1 //===- LazyCallGraph.cpp - Analysis of a Module's call graph --------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 #include "llvm/Analysis/LazyCallGraph.h"
11 #include "llvm/ADT/ScopeExit.h"
12 #include "llvm/ADT/Sequence.h"
13 #include "llvm/ADT/STLExtras.h"
14 #include "llvm/ADT/ScopeExit.h"
15 #include "llvm/IR/CallSite.h"
16 #include "llvm/IR/InstVisitor.h"
17 #include "llvm/IR/Instructions.h"
18 #include "llvm/IR/PassManager.h"
19 #include "llvm/Support/Debug.h"
20 #include "llvm/Support/GraphWriter.h"
25 #define DEBUG_TYPE "lcg"
27 void LazyCallGraph::EdgeSequence::insertEdgeInternal(Node &TargetN,
29 EdgeIndexMap.insert({&TargetN, Edges.size()});
30 Edges.emplace_back(TargetN, EK);
33 void LazyCallGraph::EdgeSequence::setEdgeKind(Node &TargetN, Edge::Kind EK) {
34 Edges[EdgeIndexMap.find(&TargetN)->second].setKind(EK);
37 bool LazyCallGraph::EdgeSequence::removeEdgeInternal(Node &TargetN) {
38 auto IndexMapI = EdgeIndexMap.find(&TargetN);
39 if (IndexMapI == EdgeIndexMap.end())
42 Edges[IndexMapI->second] = Edge();
43 EdgeIndexMap.erase(IndexMapI);
47 static void addEdge(SmallVectorImpl<LazyCallGraph::Edge> &Edges,
48 DenseMap<LazyCallGraph::Node *, int> &EdgeIndexMap,
49 LazyCallGraph::Node &N, LazyCallGraph::Edge::Kind EK) {
50 if (!EdgeIndexMap.insert({&N, Edges.size()}).second)
53 DEBUG(dbgs() << " Added callable function: " << N.getName() << "\n");
54 Edges.emplace_back(LazyCallGraph::Edge(N, EK));
57 LazyCallGraph::EdgeSequence &LazyCallGraph::Node::populateSlow() {
58 assert(!Edges && "Must not have already populated the edges for this node!");
60 DEBUG(dbgs() << " Adding functions called by '" << getName()
61 << "' to the graph.\n");
63 Edges = EdgeSequence();
65 SmallVector<Constant *, 16> Worklist;
66 SmallPtrSet<Function *, 4> Callees;
67 SmallPtrSet<Constant *, 16> Visited;
69 // Find all the potential call graph edges in this function. We track both
70 // actual call edges and indirect references to functions. The direct calls
71 // are trivially added, but to accumulate the latter we walk the instructions
72 // and add every operand which is a constant to the worklist to process
75 // Note that we consider *any* function with a definition to be a viable
76 // edge. Even if the function's definition is subject to replacement by
77 // some other module (say, a weak definition) there may still be
78 // optimizations which essentially speculate based on the definition and
79 // a way to check that the specific definition is in fact the one being
80 // used. For example, this could be done by moving the weak definition to
81 // a strong (internal) definition and making the weak definition be an
82 // alias. Then a test of the address of the weak function against the new
83 // strong definition's address would be an effective way to determine the
84 // safety of optimizing a direct call edge.
85 for (BasicBlock &BB : *F)
86 for (Instruction &I : BB) {
87 if (auto CS = CallSite(&I))
88 if (Function *Callee = CS.getCalledFunction())
89 if (!Callee->isDeclaration())
90 if (Callees.insert(Callee).second) {
91 Visited.insert(Callee);
92 addEdge(Edges->Edges, Edges->EdgeIndexMap, G->get(*Callee),
93 LazyCallGraph::Edge::Call);
96 for (Value *Op : I.operand_values())
97 if (Constant *C = dyn_cast<Constant>(Op))
98 if (Visited.insert(C).second)
99 Worklist.push_back(C);
102 // We've collected all the constant (and thus potentially function or
103 // function containing) operands to all of the instructions in the function.
104 // Process them (recursively) collecting every function found.
105 visitReferences(Worklist, Visited, [&](Function &F) {
106 addEdge(Edges->Edges, Edges->EdgeIndexMap, G->get(F),
107 LazyCallGraph::Edge::Ref);
113 void LazyCallGraph::Node::replaceFunction(Function &NewF) {
114 assert(F != &NewF && "Must not replace a function with itself!");
118 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
119 LLVM_DUMP_METHOD void LazyCallGraph::Node::dump() const {
120 dbgs() << *this << '\n';
124 LazyCallGraph::LazyCallGraph(Module &M) {
125 DEBUG(dbgs() << "Building CG for module: " << M.getModuleIdentifier()
127 for (Function &F : M)
128 if (!F.isDeclaration() && !F.hasLocalLinkage()) {
129 DEBUG(dbgs() << " Adding '" << F.getName()
130 << "' to entry set of the graph.\n");
131 addEdge(EntryEdges.Edges, EntryEdges.EdgeIndexMap, get(F), Edge::Ref);
134 // Now add entry nodes for functions reachable via initializers to globals.
135 SmallVector<Constant *, 16> Worklist;
136 SmallPtrSet<Constant *, 16> Visited;
137 for (GlobalVariable &GV : M.globals())
138 if (GV.hasInitializer())
139 if (Visited.insert(GV.getInitializer()).second)
140 Worklist.push_back(GV.getInitializer());
142 DEBUG(dbgs() << " Adding functions referenced by global initializers to the "
144 visitReferences(Worklist, Visited, [&](Function &F) {
145 addEdge(EntryEdges.Edges, EntryEdges.EdgeIndexMap, get(F),
146 LazyCallGraph::Edge::Ref);
150 LazyCallGraph::LazyCallGraph(LazyCallGraph &&G)
151 : BPA(std::move(G.BPA)), NodeMap(std::move(G.NodeMap)),
152 EntryEdges(std::move(G.EntryEdges)), SCCBPA(std::move(G.SCCBPA)),
153 SCCMap(std::move(G.SCCMap)), LeafRefSCCs(std::move(G.LeafRefSCCs)) {
157 LazyCallGraph &LazyCallGraph::operator=(LazyCallGraph &&G) {
158 BPA = std::move(G.BPA);
159 NodeMap = std::move(G.NodeMap);
160 EntryEdges = std::move(G.EntryEdges);
161 SCCBPA = std::move(G.SCCBPA);
162 SCCMap = std::move(G.SCCMap);
163 LeafRefSCCs = std::move(G.LeafRefSCCs);
168 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
169 LLVM_DUMP_METHOD void LazyCallGraph::SCC::dump() const {
170 dbgs() << *this << '\n';
175 void LazyCallGraph::SCC::verify() {
176 assert(OuterRefSCC && "Can't have a null RefSCC!");
177 assert(!Nodes.empty() && "Can't have an empty SCC!");
179 for (Node *N : Nodes) {
180 assert(N && "Can't have a null node!");
181 assert(OuterRefSCC->G->lookupSCC(*N) == this &&
182 "Node does not map to this SCC!");
183 assert(N->DFSNumber == -1 &&
184 "Must set DFS numbers to -1 when adding a node to an SCC!");
185 assert(N->LowLink == -1 &&
186 "Must set low link to -1 when adding a node to an SCC!");
188 assert(E.getNode() && "Can't have an unpopulated node!");
193 bool LazyCallGraph::SCC::isParentOf(const SCC &C) const {
197 for (Node &N : *this)
198 for (Edge &E : N->calls())
199 if (OuterRefSCC->G->lookupSCC(E.getNode()) == &C)
206 bool LazyCallGraph::SCC::isAncestorOf(const SCC &TargetC) const {
207 if (this == &TargetC)
210 LazyCallGraph &G = *OuterRefSCC->G;
212 // Start with this SCC.
213 SmallPtrSet<const SCC *, 16> Visited = {this};
214 SmallVector<const SCC *, 16> Worklist = {this};
216 // Walk down the graph until we run out of edges or find a path to TargetC.
218 const SCC &C = *Worklist.pop_back_val();
220 for (Edge &E : N->calls()) {
221 SCC *CalleeC = G.lookupSCC(E.getNode());
225 // If the callee's SCC is the TargetC, we're done.
226 if (CalleeC == &TargetC)
229 // If this is the first time we've reached this SCC, put it on the
230 // worklist to recurse through.
231 if (Visited.insert(CalleeC).second)
232 Worklist.push_back(CalleeC);
234 } while (!Worklist.empty());
240 LazyCallGraph::RefSCC::RefSCC(LazyCallGraph &G) : G(&G) {}
242 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
243 LLVM_DUMP_METHOD void LazyCallGraph::RefSCC::dump() const {
244 dbgs() << *this << '\n';
249 void LazyCallGraph::RefSCC::verify() {
250 assert(G && "Can't have a null graph!");
251 assert(!SCCs.empty() && "Can't have an empty SCC!");
253 // Verify basic properties of the SCCs.
254 SmallPtrSet<SCC *, 4> SCCSet;
255 for (SCC *C : SCCs) {
256 assert(C && "Can't have a null SCC!");
258 assert(&C->getOuterRefSCC() == this &&
259 "SCC doesn't think it is inside this RefSCC!");
260 bool Inserted = SCCSet.insert(C).second;
261 assert(Inserted && "Found a duplicate SCC!");
262 auto IndexIt = SCCIndices.find(C);
263 assert(IndexIt != SCCIndices.end() &&
264 "Found an SCC that doesn't have an index!");
267 // Check that our indices map correctly.
