include/llvm/Analysis/ScalarEvolutionExpressions.h

   1 //===- llvm/Analysis/ScalarEvolutionExpressions.h - SCEV Exprs --*- 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 // This file defines the classes used to represent and build scalar expressions.
  10 //
  11 //===----------------------------------------------------------------------===//
  12
  13 #ifndef LLVM_ANALYSIS_SCALAREVOLUTIONEXPRESSIONS_H
  14 #define LLVM_ANALYSIS_SCALAREVOLUTIONEXPRESSIONS_H
  15
  16 #include "llvm/ADT/DenseMap.h"
  17 #include "llvm/ADT/FoldingSet.h"
  18 #include "llvm/ADT/SmallPtrSet.h"
  19 #include "llvm/ADT/SmallVector.h"
  20 #include "llvm/ADT/iterator_range.h"
  21 #include "llvm/Analysis/ScalarEvolution.h"
  22 #include "llvm/IR/Constants.h"
  23 #include "llvm/IR/Value.h"
  24 #include "llvm/IR/ValueHandle.h"
  25 #include "llvm/Support/Casting.h"
  26 #include "llvm/Support/ErrorHandling.h"
  27 #include <cassert>
  28 #include <cstddef>
  29
  30 namespace llvm {
  31
  32 class APInt;
  33 class Constant;
  34 class ConstantRange;
  35 class Loop;
  36 class Type;
  37
  38   enum SCEVTypes {
  39     // These should be ordered in terms of increasing complexity to make the
  40     // folders simpler.
  41     scConstant, scTruncate, scZeroExtend, scSignExtend, scAddExpr, scMulExpr,
  42     scUDivExpr, scAddRecExpr, scUMaxExpr, scSMaxExpr, scUMinExpr, scSMinExpr,
  43     scUnknown, scCouldNotCompute
  44   };
  45
  46   /// This class represents a constant integer value.
  47   class SCEVConstant : public SCEV {
  48     friend class ScalarEvolution;
  49
  50     ConstantInt *V;
  51
  52     SCEVConstant(const FoldingSetNodeIDRef ID, ConstantInt *v) :
  53       SCEV(ID, scConstant, 1), V(v) {}
  54
  55   public:
  56     ConstantInt *getValue() const { return V; }
  57     const APInt &getAPInt() const { return getValue()->getValue(); }
  58
  59     Type *getType() const { return V->getType(); }
  60
  61     /// Methods for support type inquiry through isa, cast, and dyn_cast:
  62     static bool classof(const SCEV *S) {
  63       return S->getSCEVType() == scConstant;
  64     }
  65   };
  66
  67   static unsigned short computeExpressionSize(ArrayRef<const SCEV *> Args) {
  68     APInt Size(16, 1);
  69     for (auto *Arg : Args)
  70       Size = Size.uadd_sat(APInt(16, Arg->getExpressionSize()));
  71     return (unsigned short)Size.getZExtValue();
  72   }
  73
  74   /// This is the base class for unary cast operator classes.
  75   class SCEVCastExpr : public SCEV {
  76   protected:
  77     const SCEV *Op;
  78     Type *Ty;
  79
  80     SCEVCastExpr(const FoldingSetNodeIDRef ID,
  81                  unsigned SCEVTy, const SCEV *op, Type *ty);
  82
  83   public:
  84     const SCEV *getOperand() const { return Op; }
  85     Type *getType() const { return Ty; }
  86
  87     /// Methods for support type inquiry through isa, cast, and dyn_cast:
  88     static bool classof(const SCEV *S) {
  89       return S->getSCEVType() == scTruncate ||
  90              S->getSCEVType() == scZeroExtend ||
  91              S->getSCEVType() == scSignExtend;
  92     }
  93   };
  94
  95   /// This class represents a truncation of an integer value to a
  96   /// smaller integer value.
  97   class SCEVTruncateExpr : public SCEVCastExpr {
  98     friend class ScalarEvolution;
  99
 100     SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
 101                      const SCEV *op, Type *ty);
 102
 103   public:
 104     /// Methods for support type inquiry through isa, cast, and dyn_cast:
 105     static bool classof(const SCEV *S) {
 106       return S->getSCEVType() == scTruncate;
 107     }
 108   };
 109
 110   /// This class represents a zero extension of a small integer value
 111   /// to a larger integer value.
