[oota-llvm.git] / lib / Transforms / Vectorize / LoopVectorize.cpp

//===- LoopVectorize.cpp - A Loop Vectorizer ------------------------------===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This is the LLVM loop vectorizer. This pass modifies 'vectorizable' loops
// and generates target-independent LLVM-IR.
// The vectorizer uses the TargetTransformInfo analysis to estimate the costs
// of instructions in order to estimate the profitability of vectorization.
//
// The loop vectorizer combines consecutive loop iterations into a single
// 'wide' iteration. After this transformation the index is incremented
// by the SIMD vector width, and not by one.
//
// This pass has three parts:
// 1. The main loop pass that drives the different parts.
// 2. LoopVectorizationLegality - A unit that checks for the legality
//    of the vectorization.
// 3. InnerLoopVectorizer - A unit that performs the actual
//    widening of instructions.
// 4. LoopVectorizationCostModel - A unit that checks for the profitability
//    of vectorization. It decides on the optimal vector width, which
//    can be one, if vectorization is not profitable.
//
//===----------------------------------------------------------------------===//
//
// The reduction-variable vectorization is based on the paper:
//  D. Nuzman and R. Henderson. Multi-platform Auto-vectorization.
//
// Variable uniformity checks are inspired by:
//  Karrenberg, R. and Hack, S. Whole Function Vectorization.
//
// The interleaved access vectorization is based on the paper:
//  Dorit Nuzman, Ira Rosen and Ayal Zaks.  Auto-Vectorization of Interleaved
//  Data for SIMD
//
// Other ideas/concepts are from:
//  A. Zaks and D. Nuzman. Autovectorization in GCC-two years later.
//
//  S. Maleki, Y. Gao, M. Garzaran, T. Wong and D. Padua.  An Evaluation of
//  Vectorizing Compilers.
//
//===----------------------------------------------------------------------===//

#include "llvm/Transforms/Vectorize.h"
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/EquivalenceClasses.h"
#include "llvm/ADT/Hashing.h"
#include "llvm/ADT/MapVector.h"
#include "llvm/ADT/SetVector.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/SmallSet.h"
#include "llvm/ADT/SmallVector.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/ADT/StringExtras.h"
#include "llvm/Analysis/AliasAnalysis.h"
#include "llvm/Analysis/AliasSetTracker.h"
#include "llvm/Analysis/AssumptionCache.h"
#include "llvm/Analysis/BlockFrequencyInfo.h"
#include "llvm/Analysis/CodeMetrics.h"
#include "llvm/Analysis/LoopAccessAnalysis.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Analysis/LoopIterator.h"
#include "llvm/Analysis/LoopPass.h"
#include "llvm/Analysis/ScalarEvolution.h"
#include "llvm/Analysis/ScalarEvolutionExpander.h"
#include "llvm/Analysis/ScalarEvolutionExpressions.h"
#include "llvm/Analysis/TargetTransformInfo.h"
#include "llvm/Analysis/ValueTracking.h"
#include "llvm/IR/Constants.h"
#include "llvm/IR/DataLayout.h"
#include "llvm/IR/DebugInfo.h"
#include "llvm/IR/DerivedTypes.h"
#include "llvm/IR/DiagnosticInfo.h"
#include "llvm/IR/Dominators.h"
#include "llvm/IR/Function.h"
#include "llvm/IR/IRBuilder.h"
#include "llvm/IR/Instructions.h"
#include "llvm/IR/IntrinsicInst.h"
#include "llvm/IR/LLVMContext.h"
#include "llvm/IR/Module.h"
#include "llvm/IR/PatternMatch.h"
#include "llvm/IR/Type.h"
#include "llvm/IR/Value.h"
#include "llvm/IR/ValueHandle.h"
#include "llvm/IR/Verifier.h"
#include "llvm/Pass.h"
#include "llvm/Support/BranchProbability.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/raw_ostream.h"
#include "llvm/Transforms/Scalar.h"
#include "llvm/Transforms/Utils/BasicBlockUtils.h"
#include "llvm/Transforms/Utils/Local.h"
#include "llvm/Analysis/VectorUtils.h"
#include "llvm/Transforms/Utils/LoopUtils.h"
#include <algorithm>
#include <map>
#include <tuple>

using namespace llvm;
using namespace llvm::PatternMatch;

#define LV_NAME "loop-vectorize"
#define DEBUG_TYPE LV_NAME

STATISTIC(LoopsVectorized, "Number of loops vectorized");
STATISTIC(LoopsAnalyzed, "Number of loops analyzed for vectorization");

static cl::opt<bool>
EnableIfConversion("enable-if-conversion", cl::init(true), cl::Hidden,
                   cl::desc("Enable if-conversion during vectorization."));

/// We don't vectorize loops with a known constant trip count below this number.
static cl::opt<unsigned>
TinyTripCountVectorThreshold("vectorizer-min-trip-count", cl::init(16),
                             cl::Hidden,
                             cl::desc("Don't vectorize loops with a constant "
                                      "trip count that is smaller than this "
                                      "value."));

/// This enables versioning on the strides of symbolically striding memory
/// accesses in code like the following.
///   for (i = 0; i < N; ++i)
///     A[i * Stride1] += B[i * Stride2] ...
///
/// Will be roughly translated to
///    if (Stride1 == 1 && Stride2 == 1) {
///      for (i = 0; i < N; i+=4)
///       A[i:i+3] += ...
///    } else
///      ...
static cl::opt<bool> EnableMemAccessVersioning(
    "enable-mem-access-versioning", cl::init(true), cl::Hidden,
    cl::desc("Enable symblic stride memory access versioning"));

static cl::opt<bool> EnableInterleavedMemAccesses(
    "enable-interleaved-mem-accesses", cl::init(false), cl::Hidden,
    cl::desc("Enable vectorization on interleaved memory accesses in a loop"));

/// Maximum factor for an interleaved memory access.
static cl::opt<unsigned> MaxInterleaveGroupFactor(
    "max-interleave-group-factor", cl::Hidden,
    cl::desc("Maximum factor for an interleaved access group (default = 8)"),
    cl::init(8));

/// We don't interleave loops with a known constant trip count below this
/// number.
static const unsigned TinyTripCountInterleaveThreshold = 128;

static cl::opt<unsigned> ForceTargetNumScalarRegs(
    "force-target-num-scalar-regs", cl::init(0), cl::Hidden,
    cl::desc("A flag that overrides the target's number of scalar registers."));

static cl::opt<unsigned> ForceTargetNumVectorRegs(
    "force-target-num-vector-regs", cl::init(0), cl::Hidden,
    cl::desc("A flag that overrides the target's number of vector registers."));

/// Maximum vectorization interleave count.
static const unsigned MaxInterleaveFactor = 16;

static cl::opt<unsigned> ForceTargetMaxScalarInterleaveFactor(
    "force-target-max-scalar-interleave", cl::init(0), cl::Hidden,
    cl::desc("A flag that overrides the target's max interleave factor for "
             "scalar loops."));

static cl::opt<unsigned> ForceTargetMaxVectorInterleaveFactor(
    "force-target-max-vector-interleave", cl::init(0), cl::Hidden,
    cl::desc("A flag that overrides the target's max interleave factor for "
             "vectorized loops."));

static cl::opt<unsigned> ForceTargetInstructionCost(
    "force-target-instruction-cost", cl::init(0), cl::Hidden,
    cl::desc("A flag that overrides the target's expected cost for "
             "an instruction to a single constant value. Mostly "
             "useful for getting consistent testing."));

static cl::opt<unsigned> SmallLoopCost(
    "small-loop-cost", cl::init(20), cl::Hidden,
    cl::desc(
        "The cost of a loop that is considered 'small' by the interleaver."));

static cl::opt<bool> LoopVectorizeWithBlockFrequency(
    "loop-vectorize-with-block-frequency", cl::init(false), cl::Hidden,
    cl::desc("Enable the use of the block frequency analysis to access PGO "
             "heuristics minimizing code growth in cold regions and being more "
             "aggressive in hot regions."));

// Runtime interleave loops for load/store throughput.
static cl::opt<bool> EnableLoadStoreRuntimeInterleave(
    "enable-loadstore-runtime-interleave", cl::init(true), cl::Hidden,
    cl::desc(
        "Enable runtime interleaving until load/store ports are saturated"));

/// The number of stores in a loop that are allowed to need predication.
static cl::opt<unsigned> NumberOfStoresToPredicate(
    "vectorize-num-stores-pred", cl::init(1), cl::Hidden,
    cl::desc("Max number of stores to be predicated behind an if."));

static cl::opt<bool> EnableIndVarRegisterHeur(
    "enable-ind-var-reg-heur", cl::init(true), cl::Hidden,
    cl::desc("Count the induction variable only once when interleaving"));

static cl::opt<bool> EnableCondStoresVectorization(
    "enable-cond-stores-vec", cl::init(false), cl::Hidden,
    cl::desc("Enable if predication of stores during vectorization."));

static cl::opt<unsigned> MaxNestedScalarReductionIC(
    "max-nested-scalar-reduction-interleave", cl::init(2), cl::Hidden,
    cl::desc("The maximum interleave count to use when interleaving a scalar "
             "reduction in a nested loop."));

static cl::opt<unsigned> PragmaVectorizeMemoryCheckThreshold(
    "pragma-vectorize-memory-check-threshold", cl::init(128), cl::Hidden,
    cl::desc("The maximum allowed number of runtime memory checks with a "
             "vectorize(enable) pragma."));

namespace {

// Forward declarations.
class LoopVectorizeHints;
class LoopVectorizationLegality;
class LoopVectorizationCostModel;
class LoopVectorizationRequirements;

/// \brief This modifies LoopAccessReport to initialize message with
/// loop-vectorizer-specific part.
class VectorizationReport : public LoopAccessReport {
public:
  VectorizationReport(Instruction *I = nullptr)
      : LoopAccessReport("loop not vectorized: ", I) {}

  /// \brief This allows promotion of the loop-access analysis report into the
  /// loop-vectorizer report.  It modifies the message to add the
  /// loop-vectorizer-specific part of the message.
  explicit VectorizationReport(const LoopAccessReport &R)
      : LoopAccessReport(Twine("loop not vectorized: ") + R.str(),
                         R.getInstr()) {}
};

/// A helper function for converting Scalar types to vector types.
/// If the incoming type is void, we return void. If the VF is 1, we return
/// the scalar type.
static Type* ToVectorTy(Type *Scalar, unsigned VF) {
  if (Scalar->isVoidTy() || VF == 1)
    return Scalar;
  return VectorType::get(Scalar, VF);
}

/// InnerLoopVectorizer vectorizes loops which contain only one basic
/// block to a specified vectorization factor (VF).
/// This class performs the widening of scalars into vectors, or multiple
/// scalars. This class also implements the following features:
/// * It inserts an epilogue loop for handling loops that don't have iteration
///   counts that are known to be a multiple of the vectorization factor.
/// * It handles the code generation for reduction variables.
/// * Scalarization (implementation using scalars) of un-vectorizable
///   instructions.
/// InnerLoopVectorizer does not perform any vectorization-legality
/// checks, and relies on the caller to check for the different legality
/// aspects. The InnerLoopVectorizer relies on the
/// LoopVectorizationLegality class to provide information about the induction
/// and reduction variables that were found to a given vectorization factor.
class InnerLoopVectorizer {
public:
  InnerLoopVectorizer(Loop *OrigLoop, ScalarEvolution *SE, LoopInfo *LI,
                      DominatorTree *DT, const TargetLibraryInfo *TLI,
                      const TargetTransformInfo *TTI, unsigned VecWidth,
                      unsigned UnrollFactor)
      : OrigLoop(OrigLoop), SE(SE), LI(LI), DT(DT), TLI(TLI), TTI(TTI),
        VF(VecWidth), UF(UnrollFactor), Builder(SE->getContext()),
        Induction(nullptr), OldInduction(nullptr), WidenMap(UnrollFactor),
        TripCount(nullptr), VectorTripCount(nullptr), Legal(nullptr),
        AddedSafetyChecks(false) {}

  // Perform the actual loop widening (vectorization).
  void vectorize(LoopVectorizationLegality *L) {
    Legal = L;
    // Create a new empty loop. Unlink the old loop and connect the new one.
    createEmptyLoop();
    // Widen each instruction in the old loop to a new one in the new loop.
    // Use the Legality module to find the induction and reduction variables.
    vectorizeLoop();
    // Register the new loop and update the analysis passes.
    updateAnalysis();
  }

  // Return true if any runtime check is added.
  bool IsSafetyChecksAdded() {
    return AddedSafetyChecks;
  }

  virtual ~InnerLoopVectorizer() {}

protected:
  /// A small list of PHINodes.
  typedef SmallVector<PHINode*, 4> PhiVector;
  /// When we unroll loops we have multiple vector values for each scalar.
  /// This data structure holds the unrolled and vectorized values that
  /// originated from one scalar instruction.
  typedef SmallVector<Value*, 2> VectorParts;

  // When we if-convert we need to create edge masks. We have to cache values
  // so that we don't end up with exponential recursion/IR.
  typedef DenseMap<std::pair<BasicBlock*, BasicBlock*>,
                   VectorParts> EdgeMaskCache;

  /// \brief Add checks for strides that were assumed to be 1.
  ///
  /// Returns the last check instruction and the first check instruction in the
  /// pair as (first, last).
  std::pair<Instruction *, Instruction *> addStrideCheck(Instruction *Loc);

  /// Create an empty loop, based on the loop ranges of the old loop.
  void createEmptyLoop();
  /// Create a new induction variable inside L.
  PHINode *createInductionVariable(Loop *L, Value *Start, Value *End,
                                   Value *Step, Instruction *DL);
  /// Copy and widen the instructions from the old loop.
  virtual void vectorizeLoop();

  /// \brief The Loop exit block may have single value PHI nodes where the
  /// incoming value is 'Undef'. While vectorizing we only handled real values
  /// that were defined inside the loop. Here we fix the 'undef case'.
  /// See PR14725.
  void fixLCSSAPHIs();

  /// A helper function that computes the predicate of the block BB, assuming
  /// that the header block of the loop is set to True. It returns the *entry*
  /// mask for the block BB.
  VectorParts createBlockInMask(BasicBlock *BB);
  /// A helper function that computes the predicate of the edge between SRC
  /// and DST.
  VectorParts createEdgeMask(BasicBlock *Src, BasicBlock *Dst);

  /// A helper function to vectorize a single BB within the innermost loop.
  void vectorizeBlockInLoop(BasicBlock *BB, PhiVector *PV);

  /// Vectorize a single PHINode in a block. This method handles the induction
  /// variable canonicalization. It supports both VF = 1 for unrolled loops and
  /// arbitrary length vectors.
  void widenPHIInstruction(Instruction *PN, VectorParts &Entry,
                           unsigned UF, unsigned VF, PhiVector *PV);

  /// Insert the new loop to the loop hierarchy and pass manager
  /// and update the analysis passes.
  void updateAnalysis();

  /// This instruction is un-vectorizable. Implement it as a sequence
  /// of scalars. If \p IfPredicateStore is true we need to 'hide' each
  /// scalarized instruction behind an if block predicated on the control
  /// dependence of the instruction.
  virtual void scalarizeInstruction(Instruction *Instr,
                                    bool IfPredicateStore=false);

  /// Vectorize Load and Store instructions,
  virtual void vectorizeMemoryInstruction(Instruction *Instr);

  /// Create a broadcast instruction. This method generates a broadcast
  /// instruction (shuffle) for loop invariant values and for the induction
  /// value. If this is the induction variable then we extend it to N, N+1, ...
  /// this is needed because each iteration in the loop corresponds to a SIMD
  /// element.
  virtual Value *getBroadcastInstrs(Value *V);

  /// This function adds (StartIdx, StartIdx + Step, StartIdx + 2*Step, ...)
  /// to each vector element of Val. The sequence starts at StartIndex.
  virtual Value *getStepVector(Value *Val, int StartIdx, Value *Step);

  /// When we go over instructions in the basic block we rely on previous
  /// values within the current basic block or on loop invariant values.
  /// When we widen (vectorize) values we place them in the map. If the values
  /// are not within the map, they have to be loop invariant, so we simply
  /// broadcast them into a vector.
  VectorParts &getVectorValue(Value *V);

  /// Try to vectorize the interleaved access group that \p Instr belongs to.
  void vectorizeInterleaveGroup(Instruction *Instr);

  /// Generate a shuffle sequence that will reverse the vector Vec.
  virtual Value *reverseVector(Value *Vec);

  /// Returns (and creates if needed) the original loop trip count.
  Value *getOrCreateTripCount(Loop *NewLoop);

  /// Returns (and creates if needed) the trip count of the widened loop.
  Value *getOrCreateVectorTripCount(Loop *NewLoop);

  /// Emit a bypass check to see if the trip count would overflow, or we
  /// wouldn't have enough iterations to execute one vector loop.
  void emitMinimumIterationCountCheck(Loop *L, BasicBlock *Bypass);
  /// Emit a bypass check to see if the vector trip count is nonzero.
  void emitVectorLoopEnteredCheck(Loop *L, BasicBlock *Bypass);
  /// Emit bypass checks to check if strides we've assumed to be one really are.
  void emitStrideChecks(Loop *L, BasicBlock *Bypass);
  /// Emit bypass checks to check any memory assumptions we may have made.
  void emitMemRuntimeChecks(Loop *L, BasicBlock *Bypass);
  
  /// This is a helper class that holds the vectorizer state. It maps scalar
  /// instructions to vector instructions. When the code is 'unrolled' then
  /// then a single scalar value is mapped to multiple vector parts. The parts
  /// are stored in the VectorPart type.
  struct ValueMap {
    /// C'tor.  UnrollFactor controls the number of vectors ('parts') that
    /// are mapped.
    ValueMap(unsigned UnrollFactor) : UF(UnrollFactor) {}

    /// \return True if 'Key' is saved in the Value Map.
    bool has(Value *Key) const { return MapStorage.count(Key); }

    /// Initializes a new entry in the map. Sets all of the vector parts to the
    /// save value in 'Val'.
    /// \return A reference to a vector with splat values.
    VectorParts &splat(Value *Key, Value *Val) {
      VectorParts &Entry = MapStorage[Key];
      Entry.assign(UF, Val);
      return Entry;
    }

    ///\return A reference to the value that is stored at 'Key'.
    VectorParts &get(Value *Key) {
      VectorParts &Entry = MapStorage[Key];
      if (Entry.empty())
        Entry.resize(UF);
      assert(Entry.size() == UF);
      return Entry;
    }

  private:
    /// The unroll factor. Each entry in the map stores this number of vector
    /// elements.
    unsigned UF;

    /// Map storage. We use std::map and not DenseMap because insertions to a
    /// dense map invalidates its iterators.
    std::map<Value *, VectorParts> MapStorage;
  };

  /// The original loop.
  Loop *OrigLoop;
  /// Scev analysis to use.
  ScalarEvolution *SE;
  /// Loop Info.
  LoopInfo *LI;
  /// Dominator Tree.
  DominatorTree *DT;
  /// Alias Analysis.
  AliasAnalysis *AA;
  /// Target Library Info.
  const TargetLibraryInfo *TLI;
  /// Target Transform Info.
  const TargetTransformInfo *TTI;

  /// The vectorization SIMD factor to use. Each vector will have this many
  /// vector elements.
  unsigned VF;

protected:
  /// The vectorization unroll factor to use. Each scalar is vectorized to this
  /// many different vector instructions.
  unsigned UF;

  /// The builder that we use
  IRBuilder<> Builder;

  // --- Vectorization state ---

  /// The vector-loop preheader.
  BasicBlock *LoopVectorPreHeader;
  /// The scalar-loop preheader.
  BasicBlock *LoopScalarPreHeader;
  /// Middle Block between the vector and the scalar.
  BasicBlock *LoopMiddleBlock;
  ///The ExitBlock of the scalar loop.
  BasicBlock *LoopExitBlock;
  ///The vector loop body.
  SmallVector<BasicBlock *, 4> LoopVectorBody;
  ///The scalar loop body.
  BasicBlock *LoopScalarBody;
  /// A list of all bypass blocks. The first block is the entry of the loop.
  SmallVector<BasicBlock *, 4> LoopBypassBlocks;

  /// The new Induction variable which was added to the new block.
  PHINode *Induction;
  /// The induction variable of the old basic block.
  PHINode *OldInduction;
  /// Maps scalars to widened vectors.
  ValueMap WidenMap;
  EdgeMaskCache MaskCache;
  /// Trip count of the original loop.
  Value *TripCount;
  /// Trip count of the widened loop (TripCount - TripCount % (VF*UF))
  Value *VectorTripCount;

  LoopVectorizationLegality *Legal;

  // Record whether runtime check is added.
  bool AddedSafetyChecks;
};

class InnerLoopUnroller : public InnerLoopVectorizer {
public:
  InnerLoopUnroller(Loop *OrigLoop, ScalarEvolution *SE, LoopInfo *LI,
                    DominatorTree *DT, const TargetLibraryInfo *TLI,
                    const TargetTransformInfo *TTI, unsigned UnrollFactor)
      : InnerLoopVectorizer(OrigLoop, SE, LI, DT, TLI, TTI, 1, UnrollFactor) {}

private:
  void scalarizeInstruction(Instruction *Instr,
                            bool IfPredicateStore = false) override;
  void vectorizeMemoryInstruction(Instruction *Instr) override;
  Value *getBroadcastInstrs(Value *V) override;
  Value *getStepVector(Value *Val, int StartIdx, Value *Step) override;
  Value *reverseVector(Value *Vec) override;
};

/// \brief Look for a meaningful debug location on the instruction or it's
/// operands.
static Instruction *getDebugLocFromInstOrOperands(Instruction *I) {
  if (!I)
    return I;

  DebugLoc Empty;
  if (I->getDebugLoc() != Empty)
    return I;

  for (User::op_iterator OI = I->op_begin(), OE = I->op_end(); OI != OE; ++OI) {
    if (Instruction *OpInst = dyn_cast<Instruction>(*OI))
      if (OpInst->getDebugLoc() != Empty)
        return OpInst;
  }

  return I;
}

/// \brief Set the debug location in the builder using the debug location in the
/// instruction.
static void setDebugLocFromInst(IRBuilder<> &B, const Value *Ptr) {
  if (const Instruction *Inst = dyn_cast_or_null<Instruction>(Ptr))
    B.SetCurrentDebugLocation(Inst->getDebugLoc());
  else
    B.SetCurrentDebugLocation(DebugLoc());
}

#ifndef NDEBUG
/// \return string containing a file name and a line # for the given loop.
static std::string getDebugLocString(const Loop *L) {
  std::string Result;
  if (L) {
    raw_string_ostream OS(Result);
    if (const DebugLoc LoopDbgLoc = L->getStartLoc())
      LoopDbgLoc.print(OS);
    else
      // Just print the module name.
      OS << L->getHeader()->getParent()->getParent()->getModuleIdentifier();
    OS.flush();
  }
  return Result;
}
#endif

/// \brief Propagate known metadata from one instruction to another.
static void propagateMetadata(Instruction *To, const Instruction *From) {
  SmallVector<std::pair<unsigned, MDNode *>, 4> Metadata;
  From->getAllMetadataOtherThanDebugLoc(Metadata);

  for (auto M : Metadata) {
    unsigned Kind = M.first;

    // These are safe to transfer (this is safe for TBAA, even when we
    // if-convert, because should that metadata have had a control dependency
    // on the condition, and thus actually aliased with some other
    // non-speculated memory access when the condition was false, this would be
    // caught by the runtime overlap checks).
    if (Kind != LLVMContext::MD_tbaa &&
        Kind != LLVMContext::MD_alias_scope &&
        Kind != LLVMContext::MD_noalias &&
        Kind != LLVMContext::MD_fpmath &&
        Kind != LLVMContext::MD_nontemporal)
      continue;

    To->setMetadata(Kind, M.second);
  }
}

/// \brief Propagate known metadata from one instruction to a vector of others.
static void propagateMetadata(SmallVectorImpl<Value *> &To, const Instruction *From) {
  for (Value *V : To)
    if (Instruction *I = dyn_cast<Instruction>(V))
      propagateMetadata(I, From);
}

/// \brief The group of interleaved loads/stores sharing the same stride and
/// close to each other.
///
/// Each member in this group has an index starting from 0, and the largest
/// index should be less than interleaved factor, which is equal to the absolute
/// value of the access's stride.
///
/// E.g. An interleaved load group of factor 4:
///        for (unsigned i = 0; i < 1024; i+=4) {
///          a = A[i];                           // Member of index 0
///          b = A[i+1];                         // Member of index 1
///          d = A[i+3];                         // Member of index 3
///          ...
///        }
///
///      An interleaved store group of factor 4:
///        for (unsigned i = 0; i < 1024; i+=4) {
///          ...
///          A[i]   = a;                         // Member of index 0
///          A[i+1] = b;                         // Member of index 1
///          A[i+2] = c;                         // Member of index 2
///          A[i+3] = d;                         // Member of index 3
///        }
///
/// Note: the interleaved load group could have gaps (missing members), but
/// the interleaved store group doesn't allow gaps.
class InterleaveGroup {
public:
  InterleaveGroup(Instruction *Instr, int Stride, unsigned Align)
      : Align(Align), SmallestKey(0), LargestKey(0), InsertPos(Instr) {
    assert(Align && "The alignment should be non-zero");

    Factor = std::abs(Stride);
    assert(Factor > 1 && "Invalid interleave factor");

    Reverse = Stride < 0;
    Members[0] = Instr;
  }

  bool isReverse() const { return Reverse; }
  unsigned getFactor() const { return Factor; }
  unsigned getAlignment() const { return Align; }
  unsigned getNumMembers() const { return Members.size(); }

  /// \brief Try to insert a new member \p Instr with index \p Index and
  /// alignment \p NewAlign. The index is related to the leader and it could be
  /// negative if it is the new leader.
  ///
  /// \returns false if the instruction doesn't belong to the group.
  bool insertMember(Instruction *Instr, int Index, unsigned NewAlign) {
    assert(NewAlign && "The new member's alignment should be non-zero");

    int Key = Index + SmallestKey;

    // Skip if there is already a member with the same index.
    if (Members.count(Key))
      return false;

    if (Key > LargestKey) {
      // The largest index is always less than the interleave factor.
      if (Index >= static_cast<int>(Factor))
        return false;

      LargestKey = Key;
    } else if (Key < SmallestKey) {
      // The largest index is always less than the interleave factor.
      if (LargestKey - Key >= static_cast<int>(Factor))
        return false;

      SmallestKey = Key;
    }

    // It's always safe to select the minimum alignment.
    Align = std::min(Align, NewAlign);
    Members[Key] = Instr;
    return true;
  }

  /// \brief Get the member with the given index \p Index
  ///
  /// \returns nullptr if contains no such member.
  Instruction *getMember(unsigned Index) const {
    int Key = SmallestKey + Index;
    if (!Members.count(Key))
      return nullptr;

    return Members.find(Key)->second;
  }

  /// \brief Get the index for the given member. Unlike the key in the member
  /// map, the index starts from 0.
  unsigned getIndex(Instruction *Instr) const {
    for (auto I : Members)
      if (I.second == Instr)
        return I.first - SmallestKey;

    llvm_unreachable("InterleaveGroup contains no such member");
  }

  Instruction *getInsertPos() const { return InsertPos; }
  void setInsertPos(Instruction *Inst) { InsertPos = Inst; }

private:
  unsigned Factor; // Interleave Factor.
  bool Reverse;
  unsigned Align;
  DenseMap<int, Instruction *> Members;
  int SmallestKey;
  int LargestKey;

  // To avoid breaking dependences, vectorized instructions of an interleave
  // group should be inserted at either the first load or the last store in
  // program order.
  //
  // E.g. %even = load i32             // Insert Position
  //      %add = add i32 %even         // Use of %even
  //      %odd = load i32
  //
  //      store i32 %even
  //      %odd = add i32               // Def of %odd
  //      store i32 %odd               // Insert Position
  Instruction *InsertPos;
};

