freebsd-dev/lib/Analysis/BranchProbabilityInfo.cpp

691 lines
22 KiB
C++

//===-- BranchProbabilityInfo.cpp - Branch Probability Analysis -----------===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// Loops should be simplified before this analysis.
//
//===----------------------------------------------------------------------===//
#include "llvm/Analysis/BranchProbabilityInfo.h"
#include "llvm/ADT/PostOrderIterator.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/IR/CFG.h"
#include "llvm/IR/Constants.h"
#include "llvm/IR/Function.h"
#include "llvm/IR/Instructions.h"
#include "llvm/IR/LLVMContext.h"
#include "llvm/IR/Metadata.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/raw_ostream.h"
using namespace llvm;
#define DEBUG_TYPE "branch-prob"
INITIALIZE_PASS_BEGIN(BranchProbabilityInfo, "branch-prob",
"Branch Probability Analysis", false, true)
INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
INITIALIZE_PASS_END(BranchProbabilityInfo, "branch-prob",
"Branch Probability Analysis", false, true)
char BranchProbabilityInfo::ID = 0;
// Weights are for internal use only. They are used by heuristics to help to
// estimate edges' probability. Example:
//
// Using "Loop Branch Heuristics" we predict weights of edges for the
// block BB2.
// ...
// |
// V
// BB1<-+
// | |
// | | (Weight = 124)
// V |
// BB2--+
// |
// | (Weight = 4)
// V
// BB3
//
// Probability of the edge BB2->BB1 = 124 / (124 + 4) = 0.96875
// Probability of the edge BB2->BB3 = 4 / (124 + 4) = 0.03125
static const uint32_t LBH_TAKEN_WEIGHT = 124;
static const uint32_t LBH_NONTAKEN_WEIGHT = 4;
/// \brief Unreachable-terminating branch taken weight.
///
/// This is the weight for a branch being taken to a block that terminates
/// (eventually) in unreachable. These are predicted as unlikely as possible.
static const uint32_t UR_TAKEN_WEIGHT = 1;
/// \brief Unreachable-terminating branch not-taken weight.
///
/// This is the weight for a branch not being taken toward a block that
/// terminates (eventually) in unreachable. Such a branch is essentially never
/// taken. Set the weight to an absurdly high value so that nested loops don't
/// easily subsume it.
static const uint32_t UR_NONTAKEN_WEIGHT = 1024*1024 - 1;
/// \brief Weight for a branch taken going into a cold block.
///
/// This is the weight for a branch taken toward a block marked
/// cold. A block is marked cold if it's postdominated by a
/// block containing a call to a cold function. Cold functions
/// are those marked with attribute 'cold'.
static const uint32_t CC_TAKEN_WEIGHT = 4;
/// \brief Weight for a branch not-taken into a cold block.
///
/// This is the weight for a branch not taken toward a block marked
/// cold.
static const uint32_t CC_NONTAKEN_WEIGHT = 64;
static const uint32_t PH_TAKEN_WEIGHT = 20;
static const uint32_t PH_NONTAKEN_WEIGHT = 12;
static const uint32_t ZH_TAKEN_WEIGHT = 20;
static const uint32_t ZH_NONTAKEN_WEIGHT = 12;
static const uint32_t FPH_TAKEN_WEIGHT = 20;
static const uint32_t FPH_NONTAKEN_WEIGHT = 12;
/// \brief Invoke-terminating normal branch taken weight
///
/// This is the weight for branching to the normal destination of an invoke
/// instruction. We expect this to happen most of the time. Set the weight to an
/// absurdly high value so that nested loops subsume it.
static const uint32_t IH_TAKEN_WEIGHT = 1024 * 1024 - 1;
/// \brief Invoke-terminating normal branch not-taken weight.
///
/// This is the weight for branching to the unwind destination of an invoke
/// instruction. This is essentially never taken.
static const uint32_t IH_NONTAKEN_WEIGHT = 1;
// Standard weight value. Used when none of the heuristics set weight for
// the edge.
static const uint32_t NORMAL_WEIGHT = 16;
// Minimum weight of an edge. Please note, that weight is NEVER 0.
static const uint32_t MIN_WEIGHT = 1;
/// \brief Calculate edge weights for successors lead to unreachable.
