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ScalarEvolution.h
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1 //===- llvm/Analysis/ScalarEvolution.h - Scalar Evolution -------*- C++ -*-===//
2 //
3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4 // See https://llvm.org/LICENSE.txt for license information.
5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6 //
7 //===----------------------------------------------------------------------===//
8 //
9 // The ScalarEvolution class is an LLVM pass which can be used to analyze and
10 // categorize scalar expressions in loops. It specializes in recognizing
11 // general induction variables, representing them with the abstract and opaque
12 // SCEV class. Given this analysis, trip counts of loops and other important
13 // properties can be obtained.
14 //
15 // This analysis is primarily useful for induction variable substitution and
16 // strength reduction.
17 //
18 //===----------------------------------------------------------------------===//
19 
20 #ifndef LLVM_ANALYSIS_SCALAREVOLUTION_H
21 #define LLVM_ANALYSIS_SCALAREVOLUTION_H
22 
23 #include "llvm/ADT/APInt.h"
24 #include "llvm/ADT/ArrayRef.h"
25 #include "llvm/ADT/DenseMap.h"
26 #include "llvm/ADT/DenseMapInfo.h"
27 #include "llvm/ADT/FoldingSet.h"
28 #include "llvm/ADT/Hashing.h"
29 #include "llvm/ADT/Optional.h"
31 #include "llvm/ADT/SetVector.h"
32 #include "llvm/ADT/SmallPtrSet.h"
33 #include "llvm/ADT/SmallVector.h"
34 #include "llvm/Analysis/LoopInfo.h"
35 #include "llvm/IR/ConstantRange.h"
36 #include "llvm/IR/Function.h"
37 #include "llvm/IR/InstrTypes.h"
38 #include "llvm/IR/Instructions.h"
39 #include "llvm/IR/Operator.h"
40 #include "llvm/IR/PassManager.h"
41 #include "llvm/IR/ValueHandle.h"
42 #include "llvm/IR/ValueMap.h"
43 #include "llvm/Pass.h"
44 #include "llvm/Support/Allocator.h"
45 #include "llvm/Support/Casting.h"
46 #include "llvm/Support/Compiler.h"
47 #include <algorithm>
48 #include <cassert>
49 #include <cstdint>
50 #include <memory>
51 #include <utility>
52 
53 namespace llvm {
54 
55 class AssumptionCache;
56 class BasicBlock;
57 class Constant;
58 class ConstantInt;
59 class DataLayout;
60 class DominatorTree;
61 class GEPOperator;
62 class Instruction;
63 class LLVMContext;
64 class raw_ostream;
65 class ScalarEvolution;
66 class SCEVAddRecExpr;
67 class SCEVUnknown;
68 class StructType;
69 class TargetLibraryInfo;
70 class Type;
71 class Value;
72 
73 /// This class represents an analyzed expression in the program. These are
74 /// opaque objects that the client is not allowed to do much with directly.
75 ///
76 class SCEV : public FoldingSetNode {
77  friend struct FoldingSetTrait<SCEV>;
78 
79  /// A reference to an Interned FoldingSetNodeID for this node. The
80  /// ScalarEvolution's BumpPtrAllocator holds the data.
81  FoldingSetNodeIDRef FastID;
82 
83  // The SCEV baseclass this node corresponds to
84  const unsigned short SCEVType;
85 
86 protected:
87  // Estimated complexity of this node's expression tree size.
88  const unsigned short ExpressionSize;
89 
90  /// This field is initialized to zero and may be used in subclasses to store
91  /// miscellaneous information.
92  unsigned short SubclassData = 0;
93 
94 public:
95  /// NoWrapFlags are bitfield indices into SubclassData.
96  ///
97  /// Add and Mul expressions may have no-unsigned-wrap <NUW> or
98  /// no-signed-wrap <NSW> properties, which are derived from the IR
99  /// operator. NSW is a misnomer that we use to mean no signed overflow or
100  /// underflow.
101  ///
102  /// AddRec expressions may have a no-self-wraparound <NW> property if, in
103  /// the integer domain, abs(step) * max-iteration(loop) <=
104  /// unsigned-max(bitwidth). This means that the recurrence will never reach
105  /// its start value if the step is non-zero. Computing the same value on
106  /// each iteration is not considered wrapping, and recurrences with step = 0
107  /// are trivially <NW>. <NW> is independent of the sign of step and the
108  /// value the add recurrence starts with.
109  ///
110  /// Note that NUW and NSW are also valid properties of a recurrence, and
111  /// either implies NW. For convenience, NW will be set for a recurrence
112  /// whenever either NUW or NSW are set.
113  enum NoWrapFlags {
114  FlagAnyWrap = 0, // No guarantee.
115  FlagNW = (1 << 0), // No self-wrap.
116  FlagNUW = (1 << 1), // No unsigned wrap.
117  FlagNSW = (1 << 2), // No signed wrap.
118  NoWrapMask = (1 << 3) - 1
119  };
120 
121  explicit SCEV(const FoldingSetNodeIDRef ID, unsigned SCEVTy,
122  unsigned short ExpressionSize)
123  : FastID(ID), SCEVType(SCEVTy), ExpressionSize(ExpressionSize) {}
124  SCEV(const SCEV &) = delete;
125  SCEV &operator=(const SCEV &) = delete;
126 
127  unsigned getSCEVType() const { return SCEVType; }
128 
129  /// Return the LLVM type of this SCEV expression.
130  Type *getType() const;
131 
132  /// Return true if the expression is a constant zero.
133  bool isZero() const;
134 
135  /// Return true if the expression is a constant one.
136  bool isOne() const;
137 
138  /// Return true if the expression is a constant all-ones value.
139  bool isAllOnesValue() const;
140 
141  /// Return true if the specified scev is negated, but not a constant.
142  bool isNonConstantNegative() const;
143 
144  // Returns estimated size of the mathematical expression represented by this
145  // SCEV. The rules of its calculation are following:
146  // 1) Size of a SCEV without operands (like constants and SCEVUnknown) is 1;
147  // 2) Size SCEV with operands Op1, Op2, ..., OpN is calculated by formula:
148  // (1 + Size(Op1) + ... + Size(OpN)).
149  // This value gives us an estimation of time we need to traverse through this
150  // SCEV and all its operands recursively. We may use it to avoid performing
151  // heavy transformations on SCEVs of excessive size for sake of saving the
152  // compilation time.
153  unsigned short getExpressionSize() const {
154  return ExpressionSize;
155  }
156 
157  /// Print out the internal representation of this scalar to the specified
158  /// stream. This should really only be used for debugging purposes.
159  void print(raw_ostream &OS) const;
160 
161  /// This method is used for debugging.
162  void dump() const;
163 };
164 
165 // Specialize FoldingSetTrait for SCEV to avoid needing to compute
166 // temporary FoldingSetNodeID values.
167 template <> struct FoldingSetTrait<SCEV> : DefaultFoldingSetTrait<SCEV> {
168  static void Profile(const SCEV &X, FoldingSetNodeID &ID) { ID = X.FastID; }
169 
170  static bool Equals(const SCEV &X, const FoldingSetNodeID &ID, unsigned IDHash,
171  FoldingSetNodeID &TempID) {
172  return ID == X.FastID;
173  }
174 
175  static unsigned ComputeHash(const SCEV &X, FoldingSetNodeID &TempID) {
176  return X.FastID.ComputeHash();
177  }
178 };
179 
180 inline raw_ostream &operator<<(raw_ostream &OS, const SCEV &S) {
181  S.print(OS);
182  return OS;
183 }
184 
185 /// An object of this class is returned by queries that could not be answered.
186 /// For example, if you ask for the number of iterations of a linked-list
187 /// traversal loop, you will get one of these. None of the standard SCEV
188 /// operations are valid on this class, it is just a marker.
189 struct SCEVCouldNotCompute : public SCEV {
191 
192  /// Methods for support type inquiry through isa, cast, and dyn_cast:
193  static bool classof(const SCEV *S);
194 };
195 
196 /// This class represents an assumption made using SCEV expressions which can
197 /// be checked at run-time.
200 
201  /// A reference to an Interned FoldingSetNodeID for this node. The
202  /// ScalarEvolution's BumpPtrAllocator holds the data.
203  FoldingSetNodeIDRef FastID;
204 
205 public:
206  enum SCEVPredicateKind { P_Union, P_Equal, P_Wrap };
207 
208 protected:
210  ~SCEVPredicate() = default;
211  SCEVPredicate(const SCEVPredicate &) = default;
212  SCEVPredicate &operator=(const SCEVPredicate &) = default;
213 
214 public:
216 
217  SCEVPredicateKind getKind() const { return Kind; }
218 
219  /// Returns the estimated complexity of this predicate. This is roughly
220  /// measured in the number of run-time checks required.
221  virtual unsigned getComplexity() const { return 1; }
222 
223  /// Returns true if the predicate is always true. This means that no
224  /// assumptions were made and nothing needs to be checked at run-time.
225  virtual bool isAlwaysTrue() const = 0;
226 
227  /// Returns true if this predicate implies \p N.
228  virtual bool implies(const SCEVPredicate *N) const = 0;
229 
230  /// Prints a textual representation of this predicate with an indentation of
231  /// \p Depth.
232  virtual void print(raw_ostream &OS, unsigned Depth = 0) const = 0;
233 
234  /// Returns the SCEV to which this predicate applies, or nullptr if this is
235  /// a SCEVUnionPredicate.
236  virtual const SCEV *getExpr() const = 0;
237 };
238 
240  P.print(OS);
241  return OS;
242 }
243 
244 // Specialize FoldingSetTrait for SCEVPredicate to avoid needing to compute
245 // temporary FoldingSetNodeID values.
246 template <>
248  static void Profile(const SCEVPredicate &X, FoldingSetNodeID &ID) {
249  ID = X.FastID;
250  }
251 
252  static bool Equals(const SCEVPredicate &X, const FoldingSetNodeID &ID,
253  unsigned IDHash, FoldingSetNodeID &TempID) {
254  return ID == X.FastID;
255  }
256 
257  static unsigned ComputeHash(const SCEVPredicate &X,
258  FoldingSetNodeID &TempID) {
259  return X.FastID.ComputeHash();
260  }
261 };
262 
263 /// This class represents an assumption that two SCEV expressions are equal,
264 /// and this can be checked at run-time.
265 class SCEVEqualPredicate final : public SCEVPredicate {
266  /// We assume that LHS == RHS.
267  const SCEV *LHS;
268  const SCEV *RHS;
269 
270 public:
271  SCEVEqualPredicate(const FoldingSetNodeIDRef ID, const SCEV *LHS,
272  const SCEV *RHS);
273 
274  /// Implementation of the SCEVPredicate interface
275  bool implies(const SCEVPredicate *N) const override;
276  void print(raw_ostream &OS, unsigned Depth = 0) const override;
277  bool isAlwaysTrue() const override;
278  const SCEV *getExpr() const override;
279 
280  /// Returns the left hand side of the equality.
281  const SCEV *getLHS() const { return LHS; }
282 
283  /// Returns the right hand side of the equality.
284  const SCEV *getRHS() const { return RHS; }
285 
286  /// Methods for support type inquiry through isa, cast, and dyn_cast:
287  static bool classof(const SCEVPredicate *P) {
288  return P->getKind() == P_Equal;
289  }
290 };
291 
292 /// This class represents an assumption made on an AddRec expression. Given an
293 /// affine AddRec expression {a,+,b}, we assume that it has the nssw or nusw
294 /// flags (defined below) in the first X iterations of the loop, where X is a
295 /// SCEV expression returned by getPredicatedBackedgeTakenCount).
296 ///
297 /// Note that this does not imply that X is equal to the backedge taken
298 /// count. This means that if we have a nusw predicate for i32 {0,+,1} with a
299 /// predicated backedge taken count of X, we only guarantee that {0,+,1} has
300 /// nusw in the first X iterations. {0,+,1} may still wrap in the loop if we
301 /// have more than X iterations.
302 class SCEVWrapPredicate final : public SCEVPredicate {
303 public:
304  /// Similar to SCEV::NoWrapFlags, but with slightly different semantics
305  /// for FlagNUSW. The increment is considered to be signed, and a + b
306  /// (where b is the increment) is considered to wrap if:
307  /// zext(a + b) != zext(a) + sext(b)
308  ///
309  /// If Signed is a function that takes an n-bit tuple and maps to the
310  /// integer domain as the tuples value interpreted as twos complement,
311  /// and Unsigned a function that takes an n-bit tuple and maps to the
312  /// integer domain as as the base two value of input tuple, then a + b
313  /// has IncrementNUSW iff:
314  ///
315  /// 0 <= Unsigned(a) + Signed(b) < 2^n
316  ///
317  /// The IncrementNSSW flag has identical semantics with SCEV::FlagNSW.
318  ///
319  /// Note that the IncrementNUSW flag is not commutative: if base + inc
320  /// has IncrementNUSW, then inc + base doesn't neccessarily have this
321  /// property. The reason for this is that this is used for sign/zero
322  /// extending affine AddRec SCEV expressions when a SCEVWrapPredicate is
323  /// assumed. A {base,+,inc} expression is already non-commutative with
324  /// regards to base and inc, since it is interpreted as:
325  /// (((base + inc) + inc) + inc) ...
