[llvm] r250089 - Update the branch weight metadata in JumpThreading pass.

Manman Ren via llvm-commits llvm-commits at lists.llvm.org
Tue Oct 13 07:31:16 PDT 2015


> On Oct 12, 2015, at 8:35 PM, Manman Ren <mren at apple.com> wrote:
> 
> Hi Cong,
> 
> With this commit, building clang with PGO starts to fail with the following error:
> 
> Assertion failed: (Denominator > 0 && "Denominator cannot be 0!"), function BranchProbability, file /Users/buildslave/jenkins/sharedspace/apple-clang-stage2-RA at 2/clang/src/lib/Support/BranchProbability.cpp, line 35.
> 
> clang: error: unable to execute command: Illegal instruction: 4
> 
> I will revert this commit and see if our internal bot recovers.

Hi Cong,

Our internal bots have recovered after reverting this commit. I am working on a reduced testing case.

Thanks,
Manman

> If you need help reproducing, let me know.
> 
> Thanks,
> Manman
> 
> 
>> On Oct 12, 2015, at 12:44 PM, Cong Hou via llvm-commits <llvm-commits at lists.llvm.org> wrote:
>> 
>> Author: conghou
>> Date: Mon Oct 12 14:44:08 2015
>> New Revision: 250089
>> 
>> URL: http://llvm.org/viewvc/llvm-project?rev=250089&view=rev
>> Log:
>> Update the branch weight metadata in JumpThreading pass.
>> 
>> In JumpThreading pass, the branch weight metadata is not updated after CFG modification. Consider the jump threading on PredBB, BB, and SuccBB. After jump threading, the weight on BB->SuccBB should be adjusted as some of it is contributed by the edge PredBB->BB, which doesn't exist anymore. This patch tries to update the edge weight in metadata on BB->SuccBB by scaling it by 1 - Freq(PredBB->BB) / Freq(BB->SuccBB). 
>> 
>> Differential revision: http://reviews.llvm.org/D10979
>> 
>> 
>> Added:
>>   llvm/trunk/test/Transforms/JumpThreading/update-edge-weight.ll
>> Modified:
>>   llvm/trunk/include/llvm/Analysis/BlockFrequencyInfo.h
>>   llvm/trunk/include/llvm/Analysis/BlockFrequencyInfoImpl.h
>>   llvm/trunk/include/llvm/CodeGen/MachineBranchProbabilityInfo.h
>>   llvm/trunk/lib/Analysis/BlockFrequencyInfo.cpp
>>   llvm/trunk/lib/Analysis/BlockFrequencyInfoImpl.cpp
>>   llvm/trunk/lib/Transforms/Scalar/JumpThreading.cpp
>> 
>> Modified: llvm/trunk/include/llvm/Analysis/BlockFrequencyInfo.h
>> URL: http://llvm.org/viewvc/llvm-project/llvm/trunk/include/llvm/Analysis/BlockFrequencyInfo.h?rev=250089&r1=250088&r2=250089&view=diff
>> ==============================================================================
>> --- llvm/trunk/include/llvm/Analysis/BlockFrequencyInfo.h (original)
>> +++ llvm/trunk/include/llvm/Analysis/BlockFrequencyInfo.h Mon Oct 12 14:44:08 2015
>> @@ -45,6 +45,9 @@ public:
>>  /// floating points.
>>  BlockFrequency getBlockFreq(const BasicBlock *BB) const;
>> 
>> +  // Set the frequency of the given basic block.
>> +  void setBlockFreq(const BasicBlock *BB, uint64_t Freq);
>> +
>>  /// calculate - compute block frequency info for the given function.
