Index: head/contrib/llvm/include/llvm/Analysis/ScalarEvolution.h
===================================================================
--- head/contrib/llvm/include/llvm/Analysis/ScalarEvolution.h	(revision 312831)
+++ head/contrib/llvm/include/llvm/Analysis/ScalarEvolution.h	(revision 312832)
@@ -1,1804 +1,1823 @@
 //===- llvm/Analysis/ScalarEvolution.h - Scalar Evolution -------*- C++ -*-===//
 //
 //                     The LLVM Compiler Infrastructure
 //
 // This file is distributed under the University of Illinois Open Source
 // License. See LICENSE.TXT for details.
 //
 //===----------------------------------------------------------------------===//
 //
 // The ScalarEvolution class is an LLVM pass which can be used to analyze and
 // categorize scalar expressions in loops.  It specializes in recognizing
 // general induction variables, representing them with the abstract and opaque
 // SCEV class.  Given this analysis, trip counts of loops and other important
 // properties can be obtained.
 //
 // This analysis is primarily useful for induction variable substitution and
 // strength reduction.
 //
 //===----------------------------------------------------------------------===//
 
 #ifndef LLVM_ANALYSIS_SCALAREVOLUTION_H
 #define LLVM_ANALYSIS_SCALAREVOLUTION_H
 
 #include "llvm/ADT/DenseSet.h"
 #include "llvm/ADT/FoldingSet.h"
 #include "llvm/ADT/SetVector.h"
 #include "llvm/Analysis/LoopInfo.h"
 #include "llvm/IR/ConstantRange.h"
 #include "llvm/IR/Instructions.h"
 #include "llvm/IR/Operator.h"
 #include "llvm/IR/PassManager.h"
 #include "llvm/IR/ValueHandle.h"
 #include "llvm/IR/ValueMap.h"
 #include "llvm/Pass.h"
 #include "llvm/Support/Allocator.h"
 #include "llvm/Support/DataTypes.h"
 
 namespace llvm {
   class APInt;
   class AssumptionCache;
   class Constant;
   class ConstantInt;
   class DominatorTree;
   class Type;
   class ScalarEvolution;
   class DataLayout;
   class TargetLibraryInfo;
   class LLVMContext;
   class Operator;
   class SCEV;
   class SCEVAddRecExpr;
   class SCEVConstant;
   class SCEVExpander;
   class SCEVPredicate;
   class SCEVUnknown;
   class Function;
 
   template <> struct FoldingSetTrait<SCEV>;
   template <> struct FoldingSetTrait<SCEVPredicate>;
 
   /// This class represents an analyzed expression in the program.  These are
   /// opaque objects that the client is not allowed to do much with directly.
   ///
   class SCEV : public FoldingSetNode {
     friend struct FoldingSetTrait<SCEV>;
 
     /// A reference to an Interned FoldingSetNodeID for this node.  The
     /// ScalarEvolution's BumpPtrAllocator holds the data.
     FoldingSetNodeIDRef FastID;
 
     // The SCEV baseclass this node corresponds to
     const unsigned short SCEVType;
 
   protected:
     /// This field is initialized to zero and may be used in subclasses to store
     /// miscellaneous information.
     unsigned short SubclassData;
 
   private:
     SCEV(const SCEV &) = delete;
     void operator=(const SCEV &) = delete;
 
   public:
     /// NoWrapFlags are bitfield indices into SubclassData.
     ///
     /// Add and Mul expressions may have no-unsigned-wrap <NUW> or
     /// no-signed-wrap <NSW> properties, which are derived from the IR
     /// operator. NSW is a misnomer that we use to mean no signed overflow or
     /// underflow.
     ///
     /// AddRec expressions may have a no-self-wraparound <NW> property if, in
     /// the integer domain, abs(step) * max-iteration(loop) <=
     /// unsigned-max(bitwidth).  This means that the recurrence will never reach
     /// its start value if the step is non-zero.  Computing the same value on
     /// each iteration is not considered wrapping, and recurrences with step = 0
     /// are trivially <NW>.  <NW> is independent of the sign of step and the
     /// value the add recurrence starts with.
     ///
     /// Note that NUW and NSW are also valid properties of a recurrence, and
     /// either implies NW. For convenience, NW will be set for a recurrence
     /// whenever either NUW or NSW are set.
     enum NoWrapFlags { FlagAnyWrap = 0,          // No guarantee.
                        FlagNW      = (1 << 0),   // No self-wrap.
                        FlagNUW     = (1 << 1),   // No unsigned wrap.
                        FlagNSW     = (1 << 2),   // No signed wrap.
                        NoWrapMask  = (1 << 3) -1 };
 
     explicit SCEV(const FoldingSetNodeIDRef ID, unsigned SCEVTy) :
       FastID(ID), SCEVType(SCEVTy), SubclassData(0) {}
 
     unsigned getSCEVType() const { return SCEVType; }
 
     /// Return the LLVM type of this SCEV expression.
     ///
     Type *getType() const;
 
     /// Return true if the expression is a constant zero.
     ///
     bool isZero() const;
 
     /// Return true if the expression is a constant one.
     ///
     bool isOne() const;
 
     /// Return true if the expression is a constant all-ones value.
     ///
     bool isAllOnesValue() const;
 
     /// Return true if the specified scev is negated, but not a constant.
     bool isNonConstantNegative() const;
 
     /// Print out the internal representation of this scalar to the specified
     /// stream.  This should really only be used for debugging purposes.
     void print(raw_ostream &OS) const;
 
     /// This method is used for debugging.
     ///
     void dump() const;
   };
 
   // Specialize FoldingSetTrait for SCEV to avoid needing to compute
   // temporary FoldingSetNodeID values.
   template<> struct FoldingSetTrait<SCEV> : DefaultFoldingSetTrait<SCEV> {
     static void Profile(const SCEV &X, FoldingSetNodeID& ID) {
       ID = X.FastID;
     }
     static bool Equals(const SCEV &X, const FoldingSetNodeID &ID,
                        unsigned IDHash, FoldingSetNodeID &TempID) {
       return ID == X.FastID;
     }
     static unsigned ComputeHash(const SCEV &X, FoldingSetNodeID &TempID) {
       return X.FastID.ComputeHash();
     }
   };
 
   inline raw_ostream &operator<<(raw_ostream &OS, const SCEV &S) {
     S.print(OS);
     return OS;
   }
 
   /// An object of this class is returned by queries that could not be answered.
   /// For example, if you ask for the number of iterations of a linked-list
   /// traversal loop, you will get one of these.  None of the standard SCEV
   /// operations are valid on this class, it is just a marker.
   struct SCEVCouldNotCompute : public SCEV {
     SCEVCouldNotCompute();
 
     /// Methods for support type inquiry through isa, cast, and dyn_cast:
     static bool classof(const SCEV *S);
   };
 
   /// This class represents an assumption made using SCEV expressions which can
   /// be checked at run-time.
   class SCEVPredicate : public FoldingSetNode {
     friend struct FoldingSetTrait<SCEVPredicate>;
 
     /// A reference to an Interned FoldingSetNodeID for this node.  The
     /// ScalarEvolution's BumpPtrAllocator holds the data.
     FoldingSetNodeIDRef FastID;
 
   public:
     enum SCEVPredicateKind { P_Union, P_Equal, P_Wrap };
 
   protected:
     SCEVPredicateKind Kind;
     ~SCEVPredicate() = default;
     SCEVPredicate(const SCEVPredicate&) = default;
     SCEVPredicate &operator=(const SCEVPredicate&) = default;
 
   public:
     SCEVPredicate(const FoldingSetNodeIDRef ID, SCEVPredicateKind Kind);
 
     SCEVPredicateKind getKind() const { return Kind; }
 
     /// Returns the estimated complexity of this predicate.  This is roughly
     /// measured in the number of run-time checks required.
     virtual unsigned getComplexity() const { return 1; }
 
     /// Returns true if the predicate is always true. This means that no
     /// assumptions were made and nothing needs to be checked at run-time.
     virtual bool isAlwaysTrue() const = 0;
 
     /// Returns true if this predicate implies \p N.
     virtual bool implies(const SCEVPredicate *N) const = 0;
 
     /// Prints a textual representation of this predicate with an indentation of
     /// \p Depth.
     virtual void print(raw_ostream &OS, unsigned Depth = 0) const = 0;
 
     /// Returns the SCEV to which this predicate applies, or nullptr if this is
     /// a SCEVUnionPredicate.
     virtual const SCEV *getExpr() const = 0;
   };
 
   inline raw_ostream &operator<<(raw_ostream &OS, const SCEVPredicate &P) {
     P.print(OS);
     return OS;
   }
 
   // Specialize FoldingSetTrait for SCEVPredicate to avoid needing to compute
   // temporary FoldingSetNodeID values.
   template <>
   struct FoldingSetTrait<SCEVPredicate>
       : DefaultFoldingSetTrait<SCEVPredicate> {
 
     static void Profile(const SCEVPredicate &X, FoldingSetNodeID &ID) {
       ID = X.FastID;
     }
 
     static bool Equals(const SCEVPredicate &X, const FoldingSetNodeID &ID,
                        unsigned IDHash, FoldingSetNodeID &TempID) {
       return ID == X.FastID;
     }
     static unsigned ComputeHash(const SCEVPredicate &X,
                                 FoldingSetNodeID &TempID) {
       return X.FastID.ComputeHash();
     }
   };
 
   /// This class represents an assumption that two SCEV expressions are equal,
   /// and this can be checked at run-time. We assume that the left hand side is
   /// a SCEVUnknown and the right hand side a constant.
   class SCEVEqualPredicate final : public SCEVPredicate {
     /// We assume that LHS == RHS, where LHS is a SCEVUnknown and RHS a
     /// constant.
     const SCEVUnknown *LHS;
     const SCEVConstant *RHS;
 
   public:
     SCEVEqualPredicate(const FoldingSetNodeIDRef ID, const SCEVUnknown *LHS,
                        const SCEVConstant *RHS);
 
     /// Implementation of the SCEVPredicate interface
     bool implies(const SCEVPredicate *N) const override;
     void print(raw_ostream &OS, unsigned Depth = 0) const override;
     bool isAlwaysTrue() const override;
     const SCEV *getExpr() const override;
 
     /// Returns the left hand side of the equality.
     const SCEVUnknown *getLHS() const { return LHS; }
 
     /// Returns the right hand side of the equality.
     const SCEVConstant *getRHS() const { return RHS; }
 
     /// Methods for support type inquiry through isa, cast, and dyn_cast:
     static inline bool classof(const SCEVPredicate *P) {
       return P->getKind() == P_Equal;
     }
   };
 
   /// This class represents an assumption made on an AddRec expression. Given an
   /// affine AddRec expression {a,+,b}, we assume that it has the nssw or nusw
   /// flags (defined below) in the first X iterations of the loop, where X is a
   /// SCEV expression returned by getPredicatedBackedgeTakenCount).
   ///
   /// Note that this does not imply that X is equal to the backedge taken
   /// count. This means that if we have a nusw predicate for i32 {0,+,1} with a
   /// predicated backedge taken count of X, we only guarantee that {0,+,1} has
   /// nusw in the first X iterations. {0,+,1} may still wrap in the loop if we
   /// have more than X iterations.
   class SCEVWrapPredicate final : public SCEVPredicate {
   public:
     /// Similar to SCEV::NoWrapFlags, but with slightly different semantics
     /// for FlagNUSW. The increment is considered to be signed, and a + b
     /// (where b is the increment) is considered to wrap if:
     ///    zext(a + b) != zext(a) + sext(b)
     ///
     /// If Signed is a function that takes an n-bit tuple and maps to the
     /// integer domain as the tuples value interpreted as twos complement,
     /// and Unsigned a function that takes an n-bit tuple and maps to the
     /// integer domain as as the base two value of input tuple, then a + b
     /// has IncrementNUSW iff:
     ///
     /// 0 <= Unsigned(a) + Signed(b) < 2^n
     ///
     /// The IncrementNSSW flag has identical semantics with SCEV::FlagNSW.
     ///
     /// Note that the IncrementNUSW flag is not commutative: if base + inc
     /// has IncrementNUSW, then inc + base doesn't neccessarily have this
     /// property. The reason for this is that this is used for sign/zero
     /// extending affine AddRec SCEV expressions when a SCEVWrapPredicate is
     /// assumed. A {base,+,inc} expression is already non-commutative with
     /// regards to base and inc, since it is interpreted as:
     ///     (((base + inc) + inc) + inc) ...
     enum IncrementWrapFlags {
       IncrementAnyWrap = 0,     // No guarantee.
       IncrementNUSW = (1 << 0), // No unsigned with signed increment wrap.
       IncrementNSSW = (1 << 1), // No signed with signed increment wrap
                                 // (equivalent with SCEV::NSW)
       IncrementNoWrapMask = (1 << 2) - 1
     };
 
     /// Convenient IncrementWrapFlags manipulation methods.
     static SCEVWrapPredicate::IncrementWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
     clearFlags(SCEVWrapPredicate::IncrementWrapFlags Flags,
                SCEVWrapPredicate::IncrementWrapFlags OffFlags) {
       assert((Flags & IncrementNoWrapMask) == Flags && "Invalid flags value!");
       assert((OffFlags & IncrementNoWrapMask) == OffFlags &&
              "Invalid flags value!");
       return (SCEVWrapPredicate::IncrementWrapFlags)(Flags & ~OffFlags);
     }
 
     static SCEVWrapPredicate::IncrementWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
     maskFlags(SCEVWrapPredicate::IncrementWrapFlags Flags, int Mask) {
       assert((Flags & IncrementNoWrapMask) == Flags && "Invalid flags value!");
       assert((Mask & IncrementNoWrapMask) == Mask && "Invalid mask value!");
 
       return (SCEVWrapPredicate::IncrementWrapFlags)(Flags & Mask);
     }
 
     static SCEVWrapPredicate::IncrementWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
     setFlags(SCEVWrapPredicate::IncrementWrapFlags Flags,
              SCEVWrapPredicate::IncrementWrapFlags OnFlags) {
       assert((Flags & IncrementNoWrapMask) == Flags && "Invalid flags value!");
       assert((OnFlags & IncrementNoWrapMask) == OnFlags &&
              "Invalid flags value!");
 
       return (SCEVWrapPredicate::IncrementWrapFlags)(Flags | OnFlags);
     }
 
     /// Returns the set of SCEVWrapPredicate no wrap flags implied by a
     /// SCEVAddRecExpr.
     static SCEVWrapPredicate::IncrementWrapFlags
     getImpliedFlags(const SCEVAddRecExpr *AR, ScalarEvolution &SE);
 
   private:
     const SCEVAddRecExpr *AR;
     IncrementWrapFlags Flags;
 
   public:
     explicit SCEVWrapPredicate(const FoldingSetNodeIDRef ID,
                                const SCEVAddRecExpr *AR,
                                IncrementWrapFlags Flags);
 
     /// Returns the set assumed no overflow flags.
     IncrementWrapFlags getFlags() const { return Flags; }
     /// Implementation of the SCEVPredicate interface
     const SCEV *getExpr() const override;
     bool implies(const SCEVPredicate *N) const override;
     void print(raw_ostream &OS, unsigned Depth = 0) const override;
     bool isAlwaysTrue() const override;
 
     /// Methods for support type inquiry through isa, cast, and dyn_cast:
     static inline bool classof(const SCEVPredicate *P) {
       return P->getKind() == P_Wrap;
     }
   };
 
   /// This class represents a composition of other SCEV predicates, and is the
   /// class that most clients will interact with.  This is equivalent to a
   /// logical "AND" of all the predicates in the union.
   class SCEVUnionPredicate final : public SCEVPredicate {
   private:
     typedef DenseMap<const SCEV *, SmallVector<const SCEVPredicate *, 4>>
         PredicateMap;
 
     /// Vector with references to all predicates in this union.
     SmallVector<const SCEVPredicate *, 16> Preds;
     /// Maps SCEVs to predicates for quick look-ups.
     PredicateMap SCEVToPreds;
 
   public:
     SCEVUnionPredicate();
 
     const SmallVectorImpl<const SCEVPredicate *> &getPredicates() const {
       return Preds;
     }
 
     /// Adds a predicate to this union.
     void add(const SCEVPredicate *N);
 
     /// Returns a reference to a vector containing all predicates which apply to
     /// \p Expr.
     ArrayRef<const SCEVPredicate *> getPredicatesForExpr(const SCEV *Expr);
 
     /// Implementation of the SCEVPredicate interface
     bool isAlwaysTrue() const override;
     bool implies(const SCEVPredicate *N) const override;
     void print(raw_ostream &OS, unsigned Depth) const override;
     const SCEV *getExpr() const override;
 
     /// We estimate the complexity of a union predicate as the size number of
     /// predicates in the union.
     unsigned getComplexity() const override { return Preds.size(); }
 
     /// Methods for support type inquiry through isa, cast, and dyn_cast:
     static inline bool classof(const SCEVPredicate *P) {
       return P->getKind() == P_Union;
     }
   };
 
   /// The main scalar evolution driver. Because client code (intentionally)
   /// can't do much with the SCEV objects directly, they must ask this class
   /// for services.
   class ScalarEvolution {
   public:
     /// An enum describing the relationship between a SCEV and a loop.
     enum LoopDisposition {
       LoopVariant,    ///< The SCEV is loop-variant (unknown).
       LoopInvariant,  ///< The SCEV is loop-invariant.
       LoopComputable  ///< The SCEV varies predictably with the loop.
     };
 
     /// An enum describing the relationship between a SCEV and a basic block.
     enum BlockDisposition {
       DoesNotDominateBlock,  ///< The SCEV does not dominate the block.
       DominatesBlock,        ///< The SCEV dominates the block.
       ProperlyDominatesBlock ///< The SCEV properly dominates the block.
     };
 
     /// Convenient NoWrapFlags manipulation that hides enum casts and is
     /// visible in the ScalarEvolution name space.
     static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
     maskFlags(SCEV::NoWrapFlags Flags, int Mask) {
       return (SCEV::NoWrapFlags)(Flags & Mask);
     }
     static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
     setFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OnFlags) {
       return (SCEV::NoWrapFlags)(Flags | OnFlags);
     }
     static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
     clearFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OffFlags) {
       return (SCEV::NoWrapFlags)(Flags & ~OffFlags);
     }
 
   private:
     /// A CallbackVH to arrange for ScalarEvolution to be notified whenever a
     /// Value is deleted.
     class SCEVCallbackVH final : public CallbackVH {
       ScalarEvolution *SE;
       void deleted() override;
       void allUsesReplacedWith(Value *New) override;
     public:
       SCEVCallbackVH(Value *V, ScalarEvolution *SE = nullptr);
     };
 
     friend class SCEVCallbackVH;
     friend class SCEVExpander;
     friend class SCEVUnknown;
 
     /// The function we are analyzing.
     ///
     Function &F;
 
     /// Does the module have any calls to the llvm.experimental.guard intrinsic
     /// at all?  If this is false, we avoid doing work that will only help if
     /// thare are guards present in the IR.
     ///
     bool HasGuards;
 
     /// The target library information for the target we are targeting.
     ///
     TargetLibraryInfo &TLI;
 
     /// The tracker for @llvm.assume intrinsics in this function.
     AssumptionCache &AC;
 
     /// The dominator tree.
     ///
     DominatorTree &DT;
 
     /// The loop information for the function we are currently analyzing.
     ///
     LoopInfo &LI;
 
     /// This SCEV is used to represent unknown trip counts and things.
     std::unique_ptr<SCEVCouldNotCompute> CouldNotCompute;
 
     /// The typedef for HasRecMap.
     ///
     typedef DenseMap<const SCEV *, bool> HasRecMapType;
 
     /// This is a cache to record whether a SCEV contains any scAddRecExpr.
     HasRecMapType HasRecMap;
 
     /// The typedef for ExprValueMap.
     ///
-    typedef DenseMap<const SCEV *, SetVector<Value *>> ExprValueMapType;
+    typedef std::pair<Value *, ConstantInt *> ValueOffsetPair;
+    typedef DenseMap<const SCEV *, SetVector<ValueOffsetPair>> ExprValueMapType;
 
     /// ExprValueMap -- This map records the original values from which
     /// the SCEV expr is generated from.
+    ///
+    /// We want to represent the mapping as SCEV -> ValueOffsetPair instead
+    /// of SCEV -> Value:
+    /// Suppose we know S1 expands to V1, and
+    ///  S1 = S2 + C_a
+    ///  S3 = S2 + C_b
+    /// where C_a and C_b are different SCEVConstants. Then we'd like to
+    /// expand S3 as V1 - C_a + C_b instead of expanding S2 literally.
+    /// It is helpful when S2 is a complex SCEV expr.
+    ///
+    /// In order to do that, we represent ExprValueMap as a mapping from
+    /// SCEV to ValueOffsetPair. We will save both S1->{V1, 0} and
+    /// S2->{V1, C_a} into the map when we create SCEV for V1. When S3
+    /// is expanded, it will first expand S2 to V1 - C_a because of
+    /// S2->{V1, C_a} in the map, then expand S3 to V1 - C_a + C_b.
+    ///
+    /// Note: S->{V, Offset} in the ExprValueMap means S can be expanded
+    /// to V - Offset.
     ExprValueMapType ExprValueMap;
 
     /// The typedef for ValueExprMap.
     ///
     typedef DenseMap<SCEVCallbackVH, const SCEV *, DenseMapInfo<Value *> >
       ValueExprMapType;
 
     /// This is a cache of the values we have analyzed so far.
     ///
     ValueExprMapType ValueExprMap;
 
     /// Mark predicate values currently being processed by isImpliedCond.
     DenseSet<Value*> PendingLoopPredicates;
 
     /// Set to true by isLoopBackedgeGuardedByCond when we're walking the set of
     /// conditions dominating the backedge of a loop.
     bool WalkingBEDominatingConds;
 
     /// Set to true by isKnownPredicateViaSplitting when we're trying to prove a
     /// predicate by splitting it into a set of independent predicates.
     bool ProvingSplitPredicate;
 
     /// Information about the number of loop iterations for which a loop exit's
     /// branch condition evaluates to the not-taken path.  This is a temporary
     /// pair of exact and max expressions that are eventually summarized in
     /// ExitNotTakenInfo and BackedgeTakenInfo.
     struct ExitLimit {
       const SCEV *Exact;
       const SCEV *Max;
 
       /// A predicate union guard for this ExitLimit. The result is only
       /// valid if this predicate evaluates to 'true' at run-time.
       SCEVUnionPredicate Pred;
 
       /*implicit*/ ExitLimit(const SCEV *E) : Exact(E), Max(E) {}
 
       ExitLimit(const SCEV *E, const SCEV *M, SCEVUnionPredicate &P)
           : Exact(E), Max(M), Pred(P) {
         assert((isa<SCEVCouldNotCompute>(Exact) ||
                 !isa<SCEVCouldNotCompute>(Max)) &&
                "Exact is not allowed to be less precise than Max");
       }
 
       /// Test whether this ExitLimit contains any computed information, or
       /// whether it's all SCEVCouldNotCompute values.
       bool hasAnyInfo() const {
         return !isa<SCEVCouldNotCompute>(Exact) ||
           !isa<SCEVCouldNotCompute>(Max);
       }
 
       /// Test whether this ExitLimit contains all information.
       bool hasFullInfo() const { return !isa<SCEVCouldNotCompute>(Exact); }
     };
 
     /// Forward declaration of ExitNotTakenExtras
     struct ExitNotTakenExtras;
 
     /// Information about the number of times a particular loop exit may be
     /// reached before exiting the loop.
     struct ExitNotTakenInfo {
       AssertingVH<BasicBlock> ExitingBlock;
       const SCEV *ExactNotTaken;
 
       ExitNotTakenExtras *ExtraInfo;
       bool Complete;
 
       ExitNotTakenInfo()
           : ExitingBlock(nullptr), ExactNotTaken(nullptr), ExtraInfo(nullptr),
             Complete(true) {}
 
       ExitNotTakenInfo(BasicBlock *ExitBlock, const SCEV *Expr,
                        ExitNotTakenExtras *Ptr)
           : ExitingBlock(ExitBlock), ExactNotTaken(Expr), ExtraInfo(Ptr),
             Complete(true) {}
 
       /// Return true if all loop exits are computable.
       bool isCompleteList() const { return Complete; }
 
       /// Sets the incomplete property, indicating that one of the loop exits
       /// doesn't have a corresponding ExitNotTakenInfo entry.
       void setIncomplete() { Complete = false; }
 
       /// Returns a pointer to the predicate associated with this information,
       /// or nullptr if this doesn't exist (meaning always true).
       SCEVUnionPredicate *getPred() const {
         if (ExtraInfo)
           return &ExtraInfo->Pred;
 
         return nullptr;
       }
 
       /// Return true if the SCEV predicate associated with this information
       /// is always true.
       bool hasAlwaysTruePred() const {
         return !getPred() || getPred()->isAlwaysTrue();
       }
 
       /// Defines a simple forward iterator for ExitNotTakenInfo.
       class ExitNotTakenInfoIterator
           : public std::iterator<std::forward_iterator_tag, ExitNotTakenInfo> {
         const ExitNotTakenInfo *Start;
         unsigned Position;
 
       public:
         ExitNotTakenInfoIterator(const ExitNotTakenInfo *Start,
                                  unsigned Position)
             : Start(Start), Position(Position) {}
 
         const ExitNotTakenInfo &operator*() const {
           if (Position == 0)
             return *Start;
 
           return Start->ExtraInfo->Exits[Position - 1];
         }
 
         const ExitNotTakenInfo *operator->() const {
           if (Position == 0)
             return Start;
 
           return &Start->ExtraInfo->Exits[Position - 1];
         }
 
         bool operator==(const ExitNotTakenInfoIterator &RHS) const {
           return Start == RHS.Start && Position == RHS.Position;
         }
 
         bool operator!=(const ExitNotTakenInfoIterator &RHS) const {
           return Start != RHS.Start || Position != RHS.Position;
         }
 
         ExitNotTakenInfoIterator &operator++() { // Preincrement
           if (!Start)
             return *this;
 
           unsigned Elements =
               Start->ExtraInfo ? Start->ExtraInfo->Exits.size() + 1 : 1;
 
           ++Position;
 
           // We've run out of elements.
           if (Position == Elements) {
             Start = nullptr;
             Position = 0;
           }
 
           return *this;
         }
         ExitNotTakenInfoIterator operator++(int) { // Postincrement
           ExitNotTakenInfoIterator Tmp = *this;
           ++*this;
           return Tmp;
         }
       };
 
       /// Iterators
       ExitNotTakenInfoIterator begin() const {
         return ExitNotTakenInfoIterator(this, 0);
       }
       ExitNotTakenInfoIterator end() const {
         return ExitNotTakenInfoIterator(nullptr, 0);
       }
     };
 
     /// Describes the extra information that a ExitNotTakenInfo can have.
     struct ExitNotTakenExtras {
       /// The predicate associated with the ExitNotTakenInfo struct.
       SCEVUnionPredicate Pred;
 
       /// The extra exits in the loop. Only the ExitNotTakenExtras structure
       /// pointed to by the first ExitNotTakenInfo struct (associated with the
       /// first loop exit) will populate this vector to prevent having
       /// redundant information.
       SmallVector<ExitNotTakenInfo, 4> Exits;
     };
 
     /// A struct containing the information attached to a backedge.
     struct EdgeInfo {
       EdgeInfo(BasicBlock *Block, const SCEV *Taken, SCEVUnionPredicate &P) :
           ExitBlock(Block), Taken(Taken), Pred(std::move(P)) {}
 
       /// The exit basic block.
       BasicBlock *ExitBlock;
 
       /// The (exact) number of time we take the edge back.
       const SCEV *Taken;
 
       /// The SCEV predicated associated with Taken. If Pred doesn't evaluate
       /// to true, the information in Taken is not valid (or equivalent with
       /// a CouldNotCompute.
       SCEVUnionPredicate Pred;
     };
 
     /// Information about the backedge-taken count of a loop. This currently
     /// includes an exact count and a maximum count.
     ///
     class BackedgeTakenInfo {
       /// A list of computable exits and their not-taken counts.  Loops almost
       /// never have more than one computable exit.
       ExitNotTakenInfo ExitNotTaken;
 
       /// An expression indicating the least maximum backedge-taken count of the
       /// loop that is known, or a SCEVCouldNotCompute. This expression is only
       /// valid if the predicates associated with all loop exits are true.
       const SCEV *Max;
 
     public:
       BackedgeTakenInfo() : Max(nullptr) {}
 
       /// Initialize BackedgeTakenInfo from a list of exact exit counts.
       BackedgeTakenInfo(SmallVectorImpl<EdgeInfo> &ExitCounts, bool Complete,
                         const SCEV *MaxCount);
 
       /// Test whether this BackedgeTakenInfo contains any computed information,
       /// or whether it's all SCEVCouldNotCompute values.
       bool hasAnyInfo() const {
         return ExitNotTaken.ExitingBlock || !isa<SCEVCouldNotCompute>(Max);
       }
 
       /// Test whether this BackedgeTakenInfo contains complete information.
       bool hasFullInfo() const { return ExitNotTaken.isCompleteList(); }
 
       /// Return an expression indicating the exact backedge-taken count of the
       /// loop if it is known or SCEVCouldNotCompute otherwise. This is the
       /// number of times the loop header can be guaranteed to execute, minus
       /// one.
       ///
       /// If the SCEV predicate associated with the answer can be different
       /// from AlwaysTrue, we must add a (non null) Predicates argument.
       /// The SCEV predicate associated with the answer will be added to
       /// Predicates. A run-time check needs to be emitted for the SCEV
       /// predicate in order for the answer to be valid.
       ///
       /// Note that we should always know if we need to pass a predicate
       /// argument or not from the way the ExitCounts vector was computed.
       /// If we allowed SCEV predicates to be generated when populating this
       /// vector, this information can contain them and therefore a
       /// SCEVPredicate argument should be added to getExact.
       const SCEV *getExact(ScalarEvolution *SE,
                            SCEVUnionPredicate *Predicates = nullptr) const;
 
       /// Return the number of times this loop exit may fall through to the back
       /// edge, or SCEVCouldNotCompute. The loop is guaranteed not to exit via
       /// this block before this number of iterations, but may exit via another
       /// block.
       const SCEV *getExact(BasicBlock *ExitingBlock, ScalarEvolution *SE) const;
 
       /// Get the max backedge taken count for the loop.
       const SCEV *getMax(ScalarEvolution *SE) const;
 
       /// Return true if any backedge taken count expressions refer to the given
       /// subexpression.
       bool hasOperand(const SCEV *S, ScalarEvolution *SE) const;
 
       /// Invalidate this result and free associated memory.
       void clear();
     };
 
     /// Cache the backedge-taken count of the loops for this function as they
     /// are computed.
     DenseMap<const Loop *, BackedgeTakenInfo> BackedgeTakenCounts;
 
     /// Cache the predicated backedge-taken count of the loops for this
     /// function as they are computed.
     DenseMap<const Loop *, BackedgeTakenInfo> PredicatedBackedgeTakenCounts;
 
     /// This map contains entries for all of the PHI instructions that we
     /// attempt to compute constant evolutions for.  This allows us to avoid
     /// potentially expensive recomputation of these properties.  An instruction
     /// maps to null if we are unable to compute its exit value.
     DenseMap<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
 
     /// This map contains entries for all the expressions that we attempt to
     /// compute getSCEVAtScope information for, which can be expensive in
     /// extreme cases.
     DenseMap<const SCEV *,
              SmallVector<std::pair<const Loop *, const SCEV *>, 2> > ValuesAtScopes;
 
     /// Memoized computeLoopDisposition results.
     DenseMap<const SCEV *,
              SmallVector<PointerIntPair<const Loop *, 2, LoopDisposition>, 2>>
         LoopDispositions;
 
     /// Cache for \c loopHasNoAbnormalExits.
     DenseMap<const Loop *, bool> LoopHasNoAbnormalExits;
 
     /// Returns true if \p L contains no instruction that can abnormally exit
     /// the loop (i.e. via throwing an exception, by terminating the thread
     /// cleanly or by infinite looping in a called function).  Strictly
     /// speaking, the last one is not leaving the loop, but is identical to
     /// leaving the loop for reasoning about undefined behavior.
     bool loopHasNoAbnormalExits(const Loop *L);
 
     /// Compute a LoopDisposition value.
     LoopDisposition computeLoopDisposition(const SCEV *S, const Loop *L);
 
     /// Memoized computeBlockDisposition results.
     DenseMap<
         const SCEV *,
         SmallVector<PointerIntPair<const BasicBlock *, 2, BlockDisposition>, 2>>
         BlockDispositions;
 
     /// Compute a BlockDisposition value.
     BlockDisposition computeBlockDisposition(const SCEV *S, const BasicBlock *BB);
 
     /// Memoized results from getRange
     DenseMap<const SCEV *, ConstantRange> UnsignedRanges;
 
     /// Memoized results from getRange
     DenseMap<const SCEV *, ConstantRange> SignedRanges;
 
     /// Used to parameterize getRange
     enum RangeSignHint { HINT_RANGE_UNSIGNED, HINT_RANGE_SIGNED };
 
     /// Set the memoized range for the given SCEV.
     const ConstantRange &setRange(const SCEV *S, RangeSignHint Hint,
                                   const ConstantRange &CR) {
       DenseMap<const SCEV *, ConstantRange> &Cache =
           Hint == HINT_RANGE_UNSIGNED ? UnsignedRanges : SignedRanges;
 
       auto Pair = Cache.insert({S, CR});
       if (!Pair.second)
         Pair.first->second = CR;
       return Pair.first->second;
     }
 
     /// Determine the range for a particular SCEV.
     ConstantRange getRange(const SCEV *S, RangeSignHint Hint);
 
     /// Determines the range for the affine SCEVAddRecExpr {\p Start,+,\p Stop}.
     /// Helper for \c getRange.
     ConstantRange getRangeForAffineAR(const SCEV *Start, const SCEV *Stop,
                                       const SCEV *MaxBECount,
                                       unsigned BitWidth);
 
     /// Try to compute a range for the affine SCEVAddRecExpr {\p Start,+,\p
     /// Stop} by "factoring out" a ternary expression from the add recurrence.
     /// Helper called by \c getRange.
     ConstantRange getRangeViaFactoring(const SCEV *Start, const SCEV *Stop,
                                        const SCEV *MaxBECount,
                                        unsigned BitWidth);
 
     /// We know that there is no SCEV for the specified value.  Analyze the
     /// expression.
     const SCEV *createSCEV(Value *V);
 
     /// Provide the special handling we need to analyze PHI SCEVs.
     const SCEV *createNodeForPHI(PHINode *PN);
 
     /// Helper function called from createNodeForPHI.
     const SCEV *createAddRecFromPHI(PHINode *PN);
 
     /// Helper function called from createNodeForPHI.
     const SCEV *createNodeFromSelectLikePHI(PHINode *PN);
 
     /// Provide special handling for a select-like instruction (currently this
     /// is either a select instruction or a phi node).  \p I is the instruction
     /// being processed, and it is assumed equivalent to "Cond ? TrueVal :
     /// FalseVal".
     const SCEV *createNodeForSelectOrPHI(Instruction *I, Value *Cond,
                                          Value *TrueVal, Value *FalseVal);
 
     /// Provide the special handling we need to analyze GEP SCEVs.
     const SCEV *createNodeForGEP(GEPOperator *GEP);
 
     /// Implementation code for getSCEVAtScope; called at most once for each
     /// SCEV+Loop pair.
     ///
     const SCEV *computeSCEVAtScope(const SCEV *S, const Loop *L);
 
     /// This looks up computed SCEV values for all instructions that depend on
     /// the given instruction and removes them from the ValueExprMap map if they
     /// reference SymName. This is used during PHI resolution.
     void forgetSymbolicName(Instruction *I, const SCEV *SymName);
 
     /// Return the BackedgeTakenInfo for the given loop, lazily computing new
     /// values if the loop hasn't been analyzed yet. The returned result is
     /// guaranteed not to be predicated.
     const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
 
     /// Similar to getBackedgeTakenInfo, but will add predicates as required
     /// with the purpose of returning complete information.
     const BackedgeTakenInfo &getPredicatedBackedgeTakenInfo(const Loop *L);
 
     /// Compute the number of times the specified loop will iterate.
     /// If AllowPredicates is set, we will create new SCEV predicates as
     /// necessary in order to return an exact answer.
     BackedgeTakenInfo computeBackedgeTakenCount(const Loop *L,
                                                 bool AllowPredicates = false);
 
     /// Compute the number of times the backedge of the specified loop will
     /// execute if it exits via the specified block. If AllowPredicates is set,
     /// this call will try to use a minimal set of SCEV predicates in order to
     /// return an exact answer.
     ExitLimit computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
                                bool AllowPredicates = false);
 
     /// Compute the number of times the backedge of the specified loop will
     /// execute if its exit condition were a conditional branch of ExitCond,
     /// TBB, and FBB.
     ///
     /// \p ControlsExit is true if ExitCond directly controls the exit
     /// branch. In this case, we can assume that the loop exits only if the
     /// condition is true and can infer that failing to meet the condition prior
     /// to integer wraparound results in undefined behavior.
     ///
     /// If \p AllowPredicates is set, this call will try to use a minimal set of
     /// SCEV predicates in order to return an exact answer.
     ExitLimit computeExitLimitFromCond(const Loop *L,
                                        Value *ExitCond,
                                        BasicBlock *TBB,
                                        BasicBlock *FBB,
                                        bool ControlsExit,
                                        bool AllowPredicates = false);
 
     /// Compute the number of times the backedge of the specified loop will
     /// execute if its exit condition were a conditional branch of the ICmpInst
     /// ExitCond, TBB, and FBB. If AllowPredicates is set, this call will try
     /// to use a minimal set of SCEV predicates in order to return an exact
     /// answer.
     ExitLimit computeExitLimitFromICmp(const Loop *L,
                                        ICmpInst *ExitCond,
                                        BasicBlock *TBB,
                                        BasicBlock *FBB,
                                        bool IsSubExpr,
                                        bool AllowPredicates = false);
 
     /// Compute the number of times the backedge of the specified loop will
     /// execute if its exit condition were a switch with a single exiting case
     /// to ExitingBB.
     ExitLimit
     computeExitLimitFromSingleExitSwitch(const Loop *L, SwitchInst *Switch,
                                BasicBlock *ExitingBB, bool IsSubExpr);
 
     /// Given an exit condition of 'icmp op load X, cst', try to see if we can
     /// compute the backedge-taken count.
     ExitLimit computeLoadConstantCompareExitLimit(LoadInst *LI,
                                                   Constant *RHS,
                                                   const Loop *L,
                                                   ICmpInst::Predicate p);
 
     /// Compute the exit limit of a loop that is controlled by a
     /// "(IV >> 1) != 0" type comparison.  We cannot compute the exact trip
     /// count in these cases (since SCEV has no way of expressing them), but we
     /// can still sometimes compute an upper bound.
     ///
     /// Return an ExitLimit for a loop whose backedge is guarded by `LHS Pred
     /// RHS`.
     ExitLimit computeShiftCompareExitLimit(Value *LHS, Value *RHS,
                                            const Loop *L,
                                            ICmpInst::Predicate Pred);
 
     /// If the loop is known to execute a constant number of times (the
     /// condition evolves only from constants), try to evaluate a few iterations
     /// of the loop until we get the exit condition gets a value of ExitWhen
     /// (true or false).  If we cannot evaluate the exit count of the loop,
     /// return CouldNotCompute.
     const SCEV *computeExitCountExhaustively(const Loop *L,
                                              Value *Cond,
                                              bool ExitWhen);
 
     /// Return the number of times an exit condition comparing the specified
     /// value to zero will execute.  If not computable, return CouldNotCompute.
     /// If AllowPredicates is set, this call will try to use a minimal set of
     /// SCEV predicates in order to return an exact answer.
     ExitLimit howFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr,
                            bool AllowPredicates = false);
 
     /// Return the number of times an exit condition checking the specified
     /// value for nonzero will execute.  If not computable, return
     /// CouldNotCompute.
     ExitLimit howFarToNonZero(const SCEV *V, const Loop *L);
 
     /// Return the number of times an exit condition containing the specified
     /// less-than comparison will execute.  If not computable, return
     /// CouldNotCompute.
     ///
     /// \p isSigned specifies whether the less-than is signed.
     ///
     /// \p ControlsExit is true when the LHS < RHS condition directly controls
     /// the branch (loops exits only if condition is true). In this case, we can
     /// use NoWrapFlags to skip overflow checks.
     ///
     /// If \p AllowPredicates is set, this call will try to use a minimal set of
     /// SCEV predicates in order to return an exact answer.
     ExitLimit howManyLessThans(const SCEV *LHS, const SCEV *RHS, const Loop *L,
                                bool isSigned, bool ControlsExit,
                                bool AllowPredicates = false);
 
     ExitLimit howManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
                                   const Loop *L, bool isSigned, bool IsSubExpr,
                                   bool AllowPredicates = false);
 
     /// Return a predecessor of BB (which may not be an immediate predecessor)
     /// which has exactly one successor from which BB is reachable, or null if
     /// no such block is found.
     std::pair<BasicBlock *, BasicBlock *>
     getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
 
     /// Test whether the condition described by Pred, LHS, and RHS is true
     /// whenever the given FoundCondValue value evaluates to true.
     bool isImpliedCond(ICmpInst::Predicate Pred,
                        const SCEV *LHS, const SCEV *RHS,
                        Value *FoundCondValue,
                        bool Inverse);
 
     /// Test whether the condition described by Pred, LHS, and RHS is true
     /// whenever the condition described by FoundPred, FoundLHS, FoundRHS is
     /// true.
     bool isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
                        const SCEV *RHS, ICmpInst::Predicate FoundPred,
                        const SCEV *FoundLHS, const SCEV *FoundRHS);
 
     /// Test whether the condition described by Pred, LHS, and RHS is true
     /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
     /// true.
     bool isImpliedCondOperands(ICmpInst::Predicate Pred,
                                const SCEV *LHS, const SCEV *RHS,
                                const SCEV *FoundLHS, const SCEV *FoundRHS);
 
     /// Test whether the condition described by Pred, LHS, and RHS is true
     /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
     /// true.
     bool isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
                                      const SCEV *LHS, const SCEV *RHS,
                                      const SCEV *FoundLHS,
                                      const SCEV *FoundRHS);
 
     /// Test whether the condition described by Pred, LHS, and RHS is true
     /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
     /// true.  Utility function used by isImpliedCondOperands.  Tries to get
     /// cases like "X `sgt` 0 => X - 1 `sgt` -1".
     bool isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
                                         const SCEV *LHS, const SCEV *RHS,
                                         const SCEV *FoundLHS,
                                         const SCEV *FoundRHS);
 
     /// Return true if the condition denoted by \p LHS \p Pred \p RHS is implied
     /// by a call to \c @llvm.experimental.guard in \p BB.
     bool isImpliedViaGuard(BasicBlock *BB, ICmpInst::Predicate Pred,
                            const SCEV *LHS, const SCEV *RHS);
 
     /// Test whether the condition described by Pred, LHS, and RHS is true
     /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
     /// true.
     ///
     /// This routine tries to rule out certain kinds of integer overflow, and
     /// then tries to reason about arithmetic properties of the predicates.
     bool isImpliedCondOperandsViaNoOverflow(ICmpInst::Predicate Pred,
                                             const SCEV *LHS, const SCEV *RHS,
                                             const SCEV *FoundLHS,
                                             const SCEV *FoundRHS);
 
     /// If we know that the specified Phi is in the header of its containing
     /// loop, we know the loop executes a constant number of times, and the PHI
     /// node is just a recurrence involving constants, fold it.
     Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs,
                                                 const Loop *L);
 
     /// Test if the given expression is known to satisfy the condition described
     /// by Pred and the known constant ranges of LHS and RHS.
     ///
     bool isKnownPredicateViaConstantRanges(ICmpInst::Predicate Pred,
                                            const SCEV *LHS, const SCEV *RHS);
 
     /// Try to prove the condition described by "LHS Pred RHS" by ruling out
     /// integer overflow.
     ///
     /// For instance, this will return true for "A s< (A + C)<nsw>" if C is
     /// positive.
     bool isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
                                        const SCEV *LHS, const SCEV *RHS);
 
     /// Try to split Pred LHS RHS into logical conjunctions (and's) and try to
     /// prove them individually.
     bool isKnownPredicateViaSplitting(ICmpInst::Predicate Pred, const SCEV *LHS,
                                       const SCEV *RHS);
 
     /// Try to match the Expr as "(L + R)<Flags>".
     bool splitBinaryAdd(const SCEV *Expr, const SCEV *&L, const SCEV *&R,
                         SCEV::NoWrapFlags &Flags);
 
     /// Return true if More == (Less + C), where C is a constant.  This is
     /// intended to be used as a cheaper substitute for full SCEV subtraction.
     bool computeConstantDifference(const SCEV *Less, const SCEV *More,
                                    APInt &C);
 
     /// Drop memoized information computed for S.
     void forgetMemoizedResults(const SCEV *S);
 
     /// Return an existing SCEV for V if there is one, otherwise return nullptr.
     const SCEV *getExistingSCEV(Value *V);
 
     /// Return false iff given SCEV contains a SCEVUnknown with NULL value-
     /// pointer.
     bool checkValidity(const SCEV *S) const;
 
     /// Return true if `ExtendOpTy`({`Start`,+,`Step`}) can be proved to be
     /// equal to {`ExtendOpTy`(`Start`),+,`ExtendOpTy`(`Step`)}.  This is
     /// equivalent to proving no signed (resp. unsigned) wrap in
     /// {`Start`,+,`Step`} if `ExtendOpTy` is `SCEVSignExtendExpr`
     /// (resp. `SCEVZeroExtendExpr`).
     ///
     template<typename ExtendOpTy>
     bool proveNoWrapByVaryingStart(const SCEV *Start, const SCEV *Step,
                                    const Loop *L);
 
     /// Try to prove NSW or NUW on \p AR relying on ConstantRange manipulation.
     SCEV::NoWrapFlags proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR);
 
     bool isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
                                   ICmpInst::Predicate Pred, bool &Increasing);
 
     /// Return true if, for all loop invariant X, the predicate "LHS `Pred` X"
     /// is monotonically increasing or decreasing.  In the former case set
     /// `Increasing` to true and in the latter case set `Increasing` to false.
     ///
     /// A predicate is said to be monotonically increasing if may go from being
     /// false to being true as the loop iterates, but never the other way
     /// around.  A predicate is said to be monotonically decreasing if may go
     /// from being true to being false as the loop iterates, but never the other
     /// way around.
     bool isMonotonicPredicate(const SCEVAddRecExpr *LHS,
                               ICmpInst::Predicate Pred, bool &Increasing);
 
     /// Return SCEV no-wrap flags that can be proven based on reasoning about
     /// how poison produced from no-wrap flags on this value (e.g. a nuw add)
     /// would trigger undefined behavior on overflow.
     SCEV::NoWrapFlags getNoWrapFlagsFromUB(const Value *V);
 
     /// Return true if the SCEV corresponding to \p I is never poison.  Proving
     /// this is more complex than proving that just \p I is never poison, since
     /// SCEV commons expressions across control flow, and you can have cases
     /// like:
     ///
     ///   idx0 = a + b;
     ///   ptr[idx0] = 100;
     ///   if (<condition>) {
     ///     idx1 = a +nsw b;
     ///     ptr[idx1] = 200;
     ///   }
     ///
     /// where the SCEV expression (+ a b) is guaranteed to not be poison (and
     /// hence not sign-overflow) only if "<condition>" is true.  Since both
     /// `idx0` and `idx1` will be mapped to the same SCEV expression, (+ a b),
     /// it is not okay to annotate (+ a b) with <nsw> in the above example.
     bool isSCEVExprNeverPoison(const Instruction *I);
 
     /// This is like \c isSCEVExprNeverPoison but it specifically works for
     /// instructions that will get mapped to SCEV add recurrences.  Return true
     /// if \p I will never generate poison under the assumption that \p I is an
     /// add recurrence on the loop \p L.
     bool isAddRecNeverPoison(const Instruction *I, const Loop *L);
 
   public:
     ScalarEvolution(Function &F, TargetLibraryInfo &TLI, AssumptionCache &AC,
                     DominatorTree &DT, LoopInfo &LI);
     ~ScalarEvolution();
     ScalarEvolution(ScalarEvolution &&Arg);
 
     LLVMContext &getContext() const { return F.getContext(); }
 
     /// Test if values of the given type are analyzable within the SCEV
     /// framework. This primarily includes integer types, and it can optionally
     /// include pointer types if the ScalarEvolution class has access to
     /// target-specific information.
     bool isSCEVable(Type *Ty) const;
 
     /// Return the size in bits of the specified type, for which isSCEVable must
     /// return true.
     uint64_t getTypeSizeInBits(Type *Ty) const;
 
     /// Return a type with the same bitwidth as the given type and which
     /// represents how SCEV will treat the given type, for which isSCEVable must
     /// return true. For pointer types, this is the pointer-sized integer type.
     Type *getEffectiveSCEVType(Type *Ty) const;
 
     /// Return true if the SCEV is a scAddRecExpr or it contains
     /// scAddRecExpr. The result will be cached in HasRecMap.
     ///
     bool containsAddRecurrence(const SCEV *S);
 
     /// Return the Value set from which the SCEV expr is generated.
-    SetVector<Value *> *getSCEVValues(const SCEV *S);
+    SetVector<ValueOffsetPair> *getSCEVValues(const SCEV *S);
 
     /// Erase Value from ValueExprMap and ExprValueMap.
     void eraseValueFromMap(Value *V);
 
     /// Return a SCEV expression for the full generality of the specified
     /// expression.
     const SCEV *getSCEV(Value *V);
 
     const SCEV *getConstant(ConstantInt *V);
     const SCEV *getConstant(const APInt& Val);
     const SCEV *getConstant(Type *Ty, uint64_t V, bool isSigned = false);
     const SCEV *getTruncateExpr(const SCEV *Op, Type *Ty);
     const SCEV *getZeroExtendExpr(const SCEV *Op, Type *Ty);
     const SCEV *getSignExtendExpr(const SCEV *Op, Type *Ty);
     const SCEV *getAnyExtendExpr(const SCEV *Op, Type *Ty);
     const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
                            SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
     const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS,
                            SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
       SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
       return getAddExpr(Ops, Flags);
     }
     const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
                            SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
       SmallVector<const SCEV *, 3> Ops = {Op0, Op1, Op2};
       return getAddExpr(Ops, Flags);
     }
     const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
                            SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
     const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS,
                            SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
       SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
       return getMulExpr(Ops, Flags);
     }
     const SCEV *getMulExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
                            SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
       SmallVector<const SCEV *, 3> Ops = {Op0, Op1, Op2};
       return getMulExpr(Ops, Flags);
     }
     const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
     const SCEV *getUDivExactExpr(const SCEV *LHS, const SCEV *RHS);
     const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step,
                               const Loop *L, SCEV::NoWrapFlags Flags);
     const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
                               const Loop *L, SCEV::NoWrapFlags Flags);
     const SCEV *getAddRecExpr(const SmallVectorImpl<const SCEV *> &Operands,
                               const Loop *L, SCEV::NoWrapFlags Flags) {
       SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
       return getAddRecExpr(NewOp, L, Flags);
     }
     /// Returns an expression for a GEP
     ///
     /// \p PointeeType The type used as the basis for the pointer arithmetics
     /// \p BaseExpr The expression for the pointer operand.
     /// \p IndexExprs The expressions for the indices.
     /// \p InBounds Whether the GEP is in bounds.
     const SCEV *getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
                            const SmallVectorImpl<const SCEV *> &IndexExprs,
                            bool InBounds = false);
     const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
     const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
     const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
     const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
     const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
     const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
     const SCEV *getUnknown(Value *V);
     const SCEV *getCouldNotCompute();
 
     /// Return a SCEV for the constant 0 of a specific type.
     const SCEV *getZero(Type *Ty) { return getConstant(Ty, 0); }
 
     /// Return a SCEV for the constant 1 of a specific type.
     const SCEV *getOne(Type *Ty) { return getConstant(Ty, 1); }
 
     /// Return an expression for sizeof AllocTy that is type IntTy
     ///
     const SCEV *getSizeOfExpr(Type *IntTy, Type *AllocTy);
 
     /// Return an expression for offsetof on the given field with type IntTy
     ///
     const SCEV *getOffsetOfExpr(Type *IntTy, StructType *STy, unsigned FieldNo);
 
     /// Return the SCEV object corresponding to -V.
     ///
     const SCEV *getNegativeSCEV(const SCEV *V,
                                 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
 
     /// Return the SCEV object corresponding to ~V.
     ///
     const SCEV *getNotSCEV(const SCEV *V);
 
     /// Return LHS-RHS.  Minus is represented in SCEV as A+B*-1.
     const SCEV *getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
                              SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
 
     /// Return a SCEV corresponding to a conversion of the input value to the
     /// specified type.  If the type must be extended, it is zero extended.
     const SCEV *getTruncateOrZeroExtend(const SCEV *V, Type *Ty);
 
     /// Return a SCEV corresponding to a conversion of the input value to the
     /// specified type.  If the type must be extended, it is sign extended.
     const SCEV *getTruncateOrSignExtend(const SCEV *V, Type *Ty);
 
     /// Return a SCEV corresponding to a conversion of the input value to the
     /// specified type.  If the type must be extended, it is zero extended.  The
     /// conversion must not be narrowing.
     const SCEV *getNoopOrZeroExtend(const SCEV *V, Type *Ty);
 
     /// Return a SCEV corresponding to a conversion of the input value to the
     /// specified type.  If the type must be extended, it is sign extended.  The
     /// conversion must not be narrowing.
     const SCEV *getNoopOrSignExtend(const SCEV *V, Type *Ty);
 
     /// Return a SCEV corresponding to a conversion of the input value to the
     /// specified type. If the type must be extended, it is extended with
     /// unspecified bits. The conversion must not be narrowing.
     const SCEV *getNoopOrAnyExtend(const SCEV *V, Type *Ty);
 
     /// Return a SCEV corresponding to a conversion of the input value to the
     /// specified type.  The conversion must not be widening.
     const SCEV *getTruncateOrNoop(const SCEV *V, Type *Ty);
 
     /// Promote the operands to the wider of the types using zero-extension, and
     /// then perform a umax operation with them.
     const SCEV *getUMaxFromMismatchedTypes(const SCEV *LHS,
                                            const SCEV *RHS);
 
     /// Promote the operands to the wider of the types using zero-extension, and
     /// then perform a umin operation with them.
     const SCEV *getUMinFromMismatchedTypes(const SCEV *LHS,
                                            const SCEV *RHS);
 
     /// Transitively follow the chain of pointer-type operands until reaching a
     /// SCEV that does not have a single pointer operand. This returns a
     /// SCEVUnknown pointer for well-formed pointer-type expressions, but corner
     /// cases do exist.
     const SCEV *getPointerBase(const SCEV *V);
 
     /// Return a SCEV expression for the specified value at the specified scope
     /// in the program.  The L value specifies a loop nest to evaluate the
     /// expression at, where null is the top-level or a specified loop is
     /// immediately inside of the loop.
     ///
     /// This method can be used to compute the exit value for a variable defined
     /// in a loop by querying what the value will hold in the parent loop.
     ///
     /// In the case that a relevant loop exit value cannot be computed, the
     /// original value V is returned.
     const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
 
     /// This is a convenience function which does getSCEVAtScope(getSCEV(V), L).
     const SCEV *getSCEVAtScope(Value *V, const Loop *L);
 
     /// Test whether entry to the loop is protected by a conditional between LHS
     /// and RHS.  This is used to help avoid max expressions in loop trip
     /// counts, and to eliminate casts.
     bool isLoopEntryGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
                                   const SCEV *LHS, const SCEV *RHS);
 
     /// Test whether the backedge of the loop is protected by a conditional
     /// between LHS and RHS.  This is used to to eliminate casts.
     bool isLoopBackedgeGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
                                      const SCEV *LHS, const SCEV *RHS);
 
     /// Returns the maximum trip count of the loop if it is a single-exit
     /// loop and we can compute a small maximum for that loop.
     ///
     /// Implemented in terms of the \c getSmallConstantTripCount overload with
     /// the single exiting block passed to it. See that routine for details.
     unsigned getSmallConstantTripCount(Loop *L);
 
     /// Returns the maximum trip count of this loop as a normal unsigned
     /// value. Returns 0 if the trip count is unknown or not constant. This
     /// "trip count" assumes that control exits via ExitingBlock. More
     /// precisely, it is the number of times that control may reach ExitingBlock
     /// before taking the branch. For loops with multiple exits, it may not be
     /// the number times that the loop header executes if the loop exits
     /// prematurely via another branch.
     unsigned getSmallConstantTripCount(Loop *L, BasicBlock *ExitingBlock);
 
     /// Returns the largest constant divisor of the trip count of the
     /// loop if it is a single-exit loop and we can compute a small maximum for
     /// that loop.
     ///
     /// Implemented in terms of the \c getSmallConstantTripMultiple overload with
     /// the single exiting block passed to it. See that routine for details.
     unsigned getSmallConstantTripMultiple(Loop *L);
 
     /// Returns the largest constant divisor of the trip count of this loop as a
     /// normal unsigned value, if possible. This means that the actual trip
     /// count is always a multiple of the returned value (don't forget the trip
     /// count could very well be zero as well!). As explained in the comments
     /// for getSmallConstantTripCount, this assumes that control exits the loop
     /// via ExitingBlock.
     unsigned getSmallConstantTripMultiple(Loop *L, BasicBlock *ExitingBlock);
 
     /// Get the expression for the number of loop iterations for which this loop
     /// is guaranteed not to exit via ExitingBlock. Otherwise return
     /// SCEVCouldNotCompute.
     const SCEV *getExitCount(Loop *L, BasicBlock *ExitingBlock);
 
     /// If the specified loop has a predictable backedge-taken count, return it,
     /// otherwise return a SCEVCouldNotCompute object. The backedge-taken count
     /// is the number of times the loop header will be branched to from within
     /// the loop. This is one less than the trip count of the loop, since it
     /// doesn't count the first iteration, when the header is branched to from
     /// outside the loop.
     ///
     /// Note that it is not valid to call this method on a loop without a
     /// loop-invariant backedge-taken count (see
     /// hasLoopInvariantBackedgeTakenCount).
     ///
     const SCEV *getBackedgeTakenCount(const Loop *L);
 
     /// Similar to getBackedgeTakenCount, except it will add a set of
     /// SCEV predicates to Predicates that are required to be true in order for
     /// the answer to be correct. Predicates can be checked with run-time
     /// checks and can be used to perform loop versioning.
     const SCEV *getPredicatedBackedgeTakenCount(const Loop *L,
                                                 SCEVUnionPredicate &Predicates);
 
     /// Similar to getBackedgeTakenCount, except return the least SCEV value
     /// that is known never to be less than the actual backedge taken count.
     const SCEV *getMaxBackedgeTakenCount(const Loop *L);
 
     /// Return true if the specified loop has an analyzable loop-invariant
     /// backedge-taken count.
     bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
 
     /// This method should be called by the client when it has changed a loop in
     /// a way that may effect ScalarEvolution's ability to compute a trip count,
     /// or if the loop is deleted.  This call is potentially expensive for large
     /// loop bodies.
     void forgetLoop(const Loop *L);
 
     /// This method should be called by the client when it has changed a value
     /// in a way that may effect its value, or which may disconnect it from a
     /// def-use chain linking it to a loop.
     void forgetValue(Value *V);
 
     /// Called when the client has changed the disposition of values in
     /// this loop.
     ///
     /// We don't have a way to invalidate per-loop dispositions. Clear and
     /// recompute is simpler.
     void forgetLoopDispositions(const Loop *L) { LoopDispositions.clear(); }
 
     /// Determine the minimum number of zero bits that S is guaranteed to end in
     /// (at every loop iteration).  It is, at the same time, the minimum number
     /// of times S is divisible by 2.  For example, given {4,+,8} it returns 2.
     /// If S is guaranteed to be 0, it returns the bitwidth of S.
     uint32_t GetMinTrailingZeros(const SCEV *S);
 
     /// Determine the unsigned range for a particular SCEV.
     ///
     ConstantRange getUnsignedRange(const SCEV *S) {
       return getRange(S, HINT_RANGE_UNSIGNED);
     }
 
     /// Determine the signed range for a particular SCEV.
     ///
     ConstantRange getSignedRange(const SCEV *S) {
       return getRange(S, HINT_RANGE_SIGNED);
     }
 
     /// Test if the given expression is known to be negative.
     ///
     bool isKnownNegative(const SCEV *S);
 
     /// Test if the given expression is known to be positive.
     ///
     bool isKnownPositive(const SCEV *S);
 
     /// Test if the given expression is known to be non-negative.
     ///
     bool isKnownNonNegative(const SCEV *S);
 
     /// Test if the given expression is known to be non-positive.
     ///
     bool isKnownNonPositive(const SCEV *S);
 
     /// Test if the given expression is known to be non-zero.
     ///
     bool isKnownNonZero(const SCEV *S);
 
     /// Test if the given expression is known to satisfy the condition described
     /// by Pred, LHS, and RHS.
     ///
     bool isKnownPredicate(ICmpInst::Predicate Pred,
                           const SCEV *LHS, const SCEV *RHS);
 
     /// Return true if the result of the predicate LHS `Pred` RHS is loop
     /// invariant with respect to L.  Set InvariantPred, InvariantLHS and
     /// InvariantLHS so that InvariantLHS `InvariantPred` InvariantRHS is the
     /// loop invariant form of LHS `Pred` RHS.
     bool isLoopInvariantPredicate(ICmpInst::Predicate Pred, const SCEV *LHS,
                                   const SCEV *RHS, const Loop *L,
                                   ICmpInst::Predicate &InvariantPred,
                                   const SCEV *&InvariantLHS,
                                   const SCEV *&InvariantRHS);
 
     /// Simplify LHS and RHS in a comparison with predicate Pred. Return true
     /// iff any changes were made. If the operands are provably equal or
     /// unequal, LHS and RHS are set to the same value and Pred is set to either
     /// ICMP_EQ or ICMP_NE.
     ///
     bool SimplifyICmpOperands(ICmpInst::Predicate &Pred,
                               const SCEV *&LHS,
                               const SCEV *&RHS,
                               unsigned Depth = 0);
 
     /// Return the "disposition" of the given SCEV with respect to the given
     /// loop.
     LoopDisposition getLoopDisposition(const SCEV *S, const Loop *L);
 
     /// Return true if the value of the given SCEV is unchanging in the
     /// specified loop.
     bool isLoopInvariant(const SCEV *S, const Loop *L);
 
     /// Return true if the given SCEV changes value in a known way in the
     /// specified loop.  This property being true implies that the value is
     /// variant in the loop AND that we can emit an expression to compute the
     /// value of the expression at any particular loop iteration.
     bool hasComputableLoopEvolution(const SCEV *S, const Loop *L);
 
     /// Return the "disposition" of the given SCEV with respect to the given
     /// block.
     BlockDisposition getBlockDisposition(const SCEV *S, const BasicBlock *BB);
 
     /// Return true if elements that makes up the given SCEV dominate the
     /// specified basic block.
     bool dominates(const SCEV *S, const BasicBlock *BB);
 
     /// Return true if elements that makes up the given SCEV properly dominate
     /// the specified basic block.
     bool properlyDominates(const SCEV *S, const BasicBlock *BB);
 
     /// Test whether the given SCEV has Op as a direct or indirect operand.
     bool hasOperand(const SCEV *S, const SCEV *Op) const;
 
     /// Return the size of an element read or written by Inst.
     const SCEV *getElementSize(Instruction *Inst);
 
     /// Compute the array dimensions Sizes from the set of Terms extracted from
     /// the memory access function of this SCEVAddRecExpr (second step of
     /// delinearization).
     void findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
                              SmallVectorImpl<const SCEV *> &Sizes,
                              const SCEV *ElementSize) const;
 
     void print(raw_ostream &OS) const;
     void verify() const;
 
     /// Collect parametric terms occurring in step expressions (first step of
     /// delinearization).
     void collectParametricTerms(const SCEV *Expr,
                                 SmallVectorImpl<const SCEV *> &Terms);
 
 
 
     /// Return in Subscripts the access functions for each dimension in Sizes
     /// (third step of delinearization).
     void computeAccessFunctions(const SCEV *Expr,
                                 SmallVectorImpl<const SCEV *> &Subscripts,
                                 SmallVectorImpl<const SCEV *> &Sizes);
 
