1 //==- BlockFrequencyInfoImpl.h - Block Frequency Implementation -*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // Shared implementation of BlockFrequency for IR and Machine Instructions.
11 // See the documentation below for BlockFrequencyInfoImpl for details.
13 //===----------------------------------------------------------------------===//
15 #ifndef LLVM_ANALYSIS_BLOCKFREQUENCYINFOIMPL_H
16 #define LLVM_ANALYSIS_BLOCKFREQUENCYINFOIMPL_H
18 #include "llvm/ADT/DenseMap.h"
19 #include "llvm/ADT/GraphTraits.h"
20 #include "llvm/ADT/Optional.h"
21 #include "llvm/ADT/PostOrderIterator.h"
22 #include "llvm/ADT/iterator_range.h"
23 #include "llvm/IR/BasicBlock.h"
24 #include "llvm/Support/BlockFrequency.h"
25 #include "llvm/Support/BranchProbability.h"
26 #include "llvm/Support/DOTGraphTraits.h"
27 #include "llvm/Support/Debug.h"
28 #include "llvm/Support/Format.h"
29 #include "llvm/Support/ScaledNumber.h"
30 #include "llvm/Support/raw_ostream.h"
36 #define DEBUG_TYPE "block-freq"
41 class BranchProbabilityInfo;
45 class MachineBasicBlock;
46 class MachineBranchProbabilityInfo;
47 class MachineFunction;
49 class MachineLoopInfo;
51 namespace bfi_detail {
53 struct IrreducibleGraph;
55 // This is part of a workaround for a GCC 4.7 crash on lambdas.
56 template <class BT> struct BlockEdgesAdder;
58 /// \brief Mass of a block.
60 /// This class implements a sort of fixed-point fraction always between 0.0 and
61 /// 1.0. getMass() == UINT64_MAX indicates a value of 1.0.
63 /// Masses can be added and subtracted. Simple saturation arithmetic is used,
64 /// so arithmetic operations never overflow or underflow.
66 /// Masses can be multiplied. Multiplication treats full mass as 1.0 and uses
67 /// an inexpensive floating-point algorithm that's off-by-one (almost, but not
68 /// quite, maximum precision).
70 /// Masses can be scaled by \a BranchProbability at maximum precision.
75 BlockMass() : Mass(0) {}
76 explicit BlockMass(uint64_t Mass) : Mass(Mass) {}
78 static BlockMass getEmpty() { return BlockMass(); }
79 static BlockMass getFull() { return BlockMass(UINT64_MAX); }
81 uint64_t getMass() const { return Mass; }
83 bool isFull() const { return Mass == UINT64_MAX; }
84 bool isEmpty() const { return !Mass; }
86 bool operator!() const { return isEmpty(); }
88 /// \brief Add another mass.
90 /// Adds another mass, saturating at \a isFull() rather than overflowing.
91 BlockMass &operator+=(BlockMass X) {
92 uint64_t Sum = Mass + X.Mass;
93 Mass = Sum < Mass ? UINT64_MAX : Sum;
97 /// \brief Subtract another mass.
99 /// Subtracts another mass, saturating at \a isEmpty() rather than
101 BlockMass &operator-=(BlockMass X) {
102 uint64_t Diff = Mass - X.Mass;
103 Mass = Diff > Mass ? 0 : Diff;
107 BlockMass &operator*=(BranchProbability P) {
108 Mass = P.scale(Mass);
112 bool operator==(BlockMass X) const { return Mass == X.Mass; }
113 bool operator!=(BlockMass X) const { return Mass != X.Mass; }
114 bool operator<=(BlockMass X) const { return Mass <= X.Mass; }
115 bool operator>=(BlockMass X) const { return Mass >= X.Mass; }
116 bool operator<(BlockMass X) const { return Mass < X.Mass; }
117 bool operator>(BlockMass X) const { return Mass > X.Mass; }
119 /// \brief Convert to scaled number.
121 /// Convert to \a ScaledNumber. \a isFull() gives 1.0, while \a isEmpty()
122 /// gives slightly above 0.0.
123 ScaledNumber<uint64_t> toScaled() const;
126 raw_ostream &print(raw_ostream &OS) const;
129 inline BlockMass operator+(BlockMass L, BlockMass R) {
130 return BlockMass(L) += R;
132 inline BlockMass operator-(BlockMass L, BlockMass R) {
133 return BlockMass(L) -= R;
135 inline BlockMass operator*(BlockMass L, BranchProbability R) {
136 return BlockMass(L) *= R;
138 inline BlockMass operator*(BranchProbability L, BlockMass R) {
139 return BlockMass(R) *= L;
142 inline raw_ostream &operator<<(raw_ostream &OS, BlockMass X) {
146 } // end namespace bfi_detail
148 template <> struct isPodLike<bfi_detail::BlockMass> {
149 static const bool value = true;
152 /// \brief Base class for BlockFrequencyInfoImpl
154 /// BlockFrequencyInfoImplBase has supporting data structures and some
155 /// algorithms for BlockFrequencyInfoImplBase. Only algorithms that depend on
156 /// the block type (or that call such algorithms) are skipped here.
158 /// Nevertheless, the majority of the overall algorithm documention lives with
159 /// BlockFrequencyInfoImpl. See there for details.
160 class BlockFrequencyInfoImplBase {
162 typedef ScaledNumber<uint64_t> Scaled64;
163 typedef bfi_detail::BlockMass BlockMass;
165 /// \brief Representative of a block.
167 /// This is a simple wrapper around an index into the reverse-post-order
168 /// traversal of the blocks.
170 /// Unlike a block pointer, its order has meaning (location in the
171 /// topological sort) and it's class is the same regardless of block type.
173 typedef uint32_t IndexType;
176 bool operator==(const BlockNode &X) const { return Index == X.Index; }
177 bool operator!=(const BlockNode &X) const { return Index != X.Index; }
178 bool operator<=(const BlockNode &X) const { return Index <= X.Index; }
179 bool operator>=(const BlockNode &X) const { return Index >= X.Index; }
180 bool operator<(const BlockNode &X) const { return Index < X.Index; }
181 bool operator>(const BlockNode &X) const { return Index > X.Index; }
183 BlockNode() : Index(UINT32_MAX) {}
184 BlockNode(IndexType Index) : Index(Index) {}
186 bool isValid() const { return Index <= getMaxIndex(); }
187 static size_t getMaxIndex() { return UINT32_MAX - 1; }
190 /// \brief Stats about a block itself.
