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+//===- SyncDependenceAnalysis.cpp - Divergent Branch Dependence Calculation
+//--===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+//
+// This file implements an algorithm that returns for a divergent branch
+// the set of basic blocks whose phi nodes become divergent due to divergent
+// control. These are the blocks that are reachable by two disjoint paths from
+// the branch or loop exits that have a reaching path that is disjoint from a
+// path to the loop latch.
+//
+// The SyncDependenceAnalysis is used in the DivergenceAnalysis to model
+// control-induced divergence in phi nodes.
+//
+// -- Summary --
+// The SyncDependenceAnalysis lazily computes sync dependences [3].
+// The analysis evaluates the disjoint path criterion [2] by a reduction
+// to SSA construction. The SSA construction algorithm is implemented as
+// a simple data-flow analysis [1].
+//
+// [1] "A Simple, Fast Dominance Algorithm", SPI '01, Cooper, Harvey and Kennedy
+// [2] "Efficiently Computing Static Single Assignment Form
+// and the Control Dependence Graph", TOPLAS '91,
+// Cytron, Ferrante, Rosen, Wegman and Zadeck
+// [3] "Improving Performance of OpenCL on CPUs", CC '12, Karrenberg and Hack
+// [4] "Divergence Analysis", TOPLAS '13, Sampaio, Souza, Collange and Pereira
+//
+// -- Sync dependence --
+// Sync dependence [4] characterizes the control flow aspect of the
+// propagation of branch divergence. For example,
+//
+// %cond = icmp slt i32 %tid, 10
+// br i1 %cond, label %then, label %else
+// then:
+// br label %merge
+// else:
+// br label %merge
+// merge:
+// %a = phi i32 [ 0, %then ], [ 1, %else ]
+//
+// Suppose %tid holds the thread ID. Although %a is not data dependent on %tid
+// because %tid is not on its use-def chains, %a is sync dependent on %tid
+// because the branch "br i1 %cond" depends on %tid and affects which value %a
+// is assigned to.
+//
+// -- Reduction to SSA construction --
+// There are two disjoint paths from A to X, if a certain variant of SSA
+// construction places a phi node in X under the following set-up scheme [2].
+//
+// This variant of SSA construction ignores incoming undef values.
+// That is paths from the entry without a definition do not result in
+// phi nodes.
+//
+// entry
+// / \
+// A \
+// / \ Y
+// B C /
+// \ / \ /
+// D E
+// \ /
+// F
+// Assume that A contains a divergent branch. We are interested
+// in the set of all blocks where each block is reachable from A
+// via two disjoint paths. This would be the set {D, F} in this
+// case.
+// To generally reduce this query to SSA construction we introduce
+// a virtual variable x and assign to x different values in each
+// successor block of A.
+// entry
+// / \
+// A \
+// / \ Y
+// x = 0 x = 1 /
+// \ / \ /
+// D E
+// \ /
+// F
+// Our flavor of SSA construction for x will construct the following
+// entry
+// / \
+// A \
+// / \ Y
+// x0 = 0 x1 = 1 /
+// \ / \ /
+// x2=phi E
+// \ /
+// x3=phi
+// The blocks D and F contain phi nodes and are thus each reachable
+// by two disjoins paths from A.
+//
+// -- Remarks --
+// In case of loop exits we need to check the disjoint path criterion for loops
+// [2]. To this end, we check whether the definition of x differs between the
+// loop exit and the loop header (_after_ SSA construction).
