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1//===- CodeLayout.cpp - Implementation of code layout algorithms ----------===//2//3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.4// See https://llvm.org/LICENSE.txt for license information.5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception6//7//===----------------------------------------------------------------------===//8//9// The file implements "cache-aware" layout algorithms of basic blocks and10// functions in a binary.11//12// The algorithm tries to find a layout of nodes (basic blocks) of a given CFG13// optimizing jump locality and thus processor I-cache utilization. This is14// achieved via increasing the number of fall-through jumps and co-locating15// frequently executed nodes together. The name follows the underlying16// optimization problem, Extended-TSP, which is a generalization of classical17// (maximum) Traveling Salesmen Problem.18//19// The algorithm is a greedy heuristic that works with chains (ordered lists)20// of basic blocks. Initially all chains are isolated basic blocks. On every21// iteration, we pick a pair of chains whose merging yields the biggest increase22// in the ExtTSP score, which models how i-cache "friendly" a specific chain is.23// A pair of chains giving the maximum gain is merged into a new chain. The24// procedure stops when there is only one chain left, or when merging does not25// increase ExtTSP. In the latter case, the remaining chains are sorted by26// density in the decreasing order.27//28// An important aspect is the way two chains are merged. Unlike earlier29// algorithms (e.g., based on the approach of Pettis-Hansen), two30// chains, X and Y, are first split into three, X1, X2, and Y. Then we31// consider all possible ways of gluing the three chains (e.g., X1YX2, X1X2Y,32// X2X1Y, X2YX1, YX1X2, YX2X1) and choose the one producing the largest score.33// This improves the quality of the final result (the search space is larger)34// while keeping the implementation sufficiently fast.35//36// Reference:37//   * A. Newell and S. Pupyrev, Improved Basic Block Reordering,38//     IEEE Transactions on Computers, 202039//     https://arxiv.org/abs/1809.0467640//41//===----------------------------------------------------------------------===//42 43#include "llvm/Transforms/Utils/CodeLayout.h"44#include "llvm/Support/CommandLine.h"45#include "llvm/Support/Debug.h"46 47#include <cmath>48#include <set>49 50using namespace llvm;51using namespace llvm::codelayout;52 53#define DEBUG_TYPE "code-layout"54 55namespace llvm {56cl::opt<bool> EnableExtTspBlockPlacement(57    "enable-ext-tsp-block-placement", cl::Hidden, cl::init(false),58    cl::desc("Enable machine block placement based on the ext-tsp model, "59             "optimizing I-cache utilization."));60 61cl::opt<bool> ApplyExtTspWithoutProfile(62    "ext-tsp-apply-without-profile",63    cl::desc("Whether to apply ext-tsp placement for instances w/o profile"),64    cl::init(true), cl::Hidden);65} // namespace llvm66 67// Algorithm-specific params for Ext-TSP. The values are tuned for the best68// performance of large-scale front-end bound binaries.69static cl::opt<double> ForwardWeightCond(70    "ext-tsp-forward-weight-cond", cl::ReallyHidden, cl::init(0.1),71    cl::desc("The weight of conditional forward jumps for ExtTSP value"));72 73static cl::opt<double> ForwardWeightUncond(74    "ext-tsp-forward-weight-uncond", cl::ReallyHidden, cl::init(0.1),75    cl::desc("The weight of unconditional forward jumps for ExtTSP value"));76 77static cl::opt<double> BackwardWeightCond(78    "ext-tsp-backward-weight-cond", cl::ReallyHidden, cl::init(0.1),79    cl::desc("The weight of conditional backward jumps for ExtTSP value"));80 81static cl::opt<double> BackwardWeightUncond(82    "ext-tsp-backward-weight-uncond", cl::ReallyHidden, cl::init(0.1),83    cl::desc("The weight of unconditional backward jumps for ExtTSP value"));84 85static cl::opt<double> FallthroughWeightCond(86    "ext-tsp-fallthrough-weight-cond", cl::ReallyHidden, cl::init(1.0),87    cl::desc("The weight of conditional fallthrough jumps for ExtTSP value"));88 89static cl::opt<double> FallthroughWeightUncond(90    "ext-tsp-fallthrough-weight-uncond", cl::ReallyHidden, cl::init(1.05),91    cl::desc("The weight of unconditional fallthrough jumps for ExtTSP value"));92 93static cl::opt<unsigned> ForwardDistance(94    "ext-tsp-forward-distance", cl::ReallyHidden, cl::init(1024),95    cl::desc("The maximum distance (in bytes) of a forward jump for ExtTSP"));96 97static cl::opt<unsigned> BackwardDistance(98    "ext-tsp-backward-distance", cl::ReallyHidden, cl::init(640),99    cl::desc("The maximum distance (in bytes) of a backward jump for ExtTSP"));100 101// The maximum size of a chain created by the algorithm. The size is bounded102// so that the algorithm can efficiently process extremely large instances.103static cl::opt<unsigned>104    MaxChainSize("ext-tsp-max-chain-size", cl::ReallyHidden, cl::init(512),105                 cl::desc("The maximum size of a chain to create"));106 107// The maximum size of a chain for splitting. Larger values of the threshold108// may yield better quality at the cost of worsen run-time.109static cl::opt<unsigned> ChainSplitThreshold(110    "ext-tsp-chain-split-threshold", cl::ReallyHidden, cl::init(128),111    cl::desc("The maximum size of a chain to apply splitting"));112 113// The maximum ratio between densities of two chains for merging.114static cl::opt<double> MaxMergeDensityRatio(115    "ext-tsp-max-merge-density-ratio", cl::ReallyHidden, cl::init(100),116    cl::desc("The maximum ratio between densities of two chains for merging"));117 118// Algorithm-specific options for CDSort.119static cl::opt<unsigned> CacheEntries("cdsort-cache-entries", cl::ReallyHidden,120                                      cl::desc("The size of the cache"));121 122static cl::opt<unsigned> CacheSize("cdsort-cache-size", cl::ReallyHidden,123                                   cl::desc("The size of a line in the cache"));124 125static cl::opt<unsigned>126    CDMaxChainSize("cdsort-max-chain-size", cl::ReallyHidden,127                   cl::desc("The maximum size of a chain to create"));128 129static cl::opt<double> DistancePower(130    "cdsort-distance-power", cl::ReallyHidden,131    cl::desc("The power exponent for the distance-based locality"));132 133static cl::opt<double> FrequencyScale(134    "cdsort-frequency-scale", cl::ReallyHidden,135    cl::desc("The scale factor for the frequency-based locality"));136 137namespace {138 139// Epsilon for comparison of doubles.140constexpr double EPS = 1e-8;141 142// Compute the Ext-TSP score for a given jump.143double jumpExtTSPScore(uint64_t JumpDist, uint64_t JumpMaxDist, uint64_t Count,144                       double Weight) {145  if (JumpDist > JumpMaxDist)146    return 0;147  double Prob = 1.0 - static_cast<double>(JumpDist) / JumpMaxDist;148  return Weight * Prob * Count;149}150 151// Compute the Ext-TSP score for a jump between a given pair of blocks,152// using their sizes, (estimated) addresses and the jump execution count.153double extTSPScore(uint64_t SrcAddr, uint64_t SrcSize, uint64_t DstAddr,154                   uint64_t Count, bool IsConditional) {155  // Fallthrough156  if (SrcAddr + SrcSize == DstAddr) {157    