[BlockFrequencyInfo] Handling nested irreducible CFG with geometric series and top-down prorogation

[kula]

Summary

This patch implements the TODOs in BlockFrequencyInfoImpl.h.

1. handle nested irreducible loop.
2. true weight distribution among multi-heads of irreducible loop, instead of even split + adjustment by backedge later.
3. Use geometric series instead of loop scale for mass iteration. loop scale are still used, but for the purpose of scaling down local mass below 1.0.
4. normal code path for reducible loop is not affected.

This patch passes all regression test. Several test cases are changed accordingly. I've changed the @nonentry_header case in irreducible.ll to use
huge weight on the switch instruction to show that 'bottom' block should not be hot.

Method:

1. for loop a, found all SCCs, create SCC loops and adjust nodes in its parent node list accordingly.
2. In topological order, propagate mass on all SCCs where non-trivial SCCs incur resursion.
3. compute start term of geometric series.
4. for each header, compute its ratio of geometric series by propogation full mass starting from itself and other block hass empty mass. The cumulated backege mass is ratio.
5. find the max ratio among headers.
6. compute local scaled down mass for all headers with geometric series equation [a/(1-r)]. assume n is infinity. I've add a TODO in file to see if we should use [a*(1-r^n)/(1-r)].
7. Propagate with header mass to other blocks in loop.

[kula]

gently ping.

[dnovillo]

I have started going over this patch, but my knowledge of this area is pretty spotty. I defer to Duncan for a better opinion on this.

[kula]

Sounds good.

[kula]

Split out NFC. One bugfix.

[thanm]

Hello,

Nice work, it was interesting to poke through this code and learn a bit about how block frequencies are calculated.

General remarks:

• as w/ previous commenters I think it would be nice to have some concrete case from a real benchmark (spec or otherwise) where you can point to an improvement of some sort as a result of this change

• the original version of the code makes reference to the idea of computing block frequencies using infinite geometric series (original BlockFrequencyInfoImpl.h lines 757, 786), but it is only in the test case (test/Analysis/BlockFrequencyInfo/irreducible.ll) where an actual example is provided along with its associated geometric series. Given that the new implementation is actually doing computing series start terms and ratios, I think it would make much more sense (from a readability perspective) to promote the comments/examples from the test case to the actual code itself.

I've posted more specific nits/comments inline on the Phab review page.

Thanks, Than

include/llvm/Analysis/BlockFrequencyInfoImpl.h

723–726

This comment seems to now be stale -- rewrite?

843

recurisvely => recursively

1192

size_t would be a better type for "i" (when I do a build with this patch I get a warning about signed/unsigned comparison)

1274

typo geometirc => geometric

include/llvm/Analysis/BlockFrequencyInfoImpl.h

 #include "llvm/IR/BasicBlock.h"
 #include "llvm/Support/BlockFrequency.h"
 #include "llvm/Support/BranchProbability.h"
 #include "llvm/Support/Debug.h"
 #include "llvm/Support/ScaledNumber.h"
 #include "llvm/Support/raw_ostream.h"
 #include <deque>
 #include <list>
+#include <map>
 #include <string>
 #include <vector>
 
 #define DEBUG_TYPE "block-freq"
 
 namespace llvm {
 
 class BasicBlock;
struct FrequencyData {
     uint64_t Integer;
   };
 
   /// \brief Data about a loop.
   ///
   /// Contains the data necessary to represent a loop as a pseudo-node once it's
   /// packaged.
   struct LoopData {
-    typedef SmallVector<std::pair<BlockNode, BlockMass>, 4> ExitMap;
+    typedef std::pair<BlockNode, BlockMass> EdgeMass;
+    typedef SmallVector<EdgeMass, 4> ExitMap;
+    typedef SmallVector<EdgeMass, 4> HeaderMassList;
     typedef SmallVector<BlockNode, 4> NodeList;
-    typedef SmallVector<BlockMass, 1> HeaderMassList;
     LoopData *Parent;            ///< The parent loop.
     bool IsPackaged;             ///< Whether this has been packaged.
     uint32_t NumHeaders;         ///< 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), IsPackaged(false), NumHeaders(1), Nodes(1, Header),
-          BackedgeMass(1) {}
+        : Parent(Parent), IsPackaged(false), NumHeaders(1), Nodes(1, Header) {}
     template <class It1, class It2>
     LoopData(LoopData *Parent, It1 FirstHeader, It1 LastHeader, It2 FirstOther,
              It2 LastOther)
         : Parent(Parent), IsPackaged(false), Nodes(FirstHeader, LastHeader) {
       NumHeaders = Nodes.size();
       Nodes.insert(Nodes.end(), FirstOther, LastOther);
-      BackedgeMass.resize(NumHeaders);
+      BackedgeMass.reserve(NumHeaders);
     }
     bool isHeader(const BlockNode &Node) const {
       if (isIrreducible())
         return std::binary_search(Nodes.begin(), Nodes.begin() + NumHeaders,
                                   Node);
       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) -
-               Nodes.begin();
-      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());
     }
   };
 
   /// \brief Index of loop information.
   struct WorkingData {
     BlockNode Node; ///< This node.
     LoopData *Loop; ///< The loop this block is inside.
     BlockMass Mass; ///< Mass distribution from the entry block.
 
