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//===- Schedule.cpp - Calculate an optimized schedule ---------------------===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This pass generates an entirely new schedule tree from the data dependences
// and iteration domains. The new schedule tree is computed in two steps:
//
// 1) The isl scheduling optimizer is run
//
// The isl scheduling optimizer creates a new schedule tree that maximizes
// parallelism and tileability and minimizes data-dependence distances. The
// algorithm used is a modified version of the ``Pluto'' algorithm:
//
// U. Bondhugula, A. Hartono, J. Ramanujam, and P. Sadayappan.
// A Practical Automatic Polyhedral Parallelizer and Locality Optimizer.
// In Proceedings of the 2008 ACM SIGPLAN Conference On Programming Language
// Design and Implementation, PLDI ’08, pages 101–113. ACM, 2008.
//
// 2) A set of post-scheduling transformations is applied on the schedule tree.
//
// These optimizations include:
//
// - Tiling of the innermost tilable bands
// - Prevectorization - The choice of a possible outer loop that is strip-mined
// to the innermost level to enable inner-loop
// vectorization.
// - Some optimizations for spatial locality are also planned.
//
// For a detailed description of the schedule tree itself please see section 6
// of:
//
// Polyhedral AST generation is more than scanning polyhedra
// Tobias Grosser, Sven Verdoolaege, Albert Cohen
// ACM Transactions on Programming Languages and Systems (TOPLAS),
// 37(4), July 2015
// http://www.grosser.es/#pub-polyhedral-AST-generation
//
// This publication also contains a detailed discussion of the different options
// for polyhedral loop unrolling, full/partial tile separation and other uses
// of the schedule tree.
//
//===----------------------------------------------------------------------===//
#include "polly/ScheduleOptimizer.h"
#include "polly/CodeGen/CodeGeneration.h"
#include "polly/DependenceInfo.h"
#include "polly/LinkAllPasses.h"
#include "polly/Options.h"
#include "polly/ScopInfo.h"
#include "polly/ScopPass.h"
#include "polly/Simplify.h"
#include "polly/Support/GICHelper.h"
#include "polly/Support/ISLOStream.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/Analysis/TargetTransformInfo.h"
#include "llvm/IR/Function.h"
#include "llvm/Pass.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/raw_ostream.h"
#include "isl/constraint.h"
#include "isl/ctx.h"
#include "isl/map.h"
#include "isl/options.h"
#include "isl/printer.h"
#include "isl/schedule.h"
#include "isl/schedule_node.h"
#include "isl/space.h"
#include "isl/union_map.h"
#include "isl/union_set.h"
#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdlib>
#include <string>
#include <vector>
using namespace llvm;
using namespace polly;
#define DEBUG_TYPE "polly-opt-isl"
static cl::opt<std::string>
OptimizeDeps("polly-opt-optimize-only",
cl::desc("Only a certain kind of dependences (all/raw)"),
cl::Hidden, cl::init("all"), cl::ZeroOrMore,
cl::cat(PollyCategory));
static cl::opt<std::string>
SimplifyDeps("polly-opt-simplify-deps",
cl::desc("Dependences should be simplified (yes/no)"),
cl::Hidden, cl::init("yes"), cl::ZeroOrMore,
cl::cat(PollyCategory));
static cl::opt<int> MaxConstantTerm(
"polly-opt-max-constant-term",
cl::desc("The maximal constant term allowed (-1 is unlimited)"), cl::Hidden,
cl::init(20), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<int> MaxCoefficient(
"polly-opt-max-coefficient",
cl::desc("The maximal coefficient allowed (-1 is unlimited)"), cl::Hidden,
cl::init(20), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<std::string> FusionStrategy(
"polly-opt-fusion", cl::desc("The fusion strategy to choose (min/max)"),
cl::Hidden, cl::init("min"), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<std::string>
MaximizeBandDepth("polly-opt-maximize-bands",
cl::desc("Maximize the band depth (yes/no)"), cl::Hidden,
cl::init("yes"), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<std::string> OuterCoincidence(
"polly-opt-outer-coincidence",
cl::desc("Try to construct schedules where the outer member of each band "
"satisfies the coincidence constraints (yes/no)"),
cl::Hidden, cl::init("no"), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<int> PrevectorWidth(
"polly-prevect-width",
cl::desc(
"The number of loop iterations to strip-mine for pre-vectorization"),
cl::Hidden, cl::init(4), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<bool> FirstLevelTiling("polly-tiling",
cl::desc("Enable loop tiling"),
cl::init(true), cl::ZeroOrMore,
cl::cat(PollyCategory));
static cl::opt<int> LatencyVectorFma(
"polly-target-latency-vector-fma",
cl::desc("The minimal number of cycles between issuing two "
"dependent consecutive vector fused multiply-add "
"instructions."),
cl::Hidden, cl::init(8), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<int> ThroughputVectorFma(
"polly-target-throughput-vector-fma",
cl::desc("A throughput of the processor floating-point arithmetic units "
"expressed in the number of vector fused multiply-add "
"instructions per clock cycle."),
cl::Hidden, cl::init(1), cl::ZeroOrMore, cl::cat(PollyCategory));
// This option, along with --polly-target-2nd-cache-level-associativity,
// --polly-target-1st-cache-level-size, and --polly-target-2st-cache-level-size
// represent the parameters of the target cache, which do not have typical
// values that can be used by default. However, to apply the pattern matching
// optimizations, we use the values of the parameters of Intel Core i7-3820
// SandyBridge in case the parameters are not specified or not provided by the
// TargetTransformInfo.
static cl::opt<int> FirstCacheLevelAssociativity(
"polly-target-1st-cache-level-associativity",
cl::desc("The associativity of the first cache level."), cl::Hidden,
cl::init(-1), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<int> FirstCacheLevelDefaultAssociativity(
"polly-target-1st-cache-level-default-associativity",
cl::desc("The default associativity of the first cache level"
" (if not enough were provided by the TargetTransformInfo)."),
cl::Hidden, cl::init(8), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<int> SecondCacheLevelAssociativity(
"polly-target-2nd-cache-level-associativity",
cl::desc("The associativity of the second cache level."), cl::Hidden,
cl::init(-1), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<int> SecondCacheLevelDefaultAssociativity(
"polly-target-2nd-cache-level-default-associativity",
cl::desc("The default associativity of the second cache level"
" (if not enough were provided by the TargetTransformInfo)."),
cl::Hidden, cl::init(8), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<int> FirstCacheLevelSize(
"polly-target-1st-cache-level-size",
cl::desc("The size of the first cache level specified in bytes."),
cl::Hidden, cl::init(-1), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<int> FirstCacheLevelDefaultSize(
"polly-target-1st-cache-level-default-size",
cl::desc("The default size of the first cache level specified in bytes"
" (if not enough were provided by the TargetTransformInfo)."),
cl::Hidden, cl::init(32768), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<int> SecondCacheLevelSize(
"polly-target-2nd-cache-level-size",
cl::desc("The size of the second level specified in bytes."), cl::Hidden,
cl::init(-1), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<int> SecondCacheLevelDefaultSize(
"polly-target-2nd-cache-level-default-size",
cl::desc("The default size of the second cache level specified in bytes"
" (if not enough were provided by the TargetTransformInfo)."),
cl::Hidden, cl::init(262144), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<int> VectorRegisterBitwidth(
"polly-target-vector-register-bitwidth",
cl::desc("The size in bits of a vector register (if not set, this "
"information is taken from LLVM's target information."),
cl::Hidden, cl::init(-1), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<int> FirstLevelDefaultTileSize(
"polly-default-tile-size",
cl::desc("The default tile size (if not enough were provided by"
" --polly-tile-sizes)"),
cl::Hidden, cl::init(32), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::list<int>
FirstLevelTileSizes("polly-tile-sizes",
cl::desc("A tile size for each loop dimension, filled "
"with --polly-default-tile-size"),
cl::Hidden, cl::ZeroOrMore, cl::CommaSeparated,
cl::cat(PollyCategory));
static cl::opt<bool>
SecondLevelTiling("polly-2nd-level-tiling",
cl::desc("Enable a 2nd level loop of loop tiling"),
cl::init(false), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<int> SecondLevelDefaultTileSize(
"polly-2nd-level-default-tile-size",
