Revert "[SCEV] Move ScalarEvolutionExpander.cpp to Transforms/Utils (NFC)."

This reverts commit 51ef53f3bd23559203fe9af82ff2facbfedc1db3, as it
breaks some bots.

1 files changed, 2452 insertions, 0 deletions

diff --git a/llvm/lib/Analysis/ScalarEvolutionExpander.cpp b/llvm/lib/Analysis/ScalarEvolutionExpander.cpp
new file mode 100644
index 00000000000..dc5d02aa3a3
--- /dev/null
+++ b/llvm/lib/Analysis/ScalarEvolutionExpander.cpp
@@ -0,0 +1,2452 @@
+//===- ScalarEvolutionExpander.cpp - Scalar Evolution Analysis ------------===//
+//
+// 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 file contains the implementation of the scalar evolution expander,
+// which is used to generate the code corresponding to a given scalar evolution
+// expression.
+//
+//===----------------------------------------------------------------------===//
+
+#include "llvm/Analysis/ScalarEvolutionExpander.h"
+#include "llvm/ADT/STLExtras.h"
+#include "llvm/ADT/SmallSet.h"
+#include "llvm/Analysis/InstructionSimplify.h"
+#include "llvm/Analysis/LoopInfo.h"
+#include "llvm/Analysis/TargetTransformInfo.h"
+#include "llvm/IR/DataLayout.h"
+#include "llvm/IR/Dominators.h"
+#include "llvm/IR/IntrinsicInst.h"
+#include "llvm/IR/LLVMContext.h"
+#include "llvm/IR/Module.h"
+#include "llvm/IR/PatternMatch.h"
+#include "llvm/Support/Debug.h"
+#include "llvm/Support/raw_ostream.h"
+
+using namespace llvm;
+using namespace PatternMatch;
+
+/// ReuseOrCreateCast - Arrange for there to be a cast of V to Ty at IP,
+/// reusing an existing cast if a suitable one exists, moving an existing
+/// cast if a suitable one exists but isn't in the right place, or
+/// creating a new one.
+Value *SCEVExpander::ReuseOrCreateCast(Value *V, Type *Ty,
+                                       Instruction::CastOps Op,
+                                       BasicBlock::iterator IP) {
+  // This function must be called with the builder having a valid insertion
+  // point. It doesn't need to be the actual IP where the uses of the returned
+  // cast will be added, but it must dominate such IP.
+  // We use this precondition to produce a cast that will dominate all its
+  // uses. In particular, this is crucial for the case where the builder's
+  // insertion point *is* the point where we were asked to put the cast.
+  // Since we don't know the builder's insertion point is actually
+  // where the uses will be added (only that it dominates it), we are
+  // not allowed to move it.
+  BasicBlock::iterator BIP = Builder.GetInsertPoint();
+
+  Instruction *Ret = nullptr;
+
+  // Check to see if there is already a cast!
+  for (User *U : V->users())
+    if (U->getType() == Ty)
+      if (CastInst *CI = dyn_cast<CastInst>(U))
+        if (CI->getOpcode() == Op) {
+          // If the cast isn't where we want it, create a new cast at IP.
+          // Likewise, do not reuse a cast at BIP because it must dominate
+          // instructions that might be inserted before BIP.
+          if (BasicBlock::iterator(CI) != IP || BIP == IP) {
+            // Create a new cast, and leave the old cast in place in case
+            // it is being used as an insert point.
+            Ret = CastInst::Create(Op, V, Ty, "", &*IP);
+            Ret->takeName(CI);
+            CI->replaceAllUsesWith(Ret);
+            break;
+          }
+          Ret = CI;
+          break;
+        }
+
+  // Create a new cast.
+  if (!Ret)
+    Ret = CastInst::Create(Op, V, Ty, V->getName(), &*IP);
+
+  // We assert at the end of the function since IP might point to an
+  // instruction with different dominance properties than a cast
+  // (an invoke for example) and not dominate BIP (but the cast does).
+  assert(SE.DT.dominates(Ret, &*BIP));
+
+  rememberInstruction(Ret);
+  return Ret;
+}
+
+static BasicBlock::iterator findInsertPointAfter(Instruction *I,
+                                                 BasicBlock *MustDominate) {
+  BasicBlock::iterator IP = ++I->getIterator();
+  if (auto *II = dyn_cast<InvokeInst>(I))
+    IP = II->getNormalDest()->begin();
+
+  while (isa<PHINode>(IP))
+    ++IP;
+
+  if (isa<FuncletPadInst>(IP) || isa<LandingPadInst>(IP)) {
+    ++IP;
+  } else if (isa<CatchSwitchInst>(IP)) {
+    IP = MustDominate->getFirstInsertionPt();
+  } else {
+    assert(!IP->isEHPad() && "unexpected eh pad!");
+  }
+
+  return IP;
+}
+
+/// InsertNoopCastOfTo - Insert a cast of V to the specified type,
+/// which must be possible with a noop cast, doing what we can to share
+/// the casts.
+Value *SCEVExpander::InsertNoopCastOfTo(Value *V, Type *Ty) {
+  Instruction::CastOps Op = CastInst::getCastOpcode(V, false, Ty, false);
+  assert((Op == Instruction::BitCast ||
+          Op == Instruction::PtrToInt ||
+          Op == Instruction::IntToPtr) &&
+         "InsertNoopCastOfTo cannot perform non-noop casts!");
+  assert(SE.getTypeSizeInBits(V->getType()) == SE.getTypeSizeInBits(Ty) &&
+         "InsertNoopCastOfTo cannot change sizes!");
+
+  // Short-circuit unnecessary bitcasts.
+  if (Op == Instruction::BitCast) {
+    if (V->getType() == Ty)
+      return V;
+    if (CastInst *CI = dyn_cast<CastInst>(V)) {
+      if (CI->getOperand(0)->getType() == Ty)
+        return CI->getOperand(0);
+    }
+  }
+  // Short-circuit unnecessary inttoptr<->ptrtoint casts.
+  if ((Op == Instruction::PtrToInt || Op == Instruction::IntToPtr) &&
+      SE.getTypeSizeInBits(Ty) == SE.getTypeSizeInBits(V->getType())) {
+    if (CastInst *CI = dyn_cast<CastInst>(V))
+      if ((CI->getOpcode() == Instruction::PtrToInt ||
+           CI->getOpcode() == Instruction::IntToPtr) &&
+          SE.getTypeSizeInBits(CI->getType()) ==
+          SE.getTypeSizeInBits(CI->getOperand(0)->getType()))
+        return CI->getOperand(0);
+    if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
+      if ((CE->getOpcode() == Instruction::PtrToInt ||
+           CE->getOpcode() == Instruction::IntToPtr) &&
+          SE.getTypeSizeInBits(CE->getType()) ==
+          SE.getTypeSizeInBits(CE->getOperand(0)->getType()))
+        return CE->getOperand(0);
+  }
+
+  // Fold a cast of a constant.
+  if (Constant *C = dyn_cast<Constant>(V))
+    return ConstantExpr::getCast(Op, C, Ty);
+
+  // Cast the argument at the beginning of the entry block, after
+  // any bitcasts of other arguments.
+  if (Argument *A = dyn_cast<Argument>(V)) {
+    BasicBlock::iterator IP = A->getParent()->getEntryBlock().begin();
+    while ((isa<BitCastInst>(IP) &&
+            isa<Argument>(cast<BitCastInst>(IP)->getOperand(0)) &&
+            cast<BitCastInst>(IP)->getOperand(0) != A) ||
+           isa<DbgInfoIntrinsic>(IP))
+      ++IP;
+    return ReuseOrCreateCast(A, Ty, Op, IP);
+  }
+
+  // Cast the instruction immediately after the instruction.
+  Instruction *I = cast<Instruction>(V);
+  BasicBlock::iterator IP = findInsertPointAfter(I, Builder.GetInsertBlock());
+  return ReuseOrCreateCast(I, Ty, Op, IP);
+}
+
+/// InsertBinop - Insert the specified binary operator, doing a small amount
+/// of work to avoid inserting an obviously redundant operation, and hoisting
+/// to an outer loop when the opportunity is there and it is safe.
+Value *SCEVExpander::InsertBinop(Instruction::BinaryOps Opcode,
+                                 Value *LHS, Value *RHS,
+                                 SCEV::NoWrapFlags Flags, bool IsSafeToHoist) {
+  // Fold a binop with constant operands.
+  if (Constant *CLHS = dyn_cast<Constant>(LHS))
+    if (Constant *CRHS = dyn_cast<Constant>(RHS))
+      return ConstantExpr::get(Opcode, CLHS, CRHS);
+
+  // Do a quick scan to see if we have this binop nearby.  If so, reuse it.
+  unsigned ScanLimit = 6;
+  BasicBlock::iterator BlockBegin = Builder.GetInsertBlock()->begin();
+  // Scanning starts from the last instruction before the insertion point.
+  BasicBlock::iterator IP = Builder.GetInsertPoint();
+  if (IP != BlockBegin) {
+    --IP;
+    for (; ScanLimit; --IP, --ScanLimit) {
+      // Don't count dbg.value against the ScanLimit, to avoid perturbing the
+      // generated code.
+      if (isa<DbgInfoIntrinsic>(IP))
+        ScanLimit++;
+
+      auto canGenerateIncompatiblePoison = [&Flags](Instruction *I) {
+        // Ensure that no-wrap flags match.
+        if (isa<OverflowingBinaryOperator>(I)) {
+          if (I->hasNoSignedWrap() != (Flags & SCEV::FlagNSW))
+            return true;
+          if (I->hasNoUnsignedWrap() != (Flags & SCEV::FlagNUW))
+            return true;
+        }
+        // Conservatively, do not use any instruction which has any of exact
+        // flags installed.
+        if (isa<PossiblyExactOperator>(I) && I->isExact())
+          return true;
+        return false;
+      };
+      if (IP->getOpcode() == (unsigned)Opcode && IP->getOperand(0) == LHS &&
+          IP->getOperand(1) == RHS && !canGenerateIncompatiblePoison(&*IP))
+        return &*IP;
+      if (IP == BlockBegin) break;
+    }
+  }
+
+  // Save the original insertion point so we can restore it when we're done.
+  DebugLoc Loc = Builder.GetInsertPoint()->getDebugLoc();
+  SCEVInsertPointGuard Guard(Builder, this);
+
+  if (IsSafeToHoist) {
+    // Move the insertion point out of as many loops as we can.
+    while (const Loop *L = SE.LI.getLoopFor(Builder.GetInsertBlock())) {
+      if (!L->isLoopInvariant(LHS) || !L->isLoopInvariant(RHS)) break;
+      BasicBlock *Preheader = L->getLoopPreheader();
+      if (!Preheader) break;
+
+      // Ok, move up a level.
+      Builder.SetInsertPoint(Preheader->getTerminator());
+    }
+  }
+
+  // If we haven't found this binop, insert it.
+  Instruction *BO = cast<Instruction>(Builder.CreateBinOp(Opcode, LHS, RHS));
+  BO->setDebugLoc(Loc);
+  if (Flags & SCEV::FlagNUW)
+    BO->setHasNoUnsignedWrap();
+  if (Flags & SCEV::FlagNSW)
+    BO->setHasNoSignedWrap();
+  rememberInstruction(BO);
+
+  return BO;
+}
+
+/// FactorOutConstant - Test if S is divisible by Factor, using signed
+/// division. If so, update S with Factor divided out and return true.
+/// S need not be evenly divisible if a reasonable remainder can be
+/// computed.
+static bool FactorOutConstant(const SCEV *&S, const SCEV *&Remainder,
+                              const SCEV *Factor, ScalarEvolution &SE,
+                              const DataLayout &DL) {
+  // Everything is divisible by one.
+  if (Factor->isOne())
+    return true;
+
+  // x/x == 1.
+  if (S == Factor) {
+    S = SE.getConstant(S->getType(), 1);
+    return true;
+  }
+
+  // For a Constant, check for a multiple of the given factor.
+  if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
+    // 0/x == 0.
+    if (C->isZero())
+      return true;
+    // Check for divisibility.
+    if (const SCEVConstant *FC = dyn_cast<SCEVConstant>(Factor)) {
+      ConstantInt *CI =
+          ConstantInt::get(SE.getContext(), C->getAPInt().sdiv(FC->getAPInt()));
+      // If the quotient is zero and the remainder is non-zero, reject
+      // the value at this scale. It will be considered for subsequent
+      // smaller scales.
+      if (!CI->isZero()) {
+        const SCEV *Div = SE.getConstant(CI);
+        S = Div;
+        Remainder = SE.getAddExpr(
+            Remainder, SE.getConstant(C->getAPInt().srem(FC->getAPInt())));
+        return true;
+      }
+    }
+  }
+
+  // In a Mul, check if there is a constant operand which is a multiple
+  // of the given factor.
+  if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
+    // Size is known, check if there is a constant operand which is a multiple
+    // of the given factor. If so, we can factor it.
+    const SCEVConstant *FC = cast<SCEVConstant>(Factor);
+    if (const SCEVConstant *C = dyn_cast<SCEVConstant>(M->getOperand(0)))
+      if (!C->getAPInt().srem(FC->getAPInt())) {
+        SmallVector<const SCEV *, 4> NewMulOps(M->op_begin(), M->op_end());
+        NewMulOps[0] = SE.getConstant(C->getAPInt().sdiv(FC->getAPInt()));
+        S = SE.getMulExpr(NewMulOps);
+        return true;
+      }
+  }
+
+  // In an AddRec, check if both start and step are divisible.
+  if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
+    const SCEV *Step = A->getStepRecurrence(SE);
+    const SCEV *StepRem = SE.getConstant(Step->getType(), 0);
+    if (!FactorOutConstant(Step, StepRem, Factor, SE, DL))
+      return false;
+    if (!StepRem->isZero())
+      return false;
+    const SCEV *Start = A->getStart();
+    if (!FactorOutConstant(Start, Remainder, Factor, SE, DL))
+      return false;
+    S = SE.getAddRecExpr(Start, Step, A->getLoop(),
+                         A->getNoWrapFlags(SCEV::FlagNW));
+    return true;
+  }
+
+  return false;
+}
+
+/// SimplifyAddOperands - Sort and simplify a list of add operands. NumAddRecs
+/// is the number of SCEVAddRecExprs present, which are kept at the end of
+/// the list.
