[llvm] r367043 - [DDG] DirectedGraph as a base class for various dependence graphs such

Whitney Tsang via llvm-commits llvm-commits at lists.llvm.org
Thu Jul 25 11:23:22 PDT 2019


Author: whitneyt
Date: Thu Jul 25 11:23:22 2019
New Revision: 367043

URL: http://llvm.org/viewvc/llvm-project?rev=367043&view=rev
Log:
[DDG] DirectedGraph as a base class for various dependence graphs such
as DDG and PDG.
Summary:
This is an implementation of a directed graph base class with explicit
representation of both nodes and edges. This implementation makes the
edges explicit because we expect to assign various attributes (such as
dependence type, distribution interference weight, etc) to the edges in
the derived classes such as DDG and DIG. The DirectedGraph consists of a
list of DGNode's. Each node consists of a (possibly empty) list of
outgoing edges to other nodes in the graph. A DGEdge contains a
reference to a single target node. Note that nodes do not know about
their incoming edges so the DirectedGraph class provides a function to
find all incoming edges to a given node.

This is the first patch in a series of patches that we are planning to
contribute upstream in order to implement Data Dependence Graph and
Program Dependence Graph.

More information about the proposed design can be found here:
https://ibm.ent.box.com/v/directed-graph-and-ddg
Authored By: bmahjour
Reviewer: Meinersbur, myhsum hfinkel, fhahn, jdoerfert, kbarton
Reviewed By: Meinersbur
Subscribers: mgorny, wuzish, jsji, lebedev.ri, dexonsmith, kristina,
llvm-commits, Whitney, etiotto
Tag: LLVM
Differential Revision: https://reviews.llvm.org/D64088

Added:
    llvm/trunk/include/llvm/ADT/DirectedGraph.h
    llvm/trunk/unittests/ADT/DirectedGraphTest.cpp
Modified:
    llvm/trunk/unittests/ADT/CMakeLists.txt

Added: llvm/trunk/include/llvm/ADT/DirectedGraph.h
URL: http://llvm.org/viewvc/llvm-project/llvm/trunk/include/llvm/ADT/DirectedGraph.h?rev=367043&view=auto
==============================================================================
--- llvm/trunk/include/llvm/ADT/DirectedGraph.h (added)
+++ llvm/trunk/include/llvm/ADT/DirectedGraph.h Thu Jul 25 11:23:22 2019
@@ -0,0 +1,270 @@
+//===- llvm/ADT/DirectedGraph.h - Directed Graph ----------------*- C++ -*-===//
+//
+// 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 defines the interface and a base class implementation for a
+// directed graph.
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_ADT_DIRECTEDGRAPH_H
+#define LLVM_ADT_DIRECTEDGRAPH_H
+
+#include "llvm/ADT/GraphTraits.h"
+#include "llvm/ADT/SetVector.h"
+#include "llvm/ADT/SmallVector.h"
+#include "llvm/Support/Debug.h"
+#include "llvm/Support/raw_ostream.h"
+
+namespace llvm {
+
+/// Represent an edge in the directed graph.
+/// The edge contains the target node it connects to.
+template <class NodeType, class EdgeType> class DGEdge {
+public:
+  DGEdge() = delete;
+  /// Create an edge pointing to the given node \p N.
+  explicit DGEdge(NodeType &N) : TargetNode(N) {}
+  explicit DGEdge(const DGEdge<NodeType, EdgeType> &E)
+      : TargetNode(E.TargetNode) {}
+  DGEdge<NodeType, EdgeType> &operator=(const DGEdge<NodeType, EdgeType> &E) {
+    TargetNode = E.TargetNode;
+    return *this;
+  }
+
+  /// Static polymorphism: delegate implementation (via isEqualTo) to the
+  /// derived class.
+  bool operator==(const EdgeType &E) const { return getDerived().isEqualTo(E); }
+  bool operator!=(const EdgeType &E) const { return !operator==(E); }
+
+  /// Retrieve the target node this edge connects to.
+  const NodeType &getTargetNode() const { return TargetNode; }
+  NodeType &getTargetNode() {
+    return const_cast<NodeType &>(
+        static_cast<const DGEdge<NodeType, EdgeType> &>(*this).getTargetNode());
+  }
+
+protected:
+  // As the default implementation use address comparison for equality.
