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/*
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 *  Mathlib : A C Library of Special Functions
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 *  Copyright (C) 1998 Ross Ihaka
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 *  Copyright (C) 2000 The R Development Core Team
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 *  Copyright (C) 2003 The R Foundation
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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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 *  SYNOPSIS
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 *
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 *    #include <Rmath.h>
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 *    double lbeta(double a, double b);
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 *
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 *  DESCRIPTION
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 *
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 *    This function returns the value of the log beta function.
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 *
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 *  NOTES
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 *
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 *    This routine is a translation into C of a Fortran subroutine
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 *    by W. Fullerton of Los Alamos Scientific Laboratory.
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 */
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#include "nmath.h"
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double lbeta(double a, double b)
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{
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    double corr, p, q;
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    p = q = a;
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    if(b < p) p = b;/* := min(a,b) */
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    if(b > q) q = b;/* := max(a,b) */
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#ifdef IEEE_754
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    if(ISNAN(a) || ISNAN(b))
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	return a + b;
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#endif
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    /* both arguments must be >= 0 */
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    if (p < 0)
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	ML_ERR_return_NAN
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    else if (p == 0) {
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	return ML_POSINF;
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    }
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    else if (!R_FINITE(q)) {
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	return ML_NEGINF;
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    }
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    if (p >= 10) {
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	/* p and q are big. */
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	corr = lgammacor(p) + lgammacor(q) - lgammacor(p + q);
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	return log(q) * -0.5 + M_LN_SQRT_2PI + corr
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		+ (p - 0.5) * log(p / (p + q)) + q * log1p(-p / (p + q));
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    }
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    else if (q >= 10) {
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	/* p is small, but q is big. */
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	corr = lgammacor(q) - lgammacor(p + q);
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	return lgammafn(p) + corr + p - p * log(p + q)
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		+ (q - 0.5) * log1p(-p / (p + q));
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    }
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    else
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	/* p and q are small: p <= q < 10. */
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	return log(gammafn(p) * (gammafn(q) / gammafn(p + q)));
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}