Vendor import of llvm trunk r300890:

[FreeBSD/FreeBSD.git] / lib / Analysis / BasicAliasAnalysis.cpp

//===- 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;

bool BasicAAResult::invalidate(Function &F, const PreservedAnalyses &PA,
                               FunctionAnalysisManager::Invalidator &Inv) {
  // We don't care if this analysis itself is preserved, it has no state. But
  // we need to check that the analyses it depends on have been. Note that we
  // may be created without handles to some analyses and in that case don't
  // depend on them.
  if (Inv.invalidate<AssumptionAnalysis>(F, PA) ||
      (DT && Inv.invalidate<DominatorTreeAnalysis>(F, PA)) ||
      (LI && Inv.invalidate<LoopAnalysis>(F, PA)))
    return true;

  // Otherwise this analysis result remains valid.
  return false;
}

//===----------------------------------------------------------------------===//
// 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;
  ObjectSizeOpts Opts;
  Opts.RoundToAlign = RoundToAlign;
  if (getObjectSize(V, Size, DL, &TLI, Opts))
    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;
        }
        LLVM_FALLTHROUGH;
      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 similarly 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.
bool BasicAAResult::DecomposeGEPExpression(const Value *V,
       DecomposedGEP &Decomposed, const DataLayout &DL, AssumptionCache *AC,
       DominatorTree *DT) {
  // Limit recursion depth to limit compile time in crazy cases.
  unsigned MaxLookup = MaxLookupSearchDepth;
  SearchTimes++;

  Decomposed.StructOffset = 0;
  Decomposed.OtherOffset = 0;
  Decomposed.VarIndices.clear();
  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->isInterposable()) {
          V = GA->getAliasee();
          continue;
        }
      }
      Decomposed.Base = V;
      return false;
    }

    if (Op->getOpcode() == Instruction::BitCast ||
        Op->getOpcode() == Instruction::AddrSpaceCast) {
      V = Op->getOperand(0);
      continue;
    }

    const GEPOperator *GEPOp = dyn_cast<GEPOperator>(Op);
    if (!GEPOp) {
      if (auto CS = ImmutableCallSite(V))
        if (const Value *RV = CS.getReturnedArgOperand()) {
          V = RV;
          continue;
        }

      // 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;
        }

      Decomposed.Base = V;
      return false;
    }

    // Don't attempt to analyze GEPs over unsized objects.
    if (!GEPOp->getSourceElementType()->isSized()) {
      Decomposed.Base = V;
      return false;
    }

    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);
    // Assume all GEP operands are constants until proven otherwise.
    bool GepHasConstantOffset = true;
    for (User::const_op_iterator I = GEPOp->op_begin() + 1, E = GEPOp->op_end();
         I != E; ++I, ++GTI) {
      const Value *Index = *I;
      // Compute the (potentially symbolic) offset in bytes for this index.
      if (StructType *STy = GTI.getStructTypeOrNull()) {
        // For a struct, add the member offset.
        unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
        if (FieldNo == 0)
          continue;

        Decomposed.StructOffset +=
          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;
        Decomposed.OtherOffset +=
          DL.getTypeAllocSize(GTI.getIndexedType()) * CIdx->getSExtValue();
        continue;
      }

      GepHasConstantOffset = false;

      uint64_t Scale = DL.getTypeAllocSize(GTI.getIndexedType());
      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.
      Decomposed.OtherOffset += 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 = Decomposed.VarIndices.size(); i != e; ++i) {
        if (Decomposed.VarIndices[i].V == Index &&
            Decomposed.VarIndices[i].ZExtBits == ZExtBits &&
            Decomposed.VarIndices[i].SExtBits == SExtBits) {
          Scale += Decomposed.VarIndices[i].Scale;
          Decomposed.VarIndices.erase(Decomposed.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)};
        Decomposed.VarIndices.push_back(Entry);
      }
    }

    // Take care of wrap-arounds
    if (GepHasConstantOffset) {
      Decomposed.StructOffset =
          adjustToPointerSize(Decomposed.StructOffset, PointerSize);
      Decomposed.OtherOffset =
          adjustToPointerSize(Decomposed.OtherOffset, PointerSize);
    }

