//===- 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. LLVM_NODISCARD static SCEVWrapPredicate::IncrementWrapFlags 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); } LLVM_NODISCARD static SCEVWrapPredicate::IncrementWrapFlags 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); } LLVM_NODISCARD static SCEVWrapPredicate::IncrementWrapFlags 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. LLVM_NODISCARD 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. /// /// NB! Unlike other SCEVPredicate sub-classes this class does not live in the /// ScalarEvolution::Preds folding set. This is why the \c add function is sound. 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. LLVM_NODISCARD static SCEV::NoWrapFlags maskFlags(SCEV::NoWrapFlags Flags, int Mask) { return (SCEV::NoWrapFlags)(Flags & Mask); } LLVM_NODISCARD static SCEV::NoWrapFlags setFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OnFlags) { return (SCEV::NoWrapFlags)(Flags | OnFlags); } LLVM_NODISCARD static SCEV::NoWrapFlags 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 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. SmallPtrSet<Value *, 6> 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; /// Memoized values for the GetMinTrailingZeros DenseMap<const SCEV *, uint32_t> MinTrailingZerosCache; /// Private helper method for the GetMinTrailingZeros method uint32_t GetMinTrailingZerosImpl(const SCEV *S); /// 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 *ExactNotTaken; // The exit is not taken exactly this many times const SCEV *MaxNotTaken; // The exit is not taken at most this many times bool MaxOrZero; // Not taken either exactly MaxNotTaken or zero times /// A set of predicate guards for this ExitLimit. The result is only valid /// if all of the predicates in \c Predicates evaluate to 'true' at /// run-time. SmallPtrSet<const SCEVPredicate *, 4> Predicates; void addPredicate(const SCEVPredicate *P) { assert(!isa<SCEVUnionPredicate>(P) && "Only add leaf predicates here!"); Predicates.insert(P); } /*implicit*/ ExitLimit(const SCEV *E); ExitLimit( const SCEV *E, const SCEV *M, bool MaxOrZero, ArrayRef<const SmallPtrSetImpl<const SCEVPredicate *> *> PredSetList); ExitLimit(const SCEV *E, const SCEV *M, bool MaxOrZero, const SmallPtrSetImpl<const SCEVPredicate *> &PredSet); ExitLimit(const SCEV *E, const SCEV *M, bool MaxOrZero); /// Test whether this ExitLimit contains any computed information, or /// whether it's all SCEVCouldNotCompute values. bool hasAnyInfo() const { return !isa<SCEVCouldNotCompute>(ExactNotTaken) || !isa<SCEVCouldNotCompute>(MaxNotTaken); } /// Test whether this ExitLimit contains all information. bool hasFullInfo() const { return !isa<SCEVCouldNotCompute>(ExactNotTaken); } }; /// Information about the number of times a particular loop exit may be /// reached before exiting the loop. struct ExitNotTakenInfo { PoisoningVH<BasicBlock> ExitingBlock; const SCEV *ExactNotTaken; std::unique_ptr<SCEVUnionPredicate> Predicate; bool hasAlwaysTruePredicate() const { return !Predicate || Predicate->isAlwaysTrue(); } explicit ExitNotTakenInfo(PoisoningVH<BasicBlock> ExitingBlock, const SCEV *ExactNotTaken, std::unique_ptr<SCEVUnionPredicate> Predicate) : ExitingBlock(ExitingBlock), ExactNotTaken(ExactNotTaken), Predicate(std::move(Predicate)) {} }; /// 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. SmallVector<ExitNotTakenInfo, 1> ExitNotTaken; /// The pointer part of \c MaxAndComplete is 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. /// /// The integer part of \c MaxAndComplete is a boolean indicating if \c /// ExitNotTaken has an element for every exiting block in the loop. PointerIntPair<const SCEV *, 1> MaxAndComplete; /// True iff the backedge is taken either exactly Max or zero times. bool MaxOrZero; /// \name Helper projection functions on \c MaxAndComplete. /// @{ bool isComplete() const { return MaxAndComplete.getInt(); } const SCEV *getMax() const { return MaxAndComplete.getPointer(); } /// @} public: BackedgeTakenInfo() : MaxAndComplete(nullptr, 0), MaxOrZero(false) {} BackedgeTakenInfo(BackedgeTakenInfo &&) = default; BackedgeTakenInfo &operator=(BackedgeTakenInfo &&) = default; typedef std::pair<BasicBlock *, ExitLimit> EdgeExitInfo; /// Initialize BackedgeTakenInfo from a list of exact exit counts. BackedgeTakenInfo(SmallVectorImpl<EdgeExitInfo> &&ExitCounts, bool Complete, const SCEV *MaxCount, bool MaxOrZero); /// Test whether this BackedgeTakenInfo contains any computed information, /// or whether it's all SCEVCouldNotCompute values. bool hasAnyInfo() const { return !ExitNotTaken.empty() || !isa<SCEVCouldNotCompute>(getMax()); } /// Test