[llvm-dev] Writing loop transformations on the right representation is more productive

Prashanth N R via llvm-dev
2020-01-22T04:52:41Z

Hi Michael-

Liked your proposal and hope that it gets implemented in MLIR. Linearized
IR of LLVM is not suitable for LNO.

We have written multiple Loop Nest Optimizers (in LLVM) in past five
years.  We sent a talk proposal to LLVM developer meeting in 2017. It was
rejected. From the review comment it looked like polly was the preferred
path for Loop Nest Optimization. Hope it is not the case any more.

thanks,
-Prashanth


On Fri, Jan 3, 2020 at 4:57 PM Michael Kruse via llvm-dev <
llvm-dev at lists.llvm.org> wrote:

> In the 2018 LLVM DevMtg [1], I presented some shortcomings of how LLVM
> optimizes loops. In summary, the biggest issues are (a) the complexity
> of writing a new loop optimization pass (including needing to deal
> with a variety of low-level issues, a significant amount of required
> boilerplate, the difficulty of analysis preservation, etc.), (b)
> independent optimization heuristics and a fixed pass ordering and (c)
> code explosion due to versioning. Currently, different people are
> working on improving different loop optimization passes such as
> LoopInterchange, LoopFuse and LoopVectorize. Even if LLVM had
> 'perfect' individual loop passes, they would still have the
> aforementioned problems due to still being independent and the system
> as a whole will be suboptimal.
>
> Instead of each loop pass being a major component, the heavy lifting
> could be done by a framework of which each transformation itself is a
> small part. In this RFC, I would like to work towards a consensus on
> how such a framework could look. I already outlined a possible
> solution in the same presentation [1] and a publication [7], which is
> partially based on a previous RFC [8]. All feedback is welcome,
> including a simple '+1'.
>
> The central idea is to use a modifiable loop tree -- similar to
> LoopInfo -- as the primary representation. LLVM-IR is converted to a
> loop tree, then optimized and finally LLVM-IR is generated again for
> subtrees that are considered profitable. This is not a new concept, it
> has already been used in compilers such as IBM XL Fortran (called ASTI
> [4]) and Silicon Graphics/Open64 (called LNO [10]), and in research
> such as the Value State Dependence Graph [3].
>
> Other features include the following:
>
> 1. Candidate selection through cost functions
> 2. Cheap copies using Red/Green Trees
> 3. Application of transformations from high-level to low-level
> 4. Represents loops and predicates instead of CFGs
> 5. Data and control dependencies in one graph
> 6. Late fallback versioning at IR regeneration
> 7. Standardized API for analyses with multiple implementations
> 8. Abstract representation of statements
> 9. Expansion of use-def chains to arrays when spanning loops
>
> To elaborate on each of these:
>
> 1. Candidate selection through cost function
> --------------------------------------------
> Instead of needing to know which transformation is profitable before
> applying it, create a copy of the data structure, modify it, and
> compare it to the original. Moreover, holding multiple, differently
> optimized, copies allows evaluating each variant using a cost function
> and select the 'best' when re-generating LLVM-IR again (or re-use
the
> original LLVM-IR).
>
> Otherwise, each transformation will have to implement its own
> profitability heuristic but cannot know what other passes will do. For
> instance, the motivation for LLVM's LoopDistribution is to enable
> vectorization of loops that can be separated from other loops.
> However, it does not know whether LoopVectorize will actually
> vectorize the loop, or whether two vectorizable loops are better
> vectorized together.
>
> Instantiating every possible sequence of transformations of course is
> not feasible, so the search space needs to be pruned. This could be
> made dependent on the optimization level.
>
>
> 2. Cheap copies using Red/Green Trees
> -------------------------------------
> A red/green trees [4] is a data structure for cheap copies of DAGs.
> Basically, a green tree node references only the nodes children but
> not the parent. A node from the red tree references its corresponding
> green node and its parent (red) node. When modifying the represented
> node through copy-on-write, this allows reusing all green nodes except
> the ones from the modified node to the tree's root. The same node can
> even be used multiple times in the same copy, which can be useful for
> e.g. loop unrolling and code versioning. As a result, storing many
> optimization variants of the same code only requires copies of the
> changed parts.