    // Analyze the base pointer next.
    V = GEPOp->getOperand(0);
  } while (--MaxLookup);

  // If the chain of expressions is too deep, just return early.
  Decomposed.Base = V;
  SearchLimitReached++;
  return true;
}

/// 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();
}

/// 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;
  else if (CS.doesNotReadMemory())
    Min = FMRB_DoesNotReadMemory;

  if (CS.onlyAccessesArgMemory())
    Min = FunctionModRefBehavior(Min & FMRB_OnlyAccessesArgumentPointees);

  // If CS has operand bundles then aliasing attributes from the function it
  // calls do not directly apply to the CallSite.  This can be made more
  // precise in the future.
  if (!CS.hasOperandBundles())
    if (const Function *F = CS.getCalledFunction())
      Min =
          FunctionModRefBehavior(Min & getBestAAResults().getModRefBehavior(F));

  return 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;
  else if (F->doesNotReadMemory())
    Min = FMRB_DoesNotReadMemory;

  if (F->onlyAccessesArgMemory())
    Min = FunctionModRefBehavior(Min & FMRB_OnlyAccessesArgumentPointees);
  else if (F->onlyAccessesInaccessibleMemory())
    Min = FunctionModRefBehavior(Min & FMRB_OnlyAccessesInaccessibleMem);
  else if (F->onlyAccessesInaccessibleMemOrArgMem())
    Min = FunctionModRefBehavior(Min & FMRB_OnlyAccessesInaccessibleOrArgMem);

  return Min;
}

/// Returns true if this is a writeonly (i.e Mod only) parameter.
static bool isWriteOnlyParam(ImmutableCallSite CS, unsigned ArgIdx,
                             const TargetLibraryInfo &TLI) {
  if (CS.paramHasAttr(ArgIdx, Attribute::WriteOnly))
    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.
  // FIXME Consider handling this in InferFunctionAttr.cpp together with other
  // attributes.
  LibFunc F;
  if (CS.getCalledFunction() && TLI.getLibFunc(*CS.getCalledFunction(), F) &&
      F == LibFunc_memset_pattern16 && TLI.has(F))
    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) {

  // Checking for known builtin intrinsics and target library functions.
  if (isWriteOnlyParam(CS, ArgIdx, TLI))
    return MRI_Mod;

  if (CS.paramHasAttr(ArgIdx, Attribute::ReadOnly))
    return MRI_Ref;

  if (CS.paramHasAttr(ArgIdx, Attribute::ReadNone))
    return MRI_NoModRef;

  return AAResultBase::getArgModRefInfo(CS, ArgIdx);
}

static bool isIntrinsicCall(ImmutableCallSite CS, Intrinsic::ID IID) {
  const IntrinsicInst *II = dyn_cast<IntrinsicInst>(CS.getInstruction());
  return II && II->getIntrinsicID() == IID;
}

#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)) {

    // Optimistically assume that call doesn't touch Object and check this
    // assumption in the following loop.
    ModRefInfo Result = MRI_NoModRef;

    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) &&
           OperandNo < CS.getNumArgOperands() && !CS.isByValArgument(OperandNo)))
        continue;

      // Call doesn't access memory through this operand, so we don't care
      // if it aliases with Object.
      if (CS.doesNotAccessMemory(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.
      AliasResult AR =
          getBestAAResults().alias(MemoryLocation(*CI), MemoryLocation(Object));

      // Operand doesnt alias 'Object', continue looking for other aliases
      if (AR == NoAlias)
        continue;
      // Operand aliases 'Object', but call doesn't modify it. Strengthen
      // initial assumption and keep looking in case if there are more aliases.
      if (CS.onlyReadsMemory(OperandNo)) {
        Result = static_cast<ModRefInfo>(Result | MRI_Ref);
        continue;
      }
      // Operand aliases 'Object' but call only writes into it.
      if (CS.doesNotReadMemory(OperandNo)) {
        Result = static_cast<ModRefInfo>(Result | MRI_Mod);
        continue;
      }
      // This operand aliases 'Object' and call reads and writes into it.
      Result = MRI_ModRef;
      break;
    }

    // Early return if we improved mod ref information
    if (Result != MRI_ModRef)
      return Result;
  }