 112   class SCEVZeroExtendExpr : public SCEVCastExpr {
 113     friend class ScalarEvolution;
 114
 115     SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
 116                        const SCEV *op, Type *ty);
 117
 118   public:
 119     /// Methods for support type inquiry through isa, cast, and dyn_cast:
 120     static bool classof(const SCEV *S) {
 121       return S->getSCEVType() == scZeroExtend;
 122     }
 123   };
 124
 125   /// This class represents a sign extension of a small integer value
 126   /// to a larger integer value.
 127   class SCEVSignExtendExpr : public SCEVCastExpr {
 128     friend class ScalarEvolution;
 129
 130     SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
 131                        const SCEV *op, Type *ty);
 132
 133   public:
 134     /// Methods for support type inquiry through isa, cast, and dyn_cast:
 135     static bool classof(const SCEV *S) {
 136       return S->getSCEVType() == scSignExtend;
 137     }
 138   };
 139
 140   /// This node is a base class providing common functionality for
 141   /// n'ary operators.
 142   class SCEVNAryExpr : public SCEV {
 143   protected:
 144     // Since SCEVs are immutable, ScalarEvolution allocates operand
 145     // arrays with its SCEVAllocator, so this class just needs a simple
 146     // pointer rather than a more elaborate vector-like data structure.
 147     // This also avoids the need for a non-trivial destructor.
 148     const SCEV *const *Operands;
 149     size_t NumOperands;
 150
 151     SCEVNAryExpr(const FoldingSetNodeIDRef ID, enum SCEVTypes T,
 152                  const SCEV *const *O, size_t N)
 153         : SCEV(ID, T, computeExpressionSize(makeArrayRef(O, N))), Operands(O),
 154           NumOperands(N) {}
 155
 156   public:
 157     size_t getNumOperands() const { return NumOperands; }
 158
 159     const SCEV *getOperand(unsigned i) const {
 160       assert(i < NumOperands && "Operand index out of range!");
 161       return Operands[i];
 162     }
 163
 164     using op_iterator = const SCEV *const *;
 165     using op_range = iterator_range<op_iterator>;
 166
 167     op_iterator op_begin() const { return Operands; }
 168     op_iterator op_end() const { return Operands + NumOperands; }
 169     op_range operands() const {
 170       return make_range(op_begin(), op_end());
 171     }
 172
 173     Type *getType() const { return getOperand(0)->getType(); }
 174
 175     NoWrapFlags getNoWrapFlags(NoWrapFlags Mask = NoWrapMask) const {
 176       return (NoWrapFlags)(SubclassData & Mask);
 177     }
 178
 179     bool hasNoUnsignedWrap() const {
 180       return getNoWrapFlags(FlagNUW) != FlagAnyWrap;
 181     }
 182
 183     bool hasNoSignedWrap() const {
 184       return getNoWrapFlags(FlagNSW) != FlagAnyWrap;
 185     }
 186
 187     bool hasNoSelfWrap() const {
 188       return getNoWrapFlags(FlagNW) != FlagAnyWrap;
 189     }
 190
 191     /// Methods for support type inquiry through isa, cast, and dyn_cast:
 192     static bool classof(const SCEV *S) {
 193       return S->getSCEVType() == scAddExpr || S->getSCEVType() == scMulExpr ||
 194              S->getSCEVType() == scSMaxExpr || S->getSCEVType() == scUMaxExpr ||
 195              S->getSCEVType() == scSMinExpr || S->getSCEVType() == scUMinExpr ||
 196              S->getSCEVType() == scAddRecExpr;
 197     }
 198   };
 199
 200   /// This node is the base class for n'ary commutative operators.
 201   class SCEVCommutativeExpr : public SCEVNAryExpr {
 202   protected:
 203     SCEVCommutativeExpr(const FoldingSetNodeIDRef ID,
 204                         enum SCEVTypes T, const SCEV *const *O, size_t N)
 205       : SCEVNAryExpr(ID, T, O, N) {}
 206
 207   public:
 208     /// Methods for support type inquiry through isa, cast, and dyn_cast:
 209     static bool classof(const SCEV *S) {
 210       return S->getSCEVType() == scAddExpr || S->getSCEVType() == scMulExpr ||
 211              S->getSCEVType() == scSMaxExpr || S->getSCEVType() == scUMaxExpr ||
 212              S->getSCEVType() == scSMinExpr || S->getSCEVType() == scUMinExpr;
 213     }
 214
 215     /// Set flags for a non-recurrence without clearing previously set flags.
 216     void setNoWrapFlags(NoWrapFlags Flags) {
 217       SubclassData |= Flags;
 218     }
 219   };
 220
 221   /// This node represents an addition of some number of SCEVs.