+  bool isEqualTo(const EdgeType &E) const { return this == &E; }
+
+  // Cast the 'this' pointer to the derived type and return a reference.
+  EdgeType &getDerived() { return *static_cast<EdgeType *>(this); }
+  const EdgeType &getDerived() const {
+    return *static_cast<const EdgeType *>(this);
+  }
+
+  // The target node this edge connects to.
+  NodeType &TargetNode;
+};
+
+/// Represent a node in the directed graph.
+/// The node has a (possibly empty) list of outgoing edges.
+template <class NodeType, class EdgeType> class DGNode {
+public:
+  using EdgeListTy = SetVector<EdgeType *>;
+  using iterator = typename EdgeListTy::iterator;
+  using const_iterator = typename EdgeListTy::const_iterator;
+
+  /// Create a node with a single outgoing edge \p E.
+  explicit DGNode(EdgeType &E) : Edges() { Edges.insert(&E); }
+  DGNode() = default;
+
+  explicit DGNode(const DGNode<NodeType, EdgeType> &N) : Edges(N.Edges) {}
+  DGNode(DGNode<NodeType, EdgeType> &&N) : Edges(std::move(N.Edges)) {}
+
+  DGNode<NodeType, EdgeType> &operator=(const DGNode<NodeType, EdgeType> &N) {
+    Edges = N.Edges;
+    return *this;
+  }
+  DGNode<NodeType, EdgeType> &operator=(const DGNode<NodeType, EdgeType> &&N) {
+    Edges = std::move(N.Edges);
+    return *this;
+  }
+
+  /// Static polymorphism: delegate implementation (via isEqualTo) to the
+  /// derived class.
+  bool operator==(const NodeType &N) const { return getDerived().isEqualTo(N); }
+  bool operator!=(const NodeType &N) const { return !operator==(N); }
+
+  const_iterator begin() const { return Edges.begin(); }
+  const_iterator end() const { return Edges.end(); }
+  iterator begin() { return Edges.begin(); }
+  iterator end() { return Edges.end(); }
+  const EdgeType &front() const { return *Edges.front(); }
+  EdgeType &front() { return *Edges.front(); }
+  const EdgeType &back() const { return *Edges.back(); }
+  EdgeType &back() { return *Edges.back(); }
+
+  /// Collect in \p EL, all the edges from this node to \p N.
+  /// Return true if at least one edge was found, and false otherwise.
+  /// Note that this implementation allows more than one edge to connect
+  /// a given pair of nodes.
+  bool findEdgesTo(const NodeType &N, SmallVectorImpl<EdgeType *> &EL) const {
+    assert(EL.empty() && "Expected the list of edges to be empty.");
+    for (auto *E : Edges)
+      if (E->getTargetNode() == N)
+        EL.push_back(E);
+    return !EL.empty();
+  }
+
+  /// Add the given edge \p E to this node, if it doesn't exist already. Returns
+  /// true if the edge is added and false otherwise.
+  bool addEdge(EdgeType &E) { return Edges.insert(&E); }
+
+  /// Remove the given edge \p E from this node, if it exists.
+  void removeEdge(EdgeType &E) { Edges.remove(&E); }
+
+  /// Test whether there is an edge that goes from this node to \p N.
+  bool hasEdgeTo(const NodeType &N) const {
+    return (findEdgeTo(N) != Edges.end());
+  }
+
+  /// Retrieve the outgoing edges for the node.
+  const EdgeListTy &getEdges() const { return Edges; }
+  EdgeListTy &getEdges() {
+    return const_cast<EdgeListTy &>(
+        static_cast<const DGNode<NodeType, EdgeType> &>(*this).Edges);
+  }
+
+  /// Clear the outgoing edges.
+  void clear() { Edges.clear(); }
+
+protected:
+  // As the default implementation use address comparison for equality.
+  bool isEqualTo(const NodeType &N) const { return this == &N; }
+
+  // Cast the 'this' pointer to the derived type and return a reference.
+  NodeType &getDerived() { return *static_cast<NodeType *>(this); }
+  const NodeType &getDerived() const {
+    return *static_cast<const NodeType *>(this);
+  }
+
+  /// Find an edge to \p N. If more than one edge exists, this will return
+  /// the first one in the list of edges.
+  const_iterator findEdgeTo(const NodeType &N) const {
+    return llvm::find_if(
+        Edges, [&N](const EdgeType *E) { return E->getTargetNode() == N; });
+  }
+
+  // The list of outgoing edges.
