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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  friend class ScalarEvolutionsTest;
472 
473 public:
474  /// An enum describing the relationship between a SCEV and a loop.
476  LoopVariant, ///< The SCEV is loop-variant (unknown).
477  LoopInvariant, ///< The SCEV is loop-invariant.
478  LoopComputable ///< The SCEV varies predictably with the loop.
479  };
480 
481  /// An enum describing the relationship between a SCEV and a basic block.
483  DoesNotDominateBlock, ///< The SCEV does not dominate the block.
484  DominatesBlock, ///< The SCEV dominates the block.
485  ProperlyDominatesBlock ///< The SCEV properly dominates the block.
486  };
487 
488  /// Convenient NoWrapFlags manipulation that hides enum casts and is
489  /// visible in the ScalarEvolution name space.
491  int Mask) {
492  return (SCEV::NoWrapFlags)(Flags & Mask);
493  }
495  SCEV::NoWrapFlags OnFlags) {
496  return (SCEV::NoWrapFlags)(Flags | OnFlags);
497  }
500  return (SCEV::NoWrapFlags)(Flags & ~OffFlags);
501  }
502 
504  DominatorTree &DT, LoopInfo &LI);
506  ~ScalarEvolution();
507 
508  LLVMContext &getContext() const { return F.getContext(); }
509 
510  /// Test if values of the given type are analyzable within the SCEV
511  /// framework. This primarily includes integer types, and it can optionally
512  /// include pointer types if the ScalarEvolution class has access to
513  /// target-specific information.
514  bool isSCEVable(Type *Ty) const;
515 
516  /// Return the size in bits of the specified type, for which isSCEVable must
517  /// return true.
518  uint64_t getTypeSizeInBits(Type *Ty) const;
519 
520  /// Return a type with the same bitwidth as the given type and which
521  /// represents how SCEV will treat the given type, for which isSCEVable must
522  /// return true. For pointer types, this is the pointer-sized integer type.
523  Type *getEffectiveSCEVType(Type *Ty) const;
524 
525  // Returns a wider type among {Ty1, Ty2}.
526  Type *getWiderType(Type *Ty1, Type *Ty2) const;
527 
528  /// Return true if the SCEV is a scAddRecExpr or it contains
529  /// scAddRecExpr. The result will be cached in HasRecMap.
530  bool containsAddRecurrence(const SCEV *S);
531 
532  /// Erase Value from ValueExprMap and ExprValueMap.
533  void eraseValueFromMap(Value *V);
534 
535  /// Return a SCEV expression for the full generality of the specified
536  /// expression.
537  const SCEV *getSCEV(Value *V);
538 
539  const SCEV *getConstant(ConstantInt *V);
540  const SCEV *getConstant(const APInt &Val);
541  const SCEV *getConstant(Type *Ty, uint64_t V, bool isSigned = false);
542  const SCEV *getTruncateExpr(const SCEV *Op, Type *Ty, unsigned Depth = 0);
543  const SCEV *getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth = 0);
544  const SCEV *getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth = 0);
545  const SCEV *getAnyExtendExpr(const SCEV *Op, Type *Ty);
546  const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
548  unsigned Depth = 0);
549  const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS,
551  unsigned Depth = 0) {
552  SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
553  return getAddExpr(Ops, Flags, Depth);
554  }
555  const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
557  unsigned Depth = 0) {
558  SmallVector<const SCEV *, 3> Ops = {Op0, Op1, Op2};
559  return getAddExpr(Ops, Flags, Depth);
560  }
561  const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
563  unsigned Depth = 0);
564  const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS,
566  unsigned Depth = 0) {
567  SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
568  return getMulExpr(Ops, Flags, Depth);
569  }
570  const SCEV *getMulExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
572  unsigned Depth = 0) {
573  SmallVector<const SCEV *, 3> Ops = {Op0, Op1, Op2};
574  return getMulExpr(Ops, Flags, Depth);
575  }
576  const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
577  const SCEV *getUDivExactExpr(const SCEV *LHS, const SCEV *RHS);
578  const SCEV *getURemExpr(const SCEV *LHS, const SCEV *RHS);
579  const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step, const Loop *L,
580  SCEV::NoWrapFlags Flags);
581  const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
582  const Loop *L, SCEV::NoWrapFlags Flags);
584  const Loop *L, SCEV::NoWrapFlags Flags) {
585  SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
586  return getAddRecExpr(NewOp, L, Flags);
587  }
588 
589  /// Checks if \p SymbolicPHI can be rewritten as an AddRecExpr under some
590  /// Predicates. If successful return these <AddRecExpr, Predicates>;
591  /// The function is intended to be called from PSCEV (the caller will decide
592  /// whether to actually add the predicates and carry out the rewrites).
594  createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI);
595 
596  /// Returns an expression for a GEP
597  ///
598  /// \p GEP The GEP. The indices contained in the GEP itself are ignored,
599  /// instead we use IndexExprs.
600  /// \p IndexExprs The expressions for the indices.
601  const SCEV *getGEPExpr(GEPOperator *GEP,
602  const SmallVectorImpl<const SCEV *> &IndexExprs);
603  const SCEV *getMinMaxExpr(unsigned Kind,
605  const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
606  const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
607  const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
608  const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
609  const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
610  const SCEV *getSMinExpr(SmallVectorImpl<const SCEV *> &Operands);
611  const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
612  const SCEV *getUMinExpr(SmallVectorImpl<const SCEV *> &Operands);
613  const SCEV *getUnknown(Value *V);
614  const SCEV *getCouldNotCompute();
615 
616  /// Return a SCEV for the constant 0 of a specific type.
617  const SCEV *getZero(Type *Ty) { return getConstant(Ty, 0); }
618 
619  /// Return a SCEV for the constant 1 of a specific type.
620  const SCEV *getOne(Type *Ty) { return getConstant(Ty, 1); }
621 
622  /// Return an expression for sizeof AllocTy that is type IntTy
623  const SCEV *getSizeOfExpr(Type *IntTy, Type *AllocTy);
624 
625  /// Return an expression for offsetof on the given field with type IntTy
626  const SCEV *getOffsetOfExpr(Type *IntTy, StructType *STy, unsigned FieldNo);
627 
628  /// Return the SCEV object corresponding to -V.
629  const SCEV *getNegativeSCEV(const SCEV *V,
631 
632  /// Return the SCEV object corresponding to ~V.
633  const SCEV *getNotSCEV(const SCEV *V);
634 
635  /// Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
636  const SCEV *getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
638  unsigned Depth = 0);
639 
640  /// Return a SCEV corresponding to a conversion of the input value to the
641  /// specified type. If the type must be extended, it is zero extended.
642  const SCEV *getTruncateOrZeroExtend(const SCEV *V, Type *Ty,
643  unsigned Depth = 0);
644 
645  /// Return a SCEV corresponding to a conversion of the input value to the
646  /// specified type. If the type must be extended, it is sign extended.
647  const SCEV *getTruncateOrSignExtend(const SCEV *V, Type *Ty,
648  unsigned Depth = 0);
649 
650  /// Return a SCEV corresponding to a conversion of the input value to the
651  /// specified type. If the type must be extended, it is zero extended. The
652  /// conversion must not be narrowing.
653  const SCEV *getNoopOrZeroExtend(const SCEV *V, Type *Ty);
654 
655  /// Return a SCEV corresponding to a conversion of the input value to the
656  /// specified type. If the type must be extended, it is sign extended. The
657  /// conversion must not be narrowing.
658  const SCEV *getNoopOrSignExtend(const SCEV *V, Type *Ty);
659 
660  /// Return a SCEV corresponding to a conversion of the input value to the
661  /// specified type. If the type must be extended, it is extended with
662  /// unspecified bits. The conversion must not be narrowing.
663  const SCEV *getNoopOrAnyExtend(const SCEV *V, Type *Ty);
664 
665  /// Return a SCEV corresponding to a conversion of the input value to the
666  /// specified type. The conversion must not be widening.
667  const SCEV *getTruncateOrNoop(const SCEV *V, Type *Ty);
668 
669  /// Promote the operands to the wider of the types using zero-extension, and
670  /// then perform a umax operation with them.
671  const SCEV *getUMaxFromMismatchedTypes(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.
675  const SCEV *getUMinFromMismatchedTypes(const SCEV *LHS, const SCEV *RHS);
676 
677  /// Promote the operands to the wider of the types using zero-extension, and
678  /// then perform a umin operation with them. N-ary function.
679  const SCEV *getUMinFromMismatchedTypes(SmallVectorImpl<const SCEV *> &Ops);
680 
681  /// Transitively follow the chain of pointer-type operands until reaching a
682  /// SCEV that does not have a single pointer operand. This returns a
683  /// SCEVUnknown pointer for well-formed pointer-type expressions, but corner
684  /// cases do exist.
685  const SCEV *getPointerBase(const SCEV *V);
686 
687  /// Return a SCEV expression for the specified value at the specified scope
688  /// in the program. The L value specifies a loop nest to evaluate the
689  /// expression at, where null is the top-level or a specified loop is
690  /// immediately inside of the loop.
691  ///
692  /// This method can be used to compute the exit value for a variable defined
693  /// in a loop by querying what the value will hold in the parent loop.
694  ///
695  /// In the case that a relevant loop exit value cannot be computed, the
696  /// original value V is returned.