     /// Split this SCEVAddRecExpr into two vectors of SCEVs representing the
     /// subscripts and sizes of an array access.
     ///
     /// The delinearization is a 3 step process: the first two steps compute the
     /// sizes of each subscript and the third step computes the access functions
     /// for the delinearized array:
     ///
     /// 1. Find the terms in the step functions
     /// 2. Compute the array size
     /// 3. Compute the access function: divide the SCEV by the array size
     ///    starting with the innermost dimensions found in step 2. The Quotient
     ///    is the SCEV to be divided in the next step of the recursion. The
     ///    Remainder is the subscript of the innermost dimension. Loop over all
     ///    array dimensions computed in step 2.
     ///
     /// To compute a uniform array size for several memory accesses to the same
     /// object, one can collect in step 1 all the step terms for all the memory
     /// accesses, and compute in step 2 a unique array shape. This guarantees
     /// that the array shape will be the same across all memory accesses.
     ///
     /// FIXME: We could derive the result of steps 1 and 2 from a description of
     /// the array shape given in metadata.
     ///
     /// Example:
     ///
     /// A[][n][m]
     ///
     /// for i
     ///   for j
     ///     for k
     ///       A[j+k][2i][5i] =
     ///
     /// The initial SCEV:
     ///
     /// A[{{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k]
     ///
     /// 1. Find the different terms in the step functions:
     /// -> [2*m, 5, n*m, n*m]
     ///
     /// 2. Compute the array size: sort and unique them
     /// -> [n*m, 2*m, 5]
     /// find the GCD of all the terms = 1
     /// divide by the GCD and erase constant terms
     /// -> [n*m, 2*m]
     /// GCD = m
     /// divide by GCD -> [n, 2]
     /// remove constant terms
     /// -> [n]
     /// size of the array is A[unknown][n][m]
     ///
     /// 3. Compute the access function
     /// a. Divide {{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k by the innermost size m
     /// Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k
     /// Remainder: {{{0,+,5}_i, +, 0}_j, +, 0}_k
     /// The remainder is the subscript of the innermost array dimension: [5i].
     ///
     /// b. Divide Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k by next outer size n
     /// Quotient: {{{0,+,0}_i, +, 1}_j, +, 1}_k
     /// Remainder: {{{0,+,2}_i, +, 0}_j, +, 0}_k
     /// The Remainder is the subscript of the next array dimension: [2i].
     ///
     /// The subscript of the outermost dimension is the Quotient: [j+k].
     ///
     /// Overall, we have: A[][n][m], and the access function: A[j+k][2i][5i].
     void delinearize(const SCEV *Expr,
                      SmallVectorImpl<const SCEV *> &Subscripts,
                      SmallVectorImpl<const SCEV *> &Sizes,
                      const SCEV *ElementSize);
 
     /// Return the DataLayout associated with the module this SCEV instance is
     /// operating on.
     const DataLayout &getDataLayout() const {
       return F.getParent()->getDataLayout();
     }
 
     const SCEVPredicate *getEqualPredicate(const SCEVUnknown *LHS,
                                            const SCEVConstant *RHS);
 
     const SCEVPredicate *
     getWrapPredicate(const SCEVAddRecExpr *AR,
                      SCEVWrapPredicate::IncrementWrapFlags AddedFlags);
 
     /// Re-writes the SCEV according to the Predicates in \p A.
     const SCEV *rewriteUsingPredicate(const SCEV *S, const Loop *L,
                                       SCEVUnionPredicate &A);
     /// Tries to convert the \p S expression to an AddRec expression,
     /// adding additional predicates to \p Preds as required.
     const SCEVAddRecExpr *
     convertSCEVToAddRecWithPredicates(const SCEV *S, const Loop *L,
                                       SCEVUnionPredicate &Preds);
 
   private:
     /// Compute the backedge taken count knowing the interval difference, the
     /// stride and presence of the equality in the comparison.
     const SCEV *computeBECount(const SCEV *Delta, const SCEV *Stride,
                                bool Equality);
 
     /// Verify if an linear IV with positive stride can overflow when in a
     /// less-than comparison, knowing the invariant term of the comparison,
     /// the stride and the knowledge of NSW/NUW flags on the recurrence.
     bool doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
                             bool IsSigned, bool NoWrap);
 
     /// Verify if an linear IV with negative stride can overflow when in a
     /// greater-than comparison, knowing the invariant term of the comparison,
     /// the stride and the knowledge of NSW/NUW flags on the recurrence.
     bool doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
                             bool IsSigned, bool NoWrap);
 
   private:
     FoldingSet<SCEV> UniqueSCEVs;
     FoldingSet<SCEVPredicate> UniquePreds;
     BumpPtrAllocator SCEVAllocator;
 
     /// The head of a linked list of all SCEVUnknown values that have been
     /// allocated. This is used by releaseMemory to locate them all and call
     /// their destructors.
     SCEVUnknown *FirstUnknown;
   };
 
   /// Analysis pass that exposes the \c ScalarEvolution for a function.
   class ScalarEvolutionAnalysis
       : public AnalysisInfoMixin<ScalarEvolutionAnalysis> {
     friend AnalysisInfoMixin<ScalarEvolutionAnalysis>;
     static char PassID;
 
   public:
     typedef ScalarEvolution Result;
 
     ScalarEvolution run(Function &F, AnalysisManager<Function> &AM);
   };
 
   /// Printer pass for the \c ScalarEvolutionAnalysis results.
   class ScalarEvolutionPrinterPass
       : public PassInfoMixin<ScalarEvolutionPrinterPass> {
     raw_ostream &OS;
 
   public:
     explicit ScalarEvolutionPrinterPass(raw_ostream &OS) : OS(OS) {}
     PreservedAnalyses run(Function &F, AnalysisManager<Function> &AM);
   };
 
   class ScalarEvolutionWrapperPass : public FunctionPass {
     std::unique_ptr<ScalarEvolution> SE;
 
   public:
     static char ID;
 
     ScalarEvolutionWrapperPass();
 
     ScalarEvolution &getSE() { return *SE; }
     const ScalarEvolution &getSE() const { return *SE; }
 
     bool runOnFunction(Function &F) override;
     void releaseMemory() override;
     void getAnalysisUsage(AnalysisUsage &AU) const override;
     void print(raw_ostream &OS, const Module * = nullptr) const override;
     void verifyAnalysis() const override;
   };
 
   /// An interface layer with SCEV used to manage how we see SCEV expressions
   /// for values in the context of existing predicates. We can add new
   /// predicates, but we cannot remove them.
   ///
   /// This layer has multiple purposes:
   ///   - provides a simple interface for SCEV versioning.
   ///   - guarantees that the order of transformations applied on a SCEV
   ///     expression for a single Value is consistent across two different
   ///     getSCEV calls. This means that, for example, once we've obtained
   ///     an AddRec expression for a certain value through expression
   ///     rewriting, we will continue to get an AddRec expression for that
   ///     Value.
   ///   - lowers the number of expression rewrites.
   class PredicatedScalarEvolution {
   public:
     PredicatedScalarEvolution(ScalarEvolution &SE, Loop &L);
     const SCEVUnionPredicate &getUnionPredicate() const;
 
     /// Returns the SCEV expression of V, in the context of the current SCEV
     /// predicate.  The order of transformations applied on the expression of V
     /// returned by ScalarEvolution is guaranteed to be preserved, even when
     /// adding new predicates.
     const SCEV *getSCEV(Value *V);
 
     /// Get the (predicated) backedge count for the analyzed loop.
     const SCEV *getBackedgeTakenCount();
 
     /// Adds a new predicate.
     void addPredicate(const SCEVPredicate &Pred);
 
     /// Attempts to produce an AddRecExpr for V by adding additional SCEV
     /// predicates. If we can't transform the expression into an AddRecExpr we
     /// return nullptr and not add additional SCEV predicates to the current
     /// context.
     const SCEVAddRecExpr *getAsAddRec(Value *V);
 
     /// Proves that V doesn't overflow by adding SCEV predicate.
     void setNoOverflow(Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags);
 
     /// Returns true if we've proved that V doesn't wrap by means of a SCEV
     /// predicate.
     bool hasNoOverflow(Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags);
 
     /// Returns the ScalarEvolution analysis used.
     ScalarEvolution *getSE() const { return &SE; }
 
     /// We need to explicitly define the copy constructor because of FlagsMap.
     PredicatedScalarEvolution(const PredicatedScalarEvolution&);
 
     /// Print the SCEV mappings done by the Predicated Scalar Evolution.
     /// The printed text is indented by \p Depth.
     void print(raw_ostream &OS, unsigned Depth) const;
 
   private:
     /// Increments the version number of the predicate.  This needs to be called
     /// every time the SCEV predicate changes.
     void updateGeneration();
 
     /// Holds a SCEV and the version number of the SCEV predicate used to
     /// perform the rewrite of the expression.
     typedef std::pair<unsigned, const SCEV *> RewriteEntry;
 
     /// Maps a SCEV to the rewrite result of that SCEV at a certain version
     /// number. If this number doesn't match the current Generation, we will
     /// need to do a rewrite. To preserve the transformation order of previous
     /// rewrites, we will rewrite the previous result instead of the original
     /// SCEV.
     DenseMap<const SCEV *, RewriteEntry> RewriteMap;
 
     /// Records what NoWrap flags we've added to a Value *.
     ValueMap<Value *, SCEVWrapPredicate::IncrementWrapFlags> FlagsMap;
 
     /// The ScalarEvolution analysis.
     ScalarEvolution &SE;
 
     /// The analyzed Loop.
     const Loop &L;
 
     /// The SCEVPredicate that forms our context. We will rewrite all
     /// expressions assuming that this predicate true.
     SCEVUnionPredicate Preds;
 
     /// Marks the version of the SCEV predicate used. When rewriting a SCEV
     /// expression we mark it with the version of the predicate. We use this to
     /// figure out if the predicate has changed from the last rewrite of the
     /// SCEV. If so, we need to perform a new rewrite.
     unsigned Generation;
 
     /// The backedge taken count.
     const SCEV *BackedgeCount;
   };
 }
 
 #endif
Index: head/contrib/llvm/include/llvm/Analysis/ScalarEvolutionExpander.h
===================================================================
--- head/contrib/llvm/include/llvm/Analysis/ScalarEvolutionExpander.h	(revision 312831)
+++ head/contrib/llvm/include/llvm/Analysis/ScalarEvolutionExpander.h	(revision 312832)
@@ -1,384 +1,396 @@
 //===---- llvm/Analysis/ScalarEvolutionExpander.h - SCEV Exprs --*- C++ -*-===//
 //
 //                     The LLVM Compiler Infrastructure
 //
 // This file is distributed under the University of Illinois Open Source
 // License. See LICENSE.TXT for details.
 //
 //===----------------------------------------------------------------------===//
 //
 // This file defines the classes used to generate code from scalar expressions.
 //
 //===----------------------------------------------------------------------===//
 
 #ifndef LLVM_ANALYSIS_SCALAREVOLUTIONEXPANDER_H
 #define LLVM_ANALYSIS_SCALAREVOLUTIONEXPANDER_H
 
+#include "llvm/ADT/Optional.h"
 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
 #include "llvm/Analysis/ScalarEvolutionNormalization.h"
 #include "llvm/Analysis/TargetFolder.h"
 #include "llvm/IR/IRBuilder.h"
 #include "llvm/IR/ValueHandle.h"
 #include <set>
 
 namespace llvm {
   class TargetTransformInfo;
 
   /// Return true if the given expression is safe to expand in the sense that
   /// all materialized values are safe to speculate.
   bool isSafeToExpand(const SCEV *S, ScalarEvolution &SE);
 
   /// This class uses information about analyze scalars to
   /// rewrite expressions in canonical form.
   ///
   /// Clients should create an instance of this class when rewriting is needed,
   /// and destroy it when finished to allow the release of the associated
   /// memory.
   class SCEVExpander : public SCEVVisitor<SCEVExpander, Value*> {
     ScalarEvolution &SE;
     const DataLayout &DL;
 
     // New instructions receive a name to identifies them with the current pass.
     const char* IVName;
 
     // InsertedExpressions caches Values for reuse, so must track RAUW.
     std::map<std::pair<const SCEV *, Instruction *>, TrackingVH<Value> >
       InsertedExpressions;
     // InsertedValues only flags inserted instructions so needs no RAUW.
     std::set<AssertingVH<Value> > InsertedValues;
     std::set<AssertingVH<Value> > InsertedPostIncValues;
 
     /// A memoization of the "relevant" loop for a given SCEV.
     DenseMap<const SCEV *, const Loop *> RelevantLoops;
 
     /// \brief Addrecs referring to any of the given loops are expanded
     /// in post-inc mode. For example, expanding {1,+,1}<L> in post-inc mode
     /// returns the add instruction that adds one to the phi for {0,+,1}<L>,
     /// as opposed to a new phi starting at 1. This is only supported in
     /// non-canonical mode.
     PostIncLoopSet PostIncLoops;
 
     /// \brief When this is non-null, addrecs expanded in the loop it indicates
     /// should be inserted with increments at IVIncInsertPos.
     const Loop *IVIncInsertLoop;
 
     /// \brief When expanding addrecs in the IVIncInsertLoop loop, insert the IV
     /// increment at this position.
     Instruction *IVIncInsertPos;
 
     /// \brief Phis that complete an IV chain. Reuse
     std::set<AssertingVH<PHINode> > ChainedPhis;
 
     /// \brief When true, expressions are expanded in "canonical" form. In
     /// particular, addrecs are expanded as arithmetic based on a canonical
     /// induction variable. When false, expression are expanded in a more
     /// literal form.
     bool CanonicalMode;
 
     /// \brief When invoked from LSR, the expander is in "strength reduction"
     /// mode. The only difference is that phi's are only reused if they are
     /// already in "expanded" form.
     bool LSRMode;
 
     typedef IRBuilder<TargetFolder> BuilderType;
     BuilderType Builder;
 
     // RAII object that stores the current insertion point and restores it when
     // the object is destroyed. This includes the debug location.  Duplicated
     // from InsertPointGuard to add SetInsertPoint() which is used to updated
     // InsertPointGuards stack when insert points are moved during SCEV
     // expansion.
     class SCEVInsertPointGuard {
       IRBuilderBase &Builder;
       AssertingVH<BasicBlock> Block;
       BasicBlock::iterator Point;
       DebugLoc DbgLoc;
       SCEVExpander *SE;
 
       SCEVInsertPointGuard(const SCEVInsertPointGuard &) = delete;
       SCEVInsertPointGuard &operator=(const SCEVInsertPointGuard &) = delete;
 
     public:
       SCEVInsertPointGuard(IRBuilderBase &B, SCEVExpander *SE)
           : Builder(B), Block(B.GetInsertBlock()), Point(B.GetInsertPoint()),
             DbgLoc(B.getCurrentDebugLocation()), SE(SE) {
         SE->InsertPointGuards.push_back(this);
       }
 
       ~SCEVInsertPointGuard() {
         // These guards should always created/destroyed in FIFO order since they
         // are used to guard lexically scoped blocks of code in
         // ScalarEvolutionExpander.
         assert(SE->InsertPointGuards.back() == this);
         SE->InsertPointGuards.pop_back();
         Builder.restoreIP(IRBuilderBase::InsertPoint(Block, Point));
         Builder.SetCurrentDebugLocation(DbgLoc);
       }
 
       BasicBlock::iterator GetInsertPoint() const { return Point; }
       void SetInsertPoint(BasicBlock::iterator I) { Point = I; }
     };
 
     /// Stack of pointers to saved insert points, used to keep insert points
     /// consistent when instructions are moved.
     SmallVector<SCEVInsertPointGuard *, 8> InsertPointGuards;
 
 #ifndef NDEBUG
     const char *DebugType;
 #endif
 
     friend struct SCEVVisitor<SCEVExpander, Value*>;
 
   public:
     /// \brief Construct a SCEVExpander in "canonical" mode.
     explicit SCEVExpander(ScalarEvolution &se, const DataLayout &DL,
                           const char *name)
         : SE(se), DL(DL), IVName(name), IVIncInsertLoop(nullptr),
           IVIncInsertPos(nullptr), CanonicalMode(true), LSRMode(false),
           Builder(se.getContext(), TargetFolder(DL)) {
 #ifndef NDEBUG
       DebugType = "";
 #endif
     }
 
     ~SCEVExpander() {
       // Make sure the insert point guard stack is consistent.
       assert(InsertPointGuards.empty());
     }
 
 #ifndef NDEBUG
     void setDebugType(const char* s) { DebugType = s; }
 #endif
 
     /// \brief Erase the contents of the InsertedExpressions map so that users
     /// trying to expand the same expression into multiple BasicBlocks or
     /// different places within the same BasicBlock can do so.
     void clear() {
       InsertedExpressions.clear();
       InsertedValues.clear();
       InsertedPostIncValues.clear();
       ChainedPhis.clear();
     }
 
     /// \brief Return true for expressions that may incur non-trivial cost to
     /// evaluate at runtime.
     ///
     /// At is an optional parameter which specifies point in code where user is
     /// going to expand this expression. Sometimes this knowledge can lead to a
     /// more accurate cost estimation.
     bool isHighCostExpansion(const SCEV *Expr, Loop *L,
                              const Instruction *At = nullptr) {
       SmallPtrSet<const SCEV *, 8> Processed;
       return isHighCostExpansionHelper(Expr, L, At, Processed);
     }
 
     /// \brief 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 *getOrInsertCanonicalInductionVariable(const Loop *L, Type *Ty);
 
     /// \brief Return the induction variable increment's IV operand.
     Instruction *getIVIncOperand(Instruction *IncV, Instruction *InsertPos,
                                  bool allowScale);
 
     /// \brief Utility for hoisting an IV increment.
     bool hoistIVInc(Instruction *IncV, Instruction *InsertPos);
 
     /// \brief replace congruent phis with their most canonical
     /// representative. Return the number of phis eliminated.
     unsigned replaceCongruentIVs(Loop *L, const DominatorTree *DT,
                                  SmallVectorImpl<WeakVH> &DeadInsts,
                                  const TargetTransformInfo *TTI = nullptr);
 
     /// \brief Insert code to directly compute the specified SCEV expression
     /// into the program.  The inserted code is inserted into the specified
     /// block.
     Value *expandCodeFor(const SCEV *SH, Type *Ty, Instruction *I);
 
     /// \brief Insert code to directly compute the specified SCEV expression
     /// into the program.  The inserted code is inserted into the SCEVExpander's
     /// current insertion point. If a type is specified, the result will be
     /// expanded to have that type, with a cast if necessary.
     Value *expandCodeFor(const SCEV *SH, Type *Ty = nullptr);
 
 
     /// \brief Generates a code sequence that evaluates this predicate.
     /// The inserted instructions will be at position \p Loc.
     /// The result will be of type i1 and will have a value of 0 when the
     /// predicate is false and 1 otherwise.
     Value *expandCodeForPredicate(const SCEVPredicate *Pred, Instruction *Loc);
 
     /// \brief A specialized variant of expandCodeForPredicate, handling the
     /// case when we are expanding code for a SCEVEqualPredicate.
     Value *expandEqualPredicate(const SCEVEqualPredicate *Pred,
                                 Instruction *Loc);
 
     /// \brief Generates code that evaluates if the \p AR expression will
     /// overflow.
     Value *generateOverflowCheck(const SCEVAddRecExpr *AR, Instruction *Loc,
                                  bool Signed);
 
     /// \brief A specialized variant of expandCodeForPredicate, handling the
     /// case when we are expanding code for a SCEVWrapPredicate.
     Value *expandWrapPredicate(const SCEVWrapPredicate *P, Instruction *Loc);
 
     /// \brief A specialized variant of expandCodeForPredicate, handling the
     /// case when we are expanding code for a SCEVUnionPredicate.
     Value *expandUnionPredicate(const SCEVUnionPredicate *Pred,
                                 Instruction *Loc);
 
     /// \brief Set the current IV increment loop and position.
     void setIVIncInsertPos(const Loop *L, Instruction *Pos) {
       assert(!CanonicalMode &&
              "IV increment positions are not supported in CanonicalMode");
       IVIncInsertLoop = L;
       IVIncInsertPos = Pos;
     }
 
     /// \brief Enable post-inc expansion for addrecs referring to the given
     /// loops. Post-inc expansion is only supported in non-canonical mode.
     void setPostInc(const PostIncLoopSet &L) {
       assert(!CanonicalMode &&
              "Post-inc expansion is not supported in CanonicalMode");
       PostIncLoops = L;
     }
 
     /// \brief Disable all post-inc expansion.
     void clearPostInc() {
       PostIncLoops.clear();
 
       // When we change the post-inc loop set, cached expansions may no
       // longer be valid.
       InsertedPostIncValues.clear();
     }
 
     /// \brief Disable the behavior of expanding expressions in canonical form
     /// rather than in a more literal form. Non-canonical mode is useful for
     /// late optimization passes.
     void disableCanonicalMode() { CanonicalMode = false; }
 
     void enableLSRMode() { LSRMode = true; }
 
     /// \brief Set the current insertion point. This is useful if multiple calls
     /// to expandCodeFor() are going to be made with the same insert point and
     /// the insert point may be moved during one of the expansions (e.g. if the
     /// insert point is not a block terminator).
     void setInsertPoint(Instruction *IP) {
       assert(IP);
       Builder.SetInsertPoint(IP);
     }
 
     /// \brief Clear the current insertion point. This is useful if the
     /// instruction that had been serving as the insertion point may have been
     /// deleted.
     void clearInsertPoint() {
       Builder.ClearInsertionPoint();
     }
 
     /// \brief Return true if the specified instruction was inserted by the code
     /// rewriter.  If so, the client should not modify the instruction.
     bool isInsertedInstruction(Instruction *I) const {
       return InsertedValues.count(I) || InsertedPostIncValues.count(I);
     }
 
     void setChainedPhi(PHINode *PN) { ChainedPhis.insert(PN); }
 
-    /// \brief Try to find LLVM IR value for S available at the point At.
+    /// Try to find existing LLVM IR value for S available at the point At.
+    Value *getExactExistingExpansion(const SCEV *S, const Instruction *At,
+                                     Loop *L);
+
+    /// Try to find the ValueOffsetPair for S. The function is mainly
+    /// used to check whether S can be expanded cheaply.
+    /// If this returns a non-None value, we know we can codegen the
+    /// `ValueOffsetPair` into a suitable expansion identical with S
+    /// so that S can be expanded cheaply.
     ///
     /// L is a hint which tells in which loop to look for the suitable value.
     /// On success return value which is equivalent to the expanded S at point
     /// At. Return nullptr if value was not found.
     ///
     /// Note that this function does not perform an exhaustive search. I.e if it
     /// didn't find any value it does not mean that there is no such value.
-    Value *findExistingExpansion(const SCEV *S, const Instruction *At, Loop *L);
+    ///
+    Optional<ScalarEvolution::ValueOffsetPair>
+    getRelatedExistingExpansion(const SCEV *S, const Instruction *At, Loop *L);
 
   private:
     LLVMContext &getContext() const { return SE.getContext(); }
 
     /// \brief Recursive helper function for isHighCostExpansion.
     bool isHighCostExpansionHelper(const SCEV *S, Loop *L,
                                    const Instruction *At,
                                    SmallPtrSetImpl<const SCEV *> &Processed);
 
     /// \brief Insert the specified binary operator, doing a small amount
     /// of work to avoid inserting an obviously redundant operation.
     Value *InsertBinop(Instruction::BinaryOps Opcode, Value *LHS, Value *RHS);
 
     /// \brief 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 or creating a new
     /// one.
     Value *ReuseOrCreateCast(Value *V, Type *Ty,
                              Instruction::CastOps Op,
                              BasicBlock::iterator IP);
 
     /// \brief 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 *InsertNoopCastOfTo(Value *V, Type *Ty);
 
     /// \brief Expand a SCEVAddExpr with a pointer type into a GEP
     /// instead of using ptrtoint+arithmetic+inttoptr.
     Value *expandAddToGEP(const SCEV *const *op_begin,
                           const SCEV *const *op_end,
                           PointerType *PTy, Type *Ty, Value *V);
 
     /// \brief Find a previous Value in ExprValueMap for expand.
-    Value *FindValueInExprValueMap(const SCEV *S, const Instruction *InsertPt);
+    ScalarEvolution::ValueOffsetPair
+    FindValueInExprValueMap(const SCEV *S, const Instruction *InsertPt);
 
     Value *expand(const SCEV *S);
 
     /// \brief Determine the most "relevant" loop for the given SCEV.
     const Loop *getRelevantLoop(const SCEV *);
 
     Value *visitConstant(const SCEVConstant *S) {
       return S->getValue();
     }
 
     Value *visitTruncateExpr(const SCEVTruncateExpr *S);
 
     Value *visitZeroExtendExpr(const SCEVZeroExtendExpr *S);
 
     Value *visitSignExtendExpr(const SCEVSignExtendExpr *S);
 
     Value *visitAddExpr(const SCEVAddExpr *S);
 
     Value *visitMulExpr(const SCEVMulExpr *S);
 
     Value *visitUDivExpr(const SCEVUDivExpr *S);
 
     Value *visitAddRecExpr(const SCEVAddRecExpr *S);
 
     Value *visitSMaxExpr(const SCEVSMaxExpr *S);
 
     Value *visitUMaxExpr(const SCEVUMaxExpr *S);
 
     Value *visitUnknown(const SCEVUnknown *S) {
       return S->getValue();
     }
 
     void rememberInstruction(Value *I);
 
     bool isNormalAddRecExprPHI(PHINode *PN, Instruction *IncV, const Loop *L);
 
     bool isExpandedAddRecExprPHI(PHINode *PN, Instruction *IncV, const Loop *L);
 
     Value *expandAddRecExprLiterally(const SCEVAddRecExpr *);
     PHINode *getAddRecExprPHILiterally(const SCEVAddRecExpr *Normalized,
                                        const Loop *L,
                                        Type *ExpandTy,
                                        Type *IntTy,
                                        Type *&TruncTy,
                                        bool &InvertStep);
     Value *expandIVInc(PHINode *PN, Value *StepV, const Loop *L,
                        Type *ExpandTy, Type *IntTy, bool useSubtract);
 
     void hoistBeforePos(DominatorTree *DT, Instruction *InstToHoist,
                         Instruction *Pos, PHINode *LoopPhi);
 
     void fixupInsertPoints(Instruction *I);
   };
 }
 
 #endif
Index: head/contrib/llvm/lib/Analysis/ScalarEvolution.cpp
===================================================================
--- head/contrib/llvm/lib/Analysis/ScalarEvolution.cpp	(revision 312831)
+++ head/contrib/llvm/lib/Analysis/ScalarEvolution.cpp	(revision 312832)
@@ -1,10467 +1,10509 @@
 //===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
 //
 //                     The LLVM Compiler Infrastructure
 //
 // This file is distributed under the University of Illinois Open Source
 // License. See LICENSE.TXT for details.
 //
 //===----------------------------------------------------------------------===//
 //
 // This file contains the implementation of the scalar evolution analysis
 // engine, which is used primarily to analyze expressions involving induction
 // variables in loops.
 //
 // There are several aspects to this library.  First is the representation of
 // scalar expressions, which are represented as subclasses of the SCEV class.
 // These classes are used to represent certain types of subexpressions that we
 // can handle. We only create one SCEV of a particular shape, so
 // pointer-comparisons for equality are legal.
 //
 // One important aspect of the SCEV objects is that they are never cyclic, even
 // if there is a cycle in the dataflow for an expression (ie, a PHI node).  If
 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
 // recurrence) then we represent it directly as a recurrence node, otherwise we
 // represent it as a SCEVUnknown node.
 //
 // In addition to being able to represent expressions of various types, we also
 // have folders that are used to build the *canonical* representation for a
 // particular expression.  These folders are capable of using a variety of
 // rewrite rules to simplify the expressions.
 //
 // Once the folders are defined, we can implement the more interesting
 // higher-level code, such as the code that recognizes PHI nodes of various
 // types, computes the execution count of a loop, etc.
 //
 // TODO: We should use these routines and value representations to implement
 // dependence analysis!
 //
 //===----------------------------------------------------------------------===//
 //
 // There are several good references for the techniques used in this analysis.
 //
 //  Chains of recurrences -- a method to expedite the evaluation
 //  of closed-form functions
 //  Olaf Bachmann, Paul S. Wang, Eugene V. Zima
 //
 //  On computational properties of chains of recurrences
 //  Eugene V. Zima
 //
 //  Symbolic Evaluation of Chains of Recurrences for Loop Optimization
 //  Robert A. van Engelen
 //
 //  Efficient Symbolic Analysis for Optimizing Compilers
 //  Robert A. van Engelen
 //
 //  Using the chains of recurrences algebra for data dependence testing and
 //  induction variable substitution
 //  MS Thesis, Johnie Birch
 //
 //===----------------------------------------------------------------------===//
 
 #include "llvm/Analysis/ScalarEvolution.h"
 #include "llvm/ADT/Optional.h"
 #include "llvm/ADT/STLExtras.h"
 #include "llvm/ADT/SmallPtrSet.h"
 #include "llvm/ADT/Statistic.h"
 #include "llvm/Analysis/AssumptionCache.h"
 #include "llvm/Analysis/ConstantFolding.h"
 #include "llvm/Analysis/InstructionSimplify.h"
 #include "llvm/Analysis/LoopInfo.h"
 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
 #include "llvm/Analysis/TargetLibraryInfo.h"
 #include "llvm/Analysis/ValueTracking.h"
 #include "llvm/IR/ConstantRange.h"
 #include "llvm/IR/Constants.h"
 #include "llvm/IR/DataLayout.h"
 #include "llvm/IR/DerivedTypes.h"
 #include "llvm/IR/Dominators.h"
 #include "llvm/IR/GetElementPtrTypeIterator.h"
 #include "llvm/IR/GlobalAlias.h"
 #include "llvm/IR/GlobalVariable.h"
 #include "llvm/IR/InstIterator.h"
 #include "llvm/IR/Instructions.h"
 #include "llvm/IR/LLVMContext.h"
 #include "llvm/IR/Metadata.h"
 #include "llvm/IR/Operator.h"
 #include "llvm/IR/PatternMatch.h"
 #include "llvm/Support/CommandLine.h"
 #include "llvm/Support/Debug.h"
 #include "llvm/Support/ErrorHandling.h"
 #include "llvm/Support/MathExtras.h"
 #include "llvm/Support/raw_ostream.h"
 #include "llvm/Support/SaveAndRestore.h"
 #include <algorithm>
 using namespace llvm;
 
 #define DEBUG_TYPE "scalar-evolution"
 
 STATISTIC(NumArrayLenItCounts,
           "Number of trip counts computed with array length");
 STATISTIC(NumTripCountsComputed,
           "Number of loops with predictable loop counts");
 STATISTIC(NumTripCountsNotComputed,
           "Number of loops without predictable loop counts");
 STATISTIC(NumBruteForceTripCountsComputed,
           "Number of loops with trip counts computed by force");
 
 static cl::opt<unsigned>
 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
                         cl::desc("Maximum number of iterations SCEV will "
                                  "symbolically execute a constant "
                                  "derived loop"),
                         cl::init(100));
 
 // FIXME: Enable this with EXPENSIVE_CHECKS when the test suite is clean.
 static cl::opt<bool>
 VerifySCEV("verify-scev",
            cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
 static cl::opt<bool>
     VerifySCEVMap("verify-scev-maps",
                   cl::desc("Verify no dangling value in ScalarEvolution's "
                            "ExprValueMap (slow)"));
 
 //===----------------------------------------------------------------------===//
 //                           SCEV class definitions
 //===----------------------------------------------------------------------===//
 
 //===----------------------------------------------------------------------===//
 // Implementation of the SCEV class.
 //
 
 LLVM_DUMP_METHOD
 void SCEV::dump() const {
   print(dbgs());
   dbgs() << '\n';
 }
 
 void SCEV::print(raw_ostream &OS) const {
   switch (static_cast<SCEVTypes>(getSCEVType())) {
   case scConstant:
     cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
     return;
   case scTruncate: {
     const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
     const SCEV *Op = Trunc->getOperand();
     OS << "(trunc " << *Op->getType() << " " << *Op << " to "
        << *Trunc->getType() << ")";
     return;
   }
   case scZeroExtend: {
     const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
     const SCEV *Op = ZExt->getOperand();
     OS << "(zext " << *Op->getType() << " " << *Op << " to "
        << *ZExt->getType() << ")";
     return;
   }
   case scSignExtend: {
     const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
     const SCEV *Op = SExt->getOperand();
     OS << "(sext " << *Op->getType() << " " << *Op << " to "
        << *SExt->getType() << ")";
     return;
   }
   case scAddRecExpr: {
     const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
     OS << "{" << *AR->getOperand(0);
     for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
       OS << ",+," << *AR->getOperand(i);
     OS << "}<";
     if (AR->hasNoUnsignedWrap())
       OS << "nuw><";
     if (AR->hasNoSignedWrap())
       OS << "nsw><";
     if (AR->hasNoSelfWrap() &&
         !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
       OS << "nw><";
     AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
     OS << ">";
     return;
   }
   case scAddExpr:
   case scMulExpr:
   case scUMaxExpr:
   case scSMaxExpr: {
     const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
     const char *OpStr = nullptr;
     switch (NAry->getSCEVType()) {
     case scAddExpr: OpStr = " + "; break;
     case scMulExpr: OpStr = " * "; break;
     case scUMaxExpr: OpStr = " umax "; break;
     case scSMaxExpr: OpStr = " smax "; break;
     }
     OS << "(";
     for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
          I != E; ++I) {
       OS << **I;
       if (std::next(I) != E)
         OS << OpStr;
     }
     OS << ")";
     switch (NAry->getSCEVType()) {
     case scAddExpr:
     case scMulExpr:
       if (NAry->hasNoUnsignedWrap())
         OS << "<nuw>";
       if (NAry->hasNoSignedWrap())
         OS << "<nsw>";
     }
     return;
   }
   case scUDivExpr: {
     const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
     OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
     return;
   }
   case scUnknown: {
     const SCEVUnknown *U = cast<SCEVUnknown>(this);
     Type *AllocTy;
     if (U->isSizeOf(AllocTy)) {
       OS << "sizeof(" << *AllocTy << ")";
       return;
     }
     if (U->isAlignOf(AllocTy)) {
       OS << "alignof(" << *AllocTy << ")";
       return;
     }
 
     Type *CTy;
     Constant *FieldNo;
     if (U->isOffsetOf(CTy, FieldNo)) {
       OS << "offsetof(" << *CTy << ", ";
       FieldNo->printAsOperand(OS, false);
       OS << ")";
       return;
     }
 
     // Otherwise just print it normally.
     U->getValue()->printAsOperand(OS, false);
     return;
   }
   case scCouldNotCompute:
     OS << "***COULDNOTCOMPUTE***";
     return;
   }
   llvm_unreachable("Unknown SCEV kind!");
 }
 
 Type *SCEV::getType() const {
   switch (static_cast<SCEVTypes>(getSCEVType())) {
   case scConstant:
     return cast<SCEVConstant>(this)->getType();
   case scTruncate:
   case scZeroExtend:
   case scSignExtend:
     return cast<SCEVCastExpr>(this)->getType();
   case scAddRecExpr:
   case scMulExpr:
   case scUMaxExpr:
   case scSMaxExpr:
     return cast<SCEVNAryExpr>(this)->getType();
   case scAddExpr:
     return cast<SCEVAddExpr>(this)->getType();
   case scUDivExpr:
     return cast<SCEVUDivExpr>(this)->getType();
   case scUnknown:
     return cast<SCEVUnknown>(this)->getType();
   case scCouldNotCompute:
     llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
   }
   llvm_unreachable("Unknown SCEV kind!");
 }
 
 bool SCEV::isZero() const {
   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
     return SC->getValue()->isZero();
   return false;
 }
 
 bool SCEV::isOne() const {
   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
     return SC->getValue()->isOne();
   return false;
 }
 
 bool SCEV::isAllOnesValue() const {
   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
     return SC->getValue()->isAllOnesValue();
   return false;
 }
 
 bool SCEV::isNonConstantNegative() const {
   const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
   if (!Mul) return false;
 
   // If there is a constant factor, it will be first.
   const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
   if (!SC) return false;
 
   // Return true if the value is negative, this matches things like (-42 * V).
   return SC->getAPInt().isNegative();
 }
 
 SCEVCouldNotCompute::SCEVCouldNotCompute() :
   SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
 
 bool SCEVCouldNotCompute::classof(const SCEV *S) {
   return S->getSCEVType() == scCouldNotCompute;
 }
 
 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
   FoldingSetNodeID ID;
   ID.AddInteger(scConstant);
   ID.AddPointer(V);
   void *IP = nullptr;
   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
   SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
   UniqueSCEVs.InsertNode(S, IP);
   return S;
 }
 
 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
   return getConstant(ConstantInt::get(getContext(), Val));
 }
 
 const SCEV *
 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
   IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
   return getConstant(ConstantInt::get(ITy, V, isSigned));
 }
 
 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
                            unsigned SCEVTy, const SCEV *op, Type *ty)
   : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
 
 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
                                    const SCEV *op, Type *ty)
   : SCEVCastExpr(ID, scTruncate, op, ty) {
   assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
          "Cannot truncate non-integer value!");
 }
 
 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
                                        const SCEV *op, Type *ty)
   : SCEVCastExpr(ID, scZeroExtend, op, ty) {
   assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
          "Cannot zero extend non-integer value!");
 }
 
 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
                                        const SCEV *op, Type *ty)
   : SCEVCastExpr(ID, scSignExtend, op, ty) {
   assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
          "Cannot sign extend non-integer value!");
 }
 
 void SCEVUnknown::deleted() {
   // Clear this SCEVUnknown from various maps.
   SE->forgetMemoizedResults(this);
 
   // Remove this SCEVUnknown from the uniquing map.
   SE->UniqueSCEVs.RemoveNode(this);
 
   // Release the value.
   setValPtr(nullptr);
 }
 
 void SCEVUnknown::allUsesReplacedWith(Value *New) {
   // Clear this SCEVUnknown from various maps.
   SE->forgetMemoizedResults(this);
 
   // Remove this SCEVUnknown from the uniquing map.
   SE->UniqueSCEVs.RemoveNode(this);
 
   // Update this SCEVUnknown to point to the new value. This is needed
   // because there may still be outstanding SCEVs which still point to
   // this SCEVUnknown.
   setValPtr(New);
 }
 
 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
   if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
     if (VCE->getOpcode() == Instruction::PtrToInt)
       if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
         if (CE->getOpcode() == Instruction::GetElementPtr &&
             CE->getOperand(0)->isNullValue() &&
             CE->getNumOperands() == 2)
           if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
             if (CI->isOne()) {
               AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
                                  ->getElementType();
               return true;
             }
 
   return false;
 }
 
 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
   if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
     if (VCE->getOpcode() == Instruction::PtrToInt)
       if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
         if (CE->getOpcode() == Instruction::GetElementPtr &&
             CE->getOperand(0)->isNullValue()) {
           Type *Ty =
             cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
           if (StructType *STy = dyn_cast<StructType>(Ty))
             if (!STy->isPacked() &&
                 CE->getNumOperands() == 3 &&
                 CE->getOperand(1)->isNullValue()) {
               if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
                 if (CI->isOne() &&
                     STy->getNumElements() == 2 &&
                     STy->getElementType(0)->isIntegerTy(1)) {
                   AllocTy = STy->getElementType(1);
                   return true;
                 }
             }
         }
 
   return false;
 }
 
 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
   if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
     if (VCE->getOpcode() == Instruction::PtrToInt)
       if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
         if (CE->getOpcode() == Instruction::GetElementPtr &&
             CE->getNumOperands() == 3 &&
             CE->getOperand(0)->isNullValue() &&
             CE->getOperand(1)->isNullValue()) {
           Type *Ty =
             cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
           // Ignore vector types here so that ScalarEvolutionExpander doesn't
           // emit getelementptrs that index into vectors.
           if (Ty->isStructTy() || Ty->isArrayTy()) {
             CTy = Ty;
             FieldNo = CE->getOperand(2);
             return true;
           }
         }
 
   return false;
 }
 
 //===----------------------------------------------------------------------===//
 //                               SCEV Utilities
 //===----------------------------------------------------------------------===//
 
 namespace {
 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
 /// than the complexity of the RHS.  This comparator is used to canonicalize
 /// expressions.
 class SCEVComplexityCompare {
   const LoopInfo *const LI;
 public:
   explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
 
   // Return true or false if LHS is less than, or at least RHS, respectively.
   bool operator()(const SCEV *LHS, const SCEV *RHS) const {
     return compare(LHS, RHS) < 0;
   }
 
   // Return negative, zero, or positive, if LHS is less than, equal to, or
   // greater than RHS, respectively. A three-way result allows recursive
   // comparisons to be more efficient.
   int compare(const SCEV *LHS, const SCEV *RHS) const {
     // Fast-path: SCEVs are uniqued so we can do a quick equality check.
     if (LHS == RHS)
       return 0;
 
     // Primarily, sort the SCEVs by their getSCEVType().
     unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
     if (LType != RType)
       return (int)LType - (int)RType;
 
     // Aside from the getSCEVType() ordering, the particular ordering
     // isn't very important except that it's beneficial to be consistent,
     // so that (a + b) and (b + a) don't end up as different expressions.
     switch (static_cast<SCEVTypes>(LType)) {
     case scUnknown: {
       const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
       const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
 
       // Sort SCEVUnknown values with some loose heuristics. TODO: This is
       // not as complete as it could be.
       const Value *LV = LU->getValue(), *RV = RU->getValue();
 
       // Order pointer values after integer values. This helps SCEVExpander
       // form GEPs.
       bool LIsPointer = LV->getType()->isPointerTy(),
         RIsPointer = RV->getType()->isPointerTy();
       if (LIsPointer != RIsPointer)
         return (int)LIsPointer - (int)RIsPointer;
 
       // Compare getValueID values.
       unsigned LID = LV->getValueID(),
         RID = RV->getValueID();
       if (LID != RID)
         return (int)LID - (int)RID;
 
       // Sort arguments by their position.
       if (const Argument *LA = dyn_cast<Argument>(LV)) {
         const Argument *RA = cast<Argument>(RV);
         unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
         return (int)LArgNo - (int)RArgNo;
       }
 
       // For instructions, compare their loop depth, and their operand
       // count.  This is pretty loose.
       if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
         const Instruction *RInst = cast<Instruction>(RV);
 
         // Compare loop depths.
         const BasicBlock *LParent = LInst->getParent(),
           *RParent = RInst->getParent();
         if (LParent != RParent) {
           unsigned LDepth = LI->getLoopDepth(LParent),
             RDepth = LI->getLoopDepth(RParent);
           if (LDepth != RDepth)
             return (int)LDepth - (int)RDepth;
         }
 
         // Compare the number of operands.
         unsigned LNumOps = LInst->getNumOperands(),
           RNumOps = RInst->getNumOperands();
         return (int)LNumOps - (int)RNumOps;
       }
 
       return 0;
     }
 
     case scConstant: {
       const SCEVConstant *LC = cast<SCEVConstant>(LHS);
       const SCEVConstant *RC = cast<SCEVConstant>(RHS);
 
       // Compare constant values.
       const APInt &LA = LC->getAPInt();
       const APInt &RA = RC->getAPInt();
       unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
       if (LBitWidth != RBitWidth)
         return (int)LBitWidth - (int)RBitWidth;
       return LA.ult(RA) ? -1 : 1;
     }
 
     case scAddRecExpr: {
       const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
       const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
 
       // Compare addrec loop depths.
       const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
       if (LLoop != RLoop) {
         unsigned LDepth = LLoop->getLoopDepth(),
           RDepth = RLoop->getLoopDepth();
         if (LDepth != RDepth)
           return (int)LDepth - (int)RDepth;
       }
 
       // Addrec complexity grows with operand count.
       unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
       if (LNumOps != RNumOps)
         return (int)LNumOps - (int)RNumOps;
 
       // Lexicographically compare.
       for (unsigned i = 0; i != LNumOps; ++i) {
         long X = compare(LA->getOperand(i), RA->getOperand(i));
         if (X != 0)
           return X;
       }
 
       return 0;
     }
 
     case scAddExpr:
     case scMulExpr:
     case scSMaxExpr:
     case scUMaxExpr: {
       const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
       const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
 
       // Lexicographically compare n-ary expressions.
       unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
       if (LNumOps != RNumOps)
         return (int)LNumOps - (int)RNumOps;
 
       for (unsigned i = 0; i != LNumOps; ++i) {
         if (i >= RNumOps)
           return 1;
         long X = compare(LC->getOperand(i), RC->getOperand(i));
         if (X != 0)
           return X;
       }
       return (int)LNumOps - (int)RNumOps;
     }
 
     case scUDivExpr: {
       const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
       const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
 
       // Lexicographically compare udiv expressions.
       long X = compare(LC->getLHS(), RC->getLHS());
       if (X != 0)
         return X;
       return compare(LC->getRHS(), RC->getRHS());
     }
 
     case scTruncate:
     case scZeroExtend:
     case scSignExtend: {
       const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
       const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
 
       // Compare cast expressions by operand.
       return compare(LC->getOperand(), RC->getOperand());
     }
 
     case scCouldNotCompute:
       llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
     }
     llvm_unreachable("Unknown SCEV kind!");
   }
 };
 }  // end anonymous namespace
 
 /// Given a list of SCEV objects, order them by their complexity, and group
 /// objects of the same complexity together by value.  When this routine is
 /// finished, we know that any duplicates in the vector are consecutive and that
 /// complexity is monotonically increasing.
 ///
 /// Note that we go take special precautions to ensure that we get deterministic
 /// results from this routine.  In other words, we don't want the results of
 /// this to depend on where the addresses of various SCEV objects happened to
 /// land in memory.
 ///
 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
                               LoopInfo *LI) {
   if (Ops.size() < 2) return;  // Noop
   if (Ops.size() == 2) {
     // This is the common case, which also happens to be trivially simple.
     // Special case it.
     const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
     if (SCEVComplexityCompare(LI)(RHS, LHS))
       std::swap(LHS, RHS);
     return;
   }
 
   // Do the rough sort by complexity.
   std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
 
   // Now that we are sorted by complexity, group elements of the same
   // complexity.  Note that this is, at worst, N^2, but the vector is likely to
   // be extremely short in practice.  Note that we take this approach because we
   // do not want to depend on the addresses of the objects we are grouping.
   for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
     const SCEV *S = Ops[i];
     unsigned Complexity = S->getSCEVType();
 
     // If there are any objects of the same complexity and same value as this
     // one, group them.
     for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
       if (Ops[j] == S) { // Found a duplicate.
         // Move it to immediately after i'th element.
         std::swap(Ops[i+1], Ops[j]);
         ++i;   // no need to rescan it.
         if (i == e-2) return;  // Done!
       }
     }
   }
 }
 
 // Returns the size of the SCEV S.
 static inline int sizeOfSCEV(const SCEV *S) {
   struct FindSCEVSize {
     int Size;
     FindSCEVSize() : Size(0) {}
 
     bool follow(const SCEV *S) {
       ++Size;
       // Keep looking at all operands of S.
       return true;
     }
     bool isDone() const {
       return false;
     }
   };
 
   FindSCEVSize F;
   SCEVTraversal<FindSCEVSize> ST(F);
   ST.visitAll(S);
   return F.Size;
 }
 
 namespace {
 
 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
 public:
   // Computes the Quotient and Remainder of the division of Numerator by
   // Denominator.
   static void divide(ScalarEvolution &SE, const SCEV *Numerator,
                      const SCEV *Denominator, const SCEV **Quotient,
                      const SCEV **Remainder) {
     assert(Numerator && Denominator && "Uninitialized SCEV");
 
     SCEVDivision D(SE, Numerator, Denominator);
 
     // Check for the trivial case here to avoid having to check for it in the
     // rest of the code.
     if (Numerator == Denominator) {
       *Quotient = D.One;
       *Remainder = D.Zero;
       return;
     }
 
     if (Numerator->isZero()) {
       *Quotient = D.Zero;
       *Remainder = D.Zero;
       return;
     }
 
     // A simple case when N/1. The quotient is N.
     if (Denominator->isOne()) {
       *Quotient = Numerator;
       *Remainder = D.Zero;
       return;
     }
 
     // Split the Denominator when it is a product.
     if (const SCEVMulExpr *T = dyn_cast<SCEVMulExpr>(Denominator)) {
       const SCEV *Q, *R;
       *Quotient = Numerator;
       for (const SCEV *Op : T->operands()) {
         divide(SE, *Quotient, Op, &Q, &R);
         *Quotient = Q;
 
         // Bail out when the Numerator is not divisible by one of the terms of
         // the Denominator.
         if (!R->isZero()) {
           *Quotient = D.Zero;
           *Remainder = Numerator;
           return;
         }
       }
       *Remainder = D.Zero;
       return;
     }
 
     D.visit(Numerator);
     *Quotient = D.Quotient;
     *Remainder = D.Remainder;
   }
 
   // Except in the trivial case described above, we do not know how to divide
   // Expr by Denominator for the following functions with empty implementation.
   void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
   void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
   void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
   void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
   void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
   void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
   void visitUnknown(const SCEVUnknown *Numerator) {}
   void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
 
   void visitConstant(const SCEVConstant *Numerator) {
     if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
       APInt NumeratorVal = Numerator->getAPInt();
       APInt DenominatorVal = D->getAPInt();
       uint32_t NumeratorBW = NumeratorVal.getBitWidth();
       uint32_t DenominatorBW = DenominatorVal.getBitWidth();
 
       if (NumeratorBW > DenominatorBW)
         DenominatorVal = DenominatorVal.sext(NumeratorBW);
       else if (NumeratorBW < DenominatorBW)
         NumeratorVal = NumeratorVal.sext(DenominatorBW);
 
       APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
       APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
       APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
       Quotient = SE.getConstant(QuotientVal);
       Remainder = SE.getConstant(RemainderVal);
       return;
     }
   }
 
   void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
     const SCEV *StartQ, *StartR, *StepQ, *StepR;
     if (!Numerator->isAffine())
       return cannotDivide(Numerator);
     divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
     divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
     // Bail out if the types do not match.
     Type *Ty = Denominator->getType();
     if (Ty != StartQ->getType() || Ty != StartR->getType() ||
         Ty != StepQ->getType() || Ty != StepR->getType())
       return cannotDivide(Numerator);
     Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
                                 Numerator->getNoWrapFlags());
     Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
                                  Numerator->getNoWrapFlags());
   }
 
   void visitAddExpr(const SCEVAddExpr *Numerator) {
     SmallVector<const SCEV *, 2> Qs, Rs;
     Type *Ty = Denominator->getType();
 
     for (const SCEV *Op : Numerator->operands()) {
       const SCEV *Q, *R;
       divide(SE, Op, Denominator, &Q, &R);
 
       // Bail out if types do not match.
       if (Ty != Q->getType() || Ty != R->getType())
         return cannotDivide(Numerator);
 
       Qs.push_back(Q);
       Rs.push_back(R);
     }
 
     if (Qs.size() == 1) {
       Quotient = Qs[0];
       Remainder = Rs[0];
       return;
     }
 
     Quotient = SE.getAddExpr(Qs);
     Remainder = SE.getAddExpr(Rs);
   }
 
   void visitMulExpr(const SCEVMulExpr *Numerator) {
     SmallVector<const SCEV *, 2> Qs;
     Type *Ty = Denominator->getType();
 
     bool FoundDenominatorTerm = false;
     for (const SCEV *Op : Numerator->operands()) {
       // Bail out if types do not match.
       if (Ty != Op->getType())
         return cannotDivide(Numerator);
 
       if (FoundDenominatorTerm) {
         Qs.push_back(Op);
         continue;
       }
 
       // Check whether Denominator divides one of the product operands.
       const SCEV *Q, *R;
       divide(SE, Op, Denominator, &Q, &R);
       if (!R->isZero()) {
         Qs.push_back(Op);
         continue;
       }
 
       // Bail out if types do not match.
       if (Ty != Q->getType())
         return cannotDivide(Numerator);
 
       FoundDenominatorTerm = true;
       Qs.push_back(Q);
     }
 
     if (FoundDenominatorTerm) {
       Remainder = Zero;
       if (Qs.size() == 1)
         Quotient = Qs[0];
       else
         Quotient = SE.getMulExpr(Qs);
       return;
     }
 
     if (!isa<SCEVUnknown>(Denominator))
       return cannotDivide(Numerator);
 
     // The Remainder is obtained by replacing Denominator by 0 in Numerator.
     ValueToValueMap RewriteMap;
     RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
         cast<SCEVConstant>(Zero)->getValue();
     Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
 
     if (Remainder->isZero()) {
       // The Quotient is obtained by replacing Denominator by 1 in Numerator.
       RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
           cast<SCEVConstant>(One)->getValue();
       Quotient =
           SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
       return;
     }
 
     // Quotient is (Numerator - Remainder) divided by Denominator.
     const SCEV *Q, *R;
     const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
     // This SCEV does not seem to simplify: fail the division here.
     if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator))
       return cannotDivide(Numerator);
     divide(SE, Diff, Denominator, &Q, &R);
     if (R != Zero)
       return cannotDivide(Numerator);
     Quotient = Q;
   }
 
 private:
   SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
                const SCEV *Denominator)
       : SE(S), Denominator(Denominator) {
     Zero = SE.getZero(Denominator->getType());
     One = SE.getOne(Denominator->getType());
 
     // We generally do not know how to divide Expr by Denominator. We
     // initialize the division to a "cannot divide" state to simplify the rest
     // of the code.
     cannotDivide(Numerator);
   }
 
   // Convenience function for giving up on the division. We set the quotient to
   // be equal to zero and the remainder to be equal to the numerator.
   void cannotDivide(const SCEV *Numerator) {
     Quotient = Zero;
     Remainder = Numerator;
   }
 
   ScalarEvolution &SE;
   const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
 };
 
 }
 
 //===----------------------------------------------------------------------===//
 //                      Simple SCEV method implementations
 //===----------------------------------------------------------------------===//
 
 /// Compute BC(It, K).  The result has width W.  Assume, K > 0.
 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
                                        ScalarEvolution &SE,
                                        Type *ResultTy) {
   // Handle the simplest case efficiently.
   if (K == 1)
     return SE.getTruncateOrZeroExtend(It, ResultTy);
 
   // We are using the following formula for BC(It, K):
   //
   //   BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
   //
   // Suppose, W is the bitwidth of the return value.  We must be prepared for
   // overflow.  Hence, we must assure that the result of our computation is
   // equal to the accurate one modulo 2^W.  Unfortunately, division isn't
   // safe in modular arithmetic.
   //
   // However, this code doesn't use exactly that formula; the formula it uses
   // is something like the following, where T is the number of factors of 2 in
   // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
   // exponentiation:
   //
   //   BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
   //
   // This formula is trivially equivalent to the previous formula.  However,
   // this formula can be implemented much more efficiently.  The trick is that
   // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
   // arithmetic.  To do exact division in modular arithmetic, all we have
   // to do is multiply by the inverse.  Therefore, this step can be done at
   // width W.
   //
   // The next issue is how to safely do the division by 2^T.  The way this
   // is done is by doing the multiplication step at a width of at least W + T
   // bits.  This way, the bottom W+T bits of the product are accurate. Then,
   // when we perform the division by 2^T (which is equivalent to a right shift
   // by T), the bottom W bits are accurate.  Extra bits are okay; they'll get
   // truncated out after the division by 2^T.
   //
   // In comparison to just directly using the first formula, this technique
   // is much more efficient; using the first formula requires W * K bits,
   // but this formula less than W + K bits. Also, the first formula requires
   // a division step, whereas this formula only requires multiplies and shifts.
   //
   // It doesn't matter whether the subtraction step is done in the calculation
   // width or the input iteration count's width; if the subtraction overflows,
   // the result must be zero anyway.  We prefer here to do it in the width of
   // the induction variable because it helps a lot for certain cases; CodeGen
   // isn't smart enough to ignore the overflow, which leads to much less
   // efficient code if the width of the subtraction is wider than the native
   // register width.
   //
   // (It's possible to not widen at all by pulling out factors of 2 before
   // the multiplication; for example, K=2 can be calculated as
   // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
   // extra arithmetic, so it's not an obvious win, and it gets
   // much more complicated for K > 3.)
 
   // Protection from insane SCEVs; this bound is conservative,
   // but it probably doesn't matter.
   if (K > 1000)
     return SE.getCouldNotCompute();
 
   unsigned W = SE.getTypeSizeInBits(ResultTy);
 
   // Calculate K! / 2^T and T; we divide out the factors of two before
   // multiplying for calculating K! / 2^T to avoid overflow.
   // Other overflow doesn't matter because we only care about the bottom
   // W bits of the result.
   APInt OddFactorial(W, 1);
   unsigned T = 1;
   for (unsigned i = 3; i <= K; ++i) {
     APInt Mult(W, i);
     unsigned TwoFactors = Mult.countTrailingZeros();
     T += TwoFactors;
     Mult = Mult.lshr(TwoFactors);
     OddFactorial *= Mult;
   }
 
   // We need at least W + T bits for the multiplication step
   unsigned CalculationBits = W + T;
 
   // Calculate 2^T, at width T+W.
   APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
 
   // Calculate the multiplicative inverse of K! / 2^T;
   // this multiplication factor will perform the exact division by
   // K! / 2^T.
   APInt Mod = APInt::getSignedMinValue(W+1);
   APInt MultiplyFactor = OddFactorial.zext(W+1);
   MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
   MultiplyFactor = MultiplyFactor.trunc(W);
 
   // Calculate the product, at width T+W
   IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
                                                       CalculationBits);
   const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
   for (unsigned i = 1; i != K; ++i) {
     const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
     Dividend = SE.getMulExpr(Dividend,
                              SE.getTruncateOrZeroExtend(S, CalculationTy));
   }
 
   // Divide by 2^T
   const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
 
   // Truncate the result, and divide by K! / 2^T.
 
   return SE.getMulExpr(SE.getConstant(MultiplyFactor),
                        SE.getTruncateOrZeroExtend(DivResult, ResultTy));
 }
 
 /// Return the value of this chain of recurrences at the specified iteration
 /// number.  We can evaluate this recurrence by multiplying each element in the
 /// chain by the binomial coefficient corresponding to it.  In other words, we
 /// can evaluate {A,+,B,+,C,+,D} as:
 ///
 ///   A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
 ///
 /// where BC(It, k) stands for binomial coefficient.
 ///
 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
                                                 ScalarEvolution &SE) const {
   const SCEV *Result = getStart();
   for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
     // The computation is correct in the face of overflow provided that the
     // multiplication is performed _after_ the evaluation of the binomial
     // coefficient.
     const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
     if (isa<SCEVCouldNotCompute>(Coeff))
       return Coeff;
 
     Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
   }
   return Result;
 }
 
 //===----------------------------------------------------------------------===//
 //                    SCEV Expression folder implementations
 //===----------------------------------------------------------------------===//
 
 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
                                              Type *Ty) {
   assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
          "This is not a truncating conversion!");
   assert(isSCEVable(Ty) &&
          "This is not a conversion to a SCEVable type!");
   Ty = getEffectiveSCEVType(Ty);
 
   FoldingSetNodeID ID;
   ID.AddInteger(scTruncate);
   ID.AddPointer(Op);
   ID.AddPointer(Ty);
   void *IP = nullptr;
   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
 
   // Fold if the operand is constant.
   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
     return getConstant(
       cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
 
   // trunc(trunc(x)) --> trunc(x)
   if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
     return getTruncateExpr(ST->getOperand(), Ty);
 
   // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
   if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
     return getTruncateOrSignExtend(SS->getOperand(), Ty);
 
   // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
   if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
     return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
 
   // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
   // eliminate all the truncates, or we replace other casts with truncates.
   if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
     SmallVector<const SCEV *, 4> Operands;
     bool hasTrunc = false;
     for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
       const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
       if (!isa<SCEVCastExpr>(SA->getOperand(i)))
         hasTrunc = isa<SCEVTruncateExpr>(S);
       Operands.push_back(S);
     }
     if (!hasTrunc)
       return getAddExpr(Operands);
     UniqueSCEVs.FindNodeOrInsertPos(ID, IP);  // Mutates IP, returns NULL.
   }
 
   // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
   // eliminate all the truncates, or we replace other casts with truncates.
   if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
     SmallVector<const SCEV *, 4> Operands;
     bool hasTrunc = false;
     for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
       const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
       if (!isa<SCEVCastExpr>(SM->getOperand(i)))
         hasTrunc = isa<SCEVTruncateExpr>(S);
       Operands.push_back(S);
     }
     if (!hasTrunc)
       return getMulExpr(Operands);
     UniqueSCEVs.FindNodeOrInsertPos(ID, IP);  // Mutates IP, returns NULL.
   }
 
   // If the input value is a chrec scev, truncate the chrec's operands.
   if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
     SmallVector<const SCEV *, 4> Operands;
     for (const SCEV *Op : AddRec->operands())
       Operands.push_back(getTruncateExpr(Op, Ty));
     return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
   }
 
   // The cast wasn't folded; create an explicit cast node. We can reuse
   // the existing insert position since if we get here, we won't have
   // made any changes which would invalidate it.
   SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
                                                  Op, Ty);
   UniqueSCEVs.InsertNode(S, IP);
   return S;
 }
 
 // Get the limit of a recurrence such that incrementing by Step cannot cause
 // signed overflow as long as the value of the recurrence within the
 // loop does not exceed this limit before incrementing.
 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
                                                  ICmpInst::Predicate *Pred,
                                                  ScalarEvolution *SE) {
   unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
   if (SE->isKnownPositive(Step)) {
     *Pred = ICmpInst::ICMP_SLT;
     return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
                            SE->getSignedRange(Step).getSignedMax());
   }
   if (SE->isKnownNegative(Step)) {
     *Pred = ICmpInst::ICMP_SGT;
     return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
                            SE->getSignedRange(Step).getSignedMin());
   }
   return nullptr;
 }
 
 // Get the limit of a recurrence such that incrementing by Step cannot cause
 // unsigned overflow as long as the value of the recurrence within the loop does
 // not exceed this limit before incrementing.
 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
                                                    ICmpInst::Predicate *Pred,
                                                    ScalarEvolution *SE) {
   unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
   *Pred = ICmpInst::ICMP_ULT;
 
   return SE->getConstant(APInt::getMinValue(BitWidth) -
                          SE->getUnsignedRange(Step).getUnsignedMax());
 }
 
 namespace {
 
 struct ExtendOpTraitsBase {
   typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *);
 };
 
 // Used to make code generic over signed and unsigned overflow.
 template <typename ExtendOp> struct ExtendOpTraits {
   // Members present:
   //
   // static const SCEV::NoWrapFlags WrapType;
   //
   // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
   //
   // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
   //                                           ICmpInst::Predicate *Pred,
   //                                           ScalarEvolution *SE);
 };
 
 template <>
 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
   static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
 
   static const GetExtendExprTy GetExtendExpr;
 
   static const SCEV *getOverflowLimitForStep(const SCEV *Step,
                                              ICmpInst::Predicate *Pred,
                                              ScalarEvolution *SE) {
     return getSignedOverflowLimitForStep(Step, Pred, SE);
   }
 };
 
 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
     SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
 
 template <>
 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
   static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
 
   static const GetExtendExprTy GetExtendExpr;
 
   static const SCEV *getOverflowLimitForStep(const SCEV *Step,
                                              ICmpInst::Predicate *Pred,
                                              ScalarEvolution *SE) {
     return getUnsignedOverflowLimitForStep(Step, Pred, SE);
   }
 };
 
 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
     SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
 }
 
 // The recurrence AR has been shown to have no signed/unsigned wrap or something
 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
 // easily prove NSW/NUW for its preincrement or postincrement sibling. This
 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
 // expression "Step + sext/zext(PreIncAR)" is congruent with
 // "sext/zext(PostIncAR)"
 template <typename ExtendOpTy>
 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
                                         ScalarEvolution *SE) {
   auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
   auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
 
   const Loop *L = AR->getLoop();
   const SCEV *Start = AR->getStart();
   const SCEV *Step = AR->getStepRecurrence(*SE);
 
   // Check for a simple looking step prior to loop entry.
   const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
   if (!SA)
     return nullptr;
 
   // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
   // subtraction is expensive. For this purpose, perform a quick and dirty
   // difference, by checking for Step in the operand list.
   SmallVector<const SCEV *, 4> DiffOps;
   for (const SCEV *Op : SA->operands())
     if (Op != Step)
       DiffOps.push_back(Op);
 
   if (DiffOps.size() == SA->getNumOperands())
     return nullptr;
 
   // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
   // `Step`:
 
   // 1. NSW/NUW flags on the step increment.
   auto PreStartFlags =
     ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
   const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
   const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
       SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
 
   // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
   // "S+X does not sign/unsign-overflow".
   //
 
   const SCEV *BECount = SE->getBackedgeTakenCount(L);
   if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
       !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
     return PreStart;
 
   // 2. Direct overflow check on the step operation's expression.
   unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
   Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
   const SCEV *OperandExtendedStart =
       SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy),
                      (SE->*GetExtendExpr)(Step, WideTy));
   if ((SE->*GetExtendExpr)(Start, WideTy) == OperandExtendedStart) {
     if (PreAR && AR->getNoWrapFlags(WrapType)) {
       // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
       // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
       // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`.  Cache this fact.
       const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
     }
     return PreStart;
   }
 
   // 3. Loop precondition.
   ICmpInst::Predicate Pred;
   const SCEV *OverflowLimit =
       ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
 
   if (OverflowLimit &&
       SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
     return PreStart;
 
   return nullptr;
 }
 
 // Get the normalized zero or sign extended expression for this AddRec's Start.
 template <typename ExtendOpTy>
 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
                                         ScalarEvolution *SE) {
   auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
 
   const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE);
   if (!PreStart)
     return (SE->*GetExtendExpr)(AR->getStart(), Ty);
 
   return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty),
                         (SE->*GetExtendExpr)(PreStart, Ty));
 }
 
 // Try to prove away overflow by looking at "nearby" add recurrences.  A
 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
 //
 // Formally:
 //
 //     {S,+,X} == {S-T,+,X} + T
 //  => Ext({S,+,X}) == Ext({S-T,+,X} + T)
 //
 // If ({S-T,+,X} + T) does not overflow  ... (1)
 //
 //  RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
 //
 // If {S-T,+,X} does not overflow  ... (2)
 //
 //  RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
 //      == {Ext(S-T)+Ext(T),+,Ext(X)}
 //
 // If (S-T)+T does not overflow  ... (3)
 //
 //  RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
 //      == {Ext(S),+,Ext(X)} == LHS
 //
 // Thus, if (1), (2) and (3) are true for some T, then
 //   Ext({S,+,X}) == {Ext(S),+,Ext(X)}
 //
 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
 // does not overflow" restricted to the 0th iteration.  Therefore we only need
 // to check for (1) and (2).
 //
 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
 // is `Delta` (defined below).
 //
 template <typename ExtendOpTy>
 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
                                                 const SCEV *Step,
                                                 const Loop *L) {
   auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
 
   // We restrict `Start` to a constant to prevent SCEV from spending too much
   // time here.  It is correct (but more expensive) to continue with a
   // non-constant `Start` and do a general SCEV subtraction to compute
   // `PreStart` below.
   //
   const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
   if (!StartC)
     return false;
 
   APInt StartAI = StartC->getAPInt();
 
   for (unsigned Delta : {-2, -1, 1, 2}) {
     const SCEV *PreStart = getConstant(StartAI - Delta);
 
     FoldingSetNodeID ID;
     ID.AddInteger(scAddRecExpr);
     ID.AddPointer(PreStart);
     ID.AddPointer(Step);
     ID.AddPointer(L);
     void *IP = nullptr;
     const auto *PreAR =
       static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
 
     // Give up if we don't already have the add recurrence we need because
     // actually constructing an add recurrence is relatively expensive.
     if (PreAR && PreAR->getNoWrapFlags(WrapType)) {  // proves (2)
       const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
       ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
       const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
           DeltaS, &Pred, this);
       if (Limit && isKnownPredicate(Pred, PreAR, Limit))  // proves (1)
         return true;
     }
   }
 
   return false;
 }
 
 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
                                                Type *Ty) {
   assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
          "This is not an extending conversion!");
   assert(isSCEVable(Ty) &&
          "This is not a conversion to a SCEVable type!");
   Ty = getEffectiveSCEVType(Ty);
 
   // Fold if the operand is constant.
   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
     return getConstant(
       cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
 
   // zext(zext(x)) --> zext(x)
   if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
     return getZeroExtendExpr(SZ->getOperand(), Ty);
 
   // Before doing any expensive analysis, check to see if we've already
   // computed a SCEV for this Op and Ty.
   FoldingSetNodeID ID;
   ID.AddInteger(scZeroExtend);
   ID.AddPointer(Op);
   ID.AddPointer(Ty);
   void *IP = nullptr;
   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
 
   // zext(trunc(x)) --> zext(x) or x or trunc(x)
   if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
     // It's possible the bits taken off by the truncate were all zero bits. If
     // so, we should be able to simplify this further.
     const SCEV *X = ST->getOperand();
     ConstantRange CR = getUnsignedRange(X);
     unsigned TruncBits = getTypeSizeInBits(ST->getType());
     unsigned NewBits = getTypeSizeInBits(Ty);
     if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
             CR.zextOrTrunc(NewBits)))
       return getTruncateOrZeroExtend(X, Ty);
   }
 
   // If the input value is a chrec scev, and we can prove that the value
   // did not overflow the old, smaller, value, we can zero extend all of the
   // operands (often constants).  This allows analysis of something like
   // this:  for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
     if (AR->isAffine()) {
       const SCEV *Start = AR->getStart();
       const SCEV *Step = AR->getStepRecurrence(*this);
       unsigned BitWidth = getTypeSizeInBits(AR->getType());
       const Loop *L = AR->getLoop();
 
       if (!AR->hasNoUnsignedWrap()) {
         auto NewFlags = proveNoWrapViaConstantRanges(AR);
         const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
       }
 
       // If we have special knowledge that this addrec won't overflow,
       // we don't need to do any further analysis.
       if (AR->hasNoUnsignedWrap())
         return getAddRecExpr(
             getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
             getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
 
       // Check whether the backedge-taken count is SCEVCouldNotCompute.
       // Note that this serves two purposes: It filters out loops that are
       // simply not analyzable, and it covers the case where this code is
       // being called from within backedge-taken count analysis, such that
       // attempting to ask for the backedge-taken count would likely result
       // in infinite recursion. In the later case, the analysis code will
       // cope with a conservative value, and it will take care to purge
       // that value once it has finished.
       const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
       if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
         // Manually compute the final value for AR, checking for
         // overflow.
 
