text: //===- llvm/Analysis/LoopInfo.h - Natural Loop Calculator -------*- C++ -*-===//
  //
  //                     The LLVM Compiler Infrastructure
  //
  // This file is distributed under the University of Illinois Open Source
  // License. See LICENSE.TXT for details.
  //
  //===----------------------------------------------------------------------===//
  //
  // This file defines the LoopInfo class that is used to identify natural loops
  // and determine the loop depth of various nodes of the CFG.  A natural loop
  // has exactly one entry-point, which is called the header. Note that natural
  // loops may actually be several loops that share the same header node.
  //
  // This analysis calculates the nesting structure of loops in a function.  For
  // each natural loop identified, this analysis identifies natural loops
  // contained entirely within the loop and the basic blocks the make up the loop.
  //
  // It can calculate on the fly various bits of information, for example:
  //
  //  * whether there is a preheader for the loop
  //  * the number of back edges to the header
  //  * whether or not a particular block branches out of the loop
  //  * the successor blocks of the loop
  //  * the loop depth
  //  * etc...
  //
  // Note that this analysis specifically identifies *Loops* not cycles or SCCs
  // in the CFG.  There can be strongly connected components in the CFG which
  // this analysis will not recognize and that will not be represented by a Loop
  // instance.  In particular, a Loop might be inside such a non-loop SCC, or a
  // non-loop SCC might contain a sub-SCC which is a Loop.
  //
  //===----------------------------------------------------------------------===//
  
  #ifndef LLVM_ANALYSIS_LOOPINFO_H
  #define LLVM_ANALYSIS_LOOPINFO_H
  
  #include "llvm/ADT/DenseMap.h"
  #include "llvm/ADT/DenseSet.h"
  #include "llvm/ADT/GraphTraits.h"
  #include "llvm/ADT/SmallPtrSet.h"
  #include "llvm/ADT/SmallVector.h"
  #include "llvm/IR/CFG.h"
  #include "llvm/IR/Instruction.h"
  #include "llvm/IR/Instructions.h"
  #include "llvm/IR/PassManager.h"
  #include "llvm/Pass.h"
  #include "llvm/Support/Allocator.h"
  #include <algorithm>
  #include <utility>
  
  namespace llvm {
  
  class DominatorTree;
  class LoopInfo;
  class Loop;
  class MDNode;
  class PHINode;
  class raw_ostream;
  template <class N, bool IsPostDom> class DominatorTreeBase;
  template <class N, class M> class LoopInfoBase;
  template <class N, class M> class LoopBase;
  
  //===----------------------------------------------------------------------===//
  /// Instances of this class are used to represent loops that are detected in the
  /// flow graph.
  ///
  template <class BlockT, class LoopT> class LoopBase {
    LoopT *ParentLoop;
    // Loops contained entirely within this one.
    std::vector<LoopT *> SubLoops;
  
    // The list of blocks in this loop. First entry is the header node.
    std::vector<BlockT *> Blocks;
  
    SmallPtrSet<const BlockT *, 8> DenseBlockSet;
  
  #if LLVM_ENABLE_ABI_BREAKING_CHECKS
    /// Indicator that this loop is no longer a valid loop.
    bool IsInvalid = false;
  #endif
  
    LoopBase(const LoopBase<BlockT, LoopT> &) = delete;
    const LoopBase<BlockT, LoopT> &
    operator=(const LoopBase<BlockT, LoopT> &) = delete;
  
  public:
    /// Return the nesting level of this loop.  An outer-most loop has depth 1,
    /// for consistency with loop depth values used for basic blocks, where depth
    /// 0 is used for blocks not inside any loops.
    unsigned getLoopDepth() const {
      assert(!isInvalid() && "Loop not in a valid state!");
      unsigned D = 1;
      for (const LoopT *CurLoop = ParentLoop; CurLoop;
           CurLoop = CurLoop->ParentLoop)
        ++D;
      return D;
    }
    BlockT *getHeader() const { return getBlocks().front(); }
    LoopT *getParentLoop() const { return ParentLoop; }
  
    /// This is a raw interface for bypassing addChildLoop.
    void setParentLoop(LoopT *L) {
      assert(!isInvalid() && "Loop not in a valid state!");
      ParentLoop = L;
    }
  
    /// Return true if the specified loop is contained within in this loop.
    bool contains(const LoopT *L) const {
      assert(!isInvalid() && "Loop not in a valid state!");
      if (L == this)
        return true;
      if (!L)
        return false;
      return contains(L->getParentLoop());
    }
  
    /// Return true if the specified basic block is in this loop.
    bool contains(const BlockT *BB) const {
      assert(!isInvalid() && "Loop not in a valid state!");
      return DenseBlockSet.count(BB);
    }
  
    /// Return true if the specified instruction is in this loop.
    template <class InstT> bool contains(const InstT *Inst) const {
      return contains(Inst->getParent());
    }
  