191 struct FrequencyData {
196 /// \brief Data about a loop.
198 /// Contains the data necessary to represent a loop as a pseudo-node once it's
201 typedef SmallVector<std::pair<BlockNode, BlockMass>, 4> ExitMap;
202 typedef SmallVector<BlockNode, 4> NodeList;
203 typedef SmallVector<BlockMass, 1> HeaderMassList;
204 LoopData *Parent; ///< The parent loop.
205 bool IsPackaged; ///< Whether this has been packaged.
206 uint32_t NumHeaders; ///< Number of headers.
207 ExitMap Exits; ///< Successor edges (and weights).
208 NodeList Nodes; ///< Header and the members of the loop.
209 HeaderMassList BackedgeMass; ///< Mass returned to each loop header.
213 LoopData(LoopData *Parent, const BlockNode &Header)
214 : Parent(Parent), IsPackaged(false), NumHeaders(1), Nodes(1, Header),
216 template <class It1, class It2>
217 LoopData(LoopData *Parent, It1 FirstHeader, It1 LastHeader, It2 FirstOther,
219 : Parent(Parent), IsPackaged(false), Nodes(FirstHeader, LastHeader) {
220 NumHeaders = Nodes.size();
221 Nodes.insert(Nodes.end(), FirstOther, LastOther);
222 BackedgeMass.resize(NumHeaders);
224 bool isHeader(const BlockNode &Node) const {
226 return std::binary_search(Nodes.begin(), Nodes.begin() + NumHeaders,
228 return Node == Nodes[0];
230 BlockNode getHeader() const { return Nodes[0]; }
231 bool isIrreducible() const { return NumHeaders > 1; }
233 HeaderMassList::difference_type getHeaderIndex(const BlockNode &B) {
234 assert(isHeader(B) && "this is only valid on loop header blocks");
236 return std::lower_bound(Nodes.begin(), Nodes.begin() + NumHeaders, B) -
241 NodeList::const_iterator members_begin() const {
242 return Nodes.begin() + NumHeaders;
244 NodeList::const_iterator members_end() const { return Nodes.end(); }
245 iterator_range<NodeList::const_iterator> members() const {
246 return make_range(members_begin(), members_end());
250 /// \brief Index of loop information.
252 BlockNode Node; ///< This node.
253 LoopData *Loop; ///< The loop this block is inside.
254 BlockMass Mass; ///< Mass distribution from the entry block.
256 WorkingData(const BlockNode &Node) : Node(Node), Loop(nullptr) {}
258 bool isLoopHeader() const { return Loop && Loop->isHeader(Node); }
259 bool isDoubleLoopHeader() const {
260 return isLoopHeader() && Loop->Parent && Loop->Parent->isIrreducible() &&
261 Loop->Parent->isHeader(Node);
264 LoopData *getContainingLoop() const {
267 if (!isDoubleLoopHeader())
269 return Loop->Parent->Parent;
272 /// \brief Resolve a node to its representative.
274 /// Get the node currently representing Node, which could be a containing
277 /// This function should only be called when distributing mass. As long as
278 /// there are no irreducible edges to Node, then it will have complexity
279 /// O(1) in this context.
281 /// In general, the complexity is O(L), where L is the number of loop
282 /// headers Node has been packaged into. Since this method is called in
283 /// the context of distributing mass, L will be the number of loop headers
284 /// an early exit edge jumps out of.
285 BlockNode getResolvedNode() const {
286 auto L = getPackagedLoop();
287 return L ? L->getHeader() : Node;
289 LoopData *getPackagedLoop() const {
290 if (!Loop || !Loop->IsPackaged)
293 while (L->Parent && L->Parent->IsPackaged)
298 /// \brief Get the appropriate mass for a node.
300 /// Get appropriate mass for Node. If Node is a loop-header (whose loop
301 /// has been packaged), returns the mass of its pseudo-node. If it's a
302 /// node inside a packaged loop, it returns the loop's mass.
303 BlockMass &getMass() {
306 if (!isADoublePackage())
308 return Loop->Parent->Mass;
311 /// \brief Has ContainingLoop been packaged up?
312 bool isPackaged() const { return getResolvedNode() != Node; }
313 /// \brief Has Loop been packaged up?
314 bool isAPackage() const { return isLoopHeader() && Loop->IsPackaged; }
315 /// \brief Has Loop been packaged up twice?
316 bool isADoublePackage() const {
317 return isDoubleLoopHeader() && Loop->Parent->IsPackaged;
321 /// \brief Unscaled probability weight.
323 /// Probability weight for an edge in the graph (including the
324 /// successor/target node).
326 /// All edges in the original function are 32-bit. However, exit edges from
327 /// loop packages are taken from 64-bit exit masses, so we need 64-bits of
328 /// space in general.
330 /// In addition to the raw weight amount, Weight stores the type of the edge
331 /// in the current context (i.e., the context of the loop being processed).
332 /// Is this a local edge within the loop, an exit from the loop, or a
333 /// backedge to the loop header?
335 enum DistType { Local, Exit, Backedge };
337 BlockNode TargetNode;
339 Weight() : Type(Local), Amount(0) {}
340 Weight(DistType Type, BlockNode TargetNode, uint64_t Amount)
341 : Type(Type), TargetNode(TargetNode), Amount(Amount) {}
344 /// \brief Distribution of unscaled probability weight.
346 /// Distribution of unscaled probability weight to a set of successors.
348 /// This class collates the successor edge weights for later processing.
350 /// \a DidOverflow indicates whether \a Total did overflow while adding to
351 /// the distribution. It should never overflow twice.
352 struct Distribution {
353 typedef SmallVector<Weight, 4> WeightList;
354 WeightList Weights; ///< Individual successor weights.
355 uint64_t Total; ///< Sum of all weights.
356 bool DidOverflow; ///< Whether \a Total did overflow.
358 Distribution() : Total(0), DidOverflow(false) {}
359 void addLocal(const BlockNode &Node, uint64_t Amount) {
360 add(Node, Amount, Weight::Local);
362 void addExit(const BlockNode &Node, uint64_t Amount) {
363 add(Node, Amount, Weight::Exit);
365 void addBackedge(const BlockNode &Node, uint64_t Amount) {
366 add(Node, Amount, Weight::Backedge);
369 /// \brief Normalize the distribution.
