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183 lines
8.1 KiB
ReStructuredText
==================
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Vectorization Plan
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==================
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.. contents::
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:local:
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Abstract
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========
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The vectorization transformation can be rather complicated, involving several
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potential alternatives, especially for outer-loops [1]_ but also possibly for
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innermost loops. These alternatives may have significant performance impact,
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both positive and negative. A cost model is therefore employed to identify the
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best alternative, including the alternative of avoiding any transformation
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altogether.
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The Vectorization Plan is an explicit model for describing vectorization
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candidates. It serves for both optimizing candidates including estimating their
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cost reliably, and for performing their final translation into IR. This
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facilitates dealing with multiple vectorization candidates.
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High-level Design
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=================
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Vectorization Workflow
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----------------------
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VPlan-based vectorization involves three major steps, taking a "scenario-based
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approach" to vectorization planning:
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1. Legal Step: check if a loop can be legally vectorized; encode constraints and
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artifacts if so.
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2. Plan Step:
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a. Build initial VPlans following the constraints and decisions taken by
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Legal Step 1, and compute their cost.
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b. Apply optimizations to the VPlans, possibly forking additional VPlans.
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Prune sub-optimal VPlans having relatively high cost.
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3. Execute Step: materialize the best VPlan. Note that this is the only step
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that modifies the IR.
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Design Guidelines
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-----------------
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In what follows, the term "input IR" refers to code that is fed into the
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vectorizer whereas the term "output IR" refers to code that is generated by the
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vectorizer. The output IR contains code that has been vectorized or "widened"
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according to a loop Vectorization Factor (VF), and/or loop unroll-and-jammed
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according to an Unroll Factor (UF).
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The design of VPlan follows several high-level guidelines:
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1. Analysis-like: building and manipulating VPlans must not modify the input IR.
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In particular, if the best option is not to vectorize at all, the
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vectorization process terminates before reaching Step 3, and compilation
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should proceed as if VPlans had not been built.
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2. Align Cost & Execute: each VPlan must support both estimating the cost and
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generating the output IR code, such that the cost estimation evaluates the
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to-be-generated code reliably.
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3. Support vectorizing additional constructs:
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a. Outer-loop vectorization. In particular, VPlan must be able to model the
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control-flow of the output IR which may include multiple basic-blocks and
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nested loops.
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b. SLP vectorization.
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c. Combinations of the above, including nested vectorization: vectorizing
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both an inner loop and an outer-loop at the same time (each with its own
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VF and UF), mixed vectorization: vectorizing a loop with SLP patterns
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inside [4]_, (re)vectorizing input IR containing vector code.
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d. Function vectorization [2]_.
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4. Support multiple candidates efficiently. In particular, similar candidates
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related to a range of possible VF's and UF's must be represented efficiently.
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Potential versioning needs to be supported efficiently.
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5. Support vectorizing idioms, such as interleaved groups of strided loads or
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stores. This is achieved by modeling a sequence of output instructions using
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a "Recipe", which is responsible for computing its cost and generating its
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code.
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6. Encapsulate Single-Entry Single-Exit regions (SESE). During vectorization
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such regions may need to be, for example, predicated and linearized, or
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replicated VF*UF times to handle scalarized and predicated instructions.
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Innerloops are also modelled as SESE regions.
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Low-level Design
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================
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The low-level design of VPlan comprises of the following classes.
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:LoopVectorizationPlanner:
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A LoopVectorizationPlanner is designed to handle the vectorization of a loop
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or a loop nest. It can construct, optimize and discard one or more VPlans,
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each VPlan modelling a distinct way to vectorize the loop or the loop nest.
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Once the best VPlan is determined, including the best VF and UF, this VPlan
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drives the generation of output IR.
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:VPlan:
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A model of a vectorized candidate for a given input IR loop or loop nest. This
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candidate is represented using a Hierarchical CFG. VPlan supports estimating
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the cost and driving the generation of the output IR code it represents.