///
/// Predict that a successor which leads necessarily to an
/// unreachable-terminated block as extremely unlikely.
bool BranchProbabilityInfo::calcUnreachableHeuristics(BasicBlock *BB) {
TerminatorInst *TI = BB->getTerminator();
if (TI->getNumSuccessors() == 0) {
if (isa<UnreachableInst>(TI))
PostDominatedByUnreachable.insert(BB);
return false;
}
SmallVector<unsigned, 4> UnreachableEdges;
SmallVector<unsigned, 4> ReachableEdges;
for (succ_iterator I = succ_begin(BB), E = succ_end(BB); I != E; ++I) {
if (PostDominatedByUnreachable.count(*I))
UnreachableEdges.push_back(I.getSuccessorIndex());
else
ReachableEdges.push_back(I.getSuccessorIndex());
}
// If all successors are in the set of blocks post-dominated by unreachable,
// this block is too.
if (UnreachableEdges.size() == TI->getNumSuccessors())
PostDominatedByUnreachable.insert(BB);
// Skip probabilities if this block has a single successor or if all were
// reachable.
if (TI->getNumSuccessors() == 1 || UnreachableEdges.empty())
return false;
uint32_t UnreachableWeight =
std::max(UR_TAKEN_WEIGHT / (unsigned)UnreachableEdges.size(), MIN_WEIGHT);
for (SmallVectorImpl<unsigned>::iterator I = UnreachableEdges.begin(),
E = UnreachableEdges.end();
I != E; ++I)
setEdgeWeight(BB, *I, UnreachableWeight);
if (ReachableEdges.empty())
return true;
uint32_t ReachableWeight =
std::max(UR_NONTAKEN_WEIGHT / (unsigned)ReachableEdges.size(),
NORMAL_WEIGHT);
for (SmallVectorImpl<unsigned>::iterator I = ReachableEdges.begin(),
E = ReachableEdges.end();
I != E; ++I)
setEdgeWeight(BB, *I, ReachableWeight);
return true;
}
// Propagate existing explicit probabilities from either profile data or
// 'expect' intrinsic processing.
bool BranchProbabilityInfo::calcMetadataWeights(BasicBlock *BB) {
TerminatorInst *TI = BB->getTerminator();
if (TI->getNumSuccessors() == 1)
return false;
if (!isa<BranchInst>(TI) && !isa<SwitchInst>(TI))
return false;
MDNode *WeightsNode = TI->getMetadata(LLVMContext::MD_prof);
if (!WeightsNode)
return false;
// Check that the number of successors is manageable.
assert(TI->getNumSuccessors() < UINT32_MAX && "Too many successors");
// Ensure there are weights for all of the successors. Note that the first
// operand to the metadata node is a name, not a weight.
if (WeightsNode->getNumOperands() != TI->getNumSuccessors() + 1)
return false;
// Build up the final weights that will be used in a temporary buffer.
// Compute the sum of all weights to later decide whether they need to
// be scaled to fit in 32 bits.
uint64_t WeightSum = 0;
SmallVector<uint32_t, 2> Weights;
Weights.reserve(TI->getNumSuccessors());
for (unsigned i = 1, e = WeightsNode->getNumOperands(); i != e; ++i) {
ConstantInt *Weight =
mdconst::dyn_extract<ConstantInt>(WeightsNode->getOperand(i));
if (!Weight)
return false;
assert(Weight->getValue().getActiveBits() <= 32 &&
"Too many bits for uint32_t");
Weights.push_back(Weight->getZExtValue());
WeightSum += Weights.back();
}
assert(Weights.size() == TI->getNumSuccessors() && "Checked above");
// If the sum of weights does not fit in 32 bits, scale every weight down
// accordingly.
uint64_t ScalingFactor =
(WeightSum > UINT32_MAX) ? WeightSum / UINT32_MAX + 1 : 1;
WeightSum = 0;
for (unsigned i = 0, e = TI->getNumSuccessors(); i != e; ++i) {
uint32_t W = Weights[i] / ScalingFactor;
WeightSum += W;
setEdgeWeight(BB, i, W);
}
assert(WeightSum <= UINT32_MAX &&
"Expected weights to scale down to 32 bits");
return true;
}
/// \brief Calculate edge weights for edges leading to cold blocks.