+///
+static void SimplifyAddOperands(SmallVectorImpl<const SCEV *> &Ops,
+                                Type *Ty,
+                                ScalarEvolution &SE) {
+  unsigned NumAddRecs = 0;
+  for (unsigned i = Ops.size(); i > 0 && isa<SCEVAddRecExpr>(Ops[i-1]); --i)
+    ++NumAddRecs;
+  // Group Ops into non-addrecs and addrecs.
+  SmallVector<const SCEV *, 8> NoAddRecs(Ops.begin(), Ops.end() - NumAddRecs);
+  SmallVector<const SCEV *, 8> AddRecs(Ops.end() - NumAddRecs, Ops.end());
+  // Let ScalarEvolution sort and simplify the non-addrecs list.
+  const SCEV *Sum = NoAddRecs.empty() ?
+                    SE.getConstant(Ty, 0) :
+                    SE.getAddExpr(NoAddRecs);
+  // If it returned an add, use the operands. Otherwise it simplified
+  // the sum into a single value, so just use that.
+  Ops.clear();
+  if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Sum))
+    Ops.append(Add->op_begin(), Add->op_end());
+  else if (!Sum->isZero())
+    Ops.push_back(Sum);
+  // Then append the addrecs.
+  Ops.append(AddRecs.begin(), AddRecs.end());
+}
+
+/// SplitAddRecs - Flatten a list of add operands, moving addrec start values
+/// out to the top level. For example, convert {a + b,+,c} to a, b, {0,+,d}.
+/// This helps expose more opportunities for folding parts of the expressions
+/// into GEP indices.
+///
+static void SplitAddRecs(SmallVectorImpl<const SCEV *> &Ops,
+                         Type *Ty,
+                         ScalarEvolution &SE) {
+  // Find the addrecs.
+  SmallVector<const SCEV *, 8> AddRecs;
+  for (unsigned i = 0, e = Ops.size(); i != e; ++i)
+    while (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(Ops[i])) {
+      const SCEV *Start = A->getStart();
+      if (Start->isZero()) break;
+      const SCEV *Zero = SE.getConstant(Ty, 0);
+      AddRecs.push_back(SE.getAddRecExpr(Zero,
+                                         A->getStepRecurrence(SE),
+                                         A->getLoop(),
+                                         A->getNoWrapFlags(SCEV::FlagNW)));
+      if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Start)) {
+        Ops[i] = Zero;
+        Ops.append(Add->op_begin(), Add->op_end());
+        e += Add->getNumOperands();
+      } else {
+        Ops[i] = Start;
+      }
+    }
+  if (!AddRecs.empty()) {
+    // Add the addrecs onto the end of the list.
+    Ops.append(AddRecs.begin(), AddRecs.end());
+    // Resort the operand list, moving any constants to the front.
+    SimplifyAddOperands(Ops, Ty, SE);
+  }
+}
+
+/// expandAddToGEP - Expand an addition expression with a pointer type into
+/// a GEP instead of using ptrtoint+arithmetic+inttoptr. This helps
+/// BasicAliasAnalysis and other passes analyze the result. See the rules
+/// for getelementptr vs. inttoptr in
+/// http://llvm.org/docs/LangRef.html#pointeraliasing
+/// for details.
+///
+/// Design note: The correctness of using getelementptr here depends on
+/// ScalarEvolution not recognizing inttoptr and ptrtoint operators, as
+/// they may introduce pointer arithmetic which may not be safely converted
+/// into getelementptr.
+///
+/// Design note: It might seem desirable for this function to be more
+/// loop-aware. If some of the indices are loop-invariant while others
+/// aren't, it might seem desirable to emit multiple GEPs, keeping the
+/// loop-invariant portions of the overall computation outside the loop.
+/// However, there are a few reasons this is not done here. Hoisting simple
+/// arithmetic is a low-level optimization that often isn't very
+/// important until late in the optimization process. In fact, passes
+/// like InstructionCombining will combine GEPs, even if it means
+/// pushing loop-invariant computation down into loops, so even if the
+/// GEPs were split here, the work would quickly be undone. The
+/// LoopStrengthReduction pass, which is usually run quite late (and
+/// after the last InstructionCombining pass), takes care of hoisting
+/// loop-invariant portions of expressions, after considering what
+/// can be folded using target addressing modes.
+///
+Value *SCEVExpander::expandAddToGEP(const SCEV *const *op_begin,
+                                    const SCEV *const *op_end,
+                                    PointerType *PTy,
+                                    Type *Ty,
+                                    Value *V) {
+  Type *OriginalElTy = PTy->getElementType();
+  Type *ElTy = OriginalElTy;
+  SmallVector<Value *, 4> GepIndices;
+  SmallVector<const SCEV *, 8> Ops(op_begin, op_end);
+  bool AnyNonZeroIndices = false;
+
+  // Split AddRecs up into parts as either of the parts may be usable
+  // without the other.
+  SplitAddRecs(Ops, Ty, SE);
+
+  Type *IntIdxTy = DL.getIndexType(PTy);
+
+  // Descend down the pointer's type and attempt to convert the other
+  // operands into GEP indices, at each level. The first index in a GEP
+  // indexes into the array implied by the pointer operand; the rest of
+  // the indices index into the element or field type selected by the
+  // preceding index.
+  for (;;) {
+    // If the scale size is not 0, attempt to factor out a scale for
+    // array indexing.
+    SmallVector<const SCEV *, 8> ScaledOps;
+    if (ElTy->isSized()) {
+      const SCEV *ElSize = SE.getSizeOfExpr(IntIdxTy, ElTy);
+      if (!ElSize->isZero()) {
+        SmallVector<const SCEV *, 8> NewOps;
+        for (const SCEV *Op : Ops) {
+          const SCEV *Remainder = SE.getConstant(Ty, 0);
+          if (FactorOutConstant(Op, Remainder, ElSize, SE, DL)) {
+            // Op now has ElSize factored out.
+            ScaledOps.push_back(Op);
+            if (!Remainder->isZero())
+              NewOps.push_back(Remainder);
+            AnyNonZeroIndices = true;
+          } else {
+            // The operand was not divisible, so add it to the list of operands
+            // we'll scan next iteration.
+            NewOps.push_back(Op);
+          }
+        }
+        // If we made any changes, update Ops.
+        if (!ScaledOps.empty()) {
+          Ops = NewOps;
+          SimplifyAddOperands(Ops, Ty, SE);
+        }
+      }
+    }
+
+    // Record the scaled array index for this level of the type. If
+    // we didn't find any operands that could be factored, tentatively
+    // assume that element zero was selected (since the zero offset
+    // would obviously be folded away).
+    Value *Scaled = ScaledOps.empty() ?
+                    Constant::getNullValue(Ty) :
+                    expandCodeFor(SE.getAddExpr(ScaledOps), Ty);
+    GepIndices.push_back(Scaled);
+
+    // Collect struct field index operands.
+    while (StructType *STy = dyn_cast<StructType>(ElTy)) {
+      bool FoundFieldNo = false;
+      // An empty struct has no fields.
+      if (STy->getNumElements() == 0) break;
+      // Field offsets are known. See if a constant offset falls within any of
+      // the struct fields.
+      if (Ops.empty())
+        break;
+      if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[0]))
+        if (SE.getTypeSizeInBits(C->getType()) <= 64) {
+          const StructLayout &SL = *DL.getStructLayout(STy);
+          uint64_t FullOffset = C->getValue()->getZExtValue();
+          if (FullOffset < SL.getSizeInBytes()) {
+            unsigned ElIdx = SL.getElementContainingOffset(FullOffset);
+            GepIndices.push_back(
+                ConstantInt::get(Type::getInt32Ty(Ty->getContext()), ElIdx));
+            ElTy = STy->getTypeAtIndex(ElIdx);
+            Ops[0] =
+                SE.getConstant(Ty, FullOffset - SL.getElementOffset(ElIdx));
+            AnyNonZeroIndices = true;
+            FoundFieldNo = true;
+          }
+        }
+      // If no struct field offsets were found, tentatively assume that
+      // field zero was selected (since the zero offset would obviously
+      // be folded away).
+      if (!FoundFieldNo) {
+        ElTy = STy->getTypeAtIndex(0u);
+        GepIndices.push_back(
+          Constant::getNullValue(Type::getInt32Ty(Ty->getContext())));
+      }
+    }
+
+    if (ArrayType *ATy = dyn_cast<ArrayType>(ElTy))
+      ElTy = ATy->getElementType();
+    else
+      break;
+  }
+
+  // If none of the operands were convertible to proper GEP indices, cast
+  // the base to i8* and do an ugly getelementptr with that. It's still
+  // better than ptrtoint+arithmetic+inttoptr at least.
+  if (!AnyNonZeroIndices) {
+    // Cast the base to i8*.
+    V = InsertNoopCastOfTo(V,
+       Type::getInt8PtrTy(Ty->getContext(), PTy->getAddressSpace()));
+
+    assert(!isa<Instruction>(V) ||
+           SE.DT.dominates(cast<Instruction>(V), &*Builder.GetInsertPoint()));
+
+    // Expand the operands for a plain byte offset.
+    Value *Idx = expandCodeFor(SE.getAddExpr(Ops), Ty);
+
+    // Fold a GEP with constant operands.
+    if (Constant *CLHS = dyn_cast<Constant>(V))
+      if (Constant *CRHS = dyn_cast<Constant>(Idx))
+        return ConstantExpr::getGetElementPtr(Type::getInt8Ty(Ty->getContext()),
+                                              CLHS, CRHS);
+
+    // Do a quick scan to see if we have this GEP nearby.  If so, reuse it.
+    unsigned ScanLimit = 6;
+    BasicBlock::iterator BlockBegin = Builder.GetInsertBlock()->begin();
+    // Scanning starts from the last instruction before the insertion point.
+    BasicBlock::iterator IP = Builder.GetInsertPoint();
+    if (IP != BlockBegin) {
+      --IP;
+      for (; ScanLimit; --IP, --ScanLimit) {
+        // Don't count dbg.value against the ScanLimit, to avoid perturbing the
+        // generated code.
+        if (isa<DbgInfoIntrinsic>(IP))
+          ScanLimit++;
+        if (IP->getOpcode() == Instruction::GetElementPtr &&
+            IP->getOperand(0) == V && IP->getOperand(1) == Idx)
+          return &*IP;
+        if (IP == BlockBegin) break;
+      }
+    }
+
+    // Save the original insertion point so we can restore it when we're done.
+    SCEVInsertPointGuard Guard(Builder, this);
+
+    // Move the insertion point out of as many loops as we can.
+    while (const Loop *L = SE.LI.getLoopFor(Builder.GetInsertBlock())) {
+      if (!L->isLoopInvariant(V) || !L->isLoopInvariant(Idx)) break;
+      BasicBlock *Preheader = L->getLoopPreheader();
+      if (!Preheader) break;
+
+      // Ok, move up a level.
+      Builder.SetInsertPoint(Preheader->getTerminator());
+    }
+
+    // Emit a GEP.
+    Value *GEP = Builder.CreateGEP(Builder.getInt8Ty(), V, Idx, "uglygep");
+    rememberInstruction(GEP);
+
+    return GEP;
+  }
+
+  {
+    SCEVInsertPointGuard Guard(Builder, this);
+
+    // Move the insertion point out of as many loops as we can.
+    while (const Loop *L = SE.LI.getLoopFor(Builder.GetInsertBlock())) {
+      if (!L->isLoopInvariant(V)) break;
+
+      bool AnyIndexNotLoopInvariant = any_of(
+          GepIndices, [L](Value *Op) { return !L->isLoopInvariant(Op); });
+
+      if (AnyIndexNotLoopInvariant)
+        break;
+
+      BasicBlock *Preheader = L->getLoopPreheader();
+      if (!Preheader) break;
+
+      // Ok, move up a level.
+      Builder.SetInsertPoint(Preheader->getTerminator());
+    }
+
+    // Insert a pretty getelementptr. Note that this GEP is not marked inbounds,
+    // because ScalarEvolution may have changed the address arithmetic to
+    // compute a value which is beyond the end of the allocated object.
+    Value *Casted = V;
+    if (V->getType() != PTy)
+      Casted = InsertNoopCastOfTo(Casted, PTy);
+    Value *GEP = Builder.CreateGEP(OriginalElTy, Casted, GepIndices, "scevgep");
+    Ops.push_back(SE.getUnknown(GEP));
+    rememberInstruction(GEP);
+  }
+
+  return expand(SE.getAddExpr(Ops));
+}
+
+Value *SCEVExpander::expandAddToGEP(const SCEV *Op, PointerType *PTy, Type *Ty,
+                                    Value *V) {
+  const SCEV *const Ops[1] = {Op};
+  return expandAddToGEP(Ops, Ops + 1, PTy, Ty, V);
+}
+
+/// PickMostRelevantLoop - Given two loops pick the one that's most relevant for
+/// SCEV expansion. If they are nested, this is the most nested. If they are
+/// neighboring, pick the later.
+static const Loop *PickMostRelevantLoop(const Loop *A, const Loop *B,
+                                        DominatorTree &DT) {
+  if (!A) return B;
+  if (!B) return A;
+  if (A->contains(B)) return B;
+  if (B->contains(A)) return A;
+  if (DT.dominates(A->getHeader(), B->getHeader())) return B;
+  if (DT.dominates(B->getHeader(), A->getHeader())) return A;
+  return A; // Arbitrarily break the tie.
+}
+
+/// getRelevantLoop - Get the most relevant loop associated with the given
+/// expression, according to PickMostRelevantLoop.
+const Loop *SCEVExpander::getRelevantLoop(const SCEV *S) {
+  // Test whether we've already computed the most relevant loop for this SCEV.
+  auto Pair = RelevantLoops.insert(std::make_pair(S, nullptr));
+  if (!Pair.second)
+    return Pair.first->second;
+
+  if (isa<SCEVConstant>(S))
+    // A constant has no relevant loops.
+    return nullptr;
+  if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
+    if (const Instruction *I = dyn_cast<Instruction>(U->getValue()))
+      return Pair.first->second = SE.LI.getLoopFor(I->getParent());
+    // A non-instruction has no relevant loops.
