Math.asinh()

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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)

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).

Examples

Using Math.asinh()

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


Polyfill

As a quick and dirty hack the expression $\operatorname \left\{arsinh\right\} \left(x\right) = \ln \left\left(x + \sqrt\left\{x^\left\{2\right\} + 1\right\} \right\right)$ may be used directly for a coarse emulation by the following function:

Math.asinh = Math.asinh || function(x) {
if (x === -Infinity) {
return x;
} else {
return Math.log(x + Math.sqrt(x * x + 1));
}
};


Been formally correct it suffers from a number of issues related to floating point computations. Accurate result requires special handling of positive/negative, small/large arguments as it done e.g. in glibc or GNU Scientific Library.

Specifications

Specification Status Comment
ECMAScript 2015 (6th Edition, ECMA-262)
The definition of 'Math.asinh' in that specification.
Standard Initial definition.
ECMAScript Latest Draft (ECMA-262)
The definition of 'Math.asinh' in that specification.
Draft

Browser compatibility

Update compatibility data on GitHub
Desktop Mobile Server Chrome Edge Firefox Internet Explorer Opera Safari Android webview Chrome for Android Edge Mobile Firefox for Android Opera for Android Chrome Full support 38 Edge Full support 12 Firefox Full support 25 IE No support No Opera Full support 25 Safari Full support 8 WebView Android Full support Yes Chrome Android Full support Yes Edge Mobile Full support Yes Firefox Android Full support 25 Opera Android Full support Yes Safari iOS Full support 8 Samsung Internet Android Full support Yes nodejs Full support 0.12

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