///
/// A cold block is one post-dominated by a block with a call to a
/// cold function. Those edges are unlikely to be taken, so we give
/// them relatively low weight.
///
/// Return true if we could compute the weights for cold edges.
/// Return false, otherwise.
bool BranchProbabilityInfo::calcColdCallHeuristics(BasicBlock *BB) {
TerminatorInst *TI = BB->getTerminator();
if (TI->getNumSuccessors() == 0)
return false;
// Determine which successors are post-dominated by a cold block.
SmallVector<unsigned, 4> ColdEdges;
SmallVector<unsigned, 4> NormalEdges;
for (succ_iterator I = succ_begin(BB), E = succ_end(BB); I != E; ++I)
if (PostDominatedByColdCall.count(*I))
ColdEdges.push_back(I.getSuccessorIndex());
else
NormalEdges.push_back(I.getSuccessorIndex());
// If all successors are in the set of blocks post-dominated by cold calls,
// this block is in the set post-dominated by cold calls.
if (ColdEdges.size() == TI->getNumSuccessors())
PostDominatedByColdCall.insert(BB);
else {
// Otherwise, if the block itself contains a cold function, add it to the
// set of blocks postdominated by a cold call.
assert(!PostDominatedByColdCall.count(BB));
for (BasicBlock::iterator I = BB->begin(), E = BB->end(); I != E; ++I)
if (CallInst *CI = dyn_cast<CallInst>(I))
if (CI->hasFnAttr(Attribute::Cold)) {
PostDominatedByColdCall.insert(BB);
break;
}
}
// Skip probabilities if this block has a single successor.
if (TI->getNumSuccessors() == 1 || ColdEdges.empty())
return false;
uint32_t ColdWeight =
std::max(CC_TAKEN_WEIGHT / (unsigned) ColdEdges.size(), MIN_WEIGHT);
for (SmallVectorImpl<unsigned>::iterator I = ColdEdges.begin(),
E = ColdEdges.end();
I != E; ++I)
setEdgeWeight(BB, *I, ColdWeight);
if (NormalEdges.empty())
return true;
uint32_t NormalWeight = std::max(
CC_NONTAKEN_WEIGHT / (unsigned) NormalEdges.size(), NORMAL_WEIGHT);
for (SmallVectorImpl<unsigned>::iterator I = NormalEdges.begin(),
E = NormalEdges.end();
I != E; ++I)
setEdgeWeight(BB, *I, NormalWeight);
return true;
}
// Calculate Edge Weights using "Pointer Heuristics". Predict a comparsion
// between two pointer or pointer and NULL will fail.
bool BranchProbabilityInfo::calcPointerHeuristics(BasicBlock *BB) {
BranchInst * BI = dyn_cast<BranchInst>(BB->getTerminator());
if (!BI || !BI->isConditional())
return false;
Value *Cond = BI->getCondition();
ICmpInst *CI = dyn_cast<ICmpInst>(Cond);
if (!CI || !CI->isEquality())
return false;
Value *LHS = CI->getOperand(0);
if (!LHS->getType()->isPointerTy())
return false;
assert(CI->getOperand(1)->getType()->isPointerTy());
// p != 0 -> isProb = true
// p == 0 -> isProb = false
// p != q -> isProb = true
// p == q -> isProb = false;
unsigned TakenIdx = 0, NonTakenIdx = 1;
bool isProb = CI->getPredicate() == ICmpInst::ICMP_NE;
if (!isProb)
std::swap(TakenIdx, NonTakenIdx);
setEdgeWeight(BB, TakenIdx, PH_TAKEN_WEIGHT);
setEdgeWeight(BB, NonTakenIdx, PH_NONTAKEN_WEIGHT);
return true;
}
// Calculate Edge Weights using "Loop Branch Heuristics". Predict backedges
// as taken, exiting edges as not-taken.
bool BranchProbabilityInfo::calcLoopBranchHeuristics(BasicBlock *BB) {
Loop *L = LI->getLoopFor(BB);
if (!L)
return false;
SmallVector<unsigned, 8> BackEdges;
SmallVector<unsigned, 8> ExitingEdges;
SmallVector<unsigned, 8> InEdges; // Edges from header to the loop.
