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/BasicAliasAnalysis.h"
  #include "llvm/ADT/SmallVector.h"
  #include "llvm/ADT/Statistic.h"
  #include "llvm/Analysis/AliasAnalysis.h"
  #include "llvm/Analysis/CFG.h"
  #include "llvm/Analysis/CaptureTracking.h"
  #include "llvm/Analysis/InstructionSimplify.h"
  #include "llvm/Analysis/LoopInfo.h"
  #include "llvm/Analysis/MemoryBuiltins.h"
  #include "llvm/Analysis/ValueTracking.h"
  #include "llvm/Analysis/AssumptionCache.h"
  #include "llvm/IR/Constants.h"
  #include "llvm/IR/DataLayout.h"
  #include "llvm/IR/DerivedTypes.h"
  #include "llvm/IR/Dominators.h"
  #include "llvm/IR/GlobalAlias.h"
  #include "llvm/IR/GlobalVariable.h"
  #include "llvm/IR/Instructions.h"
  #include "llvm/IR/IntrinsicInst.h"
  #include "llvm/IR/LLVMContext.h"
  #include "llvm/IR/Operator.h"
  #include "llvm/Pass.h"
  #include "llvm/Support/ErrorHandling.h"
  #include <algorithm>
  
  #define DEBUG_TYPE "basicaa"
  
  using namespace llvm;
  
  /// Enable analysis of recursive PHI nodes.
  static cl::opt<bool> EnableRecPhiAnalysis("basicaa-recphi", cl::Hidden,
                                            cl::init(false));
  /// SearchLimitReached / SearchTimes shows how often the limit of
  /// to decompose GEPs is reached. It will affect the precision
  /// of basic alias analysis.
  STATISTIC(SearchLimitReached, "Number of times the limit to "
                                "decompose GEPs is reached");
  STATISTIC(SearchTimes, "Number of times a GEP is decomposed");
  
  /// Cutoff after which to stop analysing a set of phi nodes potentially involved
  /// in a cycle. Because we are analysing 'through' phi nodes, we need to be
  /// careful with value equivalence. We use reachability to make sure a value
  /// cannot be involved in a cycle.
  const unsigned MaxNumPhiBBsValueReachabilityCheck = 20;
  
  // The max limit of the search depth in DecomposeGEPExpression() and
  // GetUnderlyingObject(), both functions need to use the same search
  // depth otherwise the algorithm in aliasGEP will assert.
  static const unsigned MaxLookupSearchDepth = 6;
  
  //===----------------------------------------------------------------------===//
  // Useful predicates
  //===----------------------------------------------------------------------===//
  
  /// Returns 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())
        // Note even if the argument is marked nocapture, we still need to check
        // for copies made inside the function. The nocapture attribute only
        // specifies that there are no copies made that outlive the function.
        return !PointerMayBeCaptured(V, false, /*StoreCaptures=*/true);
  
    return false;
  }
  
  /// Returns 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;
  }
  
  /// Returns the size of the object specified by V or UnknownSize if unknown.
  static uint64_t getObjectSize(const Value *V, const DataLayout &DL,
                                const TargetLibraryInfo &TLI,
                                bool RoundToAlign = false) {
    uint64_t Size;
    if (getObjectSize(V, Size, DL, &TLI, RoundToAlign))
      return Size;
    return MemoryLocation::UnknownSize;
  }
  
  /// Returns 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 DataLayout &DL,
                                  const TargetLibraryInfo &TLI) {
    // Note that the meanings of the "object" are slightly different in the
    // following contexts:
    //    c1: llvm::getObjectSize()
    //    c2: llvm.objectsize() intrinsic
    //    c3: isObjectSmallerThan()
    // c1 and c2 share the same meaning; however, the meaning of "object" in c3
    // refers to the "entire object".
    //
    //  Consider this example:
    //     char *p = (char*)malloc(100)
    //     char *q = p+80;
    //
    //  In the context of c1 and c2, the "object" pointed by q refers to the
    // stretch of memory of q[0:19]. So, getObjectSize(q) should return 20.
    //
    //  However, in the context of c3, the "object" refers to the chunk of memory
    // being allocated. So, the "object" has 100 bytes, and q points to the middle
    // the "object". In case q is passed to isObjectSmallerThan() as the 1st
    // parameter, before the llvm::getObjectSize() is called to get the size of
    // entire object, we should:
    //    - either rewind the pointer q to the base-address of the object in
    //      question (in this case rewind to p), or
    //    - just give up. It is up to caller to make sure the pointer is pointing
    //      to the base address the object.
    //
    // We go for 2nd option for simplicity.
    if (!isIdentifiedObject(V))
      return false;
  
    // 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, DL, TLI, /*RoundToAlign*/ true);
  
    return ObjectSize != MemoryLocation::UnknownSize && ObjectSize < Size;
  }
  
  /// Returns true if we can prove that the object specified by V has size Size.
  static bool isObjectSize(const Value *V, uint64_t Size, const DataLayout &DL,
                           const TargetLibraryInfo &TLI) {
    uint64_t ObjectSize = getObjectSize(V, DL, TLI);
    return ObjectSize != MemoryLocation::UnknownSize && ObjectSize == Size;
  }
  
  //===----------------------------------------------------------------------===//
  // GetElementPtr Instruction Decomposition and Analysis
  //===----------------------------------------------------------------------===//
  
  /// Analyzes the specified value as a linear expression: "A*V + B", where A and
  /// B are constant integers.
  ///
  /// Returns 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*/ const Value *BasicAAResult::GetLinearExpression(
      const Value *V, APInt &Scale, APInt &Offset, unsigned &ZExtBits,
      unsigned &SExtBits, const DataLayout &DL, unsigned Depth,
      AssumptionCache *AC, DominatorTree *DT, bool &NSW, bool &NUW) {
    assert(V->getType()->isIntegerTy() && "Not an integer value");
  
    // Limit our recursion depth.
    if (Depth == 6) {
      Scale = 1;
      Offset = 0;
      return V;
    }
  
    if (const ConstantInt *Const = dyn_cast<ConstantInt>(V)) {
      // If it's a constant, just convert it to an offset and remove the variable.
      // If we've been called recursively, the Offset bit width will be greater
      // than the constant's (the Offset's always as wide as the outermost call),
      // so we'll zext here and process any extension in the isa<SExtInst> &
      // isa<ZExtInst> cases below.
      Offset += Const->getValue().zextOrSelf(Offset.getBitWidth());
      assert(Scale == 0 && "Constant values don't have a scale");
      return V;
    }
  
    if (const BinaryOperator *BOp = dyn_cast<BinaryOperator>(V)) {
      if (ConstantInt *RHSC = dyn_cast<ConstantInt>(BOp->getOperand(1))) {
  
