[swift-evolution] protocol-oriented integers (take 2)
Stephen Canon
scanon at apple.com
Wed Jan 25 13:38:28 CST 2017
> On Jan 25, 2017, at 1:58 PM, David Sweeris via swift-evolution <swift-evolution at swift.org> wrote:
>
>
>> 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.
1. Square matrices of fixed size can absolutely conform to this protocol (except for ‘/‘, as discussed earlier in the thread).
2. It’s pretty common to call the multiplicative identity matrix 1 (though “I” is more common). The rest of the integers map to square matrices in the obvious way n —> n*1 (i.e. the matrix with n on the main diagonal, and zeros elsewhere).
– Steve
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