Add an extension to support ForwardDiff

[timholy]

Because of the extensive changes on master, ForwardDiff no longer works with this package. This add an extension (Julia 1.9+) providing at least basic support.

Note that:

• this depends on Add flexibility in dispatch for iszero_tuple JuliaDiff/ForwardDiff.jl#667. I am not sure when there will be a new release of ForwardDiff, but the master branch is now 0.11-DEV.
• you have to dev ForwardDiff in the test` folder
• because of Extension-specific "cannot merge projects" JuliaLang/Pkg.jl#3636, you either have to run these tests on nightly or we have to abandon test/Project.toml and copy everything to the [extras] section of the main Project.toml.

So obviously this can't be merged yet, but I thought it would be better to submit it now.

[OlivierHnt]

Thanks for opening this PR!
I wonder though if it should be the other way around. ForwardDiff.jl adds IntervalArithmetic.jl as an extension; also this gives a stronger guarantee that their differentiation mechanism is compatible with the specifications of interval arithmetic. 🤔

[timholy]

That's actually where I started. But I grew to think it might be better this way: ForwardDiff is widely used by a lot of different things, it seems more scalable to have extensions in packages that may have fewer "interop" demands. As a practical matter, ForwardDiff's tests also take a long time to run!

But in the end I'm not sure it matters a lot; the extension mechanism ensures the code will be loaded, one way or another.

[OlivierHnt]

Good point about scalability.

So the main concern here is the reliability. Do we have a guarantee, with your PR, that iszero_tuple is used in ForwardDiff.jl in compliance with interval arithmetic specifications?

Unfortunately I am too unfamiliar with ForwardDiff.jl to know the answer. I see that it is used to define iszero(::Partials) and iszero(::Dual) which are themselves called at several places in the code.

[OlivierHnt]

I tried the tests you included in your PR and they seem to pass using the PR #593; I will add them to the test suite to keep track of FowardDiff.

[OlivierHnt]

@timholy how is the interaction between IntervalArithmetic (v0.22.14) and ForwardDiff for you?
I think the issues raised at the time in this PR have been resolved now. But I am also wondering if you are aware of more issues?

[timholy]

I haven't returned to this research topic in a while. I'll get back to it eventually, but for the time being...no idea! 🙂

[OlivierHnt]

Closing this for the time being 🙂
Feel free to reopen in the future if something comes up!