     WorkingData(const BlockNode &Node) : Node(Node), Loop(nullptr) {}
 
     bool isLoopHeader() const { return Loop && Loop->isHeader(Node); }
-    bool isDoubleLoopHeader() const {
-      return isLoopHeader() && Loop->Parent && Loop->Parent->isIrreducible() &&
-             Loop->Parent->isHeader(Node);
-    }
 
     LoopData *getContainingLoop() const {
-      if (!isLoopHeader())
-        return Loop;
-      if (!isDoubleLoopHeader())
+      if (Loop && Loop->getHeader() == Node)
         return Loop->Parent;
-      return Loop->Parent->Parent;
+      return Loop;
     }
 
     /// \brief 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
struct WorkingData {
     }
 
     /// \brief 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())
+      if (isAPackage())
         return Loop->Mass;
-      return Loop->Parent->Mass;
+      return Mass;
     }
 
     /// \brief Has ContainingLoop been packaged up?
     bool isPackaged() const { return getResolvedNode() != Node; }
     /// \brief Has Loop been packaged up?
     bool isAPackage() const { return isLoopHeader() && Loop->IsPackaged; }
-    /// \brief Has Loop been packaged up twice?
-    bool isADoublePackage() const {
-      return isDoubleLoopHeader() && Loop->Parent->IsPackaged;
-    }
   };
 
   /// \brief 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
public:
   /// 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());
-    assert(Working[Head.Index].isLoopHeader());
-    return *Working[Head.Index].Loop;
-  }
-
-  /// \brief 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.
-  iterator_range<std::list<LoopData>::iterator>
-  analyzeIrreducible(const bfi_detail::IrreducibleGraph &G, LoopData *OuterLoop,
-                     std::list<LoopData>::iterator Insert);
+  typedef std::vector<BlockNode> NodeVecTy;
+  typedef std::vector<std::pair<LoopData *, NodeVecTy>> SCCLoopVecTy;
 
   /// \brief 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);
+  /// Update \c OuterLoop. For subloops that contain nodes that are also the
+  /// header of OuterLoop, move their first header to OuterLoop header list.
+  /// Also, nodes that were packaged up need to be removed from \a
+  /// OuterLoop::Nodes.
+  void updateLoopWithIrreducible(LoopData &OuterLoop, SCCLoopVecTy &SCCs);
 
   /// \brief Distribute mass according to a distribution.
   ///
-  /// Distributes the mass in Source according to Dist.  If LoopHead.isValid(),
+  /// Distributes the mass 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);
+  void distributeMass(const BlockMass &Mass, LoopData *OuterLoop,
+                      Distribution &Dist, bool PropagateBackedge = false);
 
   /// \brief Compute the loop scale for a loop.
   void computeLoopScale(LoopData &Loop);
 
-  /// Adjust the mass of all headers in an irreducible loop.
+  /// \brief Create subloops and single nodes from irreducible graph.
   ///
-  /// 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);
+  /// Divide nodes of irreducible graph into nodes of subloops and standalone
+  /// nodes. For each subloop, save those trivial SCC that are before it
+  /// in topological order. LeftSCCs are those trivial SCCs that are after all
+  /// subloops.
+  void createSCCLoop(LoopData *OuterLoop, const bfi_detail::IrreducibleGraph &G,
+                     std::list<LoopData>::iterator Insert, NodeVecTy &LeftSCCs,
+                     SCCLoopVecTy &SCCs);
 
   /// \brief Package up a loop.
   void packageLoop(LoopData &Loop);
 
   /// \brief Unwrap loops.
   void unwrapLoops();
 
   /// \brief Finalize frequency metrics.

 ///
 ///     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
template <class BT> class BlockFrequencyInfoImpl : BlockFrequencyInfoImplBase {
   void initializeLoops();
 
   /// \brief 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);
+  bool propagateMassToSuccessors(LoopData *OuterLoop, const BlockNode &Node,
+                                 bool PropagateBackedge = false);
 
   /// \brief 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);
 
   /// \brief 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();
 
+  /// pair.first is start term, pair.second is ratio.
+  typedef std::map<BlockNode, std::pair<BlockMass, BlockMass>>
+      GeometricMeanInfo;
+
+  /// \brief Compute geometric series start term for headers.
+  ///
+  /// Propagate mass on each node of \c Loop in topological order. For
+  /// subloops, recurisvely call \c computeIrreducibleMass to calculate its
+  /// local frequency and exits weights distribution. Store calculated terms
+  /// in \c HeaderData.
+  void computeStartTerm(GeometricMeanInfo &HeaderData, LoopData *Loop,
+                        SCCLoopVecTy &SubLoops, NodeVecTy &LeftSCCs,
+                        std::list<LoopData>::iterator Insert);
+
+  /// \brief Compute geometric series ratio for headers.
+  ///
+  /// Use \c Loop::scale to scale down mass of blocks. Otherwise there will be
+  /// overflow when propagating for computing ratio. Set default \c Loop::scale
+  /// to 1.0.
+  void computeGeometricRatio(GeometricMeanInfo &HeaderData, LoopData &Loop);
+
+  /// \brief Compute loop scale and block masses of irregular loop.
+  ///
+  /// With computed start term and ratio in \c HeaderData, compute scaled block
+  /// mass.
+  void computeScaledBlockMass(GeometricMeanInfo &HeaderData, LoopData &Loop);
+
   /// \brief 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
for (size_t Index = 0; Index < RPOT.size(); ++Index) {
     HeaderData.Loop->Nodes.push_back(Index);
     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))
-      continue;
+  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))
-      continue;
-    llvm_unreachable("unhandled irreducible control flow");
     }
 }
 
