR_PREC(xt);
    int inexact =0;

    if (MPFR_IS_NAN(xt)) 
      {
        MPFR_SET_NAN(y); 
        MPFR_RET_NAN;
      }
    MPFR_CLEAR_NAN(y);

    if (MPFR_IS_INF(xt))
      { 
        MPFR_SET_INF(y);
        if (MPFR_SIGN(y) < 0) 
          MPFR_CHANGE_SIGN(y);
        MPFR_RET(0);
      }   
    
    MPFR_CLEAR_INF(y);

    if (MPFR_IS_ZERO(xt))
      return mpfr_set_ui(y,1,rnd_mode); /* cosh(0) = 1 */

    mpfr_init2(x,Nxt);
    mpfr_set4(x, xt, GMP_RNDN, 1);

    /* General case */
    {
    /* Declaration of the intermediary variable */
      mpfr_t t, te,ti;       

      /* Declaration of the size variable */
      mp_prec_t Nx = Nxt;   /* 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+3+_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 cosh */
	mpfr_exp(te,x,GMP_RNDD);         /* exp(x) */
	mpfr_ui_div(ti,1,te,GMP_RNDU);   /* 1/exp(x) */
	mpfr_add(t,te,ti,GMP_RNDN);      /* exp(x) + 1/exp(x)*/
	mpfr_div_2ui(t,t,1,GMP_RNDN);    /* 1/2(exp(x) + 1/exp(x))*/

	/* estimation of the error */
	err=Nt-3;

	/* 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);
    }
    mpfr_clear(x);
    return inexact;

}