         // Check whether the backedge-taken count can be losslessly casted to
         // the addrec's type. The count is always unsigned.
         const SCEV *CastedMaxBECount =
           getTruncateOrZeroExtend(MaxBECount, Start->getType());
         const SCEV *RecastedMaxBECount =
           getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
         if (MaxBECount == RecastedMaxBECount) {
           Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
           // Check whether Start+Step*MaxBECount has no unsigned overflow.
           const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
           const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
           const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
           const SCEV *WideMaxBECount =
             getZeroExtendExpr(CastedMaxBECount, WideTy);
           const SCEV *OperandExtendedAdd =
             getAddExpr(WideStart,
                        getMulExpr(WideMaxBECount,
                                   getZeroExtendExpr(Step, WideTy)));
           if (ZAdd == OperandExtendedAdd) {
             // Cache knowledge of AR NUW, which is propagated to this AddRec.
             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
             // Return the expression with the addrec on the outside.
             return getAddRecExpr(
                 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
                 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
           }
           // Similar to above, only this time treat the step value as signed.
           // This covers loops that count down.
           OperandExtendedAdd =
             getAddExpr(WideStart,
                        getMulExpr(WideMaxBECount,
                                   getSignExtendExpr(Step, WideTy)));
           if (ZAdd == OperandExtendedAdd) {
             // Cache knowledge of AR NW, which is propagated to this AddRec.
             // Negative step causes unsigned wrap, but it still can't self-wrap.
             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
             // Return the expression with the addrec on the outside.
             return getAddRecExpr(
                 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
                 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
           }
         }
       }
 
       // Normally, in the cases we can prove no-overflow via a
       // backedge guarding condition, we can also compute a backedge
       // taken count for the loop.  The exceptions are assumptions and
       // guards present in the loop -- SCEV is not great at exploiting
       // these to compute max backedge taken counts, but can still use
       // these to prove lack of overflow.  Use this fact to avoid
       // doing extra work that may not pay off.
       if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
           !AC.assumptions().empty()) {
         // If the backedge is guarded by a comparison with the pre-inc
         // value the addrec is safe. Also, if the entry is guarded by
         // a comparison with the start value and the backedge is
         // guarded by a comparison with the post-inc value, the addrec
         // is safe.
         if (isKnownPositive(Step)) {
           const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
                                       getUnsignedRange(Step).getUnsignedMax());
           if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
               (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
                isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
                                            AR->getPostIncExpr(*this), N))) {
             // Cache knowledge of AR NUW, which is propagated to this
             // AddRec.
             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
             // Return the expression with the addrec on the outside.
             return getAddRecExpr(
                 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
                 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
           }
         } else if (isKnownNegative(Step)) {
           const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
                                       getSignedRange(Step).getSignedMin());
           if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
               (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
                isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
                                            AR->getPostIncExpr(*this), N))) {
             // Cache knowledge of AR NW, which is propagated to this
             // AddRec.  Negative step causes unsigned wrap, but it
             // still can't self-wrap.
             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
             // Return the expression with the addrec on the outside.
             return getAddRecExpr(
                 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
                 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
           }
         }
       }
 
       if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
         const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
         return getAddRecExpr(
             getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
             getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
       }
     }
 
   if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
     // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
     if (SA->hasNoUnsignedWrap()) {
       // If the addition does not unsign overflow then we can, by definition,
       // commute the zero extension with the addition operation.
       SmallVector<const SCEV *, 4> Ops;
       for (const auto *Op : SA->operands())
         Ops.push_back(getZeroExtendExpr(Op, Ty));
       return getAddExpr(Ops, SCEV::FlagNUW);
     }
   }
 
   // The cast wasn't folded; create an explicit cast node.
   // Recompute the insert position, as it may have been invalidated.
   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
   SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
                                                    Op, Ty);
   UniqueSCEVs.InsertNode(S, IP);
   return S;
 }
 
 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
                                                Type *Ty) {
   assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
          "This is not an extending conversion!");
   assert(isSCEVable(Ty) &&
          "This is not a conversion to a SCEVable type!");
   Ty = getEffectiveSCEVType(Ty);
 
   // Fold if the operand is constant.
   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
     return getConstant(
       cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
 
   // sext(sext(x)) --> sext(x)
   if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
     return getSignExtendExpr(SS->getOperand(), Ty);
 
   // sext(zext(x)) --> zext(x)
   if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
     return getZeroExtendExpr(SZ->getOperand(), Ty);
 
   // Before doing any expensive analysis, check to see if we've already
   // computed a SCEV for this Op and Ty.
   FoldingSetNodeID ID;
   ID.AddInteger(scSignExtend);
   ID.AddPointer(Op);
   ID.AddPointer(Ty);
   void *IP = nullptr;
   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
 
   // sext(trunc(x)) --> sext(x) or x or trunc(x)
   if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
     // It's possible the bits taken off by the truncate were all sign bits. If
     // so, we should be able to simplify this further.
     const SCEV *X = ST->getOperand();
     ConstantRange CR = getSignedRange(X);
     unsigned TruncBits = getTypeSizeInBits(ST->getType());
     unsigned NewBits = getTypeSizeInBits(Ty);
     if (CR.truncate(TruncBits).signExtend(NewBits).contains(
             CR.sextOrTrunc(NewBits)))
       return getTruncateOrSignExtend(X, Ty);
   }
 
   // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
   if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
     if (SA->getNumOperands() == 2) {
       auto *SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
       auto *SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
       if (SMul && SC1) {
         if (auto *SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
           const APInt &C1 = SC1->getAPInt();
           const APInt &C2 = SC2->getAPInt();
           if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
               C2.ugt(C1) && C2.isPowerOf2())
             return getAddExpr(getSignExtendExpr(SC1, Ty),
                               getSignExtendExpr(SMul, Ty));
         }
       }
     }
 
     // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
     if (SA->hasNoSignedWrap()) {
       // If the addition does not sign overflow then we can, by definition,
       // commute the sign extension with the addition operation.
       SmallVector<const SCEV *, 4> Ops;
       for (const auto *Op : SA->operands())
         Ops.push_back(getSignExtendExpr(Op, Ty));
       return getAddExpr(Ops, SCEV::FlagNSW);
     }
   }
   // If the input value is a chrec scev, and we can prove that the value
   // did not overflow the old, smaller, value, we can sign extend all of the
   // operands (often constants).  This allows analysis of something like
   // this:  for (signed char X = 0; X < 100; ++X) { int Y = X; }
   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
     if (AR->isAffine()) {
       const SCEV *Start = AR->getStart();
       const SCEV *Step = AR->getStepRecurrence(*this);
       unsigned BitWidth = getTypeSizeInBits(AR->getType());
       const Loop *L = AR->getLoop();
 
       if (!AR->hasNoSignedWrap()) {
         auto NewFlags = proveNoWrapViaConstantRanges(AR);
         const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
       }
 
       // If we have special knowledge that this addrec won't overflow,
       // we don't need to do any further analysis.
       if (AR->hasNoSignedWrap())
         return getAddRecExpr(
             getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
             getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW);
 
       // Check whether the backedge-taken count is SCEVCouldNotCompute.
       // Note that this serves two purposes: It filters out loops that are
       // simply not analyzable, and it covers the case where this code is
       // being called from within backedge-taken count analysis, such that
       // attempting to ask for the backedge-taken count would likely result
       // in infinite recursion. In the later case, the analysis code will
       // cope with a conservative value, and it will take care to purge
       // that value once it has finished.
       const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
       if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
         // Manually compute the final value for AR, checking for
         // overflow.
 
         // Check whether the backedge-taken count can be losslessly casted to
         // the addrec's type. The count is always unsigned.
         const SCEV *CastedMaxBECount =
           getTruncateOrZeroExtend(MaxBECount, Start->getType());
         const SCEV *RecastedMaxBECount =
           getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
         if (MaxBECount == RecastedMaxBECount) {
           Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
           // Check whether Start+Step*MaxBECount has no signed overflow.
           const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
           const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
           const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
           const SCEV *WideMaxBECount =
             getZeroExtendExpr(CastedMaxBECount, WideTy);
           const SCEV *OperandExtendedAdd =
             getAddExpr(WideStart,
                        getMulExpr(WideMaxBECount,
                                   getSignExtendExpr(Step, WideTy)));
           if (SAdd == OperandExtendedAdd) {
             // Cache knowledge of AR NSW, which is propagated to this AddRec.
             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
             // Return the expression with the addrec on the outside.
             return getAddRecExpr(
                 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
                 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
           }
           // Similar to above, only this time treat the step value as unsigned.
           // This covers loops that count up with an unsigned step.
           OperandExtendedAdd =
             getAddExpr(WideStart,
                        getMulExpr(WideMaxBECount,
                                   getZeroExtendExpr(Step, WideTy)));
           if (SAdd == OperandExtendedAdd) {
             // If AR wraps around then
             //
             //    abs(Step) * MaxBECount > unsigned-max(AR->getType())
             // => SAdd != OperandExtendedAdd
             //
             // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
             // (SAdd == OperandExtendedAdd => AR is NW)
 
             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
 
             // Return the expression with the addrec on the outside.
             return getAddRecExpr(
                 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
                 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
           }
         }
       }
 
       // Normally, in the cases we can prove no-overflow via a
       // backedge guarding condition, we can also compute a backedge
       // taken count for the loop.  The exceptions are assumptions and
       // guards present in the loop -- SCEV is not great at exploiting
       // these to compute max backedge taken counts, but can still use
       // these to prove lack of overflow.  Use this fact to avoid
       // doing extra work that may not pay off.
 
       if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
           !AC.assumptions().empty()) {
         // If the backedge is guarded by a comparison with the pre-inc
         // value the addrec is safe. Also, if the entry is guarded by
         // a comparison with the start value and the backedge is
         // guarded by a comparison with the post-inc value, the addrec
         // is safe.
         ICmpInst::Predicate Pred;
         const SCEV *OverflowLimit =
             getSignedOverflowLimitForStep(Step, &Pred, this);
         if (OverflowLimit &&
             (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
              (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
               isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
                                           OverflowLimit)))) {
           // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
           const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
           return getAddRecExpr(
               getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
               getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
         }
       }
 
       // If Start and Step are constants, check if we can apply this
       // transformation:
       // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
       auto *SC1 = dyn_cast<SCEVConstant>(Start);
       auto *SC2 = dyn_cast<SCEVConstant>(Step);
       if (SC1 && SC2) {
         const APInt &C1 = SC1->getAPInt();
         const APInt &C2 = SC2->getAPInt();
         if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
             C2.isPowerOf2()) {
           Start = getSignExtendExpr(Start, Ty);
           const SCEV *NewAR = getAddRecExpr(getZero(AR->getType()), Step, L,
                                             AR->getNoWrapFlags());
           return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
         }
       }
 
       if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
         const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
         return getAddRecExpr(
             getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
             getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
       }
     }
 
   // If the input value is provably positive and we could not simplify
   // away the sext build a zext instead.
   if (isKnownNonNegative(Op))
     return getZeroExtendExpr(Op, Ty);
 
   // The cast wasn't folded; create an explicit cast node.
   // Recompute the insert position, as it may have been invalidated.
   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
   SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
                                                    Op, Ty);
   UniqueSCEVs.InsertNode(S, IP);
   return S;
 }
 
 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
 /// unspecified bits out to the given type.
 ///
 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
                                               Type *Ty) {
   assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
          "This is not an extending conversion!");
   assert(isSCEVable(Ty) &&
          "This is not a conversion to a SCEVable type!");
   Ty = getEffectiveSCEVType(Ty);
 
   // Sign-extend negative constants.
   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
     if (SC->getAPInt().isNegative())
       return getSignExtendExpr(Op, Ty);
 
   // Peel off a truncate cast.
   if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
     const SCEV *NewOp = T->getOperand();
     if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
       return getAnyExtendExpr(NewOp, Ty);
     return getTruncateOrNoop(NewOp, Ty);
   }
 
   // Next try a zext cast. If the cast is folded, use it.
   const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
   if (!isa<SCEVZeroExtendExpr>(ZExt))
     return ZExt;
 
   // Next try a sext cast. If the cast is folded, use it.
   const SCEV *SExt = getSignExtendExpr(Op, Ty);
   if (!isa<SCEVSignExtendExpr>(SExt))
     return SExt;
 
   // Force the cast to be folded into the operands of an addrec.
   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
     SmallVector<const SCEV *, 4> Ops;
     for (const SCEV *Op : AR->operands())
       Ops.push_back(getAnyExtendExpr(Op, Ty));
     return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
   }
 
   // If the expression is obviously signed, use the sext cast value.
   if (isa<SCEVSMaxExpr>(Op))
     return SExt;
 
   // Absent any other information, use the zext cast value.
   return ZExt;
 }
 
 /// Process the given Ops list, which is a list of operands to be added under
 /// the given scale, update the given map. This is a helper function for
 /// getAddRecExpr. As an example of what it does, given a sequence of operands
 /// that would form an add expression like this:
 ///
 ///    m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
 ///
 /// where A and B are constants, update the map with these values:
 ///
 ///    (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
 ///
 /// and add 13 + A*B*29 to AccumulatedConstant.
 /// This will allow getAddRecExpr to produce this:
 ///
 ///    13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
 ///
 /// This form often exposes folding opportunities that are hidden in
 /// the original operand list.
 ///
 /// Return true iff it appears that any interesting folding opportunities
 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
 /// the common case where no interesting opportunities are present, and
 /// is also used as a check to avoid infinite recursion.
 ///
 static bool
 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
                              SmallVectorImpl<const SCEV *> &NewOps,
                              APInt &AccumulatedConstant,
                              const SCEV *const *Ops, size_t NumOperands,
                              const APInt &Scale,
                              ScalarEvolution &SE) {
   bool Interesting = false;
 
   // Iterate over the add operands. They are sorted, with constants first.
   unsigned i = 0;
   while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
     ++i;
     // Pull a buried constant out to the outside.
     if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
       Interesting = true;
     AccumulatedConstant += Scale * C->getAPInt();
   }
 
   // Next comes everything else. We're especially interested in multiplies
   // here, but they're in the middle, so just visit the rest with one loop.
   for (; i != NumOperands; ++i) {
     const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
     if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
       APInt NewScale =
           Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
       if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
         // A multiplication of a constant with another add; recurse.
         const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
         Interesting |=
           CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
                                        Add->op_begin(), Add->getNumOperands(),
                                        NewScale, SE);
       } else {
         // A multiplication of a constant with some other value. Update
         // the map.
         SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
         const SCEV *Key = SE.getMulExpr(MulOps);
         auto Pair = M.insert({Key, NewScale});
         if (Pair.second) {
           NewOps.push_back(Pair.first->first);
         } else {
           Pair.first->second += NewScale;
           // The map already had an entry for this value, which may indicate
           // a folding opportunity.
           Interesting = true;
         }
       }
     } else {
       // An ordinary operand. Update the map.
       std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
           M.insert({Ops[i], Scale});
       if (Pair.second) {
         NewOps.push_back(Pair.first->first);
       } else {
         Pair.first->second += Scale;
         // The map already had an entry for this value, which may indicate
         // a folding opportunity.
         Interesting = true;
       }
     }
   }
 
   return Interesting;
 }
 
 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
 // `OldFlags' as can't-wrap behavior.  Infer a more aggressive set of
 // can't-overflow flags for the operation if possible.
 static SCEV::NoWrapFlags
 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
                       const SmallVectorImpl<const SCEV *> &Ops,
                       SCEV::NoWrapFlags Flags) {
   using namespace std::placeholders;
   typedef OverflowingBinaryOperator OBO;
 
   bool CanAnalyze =
       Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
   (void)CanAnalyze;
   assert(CanAnalyze && "don't call from other places!");
 
   int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
   SCEV::NoWrapFlags SignOrUnsignWrap =
       ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
 
   // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
   auto IsKnownNonNegative = [&](const SCEV *S) {
     return SE->isKnownNonNegative(S);
   };
 
   if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
     Flags =
         ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
 
   SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
 
   if (SignOrUnsignWrap != SignOrUnsignMask && Type == scAddExpr &&
       Ops.size() == 2 && isa<SCEVConstant>(Ops[0])) {
 
     // (A + C) --> (A + C)<nsw> if the addition does not sign overflow
     // (A + C) --> (A + C)<nuw> if the addition does not unsign overflow
 
     const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
     if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
       auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
           Instruction::Add, C, OBO::NoSignedWrap);
       if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
         Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
     }
     if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
       auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
           Instruction::Add, C, OBO::NoUnsignedWrap);
       if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
         Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
     }
   }
 
   return Flags;
 }
 
 /// Get a canonical add expression, or something simpler if possible.
 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
                                         SCEV::NoWrapFlags Flags) {
   assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
          "only nuw or nsw allowed");
   assert(!Ops.empty() && "Cannot get empty add!");
   if (Ops.size() == 1) return Ops[0];
 #ifndef NDEBUG
   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
            "SCEVAddExpr operand types don't match!");
 #endif
 
   // Sort by complexity, this groups all similar expression types together.
   GroupByComplexity(Ops, &LI);
 
   Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
 
   // If there are any constants, fold them together.
   unsigned Idx = 0;
   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
     ++Idx;
     assert(Idx < Ops.size());
     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
       // We found two constants, fold them together!
       Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt());
       if (Ops.size() == 2) return Ops[0];
       Ops.erase(Ops.begin()+1);  // Erase the folded element
       LHSC = cast<SCEVConstant>(Ops[0]);
     }
 
     // If we are left with a constant zero being added, strip it off.
     if (LHSC->getValue()->isZero()) {
       Ops.erase(Ops.begin());
       --Idx;
     }
 
     if (Ops.size() == 1) return Ops[0];
   }
 
   // Okay, check to see if the same value occurs in the operand list more than
   // once.  If so, merge them together into an multiply expression.  Since we
   // sorted the list, these values are required to be adjacent.
   Type *Ty = Ops[0]->getType();
   bool FoundMatch = false;
   for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
     if (Ops[i] == Ops[i+1]) {      //  X + Y + Y  -->  X + Y*2
       // Scan ahead to count how many equal operands there are.
       unsigned Count = 2;
       while (i+Count != e && Ops[i+Count] == Ops[i])
         ++Count;
       // Merge the values into a multiply.
       const SCEV *Scale = getConstant(Ty, Count);
       const SCEV *Mul = getMulExpr(Scale, Ops[i]);
       if (Ops.size() == Count)
         return Mul;
       Ops[i] = Mul;
       Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
       --i; e -= Count - 1;
       FoundMatch = true;
     }
   if (FoundMatch)
     return getAddExpr(Ops, Flags);
 
   // Check for truncates. If all the operands are truncated from the same
   // type, see if factoring out the truncate would permit the result to be
   // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
   // if the contents of the resulting outer trunc fold to something simple.
   for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
     const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
     Type *DstType = Trunc->getType();
     Type *SrcType = Trunc->getOperand()->getType();
     SmallVector<const SCEV *, 8> LargeOps;
     bool Ok = true;
     // Check all the operands to see if they can be represented in the
     // source type of the truncate.
     for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
       if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
         if (T->getOperand()->getType() != SrcType) {
           Ok = false;
           break;
         }
         LargeOps.push_back(T->getOperand());
       } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
         LargeOps.push_back(getAnyExtendExpr(C, SrcType));
       } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
         SmallVector<const SCEV *, 8> LargeMulOps;
         for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
           if (const SCEVTruncateExpr *T =
                 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
             if (T->getOperand()->getType() != SrcType) {
               Ok = false;
               break;
             }
             LargeMulOps.push_back(T->getOperand());
           } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
             LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
           } else {
             Ok = false;
             break;
           }
         }
         if (Ok)
           LargeOps.push_back(getMulExpr(LargeMulOps));
       } else {
         Ok = false;
         break;
       }
     }
     if (Ok) {
       // Evaluate the expression in the larger type.
       const SCEV *Fold = getAddExpr(LargeOps, Flags);
       // If it folds to something simple, use it. Otherwise, don't.
       if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
         return getTruncateExpr(Fold, DstType);
     }
   }
 
   // Skip past any other cast SCEVs.
   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
     ++Idx;
 
   // If there are add operands they would be next.
   if (Idx < Ops.size()) {
     bool DeletedAdd = false;
     while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
       // If we have an add, expand the add operands onto the end of the operands
       // list.
       Ops.erase(Ops.begin()+Idx);
       Ops.append(Add->op_begin(), Add->op_end());
       DeletedAdd = true;
     }
 
     // If we deleted at least one add, we added operands to the end of the list,
     // and they are not necessarily sorted.  Recurse to resort and resimplify
     // any operands we just acquired.
     if (DeletedAdd)
       return getAddExpr(Ops);
   }
 
   // Skip over the add expression until we get to a multiply.
   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
     ++Idx;
 
   // Check to see if there are any folding opportunities present with
   // operands multiplied by constant values.
   if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
     uint64_t BitWidth = getTypeSizeInBits(Ty);
     DenseMap<const SCEV *, APInt> M;
     SmallVector<const SCEV *, 8> NewOps;
     APInt AccumulatedConstant(BitWidth, 0);
     if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
                                      Ops.data(), Ops.size(),
                                      APInt(BitWidth, 1), *this)) {
       struct APIntCompare {
         bool operator()(const APInt &LHS, const APInt &RHS) const {
           return LHS.ult(RHS);
         }
       };
 
       // Some interesting folding opportunity is present, so its worthwhile to
       // re-generate the operands list. Group the operands by constant scale,
       // to avoid multiplying by the same constant scale multiple times.
       std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
       for (const SCEV *NewOp : NewOps)
         MulOpLists[M.find(NewOp)->second].push_back(NewOp);
       // Re-generate the operands list.
       Ops.clear();
       if (AccumulatedConstant != 0)
         Ops.push_back(getConstant(AccumulatedConstant));
       for (auto &MulOp : MulOpLists)
         if (MulOp.first != 0)
           Ops.push_back(getMulExpr(getConstant(MulOp.first),
                                    getAddExpr(MulOp.second)));
       if (Ops.empty())
         return getZero(Ty);
       if (Ops.size() == 1)
         return Ops[0];
       return getAddExpr(Ops);
     }
   }
 
   // If we are adding something to a multiply expression, make sure the
   // something is not already an operand of the multiply.  If so, merge it into
   // the multiply.
   for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
     const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
     for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
       const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
       if (isa<SCEVConstant>(MulOpSCEV))
         continue;
       for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
         if (MulOpSCEV == Ops[AddOp]) {
           // Fold W + X + (X * Y * Z)  -->  W + (X * ((Y*Z)+1))
           const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
           if (Mul->getNumOperands() != 2) {
             // If the multiply has more than two operands, we must get the
             // Y*Z term.
             SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
                                                 Mul->op_begin()+MulOp);
             MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
             InnerMul = getMulExpr(MulOps);
           }
           const SCEV *One = getOne(Ty);
           const SCEV *AddOne = getAddExpr(One, InnerMul);
           const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
           if (Ops.size() == 2) return OuterMul;
           if (AddOp < Idx) {
             Ops.erase(Ops.begin()+AddOp);
             Ops.erase(Ops.begin()+Idx-1);
           } else {
             Ops.erase(Ops.begin()+Idx);
             Ops.erase(Ops.begin()+AddOp-1);
           }
           Ops.push_back(OuterMul);
           return getAddExpr(Ops);
         }
 
       // Check this multiply against other multiplies being added together.
       for (unsigned OtherMulIdx = Idx+1;
            OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
            ++OtherMulIdx) {
         const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
         // If MulOp occurs in OtherMul, we can fold the two multiplies
         // together.
         for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
              OMulOp != e; ++OMulOp)
           if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
             // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
             const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
             if (Mul->getNumOperands() != 2) {
               SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
                                                   Mul->op_begin()+MulOp);
               MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
               InnerMul1 = getMulExpr(MulOps);
             }
             const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
             if (OtherMul->getNumOperands() != 2) {
               SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
                                                   OtherMul->op_begin()+OMulOp);
               MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
               InnerMul2 = getMulExpr(MulOps);
             }
             const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
             const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
             if (Ops.size() == 2) return OuterMul;
             Ops.erase(Ops.begin()+Idx);
             Ops.erase(Ops.begin()+OtherMulIdx-1);
             Ops.push_back(OuterMul);
             return getAddExpr(Ops);
           }
       }
     }
   }
 
   // If there are any add recurrences in the operands list, see if any other
   // added values are loop invariant.  If so, we can fold them into the
   // recurrence.
   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
     ++Idx;
 
   // Scan over all recurrences, trying to fold loop invariants into them.
   for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
     // Scan all of the other operands to this add and add them to the vector if
     // they are loop invariant w.r.t. the recurrence.
     SmallVector<const SCEV *, 8> LIOps;
     const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
     const Loop *AddRecLoop = AddRec->getLoop();
     for (unsigned i = 0, e = Ops.size(); i != e; ++i)
       if (isLoopInvariant(Ops[i], AddRecLoop)) {
         LIOps.push_back(Ops[i]);
         Ops.erase(Ops.begin()+i);
         --i; --e;
       }
 
     // If we found some loop invariants, fold them into the recurrence.
     if (!LIOps.empty()) {
       //  NLI + LI + {Start,+,Step}  -->  NLI + {LI+Start,+,Step}
       LIOps.push_back(AddRec->getStart());
 
       SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
                                              AddRec->op_end());
       // This follows from the fact that the no-wrap flags on the outer add
       // expression are applicable on the 0th iteration, when the add recurrence
       // will be equal to its start value.
       AddRecOps[0] = getAddExpr(LIOps, Flags);
 
       // Build the new addrec. Propagate the NUW and NSW flags if both the
       // outer add and the inner addrec are guaranteed to have no overflow.
       // Always propagate NW.
       Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
       const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
 
       // If all of the other operands were loop invariant, we are done.
       if (Ops.size() == 1) return NewRec;
 
       // Otherwise, add the folded AddRec by the non-invariant parts.
       for (unsigned i = 0;; ++i)
         if (Ops[i] == AddRec) {
           Ops[i] = NewRec;
           break;
         }
       return getAddExpr(Ops);
     }
 
     // Okay, if there weren't any loop invariants to be folded, check to see if
     // there are multiple AddRec's with the same loop induction variable being
     // added together.  If so, we can fold them.
     for (unsigned OtherIdx = Idx+1;
          OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
          ++OtherIdx)
       if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
         // Other + {A,+,B}<L> + {C,+,D}<L>  -->  Other + {A+C,+,B+D}<L>
         SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
                                                AddRec->op_end());
         for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
              ++OtherIdx)
           if (const auto *OtherAddRec = dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
             if (OtherAddRec->getLoop() == AddRecLoop) {
               for (unsigned i = 0, e = OtherAddRec->getNumOperands();
                    i != e; ++i) {
                 if (i >= AddRecOps.size()) {
                   AddRecOps.append(OtherAddRec->op_begin()+i,
                                    OtherAddRec->op_end());
                   break;
                 }
                 AddRecOps[i] = getAddExpr(AddRecOps[i],
                                           OtherAddRec->getOperand(i));
               }
               Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
             }
         // Step size has changed, so we cannot guarantee no self-wraparound.
         Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
         return getAddExpr(Ops);
       }
 
     // Otherwise couldn't fold anything into this recurrence.  Move onto the
     // next one.
   }
 
   // Okay, it looks like we really DO need an add expr.  Check to see if we
   // already have one, otherwise create a new one.
   FoldingSetNodeID ID;
   ID.AddInteger(scAddExpr);
   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
     ID.AddPointer(Ops[i]);
   void *IP = nullptr;
   SCEVAddExpr *S =
     static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
   if (!S) {
     const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
     std::uninitialized_copy(Ops.begin(), Ops.end(), O);
     S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
                                         O, Ops.size());
     UniqueSCEVs.InsertNode(S, IP);
   }
   S->setNoWrapFlags(Flags);
   return S;
 }
 
 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
   uint64_t k = i*j;
   if (j > 1 && k / j != i) Overflow = true;
   return k;
 }
 
 /// Compute the result of "n choose k", the binomial coefficient.  If an
 /// intermediate computation overflows, Overflow will be set and the return will
 /// be garbage. Overflow is not cleared on absence of overflow.
 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
   // We use the multiplicative formula:
   //     n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
   // At each iteration, we take the n-th term of the numeral and divide by the
   // (k-n)th term of the denominator.  This division will always produce an
   // integral result, and helps reduce the chance of overflow in the
   // intermediate computations. However, we can still overflow even when the
   // final result would fit.
 
   if (n == 0 || n == k) return 1;
   if (k > n) return 0;
 
   if (k > n/2)
     k = n-k;
 
   uint64_t r = 1;
   for (uint64_t i = 1; i <= k; ++i) {
     r = umul_ov(r, n-(i-1), Overflow);
     r /= i;
   }
   return r;
 }
 
 /// Determine if any of the operands in this SCEV are a constant or if
 /// any of the add or multiply expressions in this SCEV contain a constant.
 static bool containsConstantSomewhere(const SCEV *StartExpr) {
   SmallVector<const SCEV *, 4> Ops;
   Ops.push_back(StartExpr);
   while (!Ops.empty()) {
     const SCEV *CurrentExpr = Ops.pop_back_val();
     if (isa<SCEVConstant>(*CurrentExpr))
       return true;
 
     if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
       const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
       Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
     }
   }
   return false;
 }
 
 /// Get a canonical multiply expression, or something simpler if possible.
 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
                                         SCEV::NoWrapFlags Flags) {
   assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
          "only nuw or nsw allowed");
   assert(!Ops.empty() && "Cannot get empty mul!");
   if (Ops.size() == 1) return Ops[0];
 #ifndef NDEBUG
   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
            "SCEVMulExpr operand types don't match!");
 #endif
 
   // Sort by complexity, this groups all similar expression types together.
   GroupByComplexity(Ops, &LI);
 
   Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
 
   // If there are any constants, fold them together.
   unsigned Idx = 0;
   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
 
     // C1*(C2+V) -> C1*C2 + C1*V
     if (Ops.size() == 2)
         if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
           // If any of Add's ops are Adds or Muls with a constant,
           // apply this transformation as well.
           if (Add->getNumOperands() == 2)
             if (containsConstantSomewhere(Add))
               return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
                                 getMulExpr(LHSC, Add->getOperand(1)));
 
     ++Idx;
     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
       // We found two constants, fold them together!
       ConstantInt *Fold =
           ConstantInt::get(getContext(), LHSC->getAPInt() * RHSC->getAPInt());
       Ops[0] = getConstant(Fold);
       Ops.erase(Ops.begin()+1);  // Erase the folded element
       if (Ops.size() == 1) return Ops[0];
       LHSC = cast<SCEVConstant>(Ops[0]);
     }
 
     // If we are left with a constant one being multiplied, strip it off.
     if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
       Ops.erase(Ops.begin());
       --Idx;
     } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
       // If we have a multiply of zero, it will always be zero.
       return Ops[0];
     } else if (Ops[0]->isAllOnesValue()) {
       // If we have a mul by -1 of an add, try distributing the -1 among the
       // add operands.
       if (Ops.size() == 2) {
         if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
           SmallVector<const SCEV *, 4> NewOps;
           bool AnyFolded = false;
           for (const SCEV *AddOp : Add->operands()) {
             const SCEV *Mul = getMulExpr(Ops[0], AddOp);
             if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
             NewOps.push_back(Mul);
           }
           if (AnyFolded)
             return getAddExpr(NewOps);
         } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
           // Negation preserves a recurrence's no self-wrap property.
           SmallVector<const SCEV *, 4> Operands;
           for (const SCEV *AddRecOp : AddRec->operands())
             Operands.push_back(getMulExpr(Ops[0], AddRecOp));
 
           return getAddRecExpr(Operands, AddRec->getLoop(),
                                AddRec->getNoWrapFlags(SCEV::FlagNW));
         }
       }
     }
 
     if (Ops.size() == 1)
       return Ops[0];
   }
 
   // Skip over the add expression until we get to a multiply.
   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
     ++Idx;
 
   // If there are mul operands inline them all into this expression.
   if (Idx < Ops.size()) {
     bool DeletedMul = false;
     while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
       // If we have an mul, expand the mul operands onto the end of the operands
       // list.
       Ops.erase(Ops.begin()+Idx);
       Ops.append(Mul->op_begin(), Mul->op_end());
       DeletedMul = true;
     }
 
     // If we deleted at least one mul, we added operands to the end of the list,
     // and they are not necessarily sorted.  Recurse to resort and resimplify
     // any operands we just acquired.
     if (DeletedMul)
       return getMulExpr(Ops);
   }
 
   // If there are any add recurrences in the operands list, see if any other
   // added values are loop invariant.  If so, we can fold them into the
   // recurrence.
   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
     ++Idx;
 
   // Scan over all recurrences, trying to fold loop invariants into them.
   for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
     // Scan all of the other operands to this mul and add them to the vector if
     // they are loop invariant w.r.t. the recurrence.
     SmallVector<const SCEV *, 8> LIOps;
     const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
     const Loop *AddRecLoop = AddRec->getLoop();
     for (unsigned i = 0, e = Ops.size(); i != e; ++i)
       if (isLoopInvariant(Ops[i], AddRecLoop)) {
         LIOps.push_back(Ops[i]);
         Ops.erase(Ops.begin()+i);
         --i; --e;
       }
 
     // If we found some loop invariants, fold them into the recurrence.
     if (!LIOps.empty()) {
       //  NLI * LI * {Start,+,Step}  -->  NLI * {LI*Start,+,LI*Step}
       SmallVector<const SCEV *, 4> NewOps;
       NewOps.reserve(AddRec->getNumOperands());
       const SCEV *Scale = getMulExpr(LIOps);
       for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
         NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
 
       // Build the new addrec. Propagate the NUW and NSW flags if both the
       // outer mul and the inner addrec are guaranteed to have no overflow.
       //
       // No self-wrap cannot be guaranteed after changing the step size, but
       // will be inferred if either NUW or NSW is true.
       Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
       const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
 
       // If all of the other operands were loop invariant, we are done.
       if (Ops.size() == 1) return NewRec;
 
       // Otherwise, multiply the folded AddRec by the non-invariant parts.
       for (unsigned i = 0;; ++i)
         if (Ops[i] == AddRec) {
           Ops[i] = NewRec;
           break;
         }
       return getMulExpr(Ops);
     }
 
     // Okay, if there weren't any loop invariants to be folded, check to see if
     // there are multiple AddRec's with the same loop induction variable being
     // multiplied together.  If so, we can fold them.
 
     // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
     // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
     //       choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
     //   ]]],+,...up to x=2n}.
     // Note that the arguments to choose() are always integers with values
     // known at compile time, never SCEV objects.
     //
     // The implementation avoids pointless extra computations when the two
     // addrec's are of different length (mathematically, it's equivalent to
     // an infinite stream of zeros on the right).
     bool OpsModified = false;
     for (unsigned OtherIdx = Idx+1;
          OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
          ++OtherIdx) {
       const SCEVAddRecExpr *OtherAddRec =
         dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
       if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
         continue;
 
       bool Overflow = false;
       Type *Ty = AddRec->getType();
       bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
       SmallVector<const SCEV*, 7> AddRecOps;
       for (int x = 0, xe = AddRec->getNumOperands() +
              OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
         const SCEV *Term = getZero(Ty);
         for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
           uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
           for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
                  ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
                z < ze && !Overflow; ++z) {
             uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
             uint64_t Coeff;
             if (LargerThan64Bits)
               Coeff = umul_ov(Coeff1, Coeff2, Overflow);
             else
               Coeff = Coeff1*Coeff2;
             const SCEV *CoeffTerm = getConstant(Ty, Coeff);
             const SCEV *Term1 = AddRec->getOperand(y-z);
             const SCEV *Term2 = OtherAddRec->getOperand(z);
             Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
           }
         }
         AddRecOps.push_back(Term);
       }
       if (!Overflow) {
         const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
                                               SCEV::FlagAnyWrap);
         if (Ops.size() == 2) return NewAddRec;
         Ops[Idx] = NewAddRec;
         Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
         OpsModified = true;
         AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
         if (!AddRec)
           break;
       }
     }
     if (OpsModified)
       return getMulExpr(Ops);
 
     // Otherwise couldn't fold anything into this recurrence.  Move onto the
     // next one.
   }
 
   // Okay, it looks like we really DO need an mul expr.  Check to see if we
   // already have one, otherwise create a new one.
   FoldingSetNodeID ID;
   ID.AddInteger(scMulExpr);
   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
     ID.AddPointer(Ops[i]);
   void *IP = nullptr;
   SCEVMulExpr *S =
     static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
   if (!S) {
     const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
     std::uninitialized_copy(Ops.begin(), Ops.end(), O);
     S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
                                         O, Ops.size());
     UniqueSCEVs.InsertNode(S, IP);
   }
   S->setNoWrapFlags(Flags);
   return S;
 }
 
 /// Get a canonical unsigned division expression, or something simpler if
 /// possible.
 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
                                          const SCEV *RHS) {
   assert(getEffectiveSCEVType(LHS->getType()) ==
          getEffectiveSCEVType(RHS->getType()) &&
          "SCEVUDivExpr operand types don't match!");
 
   if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
     if (RHSC->getValue()->equalsInt(1))
       return LHS;                               // X udiv 1 --> x
     // If the denominator is zero, the result of the udiv is undefined. Don't
     // try to analyze it, because the resolution chosen here may differ from
     // the resolution chosen in other parts of the compiler.
     if (!RHSC->getValue()->isZero()) {
       // Determine if the division can be folded into the operands of
       // its operands.
       // TODO: Generalize this to non-constants by using known-bits information.
       Type *Ty = LHS->getType();
       unsigned LZ = RHSC->getAPInt().countLeadingZeros();
       unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
       // For non-power-of-two values, effectively round the value up to the
       // nearest power of two.
       if (!RHSC->getAPInt().isPowerOf2())
         ++MaxShiftAmt;
       IntegerType *ExtTy =
         IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
       if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
         if (const SCEVConstant *Step =
             dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
           // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
           const APInt &StepInt = Step->getAPInt();
           const APInt &DivInt = RHSC->getAPInt();
           if (!StepInt.urem(DivInt) &&
               getZeroExtendExpr(AR, ExtTy) ==
               getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
                             getZeroExtendExpr(Step, ExtTy),
                             AR->getLoop(), SCEV::FlagAnyWrap)) {
             SmallVector<const SCEV *, 4> Operands;
             for (const SCEV *Op : AR->operands())
               Operands.push_back(getUDivExpr(Op, RHS));
             return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
           }
           /// Get a canonical UDivExpr for a recurrence.
           /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
           // We can currently only fold X%N if X is constant.
           const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
           if (StartC && !DivInt.urem(StepInt) &&
               getZeroExtendExpr(AR, ExtTy) ==
               getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
                             getZeroExtendExpr(Step, ExtTy),
                             AR->getLoop(), SCEV::FlagAnyWrap)) {
             const APInt &StartInt = StartC->getAPInt();
             const APInt &StartRem = StartInt.urem(StepInt);
             if (StartRem != 0)
               LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
                                   AR->getLoop(), SCEV::FlagNW);
           }
         }
       // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
       if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
         SmallVector<const SCEV *, 4> Operands;
         for (const SCEV *Op : M->operands())
           Operands.push_back(getZeroExtendExpr(Op, ExtTy));
         if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
           // Find an operand that's safely divisible.
           for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
             const SCEV *Op = M->getOperand(i);
             const SCEV *Div = getUDivExpr(Op, RHSC);
             if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
               Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
                                                       M->op_end());
               Operands[i] = Div;
               return getMulExpr(Operands);
             }
           }
       }
       // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
       if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
         SmallVector<const SCEV *, 4> Operands;
         for (const SCEV *Op : A->operands())
           Operands.push_back(getZeroExtendExpr(Op, ExtTy));
         if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
           Operands.clear();
           for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
             const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
             if (isa<SCEVUDivExpr>(Op) ||
                 getMulExpr(Op, RHS) != A->getOperand(i))
               break;
             Operands.push_back(Op);
           }
           if (Operands.size() == A->getNumOperands())
             return getAddExpr(Operands);
         }
       }
 
       // Fold if both operands are constant.
       if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
         Constant *LHSCV = LHSC->getValue();
         Constant *RHSCV = RHSC->getValue();
         return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
                                                                    RHSCV)));
       }
     }
   }
 
   FoldingSetNodeID ID;
   ID.AddInteger(scUDivExpr);
   ID.AddPointer(LHS);
   ID.AddPointer(RHS);
   void *IP = nullptr;
   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
   SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
                                              LHS, RHS);
   UniqueSCEVs.InsertNode(S, IP);
   return S;
 }
 
 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
   APInt A = C1->getAPInt().abs();
   APInt B = C2->getAPInt().abs();
   uint32_t ABW = A.getBitWidth();
   uint32_t BBW = B.getBitWidth();
 
   if (ABW > BBW)
     B = B.zext(ABW);
   else if (ABW < BBW)
     A = A.zext(BBW);
 
   return APIntOps::GreatestCommonDivisor(A, B);
 }
 
 /// Get a canonical unsigned division expression, or something simpler if
 /// possible. There is no representation for an exact udiv in SCEV IR, but we
 /// can attempt to remove factors from the LHS and RHS.  We can't do this when
 /// it's not exact because the udiv may be clearing bits.
 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
                                               const SCEV *RHS) {
   // TODO: we could try to find factors in all sorts of things, but for now we
   // just deal with u/exact (multiply, constant). See SCEVDivision towards the
   // end of this file for inspiration.
 
   const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
   if (!Mul)
     return getUDivExpr(LHS, RHS);
 
   if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
     // If the mulexpr multiplies by a constant, then that constant must be the
     // first element of the mulexpr.
     if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
       if (LHSCst == RHSCst) {
         SmallVector<const SCEV *, 2> Operands;
         Operands.append(Mul->op_begin() + 1, Mul->op_end());
         return getMulExpr(Operands);
       }
 
       // We can't just assume that LHSCst divides RHSCst cleanly, it could be
       // that there's a factor provided by one of the other terms. We need to
       // check.
       APInt Factor = gcd(LHSCst, RHSCst);
       if (!Factor.isIntN(1)) {
         LHSCst =
             cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor)));
         RHSCst =
             cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor)));
         SmallVector<const SCEV *, 2> Operands;
         Operands.push_back(LHSCst);
         Operands.append(Mul->op_begin() + 1, Mul->op_end());
         LHS = getMulExpr(Operands);
         RHS = RHSCst;
         Mul = dyn_cast<SCEVMulExpr>(LHS);
         if (!Mul)
           return getUDivExactExpr(LHS, RHS);
       }
     }
   }
 
   for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
     if (Mul->getOperand(i) == RHS) {
       SmallVector<const SCEV *, 2> Operands;
       Operands.append(Mul->op_begin(), Mul->op_begin() + i);
       Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
       return getMulExpr(Operands);
     }
   }
 
   return getUDivExpr(LHS, RHS);
 }
 
 /// Get an add recurrence expression for the specified loop.  Simplify the
 /// expression as much as possible.
 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
                                            const Loop *L,
                                            SCEV::NoWrapFlags Flags) {
   SmallVector<const SCEV *, 4> Operands;
   Operands.push_back(Start);
   if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
     if (StepChrec->getLoop() == L) {
       Operands.append(StepChrec->op_begin(), StepChrec->op_end());
       return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
     }
 
   Operands.push_back(Step);
   return getAddRecExpr(Operands, L, Flags);
 }
 
 /// Get an add recurrence expression for the specified loop.  Simplify the
 /// expression as much as possible.
 const SCEV *
 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
                                const Loop *L, SCEV::NoWrapFlags Flags) {
   if (Operands.size() == 1) return Operands[0];
 #ifndef NDEBUG
   Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
   for (unsigned i = 1, e = Operands.size(); i != e; ++i)
     assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
            "SCEVAddRecExpr operand types don't match!");
   for (unsigned i = 0, e = Operands.size(); i != e; ++i)
     assert(isLoopInvariant(Operands[i], L) &&
            "SCEVAddRecExpr operand is not loop-invariant!");
 #endif
 
   if (Operands.back()->isZero()) {
     Operands.pop_back();
     return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0}  -->  X
   }
 
   // It's tempting to want to call getMaxBackedgeTakenCount count here and
   // use that information to infer NUW and NSW flags. However, computing a
   // BE count requires calling getAddRecExpr, so we may not yet have a
   // meaningful BE count at this point (and if we don't, we'd be stuck
   // with a SCEVCouldNotCompute as the cached BE count).
 
   Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
 
   // Canonicalize nested AddRecs in by nesting them in order of loop depth.
   if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
     const Loop *NestedLoop = NestedAR->getLoop();
     if (L->contains(NestedLoop)
             ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
             : (!NestedLoop->contains(L) &&
                DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
       SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
                                                   NestedAR->op_end());
       Operands[0] = NestedAR->getStart();
       // AddRecs require their operands be loop-invariant with respect to their
       // loops. Don't perform this transformation if it would break this
       // requirement.
       bool AllInvariant = all_of(
           Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
 
       if (AllInvariant) {
         // Create a recurrence for the outer loop with the same step size.
         //
         // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
         // inner recurrence has the same property.
         SCEV::NoWrapFlags OuterFlags =
           maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
 
         NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
         AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
           return isLoopInvariant(Op, NestedLoop);
         });
 
         if (AllInvariant) {
           // Ok, both add recurrences are valid after the transformation.
           //
           // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
           // the outer recurrence has the same property.
           SCEV::NoWrapFlags InnerFlags =
             maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
           return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
         }
       }
       // Reset Operands to its original state.
       Operands[0] = NestedAR;
     }
   }
 
   // Okay, it looks like we really DO need an addrec expr.  Check to see if we
   // already have one, otherwise create a new one.
   FoldingSetNodeID ID;
   ID.AddInteger(scAddRecExpr);
   for (unsigned i = 0, e = Operands.size(); i != e; ++i)
     ID.AddPointer(Operands[i]);
   ID.AddPointer(L);
   void *IP = nullptr;
   SCEVAddRecExpr *S =
     static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
   if (!S) {
     const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
     std::uninitialized_copy(Operands.begin(), Operands.end(), O);
     S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
                                            O, Operands.size(), L);
     UniqueSCEVs.InsertNode(S, IP);
   }
   S->setNoWrapFlags(Flags);
   return S;
 }
 
 const SCEV *
 ScalarEvolution::getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
                             const SmallVectorImpl<const SCEV *> &IndexExprs,
                             bool InBounds) {
   // getSCEV(Base)->getType() has the same address space as Base->getType()
   // because SCEV::getType() preserves the address space.
   Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
   // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
   // instruction to its SCEV, because the Instruction may be guarded by control
   // flow and the no-overflow bits may not be valid for the expression in any
   // context. This can be fixed similarly to how these flags are handled for
   // adds.
   SCEV::NoWrapFlags Wrap = InBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
 
   const SCEV *TotalOffset = getZero(IntPtrTy);
   // The address space is unimportant. The first thing we do on CurTy is getting
   // its element type.
   Type *CurTy = PointerType::getUnqual(PointeeType);
   for (const SCEV *IndexExpr : IndexExprs) {
     // Compute the (potentially symbolic) offset in bytes for this index.
     if (StructType *STy = dyn_cast<StructType>(CurTy)) {
       // For a struct, add the member offset.
       ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
       unsigned FieldNo = Index->getZExtValue();
       const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
 
       // Add the field offset to the running total offset.
       TotalOffset = getAddExpr(TotalOffset, FieldOffset);
 
       // Update CurTy to the type of the field at Index.
       CurTy = STy->getTypeAtIndex(Index);
     } else {
       // Update CurTy to its element type.
       CurTy = cast<SequentialType>(CurTy)->getElementType();
       // For an array, add the element offset, explicitly scaled.
       const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
       // Getelementptr indices are signed.
       IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
 
       // Multiply the index by the element size to compute the element offset.
       const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
 
       // Add the element offset to the running total offset.
       TotalOffset = getAddExpr(TotalOffset, LocalOffset);
     }
   }
 
   // Add the total offset from all the GEP indices to the base.
   return getAddExpr(BaseExpr, TotalOffset, Wrap);
 }
 
 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
                                          const SCEV *RHS) {
   SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
   return getSMaxExpr(Ops);
 }
 
 const SCEV *
 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
   assert(!Ops.empty() && "Cannot get empty smax!");
   if (Ops.size() == 1) return Ops[0];
 #ifndef NDEBUG
   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
            "SCEVSMaxExpr operand types don't match!");
 #endif
 
   // Sort by complexity, this groups all similar expression types together.
   GroupByComplexity(Ops, &LI);
 
   // If there are any constants, fold them together.
   unsigned Idx = 0;
   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
     ++Idx;
     assert(Idx < Ops.size());
     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
       // We found two constants, fold them together!
       ConstantInt *Fold = ConstantInt::get(
           getContext(), APIntOps::smax(LHSC->getAPInt(), RHSC->getAPInt()));
       Ops[0] = getConstant(Fold);
       Ops.erase(Ops.begin()+1);  // Erase the folded element
       if (Ops.size() == 1) return Ops[0];
       LHSC = cast<SCEVConstant>(Ops[0]);
     }
 
     // If we are left with a constant minimum-int, strip it off.
     if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
       Ops.erase(Ops.begin());
       --Idx;
     } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
       // If we have an smax with a constant maximum-int, it will always be
       // maximum-int.
       return Ops[0];
     }
 
     if (Ops.size() == 1) return Ops[0];
   }
 
   // Find the first SMax
   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
     ++Idx;
 
   // Check to see if one of the operands is an SMax. If so, expand its operands
   // onto our operand list, and recurse to simplify.
   if (Idx < Ops.size()) {
     bool DeletedSMax = false;
     while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
       Ops.erase(Ops.begin()+Idx);
       Ops.append(SMax->op_begin(), SMax->op_end());
       DeletedSMax = true;
     }
 
     if (DeletedSMax)
       return getSMaxExpr(Ops);
   }
 
   // Okay, check to see if the same value occurs in the operand list twice.  If
   // so, delete one.  Since we sorted the list, these values are required to
   // be adjacent.
   for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
     //  X smax Y smax Y  -->  X smax Y
     //  X smax Y         -->  X, if X is always greater than Y
     if (Ops[i] == Ops[i+1] ||
         isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
       Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
       --i; --e;
     } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
       Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
       --i; --e;
     }
 
   if (Ops.size() == 1) return Ops[0];
 
   assert(!Ops.empty() && "Reduced smax down to nothing!");
 
   // Okay, it looks like we really DO need an smax expr.  Check to see if we
   // already have one, otherwise create a new one.
   FoldingSetNodeID ID;
   ID.AddInteger(scSMaxExpr);
   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
     ID.AddPointer(Ops[i]);
   void *IP = nullptr;
   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
   const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
   std::uninitialized_copy(Ops.begin(), Ops.end(), O);
   SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
                                              O, Ops.size());
   UniqueSCEVs.InsertNode(S, IP);
   return S;
 }
 
 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
                                          const SCEV *RHS) {
   SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
   return getUMaxExpr(Ops);
 }
 
 const SCEV *
 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
   assert(!Ops.empty() && "Cannot get empty umax!");
   if (Ops.size() == 1) return Ops[0];
 #ifndef NDEBUG
   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
            "SCEVUMaxExpr operand types don't match!");
 #endif
 
   // Sort by complexity, this groups all similar expression types together.
   GroupByComplexity(Ops, &LI);
 
   // If there are any constants, fold them together.
   unsigned Idx = 0;
   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
     ++Idx;
     assert(Idx < Ops.size());
     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
       // We found two constants, fold them together!
       ConstantInt *Fold = ConstantInt::get(
           getContext(), APIntOps::umax(LHSC->getAPInt(), RHSC->getAPInt()));
       Ops[0] = getConstant(Fold);
       Ops.erase(Ops.begin()+1);  // Erase the folded element
       if (Ops.size() == 1) return Ops[0];
       LHSC = cast<SCEVConstant>(Ops[0]);
     }
 
     // If we are left with a constant minimum-int, strip it off.
     if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
       Ops.erase(Ops.begin());
       --Idx;
     } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
       // If we have an umax with a constant maximum-int, it will always be
       // maximum-int.
       return Ops[0];
     }
 
     if (Ops.size() == 1) return Ops[0];
   }
 
   // Find the first UMax
   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
     ++Idx;
 
   // Check to see if one of the operands is a UMax. If so, expand its operands
   // onto our operand list, and recurse to simplify.
   if (Idx < Ops.size()) {
     bool DeletedUMax = false;
     while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
       Ops.erase(Ops.begin()+Idx);
       Ops.append(UMax->op_begin(), UMax->op_end());
       DeletedUMax = true;
     }
 
     if (DeletedUMax)
       return getUMaxExpr(Ops);
   }
 
   // Okay, check to see if the same value occurs in the operand list twice.  If
   // so, delete one.  Since we sorted the list, these values are required to
   // be adjacent.
   for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
     //  X umax Y umax Y  -->  X umax Y
     //  X umax Y         -->  X, if X is always greater than Y
     if (Ops[i] == Ops[i+1] ||
         isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
       Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
       --i; --e;
     } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
       Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
       --i; --e;
     }
 
   if (Ops.size() == 1) return Ops[0];
 
   assert(!Ops.empty() && "Reduced umax down to nothing!");
 
   // Okay, it looks like we really DO need a umax expr.  Check to see if we
   // already have one, otherwise create a new one.
   FoldingSetNodeID ID;
   ID.AddInteger(scUMaxExpr);
   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
     ID.AddPointer(Ops[i]);
   void *IP = nullptr;
   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
   const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
   std::uninitialized_copy(Ops.begin(), Ops.end(), O);
   SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
                                              O, Ops.size());
   UniqueSCEVs.InsertNode(S, IP);
   return S;
 }
 
 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
                                          const SCEV *RHS) {
   // ~smax(~x, ~y) == smin(x, y).
   return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
 }
 
 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
                                          const SCEV *RHS) {
   // ~umax(~x, ~y) == umin(x, y)
   return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
 }
 
 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
   // We can bypass creating a target-independent
   // constant expression and then folding it back into a ConstantInt.
   // This is just a compile-time optimization.
   return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
 }
 
 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
                                              StructType *STy,
                                              unsigned FieldNo) {
   // We can bypass creating a target-independent
   // constant expression and then folding it back into a ConstantInt.
   // This is just a compile-time optimization.
   return getConstant(
       IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
 }
 
 const SCEV *ScalarEvolution::getUnknown(Value *V) {
   // Don't attempt to do anything other than create a SCEVUnknown object
   // here.  createSCEV only calls getUnknown after checking for all other
   // interesting possibilities, and any other code that calls getUnknown
   // is doing so in order to hide a value from SCEV canonicalization.
 