327  IncrementAnyWrap = 0, // No guarantee.
328  IncrementNUSW = (1 << 0), // No unsigned with signed increment wrap.
329  IncrementNSSW = (1 << 1), // No signed with signed increment wrap
330  // (equivalent with SCEV::NSW)
331  IncrementNoWrapMask = (1 << 2) - 1
332  };
333 
334  /// Convenient IncrementWrapFlags manipulation methods.
338  assert((Flags & IncrementNoWrapMask) == Flags && "Invalid flags value!");
339  assert((OffFlags & IncrementNoWrapMask) == OffFlags &&
340  "Invalid flags value!");
341  return (SCEVWrapPredicate::IncrementWrapFlags)(Flags & ~OffFlags);
342  }
343 
346  assert((Flags & IncrementNoWrapMask) == Flags && "Invalid flags value!");
347  assert((Mask & IncrementNoWrapMask) == Mask && "Invalid mask value!");
348 
350  }
351 
355  assert((Flags & IncrementNoWrapMask) == Flags && "Invalid flags value!");
356  assert((OnFlags & IncrementNoWrapMask) == OnFlags &&
357  "Invalid flags value!");
358 
359  return (SCEVWrapPredicate::IncrementWrapFlags)(Flags | OnFlags);
360  }
361 
362  /// Returns the set of SCEVWrapPredicate no wrap flags implied by a
363  /// SCEVAddRecExpr.
365  getImpliedFlags(const SCEVAddRecExpr *AR, ScalarEvolution &SE);
366 
367 private:
368  const SCEVAddRecExpr *AR;
369  IncrementWrapFlags Flags;
370 
371 public:
373  const SCEVAddRecExpr *AR,
374  IncrementWrapFlags Flags);
375 
376  /// Returns the set assumed no overflow flags.
377  IncrementWrapFlags getFlags() const { return Flags; }
378 
379  /// Implementation of the SCEVPredicate interface
380  const SCEV *getExpr() const override;
381  bool implies(const SCEVPredicate *N) const override;
382  void print(raw_ostream &OS, unsigned Depth = 0) const override;
383  bool isAlwaysTrue() const override;
384 
385  /// Methods for support type inquiry through isa, cast, and dyn_cast:
386  static bool classof(const SCEVPredicate *P) {
387  return P->getKind() == P_Wrap;
388  }
389 };
390 
391 /// This class represents a composition of other SCEV predicates, and is the
392 /// class that most clients will interact with. This is equivalent to a
393 /// logical "AND" of all the predicates in the union.
394 ///
395 /// NB! Unlike other SCEVPredicate sub-classes this class does not live in the
396 /// ScalarEvolution::Preds folding set. This is why the \c add function is sound.
397 class SCEVUnionPredicate final : public SCEVPredicate {
398 private:
399  using PredicateMap =
401 
402  /// Vector with references to all predicates in this union.
404 
405  /// Maps SCEVs to predicates for quick look-ups.
406  PredicateMap SCEVToPreds;
407 
408 public:
410 
412  return Preds;
413  }
414 
415  /// Adds a predicate to this union.
416  void add(const SCEVPredicate *N);
417 
418  /// Returns a reference to a vector containing all predicates which apply to
419  /// \p Expr.
420  ArrayRef<const SCEVPredicate *> getPredicatesForExpr(const SCEV *Expr);
421 
422  /// Implementation of the SCEVPredicate interface
423  bool isAlwaysTrue() const override;
424  bool implies(const SCEVPredicate *N) const override;
425  void print(raw_ostream &OS, unsigned Depth) const override;
426  const SCEV *getExpr() const override;
427 
428  /// We estimate the complexity of a union predicate as the size number of
429  /// predicates in the union.
430  unsigned getComplexity() const override { return Preds.size(); }
431 
432  /// Methods for support type inquiry through isa, cast, and dyn_cast:
433  static bool classof(const SCEVPredicate *P) {
434  return P->getKind() == P_Union;
435  }
436 };
437 
439  ExitLimitQuery(const Loop *L, BasicBlock *ExitingBlock, bool AllowPredicates)
440  : L(L), ExitingBlock(ExitingBlock), AllowPredicates(AllowPredicates) {}
441 
442  const Loop *L;
445 };
446 
447 template <> struct DenseMapInfo<ExitLimitQuery> {
448  static inline ExitLimitQuery getEmptyKey() {
449  return ExitLimitQuery(nullptr, nullptr, true);
450  }
451 
452  static inline ExitLimitQuery getTombstoneKey() {
453  return ExitLimitQuery(nullptr, nullptr, false);
454  }
455 
456  static unsigned getHashValue(ExitLimitQuery Val) {
457  return hash_combine(hash_combine(Val.L, Val.ExitingBlock),
458  Val.AllowPredicates);
459  }
460 
461  static bool isEqual(ExitLimitQuery LHS, ExitLimitQuery RHS) {
462  return LHS.L == RHS.L && LHS.ExitingBlock == RHS.ExitingBlock &&
463  LHS.AllowPredicates == RHS.AllowPredicates;
464  }
465 };
466 
467 /// The main scalar evolution driver. Because client code (intentionally)
468 /// can't do much with the SCEV objects directly, they must ask this class
469 /// for services.
471 public:
472  /// An enum describing the relationship between a SCEV and a loop.
474  LoopVariant, ///< The SCEV is loop-variant (unknown).
475  LoopInvariant, ///< The SCEV is loop-invariant.
476  LoopComputable ///< The SCEV varies predictably with the loop.
477  };
478 
479  /// An enum describing the relationship between a SCEV and a basic block.
481  DoesNotDominateBlock, ///< The SCEV does not dominate the block.
482  DominatesBlock, ///< The SCEV dominates the block.
483  ProperlyDominatesBlock ///< The SCEV properly dominates the block.
484  };
485 
486  /// Convenient NoWrapFlags manipulation that hides enum casts and is
487  /// visible in the ScalarEvolution name space.
489  int Mask) {
490  return (SCEV::NoWrapFlags)(Flags & Mask);
491  }
493  SCEV::NoWrapFlags OnFlags) {
494  return (SCEV::NoWrapFlags)(Flags | OnFlags);
495  }
498  return (SCEV::NoWrapFlags)(Flags & ~OffFlags);
499  }
500 
502  DominatorTree &DT, LoopInfo &LI);
504  ~ScalarEvolution();
505 
506  LLVMContext &getContext() const { return F.getContext(); }
507 
508  /// Test if values of the given type are analyzable within the SCEV
509  /// framework. This primarily includes integer types, and it can optionally
510  /// include pointer types if the ScalarEvolution class has access to
511  /// target-specific information.
512  bool isSCEVable(Type *Ty) const;
513 
514  /// Return the size in bits of the specified type, for which isSCEVable must
515  /// return true.
516  uint64_t getTypeSizeInBits(Type *Ty) const;
517 
518  /// Return a type with the same bitwidth as the given type and which
519  /// represents how SCEV will treat the given type, for which isSCEVable must
520  /// return true. For pointer types, this is the pointer-sized integer type.
521  Type *getEffectiveSCEVType(Type *Ty) const;
522 
523  // Returns a wider type among {Ty1, Ty2}.
524  Type *getWiderType(Type *Ty1, Type *Ty2) const;
525 
526  /// Return true if the SCEV is a scAddRecExpr or it contains
527  /// scAddRecExpr. The result will be cached in HasRecMap.
528  bool containsAddRecurrence(const SCEV *S);
529 
530  /// Erase Value from ValueExprMap and ExprValueMap.
531  void eraseValueFromMap(Value *V);
532 
533  /// Return a SCEV expression for the full generality of the specified
534  /// expression.
535  const SCEV *getSCEV(Value *V);
536 
537  const SCEV *getConstant(ConstantInt *V);
538  const SCEV *getConstant(const APInt &Val);
539  const SCEV *getConstant(Type *Ty, uint64_t V, bool isSigned = false);
540  const SCEV *getTruncateExpr(const SCEV *Op, Type *Ty, unsigned Depth = 0);
541  const SCEV *getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth = 0);
542  const SCEV *getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth = 0);
543  const SCEV *getAnyExtendExpr(const SCEV *Op, Type *Ty);
544  const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
546  unsigned Depth = 0);
547  const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS,
549  unsigned Depth = 0) {
550  SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
551  return getAddExpr(Ops, Flags, Depth);
552  }
553  const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
555  unsigned Depth = 0) {
556  SmallVector<const SCEV *, 3> Ops = {Op0, Op1, Op2};
557  return getAddExpr(Ops, Flags, Depth);
558  }
559  const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
561  unsigned Depth = 0);
562  const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS,
564  unsigned Depth = 0) {
565  SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
566  return getMulExpr(Ops, Flags, Depth);
567  }
568  const SCEV *getMulExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
570  unsigned Depth = 0) {
571  SmallVector<const SCEV *, 3> Ops = {Op0, Op1, Op2};
572  return getMulExpr(Ops, Flags, Depth);
573  }
574  const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
575  const SCEV *getUDivExactExpr(const SCEV *LHS, const SCEV *RHS);
576  const SCEV *getURemExpr(const SCEV *LHS, const SCEV *RHS);
577  const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step, const Loop *L,
578  SCEV::NoWrapFlags Flags);
579  const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
580  const Loop *L, SCEV::NoWrapFlags Flags);
582  const Loop *L, SCEV::NoWrapFlags Flags) {
583  SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
584  return getAddRecExpr(NewOp, L, Flags);
585  }
586 
587  /// Checks if \p SymbolicPHI can be rewritten as an AddRecExpr under some
588  /// Predicates. If successful return these <AddRecExpr, Predicates>;
589  /// The function is intended to be called from PSCEV (the caller will decide
590  /// whether to actually add the predicates and carry out the rewrites).
592  createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI);
593 
594  /// Returns an expression for a GEP
595  ///
596  /// \p GEP The GEP. The indices contained in the GEP itself are ignored,
597  /// instead we use IndexExprs.
598  /// \p IndexExprs The expressions for the indices.
599  const SCEV *getGEPExpr(GEPOperator *GEP,
600  const SmallVectorImpl<const SCEV *> &IndexExprs);
601  const SCEV *getMinMaxExpr(unsigned Kind,
603  const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
604  const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
605  const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
606  const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
607  const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
608  const SCEV *getSMinExpr(SmallVectorImpl<const SCEV *> &Operands);
609  const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
610  const SCEV *getUMinExpr(SmallVectorImpl<const SCEV *> &Operands);
611  const SCEV *getUnknown(Value *V);
612  const SCEV *getCouldNotCompute();
613 
614  /// Return a SCEV for the constant 0 of a specific type.
615  const SCEV *getZero(Type *Ty) { return getConstant(Ty, 0); }
616 
617  /// Return a SCEV for the constant 1 of a specific type.
618  const SCEV *getOne(Type *Ty) { return getConstant(Ty, 1); }
619 
620  /// Return an expression for sizeof AllocTy that is type IntTy
621  const SCEV *getSizeOfExpr(Type *IntTy, Type *AllocTy);
622 
623  /// Return an expression for offsetof on the given field with type IntTy
624  const SCEV *getOffsetOfExpr(Type *IntTy, StructType *STy, unsigned FieldNo);
625 
626  /// Return the SCEV object corresponding to -V.
627  const SCEV *getNegativeSCEV(const SCEV *V,
629 
630  /// Return the SCEV object corresponding to ~V.
631  const SCEV *getNotSCEV(const SCEV *V);
632 
633  /// Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
634  const SCEV *getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
636  unsigned Depth = 0);
637 
638  /// Return a SCEV corresponding to a conversion of the input value to the
639  /// specified type. If the type must be extended, it is zero extended.
640  const SCEV *getTruncateOrZeroExtend(const SCEV *V, Type *Ty,
641  unsigned Depth = 0);
642 
643  /// Return a SCEV corresponding to a conversion of the input value to the
644  /// specified type. If the type must be extended, it is sign extended.
645  const SCEV *getTruncateOrSignExtend(const SCEV *V, Type *Ty,
646  unsigned Depth = 0);
647 
648  /// Return a SCEV corresponding to a conversion of the input value to the
649  /// specified type. If the type must be extended, it is zero extended. The
650  /// conversion must not be narrowing.
651  const SCEV *getNoopOrZeroExtend(const SCEV *V, Type *Ty);
652 
653  /// Return a SCEV corresponding to a conversion of the input value to the
654  /// specified type. If the type must be extended, it is sign extended. The
655  /// conversion must not be narrowing.
656  const SCEV *getNoopOrSignExtend(const SCEV *V, Type *Ty);
657 
658  /// Return a SCEV corresponding to a conversion of the input value to the
659  /// specified type. If the type must be extended, it is extended with
660  /// unspecified bits. The conversion must not be narrowing.
661  const SCEV *getNoopOrAnyExtend(const SCEV *V, Type *Ty);
662 
663  /// Return a SCEV corresponding to a conversion of the input value to the
664  /// specified type. The conversion must not be widening.
665  const SCEV *getTruncateOrNoop(const SCEV *V, Type *Ty);
666 
667  /// Promote the operands to the wider of the types using zero-extension, and
668  /// then perform a umax operation with them.
669  const SCEV *getUMaxFromMismatchedTypes(const SCEV *LHS, const SCEV *RHS);
670 
671  /// Promote the operands to the wider of the types using zero-extension, and
672  /// then perform a umin operation with them.
