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 //==- BlockFrequencyInfoImpl.h - Block Frequency Implementation --*- C++ -*-==//
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
 //===----------------------------------------------------------------------===//
 //
 // Shared implementation of BlockFrequency for IR and Machine Instructions.
 // See the documentation below for BlockFrequencyInfoImpl for details.
 //
 //===----------------------------------------------------------------------===//
 
 #ifndef LLVM_ANALYSIS_BLOCKFREQUENCYINFOIMPL_H
 #define LLVM_ANALYSIS_BLOCKFREQUENCYINFOIMPL_H
 
 #include "llvm/ADT/BitVector.h"
 #include "llvm/ADT/DenseMap.h"
 #include "llvm/ADT/DenseSet.h"
 #include "llvm/ADT/GraphTraits.h"
 #include "llvm/ADT/PostOrderIterator.h"
 #include "llvm/ADT/SmallPtrSet.h"
 #include "llvm/ADT/SmallVector.h"
 #include "llvm/ADT/SparseBitVector.h"
 #include "llvm/ADT/Twine.h"
 #include "llvm/ADT/iterator_range.h"
 #include "llvm/IR/BasicBlock.h"
 #include "llvm/IR/Function.h"
 #include "llvm/IR/ValueHandle.h"
 #include "llvm/Support/BlockFrequency.h"
 #include "llvm/Support/BranchProbability.h"
 #include "llvm/Support/CommandLine.h"
 #include "llvm/Support/DOTGraphTraits.h"
 #include "llvm/Support/Debug.h"
 #include "llvm/Support/Format.h"
 #include "llvm/Support/ScaledNumber.h"
 #include "llvm/Support/raw_ostream.h"
 #include <algorithm>
 #include <cassert>
 #include <cstddef>
 #include <cstdint>
 #include <deque>
 #include <iterator>
 #include <limits>
 #include <list>
 #include <optional>
 #include <queue>
 #include <string>
 #include <utility>
 #include <vector>
 
 #define DEBUG_TYPE "block-freq"
 
 namespace llvm {
 extern llvm::cl::opt<bool> CheckBFIUnknownBlockQueries;
 
 extern llvm::cl::opt<bool> UseIterativeBFIInference;
 extern llvm::cl::opt<unsigned> IterativeBFIMaxIterationsPerBlock;
 extern llvm::cl::opt<double> IterativeBFIPrecision;
 
 class BranchProbabilityInfo;
 class Function;
 class Loop;
 class LoopInfo;
 class MachineBasicBlock;
 class MachineBranchProbabilityInfo;
 class MachineFunction;
 class MachineLoop;
 class MachineLoopInfo;
 
 namespace bfi_detail {
 
 struct IrreducibleGraph;
 
 // This is part of a workaround for a GCC 4.7 crash on lambdas.
 template <class BT> struct BlockEdgesAdder;
 
 /// Mass of a block.
 ///
 /// This class implements a sort of fixed-point fraction always between 0.0 and
 /// 1.0.  getMass() == std::numeric_limits<uint64_t>::max() indicates a value of
 /// 1.0.
 ///
 /// Masses can be added and subtracted.  Simple saturation arithmetic is used,
 /// so arithmetic operations never overflow or underflow.
 ///
 /// Masses can be multiplied.  Multiplication treats full mass as 1.0 and uses
 /// an inexpensive floating-point algorithm that's off-by-one (almost, but not
 /// quite, maximum precision).
 ///
 /// Masses can be scaled by \a BranchProbability at maximum precision.
 class BlockMass {
   uint64_t Mass = 0;
 
 public:
   BlockMass() = default;
   explicit BlockMass(uint64_t Mass) : Mass(Mass) {}
 
   static BlockMass getEmpty() { return BlockMass(); }
 
   static BlockMass getFull() {
     return BlockMass(std::numeric_limits<uint64_t>::max());
   }
 
   uint64_t getMass() const { return Mass; }
 
   bool isFull() const { return Mass == std::numeric_limits<uint64_t>::max(); }
   bool isEmpty() const { return !Mass; }
 
   bool operator!() const { return isEmpty(); }
 
   /// Add another mass.
   ///
   /// Adds another mass, saturating at \a isFull() rather than overflowing.
   BlockMass &operator+=(BlockMass X) {
     uint64_t Sum = Mass + X.Mass;
     Mass = Sum < Mass ? std::numeric_limits<uint64_t>::max() : Sum;
     return *this;
   }
 
   /// Subtract another mass.
   ///
   /// Subtracts another mass, saturating at \a isEmpty() rather than
   /// undeflowing.
   BlockMass &operator-=(BlockMass X) {
     uint64_t Diff = Mass - X.Mass;
     Mass = Diff > Mass ? 0 : Diff;
     return *this;
   }
 
   BlockMass &operator*=(BranchProbability P) {
     Mass = P.scale(Mass);
     return *this;
   }
 
   bool operator==(BlockMass X) const { return Mass == X.Mass; }
   bool operator!=(BlockMass X) const { return Mass != X.Mass; }
   bool operator<=(BlockMass X) const { return Mass <= X.Mass; }
   bool operator>=(BlockMass X) const { return Mass >= X.Mass; }
   bool operator<(BlockMass X) const { return Mass < X.Mass; }
   bool operator>(BlockMass X) const { return Mass > X.Mass; }
 
   /// Convert to scaled number.
   ///
   /// Convert to \a ScaledNumber.  \a isFull() gives 1.0, while \a isEmpty()
   /// gives slightly above 0.0.
   ScaledNumber<uint64_t> toScaled() const;
 
   void dump() const;
   raw_ostream &print(raw_ostream &OS) const;
 };
 
 inline BlockMass operator+(BlockMass L, BlockMass R) {
   return BlockMass(L) += R;
 }
 inline BlockMass operator-(BlockMass L, BlockMass R) {
   return BlockMass(L) -= R;
 }
 inline BlockMass operator*(BlockMass L, BranchProbability R) {
   return BlockMass(L) *= R;
 }
 inline BlockMass operator*(BranchProbability L, BlockMass R) {
   return BlockMass(R) *= L;
 }
 
 inline raw_ostream &operator<<(raw_ostream &OS, BlockMass X) {
   return X.print(OS);
 }
 
 } // end namespace bfi_detail
 
 /// Base class for BlockFrequencyInfoImpl
 ///
 /// BlockFrequencyInfoImplBase has supporting data structures and some
 /// algorithms for BlockFrequencyInfoImplBase.  Only algorithms that depend on
 /// the block type (or that call such algorithms) are skipped here.
 ///
 /// Nevertheless, the majority of the overall algorithm documentation lives with
 /// BlockFrequencyInfoImpl.  See there for details.
 class BlockFrequencyInfoImplBase {
 public:
   using Scaled64 = ScaledNumber<uint64_t>;
   using BlockMass = bfi_detail::BlockMass;
 
   /// Representative of a block.
   ///
   /// This is a simple wrapper around an index into the reverse-post-order
   /// traversal of the blocks.
   ///
   /// Unlike a block pointer, its order has meaning (location in the
   /// topological sort) and it's class is the same regardless of block type.
   struct BlockNode {
     using IndexType = uint32_t;
 
     IndexType Index;
 
     BlockNode() : Index(std::numeric_limits<uint32_t>::max()) {}
     BlockNode(IndexType Index) : Index(Index) {}
 
     bool operator==(const BlockNode &X) const { return Index == X.Index; }
     bool operator!=(const BlockNode &X) const { return Index != X.Index; }
     bool operator<=(const BlockNode &X) const { return Index <= X.Index; }
     bool operator>=(const BlockNode &X) const { return Index >= X.Index; }
     bool operator<(const BlockNode &X) const { return Index < X.Index; }
     bool operator>(const BlockNode &X) const { return Index > X.Index; }
 
     bool isValid() const { return Index <= getMaxIndex(); }
 
     static size_t getMaxIndex() {
        return std::numeric_limits<uint32_t>::max() - 1;
     }
   };
 
   /// Stats about a block itself.
   struct FrequencyData {
     Scaled64 Scaled;
     uint64_t Integer;
   };
 
   /// Data about a loop.
   ///
   /// Contains the data necessary to represent a loop as a pseudo-node once it's
   /// packaged.
   struct LoopData {
     using ExitMap = SmallVector<std::pair<BlockNode, BlockMass>, 4>;
     using NodeList = SmallVector<BlockNode, 4>;
     using HeaderMassList = SmallVector<BlockMass, 1>;
 
     LoopData *Parent;            ///< The parent loop.
     bool IsPackaged = false;     ///< Whether this has been packaged.
     uint32_t NumHeaders = 1;     ///< Number of headers.
     ExitMap Exits;               ///< Successor edges (and weights).
     NodeList Nodes;              ///< Header and the members of the loop.
     HeaderMassList BackedgeMass; ///< Mass returned to each loop header.
     BlockMass Mass;
     Scaled64 Scale;
 
     LoopData(LoopData *Parent, const BlockNode &Header)
       : Parent(Parent), Nodes(1, Header), BackedgeMass(1) {}
 
     template <class It1, class It2>
     LoopData(LoopData *Parent, It1 FirstHeader, It1 LastHeader, It2 FirstOther,
              It2 LastOther)
         : Parent(Parent), Nodes(FirstHeader, LastHeader) {
       NumHeaders = Nodes.size();
       Nodes.insert(Nodes.end(), FirstOther, LastOther);
       BackedgeMass.resize(NumHeaders);
     }
 
     bool isHeader(const BlockNode &Node) const {
       if (isIrreducible())
         return std::binary_search(Nodes.begin(), Nodes.begin() + NumHeaders,
                                   Node);
       return Node == Nodes[0];
     }
 
     BlockNode getHeader() const { return Nodes[0]; }
     bool isIrreducible() const { return NumHeaders > 1; }
 
     HeaderMassList::difference_type getHeaderIndex(const BlockNode &B) {
       assert(isHeader(B) && "this is only valid on loop header blocks");
       if (isIrreducible())
         return std::lower_bound(Nodes.begin(), Nodes.begin() + NumHeaders, B) -
                Nodes.begin();
       return 0;
     }
 
     NodeList::const_iterator members_begin() const {
       return Nodes.begin() + NumHeaders;
     }
 
     NodeList::const_iterator members_end() const { return Nodes.end(); }
     iterator_range<NodeList::const_iterator> members() const {
       return make_range(members_begin(), members_end());
     }
   };
 
   /// Index of loop information.
   struct WorkingData {
     BlockNode Node;           ///< This node.
     LoopData *Loop = nullptr; ///< The loop this block is inside.
     BlockMass Mass;           ///< Mass distribution from the entry block.
 