  // If the CallSite is to malloc or calloc, we can assume that it doesn't
  // modify any IR visible value.  This is only valid because we assume these
  // routines do not read values visible in the IR.  TODO: Consider special
  // casing realloc and strdup routines which access only their arguments as
  // well.  Or alternatively, replace all of this with inaccessiblememonly once
  // that's implemented fully. 
  auto *Inst = CS.getInstruction();
  if (isMallocOrCallocLikeFn(Inst, &TLI)) {
    // Be conservative if the accessed pointer may alias the allocation -
    // fallback to the generic handling below.
    if (getBestAAResults().alias(MemoryLocation(Inst), Loc) == NoAlias)
      return MRI_NoModRef;
  }

  // The semantics of memcpy intrinsics forbid overlap between their respective
  // operands, i.e., source and destination of any given memcpy must no-alias.
  // If Loc must-aliases either one of these two locations, then it necessarily
  // no-aliases the other.
  if (auto *Inst = dyn_cast<MemCpyInst>(CS.getInstruction())) {
    AliasResult SrcAA, DestAA;

    if ((SrcAA = getBestAAResults().alias(MemoryLocation::getForSource(Inst),
                                          Loc)) == MustAlias)
      // Loc is exactly the memcpy source thus disjoint from memcpy dest.
      return MRI_Ref;
    if ((DestAA = getBestAAResults().alias(MemoryLocation::getForDest(Inst),
                                           Loc)) == MustAlias)
      // The converse case.
      return MRI_Mod;

    // It's also possible for Loc to alias both src and dest, or neither.
    ModRefInfo rv = MRI_NoModRef;
    if (SrcAA != NoAlias)
      rv = static_cast<ModRefInfo>(rv | MRI_Ref);
    if (DestAA != NoAlias)
      rv = static_cast<ModRefInfo>(rv | MRI_Mod);
    return rv;
  }

  // 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 (isIntrinsicCall(CS, Intrinsic::assume))
    return MRI_NoModRef;

  // Like assumes, guard intrinsics are also marked as arbitrarily writing so
  // that proper control dependencies are maintained but they never mods any
  // particular memory location.
  //
  // *Unlike* assumes, guard intrinsics are modeled as reading memory since the
  // heap state at the point the guard is issued needs to be consistent in case
  // the guard invokes the "deopt" continuation.
  if (isIntrinsicCall(CS, Intrinsic::experimental_guard))
    return MRI_Ref;

  // Like assumes, invariant.start intrinsics were also marked as arbitrarily
  // writing so that proper control dependencies are maintained but they never
  // mod any particular memory location visible to the IR.
  // *Unlike* assumes (which are now modeled as NoModRef), invariant.start
  // intrinsic is now modeled as reading memory. This prevents hoisting the
  // invariant.start intrinsic over stores. Consider:
  // *ptr = 40;
  // *ptr = 50;
  // invariant_start(ptr)
  // int val = *ptr;
  // print(val);
  //
  // This cannot be transformed to:
  //
  // *ptr = 40;
  // invariant_start(ptr)
  // *ptr = 50;
  // int val = *ptr;
  // print(val);
  //
  // The transformation will cause the second store to be ignored (based on
  // rules of invariant.start)  and print 40, while the first program always
  // prints 50.
  if (isIntrinsicCall(CS, Intrinsic::invariant_start))
    return MRI_Ref;

  // 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 (isIntrinsicCall(CS1, Intrinsic::assume) ||
      isIntrinsicCall(CS2, Intrinsic::assume))
    return MRI_NoModRef;

  // Like assumes, guard intrinsics are also marked as arbitrarily writing so
  // that proper control dependencies are maintained but they never mod any
  // particular memory location.
  //
  // *Unlike* assumes, guard intrinsics are modeled as reading memory since the
  // heap state at the point the guard is issued needs to be consistent in case
  // the guard invokes the "deopt" continuation.