+  EdgeListTy Edges;
+};
+
+/// Directed graph
+///
+/// The graph is represented by a table of nodes.
+/// Each node contains a (possibly empty) list of outgoing edges.
+/// Each edge contains the target node it connects to.
+template <class NodeType, class EdgeType> class DirectedGraph {
+protected:
+  using NodeListTy = SmallVector<NodeType *, 10>;
+  using EdgeListTy = SmallVector<EdgeType *, 10>;
+public:
+  using iterator = typename NodeListTy::iterator;
+  using const_iterator = typename NodeListTy::const_iterator;
+  using DGraphType = DirectedGraph<NodeType, EdgeType>;
+
+  DirectedGraph() = default;
+  explicit DirectedGraph(NodeType &N) : Nodes() { addNode(N); }
+  DirectedGraph(const DGraphType &G) : Nodes(G.Nodes) {}
+  DirectedGraph(DGraphType &&RHS) : Nodes(std::move(RHS.Nodes)) {}
+  DGraphType &operator=(const DGraphType &G) {
+    Nodes = G.Nodes;
+    return *this;
+  }
+  DGraphType &operator=(const DGraphType &&G) {
+    Nodes = std::move(G.Nodes);
+    return *this;
+  }
+
+  const_iterator begin() const { return Nodes.begin(); }
+  const_iterator end() const { return Nodes.end(); }
+  iterator begin() { return Nodes.begin(); }
+  iterator end() { return Nodes.end(); }
+  const NodeType &front() const { return *Nodes.front(); }
+  NodeType &front() { return *Nodes.front(); }
+  const NodeType &back() const { return *Nodes.back(); }
+  NodeType &back() { return *Nodes.back(); }
+
+  size_t size() const { return Nodes.size(); }
+
+  /// Find the given node \p N in the table.
+  const_iterator findNode(const NodeType &N) const {
+    return llvm::find_if(Nodes,
+                         [&N](const NodeType *Node) { return *Node == N; });
+  }
+  iterator findNode(const NodeType &N) {
+    return const_cast<iterator>(
+        static_cast<const DGraphType &>(*this).findNode(N));
+  }
+
+  /// Add the given node \p N to the graph if it is not already present.
+  bool addNode(NodeType &N) {
+    if (findNode(N) != Nodes.end())
+      return false;
+    Nodes.push_back(&N);
+    return true;
+  }
+
+  /// Collect in \p EL all edges that are coming into node \p N. Return true
+  /// if at least one edge was found, and false otherwise.
+  bool findIncomingEdgesToNode(const NodeType &N, SmallVectorImpl<EdgeType*> &EL) const {
+    assert(EL.empty() && "Expected the list of edges to be empty.");
+    EdgeListTy TempList;
+    for (auto *Node : Nodes) {
+      if (*Node == N)
+        continue;
+      Node->findEdgesTo(N, TempList);
+      EL.insert(EL.end(), TempList.begin(), TempList.end());
+      TempList.clear();
+    }
+    return !EL.empty();
+  }
+
+  /// Remove the given node \p N from the graph. If the node has incoming or
+  /// outgoing edges, they are also removed. Return true if the node was found
+  /// and then removed, and false if the node was not found in the graph to
+  /// begin with.
+  bool removeNode(NodeType &N) {
+    iterator IT = findNode(N);
+    if (IT == Nodes.end())
+      return false;
+    // Remove incoming edges.
+    EdgeListTy EL;
+    for (auto *Node : Nodes) {
+      if (*Node == N)
+        continue;
+      Node->findEdgesTo(N, EL);
+      for (auto *E : EL)
+        Node->removeEdge(*E);
+      EL.clear();
+    }
+    N.clear();
+    Nodes.erase(IT);
+    return true;
+  }
+
+  /// Assuming nodes \p Src and \p Dst are already in the graph, connect node \p
+  /// Src to node \p Dst using the provided edge \p E. Return true if \p Src is
+  /// not already connected to \p Dst via \p E, and false otherwise.
+  bool connect(NodeType &Src, NodeType &Dst, EdgeType &E) {
+    assert(findNode(Src) != Nodes.end() && "Src node should be present.");
+    assert(findNode(Dst) != Nodes.end() && "Dst node should be present.");
+    assert((E.getTargetNode() == Dst) &&
+           "Target of the given edge does not match Dst.");
+    return Src.addEdge(E);
+  }
+
+protected:
+  // The list of nodes in the graph.
