xref: /llvm-project/llvm/lib/Transforms/Scalar/IndVarSimplify.cpp (revision 7ff943a9ed878e3b8ffe162b2af41a81da1a11a2)

//===- IndVarSimplify.cpp - Induction Variable Elimination ----------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
//
// This transformation analyzes and transforms the induction variables (and
// computations derived from them) into simpler forms suitable for subsequent
// analysis and transformation.
//
// If the trip count of a loop is computable, this pass also makes the following
// changes:
//   1. The exit condition for the loop is canonicalized to compare the
//      induction value against the exit value.  This turns loops like:
//        'for (i = 7; i*i < 1000; ++i)' into 'for (i = 0; i != 25; ++i)'
//   2. Any use outside of the loop of an expression derived from the indvar
//      is changed to compute the derived value outside of the loop, eliminating
//      the dependence on the exit value of the induction variable.  If the only
//      purpose of the loop is to compute the exit value of some derived
//      expression, this transformation will make the loop dead.
//
//===----------------------------------------------------------------------===//

#include "llvm/Transforms/Scalar/IndVarSimplify.h"
#include "llvm/ADT/APFloat.h"
#include "llvm/ADT/APInt.h"
#include "llvm/ADT/ArrayRef.h"
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/None.h"
#include "llvm/ADT/Optional.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/ADT/iterator_range.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Analysis/LoopPass.h"
#include "llvm/Analysis/MemorySSA.h"
#include "llvm/Analysis/MemorySSAUpdater.h"
#include "llvm/Analysis/ScalarEvolution.h"
#include "llvm/Analysis/ScalarEvolutionExpressions.h"
#include "llvm/Analysis/TargetLibraryInfo.h"
#include "llvm/Analysis/TargetTransformInfo.h"
#include "llvm/Analysis/ValueTracking.h"
#include "llvm/IR/BasicBlock.h"
#include "llvm/IR/Constant.h"
#include "llvm/IR/ConstantRange.h"
#include "llvm/IR/Constants.h"
#include "llvm/IR/DataLayout.h"
#include "llvm/IR/DerivedTypes.h"
#include "llvm/IR/Dominators.h"
#include "llvm/IR/Function.h"
#include "llvm/IR/IRBuilder.h"
#include "llvm/IR/InstrTypes.h"
#include "llvm/IR/Instruction.h"
#include "llvm/IR/Instructions.h"
#include "llvm/IR/IntrinsicInst.h"
#include "llvm/IR/Intrinsics.h"
#include "llvm/IR/Module.h"
#include "llvm/IR/Operator.h"
#include "llvm/IR/PassManager.h"
#include "llvm/IR/PatternMatch.h"
#include "llvm/IR/Type.h"
#include "llvm/IR/Use.h"
#include "llvm/IR/User.h"
#include "llvm/IR/Value.h"
#include "llvm/IR/ValueHandle.h"
#include "llvm/InitializePasses.h"
#include "llvm/Pass.h"
#include "llvm/Support/Casting.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Support/Compiler.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/ErrorHandling.h"
#include "llvm/Support/MathExtras.h"
#include "llvm/Support/raw_ostream.h"
#include "llvm/Transforms/Scalar.h"
#include "llvm/Transforms/Scalar/LoopPassManager.h"
#include "llvm/Transforms/Utils/BasicBlockUtils.h"
#include "llvm/Transforms/Utils/Local.h"
#include "llvm/Transforms/Utils/LoopUtils.h"
#include "llvm/Transforms/Utils/ScalarEvolutionExpander.h"
#include "llvm/Transforms/Utils/SimplifyIndVar.h"
#include <cassert>
#include <cstdint>
#include <utility>

using namespace llvm;
using namespace PatternMatch;

#define DEBUG_TYPE "indvars"

STATISTIC(NumWidened     , "Number of indvars widened");
STATISTIC(NumReplaced    , "Number of exit values replaced");
STATISTIC(NumLFTR        , "Number of loop exit tests replaced");
STATISTIC(NumElimExt     , "Number of IV sign/zero extends eliminated");
STATISTIC(NumElimIV      , "Number of congruent IVs eliminated");

// Trip count verification can be enabled by default under NDEBUG if we
// implement a strong expression equivalence checker in SCEV. Until then, we
// use the verify-indvars flag, which may assert in some cases.
static cl::opt<bool> VerifyIndvars(
    "verify-indvars", cl::Hidden,
    cl::desc("Verify the ScalarEvolution result after running indvars. Has no "
             "effect in release builds. (Note: this adds additional SCEV "
             "queries potentially changing the analysis result)"));

static cl::opt<ReplaceExitVal> ReplaceExitValue(
    "replexitval", cl::Hidden, cl::init(OnlyCheapRepl),
    cl::desc("Choose the strategy to replace exit value in IndVarSimplify"),
    cl::values(clEnumValN(NeverRepl, "never", "never replace exit value"),
               clEnumValN(OnlyCheapRepl, "cheap",
                          "only replace exit value when the cost is cheap"),
               clEnumValN(NoHardUse, "noharduse",
                          "only replace exit values when loop def likely dead"),
               clEnumValN(AlwaysRepl, "always",
                          "always replace exit value whenever possible")));

static cl::opt<bool> UsePostIncrementRanges(
  "indvars-post-increment-ranges", cl::Hidden,
  cl::desc("Use post increment control-dependent ranges in IndVarSimplify"),
  cl::init(true));

static cl::opt<bool>
DisableLFTR("disable-lftr", cl::Hidden, cl::init(false),
            cl::desc("Disable Linear Function Test Replace optimization"));

static cl::opt<bool>
LoopPredication("indvars-predicate-loops", cl::Hidden, cl::init(true),
                cl::desc("Predicate conditions in read only loops"));

static cl::opt<bool>
AllowIVWidening("indvars-widen-indvars", cl::Hidden, cl::init(true),
                cl::desc("Allow widening of indvars to eliminate s/zext"));

namespace {

struct RewritePhi;

class IndVarSimplify {
  LoopInfo *LI;
  ScalarEvolution *SE;
  DominatorTree *DT;
  const DataLayout &DL;
  TargetLibraryInfo *TLI;
  const TargetTransformInfo *TTI;
  std::unique_ptr<MemorySSAUpdater> MSSAU;

  SmallVector<WeakTrackingVH, 16> DeadInsts;
  bool WidenIndVars;

  bool handleFloatingPointIV(Loop *L, PHINode *PH);
  bool rewriteNonIntegerIVs(Loop *L);

  bool simplifyAndExtend(Loop *L, SCEVExpander &Rewriter, LoopInfo *LI);
  /// Try to improve our exit conditions by converting condition from signed
  /// to unsigned or rotating computation out of the loop.
  /// (See inline comment about why this is duplicated from simplifyAndExtend)
  bool canonicalizeExitCondition(Loop *L);
  /// Try to eliminate loop exits based on analyzeable exit counts
  bool optimizeLoopExits(Loop *L, SCEVExpander &Rewriter);
  /// Try to form loop invariant tests for loop exits by changing how many
  /// iterations of the loop run when that is unobservable.
  bool predicateLoopExits(Loop *L, SCEVExpander &Rewriter);

  bool rewriteFirstIterationLoopExitValues(Loop *L);

  bool linearFunctionTestReplace(Loop *L, BasicBlock *ExitingBB,
                                 const SCEV *ExitCount,
                                 PHINode *IndVar, SCEVExpander &Rewriter);

  bool sinkUnusedInvariants(Loop *L);

public:
  IndVarSimplify(LoopInfo *LI, ScalarEvolution *SE, DominatorTree *DT,
                 const DataLayout &DL, TargetLibraryInfo *TLI,
                 TargetTransformInfo *TTI, MemorySSA *MSSA, bool WidenIndVars)
      : LI(LI), SE(SE), DT(DT), DL(DL), TLI(TLI), TTI(TTI),
        WidenIndVars(WidenIndVars) {
    if (MSSA)
      MSSAU = std::make_unique<MemorySSAUpdater>(MSSA);
  }

  bool run(Loop *L);
};

} // end anonymous namespace

//===----------------------------------------------------------------------===//
// rewriteNonIntegerIVs and helpers. Prefer integer IVs.
//===----------------------------------------------------------------------===//

/// Convert APF to an integer, if possible.
static bool ConvertToSInt(const APFloat &APF, int64_t &IntVal) {
  bool isExact = false;
  // See if we can convert this to an int64_t
  uint64_t UIntVal;
  if (APF.convertToInteger(makeMutableArrayRef(UIntVal), 64, true,
                           APFloat::rmTowardZero, &isExact) != APFloat::opOK ||
      !isExact)
    return false;
  IntVal = UIntVal;
  return true;
}

/// If the loop has floating induction variable then insert corresponding
/// integer induction variable if possible.
/// For example,
/// for(double i = 0; i < 10000; ++i)
///   bar(i)
/// is converted into
/// for(int i = 0; i < 10000; ++i)
///   bar((double)i);
bool IndVarSimplify::handleFloatingPointIV(Loop *L, PHINode *PN) {
  unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
  unsigned BackEdge     = IncomingEdge^1;

  // Check incoming value.
  auto *InitValueVal = dyn_cast<ConstantFP>(PN->getIncomingValue(IncomingEdge));

  int64_t InitValue;
  if (!InitValueVal || !ConvertToSInt(InitValueVal->getValueAPF(), InitValue))
    return false;

  // Check IV increment. Reject this PN if increment operation is not
  // an add or increment value can not be represented by an integer.
  auto *Incr = dyn_cast<BinaryOperator>(PN->getIncomingValue(BackEdge));
  if (Incr == nullptr || Incr->getOpcode() != Instruction::FAdd) return false;

  // If this is not an add of the PHI with a constantfp, or if the constant fp
  // is not an integer, bail out.
  ConstantFP *IncValueVal = dyn_cast<ConstantFP>(Incr->getOperand(1));
  int64_t IncValue;
  if (IncValueVal == nullptr || Incr->getOperand(0) != PN ||
      !ConvertToSInt(IncValueVal->getValueAPF(), IncValue))
    return false;

  // Check Incr uses. One user is PN and the other user is an exit condition
  // used by the conditional terminator.
  Value::user_iterator IncrUse = Incr->user_begin();
  Instruction *U1 = cast<Instruction>(*IncrUse++);
  if (IncrUse == Incr->user_end()) return false;
  Instruction *U2 = cast<Instruction>(*IncrUse++);
  if (IncrUse != Incr->user_end()) return false;

  // Find exit condition, which is an fcmp.  If it doesn't exist, or if it isn't
  // only used by a branch, we can't transform it.
  FCmpInst *Compare = dyn_cast<FCmpInst>(U1);
  if (!Compare)
    Compare = dyn_cast<FCmpInst>(U2);
  if (!Compare || !Compare->hasOneUse() ||
      !isa<BranchInst>(Compare->user_back()))
    return false;

  BranchInst *TheBr = cast<BranchInst>(Compare->user_back());

  // We need to verify that the branch actually controls the iteration count
  // of the loop.  If not, the new IV can overflow and no one will notice.
  // The branch block must be in the loop and one of the successors must be out
  // of the loop.
  assert(TheBr->isConditional() && "Can't use fcmp if not conditional");
  if (!L->contains(TheBr->getParent()) ||
      (L->contains(TheBr->getSuccessor(0)) &&
       L->contains(TheBr->getSuccessor(1))))
    return false;

  // If it isn't a comparison with an integer-as-fp (the exit value), we can't
  // transform it.
  ConstantFP *ExitValueVal = dyn_cast<ConstantFP>(Compare->getOperand(1));
  int64_t ExitValue;
  if (ExitValueVal == nullptr ||
      !ConvertToSInt(ExitValueVal->getValueAPF(), ExitValue))
    return false;

  // Find new predicate for integer comparison.
  CmpInst::Predicate NewPred = CmpInst::BAD_ICMP_PREDICATE;
  switch (Compare->getPredicate()) {
  default: return false;  // Unknown comparison.
  case CmpInst::FCMP_OEQ:
  case CmpInst::FCMP_UEQ: NewPred = CmpInst::ICMP_EQ; break;
  case CmpInst::FCMP_ONE:
  case CmpInst::FCMP_UNE: NewPred = CmpInst::ICMP_NE; break;
  case CmpInst::FCMP_OGT:
  case CmpInst::FCMP_UGT: NewPred = CmpInst::ICMP_SGT; break;
  case CmpInst::FCMP_OGE:
  case CmpInst::FCMP_UGE: NewPred = CmpInst::ICMP_SGE; break;
  case CmpInst::FCMP_OLT:
  case CmpInst::FCMP_ULT: NewPred = CmpInst::ICMP_SLT; break;
  case CmpInst::FCMP_OLE:
  case CmpInst::FCMP_ULE: NewPred = CmpInst::ICMP_SLE; break;
  }

  // We convert the floating point induction variable to a signed i32 value if
  // we can.  This is only safe if the comparison will not overflow in a way
  // that won't be trapped by the integer equivalent operations.  Check for this
  // now.
  // TODO: We could use i64 if it is native and the range requires it.