 template <class BT>
 bool BlockFrequencyInfoImpl<BT>::computeMassInLoop(LoopData &Loop) {
   // Compute mass in loop.
   DEBUG(dbgs() << "compute-mass-in-loop: " << getLoopName(Loop) << "\n");
-
-  if (Loop.isIrreducible()) {
-    BlockMass Remaining = BlockMass::getFull();
-    for (uint32_t H = 0; H < Loop.NumHeaders; ++H) {
-      auto &Mass = Working[Loop.Nodes[H].Index].getMass();
-      Mass = Remaining * BranchProbability(1, Loop.NumHeaders - H);
-      Remaining -= Mass;
-    }
-    for (const BlockNode &M : Loop.Nodes)
-      if (!propagateMassToSuccessors(&Loop, M))
-        llvm_unreachable("unhandled irreducible control flow");
-
-    adjustLoopHeaderMass(Loop);
-  } 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;
-  }
+  assert(!Loop.isIrreducible() && "Irreducible loop don't need this");
 
   computeLoopScale(Loop);
   packageLoop(Loop);
   return true;
 }
 
 template <class BT>
 bool BlockFrequencyInfoImpl<BT>::tryToComputeMassInFunction() {
bool BlockFrequencyInfoImpl<BT>::tryToComputeMassInFunction() {
   }
   return true;
 }
 
 template <class BT> void BlockFrequencyInfoImpl<BT>::computeMassInFunction() {
   if (tryToComputeMassInFunction())
     return;
   computeIrreducibleMass(nullptr, Loops.begin());
-  if (tryToComputeMassInFunction())
-    return;
-  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 {
   typedef BT BlockT;
   typedef BlockFrequencyInfoImplBase::LoopData LoopData;
   typedef GraphTraits<const BlockT *> Successor;
 
   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 (auto I = Successor::child_begin(BB), E = Successor::child_end(BB);
          I != E; ++I)
       G.addEdge(Irr, BFI.getNode(*I), OuterLoop);
   }
 };
 }
 template <class BT>
+void BlockFrequencyInfoImpl<BT>::computeStartTerm(
+    GeometricMeanInfo &HeaderData, LoopData *Loop, SCCLoopVecTy &SubLoops,
+    NodeVecTy &LeftSCCs, std::list<LoopData>::iterator Insert) {
+  for (auto &S : SubLoops) {
+    // First propagate mass on subloop's dependence nodes.
+    for (const auto Node : S.second)
+      if (!propagateMassToSuccessors(Loop, Node, true))
+        llvm_unreachable("unhandled irreducible control flow");
+
+    // Save accumulated header mass of current subloop. After local mass of
+    // current subloop is recursively computed, we use this total mass to
+    // propagate through it.
+    BlockMass TotalInputMass = std::accumulate(
+        S.first->Nodes.begin(), S.first->Nodes.begin() + S.first->NumHeaders,
+        BlockMass::getEmpty(), [this](BlockMass &T, BlockNode &N) {
+          return T += Working[N.Index].getMass();
+        });
+
+    // Recusively compute local mass of subloop
+    auto Next = std::next(Insert);
+    computeIrreducibleMass(S.first, Insert);
+    Insert = Next;
+
+    DEBUG(dbgs() << "propagate on subloop node\n");
+    S.first->Mass = TotalInputMass;
+    if (!propagateMassToSuccessors(Loop, S.first->getHeader()))
+      llvm_unreachable("unhandled irreducible control flow");
+  }
+  DEBUG(dbgs() << "propagate on the rest of the nodes\n");
+  for (auto Node : LeftSCCs)
+    if (!propagateMassToSuccessors(Loop, Node))
+      llvm_unreachable("unhandled irreducible control flow");
+
+  if (!(Loop && Loop->isIrreducible()))
+    return;
+
+  // Add backedge weight to their target node.
+  for (const auto &I : Loop->BackedgeMass)
+    Working[I.first.Index].getMass() += I.second;
+
+  // Save all start terms
+  for (uint32_t H = 0; H < Loop->NumHeaders; ++H) {
+    auto &HeaderNode = Loop->Nodes[H];
+    auto &HeaderMass = Working[HeaderNode.Index].getMass();
+    HeaderData[HeaderNode].first = HeaderMass;
+  }
+}
+
+template <class BT>
+void BlockFrequencyInfoImpl<BT>::computeGeometricRatio(
+    GeometricMeanInfo &HeaderData, LoopData &Loop) {
+  Loop.Scale = BlockMass::getFull().toScaled();
+  LoopData::NodeList SortedNodes = Loop.Nodes;
+  std::sort(SortedNodes.begin(), SortedNodes.end());
+  for (uint32_t H = 0; H < Loop.NumHeaders; ++H) {
+    Loop.BackedgeMass.clear();
+    for (auto N : SortedNodes)
+      Working[N.Index].getMass() = BlockMass::getEmpty();
+
+    auto &HeaderNode = Loop.Nodes[H];
+    auto &HeaderMass = Working[HeaderNode.Index].getMass();
+    HeaderMass = BlockMass::getFull();
+    auto It = std::find(SortedNodes.begin(), SortedNodes.end(), HeaderNode);
+    for (int i = 0; i < SortedNodes.size(); ++i, ++It) {
+      if (It == SortedNodes.end())
+        It = SortedNodes.begin();
+      if (!propagateMassToSuccessors(&Loop, *It, true))
+        llvm_unreachable("irreducible control flow to loop header!?");
+    }
+    for (const auto &I : Loop.BackedgeMass)
+      if (I.first == HeaderNode)
+        HeaderData[HeaderNode].second += I.second;
+
+    // compute ratio to find loop scale.
+    // TODO use a(1-r^n)/(1-r) requires n, which a the loop scale we could have
+    // computed during start term computing propagation. Here it is simplified
+    // to use a/(1-r).
+    BlockMass LeftMass = BlockMass::getFull() - HeaderData[HeaderNode].second;
+    Scaled64 S = LeftMass.toScaled().inverse();
+    if (S > Loop.Scale)
+      Loop.Scale = S;
+  }
+}
+
+template <class BT>
+void BlockFrequencyInfoImpl<BT>::computeScaledBlockMass(
+    GeometricMeanInfo &HeaderData, LoopData &Loop) {
+  // Clear mass.
+  Loop.Exits.clear();
+  for (const BlockNode &N : Loop.Nodes)
+    Working[N.Index].getMass() = BlockMass::getEmpty();
+
+  // Set scaled header mass.
+  for (uint32_t H = 0; H < Loop.NumHeaders; ++H) {
+    auto &HeaderNode = Loop.Nodes[H];
+    auto &AR = HeaderData[HeaderNode];
+    BlockMass LeftMass = BlockMass::getFull() - AR.second;
+    Scaled64 S = LeftMass.toScaled().inverse();
+    // Scale down header mass by loop scale. It will be scaled back when
+    // unwrapping loops.
+    S /= Loop.Scale;
+    uint64_t HeaderMass = S.scale(AR.first.getMass());
+    Working[HeaderNode.Index].getMass() = BlockMass(HeaderMass);
+  }
+
+  for (const BlockNode &M : Loop.Nodes)
+    if (!propagateMassToSuccessors(&Loop, M))
+      llvm_unreachable("irreducible control flow to loop header!?");
+}
+
+template <class BT>
 void BlockFrequencyInfoImpl<BT>::computeIrreducibleMass(
-    LoopData *OuterLoop, std::list<LoopData>::iterator Insert) {
-  DEBUG(dbgs() << "analyze-irreducible-in-";
-        if (OuterLoop) dbgs() << "loop: " << getLoopName(*OuterLoop) << "\n";
+    LoopData *Loop, std::list<LoopData>::iterator Insert) {
+  DEBUG(dbgs() << "computeIrreducibleMass-in-";
+        if (Loop) dbgs() << "loop: " << getLoopName(*Loop) << "\n";
         else dbgs() << "function\n");
 
