private long SampleUsingInversion()
{
var px = qn;
var U = RandomState.NextDouble();
var X = 0L;
while (U > px)
{
X++;
if (X > bound)
{
X = 0;
px = qn;
U = RandomState.NextDouble();
}
else
{
U -= px;
px = ((NSamples - X + 1) * SuccessProbability * px) / (X * FailureProbability);
}
}
return(X);
}
private long SampleUsingBTPE()
{
// The following code is ported from NumPy's binomial
// sampling implementation.
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;
long m, y, k, i;
/* initialize */
r = Min(SuccessProbability, FailureProbability);
q = 1.0 - r;
fm = NSamples * r + r;
m = (long)Floor(fm);
p1 = Floor(2.195 * Sqrt(NSamples * r * q) - 4.6 * q) + 0.5;
xm = m + 0.5;
xl = xm - p1;
xr = xm + p1;
c = 0.134 + 20.5 / (15.3 + m);
a = (fm - xl) / (fm - xl * r);
laml = a * (1.0 + a / 2.0);
a = (xr - fm) / (xr * q);
lamr = a * (1.0 + a / 2.0);
p2 = p1 * (1.0 + 2.0 * c);
p3 = p2 + c / laml;
p4 = p3 + c / lamr;
/* sigh ... */
Step10:
nrq = NSamples * r * q;
u = RandomState.NextDouble() * p4;
v = RandomState.NextDouble();
if (u > p1)
{
goto Step20;
}
y = (long)Floor(xm - p1 * v + u);
goto Step60;
Step20:
if (u > p2)
{
goto Step30;
}
x = xl + (u - p1) / c;
v = v * c + 1.0 - Abs(m - x + 0.5) / p1;
if (v > 1.0)
{
goto Step10;
}
y = (long)Floor(x);
goto Step50;
Step30:
if (u > p3)
{
goto Step40;
}
y = (long)Floor(xl + Log(v) / laml);
/* Reject if v == 0.0 since cast of inf not well defined */
if ((y < 0) || (v == 0.0))
{
goto Step10;
}
v = v * (u - p2) * laml;
goto Step50;
Step40:
y = (long)Floor(xr - Log(v) / lamr);
/* Reject if v == 0.0 since cast of inf not well defined */
if ((y > NSamples) || (v == 0.0))
{
goto Step10;
}
v = v * (u - p3) * lamr;
Step50:
k = Abs(y - m);
if ((k > 20) && (k < ((nrq) / 2.0 - 1)))
{
goto Step52;
}
s = r / q;
a = s * (NSamples + 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); // lgtm [cs/loss-of-precision]
A = Log(v);
if (A < (t - rho))
{
goto Step60;
}
if (A > (t + rho))
{
goto Step10;
}
x1 = y + 1;
f1 = m + 1;
z = NSamples + 1 - m;
w = NSamples - y + 1;
x2 = x1 * x1;
f2 = f1 * f1;
z2 = z * z;
w2 = w * w;
if (A > (xm * Log(f1 / x1)
+ (NSamples - m + 0.5) * Log(z / w)
+ (y - m) * Log(w * r / (x1 * q))
+ (13680.0 - (462.0 - (132.0 - (99.0 - 140.0 / f2) / f2) / f2) / f2) / f1 / 166320.0
+ (13680.0 - (462.0 - (132.0 - (99.0 - 140.0 / z2) / z2) / z2) / z2) / z / 166320.0
+ (13680.0 - (462.0 - (132.0 - (99.0 - 140.0 / x2) / x2) / x2) / x2) / x1 / 166320.0
+ (13680.0 - (462.0 - (132.0 - (99.0 - 140.0 / w2) / w2) / w2) / w2) / w / 166320.0))
{
goto Step10;
}
Step60:
if (SuccessProbability > 0.5)
{
y = NSamples - y;
}
return(y);
}