# Math.log1p()

The ** Math.log1p()** function returns the natural logarithm (base

`e`

) of 1 + a number, that is$$\backslash forall\; x\; >\; -1,\; \backslash mathtt\{\backslash operatorname\{Math.log1p\}(x)\}\; =\; \backslash ln(1\; +\; x)$$

## Syntax

`Math.log1p(``x`)

### Parameters

`x`

- A number.

### Return value

The natural logarithm (base `e`

) of **1** plus the given number. If the number is less than **-1**, `NaN`

is returned.

## Description

For very small values of *x*, adding 1 can reduce or eliminate precision. The double floats used in JS give you about 15 digits of precision. 1 + 1e-15 = 1.000000000000001, but 1 + 1e-16 = 1.000000000000000 and therefore exactly 1.0 in that arithmetic, because digits past 15 are rounded off.

When you calculate log(1 + x), you should get an answer very close to x, if x is small (that's why these are called 'natural' logarithms). If you calculate Math.log(1 + 1.1111111111e-15) you should get an answer close to 1.1111111111e-15. Instead, you will end up taking the logarithm of 1.00000000000000111022 (the roundoff is in binary so sometimes it gets ugly), so you get the answer 1.11022...e-15, with only 3 correct digits. If, instead, you calculate Math.log1p(1.1111111111e-15) you will get a much more accurate answer 1.1111111110999995e-15 with 15 correct digits of precision (actually 16 in this case).

If the value of `x`

is less than -1, the return value is always `NaN`

.

Because `log1p()`

is a static method of `Math`

, you always use it as `Math.log1p()`

, rather than as a method of a `Math`

object you created (`Math`

is not a constructor).

## Examples

### Using `Math.log1p()`

Math.log1p(1); // 0.6931471805599453 Math.log1p(0); // 0 Math.log1p(-1); // -Infinity Math.log1p(-2); // NaN

## Polyfill

This can be emulated with the following function:

Math.log1p = Math.log1p || function(x) { return Math.log(1 + x); };

## Specifications

Specification | Status | Comment |
---|---|---|

ECMAScript 2015 (6th Edition, ECMA-262) The definition of 'Math.log1p' in that specification. |
Standard | Initial definition. |

ECMAScript 2017 Draft (ECMA-262) The definition of 'Math.log1p' in that specification. |
Draft |

## Browser compatibility

Feature | Chrome | Firefox (Gecko) | Internet Explorer | Opera | Safari |
---|---|---|---|---|---|

Basic support | 38 | 25 (25) | No support | 25 | 7.1 |

Feature | Android | Chrome for Android | Firefox Mobile (Gecko) | IE Mobile | Opera Mobile | Safari Mobile |
---|---|---|---|---|---|---|

Basic support | No support | No support | 25.0 (25) | No support | No support | 8 |

## See also

## License

© 2016 Mozilla Contributors

Licensed under the Creative Commons Attribution-ShareAlike License v2.5 or later.

https://developer.mozilla.org/en-us/docs/web/javascript/reference/global_objects/math/log1p