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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 Status Comment
ECMAScript 2015 (6th Edition, ECMA-262)
The definition of 'Math.log1p' in that specification.
Standard Initial definition.
ECMAScript Latest Draft (ECMA-262)
The definition of 'Math.log1p' in that specification.
Draft  

Browser compatibility

Update compatibility data on GitHub
DesktopMobileServer
ChromeEdgeFirefoxInternet ExplorerOperaSafariAndroid webviewChrome for AndroidEdge MobileFirefox for AndroidOpera for AndroidiOS SafariSamsung InternetNode.js
Basic supportChrome Full support 38Edge Full support YesFirefox Full support 25IE No support NoOpera Full support 25Safari Full support 8WebView Android Full support YesChrome Android Full support YesEdge Mobile Full support YesFirefox Android Full support 25Opera Android Full support YesSafari iOS Full support 8Samsung Internet Android Full support Yesnodejs Full support 0.12

Legend

Full support  
Full support
No support  
No support

See also

Autorzy i etykiety dokumentu

Ostatnia aktualizacja: wbamberg,