/// \brief Drive the analysis of interleaved memory accesses in the loop.
///
/// Use this class to analyze interleaved accesses only when we can vectorize
/// a loop. Otherwise it's meaningless to do analysis as the vectorization
/// on interleaved accesses is unsafe.
///
/// The analysis collects interleave groups and records the relationships
/// between the member and the group in a map.
class InterleavedAccessInfo {
public:
  InterleavedAccessInfo(ScalarEvolution *SE, Loop *L, DominatorTree *DT)
      : SE(SE), TheLoop(L), DT(DT) {}

  ~InterleavedAccessInfo() {
    SmallSet<InterleaveGroup *, 4> DelSet;
    // Avoid releasing a pointer twice.
    for (auto &I : InterleaveGroupMap)
      DelSet.insert(I.second);
    for (auto *Ptr : DelSet)
      delete Ptr;
  }

  /// \brief Analyze the interleaved accesses and collect them in interleave
  /// groups. Substitute symbolic strides using \p Strides.
  void analyzeInterleaving(const ValueToValueMap &Strides);

  /// \brief Check if \p Instr belongs to any interleave group.
  bool isInterleaved(Instruction *Instr) const {
    return InterleaveGroupMap.count(Instr);
  }

  /// \brief Get the interleave group that \p Instr belongs to.
  ///
  /// \returns nullptr if doesn't have such group.
  InterleaveGroup *getInterleaveGroup(Instruction *Instr) const {
    if (InterleaveGroupMap.count(Instr))
      return InterleaveGroupMap.find(Instr)->second;
    return nullptr;
  }

private:
  ScalarEvolution *SE;
  Loop *TheLoop;
  DominatorTree *DT;

  /// Holds the relationships between the members and the interleave group.
  DenseMap<Instruction *, InterleaveGroup *> InterleaveGroupMap;

  /// \brief The descriptor for a strided memory access.
  struct StrideDescriptor {
    StrideDescriptor(int Stride, const SCEV *Scev, unsigned Size,
                     unsigned Align)
        : Stride(Stride), Scev(Scev), Size(Size), Align(Align) {}

    StrideDescriptor() : Stride(0), Scev(nullptr), Size(0), Align(0) {}

    int Stride; // The access's stride. It is negative for a reverse access.
    const SCEV *Scev; // The scalar expression of this access
    unsigned Size;    // The size of the memory object.
    unsigned Align;   // The alignment of this access.
  };

  /// \brief Create a new interleave group with the given instruction \p Instr,
  /// stride \p Stride and alignment \p Align.
  ///
  /// \returns the newly created interleave group.
  InterleaveGroup *createInterleaveGroup(Instruction *Instr, int Stride,
                                         unsigned Align) {
    assert(!InterleaveGroupMap.count(Instr) &&
           "Already in an interleaved access group");
    InterleaveGroupMap[Instr] = new InterleaveGroup(Instr, Stride, Align);
    return InterleaveGroupMap[Instr];
  }

  /// \brief Release the group and remove all the relationships.
  void releaseGroup(InterleaveGroup *Group) {
    for (unsigned i = 0; i < Group->getFactor(); i++)
      if (Instruction *Member = Group->getMember(i))
        InterleaveGroupMap.erase(Member);

    delete Group;
  }

  /// \brief Collect all the accesses with a constant stride in program order.
  void collectConstStridedAccesses(
      MapVector<Instruction *, StrideDescriptor> &StrideAccesses,
      const ValueToValueMap &Strides);
};

/// Utility class for getting and setting loop vectorizer hints in the form
/// of loop metadata.
/// This class keeps a number of loop annotations locally (as member variables)
/// and can, upon request, write them back as metadata on the loop. It will
/// initially scan the loop for existing metadata, and will update the local
/// values based on information in the loop.
/// We cannot write all values to metadata, as the mere presence of some info,
/// for example 'force', means a decision has been made. So, we need to be
/// careful NOT to add them if the user hasn't specifically asked so.
class LoopVectorizeHints {
  enum HintKind {
    HK_WIDTH,
    HK_UNROLL,
    HK_FORCE
  };

  /// Hint - associates name and validation with the hint value.
  struct Hint {
    const char * Name;
    unsigned Value; // This may have to change for non-numeric values.
    HintKind Kind;

    Hint(const char * Name, unsigned Value, HintKind Kind)
      : Name(Name), Value(Value), Kind(Kind) { }

    bool validate(unsigned Val) {
      switch (Kind) {
      case HK_WIDTH:
        return isPowerOf2_32(Val) && Val <= VectorizerParams::MaxVectorWidth;
      case HK_UNROLL:
        return isPowerOf2_32(Val) && Val <= MaxInterleaveFactor;
      case HK_FORCE:
        return (Val <= 1);
      }
      return false;
    }
  };

  /// Vectorization width.
  Hint Width;
  /// Vectorization interleave factor.
  Hint Interleave;
  /// Vectorization forced
  Hint Force;

  /// Return the loop metadata prefix.
  static StringRef Prefix() { return "llvm.loop."; }

public:
  enum ForceKind {
    FK_Undefined = -1, ///< Not selected.
    FK_Disabled = 0,   ///< Forcing disabled.
    FK_Enabled = 1,    ///< Forcing enabled.
  };

  LoopVectorizeHints(const Loop *L, bool DisableInterleaving)
      : Width("vectorize.width", VectorizerParams::VectorizationFactor,
              HK_WIDTH),
        Interleave("interleave.count", DisableInterleaving, HK_UNROLL),
        Force("vectorize.enable", FK_Undefined, HK_FORCE),
        TheLoop(L) {
    // Populate values with existing loop metadata.
    getHintsFromMetadata();

    // force-vector-interleave overrides DisableInterleaving.
    if (VectorizerParams::isInterleaveForced())
      Interleave.Value = VectorizerParams::VectorizationInterleave;

    DEBUG(if (DisableInterleaving && Interleave.Value == 1) dbgs()
          << "LV: Interleaving disabled by the pass manager\n");
  }

  /// Mark the loop L as already vectorized by setting the width to 1.
  void setAlreadyVectorized() {
    Width.Value = Interleave.Value = 1;
    Hint Hints[] = {Width, Interleave};
    writeHintsToMetadata(Hints);
  }

  bool allowVectorization(Function *F, Loop *L, bool AlwaysVectorize) const {
    if (getForce() == LoopVectorizeHints::FK_Disabled) {
      DEBUG(dbgs() << "LV: Not vectorizing: #pragma vectorize disable.\n");
      emitOptimizationRemarkAnalysis(F->getContext(),
                                     vectorizeAnalysisPassName(), *F,
                                     L->getStartLoc(), emitRemark());
      return false;
    }

    if (!AlwaysVectorize && getForce() != LoopVectorizeHints::FK_Enabled) {
      DEBUG(dbgs() << "LV: Not vectorizing: No #pragma vectorize enable.\n");
      emitOptimizationRemarkAnalysis(F->getContext(),
                                     vectorizeAnalysisPassName(), *F,
                                     L->getStartLoc(), emitRemark());
      return false;
    }

    if (getWidth() == 1 && getInterleave() == 1) {
      // FIXME: Add a separate metadata to indicate when the loop has already
      // been vectorized instead of setting width and count to 1.
      DEBUG(dbgs() << "LV: Not vectorizing: Disabled/already vectorized.\n");
      // FIXME: Add interleave.disable metadata. This will allow
      // vectorize.disable to be used without disabling the pass and errors
      // to differentiate between disabled vectorization and a width of 1.
      emitOptimizationRemarkAnalysis(
          F->getContext(), vectorizeAnalysisPassName(), *F, L->getStartLoc(),
          "loop not vectorized: vectorization and interleaving are explicitly "
          "disabled, or vectorize width and interleave count are both set to "
          "1");
      return false;
    }

    return true;
  }

  /// Dumps all the hint information.
  std::string emitRemark() const {
    VectorizationReport R;
    if (Force.Value == LoopVectorizeHints::FK_Disabled)
      R << "vectorization is explicitly disabled";
    else {
      R << "use -Rpass-analysis=loop-vectorize for more info";
      if (Force.Value == LoopVectorizeHints::FK_Enabled) {
        R << " (Force=true";
        if (Width.Value != 0)
          R << ", Vector Width=" << Width.Value;
        if (Interleave.Value != 0)
          R << ", Interleave Count=" << Interleave.Value;
        R << ")";
      }
    }

    return R.str();
  }

  unsigned getWidth() const { return Width.Value; }
  unsigned getInterleave() const { return Interleave.Value; }
  enum ForceKind getForce() const { return (ForceKind)Force.Value; }
  const char *vectorizeAnalysisPassName() const {
    // If hints are provided that don't disable vectorization use the
    // AlwaysPrint pass name to force the frontend to print the diagnostic.
    if (getWidth() == 1)
      return LV_NAME;
    if (getForce() == LoopVectorizeHints::FK_Disabled)
      return LV_NAME;
    if (getForce() == LoopVectorizeHints::FK_Undefined && getWidth() == 0)
      return LV_NAME;
    return DiagnosticInfo::AlwaysPrint;
  }

  bool allowReordering() const {
    // When enabling loop hints are provided we allow the vectorizer to change
    // the order of operations that is given by the scalar loop. This is not
    // enabled by default because can be unsafe or inefficient. For example,
    // reordering floating-point operations will change the way round-off
    // error accumulates in the loop.
    return getForce() == LoopVectorizeHints::FK_Enabled || getWidth() > 1;
  }

private:
  /// Find hints specified in the loop metadata and update local values.
  void getHintsFromMetadata() {
    MDNode *LoopID = TheLoop->getLoopID();
    if (!LoopID)
      return;

    // First operand should refer to the loop id itself.
    assert(LoopID->getNumOperands() > 0 && "requires at least one operand");
    assert(LoopID->getOperand(0) == LoopID && "invalid loop id");

    for (unsigned i = 1, ie = LoopID->getNumOperands(); i < ie; ++i) {
      const MDString *S = nullptr;
      SmallVector<Metadata *, 4> Args;

      // The expected hint is either a MDString or a MDNode with the first
      // operand a MDString.
      if (const MDNode *MD = dyn_cast<MDNode>(LoopID->getOperand(i))) {
        if (!MD || MD->getNumOperands() == 0)
          continue;
        S = dyn_cast<MDString>(MD->getOperand(0));
        for (unsigned i = 1, ie = MD->getNumOperands(); i < ie; ++i)
          Args.push_back(MD->getOperand(i));
      } else {
        S = dyn_cast<MDString>(LoopID->getOperand(i));
        assert(Args.size() == 0 && "too many arguments for MDString");
      }

      if (!S)
        continue;

      // Check if the hint starts with the loop metadata prefix.
      StringRef Name = S->getString();
      if (Args.size() == 1)
        setHint(Name, Args[0]);
    }
  }

  /// Checks string hint with one operand and set value if valid.
  void setHint(StringRef Name, Metadata *Arg) {
    if (!Name.startswith(Prefix()))
      return;
    Name = Name.substr(Prefix().size(), StringRef::npos);

    const ConstantInt *C = mdconst::dyn_extract<ConstantInt>(Arg);
    if (!C) return;
    unsigned Val = C->getZExtValue();

    Hint *Hints[] = {&Width, &Interleave, &Force};
    for (auto H : Hints) {
      if (Name == H->Name) {
        if (H->validate(Val))
          H->Value = Val;
        else
          DEBUG(dbgs() << "LV: ignoring invalid hint '" << Name << "'\n");
        break;
      }
    }
  }

  /// Create a new hint from name / value pair.
  MDNode *createHintMetadata(StringRef Name, unsigned V) const {
    LLVMContext &Context = TheLoop->getHeader()->getContext();
    Metadata *MDs[] = {MDString::get(Context, Name),
                       ConstantAsMetadata::get(
                           ConstantInt::get(Type::getInt32Ty(Context), V))};
    return MDNode::get(Context, MDs);
  }

  /// Matches metadata with hint name.
  bool matchesHintMetadataName(MDNode *Node, ArrayRef<Hint> HintTypes) {
    MDString* Name = dyn_cast<MDString>(Node->getOperand(0));
    if (!Name)
      return false;

    for (auto H : HintTypes)
      if (Name->getString().endswith(H.Name))
        return true;
    return false;
  }

  /// Sets current hints into loop metadata, keeping other values intact.
  void writeHintsToMetadata(ArrayRef<Hint> HintTypes) {
    if (HintTypes.size() == 0)
      return;

    // Reserve the first element to LoopID (see below).
    SmallVector<Metadata *, 4> MDs(1);
    // If the loop already has metadata, then ignore the existing operands.
    MDNode *LoopID = TheLoop->getLoopID();
    if (LoopID) {
      for (unsigned i = 1, ie = LoopID->getNumOperands(); i < ie; ++i) {
        MDNode *Node = cast<MDNode>(LoopID->getOperand(i));
        // If node in update list, ignore old value.
        if (!matchesHintMetadataName(Node, HintTypes))
          MDs.push_back(Node);
      }
    }

    // Now, add the missing hints.
    for (auto H : HintTypes)
      MDs.push_back(createHintMetadata(Twine(Prefix(), H.Name).str(), H.Value));

    // Replace current metadata node with new one.
    LLVMContext &Context = TheLoop->getHeader()->getContext();
    MDNode *NewLoopID = MDNode::get(Context, MDs);
    // Set operand 0 to refer to the loop id itself.
    NewLoopID->replaceOperandWith(0, NewLoopID);

    TheLoop->setLoopID(NewLoopID);
  }

  /// The loop these hints belong to.
  const Loop *TheLoop;
};

static void emitAnalysisDiag(const Function *TheFunction, const Loop *TheLoop,
                             const LoopVectorizeHints &Hints,
                             const LoopAccessReport &Message) {
  const char *Name = Hints.vectorizeAnalysisPassName();
  LoopAccessReport::emitAnalysis(Message, TheFunction, TheLoop, Name);
}

static void emitMissedWarning(Function *F, Loop *L,
                              const LoopVectorizeHints &LH) {
  emitOptimizationRemarkMissed(F->getContext(), LV_NAME, *F, L->getStartLoc(),
                               LH.emitRemark());

  if (LH.getForce() == LoopVectorizeHints::FK_Enabled) {
    if (LH.getWidth() != 1)
      emitLoopVectorizeWarning(
          F->getContext(), *F, L->getStartLoc(),
          "failed explicitly specified loop vectorization");
    else if (LH.getInterleave() != 1)
      emitLoopInterleaveWarning(
          F->getContext(), *F, L->getStartLoc(),
          "failed explicitly specified loop interleaving");
  }
}

/// LoopVectorizationLegality checks if it is legal to vectorize a loop, and
/// to what vectorization factor.
/// This class does not look at the profitability of vectorization, only the
/// legality. This class has two main kinds of checks:
/// * Memory checks - The code in canVectorizeMemory checks if vectorization
///   will change the order of memory accesses in a way that will change the
///   correctness of the program.
/// * Scalars checks - The code in canVectorizeInstrs and canVectorizeMemory
/// checks for a number of different conditions, such as the availability of a
/// single induction variable, that all types are supported and vectorize-able,
/// etc. This code reflects the capabilities of InnerLoopVectorizer.
/// This class is also used by InnerLoopVectorizer for identifying
/// induction variable and the different reduction variables.
class LoopVectorizationLegality {
public:
  LoopVectorizationLegality(Loop *L, ScalarEvolution *SE, DominatorTree *DT,
                            TargetLibraryInfo *TLI, AliasAnalysis *AA,
                            Function *F, const TargetTransformInfo *TTI,
                            LoopAccessAnalysis *LAA,
                            LoopVectorizationRequirements *R,
                            const LoopVectorizeHints *H)
      : NumPredStores(0), TheLoop(L), SE(SE), TLI(TLI), TheFunction(F),
        TTI(TTI), DT(DT), LAA(LAA), LAI(nullptr), InterleaveInfo(SE, L, DT),
        Induction(nullptr), WidestIndTy(nullptr), HasFunNoNaNAttr(false),
        Requirements(R), Hints(H) {}

  /// ReductionList contains the reduction descriptors for all
  /// of the reductions that were found in the loop.
  typedef DenseMap<PHINode *, RecurrenceDescriptor> ReductionList;

  /// InductionList saves induction variables and maps them to the
  /// induction descriptor.
  typedef MapVector<PHINode*, InductionDescriptor> InductionList;

  /// Returns true if it is legal to vectorize this loop.
  /// This does not mean that it is profitable to vectorize this
  /// loop, only that it is legal to do so.
  bool canVectorize();

  /// Returns the Induction variable.
  PHINode *getInduction() { return Induction; }

  /// Returns the reduction variables found in the loop.
  ReductionList *getReductionVars() { return &Reductions; }

  /// Returns the induction variables found in the loop.
  InductionList *getInductionVars() { return &Inductions; }

  /// Returns the widest induction type.
  Type *getWidestInductionType() { return WidestIndTy; }

  /// Returns True if V is an induction variable in this loop.
  bool isInductionVariable(const Value *V);

  /// Return true if the block BB needs to be predicated in order for the loop
  /// to be vectorized.
  bool blockNeedsPredication(BasicBlock *BB);

  /// Check if this  pointer is consecutive when vectorizing. This happens
  /// when the last index of the GEP is the induction variable, or that the
  /// pointer itself is an induction variable.
  /// This check allows us to vectorize A[idx] into a wide load/store.
  /// Returns:
  /// 0 - Stride is unknown or non-consecutive.
  /// 1 - Address is consecutive.
  /// -1 - Address is consecutive, and decreasing.
  int isConsecutivePtr(Value *Ptr);

  /// Returns true if the value V is uniform within the loop.
  bool isUniform(Value *V);

  /// Returns true if this instruction will remain scalar after vectorization.
  bool isUniformAfterVectorization(Instruction* I) { return Uniforms.count(I); }

  /// Returns the information that we collected about runtime memory check.
  const RuntimePointerChecking *getRuntimePointerChecking() const {
    return LAI->getRuntimePointerChecking();
  }

  const LoopAccessInfo *getLAI() const {
    return LAI;
  }

  /// \brief Check if \p Instr belongs to any interleaved access group.
  bool isAccessInterleaved(Instruction *Instr) {
    return InterleaveInfo.isInterleaved(Instr);
  }

  /// \brief Get the interleaved access group that \p Instr belongs to.
  const InterleaveGroup *getInterleavedAccessGroup(Instruction *Instr) {
    return InterleaveInfo.getInterleaveGroup(Instr);
  }

  unsigned getMaxSafeDepDistBytes() { return LAI->getMaxSafeDepDistBytes(); }

  bool hasStride(Value *V) { return StrideSet.count(V); }
  bool mustCheckStrides() { return !StrideSet.empty(); }
  SmallPtrSet<Value *, 8>::iterator strides_begin() {
    return StrideSet.begin();
  }
  SmallPtrSet<Value *, 8>::iterator strides_end() { return StrideSet.end(); }

  /// Returns true if the target machine supports masked store operation
  /// for the given \p DataType and kind of access to \p Ptr.
  bool isLegalMaskedStore(Type *DataType, Value *Ptr) {
    return TTI->isLegalMaskedStore(DataType, isConsecutivePtr(Ptr));
  }
  /// Returns true if the target machine supports masked load operation
  /// for the given \p DataType and kind of access to \p Ptr.
  bool isLegalMaskedLoad(Type *DataType, Value *Ptr) {
    return TTI->isLegalMaskedLoad(DataType, isConsecutivePtr(Ptr));
  }
  /// Returns true if vector representation of the instruction \p I
  /// requires mask.
  bool isMaskRequired(const Instruction* I) {
    return (MaskedOp.count(I) != 0);
  }
  unsigned getNumStores() const {
    return LAI->getNumStores();
  }
  unsigned getNumLoads() const {
    return LAI->getNumLoads();
  }
  unsigned getNumPredStores() const {
    return NumPredStores;
  }
private:
  /// Check if a single basic block loop is vectorizable.
  /// At this point we know that this is a loop with a constant trip count
  /// and we only need to check individual instructions.
  bool canVectorizeInstrs();

  /// When we vectorize loops we may change the order in which
  /// we read and write from memory. This method checks if it is
  /// legal to vectorize the code, considering only memory constrains.
  /// Returns true if the loop is vectorizable
  bool canVectorizeMemory();

  /// Return true if we can vectorize this loop using the IF-conversion
  /// transformation.
  bool canVectorizeWithIfConvert();

  /// Collect the variables that need to stay uniform after vectorization.
  void collectLoopUniforms();

  /// Return true if all of the instructions in the block can be speculatively
  /// executed. \p SafePtrs is a list of addresses that are known to be legal
  /// and we know that we can read from them without segfault.
  bool blockCanBePredicated(BasicBlock *BB, SmallPtrSetImpl<Value *> &SafePtrs);

  /// \brief Collect memory access with loop invariant strides.
  ///
  /// Looks for accesses like "a[i * StrideA]" where "StrideA" is loop
  /// invariant.
  void collectStridedAccess(Value *LoadOrStoreInst);

  /// Report an analysis message to assist the user in diagnosing loops that are
  /// not vectorized.  These are handled as LoopAccessReport rather than
  /// VectorizationReport because the << operator of VectorizationReport returns
  /// LoopAccessReport.
  void emitAnalysis(const LoopAccessReport &Message) const {
    emitAnalysisDiag(TheFunction, TheLoop, *Hints, Message);
  }

  unsigned NumPredStores;

  /// The loop that we evaluate.
  Loop *TheLoop;
  /// Scev analysis.
  ScalarEvolution *SE;
  /// Target Library Info.
  TargetLibraryInfo *TLI;
  /// Parent function
  Function *TheFunction;
  /// Target Transform Info
  const TargetTransformInfo *TTI;
  /// Dominator Tree.
  DominatorTree *DT;
  // LoopAccess analysis.
  LoopAccessAnalysis *LAA;
  // And the loop-accesses info corresponding to this loop.  This pointer is
  // null until canVectorizeMemory sets it up.
  const LoopAccessInfo *LAI;

  /// The interleave access information contains groups of interleaved accesses
  /// with the same stride and close to each other.
  InterleavedAccessInfo InterleaveInfo;

  //  ---  vectorization state --- //

  /// Holds the integer induction variable. This is the counter of the
  /// loop.
  PHINode *Induction;
  /// Holds the reduction variables.
  ReductionList Reductions;
  /// Holds all of the induction variables that we found in the loop.
  /// Notice that inductions don't need to start at zero and that induction
  /// variables can be pointers.
  InductionList Inductions;
  /// Holds the widest induction type encountered.
  Type *WidestIndTy;

  /// Allowed outside users. This holds the reduction
  /// vars which can be accessed from outside the loop.
  SmallPtrSet<Value*, 4> AllowedExit;
  /// This set holds the variables which are known to be uniform after
  /// vectorization.
  SmallPtrSet<Instruction*, 4> Uniforms;

  /// Can we assume the absence of NaNs.
  bool HasFunNoNaNAttr;

  /// Vectorization requirements that will go through late-evaluation.
  LoopVectorizationRequirements *Requirements;

  /// Used to emit an analysis of any legality issues.
  const LoopVectorizeHints *Hints;

  ValueToValueMap Strides;
  SmallPtrSet<Value *, 8> StrideSet;

  /// While vectorizing these instructions we have to generate a
  /// call to the appropriate masked intrinsic
  SmallPtrSet<const Instruction*, 8> MaskedOp;
};

/// LoopVectorizationCostModel - estimates the expected speedups due to
/// vectorization.
/// In many cases vectorization is not profitable. This can happen because of
/// a number of reasons. In this class we mainly attempt to predict the
/// expected speedup/slowdowns due to the supported instruction set. We use the
/// TargetTransformInfo to query the different backends for the cost of
/// different operations.
class LoopVectorizationCostModel {
public:
  LoopVectorizationCostModel(Loop *L, ScalarEvolution *SE, LoopInfo *LI,
                             LoopVectorizationLegality *Legal,
                             const TargetTransformInfo &TTI,
                             const TargetLibraryInfo *TLI, AssumptionCache *AC,
                             const Function *F, const LoopVectorizeHints *Hints,
                             SmallPtrSetImpl<const Value *> &ValuesToIgnore)
      : TheLoop(L), SE(SE), LI(LI), Legal(Legal), TTI(TTI), TLI(TLI),
        TheFunction(F), Hints(Hints), ValuesToIgnore(ValuesToIgnore) {}

  /// Information about vectorization costs
  struct VectorizationFactor {
    unsigned Width; // Vector width with best cost
    unsigned Cost; // Cost of the loop with that width
  };
  /// \return The most profitable vectorization factor and the cost of that VF.
  /// This method checks every power of two up to VF. If UserVF is not ZERO
  /// then this vectorization factor will be selected if vectorization is
  /// possible.
  VectorizationFactor selectVectorizationFactor(bool OptForSize);

  /// \return The size (in bits) of the widest type in the code that
  /// needs to be vectorized. We ignore values that remain scalar such as
  /// 64 bit loop indices.
  unsigned getWidestType();

  /// \return The desired interleave count.
  /// If interleave count has been specified by metadata it will be returned.
  /// Otherwise, the interleave count is computed and returned. VF and LoopCost
  /// are the selected vectorization factor and the cost of the selected VF.
  unsigned selectInterleaveCount(bool OptForSize, unsigned VF,
                                 unsigned LoopCost);

  /// \return The most profitable unroll factor.
  /// This method finds the best unroll-factor based on register pressure and
  /// other parameters. VF and LoopCost are the selected vectorization factor
  /// and the cost of the selected VF.
  unsigned computeInterleaveCount(bool OptForSize, unsigned VF,
                                  unsigned LoopCost);

  /// \brief A struct that represents some properties of the register usage
  /// of a loop.
  struct RegisterUsage {
    /// Holds the number of loop invariant values that are used in the loop.
    unsigned LoopInvariantRegs;
    /// Holds the maximum number of concurrent live intervals in the loop.
    unsigned MaxLocalUsers;
    /// Holds the number of instructions in the loop.
    unsigned NumInstructions;
  };

  /// \return  information about the register usage of the loop.
  RegisterUsage calculateRegisterUsage();

private:
  /// Returns the expected execution cost. The unit of the cost does
  /// not matter because we use the 'cost' units to compare different
  /// vector widths. The cost that is returned is *not* normalized by
  /// the factor width.
  unsigned expectedCost(unsigned VF);

  /// Returns the execution time cost of an instruction for a given vector
  /// width. Vector width of one means scalar.
  unsigned getInstructionCost(Instruction *I, unsigned VF);

  /// Returns whether the instruction is a load or store and will be a emitted
  /// as a vector operation.
  bool isConsecutiveLoadOrStore(Instruction *I);

  /// Report an analysis message to assist the user in diagnosing loops that are
  /// not vectorized.  These are handled as LoopAccessReport rather than
  /// VectorizationReport because the << operator of VectorizationReport returns
  /// LoopAccessReport.
  void emitAnalysis(const LoopAccessReport &Message) const {
    emitAnalysisDiag(TheFunction, TheLoop, *Hints, Message);
  }

  /// The loop that we evaluate.
  Loop *TheLoop;
  /// Scev analysis.
  ScalarEvolution *SE;
  /// Loop Info analysis.
  LoopInfo *LI;
  /// Vectorization legality.
  LoopVectorizationLegality *Legal;
  /// Vector target information.
  const TargetTransformInfo &TTI;
  /// Target Library Info.
  const TargetLibraryInfo *TLI;
  const Function *TheFunction;
  // Loop Vectorize Hint.
  const LoopVectorizeHints *Hints;
  // Values to ignore in the cost model.
  const SmallPtrSetImpl<const Value *> &ValuesToIgnore;
};

