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# std::atanh

From cppreference.com
< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
float atanh( float arg ); | (1) | (since C++11)
double atanh( double arg ); | (2) | (since C++11)
long double atanh( long double arg ); | (3) | (since C++11)
double atanh( Integral arg ); | (4) | (since C++11)

Computes the inverse hyperbolic tangent of `arg`.

4) A set of overloads or a function template accepting an argument of any integral type. Equivalent to 2) (the argument is cast to double).

### [edit] Parameters

arg | - | value of a floating-point or Integral type

### [edit] Return value

If no errors occur, the inverse hyperbolic tangent of `arg` (tanh-1
(arg), or artanh(arg)), 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.

### [edit] 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 |arg|>1, NaN is returned and FE_INVALID is raised.
- if the argument is NaN, NaN is returned

### [edit] 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, `arg` 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.

### [edit] Example

Run this code

    #include <iostream>
    #include <cmath>
    #include <cfloat>
    #include <cerrno>
    #include <cfenv>
    #include <cstring>
    #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

### [edit] See also

asinh (C++11) | computes the inverse hyperbolic sine (arsinh(x)) (function) [edit]
acosh (C++11) | computes the inverse hyperbolic cosine (arcosh(x)) (function) [edit]
tanh | hyperbolic tangent (function) [edit]
atanh(std::complex) (C++11) | computes area hyperbolic tangent of a complex number (function template) [edit]
C documentation for atanh

### [edit] External links

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

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