# NAME

atanh, atanhf, atanhl - inverse hyperbolic tangent function

# LIBRARY

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

# 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():

``````    _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
|| _XOPEN_SOURCE >= 500
|| /* Since glibc 2.19: */ _DEFAULT_SOURCE
|| /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE``````

atanhf(), atanhl():

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

# DESCRIPTION

These functions calculate 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.

# ATTRIBUTES

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

 Interface Attribute Value atanh(), atanhf(), atanhl() Thread safety MT-Safe

# STANDARDS

C11, POSIX.1-2008.

# HISTORY

C99, POSIX.1-2001.

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

# BUGS

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