text: //===- BasicAliasAnalysis.cpp - Stateless Alias Analysis Impl -------------===//
  //
  //                     The LLVM Compiler Infrastructure
  //
  // This file is distributed under the University of Illinois Open Source
  // License. See LICENSE.TXT for details.
  //
  //===----------------------------------------------------------------------===//
  //
  // This file defines the primary stateless implementation of the
  // Alias Analysis interface that implements identities (two different
  // globals cannot alias, etc), but does no stateful analysis.
  //
  //===----------------------------------------------------------------------===//
  
  #include "llvm/Analysis/AliasAnalysis.h"
  #include "llvm/Analysis/Passes.h"
  #include "llvm/Constants.h"
  #include "llvm/DerivedTypes.h"
  #include "llvm/Function.h"
  #include "llvm/GlobalAlias.h"
  #include "llvm/GlobalVariable.h"
  #include "llvm/Instructions.h"
  #include "llvm/IntrinsicInst.h"
  #include "llvm/LLVMContext.h"
  #include "llvm/Operator.h"
  #include "llvm/Pass.h"
  #include "llvm/Analysis/CaptureTracking.h"
  #include "llvm/Analysis/MemoryBuiltins.h"
  #include "llvm/Analysis/InstructionSimplify.h"
  #include "llvm/Analysis/ValueTracking.h"
  #include "llvm/Target/TargetData.h"
  #include "llvm/Target/TargetLibraryInfo.h"
  #include "llvm/ADT/SmallPtrSet.h"
  #include "llvm/ADT/SmallVector.h"
  #include "llvm/Support/ErrorHandling.h"
  #include "llvm/Support/GetElementPtrTypeIterator.h"
  #include <algorithm>
  using namespace llvm;
  
  //===----------------------------------------------------------------------===//
  // Useful predicates
  //===----------------------------------------------------------------------===//
  
  /// isNonEscapingLocalObject - Return true if the pointer is to a function-local
  /// object that never escapes from the function.
  static bool isNonEscapingLocalObject(const Value *V) {
    // If this is a local allocation, check to see if it escapes.
    if (isa<AllocaInst>(V) || isNoAliasCall(V))
      // Set StoreCaptures to True so that we can assume in our callers that the
      // pointer is not the result of a load instruction. Currently
      // PointerMayBeCaptured doesn't have any special analysis for the
      // StoreCaptures=false case; if it did, our callers could be refined to be
      // more precise.
      return !PointerMayBeCaptured(V, false, /*StoreCaptures=*/true);
  
    // If this is an argument that corresponds to a byval or noalias argument,
    // then it has not escaped before entering the function.  Check if it escapes
    // inside the function.
    if (const Argument *A = dyn_cast<Argument>(V))
      if (A->hasByValAttr() || A->hasNoAliasAttr()) {
        // Don't bother analyzing arguments already known not to escape.
        if (A->hasNoCaptureAttr())
          return true;
        return !PointerMayBeCaptured(V, false, /*StoreCaptures=*/true);
      }
    return false;
  }
  
  /// isEscapeSource - Return true if the pointer is one which would have
  /// been considered an escape by isNonEscapingLocalObject.
  static bool isEscapeSource(const Value *V) {
    if (isa<CallInst>(V) || isa<InvokeInst>(V) || isa<Argument>(V))
      return true;
  
    // The load case works because isNonEscapingLocalObject considers all
    // stores to be escapes (it passes true for the StoreCaptures argument
    // to PointerMayBeCaptured).
    if (isa<LoadInst>(V))
      return true;
  
    return false;
  }
  
  /// getObjectSize - Return the size of the object specified by V, or
  /// UnknownSize if unknown.
  static uint64_t getObjectSize(const Value *V, const TargetData &TD,
                                bool RoundToAlign = false) {
    Type *AccessTy;
    unsigned Align;
    if (const GlobalVariable *GV = dyn_cast<GlobalVariable>(V)) {
      if (!GV->hasDefinitiveInitializer())
        return AliasAnalysis::UnknownSize;
      AccessTy = GV->getType()->getElementType();
      Align = GV->getAlignment();
    } else if (const AllocaInst *AI = dyn_cast<AllocaInst>(V)) {
      if (!AI->isArrayAllocation())
        AccessTy = AI->getType()->getElementType();
      else
        return AliasAnalysis::UnknownSize;
      Align = AI->getAlignment();
    } else if (const CallInst* CI = extractMallocCall(V)) {
      if (!RoundToAlign && !isArrayMalloc(V, &TD))
        // The size is the argument to the malloc call.
        if (const ConstantInt* C = dyn_cast<ConstantInt>(CI->getArgOperand(0)))
          return C->getZExtValue();
      return AliasAnalysis::UnknownSize;
    } else if (const Argument *A = dyn_cast<Argument>(V)) {
      if (A->hasByValAttr()) {
        AccessTy = cast<PointerType>(A->getType())->getElementType();
        Align = A->getParamAlignment();
      } else {
        return AliasAnalysis::UnknownSize;
      }
    } else {
      return AliasAnalysis::UnknownSize;
    }
  
    if (!AccessTy->isSized())
      return AliasAnalysis::UnknownSize;
  
    uint64_t Size = TD.getTypeAllocSize(AccessTy);
    // If there is an explicitly specified alignment, and we need to
    // take alignment into account, round up the size. (If the alignment
    // is implicit, getTypeAllocSize is sufficient.)
    if (RoundToAlign && Align)
      Size = RoundUpToAlignment(Size, Align);
  
    return Size;
  }
  
  /// isObjectSmallerThan - Return true if we can prove that the object specified
  /// by V is smaller than Size.
  static bool isObjectSmallerThan(const Value *V, uint64_t Size,
                                  const TargetData &TD) {
    // This function needs to use the aligned object size because we allow
    // reads a bit past the end given sufficient alignment.
    uint64_t ObjectSize = getObjectSize(V, TD, /*RoundToAlign*/true);
    
    return ObjectSize != AliasAnalysis::UnknownSize && ObjectSize < Size;
  }
  
  /// isObjectSize - Return true if we can prove that the object specified
  /// by V has size Size.
  static bool isObjectSize(const Value *V, uint64_t Size,
                           const TargetData &TD) {
    uint64_t ObjectSize = getObjectSize(V, TD);
    return ObjectSize != AliasAnalysis::UnknownSize && ObjectSize == Size;
  }
  