268 for (auto &SCCIndexPair : SCCIndices) {
269 SCC *C = SCCIndexPair.first;
270 int i = SCCIndexPair.second;
271 assert(C && "Can't have a null SCC in the indices!");
272 assert(SCCSet.count(C) && "Found an index for an SCC not in the RefSCC!");
273 assert(SCCs[i] == C && "Index doesn't point to SCC!");
276 // Check that the SCCs are in fact in post-order.
277 for (int i = 0, Size = SCCs.size(); i < Size; ++i) {
278 SCC &SourceSCC = *SCCs[i];
279 for (Node &N : SourceSCC)
283 SCC &TargetSCC = *G->lookupSCC(E.getNode());
284 if (&TargetSCC.getOuterRefSCC() == this) {
285 assert(SCCIndices.find(&TargetSCC)->second <= i &&
286 "Edge between SCCs violates post-order relationship.");
289 assert(TargetSCC.getOuterRefSCC().Parents.count(this) &&
290 "Edge to a RefSCC missing us in its parent set.");
294 // Check that our parents are actually parents.
295 for (RefSCC *ParentRC : Parents) {
296 assert(ParentRC != this && "Cannot be our own parent!");
297 auto HasConnectingEdge = [&] {
298 for (SCC &C : *ParentRC)
301 if (G->lookupRefSCC(E.getNode()) == this)
305 assert(HasConnectingEdge() && "No edge connects the parent to us!");
310 bool LazyCallGraph::RefSCC::isDescendantOf(const RefSCC &C) const {
311 // Walk up the parents of this SCC and verify that we eventually find C.
312 SmallVector<const RefSCC *, 4> AncestorWorklist;
313 AncestorWorklist.push_back(this);
315 const RefSCC *AncestorC = AncestorWorklist.pop_back_val();
316 if (AncestorC->isChildOf(C))
318 for (const RefSCC *ParentC : AncestorC->Parents)
319 AncestorWorklist.push_back(ParentC);
320 } while (!AncestorWorklist.empty());
325 /// Generic helper that updates a postorder sequence of SCCs for a potentially
326 /// cycle-introducing edge insertion.
328 /// A postorder sequence of SCCs of a directed graph has one fundamental
329 /// property: all deges in the DAG of SCCs point "up" the sequence. That is,
330 /// all edges in the SCC DAG point to prior SCCs in the sequence.
332 /// This routine both updates a postorder sequence and uses that sequence to
333 /// compute the set of SCCs connected into a cycle. It should only be called to
334 /// insert a "downward" edge which will require changing the sequence to
335 /// restore it to a postorder.
337 /// When inserting an edge from an earlier SCC to a later SCC in some postorder
338 /// sequence, all of the SCCs which may be impacted are in the closed range of
339 /// those two within the postorder sequence. The algorithm used here to restore
340 /// the state is as follows:
342 /// 1) Starting from the source SCC, construct a set of SCCs which reach the
343 /// source SCC consisting of just the source SCC. Then scan toward the
344 /// target SCC in postorder and for each SCC, if it has an edge to an SCC
345 /// in the set, add it to the set. Otherwise, the source SCC is not
346 /// a successor, move it in the postorder sequence to immediately before
347 /// the source SCC, shifting the source SCC and all SCCs in the set one
348 /// position toward the target SCC. Stop scanning after processing the
350 /// 2) If the source SCC is now past the target SCC in the postorder sequence,
351 /// and thus the new edge will flow toward the start, we are done.
352 /// 3) Otherwise, starting from the target SCC, walk all edges which reach an
353 /// SCC between the source and the target, and add them to the set of
354 /// connected SCCs, then recurse through them. Once a complete set of the
355 /// SCCs the target connects to is known, hoist the remaining SCCs between
356 /// the source and the target to be above the target. Note that there is no
357 /// need to process the source SCC, it is already known to connect.
358 /// 4) At this point, all of the SCCs in the closed range between the source
359 /// SCC and the target SCC in the postorder sequence are connected,
360 /// including the target SCC and the source SCC. Inserting the edge from
361 /// the source SCC to the target SCC will form a cycle out of precisely
362 /// these SCCs. Thus we can merge all of the SCCs in this closed range into
365 /// This process has various important properties:
366 /// - Only mutates the SCCs when adding the edge actually changes the SCC
368 /// - Never mutates SCCs which are unaffected by the change.
369 /// - Updates the postorder sequence to correctly satisfy the postorder
370 /// constraint after the edge is inserted.
371 /// - Only reorders SCCs in the closed postorder sequence from the source to
372 /// the target, so easy to bound how much has changed even in the ordering.
373 /// - Big-O is the number of edges in the closed postorder range of SCCs from
374 /// source to target.
376 /// This helper routine, in addition to updating the postorder sequence itself
377 /// will also update a map from SCCs to indices within that sequecne.
379 /// The sequence and the map must operate on pointers to the SCC type.
381 /// Two callbacks must be provided. The first computes the subset of SCCs in
382 /// the postorder closed range from the source to the target which connect to
383 /// the source SCC via some (transitive) set of edges. The second computes the
384 /// subset of the same range which the target SCC connects to via some
385 /// (transitive) set of edges. Both callbacks should populate the set argument
387 template <typename SCCT, typename PostorderSequenceT, typename SCCIndexMapT,
388 typename ComputeSourceConnectedSetCallableT,
389 typename ComputeTargetConnectedSetCallableT>
390 static iterator_range<typename PostorderSequenceT::iterator>
391 updatePostorderSequenceForEdgeInsertion(
392 SCCT &SourceSCC, SCCT &TargetSCC, PostorderSequenceT &SCCs,
393 SCCIndexMapT &SCCIndices,
394 ComputeSourceConnectedSetCallableT ComputeSourceConnectedSet,
395 ComputeTargetConnectedSetCallableT ComputeTargetConnectedSet) {
396 int SourceIdx = SCCIndices[&SourceSCC];
397 int TargetIdx = SCCIndices[&TargetSCC];
398 assert(SourceIdx < TargetIdx && "Cannot have equal indices here!");
400 SmallPtrSet<SCCT *, 4> ConnectedSet;
402 // Compute the SCCs which (transitively) reach the source.
403 ComputeSourceConnectedSet(ConnectedSet);
405 // Partition the SCCs in this part of the port-order sequence so only SCCs
406 // connecting to the source remain between it and the target. This is
407 // a benign partition as it preserves postorder.
408 auto SourceI = std::stable_partition(
409 SCCs.begin() + SourceIdx, SCCs.begin() + TargetIdx + 1,
410 [&ConnectedSet](SCCT *C) { return !ConnectedSet.count(C); });
411 for (int i = SourceIdx, e = TargetIdx + 1; i < e; ++i)
412 SCCIndices.find(SCCs[i])->second = i;
414 // If the target doesn't connect to the source, then we've corrected the
415 // post-order and there are no cycles formed.
416 if (!ConnectedSet.count(&TargetSCC)) {
417 assert(SourceI > (SCCs.begin() + SourceIdx) &&
418 "Must have moved the source to fix the post-order.");
419 assert(*std::prev(SourceI) == &TargetSCC &&
420 "Last SCC to move should have bene the target.");
422 // Return an empty range at the target SCC indicating there is nothing to
424 return make_range(std::prev(SourceI), std::prev(SourceI));
427 assert(SCCs[TargetIdx] == &TargetSCC &&
428 "Should not have moved target if connected!");
429 SourceIdx = SourceI - SCCs.begin();
430 assert(SCCs[SourceIdx] == &SourceSCC &&
431 "Bad updated index computation for the source SCC!");
434 // See whether there are any remaining intervening SCCs between the source
435 // and target. If so we need to make sure they all are reachable form the
437 if (SourceIdx + 1 < TargetIdx) {
438 ConnectedSet.clear();
439 ComputeTargetConnectedSet(ConnectedSet);
441 // Partition SCCs so that only SCCs reached from the target remain between
442 // the source and the target. This preserves postorder.
443 auto TargetI = std::stable_partition(
444 SCCs.begin() + SourceIdx + 1, SCCs.begin() + TargetIdx + 1,
445 [&ConnectedSet](SCCT *C) { return ConnectedSet.count(C); });
446 for (int i = SourceIdx + 1, e = TargetIdx + 1; i < e; ++i)
447 SCCIndices.find(SCCs[i])->second = i;
448 TargetIdx = std::prev(TargetI) - SCCs.begin();
449 assert(SCCs[TargetIdx] == &TargetSCC &&
450 "Should always end with the target!");
453 // At this point, we know that connecting source to target forms a cycle
454 // because target connects back to source, and we know that all of the SCCs
455 // between the source and target in the postorder sequence participate in that
457 return make_range(SCCs.begin() + SourceIdx, SCCs.begin() + TargetIdx);
460 SmallVector<LazyCallGraph::SCC *, 1>
461 LazyCallGraph::RefSCC::switchInternalEdgeToCall(Node &SourceN, Node &TargetN) {
462 assert(!(*SourceN)[TargetN].isCall() && "Must start with a ref edge!");
463 SmallVector<SCC *, 1> DeletedSCCs;
466 // In a debug build, verify the RefSCC is valid to start with and when this
469 auto VerifyOnExit = make_scope_exit([&]() { verify(); });
472 SCC &SourceSCC = *G->lookupSCC(SourceN);
473 SCC &TargetSCC = *G->lookupSCC(TargetN);
475 // If the two nodes are already part of the same SCC, we're also done as
476 // we've just added more connectivity.