+  // Collect weight distribution among headers since IrreducibleGraph ctor
+  // would reset block mass.
+  Distribution Dist;
+  if (Loop) {
+    for (uint32_t H = 0; H < Loop->NumHeaders; ++H) {
+      auto &HeaderNode = Loop->Nodes[H];
+      auto HeaderMass = Working[HeaderNode.Index].getMass().getMass();
+      if (HeaderMass > 0)
+        Dist.addLocal(HeaderNode, HeaderMass);
+      else
+        DEBUG(dbgs() << "   Nothing added. Header mass is zero\n");
+    }
+  } else {
+    WorkingData &Entry = Working[0];
+    Dist.addLocal(Entry.Node, UINT64_C(100));
+  }
+
   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);
+  IrreducibleGraph G(*this, Loop, addBlockEdges);
+
+  // Resolve dependency using SCC.
+  NodeVecTy LeftSCCs;
+  SCCLoopVecTy SubLoops;
+  createSCCLoop(Loop, G, Insert, LeftSCCs, SubLoops);
 
-  for (auto &L : analyzeIrreducible(G, OuterLoop, Insert))
-    computeMassInLoop(L);
+  // To calculate the geometirc series, we need start term(a) and ratio(r). The
+  // final block freq is a/(1-r).
+  GeometricMeanInfo HeaderData;
 
-  if (!OuterLoop)
+  // Distribute mass among headers according to their input relative weight.
+  distributeMass(BlockMass::getFull(), nullptr, Dist);
+
+  computeStartTerm(HeaderData, Loop, SubLoops, LeftSCCs, Insert);
+  if (!Loop)
     return;
-  updateLoopWithIrreducible(*OuterLoop);
+  if (Loop->isIrreducible()) {
+    computeGeometricRatio(HeaderData, *Loop);
+    computeScaledBlockMass(HeaderData, *Loop);
+  } else
+    computeLoopScale(*Loop);
+  packageLoop(*Loop);
 }
 
 namespace {
 // A helper function that converts a branch probability into weight.
 inline uint32_t getWeightFromBranchProb(const BranchProbability Prob) {
   return Prob.getNumerator();
 }
 } // namespace
 
 template <class BT>
-bool
-BlockFrequencyInfoImpl<BT>::propagateMassToSuccessors(LoopData *OuterLoop,
-                                                      const BlockNode &Node) {
+bool BlockFrequencyInfoImpl<BT>::propagateMassToSuccessors(
+    LoopData *OuterLoop, const BlockNode &Node, bool PropagateBackedge) {
   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 = Successor::child_begin(BB), SE = Successor::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);
+  BlockMass Mass = Working[Node.Index].getMass();
+  distributeMass(Mass, OuterLoop, Dist, PropagateBackedge);
   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";

lib/Analysis/BlockFrequencyInfoImpl.cpp

 #endif
 
   if (isLoopHeader(Resolved)) {
     DEBUG(debugSuccessor("backedge"));
     Dist.addBackedge(Resolved, Weight);
     return true;
   }
 
