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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);
541  const SCEV *getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth = 0);
542  const SCEV *getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth = 0);
543  const SCEV *getAnyExtendExpr(const SCEV *Op, Type *Ty);
544  const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
546  unsigned Depth = 0);
547  const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS,
549  unsigned Depth = 0) {
550  SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
551  return getAddExpr(Ops, Flags, Depth);
552  }
553  const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
555  unsigned Depth = 0) {
556  SmallVector<const SCEV *, 3> Ops = {Op0, Op1, Op2};
557  return getAddExpr(Ops, Flags, Depth);
558  }
559  const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
561  unsigned Depth = 0);
562  const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS,
564  unsigned Depth = 0) {
565  SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
566  return getMulExpr(Ops, Flags, Depth);
567  }
568  const SCEV *getMulExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
570  unsigned Depth = 0) {
571  SmallVector<const SCEV *, 3> Ops = {Op0, Op1, Op2};
572  return getMulExpr(Ops, Flags, Depth);
573  }
574  const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
575  const SCEV *getUDivExactExpr(const SCEV *LHS, const SCEV *RHS);
576  const SCEV *getURemExpr(const SCEV *LHS, const SCEV *RHS);
577  const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step, const Loop *L,
578  SCEV::NoWrapFlags Flags);
579  const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
580  const Loop *L, SCEV::NoWrapFlags Flags);
582  const Loop *L, SCEV::NoWrapFlags Flags) {
583  SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
584  return getAddRecExpr(NewOp, L, Flags);
585  }
586 
587  /// Checks if \p SymbolicPHI can be rewritten as an AddRecExpr under some
588  /// Predicates. If successful return these <AddRecExpr, Predicates>;
589  /// The function is intended to be called from PSCEV (the caller will decide
590  /// whether to actually add the predicates and carry out the rewrites).
592  createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI);
593 
594  /// Returns an expression for a GEP
595  ///
596  /// \p GEP The GEP. The indices contained in the GEP itself are ignored,
597  /// instead we use IndexExprs.
598  /// \p IndexExprs The expressions for the indices.
599  const SCEV *getGEPExpr(GEPOperator *GEP,
600  const SmallVectorImpl<const SCEV *> &IndexExprs);
601  const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
602  const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
603  const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
604  const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
605  const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
606  const SCEV *getSMinExpr(SmallVectorImpl<const SCEV *> &Operands);
607  const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
608  const SCEV *getUMinExpr(SmallVectorImpl<const SCEV *> &Operands);
609  const SCEV *getUnknown(Value *V);
610  const SCEV *getCouldNotCompute();
611 
612  /// Return a SCEV for the constant 0 of a specific type.
613  const SCEV *getZero(Type *Ty) { return getConstant(Ty, 0); }
614 
615  /// Return a SCEV for the constant 1 of a specific type.
616  const SCEV *getOne(Type *Ty) { return getConstant(Ty, 1); }
617 
618  /// Return an expression for sizeof AllocTy that is type IntTy
619  const SCEV *getSizeOfExpr(Type *IntTy, Type *AllocTy);
620 
621  /// Return an expression for offsetof on the given field with type IntTy
622  const SCEV *getOffsetOfExpr(Type *IntTy, StructType *STy, unsigned FieldNo);
623 
624  /// Return the SCEV object corresponding to -V.
625  const SCEV *getNegativeSCEV(const SCEV *V,
627 
628  /// Return the SCEV object corresponding to ~V.
629  const SCEV *getNotSCEV(const SCEV *V);
630 
631  /// Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
632  const SCEV *getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
634  unsigned Depth = 0);
635 
636  /// Return a SCEV corresponding to a conversion of the input value to the
637  /// specified type. If the type must be extended, it is zero extended.
638  const SCEV *getTruncateOrZeroExtend(const SCEV *V, Type *Ty);
639 
640  /// Return a SCEV corresponding to a conversion of the input value to the
641  /// specified type. If the type must be extended, it is sign extended.
642  const SCEV *getTruncateOrSignExtend(const SCEV *V, Type *Ty);
643 
644  /// Return a SCEV corresponding to a conversion of the input value to the
645  /// specified type. If the type must be extended, it is zero extended. The
646  /// conversion must not be narrowing.
647  const SCEV *getNoopOrZeroExtend(const SCEV *V, Type *Ty);
648 
649  /// Return a SCEV corresponding to a conversion of the input value to the
650  /// specified type. If the type must be extended, it is sign extended. The
651  /// conversion must not be narrowing.
652  const SCEV *getNoopOrSignExtend(const SCEV *V, Type *Ty);
653 
654  /// Return a SCEV corresponding to a conversion of the input value to the
655  /// specified type. If the type must be extended, it is extended with
656  /// unspecified bits. The conversion must not be narrowing.
657  const SCEV *getNoopOrAnyExtend(const SCEV *V, Type *Ty);
658 
659  /// Return a SCEV corresponding to a conversion of the input value to the
660  /// specified type. The conversion must not be widening.
661  const SCEV *getTruncateOrNoop(const SCEV *V, Type *Ty);
662 
663  /// Promote the operands to the wider of the types using zero-extension, and
664  /// then perform a umax operation with them.
665  const SCEV *getUMaxFromMismatchedTypes(const SCEV *LHS, const SCEV *RHS);
666 
667  /// Promote the operands to the wider of the types using zero-extension, and
668  /// then perform a umin operation with them.
669  const SCEV *getUMinFromMismatchedTypes(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. N-ary function.
673  const SCEV *getUMinFromMismatchedTypes(SmallVectorImpl<const SCEV *> &Ops);
674 
675  /// Transitively follow the chain of pointer-type operands until reaching a
676  /// SCEV that does not have a single pointer operand. This returns a
677  /// SCEVUnknown pointer for well-formed pointer-type expressions, but corner
678  /// cases do exist.
679  const SCEV *getPointerBase(const SCEV *V);
680 
681  /// Return a SCEV expression for the specified value at the specified scope
682  /// in the program. The L value specifies a loop nest to evaluate the
683  /// expression at, where null is the top-level or a specified loop is
684  /// immediately inside of the loop.
685  ///
686  /// This method can be used to compute the exit value for a variable defined
687  /// in a loop by querying what the value will hold in the parent loop.
688  ///
689  /// In the case that a relevant loop exit value cannot be computed, the
690  /// original value V is returned.
691  const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
692 
693  /// This is a convenience function which does getSCEVAtScope(getSCEV(V), L).
694  const SCEV *getSCEVAtScope(Value *V, const Loop *L);
695 
696  /// Test whether entry to the loop is protected by a conditional between LHS
697  /// and RHS. This is used to help avoid max expressions in loop trip
698  /// counts, and to eliminate casts.
699  bool isLoopEntryGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
700  const SCEV *LHS, const SCEV *RHS);
701 
702  /// Test whether the backedge of the loop is protected by a conditional
703  /// between LHS and RHS. This is used to eliminate casts.
704  bool isLoopBackedgeGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
705  const SCEV *LHS, const SCEV *RHS);
706 
707  /// Returns the maximum trip count of the loop if it is a single-exit
708  /// loop and we can compute a small maximum for that loop.
709  ///
710  /// Implemented in terms of the \c getSmallConstantTripCount overload with
711  /// the single exiting block passed to it. See that routine for details.
712  unsigned getSmallConstantTripCount(const Loop *L);
713 
714  /// Returns the maximum trip count of this loop as a normal unsigned
715  /// value. Returns 0 if the trip count is unknown or not constant. This
716  /// "trip count" assumes that control exits via ExitingBlock. More
717  /// precisely, it is the number of times that control may reach ExitingBlock
718  /// before taking the branch. For loops with multiple exits, it may not be
719  /// the number times that the loop header executes if the loop exits
720  /// prematurely via another branch.
721  unsigned getSmallConstantTripCount(const Loop *L, BasicBlock *ExitingBlock);
722 
723  /// Returns the upper bound of the loop trip count as a normal unsigned
724  /// value.
725  /// Returns 0 if the trip count is unknown or not constant.
726  unsigned getSmallConstantMaxTripCount(const Loop *L);
727 
728  /// Returns the largest constant divisor of the trip count of the
729  /// loop if it is a single-exit loop and we can compute a small maximum for
730  /// that loop.
731  ///
732  /// Implemented in terms of the \c getSmallConstantTripMultiple overload with
733  /// the single exiting block passed to it. See that routine for details.
734  unsigned getSmallConstantTripMultiple(const Loop *L);
735 
736  /// Returns the largest constant divisor of the trip count of this loop as a
737  /// normal unsigned value, if possible. This means that the actual trip
738  /// count is always a multiple of the returned value (don't forget the trip
739  /// count could very well be zero as well!). As explained in the comments
740  /// for getSmallConstantTripCount, this assumes that control exits the loop
741  /// via ExitingBlock.
742  unsigned getSmallConstantTripMultiple(const Loop *L,
743  BasicBlock *ExitingBlock);
744 
745  /// Get the expression for the number of loop iterations for which this loop
746  /// is guaranteed not to exit via ExitingBlock. Otherwise return
747  /// SCEVCouldNotCompute.
748  const SCEV *getExitCount(const Loop *L, BasicBlock *ExitingBlock);
749 
750  /// If the specified loop has a predictable backedge-taken count, return it,
751  /// otherwise return a SCEVCouldNotCompute object. The backedge-taken count is
752  /// the number of times the loop header will be branched to from within the
753  /// loop, assuming there are no abnormal exists like exception throws. This is
754  /// one less than the trip count of the loop, since it doesn't count the first
755  /// iteration, when the header is branched to from outside the loop.
756  ///
757  /// Note that it is not valid to call this method on a loop without a
758  /// loop-invariant backedge-taken count (see
759  /// hasLoopInvariantBackedgeTakenCount).
760  const SCEV *getBackedgeTakenCount(const Loop *L);
761 
762  /// Similar to getBackedgeTakenCount, except it will add a set of
763  /// SCEV predicates to Predicates that are required to be true in order for
764  /// the answer to be correct. Predicates can be checked with run-time
765  /// checks and can be used to perform loop versioning.
766  const SCEV *getPredicatedBackedgeTakenCount(const Loop *L,
767  SCEVUnionPredicate &Predicates);
768 
769  /// When successful, this returns a SCEVConstant that is greater than or equal
770  /// to (i.e. a "conservative over-approximation") of the value returend by
771  /// getBackedgeTakenCount. If such a value cannot be computed, it returns the
772  /// SCEVCouldNotCompute object.