371 /// Combines multiple edges to the same \a Weight::TargetNode and scales
372 /// down so that \a Total fits into 32-bits.
374 /// This is linear in the size of \a Weights. For the vast majority of
375 /// cases, adjacent edge weights are combined by sorting WeightList and
376 /// combining adjacent weights. However, for very large edge lists an
377 /// auxiliary hash table is used.
381 void add(const BlockNode &Node, uint64_t Amount, Weight::DistType Type);
384 /// \brief Data about each block. This is used downstream.
385 std::vector<FrequencyData> Freqs;
387 /// \brief Loop data: see initializeLoops().
388 std::vector<WorkingData> Working;
390 /// \brief Indexed information about loops.
391 std::list<LoopData> Loops;
393 /// \brief Add all edges out of a packaged loop to the distribution.
395 /// Adds all edges from LocalLoopHead to Dist. Calls addToDist() to add each
398 /// \return \c true unless there's an irreducible backedge.
399 bool addLoopSuccessorsToDist(const LoopData *OuterLoop, LoopData &Loop,
402 /// \brief Add an edge to the distribution.
404 /// Adds an edge to Succ to Dist. If \c LoopHead.isValid(), then whether the
405 /// edge is local/exit/backedge is in the context of LoopHead. Otherwise,
406 /// every edge should be a local edge (since all the loops are packaged up).
408 /// \return \c true unless aborted due to an irreducible backedge.
409 bool addToDist(Distribution &Dist, const LoopData *OuterLoop,
410 const BlockNode &Pred, const BlockNode &Succ, uint64_t Weight);
412 LoopData &getLoopPackage(const BlockNode &Head) {
413 assert(Head.Index < Working.size());
414 assert(Working[Head.Index].isLoopHeader());
415 return *Working[Head.Index].Loop;
418 /// \brief Analyze irreducible SCCs.
420 /// Separate irreducible SCCs from \c G, which is an explict graph of \c
421 /// OuterLoop (or the top-level function, if \c OuterLoop is \c nullptr).
422 /// Insert them into \a Loops before \c Insert.
424 /// \return the \c LoopData nodes representing the irreducible SCCs.
425 iterator_range<std::list<LoopData>::iterator>
426 analyzeIrreducible(const bfi_detail::IrreducibleGraph &G, LoopData *OuterLoop,
427 std::list<LoopData>::iterator Insert);
429 /// \brief Update a loop after packaging irreducible SCCs inside of it.
431 /// Update \c OuterLoop. Before finding irreducible control flow, it was
432 /// partway through \a computeMassInLoop(), so \a LoopData::Exits and \a
433 /// LoopData::BackedgeMass need to be reset. Also, nodes that were packaged
434 /// up need to be removed from \a OuterLoop::Nodes.
435 void updateLoopWithIrreducible(LoopData &OuterLoop);
437 /// \brief Distribute mass according to a distribution.
439 /// Distributes the mass in Source according to Dist. If LoopHead.isValid(),
440 /// backedges and exits are stored in its entry in Loops.
442 /// Mass is distributed in parallel from two copies of the source mass.
443 void distributeMass(const BlockNode &Source, LoopData *OuterLoop,
446 /// \brief Compute the loop scale for a loop.
447 void computeLoopScale(LoopData &Loop);
449 /// Adjust the mass of all headers in an irreducible loop.
451 /// Initially, irreducible loops are assumed to distribute their mass
452 /// equally among its headers. This can lead to wrong frequency estimates
453 /// since some headers may be executed more frequently than others.
455 /// This adjusts header mass distribution so it matches the weights of
456 /// the backedges going into each of the loop headers.
457 void adjustLoopHeaderMass(LoopData &Loop);
459 /// \brief Package up a loop.
460 void packageLoop(LoopData &Loop);
462 /// \brief Unwrap loops.
465 /// \brief Finalize frequency metrics.
467 /// Calculates final frequencies and cleans up no-longer-needed data
469 void finalizeMetrics();
471 /// \brief Clear all memory.
474 virtual std::string getBlockName(const BlockNode &Node) const;
475 std::string getLoopName(const LoopData &Loop) const;
477 virtual raw_ostream &print(raw_ostream &OS) const { return OS; }
478 void dump() const { print(dbgs()); }
480 Scaled64 getFloatingBlockFreq(const BlockNode &Node) const;
482 BlockFrequency getBlockFreq(const BlockNode &Node) const;
483 Optional<uint64_t> getBlockProfileCount(const Function &F,
484 const BlockNode &Node) const;
486 void setBlockFreq(const BlockNode &Node, uint64_t Freq);
488 raw_ostream &printBlockFreq(raw_ostream &OS, const BlockNode &Node) const;
489 raw_ostream &printBlockFreq(raw_ostream &OS,
490 const BlockFrequency &Freq) const;
492 uint64_t getEntryFreq() const {
493 assert(!Freqs.empty());
494 return Freqs[0].Integer;
496 /// \brief Virtual destructor.
498 /// Need a virtual destructor to mask the compiler warning about
500 virtual ~BlockFrequencyInfoImplBase() {}
503 namespace bfi_detail {
504 template <class BlockT> struct TypeMap {};
505 template <> struct TypeMap<BasicBlock> {
506 typedef BasicBlock BlockT;
507 typedef Function FunctionT;
508 typedef BranchProbabilityInfo BranchProbabilityInfoT;
510 typedef LoopInfo LoopInfoT;
512 template <> struct TypeMap<MachineBasicBlock> {
513 typedef MachineBasicBlock BlockT;
514 typedef MachineFunction FunctionT;
515 typedef MachineBranchProbabilityInfo BranchProbabilityInfoT;
516 typedef MachineLoop LoopT;
517 typedef MachineLoopInfo LoopInfoT;
520 /// \brief Get the name of a MachineBasicBlock.
522 /// Get the name of a MachineBasicBlock. It's templated so that including from
523 /// CodeGen is unnecessary (that would be a layering issue).
525 /// This is used mainly for debug output. The name is similar to
526 /// MachineBasicBlock::getFullName(), but skips the name of the function.
527 template <class BlockT> std::string getBlockName(const BlockT *BB) {
528 assert(BB && "Unexpected nullptr");
529 auto MachineName = "BB" + Twine(BB->getNumber());
530 if (BB->getBasicBlock())
531 return (MachineName + "[" + BB->getName() + "]").str();
532 return MachineName.str();
534 /// \brief Get the name of a BasicBlock.
