Rewrite of andersen's to be about 100x faster, cleaner, and begin to support field sensitivity

git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@42016 91177308-0d34-0410-b5e6-96231b3b80d8

1 files changed, 687 insertions, 324 deletions

diff --git a/lib/Analysis/IPA/Andersens.cpp b/lib/Analysis/IPA/Andersens.cpp
index 4c0d2468e7..fed246091d 100644
--- a/lib/Analysis/IPA/Andersens.cpp
+++ b/lib/Analysis/IPA/Andersens.cpp
@@ -7,14 +7,11 @@
 //
 //===----------------------------------------------------------------------===//
 //
-// 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.
+// This file defines an implementation of Andersen's interprocedural alias
+// analysis
 //
 // In pointer analysis terms, this is a subset-based, flow-insensitive,
-// field-insensitive, and context-insensitive algorithm pointer algorithm.
+// field-sensitive, and context-insensitive algorithm pointer algorithm.
 //
 // This algorithm is implemented as three stages:
 //   1. Object identification.
@@ -29,24 +26,23 @@
 // 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.
+// B can point to.  Constraints can handle copies, loads, and stores, and
+// address taking.
 //
 // 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.
+// Function constraints are handled as if they were structs with X fields.
+// Thus, an access to argument X of function Y is an access to node index
+// getNode(Y) + X.  This representation allows handling of indirect calls
+// without any issues.  To wit, an indirect call Y(a,b) is equivalence to
+// *(Y + 1) = a, *(Y + 2) = b.
+// The return node for a function is always located at getNode(F) +
+// CallReturnPos. The arguments start at getNode(F) + CallArgPos.
 //
 // Future Improvements:
-//   This implementation of Andersen's algorithm is extremely slow.  To make it
-//   scale reasonably well, the inclusion constraints could be sorted (easy),
-//   offline variable substitution would be a huge win (straight-forward), and
-//   online cycle elimination (trickier) might help as well.
-//
+//   Offline variable substitution, offline detection of online
+//   cycles.  Use of BDD's.
 //===----------------------------------------------------------------------===//
 
 #define DEBUG_TYPE "anders-aa"
@@ -62,31 +58,77 @@
 #include "llvm/Analysis/Passes.h"
 #include "llvm/Support/Debug.h"
 #include "llvm/ADT/Statistic.h"
+#include "llvm/ADT/SparseBitVector.h"
 #include <algorithm>
 #include <set>
-using namespace llvm;
+#include <list>
+#include <stack>
+#include <vector>
 
+using namespace llvm;
 STATISTIC(NumIters            , "Number of iterations to reach convergence");
 STATISTIC(NumConstraints      , "Number of constraints");
 STATISTIC(NumNodes            , "Number of nodes");
-STATISTIC(NumEscapingFunctions, "Number of internal functions that escape");
-STATISTIC(NumIndirectCallees  , "Number of indirect callees found");
+STATISTIC(NumUnified          , "Number of variables unified");
 
