erf, erff, erfl - cppreference.com (original) (raw)

Defined in header <math.h>
float erff( float arg ); (1) (since C99)
double erf( double arg ); (2) (since C99)
long double erfl( long double arg ); (3) (since C99)
Defined in header <tgmath.h>
#define erf( arg ) (4) (since C99)
  1. Type-generic macro: If arg has type long double, erfl is called. Otherwise, if arg has integer type or the type double, erf is called. Otherwise, erff is called.

Contents

[edit] Parameters

arg - floating-point value

[edit] Return value

If no errors occur, value of the error function of arg, that is \(\frac{2}{\sqrt{\pi} }\int_{0}^{arg}{e^{-{t^2} }\mathsf{d}t}\)∫arg
0_e_-t2
d_t_, is returned. If a range error occurs due to underflow, the correct result (after rounding), that is \(\frac{2\cdot arg}{\sqrt{\pi} }\), is returned.

[edit] Error handling

Errors are reported as specified in math_errhandling.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

[edit] Notes

Underflow is guaranteed if |arg| < DBL_MIN*(sqrt(π)/2).

\(\operatorname{erf}(\frac{x}{\sigma \sqrt{2} })\)erf() is the probability that a measurement whose errors are subject to a normal distribution with standard deviation \(\sigma\)σ is less than \(x\)x away from the mean value.

[edit] Example

#include <math.h> #include <stdio.h>   double phi(double x1, double x2) { return (erf(x2 / sqrt(2)) - erf(x1 / sqrt(2))) / 2; }   int main(void) { puts("normal variate probabilities:"); for (int n = -4; n < 4; ++n) printf("[%2d:%2d]: %5.2f%%\n", n, n + 1, 100 * phi(n, n + 1));   puts("special values:"); printf("erf(-0) = %f\n", erf(-0.0)); printf("erf(Inf) = %f\n", erf(INFINITY)); }

Output:

normal variate probabilities: [-4:-3]: 0.13% [-3:-2]: 2.14% [-2:-1]: 13.59% [-1: 0]: 34.13% [ 0: 1]: 34.13% [ 1: 2]: 13.59% [ 2: 3]: 2.14% [ 3: 4]: 0.13% special values: erf(-0) = -0.000000 erf(Inf) = 1.000000

[edit] References

[edit] See also