return jumpExtTSPScore(0, 1, Count,158                           IsConditional ? FallthroughWeightCond159                                         : FallthroughWeightUncond);160  }161  // Forward162  if (SrcAddr + SrcSize < DstAddr) {163    const uint64_t Dist = DstAddr - (SrcAddr + SrcSize);164    return jumpExtTSPScore(Dist, ForwardDistance, Count,165                           IsConditional ? ForwardWeightCond166                                         : ForwardWeightUncond);167  }168  // Backward169  const uint64_t Dist = SrcAddr + SrcSize - DstAddr;170  return jumpExtTSPScore(Dist, BackwardDistance, Count,171                         IsConditional ? BackwardWeightCond172                                       : BackwardWeightUncond);173}174 175/// A type of merging two chains, X and Y. The former chain is split into176/// X1 and X2 and then concatenated with Y in the order specified by the type.177enum class MergeTypeT : int { X_Y, Y_X, X1_Y_X2, Y_X2_X1, X2_X1_Y };178 179/// The gain of merging two chains, that is, the Ext-TSP score of the merge180/// together with the corresponding merge 'type' and 'offset'.181struct MergeGainT {182  explicit MergeGainT() = default;183  explicit MergeGainT(double Score, size_t MergeOffset, MergeTypeT MergeType)184      : Score(Score), MergeOffset(MergeOffset), MergeType(MergeType) {}185 186  double score() const { return Score; }187 188  size_t mergeOffset() const { return MergeOffset; }189 190  MergeTypeT mergeType() const { return MergeType; }191 192  void setMergeType(MergeTypeT Ty) { MergeType = Ty; }193 194  // Returns 'true' iff Other is preferred over this.195  bool operator<(const MergeGainT &Other) const {196    return (Other.Score > EPS && Other.Score > Score + EPS);197  }198 199  // Update the current gain if Other is preferred over this.200  void updateIfLessThan(const MergeGainT &Other) {201    if (*this < Other)202      *this = Other;203  }204 205private:206  double Score{-1.0};207  size_t MergeOffset{0};208  MergeTypeT MergeType{MergeTypeT::X_Y};209};210 211struct JumpT;212struct ChainT;213struct ChainEdge;214 215/// A node in the graph, typically corresponding to a basic block in the CFG or216/// a function in the call graph.217struct NodeT {218  NodeT(const NodeT &) = delete;219  NodeT(NodeT &&) = default;220  NodeT &operator=(const NodeT &) = delete;221  NodeT &operator=(NodeT &&) = default;222 223  explicit NodeT(size_t Index, uint64_t Size, uint64_t Count)224      : Index(Index), Size(Size), ExecutionCount(Count) {}225 226  bool isEntry() const { return Index == 0; }227 228  // Check if Other is a successor of the node.229  bool isSuccessor(const NodeT *Other) const;230 231  // The total execution count of outgoing jumps.232  uint64_t outCount() const;233 234  // The total execution count of incoming jumps.235  uint64_t inCount() const;236 237  // The original index of the node in graph.238  size_t Index{0};239  // The index of the node in the current chain.240  size_t CurIndex{0};241  // The size of the node in the binary.242  uint64_t Size{0};243  // The execution count of the node in the profile data.244  uint64_t ExecutionCount{0};245  // The current chain of the node.246  ChainT *CurChain{nullptr};247  // The offset of the node in the current chain.248  mutable uint64_t EstimatedAddr{0};249  // Forced successor of the node in the graph.250  NodeT *ForcedSucc{nullptr};251  // Forced predecessor of the node in the graph.252  NodeT *ForcedPred{nullptr};253  // Outgoing jumps from the node.254  std::vector<JumpT *> OutJumps;255  // Incoming jumps to the node.256  std::vector<JumpT *> InJumps;257};258 259/// An arc in the graph, typically corresponding to a jump between two nodes.260struct JumpT {261  JumpT(const JumpT &) = delete;262  JumpT(JumpT &&) = default;263  JumpT &operator=(const JumpT &) = delete;264  JumpT &operator=(JumpT &&) = default;265 266  explicit JumpT(NodeT *Source, NodeT *Target, uint64_t ExecutionCount)267      : Source(Source), Target(Target), ExecutionCount(ExecutionCount) {}268 269  // Source node of the jump.270  NodeT *Source;271  // Target node of the jump.272  NodeT *Target;273  // Execution count of the arc in the profile data.274  uint64_t ExecutionCount{0};275  // Whether the jump corresponds to a conditional branch.276  bool IsConditional{false};277  // The offset of the jump from the source node.278  uint64_t Offset{0};279};280 281/// A chain (ordered sequence) of nodes in the graph.282struct ChainT {283  ChainT(const ChainT &) = delete;284  ChainT(ChainT &&) = default;285  ChainT &operator=(const ChainT &) = delete;286  ChainT &operator=(ChainT &&) = default;287 288  explicit ChainT(uint64_t Id, NodeT *Node)289      : Id(Id), ExecutionCount(Node->ExecutionCount), Size(Node->Size),290        Nodes(1, Node) {}291 292  size_t numBlocks() const { return Nodes.size(); }293 294  double density() const { return ExecutionCount / Size; }295 296  bool isEntry() const { return Nodes[0]->Index == 0; }297 298  bool isCold() const {299    for (NodeT *Node : Nodes) {300      if (Node->ExecutionCount > 0)301        return false;302    }303    return true;304  }305 306  ChainEdge *getEdge(ChainT *Other) const {307    for (const auto &[Chain, ChainEdge] : Edges) {308      if (Chain == Other)309        return ChainEdge;310    }311    return nullptr;312  }313 314  void removeEdge(ChainT *Other) {315    auto It = Edges.begin();316    while (It != Edges.end()) {317      if (It->first == Other) {318        Edges.erase(It);319        return;320      }321      It++;322    }323  }324 325  void addEdge(ChainT *Other, ChainEdge *Edge) {326    Edges.push_back(std::make_pair(Other, Edge));327  }328 329  void merge(ChainT *Other, std::vector<NodeT *> MergedBlocks) {330    Nodes = std::move(MergedBlocks);331    // Update the chain's data.332    ExecutionCount += Other->ExecutionCount;333    Size += Other->Size;334    Id = Nodes[0]->Index;335    // Update the node's data.336    for (size_t Idx = 0; Idx < Nodes.size(); Idx++) {337      Nodes[Idx]->CurChain = this;338      Nodes[Idx]->CurIndex = Idx;339    }340  }341 342  void mergeEdges(ChainT *Other);343 344  void clear() {345    Nodes.clear();346    Nodes.shrink_to_fit();347    Edges.clear();348    Edges.shrink_to_fit();349  }350 351  // Unique chain identifier.352  uint64_t Id;353  // Cached ext-tsp score for the chain.354  double Score{0};355  // The total execution count of the chain. Since the execution count of356  // a basic block is uint64_t, using doubles here to avoid overflow.357  double ExecutionCount{0};358  // The total size of the chain.359  uint64_t Size{0};360  // Nodes of the chain.361  std::vector<NodeT *> Nodes;362  // Adjacent chains and corresponding edges (lists of jumps).363  std::vector<std::pair<ChainT *, ChainEdge *>> Edges;364};365 366/// An edge in the graph representing jumps between two chains.367/// When nodes are merged into chains, the edges are combined too so that368/// there is always at most one edge between a pair of chains.369struct ChainEdge {370  ChainEdge(const ChainEdge &) = delete;371  ChainEdge(ChainEdge &&) = default;372  ChainEdge &operator=(const ChainEdge &) = delete;373  ChainEdge &operator=(ChainEdge &&) = delete;374 375  explicit ChainEdge(JumpT *Jump)376      : SrcChain(Jump->Source->CurChain), DstChain(Jump->Target->CurChain),377        