-  if (Working[Resolved.Index].getContainingLoop() != OuterLoop) {
+  LoopData *SuccLoop = Working[Resolved.Index].getContainingLoop();
+  // Edge goes into subloop should not be exit edge.
+  if (!SuccLoop || SuccLoop->Parent != OuterLoop)
+    if (SuccLoop != OuterLoop) {
       DEBUG(debugSuccessor("  exit  "));
       Dist.addExit(Resolved, Weight);
       return true;
     }
 
   if (Resolved < Pred) {
     if (!isLoopHeader(Pred)) {
       // If OuterLoop is an irreducible loop, we can't actually handle this.
       assert((!OuterLoop || !OuterLoop->isIrreducible()) &&
              "unhandled irreducible control flow");
 
       // Irreducible backedge.  Abort.
void BlockFrequencyInfoImplBase::computeLoopScale(LoopData &Loop) {
   // appropriately describe the loop as having a large scale, without skewing
   // the final frequency computation.
   const Scaled64 InifiniteLoopScale(1, 12);
 
   // LoopScale == 1 / ExitMass
   // ExitMass == HeadMass - BackedgeMass
   BlockMass TotalBackedgeMass;
   for (auto &Mass : Loop.BackedgeMass)
-    TotalBackedgeMass += Mass;
+    TotalBackedgeMass += Mass.second;
   BlockMass ExitMass = BlockMass::getFull() - TotalBackedgeMass;
 
   // Block scale stores the inverse of the scale. If this is an infinite loop,
   // its exit mass will be zero. In this case, use an arbitrary scale for the
   // loop scale.
   Loop.Scale =
       ExitMass.isEmpty() ? InifiniteLoopScale : ExitMass.toScaled().inverse();
 
static void debugAssign(const BlockFrequencyInfoImplBase &BFI,
   if (Desc)
     dbgs() << " [" << Desc << "]";
   if (T.isValid())
     dbgs() << " to " << BFI.getBlockName(T);
   dbgs() << "\n";
 }
 #endif
 
-void BlockFrequencyInfoImplBase::distributeMass(const BlockNode &Source,
+void BlockFrequencyInfoImplBase::distributeMass(const BlockMass &Mass,
                                                 LoopData *OuterLoop,
-                                                Distribution &Dist) {
-  BlockMass Mass = Working[Source.Index].getMass();
+                                                Distribution &Dist,
+                                                bool PropagateBackedge) {
   DEBUG(dbgs() << "  => mass:  " << Mass << "\n");
 
   // Distribute mass to successors as laid out in Dist.
   DitheringDistributer D(Dist, Mass);
 
   for (const Weight &W : Dist.Weights) {
     // Check for a local edge (non-backedge and non-exit).
     BlockMass Taken = D.takeMass(W.Amount);
     if (W.Type == Weight::Local) {
       Working[W.TargetNode.Index].getMass() += Taken;
       DEBUG(debugAssign(*this, D, W.TargetNode, Taken, nullptr));
       continue;
     }
 
     // Backedges and exits only make sense if we're processing a loop.
     assert(OuterLoop && "backedge or exit outside of loop");
 
     // Check for a backedge.
     if (W.Type == Weight::Backedge) {
-      OuterLoop->BackedgeMass[OuterLoop->getHeaderIndex(W.TargetNode)] += Taken;
+      OuterLoop->BackedgeMass.push_back(std::make_pair(W.TargetNode, Taken));
       DEBUG(debugAssign(*this, D, W.TargetNode, Taken, "back"));
+      if (PropagateBackedge && OuterLoop->isIrreducible())
+        Working[W.TargetNode.Index].getMass() += Taken;
       continue;
     }
 
     // This must be an exit.
     assert(W.Type == Weight::Exit);
     OuterLoop->Exits.push_back(std::make_pair(W.TargetNode, Taken));
     DEBUG(debugAssign(*this, D, W.TargetNode, Taken, "exit"));
   }

 
 void IrreducibleGraph::indexNodes() {
   for (auto &I : Nodes)
     Lookup[I.Node.Index] = &I;
 }
 
 void IrreducibleGraph::addEdge(IrrNode &Irr, const BlockNode &Succ,
                                const BFIBase::LoopData *OuterLoop) {
-  if (OuterLoop && OuterLoop->isHeader(Succ))
+  if (OuterLoop) {
+    if (OuterLoop->isIrreducible()) {
+      // do not add retreating edge.
+      if (OuterLoop->getHeader() == Succ)
+        return;
+    } else {
+      // do not add back edge of OuterLoop
+      if (OuterLoop->isHeader(Succ))
         return;
+    }
+  }
+  // do not add exiting edge of OuterLoop
   auto L = Lookup.find(Succ.Index);
   if (L == Lookup.end())
     return;
   IrrNode &SuccIrr = *L->second;
   Irr.Edges.push_back(&SuccIrr);
   SuccIrr.Edges.push_front(&Irr);
   ++SuccIrr.NumIn;
 }