+    return nullptr;
+  }
+  if (const SCEVNAryExpr *N = dyn_cast<SCEVNAryExpr>(S)) {
+    const Loop *L = nullptr;
+    if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
+      L = AR->getLoop();
+    for (const SCEV *Op : N->operands())
+      L = PickMostRelevantLoop(L, getRelevantLoop(Op), SE.DT);
+    return RelevantLoops[N] = L;
+  }
+  if (const SCEVCastExpr *C = dyn_cast<SCEVCastExpr>(S)) {
+    const Loop *Result = getRelevantLoop(C->getOperand());
+    return RelevantLoops[C] = Result;
+  }
+  if (const SCEVUDivExpr *D = dyn_cast<SCEVUDivExpr>(S)) {
+    const Loop *Result = PickMostRelevantLoop(
+        getRelevantLoop(D->getLHS()), getRelevantLoop(D->getRHS()), SE.DT);
+    return RelevantLoops[D] = Result;
+  }
+  llvm_unreachable("Unexpected SCEV type!");
+}
+
+namespace {
+
+/// LoopCompare - Compare loops by PickMostRelevantLoop.
+class LoopCompare {
+  DominatorTree &DT;
+public:
+  explicit LoopCompare(DominatorTree &dt) : DT(dt) {}
+
+  bool operator()(std::pair<const Loop *, const SCEV *> LHS,
+                  std::pair<const Loop *, const SCEV *> RHS) const {
+    // Keep pointer operands sorted at the end.
+    if (LHS.second->getType()->isPointerTy() !=
+        RHS.second->getType()->isPointerTy())
+      return LHS.second->getType()->isPointerTy();
+
+    // Compare loops with PickMostRelevantLoop.
+    if (LHS.first != RHS.first)
+      return PickMostRelevantLoop(LHS.first, RHS.first, DT) != LHS.first;
+
+    // If one operand is a non-constant negative and the other is not,
+    // put the non-constant negative on the right so that a sub can
+    // be used instead of a negate and add.
+    if (LHS.second->isNonConstantNegative()) {
+      if (!RHS.second->isNonConstantNegative())
+        return false;
+    } else if (RHS.second->isNonConstantNegative())
+      return true;
+
+    // Otherwise they are equivalent according to this comparison.
+    return false;
+  }
+};
+
+}
+
+Value *SCEVExpander::visitAddExpr(const SCEVAddExpr *S) {
+  Type *Ty = SE.getEffectiveSCEVType(S->getType());
+
+  // Collect all the add operands in a loop, along with their associated loops.
+  // Iterate in reverse so that constants are emitted last, all else equal, and
+  // so that pointer operands are inserted first, which the code below relies on
+  // to form more involved GEPs.
+  SmallVector<std::pair<const Loop *, const SCEV *>, 8> OpsAndLoops;
+  for (std::reverse_iterator<SCEVAddExpr::op_iterator> I(S->op_end()),
+       E(S->op_begin()); I != E; ++I)
+    OpsAndLoops.push_back(std::make_pair(getRelevantLoop(*I), *I));
+
+  // Sort by loop. Use a stable sort so that constants follow non-constants and
+  // pointer operands precede non-pointer operands.
+  llvm::stable_sort(OpsAndLoops, LoopCompare(SE.DT));
+
+  // Emit instructions to add all the operands. Hoist as much as possible
+  // out of loops, and form meaningful getelementptrs where possible.
+  Value *Sum = nullptr;
+  for (auto I = OpsAndLoops.begin(), E = OpsAndLoops.end(); I != E;) {
+    const Loop *CurLoop = I->first;
+    const SCEV *Op = I->second;
+    if (!Sum) {
+      // This is the first operand. Just expand it.
+      Sum = expand(Op);
+      ++I;
+    } else if (PointerType *PTy = dyn_cast<PointerType>(Sum->getType())) {
+      // The running sum expression is a pointer. Try to form a getelementptr
+      // at this level with that as the base.
+      SmallVector<const SCEV *, 4> NewOps;
+      for (; I != E && I->first == CurLoop; ++I) {
+        // If the operand is SCEVUnknown and not instructions, peek through
+        // it, to enable more of it to be folded into the GEP.
+        const SCEV *X = I->second;
+        if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(X))
+          if (!isa<Instruction>(U->getValue()))
+            X = SE.getSCEV(U->getValue());
+        NewOps.push_back(X);
+      }
+      Sum = expandAddToGEP(NewOps.begin(), NewOps.end(), PTy, Ty, Sum);
+    } else if (PointerType *PTy = dyn_cast<PointerType>(Op->getType())) {
+      // The running sum is an integer, and there's a pointer at this level.
+      // Try to form a getelementptr. If the running sum is instructions,
+      // use a SCEVUnknown to avoid re-analyzing them.
+      SmallVector<const SCEV *, 4> NewOps;
+      NewOps.push_back(isa<Instruction>(Sum) ? SE.getUnknown(Sum) :
+                                               SE.getSCEV(Sum));
+      for (++I; I != E && I->first == CurLoop; ++I)
+        NewOps.push_back(I->second);
+      Sum = expandAddToGEP(NewOps.begin(), NewOps.end(), PTy, Ty, expand(Op));
+    } else if (Op->isNonConstantNegative()) {
+      // Instead of doing a negate and add, just do a subtract.
+      Value *W = expandCodeFor(SE.getNegativeSCEV(Op), Ty);
+      Sum = InsertNoopCastOfTo(Sum, Ty);
+      Sum = InsertBinop(Instruction::Sub, Sum, W, SCEV::FlagAnyWrap,
+                        /*IsSafeToHoist*/ true);
+      ++I;
+    } else {
+      // A simple add.
+      Value *W = expandCodeFor(Op, Ty);
+      Sum = InsertNoopCastOfTo(Sum, Ty);
+      // Canonicalize a constant to the RHS.
+      if (isa<Constant>(Sum)) std::swap(Sum, W);
+      Sum = InsertBinop(Instruction::Add, Sum, W, S->getNoWrapFlags(),
+                        /*IsSafeToHoist*/ true);
+      ++I;
+    }
+  }
+
+  return Sum;
+}
+
+Value *SCEVExpander::visitMulExpr(const SCEVMulExpr *S) {
+  Type *Ty = SE.getEffectiveSCEVType(S->getType());
+
+  // Collect all the mul operands in a loop, along with their associated loops.
+  // Iterate in reverse so that constants are emitted last, all else equal.
+  SmallVector<std::pair<const Loop *, const SCEV *>, 8> OpsAndLoops;
+  for (std::reverse_iterator<SCEVMulExpr::op_iterator> I(S->op_end()),
+       E(S->op_begin()); I != E; ++I)
+    OpsAndLoops.push_back(std::make_pair(getRelevantLoop(*I), *I));
+
+  // Sort by loop. Use a stable sort so that constants follow non-constants.
+  llvm::stable_sort(OpsAndLoops, LoopCompare(SE.DT));
+
+  // Emit instructions to mul all the operands. Hoist as much as possible
+  // out of loops.
+  Value *Prod = nullptr;
+  auto I = OpsAndLoops.begin();
+
+  // Expand the calculation of X pow N in the following manner:
+  // Let N = P1 + P2 + ... + PK, where all P are powers of 2. Then:
+  // X pow N = (X pow P1) * (X pow P2) * ... * (X pow PK).
+  const auto ExpandOpBinPowN = [this, &I, &OpsAndLoops, &Ty]() {
+    auto E = I;
+    // Calculate how many times the same operand from the same loop is included
+    // into this power.
+    uint64_t Exponent = 0;
+    const uint64_t MaxExponent = UINT64_MAX >> 1;
+    // No one sane will ever try to calculate such huge exponents, but if we
+    // need this, we stop on UINT64_MAX / 2 because we need to exit the loop
+    // below when the power of 2 exceeds our Exponent, and we want it to be
+    // 1u << 31 at most to not deal with unsigned overflow.
+    while (E != OpsAndLoops.end() && *I == *E && Exponent != MaxExponent) {
+      ++Exponent;
+      ++E;
+    }
+    assert(Exponent > 0 && "Trying to calculate a zeroth exponent of operand?");
+
+    // Calculate powers with exponents 1, 2, 4, 8 etc. and include those of them
+    // that are needed into the result.
+    Value *P = expandCodeFor(I->second, Ty);
+    Value *Result = nullptr;
+    if (Exponent & 1)
+      Result = P;
+    for (uint64_t BinExp = 2; BinExp <= Exponent; BinExp <<= 1) {
+      P = InsertBinop(Instruction::Mul, P, P, SCEV::FlagAnyWrap,
+                      /*IsSafeToHoist*/ true);
+      if (Exponent & BinExp)
+        Result = Result ? InsertBinop(Instruction::Mul, Result, P,
+                                      SCEV::FlagAnyWrap,
+                                      /*IsSafeToHoist*/ true)
+                        : P;
+    }
+
+    I = E;
+    assert(Result && "Nothing was expanded?");
+    return Result;
+  };
+
+  while (I != OpsAndLoops.end()) {
+    if (!Prod) {
+      // This is the first operand. Just expand it.
+      Prod = ExpandOpBinPowN();
+    } else if (I->second->isAllOnesValue()) {
+      // Instead of doing a multiply by negative one, just do a negate.
+      Prod = InsertNoopCastOfTo(Prod, Ty);
+      Prod = InsertBinop(Instruction::Sub, Constant::getNullValue(Ty), Prod,
+                         SCEV::FlagAnyWrap, /*IsSafeToHoist*/ true);
+      ++I;
+    } else {
+      // A simple mul.
+      Value *W = ExpandOpBinPowN();
+      Prod = InsertNoopCastOfTo(Prod, Ty);
+      // Canonicalize a constant to the RHS.
+      if (isa<Constant>(Prod)) std::swap(Prod, W);
+      const APInt *RHS;
+      if (match(W, m_Power2(RHS))) {
+        // Canonicalize Prod*(1<<C) to Prod<<C.
+        assert(!Ty->isVectorTy() && "vector types are not SCEVable");
+        auto NWFlags = S->getNoWrapFlags();
+        // clear nsw flag if shl will produce poison value.
+        if (RHS->logBase2() == RHS->getBitWidth() - 1)
+          NWFlags = ScalarEvolution::clearFlags(NWFlags, SCEV::FlagNSW);
+        Prod = InsertBinop(Instruction::Shl, Prod,
+                           ConstantInt::get(Ty, RHS->logBase2()), NWFlags,
+                           /*IsSafeToHoist*/ true);
+      } else {
+        Prod = InsertBinop(Instruction::Mul, Prod, W, S->getNoWrapFlags(),
+                           /*IsSafeToHoist*/ true);
+      }
+    }
+  }
+
+  return Prod;
+}
+
+Value *SCEVExpander::visitUDivExpr(const SCEVUDivExpr *S) {
+  Type *Ty = SE.getEffectiveSCEVType(S->getType());
+
+  Value *LHS = expandCodeFor(S->getLHS(), Ty);
+  if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(S->getRHS())) {
+    const APInt &RHS = SC->getAPInt();
+    if (RHS.isPowerOf2())
+      return InsertBinop(Instruction::LShr, LHS,
+                         ConstantInt::get(Ty, RHS.logBase2()),
+                         SCEV::FlagAnyWrap, /*IsSafeToHoist*/ true);
+  }
+
+  Value *RHS = expandCodeFor(S->getRHS(), Ty);
+  return InsertBinop(Instruction::UDiv, LHS, RHS, SCEV::FlagAnyWrap,
+                     /*IsSafeToHoist*/ SE.isKnownNonZero(S->getRHS()));
+}
+
+/// Move parts of Base into Rest to leave Base with the minimal
+/// expression that provides a pointer operand suitable for a
+/// GEP expansion.
+static void ExposePointerBase(const SCEV *&Base, const SCEV *&Rest,
+                              ScalarEvolution &SE) {
+  while (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(Base)) {
+    Base = A->getStart();
+    Rest = SE.getAddExpr(Rest,
+                         SE.getAddRecExpr(SE.getConstant(A->getType(), 0),
+                                          A->getStepRecurrence(SE),
+                                          A->getLoop(),
+                                          A->getNoWrapFlags(SCEV::FlagNW)));
+  }
+  if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(Base)) {
+    Base = A->getOperand(A->getNumOperands()-1);
+    SmallVector<const SCEV *, 8> NewAddOps(A->op_begin(), A->op_end());
+    NewAddOps.back() = Rest;
+    Rest = SE.getAddExpr(NewAddOps);
+    ExposePointerBase(Base, Rest, SE);
+  }
+}
+
+/// Determine if this is a well-behaved chain of instructions leading back to
+/// the PHI. If so, it may be reused by expanded expressions.
+bool SCEVExpander::isNormalAddRecExprPHI(PHINode *PN, Instruction *IncV,
+                                         const Loop *L) {
+  if (IncV->getNumOperands() == 0 || isa<PHINode>(IncV) ||
+      (isa<CastInst>(IncV) && !isa<BitCastInst>(IncV)))
+    return false;
+  // If any of the operands don't dominate the insert position, bail.
+  // Addrec operands are always loop-invariant, so this can only happen
+  // if there are instructions which haven't been hoisted.
+  if (L == IVIncInsertLoop) {
+    for (User::op_iterator OI = IncV->op_begin()+1,
+           OE = IncV->op_end(); OI != OE; ++OI)
+      if (Instruction *OInst = dyn_cast<Instruction>(OI))
+        if (!SE.DT.dominates(OInst, IVIncInsertPos))
+          return false;
+  }
+  // Advance to the next instruction.
+  IncV = dyn_cast<Instruction>(IncV->getOperand(0));
+  if (!IncV)
+    return false;
+
+  if (IncV->mayHaveSideEffects())
+    return false;
+
+  if (IncV == PN)
+    return true;
+
+  return isNormalAddRecExprPHI(PN, IncV, L);
+}
+
+/// getIVIncOperand returns an induction variable increment's induction
+/// variable operand.
+///
+/// If allowScale is set, any type of GEP is allowed as long as the nonIV
+/// operands dominate InsertPos.
+///
+/// If allowScale is not set, ensure that a GEP increment conforms to one of the
+/// simple patterns generated by getAddRecExprPHILiterally and
+/// expandAddtoGEP. If the pattern isn't recognized, return NULL.
