Calculates the error function of a floating-point number

#include <math.h>
double erf ( double x  );
float erff ( float x  );
long double erfl ( long double x  );

The function erf( ), called the error function, is associated with the Gaussian function or normal distribution. If the measured values of a given random variable conform to a normal distribution with the standard deviation s, then the probability that a single measurement has an error within ± a is erf( a / (s x 2) ).

The return value of erf(x) is

The function erfc( ) is the complementary error function, defined as erfc(x) = 1 - erf(x).

Example

/*
 * Given a normal distribution with mean 0 and standard deviation 1,
 * calculate the probability that the random variable is within the
 * range [0, 1.125]
 */
double sigma = 1.0;        // The standard deviation
double bound = 1.125;
double probability;        // probability that mean <= value <= bound

probability = 0.5 * erf( bound / (sigma * sqrt(2.0)) );

See Also

erfc( )