text: //===-- SimplifyIndVar.cpp - Induction variable simplification ------------===//
  //
  //                     The LLVM37 Compiler Infrastructure
  //
  // This file is distributed under the University of Illinois Open Source
  // License. See LICENSE.TXT for details.
  //
  //===----------------------------------------------------------------------===//
  //
  // This file implements induction variable simplification. It does
  // not define any actual pass or policy, but provides a single function to
  // simplify a loop's induction variables based on ScalarEvolution.
  //
  //===----------------------------------------------------------------------===//
  
  #include "llvm37/Transforms/Utils/SimplifyIndVar.h"
  #include "llvm37/ADT/STLExtras.h"
  #include "llvm37/ADT/SmallVector.h"
  #include "llvm37/ADT/Statistic.h"
  #include "llvm37/Analysis/LoopInfo.h"
  #include "llvm37/Analysis/LoopPass.h"
  #include "llvm37/Analysis/ScalarEvolutionExpressions.h"
  #include "llvm37/IR/DataLayout.h"
  #include "llvm37/IR/Dominators.h"
  #include "llvm37/IR/IRBuilder.h"
  #include "llvm37/IR/Instructions.h"
  #include "llvm37/IR/IntrinsicInst.h"
  #include "llvm37/Support/CommandLine.h"
  #include "llvm37/Support/Debug.h"
  #include "llvm37/Support/raw_ostream.h"
  
  using namespace llvm37;
  
  #define DEBUG_TYPE "indvars"
  
  STATISTIC(NumElimIdentity, "Number of IV identities eliminated");
  STATISTIC(NumElimOperand,  "Number of IV operands folded into a use");
  STATISTIC(NumElimRem     , "Number of IV remainder operations eliminated");
  STATISTIC(NumElimCmp     , "Number of IV comparisons eliminated");
  
  namespace {
    /// This is a utility for simplifying induction variables
    /// based on ScalarEvolution. It is the primary instrument of the
    /// IndvarSimplify pass, but it may also be directly invoked to cleanup after
    /// other loop passes that preserve SCEV.
    class SimplifyIndvar {
      Loop             *L;
      LoopInfo         *LI;
      ScalarEvolution  *SE;
  
      SmallVectorImpl<WeakVH> &DeadInsts;
  
      bool Changed;
  
    public:
      SimplifyIndvar(Loop *Loop, ScalarEvolution *SE, LoopInfo *LI,
                     SmallVectorImpl<WeakVH> &Dead)
          : L(Loop), LI(LI), SE(SE), DeadInsts(Dead), Changed(false) {
        assert(LI && "IV simplification requires LoopInfo");
      }
  
      bool hasChanged() const { return Changed; }
  
      /// Iteratively perform simplification on a worklist of users of the
      /// specified induction variable. This is the top-level driver that applies
      /// all simplicitions to users of an IV.
      void simplifyUsers(PHINode *CurrIV, IVVisitor *V = nullptr);
  
      Value *foldIVUser(Instruction *UseInst, Instruction *IVOperand);
  
      bool eliminateIVUser(Instruction *UseInst, Instruction *IVOperand);
      void eliminateIVComparison(ICmpInst *ICmp, Value *IVOperand);
      void eliminateIVRemainder(BinaryOperator *Rem, Value *IVOperand,
                                bool IsSigned);
      bool strengthenOverflowingOperation(BinaryOperator *OBO, Value *IVOperand);
  
      Instruction *splitOverflowIntrinsic(Instruction *IVUser,
                                          const DominatorTree *DT);
    };
  }
  
  /// Fold an IV operand into its use.  This removes increments of an
  /// aligned IV when used by a instruction that ignores the low bits.
  ///
  /// IVOperand is guaranteed SCEVable, but UseInst may not be.
  ///
  /// Return the operand of IVOperand for this induction variable if IVOperand can
  /// be folded (in case more folding opportunities have been exposed).
  /// Otherwise return null.
  Value *SimplifyIndvar::foldIVUser(Instruction *UseInst, Instruction *IVOperand) {
    Value *IVSrc = nullptr;
    unsigned OperIdx = 0;
    const SCEV *FoldedExpr = nullptr;
    switch (UseInst->getOpcode()) {
    default:
      return nullptr;
    case Instruction::UDiv:
    case Instruction::LShr:
      // We're only interested in the case where we know something about
      // the numerator and have a constant denominator.
      if (IVOperand != UseInst->getOperand(OperIdx) ||
          !isa<ConstantInt>(UseInst->getOperand(1)))
        return nullptr;
  