whether this BackedgeTakenInfo contains complete information. bool hasFullInfo() const { return isComplete(); } /// Return an expression indicating the exact *backedge-taken* /// count of the loop if it is known or SCEVCouldNotCompute /// otherwise. If execution makes it to the backedge on every /// iteration (i.e. there are no abnormal exists like exception /// throws and thread exits) then this is the number of times the /// loop header will 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 the number of times this backedge is taken is either the /// value returned by getMax or zero. bool isMaxOrZero(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; struct LoopProperties { /// Set to true if the loop contains no instruction that can have side /// effects (i.e. via throwing an exception, volatile or atomic access). bool HasNoAbnormalExits; /// Set to true if the loop 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 HasNoSideEffects; }; /// Cache for \c getLoopProperties. DenseMap<const Loop *, LoopProperties> LoopPropertiesCache; /// Return a \c LoopProperties instance for \p L, creating one if necessary. LoopProperties getLoopProperties(const Loop *L); bool loopHasNoSideEffects(const Loop *L) { return getLoopProperties(L).HasNoSideEffects; } bool loopHasNoAbnormalExits(const Loop *L) { return getLoopProperties(L).HasNoAbnormalExits; } /// 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, ConstantRange CR) { DenseMap<const SCEV *, ConstantRange> &Cache = Hint == HINT_RANGE_UNSIGNED ? UnsignedRanges : SignedRanges; auto Pair = Cache.try_emplace(S, std::move(CR)); if (!Pair.second) Pair.first->second = std::move(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); /// A helper function for createAddRecFromPHI to handle simple cases. const SCEV *createSimpleAffineAddRec(PHINode *PN, Value *BEValueV, Value *StartValueV); /// 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); // Helper functions for computeExitLimitFromCond to avoid exponential time // complexity. class ExitLimitCache { // It may look like we need key on the whole (L, TBB, FBB, ControlsExit, // AllowPredicates) tuple, but recursive calls to // computeExitLimitFromCondCached from computeExitLimitFromCondImpl only // vary the in \c ExitCond and \c ControlsExit parameters. We remember the // initial values of the other values to assert our assumption. SmallDenseMap<PointerIntPair<Value *, 1>, ExitLimit> TripCountMap; const Loop *L; BasicBlock *TBB; BasicBlock *FBB; bool AllowPredicates; public: ExitLimitCache(const Loop *L, BasicBlock *TBB, BasicBlock *FBB, bool AllowPredicates) : L(L), TBB(TBB), FBB(FBB), AllowPredicates(AllowPredicates) {} Optional<ExitLimit> find(const Loop *L, Value *ExitCond, BasicBlock *TBB, BasicBlock *FBB, bool ControlsExit, bool AllowPredicates); void insert(const Loop *L, Value *ExitCond, BasicBlock *TBB, BasicBlock *FBB, bool ControlsExit, bool AllowPredicates, const ExitLimit &EL); }; typedef ExitLimitCache ExitLimitCacheTy; ExitLimit computeExitLimitFromCondCached(ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, BasicBlock *TBB, BasicBlock *FBB, bool ControlsExit, bool AllowPredicates); ExitLimit computeExitLimitFromCondImpl(ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, BasicBlock *TBB, BasicBlock *FBB, bool ControlsExit, bool AllowPredicates); /// 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. Here LHS is an operation that includes FoundLHS as one of its /// arguments. bool isImpliedViaOperations(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const SCEV *FoundLHS, const SCEV *FoundRHS, unsigned Depth = 0); /// Test whether the condition described by Pred, LHS, and RHS is true. /// Use only simple non-recursive types of checks, such as range analysis etc. bool isKnownViaSimpleReasoning(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. 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); /// Compute \p LHS - \p RHS and returns the result as an APInt if it is a /// constant, and None if it isn't. /// /// This is intended to be a cheaper version of getMinusSCEV. We can be /// frugal here since we just bail out of actually constructing and /// canonicalizing an expression in the cases where the result isn't going /// to be a constant. Optional<APInt> computeConstantDifference(const SCEV *LHS, const SCEV *RHS); /// 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 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; // Returns a wider type among {Ty1, Ty2}. Type *getWiderType(Type *Ty1, Type *Ty2) 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<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); typedef SmallDenseMap<std::pair<const