[llvm-commits] CVS: llvm/lib/Analysis/IPA/Andersens.cpp

Chris Lattner lattner at cs.uiuc.edu
Sun May 23 16:03:02 PDT 2004


Changes in directory llvm/lib/Analysis/IPA:

Andersens.cpp added (r1.1)

---
Log message:

Add a simple implementation of Andersen's interprocedural pointer analysis


---
Diffs of the changes:  (+1029 -0)

Index: llvm/lib/Analysis/IPA/Andersens.cpp
diff -c /dev/null llvm/lib/Analysis/IPA/Andersens.cpp:1.1
*** /dev/null	Sun May 23 16:00:59 2004
--- llvm/lib/Analysis/IPA/Andersens.cpp	Sun May 23 16:00:47 2004
***************
*** 0 ****
--- 1,1029 ----
+ //===- Andersens.cpp - Andersen's Interprocedural Alias Analysis -----------==//
+ // 
+ //                     The LLVM Compiler Infrastructure
+ //
+ // This file was developed by the LLVM research group and is distributed under
+ // the University of Illinois Open Source License. See LICENSE.TXT for details.
+ // 
+ //===----------------------------------------------------------------------===//
+ //
+ // This file defines a very simple implementation of Andersen's interprocedural
+ // alias analysis.  This implementation does not include any of the fancy
+ // features that make Andersen's reasonably efficient (like cycle elimination or
+ // variable substitution), but it should be useful for getting precision
+ // numbers and can be extended in the future.
+ //
+ // In pointer analysis terms, this is a subset-based, flow-insensitive,
+ // field-insensitive, and context-insensitive algorithm pointer algorithm.
+ //
+ // This algorithm is implemented as three stages:
+ //   1. Object identification.
+ //   2. Inclusion constraint identification.
+ //   3. Inclusion constraint solving.
+ //
+ // The object identification stage identifies all of the memory objects in the
+ // program, which includes globals, heap allocated objects, and stack allocated
+ // objects.
+ //
+ // The inclusion constraint identification stage finds all inclusion constraints
+ // in the program by scanning the program, looking for pointer assignments and
+ // other statements that effect the points-to graph.  For a statement like "A =
+ // B", this statement is processed to indicate that A can point to anything that
+ // B can point to.  Constraints can handle copies, loads, and stores.
+ //
+ // The inclusion constraint solving phase iteratively propagates the inclusion
+ // constraints until a fixed point is reached.  This is an O(N^3) algorithm.
+ //
+ // In the initial pass, all indirect function calls are completely ignored.  As
+ // the analysis discovers new targets of function pointers, it iteratively
+ // resolves a precise (and conservative) call graph.  Also related, this
+ // analysis initially assumes that all internal functions have known incoming
+ // pointers.  If we find that an internal function's address escapes outside of
+ // the program, we update this assumption.
+ //
+ //===----------------------------------------------------------------------===//
+ 
+ #define DEBUG_TYPE "anders-aa"
+ #include "llvm/Constants.h"
+ #include "llvm/DerivedTypes.h"
+ #include "llvm/Instructions.h"
+ #include "llvm/Module.h"
+ #include "llvm/Pass.h"
+ #include "llvm/Support/InstIterator.h"
+ #include "llvm/Support/InstVisitor.h"
+ #include "llvm/Analysis/AliasAnalysis.h"
+ #include "Support/Debug.h"
+ #include "Support/Statistic.h"
+ #include <set>
+ using namespace llvm;
+ 
+ namespace {
+   Statistic<>
+   NumIters("anders-aa", "Number of iterations to reach convergence");
+   Statistic<>
+   NumConstraints("anders-aa", "Number of constraints");
+   Statistic<>
+   NumNodes("anders-aa", "Number of nodes");
+   Statistic<>
+   NumEscapingFunctions("anders-aa", "Number of internal functions that escape");
+   Statistic<>
+   NumIndirectCallees("anders-aa", "Number of indirect callees found");
+ 
+   class Andersens : public Pass, public AliasAnalysis,
+                     private InstVisitor<Andersens> {
+     /// Node class - This class is used to represent a memory object in the
+     /// program, and is the primitive used to build the points-to graph.
+     class Node {
+       std::vector<Node*> Pointees;
+       Value *Val;
+     public:
+       Node() : Val(0) {}
+       Node *setValue(Value *V) {
+         assert(Val == 0 && "Value already set for this node!");
+         Val = V;
+         return this;
+       }
+ 
+       /// getValue - Return the LLVM value corresponding to this node.
+       Value *getValue() const { return Val; }
+ 
+       typedef std::vector<Node*>::const_iterator iterator;
+       iterator begin() const { return Pointees.begin(); }
+       iterator end() const { return Pointees.end(); }
+ 
+       /// addPointerTo - Add a pointer to the list of pointees of this node,
+       /// returning true if this caused a new pointer to be added, or false if
+       /// we already knew about the points-to relation.
+       bool addPointerTo(Node *N) {
+         std::vector<Node*>::iterator I = std::lower_bound(Pointees.begin(),
+                                                           Pointees.end(),
+                                                           N);
+         if (I != Pointees.end() && *I == N)
+           return false;
+         Pointees.insert(I, N);
+         return true;
+       }
+ 
+       /// intersects - Return true if the points-to set of this node intersects
+       /// with the points-to set of the specified node.
+       bool intersects(Node *N) const;
+ 
+       /// intersectsIgnoring - Return true if the points-to set of this node
+       /// intersects with the points-to set of the specified node on any nodes
+       /// except for the specified node to ignore.
