xref: /external/llvm/lib/Target/Hexagon/RDFLiveness.cpp

//===--- RDFLiveness.cpp --------------------------------------------------===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// Computation of the liveness information from the data-flow graph.
//
// The main functionality of this code is to compute block live-in
// information. With the live-in information in place, the placement
// of kill flags can also be recalculated.
//
// The block live-in calculation is based on the ideas from the following
// publication:
//
// Dibyendu Das, Ramakrishna Upadrasta, Benoit Dupont de Dinechin.
// "Efficient Liveness Computation Using Merge Sets and DJ-Graphs."
// ACM Transactions on Architecture and Code Optimization, Association for
// Computing Machinery, 2012, ACM TACO Special Issue on "High-Performance
// and Embedded Architectures and Compilers", 8 (4),
// <10.1145/2086696.2086706>. <hal-00647369>
//
#include "RDFGraph.h"
#include "RDFLiveness.h"
#include "llvm/ADT/SetVector.h"
#include "llvm/CodeGen/MachineBasicBlock.h"
#include "llvm/CodeGen/MachineDominanceFrontier.h"
#include "llvm/CodeGen/MachineDominators.h"
#include "llvm/CodeGen/MachineFunction.h"
#include "llvm/CodeGen/MachineRegisterInfo.h"
#include "llvm/Target/TargetRegisterInfo.h"

using namespace llvm;
using namespace rdf;

namespace llvm {
namespace rdf {
  template<>
  raw_ostream &operator<< (raw_ostream &OS, const Print<Liveness::RefMap> &P) {
    OS << '{';
    for (auto I : P.Obj) {
      OS << ' ' << Print<RegisterRef>(I.first, P.G) << '{';
      for (auto J = I.second.begin(), E = I.second.end(); J != E; ) {
        OS << Print<NodeId>(*J, P.G);
        if (++J != E)
          OS << ',';
      }
      OS << '}';
    }
    OS << " }";
    return OS;
  }
} // namespace rdf
} // namespace llvm

// The order in the returned sequence is the order of reaching defs in the
// upward traversal: the first def is the closest to the given reference RefA,
// the next one is further up, and so on.
// The list ends at a reaching phi def, or when the reference from RefA is
// covered by the defs in the list (see FullChain).
// This function provides two modes of operation:
// (1) Returning the sequence of reaching defs for a particular reference
// node. This sequence will terminate at the first phi node [1].
// (2) Returning a partial sequence of reaching defs, where the final goal
// is to traverse past phi nodes to the actual defs arising from the code
// itself.
// In mode (2), the register reference for which the search was started
// may be different from the reference node RefA, for which this call was
// made, hence the argument RefRR, which holds the original register.
// Also, some definitions may have already been encountered in a previous
// call that will influence register covering. The register references
// already defined are passed in through DefRRs.
// In mode (1), the "continuation" considerations do not apply, and the
// RefRR is the same as the register in RefA, and the set DefRRs is empty.
//
// [1] It is possible for multiple phi nodes to be included in the returned
// sequence:
//   SubA = phi ...
//   SubB = phi ...
//   ...  = SuperAB(rdef:SubA), SuperAB"(rdef:SubB)
// However, these phi nodes are independent from one another in terms of
// the data-flow.

NodeList Liveness::getAllReachingDefs(RegisterRef RefRR,
      NodeAddr<RefNode*> RefA, bool FullChain, const RegisterSet &DefRRs) {
  SetVector<NodeId> DefQ;
  SetVector<NodeId> Owners;

  // The initial queue should not have reaching defs for shadows. The
  // whole point of a shadow is that it will have a reaching def that
  // is not aliased to the reaching defs of the related shadows.
  NodeId Start = RefA.Id;
  auto SNA = DFG.addr<RefNode*>(Start);
  if (NodeId RD = SNA.Addr->getReachingDef())
    DefQ.insert(RD);

  // Collect all the reaching defs, going up until a phi node is encountered,
  // or there are no more reaching defs. From this set, the actual set of
  // reaching defs will be selected.
  // The traversal upwards must go on until a covering def is encountered.
  // It is possible that a collection of non-covering (individually) defs
  // will be sufficient, but keep going until a covering one is found.
  for (unsigned i = 0; i < DefQ.size(); ++i) {
    auto TA = DFG.addr<DefNode*>(DefQ[i]);
    if (TA.Addr->getFlags() & NodeAttrs::PhiRef)
      continue;
    // Stop at the covering/overwriting def of the initial register reference.
    RegisterRef RR = TA.Addr->getRegRef();
    if (RAI.covers(RR, RefRR)) {
      uint16_t Flags = TA.Addr->getFlags();
      if (!(Flags & NodeAttrs::Preserving))
        continue;
    }
    // Get the next level of reaching defs. This will include multiple
    // reaching defs for shadows.
    for (auto S : DFG.getRelatedRefs(TA.Addr->getOwner(DFG), TA))
      if (auto RD = NodeAddr<RefNode*>(S).Addr->getReachingDef())
        DefQ.insert(RD);
  }

