/* cdf/fdist.c
 *
 * Copyright (C) 2002 Przemyslaw Sliwa and Jason H. Stover.
 * Copyright (C) 2006, 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_cdf.h>
#include <gsl/gsl_sf_gamma.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>

#include "error.h"
#include "beta_inc.c"

/*
 * Lower tail.
 */

double
gsl_cdf_fdist_P (const double x, const double nu1, const double nu2)
{
  double P;
  double r = nu2 / nu1;

  if (x < r)
    {
      double u = x / (r + x);

      P = beta_inc_AXPY (1.0, 0.0, nu1 / 2.0, nu2 / 2.0, u);
    }
  else
    {
      double u = r / (r + x);

      P = beta_inc_AXPY (-1.0, 1.0, nu2 / 2.0, nu1 / 2.0, u);
    }

  return P;
}

/*
 * Upper tail.
 */

double
gsl_cdf_fdist_Q (const double x, const double nu1, const double nu2)
{
  double Q;
  double r = nu2 / nu1;

  if (x < r)
    {
      double u = x / (r + x);

      Q = beta_inc_AXPY (-1.0, 1.0, nu1 / 2.0, nu2 / 2.0, u);
    }
  else
    {
      double u = r / (r + x);

      Q = beta_inc_AXPY (1.0, 0.0, nu2 / 2.0, nu1 / 2.0, u);
    }

  return Q;
}