std::asinh, std::asinhf, std::asinhl

< cpp‎ | numeric‎ | math

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

1-3) 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

acoshacoshfacoshl (C++11)(C++11)(C++11)	computes the inverse hyperbolic cosine (${\small\operatorname{arcosh}{x} }$ $arcosh(x)$ ) (function)
atanhatanhfatanhl (C++11)(C++11)(C++11)	computes the inverse hyperbolic tangent (${\small\operatorname{artanh}{x} }$ $artanh(x)$ ) (function)
sinhsinhfsinhl (C++11)(C++11)	computes hyperbolic sine (${\small\sinh{x} }$ $sinh(x)$ ) (function)
asinh(std::complex) (C++11)	computes area hyperbolic sine of a complex number (${\small\operatorname{arsinh}{z} }$ $arsinh(z)$ ) (function template)

External links

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