+       bool intersectsIgnoring(Node *N, Node *Ignoring) const;
+ 
+       // Constraint application methods.
+       bool copyFrom(Node *N);
+       bool loadFrom(Node *N);
+       bool storeThrough(Node *N);
+     };
+ 
+     /// GraphNodes - This vector is populated as part of the object
+     /// identification stage of the analysis, which populates this vector with a
+     /// node for each memory object and fills in the ValueNodes map.
+     std::vector<Node> GraphNodes;
+ 
+     /// ValueNodes - This map indicates the Node that a particular Value* is
+     /// represented by.  This contains entries for all pointers.
+     std::map<Value*, unsigned> ValueNodes;
+ 
+     /// ObjectNodes - This map contains entries for each memory object in the
+     /// program: globals, alloca's and mallocs.  
+     std::map<Value*, unsigned> ObjectNodes;
+ 
+     /// ReturnNodes - This map contains an entry for each function in the
+     /// program that returns a value.
+     std::map<Function*, unsigned> ReturnNodes;
+ 
+     /// VarargNodes - This map contains the entry used to represent all pointers
+     /// passed through the varargs portion of a function call for a particular
+     /// function.  An entry is not present in this map for functions that do not
+     /// take variable arguments.
+     std::map<Function*, unsigned> VarargNodes;
+ 
+     /// Constraint - Objects of this structure are used to represent the various
+     /// constraints identified by the algorithm.  The constraints are 'copy',
+     /// for statements like "A = B", 'load' for statements like "A = *B", and
+     /// 'store' for statements like "*A = B".
+     struct Constraint {
+       enum ConstraintType { Copy, Load, Store } Type;
+       Node *Dest, *Src;
+ 
+       Constraint(ConstraintType Ty, Node *D, Node *S)
+         : Type(Ty), Dest(D), Src(S) {}
+     };
+     
+     /// Constraints - This vector contains a list of all of the constraints
+     /// identified by the program.
+     std::vector<Constraint> Constraints;
+ 
+     /// EscapingInternalFunctions - This set contains all of the internal
+     /// functions that are found to escape from the program.  If the address of
+     /// an internal function is passed to an external function or otherwise
+     /// escapes from the analyzed portion of the program, we must assume that
+     /// any pointer arguments can alias the universal node.  This set keeps
+     /// track of those functions we are assuming to escape so far.
+     std::set<Function*> EscapingInternalFunctions;
+ 
+     /// IndirectCalls - This contains a list of all of the indirect call sites
+     /// in the program.  Since the call graph is iteratively discovered, we may
+     /// need to add constraints to our graph as we find new targets of function
+     /// pointers.
+     std::vector<CallSite> IndirectCalls;
+ 
+     /// IndirectCallees - For each call site in the indirect calls list, keep
+     /// track of the callees that we have discovered so far.  As the analysis
+     /// proceeds, more callees are discovered, until the call graph finally
+     /// stabilizes.
+     std::map<CallSite, std::vector<Function*> > IndirectCallees;
+ 
+     /// This enum defines the GraphNodes indices that correspond to important
+     /// fixed sets.
+     enum {
+       UniversalSet = 0,
+       NullPtr      = 1,
+       NullObject   = 2,
+     };
+     
+   public:
+     bool run(Module &M) {
+       InitializeAliasAnalysis(this);
+       IdentifyObjects(M);
+       CollectConstraints(M);
+       DEBUG(PrintConstraints());
+       SolveConstraints();
+       DEBUG(PrintPointsToGraph());
+ 
+       // Free the constraints list, as we don't need it to respond to alias
+       // requests.
+       ObjectNodes.clear();
+       ReturnNodes.clear();
+       VarargNodes.clear();
+       EscapingInternalFunctions.clear();
+       std::vector<Constraint>().swap(Constraints);      
+       return false;
+     }
+ 
+     void releaseMemory() {
+       // FIXME: Until we have transitively required passes working correctly,
+       // this cannot be enabled!  Otherwise, using -count-aa with the pass
+       // causes memory to be freed too early. :(
+ #if 0
+       // The memory objects and ValueNodes data structures at the only ones that
+       // are still live after construction.
+       std::vector<Node>().swap(GraphNodes);
+       ValueNodes.clear();
+ #endif
+     }
+ 
+     virtual void getAnalysisUsage(AnalysisUsage &AU) const {
+       AliasAnalysis::getAnalysisUsage(AU);
+       AU.setPreservesAll();                         // Does not transform code
+     }
+ 
+     //------------------------------------------------
+     // Implement the AliasAnalysis API
+     //  
+     AliasResult alias(const Value *V1, unsigned V1Size,
+                       const Value *V2, unsigned V2Size);
+     void getMustAliases(Value *P, std::vector<Value*> &RetVals);
+     bool pointsToConstantMemory(const Value *P);
+ 
+     virtual void deleteValue(Value *V) {
+       ValueNodes.erase(V);
+       getAnalysis<AliasAnalysis>().deleteValue(V);
+     }
+ 
+     virtual void copyValue(Value *From, Value *To) {
+       ValueNodes[To] = ValueNodes[From];
+       getAnalysis<AliasAnalysis>().copyValue(From, To);
+     }
+ 
+   private:
+     /// getNode - Return the node corresponding to the specified pointer scalar.
