[swift-evolution] protocol-oriented integers (take 2)

[David Sweeris]

> On Jan 25, 2017, at 07:59, Anton Mironov via swift-evolution <swift-evolution at swift.org> wrote:
> 
> Hi everyone,
> 
> I want to suggest a tiny extension to an Arithmetic protocol. It would be nice to have an additive identity and a multiplicative identity constants. Basically zero and one.
> 
> ```
> protocol Arithmetic {
>   /* ... */
>   static var zero: Self { get }  // additive identity: (value + .zero) == value
>   static var one: Self { get }   // multiplicative identity: (value * .one) == value
> }
> ```
> 
> These constants will ease implementation of math structures: vectors, matrices and etc.
> I’m sorry if I’m duplicating someone’s suggestion. It is really hard to search for something in a long thread.

Vectors, matrices, etc can't conform to this protocol anyway because of the * and / requirements. And while it is true that it's not uncommon to reference an all-zero matrix or vector as "0", that doesn't work for any other number... for them I think the spelling should be "additiveIdentity". It'll be easy enough to just say
protocol Addable {
    static var additiveIdentity: Self {get}
    ...
}
extension Addable where Self: Arithmetic {
    static var additiveIdentity: Self {return Self.zero}
}

IMHO, anyway.

- Dave Sweeris