   FoldingSetNodeID ID;
   ID.AddInteger(scUnknown);
   ID.AddPointer(V);
   void *IP = nullptr;
   if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
     assert(cast<SCEVUnknown>(S)->getValue() == V &&
            "Stale SCEVUnknown in uniquing map!");
     return S;
   }
   SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
                                             FirstUnknown);
   FirstUnknown = cast<SCEVUnknown>(S);
   UniqueSCEVs.InsertNode(S, IP);
   return S;
 }
 
 //===----------------------------------------------------------------------===//
 //            Basic SCEV Analysis and PHI Idiom Recognition Code
 //
 
 /// Test if values of the given type are analyzable within the SCEV
 /// framework. This primarily includes integer types, and it can optionally
 /// include pointer types if the ScalarEvolution class has access to
 /// target-specific information.
 bool ScalarEvolution::isSCEVable(Type *Ty) const {
   // Integers and pointers are always SCEVable.
   return Ty->isIntegerTy() || Ty->isPointerTy();
 }
 
 /// Return the size in bits of the specified type, for which isSCEVable must
 /// return true.
 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
   assert(isSCEVable(Ty) && "Type is not SCEVable!");
   return getDataLayout().getTypeSizeInBits(Ty);
 }
 
 /// Return a type with the same bitwidth as the given type and which represents
 /// how SCEV will treat the given type, for which isSCEVable must return
 /// true. For pointer types, this is the pointer-sized integer type.
 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
   assert(isSCEVable(Ty) && "Type is not SCEVable!");
 
   if (Ty->isIntegerTy())
     return Ty;
 
   // The only other support type is pointer.
   assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
   return getDataLayout().getIntPtrType(Ty);
 }
 
 const SCEV *ScalarEvolution::getCouldNotCompute() {
   return CouldNotCompute.get();
 }
 
 
 bool ScalarEvolution::checkValidity(const SCEV *S) const {
   // Helper class working with SCEVTraversal to figure out if a SCEV contains
   // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
   // is set iff if find such SCEVUnknown.
   //
   struct FindInvalidSCEVUnknown {
     bool FindOne;
     FindInvalidSCEVUnknown() { FindOne = false; }
     bool follow(const SCEV *S) {
       switch (static_cast<SCEVTypes>(S->getSCEVType())) {
       case scConstant:
         return false;
       case scUnknown:
         if (!cast<SCEVUnknown>(S)->getValue())
           FindOne = true;
         return false;
       default:
         return true;
       }
     }
     bool isDone() const { return FindOne; }
   };
 
   FindInvalidSCEVUnknown F;
   SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
   ST.visitAll(S);
 
   return !F.FindOne;
 }
 
 namespace {
 // Helper class working with SCEVTraversal to figure out if a SCEV contains
 // a sub SCEV of scAddRecExpr type.  FindInvalidSCEVUnknown::FoundOne is set
 // iff if such sub scAddRecExpr type SCEV is found.
 struct FindAddRecurrence {
   bool FoundOne;
   FindAddRecurrence() : FoundOne(false) {}
 
   bool follow(const SCEV *S) {
     switch (static_cast<SCEVTypes>(S->getSCEVType())) {
     case scAddRecExpr:
       FoundOne = true;
     case scConstant:
     case scUnknown:
     case scCouldNotCompute:
       return false;
     default:
       return true;
     }
   }
   bool isDone() const { return FoundOne; }
 };
 }
 
 bool ScalarEvolution::containsAddRecurrence(const SCEV *S) {
   HasRecMapType::iterator I = HasRecMap.find_as(S);
   if (I != HasRecMap.end())
     return I->second;
 
   FindAddRecurrence F;
   SCEVTraversal<FindAddRecurrence> ST(F);
   ST.visitAll(S);
   HasRecMap.insert({S, F.FoundOne});
   return F.FoundOne;
 }
 
-/// Return the Value set from S.
-SetVector<Value *> *ScalarEvolution::getSCEVValues(const SCEV *S) {
+/// Try to split a SCEVAddExpr into a pair of {SCEV, ConstantInt}.
+/// If \p S is a SCEVAddExpr and is composed of a sub SCEV S' and an
+/// offset I, then return {S', I}, else return {\p S, nullptr}.
+static std::pair<const SCEV *, ConstantInt *> splitAddExpr(const SCEV *S) {
+  const auto *Add = dyn_cast<SCEVAddExpr>(S);
+  if (!Add)
+    return {S, nullptr};
+
+  if (Add->getNumOperands() != 2)
+    return {S, nullptr};
+
+  auto *ConstOp = dyn_cast<SCEVConstant>(Add->getOperand(0));
+  if (!ConstOp)
+    return {S, nullptr};
+
+  return {Add->getOperand(1), ConstOp->getValue()};
+}
+
+/// Return the ValueOffsetPair set for \p S. \p S can be represented
+/// by the value and offset from any ValueOffsetPair in the set.
+SetVector<ScalarEvolution::ValueOffsetPair> *
+ScalarEvolution::getSCEVValues(const SCEV *S) {
   ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
   if (SI == ExprValueMap.end())
     return nullptr;
 #ifndef NDEBUG
   if (VerifySCEVMap) {
     // Check there is no dangling Value in the set returned.
     for (const auto &VE : SI->second)
-      assert(ValueExprMap.count(VE));
+      assert(ValueExprMap.count(VE.first));
   }
 #endif
   return &SI->second;
 }
 
-/// Erase Value from ValueExprMap and ExprValueMap.  If ValueExprMap.erase(V) is
-/// not used together with forgetMemoizedResults(S), eraseValueFromMap should be
-/// used instead to ensure whenever V->S is removed from ValueExprMap, V is also
-/// removed from the set of ExprValueMap[S].
+/// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V)
+/// cannot be used separately. eraseValueFromMap should be used to remove
+/// V from ValueExprMap and ExprValueMap at the same time.
 void ScalarEvolution::eraseValueFromMap(Value *V) {
   ValueExprMapType::iterator I = ValueExprMap.find_as(V);
   if (I != ValueExprMap.end()) {
     const SCEV *S = I->second;
-    SetVector<Value *> *SV = getSCEVValues(S);
-    // Remove V from the set of ExprValueMap[S]
-    if (SV)
-      SV->remove(V);
+    // Remove {V, 0} from the set of ExprValueMap[S]
+    if (SetVector<ValueOffsetPair> *SV = getSCEVValues(S))
+      SV->remove({V, nullptr});
+
+    // Remove {V, Offset} from the set of ExprValueMap[Stripped]
+    const SCEV *Stripped;
+    ConstantInt *Offset;
+    std::tie(Stripped, Offset) = splitAddExpr(S);
+    if (Offset != nullptr) {
+      if (SetVector<ValueOffsetPair> *SV = getSCEVValues(Stripped))
+        SV->remove({V, Offset});
+    }
     ValueExprMap.erase(V);
   }
 }
 
 /// Return an existing SCEV if it exists, otherwise analyze the expression and
 /// create a new one.
 const SCEV *ScalarEvolution::getSCEV(Value *V) {
   assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
 
   const SCEV *S = getExistingSCEV(V);
   if (S == nullptr) {
     S = createSCEV(V);
     // During PHI resolution, it is possible to create two SCEVs for the same
     // V, so it is needed to double check whether V->S is inserted into
-    // ValueExprMap before insert S->V into ExprValueMap.
+    // ValueExprMap before insert S->{V, 0} into ExprValueMap.
     std::pair<ValueExprMapType::iterator, bool> Pair =
         ValueExprMap.insert({SCEVCallbackVH(V, this), S});
-    if (Pair.second)
-      ExprValueMap[S].insert(V);
+    if (Pair.second) {
+      ExprValueMap[S].insert({V, nullptr});
+
+      // If S == Stripped + Offset, add Stripped -> {V, Offset} into
+      // ExprValueMap.
+      const SCEV *Stripped = S;
+      ConstantInt *Offset = nullptr;
+      std::tie(Stripped, Offset) = splitAddExpr(S);
+      // If stripped is SCEVUnknown, don't bother to save
+      // Stripped -> {V, offset}. It doesn't simplify and sometimes even
+      // increase the complexity of the expansion code.
+      // If V is GetElementPtrInst, don't save Stripped -> {V, offset}
+      // because it may generate add/sub instead of GEP in SCEV expansion.
+      if (Offset != nullptr && !isa<SCEVUnknown>(Stripped) &&
+          !isa<GetElementPtrInst>(V))
+        ExprValueMap[Stripped].insert({V, Offset});
+    }
   }
   return S;
 }
 
 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
   assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
 
   ValueExprMapType::iterator I = ValueExprMap.find_as(V);
   if (I != ValueExprMap.end()) {
     const SCEV *S = I->second;
     if (checkValidity(S))
       return S;
+    eraseValueFromMap(V);
     forgetMemoizedResults(S);
-    ValueExprMap.erase(I);
   }
   return nullptr;
 }
 
 /// Return a SCEV corresponding to -V = -1*V
 ///
 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
                                              SCEV::NoWrapFlags Flags) {
   if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
     return getConstant(
                cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
 
   Type *Ty = V->getType();
   Ty = getEffectiveSCEVType(Ty);
   return getMulExpr(
       V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
 }
 
 /// Return a SCEV corresponding to ~V = -1-V
 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
   if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
     return getConstant(
                 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
 
   Type *Ty = V->getType();
   Ty = getEffectiveSCEVType(Ty);
   const SCEV *AllOnes =
                    getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
   return getMinusSCEV(AllOnes, V);
 }
 
 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
                                           SCEV::NoWrapFlags Flags) {
   // Fast path: X - X --> 0.
   if (LHS == RHS)
     return getZero(LHS->getType());
 
   // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
   // makes it so that we cannot make much use of NUW.
   auto AddFlags = SCEV::FlagAnyWrap;
   const bool RHSIsNotMinSigned =
       !getSignedRange(RHS).getSignedMin().isMinSignedValue();
   if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
     // Let M be the minimum representable signed value. Then (-1)*RHS
     // signed-wraps if and only if RHS is M. That can happen even for
     // a NSW subtraction because e.g. (-1)*M signed-wraps even though
     // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
     // (-1)*RHS, we need to prove that RHS != M.
     //
     // If LHS is non-negative and we know that LHS - RHS does not
     // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
     // either by proving that RHS > M or that LHS >= 0.
     if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
       AddFlags = SCEV::FlagNSW;
     }
   }
 
   // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
   // RHS is NSW and LHS >= 0.
   //
   // The difficulty here is that the NSW flag may have been proven
   // relative to a loop that is to be found in a recurrence in LHS and
   // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
   // larger scope than intended.
   auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
 
   return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags);
 }
 
 const SCEV *
 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
   Type *SrcTy = V->getType();
   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
          "Cannot truncate or zero extend with non-integer arguments!");
   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
     return V;  // No conversion
   if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
     return getTruncateExpr(V, Ty);
   return getZeroExtendExpr(V, Ty);
 }
 
 const SCEV *
 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
                                          Type *Ty) {
   Type *SrcTy = V->getType();
   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
          "Cannot truncate or zero extend with non-integer arguments!");
   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
     return V;  // No conversion
   if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
     return getTruncateExpr(V, Ty);
   return getSignExtendExpr(V, Ty);
 }
 
 const SCEV *
 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
   Type *SrcTy = V->getType();
   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
          "Cannot noop or zero extend with non-integer arguments!");
   assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
          "getNoopOrZeroExtend cannot truncate!");
   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
     return V;  // No conversion
   return getZeroExtendExpr(V, Ty);
 }
 
 const SCEV *
 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
   Type *SrcTy = V->getType();
   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
          "Cannot noop or sign extend with non-integer arguments!");
   assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
          "getNoopOrSignExtend cannot truncate!");
   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
     return V;  // No conversion
   return getSignExtendExpr(V, Ty);
 }
 
 const SCEV *
 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
   Type *SrcTy = V->getType();
   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
          "Cannot noop or any extend with non-integer arguments!");
   assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
          "getNoopOrAnyExtend cannot truncate!");
   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
     return V;  // No conversion
   return getAnyExtendExpr(V, Ty);
 }
 
 const SCEV *
 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
   Type *SrcTy = V->getType();
   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
          "Cannot truncate or noop with non-integer arguments!");
   assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
          "getTruncateOrNoop cannot extend!");
   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
     return V;  // No conversion
   return getTruncateExpr(V, Ty);
 }
 
 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
                                                         const SCEV *RHS) {
   const SCEV *PromotedLHS = LHS;
   const SCEV *PromotedRHS = RHS;
 
   if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
     PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
   else
     PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
 
   return getUMaxExpr(PromotedLHS, PromotedRHS);
 }
 
 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
                                                         const SCEV *RHS) {
   const SCEV *PromotedLHS = LHS;
   const SCEV *PromotedRHS = RHS;
 
   if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
     PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
   else
     PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
 
   return getUMinExpr(PromotedLHS, PromotedRHS);
 }
 
 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
   // A pointer operand may evaluate to a nonpointer expression, such as null.
   if (!V->getType()->isPointerTy())
     return V;
 
   if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
     return getPointerBase(Cast->getOperand());
   } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
     const SCEV *PtrOp = nullptr;
     for (const SCEV *NAryOp : NAry->operands()) {
       if (NAryOp->getType()->isPointerTy()) {
         // Cannot find the base of an expression with multiple pointer operands.
         if (PtrOp)
           return V;
         PtrOp = NAryOp;
       }
     }
     if (!PtrOp)
       return V;
     return getPointerBase(PtrOp);
   }
   return V;
 }
 
 /// Push users of the given Instruction onto the given Worklist.
 static void
 PushDefUseChildren(Instruction *I,
                    SmallVectorImpl<Instruction *> &Worklist) {
   // Push the def-use children onto the Worklist stack.
   for (User *U : I->users())
     Worklist.push_back(cast<Instruction>(U));
 }
 
 void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) {
   SmallVector<Instruction *, 16> Worklist;
   PushDefUseChildren(PN, Worklist);
 
   SmallPtrSet<Instruction *, 8> Visited;
   Visited.insert(PN);
   while (!Worklist.empty()) {
     Instruction *I = Worklist.pop_back_val();
     if (!Visited.insert(I).second)
       continue;
 
     auto It = ValueExprMap.find_as(static_cast<Value *>(I));
     if (It != ValueExprMap.end()) {
       const SCEV *Old = It->second;
 
       // Short-circuit the def-use traversal if the symbolic name
       // ceases to appear in expressions.
       if (Old != SymName && !hasOperand(Old, SymName))
         continue;
 
       // SCEVUnknown for a PHI either means that it has an unrecognized
       // structure, it's a PHI that's in the progress of being computed
       // by createNodeForPHI, or it's a single-value PHI. In the first case,
       // additional loop trip count information isn't going to change anything.
       // In the second case, createNodeForPHI will perform the necessary
       // updates on its own when it gets to that point. In the third, we do
       // want to forget the SCEVUnknown.
       if (!isa<PHINode>(I) ||
           !isa<SCEVUnknown>(Old) ||
           (I != PN && Old == SymName)) {
+        eraseValueFromMap(It->first);
         forgetMemoizedResults(Old);
-        ValueExprMap.erase(It);
       }
     }
 
     PushDefUseChildren(I, Worklist);
   }
 }
 
 namespace {
 class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
 public:
   static const SCEV *rewrite(const SCEV *S, const Loop *L,
                              ScalarEvolution &SE) {
     SCEVInitRewriter Rewriter(L, SE);
     const SCEV *Result = Rewriter.visit(S);
     return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
   }
 
   SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
       : SCEVRewriteVisitor(SE), L(L), Valid(true) {}
 
   const SCEV *visitUnknown(const SCEVUnknown *Expr) {
     if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
       Valid = false;
     return Expr;
   }
 
   const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
     // Only allow AddRecExprs for this loop.
     if (Expr->getLoop() == L)
       return Expr->getStart();
     Valid = false;
     return Expr;
   }
 
   bool isValid() { return Valid; }
 
 private:
   const Loop *L;
   bool Valid;
 };
 
 class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
 public:
   static const SCEV *rewrite(const SCEV *S, const Loop *L,
                              ScalarEvolution &SE) {
     SCEVShiftRewriter Rewriter(L, SE);
     const SCEV *Result = Rewriter.visit(S);
     return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
   }
 
   SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
       : SCEVRewriteVisitor(SE), L(L), Valid(true) {}
 
   const SCEV *visitUnknown(const SCEVUnknown *Expr) {
     // Only allow AddRecExprs for this loop.
     if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
       Valid = false;
     return Expr;
   }
 
   const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
     if (Expr->getLoop() == L && Expr->isAffine())
       return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
     Valid = false;
     return Expr;
   }
   bool isValid() { return Valid; }
 
 private:
   const Loop *L;
   bool Valid;
 };
 } // end anonymous namespace
 
 SCEV::NoWrapFlags
 ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
   if (!AR->isAffine())
     return SCEV::FlagAnyWrap;
 
   typedef OverflowingBinaryOperator OBO;
   SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap;
 
   if (!AR->hasNoSignedWrap()) {
     ConstantRange AddRecRange = getSignedRange(AR);
     ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this));
 
     auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
         Instruction::Add, IncRange, OBO::NoSignedWrap);
     if (NSWRegion.contains(AddRecRange))
       Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW);
   }
 
   if (!AR->hasNoUnsignedWrap()) {
     ConstantRange AddRecRange = getUnsignedRange(AR);
     ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this));
 
     auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
         Instruction::Add, IncRange, OBO::NoUnsignedWrap);
     if (NUWRegion.contains(AddRecRange))
       Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW);
   }
 
   return Result;
 }
 
 namespace {
 /// Represents an abstract binary operation.  This may exist as a
 /// normal instruction or constant expression, or may have been
 /// derived from an expression tree.
 struct BinaryOp {
   unsigned Opcode;
   Value *LHS;
   Value *RHS;
   bool IsNSW;
   bool IsNUW;
 
   /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
   /// constant expression.
   Operator *Op;
 
   explicit BinaryOp(Operator *Op)
       : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
         IsNSW(false), IsNUW(false), Op(Op) {
     if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
       IsNSW = OBO->hasNoSignedWrap();
       IsNUW = OBO->hasNoUnsignedWrap();
     }
   }
 
   explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
                     bool IsNUW = false)
       : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW),
         Op(nullptr) {}
 };
 }
 
 
 /// Try to map \p V into a BinaryOp, and return \c None on failure.
 static Optional<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) {
   auto *Op = dyn_cast<Operator>(V);
   if (!Op)
     return None;
 
   // Implementation detail: all the cleverness here should happen without
   // creating new SCEV expressions -- our caller knowns tricks to avoid creating
   // SCEV expressions when possible, and we should not break that.
 
   switch (Op->getOpcode()) {
   case Instruction::Add:
   case Instruction::Sub:
   case Instruction::Mul:
   case Instruction::UDiv:
   case Instruction::And:
   case Instruction::Or:
   case Instruction::AShr:
   case Instruction::Shl:
     return BinaryOp(Op);
 
   case Instruction::Xor:
     if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
       // If the RHS of the xor is a signbit, then this is just an add.
       // Instcombine turns add of signbit into xor as a strength reduction step.
       if (RHSC->getValue().isSignBit())
         return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
     return BinaryOp(Op);
 
   case Instruction::LShr:
     // Turn logical shift right of a constant into a unsigned divide.
     if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
       uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();
 
       // If the shift count is not less than the bitwidth, the result of
       // the shift is undefined. Don't try to analyze it, because the
       // resolution chosen here may differ from the resolution chosen in
       // other parts of the compiler.
       if (SA->getValue().ult(BitWidth)) {
         Constant *X =
             ConstantInt::get(SA->getContext(),
                              APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
         return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
       }
     }
     return BinaryOp(Op);
 
   case Instruction::ExtractValue: {
     auto *EVI = cast<ExtractValueInst>(Op);
     if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
       break;
 
     auto *CI = dyn_cast<CallInst>(EVI->getAggregateOperand());
     if (!CI)
       break;
 
     if (auto *F = CI->getCalledFunction())
       switch (F->getIntrinsicID()) {
       case Intrinsic::sadd_with_overflow:
       case Intrinsic::uadd_with_overflow: {
         if (!isOverflowIntrinsicNoWrap(cast<IntrinsicInst>(CI), DT))
           return BinaryOp(Instruction::Add, CI->getArgOperand(0),
                           CI->getArgOperand(1));
 
         // Now that we know that all uses of the arithmetic-result component of
         // CI are guarded by the overflow check, we can go ahead and pretend
         // that the arithmetic is non-overflowing.
         if (F->getIntrinsicID() == Intrinsic::sadd_with_overflow)
           return BinaryOp(Instruction::Add, CI->getArgOperand(0),
                           CI->getArgOperand(1), /* IsNSW = */ true,
                           /* IsNUW = */ false);
         else
           return BinaryOp(Instruction::Add, CI->getArgOperand(0),
                           CI->getArgOperand(1), /* IsNSW = */ false,
                           /* IsNUW*/ true);
       }
 
       case Intrinsic::ssub_with_overflow:
       case Intrinsic::usub_with_overflow:
         return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
                         CI->getArgOperand(1));
 
       case Intrinsic::smul_with_overflow:
       case Intrinsic::umul_with_overflow:
         return BinaryOp(Instruction::Mul, CI->getArgOperand(0),
                         CI->getArgOperand(1));
       default:
         break;
       }
   }
 
   default:
     break;
   }
 
   return None;
 }
 
 const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
   const Loop *L = LI.getLoopFor(PN->getParent());
   if (!L || L->getHeader() != PN->getParent())
     return nullptr;
 
   // The loop may have multiple entrances or multiple exits; we can analyze
   // this phi as an addrec if it has a unique entry value and a unique
   // backedge value.
   Value *BEValueV = nullptr, *StartValueV = nullptr;
   for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
     Value *V = PN->getIncomingValue(i);
     if (L->contains(PN->getIncomingBlock(i))) {
       if (!BEValueV) {
         BEValueV = V;
       } else if (BEValueV != V) {
         BEValueV = nullptr;
         break;
       }
     } else if (!StartValueV) {
       StartValueV = V;
     } else if (StartValueV != V) {
       StartValueV = nullptr;
       break;
     }
   }
   if (BEValueV && StartValueV) {
     // While we are analyzing this PHI node, handle its value symbolically.
     const SCEV *SymbolicName = getUnknown(PN);
     assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
            "PHI node already processed?");
     ValueExprMap.insert({SCEVCallbackVH(PN, this), SymbolicName});
 
     // Using this symbolic name for the PHI, analyze the value coming around
     // the back-edge.
     const SCEV *BEValue = getSCEV(BEValueV);
 
     // NOTE: If BEValue is loop invariant, we know that the PHI node just
     // has a special value for the first iteration of the loop.
 
     // If the value coming around the backedge is an add with the symbolic
     // value we just inserted, then we found a simple induction variable!
     if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
       // If there is a single occurrence of the symbolic value, replace it
       // with a recurrence.
       unsigned FoundIndex = Add->getNumOperands();
       for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
         if (Add->getOperand(i) == SymbolicName)
           if (FoundIndex == e) {
             FoundIndex = i;
             break;
           }
 
       if (FoundIndex != Add->getNumOperands()) {
         // Create an add with everything but the specified operand.
         SmallVector<const SCEV *, 8> Ops;
         for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
           if (i != FoundIndex)
             Ops.push_back(Add->getOperand(i));
         const SCEV *Accum = getAddExpr(Ops);
 
         // This is not a valid addrec if the step amount is varying each
         // loop iteration, but is not itself an addrec in this loop.
         if (isLoopInvariant(Accum, L) ||
             (isa<SCEVAddRecExpr>(Accum) &&
              cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
           SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
 
           if (auto BO = MatchBinaryOp(BEValueV, DT)) {
             if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
               if (BO->IsNUW)
                 Flags = setFlags(Flags, SCEV::FlagNUW);
               if (BO->IsNSW)
                 Flags = setFlags(Flags, SCEV::FlagNSW);
             }
           } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
             // If the increment is an inbounds GEP, then we know the address
             // space cannot be wrapped around. We cannot make any guarantee
             // about signed or unsigned overflow because pointers are
             // unsigned but we may have a negative index from the base
             // pointer. We can guarantee that no unsigned wrap occurs if the
             // indices form a positive value.
             if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
               Flags = setFlags(Flags, SCEV::FlagNW);
 
               const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
               if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
                 Flags = setFlags(Flags, SCEV::FlagNUW);
             }
 
             // We cannot transfer nuw and nsw flags from subtraction
             // operations -- sub nuw X, Y is not the same as add nuw X, -Y
             // for instance.
           }
 
           const SCEV *StartVal = getSCEV(StartValueV);
           const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
 
           // Okay, for the entire analysis of this edge we assumed the PHI
           // to be symbolic.  We now need to go back and purge all of the
           // entries for the scalars that use the symbolic expression.
           forgetSymbolicName(PN, SymbolicName);
           ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
 
           // We can add Flags to the post-inc expression only if we
           // know that it us *undefined behavior* for BEValueV to
           // overflow.
           if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
             if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
               (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
 
           return PHISCEV;
         }
       }
     } else {
       // Otherwise, this could be a loop like this:
       //     i = 0;  for (j = 1; ..; ++j) { ....  i = j; }
       // In this case, j = {1,+,1}  and BEValue is j.
       // Because the other in-value of i (0) fits the evolution of BEValue
       // i really is an addrec evolution.
       //
       // We can generalize this saying that i is the shifted value of BEValue
       // by one iteration:
       //   PHI(f(0), f({1,+,1})) --> f({0,+,1})
       const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
       const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this);
       if (Shifted != getCouldNotCompute() &&
           Start != getCouldNotCompute()) {
         const SCEV *StartVal = getSCEV(StartValueV);
         if (Start == StartVal) {
           // Okay, for the entire analysis of this edge we assumed the PHI
           // to be symbolic.  We now need to go back and purge all of the
           // entries for the scalars that use the symbolic expression.
           forgetSymbolicName(PN, SymbolicName);
           ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
           return Shifted;
         }
       }
     }
 
     // Remove the temporary PHI node SCEV that has been inserted while intending
     // to create an AddRecExpr for this PHI node. We can not keep this temporary
     // as it will prevent later (possibly simpler) SCEV expressions to be added
     // to the ValueExprMap.
-    ValueExprMap.erase(PN);
+    eraseValueFromMap(PN);
   }
 
   return nullptr;
 }
 
 // Checks if the SCEV S is available at BB.  S is considered available at BB
 // if S can be materialized at BB without introducing a fault.
 static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
                                BasicBlock *BB) {
   struct CheckAvailable {
     bool TraversalDone = false;
     bool Available = true;
 
     const Loop *L = nullptr;  // The loop BB is in (can be nullptr)
     BasicBlock *BB = nullptr;
     DominatorTree &DT;
 
     CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
       : L(L), BB(BB), DT(DT) {}
 
     bool setUnavailable() {
       TraversalDone = true;
       Available = false;
       return false;
     }
 
     bool follow(const SCEV *S) {
       switch (S->getSCEVType()) {
       case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
       case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
         // These expressions are available if their operand(s) is/are.
         return true;
 
       case scAddRecExpr: {
         // We allow add recurrences that are on the loop BB is in, or some
         // outer loop.  This guarantees availability because the value of the
         // add recurrence at BB is simply the "current" value of the induction
         // variable.  We can relax this in the future; for instance an add
         // recurrence on a sibling dominating loop is also available at BB.
         const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
         if (L && (ARLoop == L || ARLoop->contains(L)))
           return true;
 
         return setUnavailable();
       }
 
       case scUnknown: {
         // For SCEVUnknown, we check for simple dominance.
         const auto *SU = cast<SCEVUnknown>(S);
         Value *V = SU->getValue();
 
         if (isa<Argument>(V))
           return false;
 
         if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
           return false;
 
         return setUnavailable();
       }
 
       case scUDivExpr:
       case scCouldNotCompute:
         // We do not try to smart about these at all.
         return setUnavailable();
       }
       llvm_unreachable("switch should be fully covered!");
     }
 
     bool isDone() { return TraversalDone; }
   };
 
   CheckAvailable CA(L, BB, DT);
   SCEVTraversal<CheckAvailable> ST(CA);
 
   ST.visitAll(S);
   return CA.Available;
 }
 
 // Try to match a control flow sequence that branches out at BI and merges back
 // at Merge into a "C ? LHS : RHS" select pattern.  Return true on a successful
 // match.
 static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
                           Value *&C, Value *&LHS, Value *&RHS) {
   C = BI->getCondition();
 
   BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
   BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
 
   if (!LeftEdge.isSingleEdge())
     return false;
 
   assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
 
   Use &LeftUse = Merge->getOperandUse(0);
   Use &RightUse = Merge->getOperandUse(1);
 
   if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
     LHS = LeftUse;
     RHS = RightUse;
     return true;
   }
 
   if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
     LHS = RightUse;
     RHS = LeftUse;
     return true;
   }
 
   return false;
 }
 
 const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
   if (PN->getNumIncomingValues() == 2) {
     const Loop *L = LI.getLoopFor(PN->getParent());
 
     // We don't want to break LCSSA, even in a SCEV expression tree.
     for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
       if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
         return nullptr;
 
     // Try to match
     //
     //  br %cond, label %left, label %right
     // left:
     //  br label %merge
     // right:
     //  br label %merge
     // merge:
     //  V = phi [ %x, %left ], [ %y, %right ]
     //
     // as "select %cond, %x, %y"
 
     BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
     assert(IDom && "At least the entry block should dominate PN");
 
     auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
     Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
 
     if (BI && BI->isConditional() &&
         BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
         IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
         IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
       return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
   }
 
   return nullptr;
 }
 
 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
   if (const SCEV *S = createAddRecFromPHI(PN))
     return S;
 
   if (const SCEV *S = createNodeFromSelectLikePHI(PN))
     return S;
 
   // If the PHI has a single incoming value, follow that value, unless the
   // PHI's incoming blocks are in a different loop, in which case doing so
   // risks breaking LCSSA form. Instcombine would normally zap these, but
   // it doesn't have DominatorTree information, so it may miss cases.
   if (Value *V = SimplifyInstruction(PN, getDataLayout(), &TLI, &DT, &AC))
     if (LI.replacementPreservesLCSSAForm(PN, V))
       return getSCEV(V);
 
   // If it's not a loop phi, we can't handle it yet.
   return getUnknown(PN);
 }
 
 const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
                                                       Value *Cond,
                                                       Value *TrueVal,
                                                       Value *FalseVal) {
   // Handle "constant" branch or select. This can occur for instance when a
   // loop pass transforms an inner loop and moves on to process the outer loop.
   if (auto *CI = dyn_cast<ConstantInt>(Cond))
     return getSCEV(CI->isOne() ? TrueVal : FalseVal);
 
   // Try to match some simple smax or umax patterns.
   auto *ICI = dyn_cast<ICmpInst>(Cond);
   if (!ICI)
     return getUnknown(I);
 
   Value *LHS = ICI->getOperand(0);
   Value *RHS = ICI->getOperand(1);
 
   switch (ICI->getPredicate()) {
   case ICmpInst::ICMP_SLT:
   case ICmpInst::ICMP_SLE:
     std::swap(LHS, RHS);
   // fall through
   case ICmpInst::ICMP_SGT:
   case ICmpInst::ICMP_SGE:
     // a >s b ? a+x : b+x  ->  smax(a, b)+x
     // a >s b ? b+x : a+x  ->  smin(a, b)+x
     if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
       const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
       const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
       const SCEV *LA = getSCEV(TrueVal);
       const SCEV *RA = getSCEV(FalseVal);
       const SCEV *LDiff = getMinusSCEV(LA, LS);
       const SCEV *RDiff = getMinusSCEV(RA, RS);
       if (LDiff == RDiff)
         return getAddExpr(getSMaxExpr(LS, RS), LDiff);
       LDiff = getMinusSCEV(LA, RS);
       RDiff = getMinusSCEV(RA, LS);
       if (LDiff == RDiff)
         return getAddExpr(getSMinExpr(LS, RS), LDiff);
     }
     break;
   case ICmpInst::ICMP_ULT:
   case ICmpInst::ICMP_ULE:
     std::swap(LHS, RHS);
   // fall through
   case ICmpInst::ICMP_UGT:
   case ICmpInst::ICMP_UGE:
     // a >u b ? a+x : b+x  ->  umax(a, b)+x
     // a >u b ? b+x : a+x  ->  umin(a, b)+x
     if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
       const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
       const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
       const SCEV *LA = getSCEV(TrueVal);
       const SCEV *RA = getSCEV(FalseVal);
       const SCEV *LDiff = getMinusSCEV(LA, LS);
       const SCEV *RDiff = getMinusSCEV(RA, RS);
       if (LDiff == RDiff)
         return getAddExpr(getUMaxExpr(LS, RS), LDiff);
       LDiff = getMinusSCEV(LA, RS);
       RDiff = getMinusSCEV(RA, LS);
       if (LDiff == RDiff)
         return getAddExpr(getUMinExpr(LS, RS), LDiff);
     }
     break;
   case ICmpInst::ICMP_NE:
     // n != 0 ? n+x : 1+x  ->  umax(n, 1)+x
     if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
         isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
       const SCEV *One = getOne(I->getType());
       const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
       const SCEV *LA = getSCEV(TrueVal);
       const SCEV *RA = getSCEV(FalseVal);
       const SCEV *LDiff = getMinusSCEV(LA, LS);
       const SCEV *RDiff = getMinusSCEV(RA, One);
       if (LDiff == RDiff)
         return getAddExpr(getUMaxExpr(One, LS), LDiff);
     }
     break;
   case ICmpInst::ICMP_EQ:
     // n == 0 ? 1+x : n+x  ->  umax(n, 1)+x
     if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
         isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
       const SCEV *One = getOne(I->getType());
       const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
       const SCEV *LA = getSCEV(TrueVal);
       const SCEV *RA = getSCEV(FalseVal);
       const SCEV *LDiff = getMinusSCEV(LA, One);
       const SCEV *RDiff = getMinusSCEV(RA, LS);
       if (LDiff == RDiff)
         return getAddExpr(getUMaxExpr(One, LS), LDiff);
     }
     break;
   default:
     break;
   }
 
   return getUnknown(I);
 }
 
 /// Expand GEP instructions into add and multiply operations. This allows them
 /// to be analyzed by regular SCEV code.
 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
   // Don't attempt to analyze GEPs over unsized objects.
   if (!GEP->getSourceElementType()->isSized())
     return getUnknown(GEP);
 
   SmallVector<const SCEV *, 4> IndexExprs;
   for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
     IndexExprs.push_back(getSCEV(*Index));
   return getGEPExpr(GEP->getSourceElementType(),
                     getSCEV(GEP->getPointerOperand()),
                     IndexExprs, GEP->isInBounds());
 }
 
 uint32_t
 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
     return C->getAPInt().countTrailingZeros();
 
   if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
     return std::min(GetMinTrailingZeros(T->getOperand()),
                     (uint32_t)getTypeSizeInBits(T->getType()));
 
   if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
     uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
     return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
              getTypeSizeInBits(E->getType()) : OpRes;
   }
 
   if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
     uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
     return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
              getTypeSizeInBits(E->getType()) : OpRes;
   }
 
   if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
     // The result is the min of all operands results.
     uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
     for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
     return MinOpRes;
   }
 
   if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
     // The result is the sum of all operands results.
     uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
     uint32_t BitWidth = getTypeSizeInBits(M->getType());
     for (unsigned i = 1, e = M->getNumOperands();
          SumOpRes != BitWidth && i != e; ++i)
       SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
                           BitWidth);
     return SumOpRes;
   }
 
   if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
     // The result is the min of all operands results.
     uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
     for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
     return MinOpRes;
   }
 
   if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
     // The result is the min of all operands results.
     uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
     for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
     return MinOpRes;
   }
 
   if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
     // The result is the min of all operands results.
     uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
     for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
     return MinOpRes;
   }
 
   if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
     // For a SCEVUnknown, ask ValueTracking.
     unsigned BitWidth = getTypeSizeInBits(U->getType());
     APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
     computeKnownBits(U->getValue(), Zeros, Ones, getDataLayout(), 0, &AC,
                      nullptr, &DT);
     return Zeros.countTrailingOnes();
   }
 
   // SCEVUDivExpr
   return 0;
 }
 
 /// Helper method to assign a range to V from metadata present in the IR.
 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
   if (Instruction *I = dyn_cast<Instruction>(V))
     if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
       return getConstantRangeFromMetadata(*MD);
 
   return None;
 }
 
 /// Determine the range for a particular SCEV.  If SignHint is
 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
 /// with a "cleaner" unsigned (resp. signed) representation.
 ConstantRange
 ScalarEvolution::getRange(const SCEV *S,
                           ScalarEvolution::RangeSignHint SignHint) {
   DenseMap<const SCEV *, ConstantRange> &Cache =
       SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
                                                        : SignedRanges;
 
   // See if we've computed this range already.
   DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
   if (I != Cache.end())
     return I->second;
 
   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
     return setRange(C, SignHint, ConstantRange(C->getAPInt()));
 
   unsigned BitWidth = getTypeSizeInBits(S->getType());
   ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
 
   // If the value has known zeros, the maximum value will have those known zeros
   // as well.
   uint32_t TZ = GetMinTrailingZeros(S);
   if (TZ != 0) {
     if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
       ConservativeResult =
           ConstantRange(APInt::getMinValue(BitWidth),
                         APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
     else
       ConservativeResult = ConstantRange(
           APInt::getSignedMinValue(BitWidth),
           APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
   }
 
   if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
     ConstantRange X = getRange(Add->getOperand(0), SignHint);
     for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
       X = X.add(getRange(Add->getOperand(i), SignHint));
     return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
   }
 
   if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
     ConstantRange X = getRange(Mul->getOperand(0), SignHint);
     for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
       X = X.multiply(getRange(Mul->getOperand(i), SignHint));
     return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
   }
 
   if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
     ConstantRange X = getRange(SMax->getOperand(0), SignHint);
     for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
       X = X.smax(getRange(SMax->getOperand(i), SignHint));
     return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
   }
 
   if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
     ConstantRange X = getRange(UMax->getOperand(0), SignHint);
     for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
       X = X.umax(getRange(UMax->getOperand(i), SignHint));
     return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
   }
 
   if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
     ConstantRange X = getRange(UDiv->getLHS(), SignHint);
     ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
     return setRange(UDiv, SignHint,
                     ConservativeResult.intersectWith(X.udiv(Y)));
   }
 
   if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
     ConstantRange X = getRange(ZExt->getOperand(), SignHint);
     return setRange(ZExt, SignHint,
                     ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
   }
 
   if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
     ConstantRange X = getRange(SExt->getOperand(), SignHint);
     return setRange(SExt, SignHint,
                     ConservativeResult.intersectWith(X.signExtend(BitWidth)));
   }
 
   if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
     ConstantRange X = getRange(Trunc->getOperand(), SignHint);
     return setRange(Trunc, SignHint,
                     ConservativeResult.intersectWith(X.truncate(BitWidth)));
   }
 
   if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
     // If there's no unsigned wrap, the value will never be less than its
     // initial value.
     if (AddRec->hasNoUnsignedWrap())
       if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
         if (!C->getValue()->isZero())
           ConservativeResult = ConservativeResult.intersectWith(
               ConstantRange(C->getAPInt(), APInt(BitWidth, 0)));
 
     // If there's no signed wrap, and all the operands have the same sign or
     // zero, the value won't ever change sign.
     if (AddRec->hasNoSignedWrap()) {
       bool AllNonNeg = true;
       bool AllNonPos = true;
       for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
         if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
         if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
       }
       if (AllNonNeg)
         ConservativeResult = ConservativeResult.intersectWith(
           ConstantRange(APInt(BitWidth, 0),
                         APInt::getSignedMinValue(BitWidth)));
       else if (AllNonPos)
         ConservativeResult = ConservativeResult.intersectWith(
           ConstantRange(APInt::getSignedMinValue(BitWidth),
                         APInt(BitWidth, 1)));
     }
 
     // TODO: non-affine addrec
     if (AddRec->isAffine()) {
       const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
       if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
           getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
         auto RangeFromAffine = getRangeForAffineAR(
             AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
             BitWidth);
         if (!RangeFromAffine.isFullSet())
           ConservativeResult =
               ConservativeResult.intersectWith(RangeFromAffine);
 
         auto RangeFromFactoring = getRangeViaFactoring(
             AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
             BitWidth);
         if (!RangeFromFactoring.isFullSet())
           ConservativeResult =
               ConservativeResult.intersectWith(RangeFromFactoring);
       }
     }
 
     return setRange(AddRec, SignHint, ConservativeResult);
   }
 
   if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
     // Check if the IR explicitly contains !range metadata.
     Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
     if (MDRange.hasValue())
       ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
 
     // Split here to avoid paying the compile-time cost of calling both
     // computeKnownBits and ComputeNumSignBits.  This restriction can be lifted
     // if needed.
     const DataLayout &DL = getDataLayout();
     if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
       // For a SCEVUnknown, ask ValueTracking.
       APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
       computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, &AC, nullptr, &DT);
       if (Ones != ~Zeros + 1)
         ConservativeResult =
             ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
     } else {
       assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
              "generalize as needed!");
       unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
       if (NS > 1)
         ConservativeResult = ConservativeResult.intersectWith(
             ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
                           APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
     }
 
     return setRange(U, SignHint, ConservativeResult);
   }
 
   return setRange(S, SignHint, ConservativeResult);
 }
 
 ConstantRange ScalarEvolution::getRangeForAffineAR(const SCEV *Start,
                                                    const SCEV *Step,
                                                    const SCEV *MaxBECount,
                                                    unsigned BitWidth) {
   assert(!isa<SCEVCouldNotCompute>(MaxBECount) &&
          getTypeSizeInBits(MaxBECount->getType()) <= BitWidth &&
          "Precondition!");
 
   ConstantRange Result(BitWidth, /* isFullSet = */ true);
 
   // Check for overflow.  This must be done with ConstantRange arithmetic
   // because we could be called from within the ScalarEvolution overflow
   // checking code.
 
   MaxBECount = getNoopOrZeroExtend(MaxBECount, Start->getType());
   ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
   ConstantRange ZExtMaxBECountRange =
       MaxBECountRange.zextOrTrunc(BitWidth * 2 + 1);
 
   ConstantRange StepSRange = getSignedRange(Step);
   ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2 + 1);
 
   ConstantRange StartURange = getUnsignedRange(Start);
   ConstantRange EndURange =
       StartURange.add(MaxBECountRange.multiply(StepSRange));
 
   // Check for unsigned overflow.
   ConstantRange ZExtStartURange = StartURange.zextOrTrunc(BitWidth * 2 + 1);
   ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2 + 1);
   if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
       ZExtEndURange) {
     APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
                                EndURange.getUnsignedMin());
     APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
                                EndURange.getUnsignedMax());
     bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
     if (!IsFullRange)
       Result =
           Result.intersectWith(ConstantRange(Min, Max + 1));
   }
 
   ConstantRange StartSRange = getSignedRange(Start);
   ConstantRange EndSRange =
       StartSRange.add(MaxBECountRange.multiply(StepSRange));
 
   // Check for signed overflow. This must be done with ConstantRange
   // arithmetic because we could be called from within the ScalarEvolution
   // overflow checking code.
   ConstantRange SExtStartSRange = StartSRange.sextOrTrunc(BitWidth * 2 + 1);
   ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2 + 1);
   if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
       SExtEndSRange) {
     APInt Min =
         APIntOps::smin(StartSRange.getSignedMin(), EndSRange.getSignedMin());
     APInt Max =
         APIntOps::smax(StartSRange.getSignedMax(), EndSRange.getSignedMax());
     bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
     if (!IsFullRange)
       Result =
           Result.intersectWith(ConstantRange(Min, Max + 1));
   }
 
   return Result;
 }
 
 ConstantRange ScalarEvolution::getRangeViaFactoring(const SCEV *Start,
                                                     const SCEV *Step,
                                                     const SCEV *MaxBECount,
                                                     unsigned BitWidth) {
   //    RangeOf({C?A:B,+,C?P:Q}) == RangeOf(C?{A,+,P}:{B,+,Q})
   // == RangeOf({A,+,P}) union RangeOf({B,+,Q})
 
   struct SelectPattern {
     Value *Condition = nullptr;
     APInt TrueValue;
     APInt FalseValue;
 
     explicit SelectPattern(ScalarEvolution &SE, unsigned BitWidth,
                            const SCEV *S) {
       Optional<unsigned> CastOp;
       APInt Offset(BitWidth, 0);
 
       assert(SE.getTypeSizeInBits(S->getType()) == BitWidth &&
              "Should be!");
 
       // Peel off a constant offset:
       if (auto *SA = dyn_cast<SCEVAddExpr>(S)) {
         // In the future we could consider being smarter here and handle
         // {Start+Step,+,Step} too.
         if (SA->getNumOperands() != 2 || !isa<SCEVConstant>(SA->getOperand(0)))
           return;
 
         Offset = cast<SCEVConstant>(SA->getOperand(0))->getAPInt();
         S = SA->getOperand(1);
       }
 
       // Peel off a cast operation
       if (auto *SCast = dyn_cast<SCEVCastExpr>(S)) {
         CastOp = SCast->getSCEVType();
         S = SCast->getOperand();
       }
 
       using namespace llvm::PatternMatch;
 
       auto *SU = dyn_cast<SCEVUnknown>(S);
       const APInt *TrueVal, *FalseVal;
       if (!SU ||
           !match(SU->getValue(), m_Select(m_Value(Condition), m_APInt(TrueVal),
                                           m_APInt(FalseVal)))) {
         Condition = nullptr;
         return;
       }
 
       TrueValue = *TrueVal;
       FalseValue = *FalseVal;
 
       // Re-apply the cast we peeled off earlier
       if (CastOp.hasValue())
         switch (*CastOp) {
         default:
           llvm_unreachable("Unknown SCEV cast type!");
 
         case scTruncate:
           TrueValue = TrueValue.trunc(BitWidth);
           FalseValue = FalseValue.trunc(BitWidth);
           break;
         case scZeroExtend:
           TrueValue = TrueValue.zext(BitWidth);
           FalseValue = FalseValue.zext(BitWidth);
           break;
         case scSignExtend:
           TrueValue = TrueValue.sext(BitWidth);
           FalseValue = FalseValue.sext(BitWidth);
           break;
         }
 
       // Re-apply the constant offset we peeled off earlier
       TrueValue += Offset;
       FalseValue += Offset;
     }
 
     bool isRecognized() { return Condition != nullptr; }
   };
 
   SelectPattern StartPattern(*this, BitWidth, Start);
   if (!StartPattern.isRecognized())
     return ConstantRange(BitWidth, /* isFullSet = */ true);
 
   SelectPattern StepPattern(*this, BitWidth, Step);
   if (!StepPattern.isRecognized())
     return ConstantRange(BitWidth, /* isFullSet = */ true);
 
   if (StartPattern.Condition != StepPattern.Condition) {
     // We don't handle this case today; but we could, by considering four
     // possibilities below instead of two. I'm not sure if there are cases where
     // that will help over what getRange already does, though.
     return ConstantRange(BitWidth, /* isFullSet = */ true);
   }
 
   // NB! Calling ScalarEvolution::getConstant is fine, but we should not try to
   // construct arbitrary general SCEV expressions here.  This function is called
   // from deep in the call stack, and calling getSCEV (on a sext instruction,
   // say) can end up caching a suboptimal value.
 
   // FIXME: without the explicit `this` receiver below, MSVC errors out with
   // C2352 and C2512 (otherwise it isn't needed).
 
   const SCEV *TrueStart = this->getConstant(StartPattern.TrueValue);
   const SCEV *TrueStep = this->getConstant(StepPattern.TrueValue);
   const SCEV *FalseStart = this->getConstant(StartPattern.FalseValue);
   const SCEV *FalseStep = this->getConstant(StepPattern.FalseValue);
 
   ConstantRange TrueRange =
       this->getRangeForAffineAR(TrueStart, TrueStep, MaxBECount, BitWidth);
   ConstantRange FalseRange =
       this->getRangeForAffineAR(FalseStart, FalseStep, MaxBECount, BitWidth);
 
   return TrueRange.unionWith(FalseRange);
 }
 
 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
   if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
   const BinaryOperator *BinOp = cast<BinaryOperator>(V);
 
   // Return early if there are no flags to propagate to the SCEV.
   SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
   if (BinOp->hasNoUnsignedWrap())
     Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
   if (BinOp->hasNoSignedWrap())
     Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
   if (Flags == SCEV::FlagAnyWrap)
     return SCEV::FlagAnyWrap;
 
   return isSCEVExprNeverPoison(BinOp) ? Flags : SCEV::FlagAnyWrap;
 }
 
 bool ScalarEvolution::isSCEVExprNeverPoison(const Instruction *I) {
   // Here we check that I is in the header of the innermost loop containing I,
   // since we only deal with instructions in the loop header. The actual loop we
   // need to check later will come from an add recurrence, but getting that
   // requires computing the SCEV of the operands, which can be expensive. This
   // check we can do cheaply to rule out some cases early.
   Loop *InnermostContainingLoop = LI.getLoopFor(I->getParent());
   if (InnermostContainingLoop == nullptr ||
       InnermostContainingLoop->getHeader() != I->getParent())
     return false;
 
   // Only proceed if we can prove that I does not yield poison.
   if (!isKnownNotFullPoison(I)) return false;
 
   // At this point we know that if I is executed, then it does not wrap
   // according to at least one of NSW or NUW. If I is not executed, then we do
   // not know if the calculation that I represents would wrap. Multiple
   // instructions can map to the same SCEV. If we apply NSW or NUW from I to
   // the SCEV, we must guarantee no wrapping for that SCEV also when it is
   // derived from other instructions that map to the same SCEV. We cannot make
   // that guarantee for cases where I is not executed. So we need to find the
   // loop that I is considered in relation to and prove that I is executed for
   // every iteration of that loop. That implies that the value that I
   // calculates does not wrap anywhere in the loop, so then we can apply the
   // flags to the SCEV.
   //
   // We check isLoopInvariant to disambiguate in case we are adding recurrences
   // from different loops, so that we know which loop to prove that I is
   // executed in.
   for (unsigned OpIndex = 0; OpIndex < I->getNumOperands(); ++OpIndex) {
     // I could be an extractvalue from a call to an overflow intrinsic.
     // TODO: We can do better here in some cases.
     if (!isSCEVable(I->getOperand(OpIndex)->getType()))
       return false;
     const SCEV *Op = getSCEV(I->getOperand(OpIndex));
     if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
       bool AllOtherOpsLoopInvariant = true;
       for (unsigned OtherOpIndex = 0; OtherOpIndex < I->getNumOperands();
            ++OtherOpIndex) {
         if (OtherOpIndex != OpIndex) {
           const SCEV *OtherOp = getSCEV(I->getOperand(OtherOpIndex));
           if (!isLoopInvariant(OtherOp, AddRec->getLoop())) {
             AllOtherOpsLoopInvariant = false;
             break;
           }
         }
       }
       if (AllOtherOpsLoopInvariant &&
           isGuaranteedToExecuteForEveryIteration(I, AddRec->getLoop()))
         return true;
     }
   }
   return false;
 }
 
 bool ScalarEvolution::isAddRecNeverPoison(const Instruction *I, const Loop *L) {
   // If we know that \c I can never be poison period, then that's enough.
   if (isSCEVExprNeverPoison(I))
     return true;
 
   // For an add recurrence specifically, we assume that infinite loops without
   // side effects are undefined behavior, and then reason as follows:
   //
   // If the add recurrence is poison in any iteration, it is poison on all
   // future iterations (since incrementing poison yields poison). If the result
   // of the add recurrence is fed into the loop latch condition and the loop
   // does not contain any throws or exiting blocks other than the latch, we now
   // have the ability to "choose" whether the backedge is taken or not (by
   // choosing a sufficiently evil value for the poison feeding into the branch)
   // for every iteration including and after the one in which \p I first became
   // poison.  There are two possibilities (let's call the iteration in which \p
   // I first became poison as K):
   //
   //  1. In the set of iterations including and after K, the loop body executes
   //     no side effects.  In this case executing the backege an infinte number
   //     of times will yield undefined behavior.
   //
   //  2. In the set of iterations including and after K, the loop body executes
   //     at least one side effect.  In this case, that specific instance of side
   //     effect is control dependent on poison, which also yields undefined
   //     behavior.
 
   auto *ExitingBB = L->getExitingBlock();
   auto *LatchBB = L->getLoopLatch();
   if (!ExitingBB || !LatchBB || ExitingBB != LatchBB)
     return false;
 
   SmallPtrSet<const Instruction *, 16> Pushed;
   SmallVector<const Instruction *, 8> PoisonStack;
 
   // We start by assuming \c I, the post-inc add recurrence, is poison.  Only
   // things that are known to be fully poison under that assumption go on the
   // PoisonStack.
   Pushed.insert(I);
   PoisonStack.push_back(I);
 
   bool LatchControlDependentOnPoison = false;
   while (!PoisonStack.empty() && !LatchControlDependentOnPoison) {
     const Instruction *Poison = PoisonStack.pop_back_val();
 
     for (auto *PoisonUser : Poison->users()) {
       if (propagatesFullPoison(cast<Instruction>(PoisonUser))) {
         if (Pushed.insert(cast<Instruction>(PoisonUser)).second)
           PoisonStack.push_back(cast<Instruction>(PoisonUser));
       } else if (auto *BI = dyn_cast<BranchInst>(PoisonUser)) {
         assert(BI->isConditional() && "Only possibility!");
         if (BI->getParent() == LatchBB) {
           LatchControlDependentOnPoison = true;
           break;
         }
       }
     }
   }
 
   return LatchControlDependentOnPoison && loopHasNoAbnormalExits(L);
 }
 
 bool ScalarEvolution::loopHasNoAbnormalExits(const Loop *L) {
   auto Itr = LoopHasNoAbnormalExits.find(L);
   if (Itr == LoopHasNoAbnormalExits.end()) {
     auto NoAbnormalExitInBB = [&](BasicBlock *BB) {
       return all_of(*BB, [](Instruction &I) {
         return isGuaranteedToTransferExecutionToSuccessor(&I);
       });
     };
 
     auto InsertPair = LoopHasNoAbnormalExits.insert(
         {L, all_of(L->getBlocks(), NoAbnormalExitInBB)});
     assert(InsertPair.second && "We just checked!");
     Itr = InsertPair.first;
   }
 
   return Itr->second;
 }
 
 const SCEV *ScalarEvolution::createSCEV(Value *V) {
   if (!isSCEVable(V->getType()))
     return getUnknown(V);
 
   if (Instruction *I = dyn_cast<Instruction>(V)) {
     // Don't attempt to analyze instructions in blocks that aren't
     // reachable. Such instructions don't matter, and they aren't required
     // to obey basic rules for definitions dominating uses which this
     // analysis depends on.
     if (!DT.isReachableFromEntry(I->getParent()))
       return getUnknown(V);
   } else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
     return getConstant(CI);
   else if (isa<ConstantPointerNull>(V))
     return getZero(V->getType());
   else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
     return GA->isInterposable() ? getUnknown(V) : getSCEV(GA->getAliasee());
   else if (!isa<ConstantExpr>(V))
     return getUnknown(V);
 
   Operator *U = cast<Operator>(V);
   if (auto BO = MatchBinaryOp(U, DT)) {
     switch (BO->Opcode) {
     case Instruction::Add: {
       // The simple thing to do would be to just call getSCEV on both operands
       // and call getAddExpr with the result. However if we're looking at a
       // bunch of things all added together, this can be quite inefficient,
       // because it leads to N-1 getAddExpr calls for N ultimate operands.
       // Instead, gather up all the operands and make a single getAddExpr call.
       // LLVM IR canonical form means we need only traverse the left operands.
       SmallVector<const SCEV *, 4> AddOps;
       do {
         if (BO->Op) {
           if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
             AddOps.push_back(OpSCEV);
             break;
           }
 
           // If a NUW or NSW flag can be applied to the SCEV for this
           // addition, then compute the SCEV for this addition by itself
           // with a separate call to getAddExpr. We need to do that
           // instead of pushing the operands of the addition onto AddOps,
           // since the flags are only known to apply to this particular
           // addition - they may not apply to other additions that can be
           // formed with operands from AddOps.
           const SCEV *RHS = getSCEV(BO->RHS);
           SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
           if (Flags != SCEV::FlagAnyWrap) {
             const SCEV *LHS = getSCEV(BO->LHS);
             if (BO->Opcode == Instruction::Sub)
               AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
             else
               AddOps.push_back(getAddExpr(LHS, RHS, Flags));
             break;
           }
         }
 
         if (BO->Opcode == Instruction::Sub)
           AddOps.push_back(getNegativeSCEV(getSCEV(BO->RHS)));
         else
           AddOps.push_back(getSCEV(BO->RHS));
 
         auto NewBO = MatchBinaryOp(BO->LHS, DT);
         if (!NewBO || (NewBO->Opcode != Instruction::Add &&
                        NewBO->Opcode != Instruction::Sub)) {
           AddOps.push_back(getSCEV(BO->LHS));
           break;
         }
         BO = NewBO;
       } while (true);
 
       return getAddExpr(AddOps);
     }
 
     case Instruction::Mul: {
       SmallVector<const SCEV *, 4> MulOps;
       do {
         if (BO->Op) {
           if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
             MulOps.push_back(OpSCEV);
             break;
           }
 
           SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
           if (Flags != SCEV::FlagAnyWrap) {
             MulOps.push_back(
                 getMulExpr(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags));
             break;
           }
         }
 
         MulOps.push_back(getSCEV(BO->RHS));
         auto NewBO = MatchBinaryOp(BO->LHS, DT);
         if (!NewBO || NewBO->Opcode != Instruction::Mul) {
           MulOps.push_back(getSCEV(BO->LHS));
           break;
         }
         BO = NewBO;
       } while (true);
 
       return getMulExpr(MulOps);
     }
     case Instruction::UDiv:
       return getUDivExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
     case Instruction::Sub: {
       SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
       if (BO->Op)
         Flags = getNoWrapFlagsFromUB(BO->Op);
       return getMinusSCEV(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags);
     }
     case Instruction::And:
       // For an expression like x&255 that merely masks off the high bits,
       // use zext(trunc(x)) as the SCEV expression.
       if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
         if (CI->isNullValue())
           return getSCEV(BO->RHS);
         if (CI->isAllOnesValue())
           return getSCEV(BO->LHS);
         const APInt &A = CI->getValue();
 
         // Instcombine's ShrinkDemandedConstant may strip bits out of
         // constants, obscuring what would otherwise be a low-bits mask.
         // Use computeKnownBits to compute what ShrinkDemandedConstant
         // knew about to reconstruct a low-bits mask value.
         unsigned LZ = A.countLeadingZeros();
         unsigned TZ = A.countTrailingZeros();
         unsigned BitWidth = A.getBitWidth();
         APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
         computeKnownBits(BO->LHS, KnownZero, KnownOne, getDataLayout(),
                          0, &AC, nullptr, &DT);
 
         APInt EffectiveMask =
             APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
         if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
           const SCEV *MulCount = getConstant(ConstantInt::get(
               getContext(), APInt::getOneBitSet(BitWidth, TZ)));
           return getMulExpr(
               getZeroExtendExpr(
                   getTruncateExpr(
                       getUDivExactExpr(getSCEV(BO->LHS), MulCount),
                       IntegerType::get(getContext(), BitWidth - LZ - TZ)),
                   BO->LHS->getType()),
               MulCount);
         }
       }
       break;
 
     case Instruction::Or:
       // If the RHS of the Or is a constant, we may have something like:
       // X*4+1 which got turned into X*4|1.  Handle this as an Add so loop
       // optimizations will transparently handle this case.
       //
       // In order for this transformation to be safe, the LHS must be of the
       // form X*(2^n) and the Or constant must be less than 2^n.
       if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
         const SCEV *LHS = getSCEV(BO->LHS);
         const APInt &CIVal = CI->getValue();
         if (GetMinTrailingZeros(LHS) >=
             (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
           // Build a plain add SCEV.
           const SCEV *S = getAddExpr(LHS, getSCEV(CI));
           // If the LHS of the add was an addrec and it has no-wrap flags,
           // transfer the no-wrap flags, since an or won't introduce a wrap.
           if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
             const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
             const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
                 OldAR->getNoWrapFlags());
           }
           return S;
         }
       }
       break;
 
     case Instruction::Xor:
       if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
         // If the RHS of xor is -1, then this is a not operation.
         if (CI->isAllOnesValue())
           return getNotSCEV(getSCEV(BO->LHS));
 
         // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
         // This is a variant of the check for xor with -1, and it handles
         // the case where instcombine has trimmed non-demanded bits out
         // of an xor with -1.
         if (auto *LBO = dyn_cast<BinaryOperator>(BO->LHS))
           if (ConstantInt *LCI = dyn_cast<ConstantInt>(LBO->getOperand(1)))
             if (LBO->getOpcode() == Instruction::And &&
                 LCI->getValue() == CI->getValue())
               if (const SCEVZeroExtendExpr *Z =
                       dyn_cast<SCEVZeroExtendExpr>(getSCEV(BO->LHS))) {
                 Type *UTy = BO->LHS->getType();
                 const SCEV *Z0 = Z->getOperand();
                 Type *Z0Ty = Z0->getType();
                 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
 
                 // If C is a low-bits mask, the zero extend is serving to
                 // mask off the high bits. Complement the operand and
                 // re-apply the zext.
                 if (APIntOps::isMask(Z0TySize, CI->getValue()))
                   return getZeroExtendExpr(getNotSCEV(Z0), UTy);
 
                 // If C is a single bit, it may be in the sign-bit position
                 // before the zero-extend. In this case, represent the xor
                 // using an add, which is equivalent, and re-apply the zext.
                 APInt Trunc = CI->getValue().trunc(Z0TySize);
                 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
                     Trunc.isSignBit())
                   return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
                                            UTy);
               }
       }
       break;
 
   case Instruction::Shl:
     // Turn shift left of a constant amount into a multiply.
     if (ConstantInt *SA = dyn_cast<ConstantInt>(BO->RHS)) {
       uint32_t BitWidth = cast<IntegerType>(SA->getType())->getBitWidth();
 
       // If the shift count is not less than the bitwidth, the result of
       // the shift is undefined. Don't try to analyze it, because the
       // resolution chosen here may differ from the resolution chosen in
       // other parts of the compiler.
       if (SA->getValue().uge(BitWidth))
         break;
 
       // It is currently not resolved how to interpret NSW for left
       // shift by BitWidth - 1, so we avoid applying flags in that
       // case. Remove this check (or this comment) once the situation
       // is resolved. See
       // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
       // and http://reviews.llvm.org/D8890 .
       auto Flags = SCEV::FlagAnyWrap;
       if (BO->Op && SA->getValue().ult(BitWidth - 1))
         Flags = getNoWrapFlagsFromUB(BO->Op);
 
       Constant *X = ConstantInt::get(getContext(),
         APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
       return getMulExpr(getSCEV(BO->LHS), getSCEV(X), Flags);
     }
     break;
 
     case Instruction::AShr:
       // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
       if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS))
         if (Operator *L = dyn_cast<Operator>(BO->LHS))
           if (L->getOpcode() == Instruction::Shl &&
               L->getOperand(1) == BO->RHS) {
             uint64_t BitWidth = getTypeSizeInBits(BO->LHS->getType());
 
             // If the shift count is not less than the bitwidth, the result of
             // the shift is undefined. Don't try to analyze it, because the
             // resolution chosen here may differ from the resolution chosen in
             // other parts of the compiler.
             if (CI->getValue().uge(BitWidth))
               break;
 
             uint64_t Amt = BitWidth - CI->getZExtValue();
             if (Amt == BitWidth)
               return getSCEV(L->getOperand(0)); // shift by zero --> noop
             return getSignExtendExpr(
                 getTruncateExpr(getSCEV(L->getOperand(0)),
                                 IntegerType::get(getContext(), Amt)),
                 BO->LHS->getType());
           }
       break;
     }
   }
 
   switch (U->getOpcode()) {
   case Instruction::Trunc:
     return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
 
   case Instruction::ZExt:
     return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
 
   case Instruction::SExt:
     return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
 
   case Instruction::BitCast:
     // BitCasts are no-op casts so we just eliminate the cast.
     if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
       return getSCEV(U->getOperand(0));
     break;
 
   // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
   // lead to pointer expressions which cannot safely be expanded to GEPs,
   // because ScalarEvolution doesn't respect the GEP aliasing rules when
   // simplifying integer expressions.
 
   case Instruction::GetElementPtr:
     return createNodeForGEP(cast<GEPOperator>(U));
 
   case Instruction::PHI:
     return createNodeForPHI(cast<PHINode>(U));
 
   case Instruction::Select:
     // U can also be a select constant expr, which let fall through.  Since
     // createNodeForSelect only works for a condition that is an `ICmpInst`, and
     // constant expressions cannot have instructions as operands, we'd have
     // returned getUnknown for a select constant expressions anyway.
     if (isa<Instruction>(U))
       return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
                                       U->getOperand(1), U->getOperand(2));
     break;
 
   case Instruction::Call:
   case Instruction::Invoke:
     if (Value *RV = CallSite(U).getReturnedArgOperand())
       return getSCEV(RV);
     break;
   }
 
   return getUnknown(V);
 }
 
 
 
 //===----------------------------------------------------------------------===//
 //                   Iteration Count Computation Code
 //
 
 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
   if (BasicBlock *ExitingBB = L->getExitingBlock())
     return getSmallConstantTripCount(L, ExitingBB);
 
   // No trip count information for multiple exits.
   return 0;
 }
 
 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
                                                     BasicBlock *ExitingBlock) {
   assert(ExitingBlock && "Must pass a non-null exiting block!");
   assert(L->isLoopExiting(ExitingBlock) &&
          "Exiting block must actually branch out of the loop!");
   const SCEVConstant *ExitCount =
       dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
   if (!ExitCount)
     return 0;
 
   ConstantInt *ExitConst = ExitCount->getValue();
 
   // Guard against huge trip counts.
   if (ExitConst->getValue().getActiveBits() > 32)
     return 0;
 
   // In case of integer overflow, this returns 0, which is correct.
   return ((unsigned)ExitConst->getZExtValue()) + 1;
 }
 
 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
   if (BasicBlock *ExitingBB = L->getExitingBlock())
     return getSmallConstantTripMultiple(L, ExitingBB);
 
   // No trip multiple information for multiple exits.
   return 0;
 }
 
 /// Returns the largest constant divisor of the trip count of this loop as a
 /// normal unsigned value, if possible. This means that the actual trip count is
 /// always a multiple of the returned value (don't forget the trip count could
 /// very well be zero as well!).
 ///
 /// Returns 1 if the trip count is unknown or not guaranteed to be the
 /// multiple of a constant (which is also the case if the trip count is simply
 /// constant, use getSmallConstantTripCount for that case), Will also return 1
 /// if the trip count is very large (>= 2^32).
 ///
 /// As explained in the comments for getSmallConstantTripCount, this assumes
 /// that control exits the loop via ExitingBlock.
 unsigned
 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
                                               BasicBlock *ExitingBlock) {
   assert(ExitingBlock && "Must pass a non-null exiting block!");
   assert(L->isLoopExiting(ExitingBlock) &&
          "Exiting block must actually branch out of the loop!");
   const SCEV *ExitCount = getExitCount(L, ExitingBlock);
   if (ExitCount == getCouldNotCompute())
     return 1;
 
   // Get the trip count from the BE count by adding 1.
   const SCEV *TCMul = getAddExpr(ExitCount, getOne(ExitCount->getType()));
   // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
   // to factor simple cases.
   if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
     TCMul = Mul->getOperand(0);
 
   const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
   if (!MulC)
     return 1;
 
   ConstantInt *Result = MulC->getValue();
 
   // Guard against huge trip counts (this requires checking
   // for zero to handle the case where the trip count == -1 and the
   // addition wraps).
   if (!Result || Result->getValue().getActiveBits() > 32 ||
       Result->getValue().getActiveBits() == 0)
     return 1;
 
   return (unsigned)Result->getZExtValue();
 }
 
 /// Get the expression for the number of loop iterations for which this loop is
 /// guaranteed not to exit via ExitingBlock. Otherwise return
 /// SCEVCouldNotCompute.
 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
   return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
 }
 
 const SCEV *
 ScalarEvolution::getPredicatedBackedgeTakenCount(const Loop *L,
                                                  SCEVUnionPredicate &Preds) {
   return getPredicatedBackedgeTakenInfo(L).getExact(this, &Preds);
 }
 
 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
   return getBackedgeTakenInfo(L).getExact(this);
 }
 
 /// Similar to getBackedgeTakenCount, except return the least SCEV value that is
 /// known never to be less than the actual backedge taken count.
 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
   return getBackedgeTakenInfo(L).getMax(this);
 }
 
 /// Push PHI nodes in the header of the given loop onto the given Worklist.
 static void
 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
   BasicBlock *Header = L->getHeader();
 
   // Push all Loop-header PHIs onto the Worklist stack.
   for (BasicBlock::iterator I = Header->begin();
        PHINode *PN = dyn_cast<PHINode>(I); ++I)
     Worklist.push_back(PN);
 }
 
 const ScalarEvolution::BackedgeTakenInfo &
 ScalarEvolution::getPredicatedBackedgeTakenInfo(const Loop *L) {
   auto &BTI = getBackedgeTakenInfo(L);
   if (BTI.hasFullInfo())
     return BTI;
 
   auto Pair = PredicatedBackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
 
   if (!Pair.second)
     return Pair.first->second;
 
   BackedgeTakenInfo Result =
       computeBackedgeTakenCount(L, /*AllowPredicates=*/true);
 
   return PredicatedBackedgeTakenCounts.find(L)->second = Result;
 }
 
 const ScalarEvolution::BackedgeTakenInfo &
 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
   // Initially insert an invalid entry for this loop. If the insertion
   // succeeds, proceed to actually compute a backedge-taken count and
   // update the value. The temporary CouldNotCompute value tells SCEV
   // code elsewhere that it shouldn't attempt to request a new
   // backedge-taken count, which could result in infinite recursion.
   std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
       BackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
   if (!Pair.second)
     return Pair.first->second;
 
   // computeBackedgeTakenCount may allocate memory for its result. Inserting it
   // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
   // must be cleared in this scope.
   BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
 
   if (Result.getExact(this) != getCouldNotCompute()) {
     assert(isLoopInvariant(Result.getExact(this), L) &&
            isLoopInvariant(Result.getMax(this), L) &&
            "Computed backedge-taken count isn't loop invariant for loop!");
     ++NumTripCountsComputed;
   }
   else if (Result.getMax(this) == getCouldNotCompute() &&
            isa<PHINode>(L->getHeader()->begin())) {
     // Only count loops that have phi nodes as not being computable.
     ++NumTripCountsNotComputed;
   }
 
   // Now that we know more about the trip count for this loop, forget any
   // existing SCEV values for PHI nodes in this loop since they are only
   // conservative estimates made without the benefit of trip count
   // information. This is similar to the code in forgetLoop, except that
   // it handles SCEVUnknown PHI nodes specially.
   if (Result.hasAnyInfo()) {
     SmallVector<Instruction *, 16> Worklist;
     PushLoopPHIs(L, Worklist);
 
     SmallPtrSet<Instruction *, 8> Visited;
     while (!Worklist.empty()) {
       Instruction *I = Worklist.pop_back_val();
       if (!Visited.insert(I).second)
         continue;
 
