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//===- llvm/Analysis/ScalarEvolution.h - Scalar Evolution -------*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
//
// 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:
// Estimated complexity of this node's expression tree size.
const unsigned short ExpressionSize;
/// 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,
unsigned short ExpressionSize)
: FastID(ID), SCEVType(SCEVTy), ExpressionSize(ExpressionSize) {}
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;
// Returns estimated size of the mathematical expression represented by this
// SCEV. The rules of its calculation are following:
// 1) Size of a SCEV without operands (like constants and SCEVUnknown) is 1;
// 2) Size SCEV with operands Op1, Op2, ..., OpN is calculated by formula:
// (1 + Size(Op1) + ... + Size(OpN)).
// This value gives us an estimation of time we need to traverse through this
// SCEV and all its operands recursively. We may use it to avoid performing
// heavy transformations on SCEVs of excessive size for sake of saving the
// compilation time.
unsigned short getExpressionSize() const {
return ExpressionSize;
}
/// 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 {
friend class ScalarEvolutionsTest;
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, unsigned Depth = 0);
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 *getMinMaxExpr(unsigned Kind,
SmallVectorImpl<const SCEV *> &Operands);
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 *getSMinExpr(SmallVectorImpl<const SCEV *> &Operands);
const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
const SCEV *getUMinExpr(SmallVectorImpl<const SCEV *> &Operands);
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,
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 sign extended.
const SCEV *getTruncateOrSignExtend(const SCEV *V, Type *Ty,
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. 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);
/// Promote the operands to the wider of the types using zero-extension, and
/// then perform a umin operation with them. N-ary function.
const SCEV *getUMinFromMismatchedTypes(SmallVectorImpl<const SCEV *> &Ops);
/// 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);
/// Return the number of times the backedge executes before the given exit
/// would be taken; if not exactly computable, return SCEVCouldNotCompute.
/// For a single exit loop, this value is equivelent to the result of
/// getBackedgeTakenCount. The loop is guaranteed to exit (via *some* exit)
/// before the backedge is executed (ExitCount + 1) times. Note that there
/// is no guarantee about *which* exit is taken on the exiting iteration.
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 *getConstantMaxBackedgeTakenCount(const Loop *L);
/// Return true if the backedge taken count is either the value returned by
/// getConstantMaxBackedgeTakenCount 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 made any change that
// would invalidate SCEV's answers, and the client wants to remove all loop
// information held internally by ScalarEvolution. This is intended to be used
// when the alternative to forget a loop is too expensive (i.e. large loop
// bodies).
void forgetAllLoops();
/// 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 invokes forgetLoop for the outermost loop of the given loop
// \p L, making ScalarEvolution forget about all this subtree. This needs to
// be done whenever we make a transform that may affect the parameters of the
// outer loop, such as exit counts for branches.
void forgetTopmostLoop(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;
// Mark SCEVUnknown Phis currently being processed by isImpliedViaMerge.
SmallPtrSet<const PHINode *, 6> PendingMerges;
/// 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(ArrayRef<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);
/// 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 figure out predicate for Phis which are SCEVUnknown
/// if it is true for every possible incoming value from their respective
/// basic blocks.
bool isImpliedViaMerge(ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS,
const SCEV *FoundLHS, const SCEV *FoundRHS,
unsigned Depth);
/// 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(ArrayRef<const SCEV *> Ops,
SCEV::NoWrapFlags Flags);
/// Get mul expr already created or create a new one.
const SCEV *getOrCreateMulExpr(ArrayRef<const SCEV *> Ops,
SCEV::NoWrapFlags Flags);
// Get addrec expr already created or create a new one.
const SCEV *getOrCreateAddRecExpr(ArrayRef<const SCEV *> Ops,
const Loop *L, SCEV::NoWrapFlags Flags);
/// Return x if \p Val is f(x) where f is a 1-1 function.
const SCEV *stripInjectiveFunctions(const SCEV *Val) const;
/// 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);
/// Try to match the pattern generated by getURemExpr(A, B). If successful,
/// Assign A and B to LHS and RHS, respectively.
bool matchURem(const SCEV *Expr, const SCEV *&LHS, const SCEV *&RHS);
/// Look for a SCEV expression with type `SCEVType` and operands `Ops` in
/// `UniqueSCEVs`.
///
/// The first component of the returned tuple is the SCEV if found and null
/// otherwise. The second component is the `FoldingSetNodeID` that was
/// constructed to look up the SCEV and the third component is the insertion
/// point.
std::tuple<const SCEV *, FoldingSetNodeID, void *>
findExistingSCEVInCache(int SCEVType, ArrayRef<const SCEV *> Ops);
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