773  const SCEV *getMaxBackedgeTakenCount(const Loop *L);
774 
775  /// Return true if the backedge taken count is either the value returned by
776  /// getMaxBackedgeTakenCount or zero.
777  bool isBackedgeTakenCountMaxOrZero(const Loop *L);
778 
779  /// Return true if the specified loop has an analyzable loop-invariant
780  /// backedge-taken count.
781  bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
782 
783  /// This method should be called by the client when it has changed a loop in
784  /// a way that may effect ScalarEvolution's ability to compute a trip count,
785  /// or if the loop is deleted. This call is potentially expensive for large
786  /// loop bodies.
787  void forgetLoop(const Loop *L);
788 
789  // This method invokes forgetLoop for the outermost loop of the given loop
790  // \p L, making ScalarEvolution forget about all this subtree. This needs to
791  // be done whenever we make a transform that may affect the parameters of the
792  // outer loop, such as exit counts for branches.
793  void forgetTopmostLoop(const Loop *L);
794 
795  /// This method should be called by the client when it has changed a value
796  /// in a way that may effect its value, or which may disconnect it from a
797  /// def-use chain linking it to a loop.
798  void forgetValue(Value *V);
799 
800  /// Called when the client has changed the disposition of values in
801  /// this loop.
802  ///
803  /// We don't have a way to invalidate per-loop dispositions. Clear and
804  /// recompute is simpler.
805  void forgetLoopDispositions(const Loop *L) { LoopDispositions.clear(); }
806 
807  /// Determine the minimum number of zero bits that S is guaranteed to end in
808  /// (at every loop iteration). It is, at the same time, the minimum number
809  /// of times S is divisible by 2. For example, given {4,+,8} it returns 2.
810  /// If S is guaranteed to be 0, it returns the bitwidth of S.
811  uint32_t GetMinTrailingZeros(const SCEV *S);
812 
813  /// Determine the unsigned range for a particular SCEV.
814  /// NOTE: This returns a copy of the reference returned by getRangeRef.
816  return getRangeRef(S, HINT_RANGE_UNSIGNED);
817  }
818 
819  /// Determine the min of the unsigned range for a particular SCEV.
821  return getRangeRef(S, HINT_RANGE_UNSIGNED).getUnsignedMin();
822  }
823 
824  /// Determine the max of the unsigned range for a particular SCEV.
826  return getRangeRef(S, HINT_RANGE_UNSIGNED).getUnsignedMax();
827  }
828 
829  /// Determine the signed range for a particular SCEV.
830  /// NOTE: This returns a copy of the reference returned by getRangeRef.
832  return getRangeRef(S, HINT_RANGE_SIGNED);
833  }
834 
835  /// Determine the min of the signed range for a particular SCEV.
837  return getRangeRef(S, HINT_RANGE_SIGNED).getSignedMin();
838  }
839 
840  /// Determine the max of the signed range for a particular SCEV.
842  return getRangeRef(S, HINT_RANGE_SIGNED).getSignedMax();
843  }
844 
845  /// Test if the given expression is known to be negative.
846  bool isKnownNegative(const SCEV *S);
847 
848  /// Test if the given expression is known to be positive.
849  bool isKnownPositive(const SCEV *S);
850 
851  /// Test if the given expression is known to be non-negative.
852  bool isKnownNonNegative(const SCEV *S);
853 
854  /// Test if the given expression is known to be non-positive.
855  bool isKnownNonPositive(const SCEV *S);
856 
857  /// Test if the given expression is known to be non-zero.
858  bool isKnownNonZero(const SCEV *S);
859 
860  /// Splits SCEV expression \p S into two SCEVs. One of them is obtained from
861  /// \p S by substitution of all AddRec sub-expression related to loop \p L
862  /// with initial value of that SCEV. The second is obtained from \p S by
863  /// substitution of all AddRec sub-expressions related to loop \p L with post
864  /// increment of this AddRec in the loop \p L. In both cases all other AddRec
865  /// sub-expressions (not related to \p L) remain the same.
866  /// If the \p S contains non-invariant unknown SCEV the function returns
867  /// CouldNotCompute SCEV in both values of std::pair.
868  /// For example, for SCEV S={0, +, 1}<L1> + {0, +, 1}<L2> and loop L=L1
869  /// the function returns pair:
870  /// first = {0, +, 1}<L2>
871  /// second = {1, +, 1}<L1> + {0, +, 1}<L2>
872  /// We can see that for the first AddRec sub-expression it was replaced with
873  /// 0 (initial value) for the first element and to {1, +, 1}<L1> (post
874  /// increment value) for the second one. In both cases AddRec expression
875  /// related to L2 remains the same.
876  std::pair<const SCEV *, const SCEV *> SplitIntoInitAndPostInc(const Loop *L,
877  const SCEV *S);
878 
879  /// We'd like to check the predicate on every iteration of the most dominated
880  /// loop between loops used in LHS and RHS.
881  /// To do this we use the following list of steps:
882  /// 1. Collect set S all loops on which either LHS or RHS depend.
883  /// 2. If S is non-empty
884  /// a. Let PD be the element of S which is dominated by all other elements.
885  /// b. Let E(LHS) be value of LHS on entry of PD.
886  /// To get E(LHS), we should just take LHS and replace all AddRecs that are
887  /// attached to PD on with their entry values.
888  /// Define E(RHS) in the same way.
889  /// c. Let B(LHS) be value of L on backedge of PD.
890  /// To get B(LHS), we should just take LHS and replace all AddRecs that are
891  /// attached to PD on with their backedge values.
892  /// Define B(RHS) in the same way.
893  /// d. Note that E(LHS) and E(RHS) are automatically available on entry of PD,
894  /// so we can assert on that.
895  /// e. Return true if isLoopEntryGuardedByCond(Pred, E(LHS), E(RHS)) &&
896  /// isLoopBackedgeGuardedByCond(Pred, B(LHS), B(RHS))
897  bool isKnownViaInduction(ICmpInst::Predicate Pred, const SCEV *LHS,
898  const SCEV *RHS);
899 
900  /// Test if the given expression is known to satisfy the condition described
901  /// by Pred, LHS, and RHS.
902  bool isKnownPredicate(ICmpInst::Predicate Pred, const SCEV *LHS,
903  const SCEV *RHS);
904 
905  /// Test if the condition described by Pred, LHS, RHS is known to be true on
906  /// every iteration of the loop of the recurrency LHS.
907  bool isKnownOnEveryIteration(ICmpInst::Predicate Pred,
908  const SCEVAddRecExpr *LHS, const SCEV *RHS);
909 
910  /// Return true if, for all loop invariant X, the predicate "LHS `Pred` X"
911  /// is monotonically increasing or decreasing. In the former case set
912  /// `Increasing` to true and in the latter case set `Increasing` to false.
913  ///
914  /// A predicate is said to be monotonically increasing if may go from being
915  /// false to being true as the loop iterates, but never the other way
916  /// around. A predicate is said to be monotonically decreasing if may go
917  /// from being true to being false as the loop iterates, but never the other
918  /// way around.
919  bool isMonotonicPredicate(const SCEVAddRecExpr *LHS, ICmpInst::Predicate Pred,
920  bool &Increasing);
921 
922  /// Return true if the result of the predicate LHS `Pred` RHS is loop
923  /// invariant with respect to L. Set InvariantPred, InvariantLHS and
924  /// InvariantLHS so that InvariantLHS `InvariantPred` InvariantRHS is the
925  /// loop invariant form of LHS `Pred` RHS.
926  bool isLoopInvariantPredicate(ICmpInst::Predicate Pred, const SCEV *LHS,
927  const SCEV *RHS, const Loop *L,
928  ICmpInst::Predicate &InvariantPred,
929  const SCEV *&InvariantLHS,
930  const SCEV *&InvariantRHS);
931 
932  /// Simplify LHS and RHS in a comparison with predicate Pred. Return true
933  /// iff any changes were made. If the operands are provably equal or
934  /// unequal, LHS and RHS are set to the same value and Pred is set to either
935  /// ICMP_EQ or ICMP_NE.
936  bool SimplifyICmpOperands(ICmpInst::Predicate &Pred, const SCEV *&LHS,
937  const SCEV *&RHS, unsigned Depth = 0);
938 
939  /// Return the "disposition" of the given SCEV with respect to the given
940  /// loop.
941  LoopDisposition getLoopDisposition(const SCEV *S, const Loop *L);
942 
943  /// Return true if the value of the given SCEV is unchanging in the
944  /// specified loop.
945  bool isLoopInvariant(const SCEV *S, const Loop *L);
946 
947  /// Determine if the SCEV can be evaluated at loop's entry. It is true if it
948  /// doesn't depend on a SCEVUnknown of an instruction which is dominated by
949  /// the header of loop L.
950  bool isAvailableAtLoopEntry(const SCEV *S, const Loop *L);
951 
952  /// Return true if the given SCEV changes value in a known way in the
953  /// specified loop. This property being true implies that the value is
954  /// variant in the loop AND that we can emit an expression to compute the
955  /// value of the expression at any particular loop iteration.
956  bool hasComputableLoopEvolution(const SCEV *S, const Loop *L);
957 
958  /// Return the "disposition" of the given SCEV with respect to the given
959  /// block.
960  BlockDisposition getBlockDisposition(const SCEV *S, const BasicBlock *BB);
961 
962  /// Return true if elements that makes up the given SCEV dominate the
963  /// specified basic block.
964  bool dominates(const SCEV *S, const BasicBlock *BB);
965 
966  /// Return true if elements that makes up the given SCEV properly dominate
967  /// the specified basic block.
968  bool properlyDominates(const SCEV *S, const BasicBlock *BB);
969 
970  /// Test whether the given SCEV has Op as a direct or indirect operand.
971  bool hasOperand(const SCEV *S, const SCEV *Op) const;
972 
973  /// Return the size of an element read or written by Inst.
974  const SCEV *getElementSize(Instruction *Inst);
975 
976  /// Compute the array dimensions Sizes from the set of Terms extracted from
977  /// the memory access function of this SCEVAddRecExpr (second step of
978  /// delinearization).
