Use widen(Int128)=BitIntgers.Int256 within FixedDecimals

[ghost]

Re-opening #6 for the new branch, rai-manual_mul_invcoeff, which is being used for the PR to JuliaMath/FixedPointDecimals.jl.

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Remove allocations for FD{Int128} by switching to widen to Int256 instead of BigInt.

Adds a dependency on the BitIntegers package, but the performance gains seem worth it to me.

[NHDaly]

Hmm, i can't figure out how to add you as reviewers, @TotalVerb or @omus. I opened it against the same branch as in JuliaMath#45 (rai-manual_mul_invcoeff), because i wanted the diffbase to be easier to read, but i didn't mean for it to stay within the RelationalAI-oss fork... Github, man. SO anyway, if you wouldn't mind leaving your Review here as if it's a JuliaMath PR, that'd be much appreciated! Thanks!

[NHDaly]

And here's the multiplication timings:

	time (ns)	allocs
FD{ Int32,2}	1.95	0
FD{ Int64,2}	8.43	0
FD{Int128,2}	72.20	0

You can see that the performance for Int128 is drastically improved, because it never has to widen into a BigInt! :)

[TotalVerb]

I have a few comments on the base branch also, but I'll leave that on the JuliaMath PR.

[TotalVerb]

Base's widemul actually has these two special cases:

widemul(x::Signed,y::Unsigned) = widen(x) * signed(widen(y))
widemul(x::Unsigned,y::Signed) = signed(widen(x)) * widen(y)

I believe we should replicate these here.

[NHDaly]

huh weird, i wonder why those are needed...? But yeah okay sounds good to me!

[NHDaly]

update: it turns out this is because apparently widemul(::Signed, ::Unsigned) returns a Signed, whereas promote would return Unsigned.

I've added your suggestion into the new take on this PR, here: JuliaMath#93

[TotalVerb]

These are monkey patching functionality that belongs in a different package (neither BitIntegers nor Base.isodd are "owned" by this package). Sometimes, this can lead to method overwriting warnings when the downstream packages are updated (although I suspect it won't in this case, but I'd prefer to avoid it overall). Would it be reasonable to simply wait for BitIntegers to merge the appropriate PRs?

[NHDaly]

:) Yeah i think that's reasonable! I agree.
I'm linking those two PRs here for posterity:
rfourquet/BitIntegers.jl#3
rfourquet/BitIntegers.jl#2

The unsigned(::Type{T}) one, rfourquet/BitIntegers.jl#2, might take a while because I think it's waiting for some progress on JuliaLang/julia#30444.

[NHDaly]

Thanks for taking a look here, @TotalVerb! I'm happy to wait for progress on JuliaMath#45. :)