1//===- llvm/Analysis/ScalarEvolutionExpressions.h - SCEV Exprs --*- C++ -*-===//
2//
3//                     The LLVM Compiler Infrastructure
4//
5// This file is distributed under the University of Illinois Open Source
6// License. See LICENSE.TXT for details.
7//
8//===----------------------------------------------------------------------===//
9//
10// This file defines the classes used to represent and build scalar expressions.
11//
12//===----------------------------------------------------------------------===//
13
14#ifndef LLVM_ANALYSIS_SCALAREVOLUTIONEXPRESSIONS_H
15#define LLVM_ANALYSIS_SCALAREVOLUTIONEXPRESSIONS_H
16
17#include "llvm/ADT/iterator_range.h"
18#include "llvm/ADT/SmallPtrSet.h"
19#include "llvm/Analysis/ScalarEvolution.h"
20#include "llvm/Support/ErrorHandling.h"
21
22namespace llvm {
23  class ConstantInt;
24  class ConstantRange;
25  class DominatorTree;
26
27  enum SCEVTypes {
28    // These should be ordered in terms of increasing complexity to make the
29    // folders simpler.
30    scConstant, scTruncate, scZeroExtend, scSignExtend, scAddExpr, scMulExpr,
31    scUDivExpr, scAddRecExpr, scUMaxExpr, scSMaxExpr,
32    scUnknown, scCouldNotCompute
33  };
34
35  //===--------------------------------------------------------------------===//
36  /// SCEVConstant - This class represents a constant integer value.
37  ///
38  class SCEVConstant : public SCEV {
39    friend class ScalarEvolution;
40
41    ConstantInt *V;
42    SCEVConstant(const FoldingSetNodeIDRef ID, ConstantInt *v) :
43      SCEV(ID, scConstant), V(v) {}
44  public:
45    ConstantInt *getValue() const { return V; }
46
47    Type *getType() const { return V->getType(); }
48
49    /// Methods for support type inquiry through isa, cast, and dyn_cast:
50    static inline bool classof(const SCEV *S) {
51      return S->getSCEVType() == scConstant;
52    }
53  };
54
55  //===--------------------------------------------------------------------===//
56  /// SCEVCastExpr - This is the base class for unary cast operator classes.
57  ///
58  class SCEVCastExpr : public SCEV {
59  protected:
60    const SCEV *Op;
61    Type *Ty;
62
63    SCEVCastExpr(const FoldingSetNodeIDRef ID,
64                 unsigned SCEVTy, const SCEV *op, Type *ty);
65
66  public:
67    const SCEV *getOperand() const { return Op; }
68    Type *getType() const { return Ty; }
69
70    /// Methods for support type inquiry through isa, cast, and dyn_cast:
71    static inline bool classof(const SCEV *S) {
72      return S->getSCEVType() == scTruncate ||
73             S->getSCEVType() == scZeroExtend ||
74             S->getSCEVType() == scSignExtend;
75    }
76  };
77
78  //===--------------------------------------------------------------------===//
79  /// SCEVTruncateExpr - This class represents a truncation of an integer value
80  /// to a smaller integer value.
81  ///
82  class SCEVTruncateExpr : public SCEVCastExpr {
83    friend class ScalarEvolution;
84
85    SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
86                     const SCEV *op, Type *ty);
87
88  public:
89    /// Methods for support type inquiry through isa, cast, and dyn_cast:
90    static inline bool classof(const SCEV *S) {
91      return S->getSCEVType() == scTruncate;
92    }
93  };
94
95  //===--------------------------------------------------------------------===//
96  /// SCEVZeroExtendExpr - This class represents a zero extension of a small
97  /// integer value to a larger integer value.
98  ///
99  class SCEVZeroExtendExpr : public SCEVCastExpr {
100    friend class ScalarEvolution;
101
102    SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
103                       const SCEV *op, Type *ty);
104
105  public:
106    /// Methods for support type inquiry through isa, cast, and dyn_cast:
107    static inline bool classof(const SCEV *S) {
108      return S->getSCEVType() == scZeroExtend;
109    }
110  };
111
112  //===--------------------------------------------------------------------===//
113  /// SCEVSignExtendExpr - This class represents a sign extension of a small
114  /// integer value to a larger integer value.
