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ScalarEvolution.h
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1 //===- llvm/Analysis/ScalarEvolution.h - Scalar Evolution -------*- C++ -*-===//
2 //
3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4 // See https://llvm.org/LICENSE.txt for license information.
5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6 //
7 //===----------------------------------------------------------------------===//
8 //
9 // The ScalarEvolution class is an LLVM pass which can be used to analyze and
10 // categorize scalar expressions in loops. It specializes in recognizing
11 // general induction variables, representing them with the abstract and opaque
12 // SCEV class. Given this analysis, trip counts of loops and other important
13 // properties can be obtained.
14 //
15 // This analysis is primarily useful for induction variable substitution and
16 // strength reduction.
17 //
18 //===----------------------------------------------------------------------===//
19 
20 #ifndef LLVM_ANALYSIS_SCALAREVOLUTION_H
21 #define LLVM_ANALYSIS_SCALAREVOLUTION_H
22 
23 #include "llvm/ADT/APInt.h"
24 #include "llvm/ADT/ArrayRef.h"
25 #include "llvm/ADT/DenseMap.h"
26 #include "llvm/ADT/DenseMapInfo.h"
27 #include "llvm/ADT/FoldingSet.h"
28 #include "llvm/ADT/Hashing.h"
29 #include "llvm/ADT/Optional.h"
31 #include "llvm/ADT/SetVector.h"
32 #include "llvm/ADT/SmallPtrSet.h"
33 #include "llvm/ADT/SmallVector.h"
34 #include "llvm/Analysis/LoopInfo.h"
35 #include "llvm/IR/ConstantRange.h"
36 #include "llvm/IR/Function.h"
37 #include "llvm/IR/InstrTypes.h"
38 #include "llvm/IR/Instructions.h"
39 #include "llvm/IR/Operator.h"
40 #include "llvm/IR/PassManager.h"
41 #include "llvm/IR/ValueHandle.h"
42 #include "llvm/IR/ValueMap.h"
43 #include "llvm/Pass.h"
44 #include "llvm/Support/Allocator.h"
45 #include "llvm/Support/Casting.h"
46 #include "llvm/Support/Compiler.h"
47 #include <algorithm>
48 #include <cassert>
49 #include <cstdint>
50 #include <memory>
51 #include <utility>
52 
53 namespace llvm {
54 
55 class AssumptionCache;
56 class BasicBlock;
57 class Constant;
58 class ConstantInt;
59 class DataLayout;
60 class DominatorTree;
61 class GEPOperator;
62 class Instruction;
63 class LLVMContext;
64 class raw_ostream;
65 class ScalarEvolution;
66 class SCEVAddRecExpr;
67 class SCEVUnknown;
68 class StructType;
69 class TargetLibraryInfo;
70 class Type;
71 class Value;
72 
73 /// This class represents an analyzed expression in the program. These are
74 /// opaque objects that the client is not allowed to do much with directly.
75 ///
76 class SCEV : public FoldingSetNode {
77  friend struct FoldingSetTrait<SCEV>;
78 
79  /// A reference to an Interned FoldingSetNodeID for this node. The
80  /// ScalarEvolution's BumpPtrAllocator holds the data.
81  FoldingSetNodeIDRef FastID;
82 
83  // The SCEV baseclass this node corresponds to
84  const unsigned short SCEVType;
85 
86 protected:
87  // Estimated complexity of this node's expression tree size.
88  const unsigned short ExpressionSize;
89 
90  /// This field is initialized to zero and may be used in subclasses to store
91  /// miscellaneous information.
92  unsigned short SubclassData = 0;
93 
94 public:
95  /// NoWrapFlags are bitfield indices into SubclassData.
96  ///
97  /// Add and Mul expressions may have no-unsigned-wrap <NUW> or
98  /// no-signed-wrap <NSW> properties, which are derived from the IR
99  /// operator. NSW is a misnomer that we use to mean no signed overflow or
100  /// underflow.
101  ///
102  /// AddRec expressions may have a no-self-wraparound <NW> property if, in
103  /// the integer domain, abs(step) * max-iteration(loop) <=
104  /// unsigned-max(bitwidth). This means that the recurrence will never reach
105  /// its start value if the step is non-zero. Computing the same value on
106  /// each iteration is not considered wrapping, and recurrences with step = 0
107  /// are trivially <NW>. <NW> is independent of the sign of step and the
108  /// value the add recurrence starts with.
109  ///
110  /// Note that NUW and NSW are also valid properties of a recurrence, and
111  /// either implies NW. For convenience, NW will be set for a recurrence
112  /// whenever either NUW or NSW are set.
113  enum NoWrapFlags {
114  FlagAnyWrap = 0, // No guarantee.
115  FlagNW = (1 << 0), // No self-wrap.
116  FlagNUW = (1 << 1), // No unsigned wrap.
117  FlagNSW = (1 << 2), // No signed wrap.
118  NoWrapMask = (1 << 3) - 1
119  };
120 
121  explicit SCEV(const FoldingSetNodeIDRef ID, unsigned SCEVTy,
122  unsigned short ExpressionSize)
123  : FastID(ID), SCEVType(SCEVTy), ExpressionSize(ExpressionSize) {}
124  SCEV(const SCEV &) = delete;
125  SCEV &operator=(const SCEV &) = delete;
126 
127  unsigned getSCEVType() const { return SCEVType; }
128 
129  /// Return the LLVM type of this SCEV expression.
130  Type *getType() const;
131 
132  /// Return true if the expression is a constant zero.
133  bool isZero() const;
134 
135  /// Return true if the expression is a constant one.
136  bool isOne() const;
137 
138  /// Return true if the expression is a constant all-ones value.
139  bool isAllOnesValue() const;
140 
141  /// Return true if the specified scev is negated, but not a constant.
142  bool isNonConstantNegative() const;
143 
144  // Returns estimated size of the mathematical expression represented by this
145  // SCEV. The rules of its calculation are following:
146  // 1) Size of a SCEV without operands (like constants and SCEVUnknown) is 1;
147  // 2) Size SCEV with operands Op1, Op2, ..., OpN is calculated by formula:
148  // (1 + Size(Op1) + ... + Size(OpN)).
149  // This value gives us an estimation of time we need to traverse through this
150  // SCEV and all its operands recursively. We may use it to avoid performing
151  // heavy transformations on SCEVs of excessive size for sake of saving the
152  // compilation time.
153  unsigned short getExpressionSize() const {
154  return ExpressionSize;
155  }
156 
157  /// Print out the internal representation of this scalar to the specified
158  /// stream. This should really only be used for debugging purposes.
159  void print(raw_ostream &OS) const;
160 
161  /// This method is used for debugging.
162  void dump() const;
163 };
164 
165 // Specialize FoldingSetTrait for SCEV to avoid needing to compute
166 // temporary FoldingSetNodeID values.
167 template <> struct FoldingSetTrait<SCEV> : DefaultFoldingSetTrait<SCEV> {
168  static void Profile(const SCEV &X, FoldingSetNodeID &ID) { ID = X.FastID; }
169 
170  static bool Equals(const SCEV &X, const FoldingSetNodeID &ID, unsigned IDHash,
171  FoldingSetNodeID &TempID) {
172  return ID == X.FastID;
173  }
174 
175  static unsigned ComputeHash(const SCEV &X, FoldingSetNodeID &TempID) {
176  return X.FastID.ComputeHash();
177  }
178 };
179 
180 inline raw_ostream &operator<<(raw_ostream &OS, const SCEV &S) {
181  S.print(OS);
182  return OS;
183 }
184 
185 /// An object of this class is returned by queries that could not be answered.
186 /// For example, if you ask for the number of iterations of a linked-list
187 /// traversal loop, you will get one of these. None of the standard SCEV
188 /// operations are valid on this class, it is just a marker.
189 struct SCEVCouldNotCompute : public SCEV {
191 
192  /// Methods for support type inquiry through isa, cast, and dyn_cast:
193  static bool classof(const SCEV *S);
194 };
195 
196 /// This class represents an assumption made using SCEV expressions which can
197 /// be checked at run-time.
200 
201  /// A reference to an Interned FoldingSetNodeID for this node. The
202  /// ScalarEvolution's BumpPtrAllocator holds the data.
203  FoldingSetNodeIDRef FastID;
204 
205 public:
206  enum SCEVPredicateKind { P_Union, P_Equal, P_Wrap };
207 
208 protected:
210  ~SCEVPredicate() = default;
211  SCEVPredicate(const SCEVPredicate &) = default;
212  SCEVPredicate &operator=(const SCEVPredicate &) = default;
213 
214 public:
216 
217  SCEVPredicateKind getKind() const { return Kind; }
218 
219  /// Returns the estimated complexity of this predicate. This is roughly
220  /// measured in the number of run-time checks required.
221  virtual unsigned getComplexity() const { return 1; }
222 
223  /// Returns true if the predicate is always true. This means that no
224  /// assumptions were made and nothing needs to be checked at run-time.
225  virtual bool isAlwaysTrue() const = 0;
226 
227  /// Returns true if this predicate implies \p N.
228  virtual bool implies(const SCEVPredicate *N) const = 0;
229 
230  /// Prints a textual representation of this predicate with an indentation of
231  /// \p Depth.
232  virtual void print(raw_ostream &OS, unsigned Depth = 0) const = 0;
233 
234  /// Returns the SCEV to which this predicate applies, or nullptr if this is
235  /// a SCEVUnionPredicate.
236  virtual const SCEV *getExpr() const = 0;
237 };
238 
240  P.print(OS);
241  return OS;
242 }
243 
244 // Specialize FoldingSetTrait for SCEVPredicate to avoid needing to compute
245 // temporary FoldingSetNodeID values.
246 template <>
248  static void Profile(const SCEVPredicate &X, FoldingSetNodeID &ID) {
249  ID = X.FastID;
250  }
251 
252  static bool Equals(const SCEVPredicate &X, const FoldingSetNodeID &ID,
253  unsigned IDHash, FoldingSetNodeID &TempID) {
254  return ID == X.FastID;
255  }
256 
257  static unsigned ComputeHash(const SCEVPredicate &X,
258  FoldingSetNodeID &TempID) {
259  return X.FastID.ComputeHash();
260  }
261 };
262 
263 /// This class represents an assumption that two SCEV expressions are equal,
264 /// and this can be checked at run-time.
265 class SCEVEqualPredicate final : public SCEVPredicate {
266  /// We assume that LHS == RHS.
267  const SCEV *LHS;
268  const SCEV *RHS;
269 
270 public:
271  SCEVEqualPredicate(const FoldingSetNodeIDRef ID, const SCEV *LHS,
272  const SCEV *RHS);
273 
274  /// Implementation of the SCEVPredicate interface
275  bool implies(const SCEVPredicate *N) const override;
276  void print(raw_ostream &OS, unsigned Depth = 0) const override;
277  bool isAlwaysTrue() const override;
278  const SCEV *getExpr() const override;
279 
280  /// Returns the left hand side of the equality.
281  const SCEV *getLHS() const { return LHS; }
282 
283  /// Returns the right hand side of the equality.
284  const SCEV *getRHS() const { return RHS; }
285 
286  /// Methods for support type inquiry through isa, cast, and dyn_cast:
287  static bool classof(const SCEVPredicate *P) {
288  return P->getKind() == P_Equal;
289  }
290 };
291 
292 /// This class represents an assumption made on an AddRec expression. Given an
293 /// affine AddRec expression {a,+,b}, we assume that it has the nssw or nusw
294 /// flags (defined below) in the first X iterations of the loop, where X is a
295 /// SCEV expression returned by getPredicatedBackedgeTakenCount).
296 ///
297 /// Note that this does not imply that X is equal to the backedge taken
298 /// count. This means that if we have a nusw predicate for i32 {0,+,1} with a
299 /// predicated backedge taken count of X, we only guarantee that {0,+,1} has
300 /// nusw in the first X iterations. {0,+,1} may still wrap in the loop if we
301 /// have more than X iterations.
302 class SCEVWrapPredicate final : public SCEVPredicate {
303 public:
304  /// Similar to SCEV::NoWrapFlags, but with slightly different semantics
305  /// for FlagNUSW. The increment is considered to be signed, and a + b
306  /// (where b is the increment) is considered to wrap if:
307  /// zext(a + b) != zext(a) + sext(b)
308  ///
309  /// If Signed is a function that takes an n-bit tuple and maps to the
310  /// integer domain as the tuples value interpreted as twos complement,
311  /// and Unsigned a function that takes an n-bit tuple and maps to the
312  /// integer domain as as the base two value of input tuple, then a + b
313  /// has IncrementNUSW iff:
314  ///
315  /// 0 <= Unsigned(a) + Signed(b) < 2^n
316  ///
317  /// The IncrementNSSW flag has identical semantics with SCEV::FlagNSW.
318  ///
319  /// Note that the IncrementNUSW flag is not commutative: if base + inc
320  /// has IncrementNUSW, then inc + base doesn't neccessarily have this
321  /// property. The reason for this is that this is used for sign/zero
322  /// extending affine AddRec SCEV expressions when a SCEVWrapPredicate is
323  /// assumed. A {base,+,inc} expression is already non-commutative with
324  /// regards to base and inc, since it is interpreted as:
325  /// (((base + inc) + inc) + inc) ...