+//
+//===----------------------------------------------------------------------===//
+#include "llvm/ADT/PostOrderIterator.h"
+#include "llvm/ADT/SmallPtrSet.h"
+#include "llvm/Analysis/PostDominators.h"
+#include "llvm/Analysis/SyncDependenceAnalysis.h"
+#include "llvm/IR/BasicBlock.h"
+#include "llvm/IR/CFG.h"
+#include "llvm/IR/Dominators.h"
+#include "llvm/IR/Function.h"
+
+#include <stack>
+#include <unordered_set>
+
+#define DEBUG_TYPE "sync-dependence"
+
+namespace llvm {
+
+ConstBlockSet SyncDependenceAnalysis::EmptyBlockSet;
+
+SyncDependenceAnalysis::SyncDependenceAnalysis(const DominatorTree &DT,
+ const PostDominatorTree &PDT,
+ const LoopInfo &LI)
+ : FuncRPOT(DT.getRoot()->getParent()), DT(DT), PDT(PDT), LI(LI) {}
+
+SyncDependenceAnalysis::~SyncDependenceAnalysis() {}
+
+using FunctionRPOT = ReversePostOrderTraversal<const Function *>;
+
+// divergence propagator for reducible CFGs
+struct DivergencePropagator {
+ const FunctionRPOT &FuncRPOT;
+ const DominatorTree &DT;
+ const PostDominatorTree &PDT;
+ const LoopInfo &LI;
+
+ // identified join points
+ std::unique_ptr<ConstBlockSet> JoinBlocks;
+
+ // reached loop exits (by a path disjoint to a path to the loop header)
+ SmallPtrSet<const BasicBlock *, 4> ReachedLoopExits;
+
+ // if DefMap[B] == C then C is the dominating definition at block B
+ // if DefMap[B] ~ undef then we haven't seen B yet
+ // if DefMap[B] == B then B is a join point of disjoint paths from X or B is
+ // an immediate successor of X (initial value).
+ using DefiningBlockMap = std::map<const BasicBlock *, const BasicBlock *>;
+ DefiningBlockMap DefMap;
+
+ // all blocks with pending visits
+ std::unordered_set<const BasicBlock *> PendingUpdates;
+
+ DivergencePropagator(const FunctionRPOT &FuncRPOT, const DominatorTree &DT,
+ const PostDominatorTree &PDT, const LoopInfo &LI)
+ : FuncRPOT(FuncRPOT), DT(DT), PDT(PDT), LI(LI),
+ JoinBlocks(new ConstBlockSet) {}
+
+ // set the definition at @block and mark @block as pending for a visit
+ void addPending(const BasicBlock &Block, const BasicBlock &DefBlock) {
+ bool WasAdded = DefMap.emplace(&Block, &DefBlock).second;
+ if (WasAdded)
+ PendingUpdates.insert(&Block);
+ }
+
+ void printDefs(raw_ostream &Out) {
+ Out << "Propagator::DefMap {\n";
+ for (const auto *Block : FuncRPOT) {
+ auto It = DefMap.find(Block);
+ Out << Block->getName() << " : ";
+ if (It == DefMap.end()) {
+ Out << "\n";
+ } else {
+ const auto *DefBlock = It->second;
+ Out << (DefBlock ? DefBlock->getName() : "<null>") << "\n";
+ }
+ }
+ Out << "}\n";
+ }
+
+ // process @succBlock with reaching definition @defBlock
+ // the original divergent branch was in @parentLoop (if any)
+ void visitSuccessor(const BasicBlock &SuccBlock, const Loop *ParentLoop,
+ const BasicBlock &DefBlock) {
+
+ // @succBlock is a loop exit
+ if (ParentLoop && !ParentLoop->contains(&SuccBlock)) {
+ DefMap.emplace(&SuccBlock, &DefBlock);
+ ReachedLoopExits.insert(&SuccBlock);
+ return;
+ }
+
+ // first reaching def?
+ auto ItLastDef = DefMap.find(&SuccBlock);
+ if (ItLastDef == DefMap.end()) {
+ addPending(SuccBlock, DefBlock);
+ return;
+ }
+
+ // a join of at least two definitions
+ if (ItLastDef->second != &DefBlock) {
+ // do we know this join already?
+ if (!JoinBlocks->insert(&SuccBlock).second)
+ return;
+
+ // update the definition
+ addPending(SuccBlock, SuccBlock);
+ }
+ }
+
+ // find all blocks reachable by two disjoint paths from @rootTerm.