115  ///
116  class SCEVSignExtendExpr : public SCEVCastExpr {
117    friend class ScalarEvolution;
118
119    SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
120                       const SCEV *op, Type *ty);
121
122  public:
123    /// Methods for support type inquiry through isa, cast, and dyn_cast:
124    static inline bool classof(const SCEV *S) {
125      return S->getSCEVType() == scSignExtend;
126    }
127  };
128
129
130  //===--------------------------------------------------------------------===//
131  /// SCEVNAryExpr - This node is a base class providing common
132  /// functionality for n'ary operators.
133  ///
134  class SCEVNAryExpr : public SCEV {
135  protected:
136    // Since SCEVs are immutable, ScalarEvolution allocates operand
137    // arrays with its SCEVAllocator, so this class just needs a simple
138    // pointer rather than a more elaborate vector-like data structure.
139    // This also avoids the need for a non-trivial destructor.
140    const SCEV *const *Operands;
141    size_t NumOperands;
142
143    SCEVNAryExpr(const FoldingSetNodeIDRef ID,
144                 enum SCEVTypes T, const SCEV *const *O, size_t N)
145      : SCEV(ID, T), Operands(O), NumOperands(N) {}
146
147  public:
148    size_t getNumOperands() const { return NumOperands; }
149    const SCEV *getOperand(unsigned i) const {
150      assert(i < NumOperands && "Operand index out of range!");
151      return Operands[i];
152    }
153
154    typedef const SCEV *const *op_iterator;
155    typedef iterator_range<op_iterator> op_range;
156    op_iterator op_begin() const { return Operands; }
157    op_iterator op_end() const { return Operands + NumOperands; }
158    op_range operands() const {
159      return make_range(op_begin(), op_end());
160    }
161
162    Type *getType() const { return getOperand(0)->getType(); }
163
164    NoWrapFlags getNoWrapFlags(NoWrapFlags Mask = NoWrapMask) const {
165      return (NoWrapFlags)(SubclassData & Mask);
166    }
167
168    /// Methods for support type inquiry through isa, cast, and dyn_cast:
169    static inline bool classof(const SCEV *S) {
170      return S->getSCEVType() == scAddExpr ||
171             S->getSCEVType() == scMulExpr ||
172             S->getSCEVType() == scSMaxExpr ||
173             S->getSCEVType() == scUMaxExpr ||
174             S->getSCEVType() == scAddRecExpr;
175    }
176  };
177
178  //===--------------------------------------------------------------------===//
179  /// SCEVCommutativeExpr - This node is the base class for n'ary commutative
180  /// operators.
181  ///
182  class SCEVCommutativeExpr : public SCEVNAryExpr {
183  protected:
184    SCEVCommutativeExpr(const FoldingSetNodeIDRef ID,
185                        enum SCEVTypes T, const SCEV *const *O, size_t N)
186      : SCEVNAryExpr(ID, T, O, N) {}
187
188  public:
189    /// Methods for support type inquiry through isa, cast, and dyn_cast:
190    static inline bool classof(const SCEV *S) {
191      return S->getSCEVType() == scAddExpr ||
192             S->getSCEVType() == scMulExpr ||
193             S->getSCEVType() == scSMaxExpr ||
194             S->getSCEVType() == scUMaxExpr;
195    }
196
197    /// Set flags for a non-recurrence without clearing previously set flags.
198    void setNoWrapFlags(NoWrapFlags Flags) {
199      SubclassData |= Flags;
200    }
201  };
202
203
204  //===--------------------------------------------------------------------===//
205  /// SCEVAddExpr - This node represents an addition of some number of SCEVs.
206  ///
207  class SCEVAddExpr : public SCEVCommutativeExpr {
208    friend class ScalarEvolution;
209
210    SCEVAddExpr(const FoldingSetNodeIDRef ID,
211                const SCEV *const *O, size_t N)
212      : SCEVCommutativeExpr(ID, scAddExpr, O, N) {
213    }
214
215  public:
216    Type *getType() const {
217      // Use the type of the last operand, which is likely to be a pointer
218      // type, if there is one. This doesn't usually matter, but it can help
219      // reduce casts when the expressions are expanded.
