X86FloatingPoint.cpp

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//===-- X86FloatingPoint.cpp - Floating point Reg -> Stack converter ------===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This file defines the pass which converts floating point instructions from
// pseudo registers into register stack instructions.  This pass uses live
// variable information to indicate where the FPn registers are used and their
// lifetimes.
//
// The x87 hardware tracks liveness of the stack registers, so it is necessary
// to implement exact liveness tracking between basic blocks. The CFG edges are
// partitioned into bundles where the same FP registers must be live in
// identical stack positions. Instructions are inserted at the end of each basic
// block to rearrange the live registers to match the outgoing bundle.
//
// This approach avoids splitting critical edges at the potential cost of more
// live register shuffling instructions when critical edges are present.
//
//===----------------------------------------------------------------------===//

#include "X86.h"
#include "X86InstrInfo.h"
#include "llvm/ADT/DepthFirstIterator.h"
#include "llvm/ADT/STLExtras.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/SmallSet.h"
#include "llvm/ADT/SmallVector.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/CodeGen/EdgeBundles.h"
#include "llvm/CodeGen/LivePhysRegs.h"
#include "llvm/CodeGen/MachineFunctionPass.h"
#include "llvm/CodeGen/MachineInstrBuilder.h"
#include "llvm/CodeGen/MachineRegisterInfo.h"
#include "llvm/CodeGen/Passes.h"
#include "llvm/CodeGen/TargetInstrInfo.h"
#include "llvm/CodeGen/TargetSubtargetInfo.h"
#include "llvm/Config/llvm-config.h"
#include "llvm/IR/InlineAsm.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/ErrorHandling.h"
#include "llvm/Support/raw_ostream.h"
#include "llvm/Target/TargetMachine.h"
#include <algorithm>
#include <bitset>
using namespace llvm;

#define DEBUG_TYPE "x86-codegen"

STATISTIC(NumFXCH, "Number of fxch instructions inserted");
STATISTIC(NumFP  , "Number of floating point instructions");

namespace {
  const unsigned ScratchFPReg = 7;

  struct FPS : public MachineFunctionPass {
    static char ID;
    FPS() : MachineFunctionPass(ID) {
      initializeEdgeBundlesPass(*PassRegistry::getPassRegistry());
      // This is really only to keep valgrind quiet.
      // The logic in isLive() is too much for it.
      memset(Stack, 0, sizeof(Stack));
      memset(RegMap, 0, sizeof(RegMap));
    }

    void getAnalysisUsage(AnalysisUsage &AU) const override {
      AU.setPreservesCFG();
      AU.addRequired<EdgeBundles>();
      AU.addPreservedID(MachineLoopInfoID);
      AU.addPreservedID(MachineDominatorsID);
      MachineFunctionPass::getAnalysisUsage(AU);
    }

    bool runOnMachineFunction(MachineFunction &MF) override;

    MachineFunctionProperties getRequiredProperties() const override {
      return MachineFunctionProperties().set(
          MachineFunctionProperties::Property::NoVRegs);
    }

    StringRef getPassName() const override { return "X86 FP Stackifier"; }

  private:
    const TargetInstrInfo *TII; // Machine instruction info.

    // Two CFG edges are related if they leave the same block, or enter the same
    // block. The transitive closure of an edge under this relation is a
    // LiveBundle. It represents a set of CFG edges where the live FP stack
    // registers must be allocated identically in the x87 stack.
    //
    // A LiveBundle is usually all the edges leaving a block, or all the edges
    // entering a block, but it can contain more edges if critical edges are
    // present.
    //
    // The set of live FP registers in a LiveBundle is calculated by bundleCFG,
    // but the exact mapping of FP registers to stack slots is fixed later.
    struct LiveBundle {
      // Bit mask of live FP registers. Bit 0 = FP0, bit 1 = FP1, &c.
      unsigned Mask;

      // Number of pre-assigned live registers in FixStack. This is 0 when the
      // stack order has not yet been fixed.
      unsigned FixCount;

      // Assigned stack order for live-in registers.
      // FixStack[i] == getStackEntry(i) for all i < FixCount.
      unsigned char FixStack[8];

      LiveBundle() : Mask(0), FixCount(0) {}

      // Have the live registers been assigned a stack order yet?
      bool isFixed() const { return !Mask || FixCount; }
    };

    // Numbered LiveBundle structs. LiveBundles[0] is used for all CFG edges
    // with no live FP registers.
    SmallVector<LiveBundle, 8> LiveBundles;

    // The edge bundle analysis provides indices into the LiveBundles vector.
    EdgeBundles *Bundles;

    // Return a bitmask of FP registers in block's live-in list.
    static unsigned calcLiveInMask(MachineBasicBlock *MBB, bool RemoveFPs) {
      unsigned Mask = 0;
      for (MachineBasicBlock::livein_iterator I = MBB->livein_begin();
           I != MBB->livein_end(); ) {
        MCPhysReg Reg = I->PhysReg;
        static_assert(X86::FP6 - X86::FP0 == 6, "sequential regnums");
        if (Reg >= X86::FP0 && Reg <= X86::FP6) {
          Mask |= 1 << (Reg - X86::FP0);
          if (RemoveFPs) {
            I = MBB->removeLiveIn(I);
            continue;
          }
        }
        ++I;
      }
      return Mask;
    }

    // Partition all the CFG edges into LiveBundles.
    void bundleCFGRecomputeKillFlags(MachineFunction &MF);

    MachineBasicBlock *MBB;     // Current basic block

    // The hardware keeps track of how many FP registers are live, so we have
    // to model that exactly. Usually, each live register corresponds to an
    // FP<n> register, but when dealing with calls, returns, and inline
    // assembly, it is sometimes necessary to have live scratch registers.
    unsigned Stack[8];          // FP<n> Registers in each stack slot...
    unsigned StackTop;          // The current top of the FP stack.

    enum {
      NumFPRegs = 8             // Including scratch pseudo-registers.
    };

    // For each live FP<n> register, point to its Stack[] entry.
    // The first entries correspond to FP0-FP6, the rest are scratch registers
    // used when we need slightly different live registers than what the
    // register allocator thinks.
    unsigned RegMap[NumFPRegs];

    // Set up our stack model to match the incoming registers to MBB.
    void setupBlockStack();

    // Shuffle live registers to match the expectations of successor blocks.
    void finishBlockStack();

#if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
    void dumpStack() const {
      dbgs() << "Stack contents:";
      for (unsigned i = 0; i != StackTop; ++i) {
        dbgs() << " FP" << Stack[i];
        assert(RegMap[Stack[i]] == i && "Stack[] doesn't match RegMap[]!");
      }
    }
#endif

    /// getSlot - Return the stack slot number a particular register number is
    /// in.
    unsigned getSlot(unsigned RegNo) const {
      assert(RegNo < NumFPRegs && "Regno out of range!");
      return RegMap[RegNo];
    }

    /// isLive - Is RegNo currently live in the stack?
    bool isLive(unsigned RegNo) const {
      unsigned Slot = getSlot(RegNo);
      return Slot < StackTop && Stack[Slot] == RegNo;
    }

    /// getStackEntry - Return the X86::FP<n> register in register ST(i).
    unsigned getStackEntry(unsigned STi) const {
      if (STi >= StackTop)
        report_fatal_error("Access past stack top!");
      return Stack[StackTop-1-STi];
    }

    /// getSTReg - Return the X86::ST(i) register which contains the specified
    /// FP<RegNo> register.
    unsigned getSTReg(unsigned RegNo) const {
      return StackTop - 1 - getSlot(RegNo) + X86::ST0;
    }

    // pushReg - Push the specified FP<n> register onto the stack.
    void pushReg(unsigned Reg) {
      assert(Reg < NumFPRegs && "Register number out of range!");
      if (StackTop >= 8)
        report_fatal_error("Stack overflow!");
      Stack[StackTop] = Reg;
      RegMap[Reg] = StackTop++;
    }

    // popReg - Pop a register from the stack.
    void popReg() {
      if (StackTop == 0)
        report_fatal_error("Cannot pop empty stack!");
      RegMap[Stack[--StackTop]] = ~0;     // Update state
    }

    bool isAtTop(unsigned RegNo) const { return getSlot(RegNo) == StackTop-1; }
    void moveToTop(unsigned RegNo, MachineBasicBlock::iterator I) {
      DebugLoc dl = I == MBB->end() ? DebugLoc() : I->getDebugLoc();
      if (isAtTop(RegNo)) return;

      unsigned STReg = getSTReg(RegNo);
      unsigned RegOnTop = getStackEntry(0);

      // Swap the slots the regs are in.
      std::swap(RegMap[RegNo], RegMap[RegOnTop]);

      // Swap stack slot contents.
      if (RegMap[RegOnTop] >= StackTop)
        report_fatal_error("Access past stack top!");
      std::swap(Stack[RegMap[RegOnTop]], Stack[StackTop-1]);

      // Emit an fxch to update the runtime processors version of the state.
      BuildMI(*MBB, I, dl, TII->get(X86::XCH_F)).addReg(STReg);
      ++NumFXCH;
    }

    void duplicateToTop(unsigned RegNo, unsigned AsReg,
                        MachineBasicBlock::iterator I) {
      DebugLoc dl = I == MBB->end() ? DebugLoc() : I->getDebugLoc();
      unsigned STReg = getSTReg(RegNo);
      pushReg(AsReg);   // New register on top of stack