 222   class SCEVAddExpr : public SCEVCommutativeExpr {
 223     friend class ScalarEvolution;
 224
 225     SCEVAddExpr(const FoldingSetNodeIDRef ID,
 226                 const SCEV *const *O, size_t N)
 227       : SCEVCommutativeExpr(ID, scAddExpr, O, N) {}
 228
 229   public:
 230     Type *getType() const {
 231       // Use the type of the last operand, which is likely to be a pointer
 232       // type, if there is one. This doesn't usually matter, but it can help
 233       // reduce casts when the expressions are expanded.
 234       return getOperand(getNumOperands() - 1)->getType();
 235     }
 236
 237     /// Methods for support type inquiry through isa, cast, and dyn_cast:
 238     static bool classof(const SCEV *S) {
 239       return S->getSCEVType() == scAddExpr;
 240     }
 241   };
 242
 243   /// This node represents multiplication of some number of SCEVs.
 244   class SCEVMulExpr : public SCEVCommutativeExpr {
 245     friend class ScalarEvolution;
 246
 247     SCEVMulExpr(const FoldingSetNodeIDRef ID,
 248                 const SCEV *const *O, size_t N)
 249       : SCEVCommutativeExpr(ID, scMulExpr, O, N) {}
 250
 251   public:
 252     /// Methods for support type inquiry through isa, cast, and dyn_cast:
 253     static bool classof(const SCEV *S) {
 254       return S->getSCEVType() == scMulExpr;
 255     }
 256   };
 257
 258   /// This class represents a binary unsigned division operation.
 259   class SCEVUDivExpr : public SCEV {
 260     friend class ScalarEvolution;
 261
 262     const SCEV *LHS;
 263     const SCEV *RHS;
 264
 265     SCEVUDivExpr(const FoldingSetNodeIDRef ID, const SCEV *lhs, const SCEV *rhs)
 266         : SCEV(ID, scUDivExpr, computeExpressionSize({lhs, rhs})), LHS(lhs),
 267           RHS(rhs) {}
 268
 269   public:
 270     const SCEV *getLHS() const { return LHS; }
 271     const SCEV *getRHS() const { return RHS; }
 272
 273     Type *getType() const {
 274       // In most cases the types of LHS and RHS will be the same, but in some
 275       // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
 276       // depend on the type for correctness, but handling types carefully can
 277       // avoid extra casts in the SCEVExpander. The LHS is more likely to be
 278       // a pointer type than the RHS, so use the RHS' type here.
 279       return getRHS()->getType();
 280     }
 281
 282     /// Methods for support type inquiry through isa, cast, and dyn_cast:
 283     static bool classof(const SCEV *S) {
 284       return S->getSCEVType() == scUDivExpr;
 285     }
 286   };
 287
 288   /// This node represents a polynomial recurrence on the trip count
 289   /// of the specified loop.  This is the primary focus of the
 290   /// ScalarEvolution framework; all the other SCEV subclasses are
 291   /// mostly just supporting infrastructure to allow SCEVAddRecExpr
 292   /// expressions to be created and analyzed.
 293   ///
 294   /// All operands of an AddRec are required to be loop invariant.
 295   ///
 296   class SCEVAddRecExpr : public SCEVNAryExpr {
 297     friend class ScalarEvolution;
 298
 299     const Loop *L;
 300
 301     SCEVAddRecExpr(const FoldingSetNodeIDRef ID,
 302                    const SCEV *const *O, size_t N, const Loop *l)
 303       : SCEVNAryExpr(ID, scAddRecExpr, O, N), L(l) {}
 304
 305   public:
 306     const SCEV *getStart() const { return Operands[0]; }
 307     const Loop *getLoop() const { return L; }
 308
 309     /// Constructs and returns the recurrence indicating how much this
 310     /// expression steps by.  If this is a polynomial of degree N, it
 311     /// returns a chrec of degree N-1.  We cannot determine whether
 312     /// the step recurrence has self-wraparound.
 313     const SCEV *getStepRecurrence(ScalarEvolution &SE) const {
 314       if (isAffine()) return getOperand(1);
 315       return SE.getAddRecExpr(SmallVector<const SCEV *, 3>(op_begin()+1,
 316                                                            op_end()),
 317                               getLoop(), FlagAnyWrap);
 318     }
 319
 320     /// Return true if this represents an expression A + B*x where A
 321     /// and B are loop invariant values.
 322     bool isAffine() const {
 323       // We know that the start value is invariant.  This expression is thus
 324       // affine iff the step is also invariant.
