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1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- 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 contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
13 //
14 // There are several aspects to this library.  First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
19 //
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node).  If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
25 //
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression.  These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
30 //
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
34 //
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
37 //
38 //===----------------------------------------------------------------------===//
39 //
40 // There are several good references for the techniques used in this analysis.
41 //
42 //  Chains of recurrences -- a method to expedite the evaluation
43 //  of closed-form functions
44 //  Olaf Bachmann, Paul S. Wang, Eugene V. Zima
45 //
46 //  On computational properties of chains of recurrences
47 //  Eugene V. Zima
48 //
49 //  Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 //  Robert A. van Engelen
51 //
52 //  Efficient Symbolic Analysis for Optimizing Compilers
53 //  Robert A. van Engelen
54 //
55 //  Using the chains of recurrences algebra for data dependence testing and
56 //  induction variable substitution
57 //  MS Thesis, Johnie Birch
58 //
59 //===----------------------------------------------------------------------===//
60 
61 #define DEBUG_TYPE "scalar-evolution"
62 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
63 #include "llvm/Constants.h"
64 #include "llvm/DerivedTypes.h"
65 #include "llvm/GlobalVariable.h"
66 #include "llvm/GlobalAlias.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/LLVMContext.h"
69 #include "llvm/Operator.h"
70 #include "llvm/Analysis/ConstantFolding.h"
71 #include "llvm/Analysis/Dominators.h"
72 #include "llvm/Analysis/InstructionSimplify.h"
73 #include "llvm/Analysis/LoopInfo.h"
74 #include "llvm/Analysis/ValueTracking.h"
75 #include "llvm/Assembly/Writer.h"
76 #include "llvm/Target/TargetData.h"
77 #include "llvm/Support/CommandLine.h"
78 #include "llvm/Support/ConstantRange.h"
79 #include "llvm/Support/Debug.h"
80 #include "llvm/Support/ErrorHandling.h"
81 #include "llvm/Support/GetElementPtrTypeIterator.h"
82 #include "llvm/Support/InstIterator.h"
83 #include "llvm/Support/MathExtras.h"
84 #include "llvm/Support/raw_ostream.h"
85 #include "llvm/ADT/Statistic.h"
86 #include "llvm/ADT/STLExtras.h"
87 #include "llvm/ADT/SmallPtrSet.h"
88 #include <algorithm>
89 using namespace llvm;
90 
91 STATISTIC(NumArrayLenItCounts,
92           "Number of trip counts computed with array length");
93 STATISTIC(NumTripCountsComputed,
94           "Number of loops with predictable loop counts");
95 STATISTIC(NumTripCountsNotComputed,
96           "Number of loops without predictable loop counts");
97 STATISTIC(NumBruteForceTripCountsComputed,
98           "Number of loops with trip counts computed by force");
99 
100 static cl::opt<unsigned>
101 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
102                         cl::desc("Maximum number of iterations SCEV will "
103                                  "symbolically execute a constant "
104                                  "derived loop"),
105                         cl::init(100));
106 
107 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
108                 "Scalar Evolution Analysis", false, true)
109 INITIALIZE_PASS_DEPENDENCY(LoopInfo)
110 INITIALIZE_PASS_DEPENDENCY(DominatorTree)
111 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
112                 "Scalar Evolution Analysis", false, true)
113 char ScalarEvolution::ID = 0;
114 
115 //===----------------------------------------------------------------------===//
116 //                           SCEV class definitions
117 //===----------------------------------------------------------------------===//
118 
119 //===----------------------------------------------------------------------===//
120 // Implementation of the SCEV class.