327  IncrementAnyWrap = 0, // No guarantee.
328  IncrementNUSW = (1 << 0), // No unsigned with signed increment wrap.
329  IncrementNSSW = (1 << 1), // No signed with signed increment wrap
330  // (equivalent with SCEV::NSW)
331  IncrementNoWrapMask = (1 << 2) - 1
332  };
333 
334  /// Convenient IncrementWrapFlags manipulation methods.
338  assert((Flags & IncrementNoWrapMask) == Flags && "Invalid flags value!");
339  assert((OffFlags & IncrementNoWrapMask) == OffFlags &&
340  "Invalid flags value!");
341  return (SCEVWrapPredicate::IncrementWrapFlags)(Flags & ~OffFlags);
342  }
343 
346  assert((Flags & IncrementNoWrapMask) == Flags && "Invalid flags value!");
347  assert((Mask & IncrementNoWrapMask) == Mask && "Invalid mask value!");
348 
350  }
351 
355  assert((Flags & IncrementNoWrapMask) == Flags && "Invalid flags value!");
356  assert((OnFlags & IncrementNoWrapMask) == OnFlags &&
357  "Invalid flags value!");
358 
359  return (SCEVWrapPredicate::IncrementWrapFlags)(Flags | OnFlags);
360  }
361 
362  /// Returns the set of SCEVWrapPredicate no wrap flags implied by a
363  /// SCEVAddRecExpr.
365  getImpliedFlags(const SCEVAddRecExpr *AR, ScalarEvolution &SE);
366 
367 private:
368  const SCEVAddRecExpr *AR;
369  IncrementWrapFlags Flags;
370 
371 public:
373  const SCEVAddRecExpr *AR,
374  IncrementWrapFlags Flags);
375 
376  /// Returns the set assumed no overflow flags.
377  IncrementWrapFlags getFlags() const { return Flags; }
378 
379  /// Implementation of the SCEVPredicate interface
380  const SCEV *getExpr() const override;
381  bool implies(const SCEVPredicate *N) const override;
382  void print(raw_ostream &OS, unsigned Depth = 0) const override;
383  bool isAlwaysTrue() const override;
384 
385  /// Methods for support type inquiry through isa, cast, and dyn_cast:
386  static bool classof(const SCEVPredicate *P) {
387  return P->getKind() == P_Wrap;
388  }
389 };
390 
391 /// This class represents a composition of other SCEV predicates, and is the
392 /// class that most clients will interact with. This is equivalent to a
393 /// logical "AND" of all the predicates in the union.
394 ///
395 /// NB! Unlike other SCEVPredicate sub-classes this class does not live in the
396 /// ScalarEvolution::Preds folding set. This is why the \c add function is sound.
397 class SCEVUnionPredicate final : public SCEVPredicate {
398 private:
399  using PredicateMap =
401 
402  /// Vector with references to all predicates in this union.
404 
405  /// Maps SCEVs to predicates for quick look-ups.
406  PredicateMap SCEVToPreds;
407 
408 public:
410 
412  return Preds;
413  }
414 
415  /// Adds a predicate to this union.
416  void add(const SCEVPredicate *N);
417 
418  /// Returns a reference to a vector containing all predicates which apply to
419  /// \p Expr.
420  ArrayRef<const SCEVPredicate *> getPredicatesForExpr(const SCEV *Expr);
421 
422  /// Implementation of the SCEVPredicate interface
423  bool isAlwaysTrue() const override;
424  bool implies(const SCEVPredicate *N) const override;
425  void print(raw_ostream &OS, unsigned Depth) const override;
426  const SCEV *getExpr() const override;
427 
428  /// We estimate the complexity of a union predicate as the size number of
429  /// predicates in the union.
430  unsigned getComplexity() const override { return Preds.size(); }
431 
432  /// Methods for support type inquiry through isa, cast, and dyn_cast:
433  static bool classof(const SCEVPredicate *P) {
434  return P->getKind() == P_Union;
435  }
436 };
437 
439  ExitLimitQuery(const Loop *L, BasicBlock *ExitingBlock, bool AllowPredicates)
440  : L(L), ExitingBlock(ExitingBlock), AllowPredicates(AllowPredicates) {}
441 
442  const Loop *L;
445 };
446 
447 template <> struct DenseMapInfo<ExitLimitQuery> {
448  static inline ExitLimitQuery getEmptyKey() {
449  return ExitLimitQuery(nullptr, nullptr, true);
450  }
451 
452  static inline ExitLimitQuery getTombstoneKey() {
453  return ExitLimitQuery(nullptr, nullptr, false);
454  }
455 
456  static unsigned getHashValue(ExitLimitQuery Val) {
457  return hash_combine(hash_combine(Val.L, Val.ExitingBlock),
458  Val.AllowPredicates);
459  }
460 
461  static bool isEqual(ExitLimitQuery LHS, ExitLimitQuery RHS) {
462  return LHS.L == RHS.L && LHS.ExitingBlock == RHS.ExitingBlock &&
463  LHS.AllowPredicates == RHS.AllowPredicates;
464  }
465 };
466 
467 /// The main scalar evolution driver. Because client code (intentionally)
468 /// can't do much with the SCEV objects directly, they must ask this class
469 /// for services.
471 public:
472  /// An enum describing the relationship between a SCEV and a loop.
474  LoopVariant, ///< The SCEV is loop-variant (unknown).
475  LoopInvariant, ///< The SCEV is loop-invariant.
476  LoopComputable ///< The SCEV varies predictably with the loop.
477  };
478 
479  /// An enum describing the relationship between a SCEV and a basic block.
481  DoesNotDominateBlock, ///< The SCEV does not dominate the block.
482  DominatesBlock, ///< The SCEV dominates the block.
483  ProperlyDominatesBlock ///< The SCEV properly dominates the block.
484  };
485 
486  /// Convenient NoWrapFlags manipulation that hides enum casts and is
487  /// visible in the ScalarEvolution name space.
489  int Mask) {
490  return (SCEV::NoWrapFlags)(Flags & Mask);
491  }
493  SCEV::NoWrapFlags OnFlags) {
494  return (SCEV::NoWrapFlags)(Flags | OnFlags);
495  }
498  return (SCEV::NoWrapFlags)(Flags & ~OffFlags);
499  }
500 
502  DominatorTree &DT, LoopInfo &LI);
504  ~ScalarEvolution();
505 
506  LLVMContext &getContext() const { return F.getContext(); }
507 
508  /// Test if values of the given type are analyzable within the SCEV
509  /// framework. This primarily includes integer types, and it can optionally
510  /// include pointer types if the ScalarEvolution class has access to
511  /// target-specific information.
512  bool isSCEVable(Type *Ty) const;
513 
514  /// Return the size in bits of the specified type, for which isSCEVable must
515  /// return true.
516  uint64_t getTypeSizeInBits(Type *Ty) const;
517 
518  /// Return a type with the same bitwidth as the given type and which
519  /// represents how SCEV will treat the given type, for which isSCEVable must
520  /// return true. For pointer types, this is the pointer-sized integer type.
521  Type *getEffectiveSCEVType(Type *Ty) const;
522 
523  // Returns a wider type among {Ty1, Ty2}.
524  Type *getWiderType(Type *Ty1, Type *Ty2) const;
525 
526  /// Return true if the SCEV is a scAddRecExpr or it contains
527  /// scAddRecExpr. The result will be cached in HasRecMap.
528  bool containsAddRecurrence(const SCEV *S);
529 
530  /// Erase Value from ValueExprMap and ExprValueMap.
531  void eraseValueFromMap(Value *V);
532 
533  /// Return a SCEV expression for the full generality of the specified
534  /// expression.
535  const SCEV *getSCEV(Value *V);
536 
537  const SCEV *getConstant(ConstantInt *V);
538  const SCEV *getConstant(const APInt &Val);
539  const SCEV *getConstant(Type *Ty, uint64_t V, bool isSigned = false);
540  const SCEV *getTruncateExpr(const SCEV *Op, Type *Ty, unsigned Depth = 0);
541  const SCEV *getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth = 0);
542  const SCEV *getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth = 0);
543  const SCEV *getAnyExtendExpr(const SCEV *Op, Type *Ty);
544  const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
546  unsigned Depth = 0);
547  const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS,
549  unsigned Depth = 0) {
550  SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
551  return getAddExpr(Ops, Flags, Depth);
552  }
553  const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
555  unsigned Depth = 0) {
556  SmallVector<const SCEV *, 3> Ops = {Op0, Op1, Op2};
557  return getAddExpr(Ops, Flags, Depth);
558  }
559  const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
561  unsigned Depth = 0);
562  const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS,
564  unsigned Depth = 0) {
565  SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
566  return getMulExpr(Ops, Flags, Depth);
567  }
568  const SCEV *getMulExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
570  unsigned Depth = 0) {
571  SmallVector<const SCEV *, 3> Ops = {Op0, Op1, Op2};
572  return getMulExpr(Ops, Flags, Depth);
573  }
574  const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
575  const SCEV *getUDivExactExpr(const SCEV *LHS, const SCEV *RHS);
576  const SCEV *getURemExpr(const SCEV *LHS, const SCEV *RHS);
577  const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step, const Loop *L,
578  SCEV::NoWrapFlags Flags);
579  const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
580  const Loop *L, SCEV::NoWrapFlags Flags);
582  const Loop *L, SCEV::NoWrapFlags Flags) {
583  SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
584  return getAddRecExpr(NewOp, L, Flags);
585  }
586 
587  /// Checks if \p SymbolicPHI can be rewritten as an AddRecExpr under some
588  /// Predicates. If successful return these <AddRecExpr, Predicates>;
589  /// The function is intended to be called from PSCEV (the caller will decide
590  /// whether to actually add the predicates and carry out the rewrites).
592  createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI);
593 
594  /// Returns an expression for a GEP
595  ///
596  /// \p GEP The GEP. The indices contained in the GEP itself are ignored,
597  /// instead we use IndexExprs.
598  /// \p IndexExprs The expressions for the indices.
599  const SCEV *getGEPExpr(GEPOperator *GEP,
600  const SmallVectorImpl<const SCEV *> &IndexExprs);
601  const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
602  const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
603  const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
604  const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
605  const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
606  const SCEV *getSMinExpr(SmallVectorImpl<const SCEV *> &Operands);
607  const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
608  const SCEV *getUMinExpr(SmallVectorImpl<const SCEV *> &Operands);
609  const SCEV *getUnknown(Value *V);
610  const SCEV *getCouldNotCompute();
611 
612  /// Return a SCEV for the constant 0 of a specific type.
613  const SCEV *getZero(Type *Ty) { return getConstant(Ty, 0); }
614 
615  /// Return a SCEV for the constant 1 of a specific type.
616  const SCEV *getOne(Type *Ty) { return getConstant(Ty, 1); }
617 
618  /// Return an expression for sizeof AllocTy that is type IntTy
619  const SCEV *getSizeOfExpr(Type *IntTy, Type *AllocTy);
620 
621  /// Return an expression for offsetof on the given field with type IntTy
622  const SCEV *getOffsetOfExpr(Type *IntTy, StructType *STy, unsigned FieldNo);
623 
624  /// Return the SCEV object corresponding to -V.
625  const SCEV *getNegativeSCEV(const SCEV *V,
627 
628  /// Return the SCEV object corresponding to ~V.
629  const SCEV *getNotSCEV(const SCEV *V);
630 
631  /// Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
632  const SCEV *getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
634  unsigned Depth = 0);
635 
636  /// Return a SCEV corresponding to a conversion of the input value to the
637  /// specified type. If the type must be extended, it is zero extended.
638  const SCEV *getTruncateOrZeroExtend(const SCEV *V, Type *Ty,
639  unsigned Depth = 0);
640 
641  /// Return a SCEV corresponding to a conversion of the input value to the
642  /// specified type. If the type must be extended, it is sign extended.
643  const SCEV *getTruncateOrSignExtend(const SCEV *V, Type *Ty,
644  unsigned Depth = 0);
645 
646  /// Return a SCEV corresponding to a conversion of the input value to the
647  /// specified type. If the type must be extended, it is zero extended. The
648  /// conversion must not be narrowing.
649  const SCEV *getNoopOrZeroExtend(const SCEV *V, Type *Ty);
650 
651  /// Return a SCEV corresponding to a conversion of the input value to the
652  /// specified type. If the type must be extended, it is sign extended. The
653  /// conversion must not be narrowing.
654  const SCEV *getNoopOrSignExtend(const SCEV *V, Type *Ty);
655 
656  /// Return a SCEV corresponding to a conversion of the input value to the
657  /// specified type. If the type must be extended, it is extended with
658  /// unspecified bits. The conversion must not be narrowing.
659  const SCEV *getNoopOrAnyExtend(const SCEV *V, Type *Ty);
660 
661  /// Return a SCEV corresponding to a conversion of the input value to the
662  /// specified type. The conversion must not be widening.
663  const SCEV *getTruncateOrNoop(const SCEV *V, Type *Ty);
664 
665  /// Promote the operands to the wider of the types using zero-extension, and
666  /// then perform a umax operation with them.
667  const SCEV *getUMaxFromMismatchedTypes(const SCEV *LHS, const SCEV *RHS);
668 
669  /// Promote the operands to the wider of the types using zero-extension, and
670  /// then perform a umin operation with them.
671  const SCEV *getUMinFromMismatchedTypes(const SCEV *LHS, const SCEV *RHS);
672 
673  /// Promote the operands to the wider of the types using zero-extension, and
674  /// then perform a umin operation with them. N-ary function.
