# std::acosh

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< cpp‎ | numeric‎ | math

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.

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