Implement reverse mode elementary functions

[Kolaru]

Unless I've missed a file somewhere, the reverse mode elementary functions required for the set based flavor by the IEEE Std 1788-2015 (section 10.5.4) are not implemented.

[dpsanders]

They are in the IntervalContractors.jl package.

[lbenet]

I think we should perhaps bring them here, since they are required by the standard.

[dpsanders]

I think we should just resurrect ValidatedNumerics.jl (or some similar name) and have it export both packages.

[lbenet]

I like the idea of resurrecting ValidatedNumerics.jl, but still think that IntervalArithmetic.jl is the right place for the reverse-mode elementary functions. IntervalContractors.jl will be essentially unchanged (except for releasing a new minor(?) version) since it imports IntervalArithmetic.jl.

[dpsanders]

I personally feel that the reverse-mode functions are really so far away in concept and style from the rest of interval arithmetic that they belong in a separate julia package.

Are they included in the simplified standard? I don't remember but think not?

[Kolaru]

They are not included in the simplified standard (see Annex A of the simplified standard, listing all things only requested in the full standard).

In regard of compliance with the full standard, where the functions are defined is probably irrelevant. Saying somethign like "IntervalArithmetic.jl, together with IntervalContractors.jl, sastifies the standard" sounds fine for me, as long at it is documented.

[lbenet]

I personally feel that the reverse-mode functions are really so far away in concept and style from the rest of interval arithmetic that they belong in a separate julia package.

I still agree with the concept part, since these functions are proposed in the full standard. If it is a question of style, maybe we should simply include a naive form here (independently coded), perhaps even use a different naming convention, and even not exporting them, to avoid collisions.

In my opinion, it sounds nicer "IntervalArithmetic.jl sastifies the standard", which serves as a basic library to build other things on top of it (as it is now).

[Kolaru]

I'm reopening this issue because while we decided to not have it in IntervalArithmetic.jl itself (IIRC), it still needs to be documented properly.

I believe we need a "Compliance with standard" section in the doc.