>
> By contrast, the red node is created on-demand. Traversing the entire
> tree should rarely be necessary (instead, use summary information in
> the green node) and when limited to subtrees that are considered
> interesting for optimization.
>
>
> 3. Apply transformations from high-level to low-level
> -----------------------------------------------------
> Optimization should be applied from very specialized to very general
> (potentially after some canonicalization). For instance, the first
> step could be detecting common idioms such as gemm and replace them
> with either a BLAS function call or apply well-studied optimizations
> like BLIS to them. After such an idiom has been detected, no other
> transformation should be applied to them.
>
> Mid-level transformations may try to map entire loop nests to cache-
> and compute hierarchies (SIMT threads, multiprocessors, offloading,
> etc) by applying transformations such as tiling, loop interchange and
> array packing.
>
> Low-level transformations commonly look at only one loop to improve
> processor pipelining and predication: Unrolling, software pipelining,
> etc.
>
>
> 4. Represents loops and predicates instead of CFGs
> -------------------------------------------------
> Control flow graphs make loop optimizations difficult, but is also not
> something a loop optimizer typically cares about. For instance, in the
> example below, loop distribution would need to understand the
> condition `c` and reconstruct the branch to fission
>
>     for (int i = 0; i < n; i += 1)
>       if (c) {
>         foo(i);
>         bar(i);
>       }
>
> into
>
>     for (int i = 0; i < n; i += 1)
>       if (c)
>         foo(i);
>     for (int i = 0; i < n; i += 1)
>       if (c)
>         bar(i);
>
> In the loop tree, control flow is represented through predicates of
> the statements.  In a first step, it is represented as
>
>     for (int i = 0; i < n; i += 1) {
>       bool __BB1_executed = 0;
>       { if (c) foo(i); __BB1_executed = 1; }
>       { if (__BB1_executed) bar(i); }
>     }
>
> The predicates (`c` and `__BB1_executed`) can be separated into a
> "necessary condition" (`c` must be true before `foo` can be
executed)
> and a "sufficient condition" (if `c` is true, `foo` must be
executed).
> These can be different to allow speculative execution of the
> statement. For instance, a necessary condition of `true` means that
> the statement can always be executed speculatively.
>
> The advantage is that control flow becomes a data-dependency problem.
> It can trivially be converted back to its CFG representation because
> `__BB1_executed` directly corresponds to the CFG edge to which it was
> connected. Data flow optimizations such as value propagation can be
> applied as well (here: `__BB1_executed == c`), such that we get
>
>     for (int i = 0; i < n; i += 1) {
>       { if (c) foo(i); }
>       { if (c) bar(i); }
>     }
>
> Which can be distributed trivially (assuming foo() and bar() do not
> cause dependencies). Whether the copy propagation is beneficial can be
> decided by a heuristic (considering whether the original flow can
> still be reconstructed) or just thrown away if the cost function does
> not select a loop tree based on the copy propagation.
>
> As a result of the predicated representation the loop tree has a
> regular pattern: sequence -> loop -> sequence -> loop -> ... .
A loop
> here is abstract in that it is something that is executed multiple
> times. This can be a sequential loop, but also a collection of SPMD
> processes, threads, vector lanes, etc.
>
> At IR regeneration, we have multiple choices of how to lower
> conditions. If we lower to LLVM-IR CFG, it may lower to
>  * Branch instructions, reusing branch conditions from previous statements
>  * Select instructions
>
> If lowering to SIMD instructions, we can generate
>  * Branch instructions for uniform predicates
>  * Execution masks for varying predicates
>  * A mix of both, since predicates can be uniform relative to previous
> taken conditions
>
> If lowering to NVPTX-style SIMT
>  * @p per-instruction execution masks
>  * Divergent branches; Every statement can be made a re-convergence
> point (by re-evaluating the condition), but will happen, at the
> latest, at the end of the loop
>  * Uniform predicates can be given the ".uni" suffix
>
> When lowering to AMD-style SIMT
>  * S_CBRANCH (explicitly managed execution mask)
>  * S_CBRANCH_I/G_FORK (stack of execution masks)
>
>
> 5. Data and control dependencies in one graph
> ---------------------------------------------
> Also as a result of the predicated from, during dependency analysis,
> control dependencies and data dependencies have the same
> representation, like in a program dependency graph. In LLVM-IR, passes
> such as AggressiveDeadCodeElimination use DominanceFrontier for this
> purpose. This would not be necessary.