697  const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
698 
699  /// This is a convenience function which does getSCEVAtScope(getSCEV(V), L).
700  const SCEV *getSCEVAtScope(Value *V, const Loop *L);
701 
702  /// Test whether entry to the loop is protected by a conditional between LHS
703  /// and RHS. This is used to help avoid max expressions in loop trip
704  /// counts, and to eliminate casts.
705  bool isLoopEntryGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
706  const SCEV *LHS, const SCEV *RHS);
707 
708  /// Test whether the backedge of the loop is protected by a conditional
709  /// between LHS and RHS. This is used to eliminate casts.
710  bool isLoopBackedgeGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
711  const SCEV *LHS, const SCEV *RHS);
712 
713  /// Returns the maximum trip count of the loop if it is a single-exit
714  /// loop and we can compute a small maximum for that loop.
715  ///
716  /// Implemented in terms of the \c getSmallConstantTripCount overload with
717  /// the single exiting block passed to it. See that routine for details.
718  unsigned getSmallConstantTripCount(const Loop *L);
719 
720  /// Returns the maximum trip count of this loop as a normal unsigned
721  /// value. Returns 0 if the trip count is unknown or not constant. This
722  /// "trip count" assumes that control exits via ExitingBlock. More
723  /// precisely, it is the number of times that control may reach ExitingBlock
724  /// before taking the branch. For loops with multiple exits, it may not be
725  /// the number times that the loop header executes if the loop exits
726  /// prematurely via another branch.
727  unsigned getSmallConstantTripCount(const Loop *L, BasicBlock *ExitingBlock);
728 
729  /// Returns the upper bound of the loop trip count as a normal unsigned
730  /// value.
731  /// Returns 0 if the trip count is unknown or not constant.
732  unsigned getSmallConstantMaxTripCount(const Loop *L);
733 
734  /// Returns the largest constant divisor of the trip count of the
735  /// loop if it is a single-exit loop and we can compute a small maximum for
736  /// that loop.
737  ///
738  /// Implemented in terms of the \c getSmallConstantTripMultiple overload with
739  /// the single exiting block passed to it. See that routine for details.
740  unsigned getSmallConstantTripMultiple(const Loop *L);
741 
742  /// Returns the largest constant divisor of the trip count of this loop as a
743  /// normal unsigned value, if possible. This means that the actual trip
744  /// count is always a multiple of the returned value (don't forget the trip
745  /// count could very well be zero as well!). As explained in the comments
746  /// for getSmallConstantTripCount, this assumes that control exits the loop
747  /// via ExitingBlock.
748  unsigned getSmallConstantTripMultiple(const Loop *L,
749  BasicBlock *ExitingBlock);
750 
751  /// Return the number of times the backedge executes before the given exit
752  /// would be taken; if not exactly computable, return SCEVCouldNotCompute.
753  /// For a single exit loop, this value is equivelent to the result of
754  /// getBackedgeTakenCount. The loop is guaranteed to exit (via *some* exit)
755  /// before the backedge is executed (ExitCount + 1) times. Note that there
756  /// is no guarantee about *which* exit is taken on the exiting iteration.
757  const SCEV *getExitCount(const Loop *L, BasicBlock *ExitingBlock);
758 
759  /// If the specified loop has a predictable backedge-taken count, return it,
760  /// otherwise return a SCEVCouldNotCompute object. The backedge-taken count is
761  /// the number of times the loop header will be branched to from within the
762  /// loop, assuming there are no abnormal exists like exception throws. This is
763  /// one less than the trip count of the loop, since it doesn't count the first
764  /// iteration, when the header is branched to from outside the loop.
765  ///
766  /// Note that it is not valid to call this method on a loop without a
767  /// loop-invariant backedge-taken count (see
768  /// hasLoopInvariantBackedgeTakenCount).
769  const SCEV *getBackedgeTakenCount(const Loop *L);
770 
771  /// Similar to getBackedgeTakenCount, except it will add a set of
772  /// SCEV predicates to Predicates that are required to be true in order for
773  /// the answer to be correct. Predicates can be checked with run-time
774  /// checks and can be used to perform loop versioning.
775  const SCEV *getPredicatedBackedgeTakenCount(const Loop *L,
776  SCEVUnionPredicate &Predicates);
777 
778  /// When successful, this returns a SCEVConstant that is greater than or equal
779  /// to (i.e. a "conservative over-approximation") of the value returend by
780  /// getBackedgeTakenCount. If such a value cannot be computed, it returns the
781  /// SCEVCouldNotCompute object.
782  const SCEV *getConstantMaxBackedgeTakenCount(const Loop *L);
783 
784  /// Return true if the backedge taken count is either the value returned by
785  /// getConstantMaxBackedgeTakenCount or zero.
786  bool isBackedgeTakenCountMaxOrZero(const Loop *L);
787 
788  /// Return true if the specified loop has an analyzable loop-invariant
789  /// backedge-taken count.
790  bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
791 
792  // This method should be called by the client when it made any change that
793  // would invalidate SCEV's answers, and the client wants to remove all loop
794  // information held internally by ScalarEvolution. This is intended to be used
795  // when the alternative to forget a loop is too expensive (i.e. large loop
796  // bodies).
797  void forgetAllLoops();
798 
799  /// This method should be called by the client when it has changed a loop in
800  /// a way that may effect ScalarEvolution's ability to compute a trip count,
801  /// or if the loop is deleted. This call is potentially expensive for large
802  /// loop bodies.
803  void forgetLoop(const Loop *L);
804 
805  // This method invokes forgetLoop for the outermost loop of the given loop
806  // \p L, making ScalarEvolution forget about all this subtree. This needs to
807  // be done whenever we make a transform that may affect the parameters of the
808  // outer loop, such as exit counts for branches.
809  void forgetTopmostLoop(const Loop *L);
810 
811  /// This method should be called by the client when it has changed a value
812  /// in a way that may effect its value, or which may disconnect it from a
813  /// def-use chain linking it to a loop.
814  void forgetValue(Value *V);
815 
816  /// Called when the client has changed the disposition of values in
817  /// this loop.
818  ///
819  /// We don't have a way to invalidate per-loop dispositions. Clear and
820  /// recompute is simpler.
821  void forgetLoopDispositions(const Loop *L) { LoopDispositions.clear(); }
822 
823  /// Determine the minimum number of zero bits that S is guaranteed to end in
824  /// (at every loop iteration). It is, at the same time, the minimum number
825  /// of times S is divisible by 2. For example, given {4,+,8} it returns 2.
826  /// If S is guaranteed to be 0, it returns the bitwidth of S.
827  uint32_t GetMinTrailingZeros(const SCEV *S);
828 
829  /// Determine the unsigned range for a particular SCEV.
830  /// NOTE: This returns a copy of the reference returned by getRangeRef.
832  return getRangeRef(S, HINT_RANGE_UNSIGNED);
833  }
834 
835  /// Determine the min of the unsigned range for a particular SCEV.
837  return getRangeRef(S, HINT_RANGE_UNSIGNED).getUnsignedMin();
838  }
839 
840  /// Determine the max of the unsigned range for a particular SCEV.
842  return getRangeRef(S, HINT_RANGE_UNSIGNED).getUnsignedMax();
843  }
844 
845  /// Determine the signed range for a particular SCEV.
846  /// NOTE: This returns a copy of the reference returned by getRangeRef.
848  return getRangeRef(S, HINT_RANGE_SIGNED);
849  }
850 
851  /// Determine the min of the signed range for a particular SCEV.
853  return getRangeRef(S, HINT_RANGE_SIGNED).getSignedMin();
854  }
855 
856  /// Determine the max of the signed range for a particular SCEV.
858  return getRangeRef(S, HINT_RANGE_SIGNED).getSignedMax();
859  }
860 
861  /// Test if the given expression is known to be negative.
862  bool isKnownNegative(const SCEV *S);
863 
864  /// Test if the given expression is known to be positive.
865  bool isKnownPositive(const SCEV *S);
866 
867  /// Test if the given expression is known to be non-negative.
868  bool isKnownNonNegative(const SCEV *S);
869 
870  /// Test if the given expression is known to be non-positive.
871  bool isKnownNonPositive(const SCEV *S);
872 
873  /// Test if the given expression is known to be non-zero.
874  bool isKnownNonZero(const SCEV *S);
875 
876  /// Splits SCEV expression \p S into two SCEVs. One of them is obtained from
877  /// \p S by substitution of all AddRec sub-expression related to loop \p L
878  /// with initial value of that SCEV. The second is obtained from \p S by
879  /// substitution of all AddRec sub-expressions related to loop \p L with post
880  /// increment of this AddRec in the loop \p L. In both cases all other AddRec
881  /// sub-expressions (not related to \p L) remain the same.
882  /// If the \p S contains non-invariant unknown SCEV the function returns
883  /// CouldNotCompute SCEV in both values of std::pair.
884  /// For example, for SCEV S={0, +, 1}<L1> + {0, +, 1}<L2> and loop L=L1
885  /// the function returns pair:
886  /// first = {0, +, 1}<L2>
887  /// second = {1, +, 1}<L1> + {0, +, 1}<L2>
888  /// We can see that for the first AddRec sub-expression it was replaced with
889  /// 0 (initial value) for the first element and to {1, +, 1}<L1> (post
890  /// increment value) for the second one. In both cases AddRec expression
891  /// related to L2 remains the same.
