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Defined in header <cmath> | ||
| (1) | ||
float atanh(float num); double atanh(double num); | (until C++23) | |
/*floating-point-type*/ atanh(/*floating-point-type*/ num); | (since C++23) (constexpr since C++26) | |
float atanhf(float num); | (2) | (since C++11) (constexpr since C++26) |
longdouble atanhl(longdouble num); | (3) | (since C++11) (constexpr since C++26) |
SIMD overload(since C++26) | ||
Defined in header <simd> | ||
template</*math-floating-point*/ V> constexpr/*deduced-simd-t*/<V> | (S) | (since C++26) |
Additional overloads(since C++11) | ||
Defined in header <cmath> | ||
template<class Integer> double atanh( Integer num); | (A) | (constexpr since C++26) |
std::atanh for all cv-unqualified floating-point types as the type of the parameter.(since C++23)S) The SIMD overload performs an element-wise std::atanh onv_num.
| (since C++26) |
A) Additional overloads are provided for all integer types, which are treated asdouble. | (since C++11) |
Contents |
| num | - | floating-point or integer value |
If no errors occur, the inverse hyperbolic tangent ofnum (tanh-1
(num), orartanh(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.
Errors are reported as specified inmath_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),
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 thanDBL_MIN,FLT_MIN, andLDBL_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 argumentnum of integer type,std::atanh(num) has the same effect asstd::atanh(static_cast<double>(num)).
#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 handlingerrno=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) = 0atanh(-0) = -0atanh(0.9) = 1.47222atanh(-1) = -inf errno == ERANGE: Numerical result out of range FE_DIVBYZERO raised
(C++11)(C++11)(C++11) | computes the inverse hyperbolic sine (\({\small\operatorname{arsinh}{x}}\)arsinh(x)) (function)[edit] |
(C++11)(C++11)(C++11) | computes the inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x}}\)arcosh(x)) (function)[edit] |
(C++11)(C++11) | computes hyperbolic tangent (\({\small\tanh{x}}\)tanh(x)) (function)[edit] |
(C++11) | computes area hyperbolic tangent of a complex number (\({\small\operatorname{artanh}{z}}\)artanh(z)) (function template)[edit] |
C documentation foratanh | |
| Weisstein, Eric W. "Inverse Hyperbolic Tangent." From MathWorld — A Wolfram Web Resource. |
