The function Φ(x) is the cumulative density function (CDF) of a standard normal (Gaussian) random variable. It is closely related to the error function erf(x).
static double Phi(double x)
{
// constants
double a1 = 0.254829592;
double a2 = -0.284496736;
double a3 = 1.421413741;
double a4 = -1.453152027;
double a5 = 1.061405429;
double p = 0.3275911;
// Save the sign of x
int sign = 1;
if (x < 0)
sign = -1;
x = Math.Abs(x) / Math.Sqrt(2.0);
// A&S formula 7.1.26
double t = 1.0 / (1.0 + p*x);
double y = 1.0 - (((((a5*t + a4)*t) + a3)*t + a2)*t + a1)*t * Math.Exp(-x*x);
return 0.5 * (1.0 + sign*y);
}
static void TestPhi()
{
// Select a few input values
double[] x =
{
-3,
-1,
0.0,
0.5,
2.1
};
// Output computed by Mathematica
// y = Phi[x]
double[] y =
{
0.00134989803163,
0.158655253931,
0.5,
0.691462461274,
0.982135579437
};
double maxError = 0.0;
for (int i = 0; i < x.Length; ++i)
{
double error = Math.Abs(y[i] - Phi(x[i]));
if (error > maxError)
maxError = error;
}
Console.WriteLine("Maximum error: {0}", maxError);
}
A&S refers to Handbook of Mathematical Functions by Abramowitz and Stegun. See Stand-alone error function for details of the algorithm.
This code is in the public domain. Do whatever you want with it, no strings attached.