892  std::pair<const SCEV *, const SCEV *> SplitIntoInitAndPostInc(const Loop *L,
893  const SCEV *S);
894 
895  /// We'd like to check the predicate on every iteration of the most dominated
896  /// loop between loops used in LHS and RHS.
897  /// To do this we use the following list of steps:
898  /// 1. Collect set S all loops on which either LHS or RHS depend.
899  /// 2. If S is non-empty
900  /// a. Let PD be the element of S which is dominated by all other elements.
901  /// b. Let E(LHS) be value of LHS on entry of PD.
902  /// To get E(LHS), we should just take LHS and replace all AddRecs that are
903  /// attached to PD on with their entry values.
904  /// Define E(RHS) in the same way.
905  /// c. Let B(LHS) be value of L on backedge of PD.
906  /// To get B(LHS), we should just take LHS and replace all AddRecs that are
907  /// attached to PD on with their backedge values.
908  /// Define B(RHS) in the same way.
909  /// d. Note that E(LHS) and E(RHS) are automatically available on entry of PD,
910  /// so we can assert on that.
911  /// e. Return true if isLoopEntryGuardedByCond(Pred, E(LHS), E(RHS)) &&
912  /// isLoopBackedgeGuardedByCond(Pred, B(LHS), B(RHS))
913  bool isKnownViaInduction(ICmpInst::Predicate Pred, const SCEV *LHS,
914  const SCEV *RHS);
915 
916  /// Test if the given expression is known to satisfy the condition described
917  /// by Pred, LHS, and RHS.
918  bool isKnownPredicate(ICmpInst::Predicate Pred, const SCEV *LHS,
919  const SCEV *RHS);
920 
921  /// Test if the condition described by Pred, LHS, RHS is known to be true on
922  /// every iteration of the loop of the recurrency LHS.
923  bool isKnownOnEveryIteration(ICmpInst::Predicate Pred,
924  const SCEVAddRecExpr *LHS, const SCEV *RHS);
925 
926  /// Return true if, for all loop invariant X, the predicate "LHS `Pred` X"
927  /// is monotonically increasing or decreasing. In the former case set
928  /// `Increasing` to true and in the latter case set `Increasing` to false.
929  ///
930  /// A predicate is said to be monotonically increasing if may go from being
931  /// false to being true as the loop iterates, but never the other way
932  /// around. A predicate is said to be monotonically decreasing if may go
933  /// from being true to being false as the loop iterates, but never the other
934  /// way around.
935  bool isMonotonicPredicate(const SCEVAddRecExpr *LHS, ICmpInst::Predicate Pred,
936  bool &Increasing);
937 
938  /// Return true if the result of the predicate LHS `Pred` RHS is loop
939  /// invariant with respect to L. Set InvariantPred, InvariantLHS and
940  /// InvariantLHS so that InvariantLHS `InvariantPred` InvariantRHS is the
941  /// loop invariant form of LHS `Pred` RHS.
942  bool isLoopInvariantPredicate(ICmpInst::Predicate Pred, const SCEV *LHS,
943  const SCEV *RHS, const Loop *L,
944  ICmpInst::Predicate &InvariantPred,
945  const SCEV *&InvariantLHS,
946  const SCEV *&InvariantRHS);
947 
948  /// Simplify LHS and RHS in a comparison with predicate Pred. Return true
949  /// iff any changes were made. If the operands are provably equal or
950  /// unequal, LHS and RHS are set to the same value and Pred is set to either
951  /// ICMP_EQ or ICMP_NE.
952  bool SimplifyICmpOperands(ICmpInst::Predicate &Pred, const SCEV *&LHS,
953  const SCEV *&RHS, unsigned Depth = 0);
954 
955  /// Return the "disposition" of the given SCEV with respect to the given
956  /// loop.
957  LoopDisposition getLoopDisposition(const SCEV *S, const Loop *L);
958 
959  /// Return true if the value of the given SCEV is unchanging in the
960  /// specified loop.
961  bool isLoopInvariant(const SCEV *S, const Loop *L);
962 
963  /// Determine if the SCEV can be evaluated at loop's entry. It is true if it
964  /// doesn't depend on a SCEVUnknown of an instruction which is dominated by
965  /// the header of loop L.
966  bool isAvailableAtLoopEntry(const SCEV *S, const Loop *L);
967 
968  /// Return true if the given SCEV changes value in a known way in the
969  /// specified loop. This property being true implies that the value is
970  /// variant in the loop AND that we can emit an expression to compute the
971  /// value of the expression at any particular loop iteration.
972  bool hasComputableLoopEvolution(const SCEV *S, const Loop *L);
973 
974  /// Return the "disposition" of the given SCEV with respect to the given
975  /// block.
976  BlockDisposition getBlockDisposition(const SCEV *S, const BasicBlock *BB);
977 
978  /// Return true if elements that makes up the given SCEV dominate the
979  /// specified basic block.
980  bool dominates(const SCEV *S, const BasicBlock *BB);
981 
982  /// Return true if elements that makes up the given SCEV properly dominate
983  /// the specified basic block.
984  bool properlyDominates(const SCEV *S, const BasicBlock *BB);
985 
986  /// Test whether the given SCEV has Op as a direct or indirect operand.
987  bool hasOperand(const SCEV *S, const SCEV *Op) const;
988 
989  /// Return the size of an element read or written by Inst.
990  const SCEV *getElementSize(Instruction *Inst);
991 
992  /// Compute the array dimensions Sizes from the set of Terms extracted from
993  /// the memory access function of this SCEVAddRecExpr (second step of
994  /// delinearization).
995  void findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
997  const SCEV *ElementSize);
998 
999  void print(raw_ostream &OS) const;
1000  void verify() const;
1001  bool invalidate(Function &F, const PreservedAnalyses &PA,
1003 
1004  /// Collect parametric terms occurring in step expressions (first step of
1005  /// delinearization).
1006  void collectParametricTerms(const SCEV *Expr,
1008 
1009  /// Return in Subscripts the access functions for each dimension in Sizes
1010  /// (third step of delinearization).
1011  void computeAccessFunctions(const SCEV *Expr,
1012  SmallVectorImpl<const SCEV *> &Subscripts,
1014 
1015  /// Split this SCEVAddRecExpr into two vectors of SCEVs representing the
1016  /// subscripts and sizes of an array access.
1017  ///
1018  /// The delinearization is a 3 step process: the first two steps compute the
1019  /// sizes of each subscript and the third step computes the access functions
1020  /// for the delinearized array:
1021  ///
1022  /// 1. Find the terms in the step functions
1023  /// 2. Compute the array size
1024  /// 3. Compute the access function: divide the SCEV by the array size
1025  /// starting with the innermost dimensions found in step 2. The Quotient
1026  /// is the SCEV to be divided in the next step of the recursion. The
1027  /// Remainder is the subscript of the innermost dimension. Loop over all
1028  /// array dimensions computed in step 2.
1029  ///
1030  /// To compute a uniform array size for several memory accesses to the same
1031  /// object, one can collect in step 1 all the step terms for all the memory
1032  /// accesses, and compute in step 2 a unique array shape. This guarantees
1033  /// that the array shape will be the same across all memory accesses.
1034  ///
1035  /// FIXME: We could derive the result of steps 1 and 2 from a description of
1036  /// the array shape given in metadata.
1037  ///
1038  /// Example:
1039  ///
1040  /// A[][n][m]
1041  ///
1042  /// for i
1043  /// for j
1044  /// for k
1045  /// A[j+k][2i][5i] =
1046  ///
1047  /// The initial SCEV:
1048  ///
1049  /// A[{{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k]
1050  ///
1051  /// 1. Find the different terms in the step functions:
1052  /// -> [2*m, 5, n*m, n*m]
1053  ///
1054  /// 2. Compute the array size: sort and unique them
1055  /// -> [n*m, 2*m, 5]
1056  /// find the GCD of all the terms = 1
1057  /// divide by the GCD and erase constant terms
1058  /// -> [n*m, 2*m]
1059  /// GCD = m
1060  /// divide by GCD -> [n, 2]
1061  /// remove constant terms
1062  /// -> [n]
1063  /// size of the array is A[unknown][n][m]
1064  ///
1065  /// 3. Compute the access function
1066  /// a. Divide {{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k by the innermost size m
1067  /// Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k
1068  /// Remainder: {{{0,+,5}_i, +, 0}_j, +, 0}_k
1069  /// The remainder is the subscript of the innermost array dimension: [5i].
1070  ///
1071  /// b. Divide Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k by next outer size n
1072  /// Quotient: {{{0,+,0}_i, +, 1}_j, +, 1}_k
1073  /// Remainder: {{{0,+,2}_i, +, 0}_j, +, 0}_k
1074  /// The Remainder is the subscript of the next array dimension: [2i].
1075  ///
1076  /// The subscript of the outermost dimension is the Quotient: [j+k].
1077  ///
1078  /// Overall, we have: A[][n][m], and the access function: A[j+k][2i][5i].
1079  void delinearize(const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
1081  const SCEV *ElementSize);
1082 
1083  /// Return the DataLayout associated with the module this SCEV instance is
1084  /// operating on.