535 template <> inline std::string getBlockName(const BasicBlock *BB) {
536 assert(BB && "Unexpected nullptr");
537 return BB->getName().str();
540 /// \brief Graph of irreducible control flow.
542 /// This graph is used for determining the SCCs in a loop (or top-level
543 /// function) that has irreducible control flow.
545 /// During the block frequency algorithm, the local graphs are defined in a
546 /// light-weight way, deferring to the \a BasicBlock or \a MachineBasicBlock
547 /// graphs for most edges, but getting others from \a LoopData::ExitMap. The
548 /// latter only has successor information.
550 /// \a IrreducibleGraph makes this graph explicit. It's in a form that can use
551 /// \a GraphTraits (so that \a analyzeIrreducible() can use \a scc_iterator),
552 /// and it explicitly lists predecessors and successors. The initialization
553 /// that relies on \c MachineBasicBlock is defined in the header.
554 struct IrreducibleGraph {
555 typedef BlockFrequencyInfoImplBase BFIBase;
559 typedef BFIBase::BlockNode BlockNode;
563 std::deque<const IrrNode *> Edges;
564 IrrNode(const BlockNode &Node) : Node(Node), NumIn(0) {}
566 typedef std::deque<const IrrNode *>::const_iterator iterator;
567 iterator pred_begin() const { return Edges.begin(); }
568 iterator succ_begin() const { return Edges.begin() + NumIn; }
569 iterator pred_end() const { return succ_begin(); }
570 iterator succ_end() const { return Edges.end(); }
573 const IrrNode *StartIrr;
574 std::vector<IrrNode> Nodes;
575 SmallDenseMap<uint32_t, IrrNode *, 4> Lookup;
577 /// \brief Construct an explicit graph containing irreducible control flow.
579 /// Construct an explicit graph of the control flow in \c OuterLoop (or the
580 /// top-level function, if \c OuterLoop is \c nullptr). Uses \c
581 /// addBlockEdges to add block successors that have not been packaged into
584 /// \a BlockFrequencyInfoImpl::computeIrreducibleMass() is the only expected
586 template <class BlockEdgesAdder>
587 IrreducibleGraph(BFIBase &BFI, const BFIBase::LoopData *OuterLoop,
588 BlockEdgesAdder addBlockEdges)
589 : BFI(BFI), StartIrr(nullptr) {
590 initialize(OuterLoop, addBlockEdges);
593 template <class BlockEdgesAdder>
594 void initialize(const BFIBase::LoopData *OuterLoop,
595 BlockEdgesAdder addBlockEdges);
596 void addNodesInLoop(const BFIBase::LoopData &OuterLoop);
597 void addNodesInFunction();
598 void addNode(const BlockNode &Node) {
599 Nodes.emplace_back(Node);
600 BFI.Working[Node.Index].getMass() = BlockMass::getEmpty();
603 template <class BlockEdgesAdder>
604 void addEdges(const BlockNode &Node, const BFIBase::LoopData *OuterLoop,
605 BlockEdgesAdder addBlockEdges);
606 void addEdge(IrrNode &Irr, const BlockNode &Succ,
607 const BFIBase::LoopData *OuterLoop);
609 template <class BlockEdgesAdder>
610 void IrreducibleGraph::initialize(const BFIBase::LoopData *OuterLoop,
611 BlockEdgesAdder addBlockEdges) {
613 addNodesInLoop(*OuterLoop);
614 for (auto N : OuterLoop->Nodes)
615 addEdges(N, OuterLoop, addBlockEdges);
617 addNodesInFunction();
618 for (uint32_t Index = 0; Index < BFI.Working.size(); ++Index)
619 addEdges(Index, OuterLoop, addBlockEdges);
621 StartIrr = Lookup[Start.Index];
623 template <class BlockEdgesAdder>
624 void IrreducibleGraph::addEdges(const BlockNode &Node,
625 const BFIBase::LoopData *OuterLoop,
626 BlockEdgesAdder addBlockEdges) {
627 auto L = Lookup.find(Node.Index);
628 if (L == Lookup.end())
630 IrrNode &Irr = *L->second;
631 const auto &Working = BFI.Working[Node.Index];
633 if (Working.isAPackage())
634 for (const auto &I : Working.Loop->Exits)
635 addEdge(Irr, I.first, OuterLoop);
637 addBlockEdges(*this, Irr, OuterLoop);
641 /// \brief Shared implementation for block frequency analysis.
643 /// This is a shared implementation of BlockFrequencyInfo and
644 /// MachineBlockFrequencyInfo, and calculates the relative frequencies of
647 /// LoopInfo defines a loop as a "non-trivial" SCC dominated by a single block,
648 /// which is called the header. A given loop, L, can have sub-loops, which are
649 /// loops within the subgraph of L that exclude its header. (A "trivial" SCC
650 /// consists of a single block that does not have a self-edge.)
652 /// In addition to loops, this algorithm has limited support for irreducible
653 /// SCCs, which are SCCs with multiple entry blocks. Irreducible SCCs are
654 /// discovered on they fly, and modelled as loops with multiple headers.
656 /// The headers of irreducible sub-SCCs consist of its entry blocks and all
657 /// nodes that are targets of a backedge within it (excluding backedges within
658 /// true sub-loops). Block frequency calculations act as if a block is
659 /// inserted that intercepts all the edges to the headers. All backedges and
660 /// entries point to this block. Its successors are the headers, which split
661 /// the frequency evenly.
663 /// This algorithm leverages BlockMass and ScaledNumber to maintain precision,
664 /// separates mass distribution from loop scaling, and dithers to eliminate
665 /// probability mass loss.
667 /// The implementation is split between BlockFrequencyInfoImpl, which knows the
668 /// type of graph being modelled (BasicBlock vs. MachineBasicBlock), and
669 /// BlockFrequencyInfoImplBase, which doesn't. The base class uses \a
670 /// BlockNode, a wrapper around a uint32_t. BlockNode is numbered from 0 in
671 /// reverse-post order. This gives two advantages: it's easy to compare the
672 /// relative ordering of two nodes, and maps keyed on BlockT can be represented
675 /// This algorithm is O(V+E), unless there is irreducible control flow, in
676 /// which case it's O(V*E) in the worst case.
678 /// These are the main stages:
680 /// 0. Reverse post-order traversal (\a initializeRPOT()).
682 /// Run a single post-order traversal and save it (in reverse) in RPOT.
