MDN will be in maintenance mode on Friday September 22nd, starting at 10 AM Pacific / 5 PM UTC, for about 1 hour.

Nossos voluntários ainda não traduziram este artigo para o Português (do Brasil) . Junte-se a nós e ajude a fazer o trabalho!
Você também pode ler o artigo em English (US).

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)




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.


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).


Using Math.log1p()

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


This can be emulated with the following function:

Math.log1p = Math.log1p || function(x) {
  return Math.log(1 + x);


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.

Browser compatibility

FeatureChromeFirefoxEdgeInternet ExplorerOperaSafari
Basic Support3825(Yes)(No)257.1
FeatureAndroidChrome for AndroidEdge mobileFirefox for AndroidIE mobileOpera AndroidiOS Safari
Basic Support(Yes)(Yes)(Yes)25(No)(Yes)8

See also

Etiquetas do documento e colaboradores

 Última atualização por: fscholz,