+Instruction *SCEVExpander::getIVIncOperand(Instruction *IncV,
+                                           Instruction *InsertPos,
+                                           bool allowScale) {
+  if (IncV == InsertPos)
+    return nullptr;
+
+  switch (IncV->getOpcode()) {
+  default:
+    return nullptr;
+  // Check for a simple Add/Sub or GEP of a loop invariant step.
+  case Instruction::Add:
+  case Instruction::Sub: {
+    Instruction *OInst = dyn_cast<Instruction>(IncV->getOperand(1));
+    if (!OInst || SE.DT.dominates(OInst, InsertPos))
+      return dyn_cast<Instruction>(IncV->getOperand(0));
+    return nullptr;
+  }
+  case Instruction::BitCast:
+    return dyn_cast<Instruction>(IncV->getOperand(0));
+  case Instruction::GetElementPtr:
+    for (auto I = IncV->op_begin() + 1, E = IncV->op_end(); I != E; ++I) {
+      if (isa<Constant>(*I))
+        continue;
+      if (Instruction *OInst = dyn_cast<Instruction>(*I)) {
+        if (!SE.DT.dominates(OInst, InsertPos))
+          return nullptr;
+      }
+      if (allowScale) {
+        // allow any kind of GEP as long as it can be hoisted.
+        continue;
+      }
+      // This must be a pointer addition of constants (pretty), which is already
+      // handled, or some number of address-size elements (ugly). Ugly geps
+      // have 2 operands. i1* is used by the expander to represent an
+      // address-size element.
+      if (IncV->getNumOperands() != 2)
+        return nullptr;
+      unsigned AS = cast<PointerType>(IncV->getType())->getAddressSpace();
+      if (IncV->getType() != Type::getInt1PtrTy(SE.getContext(), AS)
+          && IncV->getType() != Type::getInt8PtrTy(SE.getContext(), AS))
+        return nullptr;
+      break;
+    }
+    return dyn_cast<Instruction>(IncV->getOperand(0));
+  }
+}
+
+/// If the insert point of the current builder or any of the builders on the
+/// stack of saved builders has 'I' as its insert point, update it to point to
+/// the instruction after 'I'.  This is intended to be used when the instruction
+/// 'I' is being moved.  If this fixup is not done and 'I' is moved to a
+/// different block, the inconsistent insert point (with a mismatched
+/// Instruction and Block) can lead to an instruction being inserted in a block
+/// other than its parent.
+void SCEVExpander::fixupInsertPoints(Instruction *I) {
+  BasicBlock::iterator It(*I);
+  BasicBlock::iterator NewInsertPt = std::next(It);
+  if (Builder.GetInsertPoint() == It)
+    Builder.SetInsertPoint(&*NewInsertPt);
+  for (auto *InsertPtGuard : InsertPointGuards)
+    if (InsertPtGuard->GetInsertPoint() == It)
+      InsertPtGuard->SetInsertPoint(NewInsertPt);
+}
+
+/// hoistStep - Attempt to hoist a simple IV increment above InsertPos to make
+/// it available to other uses in this loop. Recursively hoist any operands,
+/// until we reach a value that dominates InsertPos.
+bool SCEVExpander::hoistIVInc(Instruction *IncV, Instruction *InsertPos) {
+  if (SE.DT.dominates(IncV, InsertPos))
+      return true;
+
+  // InsertPos must itself dominate IncV so that IncV's new position satisfies
+  // its existing users.
+  if (isa<PHINode>(InsertPos) ||
+      !SE.DT.dominates(InsertPos->getParent(), IncV->getParent()))
+    return false;
+
+  if (!SE.LI.movementPreservesLCSSAForm(IncV, InsertPos))
+    return false;
+
+  // Check that the chain of IV operands leading back to Phi can be hoisted.
+  SmallVector<Instruction*, 4> IVIncs;
+  for(;;) {
+    Instruction *Oper = getIVIncOperand(IncV, InsertPos, /*allowScale*/true);
+    if (!Oper)
+      return false;
+    // IncV is safe to hoist.
+    IVIncs.push_back(IncV);
+    IncV = Oper;
+    if (SE.DT.dominates(IncV, InsertPos))
+      break;
+  }
+  for (auto I = IVIncs.rbegin(), E = IVIncs.rend(); I != E; ++I) {
+    fixupInsertPoints(*I);
+    (*I)->moveBefore(InsertPos);
+  }
+  return true;
+}
+
+/// Determine if this cyclic phi is in a form that would have been generated by
+/// LSR. We don't care if the phi was actually expanded in this pass, as long
+/// as it is in a low-cost form, for example, no implied multiplication. This
+/// should match any patterns generated by getAddRecExprPHILiterally and
+/// expandAddtoGEP.
+bool SCEVExpander::isExpandedAddRecExprPHI(PHINode *PN, Instruction *IncV,
+                                           const Loop *L) {
+  for(Instruction *IVOper = IncV;
+      (IVOper = getIVIncOperand(IVOper, L->getLoopPreheader()->getTerminator(),
+                                /*allowScale=*/false));) {
+    if (IVOper == PN)
+      return true;
+  }
+  return false;
+}
+
+/// expandIVInc - Expand an IV increment at Builder's current InsertPos.
+/// Typically this is the LatchBlock terminator or IVIncInsertPos, but we may
+/// need to materialize IV increments elsewhere to handle difficult situations.
+Value *SCEVExpander::expandIVInc(PHINode *PN, Value *StepV, const Loop *L,
+                                 Type *ExpandTy, Type *IntTy,
+                                 bool useSubtract) {
+  Value *IncV;
+  // If the PHI is a pointer, use a GEP, otherwise use an add or sub.
+  if (ExpandTy->isPointerTy()) {
+    PointerType *GEPPtrTy = cast<PointerType>(ExpandTy);
+    // If the step isn't constant, don't use an implicitly scaled GEP, because
+    // that would require a multiply inside the loop.
+    if (!isa<ConstantInt>(StepV))
+      GEPPtrTy = PointerType::get(Type::getInt1Ty(SE.getContext()),
+                                  GEPPtrTy->getAddressSpace());
+    IncV = expandAddToGEP(SE.getSCEV(StepV), GEPPtrTy, IntTy, PN);
+    if (IncV->getType() != PN->getType()) {
+      IncV = Builder.CreateBitCast(IncV, PN->getType());
+      rememberInstruction(IncV);
+    }
+  } else {
+    IncV = useSubtract ?
+      Builder.CreateSub(PN, StepV, Twine(IVName) + ".iv.next") :
+      Builder.CreateAdd(PN, StepV, Twine(IVName) + ".iv.next");
+    rememberInstruction(IncV);
+  }
+  return IncV;
+}
+
+/// Hoist the addrec instruction chain rooted in the loop phi above the
+/// position. This routine assumes that this is possible (has been checked).
+void SCEVExpander::hoistBeforePos(DominatorTree *DT, Instruction *InstToHoist,
+                                  Instruction *Pos, PHINode *LoopPhi) {
+  do {
+    if (DT->dominates(InstToHoist, Pos))
+      break;
+    // Make sure the increment is where we want it. But don't move it
+    // down past a potential existing post-inc user.
+    fixupInsertPoints(InstToHoist);
+    InstToHoist->moveBefore(Pos);
+    Pos = InstToHoist;
+    InstToHoist = cast<Instruction>(InstToHoist->getOperand(0));
+  } while (InstToHoist != LoopPhi);
+}
+
+/// Check whether we can cheaply express the requested SCEV in terms of
+/// the available PHI SCEV by truncation and/or inversion of the step.
+static bool canBeCheaplyTransformed(ScalarEvolution &SE,
+                                    const SCEVAddRecExpr *Phi,
+                                    const SCEVAddRecExpr *Requested,
+                                    bool &InvertStep) {
+  Type *PhiTy = SE.getEffectiveSCEVType(Phi->getType());
+  Type *RequestedTy = SE.getEffectiveSCEVType(Requested->getType());
+
+  if (RequestedTy->getIntegerBitWidth() > PhiTy->getIntegerBitWidth())
+    return false;
+
+  // Try truncate it if necessary.
+  Phi = dyn_cast<SCEVAddRecExpr>(SE.getTruncateOrNoop(Phi, RequestedTy));
+  if (!Phi)
+    return false;
+
+  // Check whether truncation will help.
+  if (Phi == Requested) {
+    InvertStep = false;
+    return true;
+  }
+
+  // Check whether inverting will help: {R,+,-1} == R - {0,+,1}.
+  if (SE.getAddExpr(Requested->getStart(),
+                    SE.getNegativeSCEV(Requested)) == Phi) {
+    InvertStep = true;
+    return true;
+  }
+
+  return false;
+}
+
+static bool IsIncrementNSW(ScalarEvolution &SE, const SCEVAddRecExpr *AR) {
+  if (!isa<IntegerType>(AR->getType()))
+    return false;
+
+  unsigned BitWidth = cast<IntegerType>(AR->getType())->getBitWidth();
+  Type *WideTy = IntegerType::get(AR->getType()->getContext(), BitWidth * 2);
+  const SCEV *Step = AR->getStepRecurrence(SE);
+  const SCEV *OpAfterExtend = SE.getAddExpr(SE.getSignExtendExpr(Step, WideTy),
+                                            SE.getSignExtendExpr(AR, WideTy));
+  const SCEV *ExtendAfterOp =
+    SE.getSignExtendExpr(SE.getAddExpr(AR, Step), WideTy);
+  return ExtendAfterOp == OpAfterExtend;
+}
+
+static bool IsIncrementNUW(ScalarEvolution &SE, const SCEVAddRecExpr *AR) {
+  if (!isa<IntegerType>(AR->getType()))
+    return false;
+
+  unsigned BitWidth = cast<IntegerType>(AR->getType())->getBitWidth();
+  Type *WideTy = IntegerType::get(AR->getType()->getContext(), BitWidth * 2);
+  const SCEV *Step = AR->getStepRecurrence(SE);
+  const SCEV *OpAfterExtend = SE.getAddExpr(SE.getZeroExtendExpr(Step, WideTy),
+                                            SE.getZeroExtendExpr(AR, WideTy));
+  const SCEV *ExtendAfterOp =
+    SE.getZeroExtendExpr(SE.getAddExpr(AR, Step), WideTy);
+  return ExtendAfterOp == OpAfterExtend;
+}
+
+/// getAddRecExprPHILiterally - Helper for expandAddRecExprLiterally. Expand
+/// the base addrec, which is the addrec without any non-loop-dominating
+/// values, and return the PHI.
+PHINode *
+SCEVExpander::getAddRecExprPHILiterally(const SCEVAddRecExpr *Normalized,
+                                        const Loop *L,
+                                        Type *ExpandTy,
+                                        Type *IntTy,
+                                        Type *&TruncTy,
+                                        bool &InvertStep) {
+  assert((!IVIncInsertLoop||IVIncInsertPos) && "Uninitialized insert position");
+
+  // Reuse a previously-inserted PHI, if present.
+  BasicBlock *LatchBlock = L->getLoopLatch();
+  if (LatchBlock) {
+    PHINode *AddRecPhiMatch = nullptr;
+    Instruction *IncV = nullptr;
+    TruncTy = nullptr;
+    InvertStep = false;
+
+    // Only try partially matching scevs that need truncation and/or
+    // step-inversion if we know this loop is outside the current loop.
+    bool TryNonMatchingSCEV =
+        IVIncInsertLoop &&
+        SE.DT.properlyDominates(LatchBlock, IVIncInsertLoop->getHeader());
+
+    for (PHINode &PN : L->getHeader()->phis()) {
+      if (!SE.isSCEVable(PN.getType()))
+        continue;
+
+      const SCEVAddRecExpr *PhiSCEV = dyn_cast<SCEVAddRecExpr>(SE.getSCEV(&PN));
+      if (!PhiSCEV)
+        continue;
+
+      bool IsMatchingSCEV = PhiSCEV == Normalized;
+      // We only handle truncation and inversion of phi recurrences for the
+      // expanded expression if the expanded expression's loop dominates the
+      // loop we insert to. Check now, so we can bail out early.
+      if (!IsMatchingSCEV && !TryNonMatchingSCEV)
+          continue;
+
+      // TODO: this possibly can be reworked to avoid this cast at all.
+      Instruction *TempIncV =
+          dyn_cast<Instruction>(PN.getIncomingValueForBlock(LatchBlock));
+      if (!TempIncV)
+        continue;
+
+      // Check whether we can reuse this PHI node.
+      if (LSRMode) {
+        if (!isExpandedAddRecExprPHI(&PN, TempIncV, L))
+          continue;
+        if (L == IVIncInsertLoop && !hoistIVInc(TempIncV, IVIncInsertPos))
+          continue;
+      } else {
+        if (!isNormalAddRecExprPHI(&PN, TempIncV, L))
+          continue;
+      }
+
+      // Stop if we have found an exact match SCEV.
+      if (IsMatchingSCEV) {
+        IncV = TempIncV;
+        TruncTy = nullptr;
+        InvertStep = false;
+        AddRecPhiMatch = &PN;
+        break;
+      }
+
+      // Try whether the phi can be translated into the requested form
+      // (truncated and/or offset by a constant).
+      if ((!TruncTy || InvertStep) &&
+          canBeCheaplyTransformed(SE, PhiSCEV, Normalized, InvertStep)) {
+        // Record the phi node. But don't stop we might find an exact match
+        // later.
+        AddRecPhiMatch = &PN;
+        IncV = TempIncV;
+        TruncTy = SE.getEffectiveSCEVType(Normalized->getType());
+      }
+    }
+
+    if (AddRecPhiMatch) {
+      // Potentially, move the increment. We have made sure in
+      // isExpandedAddRecExprPHI or hoistIVInc that this is possible.
+      if (L == IVIncInsertLoop)
+        hoistBeforePos(&SE.DT, IncV, IVIncInsertPos, AddRecPhiMatch);
+
+      // Ok, the add recurrence looks usable.
+      // Remember this PHI, even in post-inc mode.
+      InsertedValues.insert(AddRecPhiMatch);
+      // Remember the increment.
