# Manual Reference Pages  - ATANH (3)

### NAME

atanh, atanhf, atanhl - inverse hyperbolic tangent function

Synopsis
Description
Errors
Bugs
Colophon

### SYNOPSIS

```
#include <math.h>

double atanh(double x);

float atanhf(float x);

long double atanhl(long double x);

```

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

atanh():

_BSD_SOURCE || _SVID_SOURCE || _XOPEN_SOURCE >= 500 || _XOPEN_SOURCE && _XOPEN_SOURCE_EXTENDED || _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L;
or cc -std=c99

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

### DESCRIPTION

The atanh() function calculates the inverse hyperbolic tangent of x; that is the value whose hyperbolic tangent is x.

### RETURN VALUE

On success, these functions return the inverse hyperbolic tangent of x.

If x is a NaN, a NaN is returned.

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

If x is +1 or -1, a pole error occurs, and the functions return HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the mathematically correct sign.

If the absolute value of x is greater than 1, a domain error occurs, and a NaN is returned.

### 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:
Domain error: x less than -1 or greater than +1
errno is set to EDOM. An invalid floating-point exception (FE_INVALID) is raised.
Pole error: x is +1 or -1
errno is set to ERANGE (but see BUGS). A divide-by-zero floating-point exception (FE_DIVBYZERO) is raised.

### CONFORMING TO

C99, POSIX.1-2001. The variant returning double also conforms to SVr4, 4.3BSD, C89.

### BUGS

In glibc 2.9 and earlier, when a pole error occurs, errno as set to EDOM instead of the POSIX-mandated ERANGE. Since version 2.10, glibc does the right thing.