  // Remove all non-phi defs that are not aliased to RefRR, and collect
  // the owners of the remaining defs.
  SetVector<NodeId> Defs;
  for (auto N : DefQ) {
    auto TA = DFG.addr<DefNode*>(N);
    bool IsPhi = TA.Addr->getFlags() & NodeAttrs::PhiRef;
    if (!IsPhi && !RAI.alias(RefRR, TA.Addr->getRegRef()))
      continue;
    Defs.insert(TA.Id);
    Owners.insert(TA.Addr->getOwner(DFG).Id);
  }

  // Return the MachineBasicBlock containing a given instruction.
  auto Block = [this] (NodeAddr<InstrNode*> IA) -> MachineBasicBlock* {
    if (IA.Addr->getKind() == NodeAttrs::Stmt)
      return NodeAddr<StmtNode*>(IA).Addr->getCode()->getParent();
    assert(IA.Addr->getKind() == NodeAttrs::Phi);
    NodeAddr<PhiNode*> PA = IA;
    NodeAddr<BlockNode*> BA = PA.Addr->getOwner(DFG);
    return BA.Addr->getCode();
  };
  // Less(A,B) iff instruction A is further down in the dominator tree than B.
  auto Less = [&Block,this] (NodeId A, NodeId B) -> bool {
    if (A == B)
      return false;
    auto OA = DFG.addr<InstrNode*>(A), OB = DFG.addr<InstrNode*>(B);
    MachineBasicBlock *BA = Block(OA), *BB = Block(OB);
    if (BA != BB)
      return MDT.dominates(BB, BA);
    // They are in the same block.
    bool StmtA = OA.Addr->getKind() == NodeAttrs::Stmt;
    bool StmtB = OB.Addr->getKind() == NodeAttrs::Stmt;
    if (StmtA) {
      if (!StmtB)   // OB is a phi and phis dominate statements.
        return true;
      auto CA = NodeAddr<StmtNode*>(OA).Addr->getCode();
      auto CB = NodeAddr<StmtNode*>(OB).Addr->getCode();
      // The order must be linear, so tie-break such equalities.
      if (CA == CB)
        return A < B;
      return MDT.dominates(CB, CA);
    } else {
      // OA is a phi.
      if (StmtB)
        return false;
      // Both are phis. There is no ordering between phis (in terms of
      // the data-flow), so tie-break this via node id comparison.
      return A < B;
    }
  };

  std::vector<NodeId> Tmp(Owners.begin(), Owners.end());
  std::sort(Tmp.begin(), Tmp.end(), Less);

  // The vector is a list of instructions, so that defs coming from
  // the same instruction don't need to be artificially ordered.
  // Then, when computing the initial segment, and iterating over an
  // instruction, pick the defs that contribute to the covering (i.e. is
  // not covered by previously added defs). Check the defs individually,
  // i.e. first check each def if is covered or not (without adding them
  // to the tracking set), and then add all the selected ones.

  // The reason for this is this example:
  // *d1<A>, *d2<B>, ... Assume A and B are aliased (can happen in phi nodes).
  // *d3<C>              If A \incl BuC, and B \incl AuC, then *d2 would be
  //                     covered if we added A first, and A would be covered
  //                     if we added B first.

  NodeList RDefs;
  RegisterSet RRs = DefRRs;

  auto DefInSet = [&Defs] (NodeAddr<RefNode*> TA) -> bool {
    return TA.Addr->getKind() == NodeAttrs::Def &&
           Defs.count(TA.Id);
  };
  for (auto T : Tmp) {
    if (!FullChain && RAI.covers(RRs, RefRR))
      break;
    auto TA = DFG.addr<InstrNode*>(T);
    bool IsPhi = DFG.IsCode<NodeAttrs::Phi>(TA);
    NodeList Ds;
    for (NodeAddr<DefNode*> DA : TA.Addr->members_if(DefInSet, DFG)) {
      auto QR = DA.Addr->getRegRef();
      // Add phi defs even if they are covered by subsequent defs. This is
      // for cases where the reached use is not covered by any of the defs
      // encountered so far: the phi def is needed to expose the liveness
      // of that use to the entry of the block.
      // Example:
      //   phi d1<R3>(,d2,), ...  Phi def d1 is covered by d2.
      //   d2<R3>(d1,,u3), ...
      //   ..., u3<D1>(d2)        This use needs to be live on entry.
      if (FullChain || IsPhi || !RAI.covers(RRs, QR))
        Ds.push_back(DA);
    }
    RDefs.insert(RDefs.end(), Ds.begin(), Ds.end());
    for (NodeAddr<DefNode*> DA : Ds) {
      // When collecting a full chain of definitions, do not consider phi
      // defs to actually define a register.
      uint16_t Flags = DA.Addr->getFlags();
      if (!FullChain || !(Flags & NodeAttrs::PhiRef))
        if (!(Flags & NodeAttrs::Preserving))
          RRs.insert(DA.Addr->getRegRef());
    }
  }

  return RDefs;
}


static const RegisterSet NoRegs;

