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//===- DivergenceAnalysis.cpp ------ Divergence Analysis ------------------===//
//                     The LLVM Compiler Infrastructure
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
// This file defines divergence analysis which determines whether a branch in a
// GPU program is divergent. It can help branch optimizations such as jump
// threading and loop unswitching to make better decisions.
// GPU programs typically use the SIMD execution model, where multiple threads
// in the same execution group have to execute in lock-step. Therefore, if the
// code contains divergent branches (i.e., threads in a group do not agree on
// which path of the branch to take), the group of threads has to execute all
// the paths from that branch with different subsets of threads enabled until
// they converge at the immediately post-dominating BB of the paths.
// Due to this execution model, some optimizations such as jump
// threading and loop unswitching can be unfortunately harmful when performed on
// divergent branches. Therefore, an analysis that computes which branches in a
// GPU program are divergent can help the compiler to selectively run these
// optimizations.
// This file defines divergence analysis which computes a conservative but
// non-trivial approximation of all divergent branches in a GPU program. It
// partially implements the approach described in
//   Divergence Analysis
//   Sampaio, Souza, Collange, Pereira
//   TOPLAS '13
// The divergence analysis identifies the sources of divergence (e.g., special
// variables that hold the thread ID), and recursively marks variables that are
// data or sync dependent on a source of divergence as divergent.
// While data dependency is a well-known concept, the notion of sync dependency
// is worth more explanation. Sync dependence 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.
// The current implementation has the following limitations:
// 1. intra-procedural. It conservatively considers the arguments of a
//    non-kernel-entry function and the return value of a function call as
//    divergent.
// 2. memory as black box. It conservatively considers values loaded from
//    generic or local address as divergent. This can be improved by leveraging
//    pointer analysis.

#include <vector>
#include "llvm/IR/Dominators.h"
#include "llvm/ADT/DenseSet.h"
#include "llvm/Analysis/Passes.h"
#include "llvm/Analysis/PostDominators.h"
#include "llvm/Analysis/TargetTransformInfo.h"
#include "llvm/IR/Function.h"
#include "llvm/IR/InstIterator.h"
#include "llvm/IR/Instructions.h"
#include "llvm/IR/IntrinsicInst.h"
#include "llvm/IR/Value.h"
#include "llvm/Pass.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/raw_ostream.h"
#include "llvm/Transforms/Scalar.h"
using namespace llvm;

#define DEBUG_TYPE "divergence"

namespace {
class DivergenceAnalysis : public FunctionPass {
  static char ID;

  DivergenceAnalysis() : FunctionPass(ID) {

  void getAnalysisUsage(AnalysisUsage &AU) const override {

  bool runOnFunction(Function &F) override;

  // Print all divergent branches in the function.
  void print(raw_ostream &OS, const Module *) const override;

  // Returns true if V is divergent.
  bool isDivergent(const Value *V) const { return DivergentValues.count(V); }
  // Returns true if V is uniform/non-divergent.
  bool isUniform(const Value *V) const { return !isDivergent(V); }

  // Stores all divergent values.
  DenseSet<const Value *> DivergentValues;
} // End of anonymous namespace

// Register this pass.
char DivergenceAnalysis::ID = 0;
INITIALIZE_PASS_BEGIN(DivergenceAnalysis, "divergence", "Divergence Analysis",
                      false, true)
INITIALIZE_PASS_END(DivergenceAnalysis, "divergence", "Divergence Analysis",
                    false, true)

namespace {

class DivergencePropagator {
  DivergencePropagator(Function &F, TargetTransformInfo &TTI,
                       DominatorTree &DT, PostDominatorTree &PDT,
                       DenseSet<const Value *> &DV)
      : F(F), TTI(TTI), DT(DT), PDT(PDT), DV(DV) {}
  void populateWithSourcesOfDivergence();
  void propagate();

  // A helper function that explores data dependents of V.
  void exploreDataDependency(Value *V);
  // A helper function that explores sync dependents of TI.
  void exploreSyncDependency(TerminatorInst *TI);
  // Computes the influence region from Start to End. This region includes all
  // basic blocks on any path from Start to End.
  void computeInfluenceRegion(BasicBlock *Start, BasicBlock *End,
                              DenseSet<BasicBlock *> &InfluenceRegion);
  // Finds all users of I that are outside the influence region, and add these
  // users to Worklist.
  void findUsersOutsideInfluenceRegion(
      Instruction &I, const DenseSet<BasicBlock *> &InfluenceRegion);

  Function &F;
  TargetTransformInfo &TTI;
  DominatorTree &DT;
  PostDominatorTree &PDT;
  std::vector<Value *> Worklist; // Stack for DFS.
  DenseSet<const Value *> &DV; // Stores all divergent values.

