[llvm-dev] [RFC] Add IR level interprocedural outliner for code size.

Daniel Berlin via llvm-dev
Tue, 01 Aug 2017 17:28:27 -0000

>
>
>
> Also as a side note, I think in the original MachineOutliner RFC thread
> there was some confusion as to whether it was possible to solve the code
> folding outlining problem exactly as a graph problem on SSA using standard
> value numbering algorithms in polynomial time.
>


> I can elaborate further, but
> 1. it is easy to see that you can map an arbitrary dag to an isomorphic
> data flow graph in an SSA IR e.g. in LLVM IR or pre-RA MIR
>


> 2. Given two dags, you can create their respective isomorphic data flow
> graphs (say, put them into two separate functions)
> 3. An exact graph based code folding outliner would be able to discover if
> the two dataflow graphs are isomorphic (that is basically what I mean by
> exact) and outline them.
> 4. Thus, graph isomorphism on dags can be solved with such an algorithm
> and thus the outlining problem is GI-hard and a polynomial time solution
> would be a big breakthrough in CS.
>

First, you'd have to reduce them in both directions to prove that ;)

All that's been shown is that you can reduce it to a hard problem.
You can also reduce it to 3-sat., but that doesn't mean anything unless you
can reduce 3-sat to it.

5. The actual problem the outliner is trying to solve is actually more
like
> finding subgraphs that are isomorphic, making the problem even harder
> (something like "given dags A and B does there exist a subgraph of A
that
> is isomorphic to a subgraph of B")
>
>
This assumes, strongly, that this reduction is the way to do it, and also
that SSA/etc imparts no structure in the reduction that enables you to
solve it faster (IE restricts the types of graphs, etc)

FWIW, the exact argument above holds for value numbering, and since the
days of kildall, it was believed not solvable in a complete fashion in less
than exponential time due to the need to do graph isomorphism on large
value graphs at join points.

Except, much like RA and other things, it turns out this is not right for
SSA, and in the past few years, it was proved you could do complete  value
numbering in polynomial time on SSA.

So with all due respect to quentin, i don't buy it yet.

Without more, i'd bet using similar techniques to solve value numbering in
polynomial time to SSA could be applied here.

This is because the complete polynomial value numbering techniques are in
fact, value graph isomorphism ....

So i'd assume the opposite (it can be done in polynomial time) without more.
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