      // Attempt to fold a binary operator with constant operand.
      // e.g. ((I + 1) >> 2) => I >> 2
      if (!isa<BinaryOperator>(IVOperand)
          || !isa<ConstantInt>(IVOperand->getOperand(1)))
        return nullptr;
  
      IVSrc = IVOperand->getOperand(0);
      // IVSrc must be the (SCEVable) IV, since the other operand is const.
      assert(SE->isSCEVable(IVSrc->getType()) && "Expect SCEVable IV operand");
  
      ConstantInt *D = cast<ConstantInt>(UseInst->getOperand(1));
      if (UseInst->getOpcode() == Instruction::LShr) {
        // Get a constant for the divisor. See createSCEV.
        uint32_t BitWidth = cast<IntegerType>(UseInst->getType())->getBitWidth();
        if (D->getValue().uge(BitWidth))
          return nullptr;
  
        D = ConstantInt::get(UseInst->getContext(),
                             APInt::getOneBitSet(BitWidth, D->getZExtValue()));
      }
      FoldedExpr = SE->getUDivExpr(SE->getSCEV(IVSrc), SE->getSCEV(D));
    }
    // We have something that might fold it's operand. Compare SCEVs.
    if (!SE->isSCEVable(UseInst->getType()))
      return nullptr;
  
    // Bypass the operand if SCEV can prove it has no effect.
    if (SE->getSCEV(UseInst) != FoldedExpr)
      return nullptr;
  
    DEBUG(dbgs() << "INDVARS: Eliminated IV operand: " << *IVOperand
          << " -> " << *UseInst << '\n');
  
    UseInst->setOperand(OperIdx, IVSrc);
    assert(SE->getSCEV(UseInst) == FoldedExpr && "bad SCEV with folded oper");
  
    ++NumElimOperand;
    Changed = true;
    if (IVOperand->use_empty())
      DeadInsts.emplace_back(IVOperand);
    return IVSrc;
  }
  
  /// SimplifyIVUsers helper for eliminating useless
  /// comparisons against an induction variable.
  void SimplifyIndvar::eliminateIVComparison(ICmpInst *ICmp, Value *IVOperand) {
    unsigned IVOperIdx = 0;
    ICmpInst::Predicate Pred = ICmp->getPredicate();
    if (IVOperand != ICmp->getOperand(0)) {
      // Swapped
      assert(IVOperand == ICmp->getOperand(1) && "Can't find IVOperand");
      IVOperIdx = 1;
      Pred = ICmpInst::getSwappedPredicate(Pred);
    }
  
    // Get the SCEVs for the ICmp operands.
    const SCEV *S = SE->getSCEV(ICmp->getOperand(IVOperIdx));
    const SCEV *X = SE->getSCEV(ICmp->getOperand(1 - IVOperIdx));
  
    // Simplify unnecessary loops away.
    const Loop *ICmpLoop = LI->getLoopFor(ICmp->getParent());
    S = SE->getSCEVAtScope(S, ICmpLoop);
    X = SE->getSCEVAtScope(X, ICmpLoop);
  
    // If the condition is always true or always false, replace it with
    // a constant value.
    if (SE->isKnownPredicate(Pred, S, X))
      ICmp->replaceAllUsesWith(ConstantInt::getTrue(ICmp->getContext()));
    else if (SE->isKnownPredicate(ICmpInst::getInversePredicate(Pred), S, X))
      ICmp->replaceAllUsesWith(ConstantInt::getFalse(ICmp->getContext()));
    else
      return;
  
    DEBUG(dbgs() << "INDVARS: Eliminated comparison: " << *ICmp << '\n');
    ++NumElimCmp;
    Changed = true;
    DeadInsts.emplace_back(ICmp);
  }
  
  /// SimplifyIVUsers helper for eliminating useless
  /// remainder operations operating on an induction variable.
  void SimplifyIndvar::eliminateIVRemainder(BinaryOperator *Rem,
                                        Value *IVOperand,
                                        bool IsSigned) {
    // We're only interested in the case where we know something about
    // the numerator.
    if (IVOperand != Rem->getOperand(0))
      return;
  
    // Get the SCEVs for the ICmp operands.
    const SCEV *S = SE->getSCEV(Rem->getOperand(0));
    const SCEV *X = SE->getSCEV(Rem->getOperand(1));
  
    // Simplify unnecessary loops away.
    const Loop *ICmpLoop = LI->getLoopFor(Rem->getParent());
    S = SE->getSCEVAtScope(S, ICmpLoop);
    X = SE->getSCEVAtScope(X, ICmpLoop);
  