675  const SCEV *getUMinFromMismatchedTypes(SmallVectorImpl<const SCEV *> &Ops);
676 
677  /// Transitively follow the chain of pointer-type operands until reaching a
678  /// SCEV that does not have a single pointer operand. This returns a
679  /// SCEVUnknown pointer for well-formed pointer-type expressions, but corner
680  /// cases do exist.
681  const SCEV *getPointerBase(const SCEV *V);
682 
683  /// Return a SCEV expression for the specified value at the specified scope
684  /// in the program. The L value specifies a loop nest to evaluate the
685  /// expression at, where null is the top-level or a specified loop is
686  /// immediately inside of the loop.
687  ///
688  /// This method can be used to compute the exit value for a variable defined
689  /// in a loop by querying what the value will hold in the parent loop.
690  ///
691  /// In the case that a relevant loop exit value cannot be computed, the
692  /// original value V is returned.
693  const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
694 
695  /// This is a convenience function which does getSCEVAtScope(getSCEV(V), L).
696  const SCEV *getSCEVAtScope(Value *V, const Loop *L);
697 
698  /// Test whether entry to the loop is protected by a conditional between LHS
699  /// and RHS. This is used to help avoid max expressions in loop trip
700  /// counts, and to eliminate casts.
701  bool isLoopEntryGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
702  const SCEV *LHS, const SCEV *RHS);
703 
704  /// Test whether the backedge of the loop is protected by a conditional
705  /// between LHS and RHS. This is used to eliminate casts.
706  bool isLoopBackedgeGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
707  const SCEV *LHS, const SCEV *RHS);
708 
709  /// Returns the maximum trip count of the loop if it is a single-exit
710  /// loop and we can compute a small maximum for that loop.
711  ///
712  /// Implemented in terms of the \c getSmallConstantTripCount overload with
713  /// the single exiting block passed to it. See that routine for details.
714  unsigned getSmallConstantTripCount(const Loop *L);
715 
716  /// Returns the maximum trip count of this loop as a normal unsigned
717  /// value. Returns 0 if the trip count is unknown or not constant. This
718  /// "trip count" assumes that control exits via ExitingBlock. More
719  /// precisely, it is the number of times that control may reach ExitingBlock
720  /// before taking the branch. For loops with multiple exits, it may not be
721  /// the number times that the loop header executes if the loop exits
722  /// prematurely via another branch.
723  unsigned getSmallConstantTripCount(const Loop *L, BasicBlock *ExitingBlock);
724 
725  /// Returns the upper bound of the loop trip count as a normal unsigned
726  /// value.
727  /// Returns 0 if the trip count is unknown or not constant.
728  unsigned getSmallConstantMaxTripCount(const Loop *L);
729 
730  /// Returns the largest constant divisor of the trip count of the
731  /// loop if it is a single-exit loop and we can compute a small maximum for
732  /// that loop.
733  ///
734  /// Implemented in terms of the \c getSmallConstantTripMultiple overload with
735  /// the single exiting block passed to it. See that routine for details.
736  unsigned getSmallConstantTripMultiple(const Loop *L);
737 
738  /// Returns the largest constant divisor of the trip count of this loop as a
739  /// normal unsigned value, if possible. This means that the actual trip
740  /// count is always a multiple of the returned value (don't forget the trip
741  /// count could very well be zero as well!). As explained in the comments
742  /// for getSmallConstantTripCount, this assumes that control exits the loop
743  /// via ExitingBlock.
744  unsigned getSmallConstantTripMultiple(const Loop *L,
745  BasicBlock *ExitingBlock);
746 
747  /// Get the expression for the number of loop iterations for which this loop
748  /// is guaranteed not to exit via ExitingBlock. Otherwise return
749  /// SCEVCouldNotCompute.
750  const SCEV *getExitCount(const Loop *L, BasicBlock *ExitingBlock);
751 
752  /// If the specified loop has a predictable backedge-taken count, return it,
753  /// otherwise return a SCEVCouldNotCompute object. The backedge-taken count is
754  /// the number of times the loop header will be branched to from within the
755  /// loop, assuming there are no abnormal exists like exception throws. This is
756  /// one less than the trip count of the loop, since it doesn't count the first
757  /// iteration, when the header is branched to from outside the loop.
758  ///
759  /// Note that it is not valid to call this method on a loop without a
760  /// loop-invariant backedge-taken count (see
761  /// hasLoopInvariantBackedgeTakenCount).
762  const SCEV *getBackedgeTakenCount(const Loop *L);
763 
764  /// Similar to getBackedgeTakenCount, except it will add a set of
765  /// SCEV predicates to Predicates that are required to be true in order for
766  /// the answer to be correct. Predicates can be checked with run-time
767  /// checks and can be used to perform loop versioning.
768  const SCEV *getPredicatedBackedgeTakenCount(const Loop *L,
769  SCEVUnionPredicate &Predicates);
770 
771  /// When successful, this returns a SCEVConstant that is greater than or equal
772  /// to (i.e. a "conservative over-approximation") of the value returend by
773  /// getBackedgeTakenCount. If such a value cannot be computed, it returns the
774  /// SCEVCouldNotCompute object.
775  const SCEV *getMaxBackedgeTakenCount(const Loop *L);
776 
777  /// Return true if the backedge taken count is either the value returned by
778  /// getMaxBackedgeTakenCount or zero.
779  bool isBackedgeTakenCountMaxOrZero(const Loop *L);
780 
781  /// Return true if the specified loop has an analyzable loop-invariant
782  /// backedge-taken count.
783  bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
784 
785  // This method should be called by the client when it made any change that
786  // would invalidate SCEV's answers, and the client wants to remove all loop
787  // information held internally by ScalarEvolution. This is intended to be used
788  // when the alternative to forget a loop is too expensive (i.e. large loop
789  // bodies).
790  void forgetAllLoops();
791 
792  /// This method should be called by the client when it has changed a loop in
793  /// a way that may effect ScalarEvolution's ability to compute a trip count,
794  /// or if the loop is deleted. This call is potentially expensive for large
795  /// loop bodies.
796  void forgetLoop(const Loop *L);
797 
798  // This method invokes forgetLoop for the outermost loop of the given loop
799  // \p L, making ScalarEvolution forget about all this subtree. This needs to
800  // be done whenever we make a transform that may affect the parameters of the
801  // outer loop, such as exit counts for branches.
802  void forgetTopmostLoop(const Loop *L);
803 
804  /// This method should be called by the client when it has changed a value
805  /// in a way that may effect its value, or which may disconnect it from a
806  /// def-use chain linking it to a loop.
807  void forgetValue(Value *V);
808 
809  /// Called when the client has changed the disposition of values in
810  /// this loop.
811  ///
812  /// We don't have a way to invalidate per-loop dispositions. Clear and
813  /// recompute is simpler.
814  void forgetLoopDispositions(const Loop *L) { LoopDispositions.clear(); }
815 
816  /// Determine the minimum number of zero bits that S is guaranteed to end in
817  /// (at every loop iteration). It is, at the same time, the minimum number
818  /// of times S is divisible by 2. For example, given {4,+,8} it returns 2.
819  /// If S is guaranteed to be 0, it returns the bitwidth of S.
820  uint32_t GetMinTrailingZeros(const SCEV *S);
821 
822  /// Determine the unsigned range for a particular SCEV.
823  /// NOTE: This returns a copy of the reference returned by getRangeRef.
825  return getRangeRef(S, HINT_RANGE_UNSIGNED);
826  }
827 
828  /// Determine the min of the unsigned range for a particular SCEV.
830  return getRangeRef(S, HINT_RANGE_UNSIGNED).getUnsignedMin();
831  }
832 
833  /// Determine the max of the unsigned range for a particular SCEV.
835  return getRangeRef(S, HINT_RANGE_UNSIGNED).getUnsignedMax();
836  }
837 
838  /// Determine the signed range for a particular SCEV.
839  /// NOTE: This returns a copy of the reference returned by getRangeRef.
841  return getRangeRef(S, HINT_RANGE_SIGNED);
842  }
843 
844  /// Determine the min of the signed range for a particular SCEV.
846  return getRangeRef(S, HINT_RANGE_SIGNED).getSignedMin();
847  }
848 
849  /// Determine the max of the signed range for a particular SCEV.
851  return getRangeRef(S, HINT_RANGE_SIGNED).getSignedMax();
852  }
853 
854  /// Test if the given expression is known to be negative.
855  bool isKnownNegative(const SCEV *S);
856 
857  /// Test if the given expression is known to be positive.
858  bool isKnownPositive(const SCEV *S);
859 
860  /// Test if the given expression is known to be non-negative.
861  bool isKnownNonNegative(const SCEV *S);
862 
863  /// Test if the given expression is known to be non-positive.
864  bool isKnownNonPositive(const SCEV *S);
865 
866  /// Test if the given expression is known to be non-zero.
867  bool isKnownNonZero(const SCEV *S);
868 
869  /// Splits SCEV expression \p S into two SCEVs. One of them is obtained from
870  /// \p S by substitution of all AddRec sub-expression related to loop \p L
871  /// with initial value of that SCEV. The second is obtained from \p S by
872  /// substitution of all AddRec sub-expressions related to loop \p L with post
873  /// increment of this AddRec in the loop \p L. In both cases all other AddRec
874  /// sub-expressions (not related to \p L) remain the same.
875  /// If the \p S contains non-invariant unknown SCEV the function returns
876  /// CouldNotCompute SCEV in both values of std::pair.
877  /// For example, for SCEV S={0, +, 1}<L1> + {0, +, 1}<L2> and loop L=L1
878  /// the function returns pair:
879  /// first = {0, +, 1}<L2>
880  /// second = {1, +, 1}<L1> + {0, +, 1}<L2>
881  /// We can see that for the first AddRec sub-expression it was replaced with
882  /// 0 (initial value) for the first element and to {1, +, 1}<L1> (post
883  /// increment value) for the second one. In both cases AddRec expression
884  /// related to L2 remains the same.
885  std::pair<const SCEV *, const SCEV *> SplitIntoInitAndPostInc(const Loop *L,
886  const SCEV *S);
887 
888  /// We'd like to check the predicate on every iteration of the most dominated
889  /// loop between loops used in LHS and RHS.
890  /// To do this we use the following list of steps:
891  /// 1. Collect set S all loops on which either LHS or RHS depend.
892  /// 2. If S is non-empty
893  /// a. Let PD be the element of S which is dominated by all other elements.
894  /// b. Let E(LHS) be value of LHS on entry of PD.
895  /// To get E(LHS), we should just take LHS and replace all AddRecs that are
896  /// attached to PD on with their entry values.
897  /// Define E(RHS) in the same way.
898  /// c. Let B(LHS) be value of L on backedge of PD.
899  /// To get B(LHS), we should just take LHS and replace all AddRecs that are
900  /// attached to PD on with their backedge values.
901  /// Define B(RHS) in the same way.
902  /// d. Note that E(LHS) and E(RHS) are automatically available on entry of PD,
903  /// so we can assert on that.
904  /// e. Return true if isLoopEntryGuardedByCond(Pred, E(LHS), E(RHS)) &&
905  /// isLoopBackedgeGuardedByCond(Pred, B(LHS), B(RHS))
906  bool isKnownViaInduction(ICmpInst::Predicate Pred, const SCEV *LHS,
907  const SCEV *RHS);
908 
909  /// Test if the given expression is known to satisfy the condition described
910  /// by Pred, LHS, and RHS.
911  bool isKnownPredicate(ICmpInst::Predicate Pred, const SCEV *LHS,
912  const SCEV *RHS);
913 
914  /// Test if the condition described by Pred, LHS, RHS is known to be true on
915  /// every iteration of the loop of the recurrency LHS.
916  bool isKnownOnEveryIteration(ICmpInst::Predicate Pred,
917  const SCEVAddRecExpr *LHS, const SCEV *RHS);
918 
919  /// Return true if, for all loop invariant X, the predicate "LHS `Pred` X"
920  /// is monotonically increasing or decreasing. In the former case set
921  /// `Increasing` to true and in the latter case set `Increasing` to false.
922  ///
923  /// A predicate is said to be monotonically increasing if may go from being
924  /// false to being true as the loop iterates, but never the other way
925  /// around. A predicate is said to be monotonically decreasing if may go
926  /// from being true to being false as the loop iterates, but never the other
927  /// way around.
928  bool isMonotonicPredicate(const SCEVAddRecExpr *LHS, ICmpInst::Predicate Pred,
929  bool &Increasing);
930 
931  /// Return true if the result of the predicate LHS `Pred` RHS is loop
932  /// invariant with respect to L. Set InvariantPred, InvariantLHS and
933  /// InvariantLHS so that InvariantLHS `InvariantPred` InvariantRHS is the
934  /// loop invariant form of LHS `Pred` RHS.
935  bool isLoopInvariantPredicate(ICmpInst::Predicate Pred, const SCEV *LHS,
936  const SCEV *RHS, const Loop *L,
937  ICmpInst::Predicate &InvariantPred,
938  const SCEV *&InvariantLHS,
939  const SCEV *&InvariantRHS);
940 
941  /// Simplify LHS and RHS in a comparison with predicate Pred. Return true
942  /// iff any changes were made. If the operands are provably equal or
943  /// unequal, LHS and RHS are set to the same value and Pred is set to either
944  /// ICMP_EQ or ICMP_NE.