673  const SCEV *getUMinFromMismatchedTypes(const SCEV *LHS, const SCEV *RHS);
674 
675  /// Promote the operands to the wider of the types using zero-extension, and
676  /// then perform a umin operation with them. N-ary function.
677  const SCEV *getUMinFromMismatchedTypes(SmallVectorImpl<const SCEV *> &Ops);
678 
679  /// Transitively follow the chain of pointer-type operands until reaching a
680  /// SCEV that does not have a single pointer operand. This returns a
681  /// SCEVUnknown pointer for well-formed pointer-type expressions, but corner
682  /// cases do exist.
683  const SCEV *getPointerBase(const SCEV *V);
684 
685  /// Return a SCEV expression for the specified value at the specified scope
686  /// in the program. The L value specifies a loop nest to evaluate the
687  /// expression at, where null is the top-level or a specified loop is
688  /// immediately inside of the loop.
689  ///
690  /// This method can be used to compute the exit value for a variable defined
691  /// in a loop by querying what the value will hold in the parent loop.
692  ///
693  /// In the case that a relevant loop exit value cannot be computed, the
694  /// original value V is returned.
695  const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
696 
697  /// This is a convenience function which does getSCEVAtScope(getSCEV(V), L).
698  const SCEV *getSCEVAtScope(Value *V, const Loop *L);
699 
700  /// Test whether entry to the loop is protected by a conditional between LHS
701  /// and RHS. This is used to help avoid max expressions in loop trip
702  /// counts, and to eliminate casts.
703  bool isLoopEntryGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
704  const SCEV *LHS, const SCEV *RHS);
705 
706  /// Test whether the backedge of the loop is protected by a conditional
707  /// between LHS and RHS. This is used to eliminate casts.
708  bool isLoopBackedgeGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
709  const SCEV *LHS, const SCEV *RHS);
710 
711  /// Returns the maximum trip count of the loop if it is a single-exit
712  /// loop and we can compute a small maximum for that loop.
713  ///
714  /// Implemented in terms of the \c getSmallConstantTripCount overload with
715  /// the single exiting block passed to it. See that routine for details.
716  unsigned getSmallConstantTripCount(const Loop *L);
717 
718  /// Returns the maximum trip count of this loop as a normal unsigned
719  /// value. Returns 0 if the trip count is unknown or not constant. This
720  /// "trip count" assumes that control exits via ExitingBlock. More
721  /// precisely, it is the number of times that control may reach ExitingBlock
722  /// before taking the branch. For loops with multiple exits, it may not be
723  /// the number times that the loop header executes if the loop exits
724  /// prematurely via another branch.
725  unsigned getSmallConstantTripCount(const Loop *L, BasicBlock *ExitingBlock);
726 
727  /// Returns the upper bound of the loop trip count as a normal unsigned
728  /// value.
729  /// Returns 0 if the trip count is unknown or not constant.
730  unsigned getSmallConstantMaxTripCount(const Loop *L);
731 
732  /// Returns the largest constant divisor of the trip count of the
733  /// loop if it is a single-exit loop and we can compute a small maximum for
734  /// that loop.
735  ///
736  /// Implemented in terms of the \c getSmallConstantTripMultiple overload with
737  /// the single exiting block passed to it. See that routine for details.
738  unsigned getSmallConstantTripMultiple(const Loop *L);
739 
740  /// Returns the largest constant divisor of the trip count of this loop as a
741  /// normal unsigned value, if possible. This means that the actual trip
742  /// count is always a multiple of the returned value (don't forget the trip
743  /// count could very well be zero as well!). As explained in the comments
744  /// for getSmallConstantTripCount, this assumes that control exits the loop
745  /// via ExitingBlock.
746  unsigned getSmallConstantTripMultiple(const Loop *L,
747  BasicBlock *ExitingBlock);
748 
749  /// Get the expression for the number of loop iterations for which this loop
750  /// is guaranteed not to exit via ExitingBlock. Otherwise return
751  /// SCEVCouldNotCompute.
752  const SCEV *getExitCount(const Loop *L, BasicBlock *ExitingBlock);
753 
754  /// If the specified loop has a predictable backedge-taken count, return it,
755  /// otherwise return a SCEVCouldNotCompute object. The backedge-taken count is
756  /// the number of times the loop header will be branched to from within the
757  /// loop, assuming there are no abnormal exists like exception throws. This is
758  /// one less than the trip count of the loop, since it doesn't count the first
759  /// iteration, when the header is branched to from outside the loop.
760  ///
761  /// Note that it is not valid to call this method on a loop without a
762  /// loop-invariant backedge-taken count (see
763  /// hasLoopInvariantBackedgeTakenCount).
764  const SCEV *getBackedgeTakenCount(const Loop *L);
765 
766  /// Similar to getBackedgeTakenCount, except it will add a set of
767  /// SCEV predicates to Predicates that are required to be true in order for
768  /// the answer to be correct. Predicates can be checked with run-time
769  /// checks and can be used to perform loop versioning.
770  const SCEV *getPredicatedBackedgeTakenCount(const Loop *L,
771  SCEVUnionPredicate &Predicates);
772 
773  /// When successful, this returns a SCEVConstant that is greater than or equal
774  /// to (i.e. a "conservative over-approximation") of the value returend by
775  /// getBackedgeTakenCount. If such a value cannot be computed, it returns the
776  /// SCEVCouldNotCompute object.
777  const SCEV *getMaxBackedgeTakenCount(const Loop *L);
778 
779  /// Return true if the backedge taken count is either the value returned by
780  /// getMaxBackedgeTakenCount or zero.
781  bool isBackedgeTakenCountMaxOrZero(const Loop *L);
782 
783  /// Return true if the specified loop has an analyzable loop-invariant
784  /// backedge-taken count.
785  bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
786 
787  // This method should be called by the client when it made any change that
788  // would invalidate SCEV's answers, and the client wants to remove all loop
789  // information held internally by ScalarEvolution. This is intended to be used
790  // when the alternative to forget a loop is too expensive (i.e. large loop
791  // bodies).
792  void forgetAllLoops();
793 
794  /// This method should be called by the client when it has changed a loop in
795  /// a way that may effect ScalarEvolution's ability to compute a trip count,
796  /// or if the loop is deleted. This call is potentially expensive for large
797  /// loop bodies.
798  void forgetLoop(const Loop *L);
799 
800  // This method invokes forgetLoop for the outermost loop of the given loop
801  // \p L, making ScalarEvolution forget about all this subtree. This needs to
802  // be done whenever we make a transform that may affect the parameters of the
803  // outer loop, such as exit counts for branches.
804  void forgetTopmostLoop(const Loop *L);
805 
806  /// This method should be called by the client when it has changed a value
807  /// in a way that may effect its value, or which may disconnect it from a
808  /// def-use chain linking it to a loop.
809  void forgetValue(Value *V);
810 
811  /// Called when the client has changed the disposition of values in
812  /// this loop.
813  ///
814  /// We don't have a way to invalidate per-loop dispositions. Clear and
815  /// recompute is simpler.
816  void forgetLoopDispositions(const Loop *L) { LoopDispositions.clear(); }
817 
818  /// Determine the minimum number of zero bits that S is guaranteed to end in
819  /// (at every loop iteration). It is, at the same time, the minimum number
820  /// of times S is divisible by 2. For example, given {4,+,8} it returns 2.
821  /// If S is guaranteed to be 0, it returns the bitwidth of S.
822  uint32_t GetMinTrailingZeros(const SCEV *S);
823 
824  /// Determine the unsigned range for a particular SCEV.
825  /// NOTE: This returns a copy of the reference returned by getRangeRef.
827  return getRangeRef(S, HINT_RANGE_UNSIGNED);
828  }
829 
830  /// Determine the min of the unsigned range for a particular SCEV.
832  return getRangeRef(S, HINT_RANGE_UNSIGNED).getUnsignedMin();
833  }
834 
835  /// Determine the max of the unsigned range for a particular SCEV.
837  return getRangeRef(S, HINT_RANGE_UNSIGNED).getUnsignedMax();
838  }
839 
840  /// Determine the signed range for a particular SCEV.
841  /// NOTE: This returns a copy of the reference returned by getRangeRef.
843  return getRangeRef(S, HINT_RANGE_SIGNED);
844  }
845 
846  /// Determine the min of the signed range for a particular SCEV.
848  return getRangeRef(S, HINT_RANGE_SIGNED).getSignedMin();
849  }
850 
851  /// Determine the max of the signed range for a particular SCEV.
853  return getRangeRef(S, HINT_RANGE_SIGNED).getSignedMax();
854  }
855 
856  /// Test if the given expression is known to be negative.
857  bool isKnownNegative(const SCEV *S);
858 
859  /// Test if the given expression is known to be positive.
860  bool isKnownPositive(const SCEV *S);
861 
862  /// Test if the given expression is known to be non-negative.
863  bool isKnownNonNegative(const SCEV *S);
864 
865  /// Test if the given expression is known to be non-positive.
866  bool isKnownNonPositive(const SCEV *S);
867 
868  /// Test if the given expression is known to be non-zero.
869  bool isKnownNonZero(const SCEV *S);
870 
871  /// Splits SCEV expression \p S into two SCEVs. One of them is obtained from
872  /// \p S by substitution of all AddRec sub-expression related to loop \p L
873  /// with initial value of that SCEV. The second is obtained from \p S by
874  /// substitution of all AddRec sub-expressions related to loop \p L with post
875  /// increment of this AddRec in the loop \p L. In both cases all other AddRec
876  /// sub-expressions (not related to \p L) remain the same.
877  /// If the \p S contains non-invariant unknown SCEV the function returns
878  /// CouldNotCompute SCEV in both values of std::pair.
879  /// For example, for SCEV S={0, +, 1}<L1> + {0, +, 1}<L2> and loop L=L1
880  /// the function returns pair:
881  /// first = {0, +, 1}<L2>
882  /// second = {1, +, 1}<L1> + {0, +, 1}<L2>
883  /// We can see that for the first AddRec sub-expression it was replaced with
884  /// 0 (initial value) for the first element and to {1, +, 1}<L1> (post
885  /// increment value) for the second one. In both cases AddRec expression
886  /// related to L2 remains the same.
887  std::pair<const SCEV *, const SCEV *> SplitIntoInitAndPostInc(const Loop *L,
888  const SCEV *S);
889 
890  /// We'd like to check the predicate on every iteration of the most dominated
891  /// loop between loops used in LHS and RHS.
892  /// To do this we use the following list of steps:
893  /// 1. Collect set S all loops on which either LHS or RHS depend.
894  /// 2. If S is non-empty
895  /// a. Let PD be the element of S which is dominated by all other elements.
896  /// b. Let E(LHS) be value of LHS on entry of PD.
897  /// To get E(LHS), we should just take LHS and replace all AddRecs that are
898  /// attached to PD on with their entry values.
899  /// Define E(RHS) in the same way.
900  /// c. Let B(LHS) be value of L on backedge of PD.
901  /// To get B(LHS), we should just take LHS and replace all AddRecs that are
902  /// attached to PD on with their backedge values.
903  /// Define B(RHS) in the same way.
904  /// d. Note that E(LHS) and E(RHS) are automatically available on entry of PD,
905  /// so we can assert on that.
906  /// e. Return true if isLoopEntryGuardedByCond(Pred, E(LHS), E(RHS)) &&
907  /// isLoopBackedgeGuardedByCond(Pred, B(LHS), B(RHS))
908  bool isKnownViaInduction(ICmpInst::Predicate Pred, const SCEV *LHS,
909  const SCEV *RHS);
910 
911  /// Test if the given expression is known to satisfy the condition described
912  /// by Pred, LHS, and RHS.
913  bool isKnownPredicate(ICmpInst::Predicate Pred, const SCEV *LHS,
914  const SCEV *RHS);
915 
916  /// Test if the condition described by Pred, LHS, RHS is known to be true on
917  /// every iteration of the loop of the recurrency LHS.
918  bool isKnownOnEveryIteration(ICmpInst::Predicate Pred,
919  const SCEVAddRecExpr *LHS, const SCEV *RHS);
920 
921  /// Return true if, for all loop invariant X, the predicate "LHS `Pred` X"
922  /// is monotonically increasing or decreasing. In the former case set
923  /// `Increasing` to true and in the latter case set `Increasing` to false.
924  ///
925  /// A predicate is said to be monotonically increasing if may go from being
926  /// false to being true as the loop iterates, but never the other way
927  /// around. A predicate is said to be monotonically decreasing if may go
928  /// from being true to being false as the loop iterates, but never the other
929  /// way around.
930  bool isMonotonicPredicate(const SCEVAddRecExpr *LHS, ICmpInst::Predicate Pred,
931  bool &Increasing);
932 
933  /// Return true if the result of the predicate LHS `Pred` RHS is loop
934  /// invariant with respect to L. Set InvariantPred, InvariantLHS and
935  /// InvariantLHS so that InvariantLHS `InvariantPred` InvariantRHS is the
936  /// loop invariant form of LHS `Pred` RHS.
