#include <config.h>
#include <math.h>
#include <gsl_math.h>
#include <gsl_sf_gamma.h>
#include <gsl_rng.h>
#include <gsl_randist.h>

/* The t-distribution has the form

   p(x) dx = (Gamma((nu + 1)/2)/(sqrt(pi nu) Gamma(nu/2))
   * (1 + (x^2)/nu)^-((nu + 1)/2) dx

   The method used here is the one described in Knuth */

double
gsl_ran_tdist (const gsl_rng * r, const double nu)
{
  if (nu <= 2)
    {
      double Y1 = gsl_ran_ugaussian (r);
      double Y2 = gsl_ran_chisq (r, nu);

      double t = Y1 / sqrt (Y2 / nu);

      return t;
    }
  else
    {
      double Y1, Y2, Z, t;
      do
	{
	  Y1 = gsl_ran_ugaussian (r);
	  Y2 = gsl_ran_exponential (r, 1 / (nu/2 - 1));

	  Z = Y1 * Y1 / (nu - 2);
	}
      while (1 - Z < 0 || exp (-Y2 - Z) > (1 - Z));

      /* Note that there is a typo in Knuth's formula, the line below
	 is taken from the original paper of Marsaglia, Mathematics of
	 Computation, 34 (1980), p 234-256 */

      t = Y1 / sqrt ((1 - 2 / nu) * (1 - Z));
      return t;
    }
}

double
gsl_ran_tdist_pdf (const double x, const double nu)
{
  double p;
  gsl_sf_result lg1, lg2;
  gsl_sf_lngamma_impl (nu / 2, &lg1);
  gsl_sf_lngamma_impl ((nu + 1) / 2, &lg2);

  p = ((exp (lg2.val - lg1.val) / sqrt (M_PI * nu)) 
       * pow ((1 + x * x / nu), -(nu + 1) / 2));
  return p;
}