+     ///
+     Node *getNode(Value *V) {
+       if (Constant *C = dyn_cast<Constant>(V))
+         return getNodeForConstantPointer(C);
+ 
+       std::map<Value*, unsigned>::iterator I = ValueNodes.find(V);
+       if (I == ValueNodes.end()) {
+         V->dump();
+         assert(I != ValueNodes.end() &&
+                "Value does not have a node in the points-to graph!");
+       }
+       return &GraphNodes[I->second];
+     }
+     
+     /// getObject - Return the node corresponding to the memory object for the
+     /// specified global or allocation instruction.
+     Node *getObject(Value *V) {
+       std::map<Value*, unsigned>::iterator I = ObjectNodes.find(V);
+       assert(I != ObjectNodes.end() &&
+              "Value does not have an object in the points-to graph!");
+       return &GraphNodes[I->second];
+     }
+ 
+     /// getReturnNode - Return the node representing the return value for the
+     /// specified function.
+     Node *getReturnNode(Function *F) {
+       std::map<Function*, unsigned>::iterator I = ReturnNodes.find(F);
+       assert(I != ReturnNodes.end() && "Function does not return a value!");
+       return &GraphNodes[I->second];
+     }
+ 
+     /// getVarargNode - Return the node representing the variable arguments
+     /// formal for the specified function.
+     Node *getVarargNode(Function *F) {
+       std::map<Function*, unsigned>::iterator I = VarargNodes.find(F);
+       assert(I != VarargNodes.end() && "Function does not take var args!");
+       return &GraphNodes[I->second];
+     }
+ 
+     /// getNodeValue - Get the node for the specified LLVM value and set the
+     /// value for it to be the specified value.
+     Node *getNodeValue(Value &V) {
+       return getNode(&V)->setValue(&V);
+     }
+ 
+     void IdentifyObjects(Module &M);
+     void CollectConstraints(Module &M);
+     void SolveConstraints();
+ 
+     Node *getNodeForConstantPointer(Constant *C);
+     Node *getNodeForConstantPointerTarget(Constant *C);
+     void AddGlobalInitializerConstraints(Node *N, Constant *C);
+     void AddConstraintsForNonInternalLinkage(Function *F);
+     void AddConstraintsForCall(CallSite CS, Function *F);
+ 
+ 
+     void PrintNode(Node *N);
+     void PrintConstraints();
+     void PrintPointsToGraph();
+ 
+     //===------------------------------------------------------------------===//
+     // Instruction visitation methods for adding constraints
+     //
+     friend class InstVisitor<Andersens>;
+     void visitReturnInst(ReturnInst &RI);
+     void visitInvokeInst(InvokeInst &II) { visitCallSite(CallSite(&II)); }
+     void visitCallInst(CallInst &CI) { visitCallSite(CallSite(&CI)); }
+     void visitCallSite(CallSite CS);
+     void visitAllocationInst(AllocationInst &AI);
+     void visitLoadInst(LoadInst &LI);
+     void visitStoreInst(StoreInst &SI);
+     void visitGetElementPtrInst(GetElementPtrInst &GEP);
+     void visitPHINode(PHINode &PN);
+     void visitCastInst(CastInst &CI);
+     void visitSelectInst(SelectInst &SI);
+     void visitVANext(VANextInst &I);
+     void visitVAArg(VAArgInst &I);
+     void visitInstruction(Instruction &I);
+   };
+ 
+   RegisterOpt<Andersens> X("anders-aa",
+                            "Andersen's Interprocedural Alias Analysis");
+   RegisterAnalysisGroup<AliasAnalysis, Andersens> Y;
+ }
+ 
+ //===----------------------------------------------------------------------===//
+ //                  AliasAnalysis Interface Implementation
+ //===----------------------------------------------------------------------===//
+ 
+ AliasAnalysis::AliasResult Andersens::alias(const Value *V1, unsigned V1Size,
+                                             const Value *V2, unsigned V2Size) {
+   Node *N1 = getNode((Value*)V1);
+   Node *N2 = getNode((Value*)V2);
+ 
+   // Check to see if the two pointers are known to not alias.  They don't alias
+   // if their points-to sets do not intersect.
+   if (!N1->intersectsIgnoring(N2, &GraphNodes[NullObject]))
+     return NoAlias;
+ 
+   return AliasAnalysis::alias(V1, V1Size, V2, V2Size);
+ }
+ 
+ /// getMustAlias - We can provide must alias information if we know that a
+ /// pointer can only point to a specific function or the null pointer.
+ /// Unfortunately we cannot determine must-alias information for global
+ /// variables or any other memory memory objects because we do not track whether
+ /// a pointer points to the beginning of an object or a field of it.
+ void Andersens::getMustAliases(Value *P, std::vector<Value*> &RetVals) {
+   Node *N = getNode(P);
+   Node::iterator I = N->begin();
+   if (I != N->end()) {
+     // If there is exactly one element in the points-to set for the object...
+     ++I;
+     if (I == N->end()) {
+       Node *Pointee = *N->begin();
+ 
+       // If a function is the only object in the points-to set, then it must be
+       // the destination.  Note that we can't handle global variables here,
+       // because we don't know if the pointer is actually pointing to a field of
+       // the global or to the beginning of it.
+       if (Value *V = Pointee->getValue()) {
+         if (Function *F = dyn_cast<Function>(V))
+           RetVals.push_back(F);
+       } else {
+         // If the object in the points-to set is the null object, then the null
+         // pointer is a must alias.
+         if (Pointee == &GraphNodes[NullObject])
+           RetVals.push_back(Constant::getNullValue(P->getType()));
+       }
+     }
+   }
+   
+   AliasAnalysis::getMustAliases(P, RetVals);
+ }
+ 
+ /// pointsToConstantMemory - If we can determine that this pointer only points
+ /// to constant memory, return true.  In practice, this means that if the
+ /// pointer can only point to constant globals, functions, or the null pointer,
+ /// return true.