 };
 } // end namespace llvm
 
 /// \brief Find extra irreducible headers.
 ///
 /// Find entry blocks and other blocks with backedges, which exist when \c G
 /// contains irreducible sub-SCCs.
 static void findIrreducibleHeaders(
-    const BlockFrequencyInfoImplBase &BFI,
-    const IrreducibleGraph &G,
+    const BlockFrequencyInfoImplBase &BFI, LoopData *OuterLoop,
     const std::vector<const IrreducibleGraph::IrrNode *> &SCC,
     LoopData::NodeList &Headers, LoopData::NodeList &Others) {
   // Map from nodes in the SCC to whether it's an entry block.
   SmallDenseMap<const IrreducibleGraph::IrrNode *, bool, 8> InSCC;
 
   // InSCC also acts the set of nodes in the graph.  Seed it.
   for (const auto *I : SCC)
     InSCC[I] = false;
 
   for (auto I = InSCC.begin(), E = InSCC.end(); I != E; ++I) {
     auto &Irr = *I->first;
-    for (const auto *P : make_range(Irr.pred_begin(), Irr.pred_end())) {
-      if (InSCC.count(P))
-        continue;
-
+    for (const auto *P : make_range(Irr.pred_begin(), Irr.pred_end()))
+      if (!InSCC.count(P)) {
         // This is an entry block.
         I->second = true;
-      Headers.push_back(Irr.Node);
-      DEBUG(dbgs() << "  => entry = " << BFI.getBlockName(Irr.Node) << "\n");
         break;
       }
-  }
-  assert(Headers.size() >= 2 &&
-         "Expected irreducible CFG; -loop-info is likely invalid");
-  if (Headers.size() == InSCC.size()) {
-    // Every block is a header.
-    std::sort(Headers.begin(), Headers.end());
-    return;
-  }
-
-  // Look for extra headers from irreducible sub-SCCs.
-  for (const auto &I : InSCC) {
-    // Entry blocks are already headers.
-    if (I.second)
-      continue;
-
-    auto &Irr = *I.first;
-    for (const auto *P : make_range(Irr.pred_begin(), Irr.pred_end())) {
-      // Skip forward edges.
-      if (P->Node < Irr.Node)
-        continue;
 
-      // Skip predecessors from entry blocks.  These can have inverted
-      // ordering.
-      if (InSCC.lookup(P))
-        continue;
-
-      // Store the extra header.
-      Headers.push_back(Irr.Node);
-      DEBUG(dbgs() << "  => extra = " << BFI.getBlockName(Irr.Node) << "\n");
+    // This SCC may share entry with ancestor SCC. In this case, pred of
+    // this node is not in OuterLoop, but more outer scope.
+    if (OuterLoop && !I->second)
+      for (uint32_t H = 0; H < OuterLoop->NumHeaders; ++H)
+        if (OuterLoop->Nodes[H] == Irr.Node) {
+          I->second = true;
           break;
         }
-    if (Headers.back() == Irr.Node)
-      // Added this as a header.
-      continue;
 
-    // This is not a header.
+    if (I->second) {
+      Headers.push_back(Irr.Node);
+      DEBUG(dbgs() << "  => entry = " << BFI.getBlockName(Irr.Node) << "\n");
+    } else {
       Others.push_back(Irr.Node);
-    DEBUG(dbgs() << "  => other = " << BFI.getBlockName(Irr.Node) << "\n");
     }
+  }
+  assert(Headers.size() >= 2 &&
+         "Expected irreducible CFG; -loop-info is likely invalid");
   std::sort(Headers.begin(), Headers.end());
   std::sort(Others.begin(), Others.end());
 }
 
-static void createIrreducibleLoop(
+static LoopData *createIrreducibleLoop(
     BlockFrequencyInfoImplBase &BFI, const IrreducibleGraph &G,
     LoopData *OuterLoop, std::list<LoopData>::iterator Insert,
     const std::vector<const IrreducibleGraph::IrrNode *> &SCC) {
   // Translate the SCC into RPO.
   DEBUG(dbgs() << " - found-scc\n");
 
   LoopData::NodeList Headers;
   LoopData::NodeList Others;
-  findIrreducibleHeaders(BFI, G, SCC, Headers, Others);
+  findIrreducibleHeaders(BFI, OuterLoop, SCC, Headers, Others);
 
   auto Loop = BFI.Loops.emplace(Insert, OuterLoop, Headers.begin(),
                                 Headers.end(), Others.begin(), Others.end());
 
   // Update loop hierarchy.
   for (const auto &N : Loop->Nodes)
-    if (BFI.Working[N.Index].isLoopHeader())
+    if (BFI.Working[N.Index].isLoopHeader() &&
+        !BFI.Working[N.Index].Loop->isIrreducible())
       BFI.Working[N.Index].Loop->Parent = &*Loop;
     else
       BFI.Working[N.Index].Loop = &*Loop;
-}
 