        // If we've been called recursively, then Offset and Scale will be wider
        // than the BOp operands. We'll always zext it here as we'll process sign
        // extensions below (see the isa<SExtInst> / isa<ZExtInst> cases).
        APInt RHS = RHSC->getValue().zextOrSelf(Offset.getBitWidth());
  
        switch (BOp->getOpcode()) {
        default:
          // We don't understand this instruction, so we can't decompose it any
          // further.
          Scale = 1;
          Offset = 0;
          return V;
        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(), DL, 0, AC,
                                 BOp, DT)) {
            Scale = 1;
            Offset = 0;
            return V;
          }
        // FALL THROUGH.
        case Instruction::Add:
          V = GetLinearExpression(BOp->getOperand(0), Scale, Offset, ZExtBits,
                                  SExtBits, DL, Depth + 1, AC, DT, NSW, NUW);
          Offset += RHS;
          break;
        case Instruction::Sub:
          V = GetLinearExpression(BOp->getOperand(0), Scale, Offset, ZExtBits,
                                  SExtBits, DL, Depth + 1, AC, DT, NSW, NUW);
          Offset -= RHS;
          break;
        case Instruction::Mul:
          V = GetLinearExpression(BOp->getOperand(0), Scale, Offset, ZExtBits,
                                  SExtBits, DL, Depth + 1, AC, DT, NSW, NUW);
          Offset *= RHS;
          Scale *= RHS;
          break;
        case Instruction::Shl:
          V = GetLinearExpression(BOp->getOperand(0), Scale, Offset, ZExtBits,
                                  SExtBits, DL, Depth + 1, AC, DT, NSW, NUW);
          Offset <<= RHS.getLimitedValue();
          Scale <<= RHS.getLimitedValue();
          // the semantics of nsw and nuw for left shifts don't match those of
          // multiplications, so we won't propagate them.
          NSW = NUW = false;
          return V;
        }
  
        if (isa<OverflowingBinaryOperator>(BOp)) {
          NUW &= BOp->hasNoUnsignedWrap();
          NSW &= BOp->hasNoSignedWrap();
        }
        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) || isa<ZExtInst>(V)) {
      Value *CastOp = cast<CastInst>(V)->getOperand(0);
      unsigned NewWidth = V->getType()->getPrimitiveSizeInBits();
      unsigned SmallWidth = CastOp->getType()->getPrimitiveSizeInBits();
      unsigned OldZExtBits = ZExtBits, OldSExtBits = SExtBits;
      const Value *Result =
          GetLinearExpression(CastOp, Scale, Offset, ZExtBits, SExtBits, DL,
                              Depth + 1, AC, DT, NSW, NUW);
  
      // zext(zext(%x)) == zext(%x), and similiarly for sext; we'll handle this
      // by just incrementing the number of bits we've extended by.
      unsigned ExtendedBy = NewWidth - SmallWidth;
  
      if (isa<SExtInst>(V) && ZExtBits == 0) {
        // sext(sext(%x, a), b) == sext(%x, a + b)
  
        if (NSW) {
          // We haven't sign-wrapped, so it's valid to decompose sext(%x + c)
          // into sext(%x) + sext(c). We'll sext the Offset ourselves:
          unsigned OldWidth = Offset.getBitWidth();
          Offset = Offset.trunc(SmallWidth).sext(NewWidth).zextOrSelf(OldWidth);
        } else {
          // We may have signed-wrapped, so don't decompose sext(%x + c) into
          // sext(%x) + sext(c)
          Scale = 1;
          Offset = 0;
          Result = CastOp;
          ZExtBits = OldZExtBits;
          SExtBits = OldSExtBits;
        }
        SExtBits += ExtendedBy;
      } else {
        // sext(zext(%x, a), b) = zext(zext(%x, a), b) = zext(%x, a + b)
  
        if (!NUW) {
          // We may have unsigned-wrapped, so don't decompose zext(%x + c) into
          // zext(%x) + zext(c)
          Scale = 1;
          Offset = 0;
          Result = CastOp;
          ZExtBits = OldZExtBits;
          SExtBits = OldSExtBits;
        }
        ZExtBits += ExtendedBy;
      }
  
      return Result;
    }
  
    Scale = 1;
    Offset = 0;
    return V;
  }
  
  /// To ensure a pointer offset fits in an integer of size PointerSize
  /// (in bits) when that size is smaller than 64. This is an issue in
  /// particular for 32b programs with negative indices that rely on two's
  /// complement wrap-arounds for precise alias information.
  static int64_t adjustToPointerSize(int64_t Offset, unsigned PointerSize) {
    assert(PointerSize <= 64 && "Invalid PointerSize!");
    unsigned ShiftBits = 64 - PointerSize;
    return (int64_t)((uint64_t)Offset << ShiftBits) >> ShiftBits;
  }
  
  /// 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 DataLayout is around, this function is capable of analyzing everything
  /// that GetUnderlyingObject can look through. To be able to do that
  /// GetUnderlyingObject and DecomposeGEPExpression must use the same search
  /// depth (MaxLookupSearchDepth). When DataLayout not is around, it just looks
  /// through pointer casts.
  /*static*/ const Value *BasicAAResult::DecomposeGEPExpression(
      const Value *V, int64_t &BaseOffs,
      SmallVectorImpl<VariableGEPIndex> &VarIndices, bool &MaxLookupReached,
      const DataLayout &DL, AssumptionCache *AC, DominatorTree *DT) {
    // Limit recursion depth to limit compile time in crazy cases.
    unsigned MaxLookup = MaxLookupSearchDepth;
    MaxLookupReached = false;
    SearchTimes++;
  
    BaseOffs = 0;
    do {
      // See if this is a bitcast or GEP.
      const Operator *Op = dyn_cast<Operator>(V);
      if (!Op) {
        // 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 ||
          Op->getOpcode() == Instruction::AddrSpaceCast) {
        V = Op->getOperand(0);
        continue;
      }
  
      const GEPOperator *GEPOp = dyn_cast<GEPOperator>(Op);
      if (!GEPOp) {
        // 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 AssumptionCache and use them here
          // (these are both now available in this function, but this should be
          // updated when GetUnderlyingObject is updated). TLI should be
          // provided also.
          if (const Value *Simplified =
                  SimplifyInstruction(const_cast<Instruction *>(I), DL)) {
            V = Simplified;
            continue;
          }
  
        return V;
      }
  
      // Don't attempt to analyze GEPs over unsized objects.
      if (!GEPOp->getSourceElementType()->isSized())
        return V;
  
      unsigned AS = GEPOp->getPointerAddressSpace();
      // Walk the indices of the GEP, accumulating them into BaseOff/VarIndices.
      gep_type_iterator GTI = gep_type_begin(GEPOp);
      unsigned PointerSize = DL.getPointerSizeInBits(AS);
      for (User::const_op_iterator I = GEPOp->op_begin() + 1, E = GEPOp->op_end();
           I != E; ++I) {
        const 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 += DL.getStructLayout(STy)->getElementOffset(FieldNo);
          continue;
        }
  
