std::cosh, std::coshf, std::coshl

Defined in header `<cmath>`
	(1)
float cosh ( float num ); double cosh ( double num ); long double cosh ( long double num );			(until C++23)
/* floating-point-type / cosh ( / floating-point-type */ num );			(since C++23) (constexpr since C++26)
float coshf( float num );		(2)	(since C++11) (constexpr since C++26)
long double coshl( long double num );		(3)	(since C++11) (constexpr since C++26)
Additional overloads (since C++11)
Defined in header `<cmath>`
template< class Integer > double cosh ( Integer num );		(A)	(constexpr since C++26)

1-3) Computes the hyperbolic cosine of num. The library provides overloads of std::cosh 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 treated as double.

(since C++11)

Parameters

num

-

floating-point or integer value

Return value

If no errors occur, the hyperbolic cosine of num (

cosh(num)

, or

e num +e -num 2

) is returned.

If a range error due to overflow occurs, +HUGE_VAL, +HUGE_VALF, or +HUGE_VALL is returned.

Error handling

Errors are reported as specified in math_errhandling.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

if the argument is ±0, 1 is returned
If the argument is ±∞, +∞ is returned
if the argument is NaN, NaN is returned

Notes

For the IEEE-compatible type double, if $|num| > 710.5$ , then std::cosh(num) overflows.

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::cosh(num) has the same effect as std::cosh(static_cast<double>(num)).

Example

Run this code

#include <cerrno>
#include <cfenv>
#include <cmath>
#include <cstring>
#include <iostream>
 
// #pragma STDC FENV_ACCESS ON
 
int main()
{
    const double x = 42;
 
    std::cout << "cosh(1) = " << std::cosh(1) << '\n'
              << "cosh(-1) = " << std::cosh(-1) << '\n'
              << "log(sinh(" << x << ")+cosh(" << x << ")) = "
              << std::log(std::sinh(x) + std::cosh(x)) << '\n';
 
    // special values
    std::cout << "cosh(+0) = " << std::cosh(0.0) << '\n'
              << "cosh(-0) = " << std::cosh(-0.0) << '\n';
 
    // error handling
    errno=0;
    std::feclearexcept(FE_ALL_EXCEPT);
 
    std::cout << "cosh(710.5) = " << std::cosh(710.5) << '\n';
 
    if (errno == ERANGE)
        std::cout << "    errno == ERANGE: " << std::strerror(errno) << '\n';
    if (std::fetestexcept(FE_OVERFLOW))
        std::cout << "    FE_OVERFLOW raised\n";
}

Possible output:

cosh(1) = 1.54308
cosh(-1) = 1.54308
log(sinh(42)+cosh(42)) = 42
cosh(+0) = 1
cosh(-0) = 1
cosh(710.5) = inf
    errno == ERANGE: Numerical result out of range
    FE_OVERFLOW raised

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sinhsinhfsinhl (C++11)(C++11)	computes hyperbolic sine (\({\small\sinh{x} }\) $sinh(x)$ ) (function)
tanhtanhftanhl (C++11)(C++11)	computes hyperbolic tangent (\({\small\tanh{x} }\) $tanh(x)$ ) (function)
acoshacoshfacoshl (C++11)(C++11)(C++11)	computes the inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x} }\) $arcosh(x)$ ) (function)
cosh(std::complex)	computes hyperbolic cosine of a complex number (\({\small\cosh{z} }\) $cosh(z)$ ) (function template)
cosh(std::valarray)	applies the function std::cosh to each element of valarray (function template)