-iterator_range<std::list<LoopData>::iterator>
-BlockFrequencyInfoImplBase::analyzeIrreducible(
-    const IrreducibleGraph &G, LoopData *OuterLoop,
-    std::list<LoopData>::iterator Insert) {
-  assert((OuterLoop == nullptr) == (Insert == Loops.begin()));
-  auto Prev = OuterLoop ? std::prev(Insert) : Loops.end();
-
-  for (auto I = scc_begin(G); !I.isAtEnd(); ++I) {
-    if (I->size() < 2)
-      continue;
-
-    // Translate the SCC into RPO.
-    createIrreducibleLoop(*this, G, OuterLoop, Insert, *I);
-  }
+  return &*Loop;
 
-  if (OuterLoop)
-    return make_range(std::next(Prev), Insert);
-  return make_range(Loops.begin(), Insert);
-}
+void BlockFrequencyInfoImplBase::updateLoopWithIrreducible(
+    LoopData &OuterLoop, SCCLoopVecTy &SubSCCs) {
+  auto &OuterNodes = OuterLoop.Nodes;
+  auto &NumHeader = OuterLoop.NumHeaders;
+  for (auto &kv : SubSCCs) {
+    LoopData *L = kv.first;
+    auto isSubLoopNode = [L](const BlockNode &N) {
+      return std::find(L->Nodes.begin(), L->Nodes.end(), N) != L->Nodes.end();
+    };
 
-void
-BlockFrequencyInfoImplBase::updateLoopWithIrreducible(LoopData &OuterLoop) {
-  OuterLoop.Exits.clear();
-  for (auto &Mass : OuterLoop.BackedgeMass)
-    Mass = BlockMass::getEmpty();
-  auto O = OuterLoop.Nodes.begin() + 1;
-  for (auto I = O, E = OuterLoop.Nodes.end(); I != E; ++I)
-    if (!Working[I->Index].isPackaged())
-      *O++ = *I;
-  OuterLoop.Nodes.erase(O, OuterLoop.Nodes.end());
-}
-
-void BlockFrequencyInfoImplBase::adjustLoopHeaderMass(LoopData &Loop) {
-  assert(Loop.isIrreducible() && "this only makes sense on irreducible loops");
-
-  // Since the loop has more than one header block, the mass flowing back into
-  // each header will be different. Adjust the mass in each header loop to
-  // reflect the masses flowing through back edges.
-  //
-  // To do this, we distribute the initial mass using the backedge masses
-  // as weights for the distribution.
-  BlockMass LoopMass = BlockMass::getFull();
-  Distribution Dist;
-
-  DEBUG(dbgs() << "adjust-loop-header-mass:\n");
-  for (uint32_t H = 0; H < Loop.NumHeaders; ++H) {
-    auto &HeaderNode = Loop.Nodes[H];
-    auto &BackedgeMass = Loop.BackedgeMass[Loop.getHeaderIndex(HeaderNode)];
-    DEBUG(dbgs() << " - Add back edge mass for node "
-                 << getBlockName(HeaderNode) << ": " << BackedgeMass << "\n");
-    if (BackedgeMass.getMass() > 0)
-      Dist.addLocal(HeaderNode, BackedgeMass.getMass());
+    // Remove headers shared with subloop.
+    auto IE = OuterNodes.begin() + NumHeader;
+    auto It = std::remove_if(OuterNodes.begin(), IE, isSubLoopNode);
+    auto NumShareHeader = std::distance(It, IE);
+    OuterNodes.erase(It, IE);
+    if (NumShareHeader > 0) {
+      assert(NumHeader >= NumShareHeader);
+      NumHeader -= NumShareHeader;
+    }
+
+    // Remove other nodes of subloop.
+    OuterNodes.erase(std::remove_if(OuterNodes.begin() + NumHeader,
+                                    OuterNodes.end(), isSubLoopNode),
+                     OuterNodes.end());
+
+    // Add back subloop header.
+    if (NumShareHeader > 0) {
+      OuterNodes.insert(OuterNodes.begin(), L->getHeader());
+      ++NumHeader;
+    } else
+      OuterNodes.push_back(L->getHeader());
+  }
+  std::sort(OuterNodes.begin(), OuterNodes.begin() + NumHeader);
+  std::sort(OuterNodes.begin() + NumHeader, OuterNodes.end());
+}
+
+void BlockFrequencyInfoImplBase::createSCCLoop(
+    LoopData *OuterLoop, const IrreducibleGraph &G,
+    std::list<LoopData>::iterator Insert, NodeVecTy &LeftSingleSCCs,
+    SCCLoopVecTy &SubSCCs) {
+  // Must get all sccs before descend since SCCIterator returns inverse
+  // topological order.
+  LoopData *PrevLoop = nullptr;
+  NodeVecTy SingleSCCs;
+  for (auto I = scc_begin(G); !I.isAtEnd(); ++I)
+    if (I->size() < 2) {
+      assert(I->size() == 1);
+      SingleSCCs.insert(SingleSCCs.begin(), (*I)[0]->Node);
+    } else {
+      // Translate the SCC into RPO.
+      auto L = createIrreducibleLoop(*this, G, OuterLoop, Insert, *I);
+      // SCCIterator gives reverse topological order, make it normal
+      if (PrevLoop)
+        SubSCCs.insert(SubSCCs.begin(), std::make_pair(PrevLoop, SingleSCCs));
       else
-      DEBUG(dbgs() << "   Nothing added. Back edge mass is zero\n");
+        LeftSingleSCCs = SingleSCCs;
+      PrevLoop = L;
+      SingleSCCs.clear();
     }
 
