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// Copyright 2014 the V8 project authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.
#include "src/base/compiler-specific.h"
#include "src/common/globals.h"
#include "src/compiler/graph.h"
#include "src/compiler/node.h"
#include "src/zone/zone-containers.h"
namespace v8 {
namespace internal {
namespace compiler {
// Determines control dependence equivalence classes for control nodes. Any two
// nodes having the same set of control dependences land in one class. These
// classes can in turn be used to:
// - Build a program structure tree (PST) for controls in the graph.
// - Determine single-entry single-exit (SESE) regions within the graph.
// Note that this implementation actually uses cycle equivalence to establish
// class numbers. Any two nodes are cycle equivalent if they occur in the same
// set of cycles. It can be shown that control dependence equivalence reduces
// to undirected cycle equivalence for strongly connected control flow graphs.
// The algorithm is based on the paper, "The program structure tree: computing
// control regions in linear time" by Johnson, Pearson & Pingali (PLDI94) which
// also contains proofs for the aforementioned equivalence. References to line
// numbers in the algorithm from figure 4 have been added [line:x].
class V8_EXPORT_PRIVATE ControlEquivalence final
: public NON_EXPORTED_BASE(ZoneObject) {
ControlEquivalence(Zone* zone, Graph* graph)
: zone_(zone),
node_data_(graph->NodeCount(), zone) {}
// Run the main algorithm starting from the {exit} control node. This causes
// the following iterations over control edges of the graph:
// 1) A breadth-first backwards traversal to determine the set of nodes that
// participate in the next step. Takes O(E) time and O(N) space.
// 2) An undirected depth-first backwards traversal that determines class
// numbers for all participating nodes. Takes O(E) time and O(N) space.
void Run(Node* exit);
// Retrieves a previously computed class number.
size_t ClassOf(Node* node) {
DCHECK_NE(kInvalidClass, GetClass(node));
return GetClass(node);
static const size_t kInvalidClass = static_cast<size_t>(-1);
enum DFSDirection { kInputDirection, kUseDirection };
struct Bracket {
DFSDirection direction; // Direction in which this bracket was added.
size_t recent_class; // Cached class when bracket was topmost.
size_t recent_size; // Cached set-size when bracket was topmost.
Node* from; // Node that this bracket originates from.
Node* to; // Node that this bracket points to.
// The set of brackets for each node during the DFS walk.
using BracketList = ZoneLinkedList<Bracket>;
struct DFSStackEntry {
DFSDirection direction; // Direction currently used in DFS walk.
Node::InputEdges::iterator input; // Iterator used for "input" direction.
Node::UseEdges::iterator use; // Iterator used for "use" direction.
Node* parent_node; // Parent node of entry during DFS walk.
Node* node; // Node that this stack entry belongs to.
// The stack is used during the undirected DFS walk.
using DFSStack = ZoneStack<DFSStackEntry>;
struct NodeData : ZoneObject {
explicit NodeData(Zone* zone)
: class_number(kInvalidClass),
on_stack(false) {}
size_t class_number; // Equivalence class number assigned to node.
BracketList blist; // List of brackets per node.
bool visited : 1; // Indicates node has already been visited.
bool on_stack : 1; // Indicates node is on DFS stack during walk.
// The per-node data computed during the DFS walk.
using Data = ZoneVector<NodeData*>;
// Called at pre-visit during DFS walk.
void VisitPre(Node* node);
// Called at mid-visit during DFS walk.
void VisitMid(Node* node, DFSDirection direction);
// Called at post-visit during DFS walk.
void VisitPost(Node* node, Node* parent_node, DFSDirection direction);
// Called when hitting a back edge in the DFS walk.
void VisitBackedge(Node* from, Node* to, DFSDirection direction);
// Performs and undirected DFS walk of the graph. Conceptually all nodes are
// expanded, splitting "input" and "use" out into separate nodes. During the
// traversal, edges towards the representative nodes are preferred.
// \ / - Pre-visit: When N1 is visited in direction D the preferred
// x N1 edge towards N is taken next, calling VisitPre(N).
// | - Mid-visit: After all edges out of N2 in direction D have
// | N been visited, we switch the direction and start considering
// | edges out of N1 now, and we call VisitMid(N).
// x N2 - Post-visit: After all edges out of N1 in direction opposite
// / \ to D have been visited, we pop N and call VisitPost(N).
// This will yield a true spanning tree (without cross or forward edges) and
// also discover proper back edges in both directions.
void RunUndirectedDFS(Node* exit);
void DetermineParticipationEnqueue(ZoneQueue<Node*>& queue, Node* node);
void DetermineParticipation(Node* exit);
NodeData* GetData(Node* node) {
size_t const index = node->id();
if (index >= node_data_.size()) node_data_.resize(index + 1);
return node_data_[index];
void AllocateData(Node* node) {
size_t const index = node->id();
if (index >= node_data_.size()) node_data_.resize(index + 1);
node_data_[index] = zone_->New<NodeData>(zone_);
int NewClassNumber() { return class_number_++; }
int NewDFSNumber() { return dfs_number_++; }
bool Participates(Node* node) { return GetData(node) != nullptr; }
// Accessors for the equivalence class stored within the per-node data.
size_t GetClass(Node* node) { return GetData(node)->class_number; }
void SetClass(Node* node, size_t number) {
GetData(node)->class_number = number;
// Accessors for the bracket list stored within the per-node data.
BracketList& GetBracketList(Node* node) {
return GetData(node)->blist;
void SetBracketList(Node* node, BracketList& list) {
GetData(node)->blist = list;
// Mutates the DFS stack by pushing an entry.
void DFSPush(DFSStack& stack, Node* node, Node* from, DFSDirection dir);
// Mutates the DFS stack by popping an entry.
void DFSPop(DFSStack& stack, Node* node);
void BracketListDelete(BracketList& blist, Node* to, DFSDirection direction);
void BracketListTRACE(BracketList& blist);
Zone* const zone_;
Graph* const graph_;
int dfs_number_; // Generates new DFS pre-order numbers on demand.
int class_number_; // Generates new equivalence class numbers on demand.
Data node_data_; // Per-node data stored as a side-table.
} // namespace compiler
} // namespace internal
} // namespace v8