# atanh - Man Page

inverse hyperbolic tangent functions

## Prolog

This manual page is part of the POSIX Programmer's Manual. The Linux implementation of this interface may differ (consult the corresponding Linux manual page for details of Linux behavior), or the interface may not be implemented on Linux.

## Synopsis

#include <math.h> double atanh(doublex); float atanhf(floatx); long double atanhl(long doublex);

## Description

The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here and the ISO C standard is unintentional. This volume of POSIX.1-2017 defers to the ISO C standard.

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

An application wishing to check for error situations should set *errno* to zero and call *feclearexcept*(FE_ALL_EXCEPT) before calling these functions. On return, if *errno* is non-zero or *fetestexcept*(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.

## Return Value

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

If *x* is ±1, a pole error shall occur, and *atanh*(), *atanhf*(), and *atanhl*() shall 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 shall occur, and either a NaN (if supported), or an implementation-defined value shall be returned.

If *x* is NaN, a NaN shall be returned.

If *x* is ±0, *x* shall be returned.

If *x* is ±Inf, a domain error shall occur, and a NaN shall be returned.

If *x* is subnormal, a range error may occur

and *x* should be returned.

If *x* is not returned, *atanh*(), *atanhf*(), and *atanhl*() shall return an implementation-defined value no greater in magnitude than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.

## Errors

These functions shall 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_ERRNO) is non-zero, then*errno*shall be set to**[EDOM]**. If the integer expression (*math_errhandling*& MATH_ERREXCEPT) is non-zero, then the invalid floating-point exception shall be raised.- Pole Error
The

*x*argument is ±1.If the integer expression (

*math_errhandling*& MATH_ERRNO) is non-zero, then*errno*shall be set to**[ERANGE]**. If the integer expression (*math_errhandling*& MATH_ERREXCEPT) is non-zero, then the divide-by-zero floating-point exception shall be raised.

These functions may fail if:

- Range Error
The value of

*x*is subnormal.If the integer expression (

*math_errhandling*& MATH_ERRNO) is non-zero, then*errno*shall be set to**[ERANGE]**. If the integer expression (*math_errhandling*& MATH_ERREXCEPT) is non-zero, then the underflow floating-point exception shall be raised.

*The following sections are informative.*

## Examples

None.

## Application Usage

On error, the expressions (*math_errhandling* & MATH_ERRNO) and (*math_errhandling* & MATH_ERREXCEPT) are independent of each other, but at least one of them must be non-zero.

## Rationale

None.

## Future Directions

None.

## See Also

feclearexcept(), fetestexcept(), tanh()

The Base Definitions volume of POSIX.1-2017, *Section 4.20*, *Treatment of Error Conditions for Mathematical Functions*, <math.h>

## Copyright

Portions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1-2017, Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 7, 2018 Edition, Copyright (C) 2018 by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. In the event of any discrepancy between this version and the original IEEE and The Open Group Standard, the original IEEE and The Open Group Standard is the referee document. The original Standard can be obtained online at http://www.opengroup.org/unix/online.html .

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