1085  const DataLayout &getDataLayout() const {
1086  return F.getParent()->getDataLayout();
1087  }
1088 
1089  const SCEVPredicate *getEqualPredicate(const SCEV *LHS, const SCEV *RHS);
1090 
1091  const SCEVPredicate *
1092  getWrapPredicate(const SCEVAddRecExpr *AR,
1094 
1095  /// Re-writes the SCEV according to the Predicates in \p A.
1096  const SCEV *rewriteUsingPredicate(const SCEV *S, const Loop *L,
1098  /// Tries to convert the \p S expression to an AddRec expression,
1099  /// adding additional predicates to \p Preds as required.
1100  const SCEVAddRecExpr *convertSCEVToAddRecWithPredicates(
1101  const SCEV *S, const Loop *L,
1103 
1104 private:
1105  /// A CallbackVH to arrange for ScalarEvolution to be notified whenever a
1106  /// Value is deleted.
1107  class SCEVCallbackVH final : public CallbackVH {
1108  ScalarEvolution *SE;
1109 
1110  void deleted() override;
1111  void allUsesReplacedWith(Value *New) override;
1112 
1113  public:
1114  SCEVCallbackVH(Value *V, ScalarEvolution *SE = nullptr);
1115  };
1116 
1117  friend class SCEVCallbackVH;
1118  friend class SCEVExpander;
1119  friend class SCEVUnknown;
1120 
1121  /// The function we are analyzing.
1122  Function &F;
1123 
1124  /// Does the module have any calls to the llvm.experimental.guard intrinsic
1125  /// at all? If this is false, we avoid doing work that will only help if
1126  /// thare are guards present in the IR.
1127  bool HasGuards;
1128 
1129  /// The target library information for the target we are targeting.
1130  TargetLibraryInfo &TLI;
1131 
1132  /// The tracker for \@llvm.assume intrinsics in this function.
1133  AssumptionCache &AC;
1134 
1135  /// The dominator tree.
1136  DominatorTree &DT;
1137 
1138  /// The loop information for the function we are currently analyzing.
1139  LoopInfo &LI;
1140 
1141  /// This SCEV is used to represent unknown trip counts and things.
1142  std::unique_ptr<SCEVCouldNotCompute> CouldNotCompute;
1143 
1144  /// The type for HasRecMap.
1146 
1147  /// This is a cache to record whether a SCEV contains any scAddRecExpr.
1148  HasRecMapType HasRecMap;
1149 
1150  /// The type for ExprValueMap.
1151  using ValueOffsetPair = std::pair<Value *, ConstantInt *>;
1153 
1154  /// ExprValueMap -- This map records the original values from which
1155  /// the SCEV expr is generated from.
1156  ///
1157  /// We want to represent the mapping as SCEV -> ValueOffsetPair instead
1158  /// of SCEV -> Value:
1159  /// Suppose we know S1 expands to V1, and
1160  /// S1 = S2 + C_a
1161  /// S3 = S2 + C_b
1162  /// where C_a and C_b are different SCEVConstants. Then we'd like to
1163  /// expand S3 as V1 - C_a + C_b instead of expanding S2 literally.
1164  /// It is helpful when S2 is a complex SCEV expr.
1165  ///
1166  /// In order to do that, we represent ExprValueMap as a mapping from
1167  /// SCEV to ValueOffsetPair. We will save both S1->{V1, 0} and
1168  /// S2->{V1, C_a} into the map when we create SCEV for V1. When S3
1169  /// is expanded, it will first expand S2 to V1 - C_a because of
1170  /// S2->{V1, C_a} in the map, then expand S3 to V1 - C_a + C_b.
1171  ///
1172  /// Note: S->{V, Offset} in the ExprValueMap means S can be expanded
1173  /// to V - Offset.
1174  ExprValueMapType ExprValueMap;
1175 
1176  /// The type for ValueExprMap.
1177  using ValueExprMapType =
1179 
1180  /// This is a cache of the values we have analyzed so far.
1181  ValueExprMapType ValueExprMap;
1182 
1183  /// Mark predicate values currently being processed by isImpliedCond.
1184  SmallPtrSet<Value *, 6> PendingLoopPredicates;
1185 
1186  /// Mark SCEVUnknown Phis currently being processed by getRangeRef.
1187  SmallPtrSet<const PHINode *, 6> PendingPhiRanges;
1188 
1189  // Mark SCEVUnknown Phis currently being processed by isImpliedViaMerge.
1190  SmallPtrSet<const PHINode *, 6> PendingMerges;
1191 
1192  /// Set to true by isLoopBackedgeGuardedByCond when we're walking the set of
1193  /// conditions dominating the backedge of a loop.
1194  bool WalkingBEDominatingConds = false;
1195 
1196  /// Set to true by isKnownPredicateViaSplitting when we're trying to prove a
1197  /// predicate by splitting it into a set of independent predicates.
1198  bool ProvingSplitPredicate = false;
1199 
1200  /// Memoized values for the GetMinTrailingZeros
1201  DenseMap<const SCEV *, uint32_t> MinTrailingZerosCache;
1202 
1203  /// Return the Value set from which the SCEV expr is generated.
1204  SetVector<ValueOffsetPair> *getSCEVValues(const SCEV *S);
1205 
1206  /// Private helper method for the GetMinTrailingZeros method
1207  uint32_t GetMinTrailingZerosImpl(const SCEV *S);
1208 
1209  /// Information about the number of loop iterations for which a loop exit's
1210  /// branch condition evaluates to the not-taken path. This is a temporary
1211  /// pair of exact and max expressions that are eventually summarized in
1212  /// ExitNotTakenInfo and BackedgeTakenInfo.
1213  struct ExitLimit {
1214  const SCEV *ExactNotTaken; // The exit is not taken exactly this many times
1215  const SCEV *MaxNotTaken; // The exit is not taken at most this many times
1216 
1217  // Not taken either exactly MaxNotTaken or zero times
1218  bool MaxOrZero = false;
1219 
1220  /// A set of predicate guards for this ExitLimit. The result is only valid
1221  /// if all of the predicates in \c Predicates evaluate to 'true' at
1222  /// run-time.
1224 
1225  void addPredicate(const SCEVPredicate *P) {
1226  assert(!isa<SCEVUnionPredicate>(P) && "Only add leaf predicates here!");
1227  Predicates.insert(P);
1228  }
1229 
1230  /*implicit*/ ExitLimit(const SCEV *E);
1231 
1232  ExitLimit(
1233  const SCEV *E, const SCEV *M, bool MaxOrZero,
1234  ArrayRef<const SmallPtrSetImpl<const SCEVPredicate *> *> PredSetList);
1235 
1236  ExitLimit(const SCEV *E, const SCEV *M, bool MaxOrZero,
1238 
1239  ExitLimit(const SCEV *E, const SCEV *M, bool MaxOrZero);
1240 
1241  /// Test whether this ExitLimit contains any computed information, or
1242  /// whether it's all SCEVCouldNotCompute values.
1243  bool hasAnyInfo() const {
1244  return !isa<SCEVCouldNotCompute>(ExactNotTaken) ||
1245  !isa<SCEVCouldNotCompute>(MaxNotTaken);
1246  }
1247 
1248  bool hasOperand(const SCEV *S) const;
1249 
1250  /// Test whether this ExitLimit contains all information.
1251  bool hasFullInfo() const {
1252  return !isa<SCEVCouldNotCompute>(ExactNotTaken);
1253  }
1254  };
1255 
1256  /// Information about the number of times a particular loop exit may be
1257  /// reached before exiting the loop.
1258  struct ExitNotTakenInfo {
1259  PoisoningVH<BasicBlock> ExitingBlock;
1260  const SCEV *ExactNotTaken;
1261  std::unique_ptr<SCEVUnionPredicate> Predicate;
1262 
1263  explicit ExitNotTakenInfo(PoisoningVH<BasicBlock> ExitingBlock,
1264  const SCEV *ExactNotTaken,
1265  std::unique_ptr<SCEVUnionPredicate> Predicate)
1266  : ExitingBlock(ExitingBlock), ExactNotTaken(ExactNotTaken),
1267  Predicate(std::move(Predicate)) {}
1268 
1269  bool hasAlwaysTruePredicate() const {
1270  return !Predicate || Predicate->isAlwaysTrue();
1271  }
1272  };
1273 
1274  /// Information about the backedge-taken count of a loop. This currently
1275  /// includes an exact count and a maximum count.
1276  ///
1277  class BackedgeTakenInfo {
1278  /// A list of computable exits and their not-taken counts. Loops almost
1279  /// never have more than one computable exit.
1280  SmallVector<ExitNotTakenInfo, 1> ExitNotTaken;
1281 
1282  /// The pointer part of \c MaxAndComplete is an expression indicating the
1283  /// least maximum backedge-taken count of the loop that is known, or a
1284  /// SCEVCouldNotCompute. This expression is only valid if the predicates
1285  /// associated with all loop exits are true.
1286  ///
1287  /// The integer part of \c MaxAndComplete is a boolean indicating if \c
1288  /// ExitNotTaken has an element for every exiting block in the loop.
1289  PointerIntPair<const SCEV *, 1> MaxAndComplete;
1290 
1291  /// True iff the backedge is taken either exactly Max or zero times.