683 /// All other stages make use of this ordering. Save a lookup from BlockT
684 /// to BlockNode (the index into RPOT) in Nodes.
686 /// 1. Loop initialization (\a initializeLoops()).
688 /// Translate LoopInfo/MachineLoopInfo into a form suitable for the rest of
689 /// the algorithm. In particular, store the immediate members of each loop
690 /// in reverse post-order.
692 /// 2. Calculate mass and scale in loops (\a computeMassInLoops()).
694 /// For each loop (bottom-up), distribute mass through the DAG resulting
695 /// from ignoring backedges and treating sub-loops as a single pseudo-node.
696 /// Track the backedge mass distributed to the loop header, and use it to
697 /// calculate the loop scale (number of loop iterations). Immediate
698 /// members that represent sub-loops will already have been visited and
699 /// packaged into a pseudo-node.
701 /// Distributing mass in a loop is a reverse-post-order traversal through
702 /// the loop. Start by assigning full mass to the Loop header. For each
703 /// node in the loop:
705 /// - Fetch and categorize the weight distribution for its successors.
706 /// If this is a packaged-subloop, the weight distribution is stored
707 /// in \a LoopData::Exits. Otherwise, fetch it from
708 /// BranchProbabilityInfo.
710 /// - Each successor is categorized as \a Weight::Local, a local edge
711 /// within the current loop, \a Weight::Backedge, a backedge to the
712 /// loop header, or \a Weight::Exit, any successor outside the loop.
713 /// The weight, the successor, and its category are stored in \a
714 /// Distribution. There can be multiple edges to each successor.
716 /// - If there's a backedge to a non-header, there's an irreducible SCC.
717 /// The usual flow is temporarily aborted. \a
718 /// computeIrreducibleMass() finds the irreducible SCCs within the
719 /// loop, packages them up, and restarts the flow.
721 /// - Normalize the distribution: scale weights down so that their sum
722 /// is 32-bits, and coalesce multiple edges to the same node.
724 /// - Distribute the mass accordingly, dithering to minimize mass loss,
725 /// as described in \a distributeMass().
727 /// In the case of irreducible loops, instead of a single loop header,
728 /// there will be several. The computation of backedge masses is similar
729 /// but instead of having a single backedge mass, there will be one
730 /// backedge per loop header. In these cases, each backedge will carry
731 /// a mass proportional to the edge weights along the corresponding
734 /// At the end of propagation, the full mass assigned to the loop will be
735 /// distributed among the loop headers proportionally according to the
736 /// mass flowing through their backedges.
738 /// Finally, calculate the loop scale from the accumulated backedge mass.
740 /// 3. Distribute mass in the function (\a computeMassInFunction()).
742 /// Finally, distribute mass through the DAG resulting from packaging all
743 /// loops in the function. This uses the same algorithm as distributing
744 /// mass in a loop, except that there are no exit or backedge edges.
746 /// 4. Unpackage loops (\a unwrapLoops()).
748 /// Initialize each block's frequency to a floating point representation of
751 /// Visit loops top-down, scaling the frequencies of its immediate members
752 /// by the loop's pseudo-node's frequency.
754 /// 5. Convert frequencies to a 64-bit range (\a finalizeMetrics()).
756 /// Using the min and max frequencies as a guide, translate floating point
757 /// frequencies to an appropriate range in uint64_t.
759 /// It has some known flaws.
761 /// - The model of irreducible control flow is a rough approximation.
763 /// Modelling irreducible control flow exactly involves setting up and
764 /// solving a group of infinite geometric series. Such precision is
765 /// unlikely to be worthwhile, since most of our algorithms give up on
766 /// irreducible control flow anyway.
768 /// Nevertheless, we might find that we need to get closer. Here's a sort
769 /// of TODO list for the model with diminishing returns, to be completed as
772 /// - The headers for the \a LoopData representing an irreducible SCC
773 /// include non-entry blocks. When these extra blocks exist, they
774 /// indicate a self-contained irreducible sub-SCC. We could treat them
775 /// as sub-loops, rather than arbitrarily shoving the problematic
776 /// blocks into the headers of the main irreducible SCC.
778 /// - Entry frequencies are assumed to be evenly split between the
779 /// headers of a given irreducible SCC, which is the only option if we
780 /// need to compute mass in the SCC before its parent loop. Instead,
781 /// we could partially compute mass in the parent loop, and stop when
782 /// we get to the SCC. Here, we have the correct ratio of entry
783 /// masses, which we can use to adjust their relative frequencies.
784 /// Compute mass in the SCC, and then continue propagation in the
787 /// - We can propagate mass iteratively through the SCC, for some fixed
788 /// number of iterations. Each iteration starts by assigning the entry
789 /// blocks their backedge mass from the prior iteration. The final
790 /// mass for each block (and each exit, and the total backedge mass
791 /// used for computing loop scale) is the sum of all iterations.
792 /// (Running this until fixed point would "solve" the geometric
793 /// series by simulation.)
794 template <class BT> class BlockFrequencyInfoImpl : BlockFrequencyInfoImplBase {
795 typedef typename bfi_detail::TypeMap<BT>::BlockT BlockT;
796 typedef typename bfi_detail::TypeMap<BT>::FunctionT FunctionT;
797 typedef typename bfi_detail::TypeMap<BT>::BranchProbabilityInfoT
798 BranchProbabilityInfoT;
799 typedef typename bfi_detail::TypeMap<BT>::LoopT LoopT;
800 typedef typename bfi_detail::TypeMap<BT>::LoopInfoT LoopInfoT;
802 // This is part of a workaround for a GCC 4.7 crash on lambdas.
803 friend struct bfi_detail::BlockEdgesAdder<BT>;
805 typedef GraphTraits<const BlockT *> Successor;
806 typedef GraphTraits<Inverse<const BlockT *>> Predecessor;
808 const BranchProbabilityInfoT *BPI;
812 // All blocks in reverse postorder.
813 std::vector<const BlockT *> RPOT;
814 DenseMap<const BlockT *, BlockNode> Nodes;
816 typedef typename std::vector<const BlockT *>::const_iterator rpot_iterator;
818 rpot_iterator rpot_begin() const { return RPOT.begin(); }
819 rpot_iterator rpot_end() const { return RPOT.end(); }
821 size_t getIndex(const rpot_iterator &I) const { return I - rpot_begin(); }
823 BlockNode getNode(const rpot_iterator &I) const {
824 return BlockNode(getIndex(I));
826 BlockNode getNode(const BlockT *BB) const { return Nodes.lookup(BB); }
828 const BlockT *getBlock(const BlockNode &Node) const {
829 assert(Node.Index < RPOT.size());
830 return RPOT[Node.Index];
833 /// \brief Run (and save) a post-order traversal.
