Cosh

Defined in header <cmath>.

Description

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 num.  (since C++23)
Additional Overloads are provided for all integer types, which are treated as double. (since C++11)

Declarations

C++23

// 1)
/* floating-point-type */ cosh( /* floating-point-type */ num );
// 2)
float coshf( float num );
// 3)
long double coshl( long double num );

Additional Overloads

// 4)
template< class Integer >
double cosh ( Integer num );

C++11

// 1)
float cosh ( float num );
// 2)
double cosh ( double num );
// 3)
long double cosh ( long double num );
// 4)
float coshf( float num );
// 5)
long double coshl( long double num );

Additional Overloads

// 6)
template< class Integer >
double cosh ( Integer num );

Parameters

num - floating-point or integer value

Return value

If no errors occur, the hyperbolic sine 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 Additional Overloads. 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)).

Examples

#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 Result

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