> Oh, a couple more things I just thought of:
>
> > public protocol Arithmetic: Equatable, IntegerLiteralConvertible {
> If your goals include supporting complex numbers, how is
> IntegerLiteralConvertible going to fit in there?
>
> > /// Initialize to zero
> > init()
> 0 is valuable as the additive identity. Should there also be a way to get 1,
> the multiplicative identity? If you need both, should these be static
> properties instead of initializers?
Interestingly, these two questions are related.
If you expose the multiplicative identity, you automatically expose a natural
way to convert from an integer N: just add `one` to itself N times.
If N is negative, take the opposite.
For complex numbers the multiplicative identity is 1 + 0i, so this means that
Complex(N) = N + 0i.
As an aside, a default generic implementation of IntegerLiteralConvertible
would run in O(log N) steps, using the “double-and-add” algorithm:
https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication#Double-and-add.
Though I don’t think this is particularly useful for our use case :-)
—
Nicola
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