  //===----------------------------------------------------------------------===//
  // GetElementPtr Instruction Decomposition and Analysis
  //===----------------------------------------------------------------------===//
  
  namespace {
    enum ExtensionKind {
      EK_NotExtended,
      EK_SignExt,
      EK_ZeroExt
    };
    
    struct VariableGEPIndex {
      const Value *V;
      ExtensionKind Extension;
      int64_t Scale;
    };
  }
  
  
  /// GetLinearExpression - Analyze the specified value as a linear expression:
  /// "A*V + B", where A and B are constant integers.  Return the scale and offset
  /// values as APInts and return V as a Value*, and return whether we looked
  /// through any sign or zero extends.  The incoming Value is known to have
  /// IntegerType and it may already be sign or zero extended.
  ///
  /// Note that this looks through extends, so the high bits may not be
  /// represented in the result.
  static Value *GetLinearExpression(Value *V, APInt &Scale, APInt &Offset,
                                    ExtensionKind &Extension,
                                    const TargetData &TD, unsigned Depth) {
    assert(V->getType()->isIntegerTy() && "Not an integer value");
  
    // Limit our recursion depth.
    if (Depth == 6) {
      Scale = 1;
      Offset = 0;
      return V;
    }
    
    if (BinaryOperator *BOp = dyn_cast<BinaryOperator>(V)) {
      if (ConstantInt *RHSC = dyn_cast<ConstantInt>(BOp->getOperand(1))) {
        switch (BOp->getOpcode()) {
        default: break;
        case Instruction::Or:
          // X|C == X+C if all the bits in C are unset in X.  Otherwise we can't
          // analyze it.
          if (!MaskedValueIsZero(BOp->getOperand(0), RHSC->getValue(), &TD))
            break;
          // FALL THROUGH.
        case Instruction::Add:
          V = GetLinearExpression(BOp->getOperand(0), Scale, Offset, Extension,
                                  TD, Depth+1);
          Offset += RHSC->getValue();
          return V;
        case Instruction::Mul:
          V = GetLinearExpression(BOp->getOperand(0), Scale, Offset, Extension,
                                  TD, Depth+1);
          Offset *= RHSC->getValue();
          Scale *= RHSC->getValue();
          return V;
        case Instruction::Shl:
          V = GetLinearExpression(BOp->getOperand(0), Scale, Offset, Extension,
                                  TD, Depth+1);
          Offset <<= RHSC->getValue().getLimitedValue();
          Scale <<= RHSC->getValue().getLimitedValue();
          return V;
        }
      }
    }
    
    // Since GEP indices are sign extended anyway, we don't care about the high
    // bits of a sign or zero extended value - just scales and offsets.  The
    // extensions have to be consistent though.
    if ((isa<SExtInst>(V) && Extension != EK_ZeroExt) ||
        (isa<ZExtInst>(V) && Extension != EK_SignExt)) {
      Value *CastOp = cast<CastInst>(V)->getOperand(0);
      unsigned OldWidth = Scale.getBitWidth();
      unsigned SmallWidth = CastOp->getType()->getPrimitiveSizeInBits();
      Scale = Scale.trunc(SmallWidth);
      Offset = Offset.trunc(SmallWidth);
      Extension = isa<SExtInst>(V) ? EK_SignExt : EK_ZeroExt;
  
      Value *Result = GetLinearExpression(CastOp, Scale, Offset, Extension,
                                          TD, Depth+1);
      Scale = Scale.zext(OldWidth);
      Offset = Offset.zext(OldWidth);
      
      return Result;
    }
    
    Scale = 1;
    Offset = 0;
    return V;
  }
  
  /// DecomposeGEPExpression - If V is a symbolic pointer expression, decompose it
  /// into a base pointer with a constant offset and a number of scaled symbolic
  /// offsets.
  ///
  /// The scaled symbolic offsets (represented by pairs of a Value* and a scale in
  /// the VarIndices vector) are Value*'s that are known to be scaled by the
  /// specified amount, but which may have other unrepresented high bits. As such,
  /// the gep cannot necessarily be reconstructed from its decomposed form.
  ///
  /// When TargetData is around, this function is capable of analyzing everything
  /// that GetUnderlyingObject can look through.  When not, it just looks
  /// through pointer casts.
  ///
  static const Value *
  DecomposeGEPExpression(const Value *V, int64_t &BaseOffs,
                         SmallVectorImpl<VariableGEPIndex> &VarIndices,
                         const TargetData *TD) {
    // Limit recursion depth to limit compile time in crazy cases.
    unsigned MaxLookup = 6;
    
    BaseOffs = 0;
    do {
      // See if this is a bitcast or GEP.
      const Operator *Op = dyn_cast<Operator>(V);
      if (Op == 0) {
        // The only non-operator case we can handle are GlobalAliases.
        if (const GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) {
          if (!GA->mayBeOverridden()) {
            V = GA->getAliasee();
            continue;
          }
        }
        return V;
      }
      
      if (Op->getOpcode() == Instruction::BitCast) {
        V = Op->getOperand(0);
        continue;
      }
  
      const GEPOperator *GEPOp = dyn_cast<GEPOperator>(Op);
      if (GEPOp == 0) {
        // If it's not a GEP, hand it off to SimplifyInstruction to see if it
        // can come up with something. This matches what GetUnderlyingObject does.
        if (const Instruction *I = dyn_cast<Instruction>(V))
          // TODO: Get a DominatorTree and use it here.
          if (const Value *Simplified =
                SimplifyInstruction(const_cast<Instruction *>(I), TD)) {
            V = Simplified;
            continue;
          }
      
        return V;
      }
      
      // Don't attempt to analyze GEPs over unsized objects.
      if (!cast<PointerType>(GEPOp->getOperand(0)->getType())
          ->getElementType()->isSized())
        return V;
      
      // If we are lacking TargetData information, we can't compute the offets of
      // elements computed by GEPs.  However, we can handle bitcast equivalent
      // GEPs.
      if (TD == 0) {
        if (!GEPOp->hasAllZeroIndices())
          return V;
        V = GEPOp->getOperand(0);
        continue;
      }
      
      // Walk the indices of the GEP, accumulating them into BaseOff/VarIndices.
      gep_type_iterator GTI = gep_type_begin(GEPOp);
      for (User::const_op_iterator I = GEPOp->op_begin()+1,
           E = GEPOp->op_end(); I != E; ++I) {
        Value *Index = *I;
        // Compute the (potentially symbolic) offset in bytes for this index.
        if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
          // For a struct, add the member offset.
          unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
          if (FieldNo == 0) continue;
          
          BaseOffs += TD->getStructLayout(STy)->getElementOffset(FieldNo);
          continue;
        }
        