+  NodeListTy Nodes;
+};
+
+} // namespace llvm
+
+#endif // LLVM_ADT_DIRECTEDGRAPH_H

Modified: llvm/trunk/unittests/ADT/CMakeLists.txt
URL: http://llvm.org/viewvc/llvm-project/llvm/trunk/unittests/ADT/CMakeLists.txt?rev=367043&r1=367042&r2=367043&view=diff
==============================================================================
--- llvm/trunk/unittests/ADT/CMakeLists.txt (original)
+++ llvm/trunk/unittests/ADT/CMakeLists.txt Thu Jul 25 11:23:22 2019
@@ -17,6 +17,7 @@ add_llvm_unittest(ADTTests
   DenseMapTest.cpp
   DenseSetTest.cpp
   DepthFirstIteratorTest.cpp
+  DirectedGraphTest.cpp
   EquivalenceClassesTest.cpp
   FallibleIteratorTest.cpp
   FoldingSet.cpp

Added: llvm/trunk/unittests/ADT/DirectedGraphTest.cpp
URL: http://llvm.org/viewvc/llvm-project/llvm/trunk/unittests/ADT/DirectedGraphTest.cpp?rev=367043&view=auto
==============================================================================
--- llvm/trunk/unittests/ADT/DirectedGraphTest.cpp (added)
+++ llvm/trunk/unittests/ADT/DirectedGraphTest.cpp Thu Jul 25 11:23:22 2019
@@ -0,0 +1,295 @@
+//===- llvm/unittest/ADT/DirectedGraphTest.cpp ------------------*- C++ -*-===//
+//
+// 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 defines concrete derivations of the directed-graph base classes
+// for testing purposes.
+//
+//===----------------------------------------------------------------------===//
+
+#include "llvm/ADT/DirectedGraph.h"
+#include "llvm/ADT/GraphTraits.h"
+#include "llvm/ADT/SCCIterator.h"
+#include "llvm/ADT/SmallPtrSet.h"
+#include "gtest/gtest.h"
+
+namespace llvm {
+
+//===--------------------------------------------------------------------===//
+// Derived nodes, edges and graph types based on DirectedGraph.
+//===--------------------------------------------------------------------===//
+
+class DGTestNode;
+class DGTestEdge;
+using DGTestNodeBase = DGNode<DGTestNode, DGTestEdge>;
+using DGTestEdgeBase = DGEdge<DGTestNode, DGTestEdge>;
+using DGTestBase = DirectedGraph<DGTestNode, DGTestEdge>;
+
+class DGTestNode : public DGTestNodeBase {
+public:
+  DGTestNode() = default;
+};
+
+class DGTestEdge : public DGTestEdgeBase {
+public:
+  DGTestEdge() = delete;
+  DGTestEdge(DGTestNode &N) : DGTestEdgeBase(N) {}
+};
+
+class DGTestGraph : public DGTestBase {
+public:
+  DGTestGraph() = default;
+  ~DGTestGraph(){};
+};
+
+using EdgeListTy = SmallVector<DGTestEdge *, 2>;
+
+//===--------------------------------------------------------------------===//
+// GraphTraits specializations for the DGTest
+//===--------------------------------------------------------------------===//
+
+template <> struct GraphTraits<DGTestNode *> {
+  using NodeRef = DGTestNode *;
+
+  static DGTestNode *DGTestGetTargetNode(DGEdge<DGTestNode, DGTestEdge> *P) {
+    return &P->getTargetNode();
+  }
+
+  // Provide a mapped iterator so that the GraphTrait-based implementations can
+  // find the target nodes without having to explicitly go through the edges.
