[swift-evolution] [Proposal draft] Enhanced floating-point protocols

[Nicola Salmoria]

> 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