1292  bool MaxOrZero = false;
1293 
1294  /// \name Helper projection functions on \c MaxAndComplete.
1295  /// @{
1296  bool isComplete() const { return MaxAndComplete.getInt(); }
1297  const SCEV *getMax() const { return MaxAndComplete.getPointer(); }
1298  /// @}
1299 
1300  public:
1301  BackedgeTakenInfo() : MaxAndComplete(nullptr, 0) {}
1302  BackedgeTakenInfo(BackedgeTakenInfo &&) = default;
1303  BackedgeTakenInfo &operator=(BackedgeTakenInfo &&) = default;
1304 
1305  using EdgeExitInfo = std::pair<BasicBlock *, ExitLimit>;
1306 
1307  /// Initialize BackedgeTakenInfo from a list of exact exit counts.
1308  BackedgeTakenInfo(ArrayRef<EdgeExitInfo> ExitCounts, bool Complete,
1309  const SCEV *MaxCount, bool MaxOrZero);
1310 
1311  /// Test whether this BackedgeTakenInfo contains any computed information,
1312  /// or whether it's all SCEVCouldNotCompute values.
1313  bool hasAnyInfo() const {
1314  return !ExitNotTaken.empty() || !isa<SCEVCouldNotCompute>(getMax());
1315  }
1316 
1317  /// Test whether this BackedgeTakenInfo contains complete information.
1318  bool hasFullInfo() const { return isComplete(); }
1319 
1320  /// Return an expression indicating the exact *backedge-taken*
1321  /// count of the loop if it is known or SCEVCouldNotCompute
1322  /// otherwise. If execution makes it to the backedge on every
1323  /// iteration (i.e. there are no abnormal exists like exception
1324  /// throws and thread exits) then this is the number of times the
1325  /// loop header will execute minus one.
1326  ///
1327  /// If the SCEV predicate associated with the answer can be different
1328  /// from AlwaysTrue, we must add a (non null) Predicates argument.
1329  /// The SCEV predicate associated with the answer will be added to
1330  /// Predicates. A run-time check needs to be emitted for the SCEV
1331  /// predicate in order for the answer to be valid.
1332  ///
1333  /// Note that we should always know if we need to pass a predicate
1334  /// argument or not from the way the ExitCounts vector was computed.
1335  /// If we allowed SCEV predicates to be generated when populating this
1336  /// vector, this information can contain them and therefore a
1337  /// SCEVPredicate argument should be added to getExact.
1338  const SCEV *getExact(const Loop *L, ScalarEvolution *SE,
1339  SCEVUnionPredicate *Predicates = nullptr) const;
1340 
1341  /// Return the number of times this loop exit may fall through to the back
1342  /// edge, or SCEVCouldNotCompute. The loop is guaranteed not to exit via
1343  /// this block before this number of iterations, but may exit via another
1344  /// block.
1345  const SCEV *getExact(BasicBlock *ExitingBlock, ScalarEvolution *SE) const;
1346 
1347  /// Get the max backedge taken count for the loop.
1348  const SCEV *getMax(ScalarEvolution *SE) const;
1349 
1350  /// Return true if the number of times this backedge is taken is either the
1351  /// value returned by getMax or zero.
1352  bool isMaxOrZero(ScalarEvolution *SE) const;
1353 
1354  /// Return true if any backedge taken count expressions refer to the given
1355  /// subexpression.
1356  bool hasOperand(const SCEV *S, ScalarEvolution *SE) const;
1357 
1358  /// Invalidate this result and free associated memory.
1359  void clear();
1360  };
1361 
1362  /// Cache the backedge-taken count of the loops for this function as they
1363  /// are computed.
1364  DenseMap<const Loop *, BackedgeTakenInfo> BackedgeTakenCounts;
1365 
1366  /// Cache the predicated backedge-taken count of the loops for this
1367  /// function as they are computed.
1368  DenseMap<const Loop *, BackedgeTakenInfo> PredicatedBackedgeTakenCounts;
1369 
1370  /// This map contains entries for all of the PHI instructions that we
1371  /// attempt to compute constant evolutions for. This allows us to avoid
1372  /// potentially expensive recomputation of these properties. An instruction
1373  /// maps to null if we are unable to compute its exit value.
1374  DenseMap<PHINode *, Constant *> ConstantEvolutionLoopExitValue;
1375 
1376  /// This map contains entries for all the expressions that we attempt to
1377  /// compute getSCEVAtScope information for, which can be expensive in
1378  /// extreme cases.
1380  ValuesAtScopes;
1381 
1382  /// Memoized computeLoopDisposition results.
1383  DenseMap<const SCEV *,
1385  LoopDispositions;
1386 
1387  struct LoopProperties {
1388  /// Set to true if the loop contains no instruction that can have side
1389  /// effects (i.e. via throwing an exception, volatile or atomic access).
1390  bool HasNoAbnormalExits;
1391 
1392  /// Set to true if the loop contains no instruction that can abnormally exit
1393  /// the loop (i.e. via throwing an exception, by terminating the thread
1394  /// cleanly or by infinite looping in a called function). Strictly
1395  /// speaking, the last one is not leaving the loop, but is identical to
1396  /// leaving the loop for reasoning about undefined behavior.
1397  bool HasNoSideEffects;
1398  };
1399 
1400  /// Cache for \c getLoopProperties.
1401  DenseMap<const Loop *, LoopProperties> LoopPropertiesCache;
1402 
1403  /// Return a \c LoopProperties instance for \p L, creating one if necessary.
1404  LoopProperties getLoopProperties(const Loop *L);
1405 
1406  bool loopHasNoSideEffects(const Loop *L) {
1407  return getLoopProperties(L).HasNoSideEffects;
1408  }
1409 
1410  bool loopHasNoAbnormalExits(const Loop *L) {
1411  return getLoopProperties(L).HasNoAbnormalExits;
1412  }
1413 
1414  /// Compute a LoopDisposition value.
1415  LoopDisposition computeLoopDisposition(const SCEV *S, const Loop *L);
1416 
1417  /// Memoized computeBlockDisposition results.
1418  DenseMap<
1419  const SCEV *,
1421  BlockDispositions;
1422 
1423  /// Compute a BlockDisposition value.
1424  BlockDisposition computeBlockDisposition(const SCEV *S, const BasicBlock *BB);
1425 
1426  /// Memoized results from getRange
1428 
1429  /// Memoized results from getRange
1431 
1432  /// Used to parameterize getRange
1433  enum RangeSignHint { HINT_RANGE_UNSIGNED, HINT_RANGE_SIGNED };
1434 
1435  /// Set the memoized range for the given SCEV.
1436  const ConstantRange &setRange(const SCEV *S, RangeSignHint Hint,
1437  ConstantRange CR) {
1439  Hint == HINT_RANGE_UNSIGNED ? UnsignedRanges : SignedRanges;
1440 
1441  auto Pair = Cache.try_emplace(S, std::move(CR));
1442  if (!Pair.second)
1443  Pair.first->second = std::move(CR);
1444  return Pair.first->second;
1445  }
1446 
1447  /// Determine the range for a particular SCEV.
1448  /// NOTE: This returns a reference to an entry in a cache. It must be
1449  /// copied if its needed for longer.
1450  const ConstantRange &getRangeRef(const SCEV *S, RangeSignHint Hint);
1451 
1452  /// Determines the range for the affine SCEVAddRecExpr {\p Start,+,\p Stop}.
1453  /// Helper for \c getRange.
1454  ConstantRange getRangeForAffineAR(const SCEV *Start, const SCEV *Stop,
1455  const SCEV *MaxBECount, unsigned BitWidth);
1456 
1457  /// Try to compute a range for the affine SCEVAddRecExpr {\p Start,+,\p
1458  /// Stop} by "factoring out" a ternary expression from the add recurrence.
1459  /// Helper called by \c getRange.
1460  ConstantRange getRangeViaFactoring(const SCEV *Start, const SCEV *Stop,
1461  const SCEV *MaxBECount, unsigned BitWidth);
1462 
1463  /// We know that there is no SCEV for the specified value. Analyze the
1464  /// expression.
1465  const SCEV *createSCEV(Value *V);
1466 
1467  /// Provide the special handling we need to analyze PHI SCEVs.
1468  const SCEV *createNodeForPHI(PHINode *PN);
1469 
1470  /// Helper function called from createNodeForPHI.
1471  const SCEV *createAddRecFromPHI(PHINode *PN);
1472 
1473  /// A helper function for createAddRecFromPHI to handle simple cases.
1474  const SCEV *createSimpleAffineAddRec(PHINode *PN, Value *BEValueV,
1475  Value *StartValueV);
1476 
1477  /// Helper function called from createNodeForPHI.
1478  const SCEV *createNodeFromSelectLikePHI(PHINode *PN);
1479 
1480  /// Provide special handling for a select-like instruction (currently this
1481  /// is either a select instruction or a phi node). \p I is the instruction
1482  /// being processed, and it is assumed equivalent to "Cond ? TrueVal :
1483  /// FalseVal".
1484  const SCEV *createNodeForSelectOrPHI(Instruction *I, Value *Cond,
1485  Value *TrueVal, Value *FalseVal);
1486 
1487  /// Provide the special handling we need to analyze GEP SCEVs.
