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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 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.
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/DenseSet.h"
#include "llvm/ADT/GraphTraits.h"
#include "llvm/ADT/Optional.h"
#include "llvm/ADT/PostOrderIterator.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/Support/BlockFrequency.h"
#include "llvm/Support/BranchProbability.h"
#include "llvm/Support/DOTGraphTraits.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/ErrorHandling.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 <string>
#include <utility>
#include <vector>
#define DEBUG_TYPE "block-freq"
namespace llvm {
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;
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 documention lives with
/// BlockFrequencyInfoImpl. See there for details.
class BlockFrequencyInfoImplBase {
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);
bool isHeader(const BlockNode &Node) const {
if (isIrreducible())
return std::binary_search(Nodes.begin(), Nodes.begin() + NumHeaders,
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) -
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() &&
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();
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);
LoopData &getLoopPackage(const BlockNode &Head) {
assert(Head.Index < Working.size());
return *Working[Head.Index].Loop;
/// Analyze irreducible SCCs.
/// Separate irreducible SCCs from \c G, which is an explict 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.
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;
Optional<uint64_t> getBlockProfileCount(const Function &F,
const BlockNode &Node) const;
Optional<uint64_t> getProfileCountFromFreq(const Function &F,
uint64_t Freq) const;
bool isIrrLoopHeader(const BlockNode &Node);
void setBlockFreq(const BlockNode &Node, uint64_t Freq);
raw_ostream &printBlockFreq(raw_ostream &OS, const BlockNode &Node) const;
raw_ostream &printBlockFreq(raw_ostream &OS,
const BlockFrequency &Freq) const;
uint64_t getEntryFreq() const {
return Freqs[0].Integer;
namespace bfi_detail {
template <class BlockT> struct TypeMap {};
template <> struct TypeMap<BasicBlock> {
using BlockT = BasicBlock;
using FunctionT = Function;
using BranchProbabilityInfoT = BranchProbabilityInfo;
using LoopT = Loop;
using LoopInfoT = LoopInfo;
template <> struct TypeMap<MachineBasicBlock> {
using BlockT = MachineBasicBlock;
using FunctionT = MachineFunction;
using BranchProbabilityInfoT = MachineBranchProbabilityInfo;
using LoopT = MachineLoop;
using LoopInfoT = MachineLoopInfo;
/// 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;
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) {
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) {
for (auto N : OuterLoop->Nodes)
addEdges(N, OuterLoop, addBlockEdges);
} else {
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())
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);
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 they 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 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 *>>;
const BranchProbabilityInfoT *BPI = nullptr;
const LoopInfoT *LI = nullptr;
const FunctionT *F = nullptr;
// All blocks in reverse postorder.
std::vector<const BlockT *> RPOT;
DenseMap<const BlockT *, BlockNode> 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); }
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));
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));
Optional<uint64_t> getBlockProfileCount(const Function &F,
const BlockT *BB) const {
return BlockFrequencyInfoImplBase::getBlockProfileCount(F, getNode(BB));
Optional<uint64_t> getProfileCountFromFreq(const Function &F,
uint64_t Freq) const {
return BlockFrequencyInfoImplBase::getProfileCountFromFreq(F, Freq);
bool isIrrLoopHeader(const BlockT *BB) {
return BlockFrequencyInfoImplBase::isIrrLoopHeader(getNode(BB));
void setBlockFreq(const BlockT *BB, uint64_t Freq);
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;
using BlockFrequencyInfoImplBase::printBlockFreq;
raw_ostream &printBlockFreq(raw_ostream &OS, const BlockT *BB) const {
return BlockFrequencyInfoImplBase::printBlockFreq(OS, getNode(BB));
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.
// Initialize.
LLVM_DEBUG(dbgs() << "\nblock-frequency: " << F.getName()
<< "\n================="
<< std::string(F.getName().size(), '=') << "\n");
// Visit loops in post-order to find the local mass distribution, and then do
// the full function.
template <class BT>
void BlockFrequencyInfoImpl<BT>::setBlockFreq(const BlockT *BB, uint64_t 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;
BlockFrequencyInfoImplBase::setBlockFreq(NewNode, Freq);
template <class BT> void BlockFrequencyInfoImpl<BT>::initializeRPOT() {
const BlockT *Entry = &F->front();
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;
for (size_t Index = 0; Index < RPOT.size(); ++Index)
template <class BT> void BlockFrequencyInfoImpl<BT>::initializeLoops() {
LLVM_DEBUG(dbgs() << "loop-detection\n");
if (LI->empty())
// 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;
BlockNode Header = getNode(Loop->getHeader());
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)
const LoopT *Loop = LI->getLoopFor(RPOT[Index]);
if (!Loop)
// Add this node to its containing loop's member list.
BlockNode Header = getNode(Loop->getHeader());
const auto &HeaderData = Working[Header.Index];
Working[Index].Loop = HeaderData.Loop;
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))
auto Next = std::next(L);
computeIrreducibleMass(&*L, L.base());
L = std::prev(Next);
if (computeMassInLoop(*L))
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;
Optional<uint64_t> MinHeaderWeight;
DenseSet<uint32_t> HeadersWithoutWeight;
for (uint32_t H = 0; H < Loop.NumHeaders; ++H) {
auto &HeaderNode = Loop.Nodes[H];
const BlockT *Block = getBlock(HeaderNode);
Optional<uint64_t> HeaderWeight = Block->getIrrLoopHeaderWeight();
if (!HeaderWeight) {
LLVM_DEBUG(dbgs() << "Missing irr loop header metadata on "
<< getBlockName(HeaderNode) << "\n");
LLVM_DEBUG(dbgs() << getBlockName(HeaderNode)
<< " has irr loop header weight "
<< HeaderWeight.getValue() << "\n");
uint64_t HeaderWeightValue = HeaderWeight.getValue();
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
// minimium 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.getValue();
LLVM_DEBUG(dbgs() << "Giving weight " << MinWeight << " to "
<< getBlockName(HeaderNode) << "\n");
if (MinWeight)
Dist.addLocal(HeaderNode, MinWeight);
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.
} 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;
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())
if (!propagateMassToSuccessors(nullptr, Node))
return false;
return true;
template <class BT> void BlockFrequencyInfoImpl<BT>::computeMassInFunction() {
if (tryToComputeMassInFunction())
computeIrreducibleMass(nullptr, Loops.begin());
if (tryToComputeMassInFunction())
llvm_unreachable("unhandled irreducible control flow");
/// \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))
if (!OuterLoop)
// A helper function that converts a branch probability into weight.
inline uint32_t getWeightFromBranchProb(const BranchProbability Prob) {
return Prob.getNumerator();
template <class BT>
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 (Optional<uint64_t> ProfileCount =
F->getFunction(), getNode(&BB)))
OS << ", count = " << ProfileCount.getValue();
if (Optional<uint64_t> IrrLoopHeaderWeight =
OS << ", irr_loop_header_weight = " << IrrLoopHeaderWeight.getValue();
OS << "\n";
// Add an extra newline for readability.
OS << "\n";
return OS;
// 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 std::string 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\"";
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 << "] : ";
OS << Node->getName() << " : ";
switch (GType) {
case GVDT_Fraction:
Graph->printBlockFreq(OS, Node);
case GVDT_Integer:
OS << Graph->getBlockFreq(Node).getFrequency();
case GVDT_Count: {
auto Count = Graph->getBlockProfileCount(Node);
if (Count)
OS << Count.getValue();
OS << "Unknown";
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\"";
return Str;
} // end namespace llvm