  // The start/stride/exit values must all fit in signed i32.
  if (!isInt<32>(InitValue) || !isInt<32>(IncValue) || !isInt<32>(ExitValue))
    return false;

  // If not actually striding (add x, 0.0), avoid touching the code.
  if (IncValue == 0)
    return false;

  // Positive and negative strides have different safety conditions.
  if (IncValue > 0) {
    // If we have a positive stride, we require the init to be less than the
    // exit value.
    if (InitValue >= ExitValue)
      return false;

    uint32_t Range = uint32_t(ExitValue-InitValue);
    // Check for infinite loop, either:
    // while (i <= Exit) or until (i > Exit)
    if (NewPred == CmpInst::ICMP_SLE || NewPred == CmpInst::ICMP_SGT) {
      if (++Range == 0) return false;  // Range overflows.
    }

    unsigned Leftover = Range % uint32_t(IncValue);

    // If this is an equality comparison, we require that the strided value
    // exactly land on the exit value, otherwise the IV condition will wrap
    // around and do things the fp IV wouldn't.
    if ((NewPred == CmpInst::ICMP_EQ || NewPred == CmpInst::ICMP_NE) &&
        Leftover != 0)
      return false;

    // If the stride would wrap around the i32 before exiting, we can't
    // transform the IV.
    if (Leftover != 0 && int32_t(ExitValue+IncValue) < ExitValue)
      return false;
  } else {
    // If we have a negative stride, we require the init to be greater than the
    // exit value.
    if (InitValue <= ExitValue)
      return false;

    uint32_t Range = uint32_t(InitValue-ExitValue);
    // Check for infinite loop, either:
    // while (i >= Exit) or until (i < Exit)
    if (NewPred == CmpInst::ICMP_SGE || NewPred == CmpInst::ICMP_SLT) {
      if (++Range == 0) return false;  // Range overflows.
    }

    unsigned Leftover = Range % uint32_t(-IncValue);

    // If this is an equality comparison, we require that the strided value
    // exactly land on the exit value, otherwise the IV condition will wrap
    // around and do things the fp IV wouldn't.
    if ((NewPred == CmpInst::ICMP_EQ || NewPred == CmpInst::ICMP_NE) &&
        Leftover != 0)
      return false;

    // If the stride would wrap around the i32 before exiting, we can't
    // transform the IV.
    if (Leftover != 0 && int32_t(ExitValue+IncValue) > ExitValue)
      return false;
  }

  IntegerType *Int32Ty = Type::getInt32Ty(PN->getContext());

  // Insert new integer induction variable.
  PHINode *NewPHI = PHINode::Create(Int32Ty, 2, PN->getName()+".int", PN);
  NewPHI->addIncoming(ConstantInt::get(Int32Ty, InitValue),
                      PN->getIncomingBlock(IncomingEdge));

  Value *NewAdd =
    BinaryOperator::CreateAdd(NewPHI, ConstantInt::get(Int32Ty, IncValue),
                              Incr->getName()+".int", Incr);
  NewPHI->addIncoming(NewAdd, PN->getIncomingBlock(BackEdge));

  ICmpInst *NewCompare = new ICmpInst(TheBr, NewPred, NewAdd,
                                      ConstantInt::get(Int32Ty, ExitValue),
                                      Compare->getName());

  // In the following deletions, PN may become dead and may be deleted.
  // Use a WeakTrackingVH to observe whether this happens.
  WeakTrackingVH WeakPH = PN;

  // Delete the old floating point exit comparison.  The branch starts using the
  // new comparison.
  NewCompare->takeName(Compare);
  Compare->replaceAllUsesWith(NewCompare);
  RecursivelyDeleteTriviallyDeadInstructions(Compare, TLI, MSSAU.get());

  // Delete the old floating point increment.
  Incr->replaceAllUsesWith(UndefValue::get(Incr->getType()));
  RecursivelyDeleteTriviallyDeadInstructions(Incr, TLI, MSSAU.get());

  // If the FP induction variable still has uses, this is because something else
  // in the loop uses its value.  In order to canonicalize the induction
  // variable, we chose to eliminate the IV and rewrite it in terms of an
  // int->fp cast.
  //
  // We give preference to sitofp over uitofp because it is faster on most
  // platforms.
  if (WeakPH) {
    Value *Conv = new SIToFPInst(NewPHI, PN->getType(), "indvar.conv",
                                 &*PN->getParent()->getFirstInsertionPt());
    PN->replaceAllUsesWith(Conv);
    RecursivelyDeleteTriviallyDeadInstructions(PN, TLI, MSSAU.get());
  }
  return true;
}

bool IndVarSimplify::rewriteNonIntegerIVs(Loop *L) {
  // First step.  Check to see if there are any floating-point recurrences.
  // If there are, change them into integer recurrences, permitting analysis by
  // the SCEV routines.
  BasicBlock *Header = L->getHeader();

  SmallVector<WeakTrackingVH, 8> PHIs;
  for (PHINode &PN : Header->phis())
    PHIs.push_back(&PN);

  bool Changed = false;
  for (unsigned i = 0, e = PHIs.size(); i != e; ++i)
    if (PHINode *PN = dyn_cast_or_null<PHINode>(&*PHIs[i]))
      Changed |= handleFloatingPointIV(L, PN);

  // If the loop previously had floating-point IV, ScalarEvolution
  // may not have been able to compute a trip count. Now that we've done some
  // re-writing, the trip count may be computable.
  if (Changed)
    SE->forgetLoop(L);
  return Changed;
}

//===---------------------------------------------------------------------===//
// rewriteFirstIterationLoopExitValues: Rewrite loop exit values if we know
// they will exit at the first iteration.
//===---------------------------------------------------------------------===//

/// Check to see if this loop has loop invariant conditions which lead to loop
/// exits. If so, we know that if the exit path is taken, it is at the first
/// loop iteration. This lets us predict exit values of PHI nodes that live in
/// loop header.
bool IndVarSimplify::rewriteFirstIterationLoopExitValues(Loop *L) {
  // Verify the input to the pass is already in LCSSA form.
  assert(L->isLCSSAForm(*DT));

  SmallVector<BasicBlock *, 8> ExitBlocks;
  L->getUniqueExitBlocks(ExitBlocks);

  bool MadeAnyChanges = false;
  for (auto *ExitBB : ExitBlocks) {
    // If there are no more PHI nodes in this exit block, then no more
    // values defined inside the loop are used on this path.
    for (PHINode &PN : ExitBB->phis()) {
      for (unsigned IncomingValIdx = 0, E = PN.getNumIncomingValues();
           IncomingValIdx != E; ++IncomingValIdx) {
        auto *IncomingBB = PN.getIncomingBlock(IncomingValIdx);

        // Can we prove that the exit must run on the first iteration if it
        // runs at all?  (i.e. early exits are fine for our purposes, but
        // traces which lead to this exit being taken on the 2nd iteration
        // aren't.)  Note that this is about whether the exit branch is
        // executed, not about whether it is taken.
        if (!L->getLoopLatch() ||
            !DT->dominates(IncomingBB, L->getLoopLatch()))
          continue;

        // Get condition that leads to the exit path.
        auto *TermInst = IncomingBB->getTerminator();

        Value *Cond = nullptr;
        if (auto *BI = dyn_cast<BranchInst>(TermInst)) {
          // Must be a conditional branch, otherwise the block
          // should not be in the loop.
          Cond = BI->getCondition();
        } else if (auto *SI = dyn_cast<SwitchInst>(TermInst))
          Cond = SI->getCondition();
        else
          continue;

        if (!L->isLoopInvariant(Cond))
          continue;

        auto *ExitVal = dyn_cast<PHINode>(PN.getIncomingValue(IncomingValIdx));

        // Only deal with PHIs in the loop header.
        if (!ExitVal || ExitVal->getParent() != L->getHeader())
          continue;

        // If ExitVal is a PHI on the loop header, then we know its
        // value along this exit because the exit can only be taken
        // on the first iteration.
        auto *LoopPreheader = L->getLoopPreheader();
        assert(LoopPreheader && "Invalid loop");
        int PreheaderIdx = ExitVal->getBasicBlockIndex(LoopPreheader);
        if (PreheaderIdx != -1) {
          assert(ExitVal->getParent() == L->getHeader() &&
                 "ExitVal must be in loop header");
          MadeAnyChanges = true;
          PN.setIncomingValue(IncomingValIdx,
                              ExitVal->getIncomingValue(PreheaderIdx));
          SE->forgetValue(&PN);
        }
      }
    }
  }
  return MadeAnyChanges;
}

//===----------------------------------------------------------------------===//
//  IV Widening - Extend the width of an IV to cover its widest uses.
//===----------------------------------------------------------------------===//

/// Update information about the induction variable that is extended by this
/// sign or zero extend operation. This is used to determine the final width of
/// the IV before actually widening it.
static void visitIVCast(CastInst *Cast, WideIVInfo &WI,
                        ScalarEvolution *SE,
                        const TargetTransformInfo *TTI) {
  bool IsSigned = Cast->getOpcode() == Instruction::SExt;
  if (!IsSigned && Cast->getOpcode() != Instruction::ZExt)
    return;

  Type *Ty = Cast->getType();
  uint64_t Width = SE->getTypeSizeInBits(Ty);
  if (!Cast->getModule()->getDataLayout().isLegalInteger(Width))
    return;

  // Check that `Cast` actually extends the induction variable (we rely on this
  // later).  This takes care of cases where `Cast` is extending a truncation of
  // the narrow induction variable, and thus can end up being narrower than the
  // "narrow" induction variable.
  uint64_t NarrowIVWidth = SE->getTypeSizeInBits(WI.NarrowIV->getType());
  if (NarrowIVWidth >= Width)
    return;

