NAME

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

Synopsis

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

// Run this code

#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

acosh
acoshf computes the inverse hyperbolic cosine
acoshl (\({\small\operatorname{arcosh}{x} }\)arcosh(x))
(C++11) (function)
(C++11)
(C++11)
atanh
atanhf computes the inverse hyperbolic tangent
atanhl (\({\small\operatorname{artanh}{x} }\)artanh(x))
(C++11) (function)
(C++11)
(C++11)
sinh
sinhf computes hyperbolic sine (\({\small\sinh{x} }\)sinh(x))
sinhl (function)
(C++11)
(C++11)
asinh(std::complex) computes area hyperbolic sine of a complex number
(C++11) (\({\small\operatorname{arsinh}{z} }\)arsinh(z))
(function template)

External links

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