      BuildMI(*MBB, I, dl, TII->get(X86::LD_Frr)).addReg(STReg);
    }

    /// popStackAfter - Pop the current value off of the top of the FP stack
    /// after the specified instruction.
    void popStackAfter(MachineBasicBlock::iterator &I);

    /// freeStackSlotAfter - Free the specified register from the register
    /// stack, so that it is no longer in a register.  If the register is
    /// currently at the top of the stack, we just pop the current instruction,
    /// otherwise we store the current top-of-stack into the specified slot,
    /// then pop the top of stack.
    void freeStackSlotAfter(MachineBasicBlock::iterator &I, unsigned Reg);

    /// freeStackSlotBefore - Just the pop, no folding. Return the inserted
    /// instruction.
    MachineBasicBlock::iterator
    freeStackSlotBefore(MachineBasicBlock::iterator I, unsigned FPRegNo);

    /// Adjust the live registers to be the set in Mask.
    void adjustLiveRegs(unsigned Mask, MachineBasicBlock::iterator I);

    /// Shuffle the top FixCount stack entries such that FP reg FixStack[0] is
    /// st(0), FP reg FixStack[1] is st(1) etc.
    void shuffleStackTop(const unsigned char *FixStack, unsigned FixCount,
                         MachineBasicBlock::iterator I);

    bool processBasicBlock(MachineFunction &MF, MachineBasicBlock &MBB);

    void handleCall(MachineBasicBlock::iterator &I);
    void handleReturn(MachineBasicBlock::iterator &I);
    void handleZeroArgFP(MachineBasicBlock::iterator &I);
    void handleOneArgFP(MachineBasicBlock::iterator &I);
    void handleOneArgFPRW(MachineBasicBlock::iterator &I);
    void handleTwoArgFP(MachineBasicBlock::iterator &I);
    void handleCompareFP(MachineBasicBlock::iterator &I);
    void handleCondMovFP(MachineBasicBlock::iterator &I);
    void handleSpecialFP(MachineBasicBlock::iterator &I);

    // Check if a COPY instruction is using FP registers.
    static bool isFPCopy(MachineInstr &MI) {
      unsigned DstReg = MI.getOperand(0).getReg();
      unsigned SrcReg = MI.getOperand(1).getReg();

      return X86::RFP80RegClass.contains(DstReg) ||
        X86::RFP80RegClass.contains(SrcReg);
    }

    void setKillFlags(MachineBasicBlock &MBB) const;
  };
  char FPS::ID = 0;
}

FunctionPass *llvm::createX86FloatingPointStackifierPass() { return new FPS(); }

/// getFPReg - Return the X86::FPx register number for the specified operand.
/// For example, this returns 3 for X86::FP3.
static unsigned getFPReg(const MachineOperand &MO) {
  assert(MO.isReg() && "Expected an FP register!");
  unsigned Reg = MO.getReg();
  assert(Reg >= X86::FP0 && Reg <= X86::FP6 && "Expected FP register!");
  return Reg - X86::FP0;
}

/// runOnMachineFunction - Loop over all of the basic blocks, transforming FP
/// register references into FP stack references.
///
bool FPS::runOnMachineFunction(MachineFunction &MF) {
  // We only need to run this pass if there are any FP registers used in this
  // function.  If it is all integer, there is nothing for us to do!
  bool FPIsUsed = false;

  static_assert(X86::FP6 == X86::FP0+6, "Register enums aren't sorted right!");
  const MachineRegisterInfo &MRI = MF.getRegInfo();
  for (unsigned i = 0; i <= 6; ++i)
    if (!MRI.reg_nodbg_empty(X86::FP0 + i)) {
      FPIsUsed = true;
      break;
    }

  // Early exit.
  if (!FPIsUsed) return false;

  Bundles = &getAnalysis<EdgeBundles>();
  TII = MF.getSubtarget().getInstrInfo();

  // Prepare cross-MBB liveness.
  bundleCFGRecomputeKillFlags(MF);

  StackTop = 0;

  // Process the function in depth first order so that we process at least one
  // of the predecessors for every reachable block in the function.
  df_iterator_default_set<MachineBasicBlock*> Processed;
  MachineBasicBlock *Entry = &MF.front();

  LiveBundle &Bundle =
    LiveBundles[Bundles->getBundle(Entry->getNumber(), false)];

  // In regcall convention, some FP registers may not be passed through
  // the stack, so they will need to be assigned to the stack first
  if ((Entry->getParent()->getFunction().getCallingConv() ==
    CallingConv::X86_RegCall) && (Bundle.Mask && !Bundle.FixCount)) {
    // In the register calling convention, up to one FP argument could be
    // saved in the first FP register.
    // If bundle.mask is non-zero and Bundle.FixCount is zero, it means
    // that the FP registers contain arguments.
    // The actual value is passed in FP0.
    // Here we fix the stack and mark FP0 as pre-assigned register.
    assert((Bundle.Mask & 0xFE) == 0 &&
      "Only FP0 could be passed as an argument");
    Bundle.FixCount = 1;
    Bundle.FixStack[0] = 0;
  }

  bool Changed = false;
  for (MachineBasicBlock *BB : depth_first_ext(Entry, Processed))
    Changed |= processBasicBlock(MF, *BB);

  // Process any unreachable blocks in arbitrary order now.
  if (MF.size() != Processed.size())
    for (MachineBasicBlock &BB : MF)
      if (Processed.insert(&BB).second)
        Changed |= processBasicBlock(MF, BB);

  LiveBundles.clear();

  return Changed;
}

/// bundleCFG - Scan all the basic blocks to determine consistent live-in and
/// live-out sets for the FP registers. Consistent means that the set of
/// registers live-out from a block is identical to the live-in set of all
/// successors. This is not enforced by the normal live-in lists since
/// registers may be implicitly defined, or not used by all successors.
void FPS::bundleCFGRecomputeKillFlags(MachineFunction &MF) {
  assert(LiveBundles.empty() && "Stale data in LiveBundles");
  LiveBundles.resize(Bundles->getNumBundles());

  // Gather the actual live-in masks for all MBBs.
  for (MachineBasicBlock &MBB : MF) {
    setKillFlags(MBB);

    const unsigned Mask = calcLiveInMask(&MBB, false);
    if (!Mask)
      continue;
    // Update MBB ingoing bundle mask.
    LiveBundles[Bundles->getBundle(MBB.getNumber(), false)].Mask |= Mask;
  }
}

/// processBasicBlock - Loop over all of the instructions in the basic block,
/// transforming FP instructions into their stack form.
///
bool FPS::processBasicBlock(MachineFunction &MF, MachineBasicBlock &BB) {
  bool Changed = false;
  MBB = &BB;

  setupBlockStack();

  for (MachineBasicBlock::iterator I = BB.begin(); I != BB.end(); ++I) {
    MachineInstr &MI = *I;
    uint64_t Flags = MI.getDesc().TSFlags;

    unsigned FPInstClass = Flags & X86II::FPTypeMask;
    if (MI.isInlineAsm())
      FPInstClass = X86II::SpecialFP;

    if (MI.isCopy() && isFPCopy(MI))
      FPInstClass = X86II::SpecialFP;

    if (MI.isImplicitDef() &&
        X86::RFP80RegClass.contains(MI.getOperand(0).getReg()))
      FPInstClass = X86II::SpecialFP;

    if (MI.isCall())
      FPInstClass = X86II::SpecialFP;

    if (FPInstClass == X86II::NotFP)
      continue;  // Efficiently ignore non-fp insts!

    MachineInstr *PrevMI = nullptr;
    if (I != BB.begin())
      PrevMI = &*std::prev(I);

    ++NumFP;  // Keep track of # of pseudo instrs
    LLVM_DEBUG(dbgs() << "\nFPInst:\t" << MI);

    // Get dead variables list now because the MI pointer may be deleted as part
    // of processing!
    SmallVector<unsigned, 8> DeadRegs;
    for (unsigned i = 0, e = MI.getNumOperands(); i != e; ++i) {
      const MachineOperand &MO = MI.getOperand(i);
      if (MO.isReg() && MO.isDead())
        DeadRegs.push_back(MO.getReg());
    }

    switch (FPInstClass) {
    case X86II::ZeroArgFP:  handleZeroArgFP(I); break;
    case X86II::OneArgFP:   handleOneArgFP(I);  break;  // fstp ST(0)
    case X86II::OneArgFPRW: handleOneArgFPRW(I); break; // ST(0) = fsqrt(ST(0))
    case X86II::TwoArgFP:   handleTwoArgFP(I);  break;
    case X86II::CompareFP:  handleCompareFP(I); break;
    case X86II::CondMovFP:  handleCondMovFP(I); break;
    case X86II::SpecialFP:  handleSpecialFP(I); break;
    default: llvm_unreachable("Unknown FP Type!");
    }

    // Check to see if any of the values defined by this instruction are dead
    // after definition.  If so, pop them.
    for (unsigned i = 0, e = DeadRegs.size(); i != e; ++i) {
      unsigned Reg = DeadRegs[i];
      // Check if Reg is live on the stack. An inline-asm register operand that
      // is in the clobber list and marked dead might not be live on the stack.
      static_assert(X86::FP7 - X86::FP0 == 7, "sequential FP regnumbers");
      if (Reg >= X86::FP0 && Reg <= X86::FP6 && isLive(Reg-X86::FP0)) {
        LLVM_DEBUG(dbgs() << "Register FP#" << Reg - X86::FP0 << " is dead!\n");
        freeStackSlotAfter(I, Reg-X86::FP0);
      }
    }

