NAME¶

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

Synopsis¶

Defined in header <cmath>
float acosh ( float num );

double acosh ( double num ); (until C++23)

long double acosh ( long double num );
/* floating-point-type */ (since C++23)
acosh ( /* floating-point-type */ num ); (constexpr since C++26)
float acoshf( float num ); (1) (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 > (A) (constexpr since C++26)
double acosh ( Integer num );

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 (since C++11)
treated as double.

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, +∞], 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

See also¶

asinh
asinhf computes the inverse hyperbolic sine
asinhl (\({\small\operatorname{arsinh}{x}}\)arsinh(x))
(C++11) (function)
(C++11)
(C++11)
atanh
atanhf computes the inverse hyperbolic tangent
atanhl (\({\small\operatorname{artanh}{x}}\)artanh(x))
(C++11) (function)
(C++11)
(C++11)
cosh
coshf computes hyperbolic cosine (\({\small\cosh{x}}\)cosh(x))
coshl (function)
(C++11)
(C++11)
acosh(std::complex) computes area hyperbolic cosine of a complex number
(C++11) (\({\small\operatorname{arcosh}{z}}\)arcosh(z))
(function template)
C documentation for
acosh

External links¶

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