  // Cast is either an sext or zext up to this point.
  // We should not widen an indvar if arithmetics on the wider indvar are more
  // expensive than those on the narrower indvar. We check only the cost of ADD
  // because at least an ADD is required to increment the induction variable. We
  // could compute more comprehensively the cost of all instructions on the
  // induction variable when necessary.
  if (TTI &&
      TTI->getArithmeticInstrCost(Instruction::Add, Ty) >
          TTI->getArithmeticInstrCost(Instruction::Add,
                                      Cast->getOperand(0)->getType())) {
    return;
  }

  if (!WI.WidestNativeType) {
    WI.WidestNativeType = SE->getEffectiveSCEVType(Ty);
    WI.IsSigned = IsSigned;
    return;
  }

  // We extend the IV to satisfy the sign of its first user, arbitrarily.
  if (WI.IsSigned != IsSigned)
    return;

  if (Width > SE->getTypeSizeInBits(WI.WidestNativeType))
    WI.WidestNativeType = SE->getEffectiveSCEVType(Ty);
}

//===----------------------------------------------------------------------===//
//  Live IV Reduction - Minimize IVs live across the loop.
//===----------------------------------------------------------------------===//

//===----------------------------------------------------------------------===//
//  Simplification of IV users based on SCEV evaluation.
//===----------------------------------------------------------------------===//

namespace {

class IndVarSimplifyVisitor : public IVVisitor {
  ScalarEvolution *SE;
  const TargetTransformInfo *TTI;
  PHINode *IVPhi;

public:
  WideIVInfo WI;

  IndVarSimplifyVisitor(PHINode *IV, ScalarEvolution *SCEV,
                        const TargetTransformInfo *TTI,
                        const DominatorTree *DTree)
    : SE(SCEV), TTI(TTI), IVPhi(IV) {
    DT = DTree;
    WI.NarrowIV = IVPhi;
  }

  // Implement the interface used by simplifyUsersOfIV.
  void visitCast(CastInst *Cast) override { visitIVCast(Cast, WI, SE, TTI); }
};

} // end anonymous namespace

/// Iteratively perform simplification on a worklist of IV users. Each
/// successive simplification may push more users which may themselves be
/// candidates for simplification.
///
/// Sign/Zero extend elimination is interleaved with IV simplification.
bool IndVarSimplify::simplifyAndExtend(Loop *L,
                                       SCEVExpander &Rewriter,
                                       LoopInfo *LI) {
  SmallVector<WideIVInfo, 8> WideIVs;

  auto *GuardDecl = L->getBlocks()[0]->getModule()->getFunction(
          Intrinsic::getName(Intrinsic::experimental_guard));
  bool HasGuards = GuardDecl && !GuardDecl->use_empty();

  SmallVector<PHINode*, 8> LoopPhis;
  for (BasicBlock::iterator I = L->getHeader()->begin(); isa<PHINode>(I); ++I) {
    LoopPhis.push_back(cast<PHINode>(I));
  }
  // Each round of simplification iterates through the SimplifyIVUsers worklist
  // for all current phis, then determines whether any IVs can be
  // widened. Widening adds new phis to LoopPhis, inducing another round of
  // simplification on the wide IVs.
  bool Changed = false;
  while (!LoopPhis.empty()) {
    // Evaluate as many IV expressions as possible before widening any IVs. This
    // forces SCEV to set no-wrap flags before evaluating sign/zero
    // extension. The first time SCEV attempts to normalize sign/zero extension,
    // the result becomes final. So for the most predictable results, we delay
    // evaluation of sign/zero extend evaluation until needed, and avoid running
    // other SCEV based analysis prior to simplifyAndExtend.
    do {
      PHINode *CurrIV = LoopPhis.pop_back_val();

      // Information about sign/zero extensions of CurrIV.
      IndVarSimplifyVisitor Visitor(CurrIV, SE, TTI, DT);

      Changed |= simplifyUsersOfIV(CurrIV, SE, DT, LI, TTI, DeadInsts, Rewriter,
                                   &Visitor);

      if (Visitor.WI.WidestNativeType) {
        WideIVs.push_back(Visitor.WI);
      }
    } while(!LoopPhis.empty());

    // Continue if we disallowed widening.
    if (!WidenIndVars)
      continue;

    for (; !WideIVs.empty(); WideIVs.pop_back()) {
      unsigned ElimExt;
      unsigned Widened;
      if (PHINode *WidePhi = createWideIV(WideIVs.back(), LI, SE, Rewriter,
                                          DT, DeadInsts, ElimExt, Widened,
                                          HasGuards, UsePostIncrementRanges)) {
        NumElimExt += ElimExt;
        NumWidened += Widened;
        Changed = true;
        LoopPhis.push_back(WidePhi);
      }
    }
  }
  return Changed;
}

//===----------------------------------------------------------------------===//
//  linearFunctionTestReplace and its kin. Rewrite the loop exit condition.
//===----------------------------------------------------------------------===//

/// Given an Value which is hoped to be part of an add recurance in the given
/// loop, return the associated Phi node if so.  Otherwise, return null.  Note
/// that this is less general than SCEVs AddRec checking.
static PHINode *getLoopPhiForCounter(Value *IncV, Loop *L) {
  Instruction *IncI = dyn_cast<Instruction>(IncV);
  if (!IncI)
    return nullptr;

  switch (IncI->getOpcode()) {
  case Instruction::Add:
  case Instruction::Sub:
    break;
  case Instruction::GetElementPtr:
    // An IV counter must preserve its type.
    if (IncI->getNumOperands() == 2)
      break;
    LLVM_FALLTHROUGH;
  default:
    return nullptr;
  }

  PHINode *Phi = dyn_cast<PHINode>(IncI->getOperand(0));
  if (Phi && Phi->getParent() == L->getHeader()) {
    if (L->isLoopInvariant(IncI->getOperand(1)))
      return Phi;
    return nullptr;
  }
  if (IncI->getOpcode() == Instruction::GetElementPtr)
    return nullptr;

  // Allow add/sub to be commuted.
  Phi = dyn_cast<PHINode>(IncI->getOperand(1));
  if (Phi && Phi->getParent() == L->getHeader()) {
    if (L->isLoopInvariant(IncI->getOperand(0)))
      return Phi;
  }
  return nullptr;
}

/// Whether the current loop exit test is based on this value.  Currently this
/// is limited to a direct use in the loop condition.
static bool isLoopExitTestBasedOn(Value *V, BasicBlock *ExitingBB) {
  BranchInst *BI = cast<BranchInst>(ExitingBB->getTerminator());
  ICmpInst *ICmp = dyn_cast<ICmpInst>(BI->getCondition());
  // TODO: Allow non-icmp loop test.
  if (!ICmp)
    return false;

  // TODO: Allow indirect use.
  return ICmp->getOperand(0) == V || ICmp->getOperand(1) == V;
}

/// linearFunctionTestReplace policy. Return true unless we can show that the
/// current exit test is already sufficiently canonical.
static bool needsLFTR(Loop *L, BasicBlock *ExitingBB) {
  assert(L->getLoopLatch() && "Must be in simplified form");

  // Avoid converting a constant or loop invariant test back to a runtime
  // test.  This is critical for when SCEV's cached ExitCount is less precise
  // than the current IR (such as after we've proven a particular exit is
  // actually dead and thus the BE count never reaches our ExitCount.)
  BranchInst *BI = cast<BranchInst>(ExitingBB->getTerminator());
  if (L->isLoopInvariant(BI->getCondition()))
    return false;

  // Do LFTR to simplify the exit condition to an ICMP.
  ICmpInst *Cond = dyn_cast<ICmpInst>(BI->getCondition());
  if (!Cond)
    return true;

  // Do LFTR to simplify the exit ICMP to EQ/NE
  ICmpInst::Predicate Pred = Cond->getPredicate();
  if (Pred != ICmpInst::ICMP_NE && Pred != ICmpInst::ICMP_EQ)
    return true;

  // Look for a loop invariant RHS
  Value *LHS = Cond->getOperand(0);
  Value *RHS = Cond->getOperand(1);
  if (!L->isLoopInvariant(RHS)) {
    if (!L->isLoopInvariant(LHS))
      return true;
    std::swap(LHS, RHS);
  }
  // Look for a simple IV counter LHS
  PHINode *Phi = dyn_cast<PHINode>(LHS);
  if (!Phi)
    Phi = getLoopPhiForCounter(LHS, L);

  if (!Phi)
    return true;

  // Do LFTR if PHI node is defined in the loop, but is *not* a counter.
  int Idx = Phi->getBasicBlockIndex(L->getLoopLatch());
  if (Idx < 0)
    return true;

  // Do LFTR if the exit condition's IV is *not* a simple counter.
  Value *IncV = Phi->getIncomingValue(Idx);
  return Phi != getLoopPhiForCounter(IncV, L);
}

/// Return true if undefined behavior would provable be executed on the path to
/// OnPathTo if Root produced a posion result.  Note that this doesn't say
/// anything about whether OnPathTo is actually executed or whether Root is
/// actually poison.  This can be used to assess whether a new use of Root can
/// be added at a location which is control equivalent with OnPathTo (such as
/// immediately before it) without introducing UB which didn't previously
/// exist.  Note that a false result conveys no information.
static bool mustExecuteUBIfPoisonOnPathTo(Instruction *Root,
                                          Instruction *OnPathTo,
                                          DominatorTree *DT) {
  // Basic approach is to assume Root is poison, propagate poison forward
  // through all users we can easily track, and then check whether any of those
  // users are provable UB and must execute before out exiting block might
  // exit.

  // The set of all recursive users we've visited (which are assumed to all be
  // poison because of said visit)
  SmallSet<const Value *, 16> KnownPoison;
  SmallVector<const Instruction*, 16> Worklist;
  Worklist.push_back(Root);
  while (!Worklist.empty()) {
    const Instruction *I = Worklist.pop_back_val();

    // If we know this must trigger UB on a path leading our target.
    if (mustTriggerUB(I, KnownPoison) && DT->dominates(I, OnPathTo))
      return true;

    // If we can't analyze propagation through this instruction, just skip it
    // and transitive users.  Safe as false is a conservative result.
    if (!propagatesPoison(cast<Operator>(I)) && I != Root)
      continue;

    if (KnownPoison.insert(I).second)
      for (const User *User : I->users())
        Worklist.push_back(cast<Instruction>(User));
  }

  // Might be non-UB, or might have a path we couldn't prove must execute on
  // way to exiting bb.
  return false;
}

/// Recursive helper for hasConcreteDef(). Unfortunately, this currently boils
/// down to checking that all operands are constant and listing instructions
/// that may hide undef.
static bool hasConcreteDefImpl(Value *V, SmallPtrSetImpl<Value*> &Visited,
                               unsigned Depth) {
  if (isa<Constant>(V))
    return !isa<UndefValue>(V);

  if (Depth >= 6)
    return false;

  // Conservatively handle non-constant non-instructions. For example, Arguments
  // may be undef.
  Instruction *I = dyn_cast<Instruction>(V);
  if (!I)
    return false;

  // Load and return values may be undef.
  if(I->mayReadFromMemory() || isa<CallInst>(I) || isa<InvokeInst>(I))
    return false;

  // Optimistically handle other instructions.
  for (Value *Op : I->operands()) {
    if (!Visited.insert(Op).second)
      continue;
    if (!hasConcreteDefImpl(Op, Visited, Depth+1))
      return false;
  }
  return true;
}

/// Return true if the given value is concrete. We must prove that undef can
/// never reach it.
///
/// TODO: If we decide that this is a good approach to checking for undef, we
/// may factor it into a common location.
static bool hasConcreteDef(Value *V) {
  SmallPtrSet<Value*, 8> Visited;
  Visited.insert(V);
  return hasConcreteDefImpl(V, Visited, 0);
}