>
> When re-generating IR, control dependencies can either be lowered to
> branching or as a boolean variables. For the purpose of loop
> optimizations, the choice of representation does not (and should not)
> make a difference.
>
>
> 6. Late fallback versioning at IR regeneration
> ------------------------------------------
> When a transformation is applied, it can attach conditions (no
> aliasing, no integer wrap, value restrictions, etc.) under which the
> transformation is valid. During LLVM-IR generation, these conditions
> are collected and emitted as run-time conditions. If the condition
> fails, the original code is executed.
>
> This avoids having every transformation emit its own fallback code.
> The fallback should never execute, or only in cases that do not do
> significant work (e.g. loop trip count is 0), such that optimizing the
> fallback itself is not necessary. In other cases, the transformation
> should implement proper loop versioning by adding the original
> statement with a `!rtc` condition.
>
>
> 7. Standardized API for analyses with multiple implementations
> --------------------------------------------------------------
> Common analyses use an interface that can be fulfilled by different
> implementations. Among these are:
>
>  * Closed form expressions
>    - None (expressions are always represented through dependencies
>      between statements)
>    - LLVM ScalarEvolution
>    - PolyhedralValueAnalysis [6]
>
> Closed form expressions can be used to remap values (typically array
> subscripts, loop lower/upper bounds), simplify expression computations
> (including predicates => is a predicate always true?), determine loop
> trip counts, etc. Most importantly, it identifies a statement
> execution (instance) relative to the loop counters.
>
>
>  * Array accesses / access range / provenance
>    - LLVM AliasAnalysis
>    - One-dimensional (always linearized)
>    - Multi-dimensional, delinearized if necessary
>    - From metadata (that a front-end emits for arrays of pointers to
>      arrays of data)
>
> Array access analysis determines whether two accesses at a specific
> index can alias each other, access ranges and connectivity.
>
>
>  * Dependencies
>    - none (cannot reorder statements)
>    - flat (depends on last execution of another statement)
>    - LLVM DependendencyAnalysis
>    - Polyhedral analysis
>
> There is intentionally no "does X depend on Y?" API as this would
make
> any analysis based on it quadratic in runtime. Instead, it has to list
> all statements another statement depends on such that a graph can be
> built and e.g. sorted topologically.
>
> Dependencies include: use-def chains via registers, memory
> flow/anti/output, general side-effects and control dependencies.
>
>
>  * Control flow
>    - Extracted from original CFG
>    - Evaluate statement conditions
>
> Control flow analysis answers questions about (post-)dominance and
> mutual exclusivity within the acyclic sequence/body of a loop.
>
>
>  * Cost heuristic
>    - TargetTransformationInfo
>
> Estimate the execution time of a (sub-)tree. Average trip counts from
> profiling [11] could be useful.
>
>
> 8. Abstract representation of statements
> ----------------------------------------
> There is no direct relationship between LLVM instructions and loop DAG
> statements. If possible, loop tree optimizations should only use the
> properties of the statement node, not its contents. Typically, a
> statement consists of multiple instructions that do not make sense to
> split. For instance, assuming that %add is not used a second time, in
> the example below
>
>     %add = add i64 %arg, 2
>     %mul = shl i64 %add, 1
>
> the two instructions should always be computed together in the same
> loop iteration. Combining instructions to statements reduces the
> computational complexity of loop optimizations and might be controlled
> by the optimization level (at lower optimization level more
> instructions would be combined). A loop node is itself a statement in
> it's parent loop node's acyclic body.