    /// Return the loops contained entirely within this loop.
    const std::vector<LoopT *> &getSubLoops() const {
      assert(!isInvalid() && "Loop not in a valid state!");
      return SubLoops;
    }
    std::vector<LoopT *> &getSubLoopsVector() {
      assert(!isInvalid() && "Loop not in a valid state!");
      return SubLoops;
    }
    typedef typename std::vector<LoopT *>::const_iterator iterator;
    typedef
        typename std::vector<LoopT *>::const_reverse_iterator reverse_iterator;
    iterator begin() const { return getSubLoops().begin(); }
    iterator end() const { return getSubLoops().end(); }
    reverse_iterator rbegin() const { return getSubLoops().rbegin(); }
    reverse_iterator rend() const { return getSubLoops().rend(); }
    bool empty() const { return getSubLoops().empty(); }
  
    /// Get a list of the basic blocks which make up this loop.
    ArrayRef<BlockT *> getBlocks() const {
      assert(!isInvalid() && "Loop not in a valid state!");
      return Blocks;
    }
    typedef typename ArrayRef<BlockT *>::const_iterator block_iterator;
    block_iterator block_begin() const { return getBlocks().begin(); }
    block_iterator block_end() const { return getBlocks().end(); }
    inline iterator_range<block_iterator> blocks() const {
      assert(!isInvalid() && "Loop not in a valid state!");
      return make_range(block_begin(), block_end());
    }
  
    /// Get the number of blocks in this loop in constant time.
    /// Invalidate the loop, indicating that it is no longer a loop.
    unsigned getNumBlocks() const {
      assert(!isInvalid() && "Loop not in a valid state!");
      return Blocks.size();
    }
  
    /// Return a direct, mutable handle to the blocks vector so that we can
    /// mutate it efficiently with techniques like `std::remove`.
    std::vector<BlockT *> &getBlocksVector() {
      assert(!isInvalid() && "Loop not in a valid state!");
      return Blocks;
    }
    /// Return a direct, mutable handle to the blocks set so that we can
    /// mutate it efficiently.
    SmallPtrSetImpl<const BlockT *> &getBlocksSet() {
      assert(!isInvalid() && "Loop not in a valid state!");
      return DenseBlockSet;
    }
  
    /// Return a direct, immutable handle to the blocks set.
    const SmallPtrSetImpl<const BlockT *> &getBlocksSet() const {
      assert(!isInvalid() && "Loop not in a valid state!");
      return DenseBlockSet;
    }
  
    /// Return true if this loop is no longer valid.  The only valid use of this
    /// helper is "assert(L.isInvalid())" or equivalent, since IsInvalid is set to
    /// true by the destructor.  In other words, if this accessor returns true,
    /// the caller has already triggered UB by calling this accessor; and so it
    /// can only be called in a context where a return value of true indicates a
    /// programmer error.
    bool isInvalid() const {
  #if LLVM_ENABLE_ABI_BREAKING_CHECKS
      return IsInvalid;
  #else
      return false;
  #endif
    }
  
    /// True if terminator in the block can branch to another block that is
    /// outside of the current loop.
    bool isLoopExiting(const BlockT *BB) const {
      assert(!isInvalid() && "Loop not in a valid state!");
      for (const auto &Succ : children<const BlockT *>(BB)) {
        if (!contains(Succ))
          return true;
      }
      return false;
    }
  
    /// Returns true if \p BB is a loop-latch.
    /// A latch block is a block that contains a branch back to the header.
    /// This function is useful when there are multiple latches in a loop
    /// because \fn getLoopLatch will return nullptr in that case.
    bool isLoopLatch(const BlockT *BB) const {
      assert(!isInvalid() && "Loop not in a valid state!");
      assert(contains(BB) && "block does not belong to the loop");
  
      BlockT *Header = getHeader();
      auto PredBegin = GraphTraits<Inverse<BlockT *>>::child_begin(Header);
      auto PredEnd = GraphTraits<Inverse<BlockT *>>::child_end(Header);
      return std::find(PredBegin, PredEnd, BB) != PredEnd;
    }
  
    /// Calculate the number of back edges to the loop header.
    unsigned getNumBackEdges() const {
      assert(!isInvalid() && "Loop not in a valid state!");
      unsigned NumBackEdges = 0;
      BlockT *H = getHeader();
  
      for (const auto Pred : children<Inverse<BlockT *>>(H))
        if (contains(Pred))
          ++NumBackEdges;
  
      return NumBackEdges;
    }
  
    //===--------------------------------------------------------------------===//
    // APIs for simple analysis of the loop.
    //
    // Note that all of these methods can fail on general loops (ie, there may not
    // be a preheader, etc).  For best success, the loop simplification and
    // induction variable canonicalization pass should be used to normalize loops
    // for easy analysis.  These methods assume canonical loops.
  
