Math.asinh()

The Math.asinh() function returns the hyperbolic arcsine of a number, that is

Math.asinh(x)=arsinh(x)= the unique ysuch thatsinh(y)=x\mathtt{\operatorname{Math.asinh}(x)} = \operatorname{arsinh}(x) = \text{ the unique } \; y \; \text{such that} \; \sinh(y) = x

Syntax

Math.asinh(x)

Parameters

x
A number.

Return value

The hyperbolic arcsine of the given number.

Description

Because asinh() is a static method of Math, you always use it as Math.asinh(), rather than as a method of a Math object you created (Math is not a constructor).

Polyfill

Math.asinh can be emulated with the following function:

if (!Math.asinh) Math.asinh = function(x) {
    var absX = Math.abs(x), w
    if (absX < 3.725290298461914e-9) // |x| < 2^-28
        return x 
    if (absX > 268435456) // |x| > 2^28
        w = Math.log(absX) + Math.LN2
    else if (absX > 2) // 2^28 >= |x| > 2
        w = Math.log(2 * absX + 1 / (Math.sqrt(x * x + 1) + absX))
    else
        var t = x * x, w = Math.log1p(absX + t / (1 + Math.sqrt(1 + t)))

    return x > 0 ? w : -w 
}

Math.log1p may also have to be polyfilled; see Math.log1p for details.

Examples

Using Math.asinh()

Math.asinh(1);  // 0.881373587019543
Math.asinh(0);  // 0

Specifications

Specification
ECMAScript (ECMA-262)
The definition of 'Math.asinh' in that specification.

Browser compatibility

DesktopMobileServer
ChromeEdgeFirefoxInternet ExplorerOperaSafariAndroid webviewChrome for AndroidFirefox for AndroidOpera for AndroidSafari on iOSSamsung InternetNode.js
asinhChrome Full support 38Edge Full support 12Firefox Full support 25IE No support NoOpera Full support 25Safari Full support 8WebView Android Full support 38Chrome Android Full support 38Firefox Android Full support 25Opera Android Full support 25Safari iOS Full support 8Samsung Internet Android Full support 3.0nodejs Full support 0.12

Legend

Full support
Full support
No support
No support

See also