text: /*
   *  AUTHOR
   *    Catherine Loader, catherine@research.bell-labs.com.
   *    October 23, 2000.
   *
   *  Merge in to R:
   *	Copyright (C) 2000, 2005 The R Core Team
   *
   *  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 2 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, a copy is available at
   *  http://www.r-project.org/Licenses/
   *
   *
   *  DESCRIPTION
   *
   *    The density function of the F distribution.
   *    To evaluate it, write it as a Binomial probability with p = x*m/(n+x*m).
   *    For m >= 2, we use the simplest conversion.
   *    For m < 2, (m-2)/2 < 0 so the conversion will not work, and we must use
   *               a second conversion.
   *    Note the division by p; this seems unavoidable
   *    for m < 2, since the F density has a singularity as x (or p) -> 0.
   */
  
  #include "nmath.h"
  #include "dpq.h"
  
  double df(double x, double m, double n, int give_log)
  {
      double p, q, f, dens;
  
  #ifdef IEEE_754
      if (ISNAN(x) || ISNAN(m) || ISNAN(n))
  	return x + m + n;
  #endif
      if (m <= 0 || n <= 0) ML_ERR_return_NAN;
      if (x < 0.)  return(R_D__0);
      if (x == 0.) return(m > 2 ? R_D__0 : (m == 2 ? R_D__1 : ML_POSINF));
      if (!R_FINITE(m) && !R_FINITE(n)) { /* both +Inf */
  	if(x == 1.) return ML_POSINF;
  	/* else */  return R_D__0;
      }
      if (!R_FINITE(n)) /* must be +Inf by now */
  	return(dgamma(x, m/2, 2./m, give_log));
      if (m > 1e14) {/* includes +Inf: code below is inaccurate there */
  	dens = dgamma(1./x, n/2, 2./n, give_log);
  	return give_log ? dens - 2*log(x): dens/(x*x);
      }
  
      f = 1./(n+x*m);
      q = n*f;
      p = x*m*f;
  
      if (m >= 2) {
  	f = m*q/2;
  	dens = dbinom_raw((m-2)/2, (m+n-2)/2, p, q, give_log);
      }
      else {
  	f = m*m*q / (2*p*(m+n));
  	dens = dbinom_raw(m/2, (m+n)/2, p, q, give_log);
      }
      return(give_log ? log(f)+dens : f*dens);
  }
  