 namespace {
+  const unsigned SelfRep = (unsigned)-1;
+  const unsigned Unvisited = (unsigned)-1;
+  // Position of the function return node relative to the function node.
+  const unsigned CallReturnPos = 2;
+  // Position of the function call node relative to the function node.
+  const unsigned CallFirstArgPos = 3;
+
   class VISIBILITY_HIDDEN Andersens : public ModulePass, public AliasAnalysis,
                                       private InstVisitor<Andersens> {
-  public:
-    static char ID; // Class identification, replacement for typeinfo
-    Andersens() : ModulePass((intptr_t)&ID) {}
-  private:
-    /// 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:
-      static const unsigned ID; // Pass identification, replacement for typeid
-      Node() : Val(0) {}
+    class Node;
+
+    /// 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",
+    /// 'store' for statements like "*A = B", and AddressOf for statements like
+    /// A = alloca;  The Offset is applied as *(A + K) = B for stores,
+    /// A = *(B + K) for loads, and A = B + K for copies.  It is
+    /// illegal on addressof constraints (Because it is statically
+    /// resolvable to A = &C where C = B + K)
+
+    struct Constraint {
+      enum ConstraintType { Copy, Load, Store, AddressOf } Type;
+      unsigned Dest;
+      unsigned Src;
+      unsigned Offset;
+
+      Constraint(ConstraintType Ty, unsigned D, unsigned S, unsigned O = 0)
+        : Type(Ty), Dest(D), Src(S), Offset(O) {
+        assert(Offset == 0 || Ty != AddressOf &&
+               "Offset is illegal on addressof constraints");
+      }
+    };
+
+    // Node class - This class is used to represent a node
+    // in the constraint graph.  Due to various optimizations,
+    // not always the case that there is a mapping from a Node to a
+    // Value.  In particular, we add artificial
+    // Node's that represent the set of pointed-to variables
+    // shared for each location equivalent Node.
+    struct Node {
+       Value *Val;
+      SparseBitVector<> *Edges;
+      SparseBitVector<> *PointsTo;
+      SparseBitVector<> *OldPointsTo;
+      bool Changed;
+      std::list<Constraint> Constraints;
+
+      // Nodes in cycles (or in equivalence classes) are united
+      // together using a standard union-find representation with path
+      // compression.  NodeRep gives the index into GraphNodes
+      // representative for this one.
+      unsigned NodeRep;    public:
+
+      Node() : Val(0), Edges(0), PointsTo(0), OldPointsTo(0), Changed(false),
+               NodeRep(SelfRep) {
+      }
+
       Node *setValue(Value *V) {
         assert(Val == 0 && "Value already set for this node!");
         Val = V;
@@ -97,21 +139,11 @@ namespace {
       ///
       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;
+      bool addPointerTo(unsigned Node) {
+        return PointsTo->test_and_set(Node);
       }
 
       /// intersects - Return true if the points-to set of this node intersects
@@ -121,12 +153,7 @@ namespace {
       /// 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);
+      bool intersectsIgnoring(Node *N, unsigned) const;
     };
 
     /// GraphNodes - This vector is populated as part of the object
@@ -152,41 +179,14 @@ namespace {
     /// 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;
+    // Map from graph node to maximum K value that is allowed (For functions,
+    // this is equivalent to the number of arguments + CallFirstArgPos)
+    std::map<unsigned, unsigned> MaxK;
 
     /// This enum defines the GraphNodes indices that correspond to important
     /// fixed sets.
@@ -195,8 +195,24 @@ namespace {
       NullPtr      = 1,
       NullObject   = 2
     };
+    // Stack for Tarjans
+    std::stack<unsigned> SCCStack;
+    // Topological Index -> Graph node
+    std::vector<unsigned> Topo2Node;
+    // Graph Node -> Topological Index;
+    std::vector<unsigned> Node2Topo;
+    // Map from Graph Node to DFS number
+    std::vector<unsigned> Node2DFS;
+    // Map from Graph Node to Deleted from graph.
+    std::vector<bool> Node2Deleted;
+    // Current DFS and RPO numbers
+    unsigned DFSNumber;
+    unsigned RPONumber;
 
   public:
+    static char ID;
+    Andersens() : ModulePass((intptr_t)&ID) {}
+
     bool runOnModule(Module &M) {
       InitializeAliasAnalysis(this);
       IdentifyObjects(M);
@@ -210,7 +226,6 @@ namespace {
       ObjectNodes.clear();
       ReturnNodes.clear();
       VarargNodes.clear();
-      EscapingInternalFunctions.clear();
       std::vector<Constraint>().swap(Constraints);
       return false;
     }
@@ -255,7 +270,7 @@ namespace {
   private:
     /// getNode - Return the node corresponding to the specified pointer scalar.
     ///
-    Node *getNode(Value *V) {
+    unsigned getNode(Value *V) {
       if (Constant *C = dyn_cast<Constant>(V))
         if (!isa<GlobalValue>(C))
           return getNodeForConstantPointer(C);
@@ -267,47 +282,55 @@ namespace {
 #endif
         assert(0 && "Value does not have a node in the points-to graph!");
       }
-      return &GraphNodes[I->second];
+      return I->second;
     }
 
     /// getObject - Return the node corresponding to the memory object for the
     /// specified global or allocation instruction.
-    Node *getObject(Value *V) {
+    unsigned 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];
+      return I->second;
     }
 
     /// getReturnNode - Return the node representing the return value for the
     /// specified function.
-    Node *getReturnNode(Function *F) {
+    unsigned 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];
+      return I->second;
     }
 