for (succ_iterator I = succ_begin(BB), E = succ_end(BB); I != E; ++I) {
if (!L->contains(*I))
ExitingEdges.push_back(I.getSuccessorIndex());
else if (L->getHeader() == *I)
BackEdges.push_back(I.getSuccessorIndex());
else
InEdges.push_back(I.getSuccessorIndex());
}
if (BackEdges.empty() && ExitingEdges.empty())
return false;
if (uint32_t numBackEdges = BackEdges.size()) {
uint32_t backWeight = LBH_TAKEN_WEIGHT / numBackEdges;
if (backWeight < NORMAL_WEIGHT)
backWeight = NORMAL_WEIGHT;
for (SmallVectorImpl<unsigned>::iterator EI = BackEdges.begin(),
EE = BackEdges.end(); EI != EE; ++EI) {
setEdgeWeight(BB, *EI, backWeight);
}
}
if (uint32_t numInEdges = InEdges.size()) {
uint32_t inWeight = LBH_TAKEN_WEIGHT / numInEdges;
if (inWeight < NORMAL_WEIGHT)
inWeight = NORMAL_WEIGHT;
for (SmallVectorImpl<unsigned>::iterator EI = InEdges.begin(),
EE = InEdges.end(); EI != EE; ++EI) {
setEdgeWeight(BB, *EI, inWeight);
}
}
if (uint32_t numExitingEdges = ExitingEdges.size()) {
uint32_t exitWeight = LBH_NONTAKEN_WEIGHT / numExitingEdges;
if (exitWeight < MIN_WEIGHT)
exitWeight = MIN_WEIGHT;
for (SmallVectorImpl<unsigned>::iterator EI = ExitingEdges.begin(),
EE = ExitingEdges.end(); EI != EE; ++EI) {
setEdgeWeight(BB, *EI, exitWeight);
}
}
return true;
}
bool BranchProbabilityInfo::calcZeroHeuristics(BasicBlock *BB) {
BranchInst * BI = dyn_cast<BranchInst>(BB->getTerminator());
if (!BI || !BI->isConditional())
return false;
Value *Cond = BI->getCondition();
ICmpInst *CI = dyn_cast<ICmpInst>(Cond);
if (!CI)
return false;
Value *RHS = CI->getOperand(1);
ConstantInt *CV = dyn_cast<ConstantInt>(RHS);
if (!CV)
return false;
// If the LHS is the result of AND'ing a value with a single bit bitmask,
// we don't have information about probabilities.
if (Instruction *LHS = dyn_cast<Instruction>(CI->getOperand(0)))
if (LHS->getOpcode() == Instruction::And)
if (ConstantInt *AndRHS = dyn_cast<ConstantInt>(LHS->getOperand(1)))
if (AndRHS->getUniqueInteger().isPowerOf2())
return false;
bool isProb;
if (CV->isZero()) {
switch (CI->getPredicate()) {
case CmpInst::ICMP_EQ:
// X == 0 -> Unlikely
isProb = false;
break;
case CmpInst::ICMP_NE:
// X != 0 -> Likely
isProb = true;
break;
case CmpInst::ICMP_SLT:
// X < 0 -> Unlikely
isProb = false;
break;
case CmpInst::ICMP_SGT:
// X > 0 -> Likely
isProb = true;
break;
default:
return false;
}
} else if (CV->isOne() && CI->getPredicate() == CmpInst::ICMP_SLT) {
// InstCombine canonicalizes X <= 0 into X < 1.
// X <= 0 -> Unlikely
isProb = false;
} else if (CV->isAllOnesValue()) {
switch (CI->getPredicate()) {
case CmpInst::ICMP_EQ:
// X == -1 -> Unlikely
isProb = false;
break;
case CmpInst::ICMP_NE:
// X != -1 -> Likely
isProb = true;
break;
case CmpInst::ICMP_SGT:
// InstCombine canonicalizes X >= 0 into X > -1.