/// \brief This holds vectorization requirements that must be verified late in
/// the process. The requirements are set by legalize and costmodel. Once
/// vectorization has been determined to be possible and profitable the
/// requirements can be verified by looking for metadata or compiler options.
/// For example, some loops require FP commutativity which is only allowed if
/// vectorization is explicitly specified or if the fast-math compiler option
/// has been provided.
/// Late evaluation of these requirements allows helpful diagnostics to be
/// composed that tells the user what need to be done to vectorize the loop. For
/// example, by specifying #pragma clang loop vectorize or -ffast-math. Late
/// evaluation should be used only when diagnostics can generated that can be
/// followed by a non-expert user.
class LoopVectorizationRequirements {
public:
  LoopVectorizationRequirements()
      : NumRuntimePointerChecks(0), UnsafeAlgebraInst(nullptr) {}

  void addUnsafeAlgebraInst(Instruction *I) {
    // First unsafe algebra instruction.
    if (!UnsafeAlgebraInst)
      UnsafeAlgebraInst = I;
  }

  void addRuntimePointerChecks(unsigned Num) { NumRuntimePointerChecks = Num; }

  bool doesNotMeet(Function *F, Loop *L, const LoopVectorizeHints &Hints) {
    const char *Name = Hints.vectorizeAnalysisPassName();
    bool Failed = false;
    if (UnsafeAlgebraInst && !Hints.allowReordering()) {
      emitOptimizationRemarkAnalysisFPCommute(
          F->getContext(), Name, *F, UnsafeAlgebraInst->getDebugLoc(),
          VectorizationReport() << "cannot prove it is safe to reorder "
                                   "floating-point operations");
      Failed = true;
    }

    // Test if runtime memcheck thresholds are exceeded.
    bool PragmaThresholdReached =
        NumRuntimePointerChecks > PragmaVectorizeMemoryCheckThreshold;
    bool ThresholdReached =
        NumRuntimePointerChecks > VectorizerParams::RuntimeMemoryCheckThreshold;
    if ((ThresholdReached && !Hints.allowReordering()) ||
        PragmaThresholdReached) {
      emitOptimizationRemarkAnalysisAliasing(
          F->getContext(), Name, *F, L->getStartLoc(),
          VectorizationReport()
              << "cannot prove it is safe to reorder memory operations");
      DEBUG(dbgs() << "LV: Too many memory checks needed.\n");
      Failed = true;
    }

    return Failed;
  }

private:
  unsigned NumRuntimePointerChecks;
  Instruction *UnsafeAlgebraInst;
};

static void addInnerLoop(Loop &L, SmallVectorImpl<Loop *> &V) {
  if (L.empty())
    return V.push_back(&L);

  for (Loop *InnerL : L)
    addInnerLoop(*InnerL, V);
}

/// The LoopVectorize Pass.
struct LoopVectorize : public FunctionPass {
  /// Pass identification, replacement for typeid
  static char ID;

  explicit LoopVectorize(bool NoUnrolling = false, bool AlwaysVectorize = true)
    : FunctionPass(ID),
      DisableUnrolling(NoUnrolling),
      AlwaysVectorize(AlwaysVectorize) {
    initializeLoopVectorizePass(*PassRegistry::getPassRegistry());
  }

  ScalarEvolution *SE;
  LoopInfo *LI;
  TargetTransformInfo *TTI;
  DominatorTree *DT;
  BlockFrequencyInfo *BFI;
  TargetLibraryInfo *TLI;
  AliasAnalysis *AA;
  AssumptionCache *AC;
  LoopAccessAnalysis *LAA;
  bool DisableUnrolling;
  bool AlwaysVectorize;

  BlockFrequency ColdEntryFreq;

  bool runOnFunction(Function &F) override {
    SE = &getAnalysis<ScalarEvolutionWrapperPass>().getSE();
    LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
    TTI = &getAnalysis<TargetTransformInfoWrapperPass>().getTTI(F);
    DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
    BFI = &getAnalysis<BlockFrequencyInfoWrapperPass>().getBFI();
    auto *TLIP = getAnalysisIfAvailable<TargetLibraryInfoWrapperPass>();
    TLI = TLIP ? &TLIP->getTLI() : nullptr;
    AA = &getAnalysis<AliasAnalysis>();
    AC = &getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F);
    LAA = &getAnalysis<LoopAccessAnalysis>();

    // Compute some weights outside of the loop over the loops. Compute this
    // using a BranchProbability to re-use its scaling math.
    const BranchProbability ColdProb(1, 5); // 20%
    ColdEntryFreq = BlockFrequency(BFI->getEntryFreq()) * ColdProb;

    // Don't attempt if
    // 1. the target claims to have no vector registers, and
    // 2. interleaving won't help ILP.
    //
    // The second condition is necessary because, even if the target has no
    // vector registers, loop vectorization may still enable scalar
    // interleaving.
    if (!TTI->getNumberOfRegisters(true) && TTI->getMaxInterleaveFactor(1) < 2)
      return false;

    // Build up a worklist of inner-loops to vectorize. This is necessary as
    // the act of vectorizing or partially unrolling a loop creates new loops
    // and can invalidate iterators across the loops.
    SmallVector<Loop *, 8> Worklist;

    for (Loop *L : *LI)
      addInnerLoop(*L, Worklist);

    LoopsAnalyzed += Worklist.size();

    // Now walk the identified inner loops.
    bool Changed = false;
    while (!Worklist.empty())
      Changed |= processLoop(Worklist.pop_back_val());

    // Process each loop nest in the function.
    return Changed;
  }

  static void AddRuntimeUnrollDisableMetaData(Loop *L) {
    SmallVector<Metadata *, 4> MDs;
    // Reserve first location for self reference to the LoopID metadata node.
    MDs.push_back(nullptr);
    bool IsUnrollMetadata = false;
    MDNode *LoopID = L->getLoopID();
    if (LoopID) {
      // First find existing loop unrolling disable metadata.
      for (unsigned i = 1, ie = LoopID->getNumOperands(); i < ie; ++i) {
        MDNode *MD = dyn_cast<MDNode>(LoopID->getOperand(i));
        if (MD) {
          const MDString *S = dyn_cast<MDString>(MD->getOperand(0));
          IsUnrollMetadata =
              S && S->getString().startswith("llvm.loop.unroll.disable");
        }
        MDs.push_back(LoopID->getOperand(i));
      }
    }

    if (!IsUnrollMetadata) {
      // Add runtime unroll disable metadata.
      LLVMContext &Context = L->getHeader()->getContext();
      SmallVector<Metadata *, 1> DisableOperands;
      DisableOperands.push_back(
          MDString::get(Context, "llvm.loop.unroll.runtime.disable"));
      MDNode *DisableNode = MDNode::get(Context, DisableOperands);
      MDs.push_back(DisableNode);
      MDNode *NewLoopID = MDNode::get(Context, MDs);
      // Set operand 0 to refer to the loop id itself.
      NewLoopID->replaceOperandWith(0, NewLoopID);
      L->setLoopID(NewLoopID);
    }
  }

  bool processLoop(Loop *L) {
    assert(L->empty() && "Only process inner loops.");

#ifndef NDEBUG
    const std::string DebugLocStr = getDebugLocString(L);
#endif /* NDEBUG */

    DEBUG(dbgs() << "\nLV: Checking a loop in \""
                 << L->getHeader()->getParent()->getName() << "\" from "
                 << DebugLocStr << "\n");

    LoopVectorizeHints Hints(L, DisableUnrolling);

    DEBUG(dbgs() << "LV: Loop hints:"
                 << " force="
                 << (Hints.getForce() == LoopVectorizeHints::FK_Disabled
                         ? "disabled"
                         : (Hints.getForce() == LoopVectorizeHints::FK_Enabled
                                ? "enabled"
                                : "?")) << " width=" << Hints.getWidth()
                 << " unroll=" << Hints.getInterleave() << "\n");

    // Function containing loop
    Function *F = L->getHeader()->getParent();

    // Looking at the diagnostic output is the only way to determine if a loop
    // was vectorized (other than looking at the IR or machine code), so it
    // is important to generate an optimization remark for each loop. Most of
    // these messages are generated by emitOptimizationRemarkAnalysis. Remarks
    // generated by emitOptimizationRemark and emitOptimizationRemarkMissed are
    // less verbose reporting vectorized loops and unvectorized loops that may
    // benefit from vectorization, respectively.

    if (!Hints.allowVectorization(F, L, AlwaysVectorize)) {
      DEBUG(dbgs() << "LV: Loop hints prevent vectorization.\n");
      return false;
    }

    // Check the loop for a trip count threshold:
    // do not vectorize loops with a tiny trip count.
    const unsigned TC = SE->getSmallConstantTripCount(L);
    if (TC > 0u && TC < TinyTripCountVectorThreshold) {
      DEBUG(dbgs() << "LV: Found a loop with a very small trip count. "
                   << "This loop is not worth vectorizing.");
      if (Hints.getForce() == LoopVectorizeHints::FK_Enabled)
        DEBUG(dbgs() << " But vectorizing was explicitly forced.\n");
      else {
        DEBUG(dbgs() << "\n");
        emitAnalysisDiag(F, L, Hints, VectorizationReport()
                                          << "vectorization is not beneficial "
                                             "and is not explicitly forced");
        return false;
      }
    }

    // Check if it is legal to vectorize the loop.
    LoopVectorizationRequirements Requirements;
    LoopVectorizationLegality LVL(L, SE, DT, TLI, AA, F, TTI, LAA,
                                  &Requirements, &Hints);
    if (!LVL.canVectorize()) {
      DEBUG(dbgs() << "LV: Not vectorizing: Cannot prove legality.\n");
      emitMissedWarning(F, L, Hints);
      return false;
    }

    // Collect values we want to ignore in the cost model. This includes
    // type-promoting instructions we identified during reduction detection.
    SmallPtrSet<const Value *, 32> ValuesToIgnore;
    CodeMetrics::collectEphemeralValues(L, AC, ValuesToIgnore);
    for (auto &Reduction : *LVL.getReductionVars()) {
      RecurrenceDescriptor &RedDes = Reduction.second;
      SmallPtrSetImpl<Instruction *> &Casts = RedDes.getCastInsts();
      ValuesToIgnore.insert(Casts.begin(), Casts.end());
    }

    // Use the cost model.
    LoopVectorizationCostModel CM(L, SE, LI, &LVL, *TTI, TLI, AC, F, &Hints,
                                  ValuesToIgnore);

    // Check the function attributes to find out if this function should be
    // optimized for size.
    bool OptForSize = Hints.getForce() != LoopVectorizeHints::FK_Enabled &&
                      F->optForSize();

    // Compute the weighted frequency of this loop being executed and see if it
    // is less than 20% of the function entry baseline frequency. Note that we
    // always have a canonical loop here because we think we *can* vectorize.
    // FIXME: This is hidden behind a flag due to pervasive problems with
    // exactly what block frequency models.
    if (LoopVectorizeWithBlockFrequency) {
      BlockFrequency LoopEntryFreq = BFI->getBlockFreq(L->getLoopPreheader());
      if (Hints.getForce() != LoopVectorizeHints::FK_Enabled &&
          LoopEntryFreq < ColdEntryFreq)
        OptForSize = true;
    }

    // Check the function attributes to see if implicit floats are allowed.
    // FIXME: This check doesn't seem possibly correct -- what if the loop is
    // an integer loop and the vector instructions selected are purely integer
    // vector instructions?
    if (F->hasFnAttribute(Attribute::NoImplicitFloat)) {
      DEBUG(dbgs() << "LV: Can't vectorize when the NoImplicitFloat"
            "attribute is used.\n");
      emitAnalysisDiag(
          F, L, Hints,
          VectorizationReport()
              << "loop not vectorized due to NoImplicitFloat attribute");
      emitMissedWarning(F, L, Hints);
      return false;
    }

    // Select the optimal vectorization factor.
    const LoopVectorizationCostModel::VectorizationFactor VF =
        CM.selectVectorizationFactor(OptForSize);

    // Select the interleave count.
    unsigned IC = CM.selectInterleaveCount(OptForSize, VF.Width, VF.Cost);

    // Get user interleave count.
    unsigned UserIC = Hints.getInterleave();

    // Identify the diagnostic messages that should be produced.
    std::string VecDiagMsg, IntDiagMsg;
    bool VectorizeLoop = true, InterleaveLoop = true;

    if (Requirements.doesNotMeet(F, L, Hints)) {
      DEBUG(dbgs() << "LV: Not vectorizing: loop did not meet vectorization "
                      "requirements.\n");
      emitMissedWarning(F, L, Hints);
      return false;
    }

    if (VF.Width == 1) {
      DEBUG(dbgs() << "LV: Vectorization is possible but not beneficial.\n");
      VecDiagMsg =
          "the cost-model indicates that vectorization is not beneficial";
      VectorizeLoop = false;
    }

    if (IC == 1 && UserIC <= 1) {
      // Tell the user interleaving is not beneficial.
      DEBUG(dbgs() << "LV: Interleaving is not beneficial.\n");
      IntDiagMsg =
          "the cost-model indicates that interleaving is not beneficial";
      InterleaveLoop = false;
      if (UserIC == 1)
        IntDiagMsg +=
            " and is explicitly disabled or interleave count is set to 1";
    } else if (IC > 1 && UserIC == 1) {
      // Tell the user interleaving is beneficial, but it explicitly disabled.
      DEBUG(dbgs()
            << "LV: Interleaving is beneficial but is explicitly disabled.");
      IntDiagMsg = "the cost-model indicates that interleaving is beneficial "
                   "but is explicitly disabled or interleave count is set to 1";
      InterleaveLoop = false;
    }

    // Override IC if user provided an interleave count.
    IC = UserIC > 0 ? UserIC : IC;

    // Emit diagnostic messages, if any.
    const char *VAPassName = Hints.vectorizeAnalysisPassName();
    if (!VectorizeLoop && !InterleaveLoop) {
      // Do not vectorize or interleaving the loop.
      emitOptimizationRemarkAnalysis(F->getContext(), VAPassName, *F,
                                     L->getStartLoc(), VecDiagMsg);
      emitOptimizationRemarkAnalysis(F->getContext(), LV_NAME, *F,
                                     L->getStartLoc(), IntDiagMsg);
      return false;
    } else if (!VectorizeLoop && InterleaveLoop) {
      DEBUG(dbgs() << "LV: Interleave Count is " << IC << '\n');
      emitOptimizationRemarkAnalysis(F->getContext(), VAPassName, *F,
                                     L->getStartLoc(), VecDiagMsg);
    } else if (VectorizeLoop && !InterleaveLoop) {
      DEBUG(dbgs() << "LV: Found a vectorizable loop (" << VF.Width << ") in "
                   << DebugLocStr << '\n');
      emitOptimizationRemarkAnalysis(F->getContext(), LV_NAME, *F,
                                     L->getStartLoc(), IntDiagMsg);
    } else if (VectorizeLoop && InterleaveLoop) {
      DEBUG(dbgs() << "LV: Found a vectorizable loop (" << VF.Width << ") in "
                   << DebugLocStr << '\n');
      DEBUG(dbgs() << "LV: Interleave Count is " << IC << '\n');
    }

    if (!VectorizeLoop) {
      assert(IC > 1 && "interleave count should not be 1 or 0");
      // If we decided that it is not legal to vectorize the loop then
      // interleave it.
      InnerLoopUnroller Unroller(L, SE, LI, DT, TLI, TTI, IC);
      Unroller.vectorize(&LVL);

      emitOptimizationRemark(F->getContext(), LV_NAME, *F, L->getStartLoc(),
                             Twine("interleaved loop (interleaved count: ") +
                                 Twine(IC) + ")");
    } else {
      // If we decided that it is *legal* to vectorize the loop then do it.
      InnerLoopVectorizer LB(L, SE, LI, DT, TLI, TTI, VF.Width, IC);
      LB.vectorize(&LVL);
      ++LoopsVectorized;

      // Add metadata to disable runtime unrolling scalar loop when there's no
      // runtime check about strides and memory. Because at this situation,
      // scalar loop is rarely used not worthy to be unrolled.
      if (!LB.IsSafetyChecksAdded())
        AddRuntimeUnrollDisableMetaData(L);

      // Report the vectorization decision.
      emitOptimizationRemark(F->getContext(), LV_NAME, *F, L->getStartLoc(),
                             Twine("vectorized loop (vectorization width: ") +
                                 Twine(VF.Width) + ", interleaved count: " +
                                 Twine(IC) + ")");
    }

    // Mark the loop as already vectorized to avoid vectorizing again.
    Hints.setAlreadyVectorized();

    DEBUG(verifyFunction(*L->getHeader()->getParent()));
    return true;
  }

  void getAnalysisUsage(AnalysisUsage &AU) const override {
    AU.addRequired<AssumptionCacheTracker>();
    AU.addRequiredID(LoopSimplifyID);
    AU.addRequiredID(LCSSAID);
    AU.addRequired<BlockFrequencyInfoWrapperPass>();
    AU.addRequired<DominatorTreeWrapperPass>();
    AU.addRequired<LoopInfoWrapperPass>();
    AU.addRequired<ScalarEvolutionWrapperPass>();
    AU.addRequired<TargetTransformInfoWrapperPass>();
    AU.addRequired<AliasAnalysis>();
    AU.addRequired<LoopAccessAnalysis>();
    AU.addPreserved<LoopInfoWrapperPass>();
    AU.addPreserved<DominatorTreeWrapperPass>();
    AU.addPreserved<AliasAnalysis>();
  }

};

} // end anonymous namespace

//===----------------------------------------------------------------------===//
// Implementation of LoopVectorizationLegality, InnerLoopVectorizer and
// LoopVectorizationCostModel.
//===----------------------------------------------------------------------===//

Value *InnerLoopVectorizer::getBroadcastInstrs(Value *V) {
  // We need to place the broadcast of invariant variables outside the loop.
  Instruction *Instr = dyn_cast<Instruction>(V);
  bool NewInstr =
      (Instr && std::find(LoopVectorBody.begin(), LoopVectorBody.end(),
                          Instr->getParent()) != LoopVectorBody.end());
  bool Invariant = OrigLoop->isLoopInvariant(V) && !NewInstr;

  // Place the code for broadcasting invariant variables in the new preheader.
  IRBuilder<>::InsertPointGuard Guard(Builder);
  if (Invariant)
    Builder.SetInsertPoint(LoopVectorPreHeader->getTerminator());

  // Broadcast the scalar into all locations in the vector.
  Value *Shuf = Builder.CreateVectorSplat(VF, V, "broadcast");

  return Shuf;
}

Value *InnerLoopVectorizer::getStepVector(Value *Val, int StartIdx,
                                          Value *Step) {
  assert(Val->getType()->isVectorTy() && "Must be a vector");
  assert(Val->getType()->getScalarType()->isIntegerTy() &&
         "Elem must be an integer");
  assert(Step->getType() == Val->getType()->getScalarType() &&
         "Step has wrong type");
  // Create the types.
  Type *ITy = Val->getType()->getScalarType();
  VectorType *Ty = cast<VectorType>(Val->getType());
  int VLen = Ty->getNumElements();
  SmallVector<Constant*, 8> Indices;

  // Create a vector of consecutive numbers from zero to VF.
  for (int i = 0; i < VLen; ++i)
    Indices.push_back(ConstantInt::get(ITy, StartIdx + i));

  // Add the consecutive indices to the vector value.
  Constant *Cv = ConstantVector::get(Indices);
  assert(Cv->getType() == Val->getType() && "Invalid consecutive vec");
  Step = Builder.CreateVectorSplat(VLen, Step);
  assert(Step->getType() == Val->getType() && "Invalid step vec");
  // FIXME: The newly created binary instructions should contain nsw/nuw flags,
  // which can be found from the original scalar operations.
  Step = Builder.CreateMul(Cv, Step);
  return Builder.CreateAdd(Val, Step, "induction");
}

int LoopVectorizationLegality::isConsecutivePtr(Value *Ptr) {
  assert(Ptr->getType()->isPointerTy() && "Unexpected non-ptr");
  // Make sure that the pointer does not point to structs.
  if (Ptr->getType()->getPointerElementType()->isAggregateType())
    return 0;

  // If this value is a pointer induction variable we know it is consecutive.
  PHINode *Phi = dyn_cast_or_null<PHINode>(Ptr);
  if (Phi && Inductions.count(Phi)) {
    InductionDescriptor II = Inductions[Phi];
    return II.getConsecutiveDirection();
  }

  GetElementPtrInst *Gep = dyn_cast_or_null<GetElementPtrInst>(Ptr);
  if (!Gep)
    return 0;

  unsigned NumOperands = Gep->getNumOperands();
  Value *GpPtr = Gep->getPointerOperand();
  // If this GEP value is a consecutive pointer induction variable and all of
  // the indices are constant then we know it is consecutive. We can
  Phi = dyn_cast<PHINode>(GpPtr);
  if (Phi && Inductions.count(Phi)) {

    // Make sure that the pointer does not point to structs.
    PointerType *GepPtrType = cast<PointerType>(GpPtr->getType());
    if (GepPtrType->getElementType()->isAggregateType())
      return 0;

    // Make sure that all of the index operands are loop invariant.
    for (unsigned i = 1; i < NumOperands; ++i)
      if (!SE->isLoopInvariant(SE->getSCEV(Gep->getOperand(i)), TheLoop))
        return 0;

    InductionDescriptor II = Inductions[Phi];
    return II.getConsecutiveDirection();
  }

  unsigned InductionOperand = getGEPInductionOperand(Gep);

  // Check that all of the gep indices are uniform except for our induction
  // operand.
  for (unsigned i = 0; i != NumOperands; ++i)
    if (i != InductionOperand &&
        !SE->isLoopInvariant(SE->getSCEV(Gep->getOperand(i)), TheLoop))
      return 0;

  // We can emit wide load/stores only if the last non-zero index is the
  // induction variable.
  const SCEV *Last = nullptr;
  if (!Strides.count(Gep))
    Last = SE->getSCEV(Gep->getOperand(InductionOperand));
  else {
    // Because of the multiplication by a stride we can have a s/zext cast.
    // We are going to replace this stride by 1 so the cast is safe to ignore.
    //
    //  %indvars.iv = phi i64 [ 0, %entry ], [ %indvars.iv.next, %for.body ]
    //  %0 = trunc i64 %indvars.iv to i32
    //  %mul = mul i32 %0, %Stride1
    //  %idxprom = zext i32 %mul to i64  << Safe cast.
    //  %arrayidx = getelementptr inbounds i32* %B, i64 %idxprom
    //
    Last = replaceSymbolicStrideSCEV(SE, Strides,
                                     Gep->getOperand(InductionOperand), Gep);
    if (const SCEVCastExpr *C = dyn_cast<SCEVCastExpr>(Last))
      Last =
          (C->getSCEVType() == scSignExtend || C->getSCEVType() == scZeroExtend)
              ? C->getOperand()
              : Last;
  }
  if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Last)) {
    const SCEV *Step = AR->getStepRecurrence(*SE);

    // The memory is consecutive because the last index is consecutive
    // and all other indices are loop invariant.
    if (Step->isOne())
      return 1;
    if (Step->isAllOnesValue())
      return -1;
  }

  return 0;
}

bool LoopVectorizationLegality::isUniform(Value *V) {
  return LAI->isUniform(V);
}

InnerLoopVectorizer::VectorParts&
InnerLoopVectorizer::getVectorValue(Value *V) {
  assert(V != Induction && "The new induction variable should not be used.");
  assert(!V->getType()->isVectorTy() && "Can't widen a vector");

  // If we have a stride that is replaced by one, do it here.
  if (Legal->hasStride(V))
    V = ConstantInt::get(V->getType(), 1);

  // If we have this scalar in the map, return it.
  if (WidenMap.has(V))
    return WidenMap.get(V);

  // If this scalar is unknown, assume that it is a constant or that it is
  // loop invariant. Broadcast V and save the value for future uses.
  Value *B = getBroadcastInstrs(V);
  return WidenMap.splat(V, B);
}

Value *InnerLoopVectorizer::reverseVector(Value *Vec) {
  assert(Vec->getType()->isVectorTy() && "Invalid type");
  SmallVector<Constant*, 8> ShuffleMask;
  for (unsigned i = 0; i < VF; ++i)
    ShuffleMask.push_back(Builder.getInt32(VF - i - 1));

  return Builder.CreateShuffleVector(Vec, UndefValue::get(Vec->getType()),
                                     ConstantVector::get(ShuffleMask),
                                     "reverse");
}

// Get a mask to interleave \p NumVec vectors into a wide vector.
// I.e.  <0, VF, VF*2, ..., VF*(NumVec-1), 1, VF+1, VF*2+1, ...>
// E.g. For 2 interleaved vectors, if VF is 4, the mask is:
//      <0, 4, 1, 5, 2, 6, 3, 7>
static Constant *getInterleavedMask(IRBuilder<> &Builder, unsigned VF,
                                    unsigned NumVec) {
  SmallVector<Constant *, 16> Mask;
  for (unsigned i = 0; i < VF; i++)
    for (unsigned j = 0; j < NumVec; j++)
      Mask.push_back(Builder.getInt32(j * VF + i));

  return ConstantVector::get(Mask);
}

// Get the strided mask starting from index \p Start.
// I.e.  <Start, Start + Stride, ..., Start + Stride*(VF-1)>
static Constant *getStridedMask(IRBuilder<> &Builder, unsigned Start,
                                unsigned Stride, unsigned VF) {
  SmallVector<Constant *, 16> Mask;
  for (unsigned i = 0; i < VF; i++)
    Mask.push_back(Builder.getInt32(Start + i * Stride));

  return ConstantVector::get(Mask);
}

// Get a mask of two parts: The first part consists of sequential integers
// starting from 0, The second part consists of UNDEFs.
// I.e. <0, 1, 2, ..., NumInt - 1, undef, ..., undef>
static Constant *getSequentialMask(IRBuilder<> &Builder, unsigned NumInt,
                                   unsigned NumUndef) {
  SmallVector<Constant *, 16> Mask;
  for (unsigned i = 0; i < NumInt; i++)
    Mask.push_back(Builder.getInt32(i));

  Constant *Undef = UndefValue::get(Builder.getInt32Ty());
  for (unsigned i = 0; i < NumUndef; i++)
    Mask.push_back(Undef);

  return ConstantVector::get(Mask);
}

// Concatenate two vectors with the same element type. The 2nd vector should
// not have more elements than the 1st vector. If the 2nd vector has less
// elements, extend it with UNDEFs.
static Value *ConcatenateTwoVectors(IRBuilder<> &Builder, Value *V1,
                                    Value *V2) {
  VectorType *VecTy1 = dyn_cast<VectorType>(V1->getType());
  VectorType *VecTy2 = dyn_cast<VectorType>(V2->getType());
  assert(VecTy1 && VecTy2 &&
         VecTy1->getScalarType() == VecTy2->getScalarType() &&
         "Expect two vectors with the same element type");

  unsigned NumElts1 = VecTy1->getNumElements();
  unsigned NumElts2 = VecTy2->getNumElements();
  assert(NumElts1 >= NumElts2 && "Unexpect the first vector has less elements");

  if (NumElts1 > NumElts2) {
    // Extend with UNDEFs.
    Constant *ExtMask =
        getSequentialMask(Builder, NumElts2, NumElts1 - NumElts2);
    V2 = Builder.CreateShuffleVector(V2, UndefValue::get(VecTy2), ExtMask);
  }

  Constant *Mask = getSequentialMask(Builder, NumElts1 + NumElts2, 0);
  return Builder.CreateShuffleVector(V1, V2, Mask);
}

// Concatenate vectors in the given list. All vectors have the same type.
static Value *ConcatenateVectors(IRBuilder<> &Builder,
                                 ArrayRef<Value *> InputList) {
  unsigned NumVec = InputList.size();
  assert(NumVec > 1 && "Should be at least two vectors");