/// Return true if this IV has any uses other than the (soon to be rewritten)
/// loop exit test.
static bool AlmostDeadIV(PHINode *Phi, BasicBlock *LatchBlock, Value *Cond) {
  int LatchIdx = Phi->getBasicBlockIndex(LatchBlock);
  Value *IncV = Phi->getIncomingValue(LatchIdx);

  for (User *U : Phi->users())
    if (U != Cond && U != IncV) return false;

  for (User *U : IncV->users())
    if (U != Cond && U != Phi) return false;
  return true;
}

/// Return true if the given phi is a "counter" in L.  A counter is an
/// add recurance (of integer or pointer type) with an arbitrary start, and a
/// step of 1.  Note that L must have exactly one latch.
static bool isLoopCounter(PHINode* Phi, Loop *L,
                          ScalarEvolution *SE) {
  assert(Phi->getParent() == L->getHeader());
  assert(L->getLoopLatch());

  if (!SE->isSCEVable(Phi->getType()))
    return false;

  const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(SE->getSCEV(Phi));
  if (!AR || AR->getLoop() != L || !AR->isAffine())
    return false;

  const SCEV *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(*SE));
  if (!Step || !Step->isOne())
    return false;

  int LatchIdx = Phi->getBasicBlockIndex(L->getLoopLatch());
  Value *IncV = Phi->getIncomingValue(LatchIdx);
  return (getLoopPhiForCounter(IncV, L) == Phi &&
          isa<SCEVAddRecExpr>(SE->getSCEV(IncV)));
}

/// Search the loop header for a loop counter (anadd rec w/step of one)
/// suitable for use by LFTR.  If multiple counters are available, select the
/// "best" one based profitable heuristics.
///
/// BECount may be an i8* pointer type. The pointer difference is already
/// valid count without scaling the address stride, so it remains a pointer
/// expression as far as SCEV is concerned.
static PHINode *FindLoopCounter(Loop *L, BasicBlock *ExitingBB,
                                const SCEV *BECount,
                                ScalarEvolution *SE, DominatorTree *DT) {
  uint64_t BCWidth = SE->getTypeSizeInBits(BECount->getType());

  Value *Cond = cast<BranchInst>(ExitingBB->getTerminator())->getCondition();

  // Loop over all of the PHI nodes, looking for a simple counter.
  PHINode *BestPhi = nullptr;
  const SCEV *BestInit = nullptr;
  BasicBlock *LatchBlock = L->getLoopLatch();
  assert(LatchBlock && "Must be in simplified form");
  const DataLayout &DL = L->getHeader()->getModule()->getDataLayout();

  for (BasicBlock::iterator I = L->getHeader()->begin(); isa<PHINode>(I); ++I) {
    PHINode *Phi = cast<PHINode>(I);
    if (!isLoopCounter(Phi, L, SE))
      continue;

    // Avoid comparing an integer IV against a pointer Limit.
    if (BECount->getType()->isPointerTy() && !Phi->getType()->isPointerTy())
      continue;

    const auto *AR = cast<SCEVAddRecExpr>(SE->getSCEV(Phi));

    // AR may be a pointer type, while BECount is an integer type.
    // AR may be wider than BECount. With eq/ne tests overflow is immaterial.
    // AR may not be a narrower type, or we may never exit.
    uint64_t PhiWidth = SE->getTypeSizeInBits(AR->getType());
    if (PhiWidth < BCWidth || !DL.isLegalInteger(PhiWidth))
      continue;

    // Avoid reusing a potentially undef value to compute other values that may
    // have originally had a concrete definition.
    if (!hasConcreteDef(Phi)) {
      // We explicitly allow unknown phis as long as they are already used by
      // the loop exit test.  This is legal since performing LFTR could not
      // increase the number of undef users.
      Value *IncPhi = Phi->getIncomingValueForBlock(LatchBlock);
      if (!isLoopExitTestBasedOn(Phi, ExitingBB) &&
          !isLoopExitTestBasedOn(IncPhi, ExitingBB))
        continue;
    }

    // Avoid introducing undefined behavior due to poison which didn't exist in
    // the original program.  (Annoyingly, the rules for poison and undef
    // propagation are distinct, so this does NOT cover the undef case above.)
    // We have to ensure that we don't introduce UB by introducing a use on an
    // iteration where said IV produces poison.  Our strategy here differs for
    // pointers and integer IVs.  For integers, we strip and reinfer as needed,
    // see code in linearFunctionTestReplace.  For pointers, we restrict
    // transforms as there is no good way to reinfer inbounds once lost.
    if (!Phi->getType()->isIntegerTy() &&
        !mustExecuteUBIfPoisonOnPathTo(Phi, ExitingBB->getTerminator(), DT))
      continue;

    const SCEV *Init = AR->getStart();

    if (BestPhi && !AlmostDeadIV(BestPhi, LatchBlock, Cond)) {
      // Don't force a live loop counter if another IV can be used.
      if (AlmostDeadIV(Phi, LatchBlock, Cond))
        continue;

      // Prefer to count-from-zero. This is a more "canonical" counter form. It
      // also prefers integer to pointer IVs.
      if (BestInit->isZero() != Init->isZero()) {
        if (BestInit->isZero())
          continue;
      }
      // If two IVs both count from zero or both count from nonzero then the
      // narrower is likely a dead phi that has been widened. Use the wider phi
      // to allow the other to be eliminated.
      else if (PhiWidth <= SE->getTypeSizeInBits(BestPhi->getType()))
        continue;
    }
    BestPhi = Phi;
    BestInit = Init;
  }
  return BestPhi;
}

/// Insert an IR expression which computes the value held by the IV IndVar
/// (which must be an loop counter w/unit stride) after the backedge of loop L
/// is taken ExitCount times.
static Value *genLoopLimit(PHINode *IndVar, BasicBlock *ExitingBB,
                           const SCEV *ExitCount, bool UsePostInc, Loop *L,
                           SCEVExpander &Rewriter, ScalarEvolution *SE) {
  assert(isLoopCounter(IndVar, L, SE));
  const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(SE->getSCEV(IndVar));
  const SCEV *IVInit = AR->getStart();

  // IVInit may be a pointer while ExitCount is an integer when FindLoopCounter
  // finds a valid pointer IV. Sign extend ExitCount in order to materialize a
  // GEP. Avoid running SCEVExpander on a new pointer value, instead reusing
  // the existing GEPs whenever possible.
  if (IndVar->getType()->isPointerTy() &&
      !ExitCount->getType()->isPointerTy()) {
    // IVOffset will be the new GEP offset that is interpreted by GEP as a
    // signed value. ExitCount on the other hand represents the loop trip count,
    // which is an unsigned value. FindLoopCounter only allows induction
    // variables that have a positive unit stride of one. This means we don't
    // have to handle the case of negative offsets (yet) and just need to zero
    // extend ExitCount.
    Type *OfsTy = SE->getEffectiveSCEVType(IVInit->getType());
    const SCEV *IVOffset = SE->getTruncateOrZeroExtend(ExitCount, OfsTy);
    if (UsePostInc)
      IVOffset = SE->getAddExpr(IVOffset, SE->getOne(OfsTy));

    // Expand the code for the iteration count.
    assert(SE->isLoopInvariant(IVOffset, L) &&
           "Computed iteration count is not loop invariant!");

    // We could handle pointer IVs other than i8*, but we need to compensate for
    // gep index scaling.
    assert(SE->getSizeOfExpr(IntegerType::getInt64Ty(IndVar->getContext()),
                             cast<PointerType>(IndVar->getType())
                                 ->getElementType())->isOne() &&
           "unit stride pointer IV must be i8*");

    const SCEV *IVLimit = SE->getAddExpr(IVInit, IVOffset);
    BranchInst *BI = cast<BranchInst>(ExitingBB->getTerminator());
    return Rewriter.expandCodeFor(IVLimit, IndVar->getType(), BI);
  } else {
    // In any other case, convert both IVInit and ExitCount to integers before
    // comparing. This may result in SCEV expansion of pointers, but in practice
    // SCEV will fold the pointer arithmetic away as such:
    // BECount = (IVEnd - IVInit - 1) => IVLimit = IVInit (postinc).
    //
    // Valid Cases: (1) both integers is most common; (2) both may be pointers
    // for simple memset-style loops.
    //
    // IVInit integer and ExitCount pointer would only occur if a canonical IV
    // were generated on top of case #2, which is not expected.

    assert(AR->getStepRecurrence(*SE)->isOne() && "only handles unit stride");
    // For unit stride, IVCount = Start + ExitCount with 2's complement
    // overflow.

    // For integer IVs, truncate the IV before computing IVInit + BECount,
    // unless we know apriori that the limit must be a constant when evaluated
    // in the bitwidth of the IV.  We prefer (potentially) keeping a truncate
    // of the IV in the loop over a (potentially) expensive expansion of the
    // widened exit count add(zext(add)) expression.
    if (SE->getTypeSizeInBits(IVInit->getType())
        > SE->getTypeSizeInBits(ExitCount->getType())) {
      if (isa<SCEVConstant>(IVInit) && isa<SCEVConstant>(ExitCount))
        ExitCount = SE->getZeroExtendExpr(ExitCount, IVInit->getType());
      else
        IVInit = SE->getTruncateExpr(IVInit, ExitCount->getType());
    }

    const SCEV *IVLimit = SE->getAddExpr(IVInit, ExitCount);

    if (UsePostInc)
      IVLimit = SE->getAddExpr(IVLimit, SE->getOne(IVLimit->getType()));

    // Expand the code for the iteration count.
    assert(SE->isLoopInvariant(IVLimit, L) &&
           "Computed iteration count is not loop invariant!");
    // Ensure that we generate the same type as IndVar, or a smaller integer
    // type. In the presence of null pointer values, we have an integer type
    // SCEV expression (IVInit) for a pointer type IV value (IndVar).
    Type *LimitTy = ExitCount->getType()->isPointerTy() ?
      IndVar->getType() : ExitCount->getType();
    BranchInst *BI = cast<BranchInst>(ExitingBB->getTerminator());
    return Rewriter.expandCodeFor(IVLimit, LimitTy, BI);
  }
}

/// This method rewrites the exit condition of the loop to be a canonical !=
/// comparison against the incremented loop induction variable.  This pass is
/// able to rewrite the exit tests of any loop where the SCEV analysis can
/// determine a loop-invariant trip count of the loop, which is actually a much
/// broader range than just linear tests.
bool IndVarSimplify::
linearFunctionTestReplace(Loop *L, BasicBlock *ExitingBB,
                          const SCEV *ExitCount,
                          PHINode *IndVar, SCEVExpander &Rewriter) {
  assert(L->getLoopLatch() && "Loop no longer in simplified form?");
  assert(isLoopCounter(IndVar, L, SE));
  Instruction * const IncVar =
    cast<Instruction>(IndVar->getIncomingValueForBlock(L->getLoopLatch()));

  // Initialize CmpIndVar to the preincremented IV.
  Value *CmpIndVar = IndVar;
  bool UsePostInc = false;

  // If the exiting block is the same as the backedge block, we prefer to
  // compare against the post-incremented value, otherwise we must compare
  // against the preincremented value.
  if (ExitingBB == L->getLoopLatch()) {
    // For pointer IVs, we chose to not strip inbounds which requires us not
    // to add a potentially UB introducing use.  We need to either a) show
    // the loop test we're modifying is already in post-inc form, or b) show
    // that adding a use must not introduce UB.
    bool SafeToPostInc =
        IndVar->getType()->isIntegerTy() ||
        isLoopExitTestBasedOn(IncVar, ExitingBB) ||
        mustExecuteUBIfPoisonOnPathTo(IncVar, ExitingBB->getTerminator(), DT);
    if (SafeToPostInc) {
      UsePostInc = true;
      CmpIndVar = IncVar;
    }
  }

