1 //===- llvm/Analysis/DDG.h --------------------------------------*- C++ -*-===//
2 //
3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4 // See https://llvm.org/LICENSE.txt for license information.
5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6 //
7 //===----------------------------------------------------------------------===//
8 //
9 // This file defines the Data-Dependence Graph (DDG).
10 //
11 //===----------------------------------------------------------------------===//
12 
13 #ifndef LLVM_ANALYSIS_DDG_H
14 #define LLVM_ANALYSIS_DDG_H
15 
16 #include "llvm/ADT/DenseMap.h"
17 #include "llvm/ADT/DirectedGraph.h"
18 #include "llvm/Analysis/DependenceAnalysis.h"
19 #include "llvm/Analysis/DependenceGraphBuilder.h"
20 #include "llvm/Analysis/LoopAnalysisManager.h"
21 #include "llvm/IR/Instructions.h"
22 
23 namespace llvm {
24 class DDGNode;
25 class DDGEdge;
26 using DDGNodeBase = DGNode<DDGNode, DDGEdge>;
27 using DDGEdgeBase = DGEdge<DDGNode, DDGEdge>;
28 using DDGBase = DirectedGraph<DDGNode, DDGEdge>;
29 class LPMUpdater;
30 
31 /// Data Dependence Graph Node
32 /// The graph can represent the following types of nodes:
33 /// 1. Single instruction node containing just one instruction.
34 /// 2. Multiple instruction node where two or more instructions from
35 ///    the same basic block are merged into one node.
36 /// 3. Pi-block node which is a group of other DDG nodes that are part of a
37 ///    strongly-connected component of the graph.
38 ///    A pi-block node contains more than one single or multiple instruction
39 ///    nodes. The root node cannot be part of a pi-block.
40 /// 4. Root node is a special node that connects to all components such that
41 ///    there is always a path from it to any node in the graph.
42 class DDGNode : public DDGNodeBase {
43 public:
44   using InstructionListType = SmallVectorImpl<Instruction *>;
45 
46   enum class NodeKind {
47     Unknown,
48     SingleInstruction,
49     MultiInstruction,
50     PiBlock,
51     Root,
52   };
53 
54   DDGNode() = delete;
DDGNode(const NodeKind K)55   DDGNode(const NodeKind K) : DDGNodeBase(), Kind(K) {}
DDGNode(const DDGNode & N)56   DDGNode(const DDGNode &N) : DDGNodeBase(N), Kind(N.Kind) {}
DDGNode(DDGNode && N)57   DDGNode(DDGNode &&N) : DDGNodeBase(std::move(N)), Kind(N.Kind) {}
58   virtual ~DDGNode() = 0;
59 
60   DDGNode &operator=(const DDGNode &N) {
61     DGNode::operator=(N);
62     Kind = N.Kind;
63     return *this;
64   }
65 
66   DDGNode &operator=(DDGNode &&N) {
67     DGNode::operator=(std::move(N));
68     Kind = N.Kind;
69     return *this;
70   }
71 
72   /// Getter for the kind of this node.
getKind()73   NodeKind getKind() const { return Kind; }
74 
75   /// Collect a list of instructions, in \p IList, for which predicate \p Pred
76   /// evaluates to true when iterating over instructions of this node. Return
77   /// true if at least one instruction was collected, and false otherwise.
78   bool collectInstructions(llvm::function_ref<bool(Instruction *)> const &Pred,
79                            InstructionListType &IList) const;
80 
81 protected:
82   /// Setter for the kind of this node.
setKind(NodeKind K)83   void setKind(NodeKind K) { Kind = K; }
84 
85 private:
86   NodeKind Kind;
87 };
88 
89 /// Subclass of DDGNode representing the root node of the graph.
90 /// There should only be one such node in a given graph.
91 class RootDDGNode : public DDGNode {
92 public:
RootDDGNode()93   RootDDGNode() : DDGNode(NodeKind::Root) {}
94   RootDDGNode(const RootDDGNode &N) = delete;
RootDDGNode(RootDDGNode && N)95   RootDDGNode(RootDDGNode &&N) : DDGNode(std::move(N)) {}
~RootDDGNode()96   ~RootDDGNode() {}
97 
98   /// Define classof to be able to use isa<>, cast<>, dyn_cast<>, etc.
classof(const DDGNode * N)99   static bool classof(const DDGNode *N) {
100     return N->getKind() == NodeKind::Root;
101   }
classof(const RootDDGNode * N)102   static bool classof(const RootDDGNode *N) { return true; }
103 };
104 
105 /// Subclass of DDGNode representing single or multi-instruction nodes.