477 if (&SourceSCC == &TargetSCC) {
478 SourceN->setEdgeKind(TargetN, Edge::Call);
482 // At this point we leverage the postorder list of SCCs to detect when the
483 // insertion of an edge changes the SCC structure in any way.
485 // First and foremost, we can eliminate the need for any changes when the
486 // edge is toward the beginning of the postorder sequence because all edges
487 // flow in that direction already. Thus adding a new one cannot form a cycle.
488 int SourceIdx = SCCIndices[&SourceSCC];
489 int TargetIdx = SCCIndices[&TargetSCC];
490 if (TargetIdx < SourceIdx) {
491 SourceN->setEdgeKind(TargetN, Edge::Call);
495 // Compute the SCCs which (transitively) reach the source.
496 auto ComputeSourceConnectedSet = [&](SmallPtrSetImpl<SCC *> &ConnectedSet) {
498 // Check that the RefSCC is still valid before computing this as the
499 // results will be nonsensical of we've broken its invariants.
502 ConnectedSet.insert(&SourceSCC);
503 auto IsConnected = [&](SCC &C) {
505 for (Edge &E : N->calls())
506 if (ConnectedSet.count(G->lookupSCC(E.getNode())))
513 make_range(SCCs.begin() + SourceIdx + 1, SCCs.begin() + TargetIdx + 1))
515 ConnectedSet.insert(C);
518 // Use a normal worklist to find which SCCs the target connects to. We still
519 // bound the search based on the range in the postorder list we care about,
520 // but because this is forward connectivity we just "recurse" through the
522 auto ComputeTargetConnectedSet = [&](SmallPtrSetImpl<SCC *> &ConnectedSet) {
524 // Check that the RefSCC is still valid before computing this as the
525 // results will be nonsensical of we've broken its invariants.
528 ConnectedSet.insert(&TargetSCC);
529 SmallVector<SCC *, 4> Worklist;
530 Worklist.push_back(&TargetSCC);
532 SCC &C = *Worklist.pop_back_val();
537 SCC &EdgeC = *G->lookupSCC(E.getNode());
538 if (&EdgeC.getOuterRefSCC() != this)
539 // Not in this RefSCC...
541 if (SCCIndices.find(&EdgeC)->second <= SourceIdx)
542 // Not in the postorder sequence between source and target.
545 if (ConnectedSet.insert(&EdgeC).second)
546 Worklist.push_back(&EdgeC);
548 } while (!Worklist.empty());
551 // Use a generic helper to update the postorder sequence of SCCs and return
552 // a range of any SCCs connected into a cycle by inserting this edge. This
553 // routine will also take care of updating the indices into the postorder
555 auto MergeRange = updatePostorderSequenceForEdgeInsertion(
556 SourceSCC, TargetSCC, SCCs, SCCIndices, ComputeSourceConnectedSet,
557 ComputeTargetConnectedSet);
559 // If the merge range is empty, then adding the edge didn't actually form any
560 // new cycles. We're done.
561 if (MergeRange.begin() == MergeRange.end()) {
562 // Now that the SCC structure is finalized, flip the kind to call.
563 SourceN->setEdgeKind(TargetN, Edge::Call);
568 // Before merging, check that the RefSCC remains valid after all the
569 // postorder updates.
573 // Otherwise we need to merge all of the SCCs in the cycle into a single
576 // NB: We merge into the target because all of these functions were already
577 // reachable from the target, meaning any SCC-wide properties deduced about it
578 // other than the set of functions within it will not have changed.
579 for (SCC *C : MergeRange) {
580 assert(C != &TargetSCC &&
581 "We merge *into* the target and shouldn't process it here!");
583 TargetSCC.Nodes.append(C->Nodes.begin(), C->Nodes.end());
584 for (Node *N : C->Nodes)
585 G->SCCMap[N] = &TargetSCC;
587 DeletedSCCs.push_back(C);
590 // Erase the merged SCCs from the list and update the indices of the
592 int IndexOffset = MergeRange.end() - MergeRange.begin();
593 auto EraseEnd = SCCs.erase(MergeRange.begin(), MergeRange.end());
594 for (SCC *C : make_range(EraseEnd, SCCs.end()))
595 SCCIndices[C] -= IndexOffset;
597 // Now that the SCC structure is finalized, flip the kind to call.
598 SourceN->setEdgeKind(TargetN, Edge::Call);
604 void LazyCallGraph::RefSCC::switchTrivialInternalEdgeToRef(Node &SourceN,
606 assert((*SourceN)[TargetN].isCall() && "Must start with a call edge!");
609 // In a debug build, verify the RefSCC is valid to start with and when this
612 auto VerifyOnExit = make_scope_exit([&]() { verify(); });
615 assert(G->lookupRefSCC(SourceN) == this &&
616 "Source must be in this RefSCC.");
617 assert(G->lookupRefSCC(TargetN) == this &&
618 "Target must be in this RefSCC.");
619 assert(G->lookupSCC(SourceN) != G->lookupSCC(TargetN) &&
620 "Source and Target must be in separate SCCs for this to be trivial!");
622 // Set the edge kind.
623 SourceN->setEdgeKind(TargetN, Edge::Ref);
626 iterator_range<LazyCallGraph::RefSCC::iterator>
627 LazyCallGraph::RefSCC::switchInternalEdgeToRef(Node &SourceN, Node &TargetN) {
628 assert((*SourceN)[TargetN].isCall() && "Must start with a call edge!");
631 // In a debug build, verify the RefSCC is valid to start with and when this
634 auto VerifyOnExit = make_scope_exit([&]() { verify(); });
637 assert(G->lookupRefSCC(SourceN) == this &&
638 "Source must be in this RefSCC.");
639 assert(G->lookupRefSCC(TargetN) == this &&
640 "Target must be in this RefSCC.");
642 SCC &TargetSCC = *G->lookupSCC(TargetN);
643 assert(G->lookupSCC(SourceN) == &TargetSCC && "Source and Target must be in "
644 "the same SCC to require the "
647 // Set the edge kind.
648 SourceN->setEdgeKind(TargetN, Edge::Ref);
650 // Otherwise we are removing a call edge from a single SCC. This may break
651 // the cycle. In order to compute the new set of SCCs, we need to do a small
652 // DFS over the nodes within the SCC to form any sub-cycles that remain as
653 // distinct SCCs and compute a postorder over the resulting SCCs.
655 // However, we specially handle the target node. The target node is known to
656 // reach all other nodes in the original SCC by definition. This means that
657 // we want the old SCC to be replaced with an SCC contaning that node as it
658 // will be the root of whatever SCC DAG results from the DFS. Assumptions
659 // about an SCC such as the set of functions called will continue to hold,
662 SCC &OldSCC = TargetSCC;
663 SmallVector<std::pair<Node *, EdgeSequence::call_iterator>, 16> DFSStack;
664 SmallVector<Node *, 16> PendingSCCStack;
665 SmallVector<SCC *, 4> NewSCCs;
667 // Prepare the nodes for a fresh DFS.
668 SmallVector<Node *, 16> Worklist;
669 Worklist.swap(OldSCC.Nodes);
670 for (Node *N : Worklist) {
671 N->DFSNumber = N->LowLink = 0;
675 // Force the target node to be in the old SCC. This also enables us to take
676 // a very significant short-cut in the standard Tarjan walk to re-form SCCs
677 // below: whenever we build an edge that reaches the target node, we know
678 // that the target node eventually connects back to all other nodes in our
679 // walk. As a consequence, we can detect and handle participants in that
680 // cycle without walking all the edges that form this connection, and instead
681 // by relying on the fundamental guarantee coming into this operation (all
682 // nodes are reachable from the target due to previously forming an SCC).
683 TargetN.DFSNumber = TargetN.LowLink = -1;
684 OldSCC.Nodes.push_back(&TargetN);
685 G->SCCMap[&TargetN] = &OldSCC;
687 // Scan down the stack and DFS across the call edges.
688 for (Node *RootN : Worklist) {
689 assert(DFSStack.empty() &&
690 "Cannot begin a new root with a non-empty DFS stack!");
691 assert(PendingSCCStack.empty() &&
692 "Cannot begin a new root with pending nodes for an SCC!");
694 // Skip any nodes we've already reached in the DFS.
695 if (RootN->DFSNumber != 0) {
696 assert(RootN->DFSNumber == -1 &&
697 "Shouldn't have any mid-DFS root nodes!");
701 RootN->DFSNumber = RootN->LowLink = 1;
702 int NextDFSNumber = 2;
704 DFSStack.push_back({RootN, (*RootN)->call_begin()});
707 EdgeSequence::call_iterator I;
708 std::tie(N, I) = DFSStack.pop_back_val();
709 auto E = (*N)->call_end();
711 Node &ChildN = I->getNode();
712 if (ChildN.DFSNumber == 0) {
713 // We haven't yet visited this child, so descend, pushing the current
714 // node onto the stack.
715 DFSStack.push_back({N, I});
717 assert(!G->SCCMap.count(&ChildN) &&
718 "Found a node with 0 DFS number but already in an SCC!");
719 ChildN.DFSNumber = ChildN.LowLink = NextDFSNumber++;
721 I = (*N)->call_begin();
722 E = (*N)->call_end();
726 // Check for the child already being part of some component.
