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/*

 *  Mathlib : A C Library of Special Functions

 *  Copyright (C) 2000-2026 The R Core Team

 *  Copyright (C) 2005-2020 The R Foundation

 *  Copyright (C) 1998 Ross Ihaka

 *

 *  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 rhyper(double NR, double NB, double n);

 *

 *  DESCRIPTION

 *

 *    Random variates from the hypergeometric distribution.

 *    Returns the number of white balls drawn when kk balls

 *    are drawn at random from an urn containing nn1 white

 *    and nn2 black balls.

 *

 *  REFERENCE

 *

 *    V. Kachitvichyanukul and B. Schmeiser (1985).

 *    ``Computer generation of hypergeometric random variates,''

 *    Journal of Statistical Computation and Simulation 22, 127-145.

 *

 *    The original algorithm had a bug -- R bug report PR#7314 --

 *    giving numbers slightly too small in case III h2pe

 *    where (m < 100 || ix <= 50) , see below.

 */

#include "nmath.h"

#include "dpq.h"

#include <limits.h>

// afc(i) :=  ln( i! )	[logarithm of the factorial i] = {R:} lgamma(i + 1) = {C:} lgammafn(i + 1)

static double afc(int i)

{

    // If (i > 7), use Stirling's approximation, otherwise use table lookup.

    const static double al[8] =

    {

	0.0,/*ln(0!)=ln(1)*/

	0.0,/*ln(1!)=ln(1)*/

	0.69314718055994530941723212145817,/*ln(2) */

	1.79175946922805500081247735838070,/*ln(6) */

	3.17805383034794561964694160129705,/*ln(24)*/

	4.78749174278204599424770093452324,

	6.57925121201010099506017829290394,

	8.52516136106541430016553103634712

	/* 10.60460290274525022841722740072165, approx. value below =

	   10.6046028788027; rel.error = 2.26 10^{-9}

	  FIXME: Use constants and if(n > ..) decisions from ./stirlerr.c

	  -----  will be even *faster* for n > 500 (or so)

	*/

    };

    if (i < 0) {

	MATHLIB_WARNING(("rhyper.c: afc(i), i=%d < 0 -- SHOULD NOT HAPPEN!\n"), i);

	return -1; // unreached

    }

    if (i <= 7)

	return al[i];

    // else i >= 8 :

    double di = i, i2 = di*di;

    return (di + 0.5) * log(di) - di + M_LN_SQRT_2PI +

	(0.0833333333333333 - 0.00277777777777778 / i2) / di;

}

//     rhyper(NR, NB, n) -- NR 'red', NB 'blue', n drawn, how many are 'red'

double rhyper(double nn1in, double nn2in, double kkin)

{

    /* check parameter validity */

    if(!R_FINITE(nn1in) || !R_FINITE(nn2in) || !R_FINITE(kkin))

	ML_WARN_return_NAN;

    nn1in = R_forceint(nn1in);

    nn2in = R_forceint(nn2in);

    kkin  = R_forceint(kkin);

    double N = nn1in + nn2in;

    if (nn1in < 0 || nn2in < 0 || kkin < 0 || kkin > nn1in + nn2in)

	ML_WARN_return_NAN;

    if (N > INT_MAX || kkin >= INT_MAX) {

	/* large n -- evade integer overflow (and inappropriate algorithms)

	   -------- */

#ifdef DEBUG_rhyper

	REprintf("rhyper(nn1=%.0f, nn2=%.0f, kk=%.0f): 'large n' case\n", nn1in, nn2in, kkin);

#endif

        // FIXME: Much faster to give rbinom() approx when appropriate; -> see Kuensch(1989)

	// Johnson, Kotz,.. p.258 (top) mention the *four* different binomial approximations

	if(kkin == 1.) { // Bernoulli

	    return rbinom(kkin, nn1in / (nn1in + nn2in));

	}

	// Slow, but safe: return  F^{-1}(U)  where F(.) = phyper(.) and  U ~ U[0,1]

	return qhyper(unif_rand(), nn1in, nn2in, kkin,

		      /*lower_tail =*/ false, /*log_p = */ false);