945  bool SimplifyICmpOperands(ICmpInst::Predicate &Pred, const SCEV *&LHS,
946  const SCEV *&RHS, unsigned Depth = 0);
947 
948  /// Return the "disposition" of the given SCEV with respect to the given
949  /// loop.
950  LoopDisposition getLoopDisposition(const SCEV *S, const Loop *L);
951 
952  /// Return true if the value of the given SCEV is unchanging in the
953  /// specified loop.
954  bool isLoopInvariant(const SCEV *S, const Loop *L);
955 
956  /// Determine if the SCEV can be evaluated at loop's entry. It is true if it
957  /// doesn't depend on a SCEVUnknown of an instruction which is dominated by
958  /// the header of loop L.
959  bool isAvailableAtLoopEntry(const SCEV *S, const Loop *L);
960 
961  /// Return true if the given SCEV changes value in a known way in the
962  /// specified loop. This property being true implies that the value is
963  /// variant in the loop AND that we can emit an expression to compute the
964  /// value of the expression at any particular loop iteration.
965  bool hasComputableLoopEvolution(const SCEV *S, const Loop *L);
966 
967  /// Return the "disposition" of the given SCEV with respect to the given
968  /// block.
969  BlockDisposition getBlockDisposition(const SCEV *S, const BasicBlock *BB);
970 
971  /// Return true if elements that makes up the given SCEV dominate the
972  /// specified basic block.
973  bool dominates(const SCEV *S, const BasicBlock *BB);
974 
975  /// Return true if elements that makes up the given SCEV properly dominate
976  /// the specified basic block.
977  bool properlyDominates(const SCEV *S, const BasicBlock *BB);
978 
979  /// Test whether the given SCEV has Op as a direct or indirect operand.
980  bool hasOperand(const SCEV *S, const SCEV *Op) const;
981 
982  /// Return the size of an element read or written by Inst.
983  const SCEV *getElementSize(Instruction *Inst);
984 
985  /// Compute the array dimensions Sizes from the set of Terms extracted from
986  /// the memory access function of this SCEVAddRecExpr (second step of
987  /// delinearization).
988  void findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
990  const SCEV *ElementSize);
991 
992  void print(raw_ostream &OS) const;
993  void verify() const;
994  bool invalidate(Function &F, const PreservedAnalyses &PA,
996 
997  /// Collect parametric terms occurring in step expressions (first step of
998  /// delinearization).
999  void collectParametricTerms(const SCEV *Expr,
1001 
1002  /// Return in Subscripts the access functions for each dimension in Sizes
1003  /// (third step of delinearization).
1004  void computeAccessFunctions(const SCEV *Expr,
1005  SmallVectorImpl<const SCEV *> &Subscripts,
1007 
1008  /// Split this SCEVAddRecExpr into two vectors of SCEVs representing the
1009  /// subscripts and sizes of an array access.
1010  ///
1011  /// The delinearization is a 3 step process: the first two steps compute the
1012  /// sizes of each subscript and the third step computes the access functions
1013  /// for the delinearized array:
1014  ///
1015  /// 1. Find the terms in the step functions
1016  /// 2. Compute the array size
1017  /// 3. Compute the access function: divide the SCEV by the array size
1018  /// starting with the innermost dimensions found in step 2. The Quotient
1019  /// is the SCEV to be divided in the next step of the recursion. The
1020  /// Remainder is the subscript of the innermost dimension. Loop over all
1021  /// array dimensions computed in step 2.
1022  ///
1023  /// To compute a uniform array size for several memory accesses to the same
1024  /// object, one can collect in step 1 all the step terms for all the memory
1025  /// accesses, and compute in step 2 a unique array shape. This guarantees
1026  /// that the array shape will be the same across all memory accesses.
1027  ///
1028  /// FIXME: We could derive the result of steps 1 and 2 from a description of
1029  /// the array shape given in metadata.
1030  ///
1031  /// Example:
1032  ///
1033  /// A[][n][m]
1034  ///
1035  /// for i
1036  /// for j
1037  /// for k
1038  /// A[j+k][2i][5i] =
1039  ///
1040  /// The initial SCEV:
1041  ///
1042  /// A[{{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k]
1043  ///
1044  /// 1. Find the different terms in the step functions:
1045  /// -> [2*m, 5, n*m, n*m]
1046  ///
1047  /// 2. Compute the array size: sort and unique them
1048  /// -> [n*m, 2*m, 5]
1049  /// find the GCD of all the terms = 1
1050  /// divide by the GCD and erase constant terms
1051  /// -> [n*m, 2*m]
1052  /// GCD = m
1053  /// divide by GCD -> [n, 2]
1054  /// remove constant terms
1055  /// -> [n]
1056  /// size of the array is A[unknown][n][m]
1057  ///
1058  /// 3. Compute the access function
1059  /// a. Divide {{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k by the innermost size m
1060  /// Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k
1061  /// Remainder: {{{0,+,5}_i, +, 0}_j, +, 0}_k
1062  /// The remainder is the subscript of the innermost array dimension: [5i].
1063  ///
1064  /// b. Divide Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k by next outer size n
1065  /// Quotient: {{{0,+,0}_i, +, 1}_j, +, 1}_k
1066  /// Remainder: {{{0,+,2}_i, +, 0}_j, +, 0}_k
1067  /// The Remainder is the subscript of the next array dimension: [2i].
1068  ///
1069  /// The subscript of the outermost dimension is the Quotient: [j+k].
1070  ///
1071  /// Overall, we have: A[][n][m], and the access function: A[j+k][2i][5i].
1072  void delinearize(const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
1074  const SCEV *ElementSize);
1075 
1076  /// Return the DataLayout associated with the module this SCEV instance is
1077  /// operating on.
1078  const DataLayout &getDataLayout() const {
1079  return F.getParent()->getDataLayout();
1080  }
1081 
1082  const SCEVPredicate *getEqualPredicate(const SCEV *LHS, const SCEV *RHS);
1083 
1084  const SCEVPredicate *
1085  getWrapPredicate(const SCEVAddRecExpr *AR,
1087 
1088  /// Re-writes the SCEV according to the Predicates in \p A.
1089  const SCEV *rewriteUsingPredicate(const SCEV *S, const Loop *L,
1090  SCEVUnionPredicate &A);
1091  /// Tries to convert the \p S expression to an AddRec expression,
1092  /// adding additional predicates to \p Preds as required.
1093  const SCEVAddRecExpr *convertSCEVToAddRecWithPredicates(
1094  const SCEV *S, const Loop *L,
1096 
1097 private:
1098  /// A CallbackVH to arrange for ScalarEvolution to be notified whenever a
1099  /// Value is deleted.
1100  class SCEVCallbackVH final : public CallbackVH {
1101  ScalarEvolution *SE;
1102 
1103  void deleted() override;
1104  void allUsesReplacedWith(Value *New) override;
1105 
1106  public:
1107  SCEVCallbackVH(Value *V, ScalarEvolution *SE = nullptr);
1108  };
1109 
1110  friend class SCEVCallbackVH;
1111  friend class SCEVExpander;
1112  friend class SCEVUnknown;
1113 
1114  /// The function we are analyzing.
1115  Function &F;
1116 
1117  /// Does the module have any calls to the llvm.experimental.guard intrinsic
1118  /// at all? If this is false, we avoid doing work that will only help if
1119  /// thare are guards present in the IR.
1120  bool HasGuards;
1121 
1122  /// The target library information for the target we are targeting.
1123  TargetLibraryInfo &TLI;
1124 
1125  /// The tracker for \@llvm.assume intrinsics in this function.
1126  AssumptionCache &AC;
1127 
1128  /// The dominator tree.
1129  DominatorTree &DT;
1130 
1131  /// The loop information for the function we are currently analyzing.
1132  LoopInfo &LI;
1133 
1134  /// This SCEV is used to represent unknown trip counts and things.
1135  std::unique_ptr<SCEVCouldNotCompute> CouldNotCompute;
1136 
1137  /// The type for HasRecMap.
1139 
1140  /// This is a cache to record whether a SCEV contains any scAddRecExpr.
1141  HasRecMapType HasRecMap;
1142 
1143  /// The type for ExprValueMap.
1144  using ValueOffsetPair = std::pair<Value *, ConstantInt *>;
1146 
1147  /// ExprValueMap -- This map records the original values from which
1148  /// the SCEV expr is generated from.
1149  ///
1150  /// We want to represent the mapping as SCEV -> ValueOffsetPair instead
1151  /// of SCEV -> Value:
1152  /// Suppose we know S1 expands to V1, and
1153  /// S1 = S2 + C_a
1154  /// S3 = S2 + C_b
1155  /// where C_a and C_b are different SCEVConstants. Then we'd like to
1156  /// expand S3 as V1 - C_a + C_b instead of expanding S2 literally.
1157  /// It is helpful when S2 is a complex SCEV expr.
1158  ///
1159  /// In order to do that, we represent ExprValueMap as a mapping from
1160  /// SCEV to ValueOffsetPair. We will save both S1->{V1, 0} and
1161  /// S2->{V1, C_a} into the map when we create SCEV for V1. When S3
1162  /// is expanded, it will first expand S2 to V1 - C_a because of
1163  /// S2->{V1, C_a} in the map, then expand S3 to V1 - C_a + C_b.
1164  ///
1165  /// Note: S->{V, Offset} in the ExprValueMap means S can be expanded
1166  /// to V - Offset.
1167  ExprValueMapType ExprValueMap;
1168 
1169  /// The type for ValueExprMap.
1170  using ValueExprMapType =
1172 
1173  /// This is a cache of the values we have analyzed so far.
1174  ValueExprMapType ValueExprMap;
1175 
1176  /// Mark predicate values currently being processed by isImpliedCond.
1177  SmallPtrSet<Value *, 6> PendingLoopPredicates;
1178 
1179  /// Mark SCEVUnknown Phis currently being processed by getRangeRef.
1180  SmallPtrSet<const PHINode *, 6> PendingPhiRanges;
1181 
1182  // Mark SCEVUnknown Phis currently being processed by isImpliedViaMerge.
1183  SmallPtrSet<const PHINode *, 6> PendingMerges;
1184 
1185  /// Set to true by isLoopBackedgeGuardedByCond when we're walking the set of
1186  /// conditions dominating the backedge of a loop.
1187  bool WalkingBEDominatingConds = false;
1188 
1189  /// Set to true by isKnownPredicateViaSplitting when we're trying to prove a
1190  /// predicate by splitting it into a set of independent predicates.
1191  bool ProvingSplitPredicate = false;
1192 
1193  /// Memoized values for the GetMinTrailingZeros
1194  DenseMap<const SCEV *, uint32_t> MinTrailingZerosCache;
1195 
1196  /// Return the Value set from which the SCEV expr is generated.
1197  SetVector<ValueOffsetPair> *getSCEVValues(const SCEV *S);
1198 
1199  /// Private helper method for the GetMinTrailingZeros method
1200  uint32_t GetMinTrailingZerosImpl(const SCEV *S);
1201 
1202  /// Information about the number of loop iterations for which a loop exit's
1203  /// branch condition evaluates to the not-taken path. This is a temporary
1204  /// pair of exact and max expressions that are eventually summarized in
1205  /// ExitNotTakenInfo and BackedgeTakenInfo.
1206  struct ExitLimit {
1207  const SCEV *ExactNotTaken; // The exit is not taken exactly this many times
1208  const SCEV *MaxNotTaken; // The exit is not taken at most this many times
1209 
1210  // Not taken either exactly MaxNotTaken or zero times
1211  bool MaxOrZero = false;
1212 
1213  /// A set of predicate guards for this ExitLimit. The result is only valid
1214  /// if all of the predicates in \c Predicates evaluate to 'true' at
1215  /// run-time.
1217 
1218  void addPredicate(const SCEVPredicate *P) {
1219  assert(!isa<SCEVUnionPredicate>(P) && "Only add leaf predicates here!");
1220  Predicates.insert(P);
1221  }
1222 
1223  /*implicit*/ ExitLimit(const SCEV *E);
1224 
1225  ExitLimit(
1226  const SCEV *E, const SCEV *M, bool MaxOrZero,
1227  ArrayRef<const SmallPtrSetImpl<const SCEVPredicate *> *> PredSetList);
1228 
1229  ExitLimit(const SCEV *E, const SCEV *M, bool MaxOrZero,
1231 
1232  ExitLimit(const SCEV *E, const SCEV *M, bool MaxOrZero);
1233 
1234  /// Test whether this ExitLimit contains any computed information, or
1235  /// whether it's all SCEVCouldNotCompute values.
1236  bool hasAnyInfo() const {
1237  return !isa<SCEVCouldNotCompute>(ExactNotTaken) ||
1238  !isa<SCEVCouldNotCompute>(MaxNotTaken);
1239  }
1240 
1241  bool hasOperand(const SCEV *S) const;
1242 
1243  /// Test whether this ExitLimit contains all information.
1244  bool hasFullInfo() const {
1245  return !isa<SCEVCouldNotCompute>(ExactNotTaken);
1246  }
1247  };
1248 
1249  /// Information about the number of times a particular loop exit may be
1250  /// reached before exiting the loop.
