std::acosh

 

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

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 (C++11)	computes the inverse hyperbolic sine (arsinh(x)) (function)
atanh (C++11)	computes the inverse hyperbolic tangent (artanh(x)) (function)
cosh	computes hyperbolic cosine (ch(x)) (function)
acosh(std::complex) (C++11)	computes area hyperbolic cosine of a complex number (function template)
C documentation for acosh

External links

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