private static void Gamma_Temme(double a, double x, out double P, out double Q)
{
double u = Math.Log(x / a);
// compute argument of error function, which is almost (x-a)/sqrt(a)
double dz = 1.0;
double z = dz;
for (int i = 3; true; i++)
{
if (i > Global.SeriesMax)
{
throw new NonconvergenceException();
}
double z_old = z;
dz *= u / i;
z += dz;
if (z == z_old)
{
break;
}
}
z = u * Math.Sqrt(a * z / 2.0);
// the first approximation is just the almost-Gaussian one
if (z > 0)
{
Q = AdvancedMath.Erfc(z) / 2.0;
P = 1.0 - Q;
}
else
{
P = AdvancedMath.Erfc(-z) / 2.0;
Q = 1.0 - P;
}
// compute Temme's correction to the Gaussian approximation
double R0 = Math.Exp(-z * z) / Math.Sqrt(Global.TwoPI * a);
double S0 = 0.0;
double ai = 1.0;
for (int i = 0; i < TemmeD.Length; i++)
{
double dS = 0.0;
double uj = 1.0;
for (int j = 0; j < TemmeD[i].Length; j++)
{
dS += TemmeD[i][j] * uj;
uj *= u;
}
S0 += dS / ai;
ai *= a;
}
double R = R0 * S0;
Q = Q + R;
P = P - R;
}