1251  struct ExitNotTakenInfo {
1252  PoisoningVH<BasicBlock> ExitingBlock;
1253  const SCEV *ExactNotTaken;
1254  std::unique_ptr<SCEVUnionPredicate> Predicate;
1255 
1256  explicit ExitNotTakenInfo(PoisoningVH<BasicBlock> ExitingBlock,
1257  const SCEV *ExactNotTaken,
1258  std::unique_ptr<SCEVUnionPredicate> Predicate)
1259  : ExitingBlock(ExitingBlock), ExactNotTaken(ExactNotTaken),
1260  Predicate(std::move(Predicate)) {}
1261 
1262  bool hasAlwaysTruePredicate() const {
1263  return !Predicate || Predicate->isAlwaysTrue();
1264  }
1265  };
1266 
1267  /// Information about the backedge-taken count of a loop. This currently
1268  /// includes an exact count and a maximum count.
1269  ///
1270  class BackedgeTakenInfo {
1271  /// A list of computable exits and their not-taken counts. Loops almost
1272  /// never have more than one computable exit.
1273  SmallVector<ExitNotTakenInfo, 1> ExitNotTaken;
1274 
1275  /// The pointer part of \c MaxAndComplete is an expression indicating the
1276  /// least maximum backedge-taken count of the loop that is known, or a
1277  /// SCEVCouldNotCompute. This expression is only valid if the predicates
1278  /// associated with all loop exits are true.
1279  ///
1280  /// The integer part of \c MaxAndComplete is a boolean indicating if \c
1281  /// ExitNotTaken has an element for every exiting block in the loop.
1282  PointerIntPair<const SCEV *, 1> MaxAndComplete;
1283 
1284  /// True iff the backedge is taken either exactly Max or zero times.
1285  bool MaxOrZero = false;
1286 
1287  /// \name Helper projection functions on \c MaxAndComplete.
1288  /// @{
1289  bool isComplete() const { return MaxAndComplete.getInt(); }
1290  const SCEV *getMax() const { return MaxAndComplete.getPointer(); }
1291  /// @}
1292 
1293  public:
1294  BackedgeTakenInfo() : MaxAndComplete(nullptr, 0) {}
1295  BackedgeTakenInfo(BackedgeTakenInfo &&) = default;
1296  BackedgeTakenInfo &operator=(BackedgeTakenInfo &&) = default;
1297 
1298  using EdgeExitInfo = std::pair<BasicBlock *, ExitLimit>;
1299 
1300  /// Initialize BackedgeTakenInfo from a list of exact exit counts.
1301  BackedgeTakenInfo(ArrayRef<EdgeExitInfo> ExitCounts, bool Complete,
1302  const SCEV *MaxCount, bool MaxOrZero);
1303 
1304  /// Test whether this BackedgeTakenInfo contains any computed information,
1305  /// or whether it's all SCEVCouldNotCompute values.
1306  bool hasAnyInfo() const {
1307  return !ExitNotTaken.empty() || !isa<SCEVCouldNotCompute>(getMax());
1308  }
1309 
1310  /// Test whether this BackedgeTakenInfo contains complete information.
1311  bool hasFullInfo() const { return isComplete(); }
1312 
1313  /// Return an expression indicating the exact *backedge-taken*
1314  /// count of the loop if it is known or SCEVCouldNotCompute
1315  /// otherwise. If execution makes it to the backedge on every
1316  /// iteration (i.e. there are no abnormal exists like exception
1317  /// throws and thread exits) then this is the number of times the
1318  /// loop header will execute minus one.
1319  ///
1320  /// If the SCEV predicate associated with the answer can be different
1321  /// from AlwaysTrue, we must add a (non null) Predicates argument.
1322  /// The SCEV predicate associated with the answer will be added to
1323  /// Predicates. A run-time check needs to be emitted for the SCEV
1324  /// predicate in order for the answer to be valid.
1325  ///
1326  /// Note that we should always know if we need to pass a predicate
1327  /// argument or not from the way the ExitCounts vector was computed.
1328  /// If we allowed SCEV predicates to be generated when populating this
1329  /// vector, this information can contain them and therefore a
1330  /// SCEVPredicate argument should be added to getExact.
1331  const SCEV *getExact(const Loop *L, ScalarEvolution *SE,
1332  SCEVUnionPredicate *Predicates = nullptr) const;
1333 
1334  /// Return the number of times this loop exit may fall through to the back
1335  /// edge, or SCEVCouldNotCompute. The loop is guaranteed not to exit via
1336  /// this block before this number of iterations, but may exit via another
1337  /// block.
1338  const SCEV *getExact(BasicBlock *ExitingBlock, ScalarEvolution *SE) const;
1339 
1340  /// Get the max backedge taken count for the loop.
1341  const SCEV *getMax(ScalarEvolution *SE) const;
1342 
1343  /// Return true if the number of times this backedge is taken is either the
1344  /// value returned by getMax or zero.
1345  bool isMaxOrZero(ScalarEvolution *SE) const;
1346 
1347  /// Return true if any backedge taken count expressions refer to the given
1348  /// subexpression.
1349  bool hasOperand(const SCEV *S, ScalarEvolution *SE) const;
1350 
1351  /// Invalidate this result and free associated memory.
1352  void clear();
1353  };
1354 
1355  /// Cache the backedge-taken count of the loops for this function as they
1356  /// are computed.
1357  DenseMap<const Loop *, BackedgeTakenInfo> BackedgeTakenCounts;
1358 
1359  /// Cache the predicated backedge-taken count of the loops for this
1360  /// function as they are computed.
1361  DenseMap<const Loop *, BackedgeTakenInfo> PredicatedBackedgeTakenCounts;
1362 
1363  /// This map contains entries for all of the PHI instructions that we
1364  /// attempt to compute constant evolutions for. This allows us to avoid
1365  /// potentially expensive recomputation of these properties. An instruction
1366  /// maps to null if we are unable to compute its exit value.
1367  DenseMap<PHINode *, Constant *> ConstantEvolutionLoopExitValue;
1368 
1369  /// This map contains entries for all the expressions that we attempt to
1370  /// compute getSCEVAtScope information for, which can be expensive in
1371  /// extreme cases.
1373  ValuesAtScopes;
1374 
1375  /// Memoized computeLoopDisposition results.
1376  DenseMap<const SCEV *,
1378  LoopDispositions;
1379 
1380  struct LoopProperties {
1381  /// Set to true if the loop contains no instruction that can have side
1382  /// effects (i.e. via throwing an exception, volatile or atomic access).
1383  bool HasNoAbnormalExits;
1384 
1385  /// Set to true if the loop contains no instruction that can abnormally exit
1386  /// the loop (i.e. via throwing an exception, by terminating the thread
1387  /// cleanly or by infinite looping in a called function). Strictly
1388  /// speaking, the last one is not leaving the loop, but is identical to
1389  /// leaving the loop for reasoning about undefined behavior.
1390  bool HasNoSideEffects;
1391  };
1392 
1393  /// Cache for \c getLoopProperties.
1394  DenseMap<const Loop *, LoopProperties> LoopPropertiesCache;
1395 
1396  /// Return a \c LoopProperties instance for \p L, creating one if necessary.
1397  LoopProperties getLoopProperties(const Loop *L);
1398 
1399  bool loopHasNoSideEffects(const Loop *L) {
1400  return getLoopProperties(L).HasNoSideEffects;
1401  }
1402 
1403  bool loopHasNoAbnormalExits(const Loop *L) {
1404  return getLoopProperties(L).HasNoAbnormalExits;
1405  }
1406 
1407  /// Compute a LoopDisposition value.
1408  LoopDisposition computeLoopDisposition(const SCEV *S, const Loop *L);
1409 
1410  /// Memoized computeBlockDisposition results.
1411  DenseMap<
1412  const SCEV *,
1414  BlockDispositions;
1415 
1416  /// Compute a BlockDisposition value.
1417  BlockDisposition computeBlockDisposition(const SCEV *S, const BasicBlock *BB);
1418 
1419  /// Memoized results from getRange
1421 
1422  /// Memoized results from getRange
1424 
1425  /// Used to parameterize getRange
1426  enum RangeSignHint { HINT_RANGE_UNSIGNED, HINT_RANGE_SIGNED };
1427 
1428  /// Set the memoized range for the given SCEV.
1429  const ConstantRange &setRange(const SCEV *S, RangeSignHint Hint,
1430  ConstantRange CR) {
1432  Hint == HINT_RANGE_UNSIGNED ? UnsignedRanges : SignedRanges;
1433 
1434  auto Pair = Cache.try_emplace(S, std::move(CR));
1435  if (!Pair.second)
1436  Pair.first->second = std::move(CR);
1437  return Pair.first->second;
1438  }
1439 
1440  /// Determine the range for a particular SCEV.
1441  /// NOTE: This returns a reference to an entry in a cache. It must be
1442  /// copied if its needed for longer.
1443  const ConstantRange &getRangeRef(const SCEV *S, RangeSignHint Hint);
1444 
1445  /// Determines the range for the affine SCEVAddRecExpr {\p Start,+,\p Stop}.
1446  /// Helper for \c getRange.
1447  ConstantRange getRangeForAffineAR(const SCEV *Start, const SCEV *Stop,
1448  const SCEV *MaxBECount, unsigned BitWidth);
1449 
1450  /// Try to compute a range for the affine SCEVAddRecExpr {\p Start,+,\p
1451  /// Stop} by "factoring out" a ternary expression from the add recurrence.
1452  /// Helper called by \c getRange.
1453  ConstantRange getRangeViaFactoring(const SCEV *Start, const SCEV *Stop,
1454  const SCEV *MaxBECount, unsigned BitWidth);
1455 
1456  /// We know that there is no SCEV for the specified value. Analyze the
1457  /// expression.
1458  const SCEV *createSCEV(Value *V);
1459 
1460  /// Provide the special handling we need to analyze PHI SCEVs.
1461  const SCEV *createNodeForPHI(PHINode *PN);
1462 
1463  /// Helper function called from createNodeForPHI.
1464  const SCEV *createAddRecFromPHI(PHINode *PN);
1465 
1466  /// A helper function for createAddRecFromPHI to handle simple cases.
1467  const SCEV *createSimpleAffineAddRec(PHINode *PN, Value *BEValueV,
1468  Value *StartValueV);
1469 
1470  /// Helper function called from createNodeForPHI.
1471  const SCEV *createNodeFromSelectLikePHI(PHINode *PN);
1472 
1473  /// Provide special handling for a select-like instruction (currently this
1474  /// is either a select instruction or a phi node). \p I is the instruction
1475  /// being processed, and it is assumed equivalent to "Cond ? TrueVal :
1476  /// FalseVal".
1477  const SCEV *createNodeForSelectOrPHI(Instruction *I, Value *Cond,
1478  Value *TrueVal, Value *FalseVal);
1479 
1480  /// Provide the special handling we need to analyze GEP SCEVs.
1481  const SCEV *createNodeForGEP(GEPOperator *GEP);
1482 
1483  /// Implementation code for getSCEVAtScope; called at most once for each
1484  /// SCEV+Loop pair.
1485  const SCEV *computeSCEVAtScope(const SCEV *S, const Loop *L);
1486 
1487  /// This looks up computed SCEV values for all instructions that depend on
1488  /// the given instruction and removes them from the ValueExprMap map if they
1489  /// reference SymName. This is used during PHI resolution.
1490  void forgetSymbolicName(Instruction *I, const SCEV *SymName);
1491 
1492  /// Return the BackedgeTakenInfo for the given loop, lazily computing new
1493  /// values if the loop hasn't been analyzed yet. The returned result is
1494  /// guaranteed not to be predicated.
1495  const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
1496 
1497  /// Similar to getBackedgeTakenInfo, but will add predicates as required
1498  /// with the purpose of returning complete information.
1499  const BackedgeTakenInfo &getPredicatedBackedgeTakenInfo(const Loop *L);
1500 
1501  /// Compute the number of times the specified loop will iterate.
1502  /// If AllowPredicates is set, we will create new SCEV predicates as
1503  /// necessary in order to return an exact answer.
1504  BackedgeTakenInfo computeBackedgeTakenCount(const Loop *L,
1505  bool AllowPredicates = false);
1506 
1507  /// Compute the number of times the backedge of the specified loop will
1508  /// execute if it exits via the specified block. If AllowPredicates is set,
1509  /// this call will try to use a minimal set of SCEV predicates in order to
1510  /// return an exact answer.
1511  ExitLimit computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
1512  bool AllowPredicates = false);
1513 
1514  /// Compute the number of times the backedge of the specified loop will
1515  /// execute if its exit condition were a conditional branch of ExitCond.
1516  ///
1517  /// \p ControlsExit is true if ExitCond directly controls the exit
1518  /// branch. In this case, we can assume that the loop exits only if the
1519  /// condition is true and can infer that failing to meet the condition prior
1520  /// to integer wraparound results in undefined behavior.
1521  ///
1522  /// If \p AllowPredicates is set, this call will try to use a minimal set of
1523  /// SCEV predicates in order to return an exact answer.
1524  ExitLimit computeExitLimitFromCond(const Loop *L, Value *ExitCond,
1525  bool ExitIfTrue, bool ControlsExit,
1526  bool AllowPredicates = false);
1527 
1528  // Helper functions for computeExitLimitFromCond to avoid exponential time
1529  // complexity.
1530 
1531  class ExitLimitCache {
1532  // It may look like we need key on the whole (L, ExitIfTrue, ControlsExit,
1533  // AllowPredicates) tuple, but recursive calls to
1534  // computeExitLimitFromCondCached from computeExitLimitFromCondImpl only
1535  // vary the in \c ExitCond and \c ControlsExit parameters. We remember the
1536  // initial values of the other values to assert our assumption.
