NAME

atanh, atanhf, atanhl — inverse hyperbolic tangent functions

SYNOPSIS

#include <math.h>

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


DESCRIPTION

^[CX] 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.1-2024 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 ^[MX]  either a NaN (if supported), or  an implementation-defined value shall be returned.

^[MX] 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.

^[MXX] If x is subnormal, x should be returned.
^[MX] If x is subnormal, a range error may occur and, 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], ^[MX]  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

^[MX] 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.

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

XBD 4.23 Treatment of Error Conditions for Mathematical Functions, <math.h>

CHANGE HISTORY

First released in Issue 4, Version 2.

Issue 5

Moved from X/OPEN UNIX extension to BASE.

Issue 6

The atanh() function is no longer marked as an extension.

The atanhf() and atanhl() functions are added for alignment with the ISO/IEC 9899:1999 standard.

The DESCRIPTION, RETURN VALUE, ERRORS, and APPLICATION USAGE sections are revised to align with the ISO/IEC 9899:1999 standard.

IEC 60559:1989 standard floating-point extensions over the ISO/IEC 9899:1999 standard are marked.

Issue 7

POSIX.1-2008, Technical Corrigendum 1, XSH/TC1-2008/0039 [320] and XSH/TC1-2008/0040 [680] are applied.

Issue 8

Austin Group Defect 1382 is applied, rearranging the text describing the behavior when x is subnormal to avoid the need for two shading changes.