NAME¶

std::atanh,std::atanhf,std::atanhl - std::atanh,std::atanhf,std::atanhl

Synopsis¶

Defined in header <cmath>
float atanh ( float num );

double atanh ( double num ); (until C++23)

long double atanh ( long double num );
/* floating-point-type */ (since C++23)
atanh ( /* floating-point-type */ num ); (constexpr since C++26)
float atanhf( float num ); (1) (2) (since C++11)
(constexpr since C++26)
long double atanhl( long double num ); (3) (since C++11)
(constexpr since C++26)
Additional overloads (since C++11)
Defined in header <cmath>
template< class Integer > (A) (constexpr since C++26)
double atanh ( Integer num );

1-3) Computes the inverse hyperbolic tangent of num.
The library provides overloads of std::atanh for all cv-unqualified floating-point
types as the type of the parameter.
(since C++23)

A) Additional overloads are provided for all integer types, which are (since C++11)
treated as double.

Parameters¶

num - floating-point or integer value

Return value¶

If no errors occur, the inverse hyperbolic tangent of num (tanh-1
(num), or artanh(num)), is returned.

If a domain error occurs, an implementation-defined value is returned (NaN where
supported).

If a pole error occurs, ±HUGE_VAL, ±HUGE_VALF, or ±HUGE_VALL is returned (with the
correct sign).

If a range error occurs due to underflow, the correct result (after rounding) is
returned.

Error handling¶

Errors are reported as specified in math_errhandling.

If the argument is not on the interval [-1, +1], a range error occurs.

If the argument is ±1, a pole error occurs.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

* if the argument is ±0, it is returned unmodified.
* if the argument is ±1, ±∞ is returned and FE_DIVBYZERO is raised.
* if |num|>1, NaN is returned and FE_INVALID is raised.
* if the argument is NaN, NaN is returned.

Notes¶

Although the C standard (to which C++ refers for this function) names this function
"arc hyperbolic tangent", the inverse functions of the hyperbolic functions are the
area functions. Their argument is the area of a hyperbolic sector, not an arc. The
correct name is "inverse hyperbolic tangent" (used by POSIX) or "area hyperbolic
tangent".

POSIX specifies that in case of underflow, num is returned unmodified, and if that
is not supported, an implementation-defined value no greater than DBL_MIN, FLT_MIN,
and LDBL_MIN is returned.

The additional overloads are not required to be provided exactly as (A). They only
need to be sufficient to ensure that for their argument num of integer type,
std::atanh(num) has the same effect as std::atanh(static_cast<double>(num)).

Example¶

// Run this code

#include <cerrno>
#include <cfenv>
#include <cfloat>
#include <cmath>
#include <cstring>
#include <iostream>
// #pragma STDC FENV_ACCESS ON

int main()
{
std::cout << "atanh(0) = " << std::atanh(0) << '\n'
<< "atanh(-0) = " << std::atanh(-0.0) << '\n'
<< "atanh(0.9) = " << std::atanh(0.9) << '\n';

// error handling
errno = 0;
std::feclearexcept(FE_ALL_EXCEPT);

std::cout << "atanh(-1) = " << std::atanh(-1) << '\n';

if (errno == ERANGE)
std::cout << " errno == ERANGE: " << std::strerror(errno) << '\n';
if (std::fetestexcept(FE_DIVBYZERO))
std::cout << " FE_DIVBYZERO raised\n";
}

Possible output:¶

atanh(0) = 0
atanh(-0) = -0
atanh(0.9) = 1.47222
atanh(-1) = -inf
errno == ERANGE: Numerical result out of range
FE_DIVBYZERO raised

See also¶

asinh
asinhf computes the inverse hyperbolic sine
asinhl (\({\small\operatorname{arsinh}{x}}\)arsinh(x))
(C++11) (function)
(C++11)
(C++11)
acosh
acoshf computes the inverse hyperbolic cosine
acoshl (\({\small\operatorname{arcosh}{x}}\)arcosh(x))
(C++11) (function)
(C++11)
(C++11)
tanh
tanhf computes hyperbolic tangent (\({\small\tanh{x}}\)tanh(x))
tanhl (function)
(C++11)
(C++11)
atanh(std::complex) computes area hyperbolic tangent of a complex number
(C++11) (\({\small\operatorname{artanh}{z}}\)artanh(z))
(function template)
C documentation for
atanh

External links¶

Weisstein, Eric W. "Inverse Hyperbolic Tangent." From MathWorld — A Wolfram Web
Resource.