NodeList Liveness::getAllReachingDefs(NodeAddr<RefNode*> RefA) {
  return getAllReachingDefs(RefA.Addr->getRegRef(), RefA, false, NoRegs);
}


NodeSet Liveness::getAllReachingDefsRec(RegisterRef RefRR,
      NodeAddr<RefNode*> RefA, NodeSet &Visited, const NodeSet &Defs) {
  // Collect all defined registers. Do not consider phis to be defining
  // anything, only collect "real" definitions.
  RegisterSet DefRRs;
  for (const auto D : Defs) {
    const auto DA = DFG.addr<const DefNode*>(D);
    if (!(DA.Addr->getFlags() & NodeAttrs::PhiRef))
      DefRRs.insert(DA.Addr->getRegRef());
  }

  auto RDs = getAllReachingDefs(RefRR, RefA, true, DefRRs);
  if (RDs.empty())
    return Defs;

  // Make a copy of the preexisting definitions and add the newly found ones.
  NodeSet TmpDefs = Defs;
  for (auto R : RDs)
    TmpDefs.insert(R.Id);

  NodeSet Result = Defs;

  for (NodeAddr<DefNode*> DA : RDs) {
    Result.insert(DA.Id);
    if (!(DA.Addr->getFlags() & NodeAttrs::PhiRef))
      continue;
    NodeAddr<PhiNode*> PA = DA.Addr->getOwner(DFG);
    if (Visited.count(PA.Id))
      continue;
    Visited.insert(PA.Id);
    // Go over all phi uses and get the reaching defs for each use.
    for (auto U : PA.Addr->members_if(DFG.IsRef<NodeAttrs::Use>, DFG)) {
      const auto &T = getAllReachingDefsRec(RefRR, U, Visited, TmpDefs);
      Result.insert(T.begin(), T.end());
    }
  }

  return Result;
}


NodeSet Liveness::getAllReachedUses(RegisterRef RefRR,
      NodeAddr<DefNode*> DefA, const RegisterSet &DefRRs) {
  NodeSet Uses;

  // If the original register is already covered by all the intervening
  // defs, no more uses can be reached.
  if (RAI.covers(DefRRs, RefRR))
    return Uses;

  // Add all directly reached uses.
  NodeId U = DefA.Addr->getReachedUse();
  while (U != 0) {
    auto UA = DFG.addr<UseNode*>(U);
    auto UR = UA.Addr->getRegRef();
    if (RAI.alias(RefRR, UR) && !RAI.covers(DefRRs, UR))
      Uses.insert(U);
    U = UA.Addr->getSibling();
  }

  // Traverse all reached defs.
  for (NodeId D = DefA.Addr->getReachedDef(), NextD; D != 0; D = NextD) {
    auto DA = DFG.addr<DefNode*>(D);
    NextD = DA.Addr->getSibling();
    auto DR = DA.Addr->getRegRef();
    // If this def is already covered, it cannot reach anything new.
    // Similarly, skip it if it is not aliased to the interesting register.
    if (RAI.covers(DefRRs, DR) || !RAI.alias(RefRR, DR))
      continue;
    NodeSet T;
    if (DA.Addr->getFlags() & NodeAttrs::Preserving) {
      // If it is a preserving def, do not update the set of intervening defs.
      T = getAllReachedUses(RefRR, DA, DefRRs);
    } else {
      RegisterSet NewDefRRs = DefRRs;
      NewDefRRs.insert(DR);
      T = getAllReachedUses(RefRR, DA, NewDefRRs);
    }
    Uses.insert(T.begin(), T.end());
  }
  return Uses;
}


void Liveness::computePhiInfo() {
  RealUseMap.clear();

  NodeList Phis;
  NodeAddr<FuncNode*> FA = DFG.getFunc();
  auto Blocks = FA.Addr->members(DFG);
  for (NodeAddr<BlockNode*> BA : Blocks) {
    auto Ps = BA.Addr->members_if(DFG.IsCode<NodeAttrs::Phi>, DFG);
    Phis.insert(Phis.end(), Ps.begin(), Ps.end());
  }

  // phi use -> (map: reaching phi -> set of registers defined in between)
  std::map<NodeId,std::map<NodeId,RegisterSet>> PhiUp;
  std::vector<NodeId> PhiUQ;  // Work list of phis for upward propagation.

