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freebsd-nq/contrib/llvm/lib/Analysis/LazyCallGraph.cpp
Dimitry Andric b40b48b876 Merge llvm, clang, lld, lldb, compiler-rt and libc++ r308421, and update 
build glue.
2017-07-19 19:41:41 +00:00

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//===- LazyCallGraph.cpp - Analysis of a Module's call graph --------------===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
#include "llvm/Analysis/LazyCallGraph.h"
#include "llvm/ADT/STLExtras.h"
#include "llvm/ADT/ScopeExit.h"
#include "llvm/ADT/Sequence.h"
#include "llvm/IR/CallSite.h"
#include "llvm/IR/InstVisitor.h"
#include "llvm/IR/Instructions.h"
#include "llvm/IR/PassManager.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/GraphWriter.h"
#include <utility>
using namespace llvm;
#define DEBUG_TYPE "lcg"
void LazyCallGraph::EdgeSequence::insertEdgeInternal(Node &TargetN,
Edge::Kind EK) {
EdgeIndexMap.insert({&TargetN, Edges.size()});
Edges.emplace_back(TargetN, EK);
}
void LazyCallGraph::EdgeSequence::setEdgeKind(Node &TargetN, Edge::Kind EK) {
Edges[EdgeIndexMap.find(&TargetN)->second].setKind(EK);
}
bool LazyCallGraph::EdgeSequence::removeEdgeInternal(Node &TargetN) {
auto IndexMapI = EdgeIndexMap.find(&TargetN);
if (IndexMapI == EdgeIndexMap.end())
return false;
Edges[IndexMapI->second] = Edge();
EdgeIndexMap.erase(IndexMapI);
return true;
}
static void addEdge(SmallVectorImpl<LazyCallGraph::Edge> &Edges,
DenseMap<LazyCallGraph::Node *, int> &EdgeIndexMap,
LazyCallGraph::Node &N, LazyCallGraph::Edge::Kind EK) {
if (!EdgeIndexMap.insert({&N, Edges.size()}).second)
return;
DEBUG(dbgs() << " Added callable function: " << N.getName() << "\n");
Edges.emplace_back(LazyCallGraph::Edge(N, EK));
}
LazyCallGraph::EdgeSequence &LazyCallGraph::Node::populateSlow() {
assert(!Edges && "Must not have already populated the edges for this node!");
DEBUG(dbgs() << " Adding functions called by '" << getName()
<< "' to the graph.\n");
Edges = EdgeSequence();
SmallVector<Constant *, 16> Worklist;
SmallPtrSet<Function *, 4> Callees;
SmallPtrSet<Constant *, 16> Visited;
// Find all the potential call graph edges in this function. We track both
// actual call edges and indirect references to functions. The direct calls
// are trivially added, but to accumulate the latter we walk the instructions
// and add every operand which is a constant to the worklist to process
// afterward.
//
// Note that we consider *any* function with a definition to be a viable
// edge. Even if the function's definition is subject to replacement by
// some other module (say, a weak definition) there may still be
// optimizations which essentially speculate based on the definition and
// a way to check that the specific definition is in fact the one being
// used. For example, this could be done by moving the weak definition to
// a strong (internal) definition and making the weak definition be an
// alias. Then a test of the address of the weak function against the new
// strong definition's address would be an effective way to determine the
// safety of optimizing a direct call edge.
for (BasicBlock &BB : *F)
for (Instruction &I : BB) {
if (auto CS = CallSite(&I))
if (Function *Callee = CS.getCalledFunction())
if (!Callee->isDeclaration())
if (Callees.insert(Callee).second) {
Visited.insert(Callee);
addEdge(Edges->Edges, Edges->EdgeIndexMap, G->get(*Callee),
LazyCallGraph::Edge::Call);
}
for (Value *Op : I.operand_values())
if (Constant *C = dyn_cast<Constant>(Op))
if (Visited.insert(C).second)
Worklist.push_back(C);
}
// We've collected all the constant (and thus potentially function or
// function containing) operands to all of the instructions in the function.
// Process them (recursively) collecting every function found.
visitReferences(Worklist, Visited, [&](Function &F) {
addEdge(Edges->Edges, Edges->EdgeIndexMap, G->get(F),
LazyCallGraph::Edge::Ref);
});
// Add implicit reference edges to any defined libcall functions (if we
// haven't found an explicit edge).
for (auto *F : G->LibFunctions)
if (!Visited.count(F))
addEdge(Edges->Edges, Edges->EdgeIndexMap, G->get(*F),
LazyCallGraph::Edge::Ref);
return *Edges;
}
void LazyCallGraph::Node::replaceFunction(Function &NewF) {
assert(F != &NewF && "Must not replace a function with itself!");
F = &NewF;
}
#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
LLVM_DUMP_METHOD void LazyCallGraph::Node::dump() const {
dbgs() << *this << '\n';
}
#endif
static bool isKnownLibFunction(Function &F, TargetLibraryInfo &TLI) {
LibFunc LF;
// Either this is a normal library function or a "vectorizable" function.
return TLI.getLibFunc(F, LF) || TLI.isFunctionVectorizable(F.getName());
}
LazyCallGraph::LazyCallGraph(Module &M, TargetLibraryInfo &TLI) {
DEBUG(dbgs() << "Building CG for module: " << M.getModuleIdentifier()
<< "\n");
for (Function &F : M) {
if (F.isDeclaration())
continue;
// If this function is a known lib function to LLVM then we want to
// synthesize reference edges to it to model the fact that LLVM can turn
// arbitrary code into a library function call.
if (isKnownLibFunction(F, TLI))
LibFunctions.insert(&F);
if (F.hasLocalLinkage())
continue;
// External linkage defined functions have edges to them from other
// modules.
DEBUG(dbgs() << " Adding '" << F.getName()
<< "' to entry set of the graph.\n");
addEdge(EntryEdges.Edges, EntryEdges.EdgeIndexMap, get(F), Edge::Ref);
}
// Now add entry nodes for functions reachable via initializers to globals.
SmallVector<Constant *, 16> Worklist;
SmallPtrSet<Constant *, 16> Visited;
for (GlobalVariable &GV : M.globals())
if (GV.hasInitializer())
if (Visited.insert(GV.getInitializer()).second)
Worklist.push_back(GV.getInitializer());
DEBUG(dbgs() << " Adding functions referenced by global initializers to the "
"entry set.\n");
visitReferences(Worklist, Visited, [&](Function &F) {
addEdge(EntryEdges.Edges, EntryEdges.EdgeIndexMap, get(F),
LazyCallGraph::Edge::Ref);
});
}
LazyCallGraph::LazyCallGraph(LazyCallGraph &&G)
: BPA(std::move(G.BPA)), NodeMap(std::move(G.NodeMap)),
EntryEdges(std::move(G.EntryEdges)), SCCBPA(std::move(G.SCCBPA)),
SCCMap(std::move(G.SCCMap)), LeafRefSCCs(std::move(G.LeafRefSCCs)),
LibFunctions(std::move(G.LibFunctions)) {
updateGraphPtrs();
}
LazyCallGraph &LazyCallGraph::operator=(LazyCallGraph &&G) {
BPA = std::move(G.BPA);
NodeMap = std::move(G.NodeMap);
EntryEdges = std::move(G.EntryEdges);
SCCBPA = std::move(G.SCCBPA);
SCCMap = std::move(G.SCCMap);
LeafRefSCCs = std::move(G.LeafRefSCCs);
LibFunctions = std::move(G.LibFunctions);
updateGraphPtrs();
return *this;
}
#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
LLVM_DUMP_METHOD void LazyCallGraph::SCC::dump() const {
dbgs() << *this << '\n';
}
#endif
#ifndef NDEBUG
void LazyCallGraph::SCC::verify() {
assert(OuterRefSCC && "Can't have a null RefSCC!");
assert(!Nodes.empty() && "Can't have an empty SCC!");
for (Node *N : Nodes) {
assert(N && "Can't have a null node!");
assert(OuterRefSCC->G->lookupSCC(*N) == this &&
"Node does not map to this SCC!");
assert(N->DFSNumber == -1 &&
"Must set DFS numbers to -1 when adding a node to an SCC!");
assert(N->LowLink == -1 &&
"Must set low link to -1 when adding a node to an SCC!");
for (Edge &E : **N)
assert(E.getNode() && "Can't have an unpopulated node!");
}
}
#endif
bool LazyCallGraph::SCC::isParentOf(const SCC &C) const {
if (this == &C)
return false;
for (Node &N : *this)
for (Edge &E : N->calls())
if (OuterRefSCC->G->lookupSCC(E.getNode()) == &C)
return true;
// No edges found.
return false;
}
bool LazyCallGraph::SCC::isAncestorOf(const SCC &TargetC) const {
if (this == &TargetC)
return false;
LazyCallGraph &G = *OuterRefSCC->G;
// Start with this SCC.
SmallPtrSet<const SCC *, 16> Visited = {this};
SmallVector<const SCC *, 16> Worklist = {this};
// Walk down the graph until we run out of edges or find a path to TargetC.
do {
const SCC &C = *Worklist.pop_back_val();
for (Node &N : C)
for (Edge &E : N->calls()) {
SCC *CalleeC = G.lookupSCC(E.getNode());
if (!CalleeC)
continue;
// If the callee's SCC is the TargetC, we're done.
if (CalleeC == &TargetC)
return true;
// If this is the first time we've reached this SCC, put it on the
// worklist to recurse through.
if (Visited.insert(CalleeC).second)
Worklist.push_back(CalleeC);
}
} while (!Worklist.empty());
// No paths found.
return false;
}
LazyCallGraph::RefSCC::RefSCC(LazyCallGraph &G) : G(&G) {}
#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
LLVM_DUMP_METHOD void LazyCallGraph::RefSCC::dump() const {
dbgs() << *this << '\n';
}
#endif
#ifndef NDEBUG
void LazyCallGraph::RefSCC::verify() {
assert(G && "Can't have a null graph!");
assert(!SCCs.empty() && "Can't have an empty SCC!");
// Verify basic properties of the SCCs.
