Web/JavaScript/Reference/Global objects/Math/log1p

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

<math display="block">\forall x > - 1,\mathtt{\operatorname{Math.log1p}(x)} = \ln(1 + x)</math>

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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).

Polyfill

This can be emulated with the following function:

Math.log1p = Math.log1p || function(x) {
  x = Number(x);
  if (x < -1 || x !== x)
    return NaN;
  if (x === 0 || x === Infinity)
    return x;
  
  var nearX = (x + 1) - 1;

  return nearX === 0 ? x : x * (Math.log(x + 1) / nearX);
};

Examples

Using Math.log1p()

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

Specifications

Specification

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

Browser compatibility

The compatibility table in this page is generated from structured data. If you'd like to contribute to the data, please check out https://github.com/mdn/browser-compat-data and send us a pull request.

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	Safari on iOS	Samsung Internet	Node.js
log1p	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 38	Chrome Android Full support 38	Firefox Android Full support 25	Opera Android Full support 25	Safari iOS Full support 8	Samsung Internet Android Full support 3.0	nodejs Full support 0.12

Legend

Full support  

Full support

No support  

No support

See also

• Math.exp()
• Math.log()
• Math.expm1()
• Math.log10()
• Math.log2()
• Math.pow()

Math.log1p() by Mozilla Contributors is licensed under CC-BY-SA 2.5.