src/nmath/lbeta.c

/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998 Ross Ihaka
 *  Copyright (C) 2000-12 The R Core Team
 *  Copyright (C) 2003 The R Foundation
 *
 *  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
 *  https://www.R-project.org/Licenses/
 *
 *  SYNOPSIS
 *
 *    #include <Rmath.h>
 *    double lbeta(double a, double b);
 *
 *  DESCRIPTION
 *
 *    This function returns the value of the log beta function.
 *
 *  NOTES
 *
 *    This routine is a translation into C of a Fortran subroutine
 *    by W. Fullerton of Los Alamos Scientific Laboratory.
 */

#include "nmath.h"

double lbeta(double a, double b)
{
    double corr, p, q;

#ifdef IEEE_754
    if(ISNAN(a) || ISNAN(b))
	return a + b;
#endif
    p = q = a;
    if(b < p) p = b;/* := min(a,b) */
    if(b > q) q = b;/* := max(a,b) */

    /* both arguments must be >= 0 */
    if (p < 0)
	ML_ERR_return_NAN
    else if (p == 0) {
	return ML_POSINF;
    }
    else if (!R_FINITE(q)) { /* q == +Inf */
	return ML_NEGINF;
    }

    if (p >= 10) {
	/* p and q are big. */
	corr = lgammacor(p) + lgammacor(q) - lgammacor(p + q);
	return log(q) * -0.5 + M_LN_SQRT_2PI + corr
		+ (p - 0.5) * log(p / (p + q)) + q * log1p(-p / (p + q));
    }
    else if (q >= 10) {
	/* p is small, but q is big. */
	corr = lgammacor(q) - lgammacor(p + q);
	return lgammafn(p) + corr + p - p * log(p + q)
		+ (q - 0.5) * log1p(-p / (p + q));
    }
    else {
	/* p and q are small: p <= q < 10. */
	/* R change for very small args */
	if (p < 1e-306) return lgamma(p) + (lgamma(q) - lgamma(p+q));
	else return log(gammafn(p) * (gammafn(q) / gammafn(p + q)));
    }
}