       ValueExprMapType::iterator It =
         ValueExprMap.find_as(static_cast<Value *>(I));
       if (It != ValueExprMap.end()) {
         const SCEV *Old = It->second;
 
         // SCEVUnknown for a PHI either means that it has an unrecognized
         // structure, or it's a PHI that's in the progress of being computed
         // by createNodeForPHI.  In the former case, additional loop trip
         // count information isn't going to change anything. In the later
         // case, createNodeForPHI will perform the necessary updates on its
         // own when it gets to that point.
         if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
+          eraseValueFromMap(It->first);
           forgetMemoizedResults(Old);
-          ValueExprMap.erase(It);
         }
         if (PHINode *PN = dyn_cast<PHINode>(I))
           ConstantEvolutionLoopExitValue.erase(PN);
       }
 
       PushDefUseChildren(I, Worklist);
     }
   }
 
   // Re-lookup the insert position, since the call to
   // computeBackedgeTakenCount above could result in a
   // recusive call to getBackedgeTakenInfo (on a different
   // loop), which would invalidate the iterator computed
   // earlier.
   return BackedgeTakenCounts.find(L)->second = Result;
 }
 
 void ScalarEvolution::forgetLoop(const Loop *L) {
   // Drop any stored trip count value.
   auto RemoveLoopFromBackedgeMap =
       [L](DenseMap<const Loop *, BackedgeTakenInfo> &Map) {
         auto BTCPos = Map.find(L);
         if (BTCPos != Map.end()) {
           BTCPos->second.clear();
           Map.erase(BTCPos);
         }
       };
 
   RemoveLoopFromBackedgeMap(BackedgeTakenCounts);
   RemoveLoopFromBackedgeMap(PredicatedBackedgeTakenCounts);
 
   // Drop information about expressions based on loop-header PHIs.
   SmallVector<Instruction *, 16> Worklist;
   PushLoopPHIs(L, Worklist);
 
   SmallPtrSet<Instruction *, 8> Visited;
   while (!Worklist.empty()) {
     Instruction *I = Worklist.pop_back_val();
     if (!Visited.insert(I).second)
       continue;
 
     ValueExprMapType::iterator It =
       ValueExprMap.find_as(static_cast<Value *>(I));
     if (It != ValueExprMap.end()) {
+      eraseValueFromMap(It->first);
       forgetMemoizedResults(It->second);
-      ValueExprMap.erase(It);
       if (PHINode *PN = dyn_cast<PHINode>(I))
         ConstantEvolutionLoopExitValue.erase(PN);
     }
 
     PushDefUseChildren(I, Worklist);
   }
 
   // Forget all contained loops too, to avoid dangling entries in the
   // ValuesAtScopes map.
   for (Loop *I : *L)
     forgetLoop(I);
 
   LoopHasNoAbnormalExits.erase(L);
 }
 
 void ScalarEvolution::forgetValue(Value *V) {
   Instruction *I = dyn_cast<Instruction>(V);
   if (!I) return;
 
   // Drop information about expressions based on loop-header PHIs.
   SmallVector<Instruction *, 16> Worklist;
   Worklist.push_back(I);
 
   SmallPtrSet<Instruction *, 8> Visited;
   while (!Worklist.empty()) {
     I = Worklist.pop_back_val();
     if (!Visited.insert(I).second)
       continue;
 
     ValueExprMapType::iterator It =
       ValueExprMap.find_as(static_cast<Value *>(I));
     if (It != ValueExprMap.end()) {
+      eraseValueFromMap(It->first);
       forgetMemoizedResults(It->second);
-      ValueExprMap.erase(It);
       if (PHINode *PN = dyn_cast<PHINode>(I))
         ConstantEvolutionLoopExitValue.erase(PN);
     }
 
     PushDefUseChildren(I, Worklist);
   }
 }
 
 /// Get the exact loop backedge taken count considering all loop exits. A
 /// computable result can only be returned for loops with a single exit.
 /// Returning the minimum taken count among all exits is incorrect because one
 /// of the loop's exit limit's may have been skipped. howFarToZero assumes that
 /// the limit of each loop test is never skipped. This is a valid assumption as
 /// long as the loop exits via that test. For precise results, it is the
 /// caller's responsibility to specify the relevant loop exit using
 /// getExact(ExitingBlock, SE).
 const SCEV *
 ScalarEvolution::BackedgeTakenInfo::getExact(
     ScalarEvolution *SE, SCEVUnionPredicate *Preds) const {
   // If any exits were not computable, the loop is not computable.
   if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
 
   // We need exactly one computable exit.
   if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
   assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
 
   const SCEV *BECount = nullptr;
   for (auto &ENT : ExitNotTaken) {
     assert(ENT.ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
 
     if (!BECount)
       BECount = ENT.ExactNotTaken;
     else if (BECount != ENT.ExactNotTaken)
       return SE->getCouldNotCompute();
     if (Preds && ENT.getPred())
       Preds->add(ENT.getPred());
 
     assert((Preds || ENT.hasAlwaysTruePred()) &&
            "Predicate should be always true!");
   }
 
   assert(BECount && "Invalid not taken count for loop exit");
   return BECount;
 }
 
 /// Get the exact not taken count for this loop exit.
 const SCEV *
 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
                                              ScalarEvolution *SE) const {
   for (auto &ENT : ExitNotTaken)
     if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePred())
       return ENT.ExactNotTaken;
 
   return SE->getCouldNotCompute();
 }
 
 /// getMax - Get the max backedge taken count for the loop.
 const SCEV *
 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
   for (auto &ENT : ExitNotTaken)
     if (!ENT.hasAlwaysTruePred())
       return SE->getCouldNotCompute();
 
   return Max ? Max : SE->getCouldNotCompute();
 }
 
 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
                                                     ScalarEvolution *SE) const {
   if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
     return true;
 
   if (!ExitNotTaken.ExitingBlock)
     return false;
 
   for (auto &ENT : ExitNotTaken)
     if (ENT.ExactNotTaken != SE->getCouldNotCompute() &&
         SE->hasOperand(ENT.ExactNotTaken, S))
       return true;
 
   return false;
 }
 
 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
 /// computable exit into a persistent ExitNotTakenInfo array.
 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
     SmallVectorImpl<EdgeInfo> &ExitCounts, bool Complete, const SCEV *MaxCount)
     : Max(MaxCount) {
 
   if (!Complete)
     ExitNotTaken.setIncomplete();
 
   unsigned NumExits = ExitCounts.size();
   if (NumExits == 0) return;
 
   ExitNotTaken.ExitingBlock = ExitCounts[0].ExitBlock;
   ExitNotTaken.ExactNotTaken = ExitCounts[0].Taken;
 
   // Determine the number of ExitNotTakenExtras structures that we need.
   unsigned ExtraInfoSize = 0;
   if (NumExits > 1)
     ExtraInfoSize = 1 + std::count_if(std::next(ExitCounts.begin()),
                                       ExitCounts.end(), [](EdgeInfo &Entry) {
                                         return !Entry.Pred.isAlwaysTrue();
                                       });
   else if (!ExitCounts[0].Pred.isAlwaysTrue())
     ExtraInfoSize = 1;
 
   ExitNotTakenExtras *ENT = nullptr;
 
   // Allocate the ExitNotTakenExtras structures and initialize the first
   // element (ExitNotTaken).
   if (ExtraInfoSize > 0) {
     ENT = new ExitNotTakenExtras[ExtraInfoSize];
     ExitNotTaken.ExtraInfo = &ENT[0];
     *ExitNotTaken.getPred() = std::move(ExitCounts[0].Pred);
   }
 
   if (NumExits == 1)
     return;
 
   assert(ENT && "ExitNotTakenExtras is NULL while having more than one exit");
 
   auto &Exits = ExitNotTaken.ExtraInfo->Exits;
 
   // Handle the rare case of multiple computable exits.
   for (unsigned i = 1, PredPos = 1; i < NumExits; ++i) {
     ExitNotTakenExtras *Ptr = nullptr;
     if (!ExitCounts[i].Pred.isAlwaysTrue()) {
       Ptr = &ENT[PredPos++];
       Ptr->Pred = std::move(ExitCounts[i].Pred);
     }
 
     Exits.emplace_back(ExitCounts[i].ExitBlock, ExitCounts[i].Taken, Ptr);
   }
 }
 
 /// Invalidate this result and free the ExitNotTakenInfo array.
 void ScalarEvolution::BackedgeTakenInfo::clear() {
   ExitNotTaken.ExitingBlock = nullptr;
   ExitNotTaken.ExactNotTaken = nullptr;
   delete[] ExitNotTaken.ExtraInfo;
 }
 
 /// Compute the number of times the backedge of the specified loop will execute.
 ScalarEvolution::BackedgeTakenInfo
 ScalarEvolution::computeBackedgeTakenCount(const Loop *L,
                                            bool AllowPredicates) {
   SmallVector<BasicBlock *, 8> ExitingBlocks;
   L->getExitingBlocks(ExitingBlocks);
 
   SmallVector<EdgeInfo, 4> ExitCounts;
   bool CouldComputeBECount = true;
   BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
   const SCEV *MustExitMaxBECount = nullptr;
   const SCEV *MayExitMaxBECount = nullptr;
 
   // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
   // and compute maxBECount.
   // Do a union of all the predicates here.
   for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
     BasicBlock *ExitBB = ExitingBlocks[i];
     ExitLimit EL = computeExitLimit(L, ExitBB, AllowPredicates);
 
     assert((AllowPredicates || EL.Pred.isAlwaysTrue()) &&
            "Predicated exit limit when predicates are not allowed!");
 
     // 1. For each exit that can be computed, add an entry to ExitCounts.
     // CouldComputeBECount is true only if all exits can be computed.
     if (EL.Exact == getCouldNotCompute())
       // We couldn't compute an exact value for this exit, so
       // we won't be able to compute an exact value for the loop.
       CouldComputeBECount = false;
     else
       ExitCounts.emplace_back(EdgeInfo(ExitBB, EL.Exact, EL.Pred));
 
     // 2. Derive the loop's MaxBECount from each exit's max number of
     // non-exiting iterations. Partition the loop exits into two kinds:
     // LoopMustExits and LoopMayExits.
     //
     // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
     // is a LoopMayExit.  If any computable LoopMustExit is found, then
     // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
     // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
     // considered greater than any computable EL.Max.
     if (EL.Max != getCouldNotCompute() && Latch &&
         DT.dominates(ExitBB, Latch)) {
       if (!MustExitMaxBECount)
         MustExitMaxBECount = EL.Max;
       else {
         MustExitMaxBECount =
           getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
       }
     } else if (MayExitMaxBECount != getCouldNotCompute()) {
       if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
         MayExitMaxBECount = EL.Max;
       else {
         MayExitMaxBECount =
           getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
       }
     }
   }
   const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
     (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
   return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
 }
 
 ScalarEvolution::ExitLimit
 ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
                                   bool AllowPredicates) {
 
   // Okay, we've chosen an exiting block.  See what condition causes us to exit
   // at this block and remember the exit block and whether all other targets
   // lead to the loop header.
   bool MustExecuteLoopHeader = true;
   BasicBlock *Exit = nullptr;
   for (auto *SBB : successors(ExitingBlock))
     if (!L->contains(SBB)) {
       if (Exit) // Multiple exit successors.
         return getCouldNotCompute();
       Exit = SBB;
     } else if (SBB != L->getHeader()) {
       MustExecuteLoopHeader = false;
     }
 
   // At this point, we know we have a conditional branch that determines whether
   // the loop is exited.  However, we don't know if the branch is executed each
   // time through the loop.  If not, then the execution count of the branch will
   // not be equal to the trip count of the loop.
   //
   // Currently we check for this by checking to see if the Exit branch goes to
   // the loop header.  If so, we know it will always execute the same number of
   // times as the loop.  We also handle the case where the exit block *is* the
   // loop header.  This is common for un-rotated loops.
   //
   // If both of those tests fail, walk up the unique predecessor chain to the
   // header, stopping if there is an edge that doesn't exit the loop. If the
   // header is reached, the execution count of the branch will be equal to the
   // trip count of the loop.
   //
   //  More extensive analysis could be done to handle more cases here.
   //
   if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
     // The simple checks failed, try climbing the unique predecessor chain
     // up to the header.
     bool Ok = false;
     for (BasicBlock *BB = ExitingBlock; BB; ) {
       BasicBlock *Pred = BB->getUniquePredecessor();
       if (!Pred)
         return getCouldNotCompute();
       TerminatorInst *PredTerm = Pred->getTerminator();
       for (const BasicBlock *PredSucc : PredTerm->successors()) {
         if (PredSucc == BB)
           continue;
         // If the predecessor has a successor that isn't BB and isn't
         // outside the loop, assume the worst.
         if (L->contains(PredSucc))
           return getCouldNotCompute();
       }
       if (Pred == L->getHeader()) {
         Ok = true;
         break;
       }
       BB = Pred;
     }
     if (!Ok)
       return getCouldNotCompute();
   }
 
   bool IsOnlyExit = (L->getExitingBlock() != nullptr);
   TerminatorInst *Term = ExitingBlock->getTerminator();
   if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
     assert(BI->isConditional() && "If unconditional, it can't be in loop!");
     // Proceed to the next level to examine the exit condition expression.
     return computeExitLimitFromCond(
         L, BI->getCondition(), BI->getSuccessor(0), BI->getSuccessor(1),
         /*ControlsExit=*/IsOnlyExit, AllowPredicates);
   }
 
   if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
     return computeExitLimitFromSingleExitSwitch(L, SI, Exit,
                                                 /*ControlsExit=*/IsOnlyExit);
 
   return getCouldNotCompute();
 }
 
 ScalarEvolution::ExitLimit
 ScalarEvolution::computeExitLimitFromCond(const Loop *L,
                                           Value *ExitCond,
                                           BasicBlock *TBB,
                                           BasicBlock *FBB,
                                           bool ControlsExit,
                                           bool AllowPredicates) {
   // Check if the controlling expression for this loop is an And or Or.
   if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
     if (BO->getOpcode() == Instruction::And) {
       // Recurse on the operands of the and.
       bool EitherMayExit = L->contains(TBB);
       ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
                                                ControlsExit && !EitherMayExit,
                                                AllowPredicates);
       ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
                                                ControlsExit && !EitherMayExit,
                                                AllowPredicates);
       const SCEV *BECount = getCouldNotCompute();
       const SCEV *MaxBECount = getCouldNotCompute();
       if (EitherMayExit) {
         // Both conditions must be true for the loop to continue executing.
         // Choose the less conservative count.
         if (EL0.Exact == getCouldNotCompute() ||
             EL1.Exact == getCouldNotCompute())
           BECount = getCouldNotCompute();
         else
           BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
         if (EL0.Max == getCouldNotCompute())
           MaxBECount = EL1.Max;
         else if (EL1.Max == getCouldNotCompute())
           MaxBECount = EL0.Max;
         else
           MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
       } else {
         // Both conditions must be true at the same time for the loop to exit.
         // For now, be conservative.
         assert(L->contains(FBB) && "Loop block has no successor in loop!");
         if (EL0.Max == EL1.Max)
           MaxBECount = EL0.Max;
         if (EL0.Exact == EL1.Exact)
           BECount = EL0.Exact;
       }
 
       SCEVUnionPredicate NP;
       NP.add(&EL0.Pred);
       NP.add(&EL1.Pred);
       // There are cases (e.g. PR26207) where computeExitLimitFromCond is able
       // to be more aggressive when computing BECount than when computing
       // MaxBECount.  In these cases it is possible for EL0.Exact and EL1.Exact
       // to match, but for EL0.Max and EL1.Max to not.
       if (isa<SCEVCouldNotCompute>(MaxBECount) &&
           !isa<SCEVCouldNotCompute>(BECount))
         MaxBECount = BECount;
 
       return ExitLimit(BECount, MaxBECount, NP);
     }
     if (BO->getOpcode() == Instruction::Or) {
       // Recurse on the operands of the or.
       bool EitherMayExit = L->contains(FBB);
       ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
                                                ControlsExit && !EitherMayExit,
                                                AllowPredicates);
       ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
                                                ControlsExit && !EitherMayExit,
                                                AllowPredicates);
       const SCEV *BECount = getCouldNotCompute();
       const SCEV *MaxBECount = getCouldNotCompute();
       if (EitherMayExit) {
         // Both conditions must be false for the loop to continue executing.
         // Choose the less conservative count.
         if (EL0.Exact == getCouldNotCompute() ||
             EL1.Exact == getCouldNotCompute())
           BECount = getCouldNotCompute();
         else
           BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
         if (EL0.Max == getCouldNotCompute())
           MaxBECount = EL1.Max;
         else if (EL1.Max == getCouldNotCompute())
           MaxBECount = EL0.Max;
         else
           MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
       } else {
         // Both conditions must be false at the same time for the loop to exit.
         // For now, be conservative.
         assert(L->contains(TBB) && "Loop block has no successor in loop!");
         if (EL0.Max == EL1.Max)
           MaxBECount = EL0.Max;
         if (EL0.Exact == EL1.Exact)
           BECount = EL0.Exact;
       }
 
       SCEVUnionPredicate NP;
       NP.add(&EL0.Pred);
       NP.add(&EL1.Pred);
       return ExitLimit(BECount, MaxBECount, NP);
     }
   }
 
   // With an icmp, it may be feasible to compute an exact backedge-taken count.
   // Proceed to the next level to examine the icmp.
   if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) {
     ExitLimit EL =
         computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
     if (EL.hasFullInfo() || !AllowPredicates)
       return EL;
 
     // Try again, but use SCEV predicates this time.
     return computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit,
                                     /*AllowPredicates=*/true);
   }
 
   // Check for a constant condition. These are normally stripped out by
   // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
   // preserve the CFG and is temporarily leaving constant conditions
   // in place.
   if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
     if (L->contains(FBB) == !CI->getZExtValue())
       // The backedge is always taken.
       return getCouldNotCompute();
     else
       // The backedge is never taken.
       return getZero(CI->getType());
   }
 
   // If it's not an integer or pointer comparison then compute it the hard way.
   return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
 }
 
 ScalarEvolution::ExitLimit
 ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
                                           ICmpInst *ExitCond,
                                           BasicBlock *TBB,
                                           BasicBlock *FBB,
                                           bool ControlsExit,
                                           bool AllowPredicates) {
 
   // If the condition was exit on true, convert the condition to exit on false
   ICmpInst::Predicate Cond;
   if (!L->contains(FBB))
     Cond = ExitCond->getPredicate();
   else
     Cond = ExitCond->getInversePredicate();
 
   // Handle common loops like: for (X = "string"; *X; ++X)
   if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
     if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
       ExitLimit ItCnt =
         computeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
       if (ItCnt.hasAnyInfo())
         return ItCnt;
     }
 
   const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
   const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
 
   // Try to evaluate any dependencies out of the loop.
   LHS = getSCEVAtScope(LHS, L);
   RHS = getSCEVAtScope(RHS, L);
 
   // At this point, we would like to compute how many iterations of the
   // loop the predicate will return true for these inputs.
   if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
     // If there is a loop-invariant, force it into the RHS.
     std::swap(LHS, RHS);
     Cond = ICmpInst::getSwappedPredicate(Cond);
   }
 
   // Simplify the operands before analyzing them.
   (void)SimplifyICmpOperands(Cond, LHS, RHS);
 
   // If we have a comparison of a chrec against a constant, try to use value
   // ranges to answer this query.
   if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
     if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
       if (AddRec->getLoop() == L) {
         // Form the constant range.
         ConstantRange CompRange(
             ICmpInst::makeConstantRange(Cond, RHSC->getAPInt()));
 
         const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
         if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
       }
 
   switch (Cond) {
   case ICmpInst::ICMP_NE: {                     // while (X != Y)
     // Convert to: while (X-Y != 0)
     ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit,
                                 AllowPredicates);
     if (EL.hasAnyInfo()) return EL;
     break;
   }
   case ICmpInst::ICMP_EQ: {                     // while (X == Y)
     // Convert to: while (X-Y == 0)
     ExitLimit EL = howFarToNonZero(getMinusSCEV(LHS, RHS), L);
     if (EL.hasAnyInfo()) return EL;
     break;
   }
   case ICmpInst::ICMP_SLT:
   case ICmpInst::ICMP_ULT: {                    // while (X < Y)
     bool IsSigned = Cond == ICmpInst::ICMP_SLT;
     ExitLimit EL = howManyLessThans(LHS, RHS, L, IsSigned, ControlsExit,
                                     AllowPredicates);
     if (EL.hasAnyInfo()) return EL;
     break;
   }
   case ICmpInst::ICMP_SGT:
   case ICmpInst::ICMP_UGT: {                    // while (X > Y)
     bool IsSigned = Cond == ICmpInst::ICMP_SGT;
     ExitLimit EL =
         howManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit,
                             AllowPredicates);
     if (EL.hasAnyInfo()) return EL;
     break;
   }
   default:
     break;
   }
 
   auto *ExhaustiveCount =
       computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
 
   if (!isa<SCEVCouldNotCompute>(ExhaustiveCount))
     return ExhaustiveCount;
 
   return computeShiftCompareExitLimit(ExitCond->getOperand(0),
                                       ExitCond->getOperand(1), L, Cond);
 }
 
 ScalarEvolution::ExitLimit
 ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
                                                       SwitchInst *Switch,
                                                       BasicBlock *ExitingBlock,
                                                       bool ControlsExit) {
   assert(!L->contains(ExitingBlock) && "Not an exiting block!");
 
   // Give up if the exit is the default dest of a switch.
   if (Switch->getDefaultDest() == ExitingBlock)
     return getCouldNotCompute();
 
   assert(L->contains(Switch->getDefaultDest()) &&
          "Default case must not exit the loop!");
   const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
   const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
 
   // while (X != Y) --> while (X-Y != 0)
   ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
   if (EL.hasAnyInfo())
     return EL;
 
   return getCouldNotCompute();
 }
 
 static ConstantInt *
 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
                                 ScalarEvolution &SE) {
   const SCEV *InVal = SE.getConstant(C);
   const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
   assert(isa<SCEVConstant>(Val) &&
          "Evaluation of SCEV at constant didn't fold correctly?");
   return cast<SCEVConstant>(Val)->getValue();
 }
 
 /// Given an exit condition of 'icmp op load X, cst', try to see if we can
 /// compute the backedge execution count.
 ScalarEvolution::ExitLimit
 ScalarEvolution::computeLoadConstantCompareExitLimit(
   LoadInst *LI,
   Constant *RHS,
   const Loop *L,
   ICmpInst::Predicate predicate) {
 
   if (LI->isVolatile()) return getCouldNotCompute();
 
   // Check to see if the loaded pointer is a getelementptr of a global.
   // TODO: Use SCEV instead of manually grubbing with GEPs.
   GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
   if (!GEP) return getCouldNotCompute();
 
   // Make sure that it is really a constant global we are gepping, with an
   // initializer, and make sure the first IDX is really 0.
   GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
   if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
       GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
       !cast<Constant>(GEP->getOperand(1))->isNullValue())
     return getCouldNotCompute();
 
   // Okay, we allow one non-constant index into the GEP instruction.
   Value *VarIdx = nullptr;
   std::vector<Constant*> Indexes;
   unsigned VarIdxNum = 0;
   for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
     if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
       Indexes.push_back(CI);
     } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
       if (VarIdx) return getCouldNotCompute();  // Multiple non-constant idx's.
       VarIdx = GEP->getOperand(i);
       VarIdxNum = i-2;
       Indexes.push_back(nullptr);
     }
 
   // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
   if (!VarIdx)
     return getCouldNotCompute();
 
   // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
   // Check to see if X is a loop variant variable value now.
   const SCEV *Idx = getSCEV(VarIdx);
   Idx = getSCEVAtScope(Idx, L);
 
   // We can only recognize very limited forms of loop index expressions, in
   // particular, only affine AddRec's like {C1,+,C2}.
   const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
   if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
       !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
       !isa<SCEVConstant>(IdxExpr->getOperand(1)))
     return getCouldNotCompute();
 
   unsigned MaxSteps = MaxBruteForceIterations;
   for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
     ConstantInt *ItCst = ConstantInt::get(
                            cast<IntegerType>(IdxExpr->getType()), IterationNum);
     ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
 
     // Form the GEP offset.
     Indexes[VarIdxNum] = Val;
 
     Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
                                                          Indexes);
     if (!Result) break;  // Cannot compute!
 
     // Evaluate the condition for this iteration.
     Result = ConstantExpr::getICmp(predicate, Result, RHS);
     if (!isa<ConstantInt>(Result)) break;  // Couldn't decide for sure
     if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
       ++NumArrayLenItCounts;
       return getConstant(ItCst);   // Found terminating iteration!
     }
   }
   return getCouldNotCompute();
 }
 
 ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit(
     Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) {
   ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV);
   if (!RHS)
     return getCouldNotCompute();
 
   const BasicBlock *Latch = L->getLoopLatch();
   if (!Latch)
     return getCouldNotCompute();
 
   const BasicBlock *Predecessor = L->getLoopPredecessor();
   if (!Predecessor)
     return getCouldNotCompute();
 
   // Return true if V is of the form "LHS `shift_op` <positive constant>".
   // Return LHS in OutLHS and shift_opt in OutOpCode.
   auto MatchPositiveShift =
       [](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) {
 
     using namespace PatternMatch;
 
     ConstantInt *ShiftAmt;
     if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
       OutOpCode = Instruction::LShr;
     else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
       OutOpCode = Instruction::AShr;
     else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
       OutOpCode = Instruction::Shl;
     else
       return false;
 
     return ShiftAmt->getValue().isStrictlyPositive();
   };
 
   // Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in
   //
   // loop:
   //   %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ]
   //   %iv.shifted = lshr i32 %iv, <positive constant>
   //
   // Return true on a succesful match.  Return the corresponding PHI node (%iv
   // above) in PNOut and the opcode of the shift operation in OpCodeOut.
   auto MatchShiftRecurrence =
       [&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) {
     Optional<Instruction::BinaryOps> PostShiftOpCode;
 
     {
       Instruction::BinaryOps OpC;
       Value *V;
 
       // If we encounter a shift instruction, "peel off" the shift operation,
       // and remember that we did so.  Later when we inspect %iv's backedge
       // value, we will make sure that the backedge value uses the same
       // operation.
       //
       // Note: the peeled shift operation does not have to be the same
       // instruction as the one feeding into the PHI's backedge value.  We only
       // really care about it being the same *kind* of shift instruction --
       // that's all that is required for our later inferences to hold.
       if (MatchPositiveShift(LHS, V, OpC)) {
         PostShiftOpCode = OpC;
         LHS = V;
       }
     }
 
     PNOut = dyn_cast<PHINode>(LHS);
     if (!PNOut || PNOut->getParent() != L->getHeader())
       return false;
 
     Value *BEValue = PNOut->getIncomingValueForBlock(Latch);
     Value *OpLHS;
 
     return
         // The backedge value for the PHI node must be a shift by a positive
         // amount
         MatchPositiveShift(BEValue, OpLHS, OpCodeOut) &&
 
         // of the PHI node itself
         OpLHS == PNOut &&
 
         // and the kind of shift should be match the kind of shift we peeled
         // off, if any.
         (!PostShiftOpCode.hasValue() || *PostShiftOpCode == OpCodeOut);
   };
 
   PHINode *PN;
   Instruction::BinaryOps OpCode;
   if (!MatchShiftRecurrence(LHS, PN, OpCode))
     return getCouldNotCompute();
 
   const DataLayout &DL = getDataLayout();
 
   // The key rationale for this optimization is that for some kinds of shift
   // recurrences, the value of the recurrence "stabilizes" to either 0 or -1
   // within a finite number of iterations.  If the condition guarding the
   // backedge (in the sense that the backedge is taken if the condition is true)
   // is false for the value the shift recurrence stabilizes to, then we know
   // that the backedge is taken only a finite number of times.
 
   ConstantInt *StableValue = nullptr;
   switch (OpCode) {
   default:
     llvm_unreachable("Impossible case!");
 
   case Instruction::AShr: {
     // {K,ashr,<positive-constant>} stabilizes to signum(K) in at most
     // bitwidth(K) iterations.
     Value *FirstValue = PN->getIncomingValueForBlock(Predecessor);
     bool KnownZero, KnownOne;
     ComputeSignBit(FirstValue, KnownZero, KnownOne, DL, 0, nullptr,
                    Predecessor->getTerminator(), &DT);
     auto *Ty = cast<IntegerType>(RHS->getType());
     if (KnownZero)
       StableValue = ConstantInt::get(Ty, 0);
     else if (KnownOne)
       StableValue = ConstantInt::get(Ty, -1, true);
     else
       return getCouldNotCompute();
 
     break;
   }
   case Instruction::LShr:
   case Instruction::Shl:
     // Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>}
     // stabilize to 0 in at most bitwidth(K) iterations.
     StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0);
     break;
   }
 
   auto *Result =
       ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI);
   assert(Result->getType()->isIntegerTy(1) &&
          "Otherwise cannot be an operand to a branch instruction");
 
   if (Result->isZeroValue()) {
     unsigned BitWidth = getTypeSizeInBits(RHS->getType());
     const SCEV *UpperBound =
         getConstant(getEffectiveSCEVType(RHS->getType()), BitWidth);
     SCEVUnionPredicate P;
     return ExitLimit(getCouldNotCompute(), UpperBound, P);
   }
 
   return getCouldNotCompute();
 }
 
 /// Return true if we can constant fold an instruction of the specified type,
 /// assuming that all operands were constants.
 static bool CanConstantFold(const Instruction *I) {
   if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
       isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
       isa<LoadInst>(I))
     return true;
 
   if (const CallInst *CI = dyn_cast<CallInst>(I))
     if (const Function *F = CI->getCalledFunction())
       return canConstantFoldCallTo(F);
   return false;
 }
 
 /// Determine whether this instruction can constant evolve within this loop
 /// assuming its operands can all constant evolve.
 static bool canConstantEvolve(Instruction *I, const Loop *L) {
   // An instruction outside of the loop can't be derived from a loop PHI.
   if (!L->contains(I)) return false;
 
   if (isa<PHINode>(I)) {
     // We don't currently keep track of the control flow needed to evaluate
     // PHIs, so we cannot handle PHIs inside of loops.
     return L->getHeader() == I->getParent();
   }
 
   // If we won't be able to constant fold this expression even if the operands
   // are constants, bail early.
   return CanConstantFold(I);
 }
 
 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
 /// recursing through each instruction operand until reaching a loop header phi.
 static PHINode *
 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
                                DenseMap<Instruction *, PHINode *> &PHIMap) {
 
   // Otherwise, we can evaluate this instruction if all of its operands are
   // constant or derived from a PHI node themselves.
   PHINode *PHI = nullptr;
   for (Value *Op : UseInst->operands()) {
     if (isa<Constant>(Op)) continue;
 
     Instruction *OpInst = dyn_cast<Instruction>(Op);
     if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
 
     PHINode *P = dyn_cast<PHINode>(OpInst);
     if (!P)
       // If this operand is already visited, reuse the prior result.
       // We may have P != PHI if this is the deepest point at which the
       // inconsistent paths meet.
       P = PHIMap.lookup(OpInst);
     if (!P) {
       // Recurse and memoize the results, whether a phi is found or not.
       // This recursive call invalidates pointers into PHIMap.
       P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
       PHIMap[OpInst] = P;
     }
     if (!P)
       return nullptr;  // Not evolving from PHI
     if (PHI && PHI != P)
       return nullptr;  // Evolving from multiple different PHIs.
     PHI = P;
   }
   // This is a expression evolving from a constant PHI!
   return PHI;
 }
 
 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
 /// in the loop that V is derived from.  We allow arbitrary operations along the
 /// way, but the operands of an operation must either be constants or a value
 /// derived from a constant PHI.  If this expression does not fit with these
 /// constraints, return null.
 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
   Instruction *I = dyn_cast<Instruction>(V);
   if (!I || !canConstantEvolve(I, L)) return nullptr;
 
   if (PHINode *PN = dyn_cast<PHINode>(I))
     return PN;
 
   // Record non-constant instructions contained by the loop.
   DenseMap<Instruction *, PHINode *> PHIMap;
   return getConstantEvolvingPHIOperands(I, L, PHIMap);
 }
 
 /// EvaluateExpression - Given an expression that passes the
 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
 /// in the loop has the value PHIVal.  If we can't fold this expression for some
 /// reason, return null.
 static Constant *EvaluateExpression(Value *V, const Loop *L,
                                     DenseMap<Instruction *, Constant *> &Vals,
                                     const DataLayout &DL,
                                     const TargetLibraryInfo *TLI) {
   // Convenient constant check, but redundant for recursive calls.
   if (Constant *C = dyn_cast<Constant>(V)) return C;
   Instruction *I = dyn_cast<Instruction>(V);
   if (!I) return nullptr;
 
   if (Constant *C = Vals.lookup(I)) return C;
 
   // An instruction inside the loop depends on a value outside the loop that we
   // weren't given a mapping for, or a value such as a call inside the loop.
   if (!canConstantEvolve(I, L)) return nullptr;
 
   // An unmapped PHI can be due to a branch or another loop inside this loop,
   // or due to this not being the initial iteration through a loop where we
   // couldn't compute the evolution of this particular PHI last time.
   if (isa<PHINode>(I)) return nullptr;
 
   std::vector<Constant*> Operands(I->getNumOperands());
 
   for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
     Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
     if (!Operand) {
       Operands[i] = dyn_cast<Constant>(I->getOperand(i));
       if (!Operands[i]) return nullptr;
       continue;
     }
     Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
     Vals[Operand] = C;
     if (!C) return nullptr;
     Operands[i] = C;
   }
 
   if (CmpInst *CI = dyn_cast<CmpInst>(I))
     return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
                                            Operands[1], DL, TLI);
   if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
     if (!LI->isVolatile())
       return ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
   }
   return ConstantFoldInstOperands(I, Operands, DL, TLI);
 }
 
 
 // If every incoming value to PN except the one for BB is a specific Constant,
 // return that, else return nullptr.
 static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) {
   Constant *IncomingVal = nullptr;
 
   for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
     if (PN->getIncomingBlock(i) == BB)
       continue;
 
     auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i));
     if (!CurrentVal)
       return nullptr;
 
     if (IncomingVal != CurrentVal) {
       if (IncomingVal)
         return nullptr;
       IncomingVal = CurrentVal;
     }
   }
 
   return IncomingVal;
 }
 
 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
 /// in the header of its containing loop, we know the loop executes a
 /// constant number of times, and the PHI node is just a recurrence
 /// involving constants, fold it.
 Constant *
 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
                                                    const APInt &BEs,
                                                    const Loop *L) {
   auto I = ConstantEvolutionLoopExitValue.find(PN);
   if (I != ConstantEvolutionLoopExitValue.end())
     return I->second;
 
   if (BEs.ugt(MaxBruteForceIterations))
     return ConstantEvolutionLoopExitValue[PN] = nullptr;  // Not going to evaluate it.
 
   Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
 
   DenseMap<Instruction *, Constant *> CurrentIterVals;
   BasicBlock *Header = L->getHeader();
   assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
 
   BasicBlock *Latch = L->getLoopLatch();
   if (!Latch)
     return nullptr;
 
   for (auto &I : *Header) {
     PHINode *PHI = dyn_cast<PHINode>(&I);
     if (!PHI) break;
     auto *StartCST = getOtherIncomingValue(PHI, Latch);
     if (!StartCST) continue;
     CurrentIterVals[PHI] = StartCST;
   }
   if (!CurrentIterVals.count(PN))
     return RetVal = nullptr;
 
   Value *BEValue = PN->getIncomingValueForBlock(Latch);
 
   // Execute the loop symbolically to determine the exit value.
   if (BEs.getActiveBits() >= 32)
     return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
 
   unsigned NumIterations = BEs.getZExtValue(); // must be in range
   unsigned IterationNum = 0;
   const DataLayout &DL = getDataLayout();
   for (; ; ++IterationNum) {
     if (IterationNum == NumIterations)
       return RetVal = CurrentIterVals[PN];  // Got exit value!
 
     // Compute the value of the PHIs for the next iteration.
     // EvaluateExpression adds non-phi values to the CurrentIterVals map.
     DenseMap<Instruction *, Constant *> NextIterVals;
     Constant *NextPHI =
         EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
     if (!NextPHI)
       return nullptr;        // Couldn't evaluate!
     NextIterVals[PN] = NextPHI;
 
     bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
 
     // Also evaluate the other PHI nodes.  However, we don't get to stop if we
     // cease to be able to evaluate one of them or if they stop evolving,
     // because that doesn't necessarily prevent us from computing PN.
     SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
     for (const auto &I : CurrentIterVals) {
       PHINode *PHI = dyn_cast<PHINode>(I.first);
       if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
       PHIsToCompute.emplace_back(PHI, I.second);
     }
     // We use two distinct loops because EvaluateExpression may invalidate any
     // iterators into CurrentIterVals.
     for (const auto &I : PHIsToCompute) {
       PHINode *PHI = I.first;
       Constant *&NextPHI = NextIterVals[PHI];
       if (!NextPHI) {   // Not already computed.
         Value *BEValue = PHI->getIncomingValueForBlock(Latch);
         NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
       }
       if (NextPHI != I.second)
         StoppedEvolving = false;
     }
 
     // If all entries in CurrentIterVals == NextIterVals then we can stop
     // iterating, the loop can't continue to change.
     if (StoppedEvolving)
       return RetVal = CurrentIterVals[PN];
 
     CurrentIterVals.swap(NextIterVals);
   }
 }
 
 const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
                                                           Value *Cond,
                                                           bool ExitWhen) {
   PHINode *PN = getConstantEvolvingPHI(Cond, L);
   if (!PN) return getCouldNotCompute();
 
   // If the loop is canonicalized, the PHI will have exactly two entries.
   // That's the only form we support here.
   if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
 
   DenseMap<Instruction *, Constant *> CurrentIterVals;
   BasicBlock *Header = L->getHeader();
   assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
 
   BasicBlock *Latch = L->getLoopLatch();
   assert(Latch && "Should follow from NumIncomingValues == 2!");
 
   for (auto &I : *Header) {
     PHINode *PHI = dyn_cast<PHINode>(&I);
     if (!PHI)
       break;
     auto *StartCST = getOtherIncomingValue(PHI, Latch);
     if (!StartCST) continue;
     CurrentIterVals[PHI] = StartCST;
   }
   if (!CurrentIterVals.count(PN))
     return getCouldNotCompute();
 
   // Okay, we find a PHI node that defines the trip count of this loop.  Execute
   // the loop symbolically to determine when the condition gets a value of
   // "ExitWhen".
   unsigned MaxIterations = MaxBruteForceIterations;   // Limit analysis.
   const DataLayout &DL = getDataLayout();
   for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
     auto *CondVal = dyn_cast_or_null<ConstantInt>(
         EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
 
     // Couldn't symbolically evaluate.
     if (!CondVal) return getCouldNotCompute();
 
     if (CondVal->getValue() == uint64_t(ExitWhen)) {
       ++NumBruteForceTripCountsComputed;
       return getConstant(Type::getInt32Ty(getContext()), IterationNum);
     }
 
     // Update all the PHI nodes for the next iteration.
     DenseMap<Instruction *, Constant *> NextIterVals;
 
     // Create a list of which PHIs we need to compute. We want to do this before
     // calling EvaluateExpression on them because that may invalidate iterators
     // into CurrentIterVals.
     SmallVector<PHINode *, 8> PHIsToCompute;
     for (const auto &I : CurrentIterVals) {
       PHINode *PHI = dyn_cast<PHINode>(I.first);
       if (!PHI || PHI->getParent() != Header) continue;
       PHIsToCompute.push_back(PHI);
     }
     for (PHINode *PHI : PHIsToCompute) {
       Constant *&NextPHI = NextIterVals[PHI];
       if (NextPHI) continue;    // Already computed!
 
       Value *BEValue = PHI->getIncomingValueForBlock(Latch);
       NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
     }
     CurrentIterVals.swap(NextIterVals);
   }
 
   // Too many iterations were needed to evaluate.
   return getCouldNotCompute();
 }
 
 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
   SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values =
       ValuesAtScopes[V];
   // Check to see if we've folded this expression at this loop before.
   for (auto &LS : Values)
     if (LS.first == L)
       return LS.second ? LS.second : V;
 
   Values.emplace_back(L, nullptr);
 
   // Otherwise compute it.
   const SCEV *C = computeSCEVAtScope(V, L);
   for (auto &LS : reverse(ValuesAtScopes[V]))
     if (LS.first == L) {
       LS.second = C;
       break;
     }
   return C;
 }
 
 /// This builds up a Constant using the ConstantExpr interface.  That way, we
 /// will return Constants for objects which aren't represented by a
 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
 /// Returns NULL if the SCEV isn't representable as a Constant.
 static Constant *BuildConstantFromSCEV(const SCEV *V) {
   switch (static_cast<SCEVTypes>(V->getSCEVType())) {
     case scCouldNotCompute:
     case scAddRecExpr:
       break;
     case scConstant:
       return cast<SCEVConstant>(V)->getValue();
     case scUnknown:
       return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
     case scSignExtend: {
       const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
       if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
         return ConstantExpr::getSExt(CastOp, SS->getType());
       break;
     }
     case scZeroExtend: {
       const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
       if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
         return ConstantExpr::getZExt(CastOp, SZ->getType());
       break;
     }
     case scTruncate: {
       const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
       if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
         return ConstantExpr::getTrunc(CastOp, ST->getType());
       break;
     }
     case scAddExpr: {
       const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
       if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
         if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
           unsigned AS = PTy->getAddressSpace();
           Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
           C = ConstantExpr::getBitCast(C, DestPtrTy);
         }
         for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
           Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
           if (!C2) return nullptr;
 
           // First pointer!
           if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
             unsigned AS = C2->getType()->getPointerAddressSpace();
             std::swap(C, C2);
             Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
             // The offsets have been converted to bytes.  We can add bytes to an
             // i8* by GEP with the byte count in the first index.
             C = ConstantExpr::getBitCast(C, DestPtrTy);
           }
 
           // Don't bother trying to sum two pointers. We probably can't
           // statically compute a load that results from it anyway.
           if (C2->getType()->isPointerTy())
             return nullptr;
 
           if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
             if (PTy->getElementType()->isStructTy())
               C2 = ConstantExpr::getIntegerCast(
                   C2, Type::getInt32Ty(C->getContext()), true);
             C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
           } else
             C = ConstantExpr::getAdd(C, C2);
         }
         return C;
       }
       break;
     }
     case scMulExpr: {
       const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
       if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
         // Don't bother with pointers at all.
         if (C->getType()->isPointerTy()) return nullptr;
         for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
           Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
           if (!C2 || C2->getType()->isPointerTy()) return nullptr;
           C = ConstantExpr::getMul(C, C2);
         }
         return C;
       }
       break;
     }
     case scUDivExpr: {
       const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
       if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
         if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
           if (LHS->getType() == RHS->getType())
             return ConstantExpr::getUDiv(LHS, RHS);
       break;
     }
     case scSMaxExpr:
     case scUMaxExpr:
       break; // TODO: smax, umax.
   }
   return nullptr;
 }
 
 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
   if (isa<SCEVConstant>(V)) return V;
 
   // If this instruction is evolved from a constant-evolving PHI, compute the
   // exit value from the loop without using SCEVs.
   if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
     if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
       const Loop *LI = this->LI[I->getParent()];
       if (LI && LI->getParentLoop() == L)  // Looking for loop exit value.
         if (PHINode *PN = dyn_cast<PHINode>(I))
           if (PN->getParent() == LI->getHeader()) {
             // Okay, there is no closed form solution for the PHI node.  Check
             // to see if the loop that contains it has a known backedge-taken
             // count.  If so, we may be able to force computation of the exit
             // value.
             const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
             if (const SCEVConstant *BTCC =
                   dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
               // Okay, we know how many times the containing loop executes.  If
               // this is a constant evolving PHI node, get the final value at
               // the specified iteration number.
               Constant *RV =
                   getConstantEvolutionLoopExitValue(PN, BTCC->getAPInt(), LI);
               if (RV) return getSCEV(RV);
             }
           }
 
       // Okay, this is an expression that we cannot symbolically evaluate
       // into a SCEV.  Check to see if it's possible to symbolically evaluate
       // the arguments into constants, and if so, try to constant propagate the
       // result.  This is particularly useful for computing loop exit values.
       if (CanConstantFold(I)) {
         SmallVector<Constant *, 4> Operands;
         bool MadeImprovement = false;
         for (Value *Op : I->operands()) {
           if (Constant *C = dyn_cast<Constant>(Op)) {
             Operands.push_back(C);
             continue;
           }
 
           // If any of the operands is non-constant and if they are
           // non-integer and non-pointer, don't even try to analyze them
           // with scev techniques.
           if (!isSCEVable(Op->getType()))
             return V;
 
           const SCEV *OrigV = getSCEV(Op);
           const SCEV *OpV = getSCEVAtScope(OrigV, L);
           MadeImprovement |= OrigV != OpV;
 
           Constant *C = BuildConstantFromSCEV(OpV);
           if (!C) return V;
           if (C->getType() != Op->getType())
             C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
                                                               Op->getType(),
                                                               false),
                                       C, Op->getType());
           Operands.push_back(C);
         }
 
         // Check to see if getSCEVAtScope actually made an improvement.
         if (MadeImprovement) {
           Constant *C = nullptr;
           const DataLayout &DL = getDataLayout();
           if (const CmpInst *CI = dyn_cast<CmpInst>(I))
             C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
                                                 Operands[1], DL, &TLI);
           else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
             if (!LI->isVolatile())
               C = ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
           } else
             C = ConstantFoldInstOperands(I, Operands, DL, &TLI);
           if (!C) return V;
           return getSCEV(C);
         }
       }
     }
 
     // This is some other type of SCEVUnknown, just return it.
     return V;
   }
 
   if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
     // Avoid performing the look-up in the common case where the specified
     // expression has no loop-variant portions.
     for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
       const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
       if (OpAtScope != Comm->getOperand(i)) {
         // Okay, at least one of these operands is loop variant but might be
         // foldable.  Build a new instance of the folded commutative expression.
         SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
                                             Comm->op_begin()+i);
         NewOps.push_back(OpAtScope);
 
         for (++i; i != e; ++i) {
           OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
           NewOps.push_back(OpAtScope);
         }
         if (isa<SCEVAddExpr>(Comm))
           return getAddExpr(NewOps);
         if (isa<SCEVMulExpr>(Comm))
           return getMulExpr(NewOps);
         if (isa<SCEVSMaxExpr>(Comm))
           return getSMaxExpr(NewOps);
         if (isa<SCEVUMaxExpr>(Comm))
           return getUMaxExpr(NewOps);
         llvm_unreachable("Unknown commutative SCEV type!");
       }
     }
     // If we got here, all operands are loop invariant.
     return Comm;
   }
 
   if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
     const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
     const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
     if (LHS == Div->getLHS() && RHS == Div->getRHS())
       return Div;   // must be loop invariant
     return getUDivExpr(LHS, RHS);
   }
 
   // If this is a loop recurrence for a loop that does not contain L, then we
   // are dealing with the final value computed by the loop.
   if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
     // First, attempt to evaluate each operand.
     // Avoid performing the look-up in the common case where the specified
     // expression has no loop-variant portions.
     for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
       const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
       if (OpAtScope == AddRec->getOperand(i))
         continue;
 
       // Okay, at least one of these operands is loop variant but might be
       // foldable.  Build a new instance of the folded commutative expression.
       SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
                                           AddRec->op_begin()+i);
       NewOps.push_back(OpAtScope);
       for (++i; i != e; ++i)
         NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
 
       const SCEV *FoldedRec =
         getAddRecExpr(NewOps, AddRec->getLoop(),
                       AddRec->getNoWrapFlags(SCEV::FlagNW));
       AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
       // The addrec may be folded to a nonrecurrence, for example, if the
       // induction variable is multiplied by zero after constant folding. Go
       // ahead and return the folded value.
       if (!AddRec)
         return FoldedRec;
       break;
     }
 
     // If the scope is outside the addrec's loop, evaluate it by using the
     // loop exit value of the addrec.
     if (!AddRec->getLoop()->contains(L)) {
       // To evaluate this recurrence, we need to know how many times the AddRec
       // loop iterates.  Compute this now.
       const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
       if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
 
       // Then, evaluate the AddRec.
       return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
     }
 
     return AddRec;
   }
 
   if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
     const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
     if (Op == Cast->getOperand())
       return Cast;  // must be loop invariant
     return getZeroExtendExpr(Op, Cast->getType());
   }
 
   if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
     const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
     if (Op == Cast->getOperand())
       return Cast;  // must be loop invariant
     return getSignExtendExpr(Op, Cast->getType());
   }
 
   if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
     const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
     if (Op == Cast->getOperand())
       return Cast;  // must be loop invariant
     return getTruncateExpr(Op, Cast->getType());
   }
 
   llvm_unreachable("Unknown SCEV type!");
 }
 
 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
   return getSCEVAtScope(getSCEV(V), L);
 }
 
 /// Finds the minimum unsigned root of the following equation:
 ///
 ///     A * X = B (mod N)
 ///
 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
 /// A and B isn't important.
 ///
 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
                                                ScalarEvolution &SE) {
   uint32_t BW = A.getBitWidth();
   assert(BW == B.getBitWidth() && "Bit widths must be the same.");
   assert(A != 0 && "A must be non-zero.");
 
   // 1. D = gcd(A, N)
   //
   // The gcd of A and N may have only one prime factor: 2. The number of
   // trailing zeros in A is its multiplicity
   uint32_t Mult2 = A.countTrailingZeros();
   // D = 2^Mult2
 
   // 2. Check if B is divisible by D.
   //
   // B is divisible by D if and only if the multiplicity of prime factor 2 for B
   // is not less than multiplicity of this prime factor for D.
   if (B.countTrailingZeros() < Mult2)
     return SE.getCouldNotCompute();
 
   // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
   // modulo (N / D).
   //
   // (N / D) may need BW+1 bits in its representation.  Hence, we'll use this
   // bit width during computations.
   APInt AD = A.lshr(Mult2).zext(BW + 1);  // AD = A / D
   APInt Mod(BW + 1, 0);
   Mod.setBit(BW - Mult2);  // Mod = N / D
   APInt I = AD.multiplicativeInverse(Mod);
 
   // 4. Compute the minimum unsigned root of the equation:
   // I * (B / D) mod (N / D)
   APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
 
   // The result is guaranteed to be less than 2^BW so we may truncate it to BW
   // bits.
   return SE.getConstant(Result.trunc(BW));
 }
 
 /// Find the roots of the quadratic equation for the given quadratic chrec
 /// {L,+,M,+,N}.  This returns either the two roots (which might be the same) or
 /// two SCEVCouldNotCompute objects.
 ///
 static Optional<std::pair<const SCEVConstant *,const SCEVConstant *>>
 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
   assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
   const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
   const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
   const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
 
   // We currently can only solve this if the coefficients are constants.
   if (!LC || !MC || !NC)
     return None;
 
   uint32_t BitWidth = LC->getAPInt().getBitWidth();
   const APInt &L = LC->getAPInt();
   const APInt &M = MC->getAPInt();
   const APInt &N = NC->getAPInt();
   APInt Two(BitWidth, 2);
   APInt Four(BitWidth, 4);
 
   {
     using namespace APIntOps;
     const APInt& C = L;
     // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
     // The B coefficient is M-N/2
     APInt B(M);
     B -= sdiv(N,Two);
 
     // The A coefficient is N/2
     APInt A(N.sdiv(Two));
 
     // Compute the B^2-4ac term.
     APInt SqrtTerm(B);
     SqrtTerm *= B;
     SqrtTerm -= Four * (A * C);
 
     if (SqrtTerm.isNegative()) {
       // The loop is provably infinite.
       return None;
     }
 
     // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
     // integer value or else APInt::sqrt() will assert.
     APInt SqrtVal(SqrtTerm.sqrt());
 
     // Compute the two solutions for the quadratic formula.
     // The divisions must be performed as signed divisions.
     APInt NegB(-B);
     APInt TwoA(A << 1);
     if (TwoA.isMinValue())
       return None;
 
     LLVMContext &Context = SE.getContext();
 
     ConstantInt *Solution1 =
       ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
     ConstantInt *Solution2 =
       ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
 
     return std::make_pair(cast<SCEVConstant>(SE.getConstant(Solution1)),
                           cast<SCEVConstant>(SE.getConstant(Solution2)));
   } // end APIntOps namespace
 }
 
 ScalarEvolution::ExitLimit
 ScalarEvolution::howFarToZero(const SCEV *V, const Loop *L, bool ControlsExit,
                               bool AllowPredicates) {
 
   // This is only used for loops with a "x != y" exit test. The exit condition
   // is now expressed as a single expression, V = x-y. So the exit test is
   // effectively V != 0.  We know and take advantage of the fact that this
   // expression only being used in a comparison by zero context.
 
   SCEVUnionPredicate P;
   // If the value is a constant
   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
     // If the value is already zero, the branch will execute zero times.
     if (C->getValue()->isZero()) return C;
     return getCouldNotCompute();  // Otherwise it will loop infinitely.
   }
 
   const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
   if (!AddRec && AllowPredicates)
     // Try to make this an AddRec using runtime tests, in the first X
     // iterations of this loop, where X is the SCEV expression found by the
     // algorithm below.
     AddRec = convertSCEVToAddRecWithPredicates(V, L, P);
 
   if (!AddRec || AddRec->getLoop() != L)
     return getCouldNotCompute();
 
   // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
   // the quadratic equation to solve it.
   if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
     if (auto Roots = SolveQuadraticEquation(AddRec, *this)) {
       const SCEVConstant *R1 = Roots->first;
       const SCEVConstant *R2 = Roots->second;
       // Pick the smallest positive root value.
       if (ConstantInt *CB = dyn_cast<ConstantInt>(ConstantExpr::getICmp(
               CmpInst::ICMP_ULT, R1->getValue(), R2->getValue()))) {
         if (!CB->getZExtValue())
           std::swap(R1, R2); // R1 is the minimum root now.
 
         // We can only use this value if the chrec ends up with an exact zero
         // value at this index.  When solving for "X*X != 5", for example, we
         // should not accept a root of 2.
         const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
         if (Val->isZero())
           return ExitLimit(R1, R1, P); // We found a quadratic root!
       }
     }
     return getCouldNotCompute();
   }
 
   // Otherwise we can only handle this if it is affine.
   if (!AddRec->isAffine())
     return getCouldNotCompute();
 
   // If this is an affine expression, the execution count of this branch is
   // the minimum unsigned root of the following equation:
   //
   //     Start + Step*N = 0 (mod 2^BW)
   //
   // equivalent to:
   //
   //             Step*N = -Start (mod 2^BW)
   //
   // where BW is the common bit width of Start and Step.
 
   // Get the initial value for the loop.
   const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
   const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
 
   // For now we handle only constant steps.
   //
   // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
   // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
   // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
   // We have not yet seen any such cases.
   const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
   if (!StepC || StepC->getValue()->equalsInt(0))
     return getCouldNotCompute();
 
   // For positive steps (counting up until unsigned overflow):
   //   N = -Start/Step (as unsigned)
   // For negative steps (counting down to zero):
   //   N = Start/-Step
   // First compute the unsigned distance from zero in the direction of Step.
   bool CountDown = StepC->getAPInt().isNegative();
   const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
 
   // Handle unitary steps, which cannot wraparound.
   // 1*N = -Start; -1*N = Start (mod 2^BW), so:
   //   N = Distance (as unsigned)
   if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
     ConstantRange CR = getUnsignedRange(Start);
     const SCEV *MaxBECount;
     if (!CountDown && CR.getUnsignedMin().isMinValue())
       // When counting up, the worst starting value is 1, not 0.
       MaxBECount = CR.getUnsignedMax().isMinValue()
         ? getConstant(APInt::getMinValue(CR.getBitWidth()))
         : getConstant(APInt::getMaxValue(CR.getBitWidth()));
     else
       MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
                                          : -CR.getUnsignedMin());
     return ExitLimit(Distance, MaxBECount, P);
   }
 
   // As a special case, handle the instance where Step is a positive power of
   // two. In this case, determining whether Step divides Distance evenly can be
   // done by counting and comparing the number of trailing zeros of Step and
   // Distance.
   if (!CountDown) {
     const APInt &StepV = StepC->getAPInt();
     // StepV.isPowerOf2() returns true if StepV is an positive power of two.  It
     // also returns true if StepV is maximally negative (eg, INT_MIN), but that
     // case is not handled as this code is guarded by !CountDown.
     if (StepV.isPowerOf2() &&
         GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) {
       // Here we've constrained the equation to be of the form
       //
       //   2^(N + k) * Distance' = (StepV == 2^N) * X (mod 2^W)  ... (0)
       //
       // where we're operating on a W bit wide integer domain and k is
       // non-negative.  The smallest unsigned solution for X is the trip count.
       //
       // (0) is equivalent to:
       //
       //      2^(N + k) * Distance' - 2^N * X = L * 2^W
       // <=>  2^N(2^k * Distance' - X) = L * 2^(W - N) * 2^N
       // <=>  2^k * Distance' - X = L * 2^(W - N)
       // <=>  2^k * Distance'     = L * 2^(W - N) + X    ... (1)
       //
       // The smallest X satisfying (1) is unsigned remainder of dividing the LHS
       // by 2^(W - N).
       //
       // <=>  X = 2^k * Distance' URem 2^(W - N)   ... (2)
       //
       // E.g. say we're solving
       //
       //   2 * Val = 2 * X  (in i8)   ... (3)
       //
       // then from (2), we get X = Val URem i8 128 (k = 0 in this case).
       //
       // Note: It is tempting to solve (3) by setting X = Val, but Val is not
       // necessarily the smallest unsigned value of X that satisfies (3).
       // E.g. if Val is i8 -127 then the smallest value of X that satisfies (3)
       // is i8 1, not i8 -127
 
       const auto *ModuloResult = getUDivExactExpr(Distance, Step);
 
       // Since SCEV does not have a URem node, we construct one using a truncate
       // and a zero extend.
 
       unsigned NarrowWidth = StepV.getBitWidth() - StepV.countTrailingZeros();
       auto *NarrowTy = IntegerType::get(getContext(), NarrowWidth);
       auto *WideTy = Distance->getType();
 
       const SCEV *Limit =
           getZeroExtendExpr(getTruncateExpr(ModuloResult, NarrowTy), WideTy);
       return ExitLimit(Limit, Limit, P);
     }
   }
 
   // If the condition controls loop exit (the loop exits only if the expression
   // is true) and the addition is no-wrap we can use unsigned divide to
   // compute the backedge count.  In this case, the step may not divide the
   // distance, but we don't care because if the condition is "missed" the loop
   // will have undefined behavior due to wrapping.
   if (ControlsExit && AddRec->hasNoSelfWrap() &&
       loopHasNoAbnormalExits(AddRec->getLoop())) {
     const SCEV *Exact =
         getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
     return ExitLimit(Exact, Exact, P);
   }
 
   // Then, try to solve the above equation provided that Start is constant.
   if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
     const SCEV *E = SolveLinEquationWithOverflow(
         StepC->getValue()->getValue(), -StartC->getValue()->getValue(), *this);
     return ExitLimit(E, E, P);
   }
   return getCouldNotCompute();
 }
 
 ScalarEvolution::ExitLimit
 ScalarEvolution::howFarToNonZero(const SCEV *V, const Loop *L) {
   // Loops that look like: while (X == 0) are very strange indeed.  We don't
   // handle them yet except for the trivial case.  This could be expanded in the
   // future as needed.
 
   // If the value is a constant, check to see if it is known to be non-zero
   // already.  If so, the backedge will execute zero times.
   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
     if (!C->getValue()->isNullValue())
       return getZero(C->getType());
     return getCouldNotCompute();  // Otherwise it will loop infinitely.
   }
 
   // We could implement others, but I really doubt anyone writes loops like
   // this, and if they did, they would already be constant folded.
   return getCouldNotCompute();
 }
 
 std::pair<BasicBlock *, BasicBlock *>
 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
   // If the block has a unique predecessor, then there is no path from the
   // predecessor to the block that does not go through the direct edge
   // from the predecessor to the block.
   if (BasicBlock *Pred = BB->getSinglePredecessor())
     return {Pred, BB};
 
   // A loop's header is defined to be a block that dominates the loop.
   // If the header has a unique predecessor outside the loop, it must be
   // a block that has exactly one successor that can reach the loop.
   if (Loop *L = LI.getLoopFor(BB))
     return {L->getLoopPredecessor(), L->getHeader()};
 
   return {nullptr, nullptr};
 }
 
 /// SCEV structural equivalence is usually sufficient for testing whether two
 /// expressions are equal, however for the purposes of looking for a condition
 /// guarding a loop, it can be useful to be a little more general, since a
 /// front-end may have replicated the controlling expression.
 ///
 static bool HasSameValue(const SCEV *A, const SCEV *B) {
   // Quick check to see if they are the same SCEV.
   if (A == B) return true;
 
   auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
     // Not all instructions that are "identical" compute the same value.  For
     // instance, two distinct alloca instructions allocating the same type are
     // identical and do not read memory; but compute distinct values.
     return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
   };
 
   // Otherwise, if they're both SCEVUnknown, it's possible that they hold
   // two different instructions with the same value. Check for this case.
   if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
     if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
       if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
         if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
           if (ComputesEqualValues(AI, BI))
             return true;
 
   // Otherwise assume they may have a different value.
   return false;
 }
 
 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
                                            const SCEV *&LHS, const SCEV *&RHS,
                                            unsigned Depth) {
   bool Changed = false;
 
   // If we hit the max recursion limit bail out.
   if (Depth >= 3)
     return false;
 
   // Canonicalize a constant to the right side.
   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
     // Check for both operands constant.
     if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
       if (ConstantExpr::getICmp(Pred,
                                 LHSC->getValue(),
                                 RHSC->getValue())->isNullValue())
         goto trivially_false;
       else
         goto trivially_true;
     }
     // Otherwise swap the operands to put the constant on the right.
     std::swap(LHS, RHS);
     Pred = ICmpInst::getSwappedPredicate(Pred);
     Changed = true;
   }
 
   // If we're comparing an addrec with a value which is loop-invariant in the
   // addrec's loop, put the addrec on the left. Also make a dominance check,
   // as both operands could be addrecs loop-invariant in each other's loop.
   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
     const Loop *L = AR->getLoop();
     if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
       std::swap(LHS, RHS);
       Pred = ICmpInst::getSwappedPredicate(Pred);
       Changed = true;
     }
   }
 
   // If there's a constant operand, canonicalize comparisons with boundary
   // cases, and canonicalize *-or-equal comparisons to regular comparisons.
   if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
     const APInt &RA = RC->getAPInt();
     switch (Pred) {
     default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
     case ICmpInst::ICMP_EQ:
     case ICmpInst::ICMP_NE:
       // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
       if (!RA)
         if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
           if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
             if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
                 ME->getOperand(0)->isAllOnesValue()) {
               RHS = AE->getOperand(1);
               LHS = ME->getOperand(1);
               Changed = true;
             }
       break;
     case ICmpInst::ICMP_UGE:
       if ((RA - 1).isMinValue()) {
         Pred = ICmpInst::ICMP_NE;
         RHS = getConstant(RA - 1);
         Changed = true;
         break;
       }
       if (RA.isMaxValue()) {
         Pred = ICmpInst::ICMP_EQ;
         Changed = true;
         break;
       }
       if (RA.isMinValue()) goto trivially_true;
 
       Pred = ICmpInst::ICMP_UGT;
       RHS = getConstant(RA - 1);
       Changed = true;
       break;
     case ICmpInst::ICMP_ULE:
       if ((RA + 1).isMaxValue()) {
         Pred = ICmpInst::ICMP_NE;
         RHS = getConstant(RA + 1);
         Changed = true;
         break;
       }
       if (RA.isMinValue()) {
         Pred = ICmpInst::ICMP_EQ;
         Changed = true;
         break;
       }
       if (RA.isMaxValue()) goto trivially_true;
 
       Pred = ICmpInst::ICMP_ULT;
       RHS = getConstant(RA + 1);
       Changed = true;
       break;
     case ICmpInst::ICMP_SGE:
       if ((RA - 1).isMinSignedValue()) {
         Pred = ICmpInst::ICMP_NE;
         RHS = getConstant(RA - 1);
         Changed = true;
         break;
       }
       if (RA.isMaxSignedValue()) {
         Pred = ICmpInst::ICMP_EQ;
         Changed = true;
         break;
       }
       if (RA.isMinSignedValue()) goto trivially_true;
 
       Pred = ICmpInst::ICMP_SGT;
       RHS = getConstant(RA - 1);
       Changed = true;
       break;
     case ICmpInst::ICMP_SLE:
       if ((RA + 1).isMaxSignedValue()) {
         Pred = ICmpInst::ICMP_NE;
         RHS = getConstant(RA + 1);
         Changed = true;
         break;
       }
       if (RA.isMinSignedValue()) {
         Pred = ICmpInst::ICMP_EQ;
         Changed = true;
         break;
       }
       if (RA.isMaxSignedValue()) goto trivially_true;
 
       Pred = ICmpInst::ICMP_SLT;
       RHS = getConstant(RA + 1);
       Changed = true;
       break;
     case ICmpInst::ICMP_UGT:
       if (RA.isMinValue()) {
         Pred = ICmpInst::ICMP_NE;
         Changed = true;
         break;
       }
       if ((RA + 1).isMaxValue()) {
         Pred = ICmpInst::ICMP_EQ;
         RHS = getConstant(RA + 1);
         Changed = true;
         break;
       }
       if (RA.isMaxValue()) goto trivially_false;
       break;
     case ICmpInst::ICMP_ULT:
       if (RA.isMaxValue()) {
         Pred = ICmpInst::ICMP_NE;
         Changed = true;
         break;
       }
       if ((RA - 1).isMinValue()) {
         Pred = ICmpInst::ICMP_EQ;
         RHS = getConstant(RA - 1);
         Changed = true;
         break;
       }
       if (RA.isMinValue()) goto trivially_false;
       break;
     case ICmpInst::ICMP_SGT:
       if (RA.isMinSignedValue()) {
         Pred = ICmpInst::ICMP_NE;
         Changed = true;
         break;
       }
       if ((RA + 1).isMaxSignedValue()) {
         Pred = ICmpInst::ICMP_EQ;
         RHS = getConstant(RA + 1);
         Changed = true;
         break;
       }
       if (RA.isMaxSignedValue()) goto trivially_false;
       break;
     case ICmpInst::ICMP_SLT:
       if (RA.isMaxSignedValue()) {
         Pred = ICmpInst::ICMP_NE;
         Changed = true;
         break;
       }
       if ((RA - 1).isMinSignedValue()) {
        Pred = ICmpInst::ICMP_EQ;
        RHS = getConstant(RA - 1);
         Changed = true;
        break;
       }
       if (RA.isMinSignedValue()) goto trivially_false;
       break;
     }
   }
 
   // Check for obvious equality.
   if (HasSameValue(LHS, RHS)) {
     if (ICmpInst::isTrueWhenEqual(Pred))
       goto trivially_true;
     if (ICmpInst::isFalseWhenEqual(Pred))
       goto trivially_false;
   }
 
   // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
   // adding or subtracting 1 from one of the operands.
   switch (Pred) {
   case ICmpInst::ICMP_SLE:
     if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
       RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
                        SCEV::FlagNSW);
       Pred = ICmpInst::ICMP_SLT;
       Changed = true;
     } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
       LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
                        SCEV::FlagNSW);
       Pred = ICmpInst::ICMP_SLT;
       Changed = true;
     }
     break;
   case ICmpInst::ICMP_SGE:
     if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
       RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
                        SCEV::FlagNSW);
       Pred = ICmpInst::ICMP_SGT;
       Changed = true;
     } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
       LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
                        SCEV::FlagNSW);
       Pred = ICmpInst::ICMP_SGT;
       Changed = true;
     }
     break;
   case ICmpInst::ICMP_ULE:
     if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
       RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
                        SCEV::FlagNUW);
       Pred = ICmpInst::ICMP_ULT;
       Changed = true;
     } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
       LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS);
       Pred = ICmpInst::ICMP_ULT;
       Changed = true;
     }
     break;
   case ICmpInst::ICMP_UGE:
     if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
       RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
       Pred = ICmpInst::ICMP_UGT;
       Changed = true;
     } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
       LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
                        SCEV::FlagNUW);
       Pred = ICmpInst::ICMP_UGT;
       Changed = true;
     }
     break;
   default:
     break;
   }
 
   // TODO: More simplifications are possible here.
 