        // For an array/pointer, add the element offset, explicitly scaled.
        if (const ConstantInt *CIdx = dyn_cast<ConstantInt>(Index)) {
          if (CIdx->isZero())
            continue;
          BaseOffs += DL.getTypeAllocSize(*GTI) * CIdx->getSExtValue();
          continue;
        }
  
        uint64_t Scale = DL.getTypeAllocSize(*GTI);
        unsigned ZExtBits = 0, SExtBits = 0;
  
        // If the integer type is smaller than the pointer size, it is implicitly
        // sign extended to pointer size.
        unsigned Width = Index->getType()->getIntegerBitWidth();
        if (PointerSize > Width)
          SExtBits += PointerSize - Width;
  
        // Use GetLinearExpression to decompose the index into a C1*V+C2 form.
        APInt IndexScale(Width, 0), IndexOffset(Width, 0);
        bool NSW = true, NUW = true;
        Index = GetLinearExpression(Index, IndexScale, IndexOffset, ZExtBits,
                                    SExtBits, DL, 0, AC, DT, NSW, NUW);
  
        // 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].ZExtBits == ZExtBits &&
              VarIndices[i].SExtBits == SExtBits) {
            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.
        Scale = adjustToPointerSize(Scale, PointerSize);
  
        if (Scale) {
          VariableGEPIndex Entry = {Index, ZExtBits, SExtBits,
                                    static_cast<int64_t>(Scale)};
          VarIndices.push_back(Entry);
        }
      }
  
      // Take care of wrap-arounds
      BaseOffs = adjustToPointerSize(BaseOffs, PointerSize);
  
      // Analyze the base pointer next.
      V = GEPOp->getOperand(0);
    } while (--MaxLookup);
  
    // If the chain of expressions is too deep, just return early.
    MaxLookupReached = true;
    SearchLimitReached++;
    return V;
  }
  
  /// 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 BasicAAResult::pointsToConstantMemory(const MemoryLocation &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(), DL);
      if (!Visited.insert(V).second) {
        Visited.clear();
        return AAResultBase::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 AAResultBase::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 AAResultBase::pointsToConstantMemory(Loc, OrLocal);
        }
        for (Value *IncValue : PN->incoming_values())
          Worklist.push_back(IncValue);
        continue;
      }
  
      // Otherwise be conservative.
      Visited.clear();
      return AAResultBase::pointsToConstantMemory(Loc, OrLocal);
  
    } while (!Worklist.empty() && --MaxLookup);
  
    Visited.clear();
    return Worklist.empty();
  }
  
  // FIXME: This code is duplicated with MemoryLocation and should be hoisted to
  // some common utility location.
  static bool isMemsetPattern16(const Function *MS,
                                const TargetLibraryInfo &TLI) {
    if (TLI.has(LibFunc::memset_pattern16) &&
        MS->getName() == "memset_pattern16") {
      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)))
        return true;
    }
    return false;
  }
  
  /// Returns the behavior when calling the given call site.
  FunctionModRefBehavior BasicAAResult::getModRefBehavior(ImmutableCallSite CS) {
    if (CS.doesNotAccessMemory())
      // Can't do better than this.
      return FMRB_DoesNotAccessMemory;
  
    FunctionModRefBehavior Min = FMRB_UnknownModRefBehavior;
  
    // If the callsite knows it only reads memory, don't return worse
    // than that.
    if (CS.onlyReadsMemory())
      Min = FMRB_OnlyReadsMemory;
  
    if (CS.onlyAccessesArgMemory())
      Min = FunctionModRefBehavior(Min & FMRB_OnlyAccessesArgumentPointees);
  
    // The AAResultBase base class has some smarts, lets use them.
    return FunctionModRefBehavior(AAResultBase::getModRefBehavior(CS) & Min);
  }
  
  /// Returns the behavior when calling the given function. For use when the call
  /// site is not known.
  FunctionModRefBehavior BasicAAResult::getModRefBehavior(const Function *F) {
    // If the function declares it doesn't access memory, we can't do better.
    if (F->doesNotAccessMemory())
      return FMRB_DoesNotAccessMemory;
  
    FunctionModRefBehavior Min = FMRB_UnknownModRefBehavior;
  
    // If the function declares it only reads memory, go with that.
    if (F->onlyReadsMemory())
      Min = FMRB_OnlyReadsMemory;
  
    if (F->onlyAccessesArgMemory())
      Min = FunctionModRefBehavior(Min & FMRB_OnlyAccessesArgumentPointees);
  
    // Otherwise be conservative.
    return FunctionModRefBehavior(AAResultBase::getModRefBehavior(F) & Min);
  }
  
  /// Returns true if this is a writeonly (i.e Mod only) parameter.  Currently,
  /// we don't have a writeonly attribute, so this only knows about builtin
  /// intrinsics and target library functions.  We could consider adding a
  /// writeonly attribute in the future and moving all of these facts to either
  /// Intrinsics.td or InferFunctionAttr.cpp
  static bool isWriteOnlyParam(ImmutableCallSite CS, unsigned ArgIdx,
                               const TargetLibraryInfo &TLI) {
    if (const IntrinsicInst *II = dyn_cast<IntrinsicInst>(CS.getInstruction()))
      switch (II->getIntrinsicID()) {
      default:
        break;
      case Intrinsic::memset:
      case Intrinsic::memcpy:
      case Intrinsic::memmove:
        // We don't currently have a writeonly attribute.  All other properties
        // of these intrinsics are nicely described via attributes in
        // Intrinsics.td and handled generically.
        if (ArgIdx == 0)
          return true;
      }
  
    // 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.  Note that all but the missing writeonly attribute are
    // handled via InferFunctionAttr.
    if (CS.getCalledFunction() && isMemsetPattern16(CS.getCalledFunction(), TLI))
      if (ArgIdx == 0)
        return true;
  
    // TODO: memset_pattern4, memset_pattern8
    // TODO: _chk variants
    // TODO: strcmp, strcpy
  
    return false;
  }
  
  ModRefInfo BasicAAResult::getArgModRefInfo(ImmutableCallSite CS,
                                             unsigned ArgIdx) {
  
    // Emulate the missing writeonly attribute by checking for known builtin
    // intrinsics and target library functions.
    if (isWriteOnlyParam(CS, ArgIdx, TLI))
      return MRI_Mod;
  
    if (CS.paramHasAttr(ArgIdx + 1, Attribute::ReadOnly))
      return MRI_Ref;
  
    if (CS.paramHasAttr(ArgIdx + 1, Attribute::ReadNone))
      return MRI_NoModRef;
  
    return AAResultBase::getArgModRefInfo(CS, ArgIdx);
  }
  
  static bool isAssumeIntrinsic(ImmutableCallSite CS) {
    const IntrinsicInst *II = dyn_cast<IntrinsicInst>(CS.getInstruction());
    return II && II->getIntrinsicID() == Intrinsic::assume;
  }
  
