[RFC/WIP] unify the concepts of Fixed and UFixed

[vchuravy]

After #27 UFixed and Fixed shared a lot of concepts and they do effectively the same thing, but sometimes a function is only implemented one way.

This is the current status of having only one type of FixedPoint and the underlying Type T defines whether it is a Unsigned or Signed type.

I added in comments the second implementation if the implementation is ambiguous and I haven't looked at the tests yet.

Merging those two concepts simplifies the code immensely, but it also highlights the subtle differences that where between Fixed and UFixed.

[timholy]

y->i? (typo)

[timholy]

I assume you're noting it's still failing, seemingly due to the "not quite 1" issue I raised above.

We might need a different implementation of convert depending on whether T<:Signed.

[timholy]

Need any help? I'd love to get this finished, tagged, and then be able to tag new versions for Colors/ColorTypes/ColorVectorSpace/Images etc.

[vchuravy]

Any help is appreciated, grad school got a bit in the way :).

I just pushed the last changes I have around, but I think I am still missing some cases.

So one of the issues is that for signed types 1 is not necessarily part of the representation and maybe using typemax and typemin is a better approach to convert FixedPoint to FloatingPoint.

[vchuravy]

oops :)

[vchuravy]

I added some comments, where I still have open questions and not necessary good answers. Essentially every bit of functionality that has a commented out version I was a bit unsure about.

[vchuravy]

A fundamental problem I am running into that using rawone doesn't make sense for Fixed... and it is a bit unintuitive that 0xFF equals 1.0 for UFixed8 = FixedPoint{UInt8, 8} where f = 8 is the number of fractional bits, with setting 0xff we are using a fractional bit to signal oneness.

Using FixedPoint{UInt8, 7} Where the first bit is the integral bit would break the major use of unsigned fixedpoint numbers in colors...

A similar problem arises with signed fixedpoint numbers, where we need one bit to signal sign and so the question is if FixedPoint{Int8, 8} is well defined at all.

Maybe my brain is just going off on a tangent and I don't see the forest because of all the trees...

[timholy]

You know, this rings a bell and is probably why I didn't unify them when I first wrote Ufixed. It has been so long, I had forgotten about these considerations. For colors/images we definitely need 0xff to correspond to 1, so perhaps these are just two different beasts and should remain separate.

Sound reasonable?

[vchuravy]

I am going to think this over, getting rid of a lot of code duplication would be really nice, but I don't really want to break the one major use case of FixedPointNumbers. (Even though UFixed should probably be called normalized numbers ;) )

[timholy]

Sounds good. I'll be out of touch for a couple of days.

When I get back, I'll soon go ahead and tag a new release of Images and all related packages, just because it's overdue. If it takes a little longer to figure this out, that's fine---no rush.

[vchuravy]

I am still interested in renaming UFixed to UNormed or UNorm. But I don't think anymore that having Fixed{Unsigned} is really useful.

[timholy]

I could go with such a renaming. (I probably won't do it myself, but happy to see it arrive, and even happier if someone helps fix the deprecations it will cause elsewhere 😉---EDIT: but don't worry about Images, that's in too much flux right now for anyone but me to touch.)