>
> Moreover, there is no reason to use only LLVM-IR to carry the
> semantics. We could also use e.g. Machine-IR or MLIR operations.
>
>
> 9. Expansion of use-def chains to arrays when spanning loops
> ------------------------------------------------------------
> Consider we would like to fission the following loop:
>
>     for (int i = 0; i < n; i += 1) {
>       { if(true) double a = f(i); }
>       { if(true) g(a); }
>     }
>
> The problem is that the split cuts the use-def dependency over `a`.
> However, the fission can still be done and results in:
>
>     double A[n];
>     for (int i = 0; i < n; i += 1)
>       { if(true) A[i] = f(i); }
>     for (int i = 0; i < n; i += 1) {
>       { if(true) g(A[i]); }
>
> The transforming pass has to consider this during its profitability
> model. The big advantage is that in terms of correctness, use-def
> chains do not manifest false dependencies.
>
>
> Possible Transformations
> ------------------------
> In principle, any transformation could be applied on this
> representation, but instruction-centric transformations such as
> InstCombine are less suitable. Obviously, loop-centric transformations
> are a better fit. Ideas for loop transformations include:
>
>  * Unroll(-and-jam)
>  * Peeling
>  * Iteration range split, concatenation
>  * Interchange
>  * Loop fusion and distribution(/fission)
>  * Tiling/stripmining/stripemining/blocking
>  * Code versioning (including loop unswitching)
>  * Maybe vectorization
>  * Accelerator offloading
>  * Parallelization
>  * Space-filling curve iteration [12]
>  * Array packing (e.g. for scratch pads), transposition
>  * Statement reordering
>  * SIMT-ization
>  * Detect and optimize reductions
>  * Loop skewing/wavefronting
>  * Loop reversal
>  * Solver-driven (polyhedral) optimization
>  * Loop idiom recognition
>
>
> Optimization Pipeline
> ---------------------
> The optimization pipeline for the hierarchy DAG is straightforward:
>
>     void optimizeLoopNest() {
>       RedOriginal = generateLoopHierarchy();
>       List = createCandidates(RedOriginal);
>       sort(List, [](Cand1,Cand2) { return estimateExecutionTime(Cand2)
>                                                    -
> estimateExecutionTime(Cand1); } );
>       if (List[0] != RedOriginal)
>         emit(List[0]);
>     }
>
> Subtree exploration is done recursively, optimizing inner nodes which
> can be (re-)used when optimizing outer nodes.
>
> The current node to optimize is compared a selection of known
> heuristics and its transformation is added to the list of candidates.
> That is, an optimization routine resemble the following, with more
> specific heuristics checked before more general ones.
>
> void exploreOptimizations(Root, Worklist) {
>    Matches = 0;
>
>    // High level: user annotations
>    if (Root.hasHint()) {
>      // Hint is mandatory: do not explore any other possibility
>      Worklist.replace(Root, applyHint(Root));
>      return;
>    }
>
>     // High level: Idiom recognition
>     if (isBLAS(Root)) {
>       Optimized = LinkAgainstBLASLibary ? convertToBlasLibCall(Root) :
>
> applyBLIS(Root):
>       Worklist.replace(Root, Optimized);
>       return;
>     }
>
>     // Mid level: recognize stencils
>     if (isStencil(Root))
>       ...