121 //
122 
dump() const123 void SCEV::dump() const {
124   print(dbgs());
125   dbgs() << '\n';
126 }
127 
print(raw_ostream & OS) const128 void SCEV::print(raw_ostream &OS) const {
129   switch (getSCEVType()) {
130   case scConstant:
131     WriteAsOperand(OS, cast<SCEVConstant>(this)->getValue(), false);
132     return;
133   case scTruncate: {
134     const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
135     const SCEV *Op = Trunc->getOperand();
136     OS << "(trunc " << *Op->getType() << " " << *Op << " to "
137        << *Trunc->getType() << ")";
138     return;
139   }
140   case scZeroExtend: {
141     const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
142     const SCEV *Op = ZExt->getOperand();
143     OS << "(zext " << *Op->getType() << " " << *Op << " to "
144        << *ZExt->getType() << ")";
145     return;
146   }
147   case scSignExtend: {
148     const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
149     const SCEV *Op = SExt->getOperand();
150     OS << "(sext " << *Op->getType() << " " << *Op << " to "
151        << *SExt->getType() << ")";
152     return;
153   }
154   case scAddRecExpr: {
155     const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
156     OS << "{" << *AR->getOperand(0);
157     for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
158       OS << ",+," << *AR->getOperand(i);
159     OS << "}<";
160     if (AR->getNoWrapFlags(FlagNUW))
161       OS << "nuw><";
162     if (AR->getNoWrapFlags(FlagNSW))
163       OS << "nsw><";
164     if (AR->getNoWrapFlags(FlagNW) &&
165         !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
166       OS << "nw><";
167     WriteAsOperand(OS, AR->getLoop()->getHeader(), /*PrintType=*/false);
168     OS << ">";
169     return;
170   }
171   case scAddExpr:
172   case scMulExpr:
173   case scUMaxExpr:
174   case scSMaxExpr: {
175     const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
176     const char *OpStr = 0;
177     switch (NAry->getSCEVType()) {
178     case scAddExpr: OpStr = " + "; break;
179     case scMulExpr: OpStr = " * "; break;
180     case scUMaxExpr: OpStr = " umax "; break;
181     case scSMaxExpr: OpStr = " smax "; break;
182     }
183     OS << "(";
184     for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
185          I != E; ++I) {
186       OS << **I;
187       if (llvm::next(I) != E)
188         OS << OpStr;
189     }
190     OS << ")";
191     return;
192   }
193   case scUDivExpr: {
194     const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
195     OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
196     return;
197   }
198   case scUnknown: {
199     const SCEVUnknown *U = cast<SCEVUnknown>(this);
200     Type *AllocTy;
201     if (U->isSizeOf(AllocTy)) {
202       OS << "sizeof(" << *AllocTy << ")";
203       return;
204     }
205     if (U->isAlignOf(AllocTy)) {
206       OS << "alignof(" << *AllocTy << ")";
207       return;
208     }
209 
210     Type *CTy;
211     Constant *FieldNo;
212     if (U->isOffsetOf(CTy, FieldNo)) {
213       OS << "offsetof(" << *CTy << ", ";
214       WriteAsOperand(OS, FieldNo, false);
215       OS << ")";
216       return;
217     }
218 
219     // Otherwise just print it normally.