>>  void calculate(const Function &F, const BranchProbabilityInfo &BPI,
>>                 const LoopInfo &LI);
>> 
>> Modified: llvm/trunk/include/llvm/Analysis/BlockFrequencyInfoImpl.h
>> URL: http://llvm.org/viewvc/llvm-project/llvm/trunk/include/llvm/Analysis/BlockFrequencyInfoImpl.h?rev=250089&r1=250088&r2=250089&view=diff
>> ==============================================================================
>> --- llvm/trunk/include/llvm/Analysis/BlockFrequencyInfoImpl.h (original)
>> +++ llvm/trunk/include/llvm/Analysis/BlockFrequencyInfoImpl.h Mon Oct 12 14:44:08 2015
>> @@ -477,6 +477,8 @@ public:
>> 
>>  BlockFrequency getBlockFreq(const BlockNode &Node) const;
>> 
>> +  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;
>> @@ -913,6 +915,7 @@ public:
>>  BlockFrequency getBlockFreq(const BlockT *BB) const {
>>    return BlockFrequencyInfoImplBase::getBlockFreq(getNode(BB));
>>  }
>> +  void setBlockFreq(const BlockT *BB, uint64_t Freq);
>>  Scaled64 getFloatingBlockFreq(const BlockT *BB) const {
>>    return BlockFrequencyInfoImplBase::getFloatingBlockFreq(getNode(BB));
>>  }
>> @@ -965,6 +968,21 @@ void BlockFrequencyInfoImpl<BT>::calcula
>>  finalizeMetrics();
>> }
>> 
>> +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;
>> +    Freqs.emplace_back();
>> +    BlockFrequencyInfoImplBase::setBlockFreq(NewNode, Freq);
>> +  }
>> +}
>> +
>> template <class BT> void BlockFrequencyInfoImpl<BT>::initializeRPOT() {
>>  const BlockT *Entry = &F->front();
>>  RPOT.reserve(F->size());
>> 
>> Modified: llvm/trunk/include/llvm/CodeGen/MachineBranchProbabilityInfo.h
>> URL: http://llvm.org/viewvc/llvm-project/llvm/trunk/include/llvm/CodeGen/MachineBranchProbabilityInfo.h?rev=250089&r1=250088&r2=250089&view=diff
>> ==============================================================================
>> --- llvm/trunk/include/llvm/CodeGen/MachineBranchProbabilityInfo.h (original)
>> +++ llvm/trunk/include/llvm/CodeGen/MachineBranchProbabilityInfo.h Mon Oct 12 14:44:08 2015
>> @@ -83,8 +83,35 @@ public:
>>  raw_ostream &printEdgeProbability(raw_ostream &OS,
>>                                    const MachineBasicBlock *Src,
>>                                    const MachineBasicBlock *Dst) const;
>> +
>> +  // Normalize a list of weights by scaling them down so that the sum of them
>> +  // doesn't exceed UINT32_MAX. Return the scale.
>> +  template <class WeightListIter>
>> +  static uint32_t normalizeEdgeWeights(WeightListIter Begin,
>> +                                       WeightListIter End);
>> };
>> 
>> +template <class WeightListIter>
>> +uint32_t
>> +MachineBranchProbabilityInfo::normalizeEdgeWeights(WeightListIter Begin,
>> +                                                   WeightListIter End) {
>> +  // First we compute the sum with 64-bits of precision.
>> +  uint64_t Sum = std::accumulate(Begin, End, uint64_t(0));
>> +
>> +  // If the computed sum fits in 32-bits, we're done.
>> +  if (Sum <= UINT32_MAX)
>> +    return 1;
>> +
>> +  // Otherwise, compute the scale necessary to cause the weights to fit, and
>> +  // re-sum with that scale applied.
>> +  assert((Sum / UINT32_MAX) < UINT32_MAX &&
>> +         "The sum of weights exceeds UINT32_MAX^2!");
>> +  uint32_t Scale = (Sum / UINT32_MAX) + 1;
>> +  for (auto I = Begin; I != End; ++I)
>> +    *I /= Scale;
>> +  return Scale;
>> +}
>> +
>> }
>> 
>> 
>> 
>> Modified: llvm/trunk/lib/Analysis/BlockFrequencyInfo.cpp
>> URL: http://llvm.org/viewvc/llvm-project/llvm/trunk/lib/Analysis/BlockFrequencyInfo.cpp?rev=250089&r1=250088&r2=250089&view=diff
>> ==============================================================================
>> --- llvm/trunk/lib/Analysis/BlockFrequencyInfo.cpp (original)
>> +++ llvm/trunk/lib/Analysis/BlockFrequencyInfo.cpp Mon Oct 12 14:44:08 2015
>> @@ -129,6 +129,12 @@ BlockFrequency BlockFrequencyInfo::getBl
>>  return BFI ? BFI->getBlockFreq(BB) : 0;
>> }
>> 
>> +void BlockFrequencyInfo::setBlockFreq(const BasicBlock *BB,
>> +                                      uint64_t Freq) {
>> +  assert(BFI && "Expected analysis to be available");
>> +  BFI->setBlockFreq(BB, Freq);
>> +}
>> +
>> /// Pop up a ghostview window with the current block frequency propagation
>> /// rendered using dot.