SmallPtrSet<SCC *, 4> SCCSet;
for (SCC *C : SCCs) {
assert(C && "Can't have a null SCC!");
C->verify();
assert(&C->getOuterRefSCC() == this &&
"SCC doesn't think it is inside this RefSCC!");
bool Inserted = SCCSet.insert(C).second;
assert(Inserted && "Found a duplicate SCC!");
auto IndexIt = SCCIndices.find(C);
assert(IndexIt != SCCIndices.end() &&
"Found an SCC that doesn't have an index!");
}
// Check that our indices map correctly.
for (auto &SCCIndexPair : SCCIndices) {
SCC *C = SCCIndexPair.first;
int i = SCCIndexPair.second;
assert(C && "Can't have a null SCC in the indices!");
assert(SCCSet.count(C) && "Found an index for an SCC not in the RefSCC!");
assert(SCCs[i] == C && "Index doesn't point to SCC!");
}
// Check that the SCCs are in fact in post-order.
for (int i = 0, Size = SCCs.size(); i < Size; ++i) {
SCC &SourceSCC = *SCCs[i];
for (Node &N : SourceSCC)
for (Edge &E : *N) {
if (!E.isCall())
continue;
SCC &TargetSCC = *G->lookupSCC(E.getNode());
if (&TargetSCC.getOuterRefSCC() == this) {
assert(SCCIndices.find(&TargetSCC)->second <= i &&
"Edge between SCCs violates post-order relationship.");
continue;
}
assert(TargetSCC.getOuterRefSCC().Parents.count(this) &&
"Edge to a RefSCC missing us in its parent set.");
}
}
// Check that our parents are actually parents.
for (RefSCC *ParentRC : Parents) {
assert(ParentRC != this && "Cannot be our own parent!");
auto HasConnectingEdge = [&] {
for (SCC &C : *ParentRC)
for (Node &N : C)
for (Edge &E : *N)
if (G->lookupRefSCC(E.getNode()) == this)
return true;
return false;
};
assert(HasConnectingEdge() && "No edge connects the parent to us!");
}
}
#endif
bool LazyCallGraph::RefSCC::isDescendantOf(const RefSCC &C) const {
// Walk up the parents of this SCC and verify that we eventually find C.
SmallVector<const RefSCC *, 4> AncestorWorklist;
AncestorWorklist.push_back(this);
do {
const RefSCC *AncestorC = AncestorWorklist.pop_back_val();
if (AncestorC->isChildOf(C))
return true;
for (const RefSCC *ParentC : AncestorC->Parents)
AncestorWorklist.push_back(ParentC);
} while (!AncestorWorklist.empty());
return false;
}
/// Generic helper that updates a postorder sequence of SCCs for a potentially
/// cycle-introducing edge insertion.
///
/// A postorder sequence of SCCs of a directed graph has one fundamental
/// property: all deges in the DAG of SCCs point "up" the sequence. That is,
/// all edges in the SCC DAG point to prior SCCs in the sequence.
///
/// This routine both updates a postorder sequence and uses that sequence to
/// compute the set of SCCs connected into a cycle. It should only be called to
/// insert a "downward" edge which will require changing the sequence to
/// restore it to a postorder.
///
/// When inserting an edge from an earlier SCC to a later SCC in some postorder
/// sequence, all of the SCCs which may be impacted are in the closed range of
/// those two within the postorder sequence. The algorithm used here to restore
/// the state is as follows:
///
/// 1) Starting from the source SCC, construct a set of SCCs which reach the
/// source SCC consisting of just the source SCC. Then scan toward the
/// target SCC in postorder and for each SCC, if it has an edge to an SCC
/// in the set, add it to the set. Otherwise, the source SCC is not
/// a successor, move it in the postorder sequence to immediately before
/// the source SCC, shifting the source SCC and all SCCs in the set one
/// position toward the target SCC. Stop scanning after processing the
/// target SCC.
/// 2) If the source SCC is now past the target SCC in the postorder sequence,
/// and thus the new edge will flow toward the start, we are done.
/// 3) Otherwise, starting from the target SCC, walk all edges which reach an
/// SCC between the source and the target, and add them to the set of
/// connected SCCs, then recurse through them. Once a complete set of the
/// SCCs the target connects to is known, hoist the remaining SCCs between
/// the source and the target to be above the target. Note that there is no
/// need to process the source SCC, it is already known to connect.
/// 4) At this point, all of the SCCs in the closed range between the source
/// SCC and the target SCC in the postorder sequence are connected,
/// including the target SCC and the source SCC. Inserting the edge from
/// the source SCC to the target SCC will form a cycle out of precisely
/// these SCCs. Thus we can merge all of the SCCs in this closed range into
/// a single SCC.
///
/// This process has various important properties:
/// - Only mutates the SCCs when adding the edge actually changes the SCC
/// structure.
/// - Never mutates SCCs which are unaffected by the change.
/// - Updates the postorder sequence to correctly satisfy the postorder
/// constraint after the edge is inserted.
/// - Only reorders SCCs in the closed postorder sequence from the source to
/// the target, so easy to bound how much has changed even in the ordering.
/// - Big-O is the number of edges in the closed postorder range of SCCs from
/// source to target.
///
/// This helper routine, in addition to updating the postorder sequence itself
/// will also update a map from SCCs to indices within that sequecne.
///
/// The sequence and the map must operate on pointers to the SCC type.
///
/// Two callbacks must be provided. The first computes the subset of SCCs in
/// the postorder closed range from the source to the target which connect to
/// the source SCC via some (transitive) set of edges. The second computes the
/// subset of the same range which the target SCC connects to via some
/// (transitive) set of edges. Both callbacks should populate the set argument
/// provided.
template <typename SCCT, typename PostorderSequenceT, typename SCCIndexMapT,
typename ComputeSourceConnectedSetCallableT,
typename ComputeTargetConnectedSetCallableT>
static iterator_range<typename PostorderSequenceT::iterator>
updatePostorderSequenceForEdgeInsertion(
SCCT &SourceSCC, SCCT &TargetSCC, PostorderSequenceT &SCCs,
SCCIndexMapT &SCCIndices,
ComputeSourceConnectedSetCallableT ComputeSourceConnectedSet,
ComputeTargetConnectedSetCallableT ComputeTargetConnectedSet) {
int SourceIdx = SCCIndices[&SourceSCC];
int TargetIdx = SCCIndices[&TargetSCC];
assert(SourceIdx < TargetIdx && "Cannot have equal indices here!");
SmallPtrSet<SCCT *, 4> ConnectedSet;
// Compute the SCCs which (transitively) reach the source.
ComputeSourceConnectedSet(ConnectedSet);
// Partition the SCCs in this part of the port-order sequence so only SCCs
// connecting to the source remain between it and the target. This is
// a benign partition as it preserves postorder.
auto SourceI = std::stable_partition(
SCCs.begin() + SourceIdx, SCCs.begin() + TargetIdx + 1,
[&ConnectedSet](SCCT *C) { return !ConnectedSet.count(C); });
for (int i = SourceIdx, e = TargetIdx + 1; i < e; ++i)
SCCIndices.find(SCCs[i])->second = i;
// If the target doesn't connect to the source, then we've corrected the
// post-order and there are no cycles formed.
if (!ConnectedSet.count(&TargetSCC)) {
assert(SourceI > (SCCs.begin() + SourceIdx) &&
"Must have moved the source to fix the post-order.");
assert(*std::prev(SourceI) == &TargetSCC &&
"Last SCC to move should have bene the target.");
// Return an empty range at the target SCC indicating there is nothing to
// merge.
return make_range(std::prev(SourceI), std::prev(SourceI));
}
assert(SCCs[TargetIdx] == &TargetSCC &&
"Should not have moved target if connected!");
SourceIdx = SourceI - SCCs.begin();
assert(SCCs[SourceIdx] == &SourceSCC &&
"Bad updated index computation for the source SCC!");
// See whether there are any remaining intervening SCCs between the source
// and target. If so we need to make sure they all are reachable form the
// target.
if (SourceIdx + 1 < TargetIdx) {
ConnectedSet.clear();
ComputeTargetConnectedSet(ConnectedSet);
// Partition SCCs so that only SCCs reached from the target remain between
// the source and the target. This preserves postorder.
auto TargetI = std::stable_partition(
SCCs.begin() + SourceIdx + 1, SCCs.begin() + TargetIdx + 1,
[&ConnectedSet](SCCT *C) { return ConnectedSet.count(C); });
for (int i = SourceIdx + 1, e = TargetIdx + 1; i < e; ++i)
SCCIndices.find(SCCs[i])->second = i;
TargetIdx = std::prev(TargetI) - SCCs.begin();
assert(SCCs[TargetIdx] == &TargetSCC &&
"Should always end with the target!");
}
// At this point, we know that connecting source to target forms a cycle
// because target connects back to source, and we know that all of the SCCs
// between the source and target in the postorder sequence participate in that
// cycle.
return make_range(SCCs.begin() + SourceIdx, SCCs.begin() + TargetIdx);
}
bool
LazyCallGraph::RefSCC::switchInternalEdgeToCall(
Node &SourceN, Node &TargetN,
function_ref<void(ArrayRef<SCC *> MergeSCCs)> MergeCB) {
assert(!(*SourceN)[TargetN].isCall() && "Must start with a ref edge!");
SmallVector<SCC *, 1> DeletedSCCs;
#ifndef NDEBUG
// In a debug build, verify the RefSCC is valid to start with and when this
// routine finishes.
verify();
auto VerifyOnExit = make_scope_exit([&]() { verify(); });
#endif
SCC &SourceSCC = *G->lookupSCC(SourceN);
SCC &TargetSCC = *G->lookupSCC(TargetN);
// If the two nodes are already part of the same SCC, we're also done as
// we've just added more connectivity.
if (&SourceSCC == &TargetSCC) {
SourceN->setEdgeKind(TargetN, Edge::Call);
return false; // No new cycle.