+      rememberInstruction(IncV);
+      return AddRecPhiMatch;
+    }
+  }
+
+  // Save the original insertion point so we can restore it when we're done.
+  SCEVInsertPointGuard Guard(Builder, this);
+
+  // Another AddRec may need to be recursively expanded below. For example, if
+  // this AddRec is quadratic, the StepV may itself be an AddRec in this
+  // loop. Remove this loop from the PostIncLoops set before expanding such
+  // AddRecs. Otherwise, we cannot find a valid position for the step
+  // (i.e. StepV can never dominate its loop header).  Ideally, we could do
+  // SavedIncLoops.swap(PostIncLoops), but we generally have a single element,
+  // so it's not worth implementing SmallPtrSet::swap.
+  PostIncLoopSet SavedPostIncLoops = PostIncLoops;
+  PostIncLoops.clear();
+
+  // Expand code for the start value into the loop preheader.
+  assert(L->getLoopPreheader() &&
+         "Can't expand add recurrences without a loop preheader!");
+  Value *StartV = expandCodeFor(Normalized->getStart(), ExpandTy,
+                                L->getLoopPreheader()->getTerminator());
+
+  // StartV must have been be inserted into L's preheader to dominate the new
+  // phi.
+  assert(!isa<Instruction>(StartV) ||
+         SE.DT.properlyDominates(cast<Instruction>(StartV)->getParent(),
+                                 L->getHeader()));
+
+  // Expand code for the step value. Do this before creating the PHI so that PHI
+  // reuse code doesn't see an incomplete PHI.
+  const SCEV *Step = Normalized->getStepRecurrence(SE);
+  // If the stride is negative, insert a sub instead of an add for the increment
+  // (unless it's a constant, because subtracts of constants are canonicalized
+  // to adds).
+  bool useSubtract = !ExpandTy->isPointerTy() && Step->isNonConstantNegative();
+  if (useSubtract)
+    Step = SE.getNegativeSCEV(Step);
+  // Expand the step somewhere that dominates the loop header.
+  Value *StepV = expandCodeFor(Step, IntTy, &L->getHeader()->front());
+
+  // The no-wrap behavior proved by IsIncrement(NUW|NSW) is only applicable if
+  // we actually do emit an addition.  It does not apply if we emit a
+  // subtraction.
+  bool IncrementIsNUW = !useSubtract && IsIncrementNUW(SE, Normalized);
+  bool IncrementIsNSW = !useSubtract && IsIncrementNSW(SE, Normalized);
+
+  // Create the PHI.
+  BasicBlock *Header = L->getHeader();
+  Builder.SetInsertPoint(Header, Header->begin());
+  pred_iterator HPB = pred_begin(Header), HPE = pred_end(Header);
+  PHINode *PN = Builder.CreatePHI(ExpandTy, std::distance(HPB, HPE),
+                                  Twine(IVName) + ".iv");
+  rememberInstruction(PN);
+
+  // Create the step instructions and populate the PHI.
+  for (pred_iterator HPI = HPB; HPI != HPE; ++HPI) {
+    BasicBlock *Pred = *HPI;
+
+    // Add a start value.
+    if (!L->contains(Pred)) {
+      PN->addIncoming(StartV, Pred);
+      continue;
+    }
+
+    // Create a step value and add it to the PHI.
+    // If IVIncInsertLoop is non-null and equal to the addrec's loop, insert the
+    // instructions at IVIncInsertPos.
+    Instruction *InsertPos = L == IVIncInsertLoop ?
+      IVIncInsertPos : Pred->getTerminator();
+    Builder.SetInsertPoint(InsertPos);
+    Value *IncV = expandIVInc(PN, StepV, L, ExpandTy, IntTy, useSubtract);
+
+    if (isa<OverflowingBinaryOperator>(IncV)) {
+      if (IncrementIsNUW)
+        cast<BinaryOperator>(IncV)->setHasNoUnsignedWrap();
+      if (IncrementIsNSW)
+        cast<BinaryOperator>(IncV)->setHasNoSignedWrap();
+    }
+    PN->addIncoming(IncV, Pred);
+  }
+
+  // After expanding subexpressions, restore the PostIncLoops set so the caller
+  // can ensure that IVIncrement dominates the current uses.
+  PostIncLoops = SavedPostIncLoops;
+
+  // Remember this PHI, even in post-inc mode.
+  InsertedValues.insert(PN);
+
+  return PN;
+}
+
+Value *SCEVExpander::expandAddRecExprLiterally(const SCEVAddRecExpr *S) {
+  Type *STy = S->getType();
+  Type *IntTy = SE.getEffectiveSCEVType(STy);
+  const Loop *L = S->getLoop();
+
+  // Determine a normalized form of this expression, which is the expression
+  // before any post-inc adjustment is made.
+  const SCEVAddRecExpr *Normalized = S;
+  if (PostIncLoops.count(L)) {
+    PostIncLoopSet Loops;
+    Loops.insert(L);
+    Normalized = cast<SCEVAddRecExpr>(normalizeForPostIncUse(S, Loops, SE));
+  }
+
+  // Strip off any non-loop-dominating component from the addrec start.
+  const SCEV *Start = Normalized->getStart();
+  const SCEV *PostLoopOffset = nullptr;
+  if (!SE.properlyDominates(Start, L->getHeader())) {
+    PostLoopOffset = Start;
+    Start = SE.getConstant(Normalized->getType(), 0);
+    Normalized = cast<SCEVAddRecExpr>(
+      SE.getAddRecExpr(Start, Normalized->getStepRecurrence(SE),
+                       Normalized->getLoop(),
+                       Normalized->getNoWrapFlags(SCEV::FlagNW)));
+  }
+
+  // Strip off any non-loop-dominating component from the addrec step.
+  const SCEV *Step = Normalized->getStepRecurrence(SE);
+  const SCEV *PostLoopScale = nullptr;
+  if (!SE.dominates(Step, L->getHeader())) {
+    PostLoopScale = Step;
+    Step = SE.getConstant(Normalized->getType(), 1);
+    if (!Start->isZero()) {
+        // The normalization below assumes that Start is constant zero, so if
+        // it isn't re-associate Start to PostLoopOffset.
+        assert(!PostLoopOffset && "Start not-null but PostLoopOffset set?");
+        PostLoopOffset = Start;
+        Start = SE.getConstant(Normalized->getType(), 0);
+    }
+    Normalized =
+      cast<SCEVAddRecExpr>(SE.getAddRecExpr(
+                             Start, Step, Normalized->getLoop(),
+                             Normalized->getNoWrapFlags(SCEV::FlagNW)));
+  }
+
+  // Expand the core addrec. If we need post-loop scaling, force it to
+  // expand to an integer type to avoid the need for additional casting.
+  Type *ExpandTy = PostLoopScale ? IntTy : STy;
+  // We can't use a pointer type for the addrec if the pointer type is
+  // non-integral.
+  Type *AddRecPHIExpandTy =
+      DL.isNonIntegralPointerType(STy) ? Normalized->getType() : ExpandTy;
+
+  // In some cases, we decide to reuse an existing phi node but need to truncate
+  // it and/or invert the step.
+  Type *TruncTy = nullptr;
+  bool InvertStep = false;
+  PHINode *PN = getAddRecExprPHILiterally(Normalized, L, AddRecPHIExpandTy,
+                                          IntTy, TruncTy, InvertStep);
+
+  // Accommodate post-inc mode, if necessary.
+  Value *Result;
+  if (!PostIncLoops.count(L))
+    Result = PN;
+  else {
+    // In PostInc mode, use the post-incremented value.
+    BasicBlock *LatchBlock = L->getLoopLatch();
+    assert(LatchBlock && "PostInc mode requires a unique loop latch!");
+    Result = PN->getIncomingValueForBlock(LatchBlock);
+
+    // For an expansion to use the postinc form, the client must call
+    // expandCodeFor with an InsertPoint that is either outside the PostIncLoop
+    // or dominated by IVIncInsertPos.
+    if (isa<Instruction>(Result) &&
+        !SE.DT.dominates(cast<Instruction>(Result),
+                         &*Builder.GetInsertPoint())) {
+      // The induction variable's postinc expansion does not dominate this use.
+      // IVUsers tries to prevent this case, so it is rare. However, it can
+      // happen when an IVUser outside the loop is not dominated by the latch
+      // block. Adjusting IVIncInsertPos before expansion begins cannot handle
+      // all cases. Consider a phi outside whose operand is replaced during
+      // expansion with the value of the postinc user. Without fundamentally
+      // changing the way postinc users are tracked, the only remedy is
+      // inserting an extra IV increment. StepV might fold into PostLoopOffset,
+      // but hopefully expandCodeFor handles that.
+      bool useSubtract =
+        !ExpandTy->isPointerTy() && Step->isNonConstantNegative();
+      if (useSubtract)
+        Step = SE.getNegativeSCEV(Step);
+      Value *StepV;
+      {
+        // Expand the step somewhere that dominates the loop header.
+        SCEVInsertPointGuard Guard(Builder, this);
+        StepV = expandCodeFor(Step, IntTy, &L->getHeader()->front());
+      }
+      Result = expandIVInc(PN, StepV, L, ExpandTy, IntTy, useSubtract);
+    }
+  }
+
+  // We have decided to reuse an induction variable of a dominating loop. Apply
+  // truncation and/or inversion of the step.
+  if (TruncTy) {
+    Type *ResTy = Result->getType();
+    // Normalize the result type.
+    if (ResTy != SE.getEffectiveSCEVType(ResTy))
+      Result = InsertNoopCastOfTo(Result, SE.getEffectiveSCEVType(ResTy));
+    // Truncate the result.
+    if (TruncTy != Result->getType()) {
+      Result = Builder.CreateTrunc(Result, TruncTy);
+      rememberInstruction(Result);
+    }
+    // Invert the result.
+    if (InvertStep) {
+      Result = Builder.CreateSub(expandCodeFor(Normalized->getStart(), TruncTy),
+                                 Result);
+      rememberInstruction(Result);
+    }
+  }
+
+  // Re-apply any non-loop-dominating scale.
+  if (PostLoopScale) {
+    assert(S->isAffine() && "Can't linearly scale non-affine recurrences.");
+    Result = InsertNoopCastOfTo(Result, IntTy);
+    Result = Builder.CreateMul(Result,
+                               expandCodeFor(PostLoopScale, IntTy));
+    rememberInstruction(Result);
+  }
+
+  // Re-apply any non-loop-dominating offset.
+  if (PostLoopOffset) {
+    if (PointerType *PTy = dyn_cast<PointerType>(ExpandTy)) {
+      if (Result->getType()->isIntegerTy()) {
+        Value *Base = expandCodeFor(PostLoopOffset, ExpandTy);
+        Result = expandAddToGEP(SE.getUnknown(Result), PTy, IntTy, Base);
+      } else {
+        Result = expandAddToGEP(PostLoopOffset, PTy, IntTy, Result);
+      }
+    } else {
+      Result = InsertNoopCastOfTo(Result, IntTy);
+      Result = Builder.CreateAdd(Result,
+                                 expandCodeFor(PostLoopOffset, IntTy));
+      rememberInstruction(Result);
+    }
+  }
+
+  return Result;
+}
+
+Value *SCEVExpander::visitAddRecExpr(const SCEVAddRecExpr *S) {
+  // In canonical mode we compute the addrec as an expression of a canonical IV
+  // using evaluateAtIteration and expand the resulting SCEV expression. This
+  // way we avoid introducing new IVs to carry on the comutation of the addrec
+  // throughout the loop.
+  //
+  // For nested addrecs evaluateAtIteration might need a canonical IV of a
+  // type wider than the addrec itself. Emitting a canonical IV of the
+  // proper type might produce non-legal types, for example expanding an i64
+  // {0,+,2,+,1} addrec would need an i65 canonical IV. To avoid this just fall
+  // back to non-canonical mode for nested addrecs.
+  if (!CanonicalMode || (S->getNumOperands() > 2))
+    return expandAddRecExprLiterally(S);
+
+  Type *Ty = SE.getEffectiveSCEVType(S->getType());
+  const Loop *L = S->getLoop();
+
+  // First check for an existing canonical IV in a suitable type.
+  PHINode *CanonicalIV = nullptr;
+  if (PHINode *PN = L->getCanonicalInductionVariable())
+    if (SE.getTypeSizeInBits(PN->getType()) >= SE.getTypeSizeInBits(Ty))
+      CanonicalIV = PN;
+
+  // Rewrite an AddRec in terms of the canonical induction variable, if
+  // its type is more narrow.
+  if (CanonicalIV &&
+      SE.getTypeSizeInBits(CanonicalIV->getType()) >
+      SE.getTypeSizeInBits(Ty)) {
+    SmallVector<const SCEV *, 4> NewOps(S->getNumOperands());
+    for (unsigned i = 0, e = S->getNumOperands(); i != e; ++i)
+      NewOps[i] = SE.getAnyExtendExpr(S->op_begin()[i], CanonicalIV->getType());
+    Value *V = expand(SE.getAddRecExpr(NewOps, S->getLoop(),
+                                       S->getNoWrapFlags(SCEV::FlagNW)));
+    BasicBlock::iterator NewInsertPt =
+        findInsertPointAfter(cast<Instruction>(V), Builder.GetInsertBlock());
+    V = expandCodeFor(SE.getTruncateExpr(SE.getUnknown(V), Ty), nullptr,
+                      &*NewInsertPt);
+    return V;
+  }
+
+  // {X,+,F} --> X + {0,+,F}
+  if (!S->getStart()->isZero()) {
+    SmallVector<const SCEV *, 4> NewOps(S->op_begin(), S->op_end());
+    NewOps[0] = SE.getConstant(Ty, 0);
+    const SCEV *Rest = SE.getAddRecExpr(NewOps, L,
+                                        S->getNoWrapFlags(SCEV::FlagNW));
+
+    // Turn things like ptrtoint+arithmetic+inttoptr into GEP. See the
+    // comments on expandAddToGEP for details.
+    const SCEV *Base = S->getStart();
+    // Dig into the expression to find the pointer base for a GEP.
+    const SCEV *ExposedRest = Rest;
+    ExposePointerBase(Base, ExposedRest, SE);
+    // If we found a pointer, expand the AddRec with a GEP.