  SmallVector<Value *, 8> ResList;
  ResList.append(InputList.begin(), InputList.end());
  do {
    SmallVector<Value *, 8> TmpList;
    for (unsigned i = 0; i < NumVec - 1; i += 2) {
      Value *V0 = ResList[i], *V1 = ResList[i + 1];
      assert((V0->getType() == V1->getType() || i == NumVec - 2) &&
             "Only the last vector may have a different type");

      TmpList.push_back(ConcatenateTwoVectors(Builder, V0, V1));
    }

    // Push the last vector if the total number of vectors is odd.
    if (NumVec % 2 != 0)
      TmpList.push_back(ResList[NumVec - 1]);

    ResList = TmpList;
    NumVec = ResList.size();
  } while (NumVec > 1);

  return ResList[0];
}

// Try to vectorize the interleave group that \p Instr belongs to.
//
// E.g. Translate following interleaved load group (factor = 3):
//   for (i = 0; i < N; i+=3) {
//     R = Pic[i];             // Member of index 0
//     G = Pic[i+1];           // Member of index 1
//     B = Pic[i+2];           // Member of index 2
//     ... // do something to R, G, B
//   }
// To:
//   %wide.vec = load <12 x i32>                       ; Read 4 tuples of R,G,B
//   %R.vec = shuffle %wide.vec, undef, <0, 3, 6, 9>   ; R elements
//   %G.vec = shuffle %wide.vec, undef, <1, 4, 7, 10>  ; G elements
//   %B.vec = shuffle %wide.vec, undef, <2, 5, 8, 11>  ; B elements
//
// Or translate following interleaved store group (factor = 3):
//   for (i = 0; i < N; i+=3) {
//     ... do something to R, G, B
//     Pic[i]   = R;           // Member of index 0
//     Pic[i+1] = G;           // Member of index 1
//     Pic[i+2] = B;           // Member of index 2
//   }
// To:
//   %R_G.vec = shuffle %R.vec, %G.vec, <0, 1, 2, ..., 7>
//   %B_U.vec = shuffle %B.vec, undef, <0, 1, 2, 3, u, u, u, u>
//   %interleaved.vec = shuffle %R_G.vec, %B_U.vec,
//        <0, 4, 8, 1, 5, 9, 2, 6, 10, 3, 7, 11>    ; Interleave R,G,B elements
//   store <12 x i32> %interleaved.vec              ; Write 4 tuples of R,G,B
void InnerLoopVectorizer::vectorizeInterleaveGroup(Instruction *Instr) {
  const InterleaveGroup *Group = Legal->getInterleavedAccessGroup(Instr);
  assert(Group && "Fail to get an interleaved access group.");

  // Skip if current instruction is not the insert position.
  if (Instr != Group->getInsertPos())
    return;

  LoadInst *LI = dyn_cast<LoadInst>(Instr);
  StoreInst *SI = dyn_cast<StoreInst>(Instr);
  Value *Ptr = LI ? LI->getPointerOperand() : SI->getPointerOperand();

  // Prepare for the vector type of the interleaved load/store.
  Type *ScalarTy = LI ? LI->getType() : SI->getValueOperand()->getType();
  unsigned InterleaveFactor = Group->getFactor();
  Type *VecTy = VectorType::get(ScalarTy, InterleaveFactor * VF);
  Type *PtrTy = VecTy->getPointerTo(Ptr->getType()->getPointerAddressSpace());

  // Prepare for the new pointers.
  setDebugLocFromInst(Builder, Ptr);
  VectorParts &PtrParts = getVectorValue(Ptr);
  SmallVector<Value *, 2> NewPtrs;
  unsigned Index = Group->getIndex(Instr);
  for (unsigned Part = 0; Part < UF; Part++) {
    // Extract the pointer for current instruction from the pointer vector. A
    // reverse access uses the pointer in the last lane.
    Value *NewPtr = Builder.CreateExtractElement(
        PtrParts[Part],
        Group->isReverse() ? Builder.getInt32(VF - 1) : Builder.getInt32(0));

    // Notice current instruction could be any index. Need to adjust the address
    // to the member of index 0.
    //
    // E.g.  a = A[i+1];     // Member of index 1 (Current instruction)
    //       b = A[i];       // Member of index 0
    // Current pointer is pointed to A[i+1], adjust it to A[i].
    //
    // E.g.  A[i+1] = a;     // Member of index 1
    //       A[i]   = b;     // Member of index 0
    //       A[i+2] = c;     // Member of index 2 (Current instruction)
    // Current pointer is pointed to A[i+2], adjust it to A[i].
    NewPtr = Builder.CreateGEP(NewPtr, Builder.getInt32(-Index));

    // Cast to the vector pointer type.
    NewPtrs.push_back(Builder.CreateBitCast(NewPtr, PtrTy));
  }

  setDebugLocFromInst(Builder, Instr);
  Value *UndefVec = UndefValue::get(VecTy);

  // Vectorize the interleaved load group.
  if (LI) {
    for (unsigned Part = 0; Part < UF; Part++) {
      Instruction *NewLoadInstr = Builder.CreateAlignedLoad(
          NewPtrs[Part], Group->getAlignment(), "wide.vec");

      for (unsigned i = 0; i < InterleaveFactor; i++) {
        Instruction *Member = Group->getMember(i);

        // Skip the gaps in the group.
        if (!Member)
          continue;

        Constant *StrideMask = getStridedMask(Builder, i, InterleaveFactor, VF);
        Value *StridedVec = Builder.CreateShuffleVector(
            NewLoadInstr, UndefVec, StrideMask, "strided.vec");

        // If this member has different type, cast the result type.
        if (Member->getType() != ScalarTy) {
          VectorType *OtherVTy = VectorType::get(Member->getType(), VF);
          StridedVec = Builder.CreateBitOrPointerCast(StridedVec, OtherVTy);
        }

        VectorParts &Entry = WidenMap.get(Member);
        Entry[Part] =
            Group->isReverse() ? reverseVector(StridedVec) : StridedVec;
      }

      propagateMetadata(NewLoadInstr, Instr);
    }
    return;
  }

  // The sub vector type for current instruction.
  VectorType *SubVT = VectorType::get(ScalarTy, VF);

  // Vectorize the interleaved store group.
  for (unsigned Part = 0; Part < UF; Part++) {
    // Collect the stored vector from each member.
    SmallVector<Value *, 4> StoredVecs;
    for (unsigned i = 0; i < InterleaveFactor; i++) {
      // Interleaved store group doesn't allow a gap, so each index has a member
      Instruction *Member = Group->getMember(i);
      assert(Member && "Fail to get a member from an interleaved store group");

      Value *StoredVec =
          getVectorValue(dyn_cast<StoreInst>(Member)->getValueOperand())[Part];
      if (Group->isReverse())
        StoredVec = reverseVector(StoredVec);

      // If this member has different type, cast it to an unified type.
      if (StoredVec->getType() != SubVT)
        StoredVec = Builder.CreateBitOrPointerCast(StoredVec, SubVT);

      StoredVecs.push_back(StoredVec);
    }

    // Concatenate all vectors into a wide vector.
    Value *WideVec = ConcatenateVectors(Builder, StoredVecs);

    // Interleave the elements in the wide vector.
    Constant *IMask = getInterleavedMask(Builder, VF, InterleaveFactor);
    Value *IVec = Builder.CreateShuffleVector(WideVec, UndefVec, IMask,
                                              "interleaved.vec");

    Instruction *NewStoreInstr =
        Builder.CreateAlignedStore(IVec, NewPtrs[Part], Group->getAlignment());
    propagateMetadata(NewStoreInstr, Instr);
  }
}

void InnerLoopVectorizer::vectorizeMemoryInstruction(Instruction *Instr) {
  // Attempt to issue a wide load.
  LoadInst *LI = dyn_cast<LoadInst>(Instr);
  StoreInst *SI = dyn_cast<StoreInst>(Instr);

  assert((LI || SI) && "Invalid Load/Store instruction");

  // Try to vectorize the interleave group if this access is interleaved.
  if (Legal->isAccessInterleaved(Instr))
    return vectorizeInterleaveGroup(Instr);

  Type *ScalarDataTy = LI ? LI->getType() : SI->getValueOperand()->getType();
  Type *DataTy = VectorType::get(ScalarDataTy, VF);
  Value *Ptr = LI ? LI->getPointerOperand() : SI->getPointerOperand();
  unsigned Alignment = LI ? LI->getAlignment() : SI->getAlignment();
  // An alignment of 0 means target abi alignment. We need to use the scalar's
  // target abi alignment in such a case.
  const DataLayout &DL = Instr->getModule()->getDataLayout();
  if (!Alignment)
    Alignment = DL.getABITypeAlignment(ScalarDataTy);
  unsigned AddressSpace = Ptr->getType()->getPointerAddressSpace();
  unsigned ScalarAllocatedSize = DL.getTypeAllocSize(ScalarDataTy);
  unsigned VectorElementSize = DL.getTypeStoreSize(DataTy) / VF;

  if (SI && Legal->blockNeedsPredication(SI->getParent()) &&
      !Legal->isMaskRequired(SI))
    return scalarizeInstruction(Instr, true);

  if (ScalarAllocatedSize != VectorElementSize)
    return scalarizeInstruction(Instr);

  // If the pointer is loop invariant or if it is non-consecutive,
  // scalarize the load.
  int ConsecutiveStride = Legal->isConsecutivePtr(Ptr);
  bool Reverse = ConsecutiveStride < 0;
  bool UniformLoad = LI && Legal->isUniform(Ptr);
  if (!ConsecutiveStride || UniformLoad)
    return scalarizeInstruction(Instr);

  Constant *Zero = Builder.getInt32(0);
  VectorParts &Entry = WidenMap.get(Instr);

  // Handle consecutive loads/stores.
  GetElementPtrInst *Gep = dyn_cast<GetElementPtrInst>(Ptr);
  if (Gep && Legal->isInductionVariable(Gep->getPointerOperand())) {
    setDebugLocFromInst(Builder, Gep);
    Value *PtrOperand = Gep->getPointerOperand();
    Value *FirstBasePtr = getVectorValue(PtrOperand)[0];
    FirstBasePtr = Builder.CreateExtractElement(FirstBasePtr, Zero);

    // Create the new GEP with the new induction variable.
    GetElementPtrInst *Gep2 = cast<GetElementPtrInst>(Gep->clone());
    Gep2->setOperand(0, FirstBasePtr);
    Gep2->setName("gep.indvar.base");
    Ptr = Builder.Insert(Gep2);
  } else if (Gep) {
    setDebugLocFromInst(Builder, Gep);
    assert(SE->isLoopInvariant(SE->getSCEV(Gep->getPointerOperand()),
                               OrigLoop) && "Base ptr must be invariant");

    // The last index does not have to be the induction. It can be
    // consecutive and be a function of the index. For example A[I+1];
    unsigned NumOperands = Gep->getNumOperands();
    unsigned InductionOperand = getGEPInductionOperand(Gep);
    // Create the new GEP with the new induction variable.
    GetElementPtrInst *Gep2 = cast<GetElementPtrInst>(Gep->clone());

    for (unsigned i = 0; i < NumOperands; ++i) {
      Value *GepOperand = Gep->getOperand(i);
      Instruction *GepOperandInst = dyn_cast<Instruction>(GepOperand);

      // Update last index or loop invariant instruction anchored in loop.
      if (i == InductionOperand ||
          (GepOperandInst && OrigLoop->contains(GepOperandInst))) {
        assert((i == InductionOperand ||
               SE->isLoopInvariant(SE->getSCEV(GepOperandInst), OrigLoop)) &&
               "Must be last index or loop invariant");

        VectorParts &GEPParts = getVectorValue(GepOperand);
        Value *Index = GEPParts[0];
        Index = Builder.CreateExtractElement(Index, Zero);
        Gep2->setOperand(i, Index);
        Gep2->setName("gep.indvar.idx");
      }
    }
    Ptr = Builder.Insert(Gep2);
  } else {
    // Use the induction element ptr.
    assert(isa<PHINode>(Ptr) && "Invalid induction ptr");
    setDebugLocFromInst(Builder, Ptr);
    VectorParts &PtrVal = getVectorValue(Ptr);
    Ptr = Builder.CreateExtractElement(PtrVal[0], Zero);
  }

  VectorParts Mask = createBlockInMask(Instr->getParent());
  // Handle Stores:
  if (SI) {
    assert(!Legal->isUniform(SI->getPointerOperand()) &&
           "We do not allow storing to uniform addresses");
    setDebugLocFromInst(Builder, SI);
    // We don't want to update the value in the map as it might be used in
    // another expression. So don't use a reference type for "StoredVal".
    VectorParts StoredVal = getVectorValue(SI->getValueOperand());
    
    for (unsigned Part = 0; Part < UF; ++Part) {
      // Calculate the pointer for the specific unroll-part.
      Value *PartPtr =
          Builder.CreateGEP(nullptr, Ptr, Builder.getInt32(Part * VF));

      if (Reverse) {
        // If we store to reverse consecutive memory locations, then we need
        // to reverse the order of elements in the stored value.
        StoredVal[Part] = reverseVector(StoredVal[Part]);
        // If the address is consecutive but reversed, then the
        // wide store needs to start at the last vector element.
        PartPtr = Builder.CreateGEP(nullptr, Ptr, Builder.getInt32(-Part * VF));
        PartPtr = Builder.CreateGEP(nullptr, PartPtr, Builder.getInt32(1 - VF));
        Mask[Part] = reverseVector(Mask[Part]);
      }

      Value *VecPtr = Builder.CreateBitCast(PartPtr,
                                            DataTy->getPointerTo(AddressSpace));

      Instruction *NewSI;
      if (Legal->isMaskRequired(SI))
        NewSI = Builder.CreateMaskedStore(StoredVal[Part], VecPtr, Alignment,
                                          Mask[Part]);
      else 
        NewSI = Builder.CreateAlignedStore(StoredVal[Part], VecPtr, Alignment);
      propagateMetadata(NewSI, SI);
    }
    return;
  }

  // Handle loads.
  assert(LI && "Must have a load instruction");
  setDebugLocFromInst(Builder, LI);
  for (unsigned Part = 0; Part < UF; ++Part) {
    // Calculate the pointer for the specific unroll-part.
    Value *PartPtr =
        Builder.CreateGEP(nullptr, Ptr, Builder.getInt32(Part * VF));

    if (Reverse) {
      // If the address is consecutive but reversed, then the
      // wide load needs to start at the last vector element.
      PartPtr = Builder.CreateGEP(nullptr, Ptr, Builder.getInt32(-Part * VF));
      PartPtr = Builder.CreateGEP(nullptr, PartPtr, Builder.getInt32(1 - VF));
      Mask[Part] = reverseVector(Mask[Part]);
    }

    Instruction* NewLI;
    Value *VecPtr = Builder.CreateBitCast(PartPtr,
                                          DataTy->getPointerTo(AddressSpace));
    if (Legal->isMaskRequired(LI))
      NewLI = Builder.CreateMaskedLoad(VecPtr, Alignment, Mask[Part],
                                       UndefValue::get(DataTy),
                                       "wide.masked.load");
    else
      NewLI = Builder.CreateAlignedLoad(VecPtr, Alignment, "wide.load");
    propagateMetadata(NewLI, LI);
    Entry[Part] = Reverse ? reverseVector(NewLI) :  NewLI;
  }
}

void InnerLoopVectorizer::scalarizeInstruction(Instruction *Instr, bool IfPredicateStore) {
  assert(!Instr->getType()->isAggregateType() && "Can't handle vectors");
  // Holds vector parameters or scalars, in case of uniform vals.
  SmallVector<VectorParts, 4> Params;

  setDebugLocFromInst(Builder, Instr);

  // Find all of the vectorized parameters.
  for (unsigned op = 0, e = Instr->getNumOperands(); op != e; ++op) {
    Value *SrcOp = Instr->getOperand(op);

    // If we are accessing the old induction variable, use the new one.
    if (SrcOp == OldInduction) {
      Params.push_back(getVectorValue(SrcOp));
      continue;
    }

    // Try using previously calculated values.
    Instruction *SrcInst = dyn_cast<Instruction>(SrcOp);

    // If the src is an instruction that appeared earlier in the basic block,
    // then it should already be vectorized.
    if (SrcInst && OrigLoop->contains(SrcInst)) {
      assert(WidenMap.has(SrcInst) && "Source operand is unavailable");
      // The parameter is a vector value from earlier.
      Params.push_back(WidenMap.get(SrcInst));
    } else {
      // The parameter is a scalar from outside the loop. Maybe even a constant.
      VectorParts Scalars;
      Scalars.append(UF, SrcOp);
      Params.push_back(Scalars);
    }
  }

  assert(Params.size() == Instr->getNumOperands() &&
         "Invalid number of operands");

  // Does this instruction return a value ?
  bool IsVoidRetTy = Instr->getType()->isVoidTy();

  Value *UndefVec = IsVoidRetTy ? nullptr :
    UndefValue::get(VectorType::get(Instr->getType(), VF));
  // Create a new entry in the WidenMap and initialize it to Undef or Null.
  VectorParts &VecResults = WidenMap.splat(Instr, UndefVec);

  Instruction *InsertPt = Builder.GetInsertPoint();
  BasicBlock *IfBlock = Builder.GetInsertBlock();
  BasicBlock *CondBlock = nullptr;

  VectorParts Cond;
  Loop *VectorLp = nullptr;
  if (IfPredicateStore) {
    assert(Instr->getParent()->getSinglePredecessor() &&
           "Only support single predecessor blocks");
    Cond = createEdgeMask(Instr->getParent()->getSinglePredecessor(),
                          Instr->getParent());
    VectorLp = LI->getLoopFor(IfBlock);
    assert(VectorLp && "Must have a loop for this block");
  }

  // For each vector unroll 'part':
  for (unsigned Part = 0; Part < UF; ++Part) {
    // For each scalar that we create:
    for (unsigned Width = 0; Width < VF; ++Width) {

      // Start if-block.
      Value *Cmp = nullptr;
      if (IfPredicateStore) {
        Cmp = Builder.CreateExtractElement(Cond[Part], Builder.getInt32(Width));
        Cmp = Builder.CreateICmp(ICmpInst::ICMP_EQ, Cmp, ConstantInt::get(Cmp->getType(), 1));
        CondBlock = IfBlock->splitBasicBlock(InsertPt, "cond.store");
        LoopVectorBody.push_back(CondBlock);
        VectorLp->addBasicBlockToLoop(CondBlock, *LI);
        // Update Builder with newly created basic block.
        Builder.SetInsertPoint(InsertPt);
      }

      Instruction *Cloned = Instr->clone();
      if (!IsVoidRetTy)
        Cloned->setName(Instr->getName() + ".cloned");
      // Replace the operands of the cloned instructions with extracted scalars.
      for (unsigned op = 0, e = Instr->getNumOperands(); op != e; ++op) {
        Value *Op = Params[op][Part];
        // Param is a vector. Need to extract the right lane.
        if (Op->getType()->isVectorTy())
          Op = Builder.CreateExtractElement(Op, Builder.getInt32(Width));
        Cloned->setOperand(op, Op);
      }

      // Place the cloned scalar in the new loop.
      Builder.Insert(Cloned);

      // If the original scalar returns a value we need to place it in a vector
      // so that future users will be able to use it.
      if (!IsVoidRetTy)
        VecResults[Part] = Builder.CreateInsertElement(VecResults[Part], Cloned,
                                                       Builder.getInt32(Width));
      // End if-block.
      if (IfPredicateStore) {
         BasicBlock *NewIfBlock = CondBlock->splitBasicBlock(InsertPt, "else");
         LoopVectorBody.push_back(NewIfBlock);
         VectorLp->addBasicBlockToLoop(NewIfBlock, *LI);
         Builder.SetInsertPoint(InsertPt);
         ReplaceInstWithInst(IfBlock->getTerminator(),
                             BranchInst::Create(CondBlock, NewIfBlock, Cmp));
         IfBlock = NewIfBlock;
      }
    }
  }
}

static Instruction *getFirstInst(Instruction *FirstInst, Value *V,
                                 Instruction *Loc) {
  if (FirstInst)
    return FirstInst;
  if (Instruction *I = dyn_cast<Instruction>(V))
    return I->getParent() == Loc->getParent() ? I : nullptr;
  return nullptr;
}

std::pair<Instruction *, Instruction *>
InnerLoopVectorizer::addStrideCheck(Instruction *Loc) {
  Instruction *tnullptr = nullptr;
  if (!Legal->mustCheckStrides())
    return std::pair<Instruction *, Instruction *>(tnullptr, tnullptr);

  IRBuilder<> ChkBuilder(Loc);

  // Emit checks.
  Value *Check = nullptr;
  Instruction *FirstInst = nullptr;
  for (SmallPtrSet<Value *, 8>::iterator SI = Legal->strides_begin(),
                                         SE = Legal->strides_end();
       SI != SE; ++SI) {
    Value *Ptr = stripIntegerCast(*SI);
    Value *C = ChkBuilder.CreateICmpNE(Ptr, ConstantInt::get(Ptr->getType(), 1),
                                       "stride.chk");
    // Store the first instruction we create.
    FirstInst = getFirstInst(FirstInst, C, Loc);
    if (Check)
      Check = ChkBuilder.CreateOr(Check, C);
    else
      Check = C;
  }

  // We have to do this trickery because the IRBuilder might fold the check to a
  // constant expression in which case there is no Instruction anchored in a
  // the block.
  LLVMContext &Ctx = Loc->getContext();
  Instruction *TheCheck =
      BinaryOperator::CreateAnd(Check, ConstantInt::getTrue(Ctx));
  ChkBuilder.Insert(TheCheck, "stride.not.one");
  FirstInst = getFirstInst(FirstInst, TheCheck, Loc);

  return std::make_pair(FirstInst, TheCheck);
}

PHINode *InnerLoopVectorizer::createInductionVariable(Loop *L,
                                                      Value *Start,
                                                      Value *End,
                                                      Value *Step,
                                                      Instruction *DL) {
  BasicBlock *Header = L->getHeader();
  BasicBlock *Latch = L->getLoopLatch();
  // As we're just creating this loop, it's possible no latch exists
  // yet. If so, use the header as this will be a single block loop.
  if (!Latch)
    Latch = Header;
    
  IRBuilder<> Builder(Header->getFirstInsertionPt());
  setDebugLocFromInst(Builder, getDebugLocFromInstOrOperands(OldInduction));
  auto *Induction = Builder.CreatePHI(Start->getType(), 2, "index");

  Builder.SetInsertPoint(Latch->getTerminator());
  
  // Create i+1 and fill the PHINode.
  Value *Next = Builder.CreateAdd(Induction, Step, "index.next");
  Induction->addIncoming(Start, L->getLoopPreheader());
  Induction->addIncoming(Next, Latch);
  // Create the compare.
  Value *ICmp = Builder.CreateICmpEQ(Next, End);
  Builder.CreateCondBr(ICmp, L->getExitBlock(), Header);
  
  // Now we have two terminators. Remove the old one from the block.
  Latch->getTerminator()->eraseFromParent();

  return Induction;
}

Value *InnerLoopVectorizer::getOrCreateTripCount(Loop *L) {
  if (TripCount)
    return TripCount;

  IRBuilder<> Builder(L->getLoopPreheader()->getTerminator());
  // Find the loop boundaries.
  const SCEV *ExitCount = SE->getBackedgeTakenCount(OrigLoop);
  assert(ExitCount != SE->getCouldNotCompute() && "Invalid loop count");

  Type *IdxTy = Legal->getWidestInductionType();
  
  // The exit count might have the type of i64 while the phi is i32. This can
  // happen if we have an induction variable that is sign extended before the
  // compare. The only way that we get a backedge taken count is that the
  // induction variable was signed and as such will not overflow. In such a case
  // truncation is legal.
  if (ExitCount->getType()->getPrimitiveSizeInBits() >
      IdxTy->getPrimitiveSizeInBits())
    ExitCount = SE->getTruncateOrNoop(ExitCount, IdxTy);

  const SCEV *BackedgeTakeCount = SE->getNoopOrZeroExtend(ExitCount, IdxTy);
  // Get the total trip count from the count by adding 1.
  ExitCount = SE->getAddExpr(BackedgeTakeCount,
                             SE->getConstant(BackedgeTakeCount->getType(), 1));

  const DataLayout &DL = L->getHeader()->getModule()->getDataLayout();

  // Expand the trip count and place the new instructions in the preheader.
  // Notice that the pre-header does not change, only the loop body.
  SCEVExpander Exp(*SE, DL, "induction");

  // Count holds the overall loop count (N).
  TripCount = Exp.expandCodeFor(ExitCount, ExitCount->getType(),
                                L->getLoopPreheader()->getTerminator());

  if (TripCount->getType()->isPointerTy())
    TripCount =
      CastInst::CreatePointerCast(TripCount, IdxTy,
                                  "exitcount.ptrcnt.to.int",
                                  L->getLoopPreheader()->getTerminator());

  return TripCount;
}

Value *InnerLoopVectorizer::getOrCreateVectorTripCount(Loop *L) {
  if (VectorTripCount)
    return VectorTripCount;
  
  Value *TC = getOrCreateTripCount(L);
  IRBuilder<> Builder(L->getLoopPreheader()->getTerminator());
  
  // Now we need to generate the expression for N - (N % VF), which is
  // the part that the vectorized body will execute.
  // The loop step is equal to the vectorization factor (num of SIMD elements)
  // times the unroll factor (num of SIMD instructions).
  Constant *Step = ConstantInt::get(TC->getType(), VF * UF);
  Value *R = Builder.CreateURem(TC, Step, "n.mod.vf");
  VectorTripCount = Builder.CreateSub(TC, R, "n.vec");

  return VectorTripCount;
}

void InnerLoopVectorizer::emitMinimumIterationCountCheck(Loop *L,
                                                         BasicBlock *Bypass) {
  Value *Count = getOrCreateTripCount(L);
  BasicBlock *BB = L->getLoopPreheader();
  IRBuilder<> Builder(BB->getTerminator());

  // Generate code to check that the loop's trip count that we computed by
  // adding one to the backedge-taken count will not overflow.
  Value *CheckMinIters =
    Builder.CreateICmpULT(Count,
                          ConstantInt::get(Count->getType(), VF * UF),
                          "min.iters.check");
  
  BasicBlock *NewBB = BB->splitBasicBlock(BB->getTerminator(),
                                          "min.iters.checked");
  if (L->getParentLoop())
    L->getParentLoop()->addBasicBlockToLoop(NewBB, *LI);
  ReplaceInstWithInst(BB->getTerminator(),
                      BranchInst::Create(Bypass, NewBB, CheckMinIters));
  LoopBypassBlocks.push_back(BB);
}

void InnerLoopVectorizer::emitVectorLoopEnteredCheck(Loop *L,
                                                     BasicBlock *Bypass) {
  Value *TC = getOrCreateVectorTripCount(L);
  BasicBlock *BB = L->getLoopPreheader();
  IRBuilder<> Builder(BB->getTerminator());
  
  // Now, compare the new count to zero. If it is zero skip the vector loop and
  // jump to the scalar loop.
  Value *Cmp = Builder.CreateICmpEQ(TC, Constant::getNullValue(TC->getType()),
                                    "cmp.zero");

  // Generate code to check that the loop's trip count that we computed by
  // adding one to the backedge-taken count will not overflow.
  BasicBlock *NewBB = BB->splitBasicBlock(BB->getTerminator(),
                                          "vector.ph");
  if (L->getParentLoop())
    L->getParentLoop()->addBasicBlockToLoop(NewBB, *LI);
  ReplaceInstWithInst(BB->getTerminator(),
                      BranchInst::Create(Bypass, NewBB, Cmp));
  LoopBypassBlocks.push_back(BB);
}

void InnerLoopVectorizer::emitStrideChecks(Loop *L,
                                           BasicBlock *Bypass) {
  BasicBlock *BB = L->getLoopPreheader();
  
  // Generate the code to check that the strides we assumed to be one are really
  // one. We want the new basic block to start at the first instruction in a
  // sequence of instructions that form a check.
  Instruction *StrideCheck;
  Instruction *FirstCheckInst;
  std::tie(FirstCheckInst, StrideCheck) = addStrideCheck(BB->getTerminator());
  if (!StrideCheck)
    return;

  // Create a new block containing the stride check.
  BB->setName("vector.stridecheck");
  auto *NewBB = BB->splitBasicBlock(BB->getTerminator(), "vector.ph");
  if (L->getParentLoop())
    L->getParentLoop()->addBasicBlockToLoop(NewBB, *LI);
  ReplaceInstWithInst(BB->getTerminator(),
                      BranchInst::Create(Bypass, NewBB, StrideCheck));
  LoopBypassBlocks.push_back(BB);
  AddedSafetyChecks = true;
}

void InnerLoopVectorizer::emitMemRuntimeChecks(Loop *L,
                                               BasicBlock *Bypass) {
  BasicBlock *BB = L->getLoopPreheader();

  // Generate the code that checks in runtime if arrays overlap. We put the
  // checks into a separate block to make the more common case of few elements
  // faster.
  Instruction *FirstCheckInst;
  Instruction *MemRuntimeCheck;
  std::tie(FirstCheckInst, MemRuntimeCheck) =
      Legal->getLAI()->addRuntimeChecks(BB->getTerminator());
  if (!MemRuntimeCheck)
    return;

  // Create a new block containing the memory check.
  BB->setName("vector.memcheck");
  auto *NewBB = BB->splitBasicBlock(BB->getTerminator(), "vector.ph");
  if (L->getParentLoop())
    L->getParentLoop()->addBasicBlockToLoop(NewBB, *LI);
  ReplaceInstWithInst(BB->getTerminator(),
                      BranchInst::Create(Bypass, NewBB, MemRuntimeCheck));
  LoopBypassBlocks.push_back(BB);
  AddedSafetyChecks = true;
}


void InnerLoopVectorizer::createEmptyLoop() {
  /*
   In this function we generate a new loop. The new loop will contain
   the vectorized instructions while the old loop will continue to run the
   scalar remainder.