+ ///
+ bool Andersens::pointsToConstantMemory(const Value *P) {
+   Node *N = getNode((Value*)P);
+   for (Node::iterator I = N->begin(), E = N->end(); I != E; ++I) {
+     if (Value *V = (*I)->getValue()) {
+       if (!isa<GlobalValue>(V) || (isa<GlobalVariable>(V) &&
+                                    !cast<GlobalVariable>(V)->isConstant()))
+         return AliasAnalysis::pointsToConstantMemory(P);
+     } else {
+       if (*I != &GraphNodes[NullObject])
+         return AliasAnalysis::pointsToConstantMemory(P);
+     }
+   }
+ 
+   return true;
+ }
+ 
+ //===----------------------------------------------------------------------===//
+ //                       Object Identification Phase
+ //===----------------------------------------------------------------------===//
+ 
+ /// IdentifyObjects - This stage scans the program, adding an entry to the
+ /// GraphNodes list for each memory object in the program (global stack or
+ /// heap), and populates the ValueNodes and ObjectNodes maps for these objects.
+ ///
+ void Andersens::IdentifyObjects(Module &M) {
+   unsigned NumObjects = 0;
+ 
+   // Object #0 is always the universal set: the object that we don't know
+   // anything about.
+   assert(NumObjects == UniversalSet && "Something changed!");
+   ++NumObjects;
+ 
+   // Object #1 always represents the null pointer.
+   assert(NumObjects == NullPtr && "Something changed!");
+   ++NumObjects;
+ 
+   // Object #2 always represents the null object (the object pointed to by null)
+   assert(NumObjects == NullObject && "Something changed!");
+   ++NumObjects;
+ 
+   // Add all the globals first.
+   for (Module::giterator I = M.gbegin(), E = M.gend(); I != E; ++I) {
+     ObjectNodes[I] = NumObjects++;
+     ValueNodes[I] = NumObjects++;
+   }
+ 
+   // Add nodes for all of the functions and the instructions inside of them.
+   for (Module::iterator F = M.begin(), E = M.end(); F != E; ++F) {
+     // The function itself is a memory object.
+     ValueNodes[F] = NumObjects++;
+     ObjectNodes[F] = NumObjects++;
+     if (isa<PointerType>(F->getFunctionType()->getReturnType()))
+       ReturnNodes[F] = NumObjects++;
+     if (F->getFunctionType()->isVarArg())
+       VarargNodes[F] = NumObjects++;
+ 
+     // Add nodes for all of the incoming pointer arguments.
+     for (Function::aiterator I = F->abegin(), E = F->aend(); I != E; ++I)
+       if (isa<PointerType>(I->getType()))
+         ValueNodes[I] = NumObjects++;
+ 
+     // Scan the function body, creating a memory object for each heap/stack
+     // allocation in the body of the function and a node to represent all
+     // pointer values defined by instructions and used as operands.
+     for (inst_iterator II = inst_begin(F), E = inst_end(F); II != E; ++II) {
+       // If this is an heap or stack allocation, create a node for the memory
+       // object.
+       if (isa<PointerType>(II->getType())) {
+         ValueNodes[&*II] = NumObjects++;
+         if (AllocationInst *AI = dyn_cast<AllocationInst>(&*II))
+           ObjectNodes[AI] = NumObjects++;
+       }
+     }
+   }
+ 
+   // Now that we know how many objects to create, make them all now!
+   GraphNodes.resize(NumObjects);
+   NumNodes += NumObjects;
+ }
+ 
+ //===----------------------------------------------------------------------===//
+ //                     Constraint Identification Phase
+ //===----------------------------------------------------------------------===//
+ 
+ /// getNodeForConstantPointer - Return the node corresponding to the constant
+ /// pointer itself.
+ Andersens::Node *Andersens::getNodeForConstantPointer(Constant *C) {
+   assert(isa<PointerType>(C->getType()) && "Not a constant pointer!");
+ 
+   if (isa<ConstantPointerNull>(C))
+     return &GraphNodes[NullPtr];
+   else if (ConstantPointerRef *CPR = dyn_cast<ConstantPointerRef>(C))
+     return getNode(CPR->getValue());
+   else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) {
+     switch (CE->getOpcode()) {
+     case Instruction::GetElementPtr:
+       return getNodeForConstantPointer(CE->getOperand(0));
+     case Instruction::Cast:
+       if (isa<PointerType>(CE->getOperand(0)->getType()))
+         return getNodeForConstantPointer(CE->getOperand(0));
+       else
+         return &GraphNodes[UniversalSet];
+     default:
+       std::cerr << "Constant Expr not yet handled: " << *CE << "\n";
+       assert(0);
+     }
+   } else {
+     assert(0 && "Unknown constant pointer!");
+   }
+ }
+ 
+ /// getNodeForConstantPointerTarget - Return the node POINTED TO by the
+ /// specified constant pointer.