   // Recursively simplify until we either hit a recursion limit or nothing
   // changes.
   if (Changed)
     return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
 
   return Changed;
 
 trivially_true:
   // Return 0 == 0.
   LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
   Pred = ICmpInst::ICMP_EQ;
   return true;
 
 trivially_false:
   // Return 0 != 0.
   LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
   Pred = ICmpInst::ICMP_NE;
   return true;
 }
 
 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
   return getSignedRange(S).getSignedMax().isNegative();
 }
 
 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
   return getSignedRange(S).getSignedMin().isStrictlyPositive();
 }
 
 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
   return !getSignedRange(S).getSignedMin().isNegative();
 }
 
 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
   return !getSignedRange(S).getSignedMax().isStrictlyPositive();
 }
 
 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
   return isKnownNegative(S) || isKnownPositive(S);
 }
 
 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
                                        const SCEV *LHS, const SCEV *RHS) {
   // Canonicalize the inputs first.
   (void)SimplifyICmpOperands(Pred, LHS, RHS);
 
   // If LHS or RHS is an addrec, check to see if the condition is true in
   // every iteration of the loop.
   // If LHS and RHS are both addrec, both conditions must be true in
   // every iteration of the loop.
   const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
   const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
   bool LeftGuarded = false;
   bool RightGuarded = false;
   if (LAR) {
     const Loop *L = LAR->getLoop();
     if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
         isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
       if (!RAR) return true;
       LeftGuarded = true;
     }
   }
   if (RAR) {
     const Loop *L = RAR->getLoop();
     if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
         isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
       if (!LAR) return true;
       RightGuarded = true;
     }
   }
   if (LeftGuarded && RightGuarded)
     return true;
 
   if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
     return true;
 
   // Otherwise see what can be done with known constant ranges.
   return isKnownPredicateViaConstantRanges(Pred, LHS, RHS);
 }
 
 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
                                            ICmpInst::Predicate Pred,
                                            bool &Increasing) {
   bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
 
 #ifndef NDEBUG
   // Verify an invariant: inverting the predicate should turn a monotonically
   // increasing change to a monotonically decreasing one, and vice versa.
   bool IncreasingSwapped;
   bool ResultSwapped = isMonotonicPredicateImpl(
       LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
 
   assert(Result == ResultSwapped && "should be able to analyze both!");
   if (ResultSwapped)
     assert(Increasing == !IncreasingSwapped &&
            "monotonicity should flip as we flip the predicate");
 #endif
 
   return Result;
 }
 
 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
                                                ICmpInst::Predicate Pred,
                                                bool &Increasing) {
 
   // A zero step value for LHS means the induction variable is essentially a
   // loop invariant value. We don't really depend on the predicate actually
   // flipping from false to true (for increasing predicates, and the other way
   // around for decreasing predicates), all we care about is that *if* the
   // predicate changes then it only changes from false to true.
   //
   // A zero step value in itself is not very useful, but there may be places
   // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
   // as general as possible.
 
   switch (Pred) {
   default:
     return false; // Conservative answer
 
   case ICmpInst::ICMP_UGT:
   case ICmpInst::ICMP_UGE:
   case ICmpInst::ICMP_ULT:
   case ICmpInst::ICMP_ULE:
     if (!LHS->hasNoUnsignedWrap())
       return false;
 
     Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
     return true;
 
   case ICmpInst::ICMP_SGT:
   case ICmpInst::ICMP_SGE:
   case ICmpInst::ICMP_SLT:
   case ICmpInst::ICMP_SLE: {
     if (!LHS->hasNoSignedWrap())
       return false;
 
     const SCEV *Step = LHS->getStepRecurrence(*this);
 
     if (isKnownNonNegative(Step)) {
       Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
       return true;
     }
 
     if (isKnownNonPositive(Step)) {
       Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
       return true;
     }
 
     return false;
   }
 
   }
 
   llvm_unreachable("switch has default clause!");
 }
 
 bool ScalarEvolution::isLoopInvariantPredicate(
     ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
     ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
     const SCEV *&InvariantRHS) {
 
   // If there is a loop-invariant, force it into the RHS, otherwise bail out.
   if (!isLoopInvariant(RHS, L)) {
     if (!isLoopInvariant(LHS, L))
       return false;
 
     std::swap(LHS, RHS);
     Pred = ICmpInst::getSwappedPredicate(Pred);
   }
 
   const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
   if (!ArLHS || ArLHS->getLoop() != L)
     return false;
 
   bool Increasing;
   if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
     return false;
 
   // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
   // true as the loop iterates, and the backedge is control dependent on
   // "ArLHS `Pred` RHS" == true then we can reason as follows:
   //
   //   * if the predicate was false in the first iteration then the predicate
   //     is never evaluated again, since the loop exits without taking the
   //     backedge.
   //   * if the predicate was true in the first iteration then it will
   //     continue to be true for all future iterations since it is
   //     monotonically increasing.
   //
   // For both the above possibilities, we can replace the loop varying
   // predicate with its value on the first iteration of the loop (which is
   // loop invariant).
   //
   // A similar reasoning applies for a monotonically decreasing predicate, by
   // replacing true with false and false with true in the above two bullets.
 
   auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
 
   if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
     return false;
 
   InvariantPred = Pred;
   InvariantLHS = ArLHS->getStart();
   InvariantRHS = RHS;
   return true;
 }
 
 bool ScalarEvolution::isKnownPredicateViaConstantRanges(
     ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
   if (HasSameValue(LHS, RHS))
     return ICmpInst::isTrueWhenEqual(Pred);
 
   // This code is split out from isKnownPredicate because it is called from
   // within isLoopEntryGuardedByCond.
 
   auto CheckRanges =
       [&](const ConstantRange &RangeLHS, const ConstantRange &RangeRHS) {
     return ConstantRange::makeSatisfyingICmpRegion(Pred, RangeRHS)
         .contains(RangeLHS);
   };
 
   // The check at the top of the function catches the case where the values are
   // known to be equal.
   if (Pred == CmpInst::ICMP_EQ)
     return false;
 
   if (Pred == CmpInst::ICMP_NE)
     return CheckRanges(getSignedRange(LHS), getSignedRange(RHS)) ||
            CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS)) ||
            isKnownNonZero(getMinusSCEV(LHS, RHS));
 
   if (CmpInst::isSigned(Pred))
     return CheckRanges(getSignedRange(LHS), getSignedRange(RHS));
 
   return CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS));
 }
 
 bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
                                                     const SCEV *LHS,
                                                     const SCEV *RHS) {
 
   // Match Result to (X + Y)<ExpectedFlags> where Y is a constant integer.
   // Return Y via OutY.
   auto MatchBinaryAddToConst =
       [this](const SCEV *Result, const SCEV *X, APInt &OutY,
              SCEV::NoWrapFlags ExpectedFlags) {
     const SCEV *NonConstOp, *ConstOp;
     SCEV::NoWrapFlags FlagsPresent;
 
     if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) ||
         !isa<SCEVConstant>(ConstOp) || NonConstOp != X)
       return false;
 
     OutY = cast<SCEVConstant>(ConstOp)->getAPInt();
     return (FlagsPresent & ExpectedFlags) == ExpectedFlags;
   };
 
   APInt C;
 
   switch (Pred) {
   default:
     break;
 
   case ICmpInst::ICMP_SGE:
     std::swap(LHS, RHS);
   case ICmpInst::ICMP_SLE:
     // X s<= (X + C)<nsw> if C >= 0
     if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative())
       return true;
 
     // (X + C)<nsw> s<= X if C <= 0
     if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) &&
         !C.isStrictlyPositive())
       return true;
     break;
 
   case ICmpInst::ICMP_SGT:
     std::swap(LHS, RHS);
   case ICmpInst::ICMP_SLT:
     // X s< (X + C)<nsw> if C > 0
     if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) &&
         C.isStrictlyPositive())
       return true;
 
     // (X + C)<nsw> s< X if C < 0
     if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative())
       return true;
     break;
   }
 
   return false;
 }
 
 bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
                                                    const SCEV *LHS,
                                                    const SCEV *RHS) {
   if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
     return false;
 
   // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
   // the stack can result in exponential time complexity.
   SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
 
   // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
   //
   // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
   // isKnownPredicate.  isKnownPredicate is more powerful, but also more
   // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
   // interesting cases seen in practice.  We can consider "upgrading" L >= 0 to
   // use isKnownPredicate later if needed.
   return isKnownNonNegative(RHS) &&
          isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
          isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS);
 }
 
 bool ScalarEvolution::isImpliedViaGuard(BasicBlock *BB,
                                         ICmpInst::Predicate Pred,
                                         const SCEV *LHS, const SCEV *RHS) {
   // No need to even try if we know the module has no guards.
   if (!HasGuards)
     return false;
 
   return any_of(*BB, [&](Instruction &I) {
     using namespace llvm::PatternMatch;
 
     Value *Condition;
     return match(&I, m_Intrinsic<Intrinsic::experimental_guard>(
                          m_Value(Condition))) &&
            isImpliedCond(Pred, LHS, RHS, Condition, false);
   });
 }
 
 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
 /// protected by a conditional between LHS and RHS.  This is used to
 /// to eliminate casts.
 bool
 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
                                              ICmpInst::Predicate Pred,
                                              const SCEV *LHS, const SCEV *RHS) {
   // Interpret a null as meaning no loop, where there is obviously no guard
   // (interprocedural conditions notwithstanding).
   if (!L) return true;
 
   if (isKnownPredicateViaConstantRanges(Pred, LHS, RHS))
     return true;
 
   BasicBlock *Latch = L->getLoopLatch();
   if (!Latch)
     return false;
 
   BranchInst *LoopContinuePredicate =
     dyn_cast<BranchInst>(Latch->getTerminator());
   if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
       isImpliedCond(Pred, LHS, RHS,
                     LoopContinuePredicate->getCondition(),
                     LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
     return true;
 
   // We don't want more than one activation of the following loops on the stack
   // -- that can lead to O(n!) time complexity.
   if (WalkingBEDominatingConds)
     return false;
 
   SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
 
   // See if we can exploit a trip count to prove the predicate.
   const auto &BETakenInfo = getBackedgeTakenInfo(L);
   const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
   if (LatchBECount != getCouldNotCompute()) {
     // We know that Latch branches back to the loop header exactly
     // LatchBECount times.  This means the backdege condition at Latch is
     // equivalent to  "{0,+,1} u< LatchBECount".
     Type *Ty = LatchBECount->getType();
     auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
     const SCEV *LoopCounter =
       getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
     if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
                       LatchBECount))
       return true;
   }
 
   // Check conditions due to any @llvm.assume intrinsics.
   for (auto &AssumeVH : AC.assumptions()) {
     if (!AssumeVH)
       continue;
     auto *CI = cast<CallInst>(AssumeVH);
     if (!DT.dominates(CI, Latch->getTerminator()))
       continue;
 
     if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
       return true;
   }
 
   // If the loop is not reachable from the entry block, we risk running into an
   // infinite loop as we walk up into the dom tree.  These loops do not matter
   // anyway, so we just return a conservative answer when we see them.
   if (!DT.isReachableFromEntry(L->getHeader()))
     return false;
 
   if (isImpliedViaGuard(Latch, Pred, LHS, RHS))
     return true;
 
   for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
        DTN != HeaderDTN; DTN = DTN->getIDom()) {
 
     assert(DTN && "should reach the loop header before reaching the root!");
 
     BasicBlock *BB = DTN->getBlock();
     if (isImpliedViaGuard(BB, Pred, LHS, RHS))
       return true;
 
     BasicBlock *PBB = BB->getSinglePredecessor();
     if (!PBB)
       continue;
 
     BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
     if (!ContinuePredicate || !ContinuePredicate->isConditional())
       continue;
 
     Value *Condition = ContinuePredicate->getCondition();
 
     // If we have an edge `E` within the loop body that dominates the only
     // latch, the condition guarding `E` also guards the backedge.  This
     // reasoning works only for loops with a single latch.
 
     BasicBlockEdge DominatingEdge(PBB, BB);
     if (DominatingEdge.isSingleEdge()) {
       // We're constructively (and conservatively) enumerating edges within the
       // loop body that dominate the latch.  The dominator tree better agree
       // with us on this:
       assert(DT.dominates(DominatingEdge, Latch) && "should be!");
 
       if (isImpliedCond(Pred, LHS, RHS, Condition,
                         BB != ContinuePredicate->getSuccessor(0)))
         return true;
     }
   }
 
   return false;
 }
 
 bool
 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
                                           ICmpInst::Predicate Pred,
                                           const SCEV *LHS, const SCEV *RHS) {
   // Interpret a null as meaning no loop, where there is obviously no guard
   // (interprocedural conditions notwithstanding).
   if (!L) return false;
 
   if (isKnownPredicateViaConstantRanges(Pred, LHS, RHS))
     return true;
 
   // Starting at the loop predecessor, climb up the predecessor chain, as long
   // as there are predecessors that can be found that have unique successors
   // leading to the original header.
   for (std::pair<BasicBlock *, BasicBlock *>
          Pair(L->getLoopPredecessor(), L->getHeader());
        Pair.first;
        Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
 
     if (isImpliedViaGuard(Pair.first, Pred, LHS, RHS))
       return true;
 
     BranchInst *LoopEntryPredicate =
       dyn_cast<BranchInst>(Pair.first->getTerminator());
     if (!LoopEntryPredicate ||
         LoopEntryPredicate->isUnconditional())
       continue;
 
     if (isImpliedCond(Pred, LHS, RHS,
                       LoopEntryPredicate->getCondition(),
                       LoopEntryPredicate->getSuccessor(0) != Pair.second))
       return true;
   }
 
   // Check conditions due to any @llvm.assume intrinsics.
   for (auto &AssumeVH : AC.assumptions()) {
     if (!AssumeVH)
       continue;
     auto *CI = cast<CallInst>(AssumeVH);
     if (!DT.dominates(CI, L->getHeader()))
       continue;
 
     if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
       return true;
   }
 
   return false;
 }
 
 namespace {
 /// RAII wrapper to prevent recursive application of isImpliedCond.
 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
 /// currently evaluating isImpliedCond.
 struct MarkPendingLoopPredicate {
   Value *Cond;
   DenseSet<Value*> &LoopPreds;
   bool Pending;
 
   MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
     : Cond(C), LoopPreds(LP) {
     Pending = !LoopPreds.insert(Cond).second;
   }
   ~MarkPendingLoopPredicate() {
     if (!Pending)
       LoopPreds.erase(Cond);
   }
 };
 } // end anonymous namespace
 
 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
                                     const SCEV *LHS, const SCEV *RHS,
                                     Value *FoundCondValue,
                                     bool Inverse) {
   MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
   if (Mark.Pending)
     return false;
 
   // Recursively handle And and Or conditions.
   if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
     if (BO->getOpcode() == Instruction::And) {
       if (!Inverse)
         return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
                isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
     } else if (BO->getOpcode() == Instruction::Or) {
       if (Inverse)
         return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
                isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
     }
   }
 
   ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
   if (!ICI) return false;
 
   // Now that we found a conditional branch that dominates the loop or controls
   // the loop latch. Check to see if it is the comparison we are looking for.
   ICmpInst::Predicate FoundPred;
   if (Inverse)
     FoundPred = ICI->getInversePredicate();
   else
     FoundPred = ICI->getPredicate();
 
   const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
   const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
 
   return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS);
 }
 
 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
                                     const SCEV *RHS,
                                     ICmpInst::Predicate FoundPred,
                                     const SCEV *FoundLHS,
                                     const SCEV *FoundRHS) {
   // Balance the types.
   if (getTypeSizeInBits(LHS->getType()) <
       getTypeSizeInBits(FoundLHS->getType())) {
     if (CmpInst::isSigned(Pred)) {
       LHS = getSignExtendExpr(LHS, FoundLHS->getType());
       RHS = getSignExtendExpr(RHS, FoundLHS->getType());
     } else {
       LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
       RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
     }
   } else if (getTypeSizeInBits(LHS->getType()) >
       getTypeSizeInBits(FoundLHS->getType())) {
     if (CmpInst::isSigned(FoundPred)) {
       FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
       FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
     } else {
       FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
       FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
     }
   }
 
   // Canonicalize the query to match the way instcombine will have
   // canonicalized the comparison.
   if (SimplifyICmpOperands(Pred, LHS, RHS))
     if (LHS == RHS)
       return CmpInst::isTrueWhenEqual(Pred);
   if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
     if (FoundLHS == FoundRHS)
       return CmpInst::isFalseWhenEqual(FoundPred);
 
   // Check to see if we can make the LHS or RHS match.
   if (LHS == FoundRHS || RHS == FoundLHS) {
     if (isa<SCEVConstant>(RHS)) {
       std::swap(FoundLHS, FoundRHS);
       FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
     } else {
       std::swap(LHS, RHS);
       Pred = ICmpInst::getSwappedPredicate(Pred);
     }
   }
 
   // Check whether the found predicate is the same as the desired predicate.
   if (FoundPred == Pred)
     return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
 
   // Check whether swapping the found predicate makes it the same as the
   // desired predicate.
   if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
     if (isa<SCEVConstant>(RHS))
       return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
     else
       return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
                                    RHS, LHS, FoundLHS, FoundRHS);
   }
 
   // Unsigned comparison is the same as signed comparison when both the operands
   // are non-negative.
   if (CmpInst::isUnsigned(FoundPred) &&
       CmpInst::getSignedPredicate(FoundPred) == Pred &&
       isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS))
     return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
 
   // Check if we can make progress by sharpening ranges.
   if (FoundPred == ICmpInst::ICMP_NE &&
       (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
 
     const SCEVConstant *C = nullptr;
     const SCEV *V = nullptr;
 
     if (isa<SCEVConstant>(FoundLHS)) {
       C = cast<SCEVConstant>(FoundLHS);
       V = FoundRHS;
     } else {
       C = cast<SCEVConstant>(FoundRHS);
       V = FoundLHS;
     }
 
     // The guarding predicate tells us that C != V. If the known range
     // of V is [C, t), we can sharpen the range to [C + 1, t).  The
     // range we consider has to correspond to same signedness as the
     // predicate we're interested in folding.
 
     APInt Min = ICmpInst::isSigned(Pred) ?
         getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
 
     if (Min == C->getAPInt()) {
       // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
       // This is true even if (Min + 1) wraps around -- in case of
       // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
 
       APInt SharperMin = Min + 1;
 
       switch (Pred) {
         case ICmpInst::ICMP_SGE:
         case ICmpInst::ICMP_UGE:
           // We know V `Pred` SharperMin.  If this implies LHS `Pred`
           // RHS, we're done.
           if (isImpliedCondOperands(Pred, LHS, RHS, V,
                                     getConstant(SharperMin)))
             return true;
 
         case ICmpInst::ICMP_SGT:
         case ICmpInst::ICMP_UGT:
           // We know from the range information that (V `Pred` Min ||
           // V == Min).  We know from the guarding condition that !(V
           // == Min).  This gives us
           //
           //       V `Pred` Min || V == Min && !(V == Min)
           //   =>  V `Pred` Min
           //
           // If V `Pred` Min implies LHS `Pred` RHS, we're done.
 
           if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
             return true;
 
         default:
           // No change
           break;
       }
     }
   }
 
   // Check whether the actual condition is beyond sufficient.
   if (FoundPred == ICmpInst::ICMP_EQ)
     if (ICmpInst::isTrueWhenEqual(Pred))
       if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
         return true;
   if (Pred == ICmpInst::ICMP_NE)
     if (!ICmpInst::isTrueWhenEqual(FoundPred))
       if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
         return true;
 
   // Otherwise assume the worst.
   return false;
 }
 
 bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr,
                                      const SCEV *&L, const SCEV *&R,
                                      SCEV::NoWrapFlags &Flags) {
   const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
   if (!AE || AE->getNumOperands() != 2)
     return false;
 
   L = AE->getOperand(0);
   R = AE->getOperand(1);
   Flags = AE->getNoWrapFlags();
   return true;
 }
 
 bool ScalarEvolution::computeConstantDifference(const SCEV *Less,
                                                 const SCEV *More,
                                                 APInt &C) {
   // We avoid subtracting expressions here because this function is usually
   // fairly deep in the call stack (i.e. is called many times).
 
   if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
     const auto *LAR = cast<SCEVAddRecExpr>(Less);
     const auto *MAR = cast<SCEVAddRecExpr>(More);
 
     if (LAR->getLoop() != MAR->getLoop())
       return false;
 
     // We look at affine expressions only; not for correctness but to keep
     // getStepRecurrence cheap.
     if (!LAR->isAffine() || !MAR->isAffine())
       return false;
 
     if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
       return false;
 
     Less = LAR->getStart();
     More = MAR->getStart();
 
     // fall through
   }
 
   if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
     const auto &M = cast<SCEVConstant>(More)->getAPInt();
     const auto &L = cast<SCEVConstant>(Less)->getAPInt();
     C = M - L;
     return true;
   }
 
   const SCEV *L, *R;
   SCEV::NoWrapFlags Flags;
   if (splitBinaryAdd(Less, L, R, Flags))
     if (const auto *LC = dyn_cast<SCEVConstant>(L))
       if (R == More) {
         C = -(LC->getAPInt());
         return true;
       }
 
   if (splitBinaryAdd(More, L, R, Flags))
     if (const auto *LC = dyn_cast<SCEVConstant>(L))
       if (R == Less) {
         C = LC->getAPInt();
         return true;
       }
 
   return false;
 }
 
 bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
     ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
     const SCEV *FoundLHS, const SCEV *FoundRHS) {
   if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
     return false;
 
   const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
   if (!AddRecLHS)
     return false;
 
   const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
   if (!AddRecFoundLHS)
     return false;
 
   // We'd like to let SCEV reason about control dependencies, so we constrain
   // both the inequalities to be about add recurrences on the same loop.  This
   // way we can use isLoopEntryGuardedByCond later.
 
   const Loop *L = AddRecFoundLHS->getLoop();
   if (L != AddRecLHS->getLoop())
     return false;
 
   //  FoundLHS u< FoundRHS u< -C =>  (FoundLHS + C) u< (FoundRHS + C) ... (1)
   //
   //  FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
   //                                                                  ... (2)
   //
   // Informal proof for (2), assuming (1) [*]:
   //
   // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
   //
   // Then
   //
   //       FoundLHS s< FoundRHS s< INT_MIN - C
   // <=>  (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C   [ using (3) ]
   // <=>  (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
   // <=>  (FoundLHS + INT_MIN + C + INT_MIN) s<
   //                        (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
   // <=>  FoundLHS + C s< FoundRHS + C
   //
   // [*]: (1) can be proved by ruling out overflow.
   //
   // [**]: This can be proved by analyzing all the four possibilities:
   //    (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
   //    (A s>= 0, B s>= 0).
   //
   // Note:
   // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
   // will not sign underflow.  For instance, say FoundLHS = (i8 -128), FoundRHS
   // = (i8 -127) and C = (i8 -100).  Then INT_MIN - C = (i8 -28), and FoundRHS
   // s< (INT_MIN - C).  Lack of sign overflow / underflow in "FoundRHS + C" is
   // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
   // C)".
 
   APInt LDiff, RDiff;
   if (!computeConstantDifference(FoundLHS, LHS, LDiff) ||
       !computeConstantDifference(FoundRHS, RHS, RDiff) ||
       LDiff != RDiff)
     return false;
 
   if (LDiff == 0)
     return true;
 
   APInt FoundRHSLimit;
 
   if (Pred == CmpInst::ICMP_ULT) {
     FoundRHSLimit = -RDiff;
   } else {
     assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
     FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - RDiff;
   }
 
   // Try to prove (1) or (2), as needed.
   return isLoopEntryGuardedByCond(L, Pred, FoundRHS,
                                   getConstant(FoundRHSLimit));
 }
 
 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
                                             const SCEV *LHS, const SCEV *RHS,
                                             const SCEV *FoundLHS,
                                             const SCEV *FoundRHS) {
   if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
     return true;
 
   if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
     return true;
 
   return isImpliedCondOperandsHelper(Pred, LHS, RHS,
                                      FoundLHS, FoundRHS) ||
          // ~x < ~y --> x > y
          isImpliedCondOperandsHelper(Pred, LHS, RHS,
                                      getNotSCEV(FoundRHS),
                                      getNotSCEV(FoundLHS));
 }
 
 
 /// If Expr computes ~A, return A else return nullptr
 static const SCEV *MatchNotExpr(const SCEV *Expr) {
   const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
   if (!Add || Add->getNumOperands() != 2 ||
       !Add->getOperand(0)->isAllOnesValue())
     return nullptr;
 
   const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
   if (!AddRHS || AddRHS->getNumOperands() != 2 ||
       !AddRHS->getOperand(0)->isAllOnesValue())
     return nullptr;
 
   return AddRHS->getOperand(1);
 }
 
 
 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
 template<typename MaxExprType>
 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
                               const SCEV *Candidate) {
   const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
   if (!MaxExpr) return false;
 
   return find(MaxExpr->operands(), Candidate) != MaxExpr->op_end();
 }
 
 
 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
 template<typename MaxExprType>
 static bool IsMinConsistingOf(ScalarEvolution &SE,
                               const SCEV *MaybeMinExpr,
                               const SCEV *Candidate) {
   const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
   if (!MaybeMaxExpr)
     return false;
 
   return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
 }
 
 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
                                            ICmpInst::Predicate Pred,
                                            const SCEV *LHS, const SCEV *RHS) {
 
   // If both sides are affine addrecs for the same loop, with equal
   // steps, and we know the recurrences don't wrap, then we only
   // need to check the predicate on the starting values.
 
   if (!ICmpInst::isRelational(Pred))
     return false;
 
   const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
   if (!LAR)
     return false;
   const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
   if (!RAR)
     return false;
   if (LAR->getLoop() != RAR->getLoop())
     return false;
   if (!LAR->isAffine() || !RAR->isAffine())
     return false;
 
   if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
     return false;
 
   SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
                          SCEV::FlagNSW : SCEV::FlagNUW;
   if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
     return false;
 
   return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
 }
 
 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
 /// expression?
 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
                                         ICmpInst::Predicate Pred,
                                         const SCEV *LHS, const SCEV *RHS) {
   switch (Pred) {
   default:
     return false;
 
   case ICmpInst::ICMP_SGE:
     std::swap(LHS, RHS);
     // fall through
   case ICmpInst::ICMP_SLE:
     return
       // min(A, ...) <= A
       IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
       // A <= max(A, ...)
       IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
 
   case ICmpInst::ICMP_UGE:
     std::swap(LHS, RHS);
     // fall through
   case ICmpInst::ICMP_ULE:
     return
       // min(A, ...) <= A
       IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
       // A <= max(A, ...)
       IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
   }
 
   llvm_unreachable("covered switch fell through?!");
 }
 
 bool
 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
                                              const SCEV *LHS, const SCEV *RHS,
                                              const SCEV *FoundLHS,
                                              const SCEV *FoundRHS) {
   auto IsKnownPredicateFull =
       [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
     return isKnownPredicateViaConstantRanges(Pred, LHS, RHS) ||
            IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
            IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
            isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
   };
 
   switch (Pred) {
   default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
   case ICmpInst::ICMP_EQ:
   case ICmpInst::ICMP_NE:
     if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
       return true;
     break;
   case ICmpInst::ICMP_SLT:
   case ICmpInst::ICMP_SLE:
     if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
         IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
       return true;
     break;
   case ICmpInst::ICMP_SGT:
   case ICmpInst::ICMP_SGE:
     if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
         IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
       return true;
     break;
   case ICmpInst::ICMP_ULT:
   case ICmpInst::ICMP_ULE:
     if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
         IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
       return true;
     break;
   case ICmpInst::ICMP_UGT:
   case ICmpInst::ICMP_UGE:
     if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
         IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
       return true;
     break;
   }
 
   return false;
 }
 
 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
                                                      const SCEV *LHS,
                                                      const SCEV *RHS,
                                                      const SCEV *FoundLHS,
                                                      const SCEV *FoundRHS) {
   if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
     // The restriction on `FoundRHS` be lifted easily -- it exists only to
     // reduce the compile time impact of this optimization.
     return false;
 
   const SCEVAddExpr *AddLHS = dyn_cast<SCEVAddExpr>(LHS);
   if (!AddLHS || AddLHS->getOperand(1) != FoundLHS ||
       !isa<SCEVConstant>(AddLHS->getOperand(0)))
     return false;
 
   APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getAPInt();
 
   // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
   // antecedent "`FoundLHS` `Pred` `FoundRHS`".
   ConstantRange FoundLHSRange =
       ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
 
   // Since `LHS` is `FoundLHS` + `AddLHS->getOperand(0)`, we can compute a range
   // for `LHS`:
   APInt Addend = cast<SCEVConstant>(AddLHS->getOperand(0))->getAPInt();
   ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(Addend));
 
   // We can also compute the range of values for `LHS` that satisfy the
   // consequent, "`LHS` `Pred` `RHS`":
   APInt ConstRHS = cast<SCEVConstant>(RHS)->getAPInt();
   ConstantRange SatisfyingLHSRange =
       ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
 
   // The antecedent implies the consequent if every value of `LHS` that
   // satisfies the antecedent also satisfies the consequent.
   return SatisfyingLHSRange.contains(LHSRange);
 }
 
 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
                                          bool IsSigned, bool NoWrap) {
   if (NoWrap) return false;
 
   unsigned BitWidth = getTypeSizeInBits(RHS->getType());
   const SCEV *One = getOne(Stride->getType());
 
   if (IsSigned) {
     APInt MaxRHS = getSignedRange(RHS).getSignedMax();
     APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
     APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
                                 .getSignedMax();
 
     // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
     return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
   }
 
   APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
   APInt MaxValue = APInt::getMaxValue(BitWidth);
   APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
                               .getUnsignedMax();
 
   // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
   return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
 }
 
 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
                                          bool IsSigned, bool NoWrap) {
   if (NoWrap) return false;
 
   unsigned BitWidth = getTypeSizeInBits(RHS->getType());
   const SCEV *One = getOne(Stride->getType());
 
   if (IsSigned) {
     APInt MinRHS = getSignedRange(RHS).getSignedMin();
     APInt MinValue = APInt::getSignedMinValue(BitWidth);
     APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
                                .getSignedMax();
 
     // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
     return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
   }
 
   APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
   APInt MinValue = APInt::getMinValue(BitWidth);
   APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
                             .getUnsignedMax();
 
   // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
   return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
 }
 
 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
                                             bool Equality) {
   const SCEV *One = getOne(Step->getType());
   Delta = Equality ? getAddExpr(Delta, Step)
                    : getAddExpr(Delta, getMinusSCEV(Step, One));
   return getUDivExpr(Delta, Step);
 }
 
 ScalarEvolution::ExitLimit
 ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS,
                                   const Loop *L, bool IsSigned,
                                   bool ControlsExit, bool AllowPredicates) {
   SCEVUnionPredicate P;
   // We handle only IV < Invariant
   if (!isLoopInvariant(RHS, L))
     return getCouldNotCompute();
 
   const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
   if (!IV && AllowPredicates)
     // Try to make this an AddRec using runtime tests, in the first X
     // iterations of this loop, where X is the SCEV expression found by the
     // algorithm below.
     IV = convertSCEVToAddRecWithPredicates(LHS, L, P);
 
   // Avoid weird loops
   if (!IV || IV->getLoop() != L || !IV->isAffine())
     return getCouldNotCompute();
 
   bool NoWrap = ControlsExit &&
                 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
 
   const SCEV *Stride = IV->getStepRecurrence(*this);
 
   // Avoid negative or zero stride values
   if (!isKnownPositive(Stride))
     return getCouldNotCompute();
 
   // Avoid proven overflow cases: this will ensure that the backedge taken count
   // will not generate any unsigned overflow. Relaxed no-overflow conditions
   // exploit NoWrapFlags, allowing to optimize in presence of undefined
   // behaviors like the case of C language.
   if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
     return getCouldNotCompute();
 
   ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
                                       : ICmpInst::ICMP_ULT;
   const SCEV *Start = IV->getStart();
   const SCEV *End = RHS;
   if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
     End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start);
 
   const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
 
   APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
                             : getUnsignedRange(Start).getUnsignedMin();
 
   APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
                              : getUnsignedRange(Stride).getUnsignedMin();
 
   unsigned BitWidth = getTypeSizeInBits(LHS->getType());
   APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
                          : APInt::getMaxValue(BitWidth) - (MinStride - 1);
 
   // Although End can be a MAX expression we estimate MaxEnd considering only
   // the case End = RHS. This is safe because in the other case (End - Start)
   // is zero, leading to a zero maximum backedge taken count.
   APInt MaxEnd =
     IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
              : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
 
   const SCEV *MaxBECount;
   if (isa<SCEVConstant>(BECount))
     MaxBECount = BECount;
   else
     MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
                                 getConstant(MinStride), false);
 
   if (isa<SCEVCouldNotCompute>(MaxBECount))
     MaxBECount = BECount;
 
   return ExitLimit(BECount, MaxBECount, P);
 }
 
 ScalarEvolution::ExitLimit
 ScalarEvolution::howManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
                                      const Loop *L, bool IsSigned,
                                      bool ControlsExit, bool AllowPredicates) {
   SCEVUnionPredicate P;
   // We handle only IV > Invariant
   if (!isLoopInvariant(RHS, L))
     return getCouldNotCompute();
 
   const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
   if (!IV && AllowPredicates)
     // Try to make this an AddRec using runtime tests, in the first X
     // iterations of this loop, where X is the SCEV expression found by the
     // algorithm below.
     IV = convertSCEVToAddRecWithPredicates(LHS, L, P);
 
   // Avoid weird loops
   if (!IV || IV->getLoop() != L || !IV->isAffine())
     return getCouldNotCompute();
 
   bool NoWrap = ControlsExit &&
                 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
 
   const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
 
   // Avoid negative or zero stride values
   if (!isKnownPositive(Stride))
     return getCouldNotCompute();
 
   // Avoid proven overflow cases: this will ensure that the backedge taken count
   // will not generate any unsigned overflow. Relaxed no-overflow conditions
   // exploit NoWrapFlags, allowing to optimize in presence of undefined
   // behaviors like the case of C language.
   if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
     return getCouldNotCompute();
 
   ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
                                       : ICmpInst::ICMP_UGT;
 
   const SCEV *Start = IV->getStart();
   const SCEV *End = RHS;
   if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS))
     End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start);
 
   const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
 
   APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
                             : getUnsignedRange(Start).getUnsignedMax();
 
   APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
                              : getUnsignedRange(Stride).getUnsignedMin();
 
   unsigned BitWidth = getTypeSizeInBits(LHS->getType());
   APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
                          : APInt::getMinValue(BitWidth) + (MinStride - 1);
 
   // Although End can be a MIN expression we estimate MinEnd considering only
   // the case End = RHS. This is safe because in the other case (Start - End)
   // is zero, leading to a zero maximum backedge taken count.
   APInt MinEnd =
     IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
              : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
 
 
   const SCEV *MaxBECount = getCouldNotCompute();
   if (isa<SCEVConstant>(BECount))
     MaxBECount = BECount;
   else
     MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
                                 getConstant(MinStride), false);
 
   if (isa<SCEVCouldNotCompute>(MaxBECount))
     MaxBECount = BECount;
 
   return ExitLimit(BECount, MaxBECount, P);
 }
 
 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(const ConstantRange &Range,
                                                     ScalarEvolution &SE) const {
   if (Range.isFullSet())  // Infinite loop.
     return SE.getCouldNotCompute();
 
   // If the start is a non-zero constant, shift the range to simplify things.
   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
     if (!SC->getValue()->isZero()) {
       SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
       Operands[0] = SE.getZero(SC->getType());
       const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
                                              getNoWrapFlags(FlagNW));
       if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
         return ShiftedAddRec->getNumIterationsInRange(
             Range.subtract(SC->getAPInt()), SE);
       // This is strange and shouldn't happen.
       return SE.getCouldNotCompute();
     }
 
   // The only time we can solve this is when we have all constant indices.
   // Otherwise, we cannot determine the overflow conditions.
   if (any_of(operands(), [](const SCEV *Op) { return !isa<SCEVConstant>(Op); }))
     return SE.getCouldNotCompute();
 
   // Okay at this point we know that all elements of the chrec are constants and
   // that the start element is zero.
 
   // First check to see if the range contains zero.  If not, the first
   // iteration exits.
   unsigned BitWidth = SE.getTypeSizeInBits(getType());
   if (!Range.contains(APInt(BitWidth, 0)))
     return SE.getZero(getType());
 
   if (isAffine()) {
     // If this is an affine expression then we have this situation:
     //   Solve {0,+,A} in Range  ===  Ax in Range
 
     // We know that zero is in the range.  If A is positive then we know that
     // the upper value of the range must be the first possible exit value.
     // If A is negative then the lower of the range is the last possible loop
     // value.  Also note that we already checked for a full range.
     APInt One(BitWidth,1);
     APInt A = cast<SCEVConstant>(getOperand(1))->getAPInt();
     APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
 
     // The exit value should be (End+A)/A.
     APInt ExitVal = (End + A).udiv(A);
     ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
 
     // Evaluate at the exit value.  If we really did fall out of the valid
     // range, then we computed our trip count, otherwise wrap around or other
     // things must have happened.
     ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
     if (Range.contains(Val->getValue()))
       return SE.getCouldNotCompute();  // Something strange happened
 
     // Ensure that the previous value is in the range.  This is a sanity check.
     assert(Range.contains(
            EvaluateConstantChrecAtConstant(this,
            ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
            "Linear scev computation is off in a bad way!");
     return SE.getConstant(ExitValue);
   } else if (isQuadratic()) {
     // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
     // quadratic equation to solve it.  To do this, we must frame our problem in
     // terms of figuring out when zero is crossed, instead of when
     // Range.getUpper() is crossed.
     SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
     NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
     const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
                                              // getNoWrapFlags(FlagNW)
                                              FlagAnyWrap);
 
     // Next, solve the constructed addrec
     if (auto Roots =
             SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE)) {
       const SCEVConstant *R1 = Roots->first;
       const SCEVConstant *R2 = Roots->second;
       // Pick the smallest positive root value.
       if (ConstantInt *CB = dyn_cast<ConstantInt>(ConstantExpr::getICmp(
               ICmpInst::ICMP_ULT, R1->getValue(), R2->getValue()))) {
         if (!CB->getZExtValue())
           std::swap(R1, R2); // R1 is the minimum root now.
 
         // Make sure the root is not off by one.  The returned iteration should
         // not be in the range, but the previous one should be.  When solving
         // for "X*X < 5", for example, we should not return a root of 2.
         ConstantInt *R1Val =
             EvaluateConstantChrecAtConstant(this, R1->getValue(), SE);
         if (Range.contains(R1Val->getValue())) {
           // The next iteration must be out of the range...
           ConstantInt *NextVal =
               ConstantInt::get(SE.getContext(), R1->getAPInt() + 1);
 
           R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
           if (!Range.contains(R1Val->getValue()))
             return SE.getConstant(NextVal);
           return SE.getCouldNotCompute(); // Something strange happened
         }
 
         // If R1 was not in the range, then it is a good return value.  Make
         // sure that R1-1 WAS in the range though, just in case.
         ConstantInt *NextVal =
             ConstantInt::get(SE.getContext(), R1->getAPInt() - 1);
         R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
         if (Range.contains(R1Val->getValue()))
           return R1;
         return SE.getCouldNotCompute(); // Something strange happened
       }
     }
   }
 
   return SE.getCouldNotCompute();
 }
 
 namespace {
 struct FindUndefs {
   bool Found;
   FindUndefs() : Found(false) {}
 
   bool follow(const SCEV *S) {
     if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
       if (isa<UndefValue>(C->getValue()))
         Found = true;
     } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
       if (isa<UndefValue>(C->getValue()))
         Found = true;
     }
 
     // Keep looking if we haven't found it yet.
     return !Found;
   }
   bool isDone() const {
     // Stop recursion if we have found an undef.
     return Found;
   }
 };
 }
 
 // Return true when S contains at least an undef value.
 static inline bool
 containsUndefs(const SCEV *S) {
   FindUndefs F;
   SCEVTraversal<FindUndefs> ST(F);
   ST.visitAll(S);
 
   return F.Found;
 }
 
 namespace {
 // Collect all steps of SCEV expressions.
 struct SCEVCollectStrides {
   ScalarEvolution &SE;
   SmallVectorImpl<const SCEV *> &Strides;
 
   SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
       : SE(SE), Strides(S) {}
 
   bool follow(const SCEV *S) {
     if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
       Strides.push_back(AR->getStepRecurrence(SE));
     return true;
   }
   bool isDone() const { return false; }
 };
 
 // Collect all SCEVUnknown and SCEVMulExpr expressions.
 struct SCEVCollectTerms {
   SmallVectorImpl<const SCEV *> &Terms;
 
   SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
       : Terms(T) {}
 
   bool follow(const SCEV *S) {
     if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
       if (!containsUndefs(S))
         Terms.push_back(S);
 
       // Stop recursion: once we collected a term, do not walk its operands.
       return false;
     }
 
     // Keep looking.
     return true;
   }
   bool isDone() const { return false; }
 };
 
 // Check if a SCEV contains an AddRecExpr.
 struct SCEVHasAddRec {
   bool &ContainsAddRec;
 
   SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) {
    ContainsAddRec = false;
   }
 
   bool follow(const SCEV *S) {
     if (isa<SCEVAddRecExpr>(S)) {
       ContainsAddRec = true;
 
       // Stop recursion: once we collected a term, do not walk its operands.
       return false;
     }
 
     // Keep looking.
     return true;
   }
   bool isDone() const { return false; }
 };
 
 // Find factors that are multiplied with an expression that (possibly as a
 // subexpression) contains an AddRecExpr. In the expression:
 //
 //  8 * (100 +  %p * %q * (%a + {0, +, 1}_loop))
 //
 // "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)"
 // that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size
 // parameters as they form a product with an induction variable.
 //
 // This collector expects all array size parameters to be in the same MulExpr.
 // It might be necessary to later add support for collecting parameters that are
 // spread over different nested MulExpr.
 struct SCEVCollectAddRecMultiplies {
   SmallVectorImpl<const SCEV *> &Terms;
   ScalarEvolution &SE;
 
   SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE)
       : Terms(T), SE(SE) {}
 
   bool follow(const SCEV *S) {
     if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) {
       bool HasAddRec = false;
       SmallVector<const SCEV *, 0> Operands;
       for (auto Op : Mul->operands()) {
         if (isa<SCEVUnknown>(Op)) {
           Operands.push_back(Op);
         } else {
           bool ContainsAddRec;
           SCEVHasAddRec ContiansAddRec(ContainsAddRec);
           visitAll(Op, ContiansAddRec);
           HasAddRec |= ContainsAddRec;
         }
       }
       if (Operands.size() == 0)
         return true;
 
       if (!HasAddRec)
         return false;
 
       Terms.push_back(SE.getMulExpr(Operands));
       // Stop recursion: once we collected a term, do not walk its operands.
       return false;
     }
 
     // Keep looking.
     return true;
   }
   bool isDone() const { return false; }
 };
 }
 
 /// Find parametric terms in this SCEVAddRecExpr. We first for parameters in
 /// two places:
 ///   1) The strides of AddRec expressions.
 ///   2) Unknowns that are multiplied with AddRec expressions.
 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
     SmallVectorImpl<const SCEV *> &Terms) {
   SmallVector<const SCEV *, 4> Strides;
   SCEVCollectStrides StrideCollector(*this, Strides);
   visitAll(Expr, StrideCollector);
 
   DEBUG({
       dbgs() << "Strides:\n";
       for (const SCEV *S : Strides)
         dbgs() << *S << "\n";
     });
 
   for (const SCEV *S : Strides) {
     SCEVCollectTerms TermCollector(Terms);
     visitAll(S, TermCollector);
   }
 
   DEBUG({
       dbgs() << "Terms:\n";
       for (const SCEV *T : Terms)
         dbgs() << *T << "\n";
     });
 
   SCEVCollectAddRecMultiplies MulCollector(Terms, *this);
   visitAll(Expr, MulCollector);
 }
 
 static bool findArrayDimensionsRec(ScalarEvolution &SE,
                                    SmallVectorImpl<const SCEV *> &Terms,
                                    SmallVectorImpl<const SCEV *> &Sizes) {
   int Last = Terms.size() - 1;
   const SCEV *Step = Terms[Last];
 
   // End of recursion.
   if (Last == 0) {
     if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
       SmallVector<const SCEV *, 2> Qs;
       for (const SCEV *Op : M->operands())
         if (!isa<SCEVConstant>(Op))
           Qs.push_back(Op);
 
       Step = SE.getMulExpr(Qs);
     }
 
     Sizes.push_back(Step);
     return true;
   }
 
   for (const SCEV *&Term : Terms) {
     // Normalize the terms before the next call to findArrayDimensionsRec.
     const SCEV *Q, *R;
     SCEVDivision::divide(SE, Term, Step, &Q, &R);
 
     // Bail out when GCD does not evenly divide one of the terms.
     if (!R->isZero())
       return false;
 
     Term = Q;
   }
 
   // Remove all SCEVConstants.
   Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
                 return isa<SCEVConstant>(E);
               }),
               Terms.end());
 
   if (Terms.size() > 0)
     if (!findArrayDimensionsRec(SE, Terms, Sizes))
       return false;
 
   Sizes.push_back(Step);
   return true;
 }
 
 // Returns true when S contains at least a SCEVUnknown parameter.
 static inline bool
 containsParameters(const SCEV *S) {
   struct FindParameter {
     bool FoundParameter;
     FindParameter() : FoundParameter(false) {}
 
     bool follow(const SCEV *S) {
       if (isa<SCEVUnknown>(S)) {
         FoundParameter = true;
         // Stop recursion: we found a parameter.
         return false;
       }
       // Keep looking.
       return true;
     }
     bool isDone() const {
       // Stop recursion if we have found a parameter.
       return FoundParameter;
     }
   };
 
   FindParameter F;
   SCEVTraversal<FindParameter> ST(F);
   ST.visitAll(S);
 
   return F.FoundParameter;
 }
 
 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
 static inline bool
 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
   for (const SCEV *T : Terms)
     if (containsParameters(T))
       return true;
   return false;
 }
 
 // Return the number of product terms in S.
 static inline int numberOfTerms(const SCEV *S) {
   if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
     return Expr->getNumOperands();
   return 1;
 }
 
 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
   if (isa<SCEVConstant>(T))
     return nullptr;
 
   if (isa<SCEVUnknown>(T))
     return T;
 
   if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
     SmallVector<const SCEV *, 2> Factors;
     for (const SCEV *Op : M->operands())
       if (!isa<SCEVConstant>(Op))
         Factors.push_back(Op);
 
     return SE.getMulExpr(Factors);
   }
 
   return T;
 }
 
 /// Return the size of an element read or written by Inst.
 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
   Type *Ty;
   if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
     Ty = Store->getValueOperand()->getType();
   else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
     Ty = Load->getType();
   else
     return nullptr;
 
   Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
   return getSizeOfExpr(ETy, Ty);
 }
 
 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
                                           SmallVectorImpl<const SCEV *> &Sizes,
                                           const SCEV *ElementSize) const {
   if (Terms.size() < 1 || !ElementSize)
     return;
 
   // Early return when Terms do not contain parameters: we do not delinearize
   // non parametric SCEVs.
   if (!containsParameters(Terms))
     return;
 
   DEBUG({
       dbgs() << "Terms:\n";
       for (const SCEV *T : Terms)
         dbgs() << *T << "\n";
     });
 
   // Remove duplicates.
   std::sort(Terms.begin(), Terms.end());
   Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
 
   // Put larger terms first.
   std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
     return numberOfTerms(LHS) > numberOfTerms(RHS);
   });
 
   ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
 
   // Try to divide all terms by the element size. If term is not divisible by
   // element size, proceed with the original term.
   for (const SCEV *&Term : Terms) {
     const SCEV *Q, *R;
     SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
     if (!Q->isZero())
       Term = Q;
   }
 
   SmallVector<const SCEV *, 4> NewTerms;
 
   // Remove constant factors.
   for (const SCEV *T : Terms)
     if (const SCEV *NewT = removeConstantFactors(SE, T))
       NewTerms.push_back(NewT);
 
   DEBUG({
       dbgs() << "Terms after sorting:\n";
       for (const SCEV *T : NewTerms)
         dbgs() << *T << "\n";
     });
 
   if (NewTerms.empty() ||
       !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
     Sizes.clear();
     return;
   }
 
   // The last element to be pushed into Sizes is the size of an element.
   Sizes.push_back(ElementSize);
 
   DEBUG({
       dbgs() << "Sizes:\n";
       for (const SCEV *S : Sizes)
         dbgs() << *S << "\n";
     });
 }
 
 void ScalarEvolution::computeAccessFunctions(
     const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
     SmallVectorImpl<const SCEV *> &Sizes) {
 
   // Early exit in case this SCEV is not an affine multivariate function.
   if (Sizes.empty())
     return;
 
   if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr))
     if (!AR->isAffine())
       return;
 
   const SCEV *Res = Expr;
   int Last = Sizes.size() - 1;
   for (int i = Last; i >= 0; i--) {
     const SCEV *Q, *R;
     SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
 
     DEBUG({
         dbgs() << "Res: " << *Res << "\n";
         dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
         dbgs() << "Res divided by Sizes[i]:\n";
         dbgs() << "Quotient: " << *Q << "\n";
         dbgs() << "Remainder: " << *R << "\n";
       });
 
     Res = Q;
 
     // Do not record the last subscript corresponding to the size of elements in
     // the array.
     if (i == Last) {
 
       // Bail out if the remainder is too complex.
       if (isa<SCEVAddRecExpr>(R)) {
         Subscripts.clear();
         Sizes.clear();
         return;
       }
 
       continue;
     }
 
     // Record the access function for the current subscript.
     Subscripts.push_back(R);
   }
 
   // Also push in last position the remainder of the last division: it will be
   // the access function of the innermost dimension.
   Subscripts.push_back(Res);
 
   std::reverse(Subscripts.begin(), Subscripts.end());
 
   DEBUG({
       dbgs() << "Subscripts:\n";
       for (const SCEV *S : Subscripts)
         dbgs() << *S << "\n";
     });
 }
 
 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
 /// sizes of an array access. Returns the remainder of the delinearization that
 /// is the offset start of the array.  The SCEV->delinearize algorithm computes
 /// the multiples of SCEV coefficients: that is a pattern matching of sub
 /// expressions in the stride and base of a SCEV corresponding to the
 /// computation of a GCD (greatest common divisor) of base and stride.  When
 /// SCEV->delinearize fails, it returns the SCEV unchanged.
 ///
 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
 ///
 ///  void foo(long n, long m, long o, double A[n][m][o]) {
 ///
 ///    for (long i = 0; i < n; i++)
 ///      for (long j = 0; j < m; j++)
 ///        for (long k = 0; k < o; k++)
 ///          A[i][j][k] = 1.0;
 ///  }
 ///
 /// the delinearization input is the following AddRec SCEV:
 ///
 ///  AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
 ///
 /// From this SCEV, we are able to say that the base offset of the access is %A
 /// because it appears as an offset that does not divide any of the strides in
 /// the loops:
 ///
 ///  CHECK: Base offset: %A
 ///
 /// and then SCEV->delinearize determines the size of some of the dimensions of
 /// the array as these are the multiples by which the strides are happening:
 ///
 ///  CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
 ///
 /// Note that the outermost dimension remains of UnknownSize because there are
 /// no strides that would help identifying the size of the last dimension: when
 /// the array has been statically allocated, one could compute the size of that
 /// dimension by dividing the overall size of the array by the size of the known
 /// dimensions: %m * %o * 8.
 ///
 /// Finally delinearize provides the access functions for the array reference
 /// that does correspond to A[i][j][k] of the above C testcase:
 ///
 ///  CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
 ///
 /// The testcases are checking the output of a function pass:
 /// DelinearizationPass that walks through all loads and stores of a function
 /// asking for the SCEV of the memory access with respect to all enclosing
 /// loops, calling SCEV->delinearize on that and printing the results.
 
 void ScalarEvolution::delinearize(const SCEV *Expr,
                                  SmallVectorImpl<const SCEV *> &Subscripts,
                                  SmallVectorImpl<const SCEV *> &Sizes,
                                  const SCEV *ElementSize) {
   // First step: collect parametric terms.
   SmallVector<const SCEV *, 4> Terms;
   collectParametricTerms(Expr, Terms);
 
   if (Terms.empty())
     return;
 
   // Second step: find subscript sizes.
   findArrayDimensions(Terms, Sizes, ElementSize);
 
   if (Sizes.empty())
     return;
 
   // Third step: compute the access functions for each subscript.
   computeAccessFunctions(Expr, Subscripts, Sizes);
 
   if (Subscripts.empty())
     return;
 
   DEBUG({
       dbgs() << "succeeded to delinearize " << *Expr << "\n";
       dbgs() << "ArrayDecl[UnknownSize]";
       for (const SCEV *S : Sizes)
         dbgs() << "[" << *S << "]";
 
       dbgs() << "\nArrayRef";
       for (const SCEV *S : Subscripts)
         dbgs() << "[" << *S << "]";
       dbgs() << "\n";
     });
 }
 
 //===----------------------------------------------------------------------===//
 //                   SCEVCallbackVH Class Implementation
 //===----------------------------------------------------------------------===//
 
 void ScalarEvolution::SCEVCallbackVH::deleted() {
   assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
   if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
     SE->ConstantEvolutionLoopExitValue.erase(PN);
   SE->eraseValueFromMap(getValPtr());
   // this now dangles!
 }
 
 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
   assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
 
   // Forget all the expressions associated with users of the old value,
   // so that future queries will recompute the expressions using the new
   // value.
   Value *Old = getValPtr();
   SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
   SmallPtrSet<User *, 8> Visited;
   while (!Worklist.empty()) {
     User *U = Worklist.pop_back_val();
     // Deleting the Old value will cause this to dangle. Postpone
     // that until everything else is done.
     if (U == Old)
       continue;
     if (!Visited.insert(U).second)
       continue;
     if (PHINode *PN = dyn_cast<PHINode>(U))
       SE->ConstantEvolutionLoopExitValue.erase(PN);
     SE->eraseValueFromMap(U);
     Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
   }
   // Delete the Old value.
   if (PHINode *PN = dyn_cast<PHINode>(Old))
     SE->ConstantEvolutionLoopExitValue.erase(PN);
   SE->eraseValueFromMap(Old);
   // this now dangles!
 }
 
 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
   : CallbackVH(V), SE(se) {}
 
 //===----------------------------------------------------------------------===//
 //                   ScalarEvolution Class Implementation
 //===----------------------------------------------------------------------===//
 
 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
                                  AssumptionCache &AC, DominatorTree &DT,
                                  LoopInfo &LI)
     : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
       CouldNotCompute(new SCEVCouldNotCompute()),
       WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
       ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64),
       FirstUnknown(nullptr) {
 
   // To use guards for proving predicates, we need to scan every instruction in
   // relevant basic blocks, and not just terminators.  Doing this is a waste of
   // time if the IR does not actually contain any calls to
   // @llvm.experimental.guard, so do a quick check and remember this beforehand.
   //
   // This pessimizes the case where a pass that preserves ScalarEvolution wants
   // to _add_ guards to the module when there weren't any before, and wants
   // ScalarEvolution to optimize based on those guards.  For now we prefer to be
   // efficient in lieu of being smart in that rather obscure case.
 
   auto *GuardDecl = F.getParent()->getFunction(
       Intrinsic::getName(Intrinsic::experimental_guard));
   HasGuards = GuardDecl && !GuardDecl->use_empty();
 }
 
 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
     : F(Arg.F), HasGuards(Arg.HasGuards), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT),
       LI(Arg.LI), CouldNotCompute(std::move(Arg.CouldNotCompute)),
       ValueExprMap(std::move(Arg.ValueExprMap)),
       WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
       BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
       PredicatedBackedgeTakenCounts(
           std::move(Arg.PredicatedBackedgeTakenCounts)),
       ConstantEvolutionLoopExitValue(
           std::move(Arg.ConstantEvolutionLoopExitValue)),
       ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
       LoopDispositions(std::move(Arg.LoopDispositions)),
       BlockDispositions(std::move(Arg.BlockDispositions)),
       UnsignedRanges(std::move(Arg.UnsignedRanges)),
       SignedRanges(std::move(Arg.SignedRanges)),
       UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
       UniquePreds(std::move(Arg.UniquePreds)),
       SCEVAllocator(std::move(Arg.SCEVAllocator)),
       FirstUnknown(Arg.FirstUnknown) {
   Arg.FirstUnknown = nullptr;
 }
 
 ScalarEvolution::~ScalarEvolution() {
   // Iterate through all the SCEVUnknown instances and call their
   // destructors, so that they release their references to their values.
   for (SCEVUnknown *U = FirstUnknown; U;) {
     SCEVUnknown *Tmp = U;
     U = U->Next;
     Tmp->~SCEVUnknown();
   }
   FirstUnknown = nullptr;
 
   ExprValueMap.clear();
   ValueExprMap.clear();
   HasRecMap.clear();
 
   // Free any extra memory created for ExitNotTakenInfo in the unlikely event
   // that a loop had multiple computable exits.
   for (auto &BTCI : BackedgeTakenCounts)
     BTCI.second.clear();
   for (auto &BTCI : PredicatedBackedgeTakenCounts)
     BTCI.second.clear();
 
   assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
   assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
   assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
 }
 
 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
   return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
 }
 
 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
                           const Loop *L) {
   // Print all inner loops first
   for (Loop *I : *L)
     PrintLoopInfo(OS, SE, I);
 
   OS << "Loop ";
   L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
   OS << ": ";
 
   SmallVector<BasicBlock *, 8> ExitBlocks;
   L->getExitBlocks(ExitBlocks);
   if (ExitBlocks.size() != 1)
     OS << "<multiple exits> ";
 
   if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
     OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
   } else {
     OS << "Unpredictable backedge-taken count. ";
   }
 
   OS << "\n"
         "Loop ";
   L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
   OS << ": ";
 
   if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
     OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
   } else {
     OS << "Unpredictable max backedge-taken count. ";
   }
 
   OS << "\n"
         "Loop ";
   L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
   OS << ": ";
 
   SCEVUnionPredicate Pred;
   auto PBT = SE->getPredicatedBackedgeTakenCount(L, Pred);
   if (!isa<SCEVCouldNotCompute>(PBT)) {
     OS << "Predicated backedge-taken count is " << *PBT << "\n";
     OS << " Predicates:\n";
     Pred.print(OS, 4);
   } else {
     OS << "Unpredictable predicated backedge-taken count. ";
   }
   OS << "\n";
 }
 
 static StringRef loopDispositionToStr(ScalarEvolution::LoopDisposition LD) {
   switch (LD) {
   case ScalarEvolution::LoopVariant:
     return "Variant";
   case ScalarEvolution::LoopInvariant:
     return "Invariant";
   case ScalarEvolution::LoopComputable:
     return "Computable";
   }
   llvm_unreachable("Unknown ScalarEvolution::LoopDisposition kind!");
 }
 
 void ScalarEvolution::print(raw_ostream &OS) const {
   // ScalarEvolution's implementation of the print method is to print
   // out SCEV values of all instructions that are interesting. Doing
   // this potentially causes it to create new SCEV objects though,
   // which technically conflicts with the const qualifier. This isn't
   // observable from outside the class though, so casting away the
   // const isn't dangerous.
   ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
 
   OS << "Classifying expressions for: ";
   F.printAsOperand(OS, /*PrintType=*/false);
   OS << "\n";
   for (Instruction &I : instructions(F))
     if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) {
       OS << I << '\n';
       OS << "  -->  ";
       const SCEV *SV = SE.getSCEV(&I);
       SV->print(OS);
       if (!isa<SCEVCouldNotCompute>(SV)) {
         OS << " U: ";
         SE.getUnsignedRange(SV).print(OS);
         OS << " S: ";
         SE.getSignedRange(SV).print(OS);
       }
 
       const Loop *L = LI.getLoopFor(I.getParent());
 
       const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
       if (AtUse != SV) {
         OS << "  -->  ";
         AtUse->print(OS);
         if (!isa<SCEVCouldNotCompute>(AtUse)) {
           OS << " U: ";
           SE.getUnsignedRange(AtUse).print(OS);
           OS << " S: ";
           SE.getSignedRange(AtUse).print(OS);
         }
       }
 
       if (L) {
         OS << "\t\t" "Exits: ";
         const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
         if (!SE.isLoopInvariant(ExitValue, L)) {
           OS << "<<Unknown>>";
         } else {
           OS << *ExitValue;
         }
 
         bool First = true;
         for (auto *Iter = L; Iter; Iter = Iter->getParentLoop()) {
           if (First) {
             OS << "\t\t" "LoopDispositions: { ";
             First = false;
           } else {
             OS << ", ";
           }
 
           Iter->getHeader()->printAsOperand(OS, /*PrintType=*/false);
           OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, Iter));
         }
 
         for (auto *InnerL : depth_first(L)) {
           if (InnerL == L)
             continue;
           if (First) {
             OS << "\t\t" "LoopDispositions: { ";
             First = false;
           } else {
             OS << ", ";
           }
 
           InnerL->getHeader()->printAsOperand(OS, /*PrintType=*/false);
           OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, InnerL));
         }
 
         OS << " }";
       }
 
       OS << "\n";
     }
 
   OS << "Determining loop execution counts for: ";
   F.printAsOperand(OS, /*PrintType=*/false);
   OS << "\n";
   for (Loop *I : LI)
     PrintLoopInfo(OS, &SE, I);
 }
 
 ScalarEvolution::LoopDisposition
 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
   auto &Values = LoopDispositions[S];
   for (auto &V : Values) {
     if (V.getPointer() == L)
       return V.getInt();
   }
   Values.emplace_back(L, LoopVariant);
   LoopDisposition D = computeLoopDisposition(S, L);
   auto &Values2 = LoopDispositions[S];
   for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
     if (V.getPointer() == L) {
       V.setInt(D);
       break;
     }
   }
   return D;
 }
 