>> void BlockFrequencyInfo::view() const {
>> 
>> Modified: llvm/trunk/lib/Analysis/BlockFrequencyInfoImpl.cpp
>> URL: http://llvm.org/viewvc/llvm-project/llvm/trunk/lib/Analysis/BlockFrequencyInfoImpl.cpp?rev=250089&r1=250088&r2=250089&view=diff
>> ==============================================================================
>> --- llvm/trunk/lib/Analysis/BlockFrequencyInfoImpl.cpp (original)
>> +++ llvm/trunk/lib/Analysis/BlockFrequencyInfoImpl.cpp Mon Oct 12 14:44:08 2015
>> @@ -530,6 +530,13 @@ BlockFrequencyInfoImplBase::getFloatingB
>>  return Freqs[Node.Index].Scaled;
>> }
>> 
>> +void BlockFrequencyInfoImplBase::setBlockFreq(const BlockNode &Node,
>> +                                              uint64_t Freq) {
>> +  assert(Node.isValid() && "Expected valid node");
>> +  assert(Node.Index < Freqs.size() && "Expected legal index");
>> +  Freqs[Node.Index].Integer = Freq;
>> +}
>> +
>> std::string
>> BlockFrequencyInfoImplBase::getBlockName(const BlockNode &Node) const {
>>  return std::string();
>> 
>> Modified: llvm/trunk/lib/Transforms/Scalar/JumpThreading.cpp
>> URL: http://llvm.org/viewvc/llvm-project/llvm/trunk/lib/Transforms/Scalar/JumpThreading.cpp?rev=250089&r1=250088&r2=250089&view=diff
>> ==============================================================================
>> --- llvm/trunk/lib/Transforms/Scalar/JumpThreading.cpp (original)
>> +++ llvm/trunk/lib/Transforms/Scalar/JumpThreading.cpp Mon Oct 12 14:44:08 2015
>> @@ -20,14 +20,20 @@
>> #include "llvm/ADT/Statistic.h"
>> #include "llvm/Analysis/GlobalsModRef.h"
>> #include "llvm/Analysis/CFG.h"
>> +#include "llvm/Analysis/BlockFrequencyInfo.h"
>> +#include "llvm/Analysis/BlockFrequencyInfoImpl.h"
>> +#include "llvm/Analysis/BranchProbabilityInfo.h"
>> #include "llvm/Analysis/ConstantFolding.h"
>> #include "llvm/Analysis/InstructionSimplify.h"
>> #include "llvm/Analysis/LazyValueInfo.h"
>> #include "llvm/Analysis/Loads.h"
>> +#include "llvm/Analysis/LoopInfo.h"
>> #include "llvm/Analysis/TargetLibraryInfo.h"
>> +#include "llvm/CodeGen/MachineBranchProbabilityInfo.h"
>> #include "llvm/IR/DataLayout.h"
>> #include "llvm/IR/IntrinsicInst.h"
>> #include "llvm/IR/LLVMContext.h"
>> +#include "llvm/IR/MDBuilder.h"
>> #include "llvm/IR/Metadata.h"
>> #include "llvm/IR/ValueHandle.h"
>> #include "llvm/Pass.h"
>> @@ -37,6 +43,8 @@
>> #include "llvm/Transforms/Utils/BasicBlockUtils.h"
>> #include "llvm/Transforms/Utils/Local.h"
>> #include "llvm/Transforms/Utils/SSAUpdater.h"
>> +#include <algorithm>
>> +#include <memory>
>> using namespace llvm;
>> 
>> #define DEBUG_TYPE "jump-threading"
>> @@ -81,6 +89,9 @@ namespace {
>>  class JumpThreading : public FunctionPass {
>>    TargetLibraryInfo *TLI;
>>    LazyValueInfo *LVI;
>> +    std::unique_ptr<BlockFrequencyInfo> BFI;