+ Andersens::Node *Andersens::getNodeForConstantPointerTarget(Constant *C) {
+   assert(isa<PointerType>(C->getType()) && "Not a constant pointer!");
+ 
+   if (isa<ConstantPointerNull>(C))
+     return &GraphNodes[NullObject];
+   else if (ConstantPointerRef *CPR = dyn_cast<ConstantPointerRef>(C))
+     return getObject(CPR->getValue());
+   else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) {
+     switch (CE->getOpcode()) {
+     case Instruction::GetElementPtr:
+       return getNodeForConstantPointerTarget(CE->getOperand(0));
+     case Instruction::Cast:
+       if (isa<PointerType>(CE->getOperand(0)->getType()))
+         return getNodeForConstantPointerTarget(CE->getOperand(0));
+       else
+         return &GraphNodes[UniversalSet];
+     default:
+       std::cerr << "Constant Expr not yet handled: " << *CE << "\n";
+       assert(0);
+     }
+   } else {
+     assert(0 && "Unknown constant pointer!");
+   }
+ }
+ 
+ /// AddGlobalInitializerConstraints - Add inclusion constraints for the memory
+ /// object N, which contains values indicated by C.
+ void Andersens::AddGlobalInitializerConstraints(Node *N, Constant *C) {
+   if (C->getType()->isFirstClassType()) {
+     if (isa<PointerType>(C->getType()))
+       N->addPointerTo(getNodeForConstantPointer(C));
+   } else if (C->isNullValue()) {
+     N->addPointerTo(&GraphNodes[NullObject]);
+     return;
+   } else {
+     // If this is an array or struct, include constraints for each element.
+     assert(isa<ConstantArray>(C) || isa<ConstantStruct>(C));
+     for (unsigned i = 0, e = C->getNumOperands(); i != e; ++i)
+       AddGlobalInitializerConstraints(N, cast<Constant>(C->getOperand(i)));
+   }
+ }
+ 
+ void Andersens::AddConstraintsForNonInternalLinkage(Function *F) {
+   for (Function::aiterator I = F->abegin(), E = F->aend(); I != E; ++I)
+     if (isa<PointerType>(I->getType()))
+       // If this is an argument of an externally accessible function, the
+       // incoming pointer might point to anything.
+       Constraints.push_back(Constraint(Constraint::Copy, getNode(I),
+                                        &GraphNodes[UniversalSet]));
+ }
+ 
+ 
+ /// CollectConstraints - This stage scans the program, adding a constraint to
+ /// the Constraints list for each instruction in the program that induces a
+ /// constraint, and setting up the initial points-to graph.
+ ///
+ void Andersens::CollectConstraints(Module &M) {
+   // First, the universal set points to itself.
+   GraphNodes[UniversalSet].addPointerTo(&GraphNodes[UniversalSet]);
+ 
+   // Next, the null pointer points to the null object.
+   GraphNodes[NullPtr].addPointerTo(&GraphNodes[NullObject]);
+ 
+   // Next, add any constraints on global variables and their initializers.
+   for (Module::giterator I = M.gbegin(), E = M.gend(); I != E; ++I) {
+     // Associate the address of the global object as pointing to the memory for
+     // the global: &G = <G memory>
+     Node *Object = getObject(I);
+     Object->setValue(I);
+     getNodeValue(*I)->addPointerTo(Object);
+ 
+     if (I->hasInitializer()) {
+       AddGlobalInitializerConstraints(Object, I->getInitializer());
+     } else {
+       // If it doesn't have an initializer (i.e. it's defined in another
+       // translation unit), it points to the universal set.
+       Constraints.push_back(Constraint(Constraint::Copy, Object,
+                                        &GraphNodes[UniversalSet]));
+     }
+   }
+   
+   for (Module::iterator F = M.begin(), E = M.end(); F != E; ++F) {
+     // Make the function address point to the function object.
+     getNodeValue(*F)->addPointerTo(getObject(F)->setValue(F));
+ 
+     // Set up the return value node.
+     if (isa<PointerType>(F->getFunctionType()->getReturnType()))
+       getReturnNode(F)->setValue(F);
+     if (F->getFunctionType()->isVarArg())
+       getVarargNode(F)->setValue(F);
+ 
+     // Set up incoming argument nodes.
+     for (Function::aiterator I = F->abegin(), E = F->aend(); I != E; ++I)
+       if (isa<PointerType>(I->getType()))
+         getNodeValue(*I);
+ 
+     if (!F->hasInternalLinkage())
+       AddConstraintsForNonInternalLinkage(F);
+ 
+     if (!F->isExternal()) {
+       // Scan the function body, creating a memory object for each heap/stack
+       // allocation in the body of the function and a node to represent all
+       // pointer values defined by instructions and used as operands.
+       visit(F);
+     } else {
+       // External functions that return pointers return the universal set.
+       if (isa<PointerType>(F->getFunctionType()->getReturnType()))
+         Constraints.push_back(Constraint(Constraint::Copy,
+                                          getReturnNode(F),
+                                          &GraphNodes[UniversalSet]));
+ 
+       // Any pointers that are passed into the function have the universal set
+       // stored into them.
+       for (Function::aiterator I = F->abegin(), E = F->aend(); I != E; ++I)
+         if (isa<PointerType>(I->getType())) {
+           // Pointers passed into external functions could have anything stored
+           // through them.
+           Constraints.push_back(Constraint(Constraint::Store, getNode(I),
+                                            &GraphNodes[UniversalSet]));
+           // Memory objects passed into external function calls can have the
+           // universal set point to them.
+           Constraints.push_back(Constraint(Constraint::Copy,
+                                            &GraphNodes[UniversalSet],
+                                            getNode(I)));
+         }
+ 
+       // If this is an external varargs function, it can also store pointers
+       // into any pointers passed through the varargs section.