+    if (PointerType *PTy = dyn_cast<PointerType>(Base->getType())) {
+      // Make sure the Base isn't something exotic, such as a multiplied
+      // or divided pointer value. In those cases, the result type isn't
+      // actually a pointer type.
+      if (!isa<SCEVMulExpr>(Base) && !isa<SCEVUDivExpr>(Base)) {
+        Value *StartV = expand(Base);
+        assert(StartV->getType() == PTy && "Pointer type mismatch for GEP!");
+        return expandAddToGEP(ExposedRest, PTy, Ty, StartV);
+      }
+    }
+
+    // Just do a normal add. Pre-expand the operands to suppress folding.
+    //
+    // The LHS and RHS values are factored out of the expand call to make the
+    // output independent of the argument evaluation order.
+    const SCEV *AddExprLHS = SE.getUnknown(expand(S->getStart()));
+    const SCEV *AddExprRHS = SE.getUnknown(expand(Rest));
+    return expand(SE.getAddExpr(AddExprLHS, AddExprRHS));
+  }
+
+  // If we don't yet have a canonical IV, create one.
+  if (!CanonicalIV) {
+    // Create and insert the PHI node for the induction variable in the
+    // specified loop.
+    BasicBlock *Header = L->getHeader();
+    pred_iterator HPB = pred_begin(Header), HPE = pred_end(Header);
+    CanonicalIV = PHINode::Create(Ty, std::distance(HPB, HPE), "indvar",
+                                  &Header->front());
+    rememberInstruction(CanonicalIV);
+
+    SmallSet<BasicBlock *, 4> PredSeen;
+    Constant *One = ConstantInt::get(Ty, 1);
+    for (pred_iterator HPI = HPB; HPI != HPE; ++HPI) {
+      BasicBlock *HP = *HPI;
+      if (!PredSeen.insert(HP).second) {
+        // There must be an incoming value for each predecessor, even the
+        // duplicates!
+        CanonicalIV->addIncoming(CanonicalIV->getIncomingValueForBlock(HP), HP);
+        continue;
+      }
+
+      if (L->contains(HP)) {
+        // Insert a unit add instruction right before the terminator
+        // corresponding to the back-edge.
+        Instruction *Add = BinaryOperator::CreateAdd(CanonicalIV, One,
+                                                     "indvar.next",
+                                                     HP->getTerminator());
+        Add->setDebugLoc(HP->getTerminator()->getDebugLoc());
+        rememberInstruction(Add);
+        CanonicalIV->addIncoming(Add, HP);
+      } else {
+        CanonicalIV->addIncoming(Constant::getNullValue(Ty), HP);
+      }
+    }
+  }
+
+  // {0,+,1} --> Insert a canonical induction variable into the loop!
+  if (S->isAffine() && S->getOperand(1)->isOne()) {
+    assert(Ty == SE.getEffectiveSCEVType(CanonicalIV->getType()) &&
+           "IVs with types different from the canonical IV should "
+           "already have been handled!");
+    return CanonicalIV;
+  }
+
+  // {0,+,F} --> {0,+,1} * F
+
+  // If this is a simple linear addrec, emit it now as a special case.
+  if (S->isAffine())    // {0,+,F} --> i*F
+    return
+      expand(SE.getTruncateOrNoop(
+        SE.getMulExpr(SE.getUnknown(CanonicalIV),
+                      SE.getNoopOrAnyExtend(S->getOperand(1),
+                                            CanonicalIV->getType())),
+        Ty));
+
+  // If this is a chain of recurrences, turn it into a closed form, using the
+  // folders, then expandCodeFor the closed form.  This allows the folders to
+  // simplify the expression without having to build a bunch of special code
+  // into this folder.
+  const SCEV *IH = SE.getUnknown(CanonicalIV);   // Get I as a "symbolic" SCEV.
+
+  // Promote S up to the canonical IV type, if the cast is foldable.
+  const SCEV *NewS = S;
+  const SCEV *Ext = SE.getNoopOrAnyExtend(S, CanonicalIV->getType());
+  if (isa<SCEVAddRecExpr>(Ext))
+    NewS = Ext;
+
+  const SCEV *V = cast<SCEVAddRecExpr>(NewS)->evaluateAtIteration(IH, SE);
+  //cerr << "Evaluated: " << *this << "\n     to: " << *V << "\n";
+
+  // Truncate the result down to the original type, if needed.
+  const SCEV *T = SE.getTruncateOrNoop(V, Ty);
+  return expand(T);
+}
+
+Value *SCEVExpander::visitTruncateExpr(const SCEVTruncateExpr *S) {
+  Type *Ty = SE.getEffectiveSCEVType(S->getType());
+  Value *V = expandCodeFor(S->getOperand(),
+                           SE.getEffectiveSCEVType(S->getOperand()->getType()));
+  Value *I = Builder.CreateTrunc(V, Ty);
+  rememberInstruction(I);
+  return I;
+}
+
+Value *SCEVExpander::visitZeroExtendExpr(const SCEVZeroExtendExpr *S) {
+  Type *Ty = SE.getEffectiveSCEVType(S->getType());
+  Value *V = expandCodeFor(S->getOperand(),
+                           SE.getEffectiveSCEVType(S->getOperand()->getType()));
+  Value *I = Builder.CreateZExt(V, Ty);
+  rememberInstruction(I);
+  return I;
+}
+
+Value *SCEVExpander::visitSignExtendExpr(const SCEVSignExtendExpr *S) {
+  Type *Ty = SE.getEffectiveSCEVType(S->getType());
+  Value *V = expandCodeFor(S->getOperand(),
+                           SE.getEffectiveSCEVType(S->getOperand()->getType()));
+  Value *I = Builder.CreateSExt(V, Ty);
+  rememberInstruction(I);
+  return I;
+}
+
+Value *SCEVExpander::visitSMaxExpr(const SCEVSMaxExpr *S) {
+  Value *LHS = expand(S->getOperand(S->getNumOperands()-1));
+  Type *Ty = LHS->getType();
+  for (int i = S->getNumOperands()-2; i >= 0; --i) {
+    // In the case of mixed integer and pointer types, do the
+    // rest of the comparisons as integer.
+    Type *OpTy = S->getOperand(i)->getType();
+    if (OpTy->isIntegerTy() != Ty->isIntegerTy()) {
+      Ty = SE.getEffectiveSCEVType(Ty);
+      LHS = InsertNoopCastOfTo(LHS, Ty);
+    }
+    Value *RHS = expandCodeFor(S->getOperand(i), Ty);
+    Value *ICmp = Builder.CreateICmpSGT(LHS, RHS);
+    rememberInstruction(ICmp);
+    Value *Sel = Builder.CreateSelect(ICmp, LHS, RHS, "smax");
+    rememberInstruction(Sel);
+    LHS = Sel;
+  }
+  // In the case of mixed integer and pointer types, cast the
+  // final result back to the pointer type.
+  if (LHS->getType() != S->getType())
+    LHS = InsertNoopCastOfTo(LHS, S->getType());
+  return LHS;
+}
+
+Value *SCEVExpander::visitUMaxExpr(const SCEVUMaxExpr *S) {
+  Value *LHS = expand(S->getOperand(S->getNumOperands()-1));
+  Type *Ty = LHS->getType();
+  for (int i = S->getNumOperands()-2; i >= 0; --i) {
+    // In the case of mixed integer and pointer types, do the
+    // rest of the comparisons as integer.
+    Type *OpTy = S->getOperand(i)->getType();
+    if (OpTy->isIntegerTy() != Ty->isIntegerTy()) {
+      Ty = SE.getEffectiveSCEVType(Ty);
+      LHS = InsertNoopCastOfTo(LHS, Ty);
+    }
+    Value *RHS = expandCodeFor(S->getOperand(i), Ty);
+    Value *ICmp = Builder.CreateICmpUGT(LHS, RHS);
+    rememberInstruction(ICmp);
+    Value *Sel = Builder.CreateSelect(ICmp, LHS, RHS, "umax");
+    rememberInstruction(Sel);
+    LHS = Sel;
+  }
+  // In the case of mixed integer and pointer types, cast the
+  // final result back to the pointer type.
+  if (LHS->getType() != S->getType())
+    LHS = InsertNoopCastOfTo(LHS, S->getType());
+  return LHS;
+}
+
+Value *SCEVExpander::visitSMinExpr(const SCEVSMinExpr *S) {
+  Value *LHS = expand(S->getOperand(S->getNumOperands() - 1));
+  Type *Ty = LHS->getType();
+  for (int i = S->getNumOperands() - 2; i >= 0; --i) {
+    // In the case of mixed integer and pointer types, do the
+    // rest of the comparisons as integer.
+    Type *OpTy = S->getOperand(i)->getType();
+    if (OpTy->isIntegerTy() != Ty->isIntegerTy()) {
+      Ty = SE.getEffectiveSCEVType(Ty);
+      LHS = InsertNoopCastOfTo(LHS, Ty);
+    }
+    Value *RHS = expandCodeFor(S->getOperand(i), Ty);
+    Value *ICmp = Builder.CreateICmpSLT(LHS, RHS);
+    rememberInstruction(ICmp);
+    Value *Sel = Builder.CreateSelect(ICmp, LHS, RHS, "smin");
+    rememberInstruction(Sel);
+    LHS = Sel;
+  }
+  // In the case of mixed integer and pointer types, cast the
+  // final result back to the pointer type.
+  if (LHS->getType() != S->getType())
+    LHS = InsertNoopCastOfTo(LHS, S->getType());
+  return LHS;
+}
+
+Value *SCEVExpander::visitUMinExpr(const SCEVUMinExpr *S) {
+  Value *LHS = expand(S->getOperand(S->getNumOperands() - 1));
+  Type *Ty = LHS->getType();
+  for (int i = S->getNumOperands() - 2; i >= 0; --i) {
+    // In the case of mixed integer and pointer types, do the
+    // rest of the comparisons as integer.
+    Type *OpTy = S->getOperand(i)->getType();
+    if (OpTy->isIntegerTy() != Ty->isIntegerTy()) {
+      Ty = SE.getEffectiveSCEVType(Ty);
+      LHS = InsertNoopCastOfTo(LHS, Ty);
+    }
+    Value *RHS = expandCodeFor(S->getOperand(i), Ty);
+    Value *ICmp = Builder.CreateICmpULT(LHS, RHS);
+    rememberInstruction(ICmp);
+    Value *Sel = Builder.CreateSelect(ICmp, LHS, RHS, "umin");
+    rememberInstruction(Sel);
+    LHS = Sel;
+  }
+  // In the case of mixed integer and pointer types, cast the
+  // final result back to the pointer type.
+  if (LHS->getType() != S->getType())
+    LHS = InsertNoopCastOfTo(LHS, S->getType());
+  return LHS;
+}
+
+Value *SCEVExpander::expandCodeFor(const SCEV *SH, Type *Ty,
+                                   Instruction *IP) {
+  setInsertPoint(IP);
+  return expandCodeFor(SH, Ty);
+}
+
+Value *SCEVExpander::expandCodeFor(const SCEV *SH, Type *Ty) {
+  // Expand the code for this SCEV.
+  Value *V = expand(SH);
+  if (Ty) {
+    assert(SE.getTypeSizeInBits(Ty) == SE.getTypeSizeInBits(SH->getType()) &&
+           "non-trivial casts should be done with the SCEVs directly!");
+    V = InsertNoopCastOfTo(V, Ty);
+  }
+  return V;
+}
+
+ScalarEvolution::ValueOffsetPair
+SCEVExpander::FindValueInExprValueMap(const SCEV *S,
+                                      const Instruction *InsertPt) {
+  SetVector<ScalarEvolution::ValueOffsetPair> *Set = SE.getSCEVValues(S);
+  // If the expansion is not in CanonicalMode, and the SCEV contains any
+  // sub scAddRecExpr type SCEV, it is required to expand the SCEV literally.
+  if (CanonicalMode || !SE.containsAddRecurrence(S)) {
+    // If S is scConstant, it may be worse to reuse an existing Value.
+    if (S->getSCEVType() != scConstant && Set) {
+      // Choose a Value from the set which dominates the insertPt.
+      // insertPt should be inside the Value's parent loop so as not to break
+      // the LCSSA form.
+      for (auto const &VOPair : *Set) {
+        Value *V = VOPair.first;
+        ConstantInt *Offset = VOPair.second;
+        Instruction *EntInst = nullptr;
+        if (V && isa<Instruction>(V) && (EntInst = cast<Instruction>(V)) &&
+            S->getType() == V->getType() &&
+            EntInst->getFunction() == InsertPt->getFunction() &&
+            SE.DT.dominates(EntInst, InsertPt) &&
+            (SE.LI.getLoopFor(EntInst->getParent()) == nullptr ||
+             SE.LI.getLoopFor(EntInst->getParent())->contains(InsertPt)))
+          return {V, Offset};
+      }
+    }
+  }
+  return {nullptr, nullptr};
+}
+
+// The expansion of SCEV will either reuse a previous Value in ExprValueMap,
+// or expand the SCEV literally. Specifically, if the expansion is in LSRMode,
+// and the SCEV contains any sub scAddRecExpr type SCEV, it will be expanded
+// literally, to prevent LSR's transformed SCEV from being reverted. Otherwise,
+// the expansion will try to reuse Value from ExprValueMap, and only when it
+// fails, expand the SCEV literally.
+Value *SCEVExpander::expand(const SCEV *S) {
+  // Compute an insertion point for this SCEV object. Hoist the instructions
+  // as far out in the loop nest as possible.
+  Instruction *InsertPt = &*Builder.GetInsertPoint();
+
+  // We can move insertion point only if there is no div or rem operations
+  // otherwise we are risky to move it over the check for zero denominator.
+  auto SafeToHoist = [](const SCEV *S) {
+    return !SCEVExprContains(S, [](const SCEV *S) {
+              if (const auto *D = dyn_cast<SCEVUDivExpr>(S)) {
+                if (const auto *SC = dyn_cast<SCEVConstant>(D->getRHS()))
+                  // Division by non-zero constants can be hoisted.
+                  return SC->getValue()->isZero();
+                // All other divisions should not be moved as they may be
+                // divisions by zero and should be kept within the
+                // conditions of the surrounding loops that guard their
+                // execution (see PR35406).