  // Go over all phis.
  for (NodeAddr<PhiNode*> PhiA : Phis) {
    // Go over all defs and collect the reached uses that are non-phi uses
    // (i.e. the "real uses").
    auto &RealUses = RealUseMap[PhiA.Id];
    auto PhiRefs = PhiA.Addr->members(DFG);

    // Have a work queue of defs whose reached uses need to be found.
    // For each def, add to the queue all reached (non-phi) defs.
    SetVector<NodeId> DefQ;
    NodeSet PhiDefs;
    for (auto R : PhiRefs) {
      if (!DFG.IsRef<NodeAttrs::Def>(R))
        continue;
      DefQ.insert(R.Id);
      PhiDefs.insert(R.Id);
    }
    for (unsigned i = 0; i < DefQ.size(); ++i) {
      NodeAddr<DefNode*> DA = DFG.addr<DefNode*>(DefQ[i]);
      NodeId UN = DA.Addr->getReachedUse();
      while (UN != 0) {
        NodeAddr<UseNode*> A = DFG.addr<UseNode*>(UN);
        if (!(A.Addr->getFlags() & NodeAttrs::PhiRef))
          RealUses[getRestrictedRegRef(A)].insert(A.Id);
        UN = A.Addr->getSibling();
      }
      NodeId DN = DA.Addr->getReachedDef();
      while (DN != 0) {
        NodeAddr<DefNode*> A = DFG.addr<DefNode*>(DN);
        for (auto T : DFG.getRelatedRefs(A.Addr->getOwner(DFG), A)) {
          uint16_t Flags = NodeAddr<DefNode*>(T).Addr->getFlags();
          // Must traverse the reached-def chain. Consider:
          //   def(D0) -> def(R0) -> def(R0) -> use(D0)
          // The reachable use of D0 passes through a def of R0.
          if (!(Flags & NodeAttrs::PhiRef))
            DefQ.insert(T.Id);
        }
        DN = A.Addr->getSibling();
      }
    }
    // Filter out these uses that appear to be reachable, but really
    // are not. For example:
    //
    // R1:0 =          d1
    //      = R1:0     u2     Reached by d1.
    //   R0 =          d3
    //      = R1:0     u4     Still reached by d1: indirectly through
    //                        the def d3.
    //   R1 =          d5
    //      = R1:0     u6     Not reached by d1 (covered collectively
    //                        by d3 and d5), but following reached
    //                        defs and uses from d1 will lead here.
    auto HasDef = [&PhiDefs] (NodeAddr<DefNode*> DA) -> bool {
      return PhiDefs.count(DA.Id);
    };
    for (auto UI = RealUses.begin(), UE = RealUses.end(); UI != UE; ) {
      // For each reached register UI->first, there is a set UI->second, of
      // uses of it. For each such use, check if it is reached by this phi,
      // i.e. check if the set of its reaching uses intersects the set of
      // this phi's defs.
      auto &Uses = UI->second;
      for (auto I = Uses.begin(), E = Uses.end(); I != E; ) {
        auto UA = DFG.addr<UseNode*>(*I);
        NodeList RDs = getAllReachingDefs(UI->first, UA);
        if (std::any_of(RDs.begin(), RDs.end(), HasDef))
          ++I;
        else
          I = Uses.erase(I);
      }
      if (Uses.empty())
        UI = RealUses.erase(UI);
      else
        ++UI;
    }

    // If this phi reaches some "real" uses, add it to the queue for upward
    // propagation.
    if (!RealUses.empty())
      PhiUQ.push_back(PhiA.Id);

    // Go over all phi uses and check if the reaching def is another phi.
    // Collect the phis that are among the reaching defs of these uses.
    // While traversing the list of reaching defs for each phi use, collect
    // the set of registers defined between this phi (Phi) and the owner phi
    // of the reaching def.
    for (auto I : PhiRefs) {
      if (!DFG.IsRef<NodeAttrs::Use>(I))
        continue;
      NodeAddr<UseNode*> UA = I;
      auto &UpMap = PhiUp[UA.Id];
      RegisterSet DefRRs;
      for (NodeAddr<DefNode*> DA : getAllReachingDefs(UA)) {
        if (DA.Addr->getFlags() & NodeAttrs::PhiRef)
          UpMap[DA.Addr->getOwner(DFG).Id] = DefRRs;
        else
          DefRRs.insert(DA.Addr->getRegRef());
      }
    }
  }

  if (Trace) {
    dbgs() << "Phi-up-to-phi map:\n";
    for (auto I : PhiUp) {
      dbgs() << "phi " << Print<NodeId>(I.first, DFG) << " -> {";
      for (auto R : I.second)
        dbgs() << ' ' << Print<NodeId>(R.first, DFG)
               << Print<RegisterSet>(R.second, DFG);
      dbgs() << " }\n";
    }
  }

