# std::asinh

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< cpp‎ | numeric‎ | math

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( Integral 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

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

### External links

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

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