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