The Math.log1p()
function returns the natural logarithm (base e
) of 1 + x
, where x
is the argument. That is
$$\backslash forall\; x\; >\; -1,\; \backslash mathtt\{\backslash operatorname\{Math.log1p\}(x)\}\; =\; \backslash ln(1\; +\; x)$$
The Math.log1p()
function returns the natural logarithm (base e
) of 1 + x
, where x
is the argument. That is
$$\backslash forall\; x\; >\; -1,\; \backslash mathtt\{\backslash operatorname\{Math.log1p\}(x)\}\; =\; \backslash ln(1\; +\; x)$$
Math.log1p(x)
x
A number.
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) where x is a small positive number, you should get an answer very close to x, because $\backslash lim\_\{x\; \backslash to\; 0\}\; \backslash frac\{\backslash log(1+x)\}\{x\}\; =\; 1$. 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), and 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).
Math.log1p()
Math.log1p(1); // 0.6931471805599453 Math.log1p(0); // 0 Math.log1p(-1); // -Infinity Math.log1p(-2); // NaN
Specification |
---|
ECMAScript Language Specification # sec-math.log1p |
Desktop | Mobile | Server | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Chrome | Edge | Firefox | Internet Explorer | Opera | Safari | WebView Android | Chrome Android | Firefox for Android | Opera Android | Safari on IOS | Samsung Internet | Deno | Node.js | |
log1p |
38 |
12 |
25 |
No |
25 |
8 |
38 |
38 |
25 |
25 |
8 |
3.0 |
1.0 |
0.12.0 |
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https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/log1p