std::acosh,std::acoshf,std::acoshl(3)

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.