    // Print out all of the instructions expanded to if -debug
    LLVM_DEBUG({
      MachineBasicBlock::iterator PrevI = PrevMI;
      if (I == PrevI) {
        dbgs() << "Just deleted pseudo instruction\n";
      } else {
        MachineBasicBlock::iterator Start = I;
        // Rewind to first instruction newly inserted.
        while (Start != BB.begin() && std::prev(Start) != PrevI)
          --Start;
        dbgs() << "Inserted instructions:\n\t";
        Start->print(dbgs());
        while (++Start != std::next(I)) {
        }
      }
      dumpStack();
    });
    (void)PrevMI;

    Changed = true;
  }

  finishBlockStack();

  return Changed;
}

/// setupBlockStack - Use the live bundles to set up our model of the stack
/// to match predecessors' live out stack.
void FPS::setupBlockStack() {
  LLVM_DEBUG(dbgs() << "\nSetting up live-ins for " << printMBBReference(*MBB)
                    << " derived from " << MBB->getName() << ".\n");
  StackTop = 0;
  // Get the live-in bundle for MBB.
  const LiveBundle &Bundle =
    LiveBundles[Bundles->getBundle(MBB->getNumber(), false)];

  if (!Bundle.Mask) {
    LLVM_DEBUG(dbgs() << "Block has no FP live-ins.\n");
    return;
  }

  // Depth-first iteration should ensure that we always have an assigned stack.
  assert(Bundle.isFixed() && "Reached block before any predecessors");

  // Push the fixed live-in registers.
  for (unsigned i = Bundle.FixCount; i > 0; --i) {
    LLVM_DEBUG(dbgs() << "Live-in st(" << (i - 1) << "): %fp"
                      << unsigned(Bundle.FixStack[i - 1]) << '\n');
    pushReg(Bundle.FixStack[i-1]);
  }

  // Kill off unwanted live-ins. This can happen with a critical edge.
  // FIXME: We could keep these live registers around as zombies. They may need
  // to be revived at the end of a short block. It might save a few instrs.
  unsigned Mask = calcLiveInMask(MBB, /*RemoveFPs=*/true);
  adjustLiveRegs(Mask, MBB->begin());
  LLVM_DEBUG(MBB->dump());
}

/// finishBlockStack - Revive live-outs that are implicitly defined out of
/// MBB. Shuffle live registers to match the expected fixed stack of any
/// predecessors, and ensure that all predecessors are expecting the same
/// stack.
void FPS::finishBlockStack() {
  // The RET handling below takes care of return blocks for us.
  if (MBB->succ_empty())
    return;

  LLVM_DEBUG(dbgs() << "Setting up live-outs for " << printMBBReference(*MBB)
                    << " derived from " << MBB->getName() << ".\n");

  // Get MBB's live-out bundle.
  unsigned BundleIdx = Bundles->getBundle(MBB->getNumber(), true);
  LiveBundle &Bundle = LiveBundles[BundleIdx];

  // We may need to kill and define some registers to match successors.
  // FIXME: This can probably be combined with the shuffle below.
  MachineBasicBlock::iterator Term = MBB->getFirstTerminator();
  adjustLiveRegs(Bundle.Mask, Term);

  if (!Bundle.Mask) {
    LLVM_DEBUG(dbgs() << "No live-outs.\n");
    return;
  }

  // Has the stack order been fixed yet?
  LLVM_DEBUG(dbgs() << "LB#" << BundleIdx << ": ");
  if (Bundle.isFixed()) {
    LLVM_DEBUG(dbgs() << "Shuffling stack to match.\n");
    shuffleStackTop(Bundle.FixStack, Bundle.FixCount, Term);
  } else {
    // Not fixed yet, we get to choose.
    LLVM_DEBUG(dbgs() << "Fixing stack order now.\n");
    Bundle.FixCount = StackTop;
    for (unsigned i = 0; i < StackTop; ++i)
      Bundle.FixStack[i] = getStackEntry(i);
  }
}


//===----------------------------------------------------------------------===//
// Efficient Lookup Table Support
//===----------------------------------------------------------------------===//

namespace {
  struct TableEntry {
    uint16_t from;
    uint16_t to;
    bool operator<(const TableEntry &TE) const { return from < TE.from; }
    friend bool operator<(const TableEntry &TE, unsigned V) {
      return TE.from < V;
    }
    friend bool LLVM_ATTRIBUTE_UNUSED operator<(unsigned V,
                                                const TableEntry &TE) {
      return V < TE.from;
    }
  };
}

static int Lookup(ArrayRef<TableEntry> Table, unsigned Opcode) {
  const TableEntry *I = std::lower_bound(Table.begin(), Table.end(), Opcode);
  if (I != Table.end() && I->from == Opcode)
    return I->to;
  return -1;
}

#ifdef NDEBUG
#define ASSERT_SORTED(TABLE)
#else
#define ASSERT_SORTED(TABLE)                                                   \
  {                                                                            \
    static std::atomic<bool> TABLE##Checked(false);                            \
    if (!TABLE##Checked.load(std::memory_order_relaxed)) {                     \
      assert(std::is_sorted(std::begin(TABLE), std::end(TABLE)) &&             \
             "All lookup tables must be sorted for efficient access!");        \
      TABLE##Checked.store(true, std::memory_order_relaxed);                   \
    }                                                                          \
  }
#endif

//===----------------------------------------------------------------------===//
// Register File -> Register Stack Mapping Methods
//===----------------------------------------------------------------------===//