220     WriteAsOperand(OS, U->getValue(), false);
221     return;
222   }
223   case scCouldNotCompute:
224     OS << "***COULDNOTCOMPUTE***";
225     return;
226   default: break;
227   }
228   llvm_unreachable("Unknown SCEV kind!");
229 }
230 
getType() const231 Type *SCEV::getType() const {
232   switch (getSCEVType()) {
233   case scConstant:
234     return cast<SCEVConstant>(this)->getType();
235   case scTruncate:
236   case scZeroExtend:
237   case scSignExtend:
238     return cast<SCEVCastExpr>(this)->getType();
239   case scAddRecExpr:
240   case scMulExpr:
241   case scUMaxExpr:
242   case scSMaxExpr:
243     return cast<SCEVNAryExpr>(this)->getType();
244   case scAddExpr:
245     return cast<SCEVAddExpr>(this)->getType();
246   case scUDivExpr:
247     return cast<SCEVUDivExpr>(this)->getType();
248   case scUnknown:
249     return cast<SCEVUnknown>(this)->getType();
250   case scCouldNotCompute:
251     llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
252     return 0;
253   default: break;
254   }
255   llvm_unreachable("Unknown SCEV kind!");
256   return 0;
257 }
258 
isZero() const259 bool SCEV::isZero() const {
260   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
261     return SC->getValue()->isZero();
262   return false;
263 }
264 
isOne() const265 bool SCEV::isOne() const {
266   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
267     return SC->getValue()->isOne();
268   return false;
269 }
270 
isAllOnesValue() const271 bool SCEV::isAllOnesValue() const {
272   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
273     return SC->getValue()->isAllOnesValue();
274   return false;
275 }
276 
SCEVCouldNotCompute()277 SCEVCouldNotCompute::SCEVCouldNotCompute() :
278   SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
279 
classof(const SCEV * S)280 bool SCEVCouldNotCompute::classof(const SCEV *S) {
281   return S->getSCEVType() == scCouldNotCompute;
282 }
283 
getConstant(ConstantInt * V)284 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
285   FoldingSetNodeID ID;
286   ID.AddInteger(scConstant);
287   ID.AddPointer(V);
288   void *IP = 0;
289   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
290   SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
291   UniqueSCEVs.InsertNode(S, IP);
292   return S;
293 }
294 
getConstant(const APInt & Val)295 const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
296   return getConstant(ConstantInt::get(getContext(), Val));
297 }
298 
299 const SCEV *
getConstant(Type * Ty,uint64_t V,bool isSigned)300 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
301   IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
302   return getConstant(ConstantInt::get(ITy, V, isSigned));
303 }
304 
SCEVCastExpr(const FoldingSetNodeIDRef ID,unsigned SCEVTy,const SCEV * op,Type * ty)305 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
306                            unsigned SCEVTy, const SCEV *op, Type *ty)
307   : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
308 
SCEVTruncateExpr(const FoldingSetNodeIDRef ID,const SCEV * op,Type * ty)309 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
310                                    const SCEV *op, Type *ty)
311   : SCEVCastExpr(ID, scTruncate, op, ty) {
312   assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
313          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
314          "Cannot truncate non-integer value!");
315 }
316 
SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,const SCEV * op,Type * ty)317 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
318                                        const SCEV *op, Type *ty)
319   : SCEVCastExpr(ID, scZeroExtend, op, ty) {
320   assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
321          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
322          "Cannot zero extend non-integer value!");
323 }
324 
SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,const SCEV * op,Type * ty)325 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
326                                        const SCEV *op, Type *ty)
327   : SCEVCastExpr(ID, scSignExtend, op, ty) {
328   assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
329          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
330          "Cannot sign extend non-integer value!");
331 }
332 
deleted()333 void SCEVUnknown::deleted() {
334   // Clear this SCEVUnknown from various maps.
335   SE->forgetMemoizedResults(this);
336 
337   // Remove this SCEVUnknown from the uniquing map.
338   SE->UniqueSCEVs.RemoveNode(this);
339 
340   // Release the value.
341   setValPtr(0);
342 }
343 
allUsesReplacedWith(Value * New)344 void SCEVUnknown::allUsesReplacedWith(Value *New) {
345   // Clear this SCEVUnknown from various maps.
346   SE->forgetMemoizedResults(this);
347 
348   // Remove this SCEVUnknown from the uniquing map.
349   SE->UniqueSCEVs.RemoveNode(this);
350 
351   // Update this SCEVUnknown to point to the new value. This is needed
352   // because there may still be outstanding SCEVs which still point to
353   // this SCEVUnknown.
