How to determine an integer in javascript

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What is the best way to write a function isInteger(x) that determines if x is an integer.

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This may sound trivial and, in fact, it is trivial with ECMAscript 6 which introduces a new Number.isInteger() function for precisely this purpose. However, prior to ECMAScript 6, this is a bit more complicated, since no equivalent of the Number.isInteger() method is provided.

The issue is that, in the ECMAScript specification, integers only exist conceptually; i.e., numeric values are always stored as floating point values.

With that in mind, the simplest and cleanest pre-ECMAScript-6 solution (which is also sufficiently robust to return false even if a non-numeric value such as a string or null is passed to the function) would be the following use of the bitwise XOR operator:

function isInteger(x) { return (x ^ 0) === x; }
The following solution would also work, although not as elegant as the one above:

function isInteger(x) { return Math.round(x) === x; }
Note that Math.ceil() or Math.floor() could be used equally well (instead of Math.round()) in the above implementation.

Or alternatively:

function isInteger(x) { return (typeof x === 'number') && (x % 1 === 0); }
One fairly common incorrect solution is the following:

function isInteger(x) { return parseInt(x, 10) === x; }
While this parseInt-based approach will work well for many values of x, once x becomes quite large, it will fail to work properly. The problem is that parseInt() coerces its first parameter to a string before parsing digits. Therefore, once the number becomes sufficiently large, its string representation will be presented in exponential form (e.g., 1e+21). Accordingly, parseInt() will then try to parse 1e+21, but will stop parsing when it reaches the e character and will therefore return a value of 1. Observe:

> String(1000000000000000000000)
> parseInt(1000000000000000000000, 10)
> parseInt(1000000000000000000000, 10) === 1000000000000000000000
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