  // It may be necessary to drop nowrap flags on the incrementing instruction
  // if either LFTR moves from a pre-inc check to a post-inc check (in which
  // case the increment might have previously been poison on the last iteration
  // only) or if LFTR switches to a different IV that was previously dynamically
  // dead (and as such may be arbitrarily poison). We remove any nowrap flags
  // that SCEV didn't infer for the post-inc addrec (even if we use a pre-inc
  // check), because the pre-inc addrec flags may be adopted from the original
  // instruction, while SCEV has to explicitly prove the post-inc nowrap flags.
  // TODO: This handling is inaccurate for one case: If we switch to a
  // dynamically dead IV that wraps on the first loop iteration only, which is
  // not covered by the post-inc addrec. (If the new IV was not dynamically
  // dead, it could not be poison on the first iteration in the first place.)
  if (auto *BO = dyn_cast<BinaryOperator>(IncVar)) {
    const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(SE->getSCEV(IncVar));
    if (BO->hasNoUnsignedWrap())
      BO->setHasNoUnsignedWrap(AR->hasNoUnsignedWrap());
    if (BO->hasNoSignedWrap())
      BO->setHasNoSignedWrap(AR->hasNoSignedWrap());
  }

  Value *ExitCnt = genLoopLimit(
      IndVar, ExitingBB, ExitCount, UsePostInc, L, Rewriter, SE);
  assert(ExitCnt->getType()->isPointerTy() ==
             IndVar->getType()->isPointerTy() &&
         "genLoopLimit missed a cast");

  // Insert a new icmp_ne or icmp_eq instruction before the branch.
  BranchInst *BI = cast<BranchInst>(ExitingBB->getTerminator());
  ICmpInst::Predicate P;
  if (L->contains(BI->getSuccessor(0)))
    P = ICmpInst::ICMP_NE;
  else
    P = ICmpInst::ICMP_EQ;

  IRBuilder<> Builder(BI);

  // The new loop exit condition should reuse the debug location of the
  // original loop exit condition.
  if (auto *Cond = dyn_cast<Instruction>(BI->getCondition()))
    Builder.SetCurrentDebugLocation(Cond->getDebugLoc());

  // For integer IVs, if we evaluated the limit in the narrower bitwidth to
  // avoid the expensive expansion of the limit expression in the wider type,
  // emit a truncate to narrow the IV to the ExitCount type.  This is safe
  // since we know (from the exit count bitwidth), that we can't self-wrap in
  // the narrower type.
  unsigned CmpIndVarSize = SE->getTypeSizeInBits(CmpIndVar->getType());
  unsigned ExitCntSize = SE->getTypeSizeInBits(ExitCnt->getType());
  if (CmpIndVarSize > ExitCntSize) {
    assert(!CmpIndVar->getType()->isPointerTy() &&
           !ExitCnt->getType()->isPointerTy());

    // Before resorting to actually inserting the truncate, use the same
    // reasoning as from SimplifyIndvar::eliminateTrunc to see if we can extend
    // the other side of the comparison instead.  We still evaluate the limit
    // in the narrower bitwidth, we just prefer a zext/sext outside the loop to
    // a truncate within in.
    bool Extended = false;
    const SCEV *IV = SE->getSCEV(CmpIndVar);
    const SCEV *TruncatedIV = SE->getTruncateExpr(SE->getSCEV(CmpIndVar),
                                                  ExitCnt->getType());
    const SCEV *ZExtTrunc =
      SE->getZeroExtendExpr(TruncatedIV, CmpIndVar->getType());

    if (ZExtTrunc == IV) {
      Extended = true;
      ExitCnt = Builder.CreateZExt(ExitCnt, IndVar->getType(),
                                   "wide.trip.count");
    } else {
      const SCEV *SExtTrunc =
        SE->getSignExtendExpr(TruncatedIV, CmpIndVar->getType());
      if (SExtTrunc == IV) {
        Extended = true;
        ExitCnt = Builder.CreateSExt(ExitCnt, IndVar->getType(),
                                     "wide.trip.count");
      }
    }

    if (Extended) {
      bool Discard;
      L->makeLoopInvariant(ExitCnt, Discard);
    } else
      CmpIndVar = Builder.CreateTrunc(CmpIndVar, ExitCnt->getType(),
                                      "lftr.wideiv");
  }
  LLVM_DEBUG(dbgs() << "INDVARS: Rewriting loop exit condition to:\n"
                    << "      LHS:" << *CmpIndVar << '\n'
                    << "       op:\t" << (P == ICmpInst::ICMP_NE ? "!=" : "==")
                    << "\n"
                    << "      RHS:\t" << *ExitCnt << "\n"
                    << "ExitCount:\t" << *ExitCount << "\n"
                    << "  was: " << *BI->getCondition() << "\n");

  Value *Cond = Builder.CreateICmp(P, CmpIndVar, ExitCnt, "exitcond");
  Value *OrigCond = BI->getCondition();
  // It's tempting to use replaceAllUsesWith here to fully replace the old
  // comparison, but that's not immediately safe, since users of the old
  // comparison may not be dominated by the new comparison. Instead, just
  // update the branch to use the new comparison; in the common case this
  // will make old comparison dead.
  BI->setCondition(Cond);
  DeadInsts.emplace_back(OrigCond);

  ++NumLFTR;
  return true;
}

//===----------------------------------------------------------------------===//
//  sinkUnusedInvariants. A late subpass to cleanup loop preheaders.
//===----------------------------------------------------------------------===//

/// If there's a single exit block, sink any loop-invariant values that
/// were defined in the preheader but not used inside the loop into the
/// exit block to reduce register pressure in the loop.
bool IndVarSimplify::sinkUnusedInvariants(Loop *L) {
  BasicBlock *ExitBlock = L->getExitBlock();
  if (!ExitBlock) return false;

  BasicBlock *Preheader = L->getLoopPreheader();
  if (!Preheader) return false;

  bool MadeAnyChanges = false;
  BasicBlock::iterator InsertPt = ExitBlock->getFirstInsertionPt();
  BasicBlock::iterator I(Preheader->getTerminator());
  while (I != Preheader->begin()) {
    --I;
    // New instructions were inserted at the end of the preheader.
    if (isa<PHINode>(I))
      break;

    // Don't move instructions which might have side effects, since the side
    // effects need to complete before instructions inside the loop.  Also don't
    // move instructions which might read memory, since the loop may modify
    // memory. Note that it's okay if the instruction might have undefined
    // behavior: LoopSimplify guarantees that the preheader dominates the exit
    // block.
    if (I->mayHaveSideEffects() || I->mayReadFromMemory())
      continue;

    // Skip debug info intrinsics.
    if (isa<DbgInfoIntrinsic>(I))
      continue;

    // Skip eh pad instructions.
    if (I->isEHPad())
      continue;

    // Don't sink alloca: we never want to sink static alloca's out of the
    // entry block, and correctly sinking dynamic alloca's requires
    // checks for stacksave/stackrestore intrinsics.
    // FIXME: Refactor this check somehow?
    if (isa<AllocaInst>(I))
      continue;

    // Determine if there is a use in or before the loop (direct or
    // otherwise).
    bool UsedInLoop = false;
    for (Use &U : I->uses()) {
      Instruction *User = cast<Instruction>(U.getUser());
      BasicBlock *UseBB = User->getParent();
      if (PHINode *P = dyn_cast<PHINode>(User)) {
        unsigned i =
          PHINode::getIncomingValueNumForOperand(U.getOperandNo());
        UseBB = P->getIncomingBlock(i);
      }
      if (UseBB == Preheader || L->contains(UseBB)) {
        UsedInLoop = true;
        break;
      }
    }

    // If there is, the def must remain in the preheader.
    if (UsedInLoop)
      continue;

    // Otherwise, sink it to the exit block.
    Instruction *ToMove = &*I;
    bool Done = false;

    if (I != Preheader->begin()) {
      // Skip debug info intrinsics.
      do {
        --I;
      } while (I->isDebugOrPseudoInst() && I != Preheader->begin());

      if (I->isDebugOrPseudoInst() && I == Preheader->begin())
        Done = true;
    } else {
      Done = true;
    }

    MadeAnyChanges = true;
    ToMove->moveBefore(*ExitBlock, InsertPt);
    if (Done) break;
    InsertPt = ToMove->getIterator();
  }

  return MadeAnyChanges;
}

static void replaceExitCond(BranchInst *BI, Value *NewCond,
                            SmallVectorImpl<WeakTrackingVH> &DeadInsts) {
  auto *OldCond = BI->getCondition();
  BI->setCondition(NewCond);
  if (OldCond->use_empty())
    DeadInsts.emplace_back(OldCond);
}

static void foldExit(const Loop *L, BasicBlock *ExitingBB, bool IsTaken,
                     SmallVectorImpl<WeakTrackingVH> &DeadInsts) {
  BranchInst *BI = cast<BranchInst>(ExitingBB->getTerminator());
  bool ExitIfTrue = !L->contains(*succ_begin(ExitingBB));
  auto *OldCond = BI->getCondition();
  auto *NewCond =
      ConstantInt::get(OldCond->getType(), IsTaken ? ExitIfTrue : !ExitIfTrue);
  replaceExitCond(BI, NewCond, DeadInsts);
}

static void replaceLoopPHINodesWithPreheaderValues(
    Loop *L, SmallVectorImpl<WeakTrackingVH> &DeadInsts) {
  assert(L->isLoopSimplifyForm() && "Should only do it in simplify form!");
  auto *LoopPreheader = L->getLoopPreheader();
  auto *LoopHeader = L->getHeader();
  for (auto &PN : LoopHeader->phis()) {
    auto *PreheaderIncoming = PN.getIncomingValueForBlock(LoopPreheader);
    PN.replaceAllUsesWith(PreheaderIncoming);
    DeadInsts.emplace_back(&PN);
  }
}

static void replaceWithInvariantCond(
    const Loop *L, BasicBlock *ExitingBB, ICmpInst::Predicate InvariantPred,
    const SCEV *InvariantLHS, const SCEV *InvariantRHS, SCEVExpander &Rewriter,
    SmallVectorImpl<WeakTrackingVH> &DeadInsts) {
  BranchInst *BI = cast<BranchInst>(ExitingBB->getTerminator());
  Rewriter.setInsertPoint(BI);
  auto *LHSV = Rewriter.expandCodeFor(InvariantLHS);
  auto *RHSV = Rewriter.expandCodeFor(InvariantRHS);
  bool ExitIfTrue = !L->contains(*succ_begin(ExitingBB));
  if (ExitIfTrue)
    InvariantPred = ICmpInst::getInversePredicate(InvariantPred);
  IRBuilder<> Builder(BI);
  auto *NewCond = Builder.CreateICmp(InvariantPred, LHSV, RHSV,
                                     BI->getCondition()->getName());
  replaceExitCond(BI, NewCond, DeadInsts);
}

static bool optimizeLoopExitWithUnknownExitCount(
    const Loop *L, BranchInst *BI, BasicBlock *ExitingBB,
    const SCEV *MaxIter, bool Inverted, bool SkipLastIter,
    ScalarEvolution *SE, SCEVExpander &Rewriter,
    SmallVectorImpl<WeakTrackingVH> &DeadInsts) {
  ICmpInst::Predicate Pred;
  Value *LHS, *RHS;
  BasicBlock *TrueSucc, *FalseSucc;
  if (!match(BI, m_Br(m_ICmp(Pred, m_Value(LHS), m_Value(RHS)),
                      m_BasicBlock(TrueSucc), m_BasicBlock(FalseSucc))))
    return false;

  assert((L->contains(TrueSucc) != L->contains(FalseSucc)) &&
         "Not a loop exit!");

