js-integers.md

Implicit integers for JavaScript

This proposal is an alternative to “Integer: Arbitrary precision integers in JavaScript” by Daniel Ehrenberg, but it also builds on his work.

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Everything mentioned here is work in progress. It is not sure that these ideas will work out:

• They may break the web.
• They may turn out to be too complicated/user-unfriendly.

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Rationale

The current proposal for Integers with arbitrary precisions has pros and cons:

• Pros: It is very clean and paves the way for more operator overloading and user-definable value types in the future.
• Cons: It is only partially backward-compatible. The already existing implicit “small integers” (incl. array indices, Array#entries(), Array#forEach(), etc.) clash with the new “big integers”.
  • That is, you can’t tell developers: “Use Integers whenever you can.”
  • Instead, best practices are: “Use Numbers for up to 53-bit ints. Use Integers if you need more bits.”

This proposal sketches an alternative approach. It has different pros and cons.

Number is a supertype of Int and Double

Number is a supertype of Int and Double: Number = Int ∪ Double

• Double:
  • typeof 123.0 === 'number'
  • Number.isDouble(123.0) === true
  • Converting to Double: Number.asDouble()
• Int:
  • typeof 123 === 'number'
  • Number.isInt(123) === true
  • Number.isInt(0xFF) === true
  • Converting to Int: Number.asInt()

More tool functions:

• Number.parseInt() : Int (new signature)
• Number.asUintN(width, theInt) (works as described in Dan’s proposal)
• Number.asIntN(width, theInt) (works as described in Dan’s proposal)

Operator overloading

Binary operators

Existing binary operators for numbers are overloaded:

• +, -
• *, /, %, **
• <<, >>, >>>

Signature:

• Signatures where results are Double:
  • Int × Double → Double (via coercion)
  • Double × Int → Double (via coercion)
  • Double × Double → Double
• Signature where the result has arbitrary precision:
  • Int × Int → Int (all operators except /, see below)

Additionally, new Int-only operators (signature: Int×Int→Int) are introduced:

• Integer division: div
  • Normal division must produce non-integer values, e.g. for 1/2
• Bitwise operators: band, bor, bxor
• Shift operators: shl, shr

Open question: Will + and * having more precision for Ints break code on the web? For example:

• Currently: 9007199254740992 + 1 === 9007199254740992
• With this proposal: 9007199254740992 + 1 === 9007199254740993

Equality

• With this proposal, === has to coerce if a Double has no decimal fraction: 1.0 === 1

Bitwise operators

The results of bitwise operators stay within 32 bits and are of type Int.

Unary operators

• Unary + must coerce to Double, because, among others, asm.js depends on it.
• Unary -: it is unclear how this operator can be made to work for Ints (which only have a single zero), given that:
  • Object.is(-0, 0) === false

Open questions

• Int operators: coerce or throw exception if operand types are wrong?
• Naming: Int makes most sense, given Number.isInteger() etc.

Various thoughts

• Static type checking tools could warn if the operands of a numeric operator mix numbers and integers.
• JSON would automatically get big integer values (more than 53 bits).

Further reading

• “Integer: Arbitrary precision integers in JavaScript” by Daniel Ehrenberg
• “ES proposal: arbitrary precision integers” by Axel Rauschmayer

@FremyCompany can you show me some code that would depend on that? (recognizing that they'd have to be multiplying integers such that the result is larger than MAX_SAFE_INTEGER, and then relying on that value being wrong)