// OpcodeTable - Sorted map of register instructions to their stack version.
// The first element is an register file pseudo instruction, the second is the
// concrete X86 instruction which uses the register stack.
//
static const TableEntry OpcodeTable[] = {
  { X86::ABS_Fp32     , X86::ABS_F     },
  { X86::ABS_Fp64     , X86::ABS_F     },
  { X86::ABS_Fp80     , X86::ABS_F     },
  { X86::ADD_Fp32m    , X86::ADD_F32m  },
  { X86::ADD_Fp64m    , X86::ADD_F64m  },
  { X86::ADD_Fp64m32  , X86::ADD_F32m  },
  { X86::ADD_Fp80m32  , X86::ADD_F32m  },
  { X86::ADD_Fp80m64  , X86::ADD_F64m  },
  { X86::ADD_FpI16m32 , X86::ADD_FI16m },
  { X86::ADD_FpI16m64 , X86::ADD_FI16m },
  { X86::ADD_FpI16m80 , X86::ADD_FI16m },
  { X86::ADD_FpI32m32 , X86::ADD_FI32m },
  { X86::ADD_FpI32m64 , X86::ADD_FI32m },
  { X86::ADD_FpI32m80 , X86::ADD_FI32m },
  { X86::CHS_Fp32     , X86::CHS_F     },
  { X86::CHS_Fp64     , X86::CHS_F     },
  { X86::CHS_Fp80     , X86::CHS_F     },
  { X86::CMOVBE_Fp32  , X86::CMOVBE_F  },
  { X86::CMOVBE_Fp64  , X86::CMOVBE_F  },
  { X86::CMOVBE_Fp80  , X86::CMOVBE_F  },
  { X86::CMOVB_Fp32   , X86::CMOVB_F   },
  { X86::CMOVB_Fp64   , X86::CMOVB_F  },
  { X86::CMOVB_Fp80   , X86::CMOVB_F  },
  { X86::CMOVE_Fp32   , X86::CMOVE_F  },
  { X86::CMOVE_Fp64   , X86::CMOVE_F   },
  { X86::CMOVE_Fp80   , X86::CMOVE_F   },
  { X86::CMOVNBE_Fp32 , X86::CMOVNBE_F },
  { X86::CMOVNBE_Fp64 , X86::CMOVNBE_F },
  { X86::CMOVNBE_Fp80 , X86::CMOVNBE_F },
  { X86::CMOVNB_Fp32  , X86::CMOVNB_F  },
  { X86::CMOVNB_Fp64  , X86::CMOVNB_F  },
  { X86::CMOVNB_Fp80  , X86::CMOVNB_F  },
  { X86::CMOVNE_Fp32  , X86::CMOVNE_F  },
  { X86::CMOVNE_Fp64  , X86::CMOVNE_F  },
  { X86::CMOVNE_Fp80  , X86::CMOVNE_F  },
  { X86::CMOVNP_Fp32  , X86::CMOVNP_F  },
  { X86::CMOVNP_Fp64  , X86::CMOVNP_F  },
  { X86::CMOVNP_Fp80  , X86::CMOVNP_F  },
  { X86::CMOVP_Fp32   , X86::CMOVP_F   },
  { X86::CMOVP_Fp64   , X86::CMOVP_F   },
  { X86::CMOVP_Fp80   , X86::CMOVP_F   },
  { X86::COS_Fp32     , X86::COS_F     },
  { X86::COS_Fp64     , X86::COS_F     },
  { X86::COS_Fp80     , X86::COS_F     },
  { X86::DIVR_Fp32m   , X86::DIVR_F32m },
  { X86::DIVR_Fp64m   , X86::DIVR_F64m },
  { X86::DIVR_Fp64m32 , X86::DIVR_F32m },
  { X86::DIVR_Fp80m32 , X86::DIVR_F32m },
  { X86::DIVR_Fp80m64 , X86::DIVR_F64m },
  { X86::DIVR_FpI16m32, X86::DIVR_FI16m},
  { X86::DIVR_FpI16m64, X86::DIVR_FI16m},
  { X86::DIVR_FpI16m80, X86::DIVR_FI16m},
  { X86::DIVR_FpI32m32, X86::DIVR_FI32m},
  { X86::DIVR_FpI32m64, X86::DIVR_FI32m},
  { X86::DIVR_FpI32m80, X86::DIVR_FI32m},
  { X86::DIV_Fp32m    , X86::DIV_F32m  },
  { X86::DIV_Fp64m    , X86::DIV_F64m  },
  { X86::DIV_Fp64m32  , X86::DIV_F32m  },
  { X86::DIV_Fp80m32  , X86::DIV_F32m  },
  { X86::DIV_Fp80m64  , X86::DIV_F64m  },
  { X86::DIV_FpI16m32 , X86::DIV_FI16m },
  { X86::DIV_FpI16m64 , X86::DIV_FI16m },
  { X86::DIV_FpI16m80 , X86::DIV_FI16m },
  { X86::DIV_FpI32m32 , X86::DIV_FI32m },
  { X86::DIV_FpI32m64 , X86::DIV_FI32m },
  { X86::DIV_FpI32m80 , X86::DIV_FI32m },
  { X86::ILD_Fp16m32  , X86::ILD_F16m  },
  { X86::ILD_Fp16m64  , X86::ILD_F16m  },
  { X86::ILD_Fp16m80  , X86::ILD_F16m  },
  { X86::ILD_Fp32m32  , X86::ILD_F32m  },
  { X86::ILD_Fp32m64  , X86::ILD_F32m  },
  { X86::ILD_Fp32m80  , X86::ILD_F32m  },
  { X86::ILD_Fp64m32  , X86::ILD_F64m  },
  { X86::ILD_Fp64m64  , X86::ILD_F64m  },
  { X86::ILD_Fp64m80  , X86::ILD_F64m  },
  { X86::ISTT_Fp16m32 , X86::ISTT_FP16m},
  { X86::ISTT_Fp16m64 , X86::ISTT_FP16m},
  { X86::ISTT_Fp16m80 , X86::ISTT_FP16m},
  { X86::ISTT_Fp32m32 , X86::ISTT_FP32m},
  { X86::ISTT_Fp32m64 , X86::ISTT_FP32m},
  { X86::ISTT_Fp32m80 , X86::ISTT_FP32m},
  { X86::ISTT_Fp64m32 , X86::ISTT_FP64m},
  { X86::ISTT_Fp64m64 , X86::ISTT_FP64m},
  { X86::ISTT_Fp64m80 , X86::ISTT_FP64m},
  { X86::IST_Fp16m32  , X86::IST_F16m  },
  { X86::IST_Fp16m64  , X86::IST_F16m  },
  { X86::IST_Fp16m80  , X86::IST_F16m  },
  { X86::IST_Fp32m32  , X86::IST_F32m  },
  { X86::IST_Fp32m64  , X86::IST_F32m  },
  { X86::IST_Fp32m80  , X86::IST_F32m  },
  { X86::IST_Fp64m32  , X86::IST_FP64m },
  { X86::IST_Fp64m64  , X86::IST_FP64m },
  { X86::IST_Fp64m80  , X86::IST_FP64m },
  { X86::LD_Fp032     , X86::LD_F0     },
  { X86::LD_Fp064     , X86::LD_F0     },
  { X86::LD_Fp080     , X86::LD_F0     },
  { X86::LD_Fp132     , X86::LD_F1     },
  { X86::LD_Fp164     , X86::LD_F1     },
  { X86::LD_Fp180     , X86::LD_F1     },
  { X86::LD_Fp32m     , X86::LD_F32m   },
  { X86::LD_Fp32m64   , X86::LD_F32m   },
  { X86::LD_Fp32m80   , X86::LD_F32m   },
  { X86::LD_Fp64m     , X86::LD_F64m   },
  { X86::LD_Fp64m80   , X86::LD_F64m   },
  { X86::LD_Fp80m     , X86::LD_F80m   },
  { X86::MUL_Fp32m    , X86::MUL_F32m  },
  { X86::MUL_Fp64m    , X86::MUL_F64m  },
  { X86::MUL_Fp64m32  , X86::MUL_F32m  },
  { X86::MUL_Fp80m32  , X86::MUL_F32m  },
  { X86::MUL_Fp80m64  , X86::MUL_F64m  },
  { X86::MUL_FpI16m32 , X86::MUL_FI16m },
  { X86::MUL_FpI16m64 , X86::MUL_FI16m },
  { X86::MUL_FpI16m80 , X86::MUL_FI16m },
  { X86::MUL_FpI32m32 , X86::MUL_FI32m },
  { X86::MUL_FpI32m64 , X86::MUL_FI32m },
  { X86::MUL_FpI32m80 , X86::MUL_FI32m },
  { X86::SIN_Fp32     , X86::SIN_F     },
  { X86::SIN_Fp64     , X86::SIN_F     },
  { X86::SIN_Fp80     , X86::SIN_F     },
  { X86::SQRT_Fp32    , X86::SQRT_F    },
  { X86::SQRT_Fp64    , X86::SQRT_F    },
  { X86::SQRT_Fp80    , X86::SQRT_F    },
  { X86::ST_Fp32m     , X86::ST_F32m   },
  { X86::ST_Fp64m     , X86::ST_F64m   },
  { X86::ST_Fp64m32   , X86::ST_F32m   },
  { X86::ST_Fp80m32   , X86::ST_F32m   },
  { X86::ST_Fp80m64   , X86::ST_F64m   },
  { X86::ST_FpP80m    , X86::ST_FP80m  },
  { X86::SUBR_Fp32m   , X86::SUBR_F32m },
  { X86::SUBR_Fp64m   , X86::SUBR_F64m },
  { X86::SUBR_Fp64m32 , X86::SUBR_F32m },
  { X86::SUBR_Fp80m32 , X86::SUBR_F32m },
  { X86::SUBR_Fp80m64 , X86::SUBR_F64m },
  { X86::SUBR_FpI16m32, X86::SUBR_FI16m},
  { X86::SUBR_FpI16m64, X86::SUBR_FI16m},
  { X86::SUBR_FpI16m80, X86::SUBR_FI16m},
  { X86::SUBR_FpI32m32, X86::SUBR_FI32m},
  { X86::SUBR_FpI32m64, X86::SUBR_FI32m},
  { X86::SUBR_FpI32m80, X86::SUBR_FI32m},
  { X86::SUB_Fp32m    , X86::SUB_F32m  },
  { X86::SUB_Fp64m    , X86::SUB_F64m  },
  { X86::SUB_Fp64m32  , X86::SUB_F32m  },
  { X86::SUB_Fp80m32  , X86::SUB_F32m  },
  { X86::SUB_Fp80m64  , X86::SUB_F64m  },
  { X86::SUB_FpI16m32 , X86::SUB_FI16m },
  { X86::SUB_FpI16m64 , X86::SUB_FI16m },
  { X86::SUB_FpI16m80 , X86::SUB_FI16m },
  { X86::SUB_FpI32m32 , X86::SUB_FI32m },
  { X86::SUB_FpI32m64 , X86::SUB_FI32m },
  { X86::SUB_FpI32m80 , X86::SUB_FI32m },
  { X86::TST_Fp32     , X86::TST_F     },
  { X86::TST_Fp64     , X86::TST_F     },
  { X86::TST_Fp80     , X86::TST_F     },
  { X86::UCOM_FpIr32  , X86::UCOM_FIr  },
  { X86::UCOM_FpIr64  , X86::UCOM_FIr  },
  { X86::UCOM_FpIr80  , X86::UCOM_FIr  },
  { X86::UCOM_Fpr32   , X86::UCOM_Fr   },
  { X86::UCOM_Fpr64   , X86::UCOM_Fr   },
  { X86::UCOM_Fpr80   , X86::UCOM_Fr   },
};

static unsigned getConcreteOpcode(unsigned Opcode) {
  ASSERT_SORTED(OpcodeTable);
  int Opc = Lookup(OpcodeTable, Opcode);
  assert(Opc != -1 && "FP Stack instruction not in OpcodeTable!");
  return Opc;
}

//===----------------------------------------------------------------------===//
// Helper Methods
//===----------------------------------------------------------------------===//

// PopTable - Sorted map of instructions to their popping version.  The first
// element is an instruction, the second is the version which pops.
//
static const TableEntry PopTable[] = {
  { X86::ADD_FrST0 , X86::ADD_FPrST0  },

  { X86::DIVR_FrST0, X86::DIVR_FPrST0 },
  { X86::DIV_FrST0 , X86::DIV_FPrST0  },

  { X86::IST_F16m  , X86::IST_FP16m   },
  { X86::IST_F32m  , X86::IST_FP32m   },

  { X86::MUL_FrST0 , X86::MUL_FPrST0  },

  { X86::ST_F32m   , X86::ST_FP32m    },
  { X86::ST_F64m   , X86::ST_FP64m    },
  { X86::ST_Frr    , X86::ST_FPrr     },

  { X86::SUBR_FrST0, X86::SUBR_FPrST0 },
  { X86::SUB_FrST0 , X86::SUB_FPrST0  },

  { X86::UCOM_FIr  , X86::UCOM_FIPr   },

  { X86::UCOM_FPr  , X86::UCOM_FPPr   },
  { X86::UCOM_Fr   , X86::UCOM_FPr    },
};