220      return getOperand(getNumOperands() - 1)->getType();
221    }
222
223    /// Methods for support type inquiry through isa, cast, and dyn_cast:
224    static inline bool classof(const SCEV *S) {
225      return S->getSCEVType() == scAddExpr;
226    }
227  };
228
229  //===--------------------------------------------------------------------===//
230  /// SCEVMulExpr - This node represents multiplication of some number of SCEVs.
231  ///
232  class SCEVMulExpr : public SCEVCommutativeExpr {
233    friend class ScalarEvolution;
234
235    SCEVMulExpr(const FoldingSetNodeIDRef ID,
236                const SCEV *const *O, size_t N)
237      : SCEVCommutativeExpr(ID, scMulExpr, O, N) {
238    }
239
240  public:
241    /// Methods for support type inquiry through isa, cast, and dyn_cast:
242    static inline bool classof(const SCEV *S) {
243      return S->getSCEVType() == scMulExpr;
244    }
245  };
246
247
248  //===--------------------------------------------------------------------===//
249  /// SCEVUDivExpr - This class represents a binary unsigned division operation.
250  ///
251  class SCEVUDivExpr : public SCEV {
252    friend class ScalarEvolution;
253
254    const SCEV *LHS;
255    const SCEV *RHS;
256    SCEVUDivExpr(const FoldingSetNodeIDRef ID, const SCEV *lhs, const SCEV *rhs)
257      : SCEV(ID, scUDivExpr), LHS(lhs), RHS(rhs) {}
258
259  public:
260    const SCEV *getLHS() const { return LHS; }
261    const SCEV *getRHS() const { return RHS; }
262
263    Type *getType() const {
264      // In most cases the types of LHS and RHS will be the same, but in some
265      // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
266      // depend on the type for correctness, but handling types carefully can
267      // avoid extra casts in the SCEVExpander. The LHS is more likely to be
268      // a pointer type than the RHS, so use the RHS' type here.
269      return getRHS()->getType();
270    }
271
272    /// Methods for support type inquiry through isa, cast, and dyn_cast:
273    static inline bool classof(const SCEV *S) {
274      return S->getSCEVType() == scUDivExpr;
275    }
276  };
277
278
279  //===--------------------------------------------------------------------===//
280  /// SCEVAddRecExpr - This node represents a polynomial recurrence on the trip
281  /// count of the specified loop.  This is the primary focus of the
282  /// ScalarEvolution framework; all the other SCEV subclasses are mostly just
283  /// supporting infrastructure to allow SCEVAddRecExpr expressions to be
284  /// created and analyzed.
285  ///
286  /// All operands of an AddRec are required to be loop invariant.
287  ///
288  class SCEVAddRecExpr : public SCEVNAryExpr {
289    friend class ScalarEvolution;
290
291    const Loop *L;
292
293    SCEVAddRecExpr(const FoldingSetNodeIDRef ID,
294                   const SCEV *const *O, size_t N, const Loop *l)
295      : SCEVNAryExpr(ID, scAddRecExpr, O, N), L(l) {}
296
297  public:
298    const SCEV *getStart() const { return Operands[0]; }
299    const Loop *getLoop() const { return L; }
300
301    /// getStepRecurrence - This method constructs and returns the recurrence
302    /// indicating how much this expression steps by.  If this is a polynomial
303    /// of degree N, it returns a chrec of degree N-1.
304    /// We cannot determine whether the step recurrence has self-wraparound.
305    const SCEV *getStepRecurrence(ScalarEvolution &SE) const {
306      if (isAffine()) return getOperand(1);
307      return SE.getAddRecExpr(SmallVector<const SCEV *, 3>(op_begin()+1,
308                                                           op_end()),
309                              getLoop(), FlagAnyWrap);
310    }
311
312    /// isAffine - Return true if this is an affine AddRec (i.e., it represents
313    /// an expressions A+B*x where A and B are loop invariant values.
314    bool isAffine() const {
315      // We know that the start value is invariant.  This expression is thus
316      // affine iff the step is also invariant.