     WorkingData(const BlockNode &Node) : Node(Node) {}
 
     bool isLoopHeader() const { return Loop && Loop->isHeader(Node); }
 
     bool isDoubleLoopHeader() const {
       return isLoopHeader() && Loop->Parent && Loop->Parent->isIrreducible() &&
              Loop->Parent->isHeader(Node);
     }
 
     LoopData *getContainingLoop() const {
       if (!isLoopHeader())
         return Loop;
       if (!isDoubleLoopHeader())
         return Loop->Parent;
       return Loop->Parent->Parent;
     }
 
     /// Resolve a node to its representative.
     ///
     /// Get the node currently representing Node, which could be a containing
     /// loop.
     ///
     /// This function should only be called when distributing mass.  As long as
     /// there are no irreducible edges to Node, then it will have complexity
     /// O(1) in this context.
     ///
     /// In general, the complexity is O(L), where L is the number of loop
     /// headers Node has been packaged into.  Since this method is called in
     /// the context of distributing mass, L will be the number of loop headers
     /// an early exit edge jumps out of.
     BlockNode getResolvedNode() const {
       auto *L = getPackagedLoop();
       return L ? L->getHeader() : Node;
     }
 
     LoopData *getPackagedLoop() const {
       if (!Loop || !Loop->IsPackaged)
         return nullptr;
       auto *L = Loop;
       while (L->Parent && L->Parent->IsPackaged)
         L = L->Parent;
       return L;
     }
 
     /// Get the appropriate mass for a node.
     ///
     /// Get appropriate mass for Node.  If Node is a loop-header (whose loop
     /// has been packaged), returns the mass of its pseudo-node.  If it's a
     /// node inside a packaged loop, it returns the loop's mass.
     BlockMass &getMass() {
       if (!isAPackage())
         return Mass;
       if (!isADoublePackage())
         return Loop->Mass;
       return Loop->Parent->Mass;
     }
 
     /// Has ContainingLoop been packaged up?
     bool isPackaged() const { return getResolvedNode() != Node; }
 
     /// Has Loop been packaged up?
     bool isAPackage() const { return isLoopHeader() && Loop->IsPackaged; }
 
     /// Has Loop been packaged up twice?
     bool isADoublePackage() const {
       return isDoubleLoopHeader() && Loop->Parent->IsPackaged;
     }
   };
 
   /// Unscaled probability weight.
   ///
   /// Probability weight for an edge in the graph (including the
   /// successor/target node).
   ///
   /// All edges in the original function are 32-bit.  However, exit edges from
   /// loop packages are taken from 64-bit exit masses, so we need 64-bits of
   /// space in general.
   ///
   /// In addition to the raw weight amount, Weight stores the type of the edge
   /// in the current context (i.e., the context of the loop being processed).
   /// Is this a local edge within the loop, an exit from the loop, or a
   /// backedge to the loop header?
   struct Weight {
     enum DistType { Local, Exit, Backedge };
     DistType Type = Local;
     BlockNode TargetNode;
     uint64_t Amount = 0;
 
     Weight() = default;
     Weight(DistType Type, BlockNode TargetNode, uint64_t Amount)
         : Type(Type), TargetNode(TargetNode), Amount(Amount) {}
   };
 
   /// Distribution of unscaled probability weight.
   ///
   /// Distribution of unscaled probability weight to a set of successors.
   ///
   /// This class collates the successor edge weights for later processing.
   ///
   /// \a DidOverflow indicates whether \a Total did overflow while adding to
   /// the distribution.  It should never overflow twice.
   struct Distribution {
     using WeightList = SmallVector<Weight, 4>;
 
     WeightList Weights;       ///< Individual successor weights.
     uint64_t Total = 0;       ///< Sum of all weights.
     bool DidOverflow = false; ///< Whether \a Total did overflow.
 
     Distribution() = default;
 
     void addLocal(const BlockNode &Node, uint64_t Amount) {
       add(Node, Amount, Weight::Local);
     }
 
     void addExit(const BlockNode &Node, uint64_t Amount) {
       add(Node, Amount, Weight::Exit);
     }
 
     void addBackedge(const BlockNode &Node, uint64_t Amount) {
       add(Node, Amount, Weight::Backedge);
     }
 
     /// Normalize the distribution.
     ///
     /// Combines multiple edges to the same \a Weight::TargetNode and scales
     /// down so that \a Total fits into 32-bits.
     ///
     /// This is linear in the size of \a Weights.  For the vast majority of
     /// cases, adjacent edge weights are combined by sorting WeightList and
     /// combining adjacent weights.  However, for very large edge lists an
     /// auxiliary hash table is used.
     void normalize();
 
   private:
     void add(const BlockNode &Node, uint64_t Amount, Weight::DistType Type);
   };
 
   /// Data about each block.  This is used downstream.
   std::vector<FrequencyData> Freqs;
 
   /// Whether each block is an irreducible loop header.
   /// This is used downstream.
   SparseBitVector<> IsIrrLoopHeader;
 
   /// Loop data: see initializeLoops().
   std::vector<WorkingData> Working;
 
   /// Indexed information about loops.
   std::list<LoopData> Loops;
 
   /// Virtual destructor.
   ///
   /// Need a virtual destructor to mask the compiler warning about
   /// getBlockName().
   virtual ~BlockFrequencyInfoImplBase() = default;
 
   /// Add all edges out of a packaged loop to the distribution.
   ///
   /// Adds all edges from LocalLoopHead to Dist.  Calls addToDist() to add each
   /// successor edge.
   ///
   /// \return \c true unless there's an irreducible backedge.
   bool addLoopSuccessorsToDist(const LoopData *OuterLoop, LoopData &Loop,
                                Distribution &Dist);
 
   /// Add an edge to the distribution.
   ///
   /// Adds an edge to Succ to Dist.  If \c LoopHead.isValid(), then whether the
   /// edge is local/exit/backedge is in the context of LoopHead.  Otherwise,
   /// every edge should be a local edge (since all the loops are packaged up).
   ///
   /// \return \c true unless aborted due to an irreducible backedge.
   bool addToDist(Distribution &Dist, const LoopData *OuterLoop,
                  const BlockNode &Pred, const BlockNode &Succ, uint64_t Weight);
 
   /// Analyze irreducible SCCs.
   ///
   /// Separate irreducible SCCs from \c G, which is an explicit graph of \c
   /// OuterLoop (or the top-level function, if \c OuterLoop is \c nullptr).
   /// Insert them into \a Loops before \c Insert.
   ///
   /// \return the \c LoopData nodes representing the irreducible SCCs.
   iterator_range<std::list<LoopData>::iterator>
   analyzeIrreducible(const bfi_detail::IrreducibleGraph &G, LoopData *OuterLoop,
                      std::list<LoopData>::iterator Insert);
 
   /// Update a loop after packaging irreducible SCCs inside of it.
   ///
   /// Update \c OuterLoop.  Before finding irreducible control flow, it was
   /// partway through \a computeMassInLoop(), so \a LoopData::Exits and \a
   /// LoopData::BackedgeMass need to be reset.  Also, nodes that were packaged
   /// up need to be removed from \a OuterLoop::Nodes.
   void updateLoopWithIrreducible(LoopData &OuterLoop);
 
   /// Distribute mass according to a distribution.
   ///
   /// Distributes the mass in Source according to Dist.  If LoopHead.isValid(),
   /// backedges and exits are stored in its entry in Loops.
   ///
   /// Mass is distributed in parallel from two copies of the source mass.
   void distributeMass(const BlockNode &Source, LoopData *OuterLoop,
                       Distribution &Dist);
 
   /// Compute the loop scale for a loop.
   void computeLoopScale(LoopData &Loop);
 
   /// Adjust the mass of all headers in an irreducible loop.
   ///
   /// Initially, irreducible loops are assumed to distribute their mass
   /// equally among its headers. This can lead to wrong frequency estimates
   /// since some headers may be executed more frequently than others.
   ///
   /// This adjusts header mass distribution so it matches the weights of
   /// the backedges going into each of the loop headers.
   void adjustLoopHeaderMass(LoopData &Loop);
 
   void distributeIrrLoopHeaderMass(Distribution &Dist);
 
   /// Package up a loop.
   void packageLoop(LoopData &Loop);
 
   /// Unwrap loops.
   void unwrapLoops();
 
   /// Finalize frequency metrics.
   ///
   /// Calculates final frequencies and cleans up no-longer-needed data
   /// structures.
   void finalizeMetrics();
 