/// popStackAfter - Pop the current value off of the top of the FP stack after
/// the specified instruction.  This attempts to be sneaky and combine the pop
/// into the instruction itself if possible.  The iterator is left pointing to
/// the last instruction, be it a new pop instruction inserted, or the old
/// instruction if it was modified in place.
///
void FPS::popStackAfter(MachineBasicBlock::iterator &I) {
  MachineInstr &MI = *I;
  const DebugLoc &dl = MI.getDebugLoc();
  ASSERT_SORTED(PopTable);

  popReg();

  // Check to see if there is a popping version of this instruction...
  int Opcode = Lookup(PopTable, I->getOpcode());
  if (Opcode != -1) {
    I->setDesc(TII->get(Opcode));
    if (Opcode == X86::UCOM_FPPr)
      I->RemoveOperand(0);
  } else {    // Insert an explicit pop
    I = BuildMI(*MBB, ++I, dl, TII->get(X86::ST_FPrr)).addReg(X86::ST0);
  }
}

/// freeStackSlotAfter - Free the specified register from the register stack, so
/// that it is no longer in a register.  If the register is currently at the top
/// of the stack, we just pop the current instruction, otherwise we store the
/// current top-of-stack into the specified slot, then pop the top of stack.
void FPS::freeStackSlotAfter(MachineBasicBlock::iterator &I, unsigned FPRegNo) {
  if (getStackEntry(0) == FPRegNo) {  // already at the top of stack? easy.
    popStackAfter(I);
    return;
  }

  // Otherwise, store the top of stack into the dead slot, killing the operand
  // without having to add in an explicit xchg then pop.
  //
  I = freeStackSlotBefore(++I, FPRegNo);
}

/// freeStackSlotBefore - Free the specified register without trying any
/// folding.
MachineBasicBlock::iterator
FPS::freeStackSlotBefore(MachineBasicBlock::iterator I, unsigned FPRegNo) {
  unsigned STReg    = getSTReg(FPRegNo);
  unsigned OldSlot  = getSlot(FPRegNo);
  unsigned TopReg   = Stack[StackTop-1];
  Stack[OldSlot]    = TopReg;
  RegMap[TopReg]    = OldSlot;
  RegMap[FPRegNo]   = ~0;
  Stack[--StackTop] = ~0;
  return BuildMI(*MBB, I, DebugLoc(), TII->get(X86::ST_FPrr))
      .addReg(STReg)
      .getInstr();
}

/// adjustLiveRegs - Kill and revive registers such that exactly the FP
/// registers with a bit in Mask are live.
void FPS::adjustLiveRegs(unsigned Mask, MachineBasicBlock::iterator I) {
  unsigned Defs = Mask;
  unsigned Kills = 0;
  for (unsigned i = 0; i < StackTop; ++i) {
    unsigned RegNo = Stack[i];
    if (!(Defs & (1 << RegNo)))
      // This register is live, but we don't want it.
      Kills |= (1 << RegNo);
    else
      // We don't need to imp-def this live register.
      Defs &= ~(1 << RegNo);
  }
  assert((Kills & Defs) == 0 && "Register needs killing and def'ing?");

  // Produce implicit-defs for free by using killed registers.
  while (Kills && Defs) {
    unsigned KReg = countTrailingZeros(Kills);
    unsigned DReg = countTrailingZeros(Defs);
    LLVM_DEBUG(dbgs() << "Renaming %fp" << KReg << " as imp %fp" << DReg
                      << "\n");
    std::swap(Stack[getSlot(KReg)], Stack[getSlot(DReg)]);
    std::swap(RegMap[KReg], RegMap[DReg]);
    Kills &= ~(1 << KReg);
    Defs &= ~(1 << DReg);
  }

  // Kill registers by popping.
  if (Kills && I != MBB->begin()) {
    MachineBasicBlock::iterator I2 = std::prev(I);
    while (StackTop) {
      unsigned KReg = getStackEntry(0);
      if (!(Kills & (1 << KReg)))
        break;
      LLVM_DEBUG(dbgs() << "Popping %fp" << KReg << "\n");
      popStackAfter(I2);
      Kills &= ~(1 << KReg);
    }
  }

  // Manually kill the rest.
  while (Kills) {
    unsigned KReg = countTrailingZeros(Kills);
    LLVM_DEBUG(dbgs() << "Killing %fp" << KReg << "\n");
    freeStackSlotBefore(I, KReg);
    Kills &= ~(1 << KReg);
  }

  // Load zeros for all the imp-defs.
  while(Defs) {
    unsigned DReg = countTrailingZeros(Defs);
    LLVM_DEBUG(dbgs() << "Defining %fp" << DReg << " as 0\n");
    BuildMI(*MBB, I, DebugLoc(), TII->get(X86::LD_F0));
    pushReg(DReg);
    Defs &= ~(1 << DReg);
  }

  // Now we should have the correct registers live.
  LLVM_DEBUG(dumpStack());
  assert(StackTop == countPopulation(Mask) && "Live count mismatch");
}

/// shuffleStackTop - emit fxch instructions before I to shuffle the top
/// FixCount entries into the order given by FixStack.
/// FIXME: Is there a better algorithm than insertion sort?
void FPS::shuffleStackTop(const unsigned char *FixStack,
                          unsigned FixCount,
                          MachineBasicBlock::iterator I) {
  // Move items into place, starting from the desired stack bottom.
  while (FixCount--) {
    // Old register at position FixCount.
    unsigned OldReg = getStackEntry(FixCount);
    // Desired register at position FixCount.
    unsigned Reg = FixStack[FixCount];
    if (Reg == OldReg)
      continue;
    // (Reg st0) (OldReg st0) = (Reg OldReg st0)
    moveToTop(Reg, I);
    if (FixCount > 0)
      moveToTop(OldReg, I);
  }
  LLVM_DEBUG(dumpStack());
}


//===----------------------------------------------------------------------===//
// Instruction transformation implementation
//===----------------------------------------------------------------------===//

void FPS::handleCall(MachineBasicBlock::iterator &I) {
  unsigned STReturns = 0;
  const MachineFunction* MF = I->getParent()->getParent();

  for (const auto &MO : I->operands()) {
    if (!MO.isReg())
      continue;

    unsigned R = MO.getReg() - X86::FP0;

    if (R < 8) {
      if (MF->getFunction().getCallingConv() != CallingConv::X86_RegCall) {
        assert(MO.isDef() && MO.isImplicit());
      }

      STReturns |= 1 << R;
    }
  }

  unsigned N = countTrailingOnes(STReturns);

  // FP registers used for function return must be consecutive starting at
  // FP0
  assert(STReturns == 0 || (isMask_32(STReturns) && N <= 2));

  // Reset the FP Stack - It is required because of possible leftovers from
  // passed arguments. The caller should assume that the FP stack is
  // returned empty (unless the callee returns values on FP stack).
  while (StackTop > 0)
    popReg();

  for (unsigned I = 0; I < N; ++I)
    pushReg(N - I - 1);
}

/// If RET has an FP register use operand, pass the first one in ST(0) and
/// the second one in ST(1).
void FPS::handleReturn(MachineBasicBlock::iterator &I) {
  MachineInstr &MI = *I;

  // Find the register operands.
  unsigned FirstFPRegOp = ~0U, SecondFPRegOp = ~0U;
  unsigned LiveMask = 0;

  for (unsigned i = 0, e = MI.getNumOperands(); i != e; ++i) {
    MachineOperand &Op = MI.getOperand(i);
    if (!Op.isReg() || Op.getReg() < X86::FP0 || Op.getReg() > X86::FP6)
      continue;
    // FP Register uses must be kills unless there are two uses of the same
    // register, in which case only one will be a kill.
    assert(Op.isUse() &&
           (Op.isKill() ||                    // Marked kill.
            getFPReg(Op) == FirstFPRegOp ||   // Second instance.
            MI.killsRegister(Op.getReg())) && // Later use is marked kill.
           "Ret only defs operands, and values aren't live beyond it");

    if (FirstFPRegOp == ~0U)
      FirstFPRegOp = getFPReg(Op);
    else {
      assert(SecondFPRegOp == ~0U && "More than two fp operands!");
      SecondFPRegOp = getFPReg(Op);
    }
    LiveMask |= (1 << getFPReg(Op));

    // Remove the operand so that later passes don't see it.
    MI.RemoveOperand(i);
    --i;
    --e;
  }

  // We may have been carrying spurious live-ins, so make sure only the
  // returned registers are left live.
  adjustLiveRegs(LiveMask, MI);
  if (!LiveMask) return;  // Quick check to see if any are possible.

