1//===- ScalarEvolutionNormalization.cpp - See below -------------*- 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 implements utilities for working with "normalized" expressions.
11// See the comments at the top of ScalarEvolutionNormalization.h for details.
12//
13//===----------------------------------------------------------------------===//
14
15#include "llvm/IR/Dominators.h"
16#include "llvm/Analysis/LoopInfo.h"
17#include "llvm/Analysis/ScalarEvolutionExpressions.h"
18#include "llvm/Analysis/ScalarEvolutionNormalization.h"
19using namespace llvm;
20
21/// IVUseShouldUsePostIncValue - We have discovered a "User" of an IV expression
22/// and now we need to decide whether the user should use the preinc or post-inc
23/// value.  If this user should use the post-inc version of the IV, return true.
24///
25/// Choosing wrong here can break dominance properties (if we choose to use the
26/// post-inc value when we cannot) or it can end up adding extra live-ranges to
27/// the loop, resulting in reg-reg copies (if we use the pre-inc value when we
28/// should use the post-inc value).
29static bool IVUseShouldUsePostIncValue(Instruction *User, Value *Operand,
30                                       const Loop *L, DominatorTree *DT) {
31  // If the user is in the loop, use the preinc value.
32  if (L->contains(User)) return false;
33
34  BasicBlock *LatchBlock = L->getLoopLatch();
35  if (!LatchBlock)
36    return false;
37
38  // Ok, the user is outside of the loop.  If it is dominated by the latch
39  // block, use the post-inc value.
40  if (DT->dominates(LatchBlock, User->getParent()))
41    return true;
42
43  // There is one case we have to be careful of: PHI nodes.  These little guys
44  // can live in blocks that are not dominated by the latch block, but (since
45  // their uses occur in the predecessor block, not the block the PHI lives in)
46  // should still use the post-inc value.  Check for this case now.
47  PHINode *PN = dyn_cast<PHINode>(User);
48  if (!PN || !Operand) return false; // not a phi, not dominated by latch block.
49
50  // Look at all of the uses of Operand by the PHI node.  If any use corresponds
51  // to a block that is not dominated by the latch block, give up and use the
52  // preincremented value.
53  for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
54    if (PN->getIncomingValue(i) == Operand &&
55        !DT->dominates(LatchBlock, PN->getIncomingBlock(i)))
56      return false;
57
58  // Okay, all uses of Operand by PN are in predecessor blocks that really are
59  // dominated by the latch block.  Use the post-incremented value.
60  return true;
61}
62
63namespace {
64
65/// Hold the state used during post-inc expression transformation, including a
66/// map of transformed expressions.
67class PostIncTransform {
68  TransformKind Kind;
69  PostIncLoopSet &Loops;
70  ScalarEvolution &SE;
71  DominatorTree &DT;
72
73  DenseMap<const SCEV*, const SCEV*> Transformed;
74
75public:
76  PostIncTransform(TransformKind kind, PostIncLoopSet &loops,
77                   ScalarEvolution &se, DominatorTree &dt):
78    Kind(kind), Loops(loops), SE(se), DT(dt) {}
79
80  const SCEV *TransformSubExpr(const SCEV *S, Instruction *User,
81                               Value *OperandValToReplace);
82
83protected:
84  const SCEV *TransformImpl(const SCEV *S, Instruction *User,
85                            Value *OperandValToReplace);
86};
87
88} // namespace
89
90/// Implement post-inc transformation for all valid expression types.
91const SCEV *PostIncTransform::
92TransformImpl(const SCEV *S, Instruction *User, Value *OperandValToReplace) {
93
94  if (const SCEVCastExpr *X = dyn_cast<SCEVCastExpr>(S)) {
95    const SCEV *O = X->getOperand();
96    const SCEV *N = TransformSubExpr(O, User, OperandValToReplace);
97    if (O != N)
98      switch (S->getSCEVType()) {
99      case scZeroExtend: return SE.getZeroExtendExpr(N, S->getType());
100      case scSignExtend: return SE.getSignExtendExpr(N, S->getType());
101      case scTruncate: return SE.getTruncateExpr(N, S->getType());
102      default: llvm_unreachable("Unexpected SCEVCastExpr kind!");
103      }
104    return S;
105  }
106
107  if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S)) {
108    // An addrec. This is the interesting part.
109    SmallVector<const SCEV *, 8> Operands;
110    const Loop *L = AR->getLoop();
111    // The addrec conceptually uses its operands at loop entry.
112    Instruction *LUser = L->getHeader()->begin();
113    // Transform each operand.
114    for (SCEVNAryExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
115         I != E; ++I) {
116      Operands.push_back(TransformSubExpr(*I, LUser, nullptr));
117    }
118    // Conservatively use AnyWrap until/unless we need FlagNW.
119    const SCEV *Result = SE.getAddRecExpr(Operands, L, SCEV::FlagAnyWrap);
120    switch (Kind) {
121    case NormalizeAutodetect:
122      // Normalize this SCEV by subtracting the expression for the final step.
123      // We only allow affine AddRecs to be normalized, otherwise we would not
124      // be able to correctly denormalize.