727 if (ChildN.DFSNumber == -1) {
728 if (G->lookupSCC(ChildN) == &OldSCC) {
729 // If the child is part of the old SCC, we know that it can reach
730 // every other node, so we have formed a cycle. Pull the entire DFS
731 // and pending stacks into it. See the comment above about setting
732 // up the old SCC for why we do this.
733 int OldSize = OldSCC.size();
734 OldSCC.Nodes.push_back(N);
735 OldSCC.Nodes.append(PendingSCCStack.begin(), PendingSCCStack.end());
736 PendingSCCStack.clear();
737 while (!DFSStack.empty())
738 OldSCC.Nodes.push_back(DFSStack.pop_back_val().first);
739 for (Node &N : make_range(OldSCC.begin() + OldSize, OldSCC.end())) {
740 N.DFSNumber = N.LowLink = -1;
741 G->SCCMap[&N] = &OldSCC;
747 // If the child has already been added to some child component, it
748 // couldn't impact the low-link of this parent because it isn't
749 // connected, and thus its low-link isn't relevant so skip it.
754 // Track the lowest linked child as the lowest link for this node.
755 assert(ChildN.LowLink > 0 && "Must have a positive low-link number!");
756 if (ChildN.LowLink < N->LowLink)
757 N->LowLink = ChildN.LowLink;
759 // Move to the next edge.
763 // Cleared the DFS early, start another round.
766 // We've finished processing N and its descendents, put it on our pending
767 // SCC stack to eventually get merged into an SCC of nodes.
768 PendingSCCStack.push_back(N);
770 // If this node is linked to some lower entry, continue walking up the
772 if (N->LowLink != N->DFSNumber)
775 // Otherwise, we've completed an SCC. Append it to our post order list of
777 int RootDFSNumber = N->DFSNumber;
778 // Find the range of the node stack by walking down until we pass the
780 auto SCCNodes = make_range(
781 PendingSCCStack.rbegin(),
782 find_if(reverse(PendingSCCStack), [RootDFSNumber](const Node *N) {
783 return N->DFSNumber < RootDFSNumber;
786 // Form a new SCC out of these nodes and then clear them off our pending
788 NewSCCs.push_back(G->createSCC(*this, SCCNodes));
789 for (Node &N : *NewSCCs.back()) {
790 N.DFSNumber = N.LowLink = -1;
791 G->SCCMap[&N] = NewSCCs.back();
793 PendingSCCStack.erase(SCCNodes.end().base(), PendingSCCStack.end());
794 } while (!DFSStack.empty());
797 // Insert the remaining SCCs before the old one. The old SCC can reach all
798 // other SCCs we form because it contains the target node of the removed edge
799 // of the old SCC. This means that we will have edges into all of the new
800 // SCCs, which means the old one must come last for postorder.
801 int OldIdx = SCCIndices[&OldSCC];
802 SCCs.insert(SCCs.begin() + OldIdx, NewSCCs.begin(), NewSCCs.end());
804 // Update the mapping from SCC* to index to use the new SCC*s, and remove the
805 // old SCC from the mapping.
806 for (int Idx = OldIdx, Size = SCCs.size(); Idx < Size; ++Idx)
807 SCCIndices[SCCs[Idx]] = Idx;
809 return make_range(SCCs.begin() + OldIdx,
810 SCCs.begin() + OldIdx + NewSCCs.size());
813 void LazyCallGraph::RefSCC::switchOutgoingEdgeToCall(Node &SourceN,
815 assert(!(*SourceN)[TargetN].isCall() && "Must start with a ref edge!");
817 assert(G->lookupRefSCC(SourceN) == this && "Source must be in this RefSCC.");
818 assert(G->lookupRefSCC(TargetN) != this &&
819 "Target must not be in this RefSCC.");
820 #ifdef EXPENSIVE_CHECKS
821 assert(G->lookupRefSCC(TargetN)->isDescendantOf(*this) &&
822 "Target must be a descendant of the Source.");
825 // Edges between RefSCCs are the same regardless of call or ref, so we can
826 // just flip the edge here.
827 SourceN->setEdgeKind(TargetN, Edge::Call);
830 // Check that the RefSCC is still valid.
835 void LazyCallGraph::RefSCC::switchOutgoingEdgeToRef(Node &SourceN,
837 assert((*SourceN)[TargetN].isCall() && "Must start with a call edge!");
839 assert(G->lookupRefSCC(SourceN) == this && "Source must be in this RefSCC.");
840 assert(G->lookupRefSCC(TargetN) != this &&
841 "Target must not be in this RefSCC.");
842 #ifdef EXPENSIVE_CHECKS
843 assert(G->lookupRefSCC(TargetN)->isDescendantOf(*this) &&
844 "Target must be a descendant of the Source.");
847 // Edges between RefSCCs are the same regardless of call or ref, so we can
848 // just flip the edge here.
849 SourceN->setEdgeKind(TargetN, Edge::Ref);
852 // Check that the RefSCC is still valid.
857 void LazyCallGraph::RefSCC::insertInternalRefEdge(Node &SourceN,
859 assert(G->lookupRefSCC(SourceN) == this && "Source must be in this RefSCC.");
860 assert(G->lookupRefSCC(TargetN) == this && "Target must be in this RefSCC.");
862 SourceN->insertEdgeInternal(TargetN, Edge::Ref);
865 // Check that the RefSCC is still valid.
870 void LazyCallGraph::RefSCC::insertOutgoingEdge(Node &SourceN, Node &TargetN,
872 // First insert it into the caller.
873 SourceN->insertEdgeInternal(TargetN, EK);
875 assert(G->lookupRefSCC(SourceN) == this && "Source must be in this RefSCC.");
877 RefSCC &TargetC = *G->lookupRefSCC(TargetN);
878 assert(&TargetC != this && "Target must not be in this RefSCC.");
879 #ifdef EXPENSIVE_CHECKS
880 assert(TargetC.isDescendantOf(*this) &&
881 "Target must be a descendant of the Source.");
884 // The only change required is to add this SCC to the parent set of the
886 TargetC.Parents.insert(this);
889 // Check that the RefSCC is still valid.
894 SmallVector<LazyCallGraph::RefSCC *, 1>
895 LazyCallGraph::RefSCC::insertIncomingRefEdge(Node &SourceN, Node &TargetN) {
896 assert(G->lookupRefSCC(TargetN) == this && "Target must be in this RefSCC.");
897 RefSCC &SourceC = *G->lookupRefSCC(SourceN);
898 assert(&SourceC != this && "Source must not be in this RefSCC.");
899 #ifdef EXPENSIVE_CHECKS
900 assert(SourceC.isDescendantOf(*this) &&
901 "Source must be a descendant of the Target.");
904 SmallVector<RefSCC *, 1> DeletedRefSCCs;
907 // In a debug build, verify the RefSCC is valid to start with and when this
910 auto VerifyOnExit = make_scope_exit([&]() { verify(); });
913 int SourceIdx = G->RefSCCIndices[&SourceC];
914 int TargetIdx = G->RefSCCIndices[this];
915 assert(SourceIdx < TargetIdx &&
916 "Postorder list doesn't see edge as incoming!");
918 // Compute the RefSCCs which (transitively) reach the source. We do this by
919 // working backwards from the source using the parent set in each RefSCC,
920 // skipping any RefSCCs that don't fall in the postorder range. This has the
921 // advantage of walking the sparser parent edge (in high fan-out graphs) but
922 // more importantly this removes examining all forward edges in all RefSCCs
923 // within the postorder range which aren't in fact connected. Only connected
924 // RefSCCs (and their edges) are visited here.
925 auto ComputeSourceConnectedSet = [&](SmallPtrSetImpl<RefSCC *> &Set) {
926 Set.insert(&SourceC);
927 SmallVector<RefSCC *, 4> Worklist;
928 Worklist.push_back(&SourceC);
930 RefSCC &RC = *Worklist.pop_back_val();
931 for (RefSCC &ParentRC : RC.parents()) {
932 // Skip any RefSCCs outside the range of source to target in the
933 // postorder sequence.
934 int ParentIdx = G->getRefSCCIndex(ParentRC);
935 assert(ParentIdx > SourceIdx && "Parent cannot precede source in postorder!");
936 if (ParentIdx > TargetIdx)
938 if (Set.insert(&ParentRC).second)
939 // First edge connecting to this parent, add it to our worklist.
940 Worklist.push_back(&ParentRC);
942 } while (!Worklist.empty());
945 // Use a normal worklist to find which SCCs the target connects to. We still
946 // bound the search based on the range in the postorder list we care about,
947 // but because this is forward connectivity we just "recurse" through the
949 auto ComputeTargetConnectedSet = [&](SmallPtrSetImpl<RefSCC *> &Set) {
951 SmallVector<RefSCC *, 4> Worklist;
952 Worklist.push_back(this);
954 RefSCC &RC = *Worklist.pop_back_val();
958 RefSCC &EdgeRC = *G->lookupRefSCC(E.getNode());
959 if (G->getRefSCCIndex(EdgeRC) <= SourceIdx)
960 // Not in the postorder sequence between source and target.
963 if (Set.insert(&EdgeRC).second)
964 Worklist.push_back(&EdgeRC);
966 } while (!Worklist.empty());
969 // Use a generic helper to update the postorder sequence of RefSCCs and return
970 // a range of any RefSCCs connected into a cycle by inserting this edge. This
971 // routine will also take care of updating the indices into the postorder
973 iterator_range<SmallVectorImpl<RefSCC *>::iterator> MergeRange =
974 updatePostorderSequenceForEdgeInsertion(
975 SourceC, *this, G->PostOrderRefSCCs, G->RefSCCIndices,
976 ComputeSourceConnectedSet, ComputeTargetConnectedSet);
978 // Build a set so we can do fast tests for whether a RefSCC will end up as
979 // part of the merged RefSCC.
