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std::asinh

Defined in header <cmath> 
float       asinh( float arg );
 (1) (since C++11) 
double      asinh( double arg );
 (2) (since C++11) 
long double asinh( long double arg );
 (3) (since C++11) 
double      asinh( IntegralType arg );
 (4) (since C++11)

Computes the inverse hyperbolic sine 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 sine of arg (sinh-1
(arg), or arsinh(arg)), 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".

Examples

#include <iostream>
#include <cmath>
 
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';
}

Output:

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

See also

(C++11)
 computes the inverse hyperbolic cosine (arcosh(x))
(function)
(C++11)
 computes the inverse hyperbolic tangent (artanh(x))
(function)
computes hyperbolic sine (sh(x))
(function)
(C++11)
 computes area hyperbolic sine of a complex number
(function template)
C documentation for asinh

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

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