  // NB! This function is *not* commutative, so we specical case two
  // possibilities for guard intrinsics.

  if (isIntrinsicCall(CS1, Intrinsic::experimental_guard))
    return getModRefBehavior(CS2) & MRI_Mod ? MRI_Ref : MRI_NoModRef;

  if (isIntrinsicCall(CS2, Intrinsic::experimental_guard))
    return getModRefBehavior(CS1) & MRI_Mod ? MRI_Mod : 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()->stripPointerCasts() ==
             GEP2->getPointerOperand()->stripPointerCasts() &&
         GEP1->getPointerOperandType() == GEP2->getPointerOperandType() &&
         "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->getSExtValue() == C2->getSExtValue())
    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;
}

// If a we have (a) a GEP and (b) a pointer based on an alloca, and the
// beginning of the object the GEP points would have a negative offset with
// repsect to the alloca, that means the GEP can not alias pointer (b).
// Note that the pointer based on the alloca may not be a GEP. For
// example, it may be the alloca itself.
// The same applies if (b) is based on a GlobalVariable. Note that just being
// based on isIdentifiedObject() is not enough - we need an identified object
// that does not permit access to negative offsets. For example, a negative
// offset from a noalias argument or call can be inbounds w.r.t the actual
// underlying object.
//
// For example, consider:
//
//   struct { int f0, int f1, ...} foo;
//   foo alloca;
//   foo* random = bar(alloca);
//   int *f0 = &alloca.f0
//   int *f1 = &random->f1;
//
// Which is lowered, approximately, to:
//
//  %alloca = alloca %struct.foo
//  %random = call %struct.foo* @random(%struct.foo* %alloca)
//  %f0 = getelementptr inbounds %struct, %struct.foo* %alloca, i32 0, i32 0
//  %f1 = getelementptr inbounds %struct, %struct.foo* %random, i32 0, i32 1
//
// Assume %f1 and %f0 alias. Then %f1 would point into the object allocated
// by %alloca. Since the %f1 GEP is inbounds, that means %random must also
// point into the same object. But since %f0 points to the beginning of %alloca,
// the highest %f1 can be is (%alloca + 3). This means %random can not be higher
// than (%alloca - 1), and so is not inbounds, a contradiction.
bool BasicAAResult::isGEPBaseAtNegativeOffset(const GEPOperator *GEPOp,
      const DecomposedGEP &DecompGEP, const DecomposedGEP &DecompObject, 
      uint64_t ObjectAccessSize) {
  // If the object access size is unknown, or the GEP isn't inbounds, bail.
  if (ObjectAccessSize == MemoryLocation::UnknownSize || !GEPOp->isInBounds())
    return false;

  // We need the object to be an alloca or a globalvariable, and want to know
  // the offset of the pointer from the object precisely, so no variable
  // indices are allowed.
  if (!(isa<AllocaInst>(DecompObject.Base) ||
        isa<GlobalVariable>(DecompObject.Base)) ||
      !DecompObject.VarIndices.empty())
    return false;

  int64_t ObjectBaseOffset = DecompObject.StructOffset +
                             DecompObject.OtherOffset;

  // If the GEP has no variable indices, we know the precise offset
  // from the base, then use it. If the GEP has variable indices, we're in
  // a bit more trouble: we can't count on the constant offsets that come
  // from non-struct sources, since these can be "rewound" by a negative
  // variable offset. So use only offsets that came from structs.
  int64_t GEPBaseOffset = DecompGEP.StructOffset;
  if (DecompGEP.VarIndices.empty())
    GEPBaseOffset += DecompGEP.OtherOffset;

  return (GEPBaseOffset >= ObjectBaseOffset + (int64_t)ObjectAccessSize);
}

/// 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) {
  DecomposedGEP DecompGEP1, DecompGEP2;
  bool GEP1MaxLookupReached =
    DecomposeGEPExpression(GEP1, DecompGEP1, DL, &AC, DT);
  bool GEP2MaxLookupReached =
    DecomposeGEPExpression(V2, DecompGEP2, DL, &AC, DT);

  int64_t GEP1BaseOffset = DecompGEP1.StructOffset + DecompGEP1.OtherOffset;
  int64_t GEP2BaseOffset = DecompGEP2.StructOffset + DecompGEP2.OtherOffset;

  assert(DecompGEP1.Base == UnderlyingV1 && DecompGEP2.Base == UnderlyingV2 &&
         "DecomposeGEPExpression returned a result different from "
         "GetUnderlyingObject");