317      return getNumOperands() == 2;
318    }
319
320    /// isQuadratic - Return true if this is an quadratic AddRec (i.e., it
321    /// represents an expressions A+B*x+C*x^2 where A, B and C are loop
322    /// invariant values.  This corresponds to an addrec of the form {L,+,M,+,N}
323    bool isQuadratic() const {
324      return getNumOperands() == 3;
325    }
326
327    /// Set flags for a recurrence without clearing any previously set flags.
328    /// For AddRec, either NUW or NSW implies NW. Keep track of this fact here
329    /// to make it easier to propagate flags.
330    void setNoWrapFlags(NoWrapFlags Flags) {
331      if (Flags & (FlagNUW | FlagNSW))
332        Flags = ScalarEvolution::setFlags(Flags, FlagNW);
333      SubclassData |= Flags;
334    }
335
336    /// evaluateAtIteration - Return the value of this chain of recurrences at
337    /// the specified iteration number.
338    const SCEV *evaluateAtIteration(const SCEV *It, ScalarEvolution &SE) const;
339
340    /// getNumIterationsInRange - Return the number of iterations of this loop
341    /// that produce values in the specified constant range.  Another way of
342    /// looking at this is that it returns the first iteration number where the
343    /// value is not in the condition, thus computing the exit count.  If the
344    /// iteration count can't be computed, an instance of SCEVCouldNotCompute is
345    /// returned.
346    const SCEV *getNumIterationsInRange(ConstantRange Range,
347                                       ScalarEvolution &SE) const;
348
349    /// getPostIncExpr - Return an expression representing the value of
350    /// this expression one iteration of the loop ahead.
351    const SCEVAddRecExpr *getPostIncExpr(ScalarEvolution &SE) const {
352      return cast<SCEVAddRecExpr>(SE.getAddExpr(this, getStepRecurrence(SE)));
353    }
354
355    /// Methods for support type inquiry through isa, cast, and dyn_cast:
356    static inline bool classof(const SCEV *S) {
357      return S->getSCEVType() == scAddRecExpr;
358    }
359
360    /// Collect parametric terms occurring in step expressions.
361    void collectParametricTerms(ScalarEvolution &SE,
362                                SmallVectorImpl<const SCEV *> &Terms) const;
363
364    /// Return in Subscripts the access functions for each dimension in Sizes.
365    void computeAccessFunctions(ScalarEvolution &SE,
366                                SmallVectorImpl<const SCEV *> &Subscripts,
367                                SmallVectorImpl<const SCEV *> &Sizes) const;
368
369    /// Split this SCEVAddRecExpr into two vectors of SCEVs representing the
370    /// subscripts and sizes of an array access.
371    ///
372    /// The delinearization is a 3 step process: the first two steps compute the
373    /// sizes of each subscript and the third step computes the access functions
374    /// for the delinearized array:
375    ///
376    /// 1. Find the terms in the step functions
377    /// 2. Compute the array size
378    /// 3. Compute the access function: divide the SCEV by the array size
379    ///    starting with the innermost dimensions found in step 2. The Quotient
380    ///    is the SCEV to be divided in the next step of the recursion. The
381    ///    Remainder is the subscript of the innermost dimension. Loop over all
382    ///    array dimensions computed in step 2.
383    ///
384    /// To compute a uniform array size for several memory accesses to the same
385    /// object, one can collect in step 1 all the step terms for all the memory
386    /// accesses, and compute in step 2 a unique array shape. This guarantees
387    /// that the array shape will be the same across all memory accesses.
388    ///
389    /// FIXME: We could derive the result of steps 1 and 2 from a description of
390    /// the array shape given in metadata.