// X >= 0 -> Likely
isProb = true;
break;
default:
return false;
}
} else {
return false;
}
unsigned TakenIdx = 0, NonTakenIdx = 1;
if (!isProb)
std::swap(TakenIdx, NonTakenIdx);
setEdgeWeight(BB, TakenIdx, ZH_TAKEN_WEIGHT);
setEdgeWeight(BB, NonTakenIdx, ZH_NONTAKEN_WEIGHT);
return true;
}
bool BranchProbabilityInfo::calcFloatingPointHeuristics(BasicBlock *BB) {
BranchInst *BI = dyn_cast<BranchInst>(BB->getTerminator());
if (!BI || !BI->isConditional())
return false;
Value *Cond = BI->getCondition();
FCmpInst *FCmp = dyn_cast<FCmpInst>(Cond);
if (!FCmp)
return false;
bool isProb;
if (FCmp->isEquality()) {
// f1 == f2 -> Unlikely
// f1 != f2 -> Likely
isProb = !FCmp->isTrueWhenEqual();
} else if (FCmp->getPredicate() == FCmpInst::FCMP_ORD) {
// !isnan -> Likely
isProb = true;
} else if (FCmp->getPredicate() == FCmpInst::FCMP_UNO) {
// isnan -> Unlikely
isProb = false;
} else {
return false;
}
unsigned TakenIdx = 0, NonTakenIdx = 1;
if (!isProb)
std::swap(TakenIdx, NonTakenIdx);
setEdgeWeight(BB, TakenIdx, FPH_TAKEN_WEIGHT);
setEdgeWeight(BB, NonTakenIdx, FPH_NONTAKEN_WEIGHT);
return true;
}
bool BranchProbabilityInfo::calcInvokeHeuristics(BasicBlock *BB) {
InvokeInst *II = dyn_cast<InvokeInst>(BB->getTerminator());
if (!II)
return false;
setEdgeWeight(BB, 0/*Index for Normal*/, IH_TAKEN_WEIGHT);
setEdgeWeight(BB, 1/*Index for Unwind*/, IH_NONTAKEN_WEIGHT);
return true;
}
void BranchProbabilityInfo::getAnalysisUsage(AnalysisUsage &AU) const {
AU.addRequired<LoopInfoWrapperPass>();
AU.setPreservesAll();
}
bool BranchProbabilityInfo::runOnFunction(Function &F) {
DEBUG(dbgs() << "---- Branch Probability Info : " << F.getName()
<< " ----\n\n");
LastF = &F; // Store the last function we ran on for printing.
LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
assert(PostDominatedByUnreachable.empty());
assert(PostDominatedByColdCall.empty());
// Walk the basic blocks in post-order so that we can build up state about
// the successors of a block iteratively.
for (auto BB : post_order(&F.getEntryBlock())) {
DEBUG(dbgs() << "Computing probabilities for " << BB->getName() << "\n");
if (calcUnreachableHeuristics(BB))
continue;
if (calcMetadataWeights(BB))
continue;
if (calcColdCallHeuristics(BB))
continue;
if (calcLoopBranchHeuristics(BB))
continue;
if (calcPointerHeuristics(BB))
continue;
if (calcZeroHeuristics(BB))
continue;
if (calcFloatingPointHeuristics(BB))
continue;
calcInvokeHeuristics(BB);
}
PostDominatedByUnreachable.clear();
PostDominatedByColdCall.clear();
return false;
}
void BranchProbabilityInfo::releaseMemory() {
Weights.clear();
}
void BranchProbabilityInfo::print(raw_ostream &OS, const Module *) const {
OS << "---- Branch Probabilities ----\n";
// We print the probabilities from the last function the analysis ran over,
// or the function it is currently running over.
assert(LastF && "Cannot print prior to running over a function");
for (Function::const_iterator BI = LastF->begin(), BE = LastF->end();
BI != BE; ++BI) {
for (succ_const_iterator SI = succ_begin(BI), SE = succ_end(BI);
SI != SE; ++SI) {
printEdgeProbability(OS << " ", BI, *SI);
}
}
}
uint32_t BranchProbabilityInfo::getSumForBlock(const BasicBlock *BB) const {
uint32_t Sum = 0;
for (succ_const_iterator I = succ_begin(BB), E = succ_end(BB); I != E; ++I) {
uint32_t Weight = getEdgeWeight(BB, I.getSuccessorIndex());
uint32_t PrevSum = Sum;
Sum += Weight;
assert(Sum >= PrevSum); (void) PrevSum;
}
return Sum;
}
bool BranchProbabilityInfo::
isEdgeHot(const BasicBlock *Src, const BasicBlock *Dst) const {
// Hot probability is at least 4/5 = 80%
// FIXME: Compare against a static "hot" BranchProbability.