354   setValPtr(New);
355 }
356 
isSizeOf(Type * & AllocTy) const357 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
358   if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
359     if (VCE->getOpcode() == Instruction::PtrToInt)
360       if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
361         if (CE->getOpcode() == Instruction::GetElementPtr &&
362             CE->getOperand(0)->isNullValue() &&
363             CE->getNumOperands() == 2)
364           if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
365             if (CI->isOne()) {
366               AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
367                                  ->getElementType();
368               return true;
369             }
370 
371   return false;
372 }
373 
isAlignOf(Type * & AllocTy) const374 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
375   if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
376     if (VCE->getOpcode() == Instruction::PtrToInt)
377       if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
378         if (CE->getOpcode() == Instruction::GetElementPtr &&
379             CE->getOperand(0)->isNullValue()) {
380           Type *Ty =
381             cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
382           if (StructType *STy = dyn_cast<StructType>(Ty))
383             if (!STy->isPacked() &&
384                 CE->getNumOperands() == 3 &&
385                 CE->getOperand(1)->isNullValue()) {
386               if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
387                 if (CI->isOne() &&
388                     STy->getNumElements() == 2 &&
389                     STy->getElementType(0)->isIntegerTy(1)) {
390                   AllocTy = STy->getElementType(1);
391                   return true;
392                 }
393             }
394         }
395 
396   return false;
397 }
398 
isOffsetOf(Type * & CTy,Constant * & FieldNo) const399 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
400   if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
401     if (VCE->getOpcode() == Instruction::PtrToInt)
402       if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
403         if (CE->getOpcode() == Instruction::GetElementPtr &&
404             CE->getNumOperands() == 3 &&
405             CE->getOperand(0)->isNullValue() &&
406             CE->getOperand(1)->isNullValue()) {
407           Type *Ty =
408             cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
409           // Ignore vector types here so that ScalarEvolutionExpander doesn't
410           // emit getelementptrs that index into vectors.
411           if (Ty->isStructTy() || Ty->isArrayTy()) {
412             CTy = Ty;
413             FieldNo = CE->getOperand(2);
414             return true;
415           }
416         }
417 
418   return false;
419 }
420 
421 //===----------------------------------------------------------------------===//
422 //                               SCEV Utilities
423 //===----------------------------------------------------------------------===//
424 
425 namespace {
426   /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
427   /// than the complexity of the RHS.  This comparator is used to canonicalize
428   /// expressions.
429   class SCEVComplexityCompare {
430     const LoopInfo *const LI;
431   public:
SCEVComplexityCompare(const LoopInfo * li)432     explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
433 
434     // Return true or false if LHS is less than, or at least RHS, respectively.
operator ()(const SCEV * LHS,const SCEV * RHS) const435     bool operator()(const SCEV *LHS, const SCEV *RHS) const {
436       return compare(LHS, RHS) < 0;
437     }
438 
439     // Return negative, zero, or positive, if LHS is less than, equal to, or
440     // greater than RHS, respectively. A three-way result allows recursive
441     // comparisons to be more efficient.
compare(const SCEV * LHS,const SCEV * RHS) const442     int compare(const SCEV *LHS, const SCEV *RHS) const {
443       // Fast-path: SCEVs are uniqued so we can do a quick equality check.
444       if (LHS == RHS)
445         return 0;
446 
447       // Primarily, sort the SCEVs by their getSCEVType().
448       unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
449       if (LType != RType)
450         return (int)LType - (int)RType;
451 
452       // Aside from the getSCEVType() ordering, the particular ordering
453       // isn't very important except that it's beneficial to be consistent,
454       // so that (a + b) and (b + a) don't end up as different expressions.
455       switch (LType) {
456       case scUnknown: {
457         const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
458         const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
459 
460         // Sort SCEVUnknown values with some loose heuristics. TODO: This is
461         // not as complete as it could be.
462         const Value *LV = LU->getValue(), *RV = RU->getValue();
463 
464         // Order pointer values after integer values. This helps SCEVExpander
465         // form GEPs.
466         bool LIsPointer = LV->getType()->isPointerTy(),
467              RIsPointer = RV->getType()->isPointerTy();
468         if (LIsPointer != RIsPointer)
469           return (int)LIsPointer - (int)RIsPointer;
470 
471         // Compare getValueID values.
