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

[Howard Lovatt]

For the Arithmetic protocol how about changing it to:

    protocol Arithmetic {
        func + (lhs: Self, rhs: Self) -> Self
        mutating func += (rhs: Self) -> Self
        ...
    }

That way naming issues are largely avoided, except for `mutating func
negate()` which has no operator and would therefore have to be a normal,
non-operator, func.

On Saturday, 16 April 2016, Nicola Salmoria via swift-evolution <
swift-evolution at swift.org> wrote:

> > 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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-- 
-- Howard.
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