937  bool isLoopInvariantPredicate(ICmpInst::Predicate Pred, const SCEV *LHS,
938  const SCEV *RHS, const Loop *L,
939  ICmpInst::Predicate &InvariantPred,
940  const SCEV *&InvariantLHS,
941  const SCEV *&InvariantRHS);
942 
943  /// Simplify LHS and RHS in a comparison with predicate Pred. Return true
944  /// iff any changes were made. If the operands are provably equal or
945  /// unequal, LHS and RHS are set to the same value and Pred is set to either
946  /// ICMP_EQ or ICMP_NE.
947  bool SimplifyICmpOperands(ICmpInst::Predicate &Pred, const SCEV *&LHS,
948  const SCEV *&RHS, unsigned Depth = 0);
949 
950  /// Return the "disposition" of the given SCEV with respect to the given
951  /// loop.
952  LoopDisposition getLoopDisposition(const SCEV *S, const Loop *L);
953 
954  /// Return true if the value of the given SCEV is unchanging in the
955  /// specified loop.
956  bool isLoopInvariant(const SCEV *S, const Loop *L);
957 
958  /// Determine if the SCEV can be evaluated at loop's entry. It is true if it
959  /// doesn't depend on a SCEVUnknown of an instruction which is dominated by
960  /// the header of loop L.
961  bool isAvailableAtLoopEntry(const SCEV *S, const Loop *L);
962 
963  /// Return true if the given SCEV changes value in a known way in the
964  /// specified loop. This property being true implies that the value is
965  /// variant in the loop AND that we can emit an expression to compute the
966  /// value of the expression at any particular loop iteration.
967  bool hasComputableLoopEvolution(const SCEV *S, const Loop *L);
968 
969  /// Return the "disposition" of the given SCEV with respect to the given
970  /// block.
971  BlockDisposition getBlockDisposition(const SCEV *S, const BasicBlock *BB);
972 
973  /// Return true if elements that makes up the given SCEV dominate the
974  /// specified basic block.
975  bool dominates(const SCEV *S, const BasicBlock *BB);
976 
977  /// Return true if elements that makes up the given SCEV properly dominate
978  /// the specified basic block.
979  bool properlyDominates(const SCEV *S, const BasicBlock *BB);
980 
981  /// Test whether the given SCEV has Op as a direct or indirect operand.
982  bool hasOperand(const SCEV *S, const SCEV *Op) const;
983 
984  /// Return the size of an element read or written by Inst.
985  const SCEV *getElementSize(Instruction *Inst);
986 
987  /// Compute the array dimensions Sizes from the set of Terms extracted from
988  /// the memory access function of this SCEVAddRecExpr (second step of
989  /// delinearization).
990  void findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
992  const SCEV *ElementSize);
993 
994  void print(raw_ostream &OS) const;
995  void verify() const;
996  bool invalidate(Function &F, const PreservedAnalyses &PA,
998 
999  /// Collect parametric terms occurring in step expressions (first step of
1000  /// delinearization).
1001  void collectParametricTerms(const SCEV *Expr,
1003 
1004  /// Return in Subscripts the access functions for each dimension in Sizes
1005  /// (third step of delinearization).
1006  void computeAccessFunctions(const SCEV *Expr,
1007  SmallVectorImpl<const SCEV *> &Subscripts,
1009 
1010  /// Split this SCEVAddRecExpr into two vectors of SCEVs representing the
1011  /// subscripts and sizes of an array access.
1012  ///
1013  /// The delinearization is a 3 step process: the first two steps compute the
1014  /// sizes of each subscript and the third step computes the access functions
1015  /// for the delinearized array:
1016  ///
1017  /// 1. Find the terms in the step functions
1018  /// 2. Compute the array size
1019  /// 3. Compute the access function: divide the SCEV by the array size
1020  /// starting with the innermost dimensions found in step 2. The Quotient
1021  /// is the SCEV to be divided in the next step of the recursion. The
1022  /// Remainder is the subscript of the innermost dimension. Loop over all
1023  /// array dimensions computed in step 2.
1024  ///
1025  /// To compute a uniform array size for several memory accesses to the same
1026  /// object, one can collect in step 1 all the step terms for all the memory
1027  /// accesses, and compute in step 2 a unique array shape. This guarantees
1028  /// that the array shape will be the same across all memory accesses.
1029  ///
1030  /// FIXME: We could derive the result of steps 1 and 2 from a description of
1031  /// the array shape given in metadata.
1032  ///
1033  /// Example:
1034  ///
1035  /// A[][n][m]
1036  ///
1037  /// for i
1038  /// for j
1039  /// for k
1040  /// A[j+k][2i][5i] =
1041  ///
1042  /// The initial SCEV:
1043  ///
1044  /// A[{{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k]
1045  ///
1046  /// 1. Find the different terms in the step functions:
1047  /// -> [2*m, 5, n*m, n*m]
1048  ///
1049  /// 2. Compute the array size: sort and unique them
1050  /// -> [n*m, 2*m, 5]
1051  /// find the GCD of all the terms = 1
1052  /// divide by the GCD and erase constant terms
1053  /// -> [n*m, 2*m]
1054  /// GCD = m
1055  /// divide by GCD -> [n, 2]
1056  /// remove constant terms
1057  /// -> [n]
1058  /// size of the array is A[unknown][n][m]
1059  ///
1060  /// 3. Compute the access function
1061  /// a. Divide {{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k by the innermost size m
1062  /// Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k
1063  /// Remainder: {{{0,+,5}_i, +, 0}_j, +, 0}_k
1064  /// The remainder is the subscript of the innermost array dimension: [5i].
1065  ///
1066  /// b. Divide Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k by next outer size n
1067  /// Quotient: {{{0,+,0}_i, +, 1}_j, +, 1}_k
1068  /// Remainder: {{{0,+,2}_i, +, 0}_j, +, 0}_k
1069  /// The Remainder is the subscript of the next array dimension: [2i].
1070  ///
1071  /// The subscript of the outermost dimension is the Quotient: [j+k].
1072  ///
1073  /// Overall, we have: A[][n][m], and the access function: A[j+k][2i][5i].
1074  void delinearize(const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
1076  const SCEV *ElementSize);
1077 
1078  /// Return the DataLayout associated with the module this SCEV instance is
1079  /// operating on.
1080  const DataLayout &getDataLayout() const {
1081  return F.getParent()->getDataLayout();
1082  }
1083 
1084  const SCEVPredicate *getEqualPredicate(const SCEV *LHS, const SCEV *RHS);
1085 
1086  const SCEVPredicate *
1087  getWrapPredicate(const SCEVAddRecExpr *AR,
1089 
1090  /// Re-writes the SCEV according to the Predicates in \p A.
1091  const SCEV *rewriteUsingPredicate(const SCEV *S, const Loop *L,
1092  SCEVUnionPredicate &A);
1093  /// Tries to convert the \p S expression to an AddRec expression,
1094  /// adding additional predicates to \p Preds as required.
1095  const SCEVAddRecExpr *convertSCEVToAddRecWithPredicates(
1096  const SCEV *S, const Loop *L,
1098 
1099 private:
1100  /// A CallbackVH to arrange for ScalarEvolution to be notified whenever a
1101  /// Value is deleted.
1102  class SCEVCallbackVH final : public CallbackVH {
1103  ScalarEvolution *SE;
1104 
1105  void deleted() override;
1106  void allUsesReplacedWith(Value *New) override;
1107 
1108  public:
1109  SCEVCallbackVH(Value *V, ScalarEvolution *SE = nullptr);
1110  };
1111 
1112  friend class SCEVCallbackVH;
1113  friend class SCEVExpander;
1114  friend class SCEVUnknown;
1115 
1116  /// The function we are analyzing.
1117  Function &F;
1118 
1119  /// Does the module have any calls to the llvm.experimental.guard intrinsic
1120  /// at all? If this is false, we avoid doing work that will only help if
1121  /// thare are guards present in the IR.
1122  bool HasGuards;
1123 
1124  /// The target library information for the target we are targeting.
1125  TargetLibraryInfo &TLI;
1126 
1127  /// The tracker for \@llvm.assume intrinsics in this function.
1128  AssumptionCache &AC;
1129 
1130  /// The dominator tree.
1131  DominatorTree &DT;
1132 
1133  /// The loop information for the function we are currently analyzing.
1134  LoopInfo &LI;
1135 
1136  /// This SCEV is used to represent unknown trip counts and things.
1137  std::unique_ptr<SCEVCouldNotCompute> CouldNotCompute;
1138 
1139  /// The type for HasRecMap.
1141 
1142  /// This is a cache to record whether a SCEV contains any scAddRecExpr.
1143  HasRecMapType HasRecMap;
1144 
1145  /// The type for ExprValueMap.
1146  using ValueOffsetPair = std::pair<Value *, ConstantInt *>;
1148 
1149  /// ExprValueMap -- This map records the original values from which
1150  /// the SCEV expr is generated from.
1151  ///
1152  /// We want to represent the mapping as SCEV -> ValueOffsetPair instead
1153  /// of SCEV -> Value:
1154  /// Suppose we know S1 expands to V1, and
1155  /// S1 = S2 + C_a
1156  /// S3 = S2 + C_b
1157  /// where C_a and C_b are different SCEVConstants. Then we'd like to
1158  /// expand S3 as V1 - C_a + C_b instead of expanding S2 literally.
1159  /// It is helpful when S2 is a complex SCEV expr.
1160  ///
1161  /// In order to do that, we represent ExprValueMap as a mapping from
1162  /// SCEV to ValueOffsetPair. We will save both S1->{V1, 0} and
1163  /// S2->{V1, C_a} into the map when we create SCEV for V1. When S3
1164  /// is expanded, it will first expand S2 to V1 - C_a because of
1165  /// S2->{V1, C_a} in the map, then expand S3 to V1 - C_a + C_b.
1166  ///
1167  /// Note: S->{V, Offset} in the ExprValueMap means S can be expanded
1168  /// to V - Offset.
1169  ExprValueMapType ExprValueMap;
1170 
1171  /// The type for ValueExprMap.
1172  using ValueExprMapType =
1174 
1175  /// This is a cache of the values we have analyzed so far.
1176  ValueExprMapType ValueExprMap;
1177 
1178  /// Mark predicate values currently being processed by isImpliedCond.
1179  SmallPtrSet<Value *, 6> PendingLoopPredicates;
1180 
1181  /// Mark SCEVUnknown Phis currently being processed by getRangeRef.
1182  SmallPtrSet<const PHINode *, 6> PendingPhiRanges;
1183 
1184  // Mark SCEVUnknown Phis currently being processed by isImpliedViaMerge.
1185  SmallPtrSet<const PHINode *, 6> PendingMerges;
1186 
1187  /// Set to true by isLoopBackedgeGuardedByCond when we're walking the set of
1188  /// conditions dominating the backedge of a loop.
1189  bool WalkingBEDominatingConds = false;
1190 
1191  /// Set to true by isKnownPredicateViaSplitting when we're trying to prove a
1192  /// predicate by splitting it into a set of independent predicates.
1193  bool ProvingSplitPredicate = false;
1194 
1195  /// Memoized values for the GetMinTrailingZeros
1196  DenseMap<const SCEV *, uint32_t> MinTrailingZerosCache;
1197 
1198  /// Return the Value set from which the SCEV expr is generated.
1199  SetVector<ValueOffsetPair> *getSCEVValues(const SCEV *S);
1200 
1201  /// Private helper method for the GetMinTrailingZeros method
1202  uint32_t GetMinTrailingZerosImpl(const SCEV *S);
1203 
1204  /// Information about the number of loop iterations for which a loop exit's
1205  /// branch condition evaluates to the not-taken path. This is a temporary
1206  /// pair of exact and max expressions that are eventually summarized in
1207  /// ExitNotTakenInfo and BackedgeTakenInfo.
1208  struct ExitLimit {
1209  const SCEV *ExactNotTaken; // The exit is not taken exactly this many times
1210  const SCEV *MaxNotTaken; // The exit is not taken at most this many times
1211 
1212  // Not taken either exactly MaxNotTaken or zero times
1213  bool MaxOrZero = false;
1214 
1215  /// A set of predicate guards for this ExitLimit. The result is only valid
1216  /// if all of the predicates in \c Predicates evaluate to 'true' at
1217  /// run-time.
1219 
1220  void addPredicate(const SCEVPredicate *P) {
1221  assert(!isa<SCEVUnionPredicate>(P) && "Only add leaf predicates here!");
1222  Predicates.insert(P);
1223  }
1224 
1225  /*implicit*/ ExitLimit(const SCEV *E);
1226 
1227  ExitLimit(
1228  const SCEV *E, const SCEV *M, bool MaxOrZero,
1229  ArrayRef<const SmallPtrSetImpl<const SCEVPredicate *> *> PredSetList);
1230 
1231  ExitLimit(const SCEV *E, const SCEV *M, bool MaxOrZero,
1233 
1234  ExitLimit(const SCEV *E, const SCEV *M, bool MaxOrZero);
1235 
1236  /// Test whether this ExitLimit contains any computed information, or
1237  /// whether it's all SCEVCouldNotCompute values.
1238  bool hasAnyInfo() const {
1239  return !isa<SCEVCouldNotCompute>(ExactNotTaken) ||
1240  !isa<SCEVCouldNotCompute>(MaxNotTaken);
1241  }
1242 
1243  bool hasOperand(const SCEV *S) const;
1244 
1245  /// Test whether this ExitLimit contains all information.