	// lower_tail=false: a thinko, is still "correct" as equiv. to  U <--> 1-U

    }

    int

	nn1 = (int)nn1in,

	nn2 = (int)nn2in,

	kk  = (int)kkin;

    /* These should become 'thread_local globals' : */

    static int ks = -1, n1s = -1, n2s = -1;

    static int m, minjx, maxjx;

    static int k, n1, n2; // <- not allowing larger integer par

    bool setup1, setup2;

    /* if new parameter values, initialize */

    if (nn1 != n1s || nn2 != n2s) { // n1 | n2 is changed: setup all

	setup1 = true;	setup2 = true;

    } else if (kk != ks) { // n1 & n2 are unchanged: setup 'k' only

	setup1 = false;	setup2 = true;

    } else { // all three unchanged ==> no setup

	setup1 = false;	setup2 = false;

    }

    if (setup1) { // n1 & n2

	n1s = nn1; n2s = nn2; // save

	if (nn1 <= nn2) {

	    n1 = nn1; n2 = nn2;

	} else { // nn2 < nn1

	    n1 = nn2; n2 = nn1;

	}

	// now have n1 <= n2

    }

    if (setup2) { // k

	ks = kk; // save

	if ((double)kk + kk >= N) { // this could overflow

	    k = (int)(N - kk);

	} else {

	    k = kk;

	}

	// now have  k < N/2 = (n1+n2)/2

    }

    if (setup1 || setup2) {

	m = (int) ((k + 1.) * (n1 + 1.) / (N + 2.)); // m := floor(adjusted mean E[.])

	minjx = imax2(0, k - n2);

	maxjx = imin2(n1, k);

#ifdef DEBUG_rhyper

	REprintf("rhyper(n1=%d, n2=%d, k=%d), setup: floor(a.mean)=: m = %d, [min,maxjx]= [%d,%d]\n",

		 nn1, nn2, kk, m, minjx, maxjx);

#endif

    }

#ifdef DEBUG_rhyper

    else

	REprintf("rhyper(n1=%d, n2=%d, k=%d); setup UNchanged\n", nn1, nn2, kk);

#endif

    // generate random variate --- Three basic cases ---------------------------

    int ix; // return value (coerced to double at the very end) .. FIXME?? what if overflows

    if (minjx == maxjx) { /* I: degenerate distribution ---------------- */

#ifdef DEBUG_rhyper

	REprintf("rhyper(), branch I (degenerate): ix := maxjx = %d\n", maxjx);

#endif

	ix = maxjx;

	goto L_finis; // return appropriate variate

    } else if (m - minjx < 10) { // II: (Scaled) algorithm HIN (inverse transformation) ----

	const static double scale = 1e25; // scaling factor against (early) underflow

	const static double con = 57.5646273248511421;

	          // 25*log(10) = log(scale) { <==> exp(con) == scale }

	static double w,

	    lw; // = log(w);  w = exp(lw) * scale = exp(lw + log(scale)) = exp(lw + con)

	if (setup1 || setup2) {

	    // NB:  n1 <= n2  here

	    if (k < n2) {

		lw = afc(n2) + afc(n1 + n2 - k) - afc(n2 - k) - afc(n1 + n2);

	    } else {

		lw = afc(n1) + afc(     k     ) - afc(k - n2) - afc(n1 + n2);

	    }

	    w = exp(lw + con);

	}

#ifdef DEBUG_rhyper

	REprintf("  branch II; w = %g %s\n", w,

		 (w > 0) ? "> 0" : "= 0 <==> Underflow __NOT GOOD__");

#endif

	if(w <= 0.)