void DivergencePropagator::populateWithSourcesOfDivergence() {
  for (auto &I : inst_range(F)) {
    if (TTI.isSourceOfDivergence(&I)) {
  for (auto &Arg : F.args()) {
    if (TTI.isSourceOfDivergence(&Arg)) {

void DivergencePropagator::exploreSyncDependency(TerminatorInst *TI) {
  // Propagation rule 1: if branch TI is divergent, all PHINodes in TI's
  // immediate post dominator are divergent. This rule handles if-then-else
  // patterns. For example,
  // if (tid < 5)
  //   a1 = 1;
  // else
  //   a2 = 2;
  // a = phi(a1, a2); // sync dependent on (tid < 5)
  BasicBlock *ThisBB = TI->getParent();
  BasicBlock *IPostDom = PDT.getNode(ThisBB)->getIDom()->getBlock();
  if (IPostDom == nullptr)

  for (auto I = IPostDom->begin(); isa<PHINode>(I); ++I) {
    // A PHINode is uniform if it returns the same value no matter which path is
    // taken.
    if (!cast<PHINode>(I)->hasConstantValue() && DV.insert(I).second)

  // Propagation rule 2: if a value defined in a loop is used outside, the user
  // is sync dependent on the condition of the loop exits that dominate the
  // user. For example,
  // int i = 0;
  // do {
  //   i++;
  //   if (foo(i)) ... // uniform
  // } while (i < tid);
  // if (bar(i)) ...   // divergent
  // A program may contain unstructured loops. Therefore, we cannot leverage
  // LoopInfo, which only recognizes natural loops.
  // The algorithm used here handles both natural and unstructured loops.  Given
  // a branch TI, we first compute its influence region, the union of all simple
  // paths from TI to its immediate post dominator (IPostDom). Then, we search
  // for all the values defined in the influence region but used outside. All
  // these users are sync dependent on TI.
  DenseSet<BasicBlock *> InfluenceRegion;
  computeInfluenceRegion(ThisBB, IPostDom, InfluenceRegion);
  // An insight that can speed up the search process is that all the in-region
  // values that are used outside must dominate TI. Therefore, instead of
  // searching every basic blocks in the influence region, we search all the
  // dominators of TI until it is outside the influence region.
  BasicBlock *InfluencedBB = ThisBB;
  while (InfluenceRegion.count(InfluencedBB)) {
    for (auto &I : *InfluencedBB)
      findUsersOutsideInfluenceRegion(I, InfluenceRegion);
    DomTreeNode *IDomNode = DT.getNode(InfluencedBB)->getIDom();
    if (IDomNode == nullptr)
    InfluencedBB = IDomNode->getBlock();

void DivergencePropagator::findUsersOutsideInfluenceRegion(
    Instruction &I, const DenseSet<BasicBlock *> &InfluenceRegion) {
  for (User *U : I.users()) {
    Instruction *UserInst = cast<Instruction>(U);
    if (!InfluenceRegion.count(UserInst->getParent())) {
      if (DV.insert(UserInst).second)

void DivergencePropagator::computeInfluenceRegion(
    BasicBlock *Start, BasicBlock *End,
    DenseSet<BasicBlock *> &InfluenceRegion) {
  assert(PDT.properlyDominates(End, Start) &&
         "End does not properly dominate Start");
  std::vector<BasicBlock *> InfluenceStack;
  while (!InfluenceStack.empty()) {
    BasicBlock *BB = InfluenceStack.back();
    for (BasicBlock *Succ : successors(BB)) {
      if (End != Succ && InfluenceRegion.insert(Succ).second)

void DivergencePropagator::exploreDataDependency(Value *V) {
  // Follow def-use chains of V.
  for (User *U : V->users()) {
    Instruction *UserInst = cast<Instruction>(U);
    if (DV.insert(UserInst).second)

void DivergencePropagator::propagate() {
  // Traverse the dependency graph using DFS.
  while (!Worklist.empty()) {
    Value *V = Worklist.back();
    if (TerminatorInst *TI = dyn_cast<TerminatorInst>(V)) {
      // Terminators with less than two successors won't introduce sync
      // dependency. Ignore them.
      if (TI->getNumSuccessors() > 1)

} /// end namespace anonymous

FunctionPass *llvm::createDivergenceAnalysisPass() {
  return new DivergenceAnalysis();

bool DivergenceAnalysis::runOnFunction(Function &F) {
  auto *TTIWP = getAnalysisIfAvailable<TargetTransformInfoWrapperPass>();
  if (TTIWP == nullptr)
    return false;

  TargetTransformInfo &TTI = TTIWP->getTTI(F);
  // Fast path: if the target does not have branch divergence, we do not mark
  // any branch as divergent.
  if (!TTI.hasBranchDivergence())
    return false;

  DivergencePropagator DP(F, TTI,
                          getAnalysis<PostDominatorTree>(), DivergentValues);
  return false;

void DivergenceAnalysis::print(raw_ostream &OS, const Module *) const {
  if (DivergentValues.empty())
  const Value *FirstDivergentValue = *DivergentValues.begin();
  const Function *F;
  if (const Argument *Arg = dyn_cast<Argument>(FirstDivergentValue)) {
    F = Arg->getParent();
  } else if (const Instruction *I =
                 dyn_cast<Instruction>(FirstDivergentValue)) {
    F = I->getParent()->getParent();
  } else {
    llvm_unreachable("Only arguments and instructions can be divergent");

  // Dumps all divergent values in F, arguments and then instructions.
  for (auto &Arg : F->args()) {
    if (DivergentValues.count(&Arg))
      OS << "DIVERGENT:  " << Arg << "\n";
  // Iterate instructions using inst_range to ensure a deterministic order.
  for (auto &I : inst_range(F)) {
    if (DivergentValues.count(&I))
      OS << "DIVERGENT:" << I << "\n";