980 SmallPtrSet<RefSCC *, 16> MergeSet(MergeRange.begin(), MergeRange.end());
982 // This RefSCC will always be part of that set, so just insert it here.
983 MergeSet.insert(this);
985 // Now that we have identified all of the SCCs which need to be merged into
986 // a connected set with the inserted edge, merge all of them into this SCC.
987 SmallVector<SCC *, 16> MergedSCCs;
989 for (RefSCC *RC : MergeRange) {
990 assert(RC != this && "We're merging into the target RefSCC, so it "
991 "shouldn't be in the range.");
993 // Merge the parents which aren't part of the merge into the our parents.
994 for (RefSCC *ParentRC : RC->Parents)
995 if (!MergeSet.count(ParentRC))
996 Parents.insert(ParentRC);
999 // Walk the inner SCCs to update their up-pointer and walk all the edges to
1000 // update any parent sets.
1001 // FIXME: We should try to find a way to avoid this (rather expensive) edge
1002 // walk by updating the parent sets in some other manner.
1003 for (SCC &InnerC : *RC) {
1004 InnerC.OuterRefSCC = this;
1005 SCCIndices[&InnerC] = SCCIndex++;
1006 for (Node &N : InnerC) {
1007 G->SCCMap[&N] = &InnerC;
1008 for (Edge &E : *N) {
1009 RefSCC &ChildRC = *G->lookupRefSCC(E.getNode());
1010 if (MergeSet.count(&ChildRC))
1012 ChildRC.Parents.erase(RC);
1013 ChildRC.Parents.insert(this);
1018 // Now merge in the SCCs. We can actually move here so try to reuse storage
1019 // the first time through.
1020 if (MergedSCCs.empty())
1021 MergedSCCs = std::move(RC->SCCs);
1023 MergedSCCs.append(RC->SCCs.begin(), RC->SCCs.end());
1025 DeletedRefSCCs.push_back(RC);
1028 // Append our original SCCs to the merged list and move it into place.
1029 for (SCC &InnerC : *this)
1030 SCCIndices[&InnerC] = SCCIndex++;
1031 MergedSCCs.append(SCCs.begin(), SCCs.end());
1032 SCCs = std::move(MergedSCCs);
1034 // Remove the merged away RefSCCs from the post order sequence.
1035 for (RefSCC *RC : MergeRange)
1036 G->RefSCCIndices.erase(RC);
1037 int IndexOffset = MergeRange.end() - MergeRange.begin();
1039 G->PostOrderRefSCCs.erase(MergeRange.begin(), MergeRange.end());
1040 for (RefSCC *RC : make_range(EraseEnd, G->PostOrderRefSCCs.end()))
1041 G->RefSCCIndices[RC] -= IndexOffset;
1043 // At this point we have a merged RefSCC with a post-order SCCs list, just
1044 // connect the nodes to form the new edge.
1045 SourceN->insertEdgeInternal(TargetN, Edge::Ref);
1047 // We return the list of SCCs which were merged so that callers can
1048 // invalidate any data they have associated with those SCCs. Note that these
1049 // SCCs are no longer in an interesting state (they are totally empty) but
1050 // the pointers will remain stable for the life of the graph itself.
1051 return DeletedRefSCCs;
1054 void LazyCallGraph::RefSCC::removeOutgoingEdge(Node &SourceN, Node &TargetN) {
1055 assert(G->lookupRefSCC(SourceN) == this &&
1056 "The source must be a member of this RefSCC.");
1058 RefSCC &TargetRC = *G->lookupRefSCC(TargetN);
1059 assert(&TargetRC != this && "The target must not be a member of this RefSCC");
1061 assert(!is_contained(G->LeafRefSCCs, this) &&
1062 "Cannot have a leaf RefSCC source.");
1065 // In a debug build, verify the RefSCC is valid to start with and when this
1066 // routine finishes.
1068 auto VerifyOnExit = make_scope_exit([&]() { verify(); });
1071 // First remove it from the node.
1072 bool Removed = SourceN->removeEdgeInternal(TargetN);
1074 assert(Removed && "Target not in the edge set for this caller?");
1076 bool HasOtherEdgeToChildRC = false;
1077 bool HasOtherChildRC = false;
1078 for (SCC *InnerC : SCCs) {
1079 for (Node &N : *InnerC) {
1080 for (Edge &E : *N) {
1081 RefSCC &OtherChildRC = *G->lookupRefSCC(E.getNode());
1082 if (&OtherChildRC == &TargetRC) {
1083 HasOtherEdgeToChildRC = true;
1086 if (&OtherChildRC != this)
1087 HasOtherChildRC = true;
1089 if (HasOtherEdgeToChildRC)
1092 if (HasOtherEdgeToChildRC)
1095 // Because the SCCs form a DAG, deleting such an edge cannot change the set
1096 // of SCCs in the graph. However, it may cut an edge of the SCC DAG, making
1097 // the source SCC no longer connected to the target SCC. If so, we need to
1098 // update the target SCC's map of its parents.
1099 if (!HasOtherEdgeToChildRC) {
1100 bool Removed = TargetRC.Parents.erase(this);
1103 "Did not find the source SCC in the target SCC's parent list!");
1105 // It may orphan an SCC if it is the last edge reaching it, but that does
1106 // not violate any invariants of the graph.
1107 if (TargetRC.Parents.empty())
1108 DEBUG(dbgs() << "LCG: Update removing " << SourceN.getFunction().getName()
1109 << " -> " << TargetN.getFunction().getName()
1110 << " edge orphaned the callee's SCC!\n");
1112 // It may make the Source SCC a leaf SCC.
1113 if (!HasOtherChildRC)
1114 G->LeafRefSCCs.push_back(this);
1118 SmallVector<LazyCallGraph::RefSCC *, 1>
1119 LazyCallGraph::RefSCC::removeInternalRefEdge(Node &SourceN, Node &TargetN) {
1120 assert(!(*SourceN)[TargetN].isCall() &&
1121 "Cannot remove a call edge, it must first be made a ref edge");
1124 // In a debug build, verify the RefSCC is valid to start with and when this
1125 // routine finishes.
1127 auto VerifyOnExit = make_scope_exit([&]() { verify(); });
1130 // First remove the actual edge.
1131 bool Removed = SourceN->removeEdgeInternal(TargetN);
1133 assert(Removed && "Target not in the edge set for this caller?");
1135 // We return a list of the resulting *new* RefSCCs in post-order.
1136 SmallVector<RefSCC *, 1> Result;
1138 // Direct recursion doesn't impact the SCC graph at all.
1139 if (&SourceN == &TargetN)
1142 // If this ref edge is within an SCC then there are sufficient other edges to
1143 // form a cycle without this edge so removing it is a no-op.
1144 SCC &SourceC = *G->lookupSCC(SourceN);
1145 SCC &TargetC = *G->lookupSCC(TargetN);
1146 if (&SourceC == &TargetC)
1149 // We build somewhat synthetic new RefSCCs by providing a postorder mapping
1150 // for each inner SCC. We also store these associated with *nodes* rather
1151 // than SCCs because this saves a round-trip through the node->SCC map and in
1152 // the common case, SCCs are small. We will verify that we always give the
1153 // same number to every node in the SCC such that these are equivalent.
1154 const int RootPostOrderNumber = 0;
1155 int PostOrderNumber = RootPostOrderNumber + 1;
1156 SmallDenseMap<Node *, int> PostOrderMapping;
1158 // Every node in the target SCC can already reach every node in this RefSCC
1159 // (by definition). It is the only node we know will stay inside this RefSCC.
1160 // Everything which transitively reaches Target will also remain in the
1161 // RefSCC. We handle this by pre-marking that the nodes in the target SCC map
1162 // back to the root post order number.
1164 // This also enables us to take a very significant short-cut in the standard
1165 // Tarjan walk to re-form RefSCCs below: whenever we build an edge that
1166 // references the target node, we know that the target node eventually
1167 // references all other nodes in our walk. As a consequence, we can detect
1168 // and handle participants in that cycle without walking all the edges that
1169 // form the connections, and instead by relying on the fundamental guarantee
1170 // coming into this operation.
1171 for (Node &N : TargetC)
1172 PostOrderMapping[&N] = RootPostOrderNumber;
1174 // Reset all the other nodes to prepare for a DFS over them, and add them to
1176 SmallVector<Node *, 8> Worklist;
1177 for (SCC *C : SCCs) {
1182 N.DFSNumber = N.LowLink = 0;
1184 Worklist.append(C->Nodes.begin(), C->Nodes.end());
1187 auto MarkNodeForSCCNumber = [&PostOrderMapping](Node &N, int Number) {
1188 N.DFSNumber = N.LowLink = -1;
1189 PostOrderMapping[&N] = Number;
1192 SmallVector<std::pair<Node *, EdgeSequence::iterator>, 4> DFSStack;
1193 SmallVector<Node *, 4> PendingRefSCCStack;
1195 assert(DFSStack.empty() &&
1196 "Cannot begin a new root with a non-empty DFS stack!");
1197 assert(PendingRefSCCStack.empty() &&
1198 "Cannot begin a new root with pending nodes for an SCC!");
1200 Node *RootN = Worklist.pop_back_val();
1201 // Skip any nodes we've already reached in the DFS.