979  void findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
981  const SCEV *ElementSize);
982 
983  void print(raw_ostream &OS) const;
984  void verify() const;
985  bool invalidate(Function &F, const PreservedAnalyses &PA,
987 
988  /// Collect parametric terms occurring in step expressions (first step of
989  /// delinearization).
990  void collectParametricTerms(const SCEV *Expr,
992 
993  /// Return in Subscripts the access functions for each dimension in Sizes
994  /// (third step of delinearization).
995  void computeAccessFunctions(const SCEV *Expr,
996  SmallVectorImpl<const SCEV *> &Subscripts,
998 
999  /// Split this SCEVAddRecExpr into two vectors of SCEVs representing the
1000  /// subscripts and sizes of an array access.
1001  ///
1002  /// The delinearization is a 3 step process: the first two steps compute the
1003  /// sizes of each subscript and the third step computes the access functions
1004  /// for the delinearized array:
1005  ///
1006  /// 1. Find the terms in the step functions
1007  /// 2. Compute the array size
1008  /// 3. Compute the access function: divide the SCEV by the array size
1009  /// starting with the innermost dimensions found in step 2. The Quotient
1010  /// is the SCEV to be divided in the next step of the recursion. The
1011  /// Remainder is the subscript of the innermost dimension. Loop over all
1012  /// array dimensions computed in step 2.
1013  ///
1014  /// To compute a uniform array size for several memory accesses to the same
1015  /// object, one can collect in step 1 all the step terms for all the memory
1016  /// accesses, and compute in step 2 a unique array shape. This guarantees
1017  /// that the array shape will be the same across all memory accesses.
1018  ///
1019  /// FIXME: We could derive the result of steps 1 and 2 from a description of
1020  /// the array shape given in metadata.
1021  ///
1022  /// Example:
1023  ///
1024  /// A[][n][m]
1025  ///
1026  /// for i
1027  /// for j
1028  /// for k
1029  /// A[j+k][2i][5i] =
1030  ///
1031  /// The initial SCEV:
1032  ///
1033  /// A[{{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k]
1034  ///
1035  /// 1. Find the different terms in the step functions:
1036  /// -> [2*m, 5, n*m, n*m]
1037  ///
1038  /// 2. Compute the array size: sort and unique them
1039  /// -> [n*m, 2*m, 5]
1040  /// find the GCD of all the terms = 1
1041  /// divide by the GCD and erase constant terms
1042  /// -> [n*m, 2*m]
1043  /// GCD = m
1044  /// divide by GCD -> [n, 2]
1045  /// remove constant terms
1046  /// -> [n]
1047  /// size of the array is A[unknown][n][m]
1048  ///
1049  /// 3. Compute the access function
1050  /// a. Divide {{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k by the innermost size m
1051  /// Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k
1052  /// Remainder: {{{0,+,5}_i, +, 0}_j, +, 0}_k
1053  /// The remainder is the subscript of the innermost array dimension: [5i].
1054  ///
1055  /// b. Divide Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k by next outer size n
1056  /// Quotient: {{{0,+,0}_i, +, 1}_j, +, 1}_k
1057  /// Remainder: {{{0,+,2}_i, +, 0}_j, +, 0}_k
1058  /// The Remainder is the subscript of the next array dimension: [2i].
1059  ///
1060  /// The subscript of the outermost dimension is the Quotient: [j+k].
1061  ///
1062  /// Overall, we have: A[][n][m], and the access function: A[j+k][2i][5i].
1063  void delinearize(const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
1065  const SCEV *ElementSize);
1066 
1067  /// Return the DataLayout associated with the module this SCEV instance is
1068  /// operating on.
1069  const DataLayout &getDataLayout() const {
1070  return F.getParent()->getDataLayout();
1071  }
1072 
1073  const SCEVPredicate *getEqualPredicate(const SCEV *LHS, const SCEV *RHS);
1074 
1075  const SCEVPredicate *
1076  getWrapPredicate(const SCEVAddRecExpr *AR,
1078 
1079  /// Re-writes the SCEV according to the Predicates in \p A.
1080  const SCEV *rewriteUsingPredicate(const SCEV *S, const Loop *L,
1081  SCEVUnionPredicate &A);
1082  /// Tries to convert the \p S expression to an AddRec expression,
1083  /// adding additional predicates to \p Preds as required.
1084  const SCEVAddRecExpr *convertSCEVToAddRecWithPredicates(
1085  const SCEV *S, const Loop *L,
1087 
1088 private:
1089  /// A CallbackVH to arrange for ScalarEvolution to be notified whenever a
1090  /// Value is deleted.
1091  class SCEVCallbackVH final : public CallbackVH {
1092  ScalarEvolution *SE;
1093 
1094  void deleted() override;
1095  void allUsesReplacedWith(Value *New) override;
1096 
1097  public:
1098  SCEVCallbackVH(Value *V, ScalarEvolution *SE = nullptr);
1099  };
1100 
1101  friend class SCEVCallbackVH;
1102  friend class SCEVExpander;
1103  friend class SCEVUnknown;
1104 
1105  /// The function we are analyzing.
1106  Function &F;
1107 
1108  /// Does the module have any calls to the llvm.experimental.guard intrinsic
1109  /// at all? If this is false, we avoid doing work that will only help if
1110  /// thare are guards present in the IR.
1111  bool HasGuards;
1112 
1113  /// The target library information for the target we are targeting.
1114  TargetLibraryInfo &TLI;
1115 
1116  /// The tracker for \@llvm.assume intrinsics in this function.
1117  AssumptionCache &AC;
1118 
1119  /// The dominator tree.
1120  DominatorTree &DT;
1121 
1122  /// The loop information for the function we are currently analyzing.
1123  LoopInfo &LI;
1124 
1125  /// This SCEV is used to represent unknown trip counts and things.
1126  std::unique_ptr<SCEVCouldNotCompute> CouldNotCompute;
1127 
1128  /// The type for HasRecMap.
1130 
1131  /// This is a cache to record whether a SCEV contains any scAddRecExpr.
1132  HasRecMapType HasRecMap;
1133 
1134  /// The type for ExprValueMap.
1135  using ValueOffsetPair = std::pair<Value *, ConstantInt *>;
1137 
1138  /// ExprValueMap -- This map records the original values from which
1139  /// the SCEV expr is generated from.
1140  ///
1141  /// We want to represent the mapping as SCEV -> ValueOffsetPair instead
1142  /// of SCEV -> Value:
1143  /// Suppose we know S1 expands to V1, and
1144  /// S1 = S2 + C_a
1145  /// S3 = S2 + C_b
1146  /// where C_a and C_b are different SCEVConstants. Then we'd like to
1147  /// expand S3 as V1 - C_a + C_b instead of expanding S2 literally.
1148  /// It is helpful when S2 is a complex SCEV expr.
1149  ///
1150  /// In order to do that, we represent ExprValueMap as a mapping from
1151  /// SCEV to ValueOffsetPair. We will save both S1->{V1, 0} and
1152  /// S2->{V1, C_a} into the map when we create SCEV for V1. When S3
1153  /// is expanded, it will first expand S2 to V1 - C_a because of
1154  /// S2->{V1, C_a} in the map, then expand S3 to V1 - C_a + C_b.
1155  ///
1156  /// Note: S->{V, Offset} in the ExprValueMap means S can be expanded
1157  /// to V - Offset.
1158  ExprValueMapType ExprValueMap;
1159 
1160  /// The type for ValueExprMap.
1161  using ValueExprMapType =
1163 
1164  /// This is a cache of the values we have analyzed so far.
1165  ValueExprMapType ValueExprMap;
1166 
1167  /// Mark predicate values currently being processed by isImpliedCond.
1168  SmallPtrSet<Value *, 6> PendingLoopPredicates;
1169 
1170  /// Mark SCEVUnknown Phis currently being processed by getRangeRef.
1171  SmallPtrSet<const PHINode *, 6> PendingPhiRanges;
1172 
1173  // Mark SCEVUnknown Phis currently being processed by isImpliedViaMerge.
1174  SmallPtrSet<const PHINode *, 6> PendingMerges;
1175 
1176  /// Set to true by isLoopBackedgeGuardedByCond when we're walking the set of
1177  /// conditions dominating the backedge of a loop.
1178  bool WalkingBEDominatingConds = false;
1179 
1180  /// Set to true by isKnownPredicateViaSplitting when we're trying to prove a
1181  /// predicate by splitting it into a set of independent predicates.
1182  bool ProvingSplitPredicate = false;
1183 
1184  /// Memoized values for the GetMinTrailingZeros
1185  DenseMap<const SCEV *, uint32_t> MinTrailingZerosCache;
1186 
1187  /// Return the Value set from which the SCEV expr is generated.
1188  SetVector<ValueOffsetPair> *getSCEVValues(const SCEV *S);
1189 
1190  /// Private helper method for the GetMinTrailingZeros method
1191  uint32_t GetMinTrailingZerosImpl(const SCEV *S);
1192 
1193  /// Information about the number of loop iterations for which a loop exit's
1194  /// branch condition evaluates to the not-taken path. This is a temporary
1195  /// pair of exact and max expressions that are eventually summarized in
1196  /// ExitNotTakenInfo and BackedgeTakenInfo.
1197  struct ExitLimit {
1198  const SCEV *ExactNotTaken; // The exit is not taken exactly this many times
1199  const SCEV *MaxNotTaken; // The exit is not taken at most this many times
1200 
1201  // Not taken either exactly MaxNotTaken or zero times
1202  bool MaxOrZero = false;
1203 
1204  /// A set of predicate guards for this ExitLimit. The result is only valid
1205  /// if all of the predicates in \c Predicates evaluate to 'true' at
1206  /// run-time.
1208 
1209  void addPredicate(const SCEVPredicate *P) {
1210  assert(!isa<SCEVUnionPredicate>(P) && "Only add leaf predicates here!");
1211  Predicates.insert(P);
1212  }
1213 
1214  /*implicit*/ ExitLimit(const SCEV *E);
1215 
1216  ExitLimit(
1217  const SCEV *E, const SCEV *M, bool MaxOrZero,
1218  ArrayRef<const SmallPtrSetImpl<const SCEVPredicate *> *> PredSetList);
1219 
1220  ExitLimit(const SCEV *E, const SCEV *M, bool MaxOrZero,
1222 
1223  ExitLimit(const SCEV *E, const SCEV *M, bool MaxOrZero);
1224 
1225  /// Test whether this ExitLimit contains any computed information, or
1226  /// whether it's all SCEVCouldNotCompute values.
