Alternatives for representing a reverse postorder numbering

Andreas Klebinger klebinger.andreas at
Thu Dec 9 13:24:17 UTC 2021

Hello Norman,

There is no invariant that Cmm control flow is reducible. So we can't
always rely on this being the case.
Depending on what you want to use this for this might or might not matter.

In terms of implementation I think the question is if doing lookups in a
LabelMap is more expensive
than making the CmmGraph representation both more polymorphic, and
putting more info into the Graph.

Which I guess mostly depends on how much mileage we get out of the
numbering. Which is impossible for
me to say in advance. If you only need/use this info for a small part of
the pipeline then keeping it as LabelMap
seems more reasonable. If you have plans to improve all sorts of passes
with this information at various stages
in the pipeline integrating it into CmmGraph seems better. It's
impossible to say without knowing the details.

All that being said I rarely have lost sleep over the overhead of
looking things up in IntMaps.
The constants are pretty good there and it seems reasonable easy to
change it later if needed.

Am 06/12/2021 um 22:50 schrieb Norman Ramsey:
> Reverse postorder numbering is a superpower for control-flow analysis
> and other back-end things.  For example,
>    - In a reducible flow graph, a node Q is a loop header if and only if
>      it is targeted by an edge P -> Q where Q's reverse postorder
>      number is not greater than P's.
>    - If a loop has multiple exits, the reverse postorder numbering of
>      the exit nodes tells exactly the order in which the nodes must
>      appear so they can be reached by multilevel `exit`/`break`
>      statements, as are found in WebAssembly.
>    - Reverse postorder numbers enable efficient computations of set
>      intersection for dominator analysis.
> One could go on.
> In a perfect world, our representation of control-flow graphs would
> provide a place to store a reverse postorder number for each
> (reachable) basic block.  Alas, we live in an imperfect world, and I
> am struggling to figure out how best to store reverse postorder
> numbers for the blocks in a `GenCmmGraph`.
>   1. One could apply ideas from "trees that grow" to the `Block` type
>      from `GHC.Cmm.Dataflow.Block`.  But this type is already one of
>      the more complicated types I have ever encountered in the wild,
>      and the thought of further complexity fills me with horror.
>   2. One could generalize quite a few types in `Cmm`.  In particular,
>      one could create an analog of the `GenCmmGraph` type.  The analog,
>      instead of taking a node type `n` as its parameter, would take a
>      block type as its parameter.  It would use `Graph'` as defined in
>      `GHC.Cmm.Dataflow.Graph`.  This change would ripple into
>      `GHC.Cmm.Dataflow` without doing a whole lot of violence to the
>      code that it there.  It would then become possible to do dataflow
>      analysis (and perhaps other operations) over graphs with annotated
>      blocks.
>      It's worth noting that the `Graph'` representation already exists,
>      but it doesn't seem to be used anywhere.  I'm not sure how it
>      survived earlier rounds of culling.
>   3. One could simple build an auxiliary `LabelMap` that includes the
>      reverse postorder number of every node.  This idea bugs me a bit.
>      I don't love spending O(log N) steps twice every time I look to
>      see the direction of a control-flow edge.  But what I *really*
>      don't love is what happens to the interfaces.  I can compute the
>      reverse postorder map twice, or I can pollute my interfaces by
>      saying "here is the dominator relation, and by the way, here also
>      are the reverse postorder numbers, which I had to compute."
> I'm currently using alternative 3: when I need reverse postorder
> numbers, I call `revPostorderFrom` (defined in `GHC.Cmm.Dataflow.Graph`),
> then zip with `[1..]`.  But I'm really tempted by alternative 2,
> which would allow me to, for example, define a graph annotated with
> reverse postorder numbers, then do both the dominator analysis and my
> translation on that graph.
> How deep into the weeds should I go?  Make dataflow analysis even more polymorphic?
> or learn to love `LabelMap`?
> Norman
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