   /// Clear all memory.
   void clear();
 
   virtual std::string getBlockName(const BlockNode &Node) const;
   std::string getLoopName(const LoopData &Loop) const;
 
   virtual raw_ostream &print(raw_ostream &OS) const { return OS; }
   void dump() const { print(dbgs()); }
 
   Scaled64 getFloatingBlockFreq(const BlockNode &Node) const;
 
   BlockFrequency getBlockFreq(const BlockNode &Node) const;
   std::optional<uint64_t>
   getBlockProfileCount(const Function &F, const BlockNode &Node,
                        bool AllowSynthetic = false) const;
   std::optional<uint64_t>
   getProfileCountFromFreq(const Function &F, BlockFrequency Freq,
                           bool AllowSynthetic = false) const;
   bool isIrrLoopHeader(const BlockNode &Node);
 
   void setBlockFreq(const BlockNode &Node, BlockFrequency Freq);
 
   BlockFrequency getEntryFreq() const {
     assert(!Freqs.empty());
     return BlockFrequency(Freqs[0].Integer);
   }
 };
 
 namespace bfi_detail {
 
 template <class BlockT> struct TypeMap {};
 template <> struct TypeMap<BasicBlock> {
   using BlockT = BasicBlock;
   using BlockKeyT = AssertingVH<const BasicBlock>;
   using FunctionT = Function;
   using BranchProbabilityInfoT = BranchProbabilityInfo;
   using LoopT = Loop;
   using LoopInfoT = LoopInfo;
 };
 template <> struct TypeMap<MachineBasicBlock> {
   using BlockT = MachineBasicBlock;
   using BlockKeyT = const MachineBasicBlock *;
   using FunctionT = MachineFunction;
   using BranchProbabilityInfoT = MachineBranchProbabilityInfo;
   using LoopT = MachineLoop;
   using LoopInfoT = MachineLoopInfo;
 };
 
 template <class BlockT, class BFIImplT>
 class BFICallbackVH;
 
 /// Get the name of a MachineBasicBlock.
 ///
 /// Get the name of a MachineBasicBlock.  It's templated so that including from
 /// CodeGen is unnecessary (that would be a layering issue).
 ///
 /// This is used mainly for debug output.  The name is similar to
 /// MachineBasicBlock::getFullName(), but skips the name of the function.
 template <class BlockT> std::string getBlockName(const BlockT *BB) {
   assert(BB && "Unexpected nullptr");
   auto MachineName = "BB" + Twine(BB->getNumber());
   if (BB->getBasicBlock())
     return (MachineName + "[" + BB->getName() + "]").str();
   return MachineName.str();
 }
 /// Get the name of a BasicBlock.
 template <> inline std::string getBlockName(const BasicBlock *BB) {
   assert(BB && "Unexpected nullptr");
   return BB->getName().str();
 }
 
 /// Graph of irreducible control flow.
 ///
 /// This graph is used for determining the SCCs in a loop (or top-level
 /// function) that has irreducible control flow.
 ///
 /// During the block frequency algorithm, the local graphs are defined in a
 /// light-weight way, deferring to the \a BasicBlock or \a MachineBasicBlock
 /// graphs for most edges, but getting others from \a LoopData::ExitMap.  The
 /// latter only has successor information.
 ///
 /// \a IrreducibleGraph makes this graph explicit.  It's in a form that can use
 /// \a GraphTraits (so that \a analyzeIrreducible() can use \a scc_iterator),
 /// and it explicitly lists predecessors and successors.  The initialization
 /// that relies on \c MachineBasicBlock is defined in the header.
 struct IrreducibleGraph {
   using BFIBase = BlockFrequencyInfoImplBase;
 
   BFIBase &BFI;
 
   using BlockNode = BFIBase::BlockNode;
   struct IrrNode {
     BlockNode Node;
     unsigned NumIn = 0;
     std::deque<const IrrNode *> Edges;
 
     IrrNode(const BlockNode &Node) : Node(Node) {}
 
     using iterator = std::deque<const IrrNode *>::const_iterator;
 
     iterator pred_begin() const { return Edges.begin(); }
     iterator succ_begin() const { return Edges.begin() + NumIn; }
     iterator pred_end() const { return succ_begin(); }
     iterator succ_end() const { return Edges.end(); }
   };
   BlockNode Start;
   const IrrNode *StartIrr = nullptr;
   std::vector<IrrNode> Nodes;
   SmallDenseMap<uint32_t, IrrNode *, 4> Lookup;
 
   /// Construct an explicit graph containing irreducible control flow.
   ///
   /// Construct an explicit graph of the control flow in \c OuterLoop (or the
   /// top-level function, if \c OuterLoop is \c nullptr).  Uses \c
   /// addBlockEdges to add block successors that have not been packaged into
   /// loops.
   ///
   /// \a BlockFrequencyInfoImpl::computeIrreducibleMass() is the only expected
   /// user of this.
   template <class BlockEdgesAdder>
   IrreducibleGraph(BFIBase &BFI, const BFIBase::LoopData *OuterLoop,
                    BlockEdgesAdder addBlockEdges) : BFI(BFI) {
     initialize(OuterLoop, addBlockEdges);
   }
 
   template <class BlockEdgesAdder>
   void initialize(const BFIBase::LoopData *OuterLoop,
                   BlockEdgesAdder addBlockEdges);
   void addNodesInLoop(const BFIBase::LoopData &OuterLoop);
   void addNodesInFunction();
 
   void addNode(const BlockNode &Node) {
     Nodes.emplace_back(Node);
     BFI.Working[Node.Index].getMass() = BlockMass::getEmpty();
   }
 
   void indexNodes();
   template <class BlockEdgesAdder>
   void addEdges(const BlockNode &Node, const BFIBase::LoopData *OuterLoop,
                 BlockEdgesAdder addBlockEdges);
   void addEdge(IrrNode &Irr, const BlockNode &Succ,
                const BFIBase::LoopData *OuterLoop);
 };
 
 template <class BlockEdgesAdder>
 void IrreducibleGraph::initialize(const BFIBase::LoopData *OuterLoop,
                                   BlockEdgesAdder addBlockEdges) {
   if (OuterLoop) {
     addNodesInLoop(*OuterLoop);
     for (auto N : OuterLoop->Nodes)
       addEdges(N, OuterLoop, addBlockEdges);
   } else {
     addNodesInFunction();
     for (uint32_t Index = 0; Index < BFI.Working.size(); ++Index)
       addEdges(Index, OuterLoop, addBlockEdges);
   }
   StartIrr = Lookup[Start.Index];
 }
 
 template <class BlockEdgesAdder>
 void IrreducibleGraph::addEdges(const BlockNode &Node,
                                 const BFIBase::LoopData *OuterLoop,
                                 BlockEdgesAdder addBlockEdges) {
   auto L = Lookup.find(Node.Index);
   if (L == Lookup.end())
     return;
   IrrNode &Irr = *L->second;
   const auto &Working = BFI.Working[Node.Index];
 
   if (Working.isAPackage())
     for (const auto &I : Working.Loop->Exits)
       addEdge(Irr, I.first, OuterLoop);
   else
     addBlockEdges(*this, Irr, OuterLoop);
 }
 