cl::desc("The default 2nd-level tile size (if not enough were provided by"
" --polly-2nd-level-tile-sizes)"),
cl::Hidden, cl::init(16), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::list<int>
SecondLevelTileSizes("polly-2nd-level-tile-sizes",
cl::desc("A tile size for each loop dimension, filled "
"with --polly-default-tile-size"),
cl::Hidden, cl::ZeroOrMore, cl::CommaSeparated,
cl::cat(PollyCategory));
static cl::opt<bool> RegisterTiling("polly-register-tiling",
cl::desc("Enable register tiling"),
cl::init(false), cl::ZeroOrMore,
cl::cat(PollyCategory));
static cl::opt<int> RegisterDefaultTileSize(
"polly-register-tiling-default-tile-size",
cl::desc("The default register tile size (if not enough were provided by"
" --polly-register-tile-sizes)"),
cl::Hidden, cl::init(2), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<int> PollyPatternMatchingNcQuotient(
"polly-pattern-matching-nc-quotient",
cl::desc("Quotient that is obtained by dividing Nc, the parameter of the"
"macro-kernel, by Nr, the parameter of the micro-kernel"),
cl::Hidden, cl::init(256), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::list<int>
RegisterTileSizes("polly-register-tile-sizes",
cl::desc("A tile size for each loop dimension, filled "
"with --polly-register-tile-size"),
cl::Hidden, cl::ZeroOrMore, cl::CommaSeparated,
cl::cat(PollyCategory));
static cl::opt<bool>
PMBasedOpts("polly-pattern-matching-based-opts",
cl::desc("Perform optimizations based on pattern matching"),
cl::init(true), cl::ZeroOrMore, cl::cat(PollyCategory));
static cl::opt<bool> OptimizedScops(
"polly-optimized-scops",
cl::desc("Polly - Dump polyhedral description of Scops optimized with "
"the isl scheduling optimizer and the set of post-scheduling "
"transformations is applied on the schedule tree"),
cl::init(false), cl::ZeroOrMore, cl::cat(PollyCategory));
STATISTIC(ScopsProcessed, "Number of scops processed");
STATISTIC(ScopsRescheduled, "Number of scops rescheduled");
STATISTIC(ScopsOptimized, "Number of scops optimized");
STATISTIC(NumAffineLoopsOptimized, "Number of affine loops optimized");
STATISTIC(NumBoxedLoopsOptimized, "Number of boxed loops optimized");
#define THREE_STATISTICS(VARNAME, DESC) \
static Statistic VARNAME[3] = { \
{DEBUG_TYPE, #VARNAME "0", DESC " (original)", {0}, {false}}, \
{DEBUG_TYPE, #VARNAME "1", DESC " (after scheduler)", {0}, {false}}, \
{DEBUG_TYPE, #VARNAME "2", DESC " (after optimizer)", {0}, {false}}}
THREE_STATISTICS(NumBands, "Number of bands");
THREE_STATISTICS(NumBandMembers, "Number of band members");
THREE_STATISTICS(NumCoincident, "Number of coincident band members");
THREE_STATISTICS(NumPermutable, "Number of permutable bands");
THREE_STATISTICS(NumFilters, "Number of filter nodes");
THREE_STATISTICS(NumExtension, "Number of extension nodes");
STATISTIC(FirstLevelTileOpts, "Number of first level tiling applied");
STATISTIC(SecondLevelTileOpts, "Number of second level tiling applied");
STATISTIC(RegisterTileOpts, "Number of register tiling applied");
STATISTIC(PrevectOpts, "Number of strip-mining for prevectorization applied");
STATISTIC(MatMulOpts,
"Number of matrix multiplication patterns detected and optimized");
/// Create an isl::union_set, which describes the isolate option based on
/// IsolateDomain.
///
/// @param IsolateDomain An isl::set whose @p OutDimsNum last dimensions should
/// belong to the current band node.
/// @param OutDimsNum A number of dimensions that should belong to
/// the current band node.
static isl::union_set getIsolateOptions(isl::set IsolateDomain,
unsigned OutDimsNum) {
unsigned Dims = IsolateDomain.dim(isl::dim::set);
assert(OutDimsNum <= Dims &&
"The isl::set IsolateDomain is used to describe the range of schedule "
"dimensions values, which should be isolated. Consequently, the "
"number of its dimensions should be greater than or equal to the "
"number of the schedule dimensions.");
isl::map IsolateRelation = isl::map::from_domain(IsolateDomain);
IsolateRelation = IsolateRelation.move_dims(isl::dim::out, 0, isl::dim::in,
Dims - OutDimsNum, OutDimsNum);
isl::set IsolateOption = IsolateRelation.wrap();
isl::id Id = isl::id::alloc(IsolateOption.get_ctx(), "isolate", nullptr);
IsolateOption = IsolateOption.set_tuple_id(Id);
return isl::union_set(IsolateOption);
}
namespace {
/// Create an isl::union_set, which describes the specified option for the
/// dimension of the current node.
///
/// @param Ctx An isl::ctx, which is used to create the isl::union_set.
/// @param Option The name of the option.
isl::union_set getDimOptions(isl::ctx Ctx, const char *Option) {
isl::space Space(Ctx, 0, 1);
auto DimOption = isl::set::universe(Space);
auto Id = isl::id::alloc(Ctx, Option, nullptr);
DimOption = DimOption.set_tuple_id(Id);
return isl::union_set(DimOption);
}
} // namespace
/// Create an isl::union_set, which describes the option of the form
/// [isolate[] -> unroll[x]].
///
/// @param Ctx An isl::ctx, which is used to create the isl::union_set.
static isl::union_set getUnrollIsolatedSetOptions(isl::ctx Ctx) {
isl::space Space = isl::space(Ctx, 0, 0, 1);
isl::map UnrollIsolatedSetOption = isl::map::universe(Space);
isl::id DimInId = isl::id::alloc(Ctx, "isolate", nullptr);
isl::id DimOutId = isl::id::alloc(Ctx, "unroll", nullptr);
UnrollIsolatedSetOption =
UnrollIsolatedSetOption.set_tuple_id(isl::dim::in, DimInId);
UnrollIsolatedSetOption =
UnrollIsolatedSetOption.set_tuple_id(isl::dim::out, DimOutId);
return UnrollIsolatedSetOption.wrap();
}
/// Make the last dimension of Set to take values from 0 to VectorWidth - 1.
///
/// @param Set A set, which should be modified.
/// @param VectorWidth A parameter, which determines the constraint.
static isl::set addExtentConstraints(isl::set Set, int VectorWidth) {
unsigned Dims = Set.dim(isl::dim::set);
isl::space Space = Set.get_space();
isl::local_space LocalSpace = isl::local_space(Space);
isl::constraint ExtConstr = isl::constraint::alloc_inequality(LocalSpace);
ExtConstr = ExtConstr.set_constant_si(0);
ExtConstr = ExtConstr.set_coefficient_si(isl::dim::set, Dims - 1, 1);
Set = Set.add_constraint(ExtConstr);
ExtConstr = isl::constraint::alloc_inequality(LocalSpace);
ExtConstr = ExtConstr.set_constant_si(VectorWidth - 1);
ExtConstr = ExtConstr.set_coefficient_si(isl::dim::set, Dims - 1, -1);
return Set.add_constraint(ExtConstr);
}
isl::set getPartialTilePrefixes(isl::set ScheduleRange, int VectorWidth) {
unsigned Dims = ScheduleRange.dim(isl::dim::set);
isl::set LoopPrefixes =
ScheduleRange.drop_constraints_involving_dims(isl::dim::set, Dims - 1, 1);
auto ExtentPrefixes = addExtentConstraints(LoopPrefixes, VectorWidth);
isl::set BadPrefixes = ExtentPrefixes.subtract(ScheduleRange);
BadPrefixes = BadPrefixes.project_out(isl::dim::set, Dims - 1, 1);
LoopPrefixes = LoopPrefixes.project_out(isl::dim::set, Dims - 1, 1);
return LoopPrefixes.subtract(BadPrefixes);
}
isl::schedule_node
ScheduleTreeOptimizer::isolateFullPartialTiles(isl::schedule_node Node,
int VectorWidth) {
assert(isl_schedule_node_get_type(Node.get()) == isl_schedule_node_band);
Node = Node.child(0).child(0);
isl::union_map SchedRelUMap = Node.get_prefix_schedule_relation();
isl::map ScheduleRelation = isl::map::from_union_map(SchedRelUMap);
isl::set ScheduleRange = ScheduleRelation.range();
isl::set IsolateDomain = getPartialTilePrefixes(ScheduleRange, VectorWidth);
auto AtomicOption = getDimOptions(IsolateDomain.get_ctx(), "atomic");
isl::union_set IsolateOption = getIsolateOptions(IsolateDomain, 1);
Node = Node.parent().parent();
isl::union_set Options = IsolateOption.unite(AtomicOption);
Node = Node.band_set_ast_build_options(Options);
return Node;
}
isl::schedule_node ScheduleTreeOptimizer::prevectSchedBand(
isl::schedule_node Node, unsigned DimToVectorize, int VectorWidth) {
assert(isl_schedule_node_get_type(Node.get()) == isl_schedule_node_band);
auto Space = isl::manage(isl_schedule_node_band_get_space(Node.get()));
auto ScheduleDimensions = Space.dim(isl::dim::set);
assert(DimToVectorize < ScheduleDimensions);
if (DimToVectorize > 0) {
Node = isl::manage(
isl_schedule_node_band_split(Node.release(), DimToVectorize));
Node = Node.child(0);
}
if (DimToVectorize < ScheduleDimensions - 1)
Node = isl::manage(isl_schedule_node_band_split(Node.release(), 1));
Space = isl::manage(isl_schedule_node_band_get_space(Node.get()));
auto Sizes = isl::multi_val::zero(Space);
Sizes = Sizes.set_val(0, isl::val(Node.get_ctx(), VectorWidth));
Node =
isl::manage(isl_schedule_node_band_tile(Node.release(), Sizes.release()));
Node = isolateFullPartialTiles(Node, VectorWidth);
Node = Node.child(0);
// Make sure the "trivially vectorizable loop" is not unrolled. Otherwise,
// we will have troubles to match it in the backend.
