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//===- DivergenceAnalysis.cpp --------- Divergence Analysis Implementation -==//
// The LLVM Compiler Infrastructure
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
// This file implements 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 "llvm/Analysis/DivergenceAnalysis.h"
#include "llvm/Analysis/Passes.h"
#include "llvm/Analysis/PostDominators.h"
#include "llvm/Analysis/TargetTransformInfo.h"
#include "llvm/IR/Dominators.h"
#include "llvm/IR/InstIterator.h"
#include "llvm/IR/Instructions.h"
#include "llvm/IR/Value.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/raw_ostream.h"
#include <vector>
using namespace llvm;
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 simple 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 : instructions(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();
// Unreachable blocks may not be in the dominator tree.
if (!DT.isReachableFromEntry(ThisBB))
// If the function has no exit blocks or doesn't reach any exit blocks, the
// post dominator may be null.
DomTreeNode *ThisNode = PDT.getNode(ThisBB);
if (!ThisNode)
BasicBlock *IPostDom = ThisNode->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)->hasConstantOrUndefValue() && 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)
// A helper function for computeInfluenceRegion that adds successors of "ThisBB"
// to the influence region.
static void
addSuccessorsToInfluenceRegion(BasicBlock *ThisBB, BasicBlock *End,
DenseSet<BasicBlock *> &InfluenceRegion,
std::vector<BasicBlock *> &InfluenceStack) {
for (BasicBlock *Succ : successors(ThisBB)) {
if (Succ != End && InfluenceRegion.insert(Succ).second)
void DivergencePropagator::computeInfluenceRegion(
BasicBlock *Start, BasicBlock *End,
DenseSet<BasicBlock *> &InfluenceRegion) {
assert(PDT.properlyDominates(End, Start) &&
"End does not properly dominate Start");
// The influence region starts from the end of "Start" to the beginning of
// "End". Therefore, "Start" should not be in the region unless "Start" is in
// a loop that doesn't contain "End".
std::vector<BasicBlock *> InfluenceStack;
addSuccessorsToInfluenceRegion(Start, End, InfluenceRegion, InfluenceStack);
while (!InfluenceStack.empty()) {
BasicBlock *BB = InfluenceStack.back();
addSuccessorsToInfluenceRegion(BB, End, InfluenceRegion, InfluenceStack);
void DivergencePropagator::exploreDataDependency(Value *V) {
// Follow def-use chains of V.
for (User *U : V->users()) {
Instruction *UserInst = cast<Instruction>(U);
if (!TTI.isAlwaysUniform(U) && 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
// 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)
FunctionPass *llvm::createDivergenceAnalysisPass() {
return new DivergenceAnalysis();
void DivergenceAnalysis::getAnalysisUsage(AnalysisUsage &AU) const {
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;
auto &PDT = getAnalysis<PostDominatorTreeWrapperPass>().getPostDomTree();
DivergencePropagator DP(F, TTI,
PDT, 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 instructions() to ensure a deterministic order.
for (auto &I : instructions(F)) {
if (DivergentValues.count(&I))
OS << "DIVERGENT:" << I << "\n";