        // For an array/pointer, add the element offset, explicitly scaled.
        if (ConstantInt *CIdx = dyn_cast<ConstantInt>(Index)) {
          if (CIdx->isZero()) continue;
          BaseOffs += TD->getTypeAllocSize(*GTI)*CIdx->getSExtValue();
          continue;
        }
        
        uint64_t Scale = TD->getTypeAllocSize(*GTI);
        ExtensionKind Extension = EK_NotExtended;
        
        // If the integer type is smaller than the pointer size, it is implicitly
        // sign extended to pointer size.
        unsigned Width = cast<IntegerType>(Index->getType())->getBitWidth();
        if (TD->getPointerSizeInBits() > Width)
          Extension = EK_SignExt;
        
        // Use GetLinearExpression to decompose the index into a C1*V+C2 form.
        APInt IndexScale(Width, 0), IndexOffset(Width, 0);
        Index = GetLinearExpression(Index, IndexScale, IndexOffset, Extension,
                                    *TD, 0);
        
        // The GEP index scale ("Scale") scales C1*V+C2, yielding (C1*V+C2)*Scale.
        // This gives us an aggregate computation of (C1*Scale)*V + C2*Scale.
        BaseOffs += IndexOffset.getSExtValue()*Scale;
        Scale *= IndexScale.getSExtValue();
        
        
        // If we already had an occurrence of this index variable, merge this
        // scale into it.  For example, we want to handle:
        //   A[x][x] -> x*16 + x*4 -> x*20
        // This also ensures that 'x' only appears in the index list once.
        for (unsigned i = 0, e = VarIndices.size(); i != e; ++i) {
          if (VarIndices[i].V == Index &&
              VarIndices[i].Extension == Extension) {
            Scale += VarIndices[i].Scale;
            VarIndices.erase(VarIndices.begin()+i);
            break;
          }
        }
        
        // Make sure that we have a scale that makes sense for this target's
        // pointer size.
        if (unsigned ShiftBits = 64-TD->getPointerSizeInBits()) {
          Scale <<= ShiftBits;
          Scale = (int64_t)Scale >> ShiftBits;
        }
        
        if (Scale) {
          VariableGEPIndex Entry = {Index, Extension,
                                    static_cast<int64_t>(Scale)};
          VarIndices.push_back(Entry);
        }
      }
      
      // Analyze the base pointer next.
      V = GEPOp->getOperand(0);
    } while (--MaxLookup);
    
    // If the chain of expressions is too deep, just return early.
    return V;
  }
  
  /// GetIndexDifference - Dest and Src are the variable indices from two
  /// decomposed GetElementPtr instructions GEP1 and GEP2 which have common base
  /// pointers.  Subtract the GEP2 indices from GEP1 to find the symbolic
  /// difference between the two pointers. 
  static void GetIndexDifference(SmallVectorImpl<VariableGEPIndex> &Dest,
                                 const SmallVectorImpl<VariableGEPIndex> &Src) {
    if (Src.empty()) return;
  
    for (unsigned i = 0, e = Src.size(); i != e; ++i) {
      const Value *V = Src[i].V;
      ExtensionKind Extension = Src[i].Extension;
      int64_t Scale = Src[i].Scale;
      
      // Find V in Dest.  This is N^2, but pointer indices almost never have more
      // than a few variable indexes.
      for (unsigned j = 0, e = Dest.size(); j != e; ++j) {
        if (Dest[j].V != V || Dest[j].Extension != Extension) continue;
        
        // If we found it, subtract off Scale V's from the entry in Dest.  If it
        // goes to zero, remove the entry.
        if (Dest[j].Scale != Scale)
          Dest[j].Scale -= Scale;
        else
          Dest.erase(Dest.begin()+j);
        Scale = 0;
        break;
      }
      
      // If we didn't consume this entry, add it to the end of the Dest list.
      if (Scale) {
        VariableGEPIndex Entry = { V, Extension, -Scale };
        Dest.push_back(Entry);
      }
    }
  }
  
  //===----------------------------------------------------------------------===//
  // BasicAliasAnalysis Pass
  //===----------------------------------------------------------------------===//
  
  #ifndef NDEBUG
  static const Function *getParent(const Value *V) {
    if (const Instruction *inst = dyn_cast<Instruction>(V))
      return inst->getParent()->getParent();
  
    if (const Argument *arg = dyn_cast<Argument>(V))
      return arg->getParent();
  
    return NULL;
  }
  
  static bool notDifferentParent(const Value *O1, const Value *O2) {
  
    const Function *F1 = getParent(O1);
    const Function *F2 = getParent(O2);
  
    return !F1 || !F2 || F1 == F2;
  }
  #endif
  
  namespace {
    /// BasicAliasAnalysis - This is the primary alias analysis implementation.
    struct BasicAliasAnalysis : public ImmutablePass, public AliasAnalysis {
      static char ID; // Class identification, replacement for typeinfo
      BasicAliasAnalysis() : ImmutablePass(ID),
                             // AliasCache rarely has more than 1 or 2 elements,
                             // so start it off fairly small so that clear()
                             // doesn't have to tromp through 64 (the default)
                             // elements on each alias query. This really wants
                             // something like a SmallDenseMap.
                             AliasCache(8) {
        initializeBasicAliasAnalysisPass(*PassRegistry::getPassRegistry());
      }
  
      virtual void initializePass() {
        InitializeAliasAnalysis(this);
      }
  
      virtual void getAnalysisUsage(AnalysisUsage &AU) const {
        AU.addRequired<AliasAnalysis>();
        AU.addRequired<TargetLibraryInfo>();
      }
  
      virtual AliasResult alias(const Location &LocA,
                                const Location &LocB) {
        assert(AliasCache.empty() && "AliasCache must be cleared after use!");
        assert(notDifferentParent(LocA.Ptr, LocB.Ptr) &&
               "BasicAliasAnalysis doesn't support interprocedural queries.");
        AliasResult Alias = aliasCheck(LocA.Ptr, LocA.Size, LocA.TBAATag,
                                       LocB.Ptr, LocB.Size, LocB.TBAATag);
        AliasCache.clear();
        return Alias;
      }
  
      virtual ModRefResult getModRefInfo(ImmutableCallSite CS,
                                         const Location &Loc);
  
      virtual ModRefResult getModRefInfo(ImmutableCallSite CS1,
                                         ImmutableCallSite CS2) {
        // The AliasAnalysis base class has some smarts, lets use them.
        return AliasAnalysis::getModRefInfo(CS1, CS2);
      }
  