 } // end namespace bfi_detail
 
 /// Shared implementation for block frequency analysis.
 ///
 /// This is a shared implementation of BlockFrequencyInfo and
 /// MachineBlockFrequencyInfo, and calculates the relative frequencies of
 /// blocks.
 ///
 /// LoopInfo defines a loop as a "non-trivial" SCC dominated by a single block,
 /// which is called the header.  A given loop, L, can have sub-loops, which are
 /// loops within the subgraph of L that exclude its header.  (A "trivial" SCC
 /// consists of a single block that does not have a self-edge.)
 ///
 /// In addition to loops, this algorithm has limited support for irreducible
 /// SCCs, which are SCCs with multiple entry blocks.  Irreducible SCCs are
 /// discovered on the fly, and modelled as loops with multiple headers.
 ///
 /// The headers of irreducible sub-SCCs consist of its entry blocks and all
 /// nodes that are targets of a backedge within it (excluding backedges within
 /// true sub-loops).  Block frequency calculations act as if a block is
 /// inserted that intercepts all the edges to the headers.  All backedges and
 /// entries point to this block.  Its successors are the headers, which split
 /// the frequency evenly.
 ///
 /// This algorithm leverages BlockMass and ScaledNumber to maintain precision,
 /// separates mass distribution from loop scaling, and dithers to eliminate
 /// probability mass loss.
 ///
 /// The implementation is split between BlockFrequencyInfoImpl, which knows the
 /// type of graph being modelled (BasicBlock vs. MachineBasicBlock), and
 /// BlockFrequencyInfoImplBase, which doesn't.  The base class uses \a
 /// BlockNode, a wrapper around a uint32_t.  BlockNode is numbered from 0 in
 /// reverse-post order.  This gives two advantages:  it's easy to compare the
 /// relative ordering of two nodes, and maps keyed on BlockT can be represented
 /// by vectors.
 ///
 /// This algorithm is O(V+E), unless there is irreducible control flow, in
 /// which case it's O(V*E) in the worst case.
 ///
 /// These are the main stages:
 ///
 ///  0. Reverse post-order traversal (\a initializeRPOT()).
 ///
 ///     Run a single post-order traversal and save it (in reverse) in RPOT.
 ///     All other stages make use of this ordering.  Save a lookup from BlockT
 ///     to BlockNode (the index into RPOT) in Nodes.
 ///
 ///  1. Loop initialization (\a initializeLoops()).
 ///
 ///     Translate LoopInfo/MachineLoopInfo into a form suitable for the rest of
 ///     the algorithm.  In particular, store the immediate members of each loop
 ///     in reverse post-order.
 ///
 ///  2. Calculate mass and scale in loops (\a computeMassInLoops()).
 ///
 ///     For each loop (bottom-up), distribute mass through the DAG resulting
 ///     from ignoring backedges and treating sub-loops as a single pseudo-node.
 ///     Track the backedge mass distributed to the loop header, and use it to
 ///     calculate the loop scale (number of loop iterations).  Immediate
 ///     members that represent sub-loops will already have been visited and
 ///     packaged into a pseudo-node.
 ///
 ///     Distributing mass in a loop is a reverse-post-order traversal through
 ///     the loop.  Start by assigning full mass to the Loop header.  For each
 ///     node in the loop:
 ///
 ///         - Fetch and categorize the weight distribution for its successors.
 ///           If this is a packaged-subloop, the weight distribution is stored
 ///           in \a LoopData::Exits.  Otherwise, fetch it from
 ///           BranchProbabilityInfo.
 ///
 ///         - Each successor is categorized as \a Weight::Local, a local edge
 ///           within the current loop, \a Weight::Backedge, a backedge to the
 ///           loop header, or \a Weight::Exit, any successor outside the loop.
 ///           The weight, the successor, and its category are stored in \a
 ///           Distribution.  There can be multiple edges to each successor.
 ///
 ///         - If there's a backedge to a non-header, there's an irreducible SCC.
 ///           The usual flow is temporarily aborted.  \a
 ///           computeIrreducibleMass() finds the irreducible SCCs within the
 ///           loop, packages them up, and restarts the flow.
 ///
 ///         - Normalize the distribution:  scale weights down so that their sum
 ///           is 32-bits, and coalesce multiple edges to the same node.
 ///
 ///         - Distribute the mass accordingly, dithering to minimize mass loss,
 ///           as described in \a distributeMass().
 ///
 ///     In the case of irreducible loops, instead of a single loop header,
 ///     there will be several. The computation of backedge masses is similar
 ///     but instead of having a single backedge mass, there will be one
 ///     backedge per loop header. In these cases, each backedge will carry
 ///     a mass proportional to the edge weights along the corresponding
 ///     path.
 ///
 ///     At the end of propagation, the full mass assigned to the loop will be
 ///     distributed among the loop headers proportionally according to the
 ///     mass flowing through their backedges.
 ///
 ///     Finally, calculate the loop scale from the accumulated backedge mass.
 ///
 ///  3. Distribute mass in the function (\a computeMassInFunction()).
 ///
 ///     Finally, distribute mass through the DAG resulting from packaging all
 ///     loops in the function.  This uses the same algorithm as distributing
 ///     mass in a loop, except that there are no exit or backedge edges.
 ///
 ///  4. Unpackage loops (\a unwrapLoops()).
 ///
 ///     Initialize each block's frequency to a floating point representation of
 ///     its mass.
 ///
 ///     Visit loops top-down, scaling the frequencies of its immediate members
 ///     by the loop's pseudo-node's frequency.
 ///
 ///  5. Convert frequencies to a 64-bit range (\a finalizeMetrics()).
 ///
 ///     Using the min and max frequencies as a guide, translate floating point
 ///     frequencies to an appropriate range in uint64_t.
 ///
 /// It has some known flaws.
 ///
 ///   - The model of irreducible control flow is a rough approximation.
 ///
 ///     Modelling irreducible control flow exactly involves setting up and
 ///     solving a group of infinite geometric series.  Such precision is
 ///     unlikely to be worthwhile, since most of our algorithms give up on
 ///     irreducible control flow anyway.
 ///
 ///     Nevertheless, we might find that we need to get closer.  Here's a sort
 ///     of TODO list for the model with diminishing returns, to be completed as
 ///     necessary.
 ///
 ///       - The headers for the \a LoopData representing an irreducible SCC
 ///         include non-entry blocks.  When these extra blocks exist, they
 ///         indicate a self-contained irreducible sub-SCC.  We could treat them
 ///         as sub-loops, rather than arbitrarily shoving the problematic
 ///         blocks into the headers of the main irreducible SCC.
 ///
 ///       - Entry frequencies are assumed to be evenly split between the
 ///         headers of a given irreducible SCC, which is the only option if we
 ///         need to compute mass in the SCC before its parent loop.  Instead,
 ///         we could partially compute mass in the parent loop, and stop when
 ///         we get to the SCC.  Here, we have the correct ratio of entry
 ///         masses, which we can use to adjust their relative frequencies.
 ///         Compute mass in the SCC, and then continue propagation in the
 ///         parent.
 ///
 ///       - We can propagate mass iteratively through the SCC, for some fixed
 ///         number of iterations.  Each iteration starts by assigning the entry
 ///         blocks their backedge mass from the prior iteration.  The final
 ///         mass for each block (and each exit, and the total backedge mass
 ///         used for computing loop scale) is the sum of all iterations.
 ///         (Running this until fixed point would "solve" the geometric
 ///         series by simulation.)
 template <class BT> class BlockFrequencyInfoImpl : BlockFrequencyInfoImplBase {
   // This is part of a workaround for a GCC 4.7 crash on lambdas.
   friend struct bfi_detail::BlockEdgesAdder<BT>;
 
   using BlockT = typename bfi_detail::TypeMap<BT>::BlockT;
   using BlockKeyT = typename bfi_detail::TypeMap<BT>::BlockKeyT;
   using FunctionT = typename bfi_detail::TypeMap<BT>::FunctionT;
   using BranchProbabilityInfoT =
       typename bfi_detail::TypeMap<BT>::BranchProbabilityInfoT;
   using LoopT = typename bfi_detail::TypeMap<BT>::LoopT;
   using LoopInfoT = typename bfi_detail::TypeMap<BT>::LoopInfoT;
   using Successor = GraphTraits<const BlockT *>;
   using Predecessor = GraphTraits<Inverse<const BlockT *>>;
   using BFICallbackVH =
       bfi_detail::BFICallbackVH<BlockT, BlockFrequencyInfoImpl>;
 
   const BranchProbabilityInfoT *BPI = nullptr;
   const LoopInfoT *LI = nullptr;
   const FunctionT *F = nullptr;
 
   // All blocks in reverse postorder.
   std::vector<const BlockT *> RPOT;
   DenseMap<BlockKeyT, std::pair<BlockNode, BFICallbackVH>> Nodes;
 
   using rpot_iterator = typename std::vector<const BlockT *>::const_iterator;
 
   rpot_iterator rpot_begin() const { return RPOT.begin(); }
   rpot_iterator rpot_end() const { return RPOT.end(); }
 
   size_t getIndex(const rpot_iterator &I) const { return I - rpot_begin(); }
 
   BlockNode getNode(const rpot_iterator &I) const {
     return BlockNode(getIndex(I));
   }
 
   BlockNode getNode(const BlockT *BB) const { return Nodes.lookup(BB).first; }
 
   const BlockT *getBlock(const BlockNode &Node) const {
     assert(Node.Index < RPOT.size());
     return RPOT[Node.Index];
   }
 
   /// Run (and save) a post-order traversal.
   ///
   /// Saves a reverse post-order traversal of all the nodes in \a F.
   void initializeRPOT();
 
   /// Initialize loop data.
   ///
   /// Build up \a Loops using \a LoopInfo.  \a LoopInfo gives us a mapping from
   /// each block to the deepest loop it's in, but we need the inverse.  For each
   /// loop, we store in reverse post-order its "immediate" members, defined as
   /// the header, the headers of immediate sub-loops, and all other blocks in
   /// the loop that are not in sub-loops.
   void initializeLoops();
 
   /// Propagate to a block's successors.
   ///
   /// In the context of distributing mass through \c OuterLoop, divide the mass
   /// currently assigned to \c Node between its successors.
   ///
   /// \return \c true unless there's an irreducible backedge.
   bool propagateMassToSuccessors(LoopData *OuterLoop, const BlockNode &Node);
 
   /// Compute mass in a particular loop.
   ///
   /// Assign mass to \c Loop's header, and then for each block in \c Loop in
   /// reverse post-order, distribute mass to its successors.  Only visits nodes
   /// that have not been packaged into sub-loops.
   ///
   /// \pre \a computeMassInLoop() has been called for each subloop of \c Loop.
   /// \return \c true unless there's an irreducible backedge.
   bool computeMassInLoop(LoopData &Loop);
 
   /// Try to compute mass in the top-level function.
   ///
   /// Assign mass to the entry block, and then for each block in reverse
   /// post-order, distribute mass to its successors.  Skips nodes that have
   /// been packaged into loops.
   ///
   /// \pre \a computeMassInLoops() has been called.
   /// \return \c true unless there's an irreducible backedge.
   bool tryToComputeMassInFunction();
 
   /// Compute mass in (and package up) irreducible SCCs.
   ///
   /// Find the irreducible SCCs in \c OuterLoop, add them to \a Loops (in front
   /// of \c Insert), and call \a computeMassInLoop() on each of them.
   ///
   /// If \c OuterLoop is \c nullptr, it refers to the top-level function.
   ///
   /// \pre \a computeMassInLoop() has been called for each subloop of \c
   /// OuterLoop.
   /// \pre \c Insert points at the last loop successfully processed by \a
   /// computeMassInLoop().
   /// \pre \c OuterLoop has irreducible SCCs.
   void computeIrreducibleMass(LoopData *OuterLoop,
                               std::list<LoopData>::iterator Insert);
 