+  using ChildIteratorType =
+      mapped_iterator<DGTestNode::iterator, decltype(&DGTestGetTargetNode)>;
+  using ChildEdgeIteratorType = DGTestNode::iterator;
+
+  static NodeRef getEntryNode(NodeRef N) { return N; }
+  static ChildIteratorType child_begin(NodeRef N) {
+    return ChildIteratorType(N->begin(), &DGTestGetTargetNode);
+  }
+  static ChildIteratorType child_end(NodeRef N) {
+    return ChildIteratorType(N->end(), &DGTestGetTargetNode);
+  }
+
+  static ChildEdgeIteratorType child_edge_begin(NodeRef N) {
+    return N->begin();
+  }
+  static ChildEdgeIteratorType child_edge_end(NodeRef N) { return N->end(); }
+};
+
+template <>
+struct GraphTraits<DGTestGraph *> : public GraphTraits<DGTestNode *> {
+  using nodes_iterator = DGTestGraph::iterator;
+  static NodeRef getEntryNode(DGTestGraph *DG) { return *DG->begin(); }
+  static nodes_iterator nodes_begin(DGTestGraph *DG) { return DG->begin(); }
+  static nodes_iterator nodes_end(DGTestGraph *DG) { return DG->end(); }
+};
+
+//===--------------------------------------------------------------------===//
+// Test various modification and query functions.
+//===--------------------------------------------------------------------===//
+
+TEST(DirectedGraphTest, AddAndConnectNodes) {
+  DGTestGraph DG;
+  DGTestNode N1, N2, N3;
+  DGTestEdge E1(N1), E2(N2), E3(N3);
+
+  // Check that new nodes can be added successfully.
+  EXPECT_TRUE(DG.addNode(N1));
+  EXPECT_TRUE(DG.addNode(N2));
+  EXPECT_TRUE(DG.addNode(N3));
+
+  // Check that duplicate nodes are not added to the graph.
+  EXPECT_FALSE(DG.addNode(N1));
+
+  // Check that nodes can be connected using valid edges with no errors.
+  EXPECT_TRUE(DG.connect(N1, N2, E2));
+  EXPECT_TRUE(DG.connect(N2, N3, E3));
+  EXPECT_TRUE(DG.connect(N3, N1, E1));
+
+  // The graph looks like this now:
+  //
+  // +---------------+
+  // v               |
+  // N1 -> N2 -> N3 -+
+
+  // Check that already connected nodes with the given edge are not connected
+  // again (ie. edges are between nodes are not duplicated).
+  EXPECT_FALSE(DG.connect(N3, N1, E1));
+
+  // Check that there are 3 nodes in the graph.
+  EXPECT_TRUE(DG.size() == 3);
+
+  // Check that the added nodes can be found in the graph.
+  EXPECT_NE(DG.findNode(N3), DG.end());
+
+  // Check that nodes that are not part of the graph are not found.
+  DGTestNode N4;
+  EXPECT_EQ(DG.findNode(N4), DG.end());
+
+  // Check that findIncommingEdgesToNode works correctly.
+  EdgeListTy EL;
+  EXPECT_TRUE(DG.findIncomingEdgesToNode(N1, EL));
+  EXPECT_TRUE(EL.size() == 1);
+  EXPECT_EQ(*EL[0], E1);
+}
+
+TEST(DirectedGraphTest, AddRemoveEdge) {
+  DGTestGraph DG;
+  DGTestNode N1, N2, N3;
+  DGTestEdge E1(N1), E2(N2), E3(N3);
+  DG.addNode(N1);
+  DG.addNode(N2);
+  DG.addNode(N3);
+  DG.connect(N1, N2, E2);
+  DG.connect(N2, N3, E3);
+  DG.connect(N3, N1, E1);
+
+  // The graph looks like this now:
+  //
+  // +---------------+
+  // v               |
+  // N1 -> N2 -> N3 -+
+
+  // Check that there are 3 nodes in the graph.
+  EXPECT_TRUE(DG.size() == 3);
+
+  // Check that the target nodes of the edges are correct.
+  EXPECT_EQ(E1.getTargetNode(), N1);
+  EXPECT_EQ(E2.getTargetNode(), N2);
+  EXPECT_EQ(E3.getTargetNode(), N3);
+
+  // Remove the edge from N1 to N2.
+  N1.removeEdge(E2);
+
+  // The graph looks like this now:
+  //
+  // N2 -> N3 -> N1
+
+  // Check that there are no incoming edges to N2.
+  EdgeListTy EL;
+  EXPECT_FALSE(DG.findIncomingEdgesToNode(N2, EL));
+  EXPECT_TRUE(EL.empty());
+
+  // Put the edge from N1 to N2 back in place.
+  N1.addEdge(E2);
+
+  // Check that E2 is the only incoming edge to N2.