391    ///
392    /// Example:
393    ///
394    /// A[][n][m]
395    ///
396    /// for i
397    ///   for j
398    ///     for k
399    ///       A[j+k][2i][5i] =
400    ///
401    /// The initial SCEV:
402    ///
403    /// A[{{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k]
404    ///
405    /// 1. Find the different terms in the step functions:
406    /// -> [2*m, 5, n*m, n*m]
407    ///
408    /// 2. Compute the array size: sort and unique them
409    /// -> [n*m, 2*m, 5]
410    /// find the GCD of all the terms = 1
411    /// divide by the GCD and erase constant terms
412    /// -> [n*m, 2*m]
413    /// GCD = m
414    /// divide by GCD -> [n, 2]
415    /// remove constant terms
416    /// -> [n]
417    /// size of the array is A[unknown][n][m]
418    ///
419    /// 3. Compute the access function
420    /// a. Divide {{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k by the innermost size m
421    /// Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k
422    /// Remainder: {{{0,+,5}_i, +, 0}_j, +, 0}_k
423    /// The remainder is the subscript of the innermost array dimension: [5i].
424    ///
425    /// b. Divide Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k by next outer size n
426    /// Quotient: {{{0,+,0}_i, +, 1}_j, +, 1}_k
427    /// Remainder: {{{0,+,2}_i, +, 0}_j, +, 0}_k
428    /// The Remainder is the subscript of the next array dimension: [2i].
429    ///
430    /// The subscript of the outermost dimension is the Quotient: [j+k].
431    ///
432    /// Overall, we have: A[][n][m], and the access function: A[j+k][2i][5i].
433    void delinearize(ScalarEvolution &SE,
434                     SmallVectorImpl<const SCEV *> &Subscripts,
435                     SmallVectorImpl<const SCEV *> &Sizes,
436                     const SCEV *ElementSize) const;
437  };
438
439  //===--------------------------------------------------------------------===//
440  /// SCEVSMaxExpr - This class represents a signed maximum selection.
441  ///
442  class SCEVSMaxExpr : public SCEVCommutativeExpr {
443    friend class ScalarEvolution;
444
445    SCEVSMaxExpr(const FoldingSetNodeIDRef ID,
446                 const SCEV *const *O, size_t N)
447      : SCEVCommutativeExpr(ID, scSMaxExpr, O, N) {
448      // Max never overflows.
449      setNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW));
450    }
451
452  public:
453    /// Methods for support type inquiry through isa, cast, and dyn_cast:
454    static inline bool classof(const SCEV *S) {
455      return S->getSCEVType() == scSMaxExpr;
456    }
457  };
458
459
460  //===--------------------------------------------------------------------===//
461  /// SCEVUMaxExpr - This class represents an unsigned maximum selection.
462  ///
463  class SCEVUMaxExpr : public SCEVCommutativeExpr {
464    friend class ScalarEvolution;
465
466    SCEVUMaxExpr(const FoldingSetNodeIDRef ID,
467                 const SCEV *const *O, size_t N)
468      : SCEVCommutativeExpr(ID, scUMaxExpr, O, N) {
469      // Max never overflows.
470      setNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW));
471    }
472
473  public:
474    /// Methods for support type inquiry through isa, cast, and dyn_cast:
475    static inline bool classof(const SCEV *S) {
476      return S->getSCEVType() == scUMaxExpr;
477    }
478  };
479
480  //===--------------------------------------------------------------------===//
481  /// SCEVUnknown - This means that we are dealing with an entirely unknown SCEV
482  /// value, and only represent it as its LLVM Value.  This is the "bottom"
483  /// value for the analysis.
484  ///
485  class SCEVUnknown : public SCEV, private CallbackVH {
486    friend class ScalarEvolution;
487
488    // Implement CallbackVH.
489    void deleted() override;
490    void allUsesReplacedWith(Value *New) override;
491
492    /// SE - The parent ScalarEvolution value. This is used to update
493    /// the parent's maps when the value associated with a SCEVUnknown
494    /// is deleted or RAUW'd.
495    ScalarEvolution *SE;
496
497    /// Next - The next pointer in the linked list of all
498    /// SCEVUnknown instances owned by a ScalarEvolution.
499    SCEVUnknown *Next;
500
501    SCEVUnknown(const FoldingSetNodeIDRef ID, Value *V,
502                ScalarEvolution *se, SCEVUnknown *next) :
503      SCEV(ID, scUnknown), CallbackVH(V), SE(se), Next(next) {}
504
505  public:
506    Value *getValue() const { return getValPtr(); }
507
508    /// isSizeOf, isAlignOf, isOffsetOf - Test whether this is a special
509    /// constant representing a type size, alignment, or field offset in
510    /// a target-independent manner, and hasn't happened to have been
511    /// folded with other operations into something unrecognizable. This
512    /// is mainly only useful for pretty-printing and other situations
513    /// where it isn't absolutely required for these to succeed.