Node = Node.band_set_ast_build_options(
isl::union_set(Node.get_ctx(), "{ unroll[x]: 1 = 0 }"));
Node = isl::manage(isl_schedule_node_band_sink(Node.release()));
Node = Node.child(0);
if (isl_schedule_node_get_type(Node.get()) == isl_schedule_node_leaf)
Node = Node.parent();
auto LoopMarker = isl::id::alloc(Node.get_ctx(), "SIMD", nullptr);
PrevectOpts++;
return Node.insert_mark(LoopMarker);
}
isl::schedule_node ScheduleTreeOptimizer::tileNode(isl::schedule_node Node,
const char *Identifier,
ArrayRef<int> TileSizes,
int DefaultTileSize) {
auto Space = isl::manage(isl_schedule_node_band_get_space(Node.get()));
auto Dims = Space.dim(isl::dim::set);
auto Sizes = isl::multi_val::zero(Space);
std::string IdentifierString(Identifier);
for (unsigned i = 0; i < Dims; i++) {
auto tileSize = i < TileSizes.size() ? TileSizes[i] : DefaultTileSize;
Sizes = Sizes.set_val(i, isl::val(Node.get_ctx(), tileSize));
}
auto TileLoopMarkerStr = IdentifierString + " - Tiles";
auto TileLoopMarker =
isl::id::alloc(Node.get_ctx(), TileLoopMarkerStr, nullptr);
Node = Node.insert_mark(TileLoopMarker);
Node = Node.child(0);
Node =
isl::manage(isl_schedule_node_band_tile(Node.release(), Sizes.release()));
Node = Node.child(0);
auto PointLoopMarkerStr = IdentifierString + " - Points";
auto PointLoopMarker =
isl::id::alloc(Node.get_ctx(), PointLoopMarkerStr, nullptr);
Node = Node.insert_mark(PointLoopMarker);
return Node.child(0);
}
isl::schedule_node ScheduleTreeOptimizer::applyRegisterTiling(
isl::schedule_node Node, ArrayRef<int> TileSizes, int DefaultTileSize) {
Node = tileNode(Node, "Register tiling", TileSizes, DefaultTileSize);
auto Ctx = Node.get_ctx();
return Node.band_set_ast_build_options(isl::union_set(Ctx, "{unroll[x]}"));
}
static bool isSimpleInnermostBand(const isl::schedule_node &Node) {
assert(isl_schedule_node_get_type(Node.get()) == isl_schedule_node_band);
assert(isl_schedule_node_n_children(Node.get()) == 1);
auto ChildType = isl_schedule_node_get_type(Node.child(0).get());
if (ChildType == isl_schedule_node_leaf)
return true;
if (ChildType != isl_schedule_node_sequence)
return false;
auto Sequence = Node.child(0);
for (int c = 0, nc = isl_schedule_node_n_children(Sequence.get()); c < nc;
++c) {
auto Child = Sequence.child(c);
if (isl_schedule_node_get_type(Child.get()) != isl_schedule_node_filter)
return false;
if (isl_schedule_node_get_type(Child.child(0).get()) !=
isl_schedule_node_leaf)
return false;
}
return true;
}
bool ScheduleTreeOptimizer::isTileableBandNode(isl::schedule_node Node) {
if (isl_schedule_node_get_type(Node.get()) != isl_schedule_node_band)
return false;
if (isl_schedule_node_n_children(Node.get()) != 1)
return false;
if (!isl_schedule_node_band_get_permutable(Node.get()))
return false;
auto Space = isl::manage(isl_schedule_node_band_get_space(Node.get()));
auto Dims = Space.dim(isl::dim::set);
if (Dims <= 1)
return false;
return isSimpleInnermostBand(Node);
}
__isl_give isl::schedule_node
ScheduleTreeOptimizer::standardBandOpts(isl::schedule_node Node, void *User) {
if (FirstLevelTiling) {
Node = tileNode(Node, "1st level tiling", FirstLevelTileSizes,
FirstLevelDefaultTileSize);
FirstLevelTileOpts++;
}
if (SecondLevelTiling) {
Node = tileNode(Node, "2nd level tiling", SecondLevelTileSizes,
SecondLevelDefaultTileSize);
SecondLevelTileOpts++;
}
if (RegisterTiling) {
Node =
applyRegisterTiling(Node, RegisterTileSizes, RegisterDefaultTileSize);
RegisterTileOpts++;
}
if (PollyVectorizerChoice == VECTORIZER_NONE)
return Node;
auto Space = isl::manage(isl_schedule_node_band_get_space(Node.get()));
auto Dims = Space.dim(isl::dim::set);
for (int i = Dims - 1; i >= 0; i--)
if (Node.band_member_get_coincident(i)) {
Node = prevectSchedBand(Node, i, PrevectorWidth);
break;
}
return Node;
}
/// Permute the two dimensions of the isl map.
///
/// Permute @p DstPos and @p SrcPos dimensions of the isl map @p Map that
/// have type @p DimType.
///
/// @param Map The isl map to be modified.
/// @param DimType The type of the dimensions.
/// @param DstPos The first dimension.
/// @param SrcPos The second dimension.
/// @return The modified map.
isl::map permuteDimensions(isl::map Map, isl::dim DimType, unsigned DstPos,
unsigned SrcPos) {
assert(DstPos < Map.dim(DimType) && SrcPos < Map.dim(DimType));
if (DstPos == SrcPos)
return Map;
isl::id DimId;
if (Map.has_tuple_id(DimType))
DimId = Map.get_tuple_id(DimType);
auto FreeDim = DimType == isl::dim::in ? isl::dim::out : isl::dim::in;
isl::id FreeDimId;
if (Map.has_tuple_id(FreeDim))
FreeDimId = Map.get_tuple_id(FreeDim);
auto MaxDim = std::max(DstPos, SrcPos);
auto MinDim = std::min(DstPos, SrcPos);
Map = Map.move_dims(FreeDim, 0, DimType, MaxDim, 1);
Map = Map.move_dims(FreeDim, 0, DimType, MinDim, 1);
Map = Map.move_dims(DimType, MinDim, FreeDim, 1, 1);
Map = Map.move_dims(DimType, MaxDim, FreeDim, 0, 1);
if (DimId)
Map = Map.set_tuple_id(DimType, DimId);
if (FreeDimId)
Map = Map.set_tuple_id(FreeDim, FreeDimId);
return Map;
}
/// Check the form of the access relation.
///
/// Check that the access relation @p AccMap has the form M[i][j], where i
/// is a @p FirstPos and j is a @p SecondPos.
///
/// @param AccMap The access relation to be checked.
/// @param FirstPos The index of the input dimension that is mapped to
/// the first output dimension.
/// @param SecondPos The index of the input dimension that is mapped to the
/// second output dimension.
/// @return True in case @p AccMap has the expected form and false,
/// otherwise.
static bool isMatMulOperandAcc(isl::set Domain, isl::map AccMap, int &FirstPos,
int &SecondPos) {
isl::space Space = AccMap.get_space();
isl::map Universe = isl::map::universe(Space);
if (Space.dim(isl::dim::out) != 2)
return false;
// MatMul has the form:
// for (i = 0; i < N; i++)
// for (j = 0; j < M; j++)
// for (k = 0; k < P; k++)
// C[i, j] += A[i, k] * B[k, j]
//
// Permutation of three outer loops: 3! = 6 possibilities.
int FirstDims[] = {0, 0, 1, 1, 2, 2};
int SecondDims[] = {1, 2, 2, 0, 0, 1};
for (int i = 0; i < 6; i += 1) {
auto PossibleMatMul =
Universe.equate(isl::dim::in, FirstDims[i], isl::dim::out, 0)
.equate(isl::dim::in, SecondDims[i], isl::dim::out, 1);
AccMap = AccMap.intersect_domain(Domain);
PossibleMatMul = PossibleMatMul.intersect_domain(Domain);
// If AccMap spans entire domain (Non-partial write),
// compute FirstPos and SecondPos.
// If AccMap != PossibleMatMul here (the two maps have been gisted at
// this point), it means that the writes are not complete, or in other
// words, it is a Partial write and Partial writes must be rejected.
if (AccMap.is_equal(PossibleMatMul)) {
if (FirstPos != -1 && FirstPos != FirstDims[i])
continue;
FirstPos = FirstDims[i];
if (SecondPos != -1 && SecondPos != SecondDims[i])
continue;
SecondPos = SecondDims[i];
return true;
}
}
return false;
}
/// Does the memory access represent a non-scalar operand of the matrix
/// multiplication.
///
/// Check that the memory access @p MemAccess is the read access to a non-scalar
/// operand of the matrix multiplication or its result.
///
/// @param MemAccess The memory access to be checked.
/// @param MMI Parameters of the matrix multiplication operands.