  // Propagate the reached registers up in the phi chain.
  //
  // The following type of situation needs careful handling:
  //
  //   phi d1<R1:0>  (1)
  //        |
  //   ... d2<R1>
  //        |
  //   phi u3<R1:0>  (2)
  //        |
  //   ... u4<R1>
  //
  // The phi node (2) defines a register pair R1:0, and reaches a "real"
  // use u4 of just R1. The same phi node is also known to reach (upwards)
  // the phi node (1). However, the use u4 is not reached by phi (1),
  // because of the intervening definition d2 of R1. The data flow between
  // phis (1) and (2) is restricted to R1:0 minus R1, i.e. R0.
  //
  // When propagating uses up the phi chains, get the all reaching defs
  // for a given phi use, and traverse the list until the propagated ref
  // is covered, or until or until reaching the final phi. Only assume
  // that the reference reaches the phi in the latter case.

  for (unsigned i = 0; i < PhiUQ.size(); ++i) {
    auto PA = DFG.addr<PhiNode*>(PhiUQ[i]);
    auto &RealUses = RealUseMap[PA.Id];
    for (auto U : PA.Addr->members_if(DFG.IsRef<NodeAttrs::Use>, DFG)) {
      NodeAddr<UseNode*> UA = U;
      auto &UpPhis = PhiUp[UA.Id];
      for (auto UP : UpPhis) {
        bool Changed = false;
        auto &MidDefs = UP.second;
        // Collect the set UpReached of uses that are reached by the current
        // phi PA, and are not covered by any intervening def between PA and
        // the upward phi UP.
        RegisterSet UpReached;
        for (auto T : RealUses) {
          if (!isRestricted(PA, UA, T.first))
            continue;
          if (!RAI.covers(MidDefs, T.first))
            UpReached.insert(T.first);
        }
        if (UpReached.empty())
          continue;
        // Update the set PRUs of real uses reached by the upward phi UP with
        // the actual set of uses (UpReached) that the UP phi reaches.
        auto &PRUs = RealUseMap[UP.first];
        for (auto R : UpReached) {
          unsigned Z = PRUs[R].size();
          PRUs[R].insert(RealUses[R].begin(), RealUses[R].end());
          Changed |= (PRUs[R].size() != Z);
        }
        if (Changed)
          PhiUQ.push_back(UP.first);
      }
    }
  }

  if (Trace) {
    dbgs() << "Real use map:\n";
    for (auto I : RealUseMap) {
      dbgs() << "phi " << Print<NodeId>(I.first, DFG);
      NodeAddr<PhiNode*> PA = DFG.addr<PhiNode*>(I.first);
      NodeList Ds = PA.Addr->members_if(DFG.IsRef<NodeAttrs::Def>, DFG);
      if (!Ds.empty()) {
        RegisterRef RR = NodeAddr<DefNode*>(Ds[0]).Addr->getRegRef();
        dbgs() << '<' << Print<RegisterRef>(RR, DFG) << '>';
      } else {
        dbgs() << "<noreg>";
      }
      dbgs() << " -> " << Print<RefMap>(I.second, DFG) << '\n';
    }
  }
}


void Liveness::computeLiveIns() {
  // Populate the node-to-block map. This speeds up the calculations
  // significantly.
  NBMap.clear();
  for (NodeAddr<BlockNode*> BA : DFG.getFunc().Addr->members(DFG)) {
    MachineBasicBlock *BB = BA.Addr->getCode();
    for (NodeAddr<InstrNode*> IA : BA.Addr->members(DFG)) {
      for (NodeAddr<RefNode*> RA : IA.Addr->members(DFG))
        NBMap.insert(std::make_pair(RA.Id, BB));
      NBMap.insert(std::make_pair(IA.Id, BB));
    }
  }

  MachineFunction &MF = DFG.getMF();

  // Compute IDF first, then the inverse.
  decltype(IIDF) IDF;
  for (auto &B : MF) {
    auto F1 = MDF.find(&B);
    if (F1 == MDF.end())
      continue;
    SetVector<MachineBasicBlock*> IDFB(F1->second.begin(), F1->second.end());
    for (unsigned i = 0; i < IDFB.size(); ++i) {
      auto F2 = MDF.find(IDFB[i]);
      if (F2 != MDF.end())
        IDFB.insert(F2->second.begin(), F2->second.end());
    }
    // Add B to the IDF(B). This will put B in the IIDF(B).
    IDFB.insert(&B);
    IDF[&B].insert(IDFB.begin(), IDFB.end());
  }

  for (auto I : IDF)
    for (auto S : I.second)
      IIDF[S].insert(I.first);

  computePhiInfo();

  NodeAddr<FuncNode*> FA = DFG.getFunc();
  auto Blocks = FA.Addr->members(DFG);

