# erf(3) — Linux manual page

```erf(3)                  Library Functions Manual                  erf(3)
```

## NAME         top

```       erf, erff, erfl - error function
```

## LIBRARY         top

```       Math library (libm, -lm)
```

## SYNOPSIS         top

```       #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         top

```       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         top

```       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         top

```       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         top

```       For an explanation of the terms used in this section, see
attributes(7).
┌─────────────────────────────────────┬───────────────┬─────────┐
│ Interface                           │ Attribute     │ Value   │
├─────────────────────────────────────┼───────────────┼─────────┤
│ erf(), erff(), erfl()               │ Thread safety │ MT-Safe │
└─────────────────────────────────────┴───────────────┴─────────┘
```

## STANDARDS         top

```       C11, POSIX.1-2008.
```

## HISTORY         top

```       C99, POSIX.1-2001.

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

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