/// @return True in case the memory access represents the read access
/// to a non-scalar operand of the matrix multiplication and
/// false, otherwise.
static bool isMatMulNonScalarReadAccess(MemoryAccess *MemAccess,
MatMulInfoTy &MMI) {
if (!MemAccess->isLatestArrayKind() || !MemAccess->isRead())
return false;
auto AccMap = MemAccess->getLatestAccessRelation();
isl::set StmtDomain = MemAccess->getStatement()->getDomain();
if (isMatMulOperandAcc(StmtDomain, AccMap, MMI.i, MMI.j) && !MMI.ReadFromC) {
MMI.ReadFromC = MemAccess;
return true;
}
if (isMatMulOperandAcc(StmtDomain, AccMap, MMI.i, MMI.k) && !MMI.A) {
MMI.A = MemAccess;
return true;
}
if (isMatMulOperandAcc(StmtDomain, AccMap, MMI.k, MMI.j) && !MMI.B) {
MMI.B = MemAccess;
return true;
}
return false;
}
/// Check accesses to operands of the matrix multiplication.
///
/// Check that accesses of the SCoP statement, which corresponds to
/// the partial schedule @p PartialSchedule, are scalar in terms of loops
/// containing the matrix multiplication, in case they do not represent
/// accesses to the non-scalar operands of the matrix multiplication or
/// its result.
///
/// @param PartialSchedule The partial schedule of the SCoP statement.
/// @param MMI Parameters of the matrix multiplication operands.
/// @return True in case the corresponding SCoP statement
/// represents matrix multiplication and false,
/// otherwise.
static bool containsOnlyMatrMultAcc(isl::map PartialSchedule,
MatMulInfoTy &MMI) {
auto InputDimId = PartialSchedule.get_tuple_id(isl::dim::in);
auto *Stmt = static_cast<ScopStmt *>(InputDimId.get_user());
unsigned OutDimNum = PartialSchedule.dim(isl::dim::out);
assert(OutDimNum > 2 && "In case of the matrix multiplication the loop nest "
"and, consequently, the corresponding scheduling "
"functions have at least three dimensions.");
auto MapI =
permuteDimensions(PartialSchedule, isl::dim::out, MMI.i, OutDimNum - 1);
auto MapJ =
permuteDimensions(PartialSchedule, isl::dim::out, MMI.j, OutDimNum - 1);
auto MapK =
permuteDimensions(PartialSchedule, isl::dim::out, MMI.k, OutDimNum - 1);
auto Accesses = getAccessesInOrder(*Stmt);
for (auto *MemA = Accesses.begin(); MemA != Accesses.end() - 1; MemA++) {
auto *MemAccessPtr = *MemA;
if (MemAccessPtr->isLatestArrayKind() && MemAccessPtr != MMI.WriteToC &&
!isMatMulNonScalarReadAccess(MemAccessPtr, MMI) &&
!(MemAccessPtr->isStrideZero(MapI)) &&
MemAccessPtr->isStrideZero(MapJ) && MemAccessPtr->isStrideZero(MapK))
return false;
}
return true;
}
/// Check for dependencies corresponding to the matrix multiplication.
///
/// Check that there is only true dependence of the form
/// S(..., k, ...) -> S(..., k + 1, …), where S is the SCoP statement
/// represented by @p Schedule and k is @p Pos. Such a dependence corresponds
/// to the dependency produced by the matrix multiplication.
///
/// @param Schedule The schedule of the SCoP statement.
/// @param D The SCoP dependencies.
/// @param Pos The parameter to describe an acceptable true dependence.
/// In case it has a negative value, try to determine its
/// acceptable value.
/// @return True in case dependencies correspond to the matrix multiplication
/// and false, otherwise.
static bool containsOnlyMatMulDep(isl::map Schedule, const Dependences *D,
int &Pos) {
isl::union_map Dep = D->getDependences(Dependences::TYPE_RAW);
isl::union_map Red = D->getDependences(Dependences::TYPE_RED);
if (Red)
Dep = Dep.unite(Red);
auto DomainSpace = Schedule.get_space().domain();
auto Space = DomainSpace.map_from_domain_and_range(DomainSpace);
auto Deltas = Dep.extract_map(Space).deltas();
int DeltasDimNum = Deltas.dim(isl::dim::set);
for (int i = 0; i < DeltasDimNum; i++) {
auto Val = Deltas.plain_get_val_if_fixed(isl::dim::set, i);
Pos = Pos < 0 && Val.is_one() ? i : Pos;
if (Val.is_nan() || !(Val.is_zero() || (i == Pos && Val.is_one())))
return false;
}
if (DeltasDimNum == 0 || Pos < 0)
return false;
return true;
}
/// Check if the SCoP statement could probably be optimized with analytical
/// modeling.
///
/// containsMatrMult tries to determine whether the following conditions
/// are true:
/// 1. The last memory access modeling an array, MA1, represents writing to
/// memory and has the form S(..., i1, ..., i2, ...) -> M(i1, i2) or
/// S(..., i2, ..., i1, ...) -> M(i1, i2), where S is the SCoP statement
/// under consideration.
/// 2. There is only one loop-carried true dependency, and it has the
/// form S(..., i3, ...) -> S(..., i3 + 1, ...), and there are no
/// loop-carried or anti dependencies.
/// 3. SCoP contains three access relations, MA2, MA3, and MA4 that represent
/// reading from memory and have the form S(..., i3, ...) -> M(i1, i3),
/// S(..., i3, ...) -> M(i3, i2), S(...) -> M(i1, i2), respectively,
/// and all memory accesses of the SCoP that are different from MA1, MA2,
/// MA3, and MA4 have stride 0, if the innermost loop is exchanged with any
/// of loops i1, i2 and i3.
///
/// @param PartialSchedule The PartialSchedule that contains a SCoP statement
/// to check.
/// @D The SCoP dependencies.
/// @MMI Parameters of the matrix multiplication operands.
static bool containsMatrMult(isl::map PartialSchedule, const Dependences *D,
MatMulInfoTy &MMI) {
auto InputDimsId = PartialSchedule.get_tuple_id(isl::dim::in);
auto *Stmt = static_cast<ScopStmt *>(InputDimsId.get_user());
if (Stmt->size() <= 1)
return false;
auto Accesses = getAccessesInOrder(*Stmt);
for (auto *MemA = Accesses.end() - 1; MemA != Accesses.begin(); MemA--) {
auto *MemAccessPtr = *MemA;
if (!MemAccessPtr->isLatestArrayKind())
continue;
if (!MemAccessPtr->isWrite())
return false;
auto AccMap = MemAccessPtr->getLatestAccessRelation();
if (!isMatMulOperandAcc(Stmt->getDomain(), AccMap, MMI.i, MMI.j))
return false;
MMI.WriteToC = MemAccessPtr;
break;
}
if (!containsOnlyMatMulDep(PartialSchedule, D, MMI.k))
return false;
if (!MMI.WriteToC || !containsOnlyMatrMultAcc(PartialSchedule, MMI))
return false;
if (!MMI.A || !MMI.B || !MMI.ReadFromC)
return false;
return true;
}
/// Permute two dimensions of the band node.
///
/// Permute FirstDim and SecondDim dimensions of the Node.
///
/// @param Node The band node to be modified.
/// @param FirstDim The first dimension to be permuted.
/// @param SecondDim The second dimension to be permuted.
static isl::schedule_node permuteBandNodeDimensions(isl::schedule_node Node,
unsigned FirstDim,
unsigned SecondDim) {
assert(isl_schedule_node_get_type(Node.get()) == isl_schedule_node_band &&
isl_schedule_node_band_n_member(Node.get()) >
std::max(FirstDim, SecondDim));
auto PartialSchedule =
isl::manage(isl_schedule_node_band_get_partial_schedule(Node.get()));
auto PartialScheduleFirstDim = PartialSchedule.get_union_pw_aff(FirstDim);
auto PartialScheduleSecondDim = PartialSchedule.get_union_pw_aff(SecondDim);
PartialSchedule =
PartialSchedule.set_union_pw_aff(SecondDim, PartialScheduleFirstDim);
PartialSchedule =
PartialSchedule.set_union_pw_aff(FirstDim, PartialScheduleSecondDim);
Node = isl::manage(isl_schedule_node_delete(Node.release()));
return Node.insert_partial_schedule(PartialSchedule);
}
isl::schedule_node ScheduleTreeOptimizer::createMicroKernel(
isl::schedule_node Node, MicroKernelParamsTy MicroKernelParams) {
Node = applyRegisterTiling(Node, {MicroKernelParams.Mr, MicroKernelParams.Nr},
1);
Node = Node.parent().parent();
return permuteBandNodeDimensions(Node, 0, 1).child(0).child(0);
}
isl::schedule_node ScheduleTreeOptimizer::createMacroKernel(
isl::schedule_node Node, MacroKernelParamsTy MacroKernelParams) {
assert(isl_schedule_node_get_type(Node.get()) == isl_schedule_node_band);
if (MacroKernelParams.Mc == 1 && MacroKernelParams.Nc == 1 &&
MacroKernelParams.Kc == 1)
return Node;
int DimOutNum = isl_schedule_node_band_n_member(Node.get());
std::vector<int> TileSizes(DimOutNum, 1);
TileSizes[DimOutNum - 3] = MacroKernelParams.Mc;
TileSizes[DimOutNum - 2] = MacroKernelParams.Nc;
TileSizes[DimOutNum - 1] = MacroKernelParams.Kc;
Node = tileNode(Node, "1st level tiling", TileSizes, 1);
Node = Node.parent().parent();
Node = permuteBandNodeDimensions(Node, DimOutNum - 2, DimOutNum - 1);
Node = permuteBandNodeDimensions(Node, DimOutNum - 3, DimOutNum - 1);
return Node.child(0).child(0);
}
/// Get the size of the widest type of the matrix multiplication operands
/// in bytes, including alignment padding.
