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//=- WebAssemblyFixIrreducibleControlFlow.cpp - Fix irreducible control flow -//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
/// \file
/// This file implements a pass that removes irreducible control flow.
/// Irreducible control flow means multiple-entry loops, which this pass
/// transforms to have a single entry.
/// Note that LLVM has a generic pass that lowers irreducible control flow, but
/// it linearizes control flow, turning diamonds into two triangles, which is
/// both unnecessary and undesirable for WebAssembly.
/// The big picture: We recursively process each "region", defined as a group
/// of blocks with a single entry and no branches back to that entry. A region
/// may be the entire function body, or the inner part of a loop, i.e., the
/// loop's body without branches back to the loop entry. In each region we fix
/// up multi-entry loops by adding a new block that can dispatch to each of the
/// loop entries, based on the value of a label "helper" variable, and we
/// replace direct branches to the entries with assignments to the label
/// variable and a branch to the dispatch block. Then the dispatch block is the
/// single entry in the loop containing the previous multiple entries. After
/// ensuring all the loops in a region are reducible, we recurse into them. The
/// total time complexity of this pass is:
/// O(NumBlocks * NumNestedLoops * NumIrreducibleLoops +
/// NumLoops * NumLoops)
/// This pass is similar to what the Relooper [1] does. Both identify looping
/// code that requires multiple entries, and resolve it in a similar way (in
/// Relooper terminology, we implement a Multiple shape in a Loop shape). Note
/// also that like the Relooper, we implement a "minimal" intervention: we only
/// use the "label" helper for the blocks we absolutely must and no others. We
/// also prioritize code size and do not duplicate code in order to resolve
/// irreducibility. The graph algorithms for finding loops and entries and so
/// forth are also similar to the Relooper. The main differences between this
/// pass and the Relooper are:
/// * We just care about irreducibility, so we just look at loops.
/// * The Relooper emits structured control flow (with ifs etc.), while we
/// emit a CFG.
/// [1] Alon Zakai. 2011. Emscripten: an LLVM-to-JavaScript compiler. In
/// Proceedings of the ACM international conference companion on Object oriented
/// programming systems languages and applications companion (SPLASH '11). ACM,
/// New York, NY, USA, 301-312. DOI=10.1145/2048147.2048224
#include "MCTargetDesc/WebAssemblyMCTargetDesc.h"
#include "WebAssembly.h"
#include "WebAssemblySubtarget.h"
#include "llvm/CodeGen/MachineInstrBuilder.h"
#include "llvm/Support/Debug.h"
using namespace llvm;
#define DEBUG_TYPE "wasm-fix-irreducible-control-flow"
namespace {
using BlockVector = SmallVector<MachineBasicBlock *, 4>;
using BlockSet = SmallPtrSet<MachineBasicBlock *, 4>;
static BlockVector getSortedEntries(const BlockSet &Entries) {
BlockVector SortedEntries(Entries.begin(), Entries.end());
[](const MachineBasicBlock *A, const MachineBasicBlock *B) {
auto ANum = A->getNumber();
auto BNum = B->getNumber();
return ANum < BNum;
return SortedEntries;
// Calculates reachability in a region. Ignores branches to blocks outside of
// the region, and ignores branches to the region entry (for the case where
// the region is the inner part of a loop).
class ReachabilityGraph {
ReachabilityGraph(MachineBasicBlock *Entry, const BlockSet &Blocks)
: Entry(Entry), Blocks(Blocks) {
#ifndef NDEBUG
// The region must have a single entry.
for (auto *MBB : Blocks) {
if (MBB != Entry) {
for (auto *Pred : MBB->predecessors()) {
bool canReach(MachineBasicBlock *From, MachineBasicBlock *To) const {
assert(inRegion(From) && inRegion(To));
auto I = Reachable.find(From);
if (I == Reachable.end())
return false;
return I->second.count(To);
// "Loopers" are blocks that are in a loop. We detect these by finding blocks
// that can reach themselves.
const BlockSet &getLoopers() const { return Loopers; }
// Get all blocks that are loop entries.
const BlockSet &getLoopEntries() const { return LoopEntries; }
// Get all blocks that enter a particular loop from outside.
const BlockSet &getLoopEnterers(MachineBasicBlock *LoopEntry) const {
auto I = LoopEnterers.find(LoopEntry);
assert(I != LoopEnterers.end());
return I->second;
MachineBasicBlock *Entry;
const BlockSet &Blocks;
BlockSet Loopers, LoopEntries;
DenseMap<MachineBasicBlock *, BlockSet> LoopEnterers;
bool inRegion(MachineBasicBlock *MBB) const { return Blocks.count(MBB); }
// Maps a block to all the other blocks it can reach.