  // There are only four possibilities here:
  // 1) we are returning a single FP value.  In this case, it has to be in
  //    ST(0) already, so just declare success by removing the value from the
  //    FP Stack.
  if (SecondFPRegOp == ~0U) {
    // Assert that the top of stack contains the right FP register.
    assert(StackTop == 1 && FirstFPRegOp == getStackEntry(0) &&
           "Top of stack not the right register for RET!");

    // Ok, everything is good, mark the value as not being on the stack
    // anymore so that our assertion about the stack being empty at end of
    // block doesn't fire.
    StackTop = 0;
    return;
  }

  // Otherwise, we are returning two values:
  // 2) If returning the same value for both, we only have one thing in the FP
  //    stack.  Consider:  RET FP1, FP1
  if (StackTop == 1) {
    assert(FirstFPRegOp == SecondFPRegOp && FirstFPRegOp == getStackEntry(0)&&
           "Stack misconfiguration for RET!");

    // Duplicate the TOS so that we return it twice.  Just pick some other FPx
    // register to hold it.
    unsigned NewReg = ScratchFPReg;
    duplicateToTop(FirstFPRegOp, NewReg, MI);
    FirstFPRegOp = NewReg;
  }

  /// Okay we know we have two different FPx operands now:
  assert(StackTop == 2 && "Must have two values live!");

  /// 3) If SecondFPRegOp is currently in ST(0) and FirstFPRegOp is currently
  ///    in ST(1).  In this case, emit an fxch.
  if (getStackEntry(0) == SecondFPRegOp) {
    assert(getStackEntry(1) == FirstFPRegOp && "Unknown regs live");
    moveToTop(FirstFPRegOp, MI);
  }

  /// 4) Finally, FirstFPRegOp must be in ST(0) and SecondFPRegOp must be in
  /// ST(1).  Just remove both from our understanding of the stack and return.
  assert(getStackEntry(0) == FirstFPRegOp && "Unknown regs live");
  assert(getStackEntry(1) == SecondFPRegOp && "Unknown regs live");
  StackTop = 0;
}

/// handleZeroArgFP - ST(0) = fld0    ST(0) = flds <mem>
///
void FPS::handleZeroArgFP(MachineBasicBlock::iterator &I) {
  MachineInstr &MI = *I;
  unsigned DestReg = getFPReg(MI.getOperand(0));

  // Change from the pseudo instruction to the concrete instruction.
  MI.RemoveOperand(0); // Remove the explicit ST(0) operand
  MI.setDesc(TII->get(getConcreteOpcode(MI.getOpcode())));

  // Result gets pushed on the stack.
  pushReg(DestReg);
}

/// handleOneArgFP - fst <mem>, ST(0)
///
void FPS::handleOneArgFP(MachineBasicBlock::iterator &I) {
  MachineInstr &MI = *I;
  unsigned NumOps = MI.getDesc().getNumOperands();
  assert((NumOps == X86::AddrNumOperands + 1 || NumOps == 1) &&
         "Can only handle fst* & ftst instructions!");

  // Is this the last use of the source register?
  unsigned Reg = getFPReg(MI.getOperand(NumOps - 1));
  bool KillsSrc = MI.killsRegister(X86::FP0 + Reg);

  // FISTP64m is strange because there isn't a non-popping versions.
  // If we have one _and_ we don't want to pop the operand, duplicate the value
  // on the stack instead of moving it.  This ensure that popping the value is
  // always ok.
  // Ditto FISTTP16m, FISTTP32m, FISTTP64m, ST_FpP80m.
  //
  if (!KillsSrc && (MI.getOpcode() == X86::IST_Fp64m32 ||
                    MI.getOpcode() == X86::ISTT_Fp16m32 ||
                    MI.getOpcode() == X86::ISTT_Fp32m32 ||
                    MI.getOpcode() == X86::ISTT_Fp64m32 ||
                    MI.getOpcode() == X86::IST_Fp64m64 ||
                    MI.getOpcode() == X86::ISTT_Fp16m64 ||
                    MI.getOpcode() == X86::ISTT_Fp32m64 ||
                    MI.getOpcode() == X86::ISTT_Fp64m64 ||
                    MI.getOpcode() == X86::IST_Fp64m80 ||
                    MI.getOpcode() == X86::ISTT_Fp16m80 ||
                    MI.getOpcode() == X86::ISTT_Fp32m80 ||
                    MI.getOpcode() == X86::ISTT_Fp64m80 ||
                    MI.getOpcode() == X86::ST_FpP80m)) {
    duplicateToTop(Reg, ScratchFPReg, I);
  } else {
    moveToTop(Reg, I);            // Move to the top of the stack...
  }

  // Convert from the pseudo instruction to the concrete instruction.
  MI.RemoveOperand(NumOps - 1); // Remove explicit ST(0) operand
  MI.setDesc(TII->get(getConcreteOpcode(MI.getOpcode())));

  if (MI.getOpcode() == X86::IST_FP64m || MI.getOpcode() == X86::ISTT_FP16m ||
      MI.getOpcode() == X86::ISTT_FP32m || MI.getOpcode() == X86::ISTT_FP64m ||
      MI.getOpcode() == X86::ST_FP80m) {
    if (StackTop == 0)
      report_fatal_error("Stack empty??");
    --StackTop;
  } else if (KillsSrc) { // Last use of operand?
    popStackAfter(I);
  }
}


/// handleOneArgFPRW: Handle instructions that read from the top of stack and
/// replace the value with a newly computed value.  These instructions may have
/// non-fp operands after their FP operands.
///
///  Examples:
///     R1 = fchs R2
///     R1 = fadd R2, [mem]
///
void FPS::handleOneArgFPRW(MachineBasicBlock::iterator &I) {
  MachineInstr &MI = *I;
#ifndef NDEBUG
  unsigned NumOps = MI.getDesc().getNumOperands();
  assert(NumOps >= 2 && "FPRW instructions must have 2 ops!!");
#endif

  // Is this the last use of the source register?
  unsigned Reg = getFPReg(MI.getOperand(1));
  bool KillsSrc = MI.killsRegister(X86::FP0 + Reg);

  if (KillsSrc) {
    // If this is the last use of the source register, just make sure it's on
    // the top of the stack.
    moveToTop(Reg, I);
    if (StackTop == 0)
      report_fatal_error("Stack cannot be empty!");
    --StackTop;
    pushReg(getFPReg(MI.getOperand(0)));
  } else {
    // If this is not the last use of the source register, _copy_ it to the top
    // of the stack.
    duplicateToTop(Reg, getFPReg(MI.getOperand(0)), I);
  }

  // Change from the pseudo instruction to the concrete instruction.
  MI.RemoveOperand(1); // Drop the source operand.
  MI.RemoveOperand(0); // Drop the destination operand.
  MI.setDesc(TII->get(getConcreteOpcode(MI.getOpcode())));
}


//===----------------------------------------------------------------------===//
// Define tables of various ways to map pseudo instructions
//

// ForwardST0Table - Map: A = B op C  into: ST(0) = ST(0) op ST(i)
static const TableEntry ForwardST0Table[] = {
  { X86::ADD_Fp32  , X86::ADD_FST0r },
  { X86::ADD_Fp64  , X86::ADD_FST0r },
  { X86::ADD_Fp80  , X86::ADD_FST0r },
  { X86::DIV_Fp32  , X86::DIV_FST0r },
  { X86::DIV_Fp64  , X86::DIV_FST0r },
  { X86::DIV_Fp80  , X86::DIV_FST0r },
  { X86::MUL_Fp32  , X86::MUL_FST0r },
  { X86::MUL_Fp64  , X86::MUL_FST0r },
  { X86::MUL_Fp80  , X86::MUL_FST0r },
  { X86::SUB_Fp32  , X86::SUB_FST0r },
  { X86::SUB_Fp64  , X86::SUB_FST0r },
  { X86::SUB_Fp80  , X86::SUB_FST0r },
};

// ReverseST0Table - Map: A = B op C  into: ST(0) = ST(i) op ST(0)
static const TableEntry ReverseST0Table[] = {
  { X86::ADD_Fp32  , X86::ADD_FST0r  },   // commutative
  { X86::ADD_Fp64  , X86::ADD_FST0r  },   // commutative
  { X86::ADD_Fp80  , X86::ADD_FST0r  },   // commutative
  { X86::DIV_Fp32  , X86::DIVR_FST0r },
  { X86::DIV_Fp64  , X86::DIVR_FST0r },
  { X86::DIV_Fp80  , X86::DIVR_FST0r },
  { X86::MUL_Fp32  , X86::MUL_FST0r  },   // commutative
  { X86::MUL_Fp64  , X86::MUL_FST0r  },   // commutative
  { X86::MUL_Fp80  , X86::MUL_FST0r  },   // commutative
  { X86::SUB_Fp32  , X86::SUBR_FST0r },
  { X86::SUB_Fp64  , X86::SUBR_FST0r },
  { X86::SUB_Fp80  , X86::SUBR_FST0r },
};

// ForwardSTiTable - Map: A = B op C  into: ST(i) = ST(0) op ST(i)
static const TableEntry ForwardSTiTable[] = {
  { X86::ADD_Fp32  , X86::ADD_FrST0  },   // commutative
  { X86::ADD_Fp64  , X86::ADD_FrST0  },   // commutative
  { X86::ADD_Fp80  , X86::ADD_FrST0  },   // commutative
  { X86::DIV_Fp32  , X86::DIVR_FrST0 },
  { X86::DIV_Fp64  , X86::DIVR_FrST0 },
  { X86::DIV_Fp80  , X86::DIVR_FrST0 },
  { X86::MUL_Fp32  , X86::MUL_FrST0  },   // commutative
  { X86::MUL_Fp64  , X86::MUL_FrST0  },   // commutative
  { X86::MUL_Fp80  , X86::MUL_FrST0  },   // commutative
  { X86::SUB_Fp32  , X86::SUBR_FrST0 },
  { X86::SUB_Fp64  , X86::SUBR_FrST0 },
  { X86::SUB_Fp80  , X86::SUBR_FrST0 },
};

