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ScalarEvolution.h
2082 lines (1733 loc) · 89.6 KB
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ScalarEvolution.h
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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/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 Loop;
class LoopInfo;
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;
}
};
/// 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,
const 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,
const BasicBlock *ExitingBlock);
/// The terms "backedge taken count" and "exit count" are used
/// interchangeably to refer to the number of times the backedge of a loop
/// has executed before the loop is exited.
enum ExitCountKind {
/// An expression exactly describing the number of times the backedge has
/// executed when a loop is exited.
Exact,
/// A constant which provides an upper bound on the exact trip count.
ConstantMaximum,
};
/// 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, const BasicBlock *ExitingBlock,
ExitCountKind Kind = Exact);
/// 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, ExitCountKind Kind = Exact);
/// 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 getBackedgeTakenCount(L, ConstantMaximum);
}
/// Return a symbolic upper bound for the backedge taken count of the loop.
/// This is more general than getConstantMaxBackedgeTakenCount as it returns
/// an arbitrary expression as opposed to only constants.
const SCEV* computeMaxBackedgeTakenCount(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);
/// 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);