DenseMap<MachineBasicBlock *, BlockSet> Reachable;
void calculate() {
// Reachability computation work list. Contains pairs of recent additions
// (A, B) where we just added a link A => B.
using BlockPair = std::pair<MachineBasicBlock *, MachineBasicBlock *>;
SmallVector<BlockPair, 4> WorkList;
// Add all relevant direct branches.
for (auto *MBB : Blocks) {
for (auto *Succ : MBB->successors()) {
if (Succ != Entry && inRegion(Succ)) {
WorkList.emplace_back(MBB, Succ);
while (!WorkList.empty()) {
MachineBasicBlock *MBB, *Succ;
std::tie(MBB, Succ) = WorkList.pop_back_val();
assert(inRegion(MBB) && Succ != Entry && inRegion(Succ));
if (MBB != Entry) {
// We recently added MBB => Succ, and that means we may have enabled
// Pred => MBB => Succ.
for (auto *Pred : MBB->predecessors()) {
if (Reachable[Pred].insert(Succ).second) {
WorkList.emplace_back(Pred, Succ);
// Blocks that can return to themselves are in a loop.
for (auto *MBB : Blocks) {
if (canReach(MBB, MBB)) {
// Find the loop entries - loopers reachable from blocks not in that loop -
// and those outside blocks that reach them, the "loop enterers".
for (auto *Looper : Loopers) {
for (auto *Pred : Looper->predecessors()) {
// Pred can reach Looper. If Looper can reach Pred, it is in the loop;
// otherwise, it is a block that enters into the loop.
if (!canReach(Looper, Pred)) {
// Finds the blocks in a single-entry loop, given the loop entry and the
// list of blocks that enter the loop.
class LoopBlocks {
LoopBlocks(MachineBasicBlock *Entry, const BlockSet &Enterers)
: Entry(Entry), Enterers(Enterers) {
BlockSet &getBlocks() { return Blocks; }
MachineBasicBlock *Entry;
const BlockSet &Enterers;
BlockSet Blocks;
void calculate() {
// Going backwards from the loop entry, if we ignore the blocks entering
// from outside, we will traverse all the blocks in the loop.
BlockVector WorkList;
BlockSet AddedToWorkList;
for (auto *Pred : Entry->predecessors()) {
if (!Enterers.count(Pred)) {
while (!WorkList.empty()) {
auto *MBB = WorkList.pop_back_val();
if (Blocks.insert(MBB).second) {
for (auto *Pred : MBB->predecessors()) {
if (!AddedToWorkList.count(Pred)) {
class WebAssemblyFixIrreducibleControlFlow final : public MachineFunctionPass {
StringRef getPassName() const override {
return "WebAssembly Fix Irreducible Control Flow";
bool runOnMachineFunction(MachineFunction &MF) override;
bool processRegion(MachineBasicBlock *Entry, BlockSet &Blocks,
MachineFunction &MF);
void makeSingleEntryLoop(BlockSet &Entries, BlockSet &Blocks,
MachineFunction &MF, const ReachabilityGraph &Graph);
static char ID; // Pass identification, replacement for typeid
WebAssemblyFixIrreducibleControlFlow() : MachineFunctionPass(ID) {}
bool WebAssemblyFixIrreducibleControlFlow::processRegion(
MachineBasicBlock *Entry, BlockSet &Blocks, MachineFunction &MF) {
bool Changed = false;
// Remove irreducibility before processing child loops, which may take
// multiple iterations.
while (true) {
ReachabilityGraph Graph(Entry, Blocks);
bool FoundIrreducibility = false;
for (auto *LoopEntry : getSortedEntries(Graph.getLoopEntries())) {
// Find mutual entries - all entries which can reach this one, and
// are reached by it (that always includes LoopEntry itself). All mutual
// entries must be in the same loop, so if we have more than one, then we
// have irreducible control flow.