}
// At this point we leverage the postorder list of SCCs to detect when the
// insertion of an edge changes the SCC structure in any way.
//
// First and foremost, we can eliminate the need for any changes when the
// edge is toward the beginning of the postorder sequence because all edges
// flow in that direction already. Thus adding a new one cannot form a cycle.
int SourceIdx = SCCIndices[&SourceSCC];
int TargetIdx = SCCIndices[&TargetSCC];
if (TargetIdx < SourceIdx) {
SourceN->setEdgeKind(TargetN, Edge::Call);
return false; // No new cycle.
}
// Compute the SCCs which (transitively) reach the source.
auto ComputeSourceConnectedSet = [&](SmallPtrSetImpl<SCC *> &ConnectedSet) {
#ifndef NDEBUG
// Check that the RefSCC is still valid before computing this as the
// results will be nonsensical of we've broken its invariants.
verify();
#endif
ConnectedSet.insert(&SourceSCC);
auto IsConnected = [&](SCC &C) {
for (Node &N : C)
for (Edge &E : N->calls())
if (ConnectedSet.count(G->lookupSCC(E.getNode())))
return true;
return false;
};
for (SCC *C :
make_range(SCCs.begin() + SourceIdx + 1, SCCs.begin() + TargetIdx + 1))
if (IsConnected(*C))
ConnectedSet.insert(C);
};
// Use a normal worklist to find which SCCs the target connects to. We still
// bound the search based on the range in the postorder list we care about,
// but because this is forward connectivity we just "recurse" through the
// edges.
auto ComputeTargetConnectedSet = [&](SmallPtrSetImpl<SCC *> &ConnectedSet) {
#ifndef NDEBUG
// Check that the RefSCC is still valid before computing this as the
// results will be nonsensical of we've broken its invariants.
verify();
#endif
ConnectedSet.insert(&TargetSCC);
SmallVector<SCC *, 4> Worklist;
Worklist.push_back(&TargetSCC);
do {
SCC &C = *Worklist.pop_back_val();
for (Node &N : C)
for (Edge &E : *N) {
if (!E.isCall())
continue;
SCC &EdgeC = *G->lookupSCC(E.getNode());
if (&EdgeC.getOuterRefSCC() != this)
// Not in this RefSCC...
continue;
if (SCCIndices.find(&EdgeC)->second <= SourceIdx)
// Not in the postorder sequence between source and target.
continue;
if (ConnectedSet.insert(&EdgeC).second)
Worklist.push_back(&EdgeC);
}
} while (!Worklist.empty());
};
// Use a generic helper to update the postorder sequence of SCCs and return
// a range of any SCCs connected into a cycle by inserting this edge. This
// routine will also take care of updating the indices into the postorder
// sequence.
auto MergeRange = updatePostorderSequenceForEdgeInsertion(
SourceSCC, TargetSCC, SCCs, SCCIndices, ComputeSourceConnectedSet,
ComputeTargetConnectedSet);
// Run the user's callback on the merged SCCs before we actually merge them.
if (MergeCB)
MergeCB(makeArrayRef(MergeRange.begin(), MergeRange.end()));
// If the merge range is empty, then adding the edge didn't actually form any
// new cycles. We're done.
if (MergeRange.begin() == MergeRange.end()) {
// Now that the SCC structure is finalized, flip the kind to call.
SourceN->setEdgeKind(TargetN, Edge::Call);
return false; // No new cycle.
}
#ifndef NDEBUG
// Before merging, check that the RefSCC remains valid after all the
// postorder updates.
verify();
#endif
// Otherwise we need to merge all of the SCCs in the cycle into a single
// result SCC.
//
// NB: We merge into the target because all of these functions were already
// reachable from the target, meaning any SCC-wide properties deduced about it
// other than the set of functions within it will not have changed.
for (SCC *C : MergeRange) {
assert(C != &TargetSCC &&
"We merge *into* the target and shouldn't process it here!");
SCCIndices.erase(C);
TargetSCC.Nodes.append(C->Nodes.begin(), C->Nodes.end());
for (Node *N : C->Nodes)
G->SCCMap[N] = &TargetSCC;
C->clear();
DeletedSCCs.push_back(C);
}
// Erase the merged SCCs from the list and update the indices of the
// remaining SCCs.
int IndexOffset = MergeRange.end() - MergeRange.begin();
auto EraseEnd = SCCs.erase(MergeRange.begin(), MergeRange.end());
for (SCC *C : make_range(EraseEnd, SCCs.end()))
SCCIndices[C] -= IndexOffset;
// Now that the SCC structure is finalized, flip the kind to call.
SourceN->setEdgeKind(TargetN, Edge::Call);
// And we're done, but we did form a new cycle.
return true;
}
void LazyCallGraph::RefSCC::switchTrivialInternalEdgeToRef(Node &SourceN,
Node &TargetN) {
assert((*SourceN)[TargetN].isCall() && "Must start with a call edge!");
#ifndef NDEBUG
// In a debug build, verify the RefSCC is valid to start with and when this
// routine finishes.
verify();
auto VerifyOnExit = make_scope_exit([&]() { verify(); });
#endif
assert(G->lookupRefSCC(SourceN) == this &&
"Source must be in this RefSCC.");
assert(G->lookupRefSCC(TargetN) == this &&
"Target must be in this RefSCC.");
assert(G->lookupSCC(SourceN) != G->lookupSCC(TargetN) &&
"Source and Target must be in separate SCCs for this to be trivial!");
// Set the edge kind.
SourceN->setEdgeKind(TargetN, Edge::Ref);
}
iterator_range<LazyCallGraph::RefSCC::iterator>
LazyCallGraph::RefSCC::switchInternalEdgeToRef(Node &SourceN, Node &TargetN) {
assert((*SourceN)[TargetN].isCall() && "Must start with a call edge!");
#ifndef NDEBUG
// In a debug build, verify the RefSCC is valid to start with and when this
// routine finishes.
verify();
auto VerifyOnExit = make_scope_exit([&]() { verify(); });
#endif
assert(G->lookupRefSCC(SourceN) == this &&
"Source must be in this RefSCC.");
assert(G->lookupRefSCC(TargetN) == this &&
"Target must be in this RefSCC.");
SCC &TargetSCC = *G->lookupSCC(TargetN);
assert(G->lookupSCC(SourceN) == &TargetSCC && "Source and Target must be in "
"the same SCC to require the "
"full CG update.");
// Set the edge kind.
SourceN->setEdgeKind(TargetN, Edge::Ref);
// Otherwise we are removing a call edge from a single SCC. This may break
// the cycle. In order to compute the new set of SCCs, we need to do a small
// DFS over the nodes within the SCC to form any sub-cycles that remain as
// distinct SCCs and compute a postorder over the resulting SCCs.
//
// However, we specially handle the target node. The target node is known to
// reach all other nodes in the original SCC by definition. This means that
// we want the old SCC to be replaced with an SCC contaning that node as it
// will be the root of whatever SCC DAG results from the DFS. Assumptions
// about an SCC such as the set of functions called will continue to hold,
// etc.
SCC &OldSCC = TargetSCC;
SmallVector<std::pair<Node *, EdgeSequence::call_iterator>, 16> DFSStack;
SmallVector<Node *, 16> PendingSCCStack;
SmallVector<SCC *, 4> NewSCCs;
// Prepare the nodes for a fresh DFS.
SmallVector<Node *, 16> Worklist;
Worklist.swap(OldSCC.Nodes);
for (Node *N : Worklist) {
N->DFSNumber = N->LowLink = 0;
G->SCCMap.erase(N);
}
// Force the target node to be in the old SCC. This also enables us to take
// a very significant short-cut in the standard Tarjan walk to re-form SCCs
// below: whenever we build an edge that reaches the target node, we know
// that the target node eventually connects back to all other nodes in our
// walk. As a consequence, we can detect and handle participants in that
// cycle without walking all the edges that form this connection, and instead
// by relying on the fundamental guarantee coming into this operation (all
// nodes are reachable from the target due to previously forming an SCC).