106 class SimpleDDGNode : public DDGNode {
107   friend class DDGBuilder;
108 
109 public:
110   SimpleDDGNode() = delete;
111   SimpleDDGNode(Instruction &I);
112   SimpleDDGNode(const SimpleDDGNode &N);
113   SimpleDDGNode(SimpleDDGNode &&N);
114   ~SimpleDDGNode();
115 
116   SimpleDDGNode &operator=(const SimpleDDGNode &N) {
117     DDGNode::operator=(N);
118     InstList = N.InstList;
119     return *this;
120   }
121 
122   SimpleDDGNode &operator=(SimpleDDGNode &&N) {
123     DDGNode::operator=(std::move(N));
124     InstList = std::move(N.InstList);
125     return *this;
126   }
127 
128   /// Get the list of instructions in this node.
getInstructions()129   const InstructionListType &getInstructions() const {
130     assert(!InstList.empty() && "Instruction List is empty.");
131     return InstList;
132   }
getInstructions()133   InstructionListType &getInstructions() {
134     return const_cast<InstructionListType &>(
135         static_cast<const SimpleDDGNode *>(this)->getInstructions());
136   }
137 
138   /// Get the first/last instruction in the node.
getFirstInstruction()139   Instruction *getFirstInstruction() const { return getInstructions().front(); }
getLastInstruction()140   Instruction *getLastInstruction() const { return getInstructions().back(); }
141 
142   /// Define classof to be able to use isa<>, cast<>, dyn_cast<>, etc.
classof(const DDGNode * N)143   static bool classof(const DDGNode *N) {
144     return N->getKind() == NodeKind::SingleInstruction ||
145            N->getKind() == NodeKind::MultiInstruction;
146   }
classof(const SimpleDDGNode * N)147   static bool classof(const SimpleDDGNode *N) { return true; }
148 
149 private:
150   /// Append the list of instructions in \p Input to this node.
appendInstructions(const InstructionListType & Input)151   void appendInstructions(const InstructionListType &Input) {
152     setKind((InstList.size() == 0 && Input.size() == 1)
153                 ? NodeKind::SingleInstruction
154                 : NodeKind::MultiInstruction);
155     InstList.insert(InstList.end(), Input.begin(), Input.end());
156   }
appendInstructions(const SimpleDDGNode & Input)157   void appendInstructions(const SimpleDDGNode &Input) {
158     appendInstructions(Input.getInstructions());
159   }
160 
161   /// List of instructions associated with a single or multi-instruction node.
162   SmallVector<Instruction *, 2> InstList;
163 };
164 
165 /// Subclass of DDGNode representing a pi-block. A pi-block represents a group
166 /// of DDG nodes that are part of a strongly-connected component of the graph.
167 /// Replacing all the SCCs with pi-blocks results in an acyclic representation
168 /// of the DDG. For example if we have:
169 /// {a -> b}, {b -> c, d}, {c -> a}
170 /// the cycle a -> b -> c -> a is abstracted into a pi-block "p" as follows:
171 /// {p -> d} with "p" containing: {a -> b}, {b -> c}, {c -> a}
172 class PiBlockDDGNode : public DDGNode {
173 public:
174   using PiNodeList = SmallVector<DDGNode *, 4>;
175 
176   PiBlockDDGNode() = delete;
177   PiBlockDDGNode(const PiNodeList &List);
178   PiBlockDDGNode(const PiBlockDDGNode &N);
179   PiBlockDDGNode(PiBlockDDGNode &&N);
180   ~PiBlockDDGNode();
181 
182   PiBlockDDGNode &operator=(const PiBlockDDGNode &N) {
183     DDGNode::operator=(N);
184     NodeList = N.NodeList;
185     return *this;
186   }
187 
188   PiBlockDDGNode &operator=(PiBlockDDGNode &&N) {
189     DDGNode::operator=(std::move(N));
190     NodeList = std::move(N.NodeList);
191     return *this;
192   }
193 
194   /// Get the list of nodes in this pi-block.