// (Note that we need to sort the entries here, as otherwise the order can
// matter: being mutual is a symmetric relationship, and each set of
// mutuals will be handled properly no matter which we see first. However,
// there can be multiple disjoint sets of mutuals, and which we process
// first changes the output.)
// Note that irreducibility may involve inner loops, e.g. imagine A
// starts one loop, and it has B inside it which starts an inner loop.
// If we add a branch from all the way on the outside to B, then in a
// sense B is no longer an "inner" loop, semantically speaking. We will
// fix that irreducibility by adding a block that dispatches to either
// either A or B, so B will no longer be an inner loop in our output.
// (A fancier approach might try to keep it as such.)
// Note that we still need to recurse into inner loops later, to handle
// the case where the irreducibility is entirely nested - we would not
// be able to identify that at this point, since the enclosing loop is
// a group of blocks all of whom can reach each other. (We'll see the
// irreducibility after removing branches to the top of that enclosing
// loop.)
BlockSet MutualLoopEntries;
for (auto *OtherLoopEntry : Graph.getLoopEntries()) {
if (OtherLoopEntry != LoopEntry &&
Graph.canReach(LoopEntry, OtherLoopEntry) &&
Graph.canReach(OtherLoopEntry, LoopEntry)) {
if (MutualLoopEntries.size() > 1) {
makeSingleEntryLoop(MutualLoopEntries, Blocks, MF, Graph);
FoundIrreducibility = true;
Changed = true;
// Only go on to actually process the inner loops when we are done
// removing irreducible control flow and changing the graph. Modifying
// the graph as we go is possible, and that might let us avoid looking at
// the already-fixed loops again if we are careful, but all that is
// complex and bug-prone. Since irreducible loops are rare, just starting
// another iteration is best.
if (FoundIrreducibility) {
for (auto *LoopEntry : Graph.getLoopEntries()) {
LoopBlocks InnerBlocks(LoopEntry, Graph.getLoopEnterers(LoopEntry));
// Each of these calls to processRegion may change the graph, but are
// guaranteed not to interfere with each other. The only changes we make
// to the graph are to add blocks on the way to a loop entry. As the
// loops are disjoint, that means we may only alter branches that exit
// another loop, which are ignored when recursing into that other loop
// anyhow.
if (processRegion(LoopEntry, InnerBlocks.getBlocks(), MF)) {
Changed = true;
return Changed;
// Given a set of entries to a single loop, create a single entry for that
// loop by creating a dispatch block for them, routing control flow using
// a helper variable. Also updates Blocks with any new blocks created, so
// that we properly track all the blocks in the region. But this does not update
// ReachabilityGraph; this will be updated in the caller of this function as
// needed.
void WebAssemblyFixIrreducibleControlFlow::makeSingleEntryLoop(
BlockSet &Entries, BlockSet &Blocks, MachineFunction &MF,
const ReachabilityGraph &Graph) {
assert(Entries.size() >= 2);
// Sort the entries to ensure a deterministic build.
BlockVector SortedEntries = getSortedEntries(Entries);
#ifndef NDEBUG
for (auto Block : SortedEntries)
assert(Block->getNumber() != -1);
if (SortedEntries.size() > 1) {
for (auto I = SortedEntries.begin(), E = SortedEntries.end() - 1; I != E;
++I) {
auto ANum = (*I)->getNumber();
auto BNum = (*(std::next(I)))->getNumber();
assert(ANum != BNum);
// Create a dispatch block which will contain a jump table to the entries.
MachineBasicBlock *Dispatch = MF.CreateMachineBasicBlock();
MF.insert(MF.end(), Dispatch);
// Add the jump table.
const auto &TII = *MF.getSubtarget<WebAssemblySubtarget>().getInstrInfo();
MachineInstrBuilder MIB =
BuildMI(Dispatch, DebugLoc(), TII.get(WebAssembly::BR_TABLE_I32));
// Add the register which will be used to tell the jump table which block to
// jump to.
MachineRegisterInfo &MRI = MF.getRegInfo();
Register Reg = MRI.createVirtualRegister(&WebAssembly::I32RegClass);
// Compute the indices in the superheader, one for each bad block, and
// add them as successors.
