std::atanh, std::atanh, std::atanhl

Defined in header <cmath>
float       atanh ( float arg );
float       atanhf( float arg );
(1) (since C++11)
double      atanh ( double arg );
(2) (since C++11)
long double atanh ( long double arg );
long double atanhl( long double arg );
(3) (since C++11)
double      atanh ( IntegralType arg );
(4) (since C++11)
1-3) 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).


arg - value of a floating-point or Integral type

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.

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


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.


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

computes the inverse hyperbolic sine (arsinh(x))
computes the inverse hyperbolic cosine (arcosh(x))
hyperbolic tangent
computes area hyperbolic tangent of a complex number
(function template)

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

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