  // Build the phi live-on-entry map.
  for (NodeAddr<BlockNode*> BA : Blocks) {
    MachineBasicBlock *MB = BA.Addr->getCode();
    auto &LON = PhiLON[MB];
    for (auto P : BA.Addr->members_if(DFG.IsCode<NodeAttrs::Phi>, DFG))
      for (auto S : RealUseMap[P.Id])
        LON[S.first].insert(S.second.begin(), S.second.end());
  }

  if (Trace) {
    dbgs() << "Phi live-on-entry map:\n";
    for (auto I : PhiLON)
      dbgs() << "block #" << I.first->getNumber() << " -> "
             << Print<RefMap>(I.second, DFG) << '\n';
  }

  // Build the phi live-on-exit map. Each phi node has some set of reached
  // "real" uses. Propagate this set backwards into the block predecessors
  // through the reaching defs of the corresponding phi uses.
  for (NodeAddr<BlockNode*> BA : Blocks) {
    auto Phis = BA.Addr->members_if(DFG.IsCode<NodeAttrs::Phi>, DFG);
    for (NodeAddr<PhiNode*> PA : Phis) {
      auto &RUs = RealUseMap[PA.Id];
      if (RUs.empty())
        continue;

      for (auto U : PA.Addr->members_if(DFG.IsRef<NodeAttrs::Use>, DFG)) {
        NodeAddr<PhiUseNode*> UA = U;
        if (UA.Addr->getReachingDef() == 0)
          continue;

        // Mark all reached "real" uses of P as live on exit in the
        // predecessor.
        // Remap all the RUs so that they have a correct reaching def.
        auto PrA = DFG.addr<BlockNode*>(UA.Addr->getPredecessor());
        auto &LOX = PhiLOX[PrA.Addr->getCode()];
        for (auto R : RUs) {
          RegisterRef RR = R.first;
          if (!isRestricted(PA, UA, RR))
            RR = getRestrictedRegRef(UA);
          // The restricted ref may be different from the ref that was
          // accessed in the "real use". This means that this phi use
          // is not the one that carries this reference, so skip it.
          if (!RAI.alias(R.first, RR))
            continue;
          for (auto D : getAllReachingDefs(RR, UA))
            LOX[RR].insert(D.Id);
        }
      }  // for U : phi uses
    }  // for P : Phis
  }  // for B : Blocks

  if (Trace) {
    dbgs() << "Phi live-on-exit map:\n";
    for (auto I : PhiLOX)
      dbgs() << "block #" << I.first->getNumber() << " -> "
             << Print<RefMap>(I.second, DFG) << '\n';
  }

  RefMap LiveIn;
  traverse(&MF.front(), LiveIn);

  // Add function live-ins to the live-in set of the function entry block.
  auto &EntryIn = LiveMap[&MF.front()];
  for (auto I = MRI.livein_begin(), E = MRI.livein_end(); I != E; ++I)
    EntryIn.insert({I->first,0});

  if (Trace) {
    // Dump the liveness map
    for (auto &B : MF) {
      BitVector LV(TRI.getNumRegs());
      for (auto I = B.livein_begin(), E = B.livein_end(); I != E; ++I)
        LV.set(I->PhysReg);
      dbgs() << "BB#" << B.getNumber() << "\t rec = {";
      for (int x = LV.find_first(); x >= 0; x = LV.find_next(x))
        dbgs() << ' ' << Print<RegisterRef>({unsigned(x),0}, DFG);
      dbgs() << " }\n";
      dbgs() << "\tcomp = " << Print<RegisterSet>(LiveMap[&B], DFG) << '\n';
    }
  }
}


void Liveness::resetLiveIns() {
  for (auto &B : DFG.getMF()) {
    // Remove all live-ins.
    std::vector<unsigned> T;
    for (auto I = B.livein_begin(), E = B.livein_end(); I != E; ++I)
      T.push_back(I->PhysReg);
    for (auto I : T)
      B.removeLiveIn(I);
    // Add the newly computed live-ins.
    auto &LiveIns = LiveMap[&B];
    for (auto I : LiveIns) {
      assert(I.Sub == 0);
      B.addLiveIn(I.Reg);
    }
  }
}


void Liveness::resetKills() {
  for (auto &B : DFG.getMF())
    resetKills(&B);
}


void Liveness::resetKills(MachineBasicBlock *B) {
  auto CopyLiveIns = [] (MachineBasicBlock *B, BitVector &LV) -> void {
    for (auto I = B->livein_begin(), E = B->livein_end(); I != E; ++I)
      LV.set(I->PhysReg);
  };

  BitVector LiveIn(TRI.getNumRegs()), Live(TRI.getNumRegs());
  CopyLiveIns(B, LiveIn);
  for (auto SI : B->successors())
    CopyLiveIns(SI, Live);

  for (auto I = B->rbegin(), E = B->rend(); I != E; ++I) {
    MachineInstr *MI = &*I;
    if (MI->isDebugValue())
      continue;

