Math.log1p() - JavaScript 编辑

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

$$\forall x > -1, \mathtt{\operatorname{Math.log1p}(x)} = \ln(1 + x)$$

The source for this interactive example is stored in a GitHub repository. If you'd like to contribute to the interactive examples project, please clone https://github.com/mdn/interactive-examples and send us a pull request.

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

Browser compatibility

BCD tables only load in the browser

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.

See also

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