472         unsigned LID = LV->getValueID(),
473                  RID = RV->getValueID();
474         if (LID != RID)
475           return (int)LID - (int)RID;
476 
477         // Sort arguments by their position.
478         if (const Argument *LA = dyn_cast<Argument>(LV)) {
479           const Argument *RA = cast<Argument>(RV);
480           unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
481           return (int)LArgNo - (int)RArgNo;
482         }
483 
484         // For instructions, compare their loop depth, and their operand
485         // count.  This is pretty loose.
486         if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
487           const Instruction *RInst = cast<Instruction>(RV);
488 
489           // Compare loop depths.
490           const BasicBlock *LParent = LInst->getParent(),
491                            *RParent = RInst->getParent();
492           if (LParent != RParent) {
493             unsigned LDepth = LI->getLoopDepth(LParent),
494                      RDepth = LI->getLoopDepth(RParent);
495             if (LDepth != RDepth)
496               return (int)LDepth - (int)RDepth;
497           }
498 
499           // Compare the number of operands.
500           unsigned LNumOps = LInst->getNumOperands(),
501                    RNumOps = RInst->getNumOperands();
502           return (int)LNumOps - (int)RNumOps;
503         }
504 
505         return 0;
506       }
507 
508       case scConstant: {
509         const SCEVConstant *LC = cast<SCEVConstant>(LHS);
510         const SCEVConstant *RC = cast<SCEVConstant>(RHS);
511 
512         // Compare constant values.
513         const APInt &LA = LC->getValue()->getValue();
514         const APInt &RA = RC->getValue()->getValue();
515         unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
516         if (LBitWidth != RBitWidth)
517           return (int)LBitWidth - (int)RBitWidth;
518         return LA.ult(RA) ? -1 : 1;
519       }
520 
521       case scAddRecExpr: {
522         const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
523         const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
524 
525         // Compare addrec loop depths.
526         const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
527         if (LLoop != RLoop) {
528           unsigned LDepth = LLoop->getLoopDepth(),
529                    RDepth = RLoop->getLoopDepth();
530           if (LDepth != RDepth)
531             return (int)LDepth - (int)RDepth;
532         }
533 
534         // Addrec complexity grows with operand count.
535         unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
536         if (LNumOps != RNumOps)
537           return (int)LNumOps - (int)RNumOps;
538 
539         // Lexicographically compare.
540         for (unsigned i = 0; i != LNumOps; ++i) {
541           long X = compare(LA->getOperand(i), RA->getOperand(i));
542           if (X != 0)
543             return X;
544         }
545 
546         return 0;
547       }
548 
549       case scAddExpr:
550       case scMulExpr:
551       case scSMaxExpr:
552       case scUMaxExpr: {
553         const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
554         const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
555 
556         // Lexicographically compare n-ary expressions.
557         unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
558         for (unsigned i = 0; i != LNumOps; ++i) {
559           if (i >= RNumOps)
560             return 1;
561           long X = compare(LC->getOperand(i), RC->getOperand(i));
562           if (X != 0)
563             return X;
564         }
565         return (int)LNumOps - (int)RNumOps;
566       }
567 
568       case scUDivExpr: {
569         const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
570         const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
571 
572         // Lexicographically compare udiv expressions.
573         long X = compare(LC->getLHS(), RC->getLHS());
574         if (X != 0)
575           return X;
576         return compare(LC->getRHS(), RC->getRHS());
577       }
578 
579       case scTruncate:
580       case scZeroExtend:
581       case scSignExtend: {
582         const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
583         const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
584 
585         // Compare cast expressions by operand.
586         return compare(LC->getOperand(), RC->getOperand());
587       }
588 
589       default:
590         break;
591       }
592 
593       llvm_unreachable("Unknown SCEV kind!");
594       return 0;
595     }
596   };
597 }
598 
599 /// GroupByComplexity - Given a list of SCEV objects, order them by their
600 /// complexity, and group objects of the same complexity together by value.