TargetN.DFSNumber = TargetN.LowLink = -1;
OldSCC.Nodes.push_back(&TargetN);
G->SCCMap[&TargetN] = &OldSCC;
// Scan down the stack and DFS across the call edges.
for (Node *RootN : Worklist) {
assert(DFSStack.empty() &&
"Cannot begin a new root with a non-empty DFS stack!");
assert(PendingSCCStack.empty() &&
"Cannot begin a new root with pending nodes for an SCC!");
// Skip any nodes we've already reached in the DFS.
if (RootN->DFSNumber != 0) {
assert(RootN->DFSNumber == -1 &&
"Shouldn't have any mid-DFS root nodes!");
continue;
}
RootN->DFSNumber = RootN->LowLink = 1;
int NextDFSNumber = 2;
DFSStack.push_back({RootN, (*RootN)->call_begin()});
do {
Node *N;
EdgeSequence::call_iterator I;
std::tie(N, I) = DFSStack.pop_back_val();
auto E = (*N)->call_end();
while (I != E) {
Node &ChildN = I->getNode();
if (ChildN.DFSNumber == 0) {
// We haven't yet visited this child, so descend, pushing the current
// node onto the stack.
DFSStack.push_back({N, I});
assert(!G->SCCMap.count(&ChildN) &&
"Found a node with 0 DFS number but already in an SCC!");
ChildN.DFSNumber = ChildN.LowLink = NextDFSNumber++;
N = &ChildN;
I = (*N)->call_begin();
E = (*N)->call_end();
continue;
}
// Check for the child already being part of some component.
if (ChildN.DFSNumber == -1) {
if (G->lookupSCC(ChildN) == &OldSCC) {
// If the child is part of the old SCC, we know that it can reach
// every other node, so we have formed a cycle. Pull the entire DFS
// and pending stacks into it. See the comment above about setting
// up the old SCC for why we do this.
int OldSize = OldSCC.size();
OldSCC.Nodes.push_back(N);
OldSCC.Nodes.append(PendingSCCStack.begin(), PendingSCCStack.end());
PendingSCCStack.clear();
while (!DFSStack.empty())
OldSCC.Nodes.push_back(DFSStack.pop_back_val().first);
for (Node &N : make_range(OldSCC.begin() + OldSize, OldSCC.end())) {
N.DFSNumber = N.LowLink = -1;
G->SCCMap[&N] = &OldSCC;
}
N = nullptr;
break;
}
// If the child has already been added to some child component, it
// couldn't impact the low-link of this parent because it isn't
// connected, and thus its low-link isn't relevant so skip it.
++I;
continue;
}
// Track the lowest linked child as the lowest link for this node.
assert(ChildN.LowLink > 0 && "Must have a positive low-link number!");
if (ChildN.LowLink < N->LowLink)
N->LowLink = ChildN.LowLink;
// Move to the next edge.
++I;
}
if (!N)
// Cleared the DFS early, start another round.
break;
// We've finished processing N and its descendents, put it on our pending
// SCC stack to eventually get merged into an SCC of nodes.
PendingSCCStack.push_back(N);
// If this node is linked to some lower entry, continue walking up the
// stack.
if (N->LowLink != N->DFSNumber)
continue;
// Otherwise, we've completed an SCC. Append it to our post order list of
// SCCs.
int RootDFSNumber = N->DFSNumber;
// Find the range of the node stack by walking down until we pass the
// root DFS number.
auto SCCNodes = make_range(
PendingSCCStack.rbegin(),
find_if(reverse(PendingSCCStack), [RootDFSNumber](const Node *N) {
return N->DFSNumber < RootDFSNumber;
}));
// Form a new SCC out of these nodes and then clear them off our pending
// stack.
NewSCCs.push_back(G->createSCC(*this, SCCNodes));
for (Node &N : *NewSCCs.back()) {
N.DFSNumber = N.LowLink = -1;
G->SCCMap[&N] = NewSCCs.back();
}
PendingSCCStack.erase(SCCNodes.end().base(), PendingSCCStack.end());
} while (!DFSStack.empty());
}
// Insert the remaining SCCs before the old one. The old SCC can reach all
// other SCCs we form because it contains the target node of the removed edge
// of the old SCC. This means that we will have edges into all of the new
// SCCs, which means the old one must come last for postorder.
int OldIdx = SCCIndices[&OldSCC];
SCCs.insert(SCCs.begin() + OldIdx, NewSCCs.begin(), NewSCCs.end());
// Update the mapping from SCC* to index to use the new SCC*s, and remove the
// old SCC from the mapping.
for (int Idx = OldIdx, Size = SCCs.size(); Idx < Size; ++Idx)
SCCIndices[SCCs[Idx]] = Idx;
return make_range(SCCs.begin() + OldIdx,
SCCs.begin() + OldIdx + NewSCCs.size());
}
void LazyCallGraph::RefSCC::switchOutgoingEdgeToCall(Node &SourceN,
Node &TargetN) {
assert(!(*SourceN)[TargetN].isCall() && "Must start with a ref edge!");
assert(G->lookupRefSCC(SourceN) == this && "Source must be in this RefSCC.");
assert(G->lookupRefSCC(TargetN) != this &&
"Target must not be in this RefSCC.");
#ifdef EXPENSIVE_CHECKS
assert(G->lookupRefSCC(TargetN)->isDescendantOf(*this) &&
"Target must be a descendant of the Source.");
#endif
// Edges between RefSCCs are the same regardless of call or ref, so we can
// just flip the edge here.
SourceN->setEdgeKind(TargetN, Edge::Call);
#ifndef NDEBUG
// Check that the RefSCC is still valid.
verify();
#endif
}
void LazyCallGraph::RefSCC::switchOutgoingEdgeToRef(Node &SourceN,
Node &TargetN) {
assert((*SourceN)[TargetN].isCall() && "Must start with a call edge!");
assert(G->lookupRefSCC(SourceN) == this && "Source must be in this RefSCC.");
assert(G->lookupRefSCC(TargetN) != this &&
"Target must not be in this RefSCC.");
#ifdef EXPENSIVE_CHECKS
assert(G->lookupRefSCC(TargetN)->isDescendantOf(*this) &&
"Target must be a descendant of the Source.");
#endif
// Edges between RefSCCs are the same regardless of call or ref, so we can
// just flip the edge here.
SourceN->setEdgeKind(TargetN, Edge::Ref);
#ifndef NDEBUG
// Check that the RefSCC is still valid.
verify();
#endif
}
void LazyCallGraph::RefSCC::insertInternalRefEdge(Node &SourceN,
Node &TargetN) {
assert(G->lookupRefSCC(SourceN) == this && "Source must be in this RefSCC.");
assert(G->lookupRefSCC(TargetN) == this && "Target must be in this RefSCC.");
SourceN->insertEdgeInternal(TargetN, Edge::Ref);
#ifndef NDEBUG
// Check that the RefSCC is still valid.
verify();
#endif
}
void LazyCallGraph::RefSCC::insertOutgoingEdge(Node &SourceN, Node &TargetN,
Edge::Kind EK) {
// First insert it into the caller.
SourceN->insertEdgeInternal(TargetN, EK);
assert(G->lookupRefSCC(SourceN) == this && "Source must be in this RefSCC.");
RefSCC &TargetC = *G->lookupRefSCC(TargetN);
assert(&TargetC != this && "Target must not be in this RefSCC.");
#ifdef EXPENSIVE_CHECKS
assert(TargetC.isDescendantOf(*this) &&
"Target must be a descendant of the Source.");
#endif
// The only change required is to add this SCC to the parent set of the
// callee.
TargetC.Parents.insert(this);
#ifndef NDEBUG
// Check that the RefSCC is still valid.
verify();
#endif
}
SmallVector<LazyCallGraph::RefSCC *, 1>
LazyCallGraph::RefSCC::insertIncomingRefEdge(Node &SourceN, Node &TargetN) {
assert(G->lookupRefSCC(TargetN) == this && "Target must be in this RefSCC.");
RefSCC &SourceC = *G->lookupRefSCC(SourceN);
assert(&SourceC != this && "Source must not be in this RefSCC.");
#ifdef EXPENSIVE_CHECKS
assert(SourceC.isDescendantOf(*this) &&
"Source must be a descendant of the Target.");
#endif
SmallVector<RefSCC *, 1> DeletedRefSCCs;
#ifndef NDEBUG
// In a debug build, verify the RefSCC is valid to start with and when this
// routine finishes.
verify();
auto VerifyOnExit = make_scope_exit([&]() { verify(); });
#endif
int SourceIdx = G->RefSCCIndices[&SourceC];
int TargetIdx = G->RefSCCIndices[this];
assert(SourceIdx < TargetIdx &&
"Postorder list doesn't see edge as incoming!");
// Compute the RefSCCs which (transitively) reach the source. We do this by
// working backwards from the source using the parent set in each RefSCC,
// skipping any RefSCCs that don't fall in the postorder range. This has the
// advantage of walking the sparser parent edge (in high fan-out graphs) but
// more importantly this removes examining all forward edges in all RefSCCs
// within the postorder range which aren't in fact connected. Only connected
// RefSCCs (and their edges) are visited here.
auto ComputeSourceConnectedSet = [&](SmallPtrSetImpl<RefSCC *> &Set) {
Set.insert(&SourceC);
SmallVector<RefSCC *, 4> Worklist;
Worklist.push_back(&SourceC);
do {
RefSCC &RC = *Worklist.pop_back_val();
for (RefSCC &ParentRC : RC.parents()) {
// Skip any RefSCCs outside the range of source to target in the
// postorder sequence.
int ParentIdx = G->getRefSCCIndex(ParentRC);
assert(ParentIdx > SourceIdx && "Parent cannot precede source in postorder!");
if (ParentIdx > TargetIdx)
continue;
if (Set.insert(&ParentRC).second)
// First edge connecting to this parent, add it to our worklist.