+  EL.clear();
+  EXPECT_TRUE(DG.findIncomingEdgesToNode(N2, EL));
+  EXPECT_EQ(*EL[0], E2);
+}
+
+TEST(DirectedGraphTest, hasEdgeTo) {
+  DGTestGraph DG;
+  DGTestNode N1, N2, N3;
+  DGTestEdge E1(N1), E2(N2), E3(N3), E4(N1);
+  DG.addNode(N1);
+  DG.addNode(N2);
+  DG.addNode(N3);
+  DG.connect(N1, N2, E2);
+  DG.connect(N2, N3, E3);
+  DG.connect(N3, N1, E1);
+  DG.connect(N2, N1, E4);
+
+  // The graph looks like this now:
+  //
+  // +-----+
+  // v     |
+  // N1 -> N2 -> N3
+  // ^           |
+  // +-----------+
+
+  EXPECT_TRUE(N2.hasEdgeTo(N1));
+  EXPECT_TRUE(N3.hasEdgeTo(N1));
+}
+
+TEST(DirectedGraphTest, AddRemoveNode) {
+  DGTestGraph DG;
+  DGTestNode N1, N2, N3;
+  DGTestEdge E1(N1), E2(N2), E3(N3);
+  DG.addNode(N1);
+  DG.addNode(N2);
+  DG.addNode(N3);
+  DG.connect(N1, N2, E2);
+  DG.connect(N2, N3, E3);
+  DG.connect(N3, N1, E1);
+
+  // The graph looks like this now:
+  //
+  // +---------------+
+  // v               |
+  // N1 -> N2 -> N3 -+
+
+  // Check that there are 3 nodes in the graph.
+  EXPECT_TRUE(DG.size() == 3);
+
+  // Check that a node in the graph can be removed, but not more than once.
+  EXPECT_TRUE(DG.removeNode(N1));
+  EXPECT_EQ(DG.findNode(N1), DG.end());
+  EXPECT_FALSE(DG.removeNode(N1));
+
+  // The graph looks like this now:
+  //
+  // N2 -> N3
+
+  // Check that there are 2 nodes in the graph and only N2 is connected to N3.
+  EXPECT_TRUE(DG.size() == 2);
+  EXPECT_TRUE(N3.getEdges().empty());
+  EdgeListTy EL;
+  EXPECT_FALSE(DG.findIncomingEdgesToNode(N2, EL));
+  EXPECT_TRUE(EL.empty());
+}
+
+TEST(DirectedGraphTest, SCC) {
+
+  DGTestGraph DG;
+  DGTestNode N1, N2, N3, N4;
+  DGTestEdge E1(N1), E2(N2), E3(N3), E4(N4);
+  DG.addNode(N1);
+  DG.addNode(N2);
+  DG.addNode(N3);
+  DG.addNode(N4);
+  DG.connect(N1, N2, E2);
+  DG.connect(N2, N3, E3);
+  DG.connect(N3, N1, E1);
+  DG.connect(N3, N4, E4);
+
+  // The graph looks like this now:
+  //
+  // +---------------+
+  // v               |
+  // N1 -> N2 -> N3 -+    N4
+  //             |        ^
+  //             +--------+
+
+  // Test that there are two SCCs:
+  // 1. {N1, N2, N3}
+  // 2. {N4}
+  using NodeListTy = SmallPtrSet<DGTestNode *, 3>;
+  SmallVector<NodeListTy, 4> ListOfSCCs;
+  for (auto &SCC : make_range(scc_begin(&DG), scc_end(&DG)))
+    ListOfSCCs.push_back(NodeListTy(SCC.begin(), SCC.end()));
+
+  EXPECT_TRUE(ListOfSCCs.size() == 2);
+
+  for (auto &SCC : ListOfSCCs) {
+    if (SCC.size() > 1)
+      continue;
+    EXPECT_TRUE(SCC.size() == 1);
+    EXPECT_TRUE(SCC.count(&N4) == 1);
+  }
+  for (auto &SCC : ListOfSCCs) {
+    if (SCC.size() <= 1)
+      continue;
+    EXPECT_TRUE(SCC.size() == 3);
+    EXPECT_TRUE(SCC.count(&N1) == 1);
+    EXPECT_TRUE(SCC.count(&N2) == 1);
+    EXPECT_TRUE(SCC.count(&N3) == 1);
+    EXPECT_TRUE(SCC.count(&N4) == 0);
+  }
+}
+
+} // namespace llvm




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