-  DitheringDistributer D(Dist, LoopMass);
+  if (SingleSCCs.empty())
+    return;
+  if (PrevLoop)
+    SubSCCs.insert(SubSCCs.begin(), std::make_pair(PrevLoop, SingleSCCs));
+  else
+    LeftSingleSCCs = SingleSCCs;
 
-  DEBUG(dbgs() << " Distribute loop mass " << LoopMass
-               << " to headers using above weights\n");
-  for (const Weight &W : Dist.Weights) {
-    BlockMass Taken = D.takeMass(W.Amount);
-    assert(W.Type == Weight::Local && "all weights should be local");
-    Working[W.TargetNode.Index].getMass() = Taken;
-    DEBUG(debugAssign(*this, D, W.TargetNode, Taken, nullptr));
-  }
+  if (OuterLoop)
+    updateLoopWithIrreducible(*OuterLoop, SubSCCs);
 }
+

test/Analysis/BlockFrequencyInfo/irreducible.ll

 define void @multientry(i1 %x) {
 ; CHECK-LABEL: Printing analysis {{.*}} for function 'multientry':
 ; CHECK-NEXT: block-frequency-info: multientry
 entry:
 ; CHECK-NEXT: entry: float = 1.0, int = [[ENTRY:[0-9]+]]
   br i1 %x, label %c1, label %c2, !prof !2
 
 c1:
-; CHECK-NEXT: c1: float = 2.0,
+; CHECK-NEXT: c1: float = 2.1429,
 ; The "correct" answer is: float = 2.142857{{[0-9]*}},
   br i1 %x, label %c2, label %exit, !prof !2
 
 c2:
-; CHECK-NEXT: c2: float = 2.0,
+; CHECK-NEXT: c2: float = 1.8571,
 ; The "correct" answer is: float = 1.857142{{[0-9]*}},
   br i1 %x, label %c1, label %exit, !prof !2
 
 exit:
 ; CHECK-NEXT: exit: float = 1.0, int = [[ENTRY]]
   ret void
 }
 

 define void @nonheader(i1 %x) {
 ; CHECK-LABEL: Printing analysis {{.*}} for function 'nonheader':
 ; CHECK-NEXT: block-frequency-info: nonheader
 entry:
 ; CHECK-NEXT: entry: float = 1.0, int = [[ENTRY:[0-9]+]]
   br i1 %x, label %left, label %right, !prof !18
 
 left:
-; CHECK-NEXT: left: float = 1.0,
+; CHECK-NEXT: left: float = 1.07{{[0-9]*}},
   br i1 %x, label %bottom, label %exit, !prof !19
 
 right:
-; CHECK-NEXT: right: float = 1.0,
+; CHECK-NEXT: right: float = 1.28{{[0-9]*}},
   br i1 %x, label %bottom, label %exit, !prof !20
 
 bottom:
-; CHECK-NEXT: bottom: float = 1.0,
+; CHECK-NEXT: bottom: float = 1.14{{[0-9]*}},
   br i1 %x, label %left, label %right, !prof !18
 
 exit:
 ; CHECK-NEXT: exit: float = 1.0, int = [[ENTRY]]
   ret void
 }
 !18 = !{!"branch_weights", i32 1, i32 1}
 !19 = !{!"branch_weights", i32 1, i32 3}
 !20 = !{!"branch_weights", i32 3, i32 1}
 
-; An irreducible SCC with an irreducible sub-SCC.  In the current version of
-; -block-freq, this means an extra header.
-;
-; This testcases uses non-trivial branch weights.  The CHECK statements here
-; will start to fail if we change -block-freq to be more accurate.  Currently,
-; loop headers are affected by the weight of their corresponding back edges.
+; This testcases uses non-trivial branch weights.
 define void @nonentry_header(i1 %x, i2 %y) {
 ; CHECK-LABEL: Printing analysis {{.*}} for function 'nonentry_header':
 ; CHECK-NEXT: block-frequency-info: nonentry_header
 entry:
 ; CHECK-NEXT: entry: float = 1.0, int = [[ENTRY:[0-9]+]]
   br i1 %x, label %left, label %right, !prof !21
 
 left:
-; CHECK-NEXT: left: float = 0.14
+; CHECK-NEXT: left: float = 0.875,
   br i1 %x, label %top, label %bottom, !prof !22
 
 right:
-; CHECK-NEXT: right: float = 0.42
+; CHECK-NEXT: right: float = 107.52,
   br i1 %x, label %top, label %bottom, !prof !22
 
 top:
-; CHECK-NEXT: top: float = 8.43
+; CHECK-NEXT: top: float = 314.69,
   switch i2 %y, label %exit [ i2 0, label %left
                               i2 1, label %right
                               i2 2, label %bottom ], !prof !23
 
 bottom:
-; CHECK-NEXT: bottom: float = 4.5,
+; CHECK-NEXT: bottom: float = 1.1291,
   br label %top
 
 exit:
 ; CHECK-NEXT: exit: float = 1.0, int = [[ENTRY]]
   ret void
 }
 !21 = !{!"branch_weights", i32 2, i32 1}
 !22 = !{!"branch_weights", i32 1, i32 1}
-!23 = !{!"branch_weights", i32 8, i32 1, i32 3, i32 12}
+!23 = !{!"branch_weights", i32 8, i32 1, i32 3000, i32 12}