Worklist.push_back(&ParentRC);
}
} while (!Worklist.empty());
};
// Use a normal worklist to find which SCCs the target connects to. We still
// bound the search based on the range in the postorder list we care about,
// but because this is forward connectivity we just "recurse" through the
// edges.
auto ComputeTargetConnectedSet = [&](SmallPtrSetImpl<RefSCC *> &Set) {
Set.insert(this);
SmallVector<RefSCC *, 4> Worklist;
Worklist.push_back(this);
do {
RefSCC &RC = *Worklist.pop_back_val();
for (SCC &C : RC)
for (Node &N : C)
for (Edge &E : *N) {
RefSCC &EdgeRC = *G->lookupRefSCC(E.getNode());
if (G->getRefSCCIndex(EdgeRC) <= SourceIdx)
// Not in the postorder sequence between source and target.
continue;
if (Set.insert(&EdgeRC).second)
Worklist.push_back(&EdgeRC);
}
} while (!Worklist.empty());
};
// Use a generic helper to update the postorder sequence of RefSCCs and return
// a range of any RefSCCs connected into a cycle by inserting this edge. This
// routine will also take care of updating the indices into the postorder
// sequence.
iterator_range<SmallVectorImpl<RefSCC *>::iterator> MergeRange =
updatePostorderSequenceForEdgeInsertion(
SourceC, *this, G->PostOrderRefSCCs, G->RefSCCIndices,
ComputeSourceConnectedSet, ComputeTargetConnectedSet);
// Build a set so we can do fast tests for whether a RefSCC will end up as
// part of the merged RefSCC.
SmallPtrSet<RefSCC *, 16> MergeSet(MergeRange.begin(), MergeRange.end());
// This RefSCC will always be part of that set, so just insert it here.
MergeSet.insert(this);
// Now that we have identified all of the SCCs which need to be merged into
// a connected set with the inserted edge, merge all of them into this SCC.
SmallVector<SCC *, 16> MergedSCCs;
int SCCIndex = 0;
for (RefSCC *RC : MergeRange) {
assert(RC != this && "We're merging into the target RefSCC, so it "
"shouldn't be in the range.");
// Merge the parents which aren't part of the merge into the our parents.
for (RefSCC *ParentRC : RC->Parents)
if (!MergeSet.count(ParentRC))
Parents.insert(ParentRC);
RC->Parents.clear();
// Walk the inner SCCs to update their up-pointer and walk all the edges to
// update any parent sets.
// FIXME: We should try to find a way to avoid this (rather expensive) edge
// walk by updating the parent sets in some other manner.
for (SCC &InnerC : *RC) {
InnerC.OuterRefSCC = this;
SCCIndices[&InnerC] = SCCIndex++;
for (Node &N : InnerC) {
G->SCCMap[&N] = &InnerC;
for (Edge &E : *N) {
RefSCC &ChildRC = *G->lookupRefSCC(E.getNode());
if (MergeSet.count(&ChildRC))
continue;
ChildRC.Parents.erase(RC);
ChildRC.Parents.insert(this);
}
}
}
// Now merge in the SCCs. We can actually move here so try to reuse storage
// the first time through.
if (MergedSCCs.empty())
MergedSCCs = std::move(RC->SCCs);
else
MergedSCCs.append(RC->SCCs.begin(), RC->SCCs.end());
RC->SCCs.clear();
DeletedRefSCCs.push_back(RC);
}
// Append our original SCCs to the merged list and move it into place.
for (SCC &InnerC : *this)
SCCIndices[&InnerC] = SCCIndex++;
MergedSCCs.append(SCCs.begin(), SCCs.end());
SCCs = std::move(MergedSCCs);
// Remove the merged away RefSCCs from the post order sequence.
for (RefSCC *RC : MergeRange)
G->RefSCCIndices.erase(RC);
int IndexOffset = MergeRange.end() - MergeRange.begin();
auto EraseEnd =
G->PostOrderRefSCCs.erase(MergeRange.begin(), MergeRange.end());
for (RefSCC *RC : make_range(EraseEnd, G->PostOrderRefSCCs.end()))
G->RefSCCIndices[RC] -= IndexOffset;
// At this point we have a merged RefSCC with a post-order SCCs list, just
// connect the nodes to form the new edge.
SourceN->insertEdgeInternal(TargetN, Edge::Ref);
// We return the list of SCCs which were merged so that callers can
// invalidate any data they have associated with those SCCs. Note that these
// SCCs are no longer in an interesting state (they are totally empty) but
// the pointers will remain stable for the life of the graph itself.
return DeletedRefSCCs;
}
void LazyCallGraph::RefSCC::removeOutgoingEdge(Node &SourceN, Node &TargetN) {
assert(G->lookupRefSCC(SourceN) == this &&
"The source must be a member of this RefSCC.");
RefSCC &TargetRC = *G->lookupRefSCC(TargetN);
assert(&TargetRC != this && "The target must not be a member of this RefSCC");
assert(!is_contained(G->LeafRefSCCs, this) &&
"Cannot have a leaf RefSCC source.");
#ifndef NDEBUG
// In a debug build, verify the RefSCC is valid to start with and when this
// routine finishes.
verify();
auto VerifyOnExit = make_scope_exit([&]() { verify(); });
#endif
// First remove it from the node.
bool Removed = SourceN->removeEdgeInternal(TargetN);
(void)Removed;
assert(Removed && "Target not in the edge set for this caller?");
bool HasOtherEdgeToChildRC = false;
bool HasOtherChildRC = false;
for (SCC *InnerC : SCCs) {
for (Node &N : *InnerC) {
for (Edge &E : *N) {
RefSCC &OtherChildRC = *G->lookupRefSCC(E.getNode());
if (&OtherChildRC == &TargetRC) {
HasOtherEdgeToChildRC = true;
break;
}
if (&OtherChildRC != this)
HasOtherChildRC = true;
}
if (HasOtherEdgeToChildRC)
break;
}
if (HasOtherEdgeToChildRC)
break;
}
// Because the SCCs form a DAG, deleting such an edge cannot change the set
// of SCCs in the graph. However, it may cut an edge of the SCC DAG, making
// the source SCC no longer connected to the target SCC. If so, we need to
// update the target SCC's map of its parents.
if (!HasOtherEdgeToChildRC) {
bool Removed = TargetRC.Parents.erase(this);
(void)Removed;
assert(Removed &&
"Did not find the source SCC in the target SCC's parent list!");
// It may orphan an SCC if it is the last edge reaching it, but that does
// not violate any invariants of the graph.
if (TargetRC.Parents.empty())
DEBUG(dbgs() << "LCG: Update removing " << SourceN.getFunction().getName()
<< " -> " << TargetN.getFunction().getName()
<< " edge orphaned the callee's SCC!\n");
// It may make the Source SCC a leaf SCC.
if (!HasOtherChildRC)
G->LeafRefSCCs.push_back(this);
}
}
SmallVector<LazyCallGraph::RefSCC *, 1>
LazyCallGraph::RefSCC::removeInternalRefEdge(Node &SourceN, Node &TargetN) {
assert(!(*SourceN)[TargetN].isCall() &&
"Cannot remove a call edge, it must first be made a ref edge");
#ifndef NDEBUG
// In a debug build, verify the RefSCC is valid to start with and when this
// routine finishes.
verify();
auto VerifyOnExit = make_scope_exit([&]() { verify(); });
#endif
// First remove the actual edge.
bool Removed = SourceN->removeEdgeInternal(TargetN);
(void)Removed;
assert(Removed && "Target not in the edge set for this caller?");
// We return a list of the resulting *new* RefSCCs in post-order.
SmallVector<RefSCC *, 1> Result;
// Direct recursion doesn't impact the SCC graph at all.
if (&SourceN == &TargetN)
return Result;
// If this ref edge is within an SCC then there are sufficient other edges to
// form a cycle without this edge so removing it is a no-op.
SCC &SourceC = *G->lookupSCC(SourceN);
SCC &TargetC = *G->lookupSCC(TargetN);
if (&SourceC == &TargetC)
return Result;
// We build somewhat synthetic new RefSCCs by providing a postorder mapping
// for each inner SCC. We also store these associated with *nodes* rather
// than SCCs because this saves a round-trip through the node->SCC map and in
// the common case, SCCs are small. We will verify that we always give the
// same number to every node in the SCC such that these are equivalent.
const int RootPostOrderNumber = 0;
int PostOrderNumber = RootPostOrderNumber + 1;
SmallDenseMap<Node *, int> PostOrderMapping;
// Every node in the target SCC can already reach every node in this RefSCC
// (by definition). It is the only node we know will stay inside this RefSCC.
// Everything which transitively reaches Target will also remain in the
// RefSCC. We handle this by pre-marking that the nodes in the target SCC map
// back to the root post order number.
//
// This also enables us to take a very significant short-cut in the standard
// Tarjan walk to re-form RefSCCs below: whenever we build an edge that
// references the target node, we know that the target node eventually
// references all other nodes in our walk. As a consequence, we can detect
// and handle participants in that cycle without walking all the edges that
// form the connections, and instead by relying on the fundamental guarantee
// coming into this operation.
for (Node &N : TargetC)
PostOrderMapping[&N] = RootPostOrderNumber;
// Reset all the other nodes to prepare for a DFS over them, and add them to
// our worklist.