      /// pointsToConstantMemory - Chase pointers until we find a (constant
      /// global) or not.
      virtual bool pointsToConstantMemory(const Location &Loc, bool OrLocal);
  
      /// getModRefBehavior - Return the behavior when calling the given
      /// call site.
      virtual ModRefBehavior getModRefBehavior(ImmutableCallSite CS);
  
      /// getModRefBehavior - Return the behavior when calling the given function.
      /// For use when the call site is not known.
      virtual ModRefBehavior getModRefBehavior(const Function *F);
  
      /// getAdjustedAnalysisPointer - This method is used when a pass implements
      /// an analysis interface through multiple inheritance.  If needed, it
      /// should override this to adjust the this pointer as needed for the
      /// specified pass info.
      virtual void *getAdjustedAnalysisPointer(const void *ID) {
        if (ID == &AliasAnalysis::ID)
          return (AliasAnalysis*)this;
        return this;
      }
      
    private:
      // AliasCache - Track alias queries to guard against recursion.
      typedef std::pair<Location, Location> LocPair;
      typedef DenseMap<LocPair, AliasResult> AliasCacheTy;
      AliasCacheTy AliasCache;
  
      // Visited - Track instructions visited by pointsToConstantMemory.
      SmallPtrSet<const Value*, 16> Visited;
  
      // aliasGEP - Provide a bunch of ad-hoc rules to disambiguate a GEP
      // instruction against another.
      AliasResult aliasGEP(const GEPOperator *V1, uint64_t V1Size,
                           const Value *V2, uint64_t V2Size,
                           const MDNode *V2TBAAInfo,
                           const Value *UnderlyingV1, const Value *UnderlyingV2);
  
      // aliasPHI - Provide a bunch of ad-hoc rules to disambiguate a PHI
      // instruction against another.
      AliasResult aliasPHI(const PHINode *PN, uint64_t PNSize,
                           const MDNode *PNTBAAInfo,
                           const Value *V2, uint64_t V2Size,
                           const MDNode *V2TBAAInfo);
  
      /// aliasSelect - Disambiguate a Select instruction against another value.
      AliasResult aliasSelect(const SelectInst *SI, uint64_t SISize,
                              const MDNode *SITBAAInfo,
                              const Value *V2, uint64_t V2Size,
                              const MDNode *V2TBAAInfo);
  
      AliasResult aliasCheck(const Value *V1, uint64_t V1Size,
                             const MDNode *V1TBAATag,
                             const Value *V2, uint64_t V2Size,
                             const MDNode *V2TBAATag);
    };
  }  // End of anonymous namespace
  
  // Register this pass...
  char BasicAliasAnalysis::ID = 0;
  INITIALIZE_AG_PASS_BEGIN(BasicAliasAnalysis, AliasAnalysis, "basicaa",
                     "Basic Alias Analysis (stateless AA impl)",
                     false, true, false)
  INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfo)
  INITIALIZE_AG_PASS_END(BasicAliasAnalysis, AliasAnalysis, "basicaa",
                     "Basic Alias Analysis (stateless AA impl)",
                     false, true, false)
  
  
  ImmutablePass *llvm::createBasicAliasAnalysisPass() {
    return new BasicAliasAnalysis();
  }
  
  /// pointsToConstantMemory - Returns whether the given pointer value
  /// points to memory that is local to the function, with global constants being
  /// considered local to all functions.
  bool
  BasicAliasAnalysis::pointsToConstantMemory(const Location &Loc, bool OrLocal) {
    assert(Visited.empty() && "Visited must be cleared after use!");
  
    unsigned MaxLookup = 8;
    SmallVector<const Value *, 16> Worklist;
    Worklist.push_back(Loc.Ptr);
    do {
      const Value *V = GetUnderlyingObject(Worklist.pop_back_val(), TD);
      if (!Visited.insert(V)) {
        Visited.clear();
        return AliasAnalysis::pointsToConstantMemory(Loc, OrLocal);
      }
  
      // An alloca instruction defines local memory.
      if (OrLocal && isa<AllocaInst>(V))
        continue;
  
      // A global constant counts as local memory for our purposes.
      if (const GlobalVariable *GV = dyn_cast<GlobalVariable>(V)) {
        // Note: this doesn't require GV to be "ODR" because it isn't legal for a
        // global to be marked constant in some modules and non-constant in
        // others.  GV may even be a declaration, not a definition.
        if (!GV->isConstant()) {
          Visited.clear();
          return AliasAnalysis::pointsToConstantMemory(Loc, OrLocal);
        }
        continue;
      }
  
      // If both select values point to local memory, then so does the select.
      if (const SelectInst *SI = dyn_cast<SelectInst>(V)) {
        Worklist.push_back(SI->getTrueValue());
        Worklist.push_back(SI->getFalseValue());
        continue;
      }
  
      // If all values incoming to a phi node point to local memory, then so does
      // the phi.
      if (const PHINode *PN = dyn_cast<PHINode>(V)) {
        // Don't bother inspecting phi nodes with many operands.
        if (PN->getNumIncomingValues() > MaxLookup) {
          Visited.clear();
          return AliasAnalysis::pointsToConstantMemory(Loc, OrLocal);
        }
        for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
          Worklist.push_back(PN->getIncomingValue(i));
        continue;
      }
  
      // Otherwise be conservative.
      Visited.clear();
      return AliasAnalysis::pointsToConstantMemory(Loc, OrLocal);
  
    } while (!Worklist.empty() && --MaxLookup);
  
    Visited.clear();
    return Worklist.empty();
  }
  
  /// getModRefBehavior - Return the behavior when calling the given call site.
  AliasAnalysis::ModRefBehavior
  BasicAliasAnalysis::getModRefBehavior(ImmutableCallSite CS) {
    if (CS.doesNotAccessMemory())
      // Can't do better than this.
      return DoesNotAccessMemory;
  
    ModRefBehavior Min = UnknownModRefBehavior;
  
    // If the callsite knows it only reads memory, don't return worse
    // than that.
    if (CS.onlyReadsMemory())
      Min = OnlyReadsMemory;
  
    // The AliasAnalysis base class has some smarts, lets use them.
    return ModRefBehavior(AliasAnalysis::getModRefBehavior(CS) & Min);
  }
  
  /// getModRefBehavior - Return the behavior when calling the given function.
  /// For use when the call site is not known.
  AliasAnalysis::ModRefBehavior
  BasicAliasAnalysis::getModRefBehavior(const Function *F) {
    // If the function declares it doesn't access memory, we can't do better.
    if (F->doesNotAccessMemory())
      return DoesNotAccessMemory;
  