1246  bool hasFullInfo() const {
1247  return !isa<SCEVCouldNotCompute>(ExactNotTaken);
1248  }
1249  };
1250 
1251  /// Information about the number of times a particular loop exit may be
1252  /// reached before exiting the loop.
1253  struct ExitNotTakenInfo {
1254  PoisoningVH<BasicBlock> ExitingBlock;
1255  const SCEV *ExactNotTaken;
1256  std::unique_ptr<SCEVUnionPredicate> Predicate;
1257 
1258  explicit ExitNotTakenInfo(PoisoningVH<BasicBlock> ExitingBlock,
1259  const SCEV *ExactNotTaken,
1260  std::unique_ptr<SCEVUnionPredicate> Predicate)
1261  : ExitingBlock(ExitingBlock), ExactNotTaken(ExactNotTaken),
1262  Predicate(std::move(Predicate)) {}
1263 
1264  bool hasAlwaysTruePredicate() const {
1265  return !Predicate || Predicate->isAlwaysTrue();
1266  }
1267  };
1268 
1269  /// Information about the backedge-taken count of a loop. This currently
1270  /// includes an exact count and a maximum count.
1271  ///
1272  class BackedgeTakenInfo {
1273  /// A list of computable exits and their not-taken counts. Loops almost
1274  /// never have more than one computable exit.
1275  SmallVector<ExitNotTakenInfo, 1> ExitNotTaken;
1276 
1277  /// The pointer part of \c MaxAndComplete is an expression indicating the
1278  /// least maximum backedge-taken count of the loop that is known, or a
1279  /// SCEVCouldNotCompute. This expression is only valid if the predicates
1280  /// associated with all loop exits are true.
1281  ///
1282  /// The integer part of \c MaxAndComplete is a boolean indicating if \c
1283  /// ExitNotTaken has an element for every exiting block in the loop.
1284  PointerIntPair<const SCEV *, 1> MaxAndComplete;
1285 
1286  /// True iff the backedge is taken either exactly Max or zero times.
1287  bool MaxOrZero = false;
1288 
1289  /// \name Helper projection functions on \c MaxAndComplete.
1290  /// @{
1291  bool isComplete() const { return MaxAndComplete.getInt(); }
1292  const SCEV *getMax() const { return MaxAndComplete.getPointer(); }
1293  /// @}
1294 
1295  public:
1296  BackedgeTakenInfo() : MaxAndComplete(nullptr, 0) {}
1297  BackedgeTakenInfo(BackedgeTakenInfo &&) = default;
1298  BackedgeTakenInfo &operator=(BackedgeTakenInfo &&) = default;
1299 
1300  using EdgeExitInfo = std::pair<BasicBlock *, ExitLimit>;
1301 
1302  /// Initialize BackedgeTakenInfo from a list of exact exit counts.
1303  BackedgeTakenInfo(ArrayRef<EdgeExitInfo> ExitCounts, bool Complete,
1304  const SCEV *MaxCount, bool MaxOrZero);
1305 
1306  /// Test whether this BackedgeTakenInfo contains any computed information,
1307  /// or whether it's all SCEVCouldNotCompute values.
1308  bool hasAnyInfo() const {
1309  return !ExitNotTaken.empty() || !isa<SCEVCouldNotCompute>(getMax());
1310  }
1311 
1312  /// Test whether this BackedgeTakenInfo contains complete information.
1313  bool hasFullInfo() const { return isComplete(); }
1314 
1315  /// Return an expression indicating the exact *backedge-taken*
1316  /// count of the loop if it is known or SCEVCouldNotCompute
1317  /// otherwise. If execution makes it to the backedge on every
1318  /// iteration (i.e. there are no abnormal exists like exception
1319  /// throws and thread exits) then this is the number of times the
1320  /// loop header will execute minus one.
1321  ///
1322  /// If the SCEV predicate associated with the answer can be different
1323  /// from AlwaysTrue, we must add a (non null) Predicates argument.
1324  /// The SCEV predicate associated with the answer will be added to
1325  /// Predicates. A run-time check needs to be emitted for the SCEV
1326  /// predicate in order for the answer to be valid.
1327  ///
1328  /// Note that we should always know if we need to pass a predicate
1329  /// argument or not from the way the ExitCounts vector was computed.
1330  /// If we allowed SCEV predicates to be generated when populating this
1331  /// vector, this information can contain them and therefore a
1332  /// SCEVPredicate argument should be added to getExact.
1333  const SCEV *getExact(const Loop *L, ScalarEvolution *SE,
1334  SCEVUnionPredicate *Predicates = nullptr) const;
1335 
1336  /// Return the number of times this loop exit may fall through to the back
1337  /// edge, or SCEVCouldNotCompute. The loop is guaranteed not to exit via
1338  /// this block before this number of iterations, but may exit via another
1339  /// block.
1340  const SCEV *getExact(BasicBlock *ExitingBlock, ScalarEvolution *SE) const;
1341 
1342  /// Get the max backedge taken count for the loop.
1343  const SCEV *getMax(ScalarEvolution *SE) const;
1344 
1345  /// Return true if the number of times this backedge is taken is either the
1346  /// value returned by getMax or zero.
1347  bool isMaxOrZero(ScalarEvolution *SE) const;
1348 
1349  /// Return true if any backedge taken count expressions refer to the given
1350  /// subexpression.
1351  bool hasOperand(const SCEV *S, ScalarEvolution *SE) const;
1352 
1353  /// Invalidate this result and free associated memory.
1354  void clear();
1355  };
1356 
1357  /// Cache the backedge-taken count of the loops for this function as they
1358  /// are computed.
1359  DenseMap<const Loop *, BackedgeTakenInfo> BackedgeTakenCounts;
1360 
1361  /// Cache the predicated backedge-taken count of the loops for this
1362  /// function as they are computed.
1363  DenseMap<const Loop *, BackedgeTakenInfo> PredicatedBackedgeTakenCounts;
1364 
1365  /// This map contains entries for all of the PHI instructions that we
1366  /// attempt to compute constant evolutions for. This allows us to avoid
1367  /// potentially expensive recomputation of these properties. An instruction
1368  /// maps to null if we are unable to compute its exit value.
1369  DenseMap<PHINode *, Constant *> ConstantEvolutionLoopExitValue;
1370 
1371  /// This map contains entries for all the expressions that we attempt to
1372  /// compute getSCEVAtScope information for, which can be expensive in
1373  /// extreme cases.
1375  ValuesAtScopes;
1376 
1377  /// Memoized computeLoopDisposition results.
1378  DenseMap<const SCEV *,
1380  LoopDispositions;
1381 
1382  struct LoopProperties {
1383  /// Set to true if the loop contains no instruction that can have side
1384  /// effects (i.e. via throwing an exception, volatile or atomic access).
1385  bool HasNoAbnormalExits;
1386 
1387  /// Set to true if the loop contains no instruction that can abnormally exit
1388  /// the loop (i.e. via throwing an exception, by terminating the thread
1389  /// cleanly or by infinite looping in a called function). Strictly
1390  /// speaking, the last one is not leaving the loop, but is identical to
1391  /// leaving the loop for reasoning about undefined behavior.
1392  bool HasNoSideEffects;
1393  };
1394 
1395  /// Cache for \c getLoopProperties.
1396  DenseMap<const Loop *, LoopProperties> LoopPropertiesCache;
1397 
1398  /// Return a \c LoopProperties instance for \p L, creating one if necessary.
1399  LoopProperties getLoopProperties(const Loop *L);
1400 
1401  bool loopHasNoSideEffects(const Loop *L) {
1402  return getLoopProperties(L).HasNoSideEffects;
1403  }
1404 
1405  bool loopHasNoAbnormalExits(const Loop *L) {
1406  return getLoopProperties(L).HasNoAbnormalExits;
1407  }
1408 
1409  /// Compute a LoopDisposition value.
1410  LoopDisposition computeLoopDisposition(const SCEV *S, const Loop *L);
1411 
1412  /// Memoized computeBlockDisposition results.
1413  DenseMap<
1414  const SCEV *,
1416  BlockDispositions;
1417 
1418  /// Compute a BlockDisposition value.
1419  BlockDisposition computeBlockDisposition(const SCEV *S, const BasicBlock *BB);
1420 
1421  /// Memoized results from getRange
1423 
1424  /// Memoized results from getRange
1426 
1427  /// Used to parameterize getRange
1428  enum RangeSignHint { HINT_RANGE_UNSIGNED, HINT_RANGE_SIGNED };
1429 
1430  /// Set the memoized range for the given SCEV.
1431  const ConstantRange &setRange(const SCEV *S, RangeSignHint Hint,
1432  ConstantRange CR) {
1434  Hint == HINT_RANGE_UNSIGNED ? UnsignedRanges : SignedRanges;
1435 
1436  auto Pair = Cache.try_emplace(S, std::move(CR));
1437  if (!Pair.second)
1438  Pair.first->second = std::move(CR);
1439  return Pair.first->second;
1440  }
1441 
1442  /// Determine the range for a particular SCEV.
1443  /// NOTE: This returns a reference to an entry in a cache. It must be
1444  /// copied if its needed for longer.
1445  const ConstantRange &getRangeRef(const SCEV *S, RangeSignHint Hint);
1446 
1447  /// Determines the range for the affine SCEVAddRecExpr {\p Start,+,\p Stop}.
1448  /// Helper for \c getRange.
1449  ConstantRange getRangeForAffineAR(const SCEV *Start, const SCEV *Stop,
1450  const SCEV *MaxBECount, unsigned BitWidth);
1451 
1452  /// Try to compute a range for the affine SCEVAddRecExpr {\p Start,+,\p
1453  /// Stop} by "factoring out" a ternary expression from the add recurrence.
1454  /// Helper called by \c getRange.
1455  ConstantRange getRangeViaFactoring(const SCEV *Start, const SCEV *Stop,
1456  const SCEV *MaxBECount, unsigned BitWidth);
1457 
1458  /// We know that there is no SCEV for the specified value. Analyze the
1459  /// expression.
1460  const SCEV *createSCEV(Value *V);
1461 
1462  /// Provide the special handling we need to analyze PHI SCEVs.
1463  const SCEV *createNodeForPHI(PHINode *PN);
1464 
1465  /// Helper function called from createNodeForPHI.
1466  const SCEV *createAddRecFromPHI(PHINode *PN);
1467 
1468  /// A helper function for createAddRecFromPHI to handle simple cases.
1469  const SCEV *createSimpleAffineAddRec(PHINode *PN, Value *BEValueV,
1470  Value *StartValueV);
1471 
1472  /// Helper function called from createNodeForPHI.
1473  const SCEV *createNodeFromSelectLikePHI(PHINode *PN);
1474 
1475  /// Provide special handling for a select-like instruction (currently this
1476  /// is either a select instruction or a phi node). \p I is the instruction
1477  /// being processed, and it is assumed equivalent to "Cond ? TrueVal :
1478  /// FalseVal".
1479  const SCEV *createNodeForSelectOrPHI(Instruction *I, Value *Cond,
1480  Value *TrueVal, Value *FalseVal);
1481 
1482  /// Provide the special handling we need to analyze GEP SCEVs.
1483  const SCEV *createNodeForGEP(GEPOperator *GEP);
1484 
1485  /// Implementation code for getSCEVAtScope; called at most once for each
1486  /// SCEV+Loop pair.
1487  const SCEV *computeSCEVAtScope(const SCEV *S, const Loop *L);
1488 
1489  /// This looks up computed SCEV values for all instructions that depend on
1490  /// the given instruction and removes them from the ValueExprMap map if they
1491  /// reference SymName. This is used during PHI resolution.
1492  void forgetSymbolicName(Instruction *I, const SCEV *SymName);
1493 
1494  /// Return the BackedgeTakenInfo for the given loop, lazily computing new
1495  /// values if the loop hasn't been analyzed yet. The returned result is
1496  /// guaranteed not to be predicated.
1497  const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
1498 
1499  /// Similar to getBackedgeTakenInfo, but will add predicates as required
1500  /// with the purpose of returning complete information.
1501  const BackedgeTakenInfo &getPredicatedBackedgeTakenInfo(const Loop *L);
1502 
1503  /// Compute the number of times the specified loop will iterate.
1504  /// If AllowPredicates is set, we will create new SCEV predicates as
1505  /// necessary in order to return an exact answer.
1506  BackedgeTakenInfo computeBackedgeTakenCount(const Loop *L,
1507  bool AllowPredicates = false);
1508 
1509  /// Compute the number of times the backedge of the specified loop will
1510  /// execute if it exits via the specified block. If AllowPredicates is set,
1511  /// this call will try to use a minimal set of SCEV predicates in order to
1512  /// return an exact answer.
1513  ExitLimit computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
1514  bool AllowPredicates = false);
1515 
1516  /// Compute the number of times the backedge of the specified loop will
1517  /// execute if its exit condition were a conditional branch of ExitCond.
1518  ///
1519  /// \p ControlsExit is true if ExitCond directly controls the exit
1520  /// branch. In this case, we can assume that the loop exits only if the
1521  /// condition is true and can infer that failing to meet the condition prior
1522  /// to integer wraparound results in undefined behavior.
1523  ///
1524  /// If \p AllowPredicates is set, this call will try to use a minimal set of
1525  /// SCEV predicates in order to return an exact answer.