+       if (F->getFunctionType()->isVarArg())
+         Constraints.push_back(Constraint(Constraint::Store, getVarargNode(F),
+                                          &GraphNodes[UniversalSet]));
+     }
+   }
+   NumConstraints += Constraints.size();
+ }
+ 
+ 
+ void Andersens::visitInstruction(Instruction &I) {
+ #ifdef NDEBUG
+   return;          // This function is just a big assert.
+ #endif
+   if (isa<BinaryOperator>(I))
+     return;
+   // Most instructions don't have any effect on pointer values.
+   switch (I.getOpcode()) {
+   case Instruction::Br:
+   case Instruction::Switch:
+   case Instruction::Unwind:
+   case Instruction::Free:
+   case Instruction::Shl:
+   case Instruction::Shr:
+     return;
+   default:
+     // Is this something we aren't handling yet?
+     std::cerr << "Unknown instruction: " << I;
+     abort();
+   }
+ }
+ 
+ void Andersens::visitAllocationInst(AllocationInst &AI) {
+   getNodeValue(AI)->addPointerTo(getObject(&AI)->setValue(&AI));
+ }
+ 
+ void Andersens::visitReturnInst(ReturnInst &RI) {
+   if (RI.getNumOperands() && isa<PointerType>(RI.getOperand(0)->getType()))
+     // return V   -->   <Copy/retval{F}/v>
+     Constraints.push_back(Constraint(Constraint::Copy,
+                                      getReturnNode(RI.getParent()->getParent()),
+                                      getNode(RI.getOperand(0))));
+ }
+ 
+ void Andersens::visitLoadInst(LoadInst &LI) {
+   if (isa<PointerType>(LI.getType()))
+     // P1 = load P2  -->  <Load/P1/P2>
+     Constraints.push_back(Constraint(Constraint::Load, getNodeValue(LI),
+                                      getNode(LI.getOperand(0))));
+ }
+ 
+ void Andersens::visitStoreInst(StoreInst &SI) {
+   if (isa<PointerType>(SI.getOperand(0)->getType()))
+     // store P1, P2  -->  <Store/P2/P1>
+     Constraints.push_back(Constraint(Constraint::Store,
+                                      getNode(SI.getOperand(1)),
+                                      getNode(SI.getOperand(0))));
+ }
+ 
+ void Andersens::visitGetElementPtrInst(GetElementPtrInst &GEP) {
+   // P1 = getelementptr P2, ... --> <Copy/P1/P2>
+   Constraints.push_back(Constraint(Constraint::Copy, getNodeValue(GEP),
+                                    getNode(GEP.getOperand(0))));
+ }
+ 
+ void Andersens::visitPHINode(PHINode &PN) {
+   if (isa<PointerType>(PN.getType())) {
+     Node *PNN = getNodeValue(PN);
+     for (unsigned i = 0, e = PN.getNumIncomingValues(); i != e; ++i)
+       // P1 = phi P2, P3  -->  <Copy/P1/P2>, <Copy/P1/P3>, ...
+       Constraints.push_back(Constraint(Constraint::Copy, PNN,
+                                        getNode(PN.getIncomingValue(i))));
+   }
+ }
+ 
+ void Andersens::visitCastInst(CastInst &CI) {
+   Value *Op = CI.getOperand(0);
+   if (isa<PointerType>(CI.getType())) {
+     if (isa<PointerType>(Op->getType())) {
+       // P1 = cast P2  --> <Copy/P1/P2>
+       Constraints.push_back(Constraint(Constraint::Copy, getNodeValue(CI),
+                                        getNode(CI.getOperand(0))));
+     } else {
+       // P1 = cast int --> <Copy/P1/Univ>
+       Constraints.push_back(Constraint(Constraint::Copy, getNodeValue(CI),
+                                        &GraphNodes[UniversalSet]));
+     }
+   } else if (isa<PointerType>(Op->getType())) {
+     // int = cast P1 --> <Copy/Univ/P1>
+     Constraints.push_back(Constraint(Constraint::Copy,
+                                      &GraphNodes[UniversalSet],
+                                      getNode(CI.getOperand(0))));
+   }
+ }
+ 
+ void Andersens::visitSelectInst(SelectInst &SI) {
+   if (isa<PointerType>(SI.getType())) {
+     Node *SIN = getNodeValue(SI);
+     // P1 = select C, P2, P3   ---> <Copy/P1/P2>, <Copy/P1/P3>
+     Constraints.push_back(Constraint(Constraint::Copy, SIN,
+                                      getNode(SI.getOperand(1))));
+     Constraints.push_back(Constraint(Constraint::Copy, SIN,
+                                      getNode(SI.getOperand(2))));
+   }
+ }
+ 
+ void Andersens::visitVANext(VANextInst &I) {
+   // FIXME: Implement
+   assert(0 && "vanext not handled yet!");
+ }
+ void Andersens::visitVAArg(VAArgInst &I) {
+   assert(0 && "vaarg not handled yet!");
+ }
+ 
+ /// AddConstraintsForCall - Add constraints for a call with actual arguments
+ /// specified by CS to the function specified by F.  Note that the types of
+ /// arguments might not match up in the case where this is an indirect call and
+ /// the function pointer has been casted.  If this is the case, do something
+ /// reasonable.
+ void Andersens::AddConstraintsForCall(CallSite CS, Function *F) {
+   if (isa<PointerType>(CS.getType())) {
+     Node *CSN = getNode(CS.getInstruction());
+     if (isa<PointerType>(F->getFunctionType()->getReturnType())) {
+       Constraints.push_back(Constraint(Constraint::Copy, CSN,
+                                        getReturnNode(F)));
+     } else {
+       // If the function returns a non-pointer value, handle this just like we
+       // treat a nonpointer cast to pointer.