+                return true;
+              }
+              return false;
+            });
+  };
+  if (SafeToHoist(S)) {
+    for (Loop *L = SE.LI.getLoopFor(Builder.GetInsertBlock());;
+         L = L->getParentLoop()) {
+      if (SE.isLoopInvariant(S, L)) {
+        if (!L) break;
+        if (BasicBlock *Preheader = L->getLoopPreheader())
+          InsertPt = Preheader->getTerminator();
+        else
+          // LSR sets the insertion point for AddRec start/step values to the
+          // block start to simplify value reuse, even though it's an invalid
+          // position. SCEVExpander must correct for this in all cases.
+          InsertPt = &*L->getHeader()->getFirstInsertionPt();
+      } else {
+        // If the SCEV is computable at this level, insert it into the header
+        // after the PHIs (and after any other instructions that we've inserted
+        // there) so that it is guaranteed to dominate any user inside the loop.
+        if (L && SE.hasComputableLoopEvolution(S, L) && !PostIncLoops.count(L))
+          InsertPt = &*L->getHeader()->getFirstInsertionPt();
+        while (InsertPt->getIterator() != Builder.GetInsertPoint() &&
+               (isInsertedInstruction(InsertPt) ||
+                isa<DbgInfoIntrinsic>(InsertPt)))
+          InsertPt = &*std::next(InsertPt->getIterator());
+        break;
+      }
+    }
+  }
+
+  // IndVarSimplify sometimes sets the insertion point at the block start, even
+  // when there are PHIs at that point.  We must correct for this.
+  if (isa<PHINode>(*InsertPt))
+    InsertPt = &*InsertPt->getParent()->getFirstInsertionPt();
+
+  // Check to see if we already expanded this here.
+  auto I = InsertedExpressions.find(std::make_pair(S, InsertPt));
+  if (I != InsertedExpressions.end())
+    return I->second;
+
+  SCEVInsertPointGuard Guard(Builder, this);
+  Builder.SetInsertPoint(InsertPt);
+
+  // Expand the expression into instructions.
+  ScalarEvolution::ValueOffsetPair VO = FindValueInExprValueMap(S, InsertPt);
+  Value *V = VO.first;
+
+  if (!V)
+    V = visit(S);
+  else if (VO.second) {
+    if (PointerType *Vty = dyn_cast<PointerType>(V->getType())) {
+      Type *Ety = Vty->getPointerElementType();
+      int64_t Offset = VO.second->getSExtValue();
+      int64_t ESize = SE.getTypeSizeInBits(Ety);
+      if ((Offset * 8) % ESize == 0) {
+        ConstantInt *Idx =
+            ConstantInt::getSigned(VO.second->getType(), -(Offset * 8) / ESize);
+        V = Builder.CreateGEP(Ety, V, Idx, "scevgep");
+      } else {
+        ConstantInt *Idx =
+            ConstantInt::getSigned(VO.second->getType(), -Offset);
+        unsigned AS = Vty->getAddressSpace();
+        V = Builder.CreateBitCast(V, Type::getInt8PtrTy(SE.getContext(), AS));
+        V = Builder.CreateGEP(Type::getInt8Ty(SE.getContext()), V, Idx,
+                              "uglygep");
+        V = Builder.CreateBitCast(V, Vty);
+      }
+    } else {
+      V = Builder.CreateSub(V, VO.second);
+    }
+  }
+  // Remember the expanded value for this SCEV at this location.
+  //
+  // This is independent of PostIncLoops. The mapped value simply materializes
+  // the expression at this insertion point. If the mapped value happened to be
+  // a postinc expansion, it could be reused by a non-postinc user, but only if
+  // its insertion point was already at the head of the loop.
+  InsertedExpressions[std::make_pair(S, InsertPt)] = V;
+  return V;
+}
+
+void SCEVExpander::rememberInstruction(Value *I) {
+  if (!PostIncLoops.empty())
+    InsertedPostIncValues.insert(I);
+  else
+    InsertedValues.insert(I);
+}
+
+/// getOrInsertCanonicalInductionVariable - This method returns the
+/// canonical induction variable of the specified type for the specified
+/// loop (inserting one if there is none).  A canonical induction variable
+/// starts at zero and steps by one on each iteration.
+PHINode *
+SCEVExpander::getOrInsertCanonicalInductionVariable(const Loop *L,
+                                                    Type *Ty) {
+  assert(Ty->isIntegerTy() && "Can only insert integer induction variables!");
+
+  // Build a SCEV for {0,+,1}<L>.
+  // Conservatively use FlagAnyWrap for now.
+  const SCEV *H = SE.getAddRecExpr(SE.getConstant(Ty, 0),
+                                   SE.getConstant(Ty, 1), L, SCEV::FlagAnyWrap);
+
+  // Emit code for it.
+  SCEVInsertPointGuard Guard(Builder, this);
+  PHINode *V =
+      cast<PHINode>(expandCodeFor(H, nullptr, &L->getHeader()->front()));
+
+  return V;
+}
+
+/// replaceCongruentIVs - Check for congruent phis in this loop header and
+/// replace them with their most canonical representative. Return the number of
+/// phis eliminated.
+///
+/// This does not depend on any SCEVExpander state but should be used in
+/// the same context that SCEVExpander is used.
+unsigned
+SCEVExpander::replaceCongruentIVs(Loop *L, const DominatorTree *DT,
+                                  SmallVectorImpl<WeakTrackingVH> &DeadInsts,
+                                  const TargetTransformInfo *TTI) {
+  // Find integer phis in order of increasing width.
+  SmallVector<PHINode*, 8> Phis;
+  for (PHINode &PN : L->getHeader()->phis())
+    Phis.push_back(&PN);
+
+  if (TTI)
+    llvm::sort(Phis, [](Value *LHS, Value *RHS) {
+      // Put pointers at the back and make sure pointer < pointer = false.
+      if (!LHS->getType()->isIntegerTy() || !RHS->getType()->isIntegerTy())
+        return RHS->getType()->isIntegerTy() && !LHS->getType()->isIntegerTy();
+      return RHS->getType()->getPrimitiveSizeInBits() <
+             LHS->getType()->getPrimitiveSizeInBits();
+    });
+
+  unsigned NumElim = 0;
+  DenseMap<const SCEV *, PHINode *> ExprToIVMap;
+  // Process phis from wide to narrow. Map wide phis to their truncation
+  // so narrow phis can reuse them.
+  for (PHINode *Phi : Phis) {
+    auto SimplifyPHINode = [&](PHINode *PN) -> Value * {
+      if (Value *V = SimplifyInstruction(PN, {DL, &SE.TLI, &SE.DT, &SE.AC}))
+        return V;
+      if (!SE.isSCEVable(PN->getType()))
+        return nullptr;
+      auto *Const = dyn_cast<SCEVConstant>(SE.getSCEV(PN));
+      if (!Const)
+        return nullptr;
+      return Const->getValue();
+    };
+
+    // Fold constant phis. They may be congruent to other constant phis and
+    // would confuse the logic below that expects proper IVs.
+    if (Value *V = SimplifyPHINode(Phi)) {
+      if (V->getType() != Phi->getType())
+        continue;
+      Phi->replaceAllUsesWith(V);
+      DeadInsts.emplace_back(Phi);
+      ++NumElim;
+      DEBUG_WITH_TYPE(DebugType, dbgs()
+                      << "INDVARS: Eliminated constant iv: " << *Phi << '\n');
+      continue;
+    }
+
+    if (!SE.isSCEVable(Phi->getType()))
+      continue;
+
+    PHINode *&OrigPhiRef = ExprToIVMap[SE.getSCEV(Phi)];
+    if (!OrigPhiRef) {
+      OrigPhiRef = Phi;
+      if (Phi->getType()->isIntegerTy() && TTI &&
+          TTI->isTruncateFree(Phi->getType(), Phis.back()->getType())) {
+        // This phi can be freely truncated to the narrowest phi type. Map the
+        // truncated expression to it so it will be reused for narrow types.
+        const SCEV *TruncExpr =
+          SE.getTruncateExpr(SE.getSCEV(Phi), Phis.back()->getType());
+        ExprToIVMap[TruncExpr] = Phi;
+      }
+      continue;
+    }
+
+    // Replacing a pointer phi with an integer phi or vice-versa doesn't make
+    // sense.
+    if (OrigPhiRef->getType()->isPointerTy() != Phi->getType()->isPointerTy())
+      continue;
+
+    if (BasicBlock *LatchBlock = L->getLoopLatch()) {
+      Instruction *OrigInc = dyn_cast<Instruction>(
+          OrigPhiRef->getIncomingValueForBlock(LatchBlock));
+      Instruction *IsomorphicInc =
+          dyn_cast<Instruction>(Phi->getIncomingValueForBlock(LatchBlock));
+
+      if (OrigInc && IsomorphicInc) {
+        // If this phi has the same width but is more canonical, replace the
+        // original with it. As part of the "more canonical" determination,
+        // respect a prior decision to use an IV chain.
+        if (OrigPhiRef->getType() == Phi->getType() &&
+            !(ChainedPhis.count(Phi) ||
+              isExpandedAddRecExprPHI(OrigPhiRef, OrigInc, L)) &&
+            (ChainedPhis.count(Phi) ||
+             isExpandedAddRecExprPHI(Phi, IsomorphicInc, L))) {
+          std::swap(OrigPhiRef, Phi);
+          std::swap(OrigInc, IsomorphicInc);
+        }
+        // Replacing the congruent phi is sufficient because acyclic
+        // redundancy elimination, CSE/GVN, should handle the
+        // rest. However, once SCEV proves that a phi is congruent,
+        // it's often the head of an IV user cycle that is isomorphic
+        // with the original phi. It's worth eagerly cleaning up the
+        // common case of a single IV increment so that DeleteDeadPHIs
+        // can remove cycles that had postinc uses.
+        const SCEV *TruncExpr =
+            SE.getTruncateOrNoop(SE.getSCEV(OrigInc), IsomorphicInc->getType());
+        if (OrigInc != IsomorphicInc &&
+            TruncExpr == SE.getSCEV(IsomorphicInc) &&
+            SE.LI.replacementPreservesLCSSAForm(IsomorphicInc, OrigInc) &&
+            hoistIVInc(OrigInc, IsomorphicInc)) {
+          DEBUG_WITH_TYPE(DebugType,
+                          dbgs() << "INDVARS: Eliminated congruent iv.inc: "
+                                 << *IsomorphicInc << '\n');
+          Value *NewInc = OrigInc;
+          if (OrigInc->getType() != IsomorphicInc->getType()) {
+            Instruction *IP = nullptr;
+            if (PHINode *PN = dyn_cast<PHINode>(OrigInc))
+              IP = &*PN->getParent()->getFirstInsertionPt();
+            else
+              IP = OrigInc->getNextNode();
+
+            IRBuilder<> Builder(IP);
+            Builder.SetCurrentDebugLocation(IsomorphicInc->getDebugLoc());
+            NewInc = Builder.CreateTruncOrBitCast(
+                OrigInc, IsomorphicInc->getType(), IVName);
+          }
+          IsomorphicInc->replaceAllUsesWith(NewInc);
+          DeadInsts.emplace_back(IsomorphicInc);
+        }
+      }
+    }
+    DEBUG_WITH_TYPE(DebugType, dbgs() << "INDVARS: Eliminated congruent iv: "
+                                      << *Phi << '\n');
+    ++NumElim;
+    Value *NewIV = OrigPhiRef;
+    if (OrigPhiRef->getType() != Phi->getType()) {
+      IRBuilder<> Builder(&*L->getHeader()->getFirstInsertionPt());
+      Builder.SetCurrentDebugLocation(Phi->getDebugLoc());
+      NewIV = Builder.CreateTruncOrBitCast(OrigPhiRef, Phi->getType(), IVName);
+    }
+    Phi->replaceAllUsesWith(NewIV);
+    DeadInsts.emplace_back(Phi);
+  }
+  return NumElim;
+}
+
+Value *SCEVExpander::getExactExistingExpansion(const SCEV *S,
+                                               const Instruction *At, Loop *L) {
+  Optional<ScalarEvolution::ValueOffsetPair> VO =
+      getRelatedExistingExpansion(S, At, L);
+  if (VO && VO.getValue().second == nullptr)
+    return VO.getValue().first;
+  return nullptr;
+}
+
+Optional<ScalarEvolution::ValueOffsetPair>
+SCEVExpander::getRelatedExistingExpansion(const SCEV *S, const Instruction *At,
+                                          Loop *L) {
+  using namespace llvm::PatternMatch;
+
+  SmallVector<BasicBlock *, 4> ExitingBlocks;
+  L->getExitingBlocks(ExitingBlocks);
+
+  // Look for suitable value in simple conditions at the loop exits.
+  for (BasicBlock *BB : ExitingBlocks) {
+    ICmpInst::Predicate Pred;
+    Instruction *LHS, *RHS;
+
+    if (!match(BB->getTerminator(),
+               m_Br(m_ICmp(Pred, m_Instruction(LHS), m_Instruction(RHS)),
+                    m_BasicBlock(), m_BasicBlock())))
+      continue;
+
+    if (SE.getSCEV(LHS) == S && SE.DT.dominates(LHS, At))
+      return ScalarEvolution::ValueOffsetPair(LHS, nullptr);
+
+    if (SE.getSCEV(RHS) == S && SE.DT.dominates(RHS, At))
+      return ScalarEvolution::ValueOffsetPair(RHS, nullptr);
+  }
+
+  // Use expand's logic which is used for reusing a previous Value in
+  // ExprValueMap.
+  ScalarEvolution::ValueOffsetPair VO = FindValueInExprValueMap(S, At);
+  if (VO.first)
+    return VO;
+
+  // There is potential to make this significantly smarter, but this simple
+  // heuristic already gets some interesting cases.
+
+  // Can not find suitable value.
+  return None;
+}
+
+bool SCEVExpander::isHighCostExpansionHelper(
+    const SCEV *S, Loop *L, const Instruction *At,
+    SmallPtrSetImpl<const SCEV *> &Processed) {
+
+  // If we can find an existing value for this scev available at the point "At"
+  // then consider the expression cheap.