514    bool isSizeOf(Type *&AllocTy) const;
515    bool isAlignOf(Type *&AllocTy) const;
516    bool isOffsetOf(Type *&STy, Constant *&FieldNo) const;
517
518    Type *getType() const { return getValPtr()->getType(); }
519
520    /// Methods for support type inquiry through isa, cast, and dyn_cast:
521    static inline bool classof(const SCEV *S) {
522      return S->getSCEVType() == scUnknown;
523    }
524  };
525
526  /// SCEVVisitor - This class defines a simple visitor class that may be used
527  /// for various SCEV analysis purposes.
528  template<typename SC, typename RetVal=void>
529  struct SCEVVisitor {
530    RetVal visit(const SCEV *S) {
531      switch (S->getSCEVType()) {
532      case scConstant:
533        return ((SC*)this)->visitConstant((const SCEVConstant*)S);
534      case scTruncate:
535        return ((SC*)this)->visitTruncateExpr((const SCEVTruncateExpr*)S);
536      case scZeroExtend:
537        return ((SC*)this)->visitZeroExtendExpr((const SCEVZeroExtendExpr*)S);
538      case scSignExtend:
539        return ((SC*)this)->visitSignExtendExpr((const SCEVSignExtendExpr*)S);
540      case scAddExpr:
541        return ((SC*)this)->visitAddExpr((const SCEVAddExpr*)S);
542      case scMulExpr:
543        return ((SC*)this)->visitMulExpr((const SCEVMulExpr*)S);
544      case scUDivExpr:
545        return ((SC*)this)->visitUDivExpr((const SCEVUDivExpr*)S);
546      case scAddRecExpr:
547        return ((SC*)this)->visitAddRecExpr((const SCEVAddRecExpr*)S);
548      case scSMaxExpr:
549        return ((SC*)this)->visitSMaxExpr((const SCEVSMaxExpr*)S);
550      case scUMaxExpr:
551        return ((SC*)this)->visitUMaxExpr((const SCEVUMaxExpr*)S);
552      case scUnknown:
553        return ((SC*)this)->visitUnknown((const SCEVUnknown*)S);
554      case scCouldNotCompute:
555        return ((SC*)this)->visitCouldNotCompute((const SCEVCouldNotCompute*)S);
556      default:
557        llvm_unreachable("Unknown SCEV type!");
558      }
559    }
560
561    RetVal visitCouldNotCompute(const SCEVCouldNotCompute *S) {
562      llvm_unreachable("Invalid use of SCEVCouldNotCompute!");
563    }
564  };
565
566  /// Visit all nodes in the expression tree using worklist traversal.
567  ///
568  /// Visitor implements:
569  ///   // return true to follow this node.
570  ///   bool follow(const SCEV *S);
571  ///   // return true to terminate the search.
572  ///   bool isDone();
573  template<typename SV>
574  class SCEVTraversal {
575    SV &Visitor;
576    SmallVector<const SCEV *, 8> Worklist;
577    SmallPtrSet<const SCEV *, 8> Visited;
578
579    void push(const SCEV *S) {
580      if (Visited.insert(S) && Visitor.follow(S))
581        Worklist.push_back(S);
582    }
583  public:
584    SCEVTraversal(SV& V): Visitor(V) {}
585
586    void visitAll(const SCEV *Root) {
587      push(Root);
588      while (!Worklist.empty() && !Visitor.isDone()) {
589        const SCEV *S = Worklist.pop_back_val();
590
591        switch (S->getSCEVType()) {
592        case scConstant:
593        case scUnknown:
594          break;
595        case scTruncate:
596        case scZeroExtend:
597        case scSignExtend:
598          push(cast<SCEVCastExpr>(S)->getOperand());
599          break;
600        case scAddExpr:
601        case scMulExpr:
602        case scSMaxExpr:
603        case scUMaxExpr:
604        case scAddRecExpr: {
605          const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
606          for (SCEVNAryExpr::op_iterator I = NAry->op_begin(),
607                 E = NAry->op_end(); I != E; ++I) {
608            push(*I);
609          }
610          break;
611        }
612        case scUDivExpr: {
613          const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
614          push(UDiv->getLHS());
615          push(UDiv->getRHS());
616          break;
617        }
618        case scCouldNotCompute:
619          llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
620        default:
621          llvm_unreachable("Unknown SCEV kind!");
622        }
623      }
624    }
625  };
626
627  /// Use SCEVTraversal to visit all nodes in the givien expression tree.