   /// Compute mass in all loops.
   ///
   /// For each loop bottom-up, call \a computeMassInLoop().
   ///
   /// \a computeMassInLoop() aborts (and returns \c false) on loops that
   /// contain a irreducible sub-SCCs.  Use \a computeIrreducibleMass() and then
   /// re-enter \a computeMassInLoop().
   ///
   /// \post \a computeMassInLoop() has returned \c true for every loop.
   void computeMassInLoops();
 
   /// Compute mass in the top-level function.
   ///
   /// Uses \a tryToComputeMassInFunction() and \a computeIrreducibleMass() to
   /// compute mass in the top-level function.
   ///
   /// \post \a tryToComputeMassInFunction() has returned \c true.
   void computeMassInFunction();
 
   std::string getBlockName(const BlockNode &Node) const override {
     return bfi_detail::getBlockName(getBlock(Node));
   }
 
   /// The current implementation for computing relative block frequencies does
   /// not handle correctly control-flow graphs containing irreducible loops. To
   /// resolve the problem, we apply a post-processing step, which iteratively
   /// updates block frequencies based on the frequencies of their predesessors.
   /// This corresponds to finding the stationary point of the Markov chain by
   /// an iterative method aka "PageRank computation".
   /// The algorithm takes at most O(|E| * IterativeBFIMaxIterations) steps but
   /// typically converges faster.
   ///
   /// Decide whether we want to apply iterative inference for a given function.
   bool needIterativeInference() const;
 
   /// Apply an iterative post-processing to infer correct counts for irr loops.
   void applyIterativeInference();
 
   using ProbMatrixType = std::vector<std::vector<std::pair<size_t, Scaled64>>>;
 
   /// Run iterative inference for a probability matrix and initial frequencies.
   void iterativeInference(const ProbMatrixType &ProbMatrix,
                           std::vector<Scaled64> &Freq) const;
 
   /// Find all blocks to apply inference on, that is, reachable from the entry
   /// and backward reachable from exists along edges with positive probability.
   void findReachableBlocks(std::vector<const BlockT *> &Blocks) const;
 
   /// Build a matrix of probabilities with transitions (edges) between the
   /// blocks: ProbMatrix[I] holds pairs (J, P), where Pr[J -> I | J] = P
   void initTransitionProbabilities(
       const std::vector<const BlockT *> &Blocks,
       const DenseMap<const BlockT *, size_t> &BlockIndex,
       ProbMatrixType &ProbMatrix) const;
 
 #ifndef NDEBUG
   /// Compute the discrepancy between current block frequencies and the
   /// probability matrix.
   Scaled64 discrepancy(const ProbMatrixType &ProbMatrix,
                        const std::vector<Scaled64> &Freq) const;
 #endif
 
 public:
   BlockFrequencyInfoImpl() = default;
 
   const FunctionT *getFunction() const { return F; }
 
   void calculate(const FunctionT &F, const BranchProbabilityInfoT &BPI,
                  const LoopInfoT &LI);
 
   using BlockFrequencyInfoImplBase::getEntryFreq;
 
   BlockFrequency getBlockFreq(const BlockT *BB) const {
     return BlockFrequencyInfoImplBase::getBlockFreq(getNode(BB));
   }
 
   std::optional<uint64_t>
   getBlockProfileCount(const Function &F, const BlockT *BB,
                        bool AllowSynthetic = false) const {
     return BlockFrequencyInfoImplBase::getBlockProfileCount(F, getNode(BB),
                                                             AllowSynthetic);
   }
 
   std::optional<uint64_t>
   getProfileCountFromFreq(const Function &F, BlockFrequency Freq,
                           bool AllowSynthetic = false) const {
     return BlockFrequencyInfoImplBase::getProfileCountFromFreq(F, Freq,
                                                                AllowSynthetic);
   }
 
   bool isIrrLoopHeader(const BlockT *BB) {
     return BlockFrequencyInfoImplBase::isIrrLoopHeader(getNode(BB));
   }
 
   void setBlockFreq(const BlockT *BB, BlockFrequency Freq);
 
   void forgetBlock(const BlockT *BB) {
     // We don't erase corresponding items from `Freqs`, `RPOT` and other to
     // avoid invalidating indices. Doing so would have saved some memory, but
     // it's not worth it.
     Nodes.erase(BB);
   }
 
   Scaled64 getFloatingBlockFreq(const BlockT *BB) const {
     return BlockFrequencyInfoImplBase::getFloatingBlockFreq(getNode(BB));
   }
 
   const BranchProbabilityInfoT &getBPI() const { return *BPI; }
 
   /// Print the frequencies for the current function.
   ///
   /// Prints the frequencies for the blocks in the current function.
   ///
   /// Blocks are printed in the natural iteration order of the function, rather
   /// than reverse post-order.  This provides two advantages:  writing -analyze
   /// tests is easier (since blocks come out in source order), and even
   /// unreachable blocks are printed.
   ///
   /// \a BlockFrequencyInfoImplBase::print() only knows reverse post-order, so
   /// we need to override it here.
   raw_ostream &print(raw_ostream &OS) const override;
 
   using BlockFrequencyInfoImplBase::dump;
 
   void verifyMatch(BlockFrequencyInfoImpl<BT> &Other) const;
 };
 
 namespace bfi_detail {
 
 template <class BFIImplT>
 class BFICallbackVH<BasicBlock, BFIImplT> : public CallbackVH {
   BFIImplT *BFIImpl;
 
 public:
   BFICallbackVH() = default;
 
   BFICallbackVH(const BasicBlock *BB, BFIImplT *BFIImpl)
       : CallbackVH(BB), BFIImpl(BFIImpl) {}
 
   virtual ~BFICallbackVH() = default;
 
   void deleted() override {
     BFIImpl->forgetBlock(cast<BasicBlock>(getValPtr()));
   }
 };
 
 /// Dummy implementation since MachineBasicBlocks aren't Values, so ValueHandles
 /// don't apply to them.
 template <class BFIImplT>
 class BFICallbackVH<MachineBasicBlock, BFIImplT> {
 public:
   BFICallbackVH() = default;
   BFICallbackVH(const MachineBasicBlock *, BFIImplT *) {}
 };
 
 } // end namespace bfi_detail
 
 template <class BT>
 void BlockFrequencyInfoImpl<BT>::calculate(const FunctionT &F,
                                            const BranchProbabilityInfoT &BPI,
                                            const LoopInfoT &LI) {
   // Save the parameters.
   this->BPI = &BPI;
   this->LI = &LI;
   this->F = &F;
 
   // Clean up left-over data structures.
   BlockFrequencyInfoImplBase::clear();
   RPOT.clear();
   Nodes.clear();
 
   // Initialize.
   LLVM_DEBUG(dbgs() << "\nblock-frequency: " << F.getName()
                     << "\n================="
                     << std::string(F.getName().size(), '=') << "\n");
   initializeRPOT();
   initializeLoops();
 
   // Visit loops in post-order to find the local mass distribution, and then do
   // the full function.
   computeMassInLoops();
   computeMassInFunction();
   unwrapLoops();
   // Apply a post-processing step improving computed frequencies for functions
   // with irreducible loops.
   if (needIterativeInference())
     applyIterativeInference();
   finalizeMetrics();
 
   if (CheckBFIUnknownBlockQueries) {
     // To detect BFI queries for unknown blocks, add entries for unreachable
     // blocks, if any. This is to distinguish between known/existing unreachable
     // blocks and unknown blocks.
     for (const BlockT &BB : F)
       if (!Nodes.count(&BB))
         setBlockFreq(&BB, BlockFrequency());
   }
 }
 
 template <class BT>
 void BlockFrequencyInfoImpl<BT>::setBlockFreq(const BlockT *BB,
                                               BlockFrequency Freq) {
   if (Nodes.count(BB))
     BlockFrequencyInfoImplBase::setBlockFreq(getNode(BB), Freq);
   else {
     // If BB is a newly added block after BFI is done, we need to create a new
     // BlockNode for it assigned with a new index. The index can be determined
     // by the size of Freqs.
     BlockNode NewNode(Freqs.size());
     Nodes[BB] = {NewNode, BFICallbackVH(BB, this)};
     Freqs.emplace_back();
     BlockFrequencyInfoImplBase::setBlockFreq(NewNode, Freq);
   }
 }
 
 template <class BT> void BlockFrequencyInfoImpl<BT>::initializeRPOT() {
   const BlockT *Entry = &F->front();
   RPOT.reserve(F->size());
   std::copy(po_begin(Entry), po_end(Entry), std::back_inserter(RPOT));
   std::reverse(RPOT.begin(), RPOT.end());
 
   assert(RPOT.size() - 1 <= BlockNode::getMaxIndex() &&
          "More nodes in function than Block Frequency Info supports");
 
   LLVM_DEBUG(dbgs() << "reverse-post-order-traversal\n");
   for (rpot_iterator I = rpot_begin(), E = rpot_end(); I != E; ++I) {
     BlockNode Node = getNode(I);
     LLVM_DEBUG(dbgs() << " - " << getIndex(I) << ": " << getBlockName(Node)
                       << "\n");
     Nodes[*I] = {Node, BFICallbackVH(*I, this)};
   }
 
   Working.reserve(RPOT.size());
   for (size_t Index = 0; Index < RPOT.size(); ++Index)
     Working.emplace_back(Index);
   Freqs.resize(RPOT.size());
 }
 
 template <class BT> void BlockFrequencyInfoImpl<BT>::initializeLoops() {
   LLVM_DEBUG(dbgs() << "loop-detection\n");
   if (LI->empty())
     return;
 
