The R Project SVN R

/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 2000-2026 The R Core Team
 *  Copyright (C) 1998 Ross Ihaka
 *  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).

 * Fixed two signs s/+/-/ in Stirling terms -- PR#19049 (2026-04)
 */

#define CALLED_FROM_rbinom
#include <R_ext/Random.h>
#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 u, v, x;
    double p, q, np, g, r;
    int i, ix, k, n;

    if (!R_FINITE(nin)) ML_WARN_return_NAN;
    r = R_forceint(nin);
    if (r != nin) ML_WARN_return_NAN;
    if (!R_FINITE(pp) ||
    /* n=0, p=0, p=1 are not errors <TSL>*/
    r < 0 || pp < 0. || pp > 1.)    ML_WARN_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) { // (n, p) have changed: recompute "constants" if(np >= 30.)
    psave = pp;
    nsave = n;
    if (np < 30.0) {
        /* inverse cdf logic for mean less than 30 */
        qn = /* (1-p)^n = q^n, but (1-p) may have underflown to 1 : */
        p > 0.25 ? R_pow_di(q, n) : exp(n * log1p(-p));
        goto L_np_small;
    } else {
        double 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);
        double 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 { // pp == psave  &&  n == nsave
    if (np < 30.0) // use qn {etc}
        goto L_np_small;
    }

    /*-------------------------- np = n*p >= 30 : ------------------- */
    Binomtype rbinom_kind = R_binom_kind(); /* ../main/RNG.c */
    repeat {
      u = unif_rand() * p4;
      v = unif_rand();
      /* triangular region */
      if (u <= p1) {
      ix = (int)(xm - p1 * v + u);
      goto finis;
      }
      /* else -- parallelogram region */
      if (u <= p2) { /* p1 < 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: p3 < u <= p4 */
      ix = (int)(xr - log(v) / xlr);
      if (ix > n)
          continue;
      v = v * (u - p3) * xlr;
      } else { /* left tail:  p2 < u <= p3 */
      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 */
      double f = 1.;
      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 { /* 21 <=  k  <=  npq/2 - 2 : ==> 21 <= npq/2 - 2  <==> npq >= 46
          * squeezing using upper and lower bounds on log(f(x)) */

      const double one_6th = (rbinom_kind == BTPE) ? 0.16666666666666666 : 0.1666666666666;
      double
          amaxp = (k / npq) * ((k * (k / 3. + 0.625) + one_6th) / 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 */
          double x1 = ix + 1,
          f1 = fm + 1.,
          z = n + 1 - fm,
          w = n - ix + 1.,
          z2 = z * z,
          x2 = x1 * x1,
          f2 = f1 * f1,
          w2 = w * w;

          if(rbinom_kind == BTPE) {
          if (alv <= xm * log(f1 / x1) + (n - m + 0.5) * log(z / w) + (ix - m) * log(w * p / (x1 * q)) +
              ((13860. - (462. - (132. - (99. - 140. / f2) / f2) / f2) / f2) / f1 +
               (13860. - (462. - (132. - (99. - 140. / z2) / z2) / z2) / z2) / z )/ 166320. - /* was '+' */
              ((13860. - (462. - (132. - (99. - 140. / x2) / x2) / x2) / x2) / x1 +
               (13860. - (462. - (132. - (99. - 140. / w2) / w2) / w2) / w2) / w )/ 166320.  )
          goto finis;
          }
          else { // rbinom_kind == BUGGY_BTPE
          if (alv <= xm * log(f1 / x1) + (n - m + 0.5) * log(z / w) + (ix - m) * log(w * p / (x1 * q)) +
              (13860. - (462. - (132. - (99. - 140. / f2) / f2) / f2) / f2) / f1 / 166320. +
              (13860. - (462. - (132. - (99. - 140. / z2) / z2) / z2) / z2) / z  / 166320. + // wrong
              (13860. - (462. - (132. - (99. - 140. / x2) / x2) / x2) / x2) / x1 / 166320. + // wrong
              (13860. - (462. - (132. - (99. - 140. / w2) / w2) / w2) / w2) / w  / 166320.  )
          goto finis;
          }
      }
      }
    } // end repeat {}

 L_np_small:
    /*---------------------- np = n*p < 30 : ------------------------- */

  repeat {
     // fn(qn, g, r)
     ix = 0;
     double f = qn,
     u = unif_rand();
     repeat {
     if (u < f)
         goto finis;
     if (ix > 110) // <-- why '110' ? -- always sufficient?
         break; // "reject" : try next u = unif()
     u -= f;
     ix++;
     f *= (g / ix - r);
     }
  }
 finis:
    if (psave > 0.5)
     ix = n - ix;
  return (double)ix;
}