     /// getVarargNode - Return the node representing the variable arguments
     /// formal for the specified function.
-    Node *getVarargNode(Function *F) {
+    unsigned 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];
+      return 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);
+    unsigned getNodeValue(Value &V) {
+      unsigned Index = getNode(&V);
+      GraphNodes[Index].setValue(&V);
+      return Index;
     }
 
+    unsigned UniteNodes(unsigned First, unsigned Second);
+    unsigned FindNode(unsigned Node);
+
     void IdentifyObjects(Module &M);
     void CollectConstraints(Module &M);
+    bool AnalyzeUsesOfFunction(Value *);
+    void CreateConstraintGraph();
     void SolveConstraints();
+    void QueryNode(unsigned Node);
 
-    Node *getNodeForConstantPointer(Constant *C);
-    Node *getNodeForConstantPointerTarget(Constant *C);
-    void AddGlobalInitializerConstraints(Node *N, Constant *C);
+    unsigned getNodeForConstantPointer(Constant *C);
+    unsigned getNodeForConstantPointerTarget(Constant *C);
+    void AddGlobalInitializerConstraints(unsigned, Constant *C);
 
     void AddConstraintsForNonInternalLinkage(Function *F);
     void AddConstraintsForCall(CallSite CS, Function *F);
@@ -337,6 +360,7 @@ namespace {
     void visitSelectInst(SelectInst &SI);
     void visitVAArg(VAArgInst &I);
     void visitInstruction(Instruction &I);
+
   };
 
   char Andersens::ID = 0;
@@ -353,12 +377,12 @@ ModulePass *llvm::createAndersensPass() { return new Andersens(); }
 
 AliasAnalysis::AliasResult Andersens::alias(const Value *V1, unsigned V1Size,
                                             const Value *V2, unsigned V2Size) {
-  Node *N1 = getNode(const_cast<Value*>(V1));
-  Node *N2 = getNode(const_cast<Value*>(V2));
+  Node *N1 = &GraphNodes[FindNode(getNode(const_cast<Value*>(V1)))];
+  Node *N2 = &GraphNodes[FindNode(getNode(const_cast<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]))
+  if (!N1->intersectsIgnoring(N2, NullObject))
     return NoAlias;
 
   return AliasAnalysis::alias(V1, V1Size, V2, V2Size);
@@ -376,14 +400,12 @@ Andersens::getModRefInfo(CallSite CS, Value *P, unsigned Size) {
   // is, after all, a "research quality" implementation of Andersen's analysis.
   if (Function *F = CS.getCalledFunction())
     if (F->isDeclaration()) {
-      Node *N1 = getNode(P);
+      Node *N1 = &GraphNodes[FindNode(getNode(P))];
 
-      if (N1->begin() == N1->end())
-        return NoModRef;  // P doesn't point to anything.
+      if (N1->PointsTo->empty())
+        return NoModRef;
 
-      // Get the first pointee.
-      Node *FirstPointee = *N1->begin();
-      if (FirstPointee != &GraphNodes[UniversalSet])
+      if (!N1->PointsTo->test(UniversalSet))
         return NoModRef;  // P doesn't point to the universal set.
     }
 
@@ -401,30 +423,23 @@ Andersens::getModRefInfo(CallSite CS1, CallSite CS2) {
 /// 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()));
-      }
+  Node *N = &GraphNodes[FindNode(getNode(P))];
+  if (N->PointsTo->count() == 1) {
+    Node *Pointee = &GraphNodes[N->PointsTo->find_first()];
+    // 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);
 }
 
@@ -434,14 +449,20 @@ void Andersens::getMustAliases(Value *P, std::vector<Value*> &RetVals) {
 /// 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()) {
+  Node *N = &GraphNodes[FindNode(getNode((Value*)P))];
+  unsigned i;
+
+  for (SparseBitVector<>::iterator bi = N->PointsTo->begin();
+       bi != N->PointsTo->end();
+       ++bi) {
+    i = *bi;
+    Node *Pointee = &GraphNodes[i];
+    if (Value *V = Pointee->getValue()) {
       if (!isa<GlobalValue>(V) || (isa<GlobalVariable>(V) &&
                                    !cast<GlobalVariable>(V)->isConstant()))
         return AliasAnalysis::pointsToConstantMemory(P);
     } else {
-      if (*I != &GraphNodes[NullObject])
+      if (i != NullObject)
         return AliasAnalysis::pointsToConstantMemory(P);
     }
   }
@@ -483,6 +504,7 @@ void Andersens::IdentifyObjects(Module &M) {
   // 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.
+    unsigned First = NumObjects;
     ValueNodes[F] = NumObjects++;
     ObjectNodes[F] = NumObjects++;
     if (isa<PointerType>(F->getFunctionType()->getReturnType()))
@@ -490,11 +512,14 @@ void Andersens::IdentifyObjects(Module &M) {
     if (F->getFunctionType()->isVarArg())
       VarargNodes[F] = NumObjects++;
 
