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# erf - Man Page

error function

## Library

Math library (libm, -lm)

## 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():

```    _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L || _XOPEN_SOURCE
|| /* Since glibc 2.19: */ _DEFAULT_SOURCE
|| /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE```

erff(), erfl():

```    _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
|| /* Since glibc 2.19: */ _DEFAULT_SOURCE
|| /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE```

## Description

These functions return 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 value of the error function of x, a value in the range [-1,Ā 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.

## Attributes

For an explanation of the terms used in this section, see attributes(7).

InterfaceAttributeValue

## Standards

C11, POSIX.1-2008.

## History

C99, POSIX.1-2001.

The variant returning double also conforms to SVr4, 4.3BSD.