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+//===- 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/APInt.h"
+#include "llvm/ADT/ArrayRef.h"
+#include "llvm/ADT/DenseMap.h"
+#include "llvm/ADT/DenseMapInfo.h"
+#include "llvm/ADT/FoldingSet.h"
+#include "llvm/ADT/Hashing.h"
+#include "llvm/ADT/Optional.h"
+#include "llvm/ADT/PointerIntPair.h"
+#include "llvm/ADT/SetVector.h"
+#include "llvm/ADT/SmallPtrSet.h"
+#include "llvm/ADT/SmallVector.h"
+#include "llvm/Analysis/LoopInfo.h"
+#include "llvm/IR/ConstantRange.h"
+#include "llvm/IR/Function.h"
+#include "llvm/IR/InstrTypes.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/Casting.h"
+#include "llvm/Support/Compiler.h"
+#include <algorithm>
+#include <cassert>
+#include <cstdint>
+#include <memory>
+#include <utility>
+
+namespace llvm {
+
+class AssumptionCache;
+class BasicBlock;
+class Constant;
+class ConstantInt;
+class DataLayout;
+class DominatorTree;
+class GEPOperator;
+class Instruction;
+class LLVMContext;
+class raw_ostream;
+class ScalarEvolution;
+class SCEVAddRecExpr;
+class SCEVUnknown;
+class StructType;
+class TargetLibraryInfo;
+class Type;
+class Value;
+
+/// 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 = 0;
+
+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) {}
+ SCEV(const SCEV &) = delete;
+ SCEV &operator=(const SCEV &) = delete;
+
+ 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.
+class SCEVEqualPredicate final : public SCEVPredicate {
+ /// We assume that LHS == RHS.
+ const SCEV *LHS;
+ const SCEV *RHS;
+
+public:
+ SCEVEqualPredicate(const FoldingSetNodeIDRef ID, const SCEV *LHS,
+ const SCEV *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 SCEV *getLHS() const { return LHS; }
+
+ /// Returns the right hand side of the equality.
+ const SCEV *getRHS() const { return RHS; }
+
+ /// Methods for support type inquiry through isa, cast, and dyn_cast:
+ static 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 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:
+ using PredicateMap =
+ DenseMap<const SCEV *, SmallVector<const SCEVPredicate *, 4>>;
+
+ /// 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 bool classof(const SCEVPredicate *P) {
+ return P->getKind() == P_Union;
+ }
+};
+
+struct ExitLimitQuery {
+ ExitLimitQuery(const Loop *L, BasicBlock *ExitingBlock, bool AllowPredicates)
+ : L(L), ExitingBlock(ExitingBlock), AllowPredicates(AllowPredicates) {}
+
+ const Loop *L;
+ BasicBlock *ExitingBlock;
+ bool AllowPredicates;
+};
+
+template <> struct DenseMapInfo<ExitLimitQuery> {
+ static inline ExitLimitQuery getEmptyKey() {
+ return ExitLimitQuery(nullptr, nullptr, true);
+ }
+
+ static inline ExitLimitQuery getTombstoneKey() {
+ return ExitLimitQuery(nullptr, nullptr, false);
+ }
+
+ static unsigned getHashValue(ExitLimitQuery Val) {
+ return hash_combine(hash_combine(Val.L, Val.ExitingBlock),
+ Val.AllowPredicates);
+ }
+
+ static bool isEqual(ExitLimitQuery LHS, ExitLimitQuery RHS) {
+ return LHS.L == RHS.L && LHS.ExitingBlock == RHS.ExitingBlock &&
+ LHS.AllowPredicates == RHS.AllowPredicates;
+ }
+};
+
+/// 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);
+ }
+
+ ScalarEvolution(Function &F, TargetLibraryInfo &TLI, AssumptionCache &AC,
+ DominatorTree &DT, LoopInfo &LI);
+ ScalarEvolution(ScalarEvolution &&Arg);
+ ~ScalarEvolution();
+
+ 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);
+
+ /// 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, unsigned Depth = 0);
+ const SCEV *getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth = 0);
+ 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 *getURemExpr(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);
+ }
+
+ /// Checks if \p SymbolicPHI can be rewritten as an AddRecExpr under some
+ /// Predicates. If successful return these <AddRecExpr, Predicates>;
+ /// The function is intended to be called from PSCEV (the caller will decide
+ /// whether to actually add the predicates and carry out the rewrites).
+ Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
+ createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI);
+
+ /// 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 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.
+ /// NOTE: This returns a copy of the reference returned by getRangeRef.
+ ConstantRange getUnsignedRange(const SCEV *S) {
+ return getRangeRef(S, HINT_RANGE_UNSIGNED);
+ }
+
+ /// Determine the min of the unsigned range for a particular SCEV.
+ APInt getUnsignedRangeMin(const SCEV *S) {
+ return getRangeRef(S, HINT_RANGE_UNSIGNED).getUnsignedMin();
+ }
+
+ /// Determine the max of the unsigned range for a particular SCEV.
+ APInt getUnsignedRangeMax(const SCEV *S) {
+ return getRangeRef(S, HINT_RANGE_UNSIGNED).getUnsignedMax();
+ }
+
+ /// Determine the signed range for a particular SCEV.
+ /// NOTE: This returns a copy of the reference returned by getRangeRef.
+ ConstantRange getSignedRange(const SCEV *S) {
+ return getRangeRef(S, HINT_RANGE_SIGNED);
+ }
+
+ /// Determine the min of the signed range for a particular SCEV.
+ APInt getSignedRangeMin(const SCEV *S) {
+ return getRangeRef(S, HINT_RANGE_SIGNED).getSignedMin();
+ }
+
+ /// Determine the max of the signed range for a particular SCEV.
+ APInt getSignedRangeMax(const SCEV *S) {
+ return getRangeRef(S, HINT_RANGE_SIGNED).getSignedMax();
+ }
+
+ /// 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);
+
+ /// Splits SCEV expression \p S into two SCEVs. One of them is obtained from
+ /// \p S by substitution of all AddRec sub-expression related to loop \p L
+ /// with initial value of that SCEV. The second is obtained from \p S by
+ /// substitution of all AddRec sub-expressions related to loop \p L with post
+ /// increment of this AddRec in the loop \p L. In both cases all other AddRec
+ /// sub-expressions (not related to \p L) remain the same.
+ /// If the \p S contains non-invariant unknown SCEV the function returns
+ /// CouldNotCompute SCEV in both values of std::pair.
+ /// For example, for SCEV S={0, +, 1}<L1> + {0, +, 1}<L2> and loop L=L1
+ /// the function returns pair:
+ /// first = {0, +, 1}<L2>
+ /// second = {1, +, 1}<L1> + {0, +, 1}<L2>
+ /// We can see that for the first AddRec sub-expression it was replaced with
+ /// 0 (initial value) for the first element and to {1, +, 1}<L1> (post
+ /// increment value) for the second one. In both cases AddRec expression
+ /// related to L2 remains the same.
+ std::pair<const SCEV *, const SCEV *> SplitIntoInitAndPostInc(const Loop *L,
+ const SCEV *S);
+
+ /// We'd like to check the predicate on every iteration of the most dominated
+ /// loop between loops used in LHS and RHS.
+ /// To do this we use the following list of steps:
+ /// 1. Collect set S all loops on which either LHS or RHS depend.
+ /// 2. If S is non-empty
+ /// a. Let PD be the element of S which is dominated by all other elements.
+ /// b. Let E(LHS) be value of LHS on entry of PD.
+ /// To get E(LHS), we should just take LHS and replace all AddRecs that are
+ /// attached to PD on with their entry values.
+ /// Define E(RHS) in the same way.
+ /// c. Let B(LHS) be value of L on backedge of PD.
+ /// To get B(LHS), we should just take LHS and replace all AddRecs that are
+ /// attached to PD on with their backedge values.
+ /// Define B(RHS) in the same way.
+ /// d. Note that E(LHS) and E(RHS) are automatically available on entry of PD,
+ /// so we can assert on that.