628  template<typename SV>
629  void visitAll(const SCEV *Root, SV& Visitor) {
630    SCEVTraversal<SV> T(Visitor);
631    T.visitAll(Root);
632  }
633
634  typedef DenseMap<const Value*, Value*> ValueToValueMap;
635
636  /// The SCEVParameterRewriter takes a scalar evolution expression and updates
637  /// the SCEVUnknown components following the Map (Value -> Value).
638  struct SCEVParameterRewriter
639    : public SCEVVisitor<SCEVParameterRewriter, const SCEV*> {
640  public:
641    static const SCEV *rewrite(const SCEV *Scev, ScalarEvolution &SE,
642                               ValueToValueMap &Map,
643                               bool InterpretConsts = false) {
644      SCEVParameterRewriter Rewriter(SE, Map, InterpretConsts);
645      return Rewriter.visit(Scev);
646    }
647
648    SCEVParameterRewriter(ScalarEvolution &S, ValueToValueMap &M, bool C)
649      : SE(S), Map(M), InterpretConsts(C) {}
650
651    const SCEV *visitConstant(const SCEVConstant *Constant) {
652      return Constant;
653    }
654
655    const SCEV *visitTruncateExpr(const SCEVTruncateExpr *Expr) {
656      const SCEV *Operand = visit(Expr->getOperand());
657      return SE.getTruncateExpr(Operand, Expr->getType());
658    }
659
660    const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
661      const SCEV *Operand = visit(Expr->getOperand());
662      return SE.getZeroExtendExpr(Operand, Expr->getType());
663    }
664
665    const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
666      const SCEV *Operand = visit(Expr->getOperand());
667      return SE.getSignExtendExpr(Operand, Expr->getType());
668    }
669
670    const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
671      SmallVector<const SCEV *, 2> Operands;
672      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
673        Operands.push_back(visit(Expr->getOperand(i)));
674      return SE.getAddExpr(Operands);
675    }
676
677    const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
678      SmallVector<const SCEV *, 2> Operands;
679      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
680        Operands.push_back(visit(Expr->getOperand(i)));
681      return SE.getMulExpr(Operands);
682    }
683
684    const SCEV *visitUDivExpr(const SCEVUDivExpr *Expr) {
685      return SE.getUDivExpr(visit(Expr->getLHS()), visit(Expr->getRHS()));
686    }
687
688    const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
689      SmallVector<const SCEV *, 2> Operands;
690      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
691        Operands.push_back(visit(Expr->getOperand(i)));
692      return SE.getAddRecExpr(Operands, Expr->getLoop(),
693                              Expr->getNoWrapFlags());
694    }
695
696    const SCEV *visitSMaxExpr(const SCEVSMaxExpr *Expr) {
697      SmallVector<const SCEV *, 2> Operands;
698      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
699        Operands.push_back(visit(Expr->getOperand(i)));
700      return SE.getSMaxExpr(Operands);
701    }
702
703    const SCEV *visitUMaxExpr(const SCEVUMaxExpr *Expr) {
704      SmallVector<const SCEV *, 2> Operands;
705      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
706        Operands.push_back(visit(Expr->getOperand(i)));
707      return SE.getUMaxExpr(Operands);
708    }
709
710    const SCEV *visitUnknown(const SCEVUnknown *Expr) {
711      Value *V = Expr->getValue();
712      if (Map.count(V)) {
713        Value *NV = Map[V];
714        if (InterpretConsts && isa<ConstantInt>(NV))
715          return SE.getConstant(cast<ConstantInt>(NV));
716        return SE.getUnknown(NV);
717      }
718      return Expr;
719    }
720
721    const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
722      return Expr;
723    }
724
725  private:
726    ScalarEvolution &SE;
727    ValueToValueMap &Map;
728    bool InterpretConsts;
729  };
730
731  typedef DenseMap<const Loop*, const SCEV*> LoopToScevMapT;
732
733  /// The SCEVApplyRewriter takes a scalar evolution expression and applies
734  /// the Map (Loop -> SCEV) to all AddRecExprs.
