How do we implement Ratio and Complex?

[stylewarning]

There is difficulty in implementing these as native Lisp objects, because:

• Problem 1: reduction of #C(k 0) to k; or k/1 to k

• Problem 2: Lisp doesn't allow arbitrary field elements as components (Complex :a cannot use Lisp's complex numbers)

How do we implement Complex Single-Float as specialized on (COMPLEX SINGLE-FLOAT), but also allow Num :a => Complex :a to exist?

[stylewarning]

See also lisp-type

[bitmappergit]

I don't think Ratio is an issue once #51 is solved due to the reduction of those to integers being the first thing that happens, which would then have something like ((Num :a) => :a) for their type, and ratios must have an instance of Num to implement Fractional.

[eliaslfox]

I think @stylewarning is referring to the fact that SBCL will convert #C(k 0) into a real type at runtime.

[stylewarning]

Yes:

CL-USER> 4/3
4/3
CL-USER> (type-of *)
RATIO
CL-USER> 4/2
2
CL-USER> (type-of *)
(INTEGER 0 4611686018427387903)
CL-USER> #C(2 1)
#C(2 1)
CL-USER> (type-of *)
(COMPLEX (INTEGER 1 2))
CL-USER> #C(2 0)
2
CL-USER> (type-of *)
(INTEGER 0 4611686018427387903)

[bitmappergit]

Ah, sorry, I misunderstood the issue.

It might just be best to represent these as a datatype like in Haskell, and handle this in the codegen?