  // 'LHS pred RHS' should now mean that we stay in loop.
  if (L->contains(FalseSucc))
    Pred = CmpInst::getInversePredicate(Pred);

  // If we are proving loop exit, invert the predicate.
  if (Inverted)
    Pred = CmpInst::getInversePredicate(Pred);

  const SCEV *LHSS = SE->getSCEVAtScope(LHS, L);
  const SCEV *RHSS = SE->getSCEVAtScope(RHS, L);
  // Can we prove it to be trivially true?
  if (SE->isKnownPredicateAt(Pred, LHSS, RHSS, BI)) {
    foldExit(L, ExitingBB, Inverted, DeadInsts);
    return true;
  }
  // Further logic works for non-inverted condition only.
  if (Inverted)
    return false;

  auto *ARTy = LHSS->getType();
  auto *MaxIterTy = MaxIter->getType();
  // If possible, adjust types.
  if (SE->getTypeSizeInBits(ARTy) > SE->getTypeSizeInBits(MaxIterTy))
    MaxIter = SE->getZeroExtendExpr(MaxIter, ARTy);
  else if (SE->getTypeSizeInBits(ARTy) < SE->getTypeSizeInBits(MaxIterTy)) {
    const SCEV *MinusOne = SE->getMinusOne(ARTy);
    auto *MaxAllowedIter = SE->getZeroExtendExpr(MinusOne, MaxIterTy);
    if (SE->isKnownPredicateAt(ICmpInst::ICMP_ULE, MaxIter, MaxAllowedIter, BI))
      MaxIter = SE->getTruncateExpr(MaxIter, ARTy);
  }

  if (SkipLastIter) {
    const SCEV *One = SE->getOne(MaxIter->getType());
    MaxIter = SE->getMinusSCEV(MaxIter, One);
  }

  // Check if there is a loop-invariant predicate equivalent to our check.
  auto LIP = SE->getLoopInvariantExitCondDuringFirstIterations(Pred, LHSS, RHSS,
                                                               L, BI, MaxIter);
  if (!LIP)
    return false;

  // Can we prove it to be trivially true?
  if (SE->isKnownPredicateAt(LIP->Pred, LIP->LHS, LIP->RHS, BI))
    foldExit(L, ExitingBB, Inverted, DeadInsts);
  else
    replaceWithInvariantCond(L, ExitingBB, LIP->Pred, LIP->LHS, LIP->RHS,
                             Rewriter, DeadInsts);

  return true;
}

bool IndVarSimplify::canonicalizeExitCondition(Loop *L) {
  // Note: This is duplicating a particular part on SimplifyIndVars reasoning.
  // We need to duplicate it because given icmp zext(small-iv), C, IVUsers
  // never reaches the icmp since the zext doesn't fold to an AddRec unless
  // it already has flags.  The alternative to this would be to extending the
  // set of "interesting" IV users to include the icmp, but doing that
  // regresses results in practice by querying SCEVs before trip counts which
  // rely on them which results in SCEV caching sub-optimal answers.  The
  // concern about caching sub-optimal results is why we only query SCEVs of
  // the loop invariant RHS here.
  SmallVector<BasicBlock*, 16> ExitingBlocks;
  L->getExitingBlocks(ExitingBlocks);
  bool Changed = false;
  for (auto *ExitingBB : ExitingBlocks) {
    auto *BI = dyn_cast<BranchInst>(ExitingBB->getTerminator());
    if (!BI)
      continue;
    assert(BI->isConditional() && "exit branch must be conditional");

    auto *ICmp = dyn_cast<ICmpInst>(BI->getCondition());
    if (!ICmp || !ICmp->hasOneUse() || ICmp->isUnsigned())
      continue;

    auto *LHS = ICmp->getOperand(0);
    auto *RHS = ICmp->getOperand(1);
    // For the range reasoning, avoid computing SCEVs in the loop to avoid
    // poisoning cache with sub-optimal results.  For the must-execute case,
    // this is a neccessary precondition for correctness.
    if (!L->isLoopInvariant(RHS))
      continue;

    // Match (icmp signed-cond zext, RHS)
    Value *LHSOp = nullptr;
    if (!match(LHS, m_ZExt(m_Value(LHSOp))))
      continue;

    const DataLayout &DL = ExitingBB->getModule()->getDataLayout();
    const unsigned InnerBitWidth = DL.getTypeSizeInBits(LHSOp->getType());
    const unsigned OuterBitWidth = DL.getTypeSizeInBits(RHS->getType());
    auto FullCR = ConstantRange::getFull(InnerBitWidth);
    FullCR = FullCR.zeroExtend(OuterBitWidth);
    if (FullCR.contains(SE->getUnsignedRange(SE->getSCEV(RHS)))) {
      // We have now matched icmp signed-cond zext(X), zext(Y'), and can thus
      // replace the signed condition with the unsigned version.
      ICmp->setPredicate(ICmp->getUnsignedPredicate());
      Changed = true;
      // Note: No SCEV invalidation needed.  We've changed the predicate, but
      // have not changed exit counts, or the values produced by the compare.
      continue;
    }

    // If we have a loop which would be undefined if infinite, and it has at
    // most one possible dynamic exit, then we can conclude that exit must
    // be taken.  If that exit must be taken, and we know the LHS can only
    // take values in the positive domain, then we can conclude RHS must
    // also be in that same range, and replace a signed compare with an
    // unsigned one.
    // If the exit might not be taken in a well defined program.
    if (ExitingBlocks.size() == 1 && SE->loopHasNoAbnormalExits(L) &&
        SE->loopIsFiniteByAssumption(L)) {
      // We have now matched icmp signed-cond zext(X), zext(Y'), and can thus
      // replace the signed condition with the unsigned version.
      ICmp->setPredicate(ICmp->getUnsignedPredicate());
      Changed = true;

      // Given we've changed exit counts, notify SCEV.
      // Some nested loops may share same folded exit basic block,
      // thus we need to notify top most loop.
      SE->forgetTopmostLoop(L);
      continue;
    }
  }

  // Now that we've canonicalized the condition to match the extend,
  // see if we can rotate the extend out of the loop.
  for (auto *ExitingBB : ExitingBlocks) {
    auto *BI = dyn_cast<BranchInst>(ExitingBB->getTerminator());
    if (!BI)
      continue;
    assert(BI->isConditional() && "exit branch must be conditional");

    auto *ICmp = dyn_cast<ICmpInst>(BI->getCondition());
    if (!ICmp || !ICmp->hasOneUse() || !ICmp->isUnsigned())
      continue;

    auto *LHS = ICmp->getOperand(0);
    auto *RHS = ICmp->getOperand(1);
    if (L->isLoopInvariant(LHS) || !L->isLoopInvariant(RHS))
      // Nothing to rotate
      continue;

    if (!LHS->hasOneUse())
      // Can't rotate without increasing instruction count
      continue;

    // Match (icmp unsigned-cond zext, RHS)
    // TODO: Extend to handle corresponding sext/signed-cmp case
    // TODO: Extend to other invertible functions
    Value *LHSOp = nullptr;
    if (!match(LHS, m_ZExt(m_Value(LHSOp))))
      continue;

    // Given a icmp unsigned-cond zext(Op) where zext(trunc(RHS)) == RHS
    // replace with an icmp of the form icmp unsigned-cond Op, trunc(RHS)
    // when zext is loop varying and RHS is loop invariant.  This converts
    // loop varying work to loop-invariant work.
    auto doRotateTransform = [&]() {
      assert(ICmp->isUnsigned() && "must have proven unsigned already");
      auto *NewRHS =
        CastInst::Create(Instruction::Trunc, RHS, LHSOp->getType(), "",
                         L->getLoopPreheader()->getTerminator());
      ICmp->setOperand(0, LHSOp);
      ICmp->setOperand(1, NewRHS);
      if (LHS->use_empty())
        DeadInsts.push_back(LHS);
    };


    const DataLayout &DL = ExitingBB->getModule()->getDataLayout();
    const unsigned InnerBitWidth = DL.getTypeSizeInBits(LHSOp->getType());
    const unsigned OuterBitWidth = DL.getTypeSizeInBits(RHS->getType());
    auto FullCR = ConstantRange::getFull(InnerBitWidth);
    FullCR = FullCR.zeroExtend(OuterBitWidth);
    if (FullCR.contains(SE->getUnsignedRange(SE->getSCEV(RHS)))) {
      doRotateTransform();
      Changed = true;
      // Note, we are leaving SCEV in an unfortunately imprecise case here
      // as rotation tends to reveal information about trip counts not
      // previously visible.
      continue;
    }

    // If we have a loop which would be undefined if infinite, and it has at
    // most one possible dynamic exit, then we can conclude that exit must
    // be taken.  If that exit must be taken, and we know the LHS can only
    // take values in the positive domain, then we can conclude RHS must
    // also be in that same range.
    if (ExitingBlocks.size() == 1 && SE->loopHasNoAbnormalExits(L) &&
        SE->loopIsFiniteByAssumption(L)) {
      doRotateTransform();
      Changed = true;
      // Given we've changed exit counts, notify SCEV.
      // Some nested loops may share same folded exit basic block,
      // thus we need to notify top most loop.
      SE->forgetTopmostLoop(L);
      continue;
    }
  }

  return Changed;
}

bool IndVarSimplify::optimizeLoopExits(Loop *L, SCEVExpander &Rewriter) {
  SmallVector<BasicBlock*, 16> ExitingBlocks;
  L->getExitingBlocks(ExitingBlocks);

  // Remove all exits which aren't both rewriteable and execute on every
  // iteration.
  llvm::erase_if(ExitingBlocks, [&](BasicBlock *ExitingBB) {
    // If our exitting block exits multiple loops, we can only rewrite the
    // innermost one.  Otherwise, we're changing how many times the innermost
    // loop runs before it exits.
    if (LI->getLoopFor(ExitingBB) != L)
      return true;

    // Can't rewrite non-branch yet.
    BranchInst *BI = dyn_cast<BranchInst>(ExitingBB->getTerminator());
    if (!BI)
      return true;

    // If already constant, nothing to do.
    if (isa<Constant>(BI->getCondition()))
      return true;

    // Likewise, the loop latch must be dominated by the exiting BB.
    if (!DT->dominates(ExitingBB, L->getLoopLatch()))
      return true;

    return false;
  });

  if (ExitingBlocks.empty())
    return false;

  // Get a symbolic upper bound on the loop backedge taken count.
  const SCEV *MaxExitCount = SE->getSymbolicMaxBackedgeTakenCount(L);
  if (isa<SCEVCouldNotCompute>(MaxExitCount))
    return false;