  #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 nullptr;
  }
  
  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
  
  AliasResult BasicAAResult::alias(const MemoryLocation &LocA,
                                   const MemoryLocation &LocB) {
    assert(notDifferentParent(LocA.Ptr, LocB.Ptr) &&
           "BasicAliasAnalysis doesn't support interprocedural queries.");
  
    // If we have a directly cached entry for these locations, we have recursed
    // through this once, so just return the cached results. Notably, when this
    // happens, we don't clear the cache.
    auto CacheIt = AliasCache.find(LocPair(LocA, LocB));
    if (CacheIt != AliasCache.end())
      return CacheIt->second;
  
    AliasResult Alias = aliasCheck(LocA.Ptr, LocA.Size, LocA.AATags, LocB.Ptr,
                                   LocB.Size, LocB.AATags);
    // AliasCache rarely has more than 1 or 2 elements, always use
    // shrink_and_clear so it quickly returns to the inline capacity of the
    // SmallDenseMap if it ever grows larger.
    // FIXME: This should really be shrink_to_inline_capacity_and_clear().
    AliasCache.shrink_and_clear();
    VisitedPhiBBs.clear();
    return Alias;
  }
  
  /// Checks 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.
  ModRefInfo BasicAAResult::getModRefInfo(ImmutableCallSite CS,
                                          const MemoryLocation &Loc) {
    assert(notDifferentParent(CS.getInstruction(), Loc.Ptr) &&
           "AliasAnalysis query involving multiple functions!");
  
    const Value *Object = GetUnderlyingObject(Loc.Ptr, DL);
  
    // 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 MRI_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 OperandNo = 0;
      for (auto CI = CS.data_operands_begin(), CE = CS.data_operands_end();
           CI != CE; ++CI, ++OperandNo) {
        // 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(OperandNo) && !CS.isByValArgument(OperandNo)))
          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.
        AliasResult AR =
            getBestAAResults().alias(MemoryLocation(*CI), MemoryLocation(Object));
        if (AR) {
          PassedAsArg = true;
          break;
        }
      }
  
      if (!PassedAsArg)
        return MRI_NoModRef;
    }
  
    // While the assume intrinsic is marked as arbitrarily writing so that
    // proper control dependencies will be maintained, it never aliases any
    // particular memory location.
    if (isAssumeIntrinsic(CS))
      return MRI_NoModRef;
  
    // The AAResultBase base class has some smarts, lets use them.
    return AAResultBase::getModRefInfo(CS, Loc);
  }
  
  ModRefInfo BasicAAResult::getModRefInfo(ImmutableCallSite CS1,
                                          ImmutableCallSite CS2) {
    // While the assume intrinsic is marked as arbitrarily writing so that
    // proper control dependencies will be maintained, it never aliases any
    // particular memory location.
    if (isAssumeIntrinsic(CS1) || isAssumeIntrinsic(CS2))
      return MRI_NoModRef;
  
    // The AAResultBase base class has some smarts, lets use them.
    return AAResultBase::getModRefInfo(CS1, CS2);
  }
  
  /// Provide ad-hoc rules to disambiguate accesses through two GEP operators,
  /// both having the exact same pointer operand.
  static AliasResult aliasSameBasePointerGEPs(const GEPOperator *GEP1,
                                              uint64_t V1Size,
                                              const GEPOperator *GEP2,
                                              uint64_t V2Size,
                                              const DataLayout &DL) {
  
    assert(GEP1->getPointerOperand() == GEP2->getPointerOperand() &&
           "Expected GEPs with the same pointer operand");
  
    // Try to determine whether GEP1 and GEP2 index through arrays, into structs,
    // such that the struct field accesses provably cannot alias.
    // We also need at least two indices (the pointer, and the struct field).
    if (GEP1->getNumIndices() != GEP2->getNumIndices() ||
        GEP1->getNumIndices() < 2)
      return MayAlias;
  
    // If we don't know the size of the accesses through both GEPs, we can't
    // determine whether the struct fields accessed can't alias.
    if (V1Size == MemoryLocation::UnknownSize ||
        V2Size == MemoryLocation::UnknownSize)
      return MayAlias;
  
    ConstantInt *C1 =
        dyn_cast<ConstantInt>(GEP1->getOperand(GEP1->getNumOperands() - 1));
    ConstantInt *C2 =
        dyn_cast<ConstantInt>(GEP2->getOperand(GEP2->getNumOperands() - 1));
  
    // If the last (struct) indices are constants and are equal, the other indices
    // might be also be dynamically equal, so the GEPs can alias.
    if (C1 && C2 && C1 == C2)
      return MayAlias;
  
    // Find the last-indexed type of the GEP, i.e., the type you'd get if
    // you stripped the last index.
    // On the way, look at each indexed type.  If there's something other
    // than an array, different indices can lead to different final types.
    SmallVector<Value *, 8> IntermediateIndices;
  
    // Insert the first index; we don't need to check the type indexed
    // through it as it only drops the pointer indirection.
    assert(GEP1->getNumIndices() > 1 && "Not enough GEP indices to examine");
    IntermediateIndices.push_back(GEP1->getOperand(1));
  
    // Insert all the remaining indices but the last one.
    // Also, check that they all index through arrays.
    for (unsigned i = 1, e = GEP1->getNumIndices() - 1; i != e; ++i) {
      if (!isa<ArrayType>(GetElementPtrInst::getIndexedType(
              GEP1->getSourceElementType(), IntermediateIndices)))
        return MayAlias;
      IntermediateIndices.push_back(GEP1->getOperand(i + 1));
    }
  
    auto *Ty = GetElementPtrInst::getIndexedType(
      GEP1->getSourceElementType(), IntermediateIndices);
    StructType *LastIndexedStruct = dyn_cast<StructType>(Ty);
  
    if (isa<SequentialType>(Ty)) {
      // We know that:
      // - both GEPs begin indexing from the exact same pointer;
      // - the last indices in both GEPs are constants, indexing into a sequential
      //   type (array or pointer);
      // - both GEPs only index through arrays prior to that.
      //
      // Because array indices greater than the number of elements are valid in
      // GEPs, unless we know the intermediate indices are identical between
      // GEP1 and GEP2 we cannot guarantee that the last indexed arrays don't
      // partially overlap. We also need to check that the loaded size matches
      // the element size, otherwise we could still have overlap.
      const uint64_t ElementSize =
          DL.getTypeStoreSize(cast<SequentialType>(Ty)->getElementType());
      if (V1Size != ElementSize || V2Size != ElementSize)
        return MayAlias;
  
      for (unsigned i = 0, e = GEP1->getNumIndices() - 1; i != e; ++i)
        if (GEP1->getOperand(i + 1) != GEP2->getOperand(i + 1))
          return MayAlias;
  
      // Now we know that the array/pointer that GEP1 indexes into and that
      // that GEP2 indexes into must either precisely overlap or be disjoint.
      // Because they cannot partially overlap and because fields in an array
      // cannot overlap, if we can prove the final indices are different between
      // GEP1 and GEP2, we can conclude GEP1 and GEP2 don't alias.
      