1227  bool hasAnyInfo() const {
1228  return !isa<SCEVCouldNotCompute>(ExactNotTaken) ||
1229  !isa<SCEVCouldNotCompute>(MaxNotTaken);
1230  }
1231 
1232  bool hasOperand(const SCEV *S) const;
1233 
1234  /// Test whether this ExitLimit contains all information.
1235  bool hasFullInfo() const {
1236  return !isa<SCEVCouldNotCompute>(ExactNotTaken);
1237  }
1238  };
1239 
1240  /// Information about the number of times a particular loop exit may be
1241  /// reached before exiting the loop.
1242  struct ExitNotTakenInfo {
1243  PoisoningVH<BasicBlock> ExitingBlock;
1244  const SCEV *ExactNotTaken;
1245  std::unique_ptr<SCEVUnionPredicate> Predicate;
1246 
1247  explicit ExitNotTakenInfo(PoisoningVH<BasicBlock> ExitingBlock,
1248  const SCEV *ExactNotTaken,
1249  std::unique_ptr<SCEVUnionPredicate> Predicate)
1250  : ExitingBlock(ExitingBlock), ExactNotTaken(ExactNotTaken),
1251  Predicate(std::move(Predicate)) {}
1252 
1253  bool hasAlwaysTruePredicate() const {
1254  return !Predicate || Predicate->isAlwaysTrue();
1255  }
1256  };
1257 
1258  /// Information about the backedge-taken count of a loop. This currently
1259  /// includes an exact count and a maximum count.
1260  ///
1261  class BackedgeTakenInfo {
1262  /// A list of computable exits and their not-taken counts. Loops almost
1263  /// never have more than one computable exit.
1264  SmallVector<ExitNotTakenInfo, 1> ExitNotTaken;
1265 
1266  /// The pointer part of \c MaxAndComplete is an expression indicating the
1267  /// least maximum backedge-taken count of the loop that is known, or a
1268  /// SCEVCouldNotCompute. This expression is only valid if the predicates
1269  /// associated with all loop exits are true.
1270  ///
1271  /// The integer part of \c MaxAndComplete is a boolean indicating if \c
1272  /// ExitNotTaken has an element for every exiting block in the loop.
1273  PointerIntPair<const SCEV *, 1> MaxAndComplete;
1274 
1275  /// True iff the backedge is taken either exactly Max or zero times.
1276  bool MaxOrZero = false;
1277 
1278  /// \name Helper projection functions on \c MaxAndComplete.
1279  /// @{
1280  bool isComplete() const { return MaxAndComplete.getInt(); }
1281  const SCEV *getMax() const { return MaxAndComplete.getPointer(); }
1282  /// @}
1283 
1284  public:
1285  BackedgeTakenInfo() : MaxAndComplete(nullptr, 0) {}
1286  BackedgeTakenInfo(BackedgeTakenInfo &&) = default;
1287  BackedgeTakenInfo &operator=(BackedgeTakenInfo &&) = default;
1288 
1289  using EdgeExitInfo = std::pair<BasicBlock *, ExitLimit>;
1290 
1291  /// Initialize BackedgeTakenInfo from a list of exact exit counts.
1292  BackedgeTakenInfo(ArrayRef<EdgeExitInfo> ExitCounts, bool Complete,
1293  const SCEV *MaxCount, bool MaxOrZero);
1294 
1295  /// Test whether this BackedgeTakenInfo contains any computed information,
1296  /// or whether it's all SCEVCouldNotCompute values.
1297  bool hasAnyInfo() const {
1298  return !ExitNotTaken.empty() || !isa<SCEVCouldNotCompute>(getMax());
1299  }
1300 
1301  /// Test whether this BackedgeTakenInfo contains complete information.
1302  bool hasFullInfo() const { return isComplete(); }
1303 
1304  /// Return an expression indicating the exact *backedge-taken*
1305  /// count of the loop if it is known or SCEVCouldNotCompute
1306  /// otherwise. If execution makes it to the backedge on every
1307  /// iteration (i.e. there are no abnormal exists like exception
1308  /// throws and thread exits) then this is the number of times the
1309  /// loop header will execute minus one.
1310  ///
1311  /// If the SCEV predicate associated with the answer can be different
1312  /// from AlwaysTrue, we must add a (non null) Predicates argument.
1313  /// The SCEV predicate associated with the answer will be added to
1314  /// Predicates. A run-time check needs to be emitted for the SCEV
1315  /// predicate in order for the answer to be valid.
1316  ///
1317  /// Note that we should always know if we need to pass a predicate
1318  /// argument or not from the way the ExitCounts vector was computed.
1319  /// If we allowed SCEV predicates to be generated when populating this
1320  /// vector, this information can contain them and therefore a
1321  /// SCEVPredicate argument should be added to getExact.
1322  const SCEV *getExact(const Loop *L, ScalarEvolution *SE,
1323  SCEVUnionPredicate *Predicates = nullptr) const;
1324 
1325  /// Return the number of times this loop exit may fall through to the back
1326  /// edge, or SCEVCouldNotCompute. The loop is guaranteed not to exit via
1327  /// this block before this number of iterations, but may exit via another
1328  /// block.
1329  const SCEV *getExact(BasicBlock *ExitingBlock, ScalarEvolution *SE) const;
1330 
1331  /// Get the max backedge taken count for the loop.
1332  const SCEV *getMax(ScalarEvolution *SE) const;
1333 
1334  /// Return true if the number of times this backedge is taken is either the
1335  /// value returned by getMax or zero.
1336  bool isMaxOrZero(ScalarEvolution *SE) const;
1337 
1338  /// Return true if any backedge taken count expressions refer to the given
1339  /// subexpression.
1340  bool hasOperand(const SCEV *S, ScalarEvolution *SE) const;
1341 
1342  /// Invalidate this result and free associated memory.
1343  void clear();
1344  };
1345 
1346  /// Cache the backedge-taken count of the loops for this function as they
1347  /// are computed.
1348  DenseMap<const Loop *, BackedgeTakenInfo> BackedgeTakenCounts;
1349 
1350  /// Cache the predicated backedge-taken count of the loops for this
1351  /// function as they are computed.
1352  DenseMap<const Loop *, BackedgeTakenInfo> PredicatedBackedgeTakenCounts;
1353 
1354  /// This map contains entries for all of the PHI instructions that we
1355  /// attempt to compute constant evolutions for. This allows us to avoid
1356  /// potentially expensive recomputation of these properties. An instruction
1357  /// maps to null if we are unable to compute its exit value.
1358  DenseMap<PHINode *, Constant *> ConstantEvolutionLoopExitValue;
1359 
1360  /// This map contains entries for all the expressions that we attempt to
1361  /// compute getSCEVAtScope information for, which can be expensive in
1362  /// extreme cases.
1364  ValuesAtScopes;
1365 
1366  /// Memoized computeLoopDisposition results.
1367  DenseMap<const SCEV *,
1369  LoopDispositions;
1370 
1371  struct LoopProperties {
1372  /// Set to true if the loop contains no instruction that can have side
1373  /// effects (i.e. via throwing an exception, volatile or atomic access).
1374  bool HasNoAbnormalExits;
1375 
1376  /// Set to true if the loop contains no instruction that can abnormally exit
1377  /// the loop (i.e. via throwing an exception, by terminating the thread
1378  /// cleanly or by infinite looping in a called function). Strictly
1379  /// speaking, the last one is not leaving the loop, but is identical to
1380  /// leaving the loop for reasoning about undefined behavior.
1381  bool HasNoSideEffects;
1382  };
1383 
1384  /// Cache for \c getLoopProperties.
1385  DenseMap<const Loop *, LoopProperties> LoopPropertiesCache;
1386 
1387  /// Return a \c LoopProperties instance for \p L, creating one if necessary.
1388  LoopProperties getLoopProperties(const Loop *L);
1389 
1390  bool loopHasNoSideEffects(const Loop *L) {
1391  return getLoopProperties(L).HasNoSideEffects;
1392  }
1393 
1394  bool loopHasNoAbnormalExits(const Loop *L) {
1395  return getLoopProperties(L).HasNoAbnormalExits;
1396  }
1397 
1398  /// Compute a LoopDisposition value.
1399  LoopDisposition computeLoopDisposition(const SCEV *S, const Loop *L);
1400 
1401  /// Memoized computeBlockDisposition results.
1402  DenseMap<
1403  const SCEV *,
1405  BlockDispositions;
1406 
1407  /// Compute a BlockDisposition value.
1408  BlockDisposition computeBlockDisposition(const SCEV *S, const BasicBlock *BB);
1409 
1410  /// Memoized results from getRange
1412 
1413  /// Memoized results from getRange
1415 
1416  /// Used to parameterize getRange
1417  enum RangeSignHint { HINT_RANGE_UNSIGNED, HINT_RANGE_SIGNED };
1418 
1419  /// Set the memoized range for the given SCEV.
1420  const ConstantRange &setRange(const SCEV *S, RangeSignHint Hint,
1421  ConstantRange CR) {
1423  Hint == HINT_RANGE_UNSIGNED ? UnsignedRanges : SignedRanges;
1424 
1425  auto Pair = Cache.try_emplace(S, std::move(CR));
1426  if (!Pair.second)
1427  Pair.first->second = std::move(CR);
1428  return Pair.first->second;
1429  }
1430 
1431  /// Determine the range for a particular SCEV.
1432  /// NOTE: This returns a reference to an entry in a cache. It must be
1433  /// copied if its needed for longer.
1434  const ConstantRange &getRangeRef(const SCEV *S, RangeSignHint Hint);
1435 
1436  /// Determines the range for the affine SCEVAddRecExpr {\p Start,+,\p Stop}.
1437  /// Helper for \c getRange.
1438  ConstantRange getRangeForAffineAR(const SCEV *Start, const SCEV *Stop,
1439  const SCEV *MaxBECount, unsigned BitWidth);
1440 
1441  /// Try to compute a range for the affine SCEVAddRecExpr {\p Start,+,\p
1442  /// Stop} by "factoring out" a ternary expression from the add recurrence.
1443  /// Helper called by \c getRange.