Jumps(1, Jump) {}378 379  ChainT *srcChain() const { return SrcChain; }380 381  ChainT *dstChain() const { return DstChain; }382 383  bool isSelfEdge() const { return SrcChain == DstChain; }384 385  const std::vector<JumpT *> &jumps() const { return Jumps; }386 387  void appendJump(JumpT *Jump) { Jumps.push_back(Jump); }388 389  void moveJumps(ChainEdge *Other) {390    llvm::append_range(Jumps, Other->Jumps);391    Other->Jumps.clear();392    Other->Jumps.shrink_to_fit();393  }394 395  void changeEndpoint(ChainT *From, ChainT *To) {396    if (From == SrcChain)397      SrcChain = To;398    if (From == DstChain)399      DstChain = To;400  }401 402  bool hasCachedMergeGain(ChainT *Src, ChainT *Dst) const {403    return Src == SrcChain ? CacheValidForward : CacheValidBackward;404  }405 406  MergeGainT getCachedMergeGain(ChainT *Src, ChainT *Dst) const {407    return Src == SrcChain ? CachedGainForward : CachedGainBackward;408  }409 410  void setCachedMergeGain(ChainT *Src, ChainT *Dst, MergeGainT MergeGain) {411    if (Src == SrcChain) {412      CachedGainForward = MergeGain;413      CacheValidForward = true;414    } else {415      CachedGainBackward = MergeGain;416      CacheValidBackward = true;417    }418  }419 420  void invalidateCache() {421    CacheValidForward = false;422    CacheValidBackward = false;423  }424 425  void setMergeGain(MergeGainT Gain) { CachedGain = Gain; }426 427  MergeGainT getMergeGain() const { return CachedGain; }428 429  double gain() const { return CachedGain.score(); }430 431private:432  // Source chain.433  ChainT *SrcChain{nullptr};434  // Destination chain.435  ChainT *DstChain{nullptr};436  // Original jumps in the binary with corresponding execution counts.437  std::vector<JumpT *> Jumps;438  // Cached gain value for merging the pair of chains.439  MergeGainT CachedGain;440 441  // Cached gain values for merging the pair of chains. Since the gain of442  // merging (Src, Dst) and (Dst, Src) might be different, we store both values443  // here and a flag indicating which of the options results in a higher gain.444  // Cached gain values.445  MergeGainT CachedGainForward;446  MergeGainT CachedGainBackward;447  // Whether the cached value must be recomputed.448  bool CacheValidForward{false};449  bool CacheValidBackward{false};450};451 452bool NodeT::isSuccessor(const NodeT *Other) const {453  for (JumpT *Jump : OutJumps)454    if (Jump->Target == Other)455      return true;456  return false;457}458 459uint64_t NodeT::outCount() const {460  uint64_t Count = 0;461  for (JumpT *Jump : OutJumps)462    Count += Jump->ExecutionCount;463  return Count;464}465 466uint64_t NodeT::inCount() const {467  uint64_t Count = 0;468  for (JumpT *Jump : InJumps)469    Count += Jump->ExecutionCount;470  return Count;471}472 473void ChainT::mergeEdges(ChainT *Other) {474  // Update edges adjacent to chain Other.475  for (const auto &[DstChain, DstEdge] : Other->Edges) {476    ChainT *TargetChain = DstChain == Other ? this : DstChain;477    ChainEdge *CurEdge = getEdge(TargetChain);478    if (CurEdge == nullptr) {479      DstEdge->changeEndpoint(Other, this);480      this->addEdge(TargetChain, DstEdge);481      if (DstChain != this && DstChain != Other)482        DstChain->addEdge(this, DstEdge);483    } else {484      CurEdge->moveJumps(DstEdge);485    }486    // Cleanup leftover edge.487    if (DstChain != Other)488      DstChain->removeEdge(Other);489  }490}491 492using NodeIter = std::vector<NodeT *>::const_iterator;493static std::vector<NodeT *> EmptyList;494 495/// A wrapper around three concatenated vectors (chains) of nodes; it is used496/// to avoid extra instantiation of the vectors.497struct MergedNodesT {498  MergedNodesT(NodeIter Begin1, NodeIter End1,499               NodeIter Begin2 = EmptyList.begin(),500               NodeIter End2 = EmptyList.end(),501               NodeIter Begin3 = EmptyList.begin(),502               NodeIter End3 = EmptyList.end())503      : Begin1(Begin1), End1(End1), Begin2(Begin2), End2(End2), Begin3(Begin3),504        End3(End3) {}505 506  template <typename F> void forEach(const F &Func) const {507    for (auto It = Begin1; It != End1; It++)508      Func(*It);509    for (auto It = Begin2; It != End2; It++)510      Func(*It);511    for (auto It = Begin3; It != End3; It++)512      Func(*It);513  }514 515  std::vector<NodeT *> getNodes() const {516    std::vector<NodeT *> Result;517    Result.reserve(std::distance(Begin1, End1) + std::distance(Begin2, End2) +518                   std::distance(Begin3, End3));519    Result.insert(Result.end(), Begin1, End1);520    Result.insert(Result.end(), Begin2, End2);521    Result.insert(Result.end(), Begin3, End3);522    return Result;523  }524 525  const NodeT *getFirstNode() const { return *Begin1; }526 527private:528  NodeIter Begin1;529  NodeIter End1;530  NodeIter Begin2;531  NodeIter End2;532  NodeIter Begin3;533  NodeIter End3;534};535 536/// A wrapper around two concatenated vectors (chains) of jumps.537struct MergedJumpsT {538  MergedJumpsT(const std::vector<JumpT *> *Jumps1,539               const std::vector<JumpT *> *Jumps2 = nullptr) {540    assert(!Jumps1->empty() && "cannot merge empty jump list");541    JumpArray[0] = Jumps1;542    JumpArray[1] = Jumps2;543  }544 545  template <typename F> void forEach(const F &Func) const {546    for (auto Jumps : JumpArray)547      if (Jumps != nullptr)548        for (JumpT *Jump : *Jumps)549          Func(Jump);550  }551 552private:553  std::array<const std::vector<JumpT *> *, 2> JumpArray{nullptr, nullptr};554};555 556/// Merge two chains of nodes respecting a given 'type' and 'offset'.557///558/// If MergeType == 0, then the result is a concatenation of two chains.559/// Otherwise, the first chain is cut into two sub-chains at the offset,560/// and merged using all possible ways of concatenating three chains.561MergedNodesT mergeNodes(const std::vector<NodeT *> &X,562                        const std::vector<NodeT *> &Y, size_t MergeOffset,563                        MergeTypeT MergeType) {564  // Split the first chain, X, into X1 and X2.565  NodeIter BeginX1 = X.begin();566  NodeIter EndX1 = X.begin() + MergeOffset;567  NodeIter BeginX2 = X.begin() + MergeOffset;568  NodeIter EndX2 = X.end();569  NodeIter BeginY = Y.begin();570  NodeIter EndY = Y.end();571 572  // Construct a new chain from the three existing ones.573  switch (MergeType) {574  case MergeTypeT::X_Y:575    return MergedNodesT(BeginX1, EndX2, BeginY, EndY);576  case MergeTypeT::Y_X:577    return MergedNodesT(BeginY, EndY, BeginX1, EndX2);578  case MergeTypeT::X1_Y_X2:579    return MergedNodesT(BeginX1, EndX1, BeginY, EndY, BeginX2, EndX2);580  case MergeTypeT::Y_X2_X1:581    return MergedNodesT(BeginY, EndY, BeginX2, EndX2, BeginX1, EndX1);582  case MergeTypeT::X2_X1_Y:583    return MergedNodesT(BeginX2, EndX2, BeginX1, EndX1, BeginY, EndY);584  }585  llvm_unreachable("unexpected chain merge type");586}587 588/// The implementation of the ExtTSP algorithm.589class ExtTSPImpl {590public:591  ExtTSPImpl(ArrayRef<uint64_t> NodeSizes, ArrayRef<uint64_t> NodeCounts,592             ArrayRef<EdgeCount> EdgeCounts)593      : NumNodes(NodeSizes.size()) {594    initialize(NodeSizes, NodeCounts, EdgeCounts);595  }596 597  /// Run the algorithm and return an optimized ordering of nodes.598  