   // Visit loops top down and assign them an index.
   std::deque<std::pair<const LoopT *, LoopData *>> Q;
   for (const LoopT *L : *LI)
     Q.emplace_back(L, nullptr);
   while (!Q.empty()) {
     const LoopT *Loop = Q.front().first;
     LoopData *Parent = Q.front().second;
     Q.pop_front();
 
     BlockNode Header = getNode(Loop->getHeader());
     assert(Header.isValid());
 
     Loops.emplace_back(Parent, Header);
     Working[Header.Index].Loop = &Loops.back();
     LLVM_DEBUG(dbgs() << " - loop = " << getBlockName(Header) << "\n");
 
     for (const LoopT *L : *Loop)
       Q.emplace_back(L, &Loops.back());
   }
 
   // Visit nodes in reverse post-order and add them to their deepest containing
   // loop.
   for (size_t Index = 0; Index < RPOT.size(); ++Index) {
     // Loop headers have already been mostly mapped.
     if (Working[Index].isLoopHeader()) {
       LoopData *ContainingLoop = Working[Index].getContainingLoop();
       if (ContainingLoop)
         ContainingLoop->Nodes.push_back(Index);
       continue;
     }
 
     const LoopT *Loop = LI->getLoopFor(RPOT[Index]);
     if (!Loop)
       continue;
 
     // Add this node to its containing loop's member list.
     BlockNode Header = getNode(Loop->getHeader());
     assert(Header.isValid());
     const auto &HeaderData = Working[Header.Index];
     assert(HeaderData.isLoopHeader());
 
     Working[Index].Loop = HeaderData.Loop;
     HeaderData.Loop->Nodes.push_back(Index);
     LLVM_DEBUG(dbgs() << " - loop = " << getBlockName(Header)
                       << ": member = " << getBlockName(Index) << "\n");
   }
 }
 
 template <class BT> void BlockFrequencyInfoImpl<BT>::computeMassInLoops() {
   // Visit loops with the deepest first, and the top-level loops last.
   for (auto L = Loops.rbegin(), E = Loops.rend(); L != E; ++L) {
     if (computeMassInLoop(*L))
       continue;
     auto Next = std::next(L);
     computeIrreducibleMass(&*L, L.base());
     L = std::prev(Next);
     if (computeMassInLoop(*L))
       continue;
     llvm_unreachable("unhandled irreducible control flow");
   }
 }
 
 template <class BT>
 bool BlockFrequencyInfoImpl<BT>::computeMassInLoop(LoopData &Loop) {
   // Compute mass in loop.
   LLVM_DEBUG(dbgs() << "compute-mass-in-loop: " << getLoopName(Loop) << "\n");
 
   if (Loop.isIrreducible()) {
     LLVM_DEBUG(dbgs() << "isIrreducible = true\n");
     Distribution Dist;
     unsigned NumHeadersWithWeight = 0;
     std::optional<uint64_t> MinHeaderWeight;
     DenseSet<uint32_t> HeadersWithoutWeight;
     HeadersWithoutWeight.reserve(Loop.NumHeaders);
     for (uint32_t H = 0; H < Loop.NumHeaders; ++H) {
       auto &HeaderNode = Loop.Nodes[H];
       const BlockT *Block = getBlock(HeaderNode);
       IsIrrLoopHeader.set(Loop.Nodes[H].Index);
       std::optional<uint64_t> HeaderWeight = Block->getIrrLoopHeaderWeight();
       if (!HeaderWeight) {
         LLVM_DEBUG(dbgs() << "Missing irr loop header metadata on "
                           << getBlockName(HeaderNode) << "\n");
         HeadersWithoutWeight.insert(H);
         continue;
       }
       LLVM_DEBUG(dbgs() << getBlockName(HeaderNode)
                         << " has irr loop header weight " << *HeaderWeight
                         << "\n");
       NumHeadersWithWeight++;
       uint64_t HeaderWeightValue = *HeaderWeight;
       if (!MinHeaderWeight || HeaderWeightValue < MinHeaderWeight)
         MinHeaderWeight = HeaderWeightValue;
       if (HeaderWeightValue) {
         Dist.addLocal(HeaderNode, HeaderWeightValue);
       }
     }
     // As a heuristic, if some headers don't have a weight, give them the
     // minimum weight seen (not to disrupt the existing trends too much by
     // using a weight that's in the general range of the other headers' weights,
     // and the minimum seems to perform better than the average.)
     // FIXME: better update in the passes that drop the header weight.
     // If no headers have a weight, give them even weight (use weight 1).
     if (!MinHeaderWeight)
       MinHeaderWeight = 1;
     for (uint32_t H : HeadersWithoutWeight) {
       auto &HeaderNode = Loop.Nodes[H];
       assert(!getBlock(HeaderNode)->getIrrLoopHeaderWeight() &&
              "Shouldn't have a weight metadata");
       uint64_t MinWeight = *MinHeaderWeight;
       LLVM_DEBUG(dbgs() << "Giving weight " << MinWeight << " to "
                         << getBlockName(HeaderNode) << "\n");
       if (MinWeight)
         Dist.addLocal(HeaderNode, MinWeight);
     }
     distributeIrrLoopHeaderMass(Dist);
     for (const BlockNode &M : Loop.Nodes)
       if (!propagateMassToSuccessors(&Loop, M))
         llvm_unreachable("unhandled irreducible control flow");
     if (NumHeadersWithWeight == 0)
       // No headers have a metadata. Adjust header mass.
       adjustLoopHeaderMass(Loop);
   } else {
     Working[Loop.getHeader().Index].getMass() = BlockMass::getFull();
     if (!propagateMassToSuccessors(&Loop, Loop.getHeader()))
       llvm_unreachable("irreducible control flow to loop header!?");
     for (const BlockNode &M : Loop.members())
       if (!propagateMassToSuccessors(&Loop, M))
         // Irreducible backedge.
         return false;
   }
 
   computeLoopScale(Loop);
   packageLoop(Loop);
   return true;
 }
 
 template <class BT>
 bool BlockFrequencyInfoImpl<BT>::tryToComputeMassInFunction() {
   // Compute mass in function.
   LLVM_DEBUG(dbgs() << "compute-mass-in-function\n");
   assert(!Working.empty() && "no blocks in function");
   assert(!Working[0].isLoopHeader() && "entry block is a loop header");
 
   Working[0].getMass() = BlockMass::getFull();
   for (rpot_iterator I = rpot_begin(), IE = rpot_end(); I != IE; ++I) {
     // Check for nodes that have been packaged.
     BlockNode Node = getNode(I);
     if (Working[Node.Index].isPackaged())
       continue;
 
     if (!propagateMassToSuccessors(nullptr, Node))
       return false;
   }
   return true;
 }
 
 template <class BT> void BlockFrequencyInfoImpl<BT>::computeMassInFunction() {
   if (tryToComputeMassInFunction())
     return;
   computeIrreducibleMass(nullptr, Loops.begin());
   if (tryToComputeMassInFunction())
     return;
   llvm_unreachable("unhandled irreducible control flow");
 }
 
 template <class BT>
 bool BlockFrequencyInfoImpl<BT>::needIterativeInference() const {
   if (!UseIterativeBFIInference)
     return false;
   if (!F->getFunction().hasProfileData())
     return false;
   // Apply iterative inference only if the function contains irreducible loops;
   // otherwise, computed block frequencies are reasonably correct.
   for (auto L = Loops.rbegin(), E = Loops.rend(); L != E; ++L) {
     if (L->isIrreducible())
       return true;
   }
   return false;
 }
 
 template <class BT> void BlockFrequencyInfoImpl<BT>::applyIterativeInference() {
   // Extract blocks for processing: a block is considered for inference iff it
   // can be reached from the entry by edges with a positive probability.
   // Non-processed blocks are assigned with the zero frequency and are ignored
   // in the computation
   std::vector<const BlockT *> ReachableBlocks;
   findReachableBlocks(ReachableBlocks);
   if (ReachableBlocks.empty())
     return;
 
   // The map is used to index successors/predecessors of reachable blocks in
   // the ReachableBlocks vector
   DenseMap<const BlockT *, size_t> BlockIndex;
   // Extract initial frequencies for the reachable blocks
   auto Freq = std::vector<Scaled64>(ReachableBlocks.size());
   Scaled64 SumFreq;
   for (size_t I = 0; I < ReachableBlocks.size(); I++) {
     const BlockT *BB = ReachableBlocks[I];
     BlockIndex[BB] = I;
     Freq[I] = getFloatingBlockFreq(BB);
     SumFreq += Freq[I];
   }
   assert(!SumFreq.isZero() && "empty initial block frequencies");
 
   LLVM_DEBUG(dbgs() << "Applying iterative inference for " << F->getName()
                     << " with " << ReachableBlocks.size() << " blocks\n");
 
   // Normalizing frequencies so they sum up to 1.0
   for (auto &Value : Freq) {
     Value /= SumFreq;
   }
 
   // Setting up edge probabilities using sparse matrix representation:
   // ProbMatrix[I] holds a vector of pairs (J, P) where Pr[J -> I | J] = P
   ProbMatrixType ProbMatrix;
   initTransitionProbabilities(ReachableBlocks, BlockIndex, ProbMatrix);
 
   // Run the propagation
   iterativeInference(ProbMatrix, Freq);
 