+ // This method works for both divergent terminators and loops with
+ // divergent exits.
+ // @rootBlock is either the block containing the branch or the header of the
+ // divergent loop.
+ // @nodeSuccessors is the set of successors of the node (Loop or Terminator)
+ // headed by @rootBlock.
+ // @parentLoop is the parent loop of the Loop or the loop that contains the
+ // Terminator.
+ template <typename SuccessorIterable>
+ std::unique_ptr<ConstBlockSet>
+ computeJoinPoints(const BasicBlock &RootBlock,
+ SuccessorIterable NodeSuccessors, const Loop *ParentLoop, const BasicBlock * PdBoundBlock) {
+ assert(JoinBlocks);
+
+ // bootstrap with branch targets
+ for (const auto *SuccBlock : NodeSuccessors) {
+ DefMap.emplace(SuccBlock, SuccBlock);
+
+ if (ParentLoop && !ParentLoop->contains(SuccBlock)) {
+ // immediate loop exit from node.
+ ReachedLoopExits.insert(SuccBlock);
+ continue;
+ } else {
+ // regular successor
+ PendingUpdates.insert(SuccBlock);
+ }
+ }
+
+ auto ItBeginRPO = FuncRPOT.begin();
+
+ // skip until term (TODO RPOT won't let us start at @term directly)
+ for (; *ItBeginRPO != &RootBlock; ++ItBeginRPO) {}
+
+ auto ItEndRPO = FuncRPOT.end();
+ assert(ItBeginRPO != ItEndRPO);
+
+ // propagate definitions at the immediate successors of the node in RPO
+ auto ItBlockRPO = ItBeginRPO;
+ while (++ItBlockRPO != ItEndRPO && *ItBlockRPO != PdBoundBlock) {
+ const auto *Block = *ItBlockRPO;
+
+ // skip @block if not pending update
+ auto ItPending = PendingUpdates.find(Block);
+ if (ItPending == PendingUpdates.end())
+ continue;
+ PendingUpdates.erase(ItPending);
+
+ // propagate definition at @block to its successors
+ auto ItDef = DefMap.find(Block);
+ const auto *DefBlock = ItDef->second;
+ assert(DefBlock);
+
+ auto *BlockLoop = LI.getLoopFor(Block);
+ if (ParentLoop &&
+ (ParentLoop != BlockLoop && ParentLoop->contains(BlockLoop))) {
+ // if the successor is the header of a nested loop pretend its a
+ // single node with the loop's exits as successors
+ SmallVector<BasicBlock *, 4> BlockLoopExits;
+ BlockLoop->getExitBlocks(BlockLoopExits);
+ for (const auto *BlockLoopExit : BlockLoopExits) {
+ visitSuccessor(*BlockLoopExit, ParentLoop, *DefBlock);
+ }
+
+ } else {
+ // the successors are either on the same loop level or loop exits
+ for (const auto *SuccBlock : successors(Block)) {
+ visitSuccessor(*SuccBlock, ParentLoop, *DefBlock);
+ }
+ }
+ }
+
+ // We need to know the definition at the parent loop header to decide
+ // whether the definition at the header is different from the definition at
+ // the loop exits, which would indicate a divergent loop exits.
+ //
+ // A // loop header
+ // |
+ // B // nested loop header
+ // |
+ // C -> X (exit from B loop) -..-> (A latch)
+ // |
+ // D -> back to B (B latch)
+ // |
+ // proper exit from both loops
+ //
+ // D post-dominates B as it is the only proper exit from the "A loop".
+ // If C has a divergent branch, propagation will therefore stop at D.
+ // That implies that B will never receive a definition.
+ // But that definition can only be the same as at D (D itself in thise case)
+ // because all paths to anywhere have to pass through D.