+  if (At && getRelatedExistingExpansion(S, At, L))
+    return false;
+
+  // Zero/One operand expressions
+  switch (S->getSCEVType()) {
+  case scUnknown:
+  case scConstant:
+    return false;
+  case scTruncate:
+    return isHighCostExpansionHelper(cast<SCEVTruncateExpr>(S)->getOperand(),
+                                     L, At, Processed);
+  case scZeroExtend:
+    return isHighCostExpansionHelper(cast<SCEVZeroExtendExpr>(S)->getOperand(),
+                                     L, At, Processed);
+  case scSignExtend:
+    return isHighCostExpansionHelper(cast<SCEVSignExtendExpr>(S)->getOperand(),
+                                     L, At, Processed);
+  }
+
+  if (!Processed.insert(S).second)
+    return false;
+
+  if (auto *UDivExpr = dyn_cast<SCEVUDivExpr>(S)) {
+    // If the divisor is a power of two and the SCEV type fits in a native
+    // integer (and the LHS not expensive), consider the division cheap
+    // irrespective of whether it occurs in the user code since it can be
+    // lowered into a right shift.
+    if (auto *SC = dyn_cast<SCEVConstant>(UDivExpr->getRHS()))
+      if (SC->getAPInt().isPowerOf2()) {
+        if (isHighCostExpansionHelper(UDivExpr->getLHS(), L, At, Processed))
+          return true;
+        const DataLayout &DL =
+            L->getHeader()->getParent()->getParent()->getDataLayout();
+        unsigned Width = cast<IntegerType>(UDivExpr->getType())->getBitWidth();
+        return DL.isIllegalInteger(Width);
+      }
+
+    // UDivExpr is very likely a UDiv that ScalarEvolution's HowFarToZero or
+    // HowManyLessThans produced to compute a precise expression, rather than a
+    // UDiv from the user's code. If we can't find a UDiv in the code with some
+    // simple searching, assume the former consider UDivExpr expensive to
+    // compute.
+    BasicBlock *ExitingBB = L->getExitingBlock();
+    if (!ExitingBB)
+      return true;
+
+    // At the beginning of this function we already tried to find existing value
+    // for plain 'S'. Now try to lookup 'S + 1' since it is common pattern
+    // involving division. This is just a simple search heuristic.
+    if (!At)
+      At = &ExitingBB->back();
+    if (!getRelatedExistingExpansion(
+            SE.getAddExpr(S, SE.getConstant(S->getType(), 1)), At, L))
+      return true;
+  }
+
+  // HowManyLessThans uses a Max expression whenever the loop is not guarded by
+  // the exit condition.
+  if (isa<SCEVMinMaxExpr>(S))
+    return true;
+
+  // Recurse past nary expressions, which commonly occur in the
+  // BackedgeTakenCount. They may already exist in program code, and if not,
+  // they are not too expensive rematerialize.
+  if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(S)) {
+    for (auto *Op : NAry->operands())
+      if (isHighCostExpansionHelper(Op, L, At, Processed))
+        return true;
+  }
+
+  // If we haven't recognized an expensive SCEV pattern, assume it's an
+  // expression produced by program code.
+  return false;
+}
+
+Value *SCEVExpander::expandCodeForPredicate(const SCEVPredicate *Pred,
+                                            Instruction *IP) {
+  assert(IP);
+  switch (Pred->getKind()) {
+  case SCEVPredicate::P_Union:
+    return expandUnionPredicate(cast<SCEVUnionPredicate>(Pred), IP);
+  case SCEVPredicate::P_Equal:
+    return expandEqualPredicate(cast<SCEVEqualPredicate>(Pred), IP);
+  case SCEVPredicate::P_Wrap: {
+    auto *AddRecPred = cast<SCEVWrapPredicate>(Pred);
+    return expandWrapPredicate(AddRecPred, IP);
+  }
+  }
+  llvm_unreachable("Unknown SCEV predicate type");
+}
+
+Value *SCEVExpander::expandEqualPredicate(const SCEVEqualPredicate *Pred,
+                                          Instruction *IP) {
+  Value *Expr0 = expandCodeFor(Pred->getLHS(), Pred->getLHS()->getType(), IP);
+  Value *Expr1 = expandCodeFor(Pred->getRHS(), Pred->getRHS()->getType(), IP);
+
+  Builder.SetInsertPoint(IP);
+  auto *I = Builder.CreateICmpNE(Expr0, Expr1, "ident.check");
+  return I;
+}
+
+Value *SCEVExpander::generateOverflowCheck(const SCEVAddRecExpr *AR,
+                                           Instruction *Loc, bool Signed) {
+  assert(AR->isAffine() && "Cannot generate RT check for "
+                           "non-affine expression");
+
+  SCEVUnionPredicate Pred;
+  const SCEV *ExitCount =
+      SE.getPredicatedBackedgeTakenCount(AR->getLoop(), Pred);
+
+  assert(ExitCount != SE.getCouldNotCompute() && "Invalid loop count");
+
+  const SCEV *Step = AR->getStepRecurrence(SE);
+  const SCEV *Start = AR->getStart();
+
+  Type *ARTy = AR->getType();
+  unsigned SrcBits = SE.getTypeSizeInBits(ExitCount->getType());
+  unsigned DstBits = SE.getTypeSizeInBits(ARTy);
+
+  // The expression {Start,+,Step} has nusw/nssw if
+  //   Step < 0, Start - |Step| * Backedge <= Start
+  //   Step >= 0, Start + |Step| * Backedge > Start
+  // and |Step| * Backedge doesn't unsigned overflow.
+
+  IntegerType *CountTy = IntegerType::get(Loc->getContext(), SrcBits);
+  Builder.SetInsertPoint(Loc);
+  Value *TripCountVal = expandCodeFor(ExitCount, CountTy, Loc);
+
+  IntegerType *Ty =
+      IntegerType::get(Loc->getContext(), SE.getTypeSizeInBits(ARTy));
+  Type *ARExpandTy = DL.isNonIntegralPointerType(ARTy) ? ARTy : Ty;
+
+  Value *StepValue = expandCodeFor(Step, Ty, Loc);
+  Value *NegStepValue = expandCodeFor(SE.getNegativeSCEV(Step), Ty, Loc);
+  Value *StartValue = expandCodeFor(Start, ARExpandTy, Loc);
+
+  ConstantInt *Zero =
+      ConstantInt::get(Loc->getContext(), APInt::getNullValue(DstBits));
+
+  Builder.SetInsertPoint(Loc);
+  // Compute |Step|
+  Value *StepCompare = Builder.CreateICmp(ICmpInst::ICMP_SLT, StepValue, Zero);
+  Value *AbsStep = Builder.CreateSelect(StepCompare, NegStepValue, StepValue);
+
+  // Get the backedge taken count and truncate or extended to the AR type.
+  Value *TruncTripCount = Builder.CreateZExtOrTrunc(TripCountVal, Ty);
+  auto *MulF = Intrinsic::getDeclaration(Loc->getModule(),
+                                         Intrinsic::umul_with_overflow, Ty);
+
+  // Compute |Step| * Backedge
+  CallInst *Mul = Builder.CreateCall(MulF, {AbsStep, TruncTripCount}, "mul");
+  Value *MulV = Builder.CreateExtractValue(Mul, 0, "mul.result");
+  Value *OfMul = Builder.CreateExtractValue(Mul, 1, "mul.overflow");
+
+  // Compute:
+  //   Start + |Step| * Backedge < Start
+  //   Start - |Step| * Backedge > Start
+  Value *Add = nullptr, *Sub = nullptr;
+  if (PointerType *ARPtrTy = dyn_cast<PointerType>(ARExpandTy)) {
+    const SCEV *MulS = SE.getSCEV(MulV);
+    const SCEV *NegMulS = SE.getNegativeSCEV(MulS);
+    Add = Builder.CreateBitCast(expandAddToGEP(MulS, ARPtrTy, Ty, StartValue),
+                                ARPtrTy);
+    Sub = Builder.CreateBitCast(
+        expandAddToGEP(NegMulS, ARPtrTy, Ty, StartValue), ARPtrTy);
+  } else {
+    Add = Builder.CreateAdd(StartValue, MulV);
+    Sub = Builder.CreateSub(StartValue, MulV);
+  }
+
+  Value *EndCompareGT = Builder.CreateICmp(
+      Signed ? ICmpInst::ICMP_SGT : ICmpInst::ICMP_UGT, Sub, StartValue);
+
+  Value *EndCompareLT = Builder.CreateICmp(
+      Signed ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT, Add, StartValue);
+
+  // Select the answer based on the sign of Step.
+  Value *EndCheck =
+      Builder.CreateSelect(StepCompare, EndCompareGT, EndCompareLT);
+
+  // If the backedge taken count type is larger than the AR type,
+  // check that we don't drop any bits by truncating it. If we are
+  // dropping bits, then we have overflow (unless the step is zero).
+  if (SE.getTypeSizeInBits(CountTy) > SE.getTypeSizeInBits(Ty)) {
+    auto MaxVal = APInt::getMaxValue(DstBits).zext(SrcBits);
+    auto *BackedgeCheck =
+        Builder.CreateICmp(ICmpInst::ICMP_UGT, TripCountVal,
+                           ConstantInt::get(Loc->getContext(), MaxVal));
+    BackedgeCheck = Builder.CreateAnd(
+        BackedgeCheck, Builder.CreateICmp(ICmpInst::ICMP_NE, StepValue, Zero));
+
+    EndCheck = Builder.CreateOr(EndCheck, BackedgeCheck);
+  }
+
+  EndCheck = Builder.CreateOr(EndCheck, OfMul);
+  return EndCheck;
+}
+
+Value *SCEVExpander::expandWrapPredicate(const SCEVWrapPredicate *Pred,
+                                         Instruction *IP) {
+  const auto *A = cast<SCEVAddRecExpr>(Pred->getExpr());
+  Value *NSSWCheck = nullptr, *NUSWCheck = nullptr;
+
+  // Add a check for NUSW
+  if (Pred->getFlags() & SCEVWrapPredicate::IncrementNUSW)
+    NUSWCheck = generateOverflowCheck(A, IP, false);
+
+  // Add a check for NSSW
+  if (Pred->getFlags() & SCEVWrapPredicate::IncrementNSSW)
+    NSSWCheck = generateOverflowCheck(A, IP, true);
+
+  if (NUSWCheck && NSSWCheck)
+    return Builder.CreateOr(NUSWCheck, NSSWCheck);
+
+  if (NUSWCheck)
+    return NUSWCheck;
+
+  if (NSSWCheck)
+    return NSSWCheck;
+
+  return ConstantInt::getFalse(IP->getContext());
+}
+
+Value *SCEVExpander::expandUnionPredicate(const SCEVUnionPredicate *Union,
+                                          Instruction *IP) {
+  auto *BoolType = IntegerType::get(IP->getContext(), 1);
+  Value *Check = ConstantInt::getNullValue(BoolType);
+
+  // Loop over all checks in this set.
+  for (auto Pred : Union->getPredicates()) {
+    auto *NextCheck = expandCodeForPredicate(Pred, IP);
+    Builder.SetInsertPoint(IP);
+    Check = Builder.CreateOr(Check, NextCheck);
+  }
+
+  return Check;
+}
+
+namespace {
+// Search for a SCEV subexpression that is not safe to expand.  Any expression
+// that may expand to a !isSafeToSpeculativelyExecute value is unsafe, namely
+// UDiv expressions. We don't know if the UDiv is derived from an IR divide
+// instruction, but the important thing is that we prove the denominator is
+// nonzero before expansion.
+//
+// IVUsers already checks that IV-derived expressions are safe. So this check is
+// only needed when the expression includes some subexpression that is not IV
+// derived.
+//
+// Currently, we only allow division by a nonzero constant here. If this is
+// inadequate, we could easily allow division by SCEVUnknown by using
+// ValueTracking to check isKnownNonZero().
+//
+// We cannot generally expand recurrences unless the step dominates the loop
+// header. The expander handles the special case of affine recurrences by
+// scaling the recurrence outside the loop, but this technique isn't generally
+// applicable. Expanding a nested recurrence outside a loop requires computing
+// binomial coefficients. This could be done, but the recurrence has to be in a
+// perfectly reduced form, which can't be guaranteed.
+struct SCEVFindUnsafe {
+  ScalarEvolution &SE;
+  bool IsUnsafe;
+
+  SCEVFindUnsafe(ScalarEvolution &se): SE(se), IsUnsafe(false) {}
+
+  bool follow(const SCEV *S) {
+    if (const SCEVUDivExpr *D = dyn_cast<SCEVUDivExpr>(S)) {
+      const SCEVConstant *SC = dyn_cast<SCEVConstant>(D->getRHS());
+      if (!SC || SC->getValue()->isZero()) {
+        IsUnsafe = true;
+        return false;
+      }
+    }
+    if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S)) {
+      const SCEV *Step = AR->getStepRecurrence(SE);
+      if (!AR->isAffine() && !SE.dominates(Step, AR->getLoop()->getHeader())) {
+        IsUnsafe = true;
+        return false;
+      }
+    }
+    return true;
+  }
+  bool isDone() const { return IsUnsafe; }
+};
+}
+
+namespace llvm {
+bool isSafeToExpand(const SCEV *S, ScalarEvolution &SE) {
+  SCEVFindUnsafe Search(SE);
+  visitAll(S, Search);
+  return !Search.IsUnsafe;
+}
+
+bool isSafeToExpandAt(const SCEV *S, const Instruction *InsertionPoint,
+                      ScalarEvolution &SE) {
+  if (!isSafeToExpand(S, SE))
+    return false;
+  // We have to prove that the expanded site of S dominates InsertionPoint.
+  // This is easy when not in the same block, but hard when S is an instruction
+  // to be expanded somewhere inside the same block as our insertion point.
+  // What we really need here is something analogous to an OrderedBasicBlock,
+  // but for the moment, we paper over the problem by handling two common and
+  // cheap to check cases.
+  if (SE.properlyDominates(S, InsertionPoint->getParent()))
+    return true;
+  if (SE.dominates(S, InsertionPoint->getParent())) {
+    if (InsertionPoint->getParent()->getTerminator() == InsertionPoint)
+      return true;
+    if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S))
+      for (const Value *V : InsertionPoint->operand_values())
+        if (V == U->getValue())
+          return true;
+  }
+  return false;
+}
+}