max integer value in JavaScript

Question

I\'m reading the second chapter of the book Eloquent JavaScript. The author states that:

Any whole number less than 2^52 (which is more than 10^

Answer 1

You can think of 52 bits integer in JS, but remember that bitwise logical operators & | >> etc.. will only deal with 32 less significant bits discarding the rest.

Answer 2

You can find some information on JavaScript's Number type here: ECMA-262 5th Edition: The Number Type.

As it mentions, numbers are represented as a 64-bit floating-point number, with 53 bits of mantissa (significant digits) and 11 bits for the exponent (IEEE 754). The result is then obtained with: mantissa * 2^exponent.

This means that up to 2^53 values can be represented in the mantissa (of those a few numbers have special meanings, and the others are positive and negative integers).

The number 2^53 (9007199254740992) can't be represented in the mantissa, and you have to use an exponent. As an example, you can represent 2^53 as (9007199254740992 / 2) * 2^1, ie. mantissa = 9007199254740992 / 2 = 4503599627370496 and exponent = 1.

Let's check what happens with 2^53+1 (9007199254740993). Here we have to do the same, mantissa = 9007199254740993 / 2 = 4503599627370496. Oops, isn't this the same mantissa we had for 2^53? Looks like there's been some rounding error! :)

(Note: the above examples are not actually how it really works: the mantissa is always interpreted as having a dot after the first digit, which means that eg. the number 3 is actually stored as 1.5*2. I omitted this in the above explanation to make it easier to follow.)

You can find some more information on floating-point numbers (in general) here: What Every Computer Scientist Should Know About Floating-Point Arithmetic.

Answer 3

This is not a strongly typed programming language. JS has an object Number. You can even get an infinite number: document.write(Math.exp(1000));.

document.write(Number.MIN_VALUE + "<br>");
document.write(Number.MAX_VALUE + "<br>");

document.write(Number.POSITIVE_INFINITY + "<br>");
document.write(Number.NEGATIVE_INFINITY + "<br>");

    alert([
         Number.MAX_VALUE/(1e293),
         Number.MAX_VALUE/(1e292),
         Number.MAX_VALUE/(1e291),
         Number.MAX_VALUE/(1e290),
    ].join('\n'))

Hope it's a useful answer. Thanks!

UPDATE: max int is - +/- 9007199254740992