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/*
* Mathlib : A C Library of Special Functions
* Copyright (C) 1998 Ross Ihaka
* Copyright (C) 2000-2014 The R Core Team
* Copyright (C) 2007 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 rbinom(double nin, double pp)
*
* DESCRIPTION
*
* Random variates from the binomial distribution.
*
* REFERENCE
*
* Kachitvichyanukul, V. and Schmeiser, B. W. (1988).
* Binomial random variate generation.
* Communications of the ACM 31, 216-222.
* (Algorithm BTPEC).
*/
#include "nmath.h"
#include "dpq.h"
#include <stdlib.h>
#include <limits.h>
#define repeat for(;;)
double rbinom(double nin, double pp)
{
/* FIXME: These should become THREAD_specific globals : */
static double c, fm, npq, p1, p2, p3, p4, qn;
static double xl, xll, xlr, xm, xr;
static double psave = -1.0;
static int nsave = -1;
static int m;
double f, f1, f2, u, v, w, w2, x, x1, x2, z, z2;
double p, q, np, g, r, al, alv, amaxp, ffm, ynorm;
int i, ix, k, n;
if (!R_FINITE(nin)) ML_ERR_return_NAN;
r = R_forceint(nin);
if (r != nin) ML_ERR_return_NAN;
if (!R_FINITE(pp) ||
/* n=0, p=0, p=1 are not errors <TSL>*/
r < 0 || pp < 0. || pp > 1.) ML_ERR_return_NAN;
if (r == 0 || pp == 0.) return 0;
if (pp == 1.) return r;
if (r >= INT_MAX)/* evade integer overflow,
and r == INT_MAX gave only even values */
return qbinom(unif_rand(), r, pp, /*lower_tail*/ 0, /*log_p*/ 0);
/* else */
n = (int) r;
p = fmin2(pp, 1. - pp);
q = 1. - p;
np = n * p;
r = p / q;
g = r * (n + 1);
/* Setup, perform only when parameters change [using static (globals): */
/* FIXING: Want this thread safe
-- use as little (thread globals) as possible
*/
if (pp != psave || n != nsave) {
psave = pp;
nsave = n;
if (np < 30.0) {
/* inverse cdf logic for mean less than 30 */
qn = R_pow_di(q, n);
goto L_np_small;
} else {
ffm = np + p;
m = (int) ffm;
fm = m;
npq = np * q;
p1 = (int)(2.195 * sqrt(npq) - 4.6 * q) + 0.5;
xm = fm + 0.5;
xl = xm - p1;
xr = xm + p1;
c = 0.134 + 20.5 / (15.3 + fm);
al = (ffm - xl) / (ffm - xl * p);
xll = al * (1.0 + 0.5 * al);
al = (xr - ffm) / (xr * q);
xlr = al * (1.0 + 0.5 * al);
p2 = p1 * (1.0 + c + c);
p3 = p2 + c / xll;
p4 = p3 + c / xlr;
}
} else if (n == nsave) {
if (np < 30.0)
goto L_np_small;
}
/*-------------------------- np = n*p >= 30 : ------------------- */
repeat {
u = unif_rand() * p4;
v = unif_rand();
/* triangular region */
if (u <= p1) {
ix = (int)(xm - p1 * v + u);
goto finis;
}
/* parallelogram region */
if (u <= p2) {
x = xl + (u - p1) / c;
v = v * c + 1.0 - fabs(xm - x) / p1;
if (v > 1.0 || v <= 0.)
continue;
ix = (int) x;
} else {
if (u > p3) { /* right tail */
ix = (int)(xr - log(v) / xlr);
if (ix > n)
continue;
v = v * (u - p3) * xlr;
} else {/* left tail */
ix = (int)(xl + log(v) / xll);
if (ix < 0)
continue;
v = v * (u - p2) * xll;
}
}
/* determine appropriate way to perform accept/reject test */
k = abs(ix - m);
if (k <= 20 || k >= npq / 2 - 1) {
/* explicit evaluation */
f = 1.0;
if (m < ix) {
for (i = m + 1; i <= ix; i++)
f *= (g / i - r);
} else if (m != ix) {
for (i = ix + 1; i <= m; i++)
f /= (g / i - r);
}
if (v <= f)
goto finis;
} else {
/* squeezing using upper and lower bounds on log(f(x)) */
amaxp = (k / npq) * ((k * (k / 3. + 0.625) + 0.1666666666666) / npq + 0.5);
ynorm = -k * k / (2.0 * npq);
alv = log(v);
if (alv < ynorm - amaxp)
goto finis;
if (alv <= ynorm + amaxp) {
/* stirling's formula to machine accuracy */
/* for the final acceptance/rejection test */
x1 = ix + 1;
f1 = fm + 1.0;
z = n + 1 - fm;
w = n - ix + 1.0;
z2 = z * z;
x2 = x1 * x1;
f2 = f1 * f1;
w2 = w * w;
if (alv <= xm * log(f1 / x1) + (n - m + 0.5) * log(z / w) + (ix - m) * log(w * p / (x1 * q)) + (13860.0 - (462.0 - (132.0 - (99.0 - 140.0 / f2) / f2) / f2) / f2) / f1 / 166320.0 + (13860.0 - (462.0 - (132.0 - (99.0 - 140.0 / z2) / z2) / z2) / z2) / z / 166320.0 + (13860.0 - (462.0 - (132.0 - (99.0 - 140.0 / x2) / x2) / x2) / x2) / x1 / 166320.0 + (13860.0 - (462.0 - (132.0 - (99.0 - 140.0 / w2) / w2) / w2) / w2) / w / 166320.)
goto finis;
}
}
}
L_np_small:
/*---------------------- np = n*p < 30 : ------------------------- */
repeat {
ix = 0;
f = qn;
u = unif_rand();
repeat {
if (u < f)
goto finis;
if (ix > 110)
break;
u -= f;
ix++;
f *= (g / ix - r);
}
}
finis:
if (psave > 0.5)
ix = n - ix;
return (double)ix;
}
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