  // Visit our exit blocks in order of dominance. We know from the fact that
  // all exits must dominate the latch, so there is a total dominance order
  // between them.
  llvm::sort(ExitingBlocks, [&](BasicBlock *A, BasicBlock *B) {
               // std::sort sorts in ascending order, so we want the inverse of
               // the normal dominance relation.
               if (A == B) return false;
               if (DT->properlyDominates(A, B))
                 return true;
               else {
                 assert(DT->properlyDominates(B, A) &&
                        "expected total dominance order!");
                 return false;
               }
  });
#ifdef ASSERT
  for (unsigned i = 1; i < ExitingBlocks.size(); i++) {
    assert(DT->dominates(ExitingBlocks[i-1], ExitingBlocks[i]));
  }
#endif

  bool Changed = false;
  bool SkipLastIter = false;
  SmallSet<const SCEV*, 8> DominatingExitCounts;
  for (BasicBlock *ExitingBB : ExitingBlocks) {
    const SCEV *ExitCount = SE->getExitCount(L, ExitingBB);
    if (isa<SCEVCouldNotCompute>(ExitCount)) {
      // Okay, we do not know the exit count here. Can we at least prove that it
      // will remain the same within iteration space?
      auto *BI = cast<BranchInst>(ExitingBB->getTerminator());
      auto OptimizeCond = [&](bool Inverted, bool SkipLastIter) {
        return optimizeLoopExitWithUnknownExitCount(
            L, BI, ExitingBB, MaxExitCount, Inverted, SkipLastIter, SE,
            Rewriter, DeadInsts);
      };

      // TODO: We might have proved that we can skip the last iteration for
      // this check. In this case, we only want to check the condition on the
      // pre-last iteration (MaxExitCount - 1). However, there is a nasty
      // corner case:
      //
      //   for (i = len; i != 0; i--) { ... check (i ult X) ... }
      //
      // If we could not prove that len != 0, then we also could not prove that
      // (len - 1) is not a UINT_MAX. If we simply query (len - 1), then
      // OptimizeCond will likely not prove anything for it, even if it could
      // prove the same fact for len.
      //
      // As a temporary solution, we query both last and pre-last iterations in
      // hope that we will be able to prove triviality for at least one of
      // them. We can stop querying MaxExitCount for this case once SCEV
      // understands that (MaxExitCount - 1) will not overflow here.
      if (OptimizeCond(false, false) || OptimizeCond(true, false))
        Changed = true;
      else if (SkipLastIter)
        if (OptimizeCond(false, true) || OptimizeCond(true, true))
          Changed = true;
      continue;
    }

    if (MaxExitCount == ExitCount)
      // If the loop has more than 1 iteration, all further checks will be
      // executed 1 iteration less.
      SkipLastIter = true;

    // If we know we'd exit on the first iteration, rewrite the exit to
    // reflect this.  This does not imply the loop must exit through this
    // exit; there may be an earlier one taken on the first iteration.
    // We know that the backedge can't be taken, so we replace all
    // the header PHIs with values coming from the preheader.
    if (ExitCount->isZero()) {
      foldExit(L, ExitingBB, true, DeadInsts);
      replaceLoopPHINodesWithPreheaderValues(L, DeadInsts);
      Changed = true;
      continue;
    }

    assert(ExitCount->getType()->isIntegerTy() &&
           MaxExitCount->getType()->isIntegerTy() &&
           "Exit counts must be integers");

    Type *WiderType =
      SE->getWiderType(MaxExitCount->getType(), ExitCount->getType());
    ExitCount = SE->getNoopOrZeroExtend(ExitCount, WiderType);
    MaxExitCount = SE->getNoopOrZeroExtend(MaxExitCount, WiderType);
    assert(MaxExitCount->getType() == ExitCount->getType());

    // Can we prove that some other exit must be taken strictly before this
    // one?
    if (SE->isLoopEntryGuardedByCond(L, CmpInst::ICMP_ULT,
                                     MaxExitCount, ExitCount)) {
      foldExit(L, ExitingBB, false, DeadInsts);
      Changed = true;
      continue;
    }

    // As we run, keep track of which exit counts we've encountered.  If we
    // find a duplicate, we've found an exit which would have exited on the
    // exiting iteration, but (from the visit order) strictly follows another
    // which does the same and is thus dead.
    if (!DominatingExitCounts.insert(ExitCount).second) {
      foldExit(L, ExitingBB, false, DeadInsts);
      Changed = true;
      continue;
    }

    // TODO: There might be another oppurtunity to leverage SCEV's reasoning
    // here.  If we kept track of the min of dominanting exits so far, we could
    // discharge exits with EC >= MDEC. This is less powerful than the existing
    // transform (since later exits aren't considered), but potentially more
    // powerful for any case where SCEV can prove a >=u b, but neither a == b
    // or a >u b.  Such a case is not currently known.
  }
  return Changed;
}

bool IndVarSimplify::predicateLoopExits(Loop *L, SCEVExpander &Rewriter) {
  SmallVector<BasicBlock*, 16> ExitingBlocks;
  L->getExitingBlocks(ExitingBlocks);

  // Finally, see if we can rewrite our exit conditions into a loop invariant
  // form. If we have a read-only loop, and we can tell that we must exit down
  // a path which does not need any of the values computed within the loop, we
  // can rewrite the loop to exit on the first iteration.  Note that this
  // doesn't either a) tell us the loop exits on the first iteration (unless
  // *all* exits are predicateable) or b) tell us *which* exit might be taken.
  // This transformation looks a lot like a restricted form of dead loop
  // elimination, but restricted to read-only loops and without neccesssarily
  // needing to kill the loop entirely.
  if (!LoopPredication)
    return false;

  // Note: ExactBTC is the exact backedge taken count *iff* the loop exits
  // through *explicit* control flow.  We have to eliminate the possibility of
  // implicit exits (see below) before we know it's truly exact.
  const SCEV *ExactBTC = SE->getBackedgeTakenCount(L);
  if (isa<SCEVCouldNotCompute>(ExactBTC) || !isSafeToExpand(ExactBTC, *SE))
    return false;

  assert(SE->isLoopInvariant(ExactBTC, L) && "BTC must be loop invariant");
  assert(ExactBTC->getType()->isIntegerTy() && "BTC must be integer");

  auto BadExit = [&](BasicBlock *ExitingBB) {
    // If our exiting block exits multiple loops, we can only rewrite the
    // innermost one.  Otherwise, we're changing how many times the innermost
    // loop runs before it exits.
    if (LI->getLoopFor(ExitingBB) != L)
      return true;

    // Can't rewrite non-branch yet.
    BranchInst *BI = dyn_cast<BranchInst>(ExitingBB->getTerminator());
    if (!BI)
      return true;

    // If already constant, nothing to do.
    if (isa<Constant>(BI->getCondition()))
      return true;

    // If the exit block has phis, we need to be able to compute the values
    // within the loop which contains them.  This assumes trivially lcssa phis
    // have already been removed; TODO: generalize
    BasicBlock *ExitBlock =
    BI->getSuccessor(L->contains(BI->getSuccessor(0)) ? 1 : 0);
    if (!ExitBlock->phis().empty())
      return true;

    const SCEV *ExitCount = SE->getExitCount(L, ExitingBB);
    if (isa<SCEVCouldNotCompute>(ExitCount) || !isSafeToExpand(ExitCount, *SE))
      return true;

    assert(SE->isLoopInvariant(ExitCount, L) &&
           "Exit count must be loop invariant");
    assert(ExitCount->getType()->isIntegerTy() && "Exit count must be integer");
    return false;
  };

  // If we have any exits which can't be predicated themselves, than we can't
  // predicate any exit which isn't guaranteed to execute before it.  Consider
  // two exits (a) and (b) which would both exit on the same iteration.  If we
  // can predicate (b), but not (a), and (a) preceeds (b) along some path, then
  // we could convert a loop from exiting through (a) to one exiting through
  // (b).  Note that this problem exists only for exits with the same exit
  // count, and we could be more aggressive when exit counts are known inequal.
  llvm::sort(ExitingBlocks,
            [&](BasicBlock *A, BasicBlock *B) {
              // std::sort sorts in ascending order, so we want the inverse of
              // the normal dominance relation, plus a tie breaker for blocks
              // unordered by dominance.
              if (DT->properlyDominates(A, B)) return true;
              if (DT->properlyDominates(B, A)) return false;
              return A->getName() < B->getName();
            });
  // Check to see if our exit blocks are a total order (i.e. a linear chain of
  // exits before the backedge).  If they aren't, reasoning about reachability
  // is complicated and we choose not to for now.
  for (unsigned i = 1; i < ExitingBlocks.size(); i++)
    if (!DT->dominates(ExitingBlocks[i-1], ExitingBlocks[i]))
      return false;

  // Given our sorted total order, we know that exit[j] must be evaluated
  // after all exit[i] such j > i.
  for (unsigned i = 0, e = ExitingBlocks.size(); i < e; i++)
    if (BadExit(ExitingBlocks[i])) {
      ExitingBlocks.resize(i);
      break;
    }

  if (ExitingBlocks.empty())
    return false;

  // We rely on not being able to reach an exiting block on a later iteration
  // then it's statically compute exit count.  The implementaton of
  // getExitCount currently has this invariant, but assert it here so that
  // breakage is obvious if this ever changes..
  assert(llvm::all_of(ExitingBlocks, [&](BasicBlock *ExitingBB) {
        return DT->dominates(ExitingBB, L->getLoopLatch());
      }));

  // At this point, ExitingBlocks consists of only those blocks which are
  // predicatable.  Given that, we know we have at least one exit we can
  // predicate if the loop is doesn't have side effects and doesn't have any
  // implicit exits (because then our exact BTC isn't actually exact).
  // @Reviewers - As structured, this is O(I^2) for loop nests.  Any
  // suggestions on how to improve this?  I can obviously bail out for outer
  // loops, but that seems less than ideal.  MemorySSA can find memory writes,
  // is that enough for *all* side effects?
  for (BasicBlock *BB : L->blocks())
    for (auto &I : *BB)
      // TODO:isGuaranteedToTransfer
      if (I.mayHaveSideEffects())
        return false;

  bool Changed = false;
  // Finally, do the actual predication for all predicatable blocks.  A couple
  // of notes here:
  // 1) We don't bother to constant fold dominated exits with identical exit
  //    counts; that's simply a form of CSE/equality propagation and we leave
  //    it for dedicated passes.
  // 2) We insert the comparison at the branch.  Hoisting introduces additional
  //    legality constraints and we leave that to dedicated logic.  We want to
  //    predicate even if we can't insert a loop invariant expression as
  //    peeling or unrolling will likely reduce the cost of the otherwise loop
  //    varying check.
  Rewriter.setInsertPoint(L->getLoopPreheader()->getTerminator());
  IRBuilder<> B(L->getLoopPreheader()->getTerminator());
  Value *ExactBTCV = nullptr; // Lazily generated if needed.
  for (BasicBlock *ExitingBB : ExitingBlocks) {
    const SCEV *ExitCount = SE->getExitCount(L, ExitingBB);

    auto *BI = cast<BranchInst>(ExitingBB->getTerminator());
    Value *NewCond;
    if (ExitCount == ExactBTC) {
      NewCond = L->contains(BI->getSuccessor(0)) ?
        B.getFalse() : B.getTrue();
    } else {
      Value *ECV = Rewriter.expandCodeFor(ExitCount);
      if (!ExactBTCV)
        ExactBTCV = Rewriter.expandCodeFor(ExactBTC);
      Value *RHS = ExactBTCV;
      if (ECV->getType() != RHS->getType()) {
        Type *WiderTy = SE->getWiderType(ECV->getType(), RHS->getType());
        ECV = B.CreateZExt(ECV, WiderTy);
        RHS = B.CreateZExt(RHS, WiderTy);
      }
      auto Pred = L->contains(BI->getSuccessor(0)) ?
        ICmpInst::ICMP_NE : ICmpInst::ICMP_EQ;
      NewCond = B.CreateICmp(Pred, ECV, RHS);
    }
    Value *OldCond = BI->getCondition();
    BI->setCondition(NewCond);
    if (OldCond->use_empty())
      DeadInsts.emplace_back(OldCond);
    Changed = true;
  }

  return Changed;
}

//===----------------------------------------------------------------------===//
//  IndVarSimplify driver. Manage several subpasses of IV simplification.
//===----------------------------------------------------------------------===//

bool IndVarSimplify::run(Loop *L) {
  // We need (and expect!) the incoming loop to be in LCSSA.
  assert(L->isRecursivelyLCSSAForm(*DT, *LI) &&
         "LCSSA required to run indvars!");