    // i % n  -->  i  if i is in [0,n).
    if ((!IsSigned || SE->isKnownNonNegative(S)) &&
        SE->isKnownPredicate(IsSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
                             S, X))
      Rem->replaceAllUsesWith(Rem->getOperand(0));
    else {
      // (i+1) % n  -->  (i+1)==n?0:(i+1)  if i is in [0,n).
      const SCEV *LessOne =
        SE->getMinusSCEV(S, SE->getConstant(S->getType(), 1));
      if (IsSigned && !SE->isKnownNonNegative(LessOne))
        return;
  
      if (!SE->isKnownPredicate(IsSigned ?
                                ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
                                LessOne, X))
        return;
  
      ICmpInst *ICmp = new ICmpInst(Rem, ICmpInst::ICMP_EQ,
                                    Rem->getOperand(0), Rem->getOperand(1));
      SelectInst *Sel =
        SelectInst::Create(ICmp,
                           ConstantInt::get(Rem->getType(), 0),
                           Rem->getOperand(0), "tmp", Rem);
      Rem->replaceAllUsesWith(Sel);
    }
  
    DEBUG(dbgs() << "INDVARS: Simplified rem: " << *Rem << '\n');
    ++NumElimRem;
    Changed = true;
    DeadInsts.emplace_back(Rem);
  }
  
  /// Eliminate an operation that consumes a simple IV and has
  /// no observable side-effect given the range of IV values.
  /// IVOperand is guaranteed SCEVable, but UseInst may not be.
  bool SimplifyIndvar::eliminateIVUser(Instruction *UseInst,
                                       Instruction *IVOperand) {
    if (ICmpInst *ICmp = dyn_cast<ICmpInst>(UseInst)) {
      eliminateIVComparison(ICmp, IVOperand);
      return true;
    }
    if (BinaryOperator *Rem = dyn_cast<BinaryOperator>(UseInst)) {
      bool IsSigned = Rem->getOpcode() == Instruction::SRem;
      if (IsSigned || Rem->getOpcode() == Instruction::URem) {
        eliminateIVRemainder(Rem, IVOperand, IsSigned);
        return true;
      }
    }
  
    // Eliminate any operation that SCEV can prove is an identity function.
    if (!SE->isSCEVable(UseInst->getType()) ||
        (UseInst->getType() != IVOperand->getType()) ||
        (SE->getSCEV(UseInst) != SE->getSCEV(IVOperand)))
      return false;
  
    DEBUG(dbgs() << "INDVARS: Eliminated identity: " << *UseInst << '\n');
  
    UseInst->replaceAllUsesWith(IVOperand);
    ++NumElimIdentity;
    Changed = true;
    DeadInsts.emplace_back(UseInst);
    return true;
  }
  
  /// Annotate BO with nsw / nuw if it provably does not signed-overflow /
  /// unsigned-overflow.  Returns true if anything changed, false otherwise.
  bool SimplifyIndvar::strengthenOverflowingOperation(BinaryOperator *BO,
                                                      Value *IVOperand) {
  
    // Fastpath: we don't have any work to do if `BO` is `nuw` and `nsw`.
    if (BO->hasNoUnsignedWrap() && BO->hasNoSignedWrap())
      return false;
  
    const SCEV *(ScalarEvolution::*GetExprForBO)(const SCEV *, const SCEV *,
                                                 SCEV::NoWrapFlags);
  
    switch (BO->getOpcode()) {
    default:
      return false;
  
    case Instruction::Add:
      GetExprForBO = &ScalarEvolution::getAddExpr;
      break;
  
    case Instruction::Sub:
      GetExprForBO = &ScalarEvolution::getMinusSCEV;
      break;
  
    case Instruction::Mul:
      GetExprForBO = &ScalarEvolution::getMulExpr;
      break;
    }
  
    unsigned BitWidth = cast<IntegerType>(BO->getType())->getBitWidth();
    Type *WideTy = IntegerType::get(BO->getContext(), BitWidth * 2);
    const SCEV *LHS = SE->getSCEV(BO->getOperand(0));
    const SCEV *RHS = SE->getSCEV(BO->getOperand(1));
  
    bool Changed = false;
  
    if (!BO->hasNoUnsignedWrap()) {
      const SCEV *ExtendAfterOp = SE->getZeroExtendExpr(SE->getSCEV(BO), WideTy);
      const SCEV *OpAfterExtend = (SE->*GetExprForBO)(
        SE->getZeroExtendExpr(LHS, WideTy), SE->getZeroExtendExpr(RHS, WideTy),
        SCEV::FlagAnyWrap);
      if (ExtendAfterOp == OpAfterExtend) {
        BO->setHasNoUnsignedWrap();
        SE->forgetValue(BO);
        Changed = true;
      }
    }
  
