RFC: Trace-based layout.

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1

I plan on rewriting the block placement algorithm to proceed by traces.

A trace is a chain of blocks where each block in the chain may fall through to
the successor in the chain.

The overall algorithm would be to first produce traces for a function, and then
order those traces to try and get cache locality.

Currently block placement uses a greedy single step approach to layout. It
produces chains working from inner to outer loops. Unlike a trace, a chain may
contain non-fallthrough edges. This causes problems with loop layout. The main
problems with loop layout are: loop rotation and cold blocks in a loop.

Overview of proposed solution:

Phase 1:
Greedily produce a set of traces through the function. A trace is a list of
blocks with each block in the list falling through (possibly conditionally) to
the next block in the list. Loop rotation will occur naturally in this phase via
the triangle replacement algorithm below. Handling single trace loops requires a
tweak, see the detailed design.

Phase 2:
After producing what we believe are the best traces, they need to be ordered.
They will be ordered topologically, except that traces that are cold enough (As
measured by their warmest block) will be floated later, This may push them out
of a loop or to the end of the function.

Detailed Design

Note whenever an edge is used as a number, I am referring to the edge frequency.

Phase 1: Producing traces
Traces are produced according to the following algorithm:

  • Sort the edges according to weight, stable-sorting them according the incoming
    block and edge ordering.
  • Place each block in a trace of length 1.
  • For each edge in order:
  • If the source is at the end of a trace, and the target is at the beginning
    of a trace, glue those 2 traces into 1 longer trace.
  • If an edge has a target or source in the middle of another trace, consider
    tail duplication. The benefit calculation is the same as the existing
    code.
  • If an edge has a source or target in the middle, check them to see if they
    can be replaced as a triangle. (Triangle replacement described below)
  • Compare the benefit of choosing the edge, along with any triangles
    found, with the cost of breaking the existing edges.
  • If it is a net benefit, perform the switch.
  • Triangle checking:
    Consider a trace in 2 parts: A1->A2, and the current edge under consideration
    is A1->B (the case for C->A2 is mirror, and both may need to be done)
  • First find the best alternative C->B
  • Check for an alternative for A2: D->A2
  • Find D’s best Alternative: D->E
  • Compare the frequencies: A1->A2 + C->B + D->E vs A1->B + D->A2
  • If the 2nd sum is bigger, do the switch.
  • Loop Rotation Tweak:
    If A contains a backedge A2->A1, then when considering A1->B or C->A2, we
    can include that backedge in the gain:
    A1->A2 + C->D + E->B vs A1->B + C->A2 + A2->A

Phase 2: Order traces.
First we compute the frequency of a trace by finding the max frequency of any of
its blocks.
Then we attempt to place the traces topologically. When a trace cannot be placed
topologically, we prefer warmer traces first.

Questions and comments welcome.

2

Is this an existing published algorithm? Do you have a link to a paper?

– Sean Silva

3

It is essentially block layout algorithm 2 here, with limited non-greedy lookahead. (The triangle detection)
https://www.ece.cmu.edu/~ece447/s13/lib/exe/fetch.php?media=p16-pettis.pdf

4

This algorithm should be easy enough to implement and experiment with out of tree. A reasonable goal would be to identify cases that the current, more sophisticated algorithm are handling poorly. At that point, it would be much more useful to fix the current algorithm’s heuristics rather than introducing another less sophisticated alternative.

The current algorithm deals well with partial profile information and maintains a number of layout properties relative to the CFG structure. I’m not the best person to explain all of this, but you will certainly need to understand the original goals, show concrete examples of how it “fails” and can’t be easily fixed, before you propose replacing it.

-Andy

5

I plan on rewriting the block placement algorithm to proceed by traces.

A trace is a chain of blocks where each block in the chain may fall
through to
the successor in the chain.

The overall algorithm would be to first produce traces for a function, and
then
order those traces to try and get cache locality.

Currently block placement uses a greedy single step approach to layout. It
produces chains working from inner to outer loops. Unlike a trace, a chain
may
contain non-fallthrough edges. This causes problems with loop layout. The
main
problems with loop layout are: loop rotation and cold blocks in a loop.

Overview of proposed solution:

Phase 1:
Greedily produce a set of traces through the function. A trace is a list of
blocks with each block in the list falling through (possibly
conditionally) to
the next block in the list. Loop rotation will occur naturally in this
phase via
the triangle replacement algorithm below. Handling single trace loops
requires a
tweak, see the detailed design.

Phase 2:
After producing what we believe are the best traces, they need to be
ordered.
They will be ordered topologically, except that traces that are cold
enough (As
measured by their warmest block) will be floated later, This may push them
out
of a loop or to the end of the function.

Detailed Design

Note whenever an edge is used as a number, I am referring to the edge
frequency.

