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/*
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 *  AUTHOR
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 *    Catherine Loader, catherine@research.bell-labs.com.
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 *    October 23, 2000.
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 *
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 *  Merge in to R:
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 *	Copyright (C) 2000, 2005 The R Core Development Team
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 *
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 *  This program is free software; you can redistribute it and/or modify
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 *  it under the terms of the GNU General Public License as published by
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 *  the Free Software Foundation; either version 2 of the License, or
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 *  (at your option) any later version.
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 *
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 *  This program is distributed in the hope that it will be useful,
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 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
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 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
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 *  GNU General Public License for more details.
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 *
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 *  You should have received a copy of the GNU General Public License
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 *  along with this program; if not, a copy is available at
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 *  http://www.r-project.org/Licenses/
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 *
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 *
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 *  DESCRIPTION
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 *
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 *    The density function of the F distribution.
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 *    To evaluate it, write it as a Binomial probability with p = x*m/(n+x*m).
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 *    For m >= 2, we use the simplest conversion.
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 *    For m < 2, (m-2)/2 < 0 so the conversion will not work, and we must use
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 *               a second conversion.
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 *    Note the division by p; this seems unavoidable
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 *    for m < 2, since the F density has a singularity as x (or p) -> 0.
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 */
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#include "nmath.h"
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#include "dpq.h"
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double df(double x, double m, double n, int give_log)
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{
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    double p, q, f, dens;
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#ifdef IEEE_754
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    if (ISNAN(x) || ISNAN(m) || ISNAN(n))
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	return x + m + n;
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#endif
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    if (m <= 0 || n <= 0) ML_ERR_return_NAN;
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    if (x < 0.)  return(R_D__0);
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    if (x == 0.) return(m > 2 ? R_D__0 : (m == 2 ? R_D__1 : ML_POSINF));
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    if (!R_FINITE(m) && !R_FINITE(n)) { /* both +Inf */
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	if(x == 1.) return ML_POSINF;
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	/* else */  return R_D__0;
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    }
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    if (!R_FINITE(n)) /* must be +Inf by now */
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	return(dgamma(x, m/2, 2./m, give_log));
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    if (m > 1e14) {/* includes +Inf: code below is inaccurate there */
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	dens = dgamma(1./x, n/2, 2./n, give_log);
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	return give_log ? dens - 2*log(x): dens/(x*x);
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    }
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    f = 1./(n+x*m);
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    q = n*f;
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    p = x*m*f;
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    if (m >= 2) {
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	f = m*q/2;
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	dens = dbinom_raw((m-2)/2, (m+n-2)/2, p, q, give_log);
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    }
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    else {
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	f = m*m*q / (2*p*(m+n));
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	dens = dbinom_raw(m/2, (m+n)/2, p, q, give_log);
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    }
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    return(give_log ? log(f)+dens : f*dens);
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}