    /// Return all blocks inside the loop that have successors outside of the
    /// loop. These are the blocks _inside of the current loop_ which branch out.
    /// The returned list is always unique.
    void getExitingBlocks(SmallVectorImpl<BlockT *> &ExitingBlocks) const;
  
    /// If getExitingBlocks would return exactly one block, return that block.
    /// Otherwise return null.
    BlockT *getExitingBlock() const;
  
    /// Return all of the successor blocks of this loop. These are the blocks
    /// _outside of the current loop_ which are branched to.
    void getExitBlocks(SmallVectorImpl<BlockT *> &ExitBlocks) const;
  
    /// If getExitBlocks would return exactly one block, return that block.
    /// Otherwise return null.
    BlockT *getExitBlock() const;
  
    /// Edge type.
    typedef std::pair<const BlockT *, const BlockT *> Edge;
  
    /// Return all pairs of (_inside_block_,_outside_block_).
    void getExitEdges(SmallVectorImpl<Edge> &ExitEdges) const;
  
    /// If there is a preheader for this loop, return it. A loop has a preheader
    /// if there is only one edge to the header of the loop from outside of the
    /// loop. If this is the case, the block branching to the header of the loop
    /// is the preheader node.
    ///
    /// This method returns null if there is no preheader for the loop.
    BlockT *getLoopPreheader() const;
  
    /// If the given loop's header has exactly one unique predecessor outside the
    /// loop, return it. Otherwise return null.
    ///  This is less strict that the loop "preheader" concept, which requires
    /// the predecessor to have exactly one successor.
    BlockT *getLoopPredecessor() const;
  
    /// If there is a single latch block for this loop, return it.
    /// A latch block is a block that contains a branch back to the header.
    BlockT *getLoopLatch() const;
  
    /// Return all loop latch blocks of this loop. A latch block is a block that
    /// contains a branch back to the header.
    void getLoopLatches(SmallVectorImpl<BlockT *> &LoopLatches) const {
      assert(!isInvalid() && "Loop not in a valid state!");
      BlockT *H = getHeader();
      for (const auto Pred : children<Inverse<BlockT *>>(H))
        if (contains(Pred))
          LoopLatches.push_back(Pred);
    }
  
    //===--------------------------------------------------------------------===//
    // APIs for updating loop information after changing the CFG
    //
  
    /// This method is used by other analyses to update loop information.
    /// NewBB is set to be a new member of the current loop.
    /// Because of this, it is added as a member of all parent loops, and is added
    /// to the specified LoopInfo object as being in the current basic block.  It
    /// is not valid to replace the loop header with this method.
    void addBasicBlockToLoop(BlockT *NewBB, LoopInfoBase<BlockT, LoopT> &LI);
  
    /// This is used when splitting loops up. It replaces the OldChild entry in
    /// our children list with NewChild, and updates the parent pointer of
    /// OldChild to be null and the NewChild to be this loop.
    /// This updates the loop depth of the new child.
    void replaceChildLoopWith(LoopT *OldChild, LoopT *NewChild);
  
    /// Add the specified loop to be a child of this loop.
    /// This updates the loop depth of the new child.
    void addChildLoop(LoopT *NewChild) {
      assert(!isInvalid() && "Loop not in a valid state!");
      assert(!NewChild->ParentLoop && "NewChild already has a parent!");
      NewChild->ParentLoop = static_cast<LoopT *>(this);
      SubLoops.push_back(NewChild);
    }
  
    /// This removes the specified child from being a subloop of this loop. The
    /// loop is not deleted, as it will presumably be inserted into another loop.
    LoopT *removeChildLoop(iterator I) {
      assert(!isInvalid() && "Loop not in a valid state!");
      assert(I != SubLoops.end() && "Cannot remove end iterator!");
      LoopT *Child = *I;
      assert(Child->ParentLoop == this && "Child is not a child of this loop!");
      SubLoops.erase(SubLoops.begin() + (I - begin()));
      Child->ParentLoop = nullptr;
      return Child;
    }
  
    /// This removes the specified child from being a subloop of this loop. The
    /// loop is not deleted, as it will presumably be inserted into another loop.
    LoopT *removeChildLoop(LoopT *Child) {
      return removeChildLoop(llvm::find(*this, Child));
    }
  
    /// This adds a basic block directly to the basic block list.
    /// This should only be used by transformations that create new loops.  Other
    /// transformations should use addBasicBlockToLoop.
    void addBlockEntry(BlockT *BB) {
      assert(!isInvalid() && "Loop not in a valid state!");
      Blocks.push_back(BB);
      DenseBlockSet.insert(BB);
    }
  
    /// interface to reverse Blocks[from, end of loop] in this loop
    void reverseBlock(unsigned from) {
      assert(!isInvalid() && "Loop not in a valid state!");
      std::reverse(Blocks.begin() + from, Blocks.end());
    }
  
    /// interface to do reserve() for Blocks
    void reserveBlocks(unsigned size) {
      assert(!isInvalid() && "Loop not in a valid state!");
      Blocks.reserve(size);
    }
  
