RFC: int semantics

text/0001-int.md

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+---
+Feature Name: rescript-integers
+Start Date: 2024-11-19
+RFC PR: https://github.com/rescript-lang/rfcs/pull/1
+ReScript Issue: (leave this empty)
+---
+
+## Summary
+
+Semantics deifinition of the ReScript's `int` type and integer primitives.
+
+## Motivation
+
+ReScript has three numeric primitive types, `int`, `float` and `bigint`.
+
+The semantics of `float` and `bigint` completely match JavaScript's ones, but `int` is unique to ReScript and originally came from OCaml's `int` type.
+
+`int` stands for 32-bit signed integers. It's a bit unusual for a language to have int32 only and no other precision — mostly for historical reasons, and it isn't very clear due to differences in behavior with JavaScript.
+
+This RFC describes its semantics and chosen trade-offs as precisely as possible.
+
+## Definition
+
+TBD
+
+```res
+type int
+
+let n = 100
+```
+
+Using unbounded integer literals may result in compile-time errors with messages such as `"Integer literal exceeds the range of representable integers of type int."`
+
+## Primitives
+
+Let `max_value` be $2^{31}-1$ and `min_value` be $-2^{31}$.
+
+### `fromNumber(x: number)`
+
+1. If `x` is JavaScript's `Infinity`, return `max_value`.
+2. If `x` is JavaScript's `-Infinity`, return `min_value`.
+3. Let `int32` be [`ToInt32`]`(x)`, return `int32`.
+
+The actions 1 and 2 are intended to reduce confusion when converting from an infinate value. (e.g. https://github.com/rescript-lang/rescript/issues/6737) However, it can be omitted if it is obvious that the `x` is not `Infinity` or `-Infinity`.
+
+The [`ToInt32`] behavior follows the definition in ECMA-262 as is. In action, the ReScript compiler uses `bitwiseOR(number, 0)`. This is what appears in the output as `number | 0`. And this removes all special numbers defined in IEEE-754. `int` never contain the following values:
+
+- `NaN`
+- `Infinity` and `-Infinity`
+- `-0`
+
+`fromNumber(x)` must be idempotent.
+
+### `add(x: int, y: int)`
+
+1. Let `number` be mathmatically $x + y$.
+2. Let `int32` be `fromNumber(number)`, return `int32`.
+
+### `subtract(x, y)`
+
+1. Let `number` be mathmatically $x - y$.
+2. Let `int32` be `fromNumber(number)`, return `int32`.
+
+### `multiply(x, y)`
+
+1. Let `number` be mathmatically $x * y$.
+2. Let `int32` be `fromNumber(number)`, return `int32`.
+
+The `multiply(x, y)` must produce the same result as `add(x)` accumulated `y` times.
+
+```res
+let multiply = (x, y) => {
+  let id = 0
+  let rec multiply = (x, y, acc) => {
+    switch y {
+    | 0 => acc
+    | n => multiply(x, n - 1, add(x, acc))
+    }
+  }
+  multiply(x, y, id)
+}
+```
+
+### `exponentiate(x, y)`
+
+1. Let `number` be mathmatically $x ^ y$.
+2. Let `int32` be `fromNumber(number)`, return `int32`.
+
+The `exponentiate(x, y)` must produce the same result as `multiply(x)` accumulated `y` times.
+
+```res
+let exponentiate = (x, y) => {
+  let id = 1
+  let rec exponentiate = (x, y, acc) => {
+    switch y {
+    | 0 => acc
+    | n => exponentiate(x, n - 1, multiply(x, acc))
+    }
+  }
+  exponentiate(x, y, id)
+}
+```
+
+### `divide(x, y)`
+
+1. If `y` equals `0`, raise `Divide_by_zero`.
+2. Let `number` be mathmatically $x / y$.
+3. Let `int32` be `fromNumber(number)`, return `int32`.
+
+### `remainder(x, y)`
+
+1. If `y` equals `0`, raise `Divide_by_zero`.
+
+### `abs(x)`
+
+1. If `x` is `min_value`, raise `Overflow_value`.
+
+## API consideration
+
+TBD
+
+## Questions
+
+### Why do we even use `int`?
+
+The use of `int` is primarily for backward compatibility — not with OCaml, but with all existing ReScript codebases.
+
+Additionally, using `int` is beneficial for JavaScript programs since major JavaScript engines treat integers differently.
+
+Depending on the implementation, integer values (especially 32-bit integers) may have a distinct memory representation compared to floating-point numbers. For example, V8 (the JavaScript engine in Chromium) employs an internal element kind called "SMI" (Small integers). This provides an efficient memory representation for signed 32-bit integers and enhances runtime performance by avoiding heap allocation.
+
+At compile time, the compiler ensures that certain operations are restricted to using only `int` types. This increases the likelihood of utilizing the optimized execution paths for SMIs and reduces the potential for runtime de-optimization caused by element kind transitions.
+
+### Why do we truncate values instead of bounds-checking?
+
+It is also for backward compatibility. Bounds-checking and failure early may be more useful for fast feedback loop, but we don't want to break any programs that (accidentally) worked before.
+
+The `number | 0` is actually the most concise output form we can consistently use. Introducing any other runtime codes universally would lead to significant code bloat in the output.
+
+### Can we somehow make it match JavaScript's `number`?
+
+Perhaps in the future, we can make our number literals actually match JavaScript's number semantics. We could also rename `int` to `int32` and assign another literal like `0l`, as it was in OCaml syntax.
+
+However, this is not something that will happen in the near future. It won't occur until we are confident in our migration strategy to avoid breaking existing codebases. If done incorrectly, it could completely break compatibility with existing code.
+
+## Future posibilities
+
+Guaranteeing the use of int32 types may offer additional advantages in the future when targeting WebAssembly or alternative native backends.
+
+[`ToInt32`]: https://262.ecma-international.org/#sec-toint32