is // required to return Rational? Alternatively, an interface for rationals

[nsajko]

I want to implement // for my own types. The return type would subtype Real and it'd also overload numerator and denominator, but it wouldn't subtype Rational. Would that be allowed?

The motivation is twofold:

• (Regular) continued fractions seem to be a good choice for encoding rational numbers. It'd be nice if such a type/package could overload // to return the same type, instead of Rational.
• Rational doesn't generally support type domain numbers, because it requires the numerator and denominator to have the same type. Thus a new, "type domain rational", type would be nice, and // would ideally return type domain numbers given type domain numbers as input.

[nhz2]

// can also return Complex, though there are still some overflow issues Ref #53435.

I also find it strange that there is a method of // for //(x::Number, y::Complex) but no method for //(x::Number, y::Real)

I think it might make sense to define a generic //(x::Number, y::Number) = rational(x) / rational(y) where rational would be a function to promote a number to any type that supports exact division.

[nhz2]

An important question is what should rational(x::Float64) do? Should it return an exact Rational{BigInt} or throw an error?