       [ ] <-- loop iteration number check.
    /   |
   /    v
  |    [ ] <-- vector loop bypass (may consist of multiple blocks).
  |  /  |
  | /   v
  ||   [ ]     <-- vector pre header.
  |/    |
  |     v
  |    [  ] \
  |    [  ]_|   <-- vector loop.
  |     |
  |     v
  |   -[ ]   <--- middle-block.
  |  /  |
  | /   v
  -|- >[ ]     <--- new preheader.
   |    |
   |    v
   |   [ ] \
   |   [ ]_|   <-- old scalar loop to handle remainder.
    \   |
     \  v
      >[ ]     <-- exit block.
   ...
   */

  BasicBlock *OldBasicBlock = OrigLoop->getHeader();
  BasicBlock *VectorPH = OrigLoop->getLoopPreheader();
  BasicBlock *ExitBlock = OrigLoop->getExitBlock();
  assert(VectorPH && "Invalid loop structure");
  assert(ExitBlock && "Must have an exit block");

  // Some loops have a single integer induction variable, while other loops
  // don't. One example is c++ iterators that often have multiple pointer
  // induction variables. In the code below we also support a case where we
  // don't have a single induction variable.
  //
  // We try to obtain an induction variable from the original loop as hard
  // as possible. However if we don't find one that:
  //   - is an integer
  //   - counts from zero, stepping by one
  //   - is the size of the widest induction variable type
  // then we create a new one.
  OldInduction = Legal->getInduction();
  Type *IdxTy = Legal->getWidestInductionType();

  // Split the single block loop into the two loop structure described above.
  BasicBlock *VecBody =
      VectorPH->splitBasicBlock(VectorPH->getTerminator(), "vector.body");
  BasicBlock *MiddleBlock =
  VecBody->splitBasicBlock(VecBody->getTerminator(), "middle.block");
  BasicBlock *ScalarPH =
  MiddleBlock->splitBasicBlock(MiddleBlock->getTerminator(), "scalar.ph");

  // Create and register the new vector loop.
  Loop* Lp = new Loop();
  Loop *ParentLoop = OrigLoop->getParentLoop();

  // Insert the new loop into the loop nest and register the new basic blocks
  // before calling any utilities such as SCEV that require valid LoopInfo.
  if (ParentLoop) {
    ParentLoop->addChildLoop(Lp);
    ParentLoop->addBasicBlockToLoop(ScalarPH, *LI);
    ParentLoop->addBasicBlockToLoop(MiddleBlock, *LI);
  } else {
    LI->addTopLevelLoop(Lp);
  }
  Lp->addBasicBlockToLoop(VecBody, *LI);

  // Find the loop boundaries.
  Value *Count = getOrCreateTripCount(Lp);

  Value *StartIdx = ConstantInt::get(IdxTy, 0);

  // We need to test whether the backedge-taken count is uint##_max. Adding one
  // to it will cause overflow and an incorrect loop trip count in the vector
  // body. In case of overflow we want to directly jump to the scalar remainder
  // loop.
  emitMinimumIterationCountCheck(Lp, ScalarPH);
  // Now, compare the new count to zero. If it is zero skip the vector loop and
  // jump to the scalar loop.
  emitVectorLoopEnteredCheck(Lp, ScalarPH);
  // Generate the code to check that the strides we assumed to be one are really
  // one. We want the new basic block to start at the first instruction in a
  // sequence of instructions that form a check.
  emitStrideChecks(Lp, ScalarPH);
  // Generate the code that checks in runtime if arrays overlap. We put the
  // checks into a separate block to make the more common case of few elements
  // faster.
  emitMemRuntimeChecks(Lp, ScalarPH);
  
  // Generate the induction variable.
  // The loop step is equal to the vectorization factor (num of SIMD elements)
  // times the unroll factor (num of SIMD instructions).
  Value *CountRoundDown = getOrCreateVectorTripCount(Lp);
  Constant *Step = ConstantInt::get(IdxTy, VF * UF);
  Induction =
    createInductionVariable(Lp, StartIdx, CountRoundDown, Step,
                            getDebugLocFromInstOrOperands(OldInduction));

  // We are going to resume the execution of the scalar loop.
  // Go over all of the induction variables that we found and fix the
  // PHIs that are left in the scalar version of the loop.
  // The starting values of PHI nodes depend on the counter of the last
  // iteration in the vectorized loop.
  // If we come from a bypass edge then we need to start from the original
  // start value.

  // This variable saves the new starting index for the scalar loop. It is used
  // to test if there are any tail iterations left once the vector loop has
  // completed.
  LoopVectorizationLegality::InductionList::iterator I, E;
  LoopVectorizationLegality::InductionList *List = Legal->getInductionVars();
  for (I = List->begin(), E = List->end(); I != E; ++I) {
    PHINode *OrigPhi = I->first;
    InductionDescriptor II = I->second;

    // Create phi nodes to merge from the  backedge-taken check block.
    PHINode *BCResumeVal = PHINode::Create(OrigPhi->getType(), 3,
                                           "bc.resume.val",
                                           ScalarPH->getTerminator());
    Value *EndValue;
    if (OrigPhi == OldInduction) {
      // We know what the end value is.
      EndValue = CountRoundDown;
    } else {
      IRBuilder<> B(LoopBypassBlocks.back()->getTerminator());
      Value *CRD = B.CreateSExtOrTrunc(CountRoundDown,
                                       II.getStepValue()->getType(),
                                       "cast.crd");
      EndValue = II.transform(B, CRD);
      EndValue->setName("ind.end");
    }

    // The new PHI merges the original incoming value, in case of a bypass,
    // or the value at the end of the vectorized loop.
    BCResumeVal->addIncoming(EndValue, MiddleBlock);

    // Fix the scalar body counter (PHI node).
    unsigned BlockIdx = OrigPhi->getBasicBlockIndex(ScalarPH);

    // The old induction's phi node in the scalar body needs the truncated
    // value.
    for (unsigned I = 0, E = LoopBypassBlocks.size(); I != E; ++I)
      BCResumeVal->addIncoming(II.getStartValue(), LoopBypassBlocks[I]);
    OrigPhi->setIncomingValue(BlockIdx, BCResumeVal);
  }

  // Add a check in the middle block to see if we have completed
  // all of the iterations in the first vector loop.
  // If (N - N%VF) == N, then we *don't* need to run the remainder.
  Value *CmpN = CmpInst::Create(Instruction::ICmp, CmpInst::ICMP_EQ, Count,
                                CountRoundDown, "cmp.n",
                                MiddleBlock->getTerminator());
  ReplaceInstWithInst(MiddleBlock->getTerminator(),
                      BranchInst::Create(ExitBlock, ScalarPH, CmpN));

  // Get ready to start creating new instructions into the vectorized body.
  Builder.SetInsertPoint(VecBody->getFirstInsertionPt());

  // Save the state.
  LoopVectorPreHeader = Lp->getLoopPreheader();
  LoopScalarPreHeader = ScalarPH;
  LoopMiddleBlock = MiddleBlock;
  LoopExitBlock = ExitBlock;
  LoopVectorBody.push_back(VecBody);
  LoopScalarBody = OldBasicBlock;

  LoopVectorizeHints Hints(Lp, true);
  Hints.setAlreadyVectorized();
}

namespace {
struct CSEDenseMapInfo {
  static bool canHandle(Instruction *I) {
    return isa<InsertElementInst>(I) || isa<ExtractElementInst>(I) ||
           isa<ShuffleVectorInst>(I) || isa<GetElementPtrInst>(I);
  }
  static inline Instruction *getEmptyKey() {
    return DenseMapInfo<Instruction *>::getEmptyKey();
  }
  static inline Instruction *getTombstoneKey() {
    return DenseMapInfo<Instruction *>::getTombstoneKey();
  }
  static unsigned getHashValue(Instruction *I) {
    assert(canHandle(I) && "Unknown instruction!");
    return hash_combine(I->getOpcode(), hash_combine_range(I->value_op_begin(),
                                                           I->value_op_end()));
  }
  static bool isEqual(Instruction *LHS, Instruction *RHS) {
    if (LHS == getEmptyKey() || RHS == getEmptyKey() ||
        LHS == getTombstoneKey() || RHS == getTombstoneKey())
      return LHS == RHS;
    return LHS->isIdenticalTo(RHS);
  }
};
}

/// \brief Check whether this block is a predicated block.
/// Due to if predication of stores we might create a sequence of "if(pred) a[i]
/// = ...;  " blocks. We start with one vectorized basic block. For every
/// conditional block we split this vectorized block. Therefore, every second
/// block will be a predicated one.
static bool isPredicatedBlock(unsigned BlockNum) {
  return BlockNum % 2;
}

///\brief Perform cse of induction variable instructions.
static void cse(SmallVector<BasicBlock *, 4> &BBs) {
  // Perform simple cse.
  SmallDenseMap<Instruction *, Instruction *, 4, CSEDenseMapInfo> CSEMap;
  for (unsigned i = 0, e = BBs.size(); i != e; ++i) {
    BasicBlock *BB = BBs[i];
    for (BasicBlock::iterator I = BB->begin(), E = BB->end(); I != E;) {
      Instruction *In = I++;

      if (!CSEDenseMapInfo::canHandle(In))
        continue;

      // Check if we can replace this instruction with any of the
      // visited instructions.
      if (Instruction *V = CSEMap.lookup(In)) {
        In->replaceAllUsesWith(V);
        In->eraseFromParent();
        continue;
      }
      // Ignore instructions in conditional blocks. We create "if (pred) a[i] =
      // ...;" blocks for predicated stores. Every second block is a predicated
      // block.
      if (isPredicatedBlock(i))
        continue;

      CSEMap[In] = In;
    }
  }
}

/// \brief Adds a 'fast' flag to floating point operations.
static Value *addFastMathFlag(Value *V) {
  if (isa<FPMathOperator>(V)){
    FastMathFlags Flags;
    Flags.setUnsafeAlgebra();
    cast<Instruction>(V)->setFastMathFlags(Flags);
  }
  return V;
}

/// Estimate the overhead of scalarizing a value. Insert and Extract are set if
/// the result needs to be inserted and/or extracted from vectors.
static unsigned getScalarizationOverhead(Type *Ty, bool Insert, bool Extract,
                                         const TargetTransformInfo &TTI) {
  if (Ty->isVoidTy())
    return 0;

  assert(Ty->isVectorTy() && "Can only scalarize vectors");
  unsigned Cost = 0;

  for (int i = 0, e = Ty->getVectorNumElements(); i < e; ++i) {
    if (Insert)
      Cost += TTI.getVectorInstrCost(Instruction::InsertElement, Ty, i);
    if (Extract)
      Cost += TTI.getVectorInstrCost(Instruction::ExtractElement, Ty, i);
  }

  return Cost;
}

// Estimate cost of a call instruction CI if it were vectorized with factor VF.
// Return the cost of the instruction, including scalarization overhead if it's
// needed. The flag NeedToScalarize shows if the call needs to be scalarized -
// i.e. either vector version isn't available, or is too expensive.
static unsigned getVectorCallCost(CallInst *CI, unsigned VF,
                                  const TargetTransformInfo &TTI,
                                  const TargetLibraryInfo *TLI,
                                  bool &NeedToScalarize) {
  Function *F = CI->getCalledFunction();
  StringRef FnName = CI->getCalledFunction()->getName();
  Type *ScalarRetTy = CI->getType();
  SmallVector<Type *, 4> Tys, ScalarTys;
  for (auto &ArgOp : CI->arg_operands())
    ScalarTys.push_back(ArgOp->getType());

  // Estimate cost of scalarized vector call. The source operands are assumed
  // to be vectors, so we need to extract individual elements from there,
  // execute VF scalar calls, and then gather the result into the vector return
  // value.
  unsigned ScalarCallCost = TTI.getCallInstrCost(F, ScalarRetTy, ScalarTys);
  if (VF == 1)
    return ScalarCallCost;

  // Compute corresponding vector type for return value and arguments.
  Type *RetTy = ToVectorTy(ScalarRetTy, VF);
  for (unsigned i = 0, ie = ScalarTys.size(); i != ie; ++i)
    Tys.push_back(ToVectorTy(ScalarTys[i], VF));

  // Compute costs of unpacking argument values for the scalar calls and
  // packing the return values to a vector.
  unsigned ScalarizationCost =
      getScalarizationOverhead(RetTy, true, false, TTI);
  for (unsigned i = 0, ie = Tys.size(); i != ie; ++i)
    ScalarizationCost += getScalarizationOverhead(Tys[i], false, true, TTI);

  unsigned Cost = ScalarCallCost * VF + ScalarizationCost;

  // If we can't emit a vector call for this function, then the currently found
  // cost is the cost we need to return.
  NeedToScalarize = true;
  if (!TLI || !TLI->isFunctionVectorizable(FnName, VF) || CI->isNoBuiltin())
    return Cost;

  // If the corresponding vector cost is cheaper, return its cost.
  unsigned VectorCallCost = TTI.getCallInstrCost(nullptr, RetTy, Tys);
  if (VectorCallCost < Cost) {
    NeedToScalarize = false;
    return VectorCallCost;
  }
  return Cost;
}

// Estimate cost of an intrinsic call instruction CI if it were vectorized with
// factor VF.  Return the cost of the instruction, including scalarization
// overhead if it's needed.
static unsigned getVectorIntrinsicCost(CallInst *CI, unsigned VF,
                                       const TargetTransformInfo &TTI,
                                       const TargetLibraryInfo *TLI) {
  Intrinsic::ID ID = getIntrinsicIDForCall(CI, TLI);
  assert(ID && "Expected intrinsic call!");

  Type *RetTy = ToVectorTy(CI->getType(), VF);
  SmallVector<Type *, 4> Tys;
  for (unsigned i = 0, ie = CI->getNumArgOperands(); i != ie; ++i)
    Tys.push_back(ToVectorTy(CI->getArgOperand(i)->getType(), VF));

  return TTI.getIntrinsicInstrCost(ID, RetTy, Tys);
}

void InnerLoopVectorizer::vectorizeLoop() {
  //===------------------------------------------------===//
  //
  // Notice: any optimization or new instruction that go
  // into the code below should be also be implemented in
  // the cost-model.
  //
  //===------------------------------------------------===//
  Constant *Zero = Builder.getInt32(0);

  // In order to support reduction variables we need to be able to vectorize
  // Phi nodes. Phi nodes have cycles, so we need to vectorize them in two
  // stages. First, we create a new vector PHI node with no incoming edges.
  // We use this value when we vectorize all of the instructions that use the
  // PHI. Next, after all of the instructions in the block are complete we
  // add the new incoming edges to the PHI. At this point all of the
  // instructions in the basic block are vectorized, so we can use them to
  // construct the PHI.
  PhiVector RdxPHIsToFix;

  // Scan the loop in a topological order to ensure that defs are vectorized
  // before users.
  LoopBlocksDFS DFS(OrigLoop);
  DFS.perform(LI);

  // Vectorize all of the blocks in the original loop.
  for (LoopBlocksDFS::RPOIterator bb = DFS.beginRPO(),
       be = DFS.endRPO(); bb != be; ++bb)
    vectorizeBlockInLoop(*bb, &RdxPHIsToFix);

  // At this point every instruction in the original loop is widened to
  // a vector form. We are almost done. Now, we need to fix the PHI nodes
  // that we vectorized. The PHI nodes are currently empty because we did
  // not want to introduce cycles. Notice that the remaining PHI nodes
  // that we need to fix are reduction variables.

  // Create the 'reduced' values for each of the induction vars.
  // The reduced values are the vector values that we scalarize and combine
  // after the loop is finished.
  for (PhiVector::iterator it = RdxPHIsToFix.begin(), e = RdxPHIsToFix.end();
       it != e; ++it) {
    PHINode *RdxPhi = *it;
    assert(RdxPhi && "Unable to recover vectorized PHI");

    // Find the reduction variable descriptor.
    assert(Legal->getReductionVars()->count(RdxPhi) &&
           "Unable to find the reduction variable");
    RecurrenceDescriptor RdxDesc = (*Legal->getReductionVars())[RdxPhi];

    RecurrenceDescriptor::RecurrenceKind RK = RdxDesc.getRecurrenceKind();
    TrackingVH<Value> ReductionStartValue = RdxDesc.getRecurrenceStartValue();
    Instruction *LoopExitInst = RdxDesc.getLoopExitInstr();
    RecurrenceDescriptor::MinMaxRecurrenceKind MinMaxKind =
        RdxDesc.getMinMaxRecurrenceKind();
    setDebugLocFromInst(Builder, ReductionStartValue);

    // We need to generate a reduction vector from the incoming scalar.
    // To do so, we need to generate the 'identity' vector and override
    // one of the elements with the incoming scalar reduction. We need
    // to do it in the vector-loop preheader.
    Builder.SetInsertPoint(LoopBypassBlocks[1]->getTerminator());

    // This is the vector-clone of the value that leaves the loop.
    VectorParts &VectorExit = getVectorValue(LoopExitInst);
    Type *VecTy = VectorExit[0]->getType();

    // Find the reduction identity variable. Zero for addition, or, xor,
    // one for multiplication, -1 for And.
    Value *Identity;
    Value *VectorStart;
    if (RK == RecurrenceDescriptor::RK_IntegerMinMax ||
        RK == RecurrenceDescriptor::RK_FloatMinMax) {
      // MinMax reduction have the start value as their identify.
      if (VF == 1) {
        VectorStart = Identity = ReductionStartValue;
      } else {
        VectorStart = Identity =
            Builder.CreateVectorSplat(VF, ReductionStartValue, "minmax.ident");
      }
    } else {
      // Handle other reduction kinds:
      Constant *Iden = RecurrenceDescriptor::getRecurrenceIdentity(
          RK, VecTy->getScalarType());
      if (VF == 1) {
        Identity = Iden;
        // This vector is the Identity vector where the first element is the
        // incoming scalar reduction.
        VectorStart = ReductionStartValue;
      } else {
        Identity = ConstantVector::getSplat(VF, Iden);

        // This vector is the Identity vector where the first element is the
        // incoming scalar reduction.
        VectorStart =
            Builder.CreateInsertElement(Identity, ReductionStartValue, Zero);
      }
    }

    // Fix the vector-loop phi.

    // Reductions do not have to start at zero. They can start with
    // any loop invariant values.
    VectorParts &VecRdxPhi = WidenMap.get(RdxPhi);
    BasicBlock *Latch = OrigLoop->getLoopLatch();
    Value *LoopVal = RdxPhi->getIncomingValueForBlock(Latch);
    VectorParts &Val = getVectorValue(LoopVal);
    for (unsigned part = 0; part < UF; ++part) {
      // Make sure to add the reduction stat value only to the
      // first unroll part.
      Value *StartVal = (part == 0) ? VectorStart : Identity;
      cast<PHINode>(VecRdxPhi[part])->addIncoming(StartVal,
                                                  LoopVectorPreHeader);
      cast<PHINode>(VecRdxPhi[part])->addIncoming(Val[part],
                                                  LoopVectorBody.back());
    }

    // Before each round, move the insertion point right between
    // the PHIs and the values we are going to write.
    // This allows us to write both PHINodes and the extractelement
    // instructions.
    Builder.SetInsertPoint(LoopMiddleBlock->getFirstInsertionPt());

    VectorParts RdxParts = getVectorValue(LoopExitInst);
    setDebugLocFromInst(Builder, LoopExitInst);

    // If the vector reduction can be performed in a smaller type, we truncate
    // then extend the loop exit value to enable InstCombine to evaluate the
    // entire expression in the smaller type.
    if (VF > 1 && RdxPhi->getType() != RdxDesc.getRecurrenceType()) {
      Type *RdxVecTy = VectorType::get(RdxDesc.getRecurrenceType(), VF);
      Builder.SetInsertPoint(LoopVectorBody.back()->getTerminator());
      for (unsigned part = 0; part < UF; ++part) {
        Value *Trunc = Builder.CreateTrunc(RdxParts[part], RdxVecTy);
        Value *Extnd = RdxDesc.isSigned() ? Builder.CreateSExt(Trunc, VecTy)
                                          : Builder.CreateZExt(Trunc, VecTy);
        for (Value::user_iterator UI = RdxParts[part]->user_begin();
             UI != RdxParts[part]->user_end();)
          if (*UI != Trunc) {
            (*UI++)->replaceUsesOfWith(RdxParts[part], Extnd);
            RdxParts[part] = Extnd;
          } else {
            ++UI;
          }
      }
      Builder.SetInsertPoint(LoopMiddleBlock->getFirstInsertionPt());
      for (unsigned part = 0; part < UF; ++part)
        RdxParts[part] = Builder.CreateTrunc(RdxParts[part], RdxVecTy);
    }

    // Reduce all of the unrolled parts into a single vector.
    Value *ReducedPartRdx = RdxParts[0];
    unsigned Op = RecurrenceDescriptor::getRecurrenceBinOp(RK);
    setDebugLocFromInst(Builder, ReducedPartRdx);
    for (unsigned part = 1; part < UF; ++part) {
      if (Op != Instruction::ICmp && Op != Instruction::FCmp)
        // Floating point operations had to be 'fast' to enable the reduction.
        ReducedPartRdx = addFastMathFlag(
            Builder.CreateBinOp((Instruction::BinaryOps)Op, RdxParts[part],
                                ReducedPartRdx, "bin.rdx"));
      else
        ReducedPartRdx = RecurrenceDescriptor::createMinMaxOp(
            Builder, MinMaxKind, ReducedPartRdx, RdxParts[part]);
    }

    if (VF > 1) {
      // VF is a power of 2 so we can emit the reduction using log2(VF) shuffles
      // and vector ops, reducing the set of values being computed by half each
      // round.
      assert(isPowerOf2_32(VF) &&
             "Reduction emission only supported for pow2 vectors!");
      Value *TmpVec = ReducedPartRdx;
      SmallVector<Constant*, 32> ShuffleMask(VF, nullptr);
      for (unsigned i = VF; i != 1; i >>= 1) {
        // Move the upper half of the vector to the lower half.
        for (unsigned j = 0; j != i/2; ++j)
          ShuffleMask[j] = Builder.getInt32(i/2 + j);

        // Fill the rest of the mask with undef.
        std::fill(&ShuffleMask[i/2], ShuffleMask.end(),
                  UndefValue::get(Builder.getInt32Ty()));

        Value *Shuf =
        Builder.CreateShuffleVector(TmpVec,
                                    UndefValue::get(TmpVec->getType()),
                                    ConstantVector::get(ShuffleMask),
                                    "rdx.shuf");

        if (Op != Instruction::ICmp && Op != Instruction::FCmp)
          // Floating point operations had to be 'fast' to enable the reduction.
          TmpVec = addFastMathFlag(Builder.CreateBinOp(
              (Instruction::BinaryOps)Op, TmpVec, Shuf, "bin.rdx"));
        else
          TmpVec = RecurrenceDescriptor::createMinMaxOp(Builder, MinMaxKind,
                                                        TmpVec, Shuf);
      }

      // The result is in the first element of the vector.
      ReducedPartRdx = Builder.CreateExtractElement(TmpVec,
                                                    Builder.getInt32(0));

      // If the reduction can be performed in a smaller type, we need to extend
      // the reduction to the wider type before we branch to the original loop.
      if (RdxPhi->getType() != RdxDesc.getRecurrenceType())
        ReducedPartRdx =
            RdxDesc.isSigned()
                ? Builder.CreateSExt(ReducedPartRdx, RdxPhi->getType())
                : Builder.CreateZExt(ReducedPartRdx, RdxPhi->getType());
    }

    // Create a phi node that merges control-flow from the backedge-taken check
    // block and the middle block.
    PHINode *BCBlockPhi = PHINode::Create(RdxPhi->getType(), 2, "bc.merge.rdx",
                                          LoopScalarPreHeader->getTerminator());
    for (unsigned I = 0, E = LoopBypassBlocks.size(); I != E; ++I)
      BCBlockPhi->addIncoming(ReductionStartValue, LoopBypassBlocks[I]);
    BCBlockPhi->addIncoming(ReducedPartRdx, LoopMiddleBlock);

    // Now, we need to fix the users of the reduction variable
    // inside and outside of the scalar remainder loop.
    // We know that the loop is in LCSSA form. We need to update the
    // PHI nodes in the exit blocks.
    for (BasicBlock::iterator LEI = LoopExitBlock->begin(),
         LEE = LoopExitBlock->end(); LEI != LEE; ++LEI) {
      PHINode *LCSSAPhi = dyn_cast<PHINode>(LEI);
      if (!LCSSAPhi) break;

      // All PHINodes need to have a single entry edge, or two if
      // we already fixed them.
      assert(LCSSAPhi->getNumIncomingValues() < 3 && "Invalid LCSSA PHI");

      // We found our reduction value exit-PHI. Update it with the
      // incoming bypass edge.
      if (LCSSAPhi->getIncomingValue(0) == LoopExitInst) {
        // Add an edge coming from the bypass.
        LCSSAPhi->addIncoming(ReducedPartRdx, LoopMiddleBlock);
        break;
      }
    }// end of the LCSSA phi scan.