std::vector<uint64_t> run() {599    // Pass 1: Merge nodes with their mutually forced successors600    mergeForcedPairs();601 602    // Pass 2: Merge pairs of chains while improving the ExtTSP objective603    mergeChainPairs();604 605    // Pass 3: Merge cold nodes to reduce code size606    mergeColdChains();607 608    // Collect nodes from all chains609    return concatChains();610  }611 612private:613  /// Initialize the algorithm's data structures.614  void initialize(const ArrayRef<uint64_t> &NodeSizes,615                  const ArrayRef<uint64_t> &NodeCounts,616                  const ArrayRef<EdgeCount> &EdgeCounts) {617    // Initialize nodes.618    AllNodes.reserve(NumNodes);619    for (uint64_t Idx = 0; Idx < NumNodes; Idx++) {620      uint64_t Size = std::max<uint64_t>(NodeSizes[Idx], 1ULL);621      uint64_t ExecutionCount = NodeCounts[Idx];622      // The execution count of the entry node is set to at least one.623      if (Idx == 0 && ExecutionCount == 0)624        ExecutionCount = 1;625      AllNodes.emplace_back(Idx, Size, ExecutionCount);626    }627 628    // Initialize jumps between the nodes.629    SuccNodes.resize(NumNodes);630    PredNodes.resize(NumNodes);631    std::vector<uint64_t> OutDegree(NumNodes, 0);632    AllJumps.reserve(EdgeCounts.size());633    for (auto Edge : EdgeCounts) {634      ++OutDegree[Edge.src];635      // Ignore self-edges.636      if (Edge.src == Edge.dst)637        continue;638 639      SuccNodes[Edge.src].push_back(Edge.dst);640      PredNodes[Edge.dst].push_back(Edge.src);641      if (Edge.count > 0) {642        NodeT &PredNode = AllNodes[Edge.src];643        NodeT &SuccNode = AllNodes[Edge.dst];644        AllJumps.emplace_back(&PredNode, &SuccNode, Edge.count);645        SuccNode.InJumps.push_back(&AllJumps.back());646        PredNode.OutJumps.push_back(&AllJumps.back());647        // Adjust execution counts.648        PredNode.ExecutionCount = std::max(PredNode.ExecutionCount, Edge.count);649        SuccNode.ExecutionCount = std::max(SuccNode.ExecutionCount, Edge.count);650      }651    }652    for (JumpT &Jump : AllJumps) {653      assert(OutDegree[Jump.Source->Index] > 0 &&654             "incorrectly computed out-degree of the block");655      Jump.IsConditional = OutDegree[Jump.Source->Index] > 1;656    }657 658    // Initialize chains.659    AllChains.reserve(NumNodes);660    HotChains.reserve(NumNodes);661    for (NodeT &Node : AllNodes) {662      // Create a chain.663      AllChains.emplace_back(Node.Index, &Node);664      Node.CurChain = &AllChains.back();665      if (Node.ExecutionCount > 0)666        HotChains.push_back(&AllChains.back());667    }668 669    // Initialize chain edges.670    AllEdges.reserve(AllJumps.size());671    for (NodeT &PredNode : AllNodes) {672      for (JumpT *Jump : PredNode.OutJumps) {673        assert(Jump->ExecutionCount > 0 && "incorrectly initialized jump");674        NodeT *SuccNode = Jump->Target;675        ChainEdge *CurEdge = PredNode.CurChain->getEdge(SuccNode->CurChain);676        // This edge is already present in the graph.677        if (CurEdge != nullptr) {678          assert(SuccNode->CurChain->getEdge(PredNode.CurChain) != nullptr);679          CurEdge->appendJump(Jump);680          continue;681        }682        // This is a new edge.683        AllEdges.emplace_back(Jump);684        PredNode.CurChain->addEdge(SuccNode->CurChain, &AllEdges.back());685        SuccNode->CurChain->addEdge(PredNode.CurChain, &AllEdges.back());686      }687    }688  }689 690  /// For a pair of nodes, A and B, node B is the forced successor of A,691  /// if (i) all jumps (based on profile) from A goes to B and (ii) all jumps692  /// to B are from A. Such nodes should be adjacent in the optimal ordering;693  /// the method finds and merges such pairs of nodes.694  void mergeForcedPairs() {695    // Find forced pairs of blocks.696    for (NodeT &Node : AllNodes) {697      if (SuccNodes[Node.Index].size() == 1 &&698          PredNodes[SuccNodes[Node.Index][0]].size() == 1 &&699          SuccNodes[Node.Index][0] != 0) {700        size_t SuccIndex = SuccNodes[Node.Index][0];701        Node.ForcedSucc = &AllNodes[SuccIndex];702        AllNodes[SuccIndex].ForcedPred = &Node;703      }704    }705 706    // There might be 'cycles' in the forced dependencies, since profile707    // data isn't 100% accurate. Typically this is observed in loops, when the708    // loop edges are the hottest successors for the basic blocks of the loop.709    // Break the cycles by choosing the node with the smallest index as the710    // head. This helps to keep the original order of the loops, which likely711    // have already been rotated in the optimized manner.712    for (NodeT &Node : AllNodes) {713      if (Node.ForcedSucc == nullptr || Node.ForcedPred == nullptr)714        continue;715 716      NodeT *SuccNode = Node.ForcedSucc;717      while (SuccNode != nullptr && SuccNode != &Node) {718        SuccNode = SuccNode->ForcedSucc;719      }720      if (SuccNode == nullptr)721        continue;722      // Break the cycle.723      AllNodes[Node.ForcedPred->Index].ForcedSucc = nullptr;724      Node.ForcedPred = nullptr;725    }726 727    // Merge nodes with their fallthrough successors.728    for (NodeT &Node : AllNodes) {729      if (Node.ForcedPred == nullptr && Node.ForcedSucc != nullptr) {730        const NodeT *CurBlock = &Node;731        while (CurBlock->ForcedSucc != nullptr) {732          const NodeT *NextBlock = CurBlock->ForcedSucc;733          mergeChains(Node.CurChain, NextBlock->CurChain, 0, MergeTypeT::X_Y);734          CurBlock = NextBlock;735        }736      }737    }738  }739 740  /// Merge pairs of chains while improving the ExtTSP objective.741  void mergeChainPairs() {742    /// Deterministically compare pairs of chains.743    auto compareChainPairs = [](const ChainT *A1, const ChainT *B1,744                                const ChainT *A2, const ChainT *B2) {745      return std::make_tuple(A1->Id, B1->Id) < std::make_tuple(A2->Id, B2->Id);746    };747 748    while (HotChains.size() > 1) {749      ChainT *BestChainPred = nullptr;750      ChainT *BestChainSucc = nullptr;751      MergeGainT BestGain;752      // Iterate over all pairs of chains.753      for (ChainT *ChainPred : HotChains) {754        // Get candidates for merging with the current chain.755        for (const auto &[ChainSucc, Edge] : ChainPred->Edges) {756          // Ignore loop edges.757          if (Edge->isSelfEdge())758            continue;759          // Skip the merge if the combined chain violates the maximum specified760          // size.761          if (ChainPred->numBlocks() + ChainSucc->numBlocks() >= MaxChainSize)762            continue;763          // Don't merge the chains if they have vastly different densities.764          // Skip the merge if the ratio between the densities exceeds765          // MaxMergeDensityRatio. Smaller values of the option result in fewer766          // merges, and hence, more chains.767          const double ChainPredDensity = ChainPred->density();768          const double ChainSuccDensity = ChainSucc->density();769          assert(ChainPredDensity > 0.0 && ChainSuccDensity > 0.0 &&770                 "incorrectly computed chain densities");771          auto [MinDensity, MaxDensity] =772              std::minmax(ChainPredDensity, ChainSuccDensity);773          