  // If LoopSimplify form is not available, stay out of trouble. Some notes:
  //  - LSR currently only supports LoopSimplify-form loops. Indvars'
  //    canonicalization can be a pessimization without LSR to "clean up"
  //    afterwards.
  //  - We depend on having a preheader; in particular,
  //    Loop::getCanonicalInductionVariable only supports loops with preheaders,
  //    and we're in trouble if we can't find the induction variable even when
  //    we've manually inserted one.
  //  - LFTR relies on having a single backedge.
  if (!L->isLoopSimplifyForm())
    return false;

#ifndef NDEBUG
  // Used below for a consistency check only
  // Note: Since the result returned by ScalarEvolution may depend on the order
  // in which previous results are added to its cache, the call to
  // getBackedgeTakenCount() may change following SCEV queries.
  const SCEV *BackedgeTakenCount;
  if (VerifyIndvars)
    BackedgeTakenCount = SE->getBackedgeTakenCount(L);
#endif

  bool Changed = false;
  // If there are any floating-point recurrences, attempt to
  // transform them to use integer recurrences.
  Changed |= rewriteNonIntegerIVs(L);

  // Create a rewriter object which we'll use to transform the code with.
  SCEVExpander Rewriter(*SE, DL, "indvars");
#ifndef NDEBUG
  Rewriter.setDebugType(DEBUG_TYPE);
#endif

  // Eliminate redundant IV users.
  //
  // Simplification works best when run before other consumers of SCEV. We
  // attempt to avoid evaluating SCEVs for sign/zero extend operations until
  // other expressions involving loop IVs have been evaluated. This helps SCEV
  // set no-wrap flags before normalizing sign/zero extension.
  Rewriter.disableCanonicalMode();
  Changed |= simplifyAndExtend(L, Rewriter, LI);

  // Check to see if we can compute the final value of any expressions
  // that are recurrent in the loop, and substitute the exit values from the
  // loop into any instructions outside of the loop that use the final values
  // of the current expressions.
  if (ReplaceExitValue != NeverRepl) {
    if (int Rewrites = rewriteLoopExitValues(L, LI, TLI, SE, TTI, Rewriter, DT,
                                             ReplaceExitValue, DeadInsts)) {
      NumReplaced += Rewrites;
      Changed = true;
    }
  }

  // Eliminate redundant IV cycles.
  NumElimIV += Rewriter.replaceCongruentIVs(L, DT, DeadInsts);

  // Try to convert exit conditions to unsigned and rotate computation
  // out of the loop.  Note: Handles invalidation internally if needed.
  Changed |= canonicalizeExitCondition(L);

  // Try to eliminate loop exits based on analyzeable exit counts
  if (optimizeLoopExits(L, Rewriter))  {
    Changed = true;
    // Given we've changed exit counts, notify SCEV
    // Some nested loops may share same folded exit basic block,
    // thus we need to notify top most loop.
    SE->forgetTopmostLoop(L);
  }

  // Try to form loop invariant tests for loop exits by changing how many
  // iterations of the loop run when that is unobservable.
  if (predicateLoopExits(L, Rewriter)) {
    Changed = true;
    // Given we've changed exit counts, notify SCEV
    SE->forgetLoop(L);
  }

  // If we have a trip count expression, rewrite the loop's exit condition
  // using it.
  if (!DisableLFTR) {
    BasicBlock *PreHeader = L->getLoopPreheader();
    BranchInst *PreHeaderBR = cast<BranchInst>(PreHeader->getTerminator());

    SmallVector<BasicBlock*, 16> ExitingBlocks;
    L->getExitingBlocks(ExitingBlocks);
    for (BasicBlock *ExitingBB : ExitingBlocks) {
      // Can't rewrite non-branch yet.
      if (!isa<BranchInst>(ExitingBB->getTerminator()))
        continue;

      // If our exitting block exits multiple loops, we can only rewrite the
      // innermost one.  Otherwise, we're changing how many times the innermost
      // loop runs before it exits.
      if (LI->getLoopFor(ExitingBB) != L)
        continue;

      if (!needsLFTR(L, ExitingBB))
        continue;

      const SCEV *ExitCount = SE->getExitCount(L, ExitingBB);
      if (isa<SCEVCouldNotCompute>(ExitCount))
        continue;

      // This was handled above, but as we form SCEVs, we can sometimes refine
      // existing ones; this allows exit counts to be folded to zero which
      // weren't when optimizeLoopExits saw them.  Arguably, we should iterate
      // until stable to handle cases like this better.
      if (ExitCount->isZero())
        continue;

      PHINode *IndVar = FindLoopCounter(L, ExitingBB, ExitCount, SE, DT);
      if (!IndVar)
        continue;

      // Avoid high cost expansions.  Note: This heuristic is questionable in
      // that our definition of "high cost" is not exactly principled.
      if (Rewriter.isHighCostExpansion(ExitCount, L, SCEVCheapExpansionBudget,
                                       TTI, PreHeaderBR))
        continue;

      // Check preconditions for proper SCEVExpander operation. SCEV does not
      // express SCEVExpander's dependencies, such as LoopSimplify. Instead
      // any pass that uses the SCEVExpander must do it. This does not work
      // well for loop passes because SCEVExpander makes assumptions about
      // all loops, while LoopPassManager only forces the current loop to be
      // simplified.
      //
      // FIXME: SCEV expansion has no way to bail out, so the caller must
      // explicitly check any assumptions made by SCEV. Brittle.
      const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(ExitCount);
      if (!AR || AR->getLoop()->getLoopPreheader())
        Changed |= linearFunctionTestReplace(L, ExitingBB,
                                             ExitCount, IndVar,
                                             Rewriter);
    }
  }
  // Clear the rewriter cache, because values that are in the rewriter's cache
  // can be deleted in the loop below, causing the AssertingVH in the cache to
  // trigger.
  Rewriter.clear();

  // Now that we're done iterating through lists, clean up any instructions
  // which are now dead.
  while (!DeadInsts.empty()) {
    Value *V = DeadInsts.pop_back_val();

    if (PHINode *PHI = dyn_cast_or_null<PHINode>(V))
      Changed |= RecursivelyDeleteDeadPHINode(PHI, TLI, MSSAU.get());
    else if (Instruction *Inst = dyn_cast_or_null<Instruction>(V))
      Changed |=
          RecursivelyDeleteTriviallyDeadInstructions(Inst, TLI, MSSAU.get());
  }

  // The Rewriter may not be used from this point on.

  // Loop-invariant instructions in the preheader that aren't used in the
  // loop may be sunk below the loop to reduce register pressure.
  Changed |= sinkUnusedInvariants(L);

  // rewriteFirstIterationLoopExitValues does not rely on the computation of
  // trip count and therefore can further simplify exit values in addition to
  // rewriteLoopExitValues.
  Changed |= rewriteFirstIterationLoopExitValues(L);

  // Clean up dead instructions.
  Changed |= DeleteDeadPHIs(L->getHeader(), TLI, MSSAU.get());

  // Check a post-condition.
  assert(L->isRecursivelyLCSSAForm(*DT, *LI) &&
         "Indvars did not preserve LCSSA!");

  // Verify that LFTR, and any other change have not interfered with SCEV's
  // ability to compute trip count.  We may have *changed* the exit count, but
  // only by reducing it.
#ifndef NDEBUG
  if (VerifyIndvars && !isa<SCEVCouldNotCompute>(BackedgeTakenCount)) {
    SE->forgetLoop(L);
    const SCEV *NewBECount = SE->getBackedgeTakenCount(L);
    if (SE->getTypeSizeInBits(BackedgeTakenCount->getType()) <
        SE->getTypeSizeInBits(NewBECount->getType()))
      NewBECount = SE->getTruncateOrNoop(NewBECount,
                                         BackedgeTakenCount->getType());
    else
      BackedgeTakenCount = SE->getTruncateOrNoop(BackedgeTakenCount,
                                                 NewBECount->getType());
    assert(!SE->isKnownPredicate(ICmpInst::ICMP_ULT, BackedgeTakenCount,
                                 NewBECount) && "indvars must preserve SCEV");
  }
  if (VerifyMemorySSA && MSSAU)
    MSSAU->getMemorySSA()->verifyMemorySSA();
#endif

  return Changed;
}

PreservedAnalyses IndVarSimplifyPass::run(Loop &L, LoopAnalysisManager &AM,
                                          LoopStandardAnalysisResults &AR,
                                          LPMUpdater &) {
  Function *F = L.getHeader()->getParent();
  const DataLayout &DL = F->getParent()->getDataLayout();

  IndVarSimplify IVS(&AR.LI, &AR.SE, &AR.DT, DL, &AR.TLI, &AR.TTI, AR.MSSA,
                     WidenIndVars && AllowIVWidening);
  if (!IVS.run(&L))
    return PreservedAnalyses::all();

  auto PA = getLoopPassPreservedAnalyses();
  PA.preserveSet<CFGAnalyses>();
  if (AR.MSSA)
    PA.preserve<MemorySSAAnalysis>();
  return PA;
}

namespace {

struct IndVarSimplifyLegacyPass : public LoopPass {
  static char ID; // Pass identification, replacement for typeid

  IndVarSimplifyLegacyPass() : LoopPass(ID) {
    initializeIndVarSimplifyLegacyPassPass(*PassRegistry::getPassRegistry());
  }

  bool runOnLoop(Loop *L, LPPassManager &LPM) override {
    if (skipLoop(L))
      return false;

    auto *LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
    auto *SE = &getAnalysis<ScalarEvolutionWrapperPass>().getSE();
    auto *DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
    auto *TLIP = getAnalysisIfAvailable<TargetLibraryInfoWrapperPass>();
    auto *TLI = TLIP ? &TLIP->getTLI(*L->getHeader()->getParent()) : nullptr;
    auto *TTIP = getAnalysisIfAvailable<TargetTransformInfoWrapperPass>();
    auto *TTI = TTIP ? &TTIP->getTTI(*L->getHeader()->getParent()) : nullptr;
    const DataLayout &DL = L->getHeader()->getModule()->getDataLayout();
    auto *MSSAAnalysis = getAnalysisIfAvailable<MemorySSAWrapperPass>();
    MemorySSA *MSSA = nullptr;
    if (MSSAAnalysis)
      MSSA = &MSSAAnalysis->getMSSA();

    IndVarSimplify IVS(LI, SE, DT, DL, TLI, TTI, MSSA, AllowIVWidening);
    return IVS.run(L);
  }

  void getAnalysisUsage(AnalysisUsage &AU) const override {
    AU.setPreservesCFG();
    AU.addPreserved<MemorySSAWrapperPass>();
    getLoopAnalysisUsage(AU);
  }
};

} // end anonymous namespace

char IndVarSimplifyLegacyPass::ID = 0;

INITIALIZE_PASS_BEGIN(IndVarSimplifyLegacyPass, "indvars",
                      "Induction Variable Simplification", false, false)
INITIALIZE_PASS_DEPENDENCY(LoopPass)
INITIALIZE_PASS_END(IndVarSimplifyLegacyPass, "indvars",
                    "Induction Variable Simplification", false, false)

Pass *llvm::createIndVarSimplifyPass() {
  return new IndVarSimplifyLegacyPass();
}