+ /// e. Return true if isLoopEntryGuardedByCond(Pred, E(LHS), E(RHS)) &&
+ /// isLoopBackedgeGuardedByCond(Pred, B(LHS), B(RHS))
+ bool isKnownViaInduction(ICmpInst::Predicate Pred, const SCEV *LHS,
+ const SCEV *RHS);
+
+ /// 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);
+
+ /// Test if the condition described by Pred, LHS, RHS is known to be true on
+ /// every iteration of the loop of the recurrency LHS.
+ bool isKnownOnEveryIteration(ICmpInst::Predicate Pred,
+ const SCEVAddRecExpr *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 SCEV *LHS, const SCEV *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:
+ /// 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 type for HasRecMap.
+ using HasRecMapType = DenseMap<const SCEV *, bool>;
+
+ /// This is a cache to record whether a SCEV contains any scAddRecExpr.
+ HasRecMapType HasRecMap;
+
+ /// The type for ExprValueMap.
+ using ValueOffsetPair = std::pair<Value *, ConstantInt *>;
+ using ExprValueMapType = DenseMap<const SCEV *, SetVector<ValueOffsetPair>>;
+
+ /// 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 type for ValueExprMap.
+ using ValueExprMapType =
+ DenseMap<SCEVCallbackVH, const SCEV *, DenseMapInfo<Value *>>;
+
+ /// 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;
+
+ /// Mark SCEVUnknown Phis currently being processed by getRangeRef.
+ SmallPtrSet<const PHINode *, 6> PendingPhiRanges;
+
+ /// Set to true by isLoopBackedgeGuardedByCond when we're walking the set of
+ /// conditions dominating the backedge of a loop.
+ bool WalkingBEDominatingConds = false;
+
+ /// Set to true by isKnownPredicateViaSplitting when we're trying to prove a
+ /// predicate by splitting it into a set of independent predicates.
+ bool ProvingSplitPredicate = false;
+
+ /// Memoized values for the GetMinTrailingZeros
+ DenseMap<const SCEV *, uint32_t> MinTrailingZerosCache;
+
+ /// Return the Value set from which the SCEV expr is generated.
+ SetVector<ValueOffsetPair> *getSCEVValues(const SCEV *S);
+
+ /// 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
+
+ // Not taken either exactly MaxNotTaken or zero times
+ bool MaxOrZero = false;
+
+ /// 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);
+ }
+
+ bool hasOperand(const SCEV *S) const;
+
+ /// 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;
+
+ explicit ExitNotTakenInfo(PoisoningVH<BasicBlock> ExitingBlock,
+ const SCEV *ExactNotTaken,
+ std::unique_ptr<SCEVUnionPredicate> Predicate)
+ : ExitingBlock(ExitingBlock), ExactNotTaken(ExactNotTaken),
+ Predicate(std::move(Predicate)) {}
+
+ bool hasAlwaysTruePredicate() const {
+ return !Predicate || Predicate->isAlwaysTrue();
+ }
+ };
+
+ /// 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 = false;
+
+ /// \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) {}
+ BackedgeTakenInfo(BackedgeTakenInfo &&) = default;
+ BackedgeTakenInfo &operator=(BackedgeTakenInfo &&) = default;
+
+ using EdgeExitInfo = std::pair<BasicBlock *, ExitLimit>;
+
+ /// 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(const Loop *L, 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.
+ /// NOTE: This returns a reference to an entry in a cache. It must be
+ /// copied if its needed for longer.
+ const ConstantRange &getRangeRef(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.