getNodes()195   const PiNodeList &getNodes() const {
196     assert(!NodeList.empty() && "Node list is empty.");
197     return NodeList;
198   }
getNodes()199   PiNodeList &getNodes() {
200     return const_cast<PiNodeList &>(
201         static_cast<const PiBlockDDGNode *>(this)->getNodes());
202   }
203 
204   /// Define classof to be able to use isa<>, cast<>, dyn_cast<>, etc.
classof(const DDGNode * N)205   static bool classof(const DDGNode *N) {
206     return N->getKind() == NodeKind::PiBlock;
207   }
208 
209 private:
210   /// List of nodes in this pi-block.
211   PiNodeList NodeList;
212 };
213 
214 /// Data Dependency Graph Edge.
215 /// An edge in the DDG can represent a def-use relationship or
216 /// a memory dependence based on the result of DependenceAnalysis.
217 /// A rooted edge connects the root node to one of the components
218 /// of the graph.
219 class DDGEdge : public DDGEdgeBase {
220 public:
221   /// The kind of edge in the DDG
222   enum class EdgeKind {
223     Unknown,
224     RegisterDefUse,
225     MemoryDependence,
226     Rooted,
227     Last = Rooted // Must be equal to the largest enum value.
228   };
229 
230   explicit DDGEdge(DDGNode &N) = delete;
DDGEdge(DDGNode & N,EdgeKind K)231   DDGEdge(DDGNode &N, EdgeKind K) : DDGEdgeBase(N), Kind(K) {}
DDGEdge(const DDGEdge & E)232   DDGEdge(const DDGEdge &E) : DDGEdgeBase(E), Kind(E.getKind()) {}
DDGEdge(DDGEdge && E)233   DDGEdge(DDGEdge &&E) : DDGEdgeBase(std::move(E)), Kind(E.Kind) {}
234   DDGEdge &operator=(const DDGEdge &E) {
235     DDGEdgeBase::operator=(E);
236     Kind = E.Kind;
237     return *this;
238   }
239 
240   DDGEdge &operator=(DDGEdge &&E) {
241     DDGEdgeBase::operator=(std::move(E));
242     Kind = E.Kind;
243     return *this;
244   }
245 
246   /// Get the edge kind
getKind()247   EdgeKind getKind() const { return Kind; };
248 
249   /// Return true if this is a def-use edge, and false otherwise.
isDefUse()250   bool isDefUse() const { return Kind == EdgeKind::RegisterDefUse; }
251 
252   /// Return true if this is a memory dependence edge, and false otherwise.
isMemoryDependence()253   bool isMemoryDependence() const { return Kind == EdgeKind::MemoryDependence; }
254 
255   /// Return true if this is an edge stemming from the root node, and false
256   /// otherwise.
isRooted()257   bool isRooted() const { return Kind == EdgeKind::Rooted; }
258 
259 private:
260   EdgeKind Kind;
261 };
262 
263 /// Encapsulate some common data and functionality needed for different
264 /// variations of data dependence graphs.
265 template <typename NodeType> class DependenceGraphInfo {
266 public:
267   using DependenceList = SmallVector<std::unique_ptr<Dependence>, 1>;
268 
269   DependenceGraphInfo() = delete;
270   DependenceGraphInfo(const DependenceGraphInfo &G) = delete;
DependenceGraphInfo(const std::string & N,const DependenceInfo & DepInfo)271   DependenceGraphInfo(const std::string &N, const DependenceInfo &DepInfo)
272       : Name(N), DI(DepInfo), Root(nullptr) {}
DependenceGraphInfo(DependenceGraphInfo && G)273   DependenceGraphInfo(DependenceGraphInfo &&G)
274       : Name(std::move(G.Name)), DI(std::move(G.DI)), Root(G.Root) {}
~DependenceGraphInfo()275   virtual ~DependenceGraphInfo() {}
276 
277   /// Return the label that is used to name this graph.
getName()278   const StringRef getName() const { return Name; }
279 
280   /// Return the root node of the graph.
getRoot()281   NodeType &getRoot() const {
282     assert(Root && "Root node is not available yet. Graph construction may "
283                    "still be in progress\n");
284     return *Root;
285   }
286 
287   /// Collect all the data dependency infos coming from any pair of memory
288   /// accesses from \p Src to \p Dst, and store them into \p Deps. Return true
289   /// if a dependence exists, and false otherwise.