DenseMap<MachineBasicBlock *, unsigned> Indices;
for (auto *Entry : SortedEntries) {
auto Pair = Indices.insert(std::make_pair(Entry, 0));
unsigned Index = MIB.getInstr()->getNumExplicitOperands() - 1;
Pair.first->second = Index;
// Rewrite the problematic successors for every block that wants to reach
// the bad blocks. For simplicity, we just introduce a new block for every
// edge we need to rewrite. (Fancier things are possible.)
BlockVector AllPreds;
for (auto *Entry : SortedEntries) {
for (auto *Pred : Entry->predecessors()) {
if (Pred != Dispatch) {
// This set stores predecessors within this loop.
DenseSet<MachineBasicBlock *> InLoop;
for (auto *Pred : AllPreds) {
for (auto *Entry : Pred->successors()) {
if (!Entries.count(Entry))
if (Graph.canReach(Entry, Pred)) {
// Record if each entry has a layout predecessor. This map stores
// <<loop entry, Predecessor is within the loop?>, layout predecessor>
DenseMap<PointerIntPair<MachineBasicBlock *, 1, bool>, MachineBasicBlock *>
for (auto *Pred : AllPreds) {
bool PredInLoop = InLoop.count(Pred);
for (auto *Entry : Pred->successors())
if (Entries.count(Entry) && Pred->isLayoutSuccessor(Entry))
EntryToLayoutPred[{Entry, PredInLoop}] = Pred;
// We need to create at most two routing blocks per entry: one for
// predecessors outside the loop and one for predecessors inside the loop.
// This map stores
// <<loop entry, Predecessor is within the loop?>, routing block>
DenseMap<PointerIntPair<MachineBasicBlock *, 1, bool>, MachineBasicBlock *>
for (auto *Pred : AllPreds) {
bool PredInLoop = InLoop.count(Pred);
for (auto *Entry : Pred->successors()) {
if (!Entries.count(Entry) || Map.count({Entry, PredInLoop}))
// If there exists a layout predecessor of this entry and this predecessor
// is not that, we rather create a routing block after that layout
// predecessor to save a branch.
if (auto *OtherPred = EntryToLayoutPred.lookup({Entry, PredInLoop}))
if (OtherPred != Pred)
// This is a successor we need to rewrite.
MachineBasicBlock *Routing = MF.CreateMachineBasicBlock();
? MachineFunction::iterator(Entry)
: MF.end(),
// Set the jump table's register of the index of the block we wish to
// jump to, and jump to the jump table.
BuildMI(Routing, DebugLoc(), TII.get(WebAssembly::CONST_I32), Reg)
BuildMI(Routing, DebugLoc(), TII.get(WebAssembly::BR)).addMBB(Dispatch);
Map[{Entry, PredInLoop}] = Routing;
for (auto *Pred : AllPreds) {
bool PredInLoop = InLoop.count(Pred);
// Remap the terminator operands and the successor list.
for (MachineInstr &Term : Pred->terminators())
for (auto &Op : Term.explicit_uses())
if (Op.isMBB() && Indices.count(Op.getMBB()))
Op.setMBB(Map[{Op.getMBB(), PredInLoop}]);
for (auto *Succ : Pred->successors()) {
if (!Entries.count(Succ))
auto *Routing = Map[{Succ, PredInLoop}];
Pred->replaceSuccessor(Succ, Routing);
// Create a fake default label, because br_table requires one.
->getOperand(MIB.getInstr()->getNumExplicitOperands() - 1)
} // end anonymous namespace
char WebAssemblyFixIrreducibleControlFlow::ID = 0;
INITIALIZE_PASS(WebAssemblyFixIrreducibleControlFlow, DEBUG_TYPE,
"Removes irreducible control flow", false, false)
FunctionPass *llvm::createWebAssemblyFixIrreducibleControlFlow() {
return new WebAssemblyFixIrreducibleControlFlow();
bool WebAssemblyFixIrreducibleControlFlow::runOnMachineFunction(
MachineFunction &MF) {
LLVM_DEBUG(dbgs() << "********** Fixing Irreducible Control Flow **********\n"
"********** Function: "
<< MF.getName() << '\n');
// Start the recursive process on the entire function body.
BlockSet AllBlocks;
for (auto &MBB : MF) {
if (LLVM_UNLIKELY(processRegion(&*MF.begin(), AllBlocks, MF))) {
// We rewrote part of the function; recompute relevant things.
return true;
return false;