    // For intrinsics, we can check the table.
    if (unsigned iid = F->getIntrinsicID()) {
  #define GET_INTRINSIC_MODREF_BEHAVIOR
  #include "llvm/Intrinsics.gen"
  #undef GET_INTRINSIC_MODREF_BEHAVIOR
    }
  
    ModRefBehavior Min = UnknownModRefBehavior;
  
    // If the function declares it only reads memory, go with that.
    if (F->onlyReadsMemory())
      Min = OnlyReadsMemory;
  
    // Otherwise be conservative.
    return ModRefBehavior(AliasAnalysis::getModRefBehavior(F) & Min);
  }
  
  /// getModRefInfo - Check to see if the specified callsite can clobber the
  /// specified memory object.  Since we only look at local properties of this
  /// function, we really can't say much about this query.  We do, however, use
  /// simple "address taken" analysis on local objects.
  AliasAnalysis::ModRefResult
  BasicAliasAnalysis::getModRefInfo(ImmutableCallSite CS,
                                    const Location &Loc) {
    assert(notDifferentParent(CS.getInstruction(), Loc.Ptr) &&
           "AliasAnalysis query involving multiple functions!");
  
    const Value *Object = GetUnderlyingObject(Loc.Ptr, TD);
    
    // If this is a tail call and Loc.Ptr points to a stack location, we know that
    // the tail call cannot access or modify the local stack.
    // We cannot exclude byval arguments here; these belong to the caller of
    // the current function not to the current function, and a tail callee
    // may reference them.
    if (isa<AllocaInst>(Object))
      if (const CallInst *CI = dyn_cast<CallInst>(CS.getInstruction()))
        if (CI->isTailCall())
          return NoModRef;
    
    // If the pointer is to a locally allocated object that does not escape,
    // then the call can not mod/ref the pointer unless the call takes the pointer
    // as an argument, and itself doesn't capture it.
    if (!isa<Constant>(Object) && CS.getInstruction() != Object &&
        isNonEscapingLocalObject(Object)) {
      bool PassedAsArg = false;
      unsigned ArgNo = 0;
      for (ImmutableCallSite::arg_iterator CI = CS.arg_begin(), CE = CS.arg_end();
           CI != CE; ++CI, ++ArgNo) {
        // Only look at the no-capture or byval pointer arguments.  If this
        // pointer were passed to arguments that were neither of these, then it
        // couldn't be no-capture.
        if (!(*CI)->getType()->isPointerTy() ||
            (!CS.doesNotCapture(ArgNo) && !CS.isByValArgument(ArgNo)))
          continue;
        
        // If this is a no-capture pointer argument, see if we can tell that it
        // is impossible to alias the pointer we're checking.  If not, we have to
        // assume that the call could touch the pointer, even though it doesn't
        // escape.
        if (!isNoAlias(Location(*CI), Location(Object))) {
          PassedAsArg = true;
          break;
        }
      }
      
      if (!PassedAsArg)
        return NoModRef;
    }
  
    const TargetLibraryInfo &TLI = getAnalysis<TargetLibraryInfo>();
    ModRefResult Min = ModRef;
  
    // Finally, handle specific knowledge of intrinsics.
    const IntrinsicInst *II = dyn_cast<IntrinsicInst>(CS.getInstruction());
    if (II != 0)
      switch (II->getIntrinsicID()) {
      default: break;
      case Intrinsic::memcpy:
      case Intrinsic::memmove: {
        uint64_t Len = UnknownSize;
        if (ConstantInt *LenCI = dyn_cast<ConstantInt>(II->getArgOperand(2)))
          Len = LenCI->getZExtValue();
        Value *Dest = II->getArgOperand(0);
        Value *Src = II->getArgOperand(1);
        // If it can't overlap the source dest, then it doesn't modref the loc.
        if (isNoAlias(Location(Dest, Len), Loc)) {
          if (isNoAlias(Location(Src, Len), Loc))
            return NoModRef;
          // If it can't overlap the dest, then worst case it reads the loc.
          Min = Ref;
        } else if (isNoAlias(Location(Src, Len), Loc)) {
          // If it can't overlap the source, then worst case it mutates the loc.
          Min = Mod;
        }
        break;
      }
      case Intrinsic::memset:
        // Since memset is 'accesses arguments' only, the AliasAnalysis base class
        // will handle it for the variable length case.
        if (ConstantInt *LenCI = dyn_cast<ConstantInt>(II->getArgOperand(2))) {
          uint64_t Len = LenCI->getZExtValue();
          Value *Dest = II->getArgOperand(0);
          if (isNoAlias(Location(Dest, Len), Loc))
            return NoModRef;
        }
        // We know that memset doesn't load anything.
        Min = Mod;
        break;
      case Intrinsic::lifetime_start:
      case Intrinsic::lifetime_end:
      case Intrinsic::invariant_start: {
        uint64_t PtrSize =
          cast<ConstantInt>(II->getArgOperand(0))->getZExtValue();
        if (isNoAlias(Location(II->getArgOperand(1),
                               PtrSize,
                               II->getMetadata(LLVMContext::MD_tbaa)),
                      Loc))
          return NoModRef;
        break;
      }
      case Intrinsic::invariant_end: {
        uint64_t PtrSize =
          cast<ConstantInt>(II->getArgOperand(1))->getZExtValue();
        if (isNoAlias(Location(II->getArgOperand(2),
                               PtrSize,
                               II->getMetadata(LLVMContext::MD_tbaa)),
                      Loc))
          return NoModRef;
        break;
      }
      case Intrinsic::arm_neon_vld1: {
        // LLVM's vld1 and vst1 intrinsics currently only support a single
        // vector register.
        uint64_t Size =
          TD ? TD->getTypeStoreSize(II->getType()) : UnknownSize;
        if (isNoAlias(Location(II->getArgOperand(0), Size,
                               II->getMetadata(LLVMContext::MD_tbaa)),
                      Loc))
          return NoModRef;
        break;
      }
      case Intrinsic::arm_neon_vst1: {
        uint64_t Size =
          TD ? TD->getTypeStoreSize(II->getArgOperand(1)->getType()) : UnknownSize;
        if (isNoAlias(Location(II->getArgOperand(0), Size,
                               II->getMetadata(LLVMContext::MD_tbaa)),
                      Loc))
          return NoModRef;
        break;
      }
      }
  