    // Fix the scalar loop reduction variable with the incoming reduction sum
    // from the vector body and from the backedge value.
    int IncomingEdgeBlockIdx =
    (RdxPhi)->getBasicBlockIndex(OrigLoop->getLoopLatch());
    assert(IncomingEdgeBlockIdx >= 0 && "Invalid block index");
    // Pick the other block.
    int SelfEdgeBlockIdx = (IncomingEdgeBlockIdx ? 0 : 1);
    (RdxPhi)->setIncomingValue(SelfEdgeBlockIdx, BCBlockPhi);
    (RdxPhi)->setIncomingValue(IncomingEdgeBlockIdx, LoopExitInst);
  }// end of for each redux variable.

  fixLCSSAPHIs();

  // Remove redundant induction instructions.
  cse(LoopVectorBody);
}

void InnerLoopVectorizer::fixLCSSAPHIs() {
  for (BasicBlock::iterator LEI = LoopExitBlock->begin(),
       LEE = LoopExitBlock->end(); LEI != LEE; ++LEI) {
    PHINode *LCSSAPhi = dyn_cast<PHINode>(LEI);
    if (!LCSSAPhi) break;
    if (LCSSAPhi->getNumIncomingValues() == 1)
      LCSSAPhi->addIncoming(UndefValue::get(LCSSAPhi->getType()),
                            LoopMiddleBlock);
  }
}

InnerLoopVectorizer::VectorParts
InnerLoopVectorizer::createEdgeMask(BasicBlock *Src, BasicBlock *Dst) {
  assert(std::find(pred_begin(Dst), pred_end(Dst), Src) != pred_end(Dst) &&
         "Invalid edge");

  // Look for cached value.
  std::pair<BasicBlock*, BasicBlock*> Edge(Src, Dst);
  EdgeMaskCache::iterator ECEntryIt = MaskCache.find(Edge);
  if (ECEntryIt != MaskCache.end())
    return ECEntryIt->second;

  VectorParts SrcMask = createBlockInMask(Src);

  // The terminator has to be a branch inst!
  BranchInst *BI = dyn_cast<BranchInst>(Src->getTerminator());
  assert(BI && "Unexpected terminator found");

  if (BI->isConditional()) {
    VectorParts EdgeMask = getVectorValue(BI->getCondition());

    if (BI->getSuccessor(0) != Dst)
      for (unsigned part = 0; part < UF; ++part)
        EdgeMask[part] = Builder.CreateNot(EdgeMask[part]);

    for (unsigned part = 0; part < UF; ++part)
      EdgeMask[part] = Builder.CreateAnd(EdgeMask[part], SrcMask[part]);

    MaskCache[Edge] = EdgeMask;
    return EdgeMask;
  }

  MaskCache[Edge] = SrcMask;
  return SrcMask;
}

InnerLoopVectorizer::VectorParts
InnerLoopVectorizer::createBlockInMask(BasicBlock *BB) {
  assert(OrigLoop->contains(BB) && "Block is not a part of a loop");

  // Loop incoming mask is all-one.
  if (OrigLoop->getHeader() == BB) {
    Value *C = ConstantInt::get(IntegerType::getInt1Ty(BB->getContext()), 1);
    return getVectorValue(C);
  }

  // This is the block mask. We OR all incoming edges, and with zero.
  Value *Zero = ConstantInt::get(IntegerType::getInt1Ty(BB->getContext()), 0);
  VectorParts BlockMask = getVectorValue(Zero);

  // For each pred:
  for (pred_iterator it = pred_begin(BB), e = pred_end(BB); it != e; ++it) {
    VectorParts EM = createEdgeMask(*it, BB);
    for (unsigned part = 0; part < UF; ++part)
      BlockMask[part] = Builder.CreateOr(BlockMask[part], EM[part]);
  }

  return BlockMask;
}

void InnerLoopVectorizer::widenPHIInstruction(Instruction *PN,
                                              InnerLoopVectorizer::VectorParts &Entry,
                                              unsigned UF, unsigned VF, PhiVector *PV) {
  PHINode* P = cast<PHINode>(PN);
  // Handle reduction variables:
  if (Legal->getReductionVars()->count(P)) {
    for (unsigned part = 0; part < UF; ++part) {
      // This is phase one of vectorizing PHIs.
      Type *VecTy = (VF == 1) ? PN->getType() :
      VectorType::get(PN->getType(), VF);
      Entry[part] = PHINode::Create(VecTy, 2, "vec.phi",
                                    LoopVectorBody.back()-> getFirstInsertionPt());
    }
    PV->push_back(P);
    return;
  }

  setDebugLocFromInst(Builder, P);
  // Check for PHI nodes that are lowered to vector selects.
  if (P->getParent() != OrigLoop->getHeader()) {
    // We know that all PHIs in non-header blocks are converted into
    // selects, so we don't have to worry about the insertion order and we
    // can just use the builder.
    // At this point we generate the predication tree. There may be
    // duplications since this is a simple recursive scan, but future
    // optimizations will clean it up.

    unsigned NumIncoming = P->getNumIncomingValues();

    // Generate a sequence of selects of the form:
    // SELECT(Mask3, In3,
    //      SELECT(Mask2, In2,
    //                   ( ...)))
    for (unsigned In = 0; In < NumIncoming; In++) {
      VectorParts Cond = createEdgeMask(P->getIncomingBlock(In),
                                        P->getParent());
      VectorParts &In0 = getVectorValue(P->getIncomingValue(In));

      for (unsigned part = 0; part < UF; ++part) {
        // We might have single edge PHIs (blocks) - use an identity
        // 'select' for the first PHI operand.
        if (In == 0)
          Entry[part] = Builder.CreateSelect(Cond[part], In0[part],
                                             In0[part]);
        else
          // Select between the current value and the previous incoming edge
          // based on the incoming mask.
          Entry[part] = Builder.CreateSelect(Cond[part], In0[part],
                                             Entry[part], "predphi");
      }
    }
    return;
  }

  // This PHINode must be an induction variable.
  // Make sure that we know about it.
  assert(Legal->getInductionVars()->count(P) &&
         "Not an induction variable");

  InductionDescriptor II = Legal->getInductionVars()->lookup(P);

  // FIXME: The newly created binary instructions should contain nsw/nuw flags,
  // which can be found from the original scalar operations.
  switch (II.getKind()) {
    case InductionDescriptor::IK_NoInduction:
      llvm_unreachable("Unknown induction");
    case InductionDescriptor::IK_IntInduction: {
      assert(P->getType() == II.getStartValue()->getType() && "Types must match");
      // Handle other induction variables that are now based on the
      // canonical one.
      Value *V = Induction;
      if (P != OldInduction) {
        V = Builder.CreateSExtOrTrunc(Induction, P->getType());
        V = II.transform(Builder, V);
        V->setName("offset.idx");
      }
      Value *Broadcasted = getBroadcastInstrs(V);
      // After broadcasting the induction variable we need to make the vector
      // consecutive by adding 0, 1, 2, etc.
      for (unsigned part = 0; part < UF; ++part)
        Entry[part] = getStepVector(Broadcasted, VF * part, II.getStepValue());
      return;
    }
    case InductionDescriptor::IK_PtrInduction:
      // Handle the pointer induction variable case.
      assert(P->getType()->isPointerTy() && "Unexpected type.");
      // This is the normalized GEP that starts counting at zero.
      Value *PtrInd = Induction;
      PtrInd = Builder.CreateSExtOrTrunc(PtrInd, II.getStepValue()->getType());
      // This is the vector of results. Notice that we don't generate
      // vector geps because scalar geps result in better code.
      for (unsigned part = 0; part < UF; ++part) {
        if (VF == 1) {
          int EltIndex = part;
          Constant *Idx = ConstantInt::get(PtrInd->getType(), EltIndex);
          Value *GlobalIdx = Builder.CreateAdd(PtrInd, Idx);
          Value *SclrGep = II.transform(Builder, GlobalIdx);
          SclrGep->setName("next.gep");
          Entry[part] = SclrGep;
          continue;
        }

        Value *VecVal = UndefValue::get(VectorType::get(P->getType(), VF));
        for (unsigned int i = 0; i < VF; ++i) {
          int EltIndex = i + part * VF;
          Constant *Idx = ConstantInt::get(PtrInd->getType(), EltIndex);
          Value *GlobalIdx = Builder.CreateAdd(PtrInd, Idx);
          Value *SclrGep = II.transform(Builder, GlobalIdx);
          SclrGep->setName("next.gep");
          VecVal = Builder.CreateInsertElement(VecVal, SclrGep,
                                               Builder.getInt32(i),
                                               "insert.gep");
        }
        Entry[part] = VecVal;
      }
      return;
  }
}

void InnerLoopVectorizer::vectorizeBlockInLoop(BasicBlock *BB, PhiVector *PV) {
  // For each instruction in the old loop.
  for (BasicBlock::iterator it = BB->begin(), e = BB->end(); it != e; ++it) {
    VectorParts &Entry = WidenMap.get(it);
    switch (it->getOpcode()) {
    case Instruction::Br:
      // Nothing to do for PHIs and BR, since we already took care of the
      // loop control flow instructions.
      continue;
    case Instruction::PHI: {
      // Vectorize PHINodes.
      widenPHIInstruction(it, Entry, UF, VF, PV);
      continue;
    }// End of PHI.

    case Instruction::Add:
    case Instruction::FAdd:
    case Instruction::Sub:
    case Instruction::FSub:
    case Instruction::Mul:
    case Instruction::FMul:
    case Instruction::UDiv:
    case Instruction::SDiv:
    case Instruction::FDiv:
    case Instruction::URem:
    case Instruction::SRem:
    case Instruction::FRem:
    case Instruction::Shl:
    case Instruction::LShr:
    case Instruction::AShr:
    case Instruction::And:
    case Instruction::Or:
    case Instruction::Xor: {
      // Just widen binops.
      BinaryOperator *BinOp = dyn_cast<BinaryOperator>(it);
      setDebugLocFromInst(Builder, BinOp);
      VectorParts &A = getVectorValue(it->getOperand(0));
      VectorParts &B = getVectorValue(it->getOperand(1));

      // Use this vector value for all users of the original instruction.
      for (unsigned Part = 0; Part < UF; ++Part) {
        Value *V = Builder.CreateBinOp(BinOp->getOpcode(), A[Part], B[Part]);

        if (BinaryOperator *VecOp = dyn_cast<BinaryOperator>(V))
          VecOp->copyIRFlags(BinOp);

        Entry[Part] = V;
      }

      propagateMetadata(Entry, it);
      break;
    }
    case Instruction::Select: {
      // Widen selects.
      // If the selector is loop invariant we can create a select
      // instruction with a scalar condition. Otherwise, use vector-select.
      bool InvariantCond = SE->isLoopInvariant(SE->getSCEV(it->getOperand(0)),
                                               OrigLoop);
      setDebugLocFromInst(Builder, it);

      // The condition can be loop invariant  but still defined inside the
      // loop. This means that we can't just use the original 'cond' value.
      // We have to take the 'vectorized' value and pick the first lane.
      // Instcombine will make this a no-op.
      VectorParts &Cond = getVectorValue(it->getOperand(0));
      VectorParts &Op0  = getVectorValue(it->getOperand(1));
      VectorParts &Op1  = getVectorValue(it->getOperand(2));

      Value *ScalarCond = (VF == 1) ? Cond[0] :
        Builder.CreateExtractElement(Cond[0], Builder.getInt32(0));

      for (unsigned Part = 0; Part < UF; ++Part) {
        Entry[Part] = Builder.CreateSelect(
          InvariantCond ? ScalarCond : Cond[Part],
          Op0[Part],
          Op1[Part]);
      }

      propagateMetadata(Entry, it);
      break;
    }

    case Instruction::ICmp:
    case Instruction::FCmp: {
      // Widen compares. Generate vector compares.
      bool FCmp = (it->getOpcode() == Instruction::FCmp);
      CmpInst *Cmp = dyn_cast<CmpInst>(it);
      setDebugLocFromInst(Builder, it);
      VectorParts &A = getVectorValue(it->getOperand(0));
      VectorParts &B = getVectorValue(it->getOperand(1));
      for (unsigned Part = 0; Part < UF; ++Part) {
        Value *C = nullptr;
        if (FCmp)
          C = Builder.CreateFCmp(Cmp->getPredicate(), A[Part], B[Part]);
        else
          C = Builder.CreateICmp(Cmp->getPredicate(), A[Part], B[Part]);
        Entry[Part] = C;
      }

      propagateMetadata(Entry, it);
      break;
    }

    case Instruction::Store:
    case Instruction::Load:
      vectorizeMemoryInstruction(it);
        break;
    case Instruction::ZExt:
    case Instruction::SExt:
    case Instruction::FPToUI:
    case Instruction::FPToSI:
    case Instruction::FPExt:
    case Instruction::PtrToInt:
    case Instruction::IntToPtr:
    case Instruction::SIToFP:
    case Instruction::UIToFP:
    case Instruction::Trunc:
    case Instruction::FPTrunc:
    case Instruction::BitCast: {
      CastInst *CI = dyn_cast<CastInst>(it);
      setDebugLocFromInst(Builder, it);
      /// Optimize the special case where the source is the induction
      /// variable. Notice that we can only optimize the 'trunc' case
      /// because: a. FP conversions lose precision, b. sext/zext may wrap,
      /// c. other casts depend on pointer size.
      if (CI->getOperand(0) == OldInduction &&
          it->getOpcode() == Instruction::Trunc) {
        Value *ScalarCast = Builder.CreateCast(CI->getOpcode(), Induction,
                                               CI->getType());
        Value *Broadcasted = getBroadcastInstrs(ScalarCast);
        InductionDescriptor II = Legal->getInductionVars()->lookup(OldInduction);
        Constant *Step =
            ConstantInt::getSigned(CI->getType(), II.getStepValue()->getSExtValue());
        for (unsigned Part = 0; Part < UF; ++Part)
          Entry[Part] = getStepVector(Broadcasted, VF * Part, Step);
        propagateMetadata(Entry, it);
        break;
      }
      /// Vectorize casts.
      Type *DestTy = (VF == 1) ? CI->getType() :
                                 VectorType::get(CI->getType(), VF);

      VectorParts &A = getVectorValue(it->getOperand(0));
      for (unsigned Part = 0; Part < UF; ++Part)
        Entry[Part] = Builder.CreateCast(CI->getOpcode(), A[Part], DestTy);
      propagateMetadata(Entry, it);
      break;
    }

    case Instruction::Call: {
      // Ignore dbg intrinsics.
      if (isa<DbgInfoIntrinsic>(it))
        break;
      setDebugLocFromInst(Builder, it);

      Module *M = BB->getParent()->getParent();
      CallInst *CI = cast<CallInst>(it);

      StringRef FnName = CI->getCalledFunction()->getName();
      Function *F = CI->getCalledFunction();
      Type *RetTy = ToVectorTy(CI->getType(), VF);
      SmallVector<Type *, 4> Tys;
      for (unsigned i = 0, ie = CI->getNumArgOperands(); i != ie; ++i)
        Tys.push_back(ToVectorTy(CI->getArgOperand(i)->getType(), VF));

      Intrinsic::ID ID = getIntrinsicIDForCall(CI, TLI);
      if (ID &&
          (ID == Intrinsic::assume || ID == Intrinsic::lifetime_end ||
           ID == Intrinsic::lifetime_start)) {
        scalarizeInstruction(it);
        break;
      }
      // The flag shows whether we use Intrinsic or a usual Call for vectorized
      // version of the instruction.
      // Is it beneficial to perform intrinsic call compared to lib call?
      bool NeedToScalarize;
      unsigned CallCost = getVectorCallCost(CI, VF, *TTI, TLI, NeedToScalarize);
      bool UseVectorIntrinsic =
          ID && getVectorIntrinsicCost(CI, VF, *TTI, TLI) <= CallCost;
      if (!UseVectorIntrinsic && NeedToScalarize) {
        scalarizeInstruction(it);
        break;
      }

      for (unsigned Part = 0; Part < UF; ++Part) {
        SmallVector<Value *, 4> Args;
        for (unsigned i = 0, ie = CI->getNumArgOperands(); i != ie; ++i) {
          Value *Arg = CI->getArgOperand(i);
          // Some intrinsics have a scalar argument - don't replace it with a
          // vector.
          if (!UseVectorIntrinsic || !hasVectorInstrinsicScalarOpd(ID, i)) {
            VectorParts &VectorArg = getVectorValue(CI->getArgOperand(i));
            Arg = VectorArg[Part];
          }
          Args.push_back(Arg);
        }

        Function *VectorF;
        if (UseVectorIntrinsic) {
          // Use vector version of the intrinsic.
          Type *TysForDecl[] = {CI->getType()};
          if (VF > 1)
            TysForDecl[0] = VectorType::get(CI->getType()->getScalarType(), VF);
          VectorF = Intrinsic::getDeclaration(M, ID, TysForDecl);
        } else {
          // Use vector version of the library call.
          StringRef VFnName = TLI->getVectorizedFunction(FnName, VF);
          assert(!VFnName.empty() && "Vector function name is empty.");
          VectorF = M->getFunction(VFnName);
          if (!VectorF) {
            // Generate a declaration
            FunctionType *FTy = FunctionType::get(RetTy, Tys, false);
            VectorF =
                Function::Create(FTy, Function::ExternalLinkage, VFnName, M);
            VectorF->copyAttributesFrom(F);
          }
        }
        assert(VectorF && "Can't create vector function.");
        Entry[Part] = Builder.CreateCall(VectorF, Args);
      }

      propagateMetadata(Entry, it);
      break;
    }

    default:
      // All other instructions are unsupported. Scalarize them.
      scalarizeInstruction(it);
      break;
    }// end of switch.
  }// end of for_each instr.
}

void InnerLoopVectorizer::updateAnalysis() {
  // Forget the original basic block.
  SE->forgetLoop(OrigLoop);

  // Update the dominator tree information.
  assert(DT->properlyDominates(LoopBypassBlocks.front(), LoopExitBlock) &&
         "Entry does not dominate exit.");

  for (unsigned I = 1, E = LoopBypassBlocks.size(); I != E; ++I)
    DT->addNewBlock(LoopBypassBlocks[I], LoopBypassBlocks[I-1]);
  DT->addNewBlock(LoopVectorPreHeader, LoopBypassBlocks.back());

  // Due to if predication of stores we might create a sequence of "if(pred)
  // a[i] = ...;  " blocks.
  for (unsigned i = 0, e = LoopVectorBody.size(); i != e; ++i) {
    if (i == 0)
      DT->addNewBlock(LoopVectorBody[0], LoopVectorPreHeader);
    else if (isPredicatedBlock(i)) {
      DT->addNewBlock(LoopVectorBody[i], LoopVectorBody[i-1]);
    } else {
      DT->addNewBlock(LoopVectorBody[i], LoopVectorBody[i-2]);
    }
  }

  DT->addNewBlock(LoopMiddleBlock, LoopVectorBody.back());
  DT->addNewBlock(LoopScalarPreHeader, LoopBypassBlocks[0]);
  DT->changeImmediateDominator(LoopScalarBody, LoopScalarPreHeader);
  DT->changeImmediateDominator(LoopExitBlock, LoopBypassBlocks[0]);

  DEBUG(DT->verifyDomTree());
}

/// \brief Check whether it is safe to if-convert this phi node.
///
/// Phi nodes with constant expressions that can trap are not safe to if
/// convert.
static bool canIfConvertPHINodes(BasicBlock *BB) {
  for (BasicBlock::iterator I = BB->begin(), E = BB->end(); I != E; ++I) {
    PHINode *Phi = dyn_cast<PHINode>(I);
    if (!Phi)
      return true;
    for (unsigned p = 0, e = Phi->getNumIncomingValues(); p != e; ++p)
      if (Constant *C = dyn_cast<Constant>(Phi->getIncomingValue(p)))
        if (C->canTrap())
          return false;
  }
  return true;
}

bool LoopVectorizationLegality::canVectorizeWithIfConvert() {
  if (!EnableIfConversion) {
    emitAnalysis(VectorizationReport() << "if-conversion is disabled");
    return false;
  }

  assert(TheLoop->getNumBlocks() > 1 && "Single block loops are vectorizable");

  // A list of pointers that we can safely read and write to.
  SmallPtrSet<Value *, 8> SafePointes;

  // Collect safe addresses.
  for (Loop::block_iterator BI = TheLoop->block_begin(),
         BE = TheLoop->block_end(); BI != BE; ++BI) {
    BasicBlock *BB = *BI;

    if (blockNeedsPredication(BB))
      continue;

    for (BasicBlock::iterator I = BB->begin(), E = BB->end(); I != E; ++I) {
      if (LoadInst *LI = dyn_cast<LoadInst>(I))
        SafePointes.insert(LI->getPointerOperand());
      else if (StoreInst *SI = dyn_cast<StoreInst>(I))
        SafePointes.insert(SI->getPointerOperand());
    }
  }

  // Collect the blocks that need predication.
  BasicBlock *Header = TheLoop->getHeader();
  for (Loop::block_iterator BI = TheLoop->block_begin(),
         BE = TheLoop->block_end(); BI != BE; ++BI) {
    BasicBlock *BB = *BI;

    // We don't support switch statements inside loops.
    if (!isa<BranchInst>(BB->getTerminator())) {
      emitAnalysis(VectorizationReport(BB->getTerminator())
                   << "loop contains a switch statement");
      return false;
    }

    // We must be able to predicate all blocks that need to be predicated.
    if (blockNeedsPredication(BB)) {
      if (!blockCanBePredicated(BB, SafePointes)) {
        emitAnalysis(VectorizationReport(BB->getTerminator())
                     << "control flow cannot be substituted for a select");
        return false;
      }
    } else if (BB != Header && !canIfConvertPHINodes(BB)) {
      emitAnalysis(VectorizationReport(BB->getTerminator())
                   << "control flow cannot be substituted for a select");
      return false;
    }
  }

  // We can if-convert this loop.
  return true;
}

bool LoopVectorizationLegality::canVectorize() {
  // We must have a loop in canonical form. Loops with indirectbr in them cannot
  // be canonicalized.
  if (!TheLoop->getLoopPreheader()) {
    emitAnalysis(
        VectorizationReport() <<
        "loop control flow is not understood by vectorizer");
    return false;
  }

  // We can only vectorize innermost loops.
  if (!TheLoop->empty()) {
    emitAnalysis(VectorizationReport() << "loop is not the innermost loop");
    return false;
  }

  // We must have a single backedge.
  if (TheLoop->getNumBackEdges() != 1) {
    emitAnalysis(
        VectorizationReport() <<
        "loop control flow is not understood by vectorizer");
    return false;
  }

  // We must have a single exiting block.
  if (!TheLoop->getExitingBlock()) {
    emitAnalysis(
        VectorizationReport() <<
        "loop control flow is not understood by vectorizer");
    return false;
  }

  // We only handle bottom-tested loops, i.e. loop in which the condition is
  // checked at the end of each iteration. With that we can assume that all
  // instructions in the loop are executed the same number of times.
  if (TheLoop->getExitingBlock() != TheLoop->getLoopLatch()) {
    emitAnalysis(
        VectorizationReport() <<
        "loop control flow is not understood by vectorizer");
    return false;
  }

  // We need to have a loop header.
  DEBUG(dbgs() << "LV: Found a loop: " <<
        TheLoop->getHeader()->getName() << '\n');

  // Check if we can if-convert non-single-bb loops.
  unsigned NumBlocks = TheLoop->getNumBlocks();
  if (NumBlocks != 1 && !canVectorizeWithIfConvert()) {
    DEBUG(dbgs() << "LV: Can't if-convert the loop.\n");
    return false;
  }

  // ScalarEvolution needs to be able to find the exit count.
  const SCEV *ExitCount = SE->getBackedgeTakenCount(TheLoop);
  if (ExitCount == SE->getCouldNotCompute()) {
    emitAnalysis(VectorizationReport() <<
                 "could not determine number of loop iterations");
    DEBUG(dbgs() << "LV: SCEV could not compute the loop exit count.\n");
    return false;
  }

  // Check if we can vectorize the instructions and CFG in this loop.
  if (!canVectorizeInstrs()) {
    DEBUG(dbgs() << "LV: Can't vectorize the instructions or CFG\n");
    return false;
  }

  // Go over each instruction and look at memory deps.
  if (!canVectorizeMemory()) {
    DEBUG(dbgs() << "LV: Can't vectorize due to memory conflicts\n");
    return false;
  }

  // Collect all of the variables that remain uniform after vectorization.
  collectLoopUniforms();

  DEBUG(dbgs() << "LV: We can vectorize this loop"
               << (LAI->getRuntimePointerChecking()->Need
                       ? " (with a runtime bound check)"
                       : "")
               << "!\n");

  bool UseInterleaved = TTI->enableInterleavedAccessVectorization();

  // If an override option has been passed in for interleaved accesses, use it.
  if (EnableInterleavedMemAccesses.getNumOccurrences() > 0)
    UseInterleaved = EnableInterleavedMemAccesses;

  // Analyze interleaved memory accesses.
  if (UseInterleaved)
     InterleaveInfo.analyzeInterleaving(Strides);

  // Okay! We can vectorize. At this point we don't have any other mem analysis
  // which may limit our maximum vectorization factor, so just return true with
  // no restrictions.
  return true;
}

static Type *convertPointerToIntegerType(const DataLayout &DL, Type *Ty) {
  if (Ty->isPointerTy())
    return DL.getIntPtrType(Ty);

  // It is possible that char's or short's overflow when we ask for the loop's
  // trip count, work around this by changing the type size.
  if (Ty->getScalarSizeInBits() < 32)
    return Type::getInt32Ty(Ty->getContext());

  return Ty;
}

static Type* getWiderType(const DataLayout &DL, Type *Ty0, Type *Ty1) {
  Ty0 = convertPointerToIntegerType(DL, Ty0);
  Ty1 = convertPointerToIntegerType(DL, Ty1);
  if (Ty0->getScalarSizeInBits() > Ty1->getScalarSizeInBits())
    return Ty0;
  return Ty1;
}

/// \brief Check that the instruction has outside loop users and is not an
/// identified reduction variable.
static bool hasOutsideLoopUser(const Loop *TheLoop, Instruction *Inst,
                               SmallPtrSetImpl<Value *> &Reductions) {
  // Reduction instructions are allowed to have exit users. All other
  // instructions must not have external users.
  if (!Reductions.count(Inst))
    //Check that all of the users of the loop are inside the BB.
    for (User *U : Inst->users()) {
      Instruction *UI = cast<Instruction>(U);
      // This user may be a reduction exit value.
      if (!TheLoop->contains(UI)) {
        DEBUG(dbgs() << "LV: Found an outside user for : " << *UI << '\n');
        return true;
      }
    }
  return false;
}

bool LoopVectorizationLegality::canVectorizeInstrs() {
  BasicBlock *Header = TheLoop->getHeader();

  // Look for the attribute signaling the absence of NaNs.
  Function &F = *Header->getParent();
  const DataLayout &DL = F.getParent()->getDataLayout();
  if (F.hasFnAttribute("no-nans-fp-math"))
    HasFunNoNaNAttr =
        F.getFnAttribute("no-nans-fp-math").getValueAsString() == "true";

  // For each block in the loop.
  for (Loop::block_iterator bb = TheLoop->block_begin(),
       be = TheLoop->block_end(); bb != be; ++bb) {

    // Scan the instructions in the block and look for hazards.
    for (BasicBlock::iterator it = (*bb)->begin(), e = (*bb)->end(); it != e;
         ++it) {

      if (PHINode *Phi = dyn_cast<PHINode>(it)) {
        Type *PhiTy = Phi->getType();
        // Check that this PHI type is allowed.
        if (!PhiTy->isIntegerTy() &&
            !PhiTy->isFloatingPointTy() &&
            !PhiTy->isPointerTy()) {
          emitAnalysis(VectorizationReport(it)
                       << "loop control flow is not understood by vectorizer");
          DEBUG(dbgs() << "LV: Found an non-int non-pointer PHI.\n");
          return false;
        }

        // If this PHINode is not in the header block, then we know that we
        // can convert it to select during if-conversion. No need to check if
        // the PHIs in this block are induction or reduction variables.
        if (*bb != Header) {
          // Check that this instruction has no outside users or is an
          // identified reduction value with an outside user.
          if (!hasOutsideLoopUser(TheLoop, it, AllowedExit))
            continue;
          emitAnalysis(VectorizationReport(it) <<
                       "value could not be identified as "
                       "an induction or reduction variable");
          return false;
        }