return getEdgeProbability(Src, Dst) > BranchProbability(4, 5);
}
BasicBlock *BranchProbabilityInfo::getHotSucc(BasicBlock *BB) const {
uint32_t Sum = 0;
uint32_t MaxWeight = 0;
BasicBlock *MaxSucc = nullptr;
for (succ_iterator I = succ_begin(BB), E = succ_end(BB); I != E; ++I) {
BasicBlock *Succ = *I;
uint32_t Weight = getEdgeWeight(BB, Succ);
uint32_t PrevSum = Sum;
Sum += Weight;
assert(Sum > PrevSum); (void) PrevSum;
if (Weight > MaxWeight) {
MaxWeight = Weight;
MaxSucc = Succ;
}
}
// Hot probability is at least 4/5 = 80%
if (BranchProbability(MaxWeight, Sum) > BranchProbability(4, 5))
return MaxSucc;
return nullptr;
}
/// Get the raw edge weight for the edge. If can't find it, return
/// DEFAULT_WEIGHT value. Here an edge is specified using PredBlock and an index
/// to the successors.
uint32_t BranchProbabilityInfo::
getEdgeWeight(const BasicBlock *Src, unsigned IndexInSuccessors) const {
DenseMap<Edge, uint32_t>::const_iterator I =
Weights.find(std::make_pair(Src, IndexInSuccessors));
if (I != Weights.end())
return I->second;
return DEFAULT_WEIGHT;
}
uint32_t BranchProbabilityInfo::getEdgeWeight(const BasicBlock *Src,
succ_const_iterator Dst) const {
return getEdgeWeight(Src, Dst.getSuccessorIndex());
}
/// Get the raw edge weight calculated for the block pair. This returns the sum
/// of all raw edge weights from Src to Dst.
uint32_t BranchProbabilityInfo::
getEdgeWeight(const BasicBlock *Src, const BasicBlock *Dst) const {
uint32_t Weight = 0;
bool FoundWeight = false;
DenseMap<Edge, uint32_t>::const_iterator MapI;
for (succ_const_iterator I = succ_begin(Src), E = succ_end(Src); I != E; ++I)
if (*I == Dst) {
MapI = Weights.find(std::make_pair(Src, I.getSuccessorIndex()));
if (MapI != Weights.end()) {
FoundWeight = true;
Weight += MapI->second;
}
}
return (!FoundWeight) ? DEFAULT_WEIGHT : Weight;
}
/// Set the edge weight for a given edge specified by PredBlock and an index
/// to the successors.
void BranchProbabilityInfo::
setEdgeWeight(const BasicBlock *Src, unsigned IndexInSuccessors,
uint32_t Weight) {
Weights[std::make_pair(Src, IndexInSuccessors)] = Weight;
DEBUG(dbgs() << "set edge " << Src->getName() << " -> "
<< IndexInSuccessors << " successor weight to "
<< Weight << "\n");
}
/// Get an edge's probability, relative to other out-edges from Src.
BranchProbability BranchProbabilityInfo::
getEdgeProbability(const BasicBlock *Src, unsigned IndexInSuccessors) const {
uint32_t N = getEdgeWeight(Src, IndexInSuccessors);
uint32_t D = getSumForBlock(Src);
return BranchProbability(N, D);
}
/// Get the probability of going from Src to Dst. It returns the sum of all
/// probabilities for edges from Src to Dst.
BranchProbability BranchProbabilityInfo::
getEdgeProbability(const BasicBlock *Src, const BasicBlock *Dst) const {
uint32_t N = getEdgeWeight(Src, Dst);
uint32_t D = getSumForBlock(Src);
return BranchProbability(N, D);
}
raw_ostream &
BranchProbabilityInfo::printEdgeProbability(raw_ostream &OS,
const BasicBlock *Src,
const BasicBlock *Dst) const {
const BranchProbability Prob = getEdgeProbability(Src, Dst);
OS << "edge " << Src->getName() << " -> " << Dst->getName()
<< " probability is " << Prob
<< (isEdgeHot(Src, Dst) ? " [HOT edge]\n" : "\n");
return OS;
}