1202 if (RootN->DFSNumber != 0) {
1203 assert(RootN->DFSNumber == -1 &&
1204 "Shouldn't have any mid-DFS root nodes!");
1208 RootN->DFSNumber = RootN->LowLink = 1;
1209 int NextDFSNumber = 2;
1211 DFSStack.push_back({RootN, (*RootN)->begin()});
1214 EdgeSequence::iterator I;
1215 std::tie(N, I) = DFSStack.pop_back_val();
1216 auto E = (*N)->end();
1218 assert(N->DFSNumber != 0 && "We should always assign a DFS number "
1219 "before processing a node.");
1222 Node &ChildN = I->getNode();
1223 if (ChildN.DFSNumber == 0) {
1224 // Mark that we should start at this child when next this node is the
1225 // top of the stack. We don't start at the next child to ensure this
1226 // child's lowlink is reflected.
1227 DFSStack.push_back({N, I});
1229 // Continue, resetting to the child node.
1230 ChildN.LowLink = ChildN.DFSNumber = NextDFSNumber++;
1232 I = ChildN->begin();
1236 if (ChildN.DFSNumber == -1) {
1237 // Check if this edge's target node connects to the deleted edge's
1238 // target node. If so, we know that every node connected will end up
1239 // in this RefSCC, so collapse the entire current stack into the root
1240 // slot in our SCC numbering. See above for the motivation of
1241 // optimizing the target connected nodes in this way.
1242 auto PostOrderI = PostOrderMapping.find(&ChildN);
1243 if (PostOrderI != PostOrderMapping.end() &&
1244 PostOrderI->second == RootPostOrderNumber) {
1245 MarkNodeForSCCNumber(*N, RootPostOrderNumber);
1246 while (!PendingRefSCCStack.empty())
1247 MarkNodeForSCCNumber(*PendingRefSCCStack.pop_back_val(),
1248 RootPostOrderNumber);
1249 while (!DFSStack.empty())
1250 MarkNodeForSCCNumber(*DFSStack.pop_back_val().first,
1251 RootPostOrderNumber);
1252 // Ensure we break all the way out of the enclosing loop.
1257 // If this child isn't currently in this RefSCC, no need to process
1258 // it. However, we do need to remove this RefSCC from its RefSCC's
1260 RefSCC &ChildRC = *G->lookupRefSCC(ChildN);
1261 ChildRC.Parents.erase(this);
1266 // Track the lowest link of the children, if any are still in the stack.
1267 // Any child not on the stack will have a LowLink of -1.
1268 assert(ChildN.LowLink != 0 &&
1269 "Low-link must not be zero with a non-zero DFS number.");
1270 if (ChildN.LowLink >= 0 && ChildN.LowLink < N->LowLink)
1271 N->LowLink = ChildN.LowLink;
1275 // We short-circuited this node.
1278 // We've finished processing N and its descendents, put it on our pending
1279 // stack to eventually get merged into a RefSCC.
1280 PendingRefSCCStack.push_back(N);
1282 // If this node is linked to some lower entry, continue walking up the
1284 if (N->LowLink != N->DFSNumber) {
1285 assert(!DFSStack.empty() &&
1286 "We never found a viable root for a RefSCC to pop off!");
1290 // Otherwise, form a new RefSCC from the top of the pending node stack.
1291 int RootDFSNumber = N->DFSNumber;
1292 // Find the range of the node stack by walking down until we pass the
1294 auto RefSCCNodes = make_range(
1295 PendingRefSCCStack.rbegin(),
1296 find_if(reverse(PendingRefSCCStack), [RootDFSNumber](const Node *N) {
1297 return N->DFSNumber < RootDFSNumber;
1300 // Mark the postorder number for these nodes and clear them off the
1301 // stack. We'll use the postorder number to pull them into RefSCCs at the
1302 // end. FIXME: Fuse with the loop above.
1303 int RefSCCNumber = PostOrderNumber++;
1304 for (Node *N : RefSCCNodes)
1305 MarkNodeForSCCNumber(*N, RefSCCNumber);
1307 PendingRefSCCStack.erase(RefSCCNodes.end().base(),
1308 PendingRefSCCStack.end());
1309 } while (!DFSStack.empty());
1311 assert(DFSStack.empty() && "Didn't flush the entire DFS stack!");
1312 assert(PendingRefSCCStack.empty() && "Didn't flush all pending nodes!");
1313 } while (!Worklist.empty());
1315 // We now have a post-order numbering for RefSCCs and a mapping from each
1316 // node in this RefSCC to its final RefSCC. We create each new RefSCC node
1317 // (re-using this RefSCC node for the root) and build a radix-sort style map
1318 // from postorder number to the RefSCC. We then append SCCs to each of these
1319 // RefSCCs in the order they occured in the original SCCs container.
1320 for (int i = 1; i < PostOrderNumber; ++i)
1321 Result.push_back(G->createRefSCC(*G));
1323 // Insert the resulting postorder sequence into the global graph postorder
1324 // sequence before the current RefSCC in that sequence. The idea being that
1325 // this RefSCC is the target of the reference edge removed, and thus has
1326 // a direct or indirect edge to every other RefSCC formed and so must be at
1327 // the end of any postorder traversal.
1329 // FIXME: It'd be nice to change the APIs so that we returned an iterator
1330 // range over the global postorder sequence and generally use that sequence
1331 // rather than building a separate result vector here.
1332 if (!Result.empty()) {
1333 int Idx = G->getRefSCCIndex(*this);
1334 G->PostOrderRefSCCs.insert(G->PostOrderRefSCCs.begin() + Idx,
1335 Result.begin(), Result.end());
1336 for (int i : seq<int>(Idx, G->PostOrderRefSCCs.size()))
1337 G->RefSCCIndices[G->PostOrderRefSCCs[i]] = i;
1338 assert(G->PostOrderRefSCCs[G->getRefSCCIndex(*this)] == this &&
1339 "Failed to update this RefSCC's index after insertion!");
1342 for (SCC *C : SCCs) {
1343 auto PostOrderI = PostOrderMapping.find(&*C->begin());
1344 assert(PostOrderI != PostOrderMapping.end() &&
1345 "Cannot have missing mappings for nodes!");
1346 int SCCNumber = PostOrderI->second;
1349 assert(PostOrderMapping.find(&N)->second == SCCNumber &&
1350 "Cannot have different numbers for nodes in the same SCC!");
1353 // The root node is handled separately by removing the SCCs.
1356 RefSCC &RC = *Result[SCCNumber - 1];
1357 int SCCIndex = RC.SCCs.size();
1358 RC.SCCs.push_back(C);
1359 RC.SCCIndices[C] = SCCIndex;
1360 C->OuterRefSCC = &RC;
1363 // FIXME: We re-walk the edges in each RefSCC to establish whether it is
1364 // a leaf and connect it to the rest of the graph's parents lists. This is
1365 // really wasteful. We should instead do this during the DFS to avoid yet
1366 // another edge walk.
1367 for (RefSCC *RC : Result)
1368 G->connectRefSCC(*RC);
1370 // Now erase all but the root's SCCs.
1371 SCCs.erase(remove_if(SCCs,
1373 return PostOrderMapping.lookup(&*C->begin()) !=
1374 RootPostOrderNumber;
1378 for (int i = 0, Size = SCCs.size(); i < Size; ++i)
1379 SCCIndices[SCCs[i]] = i;
1382 // Now we need to reconnect the current (root) SCC to the graph. We do this
1383 // manually because we can special case our leaf handling and detect errors.
1387 for (Node &N : *C) {
1388 for (Edge &E : *N) {
1389 RefSCC &ChildRC = *G->lookupRefSCC(E.getNode());
1390 if (&ChildRC == this)
1392 ChildRC.Parents.insert(this);
1399 if (!Result.empty())
1400 assert(!IsLeaf && "This SCC cannot be a leaf as we have split out new "
1401 "SCCs by removing this edge.");
1402 if (none_of(G->LeafRefSCCs, [&](RefSCC *C) { return C == this; }))
1403 assert(!IsLeaf && "This SCC cannot be a leaf as it already had child "
1404 "SCCs before we removed this edge.");
1406 // And connect both this RefSCC and all the new ones to the correct parents.
1407 // The easiest way to do this is just to re-analyze the old parent set.
1408 SmallVector<RefSCC *, 4> OldParents(Parents.begin(), Parents.end());
1410 for (RefSCC *ParentRC : OldParents)
1411 for (SCC &ParentC : *ParentRC)
1412 for (Node &ParentN : ParentC)
1413 for (Edge &E : *ParentN) {
1414 RefSCC &RC = *G->lookupRefSCC(E.getNode());
1415 if (&RC != ParentRC)
1416 RC.Parents.insert(ParentRC);
1419 // If this SCC stopped being a leaf through this edge removal, remove it from
1420 // the leaf SCC list. Note that this DTRT in the case where this was never
1422 // FIXME: As LeafRefSCCs could be very large, we might want to not walk the
1423 // entire list if this RefSCC wasn't a leaf before the edge removal.
1424 if (!Result.empty())
1425 G->LeafRefSCCs.erase(
1426 std::remove(G->LeafRefSCCs.begin(), G->LeafRefSCCs.end(), this),
1427 G->LeafRefSCCs.end());
1430 // Verify all of the new RefSCCs.
1431 for (RefSCC *RC : Result)
1435 // Return the new list of SCCs.