      // If the last indices are constants, we've already checked they don't
      // equal each other so we can exit early.
      if (C1 && C2)
        return NoAlias;
      if (isKnownNonEqual(GEP1->getOperand(GEP1->getNumOperands() - 1),
                          GEP2->getOperand(GEP2->getNumOperands() - 1),
                          DL))
        return NoAlias;
      return MayAlias;
    } else if (!LastIndexedStruct || !C1 || !C2) {
      return MayAlias;
    }
  
    // We know that:
    // - both GEPs begin indexing from the exact same pointer;
    // - the last indices in both GEPs are constants, indexing into a struct;
    // - said indices are different, hence, the pointed-to fields are different;
    // - both GEPs only index through arrays prior to that.
    //
    // This lets us determine that the struct that GEP1 indexes into and the
    // struct that GEP2 indexes into must either precisely overlap or be
    // completely disjoint.  Because they cannot partially overlap, indexing into
    // different non-overlapping fields of the struct will never alias.
  
    // Therefore, the only remaining thing needed to show that both GEPs can't
    // alias is that the fields are not overlapping.
    const StructLayout *SL = DL.getStructLayout(LastIndexedStruct);
    const uint64_t StructSize = SL->getSizeInBytes();
    const uint64_t V1Off = SL->getElementOffset(C1->getZExtValue());
    const uint64_t V2Off = SL->getElementOffset(C2->getZExtValue());
  
    auto EltsDontOverlap = [StructSize](uint64_t V1Off, uint64_t V1Size,
                                        uint64_t V2Off, uint64_t V2Size) {
      return V1Off < V2Off && V1Off + V1Size <= V2Off &&
             ((V2Off + V2Size <= StructSize) ||
              (V2Off + V2Size - StructSize <= V1Off));
    };
  
    if (EltsDontOverlap(V1Off, V1Size, V2Off, V2Size) ||
        EltsDontOverlap(V2Off, V2Size, V1Off, V1Size))
      return NoAlias;
  
    return MayAlias;
  }
  
  /// Provides 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, DL), UnderlyingV2 is the same for
  /// V2.
  AliasResult BasicAAResult::aliasGEP(const GEPOperator *GEP1, uint64_t V1Size,
                                      const AAMDNodes &V1AAInfo, const Value *V2,
                                      uint64_t V2Size, const AAMDNodes &V2AAInfo,
                                      const Value *UnderlyingV1,
                                      const Value *UnderlyingV2) {
    int64_t GEP1BaseOffset;
    bool GEP1MaxLookupReached;
    SmallVector<VariableGEPIndex, 4> GEP1VariableIndices;
  
    // If we have two gep instructions with must-alias or not-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, MemoryLocation::UnknownSize, AAMDNodes(),
                     UnderlyingV2, MemoryLocation::UnknownSize, AAMDNodes());
  
      // Check for geps of non-aliasing underlying pointers where the offsets are
      // identical.
      if ((BaseAlias == MayAlias) && V1Size == V2Size) {
        // Do the base pointers alias assuming type and size.
        AliasResult PreciseBaseAlias = aliasCheck(UnderlyingV1, V1Size, V1AAInfo,
                                                  UnderlyingV2, V2Size, V2AAInfo);
        if (PreciseBaseAlias == NoAlias) {
          // See if the computed offset from the common pointer tells us about the
          // relation of the resulting pointer.
          int64_t GEP2BaseOffset;
          bool GEP2MaxLookupReached;
          SmallVector<VariableGEPIndex, 4> GEP2VariableIndices;
          const Value *GEP2BasePtr =
              DecomposeGEPExpression(GEP2, GEP2BaseOffset, GEP2VariableIndices,
                                     GEP2MaxLookupReached, DL, &AC, DT);
          const Value *GEP1BasePtr =
              DecomposeGEPExpression(GEP1, GEP1BaseOffset, GEP1VariableIndices,
                                     GEP1MaxLookupReached, DL, &AC, DT);
          // DecomposeGEPExpression and GetUnderlyingObject should return the
          // same result except when DecomposeGEPExpression has no DataLayout.
          // FIXME: They always have a DataLayout, so this should become an
          // assert.
          if (GEP1BasePtr != UnderlyingV1 || GEP2BasePtr != UnderlyingV2) {
            return MayAlias;
          }
          // If the max search depth is reached the result is undefined
          if (GEP2MaxLookupReached || GEP1MaxLookupReached)
            return MayAlias;
  
          // Same offsets.
          if (GEP1BaseOffset == GEP2BaseOffset &&
              GEP1VariableIndices == GEP2VariableIndices)
            return NoAlias;
          GEP1VariableIndices.clear();
        }
      }
  
      // 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,
                                 GEP1MaxLookupReached, DL, &AC, DT);
  
      int64_t GEP2BaseOffset;
      bool GEP2MaxLookupReached;
      SmallVector<VariableGEPIndex, 4> GEP2VariableIndices;
      const Value *GEP2BasePtr =
          DecomposeGEPExpression(GEP2, GEP2BaseOffset, GEP2VariableIndices,
                                 GEP2MaxLookupReached, DL, &AC, DT);
  
      // DecomposeGEPExpression and GetUnderlyingObject should return the
      // same result except when DecomposeGEPExpression has no DataLayout.
      // FIXME: They always have a DataLayout, so this should become an assert.
      if (GEP1BasePtr != UnderlyingV1 || GEP2BasePtr != UnderlyingV2) {
        return MayAlias;
      }
  
      // If we know the two GEPs are based off of the exact same pointer (and not
      // just the same underlying object), see if that tells us anything about
      // the resulting pointers.
      if (GEP1->getPointerOperand() == GEP2->getPointerOperand()) {
        AliasResult R = aliasSameBasePointerGEPs(GEP1, V1Size, GEP2, V2Size, DL);
        // If we couldn't find anything interesting, don't abandon just yet.
        if (R != MayAlias)
          return R;
      }
  
      // If the max search depth is reached, the result is undefined
      if (GEP2MaxLookupReached || GEP1MaxLookupReached)
        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 == MemoryLocation::UnknownSize &&
          V2Size == MemoryLocation::UnknownSize)
        return MayAlias;
  
