Asinh

Defined in header <cmath>.

Description

Computes the inverse hyperbolic sine of num. ​ The library provides overloads of std::asinh for all cv-unqualified floating-point types as the type of the parameter num  (od C++23).
​Additional Overloads are provided for all integer types, which are treated as double.

Declarations

C++23

// 1)
/* floating-point-type */ asinh( /* floating-point-type */ num );
// 2)
float asinhf( float num );
// 3)
long double asinhl( long double num );

Additional Overloads

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

C++11

//1 )
float asinh ( float num );
// 2)
double asinh ( double num );
// 3)
long double asinh ( long double num );
// 4)
float asinhf( float num );
// 5)
long double asinhl( long double num );

Additional Overloads

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

Parameters

num - floating-point or integer value

Return value

If no errors occur, the inverse hyperbolic sine of num (sinh^-1(num), or arsinh(num)) 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

Although the C standard (to which C++ refers for this function) names this function "arc hyperbolic sine", 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 sine" (used by POSIX) or "area hyperbolic sine".

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

Examples

#include <cmath>
#include <iostream>
 
int main()
{
    std::cout 
        << "asinh(1) = " 
        << std::asinh(1) << '\n'
        << "asinh(-1) = " 
        << std::asinh(-1) << '\n';
 
    // special values
    std::cout 
        << "asinh(+0) = " 
        << std::asinh(+0.0) << '\n'
        << "asinh(-0) = " 
        <<  std::asinh(-0.0) << '\n';
}

Result

asinh(1) = 0.881374
asinh(-1) = -0.881374
asinh(+0) = 0
asinh(-0) = -0