std::acosh, std::acoshf, std::acoshl

Defined in header `<cmath>`
	(1)
float acosh ( float num ); double acosh ( double num ); long double acosh ( long 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)
long double acoshl( long double num );		(3)	(since C++11) (constexpr since C++26)
Additional overloads (since C++11)
Defined in header `<cmath>`
template< class Integer > double acosh ( Integer num );		(A)	(constexpr since C++26)

1-3) Computes the inverse hyperbolic cosine of num. The library provides overloads of std::acosh for all cv-unqualified floating-point types as the type of the parameter. (since C++23)

A) Additional overloads are provided for all integer types, which are treated as double.

(since C++11)

Parameters

num

-

floating-point or integer value

Return value

If no errors occur, the inverse hyperbolic cosine of num ( $cosh -1 (num)$ , or $arcosh(num)$ ) on the interval $[0, +\infty]$ , is returned.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

Error handling

Errors are reported as specified in math_errhandling.

If the argument is less than 1, a domain error occurs.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

if the argument is less than 1, FE_INVALID is raised an NaN is returned
if the argument is 1, +0 is returned
if the argument is +∞, +∞ is returned
if the argument is NaN, NaN is returned

Notes

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 argument num of integer type, std::acosh(num) has the same effect as std::acosh(static_cast<double>(num)).

Examples

Run this code

#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 handling
    errno = 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) = 0
acosh(10) = 2.99322
acosh(DBL_MAX) = 710.476
acosh(Inf) = inf
acosh(0.5) = -nan
    errno == EDOM: Numerical argument out of domain
    FE_INVALID raised

External links

Weisstein, Eric W. "Inverse Hyperbolic Cosine." From MathWorld — A Wolfram Web Resource.

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asinhasinhfasinhl (C++11)(C++11)(C++11)	computes the inverse hyperbolic sine (\({\small\operatorname{arsinh}{x} }\) $arsinh(x)$ ) (function)
atanhatanhfatanhl (C++11)(C++11)(C++11)	computes the inverse hyperbolic tangent (\({\small\operatorname{artanh}{x} }\) $artanh(x)$ ) (function)
coshcoshfcoshl (C++11)(C++11)	computes hyperbolic cosine (\({\small\cosh{x} }\) $cosh(x)$ ) (function)
acosh(std::complex) (C++11)	computes area hyperbolic cosine of a complex number (\({\small\operatorname{arcosh}{z} }\) $arcosh(z)$ ) (function template)