    // We can bound the aliasing properties of memset_pattern16 just as we can
    // for memcpy/memset.  This is particularly important because the 
    // LoopIdiomRecognizer likes to turn loops into calls to memset_pattern16
    // whenever possible.
    else if (TLI.has(LibFunc::memset_pattern16) &&
             CS.getCalledFunction() &&
             CS.getCalledFunction()->getName() == "memset_pattern16") {
      const Function *MS = CS.getCalledFunction();
      FunctionType *MemsetType = MS->getFunctionType();
      if (!MemsetType->isVarArg() && MemsetType->getNumParams() == 3 &&
          isa<PointerType>(MemsetType->getParamType(0)) &&
          isa<PointerType>(MemsetType->getParamType(1)) &&
          isa<IntegerType>(MemsetType->getParamType(2))) {
        uint64_t Len = UnknownSize;
        if (const ConstantInt *LenCI = dyn_cast<ConstantInt>(CS.getArgument(2)))
          Len = LenCI->getZExtValue();
        const Value *Dest = CS.getArgument(0);
        const Value *Src = CS.getArgument(1);
        // If it can't overlap the source dest, then it doesn't modref the loc.
        if (isNoAlias(Location(Dest, Len), Loc)) {
          // Always reads 16 bytes of the source.
          if (isNoAlias(Location(Src, 16), Loc))
            return NoModRef;
          // If it can't overlap the dest, then worst case it reads the loc.
          Min = Ref;
        // Always reads 16 bytes of the source.
        } else if (isNoAlias(Location(Src, 16), Loc)) {
          // If it can't overlap the source, then worst case it mutates the loc.
          Min = Mod;
        }
      }
    }
  
    // The AliasAnalysis base class has some smarts, lets use them.
    return ModRefResult(AliasAnalysis::getModRefInfo(CS, Loc) & Min);
  }
  
  /// aliasGEP - Provide a bunch of ad-hoc rules to disambiguate a GEP instruction
  /// against another pointer.  We know that V1 is a GEP, but we don't know
  /// anything about V2.  UnderlyingV1 is GetUnderlyingObject(GEP1, TD),
  /// UnderlyingV2 is the same for V2.
  ///
  AliasAnalysis::AliasResult
  BasicAliasAnalysis::aliasGEP(const GEPOperator *GEP1, uint64_t V1Size,
                               const Value *V2, uint64_t V2Size,
                               const MDNode *V2TBAAInfo,
                               const Value *UnderlyingV1,
                               const Value *UnderlyingV2) {
    int64_t GEP1BaseOffset;
    SmallVector<VariableGEPIndex, 4> GEP1VariableIndices;
  
    // If we have two gep instructions with must-alias'ing base pointers, figure
    // out if the indexes to the GEP tell us anything about the derived pointer.
    if (const GEPOperator *GEP2 = dyn_cast<GEPOperator>(V2)) {
      // Do the base pointers alias?
      AliasResult BaseAlias = aliasCheck(UnderlyingV1, UnknownSize, 0,
                                         UnderlyingV2, UnknownSize, 0);
      
      // If we get a No or May, then return it immediately, no amount of analysis
      // will improve this situation.
      if (BaseAlias != MustAlias) return BaseAlias;
      
      // Otherwise, we have a MustAlias.  Since the base pointers alias each other
      // exactly, see if the computed offset from the common pointer tells us
      // about the relation of the resulting pointer.
      const Value *GEP1BasePtr =
        DecomposeGEPExpression(GEP1, GEP1BaseOffset, GEP1VariableIndices, TD);
      
      int64_t GEP2BaseOffset;
      SmallVector<VariableGEPIndex, 4> GEP2VariableIndices;
      const Value *GEP2BasePtr =
        DecomposeGEPExpression(GEP2, GEP2BaseOffset, GEP2VariableIndices, TD);
      
      // If DecomposeGEPExpression isn't able to look all the way through the
      // addressing operation, we must not have TD and this is too complex for us
      // to handle without it.
      if (GEP1BasePtr != UnderlyingV1 || GEP2BasePtr != UnderlyingV2) {
        assert(TD == 0 &&
               "DecomposeGEPExpression and GetUnderlyingObject disagree!");
        return MayAlias;
      }
      
      // Subtract the GEP2 pointer from the GEP1 pointer to find out their
      // symbolic difference.
      GEP1BaseOffset -= GEP2BaseOffset;
      GetIndexDifference(GEP1VariableIndices, GEP2VariableIndices);
      
    } else {
      // Check to see if these two pointers are related by the getelementptr
      // instruction.  If one pointer is a GEP with a non-zero index of the other
      // pointer, we know they cannot alias.
  
      // If both accesses are unknown size, we can't do anything useful here.
      if (V1Size == UnknownSize && V2Size == UnknownSize)
        return MayAlias;
  
      AliasResult R = aliasCheck(UnderlyingV1, UnknownSize, 0,
                                 V2, V2Size, V2TBAAInfo);
      if (R != MustAlias)
        // If V2 may alias GEP base pointer, conservatively returns MayAlias.
        // If V2 is known not to alias GEP base pointer, then the two values
        // cannot alias per GEP semantics: "A pointer value formed from a
        // getelementptr instruction is associated with the addresses associated
        // with the first operand of the getelementptr".
        return R;
  
      const Value *GEP1BasePtr =
        DecomposeGEPExpression(GEP1, GEP1BaseOffset, GEP1VariableIndices, TD);
      
      // If DecomposeGEPExpression isn't able to look all the way through the
      // addressing operation, we must not have TD and this is too complex for us
      // to handle without it.
      if (GEP1BasePtr != UnderlyingV1) {
        assert(TD == 0 &&
               "DecomposeGEPExpression and GetUnderlyingObject disagree!");
        return MayAlias;
      }
    }
    
    // In the two GEP Case, if there is no difference in the offsets of the
    // computed pointers, the resultant pointers are a must alias.  This
    // hapens when we have two lexically identical GEP's (for example).
    //
    // In the other case, if we have getelementptr <ptr>, 0, 0, 0, 0, ... and V2
    // must aliases the GEP, the end result is a must alias also.
    if (GEP1BaseOffset == 0 && GEP1VariableIndices.empty())
      return MustAlias;
  
    // If there is a constant difference between the pointers, but the difference
    // is less than the size of the associated memory object, then we know
    // that the objects are partially overlapping.  If the difference is
    // greater, we know they do not overlap.
    if (GEP1BaseOffset != 0 && GEP1VariableIndices.empty()) {
      if (GEP1BaseOffset >= 0) {
        if (V2Size != UnknownSize) {
          if ((uint64_t)GEP1BaseOffset < V2Size)
            return PartialAlias;
          return NoAlias;
        }
      } else {
        if (V1Size != UnknownSize) {
          if (-(uint64_t)GEP1BaseOffset < V1Size)
            return PartialAlias;
          return NoAlias;
        }
      }
    }
  