///
/// @param MMI Parameters of the matrix multiplication operands.
/// @return The size of the widest type of the matrix multiplication operands
/// in bytes, including alignment padding.
static uint64_t getMatMulAlignTypeSize(MatMulInfoTy MMI) {
auto *S = MMI.A->getStatement()->getParent();
auto &DL = S->getFunction().getParent()->getDataLayout();
auto ElementSizeA = DL.getTypeAllocSize(MMI.A->getElementType());
auto ElementSizeB = DL.getTypeAllocSize(MMI.B->getElementType());
auto ElementSizeC = DL.getTypeAllocSize(MMI.WriteToC->getElementType());
return std::max({ElementSizeA, ElementSizeB, ElementSizeC});
}
/// Get the size of the widest type of the matrix multiplication operands
/// in bits.
///
/// @param MMI Parameters of the matrix multiplication operands.
/// @return The size of the widest type of the matrix multiplication operands
/// in bits.
static uint64_t getMatMulTypeSize(MatMulInfoTy MMI) {
auto *S = MMI.A->getStatement()->getParent();
auto &DL = S->getFunction().getParent()->getDataLayout();
auto ElementSizeA = DL.getTypeSizeInBits(MMI.A->getElementType());
auto ElementSizeB = DL.getTypeSizeInBits(MMI.B->getElementType());
auto ElementSizeC = DL.getTypeSizeInBits(MMI.WriteToC->getElementType());
return std::max({ElementSizeA, ElementSizeB, ElementSizeC});
}
/// Get parameters of the BLIS micro kernel.
///
/// We choose the Mr and Nr parameters of the micro kernel to be large enough
/// such that no stalls caused by the combination of latencies and dependencies
/// are introduced during the updates of the resulting matrix of the matrix
/// multiplication. However, they should also be as small as possible to
/// release more registers for entries of multiplied matrices.
///
/// @param TTI Target Transform Info.
/// @param MMI Parameters of the matrix multiplication operands.
/// @return The structure of type MicroKernelParamsTy.
/// @see MicroKernelParamsTy
static struct MicroKernelParamsTy
getMicroKernelParams(const TargetTransformInfo *TTI, MatMulInfoTy MMI) {
assert(TTI && "The target transform info should be provided.");
// Nvec - Number of double-precision floating-point numbers that can be hold
// by a vector register. Use 2 by default.
long RegisterBitwidth = VectorRegisterBitwidth;
if (RegisterBitwidth == -1)
RegisterBitwidth = TTI->getRegisterBitWidth(true);
auto ElementSize = getMatMulTypeSize(MMI);
assert(ElementSize > 0 && "The element size of the matrix multiplication "
"operands should be greater than zero.");
auto Nvec = RegisterBitwidth / ElementSize;
if (Nvec == 0)
Nvec = 2;
int Nr =
ceil(sqrt(Nvec * LatencyVectorFma * ThroughputVectorFma) / Nvec) * Nvec;
int Mr = ceil(Nvec * LatencyVectorFma * ThroughputVectorFma / Nr);
return {Mr, Nr};
}
namespace {
/// Determine parameters of the target cache.
///
/// @param TTI Target Transform Info.
void getTargetCacheParameters(const llvm::TargetTransformInfo *TTI) {
auto L1DCache = llvm::TargetTransformInfo::CacheLevel::L1D;
auto L2DCache = llvm::TargetTransformInfo::CacheLevel::L2D;
if (FirstCacheLevelSize == -1) {
if (TTI->getCacheSize(L1DCache).hasValue())
FirstCacheLevelSize = TTI->getCacheSize(L1DCache).getValue();
else
FirstCacheLevelSize = static_cast<int>(FirstCacheLevelDefaultSize);
}
if (SecondCacheLevelSize == -1) {
if (TTI->getCacheSize(L2DCache).hasValue())
SecondCacheLevelSize = TTI->getCacheSize(L2DCache).getValue();
else
SecondCacheLevelSize = static_cast<int>(SecondCacheLevelDefaultSize);
}
if (FirstCacheLevelAssociativity == -1) {
if (TTI->getCacheAssociativity(L1DCache).hasValue())
FirstCacheLevelAssociativity =
TTI->getCacheAssociativity(L1DCache).getValue();
else
FirstCacheLevelAssociativity =
static_cast<int>(FirstCacheLevelDefaultAssociativity);
}
if (SecondCacheLevelAssociativity == -1) {
if (TTI->getCacheAssociativity(L2DCache).hasValue())
SecondCacheLevelAssociativity =
TTI->getCacheAssociativity(L2DCache).getValue();
else
SecondCacheLevelAssociativity =
static_cast<int>(SecondCacheLevelDefaultAssociativity);
}
}
} // namespace
/// Get parameters of the BLIS macro kernel.
///
/// During the computation of matrix multiplication, blocks of partitioned
/// matrices are mapped to different layers of the memory hierarchy.
/// To optimize data reuse, blocks should be ideally kept in cache between
/// iterations. Since parameters of the macro kernel determine sizes of these
/// blocks, there are upper and lower bounds on these parameters.
///
/// @param TTI Target Transform Info.
/// @param MicroKernelParams Parameters of the micro-kernel
/// to be taken into account.
/// @param MMI Parameters of the matrix multiplication operands.
/// @return The structure of type MacroKernelParamsTy.
/// @see MacroKernelParamsTy
/// @see MicroKernelParamsTy
static struct MacroKernelParamsTy
getMacroKernelParams(const llvm::TargetTransformInfo *TTI,
const MicroKernelParamsTy &MicroKernelParams,
MatMulInfoTy MMI) {
getTargetCacheParameters(TTI);
// According to www.cs.utexas.edu/users/flame/pubs/TOMS-BLIS-Analytical.pdf,
// it requires information about the first two levels of a cache to determine
// all the parameters of a macro-kernel. It also checks that an associativity
// degree of a cache level is greater than two. Otherwise, another algorithm
// for determination of the parameters should be used.
if (!(MicroKernelParams.Mr > 0 && MicroKernelParams.Nr > 0 &&
FirstCacheLevelSize > 0 && SecondCacheLevelSize > 0 &&
FirstCacheLevelAssociativity > 2 && SecondCacheLevelAssociativity > 2))
return {1, 1, 1};
// The quotient should be greater than zero.
if (PollyPatternMatchingNcQuotient <= 0)
return {1, 1, 1};
int Car = floor(
(FirstCacheLevelAssociativity - 1) /
(1 + static_cast<double>(MicroKernelParams.Nr) / MicroKernelParams.Mr));
// Car can be computed to be zero since it is floor to int.
// On Mac OS, division by 0 does not raise a signal. This causes negative
// tile sizes to be computed. Prevent division by Cac==0 by early returning
// if this happens.
if (Car == 0)
return {1, 1, 1};
auto ElementSize = getMatMulAlignTypeSize(MMI);
assert(ElementSize > 0 && "The element size of the matrix multiplication "
"operands should be greater than zero.");
int Kc = (Car * FirstCacheLevelSize) /
(MicroKernelParams.Mr * FirstCacheLevelAssociativity * ElementSize);
double Cac =
static_cast<double>(Kc * ElementSize * SecondCacheLevelAssociativity) /
SecondCacheLevelSize;
int Mc = floor((SecondCacheLevelAssociativity - 2) / Cac);
int Nc = PollyPatternMatchingNcQuotient * MicroKernelParams.Nr;
assert(Mc > 0 && Nc > 0 && Kc > 0 &&
"Matrix block sizes should be greater than zero");
return {Mc, Nc, Kc};
}
/// Create an access relation that is specific to
/// the matrix multiplication pattern.
///
/// Create an access relation of the following form:
/// [O0, O1, O2, O3, O4, O5, O6, O7, O8] -> [OI, O5, OJ]
/// where I is @p FirstDim, J is @p SecondDim.
///
/// It can be used, for example, to create relations that helps to consequently
/// access elements of operands of a matrix multiplication after creation of
/// the BLIS micro and macro kernels.
///
/// @see ScheduleTreeOptimizer::createMicroKernel
/// @see ScheduleTreeOptimizer::createMacroKernel
///
/// Subsequently, the described access relation is applied to the range of
/// @p MapOldIndVar, that is used to map original induction variables to
/// the ones, which are produced by schedule transformations. It helps to
/// define relations using a new space and, at the same time, keep them
/// in the original one.
///
/// @param MapOldIndVar The relation, which maps original induction variables
/// to the ones, which are produced by schedule
/// transformations.