    /// This method is used to move BB (which must be part of this loop) to be the
    /// loop header of the loop (the block that dominates all others).
    void moveToHeader(BlockT *BB) {
      assert(!isInvalid() && "Loop not in a valid state!");
      if (Blocks[0] == BB)
        return;
      for (unsigned i = 0;; ++i) {
        assert(i != Blocks.size() && "Loop does not contain BB!");
        if (Blocks[i] == BB) {
          Blocks[i] = Blocks[0];
          Blocks[0] = BB;
          return;
        }
      }
    }
  
    /// This removes the specified basic block from the current loop, updating the
    /// Blocks as appropriate. This does not update the mapping in the LoopInfo
    /// class.
    void removeBlockFromLoop(BlockT *BB) {
      assert(!isInvalid() && "Loop not in a valid state!");
      auto I = find(Blocks, BB);
      assert(I != Blocks.end() && "N is not in this list!");
      Blocks.erase(I);
  
      DenseBlockSet.erase(BB);
    }
  
    /// Verify loop structure
    void verifyLoop() const;
  
    /// Verify loop structure of this loop and all nested loops.
    void verifyLoopNest(DenseSet<const LoopT *> *Loops) const;
  
    /// Print loop with all the BBs inside it.
    void print(raw_ostream &OS, unsigned Depth = 0, bool Verbose = false) const;
  
  protected:
    friend class LoopInfoBase<BlockT, LoopT>;
  
    /// This creates an empty loop.
    LoopBase() : ParentLoop(nullptr) {}
  
    explicit LoopBase(BlockT *BB) : ParentLoop(nullptr) {
      Blocks.push_back(BB);
      DenseBlockSet.insert(BB);
    }
  
    // Since loop passes like SCEV are allowed to key analysis results off of
    // `Loop` pointers, we cannot re-use pointers within a loop pass manager.
    // This means loop passes should not be `delete` ing `Loop` objects directly
    // (and risk a later `Loop` allocation re-using the address of a previous one)
    // but should be using LoopInfo::markAsRemoved, which keeps around the `Loop`
    // pointer till the end of the lifetime of the `LoopInfo` object.
    //
    // To make it easier to follow this rule, we mark the destructor as
    // non-public.
    ~LoopBase() {
      for (auto *SubLoop : SubLoops)
        SubLoop->~LoopT();
  
  #if LLVM_ENABLE_ABI_BREAKING_CHECKS
      IsInvalid = true;
  #endif
      SubLoops.clear();
      Blocks.clear();
      DenseBlockSet.clear();
      ParentLoop = nullptr;
    }
  };
  
  template <class BlockT, class LoopT>
  raw_ostream &operator<<(raw_ostream &OS, const LoopBase<BlockT, LoopT> &Loop) {
    Loop.print(OS);
    return OS;
  }
  
  // Implementation in LoopInfoImpl.h
  extern template class LoopBase<BasicBlock, Loop>;
  
  /// Represents a single loop in the control flow graph.  Note that not all SCCs
  /// in the CFG are necessarily loops.
  class Loop : public LoopBase<BasicBlock, Loop> {
  public:
    /// A range representing the start and end location of a loop.
    class LocRange {
      DebugLoc Start;
      DebugLoc End;
  
    public:
      LocRange() {}
      LocRange(DebugLoc Start) : Start(std::move(Start)), End(std::move(Start)) {}
      LocRange(DebugLoc Start, DebugLoc End)
          : Start(std::move(Start)), End(std::move(End)) {}
  
      const DebugLoc &getStart() const { return Start; }
      const DebugLoc &getEnd() const { return End; }
  
      /// Check for null.
      ///
      explicit operator bool() const { return Start && End; }
    };
  
    /// Return true if the specified value is loop invariant.
    bool isLoopInvariant(const Value *V) const;
  
    /// Return true if all the operands of the specified instruction are loop
    /// invariant.
    bool hasLoopInvariantOperands(const Instruction *I) const;
  
    /// If the given value is an instruction inside of the loop and it can be
    /// hoisted, do so to make it trivially loop-invariant.
    /// Return true if the value after any hoisting is loop invariant. This
    /// function can be used as a slightly more aggressive replacement for
    /// isLoopInvariant.
    ///
    /// If InsertPt is specified, it is the point to hoist instructions to.
    /// If null, the terminator of the loop preheader is used.
    bool makeLoopInvariant(Value *V, bool &Changed,
                           Instruction *InsertPt = nullptr) const;
  
    /// If the given instruction is inside of the loop and it can be hoisted, do
    /// so to make it trivially loop-invariant.
    /// Return true if the instruction after any hoisting is loop invariant. This
    /// function can be used as a slightly more aggressive replacement for
    /// isLoopInvariant.
    ///
    /// If InsertPt is specified, it is the point to hoist instructions to.
    /// If null, the terminator of the loop preheader is used.
    ///
    bool makeLoopInvariant(Instruction *I, bool &Changed,
                           Instruction *InsertPt = nullptr) const;
  