1439 void LazyCallGraph::RefSCC::handleTrivialEdgeInsertion(Node &SourceN,
1441 // The only trivial case that requires any graph updates is when we add new
1442 // ref edge and may connect different RefSCCs along that path. This is only
1443 // because of the parents set. Every other part of the graph remains constant
1444 // after this edge insertion.
1445 assert(G->lookupRefSCC(SourceN) == this && "Source must be in this RefSCC.");
1446 RefSCC &TargetRC = *G->lookupRefSCC(TargetN);
1447 if (&TargetRC == this) {
1452 #ifdef EXPENSIVE_CHECKS
1453 assert(TargetRC.isDescendantOf(*this) &&
1454 "Target must be a descendant of the Source.");
1456 // The only change required is to add this RefSCC to the parent set of the
1457 // target. This is a set and so idempotent if the edge already existed.
1458 TargetRC.Parents.insert(this);
1461 void LazyCallGraph::RefSCC::insertTrivialCallEdge(Node &SourceN,
1464 // Check that the RefSCC is still valid when we finish.
1465 auto ExitVerifier = make_scope_exit([this] { verify(); });
1467 #ifdef EXPENSIVE_CHECKS
1468 // Check that we aren't breaking some invariants of the SCC graph. Note that
1469 // this is quadratic in the number of edges in the call graph!
1470 SCC &SourceC = *G->lookupSCC(SourceN);
1471 SCC &TargetC = *G->lookupSCC(TargetN);
1472 if (&SourceC != &TargetC)
1473 assert(SourceC.isAncestorOf(TargetC) &&
1474 "Call edge is not trivial in the SCC graph!");
1475 #endif // EXPENSIVE_CHECKS
1478 // First insert it into the source or find the existing edge.
1480 SourceN->EdgeIndexMap.insert({&TargetN, SourceN->Edges.size()});
1481 if (!InsertResult.second) {
1482 // Already an edge, just update it.
1483 Edge &E = SourceN->Edges[InsertResult.first->second];
1485 return; // Nothing to do!
1486 E.setKind(Edge::Call);
1488 // Create the new edge.
1489 SourceN->Edges.emplace_back(TargetN, Edge::Call);
1492 // Now that we have the edge, handle the graph fallout.
1493 handleTrivialEdgeInsertion(SourceN, TargetN);
1496 void LazyCallGraph::RefSCC::insertTrivialRefEdge(Node &SourceN, Node &TargetN) {
1498 // Check that the RefSCC is still valid when we finish.
1499 auto ExitVerifier = make_scope_exit([this] { verify(); });
1501 #ifdef EXPENSIVE_CHECKS
1502 // Check that we aren't breaking some invariants of the RefSCC graph.
1503 RefSCC &SourceRC = *G->lookupRefSCC(SourceN);
1504 RefSCC &TargetRC = *G->lookupRefSCC(TargetN);
1505 if (&SourceRC != &TargetRC)
1506 assert(SourceRC.isAncestorOf(TargetRC) &&
1507 "Ref edge is not trivial in the RefSCC graph!");
1508 #endif // EXPENSIVE_CHECKS
1511 // First insert it into the source or find the existing edge.
1513 SourceN->EdgeIndexMap.insert({&TargetN, SourceN->Edges.size()});
1514 if (!InsertResult.second)
1515 // Already an edge, we're done.
1518 // Create the new edge.
1519 SourceN->Edges.emplace_back(TargetN, Edge::Ref);
1521 // Now that we have the edge, handle the graph fallout.
1522 handleTrivialEdgeInsertion(SourceN, TargetN);
1525 void LazyCallGraph::RefSCC::replaceNodeFunction(Node &N, Function &NewF) {
1526 Function &OldF = N.getFunction();
1529 // Check that the RefSCC is still valid when we finish.
1530 auto ExitVerifier = make_scope_exit([this] { verify(); });
1532 assert(G->lookupRefSCC(N) == this &&
1533 "Cannot replace the function of a node outside this RefSCC.");
1535 assert(G->NodeMap.find(&NewF) == G->NodeMap.end() &&
1536 "Must not have already walked the new function!'");
1538 // It is important that this replacement not introduce graph changes so we
1539 // insist that the caller has already removed every use of the original
1540 // function and that all uses of the new function correspond to existing
1541 // edges in the graph. The common and expected way to use this is when
1542 // replacing the function itself in the IR without changing the call graph
1543 // shape and just updating the analysis based on that.
1544 assert(&OldF != &NewF && "Cannot replace a function with itself!");
1545 assert(OldF.use_empty() &&
1546 "Must have moved all uses from the old function to the new!");
1549 N.replaceFunction(NewF);
1551 // Update various call graph maps.
1552 G->NodeMap.erase(&OldF);
1553 G->NodeMap[&NewF] = &N;
1556 void LazyCallGraph::insertEdge(Node &SourceN, Node &TargetN, Edge::Kind EK) {
1557 assert(SCCMap.empty() &&
1558 "This method cannot be called after SCCs have been formed!");
1560 return SourceN->insertEdgeInternal(TargetN, EK);
1563 void LazyCallGraph::removeEdge(Node &SourceN, Node &TargetN) {
1564 assert(SCCMap.empty() &&
1565 "This method cannot be called after SCCs have been formed!");
1567 bool Removed = SourceN->removeEdgeInternal(TargetN);
1569 assert(Removed && "Target not in the edge set for this caller?");
1572 void LazyCallGraph::removeDeadFunction(Function &F) {
1573 // FIXME: This is unnecessarily restrictive. We should be able to remove
1574 // functions which recursively call themselves.
1575 assert(F.use_empty() &&
1576 "This routine should only be called on trivially dead functions!");
1578 auto NI = NodeMap.find(&F);
1579 if (NI == NodeMap.end())
1580 // Not in the graph at all!
1583 Node &N = *NI->second;
1586 // Remove this from the entry edges if present.
1587 EntryEdges.removeEdgeInternal(N);
1589 if (SCCMap.empty()) {
1590 // No SCCs have been formed, so removing this is fine and there is nothing
1591 // else necessary at this point but clearing out the node.
1596 // Cannot remove a function which has yet to be visited in the DFS walk, so
1597 // if we have a node at all then we must have an SCC and RefSCC.
1598 auto CI = SCCMap.find(&N);
1599 assert(CI != SCCMap.end() &&
1600 "Tried to remove a node without an SCC after DFS walk started!");
1601 SCC &C = *CI->second;
1603 RefSCC &RC = C.getOuterRefSCC();
1605 // This node must be the only member of its SCC as it has no callers, and
1606 // that SCC must be the only member of a RefSCC as it has no references.
1607 // Validate these properties first.
1608 assert(C.size() == 1 && "Dead functions must be in a singular SCC");
1609 assert(RC.size() == 1 && "Dead functions must be in a singular RefSCC");
1611 // Clean up any remaining reference edges. Note that we walk an unordered set
1612 // here but are just removing and so the order doesn't matter.
1613 for (RefSCC &ParentRC : RC.parents())
1614 for (SCC &ParentC : ParentRC)
1615 for (Node &ParentN : ParentC)
1617 ParentN->removeEdgeInternal(N);
1619 // Now remove this RefSCC from any parents sets and the leaf list.
1621 if (RefSCC *TargetRC = lookupRefSCC(E.getNode()))
1622 TargetRC->Parents.erase(&RC);
1623 // FIXME: This is a linear operation which could become hot and benefit from
1625 auto LRI = find(LeafRefSCCs, &RC);
1626 if (LRI != LeafRefSCCs.end())
1627 LeafRefSCCs.erase(LRI);
1629 auto RCIndexI = RefSCCIndices.find(&RC);
1630 int RCIndex = RCIndexI->second;
1631 PostOrderRefSCCs.erase(PostOrderRefSCCs.begin() + RCIndex);
1632 RefSCCIndices.erase(RCIndexI);
1633 for (int i = RCIndex, Size = PostOrderRefSCCs.size(); i < Size; ++i)
1634 RefSCCIndices[PostOrderRefSCCs[i]] = i;
1636 // Finally clear out all the data structures from the node down through the
1642 // Nothing to delete as all the objects are allocated in stable bump pointer
1646 LazyCallGraph::Node &LazyCallGraph::insertInto(Function &F, Node *&MappedN) {
1647 return *new (MappedN = BPA.Allocate()) Node(*this, F);
1650 void LazyCallGraph::updateGraphPtrs() {
1651 // Process all nodes updating the graph pointers.
1653 SmallVector<Node *, 16> Worklist;
1654 for (Edge &E : EntryEdges)
1655 Worklist.push_back(&E.getNode());
1657 while (!Worklist.empty()) {
1658 Node &N = *Worklist.pop_back_val();
1662 Worklist.push_back(&E.getNode());
1666 // Process all SCCs updating the graph pointers.
1668 SmallVector<RefSCC *, 16> Worklist(LeafRefSCCs.begin(), LeafRefSCCs.end());
1670 while (!Worklist.empty()) {
1671 RefSCC &C = *Worklist.pop_back_val();
1673 for (RefSCC &ParentC : C.parents())
1674 Worklist.push_back(&ParentC);
1679 template <typename RootsT, typename GetBeginT, typename GetEndT,
1680 typename GetNodeT, typename FormSCCCallbackT>
1681 void LazyCallGraph::buildGenericSCCs(RootsT &&Roots, GetBeginT &&GetBegin,
1682 GetEndT &&GetEnd, GetNodeT &&GetNode,
1683 FormSCCCallbackT &&FormSCC) {
1684 typedef decltype(GetBegin(std::declval<Node &>())) EdgeItT;
1686 SmallVector<std::pair<Node *, EdgeItT>, 16> DFSStack;
1687 SmallVector<Node *, 16> PendingSCCStack;
1689 // Scan down the stack and DFS across the call edges.