const double Ratio = MaxDensity / MinDensity;774          if (Ratio > MaxMergeDensityRatio)775            continue;776 777          // Compute the gain of merging the two chains.778          MergeGainT CurGain = getBestMergeGain(ChainPred, ChainSucc, Edge);779          if (CurGain.score() <= EPS)780            continue;781 782          if (BestGain < CurGain ||783              (std::abs(CurGain.score() - BestGain.score()) < EPS &&784               compareChainPairs(ChainPred, ChainSucc, BestChainPred,785                                 BestChainSucc))) {786            BestGain = CurGain;787            BestChainPred = ChainPred;788            BestChainSucc = ChainSucc;789          }790        }791      }792 793      // Stop merging when there is no improvement.794      if (BestGain.score() <= EPS)795        break;796 797      // Merge the best pair of chains.798      mergeChains(BestChainPred, BestChainSucc, BestGain.mergeOffset(),799                  BestGain.mergeType());800    }801  }802 803  /// Merge remaining nodes into chains w/o taking jump counts into804  /// consideration. This allows to maintain the original node order in the805  /// absence of profile data.806  void mergeColdChains() {807    for (size_t SrcBB = 0; SrcBB < NumNodes; SrcBB++) {808      // Iterating in reverse order to make sure original fallthrough jumps are809      // merged first; this might be beneficial for code size.810      size_t NumSuccs = SuccNodes[SrcBB].size();811      for (size_t Idx = 0; Idx < NumSuccs; Idx++) {812        size_t DstBB = SuccNodes[SrcBB][NumSuccs - Idx - 1];813        ChainT *SrcChain = AllNodes[SrcBB].CurChain;814        ChainT *DstChain = AllNodes[DstBB].CurChain;815        if (SrcChain != DstChain && !DstChain->isEntry() &&816            SrcChain->Nodes.back()->Index == SrcBB &&817            DstChain->Nodes.front()->Index == DstBB &&818            SrcChain->isCold() == DstChain->isCold()) {819          mergeChains(SrcChain, DstChain, 0, MergeTypeT::X_Y);820        }821      }822    }823  }824 825  /// Compute the Ext-TSP score for a given node order and a list of jumps.826  double extTSPScore(const MergedNodesT &Nodes,827                     const MergedJumpsT &Jumps) const {828    uint64_t CurAddr = 0;829    Nodes.forEach([&](const NodeT *Node) {830      Node->EstimatedAddr = CurAddr;831      CurAddr += Node->Size;832    });833 834    double Score = 0;835    Jumps.forEach([&](const JumpT *Jump) {836      const NodeT *SrcBlock = Jump->Source;837      const NodeT *DstBlock = Jump->Target;838      Score += ::extTSPScore(SrcBlock->EstimatedAddr, SrcBlock->Size,839                             DstBlock->EstimatedAddr, Jump->ExecutionCount,840                             Jump->IsConditional);841    });842    return Score;843  }844 845  /// Compute the gain of merging two chains.846  ///847  /// The function considers all possible ways of merging two chains and848  /// computes the one having the largest increase in ExtTSP objective. The849  /// result is a pair with the first element being the gain and the second850  /// element being the corresponding merging type.851  MergeGainT getBestMergeGain(ChainT *ChainPred, ChainT *ChainSucc,852                              ChainEdge *Edge) const {853    if (Edge->hasCachedMergeGain(ChainPred, ChainSucc))854      return Edge->getCachedMergeGain(ChainPred, ChainSucc);855 856    assert(!Edge->jumps().empty() && "trying to merge chains w/o jumps");857    // Precompute jumps between ChainPred and ChainSucc.858    ChainEdge *EdgePP = ChainPred->getEdge(ChainPred);859    MergedJumpsT Jumps(&Edge->jumps(), EdgePP ? &EdgePP->jumps() : nullptr);860 861    // This object holds the best chosen gain of merging two chains.862    MergeGainT Gain = MergeGainT();863 864    /// Given a merge offset and a list of merge types, try to merge two chains865    /// and update Gain with a better alternative.866    auto tryChainMerging = [&](size_t Offset,867                               const std::vector<MergeTypeT> &MergeTypes) {868      // Skip merging corresponding to concatenation w/o splitting.869      if (Offset == 0 || Offset == ChainPred->Nodes.size())870        return;871      // Skip merging if it breaks Forced successors.872      NodeT *Node = ChainPred->Nodes[Offset - 1];873      if (Node->ForcedSucc != nullptr)874        return;875      // Apply the merge, compute the corresponding gain, and update the best876      // value, if the merge is beneficial.877      for (const MergeTypeT &MergeType : MergeTypes) {878        Gain.updateIfLessThan(879            computeMergeGain(ChainPred, ChainSucc, Jumps, Offset, MergeType));880      }881    };882 883    // Try to concatenate two chains w/o splitting.884    Gain.updateIfLessThan(885        computeMergeGain(ChainPred, ChainSucc, Jumps, 0, MergeTypeT::X_Y));886 887    // Attach (a part of) ChainPred before the first node of ChainSucc.888    for (JumpT *Jump : ChainSucc->Nodes.front()->InJumps) {889      const NodeT *SrcBlock = Jump->Source;890      if (SrcBlock->CurChain != ChainPred)891        continue;892      size_t Offset = SrcBlock->CurIndex + 1;893      tryChainMerging(Offset, {MergeTypeT::X1_Y_X2, MergeTypeT::X2_X1_Y});894    }895 896    // Attach (a part of) ChainPred after the last node of ChainSucc.897    for (JumpT *Jump : ChainSucc->Nodes.back()->OutJumps) {898      const NodeT *DstBlock = Jump->Target;899      if (DstBlock->CurChain != ChainPred)900        continue;901      size_t Offset = DstBlock->CurIndex;902      tryChainMerging(Offset, {MergeTypeT::X1_Y_X2, MergeTypeT::Y_X2_X1});903    }904 905    // Try to break ChainPred in various ways and concatenate with ChainSucc.906    if (ChainPred->Nodes.size() <= ChainSplitThreshold) {907      for (size_t Offset = 1; Offset < ChainPred->Nodes.size(); Offset++) {908        // Do not split the chain along a fall-through jump. One of the two909        // loops above may still "break" such a jump whenever it results in a910        // new fall-through.911        const NodeT *BB = ChainPred->Nodes[Offset - 1];912        const NodeT *BB2 = ChainPred->Nodes[Offset];913        if (BB->isSuccessor(BB2))914          continue;915 916        // In practice, applying X2_Y_X1 merging almost never provides benefits;917        // thus, we exclude it from consideration to reduce the search space.918        tryChainMerging(Offset, {MergeTypeT::X1_Y_X2, MergeTypeT::Y_X2_X1,919                                 MergeTypeT::X2_X1_Y});920      }921    }922 923    Edge->setCachedMergeGain(ChainPred, ChainSucc, Gain);924    return Gain;925  }926 927  /// Compute the score gain of merging two chains, respecting a given928  /// merge 'type' and 'offset'.929  ///930  /// The two chains are not modified in the method.931  MergeGainT computeMergeGain(const ChainT *ChainPred, const ChainT *ChainSucc,932                              const MergedJumpsT &Jumps, size_t MergeOffset,933                              MergeTypeT MergeType) const {934    MergedNodesT MergedNodes =935        mergeNodes(ChainPred->Nodes, ChainSucc->Nodes, MergeOffset, MergeType);936 937    // Do not allow a merge that does not preserve the original entry point.938    if ((ChainPred->isEntry() || ChainSucc->isEntry()) &&939        !MergedNodes.getFirstNode()->isEntry())940      return MergeGainT();941 