public static double UpperIncomplete(double a, double x)
{
const double big = 4.503599627370496e15;
const double biginv = 2.22044604925031308085e-16;
double ans, ax, c, yc, r, t, y, z;
double pk, pkm1, pkm2, qk, qkm1, qkm2;
if (x <= 0 || a <= 0)
return 1.0;
if (x < 1.0 || x < a)
return 1.0 - LowerIncomplete(a, x);
if (Double.IsPositiveInfinity(x))
return 0;
ax = a * Math.Log(x) - x - Log(a);
if (ax < -Constants.LogMax)
return 0.0;
ax = Math.Exp(ax);
// continued fraction
y = 1.0 - a;
z = x + y + 1.0;
c = 0.0;
pkm2 = 1.0;
qkm2 = x;
pkm1 = x + 1.0;
qkm1 = z * x;
ans = pkm1 / qkm1;
do
{
c += 1.0;
y += 1.0;
z += 2.0;
yc = y * c;
pk = pkm1 * z - pkm2 * yc;
qk = qkm1 * z - qkm2 * yc;
if (qk != 0)
{
r = pk / qk;
t = Math.Abs((ans - r) / r);
ans = r;
}
else
t = 1.0;
pkm2 = pkm1;
pkm1 = pk;
qkm2 = qkm1;
qkm1 = qk;
if (Math.Abs(pk) > big)
{
pkm2 *= biginv;
pkm1 *= biginv;
qkm2 *= biginv;
qkm1 *= biginv;
}
} while (t > Constants.DoubleEpsilon);
return ans * ax;
}