1537  SmallDenseMap<PointerIntPair<Value *, 1>, ExitLimit> TripCountMap;
1538 
1539  const Loop *L;
1540  bool ExitIfTrue;
1541  bool AllowPredicates;
1542 
1543  public:
1544  ExitLimitCache(const Loop *L, bool ExitIfTrue, bool AllowPredicates)
1545  : L(L), ExitIfTrue(ExitIfTrue), AllowPredicates(AllowPredicates) {}
1546 
1547  Optional<ExitLimit> find(const Loop *L, Value *ExitCond, bool ExitIfTrue,
1548  bool ControlsExit, bool AllowPredicates);
1549 
1550  void insert(const Loop *L, Value *ExitCond, bool ExitIfTrue,
1551  bool ControlsExit, bool AllowPredicates, const ExitLimit &EL);
1552  };
1553 
1554  using ExitLimitCacheTy = ExitLimitCache;
1555 
1556  ExitLimit computeExitLimitFromCondCached(ExitLimitCacheTy &Cache,
1557  const Loop *L, Value *ExitCond,
1558  bool ExitIfTrue,
1559  bool ControlsExit,
1560  bool AllowPredicates);
1561  ExitLimit computeExitLimitFromCondImpl(ExitLimitCacheTy &Cache, const Loop *L,
1562  Value *ExitCond, bool ExitIfTrue,
1563  bool ControlsExit,
1564  bool AllowPredicates);
1565 
1566  /// Compute the number of times the backedge of the specified loop will
1567  /// execute if its exit condition were a conditional branch of the ICmpInst
1568  /// ExitCond and ExitIfTrue. If AllowPredicates is set, this call will try
1569  /// to use a minimal set of SCEV predicates in order to return an exact
1570  /// answer.
1571  ExitLimit computeExitLimitFromICmp(const Loop *L, ICmpInst *ExitCond,
1572  bool ExitIfTrue,
1573  bool IsSubExpr,
1574  bool AllowPredicates = false);
1575 
1576  /// Compute the number of times the backedge of the specified loop will
1577  /// execute if its exit condition were a switch with a single exiting case
1578  /// to ExitingBB.
1579  ExitLimit computeExitLimitFromSingleExitSwitch(const Loop *L,
1580  SwitchInst *Switch,
1581  BasicBlock *ExitingBB,
1582  bool IsSubExpr);
1583 
1584  /// Given an exit condition of 'icmp op load X, cst', try to see if we can
1585  /// compute the backedge-taken count.
1586  ExitLimit computeLoadConstantCompareExitLimit(LoadInst *LI, Constant *RHS,
1587  const Loop *L,
1589 
1590  /// Compute the exit limit of a loop that is controlled by a
1591  /// "(IV >> 1) != 0" type comparison. We cannot compute the exact trip
1592  /// count in these cases (since SCEV has no way of expressing them), but we
1593  /// can still sometimes compute an upper bound.
1594  ///
1595  /// Return an ExitLimit for a loop whose backedge is guarded by `LHS Pred
1596  /// RHS`.
1597  ExitLimit computeShiftCompareExitLimit(Value *LHS, Value *RHS, const Loop *L,
1598  ICmpInst::Predicate Pred);
1599 
1600  /// If the loop is known to execute a constant number of times (the
1601  /// condition evolves only from constants), try to evaluate a few iterations
1602  /// of the loop until we get the exit condition gets a value of ExitWhen
1603  /// (true or false). If we cannot evaluate the exit count of the loop,
1604  /// return CouldNotCompute.
1605  const SCEV *computeExitCountExhaustively(const Loop *L, Value *Cond,
1606  bool ExitWhen);
1607 
1608  /// Return the number of times an exit condition comparing the specified
1609  /// value to zero will execute. If not computable, return CouldNotCompute.
1610  /// If AllowPredicates is set, this call will try to use a minimal set of
1611  /// SCEV predicates in order to return an exact answer.
1612  ExitLimit howFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr,
1613  bool AllowPredicates = false);
1614 
1615  /// Return the number of times an exit condition checking the specified
1616  /// value for nonzero will execute. If not computable, return
1617  /// CouldNotCompute.
1618  ExitLimit howFarToNonZero(const SCEV *V, const Loop *L);
1619 
1620  /// Return the number of times an exit condition containing the specified
1621  /// less-than comparison will execute. If not computable, return
1622  /// CouldNotCompute.
1623  ///
1624  /// \p isSigned specifies whether the less-than is signed.
1625  ///
1626  /// \p ControlsExit is true when the LHS < RHS condition directly controls
1627  /// the branch (loops exits only if condition is true). In this case, we can
1628  /// use NoWrapFlags to skip overflow checks.
1629  ///
1630  /// If \p AllowPredicates is set, this call will try to use a minimal set of
1631  /// SCEV predicates in order to return an exact answer.
1632  ExitLimit howManyLessThans(const SCEV *LHS, const SCEV *RHS, const Loop *L,
1633  bool isSigned, bool ControlsExit,
1634  bool AllowPredicates = false);
1635 
1636  ExitLimit howManyGreaterThans(const SCEV *LHS, const SCEV *RHS, const Loop *L,
1637  bool isSigned, bool IsSubExpr,
1638  bool AllowPredicates = false);
1639 
1640  /// Return a predecessor of BB (which may not be an immediate predecessor)
1641  /// which has exactly one successor from which BB is reachable, or null if
1642  /// no such block is found.
1643  std::pair<BasicBlock *, BasicBlock *>
1644  getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
1645 
1646  /// Test whether the condition described by Pred, LHS, and RHS is true
1647  /// whenever the given FoundCondValue value evaluates to true.
1648  bool isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
1649  Value *FoundCondValue, bool Inverse);
1650 
1651  /// Test whether the condition described by Pred, LHS, and RHS is true
1652  /// whenever the condition described by FoundPred, FoundLHS, FoundRHS is
1653  /// true.
1654  bool isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
1655  ICmpInst::Predicate FoundPred, const SCEV *FoundLHS,
1656  const SCEV *FoundRHS);
1657 
1658  /// Test whether the condition described by Pred, LHS, and RHS is true
1659  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1660  /// true.
1661  bool isImpliedCondOperands(ICmpInst::Predicate Pred, const SCEV *LHS,
1662  const SCEV *RHS, const SCEV *FoundLHS,
1663  const SCEV *FoundRHS);
1664 
1665  /// Test whether the condition described by Pred, LHS, and RHS is true
1666  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1667  /// true. Here LHS is an operation that includes FoundLHS as one of its
1668  /// arguments.
1669  bool isImpliedViaOperations(ICmpInst::Predicate Pred,
1670  const SCEV *LHS, const SCEV *RHS,
1671  const SCEV *FoundLHS, const SCEV *FoundRHS,
1672  unsigned Depth = 0);
1673 
1674  /// Test whether the condition described by Pred, LHS, and RHS is true.
1675  /// Use only simple non-recursive types of checks, such as range analysis etc.
1676  bool isKnownViaNonRecursiveReasoning(ICmpInst::Predicate Pred,
1677  const SCEV *LHS, const SCEV *RHS);
1678 
1679  /// Test whether the condition described by Pred, LHS, and RHS is true
1680  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1681  /// true.
1682  bool isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, const SCEV *LHS,
1683  const SCEV *RHS, const SCEV *FoundLHS,
1684  const SCEV *FoundRHS);
1685 
1686  /// Test whether the condition described by Pred, LHS, and RHS is true
1687  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1688  /// true. Utility function used by isImpliedCondOperands. Tries to get
1689  /// cases like "X `sgt` 0 => X - 1 `sgt` -1".
1690  bool isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred, const SCEV *LHS,
1691  const SCEV *RHS, const SCEV *FoundLHS,
1692  const SCEV *FoundRHS);
1693 
1694  /// Return true if the condition denoted by \p LHS \p Pred \p RHS is implied
1695  /// by a call to \c @llvm.experimental.guard in \p BB.
1696  bool isImpliedViaGuard(BasicBlock *BB, ICmpInst::Predicate Pred,
1697  const SCEV *LHS, const SCEV *RHS);
1698 
1699  /// Test whether the condition described by Pred, LHS, and RHS is true
1700  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1701  /// true.
1702  ///
1703  /// This routine tries to rule out certain kinds of integer overflow, and
1704  /// then tries to reason about arithmetic properties of the predicates.
1705  bool isImpliedCondOperandsViaNoOverflow(ICmpInst::Predicate Pred,
1706  const SCEV *LHS, const SCEV *RHS,
1707  const SCEV *FoundLHS,
1708  const SCEV *FoundRHS);
1709 
1710  /// Test whether the condition described by Pred, LHS, and RHS is true
1711  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1712  /// true.
1713  ///
1714  /// This routine tries to figure out predicate for Phis which are SCEVUnknown
1715  /// if it is true for every possible incoming value from their respective
1716  /// basic blocks.
1717  bool isImpliedViaMerge(ICmpInst::Predicate Pred,
1718  const SCEV *LHS, const SCEV *RHS,
1719  const SCEV *FoundLHS, const SCEV *FoundRHS,
1720  unsigned Depth);
1721 
1722  /// If we know that the specified Phi is in the header of its containing
1723  /// loop, we know the loop executes a constant number of times, and the PHI
1724  /// node is just a recurrence involving constants, fold it.
1725  Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt &BEs,
1726  const Loop *L);
1727 
1728  /// Test if the given expression is known to satisfy the condition described
1729  /// by Pred and the known constant ranges of LHS and RHS.
1730  bool isKnownPredicateViaConstantRanges(ICmpInst::Predicate Pred,
1731  const SCEV *LHS, const SCEV *RHS);
1732 
1733  /// Try to prove the condition described by "LHS Pred RHS" by ruling out
1734  /// integer overflow.
1735  ///
1736  /// For instance, this will return true for "A s< (A + C)<nsw>" if C is
1737  /// positive.
1738  bool isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred, const SCEV *LHS,
1739  const SCEV *RHS);
1740 
1741  /// Try to split Pred LHS RHS into logical conjunctions (and's) and try to
1742  /// prove them individually.
1743  bool isKnownPredicateViaSplitting(ICmpInst::Predicate Pred, const SCEV *LHS,
1744  const SCEV *RHS);
1745 
1746  /// Try to match the Expr as "(L + R)<Flags>".
1747  bool splitBinaryAdd(const SCEV *Expr, const SCEV *&L, const SCEV *&R,
1748  SCEV::NoWrapFlags &Flags);
1749 
1750  /// Compute \p LHS - \p RHS and returns the result as an APInt if it is a
1751  /// constant, and None if it isn't.
1752  ///
1753  /// This is intended to be a cheaper version of getMinusSCEV. We can be
1754  /// frugal here since we just bail out of actually constructing and
1755  /// canonicalizing an expression in the cases where the result isn't going
1756  /// to be a constant.
1757  Optional<APInt> computeConstantDifference(const SCEV *LHS, const SCEV *RHS);
1758 
1759  /// Drop memoized information computed for S.
1760  void forgetMemoizedResults(const SCEV *S);
1761 
1762  /// Return an existing SCEV for V if there is one, otherwise return nullptr.
1763  const SCEV *getExistingSCEV(Value *V);
1764 
1765  /// Return false iff given SCEV contains a SCEVUnknown with NULL value-
1766  /// pointer.
1767  bool checkValidity(const SCEV *S) const;
1768 
1769  /// Return true if `ExtendOpTy`({`Start`,+,`Step`}) can be proved to be
1770  /// equal to {`ExtendOpTy`(`Start`),+,`ExtendOpTy`(`Step`)}. This is
1771  /// equivalent to proving no signed (resp. unsigned) wrap in
1772  /// {`Start`,+,`Step`} if `ExtendOpTy` is `SCEVSignExtendExpr`
1773  /// (resp. `SCEVZeroExtendExpr`).
1774  template <typename ExtendOpTy>
1775  bool proveNoWrapByVaryingStart(const SCEV *Start, const SCEV *Step,
1776  const Loop *L);
1777 
1778  /// Try to prove NSW or NUW on \p AR relying on ConstantRange manipulation.
1779  SCEV::NoWrapFlags proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR);
1780 
1781  bool isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
1782  ICmpInst::Predicate Pred, bool &Increasing);
1783 
1784  /// Return SCEV no-wrap flags that can be proven based on reasoning about
1785  /// how poison produced from no-wrap flags on this value (e.g. a nuw add)
1786  /// would trigger undefined behavior on overflow.
1787  SCEV::NoWrapFlags getNoWrapFlagsFromUB(const Value *V);
1788 
1789  /// Return true if the SCEV corresponding to \p I is never poison. Proving
1790  /// this is more complex than proving that just \p I is never poison, since
1791  /// SCEV commons expressions across control flow, and you can have cases
1792  /// like:
1793  ///
1794  /// idx0 = a + b;
1795  /// ptr[idx0] = 100;
1796  /// if (<condition>) {
1797  /// idx1 = a +nsw b;
1798  /// ptr[idx1] = 200;
1799  /// }
1800  ///
1801  /// where the SCEV expression (+ a b) is guaranteed to not be poison (and
1802  /// hence not sign-overflow) only if "<condition>" is true. Since both
1803  /// `idx0` and `idx1` will be mapped to the same SCEV expression, (+ a b),
1804  /// it is not okay to annotate (+ a b) with <nsw> in the above example.