// ReverseSTiTable - Map: A = B op C  into: ST(i) = ST(i) op ST(0)
static const TableEntry ReverseSTiTable[] = {
  { X86::ADD_Fp32  , X86::ADD_FrST0 },
  { X86::ADD_Fp64  , X86::ADD_FrST0 },
  { X86::ADD_Fp80  , X86::ADD_FrST0 },
  { X86::DIV_Fp32  , X86::DIV_FrST0 },
  { X86::DIV_Fp64  , X86::DIV_FrST0 },
  { X86::DIV_Fp80  , X86::DIV_FrST0 },
  { X86::MUL_Fp32  , X86::MUL_FrST0 },
  { X86::MUL_Fp64  , X86::MUL_FrST0 },
  { X86::MUL_Fp80  , X86::MUL_FrST0 },
  { X86::SUB_Fp32  , X86::SUB_FrST0 },
  { X86::SUB_Fp64  , X86::SUB_FrST0 },
  { X86::SUB_Fp80  , X86::SUB_FrST0 },
};


/// handleTwoArgFP - Handle instructions like FADD and friends which are virtual
/// instructions which need to be simplified and possibly transformed.
///
/// Result: ST(0) = fsub  ST(0), ST(i)
///         ST(i) = fsub  ST(0), ST(i)
///         ST(0) = fsubr ST(0), ST(i)
///         ST(i) = fsubr ST(0), ST(i)
///
void FPS::handleTwoArgFP(MachineBasicBlock::iterator &I) {
  ASSERT_SORTED(ForwardST0Table); ASSERT_SORTED(ReverseST0Table);
  ASSERT_SORTED(ForwardSTiTable); ASSERT_SORTED(ReverseSTiTable);
  MachineInstr &MI = *I;

  unsigned NumOperands = MI.getDesc().getNumOperands();
  assert(NumOperands == 3 && "Illegal TwoArgFP instruction!");
  unsigned Dest = getFPReg(MI.getOperand(0));
  unsigned Op0 = getFPReg(MI.getOperand(NumOperands - 2));
  unsigned Op1 = getFPReg(MI.getOperand(NumOperands - 1));
  bool KillsOp0 = MI.killsRegister(X86::FP0 + Op0);
  bool KillsOp1 = MI.killsRegister(X86::FP0 + Op1);
  DebugLoc dl = MI.getDebugLoc();

  unsigned TOS = getStackEntry(0);

  // One of our operands must be on the top of the stack.  If neither is yet, we
  // need to move one.
  if (Op0 != TOS && Op1 != TOS) {   // No operand at TOS?
    // We can choose to move either operand to the top of the stack.  If one of
    // the operands is killed by this instruction, we want that one so that we
    // can update right on top of the old version.
    if (KillsOp0) {
      moveToTop(Op0, I);         // Move dead operand to TOS.
      TOS = Op0;
    } else if (KillsOp1) {
      moveToTop(Op1, I);
      TOS = Op1;
    } else {
      // All of the operands are live after this instruction executes, so we
      // cannot update on top of any operand.  Because of this, we must
      // duplicate one of the stack elements to the top.  It doesn't matter
      // which one we pick.
      //
      duplicateToTop(Op0, Dest, I);
      Op0 = TOS = Dest;
      KillsOp0 = true;
    }
  } else if (!KillsOp0 && !KillsOp1) {
    // If we DO have one of our operands at the top of the stack, but we don't
    // have a dead operand, we must duplicate one of the operands to a new slot
    // on the stack.
    duplicateToTop(Op0, Dest, I);
    Op0 = TOS = Dest;
    KillsOp0 = true;
  }

  // Now we know that one of our operands is on the top of the stack, and at
  // least one of our operands is killed by this instruction.
  assert((TOS == Op0 || TOS == Op1) && (KillsOp0 || KillsOp1) &&
         "Stack conditions not set up right!");

  // We decide which form to use based on what is on the top of the stack, and
  // which operand is killed by this instruction.
  ArrayRef<TableEntry> InstTable;
  bool isForward = TOS == Op0;
  bool updateST0 = (TOS == Op0 && !KillsOp1) || (TOS == Op1 && !KillsOp0);
  if (updateST0) {
    if (isForward)
      InstTable = ForwardST0Table;
    else
      InstTable = ReverseST0Table;
  } else {
    if (isForward)
      InstTable = ForwardSTiTable;
    else
      InstTable = ReverseSTiTable;
  }

  int Opcode = Lookup(InstTable, MI.getOpcode());
  assert(Opcode != -1 && "Unknown TwoArgFP pseudo instruction!");

  // NotTOS - The register which is not on the top of stack...
  unsigned NotTOS = (TOS == Op0) ? Op1 : Op0;

  // Replace the old instruction with a new instruction
  MBB->remove(&*I++);
  I = BuildMI(*MBB, I, dl, TII->get(Opcode)).addReg(getSTReg(NotTOS));

  // If both operands are killed, pop one off of the stack in addition to
  // overwriting the other one.
  if (KillsOp0 && KillsOp1 && Op0 != Op1) {
    assert(!updateST0 && "Should have updated other operand!");
    popStackAfter(I);   // Pop the top of stack
  }

  // Update stack information so that we know the destination register is now on
  // the stack.
  unsigned UpdatedSlot = getSlot(updateST0 ? TOS : NotTOS);
  assert(UpdatedSlot < StackTop && Dest < 7);
  Stack[UpdatedSlot]   = Dest;
  RegMap[Dest]         = UpdatedSlot;
  MBB->getParent()->DeleteMachineInstr(&MI); // Remove the old instruction
}

/// handleCompareFP - Handle FUCOM and FUCOMI instructions, which have two FP
/// register arguments and no explicit destinations.
///
void FPS::handleCompareFP(MachineBasicBlock::iterator &I) {
  ASSERT_SORTED(ForwardST0Table); ASSERT_SORTED(ReverseST0Table);
  ASSERT_SORTED(ForwardSTiTable); ASSERT_SORTED(ReverseSTiTable);
  MachineInstr &MI = *I;

  unsigned NumOperands = MI.getDesc().getNumOperands();
  assert(NumOperands == 2 && "Illegal FUCOM* instruction!");
  unsigned Op0 = getFPReg(MI.getOperand(NumOperands - 2));
  unsigned Op1 = getFPReg(MI.getOperand(NumOperands - 1));
  bool KillsOp0 = MI.killsRegister(X86::FP0 + Op0);
  bool KillsOp1 = MI.killsRegister(X86::FP0 + Op1);

  // Make sure the first operand is on the top of stack, the other one can be
  // anywhere.
  moveToTop(Op0, I);

  // Change from the pseudo instruction to the concrete instruction.
  MI.getOperand(0).setReg(getSTReg(Op1));
  MI.RemoveOperand(1);
  MI.setDesc(TII->get(getConcreteOpcode(MI.getOpcode())));

  // If any of the operands are killed by this instruction, free them.
  if (KillsOp0) freeStackSlotAfter(I, Op0);
  if (KillsOp1 && Op0 != Op1) freeStackSlotAfter(I, Op1);
}

/// handleCondMovFP - Handle two address conditional move instructions.  These
/// instructions move a st(i) register to st(0) iff a condition is true.  These
/// instructions require that the first operand is at the top of the stack, but
/// otherwise don't modify the stack at all.
void FPS::handleCondMovFP(MachineBasicBlock::iterator &I) {
  MachineInstr &MI = *I;

  unsigned Op0 = getFPReg(MI.getOperand(0));
  unsigned Op1 = getFPReg(MI.getOperand(2));
  bool KillsOp1 = MI.killsRegister(X86::FP0 + Op1);

  // The first operand *must* be on the top of the stack.
  moveToTop(Op0, I);

  // Change the second operand to the stack register that the operand is in.
  // Change from the pseudo instruction to the concrete instruction.
  MI.RemoveOperand(0);
  MI.RemoveOperand(1);
  MI.getOperand(0).setReg(getSTReg(Op1));
  MI.setDesc(TII->get(getConcreteOpcode(MI.getOpcode())));

  // If we kill the second operand, make sure to pop it from the stack.
  if (Op0 != Op1 && KillsOp1) {
    // Get this value off of the register stack.
    freeStackSlotAfter(I, Op1);
  }
}


/// handleSpecialFP - Handle special instructions which behave unlike other
/// floating point instructions.  This is primarily intended for use by pseudo
/// instructions.
///
void FPS::handleSpecialFP(MachineBasicBlock::iterator &Inst) {
  MachineInstr &MI = *Inst;

  if (MI.isCall()) {
    handleCall(Inst);
    return;
  }

  if (MI.isReturn()) {
    handleReturn(Inst);
    return;
  }

  switch (MI.getOpcode()) {
  default: llvm_unreachable("Unknown SpecialFP instruction!");
  case TargetOpcode::COPY: {
    // We handle three kinds of copies: FP <- FP, FP <- ST, and ST <- FP.
    const MachineOperand &MO1 = MI.getOperand(1);
    const MachineOperand &MO0 = MI.getOperand(0);
    bool KillsSrc = MI.killsRegister(MO1.getReg());