>> +    std::unique_ptr<BranchProbabilityInfo> BPI;
>> +    bool HasProfileData;
>> #ifdef NDEBUG
>>    SmallPtrSet<BasicBlock*, 16> LoopHeaders;
>> #else
>> @@ -119,6 +130,11 @@ namespace {
>>      AU.addRequired<TargetLibraryInfoWrapperPass>();
>>    }
>> 
>> +    void releaseMemory() override {
>> +      BFI.reset();
>> +      BPI.reset();
>> +    }
>> +
>>    void FindLoopHeaders(Function &F);
>>    bool ProcessBlock(BasicBlock *BB);
>>    bool ThreadEdge(BasicBlock *BB, const SmallVectorImpl<BasicBlock*> &PredBBs,
>> @@ -139,6 +155,12 @@ namespace {
>> 
>>    bool SimplifyPartiallyRedundantLoad(LoadInst *LI);
>>    bool TryToUnfoldSelect(CmpInst *CondCmp, BasicBlock *BB);
>> +
>> +  private:
>> +    BasicBlock *SplitBlockPreds(BasicBlock *BB, ArrayRef<BasicBlock *> Preds,
>> +                                const char *Suffix);
>> +    void UpdateBlockFreqAndEdgeWeight(BasicBlock *PredBB, BasicBlock *BB,
>> +                                      BasicBlock *NewBB, BasicBlock *SuccBB);
>>  };
>> }
>> 
>> @@ -162,6 +184,16 @@ bool JumpThreading::runOnFunction(Functi
>>  DEBUG(dbgs() << "Jump threading on function '" << F.getName() << "'\n");
>>  TLI = &getAnalysis<TargetLibraryInfoWrapperPass>().getTLI();
>>  LVI = &getAnalysis<LazyValueInfo>();
>> +  BFI.reset();
>> +  BPI.reset();
>> +  // When profile data is available, we need to update edge weights after
>> +  // successful jump threading, which requires both BPI and BFI being available.
>> +  HasProfileData = F.getEntryCount().hasValue();
>> +  if (HasProfileData) {
>> +    LoopInfo LI{DominatorTree(F)};
>> +    BPI.reset(new BranchProbabilityInfo(F, LI));
>> +    BFI.reset(new BlockFrequencyInfo(F, *BPI, LI));
>> +  }
>> 
>>  // Remove unreachable blocks from function as they may result in infinite
>>  // loop. We do threading if we found something profitable. Jump threading a
>> @@ -977,8 +1009,7 @@ bool JumpThreading::SimplifyPartiallyRed
>>    }
>> 
>>    // Split them out to their own block.
>> -    UnavailablePred =
>> -      SplitBlockPredecessors(LoadBB, PredsToSplit, "thread-pre-split");
>> +    UnavailablePred = SplitBlockPreds(LoadBB, PredsToSplit, "thread-pre-split");
>>  }
>> 
>>  // If the value isn't available in all predecessors, then there will be
>> @@ -1403,7 +1434,7 @@ bool JumpThreading::ThreadEdge(BasicBloc
>>  else {
>>    DEBUG(dbgs() << "  Factoring out " << PredBBs.size()
>>          << " common predecessors.\n");
>> -    PredBB = SplitBlockPredecessors(BB, PredBBs, ".thr_comm");
>> +    PredBB = SplitBlockPreds(BB, PredBBs, ".thr_comm");
>>  }
>> 
>>  // And finally, do it!
>> @@ -1424,6 +1455,13 @@ bool JumpThreading::ThreadEdge(BasicBloc
>>                                         BB->getParent(), BB);
>>  NewBB->moveAfter(PredBB);
>> 
>> +  // Set the block frequency of NewBB.