      AliasResult R = aliasCheck(UnderlyingV1, MemoryLocation::UnknownSize,
                                 AAMDNodes(), V2, V2Size, V2AAInfo);
      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,
                                 GEP1MaxLookupReached, DL, &AC, DT);
  
      // DecomposeGEPExpression and GetUnderlyingObject should return the
      // same result except when DecomposeGEPExpression has no DataLayout.
      // FIXME: They always have a DataLayout, so this should become an assert.
      if (GEP1BasePtr != UnderlyingV1) {
        return MayAlias;
      }
      // If the max search depth is reached the result is undefined
      if (GEP1MaxLookupReached)
        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
    // happens 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 != MemoryLocation::UnknownSize) {
          if ((uint64_t)GEP1BaseOffset < V2Size)
            return PartialAlias;
          return NoAlias;
        }
      } else {
        // We have the situation where:
        // +                +
        // | BaseOffset     |
        // ---------------->|
        // |-->V1Size       |-------> V2Size
        // GEP1             V2
        // We need to know that V2Size is not unknown, otherwise we might have
        // stripped a gep with negative index ('gep <ptr>, -1, ...).
        if (V1Size != MemoryLocation::UnknownSize &&
            V2Size != MemoryLocation::UnknownSize) {
          if (-(uint64_t)GEP1BaseOffset < V1Size)
            return PartialAlias;
          return NoAlias;
        }
      }
    }
  
    if (!GEP1VariableIndices.empty()) {
      uint64_t Modulo = 0;
      bool AllPositive = true;
      for (unsigned i = 0, e = GEP1VariableIndices.size(); i != e; ++i) {
  
        // Try to distinguish something like &A[i][1] against &A[42][0].
        // Grab the least significant bit set in any of the scales. We
        // don't need std::abs here (even if the scale's negative) as we'll
        // be ^'ing Modulo with itself later.
        Modulo |= (uint64_t)GEP1VariableIndices[i].Scale;
  
        if (AllPositive) {
          // If the Value could change between cycles, then any reasoning about
          // the Value this cycle may not hold in the next cycle. We'll just
          // give up if we can't determine conditions that hold for every cycle:
          const Value *V = GEP1VariableIndices[i].V;
  
          bool SignKnownZero, SignKnownOne;
          ComputeSignBit(const_cast<Value *>(V), SignKnownZero, SignKnownOne, DL,
                         0, &AC, nullptr, DT);
  
          // Zero-extension widens the variable, and so forces the sign
          // bit to zero.
          bool IsZExt = GEP1VariableIndices[i].ZExtBits > 0 || isa<ZExtInst>(V);
          SignKnownZero |= IsZExt;
          SignKnownOne &= !IsZExt;
  
          // If the variable begins with a zero then we know it's
          // positive, regardless of whether the value is signed or
          // unsigned.
          int64_t Scale = GEP1VariableIndices[i].Scale;
          AllPositive =
              (SignKnownZero && Scale >= 0) || (SignKnownOne && Scale < 0);
        }
      }
  
      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 != MemoryLocation::UnknownSize &&
          V2Size != MemoryLocation::UnknownSize && ModOffset >= V2Size &&
          V1Size <= Modulo - ModOffset)
        return NoAlias;
  
      // If we know all the variables are positive, then GEP1 >= GEP1BasePtr.
      // If GEP1BasePtr > V2 (GEP1BaseOffset > 0) then we know the pointers
      // don't alias if V2Size can fit in the gap between V2 and GEP1BasePtr.
      if (AllPositive && GEP1BaseOffset > 0 && V2Size <= (uint64_t)GEP1BaseOffset)
        return NoAlias;
  
      if (constantOffsetHeuristic(GEP1VariableIndices, V1Size, V2Size,
                                  GEP1BaseOffset, &AC, DT))
        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 AliasResult MergeAliasResults(AliasResult A, AliasResult B) {
    // If the results agree, take it.
    if (A == B)
      return A;
    // A mix of PartialAlias and MustAlias is PartialAlias.
    if ((A == PartialAlias && B == MustAlias) ||
        (B == PartialAlias && A == MustAlias))
      return PartialAlias;
    // Otherwise, we don't know anything.
    return MayAlias;
  }
  
  /// Provides a bunch of ad-hoc rules to disambiguate a Select instruction
  /// against another.
  AliasResult BasicAAResult::aliasSelect(const SelectInst *SI, uint64_t SISize,
                                         const AAMDNodes &SIAAInfo,
                                         const Value *V2, uint64_t V2Size,
                                         const AAMDNodes &V2AAInfo) {
    // 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, SIAAInfo,
                                       SI2->getTrueValue(), V2Size, V2AAInfo);
        if (Alias == MayAlias)
          return MayAlias;
        AliasResult ThisAlias =
            aliasCheck(SI->getFalseValue(), SISize, SIAAInfo,
                       SI2->getFalseValue(), V2Size, V2AAInfo);
        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, V2AAInfo, SI->getTrueValue(), SISize, SIAAInfo);
    if (Alias == MayAlias)
      return MayAlias;
  
    AliasResult ThisAlias =
        aliasCheck(V2, V2Size, V2AAInfo, SI->getFalseValue(), SISize, SIAAInfo);
    return MergeAliasResults(ThisAlias, Alias);
  }
  
  /// Provide a bunch of ad-hoc rules to disambiguate a PHI instruction against
  /// another.
  AliasResult BasicAAResult::aliasPHI(const PHINode *PN, uint64_t PNSize,
                                      const AAMDNodes &PNAAInfo, const Value *V2,
                                      uint64_t V2Size,
                                      const AAMDNodes &V2AAInfo) {
    // Track phi nodes we have visited. We use this information when we determine
    // value equivalence.
    VisitedPhiBBs.insert(PN->getParent());
  
    // 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()) {
        LocPair Locs(MemoryLocation(PN, PNSize, PNAAInfo),
                     MemoryLocation(V2, V2Size, V2AAInfo));
        if (PN > V2)
          std::swap(Locs.first, Locs.second);
        // Analyse the PHIs' inputs under the assumption that the PHIs are
        // NoAlias.
        // If the PHIs are May/MustAlias there must be (recursively) an input
        // operand from outside the PHIs' cycle that is MayAlias/MustAlias or
        // there must be an operation on the PHIs within the PHIs' value cycle
        // that causes a MayAlias.
        // Pretend the phis do not alias.
        AliasResult Alias = NoAlias;
        assert(AliasCache.count(Locs) &&
               "There must exist an entry for the phi node");
        AliasResult OrigAliasResult = AliasCache[Locs];
        AliasCache[Locs] = NoAlias;
  
        for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
          AliasResult ThisAlias =
              aliasCheck(PN->getIncomingValue(i), PNSize, PNAAInfo,
                         PN2->getIncomingValueForBlock(PN->getIncomingBlock(i)),
                         V2Size, V2AAInfo);
          Alias = MergeAliasResults(ThisAlias, Alias);
          if (Alias == MayAlias)
            break;
        }
  