  // If the GEP's offset relative to its base is such that the base would
  // fall below the start of the object underlying V2, then the GEP and V2
  // cannot alias.
  if (!GEP1MaxLookupReached && !GEP2MaxLookupReached &&
      isGEPBaseAtNegativeOffset(GEP1, DecompGEP1, DecompGEP2, V2Size))
    return NoAlias;
  // 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)) {
    // Check for the GEP base being at a negative offset, this time in the other
    // direction.
    if (!GEP1MaxLookupReached && !GEP2MaxLookupReached &&
        isGEPBaseAtNegativeOffset(GEP2, DecompGEP2, DecompGEP1, V1Size))
      return NoAlias;
    // 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.
        // If the max search depth is reached the result is undefined
        if (GEP2MaxLookupReached || GEP1MaxLookupReached)
          return MayAlias;

        // Same offsets.
        if (GEP1BaseOffset == GEP2BaseOffset &&
            DecompGEP1.VarIndices == DecompGEP2.VarIndices)
          return NoAlias;
      }
    }

    // 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.
    // 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()->stripPointerCasts() ==
            GEP2->getPointerOperand()->stripPointerCasts() &&
        GEP1->getPointerOperandType() == GEP2->getPointerOperandType()) {
      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(DecompGEP1.VarIndices, DecompGEP2.VarIndices);

  } 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, MemoryLocation::UnknownSize,
                               V2AAInfo, nullptr, UnderlyingV2);
    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: "Any memory access must be done through
      // a pointer value associated with an address range of the memory access,
      // otherwise the behavior is undefined.".
      return R;

    // 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 && DecompGEP1.VarIndices.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 && DecompGEP1.VarIndices.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 (!DecompGEP1.VarIndices.empty()) {
    uint64_t Modulo = 0;
    bool AllPositive = true;
    for (unsigned i = 0, e = DecompGEP1.VarIndices.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)DecompGEP1.VarIndices[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 = DecompGEP1.VarIndices[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 = DecompGEP1.VarIndices[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 = DecompGEP1.VarIndices[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(DecompGEP1.VarIndices, 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,
                                       const Value *UnderV2) {
  // 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, UnderV2);
  if (Alias == MayAlias)
    return MayAlias;

  AliasResult ThisAlias =
      aliasCheck(V2, V2Size, V2AAInfo, SI->getFalseValue(), SISize, SIAAInfo,
                 UnderV2);
  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,
                                    const Value *UnderV2) {
  // 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, UnderV2);

  // 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, UnderV2);
    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, 
                                      const Value *O1, const Value *O2) {
  // 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.
  if (O1 == nullptr)
    O1 = GetUnderlyingObject(V1, DL, MaxLookupSearchDepth);

  if (O2 == nullptr)
    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(O1, O2);
    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, O2);
    if (Result != MayAlias)
      return AliasCache[Locs] = Result;
  }

  if (isa<SelectInst>(V2) && !isa<SelectInst>(V1)) {
    std::swap(V1, V2);
    std::swap(O1, O2);
    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, O2);
    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
//===----------------------------------------------------------------------===//

AnalysisKey BasicAA::Key;

BasicAAResult BasicAA::run(Function &F, FunctionAnalysisManager &AM) {
  return BasicAAResult(F.getParent()->getDataLayout(),
                       AM.getResult<TargetLibraryAnalysis>(F),
                       AM.getResult<AssumptionAnalysis>(F),
                       &AM.getResult<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(DominatorTreeWrapperPass)
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 = getAnalysis<DominatorTreeWrapperPass>();
  auto *LIWP = getAnalysisIfAvailable<LoopInfoWrapperPass>();

  Result.reset(new BasicAAResult(F.getParent()->getDataLayout(), TLIWP.getTLI(),
                                 ACT.getAssumptionCache(F), &DTWP.getDomTree(),
                                 LIWP ? &LIWP->getLoopInfo() : nullptr));

  return false;
}

void BasicAAWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
  AU.setPreservesAll();
  AU.addRequired<AssumptionCacheTracker>();
  AU.addRequired<DominatorTreeWrapperPass>();
  AU.addRequired<TargetLibraryInfoWrapperPass>();
}

BasicAAResult llvm::createLegacyPMBasicAAResult(Pass &P, Function &F) {
  return BasicAAResult(
      F.getParent()->getDataLayout(),
      P.getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(),
      P.getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F));
}