SmallVector<Node *, 8> Worklist;
for (SCC *C : SCCs) {
if (C == &TargetC)
continue;
for (Node &N : *C)
N.DFSNumber = N.LowLink = 0;
Worklist.append(C->Nodes.begin(), C->Nodes.end());
}
auto MarkNodeForSCCNumber = [&PostOrderMapping](Node &N, int Number) {
N.DFSNumber = N.LowLink = -1;
PostOrderMapping[&N] = Number;
};
SmallVector<std::pair<Node *, EdgeSequence::iterator>, 4> DFSStack;
SmallVector<Node *, 4> PendingRefSCCStack;
do {
assert(DFSStack.empty() &&
"Cannot begin a new root with a non-empty DFS stack!");
assert(PendingRefSCCStack.empty() &&
"Cannot begin a new root with pending nodes for an SCC!");
Node *RootN = Worklist.pop_back_val();
// Skip any nodes we've already reached in the DFS.
if (RootN->DFSNumber != 0) {
assert(RootN->DFSNumber == -1 &&
"Shouldn't have any mid-DFS root nodes!");
continue;
}
RootN->DFSNumber = RootN->LowLink = 1;
int NextDFSNumber = 2;
DFSStack.push_back({RootN, (*RootN)->begin()});
do {
Node *N;
EdgeSequence::iterator I;
std::tie(N, I) = DFSStack.pop_back_val();
auto E = (*N)->end();
assert(N->DFSNumber != 0 && "We should always assign a DFS number "
"before processing a node.");
while (I != E) {
Node &ChildN = I->getNode();
if (ChildN.DFSNumber == 0) {
// Mark that we should start at this child when next this node is the
// top of the stack. We don't start at the next child to ensure this
// child's lowlink is reflected.
DFSStack.push_back({N, I});
// Continue, resetting to the child node.
ChildN.LowLink = ChildN.DFSNumber = NextDFSNumber++;
N = &ChildN;
I = ChildN->begin();
E = ChildN->end();
continue;
}
if (ChildN.DFSNumber == -1) {
// Check if this edge's target node connects to the deleted edge's
// target node. If so, we know that every node connected will end up
// in this RefSCC, so collapse the entire current stack into the root
// slot in our SCC numbering. See above for the motivation of
// optimizing the target connected nodes in this way.
auto PostOrderI = PostOrderMapping.find(&ChildN);
if (PostOrderI != PostOrderMapping.end() &&
PostOrderI->second == RootPostOrderNumber) {
MarkNodeForSCCNumber(*N, RootPostOrderNumber);
while (!PendingRefSCCStack.empty())
MarkNodeForSCCNumber(*PendingRefSCCStack.pop_back_val(),
RootPostOrderNumber);
while (!DFSStack.empty())
MarkNodeForSCCNumber(*DFSStack.pop_back_val().first,
RootPostOrderNumber);
// Ensure we break all the way out of the enclosing loop.
N = nullptr;
break;
}
// If this child isn't currently in this RefSCC, no need to process
// it. However, we do need to remove this RefSCC from its RefSCC's
// parent set.
RefSCC &ChildRC = *G->lookupRefSCC(ChildN);
ChildRC.Parents.erase(this);
++I;
continue;
}
// Track the lowest link of the children, if any are still in the stack.
// Any child not on the stack will have a LowLink of -1.
assert(ChildN.LowLink != 0 &&
"Low-link must not be zero with a non-zero DFS number.");
if (ChildN.LowLink >= 0 && ChildN.LowLink < N->LowLink)
N->LowLink = ChildN.LowLink;
++I;
}
if (!N)
// We short-circuited this node.
break;
// We've finished processing N and its descendents, put it on our pending
// stack to eventually get merged into a RefSCC.
PendingRefSCCStack.push_back(N);
// If this node is linked to some lower entry, continue walking up the
// stack.
if (N->LowLink != N->DFSNumber) {
assert(!DFSStack.empty() &&
"We never found a viable root for a RefSCC to pop off!");
continue;
}
// Otherwise, form a new RefSCC from the top of the pending node stack.
int RootDFSNumber = N->DFSNumber;
// Find the range of the node stack by walking down until we pass the
// root DFS number.
auto RefSCCNodes = make_range(
PendingRefSCCStack.rbegin(),
find_if(reverse(PendingRefSCCStack), [RootDFSNumber](const Node *N) {
return N->DFSNumber < RootDFSNumber;
}));
// Mark the postorder number for these nodes and clear them off the
// stack. We'll use the postorder number to pull them into RefSCCs at the
// end. FIXME: Fuse with the loop above.
int RefSCCNumber = PostOrderNumber++;
for (Node *N : RefSCCNodes)
MarkNodeForSCCNumber(*N, RefSCCNumber);
PendingRefSCCStack.erase(RefSCCNodes.end().base(),
PendingRefSCCStack.end());
} while (!DFSStack.empty());
assert(DFSStack.empty() && "Didn't flush the entire DFS stack!");
assert(PendingRefSCCStack.empty() && "Didn't flush all pending nodes!");
} while (!Worklist.empty());
// We now have a post-order numbering for RefSCCs and a mapping from each
// node in this RefSCC to its final RefSCC. We create each new RefSCC node
// (re-using this RefSCC node for the root) and build a radix-sort style map
// from postorder number to the RefSCC. We then append SCCs to each of these
// RefSCCs in the order they occured in the original SCCs container.
for (int i = 1; i < PostOrderNumber; ++i)
Result.push_back(G->createRefSCC(*G));
// Insert the resulting postorder sequence into the global graph postorder
// sequence before the current RefSCC in that sequence. The idea being that
// this RefSCC is the target of the reference edge removed, and thus has
// a direct or indirect edge to every other RefSCC formed and so must be at
// the end of any postorder traversal.
//
// FIXME: It'd be nice to change the APIs so that we returned an iterator
// range over the global postorder sequence and generally use that sequence
// rather than building a separate result vector here.
if (!Result.empty()) {
int Idx = G->getRefSCCIndex(*this);
G->PostOrderRefSCCs.insert(G->PostOrderRefSCCs.begin() + Idx,
Result.begin(), Result.end());
for (int i : seq<int>(Idx, G->PostOrderRefSCCs.size()))
G->RefSCCIndices[G->PostOrderRefSCCs[i]] = i;
assert(G->PostOrderRefSCCs[G->getRefSCCIndex(*this)] == this &&
"Failed to update this RefSCC's index after insertion!");
}
for (SCC *C : SCCs) {
auto PostOrderI = PostOrderMapping.find(&*C->begin());
assert(PostOrderI != PostOrderMapping.end() &&
"Cannot have missing mappings for nodes!");
int SCCNumber = PostOrderI->second;
#ifndef NDEBUG
for (Node &N : *C)
assert(PostOrderMapping.find(&N)->second == SCCNumber &&
"Cannot have different numbers for nodes in the same SCC!");
#endif
if (SCCNumber == 0)
// The root node is handled separately by removing the SCCs.
continue;
RefSCC &RC = *Result[SCCNumber - 1];
int SCCIndex = RC.SCCs.size();
RC.SCCs.push_back(C);
RC.SCCIndices[C] = SCCIndex;
C->OuterRefSCC = &RC;
}
// FIXME: We re-walk the edges in each RefSCC to establish whether it is
// a leaf and connect it to the rest of the graph's parents lists. This is
// really wasteful. We should instead do this during the DFS to avoid yet
// another edge walk.
for (RefSCC *RC : Result)
G->connectRefSCC(*RC);
// Now erase all but the root's SCCs.
SCCs.erase(remove_if(SCCs,
[&](SCC *C) {
return PostOrderMapping.lookup(&*C->begin()) !=
RootPostOrderNumber;
}),
SCCs.end());
SCCIndices.clear();
for (int i = 0, Size = SCCs.size(); i < Size; ++i)
SCCIndices[SCCs[i]] = i;
#ifndef NDEBUG
// Now we need to reconnect the current (root) SCC to the graph. We do this
// manually because we can special case our leaf handling and detect errors.
bool IsLeaf = true;
#endif
for (SCC *C : SCCs)
for (Node &N : *C) {
for (Edge &E : *N) {
RefSCC &ChildRC = *G->lookupRefSCC(E.getNode());
if (&ChildRC == this)
continue;
ChildRC.Parents.insert(this);
#ifndef NDEBUG
IsLeaf = false;
#endif
}
}
#ifndef NDEBUG
if (!Result.empty())
assert(!IsLeaf && "This SCC cannot be a leaf as we have split out new "
"SCCs by removing this edge.");
if (none_of(G->LeafRefSCCs, [&](RefSCC *C) { return C == this; }))
assert(!IsLeaf && "This SCC cannot be a leaf as it already had child "
"SCCs before we removed this edge.");
#endif
// And connect both this RefSCC and all the new ones to the correct parents.
// The easiest way to do this is just to re-analyze the old parent set.
SmallVector<RefSCC *, 4> OldParents(Parents.begin(), Parents.end());
Parents.clear();
for (RefSCC *ParentRC : OldParents)
for (SCC &ParentC : *ParentRC)
for (Node &ParentN : ParentC)
for (Edge &E : *ParentN) {
RefSCC &RC = *G->lookupRefSCC(E.getNode());
if (&RC != ParentRC)
RC.Parents.insert(ParentRC);
}
// If this SCC stopped being a leaf through this edge removal, remove it from
// the leaf SCC list. Note that this DTRT in the case where this was never
// a leaf.