        // Reset if speculation failed.
        if (Alias != NoAlias)
          AliasCache[Locs] = OrigAliasResult;
  
        return Alias;
      }
  
    SmallPtrSet<Value *, 4> UniqueSrc;
    SmallVector<Value *, 4> V1Srcs;
    bool isRecursive = false;
    for (Value *PV1 : PN->incoming_values()) {
      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 (EnableRecPhiAnalysis)
        if (GEPOperator *PV1GEP = dyn_cast<GEPOperator>(PV1)) {
          // Check whether the incoming value is a GEP that advances the pointer
          // result of this PHI node (e.g. in a loop). If this is the case, we
          // would recurse and always get a MayAlias. Handle this case specially
          // below.
          if (PV1GEP->getPointerOperand() == PN && PV1GEP->getNumIndices() == 1 &&
              isa<ConstantInt>(PV1GEP->idx_begin())) {
            isRecursive = true;
            continue;
          }
        }
  
      if (UniqueSrc.insert(PV1).second)
        V1Srcs.push_back(PV1);
    }
  
    // If this PHI node is recursive, set the size of the accessed memory to
    // unknown to represent all the possible values the GEP could advance the
    // pointer to.
    if (isRecursive)
      PNSize = MemoryLocation::UnknownSize;
  
    AliasResult Alias =
        aliasCheck(V2, V2Size, V2AAInfo, V1Srcs[0], PNSize, PNAAInfo);
  
    // 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, V2AAInfo, V, PNSize, PNAAInfo);
      Alias = MergeAliasResults(ThisAlias, Alias);
      if (Alias == MayAlias)
        break;
    }
  
    return Alias;
  }
  
  /// Provides a bunch of ad-hoc rules to disambiguate in common cases, such as
  /// array references.
  AliasResult BasicAAResult::aliasCheck(const Value *V1, uint64_t V1Size,
                                        AAMDNodes V1AAInfo, const Value *V2,
                                        uint64_t V2Size, AAMDNodes V2AAInfo) {
    // 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();
  
    // If V1 or V2 is undef, the result is NoAlias because we can always pick a
    // value for undef that aliases nothing in the program.
    if (isa<UndefValue>(V1) || isa<UndefValue>(V2))
      return NoAlias;
  
    // Are we checking for alias of the same value?
    // Because we look 'through' phi nodes, we could look at "Value" pointers from
    // different iterations. We must therefore make sure that this is not the
    // case. The function isValueEqualInPotentialCycles ensures that this cannot
    // happen by looking at the visited phi nodes and making sure they cannot
    // reach the value.
    if (isValueEqualInPotentialCycles(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, DL, MaxLookupSearchDepth);
    const Value *O2 = GetUnderlyingObject(V2, DL, MaxLookupSearchDepth);
  
    // 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;
  
      // Function arguments can't alias with things that are known to be
      // unambigously identified at the function level.
      if ((isa<Argument>(O1) && isIdentifiedFunctionLocal(O2)) ||
          (isa<Argument>(O2) && isIdentifiedFunctionLocal(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 ((V1Size != MemoryLocation::UnknownSize &&
         isObjectSmallerThan(O2, V1Size, DL, TLI)) ||
        (V2Size != MemoryLocation::UnknownSize &&
         isObjectSmallerThan(O1, V2Size, DL, TLI)))
      return NoAlias;
  
    // Check the cache before climbing up use-def chains. This also terminates
    // otherwise infinitely recursive queries.
    LocPair Locs(MemoryLocation(V1, V1Size, V1AAInfo),
                 MemoryLocation(V2, V2Size, V2AAInfo));
    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);
      std::swap(V1AAInfo, V2AAInfo);
    }
    if (const GEPOperator *GV1 = dyn_cast<GEPOperator>(V1)) {
      AliasResult Result =
          aliasGEP(GV1, V1Size, V1AAInfo, V2, V2Size, V2AAInfo, O1, O2);
      if (Result != MayAlias)
        return AliasCache[Locs] = Result;
    }
  
    if (isa<PHINode>(V2) && !isa<PHINode>(V1)) {
      std::swap(V1, V2);
      std::swap(V1Size, V2Size);
      std::swap(V1AAInfo, V2AAInfo);
    }
    if (const PHINode *PN = dyn_cast<PHINode>(V1)) {
      AliasResult Result = aliasPHI(PN, V1Size, V1AAInfo, V2, V2Size, V2AAInfo);
      if (Result != MayAlias)
        return AliasCache[Locs] = Result;
    }
  
    if (isa<SelectInst>(V2) && !isa<SelectInst>(V1)) {
      std::swap(V1, V2);
      std::swap(V1Size, V2Size);
      std::swap(V1AAInfo, V2AAInfo);
    }
    if (const SelectInst *S1 = dyn_cast<SelectInst>(V1)) {
      AliasResult Result =
          aliasSelect(S1, V1Size, V1AAInfo, V2, V2Size, V2AAInfo);
      if (Result != MayAlias)
        return AliasCache[Locs] = Result;
    }
  
    // If both pointers are pointing into the same object and one of them
    // accesses the entire object, then the accesses must overlap in some way.
    if (O1 == O2)
      if ((V1Size != MemoryLocation::UnknownSize &&
           isObjectSize(O1, V1Size, DL, TLI)) ||
          (V2Size != MemoryLocation::UnknownSize &&
           isObjectSize(O2, V2Size, DL, TLI)))
        return AliasCache[Locs] = PartialAlias;
  
    // Recurse back into the best AA results we have, potentially with refined
    // memory locations. We have already ensured that BasicAA has a MayAlias
    // cache result for these, so any recursion back into BasicAA won't loop.
    AliasResult Result = getBestAAResults().alias(Locs.first, Locs.second);
    return AliasCache[Locs] = Result;
  }
  
  /// Check whether two Values can be considered equivalent.
  ///
  /// In addition to pointer equivalence of \p V1 and \p V2 this checks whether
  /// they can not be part of a cycle in the value graph by looking at all
  /// visited phi nodes an making sure that the phis cannot reach the value. We
  /// have to do this because we are looking through phi nodes (That is we say
  /// noalias(V, phi(VA, VB)) if noalias(V, VA) and noalias(V, VB).
  bool BasicAAResult::isValueEqualInPotentialCycles(const Value *V,
                                                    const Value *V2) {
    if (V != V2)
      return false;
  
    const Instruction *Inst = dyn_cast<Instruction>(V);
    if (!Inst)
      return true;
  
    if (VisitedPhiBBs.empty())
      return true;
  
    if (VisitedPhiBBs.size() > MaxNumPhiBBsValueReachabilityCheck)
      return false;
  