 325       return getNumOperands() == 2;
 326     }
 327
 328     /// Return true if this represents an expression A + B*x + C*x^2
 329     /// where A, B and C are loop invariant values.  This corresponds
 330     /// to an addrec of the form {L,+,M,+,N}
 331     bool isQuadratic() const {
 332       return getNumOperands() == 3;
 333     }
 334
 335     /// Set flags for a recurrence without clearing any previously set flags.
 336     /// For AddRec, either NUW or NSW implies NW. Keep track of this fact here
 337     /// to make it easier to propagate flags.
 338     void setNoWrapFlags(NoWrapFlags Flags) {
 339       if (Flags & (FlagNUW | FlagNSW))
 340         Flags = ScalarEvolution::setFlags(Flags, FlagNW);
 341       SubclassData |= Flags;
 342     }
 343
 344     /// Return the value of this chain of recurrences at the specified
 345     /// iteration number.
 346     const SCEV *evaluateAtIteration(const SCEV *It, ScalarEvolution &SE) const;
 347
 348     /// Return the number of iterations of this loop that produce
 349     /// values in the specified constant range.  Another way of
 350     /// looking at this is that it returns the first iteration number
 351     /// where the value is not in the condition, thus computing the
 352     /// exit count.  If the iteration count can't be computed, an
 353     /// instance of SCEVCouldNotCompute is returned.
 354     const SCEV *getNumIterationsInRange(const ConstantRange &Range,
 355                                         ScalarEvolution &SE) const;
 356
 357     /// Return an expression representing the value of this expression
 358     /// one iteration of the loop ahead.
 359     const SCEVAddRecExpr *getPostIncExpr(ScalarEvolution &SE) const;
 360
 361     /// Methods for support type inquiry through isa, cast, and dyn_cast:
 362     static bool classof(const SCEV *S) {
 363       return S->getSCEVType() == scAddRecExpr;
 364     }
 365   };
 366
 367   /// This node is the base class min/max selections.
 368   class SCEVMinMaxExpr : public SCEVCommutativeExpr {
 369     friend class ScalarEvolution;
 370
 371     static bool isMinMaxType(enum SCEVTypes T) {
 372       return T == scSMaxExpr || T == scUMaxExpr || T == scSMinExpr ||
 373              T == scUMinExpr;
 374     }
 375
 376   protected:
 377     /// Note: Constructing subclasses via this constructor is allowed
 378     SCEVMinMaxExpr(const FoldingSetNodeIDRef ID, enum SCEVTypes T,
 379                    const SCEV *const *O, size_t N)
 380         : SCEVCommutativeExpr(ID, T, O, N) {
 381       assert(isMinMaxType(T));
 382       // Min and max never overflow
 383       setNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW));
 384     }
 385
 386   public:
 387     static bool classof(const SCEV *S) {
 388       return isMinMaxType(static_cast<SCEVTypes>(S->getSCEVType()));
 389     }
 390
 391     static enum SCEVTypes negate(enum SCEVTypes T) {
 392       switch (T) {
 393       case scSMaxExpr:
 394         return scSMinExpr;
 395       case scSMinExpr:
 396         return scSMaxExpr;
 397       case scUMaxExpr:
 398         return scUMinExpr;
 399       case scUMinExpr:
 400         return scUMaxExpr;
 401       default:
 402         llvm_unreachable("Not a min or max SCEV type!");
 403       }
 404     }
 405   };
 406
 407   /// This class represents a signed maximum selection.
 408   class SCEVSMaxExpr : public SCEVMinMaxExpr {
 409     friend class ScalarEvolution;
 410
 411     SCEVSMaxExpr(const FoldingSetNodeIDRef ID, const SCEV *const *O, size_t N)
 412         : SCEVMinMaxExpr(ID, scSMaxExpr, O, N) {}
 413
 414   public:
 415     /// Methods for support type inquiry through isa, cast, and dyn_cast:
 416     static bool classof(const SCEV *S) {
 417       return S->getSCEVType() == scSMaxExpr;
 418     }
 419   };
 420
 421   /// This class represents an unsigned maximum selection.
 422   class SCEVUMaxExpr : public SCEVMinMaxExpr {
 423     friend class ScalarEvolution;
 424
 425     SCEVUMaxExpr(const FoldingSetNodeIDRef ID, const SCEV *const *O, size_t N)
 426         : SCEVMinMaxExpr(ID, scUMaxExpr, O, N) {}
 427
 428   public:
 429     /// Methods for support type inquiry through isa, cast, and dyn_cast:
 430     static bool classof(const SCEV *S) {
 431       return S->getSCEVType() == scUMaxExpr;
 432     }
 433   };
 434
 435   /// This class represents a signed minimum selection.