    MI->clearKillInfo();
    for (auto &Op : MI->operands()) {
      // An implicit def of a super-register may not necessarily start a
      // live range of it, since an implicit use could be used to keep parts
      // of it live. Instead of analyzing the implicit operands, ignore
      // implicit defs.
      if (!Op.isReg() || !Op.isDef() || Op.isImplicit())
        continue;
      unsigned R = Op.getReg();
      if (!TargetRegisterInfo::isPhysicalRegister(R))
        continue;
      for (MCSubRegIterator SR(R, &TRI, true); SR.isValid(); ++SR)
        Live.reset(*SR);
    }
    for (auto &Op : MI->operands()) {
      if (!Op.isReg() || !Op.isUse())
        continue;
      unsigned R = Op.getReg();
      if (!TargetRegisterInfo::isPhysicalRegister(R))
        continue;
      bool IsLive = false;
      for (MCRegAliasIterator AR(R, &TRI, true); AR.isValid(); ++AR) {
        if (!Live[*AR])
          continue;
        IsLive = true;
        break;
      }
      if (IsLive)
        continue;
      Op.setIsKill(true);
      for (MCSubRegIterator SR(R, &TRI, true); SR.isValid(); ++SR)
        Live.set(*SR);
    }
  }
}


// For shadows, determine if RR is aliased to a reaching def of any other
// shadow associated with RA. If it is not, then RR is "restricted" to RA,
// and so it can be considered a value specific to RA. This is important
// for accurately determining values associated with phi uses.
// For non-shadows, this function returns "true".
bool Liveness::isRestricted(NodeAddr<InstrNode*> IA, NodeAddr<RefNode*> RA,
      RegisterRef RR) const {
  NodeId Start = RA.Id;
  for (NodeAddr<RefNode*> TA = DFG.getNextShadow(IA, RA);
       TA.Id != 0 && TA.Id != Start; TA = DFG.getNextShadow(IA, TA)) {
    NodeId RD = TA.Addr->getReachingDef();
    if (RD == 0)
      continue;
    if (RAI.alias(RR, DFG.addr<DefNode*>(RD).Addr->getRegRef()))
      return false;
  }
  return true;
}


RegisterRef Liveness::getRestrictedRegRef(NodeAddr<RefNode*> RA) const {
  assert(DFG.IsRef<NodeAttrs::Use>(RA));
  if (RA.Addr->getFlags() & NodeAttrs::Shadow) {
    NodeId RD = RA.Addr->getReachingDef();
    assert(RD);
    RA = DFG.addr<DefNode*>(RD);
  }
  return RA.Addr->getRegRef();
}


unsigned Liveness::getPhysReg(RegisterRef RR) const {
  if (!TargetRegisterInfo::isPhysicalRegister(RR.Reg))
    return 0;
  return RR.Sub ? TRI.getSubReg(RR.Reg, RR.Sub) : RR.Reg;
}


// Helper function to obtain the basic block containing the reaching def
// of the given use.
MachineBasicBlock *Liveness::getBlockWithRef(NodeId RN) const {
  auto F = NBMap.find(RN);
  if (F != NBMap.end())
    return F->second;
  llvm_unreachable("Node id not in map");
}


void Liveness::traverse(MachineBasicBlock *B, RefMap &LiveIn) {
  // The LiveIn map, for each (physical) register, contains the set of live
  // reaching defs of that register that are live on entry to the associated
  // block.

  // The summary of the traversal algorithm:
  //
  // R is live-in in B, if there exists a U(R), such that rdef(R) dom B
  // and (U \in IDF(B) or B dom U).
  //
  // for (C : children) {
  //   LU = {}
  //   traverse(C, LU)
  //   LiveUses += LU
  // }
  //
  // LiveUses -= Defs(B);
  // LiveUses += UpwardExposedUses(B);
  // for (C : IIDF[B])
  //   for (U : LiveUses)
  //     if (Rdef(U) dom C)
  //       C.addLiveIn(U)
  //

  // Go up the dominator tree (depth-first).
  MachineDomTreeNode *N = MDT.getNode(B);
  for (auto I : *N) {
    RefMap L;
    MachineBasicBlock *SB = I->getBlock();
    traverse(SB, L);

    for (auto S : L)
      LiveIn[S.first].insert(S.second.begin(), S.second.end());
  }

  if (Trace) {
    dbgs() << LLVM_FUNCTION_NAME << " in BB#" << B->getNumber()
           << " after recursion into";
    for (auto I : *N)
      dbgs() << ' ' << I->getBlock()->getNumber();
    dbgs() << "\n  LiveIn: " << Print<RefMap>(LiveIn, DFG);
    dbgs() << "\n  Local:  " << Print<RegisterSet>(LiveMap[B], DFG) << '\n';
  }

  // Add phi uses that are live on exit from this block.
  RefMap &PUs = PhiLOX[B];
  for (auto S : PUs)
    LiveIn[S.first].insert(S.second.begin(), S.second.end());

  if (Trace) {
    dbgs() << "after LOX\n";
    dbgs() << "  LiveIn: " << Print<RefMap>(LiveIn, DFG) << '\n';
    dbgs() << "  Local:  " << Print<RegisterSet>(LiveMap[B], DFG) << '\n';
  }