1444  ConstantRange getRangeViaFactoring(const SCEV *Start, const SCEV *Stop,
1445  const SCEV *MaxBECount, unsigned BitWidth);
1446 
1447  /// We know that there is no SCEV for the specified value. Analyze the
1448  /// expression.
1449  const SCEV *createSCEV(Value *V);
1450 
1451  /// Provide the special handling we need to analyze PHI SCEVs.
1452  const SCEV *createNodeForPHI(PHINode *PN);
1453 
1454  /// Helper function called from createNodeForPHI.
1455  const SCEV *createAddRecFromPHI(PHINode *PN);
1456 
1457  /// A helper function for createAddRecFromPHI to handle simple cases.
1458  const SCEV *createSimpleAffineAddRec(PHINode *PN, Value *BEValueV,
1459  Value *StartValueV);
1460 
1461  /// Helper function called from createNodeForPHI.
1462  const SCEV *createNodeFromSelectLikePHI(PHINode *PN);
1463 
1464  /// Provide special handling for a select-like instruction (currently this
1465  /// is either a select instruction or a phi node). \p I is the instruction
1466  /// being processed, and it is assumed equivalent to "Cond ? TrueVal :
1467  /// FalseVal".
1468  const SCEV *createNodeForSelectOrPHI(Instruction *I, Value *Cond,
1469  Value *TrueVal, Value *FalseVal);
1470 
1471  /// Provide the special handling we need to analyze GEP SCEVs.
1472  const SCEV *createNodeForGEP(GEPOperator *GEP);
1473 
1474  /// Implementation code for getSCEVAtScope; called at most once for each
1475  /// SCEV+Loop pair.
1476  const SCEV *computeSCEVAtScope(const SCEV *S, const Loop *L);
1477 
1478  /// This looks up computed SCEV values for all instructions that depend on
1479  /// the given instruction and removes them from the ValueExprMap map if they
1480  /// reference SymName. This is used during PHI resolution.
1481  void forgetSymbolicName(Instruction *I, const SCEV *SymName);
1482 
1483  /// Return the BackedgeTakenInfo for the given loop, lazily computing new
1484  /// values if the loop hasn't been analyzed yet. The returned result is
1485  /// guaranteed not to be predicated.
1486  const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
1487 
1488  /// Similar to getBackedgeTakenInfo, but will add predicates as required
1489  /// with the purpose of returning complete information.
1490  const BackedgeTakenInfo &getPredicatedBackedgeTakenInfo(const Loop *L);
1491 
1492  /// Compute the number of times the specified loop will iterate.
1493  /// If AllowPredicates is set, we will create new SCEV predicates as
1494  /// necessary in order to return an exact answer.
1495  BackedgeTakenInfo computeBackedgeTakenCount(const Loop *L,
1496  bool AllowPredicates = false);
1497 
1498  /// Compute the number of times the backedge of the specified loop will
1499  /// execute if it exits via the specified block. If AllowPredicates is set,
1500  /// this call will try to use a minimal set of SCEV predicates in order to
1501  /// return an exact answer.
1502  ExitLimit computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
1503  bool AllowPredicates = false);
1504 
1505  /// Compute the number of times the backedge of the specified loop will
1506  /// execute if its exit condition were a conditional branch of ExitCond.
1507  ///
1508  /// \p ControlsExit is true if ExitCond directly controls the exit
1509  /// branch. In this case, we can assume that the loop exits only if the
1510  /// condition is true and can infer that failing to meet the condition prior
1511  /// to integer wraparound results in undefined behavior.
1512  ///
1513  /// If \p AllowPredicates is set, this call will try to use a minimal set of
1514  /// SCEV predicates in order to return an exact answer.
1515  ExitLimit computeExitLimitFromCond(const Loop *L, Value *ExitCond,
1516  bool ExitIfTrue, bool ControlsExit,
1517  bool AllowPredicates = false);
1518 
1519  // Helper functions for computeExitLimitFromCond to avoid exponential time
1520  // complexity.
1521 
1522  class ExitLimitCache {
1523  // It may look like we need key on the whole (L, ExitIfTrue, ControlsExit,
1524  // AllowPredicates) tuple, but recursive calls to
1525  // computeExitLimitFromCondCached from computeExitLimitFromCondImpl only
1526  // vary the in \c ExitCond and \c ControlsExit parameters. We remember the
1527  // initial values of the other values to assert our assumption.
1528  SmallDenseMap<PointerIntPair<Value *, 1>, ExitLimit> TripCountMap;
1529 
1530  const Loop *L;
1531  bool ExitIfTrue;
1532  bool AllowPredicates;
1533 
1534  public:
1535  ExitLimitCache(const Loop *L, bool ExitIfTrue, bool AllowPredicates)
1536  : L(L), ExitIfTrue(ExitIfTrue), AllowPredicates(AllowPredicates) {}
1537 
1538  Optional<ExitLimit> find(const Loop *L, Value *ExitCond, bool ExitIfTrue,
1539  bool ControlsExit, bool AllowPredicates);
1540 
1541  void insert(const Loop *L, Value *ExitCond, bool ExitIfTrue,
1542  bool ControlsExit, bool AllowPredicates, const ExitLimit &EL);
1543  };
1544 
1545  using ExitLimitCacheTy = ExitLimitCache;
1546 
1547  ExitLimit computeExitLimitFromCondCached(ExitLimitCacheTy &Cache,
1548  const Loop *L, Value *ExitCond,
1549  bool ExitIfTrue,
1550  bool ControlsExit,
1551  bool AllowPredicates);
1552  ExitLimit computeExitLimitFromCondImpl(ExitLimitCacheTy &Cache, const Loop *L,
1553  Value *ExitCond, bool ExitIfTrue,
1554  bool ControlsExit,
1555  bool AllowPredicates);
1556 
1557  /// Compute the number of times the backedge of the specified loop will
1558  /// execute if its exit condition were a conditional branch of the ICmpInst
1559  /// ExitCond and ExitIfTrue. If AllowPredicates is set, this call will try
1560  /// to use a minimal set of SCEV predicates in order to return an exact
1561  /// answer.
1562  ExitLimit computeExitLimitFromICmp(const Loop *L, ICmpInst *ExitCond,
1563  bool ExitIfTrue,
1564  bool IsSubExpr,
1565  bool AllowPredicates = false);
1566 
1567  /// Compute the number of times the backedge of the specified loop will
1568  /// execute if its exit condition were a switch with a single exiting case
1569  /// to ExitingBB.
1570  ExitLimit computeExitLimitFromSingleExitSwitch(const Loop *L,
1571  SwitchInst *Switch,
1572  BasicBlock *ExitingBB,
1573  bool IsSubExpr);
1574 
1575  /// Given an exit condition of 'icmp op load X, cst', try to see if we can
1576  /// compute the backedge-taken count.
1577  ExitLimit computeLoadConstantCompareExitLimit(LoadInst *LI, Constant *RHS,
1578  const Loop *L,
1580 
1581  /// Compute the exit limit of a loop that is controlled by a
1582  /// "(IV >> 1) != 0" type comparison. We cannot compute the exact trip
1583  /// count in these cases (since SCEV has no way of expressing them), but we
1584  /// can still sometimes compute an upper bound.
1585  ///
1586  /// Return an ExitLimit for a loop whose backedge is guarded by `LHS Pred
1587  /// RHS`.
1588  ExitLimit computeShiftCompareExitLimit(Value *LHS, Value *RHS, const Loop *L,
1589  ICmpInst::Predicate Pred);
1590 
1591  /// If the loop is known to execute a constant number of times (the
1592  /// condition evolves only from constants), try to evaluate a few iterations
1593  /// of the loop until we get the exit condition gets a value of ExitWhen
1594  /// (true or false). If we cannot evaluate the exit count of the loop,
1595  /// return CouldNotCompute.
1596  const SCEV *computeExitCountExhaustively(const Loop *L, Value *Cond,
1597  bool ExitWhen);
1598 
1599  /// Return the number of times an exit condition comparing the specified
1600  /// value to zero will execute. If not computable, return CouldNotCompute.
1601  /// If AllowPredicates is set, this call will try to use a minimal set of
1602  /// SCEV predicates in order to return an exact answer.
1603  ExitLimit howFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr,
1604  bool AllowPredicates = false);
1605 
1606  /// Return the number of times an exit condition checking the specified
1607  /// value for nonzero will execute. If not computable, return
1608  /// CouldNotCompute.
1609  ExitLimit howFarToNonZero(const SCEV *V, const Loop *L);
1610 
1611  /// Return the number of times an exit condition containing the specified
1612  /// less-than comparison will execute. If not computable, return
1613  /// CouldNotCompute.
1614  ///
1615  /// \p isSigned specifies whether the less-than is signed.
1616  ///
1617  /// \p ControlsExit is true when the LHS < RHS condition directly controls
1618  /// the branch (loops exits only if condition is true). In this case, we can
1619  /// use NoWrapFlags to skip overflow checks.
1620  ///
1621  /// If \p AllowPredicates is set, this call will try to use a minimal set of
1622  /// SCEV predicates in order to return an exact answer.
1623  ExitLimit howManyLessThans(const SCEV *LHS, const SCEV *RHS, const Loop *L,
1624  bool isSigned, bool ControlsExit,
1625  bool AllowPredicates = false);
1626 
1627  ExitLimit howManyGreaterThans(const SCEV *LHS, const SCEV *RHS, const Loop *L,
1628  bool isSigned, bool IsSubExpr,
1629  bool AllowPredicates = false);
1630 
1631  /// Return a predecessor of BB (which may not be an immediate predecessor)
1632  /// which has exactly one successor from which BB is reachable, or null if
1633  /// no such block is found.
1634  std::pair<BasicBlock *, BasicBlock *>
1635  getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
1636 
1637  /// Test whether the condition described by Pred, LHS, and RHS is true
1638  /// whenever the given FoundCondValue value evaluates to true.
1639  bool isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
1640  Value *FoundCondValue, bool Inverse);
1641 
1642  /// Test whether the condition described by Pred, LHS, and RHS is true
1643  /// whenever the condition described by FoundPred, FoundLHS, FoundRHS is
1644  /// true.
1645  bool isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
1646  ICmpInst::Predicate FoundPred, const SCEV *FoundLHS,
1647  const SCEV *FoundRHS);
1648 
1649  /// Test whether the condition described by Pred, LHS, and RHS is true
1650  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1651  /// true.