1488  const SCEV *createNodeForGEP(GEPOperator *GEP);
1489 
1490  /// Implementation code for getSCEVAtScope; called at most once for each
1491  /// SCEV+Loop pair.
1492  const SCEV *computeSCEVAtScope(const SCEV *S, const Loop *L);
1493 
1494  /// This looks up computed SCEV values for all instructions that depend on
1495  /// the given instruction and removes them from the ValueExprMap map if they
1496  /// reference SymName. This is used during PHI resolution.
1497  void forgetSymbolicName(Instruction *I, const SCEV *SymName);
1498 
1499  /// Return the BackedgeTakenInfo for the given loop, lazily computing new
1500  /// values if the loop hasn't been analyzed yet. The returned result is
1501  /// guaranteed not to be predicated.
1502  const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
1503 
1504  /// Similar to getBackedgeTakenInfo, but will add predicates as required
1505  /// with the purpose of returning complete information.
1506  const BackedgeTakenInfo &getPredicatedBackedgeTakenInfo(const Loop *L);
1507 
1508  /// Compute the number of times the specified loop will iterate.
1509  /// If AllowPredicates is set, we will create new SCEV predicates as
1510  /// necessary in order to return an exact answer.
1511  BackedgeTakenInfo computeBackedgeTakenCount(const Loop *L,
1512  bool AllowPredicates = false);
1513 
1514  /// Compute the number of times the backedge of the specified loop will
1515  /// execute if it exits via the specified block. If AllowPredicates is set,
1516  /// this call will try to use a minimal set of SCEV predicates in order to
1517  /// return an exact answer.
1518  ExitLimit computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
1519  bool AllowPredicates = false);
1520 
1521  /// Compute the number of times the backedge of the specified loop will
1522  /// execute if its exit condition were a conditional branch of ExitCond.
1523  ///
1524  /// \p ControlsExit is true if ExitCond directly controls the exit
1525  /// branch. In this case, we can assume that the loop exits only if the
1526  /// condition is true and can infer that failing to meet the condition prior
1527  /// to integer wraparound results in undefined behavior.
1528  ///
1529  /// If \p AllowPredicates is set, this call will try to use a minimal set of
1530  /// SCEV predicates in order to return an exact answer.
1531  ExitLimit computeExitLimitFromCond(const Loop *L, Value *ExitCond,
1532  bool ExitIfTrue, bool ControlsExit,
1533  bool AllowPredicates = false);
1534 
1535  // Helper functions for computeExitLimitFromCond to avoid exponential time
1536  // complexity.
1537 
1538  class ExitLimitCache {
1539  // It may look like we need key on the whole (L, ExitIfTrue, ControlsExit,
1540  // AllowPredicates) tuple, but recursive calls to
1541  // computeExitLimitFromCondCached from computeExitLimitFromCondImpl only
1542  // vary the in \c ExitCond and \c ControlsExit parameters. We remember the
1543  // initial values of the other values to assert our assumption.
1544  SmallDenseMap<PointerIntPair<Value *, 1>, ExitLimit> TripCountMap;
1545 
1546  const Loop *L;
1547  bool ExitIfTrue;
1548  bool AllowPredicates;
1549 
1550  public:
1551  ExitLimitCache(const Loop *L, bool ExitIfTrue, bool AllowPredicates)
1552  : L(L), ExitIfTrue(ExitIfTrue), AllowPredicates(AllowPredicates) {}
1553 
1554  Optional<ExitLimit> find(const Loop *L, Value *ExitCond, bool ExitIfTrue,
1555  bool ControlsExit, bool AllowPredicates);
1556 
1557  void insert(const Loop *L, Value *ExitCond, bool ExitIfTrue,
1558  bool ControlsExit, bool AllowPredicates, const ExitLimit &EL);
1559  };
1560 
1561  using ExitLimitCacheTy = ExitLimitCache;
1562 
1563  ExitLimit computeExitLimitFromCondCached(ExitLimitCacheTy &Cache,
1564  const Loop *L, Value *ExitCond,
1565  bool ExitIfTrue,
1566  bool ControlsExit,
1567  bool AllowPredicates);
1568  ExitLimit computeExitLimitFromCondImpl(ExitLimitCacheTy &Cache, const Loop *L,
1569  Value *ExitCond, bool ExitIfTrue,
1570  bool ControlsExit,
1571  bool AllowPredicates);
1572 
1573  /// Compute the number of times the backedge of the specified loop will
1574  /// execute if its exit condition were a conditional branch of the ICmpInst
1575  /// ExitCond and ExitIfTrue. If AllowPredicates is set, this call will try
1576  /// to use a minimal set of SCEV predicates in order to return an exact
1577  /// answer.
1578  ExitLimit computeExitLimitFromICmp(const Loop *L, ICmpInst *ExitCond,
1579  bool ExitIfTrue,
1580  bool IsSubExpr,
1581  bool AllowPredicates = false);
1582 
1583  /// Compute the number of times the backedge of the specified loop will
1584  /// execute if its exit condition were a switch with a single exiting case
1585  /// to ExitingBB.
1586  ExitLimit computeExitLimitFromSingleExitSwitch(const Loop *L,
1587  SwitchInst *Switch,
1588  BasicBlock *ExitingBB,
1589  bool IsSubExpr);
1590 
1591  /// Given an exit condition of 'icmp op load X, cst', try to see if we can
1592  /// compute the backedge-taken count.
1593  ExitLimit computeLoadConstantCompareExitLimit(LoadInst *LI, Constant *RHS,
1594  const Loop *L,
1596 
1597  /// Compute the exit limit of a loop that is controlled by a
1598  /// "(IV >> 1) != 0" type comparison. We cannot compute the exact trip
1599  /// count in these cases (since SCEV has no way of expressing them), but we
1600  /// can still sometimes compute an upper bound.
1601  ///
1602  /// Return an ExitLimit for a loop whose backedge is guarded by `LHS Pred
1603  /// RHS`.
1604  ExitLimit computeShiftCompareExitLimit(Value *LHS, Value *RHS, const Loop *L,
1605  ICmpInst::Predicate Pred);
1606 
1607  /// If the loop is known to execute a constant number of times (the
1608  /// condition evolves only from constants), try to evaluate a few iterations
1609  /// of the loop until we get the exit condition gets a value of ExitWhen
1610  /// (true or false). If we cannot evaluate the exit count of the loop,
1611  /// return CouldNotCompute.
1612  const SCEV *computeExitCountExhaustively(const Loop *L, Value *Cond,
1613  bool ExitWhen);
1614 
1615  /// Return the number of times an exit condition comparing the specified
1616  /// value to zero will execute. If not computable, return CouldNotCompute.
1617  /// If AllowPredicates is set, this call will try to use a minimal set of
1618  /// SCEV predicates in order to return an exact answer.
1619  ExitLimit howFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr,
1620  bool AllowPredicates = false);
1621 
1622  /// Return the number of times an exit condition checking the specified
1623  /// value for nonzero will execute. If not computable, return
1624  /// CouldNotCompute.
1625  ExitLimit howFarToNonZero(const SCEV *V, const Loop *L);
1626 
1627  /// Return the number of times an exit condition containing the specified
1628  /// less-than comparison will execute. If not computable, return
1629  /// CouldNotCompute.
1630  ///
1631  /// \p isSigned specifies whether the less-than is signed.
1632  ///
1633  /// \p ControlsExit is true when the LHS < RHS condition directly controls
1634  /// the branch (loops exits only if condition is true). In this case, we can
1635  /// use NoWrapFlags to skip overflow checks.
1636  ///
1637  /// If \p AllowPredicates is set, this call will try to use a minimal set of
1638  /// SCEV predicates in order to return an exact answer.
1639  ExitLimit howManyLessThans(const SCEV *LHS, const SCEV *RHS, const Loop *L,
1640  bool isSigned, bool ControlsExit,
1641  bool AllowPredicates = false);
1642 
1643  ExitLimit howManyGreaterThans(const SCEV *LHS, const SCEV *RHS, const Loop *L,
1644  bool isSigned, bool IsSubExpr,
1645  bool AllowPredicates = false);
1646 
1647  /// Return a predecessor of BB (which may not be an immediate predecessor)
1648  /// which has exactly one successor from which BB is reachable, or null if
1649  /// no such block is found.
1650  std::pair<BasicBlock *, BasicBlock *>
1651  getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
1652 
1653  /// Test whether the condition described by Pred, LHS, and RHS is true
1654  /// whenever the given FoundCondValue value evaluates to true.
1655  bool isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
1656  Value *FoundCondValue, bool Inverse);
1657 
1658  /// Test whether the condition described by Pred, LHS, and RHS is true
1659  /// whenever the condition described by FoundPred, FoundLHS, FoundRHS is
1660  /// true.
1661  bool isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
1662  ICmpInst::Predicate FoundPred, 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.
1668  bool isImpliedCondOperands(ICmpInst::Predicate Pred, const SCEV *LHS,
1669  const SCEV *RHS, const SCEV *FoundLHS,
1670  const SCEV *FoundRHS);
1671 
1672  /// Test whether the condition described by Pred, LHS, and RHS is true
1673  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1674  /// true. Here LHS is an operation that includes FoundLHS as one of its
1675  /// arguments.
