Stand-alone C++ implementation of 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.


#include <cmath>

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 = fabs(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*exp(-x*x);

    return sign*y;
}

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 
    };

    int numTests = sizeof(x)/sizeof(double);

    double maxError = 0.0;
    for (int i = 0; i < numTests; ++i)
    {
        double error = fabs(y[i] - erf(x[i]));
        if (error > maxError)
            maxError = error;
    }

    std::cout << "Maximum error: " << maxError << "\n";
}    

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