Phase 1: Producing traces
Traces are produced according to the following algorithm:
* Sort the edges according to weight, stable-sorting them according the
incoming
block and edge ordering.
* Place each block in a trace of length 1.
* For each edge in order:
    * If the source is at the end of a trace, and the target is at the
beginning
      of a trace, glue those 2 traces into 1 longer trace.
    * If an edge has a target or source in the middle of another trace,
consider
      tail duplication. The benefit calculation is the same as the existing
      code.
    * If an edge has a source or target in the middle, check them to see
if they
      can be replaced as a triangle. (Triangle replacement described below)
      * Compare the benefit of choosing the edge, along with any triangles
        found, with the cost of breaking the existing edges.
        * If it is a net benefit, perform the switch.
* Triangle checking:
    Consider a trace in 2 parts: A1->A2, and the current edge under
consideration
    is A1->B (the case for C->A2 is mirror, and both may need to be done)
    * First find the best alternative C->B
    * Check for an alternative for A2: D->A2
    * Find D's best Alternative: D->E
    * Compare the frequencies: A1->A2 + C->B + D->E vs A1->B + D->A2
    * If the 2nd sum is bigger, do the switch.
  * Loop Rotation Tweak:
    If A contains a backedge A2->A1, then when considering A1->B or C->A2,
we
    can include that backedge in the gain:
    A1->A2 + C->D + E->B vs A1->B + C->A2 + A2->A

Phase 2: Order traces.
First we compute the frequency of a trace by finding the max frequency of
any of
its blocks.
Then we attempt to place the traces topologically. When a trace cannot be
placed
topologically, we prefer warmer traces first.

Questions and comments welcome.
_______________________________________________

This algorithm should be easy enough to implement and experiment with out
of tree. A reasonable goal would be to identify cases that the current,
more sophisticated algorithm are handling poorly. At that point, it would
be much more useful to fix the current algorithm’s heuristics rather than
introducing another less sophisticated alternative.

I wrote many of the current algorithms heuristics, and they feel like hacks
to work around specific problems.

What I'm proposing is more, not less sophisticated. Handling loop rotation
as part of a general lookahead problem is more sophisticated than the
existing method of laying out the loop and praying that one of the n
rotations will be a good one.
Even the tail-duplication support I added is kind of a hack. It would be
better to do block cloning to handle cases where tail-duplication currently
fails

The current algorithm deals well with partial profile information and
maintains a number of layout properties relative to the CFG structure. I’m
not the best person to explain all of this, but you will certainly need to
understand the original goals, show concrete examples of how it “fails” and
can’t be easily fixed, before you propose replacing it.

I'll make sure to include test cases with any diffs I mail out.

6

The “Algo2” that you referred to is the least sophisticated layout algorithm I can imagine. I’ve always found it to be extremely unsatisfying when it comes to partial profile, unbiased branches, or general debugging sanity.

When I say the existing algorithm is more sophisticated, I mean that it is designed to meet a couple basic requirements:

  • contiguous loops
  • topologically ordered regions with a loop
    With the exception that clearly cold paths are moved to the end of the function.

I’m not sure how well your "triangle look-ahead” algorithm works, but if you can also meet those requirements then I would say it’s also very sophisticated. I haven’t spent any time evaluating the current LLVM algorithm, so won’t defend it over another approach that meets the same goals.

I am very curious to see examples of situations where your approach yields better performance.

Ok. I’m not opposed to someone who has a lot of experience with the current algorithm rewriting it. I’m just concerned that it will result in a lot of arbitrary code shuffling, making it difficult to make sense of the codegen output, and result in worse block layout for the typical situation: many missing branch weights, or workloads that deviate from the profile.

-Andy

7

Chiming in to this discussion just a little bit late…

I share Andy’s concerns about whether the proposed trace algorithm subtly improves on the existing code. I’m perfectly happy to be convinced, but the burden of proof here is high.

Thinking about the current algorithm, I find it helpful to think in terms of extended basic blocks. At it’s most basic, the existing code (and your alternate proposal unless I’m misreading it) eagerly forms extended basic blocks with a single exit, but potentially many early exits before a single N-way terminator. At this stage, we’re only handling “obvious” cases where the exit path is substantially colder than the fall-through which continues within the same EBB.

The “interesting bits” of both the current code and your new algorithm can be phrased as merging these EBBs to form super-blocks. Once we start merging EBBs, we have to allow multiple entries into our super-blocks. One nice property of loops, triangles, and diamonds is that control flow entirely within a super-block is invisible to other super-blocks. Note there’s, for example, a policy choice as to whether cold loop blocks are placed into the loops super-block (hiding the control flow) or into a separate super-block (outlining the cold path far away).

I suspect the current code could be substantially improved by making the abstractions of EBBs and super-blocks explicit in the code. Then the heuristic pieces would be much more obvious and easier to evaluate in isolation.

Philip