Stand-alone C++ implementation of 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).
#include <cmath>
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 = fabs(x)/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*exp(-x*x);
return 0.5*(1.0 + sign*y);
}
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
};
int numTests = sizeof(x)/sizeof(double);
double maxError = 0.0;
for (int i = 0; i < numTests; ++i)
{
double error = fabs(y[i] - phi(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.