# Math.log1p()

The Math.log1p() function returns the natural logarithm (base e) of 1 + a number, that is

$∀x>-1,Math.log1p(x)=ln(1+x)\forall x > -1, \mathtt{\operatorname{Math.log1p}(x)} = \ln(1 + x)$

## Syntax

JavaScript
Math.log1p(<var>x</var>)

### 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()

JavaScript
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:

JavaScript
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