Stand-alone C# code for
the error function erf(x)

The following code first appeared as Python code in my blog post Stand-alone error function erf. See that post for documentation. See also Relating erf and Φ.

    using System;
    
    static double Erf(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);

        // 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 sign*y;
    }
    
    static void TestErf()
    {
        // Select a few input values
        double[] x = 
        {
            -3, 
            -1, 
            0.0, 
            0.5, 
            2.1 
        };

        // Output computed by Mathematica
        // y = Erf[x]
        double[] y = 
        { 
            -0.999977909503, 
            -0.842700792950, 
            0.0, 
            0.520499877813, 
            0.997020533344 
        };

        double maxError = 0.0;
        for (int i = 0; i < x.Length; ++i)
        {
            double error = Math.Abs(y[i] - Erf(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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