601 /// When this routine is finished, we know that any duplicates in the vector are
602 /// consecutive and that complexity is monotonically increasing.
603 ///
604 /// Note that we go take special precautions to ensure that we get deterministic
605 /// results from this routine.  In other words, we don't want the results of
606 /// this to depend on where the addresses of various SCEV objects happened to
607 /// land in memory.
608 ///
GroupByComplexity(SmallVectorImpl<const SCEV * > & Ops,LoopInfo * LI)609 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
610                               LoopInfo *LI) {
611   if (Ops.size() < 2) return;  // Noop
612   if (Ops.size() == 2) {
613     // This is the common case, which also happens to be trivially simple.
614     // Special case it.
615     const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
616     if (SCEVComplexityCompare(LI)(RHS, LHS))
617       std::swap(LHS, RHS);
618     return;
619   }
620 
621   // Do the rough sort by complexity.
622   std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
623 
624   // Now that we are sorted by complexity, group elements of the same
625   // complexity.  Note that this is, at worst, N^2, but the vector is likely to
626   // be extremely short in practice.  Note that we take this approach because we
627   // do not want to depend on the addresses of the objects we are grouping.
628   for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
629     const SCEV *S = Ops[i];
630     unsigned Complexity = S->getSCEVType();
631 
632     // If there are any objects of the same complexity and same value as this
633     // one, group them.
634     for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
635       if (Ops[j] == S) { // Found a duplicate.
636         // Move it to immediately after i'th element.
637         std::swap(Ops[i+1], Ops[j]);
638         ++i;   // no need to rescan it.
639         if (i == e-2) return;  // Done!
640       }
641     }
642   }
643 }
644 
645 
646 
647 //===----------------------------------------------------------------------===//
648 //                      Simple SCEV method implementations
649 //===----------------------------------------------------------------------===//
650 
651 /// BinomialCoefficient - Compute BC(It, K).  The result has width W.
652 /// Assume, K > 0.
BinomialCoefficient(const SCEV * It,unsigned K,ScalarEvolution & SE,Type * ResultTy)653 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
654                                        ScalarEvolution &SE,
655                                        Type *ResultTy) {
656   // Handle the simplest case efficiently.
657   if (K == 1)
658     return SE.getTruncateOrZeroExtend(It, ResultTy);
659 
660   // We are using the following formula for BC(It, K):
661   //
662   //   BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
663   //
664   // Suppose, W is the bitwidth of the return value.  We must be prepared for
665   // overflow.  Hence, we must assure that the result of our computation is
666   // equal to the accurate one modulo 2^W.  Unfortunately, division isn't
667   // safe in modular arithmetic.
668   //
669   // However, this code doesn't use exactly that formula; the formula it uses
670   // is something like the following, where T is the number of factors of 2 in
671   // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
672   // exponentiation:
673   //
674   //   BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
675   //
676   // This formula is trivially equivalent to the previous formula.  However,
677   // this formula can be implemented much more efficiently.  The trick is that
678   // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
679   // arithmetic.  To do exact division in modular arithmetic, all we have
680   // to do is multiply by the inverse.  Therefore, this step can be done at
681   // width W.
682   //
683   // The next issue is how to safely do the division by 2^T.  The way this
684   // is done is by doing the multiplication step at a width of at least W + T
685   // bits.  This way, the bottom W+T bits of the product are accurate. Then,
686   // when we perform the division by 2^T (which is equivalent to a right shift
687   // by T), the bottom W bits are accurate.  Extra bits are okay; they'll get
688   // truncated out after the division by 2^T.
689   //
690   // In comparison to just directly using the first formula, this technique
691   // is much more efficient; using the first formula requires W * K bits,
692   // but this formula less than W + K bits. Also, the first formula requires
693   // a division step, whereas this formula only requires multiplies and shifts.