    if (!BO->hasNoSignedWrap()) {
      const SCEV *ExtendAfterOp = SE->getSignExtendExpr(SE->getSCEV(BO), WideTy);
      const SCEV *OpAfterExtend = (SE->*GetExprForBO)(
        SE->getSignExtendExpr(LHS, WideTy), SE->getSignExtendExpr(RHS, WideTy),
        SCEV::FlagAnyWrap);
      if (ExtendAfterOp == OpAfterExtend) {
        BO->setHasNoSignedWrap();
        SE->forgetValue(BO);
        Changed = true;
      }
    }
  
    return Changed;
  }
  
  /// \brief Split sadd.with.overflow into add + sadd.with.overflow to allow
  /// analysis and optimization.
  ///
  /// \return A new value representing the non-overflowing add if possible,
  /// otherwise return the original value.
  Instruction *SimplifyIndvar::splitOverflowIntrinsic(Instruction *IVUser,
                                                      const DominatorTree *DT) {
    IntrinsicInst *II = dyn_cast<IntrinsicInst>(IVUser);
    if (!II || II->getIntrinsicID() != Intrinsic::sadd_with_overflow)
      return IVUser;
  
    // Find a branch guarded by the overflow check.
    BranchInst *Branch = nullptr;
    Instruction *AddVal = nullptr;
    for (User *U : II->users()) {
      if (ExtractValueInst *ExtractInst = dyn_cast<ExtractValueInst>(U)) {
        if (ExtractInst->getNumIndices() != 1)
          continue;
        if (ExtractInst->getIndices()[0] == 0)
          AddVal = ExtractInst;
        else if (ExtractInst->getIndices()[0] == 1 && ExtractInst->hasOneUse())
          Branch = dyn_cast<BranchInst>(ExtractInst->user_back());
      }
    }
    if (!AddVal || !Branch)
      return IVUser;
  
    BasicBlock *ContinueBB = Branch->getSuccessor(1);
    if (std::next(pred_begin(ContinueBB)) != pred_end(ContinueBB))
      return IVUser;
  
    // Check if all users of the add are provably NSW.
    bool AllNSW = true;
    for (Use &U : AddVal->uses()) {
      if (Instruction *UseInst = dyn_cast<Instruction>(U.getUser())) {
        BasicBlock *UseBB = UseInst->getParent();
        if (PHINode *PHI = dyn_cast<PHINode>(UseInst))
          UseBB = PHI->getIncomingBlock(U);
        if (!DT->dominates(ContinueBB, UseBB)) {
          AllNSW = false;
          break;
        }
      }
    }
    if (!AllNSW)
      return IVUser;
  
    // Go for it...
    IRBuilder<> Builder(IVUser);
    Instruction *AddInst = dyn_cast<Instruction>(
      Builder.CreateNSWAdd(II->getOperand(0), II->getOperand(1)));
  
    // The caller expects the new add to have the same form as the intrinsic. The
    // IV operand position must be the same.
    assert((AddInst->getOpcode() == Instruction::Add &&
            AddInst->getOperand(0) == II->getOperand(0)) &&
           "Bad add instruction created from overflow intrinsic.");
  
    AddVal->replaceAllUsesWith(AddInst);
    DeadInsts.emplace_back(AddVal);
    return AddInst;
  }
  
  /// Add all uses of Def to the current IV's worklist.
  static void pushIVUsers(
    Instruction *Def,
    SmallPtrSet<Instruction*,16> &Simplified,
    SmallVectorImpl< std::pair<Instruction*,Instruction*> > &SimpleIVUsers) {
  
    for (User *U : Def->users()) {
      Instruction *UI = cast<Instruction>(U);
  
      // Avoid infinite or exponential worklist processing.
      // Also ensure unique worklist users.
      // If Def is a LoopPhi, it may not be in the Simplified set, so check for
      // self edges first.
      if (UI != Def && Simplified.insert(UI).second)
        SimpleIVUsers.push_back(std::make_pair(UI, Def));
    }
  }
  
  /// Return true if this instruction generates a simple SCEV
  /// expression in terms of that IV.
  ///
  /// This is similar to IVUsers' isInteresting() but processes each instruction
  /// non-recursively when the operand is already known to be a simpleIVUser.
  ///
  static bool isSimpleIVUser(Instruction *I, const Loop *L, ScalarEvolution *SE) {
    if (!SE->isSCEVable(I->getType()))
      return false;
  
    // Get the symbolic expression for this instruction.
    const SCEV *S = SE->getSCEV(I);
  
