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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/ | |
* | |
* THIS FILE WAS MODIFIED; USE AT YOUR OWN RISK! | |
*/ | |
#include <math.h> | |
#include <stdio.h> | |
#include <limits.h> | |
#include <stdlib.h> | |
#include <time.h> | |
double unif_rand() { | |
return (double) (rand()) / (double) RAND_MAX; | |
} | |
double rbinom(double nin, double pp) | |
{ | |
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; | |
r = round(nin); | |
if (r < 0 || pp < 0. || pp > 1.) return -1; | |
if (r == 0 || pp == 0.) { | |
return 0; | |
} | |
if (pp == 1.) return r; | |
if (r >= INT_MAX) return -1; | |
/* else */ | |
n = (int) r; | |
if(pp < 1.0 - pp) { | |
p = pp; | |
} else { | |
p = 1.0 - 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 = pow(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 : ------------------- */ | |
while(1) { | |
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 : ------------------------- */ | |
while(1) { | |
ix = 0; | |
f = qn; | |
u = unif_rand(); | |
while(1) { | |
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; | |
} | |
int main() { | |
srand((unsigned) time(0)); | |
printf("%f\n", rbinom(1000000, 0.2)); | |
return 0; | |
} |
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