+       Constraints.push_back(Constraint(Constraint::Copy, CSN,
+                                        &GraphNodes[UniversalSet]));
+     }
+   } else if (isa<PointerType>(F->getFunctionType()->getReturnType())) {
+     Constraints.push_back(Constraint(Constraint::Copy,
+                                      &GraphNodes[UniversalSet],
+                                      getReturnNode(F)));
+   }
+   
+   Function::aiterator AI = F->abegin(), AE = F->aend();
+   CallSite::arg_iterator ArgI = CS.arg_begin(), ArgE = CS.arg_end();
+   for (; AI != AE && ArgI != ArgE; ++AI, ++ArgI)
+     if (isa<PointerType>(AI->getType())) {
+       if (isa<PointerType>((*ArgI)->getType())) {
+         // Copy the actual argument into the formal argument.
+         Constraints.push_back(Constraint(Constraint::Copy, getNode(AI),
+                                          getNode(*ArgI)));
+       } else {
+         Constraints.push_back(Constraint(Constraint::Copy, getNode(AI),
+                                          &GraphNodes[UniversalSet]));
+       }
+     } else if (isa<PointerType>((*ArgI)->getType())) {
+       Constraints.push_back(Constraint(Constraint::Copy,
+                                        &GraphNodes[UniversalSet],
+                                        getNode(*ArgI)));
+     }
+   
+   // Copy all pointers passed through the varargs section to the varargs node.
+   if (F->getFunctionType()->isVarArg())
+     for (; ArgI != ArgE; ++ArgI)
+       if (isa<PointerType>((*ArgI)->getType()))
+         Constraints.push_back(Constraint(Constraint::Copy, getVarargNode(F),
+                                          getNode(*ArgI)));
+   // If more arguments are passed in than we track, just drop them on the floor.
+ }
+ 
+ void Andersens::visitCallSite(CallSite CS) {
+   if (isa<PointerType>(CS.getType()))
+     getNodeValue(*CS.getInstruction());
+ 
+   if (Function *F = CS.getCalledFunction()) {
+     AddConstraintsForCall(CS, F);
+   } else {
+     // We don't handle indirect call sites yet.  Keep track of them for when we
+     // discover the call graph incrementally.
+     IndirectCalls.push_back(CS);
+   }
+ }
+ 
+ //===----------------------------------------------------------------------===//
+ //                         Constraint Solving Phase
+ //===----------------------------------------------------------------------===//
+ 
+ /// intersects - Return true if the points-to set of this node intersects
+ /// with the points-to set of the specified node.
+ bool Andersens::Node::intersects(Node *N) const {
+   iterator I1 = begin(), I2 = N->begin(), E1 = end(), E2 = N->end();
+   while (I1 != E1 && I2 != E2) {
+     if (*I1 == *I2) return true;
+     if (*I1 < *I2)
+       ++I1;
+     else
+       ++I2;
+   }
+   return false;
+ }
+ 
+ /// intersectsIgnoring - Return true if the points-to set of this node
+ /// intersects with the points-to set of the specified node on any nodes
+ /// except for the specified node to ignore.
+ bool Andersens::Node::intersectsIgnoring(Node *N, Node *Ignoring) const {
+   iterator I1 = begin(), I2 = N->begin(), E1 = end(), E2 = N->end();
+   while (I1 != E1 && I2 != E2) {
+     if (*I1 == *I2) {
+       if (*I1 != Ignoring) return true;
+       ++I1; ++I2;
+     } else if (*I1 < *I2)
+       ++I1;
+     else
+       ++I2;
+   }
+   return false;
+ }
+ 
+ // Copy constraint: all edges out of the source node get copied to the
+ // destination node.  This returns true if a change is made.
+ bool Andersens::Node::copyFrom(Node *N) {
+   // Use a mostly linear-time merge since both of the lists are sorted.
+   bool Changed = false;
+   iterator I = N->begin(), E = N->end();
+   unsigned i = 0;
+   while (I != E && i != Pointees.size()) {
+     if (Pointees[i] < *I) {
+       ++i;
+     } else if (Pointees[i] == *I) {
+       ++i; ++I;
+     } else {
+       // We found a new element to copy over.
+       Changed = true;
+       Pointees.insert(Pointees.begin()+i, *I);
+        ++i; ++I;
+     }
+   }
+ 
+   if (I != E) {
+     Pointees.insert(Pointees.end(), I, E);
+     Changed = true;
+   }
+ 
+   return Changed;
+ }
+ 
+ bool Andersens::Node::loadFrom(Node *N) {
+   bool Changed = false;
+   for (iterator I = N->begin(), E = N->end(); I != E; ++I)
+     Changed |= copyFrom(*I);
+   return Changed;
+ }
+ 
+ bool Andersens::Node::storeThrough(Node *N) {
+   bool Changed = false;
+   for (iterator I = begin(), E = end(); I != E; ++I)
+     Changed |= (*I)->copyFrom(N);
+   return Changed;
+ }
+ 
+ 
+ /// SolveConstraints - This stage iteratively processes the constraints list
+ /// propagating constraints (adding edges to the Nodes in the points-to graph)
+ /// until a fixed point is reached.
+ ///
+ void Andersens::SolveConstraints() {
+   bool Changed = true;
+   unsigned Iteration = 0;
+   while (Changed) {
+     Changed = false;
+     ++NumIters;
+     DEBUG(std::cerr << "Starting iteration #" << Iteration++ << "!\n");
+ 
+     // Loop over all of the constraints, applying them in turn.