/// @param FirstDim, SecondDim The input dimensions that are used to define
/// the specified access relation.
/// @return The specified access relation.
isl::map getMatMulAccRel(isl::map MapOldIndVar, unsigned FirstDim,
unsigned SecondDim) {
auto AccessRelSpace = isl::space(MapOldIndVar.get_ctx(), 0, 9, 3);
auto AccessRel = isl::map::universe(AccessRelSpace);
AccessRel = AccessRel.equate(isl::dim::in, FirstDim, isl::dim::out, 0);
AccessRel = AccessRel.equate(isl::dim::in, 5, isl::dim::out, 1);
AccessRel = AccessRel.equate(isl::dim::in, SecondDim, isl::dim::out, 2);
return MapOldIndVar.apply_range(AccessRel);
}
isl::schedule_node createExtensionNode(isl::schedule_node Node,
isl::map ExtensionMap) {
auto Extension = isl::union_map(ExtensionMap);
auto NewNode = isl::schedule_node::from_extension(Extension);
return Node.graft_before(NewNode);
}
/// Apply the packing transformation.
///
/// The packing transformation can be described as a data-layout
/// transformation that requires to introduce a new array, copy data
/// to the array, and change memory access locations to reference the array.
/// It can be used to ensure that elements of the new array are read in-stride
/// access, aligned to cache lines boundaries, and preloaded into certain cache
/// levels.
///
/// As an example let us consider the packing of the array A that would help
/// to read its elements with in-stride access. An access to the array A
/// is represented by an access relation that has the form
/// S[i, j, k] -> A[i, k]. The scheduling function of the SCoP statement S has
/// the form S[i,j, k] -> [floor((j mod Nc) / Nr), floor((i mod Mc) / Mr),
/// k mod Kc, j mod Nr, i mod Mr].
///
/// To ensure that elements of the array A are read in-stride access, we add
/// a new array Packed_A[Mc/Mr][Kc][Mr] to the SCoP, using
/// Scop::createScopArrayInfo, change the access relation
/// S[i, j, k] -> A[i, k] to
/// S[i, j, k] -> Packed_A[floor((i mod Mc) / Mr), k mod Kc, i mod Mr], using
/// MemoryAccess::setNewAccessRelation, and copy the data to the array, using
/// the copy statement created by Scop::addScopStmt.
///
/// @param Node The schedule node to be optimized.
/// @param MapOldIndVar The relation, which maps original induction variables
/// to the ones, which are produced by schedule
/// transformations.
/// @param MicroParams, MacroParams Parameters of the BLIS kernel
/// to be taken into account.
/// @param MMI Parameters of the matrix multiplication operands.
/// @return The optimized schedule node.
static isl::schedule_node
optimizeDataLayoutMatrMulPattern(isl::schedule_node Node, isl::map MapOldIndVar,
MicroKernelParamsTy MicroParams,
MacroKernelParamsTy MacroParams,
MatMulInfoTy &MMI) {
auto InputDimsId = MapOldIndVar.get_tuple_id(isl::dim::in);
auto *Stmt = static_cast<ScopStmt *>(InputDimsId.get_user());
// Create a copy statement that corresponds to the memory access to the
// matrix B, the second operand of the matrix multiplication.
Node = Node.parent().parent().parent().parent().parent().parent();
Node = isl::manage(isl_schedule_node_band_split(Node.release(), 2)).child(0);
auto AccRel = getMatMulAccRel(MapOldIndVar, 3, 7);
unsigned FirstDimSize = MacroParams.Nc / MicroParams.Nr;
unsigned SecondDimSize = MacroParams.Kc;
unsigned ThirdDimSize = MicroParams.Nr;
auto *SAI = Stmt->getParent()->createScopArrayInfo(
MMI.B->getElementType(), "Packed_B",
{FirstDimSize, SecondDimSize, ThirdDimSize});
AccRel = AccRel.set_tuple_id(isl::dim::out, SAI->getBasePtrId());
auto OldAcc = MMI.B->getLatestAccessRelation();
MMI.B->setNewAccessRelation(AccRel);
auto ExtMap = MapOldIndVar.project_out(isl::dim::out, 2,
MapOldIndVar.dim(isl::dim::out) - 2);
ExtMap = ExtMap.reverse();
ExtMap = ExtMap.fix_si(isl::dim::out, MMI.i, 0);
auto Domain = Stmt->getDomain();
// Restrict the domains of the copy statements to only execute when also its
// originating statement is executed.
auto DomainId = Domain.get_tuple_id();
auto *NewStmt = Stmt->getParent()->addScopStmt(
OldAcc, MMI.B->getLatestAccessRelation(), Domain);
ExtMap = ExtMap.set_tuple_id(isl::dim::out, DomainId);
ExtMap = ExtMap.intersect_range(Domain);
ExtMap = ExtMap.set_tuple_id(isl::dim::out, NewStmt->getDomainId());
Node = createExtensionNode(Node, ExtMap);
// Create a copy statement that corresponds to the memory access
// to the matrix A, the first operand of the matrix multiplication.
Node = Node.child(0);
AccRel = getMatMulAccRel(MapOldIndVar, 4, 6);
FirstDimSize = MacroParams.Mc / MicroParams.Mr;
ThirdDimSize = MicroParams.Mr;
SAI = Stmt->getParent()->createScopArrayInfo(
MMI.A->getElementType(), "Packed_A",
{FirstDimSize, SecondDimSize, ThirdDimSize});
AccRel = AccRel.set_tuple_id(isl::dim::out, SAI->getBasePtrId());
OldAcc = MMI.A->getLatestAccessRelation();
MMI.A->setNewAccessRelation(AccRel);
ExtMap = MapOldIndVar.project_out(isl::dim::out, 3,
MapOldIndVar.dim(isl::dim::out) - 3);
ExtMap = ExtMap.reverse();
ExtMap = ExtMap.fix_si(isl::dim::out, MMI.j, 0);
NewStmt = Stmt->getParent()->addScopStmt(
OldAcc, MMI.A->getLatestAccessRelation(), Domain);
// Restrict the domains of the copy statements to only execute when also its
// originating statement is executed.
ExtMap = ExtMap.set_tuple_id(isl::dim::out, DomainId);
ExtMap = ExtMap.intersect_range(Domain);
ExtMap = ExtMap.set_tuple_id(isl::dim::out, NewStmt->getDomainId());
Node = createExtensionNode(Node, ExtMap);
return Node.child(0).child(0).child(0).child(0).child(0);
}
/// Get a relation mapping induction variables produced by schedule
/// transformations to the original ones.
///
/// @param Node The schedule node produced as the result of creation
/// of the BLIS kernels.
/// @param MicroKernelParams, MacroKernelParams Parameters of the BLIS kernel
/// to be taken into account.
/// @return The relation mapping original induction variables to the ones
/// produced by schedule transformation.
/// @see ScheduleTreeOptimizer::createMicroKernel
/// @see ScheduleTreeOptimizer::createMacroKernel
/// @see getMacroKernelParams
isl::map
getInductionVariablesSubstitution(isl::schedule_node Node,
MicroKernelParamsTy MicroKernelParams,
MacroKernelParamsTy MacroKernelParams) {
auto Child = Node.child(0);
auto UnMapOldIndVar = Child.get_prefix_schedule_union_map();
auto MapOldIndVar = isl::map::from_union_map(UnMapOldIndVar);
if (MapOldIndVar.dim(isl::dim::out) > 9)
return MapOldIndVar.project_out(isl::dim::out, 0,
MapOldIndVar.dim(isl::dim::out) - 9);
return MapOldIndVar;
}
/// Isolate a set of partial tile prefixes and unroll the isolated part.
///
/// The set should ensure that it contains only partial tile prefixes that have
/// exactly Mr x Nr iterations of the two innermost loops produced by
/// the optimization of the matrix multiplication. Mr and Nr are parameters of
/// the micro-kernel.
///
/// In case of parametric bounds, this helps to auto-vectorize the unrolled
/// innermost loops, using the SLP vectorizer.
///
/// @param Node The schedule node to be modified.
/// @param MicroKernelParams Parameters of the micro-kernel
/// to be taken into account.
/// @return The modified isl_schedule_node.
static isl::schedule_node
isolateAndUnrollMatMulInnerLoops(isl::schedule_node Node,
struct MicroKernelParamsTy MicroKernelParams) {
isl::schedule_node Child = Node.get_child(0);
isl::union_map UnMapOldIndVar = Child.get_prefix_schedule_relation();
isl::set Prefix = isl::map::from_union_map(UnMapOldIndVar).range();
unsigned Dims = Prefix.dim(isl::dim::set);
Prefix = Prefix.project_out(isl::dim::set, Dims - 1, 1);
Prefix = getPartialTilePrefixes(Prefix, MicroKernelParams.Nr);
Prefix = getPartialTilePrefixes(Prefix, MicroKernelParams.Mr);
isl::union_set IsolateOption =
getIsolateOptions(Prefix.add_dims(isl::dim::set, 3), 3);
isl::ctx Ctx = Node.get_ctx();
auto Options = IsolateOption.unite(getDimOptions(Ctx, "unroll"));
Options = Options.unite(getUnrollIsolatedSetOptions(Ctx));
Node = Node.band_set_ast_build_options(Options);
Node = Node.parent().parent().parent();
IsolateOption = getIsolateOptions(Prefix, 3);
Options = IsolateOption.unite(getDimOptions(Ctx, "separate"));
Node = Node.band_set_ast_build_options(Options);
Node = Node.child(0).child(0).child(0);
return Node;
}
/// Mark @p BasePtr with "Inter iteration alias-free" mark node.