    // Make sure that the visited phis cannot reach the Value. This ensures that
    // the Values cannot come from different iterations of a potential cycle the
    // phi nodes could be involved in.
    for (auto *P : VisitedPhiBBs)
      if (isPotentiallyReachable(&P->front(), Inst, DT, LI))
        return false;
  
    return true;
  }
  
  /// Computes the symbolic difference between two de-composed GEPs.
  ///
  /// Dest and Src are the variable indices from two decomposed GetElementPtr
  /// instructions GEP1 and GEP2 which have common base pointers.
  void BasicAAResult::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;
      unsigned ZExtBits = Src[i].ZExtBits, SExtBits = Src[i].SExtBits;
      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 (!isValueEqualInPotentialCycles(Dest[j].V, V) ||
            Dest[j].ZExtBits != ZExtBits || Dest[j].SExtBits != SExtBits)
          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, ZExtBits, SExtBits, -Scale};
        Dest.push_back(Entry);
      }
    }
  }
  
  bool BasicAAResult::constantOffsetHeuristic(
      const SmallVectorImpl<VariableGEPIndex> &VarIndices, uint64_t V1Size,
      uint64_t V2Size, int64_t BaseOffset, AssumptionCache *AC,
      DominatorTree *DT) {
    if (VarIndices.size() != 2 || V1Size == MemoryLocation::UnknownSize ||
        V2Size == MemoryLocation::UnknownSize)
      return false;
  
    const VariableGEPIndex &Var0 = VarIndices[0], &Var1 = VarIndices[1];
  
    if (Var0.ZExtBits != Var1.ZExtBits || Var0.SExtBits != Var1.SExtBits ||
        Var0.Scale != -Var1.Scale)
      return false;
  
    unsigned Width = Var1.V->getType()->getIntegerBitWidth();
  
    // We'll strip off the Extensions of Var0 and Var1 and do another round
    // of GetLinearExpression decomposition. In the example above, if Var0
    // is zext(%x + 1) we should get V1 == %x and V1Offset == 1.
  
    APInt V0Scale(Width, 0), V0Offset(Width, 0), V1Scale(Width, 0),
        V1Offset(Width, 0);
    bool NSW = true, NUW = true;
    unsigned V0ZExtBits = 0, V0SExtBits = 0, V1ZExtBits = 0, V1SExtBits = 0;
    const Value *V0 = GetLinearExpression(Var0.V, V0Scale, V0Offset, V0ZExtBits,
                                          V0SExtBits, DL, 0, AC, DT, NSW, NUW);
    NSW = true, NUW = true;
    const Value *V1 = GetLinearExpression(Var1.V, V1Scale, V1Offset, V1ZExtBits,
                                          V1SExtBits, DL, 0, AC, DT, NSW, NUW);
  
    if (V0Scale != V1Scale || V0ZExtBits != V1ZExtBits ||
        V0SExtBits != V1SExtBits || !isValueEqualInPotentialCycles(V0, V1))
      return false;
  
    // We have a hit - Var0 and Var1 only differ by a constant offset!
  
    // If we've been sext'ed then zext'd the maximum difference between Var0 and
    // Var1 is possible to calculate, but we're just interested in the absolute
    // minimum difference between the two. The minimum distance may occur due to
    // wrapping; consider "add i3 %i, 5": if %i == 7 then 7 + 5 mod 8 == 4, and so
    // the minimum distance between %i and %i + 5 is 3.
    APInt MinDiff = V0Offset - V1Offset, Wrapped = -MinDiff;
    MinDiff = APIntOps::umin(MinDiff, Wrapped);
    uint64_t MinDiffBytes = MinDiff.getZExtValue() * std::abs(Var0.Scale);
  
    // We can't definitely say whether GEP1 is before or after V2 due to wrapping
    // arithmetic (i.e. for some values of GEP1 and V2 GEP1 < V2, and for other
    // values GEP1 > V2). We'll therefore only declare NoAlias if both V1Size and
    // V2Size can fit in the MinDiffBytes gap.
    return V1Size + std::abs(BaseOffset) <= MinDiffBytes &&
           V2Size + std::abs(BaseOffset) <= MinDiffBytes;
  }
  
  //===----------------------------------------------------------------------===//
  // BasicAliasAnalysis Pass
  //===----------------------------------------------------------------------===//
  
  char BasicAA::PassID;
  
  BasicAAResult BasicAA::run(Function &F, AnalysisManager<Function> *AM) {
    return BasicAAResult(F.getParent()->getDataLayout(),
                         AM->getResult<TargetLibraryAnalysis>(F),
                         AM->getResult<AssumptionAnalysis>(F),
                         AM->getCachedResult<DominatorTreeAnalysis>(F),
                         AM->getCachedResult<LoopAnalysis>(F));
  }
  
  BasicAAWrapperPass::BasicAAWrapperPass() : FunctionPass(ID) {
      initializeBasicAAWrapperPassPass(*PassRegistry::getPassRegistry());
  }
  
  char BasicAAWrapperPass::ID = 0;
  void BasicAAWrapperPass::anchor() {}
  
  INITIALIZE_PASS_BEGIN(BasicAAWrapperPass, "basicaa",
                        "Basic Alias Analysis (stateless AA impl)", true, true)
  INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
  INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
  INITIALIZE_PASS_END(BasicAAWrapperPass, "basicaa",
                      "Basic Alias Analysis (stateless AA impl)", true, true)
  
  FunctionPass *llvm::createBasicAAWrapperPass() {
    return new BasicAAWrapperPass();
  }
  
  bool BasicAAWrapperPass::runOnFunction(Function &F) {
    auto &ACT = getAnalysis<AssumptionCacheTracker>();
    auto &TLIWP = getAnalysis<TargetLibraryInfoWrapperPass>();
    auto *DTWP = getAnalysisIfAvailable<DominatorTreeWrapperPass>();
    auto *LIWP = getAnalysisIfAvailable<LoopInfoWrapperPass>();
  
    Result.reset(new BasicAAResult(F.getParent()->getDataLayout(), TLIWP.getTLI(),
                                   ACT.getAssumptionCache(F),
                                   DTWP ? &DTWP->getDomTree() : nullptr,
                                   LIWP ? &LIWP->getLoopInfo() : nullptr));
  
    return false;
  }
  
  void BasicAAWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
    AU.setPreservesAll();
    AU.addRequired<AssumptionCacheTracker>();
    AU.addRequired<TargetLibraryInfoWrapperPass>();
  }
  
  BasicAAResult llvm::createLegacyPMBasicAAResult(Pass &P, Function &F) {
    return BasicAAResult(
        F.getParent()->getDataLayout(),
        P.getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(),
        P.getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F));
  }
  