942    // The gain for the new chain.943    double NewScore = extTSPScore(MergedNodes, Jumps);944    double CurScore = ChainPred->Score;945    return MergeGainT(NewScore - CurScore, MergeOffset, MergeType);946  }947 948  /// Merge chain From into chain Into, update the list of active chains,949  /// adjacency information, and the corresponding cached values.950  void mergeChains(ChainT *Into, ChainT *From, size_t MergeOffset,951                   MergeTypeT MergeType) {952    assert(Into != From && "a chain cannot be merged with itself");953 954    // Merge the nodes.955    MergedNodesT MergedNodes =956        mergeNodes(Into->Nodes, From->Nodes, MergeOffset, MergeType);957    Into->merge(From, MergedNodes.getNodes());958 959    // Merge the edges.960    Into->mergeEdges(From);961    From->clear();962 963    // Update cached ext-tsp score for the new chain.964    ChainEdge *SelfEdge = Into->getEdge(Into);965    if (SelfEdge != nullptr) {966      MergedNodes = MergedNodesT(Into->Nodes.begin(), Into->Nodes.end());967      MergedJumpsT MergedJumps(&SelfEdge->jumps());968      Into->Score = extTSPScore(MergedNodes, MergedJumps);969    }970 971    // Remove the chain from the list of active chains.972    llvm::erase(HotChains, From);973 974    // Invalidate caches.975    for (auto EdgeIt : Into->Edges)976      EdgeIt.second->invalidateCache();977  }978 979  /// Concatenate all chains into the final order.980  std::vector<uint64_t> concatChains() {981    // Collect non-empty chains.982    std::vector<const ChainT *> SortedChains;983    for (ChainT &Chain : AllChains) {984      if (!Chain.Nodes.empty())985        SortedChains.push_back(&Chain);986    }987 988    // Sorting chains by density in the decreasing order.989    std::sort(SortedChains.begin(), SortedChains.end(),990              [&](const ChainT *L, const ChainT *R) {991                // Place the entry point at the beginning of the order.992                if (L->isEntry() != R->isEntry())993                  return L->isEntry();994 995                // Compare by density and break ties by chain identifiers.996                return std::make_tuple(-L->density(), L->Id) <997                       std::make_tuple(-R->density(), R->Id);998              });999 1000    // Collect the nodes in the order specified by their chains.1001    std::vector<uint64_t> Order;1002    Order.reserve(NumNodes);1003    for (const ChainT *Chain : SortedChains)1004      for (NodeT *Node : Chain->Nodes)1005        Order.push_back(Node->Index);1006    return Order;1007  }1008 1009private:1010  /// The number of nodes in the graph.1011  const size_t NumNodes;1012 1013  /// Successors of each node.1014  std::vector<std::vector<uint64_t>> SuccNodes;1015 1016  /// Predecessors of each node.1017  std::vector<std::vector<uint64_t>> PredNodes;1018 1019  /// All nodes (basic blocks) in the graph.1020  std::vector<NodeT> AllNodes;1021 1022  /// All jumps between the nodes.1023  std::vector<JumpT> AllJumps;1024 1025  /// All chains of nodes.1026  std::vector<ChainT> AllChains;1027 1028  /// All edges between the chains.1029  std::vector<ChainEdge> AllEdges;1030 1031  /// Active chains. The vector gets updated at runtime when chains are merged.1032  std::vector<ChainT *> HotChains;1033};1034 1035/// The implementation of the Cache-Directed Sort (CDSort) algorithm for1036/// ordering functions represented by a call graph.1037class CDSortImpl {1038public:1039  CDSortImpl(const CDSortConfig &Config, ArrayRef<uint64_t> NodeSizes,1040             ArrayRef<uint64_t> NodeCounts, ArrayRef<EdgeCount> EdgeCounts,1041             ArrayRef<uint64_t> EdgeOffsets)1042      : Config(Config), NumNodes(NodeSizes.size()) {1043    initialize(NodeSizes, NodeCounts, EdgeCounts, EdgeOffsets);1044  }1045 1046  /// Run the algorithm and return an ordered set of function clusters.1047  std::vector<uint64_t> run() {1048    // Merge pairs of chains while improving the objective.1049    mergeChainPairs();1050 1051    // Collect nodes from all the chains.1052    return concatChains();1053  }1054 1055private:1056  /// Initialize the algorithm's data structures.1057  void initialize(const ArrayRef<uint64_t> &NodeSizes,1058                  const ArrayRef<uint64_t> &NodeCounts,1059                  const ArrayRef<EdgeCount> &EdgeCounts,1060                  const ArrayRef<uint64_t> &EdgeOffsets) {1061    // Initialize nodes.1062    AllNodes.reserve(NumNodes);1063    for (uint64_t Node = 0; Node < NumNodes; Node++) {1064      uint64_t Size = std::max<uint64_t>(NodeSizes[Node], 1ULL);1065      uint64_t ExecutionCount = NodeCounts[Node];1066      AllNodes.emplace_back(Node, Size, ExecutionCount);1067      TotalSamples += ExecutionCount;1068      if (ExecutionCount > 0)1069        TotalSize += Size;1070    }1071 1072    // Initialize jumps between the nodes.1073    SuccNodes.resize(NumNodes);1074    PredNodes.resize(NumNodes);1075    AllJumps.reserve(EdgeCounts.size());1076    for (size_t I = 0; I < EdgeCounts.size(); I++) {1077      auto [Pred, Succ, Count] = EdgeCounts[I];1078      // Ignore recursive calls.1079      if (Pred == Succ)1080        continue;1081 1082      SuccNodes[Pred].push_back(Succ);1083      PredNodes[Succ].push_back(Pred);1084      if (Count > 0) {1085        NodeT &PredNode = AllNodes[Pred];1086        NodeT &SuccNode = AllNodes[Succ];1087        AllJumps.emplace_back(&PredNode, &SuccNode, Count);1088        AllJumps.back().Offset = EdgeOffsets[I];1089        SuccNode.InJumps.push_back(&AllJumps.back());1090        PredNode.OutJumps.push_back(&AllJumps.back());1091        // Adjust execution counts.1092        PredNode.ExecutionCount = std::max(PredNode.ExecutionCount, Count);1093        SuccNode.ExecutionCount = std::max(SuccNode.ExecutionCount, Count);1094      }1095    }1096 1097    // Initialize chains.1098    AllChains.reserve(NumNodes);1099    for (NodeT &Node : AllNodes) {1100      // Adjust execution counts.1101      Node.ExecutionCount = std::max(Node.ExecutionCount, Node.inCount());1102      Node.ExecutionCount = std::max(Node.ExecutionCount, Node.outCount());1103      // Create chain.1104      AllChains.emplace_back(Node.Index, &Node);1105      Node.CurChain = &AllChains.back();1106    }1107 1108    // Initialize chain edges.1109    AllEdges.reserve(AllJumps.size());1110    for (NodeT &PredNode : AllNodes) {1111      for (JumpT *Jump : PredNode.OutJumps) {1112        NodeT *SuccNode = Jump->Target;1113        ChainEdge *CurEdge = PredNode.CurChain->getEdge(SuccNode->CurChain);1114        // This edge is already present in the graph.1115        if (CurEdge != nullptr) {1116          assert(SuccNode->CurChain->getEdge(PredNode.CurChain) != nullptr);1117          CurEdge->appendJump(Jump);1118          continue;1119        }1120        // This is a new edge.1121        AllEdges.emplace_back(Jump);1122        PredNode.CurChain->addEdge(SuccNode->CurChain, &AllEdges.back());1123        SuccNode->CurChain->addEdge(PredNode.CurChain, &AllEdges.back());1124      }1125    }1126  }1127 1128  /// Merge pairs of chains while there is an improvement in the objective.1129  void mergeChainPairs() {1130    // Create a priority queue containing all edges ordered by the merge gain.1131    auto GainComparator = [](ChainEdge *L, ChainEdge *R) {1132      return