>
>     // Mid level: Map to compute hierarchy (here: simd -> SMT -> core
> -> socket for CPUs)
>     if (isParallel(Root) fitsWorkingSet(Root.getBody(), LLCSize) &&
&&
>       isParallel(Root.getPerfectlyNestedLoop(1)) &&
>        fitsWorkingSet(Root.getPerfectlyNestedLoop(2).getBody(), L2Size)
&&
>       isParallel(Root.getPerfectlyNestedLoop(2)) &&
>        fitsWorkingSet(Root.getPerfectlyNestedLoop(3).getBody(), L1Size)
&&
>       isVectorizable(Root.getPerfectlyNestedLoop(3))) {
>         Optimized = applyVectorization(Root.getPerfectlyNestedLoop(3));
>         Optimized = applyParallel(Optimized.getParent(), /*places=*/SMT);
>         Optimized = applyParallel(Optimized.getParent(), /*places=*/Cores);
>         Optimized = applyParallel(Optimized.getParent(),
> /*places=*/Sockets);
>
>         // Still explore CPU pipeline optimizations of innermost
>         Worklist.insert(Root,Optimized);
>         Matches += 1;
>     }
>
>     if (Matches >= Threshold)
>       return;
>
>     // Low level: optimize working set for L1 cache size using tiling
>     Band = maximumTilableNest(Root);
>     WorkingSetSizePerIteration = estimatWorkingSet(Band.back().getBody());
>     TileSize = floor(nthroot(L1CacheSize / WorkingSetSizePerIteration,
> Band.size()));
>     if (TileSize > 1) {
>        Worklist.insert(applyTiling(Root, TilesSize.splat(Band.size()));
>        Matches += 1;
>     }
>
>     if (Matches >= Threshold)
>       return;
>
>     // Low level: vectorization for each SIMD level (potentially
>     // carried-out by VPlan)
>     foreach (Width : promisingSimdWidths(Root)) {
>       Vectorized = applyVectorization(Root, Width);
>       if (Vectorized.isSatisfiable()) {
>         Worklist.insert(Vectorized);
>         Matches += 1;
>       }
>     }
>
>     if (Matches >= Threshold)
>       return;
>
>     // Low level: rely on heuristic to find best unrolling factor
>     if (Factor = unrollFactorHeuristic(Root))  {
>       Worklist.insert(applyUnroll(Root, Factor).getRoot());
>       Matches += 1;
>     }
>
>     if (Matches >= Threshold)
>       return;
>
>     ...
> }
>
>
> The "levels" encode precedence optimizations. Depending on the
> optimization level, we might only apply the most promising
> optimization.
>
> Instead of this brute force implementation, for predefined
> optimization levels, the search space exploration should be guided:
> Encode the order of the most useful transformations in the search
> space exploration. For instance, find all idioms first, then apply
> memory hierarchy optimizations, then compute hierarchy, then CPU
> pipeline optimizations. Since this is very transformation specific, I
> do not expect to write a 'pass manager' where transformations can
> register itself to (except for exhaustive searches when explicitly
> enabled). Instead, I'd write this in code that classifies loop nests
> (e.g. compute bound, bandwidth bound, known idioms, tensor
> contractions, stencils, etc.) and choses appropriate optimization
> paths. We can, of course, make this more generic over time.
>
>
>
> Writing an optimization pass
> -----------------------------
>
> Optimizations themselves are written in the following steps:
> 1. Check preconditions
> 2. Quick profitability analysis to skip obviously bad transformations
> 3. Create new green nodes to represent the changed loop nest; reuse
> unchanged green nodes as much as possible
> 4. Create a red node to insert into the parent
> 5. Preserve analyses (most analyses should be able to use analysis
> stored in reused green nodes and/or lazyly reevaluate new nodes)
> 6. Check whether the transformation was valid
>
> Especially the possibility to analyze the correctness after the
> transformation was applied could significantly reduce the amount of
> code needed to verify the correctness.
>
> A transformation like loop fusion could look like:
>
>   void applyFuse(Red1, Red2) {
>    // Assume Red1 and Red2 are consecutive sibling loops
>
>   // Bail out on untypical things (atomic accesses, exceptions,
> convergent instructions, ...)
>   if (!Red1->isSimple() || !Red2->isSimple())
>     return;
>
>   // Consistency checks (can be less less strict by moving conditions
> into the fused body).
>   if (Red1->getIterationCount() != Red2->getIterationCount())
>     return;
>   if (Red1->getPredicate() != Red2->getPredicate())
>     return;
>
>   // Create new loop hierarchy with fused loops.
>   GreenFused = new GreenLoop({ Red1->getGreen(), Red2->getGreen() },
>
>  Red1->getIterationCount());
>   RedFused = new RedNode(GreenFused, Red1->getParent());
>   NewRoot = RedFused->getRoot();
>
>   // Preserve analysis.