694   //
695   // It doesn't matter whether the subtraction step is done in the calculation
696   // width or the input iteration count's width; if the subtraction overflows,
697   // the result must be zero anyway.  We prefer here to do it in the width of
698   // the induction variable because it helps a lot for certain cases; CodeGen
699   // isn't smart enough to ignore the overflow, which leads to much less
700   // efficient code if the width of the subtraction is wider than the native
701   // register width.
702   //
703   // (It's possible to not widen at all by pulling out factors of 2 before
704   // the multiplication; for example, K=2 can be calculated as
705   // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
706   // extra arithmetic, so it's not an obvious win, and it gets
707   // much more complicated for K > 3.)
708 
709   // Protection from insane SCEVs; this bound is conservative,
710   // but it probably doesn't matter.
711   if (K > 1000)
712     return SE.getCouldNotCompute();
713 
714   unsigned W = SE.getTypeSizeInBits(ResultTy);
715 
716   // Calculate K! / 2^T and T; we divide out the factors of two before
717   // multiplying for calculating K! / 2^T to avoid overflow.
718   // Other overflow doesn't matter because we only care about the bottom
719   // W bits of the result.
720   APInt OddFactorial(W, 1);
721   unsigned T = 1;
722   for (unsigned i = 3; i <= K; ++i) {
723     APInt Mult(W, i);
724     unsigned TwoFactors = Mult.countTrailingZeros();
725     T += TwoFactors;
726     Mult = Mult.lshr(TwoFactors);
727     OddFactorial *= Mult;
728   }
729 
730   // We need at least W + T bits for the multiplication step
731   unsigned CalculationBits = W + T;
732 
733   // Calculate 2^T, at width T+W.
734   APInt DivFactor = APInt(CalculationBits, 1).shl(T);
735 
736   // Calculate the multiplicative inverse of K! / 2^T;
737   // this multiplication factor will perform the exact division by
738   // K! / 2^T.
739   APInt Mod = APInt::getSignedMinValue(W+1);
740   APInt MultiplyFactor = OddFactorial.zext(W+1);
741   MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
742   MultiplyFactor = MultiplyFactor.trunc(W);
743 
744   // Calculate the product, at width T+W
745   IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
746                                                       CalculationBits);
747   const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
748   for (unsigned i = 1; i != K; ++i) {
749     const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
750     Dividend = SE.getMulExpr(Dividend,
751                              SE.getTruncateOrZeroExtend(S, CalculationTy));
752   }
753 
754   // Divide by 2^T
755   const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
756 
757   // Truncate the result, and divide by K! / 2^T.
758 
759   return SE.getMulExpr(SE.getConstant(MultiplyFactor),
760                        SE.getTruncateOrZeroExtend(DivResult, ResultTy));
761 }
762 
763 /// evaluateAtIteration - Return the value of this chain of recurrences at
764 /// the specified iteration number.  We can evaluate this recurrence by
765 /// multiplying each element in the chain by the binomial coefficient
766 /// corresponding to it.  In other words, we can evaluate {A,+,B,+,C,+,D} as:
767 ///
768 ///   A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
769 ///
770 /// where BC(It, k) stands for binomial coefficient.
771 ///
evaluateAtIteration(const SCEV * It,ScalarEvolution & SE) const772 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
773                                                 ScalarEvolution &SE) const {
774   const SCEV *Result = getStart();
775   for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
776     // The computation is correct in the face of overflow provided that the
777     // multiplication is performed _after_ the evaluation of the binomial
778     // coefficient.
