3 ms·

From what I understand, the big advantage of the e-graphs approach is, that the quality of the output is (within limits) a function the time and memory given.

From what I understand, the big advantage of the e-graphs approach is, that the quality of the output is (within limits) a function the time and memory given. The more memory, the more nodes can be generated in the e-graph and the more time for search, the better the selected node. It might never be as fast as copy-and-patch or as good as LLVM or GCC, but this flexibility is a value in itself.

thechao 3y ago
When we first reviewed the equality saturation paper, we thought there was one major pro, and one major con: [pro] phase-ordering invariant; [con] at the time there was no (believable) way to extract the transformed graph in a non-hand-wavy-way. Personally, I think e-graphs should be combined with Massalin superoptimization — they're natural "duals" — and just turn the whole exercise into a hill-climbing process. You can tune the total effort by the set of passes used, the amount of time to drive the graph to saturation, and the method (and time) for graph extraction.
- vlovich123 3y ago
  Can you memoize across invocations so that the time spent optimizing is cumulative across all builds?
  - fwip 3y ago
    Speaking as an e-graph rookie - I believe so, with caveats. You can certainly store the chosen extractions/optimizations and re-use any that don't change. For example, if a long chain of rewrites yields A ==> B ==> ... ==> Z, you could short-circuit that and assume that Z is still what you want to replace A with. Perhaps each time you compiled, you could only rewrite the 'changed' sections of the program, along with a randomly selected portion to explore for greater-optimization. (Although, you may just want to go all the way and write a tool that constantly adds to your equivalence DB in the background, with compilation just a matter of running your extraction heuristics.) You probably wouldn't want to store every possible rewrite, though, as the space complexity or retrieval cost is likely a bigger deal than the time complexity (you wouldn't load 2+2=4 from a database, you'd just do the addition). But, if you restore only a subset of equivalencies that are known to be useful, there's not a simple way to keep the optimization from re-exploring the "rejected candidates" (without shutting off the eclass entirely) - and, it's even not clear to me that you'd want to, as changing program context may end up meaning that M becomes a better replacement candidate for A than Z. (Boring prerequisites for this approach also include: consistent serialization of terms, avoiding storage of infinite equivalencies, like `A => A + 0 => A + 0 + 0 ==> ...` (and possibly of exponential equivalencies like the kind associativity rules can produce), and strong heuristics to capture "high-value" equivalencies that are both useful and cheaper to lookup than re-derive.)
    - thechao 3y ago
      I always thought that it'd be nice to build an expository version of eq-sat that just operated on straight-line code, and didn't try to use the complicated e-graph structure (does it still use pi-nodes? I've not looked at the paper in a decade). The major complexity of eq-sat is in the novel extraction heuristics, and the complicated data-structures only mask that. EDIT: Right. Blech. Theta & Phi nodes.
cfallin 3y ago
We actually take a fairly unconventional approach to e-graphs: we have a few linear passes and we do all rewrites eagerly, so we use them to provide a general framework for the fixpoint problem into which we plug in all our rewrites, but we don't have the usual "apply as much CPU time as you want to get better results" property of conventional equality saturation. I gave a talk about this approach, aegraphs (acyclic e-graphs), here: slides (https://cfallin.org/pubs/egraphs2023_aegraphs_slides.pdf https://cfallin.org/pubs/egraphs2023_aegraphs_slides.pdf), video (https://vimeo.com/843540328 https://vimeo.com/843540328) (disclosure: Cranelift tech lead 2020-2022 and main author of the e-graphs mid-end, as well as regalloc, isel and its custom DSL, and other bits, along with the excellent team)
- scoopr 3y ago
  I found the video to be great! Informative and understandable even when I'm just casually interested in compilers, with not a lot of real world experience writing them.

thechao 3y ago

When we first reviewed the equality saturation paper, we thought there was one major pro, and one major con: [pro] phase-ordering invariant; [con] at the time there was no (believable) way to extract the transformed graph in a non-hand-wavy-way. Personally, I think e-graphs should be combined with Massalin superoptimization — they're natural "duals" — and just turn the whole exercise into a hill-climbing process. You can tune the total effort by the set of passes used, the amount of time to drive the graph to saturation, and the method (and time) for graph extraction.

vlovich123 3y ago
Can you memoize across invocations so that the time spent optimizing is cumulative across all builds?
- fwip 3y ago
  Speaking as an e-graph rookie - I believe so, with caveats. You can certainly store the chosen extractions/optimizations and re-use any that don't change. For example, if a long chain of rewrites yields A ==> B ==> ... ==> Z, you could short-circuit that and assume that Z is still what you want to replace A with. Perhaps each time you compiled, you could only rewrite the 'changed' sections of the program, along with a randomly selected portion to explore for greater-optimization. (Although, you may just want to go all the way and write a tool that constantly adds to your equivalence DB in the background, with compilation just a matter of running your extraction heuristics.) You probably wouldn't want to store every possible rewrite, though, as the space complexity or retrieval cost is likely a bigger deal than the time complexity (you wouldn't load 2+2=4 from a database, you'd just do the addition). But, if you restore only a subset of equivalencies that are known to be useful, there's not a simple way to keep the optimization from re-exploring the "rejected candidates" (without shutting off the eclass entirely) - and, it's even not clear to me that you'd want to, as changing program context may end up meaning that M becomes a better replacement candidate for A than Z. (Boring prerequisites for this approach also include: consistent serialization of terms, avoiding storage of infinite equivalencies, like `A => A + 0 => A + 0 + 0 ==> ...` (and possibly of exponential equivalencies like the kind associativity rules can produce), and strong heuristics to capture "high-value" equivalencies that are both useful and cheaper to lookup than re-derive.)
  - thechao 3y ago
    I always thought that it'd be nice to build an expository version of eq-sat that just operated on straight-line code, and didn't try to use the complicated e-graph structure (does it still use pi-nodes? I've not looked at the paper in a decade). The major complexity of eq-sat is in the novel extraction heuristics, and the complicated data-structures only mask that. EDIT: Right. Blech. Theta & Phi nodes.

cfallin 3y ago

We actually take a fairly unconventional approach to e-graphs: we have a few linear passes and we do all rewrites eagerly, so we use them to provide a general framework for the fixpoint problem into which we plug in all our rewrites, but we don't have the usual "apply as much CPU time as you want to get better results" property of conventional equality saturation. I gave a talk about this approach, aegraphs (acyclic e-graphs), here: slides (https://cfallin.org/pubs/egraphs2023_aegraphs_slides.pdf https://cfallin.org/pubs/egraphs2023_aegraphs_slides.pdf), video (https://vimeo.com/843540328 https://vimeo.com/843540328) (disclosure: Cranelift tech lead 2020-2022 and main author of the e-graphs mid-end, as well as regalloc, isel and its custom DSL, and other bits, along with the excellent team)

scoopr 3y ago
I found the video to be great! Informative and understandable even when I'm just casually interested in compilers, with not a lot of real world experience writing them.