std::acosh,std::acoshf,std::acoshl (3) - Linux Manuals

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


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


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).


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


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".


// Run this code

  #include <iostream>
  #include <cmath>
  #include <cfloat>
  #include <cerrno>
  #include <cfenv>
  #include <cstring>
  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::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.

See also

asinhl computes the inverse hyperbolic sine (arsinh(x))

atanhl computes the inverse hyperbolic tangent (artanh(x))

coshl computes hyperbolic cosine (ch(x))


acosh(std::complex) computes area hyperbolic cosine of a complex number
                    (function template)