1690 for (Node *RootN : Roots) {
1691 assert(DFSStack.empty() &&
1692 "Cannot begin a new root with a non-empty DFS stack!");
1693 assert(PendingSCCStack.empty() &&
1694 "Cannot begin a new root with pending nodes for an SCC!");
1696 // Skip any nodes we've already reached in the DFS.
1697 if (RootN->DFSNumber != 0) {
1698 assert(RootN->DFSNumber == -1 &&
1699 "Shouldn't have any mid-DFS root nodes!");
1703 RootN->DFSNumber = RootN->LowLink = 1;
1704 int NextDFSNumber = 2;
1706 DFSStack.push_back({RootN, GetBegin(*RootN)});
1710 std::tie(N, I) = DFSStack.pop_back_val();
1711 auto E = GetEnd(*N);
1713 Node &ChildN = GetNode(I);
1714 if (ChildN.DFSNumber == 0) {
1715 // We haven't yet visited this child, so descend, pushing the current
1716 // node onto the stack.
1717 DFSStack.push_back({N, I});
1719 ChildN.DFSNumber = ChildN.LowLink = NextDFSNumber++;
1726 // If the child has already been added to some child component, it
1727 // couldn't impact the low-link of this parent because it isn't
1728 // connected, and thus its low-link isn't relevant so skip it.
1729 if (ChildN.DFSNumber == -1) {
1734 // Track the lowest linked child as the lowest link for this node.
1735 assert(ChildN.LowLink > 0 && "Must have a positive low-link number!");
1736 if (ChildN.LowLink < N->LowLink)
1737 N->LowLink = ChildN.LowLink;
1739 // Move to the next edge.
1743 // We've finished processing N and its descendents, put it on our pending
1744 // SCC stack to eventually get merged into an SCC of nodes.
1745 PendingSCCStack.push_back(N);
1747 // If this node is linked to some lower entry, continue walking up the
1749 if (N->LowLink != N->DFSNumber)
1752 // Otherwise, we've completed an SCC. Append it to our post order list of
1754 int RootDFSNumber = N->DFSNumber;
1755 // Find the range of the node stack by walking down until we pass the
1757 auto SCCNodes = make_range(
1758 PendingSCCStack.rbegin(),
1759 find_if(reverse(PendingSCCStack), [RootDFSNumber](const Node *N) {
1760 return N->DFSNumber < RootDFSNumber;
1762 // Form a new SCC out of these nodes and then clear them off our pending
1765 PendingSCCStack.erase(SCCNodes.end().base(), PendingSCCStack.end());
1766 } while (!DFSStack.empty());
1770 /// Build the internal SCCs for a RefSCC from a sequence of nodes.
1772 /// Appends the SCCs to the provided vector and updates the map with their
1773 /// indices. Both the vector and map must be empty when passed into this
1775 void LazyCallGraph::buildSCCs(RefSCC &RC, node_stack_range Nodes) {
1776 assert(RC.SCCs.empty() && "Already built SCCs!");
1777 assert(RC.SCCIndices.empty() && "Already mapped SCC indices!");
1779 for (Node *N : Nodes) {
1780 assert(N->LowLink >= (*Nodes.begin())->LowLink &&
1781 "We cannot have a low link in an SCC lower than its root on the "
1784 // This node will go into the next RefSCC, clear out its DFS and low link
1786 N->DFSNumber = N->LowLink = 0;
1789 // Each RefSCC contains a DAG of the call SCCs. To build these, we do
1790 // a direct walk of the call edges using Tarjan's algorithm. We reuse the
1791 // internal storage as we won't need it for the outer graph's DFS any longer.
1793 Nodes, [](Node &N) { return N->call_begin(); },
1794 [](Node &N) { return N->call_end(); },
1795 [](EdgeSequence::call_iterator I) -> Node & { return I->getNode(); },
1796 [this, &RC](node_stack_range Nodes) {
1797 RC.SCCs.push_back(createSCC(RC, Nodes));
1798 for (Node &N : *RC.SCCs.back()) {
1799 N.DFSNumber = N.LowLink = -1;
1800 SCCMap[&N] = RC.SCCs.back();
1804 // Wire up the SCC indices.
1805 for (int i = 0, Size = RC.SCCs.size(); i < Size; ++i)
1806 RC.SCCIndices[RC.SCCs[i]] = i;
1809 void LazyCallGraph::buildRefSCCs() {
1810 if (EntryEdges.empty() || !PostOrderRefSCCs.empty())
1811 // RefSCCs are either non-existent or already built!
1814 assert(RefSCCIndices.empty() && "Already mapped RefSCC indices!");
1816 SmallVector<Node *, 16> Roots;
1817 for (Edge &E : *this)
1818 Roots.push_back(&E.getNode());
1820 // The roots will be popped of a stack, so use reverse to get a less
1821 // surprising order. This doesn't change any of the semantics anywhere.
1822 std::reverse(Roots.begin(), Roots.end());
1827 // We need to populate each node as we begin to walk its edges.
1831 [](Node &N) { return N->end(); },
1832 [](EdgeSequence::iterator I) -> Node & { return I->getNode(); },
1833 [this](node_stack_range Nodes) {
1834 RefSCC *NewRC = createRefSCC(*this);
1835 buildSCCs(*NewRC, Nodes);
1836 connectRefSCC(*NewRC);
1838 // Push the new node into the postorder list and remember its position
1839 // in the index map.
1841 RefSCCIndices.insert({NewRC, PostOrderRefSCCs.size()}).second;
1843 assert(Inserted && "Cannot already have this RefSCC in the index map!");
1844 PostOrderRefSCCs.push_back(NewRC);
1851 // FIXME: We should move callers of this to embed the parent linking and leaf
1852 // tracking into their DFS in order to remove a full walk of all edges.
1853 void LazyCallGraph::connectRefSCC(RefSCC &RC) {
1854 // Walk all edges in the RefSCC (this remains linear as we only do this once
1855 // when we build the RefSCC) to connect it to the parent sets of its
1860 for (Edge &E : *N) {
1861 RefSCC &ChildRC = *lookupRefSCC(E.getNode());
1862 if (&ChildRC == &RC)
1864 ChildRC.Parents.insert(&RC);
1868 // For the SCCs where we find no child SCCs, add them to the leaf list.
1870 LeafRefSCCs.push_back(&RC);
1873 AnalysisKey LazyCallGraphAnalysis::Key;
1875 LazyCallGraphPrinterPass::LazyCallGraphPrinterPass(raw_ostream &OS) : OS(OS) {}
1877 static void printNode(raw_ostream &OS, LazyCallGraph::Node &N) {
1878 OS << " Edges in function: " << N.getFunction().getName() << "\n";
1879 for (LazyCallGraph::Edge &E : N.populate())
1880 OS << " " << (E.isCall() ? "call" : "ref ") << " -> "
1881 << E.getFunction().getName() << "\n";
1886 static void printSCC(raw_ostream &OS, LazyCallGraph::SCC &C) {
1887 ptrdiff_t Size = std::distance(C.begin(), C.end());
1888 OS << " SCC with " << Size << " functions:\n";
1890 for (LazyCallGraph::Node &N : C)
1891 OS << " " << N.getFunction().getName() << "\n";
1894 static void printRefSCC(raw_ostream &OS, LazyCallGraph::RefSCC &C) {
1895 ptrdiff_t Size = std::distance(C.begin(), C.end());
1896 OS << " RefSCC with " << Size << " call SCCs:\n";
1898 for (LazyCallGraph::SCC &InnerC : C)
1899 printSCC(OS, InnerC);
1904 PreservedAnalyses LazyCallGraphPrinterPass::run(Module &M,
1905 ModuleAnalysisManager &AM) {
1906 LazyCallGraph &G = AM.getResult<LazyCallGraphAnalysis>(M);
1908 OS << "Printing the call graph for module: " << M.getModuleIdentifier()
1911 for (Function &F : M)
1912 printNode(OS, G.get(F));
1915 for (LazyCallGraph::RefSCC &C : G.postorder_ref_sccs())
1918 return PreservedAnalyses::all();
1921 LazyCallGraphDOTPrinterPass::LazyCallGraphDOTPrinterPass(raw_ostream &OS)
1924 static void printNodeDOT(raw_ostream &OS, LazyCallGraph::Node &N) {
1925 std::string Name = "\"" + DOT::EscapeString(N.getFunction().getName()) + "\"";
1927 for (LazyCallGraph::Edge &E : N.populate()) {
1928 OS << " " << Name << " -> \""
1929 << DOT::EscapeString(E.getFunction().getName()) << "\"";
1930 if (!E.isCall()) // It is a ref edge.
1931 OS << " [style=dashed,label=\"ref\"]";
1938 PreservedAnalyses LazyCallGraphDOTPrinterPass::run(Module &M,
1939 ModuleAnalysisManager &AM) {
1940 LazyCallGraph &G = AM.getResult<LazyCallGraphAnalysis>(M);
1942 OS << "digraph \"" << DOT::EscapeString(M.getModuleIdentifier()) << "\" {\n";
1944 for (Function &F : M)
1945 printNodeDOT(OS, G.get(F));
1949 return PreservedAnalyses::all();