 436   class SCEVSMinExpr : public SCEVMinMaxExpr {
 437     friend class ScalarEvolution;
 438
 439     SCEVSMinExpr(const FoldingSetNodeIDRef ID, const SCEV *const *O, size_t N)
 440         : SCEVMinMaxExpr(ID, scSMinExpr, O, N) {}
 441
 442   public:
 443     /// Methods for support type inquiry through isa, cast, and dyn_cast:
 444     static bool classof(const SCEV *S) {
 445       return S->getSCEVType() == scSMinExpr;
 446     }
 447   };
 448
 449   /// This class represents an unsigned minimum selection.
 450   class SCEVUMinExpr : public SCEVMinMaxExpr {
 451     friend class ScalarEvolution;
 452
 453     SCEVUMinExpr(const FoldingSetNodeIDRef ID, const SCEV *const *O, size_t N)
 454         : SCEVMinMaxExpr(ID, scUMinExpr, O, N) {}
 455
 456   public:
 457     /// Methods for support type inquiry through isa, cast, and dyn_cast:
 458     static bool classof(const SCEV *S) {
 459       return S->getSCEVType() == scUMinExpr;
 460     }
 461   };
 462
 463   /// This means that we are dealing with an entirely unknown SCEV
 464   /// value, and only represent it as its LLVM Value.  This is the
 465   /// "bottom" value for the analysis.
 466   class SCEVUnknown final : public SCEV, private CallbackVH {
 467     friend class ScalarEvolution;
 468
 469     /// The parent ScalarEvolution value. This is used to update the
 470     /// parent's maps when the value associated with a SCEVUnknown is
 471     /// deleted or RAUW'd.
 472     ScalarEvolution *SE;
 473
 474     /// The next pointer in the linked list of all SCEVUnknown
 475     /// instances owned by a ScalarEvolution.
 476     SCEVUnknown *Next;
 477
 478     SCEVUnknown(const FoldingSetNodeIDRef ID, Value *V,
 479                 ScalarEvolution *se, SCEVUnknown *next) :
 480       SCEV(ID, scUnknown, 1), CallbackVH(V), SE(se), Next(next) {}
 481
 482     // Implement CallbackVH.
 483     void deleted() override;
 484     void allUsesReplacedWith(Value *New) override;
 485
 486   public:
 487     Value *getValue() const { return getValPtr(); }
 488
 489     /// @{
 490     /// Test whether this is a special constant representing a type
 491     /// size, alignment, or field offset in a target-independent
 492     /// manner, and hasn't happened to have been folded with other
 493     /// operations into something unrecognizable. This is mainly only
 494     /// useful for pretty-printing and other situations where it isn't
 495     /// absolutely required for these to succeed.
 496     bool isSizeOf(Type *&AllocTy) const;
 497     bool isAlignOf(Type *&AllocTy) const;
 498     bool isOffsetOf(Type *&STy, Constant *&FieldNo) const;
 499     /// @}
 500
 501     Type *getType() const { return getValPtr()->getType(); }
 502
 503     /// Methods for support type inquiry through isa, cast, and dyn_cast:
 504     static bool classof(const SCEV *S) {
 505       return S->getSCEVType() == scUnknown;
 506     }
 507   };
 508
 509   /// This class defines a simple visitor class that may be used for
 510   /// various SCEV analysis purposes.
