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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, 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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 *   To compute the binomial probability, call dbinom(x,n,p).
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 *   This checks for argument validity, and calls dbinom_raw().
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 *
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 *   dbinom_raw() does the actual computation; note this is called by
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 *   other functions in addition to dbinom().
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 *     (1) dbinom_raw() has both p and q arguments, when one may be represented
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 *         more accurately than the other (in particular, in df()).
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 *     (2) dbinom_raw() does NOT check that inputs x and n are integers. This
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 *         should be done in the calling function, where necessary.
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 *         -- but is not the case at all when called e.g., from df() or dbeta() !
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 *     (3) Also does not check for 0 <= p <= 1 and 0 <= q <= 1 or NaN's.
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 *         Do this in the calling function.
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 */
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#include "nmath.h"
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#include "dpq.h"
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double attribute_hidden
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dbinom_raw(double x, double n, double p, double q, int give_log)
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{
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    double lf, lc;
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    if (p == 0) return((x == 0) ? R_D__1 : R_D__0);
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    if (q == 0) return((x == n) ? R_D__1 : R_D__0);
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    if (x == 0) {
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	if(n == 0) return R_D__1;
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	lc = (p < 0.1) ? -bd0(n,n*q) - n*p : n*log(q);
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	return( R_D_exp(lc) );
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    }
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    if (x == n) {
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	lc = (q < 0.1) ? -bd0(n,n*p) - n*q : n*log(p);
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	return( R_D_exp(lc) );
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    }
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    if (x < 0 || x > n) return( R_D__0 );
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    /* n*p or n*q can underflow to zero if n and p or q are small.  This
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       used to occur in dbeta, and gives NaN as from R 2.3.0.  */
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    lc = stirlerr(n) - stirlerr(x) - stirlerr(n-x) - bd0(x,n*p) - bd0(n-x,n*q);
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    /* f = (M_2PI*x*(n-x))/n; could overflow or underflow */
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    lf = log(M_2PI) + log(x) + log(n-x) - log(n);
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    return R_D_exp(lc - 0.5*lf);
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}
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double dbinom(double x, double n, double p, int give_log)
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{
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#ifdef IEEE_754
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    /* NaNs propagated correctly */
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    if (ISNAN(x) || ISNAN(n) || ISNAN(p)) return x + n + p;
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#endif
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    if (p < 0 || p > 1 || R_D_negInonint(n))
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	ML_ERR_return_NAN;
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    R_D_nonint_check(x);
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    if (x < 0 || !R_FINITE(x)) return R_D__0;
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    n = R_D_forceint(n);
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    x = R_D_forceint(x);
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    return dbinom_raw(x, n, p, 1-p, give_log);
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}