835 /// Saves a reverse post-order traversal of all the nodes in \a F.
836 void initializeRPOT();
838 /// \brief Initialize loop data.
840 /// Build up \a Loops using \a LoopInfo. \a LoopInfo gives us a mapping from
841 /// each block to the deepest loop it's in, but we need the inverse. For each
842 /// loop, we store in reverse post-order its "immediate" members, defined as
843 /// the header, the headers of immediate sub-loops, and all other blocks in
844 /// the loop that are not in sub-loops.
845 void initializeLoops();
847 /// \brief Propagate to a block's successors.
849 /// In the context of distributing mass through \c OuterLoop, divide the mass
850 /// currently assigned to \c Node between its successors.
852 /// \return \c true unless there's an irreducible backedge.
853 bool propagateMassToSuccessors(LoopData *OuterLoop, const BlockNode &Node);
855 /// \brief Compute mass in a particular loop.
857 /// Assign mass to \c Loop's header, and then for each block in \c Loop in
858 /// reverse post-order, distribute mass to its successors. Only visits nodes
859 /// that have not been packaged into sub-loops.
861 /// \pre \a computeMassInLoop() has been called for each subloop of \c Loop.
862 /// \return \c true unless there's an irreducible backedge.
863 bool computeMassInLoop(LoopData &Loop);
865 /// \brief Try to compute mass in the top-level function.
867 /// Assign mass to the entry block, and then for each block in reverse
868 /// post-order, distribute mass to its successors. Skips nodes that have
869 /// been packaged into loops.
871 /// \pre \a computeMassInLoops() has been called.
872 /// \return \c true unless there's an irreducible backedge.
873 bool tryToComputeMassInFunction();
875 /// \brief Compute mass in (and package up) irreducible SCCs.
877 /// Find the irreducible SCCs in \c OuterLoop, add them to \a Loops (in front
878 /// of \c Insert), and call \a computeMassInLoop() on each of them.
880 /// If \c OuterLoop is \c nullptr, it refers to the top-level function.
882 /// \pre \a computeMassInLoop() has been called for each subloop of \c
884 /// \pre \c Insert points at the last loop successfully processed by \a
885 /// computeMassInLoop().
886 /// \pre \c OuterLoop has irreducible SCCs.
887 void computeIrreducibleMass(LoopData *OuterLoop,
888 std::list<LoopData>::iterator Insert);
890 /// \brief Compute mass in all loops.
892 /// For each loop bottom-up, call \a computeMassInLoop().
894 /// \a computeMassInLoop() aborts (and returns \c false) on loops that
895 /// contain a irreducible sub-SCCs. Use \a computeIrreducibleMass() and then
896 /// re-enter \a computeMassInLoop().
898 /// \post \a computeMassInLoop() has returned \c true for every loop.
899 void computeMassInLoops();
901 /// \brief Compute mass in the top-level function.
903 /// Uses \a tryToComputeMassInFunction() and \a computeIrreducibleMass() to
904 /// compute mass in the top-level function.
906 /// \post \a tryToComputeMassInFunction() has returned \c true.
907 void computeMassInFunction();
909 std::string getBlockName(const BlockNode &Node) const override {
910 return bfi_detail::getBlockName(getBlock(Node));
914 const FunctionT *getFunction() const { return F; }
916 void calculate(const FunctionT &F, const BranchProbabilityInfoT &BPI,
917 const LoopInfoT &LI);
918 BlockFrequencyInfoImpl() : BPI(nullptr), LI(nullptr), F(nullptr) {}
920 using BlockFrequencyInfoImplBase::getEntryFreq;
921 BlockFrequency getBlockFreq(const BlockT *BB) const {
922 return BlockFrequencyInfoImplBase::getBlockFreq(getNode(BB));
924 Optional<uint64_t> getBlockProfileCount(const Function &F,
925 const BlockT *BB) const {
926 return BlockFrequencyInfoImplBase::getBlockProfileCount(F, getNode(BB));
928 void setBlockFreq(const BlockT *BB, uint64_t Freq);
929 Scaled64 getFloatingBlockFreq(const BlockT *BB) const {
930 return BlockFrequencyInfoImplBase::getFloatingBlockFreq(getNode(BB));
933 const BranchProbabilityInfoT &getBPI() const { return *BPI; }
935 /// \brief Print the frequencies for the current function.
937 /// Prints the frequencies for the blocks in the current function.
939 /// Blocks are printed in the natural iteration order of the function, rather
940 /// than reverse post-order. This provides two advantages: writing -analyze
941 /// tests is easier (since blocks come out in source order), and even
942 /// unreachable blocks are printed.
944 /// \a BlockFrequencyInfoImplBase::print() only knows reverse post-order, so
945 /// we need to override it here.
946 raw_ostream &print(raw_ostream &OS) const override;
947 using BlockFrequencyInfoImplBase::dump;
949 using BlockFrequencyInfoImplBase::printBlockFreq;
950 raw_ostream &printBlockFreq(raw_ostream &OS, const BlockT *BB) const {
951 return BlockFrequencyInfoImplBase::printBlockFreq(OS, getNode(BB));
956 void BlockFrequencyInfoImpl<BT>::calculate(const FunctionT &F,
957 const BranchProbabilityInfoT &BPI,
958 const LoopInfoT &LI) {
959 // Save the parameters.
964 // Clean up left-over data structures.
965 BlockFrequencyInfoImplBase::clear();
970 DEBUG(dbgs() << "\nblock-frequency: " << F.getName() << "\n================="
971 << std::string(F.getName().size(), '=') << "\n");
975 // Visit loops in post-order to find the local mass distribution, and then do
976 // the full function.
977 computeMassInLoops();
978 computeMassInFunction();
984 void BlockFrequencyInfoImpl<BT>::setBlockFreq(const BlockT *BB, uint64_t Freq) {
986 BlockFrequencyInfoImplBase::setBlockFreq(getNode(BB), Freq);
988 // If BB is a newly added block after BFI is done, we need to create a new
989 // BlockNode for it assigned with a new index. The index can be determined
990 // by the size of Freqs.