        // We only allow if-converted PHIs with exactly two incoming values.
        if (Phi->getNumIncomingValues() != 2) {
          emitAnalysis(VectorizationReport(it)
                       << "control flow not understood by vectorizer");
          DEBUG(dbgs() << "LV: Found an invalid PHI.\n");
          return false;
        }

        InductionDescriptor ID;
        if (InductionDescriptor::isInductionPHI(Phi, SE, ID)) {
          Inductions[Phi] = ID;
          // Get the widest type.
          if (!WidestIndTy)
            WidestIndTy = convertPointerToIntegerType(DL, PhiTy);
          else
            WidestIndTy = getWiderType(DL, PhiTy, WidestIndTy);

          // Int inductions are special because we only allow one IV.
          if (ID.getKind() == InductionDescriptor::IK_IntInduction &&
              ID.getStepValue()->isOne() &&
              isa<Constant>(ID.getStartValue()) &&
                cast<Constant>(ID.getStartValue())->isNullValue()) {
            // Use the phi node with the widest type as induction. Use the last
            // one if there are multiple (no good reason for doing this other
            // than it is expedient). We've checked that it begins at zero and
            // steps by one, so this is a canonical induction variable.
            if (!Induction || PhiTy == WidestIndTy)
              Induction = Phi;
          }

          DEBUG(dbgs() << "LV: Found an induction variable.\n");

          // Until we explicitly handle the case of an induction variable with
          // an outside loop user we have to give up vectorizing this loop.
          if (hasOutsideLoopUser(TheLoop, it, AllowedExit)) {
            emitAnalysis(VectorizationReport(it) <<
                         "use of induction value outside of the "
                         "loop is not handled by vectorizer");
            return false;
          }

          continue;
        }

        if (RecurrenceDescriptor::isReductionPHI(Phi, TheLoop,
                                                 Reductions[Phi])) {
          if (Reductions[Phi].hasUnsafeAlgebra())
            Requirements->addUnsafeAlgebraInst(
                Reductions[Phi].getUnsafeAlgebraInst());
          AllowedExit.insert(Reductions[Phi].getLoopExitInstr());
          continue;
        }

        emitAnalysis(VectorizationReport(it) <<
                     "value that could not be identified as "
                     "reduction is used outside the loop");
        DEBUG(dbgs() << "LV: Found an unidentified PHI."<< *Phi <<"\n");
        return false;
      }// end of PHI handling

      // We handle calls that:
      //   * Are debug info intrinsics.
      //   * Have a mapping to an IR intrinsic.
      //   * Have a vector version available.
      CallInst *CI = dyn_cast<CallInst>(it);
      if (CI && !getIntrinsicIDForCall(CI, TLI) && !isa<DbgInfoIntrinsic>(CI) &&
          !(CI->getCalledFunction() && TLI &&
            TLI->isFunctionVectorizable(CI->getCalledFunction()->getName()))) {
        emitAnalysis(VectorizationReport(it) <<
                     "call instruction cannot be vectorized");
        DEBUG(dbgs() << "LV: Found a non-intrinsic, non-libfunc callsite.\n");
        return false;
      }

      // Intrinsics such as powi,cttz and ctlz are legal to vectorize if the
      // second argument is the same (i.e. loop invariant)
      if (CI &&
          hasVectorInstrinsicScalarOpd(getIntrinsicIDForCall(CI, TLI), 1)) {
        if (!SE->isLoopInvariant(SE->getSCEV(CI->getOperand(1)), TheLoop)) {
          emitAnalysis(VectorizationReport(it)
                       << "intrinsic instruction cannot be vectorized");
          DEBUG(dbgs() << "LV: Found unvectorizable intrinsic " << *CI << "\n");
          return false;
        }
      }

      // Check that the instruction return type is vectorizable.
      // Also, we can't vectorize extractelement instructions.
      if ((!VectorType::isValidElementType(it->getType()) &&
           !it->getType()->isVoidTy()) || isa<ExtractElementInst>(it)) {
        emitAnalysis(VectorizationReport(it)
                     << "instruction return type cannot be vectorized");
        DEBUG(dbgs() << "LV: Found unvectorizable type.\n");
        return false;
      }

      // Check that the stored type is vectorizable.
      if (StoreInst *ST = dyn_cast<StoreInst>(it)) {
        Type *T = ST->getValueOperand()->getType();
        if (!VectorType::isValidElementType(T)) {
          emitAnalysis(VectorizationReport(ST) <<
                       "store instruction cannot be vectorized");
          return false;
        }
        if (EnableMemAccessVersioning)
          collectStridedAccess(ST);
      }

      if (EnableMemAccessVersioning)
        if (LoadInst *LI = dyn_cast<LoadInst>(it))
          collectStridedAccess(LI);

      // Reduction instructions are allowed to have exit users.
      // All other instructions must not have external users.
      if (hasOutsideLoopUser(TheLoop, it, AllowedExit)) {
        emitAnalysis(VectorizationReport(it) <<
                     "value cannot be used outside the loop");
        return false;
      }

    } // next instr.

  }

  if (!Induction) {
    DEBUG(dbgs() << "LV: Did not find one integer induction var.\n");
    if (Inductions.empty()) {
      emitAnalysis(VectorizationReport()
                   << "loop induction variable could not be identified");
      return false;
    }
  }

  // Now we know the widest induction type, check if our found induction
  // is the same size. If it's not, unset it here and InnerLoopVectorizer
  // will create another.
  if (Induction && WidestIndTy != Induction->getType())
    Induction = nullptr;

  return true;
}

void LoopVectorizationLegality::collectStridedAccess(Value *MemAccess) {
  Value *Ptr = nullptr;
  if (LoadInst *LI = dyn_cast<LoadInst>(MemAccess))
    Ptr = LI->getPointerOperand();
  else if (StoreInst *SI = dyn_cast<StoreInst>(MemAccess))
    Ptr = SI->getPointerOperand();
  else
    return;

  Value *Stride = getStrideFromPointer(Ptr, SE, TheLoop);
  if (!Stride)
    return;

  DEBUG(dbgs() << "LV: Found a strided access that we can version");
  DEBUG(dbgs() << "  Ptr: " << *Ptr << " Stride: " << *Stride << "\n");
  Strides[Ptr] = Stride;
  StrideSet.insert(Stride);
}

void LoopVectorizationLegality::collectLoopUniforms() {
  // We now know that the loop is vectorizable!
  // Collect variables that will remain uniform after vectorization.
  std::vector<Value*> Worklist;
  BasicBlock *Latch = TheLoop->getLoopLatch();

  // Start with the conditional branch and walk up the block.
  Worklist.push_back(Latch->getTerminator()->getOperand(0));

  // Also add all consecutive pointer values; these values will be uniform
  // after vectorization (and subsequent cleanup) and, until revectorization is
  // supported, all dependencies must also be uniform.
  for (Loop::block_iterator B = TheLoop->block_begin(),
       BE = TheLoop->block_end(); B != BE; ++B)
    for (BasicBlock::iterator I = (*B)->begin(), IE = (*B)->end();
         I != IE; ++I)
      if (I->getType()->isPointerTy() && isConsecutivePtr(I))
        Worklist.insert(Worklist.end(), I->op_begin(), I->op_end());

  while (!Worklist.empty()) {
    Instruction *I = dyn_cast<Instruction>(Worklist.back());
    Worklist.pop_back();

    // Look at instructions inside this loop.
    // Stop when reaching PHI nodes.
    // TODO: we need to follow values all over the loop, not only in this block.
    if (!I || !TheLoop->contains(I) || isa<PHINode>(I))
      continue;

    // This is a known uniform.
    Uniforms.insert(I);

    // Insert all operands.
    Worklist.insert(Worklist.end(), I->op_begin(), I->op_end());
  }
}

bool LoopVectorizationLegality::canVectorizeMemory() {
  LAI = &LAA->getInfo(TheLoop, Strides);
  auto &OptionalReport = LAI->getReport();
  if (OptionalReport)
    emitAnalysis(VectorizationReport(*OptionalReport));
  if (!LAI->canVectorizeMemory())
    return false;

  if (LAI->hasStoreToLoopInvariantAddress()) {
    emitAnalysis(
        VectorizationReport()
        << "write to a loop invariant address could not be vectorized");
    DEBUG(dbgs() << "LV: We don't allow storing to uniform addresses\n");
    return false;
  }

  Requirements->addRuntimePointerChecks(LAI->getNumRuntimePointerChecks());

  return true;
}

bool LoopVectorizationLegality::isInductionVariable(const Value *V) {
  Value *In0 = const_cast<Value*>(V);
  PHINode *PN = dyn_cast_or_null<PHINode>(In0);
  if (!PN)
    return false;

  return Inductions.count(PN);
}

bool LoopVectorizationLegality::blockNeedsPredication(BasicBlock *BB)  {
  return LoopAccessInfo::blockNeedsPredication(BB, TheLoop, DT);
}

bool LoopVectorizationLegality::blockCanBePredicated(BasicBlock *BB,
                                           SmallPtrSetImpl<Value *> &SafePtrs) {
  
  for (BasicBlock::iterator it = BB->begin(), e = BB->end(); it != e; ++it) {
    // Check that we don't have a constant expression that can trap as operand.
    for (Instruction::op_iterator OI = it->op_begin(), OE = it->op_end();
         OI != OE; ++OI) {
      if (Constant *C = dyn_cast<Constant>(*OI))
        if (C->canTrap())
          return false;
    }
    // We might be able to hoist the load.
    if (it->mayReadFromMemory()) {
      LoadInst *LI = dyn_cast<LoadInst>(it);
      if (!LI)
        return false;
      if (!SafePtrs.count(LI->getPointerOperand())) {
        if (isLegalMaskedLoad(LI->getType(), LI->getPointerOperand())) {
          MaskedOp.insert(LI);
          continue;
        }
        return false;
      }
    }

    // We don't predicate stores at the moment.
    if (it->mayWriteToMemory()) {
      StoreInst *SI = dyn_cast<StoreInst>(it);
      // We only support predication of stores in basic blocks with one
      // predecessor.
      if (!SI)
        return false;

      bool isSafePtr = (SafePtrs.count(SI->getPointerOperand()) != 0);
      bool isSinglePredecessor = SI->getParent()->getSinglePredecessor();
      
      if (++NumPredStores > NumberOfStoresToPredicate || !isSafePtr ||
          !isSinglePredecessor) {
        // Build a masked store if it is legal for the target, otherwise scalarize
        // the block.
        bool isLegalMaskedOp =
          isLegalMaskedStore(SI->getValueOperand()->getType(),
                             SI->getPointerOperand());
        if (isLegalMaskedOp) {
          --NumPredStores;
          MaskedOp.insert(SI);
          continue;
        }
        return false;
      }
    }
    if (it->mayThrow())
      return false;

    // The instructions below can trap.
    switch (it->getOpcode()) {
    default: continue;
    case Instruction::UDiv:
    case Instruction::SDiv:
    case Instruction::URem:
    case Instruction::SRem:
      return false;
    }
  }

  return true;
}

void InterleavedAccessInfo::collectConstStridedAccesses(
    MapVector<Instruction *, StrideDescriptor> &StrideAccesses,
    const ValueToValueMap &Strides) {
  // Holds load/store instructions in program order.
  SmallVector<Instruction *, 16> AccessList;

  for (auto *BB : TheLoop->getBlocks()) {
    bool IsPred = LoopAccessInfo::blockNeedsPredication(BB, TheLoop, DT);

    for (auto &I : *BB) {
      if (!isa<LoadInst>(&I) && !isa<StoreInst>(&I))
        continue;
      // FIXME: Currently we can't handle mixed accesses and predicated accesses
      if (IsPred)
        return;

      AccessList.push_back(&I);
    }
  }

  if (AccessList.empty())
    return;

  auto &DL = TheLoop->getHeader()->getModule()->getDataLayout();
  for (auto I : AccessList) {
    LoadInst *LI = dyn_cast<LoadInst>(I);
    StoreInst *SI = dyn_cast<StoreInst>(I);

    Value *Ptr = LI ? LI->getPointerOperand() : SI->getPointerOperand();
    int Stride = isStridedPtr(SE, Ptr, TheLoop, Strides);

    // The factor of the corresponding interleave group.
    unsigned Factor = std::abs(Stride);

    // Ignore the access if the factor is too small or too large.
    if (Factor < 2 || Factor > MaxInterleaveGroupFactor)
      continue;

    const SCEV *Scev = replaceSymbolicStrideSCEV(SE, Strides, Ptr);
    PointerType *PtrTy = dyn_cast<PointerType>(Ptr->getType());
    unsigned Size = DL.getTypeAllocSize(PtrTy->getElementType());

    // An alignment of 0 means target ABI alignment.
    unsigned Align = LI ? LI->getAlignment() : SI->getAlignment();
    if (!Align)
      Align = DL.getABITypeAlignment(PtrTy->getElementType());

    StrideAccesses[I] = StrideDescriptor(Stride, Scev, Size, Align);
  }
}

// Analyze interleaved accesses and collect them into interleave groups.
//
// Notice that the vectorization on interleaved groups will change instruction
// orders and may break dependences. But the memory dependence check guarantees
// that there is no overlap between two pointers of different strides, element
// sizes or underlying bases.
//
// For pointers sharing the same stride, element size and underlying base, no
// need to worry about Read-After-Write dependences and Write-After-Read
// dependences.
//
// E.g. The RAW dependence:  A[i] = a;
//                           b = A[i];
// This won't exist as it is a store-load forwarding conflict, which has
// already been checked and forbidden in the dependence check.
//
// E.g. The WAR dependence:  a = A[i];  // (1)
//                           A[i] = b;  // (2)
// The store group of (2) is always inserted at or below (2), and the load group
// of (1) is always inserted at or above (1). The dependence is safe.
void InterleavedAccessInfo::analyzeInterleaving(
    const ValueToValueMap &Strides) {
  DEBUG(dbgs() << "LV: Analyzing interleaved accesses...\n");

  // Holds all the stride accesses.
  MapVector<Instruction *, StrideDescriptor> StrideAccesses;
  collectConstStridedAccesses(StrideAccesses, Strides);

  if (StrideAccesses.empty())
    return;

  // Holds all interleaved store groups temporarily.
  SmallSetVector<InterleaveGroup *, 4> StoreGroups;

  // Search the load-load/write-write pair B-A in bottom-up order and try to
  // insert B into the interleave group of A according to 3 rules:
  //   1. A and B have the same stride.
  //   2. A and B have the same memory object size.
  //   3. B belongs to the group according to the distance.
  //
  // The bottom-up order can avoid breaking the Write-After-Write dependences
  // between two pointers of the same base.
  // E.g.  A[i]   = a;   (1)
  //       A[i]   = b;   (2)
  //       A[i+1] = c    (3)
  // We form the group (2)+(3) in front, so (1) has to form groups with accesses
  // above (1), which guarantees that (1) is always above (2).
  for (auto I = StrideAccesses.rbegin(), E = StrideAccesses.rend(); I != E;
       ++I) {
    Instruction *A = I->first;
    StrideDescriptor DesA = I->second;

    InterleaveGroup *Group = getInterleaveGroup(A);
    if (!Group) {
      DEBUG(dbgs() << "LV: Creating an interleave group with:" << *A << '\n');
      Group = createInterleaveGroup(A, DesA.Stride, DesA.Align);
    }

    if (A->mayWriteToMemory())
      StoreGroups.insert(Group);

    for (auto II = std::next(I); II != E; ++II) {
      Instruction *B = II->first;
      StrideDescriptor DesB = II->second;

      // Ignore if B is already in a group or B is a different memory operation.
      if (isInterleaved(B) || A->mayReadFromMemory() != B->mayReadFromMemory())
        continue;

      // Check the rule 1 and 2.
      if (DesB.Stride != DesA.Stride || DesB.Size != DesA.Size)
        continue;

      // Calculate the distance and prepare for the rule 3.
      const SCEVConstant *DistToA =
          dyn_cast<SCEVConstant>(SE->getMinusSCEV(DesB.Scev, DesA.Scev));
      if (!DistToA)
        continue;

      int DistanceToA = DistToA->getValue()->getValue().getSExtValue();

      // Skip if the distance is not multiple of size as they are not in the
      // same group.
      if (DistanceToA % static_cast<int>(DesA.Size))
        continue;

      // The index of B is the index of A plus the related index to A.
      int IndexB =
          Group->getIndex(A) + DistanceToA / static_cast<int>(DesA.Size);

      // Try to insert B into the group.
      if (Group->insertMember(B, IndexB, DesB.Align)) {
        DEBUG(dbgs() << "LV: Inserted:" << *B << '\n'
                     << "    into the interleave group with" << *A << '\n');
        InterleaveGroupMap[B] = Group;

        // Set the first load in program order as the insert position.
        if (B->mayReadFromMemory())
          Group->setInsertPos(B);
      }
    } // Iteration on instruction B
  }   // Iteration on instruction A

  // Remove interleaved store groups with gaps.
  for (InterleaveGroup *Group : StoreGroups)
    if (Group->getNumMembers() != Group->getFactor())
      releaseGroup(Group);
}

LoopVectorizationCostModel::VectorizationFactor
LoopVectorizationCostModel::selectVectorizationFactor(bool OptForSize) {
  // Width 1 means no vectorize
  VectorizationFactor Factor = { 1U, 0U };
  if (OptForSize && Legal->getRuntimePointerChecking()->Need) {
    emitAnalysis(VectorizationReport() <<
                 "runtime pointer checks needed. Enable vectorization of this "
                 "loop with '#pragma clang loop vectorize(enable)' when "
                 "compiling with -Os/-Oz");
    DEBUG(dbgs() <<
          "LV: Aborting. Runtime ptr check is required with -Os/-Oz.\n");
    return Factor;
  }

  if (!EnableCondStoresVectorization && Legal->getNumPredStores()) {
    emitAnalysis(VectorizationReport() <<
                 "store that is conditionally executed prevents vectorization");
    DEBUG(dbgs() << "LV: No vectorization. There are conditional stores.\n");
    return Factor;
  }

  // Find the trip count.
  unsigned TC = SE->getSmallConstantTripCount(TheLoop);
  DEBUG(dbgs() << "LV: Found trip count: " << TC << '\n');

  unsigned WidestType = getWidestType();
  unsigned WidestRegister = TTI.getRegisterBitWidth(true);
  unsigned MaxSafeDepDist = -1U;
  if (Legal->getMaxSafeDepDistBytes() != -1U)
    MaxSafeDepDist = Legal->getMaxSafeDepDistBytes() * 8;
  WidestRegister = ((WidestRegister < MaxSafeDepDist) ?
                    WidestRegister : MaxSafeDepDist);
  unsigned MaxVectorSize = WidestRegister / WidestType;
  DEBUG(dbgs() << "LV: The Widest type: " << WidestType << " bits.\n");
  DEBUG(dbgs() << "LV: The Widest register is: "
          << WidestRegister << " bits.\n");

  if (MaxVectorSize == 0) {
    DEBUG(dbgs() << "LV: The target has no vector registers.\n");
    MaxVectorSize = 1;
  }

  assert(MaxVectorSize <= 64 && "Did not expect to pack so many elements"
         " into one vector!");

  unsigned VF = MaxVectorSize;

  // If we optimize the program for size, avoid creating the tail loop.
  if (OptForSize) {
    // If we are unable to calculate the trip count then don't try to vectorize.
    if (TC < 2) {
      emitAnalysis
        (VectorizationReport() <<
         "unable to calculate the loop count due to complex control flow");
      DEBUG(dbgs() << "LV: Aborting. A tail loop is required with -Os/-Oz.\n");
      return Factor;
    }

    // Find the maximum SIMD width that can fit within the trip count.
    VF = TC % MaxVectorSize;

    if (VF == 0)
      VF = MaxVectorSize;
    else {
      // If the trip count that we found modulo the vectorization factor is not
      // zero then we require a tail.
      emitAnalysis(VectorizationReport() <<
                   "cannot optimize for size and vectorize at the "
                   "same time. Enable vectorization of this loop "
                   "with '#pragma clang loop vectorize(enable)' "
                   "when compiling with -Os/-Oz");
      DEBUG(dbgs() << "LV: Aborting. A tail loop is required with -Os/-Oz.\n");
      return Factor;
    }
  }

  int UserVF = Hints->getWidth();
  if (UserVF != 0) {
    assert(isPowerOf2_32(UserVF) && "VF needs to be a power of two");
    DEBUG(dbgs() << "LV: Using user VF " << UserVF << ".\n");

    Factor.Width = UserVF;
    return Factor;
  }

  float Cost = expectedCost(1);
#ifndef NDEBUG
  const float ScalarCost = Cost;
#endif /* NDEBUG */
  unsigned Width = 1;
  DEBUG(dbgs() << "LV: Scalar loop costs: " << (int)ScalarCost << ".\n");

  bool ForceVectorization = Hints->getForce() == LoopVectorizeHints::FK_Enabled;
  // Ignore scalar width, because the user explicitly wants vectorization.
  if (ForceVectorization && VF > 1) {
    Width = 2;
    Cost = expectedCost(Width) / (float)Width;
  }

  for (unsigned i=2; i <= VF; i*=2) {
    // Notice that the vector loop needs to be executed less times, so
    // we need to divide the cost of the vector loops by the width of
    // the vector elements.
    float VectorCost = expectedCost(i) / (float)i;
    DEBUG(dbgs() << "LV: Vector loop of width " << i << " costs: " <<
          (int)VectorCost << ".\n");
    if (VectorCost < Cost) {
      Cost = VectorCost;
      Width = i;
    }
  }

  DEBUG(if (ForceVectorization && Width > 1 && Cost >= ScalarCost) dbgs()
        << "LV: Vectorization seems to be not beneficial, "
        << "but was forced by a user.\n");
  DEBUG(dbgs() << "LV: Selecting VF: "<< Width << ".\n");
  Factor.Width = Width;
  Factor.Cost = Width * Cost;
  return Factor;
}

unsigned LoopVectorizationCostModel::getWidestType() {
  unsigned MaxWidth = 8;
  const DataLayout &DL = TheFunction->getParent()->getDataLayout();

  // For each block.
  for (Loop::block_iterator bb = TheLoop->block_begin(),
       be = TheLoop->block_end(); bb != be; ++bb) {
    BasicBlock *BB = *bb;

    // For each instruction in the loop.
    for (BasicBlock::iterator it = BB->begin(), e = BB->end(); it != e; ++it) {
      Type *T = it->getType();

      // Skip ignored values.
      if (ValuesToIgnore.count(it))
        continue;

      // Only examine Loads, Stores and PHINodes.
      if (!isa<LoadInst>(it) && !isa<StoreInst>(it) && !isa<PHINode>(it))
        continue;

      // Examine PHI nodes that are reduction variables. Update the type to
      // account for the recurrence type.
      if (PHINode *PN = dyn_cast<PHINode>(it)) {
        if (!Legal->getReductionVars()->count(PN))
          continue;
        RecurrenceDescriptor RdxDesc = (*Legal->getReductionVars())[PN];
        T = RdxDesc.getRecurrenceType();
      }

      // Examine the stored values.
      if (StoreInst *ST = dyn_cast<StoreInst>(it))
        T = ST->getValueOperand()->getType();

      // Ignore loaded pointer types and stored pointer types that are not
      // consecutive. However, we do want to take consecutive stores/loads of
      // pointer vectors into account.
      if (T->isPointerTy() && !isConsecutiveLoadOrStore(it))
        continue;

      MaxWidth = std::max(MaxWidth,
                          (unsigned)DL.getTypeSizeInBits(T->getScalarType()));
    }
  }

  return MaxWidth;
}

unsigned LoopVectorizationCostModel::selectInterleaveCount(bool OptForSize,
                                                           unsigned VF,
                                                           unsigned LoopCost) {

  // -- The interleave heuristics --
  // We interleave the loop in order to expose ILP and reduce the loop overhead.
  // There are many micro-architectural considerations that we can't predict
  // at this level. For example, frontend pressure (on decode or fetch) due to
  // code size, or the number and capabilities of the execution ports.
  //
  // We use the following heuristics to select the interleave count:
  // 1. If the code has reductions, then we interleave to break the cross
  // iteration dependency.
  // 2. If the loop is really small, then we interleave to reduce the loop
  // overhead.
  // 3. We don't interleave if we think that we will spill registers to memory
  // due to the increased register pressure.

