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I maintain a JavaScript hashing library and the language's handling of large integers is terrible. SHA-256/SHA-384/SHA-512 as well as SHA-3 all use 64-bit primitives so I need to do some hacks to emulate a 64-bit integer. Bit shifting large numbers gets even more nebulous...

Do you know if moving to BigInt would cause performance issues?

The point is that not all integers over `Number.MAX_SAFE_INTEGER` can be represented. Some can, of course.

That 2^53 - 1 comes from the 64-Bit floating point representation JS uses for the normal number type.

    (Number.MAX_SAFE_INTEGER + 1) === (Number.MAX_SAFE_INTEGER + 2)
    > true

edit: yeah, just as you wrote in the reply to the other comment

> The point is that not all integers over `Number.MAX_SAFE_INTEGER` can be represented. Some can, of course.

Right. This contradicts the article.

> 2^53 - 1 comes from the 64-Bit floating point representation JS uses

Right.

Ah, now I see it the whole point - "reliably representable" not meaning the same as "safe", gotcha.

Sort of. I'm pointing out what seems to me to be an incorrect statement in the article. I think it's reasonable to have special terminology for the sequence of contiguous integers which can be represented exactly in the Number type. Safe seems a reasonable choice, provided it's used carefully.

MAX_SAFE_INTEGER seems a better choice of identifier than something like MAX_VALUE_OF_EXACTLY_REPRESENTABLE_CONTIGUOUS_SEQUENCE_OF_INTEGERS, of course, despite that it's less precise. (Even that absurdly long identifier isn't perfectly precise, as we can define a trivial sequence of a single value like Number.MAX_VALUE.) The documentation explaining it should be precise, though.

I think you misread the sentence. It's not the largest value JS can represent, it's the largest value it can "reliably represent". After 2^53 - 1 you get incorrect results when dealing with integers, making the results not "reliable".

When an integer can be reliably represented, that presumably means that JavaScript's definition of the Number type is such that it guarantees that a given integer can be represented exactly by the Number type. It doesn't mean you can safely do arbitrary integer arithmetic on it and get back another integer, also represented exactly. Trivially, there are no such values.

Every non-negative integer up to and including Number.MAX_SAFE_INTEGER can be represented exactly by the Number type, in any compliant JavaScript implementation. It's also true though that Number.MAX_VALUE is itself defined to be an integer. It's therefore not true to say that Number.MAX_SAFE_INTEGER is the greatest integer that can be exactly represented by JavaScript's Number type.

Instead, Number.MAX_SAFE_INTEGER is the greatest integer such that Number.MAX_SAFE_INTEGER can be represented precisely by the Number type, and all non-negative integers less than Number.MAX_SAFE_INTEGER can be represented exactly by the Number type. (See also my second edit to my earlier post.)

It seems incorrect then that the article states:

> 2^53 - 1, which is the largest number JavaScript can reliably represent with the Number primitive and represented by the Number.MAX_SAFE_INTEGER constant

There's discussion of the term safely represent on the MAX_SAFE_INTEGER page. [0]

[0] https://developer.mozilla.org/en-US/docs/Web/JavaScript/Refe...

I can't agree with your pedantry here.

> When an integer can be reliably represented, that presumably

You are right that the wording is not precise, but now you're putting a lot of meaning into what you admit is an assumption.

> means that JavaScript's definition of the Number type is such that it guarantees that a given integer can be represented exactly by the Number type. It doesn't mean you can safely do arbitrary integer arithmetic

Who said arbitrary? The natural numbers are canonically represented by a successor function, denoted S(n). So we're talking about the highest natural that can be represented as such.

> you're putting a lot of meaning into what you admit is an assumption

Can you suggest another interpretation? It's a point about representing a number, and is not a point about arithmetic, so I'm not seeing what else it could mean.

Either way we're agreed that it wants reworking. Technical documentation should not be incorrect, as I believe it to be, and it should not be ambiguous, as you believe it to be.

> Who said arbitrary?

Look at what I was responding to: After 2^53 - 1 you get incorrect results when dealing with integers, making the results not "reliable". That's not very precise, as dealing with might refer to the problem of exactly representing the integer values in the Number type, or it might refer to the problem of doing arithmetic with those values and getting exact results.

To rephrase my point: with the exception of 0, there is no Number value x such that, for all integer Number values y, the integer x + y can be represented exactly as a Number. It's not 'safe' to compute Number.MAX_SAFE_INTEGER + 1 despite that both terms are 'safe' integers.

Which is to say, we need to be clear that we're reasoning about the problem of exactly representing integer values in the Number type.

> The natural numbers are canonically represented by a successor function, denoted S(n). So we're talking about the highest natural that can be represented as such.

I don't see your point here. I've already discussed the difference between Number.MAX_SAFE_INTEGER and the much greater integer Number.MAX_VALUE.