/*

 *  AUTHOR

 *    Catherine Loader, catherine@research.bell-labs.com.

 *    October 23, 2000.

 *

 *  Merge in to R:

 *  Copyright (C) 2000-2014 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

 *  https://www.R-project.org/Licenses/

 *

 *

 * DESCRIPTION

 *

 *    Given a sequence of r successes and b failures, we sample n (\le b+r)

 *    items without replacement. The hypergeometric probability is the

 *    probability of x successes:

 *

 *           choose(r, x) * choose(b, n-x)

 *  p(x; r,b,n) =  -----------------------------  =

 *             choose(r+b, n)

 *

 *          dbinom(x,r,p) * dbinom(n-x,b,p)

 *        = --------------------------------

 *             dbinom(n,r+b,p)

 *

 *    for any p. For numerical stability, we take p=n/(r+b); with this choice,

 *    the denominator is not exponentially small.

 */

#include "nmath.h"

#include "dpq.h"

double dhyper(double x, double r, double b, double n, int give_log)

{

    double p, q, p1, p2, p3;

#ifdef IEEE_754

    if (ISNAN(x) || ISNAN(r) || ISNAN(b) || ISNAN(n))

  return x + r + b + n;

#endif

    if (R_D_negInonint(r) || R_D_negInonint(b) || R_D_negInonint(n) || n > r+b)

  ML_WARN_return_NAN;

    if(x < 0) return(R_D__0);

    R_D_nonint_check(x);// incl warning

    x = R_forceint(x);

    r = R_forceint(r);

    b = R_forceint(b);

    n = R_forceint(n);

    if (n < x || r < x || n - x > b) return(R_D__0);

    if (n == 0) return((x == 0) ? R_D__1 : R_D__0);

    p = ((double)n)/((double)(r+b));

    q = ((double)(r+b-n))/((double)(r+b));

    p1 = dbinom_raw(x, r, p,q,give_log);

    p2 = dbinom_raw(n-x,b, p,q,give_log);

    p3 = dbinom_raw(n,r+b, p,q,give_log);

    return( (give_log) ? p1 + p2 - p3 : p1*p2/p3 );

}