///
/// @param Node The child of the mark node to be inserted.
/// @param BasePtr The pointer to be marked.
/// @return The modified isl_schedule_node.
static isl::schedule_node markInterIterationAliasFree(isl::schedule_node Node,
Value *BasePtr) {
if (!BasePtr)
return Node;
auto Id =
isl::id::alloc(Node.get_ctx(), "Inter iteration alias-free", BasePtr);
return Node.insert_mark(Id).child(0);
}
/// Insert "Loop Vectorizer Disabled" mark node.
///
/// @param Node The child of the mark node to be inserted.
/// @return The modified isl_schedule_node.
static isl::schedule_node markLoopVectorizerDisabled(isl::schedule_node Node) {
auto Id = isl::id::alloc(Node.get_ctx(), "Loop Vectorizer Disabled", nullptr);
return Node.insert_mark(Id).child(0);
}
/// Restore the initial ordering of dimensions of the band node
///
/// In case the band node represents all the dimensions of the iteration
/// domain, recreate the band node to restore the initial ordering of the
/// dimensions.
///
/// @param Node The band node to be modified.
/// @return The modified schedule node.
static isl::schedule_node
getBandNodeWithOriginDimOrder(isl::schedule_node Node) {
assert(isl_schedule_node_get_type(Node.get()) == isl_schedule_node_band);
if (isl_schedule_node_get_type(Node.child(0).get()) != isl_schedule_node_leaf)
return Node;
auto Domain = Node.get_universe_domain();
assert(isl_union_set_n_set(Domain.get()) == 1);
if (Node.get_schedule_depth() != 0 ||
(isl::set(Domain).dim(isl::dim::set) !=
isl_schedule_node_band_n_member(Node.get())))
return Node;
Node = isl::manage(isl_schedule_node_delete(Node.copy()));
auto PartialSchedulePwAff = Domain.identity_union_pw_multi_aff();
auto PartialScheduleMultiPwAff =
isl::multi_union_pw_aff(PartialSchedulePwAff);
PartialScheduleMultiPwAff =
PartialScheduleMultiPwAff.reset_tuple_id(isl::dim::set);
return Node.insert_partial_schedule(PartialScheduleMultiPwAff);
}
isl::schedule_node
ScheduleTreeOptimizer::optimizeMatMulPattern(isl::schedule_node Node,
const TargetTransformInfo *TTI,
MatMulInfoTy &MMI) {
assert(TTI && "The target transform info should be provided.");
Node = markInterIterationAliasFree(
Node, MMI.WriteToC->getLatestScopArrayInfo()->getBasePtr());
int DimOutNum = isl_schedule_node_band_n_member(Node.get());
assert(DimOutNum > 2 && "In case of the matrix multiplication the loop nest "
"and, consequently, the corresponding scheduling "
"functions have at least three dimensions.");
Node = getBandNodeWithOriginDimOrder(Node);
Node = permuteBandNodeDimensions(Node, MMI.i, DimOutNum - 3);
int NewJ = MMI.j == DimOutNum - 3 ? MMI.i : MMI.j;
int NewK = MMI.k == DimOutNum - 3 ? MMI.i : MMI.k;
Node = permuteBandNodeDimensions(Node, NewJ, DimOutNum - 2);
NewK = NewK == DimOutNum - 2 ? NewJ : NewK;
Node = permuteBandNodeDimensions(Node, NewK, DimOutNum - 1);
auto MicroKernelParams = getMicroKernelParams(TTI, MMI);
auto MacroKernelParams = getMacroKernelParams(TTI, MicroKernelParams, MMI);
Node = createMacroKernel(Node, MacroKernelParams);
Node = createMicroKernel(Node, MicroKernelParams);
if (MacroKernelParams.Mc == 1 || MacroKernelParams.Nc == 1 ||
MacroKernelParams.Kc == 1)
return Node;
auto MapOldIndVar = getInductionVariablesSubstitution(Node, MicroKernelParams,
MacroKernelParams);
if (!MapOldIndVar)
return Node;
Node = markLoopVectorizerDisabled(Node.parent()).child(0);
Node = isolateAndUnrollMatMulInnerLoops(Node, MicroKernelParams);
return optimizeDataLayoutMatrMulPattern(Node, MapOldIndVar, MicroKernelParams,
MacroKernelParams, MMI);
}
bool ScheduleTreeOptimizer::isMatrMultPattern(isl::schedule_node Node,
const Dependences *D,
MatMulInfoTy &MMI) {
auto PartialSchedule = isl::manage(
isl_schedule_node_band_get_partial_schedule_union_map(Node.get()));
Node = Node.child(0);
auto LeafType = isl_schedule_node_get_type(Node.get());
Node = Node.parent();
if (LeafType != isl_schedule_node_leaf ||
isl_schedule_node_band_n_member(Node.get()) < 3 ||
Node.get_schedule_depth() != 0 ||
isl_union_map_n_map(PartialSchedule.get()) != 1)
return false;
auto NewPartialSchedule = isl::map::from_union_map(PartialSchedule);
if (containsMatrMult(NewPartialSchedule, D, MMI))
return true;
return false;
}
__isl_give isl_schedule_node *
ScheduleTreeOptimizer::optimizeBand(__isl_take isl_schedule_node *Node,
void *User) {
if (!isTileableBandNode(isl::manage_copy(Node)))
return Node;
const OptimizerAdditionalInfoTy *OAI =
static_cast<const OptimizerAdditionalInfoTy *>(User);
MatMulInfoTy MMI;
if (PMBasedOpts && User &&
isMatrMultPattern(isl::manage_copy(Node), OAI->D, MMI)) {
LLVM_DEBUG(dbgs() << "The matrix multiplication pattern was detected\n");
MatMulOpts++;
return optimizeMatMulPattern(isl::manage(Node), OAI->TTI, MMI).release();
}
return standardBandOpts(isl::manage(Node), User).release();
}
isl::schedule
ScheduleTreeOptimizer::optimizeSchedule(isl::schedule Schedule,
const OptimizerAdditionalInfoTy *OAI) {
auto Root = Schedule.get_root();
Root = optimizeScheduleNode(Root, OAI);
return Root.get_schedule();
}
isl::schedule_node ScheduleTreeOptimizer::optimizeScheduleNode(
isl::schedule_node Node, const OptimizerAdditionalInfoTy *OAI) {
Node = isl::manage(isl_schedule_node_map_descendant_bottom_up(
Node.release(), optimizeBand,
const_cast<void *>(static_cast<const void *>(OAI))));
return Node;
}
bool ScheduleTreeOptimizer::isProfitableSchedule(Scop &S,
isl::schedule NewSchedule) {
// To understand if the schedule has been optimized we check if the schedule
// has changed at all.
// TODO: We can improve this by tracking if any necessarily beneficial
// transformations have been performed. This can e.g. be tiling, loop
// interchange, or ...) We can track this either at the place where the
// transformation has been performed or, in case of automatic ILP based
// optimizations, by comparing (yet to be defined) performance metrics
// before/after the scheduling optimizer
// (e.g., #stride-one accesses)
if (S.containsExtensionNode(NewSchedule))
return true;
auto NewScheduleMap = NewSchedule.get_map();
auto OldSchedule = S.getSchedule();
assert(OldSchedule && "Only IslScheduleOptimizer can insert extension nodes "
"that make Scop::getSchedule() return nullptr.");
bool changed = !OldSchedule.is_equal(NewScheduleMap);
return changed;
}
namespace {
class IslScheduleOptimizer : public ScopPass {
public:
static char ID;
explicit IslScheduleOptimizer() : ScopPass(ID) {}
~IslScheduleOptimizer() override { isl_schedule_free(LastSchedule); }
/// Optimize the schedule of the SCoP @p S.
bool runOnScop(Scop &S) override;
/// Print the new schedule for the SCoP @p S.
void printScop(raw_ostream &OS, Scop &S) const override;
/// Register all analyses and transformation required.
void getAnalysisUsage(AnalysisUsage &AU) const override;
/// Release the internal memory.
void releaseMemory() override {
isl_schedule_free(LastSchedule);
LastSchedule = nullptr;
}
private:
isl_schedule *LastSchedule = nullptr;
};
} // namespace
char IslScheduleOptimizer::ID = 0;
/// Collect statistics for the schedule tree.
///
/// @param Schedule The schedule tree to analyze. If not a schedule tree it is
/// ignored.
/// @param Version The version of the schedule tree that is analyzed.
/// 0 for the original schedule tree before any transformation.
/// 1 for the schedule tree after isl's rescheduling.