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:Hierarchical CFG:
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A control-flow graph whose nodes are basic-blocks or Hierarchical CFG's. The
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Hierarchical CFG data structure is similar to the Tile Tree [5]_, where
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cross-Tile edges are lifted to connect Tiles instead of the original
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basic-blocks as in Sharir [6]_, promoting the Tile encapsulation. The terms
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Region and Block are used rather than Tile [5]_ to avoid confusion with loop
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tiling.
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:VPBlockBase:
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The building block of the Hierarchical CFG. A pure-virtual base-class of
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VPBasicBlock and VPRegionBlock, see below. VPBlockBase models the hierarchical
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control-flow relations with other VPBlocks. Note that in contrast to the IR
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BasicBlock, a VPBlockBase models its control-flow successors and predecessors
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directly, rather than through a Terminator branch or through predecessor
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branches that "use" the VPBlockBase.
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:VPBasicBlock:
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VPBasicBlock is a subclass of VPBlockBase, and serves as the leaves of the
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Hierarchical CFG. It represents a sequence of output IR instructions that will
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appear consecutively in an output IR basic-block. The instructions of this
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basic-block originate from one or more VPBasicBlocks. VPBasicBlock holds a
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sequence of zero or more VPRecipes that model the cost and generation of the
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output IR instructions.
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:VPRegionBlock:
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VPRegionBlock is a subclass of VPBlockBase. It models a collection of
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VPBasicBlocks and VPRegionBlocks which form a SESE subgraph of the output IR
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CFG. A VPRegionBlock may indicate that its contents are to be replicated a
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constant number of times when output IR is generated, effectively representing
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a loop with constant trip-count that will be completely unrolled. This is used
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to support scalarized and predicated instructions with a single model for
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multiple candidate VF's and UF's.
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:VPRecipeBase:
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A pure-virtual base class modeling a sequence of one or more output IR
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instructions, possibly based on one or more input IR instructions. These
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input IR instructions are referred to as "Ingredients" of the Recipe. A Recipe
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may specify how its ingredients are to be transformed to produce the output IR
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instructions; e.g., cloned once, replicated multiple times or widened
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according to selected VF.
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:VPTransformState:
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Stores information used for generating output IR, passed from
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LoopVectorizationPlanner to its selected VPlan for execution, and used to pass
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additional information down to VPBlocks and VPRecipes.
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Related LLVM components
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-----------------------
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1. SLP Vectorizer: one can compare the VPlan model with LLVM's existing SLP
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tree, where TSLP [3]_ adds Plan Step 2.b.
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2. RegionInfo: one can compare VPlan's H-CFG with the Region Analysis as used by
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Polly [7]_.
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References
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----------
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.. [1] "Outer-loop vectorization: revisited for short SIMD architectures", Dorit
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Nuzman and Ayal Zaks, PACT 2008.
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.. [2] "Proposal for function vectorization and loop vectorization with function
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calls", Xinmin Tian, [`cfe-dev
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<http://lists.llvm.org/pipermail/cfe-dev/2016-March/047732.html>`_].,
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March 2, 2016.
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See also `review <https://reviews.llvm.org/D22792>`_.
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.. [3] "Throttling Automatic Vectorization: When Less is More", Vasileios
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Porpodas and Tim Jones, PACT 2015 and LLVM Developers' Meeting 2015.
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.. [4] "Exploiting mixed SIMD parallelism by reducing data reorganization
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overhead", Hao Zhou and Jingling Xue, CGO 2016.
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.. [5] "Register Allocation via Hierarchical Graph Coloring", David Callahan and
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Brian Koblenz, PLDI 1991
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.. [6] "Structural analysis: A new approach to flow analysis in optimizing
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compilers", M. Sharir, Journal of Computer Languages, Jan. 1980
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.. [7] "Enabling Polyhedral Optimizations in LLVM", Tobias Grosser, Diploma
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thesis, 2011.
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.. [8] "Introducing VPlan to the Loop Vectorizer", Gil Rapaport and Ayal Zaks,
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European LLVM Developers' Meeting 2017.
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