1676  bool isImpliedViaOperations(ICmpInst::Predicate Pred,
1677  const SCEV *LHS, const SCEV *RHS,
1678  const SCEV *FoundLHS, const SCEV *FoundRHS,
1679  unsigned Depth = 0);
1680 
1681  /// Test whether the condition described by Pred, LHS, and RHS is true.
1682  /// Use only simple non-recursive types of checks, such as range analysis etc.
1683  bool isKnownViaNonRecursiveReasoning(ICmpInst::Predicate Pred,
1684  const SCEV *LHS, const SCEV *RHS);
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.
1689  bool isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, const SCEV *LHS,
1690  const SCEV *RHS, const SCEV *FoundLHS,
1691  const SCEV *FoundRHS);
1692 
1693  /// Test whether the condition described by Pred, LHS, and RHS is true
1694  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1695  /// true. Utility function used by isImpliedCondOperands. Tries to get
1696  /// cases like "X `sgt` 0 => X - 1 `sgt` -1".
1697  bool isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred, const SCEV *LHS,
1698  const SCEV *RHS, const SCEV *FoundLHS,
1699  const SCEV *FoundRHS);
1700 
1701  /// Return true if the condition denoted by \p LHS \p Pred \p RHS is implied
1702  /// by a call to \c @llvm.experimental.guard in \p BB.
1703  bool isImpliedViaGuard(BasicBlock *BB, ICmpInst::Predicate Pred,
1704  const SCEV *LHS, const SCEV *RHS);
1705 
1706  /// Test whether the condition described by Pred, LHS, and RHS is true
1707  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1708  /// true.
1709  ///
1710  /// This routine tries to rule out certain kinds of integer overflow, and
1711  /// then tries to reason about arithmetic properties of the predicates.
1712  bool isImpliedCondOperandsViaNoOverflow(ICmpInst::Predicate Pred,
1713  const SCEV *LHS, const SCEV *RHS,
1714  const SCEV *FoundLHS,
1715  const SCEV *FoundRHS);
1716 
1717  /// Test whether the condition described by Pred, LHS, and RHS is true
1718  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1719  /// true.
1720  ///
1721  /// This routine tries to figure out predicate for Phis which are SCEVUnknown
1722  /// if it is true for every possible incoming value from their respective
1723  /// basic blocks.
1724  bool isImpliedViaMerge(ICmpInst::Predicate Pred,
1725  const SCEV *LHS, const SCEV *RHS,
1726  const SCEV *FoundLHS, const SCEV *FoundRHS,
1727  unsigned Depth);
1728 
1729  /// If we know that the specified Phi is in the header of its containing
1730  /// loop, we know the loop executes a constant number of times, and the PHI
1731  /// node is just a recurrence involving constants, fold it.
1732  Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt &BEs,
1733  const Loop *L);
1734 
1735  /// Test if the given expression is known to satisfy the condition described
1736  /// by Pred and the known constant ranges of LHS and RHS.
1737  bool isKnownPredicateViaConstantRanges(ICmpInst::Predicate Pred,
1738  const SCEV *LHS, const SCEV *RHS);
1739 
1740  /// Try to prove the condition described by "LHS Pred RHS" by ruling out
1741  /// integer overflow.
1742  ///
1743  /// For instance, this will return true for "A s< (A + C)<nsw>" if C is
1744  /// positive.
1745  bool isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred, const SCEV *LHS,
1746  const SCEV *RHS);
1747 
1748  /// Try to split Pred LHS RHS into logical conjunctions (and's) and try to
1749  /// prove them individually.
1750  bool isKnownPredicateViaSplitting(ICmpInst::Predicate Pred, const SCEV *LHS,
1751  const SCEV *RHS);
1752 
1753  /// Try to match the Expr as "(L + R)<Flags>".
1754  bool splitBinaryAdd(const SCEV *Expr, const SCEV *&L, const SCEV *&R,
1755  SCEV::NoWrapFlags &Flags);
1756 
1757  /// Compute \p LHS - \p RHS and returns the result as an APInt if it is a
1758  /// constant, and None if it isn't.
1759  ///
1760  /// This is intended to be a cheaper version of getMinusSCEV. We can be
1761  /// frugal here since we just bail out of actually constructing and
1762  /// canonicalizing an expression in the cases where the result isn't going
1763  /// to be a constant.
1764  Optional<APInt> computeConstantDifference(const SCEV *LHS, const SCEV *RHS);
1765 
1766  /// Drop memoized information computed for S.
1767  void forgetMemoizedResults(const SCEV *S);
1768 
1769  /// Return an existing SCEV for V if there is one, otherwise return nullptr.
1770  const SCEV *getExistingSCEV(Value *V);
1771 
1772  /// Return false iff given SCEV contains a SCEVUnknown with NULL value-
1773  /// pointer.
1774  bool checkValidity(const SCEV *S) const;
1775 
1776  /// Return true if `ExtendOpTy`({`Start`,+,`Step`}) can be proved to be
1777  /// equal to {`ExtendOpTy`(`Start`),+,`ExtendOpTy`(`Step`)}. This is
1778  /// equivalent to proving no signed (resp. unsigned) wrap in
1779  /// {`Start`,+,`Step`} if `ExtendOpTy` is `SCEVSignExtendExpr`
1780  /// (resp. `SCEVZeroExtendExpr`).
1781  template <typename ExtendOpTy>
1782  bool proveNoWrapByVaryingStart(const SCEV *Start, const SCEV *Step,
1783  const Loop *L);
1784 
1785  /// Try to prove NSW or NUW on \p AR relying on ConstantRange manipulation.
1786  SCEV::NoWrapFlags proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR);
1787 
1788  bool isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
1789  ICmpInst::Predicate Pred, bool &Increasing);
1790 
1791  /// Return SCEV no-wrap flags that can be proven based on reasoning about
1792  /// how poison produced from no-wrap flags on this value (e.g. a nuw add)
1793  /// would trigger undefined behavior on overflow.
1794  SCEV::NoWrapFlags getNoWrapFlagsFromUB(const Value *V);
1795 
1796  /// Return true if the SCEV corresponding to \p I is never poison. Proving
1797  /// this is more complex than proving that just \p I is never poison, since
1798  /// SCEV commons expressions across control flow, and you can have cases
1799  /// like:
1800  ///
1801  /// idx0 = a + b;
1802  /// ptr[idx0] = 100;
1803  /// if (<condition>) {
1804  /// idx1 = a +nsw b;
1805  /// ptr[idx1] = 200;
1806  /// }
1807  ///
1808  /// where the SCEV expression (+ a b) is guaranteed to not be poison (and
1809  /// hence not sign-overflow) only if "<condition>" is true. Since both
1810  /// `idx0` and `idx1` will be mapped to the same SCEV expression, (+ a b),
1811  /// it is not okay to annotate (+ a b) with <nsw> in the above example.
1812  bool isSCEVExprNeverPoison(const Instruction *I);
1813 
1814  /// This is like \c isSCEVExprNeverPoison but it specifically works for
1815  /// instructions that will get mapped to SCEV add recurrences. Return true
1816  /// if \p I will never generate poison under the assumption that \p I is an
1817  /// add recurrence on the loop \p L.
1818  bool isAddRecNeverPoison(const Instruction *I, const Loop *L);
1819 
1820  /// Similar to createAddRecFromPHI, but with the additional flexibility of
1821  /// suggesting runtime overflow checks in case casts are encountered.
1822  /// If successful, the analysis records that for this loop, \p SymbolicPHI,
1823  /// which is the UnknownSCEV currently representing the PHI, can be rewritten
1824  /// into an AddRec, assuming some predicates; The function then returns the
1825  /// AddRec and the predicates as a pair, and caches this pair in
1826  /// PredicatedSCEVRewrites.
1827  /// If the analysis is not successful, a mapping from the \p SymbolicPHI to
1828  /// itself (with no predicates) is recorded, and a nullptr with an empty
1829  /// predicates vector is returned as a pair.
1831  createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI);
1832 
1833  /// Compute the backedge taken count knowing the interval difference, the
1834  /// stride and presence of the equality in the comparison.
1835  const SCEV *computeBECount(const SCEV *Delta, const SCEV *Stride,
1836  bool Equality);
1837 
1838  /// Compute the maximum backedge count based on the range of values
1839  /// permitted by Start, End, and Stride. This is for loops of the form
1840  /// {Start, +, Stride} LT End.
1841  ///
1842  /// Precondition: the induction variable is known to be positive. We *don't*
1843  /// assert these preconditions so please be careful.
1844  const SCEV *computeMaxBECountForLT(const SCEV *Start, const SCEV *Stride,
1845  const SCEV *End, unsigned BitWidth,
1846  bool IsSigned);
1847 
1848  /// Verify if an linear IV with positive stride can overflow when in a
1849  /// less-than comparison, knowing the invariant term of the comparison,
1850  /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1851  bool doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride, bool IsSigned,
1852  bool NoWrap);
1853 
1854  /// Verify if an linear IV with negative stride can overflow when in a
1855  /// greater-than comparison, knowing the invariant term of the comparison,
1856  /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1857  bool doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride, bool IsSigned,
1858  bool NoWrap);
1859 
1860  /// Get add expr already created or create a new one.