991 BlockNode NewNode(Freqs.size());
993 Freqs.emplace_back();
994 BlockFrequencyInfoImplBase::setBlockFreq(NewNode, Freq);
998 template <class BT> void BlockFrequencyInfoImpl<BT>::initializeRPOT() {
999 const BlockT *Entry = &F->front();
1000 RPOT.reserve(F->size());
1001 std::copy(po_begin(Entry), po_end(Entry), std::back_inserter(RPOT));
1002 std::reverse(RPOT.begin(), RPOT.end());
1004 assert(RPOT.size() - 1 <= BlockNode::getMaxIndex() &&
1005 "More nodes in function than Block Frequency Info supports");
1007 DEBUG(dbgs() << "reverse-post-order-traversal\n");
1008 for (rpot_iterator I = rpot_begin(), E = rpot_end(); I != E; ++I) {
1009 BlockNode Node = getNode(I);
1010 DEBUG(dbgs() << " - " << getIndex(I) << ": " << getBlockName(Node) << "\n");
1014 Working.reserve(RPOT.size());
1015 for (size_t Index = 0; Index < RPOT.size(); ++Index)
1016 Working.emplace_back(Index);
1017 Freqs.resize(RPOT.size());
1020 template <class BT> void BlockFrequencyInfoImpl<BT>::initializeLoops() {
1021 DEBUG(dbgs() << "loop-detection\n");
1025 // Visit loops top down and assign them an index.
1026 std::deque<std::pair<const LoopT *, LoopData *>> Q;
1027 for (const LoopT *L : *LI)
1028 Q.emplace_back(L, nullptr);
1029 while (!Q.empty()) {
1030 const LoopT *Loop = Q.front().first;
1031 LoopData *Parent = Q.front().second;
1034 BlockNode Header = getNode(Loop->getHeader());
1035 assert(Header.isValid());
1037 Loops.emplace_back(Parent, Header);
1038 Working[Header.Index].Loop = &Loops.back();
1039 DEBUG(dbgs() << " - loop = " << getBlockName(Header) << "\n");
1041 for (const LoopT *L : *Loop)
1042 Q.emplace_back(L, &Loops.back());
1045 // Visit nodes in reverse post-order and add them to their deepest containing
1047 for (size_t Index = 0; Index < RPOT.size(); ++Index) {
1048 // Loop headers have already been mostly mapped.
1049 if (Working[Index].isLoopHeader()) {
1050 LoopData *ContainingLoop = Working[Index].getContainingLoop();
1052 ContainingLoop->Nodes.push_back(Index);
1056 const LoopT *Loop = LI->getLoopFor(RPOT[Index]);
1060 // Add this node to its containing loop's member list.
1061 BlockNode Header = getNode(Loop->getHeader());
1062 assert(Header.isValid());
1063 const auto &HeaderData = Working[Header.Index];
1064 assert(HeaderData.isLoopHeader());
1066 Working[Index].Loop = HeaderData.Loop;
1067 HeaderData.Loop->Nodes.push_back(Index);
1068 DEBUG(dbgs() << " - loop = " << getBlockName(Header)
1069 << ": member = " << getBlockName(Index) << "\n");
1073 template <class BT> void BlockFrequencyInfoImpl<BT>::computeMassInLoops() {
1074 // Visit loops with the deepest first, and the top-level loops last.
1075 for (auto L = Loops.rbegin(), E = Loops.rend(); L != E; ++L) {
1076 if (computeMassInLoop(*L))
1078 auto Next = std::next(L);
1079 computeIrreducibleMass(&*L, L.base());
1080 L = std::prev(Next);
1081 if (computeMassInLoop(*L))
1083 llvm_unreachable("unhandled irreducible control flow");
1088 bool BlockFrequencyInfoImpl<BT>::computeMassInLoop(LoopData &Loop) {
1089 // Compute mass in loop.
1090 DEBUG(dbgs() << "compute-mass-in-loop: " << getLoopName(Loop) << "\n");
1092 if (Loop.isIrreducible()) {
1093 BlockMass Remaining = BlockMass::getFull();
1094 for (uint32_t H = 0; H < Loop.NumHeaders; ++H) {
1095 auto &Mass = Working[Loop.Nodes[H].Index].getMass();
1096 Mass = Remaining * BranchProbability(1, Loop.NumHeaders - H);
1099 for (const BlockNode &M : Loop.Nodes)
1100 if (!propagateMassToSuccessors(&Loop, M))
1101 llvm_unreachable("unhandled irreducible control flow");
1103 adjustLoopHeaderMass(Loop);
1105 Working[Loop.getHeader().Index].getMass() = BlockMass::getFull();
1106 if (!propagateMassToSuccessors(&Loop, Loop.getHeader()))
1107 llvm_unreachable("irreducible control flow to loop header!?");
1108 for (const BlockNode &M : Loop.members())
1109 if (!propagateMassToSuccessors(&Loop, M))
1110 // Irreducible backedge.
1114 computeLoopScale(Loop);
1120 bool BlockFrequencyInfoImpl<BT>::tryToComputeMassInFunction() {
1121 // Compute mass in function.
1122 DEBUG(dbgs() << "compute-mass-in-function\n");
1123 assert(!Working.empty() && "no blocks in function");
1124 assert(!Working[0].isLoopHeader() && "entry block is a loop header");
1126 Working[0].getMass() = BlockMass::getFull();
1127 for (rpot_iterator I = rpot_begin(), IE = rpot_end(); I != IE; ++I) {
1128 // Check for nodes that have been packaged.
1129 BlockNode Node = getNode(I);
1130 if (Working[Node.Index].isPackaged())
1133 if (!propagateMassToSuccessors(nullptr, Node))
1139 template <class BT> void BlockFrequencyInfoImpl<BT>::computeMassInFunction() {
1140 if (tryToComputeMassInFunction())
1142 computeIrreducibleMass(nullptr, Loops.begin());
1143 if (tryToComputeMassInFunction())
1145 llvm_unreachable("unhandled irreducible control flow");
1148 /// \note This should be a lambda, but that crashes GCC 4.7.