+     for (unsigned i = 0, e = Constraints.size(); i != e; ++i) {
+       Constraint &C = Constraints[i];
+       switch (C.Type) {
+       case Constraint::Copy:
+         Changed |= C.Dest->copyFrom(C.Src);
+         break;
+       case Constraint::Load:
+         Changed |= C.Dest->loadFrom(C.Src);
+         break;
+       case Constraint::Store:
+         Changed |= C.Dest->storeThrough(C.Src);
+         break;
+       default:
+         assert(0 && "Unknown constraint!");
+       }
+     }
+ 
+     if (Changed) {
+       // Check to see if any internal function's addresses have been passed to
+       // external functions.  If so, we have to assume that their incoming
+       // arguments could be anything.  If there are any internal functions in
+       // the universal node that we don't know about, we must iterate.
+       for (Node::iterator I = GraphNodes[UniversalSet].begin(),
+              E = GraphNodes[UniversalSet].end(); I != E; ++I)
+         if (Function *F = dyn_cast_or_null<Function>((*I)->getValue()))
+           if (F->hasInternalLinkage() &&
+               EscapingInternalFunctions.insert(F).second) {
+             // We found a function that is just now escaping.  Mark it as if it
+             // didn't have internal linkage.
+             AddConstraintsForNonInternalLinkage(F);
+             DEBUG(std::cerr << "Found escaping internal function: "
+                             << F->getName() << "\n");
+             ++NumEscapingFunctions;
+           }
+ 
+       // Check to see if we have discovered any new callees of the indirect call
+       // sites.  If so, add constraints to the analysis.
+       for (unsigned i = 0, e = IndirectCalls.size(); i != e; ++i) {
+         CallSite CS = IndirectCalls[i];
+         std::vector<Function*> &KnownCallees = IndirectCallees[CS];
+         Node *CN = getNode(CS.getCalledValue());
+ 
+         for (Node::iterator NI = CN->begin(), E = CN->end(); NI != E; ++NI)
+           if (Function *F = dyn_cast_or_null<Function>((*NI)->getValue())) {
+             std::vector<Function*>::iterator IP =
+               std::lower_bound(KnownCallees.begin(), KnownCallees.end(), F);
+             if (IP == KnownCallees.end() || *IP != F) {
+               // Add the constraints for the call now.
+               AddConstraintsForCall(CS, F);
+               DEBUG(std::cerr << "Found actual callee '"
+                               << F->getName() << "' for call: "
+                               << *CS.getInstruction() << "\n");
+               ++NumIndirectCallees;
+               KnownCallees.insert(IP, F);
+             }
+           }
+       }
+     }
+   }
+ }
+ 
+ 
+ 
+ //===----------------------------------------------------------------------===//
+ //                               Debugging Output
+ //===----------------------------------------------------------------------===//
+ 
+ void Andersens::PrintNode(Node *N) {
+   if (N == &GraphNodes[UniversalSet]) {
+     std::cerr << "<universal>";
+     return;
+   } else if (N == &GraphNodes[NullPtr]) {
+     std::cerr << "<nullptr>";
+     return;
+   } else if (N == &GraphNodes[NullObject]) {
+     std::cerr << "<null>";
+     return;
+   }
+ 
+   assert(N->getValue() != 0 && "Never set node label!");
+   Value *V = N->getValue();
+   if (Function *F = dyn_cast<Function>(V)) {
+     if (isa<PointerType>(F->getFunctionType()->getReturnType()) &&
+         N == getReturnNode(F)) {
+       std::cerr << F->getName() << ":retval";
+       return;
+     } else if (F->getFunctionType()->isVarArg() && N == getVarargNode(F)) {
+       std::cerr << F->getName() << ":vararg";
+       return;
+     }
+   }
+ 
+   if (Instruction *I = dyn_cast<Instruction>(V))
+     std::cerr << I->getParent()->getParent()->getName() << ":";
+   else if (Argument *Arg = dyn_cast<Argument>(V))
+     std::cerr << Arg->getParent()->getName() << ":";
+ 
+   if (V->hasName())
+     std::cerr << V->getName();
+   else
+     std::cerr << "(unnamed)";
+ 
+   if (isa<GlobalValue>(V) || isa<AllocationInst>(V))
+     if (N == getObject(V))
+       std::cerr << "<mem>";
+ }
+ 
+ void Andersens::PrintConstraints() {
+   std::cerr << "Constraints:\n";
+   for (unsigned i = 0, e = Constraints.size(); i != e; ++i) {
+     std::cerr << "  #" << i << ":  ";
+     Constraint &C = Constraints[i];
+     if (C.Type == Constraint::Store)
+       std::cerr << "*";
+     PrintNode(C.Dest);
+     std::cerr << " = ";
+     if (C.Type == Constraint::Load)
+       std::cerr << "*";
+     PrintNode(C.Src);
+     std::cerr << "\n";
+   }
+ }
+ 
+ void Andersens::PrintPointsToGraph() {
+   std::cerr << "Points-to graph:\n";
+   for (unsigned i = 0, e = GraphNodes.size(); i != e; ++i) {
+     Node *N = &GraphNodes[i];
+     std::cerr << "[" << (N->end() - N->begin()) << "] ";
+     PrintNode(N);
+     std::cerr << "\t--> ";
+     for (Node::iterator I = N->begin(), E = N->end(); I != E; ++I) {
+       if (I != N->begin()) std::cerr << ", ";
+       PrintNode(*I);
+     }
+     std::cerr << "\n";
+   }
+ }





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