1861  const SCEV *getOrCreateAddExpr(ArrayRef<const SCEV *> Ops,
1862  SCEV::NoWrapFlags Flags);
1863 
1864  /// Get mul expr already created or create a new one.
1865  const SCEV *getOrCreateMulExpr(ArrayRef<const SCEV *> Ops,
1866  SCEV::NoWrapFlags Flags);
1867 
1868  // Get addrec expr already created or create a new one.
1869  const SCEV *getOrCreateAddRecExpr(ArrayRef<const SCEV *> Ops,
1870  const Loop *L, SCEV::NoWrapFlags Flags);
1871 
1872  /// Return x if \p Val is f(x) where f is a 1-1 function.
1873  const SCEV *stripInjectiveFunctions(const SCEV *Val) const;
1874 
1875  /// Find all of the loops transitively used in \p S, and fill \p LoopsUsed.
1876  /// A loop is considered "used" by an expression if it contains
1877  /// an add rec on said loop.
1878  void getUsedLoops(const SCEV *S, SmallPtrSetImpl<const Loop *> &LoopsUsed);
1879 
1880  /// Find all of the loops transitively used in \p S, and update \c LoopUsers
1881  /// accordingly.
1882  void addToLoopUseLists(const SCEV *S);
1883 
1884  /// Try to match the pattern generated by getURemExpr(A, B). If successful,
1885  /// Assign A and B to LHS and RHS, respectively.
1886  bool matchURem(const SCEV *Expr, const SCEV *&LHS, const SCEV *&RHS);
1887 
1888  /// Look for a SCEV expression with type `SCEVType` and operands `Ops` in
1889  /// `UniqueSCEVs`.
1890  ///
1891  /// The first component of the returned tuple is the SCEV if found and null
1892  /// otherwise. The second component is the `FoldingSetNodeID` that was
1893  /// constructed to look up the SCEV and the third component is the insertion
1894  /// point.
1895  std::tuple<const SCEV *, FoldingSetNodeID, void *>
1896  findExistingSCEVInCache(int SCEVType, ArrayRef<const SCEV *> Ops);
1897 
1898  FoldingSet<SCEV> UniqueSCEVs;
1899  FoldingSet<SCEVPredicate> UniquePreds;
1900  BumpPtrAllocator SCEVAllocator;
1901 
1902  /// This maps loops to a list of SCEV expressions that (transitively) use said
1903  /// loop.
1905 
1906  /// Cache tentative mappings from UnknownSCEVs in a Loop, to a SCEV expression
1907  /// they can be rewritten into under certain predicates.
1909  std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
1910  PredicatedSCEVRewrites;
1911 
1912  /// The head of a linked list of all SCEVUnknown values that have been
1913  /// allocated. This is used by releaseMemory to locate them all and call
1914  /// their destructors.
1915  SCEVUnknown *FirstUnknown = nullptr;
1916 };
1917 
1918 /// Analysis pass that exposes the \c ScalarEvolution for a function.
1920  : public AnalysisInfoMixin<ScalarEvolutionAnalysis> {
1922 
1923  static AnalysisKey Key;
1924 
1925 public:
1927 
1929 };
1930 
1931 /// Printer pass for the \c ScalarEvolutionAnalysis results.
1933  : public PassInfoMixin<ScalarEvolutionPrinterPass> {
1934  raw_ostream &OS;
1935 
1936 public:
1937  explicit ScalarEvolutionPrinterPass(raw_ostream &OS) : OS(OS) {}
1938 
1940 };
1941 
1943  std::unique_ptr<ScalarEvolution> SE;
1944 
1945 public:
1946  static char ID;
1947 
1949 
1950  ScalarEvolution &getSE() { return *SE; }
1951  const ScalarEvolution &getSE() const { return *SE; }
1952 
1953  bool runOnFunction(Function &F) override;
1954  void releaseMemory() override;
1955  void getAnalysisUsage(AnalysisUsage &AU) const override;
1956  void print(raw_ostream &OS, const Module * = nullptr) const override;
1957  void verifyAnalysis() const override;
1958 };
1959 
1960 /// An interface layer with SCEV used to manage how we see SCEV expressions
1961 /// for values in the context of existing predicates. We can add new
1962 /// predicates, but we cannot remove them.
1963 ///
1964 /// This layer has multiple purposes:
1965 /// - provides a simple interface for SCEV versioning.
1966 /// - guarantees that the order of transformations applied on a SCEV
1967 /// expression for a single Value is consistent across two different
1968 /// getSCEV calls. This means that, for example, once we've obtained
1969 /// an AddRec expression for a certain value through expression
1970 /// rewriting, we will continue to get an AddRec expression for that
1971 /// Value.
1972 /// - lowers the number of expression rewrites.
1974 public:
1976 
1977  const SCEVUnionPredicate &getUnionPredicate() const;
1978 
1979  /// Returns the SCEV expression of V, in the context of the current SCEV
1980  /// predicate. The order of transformations applied on the expression of V
1981  /// returned by ScalarEvolution is guaranteed to be preserved, even when
1982  /// adding new predicates.
1983  const SCEV *getSCEV(Value *V);
1984 
1985  /// Get the (predicated) backedge count for the analyzed loop.
1986  const SCEV *getBackedgeTakenCount();
1987 
1988  /// Adds a new predicate.
1989  void addPredicate(const SCEVPredicate &Pred);
1990 
1991  /// Attempts to produce an AddRecExpr for V by adding additional SCEV
1992  /// predicates. If we can't transform the expression into an AddRecExpr we
1993  /// return nullptr and not add additional SCEV predicates to the current
1994  /// context.
1995  const SCEVAddRecExpr *getAsAddRec(Value *V);
1996 
1997  /// Proves that V doesn't overflow by adding SCEV predicate.
1998  void setNoOverflow(Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags);
1999 
2000  /// Returns true if we've proved that V doesn't wrap by means of a SCEV
2001  /// predicate.
2002  bool hasNoOverflow(Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags);
2003 
2004  /// Returns the ScalarEvolution analysis used.
2005  ScalarEvolution *getSE() const { return &SE; }
2006 
2007  /// We need to explicitly define the copy constructor because of FlagsMap.
2009 
2010  /// Print the SCEV mappings done by the Predicated Scalar Evolution.
2011  /// The printed text is indented by \p Depth.
2012  void print(raw_ostream &OS, unsigned Depth) const;
2013 
2014  /// Check if \p AR1 and \p AR2 are equal, while taking into account
2015  /// Equal predicates in Preds.
2016  bool areAddRecsEqualWithPreds(const SCEVAddRecExpr *AR1,
2017  const SCEVAddRecExpr *AR2) const;
2018 
2019 private:
2020  /// Increments the version number of the predicate. This needs to be called
2021  /// every time the SCEV predicate changes.
2022  void updateGeneration();
2023 
2024  /// Holds a SCEV and the version number of the SCEV predicate used to
2025  /// perform the rewrite of the expression.
2026  using RewriteEntry = std::pair<unsigned, const SCEV *>;
2027 
2028  /// Maps a SCEV to the rewrite result of that SCEV at a certain version
2029  /// number. If this number doesn't match the current Generation, we will
2030  /// need to do a rewrite. To preserve the transformation order of previous
2031  /// rewrites, we will rewrite the previous result instead of the original
2032  /// SCEV.
2034 
2035  /// Records what NoWrap flags we've added to a Value *.
2037 
2038  /// The ScalarEvolution analysis.
2039  ScalarEvolution &SE;
2040 
2041  /// The analyzed Loop.
2042  const Loop &L;
2043 
2044  /// The SCEVPredicate that forms our context. We will rewrite all
2045  /// expressions assuming that this predicate true.
2046  SCEVUnionPredicate Preds;
2047 
2048  /// Marks the version of the SCEV predicate used. When rewriting a SCEV
2049  /// expression we mark it with the version of the predicate. We use this to
2050  /// figure out if the predicate has changed from the last rewrite of the
2051  /// SCEV. If so, we need to perform a new rewrite.
2052  unsigned Generation = 0;
2053 
2054  /// The backedge taken count.
2055  const SCEV *BackedgeCount = nullptr;
2056 };
2057 
2058 } // end namespace llvm
2059 
2060 #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:111
static GCMetadataPrinterRegistry::Add< ErlangGCPrinter > X("erlang", "erlang-compatible garbage collector")
const ScalarEvolution & getSE() const
static Type * getWiderType(const DataLayout &DL, Type *Ty0, Type *Ty1)
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:66
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:169
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:238
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
mir Rename Register Operands
This file implements a class to represent arbitrary precision integral constant values and operations...
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:373
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:154
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:46
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:141
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:390
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:732
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:205
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:1186
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)
static uint64_t add(uint64_t LeftOp, uint64_t RightOp)
Definition: FileCheck.cpp:215
This is a &#39;vector&#39; (really, a variable-sized array), optimized for the case when the array is small...
Definition: SmallVector.h:837
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:599
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:225
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:509
#define I(x, y, z)
Definition: MD5.cpp:58
#define N
static GCRegistry::Add< ErlangGC > A("erlang", "erlang-compatible garbage collector")
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:2047
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:153
API to communicate dependencies between analyses during invalidation.
Definition: PassManager.h:649
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:575
LLVM Value Representation.
Definition: Value.h:74
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:71
IncrementWrapFlags getFlags() const
Returns the set assumed no overflow flags.