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Defined in header <cmath> | ||
| (1) | ||
float acosh(float num); double acosh(double num); | (until C++23) | |
/*floating-point-type*/ acosh(/*floating-point-type*/ num); | (since C++23) (constexpr since C++26) | |
float acoshf(float num); | (2) | (since C++11) (constexpr since C++26) |
longdouble acoshl(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 acosh( Integer num); | (A) | (constexpr since C++26) |
std::acosh 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::acosh 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 cosine ofnum (cosh-1
(num), orarcosh(num)) on the interval[0, +∞], is returned.
If a domain error occurs, an implementation-defined value is returned (NaN where supported).
Errors are reported as specified inmath_errhandling.
If the argument is less than 1, a domain 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 cosine", 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 cosine" (used by POSIX) or "area hyperbolic cosine".
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::acosh(num) has the same effect asstd::acosh(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<<"acosh(1) = "<< std::acosh(1)<<'\n'<<"acosh(10) = "<< std::acosh(10)<<'\n'<<"acosh(DBL_MAX) = "<< std::acosh(DBL_MAX)<<'\n'<<"acosh(Inf) = "<< std::acosh(INFINITY)<<'\n'; // error handlingerrno=0;std::feclearexcept(FE_ALL_EXCEPT); std::cout<<"acosh(0.5) = "<< std::acosh(0.5)<<'\n'; if(errno==EDOM)std::cout<<" errno == EDOM: "<<std::strerror(errno)<<'\n';if(std::fetestexcept(FE_INVALID))std::cout<<" FE_INVALID raised\n";}
Possible output:
acosh(1) = 0acosh(10) = 2.99322acosh(DBL_MAX) = 710.476acosh(Inf) = infacosh(0.5) = -nan errno == EDOM: Numerical argument out of domain FE_INVALID 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 tangent (\({\small\operatorname{artanh}{x}}\)artanh(x)) (function)[edit] |
(C++11)(C++11) | computes hyperbolic cosine (\({\small\cosh{x}}\)cosh(x)) (function)[edit] |
(C++11) | computes area hyperbolic cosine of a complex number (\({\small\operatorname{arcosh}{z}}\)arcosh(z)) (function template)[edit] |
C documentation foracosh | |
| Weisstein, Eric W. "Inverse Hyperbolic Cosine." From MathWorld — A Wolfram Web Resource. |
