# 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

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

## Browser compatibility

Update compatibility data on GitHub
Desktop Mobile Server Chrome Edge Firefox Internet Explorer Opera Safari Android webview Chrome for Android 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 38 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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