1805  bool isSCEVExprNeverPoison(const Instruction *I);
1806 
1807  /// This is like \c isSCEVExprNeverPoison but it specifically works for
1808  /// instructions that will get mapped to SCEV add recurrences. Return true
1809  /// if \p I will never generate poison under the assumption that \p I is an
1810  /// add recurrence on the loop \p L.
1811  bool isAddRecNeverPoison(const Instruction *I, const Loop *L);
1812 
1813  /// Similar to createAddRecFromPHI, but with the additional flexibility of
1814  /// suggesting runtime overflow checks in case casts are encountered.
1815  /// If successful, the analysis records that for this loop, \p SymbolicPHI,
1816  /// which is the UnknownSCEV currently representing the PHI, can be rewritten
1817  /// into an AddRec, assuming some predicates; The function then returns the
1818  /// AddRec and the predicates as a pair, and caches this pair in
1819  /// PredicatedSCEVRewrites.
1820  /// If the analysis is not successful, a mapping from the \p SymbolicPHI to
1821  /// itself (with no predicates) is recorded, and a nullptr with an empty
1822  /// predicates vector is returned as a pair.
1824  createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI);
1825 
1826  /// Compute the backedge taken count knowing the interval difference, the
1827  /// stride and presence of the equality in the comparison.
1828  const SCEV *computeBECount(const SCEV *Delta, const SCEV *Stride,
1829  bool Equality);
1830 
1831  /// Compute the maximum backedge count based on the range of values
1832  /// permitted by Start, End, and Stride. This is for loops of the form
1833  /// {Start, +, Stride} LT End.
1834  ///
1835  /// Precondition: the induction variable is known to be positive. We *don't*
1836  /// assert these preconditions so please be careful.
1837  const SCEV *computeMaxBECountForLT(const SCEV *Start, const SCEV *Stride,
1838  const SCEV *End, unsigned BitWidth,
1839  bool IsSigned);
1840 
1841  /// Verify if an linear IV with positive stride can overflow when in a
1842  /// less-than comparison, knowing the invariant term of the comparison,
1843  /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1844  bool doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride, bool IsSigned,
1845  bool NoWrap);
1846 
1847  /// Verify if an linear IV with negative stride can overflow when in a
1848  /// greater-than comparison, knowing the invariant term of the comparison,
1849  /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1850  bool doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride, bool IsSigned,
1851  bool NoWrap);
1852 
1853  /// Get add expr already created or create a new one.
1854  const SCEV *getOrCreateAddExpr(ArrayRef<const SCEV *> Ops,
1855  SCEV::NoWrapFlags Flags);
1856 
1857  /// Get mul expr already created or create a new one.
1858  const SCEV *getOrCreateMulExpr(ArrayRef<const SCEV *> Ops,
1859  SCEV::NoWrapFlags Flags);
1860 
1861  // Get addrec expr already created or create a new one.
1862  const SCEV *getOrCreateAddRecExpr(ArrayRef<const SCEV *> Ops,
1863  const Loop *L, SCEV::NoWrapFlags Flags);
1864 
1865  /// Return x if \p Val is f(x) where f is a 1-1 function.
1866  const SCEV *stripInjectiveFunctions(const SCEV *Val) const;
1867 
1868  /// Find all of the loops transitively used in \p S, and fill \p LoopsUsed.
1869  /// A loop is considered "used" by an expression if it contains
1870  /// an add rec on said loop.
1871  void getUsedLoops(const SCEV *S, SmallPtrSetImpl<const Loop *> &LoopsUsed);
1872 
1873  /// Find all of the loops transitively used in \p S, and update \c LoopUsers
1874  /// accordingly.
1875  void addToLoopUseLists(const SCEV *S);
1876 
1877  /// Try to match the pattern generated by getURemExpr(A, B). If successful,
1878  /// Assign A and B to LHS and RHS, respectively.
1879  bool matchURem(const SCEV *Expr, const SCEV *&LHS, const SCEV *&RHS);
1880 
1881  /// Look for a SCEV expression with type `SCEVType` and operands `Ops` in
1882  /// `UniqueSCEVs`.
1883  ///
1884  /// The first component of the returned tuple is the SCEV if found and null
1885  /// otherwise. The second component is the `FoldingSetNodeID` that was
1886  /// constructed to look up the SCEV and the third component is the insertion
1887  /// point.
1888  std::tuple<const SCEV *, FoldingSetNodeID, void *>
1889  findExistingSCEVInCache(int SCEVType, ArrayRef<const SCEV *> Ops);
1890 
1891  FoldingSet<SCEV> UniqueSCEVs;
1892  FoldingSet<SCEVPredicate> UniquePreds;
1893  BumpPtrAllocator SCEVAllocator;
1894 
1895  /// This maps loops to a list of SCEV expressions that (transitively) use said
1896  /// loop.
1898 
1899  /// Cache tentative mappings from UnknownSCEVs in a Loop, to a SCEV expression
1900  /// they can be rewritten into under certain predicates.
1902  std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
1903  PredicatedSCEVRewrites;
1904 
1905  /// The head of a linked list of all SCEVUnknown values that have been
1906  /// allocated. This is used by releaseMemory to locate them all and call
1907  /// their destructors.
1908  SCEVUnknown *FirstUnknown = nullptr;
1909 };
1910 
1911 /// Analysis pass that exposes the \c ScalarEvolution for a function.
1913  : public AnalysisInfoMixin<ScalarEvolutionAnalysis> {
1915 
1916  static AnalysisKey Key;
1917 
1918 public:
1920 
1922 };
1923 
1924 /// Printer pass for the \c ScalarEvolutionAnalysis results.
1926  : public PassInfoMixin<ScalarEvolutionPrinterPass> {
1927  raw_ostream &OS;
1928 
1929 public:
1930  explicit ScalarEvolutionPrinterPass(raw_ostream &OS) : OS(OS) {}
1931 
1933 };
1934 
1936  std::unique_ptr<ScalarEvolution> SE;
1937 
1938 public:
1939  static char ID;
1940 
1942 
1943  ScalarEvolution &getSE() { return *SE; }
1944  const ScalarEvolution &getSE() const { return *SE; }
1945 
1946  bool runOnFunction(Function &F) override;
1947  void releaseMemory() override;
1948  void getAnalysisUsage(AnalysisUsage &AU) const override;
1949  void print(raw_ostream &OS, const Module * = nullptr) const override;
1950  void verifyAnalysis() const override;
1951 };
1952 
1953 /// An interface layer with SCEV used to manage how we see SCEV expressions
1954 /// for values in the context of existing predicates. We can add new
1955 /// predicates, but we cannot remove them.
1956 ///
1957 /// This layer has multiple purposes:
1958 /// - provides a simple interface for SCEV versioning.
1959 /// - guarantees that the order of transformations applied on a SCEV
1960 /// expression for a single Value is consistent across two different
1961 /// getSCEV calls. This means that, for example, once we've obtained
1962 /// an AddRec expression for a certain value through expression
1963 /// rewriting, we will continue to get an AddRec expression for that
1964 /// Value.
1965 /// - lowers the number of expression rewrites.
1967 public:
1969 
1970  const SCEVUnionPredicate &getUnionPredicate() const;
1971 
1972  /// Returns the SCEV expression of V, in the context of the current SCEV
1973  /// predicate. The order of transformations applied on the expression of V
1974  /// returned by ScalarEvolution is guaranteed to be preserved, even when
1975  /// adding new predicates.
1976  const SCEV *getSCEV(Value *V);
1977 
1978  /// Get the (predicated) backedge count for the analyzed loop.
1979  const SCEV *getBackedgeTakenCount();
1980 
1981  /// Adds a new predicate.
1982  void addPredicate(const SCEVPredicate &Pred);
1983 
1984  /// Attempts to produce an AddRecExpr for V by adding additional SCEV
1985  /// predicates. If we can't transform the expression into an AddRecExpr we
1986  /// return nullptr and not add additional SCEV predicates to the current
1987  /// context.
1988  const SCEVAddRecExpr *getAsAddRec(Value *V);
1989 
1990  /// Proves that V doesn't overflow by adding SCEV predicate.
1991  void setNoOverflow(Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags);
1992 
1993  /// Returns true if we've proved that V doesn't wrap by means of a SCEV
1994  /// predicate.
1995  bool hasNoOverflow(Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags);
1996 
1997  /// Returns the ScalarEvolution analysis used.
1998  ScalarEvolution *getSE() const { return &SE; }
1999 
2000  /// We need to explicitly define the copy constructor because of FlagsMap.
2002 
2003  /// Print the SCEV mappings done by the Predicated Scalar Evolution.
2004  /// The printed text is indented by \p Depth.
2005  void print(raw_ostream &OS, unsigned Depth) const;
2006 
2007  /// Check if \p AR1 and \p AR2 are equal, while taking into account
2008  /// Equal predicates in Preds.
2009  bool areAddRecsEqualWithPreds(const SCEVAddRecExpr *AR1,
2010  const SCEVAddRecExpr *AR2) const;
2011 
2012 private:
2013  /// Increments the version number of the predicate. This needs to be called
2014  /// every time the SCEV predicate changes.
2015  void updateGeneration();
2016 
2017  /// Holds a SCEV and the version number of the SCEV predicate used to
2018  /// perform the rewrite of the expression.
2019  using RewriteEntry = std::pair<unsigned, const SCEV *>;
2020 
2021  /// Maps a SCEV to the rewrite result of that SCEV at a certain version
2022  /// number. If this number doesn't match the current Generation, we will
2023  /// need to do a rewrite. To preserve the transformation order of previous
2024  /// rewrites, we will rewrite the previous result instead of the original
2025  /// SCEV.
2027 
2028  /// Records what NoWrap flags we've added to a Value *.
2030 
2031  /// The ScalarEvolution analysis.
2032  ScalarEvolution &SE;
2033 
2034  /// The analyzed Loop.
2035  const Loop &L;
2036 
2037  /// The SCEVPredicate that forms our context. We will rewrite all
2038  /// expressions assuming that this predicate true.
2039  SCEVUnionPredicate Preds;
2040 
2041  /// Marks the version of the SCEV predicate used. When rewriting a SCEV
2042  /// expression we mark it with the version of the predicate. We use this to
2043  /// figure out if the predicate has changed from the last rewrite of the
2044  /// SCEV. If so, we need to perform a new rewrite.
2045  unsigned Generation = 0;
2046 
2047  /// The backedge taken count.
2048  const SCEV *BackedgeCount = nullptr;
2049 };
2050 
2051 } // end namespace llvm
2052 
2053 #endif // LLVM_ANALYSIS_SCALAREVOLUTION_H
ExitLimitQuery(const Loop *L, BasicBlock *ExitingBlock, bool AllowPredicates)
bool isKnownPositive(const Value *V, const DataLayout &DL, unsigned Depth=0, AssumptionCache *AC=nullptr, const Instruction *CxtI=nullptr, const DominatorTree *DT=nullptr, bool UseInstrInfo=true)
Returns true if the given value is known be positive (i.e.
A parsed version of the target data layout string in and methods for querying it. ...
Definition: DataLayout.h:110
Type
MessagePack types as defined in the standard, with the exception of Integer being divided into a sign...
Definition: MsgPackReader.h:48
static GCMetadataPrinterRegistry::Add< ErlangGCPrinter > X("erlang", "erlang-compatible garbage collector")
const ScalarEvolution & getSE() const
static Type * getWiderType(const DataLayout &DL, Type *Ty0, Type *Ty1)
static bool isLoopInvariant(Value *V, const Loop *L, const DominatorTree *DT)
Perform a quick domtree based check for loop invariance assuming that V is used within the loop...
This class represents lattice values for constants.
Definition: AllocatorList.h:23
SCEV & operator=(const SCEV &)=delete
PointerTy getPointer() const
Various leaf nodes.
Definition: ISDOpcodes.h:59
static unsigned ComputeHash(const SCEVPredicate &X, FoldingSetNodeID &TempID)
A Module instance is used to store all the information related to an LLVM module. ...
Definition: Module.h:65
void dump() const
This method is used for debugging.
const unsigned short ExpressionSize
The main scalar evolution driver.
bool isZero() const
Return true if the expression is a constant zero.
const SCEV * getAddRecExpr(const SmallVectorImpl< const SCEV *> &Operands, const Loop *L, SCEV::NoWrapFlags Flags)
IncrementWrapFlags
Similar to SCEV::NoWrapFlags, but with slightly different semantics for FlagNUSW. ...
static LLVM_NODISCARD SCEV::NoWrapFlags setFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OnFlags)
static bool Equals(const SCEVPredicate &X, const FoldingSetNodeID &ID, unsigned IDHash, FoldingSetNodeID &TempID)
A cache of @llvm.assume calls within a function.
APInt getSignedRangeMin(const SCEV *S)
Determine the min of the signed range for a particular SCEV.
F(f)
An instruction for reading from memory.
Definition: Instructions.h:167
Hexagon Common GEP
An object of this class is returned by queries that could not be answered.
This file defines the MallocAllocator and BumpPtrAllocator interfaces.
APInt getSignedRangeMax(const SCEV *S)
Determine the max of the signed range for a particular SCEV.
A templated base class for SmallPtrSet which provides the typesafe interface that is common across al...
Definition: SmallPtrSet.h:343
const SCEV * getZero(Type *Ty)
Return a SCEV for the constant 0 of a specific type.