>> +  if (HasProfileData) {
>> +    auto NewBBFreq =
>> +        BFI->getBlockFreq(PredBB) * BPI->getEdgeProbability(PredBB, BB);
>> +    BFI->setBlockFreq(NewBB, NewBBFreq.getFrequency());
>> +  }
>> +
>>  BasicBlock::iterator BI = BB->begin();
>>  for (; PHINode *PN = dyn_cast<PHINode>(BI); ++BI)
>>    ValueMapping[PN] = PN->getIncomingValueForBlock(PredBB);
>> @@ -1447,7 +1485,7 @@ bool JumpThreading::ThreadEdge(BasicBloc
>> 
>>  // We didn't copy the terminator from BB over to NewBB, because there is now
>>  // an unconditional jump to SuccBB.  Insert the unconditional jump.
>> -  BranchInst *NewBI =BranchInst::Create(SuccBB, NewBB);
>> +  BranchInst *NewBI = BranchInst::Create(SuccBB, NewBB);
>>  NewBI->setDebugLoc(BB->getTerminator()->getDebugLoc());
>> 
>>  // Check to see if SuccBB has PHI nodes. If so, we need to add entries to the
>> @@ -1508,11 +1546,86 @@ bool JumpThreading::ThreadEdge(BasicBloc
>>  // frequently happens because of phi translation.
>>  SimplifyInstructionsInBlock(NewBB, TLI);
>> 
>> +  // Update the edge weight from BB to SuccBB, which should be less than before.
>> +  UpdateBlockFreqAndEdgeWeight(PredBB, BB, NewBB, SuccBB);
>> +
>>  // Threaded an edge!
>>  ++NumThreads;
>>  return true;
>> }
>> 
>> +/// Create a new basic block that will be the predecessor of BB and successor of
>> +/// all blocks in Preds. When profile data is availble, update the frequency of
>> +/// this new block.
>> +BasicBlock *JumpThreading::SplitBlockPreds(BasicBlock *BB,
>> +                                           ArrayRef<BasicBlock *> Preds,
>> +                                           const char *Suffix) {
>> +  // Collect the frequencies of all predecessors of BB, which will be used to
>> +  // update the edge weight on BB->SuccBB.
>> +  BlockFrequency PredBBFreq(0);
>> +  if (HasProfileData)
>> +    for (auto Pred : Preds)
>> +      PredBBFreq += BFI->getBlockFreq(Pred) * BPI->getEdgeProbability(Pred, BB);
>> +
>> +  BasicBlock *PredBB = SplitBlockPredecessors(BB, Preds, Suffix);
>> +
>> +  // Set the block frequency of the newly created PredBB, which is the sum of
>> +  // frequencies of Preds.
>> +  if (HasProfileData)
>> +    BFI->setBlockFreq(PredBB, PredBBFreq.getFrequency());
>> +  return PredBB;
>> +}
>> +
>> +/// Update the block frequency of BB and branch weight and the metadata on the
>> +/// edge BB->SuccBB. This is done by scaling the weight of BB->SuccBB by 1 -
>> +/// Freq(PredBB->BB) / Freq(BB->SuccBB).
>> +void JumpThreading::UpdateBlockFreqAndEdgeWeight(BasicBlock *PredBB,
>> +                                                 BasicBlock *BB,
>> +                                                 BasicBlock *NewBB,
>> +                                                 BasicBlock *SuccBB) {
>> +  if (!HasProfileData)
>> +    return;
>> +
>> +  assert(BFI && BPI && "BFI & BPI should have been created here");
>> +
>> +  // As the edge from PredBB to BB is deleted, we have to update the block
>> +  // frequency of BB.
>> +  auto BBOrigFreq = BFI->getBlockFreq(BB);
>> +  auto NewBBFreq = BFI->getBlockFreq(NewBB);
>> +  auto BB2SuccBBFreq = BBOrigFreq * BPI->getEdgeProbability(BB, SuccBB);
>> +  auto BBNewFreq = BBOrigFreq - NewBBFreq;
>> +  BFI->setBlockFreq(BB, BBNewFreq.getFrequency());
>> +
>> +  // Collect updated outgoing edges' frequencies from BB and use them to update
>> +  // edge weights.
