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
.
double
).arg | - | value of a floating-point or Integral type |
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.
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),
FE_DIVBYZERO
is raised. FE_INVALID
is raised. 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> #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
(C++11)
| computes the inverse hyperbolic sine (arsinh(x)) (function) |
(C++11)
| computes the inverse hyperbolic cosine (arcosh(x)) (function) |
hyperbolic tangent (function) |
|
(C++11)
| computes area hyperbolic tangent of a complex number (function template) |
C documentation for atanh |
Weisstein, Eric W. "Inverse Hyperbolic Tangent." From MathWorld--A Wolfram Web Resource.
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