    // Try to distinguish something like &A[i][1] against &A[42][0].
    // Grab the least significant bit set in any of the scales.
    if (!GEP1VariableIndices.empty()) {
      uint64_t Modulo = 0;
      for (unsigned i = 0, e = GEP1VariableIndices.size(); i != e; ++i)
        Modulo |= (uint64_t)GEP1VariableIndices[i].Scale;
      Modulo = Modulo ^ (Modulo & (Modulo - 1));
  
      // We can compute the difference between the two addresses
      // mod Modulo. Check whether that difference guarantees that the
      // two locations do not alias.
      uint64_t ModOffset = (uint64_t)GEP1BaseOffset & (Modulo - 1);
      if (V1Size != UnknownSize && V2Size != UnknownSize &&
          ModOffset >= V2Size && V1Size <= Modulo - ModOffset)
        return NoAlias;
    }
  
    // Statically, we can see that the base objects are the same, but the
    // pointers have dynamic offsets which we can't resolve. And none of our
    // little tricks above worked.
    //
    // TODO: Returning PartialAlias instead of MayAlias is a mild hack; the
    // practical effect of this is protecting TBAA in the case of dynamic
    // indices into arrays of unions or malloc'd memory.
    return PartialAlias;
  }
  
  static AliasAnalysis::AliasResult
  MergeAliasResults(AliasAnalysis::AliasResult A, AliasAnalysis::AliasResult B) {
    // If the results agree, take it.
    if (A == B)
      return A;
    // A mix of PartialAlias and MustAlias is PartialAlias.
    if ((A == AliasAnalysis::PartialAlias && B == AliasAnalysis::MustAlias) ||
        (B == AliasAnalysis::PartialAlias && A == AliasAnalysis::MustAlias))
      return AliasAnalysis::PartialAlias;
    // Otherwise, we don't know anything.
    return AliasAnalysis::MayAlias;
  }
  
  /// aliasSelect - Provide a bunch of ad-hoc rules to disambiguate a Select
  /// instruction against another.
  AliasAnalysis::AliasResult
  BasicAliasAnalysis::aliasSelect(const SelectInst *SI, uint64_t SISize,
                                  const MDNode *SITBAAInfo,
                                  const Value *V2, uint64_t V2Size,
                                  const MDNode *V2TBAAInfo) {
    // If the values are Selects with the same condition, we can do a more precise
    // check: just check for aliases between the values on corresponding arms.
    if (const SelectInst *SI2 = dyn_cast<SelectInst>(V2))
      if (SI->getCondition() == SI2->getCondition()) {
        AliasResult Alias =
          aliasCheck(SI->getTrueValue(), SISize, SITBAAInfo,
                     SI2->getTrueValue(), V2Size, V2TBAAInfo);
        if (Alias == MayAlias)
          return MayAlias;
        AliasResult ThisAlias =
          aliasCheck(SI->getFalseValue(), SISize, SITBAAInfo,
                     SI2->getFalseValue(), V2Size, V2TBAAInfo);
        return MergeAliasResults(ThisAlias, Alias);
      }
  
    // If both arms of the Select node NoAlias or MustAlias V2, then returns
    // NoAlias / MustAlias. Otherwise, returns MayAlias.
    AliasResult Alias =
      aliasCheck(V2, V2Size, V2TBAAInfo, SI->getTrueValue(), SISize, SITBAAInfo);
    if (Alias == MayAlias)
      return MayAlias;
  
    AliasResult ThisAlias =
      aliasCheck(V2, V2Size, V2TBAAInfo, SI->getFalseValue(), SISize, SITBAAInfo);
    return MergeAliasResults(ThisAlias, Alias);
  }
  
  // aliasPHI - Provide a bunch of ad-hoc rules to disambiguate a PHI instruction
  // against another.
  AliasAnalysis::AliasResult
  BasicAliasAnalysis::aliasPHI(const PHINode *PN, uint64_t PNSize,
                               const MDNode *PNTBAAInfo,
                               const Value *V2, uint64_t V2Size,
                               const MDNode *V2TBAAInfo) {
    // If the values are PHIs in the same block, we can do a more precise
    // as well as efficient check: just check for aliases between the values
    // on corresponding edges.
    if (const PHINode *PN2 = dyn_cast<PHINode>(V2))
      if (PN2->getParent() == PN->getParent()) {
        AliasResult Alias =
          aliasCheck(PN->getIncomingValue(0), PNSize, PNTBAAInfo,
                     PN2->getIncomingValueForBlock(PN->getIncomingBlock(0)),
                     V2Size, V2TBAAInfo);
        if (Alias == MayAlias)
          return MayAlias;
        for (unsigned i = 1, e = PN->getNumIncomingValues(); i != e; ++i) {
          AliasResult ThisAlias =
            aliasCheck(PN->getIncomingValue(i), PNSize, PNTBAAInfo,
                       PN2->getIncomingValueForBlock(PN->getIncomingBlock(i)),
                       V2Size, V2TBAAInfo);
          Alias = MergeAliasResults(ThisAlias, Alias);
          if (Alias == MayAlias)
            break;
        }
        return Alias;
      }
  
    SmallPtrSet<Value*, 4> UniqueSrc;
    SmallVector<Value*, 4> V1Srcs;
    for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
      Value *PV1 = PN->getIncomingValue(i);
      if (isa<PHINode>(PV1))
        // If any of the source itself is a PHI, return MayAlias conservatively
        // to avoid compile time explosion. The worst possible case is if both
        // sides are PHI nodes. In which case, this is O(m x n) time where 'm'
        // and 'n' are the number of PHI sources.
        return MayAlias;
      if (UniqueSrc.insert(PV1))
        V1Srcs.push_back(PV1);
    }
  
    AliasResult Alias = aliasCheck(V2, V2Size, V2TBAAInfo,
                                   V1Srcs[0], PNSize, PNTBAAInfo);
    // Early exit if the check of the first PHI source against V2 is MayAlias.
    // Other results are not possible.
    if (Alias == MayAlias)
      return MayAlias;
  
    // If all sources of the PHI node NoAlias or MustAlias V2, then returns
    // NoAlias / MustAlias. Otherwise, returns MayAlias.
    for (unsigned i = 1, e = V1Srcs.size(); i != e; ++i) {
      Value *V = V1Srcs[i];
  