+
     // Add nodes for all of the incoming pointer arguments.
     for (Function::arg_iterator I = F->arg_begin(), E = F->arg_end();
          I != E; ++I)
       if (isa<PointerType>(I->getType()))
         ValueNodes[I] = NumObjects++;
+    MaxK[First] = NumObjects - First;
+    MaxK[First + 1] = NumObjects - First - 1;
 
     // 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
@@ -521,11 +546,11 @@ void Andersens::IdentifyObjects(Module &M) {
 
 /// getNodeForConstantPointer - Return the node corresponding to the constant
 /// pointer itself.
-Andersens::Node *Andersens::getNodeForConstantPointer(Constant *C) {
+unsigned Andersens::getNodeForConstantPointer(Constant *C) {
   assert(isa<PointerType>(C->getType()) && "Not a constant pointer!");
 
   if (isa<ConstantPointerNull>(C) || isa<UndefValue>(C))
-    return &GraphNodes[NullPtr];
+    return NullPtr;
   else if (GlobalValue *GV = dyn_cast<GlobalValue>(C))
     return getNode(GV);
   else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) {
@@ -533,7 +558,7 @@ Andersens::Node *Andersens::getNodeForConstantPointer(Constant *C) {
     case Instruction::GetElementPtr:
       return getNodeForConstantPointer(CE->getOperand(0));
     case Instruction::IntToPtr:
-      return &GraphNodes[UniversalSet];
+      return UniversalSet;
     case Instruction::BitCast:
       return getNodeForConstantPointer(CE->getOperand(0));
     default:
@@ -548,11 +573,11 @@ Andersens::Node *Andersens::getNodeForConstantPointer(Constant *C) {
 
 /// getNodeForConstantPointerTarget - Return the node POINTED TO by the
 /// specified constant pointer.
-Andersens::Node *Andersens::getNodeForConstantPointerTarget(Constant *C) {
+unsigned Andersens::getNodeForConstantPointerTarget(Constant *C) {
   assert(isa<PointerType>(C->getType()) && "Not a constant pointer!");
 
   if (isa<ConstantPointerNull>(C))
-    return &GraphNodes[NullObject];
+    return NullObject;
   else if (GlobalValue *GV = dyn_cast<GlobalValue>(C))
     return getObject(GV);
   else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) {
@@ -560,7 +585,7 @@ Andersens::Node *Andersens::getNodeForConstantPointerTarget(Constant *C) {
     case Instruction::GetElementPtr:
       return getNodeForConstantPointerTarget(CE->getOperand(0));
     case Instruction::IntToPtr:
-      return &GraphNodes[UniversalSet];
+      return UniversalSet;
     case Instruction::BitCast:
       return getNodeForConstantPointerTarget(CE->getOperand(0));
     default:
@@ -575,19 +600,22 @@ Andersens::Node *Andersens::getNodeForConstantPointerTarget(Constant *C) {
 
 /// AddGlobalInitializerConstraints - Add inclusion constraints for the memory
 /// object N, which contains values indicated by C.
-void Andersens::AddGlobalInitializerConstraints(Node *N, Constant *C) {
+void Andersens::AddGlobalInitializerConstraints(unsigned NodeIndex,
+                                                Constant *C) {
   if (C->getType()->isFirstClassType()) {
     if (isa<PointerType>(C->getType()))
-      N->copyFrom(getNodeForConstantPointer(C));
-
+      Constraints.push_back(Constraint(Constraint::Copy, NodeIndex,
+                                       getNodeForConstantPointer(C)));
   } else if (C->isNullValue()) {
-    N->addPointerTo(&GraphNodes[NullObject]);
+    Constraints.push_back(Constraint(Constraint::Copy, NodeIndex,
+                                     NullObject));
     return;
   } else if (!isa<UndefValue>(C)) {
     // 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)));
+      AddGlobalInitializerConstraints(NodeIndex,
+                                      cast<Constant>(C->getOperand(i)));
   }
 }
 