735  struct SCEVApplyRewriter
736    : public SCEVVisitor<SCEVApplyRewriter, const SCEV*> {
737  public:
738    static const SCEV *rewrite(const SCEV *Scev, LoopToScevMapT &Map,
739                               ScalarEvolution &SE) {
740      SCEVApplyRewriter Rewriter(SE, Map);
741      return Rewriter.visit(Scev);
742    }
743
744    SCEVApplyRewriter(ScalarEvolution &S, LoopToScevMapT &M)
745      : SE(S), Map(M) {}
746
747    const SCEV *visitConstant(const SCEVConstant *Constant) {
748      return Constant;
749    }
750
751    const SCEV *visitTruncateExpr(const SCEVTruncateExpr *Expr) {
752      const SCEV *Operand = visit(Expr->getOperand());
753      return SE.getTruncateExpr(Operand, Expr->getType());
754    }
755
756    const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
757      const SCEV *Operand = visit(Expr->getOperand());
758      return SE.getZeroExtendExpr(Operand, Expr->getType());
759    }
760
761    const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
762      const SCEV *Operand = visit(Expr->getOperand());
763      return SE.getSignExtendExpr(Operand, Expr->getType());
764    }
765
766    const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
767      SmallVector<const SCEV *, 2> Operands;
768      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
769        Operands.push_back(visit(Expr->getOperand(i)));
770      return SE.getAddExpr(Operands);
771    }
772
773    const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
774      SmallVector<const SCEV *, 2> Operands;
775      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
776        Operands.push_back(visit(Expr->getOperand(i)));
777      return SE.getMulExpr(Operands);
778    }
779
780    const SCEV *visitUDivExpr(const SCEVUDivExpr *Expr) {
781      return SE.getUDivExpr(visit(Expr->getLHS()), visit(Expr->getRHS()));
782    }
783
784    const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
785      SmallVector<const SCEV *, 2> Operands;
786      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
787        Operands.push_back(visit(Expr->getOperand(i)));
788
789      const Loop *L = Expr->getLoop();
790      const SCEV *Res = SE.getAddRecExpr(Operands, L, Expr->getNoWrapFlags());
791
792      if (0 == Map.count(L))
793        return Res;
794
795      const SCEVAddRecExpr *Rec = (const SCEVAddRecExpr *) Res;
796      return Rec->evaluateAtIteration(Map[L], SE);
797    }
798
799    const SCEV *visitSMaxExpr(const SCEVSMaxExpr *Expr) {
800      SmallVector<const SCEV *, 2> Operands;
801      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
802        Operands.push_back(visit(Expr->getOperand(i)));
803      return SE.getSMaxExpr(Operands);
804    }
805
806    const SCEV *visitUMaxExpr(const SCEVUMaxExpr *Expr) {
807      SmallVector<const SCEV *, 2> Operands;
808      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
809        Operands.push_back(visit(Expr->getOperand(i)));
810      return SE.getUMaxExpr(Operands);
811    }
812
813    const SCEV *visitUnknown(const SCEVUnknown *Expr) {
814      return Expr;
815    }
816
817    const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
818      return Expr;
819    }
820
821  private:
822    ScalarEvolution &SE;
823    LoopToScevMapT &Map;
824  };
825
826/// Applies the Map (Loop -> SCEV) to the given Scev.
827static inline const SCEV *apply(const SCEV *Scev, LoopToScevMapT &Map,
828                                ScalarEvolution &SE) {
829  return SCEVApplyRewriter::rewrite(Scev, Map, SE);
830}
831
832}
833
834#endif
835