290   bool getDependencies(const NodeType &Src, const NodeType &Dst,
291                        DependenceList &Deps) const;
292 
293 protected:
294   // Name of the graph.
295   std::string Name;
296 
297   // Store a copy of DependenceInfo in the graph, so that individual memory
298   // dependencies don't need to be stored. Instead when the dependence is
299   // queried it is recomputed using @DI.
300   const DependenceInfo DI;
301 
302   // A special node in the graph that has an edge to every connected component of
303   // the graph, to ensure all nodes are reachable in a graph walk.
304   NodeType *Root = nullptr;
305 };
306 
307 using DDGInfo = DependenceGraphInfo<DDGNode>;
308 
309 /// Data Dependency Graph
310 class DataDependenceGraph : public DDGBase, public DDGInfo {
311   friend AbstractDependenceGraphBuilder<DataDependenceGraph>;
312   friend class DDGBuilder;
313 
314 public:
315   using NodeType = DDGNode;
316   using EdgeType = DDGEdge;
317 
318   DataDependenceGraph() = delete;
319   DataDependenceGraph(const DataDependenceGraph &G) = delete;
DataDependenceGraph(DataDependenceGraph && G)320   DataDependenceGraph(DataDependenceGraph &&G)
321       : DDGBase(std::move(G)), DDGInfo(std::move(G)) {}
322   DataDependenceGraph(Function &F, DependenceInfo &DI);
323   DataDependenceGraph(Loop &L, LoopInfo &LI, DependenceInfo &DI);
324   ~DataDependenceGraph();
325 
326   /// If node \p N belongs to a pi-block return a pointer to the pi-block,
327   /// otherwise return null.
328   const PiBlockDDGNode *getPiBlock(const NodeType &N) const;
329 
330 protected:
331   /// Add node \p N to the graph, if it's not added yet, and keep track of the
332   /// root node as well as pi-blocks and their members. Return true if node is
333   /// successfully added.
334   bool addNode(NodeType &N);
335 
336 private:
337   using PiBlockMapType = DenseMap<const NodeType *, const PiBlockDDGNode *>;
338 
339   /// Mapping from graph nodes to their containing pi-blocks. If a node is not
340   /// part of a pi-block, it will not appear in this map.
341   PiBlockMapType PiBlockMap;
342 };
343 
344 /// Concrete implementation of a pure data dependence graph builder. This class
345 /// provides custom implementation for the pure-virtual functions used in the
346 /// generic dependence graph build algorithm.
347 ///
348 /// For information about time complexity of the build algorithm see the
349 /// comments near the declaration of AbstractDependenceGraphBuilder.
350 class DDGBuilder : public AbstractDependenceGraphBuilder<DataDependenceGraph> {
351 public:
DDGBuilder(DataDependenceGraph & G,DependenceInfo & D,const BasicBlockListType & BBs)352   DDGBuilder(DataDependenceGraph &G, DependenceInfo &D,
353              const BasicBlockListType &BBs)
354       : AbstractDependenceGraphBuilder(G, D, BBs) {}
createRootNode()355   DDGNode &createRootNode() final override {
356     auto *RN = new RootDDGNode();
357     assert(RN && "Failed to allocate memory for DDG root node.");
358     Graph.addNode(*RN);
359     return *RN;
360   }
createFineGrainedNode(Instruction & I)361   DDGNode &createFineGrainedNode(Instruction &I) final override {
362     auto *SN = new SimpleDDGNode(I);
363     assert(SN && "Failed to allocate memory for simple DDG node.");
364     Graph.addNode(*SN);
365     return *SN;
366   }
createPiBlock(const NodeListType & L)367   DDGNode &createPiBlock(const NodeListType &L) final override {
368     auto *Pi = new PiBlockDDGNode(L);
369     assert(Pi && "Failed to allocate memory for pi-block node.");
370     Graph.addNode(*Pi);
371     return *Pi;
372   }
createDefUseEdge(DDGNode & Src,DDGNode & Tgt)373   DDGEdge &createDefUseEdge(DDGNode &Src, DDGNode &Tgt) final override {
