atanh man page

Prolog

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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

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.1‐2008 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.

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.

See Also

feclearexcept(), fetestexcept(), tanh()

The Base Definitions volume of POSIX.1‐2008, Section 4.19, Treatment of Error Conditions for Mathematical Functions, <math.h>

Info

2013 IEEE/The Open Group POSIX Programmer's Manual