1149 namespace bfi_detail {
1150 template <class BT> struct BlockEdgesAdder {
1152 typedef BlockFrequencyInfoImplBase::LoopData LoopData;
1153 typedef GraphTraits<const BlockT *> Successor;
1155 const BlockFrequencyInfoImpl<BT> &BFI;
1156 explicit BlockEdgesAdder(const BlockFrequencyInfoImpl<BT> &BFI)
1158 void operator()(IrreducibleGraph &G, IrreducibleGraph::IrrNode &Irr,
1159 const LoopData *OuterLoop) {
1160 const BlockT *BB = BFI.RPOT[Irr.Node.Index];
1161 for (auto I = Successor::child_begin(BB), E = Successor::child_end(BB);
1163 G.addEdge(Irr, BFI.getNode(*I), OuterLoop);
1168 void BlockFrequencyInfoImpl<BT>::computeIrreducibleMass(
1169 LoopData *OuterLoop, std::list<LoopData>::iterator Insert) {
1170 DEBUG(dbgs() << "analyze-irreducible-in-";
1171 if (OuterLoop) dbgs() << "loop: " << getLoopName(*OuterLoop) << "\n";
1172 else dbgs() << "function\n");
1174 using namespace bfi_detail;
1175 // Ideally, addBlockEdges() would be declared here as a lambda, but that
1177 BlockEdgesAdder<BT> addBlockEdges(*this);
1178 IrreducibleGraph G(*this, OuterLoop, addBlockEdges);
1180 for (auto &L : analyzeIrreducible(G, OuterLoop, Insert))
1181 computeMassInLoop(L);
1185 updateLoopWithIrreducible(*OuterLoop);
1188 // A helper function that converts a branch probability into weight.
1189 inline uint32_t getWeightFromBranchProb(const BranchProbability Prob) {
1190 return Prob.getNumerator();
1195 BlockFrequencyInfoImpl<BT>::propagateMassToSuccessors(LoopData *OuterLoop,
1196 const BlockNode &Node) {
1197 DEBUG(dbgs() << " - node: " << getBlockName(Node) << "\n");
1198 // Calculate probability for successors.
1200 if (auto *Loop = Working[Node.Index].getPackagedLoop()) {
1201 assert(Loop != OuterLoop && "Cannot propagate mass in a packaged loop");
1202 if (!addLoopSuccessorsToDist(OuterLoop, *Loop, Dist))
1203 // Irreducible backedge.
1206 const BlockT *BB = getBlock(Node);
1207 for (auto SI = Successor::child_begin(BB), SE = Successor::child_end(BB);
1209 if (!addToDist(Dist, OuterLoop, Node, getNode(*SI),
1210 getWeightFromBranchProb(BPI->getEdgeProbability(BB, SI))))
1211 // Irreducible backedge.
1215 // Distribute mass to successors, saving exit and backedge data in the
1217 distributeMass(Node, OuterLoop, Dist);
1222 raw_ostream &BlockFrequencyInfoImpl<BT>::print(raw_ostream &OS) const {
1225 OS << "block-frequency-info: " << F->getName() << "\n";
1226 for (const BlockT &BB : *F) {
1227 OS << " - " << bfi_detail::getBlockName(&BB) << ": float = ";
1228 getFloatingBlockFreq(&BB).print(OS, 5)
1229 << ", int = " << getBlockFreq(&BB).getFrequency() << "\n";
1232 // Add an extra newline for readability.
1237 // Graph trait base class for block frequency information graph
1240 enum GVDAGType { GVDT_None, GVDT_Fraction, GVDT_Integer, GVDT_Count };
1242 template <class BlockFrequencyInfoT, class BranchProbabilityInfoT>
1243 struct BFIDOTGraphTraitsBase : public DefaultDOTGraphTraits {
1244 explicit BFIDOTGraphTraitsBase(bool isSimple = false)
1245 : DefaultDOTGraphTraits(isSimple) {}
1247 typedef GraphTraits<BlockFrequencyInfoT *> GTraits;
1248 typedef typename GTraits::NodeType NodeType;
1249 typedef typename GTraits::ChildIteratorType EdgeIter;
1250 typedef typename GTraits::nodes_iterator NodeIter;
1252 uint64_t MaxFrequency = 0;
1253 static std::string getGraphName(const BlockFrequencyInfoT *G) {
1254 return G->getFunction()->getName();
1257 std::string getNodeAttributes(const NodeType *Node,
1258 const BlockFrequencyInfoT *Graph,
1259 unsigned HotPercentThreshold = 0) {
1261 if (!HotPercentThreshold)
1264 // Compute MaxFrequency on the fly:
1265 if (!MaxFrequency) {
1266 for (NodeIter I = GTraits::nodes_begin(Graph),
1267 E = GTraits::nodes_end(Graph);
1271 std::max(MaxFrequency, Graph->getBlockFreq(&N).getFrequency());
1274 BlockFrequency Freq = Graph->getBlockFreq(Node);
1275 BlockFrequency HotFreq =
1276 (BlockFrequency(MaxFrequency) *
1277 BranchProbability::getBranchProbability(HotPercentThreshold, 100));
1282 raw_string_ostream OS(Result);
1283 OS << "color=\"red\"";
1288 std::string getNodeLabel(const NodeType *Node,
1289 const BlockFrequencyInfoT *Graph, GVDAGType GType) {
1291 raw_string_ostream OS(Result);
1293 OS << Node->getName().str() << " : ";
1296 Graph->printBlockFreq(OS, Node);
1299 OS << Graph->getBlockFreq(Node).getFrequency();
1302 auto Count = Graph->getBlockProfileCount(Node);
1304 OS << Count.getValue();
1310 llvm_unreachable("If we are not supposed to render a graph we should "
1311 "never reach this point.");
1316 std::string getEdgeAttributes(const NodeType *Node, EdgeIter EI,
1317 const BlockFrequencyInfoT *BFI,
1318 const BranchProbabilityInfoT *BPI,
1319 unsigned HotPercentThreshold = 0) {
1324 BranchProbability BP = BPI->getEdgeProbability(Node, EI);
1325 uint32_t N = BP.getNumerator();
1326 uint32_t D = BP.getDenominator();
1327 double Percent = 100.0 * N / D;
1328 raw_string_ostream OS(Str);
1329 OS << format("label=\"%.1f%%\"", Percent);
1331 if (HotPercentThreshold) {
1332 BlockFrequency EFreq = BFI->getBlockFreq(Node) * BP;
1333 BlockFrequency HotFreq = BlockFrequency(MaxFrequency) *
1334 BranchProbability(HotPercentThreshold, 100);
1336 if (EFreq >= HotFreq) {
1337 OS << ",color=\"red\"";
1346 } // end namespace llvm