Fusion level axioms

[zasdfgbnm]

Fixes #320. Add a new optimization pass that append extent > 0 as axioms of the fusion.

Currently, we are not doing concretization of extent zero, so this assumption is actually wrong. But fortunately, it is not too wrong, given the fact that:

• no test / benchmark fail
• AFAICT, except at parallel dimension map (where we already assume extent > 0), the only difference that extent > 0 vs extent >= 0 is when extent is a denominator. Considering that we already have preserve_error = false by default, so changing from extent >= 0 to extent > 0 will hopefully be a no-op for lowering.

But this do help on vectorization analysis. Currently, I am seeing a lot of things like where(abs(i1) == i1, i2, i3), and the added axioms should help on eliminate this trivial computation.

Also note that I removed the explicit assumption on parallel dimension map, which means that, if we are using fusion executor manually, we must run pre-segmentation pass before scheduling in order to get the same behavior as using executor cache. In the future, I think this is the direction to go as we are adding more and more pre-segmentation passes. Especially, I am thinking about moving replaceSymbolicSizes from a lowering pass into a pre-segmentation or maybe pre-concretization pass. This would reduce the number of Val* and generally speeding up all expr simplification and sameAs check.

I am OK with holding this PR until zero extent concretization is merged. But I don't think this is necessary. (Just be a bad guy and break things😈)

[zasdfgbnm]

!build

[naoyam]

Agree this should be relatively safe. I still think we should consider a different IterType for size-zero domains.

[zasdfgbnm]

@naoyam Clang-tidy is broken due to unrelated thing:

Fuser/.github/workflows/lint.yml

Lines 60 to 63 in 1ca8581

	git fetch origin main
	git checkout origin/main
	head_commit=$(git rev-parse HEAD)
	git checkout $this_commit

I think I need admin power to force merge.
Edit: the clang-tidy error is easy to fix. Will fix it in this PR.

[zasdfgbnm]

And I agree with a separate IterType for zero extent.

[zasdfgbnm]

@naoyam Clang-tidy is broken due to unrelated thing:

Fuser/.github/workflows/lint.yml

Lines 60 to 63 in 1ca8581

	git fetch origin main
	git checkout origin/main
	head_commit=$(git rev-parse HEAD)
	git checkout $this_commit

I think I need admin power to force merge.

Maybe not, I think the clang-tidy error is easy to fix. Let me try it.

[zasdfgbnm]

cc @rdspring1 @jjsjann123

[zasdfgbnm]

!build

[jacobhinkle]

I think we can guarantee positivity somewhat soon, and kill a few birds with one stone. #449 is a start, and #448 is the followup (haven't started that just yet but hopefully will soon).