# man pages section 3: Extended Library Functions, Volume 2

Updated: Thursday, June 13, 2019

## atanhl(3M)

### Name

atanh, atanhf, atanhl - inverse hyperbolic tangent functions

### Synopsis

```c99 [ flag... ] file... –lm [ library... ]
#include <math.h>

double atanh(double x);```
`float atanhf(float x);`
`long double atanhl(long double x);`

### Description

These functions compute the inverse hyperbolic tangent of their argument x.

### Return Values

Upon successful completion, these functions return the inverse hyperbolic tangent of their argument.

If x is ±1, a pole error occurs and atanh(), atanhf(), and atanhl() return the value of the macro HUGE_VAL, HUGE_VALF, and HUGE_VALL, respectively, with the same sign as the correct value of the function.

For finite |x| > 1, a domain error occurs and a NaN is returned.

If x is NaN, NaN is returned.

If x is +0, x is returned.

If x is +Inf, a domain error occurs and a NaN is returned.

For exceptional cases, matherr(3M) tabulates the values to be returned by atanh() as specified by SVID3 and XPG3.

### Errors

These functions will fail if:

Domain Error

The x argument is finite and not in the range [-1,1], or is ±Inf.

If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, the invalid floating-point exception is raised.

The atanh() function sets errno to EDOM if the absolute value of x is greater than 1.0.

Pole Error

The x argument is ±1.

If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the divide-by-zero floating-point exception is raised.

The atanh() function sets errno to ERANGE if the absolute value of x is equal to 1.0.

### Usage

An application wanting to check for exceptions should call feclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, if fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an exception has been raised. An application should either examine the return value or check the floating point exception flags to detect exceptions.

An application can also set errno to 0 before calling atanh(). On return, if errno is non-zero, an error has occurred. The atanhf() and atanhl() functions do not set errno.

### Attributes

See attributes(7) for descriptions of the following attributes:

ATTRIBUTE TYPE
ATTRIBUTE VALUE
Interface Stability
Committed
Availability
system/library/math
MT-Level
MT-Safe
Standard