 511   template<typename SC, typename RetVal=void>
 512   struct SCEVVisitor {
 513     RetVal visit(const SCEV *S) {
 514       switch (S->getSCEVType()) {
 515       case scConstant:
 516         return ((SC*)this)->visitConstant((const SCEVConstant*)S);
 517       case scTruncate:
 518         return ((SC*)this)->visitTruncateExpr((const SCEVTruncateExpr*)S);
 519       case scZeroExtend:
 520         return ((SC*)this)->visitZeroExtendExpr((const SCEVZeroExtendExpr*)S);
 521       case scSignExtend:
 522         return ((SC*)this)->visitSignExtendExpr((const SCEVSignExtendExpr*)S);
 523       case scAddExpr:
 524         return ((SC*)this)->visitAddExpr((const SCEVAddExpr*)S);
 525       case scMulExpr:
 526         return ((SC*)this)->visitMulExpr((const SCEVMulExpr*)S);
 527       case scUDivExpr:
 528         return ((SC*)this)->visitUDivExpr((const SCEVUDivExpr*)S);
 529       case scAddRecExpr:
 530         return ((SC*)this)->visitAddRecExpr((const SCEVAddRecExpr*)S);
 531       case scSMaxExpr:
 532         return ((SC*)this)->visitSMaxExpr((const SCEVSMaxExpr*)S);
 533       case scUMaxExpr:
 534         return ((SC*)this)->visitUMaxExpr((const SCEVUMaxExpr*)S);
 535       case scSMinExpr:
 536         return ((SC *)this)->visitSMinExpr((const SCEVSMinExpr *)S);
 537       case scUMinExpr:
 538         return ((SC *)this)->visitUMinExpr((const SCEVUMinExpr *)S);
 539       case scUnknown:
 540         return ((SC*)this)->visitUnknown((const SCEVUnknown*)S);
 541       case scCouldNotCompute:
 542         return ((SC*)this)->visitCouldNotCompute((const SCEVCouldNotCompute*)S);
 543       default:
 544         llvm_unreachable("Unknown SCEV type!");
 545       }
 546     }
 547
 548     RetVal visitCouldNotCompute(const SCEVCouldNotCompute *S) {
 549       llvm_unreachable("Invalid use of SCEVCouldNotCompute!");
 550     }
 551   };
 552
 553   /// Visit all nodes in the expression tree using worklist traversal.
 554   ///
 555   /// Visitor implements:
 556   ///   // return true to follow this node.
 557   ///   bool follow(const SCEV *S);
 558   ///   // return true to terminate the search.
 559   ///   bool isDone();
 560   template<typename SV>
 561   class SCEVTraversal {
 562     SV &Visitor;
 563     SmallVector<const SCEV *, 8> Worklist;
 564     SmallPtrSet<const SCEV *, 8> Visited;
 565
 566     void push(const SCEV *S) {
 567       if (Visited.insert(S).second && Visitor.follow(S))
 568         Worklist.push_back(S);
 569     }
 570
 571   public:
 572     SCEVTraversal(SV& V): Visitor(V) {}
 573
 574     void visitAll(const SCEV *Root) {
 575       push(Root);
 576       while (!Worklist.empty() && !Visitor.isDone()) {
 577         const SCEV *S = Worklist.pop_back_val();
 578
 579         switch (S->getSCEVType()) {
 580         case scConstant:
 581         case scUnknown:
 582           break;
 583         case scTruncate:
 584         case scZeroExtend:
 585         case scSignExtend:
 586           push(cast<SCEVCastExpr>(S)->getOperand());
 587           break;
 588         case scAddExpr:
 589         case scMulExpr:
 590         case scSMaxExpr:
 591         case scUMaxExpr:
 592         case scSMinExpr:
 593         case scUMinExpr:
 594         case scAddRecExpr:
 595           for (const auto *Op : cast<SCEVNAryExpr>(S)->operands())
 596             push(Op);
 597           break;
 598         case scUDivExpr: {
 599           const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
 600           push(UDiv->getLHS());
 601           push(UDiv->getRHS());
 602           break;
 603         }
 604         case scCouldNotCompute:
 605           llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
 606         default:
 607           llvm_unreachable("Unknown SCEV kind!");
 608         }
 609       }
 610     }
 611   };
 612
 613   /// Use SCEVTraversal to visit all nodes in the given expression tree.
 614   template<typename SV>
 615   void visitAll(const SCEV *Root, SV& Visitor) {
 616     SCEVTraversal<SV> T(Visitor);
 617     T.visitAll(Root);
 618   }
 619
 620   /// Return true if any node in \p Root satisfies the predicate \p Pred.
 621   template <typename PredTy>
 622   bool SCEVExprContains(const SCEV *Root, PredTy Pred) {
 623     struct FindClosure {
 624       bool Found = false;
 625       PredTy Pred;
 626
 627       FindClosure(PredTy Pred) : Pred(Pred) {}
 628
 629       bool follow(const SCEV *S) {
 630         if (!Pred(S))
 631           return true;
 632
 633         Found = true;
 634         return false;
 635       }
 636
 637       bool isDone() const { return Found; }
 638     };
 639
 640     FindClosure FC(Pred);
 641     visitAll(Root, FC);
 642     return FC.Found;
 643   }
 644
 645   /// This visitor recursively visits a SCEV expression and re-writes it.
 646   /// The result from each visit is cached, so it will return the same
 647   /// SCEV for the same input.