>   // In this case not really necessary since the green nodes of the
>   // loop bodies are reused.
>   DependenceAnalysis->transferAnalysis(Red1->getBody(),
>
RedFused->getBody()[0],
> ClosedExprAnalysis->makeIdentityMapping(Red1->getIterator(),
>
> RedFused->getIterator()));
>   DependenceAnalysis->transferAnalysis(Red2->getBody(),
>
RedFused->getBody()[1],
>    ClosedExprAnalysis->makeIdentityMapping(Red2->getIterator(),
>
> RedFused->getIterator()));
>
>   ValidityCondition = DependenceAnalysis->isValid(NewRoot);
>   if (ValidityCondition.isSatisfiable()) {
>     RedFused.addAssumption(ValidityCondition);
>     Candidates.push_back(NewRoot);
>   }
> }
>
>
>
> Questions & Answers
> -------------------
>
> Q: Is the loop hierarchy a tree or DAG?
> A: Both. A green node can be reused multiple times in the same
> structure (e.g. due to unrolling, versioning, peelings, etc), but a
> red node is specific to the position in its parent; there can be
> multiple red nodes for the same green node.
>
>
> Q: No SSA?
> A: Since the location of a definition depends on the parent in a green
> DAG, possibly from different loop hierarchies after transformations,
> it is not possible to directly reference the definition with its use.
> However, it is possible in the red tree, but runs against the goal of
> avoiding heavy red nodes. Instead, to find the previous definition,
> one has to traverse the green no up to find at which sibling level the
> value is defined. However, this should not be a common query; loop
> optimizations should use dependency information instead.
>
>
> Q: Loops with multiple exits?
> A: If every exiting edge a unique number to its __???_executed
> variable, it can be handled like a switch.
>
>
> Q: Unstructured control flow?
> A: Unstructured control flow only introduces disjunctions to statement
> predicated. That is, the predicate
>
>     a or b
>
> corresponds to block BB2 the CFG
>
>     BB0:
>       br i1 %a, label %BB2, label %BB2
>
>     BB1:
>       br i1 %b, label %BB2, label %BB3
>
>     BB2:
>
> In structured control flow, BB1 and/or BB2 would be post-dominated by
> BB2 and the disjunction disappear.
>
>
> Q: Irreducible loops?
> A: Can be folded into the first iteration of the loop by including a
> condition for statements not executed during the first iteration.
>
>
> Q: The unreachable terminator?
> A: If due to a non-returning function call, this introduces a loop
> exit (which will also introduce control a dependency to everything
> that follows) to the surrounding loops. If due to an assumption, we
> may add the branching condition to the sufficient condition, but not
> to the necessary condition.
>
>
> Q: Infinite loops?
> A: The closed-form expression identifying a statement instances and
> loop trip count have no upper bound. Either use arbitrary range
> arithmetic, use relative dependence vectors and/or fall back on
> pessimistic assumptions. In addition, like with the unreachable
> terminator, this may be handled as another loop exit.
>
>
> Q: IndirectBr?
> Since the list of possible targets is part of the instructions, can be
> handled like a switch over the target address
>
>
> Q: Loop guards?
> A: Loop guards manifests as the execution condition of the loop
> statement's predicate. A loop whose predicate evaluates to false can
> be considered a loop with 0 iterations. The IR generator can also emit
> the predicate as a loop guard. It might be useful to ensure that if
> the predicate evaluates to true, the loop has at least one iteration
> and the loop-condition is not evaluated for the first iteration (like
> LoopRotation).
>
>
> Q: Exceptions?
> A: Could also be handled with control dependencies, but I would
> instead mark the surrounding loops with "contains unpredictable
> control flow" to be ignored by most transformations. Similar to
> `!isSimple()` of LoadInst and StoreInst.
>
>
> Q: Relation to the new/legacy pass manager?
> A: LLVM's pass managers are unfortunately not designed to apply to
> subtrees nor persistent data structures besides the LLVM-IR itself.