/// 2 for the schedule tree after optimizations are applied
/// (tiling, pattern matching)
static void walkScheduleTreeForStatistics(isl::schedule Schedule, int Version) {
auto Root = Schedule.get_root();
if (!Root)
return;
isl_schedule_node_foreach_descendant_top_down(
Root.get(),
[](__isl_keep isl_schedule_node *nodeptr, void *user) -> isl_bool {
isl::schedule_node Node = isl::manage_copy(nodeptr);
int Version = *static_cast<int *>(user);
switch (isl_schedule_node_get_type(Node.get())) {
case isl_schedule_node_band: {
NumBands[Version]++;
if (isl_schedule_node_band_get_permutable(Node.get()) ==
isl_bool_true)
NumPermutable[Version]++;
int CountMembers = isl_schedule_node_band_n_member(Node.get());
NumBandMembers[Version] += CountMembers;
for (int i = 0; i < CountMembers; i += 1) {
if (Node.band_member_get_coincident(i))
NumCoincident[Version]++;
}
break;
}
case isl_schedule_node_filter:
NumFilters[Version]++;
break;
case isl_schedule_node_extension:
NumExtension[Version]++;
break;
default:
break;
}
return isl_bool_true;
},
&Version);
}
bool IslScheduleOptimizer::runOnScop(Scop &S) {
// Skip SCoPs in case they're already optimised by PPCGCodeGeneration
if (S.isToBeSkipped())
return false;
// Skip empty SCoPs but still allow code generation as it will delete the
// loops present but not needed.
if (S.getSize() == 0) {
S.markAsOptimized();
return false;
}
const Dependences &D =
getAnalysis<DependenceInfo>().getDependences(Dependences::AL_Statement);
if (D.getSharedIslCtx() != S.getSharedIslCtx()) {
LLVM_DEBUG(dbgs() << "DependenceInfo for another SCoP/isl_ctx\n");
return false;
}
if (!D.hasValidDependences())
return false;
isl_schedule_free(LastSchedule);
LastSchedule = nullptr;
// Build input data.
int ValidityKinds =
Dependences::TYPE_RAW | Dependences::TYPE_WAR | Dependences::TYPE_WAW;
int ProximityKinds;
if (OptimizeDeps == "all")
ProximityKinds =
Dependences::TYPE_RAW | Dependences::TYPE_WAR | Dependences::TYPE_WAW;
else if (OptimizeDeps == "raw")
ProximityKinds = Dependences::TYPE_RAW;
else {
errs() << "Do not know how to optimize for '" << OptimizeDeps << "'"
<< " Falling back to optimizing all dependences.\n";
ProximityKinds =
Dependences::TYPE_RAW | Dependences::TYPE_WAR | Dependences::TYPE_WAW;
}
isl::union_set Domain = S.getDomains();
if (!Domain)
return false;
ScopsProcessed++;
walkScheduleTreeForStatistics(S.getScheduleTree(), 0);
isl::union_map Validity = D.getDependences(ValidityKinds);
isl::union_map Proximity = D.getDependences(ProximityKinds);
// Simplify the dependences by removing the constraints introduced by the
// domains. This can speed up the scheduling time significantly, as large
// constant coefficients will be removed from the dependences. The
// introduction of some additional dependences reduces the possible
// transformations, but in most cases, such transformation do not seem to be
// interesting anyway. In some cases this option may stop the scheduler to
// find any schedule.
if (SimplifyDeps == "yes") {
Validity = Validity.gist_domain(Domain);
Validity = Validity.gist_range(Domain);
Proximity = Proximity.gist_domain(Domain);
Proximity = Proximity.gist_range(Domain);
} else if (SimplifyDeps != "no") {
errs() << "warning: Option -polly-opt-simplify-deps should either be 'yes' "
"or 'no'. Falling back to default: 'yes'\n";
}
LLVM_DEBUG(dbgs() << "\n\nCompute schedule from: ");
LLVM_DEBUG(dbgs() << "Domain := " << Domain << ";\n");
LLVM_DEBUG(dbgs() << "Proximity := " << Proximity << ";\n");
LLVM_DEBUG(dbgs() << "Validity := " << Validity << ";\n");
unsigned IslSerializeSCCs;
if (FusionStrategy == "max") {
IslSerializeSCCs = 0;
} else if (FusionStrategy == "min") {
IslSerializeSCCs = 1;
} else {
errs() << "warning: Unknown fusion strategy. Falling back to maximal "
"fusion.\n";
IslSerializeSCCs = 0;
}
int IslMaximizeBands;
if (MaximizeBandDepth == "yes") {
IslMaximizeBands = 1;
} else if (MaximizeBandDepth == "no") {
IslMaximizeBands = 0;
} else {
errs() << "warning: Option -polly-opt-maximize-bands should either be 'yes'"
" or 'no'. Falling back to default: 'yes'\n";
IslMaximizeBands = 1;
}
int IslOuterCoincidence;
if (OuterCoincidence == "yes") {
IslOuterCoincidence = 1;
} else if (OuterCoincidence == "no") {
IslOuterCoincidence = 0;
} else {
errs() << "warning: Option -polly-opt-outer-coincidence should either be "
"'yes' or 'no'. Falling back to default: 'no'\n";
IslOuterCoincidence = 0;
}
isl_ctx *Ctx = S.getIslCtx().get();
isl_options_set_schedule_outer_coincidence(Ctx, IslOuterCoincidence);
isl_options_set_schedule_serialize_sccs(Ctx, IslSerializeSCCs);
isl_options_set_schedule_maximize_band_depth(Ctx, IslMaximizeBands);
isl_options_set_schedule_max_constant_term(Ctx, MaxConstantTerm);
isl_options_set_schedule_max_coefficient(Ctx, MaxCoefficient);
isl_options_set_tile_scale_tile_loops(Ctx, 0);
auto OnErrorStatus = isl_options_get_on_error(Ctx);
isl_options_set_on_error(Ctx, ISL_ON_ERROR_CONTINUE);
auto SC = isl::schedule_constraints::on_domain(Domain);
SC = SC.set_proximity(Proximity);
SC = SC.set_validity(Validity);
SC = SC.set_coincidence(Validity);
auto Schedule = SC.compute_schedule();
isl_options_set_on_error(Ctx, OnErrorStatus);
walkScheduleTreeForStatistics(Schedule, 1);
// In cases the scheduler is not able to optimize the code, we just do not
// touch the schedule.
if (!Schedule)
return false;
ScopsRescheduled++;
LLVM_DEBUG({
auto *P = isl_printer_to_str(Ctx);
P = isl_printer_set_yaml_style(P, ISL_YAML_STYLE_BLOCK);
P = isl_printer_print_schedule(P, Schedule.get());
auto *str = isl_printer_get_str(P);
dbgs() << "NewScheduleTree: \n" << str << "\n";
free(str);
isl_printer_free(P);
});
Function &F = S.getFunction();
auto *TTI = &getAnalysis<TargetTransformInfoWrapperPass>().getTTI(F);
const OptimizerAdditionalInfoTy OAI = {TTI, const_cast<Dependences *>(&D)};
auto NewSchedule = ScheduleTreeOptimizer::optimizeSchedule(Schedule, &OAI);
walkScheduleTreeForStatistics(NewSchedule, 2);
if (!ScheduleTreeOptimizer::isProfitableSchedule(S, NewSchedule))
return false;
auto ScopStats = S.getStatistics();
ScopsOptimized++;
NumAffineLoopsOptimized += ScopStats.NumAffineLoops;
NumBoxedLoopsOptimized += ScopStats.NumBoxedLoops;
S.setScheduleTree(NewSchedule);
S.markAsOptimized();
if (OptimizedScops)
errs() << S;
return false;
}
void IslScheduleOptimizer::printScop(raw_ostream &OS, Scop &) const {
isl_printer *p;
char *ScheduleStr;
OS << "Calculated schedule:\n";
if (!LastSchedule) {
OS << "n/a\n";
return;
}
p = isl_printer_to_str(isl_schedule_get_ctx(LastSchedule));
p = isl_printer_print_schedule(p, LastSchedule);
ScheduleStr = isl_printer_get_str(p);
isl_printer_free(p);
OS << ScheduleStr << "\n";
}
void IslScheduleOptimizer::getAnalysisUsage(AnalysisUsage &AU) const {
ScopPass::getAnalysisUsage(AU);
AU.addRequired<DependenceInfo>();
AU.addRequired<TargetTransformInfoWrapperPass>();
AU.addPreserved<DependenceInfo>();
}
Pass *polly::createIslScheduleOptimizerPass() {
return new IslScheduleOptimizer();
}
INITIALIZE_PASS_BEGIN(IslScheduleOptimizer, "polly-opt-isl",
"Polly - Optimize schedule of SCoP", false, false);
INITIALIZE_PASS_DEPENDENCY(DependenceInfo);
INITIALIZE_PASS_DEPENDENCY(ScopInfoRegionPass);
INITIALIZE_PASS_DEPENDENCY(TargetTransformInfoWrapperPass);
INITIALIZE_PASS_END(IslScheduleOptimizer, "polly-opt-isl",
"Polly - Optimize schedule of SCoP", false, false)