 648   template<typename SC>
 649   class SCEVRewriteVisitor : public SCEVVisitor<SC, const SCEV *> {
 650   protected:
 651     ScalarEvolution &SE;
 652     // Memoize the result of each visit so that we only compute once for
 653     // the same input SCEV. This is to avoid redundant computations when
 654     // a SCEV is referenced by multiple SCEVs. Without memoization, this
 655     // visit algorithm would have exponential time complexity in the worst
 656     // case, causing the compiler to hang on certain tests.
 657     DenseMap<const SCEV *, const SCEV *> RewriteResults;
 658
 659   public:
 660     SCEVRewriteVisitor(ScalarEvolution &SE) : SE(SE) {}
 661
 662     const SCEV *visit(const SCEV *S) {
 663       auto It = RewriteResults.find(S);
 664       if (It != RewriteResults.end())
 665         return It->second;
 666       auto* Visited = SCEVVisitor<SC, const SCEV *>::visit(S);
 667       auto Result = RewriteResults.try_emplace(S, Visited);
 668       assert(Result.second && "Should insert a new entry");
 669       return Result.first->second;
 670     }
 671
 672     const SCEV *visitConstant(const SCEVConstant *Constant) {
 673       return Constant;
 674     }
 675
 676     const SCEV *visitTruncateExpr(const SCEVTruncateExpr *Expr) {
 677       const SCEV *Operand = ((SC*)this)->visit(Expr->getOperand());
 678       return Operand == Expr->getOperand()
 679                  ? Expr
 680                  : SE.getTruncateExpr(Operand, Expr->getType());
 681     }
 682
 683     const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
 684       const SCEV *Operand = ((SC*)this)->visit(Expr->getOperand());
 685       return Operand == Expr->getOperand()
 686                  ? Expr
 687                  : SE.getZeroExtendExpr(Operand, Expr->getType());
 688     }
 689
 690     const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
 691       const SCEV *Operand = ((SC*)this)->visit(Expr->getOperand());
 692       return Operand == Expr->getOperand()
 693                  ? Expr
 694                  : SE.getSignExtendExpr(Operand, Expr->getType());
 695     }
 696
 697     const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
 698       SmallVector<const SCEV *, 2> Operands;
 699       bool Changed = false;
 700       for (auto *Op : Expr->operands()) {
 701         Operands.push_back(((SC*)this)->visit(Op));
 702         Changed |= Op != Operands.back();
 703       }
 704       return !Changed ? Expr : SE.getAddExpr(Operands);
 705     }
 706
 707     const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
 708       SmallVector<const SCEV *, 2> Operands;
 709       bool Changed = false;
 710       for (auto *Op : Expr->operands()) {
 711         Operands.push_back(((SC*)this)->visit(Op));
 712         Changed |= Op != Operands.back();
 713       }
 714       return !Changed ? Expr : SE.getMulExpr(Operands);
 715     }
 716
 717     const SCEV *visitUDivExpr(const SCEVUDivExpr *Expr) {
 718       auto *LHS = ((SC *)this)->visit(Expr->getLHS());
 719       auto *RHS = ((SC *)this)->visit(Expr->getRHS());
 720       bool Changed = LHS != Expr->getLHS() || RHS != Expr->getRHS();
 721       return !Changed ? Expr : SE.getUDivExpr(LHS, RHS);
 722     }
 723
 724     const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
 725       SmallVector<const SCEV *, 2> Operands;
 726       bool Changed = false;
 727       for (auto *Op : Expr->operands()) {
 728         Operands.push_back(((SC*)this)->visit(Op));
 729         Changed |= Op != Operands.back();
 730       }
 731       return !Changed ? Expr
 732                       : SE.getAddRecExpr(Operands, Expr->getLoop(),
 733                                          Expr->getNoWrapFlags());
 734     }
 735
 736     const SCEV *visitSMaxExpr(const SCEVSMaxExpr *Expr) {
 737       SmallVector<const SCEV *, 2> Operands;
 738       bool Changed = false;
 739       for (auto *Op : Expr->operands()) {
 740         Operands.push_back(((SC *)this)->visit(Op));
 741         Changed |= Op != Operands.back();
 742       }
 743       return !Changed ? Expr : SE.getSMaxExpr(Operands);