std::make_tuple(-L->gain(), L->srcChain()->Id, L->dstChain()->Id) <1133             std::make_tuple(-R->gain(), R->srcChain()->Id, R->dstChain()->Id);1134    };1135    std::set<ChainEdge *, decltype(GainComparator)> Queue(GainComparator);1136 1137    // Insert the edges into the queue.1138    [[maybe_unused]] size_t NumActiveChains = 0;1139    for (NodeT &Node : AllNodes) {1140      if (Node.ExecutionCount == 0)1141        continue;1142      ++NumActiveChains;1143      for (const auto &[_, Edge] : Node.CurChain->Edges) {1144        // Ignore self-edges.1145        if (Edge->isSelfEdge())1146          continue;1147        // Ignore already processed edges.1148        if (Edge->gain() != -1.0)1149          continue;1150 1151        // Compute the gain of merging the two chains.1152        MergeGainT Gain = getBestMergeGain(Edge);1153        Edge->setMergeGain(Gain);1154 1155        if (Edge->gain() > EPS)1156          Queue.insert(Edge);1157      }1158    }1159 1160    // Merge the chains while the gain of merging is positive.1161    while (!Queue.empty()) {1162      // Extract the best (top) edge for merging.1163      ChainEdge *BestEdge = *Queue.begin();1164      Queue.erase(Queue.begin());1165      ChainT *BestSrcChain = BestEdge->srcChain();1166      ChainT *BestDstChain = BestEdge->dstChain();1167 1168      // Remove outdated edges from the queue.1169      for (const auto &[_, ChainEdge] : BestSrcChain->Edges)1170        Queue.erase(ChainEdge);1171      for (const auto &[_, ChainEdge] : BestDstChain->Edges)1172        Queue.erase(ChainEdge);1173 1174      // Merge the best pair of chains.1175      MergeGainT BestGain = BestEdge->getMergeGain();1176      mergeChains(BestSrcChain, BestDstChain, BestGain.mergeOffset(),1177                  BestGain.mergeType());1178      --NumActiveChains;1179 1180      // Insert newly created edges into the queue.1181      for (const auto &[_, Edge] : BestSrcChain->Edges) {1182        // Ignore loop edges.1183        if (Edge->isSelfEdge())1184          continue;1185        if (Edge->srcChain()->numBlocks() + Edge->dstChain()->numBlocks() >1186            Config.MaxChainSize)1187          continue;1188 1189        // Compute the gain of merging the two chains.1190        MergeGainT Gain = getBestMergeGain(Edge);1191        Edge->setMergeGain(Gain);1192 1193        if (Edge->gain() > EPS)1194          Queue.insert(Edge);1195      }1196    }1197 1198    LLVM_DEBUG(dbgs() << "Cache-directed function sorting reduced the number"1199                      << " of chains from " << NumNodes << " to "1200                      << NumActiveChains << "\n");1201  }1202 1203  /// Compute the gain of merging two chains.1204  ///1205  /// The function considers all possible ways of merging two chains and1206  /// computes the one having the largest increase in ExtTSP objective. The1207  /// result is a pair with the first element being the gain and the second1208  /// element being the corresponding merging type.1209  MergeGainT getBestMergeGain(ChainEdge *Edge) const {1210    assert(!Edge->jumps().empty() && "trying to merge chains w/o jumps");1211    // Precompute jumps between ChainPred and ChainSucc.1212    MergedJumpsT Jumps(&Edge->jumps());1213    ChainT *SrcChain = Edge->srcChain();1214    ChainT *DstChain = Edge->dstChain();1215 1216    // This object holds the best currently chosen gain of merging two chains.1217    MergeGainT Gain = MergeGainT();1218 1219    /// Given a list of merge types, try to merge two chains and update Gain1220    /// with a better alternative.1221    auto tryChainMerging = [&](const std::vector<MergeTypeT> &MergeTypes) {1222      // Apply the merge, compute the corresponding gain, and update the best1223      // value, if the merge is beneficial.1224      for (const MergeTypeT &MergeType : MergeTypes) {1225        MergeGainT NewGain =1226            computeMergeGain(SrcChain, DstChain, Jumps, MergeType);1227 1228        // When forward and backward gains are the same, prioritize merging that1229        // preserves the original order of the functions in the binary.1230        if (std::abs(Gain.score() - NewGain.score()) < EPS) {1231          if ((MergeType == MergeTypeT::X_Y && SrcChain->Id < DstChain->Id) ||1232              (MergeType == MergeTypeT::Y_X && SrcChain->Id > DstChain->Id)) {1233            Gain = NewGain;1234          }1235        } else if (NewGain.score() > Gain.score() + EPS) {1236          Gain = NewGain;1237        }1238      }1239    };1240 1241    // Try to concatenate two chains w/o splitting.1242    tryChainMerging({MergeTypeT::X_Y, MergeTypeT::Y_X});1243 1244    return Gain;1245  }1246 1247  /// Compute the score gain of merging two chains, respecting a given type.1248  ///1249  /// The two chains are not modified in the method.1250  MergeGainT computeMergeGain(ChainT *ChainPred, ChainT *ChainSucc,1251                              const MergedJumpsT &Jumps,1252                              MergeTypeT MergeType) const {1253    // This doesn't depend on the ordering of the nodes1254    double FreqGain = freqBasedLocalityGain(ChainPred, ChainSucc);1255 1256    // Merge offset is always 0, as the chains are not split.1257    size_t MergeOffset = 0;1258    auto MergedBlocks =1259        mergeNodes(ChainPred->Nodes, ChainSucc->Nodes, MergeOffset, MergeType);1260    double DistGain = distBasedLocalityGain(MergedBlocks, Jumps);1261 1262    double GainScore = DistGain + Config.FrequencyScale * FreqGain;1263    // Scale the result to increase the importance of merging short chains.1264    if (GainScore >= 0.0)1265      GainScore /= std::min(ChainPred->Size, ChainSucc->Size);1266 1267    return MergeGainT(GainScore, MergeOffset, MergeType);1268  }1269 1270  /// Compute the change of the frequency locality after merging the chains.1271  double freqBasedLocalityGain(ChainT *ChainPred, ChainT *ChainSucc) const {1272    auto missProbability = [&](double ChainDensity) {1273      double PageSamples = ChainDensity * Config.CacheSize;1274      if (PageSamples >= TotalSamples)1275        return 0.0;1276      double P = PageSamples / TotalSamples;1277      return pow(1.0 - P, static_cast<double>(Config.CacheEntries));1278    };1279 1280    // Cache misses on the chains before merging.1281    double CurScore =1282        ChainPred->ExecutionCount * missProbability(ChainPred->density()) +1283        ChainSucc->ExecutionCount * missProbability(ChainSucc->density());1284 1285    // Cache misses on the merged chain1286    double MergedCounts = ChainPred->ExecutionCount + ChainSucc->ExecutionCount;1287    double MergedSize = ChainPred->Size + ChainSucc->Size;1288    double MergedDensity = MergedCounts / MergedSize;1289    double NewScore = MergedCounts * missProbability(MergedDensity);1290 1291    return CurScore - NewScore;1292  }1293 1294  /// Compute the distance locality for a jump / call.1295  double distScore(uint64_t SrcAddr, uint64_t DstAddr, uint64_t Count) const {1296    uint64_t Dist = SrcAddr <= DstAddr ? DstAddr - SrcAddr : SrcAddr - DstAddr;1297    double D = Dist == 0 ? 