 ScalarEvolution::LoopDisposition
 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
   switch (static_cast<SCEVTypes>(S->getSCEVType())) {
   case scConstant:
     return LoopInvariant;
   case scTruncate:
   case scZeroExtend:
   case scSignExtend:
     return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
   case scAddRecExpr: {
     const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
 
     // If L is the addrec's loop, it's computable.
     if (AR->getLoop() == L)
       return LoopComputable;
 
     // Add recurrences are never invariant in the function-body (null loop).
     if (!L)
       return LoopVariant;
 
     // This recurrence is variant w.r.t. L if L contains AR's loop.
     if (L->contains(AR->getLoop()))
       return LoopVariant;
 
     // This recurrence is invariant w.r.t. L if AR's loop contains L.
     if (AR->getLoop()->contains(L))
       return LoopInvariant;
 
     // This recurrence is variant w.r.t. L if any of its operands
     // are variant.
     for (auto *Op : AR->operands())
       if (!isLoopInvariant(Op, L))
         return LoopVariant;
 
     // Otherwise it's loop-invariant.
     return LoopInvariant;
   }
   case scAddExpr:
   case scMulExpr:
   case scUMaxExpr:
   case scSMaxExpr: {
     bool HasVarying = false;
     for (auto *Op : cast<SCEVNAryExpr>(S)->operands()) {
       LoopDisposition D = getLoopDisposition(Op, L);
       if (D == LoopVariant)
         return LoopVariant;
       if (D == LoopComputable)
         HasVarying = true;
     }
     return HasVarying ? LoopComputable : LoopInvariant;
   }
   case scUDivExpr: {
     const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
     LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
     if (LD == LoopVariant)
       return LoopVariant;
     LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
     if (RD == LoopVariant)
       return LoopVariant;
     return (LD == LoopInvariant && RD == LoopInvariant) ?
            LoopInvariant : LoopComputable;
   }
   case scUnknown:
     // All non-instruction values are loop invariant.  All instructions are loop
     // invariant if they are not contained in the specified loop.
     // Instructions are never considered invariant in the function body
     // (null loop) because they are defined within the "loop".
     if (auto *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
       return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
     return LoopInvariant;
   case scCouldNotCompute:
     llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
   }
   llvm_unreachable("Unknown SCEV kind!");
 }
 
 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
   return getLoopDisposition(S, L) == LoopInvariant;
 }
 
 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
   return getLoopDisposition(S, L) == LoopComputable;
 }
 
 ScalarEvolution::BlockDisposition
 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
   auto &Values = BlockDispositions[S];
   for (auto &V : Values) {
     if (V.getPointer() == BB)
       return V.getInt();
   }
   Values.emplace_back(BB, DoesNotDominateBlock);
   BlockDisposition D = computeBlockDisposition(S, BB);
   auto &Values2 = BlockDispositions[S];
   for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
     if (V.getPointer() == BB) {
       V.setInt(D);
       break;
     }
   }
   return D;
 }
 
 ScalarEvolution::BlockDisposition
 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
   switch (static_cast<SCEVTypes>(S->getSCEVType())) {
   case scConstant:
     return ProperlyDominatesBlock;
   case scTruncate:
   case scZeroExtend:
   case scSignExtend:
     return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
   case scAddRecExpr: {
     // This uses a "dominates" query instead of "properly dominates" query
     // to test for proper dominance too, because the instruction which
     // produces the addrec's value is a PHI, and a PHI effectively properly
     // dominates its entire containing block.
     const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
     if (!DT.dominates(AR->getLoop()->getHeader(), BB))
       return DoesNotDominateBlock;
   }
   // FALL THROUGH into SCEVNAryExpr handling.
   case scAddExpr:
   case scMulExpr:
   case scUMaxExpr:
   case scSMaxExpr: {
     const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
     bool Proper = true;
     for (const SCEV *NAryOp : NAry->operands()) {
       BlockDisposition D = getBlockDisposition(NAryOp, BB);
       if (D == DoesNotDominateBlock)
         return DoesNotDominateBlock;
       if (D == DominatesBlock)
         Proper = false;
     }
     return Proper ? ProperlyDominatesBlock : DominatesBlock;
   }
   case scUDivExpr: {
     const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
     const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
     BlockDisposition LD = getBlockDisposition(LHS, BB);
     if (LD == DoesNotDominateBlock)
       return DoesNotDominateBlock;
     BlockDisposition RD = getBlockDisposition(RHS, BB);
     if (RD == DoesNotDominateBlock)
       return DoesNotDominateBlock;
     return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
       ProperlyDominatesBlock : DominatesBlock;
   }
   case scUnknown:
     if (Instruction *I =
           dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
       if (I->getParent() == BB)
         return DominatesBlock;
       if (DT.properlyDominates(I->getParent(), BB))
         return ProperlyDominatesBlock;
       return DoesNotDominateBlock;
     }
     return ProperlyDominatesBlock;
   case scCouldNotCompute:
     llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
   }
   llvm_unreachable("Unknown SCEV kind!");
 }
 
 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
   return getBlockDisposition(S, BB) >= DominatesBlock;
 }
 
 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
   return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
 }
 
 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
   // Search for a SCEV expression node within an expression tree.
   // Implements SCEVTraversal::Visitor.
   struct SCEVSearch {
     const SCEV *Node;
     bool IsFound;
 
     SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
 
     bool follow(const SCEV *S) {
       IsFound |= (S == Node);
       return !IsFound;
     }
     bool isDone() const { return IsFound; }
   };
 
   SCEVSearch Search(Op);
   visitAll(S, Search);
   return Search.IsFound;
 }
 
 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
   ValuesAtScopes.erase(S);
   LoopDispositions.erase(S);
   BlockDispositions.erase(S);
   UnsignedRanges.erase(S);
   SignedRanges.erase(S);
   ExprValueMap.erase(S);
   HasRecMap.erase(S);
 
   auto RemoveSCEVFromBackedgeMap =
       [S, this](DenseMap<const Loop *, BackedgeTakenInfo> &Map) {
         for (auto I = Map.begin(), E = Map.end(); I != E;) {
           BackedgeTakenInfo &BEInfo = I->second;
           if (BEInfo.hasOperand(S, this)) {
             BEInfo.clear();
             Map.erase(I++);
           } else
             ++I;
         }
       };
 
   RemoveSCEVFromBackedgeMap(BackedgeTakenCounts);
   RemoveSCEVFromBackedgeMap(PredicatedBackedgeTakenCounts);
 }
 
 typedef DenseMap<const Loop *, std::string> VerifyMap;
 
 /// replaceSubString - Replaces all occurrences of From in Str with To.
 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
   size_t Pos = 0;
   while ((Pos = Str.find(From, Pos)) != std::string::npos) {
     Str.replace(Pos, From.size(), To.data(), To.size());
     Pos += To.size();
   }
 }
 
 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
 static void
 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
   std::string &S = Map[L];
   if (S.empty()) {
     raw_string_ostream OS(S);
     SE.getBackedgeTakenCount(L)->print(OS);
 
     // false and 0 are semantically equivalent. This can happen in dead loops.
     replaceSubString(OS.str(), "false", "0");
     // Remove wrap flags, their use in SCEV is highly fragile.
     // FIXME: Remove this when SCEV gets smarter about them.
     replaceSubString(OS.str(), "<nw>", "");
     replaceSubString(OS.str(), "<nsw>", "");
     replaceSubString(OS.str(), "<nuw>", "");
   }
 
   for (auto *R : reverse(*L))
     getLoopBackedgeTakenCounts(R, Map, SE); // recurse.
 }
 
 void ScalarEvolution::verify() const {
   ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
 
   // Gather stringified backedge taken counts for all loops using SCEV's caches.
   // FIXME: It would be much better to store actual values instead of strings,
   //        but SCEV pointers will change if we drop the caches.
   VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
   for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
     getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
 
   // Gather stringified backedge taken counts for all loops using a fresh
   // ScalarEvolution object.
   ScalarEvolution SE2(F, TLI, AC, DT, LI);
   for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
     getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE2);
 
   // Now compare whether they're the same with and without caches. This allows
   // verifying that no pass changed the cache.
   assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
          "New loops suddenly appeared!");
 
   for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
                            OldE = BackedgeDumpsOld.end(),
                            NewI = BackedgeDumpsNew.begin();
        OldI != OldE; ++OldI, ++NewI) {
     assert(OldI->first == NewI->first && "Loop order changed!");
 
     // Compare the stringified SCEVs. We don't care if undef backedgetaken count
     // changes.
     // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
     // means that a pass is buggy or SCEV has to learn a new pattern but is
     // usually not harmful.
     if (OldI->second != NewI->second &&
         OldI->second.find("undef") == std::string::npos &&
         NewI->second.find("undef") == std::string::npos &&
         OldI->second != "***COULDNOTCOMPUTE***" &&
         NewI->second != "***COULDNOTCOMPUTE***") {
       dbgs() << "SCEVValidator: SCEV for loop '"
              << OldI->first->getHeader()->getName()
              << "' changed from '" << OldI->second
              << "' to '" << NewI->second << "'!\n";
       std::abort();
     }
   }
 
   // TODO: Verify more things.
 }
 
 char ScalarEvolutionAnalysis::PassID;
 
 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
                                              AnalysisManager<Function> &AM) {
   return ScalarEvolution(F, AM.getResult<TargetLibraryAnalysis>(F),
                          AM.getResult<AssumptionAnalysis>(F),
                          AM.getResult<DominatorTreeAnalysis>(F),
                          AM.getResult<LoopAnalysis>(F));
 }
 
 PreservedAnalyses
 ScalarEvolutionPrinterPass::run(Function &F, AnalysisManager<Function> &AM) {
   AM.getResult<ScalarEvolutionAnalysis>(F).print(OS);
   return PreservedAnalyses::all();
 }
 
 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
                       "Scalar Evolution Analysis", false, true)
 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
                     "Scalar Evolution Analysis", false, true)
 char ScalarEvolutionWrapperPass::ID = 0;
 
 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
   initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
 }
 
 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
   SE.reset(new ScalarEvolution(
       F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(),
       getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
       getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
       getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
   return false;
 }
 
 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
 
 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
   SE->print(OS);
 }
 
 void ScalarEvolutionWrapperPass::verifyAnalysis() const {
   if (!VerifySCEV)
     return;
 
   SE->verify();
 }
 
 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
   AU.setPreservesAll();
   AU.addRequiredTransitive<AssumptionCacheTracker>();
   AU.addRequiredTransitive<LoopInfoWrapperPass>();
   AU.addRequiredTransitive<DominatorTreeWrapperPass>();
   AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
 }
 
 const SCEVPredicate *
 ScalarEvolution::getEqualPredicate(const SCEVUnknown *LHS,
                                    const SCEVConstant *RHS) {
   FoldingSetNodeID ID;
   // Unique this node based on the arguments
   ID.AddInteger(SCEVPredicate::P_Equal);
   ID.AddPointer(LHS);
   ID.AddPointer(RHS);
   void *IP = nullptr;
   if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
     return S;
   SCEVEqualPredicate *Eq = new (SCEVAllocator)
       SCEVEqualPredicate(ID.Intern(SCEVAllocator), LHS, RHS);
   UniquePreds.InsertNode(Eq, IP);
   return Eq;
 }
 
 const SCEVPredicate *ScalarEvolution::getWrapPredicate(
     const SCEVAddRecExpr *AR,
     SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
   FoldingSetNodeID ID;
   // Unique this node based on the arguments
   ID.AddInteger(SCEVPredicate::P_Wrap);
   ID.AddPointer(AR);
   ID.AddInteger(AddedFlags);
   void *IP = nullptr;
   if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
     return S;
   auto *OF = new (SCEVAllocator)
       SCEVWrapPredicate(ID.Intern(SCEVAllocator), AR, AddedFlags);
   UniquePreds.InsertNode(OF, IP);
   return OF;
 }
 
 namespace {
 
 class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> {
 public:
   // Rewrites \p S in the context of a loop L and the predicate A.
   // If Assume is true, rewrite is free to add further predicates to A
   // such that the result will be an AddRecExpr.
   static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
                              SCEVUnionPredicate &A, bool Assume) {
     SCEVPredicateRewriter Rewriter(L, SE, A, Assume);
     return Rewriter.visit(S);
   }
 
   SCEVPredicateRewriter(const Loop *L, ScalarEvolution &SE,
                         SCEVUnionPredicate &P, bool Assume)
       : SCEVRewriteVisitor(SE), P(P), L(L), Assume(Assume) {}
 
   const SCEV *visitUnknown(const SCEVUnknown *Expr) {
     auto ExprPreds = P.getPredicatesForExpr(Expr);
     for (auto *Pred : ExprPreds)
       if (const auto *IPred = dyn_cast<SCEVEqualPredicate>(Pred))
         if (IPred->getLHS() == Expr)
           return IPred->getRHS();
 
     return Expr;
   }
 
   const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
     const SCEV *Operand = visit(Expr->getOperand());
     const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
     if (AR && AR->getLoop() == L && AR->isAffine()) {
       // This couldn't be folded because the operand didn't have the nuw
       // flag. Add the nusw flag as an assumption that we could make.
       const SCEV *Step = AR->getStepRecurrence(SE);
       Type *Ty = Expr->getType();
       if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNUSW))
         return SE.getAddRecExpr(SE.getZeroExtendExpr(AR->getStart(), Ty),
                                 SE.getSignExtendExpr(Step, Ty), L,
                                 AR->getNoWrapFlags());
     }
     return SE.getZeroExtendExpr(Operand, Expr->getType());
   }
 
   const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
     const SCEV *Operand = visit(Expr->getOperand());
     const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
     if (AR && AR->getLoop() == L && AR->isAffine()) {
       // This couldn't be folded because the operand didn't have the nsw
       // flag. Add the nssw flag as an assumption that we could make.
       const SCEV *Step = AR->getStepRecurrence(SE);
       Type *Ty = Expr->getType();
       if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNSSW))
         return SE.getAddRecExpr(SE.getSignExtendExpr(AR->getStart(), Ty),
                                 SE.getSignExtendExpr(Step, Ty), L,
                                 AR->getNoWrapFlags());
     }
     return SE.getSignExtendExpr(Operand, Expr->getType());
   }
 
 private:
   bool addOverflowAssumption(const SCEVAddRecExpr *AR,
                              SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
     auto *A = SE.getWrapPredicate(AR, AddedFlags);
     if (!Assume) {
       // Check if we've already made this assumption.
       if (P.implies(A))
         return true;
       return false;
     }
     P.add(A);
     return true;
   }
 
   SCEVUnionPredicate &P;
   const Loop *L;
   bool Assume;
 };
 } // end anonymous namespace
 
 const SCEV *ScalarEvolution::rewriteUsingPredicate(const SCEV *S, const Loop *L,
                                                    SCEVUnionPredicate &Preds) {
   return SCEVPredicateRewriter::rewrite(S, L, *this, Preds, false);
 }
 
 const SCEVAddRecExpr *
 ScalarEvolution::convertSCEVToAddRecWithPredicates(const SCEV *S, const Loop *L,
                                                    SCEVUnionPredicate &Preds) {
   SCEVUnionPredicate TransformPreds;
   S = SCEVPredicateRewriter::rewrite(S, L, *this, TransformPreds, true);
   auto *AddRec = dyn_cast<SCEVAddRecExpr>(S);
 
   if (!AddRec)
     return nullptr;
 
   // Since the transformation was successful, we can now transfer the SCEV
   // predicates.
   Preds.add(&TransformPreds);
   return AddRec;
 }
 
 /// SCEV predicates
 SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID,
                              SCEVPredicateKind Kind)
     : FastID(ID), Kind(Kind) {}
 
 SCEVEqualPredicate::SCEVEqualPredicate(const FoldingSetNodeIDRef ID,
                                        const SCEVUnknown *LHS,
                                        const SCEVConstant *RHS)
     : SCEVPredicate(ID, P_Equal), LHS(LHS), RHS(RHS) {}
 
 bool SCEVEqualPredicate::implies(const SCEVPredicate *N) const {
   const auto *Op = dyn_cast<SCEVEqualPredicate>(N);
 
   if (!Op)
     return false;
 
   return Op->LHS == LHS && Op->RHS == RHS;
 }
 
 bool SCEVEqualPredicate::isAlwaysTrue() const { return false; }
 
 const SCEV *SCEVEqualPredicate::getExpr() const { return LHS; }
 
 void SCEVEqualPredicate::print(raw_ostream &OS, unsigned Depth) const {
   OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n";
 }
 
 SCEVWrapPredicate::SCEVWrapPredicate(const FoldingSetNodeIDRef ID,
                                      const SCEVAddRecExpr *AR,
                                      IncrementWrapFlags Flags)
     : SCEVPredicate(ID, P_Wrap), AR(AR), Flags(Flags) {}
 
 const SCEV *SCEVWrapPredicate::getExpr() const { return AR; }
 
 bool SCEVWrapPredicate::implies(const SCEVPredicate *N) const {
   const auto *Op = dyn_cast<SCEVWrapPredicate>(N);
 
   return Op && Op->AR == AR && setFlags(Flags, Op->Flags) == Flags;
 }
 
 bool SCEVWrapPredicate::isAlwaysTrue() const {
   SCEV::NoWrapFlags ScevFlags = AR->getNoWrapFlags();
   IncrementWrapFlags IFlags = Flags;
 
   if (ScalarEvolution::setFlags(ScevFlags, SCEV::FlagNSW) == ScevFlags)
     IFlags = clearFlags(IFlags, IncrementNSSW);
 
   return IFlags == IncrementAnyWrap;
 }
 
 void SCEVWrapPredicate::print(raw_ostream &OS, unsigned Depth) const {
   OS.indent(Depth) << *getExpr() << " Added Flags: ";
   if (SCEVWrapPredicate::IncrementNUSW & getFlags())
     OS << "<nusw>";
   if (SCEVWrapPredicate::IncrementNSSW & getFlags())
     OS << "<nssw>";
   OS << "\n";
 }
 
 SCEVWrapPredicate::IncrementWrapFlags
 SCEVWrapPredicate::getImpliedFlags(const SCEVAddRecExpr *AR,
                                    ScalarEvolution &SE) {
   IncrementWrapFlags ImpliedFlags = IncrementAnyWrap;
   SCEV::NoWrapFlags StaticFlags = AR->getNoWrapFlags();
 
   // We can safely transfer the NSW flag as NSSW.
   if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNSW) == StaticFlags)
     ImpliedFlags = IncrementNSSW;
 
   if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNUW) == StaticFlags) {
     // If the increment is positive, the SCEV NUW flag will also imply the
     // WrapPredicate NUSW flag.
     if (const auto *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(SE)))
       if (Step->getValue()->getValue().isNonNegative())
         ImpliedFlags = setFlags(ImpliedFlags, IncrementNUSW);
   }
 
   return ImpliedFlags;
 }
 
 /// Union predicates don't get cached so create a dummy set ID for it.
 SCEVUnionPredicate::SCEVUnionPredicate()
     : SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {}
 
 bool SCEVUnionPredicate::isAlwaysTrue() const {
   return all_of(Preds,
                 [](const SCEVPredicate *I) { return I->isAlwaysTrue(); });
 }
 
 ArrayRef<const SCEVPredicate *>
 SCEVUnionPredicate::getPredicatesForExpr(const SCEV *Expr) {
   auto I = SCEVToPreds.find(Expr);
   if (I == SCEVToPreds.end())
     return ArrayRef<const SCEVPredicate *>();
   return I->second;
 }
 
 bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const {
   if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N))
     return all_of(Set->Preds,
                   [this](const SCEVPredicate *I) { return this->implies(I); });
 
   auto ScevPredsIt = SCEVToPreds.find(N->getExpr());
   if (ScevPredsIt == SCEVToPreds.end())
     return false;
   auto &SCEVPreds = ScevPredsIt->second;
 
   return any_of(SCEVPreds,
                 [N](const SCEVPredicate *I) { return I->implies(N); });
 }
 
 const SCEV *SCEVUnionPredicate::getExpr() const { return nullptr; }
 
 void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const {
   for (auto Pred : Preds)
     Pred->print(OS, Depth);
 }
 
 void SCEVUnionPredicate::add(const SCEVPredicate *N) {
   if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N)) {
     for (auto Pred : Set->Preds)
       add(Pred);
     return;
   }
 
   if (implies(N))
     return;
 
   const SCEV *Key = N->getExpr();
   assert(Key && "Only SCEVUnionPredicate doesn't have an "
                 " associated expression!");
 
   SCEVToPreds[Key].push_back(N);
   Preds.push_back(N);
 }
 
 PredicatedScalarEvolution::PredicatedScalarEvolution(ScalarEvolution &SE,
                                                      Loop &L)
     : SE(SE), L(L), Generation(0), BackedgeCount(nullptr) {}
 
 const SCEV *PredicatedScalarEvolution::getSCEV(Value *V) {
   const SCEV *Expr = SE.getSCEV(V);
   RewriteEntry &Entry = RewriteMap[Expr];
 
   // If we already have an entry and the version matches, return it.
   if (Entry.second && Generation == Entry.first)
     return Entry.second;
 
   // We found an entry but it's stale. Rewrite the stale entry
   // acording to the current predicate.
   if (Entry.second)
     Expr = Entry.second;
 
   const SCEV *NewSCEV = SE.rewriteUsingPredicate(Expr, &L, Preds);
   Entry = {Generation, NewSCEV};
 
   return NewSCEV;
 }
 
 const SCEV *PredicatedScalarEvolution::getBackedgeTakenCount() {
   if (!BackedgeCount) {
     SCEVUnionPredicate BackedgePred;
     BackedgeCount = SE.getPredicatedBackedgeTakenCount(&L, BackedgePred);
     addPredicate(BackedgePred);
   }
   return BackedgeCount;
 }
 
 void PredicatedScalarEvolution::addPredicate(const SCEVPredicate &Pred) {
   if (Preds.implies(&Pred))
     return;
   Preds.add(&Pred);
   updateGeneration();
 }
 
 const SCEVUnionPredicate &PredicatedScalarEvolution::getUnionPredicate() const {
   return Preds;
 }
 
 void PredicatedScalarEvolution::updateGeneration() {
   // If the generation number wrapped recompute everything.
   if (++Generation == 0) {
     for (auto &II : RewriteMap) {
       const SCEV *Rewritten = II.second.second;
       II.second = {Generation, SE.rewriteUsingPredicate(Rewritten, &L, Preds)};
     }
   }
 }
 
 void PredicatedScalarEvolution::setNoOverflow(
     Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
   const SCEV *Expr = getSCEV(V);
   const auto *AR = cast<SCEVAddRecExpr>(Expr);
 
   auto ImpliedFlags = SCEVWrapPredicate::getImpliedFlags(AR, SE);
 
   // Clear the statically implied flags.
   Flags = SCEVWrapPredicate::clearFlags(Flags, ImpliedFlags);
   addPredicate(*SE.getWrapPredicate(AR, Flags));
 
   auto II = FlagsMap.insert({V, Flags});
   if (!II.second)
     II.first->second = SCEVWrapPredicate::setFlags(Flags, II.first->second);
 }
 
 bool PredicatedScalarEvolution::hasNoOverflow(
     Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
   const SCEV *Expr = getSCEV(V);
   const auto *AR = cast<SCEVAddRecExpr>(Expr);
 
   Flags = SCEVWrapPredicate::clearFlags(
       Flags, SCEVWrapPredicate::getImpliedFlags(AR, SE));
 
   auto II = FlagsMap.find(V);
 
   if (II != FlagsMap.end())
     Flags = SCEVWrapPredicate::clearFlags(Flags, II->second);
 
   return Flags == SCEVWrapPredicate::IncrementAnyWrap;
 }
 
 const SCEVAddRecExpr *PredicatedScalarEvolution::getAsAddRec(Value *V) {
   const SCEV *Expr = this->getSCEV(V);
   auto *New = SE.convertSCEVToAddRecWithPredicates(Expr, &L, Preds);
 
   if (!New)
     return nullptr;
 
   updateGeneration();
   RewriteMap[SE.getSCEV(V)] = {Generation, New};
   return New;
 }
 
 PredicatedScalarEvolution::PredicatedScalarEvolution(
     const PredicatedScalarEvolution &Init)
     : RewriteMap(Init.RewriteMap), SE(Init.SE), L(Init.L), Preds(Init.Preds),
       Generation(Init.Generation), BackedgeCount(Init.BackedgeCount) {
   for (const auto &I : Init.FlagsMap)
     FlagsMap.insert(I);
 }
 
 void PredicatedScalarEvolution::print(raw_ostream &OS, unsigned Depth) const {
   // For each block.
   for (auto *BB : L.getBlocks())
     for (auto &I : *BB) {
       if (!SE.isSCEVable(I.getType()))
         continue;
 
       auto *Expr = SE.getSCEV(&I);
       auto II = RewriteMap.find(Expr);
 
       if (II == RewriteMap.end())
         continue;
 
       // Don't print things that are not interesting.
       if (II->second.second == Expr)
         continue;
 
       OS.indent(Depth) << "[PSE]" << I << ":\n";
       OS.indent(Depth + 2) << *Expr << "\n";
       OS.indent(Depth + 2) << "--> " << *II->second.second << "\n";
     }
 }
Index: head/contrib/llvm/lib/Analysis/ScalarEvolutionExpander.cpp
===================================================================
--- head/contrib/llvm/lib/Analysis/ScalarEvolutionExpander.cpp	(revision 312831)
+++ head/contrib/llvm/lib/Analysis/ScalarEvolutionExpander.cpp	(revision 312832)
@@ -1,2210 +1,2244 @@
 //===- ScalarEvolutionExpander.cpp - Scalar Evolution Analysis ------------===//
 //
 //                     The LLVM Compiler Infrastructure
 //
 // This file is distributed under the University of Illinois Open Source
 // License. See LICENSE.TXT for details.
 //
 //===----------------------------------------------------------------------===//
 //
 // 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. Clear its operand
             // so that it doesn't hold anything live.
             Ret = CastInst::Create(Op, V, Ty, "", &*IP);
             Ret->takeName(CI);
             CI->replaceAllUsesWith(Ret);
             CI->setOperand(0, UndefValue::get(V->getType()));
             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.
 Value *SCEVExpander::InsertBinop(Instruction::BinaryOps Opcode,
                                  Value *LHS, Value *RHS) {
   // 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++;
       if (IP->getOpcode() == (unsigned)Opcode && IP->getOperand(0) == LHS &&
           IP->getOperand(1) == RHS)
         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);
 
   // 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);
   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.
 /// TODO: When ScalarEvolution gets a SCEVSDivExpr, this can be made
 /// unnecessary; in its place, just signed-divide Ops[i] by the scale and
 /// check to see if the divide was folded.
 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 *IntPtrTy = DL.getIntPtrType(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(IntPtrTy, 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 =
           std::any_of(GepIndices.begin(), GepIndices.end(),
                       [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));
 }
 
 /// 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.
   std::stable_sort(OpsAndLoops.begin(), OpsAndLoops.end(), 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);
       ++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);
       ++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.
   std::stable_sort(OpsAndLoops.begin(), OpsAndLoops.end(), LoopCompare(SE.DT));
 
   // Emit instructions to mul all the operands. Hoist as much as possible
   // out of loops.
   Value *Prod = nullptr;
   for (const auto &I : OpsAndLoops) {
     const SCEV *Op = I.second;
     if (!Prod) {
       // This is the first operand. Just expand it.
       Prod = expand(Op);
     } else if (Op->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);
     } else {
       // A simple mul.
       Value *W = expandCodeFor(Op, Ty);
       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");
         Prod = InsertBinop(Instruction::Shl, Prod,
                            ConstantInt::get(Ty, RHS->logBase2()));
       } else {
         Prod = InsertBinop(Instruction::Mul, Prod, W);
       }
     }
   }
 
   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()));
   }
 
   Value *RHS = expandCodeFor(S->getRHS(), Ty);
   return InsertBinop(Instruction::UDiv, LHS, RHS);
 }
 
 /// 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());
     const SCEV *const StepArray[1] = { SE.getSCEV(StepV) };
     IncV = expandAddToGEP(StepArray, StepArray+1, 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;
 }
 
 /// \brief 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);
 }
 
 /// \brief 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 (auto &I : *L->getHeader()) {
       auto *PN = dyn_cast<PHINode>(&I);
       if (!PN || !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;
 
       Instruction *TempIncV =
           cast<Instruction>(PN->getIncomingValueForBlock(LatchBlock));
 
       // 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.
   Value *StartV =
       expandCodeFor(Normalized->getStart(), ExpandTy, &L->getHeader()->front());
 
   // StartV must be hoisted 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>(TransformForPostIncUse(
         Normalize, S, nullptr, nullptr, Loops, SE, SE.DT));
   }
 
   // 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;
   // 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, ExpandTy, 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 outide 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 invertion 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)) {
       const SCEV *const OffsetArray[1] = { PostLoopOffset };
       Result = expandAddToGEP(OffsetArray, OffsetArray+1, 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) {
   if (!CanonicalMode) 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();
     const SCEV *RestArray[1] = { Rest };
     // Dig into the expression to find the pointer base for a GEP.
     ExposePointerBase(Base, RestArray[0], 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(RestArray, RestArray+1, 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.
     if (S->getOperand(i)->getType() != Ty) {
       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.
     if (S->getOperand(i)->getType() != Ty) {
       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::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;
 }
 
-Value *SCEVExpander::FindValueInExprValueMap(const SCEV *S,
-                                             const Instruction *InsertPt) {
-  SetVector<Value *> *Set = SE.getSCEVValues(S);
+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 &Ent : *Set) {
+      for (auto const &VOPair : *Set) {
+        Value *V = VOPair.first;
+        ConstantInt *Offset = VOPair.second;
         Instruction *EntInst = nullptr;
-        if (Ent && isa<Instruction>(Ent) &&
-            (EntInst = cast<Instruction>(Ent)) &&
-            S->getType() == Ent->getType() &&
+        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 Ent;
-        }
+             SE.LI.getLoopFor(EntInst->getParent())->contains(InsertPt)))
+          return {V, Offset};
       }
     }
   }
-  return nullptr;
+  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();
   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;
     }
 
   // 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.
-  Value *V = FindValueInExprValueMap(S, InsertPt);
+  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<WeakVH> &DeadInsts,
                                            const TargetTransformInfo *TTI) {
   // Find integer phis in order of increasing width.
   SmallVector<PHINode*, 8> Phis;
   for (auto &I : *L->getHeader()) {
     if (auto *PN = dyn_cast<PHINode>(&I))
       Phis.push_back(PN);
     else
       break;
   }
 
   if (TTI)
     std::sort(Phis.begin(), Phis.end(), [](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::findExistingExpansion(const SCEV *S,
-                                           const Instruction *At, Loop *L) {
+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;
     BasicBlock *TrueBB, *FalseBB;
 
     if (!match(BB->getTerminator(),
                m_Br(m_ICmp(Pred, m_Instruction(LHS), m_Instruction(RHS)),
                     TrueBB, FalseBB)))
       continue;
 
     if (SE.getSCEV(LHS) == S && SE.DT.dominates(LHS, At))
-      return LHS;
+      return ScalarEvolution::ValueOffsetPair(LHS, nullptr);
 
     if (SE.getSCEV(RHS) == S && SE.DT.dominates(RHS, At))
-      return RHS;
+      return ScalarEvolution::ValueOffsetPair(RHS, nullptr);
   }
 
   // Use expand's logic which is used for reusing a previous Value in
   // ExprValueMap.
-  if (Value *Val = FindValueInExprValueMap(S, At))
-    return Val;
+  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 nullptr;
+  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 avaliable at the point "At"
   // then consider the expression cheap.
-  if (At && findExistingExpansion(S, At, L) != nullptr)
+  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, 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()) {
         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 (!findExistingExpansion(
+    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<SCEVSMaxExpr>(S) || isa<SCEVUMaxExpr>(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();
 
   unsigned SrcBits = SE.getTypeSizeInBits(ExitCount->getType());
   unsigned DstBits = SE.getTypeSizeInBits(AR->getType());
 
   // 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(AR->getType()));
 
   Value *StepValue = expandCodeFor(Step, Ty, Loc);
   Value *NegStepValue = expandCodeFor(SE.getNegativeSCEV(Step), Ty, Loc);
   Value *StartValue = expandCodeFor(Start, Ty, 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 = Builder.CreateAdd(StartValue, MulV);
   Value *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
   // droping 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;
 }
 }
Index: head/contrib/llvm/lib/Transforms/Scalar/IndVarSimplify.cpp
===================================================================
--- head/contrib/llvm/lib/Transforms/Scalar/IndVarSimplify.cpp	(revision 312831)
+++ head/contrib/llvm/lib/Transforms/Scalar/IndVarSimplify.cpp	(revision 312832)
@@ -1,2288 +1,2288 @@
 //===- IndVarSimplify.cpp - Induction Variable Elimination ----------------===//
 //
 //                     The LLVM Compiler Infrastructure
 //
 // This file is distributed under the University of Illinois Open Source
 // License. See LICENSE.TXT for details.
 //
 //===----------------------------------------------------------------------===//
 //
 // This transformation analyzes and transforms the induction variables (and
 // computations derived from them) into simpler forms suitable for subsequent
 // analysis and transformation.
 //
 // If the trip count of a loop is computable, this pass also makes the following
 // changes:
 //   1. The exit condition for the loop is canonicalized to compare the
 //      induction value against the exit value.  This turns loops like:
 //        'for (i = 7; i*i < 1000; ++i)' into 'for (i = 0; i != 25; ++i)'
 //   2. Any use outside of the loop of an expression derived from the indvar
 //      is changed to compute the derived value outside of the loop, eliminating
 //      the dependence on the exit value of the induction variable.  If the only
 //      purpose of the loop is to compute the exit value of some derived
 //      expression, this transformation will make the loop dead.
 //
 //===----------------------------------------------------------------------===//
 
 #include "llvm/Transforms/Scalar/IndVarSimplify.h"
 #include "llvm/Transforms/Scalar.h"
 #include "llvm/ADT/SmallVector.h"
 #include "llvm/ADT/Statistic.h"
 #include "llvm/Analysis/GlobalsModRef.h"
 #include "llvm/Analysis/LoopInfo.h"
 #include "llvm/Analysis/LoopPass.h"
 #include "llvm/Analysis/LoopPassManager.h"
 #include "llvm/Analysis/ScalarEvolutionExpander.h"
 #include "llvm/Analysis/ScalarEvolutionAliasAnalysis.h"
 #include "llvm/Analysis/TargetLibraryInfo.h"
 #include "llvm/Analysis/TargetTransformInfo.h"
 #include "llvm/IR/BasicBlock.h"
 #include "llvm/IR/CFG.h"
 #include "llvm/IR/Constants.h"
 #include "llvm/IR/DataLayout.h"
 #include "llvm/IR/Dominators.h"
 #include "llvm/IR/Instructions.h"
 #include "llvm/IR/IntrinsicInst.h"
 #include "llvm/IR/LLVMContext.h"
 #include "llvm/IR/PatternMatch.h"
 #include "llvm/IR/Type.h"
 #include "llvm/Support/CommandLine.h"
 #include "llvm/Support/Debug.h"
 #include "llvm/Support/raw_ostream.h"
 #include "llvm/Transforms/Utils/BasicBlockUtils.h"
 #include "llvm/Transforms/Utils/Local.h"
 #include "llvm/Transforms/Utils/LoopUtils.h"
 #include "llvm/Transforms/Utils/SimplifyIndVar.h"
 using namespace llvm;
 
 #define DEBUG_TYPE "indvars"
 
 STATISTIC(NumWidened     , "Number of indvars widened");
 STATISTIC(NumReplaced    , "Number of exit values replaced");
 STATISTIC(NumLFTR        , "Number of loop exit tests replaced");
 STATISTIC(NumElimExt     , "Number of IV sign/zero extends eliminated");
 STATISTIC(NumElimIV      , "Number of congruent IVs eliminated");
 
 // Trip count verification can be enabled by default under NDEBUG if we
 // implement a strong expression equivalence checker in SCEV. Until then, we
 // use the verify-indvars flag, which may assert in some cases.
 static cl::opt<bool> VerifyIndvars(
   "verify-indvars", cl::Hidden,
   cl::desc("Verify the ScalarEvolution result after running indvars"));
 
 enum ReplaceExitVal { NeverRepl, OnlyCheapRepl, AlwaysRepl };
 
 static cl::opt<ReplaceExitVal> ReplaceExitValue(
     "replexitval", cl::Hidden, cl::init(OnlyCheapRepl),
     cl::desc("Choose the strategy to replace exit value in IndVarSimplify"),
     cl::values(clEnumValN(NeverRepl, "never", "never replace exit value"),
                clEnumValN(OnlyCheapRepl, "cheap",
                           "only replace exit value when the cost is cheap"),
                clEnumValN(AlwaysRepl, "always",
                           "always replace exit value whenever possible"),
                clEnumValEnd));
 
 namespace {
 struct RewritePhi;
 
 class IndVarSimplify {
   LoopInfo *LI;
   ScalarEvolution *SE;
   DominatorTree *DT;
   const DataLayout &DL;
   TargetLibraryInfo *TLI;
   const TargetTransformInfo *TTI;
 
   SmallVector<WeakVH, 16> DeadInsts;
   bool Changed = false;
 
   bool isValidRewrite(Value *FromVal, Value *ToVal);
 
   void handleFloatingPointIV(Loop *L, PHINode *PH);
   void rewriteNonIntegerIVs(Loop *L);
 
   void simplifyAndExtend(Loop *L, SCEVExpander &Rewriter, LoopInfo *LI);
 
   bool canLoopBeDeleted(Loop *L, SmallVector<RewritePhi, 8> &RewritePhiSet);
   void rewriteLoopExitValues(Loop *L, SCEVExpander &Rewriter);
   void rewriteFirstIterationLoopExitValues(Loop *L);
 
   Value *linearFunctionTestReplace(Loop *L, const SCEV *BackedgeTakenCount,
                                    PHINode *IndVar, SCEVExpander &Rewriter);
 
   void sinkUnusedInvariants(Loop *L);
 
   Value *expandSCEVIfNeeded(SCEVExpander &Rewriter, const SCEV *S, Loop *L,
                             Instruction *InsertPt, Type *Ty);
 
 public:
   IndVarSimplify(LoopInfo *LI, ScalarEvolution *SE, DominatorTree *DT,
                  const DataLayout &DL, TargetLibraryInfo *TLI,
                  TargetTransformInfo *TTI)
       : LI(LI), SE(SE), DT(DT), DL(DL), TLI(TLI), TTI(TTI) {}
 
   bool run(Loop *L);
 };
 }
 
 /// Return true if the SCEV expansion generated by the rewriter can replace the
 /// original value. SCEV guarantees that it produces the same value, but the way
 /// it is produced may be illegal IR.  Ideally, this function will only be
 /// called for verification.
 bool IndVarSimplify::isValidRewrite(Value *FromVal, Value *ToVal) {
   // If an SCEV expression subsumed multiple pointers, its expansion could
   // reassociate the GEP changing the base pointer. This is illegal because the
   // final address produced by a GEP chain must be inbounds relative to its
   // underlying object. Otherwise basic alias analysis, among other things,
   // could fail in a dangerous way. Ultimately, SCEV will be improved to avoid
   // producing an expression involving multiple pointers. Until then, we must
   // bail out here.
   //
   // Retrieve the pointer operand of the GEP. Don't use GetUnderlyingObject
   // because it understands lcssa phis while SCEV does not.
   Value *FromPtr = FromVal;
   Value *ToPtr = ToVal;
   if (auto *GEP = dyn_cast<GEPOperator>(FromVal)) {
     FromPtr = GEP->getPointerOperand();
   }
   if (auto *GEP = dyn_cast<GEPOperator>(ToVal)) {
     ToPtr = GEP->getPointerOperand();
   }
   if (FromPtr != FromVal || ToPtr != ToVal) {
     // Quickly check the common case
     if (FromPtr == ToPtr)
       return true;
 
     // SCEV may have rewritten an expression that produces the GEP's pointer
     // operand. That's ok as long as the pointer operand has the same base
     // pointer. Unlike GetUnderlyingObject(), getPointerBase() will find the
     // base of a recurrence. This handles the case in which SCEV expansion
     // converts a pointer type recurrence into a nonrecurrent pointer base
     // indexed by an integer recurrence.
 
     // If the GEP base pointer is a vector of pointers, abort.
     if (!FromPtr->getType()->isPointerTy() || !ToPtr->getType()->isPointerTy())
       return false;
 
     const SCEV *FromBase = SE->getPointerBase(SE->getSCEV(FromPtr));
     const SCEV *ToBase = SE->getPointerBase(SE->getSCEV(ToPtr));
     if (FromBase == ToBase)
       return true;
 
     DEBUG(dbgs() << "INDVARS: GEP rewrite bail out "
           << *FromBase << " != " << *ToBase << "\n");
 
     return false;
   }
   return true;
 }
 
 /// Determine the insertion point for this user. By default, insert immediately
 /// before the user. SCEVExpander or LICM will hoist loop invariants out of the
 /// loop. For PHI nodes, there may be multiple uses, so compute the nearest
 /// common dominator for the incoming blocks.
 static Instruction *getInsertPointForUses(Instruction *User, Value *Def,
                                           DominatorTree *DT, LoopInfo *LI) {
   PHINode *PHI = dyn_cast<PHINode>(User);
   if (!PHI)
     return User;
 
   Instruction *InsertPt = nullptr;
   for (unsigned i = 0, e = PHI->getNumIncomingValues(); i != e; ++i) {
     if (PHI->getIncomingValue(i) != Def)
       continue;
 
     BasicBlock *InsertBB = PHI->getIncomingBlock(i);
     if (!InsertPt) {
       InsertPt = InsertBB->getTerminator();
       continue;
     }
     InsertBB = DT->findNearestCommonDominator(InsertPt->getParent(), InsertBB);
     InsertPt = InsertBB->getTerminator();
   }
   assert(InsertPt && "Missing phi operand");
 
   auto *DefI = dyn_cast<Instruction>(Def);
   if (!DefI)
     return InsertPt;
 
   assert(DT->dominates(DefI, InsertPt) && "def does not dominate all uses");
 
   auto *L = LI->getLoopFor(DefI->getParent());
   assert(!L || L->contains(LI->getLoopFor(InsertPt->getParent())));
 
   for (auto *DTN = (*DT)[InsertPt->getParent()]; DTN; DTN = DTN->getIDom())
     if (LI->getLoopFor(DTN->getBlock()) == L)
       return DTN->getBlock()->getTerminator();
 
   llvm_unreachable("DefI dominates InsertPt!");
 }
 
 //===----------------------------------------------------------------------===//
 // rewriteNonIntegerIVs and helpers. Prefer integer IVs.
 //===----------------------------------------------------------------------===//
 
 /// Convert APF to an integer, if possible.
 static bool ConvertToSInt(const APFloat &APF, int64_t &IntVal) {
   bool isExact = false;
   // See if we can convert this to an int64_t
   uint64_t UIntVal;
   if (APF.convertToInteger(&UIntVal, 64, true, APFloat::rmTowardZero,
                            &isExact) != APFloat::opOK || !isExact)
     return false;
   IntVal = UIntVal;
   return true;
 }
 
 /// If the loop has floating induction variable then insert corresponding
 /// integer induction variable if possible.
 /// For example,
 /// for(double i = 0; i < 10000; ++i)
 ///   bar(i)
 /// is converted into
 /// for(int i = 0; i < 10000; ++i)
 ///   bar((double)i);
 ///
 void IndVarSimplify::handleFloatingPointIV(Loop *L, PHINode *PN) {
   unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
   unsigned BackEdge     = IncomingEdge^1;
 
   // Check incoming value.
   auto *InitValueVal = dyn_cast<ConstantFP>(PN->getIncomingValue(IncomingEdge));
 
   int64_t InitValue;
   if (!InitValueVal || !ConvertToSInt(InitValueVal->getValueAPF(), InitValue))
     return;
 
   // Check IV increment. Reject this PN if increment operation is not
   // an add or increment value can not be represented by an integer.
   auto *Incr = dyn_cast<BinaryOperator>(PN->getIncomingValue(BackEdge));
   if (Incr == nullptr || Incr->getOpcode() != Instruction::FAdd) return;
 
   // If this is not an add of the PHI with a constantfp, or if the constant fp
   // is not an integer, bail out.
   ConstantFP *IncValueVal = dyn_cast<ConstantFP>(Incr->getOperand(1));
   int64_t IncValue;
   if (IncValueVal == nullptr || Incr->getOperand(0) != PN ||
       !ConvertToSInt(IncValueVal->getValueAPF(), IncValue))
     return;
 
   // Check Incr uses. One user is PN and the other user is an exit condition
   // used by the conditional terminator.
   Value::user_iterator IncrUse = Incr->user_begin();
   Instruction *U1 = cast<Instruction>(*IncrUse++);
   if (IncrUse == Incr->user_end()) return;
   Instruction *U2 = cast<Instruction>(*IncrUse++);
   if (IncrUse != Incr->user_end()) return;
 
   // Find exit condition, which is an fcmp.  If it doesn't exist, or if it isn't
   // only used by a branch, we can't transform it.
   FCmpInst *Compare = dyn_cast<FCmpInst>(U1);
   if (!Compare)
     Compare = dyn_cast<FCmpInst>(U2);
   if (!Compare || !Compare->hasOneUse() ||
       !isa<BranchInst>(Compare->user_back()))
     return;
 
   BranchInst *TheBr = cast<BranchInst>(Compare->user_back());
 
   // We need to verify that the branch actually controls the iteration count
   // of the loop.  If not, the new IV can overflow and no one will notice.
   // The branch block must be in the loop and one of the successors must be out
   // of the loop.
   assert(TheBr->isConditional() && "Can't use fcmp if not conditional");
   if (!L->contains(TheBr->getParent()) ||
       (L->contains(TheBr->getSuccessor(0)) &&
        L->contains(TheBr->getSuccessor(1))))
     return;
 
 
   // If it isn't a comparison with an integer-as-fp (the exit value), we can't
   // transform it.
   ConstantFP *ExitValueVal = dyn_cast<ConstantFP>(Compare->getOperand(1));
   int64_t ExitValue;
   if (ExitValueVal == nullptr ||
       !ConvertToSInt(ExitValueVal->getValueAPF(), ExitValue))
     return;
 
   // Find new predicate for integer comparison.
   CmpInst::Predicate NewPred = CmpInst::BAD_ICMP_PREDICATE;
   switch (Compare->getPredicate()) {
   default: return;  // Unknown comparison.
   case CmpInst::FCMP_OEQ:
   case CmpInst::FCMP_UEQ: NewPred = CmpInst::ICMP_EQ; break;
   case CmpInst::FCMP_ONE:
   case CmpInst::FCMP_UNE: NewPred = CmpInst::ICMP_NE; break;
   case CmpInst::FCMP_OGT:
   case CmpInst::FCMP_UGT: NewPred = CmpInst::ICMP_SGT; break;
   case CmpInst::FCMP_OGE:
   case CmpInst::FCMP_UGE: NewPred = CmpInst::ICMP_SGE; break;
   case CmpInst::FCMP_OLT:
   case CmpInst::FCMP_ULT: NewPred = CmpInst::ICMP_SLT; break;
   case CmpInst::FCMP_OLE:
   case CmpInst::FCMP_ULE: NewPred = CmpInst::ICMP_SLE; break;
   }
 
   // We convert the floating point induction variable to a signed i32 value if
   // we can.  This is only safe if the comparison will not overflow in a way
   // that won't be trapped by the integer equivalent operations.  Check for this
   // now.
   // TODO: We could use i64 if it is native and the range requires it.
 
   // The start/stride/exit values must all fit in signed i32.
   if (!isInt<32>(InitValue) || !isInt<32>(IncValue) || !isInt<32>(ExitValue))
     return;
 
   // If not actually striding (add x, 0.0), avoid touching the code.
   if (IncValue == 0)
     return;
 
   // Positive and negative strides have different safety conditions.
   if (IncValue > 0) {
     // If we have a positive stride, we require the init to be less than the
     // exit value.
     if (InitValue >= ExitValue)
       return;
 
     uint32_t Range = uint32_t(ExitValue-InitValue);
     // Check for infinite loop, either:
     // while (i <= Exit) or until (i > Exit)
     if (NewPred == CmpInst::ICMP_SLE || NewPred == CmpInst::ICMP_SGT) {
       if (++Range == 0) return;  // Range overflows.
     }
 
     unsigned Leftover = Range % uint32_t(IncValue);
 
     // If this is an equality comparison, we require that the strided value
     // exactly land on the exit value, otherwise the IV condition will wrap
     // around and do things the fp IV wouldn't.
     if ((NewPred == CmpInst::ICMP_EQ || NewPred == CmpInst::ICMP_NE) &&
         Leftover != 0)
       return;
 
     // If the stride would wrap around the i32 before exiting, we can't
     // transform the IV.
     if (Leftover != 0 && int32_t(ExitValue+IncValue) < ExitValue)
       return;
 
   } else {
     // If we have a negative stride, we require the init to be greater than the
     // exit value.
     if (InitValue <= ExitValue)
       return;
 
     uint32_t Range = uint32_t(InitValue-ExitValue);
     // Check for infinite loop, either:
     // while (i >= Exit) or until (i < Exit)
     if (NewPred == CmpInst::ICMP_SGE || NewPred == CmpInst::ICMP_SLT) {
       if (++Range == 0) return;  // Range overflows.
     }
 
     unsigned Leftover = Range % uint32_t(-IncValue);
 
     // If this is an equality comparison, we require that the strided value
     // exactly land on the exit value, otherwise the IV condition will wrap
     // around and do things the fp IV wouldn't.
     if ((NewPred == CmpInst::ICMP_EQ || NewPred == CmpInst::ICMP_NE) &&
         Leftover != 0)
       return;
 
     // If the stride would wrap around the i32 before exiting, we can't
     // transform the IV.
     if (Leftover != 0 && int32_t(ExitValue+IncValue) > ExitValue)
       return;
   }
 
   IntegerType *Int32Ty = Type::getInt32Ty(PN->getContext());
 
   // Insert new integer induction variable.
   PHINode *NewPHI = PHINode::Create(Int32Ty, 2, PN->getName()+".int", PN);
   NewPHI->addIncoming(ConstantInt::get(Int32Ty, InitValue),
                       PN->getIncomingBlock(IncomingEdge));
 
   Value *NewAdd =
     BinaryOperator::CreateAdd(NewPHI, ConstantInt::get(Int32Ty, IncValue),
                               Incr->getName()+".int", Incr);
   NewPHI->addIncoming(NewAdd, PN->getIncomingBlock(BackEdge));
 
   ICmpInst *NewCompare = new ICmpInst(TheBr, NewPred, NewAdd,
                                       ConstantInt::get(Int32Ty, ExitValue),
                                       Compare->getName());
 
   // In the following deletions, PN may become dead and may be deleted.
   // Use a WeakVH to observe whether this happens.
   WeakVH WeakPH = PN;
 
   // Delete the old floating point exit comparison.  The branch starts using the
   // new comparison.
   NewCompare->takeName(Compare);
   Compare->replaceAllUsesWith(NewCompare);
   RecursivelyDeleteTriviallyDeadInstructions(Compare, TLI);
 
   // Delete the old floating point increment.
   Incr->replaceAllUsesWith(UndefValue::get(Incr->getType()));
   RecursivelyDeleteTriviallyDeadInstructions(Incr, TLI);
 
   // If the FP induction variable still has uses, this is because something else
   // in the loop uses its value.  In order to canonicalize the induction
   // variable, we chose to eliminate the IV and rewrite it in terms of an
   // int->fp cast.
   //
   // We give preference to sitofp over uitofp because it is faster on most
   // platforms.
   if (WeakPH) {
     Value *Conv = new SIToFPInst(NewPHI, PN->getType(), "indvar.conv",
                                  &*PN->getParent()->getFirstInsertionPt());
     PN->replaceAllUsesWith(Conv);
     RecursivelyDeleteTriviallyDeadInstructions(PN, TLI);
   }
   Changed = true;
 }
 
 void IndVarSimplify::rewriteNonIntegerIVs(Loop *L) {
   // First step.  Check to see if there are any floating-point recurrences.
   // If there are, change them into integer recurrences, permitting analysis by
   // the SCEV routines.
   //
   BasicBlock *Header = L->getHeader();
 
   SmallVector<WeakVH, 8> PHIs;
   for (BasicBlock::iterator I = Header->begin();
        PHINode *PN = dyn_cast<PHINode>(I); ++I)
     PHIs.push_back(PN);
 
   for (unsigned i = 0, e = PHIs.size(); i != e; ++i)
     if (PHINode *PN = dyn_cast_or_null<PHINode>(&*PHIs[i]))
       handleFloatingPointIV(L, PN);
 
   // If the loop previously had floating-point IV, ScalarEvolution
   // may not have been able to compute a trip count. Now that we've done some
   // re-writing, the trip count may be computable.
   if (Changed)
     SE->forgetLoop(L);
 }
 
 namespace {
 // Collect information about PHI nodes which can be transformed in
 // rewriteLoopExitValues.
 struct RewritePhi {
   PHINode *PN;
   unsigned Ith;  // Ith incoming value.
   Value *Val;    // Exit value after expansion.
   bool HighCost; // High Cost when expansion.
 
   RewritePhi(PHINode *P, unsigned I, Value *V, bool H)
       : PN(P), Ith(I), Val(V), HighCost(H) {}
 };
 }
 
 Value *IndVarSimplify::expandSCEVIfNeeded(SCEVExpander &Rewriter, const SCEV *S,
                                           Loop *L, Instruction *InsertPt,
                                           Type *ResultTy) {
   // Before expanding S into an expensive LLVM expression, see if we can use an
   // already existing value as the expansion for S.
-  if (Value *ExistingValue = Rewriter.findExistingExpansion(S, InsertPt, L))
+  if (Value *ExistingValue = Rewriter.getExactExistingExpansion(S, InsertPt, L))
     if (ExistingValue->getType() == ResultTy)
       return ExistingValue;
 
   // We didn't find anything, fall back to using SCEVExpander.
   return Rewriter.expandCodeFor(S, ResultTy, InsertPt);
 }
 
 //===----------------------------------------------------------------------===//
 // rewriteLoopExitValues - Optimize IV users outside the loop.
 // As a side effect, reduces the amount of IV processing within the loop.
 //===----------------------------------------------------------------------===//
 
 /// Check to see if this loop has a computable loop-invariant execution count.
 /// If so, this means that we can compute the final value of any expressions
 /// that are recurrent in the loop, and substitute the exit values from the loop
 /// into any instructions outside of the loop that use the final values of the
 /// current expressions.
 ///
 /// This is mostly redundant with the regular IndVarSimplify activities that
 /// happen later, except that it's more powerful in some cases, because it's
 /// able to brute-force evaluate arbitrary instructions as long as they have
 /// constant operands at the beginning of the loop.
 void IndVarSimplify::rewriteLoopExitValues(Loop *L, SCEVExpander &Rewriter) {
   // Check a pre-condition.
   assert(L->isRecursivelyLCSSAForm(*DT) && "Indvars did not preserve LCSSA!");
 
   SmallVector<BasicBlock*, 8> ExitBlocks;
   L->getUniqueExitBlocks(ExitBlocks);
 
   SmallVector<RewritePhi, 8> RewritePhiSet;
   // Find all values that are computed inside the loop, but used outside of it.
   // Because of LCSSA, these values will only occur in LCSSA PHI Nodes.  Scan
   // the exit blocks of the loop to find them.
   for (BasicBlock *ExitBB : ExitBlocks) {
     // If there are no PHI nodes in this exit block, then no values defined
     // inside the loop are used on this path, skip it.
     PHINode *PN = dyn_cast<PHINode>(ExitBB->begin());
     if (!PN) continue;
 
     unsigned NumPreds = PN->getNumIncomingValues();
 
     // Iterate over all of the PHI nodes.
     BasicBlock::iterator BBI = ExitBB->begin();
     while ((PN = dyn_cast<PHINode>(BBI++))) {
       if (PN->use_empty())
         continue; // dead use, don't replace it
 
       if (!SE->isSCEVable(PN->getType()))
         continue;
 
       // It's necessary to tell ScalarEvolution about this explicitly so that
       // it can walk the def-use list and forget all SCEVs, as it may not be
       // watching the PHI itself. Once the new exit value is in place, there
       // may not be a def-use connection between the loop and every instruction
       // which got a SCEVAddRecExpr for that loop.
       SE->forgetValue(PN);
 
       // Iterate over all of the values in all the PHI nodes.
       for (unsigned i = 0; i != NumPreds; ++i) {
         // If the value being merged in is not integer or is not defined
         // in the loop, skip it.
         Value *InVal = PN->getIncomingValue(i);
         if (!isa<Instruction>(InVal))
           continue;
 
         // If this pred is for a subloop, not L itself, skip it.
         if (LI->getLoopFor(PN->getIncomingBlock(i)) != L)
           continue; // The Block is in a subloop, skip it.
 