1526  ExitLimit computeExitLimitFromCond(const Loop *L, Value *ExitCond,
1527  bool ExitIfTrue, bool ControlsExit,
1528  bool AllowPredicates = false);
1529 
1530  // Helper functions for computeExitLimitFromCond to avoid exponential time
1531  // complexity.
1532 
1533  class ExitLimitCache {
1534  // It may look like we need key on the whole (L, ExitIfTrue, ControlsExit,
1535  // AllowPredicates) tuple, but recursive calls to
1536  // computeExitLimitFromCondCached from computeExitLimitFromCondImpl only
1537  // vary the in \c ExitCond and \c ControlsExit parameters. We remember the
1538  // initial values of the other values to assert our assumption.
1539  SmallDenseMap<PointerIntPair<Value *, 1>, ExitLimit> TripCountMap;
1540 
1541  const Loop *L;
1542  bool ExitIfTrue;
1543  bool AllowPredicates;
1544 
1545  public:
1546  ExitLimitCache(const Loop *L, bool ExitIfTrue, bool AllowPredicates)
1547  : L(L), ExitIfTrue(ExitIfTrue), AllowPredicates(AllowPredicates) {}
1548 
1549  Optional<ExitLimit> find(const Loop *L, Value *ExitCond, bool ExitIfTrue,
1550  bool ControlsExit, bool AllowPredicates);
1551 
1552  void insert(const Loop *L, Value *ExitCond, bool ExitIfTrue,
1553  bool ControlsExit, bool AllowPredicates, const ExitLimit &EL);
1554  };
1555 
1556  using ExitLimitCacheTy = ExitLimitCache;
1557 
1558  ExitLimit computeExitLimitFromCondCached(ExitLimitCacheTy &Cache,
1559  const Loop *L, Value *ExitCond,
1560  bool ExitIfTrue,
1561  bool ControlsExit,
1562  bool AllowPredicates);
1563  ExitLimit computeExitLimitFromCondImpl(ExitLimitCacheTy &Cache, const Loop *L,
1564  Value *ExitCond, bool ExitIfTrue,
1565  bool ControlsExit,
1566  bool AllowPredicates);
1567 
1568  /// Compute the number of times the backedge of the specified loop will
1569  /// execute if its exit condition were a conditional branch of the ICmpInst
1570  /// ExitCond and ExitIfTrue. If AllowPredicates is set, this call will try
1571  /// to use a minimal set of SCEV predicates in order to return an exact
1572  /// answer.
1573  ExitLimit computeExitLimitFromICmp(const Loop *L, ICmpInst *ExitCond,
1574  bool ExitIfTrue,
1575  bool IsSubExpr,
1576  bool AllowPredicates = false);
1577 
1578  /// Compute the number of times the backedge of the specified loop will
1579  /// execute if its exit condition were a switch with a single exiting case
1580  /// to ExitingBB.
1581  ExitLimit computeExitLimitFromSingleExitSwitch(const Loop *L,
1582  SwitchInst *Switch,
1583  BasicBlock *ExitingBB,
1584  bool IsSubExpr);
1585 
1586  /// Given an exit condition of 'icmp op load X, cst', try to see if we can
1587  /// compute the backedge-taken count.
1588  ExitLimit computeLoadConstantCompareExitLimit(LoadInst *LI, Constant *RHS,
1589  const Loop *L,
1591 
1592  /// Compute the exit limit of a loop that is controlled by a
1593  /// "(IV >> 1) != 0" type comparison. We cannot compute the exact trip
1594  /// count in these cases (since SCEV has no way of expressing them), but we
1595  /// can still sometimes compute an upper bound.
1596  ///
1597  /// Return an ExitLimit for a loop whose backedge is guarded by `LHS Pred
1598  /// RHS`.
1599  ExitLimit computeShiftCompareExitLimit(Value *LHS, Value *RHS, const Loop *L,
1600  ICmpInst::Predicate Pred);
1601 
1602  /// If the loop is known to execute a constant number of times (the
1603  /// condition evolves only from constants), try to evaluate a few iterations
1604  /// of the loop until we get the exit condition gets a value of ExitWhen
1605  /// (true or false). If we cannot evaluate the exit count of the loop,
1606  /// return CouldNotCompute.
1607  const SCEV *computeExitCountExhaustively(const Loop *L, Value *Cond,
1608  bool ExitWhen);
1609 
1610  /// Return the number of times an exit condition comparing the specified
1611  /// value to zero will execute. If not computable, return CouldNotCompute.
1612  /// If AllowPredicates is set, this call will try to use a minimal set of
1613  /// SCEV predicates in order to return an exact answer.
1614  ExitLimit howFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr,
1615  bool AllowPredicates = false);
1616 
1617  /// Return the number of times an exit condition checking the specified
1618  /// value for nonzero will execute. If not computable, return
1619  /// CouldNotCompute.
1620  ExitLimit howFarToNonZero(const SCEV *V, const Loop *L);
1621 
1622  /// Return the number of times an exit condition containing the specified
1623  /// less-than comparison will execute. If not computable, return
1624  /// CouldNotCompute.
1625  ///
1626  /// \p isSigned specifies whether the less-than is signed.
1627  ///
1628  /// \p ControlsExit is true when the LHS < RHS condition directly controls
1629  /// the branch (loops exits only if condition is true). In this case, we can
1630  /// use NoWrapFlags to skip overflow checks.
1631  ///
1632  /// If \p AllowPredicates is set, this call will try to use a minimal set of
1633  /// SCEV predicates in order to return an exact answer.
1634  ExitLimit howManyLessThans(const SCEV *LHS, const SCEV *RHS, const Loop *L,
1635  bool isSigned, bool ControlsExit,
1636  bool AllowPredicates = false);
1637 
1638  ExitLimit howManyGreaterThans(const SCEV *LHS, const SCEV *RHS, const Loop *L,
1639  bool isSigned, bool IsSubExpr,
1640  bool AllowPredicates = false);
1641 
1642  /// Return a predecessor of BB (which may not be an immediate predecessor)
1643  /// which has exactly one successor from which BB is reachable, or null if
1644  /// no such block is found.
1645  std::pair<BasicBlock *, BasicBlock *>
1646  getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
1647 
1648  /// Test whether the condition described by Pred, LHS, and RHS is true
1649  /// whenever the given FoundCondValue value evaluates to true.
1650  bool isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
1651  Value *FoundCondValue, bool Inverse);
1652 
1653  /// Test whether the condition described by Pred, LHS, and RHS is true
1654  /// whenever the condition described by FoundPred, FoundLHS, FoundRHS is
1655  /// true.
1656  bool isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
1657  ICmpInst::Predicate FoundPred, const SCEV *FoundLHS,
1658  const SCEV *FoundRHS);
1659 
1660  /// Test whether the condition described by Pred, LHS, and RHS is true
1661  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1662  /// true.
1663  bool isImpliedCondOperands(ICmpInst::Predicate Pred, const SCEV *LHS,
1664  const SCEV *RHS, const SCEV *FoundLHS,
1665  const SCEV *FoundRHS);
1666 
1667  /// Test whether the condition described by Pred, LHS, and RHS is true
1668  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1669  /// true. Here LHS is an operation that includes FoundLHS as one of its
1670  /// arguments.
1671  bool isImpliedViaOperations(ICmpInst::Predicate Pred,
1672  const SCEV *LHS, const SCEV *RHS,
1673  const SCEV *FoundLHS, const SCEV *FoundRHS,
1674  unsigned Depth = 0);
1675 
1676  /// Test whether the condition described by Pred, LHS, and RHS is true.
1677  /// Use only simple non-recursive types of checks, such as range analysis etc.
1678  bool isKnownViaNonRecursiveReasoning(ICmpInst::Predicate Pred,
1679  const SCEV *LHS, const SCEV *RHS);
1680 
1681  /// Test whether the condition described by Pred, LHS, and RHS is true
1682  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1683  /// true.
1684  bool isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, const SCEV *LHS,
1685  const SCEV *RHS, const SCEV *FoundLHS,
1686  const SCEV *FoundRHS);
1687 
1688  /// Test whether the condition described by Pred, LHS, and RHS is true
1689  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1690  /// true. Utility function used by isImpliedCondOperands. Tries to get
1691  /// cases like "X `sgt` 0 => X - 1 `sgt` -1".
1692  bool isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred, const SCEV *LHS,
1693  const SCEV *RHS, const SCEV *FoundLHS,
1694  const SCEV *FoundRHS);
1695 
1696  /// Return true if the condition denoted by \p LHS \p Pred \p RHS is implied
1697  /// by a call to \c @llvm.experimental.guard in \p BB.
1698  bool isImpliedViaGuard(BasicBlock *BB, ICmpInst::Predicate Pred,
1699  const SCEV *LHS, const SCEV *RHS);
1700 
1701  /// Test whether the condition described by Pred, LHS, and RHS is true
1702  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1703  /// true.
1704  ///
1705  /// This routine tries to rule out certain kinds of integer overflow, and
1706  /// then tries to reason about arithmetic properties of the predicates.
1707  bool isImpliedCondOperandsViaNoOverflow(ICmpInst::Predicate Pred,
1708  const SCEV *LHS, const SCEV *RHS,
1709  const SCEV *FoundLHS,
1710  const SCEV *FoundRHS);
1711 
1712  /// Test whether the condition described by Pred, LHS, and RHS is true
1713  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1714  /// true.
1715  ///
1716  /// This routine tries to figure out predicate for Phis which are SCEVUnknown
1717  /// if it is true for every possible incoming value from their respective
1718  /// basic blocks.
1719  bool isImpliedViaMerge(ICmpInst::Predicate Pred,
1720  const SCEV *LHS, const SCEV *RHS,
1721  const SCEV *FoundLHS, const SCEV *FoundRHS,
1722  unsigned Depth);
1723 
1724  /// If we know that the specified Phi is in the header of its containing
1725  /// loop, we know the loop executes a constant number of times, and the PHI
1726  /// node is just a recurrence involving constants, fold it.
1727  Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt &BEs,
1728  const Loop *L);
1729 
1730  /// Test if the given expression is known to satisfy the condition described
1731  /// by Pred and the known constant ranges of LHS and RHS.
1732  bool isKnownPredicateViaConstantRanges(ICmpInst::Predicate Pred,
1733  const SCEV *LHS, const SCEV *RHS);
1734 
1735  /// Try to prove the condition described by "LHS Pred RHS" by ruling out
1736  /// integer overflow.
1737  ///
1738  /// For instance, this will return true for "A s< (A + C)<nsw>" if C is
1739  /// positive.
1740  bool isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred, const SCEV *LHS,
1741  const SCEV *RHS);
1742 
1743  /// Try to split Pred LHS RHS into logical conjunctions (and's) and try to
1744  /// prove them individually.
1745  bool isKnownPredicateViaSplitting(ICmpInst::Predicate Pred, const SCEV *LHS,
1746  const SCEV *RHS);
1747 
1748  /// Try to match the Expr as "(L + R)<Flags>".
1749  bool splitBinaryAdd(const SCEV *Expr, const SCEV *&L, const SCEV *&R,
1750  SCEV::NoWrapFlags &Flags);
1751 
1752  /// Compute \p LHS - \p RHS and returns the result as an APInt if it is a
1753  /// constant, and None if it isn't.
1754  ///
1755  /// This is intended to be a cheaper version of getMinusSCEV. We can be
1756  /// frugal here since we just bail out of actually constructing and
1757  /// canonicalizing an expression in the cases where the result isn't going
1758  /// to be a constant.
1759  Optional<APInt> computeConstantDifference(const SCEV *LHS, const SCEV *RHS);
1760 
1761  /// Drop memoized information computed for S.
1762  void forgetMemoizedResults(const SCEV *S);
1763 
1764  /// Return an existing SCEV for V if there is one, otherwise return nullptr.
1765  const SCEV *getExistingSCEV(Value *V);
1766 
1767  /// Return false iff given SCEV contains a SCEVUnknown with NULL value-
1768  /// pointer.
1769  bool checkValidity(const SCEV *S) const;
1770 
1771  /// Return true if `ExtendOpTy`({`Start`,+,`Step`}) can be proved to be
1772  /// equal to {`ExtendOpTy`(`Start`),+,`ExtendOpTy`(`Step`)}. This is
1773  /// equivalent to proving no signed (resp. unsigned) wrap in
1774  /// {`Start`,+,`Step`} if `ExtendOpTy` is `SCEVSignExtendExpr`
1775  /// (resp. `SCEVZeroExtendExpr`).
1776  template <typename ExtendOpTy>
1777  bool proveNoWrapByVaryingStart(const SCEV *Start, const SCEV *Step,
1778  const Loop *L);
1779 
1780  /// Try to prove NSW or NUW on \p AR relying on ConstantRange manipulation.
1781  SCEV::NoWrapFlags proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR);
1782 
1783  bool isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
1784  ICmpInst::Predicate Pred, bool &Increasing);
1785 
1786  /// Return SCEV no-wrap flags that can be proven based on reasoning about
1787  /// how poison produced from no-wrap flags on this value (e.g. a nuw add)
1788  /// would trigger undefined behavior on overflow.