0.1 : static_cast<double>(Dist);1298    return static_cast<double>(Count) * std::pow(D, -Config.DistancePower);1299  }1300 1301  /// Compute the change of the distance locality after merging the chains.1302  double distBasedLocalityGain(const MergedNodesT &Nodes,1303                               const MergedJumpsT &Jumps) const {1304    uint64_t CurAddr = 0;1305    Nodes.forEach([&](const NodeT *Node) {1306      Node->EstimatedAddr = CurAddr;1307      CurAddr += Node->Size;1308    });1309 1310    double CurScore = 0;1311    double NewScore = 0;1312    Jumps.forEach([&](const JumpT *Jump) {1313      uint64_t SrcAddr = Jump->Source->EstimatedAddr + Jump->Offset;1314      uint64_t DstAddr = Jump->Target->EstimatedAddr;1315      NewScore += distScore(SrcAddr, DstAddr, Jump->ExecutionCount);1316      CurScore += distScore(0, TotalSize, Jump->ExecutionCount);1317    });1318    return NewScore - CurScore;1319  }1320 1321  /// Merge chain From into chain Into, update the list of active chains,1322  /// adjacency information, and the corresponding cached values.1323  void mergeChains(ChainT *Into, ChainT *From, size_t MergeOffset,1324                   MergeTypeT MergeType) {1325    assert(Into != From && "a chain cannot be merged with itself");1326 1327    // Merge the nodes.1328    MergedNodesT MergedNodes =1329        mergeNodes(Into->Nodes, From->Nodes, MergeOffset, MergeType);1330    Into->merge(From, MergedNodes.getNodes());1331 1332    // Merge the edges.1333    Into->mergeEdges(From);1334    From->clear();1335  }1336 1337  /// Concatenate all chains into the final order.1338  std::vector<uint64_t> concatChains() {1339    // Collect chains and calculate density stats for their sorting.1340    std::vector<const ChainT *> SortedChains;1341    DenseMap<const ChainT *, double> ChainDensity;1342    for (ChainT &Chain : AllChains) {1343      if (!Chain.Nodes.empty()) {1344        SortedChains.push_back(&Chain);1345        // Using doubles to avoid overflow of ExecutionCounts.1346        double Size = 0;1347        double ExecutionCount = 0;1348        for (NodeT *Node : Chain.Nodes) {1349          Size += static_cast<double>(Node->Size);1350          ExecutionCount += static_cast<double>(Node->ExecutionCount);1351        }1352        assert(Size > 0 && "a chain of zero size");1353        ChainDensity[&Chain] = ExecutionCount / Size;1354      }1355    }1356 1357    // Sort chains by density in the decreasing order.1358    std::sort(SortedChains.begin(), SortedChains.end(),1359              [&](const ChainT *L, const ChainT *R) {1360                const double DL = ChainDensity[L];1361                const double DR = ChainDensity[R];1362                // Compare by density and break ties by chain identifiers.1363                return std::make_tuple(-DL, L->Id) <1364                       std::make_tuple(-DR, R->Id);1365              });1366 1367    // Collect the nodes in the order specified by their chains.1368    std::vector<uint64_t> Order;1369    Order.reserve(NumNodes);1370    for (const ChainT *Chain : SortedChains)1371      for (NodeT *Node : Chain->Nodes)1372        Order.push_back(Node->Index);1373    return Order;1374  }1375 1376private:1377  /// Config for the algorithm.1378  const CDSortConfig Config;1379 1380  /// The number of nodes in the graph.1381  const size_t NumNodes;1382 1383  /// Successors of each node.1384  std::vector<std::vector<uint64_t>> SuccNodes;1385 1386  /// Predecessors of each node.1387  std::vector<std::vector<uint64_t>> PredNodes;1388 1389  /// All nodes (functions) in the graph.1390  std::vector<NodeT> AllNodes;1391 1392  /// All jumps (function calls) between the nodes.1393  std::vector<JumpT> AllJumps;1394 1395  /// All chains of nodes.1396  std::vector<ChainT> AllChains;1397 1398  /// All edges between the chains.1399  std::vector<ChainEdge> AllEdges;1400 1401  /// The total number of samples in the graph.1402  uint64_t TotalSamples{0};1403 1404  /// The total size of the nodes in the graph.1405  uint64_t TotalSize{0};1406};1407 1408} // end of anonymous namespace1409 1410std::vector<uint64_t>1411codelayout::computeExtTspLayout(ArrayRef<uint64_t> NodeSizes,1412                                ArrayRef<uint64_t> NodeCounts,1413                                ArrayRef<EdgeCount> EdgeCounts) {1414  // Verify correctness of the input data.1415  assert(NodeCounts.size() == NodeSizes.size() && "Incorrect input");1416  assert(NodeSizes.size() > 2 && "Incorrect input");1417 1418  // Apply the reordering algorithm.1419  ExtTSPImpl Alg(NodeSizes, NodeCounts, EdgeCounts);1420  std::vector<uint64_t> Result = Alg.run();1421 1422  // Verify correctness of the output.1423  assert(Result.front() == 0 && "Original entry point is not preserved");1424  assert(Result.size() == NodeSizes.size() && "Incorrect size of layout");1425  return Result;1426}1427 1428double codelayout::calcExtTspScore(ArrayRef<uint64_t> Order,1429                                   ArrayRef<uint64_t> NodeSizes,1430                                   ArrayRef<EdgeCount> EdgeCounts) {1431  // Estimate addresses of the blocks in memory.1432  SmallVector<uint64_t> Addr(NodeSizes.size(), 0);1433  for (uint64_t Idx = 1; Idx < Order.size(); Idx++)1434    Addr[Order[Idx]] = Addr[Order[Idx - 1]] + NodeSizes[Order[Idx - 1]];1435  SmallVector<uint64_t> OutDegree(NodeSizes.size(), 0);1436  for (auto &Edge : EdgeCounts)1437    ++OutDegree[Edge.src];1438 1439  // Increase the score for each jump.1440  double Score = 0;1441  for (auto &Edge : EdgeCounts) {1442    bool IsConditional = OutDegree[Edge.src] > 1;1443    Score += ::extTSPScore(Addr[Edge.src], NodeSizes[Edge.src], Addr[Edge.dst],1444                           Edge.count, IsConditional);1445  }1446  return Score;1447}1448 1449double codelayout::calcExtTspScore(ArrayRef<uint64_t> NodeSizes,1450                                   ArrayRef<EdgeCount> EdgeCounts) {1451  SmallVector<uint64_t> Order(NodeSizes.size());1452  for (uint64_t Idx = 0; Idx < NodeSizes.size(); Idx++)1453    Order[Idx] = Idx;1454  return calcExtTspScore(Order, NodeSizes, EdgeCounts);1455}1456 1457std::vector<uint64_t> codelayout::computeCacheDirectedLayout(1458    const CDSortConfig &Config, ArrayRef<uint64_t> FuncSizes,1459    ArrayRef<uint64_t> FuncCounts, ArrayRef<EdgeCount> CallCounts,1460    ArrayRef<uint64_t> CallOffsets) {1461  // Verify correctness of the input data.1462  assert(FuncCounts.size() == FuncSizes.size() && "Incorrect input");1463 1464  // Apply the reordering algorithm.1465  CDSortImpl Alg(Config, FuncSizes, FuncCounts, CallCounts, CallOffsets);1466  std::vector<uint64_t> Result = Alg.run();1467  assert(Result.size() == FuncSizes.size() && "Incorrect size of layout");1468  return Result;1469}1470 1471std::vector<uint64_t> codelayout::computeCacheDirectedLayout(1472    ArrayRef<uint64_t> FuncSizes, ArrayRef<uint64_t> FuncCounts,1473    ArrayRef<EdgeCount> CallCounts, ArrayRef<uint64_t> CallOffsets) {1474  CDSortConfig Config;1475  // Populate the config from the command-line options.1476  if (CacheEntries.getNumOccurrences() > 0)1477    Config.CacheEntries = CacheEntries;1478  if (CacheSize.getNumOccurrences() > 0)1479    Config.CacheSize = CacheSize;1480  if (CDMaxChainSize.getNumOccurrences() > 0)1481    Config.MaxChainSize = CDMaxChainSize;1482  if (DistancePower.getNumOccurrences() > 0)1483    Config.DistancePower = DistancePower;1484  if (FrequencyScale.getNumOccurrences() > 0)1485    Config.FrequencyScale = FrequencyScale;1486  return computeCacheDirectedLayout(Config, FuncSizes, FuncCounts, CallCounts,1487                                    CallOffsets);1488}1489