1652  bool isImpliedCondOperands(ICmpInst::Predicate Pred, const SCEV *LHS,
1653  const SCEV *RHS, const SCEV *FoundLHS,
1654  const SCEV *FoundRHS);
1655 
1656  /// Test whether the condition described by Pred, LHS, and RHS is true
1657  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1658  /// true. Here LHS is an operation that includes FoundLHS as one of its
1659  /// arguments.
1660  bool isImpliedViaOperations(ICmpInst::Predicate Pred,
1661  const SCEV *LHS, const SCEV *RHS,
1662  const SCEV *FoundLHS, const SCEV *FoundRHS,
1663  unsigned Depth = 0);
1664 
1665  /// Test whether the condition described by Pred, LHS, and RHS is true.
1666  /// Use only simple non-recursive types of checks, such as range analysis etc.
1667  bool isKnownViaNonRecursiveReasoning(ICmpInst::Predicate Pred,
1668  const SCEV *LHS, const SCEV *RHS);
1669 
1670  /// Test whether the condition described by Pred, LHS, and RHS is true
1671  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1672  /// true.
1673  bool isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, const SCEV *LHS,
1674  const SCEV *RHS, const SCEV *FoundLHS,
1675  const SCEV *FoundRHS);
1676 
1677  /// Test whether the condition described by Pred, LHS, and RHS is true
1678  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1679  /// true. Utility function used by isImpliedCondOperands. Tries to get
1680  /// cases like "X `sgt` 0 => X - 1 `sgt` -1".
1681  bool isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred, const SCEV *LHS,
1682  const SCEV *RHS, const SCEV *FoundLHS,
1683  const SCEV *FoundRHS);
1684 
1685  /// Return true if the condition denoted by \p LHS \p Pred \p RHS is implied
1686  /// by a call to \c @llvm.experimental.guard in \p BB.
1687  bool isImpliedViaGuard(BasicBlock *BB, ICmpInst::Predicate Pred,
1688  const SCEV *LHS, const SCEV *RHS);
1689 
1690  /// Test whether the condition described by Pred, LHS, and RHS is true
1691  /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1692  /// true.
1693  ///
1694  /// This routine tries to rule out certain kinds of integer overflow, and
1695  /// then tries to reason about arithmetic properties of the predicates.
1696  bool isImpliedCondOperandsViaNoOverflow(ICmpInst::Predicate Pred,
1697  const SCEV *LHS, const SCEV *RHS,
1698  const SCEV *FoundLHS,
1699  const SCEV *FoundRHS);
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 figure out predicate for Phis which are SCEVUnknown
1706  /// if it is true for every possible incoming value from their respective
1707  /// basic blocks.
1708  bool isImpliedViaMerge(ICmpInst::Predicate Pred,
1709  const SCEV *LHS, const SCEV *RHS,
1710  const SCEV *FoundLHS, const SCEV *FoundRHS,
1711  unsigned Depth);
1712 
1713  /// If we know that the specified Phi is in the header of its containing
1714  /// loop, we know the loop executes a constant number of times, and the PHI
1715  /// node is just a recurrence involving constants, fold it.
1716  Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt &BEs,
1717  const Loop *L);
1718 
1719  /// Test if the given expression is known to satisfy the condition described
1720  /// by Pred and the known constant ranges of LHS and RHS.
1721  bool isKnownPredicateViaConstantRanges(ICmpInst::Predicate Pred,
1722  const SCEV *LHS, const SCEV *RHS);
1723 
1724  /// Try to prove the condition described by "LHS Pred RHS" by ruling out
1725  /// integer overflow.
1726  ///
1727  /// For instance, this will return true for "A s< (A + C)<nsw>" if C is
1728  /// positive.
1729  bool isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred, const SCEV *LHS,
1730  const SCEV *RHS);
1731 
1732  /// Try to split Pred LHS RHS into logical conjunctions (and's) and try to
1733  /// prove them individually.
1734  bool isKnownPredicateViaSplitting(ICmpInst::Predicate Pred, const SCEV *LHS,
1735  const SCEV *RHS);
1736 
1737  /// Try to match the Expr as "(L + R)<Flags>".
1738  bool splitBinaryAdd(const SCEV *Expr, const SCEV *&L, const SCEV *&R,
1739  SCEV::NoWrapFlags &Flags);
1740 
1741  /// Compute \p LHS - \p RHS and returns the result as an APInt if it is a
1742  /// constant, and None if it isn't.
1743  ///
1744  /// This is intended to be a cheaper version of getMinusSCEV. We can be
1745  /// frugal here since we just bail out of actually constructing and
1746  /// canonicalizing an expression in the cases where the result isn't going
1747  /// to be a constant.
1748  Optional<APInt> computeConstantDifference(const SCEV *LHS, const SCEV *RHS);
1749 
1750  /// Drop memoized information computed for S.
1751  void forgetMemoizedResults(const SCEV *S);
1752 
1753  /// Return an existing SCEV for V if there is one, otherwise return nullptr.
1754  const SCEV *getExistingSCEV(Value *V);
1755 
1756  /// Return false iff given SCEV contains a SCEVUnknown with NULL value-
1757  /// pointer.
1758  bool checkValidity(const SCEV *S) const;
1759 
1760  /// Return true if `ExtendOpTy`({`Start`,+,`Step`}) can be proved to be
1761  /// equal to {`ExtendOpTy`(`Start`),+,`ExtendOpTy`(`Step`)}. This is
1762  /// equivalent to proving no signed (resp. unsigned) wrap in
1763  /// {`Start`,+,`Step`} if `ExtendOpTy` is `SCEVSignExtendExpr`
1764  /// (resp. `SCEVZeroExtendExpr`).
1765  template <typename ExtendOpTy>
1766  bool proveNoWrapByVaryingStart(const SCEV *Start, const SCEV *Step,
1767  const Loop *L);
1768 
1769  /// Try to prove NSW or NUW on \p AR relying on ConstantRange manipulation.
1770  SCEV::NoWrapFlags proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR);
1771 
1772  bool isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
1773  ICmpInst::Predicate Pred, bool &Increasing);
1774 
1775  /// Return SCEV no-wrap flags that can be proven based on reasoning about
1776  /// how poison produced from no-wrap flags on this value (e.g. a nuw add)
1777  /// would trigger undefined behavior on overflow.
1778  SCEV::NoWrapFlags getNoWrapFlagsFromUB(const Value *V);
1779 
1780  /// Return true if the SCEV corresponding to \p I is never poison. Proving
1781  /// this is more complex than proving that just \p I is never poison, since
1782  /// SCEV commons expressions across control flow, and you can have cases
1783  /// like:
1784  ///
1785  /// idx0 = a + b;
1786  /// ptr[idx0] = 100;
1787  /// if (<condition>) {
1788  /// idx1 = a +nsw b;
1789  /// ptr[idx1] = 200;
1790  /// }
1791  ///
1792  /// where the SCEV expression (+ a b) is guaranteed to not be poison (and
1793  /// hence not sign-overflow) only if "<condition>" is true. Since both
1794  /// `idx0` and `idx1` will be mapped to the same SCEV expression, (+ a b),
1795  /// it is not okay to annotate (+ a b) with <nsw> in the above example.
1796  bool isSCEVExprNeverPoison(const Instruction *I);
1797 
1798  /// This is like \c isSCEVExprNeverPoison but it specifically works for
1799  /// instructions that will get mapped to SCEV add recurrences. Return true
1800  /// if \p I will never generate poison under the assumption that \p I is an
1801  /// add recurrence on the loop \p L.
1802  bool isAddRecNeverPoison(const Instruction *I, const Loop *L);
1803 
1804  /// Similar to createAddRecFromPHI, but with the additional flexibility of
1805  /// suggesting runtime overflow checks in case casts are encountered.
1806  /// If successful, the analysis records that for this loop, \p SymbolicPHI,
1807  /// which is the UnknownSCEV currently representing the PHI, can be rewritten
1808  /// into an AddRec, assuming some predicates; The function then returns the
1809  /// AddRec and the predicates as a pair, and caches this pair in
1810  /// PredicatedSCEVRewrites.
1811  /// If the analysis is not successful, a mapping from the \p SymbolicPHI to
1812  /// itself (with no predicates) is recorded, and a nullptr with an empty
1813  /// predicates vector is returned as a pair.
1815  createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI);
1816 
1817  /// Compute the backedge taken count knowing the interval difference, the
1818  /// stride and presence of the equality in the comparison.
1819  const SCEV *computeBECount(const SCEV *Delta, const SCEV *Stride,
1820  bool Equality);
1821 
1822  /// Compute the maximum backedge count based on the range of values
1823  /// permitted by Start, End, and Stride. This is for loops of the form
1824  /// {Start, +, Stride} LT End.
1825  ///
1826  /// Precondition: the induction variable is known to be positive. We *don't*
1827  /// assert these preconditions so please be careful.
1828  const SCEV *computeMaxBECountForLT(const SCEV *Start, const SCEV *Stride,
1829  const SCEV *End, unsigned BitWidth,
1830  bool IsSigned);
1831 
1832  /// Verify if an linear IV with positive stride can overflow when in a
1833  /// less-than comparison, knowing the invariant term of the comparison,
1834  /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1835  bool doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride, bool IsSigned,
1836  bool NoWrap);
1837 
1838  /// Verify if an linear IV with negative stride can overflow when in a
1839  /// greater-than comparison, knowing the invariant term of the comparison,
1840  /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1841  bool doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride, bool IsSigned,
1842  bool NoWrap);
1843 
1844  /// Get add expr already created or create a new one.
1845  const SCEV *getOrCreateAddExpr(ArrayRef<const SCEV *> Ops,
1846  SCEV::NoWrapFlags Flags);
1847 
1848  /// Get mul expr already created or create a new one.
1849  const SCEV *getOrCreateMulExpr(ArrayRef<const SCEV *> Ops,
1850  SCEV::NoWrapFlags Flags);
1851 
1852  // Get addrec expr already created or create a new one.
1853  const SCEV *getOrCreateAddRecExpr(ArrayRef<const SCEV *> Ops,
1854  const Loop *L, SCEV::NoWrapFlags Flags);
1855 
1856  /// Return x if \p Val is f(x) where f is a 1-1 function.
