Return to sinh.c CVS log

Up to [local] / OpenXM_contrib / gmp / mpfr

Initial revision

/* mpfr_sinh -- hyperbolic sine

Copyright 2001, 2002 Free Software Foundation, Inc.

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 sinh is done by

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

int
mpfr_sinh (mpfr_ptr y, mpfr_srcptr xt, mp_rnd_t rnd_mode)
{
    /****** Declarations ******/
    mpfr_t x;
    mp_prec_t Nxt = MPFR_PREC(xt);
    int flag_neg=0, 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);
        MPFR_SET_SAME_SIGN(y, xt);
        MPFR_RET(0);
      }

    MPFR_CLEAR_INF(y);
  
    if (MPFR_IS_ZERO(xt))
      {
        MPFR_SET_ZERO(y);   /* sinh(0) = 0 */
        MPFR_SET_SAME_SIGN(y, xt);
        MPFR_RET(0);
      }

    mpfr_init2 (x, Nxt);
    mpfr_set (x, xt, GMP_RNDN);

    if(MPFR_SIGN(x)<0)
      {
        MPFR_CHANGE_SIGN(x);
        flag_neg=1;
      }

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

      /* 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 + _mpfr_ceil_log2 (5) + _mpfr_ceil_log2 (Nt);

      /* initialise of intermediary	variable */
      mpfr_init (t);
      mpfr_init (te);
      mpfr_init (ti);

      /* First computation of sinh */
      do {

	/* reactualisation of the precision */

	mpfr_set_prec (t, Nt);
	mpfr_set_prec (te, Nt);
	mpfr_set_prec (ti, Nt);

	/* compute sinh */
	mpfr_exp (te, x, GMP_RNDD);        /* exp(x) */
	mpfr_ui_div (ti, 1, te, GMP_RNDU); /* 1/exp(x) */
        mpfr_sub (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)) */

        /* it may be that t is zero (in fact, it can only occur when te=1,
           and thus ti=1 too) */

        if (MPFR_IS_ZERO(t))
          err = -1;
        else
          {
            /* calculation of the error */
            d = MPFR_EXP(te) - MPFR_EXP(t) + 2;
	
            /* estimation of the error */
            /* err = Nt-(_mpfr_ceil_log2(1+pow(2,d)));*/
            err = Nt - (MAX(d,0) + 1);
          }

	/* actualisation of the precision */
        Nt += 10; 

      } while ((err < 0) || !mpfr_can_round(t, err, GMP_RNDN, rnd_mode, Ny));

      if (flag_neg == 1)
          MPFR_CHANGE_SIGN(t);

      inexact = mpfr_set (y, t, rnd_mode);
      mpfr_clear (t);
      mpfr_clear (ti);
      mpfr_clear (te);
    }
    mpfr_clear (x);

    return inexact;
}