  // When we optimize for size, we don't interleave.
  if (OptForSize)
    return 1;

  // We used the distance for the interleave count.
  if (Legal->getMaxSafeDepDistBytes() != -1U)
    return 1;

  // Do not interleave loops with a relatively small trip count.
  unsigned TC = SE->getSmallConstantTripCount(TheLoop);
  if (TC > 1 && TC < TinyTripCountInterleaveThreshold)
    return 1;

  unsigned TargetNumRegisters = TTI.getNumberOfRegisters(VF > 1);
  DEBUG(dbgs() << "LV: The target has " << TargetNumRegisters <<
        " registers\n");

  if (VF == 1) {
    if (ForceTargetNumScalarRegs.getNumOccurrences() > 0)
      TargetNumRegisters = ForceTargetNumScalarRegs;
  } else {
    if (ForceTargetNumVectorRegs.getNumOccurrences() > 0)
      TargetNumRegisters = ForceTargetNumVectorRegs;
  }

  LoopVectorizationCostModel::RegisterUsage R = calculateRegisterUsage();
  // We divide by these constants so assume that we have at least one
  // instruction that uses at least one register.
  R.MaxLocalUsers = std::max(R.MaxLocalUsers, 1U);
  R.NumInstructions = std::max(R.NumInstructions, 1U);

  // We calculate the interleave count using the following formula.
  // Subtract the number of loop invariants from the number of available
  // registers. These registers are used by all of the interleaved instances.
  // Next, divide the remaining registers by the number of registers that is
  // required by the loop, in order to estimate how many parallel instances
  // fit without causing spills. All of this is rounded down if necessary to be
  // a power of two. We want power of two interleave count to simplify any
  // addressing operations or alignment considerations.
  unsigned IC = PowerOf2Floor((TargetNumRegisters - R.LoopInvariantRegs) /
                              R.MaxLocalUsers);

  // Don't count the induction variable as interleaved.
  if (EnableIndVarRegisterHeur)
    IC = PowerOf2Floor((TargetNumRegisters - R.LoopInvariantRegs - 1) /
                       std::max(1U, (R.MaxLocalUsers - 1)));

  // Clamp the interleave ranges to reasonable counts.
  unsigned MaxInterleaveCount = TTI.getMaxInterleaveFactor(VF);

  // Check if the user has overridden the max.
  if (VF == 1) {
    if (ForceTargetMaxScalarInterleaveFactor.getNumOccurrences() > 0)
      MaxInterleaveCount = ForceTargetMaxScalarInterleaveFactor;
  } else {
    if (ForceTargetMaxVectorInterleaveFactor.getNumOccurrences() > 0)
      MaxInterleaveCount = ForceTargetMaxVectorInterleaveFactor;
  }

  // If we did not calculate the cost for VF (because the user selected the VF)
  // then we calculate the cost of VF here.
  if (LoopCost == 0)
    LoopCost = expectedCost(VF);

  // Clamp the calculated IC to be between the 1 and the max interleave count
  // that the target allows.
  if (IC > MaxInterleaveCount)
    IC = MaxInterleaveCount;
  else if (IC < 1)
    IC = 1;

  // Interleave if we vectorized this loop and there is a reduction that could
  // benefit from interleaving.
  if (VF > 1 && Legal->getReductionVars()->size()) {
    DEBUG(dbgs() << "LV: Interleaving because of reductions.\n");
    return IC;
  }

  // Note that if we've already vectorized the loop we will have done the
  // runtime check and so interleaving won't require further checks.
  bool InterleavingRequiresRuntimePointerCheck =
      (VF == 1 && Legal->getRuntimePointerChecking()->Need);

  // We want to interleave small loops in order to reduce the loop overhead and
  // potentially expose ILP opportunities.
  DEBUG(dbgs() << "LV: Loop cost is " << LoopCost << '\n');
  if (!InterleavingRequiresRuntimePointerCheck && LoopCost < SmallLoopCost) {
    // We assume that the cost overhead is 1 and we use the cost model
    // to estimate the cost of the loop and interleave until the cost of the
    // loop overhead is about 5% of the cost of the loop.
    unsigned SmallIC =
        std::min(IC, (unsigned)PowerOf2Floor(SmallLoopCost / LoopCost));

    // Interleave until store/load ports (estimated by max interleave count) are
    // saturated.
    unsigned NumStores = Legal->getNumStores();
    unsigned NumLoads = Legal->getNumLoads();
    unsigned StoresIC = IC / (NumStores ? NumStores : 1);
    unsigned LoadsIC = IC / (NumLoads ? NumLoads : 1);

    // If we have a scalar reduction (vector reductions are already dealt with
    // by this point), we can increase the critical path length if the loop
    // we're interleaving is inside another loop. Limit, by default to 2, so the
    // critical path only gets increased by one reduction operation.
    if (Legal->getReductionVars()->size() &&
        TheLoop->getLoopDepth() > 1) {
      unsigned F = static_cast<unsigned>(MaxNestedScalarReductionIC);
      SmallIC = std::min(SmallIC, F);
      StoresIC = std::min(StoresIC, F);
      LoadsIC = std::min(LoadsIC, F);
    }

    if (EnableLoadStoreRuntimeInterleave &&
        std::max(StoresIC, LoadsIC) > SmallIC) {
      DEBUG(dbgs() << "LV: Interleaving to saturate store or load ports.\n");
      return std::max(StoresIC, LoadsIC);
    }

    DEBUG(dbgs() << "LV: Interleaving to reduce branch cost.\n");
    return SmallIC;
  }

  // Interleave if this is a large loop (small loops are already dealt with by
  // this
  // point) that could benefit from interleaving.
  bool HasReductions = (Legal->getReductionVars()->size() > 0);
  if (TTI.enableAggressiveInterleaving(HasReductions)) {
    DEBUG(dbgs() << "LV: Interleaving to expose ILP.\n");
    return IC;
  }

  DEBUG(dbgs() << "LV: Not Interleaving.\n");
  return 1;
}

LoopVectorizationCostModel::RegisterUsage
LoopVectorizationCostModel::calculateRegisterUsage() {
  // This function calculates the register usage by measuring the highest number
  // of values that are alive at a single location. Obviously, this is a very
  // rough estimation. We scan the loop in a topological order in order and
  // assign a number to each instruction. We use RPO to ensure that defs are
  // met before their users. We assume that each instruction that has in-loop
  // users starts an interval. We record every time that an in-loop value is
  // used, so we have a list of the first and last occurrences of each
  // instruction. Next, we transpose this data structure into a multi map that
  // holds the list of intervals that *end* at a specific location. This multi
  // map allows us to perform a linear search. We scan the instructions linearly
  // and record each time that a new interval starts, by placing it in a set.
  // If we find this value in the multi-map then we remove it from the set.
  // The max register usage is the maximum size of the set.
  // We also search for instructions that are defined outside the loop, but are
  // used inside the loop. We need this number separately from the max-interval
  // usage number because when we unroll, loop-invariant values do not take
  // more register.
  LoopBlocksDFS DFS(TheLoop);
  DFS.perform(LI);

  RegisterUsage R;
  R.NumInstructions = 0;

  // Each 'key' in the map opens a new interval. The values
  // of the map are the index of the 'last seen' usage of the
  // instruction that is the key.
  typedef DenseMap<Instruction*, unsigned> IntervalMap;
  // Maps instruction to its index.
  DenseMap<unsigned, Instruction*> IdxToInstr;
  // Marks the end of each interval.
  IntervalMap EndPoint;
  // Saves the list of instruction indices that are used in the loop.
  SmallSet<Instruction*, 8> Ends;
  // Saves the list of values that are used in the loop but are
  // defined outside the loop, such as arguments and constants.
  SmallPtrSet<Value*, 8> LoopInvariants;

  unsigned Index = 0;
  for (LoopBlocksDFS::RPOIterator bb = DFS.beginRPO(),
       be = DFS.endRPO(); bb != be; ++bb) {
    R.NumInstructions += (*bb)->size();
    for (BasicBlock::iterator it = (*bb)->begin(), e = (*bb)->end(); it != e;
         ++it) {
      Instruction *I = it;
      IdxToInstr[Index++] = I;

      // Save the end location of each USE.
      for (unsigned i = 0; i < I->getNumOperands(); ++i) {
        Value *U = I->getOperand(i);
        Instruction *Instr = dyn_cast<Instruction>(U);

        // Ignore non-instruction values such as arguments, constants, etc.
        if (!Instr) continue;

        // If this instruction is outside the loop then record it and continue.
        if (!TheLoop->contains(Instr)) {
          LoopInvariants.insert(Instr);
          continue;
        }

        // Overwrite previous end points.
        EndPoint[Instr] = Index;
        Ends.insert(Instr);
      }
    }
  }

  // Saves the list of intervals that end with the index in 'key'.
  typedef SmallVector<Instruction*, 2> InstrList;
  DenseMap<unsigned, InstrList> TransposeEnds;

  // Transpose the EndPoints to a list of values that end at each index.
  for (IntervalMap::iterator it = EndPoint.begin(), e = EndPoint.end();
       it != e; ++it)
    TransposeEnds[it->second].push_back(it->first);

  SmallSet<Instruction*, 8> OpenIntervals;
  unsigned MaxUsage = 0;


  DEBUG(dbgs() << "LV(REG): Calculating max register usage:\n");
  for (unsigned int i = 0; i < Index; ++i) {
    Instruction *I = IdxToInstr[i];
    // Ignore instructions that are never used within the loop.
    if (!Ends.count(I)) continue;

    // Skip ignored values.
    if (ValuesToIgnore.count(I))
      continue;

    // Remove all of the instructions that end at this location.
    InstrList &List = TransposeEnds[i];
    for (unsigned int j=0, e = List.size(); j < e; ++j)
      OpenIntervals.erase(List[j]);

    // Count the number of live interals.
    MaxUsage = std::max(MaxUsage, OpenIntervals.size());

    DEBUG(dbgs() << "LV(REG): At #" << i << " Interval # " <<
          OpenIntervals.size() << '\n');

    // Add the current instruction to the list of open intervals.
    OpenIntervals.insert(I);
  }

  unsigned Invariant = LoopInvariants.size();
  DEBUG(dbgs() << "LV(REG): Found max usage: " << MaxUsage << '\n');
  DEBUG(dbgs() << "LV(REG): Found invariant usage: " << Invariant << '\n');
  DEBUG(dbgs() << "LV(REG): LoopSize: " << R.NumInstructions << '\n');

  R.LoopInvariantRegs = Invariant;
  R.MaxLocalUsers = MaxUsage;
  return R;
}

unsigned LoopVectorizationCostModel::expectedCost(unsigned VF) {
  unsigned Cost = 0;

  // For each block.
  for (Loop::block_iterator bb = TheLoop->block_begin(),
       be = TheLoop->block_end(); bb != be; ++bb) {
    unsigned BlockCost = 0;
    BasicBlock *BB = *bb;

    // For each instruction in the old loop.
    for (BasicBlock::iterator it = BB->begin(), e = BB->end(); it != e; ++it) {
      // Skip dbg intrinsics.
      if (isa<DbgInfoIntrinsic>(it))
        continue;

      // Skip ignored values.
      if (ValuesToIgnore.count(it))
        continue;

      unsigned C = getInstructionCost(it, VF);

      // Check if we should override the cost.
      if (ForceTargetInstructionCost.getNumOccurrences() > 0)
        C = ForceTargetInstructionCost;

      BlockCost += C;
      DEBUG(dbgs() << "LV: Found an estimated cost of " << C << " for VF " <<
            VF << " For instruction: " << *it << '\n');
    }

    // We assume that if-converted blocks have a 50% chance of being executed.
    // When the code is scalar then some of the blocks are avoided due to CF.
    // When the code is vectorized we execute all code paths.
    if (VF == 1 && Legal->blockNeedsPredication(*bb))
      BlockCost /= 2;

    Cost += BlockCost;
  }

  return Cost;
}

/// \brief Check whether the address computation for a non-consecutive memory
/// access looks like an unlikely candidate for being merged into the indexing
/// mode.
///
/// We look for a GEP which has one index that is an induction variable and all
/// other indices are loop invariant. If the stride of this access is also
/// within a small bound we decide that this address computation can likely be
/// merged into the addressing mode.
/// In all other cases, we identify the address computation as complex.
static bool isLikelyComplexAddressComputation(Value *Ptr,
                                              LoopVectorizationLegality *Legal,
                                              ScalarEvolution *SE,
                                              const Loop *TheLoop) {
  GetElementPtrInst *Gep = dyn_cast<GetElementPtrInst>(Ptr);
  if (!Gep)
    return true;

  // We are looking for a gep with all loop invariant indices except for one
  // which should be an induction variable.
  unsigned NumOperands = Gep->getNumOperands();
  for (unsigned i = 1; i < NumOperands; ++i) {
    Value *Opd = Gep->getOperand(i);
    if (!SE->isLoopInvariant(SE->getSCEV(Opd), TheLoop) &&
        !Legal->isInductionVariable(Opd))
      return true;
  }

  // Now we know we have a GEP ptr, %inv, %ind, %inv. Make sure that the step
  // can likely be merged into the address computation.
  unsigned MaxMergeDistance = 64;

  const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(SE->getSCEV(Ptr));
  if (!AddRec)
    return true;

  // Check the step is constant.
  const SCEV *Step = AddRec->getStepRecurrence(*SE);
  // Calculate the pointer stride and check if it is consecutive.
  const SCEVConstant *C = dyn_cast<SCEVConstant>(Step);
  if (!C)
    return true;

  const APInt &APStepVal = C->getValue()->getValue();

  // Huge step value - give up.
  if (APStepVal.getBitWidth() > 64)
    return true;

  int64_t StepVal = APStepVal.getSExtValue();

  return StepVal > MaxMergeDistance;
}

static bool isStrideMul(Instruction *I, LoopVectorizationLegality *Legal) {
  if (Legal->hasStride(I->getOperand(0)) || Legal->hasStride(I->getOperand(1)))
    return true;
  return false;
}

unsigned
LoopVectorizationCostModel::getInstructionCost(Instruction *I, unsigned VF) {
  // If we know that this instruction will remain uniform, check the cost of
  // the scalar version.
  if (Legal->isUniformAfterVectorization(I))
    VF = 1;

  Type *RetTy = I->getType();
  Type *VectorTy = ToVectorTy(RetTy, VF);

  // TODO: We need to estimate the cost of intrinsic calls.
  switch (I->getOpcode()) {
  case Instruction::GetElementPtr:
    // We mark this instruction as zero-cost because the cost of GEPs in
    // vectorized code depends on whether the corresponding memory instruction
    // is scalarized or not. Therefore, we handle GEPs with the memory
    // instruction cost.
    return 0;
  case Instruction::Br: {
    return TTI.getCFInstrCost(I->getOpcode());
  }
  case Instruction::PHI:
    //TODO: IF-converted IFs become selects.
    return 0;
  case Instruction::Add:
  case Instruction::FAdd:
  case Instruction::Sub:
  case Instruction::FSub:
  case Instruction::Mul:
  case Instruction::FMul:
  case Instruction::UDiv:
  case Instruction::SDiv:
  case Instruction::FDiv:
  case Instruction::URem:
  case Instruction::SRem:
  case Instruction::FRem:
  case Instruction::Shl:
  case Instruction::LShr:
  case Instruction::AShr:
  case Instruction::And:
  case Instruction::Or:
  case Instruction::Xor: {
    // Since we will replace the stride by 1 the multiplication should go away.
    if (I->getOpcode() == Instruction::Mul && isStrideMul(I, Legal))
      return 0;
    // Certain instructions can be cheaper to vectorize if they have a constant
    // second vector operand. One example of this are shifts on x86.
    TargetTransformInfo::OperandValueKind Op1VK =
      TargetTransformInfo::OK_AnyValue;
    TargetTransformInfo::OperandValueKind Op2VK =
      TargetTransformInfo::OK_AnyValue;
    TargetTransformInfo::OperandValueProperties Op1VP =
        TargetTransformInfo::OP_None;
    TargetTransformInfo::OperandValueProperties Op2VP =
        TargetTransformInfo::OP_None;
    Value *Op2 = I->getOperand(1);

    // Check for a splat of a constant or for a non uniform vector of constants.
    if (isa<ConstantInt>(Op2)) {
      ConstantInt *CInt = cast<ConstantInt>(Op2);
      if (CInt && CInt->getValue().isPowerOf2())
        Op2VP = TargetTransformInfo::OP_PowerOf2;
      Op2VK = TargetTransformInfo::OK_UniformConstantValue;
    } else if (isa<ConstantVector>(Op2) || isa<ConstantDataVector>(Op2)) {
      Op2VK = TargetTransformInfo::OK_NonUniformConstantValue;
      Constant *SplatValue = cast<Constant>(Op2)->getSplatValue();
      if (SplatValue) {
        ConstantInt *CInt = dyn_cast<ConstantInt>(SplatValue);
        if (CInt && CInt->getValue().isPowerOf2())
          Op2VP = TargetTransformInfo::OP_PowerOf2;
        Op2VK = TargetTransformInfo::OK_UniformConstantValue;
      }
    }

    return TTI.getArithmeticInstrCost(I->getOpcode(), VectorTy, Op1VK, Op2VK,
                                      Op1VP, Op2VP);
  }
  case Instruction::Select: {
    SelectInst *SI = cast<SelectInst>(I);
    const SCEV *CondSCEV = SE->getSCEV(SI->getCondition());
    bool ScalarCond = (SE->isLoopInvariant(CondSCEV, TheLoop));
    Type *CondTy = SI->getCondition()->getType();
    if (!ScalarCond)
      CondTy = VectorType::get(CondTy, VF);

    return TTI.getCmpSelInstrCost(I->getOpcode(), VectorTy, CondTy);
  }
  case Instruction::ICmp:
  case Instruction::FCmp: {
    Type *ValTy = I->getOperand(0)->getType();
    VectorTy = ToVectorTy(ValTy, VF);
    return TTI.getCmpSelInstrCost(I->getOpcode(), VectorTy);
  }
  case Instruction::Store:
  case Instruction::Load: {
    StoreInst *SI = dyn_cast<StoreInst>(I);
    LoadInst *LI = dyn_cast<LoadInst>(I);
    Type *ValTy = (SI ? SI->getValueOperand()->getType() :
                   LI->getType());
    VectorTy = ToVectorTy(ValTy, VF);

    unsigned Alignment = SI ? SI->getAlignment() : LI->getAlignment();
    unsigned AS = SI ? SI->getPointerAddressSpace() :
      LI->getPointerAddressSpace();
    Value *Ptr = SI ? SI->getPointerOperand() : LI->getPointerOperand();
    // We add the cost of address computation here instead of with the gep
    // instruction because only here we know whether the operation is
    // scalarized.
    if (VF == 1)
      return TTI.getAddressComputationCost(VectorTy) +
        TTI.getMemoryOpCost(I->getOpcode(), VectorTy, Alignment, AS);

    // For an interleaved access, calculate the total cost of the whole
    // interleave group.
    if (Legal->isAccessInterleaved(I)) {
      auto Group = Legal->getInterleavedAccessGroup(I);
      assert(Group && "Fail to get an interleaved access group.");

      // Only calculate the cost once at the insert position.
      if (Group->getInsertPos() != I)
        return 0;

      unsigned InterleaveFactor = Group->getFactor();
      Type *WideVecTy =
          VectorType::get(VectorTy->getVectorElementType(),
                          VectorTy->getVectorNumElements() * InterleaveFactor);

      // Holds the indices of existing members in an interleaved load group.
      // An interleaved store group doesn't need this as it dones't allow gaps.
      SmallVector<unsigned, 4> Indices;
      if (LI) {
        for (unsigned i = 0; i < InterleaveFactor; i++)
          if (Group->getMember(i))
            Indices.push_back(i);
      }

      // Calculate the cost of the whole interleaved group.
      unsigned Cost = TTI.getInterleavedMemoryOpCost(
          I->getOpcode(), WideVecTy, Group->getFactor(), Indices,
          Group->getAlignment(), AS);

      if (Group->isReverse())
        Cost +=
            Group->getNumMembers() *
            TTI.getShuffleCost(TargetTransformInfo::SK_Reverse, VectorTy, 0);

      // FIXME: The interleaved load group with a huge gap could be even more
      // expensive than scalar operations. Then we could ignore such group and
      // use scalar operations instead.
      return Cost;
    }

    // Scalarized loads/stores.
    int ConsecutiveStride = Legal->isConsecutivePtr(Ptr);
    bool Reverse = ConsecutiveStride < 0;
    const DataLayout &DL = I->getModule()->getDataLayout();
    unsigned ScalarAllocatedSize = DL.getTypeAllocSize(ValTy);
    unsigned VectorElementSize = DL.getTypeStoreSize(VectorTy) / VF;
    if (!ConsecutiveStride || ScalarAllocatedSize != VectorElementSize) {
      bool IsComplexComputation =
        isLikelyComplexAddressComputation(Ptr, Legal, SE, TheLoop);
      unsigned Cost = 0;
      // The cost of extracting from the value vector and pointer vector.
      Type *PtrTy = ToVectorTy(Ptr->getType(), VF);
      for (unsigned i = 0; i < VF; ++i) {
        //  The cost of extracting the pointer operand.
        Cost += TTI.getVectorInstrCost(Instruction::ExtractElement, PtrTy, i);
        // In case of STORE, the cost of ExtractElement from the vector.
        // In case of LOAD, the cost of InsertElement into the returned
        // vector.
        Cost += TTI.getVectorInstrCost(SI ? Instruction::ExtractElement :
                                            Instruction::InsertElement,
                                            VectorTy, i);
      }

      // The cost of the scalar loads/stores.
      Cost += VF * TTI.getAddressComputationCost(PtrTy, IsComplexComputation);
      Cost += VF * TTI.getMemoryOpCost(I->getOpcode(), ValTy->getScalarType(),
                                       Alignment, AS);
      return Cost;
    }

    // Wide load/stores.
    unsigned Cost = TTI.getAddressComputationCost(VectorTy);
    if (Legal->isMaskRequired(I))
      Cost += TTI.getMaskedMemoryOpCost(I->getOpcode(), VectorTy, Alignment,
                                        AS);
    else
      Cost += TTI.getMemoryOpCost(I->getOpcode(), VectorTy, Alignment, AS);

    if (Reverse)
      Cost += TTI.getShuffleCost(TargetTransformInfo::SK_Reverse,
                                  VectorTy, 0);
    return Cost;
  }
  case Instruction::ZExt:
  case Instruction::SExt:
  case Instruction::FPToUI:
  case Instruction::FPToSI:
  case Instruction::FPExt:
  case Instruction::PtrToInt:
  case Instruction::IntToPtr:
  case Instruction::SIToFP:
  case Instruction::UIToFP:
  case Instruction::Trunc:
  case Instruction::FPTrunc:
  case Instruction::BitCast: {
    // We optimize the truncation of induction variable.
    // The cost of these is the same as the scalar operation.
    if (I->getOpcode() == Instruction::Trunc &&
        Legal->isInductionVariable(I->getOperand(0)))
      return TTI.getCastInstrCost(I->getOpcode(), I->getType(),
                                  I->getOperand(0)->getType());

    Type *SrcVecTy = ToVectorTy(I->getOperand(0)->getType(), VF);
    return TTI.getCastInstrCost(I->getOpcode(), VectorTy, SrcVecTy);
  }
  case Instruction::Call: {
    bool NeedToScalarize;
    CallInst *CI = cast<CallInst>(I);
    unsigned CallCost = getVectorCallCost(CI, VF, TTI, TLI, NeedToScalarize);
    if (getIntrinsicIDForCall(CI, TLI))
      return std::min(CallCost, getVectorIntrinsicCost(CI, VF, TTI, TLI));
    return CallCost;
  }
  default: {
    // We are scalarizing the instruction. Return the cost of the scalar
    // instruction, plus the cost of insert and extract into vector
    // elements, times the vector width.
    unsigned Cost = 0;

    if (!RetTy->isVoidTy() && VF != 1) {
      unsigned InsCost = TTI.getVectorInstrCost(Instruction::InsertElement,
                                                VectorTy);
      unsigned ExtCost = TTI.getVectorInstrCost(Instruction::ExtractElement,
                                                VectorTy);

      // The cost of inserting the results plus extracting each one of the
      // operands.
      Cost += VF * (InsCost + ExtCost * I->getNumOperands());
    }

    // The cost of executing VF copies of the scalar instruction. This opcode
    // is unknown. Assume that it is the same as 'mul'.
    Cost += VF * TTI.getArithmeticInstrCost(Instruction::Mul, VectorTy);
    return Cost;
  }
  }// end of switch.
}

char LoopVectorize::ID = 0;
static const char lv_name[] = "Loop Vectorization";
INITIALIZE_PASS_BEGIN(LoopVectorize, LV_NAME, lv_name, false, false)
INITIALIZE_PASS_DEPENDENCY(TargetTransformInfoWrapperPass)
INITIALIZE_AG_DEPENDENCY(AliasAnalysis)
INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
INITIALIZE_PASS_DEPENDENCY(BlockFrequencyInfoWrapperPass)
INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
INITIALIZE_PASS_DEPENDENCY(ScalarEvolutionWrapperPass)
INITIALIZE_PASS_DEPENDENCY(LCSSA)
INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
INITIALIZE_PASS_DEPENDENCY(LoopSimplify)
INITIALIZE_PASS_DEPENDENCY(LoopAccessAnalysis)
INITIALIZE_PASS_END(LoopVectorize, LV_NAME, lv_name, false, false)

namespace llvm {
  Pass *createLoopVectorizePass(bool NoUnrolling, bool AlwaysVectorize) {
    return new LoopVectorize(NoUnrolling, AlwaysVectorize);
  }
}

bool LoopVectorizationCostModel::isConsecutiveLoadOrStore(Instruction *Inst) {
  // Check for a store.
  if (StoreInst *ST = dyn_cast<StoreInst>(Inst))
    return Legal->isConsecutivePtr(ST->getPointerOperand()) != 0;

  // Check for a load.
  if (LoadInst *LI = dyn_cast<LoadInst>(Inst))
    return Legal->isConsecutivePtr(LI->getPointerOperand()) != 0;

  return false;
}


void InnerLoopUnroller::scalarizeInstruction(Instruction *Instr,
                                             bool IfPredicateStore) {
  assert(!Instr->getType()->isAggregateType() && "Can't handle vectors");
  // Holds vector parameters or scalars, in case of uniform vals.
  SmallVector<VectorParts, 4> Params;

  setDebugLocFromInst(Builder, Instr);

  // Find all of the vectorized parameters.
  for (unsigned op = 0, e = Instr->getNumOperands(); op != e; ++op) {
    Value *SrcOp = Instr->getOperand(op);

    // If we are accessing the old induction variable, use the new one.
    if (SrcOp == OldInduction) {
      Params.push_back(getVectorValue(SrcOp));
      continue;
    }

    // Try using previously calculated values.
    Instruction *SrcInst = dyn_cast<Instruction>(SrcOp);

    // If the src is an instruction that appeared earlier in the basic block
    // then it should already be vectorized.
    if (SrcInst && OrigLoop->contains(SrcInst)) {
      assert(WidenMap.has(SrcInst) && "Source operand is unavailable");
      // The parameter is a vector value from earlier.
      Params.push_back(WidenMap.get(SrcInst));
    } else {
      // The parameter is a scalar from outside the loop. Maybe even a constant.
      VectorParts Scalars;
      Scalars.append(UF, SrcOp);
      Params.push_back(Scalars);
    }
  }

  assert(Params.size() == Instr->getNumOperands() &&
         "Invalid number of operands");

  // Does this instruction return a value ?
  bool IsVoidRetTy = Instr->getType()->isVoidTy();

  Value *UndefVec = IsVoidRetTy ? nullptr :
  UndefValue::get(Instr->getType());
  // Create a new entry in the WidenMap and initialize it to Undef or Null.
  VectorParts &VecResults = WidenMap.splat(Instr, UndefVec);

  Instruction *InsertPt = Builder.GetInsertPoint();
  BasicBlock *IfBlock = Builder.GetInsertBlock();
  BasicBlock *CondBlock = nullptr;

  VectorParts Cond;
  Loop *VectorLp = nullptr;
  if (IfPredicateStore) {
    assert(Instr->getParent()->getSinglePredecessor() &&
           "Only support single predecessor blocks");
    Cond = createEdgeMask(Instr->getParent()->getSinglePredecessor(),
                          Instr->getParent());
    VectorLp = LI->getLoopFor(IfBlock);
    assert(VectorLp && "Must have a loop for this block");
  }

  // For each vector unroll 'part':
  for (unsigned Part = 0; Part < UF; ++Part) {
    // For each scalar that we create:

    // Start an "if (pred) a[i] = ..." block.
    Value *Cmp = nullptr;
    if (IfPredicateStore) {
      if (Cond[Part]->getType()->isVectorTy())
        Cond[Part] =
            Builder.CreateExtractElement(Cond[Part], Builder.getInt32(0));
      Cmp = Builder.CreateICmp(ICmpInst::ICMP_EQ, Cond[Part],
                               ConstantInt::get(Cond[Part]->getType(), 1));
      CondBlock = IfBlock->splitBasicBlock(InsertPt, "cond.store");
      LoopVectorBody.push_back(CondBlock);
      VectorLp->addBasicBlockToLoop(CondBlock, *LI);
      // Update Builder with newly created basic block.
      Builder.SetInsertPoint(InsertPt);
    }

    Instruction *Cloned = Instr->clone();
      if (!IsVoidRetTy)
        Cloned->setName(Instr->getName() + ".cloned");
      // Replace the operands of the cloned instructions with extracted scalars.
      for (unsigned op = 0, e = Instr->getNumOperands(); op != e; ++op) {
        Value *Op = Params[op][Part];
        Cloned->setOperand(op, Op);
      }

      // Place the cloned scalar in the new loop.
      Builder.Insert(Cloned);

      // If the original scalar returns a value we need to place it in a vector
      // so that future users will be able to use it.
      if (!IsVoidRetTy)
        VecResults[Part] = Cloned;

    // End if-block.
      if (IfPredicateStore) {
        BasicBlock *NewIfBlock = CondBlock->splitBasicBlock(InsertPt, "else");
        LoopVectorBody.push_back(NewIfBlock);
        VectorLp->addBasicBlockToLoop(NewIfBlock, *LI);
        Builder.SetInsertPoint(InsertPt);
        ReplaceInstWithInst(IfBlock->getTerminator(),
                            BranchInst::Create(CondBlock, NewIfBlock, Cmp));
        IfBlock = NewIfBlock;
      }
  }
}

void InnerLoopUnroller::vectorizeMemoryInstruction(Instruction *Instr) {
  StoreInst *SI = dyn_cast<StoreInst>(Instr);
  bool IfPredicateStore = (SI && Legal->blockNeedsPredication(SI->getParent()));

  return scalarizeInstruction(Instr, IfPredicateStore);
}

Value *InnerLoopUnroller::reverseVector(Value *Vec) {
  return Vec;
}

Value *InnerLoopUnroller::getBroadcastInstrs(Value *V) {
  return V;
}

Value *InnerLoopUnroller::getStepVector(Value *Val, int StartIdx, Value *Step) {
  // When unrolling and the VF is 1, we only need to add a simple scalar.
  Type *ITy = Val->getType();
  assert(!ITy->isVectorTy() && "Val must be a scalar");
  Constant *C = ConstantInt::get(ITy, StartIdx);
  return Builder.CreateAdd(Val, Builder.CreateMul(C, Step), "induction");
}