374     auto *E = new DDGEdge(Tgt, DDGEdge::EdgeKind::RegisterDefUse);
375     assert(E && "Failed to allocate memory for edge");
376     Graph.connect(Src, Tgt, *E);
377     return *E;
378   }
createMemoryEdge(DDGNode & Src,DDGNode & Tgt)379   DDGEdge &createMemoryEdge(DDGNode &Src, DDGNode &Tgt) final override {
380     auto *E = new DDGEdge(Tgt, DDGEdge::EdgeKind::MemoryDependence);
381     assert(E && "Failed to allocate memory for edge");
382     Graph.connect(Src, Tgt, *E);
383     return *E;
384   }
createRootedEdge(DDGNode & Src,DDGNode & Tgt)385   DDGEdge &createRootedEdge(DDGNode &Src, DDGNode &Tgt) final override {
386     auto *E = new DDGEdge(Tgt, DDGEdge::EdgeKind::Rooted);
387     assert(E && "Failed to allocate memory for edge");
388     assert(isa<RootDDGNode>(Src) && "Expected root node");
389     Graph.connect(Src, Tgt, *E);
390     return *E;
391   }
392 
getNodesInPiBlock(const DDGNode & N)393   const NodeListType &getNodesInPiBlock(const DDGNode &N) final override {
394     auto *PiNode = dyn_cast<const PiBlockDDGNode>(&N);
395     assert(PiNode && "Expected a pi-block node.");
396     return PiNode->getNodes();
397   }
398 
399   /// Return true if the two nodes \pSrc and \pTgt are both simple nodes and
400   /// the consecutive instructions after merging belong to the same basic block.
401   bool areNodesMergeable(const DDGNode &Src,
402                          const DDGNode &Tgt) const final override;
403   void mergeNodes(DDGNode &Src, DDGNode &Tgt) final override;
404   bool shouldSimplify() const final override;
405   bool shouldCreatePiBlocks() const final override;
406 };
407 
408 raw_ostream &operator<<(raw_ostream &OS, const DDGNode &N);
409 raw_ostream &operator<<(raw_ostream &OS, const DDGNode::NodeKind K);
410 raw_ostream &operator<<(raw_ostream &OS, const DDGEdge &E);
411 raw_ostream &operator<<(raw_ostream &OS, const DDGEdge::EdgeKind K);
412 raw_ostream &operator<<(raw_ostream &OS, const DataDependenceGraph &G);
413 
414 //===--------------------------------------------------------------------===//
415 // DDG Analysis Passes
416 //===--------------------------------------------------------------------===//
417 
418 /// Analysis pass that builds the DDG for a loop.
419 class DDGAnalysis : public AnalysisInfoMixin<DDGAnalysis> {
420 public:
421   using Result = std::unique_ptr<DataDependenceGraph>;
422   Result run(Loop &L, LoopAnalysisManager &AM, LoopStandardAnalysisResults &AR);
423 
424 private:
425   friend AnalysisInfoMixin<DDGAnalysis>;
426   static AnalysisKey Key;
427 };
428 
429 /// Textual printer pass for the DDG of a loop.
430 class DDGAnalysisPrinterPass : public PassInfoMixin<DDGAnalysisPrinterPass> {
431 public:
DDGAnalysisPrinterPass(raw_ostream & OS)432   explicit DDGAnalysisPrinterPass(raw_ostream &OS) : OS(OS) {}
433   PreservedAnalyses run(Loop &L, LoopAnalysisManager &AM,
434                         LoopStandardAnalysisResults &AR, LPMUpdater &U);
435 
436 private:
437   raw_ostream &OS;
438 };
439 
440 //===--------------------------------------------------------------------===//
441 // DependenceGraphInfo Implementation
442 //===--------------------------------------------------------------------===//
443 
444 template <typename NodeType>
getDependencies(const NodeType & Src,const NodeType & Dst,DependenceList & Deps)445 bool DependenceGraphInfo<NodeType>::getDependencies(
446     const NodeType &Src, const NodeType &Dst, DependenceList &Deps) const {
447   assert(Deps.empty() && "Expected empty output list at the start.");
448 
449   // List of memory access instructions from src and dst nodes.
