## Name

erf, erff, erfl — error function

## Synopsis

`#include <math.h>`
 ```double erf(``` double x`)`;

 ```float erff(``` float x`)`;

 ```long double erfl(``` long double x`)`;

Note
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`
Note Link with `−lm`.

## 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, 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).

 Interface Attribute Value `erf`(), `erff`(), `erfl`() Thread safety MT-Safe

## CONFORMING TO

C99, POSIX.1-2001, POSIX.1-2008.

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

cerf(3), erfc(3), exp(3)

## COLOPHON

This page is part of release 5.11 of the Linux `man-pages` project. A description of the project, information about reporting bugs, and the latest version of this page, can be found at https://www.kernel.org/doc/man−pages/.

 Copyright 1993 David Metcalfe (david(@)prism.demon.co.uk) and Copyright 2008, Linux Foundation, written by Michael Kerrisk      %%%LICENSE_START(VERBATIM) Permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and this permission notice are preserved on all copies. Permission is granted to copy and distribute modified versions of this manual under the conditions for verbatim copying, provided that the entire resulting derived work is distributed under the terms of a permission notice identical to this one. Since the Linux kernel and libraries are constantly changing, this manual page may be incorrect or out-of-date.  The author(s) assume no responsibility for errors or omissions, or for damages resulting from the use of the information contained herein.  The author(s) may not have taken the same level of care in the production of this manual, which is licensed free of charge, as they might when working professionally. Formatted or processed versions of this manual, if unaccompanied by the source, must acknowledge the copyright and authors of this work. %%%LICENSE_END References consulted:     Linux libc source code     Lewine's _POSIX Programmer's Guide_ (O'Reilly & Associates, 1991)     386BSD man pages Modified 1993-07-24 by Rik Faith (faith(@)cs.unc.edu) Modified 2002-07-27 by Walter Harms (walter.harms(@)informatik.uni-oldenburg.de)