Sinh

Defined in header <cmath>.

Description

Computes the hyperbolic sine of num.
The library provides overloads of std::sinh 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 */ sinh( /* floating-point-type */ num );
// 2)
float sinhf( float num );
// 3)
long double sinhl( long double num );

Additional Overloads

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

C++11

// 1)
float sinh ( float num );
// 2)
double sinh ( double num );
// 3)
long double sinh ( long double num );
// 4)
float sinhf( float num );
// 5)
long double sinhl( long double num );

Additional Overloads

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

Parameters

​num - floating-point or integer value

Return value

If no errors occur, the hyperbolic sine of num (sinh(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.

If a range error occurs due to underflow, the correct result (after rounding) 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 or ±∞, it is returned unmodified if the argument is NaN, NaN is returned

Notes

POSIX specifies that in case of underflow, num is returned unmodified, and if that is not supported, and implementation-defined value no greater than DBL_MIN, FLT_MIN, and LDBL_MIN is returned.

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::sinh(num) has the same effect as std::sinh(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 
        << "sinh(1) = " 
        << std::sinh(1) << '\n'
        << "sinh(-1) = " 
        << std::sinh(-1) << '\n'
        << "log(sinh(" 
        << x << ")+cosh(" << x << ")) = "
        << std::log(std::sinh(x) + std::cosh(x)) << '\n';
 
    // special values
    std::cout 
        << "sinh(+0) = " 
        << std::sinh(0.0) << '\n'
        << "sinh(-0) = " 
        << std::sinh(-0.0) << '\n';
 
    // error handling
    errno = 0;
    std::feclearexcept(FE_ALL_EXCEPT);
 
    std::cout 
        << "sinh(710.5) = " 
        << std::sinh(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

sinh(1) = 1.1752
sinh(-1) = -1.1752
log(sinh(42)+cosh(42)) = 42
sinh(+0) = 0
sinh(-0) = -0
sinh(710.5) = inf
errno == ERANGE: Numerical result out of range
FE_OVERFLOW raised