/* sys/invhyp.c

 * 

 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Brian Gough

 * 

 * This program is free software; you can redistribute it and/or modify

 * it under the terms of the GNU General Public License as published by

 * the Free Software Foundation; either version 3 of the License, or (at

 * your option) any later version.

 * 

 * This program 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

 * General Public License for more details.

 * 

 * You should have received a copy of the GNU General Public License

 * along with this program; if not, write to the Free Software

 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.

 */

#include <config.h>

#include <math.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_machine.h>

double

gsl_acosh (const double x)

{

  if (x > 1.0 / GSL_SQRT_DBL_EPSILON)

    {

      return log (x) + M_LN2;

    }

  else if (x > 2)

    {

      return log (2 * x - 1 / (sqrt (x * x - 1) + x));

    }

  else if (x > 1)

    {

      double t = x - 1;

      return log1p (t + sqrt (2 * t + t * t));

    }

  else if (x == 1)

    {

      return 0;

    }

  else

    {

      return GSL_NAN;

    }

}

double

gsl_asinh (const double x)

{

  double a = fabs (x);

  double s = (x < 0) ? -1 : 1;

  if (a > 1 / GSL_SQRT_DBL_EPSILON)

    {

      return s * (log (a) + M_LN2);

    }

  else if (a > 2)

    {

      return s * log (2 * a + 1 / (a + sqrt (a * a + 1)));

    }

  else if (a > GSL_SQRT_DBL_EPSILON)

    {

      double a2 = a * a;

      return s * log1p (a + a2 / (1 + sqrt (1 + a2)));

    }

  else

    {

      return x;

    }

}

double

gsl_atanh (const double x)

{

  double a = fabs (x);

  double s = (x < 0) ? -1 : 1;

  if (a > 1)

    {

      return GSL_NAN;

    }

  else if (a == 1)

    {

      return (x < 0) ? GSL_NEGINF : GSL_POSINF;

    }

  else if (a >= 0.5)

    {

      return s * 0.5 * log1p (2 * a / (1 - a));

    }

  else if (a > GSL_DBL_EPSILON)

    {

      return s * 0.5 * log1p (2 * a + 2 * a * a / (1 - a));

    }

  else

    {

      return x;

    }

}