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GenNumpy.cpp
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GenNumpy.cpp
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#include "GenNumpy.h"
#include <algorithm>
#include <string>
GenNumpy::GenNumpy()
{
p_binomial = new binomial_t();
p_binomial->has_binomial = 0;
}
GenNumpy::~GenNumpy()
{
delete p_binomial;
}
std::string GenNumpy::getName()
{
return "Numpy";
}
int GenNumpy::gen(int n, double p)
{
if (p * n <= 30)
{
return random_binomial_inversion(n, p);
}
else
{
return genBTPE(n, p);
}
}
int GenNumpy::random_binomial_inversion(int n, double p)
{
double q, qn, np, px, U;
int X, bound;
if (!(p_binomial->has_binomial) || (p_binomial->nsave != n) ||
(p_binomial->psave != p)) {
p_binomial->nsave = n;
p_binomial->psave = p;
p_binomial->has_binomial = 1;
p_binomial->q = q = 1.0 - p;
p_binomial->r = qn = exp(n * log(q));
p_binomial->c = np = n * p;
p_binomial->m = bound = (int)std::min(double(n), np + 10.0 * sqrt(np * q + 1));
}
else {
q = p_binomial->q;
qn = p_binomial->r;
np = p_binomial->c;
bound = p_binomial->m;
}
X = 0;
px = qn;
do
U = (double)rand() / RAND_MAX;
while (U == 0.0);
while (U > px) {
X++;
if (X > bound) {
X = 0;
px = qn;
do
U = (double)rand() / RAND_MAX;
while (U == 0.0);
}
else {
U -= px;
px = ((n - X + 1) * p * px) / (X * q);
}
}
return X;
}
int GenNumpy::genBTPE(int n, double p)
{
double r, q, fm, p1, xm, xl, xr, c, laml, lamr, p2, p3, p4;
double a, u, v, s, F, rho, t, A, nrq, x1, x2, f1, f2, z, z2, w, w2, x;
int m, y, k, i;
if (!(p_binomial->has_binomial) || (p_binomial->nsave != n) ||
(p_binomial->psave != p)) {
/* initialize */
p_binomial->nsave = n;
p_binomial->psave = p;
p_binomial->has_binomial = 1;
p_binomial->r = r = std::min(p, 1.0 - p);
p_binomial->q = q = 1.0 - r;
p_binomial->fm = fm = n * r + r;
p_binomial->m = m = (int)floor(p_binomial->fm);
p_binomial->p1 = p1 = floor(2.195 * sqrt(n * r * q) - 4.6 * q) + 0.5;
p_binomial->xm = xm = m + 0.5;
p_binomial->xl = xl = xm - p1;
p_binomial->xr = xr = xm + p1;
p_binomial->c = c = 0.134 + 20.5 / (15.3 + m);
a = (fm - xl) / (fm - xl * r);
p_binomial->laml = laml = a * (1.0 + a / 2.0);
a = (xr - fm) / (xr * q);
p_binomial->lamr = lamr = a * (1.0 + a / 2.0);
if (lamr == 0.0)
{
int x = 0;
}
p_binomial->p2 = p2 = p1 * (1.0 + 2.0 * c);
p_binomial->p3 = p3 = p2 + c / laml;
p_binomial->p4 = p4 = p3 + c / lamr;
}
else {
r = p_binomial->r;
q = p_binomial->q;
fm = p_binomial->fm;
m = p_binomial->m;
p1 = p_binomial->p1;
xm = p_binomial->xm;
xl = p_binomial->xl;
xr = p_binomial->xr;
c = p_binomial->c;
laml = p_binomial->laml;
lamr = p_binomial->lamr;
p2 = p_binomial->p2;
p3 = p_binomial->p3;
p4 = p_binomial->p4;
}
/* sigh ... */
Step10:
nrq = n * r * q;
u = (double)rand() / RAND_MAX * p4;
do
v = (double)rand() / RAND_MAX;
while (v == 0.0);
if (u > p1)
goto Step20;
y = (int)floor(xm - p1 * v + u);
goto Step60;
Step20:
if (u > p2)
goto Step30;
x = xl + (u - p1) / c;
v = v * c + 1.0 - fabs(m - x + 0.5) / p1;
if (v > 1.0)
goto Step10;
y = (int)floor(x);
goto Step50;
Step30:
if (u > p3)
goto Step40;
y = (int)floor(xl + log(v) / laml);
/* Reject if v==0.0 since previous cast is undefined */
if ((y < 0) || (v == 0.0))
goto Step10;
v = v * (u - p2) * laml;
goto Step50;
Step40:
y = (int)floor(xr - log(v) / lamr);
/* Reject if v==0.0 since previous cast is undefined */
if ((y > n) || (v == 0.0))
goto Step10;
v = v * (u - p3) * lamr;
Step50:
k = llabs(y - m);
if ((k > 20) && (k < ((nrq) / 2.0 - 1)))
goto Step52;
s = r / q;
a = s * (n + 1);
F = 1.0;
if (m < y) {
for (i = m + 1; i <= y; i++) {
F *= (a / i - s);
}
}
else if (m > y) {
for (i = y + 1; i <= m; i++) {
F /= (a / i - s);
}
}
if (v > F)
goto Step10;
goto Step60;
Step52:
rho =
(k / (nrq)) * ((k * (k / 3.0 + 0.625) + 0.16666666666666666) / nrq + 0.5);
t = -k * k / (2 * nrq);
/* log(0.0) ok here */
A = log(v);
if (A < (t - rho))
goto Step60;
if (A > (t + rho))
goto Step10;
x1 = y + 1;
f1 = m + 1;
z = n + 1 - m;
w = n - y + 1;
x2 = x1 * x1;
f2 = f1 * f1;
z2 = z * z;
w2 = w * w;
if (A > (xm * log(f1 / x1) + (n - m + 0.5) * log(z / w) +
(y - m) * log(w * r / (x1 * q)) +
(13680. - (462. - (132. - (99. - 140. / f2) / f2) / f2) / f2) / f1 /
166320. +
(13680. - (462. - (132. - (99. - 140. / z2) / z2) / z2) / z2) / z /
166320. +
(13680. - (462. - (132. - (99. - 140. / x2) / x2) / x2) / x2) / x1 /
166320. +
(13680. - (462. - (132. - (99. - 140. / w2) / w2) / w2) / w2) / w /
166320.)) {
goto Step10;
}
Step60:
if (p > 0.5) {
y = n - y;
}
return y;
}