The SCEV is loop-invariant.
static LLVM_NODISCARD SCEVWrapPredicate::IncrementWrapFlags setFlags(SCEVWrapPredicate::IncrementWrapFlags Flags, SCEVWrapPredicate::IncrementWrapFlags OnFlags)
Definition: BitVector.h:937
const SCEV * getAddExpr(const SCEV *LHS, const SCEV *RHS, SCEV::NoWrapFlags Flags=SCEV::FlagAnyWrap, unsigned Depth=0)
const DataLayout & getDataLayout() const
Get the data layout for the module&#39;s target platform.
Definition: Module.cpp:369
Class to represent struct types.
Definition: DerivedTypes.h:232
APInt getUnsignedRangeMax(const SCEV *S)
Determine the max of the unsigned range for a particular SCEV.
This class consists of common code factored out of the SmallVector class to reduce code duplication b...
Definition: APFloat.h:41
unsigned short SubclassData
This field is initialized to zero and may be used in subclasses to store miscellaneous information...
LLVMContext & getContext() const
BasicBlock * ExitingBlock
This file implements a class to represent arbitrary precision integral constant values and operations...
static int64_t getConstant(const MachineInstr *MI)
Key
PAL metadata keys.
ConstantRange getSignedRange(const SCEV *S)
Determine the signed range for a particular SCEV.
This node represents a polynomial recurrence on the trip count of the specified loop.
IntType getInt() const
A CRTP mix-in to automatically provide informational APIs needed for passes.
Definition: PassManager.h:365
static bool classof(const SCEVPredicate *P)
Methods for support type inquiry through isa, cast, and dyn_cast:
ArrayRef - Represent a constant reference to an array (0 or more elements consecutively in memory)...
Definition: APInt.h:32
bool isKnownNonNegative(const Value *V, const DataLayout &DL, unsigned Depth=0, AssumptionCache *AC=nullptr, const Instruction *CxtI=nullptr, const DominatorTree *DT=nullptr, bool UseInstrInfo=true)
Returns true if the give value is known to be non-negative.
Concrete subclass of DominatorTreeBase that is used to compute a normal dominator tree...
Definition: Dominators.h:144
void forgetLoopDispositions(const Loop *L)
Called when the client has changed the disposition of values in this loop.
Value handle that poisons itself if the Value is deleted.
Definition: ValueHandle.h:440
unsigned ComputeHash() const
ComputeHash - Compute a strong hash value for this FoldingSetNodeIDRef, used to lookup the node in th...
Definition: FoldingSet.cpp:29
unsigned short getExpressionSize() const
FoldingSetNodeID - This class is used to gather all the unique data bits of a node.
Definition: FoldingSet.h:305
Printer pass for the ScalarEvolutionAnalysis results.
static bool runOnFunction(Function &F, bool PostInlining)
#define P(N)
This means that we are dealing with an entirely unknown SCEV value, and only represent it as its LLVM...
APInt getUnsignedRangeMin(const SCEV *S)
Determine the min of the unsigned range for a particular SCEV.
FoldingSetTrait - This trait class is used to define behavior of how to "profile" (in the FoldingSet ...
Definition: FoldingSet.h:249
A set of analyses that are preserved following a run of a transformation pass.
Definition: PassManager.h:153
const SCEV * getOne(Type *Ty)
Return a SCEV for the constant 1 of a specific type.
static bool Equals(const SCEV &X, const FoldingSetNodeID &ID, unsigned IDHash, FoldingSetNodeID &TempID)
SCEVPredicateKind getKind() const
LLVM Basic Block Representation.
Definition: BasicBlock.h:57
PointerIntPair - This class implements a pair of a pointer and small integer.
The instances of the Type class are immutable: once they are created, they are never changed...
Definition: Type.h:45
This is an important class for using LLVM in a threaded context.
Definition: LLVMContext.h:64
Allocate memory in an ever growing pool, as if by bump-pointer.
Definition: Allocator.h:140
static GCRegistry::Add< CoreCLRGC > E("coreclr", "CoreCLR-compatible GC")
This is an important base class in LLVM.
Definition: Constant.h:41
std::pair< iterator, bool > insert(PtrType Ptr)
Inserts Ptr if and only if there is no element in the container equal to Ptr.
Definition: SmallPtrSet.h:370
A CRTP mix-in that provides informational APIs needed for analysis passes.
Definition: PassManager.h:382
ScalarEvolutionPrinterPass(raw_ostream &OS)
Represent the analysis usage information of a pass.
This instruction compares its operands according to the predicate given to the constructor.
Predicate
This enumeration lists the possible predicates for CmpInst subclasses.
Definition: InstrTypes.h:646
FunctionPass class - This class is used to implement most global optimizations.
Definition: Pass.h:284
amdgpu Simplify well known AMD library false FunctionCallee Value * Arg
static LLVM_NODISCARD SCEV::NoWrapFlags clearFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OffFlags)
const SCEV * getLHS() const
Returns the left hand side of the equality.
LLVMContext & getContext() const
getContext - Return a reference to the LLVMContext associated with this function. ...
Definition: Function.cpp:192
const SCEV * getRHS() const
Returns the right hand side of the equality.
ScalarEvolution * getSE() const
Returns the ScalarEvolution analysis used.
size_t size() const
Definition: SmallVector.h:52
auto find(R &&Range, const T &Val) -> decltype(adl_begin(Range))
Provide wrappers to std::find which take ranges instead of having to pass begin/end explicitly...
Definition: STLExtras.h:1206
FoldingSet - This template class is used to instantiate a specialized implementation of the folding s...
Definition: FoldingSet.h:473
bool verify(const TargetRegisterInfo &TRI) const
Check that information hold by this instance make sense for the given TRI.
static unsigned ComputeHash(const SCEV &X, FoldingSetNodeID &TempID)
static ExitLimitQuery getEmptyKey()
The SCEV is loop-variant (unknown).
This class represents an assumption made using SCEV expressions which can be checked at run-time...
void print(raw_ostream &OS) const
Print out the internal representation of this scalar to the specified stream.
unsigned getSCEVType() const
bool isNonConstantNegative() const
Return true if the specified scev is negated, but not a constant.
See the file comment.
Definition: ValueMap.h:85
SmallPtrSet - This class implements a set which is optimized for holding SmallSize or less elements...
Definition: SmallPtrSet.h:417
This is the shared class of boolean and integer constants.
Definition: Constants.h:83
bool isAllOnesValue() const
Return true if the expression is a constant all-ones value.
Type * getType() const
Return the LLVM type of this SCEV expression.
static LLVM_NODISCARD SCEVWrapPredicate::IncrementWrapFlags clearFlags(SCEVWrapPredicate::IncrementWrapFlags Flags, SCEVWrapPredicate::IncrementWrapFlags OffFlags)
Convenient IncrementWrapFlags manipulation methods.
static bool isEqual(ExitLimitQuery LHS, ExitLimitQuery RHS)
This is a &#39;vector&#39; (really, a variable-sized array), optimized for the case when the array is small...
Definition: SmallVector.h:841
Provides information about what library functions are available for the current target.
The SCEV dominates the block.
Predicate
Predicate - These are "(BI << 5) | BO" for various predicates.
Definition: PPCPredicates.h:26
This class represents a range of values.
Definition: ConstantRange.h:47
An interface layer with SCEV used to manage how we see SCEV expressions for values in the context of ...
static LLVM_NODISCARD SCEVWrapPredicate::IncrementWrapFlags maskFlags(SCEVWrapPredicate::IncrementWrapFlags Flags, int Mask)
static void Profile(const SCEV &X, FoldingSetNodeID &ID)
static void Profile(const SCEVPredicate &X, FoldingSetNodeID &ID)
LoopDisposition
An enum describing the relationship between a SCEV and a loop.
Class for arbitrary precision integers.
Definition: APInt.h:69
virtual void print(raw_ostream &OS, unsigned Depth=0) const =0
Prints a textual representation of this predicate with an indentation of Depth.
hash_code hash_combine(const Ts &...args)
Combine values into a single hash_code.
Definition: Hashing.h:600
bool isKnownNonZero(const Value *V, const DataLayout &DL, unsigned Depth=0, AssumptionCache *AC=nullptr, const Instruction *CxtI=nullptr, const DominatorTree *DT=nullptr, bool UseInstrInfo=true)
Return true if the given value is known to be non-zero when defined.
This class uses information about analyze scalars to rewrite expressions in canonical form...
static void clear(coro::Shape &Shape)
Definition: Coroutines.cpp:211
const DataLayout & getDataLayout() const
Return the DataLayout associated with the module this SCEV instance is operating on.
static bool classof(const SCEVPredicate *P)
Methods for support type inquiry through isa, cast, and dyn_cast:
Analysis pass that exposes the ScalarEvolution for a function.
unsigned getComplexity() const override
We estimate the complexity of a union predicate as the size number of predicates in the union...
static ExitLimitQuery getTombstoneKey()
The SCEV does not dominate the block.
FoldingSetNodeIDRef - This class describes a reference to an interned FoldingSetNodeID, which can be a useful to store node id data rather than using plain FoldingSetNodeIDs, since the 32-element SmallVector is often much larger than necessary, and the possibility of heap allocation means it requires a non-trivial destructor call.
Definition: FoldingSet.h:277
MCExpr const & getExpr(MCExpr const &Expr)
Node - This class is used to maintain the singly linked bucket list in a folding set.
Definition: FoldingSet.h:135
This class represents an analyzed expression in the program.
bool isKnownNegative(const Value *V, const DataLayout &DL, unsigned Depth=0, AssumptionCache *AC=nullptr, const Instruction *CxtI=nullptr, const DominatorTree *DT=nullptr, bool UseInstrInfo=true)
Returns true if the given value is known be negative (i.e.
LLVM_NODISCARD bool empty() const
Definition: SmallVector.h:55
const SCEV * getMulExpr(const SCEV *LHS, const SCEV *RHS, SCEV::NoWrapFlags Flags=SCEV::FlagAnyWrap, unsigned Depth=0)
Represents a single loop in the control flow graph.
Definition: LoopInfo.h:464
#define I(x, y, z)
Definition: MD5.cpp:58
#define N
BlockDisposition
An enum describing the relationship between a SCEV and a basic block.
static LLVM_NODISCARD SCEV::NoWrapFlags maskFlags(SCEV::NoWrapFlags Flags, int Mask)
Convenient NoWrapFlags manipulation that hides enum casts and is visible in the ScalarEvolution name ...
raw_ostream & operator<<(raw_ostream &OS, const APInt &I)
Definition: APInt.h:2038
virtual unsigned getComplexity() const
Returns the estimated complexity of this predicate.
#define LLVM_NODISCARD
LLVM_NODISCARD - Warn if a type or return value is discarded.
Definition: Compiler.h:128
API to communicate dependencies between analyses during invalidation.
Definition: PassManager.h:641
ConstantRange getUnsignedRange(const SCEV *S)
Determine the unsigned range for a particular SCEV.
const SmallVectorImpl< const SCEVPredicate * > & getPredicates() const
Multiway switch.
assert(ImpDefSCC.getReg()==AMDGPU::SCC &&ImpDefSCC.isDef())
This class represents a composition of other SCEV predicates, and is the class that most clients will...
bool isOne() const
Return true if the expression is a constant one.
const SCEV * getMulExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2, SCEV::NoWrapFlags Flags=SCEV::FlagAnyWrap, unsigned Depth=0)
Module * getParent()
Get the module that this global value is contained inside of...
Definition: GlobalValue.h:565
LLVM Value Representation.
Definition: Value.h:72
A vector that has set insertion semantics.
Definition: SetVector.h:40
std::underlying_type< E >::type Mask()
Get a bitmask with 1s in all places up to the high-order bit of E&#39;s largest value.
Definition: BitmaskEnum.h:80
DefaultFoldingSetTrait - This class provides default implementations for FoldingSetTrait implementati...
Definition: FoldingSet.h:220
SCEVPredicateKind Kind
This class implements an extremely fast bulk output stream that can only output to a stream...
Definition: raw_ostream.h:45
static unsigned getHashValue(ExitLimitQuery Val)
Value handle with callbacks on RAUW and destruction.
Definition: ValueHandle.h:379
A container for analyses that lazily runs them and caches their results.
static Optional< bool > isImpliedCondOperands(CmpInst::Predicate Pred, const Value *ALHS, const Value *ARHS, const Value *BLHS, const Value *BRHS, const DataLayout &DL, unsigned Depth)
Return true if "icmp Pred BLHS BRHS" is true whenever "icmp Pred ALHS ARHS" is true.
SCEV(const FoldingSetNodeIDRef ID, unsigned SCEVTy, unsigned short ExpressionSize)
This header defines various interfaces for pass management in LLVM.
const SCEV * getAddExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2, SCEV::NoWrapFlags Flags=SCEV::FlagAnyWrap, unsigned Depth=0)
This class represents an assumption made on an AddRec expression.
static bool classof(const SCEVPredicate *P)
Methods for support type inquiry through isa, cast, and dyn_cast:
NoWrapFlags
NoWrapFlags are bitfield indices into SubclassData.
This class represents an assumption that two SCEV expressions are equal, and this can be checked at r...
A special type used by analysis passes to provide an address that identifies that particular analysis...
Definition: PassManager.h:70
IncrementWrapFlags getFlags() const
Returns the set assumed no overflow flags.