@@ -600,7 +628,7 @@ void Andersens::AddConstraintsForNonInternalLinkage(Function *F) {
       // 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]));
+                                       UniversalSet));
 }
 
 /// AddConstraintsForCall - If this is a call to a "known" function, add the
@@ -653,14 +681,20 @@ bool Andersens::AddConstraintsForExternalCall(CallSite CS, Function *F) {
 
 
   // These functions do induce points-to edges.
-  if (F->getName() == "llvm.memcpy.i32" || F->getName() == "llvm.memcpy.i64" || 
+  if (F->getName() == "llvm.memcpy.i32" || F->getName() == "llvm.memcpy.i64" ||
       F->getName() == "llvm.memmove.i32" ||F->getName() == "llvm.memmove.i64" ||
       F->getName() == "memmove") {
-    // Note: this is a poor approximation, this says Dest = Src, instead of
-    // *Dest = *Src.
-    Constraints.push_back(Constraint(Constraint::Copy,
-                                     getNode(CS.getArgument(0)),
-                                     getNode(CS.getArgument(1))));
+
+    // *Dest = *Src, which requires an artificial graph node to represent the
+    // constraint.  It is broken up into *Dest = temp, temp = *Src
+    unsigned FirstArg = getNode(CS.getArgument(0));
+    unsigned SecondArg = getNode(CS.getArgument(1));
+    unsigned TempArg = GraphNodes.size();
+    GraphNodes.push_back(Node());
+    Constraints.push_back(Constraint(Constraint::Store,
+                                     FirstArg, TempArg));
+    Constraints.push_back(Constraint(Constraint::Load,
+                                     TempArg, SecondArg));
     return true;
   }
 
@@ -679,49 +713,99 @@ bool Andersens::AddConstraintsForExternalCall(CallSite CS, Function *F) {
 
 
 
+/// AnalyzeUsesOfFunction - Look at all of the users of the specified function.
+/// If this is used by anything complex (i.e., the address escapes), return
+/// true.
+bool Andersens::AnalyzeUsesOfFunction(Value *V) {
+
+  if (!isa<PointerType>(V->getType())) return true;
+
+  for (Value::use_iterator UI = V->use_begin(), E = V->use_end(); UI != E; ++UI)
+    if (dyn_cast<LoadInst>(*UI)) {
+      return false;
+    } else if (StoreInst *SI = dyn_cast<StoreInst>(*UI)) {
+      if (V == SI->getOperand(1)) {
+        return false;
+      } else if (SI->getOperand(1)) {
+        return true;  // Storing the pointer
+      }
+    } else if (GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(*UI)) {
+      if (AnalyzeUsesOfFunction(GEP)) return true;
+    } else if (CallInst *CI = dyn_cast<CallInst>(*UI)) {
+      // Make sure that this is just the function being called, not that it is
+      // passing into the function.
+      for (unsigned i = 1, e = CI->getNumOperands(); i != e; ++i)
+        if (CI->getOperand(i) == V) return true;
+    } else if (InvokeInst *II = dyn_cast<InvokeInst>(*UI)) {
+      // Make sure that this is just the function being called, not that it is
+      // passing into the function.
+      for (unsigned i = 3, e = II->getNumOperands(); i != e; ++i)
+        if (II->getOperand(i) == V) return true;
+    } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(*UI)) {
+      if (CE->getOpcode() == Instruction::GetElementPtr ||
+          CE->getOpcode() == Instruction::BitCast) {
+        if (AnalyzeUsesOfFunction(CE))
+          return true;
+      } else {
+        return true;
+      }
+    } else if (ICmpInst *ICI = dyn_cast<ICmpInst>(*UI)) {
+      if (!isa<ConstantPointerNull>(ICI->getOperand(1)))
+        return true;  // Allow comparison against null.
+    } else if (dyn_cast<FreeInst>(*UI)) {
+      return false;
+    } else {
+      return true;
+    }
+  return false;
+}
+
 /// 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]);
-  //Constraints.push_back(Constraint(Constraint::Load, &GraphNodes[UniversalSet],
-  //                                 &GraphNodes[UniversalSet]));
-  Constraints.push_back(Constraint(Constraint::Store, &GraphNodes[UniversalSet],
-                                   &GraphNodes[UniversalSet]));
+  Constraints.push_back(Constraint(Constraint::AddressOf, UniversalSet,
+                                   UniversalSet));
+  Constraints.push_back(Constraint(Constraint::Store, UniversalSet,
+                                   UniversalSet));
 