 744     }
 745
 746     const SCEV *visitUMaxExpr(const SCEVUMaxExpr *Expr) {
 747       SmallVector<const SCEV *, 2> Operands;
 748       bool Changed = false;
 749       for (auto *Op : Expr->operands()) {
 750         Operands.push_back(((SC*)this)->visit(Op));
 751         Changed |= Op != Operands.back();
 752       }
 753       return !Changed ? Expr : SE.getUMaxExpr(Operands);
 754     }
 755
 756     const SCEV *visitSMinExpr(const SCEVSMinExpr *Expr) {
 757       SmallVector<const SCEV *, 2> Operands;
 758       bool Changed = false;
 759       for (auto *Op : Expr->operands()) {
 760         Operands.push_back(((SC *)this)->visit(Op));
 761         Changed |= Op != Operands.back();
 762       }
 763       return !Changed ? Expr : SE.getSMinExpr(Operands);
 764     }
 765
 766     const SCEV *visitUMinExpr(const SCEVUMinExpr *Expr) {
 767       SmallVector<const SCEV *, 2> Operands;
 768       bool Changed = false;
 769       for (auto *Op : Expr->operands()) {
 770         Operands.push_back(((SC *)this)->visit(Op));
 771         Changed |= Op != Operands.back();
 772       }
 773       return !Changed ? Expr : SE.getUMinExpr(Operands);
 774     }
 775
 776     const SCEV *visitUnknown(const SCEVUnknown *Expr) {
 777       return Expr;
 778     }
 779
 780     const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
 781       return Expr;
 782     }
 783   };
 784
 785   using ValueToValueMap = DenseMap<const Value *, Value *>;
 786
 787   /// The SCEVParameterRewriter takes a scalar evolution expression and updates
 788   /// the SCEVUnknown components following the Map (Value -> Value).
 789   class SCEVParameterRewriter : public SCEVRewriteVisitor<SCEVParameterRewriter> {
 790   public:
 791     static const SCEV *rewrite(const SCEV *Scev, ScalarEvolution &SE,
 792                                ValueToValueMap &Map,
 793                                bool InterpretConsts = false) {
 794       SCEVParameterRewriter Rewriter(SE, Map, InterpretConsts);
 795       return Rewriter.visit(Scev);
 796     }
 797
 798     SCEVParameterRewriter(ScalarEvolution &SE, ValueToValueMap &M, bool C)
 799       : SCEVRewriteVisitor(SE), Map(M), InterpretConsts(C) {}
 800
 801     const SCEV *visitUnknown(const SCEVUnknown *Expr) {
 802       Value *V = Expr->getValue();
 803       if (Map.count(V)) {
 804         Value *NV = Map[V];
 805         if (InterpretConsts && isa<ConstantInt>(NV))
 806           return SE.getConstant(cast<ConstantInt>(NV));
 807         return SE.getUnknown(NV);
 808       }
 809       return Expr;
 810     }
 811
 812   private:
 813     ValueToValueMap &Map;
 814     bool InterpretConsts;
 815   };
 816
 817   using LoopToScevMapT = DenseMap<const Loop *, const SCEV *>;
 818
 819   /// The SCEVLoopAddRecRewriter takes a scalar evolution expression and applies
 820   /// the Map (Loop -> SCEV) to all AddRecExprs.
 821   class SCEVLoopAddRecRewriter
 822       : public SCEVRewriteVisitor<SCEVLoopAddRecRewriter> {
 823   public:
 824     SCEVLoopAddRecRewriter(ScalarEvolution &SE, LoopToScevMapT &M)
 825         : SCEVRewriteVisitor(SE), Map(M) {}
 826
 827     static const SCEV *rewrite(const SCEV *Scev, LoopToScevMapT &Map,
 828                                ScalarEvolution &SE) {
 829       SCEVLoopAddRecRewriter Rewriter(SE, Map);
 830       return Rewriter.visit(Scev);
 831     }
 832
 833     const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
 834       SmallVector<const SCEV *, 2> Operands;
 835       for (const SCEV *Op : Expr->operands())
 836         Operands.push_back(visit(Op));
 837
 838       const Loop *L = Expr->getLoop();
 839       const SCEV *Res = SE.getAddRecExpr(Operands, L, Expr->getNoWrapFlags());
 840
 841       if (0 == Map.count(L))
 842         return Res;
 843
 844       const SCEVAddRecExpr *Rec = cast<SCEVAddRecExpr>(Res);
 845       return Rec->evaluateAtIteration(Map[L], SE);
 846     }
 847
 848   private:
 849     LoopToScevMapT &Map;
 850   };
 851
 852 } // end namespace llvm
 853
 854 #endif // LLVM_ANALYSIS_SCALAREVOLUTIONEXPRESSIONS_H