+ ///
+ /// \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,
+ bool ExitIfTrue, 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, ExitIfTrue, 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;
+ bool ExitIfTrue;
+ bool AllowPredicates;
+
+ public:
+ ExitLimitCache(const Loop *L, bool ExitIfTrue, bool AllowPredicates)
+ : L(L), ExitIfTrue(ExitIfTrue), AllowPredicates(AllowPredicates) {}
+
+ Optional<ExitLimit> find(const Loop *L, Value *ExitCond, bool ExitIfTrue,
+ bool ControlsExit, bool AllowPredicates);
+
+ void insert(const Loop *L, Value *ExitCond, bool ExitIfTrue,
+ bool ControlsExit, bool AllowPredicates, const ExitLimit &EL);
+ };
+
+ using ExitLimitCacheTy = ExitLimitCache;
+
+ ExitLimit computeExitLimitFromCondCached(ExitLimitCacheTy &Cache,
+ const Loop *L, Value *ExitCond,
+ bool ExitIfTrue,
+ bool ControlsExit,
+ bool AllowPredicates);
+ ExitLimit computeExitLimitFromCondImpl(ExitLimitCacheTy &Cache, const Loop *L,
+ Value *ExitCond, bool ExitIfTrue,
+ 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 and ExitIfTrue. 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,
+ bool ExitIfTrue,
+ 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 isKnownViaNonRecursiveReasoning(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);
+
+ /// Similar to createAddRecFromPHI, but with the additional flexibility of
+ /// suggesting runtime overflow checks in case casts are encountered.
+ /// If successful, the analysis records that for this loop, \p SymbolicPHI,
+ /// which is the UnknownSCEV currently representing the PHI, can be rewritten
+ /// into an AddRec, assuming some predicates; The function then returns the
+ /// AddRec and the predicates as a pair, and caches this pair in
+ /// PredicatedSCEVRewrites.
+ /// If the analysis is not successful, a mapping from the \p SymbolicPHI to
+ /// itself (with no predicates) is recorded, and a nullptr with an empty
+ /// predicates vector is returned as a pair.
+ Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
+ createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI);
+
+ /// 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);
+
+ /// Compute the maximum backedge count based on the range of values
+ /// permitted by Start, End, and Stride. This is for loops of the form
+ /// {Start, +, Stride} LT End.
+ ///
+ /// Precondition: the induction variable is known to be positive. We *don't*
+ /// assert these preconditions so please be careful.
+ const SCEV *computeMaxBECountForLT(const SCEV *Start, const SCEV *Stride,
+ const SCEV *End, unsigned BitWidth,
+ bool IsSigned);
+
+ /// 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);
+
+ /// Find all of the loops transitively used in \p S, and fill \p LoopsUsed.
+ /// A loop is considered "used" by an expression if it contains
+ /// an add rec on said loop.
+ void getUsedLoops(const SCEV *S, SmallPtrSetImpl<const Loop *> &LoopsUsed);
+
+ /// Find all of the loops transitively used in \p S, and update \c LoopUsers
+ /// accordingly.
+ void addToLoopUseLists(const SCEV *S);
+
+ FoldingSet<SCEV> UniqueSCEVs;
+ FoldingSet<SCEVPredicate> UniquePreds;
+ BumpPtrAllocator SCEVAllocator;
+
+ /// This maps loops to a list of SCEV expressions that (transitively) use said
+ /// loop.
+ DenseMap<const Loop *, SmallVector<const SCEV *, 4>> LoopUsers;
+
+ /// Cache tentative mappings from UnknownSCEVs in a Loop, to a SCEV expression
+ /// they can be rewritten into under certain predicates.
+ DenseMap<std::pair<const SCEVUnknown *, const Loop *>,
+ std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
+ PredicatedSCEVRewrites;
+
+ /// 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 = nullptr;
+};
+
+/// Analysis pass that exposes the \c ScalarEvolution for a function.
+class ScalarEvolutionAnalysis
+ : public AnalysisInfoMixin<ScalarEvolutionAnalysis> {
+ friend AnalysisInfoMixin<ScalarEvolutionAnalysis>;
+
+ static AnalysisKey Key;
+
+public:
+ using Result = ScalarEvolution;
+
+ 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;
+
+ /// Check if \p AR1 and \p AR2 are equal, while taking into account
+ /// Equal predicates in Preds.
+ bool areAddRecsEqualWithPreds(const SCEVAddRecExpr *AR1,
+ const SCEVAddRecExpr *AR2) 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.
+ using RewriteEntry = std::pair<unsigned, const SCEV *>;
+
+ /// 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 = 0;
+
+ /// The backedge taken count.
+ const SCEV *BackedgeCount = nullptr;
+};
+
+} // end namespace llvm
+
+#endif // LLVM_ANALYSIS_SCALAREVOLUTION_H