    /// Check to see if the loop has a canonical induction variable: an integer
    /// recurrence that starts at 0 and increments by one each time through the
    /// loop. If so, return the phi node that corresponds to it.
    ///
    /// The IndVarSimplify pass transforms loops to have a canonical induction
    /// variable.
    ///
    PHINode *getCanonicalInductionVariable() const;
  
    /// Return true if the Loop is in LCSSA form.
    bool isLCSSAForm(DominatorTree &DT) const;
  
    /// Return true if this Loop and all inner subloops are in LCSSA form.
    bool isRecursivelyLCSSAForm(DominatorTree &DT, const LoopInfo &LI) const;
  
    /// Return true if the Loop is in the form that the LoopSimplify form
    /// transforms loops to, which is sometimes called normal form.
    bool isLoopSimplifyForm() const;
  
    /// Return true if the loop body is safe to clone in practice.
    bool isSafeToClone() const;
  
    /// Returns true if the loop is annotated parallel.
    ///
    /// A parallel loop can be assumed to not contain any dependencies between
    /// iterations by the compiler. That is, any loop-carried dependency checking
    /// can be skipped completely when parallelizing the loop on the target
    /// machine. Thus, if the parallel loop information originates from the
    /// programmer, e.g. via the OpenMP parallel for pragma, it is the
    /// programmer's responsibility to ensure there are no loop-carried
    /// dependencies. The final execution order of the instructions across
    /// iterations is not guaranteed, thus, the end result might or might not
    /// implement actual concurrent execution of instructions across multiple
    /// iterations.
    bool isAnnotatedParallel() const;
  
    /// Return the llvm.loop loop id metadata node for this loop if it is present.
    ///
    /// If this loop contains the same llvm.loop metadata on each branch to the
    /// header then the node is returned. If any latch instruction does not
    /// contain llvm.loop or if multiple latches contain different nodes then
    /// 0 is returned.
    MDNode *getLoopID() const;
    /// Set the llvm.loop loop id metadata for this loop.
    ///
    /// The LoopID metadata node will be added to each terminator instruction in
    /// the loop that branches to the loop header.
    ///
    /// The LoopID metadata node should have one or more operands and the first
    /// operand should be the node itself.
    void setLoopID(MDNode *LoopID) const;
  
    /// Add llvm.loop.unroll.disable to this loop's loop id metadata.
    ///
    /// Remove existing unroll metadata and add unroll disable metadata to
    /// indicate the loop has already been unrolled.  This prevents a loop
    /// from being unrolled more than is directed by a pragma if the loop
    /// unrolling pass is run more than once (which it generally is).
    void setLoopAlreadyUnrolled();
  
    /// Return true if no exit block for the loop has a predecessor that is
    /// outside the loop.
    bool hasDedicatedExits() const;
  
    /// Return all unique successor blocks of this loop.
    /// These are the blocks _outside of the current loop_ which are branched to.
    /// This assumes that loop exits are in canonical form, i.e. all exits are
    /// dedicated exits.
    void getUniqueExitBlocks(SmallVectorImpl<BasicBlock *> &ExitBlocks) const;
  
    /// If getUniqueExitBlocks would return exactly one block, return that block.
    /// Otherwise return null.
    BasicBlock *getUniqueExitBlock() const;
  
    void dump() const;
    void dumpVerbose() const;
  
    /// Return the debug location of the start of this loop.
    /// This looks for a BB terminating instruction with a known debug
    /// location by looking at the preheader and header blocks. If it
    /// cannot find a terminating instruction with location information,
    /// it returns an unknown location.
    DebugLoc getStartLoc() const;
  
    /// Return the source code span of the loop.
    LocRange getLocRange() const;
  
    StringRef getName() const {
      if (BasicBlock *Header = getHeader())
        if (Header->hasName())
          return Header->getName();
      return "<unnamed loop>";
    }
  
  private:
    Loop() = default;
  
    friend class LoopInfoBase<BasicBlock, Loop>;
    friend class LoopBase<BasicBlock, Loop>;
    explicit Loop(BasicBlock *BB) : LoopBase<BasicBlock, Loop>(BB) {}
    ~Loop() = default;
  };
  