	    MATHLIB_ERROR(_("w = %g <= 0: Underflow in rhyper()  SHOULD NOT HAPPEN!"), w);

	// FIXME: MM has code "rhyper.c+M3" for switching to log space if w == 0

	double p, u;

      L10:

	p = w;

	ix = minjx;

	u = unif_rand() * scale;

#ifdef DEBUG_rhyper

	REprintf("  _new_ u = %g\n", u);

#endif

	while (u > p) {

	    u -= p;

	    p *= ((double) n1 - ix) * (k - ix);

	    ix++;

	    p = p / ix / (n2 - k + ix);

#ifdef DEBUG_rhyper

	    REprintf("       ix=%3d, u=%11g, p=%20.14g (u-p=%g)\n", ix, u, p, u-p);

#endif

	    if (ix > maxjx)

		goto L10;

	    // FIXME  if(p == 0.)  we also "have lost"  => goto L10

	}

    } else { /* III : H2PE Algorithm --------------------------------------- */

	static double a, xl, xr, lamdl, lamdr, p1, p2, p3;

	if (setup1 || setup2) {

	    double

		s = sqrt((N - k) * k * n1 * n2 / (N - 1) / N / N),

		/* remark: d is defined in reference without int. */

		/* the truncation centers the cell boundaries at 0.5 */

		d = (int) (1.5 * s) + .5;

	    xl = m - d + .5;

	    xr = m + d + .5;

	    a = afc(m) + afc(n1 - m) + afc(k - m) + afc(n2 - k + m);

	    double

		kl = exp(a - afc((int) (xl)) - afc((int) (n1 - xl))

			 - afc((int) (k - xl))

			 - afc((int) (n2 - k + xl))),

		kr = exp(a - afc((int) (xr - 1))

			 - afc((int) (n1 - xr + 1))

			 - afc((int) (k - xr + 1))

			 - afc((int) (n2 - k + xr - 1)));

	    lamdl = -log(xl * (n2 - k + xl) / (n1 - xl + 1) / (k - xl + 1));

	    lamdr = -log((n1 - xr + 1) * (k - xr + 1) / xr / (n2 - k + xr));

	    p1 = d + d;

	    p2 = p1 + kl / lamdl;

	    p3 = p2 + kr / lamdr;

#ifdef DEBUG_rhyper

	    REprintf("rhyper(), branch III {accept/reject}: (xl,xr)= (%g,%g); lamdl,r = (%g,%g)\n",

		     xl, xr, lamdl, lamdr);

	    REprintf(" --------> (p1,p2,p3) = (%g,%g,%g)\n", p1,p2,p3);

	}

	else

	    REprintf("rhyper(), branch III {accept/reject}: NO setup needed; lamdl,r = (%g,%g)\n",

		     lamdl, lamdr);

#else

        }

#endif

	/* acceptance/rejection test */

	bool reject = true;

        int n_uv = 0;

    do { // L30: -------------- acceptance / rejection : loop while reject=true -------------

	double

	    u = unif_rand() * p3,

	    v = unif_rand();

	n_uv++;

	if(n_uv >= 10000) {

	    REprintf("rhyper(*, n1=%d, n2=%d, k=%d): branch III: giving up after %d rejections\n",

		     nn1, nn2, kk, n_uv);

	    ML_WARN_return_NAN;

        }

#ifdef DEBUG_rhyper

	REprintf(" ... L30 [%d]: new (u=%g, v ~ U[0,1]=%g): ", n_uv, u,v);

#endif

	if (u < p1) {		/* rectangular region */

	    ix = (int) (xl + u);

#ifdef DEBUG_rhyper

	    REprintf(" rectangular: ix=%d\n", ix);

#endif

	} else if (u <= p2) {	/* left tail */

	    ix = (int) (xl + log(v) / lamdl);

#ifdef DEBUG_rhyper

	    REprintf(" left tail: ix=%d %s", ix, (ix < minjx)? "< minjx (=> L30)\n" : ">= minjx;");

#endif

	    if (ix < minjx)

		continue; // goto L30

	    v = v * (u - p1) * lamdl;

	} else {		/* right tail */

	    ix = (int) (xr - log(v) / lamdr);

#ifdef DEBUG_rhyper

	    REprintf(" right tail: ix=%d %s", ix, (ix > maxjx)? "> maxjx (=> L30)\n" : "< maxjx;");