   // Next, the null pointer points to the null object.
-  GraphNodes[NullPtr].addPointerTo(&GraphNodes[NullObject]);
+  Constraints.push_back(Constraint(Constraint::AddressOf, NullPtr, NullObject));
 
   // Next, add any constraints on global variables and their initializers.
   for (Module::global_iterator I = M.global_begin(), E = M.global_end();
        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);
+    unsigned ObjectIndex = getObject(I);
+    Node *Object = &GraphNodes[ObjectIndex];
     Object->setValue(I);
-    getNodeValue(*I)->addPointerTo(Object);
+    Constraints.push_back(Constraint(Constraint::AddressOf, getNodeValue(*I),
+                                     ObjectIndex));
 
     if (I->hasInitializer()) {
-      AddGlobalInitializerConstraints(Object, I->getInitializer());
+      AddGlobalInitializerConstraints(ObjectIndex, 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]));
+      Constraints.push_back(Constraint(Constraint::Copy, ObjectIndex,
+                                       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));
-
+    unsigned ObjectIndex = getObject(F);
+    GraphNodes[ObjectIndex].setValue(F);
+    Constraints.push_back(Constraint(Constraint::AddressOf, getNodeValue(*F),
+                                     ObjectIndex));
     // Set up the return value node.
     if (isa<PointerType>(F->getFunctionType()->getReturnType()))
-      getReturnNode(F)->setValue(F);
+      GraphNodes[getReturnNode(F)].setValue(F);
     if (F->getFunctionType()->isVarArg())
-      getVarargNode(F)->setValue(F);
+      GraphNodes[getVarargNode(F)].setValue(F);
 
     // Set up incoming argument nodes.
     for (Function::arg_iterator I = F->arg_begin(), E = F->arg_end();
@@ -729,7 +813,10 @@ void Andersens::CollectConstraints(Module &M) {
       if (isa<PointerType>(I->getType()))
         getNodeValue(*I);
 
-    if (!F->hasInternalLinkage())
+    // At some point we should just add constraints for the escaping functions
+    // at solve time, but this slows down solving. For now, we simply mark
+    // address taken functions as escaping and treat them as external.
+    if (!F->hasInternalLinkage() || AnalyzeUsesOfFunction(F))
       AddConstraintsForNonInternalLinkage(F);
 
     if (!F->isDeclaration()) {
@@ -742,7 +829,7 @@ void Andersens::CollectConstraints(Module &M) {
       if (isa<PointerType>(F->getFunctionType()->getReturnType()))
         Constraints.push_back(Constraint(Constraint::Copy,
                                          getReturnNode(F),
-                                         &GraphNodes[UniversalSet]));
+                                         UniversalSet));
 
       // Any pointers that are passed into the function have the universal set
       // stored into them.
@@ -752,11 +839,11 @@ void Andersens::CollectConstraints(Module &M) {
           // Pointers passed into external functions could have anything stored
           // through them.
           Constraints.push_back(Constraint(Constraint::Store, getNode(I),
-                                           &GraphNodes[UniversalSet]));
+                                           UniversalSet));
           // Memory objects passed into external function calls can have the
           // universal set point to them.
           Constraints.push_back(Constraint(Constraint::Copy,
-                                           &GraphNodes[UniversalSet],
+                                           UniversalSet,
                                            getNode(I)));
         }
 
@@ -764,7 +851,7 @@ void Andersens::CollectConstraints(Module &M) {
       // into any pointers passed through the varargs section.
       if (F->getFunctionType()->isVarArg())
         Constraints.push_back(Constraint(Constraint::Store, getVarargNode(F),
-                                         &GraphNodes[UniversalSet]));
+                                         UniversalSet));
     }
   }
   NumConstraints += Constraints.size();
@@ -795,7 +882,10 @@ void Andersens::visitInstruction(Instruction &I) {
 }
 