  //===----------------------------------------------------------------------===//
  /// This class builds and contains all of the top-level loop
  /// structures in the specified function.
  ///
  
  template <class BlockT, class LoopT> class LoopInfoBase {
    // BBMap - Mapping of basic blocks to the inner most loop they occur in
    DenseMap<const BlockT *, LoopT *> BBMap;
    std::vector<LoopT *> TopLevelLoops;
    BumpPtrAllocator LoopAllocator;
  
    friend class LoopBase<BlockT, LoopT>;
    friend class LoopInfo;
  
    void operator=(const LoopInfoBase &) = delete;
    LoopInfoBase(const LoopInfoBase &) = delete;
  
  public:
    LoopInfoBase() {}
    ~LoopInfoBase() { releaseMemory(); }
  
    LoopInfoBase(LoopInfoBase &&Arg)
        : BBMap(std::move(Arg.BBMap)),
          TopLevelLoops(std::move(Arg.TopLevelLoops)),
          LoopAllocator(std::move(Arg.LoopAllocator)) {
      // We have to clear the arguments top level loops as we've taken ownership.
      Arg.TopLevelLoops.clear();
    }
    LoopInfoBase &operator=(LoopInfoBase &&RHS) {
      BBMap = std::move(RHS.BBMap);
  
      for (auto *L : TopLevelLoops)
        L->~LoopT();
  
      TopLevelLoops = std::move(RHS.TopLevelLoops);
      LoopAllocator = std::move(RHS.LoopAllocator);
      RHS.TopLevelLoops.clear();
      return *this;
    }
  
    void releaseMemory() {
      BBMap.clear();
  
      for (auto *L : TopLevelLoops)
        L->~LoopT();
      TopLevelLoops.clear();
      LoopAllocator.Reset();
    }
  
    template <typename... ArgsTy> LoopT *AllocateLoop(ArgsTy &&... Args) {
      LoopT *Storage = LoopAllocator.Allocate<LoopT>();
      return new (Storage) LoopT(std::forward<ArgsTy>(Args)...);
    }
  
    /// iterator/begin/end - The interface to the top-level loops in the current
    /// function.
    ///
    typedef typename std::vector<LoopT *>::const_iterator iterator;
    typedef
        typename std::vector<LoopT *>::const_reverse_iterator reverse_iterator;
    iterator begin() const { return TopLevelLoops.begin(); }
    iterator end() const { return TopLevelLoops.end(); }
    reverse_iterator rbegin() const { return TopLevelLoops.rbegin(); }
    reverse_iterator rend() const { return TopLevelLoops.rend(); }
    bool empty() const { return TopLevelLoops.empty(); }
  
    /// Return all of the loops in the function in preorder across the loop
    /// nests, with siblings in forward program order.
    ///
    /// Note that because loops form a forest of trees, preorder is equivalent to
    /// reverse postorder.
    SmallVector<LoopT *, 4> getLoopsInPreorder();
  
    /// Return all of the loops in the function in preorder across the loop
    /// nests, with siblings in *reverse* program order.
    ///
    /// Note that because loops form a forest of trees, preorder is equivalent to
    /// reverse postorder.
    ///
    /// Also note that this is *not* a reverse preorder. Only the siblings are in
    /// reverse program order.
    SmallVector<LoopT *, 4> getLoopsInReverseSiblingPreorder();
  
    /// Return the inner most loop that BB lives in. If a basic block is in no
    /// loop (for example the entry node), null is returned.
    LoopT *getLoopFor(const BlockT *BB) const { return BBMap.lookup(BB); }
  
    /// Same as getLoopFor.
    const LoopT *operator[](const BlockT *BB) const { return getLoopFor(BB); }
  
    /// Return the loop nesting level of the specified block. A depth of 0 means
    /// the block is not inside any loop.
    unsigned getLoopDepth(const BlockT *BB) const {
      const LoopT *L = getLoopFor(BB);
      return L ? L->getLoopDepth() : 0;
    }
  
    // True if the block is a loop header node
    bool isLoopHeader(const BlockT *BB) const {
      const LoopT *L = getLoopFor(BB);
      return L && L->getHeader() == BB;
    }
  
    /// This removes the specified top-level loop from this loop info object.
    /// The loop is not deleted, as it will presumably be inserted into
    /// another loop.
    LoopT *removeLoop(iterator I) {
      assert(I != end() && "Cannot remove end iterator!");
      LoopT *L = *I;
      assert(!L->getParentLoop() && "Not a top-level loop!");
      TopLevelLoops.erase(TopLevelLoops.begin() + (I - begin()));
      return L;
    }
  
    /// Change the top-level loop that contains BB to the specified loop.
    /// This should be used by transformations that restructure the loop hierarchy
    /// tree.
    void changeLoopFor(BlockT *BB, LoopT *L) {
      if (!L) {
        BBMap.erase(BB);
        return;
      }
      BBMap[BB] = L;
    }
  
    /// Replace the specified loop in the top-level loops list with the indicated
    /// loop.
    void changeTopLevelLoop(LoopT *OldLoop, LoopT *NewLoop) {
      auto I = find(TopLevelLoops, OldLoop);
      assert(I != TopLevelLoops.end() && "Old loop not at top level!");
      *I = NewLoop;
      assert(!NewLoop->ParentLoop && !OldLoop->ParentLoop &&
             "Loops already embedded into a subloop!");
    }
  
    /// This adds the specified loop to the collection of top-level loops.
    void addTopLevelLoop(LoopT *New) {
      assert(!New->getParentLoop() && "Loop already in subloop!");
      TopLevelLoops.push_back(New);
    }
  