1789  SCEV::NoWrapFlags getNoWrapFlagsFromUB(const Value *V);
1790 
1791  /// Return true if the SCEV corresponding to \p I is never poison. Proving
1792  /// this is more complex than proving that just \p I is never poison, since
1793  /// SCEV commons expressions across control flow, and you can have cases
1794  /// like:
1795  ///
1796  /// idx0 = a + b;
1797  /// ptr[idx0] = 100;
1798  /// if (<condition>) {
1799  /// idx1 = a +nsw b;
1800  /// ptr[idx1] = 200;
1801  /// }
1802  ///
1803  /// where the SCEV expression (+ a b) is guaranteed to not be poison (and
1804  /// hence not sign-overflow) only if "<condition>" is true. Since both
1805  /// `idx0` and `idx1` will be mapped to the same SCEV expression, (+ a b),
1806  /// it is not okay to annotate (+ a b) with <nsw> in the above example.
1807  bool isSCEVExprNeverPoison(const Instruction *I);
1808 
1809  /// This is like \c isSCEVExprNeverPoison but it specifically works for
1810  /// instructions that will get mapped to SCEV add recurrences. Return true
1811  /// if \p I will never generate poison under the assumption that \p I is an
1812  /// add recurrence on the loop \p L.
1813  bool isAddRecNeverPoison(const Instruction *I, const Loop *L);
1814 
1815  /// Similar to createAddRecFromPHI, but with the additional flexibility of
1816  /// suggesting runtime overflow checks in case casts are encountered.
1817  /// If successful, the analysis records that for this loop, \p SymbolicPHI,
1818  /// which is the UnknownSCEV currently representing the PHI, can be rewritten
1819  /// into an AddRec, assuming some predicates; The function then returns the
1820  /// AddRec and the predicates as a pair, and caches this pair in
1821  /// PredicatedSCEVRewrites.
1822  /// If the analysis is not successful, a mapping from the \p SymbolicPHI to
1823  /// itself (with no predicates) is recorded, and a nullptr with an empty
1824  /// predicates vector is returned as a pair.
1826  createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI);
1827 
1828  /// Compute the backedge taken count knowing the interval difference, the
1829  /// stride and presence of the equality in the comparison.
1830  const SCEV *computeBECount(const SCEV *Delta, const SCEV *Stride,
1831  bool Equality);
1832 
1833  /// Compute the maximum backedge count based on the range of values
1834  /// permitted by Start, End, and Stride. This is for loops of the form
1835  /// {Start, +, Stride} LT End.
1836  ///
1837  /// Precondition: the induction variable is known to be positive. We *don't*
1838  /// assert these preconditions so please be careful.
1839  const SCEV *computeMaxBECountForLT(const SCEV *Start, const SCEV *Stride,
1840  const SCEV *End, unsigned BitWidth,
1841  bool IsSigned);
1842 
1843  /// Verify if an linear IV with positive stride can overflow when in a
1844  /// less-than comparison, knowing the invariant term of the comparison,
1845  /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1846  bool doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride, bool IsSigned,
1847  bool NoWrap);
1848 
1849  /// Verify if an linear IV with negative stride can overflow when in a
1850  /// greater-than comparison, knowing the invariant term of the comparison,
1851  /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1852  bool doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride, bool IsSigned,
1853  bool NoWrap);
1854 
1855  /// Get add expr already created or create a new one.
1856  const SCEV *getOrCreateAddExpr(ArrayRef<const SCEV *> Ops,
1857  SCEV::NoWrapFlags Flags);
1858 
1859  /// Get mul expr already created or create a new one.
1860  const SCEV *getOrCreateMulExpr(ArrayRef<const SCEV *> Ops,
1861  SCEV::NoWrapFlags Flags);
1862 
1863  // Get addrec expr already created or create a new one.
1864  const SCEV *getOrCreateAddRecExpr(ArrayRef<const SCEV *> Ops,
1865  const Loop *L, SCEV::NoWrapFlags Flags);
1866 
1867  /// Return x if \p Val is f(x) where f is a 1-1 function.
1868  const SCEV *stripInjectiveFunctions(const SCEV *Val) const;
1869 
1870  /// Find all of the loops transitively used in \p S, and fill \p LoopsUsed.
1871  /// A loop is considered "used" by an expression if it contains
1872  /// an add rec on said loop.
1873  void getUsedLoops(const SCEV *S, SmallPtrSetImpl<const Loop *> &LoopsUsed);
1874 
1875  /// Find all of the loops transitively used in \p S, and update \c LoopUsers
1876  /// accordingly.
1877  void addToLoopUseLists(const SCEV *S);
1878 
1879  /// Try to match the pattern generated by getURemExpr(A, B). If successful,
1880  /// Assign A and B to LHS and RHS, respectively.
1881  bool matchURem(const SCEV *Expr, const SCEV *&LHS, const SCEV *&RHS);
1882 
1883  /// Look for a SCEV expression with type `SCEVType` and operands `Ops` in
1884  /// `UniqueSCEVs`.
1885  ///
1886  /// The first component of the returned tuple is the SCEV if found and null
1887  /// otherwise. The second component is the `FoldingSetNodeID` that was
1888  /// constructed to look up the SCEV and the third component is the insertion
1889  /// point.
1890  std::tuple<const SCEV *, FoldingSetNodeID, void *>
1891  findExistingSCEVInCache(int SCEVType, ArrayRef<const SCEV *> Ops);
1892 
1893  FoldingSet<SCEV> UniqueSCEVs;
1894  FoldingSet<SCEVPredicate> UniquePreds;
1895  BumpPtrAllocator SCEVAllocator;
1896 
1897  /// This maps loops to a list of SCEV expressions that (transitively) use said
1898  /// loop.
1900 
1901  /// Cache tentative mappings from UnknownSCEVs in a Loop, to a SCEV expression
1902  /// they can be rewritten into under certain predicates.
1904  std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
1905  PredicatedSCEVRewrites;
1906 
1907  /// The head of a linked list of all SCEVUnknown values that have been
1908  /// allocated. This is used by releaseMemory to locate them all and call
1909  /// their destructors.
1910  SCEVUnknown *FirstUnknown = nullptr;
1911 };
1912 
1913 /// Analysis pass that exposes the \c ScalarEvolution for a function.
1915  : public AnalysisInfoMixin<ScalarEvolutionAnalysis> {
1917 
1918  static AnalysisKey Key;
1919 
1920 public:
1922 
1924 };
1925 
1926 /// Printer pass for the \c ScalarEvolutionAnalysis results.
1928  : public PassInfoMixin<ScalarEvolutionPrinterPass> {
1929  raw_ostream &OS;
1930 
1931 public:
1932  explicit ScalarEvolutionPrinterPass(raw_ostream &OS) : OS(OS) {}
1933 
1935 };
1936 
1938  std::unique_ptr<ScalarEvolution> SE;
1939 
1940 public:
1941  static char ID;
1942 
1944 
1945  ScalarEvolution &getSE() { return *SE; }
1946  const ScalarEvolution &getSE() const { return *SE; }
1947 
1948  bool runOnFunction(Function &F) override;
1949  void releaseMemory() override;
1950  void getAnalysisUsage(AnalysisUsage &AU) const override;
1951  void print(raw_ostream &OS, const Module * = nullptr) const override;
1952  void verifyAnalysis() const override;
1953 };
1954 
1955 /// An interface layer with SCEV used to manage how we see SCEV expressions
1956 /// for values in the context of existing predicates. We can add new
1957 /// predicates, but we cannot remove them.
1958 ///
1959 /// This layer has multiple purposes:
1960 /// - provides a simple interface for SCEV versioning.
1961 /// - guarantees that the order of transformations applied on a SCEV
1962 /// expression for a single Value is consistent across two different
1963 /// getSCEV calls. This means that, for example, once we've obtained
1964 /// an AddRec expression for a certain value through expression
1965 /// rewriting, we will continue to get an AddRec expression for that
1966 /// Value.
1967 /// - lowers the number of expression rewrites.
1969 public:
1971 
1972  const SCEVUnionPredicate &getUnionPredicate() const;
1973 
1974  /// Returns the SCEV expression of V, in the context of the current SCEV
1975  /// predicate. The order of transformations applied on the expression of V
1976  /// returned by ScalarEvolution is guaranteed to be preserved, even when
1977  /// adding new predicates.
1978  const SCEV *getSCEV(Value *V);
1979 
1980  /// Get the (predicated) backedge count for the analyzed loop.
1981  const SCEV *getBackedgeTakenCount();
1982 
1983  /// Adds a new predicate.
1984  void addPredicate(const SCEVPredicate &Pred);
1985 
1986  /// Attempts to produce an AddRecExpr for V by adding additional SCEV
1987  /// predicates. If we can't transform the expression into an AddRecExpr we
1988  /// return nullptr and not add additional SCEV predicates to the current
1989  /// context.
1990  const SCEVAddRecExpr *getAsAddRec(Value *V);
1991 
1992  /// Proves that V doesn't overflow by adding SCEV predicate.
1993  void setNoOverflow(Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags);
1994 
1995  /// Returns true if we've proved that V doesn't wrap by means of a SCEV
1996  /// predicate.
1997  bool hasNoOverflow(Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags);
1998 
1999  /// Returns the ScalarEvolution analysis used.
2000  ScalarEvolution *getSE() const { return &SE; }
2001 
2002  /// We need to explicitly define the copy constructor because of FlagsMap.
2004 
2005  /// Print the SCEV mappings done by the Predicated Scalar Evolution.
2006  /// The printed text is indented by \p Depth.
2007  void print(raw_ostream &OS, unsigned Depth) const;
2008 
2009  /// Check if \p AR1 and \p AR2 are equal, while taking into account
2010  /// Equal predicates in Preds.
2011  bool areAddRecsEqualWithPreds(const SCEVAddRecExpr *AR1,
2012  const SCEVAddRecExpr *AR2) const;
2013 
2014 private:
2015  /// Increments the version number of the predicate. This needs to be called
2016  /// every time the SCEV predicate changes.
2017  void updateGeneration();
2018 
2019  /// Holds a SCEV and the version number of the SCEV predicate used to
2020  /// perform the rewrite of the expression.
2021  using RewriteEntry = std::pair<unsigned, const SCEV *>;
2022 
2023  /// Maps a SCEV to the rewrite result of that SCEV at a certain version
2024  /// number. If this number doesn't match the current Generation, we will
2025  /// need to do a rewrite. To preserve the transformation order of previous
2026  /// rewrites, we will rewrite the previous result instead of the original
2027  /// SCEV.
2029 
2030  /// Records what NoWrap flags we've added to a Value *.
2032 
2033  /// The ScalarEvolution analysis.
2034  ScalarEvolution &SE;
2035 
2036  /// The analyzed Loop.
2037  const Loop &L;
2038 
2039  /// The SCEVPredicate that forms our context. We will rewrite all
2040  /// expressions assuming that this predicate true.
2041  SCEVUnionPredicate Preds;
2042 
2043  /// Marks the version of the SCEV predicate used. When rewriting a SCEV
2044  /// expression we mark it with the version of the predicate. We use this to
2045  /// figure out if the predicate has changed from the last rewrite of the
2046  /// SCEV. If so, we need to perform a new rewrite.
2047  unsigned Generation = 0;
2048 
2049  /// The backedge taken count.
2050  const SCEV *BackedgeCount = nullptr;
2051 };
2052 
2053 } // end namespace llvm
2054 
2055 #endif // LLVM_ANALYSIS_SCALAREVOLUTION_H
ExitLimitQuery(const Loop *L, BasicBlock *ExitingBlock, bool AllowPredicates)
bool isKnownPositive(const Value *V, const DataLayout &DL, unsigned Depth=0, AssumptionCache *AC=nullptr, const Instruction *CxtI=nullptr, const DominatorTree *DT=nullptr, bool UseInstrInfo=true)
Returns true if the given value is known be positive (i.e.
A parsed version of the target data layout string in and methods for querying it. ...
Definition: DataLayout.h:110
Type
MessagePack types as defined in the standard, with the exception of Integer being divided into a sign...
Definition: MsgPackReader.h:48
static GCMetadataPrinterRegistry::Add< ErlangGCPrinter > X("erlang", "erlang-compatible garbage collector")
const ScalarEvolution & getSE() const
static Type * getWiderType(const DataLayout &DL, Type *Ty0, Type *Ty1)
This class represents lattice values for constants.
Definition: AllocatorList.h:23
SCEV & operator=(const SCEV &)=delete
PointerTy getPointer() const
Various leaf nodes.
Definition: ISDOpcodes.h:59
static unsigned ComputeHash(const SCEVPredicate &X, FoldingSetNodeID &TempID)
A Module instance is used to store all the information related to an LLVM module. ...
Definition: Module.h:65
void dump() const
This method is used for debugging.
const unsigned short ExpressionSize
The main scalar evolution driver.
bool isZero() const
Return true if the expression is a constant zero.
const SCEV * getAddRecExpr(const SmallVectorImpl< const SCEV *> &Operands, const Loop *L, SCEV::NoWrapFlags Flags)
IncrementWrapFlags
Similar to SCEV::NoWrapFlags, but with slightly different semantics for FlagNUSW. ...
static LLVM_NODISCARD SCEV::NoWrapFlags setFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OnFlags)
static bool Equals(const SCEVPredicate &X, const FoldingSetNodeID &ID, unsigned IDHash, FoldingSetNodeID &TempID)
A cache of @llvm.assume calls within a function.
APInt getSignedRangeMin(const SCEV *S)
Determine the min of the signed range for a particular SCEV.