+ //
+ const BasicBlock *ParentLoopHeader =
+ ParentLoop ? ParentLoop->getHeader() : nullptr;
+ if (ParentLoop && ParentLoop->contains(PdBoundBlock)) {
+ DefMap[ParentLoopHeader] = DefMap[PdBoundBlock];
+ }
+
+ // analyze reached loop exits
+ if (!ReachedLoopExits.empty()) {
+ assert(ParentLoop);
+ const auto *HeaderDefBlock = DefMap[ParentLoopHeader];
+ LLVM_DEBUG(printDefs(dbgs()));
+ assert(HeaderDefBlock && "no definition in header of carrying loop");
+
+ for (const auto *ExitBlock : ReachedLoopExits) {
+ auto ItExitDef = DefMap.find(ExitBlock);
+ assert((ItExitDef != DefMap.end()) &&
+ "no reaching def at reachable loop exit");
+ if (ItExitDef->second != HeaderDefBlock) {
+ JoinBlocks->insert(ExitBlock);
+ }
+ }
+ }
+
+ return std::move(JoinBlocks);
+ }
+};
+
+const ConstBlockSet &SyncDependenceAnalysis::join_blocks(const Loop &Loop) {
+ using LoopExitVec = SmallVector<BasicBlock *, 4>;
+ LoopExitVec LoopExits;
+ Loop.getExitBlocks(LoopExits);
+ if (LoopExits.size() < 1) {
+ return EmptyBlockSet;
+ }
+
+ // already available in cache?
+ auto ItCached = CachedLoopExitJoins.find(&Loop);
+ if (ItCached != CachedLoopExitJoins.end()) {
+ return *ItCached->second;
+ }
+
+ // dont propagte beyond the immediate post dom of the loop
+ const auto *PdNode = PDT.getNode(const_cast<BasicBlock *>(Loop.getHeader()));
+ const auto *IpdNode = PdNode->getIDom();
+ const auto *PdBoundBlock = IpdNode ? IpdNode->getBlock() : nullptr;
+ while (PdBoundBlock && Loop.contains(PdBoundBlock)) {
+ IpdNode = IpdNode->getIDom();
+ PdBoundBlock = IpdNode ? IpdNode->getBlock() : nullptr;
+ }
+
+ // compute all join points
+ DivergencePropagator Propagator{FuncRPOT, DT, PDT, LI};
+ auto JoinBlocks = Propagator.computeJoinPoints<const LoopExitVec &>(
+ *Loop.getHeader(), LoopExits, Loop.getParentLoop(), PdBoundBlock);
+
+ auto ItInserted = CachedLoopExitJoins.emplace(&Loop, std::move(JoinBlocks));
+ assert(ItInserted.second);
+ return *ItInserted.first->second;
+}
+
+const ConstBlockSet &
+SyncDependenceAnalysis::join_blocks(const Instruction &Term) {
+ // trivial case
+ if (Term.getNumSuccessors() < 1) {
+ return EmptyBlockSet;
+ }
+
+ // already available in cache?
+ auto ItCached = CachedBranchJoins.find(&Term);
+ if (ItCached != CachedBranchJoins.end())
+ return *ItCached->second;
+
+ // dont propagate beyond the immediate post dominator of the branch
+ const auto *PdNode = PDT.getNode(const_cast<BasicBlock *>(Term.getParent()));
+ const auto *IpdNode = PdNode->getIDom();
+ const auto *PdBoundBlock = IpdNode ? IpdNode->getBlock() : nullptr;
+
+ // compute all join points
+ DivergencePropagator Propagator{FuncRPOT, DT, PDT, LI};
+ const auto &TermBlock = *Term.getParent();
+ auto JoinBlocks = Propagator.computeJoinPoints<succ_const_range>(
+ TermBlock, successors(Term.getParent()), LI.getLoopFor(&TermBlock), PdBoundBlock);
+
+ auto ItInserted = CachedBranchJoins.emplace(&Term, std::move(JoinBlocks));
+ assert(ItInserted.second);
+ return *ItInserted.first->second;
+}
+
+} // namespace llvm
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