125      // e.g. {1,+,3,+,2} == {-2,+,1,+,2} + {3,+,2}
126      // Normalized form:   {-2,+,1,+,2}
127      // Denormalized form: {1,+,3,+,2}
128      //
129      // However, denormalization would use the a different step expression than
130      // normalization (see getPostIncExpr), generating the wrong final
131      // expression: {-2,+,1,+,2} + {1,+,2} => {-1,+,3,+,2}
132      if (AR->isAffine() &&
133          IVUseShouldUsePostIncValue(User, OperandValToReplace, L, &DT)) {
134        const SCEV *TransformedStep =
135          TransformSubExpr(AR->getStepRecurrence(SE),
136                           User, OperandValToReplace);
137        Result = SE.getMinusSCEV(Result, TransformedStep);
138        Loops.insert(L);
139      }
140#if 0
141      // This assert is conceptually correct, but ScalarEvolution currently
142      // sometimes fails to canonicalize two equal SCEVs to exactly the same
143      // form. It's possibly a pessimization when this happens, but it isn't a
144      // correctness problem, so disable this assert for now.
145      assert(S == TransformSubExpr(Result, User, OperandValToReplace) &&
146             "SCEV normalization is not invertible!");
147#endif
148      break;
149    case Normalize:
150      // We want to normalize step expression, because otherwise we might not be
151      // able to denormalize to the original expression.
152      //
153      // Here is an example what will happen if we don't normalize step:
154      //  ORIGINAL ISE:
155      //    {(100 /u {1,+,1}<%bb16>),+,(100 /u {1,+,1}<%bb16>)}<%bb25>
156      //  NORMALIZED ISE:
157      //    {((-1 * (100 /u {1,+,1}<%bb16>)) + (100 /u {0,+,1}<%bb16>)),+,
158      //     (100 /u {0,+,1}<%bb16>)}<%bb25>
159      //  DENORMALIZED BACK ISE:
160      //    {((2 * (100 /u {1,+,1}<%bb16>)) + (-1 * (100 /u {2,+,1}<%bb16>))),+,
161      //     (100 /u {1,+,1}<%bb16>)}<%bb25>
162      //  Note that the initial value changes after normalization +
163      //  denormalization, which isn't correct.
164      if (Loops.count(L)) {
165        const SCEV *TransformedStep =
166          TransformSubExpr(AR->getStepRecurrence(SE),
167                           User, OperandValToReplace);
168        Result = SE.getMinusSCEV(Result, TransformedStep);
169      }
170#if 0
171      // See the comment on the assert above.
172      assert(S == TransformSubExpr(Result, User, OperandValToReplace) &&
173             "SCEV normalization is not invertible!");
174#endif
175      break;
176    case Denormalize:
177      // Here we want to normalize step expressions for the same reasons, as
178      // stated above.
179      if (Loops.count(L)) {
180        const SCEV *TransformedStep =
181          TransformSubExpr(AR->getStepRecurrence(SE),
182                           User, OperandValToReplace);
183        Result = SE.getAddExpr(Result, TransformedStep);
184      }
185      break;
186    }
187    return Result;
188  }
189
190  if (const SCEVNAryExpr *X = dyn_cast<SCEVNAryExpr>(S)) {
191    SmallVector<const SCEV *, 8> Operands;
192    bool Changed = false;
193    // Transform each operand.
194    for (SCEVNAryExpr::op_iterator I = X->op_begin(), E = X->op_end();
195         I != E; ++I) {
196      const SCEV *O = *I;
197      const SCEV *N = TransformSubExpr(O, User, OperandValToReplace);
198      Changed |= N != O;
199      Operands.push_back(N);
200    }
201    // If any operand actually changed, return a transformed result.
202    if (Changed)
203      switch (S->getSCEVType()) {
204      case scAddExpr: return SE.getAddExpr(Operands);
205      case scMulExpr: return SE.getMulExpr(Operands);
206      case scSMaxExpr: return SE.getSMaxExpr(Operands);
207      case scUMaxExpr: return SE.getUMaxExpr(Operands);
208      default: llvm_unreachable("Unexpected SCEVNAryExpr kind!");
209      }
210    return S;
211  }
212
213  if (const SCEVUDivExpr *X = dyn_cast<SCEVUDivExpr>(S)) {
214    const SCEV *LO = X->getLHS();
215    const SCEV *RO = X->getRHS();
216    const SCEV *LN = TransformSubExpr(LO, User, OperandValToReplace);
217    const SCEV *RN = TransformSubExpr(RO, User, OperandValToReplace);
218    if (LO != LN || RO != RN)
219      return SE.getUDivExpr(LN, RN);
220    return S;
221  }
222
223  llvm_unreachable("Unexpected SCEV kind!");
224}
225
226/// Manage recursive transformation across an expression DAG. Revisiting
227/// expressions would lead to exponential recursion.
228const SCEV *PostIncTransform::
229TransformSubExpr(const SCEV *S, Instruction *User, Value *OperandValToReplace) {
230
231  if (isa<SCEVConstant>(S) || isa<SCEVUnknown>(S))
232    return S;
233
234  const SCEV *Result = Transformed.lookup(S);
235  if (Result)
236    return Result;
237
238  Result = TransformImpl(S, User, OperandValToReplace);
239  Transformed[S] = Result;
240  return Result;
241}
242
243/// Top level driver for transforming an expression DAG into its requested
244/// post-inc form (either "Normalized" or "Denormalized").
245const SCEV *llvm::TransformForPostIncUse(TransformKind Kind,
246                                         const SCEV *S,
247                                         Instruction *User,
248                                         Value *OperandValToReplace,
249                                         PostIncLoopSet &Loops,
250                                         ScalarEvolution &SE,
251                                         DominatorTree &DT) {
252  PostIncTransform Transform(Kind, Loops, SE, DT);
253  return Transform.TransformSubExpr(S, User, OperandValToReplace);
254}
255