SCEV *, Type *>, const SCEV *, 8> ExtendCacheTy; const SCEV *getZeroExtendExpr(const SCEV *Op, Type *Ty); const SCEV *getZeroExtendExprCached(const SCEV *Op, Type *Ty, ExtendCacheTy &Cache); const SCEV *getZeroExtendExprImpl(const SCEV *Op, Type *Ty, ExtendCacheTy &Cache); const SCEV *getSignExtendExpr(const SCEV *Op, Type *Ty); const SCEV *getSignExtendExprCached(const SCEV *Op, Type *Ty, ExtendCacheTy &Cache); const SCEV *getSignExtendExprImpl(const SCEV *Op, Type *Ty, ExtendCacheTy &Cache); const SCEV *getAnyExtendExpr(const SCEV *Op, Type *Ty); const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops, SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap, unsigned Depth = 0); const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS, SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap, unsigned Depth = 0) { SmallVector<const SCEV *, 2> Ops = {LHS, RHS}; return getAddExpr(Ops, Flags, Depth); } const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2, SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap, unsigned Depth = 0) { SmallVector<const SCEV *, 3> Ops = {Op0, Op1, Op2}; return getAddExpr(Ops, Flags, Depth); } const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops, SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap, unsigned Depth = 0); const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS, SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap, unsigned Depth = 0) { SmallVector<const SCEV *, 2> Ops = {LHS, RHS}; return getMulExpr(Ops, Flags, Depth); } const SCEV *getMulExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2, SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap, unsigned Depth = 0) { SmallVector<const SCEV *, 3> Ops = {Op0, Op1, Op2}; return getMulExpr(Ops, Flags, Depth); } 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 GEP The GEP. The indices contained in the GEP itself are ignored, /// instead we use IndexExprs. /// \p IndexExprs The expressions for the indices. const SCEV *getGEPExpr(GEPOperator *GEP, const SmallVectorImpl<const SCEV *> &IndexExprs); 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, unsigned Depth = 0); /// 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(const 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(const Loop *L, BasicBlock *ExitingBlock); /// Returns the upper bound of the loop trip count as a normal unsigned /// value. /// Returns 0 if the trip count is unknown or not constant. unsigned getSmallConstantMaxTripCount(const Loop *L); /// 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(const 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(const 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(const 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, assuming there are no abnormal exists like exception throws. 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); /// When successful, this returns a SCEVConstant that is greater than or equal /// to (i.e. a "conservative over-approximation") of the value returend by /// getBackedgeTakenCount. If such a value cannot be computed, it returns the /// SCEVCouldNotCompute object. const SCEV *getMaxBackedgeTakenCount(const Loop *L); /// Return true if the backedge taken count is either the value returned by /// getMaxBackedgeTakenCount or zero. bool isBackedgeTakenCountMaxOrZero(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, 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 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); /// Determine if the SCEV can be evaluated at loop's entry. It is true if it /// doesn't depend on a SCEVUnknown of an instruction which is dominated by /// the header of loop L. bool isAvailableAtLoopEntry(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); void print(raw_ostream &OS) const; void verify() const; bool invalidate(Function &F, const PreservedAnalyses &PA, FunctionAnalysisManager::Invalidator &Inv); /// 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, SmallPtrSetImpl<const SCEVPredicate *> &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); /// Get add expr already created or create a new one. const SCEV *getOrCreateAddExpr(SmallVectorImpl<const SCEV *> &Ops, SCEV::NoWrapFlags Flags); /// Get mul expr already created or create a new one. const SCEV *getOrCreateMulExpr(SmallVectorImpl<const SCEV *> &Ops, SCEV::NoWrapFlags Flags); 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 AnalysisKey Key; public: typedef ScalarEvolution Result; ScalarEvolution run(Function &F, FunctionAnalysisManager &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, FunctionAnalysisManager &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