>> +  SmallVector<uint64_t, 4> BBSuccFreq;
>> +  for (auto I = succ_begin(BB), E = succ_end(BB); I != E; ++I) {
>> +    auto SuccFreq = (*I == SuccBB)
>> +                        ? BB2SuccBBFreq - NewBBFreq
>> +                        : BBOrigFreq * BPI->getEdgeProbability(BB, *I);
>> +    BBSuccFreq.push_back(SuccFreq.getFrequency());
>> +  }
>> +
>> +  // Normalize edge weights in Weights64 so that the sum of them can fit in
>> +  MachineBranchProbabilityInfo::normalizeEdgeWeights(BBSuccFreq.begin(),
>> +                                                     BBSuccFreq.end());
>> +
>> +  SmallVector<uint32_t, 4> Weights;
>> +  for (auto Freq : BBSuccFreq)
>> +    Weights.push_back(static_cast<uint32_t>(Freq));
>> +
>> +  // Update edge weights in BPI.
>> +  for (int I = 0, E = Weights.size(); I < E; I++)
>> +    BPI->setEdgeWeight(BB, I, Weights[I]);
>> +
>> +  if (Weights.size() >= 2) {
>> +    auto TI = BB->getTerminator();
>> +    TI->setMetadata(
>> +        LLVMContext::MD_prof,
>> +        MDBuilder(TI->getParent()->getContext()).createBranchWeights(Weights));
>> +  }
>> +}
>> +
>> /// DuplicateCondBranchOnPHIIntoPred - PredBB contains an unconditional branch
>> /// to BB which contains an i1 PHI node and a conditional branch on that PHI.
>> /// If we can duplicate the contents of BB up into PredBB do so now, this
>> @@ -1546,7 +1659,7 @@ bool JumpThreading::DuplicateCondBranchO
>>  else {
>>    DEBUG(dbgs() << "  Factoring out " << PredBBs.size()
>>          << " common predecessors.\n");
>> -    PredBB = SplitBlockPredecessors(BB, PredBBs, ".thr_comm");
>> +    PredBB = SplitBlockPreds(BB, PredBBs, ".thr_comm");
>>  }
>> 
>>  // Okay, we decided to do this!  Clone all the instructions in BB onto the end
>> 
>> Added: llvm/trunk/test/Transforms/JumpThreading/update-edge-weight.ll
>> URL: http://llvm.org/viewvc/llvm-project/llvm/trunk/test/Transforms/JumpThreading/update-edge-weight.ll?rev=250089&view=auto
>> ==============================================================================
>> --- llvm/trunk/test/Transforms/JumpThreading/update-edge-weight.ll (added)
>> +++ llvm/trunk/test/Transforms/JumpThreading/update-edge-weight.ll Mon Oct 12 14:44:08 2015
>> @@ -0,0 +1,43 @@
>> +; RUN: opt -S -jump-threading %s | FileCheck %s
>> +
>> +; Test if edge weights are properly updated after jump threading.
>> +
>> +; CHECK: !2 = !{!"branch_weights", i32 22, i32 7}
>> +
>> +define void @foo(i32 %n) !prof !0 {
>> +entry:
>> +  %cmp = icmp sgt i32 %n, 10
>> +  br i1 %cmp, label %if.then.1, label %if.else.1, !prof !1
>> +
>> +if.then.1:
>> +  tail call void @a()
>> +  br label %if.cond
>> +
>> +if.else.1:
>> +  tail call void @b()
>> +  br label %if.cond
>> +
>> +if.cond:
>> +  %cmp1 = icmp sgt i32 %n, 5
>> +  br i1 %cmp1, label %if.then.2, label %if.else.2, !prof !2
>> +
>> +if.then.2:
>> +  tail call void @c()
>> +  br label %if.end
>> +
>> +if.else.2:
>> +  tail call void @d()
>> +  br label %if.end
>> +
>> +if.end:
>> +  ret void
>> +}
>> +
>> +declare void @a()
>> +declare void @b()
>> +declare void @c()
>> +declare void @d()
>> +
>> +!0 = !{!"function_entry_count", i64 1}
>> +!1 = !{!"branch_weights", i32 10, i32 5}
>> +!2 = !{!"branch_weights", i32 10, i32 1}
>> 
>> 
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