Math.asinh

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

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

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).

Examples

Using Math.asinh()

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

Polyfill

As a quick and dirty hack the expression $\operatorname {arsinh} (x) = \ln \left(x + \sqrt{x^{2} + 1} \right)$ 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

Browser compatibility

See also

• Math.acosh()
• Math.atanh()
• Math.cosh()
• Math.sinh()
• Math.tanh()