F(f)
An instruction for reading from memory.
Definition: Instructions.h:167
Hexagon Common GEP
An object of this class is returned by queries that could not be answered.
This file defines the MallocAllocator and BumpPtrAllocator interfaces.
APInt getSignedRangeMax(const SCEV *S)
Determine the max of the signed range for a particular SCEV.
A templated base class for SmallPtrSet which provides the typesafe interface that is common across al...
Definition: SmallPtrSet.h:343
const SCEV * getZero(Type *Ty)
Return a SCEV for the constant 0 of a specific type.
The SCEV is loop-invariant.
static LLVM_NODISCARD SCEVWrapPredicate::IncrementWrapFlags setFlags(SCEVWrapPredicate::IncrementWrapFlags Flags, SCEVWrapPredicate::IncrementWrapFlags OnFlags)
Definition: BitVector.h:937
const SCEV * getAddExpr(const SCEV *LHS, const SCEV *RHS, SCEV::NoWrapFlags Flags=SCEV::FlagAnyWrap, unsigned Depth=0)
const DataLayout & getDataLayout() const
Get the data layout for the module&#39;s target platform.
Definition: Module.cpp:369
Class to represent struct types.
Definition: DerivedTypes.h:232
APInt getUnsignedRangeMax(const SCEV *S)
Determine the max of the unsigned range for a particular SCEV.
This class consists of common code factored out of the SmallVector class to reduce code duplication b...
Definition: APFloat.h:41
unsigned short SubclassData
This field is initialized to zero and may be used in subclasses to store miscellaneous information...
LLVMContext & getContext() const
BasicBlock * ExitingBlock
This file implements a class to represent arbitrary precision integral constant values and operations...
static int64_t getConstant(const MachineInstr *MI)
Key
PAL metadata keys.
ConstantRange getSignedRange(const SCEV *S)
Determine the signed range for a particular SCEV.
This node represents a polynomial recurrence on the trip count of the specified loop.
IntType getInt() const
A CRTP mix-in to automatically provide informational APIs needed for passes.
Definition: PassManager.h:372
static bool classof(const SCEVPredicate *P)
Methods for support type inquiry through isa, cast, and dyn_cast:
ArrayRef - Represent a constant reference to an array (0 or more elements consecutively in memory)...
Definition: APInt.h:32
bool isKnownNonNegative(const Value *V, const DataLayout &DL, unsigned Depth=0, AssumptionCache *AC=nullptr, const Instruction *CxtI=nullptr, const DominatorTree *DT=nullptr, bool UseInstrInfo=true)
Returns true if the give value is known to be non-negative.
Concrete subclass of DominatorTreeBase that is used to compute a normal dominator tree...
Definition: Dominators.h:144
void forgetLoopDispositions(const Loop *L)
Called when the client has changed the disposition of values in this loop.
Value handle that poisons itself if the Value is deleted.
Definition: ValueHandle.h:440
unsigned ComputeHash() const
ComputeHash - Compute a strong hash value for this FoldingSetNodeIDRef, used to lookup the node in th...
Definition: FoldingSet.cpp:29
unsigned short getExpressionSize() const
FoldingSetNodeID - This class is used to gather all the unique data bits of a node.
Definition: FoldingSet.h:305
Printer pass for the ScalarEvolutionAnalysis results.
static bool runOnFunction(Function &F, bool PostInlining)
#define P(N)
This means that we are dealing with an entirely unknown SCEV value, and only represent it as its LLVM...
APInt getUnsignedRangeMin(const SCEV *S)
Determine the min of the unsigned range for a particular SCEV.
FoldingSetTrait - This trait class is used to define behavior of how to "profile" (in the FoldingSet ...
Definition: FoldingSet.h:249
A set of analyses that are preserved following a run of a transformation pass.
Definition: PassManager.h:153
const SCEV * getOne(Type *Ty)
Return a SCEV for the constant 1 of a specific type.
static bool Equals(const SCEV &X, const FoldingSetNodeID &ID, unsigned IDHash, FoldingSetNodeID &TempID)
SCEVPredicateKind getKind() const
LLVM Basic Block Representation.
Definition: BasicBlock.h:57
PointerIntPair - This class implements a pair of a pointer and small integer.
The instances of the Type class are immutable: once they are created, they are never changed...
Definition: Type.h:45
This is an important class for using LLVM in a threaded context.
Definition: LLVMContext.h:64
Allocate memory in an ever growing pool, as if by bump-pointer.
Definition: Allocator.h:140
static GCRegistry::Add< CoreCLRGC > E("coreclr", "CoreCLR-compatible GC")
This is an important base class in LLVM.
Definition: Constant.h:41
std::pair< iterator, bool > insert(PtrType Ptr)
Inserts Ptr if and only if there is no element in the container equal to Ptr.
Definition: SmallPtrSet.h:370
A CRTP mix-in that provides informational APIs needed for analysis passes.
Definition: PassManager.h:389
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:709
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:196
const SCEV * getRHS() const
Returns the right hand side of the equality.
ScalarEvolution * getSE() const
Returns the ScalarEvolution analysis used.
size_t size() const
Definition: SmallVector.h:52
auto find(R &&Range, const T &Val) -> decltype(adl_begin(Range))
Provide wrappers to std::find which take ranges instead of having to pass begin/end explicitly...
Definition: STLExtras.h:1206
FoldingSet - This template class is used to instantiate a specialized implementation of the folding s...
Definition: FoldingSet.h:473
bool verify(const TargetRegisterInfo &TRI) const
Check that information hold by this instance make sense for the given TRI.
static unsigned ComputeHash(const SCEV &X, FoldingSetNodeID &TempID)
static ExitLimitQuery getEmptyKey()
The SCEV is loop-variant (unknown).
This class represents an assumption made using SCEV expressions which can be checked at run-time...
void print(raw_ostream &OS) const
Print out the internal representation of this scalar to the specified stream.
unsigned getSCEVType() const
bool isNonConstantNegative() const
Return true if the specified scev is negated, but not a constant.
See the file comment.
Definition: ValueMap.h:85
SmallPtrSet - This class implements a set which is optimized for holding SmallSize or less elements...
Definition: SmallPtrSet.h:417
This is the shared class of boolean and integer constants.
Definition: Constants.h:83
bool isAllOnesValue() const
Return true if the expression is a constant all-ones value.
Type * getType() const
Return the LLVM type of this SCEV expression.
static LLVM_NODISCARD SCEVWrapPredicate::IncrementWrapFlags clearFlags(SCEVWrapPredicate::IncrementWrapFlags Flags, SCEVWrapPredicate::IncrementWrapFlags OffFlags)
Convenient IncrementWrapFlags manipulation methods.
static bool isEqual(ExitLimitQuery LHS, ExitLimitQuery RHS)
static uint64_t add(uint64_t LeftOp, uint64_t RightOp)
Definition: FileCheck.cpp:124
This is a &#39;vector&#39; (really, a variable-sized array), optimized for the case when the array is small...
Definition: SmallVector.h:841
Provides information about what library functions are available for the current target.
The SCEV dominates the block.
Predicate
Predicate - These are "(BI << 5) | BO" for various predicates.
Definition: PPCPredicates.h:26
This class represents a range of values.
Definition: ConstantRange.h:47
An interface layer with SCEV used to manage how we see SCEV expressions for values in the context of ...
static LLVM_NODISCARD SCEVWrapPredicate::IncrementWrapFlags maskFlags(SCEVWrapPredicate::IncrementWrapFlags Flags, int Mask)
static void Profile(const SCEV &X, FoldingSetNodeID &ID)
static void Profile(const SCEVPredicate &X, FoldingSetNodeID &ID)
LoopDisposition
An enum describing the relationship between a SCEV and a loop.
Class for arbitrary precision integers.
Definition: APInt.h:69
virtual void print(raw_ostream &OS, unsigned Depth=0) const =0
Prints a textual representation of this predicate with an indentation of Depth.
hash_code hash_combine(const Ts &...args)
Combine values into a single hash_code.
Definition: Hashing.h:600
bool isKnownNonZero(const Value *V, const DataLayout &DL, unsigned Depth=0, AssumptionCache *AC=nullptr, const Instruction *CxtI=nullptr, const DominatorTree *DT=nullptr, bool UseInstrInfo=true)
Return true if the given value is known to be non-zero when defined.
This class uses information about analyze scalars to rewrite expressions in canonical form...
static void clear(coro::Shape &Shape)
Definition: Coroutines.cpp:211
const DataLayout & getDataLayout() const
Return the DataLayout associated with the module this SCEV instance is operating on.
static bool classof(const SCEVPredicate *P)
Methods for support type inquiry through isa, cast, and dyn_cast:
Analysis pass that exposes the ScalarEvolution for a function.
unsigned getComplexity() const override
We estimate the complexity of a union predicate as the size number of predicates in the union...
static ExitLimitQuery getTombstoneKey()
The SCEV does not dominate the block.
FoldingSetNodeIDRef - This class describes a reference to an interned FoldingSetNodeID, which can be a useful to store node id data rather than using plain FoldingSetNodeIDs, since the 32-element SmallVector is often much larger than necessary, and the possibility of heap allocation means it requires a non-trivial destructor call.
Definition: FoldingSet.h:277
MCExpr const & getExpr(MCExpr const &Expr)
Node - This class is used to maintain the singly linked bucket list in a folding set.
Definition: FoldingSet.h:135
This class represents an analyzed expression in the program.
bool isKnownNegative(const Value *V, const DataLayout &DL, unsigned Depth=0, AssumptionCache *AC=nullptr, const Instruction *CxtI=nullptr, const DominatorTree *DT=nullptr, bool UseInstrInfo=true)
Returns true if the given value is known be negative (i.e.
LLVM_NODISCARD bool empty() const
Definition: SmallVector.h:55
const SCEV * getMulExpr(const SCEV *LHS, const SCEV *RHS, SCEV::NoWrapFlags Flags=SCEV::FlagAnyWrap, unsigned Depth=0)
Represents a single loop in the control flow graph.
Definition: LoopInfo.h:465
#define I(x, y, z)
Definition: MD5.cpp:58
#define N
BlockDisposition
An enum describing the relationship between a SCEV and a basic block.
static LLVM_NODISCARD SCEV::NoWrapFlags maskFlags(SCEV::NoWrapFlags Flags, int Mask)
Convenient NoWrapFlags manipulation that hides enum casts and is visible in the ScalarEvolution name ...
raw_ostream & operator<<(raw_ostream &OS, const APInt &I)
Definition: APInt.h:2038
virtual unsigned getComplexity() const
Returns the estimated complexity of this predicate.
#define LLVM_NODISCARD
LLVM_NODISCARD - Warn if a type or return value is discarded.
Definition: Compiler.h:128
API to communicate dependencies between analyses during invalidation.
Definition: PassManager.h:648
ConstantRange getUnsignedRange(const SCEV *S)
Determine the unsigned range for a particular SCEV.
const SmallVectorImpl< const SCEVPredicate * > & getPredicates() const
Multiway switch.
assert(ImpDefSCC.getReg()==AMDGPU::SCC &&ImpDefSCC.isDef())
This class represents a composition of other SCEV predicates, and is the class that most clients will...
bool isOne() const
Return true if the expression is a constant one.
const SCEV * getMulExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2, SCEV::NoWrapFlags Flags=SCEV::FlagAnyWrap, unsigned Depth=0)
Module * getParent()
Get the module that this global value is contained inside of...
Definition: GlobalValue.h:565
LLVM Value Representation.
Definition: Value.h:72
A vector that has set insertion semantics.
Definition: SetVector.h:40
std::underlying_type< E >::type Mask()
Get a bitmask with 1s in all places up to the high-order bit of E&#39;s largest value.
Definition: BitmaskEnum.h:80
DefaultFoldingSetTrait - This class provides default implementations for FoldingSetTrait implementati...
Definition: FoldingSet.h:220
SCEVPredicateKind Kind
This class implements an extremely fast bulk output stream that can only output to a stream...
Definition: raw_ostream.h:45
static unsigned getHashValue(ExitLimitQuery Val)
Value handle with callbacks on RAUW and destruction.
Definition: ValueHandle.h:379
A container for analyses that lazily runs them and caches their results.
static Optional< bool > isImpliedCondOperands(CmpInst::Predicate Pred, const Value *ALHS, const Value *ARHS, const Value *BLHS, const Value *BRHS, const DataLayout &DL, unsigned Depth)
Return true if "icmp Pred BLHS BRHS" is true whenever "icmp Pred ALHS ARHS" is true.
SCEV(const FoldingSetNodeIDRef ID, unsigned SCEVTy, unsigned short ExpressionSize)
This header defines various interfaces for pass management in LLVM.
const SCEV * getAddExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2, SCEV::NoWrapFlags Flags=SCEV::FlagAnyWrap, unsigned Depth=0)
This class represents an assumption made on an AddRec expression.
static bool classof(const SCEVPredicate *P)
Methods for support type inquiry through isa, cast, and dyn_cast:
NoWrapFlags
NoWrapFlags are bitfield indices into SubclassData.
This class represents an assumption that two SCEV expressions are equal, and this can be checked at r...
A special type used by analysis passes to provide an address that identifies that particular analysis...
Definition: PassManager.h:70
IncrementWrapFlags getFlags() const
Returns the set assumed no overflow flags.