    /// This method completely removes BB from all data structures,
    /// including all of the Loop objects it is nested in and our mapping from
    /// BasicBlocks to loops.
    void removeBlock(BlockT *BB) {
      auto I = BBMap.find(BB);
      if (I != BBMap.end()) {
        for (LoopT *L = I->second; L; L = L->getParentLoop())
          L->removeBlockFromLoop(BB);
  
        BBMap.erase(I);
      }
    }
  
    // Internals
  
    static bool isNotAlreadyContainedIn(const LoopT *SubLoop,
                                        const LoopT *ParentLoop) {
      if (!SubLoop)
        return true;
      if (SubLoop == ParentLoop)
        return false;
      return isNotAlreadyContainedIn(SubLoop->getParentLoop(), ParentLoop);
    }
  
    /// Create the loop forest using a stable algorithm.
    void analyze(const DominatorTreeBase<BlockT, false> &DomTree);
  
    // Debugging
    void print(raw_ostream &OS) const;
  
    void verify(const DominatorTreeBase<BlockT, false> &DomTree) const;
  
    /// Destroy a loop that has been removed from the `LoopInfo` nest.
    ///
    /// This runs the destructor of the loop object making it invalid to
    /// reference afterward. The memory is retained so that the *pointer* to the
    /// loop remains valid.
    ///
    /// The caller is responsible for removing this loop from the loop nest and
    /// otherwise disconnecting it from the broader `LoopInfo` data structures.
    /// Callers that don't naturally handle this themselves should probably call
    /// `erase' instead.
    void destroy(LoopT *L) {
      L->~LoopT();
  
      // Since LoopAllocator is a BumpPtrAllocator, this Deallocate only poisons
      // \c L, but the pointer remains valid for non-dereferencing uses.
      LoopAllocator.Deallocate(L);
    }
  };
  
  // Implementation in LoopInfoImpl.h
  extern template class LoopInfoBase<BasicBlock, Loop>;
  
  class LoopInfo : public LoopInfoBase<BasicBlock, Loop> {
    typedef LoopInfoBase<BasicBlock, Loop> BaseT;
  
    friend class LoopBase<BasicBlock, Loop>;
  
    void operator=(const LoopInfo &) = delete;
    LoopInfo(const LoopInfo &) = delete;
  
  public:
    LoopInfo() {}
    explicit LoopInfo(const DominatorTreeBase<BasicBlock, false> &DomTree);
  
    LoopInfo(LoopInfo &&Arg) : BaseT(std::move(static_cast<BaseT &>(Arg))) {}
    LoopInfo &operator=(LoopInfo &&RHS) {
      BaseT::operator=(std::move(static_cast<BaseT &>(RHS)));
      return *this;
    }
  
    /// Handle invalidation explicitly.
    bool invalidate(Function &F, const PreservedAnalyses &PA,
                    FunctionAnalysisManager::Invalidator &);
  
    // Most of the public interface is provided via LoopInfoBase.
  
    /// Update LoopInfo after removing the last backedge from a loop. This updates
    /// the loop forest and parent loops for each block so that \c L is no longer
    /// referenced, but does not actually delete \c L immediately. The pointer
    /// will remain valid until this LoopInfo's memory is released.
    void erase(Loop *L);
  
    /// Returns true if replacing From with To everywhere is guaranteed to
    /// preserve LCSSA form.
    bool replacementPreservesLCSSAForm(Instruction *From, Value *To) {
      // Preserving LCSSA form is only problematic if the replacing value is an
      // instruction.
      Instruction *I = dyn_cast<Instruction>(To);
      if (!I)
        return true;
      // If both instructions are defined in the same basic block then replacement
      // cannot break LCSSA form.
      if (I->getParent() == From->getParent())
        return true;
      // If the instruction is not defined in a loop then it can safely replace
      // anything.
      Loop *ToLoop = getLoopFor(I->getParent());
      if (!ToLoop)
        return true;
      // If the replacing instruction is defined in the same loop as the original
      // instruction, or in a loop that contains it as an inner loop, then using
      // it as a replacement will not break LCSSA form.
      return ToLoop->contains(getLoopFor(From->getParent()));
    }
  
    /// Checks if moving a specific instruction can break LCSSA in any loop.
    ///
    /// Return true if moving \p Inst to before \p NewLoc will break LCSSA,
    /// assuming that the function containing \p Inst and \p NewLoc is currently
    /// in LCSSA form.
    bool movementPreservesLCSSAForm(Instruction *Inst, Instruction *NewLoc) {
      assert(Inst->getFunction() == NewLoc->getFunction() &&
             "Can't reason about IPO!");
  
      auto *OldBB = Inst->getParent();
      auto *NewBB = NewLoc->getParent();
  
      // Movement within the same loop does not break LCSSA (the equality check is
      // to avoid doing a hashtable lookup in case of intra-block movement).
      if (OldBB == NewBB)
        return true;
  
      auto *OldLoop = getLoopFor(OldBB);
      auto *NewLoop = getLoopFor(NewBB);
  
      if (OldLoop == NewLoop)
        return true;
  
      // Check if Outer contains Inner; with the null loop counting as the
      // "outermost" loop.
      auto Contains = [](const Loop *Outer, const Loop *Inner) {
        return !Outer || Outer->contains(Inner);
      };
  
      // To check that the movement of Inst to before NewLoc does not break LCSSA,
      // we need to check two sets of uses for possible LCSSA violations at
      // NewLoc: the users of NewInst, and the operands of NewInst.
  