  // Stop tracking all uses defined in this block: erase those records
  // where the reaching def is located in B and which cover all reached
  // uses.
  auto Copy = LiveIn;
  LiveIn.clear();

  for (auto I : Copy) {
    auto &Defs = LiveIn[I.first];
    NodeSet Rest;
    for (auto R : I.second) {
      auto DA = DFG.addr<DefNode*>(R);
      RegisterRef DDR = DA.Addr->getRegRef();
      NodeAddr<InstrNode*> IA = DA.Addr->getOwner(DFG);
      NodeAddr<BlockNode*> BA = IA.Addr->getOwner(DFG);
      // Defs from a different block need to be preserved. Defs from this
      // block will need to be processed further, except for phi defs, the
      // liveness of which is handled through the PhiLON/PhiLOX maps.
      if (B != BA.Addr->getCode())
        Defs.insert(R);
      else {
        bool IsPreserving = DA.Addr->getFlags() & NodeAttrs::Preserving;
        if (IA.Addr->getKind() != NodeAttrs::Phi && !IsPreserving) {
          bool Covering = RAI.covers(DDR, I.first);
          NodeId U = DA.Addr->getReachedUse();
          while (U && Covering) {
            auto DUA = DFG.addr<UseNode*>(U);
            RegisterRef Q = DUA.Addr->getRegRef();
            Covering = RAI.covers(DA.Addr->getRegRef(), Q);
            U = DUA.Addr->getSibling();
          }
          if (!Covering)
            Rest.insert(R);
        }
      }
    }

    // Non-covering defs from B.
    for (auto R : Rest) {
      auto DA = DFG.addr<DefNode*>(R);
      RegisterRef DRR = DA.Addr->getRegRef();
      RegisterSet RRs;
      for (NodeAddr<DefNode*> TA : getAllReachingDefs(DA)) {
        NodeAddr<InstrNode*> IA = TA.Addr->getOwner(DFG);
        NodeAddr<BlockNode*> BA = IA.Addr->getOwner(DFG);
        // Preserving defs do not count towards covering.
        if (!(TA.Addr->getFlags() & NodeAttrs::Preserving))
          RRs.insert(TA.Addr->getRegRef());
        if (BA.Addr->getCode() == B)
          continue;
        if (RAI.covers(RRs, DRR))
          break;
        Defs.insert(TA.Id);
      }
    }
  }

  emptify(LiveIn);

  if (Trace) {
    dbgs() << "after defs in block\n";
    dbgs() << "  LiveIn: " << Print<RefMap>(LiveIn, DFG) << '\n';
    dbgs() << "  Local:  " << Print<RegisterSet>(LiveMap[B], DFG) << '\n';
  }

  // Scan the block for upward-exposed uses and add them to the tracking set.
  for (auto I : DFG.getFunc().Addr->findBlock(B, DFG).Addr->members(DFG)) {
    NodeAddr<InstrNode*> IA = I;
    if (IA.Addr->getKind() != NodeAttrs::Stmt)
      continue;
    for (NodeAddr<UseNode*> UA : IA.Addr->members_if(DFG.IsUse, DFG)) {
      RegisterRef RR = UA.Addr->getRegRef();
      for (auto D : getAllReachingDefs(UA))
        if (getBlockWithRef(D.Id) != B)
          LiveIn[RR].insert(D.Id);
    }
  }

  if (Trace) {
    dbgs() << "after uses in block\n";
    dbgs() << "  LiveIn: " << Print<RefMap>(LiveIn, DFG) << '\n';
    dbgs() << "  Local:  " << Print<RegisterSet>(LiveMap[B], DFG) << '\n';
  }

  // Phi uses should not be propagated up the dominator tree, since they
  // are not dominated by their corresponding reaching defs.
  auto &Local = LiveMap[B];
  auto &LON = PhiLON[B];
  for (auto R : LON)
    Local.insert(R.first);

  if (Trace) {
    dbgs() << "after phi uses in block\n";
    dbgs() << "  LiveIn: " << Print<RefMap>(LiveIn, DFG) << '\n';
    dbgs() << "  Local:  " << Print<RegisterSet>(Local, DFG) << '\n';
  }

  for (auto C : IIDF[B]) {
    auto &LiveC = LiveMap[C];
    for (auto S : LiveIn)
      for (auto R : S.second)
        if (MDT.properlyDominates(getBlockWithRef(R), C))
          LiveC.insert(S.first);
  }
}


void Liveness::emptify(RefMap &M) {
  for (auto I = M.begin(), E = M.end(); I != E; )
    I = I->second.empty() ? M.erase(I) : std::next(I);
}