1857  const SCEV *stripInjectiveFunctions(const SCEV *Val) const;
1858 
1859  /// Find all of the loops transitively used in \p S, and fill \p LoopsUsed.
1860  /// A loop is considered "used" by an expression if it contains
1861  /// an add rec on said loop.
1862  void getUsedLoops(const SCEV *S, SmallPtrSetImpl<const Loop *> &LoopsUsed);
1863 
1864  /// Find all of the loops transitively used in \p S, and update \c LoopUsers
1865  /// accordingly.
1866  void addToLoopUseLists(const SCEV *S);
1867 
1868  /// Try to match the pattern generated by getURemExpr(A, B). If successful,
1869  /// Assign A and B to LHS and RHS, respectively.
1870  bool matchURem(const SCEV *Expr, const SCEV *&LHS, const SCEV *&RHS);
1871 
1872  FoldingSet<SCEV> UniqueSCEVs;
1873  FoldingSet<SCEVPredicate> UniquePreds;
1874  BumpPtrAllocator SCEVAllocator;
1875 
1876  /// This maps loops to a list of SCEV expressions that (transitively) use said
1877  /// loop.
1879 
1880  /// Cache tentative mappings from UnknownSCEVs in a Loop, to a SCEV expression
1881  /// they can be rewritten into under certain predicates.
1883  std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
1884  PredicatedSCEVRewrites;
1885 
1886  /// The head of a linked list of all SCEVUnknown values that have been
1887  /// allocated. This is used by releaseMemory to locate them all and call
1888  /// their destructors.
1889  SCEVUnknown *FirstUnknown = nullptr;
1890 };
1891 
1892 /// Analysis pass that exposes the \c ScalarEvolution for a function.
1894  : public AnalysisInfoMixin<ScalarEvolutionAnalysis> {
1896 
1897  static AnalysisKey Key;
1898 
1899 public:
1901 
1903 };
1904 
1905 /// Printer pass for the \c ScalarEvolutionAnalysis results.
1907  : public PassInfoMixin<ScalarEvolutionPrinterPass> {
1908  raw_ostream &OS;
1909 
1910 public:
1911  explicit ScalarEvolutionPrinterPass(raw_ostream &OS) : OS(OS) {}
1912 
1914 };
1915 
1917  std::unique_ptr<ScalarEvolution> SE;
1918 
1919 public:
1920  static char ID;
1921 
1923 
1924  ScalarEvolution &getSE() { return *SE; }
1925  const ScalarEvolution &getSE() const { return *SE; }
1926 
1927  bool runOnFunction(Function &F) override;
1928  void releaseMemory() override;
1929  void getAnalysisUsage(AnalysisUsage &AU) const override;
1930  void print(raw_ostream &OS, const Module * = nullptr) const override;
1931  void verifyAnalysis() const override;
1932 };
1933 
1934 /// An interface layer with SCEV used to manage how we see SCEV expressions
1935 /// for values in the context of existing predicates. We can add new
1936 /// predicates, but we cannot remove them.
1937 ///
1938 /// This layer has multiple purposes:
1939 /// - provides a simple interface for SCEV versioning.
1940 /// - guarantees that the order of transformations applied on a SCEV
1941 /// expression for a single Value is consistent across two different
1942 /// getSCEV calls. This means that, for example, once we've obtained
1943 /// an AddRec expression for a certain value through expression
1944 /// rewriting, we will continue to get an AddRec expression for that
1945 /// Value.
1946 /// - lowers the number of expression rewrites.
1948 public:
1950 
1951  const SCEVUnionPredicate &getUnionPredicate() const;
1952 
1953  /// Returns the SCEV expression of V, in the context of the current SCEV
1954  /// predicate. The order of transformations applied on the expression of V
1955  /// returned by ScalarEvolution is guaranteed to be preserved, even when
1956  /// adding new predicates.
1957  const SCEV *getSCEV(Value *V);
1958 
1959  /// Get the (predicated) backedge count for the analyzed loop.
1960  const SCEV *getBackedgeTakenCount();
1961 
1962  /// Adds a new predicate.
1963  void addPredicate(const SCEVPredicate &Pred);
1964 
1965  /// Attempts to produce an AddRecExpr for V by adding additional SCEV
1966  /// predicates. If we can't transform the expression into an AddRecExpr we
1967  /// return nullptr and not add additional SCEV predicates to the current
1968  /// context.
1969  const SCEVAddRecExpr *getAsAddRec(Value *V);
1970 
1971  /// Proves that V doesn't overflow by adding SCEV predicate.
1972  void setNoOverflow(Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags);
1973 
1974  /// Returns true if we've proved that V doesn't wrap by means of a SCEV
1975  /// predicate.
1976  bool hasNoOverflow(Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags);
1977 
1978  /// Returns the ScalarEvolution analysis used.
1979  ScalarEvolution *getSE() const { return &SE; }
1980 
1981  /// We need to explicitly define the copy constructor because of FlagsMap.
1983 
1984  /// Print the SCEV mappings done by the Predicated Scalar Evolution.
1985  /// The printed text is indented by \p Depth.
1986  void print(raw_ostream &OS, unsigned Depth) const;
1987 
1988  /// Check if \p AR1 and \p AR2 are equal, while taking into account
1989  /// Equal predicates in Preds.
1990  bool areAddRecsEqualWithPreds(const SCEVAddRecExpr *AR1,
1991  const SCEVAddRecExpr *AR2) const;
1992 
1993 private:
1994  /// Increments the version number of the predicate. This needs to be called
1995  /// every time the SCEV predicate changes.
1996  void updateGeneration();
1997 
1998  /// Holds a SCEV and the version number of the SCEV predicate used to
1999  /// perform the rewrite of the expression.
2000  using RewriteEntry = std::pair<unsigned, const SCEV *>;
2001 
2002  /// Maps a SCEV to the rewrite result of that SCEV at a certain version
2003  /// number. If this number doesn't match the current Generation, we will
2004  /// need to do a rewrite. To preserve the transformation order of previous
2005  /// rewrites, we will rewrite the previous result instead of the original
2006  /// SCEV.
2008 
2009  /// Records what NoWrap flags we've added to a Value *.
2011 
2012  /// The ScalarEvolution analysis.
2013  ScalarEvolution &SE;
2014 
2015  /// The analyzed Loop.
2016  const Loop &L;
2017 
2018  /// The SCEVPredicate that forms our context. We will rewrite all
2019  /// expressions assuming that this predicate true.
2020  SCEVUnionPredicate Preds;
2021 
2022  /// Marks the version of the SCEV predicate used. When rewriting a SCEV
2023  /// expression we mark it with the version of the predicate. We use this to
2024  /// figure out if the predicate has changed from the last rewrite of the
2025  /// SCEV. If so, we need to perform a new rewrite.
2026  unsigned Generation = 0;
2027 
2028  /// The backedge taken count.
2029  const SCEV *BackedgeCount = nullptr;
2030 };
2031 
2032 } // end namespace llvm
2033 
2034 #endif // LLVM_ANALYSIS_SCALAREVOLUTION_H
ExitLimitQuery(const Loop *L, BasicBlock *ExitingBlock, bool AllowPredicates)
bool isKnownPositive(const Value *V, const DataLayout &DL, unsigned Depth=0, AssumptionCache *AC=nullptr, const Instruction *CxtI=nullptr, const DominatorTree *DT=nullptr, bool UseInstrInfo=true)
Returns true if the given value is known be positive (i.e.
A parsed version of the target data layout string in and methods for querying it. ...
Definition: DataLayout.h:110
Type
MessagePack types as defined in the standard, with the exception of Integer being divided into a sign...
Definition: MsgPackReader.h:48
static GCMetadataPrinterRegistry::Add< ErlangGCPrinter > X("erlang", "erlang-compatible garbage collector")
const ScalarEvolution & getSE() const
static Type * getWiderType(const DataLayout &DL, Type *Ty0, Type *Ty1)
static bool isLoopInvariant(Value *V, const Loop *L, const DominatorTree *DT)
Perform a quick domtree based check for loop invariance assuming that V is used within the loop...
This class represents lattice values for constants.
Definition: AllocatorList.h:23
SCEV & operator=(const SCEV &)=delete
PointerTy getPointer() const
Various leaf nodes.
Definition: ISDOpcodes.h:59
static unsigned ComputeHash(const SCEVPredicate &X, FoldingSetNodeID &TempID)
A Module instance is used to store all the information related to an LLVM module. ...
Definition: Module.h:64
void dump() const
This method is used for debugging.
const unsigned short ExpressionSize
The main scalar evolution driver.
bool isZero() const
Return true if the expression is a constant zero.
const SCEV * getAddRecExpr(const SmallVectorImpl< const SCEV *> &Operands, const Loop *L, SCEV::NoWrapFlags Flags)
IncrementWrapFlags
Similar to SCEV::NoWrapFlags, but with slightly different semantics for FlagNUSW. ...
static LLVM_NODISCARD SCEV::NoWrapFlags setFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OnFlags)
static bool Equals(const SCEVPredicate &X, const FoldingSetNodeID &ID, unsigned IDHash, FoldingSetNodeID &TempID)
A cache of @llvm.assume calls within a function.
APInt getSignedRangeMin(const SCEV *S)
Determine the min of the signed range for a particular SCEV.
F(f)
An instruction for reading from memory.
Definition: Instructions.h:167
Hexagon Common GEP
An object of this class is returned by queries that could not be answered.
This file defines the MallocAllocator and BumpPtrAllocator interfaces.
APInt getSignedRangeMax(const SCEV *S)
Determine the max of the signed range for a particular SCEV.
A templated base class for SmallPtrSet which provides the typesafe interface that is common across al...
Definition: SmallPtrSet.h:343
const SCEV * getZero(Type *Ty)
Return a SCEV for the constant 0 of a specific type.
The SCEV is loop-invariant.
static LLVM_NODISCARD SCEVWrapPredicate::IncrementWrapFlags setFlags(SCEVWrapPredicate::IncrementWrapFlags Flags, SCEVWrapPredicate::IncrementWrapFlags OnFlags)
Definition: BitVector.h:937
const SCEV * getAddExpr(const SCEV *LHS, const SCEV *RHS, SCEV::NoWrapFlags Flags=SCEV::FlagAnyWrap, unsigned Depth=0)
const DataLayout & getDataLayout() const
Get the data layout for the module&#39;s target platform.
