# Manual Reference Pages  - ERF (3)

### NAME

erf, erff, erfl, - error function

Synopsis
Description
Return Value
Errors
Colophon

### SYNOPSIS

```
#include <math.h>

double erf(double x);

float erff(float x);

long double erfl(long double x);

```

Feature Test Macro Requirements for glibc (see feature_test_macros(7)):

erf():

_BSD_SOURCE || _SVID_SOURCE || _XOPEN_SOURCE || _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L;
or cc -std=c99

erff(), erfl():
_BSD_SOURCE || _SVID_SOURCE || _XOPEN_SOURCE >= 600 || _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L;
or cc -std=c99

### DESCRIPTION

The erf() function returns the error function of x, defined as
erf(x) = 2/sqrt(pi)* integral from 0 to x of exp(-t*t) dt

### RETURN VALUE

On success, these functions return the error function of x, a value in the range [-1, 1].

If x is a NaN, a NaN is returned.

If x is +0 (-0), +0 (-0) is returned.

If x is positive infinity (negative infinity), +1 (-1) is returned.

If x is subnormal, a range error occurs, and the return value is 2*x/sqrt(pi).

### ERRORS

See math_error(7) for information on how to determine whether an error has occurred when calling these functions.

The following errors can occur:
Range error: result underflow (x is subnormal)
An underflow floating-point exception (FE_UNDERFLOW) is raised.
These functions do not set errno.

### CONFORMING TO

C99, POSIX.1-2001. The variant returning double also conforms to SVr4, 4.3BSD.