         // Check that InVal is defined in the loop.
         Instruction *Inst = cast<Instruction>(InVal);
         if (!L->contains(Inst))
           continue;
 
         // Okay, this instruction has a user outside of the current loop
         // and varies predictably *inside* the loop.  Evaluate the value it
         // contains when the loop exits, if possible.
         const SCEV *ExitValue = SE->getSCEVAtScope(Inst, L->getParentLoop());
         if (!SE->isLoopInvariant(ExitValue, L) ||
             !isSafeToExpand(ExitValue, *SE))
           continue;
 
         // Computing the value outside of the loop brings no benefit if :
         //  - it is definitely used inside the loop in a way which can not be
         //    optimized away.
         //  - no use outside of the loop can take advantage of hoisting the
         //    computation out of the loop
         if (ExitValue->getSCEVType()>=scMulExpr) {
           unsigned NumHardInternalUses = 0;
           unsigned NumSoftExternalUses = 0;
           unsigned NumUses = 0;
           for (auto IB = Inst->user_begin(), IE = Inst->user_end();
                IB != IE && NumUses <= 6; ++IB) {
             Instruction *UseInstr = cast<Instruction>(*IB);
             unsigned Opc = UseInstr->getOpcode();
             NumUses++;
             if (L->contains(UseInstr)) {
               if (Opc == Instruction::Call || Opc == Instruction::Ret)
                 NumHardInternalUses++;
             } else {
               if (Opc == Instruction::PHI) {
                 // Do not count the Phi as a use. LCSSA may have inserted
                 // plenty of trivial ones.
                 NumUses--;
                 for (auto PB = UseInstr->user_begin(),
                           PE = UseInstr->user_end();
                      PB != PE && NumUses <= 6; ++PB, ++NumUses) {
                   unsigned PhiOpc = cast<Instruction>(*PB)->getOpcode();
                   if (PhiOpc != Instruction::Call && PhiOpc != Instruction::Ret)
                     NumSoftExternalUses++;
                 }
                 continue;
               }
               if (Opc != Instruction::Call && Opc != Instruction::Ret)
                 NumSoftExternalUses++;
             }
           }
           if (NumUses <= 6 && NumHardInternalUses && !NumSoftExternalUses)
             continue;
         }
 
         bool HighCost = Rewriter.isHighCostExpansion(ExitValue, L, Inst);
         Value *ExitVal =
             expandSCEVIfNeeded(Rewriter, ExitValue, L, Inst, PN->getType());
 
         DEBUG(dbgs() << "INDVARS: RLEV: AfterLoopVal = " << *ExitVal << '\n'
                      << "  LoopVal = " << *Inst << "\n");
 
         if (!isValidRewrite(Inst, ExitVal)) {
           DeadInsts.push_back(ExitVal);
           continue;
         }
 
         // Collect all the candidate PHINodes to be rewritten.
         RewritePhiSet.emplace_back(PN, i, ExitVal, HighCost);
       }
     }
   }
 
   bool LoopCanBeDel = canLoopBeDeleted(L, RewritePhiSet);
 
   // Transformation.
   for (const RewritePhi &Phi : RewritePhiSet) {
     PHINode *PN = Phi.PN;
     Value *ExitVal = Phi.Val;
 
     // Only do the rewrite when the ExitValue can be expanded cheaply.
     // If LoopCanBeDel is true, rewrite exit value aggressively.
     if (ReplaceExitValue == OnlyCheapRepl && !LoopCanBeDel && Phi.HighCost) {
       DeadInsts.push_back(ExitVal);
       continue;
     }
 
     Changed = true;
     ++NumReplaced;
     Instruction *Inst = cast<Instruction>(PN->getIncomingValue(Phi.Ith));
     PN->setIncomingValue(Phi.Ith, ExitVal);
 
     // If this instruction is dead now, delete it. Don't do it now to avoid
     // invalidating iterators.
     if (isInstructionTriviallyDead(Inst, TLI))
       DeadInsts.push_back(Inst);
 
     // Replace PN with ExitVal if that is legal and does not break LCSSA.
     if (PN->getNumIncomingValues() == 1 &&
         LI->replacementPreservesLCSSAForm(PN, ExitVal)) {
       PN->replaceAllUsesWith(ExitVal);
       PN->eraseFromParent();
     }
   }
 
   // The insertion point instruction may have been deleted; clear it out
   // so that the rewriter doesn't trip over it later.
   Rewriter.clearInsertPoint();
 }
 
 //===---------------------------------------------------------------------===//
 // rewriteFirstIterationLoopExitValues: Rewrite loop exit values if we know
 // they will exit at the first iteration.
 //===---------------------------------------------------------------------===//
 
 /// Check to see if this loop has loop invariant conditions which lead to loop
 /// exits. If so, we know that if the exit path is taken, it is at the first
 /// loop iteration. This lets us predict exit values of PHI nodes that live in
 /// loop header.
 void IndVarSimplify::rewriteFirstIterationLoopExitValues(Loop *L) {
   // Verify the input to the pass is already in LCSSA form.
   assert(L->isLCSSAForm(*DT));
 
   SmallVector<BasicBlock *, 8> ExitBlocks;
   L->getUniqueExitBlocks(ExitBlocks);
   auto *LoopHeader = L->getHeader();
   assert(LoopHeader && "Invalid loop");
 
   for (auto *ExitBB : ExitBlocks) {
     BasicBlock::iterator BBI = ExitBB->begin();
     // If there are no more PHI nodes in this exit block, then no more
     // values defined inside the loop are used on this path.
     while (auto *PN = dyn_cast<PHINode>(BBI++)) {
       for (unsigned IncomingValIdx = 0, E = PN->getNumIncomingValues();
           IncomingValIdx != E; ++IncomingValIdx) {
         auto *IncomingBB = PN->getIncomingBlock(IncomingValIdx);
 
         // We currently only support loop exits from loop header. If the
         // incoming block is not loop header, we need to recursively check
         // all conditions starting from loop header are loop invariants.
         // Additional support might be added in the future.
         if (IncomingBB != LoopHeader)
           continue;
 
         // Get condition that leads to the exit path.
         auto *TermInst = IncomingBB->getTerminator();
 
         Value *Cond = nullptr;
         if (auto *BI = dyn_cast<BranchInst>(TermInst)) {
           // Must be a conditional branch, otherwise the block
           // should not be in the loop.
           Cond = BI->getCondition();
         } else if (auto *SI = dyn_cast<SwitchInst>(TermInst))
           Cond = SI->getCondition();
         else
           continue;
 
         if (!L->isLoopInvariant(Cond))
           continue;
 
         auto *ExitVal =
             dyn_cast<PHINode>(PN->getIncomingValue(IncomingValIdx));
 
         // Only deal with PHIs.
         if (!ExitVal)
           continue;
 
         // If ExitVal is a PHI on the loop header, then we know its
         // value along this exit because the exit can only be taken
         // on the first iteration.
         auto *LoopPreheader = L->getLoopPreheader();
         assert(LoopPreheader && "Invalid loop");
         int PreheaderIdx = ExitVal->getBasicBlockIndex(LoopPreheader);
         if (PreheaderIdx != -1) {
           assert(ExitVal->getParent() == LoopHeader &&
                  "ExitVal must be in loop header");
           PN->setIncomingValue(IncomingValIdx,
               ExitVal->getIncomingValue(PreheaderIdx));
         }
       }
     }
   }
 }
 
 /// Check whether it is possible to delete the loop after rewriting exit
 /// value. If it is possible, ignore ReplaceExitValue and do rewriting
 /// aggressively.
 bool IndVarSimplify::canLoopBeDeleted(
     Loop *L, SmallVector<RewritePhi, 8> &RewritePhiSet) {
 
   BasicBlock *Preheader = L->getLoopPreheader();
   // If there is no preheader, the loop will not be deleted.
   if (!Preheader)
     return false;
 
   // In LoopDeletion pass Loop can be deleted when ExitingBlocks.size() > 1.
   // We obviate multiple ExitingBlocks case for simplicity.
   // TODO: If we see testcase with multiple ExitingBlocks can be deleted
   // after exit value rewriting, we can enhance the logic here.
   SmallVector<BasicBlock *, 4> ExitingBlocks;
   L->getExitingBlocks(ExitingBlocks);
   SmallVector<BasicBlock *, 8> ExitBlocks;
   L->getUniqueExitBlocks(ExitBlocks);
   if (ExitBlocks.size() > 1 || ExitingBlocks.size() > 1)
     return false;
 
   BasicBlock *ExitBlock = ExitBlocks[0];
   BasicBlock::iterator BI = ExitBlock->begin();
   while (PHINode *P = dyn_cast<PHINode>(BI)) {
     Value *Incoming = P->getIncomingValueForBlock(ExitingBlocks[0]);
 
     // If the Incoming value of P is found in RewritePhiSet, we know it
     // could be rewritten to use a loop invariant value in transformation
     // phase later. Skip it in the loop invariant check below.
     bool found = false;
     for (const RewritePhi &Phi : RewritePhiSet) {
       unsigned i = Phi.Ith;
       if (Phi.PN == P && (Phi.PN)->getIncomingValue(i) == Incoming) {
         found = true;
         break;
       }
     }
 
     Instruction *I;
     if (!found && (I = dyn_cast<Instruction>(Incoming)))
       if (!L->hasLoopInvariantOperands(I))
         return false;
 
     ++BI;
   }
 
   for (auto *BB : L->blocks())
     if (any_of(*BB, [](Instruction &I) { return I.mayHaveSideEffects(); }))
       return false;
 
   return true;
 }
 
 //===----------------------------------------------------------------------===//
 //  IV Widening - Extend the width of an IV to cover its widest uses.
 //===----------------------------------------------------------------------===//
 
 namespace {
 // Collect information about induction variables that are used by sign/zero
 // extend operations. This information is recorded by CollectExtend and provides
 // the input to WidenIV.
 struct WideIVInfo {
   PHINode *NarrowIV = nullptr;
   Type *WidestNativeType = nullptr; // Widest integer type created [sz]ext
   bool IsSigned = false;            // Was a sext user seen before a zext?
 };
 }
 
 /// Update information about the induction variable that is extended by this
 /// sign or zero extend operation. This is used to determine the final width of
 /// the IV before actually widening it.
 static void visitIVCast(CastInst *Cast, WideIVInfo &WI, ScalarEvolution *SE,
                         const TargetTransformInfo *TTI) {
   bool IsSigned = Cast->getOpcode() == Instruction::SExt;
   if (!IsSigned && Cast->getOpcode() != Instruction::ZExt)
     return;
 
   Type *Ty = Cast->getType();
   uint64_t Width = SE->getTypeSizeInBits(Ty);
   if (!Cast->getModule()->getDataLayout().isLegalInteger(Width))
     return;
 
   // Check that `Cast` actually extends the induction variable (we rely on this
   // later).  This takes care of cases where `Cast` is extending a truncation of
   // the narrow induction variable, and thus can end up being narrower than the
   // "narrow" induction variable.
   uint64_t NarrowIVWidth = SE->getTypeSizeInBits(WI.NarrowIV->getType());
   if (NarrowIVWidth >= Width)
     return;
 
   // Cast is either an sext or zext up to this point.
   // We should not widen an indvar if arithmetics on the wider indvar are more
   // expensive than those on the narrower indvar. We check only the cost of ADD
   // because at least an ADD is required to increment the induction variable. We
   // could compute more comprehensively the cost of all instructions on the
   // induction variable when necessary.
   if (TTI &&
       TTI->getArithmeticInstrCost(Instruction::Add, Ty) >
           TTI->getArithmeticInstrCost(Instruction::Add,
                                       Cast->getOperand(0)->getType())) {
     return;
   }
 
   if (!WI.WidestNativeType) {
     WI.WidestNativeType = SE->getEffectiveSCEVType(Ty);
     WI.IsSigned = IsSigned;
     return;
   }
 
   // We extend the IV to satisfy the sign of its first user, arbitrarily.
   if (WI.IsSigned != IsSigned)
     return;
 
   if (Width > SE->getTypeSizeInBits(WI.WidestNativeType))
     WI.WidestNativeType = SE->getEffectiveSCEVType(Ty);
 }
 
 namespace {
 
 /// Record a link in the Narrow IV def-use chain along with the WideIV that
 /// computes the same value as the Narrow IV def.  This avoids caching Use*
 /// pointers.
 struct NarrowIVDefUse {
   Instruction *NarrowDef = nullptr;
   Instruction *NarrowUse = nullptr;
   Instruction *WideDef = nullptr;
 
   // True if the narrow def is never negative.  Tracking this information lets
   // us use a sign extension instead of a zero extension or vice versa, when
   // profitable and legal.
   bool NeverNegative = false;
 
   NarrowIVDefUse(Instruction *ND, Instruction *NU, Instruction *WD,
                  bool NeverNegative)
       : NarrowDef(ND), NarrowUse(NU), WideDef(WD),
         NeverNegative(NeverNegative) {}
 };
 
 /// The goal of this transform is to remove sign and zero extends without
 /// creating any new induction variables. To do this, it creates a new phi of
 /// the wider type and redirects all users, either removing extends or inserting
 /// truncs whenever we stop propagating the type.
 ///
 class WidenIV {
   // Parameters
   PHINode *OrigPhi;
   Type *WideType;
   bool IsSigned;
 
   // Context
   LoopInfo        *LI;
   Loop            *L;
   ScalarEvolution *SE;
   DominatorTree   *DT;
 
   // Result
   PHINode *WidePhi;
   Instruction *WideInc;
   const SCEV *WideIncExpr;
   SmallVectorImpl<WeakVH> &DeadInsts;
 
   SmallPtrSet<Instruction*,16> Widened;
   SmallVector<NarrowIVDefUse, 8> NarrowIVUsers;
 
 public:
   WidenIV(const WideIVInfo &WI, LoopInfo *LInfo,
           ScalarEvolution *SEv, DominatorTree *DTree,
           SmallVectorImpl<WeakVH> &DI) :
     OrigPhi(WI.NarrowIV),
     WideType(WI.WidestNativeType),
     IsSigned(WI.IsSigned),
     LI(LInfo),
     L(LI->getLoopFor(OrigPhi->getParent())),
     SE(SEv),
     DT(DTree),
     WidePhi(nullptr),
     WideInc(nullptr),
     WideIncExpr(nullptr),
     DeadInsts(DI) {
     assert(L->getHeader() == OrigPhi->getParent() && "Phi must be an IV");
   }
 
   PHINode *createWideIV(SCEVExpander &Rewriter);
 
 protected:
   Value *createExtendInst(Value *NarrowOper, Type *WideType, bool IsSigned,
                           Instruction *Use);
 
   Instruction *cloneIVUser(NarrowIVDefUse DU, const SCEVAddRecExpr *WideAR);
   Instruction *cloneArithmeticIVUser(NarrowIVDefUse DU,
                                      const SCEVAddRecExpr *WideAR);
   Instruction *cloneBitwiseIVUser(NarrowIVDefUse DU);
 
   const SCEVAddRecExpr *getWideRecurrence(Instruction *NarrowUse);
 
   const SCEVAddRecExpr* getExtendedOperandRecurrence(NarrowIVDefUse DU);
 
   const SCEV *getSCEVByOpCode(const SCEV *LHS, const SCEV *RHS,
                               unsigned OpCode) const;
 
   Instruction *widenIVUse(NarrowIVDefUse DU, SCEVExpander &Rewriter);
 
   bool widenLoopCompare(NarrowIVDefUse DU);
 
   void pushNarrowIVUsers(Instruction *NarrowDef, Instruction *WideDef);
 };
 } // anonymous namespace
 
 /// Perform a quick domtree based check for loop invariance assuming that V is
 /// used within the loop. LoopInfo::isLoopInvariant() seems gratuitous for this
 /// purpose.
 static bool isLoopInvariant(Value *V, const Loop *L, const DominatorTree *DT) {
   Instruction *Inst = dyn_cast<Instruction>(V);
   if (!Inst)
     return true;
 
   return DT->properlyDominates(Inst->getParent(), L->getHeader());
 }
 
 Value *WidenIV::createExtendInst(Value *NarrowOper, Type *WideType,
                                  bool IsSigned, Instruction *Use) {
   // Set the debug location and conservative insertion point.
   IRBuilder<> Builder(Use);
   // Hoist the insertion point into loop preheaders as far as possible.
   for (const Loop *L = LI->getLoopFor(Use->getParent());
        L && L->getLoopPreheader() && isLoopInvariant(NarrowOper, L, DT);
        L = L->getParentLoop())
     Builder.SetInsertPoint(L->getLoopPreheader()->getTerminator());
 
   return IsSigned ? Builder.CreateSExt(NarrowOper, WideType) :
                     Builder.CreateZExt(NarrowOper, WideType);
 }
 
 /// Instantiate a wide operation to replace a narrow operation. This only needs
 /// to handle operations that can evaluation to SCEVAddRec. It can safely return
 /// 0 for any operation we decide not to clone.
 Instruction *WidenIV::cloneIVUser(NarrowIVDefUse DU,
                                   const SCEVAddRecExpr *WideAR) {
   unsigned Opcode = DU.NarrowUse->getOpcode();
   switch (Opcode) {
   default:
     return nullptr;
   case Instruction::Add:
   case Instruction::Mul:
   case Instruction::UDiv:
   case Instruction::Sub:
     return cloneArithmeticIVUser(DU, WideAR);
 
   case Instruction::And:
   case Instruction::Or:
   case Instruction::Xor:
   case Instruction::Shl:
   case Instruction::LShr:
   case Instruction::AShr:
     return cloneBitwiseIVUser(DU);
   }
 }
 
 Instruction *WidenIV::cloneBitwiseIVUser(NarrowIVDefUse DU) {
   Instruction *NarrowUse = DU.NarrowUse;
   Instruction *NarrowDef = DU.NarrowDef;
   Instruction *WideDef = DU.WideDef;
 
   DEBUG(dbgs() << "Cloning bitwise IVUser: " << *NarrowUse << "\n");
 
   // Replace NarrowDef operands with WideDef. Otherwise, we don't know anything
   // about the narrow operand yet so must insert a [sz]ext. It is probably loop
   // invariant and will be folded or hoisted. If it actually comes from a
   // widened IV, it should be removed during a future call to widenIVUse.
   Value *LHS = (NarrowUse->getOperand(0) == NarrowDef)
                    ? WideDef
                    : createExtendInst(NarrowUse->getOperand(0), WideType,
                                       IsSigned, NarrowUse);
   Value *RHS = (NarrowUse->getOperand(1) == NarrowDef)
                    ? WideDef
                    : createExtendInst(NarrowUse->getOperand(1), WideType,
                                       IsSigned, NarrowUse);
 
   auto *NarrowBO = cast<BinaryOperator>(NarrowUse);
   auto *WideBO = BinaryOperator::Create(NarrowBO->getOpcode(), LHS, RHS,
                                         NarrowBO->getName());
   IRBuilder<> Builder(NarrowUse);
   Builder.Insert(WideBO);
   WideBO->copyIRFlags(NarrowBO);
   return WideBO;
 }
 
 Instruction *WidenIV::cloneArithmeticIVUser(NarrowIVDefUse DU,
                                             const SCEVAddRecExpr *WideAR) {
   Instruction *NarrowUse = DU.NarrowUse;
   Instruction *NarrowDef = DU.NarrowDef;
   Instruction *WideDef = DU.WideDef;
 
   DEBUG(dbgs() << "Cloning arithmetic IVUser: " << *NarrowUse << "\n");
 
   unsigned IVOpIdx = (NarrowUse->getOperand(0) == NarrowDef) ? 0 : 1;
 
   // We're trying to find X such that
   //
   //  Widen(NarrowDef `op` NonIVNarrowDef) == WideAR == WideDef `op.wide` X
   //
   // We guess two solutions to X, sext(NonIVNarrowDef) and zext(NonIVNarrowDef),
   // and check using SCEV if any of them are correct.
 
   // Returns true if extending NonIVNarrowDef according to `SignExt` is a
   // correct solution to X.
   auto GuessNonIVOperand = [&](bool SignExt) {
     const SCEV *WideLHS;
     const SCEV *WideRHS;
 
     auto GetExtend = [this, SignExt](const SCEV *S, Type *Ty) {
       if (SignExt)
         return SE->getSignExtendExpr(S, Ty);
       return SE->getZeroExtendExpr(S, Ty);
     };
 
     if (IVOpIdx == 0) {
       WideLHS = SE->getSCEV(WideDef);
       const SCEV *NarrowRHS = SE->getSCEV(NarrowUse->getOperand(1));
       WideRHS = GetExtend(NarrowRHS, WideType);
     } else {
       const SCEV *NarrowLHS = SE->getSCEV(NarrowUse->getOperand(0));
       WideLHS = GetExtend(NarrowLHS, WideType);
       WideRHS = SE->getSCEV(WideDef);
     }
 
     // WideUse is "WideDef `op.wide` X" as described in the comment.
     const SCEV *WideUse = nullptr;
 
     switch (NarrowUse->getOpcode()) {
     default:
       llvm_unreachable("No other possibility!");
 
     case Instruction::Add:
       WideUse = SE->getAddExpr(WideLHS, WideRHS);
       break;
 
     case Instruction::Mul:
       WideUse = SE->getMulExpr(WideLHS, WideRHS);
       break;
 
     case Instruction::UDiv:
       WideUse = SE->getUDivExpr(WideLHS, WideRHS);
       break;
 
     case Instruction::Sub:
       WideUse = SE->getMinusSCEV(WideLHS, WideRHS);
       break;
     }
 
     return WideUse == WideAR;
   };
 
   bool SignExtend = IsSigned;
   if (!GuessNonIVOperand(SignExtend)) {
     SignExtend = !SignExtend;
     if (!GuessNonIVOperand(SignExtend))
       return nullptr;
   }
 
   Value *LHS = (NarrowUse->getOperand(0) == NarrowDef)
                    ? WideDef
                    : createExtendInst(NarrowUse->getOperand(0), WideType,
                                       SignExtend, NarrowUse);
   Value *RHS = (NarrowUse->getOperand(1) == NarrowDef)
                    ? WideDef
                    : createExtendInst(NarrowUse->getOperand(1), WideType,
                                       SignExtend, NarrowUse);
 
   auto *NarrowBO = cast<BinaryOperator>(NarrowUse);
   auto *WideBO = BinaryOperator::Create(NarrowBO->getOpcode(), LHS, RHS,
                                         NarrowBO->getName());
 
   IRBuilder<> Builder(NarrowUse);
   Builder.Insert(WideBO);
   WideBO->copyIRFlags(NarrowBO);
   return WideBO;
 }
 
 const SCEV *WidenIV::getSCEVByOpCode(const SCEV *LHS, const SCEV *RHS,
                                      unsigned OpCode) const {
   if (OpCode == Instruction::Add)
     return SE->getAddExpr(LHS, RHS);
   if (OpCode == Instruction::Sub)
     return SE->getMinusSCEV(LHS, RHS);
   if (OpCode == Instruction::Mul)
     return SE->getMulExpr(LHS, RHS);
 
   llvm_unreachable("Unsupported opcode.");
 }
 
 /// No-wrap operations can transfer sign extension of their result to their
 /// operands. Generate the SCEV value for the widened operation without
 /// actually modifying the IR yet. If the expression after extending the
 /// operands is an AddRec for this loop, return it.
 const SCEVAddRecExpr* WidenIV::getExtendedOperandRecurrence(NarrowIVDefUse DU) {
 
   // Handle the common case of add<nsw/nuw>
   const unsigned OpCode = DU.NarrowUse->getOpcode();
   // Only Add/Sub/Mul instructions supported yet.
   if (OpCode != Instruction::Add && OpCode != Instruction::Sub &&
       OpCode != Instruction::Mul)
     return nullptr;
 
   // One operand (NarrowDef) has already been extended to WideDef. Now determine
   // if extending the other will lead to a recurrence.
   const unsigned ExtendOperIdx =
       DU.NarrowUse->getOperand(0) == DU.NarrowDef ? 1 : 0;
   assert(DU.NarrowUse->getOperand(1-ExtendOperIdx) == DU.NarrowDef && "bad DU");
 
   const SCEV *ExtendOperExpr = nullptr;
   const OverflowingBinaryOperator *OBO =
     cast<OverflowingBinaryOperator>(DU.NarrowUse);
   if (IsSigned && OBO->hasNoSignedWrap())
     ExtendOperExpr = SE->getSignExtendExpr(
       SE->getSCEV(DU.NarrowUse->getOperand(ExtendOperIdx)), WideType);
   else if(!IsSigned && OBO->hasNoUnsignedWrap())
     ExtendOperExpr = SE->getZeroExtendExpr(
       SE->getSCEV(DU.NarrowUse->getOperand(ExtendOperIdx)), WideType);
   else
     return nullptr;
 
   // When creating this SCEV expr, don't apply the current operations NSW or NUW
   // flags. This instruction may be guarded by control flow that the no-wrap
   // behavior depends on. Non-control-equivalent instructions can be mapped to
   // the same SCEV expression, and it would be incorrect to transfer NSW/NUW
   // semantics to those operations.
   const SCEV *lhs = SE->getSCEV(DU.WideDef);
   const SCEV *rhs = ExtendOperExpr;
 
   // Let's swap operands to the initial order for the case of non-commutative
   // operations, like SUB. See PR21014.
   if (ExtendOperIdx == 0)
     std::swap(lhs, rhs);
   const SCEVAddRecExpr *AddRec =
       dyn_cast<SCEVAddRecExpr>(getSCEVByOpCode(lhs, rhs, OpCode));
 
   if (!AddRec || AddRec->getLoop() != L)
     return nullptr;
   return AddRec;
 }
 
 /// Is this instruction potentially interesting for further simplification after
 /// widening it's type? In other words, can the extend be safely hoisted out of
 /// the loop with SCEV reducing the value to a recurrence on the same loop. If
 /// so, return the sign or zero extended recurrence. Otherwise return NULL.
 const SCEVAddRecExpr *WidenIV::getWideRecurrence(Instruction *NarrowUse) {
   if (!SE->isSCEVable(NarrowUse->getType()))
     return nullptr;
 
   const SCEV *NarrowExpr = SE->getSCEV(NarrowUse);
   if (SE->getTypeSizeInBits(NarrowExpr->getType())
       >= SE->getTypeSizeInBits(WideType)) {
     // NarrowUse implicitly widens its operand. e.g. a gep with a narrow
     // index. So don't follow this use.
     return nullptr;
   }
 
   const SCEV *WideExpr = IsSigned ?
     SE->getSignExtendExpr(NarrowExpr, WideType) :
     SE->getZeroExtendExpr(NarrowExpr, WideType);
   const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(WideExpr);
   if (!AddRec || AddRec->getLoop() != L)
     return nullptr;
   return AddRec;
 }
 
 /// This IV user cannot be widen. Replace this use of the original narrow IV
 /// with a truncation of the new wide IV to isolate and eliminate the narrow IV.
 static void truncateIVUse(NarrowIVDefUse DU, DominatorTree *DT, LoopInfo *LI) {
   DEBUG(dbgs() << "INDVARS: Truncate IV " << *DU.WideDef
         << " for user " << *DU.NarrowUse << "\n");
   IRBuilder<> Builder(
       getInsertPointForUses(DU.NarrowUse, DU.NarrowDef, DT, LI));
   Value *Trunc = Builder.CreateTrunc(DU.WideDef, DU.NarrowDef->getType());
   DU.NarrowUse->replaceUsesOfWith(DU.NarrowDef, Trunc);
 }
 
 /// If the narrow use is a compare instruction, then widen the compare
 //  (and possibly the other operand).  The extend operation is hoisted into the
 // loop preheader as far as possible.
 bool WidenIV::widenLoopCompare(NarrowIVDefUse DU) {
   ICmpInst *Cmp = dyn_cast<ICmpInst>(DU.NarrowUse);
   if (!Cmp)
     return false;
 
   // We can legally widen the comparison in the following two cases:
   //
   //  - The signedness of the IV extension and comparison match
   //
   //  - The narrow IV is always positive (and thus its sign extension is equal
   //    to its zero extension).  For instance, let's say we're zero extending
   //    %narrow for the following use
   //
   //      icmp slt i32 %narrow, %val   ... (A)
   //
   //    and %narrow is always positive.  Then
   //
   //      (A) == icmp slt i32 sext(%narrow), sext(%val)
   //          == icmp slt i32 zext(%narrow), sext(%val)
 
   if (!(DU.NeverNegative || IsSigned == Cmp->isSigned()))
     return false;
 
   Value *Op = Cmp->getOperand(Cmp->getOperand(0) == DU.NarrowDef ? 1 : 0);
   unsigned CastWidth = SE->getTypeSizeInBits(Op->getType());
   unsigned IVWidth = SE->getTypeSizeInBits(WideType);
   assert (CastWidth <= IVWidth && "Unexpected width while widening compare.");
 
   // Widen the compare instruction.
   IRBuilder<> Builder(
       getInsertPointForUses(DU.NarrowUse, DU.NarrowDef, DT, LI));
   DU.NarrowUse->replaceUsesOfWith(DU.NarrowDef, DU.WideDef);
 
   // Widen the other operand of the compare, if necessary.
   if (CastWidth < IVWidth) {
     Value *ExtOp = createExtendInst(Op, WideType, Cmp->isSigned(), Cmp);
     DU.NarrowUse->replaceUsesOfWith(Op, ExtOp);
   }
   return true;
 }
 
 /// Determine whether an individual user of the narrow IV can be widened. If so,
 /// return the wide clone of the user.
 Instruction *WidenIV::widenIVUse(NarrowIVDefUse DU, SCEVExpander &Rewriter) {
 
   // Stop traversing the def-use chain at inner-loop phis or post-loop phis.
   if (PHINode *UsePhi = dyn_cast<PHINode>(DU.NarrowUse)) {
     if (LI->getLoopFor(UsePhi->getParent()) != L) {
       // For LCSSA phis, sink the truncate outside the loop.
       // After SimplifyCFG most loop exit targets have a single predecessor.
       // Otherwise fall back to a truncate within the loop.
       if (UsePhi->getNumOperands() != 1)
         truncateIVUse(DU, DT, LI);
       else {
         // Widening the PHI requires us to insert a trunc.  The logical place
         // for this trunc is in the same BB as the PHI.  This is not possible if
         // the BB is terminated by a catchswitch.
         if (isa<CatchSwitchInst>(UsePhi->getParent()->getTerminator()))
           return nullptr;
 
         PHINode *WidePhi =
           PHINode::Create(DU.WideDef->getType(), 1, UsePhi->getName() + ".wide",
                           UsePhi);
         WidePhi->addIncoming(DU.WideDef, UsePhi->getIncomingBlock(0));
         IRBuilder<> Builder(&*WidePhi->getParent()->getFirstInsertionPt());
         Value *Trunc = Builder.CreateTrunc(WidePhi, DU.NarrowDef->getType());
         UsePhi->replaceAllUsesWith(Trunc);
         DeadInsts.emplace_back(UsePhi);
         DEBUG(dbgs() << "INDVARS: Widen lcssa phi " << *UsePhi
               << " to " << *WidePhi << "\n");
       }
       return nullptr;
     }
   }
   // Our raison d'etre! Eliminate sign and zero extension.
   if (IsSigned ? isa<SExtInst>(DU.NarrowUse) : isa<ZExtInst>(DU.NarrowUse)) {
     Value *NewDef = DU.WideDef;
     if (DU.NarrowUse->getType() != WideType) {
       unsigned CastWidth = SE->getTypeSizeInBits(DU.NarrowUse->getType());
       unsigned IVWidth = SE->getTypeSizeInBits(WideType);
       if (CastWidth < IVWidth) {
         // The cast isn't as wide as the IV, so insert a Trunc.
         IRBuilder<> Builder(DU.NarrowUse);
         NewDef = Builder.CreateTrunc(DU.WideDef, DU.NarrowUse->getType());
       }
       else {
         // A wider extend was hidden behind a narrower one. This may induce
         // another round of IV widening in which the intermediate IV becomes
         // dead. It should be very rare.
         DEBUG(dbgs() << "INDVARS: New IV " << *WidePhi
               << " not wide enough to subsume " << *DU.NarrowUse << "\n");
         DU.NarrowUse->replaceUsesOfWith(DU.NarrowDef, DU.WideDef);
         NewDef = DU.NarrowUse;
       }
     }
     if (NewDef != DU.NarrowUse) {
       DEBUG(dbgs() << "INDVARS: eliminating " << *DU.NarrowUse
             << " replaced by " << *DU.WideDef << "\n");
       ++NumElimExt;
       DU.NarrowUse->replaceAllUsesWith(NewDef);
       DeadInsts.emplace_back(DU.NarrowUse);
     }
     // Now that the extend is gone, we want to expose it's uses for potential
     // further simplification. We don't need to directly inform SimplifyIVUsers
     // of the new users, because their parent IV will be processed later as a
     // new loop phi. If we preserved IVUsers analysis, we would also want to
     // push the uses of WideDef here.
 
     // No further widening is needed. The deceased [sz]ext had done it for us.
     return nullptr;
   }
 
   // Does this user itself evaluate to a recurrence after widening?
   const SCEVAddRecExpr *WideAddRec = getWideRecurrence(DU.NarrowUse);
   if (!WideAddRec)
     WideAddRec = getExtendedOperandRecurrence(DU);
 
   if (!WideAddRec) {
     // If use is a loop condition, try to promote the condition instead of
     // truncating the IV first.
     if (widenLoopCompare(DU))
       return nullptr;
 
     // This user does not evaluate to a recurence after widening, so don't
     // follow it. Instead insert a Trunc to kill off the original use,
     // eventually isolating the original narrow IV so it can be removed.
     truncateIVUse(DU, DT, LI);
     return nullptr;
   }
   // Assume block terminators cannot evaluate to a recurrence. We can't to
   // insert a Trunc after a terminator if there happens to be a critical edge.
   assert(DU.NarrowUse != DU.NarrowUse->getParent()->getTerminator() &&
          "SCEV is not expected to evaluate a block terminator");
 
   // Reuse the IV increment that SCEVExpander created as long as it dominates
   // NarrowUse.
   Instruction *WideUse = nullptr;
   if (WideAddRec == WideIncExpr && Rewriter.hoistIVInc(WideInc, DU.NarrowUse))
     WideUse = WideInc;
   else {
     WideUse = cloneIVUser(DU, WideAddRec);
     if (!WideUse)
       return nullptr;
   }
   // Evaluation of WideAddRec ensured that the narrow expression could be
   // extended outside the loop without overflow. This suggests that the wide use
   // evaluates to the same expression as the extended narrow use, but doesn't
   // absolutely guarantee it. Hence the following failsafe check. In rare cases
   // where it fails, we simply throw away the newly created wide use.
   if (WideAddRec != SE->getSCEV(WideUse)) {
     DEBUG(dbgs() << "Wide use expression mismatch: " << *WideUse
           << ": " << *SE->getSCEV(WideUse) << " != " << *WideAddRec << "\n");
     DeadInsts.emplace_back(WideUse);
     return nullptr;
   }
 
   // Returning WideUse pushes it on the worklist.
   return WideUse;
 }
 
 /// Add eligible users of NarrowDef to NarrowIVUsers.
 ///
 void WidenIV::pushNarrowIVUsers(Instruction *NarrowDef, Instruction *WideDef) {
   const SCEV *NarrowSCEV = SE->getSCEV(NarrowDef);
   bool NeverNegative =
       SE->isKnownPredicate(ICmpInst::ICMP_SGE, NarrowSCEV,
                            SE->getConstant(NarrowSCEV->getType(), 0));
   for (User *U : NarrowDef->users()) {
     Instruction *NarrowUser = cast<Instruction>(U);
 
     // Handle data flow merges and bizarre phi cycles.
     if (!Widened.insert(NarrowUser).second)
       continue;
 
     NarrowIVUsers.emplace_back(NarrowDef, NarrowUser, WideDef, NeverNegative);
   }
 }
 
 /// Process a single induction variable. First use the SCEVExpander to create a
 /// wide induction variable that evaluates to the same recurrence as the
 /// original narrow IV. Then use a worklist to forward traverse the narrow IV's
 /// def-use chain. After widenIVUse has processed all interesting IV users, the
 /// narrow IV will be isolated for removal by DeleteDeadPHIs.
 ///
 /// It would be simpler to delete uses as they are processed, but we must avoid
 /// invalidating SCEV expressions.
 ///
 PHINode *WidenIV::createWideIV(SCEVExpander &Rewriter) {
   // Is this phi an induction variable?
   const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(SE->getSCEV(OrigPhi));
   if (!AddRec)
     return nullptr;
 
   // Widen the induction variable expression.
   const SCEV *WideIVExpr = IsSigned ?
     SE->getSignExtendExpr(AddRec, WideType) :
     SE->getZeroExtendExpr(AddRec, WideType);
 
   assert(SE->getEffectiveSCEVType(WideIVExpr->getType()) == WideType &&
          "Expect the new IV expression to preserve its type");
 
   // Can the IV be extended outside the loop without overflow?
   AddRec = dyn_cast<SCEVAddRecExpr>(WideIVExpr);
   if (!AddRec || AddRec->getLoop() != L)
     return nullptr;
 
   // An AddRec must have loop-invariant operands. Since this AddRec is
   // materialized by a loop header phi, the expression cannot have any post-loop
   // operands, so they must dominate the loop header.
   assert(
       SE->properlyDominates(AddRec->getStart(), L->getHeader()) &&
       SE->properlyDominates(AddRec->getStepRecurrence(*SE), L->getHeader()) &&
       "Loop header phi recurrence inputs do not dominate the loop");
 
   // The rewriter provides a value for the desired IV expression. This may
   // either find an existing phi or materialize a new one. Either way, we
   // expect a well-formed cyclic phi-with-increments. i.e. any operand not part
   // of the phi-SCC dominates the loop entry.
   Instruction *InsertPt = &L->getHeader()->front();
   WidePhi = cast<PHINode>(Rewriter.expandCodeFor(AddRec, WideType, InsertPt));
 
   // Remembering the WideIV increment generated by SCEVExpander allows
   // widenIVUse to reuse it when widening the narrow IV's increment. We don't
   // employ a general reuse mechanism because the call above is the only call to
   // SCEVExpander. Henceforth, we produce 1-to-1 narrow to wide uses.
   if (BasicBlock *LatchBlock = L->getLoopLatch()) {
     WideInc =
       cast<Instruction>(WidePhi->getIncomingValueForBlock(LatchBlock));
     WideIncExpr = SE->getSCEV(WideInc);
   }
 
   DEBUG(dbgs() << "Wide IV: " << *WidePhi << "\n");
   ++NumWidened;
 
   // Traverse the def-use chain using a worklist starting at the original IV.
   assert(Widened.empty() && NarrowIVUsers.empty() && "expect initial state" );
 
   Widened.insert(OrigPhi);
   pushNarrowIVUsers(OrigPhi, WidePhi);
 
   while (!NarrowIVUsers.empty()) {
     NarrowIVDefUse DU = NarrowIVUsers.pop_back_val();
 
     // Process a def-use edge. This may replace the use, so don't hold a
     // use_iterator across it.
     Instruction *WideUse = widenIVUse(DU, Rewriter);
 
     // Follow all def-use edges from the previous narrow use.
     if (WideUse)
       pushNarrowIVUsers(DU.NarrowUse, WideUse);
 
     // widenIVUse may have removed the def-use edge.
     if (DU.NarrowDef->use_empty())
       DeadInsts.emplace_back(DU.NarrowDef);
   }
   return WidePhi;
 }
 
 //===----------------------------------------------------------------------===//
 //  Live IV Reduction - Minimize IVs live across the loop.
 //===----------------------------------------------------------------------===//
 
 
 //===----------------------------------------------------------------------===//
 //  Simplification of IV users based on SCEV evaluation.
 //===----------------------------------------------------------------------===//
 
 namespace {
 class IndVarSimplifyVisitor : public IVVisitor {
   ScalarEvolution *SE;
   const TargetTransformInfo *TTI;
   PHINode *IVPhi;
 
 public:
   WideIVInfo WI;
 
   IndVarSimplifyVisitor(PHINode *IV, ScalarEvolution *SCEV,
                         const TargetTransformInfo *TTI,
                         const DominatorTree *DTree)
     : SE(SCEV), TTI(TTI), IVPhi(IV) {
     DT = DTree;
     WI.NarrowIV = IVPhi;
   }
 
   // Implement the interface used by simplifyUsersOfIV.
   void visitCast(CastInst *Cast) override { visitIVCast(Cast, WI, SE, TTI); }
 };
 }
 
 /// Iteratively perform simplification on a worklist of IV users. Each
 /// successive simplification may push more users which may themselves be
 /// candidates for simplification.
 ///
 /// Sign/Zero extend elimination is interleaved with IV simplification.
 ///
 void IndVarSimplify::simplifyAndExtend(Loop *L,
                                        SCEVExpander &Rewriter,
                                        LoopInfo *LI) {
   SmallVector<WideIVInfo, 8> WideIVs;
 
   SmallVector<PHINode*, 8> LoopPhis;
   for (BasicBlock::iterator I = L->getHeader()->begin(); isa<PHINode>(I); ++I) {
     LoopPhis.push_back(cast<PHINode>(I));
   }
   // Each round of simplification iterates through the SimplifyIVUsers worklist
   // for all current phis, then determines whether any IVs can be
   // widened. Widening adds new phis to LoopPhis, inducing another round of
   // simplification on the wide IVs.
   while (!LoopPhis.empty()) {
     // Evaluate as many IV expressions as possible before widening any IVs. This
     // forces SCEV to set no-wrap flags before evaluating sign/zero
     // extension. The first time SCEV attempts to normalize sign/zero extension,
     // the result becomes final. So for the most predictable results, we delay
     // evaluation of sign/zero extend evaluation until needed, and avoid running
     // other SCEV based analysis prior to simplifyAndExtend.
     do {
       PHINode *CurrIV = LoopPhis.pop_back_val();
 
       // Information about sign/zero extensions of CurrIV.
       IndVarSimplifyVisitor Visitor(CurrIV, SE, TTI, DT);
 
       Changed |= simplifyUsersOfIV(CurrIV, SE, DT, LI, DeadInsts, &Visitor);
 
       if (Visitor.WI.WidestNativeType) {
         WideIVs.push_back(Visitor.WI);
       }
     } while(!LoopPhis.empty());
 
     for (; !WideIVs.empty(); WideIVs.pop_back()) {
       WidenIV Widener(WideIVs.back(), LI, SE, DT, DeadInsts);
       if (PHINode *WidePhi = Widener.createWideIV(Rewriter)) {
         Changed = true;
         LoopPhis.push_back(WidePhi);
       }
     }
   }
 }
 
 //===----------------------------------------------------------------------===//
 //  linearFunctionTestReplace and its kin. Rewrite the loop exit condition.
 //===----------------------------------------------------------------------===//
 
 /// Return true if this loop's backedge taken count expression can be safely and
 /// cheaply expanded into an instruction sequence that can be used by
 /// linearFunctionTestReplace.
 ///
 /// TODO: This fails for pointer-type loop counters with greater than one byte
 /// strides, consequently preventing LFTR from running. For the purpose of LFTR
 /// we could skip this check in the case that the LFTR loop counter (chosen by
 /// FindLoopCounter) is also pointer type. Instead, we could directly convert
 /// the loop test to an inequality test by checking the target data's alignment
 /// of element types (given that the initial pointer value originates from or is
 /// used by ABI constrained operation, as opposed to inttoptr/ptrtoint).
 /// However, we don't yet have a strong motivation for converting loop tests
 /// into inequality tests.
 static bool canExpandBackedgeTakenCount(Loop *L, ScalarEvolution *SE,
                                         SCEVExpander &Rewriter) {
   const SCEV *BackedgeTakenCount = SE->getBackedgeTakenCount(L);
   if (isa<SCEVCouldNotCompute>(BackedgeTakenCount) ||
       BackedgeTakenCount->isZero())
     return false;
 
   if (!L->getExitingBlock())
     return false;
 
   // Can't rewrite non-branch yet.
   if (!isa<BranchInst>(L->getExitingBlock()->getTerminator()))
     return false;
 
   if (Rewriter.isHighCostExpansion(BackedgeTakenCount, L))
     return false;
 
   return true;
 }
 
 /// Return the loop header phi IFF IncV adds a loop invariant value to the phi.
 static PHINode *getLoopPhiForCounter(Value *IncV, Loop *L, DominatorTree *DT) {
   Instruction *IncI = dyn_cast<Instruction>(IncV);
   if (!IncI)
     return nullptr;
 
   switch (IncI->getOpcode()) {
   case Instruction::Add:
   case Instruction::Sub:
     break;
   case Instruction::GetElementPtr:
     // An IV counter must preserve its type.
     if (IncI->getNumOperands() == 2)
       break;
   default:
     return nullptr;
   }
 
   PHINode *Phi = dyn_cast<PHINode>(IncI->getOperand(0));
   if (Phi && Phi->getParent() == L->getHeader()) {
     if (isLoopInvariant(IncI->getOperand(1), L, DT))
       return Phi;
     return nullptr;
   }
   if (IncI->getOpcode() == Instruction::GetElementPtr)
     return nullptr;
 
   // Allow add/sub to be commuted.
   Phi = dyn_cast<PHINode>(IncI->getOperand(1));
   if (Phi && Phi->getParent() == L->getHeader()) {
     if (isLoopInvariant(IncI->getOperand(0), L, DT))
       return Phi;
   }
   return nullptr;
 }
 
 /// Return the compare guarding the loop latch, or NULL for unrecognized tests.
 static ICmpInst *getLoopTest(Loop *L) {
   assert(L->getExitingBlock() && "expected loop exit");
 
   BasicBlock *LatchBlock = L->getLoopLatch();
   // Don't bother with LFTR if the loop is not properly simplified.
   if (!LatchBlock)
     return nullptr;
 
   BranchInst *BI = dyn_cast<BranchInst>(L->getExitingBlock()->getTerminator());
   assert(BI && "expected exit branch");
 
   return dyn_cast<ICmpInst>(BI->getCondition());
 }
 
 /// linearFunctionTestReplace policy. Return true unless we can show that the
 /// current exit test is already sufficiently canonical.
 static bool needsLFTR(Loop *L, DominatorTree *DT) {
   // Do LFTR to simplify the exit condition to an ICMP.
   ICmpInst *Cond = getLoopTest(L);
   if (!Cond)
     return true;
 
   // Do LFTR to simplify the exit ICMP to EQ/NE
   ICmpInst::Predicate Pred = Cond->getPredicate();
   if (Pred != ICmpInst::ICMP_NE && Pred != ICmpInst::ICMP_EQ)
     return true;
 
   // Look for a loop invariant RHS
   Value *LHS = Cond->getOperand(0);
   Value *RHS = Cond->getOperand(1);
   if (!isLoopInvariant(RHS, L, DT)) {
     if (!isLoopInvariant(LHS, L, DT))
       return true;
     std::swap(LHS, RHS);
   }
   // Look for a simple IV counter LHS
   PHINode *Phi = dyn_cast<PHINode>(LHS);
   if (!Phi)
     Phi = getLoopPhiForCounter(LHS, L, DT);
 
   if (!Phi)
     return true;
 
   // Do LFTR if PHI node is defined in the loop, but is *not* a counter.
   int Idx = Phi->getBasicBlockIndex(L->getLoopLatch());
   if (Idx < 0)
     return true;
 
   // Do LFTR if the exit condition's IV is *not* a simple counter.
   Value *IncV = Phi->getIncomingValue(Idx);
   return Phi != getLoopPhiForCounter(IncV, L, DT);
 }
 
 /// Recursive helper for hasConcreteDef(). Unfortunately, this currently boils
 /// down to checking that all operands are constant and listing instructions
 /// that may hide undef.
 static bool hasConcreteDefImpl(Value *V, SmallPtrSetImpl<Value*> &Visited,
                                unsigned Depth) {
   if (isa<Constant>(V))
     return !isa<UndefValue>(V);
 
   if (Depth >= 6)
     return false;
 
   // Conservatively handle non-constant non-instructions. For example, Arguments
   // may be undef.
   Instruction *I = dyn_cast<Instruction>(V);
   if (!I)
     return false;
 
   // Load and return values may be undef.
   if(I->mayReadFromMemory() || isa<CallInst>(I) || isa<InvokeInst>(I))
     return false;
 
   // Optimistically handle other instructions.
   for (Value *Op : I->operands()) {
     if (!Visited.insert(Op).second)
       continue;
     if (!hasConcreteDefImpl(Op, Visited, Depth+1))
       return false;
   }
   return true;
 }
 
 /// Return true if the given value is concrete. We must prove that undef can
 /// never reach it.
 ///
 /// TODO: If we decide that this is a good approach to checking for undef, we
 /// may factor it into a common location.
 static bool hasConcreteDef(Value *V) {
   SmallPtrSet<Value*, 8> Visited;
   Visited.insert(V);
   return hasConcreteDefImpl(V, Visited, 0);
 }
 
 /// Return true if this IV has any uses other than the (soon to be rewritten)
 /// loop exit test.
 static bool AlmostDeadIV(PHINode *Phi, BasicBlock *LatchBlock, Value *Cond) {
   int LatchIdx = Phi->getBasicBlockIndex(LatchBlock);
   Value *IncV = Phi->getIncomingValue(LatchIdx);
 
   for (User *U : Phi->users())
     if (U != Cond && U != IncV) return false;
 
   for (User *U : IncV->users())
     if (U != Cond && U != Phi) return false;
   return true;
 }
 
 /// Find an affine IV in canonical form.
 ///
 /// BECount may be an i8* pointer type. The pointer difference is already
 /// valid count without scaling the address stride, so it remains a pointer
 /// expression as far as SCEV is concerned.
 ///
 /// Currently only valid for LFTR. See the comments on hasConcreteDef below.
 ///
 /// FIXME: Accept -1 stride and set IVLimit = IVInit - BECount
 ///
 /// FIXME: Accept non-unit stride as long as SCEV can reduce BECount * Stride.
 /// This is difficult in general for SCEV because of potential overflow. But we
 /// could at least handle constant BECounts.
 static PHINode *FindLoopCounter(Loop *L, const SCEV *BECount,
                                 ScalarEvolution *SE, DominatorTree *DT) {
   uint64_t BCWidth = SE->getTypeSizeInBits(BECount->getType());
 
   Value *Cond =
     cast<BranchInst>(L->getExitingBlock()->getTerminator())->getCondition();
 
   // Loop over all of the PHI nodes, looking for a simple counter.
   PHINode *BestPhi = nullptr;
   const SCEV *BestInit = nullptr;
   BasicBlock *LatchBlock = L->getLoopLatch();
   assert(LatchBlock && "needsLFTR should guarantee a loop latch");
   const DataLayout &DL = L->getHeader()->getModule()->getDataLayout();
 
   for (BasicBlock::iterator I = L->getHeader()->begin(); isa<PHINode>(I); ++I) {
     PHINode *Phi = cast<PHINode>(I);
     if (!SE->isSCEVable(Phi->getType()))
       continue;
 
     // Avoid comparing an integer IV against a pointer Limit.
     if (BECount->getType()->isPointerTy() && !Phi->getType()->isPointerTy())
       continue;
 
     const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(SE->getSCEV(Phi));
     if (!AR || AR->getLoop() != L || !AR->isAffine())
       continue;
 
     // AR may be a pointer type, while BECount is an integer type.
     // AR may be wider than BECount. With eq/ne tests overflow is immaterial.
     // AR may not be a narrower type, or we may never exit.
     uint64_t PhiWidth = SE->getTypeSizeInBits(AR->getType());
     if (PhiWidth < BCWidth || !DL.isLegalInteger(PhiWidth))
       continue;
 
     const SCEV *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(*SE));
     if (!Step || !Step->isOne())
       continue;
 
     int LatchIdx = Phi->getBasicBlockIndex(LatchBlock);
     Value *IncV = Phi->getIncomingValue(LatchIdx);
     if (getLoopPhiForCounter(IncV, L, DT) != Phi)
       continue;
 
     // Avoid reusing a potentially undef value to compute other values that may
     // have originally had a concrete definition.
     if (!hasConcreteDef(Phi)) {
       // We explicitly allow unknown phis as long as they are already used by
       // the loop test. In this case we assume that performing LFTR could not
       // increase the number of undef users.
       if (ICmpInst *Cond = getLoopTest(L)) {
         if (Phi != getLoopPhiForCounter(Cond->getOperand(0), L, DT) &&
             Phi != getLoopPhiForCounter(Cond->getOperand(1), L, DT)) {
           continue;
         }
       }
     }
     const SCEV *Init = AR->getStart();
 
     if (BestPhi && !AlmostDeadIV(BestPhi, LatchBlock, Cond)) {
       // Don't force a live loop counter if another IV can be used.
       if (AlmostDeadIV(Phi, LatchBlock, Cond))
         continue;
 
       // Prefer to count-from-zero. This is a more "canonical" counter form. It
       // also prefers integer to pointer IVs.
       if (BestInit->isZero() != Init->isZero()) {
         if (BestInit->isZero())
           continue;
       }
       // If two IVs both count from zero or both count from nonzero then the
       // narrower is likely a dead phi that has been widened. Use the wider phi
       // to allow the other to be eliminated.
       else if (PhiWidth <= SE->getTypeSizeInBits(BestPhi->getType()))
         continue;
     }
     BestPhi = Phi;
     BestInit = Init;
   }
   return BestPhi;
 }
 
 /// Help linearFunctionTestReplace by generating a value that holds the RHS of
 /// the new loop test.
 static Value *genLoopLimit(PHINode *IndVar, const SCEV *IVCount, Loop *L,
                            SCEVExpander &Rewriter, ScalarEvolution *SE) {
   const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(SE->getSCEV(IndVar));
   assert(AR && AR->getLoop() == L && AR->isAffine() && "bad loop counter");
   const SCEV *IVInit = AR->getStart();
 
   // IVInit may be a pointer while IVCount is an integer when FindLoopCounter
   // finds a valid pointer IV. Sign extend BECount in order to materialize a
   // GEP. Avoid running SCEVExpander on a new pointer value, instead reusing
   // the existing GEPs whenever possible.
   if (IndVar->getType()->isPointerTy() && !IVCount->getType()->isPointerTy()) {
     // IVOffset will be the new GEP offset that is interpreted by GEP as a
     // signed value. IVCount on the other hand represents the loop trip count,
     // which is an unsigned value. FindLoopCounter only allows induction
     // variables that have a positive unit stride of one. This means we don't
     // have to handle the case of negative offsets (yet) and just need to zero
     // extend IVCount.
     Type *OfsTy = SE->getEffectiveSCEVType(IVInit->getType());
     const SCEV *IVOffset = SE->getTruncateOrZeroExtend(IVCount, OfsTy);
 
     // Expand the code for the iteration count.
     assert(SE->isLoopInvariant(IVOffset, L) &&
            "Computed iteration count is not loop invariant!");
     BranchInst *BI = cast<BranchInst>(L->getExitingBlock()->getTerminator());
     Value *GEPOffset = Rewriter.expandCodeFor(IVOffset, OfsTy, BI);
 
     Value *GEPBase = IndVar->getIncomingValueForBlock(L->getLoopPreheader());
     assert(AR->getStart() == SE->getSCEV(GEPBase) && "bad loop counter");
     // We could handle pointer IVs other than i8*, but we need to compensate for
     // gep index scaling. See canExpandBackedgeTakenCount comments.
     assert(SE->getSizeOfExpr(IntegerType::getInt64Ty(IndVar->getContext()),
                              cast<PointerType>(GEPBase->getType())
                                  ->getElementType())->isOne() &&
            "unit stride pointer IV must be i8*");
 
     IRBuilder<> Builder(L->getLoopPreheader()->getTerminator());
     return Builder.CreateGEP(nullptr, GEPBase, GEPOffset, "lftr.limit");
   } else {
     // In any other case, convert both IVInit and IVCount to integers before
     // comparing. This may result in SCEV expension of pointers, but in practice
     // SCEV will fold the pointer arithmetic away as such:
     // BECount = (IVEnd - IVInit - 1) => IVLimit = IVInit (postinc).
     //
     // Valid Cases: (1) both integers is most common; (2) both may be pointers
     // for simple memset-style loops.
     //
     // IVInit integer and IVCount pointer would only occur if a canonical IV
     // were generated on top of case #2, which is not expected.
 
     const SCEV *IVLimit = nullptr;
     // For unit stride, IVCount = Start + BECount with 2's complement overflow.
     // For non-zero Start, compute IVCount here.
     if (AR->getStart()->isZero())
       IVLimit = IVCount;
     else {
       assert(AR->getStepRecurrence(*SE)->isOne() && "only handles unit stride");
       const SCEV *IVInit = AR->getStart();
 
       // For integer IVs, truncate the IV before computing IVInit + BECount.
       if (SE->getTypeSizeInBits(IVInit->getType())
           > SE->getTypeSizeInBits(IVCount->getType()))
         IVInit = SE->getTruncateExpr(IVInit, IVCount->getType());
 
       IVLimit = SE->getAddExpr(IVInit, IVCount);
     }
     // Expand the code for the iteration count.
     BranchInst *BI = cast<BranchInst>(L->getExitingBlock()->getTerminator());
     IRBuilder<> Builder(BI);
     assert(SE->isLoopInvariant(IVLimit, L) &&
            "Computed iteration count is not loop invariant!");
     // Ensure that we generate the same type as IndVar, or a smaller integer
     // type. In the presence of null pointer values, we have an integer type
     // SCEV expression (IVInit) for a pointer type IV value (IndVar).
     Type *LimitTy = IVCount->getType()->isPointerTy() ?
       IndVar->getType() : IVCount->getType();
     return Rewriter.expandCodeFor(IVLimit, LimitTy, BI);
   }
 }
 
 /// This method rewrites the exit condition of the loop to be a canonical !=
 /// comparison against the incremented loop induction variable.  This pass is
 /// able to rewrite the exit tests of any loop where the SCEV analysis can
 /// determine a loop-invariant trip count of the loop, which is actually a much
 /// broader range than just linear tests.
 Value *IndVarSimplify::
 linearFunctionTestReplace(Loop *L,
                           const SCEV *BackedgeTakenCount,
                           PHINode *IndVar,
                           SCEVExpander &Rewriter) {
   assert(canExpandBackedgeTakenCount(L, SE, Rewriter) && "precondition");
 
   // Initialize CmpIndVar and IVCount to their preincremented values.
   Value *CmpIndVar = IndVar;
   const SCEV *IVCount = BackedgeTakenCount;
 
   // If the exiting block is the same as the backedge block, we prefer to
   // compare against the post-incremented value, otherwise we must compare
   // against the preincremented value.
   if (L->getExitingBlock() == L->getLoopLatch()) {
     // Add one to the "backedge-taken" count to get the trip count.
     // This addition may overflow, which is valid as long as the comparison is
     // truncated to BackedgeTakenCount->getType().
     IVCount = SE->getAddExpr(BackedgeTakenCount,
                              SE->getOne(BackedgeTakenCount->getType()));
     // The BackedgeTaken expression contains the number of times that the
     // backedge branches to the loop header.  This is one less than the
     // number of times the loop executes, so use the incremented indvar.
     CmpIndVar = IndVar->getIncomingValueForBlock(L->getExitingBlock());
   }
 
   Value *ExitCnt = genLoopLimit(IndVar, IVCount, L, Rewriter, SE);
   assert(ExitCnt->getType()->isPointerTy() ==
              IndVar->getType()->isPointerTy() &&
          "genLoopLimit missed a cast");
 
   // Insert a new icmp_ne or icmp_eq instruction before the branch.
   BranchInst *BI = cast<BranchInst>(L->getExitingBlock()->getTerminator());
   ICmpInst::Predicate P;
   if (L->contains(BI->getSuccessor(0)))
     P = ICmpInst::ICMP_NE;
   else
     P = ICmpInst::ICMP_EQ;
 
   DEBUG(dbgs() << "INDVARS: Rewriting loop exit condition to:\n"
                << "      LHS:" << *CmpIndVar << '\n'
                << "       op:\t"
                << (P == ICmpInst::ICMP_NE ? "!=" : "==") << "\n"
                << "      RHS:\t" << *ExitCnt << "\n"
                << "  IVCount:\t" << *IVCount << "\n");
 
   IRBuilder<> Builder(BI);
 
   // LFTR can ignore IV overflow and truncate to the width of
   // BECount. This avoids materializing the add(zext(add)) expression.
   unsigned CmpIndVarSize = SE->getTypeSizeInBits(CmpIndVar->getType());
   unsigned ExitCntSize = SE->getTypeSizeInBits(ExitCnt->getType());
   if (CmpIndVarSize > ExitCntSize) {
     const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(SE->getSCEV(IndVar));
     const SCEV *ARStart = AR->getStart();
     const SCEV *ARStep = AR->getStepRecurrence(*SE);
     // For constant IVCount, avoid truncation.
     if (isa<SCEVConstant>(ARStart) && isa<SCEVConstant>(IVCount)) {
       const APInt &Start = cast<SCEVConstant>(ARStart)->getAPInt();
       APInt Count = cast<SCEVConstant>(IVCount)->getAPInt();
       // Note that the post-inc value of BackedgeTakenCount may have overflowed
       // above such that IVCount is now zero.
       if (IVCount != BackedgeTakenCount && Count == 0) {
         Count = APInt::getMaxValue(Count.getBitWidth()).zext(CmpIndVarSize);
         ++Count;
       }
       else
         Count = Count.zext(CmpIndVarSize);
       APInt NewLimit;
       if (cast<SCEVConstant>(ARStep)->getValue()->isNegative())
         NewLimit = Start - Count;
       else
         NewLimit = Start + Count;
       ExitCnt = ConstantInt::get(CmpIndVar->getType(), NewLimit);
 
       DEBUG(dbgs() << "  Widen RHS:\t" << *ExitCnt << "\n");
     } else {
       CmpIndVar = Builder.CreateTrunc(CmpIndVar, ExitCnt->getType(),
                                       "lftr.wideiv");
     }
   }
   Value *Cond = Builder.CreateICmp(P, CmpIndVar, ExitCnt, "exitcond");
   Value *OrigCond = BI->getCondition();
   // It's tempting to use replaceAllUsesWith here to fully replace the old
   // comparison, but that's not immediately safe, since users of the old
   // comparison may not be dominated by the new comparison. Instead, just
   // update the branch to use the new comparison; in the common case this
   // will make old comparison dead.
   BI->setCondition(Cond);
   DeadInsts.push_back(OrigCond);
 
   ++NumLFTR;
   Changed = true;
   return Cond;
 }
 
 //===----------------------------------------------------------------------===//
 //  sinkUnusedInvariants. A late subpass to cleanup loop preheaders.
 //===----------------------------------------------------------------------===//
 
 /// If there's a single exit block, sink any loop-invariant values that
 /// were defined in the preheader but not used inside the loop into the
 /// exit block to reduce register pressure in the loop.
 void IndVarSimplify::sinkUnusedInvariants(Loop *L) {
   BasicBlock *ExitBlock = L->getExitBlock();
   if (!ExitBlock) return;
 
   BasicBlock *Preheader = L->getLoopPreheader();
   if (!Preheader) return;
 
   Instruction *InsertPt = &*ExitBlock->getFirstInsertionPt();
   BasicBlock::iterator I(Preheader->getTerminator());
   while (I != Preheader->begin()) {
     --I;
     // New instructions were inserted at the end of the preheader.
     if (isa<PHINode>(I))
       break;
 
     // Don't move instructions which might have side effects, since the side
     // effects need to complete before instructions inside the loop.  Also don't
     // move instructions which might read memory, since the loop may modify
     // memory. Note that it's okay if the instruction might have undefined
     // behavior: LoopSimplify guarantees that the preheader dominates the exit
     // block.
     if (I->mayHaveSideEffects() || I->mayReadFromMemory())
       continue;
 
     // Skip debug info intrinsics.
     if (isa<DbgInfoIntrinsic>(I))
       continue;
 
     // Skip eh pad instructions.
     if (I->isEHPad())
       continue;
 
     // Don't sink alloca: we never want to sink static alloca's out of the
     // entry block, and correctly sinking dynamic alloca's requires
     // checks for stacksave/stackrestore intrinsics.
     // FIXME: Refactor this check somehow?
     if (isa<AllocaInst>(I))
       continue;
 
     // Determine if there is a use in or before the loop (direct or
     // otherwise).
     bool UsedInLoop = false;
     for (Use &U : I->uses()) {
       Instruction *User = cast<Instruction>(U.getUser());
       BasicBlock *UseBB = User->getParent();
       if (PHINode *P = dyn_cast<PHINode>(User)) {
         unsigned i =
           PHINode::getIncomingValueNumForOperand(U.getOperandNo());
         UseBB = P->getIncomingBlock(i);
       }
       if (UseBB == Preheader || L->contains(UseBB)) {
         UsedInLoop = true;
         break;
       }
     }
 
     // If there is, the def must remain in the preheader.
     if (UsedInLoop)
       continue;
 
     // Otherwise, sink it to the exit block.
     Instruction *ToMove = &*I;
     bool Done = false;
 
     if (I != Preheader->begin()) {
       // Skip debug info intrinsics.
       do {
         --I;
       } while (isa<DbgInfoIntrinsic>(I) && I != Preheader->begin());
 
       if (isa<DbgInfoIntrinsic>(I) && I == Preheader->begin())
         Done = true;
     } else {
       Done = true;
     }
 
     ToMove->moveBefore(InsertPt);
     if (Done) break;
     InsertPt = ToMove;
   }
 }
 
 //===----------------------------------------------------------------------===//
 //  IndVarSimplify driver. Manage several subpasses of IV simplification.
 //===----------------------------------------------------------------------===//
 
 bool IndVarSimplify::run(Loop *L) {
   // We need (and expect!) the incoming loop to be in LCSSA.
   assert(L->isRecursivelyLCSSAForm(*DT) && "LCSSA required to run indvars!");
 
   // If LoopSimplify form is not available, stay out of trouble. Some notes:
   //  - LSR currently only supports LoopSimplify-form loops. Indvars'
   //    canonicalization can be a pessimization without LSR to "clean up"
   //    afterwards.
   //  - We depend on having a preheader; in particular,
   //    Loop::getCanonicalInductionVariable only supports loops with preheaders,
   //    and we're in trouble if we can't find the induction variable even when
   //    we've manually inserted one.
   if (!L->isLoopSimplifyForm())
     return false;
 
   // If there are any floating-point recurrences, attempt to
   // transform them to use integer recurrences.
   rewriteNonIntegerIVs(L);
 
   const SCEV *BackedgeTakenCount = SE->getBackedgeTakenCount(L);
 
   // Create a rewriter object which we'll use to transform the code with.
   SCEVExpander Rewriter(*SE, DL, "indvars");
 #ifndef NDEBUG
   Rewriter.setDebugType(DEBUG_TYPE);
 #endif
 
   // Eliminate redundant IV users.
   //
   // Simplification works best when run before other consumers of SCEV. We
   // attempt to avoid evaluating SCEVs for sign/zero extend operations until
   // other expressions involving loop IVs have been evaluated. This helps SCEV
   // set no-wrap flags before normalizing sign/zero extension.
   Rewriter.disableCanonicalMode();
   simplifyAndExtend(L, Rewriter, LI);
 
   // Check to see if this loop has a computable loop-invariant execution count.
   // If so, this means that we can compute the final value of any expressions
   // that are recurrent in the loop, and substitute the exit values from the
   // loop into any instructions outside of the loop that use the final values of
   // the current expressions.
   //
   if (ReplaceExitValue != NeverRepl &&
       !isa<SCEVCouldNotCompute>(BackedgeTakenCount))
     rewriteLoopExitValues(L, Rewriter);
 
   // Eliminate redundant IV cycles.
   NumElimIV += Rewriter.replaceCongruentIVs(L, DT, DeadInsts);
 
   // If we have a trip count expression, rewrite the loop's exit condition
   // using it.  We can currently only handle loops with a single exit.
   if (canExpandBackedgeTakenCount(L, SE, Rewriter) && needsLFTR(L, DT)) {
     PHINode *IndVar = FindLoopCounter(L, BackedgeTakenCount, SE, DT);
     if (IndVar) {
       // Check preconditions for proper SCEVExpander operation. SCEV does not
       // express SCEVExpander's dependencies, such as LoopSimplify. Instead any
       // pass that uses the SCEVExpander must do it. This does not work well for
       // loop passes because SCEVExpander makes assumptions about all loops,
       // while LoopPassManager only forces the current loop to be simplified.
       //
       // FIXME: SCEV expansion has no way to bail out, so the caller must
       // explicitly check any assumptions made by SCEV. Brittle.
       const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(BackedgeTakenCount);
       if (!AR || AR->getLoop()->getLoopPreheader())
         (void)linearFunctionTestReplace(L, BackedgeTakenCount, IndVar,
                                         Rewriter);
     }
   }
   // Clear the rewriter cache, because values that are in the rewriter's cache
   // can be deleted in the loop below, causing the AssertingVH in the cache to
   // trigger.
   Rewriter.clear();
 
   // Now that we're done iterating through lists, clean up any instructions
   // which are now dead.
   while (!DeadInsts.empty())
     if (Instruction *Inst =
             dyn_cast_or_null<Instruction>(DeadInsts.pop_back_val()))
       RecursivelyDeleteTriviallyDeadInstructions(Inst, TLI);
 
   // The Rewriter may not be used from this point on.
 
   // Loop-invariant instructions in the preheader that aren't used in the
   // loop may be sunk below the loop to reduce register pressure.
   sinkUnusedInvariants(L);
 
   // rewriteFirstIterationLoopExitValues does not rely on the computation of
   // trip count and therefore can further simplify exit values in addition to
   // rewriteLoopExitValues.
   rewriteFirstIterationLoopExitValues(L);
 
   // Clean up dead instructions.
   Changed |= DeleteDeadPHIs(L->getHeader(), TLI);
 
   // Check a post-condition.
   assert(L->isRecursivelyLCSSAForm(*DT) && "Indvars did not preserve LCSSA!");
 
   // Verify that LFTR, and any other change have not interfered with SCEV's
   // ability to compute trip count.
 #ifndef NDEBUG
   if (VerifyIndvars && !isa<SCEVCouldNotCompute>(BackedgeTakenCount)) {
     SE->forgetLoop(L);
     const SCEV *NewBECount = SE->getBackedgeTakenCount(L);
     if (SE->getTypeSizeInBits(BackedgeTakenCount->getType()) <
         SE->getTypeSizeInBits(NewBECount->getType()))
       NewBECount = SE->getTruncateOrNoop(NewBECount,
                                          BackedgeTakenCount->getType());
     else
       BackedgeTakenCount = SE->getTruncateOrNoop(BackedgeTakenCount,
                                                  NewBECount->getType());
     assert(BackedgeTakenCount == NewBECount && "indvars must preserve SCEV");
   }
 #endif
 
   return Changed;
 }
 
 PreservedAnalyses IndVarSimplifyPass::run(Loop &L, AnalysisManager<Loop> &AM) {
   auto &FAM = AM.getResult<FunctionAnalysisManagerLoopProxy>(L).getManager();
   Function *F = L.getHeader()->getParent();
   const DataLayout &DL = F->getParent()->getDataLayout();
 
   auto *LI = FAM.getCachedResult<LoopAnalysis>(*F);
   auto *SE = FAM.getCachedResult<ScalarEvolutionAnalysis>(*F);
   auto *DT = FAM.getCachedResult<DominatorTreeAnalysis>(*F);
 
   assert((LI && SE && DT) &&
          "Analyses required for indvarsimplify not available!");
 
   // Optional analyses.
   auto *TTI = FAM.getCachedResult<TargetIRAnalysis>(*F);
   auto *TLI = FAM.getCachedResult<TargetLibraryAnalysis>(*F);
 
   IndVarSimplify IVS(LI, SE, DT, DL, TLI, TTI);
   if (!IVS.run(&L))
     return PreservedAnalyses::all();
 
   // FIXME: This should also 'preserve the CFG'.
   return getLoopPassPreservedAnalyses();
 }
 
 namespace {
 struct IndVarSimplifyLegacyPass : public LoopPass {
   static char ID; // Pass identification, replacement for typeid
   IndVarSimplifyLegacyPass() : LoopPass(ID) {
     initializeIndVarSimplifyLegacyPassPass(*PassRegistry::getPassRegistry());
   }
 
   bool runOnLoop(Loop *L, LPPassManager &LPM) override {
     if (skipLoop(L))
       return false;
 
     auto *LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
     auto *SE = &getAnalysis<ScalarEvolutionWrapperPass>().getSE();
     auto *DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
     auto *TLIP = getAnalysisIfAvailable<TargetLibraryInfoWrapperPass>();
     auto *TLI = TLIP ? &TLIP->getTLI() : nullptr;
     auto *TTIP = getAnalysisIfAvailable<TargetTransformInfoWrapperPass>();
     auto *TTI = TTIP ? &TTIP->getTTI(*L->getHeader()->getParent()) : nullptr;
     const DataLayout &DL = L->getHeader()->getModule()->getDataLayout();
 
     IndVarSimplify IVS(LI, SE, DT, DL, TLI, TTI);
     return IVS.run(L);
   }
 
   void getAnalysisUsage(AnalysisUsage &AU) const override {
     AU.setPreservesCFG();
     getLoopAnalysisUsage(AU);
   }
 };
 }
 
 char IndVarSimplifyLegacyPass::ID = 0;
 INITIALIZE_PASS_BEGIN(IndVarSimplifyLegacyPass, "indvars",
                       "Induction Variable Simplification", false, false)
 INITIALIZE_PASS_DEPENDENCY(LoopPass)
 INITIALIZE_PASS_END(IndVarSimplifyLegacyPass, "indvars",
                     "Induction Variable Simplification", false, false)
 
 Pass *llvm::createIndVarSimplifyPass() {
   return new IndVarSimplifyLegacyPass();
 }