> Instead, the loop tree optimizer would be its own monolithic pass on
> the pass manager level (like MachinePassManager and VPlan). My idea is
> to add it somewhere before LoopVectorize, but after the inliner,
> potentially replace most other loop transformations. There should be
> just one instance of the pass in the pipeline since creating an
> alternative representation of LLVM-IR is not that cheap. It does not
> need IR normalization (LoopSimplify, LICM, LoopRotate, LCSSA); these
> can be performed on the loop tree and emitted into the LLVM-IR if a
> non-modified tree is chosen. Possibly some of these passes can be
> removed.
> In order to preserve user-directed transformations (such as "#pragma
> clang loop distribute"), it may also be interesting to put it earlier
> into the pipeline to avoid that other passes such as LoopFullUnroll
> change the loop before the transformation can be applied.
> Alternatively, such passes can be taught the check the presence of a
> user-directed transformation before applying its transformation.
>
>
> Q: Relation to LoopVectorize/VPlan?
> A: VPlan has similar design goals [9] but is intended for
> vectorization only. It also has a hierarchical data structure, but
> uses a CFG for acyclic control flow. It is also intended to have
> multiple variants of the same source IR from which the best is
> selected via a cost function. However, it lacks cheap copies. Instead
> of instructions, it uses recipes/"meta-instructions" that handle
what
> happens to instructions after vectorization, e.g. do that operation on
> each vector lane ("WIDEN"). VPlan is more oriented towards
modifying
> instructions instead of statements as collection of instructions. With
> the loop hierarchy, I do not plan to redo the work of VPlan, but also
> do not see a reason why it should not also be able to do
> vectorization.
>
>
> Q: Relation to Polly?
> A: Polly uses ISL's schedule tree as the representation of the loop
> hierarchy. Its creation may fail of something not representable in a
> schedule tree is found. Polly tries to find the maximum representable
> region, but once it is chosen, it cannot be changed (e.g. because
> optimizing it takes too long). The schedule tree is stored internally
> by ISL as a kind of green tree, but is walked over by an iterator that
> remembers the path to the root. While this could be used to select a
> best schedule tree using a cost function, Polly relies mostly on ISL's
> reschedule algorithm to find a profitable transformation.
>
>
> Q: Relation to MLIR?
> A: MLIR is more similar to LLVM-IR than a loop hierarchy. For
> instance, it also does not feature cheap copies. An advantage is that
> loops and multi-dimensional arrays can be represented in the language
> without the need of being rediscovered, but have to be inserted by a
> front-end. That is, if Clang was generating MLIR, loops and arrays
> still have to be rediscovered. However, a loop hierarchy optimizer
> could be applied to MLIR just as well as to LLVM-IR.
>
>
> References
> ----------
> [1] http://llvm.org/devmtg/2018-10/talk-abstracts.html#talk11
> [2] https://ieeexplore.ieee.org/abstract/document/5389392/
> [3] http://sro.sussex.ac.uk/id/eprint/7576/1/Stanier,_James.pdf
> [4]
>
https://blogs.msdn.microsoft.com/ericlippert/2012/06/08/persistence-facades-and-roslyns-red-green-trees/
> [5] https://github.com/Meinersbur/llvm-project/tree/LOF/llvm/lib/LOF
> [6] https://llvm.org/devmtg/2017-10/#src2
> [7] https://arxiv.org/abs/1811.00632
> [8] https://lists.llvm.org/pipermail/llvm-dev/2017-October/118125.html
> [9] https://llvm.org/docs/Proposals/VectorizationPlan.html
> [10] https://github.com/open64-compiler/open64/tree/master/osprey/be/lno
> [11] https://reviews.llvm.org/D70688
> [12] https://arxiv.org/abs/1801.07399
> _______________________________________________
> LLVM Developers mailing list
> llvm-dev at lists.llvm.org
> https://lists.llvm.org/cgi-bin/mailman/listinfo/llvm-dev
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL:
<http://lists.llvm.org/pipermail/llvm-dev/attachments/20200122/57a23b57/attachment-0001.html>