Stand-alone C# code for Φ(x)

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.

Other versions: C++, Python

Stand-alone numerical code

 

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