    // FP <- FP copy.
    unsigned DstFP = getFPReg(MO0);
    unsigned SrcFP = getFPReg(MO1);
    assert(isLive(SrcFP) && "Cannot copy dead register");
    if (KillsSrc) {
      // If the input operand is killed, we can just change the owner of the
      // incoming stack slot into the result.
      unsigned Slot = getSlot(SrcFP);
      Stack[Slot] = DstFP;
      RegMap[DstFP] = Slot;
    } else {
      // For COPY we just duplicate the specified value to a new stack slot.
      // This could be made better, but would require substantial changes.
      duplicateToTop(SrcFP, DstFP, Inst);
    }
    break;
  }

  case TargetOpcode::IMPLICIT_DEF: {
    // All FP registers must be explicitly defined, so load a 0 instead.
    unsigned Reg = MI.getOperand(0).getReg() - X86::FP0;
    LLVM_DEBUG(dbgs() << "Emitting LD_F0 for implicit FP" << Reg << '\n');
    BuildMI(*MBB, Inst, MI.getDebugLoc(), TII->get(X86::LD_F0));
    pushReg(Reg);
    break;
  }

  case TargetOpcode::INLINEASM: {
    // The inline asm MachineInstr currently only *uses* FP registers for the
    // 'f' constraint.  These should be turned into the current ST(x) register
    // in the machine instr.
    //
    // There are special rules for x87 inline assembly. The compiler must know
    // exactly how many registers are popped and pushed implicitly by the asm.
    // Otherwise it is not possible to restore the stack state after the inline
    // asm.
    //
    // There are 3 kinds of input operands:
    //
    // 1. Popped inputs. These must appear at the stack top in ST0-STn. A
    //    popped input operand must be in a fixed stack slot, and it is either
    //    tied to an output operand, or in the clobber list. The MI has ST use
    //    and def operands for these inputs.
    //
    // 2. Fixed inputs. These inputs appear in fixed stack slots, but are
    //    preserved by the inline asm. The fixed stack slots must be STn-STm
    //    following the popped inputs. A fixed input operand cannot be tied to
    //    an output or appear in the clobber list. The MI has ST use operands
    //    and no defs for these inputs.
    //
    // 3. Preserved inputs. These inputs use the "f" constraint which is
    //    represented as an FP register. The inline asm won't change these
    //    stack slots.
    //
    // Outputs must be in ST registers, FP outputs are not allowed. Clobbered
    // registers do not count as output operands. The inline asm changes the
    // stack as if it popped all the popped inputs and then pushed all the
    // output operands.

    // Scan the assembly for ST registers used, defined and clobbered. We can
    // only tell clobbers from defs by looking at the asm descriptor.
    unsigned STUses = 0, STDefs = 0, STClobbers = 0, STDeadDefs = 0;
    unsigned NumOps = 0;
    SmallSet<unsigned, 1> FRegIdx;
    unsigned RCID;

    for (unsigned i = InlineAsm::MIOp_FirstOperand, e = MI.getNumOperands();
         i != e && MI.getOperand(i).isImm(); i += 1 + NumOps) {
      unsigned Flags = MI.getOperand(i).getImm();

      NumOps = InlineAsm::getNumOperandRegisters(Flags);
      if (NumOps != 1)
        continue;
      const MachineOperand &MO = MI.getOperand(i + 1);
      if (!MO.isReg())
        continue;
      unsigned STReg = MO.getReg() - X86::FP0;
      if (STReg >= 8)
        continue;

      // If the flag has a register class constraint, this must be an operand
      // with constraint "f". Record its index and continue.
      if (InlineAsm::hasRegClassConstraint(Flags, RCID)) {
        FRegIdx.insert(i + 1);
        continue;
      }

      switch (InlineAsm::getKind(Flags)) {
      case InlineAsm::Kind_RegUse:
        STUses |= (1u << STReg);
        break;
      case InlineAsm::Kind_RegDef:
      case InlineAsm::Kind_RegDefEarlyClobber:
        STDefs |= (1u << STReg);
        if (MO.isDead())
          STDeadDefs |= (1u << STReg);
        break;
      case InlineAsm::Kind_Clobber:
        STClobbers |= (1u << STReg);
        break;
      default:
        break;
      }
    }

    if (STUses && !isMask_32(STUses))
      MI.emitError("fixed input regs must be last on the x87 stack");
    unsigned NumSTUses = countTrailingOnes(STUses);

    // Defs must be contiguous from the stack top. ST0-STn.
    if (STDefs && !isMask_32(STDefs)) {
      MI.emitError("output regs must be last on the x87 stack");
      STDefs = NextPowerOf2(STDefs) - 1;
    }
    unsigned NumSTDefs = countTrailingOnes(STDefs);

    // So must the clobbered stack slots. ST0-STm, m >= n.
    if (STClobbers && !isMask_32(STDefs | STClobbers))
      MI.emitError("clobbers must be last on the x87 stack");

    // Popped inputs are the ones that are also clobbered or defined.
    unsigned STPopped = STUses & (STDefs | STClobbers);
    if (STPopped && !isMask_32(STPopped))
      MI.emitError("implicitly popped regs must be last on the x87 stack");
    unsigned NumSTPopped = countTrailingOnes(STPopped);

    LLVM_DEBUG(dbgs() << "Asm uses " << NumSTUses << " fixed regs, pops "
                      << NumSTPopped << ", and defines " << NumSTDefs
                      << " regs.\n");

#ifndef NDEBUG
    // If any input operand uses constraint "f", all output register
    // constraints must be early-clobber defs.
    for (unsigned I = 0, E = MI.getNumOperands(); I < E; ++I)
      if (FRegIdx.count(I)) {
        assert((1 << getFPReg(MI.getOperand(I)) & STDefs) == 0 &&
               "Operands with constraint \"f\" cannot overlap with defs");
      }
#endif

    // Collect all FP registers (register operands with constraints "t", "u",
    // and "f") to kill afer the instruction.
    unsigned FPKills = ((1u << NumFPRegs) - 1) & ~0xff;
    for (unsigned i = 0, e = MI.getNumOperands(); i != e; ++i) {
      MachineOperand &Op = MI.getOperand(i);
      if (!Op.isReg() || Op.getReg() < X86::FP0 || Op.getReg() > X86::FP6)
        continue;
      unsigned FPReg = getFPReg(Op);

      // If we kill this operand, make sure to pop it from the stack after the
      // asm.  We just remember it for now, and pop them all off at the end in
      // a batch.
      if (Op.isUse() && Op.isKill())
        FPKills |= 1U << FPReg;
    }

    // Do not include registers that are implicitly popped by defs/clobbers.
    FPKills &= ~(STDefs | STClobbers);

    // Now we can rearrange the live registers to match what was requested.
    unsigned char STUsesArray[8];

    for (unsigned I = 0; I < NumSTUses; ++I)
      STUsesArray[I] = I;

    shuffleStackTop(STUsesArray, NumSTUses, Inst);
    LLVM_DEBUG({
      dbgs() << "Before asm: ";
      dumpStack();
    });

    // With the stack layout fixed, rewrite the FP registers.
    for (unsigned i = 0, e = MI.getNumOperands(); i != e; ++i) {
      MachineOperand &Op = MI.getOperand(i);
      if (!Op.isReg() || Op.getReg() < X86::FP0 || Op.getReg() > X86::FP6)
        continue;

      unsigned FPReg = getFPReg(Op);

      if (FRegIdx.count(i))
        // Operand with constraint "f".
        Op.setReg(getSTReg(FPReg));
      else
        // Operand with a single register class constraint ("t" or "u").
        Op.setReg(X86::ST0 + FPReg);
    }

    // Simulate the inline asm popping its inputs and pushing its outputs.
    StackTop -= NumSTPopped;

    for (unsigned i = 0; i < NumSTDefs; ++i)
      pushReg(NumSTDefs - i - 1);

    // If this asm kills any FP registers (is the last use of them) we must
    // explicitly emit pop instructions for them.  Do this now after the asm has
    // executed so that the ST(x) numbers are not off (which would happen if we
    // did this inline with operand rewriting).
    //
    // Note: this might be a non-optimal pop sequence.  We might be able to do
    // better by trying to pop in stack order or something.
    while (FPKills) {
      unsigned FPReg = countTrailingZeros(FPKills);
      if (isLive(FPReg))
        freeStackSlotAfter(Inst, FPReg);
      FPKills &= ~(1U << FPReg);
    }

    // Don't delete the inline asm!
    return;
  }
  }

  Inst = MBB->erase(Inst);  // Remove the pseudo instruction

  // We want to leave I pointing to the previous instruction, but what if we
  // just erased the first instruction?
  if (Inst == MBB->begin()) {
    LLVM_DEBUG(dbgs() << "Inserting dummy KILL\n");
    Inst = BuildMI(*MBB, Inst, DebugLoc(), TII->get(TargetOpcode::KILL));
  } else
    --Inst;
}

void FPS::setKillFlags(MachineBasicBlock &MBB) const {
  const TargetRegisterInfo &TRI =
      *MBB.getParent()->getSubtarget().getRegisterInfo();
  LivePhysRegs LPR(TRI);

  LPR.addLiveOuts(MBB);

  for (MachineBasicBlock::reverse_iterator I = MBB.rbegin(), E = MBB.rend();
       I != E; ++I) {
    if (I->isDebugInstr())
      continue;

    std::bitset<8> Defs;
    SmallVector<MachineOperand *, 2> Uses;
    MachineInstr &MI = *I;

    for (auto &MO : I->operands()) {
      if (!MO.isReg())
        continue;

      unsigned Reg = MO.getReg() - X86::FP0;

      if (Reg >= 8)
        continue;

      if (MO.isDef()) {
        Defs.set(Reg);
        if (!LPR.contains(MO.getReg()))
          MO.setIsDead();
      } else
        Uses.push_back(&MO);
    }

    for (auto *MO : Uses)
      if (Defs.test(getFPReg(*MO)) || !LPR.contains(MO->getReg()))
        MO->setIsKill();

    LPR.stepBackward(MI);
  }
}