 void Andersens::visitAllocationInst(AllocationInst &AI) {
-  getNodeValue(AI)->addPointerTo(getObject(&AI)->setValue(&AI));
+  unsigned ObjectIndex = getObject(&AI);
+  GraphNodes[ObjectIndex].setValue(&AI);
+  Constraints.push_back(Constraint(Constraint::AddressOf, getNodeValue(AI),
+                                   ObjectIndex));
 }
 
 void Andersens::visitReturnInst(ReturnInst &RI) {
@@ -829,7 +919,7 @@ void Andersens::visitGetElementPtrInst(GetElementPtrInst &GEP) {
 
 void Andersens::visitPHINode(PHINode &PN) {
   if (isa<PointerType>(PN.getType())) {
-    Node *PNN = getNodeValue(PN);
+    unsigned 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,
@@ -848,7 +938,7 @@ void Andersens::visitCastInst(CastInst &CI) {
       // P1 = cast int --> <Copy/P1/Univ>
 #if 0
       Constraints.push_back(Constraint(Constraint::Copy, getNodeValue(CI),
-                                       &GraphNodes[UniversalSet]));
+                                       UniversalSet));
 #else
       getNodeValue(CI);
 #endif
@@ -857,7 +947,7 @@ void Andersens::visitCastInst(CastInst &CI) {
     // int = cast P1 --> <Copy/Univ/P1>
 #if 0
     Constraints.push_back(Constraint(Constraint::Copy,
-                                     &GraphNodes[UniversalSet],
+                                     UniversalSet,
                                      getNode(CI.getOperand(0))));
 #else
     getNode(CI.getOperand(0));
@@ -867,7 +957,7 @@ void Andersens::visitCastInst(CastInst &CI) {
 
 void Andersens::visitSelectInst(SelectInst &SI) {
   if (isa<PointerType>(SI.getType())) {
-    Node *SIN = getNodeValue(SI);
+    unsigned 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))));
@@ -886,48 +976,72 @@ void Andersens::visitVAArg(VAArgInst &I) {
 /// the function pointer has been casted.  If this is the case, do something
 /// reasonable.
 void Andersens::AddConstraintsForCall(CallSite CS, Function *F) {
-  // If this is a call to an external function, handle it directly to get some
-  // taste of context sensitivity.
-  if (F->isDeclaration() && AddConstraintsForExternalCall(CS, F))
+  Value *CallValue = CS.getCalledValue();
+  bool IsDeref = F == NULL;
+
+  // If this is a call to an external function, try to handle it directly to get
+  // some taste of context sensitivity.
+  if (F && F->isDeclaration() && AddConstraintsForExternalCall(CS, F))
     return;
 
   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)));
+    unsigned CSN = getNode(CS.getInstruction());
+    if (!F || isa<PointerType>(F->getFunctionType()->getReturnType())) {
+      if (IsDeref)
+        Constraints.push_back(Constraint(Constraint::Load, CSN,
+                                         getNode(CallValue), CallReturnPos));
+      else
+        Constraints.push_back(Constraint(Constraint::Copy, CSN,
+                                         getNode(CallValue) + CallReturnPos));
     } 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]));
+                                       UniversalSet));
     }
-  } else if (isa<PointerType>(F->getFunctionType()->getReturnType())) {
+  } else if (F && isa<PointerType>(F->getFunctionType()->getReturnType())) {
     Constraints.push_back(Constraint(Constraint::Copy,
-                                     &GraphNodes[UniversalSet],
-                                     getReturnNode(F)));
+                                     UniversalSet,
+                                     getNode(CallValue) + CallReturnPos));
   }
 
-  Function::arg_iterator AI = F->arg_begin(), AE = F->arg_end();
   CallSite::arg_iterator ArgI = CS.arg_begin(), ArgE = CS.arg_end();
-  for (; AI != AE && ArgI != ArgE; ++AI, ++ArgI)
-    if (isa<PointerType>(AI->getType())) {
+  if (F) {
+    // Direct Call
+    Function::arg_iterator AI = F->arg_begin(), AE = F->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),
+                                           UniversalSet));
+        }
+      } else if (isa<PointerType>((*ArgI)->getType())) {
+        Constraints.push_back(Constraint(Constraint::Copy,
+                                         UniversalSet,
+                                         getNode(*ArgI)));
+      }
+  } else {
+    //Indirect Call
+    unsigned ArgPos = CallFirstArgPos;
+    for (; ArgI != ArgE; ++ArgI) {