Definition: Module.cpp:369
Class to represent struct types.
Definition: DerivedTypes.h:232
APInt getUnsignedRangeMax(const SCEV *S)
Determine the max of the unsigned range for a particular SCEV.
This class consists of common code factored out of the SmallVector class to reduce code duplication b...
Definition: APFloat.h:41
unsigned short SubclassData
This field is initialized to zero and may be used in subclasses to store miscellaneous information...
LLVMContext & getContext() const
BasicBlock * ExitingBlock
This file implements a class to represent arbitrary precision integral constant values and operations...
static int64_t getConstant(const MachineInstr *MI)
Key
PAL metadata keys.
ConstantRange getSignedRange(const SCEV *S)
Determine the signed range for a particular SCEV.
This node represents a polynomial recurrence on the trip count of the specified loop.
IntType getInt() const
A CRTP mix-in to automatically provide informational APIs needed for passes.
Definition: PassManager.h:365
static bool classof(const SCEVPredicate *P)
Methods for support type inquiry through isa, cast, and dyn_cast:
ArrayRef - Represent a constant reference to an array (0 or more elements consecutively in memory)...
Definition: APInt.h:32
bool isKnownNonNegative(const Value *V, const DataLayout &DL, unsigned Depth=0, AssumptionCache *AC=nullptr, const Instruction *CxtI=nullptr, const DominatorTree *DT=nullptr, bool UseInstrInfo=true)
Returns true if the give value is known to be non-negative.
Concrete subclass of DominatorTreeBase that is used to compute a normal dominator tree...
Definition: Dominators.h:144
void forgetLoopDispositions(const Loop *L)
Called when the client has changed the disposition of values in this loop.
Value handle that poisons itself if the Value is deleted.
Definition: ValueHandle.h:440
unsigned ComputeHash() const
ComputeHash - Compute a strong hash value for this FoldingSetNodeIDRef, used to lookup the node in th...
Definition: FoldingSet.cpp:29
unsigned short getExpressionSize() const
FoldingSetNodeID - This class is used to gather all the unique data bits of a node.
Definition: FoldingSet.h:305
Printer pass for the ScalarEvolutionAnalysis results.
static bool runOnFunction(Function &F, bool PostInlining)
#define P(N)
This means that we are dealing with an entirely unknown SCEV value, and only represent it as its LLVM...
APInt getUnsignedRangeMin(const SCEV *S)
Determine the min of the unsigned range for a particular SCEV.
FoldingSetTrait - This trait class is used to define behavior of how to "profile" (in the FoldingSet ...
Definition: FoldingSet.h:249
A set of analyses that are preserved following a run of a transformation pass.
Definition: PassManager.h:153
const SCEV * getOne(Type *Ty)
Return a SCEV for the constant 1 of a specific type.
static bool Equals(const SCEV &X, const FoldingSetNodeID &ID, unsigned IDHash, FoldingSetNodeID &TempID)
SCEVPredicateKind getKind() const
LLVM Basic Block Representation.
Definition: BasicBlock.h:57
PointerIntPair - This class implements a pair of a pointer and small integer.
The instances of the Type class are immutable: once they are created, they are never changed...
Definition: Type.h:45
This is an important class for using LLVM in a threaded context.
Definition: LLVMContext.h:68
Allocate memory in an ever growing pool, as if by bump-pointer.
Definition: Allocator.h:140
static GCRegistry::Add< CoreCLRGC > E("coreclr", "CoreCLR-compatible GC")
This is an important base class in LLVM.
Definition: Constant.h:41
std::pair< iterator, bool > insert(PtrType Ptr)
Inserts Ptr if and only if there is no element in the container equal to Ptr.
Definition: SmallPtrSet.h:370
A CRTP mix-in that provides informational APIs needed for analysis passes.
Definition: PassManager.h:382
ScalarEvolutionPrinterPass(raw_ostream &OS)
Represent the analysis usage information of a pass.
This instruction compares its operands according to the predicate given to the constructor.
Predicate
This enumeration lists the possible predicates for CmpInst subclasses.
Definition: InstrTypes.h:646
FunctionPass class - This class is used to implement most global optimizations.
Definition: Pass.h:284
amdgpu Simplify well known AMD library false FunctionCallee Value * Arg
static LLVM_NODISCARD SCEV::NoWrapFlags clearFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OffFlags)
const SCEV * getLHS() const
Returns the left hand side of the equality.
LLVMContext & getContext() const
getContext - Return a reference to the LLVMContext associated with this function. ...
Definition: Function.cpp:192
const SCEV * getRHS() const
Returns the right hand side of the equality.
ScalarEvolution * getSE() const
Returns the ScalarEvolution analysis used.
size_t size() const
Definition: SmallVector.h:52
auto find(R &&Range, const T &Val) -> decltype(adl_begin(Range))
Provide wrappers to std::find which take ranges instead of having to pass begin/end explicitly...
Definition: STLExtras.h:1206
FoldingSet - This template class is used to instantiate a specialized implementation of the folding s...
Definition: FoldingSet.h:473
bool verify(const TargetRegisterInfo &TRI) const
Check that information hold by this instance make sense for the given TRI.
static unsigned ComputeHash(const SCEV &X, FoldingSetNodeID &TempID)
static ExitLimitQuery getEmptyKey()
The SCEV is loop-variant (unknown).
This class represents an assumption made using SCEV expressions which can be checked at run-time...
void print(raw_ostream &OS) const
Print out the internal representation of this scalar to the specified stream.
unsigned getSCEVType() const
bool isNonConstantNegative() const
Return true if the specified scev is negated, but not a constant.
See the file comment.
Definition: ValueMap.h:85
SmallPtrSet - This class implements a set which is optimized for holding SmallSize or less elements...
Definition: SmallPtrSet.h:417
This is the shared class of boolean and integer constants.
Definition: Constants.h:83
bool isAllOnesValue() const
Return true if the expression is a constant all-ones value.
Type * getType() const
Return the LLVM type of this SCEV expression.
static LLVM_NODISCARD SCEVWrapPredicate::IncrementWrapFlags clearFlags(SCEVWrapPredicate::IncrementWrapFlags Flags, SCEVWrapPredicate::IncrementWrapFlags OffFlags)
Convenient IncrementWrapFlags manipulation methods.
static bool isEqual(ExitLimitQuery LHS, ExitLimitQuery RHS)
This is a &#39;vector&#39; (really, a variable-sized array), optimized for the case when the array is small...
Definition: SmallVector.h:839
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:46
An interface layer with SCEV used to manage how we see SCEV expressions for values in the context of ...
static LLVM_NODISCARD SCEVWrapPredicate::IncrementWrapFlags maskFlags(SCEVWrapPredicate::IncrementWrapFlags Flags, int Mask)
static void Profile(const SCEV &X, FoldingSetNodeID &ID)
static void Profile(const SCEVPredicate &X, FoldingSetNodeID &ID)
LoopDisposition
An enum describing the relationship between a SCEV and a loop.
Class for arbitrary precision integers.
Definition: APInt.h:69
virtual void print(raw_ostream &OS, unsigned Depth=0) const =0
Prints a textual representation of this predicate with an indentation of Depth.
hash_code hash_combine(const Ts &...args)
Combine values into a single hash_code.
Definition: Hashing.h:600
bool isKnownNonZero(const Value *V, const DataLayout &DL, unsigned Depth=0, AssumptionCache *AC=nullptr, const Instruction *CxtI=nullptr, const DominatorTree *DT=nullptr, bool UseInstrInfo=true)
Return true if the given value is known to be non-zero when defined.
This class uses information about analyze scalars to rewrite expressions in canonical form...
static void clear(coro::Shape &Shape)
Definition: Coroutines.cpp:211
const DataLayout & getDataLayout() const
Return the DataLayout associated with the module this SCEV instance is operating on.
static bool classof(const SCEVPredicate *P)
Methods for support type inquiry through isa, cast, and dyn_cast:
Analysis pass that exposes the ScalarEvolution for a function.
unsigned getComplexity() const override
We estimate the complexity of a union predicate as the size number of predicates in the union...
static ExitLimitQuery getTombstoneKey()
The SCEV does not dominate the block.
FoldingSetNodeIDRef - This class describes a reference to an interned FoldingSetNodeID, which can be a useful to store node id data rather than using plain FoldingSetNodeIDs, since the 32-element SmallVector is often much larger than necessary, and the possibility of heap allocation means it requires a non-trivial destructor call.
Definition: FoldingSet.h:277
MCExpr const & getExpr(MCExpr const &Expr)
Node - This class is used to maintain the singly linked bucket list in a folding set.
Definition: FoldingSet.h:135
This class represents an analyzed expression in the program.
bool isKnownNegative(const Value *V, const DataLayout &DL, unsigned Depth=0, AssumptionCache *AC=nullptr, const Instruction *CxtI=nullptr, const DominatorTree *DT=nullptr, bool UseInstrInfo=true)
Returns true if the given value is known be negative (i.e.
LLVM_NODISCARD bool empty() const
Definition: SmallVector.h:55
const SCEV * getMulExpr(const SCEV *LHS, const SCEV *RHS, SCEV::NoWrapFlags Flags=SCEV::FlagAnyWrap, unsigned Depth=0)
Represents a single loop in the control flow graph.
Definition: LoopInfo.h:464
#define I(x, y, z)
Definition: MD5.cpp:58
#define N
BlockDisposition
An enum describing the relationship between a SCEV and a basic block.
static LLVM_NODISCARD SCEV::NoWrapFlags maskFlags(SCEV::NoWrapFlags Flags, int Mask)
Convenient NoWrapFlags manipulation that hides enum casts and is visible in the ScalarEvolution name ...
raw_ostream & operator<<(raw_ostream &OS, const APInt &I)
Definition: APInt.h:2038
virtual unsigned getComplexity() const
Returns the estimated complexity of this predicate.
#define LLVM_NODISCARD
LLVM_NODISCARD - Warn if a type or return value is discarded.
Definition: Compiler.h:128
API to communicate dependencies between analyses during invalidation.
Definition: PassManager.h:641
ConstantRange getUnsignedRange(const SCEV *S)
Determine the unsigned range for a particular SCEV.
const unsigned Kind
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.