// FIXME: As LeafRefSCCs could be very large, we might want to not walk the
// entire list if this RefSCC wasn't a leaf before the edge removal.
if (!Result.empty())
G->LeafRefSCCs.erase(
std::remove(G->LeafRefSCCs.begin(), G->LeafRefSCCs.end(), this),
G->LeafRefSCCs.end());
#ifndef NDEBUG
// Verify all of the new RefSCCs.
for (RefSCC *RC : Result)
RC->verify();
#endif
// Return the new list of SCCs.
return Result;
}
void LazyCallGraph::RefSCC::handleTrivialEdgeInsertion(Node &SourceN,
Node &TargetN) {
// The only trivial case that requires any graph updates is when we add new
// ref edge and may connect different RefSCCs along that path. This is only
// because of the parents set. Every other part of the graph remains constant
// after this edge insertion.
assert(G->lookupRefSCC(SourceN) == this && "Source must be in this RefSCC.");
RefSCC &TargetRC = *G->lookupRefSCC(TargetN);
if (&TargetRC == this) {
return;
}
#ifdef EXPENSIVE_CHECKS
assert(TargetRC.isDescendantOf(*this) &&
"Target must be a descendant of the Source.");
#endif
// The only change required is to add this RefSCC to the parent set of the
// target. This is a set and so idempotent if the edge already existed.
TargetRC.Parents.insert(this);
}
void LazyCallGraph::RefSCC::insertTrivialCallEdge(Node &SourceN,
Node &TargetN) {
#ifndef NDEBUG
// Check that the RefSCC is still valid when we finish.
auto ExitVerifier = make_scope_exit([this] { verify(); });
#ifdef EXPENSIVE_CHECKS
// Check that we aren't breaking some invariants of the SCC graph. Note that
// this is quadratic in the number of edges in the call graph!
SCC &SourceC = *G->lookupSCC(SourceN);
SCC &TargetC = *G->lookupSCC(TargetN);
if (&SourceC != &TargetC)
assert(SourceC.isAncestorOf(TargetC) &&
"Call edge is not trivial in the SCC graph!");
#endif // EXPENSIVE_CHECKS
#endif // NDEBUG
// First insert it into the source or find the existing edge.
auto InsertResult =
SourceN->EdgeIndexMap.insert({&TargetN, SourceN->Edges.size()});
if (!InsertResult.second) {
// Already an edge, just update it.
Edge &E = SourceN->Edges[InsertResult.first->second];
if (E.isCall())
return; // Nothing to do!
E.setKind(Edge::Call);
} else {
// Create the new edge.
SourceN->Edges.emplace_back(TargetN, Edge::Call);
}
// Now that we have the edge, handle the graph fallout.
handleTrivialEdgeInsertion(SourceN, TargetN);
}
void LazyCallGraph::RefSCC::insertTrivialRefEdge(Node &SourceN, Node &TargetN) {
#ifndef NDEBUG
// Check that the RefSCC is still valid when we finish.
auto ExitVerifier = make_scope_exit([this] { verify(); });
#ifdef EXPENSIVE_CHECKS
// Check that we aren't breaking some invariants of the RefSCC graph.
RefSCC &SourceRC = *G->lookupRefSCC(SourceN);
RefSCC &TargetRC = *G->lookupRefSCC(TargetN);
if (&SourceRC != &TargetRC)
assert(SourceRC.isAncestorOf(TargetRC) &&
"Ref edge is not trivial in the RefSCC graph!");
#endif // EXPENSIVE_CHECKS
#endif // NDEBUG
// First insert it into the source or find the existing edge.
auto InsertResult =
SourceN->EdgeIndexMap.insert({&TargetN, SourceN->Edges.size()});
if (!InsertResult.second)
// Already an edge, we're done.
return;
// Create the new edge.
SourceN->Edges.emplace_back(TargetN, Edge::Ref);
// Now that we have the edge, handle the graph fallout.
handleTrivialEdgeInsertion(SourceN, TargetN);
}
void LazyCallGraph::RefSCC::replaceNodeFunction(Node &N, Function &NewF) {
Function &OldF = N.getFunction();
#ifndef NDEBUG
// Check that the RefSCC is still valid when we finish.
auto ExitVerifier = make_scope_exit([this] { verify(); });
assert(G->lookupRefSCC(N) == this &&
"Cannot replace the function of a node outside this RefSCC.");
assert(G->NodeMap.find(&NewF) == G->NodeMap.end() &&
"Must not have already walked the new function!'");
// It is important that this replacement not introduce graph changes so we
// insist that the caller has already removed every use of the original
// function and that all uses of the new function correspond to existing
// edges in the graph. The common and expected way to use this is when
// replacing the function itself in the IR without changing the call graph
// shape and just updating the analysis based on that.
assert(&OldF != &NewF && "Cannot replace a function with itself!");
assert(OldF.use_empty() &&
"Must have moved all uses from the old function to the new!");
#endif
N.replaceFunction(NewF);
// Update various call graph maps.
G->NodeMap.erase(&OldF);
G->NodeMap[&NewF] = &N;
}
void LazyCallGraph::insertEdge(Node &SourceN, Node &TargetN, Edge::Kind EK) {
assert(SCCMap.empty() &&
"This method cannot be called after SCCs have been formed!");
return SourceN->insertEdgeInternal(TargetN, EK);
}
void LazyCallGraph::removeEdge(Node &SourceN, Node &TargetN) {
assert(SCCMap.empty() &&
"This method cannot be called after SCCs have been formed!");
bool Removed = SourceN->removeEdgeInternal(TargetN);
(void)Removed;
assert(Removed && "Target not in the edge set for this caller?");
}
void LazyCallGraph::removeDeadFunction(Function &F) {
// FIXME: This is unnecessarily restrictive. We should be able to remove
// functions which recursively call themselves.
assert(F.use_empty() &&
"This routine should only be called on trivially dead functions!");
// We shouldn't remove library functions as they are never really dead while
// the call graph is in use -- every function definition refers to them.
assert(!isLibFunction(F) &&
"Must not remove lib functions from the call graph!");
auto NI = NodeMap.find(&F);
if (NI == NodeMap.end())
// Not in the graph at all!
return;
Node &N = *NI->second;
NodeMap.erase(NI);
// Remove this from the entry edges if present.
EntryEdges.removeEdgeInternal(N);
if (SCCMap.empty()) {
// No SCCs have been formed, so removing this is fine and there is nothing
// else necessary at this point but clearing out the node.
N.clear();
return;
}
// Cannot remove a function which has yet to be visited in the DFS walk, so
// if we have a node at all then we must have an SCC and RefSCC.
auto CI = SCCMap.find(&N);
assert(CI != SCCMap.end() &&
"Tried to remove a node without an SCC after DFS walk started!");
SCC &C = *CI->second;
SCCMap.erase(CI);
RefSCC &RC = C.getOuterRefSCC();
// This node must be the only member of its SCC as it has no callers, and
// that SCC must be the only member of a RefSCC as it has no references.
// Validate these properties first.
assert(C.size() == 1 && "Dead functions must be in a singular SCC");
assert(RC.size() == 1 && "Dead functions must be in a singular RefSCC");
// Clean up any remaining reference edges. Note that we walk an unordered set
// here but are just removing and so the order doesn't matter.
for (RefSCC &ParentRC : RC.parents())
for (SCC &ParentC : ParentRC)
for (Node &ParentN : ParentC)
if (ParentN)
ParentN->removeEdgeInternal(N);
// Now remove this RefSCC from any parents sets and the leaf list.
for (Edge &E : *N)
if (RefSCC *TargetRC = lookupRefSCC(E.getNode()))
TargetRC->Parents.erase(&RC);
// FIXME: This is a linear operation which could become hot and benefit from
// an index map.
auto LRI = find(LeafRefSCCs, &RC);
if (LRI != LeafRefSCCs.end())
LeafRefSCCs.erase(LRI);
auto RCIndexI = RefSCCIndices.find(&RC);
int RCIndex = RCIndexI->second;
PostOrderRefSCCs.erase(PostOrderRefSCCs.begin() + RCIndex);
RefSCCIndices.erase(RCIndexI);
for (int i = RCIndex, Size = PostOrderRefSCCs.size(); i < Size; ++i)
RefSCCIndices[PostOrderRefSCCs[i]] = i;
// Finally clear out all the data structures from the node down through the
// components.
N.clear();
C.clear();
RC.clear();
// Nothing to delete as all the objects are allocated in stable bump pointer
// allocators.
}
LazyCallGraph::Node &LazyCallGraph::insertInto(Function &F, Node *&MappedN) {
return *new (MappedN = BPA.Allocate()) Node(*this, F);
}
void LazyCallGraph::updateGraphPtrs() {
// Process all nodes updating the graph pointers.
{
SmallVector<Node *, 16> Worklist;
for (Edge &E : EntryEdges)
Worklist.push_back(&E.getNode());
while (!Worklist.empty()) {
Node &N = *Worklist.pop_back_val();
N.G = this;
if (N)
for (Edge &E : *N)
Worklist.push_back(&E.getNode());
}
}
// Process all SCCs updating the graph pointers.
