The Math.log1p()
function returns the natural logarithm (base e
) of 1 + a number, that is
Math.log1p(x)
x
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).
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); };
Math.log1p()
Math.log1p(1); // 0.6931471805599453 Math.log1p(0); // 0 Math.log1p(-1); // -Infinity Math.log1p(-2); // NaN
Desktop | ||||||
---|---|---|---|---|---|---|
log1p |
38 | 12 | 25 | No | 25 | 8 |
Mobile | ||||||
---|---|---|---|---|---|---|
log1p |
38 | 38 | 25 | 25 | 8 | 3.0 |
Server | |
---|---|
log1p |
0.12 |
© 2005–2018 Mozilla Developer Network and individual contributors.
Licensed under the Creative Commons Attribution-ShareAlike License v2.5 or later.
https://wiki.developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/log1p