      // If we know we're hoisting Inst out of an inner loop to an outer loop,
      // then the uses *of* Inst don't need to be checked.
  
      if (!Contains(NewLoop, OldLoop)) {
        for (Use &U : Inst->uses()) {
          auto *UI = cast<Instruction>(U.getUser());
          auto *UBB = isa<PHINode>(UI) ? cast<PHINode>(UI)->getIncomingBlock(U)
                                       : UI->getParent();
          if (UBB != NewBB && getLoopFor(UBB) != NewLoop)
            return false;
        }
      }
  
      // If we know we're sinking Inst from an outer loop into an inner loop, then
      // the *operands* of Inst don't need to be checked.
  
      if (!Contains(OldLoop, NewLoop)) {
        // See below on why we can't handle phi nodes here.
        if (isa<PHINode>(Inst))
          return false;
  
        for (Use &U : Inst->operands()) {
          auto *DefI = dyn_cast<Instruction>(U.get());
          if (!DefI)
            return false;
  
          // This would need adjustment if we allow Inst to be a phi node -- the
          // new use block won't simply be NewBB.
  
          auto *DefBlock = DefI->getParent();
          if (DefBlock != NewBB && getLoopFor(DefBlock) != NewLoop)
            return false;
        }
      }
  
      return true;
    }
  };
  
  // Allow clients to walk the list of nested loops...
  template <> struct GraphTraits<const Loop *> {
    typedef const Loop *NodeRef;
    typedef LoopInfo::iterator ChildIteratorType;
  
    static NodeRef getEntryNode(const Loop *L) { return L; }
    static ChildIteratorType child_begin(NodeRef N) { return N->begin(); }
    static ChildIteratorType child_end(NodeRef N) { return N->end(); }
  };
  
  template <> struct GraphTraits<Loop *> {
    typedef Loop *NodeRef;
    typedef LoopInfo::iterator ChildIteratorType;
  
    static NodeRef getEntryNode(Loop *L) { return L; }
    static ChildIteratorType child_begin(NodeRef N) { return N->begin(); }
    static ChildIteratorType child_end(NodeRef N) { return N->end(); }
  };
  
  /// Analysis pass that exposes the \c LoopInfo for a function.
  class LoopAnalysis : public AnalysisInfoMixin<LoopAnalysis> {
    friend AnalysisInfoMixin<LoopAnalysis>;
    static AnalysisKey Key;
  
  public:
    typedef LoopInfo Result;
  
    LoopInfo run(Function &F, FunctionAnalysisManager &AM);
  };
  
  /// Printer pass for the \c LoopAnalysis results.
  class LoopPrinterPass : public PassInfoMixin<LoopPrinterPass> {
    raw_ostream &OS;
  
  public:
    explicit LoopPrinterPass(raw_ostream &OS) : OS(OS) {}
    PreservedAnalyses run(Function &F, FunctionAnalysisManager &AM);
  };
  
  /// Verifier pass for the \c LoopAnalysis results.
  struct LoopVerifierPass : public PassInfoMixin<LoopVerifierPass> {
    PreservedAnalyses run(Function &F, FunctionAnalysisManager &AM);
  };
  
  /// The legacy pass manager's analysis pass to compute loop information.
  class LoopInfoWrapperPass : public FunctionPass {
    LoopInfo LI;
  
  public:
    static char ID; // Pass identification, replacement for typeid
  
    LoopInfoWrapperPass() : FunctionPass(ID) {
      initializeLoopInfoWrapperPassPass(*PassRegistry::getPassRegistry());
    }
  
    LoopInfo &getLoopInfo() { return LI; }
    const LoopInfo &getLoopInfo() const { return LI; }
  
    /// Calculate the natural loop information for a given function.
    bool runOnFunction(Function &F) override;
  
    void verifyAnalysis() const override;
  
    void releaseMemory() override { LI.releaseMemory(); }
  
    void print(raw_ostream &O, const Module *M = nullptr) const override;
  
    void getAnalysisUsage(AnalysisUsage &AU) const override;
  };
  
  /// Function to print a loop's contents as LLVM's text IR assembly.
  void printLoop(Loop &L, raw_ostream &OS, const std::string &Banner = "");
  
  } // End llvm namespace
  
  #endif
  