   // Assign computed frequency values
   for (const BlockT &BB : *F) {
     auto Node = getNode(&BB);
     if (!Node.isValid())
       continue;
     if (auto It = BlockIndex.find(&BB); It != BlockIndex.end())
       Freqs[Node.Index].Scaled = Freq[It->second];
     else
       Freqs[Node.Index].Scaled = Scaled64::getZero();
   }
 }
 
 template <class BT>
 void BlockFrequencyInfoImpl<BT>::iterativeInference(
     const ProbMatrixType &ProbMatrix, std::vector<Scaled64> &Freq) const {
   assert(0.0 < IterativeBFIPrecision && IterativeBFIPrecision < 1.0 &&
          "incorrectly specified precision");
   // Convert double precision to Scaled64
   const auto Precision =
       Scaled64::getInverse(static_cast<uint64_t>(1.0 / IterativeBFIPrecision));
   const size_t MaxIterations = IterativeBFIMaxIterationsPerBlock * Freq.size();
 
 #ifndef NDEBUG
   LLVM_DEBUG(dbgs() << "  Initial discrepancy = "
                     << discrepancy(ProbMatrix, Freq).toString() << "\n");
 #endif
 
   // Successors[I] holds unique sucessors of the I-th block
   auto Successors = std::vector<std::vector<size_t>>(Freq.size());
   for (size_t I = 0; I < Freq.size(); I++) {
     for (const auto &Jump : ProbMatrix[I]) {
       Successors[Jump.first].push_back(I);
     }
   }
 
   // To speedup computation, we maintain a set of "active" blocks whose
   // frequencies need to be updated based on the incoming edges.
   // The set is dynamic and changes after every update. Initially all blocks
   // with a positive frequency are active
   auto IsActive = BitVector(Freq.size(), false);
   std::queue<size_t> ActiveSet;
   for (size_t I = 0; I < Freq.size(); I++) {
     if (Freq[I] > 0) {
       ActiveSet.push(I);
       IsActive[I] = true;
     }
   }
 
   // Iterate over the blocks propagating frequencies
   size_t It = 0;
   while (It++ < MaxIterations && !ActiveSet.empty()) {
     size_t I = ActiveSet.front();
     ActiveSet.pop();
     IsActive[I] = false;
 
     // Compute a new frequency for the block: NewFreq := Freq \times ProbMatrix.
     // A special care is taken for self-edges that needs to be scaled by
     // (1.0 - SelfProb), where SelfProb is the sum of probabilities on the edges
     Scaled64 NewFreq;
     Scaled64 OneMinusSelfProb = Scaled64::getOne();
     for (const auto &Jump : ProbMatrix[I]) {
       if (Jump.first == I) {
         OneMinusSelfProb -= Jump.second;
       } else {
         NewFreq += Freq[Jump.first] * Jump.second;
       }
     }
     if (OneMinusSelfProb != Scaled64::getOne())
       NewFreq /= OneMinusSelfProb;
 
     // If the block's frequency has changed enough, then
     // make sure the block and its successors are in the active set
     auto Change = Freq[I] >= NewFreq ? Freq[I] - NewFreq : NewFreq - Freq[I];
     if (Change > Precision) {
       ActiveSet.push(I);
       IsActive[I] = true;
       for (size_t Succ : Successors[I]) {
         if (!IsActive[Succ]) {
           ActiveSet.push(Succ);
           IsActive[Succ] = true;
         }
       }
     }
 
     // Update the frequency for the block
     Freq[I] = NewFreq;
   }
 
   LLVM_DEBUG(dbgs() << "  Completed " << It << " inference iterations"
                     << format(" (%0.0f per block)", double(It) / Freq.size())
                     << "\n");
 #ifndef NDEBUG
   LLVM_DEBUG(dbgs() << "  Final   discrepancy = "
                     << discrepancy(ProbMatrix, Freq).toString() << "\n");
 #endif
 }
 
 template <class BT>
 void BlockFrequencyInfoImpl<BT>::findReachableBlocks(
     std::vector<const BlockT *> &Blocks) const {
   // Find all blocks to apply inference on, that is, reachable from the entry
   // along edges with non-zero probablities
   std::queue<const BlockT *> Queue;
   SmallPtrSet<const BlockT *, 8> Reachable;
   const BlockT *Entry = &F->front();
   Queue.push(Entry);
   Reachable.insert(Entry);
   while (!Queue.empty()) {
     const BlockT *SrcBB = Queue.front();
     Queue.pop();
     for (const BlockT *DstBB : children<const BlockT *>(SrcBB)) {
       auto EP = BPI->getEdgeProbability(SrcBB, DstBB);
       if (EP.isZero())
         continue;
       if (Reachable.insert(DstBB).second)
         Queue.push(DstBB);
     }
   }
 
   // Find all blocks to apply inference on, that is, backward reachable from
   // the entry along (backward) edges with non-zero probablities
   SmallPtrSet<const BlockT *, 8> InverseReachable;
   for (const BlockT &BB : *F) {
     // An exit block is a block without any successors
     bool HasSucc = !llvm::children<const BlockT *>(&BB).empty();
     if (!HasSucc && Reachable.count(&BB)) {
       Queue.push(&BB);
       InverseReachable.insert(&BB);
     }
   }
   while (!Queue.empty()) {
     const BlockT *SrcBB = Queue.front();
     Queue.pop();
     for (const BlockT *DstBB : inverse_children<const BlockT *>(SrcBB)) {
       auto EP = BPI->getEdgeProbability(DstBB, SrcBB);
       if (EP.isZero())
         continue;
       if (InverseReachable.insert(DstBB).second)
         Queue.push(DstBB);
     }
   }
 
   // Collect the result
   Blocks.reserve(F->size());
   for (const BlockT &BB : *F) {
     if (Reachable.count(&BB) && InverseReachable.count(&BB)) {
       Blocks.push_back(&BB);
     }
   }
 }
 
 template <class BT>
 void BlockFrequencyInfoImpl<BT>::initTransitionProbabilities(
     const std::vector<const BlockT *> &Blocks,
     const DenseMap<const BlockT *, size_t> &BlockIndex,
     ProbMatrixType &ProbMatrix) const {
   const size_t NumBlocks = Blocks.size();
   auto Succs = std::vector<std::vector<std::pair<size_t, Scaled64>>>(NumBlocks);
   auto SumProb = std::vector<Scaled64>(NumBlocks);
 
   // Find unique successors and corresponding probabilities for every block
   for (size_t Src = 0; Src < NumBlocks; Src++) {
     const BlockT *BB = Blocks[Src];
     SmallPtrSet<const BlockT *, 2> UniqueSuccs;
     for (const auto SI : children<const BlockT *>(BB)) {
       // Ignore cold blocks
       if (!BlockIndex.contains(SI))
         continue;
       // Ignore parallel edges between BB and SI blocks
       if (!UniqueSuccs.insert(SI).second)
         continue;
       // Ignore jumps with zero probability
       auto EP = BPI->getEdgeProbability(BB, SI);
       if (EP.isZero())
         continue;
 
       auto EdgeProb =
           Scaled64::getFraction(EP.getNumerator(), EP.getDenominator());
       size_t Dst = BlockIndex.find(SI)->second;
       Succs[Src].push_back(std::make_pair(Dst, EdgeProb));
       SumProb[Src] += EdgeProb;
     }
   }
 
   // Add transitions for every jump with positive branch probability
   ProbMatrix = ProbMatrixType(NumBlocks);
   for (size_t Src = 0; Src < NumBlocks; Src++) {
     // Ignore blocks w/o successors
     if (Succs[Src].empty())
       continue;
 
     assert(!SumProb[Src].isZero() && "Zero sum probability of non-exit block");
     for (auto &Jump : Succs[Src]) {
       size_t Dst = Jump.first;
       Scaled64 Prob = Jump.second;
       ProbMatrix[Dst].push_back(std::make_pair(Src, Prob / SumProb[Src]));
     }
   }
 
   // Add transitions from sinks to the source
   size_t EntryIdx = BlockIndex.find(&F->front())->second;
   for (size_t Src = 0; Src < NumBlocks; Src++) {
     if (Succs[Src].empty()) {
       ProbMatrix[EntryIdx].push_back(std::make_pair(Src, Scaled64::getOne()));
     }
   }
 }
 
 #ifndef NDEBUG
 template <class BT>
 BlockFrequencyInfoImplBase::Scaled64 BlockFrequencyInfoImpl<BT>::discrepancy(
     const ProbMatrixType &ProbMatrix, const std::vector<Scaled64> &Freq) const {
   assert(Freq[0] > 0 && "Incorrectly computed frequency of the entry block");
   Scaled64 Discrepancy;
   for (size_t I = 0; I < ProbMatrix.size(); I++) {
     Scaled64 Sum;
     for (const auto &Jump : ProbMatrix[I]) {
       Sum += Freq[Jump.first] * Jump.second;
     }
     Discrepancy += Freq[I] >= Sum ? Freq[I] - Sum : Sum - Freq[I];
   }
   // Normalizing by the frequency of the entry block
   return Discrepancy / Freq[0];
 }
 #endif
 
 /// \note This should be a lambda, but that crashes GCC 4.7.
 namespace bfi_detail {
 
 template <class BT> struct BlockEdgesAdder {
   using BlockT = BT;
   using LoopData = BlockFrequencyInfoImplBase::LoopData;
   using Successor = GraphTraits<const BlockT *>;
 
   const BlockFrequencyInfoImpl<BT> &BFI;
 
   explicit BlockEdgesAdder(const BlockFrequencyInfoImpl<BT> &BFI)
       : BFI(BFI) {}
 
   void operator()(IrreducibleGraph &G, IrreducibleGraph::IrrNode &Irr,
                   const LoopData *OuterLoop) {
     const BlockT *BB = BFI.RPOT[Irr.Node.Index];
     for (const auto *Succ : children<const BlockT *>(BB))
       G.addEdge(Irr, BFI.getNode(Succ), OuterLoop);
   }
 };
 