    // Only consider affine recurrences.
    const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S);
    if (AR && AR->getLoop() == L)
      return true;
  
    return false;
  }
  
  /// Iteratively perform simplification on a worklist of users
  /// of the specified induction variable. Each successive simplification may push
  /// more users which may themselves be candidates for simplification.
  ///
  /// This algorithm does not require IVUsers analysis. Instead, it simplifies
  /// instructions in-place during analysis. Rather than rewriting induction
  /// variables bottom-up from their users, it transforms a chain of IVUsers
  /// top-down, updating the IR only when it encouters a clear optimization
  /// opportunitiy.
  ///
  /// Once DisableIVRewrite is default, LSR will be the only client of IVUsers.
  ///
  void SimplifyIndvar::simplifyUsers(PHINode *CurrIV, IVVisitor *V) {
    if (!SE->isSCEVable(CurrIV->getType()))
      return;
  
    // Instructions processed by SimplifyIndvar for CurrIV.
    SmallPtrSet<Instruction*,16> Simplified;
  
    // Use-def pairs if IV users waiting to be processed for CurrIV.
    SmallVector<std::pair<Instruction*, Instruction*>, 8> SimpleIVUsers;
  
    // Push users of the current LoopPhi. In rare cases, pushIVUsers may be
    // called multiple times for the same LoopPhi. This is the proper thing to
    // do for loop header phis that use each other.
    pushIVUsers(CurrIV, Simplified, SimpleIVUsers);
  
    while (!SimpleIVUsers.empty()) {
      std::pair<Instruction*, Instruction*> UseOper =
        SimpleIVUsers.pop_back_val();
      Instruction *UseInst = UseOper.first;
  
      // Bypass back edges to avoid extra work.
      if (UseInst == CurrIV) continue;
  
      if (V && V->shouldSplitOverflowInstrinsics()) {
        UseInst = splitOverflowIntrinsic(UseInst, V->getDomTree());
        if (!UseInst)
          continue;
      }
  
      Instruction *IVOperand = UseOper.second;
      for (unsigned N = 0; IVOperand; ++N) {
        assert(N <= Simplified.size() && "runaway iteration");
  
        Value *NewOper = foldIVUser(UseOper.first, IVOperand);
        if (!NewOper)
          break; // done folding
        IVOperand = dyn_cast<Instruction>(NewOper);
      }
      if (!IVOperand)
        continue;
  
      if (eliminateIVUser(UseOper.first, IVOperand)) {
        pushIVUsers(IVOperand, Simplified, SimpleIVUsers);
        continue;
      }
  
      if (BinaryOperator *BO = dyn_cast<BinaryOperator>(UseOper.first)) {
        if (isa<OverflowingBinaryOperator>(BO) &&
            strengthenOverflowingOperation(BO, IVOperand)) {
          // re-queue uses of the now modified binary operator and fall
          // through to the checks that remain.
          pushIVUsers(IVOperand, Simplified, SimpleIVUsers);
        }
      }
  
      CastInst *Cast = dyn_cast<CastInst>(UseOper.first);
      if (V && Cast) {
        V->visitCast(Cast);
        continue;
      }
      if (isSimpleIVUser(UseOper.first, L, SE)) {
        pushIVUsers(UseOper.first, Simplified, SimpleIVUsers);
      }
    }
  }
  
  namespace llvm37 {
  
  void IVVisitor::anchor() { }
  
  /// Simplify instructions that use this induction variable
  /// by using ScalarEvolution to analyze the IV's recurrence.
  bool simplifyUsersOfIV(PHINode *CurrIV, ScalarEvolution *SE, LPPassManager *LPM,
                         SmallVectorImpl<WeakVH> &Dead, IVVisitor *V)
  {
    LoopInfo *LI = &LPM->getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
    SimplifyIndvar SIV(LI->getLoopFor(CurrIV->getParent()), SE, LI, Dead);
    SIV.simplifyUsers(CurrIV, V);
    return SIV.hasChanged();
  }
  
  /// Simplify users of induction variables within this
  /// loop. This does not actually change or add IVs.
  bool simplifyLoopIVs(Loop *L, ScalarEvolution *SE, LPPassManager *LPM,
                       SmallVectorImpl<WeakVH> &Dead) {
    bool Changed = false;
    for (BasicBlock::iterator I = L->getHeader()->begin(); isa<PHINode>(I); ++I) {
      Changed |= simplifyUsersOfIV(cast<PHINode>(I), SE, LPM, Dead);
    }
    return Changed;
  }
  
  } // namespace llvm37
  