450   SmallVector<Instruction *, 8> SrcIList, DstIList;
451   auto isMemoryAccess = [](const Instruction *I) {
452     return I->mayReadOrWriteMemory();
453   };
454   Src.collectInstructions(isMemoryAccess, SrcIList);
455   Dst.collectInstructions(isMemoryAccess, DstIList);
456 
457   for (auto *SrcI : SrcIList)
458     for (auto *DstI : DstIList)
459       if (auto Dep =
460               const_cast<DependenceInfo *>(&DI)->depends(SrcI, DstI, true))
461         Deps.push_back(std::move(Dep));
462 
463   return !Deps.empty();
464 }
465 
466 //===--------------------------------------------------------------------===//
467 // GraphTraits specializations for the DDG
468 //===--------------------------------------------------------------------===//
469 
470 /// non-const versions of the grapth trait specializations for DDG
471 template <> struct GraphTraits<DDGNode *> {
472   using NodeRef = DDGNode *;
473 
474   static DDGNode *DDGGetTargetNode(DGEdge<DDGNode, DDGEdge> *P) {
475     return &P->getTargetNode();
476   }
477 
478   // Provide a mapped iterator so that the GraphTrait-based implementations can
479   // find the target nodes without having to explicitly go through the edges.
480   using ChildIteratorType =
481       mapped_iterator<DDGNode::iterator, decltype(&DDGGetTargetNode)>;
482   using ChildEdgeIteratorType = DDGNode::iterator;
483 
484   static NodeRef getEntryNode(NodeRef N) { return N; }
485   static ChildIteratorType child_begin(NodeRef N) {
486     return ChildIteratorType(N->begin(), &DDGGetTargetNode);
487   }
488   static ChildIteratorType child_end(NodeRef N) {
489     return ChildIteratorType(N->end(), &DDGGetTargetNode);
490   }
491 
492   static ChildEdgeIteratorType child_edge_begin(NodeRef N) {
493     return N->begin();
494   }
495   static ChildEdgeIteratorType child_edge_end(NodeRef N) { return N->end(); }
496 };
497 
498 template <>
499 struct GraphTraits<DataDependenceGraph *> : public GraphTraits<DDGNode *> {
500   using nodes_iterator = DataDependenceGraph::iterator;
501   static NodeRef getEntryNode(DataDependenceGraph *DG) {
502     return &DG->getRoot();
503   }
504   static nodes_iterator nodes_begin(DataDependenceGraph *DG) {
505     return DG->begin();
506   }
507   static nodes_iterator nodes_end(DataDependenceGraph *DG) { return DG->end(); }
508 };
509 
510 /// const versions of the grapth trait specializations for DDG
511 template <> struct GraphTraits<const DDGNode *> {
512   using NodeRef = const DDGNode *;
513 
514   static const DDGNode *DDGGetTargetNode(const DGEdge<DDGNode, DDGEdge> *P) {
515     return &P->getTargetNode();
516   }
517 
518   // Provide a mapped iterator so that the GraphTrait-based implementations can
519   // find the target nodes without having to explicitly go through the edges.
520   using ChildIteratorType =
521       mapped_iterator<DDGNode::const_iterator, decltype(&DDGGetTargetNode)>;
522   using ChildEdgeIteratorType = DDGNode::const_iterator;
523 
524   static NodeRef getEntryNode(NodeRef N) { return N; }
525   static ChildIteratorType child_begin(NodeRef N) {
526     return ChildIteratorType(N->begin(), &DDGGetTargetNode);
527   }
528   static ChildIteratorType child_end(NodeRef N) {
529     return ChildIteratorType(N->end(), &DDGGetTargetNode);
530   }
531 
532   static ChildEdgeIteratorType child_edge_begin(NodeRef N) {
533     return N->begin();
534   }
535   static ChildEdgeIteratorType child_edge_end(NodeRef N) { return N->end(); }
536 };
537 
538 template <>
539 struct GraphTraits<const DataDependenceGraph *>
540     : public GraphTraits<const DDGNode *> {
541   using nodes_iterator = DataDependenceGraph::const_iterator;
542   static NodeRef getEntryNode(const DataDependenceGraph *DG) {
543     return &DG->getRoot();
544   }
545   static nodes_iterator nodes_begin(const DataDependenceGraph *DG) {
546     return DG->begin();
547   }
548   static nodes_iterator nodes_end(const DataDependenceGraph *DG) {
549     return DG->end();
550   }
551 };
552 
553 } // namespace llvm
554 
555 #endif // LLVM_ANALYSIS_DDG_H
556