#endif

	    if (ix > maxjx)

		continue; // goto L30

	    v = v * (u - p2) * lamdr;

	}

#ifdef DEBUG_rhyper

	if(u >= p1) REprintf(" new v = %g\n", v);

#endif

	if (m < 100 || ix <= 50) {

	    /* explicit evaluation */

	    /* The original algorithm (and TOMS 668) have

		   f = f * i * (n2 - k + i) / (n1 - i) / (k - i);

	       in the (m > ix) case, but the definition of the

	       recurrence relation on p134 shows that the +1 is

	       needed. */

	    double f = 1.0;

	    if (m < ix) {

		for (int i = m + 1; i <= ix; i++)

		    f = f * (n1 - i + 1) * (k - i + 1) / (n2 - k + i) / i;

	    } else if (m > ix) {

		for (int i = ix + 1; i <= m; i++)

		    f = f * i * (n2 - k + i) / (n1 - i + 1) / (k - i + 1);

	    }

#ifdef DEBUG_rhyper

	    REprintf(" small m or ix: f = %g\n", f);

#endif

	    if (v <= f) {

		reject = false;

	    }

	} else {

	    const static double deltal = 0.0078;

	    const static double deltau = 0.0034;

#ifdef DEBUG_rhyper

	    REprintf(" ... accept/reject 'large' case v=%g\n", v);

#endif

	    /* squeeze using upper and lower bounds */

	    double

		y = ix,

		y1 = y + 1.0,

		ym = y - m,

		yn = n1 - y + 1.0,

		yk = k  - y + 1.0,

		nk = n2 - k + y1,

		r = -ym / y1,

		s =  ym / yn,

		t =  ym / yk,

		e = -ym / nk,

		g = yn * yk / (y1 * nk) - 1.0,

		dg = (g < 0.0) ? 1. + g : 1.,

		gu = g * (1.0 + g * (-0.5 + g / 3.0)),

		gl = gu - .25 * (g * g * g * g) / dg,

		xm = m + 0.5,

		xn = n1 - m + 0.5,

		xk = k - m + 0.5,

		nm = n2 - k + xm,

		ub = y * gu - m * gl + deltau

		+ xm * r * (1. + r * (-0.5 + r / 3.0))

		+ xn * s * (1. + s * (-0.5 + s / 3.0))

		+ xk * t * (1. + t * (-0.5 + t / 3.0))

		+ nm * e * (1. + e * (-0.5 + e / 3.0));

	    /* test against upper bound */

	    double alv = log(v);

	    if (alv > ub) {

		reject = true;

	    } else {

		/* test against lower bound */

		double dr = xm * (r * r * r * r);

		if (r < 0.)

		    dr /= (1.0 + r);

		double ds = xn * (s * s * s * s);

		if (s < 0.0)

		    ds /= (1.0 + s);

		double dt = xk * (t * t * t * t);

		if (t < 0.0)

		    dt /= (1.0 + t);

		double de = nm * (e * e * e * e);

		if (e < 0.0)

		    de /= (1.0 + e);

		if (alv < ub - 0.25 * (dr + ds + dt + de)

		    + (y + m) * (gl - gu) - deltal) {

		    reject = false;

		}

		else {

		    /* * Stirling's formula to machine accuracy

		     */

		    if (alv <= (a - afc(ix) - afc(n1 - ix)

				- afc(k - ix) - afc(n2 - k + ix))) {

			reject = false;

		    } else {

			reject = true;

		    }

		}

	    }

	} // end{ III "large" }

    } while (reject);

    } // end{branch III}

L_finis:  /* return appropriate variate */

#ifdef DEBUG_rhyper

    REprintf(" L_finis: ix = %d, then", ix);

#endif

    if ((double)kk + kk >= N) {

	if (nn1 > nn2) {

	    ix = kk - nn2 + ix;

	} else {

	    ix = nn1 - ix;

	}

    } else if (nn1 > nn2) {

	ix = kk - ix;

    }

#ifdef DEBUG_rhyper

    REprintf(" %d\n", ix);

#endif

    return ix;

}