      AliasResult ThisAlias = aliasCheck(V2, V2Size, V2TBAAInfo,
                                         V, PNSize, PNTBAAInfo);
      Alias = MergeAliasResults(ThisAlias, Alias);
      if (Alias == MayAlias)
        break;
    }
  
    return Alias;
  }
  
  // aliasCheck - Provide a bunch of ad-hoc rules to disambiguate in common cases,
  // such as array references.
  //
  AliasAnalysis::AliasResult
  BasicAliasAnalysis::aliasCheck(const Value *V1, uint64_t V1Size,
                                 const MDNode *V1TBAAInfo,
                                 const Value *V2, uint64_t V2Size,
                                 const MDNode *V2TBAAInfo) {
    // If either of the memory references is empty, it doesn't matter what the
    // pointer values are.
    if (V1Size == 0 || V2Size == 0)
      return NoAlias;
  
    // Strip off any casts if they exist.
    V1 = V1->stripPointerCasts();
    V2 = V2->stripPointerCasts();
  
    // Are we checking for alias of the same value?
    if (V1 == V2) return MustAlias;
  
    if (!V1->getType()->isPointerTy() || !V2->getType()->isPointerTy())
      return NoAlias;  // Scalars cannot alias each other
  
    // Figure out what objects these things are pointing to if we can.
    const Value *O1 = GetUnderlyingObject(V1, TD);
    const Value *O2 = GetUnderlyingObject(V2, TD);
  
    // Null values in the default address space don't point to any object, so they
    // don't alias any other pointer.
    if (const ConstantPointerNull *CPN = dyn_cast<ConstantPointerNull>(O1))
      if (CPN->getType()->getAddressSpace() == 0)
        return NoAlias;
    if (const ConstantPointerNull *CPN = dyn_cast<ConstantPointerNull>(O2))
      if (CPN->getType()->getAddressSpace() == 0)
        return NoAlias;
  
    if (O1 != O2) {
      // If V1/V2 point to two different objects we know that we have no alias.
      if (isIdentifiedObject(O1) && isIdentifiedObject(O2))
        return NoAlias;
  
      // Constant pointers can't alias with non-const isIdentifiedObject objects.
      if ((isa<Constant>(O1) && isIdentifiedObject(O2) && !isa<Constant>(O2)) ||
          (isa<Constant>(O2) && isIdentifiedObject(O1) && !isa<Constant>(O1)))
        return NoAlias;
  
      // Arguments can't alias with local allocations or noalias calls
      // in the same function.
      if (((isa<Argument>(O1) && (isa<AllocaInst>(O2) || isNoAliasCall(O2))) ||
           (isa<Argument>(O2) && (isa<AllocaInst>(O1) || isNoAliasCall(O1)))))
        return NoAlias;
  
      // Most objects can't alias null.
      if ((isa<ConstantPointerNull>(O2) && isKnownNonNull(O1)) ||
          (isa<ConstantPointerNull>(O1) && isKnownNonNull(O2)))
        return NoAlias;
    
      // If one pointer is the result of a call/invoke or load and the other is a
      // non-escaping local object within the same function, then we know the
      // object couldn't escape to a point where the call could return it.
      //
      // Note that if the pointers are in different functions, there are a
      // variety of complications. A call with a nocapture argument may still
      // temporary store the nocapture argument's value in a temporary memory
      // location if that memory location doesn't escape. Or it may pass a
      // nocapture value to other functions as long as they don't capture it.
      if (isEscapeSource(O1) && isNonEscapingLocalObject(O2))
        return NoAlias;
      if (isEscapeSource(O2) && isNonEscapingLocalObject(O1))
        return NoAlias;
    }
  
    // If the size of one access is larger than the entire object on the other
    // side, then we know such behavior is undefined and can assume no alias.
    if (TD)
      if ((V1Size != UnknownSize && isObjectSmallerThan(O2, V1Size, *TD)) ||
          (V2Size != UnknownSize && isObjectSmallerThan(O1, V2Size, *TD)))
        return NoAlias;
    
    // Check the cache before climbing up use-def chains. This also terminates
    // otherwise infinitely recursive queries.
    LocPair Locs(Location(V1, V1Size, V1TBAAInfo),
                 Location(V2, V2Size, V2TBAAInfo));
    if (V1 > V2)
      std::swap(Locs.first, Locs.second);
    std::pair<AliasCacheTy::iterator, bool> Pair =
      AliasCache.insert(std::make_pair(Locs, MayAlias));
    if (!Pair.second)
      return Pair.first->second;
  
    // FIXME: This isn't aggressively handling alias(GEP, PHI) for example: if the
    // GEP can't simplify, we don't even look at the PHI cases.
    if (!isa<GEPOperator>(V1) && isa<GEPOperator>(V2)) {
      std::swap(V1, V2);
      std::swap(V1Size, V2Size);
      std::swap(O1, O2);
    }
    if (const GEPOperator *GV1 = dyn_cast<GEPOperator>(V1)) {
      AliasResult Result = aliasGEP(GV1, V1Size, V2, V2Size, V2TBAAInfo, O1, O2);
      if (Result != MayAlias) return AliasCache[Locs] = Result;
    }
  
    if (isa<PHINode>(V2) && !isa<PHINode>(V1)) {
      std::swap(V1, V2);
      std::swap(V1Size, V2Size);
    }
    if (const PHINode *PN = dyn_cast<PHINode>(V1)) {
      AliasResult Result = aliasPHI(PN, V1Size, V1TBAAInfo,
                                    V2, V2Size, V2TBAAInfo);
      if (Result != MayAlias) return AliasCache[Locs] = Result;
    }
  
    if (isa<SelectInst>(V2) && !isa<SelectInst>(V1)) {
      std::swap(V1, V2);
      std::swap(V1Size, V2Size);
    }
    if (const SelectInst *S1 = dyn_cast<SelectInst>(V1)) {
      AliasResult Result = aliasSelect(S1, V1Size, V1TBAAInfo,
                                       V2, V2Size, V2TBAAInfo);
      if (Result != MayAlias) return AliasCache[Locs] = Result;
    }
  
    // If both pointers are pointing into the same object and one of them
    // accesses is accessing the entire object, then the accesses must
    // overlap in some way.
    if (TD && O1 == O2)
      if ((V1Size != UnknownSize && isObjectSize(O1, V1Size, *TD)) ||
          (V2Size != UnknownSize && isObjectSize(O2, V2Size, *TD)))
        return AliasCache[Locs] = PartialAlias;
  
    AliasResult Result =
      AliasAnalysis::alias(Location(V1, V1Size, V1TBAAInfo),
                           Location(V2, V2Size, V2TBAAInfo));
    return AliasCache[Locs] = Result;
  }
  