 } // end namespace bfi_detail
 
 template <class BT>
 void BlockFrequencyInfoImpl<BT>::computeIrreducibleMass(
     LoopData *OuterLoop, std::list<LoopData>::iterator Insert) {
   LLVM_DEBUG(dbgs() << "analyze-irreducible-in-";
              if (OuterLoop) dbgs()
              << "loop: " << getLoopName(*OuterLoop) << "\n";
              else dbgs() << "function\n");
 
   using namespace bfi_detail;
 
   // Ideally, addBlockEdges() would be declared here as a lambda, but that
   // crashes GCC 4.7.
   BlockEdgesAdder<BT> addBlockEdges(*this);
   IrreducibleGraph G(*this, OuterLoop, addBlockEdges);
 
   for (auto &L : analyzeIrreducible(G, OuterLoop, Insert))
     computeMassInLoop(L);
 
   if (!OuterLoop)
     return;
   updateLoopWithIrreducible(*OuterLoop);
 }
 
 // A helper function that converts a branch probability into weight.
 inline uint32_t getWeightFromBranchProb(const BranchProbability Prob) {
   return Prob.getNumerator();
 }
 
 template <class BT>
 bool
 BlockFrequencyInfoImpl<BT>::propagateMassToSuccessors(LoopData *OuterLoop,
                                                       const BlockNode &Node) {
   LLVM_DEBUG(dbgs() << " - node: " << getBlockName(Node) << "\n");
   // Calculate probability for successors.
   Distribution Dist;
   if (auto *Loop = Working[Node.Index].getPackagedLoop()) {
     assert(Loop != OuterLoop && "Cannot propagate mass in a packaged loop");
     if (!addLoopSuccessorsToDist(OuterLoop, *Loop, Dist))
       // Irreducible backedge.
       return false;
   } else {
     const BlockT *BB = getBlock(Node);
     for (auto SI = GraphTraits<const BlockT *>::child_begin(BB),
               SE = GraphTraits<const BlockT *>::child_end(BB);
          SI != SE; ++SI)
       if (!addToDist(
               Dist, OuterLoop, Node, getNode(*SI),
               getWeightFromBranchProb(BPI->getEdgeProbability(BB, SI))))
         // Irreducible backedge.
         return false;
   }
 
   // Distribute mass to successors, saving exit and backedge data in the
   // loop header.
   distributeMass(Node, OuterLoop, Dist);
   return true;
 }
 
 template <class BT>
 raw_ostream &BlockFrequencyInfoImpl<BT>::print(raw_ostream &OS) const {
   if (!F)
     return OS;
   OS << "block-frequency-info: " << F->getName() << "\n";
   for (const BlockT &BB : *F) {
     OS << " - " << bfi_detail::getBlockName(&BB) << ": float = ";
     getFloatingBlockFreq(&BB).print(OS, 5)
         << ", int = " << getBlockFreq(&BB).getFrequency();
     if (std::optional<uint64_t> ProfileCount =
         BlockFrequencyInfoImplBase::getBlockProfileCount(
             F->getFunction(), getNode(&BB)))
       OS << ", count = " << *ProfileCount;
     if (std::optional<uint64_t> IrrLoopHeaderWeight =
             BB.getIrrLoopHeaderWeight())
       OS << ", irr_loop_header_weight = " << *IrrLoopHeaderWeight;
     OS << "\n";
   }
 
   // Add an extra newline for readability.
   OS << "\n";
   return OS;
 }
 
 template <class BT>
 void BlockFrequencyInfoImpl<BT>::verifyMatch(
     BlockFrequencyInfoImpl<BT> &Other) const {
   bool Match = true;
   DenseMap<const BlockT *, BlockNode> ValidNodes;
   DenseMap<const BlockT *, BlockNode> OtherValidNodes;
   for (auto &Entry : Nodes) {
     const BlockT *BB = Entry.first;
     if (BB) {
       ValidNodes[BB] = Entry.second.first;
     }
   }
   for (auto &Entry : Other.Nodes) {
     const BlockT *BB = Entry.first;
     if (BB) {
       OtherValidNodes[BB] = Entry.second.first;
     }
   }
   unsigned NumValidNodes = ValidNodes.size();
   unsigned NumOtherValidNodes = OtherValidNodes.size();
   if (NumValidNodes != NumOtherValidNodes) {
     Match = false;
     dbgs() << "Number of blocks mismatch: " << NumValidNodes << " vs "
            << NumOtherValidNodes << "\n";
   } else {
     for (auto &Entry : ValidNodes) {
       const BlockT *BB = Entry.first;
       BlockNode Node = Entry.second;
       if (auto It = OtherValidNodes.find(BB); It != OtherValidNodes.end()) {
         BlockNode OtherNode = It->second;
         const auto &Freq = Freqs[Node.Index];
         const auto &OtherFreq = Other.Freqs[OtherNode.Index];
         if (Freq.Integer != OtherFreq.Integer) {
           Match = false;
           dbgs() << "Freq mismatch: " << bfi_detail::getBlockName(BB) << " "
                  << Freq.Integer << " vs " << OtherFreq.Integer << "\n";
         }
       } else {
         Match = false;
         dbgs() << "Block " << bfi_detail::getBlockName(BB) << " index "
                << Node.Index << " does not exist in Other.\n";
       }
     }
     // If there's a valid node in OtherValidNodes that's not in ValidNodes,
     // either the above num check or the check on OtherValidNodes will fail.
   }
   if (!Match) {
     dbgs() << "This\n";
     print(dbgs());
     dbgs() << "Other\n";
     Other.print(dbgs());
   }
   assert(Match && "BFI mismatch");
 }
 
 // Graph trait base class for block frequency information graph
 // viewer.
 
 enum GVDAGType { GVDT_None, GVDT_Fraction, GVDT_Integer, GVDT_Count };
 
 template <class BlockFrequencyInfoT, class BranchProbabilityInfoT>
 struct BFIDOTGraphTraitsBase : public DefaultDOTGraphTraits {
   using GTraits = GraphTraits<BlockFrequencyInfoT *>;
   using NodeRef = typename GTraits::NodeRef;
   using EdgeIter = typename GTraits::ChildIteratorType;
   using NodeIter = typename GTraits::nodes_iterator;
 
   uint64_t MaxFrequency = 0;
 
   explicit BFIDOTGraphTraitsBase(bool isSimple = false)
       : DefaultDOTGraphTraits(isSimple) {}
 
   static StringRef getGraphName(const BlockFrequencyInfoT *G) {
     return G->getFunction()->getName();
   }
 
   std::string getNodeAttributes(NodeRef Node, const BlockFrequencyInfoT *Graph,
                                 unsigned HotPercentThreshold = 0) {
     std::string Result;
     if (!HotPercentThreshold)
       return Result;
 
     // Compute MaxFrequency on the fly:
     if (!MaxFrequency) {
       for (NodeIter I = GTraits::nodes_begin(Graph),
                     E = GTraits::nodes_end(Graph);
            I != E; ++I) {
         NodeRef N = *I;
         MaxFrequency =
             std::max(MaxFrequency, Graph->getBlockFreq(N).getFrequency());
       }
     }
     BlockFrequency Freq = Graph->getBlockFreq(Node);
     BlockFrequency HotFreq =
         (BlockFrequency(MaxFrequency) *
          BranchProbability::getBranchProbability(HotPercentThreshold, 100));
 
     if (Freq < HotFreq)
       return Result;
 
     raw_string_ostream OS(Result);
     OS << "color=\"red\"";
     OS.flush();
     return Result;
   }
 
   std::string getNodeLabel(NodeRef Node, const BlockFrequencyInfoT *Graph,
                            GVDAGType GType, int layout_order = -1) {
     std::string Result;
     raw_string_ostream OS(Result);
 
     if (layout_order != -1)
       OS << Node->getName() << "[" << layout_order << "] : ";
     else
       OS << Node->getName() << " : ";
     switch (GType) {
     case GVDT_Fraction:
       OS << printBlockFreq(*Graph, *Node);
       break;
     case GVDT_Integer:
       OS << Graph->getBlockFreq(Node).getFrequency();
       break;
     case GVDT_Count: {
       auto Count = Graph->getBlockProfileCount(Node);
       if (Count)
         OS << *Count;
       else
         OS << "Unknown";
       break;
     }
     case GVDT_None:
       llvm_unreachable("If we are not supposed to render a graph we should "
                        "never reach this point.");
     }
     return Result;
   }
 
   std::string getEdgeAttributes(NodeRef Node, EdgeIter EI,
                                 const BlockFrequencyInfoT *BFI,
                                 const BranchProbabilityInfoT *BPI,
                                 unsigned HotPercentThreshold = 0) {
     std::string Str;
     if (!BPI)
       return Str;
 
     BranchProbability BP = BPI->getEdgeProbability(Node, EI);
     uint32_t N = BP.getNumerator();
     uint32_t D = BP.getDenominator();
     double Percent = 100.0 * N / D;
     raw_string_ostream OS(Str);
     OS << format("label=\"%.1f%%\"", Percent);
 
     if (HotPercentThreshold) {
       BlockFrequency EFreq = BFI->getBlockFreq(Node) * BP;
       BlockFrequency HotFreq = BlockFrequency(MaxFrequency) *
                                BranchProbability(HotPercentThreshold, 100);
 
       if (EFreq >= HotFreq) {
         OS << ",color=\"red\"";
       }
     }
 
     OS.flush();
     return Str;
   }
 };
 
 } // end namespace llvm
 
 #undef DEBUG_TYPE
 
 #endif // LLVM_ANALYSIS_BLOCKFREQUENCYINFOIMPL_H

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