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

Specifications

Browser compatibility

Desktop Mobile
Chrome Edge Firefox Internet Explorer Opera Safari WebView Android Chrome Android Firefox for Android Opera Android Safari on IOS Samsung Internet
log1p
38
12
25
No
25
8
38
38
25
25
8
3.0

See also

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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