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

Defined in header `<cmath>`
float acosh ( float arg ); float acoshf( float arg );	(1)	(since C++11)
double acosh ( double arg );	(2)	(since C++11)
long double acosh ( long double arg ); long double acoshl( long double arg );	(3)	(since C++11)
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 $[0, +\infty]$ , 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

External links

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

Compiler support
Freestanding and hosted
Language
Standard library headers
Named requirements
Feature test macros (C++20)
Language support library
Concepts library (C++20)
Metaprogramming library (C++11)
Diagnostics library
General utilities library
Strings library
Containers library
Iterators library
Ranges library (C++20)
Algorithms library
Numerics library
Localizations library
Input/output library
Filesystem library (C++17)
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Technical specifications
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External libraries

Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Floating-point environment (C++11)
Complex numbers
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Pseudo-random number generation
Factor operations
gcd (C++17)
lcm (C++17)
Interpolations
midpoint (C++20)
lerp (C++20)
Generic numeric operations
iota (C++11)
ranges::iota (C++23)
accumulate
inner_product
adjacent_difference
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reduce (C++17)
transform_reduce (C++17)
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exclusive_scan (C++17)
transform_inclusive_scan (C++17)
transform_exclusive_scan (C++17)
Bit operations
bit_cast (C++20)
byteswap (C++23)
has_single_bit (C++20)
bit_ceil (C++20)
bit_floor (C++20)
bit_width (C++20)
rotl (C++20)
rotr (C++20)
countl_zero (C++20)
countl_one (C++20)
countr_zero (C++20)
countr_one (C++20)
popcount (C++20)
endian (C++20)

asinhasinhfasinhl (C++11)(C++11)(C++11)	computes the inverse hyperbolic sine (\({\small\operatorname{arsinh}{x} }\) $arsinh(x)$ ) (function)
atanhatanhfatanhl (C++11)(C++11)(C++11)	computes the inverse hyperbolic tangent (\({\small\operatorname{artanh}{x} }\) $artanh(x)$ ) (function)
coshcoshfcoshl (C++11)(C++11)	computes hyperbolic cosine (\({\small\cosh{x} }\) $cosh(x)$ ) (function)
acosh(std::complex) (C++11)	computes area hyperbolic cosine of a complex number (\({\small\operatorname{arcosh}{z} }\) $arcosh(z)$ ) (function template)