{
SmallVector<RefSCC *, 16> Worklist(LeafRefSCCs.begin(), LeafRefSCCs.end());
while (!Worklist.empty()) {
RefSCC &C = *Worklist.pop_back_val();
C.G = this;
for (RefSCC &ParentC : C.parents())
Worklist.push_back(&ParentC);
}
}
}
template <typename RootsT, typename GetBeginT, typename GetEndT,
typename GetNodeT, typename FormSCCCallbackT>
void LazyCallGraph::buildGenericSCCs(RootsT &&Roots, GetBeginT &&GetBegin,
GetEndT &&GetEnd, GetNodeT &&GetNode,
FormSCCCallbackT &&FormSCC) {
typedef decltype(GetBegin(std::declval<Node &>())) EdgeItT;
SmallVector<std::pair<Node *, EdgeItT>, 16> DFSStack;
SmallVector<Node *, 16> PendingSCCStack;
// Scan down the stack and DFS across the call edges.
for (Node *RootN : Roots) {
assert(DFSStack.empty() &&
"Cannot begin a new root with a non-empty DFS stack!");
assert(PendingSCCStack.empty() &&
"Cannot begin a new root with pending nodes for an SCC!");
// Skip any nodes we've already reached in the DFS.
if (RootN->DFSNumber != 0) {
assert(RootN->DFSNumber == -1 &&
"Shouldn't have any mid-DFS root nodes!");
continue;
}
RootN->DFSNumber = RootN->LowLink = 1;
int NextDFSNumber = 2;
DFSStack.push_back({RootN, GetBegin(*RootN)});
do {
Node *N;
EdgeItT I;
std::tie(N, I) = DFSStack.pop_back_val();
auto E = GetEnd(*N);
while (I != E) {
Node &ChildN = GetNode(I);
if (ChildN.DFSNumber == 0) {
// We haven't yet visited this child, so descend, pushing the current
// node onto the stack.
DFSStack.push_back({N, I});
ChildN.DFSNumber = ChildN.LowLink = NextDFSNumber++;
N = &ChildN;
I = GetBegin(*N);
E = GetEnd(*N);
continue;
}
// If the child has already been added to some child component, it
// couldn't impact the low-link of this parent because it isn't
// connected, and thus its low-link isn't relevant so skip it.
if (ChildN.DFSNumber == -1) {
++I;
continue;
}
// Track the lowest linked child as the lowest link for this node.
assert(ChildN.LowLink > 0 && "Must have a positive low-link number!");
if (ChildN.LowLink < N->LowLink)
N->LowLink = ChildN.LowLink;
// Move to the next edge.
++I;
}
// We've finished processing N and its descendents, put it on our pending
// SCC stack to eventually get merged into an SCC of nodes.
PendingSCCStack.push_back(N);
// If this node is linked to some lower entry, continue walking up the
// stack.
if (N->LowLink != N->DFSNumber)
continue;
// Otherwise, we've completed an SCC. Append it to our post order list of
// SCCs.
int RootDFSNumber = N->DFSNumber;
// Find the range of the node stack by walking down until we pass the
// root DFS number.
auto SCCNodes = make_range(
PendingSCCStack.rbegin(),
find_if(reverse(PendingSCCStack), [RootDFSNumber](const Node *N) {
return N->DFSNumber < RootDFSNumber;
}));
// Form a new SCC out of these nodes and then clear them off our pending
// stack.
FormSCC(SCCNodes);
PendingSCCStack.erase(SCCNodes.end().base(), PendingSCCStack.end());
} while (!DFSStack.empty());
}
}
/// Build the internal SCCs for a RefSCC from a sequence of nodes.
///
/// Appends the SCCs to the provided vector and updates the map with their
/// indices. Both the vector and map must be empty when passed into this
/// routine.
void LazyCallGraph::buildSCCs(RefSCC &RC, node_stack_range Nodes) {
assert(RC.SCCs.empty() && "Already built SCCs!");
assert(RC.SCCIndices.empty() && "Already mapped SCC indices!");
for (Node *N : Nodes) {
assert(N->LowLink >= (*Nodes.begin())->LowLink &&
"We cannot have a low link in an SCC lower than its root on the "
"stack!");
// This node will go into the next RefSCC, clear out its DFS and low link
// as we scan.
N->DFSNumber = N->LowLink = 0;
}
// Each RefSCC contains a DAG of the call SCCs. To build these, we do
// a direct walk of the call edges using Tarjan's algorithm. We reuse the
// internal storage as we won't need it for the outer graph's DFS any longer.
buildGenericSCCs(
Nodes, [](Node &N) { return N->call_begin(); },
[](Node &N) { return N->call_end(); },
[](EdgeSequence::call_iterator I) -> Node & { return I->getNode(); },
[this, &RC](node_stack_range Nodes) {
RC.SCCs.push_back(createSCC(RC, Nodes));
for (Node &N : *RC.SCCs.back()) {
N.DFSNumber = N.LowLink = -1;
SCCMap[&N] = RC.SCCs.back();
}
});
// Wire up the SCC indices.
for (int i = 0, Size = RC.SCCs.size(); i < Size; ++i)
RC.SCCIndices[RC.SCCs[i]] = i;
}
void LazyCallGraph::buildRefSCCs() {
if (EntryEdges.empty() || !PostOrderRefSCCs.empty())
// RefSCCs are either non-existent or already built!
return;
assert(RefSCCIndices.empty() && "Already mapped RefSCC indices!");
SmallVector<Node *, 16> Roots;
for (Edge &E : *this)
Roots.push_back(&E.getNode());
// The roots will be popped of a stack, so use reverse to get a less
// surprising order. This doesn't change any of the semantics anywhere.
std::reverse(Roots.begin(), Roots.end());
buildGenericSCCs(
Roots,
[](Node &N) {
// We need to populate each node as we begin to walk its edges.
N.populate();
return N->begin();
},
[](Node &N) { return N->end(); },
[](EdgeSequence::iterator I) -> Node & { return I->getNode(); },
[this](node_stack_range Nodes) {
RefSCC *NewRC = createRefSCC(*this);
buildSCCs(*NewRC, Nodes);
connectRefSCC(*NewRC);
// Push the new node into the postorder list and remember its position
// in the index map.
bool Inserted =
RefSCCIndices.insert({NewRC, PostOrderRefSCCs.size()}).second;
(void)Inserted;
assert(Inserted && "Cannot already have this RefSCC in the index map!");
PostOrderRefSCCs.push_back(NewRC);
#ifndef NDEBUG
NewRC->verify();
#endif
});
}
// FIXME: We should move callers of this to embed the parent linking and leaf
// tracking into their DFS in order to remove a full walk of all edges.
void LazyCallGraph::connectRefSCC(RefSCC &RC) {
// Walk all edges in the RefSCC (this remains linear as we only do this once
// when we build the RefSCC) to connect it to the parent sets of its
// children.
bool IsLeaf = true;
for (SCC &C : RC)
for (Node &N : C)
for (Edge &E : *N) {
RefSCC &ChildRC = *lookupRefSCC(E.getNode());
if (&ChildRC == &RC)
continue;
ChildRC.Parents.insert(&RC);
IsLeaf = false;
}
// For the SCCs where we find no child SCCs, add them to the leaf list.
if (IsLeaf)
LeafRefSCCs.push_back(&RC);
}
AnalysisKey LazyCallGraphAnalysis::Key;
LazyCallGraphPrinterPass::LazyCallGraphPrinterPass(raw_ostream &OS) : OS(OS) {}
static void printNode(raw_ostream &OS, LazyCallGraph::Node &N) {
OS << " Edges in function: " << N.getFunction().getName() << "\n";
for (LazyCallGraph::Edge &E : N.populate())
OS << " " << (E.isCall() ? "call" : "ref ") << " -> "
<< E.getFunction().getName() << "\n";
OS << "\n";
}
static void printSCC(raw_ostream &OS, LazyCallGraph::SCC &C) {
ptrdiff_t Size = std::distance(C.begin(), C.end());
OS << " SCC with " << Size << " functions:\n";
for (LazyCallGraph::Node &N : C)
OS << " " << N.getFunction().getName() << "\n";
}
static void printRefSCC(raw_ostream &OS, LazyCallGraph::RefSCC &C) {
ptrdiff_t Size = std::distance(C.begin(), C.end());
OS << " RefSCC with " << Size << " call SCCs:\n";
for (LazyCallGraph::SCC &InnerC : C)
printSCC(OS, InnerC);
OS << "\n";
}
PreservedAnalyses LazyCallGraphPrinterPass::run(Module &M,
ModuleAnalysisManager &AM) {
LazyCallGraph &G = AM.getResult<LazyCallGraphAnalysis>(M);
OS << "Printing the call graph for module: " << M.getModuleIdentifier()
<< "\n\n";
for (Function &F : M)
printNode(OS, G.get(F));
G.buildRefSCCs();
for (LazyCallGraph::RefSCC &C : G.postorder_ref_sccs())
printRefSCC(OS, C);
return PreservedAnalyses::all();
}
LazyCallGraphDOTPrinterPass::LazyCallGraphDOTPrinterPass(raw_ostream &OS)
: OS(OS) {}
static void printNodeDOT(raw_ostream &OS, LazyCallGraph::Node &N) {
std::string Name = "\"" + DOT::EscapeString(N.getFunction().getName()) + "\"";
for (LazyCallGraph::Edge &E : N.populate()) {
OS << " " << Name << " -> \""
<< DOT::EscapeString(E.getFunction().getName()) << "\"";
if (!E.isCall()) // It is a ref edge.
OS << " [style=dashed,label=\"ref\"]";
OS << ";\n";
}
OS << "\n";
}
PreservedAnalyses LazyCallGraphDOTPrinterPass::run(Module &M,
ModuleAnalysisManager &AM) {
LazyCallGraph &G = AM.getResult<LazyCallGraphAnalysis>(M);
OS << "digraph \"" << DOT::EscapeString(M.getModuleIdentifier()) << "\" {\n";
for (Function &F : M)
printNodeDOT(OS, G.get(F));
OS << "}\n";
return PreservedAnalyses::all();
}
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