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llvm-mirror/include/llvm/Analysis/ScalarEvolution.h
Philip Reames b4f1faa3f8 [SCEV] Revise a method description to match actual behavior [NFC] 
Reword the ScalarEvolution::getExitCount comment in the same terminology as used by getBackedgeTakenCount since they're equivelent for single exit loops.  Also, strengthen the comment to indicate exiting on the exact iteration specified is guaranteed.  Several transforms implicitly rely on this; and the actual implementation checks for it (via dominating latch checks).  So, spell out the guarantee in the comment.

llvm-svn: 363867
2019-06-19 19:23:19 +00:00

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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 {
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 *getMaxBackedgeTakenCount(const Loop *L);
/// Return true if the backedge taken count is either the value returned by
/// getMaxBackedgeTakenCount or zero.
bool isBackedgeTakenCountMaxOrZero(const Loop *L);
/// Return true if the specified loop has an analyzable loop-invariant
/// backedge-taken count.
bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
// This method should be called by the client when it 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
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