# 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 