NAME

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

Synopsis

Defined in header <cmath>
float acosh ( float arg ); (1) (since C++11)
float acoshf( float arg );
double acosh ( double arg ); (2) (since C++11)
long double acosh ( long double arg ); (3) (since C++11)
long double acoshl( long double arg );
double acosh ( IntegralType arg ); (4) (since C++11)

1-3) Computes the inverse hyperbolic cosine of arg.
4) A set of overloads or a function template accepting an argument of any integral
type. Equivalent to 2) (the argument is cast to double).

Parameters

arg - value of a floating-point or Integral type

Return value

If no errors occur, the inverse hyperbolic cosine of arg (cosh-1
(arg), or arcosh(arg)) 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".

Examples

// Run this code

#include <iostream>
#include <cmath>
#include <cfloat>
#include <cerrno>
#include <cfenv>
#include <cstring>
#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)

External links

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