779     const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
780     if (isa<SCEVCouldNotCompute>(Coeff))
781       return Coeff;
782 
783     Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
784   }
785   return Result;
786 }
787 
788 //===----------------------------------------------------------------------===//
789 //                    SCEV Expression folder implementations
790 //===----------------------------------------------------------------------===//
791 
getTruncateExpr(const SCEV * Op,Type * Ty)792 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
793                                              Type *Ty) {
794   assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
795          "This is not a truncating conversion!");
796   assert(isSCEVable(Ty) &&
797          "This is not a conversion to a SCEVable type!");
798   Ty = getEffectiveSCEVType(Ty);
799 
800   FoldingSetNodeID ID;
801   ID.AddInteger(scTruncate);
802   ID.AddPointer(Op);
803   ID.AddPointer(Ty);
804   void *IP = 0;
805   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
806 
807   // Fold if the operand is constant.
808   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
809     return getConstant(
810       cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(),
811                                                getEffectiveSCEVType(Ty))));
812 
813   // trunc(trunc(x)) --> trunc(x)
814   if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
815     return getTruncateExpr(ST->getOperand(), Ty);
816 
817   // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
818   if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
819     return getTruncateOrSignExtend(SS->getOperand(), Ty);
820 
821   // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
822   if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
823     return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
824 
825   // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
826   // eliminate all the truncates.
827   if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
828     SmallVector<const SCEV *, 4> Operands;
829     bool hasTrunc = false;
830     for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
831       const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
832       hasTrunc = isa<SCEVTruncateExpr>(S);
833       Operands.push_back(S);
834     }
835     if (!hasTrunc)
836       return getAddExpr(Operands);
837     UniqueSCEVs.FindNodeOrInsertPos(ID, IP);  // Mutates IP, returns NULL.
838   }
839 
840   // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
841   // eliminate all the truncates.
842   if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
843     SmallVector<const SCEV *, 4> Operands;
844     bool hasTrunc = false;
845     for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
846       const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
847       hasTrunc = isa<SCEVTruncateExpr>(S);
848       Operands.push_back(S);
849     }
850     if (!hasTrunc)
851       return getMulExpr(Operands);
852     UniqueSCEVs.FindNodeOrInsertPos(ID, IP);  // Mutates IP, returns NULL.
853   }
854 
855   // If the input value is a chrec scev, truncate the chrec's operands.
856   if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
857     SmallVector<const SCEV *, 4> Operands;
858     for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
859       Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
860     return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
861   }
862 
863   // As a special case, fold trunc(undef) to undef. We don't want to
864   // know too much about SCEVUnknowns, but this special case is handy
865   // and harmless.
866   if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
867     if (isa<UndefValue>(U->getValue()))
868       return getSCEV(UndefValue::get(Ty));
869 
870   // The cast wasn't folded; create an explicit cast node. We can reuse
871   // the existing insert position since if we get here, we won't have
872   // made any changes which would invalidate it.
873   SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
874                                                  Op, Ty);
875   UniqueSCEVs.InsertNode(S, IP);
876   return S;
877 }
878 
getZeroExtendExpr(const SCEV * Op,Type * Ty)879 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
880                                                Type *Ty) {
881   assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
882          "This is not an extending conversion!");
883   assert(isSCEVable(Ty) &&
884          "This is not a conversion to a SCEVable type!");
885   Ty = getEffectiveSCEVType(Ty);
886 
887   // Fold if the operand is constant.
888   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
889     return getConstant(
890       cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(),
891                                               getEffectiveSCEVType(Ty))));
892 
893   // zext(zext(x)) --> zext(x)
894   if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
895     return getZeroExtendExpr(SZ->getOperand(), Ty);
896 
897   // Before doing any expensive analysis, check to see if we've already
898   // computed a SCEV for this Op and Ty.
899   FoldingSetNodeID ID;
900   ID.AddInteger(scZeroExtend);
901   ID.AddPointer(Op);
902   ID.AddPointer(Ty);
903   void *IP = 0;
904   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
905 
906   // zext(trunc(x)) --> zext(x) or x or trunc(x)
907   if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
908     // It's possible the bits taken off by the truncate were all zero bits. If
909     // so, we should be able to simplify this further.
910     const SCEV *X = ST->getOperand();
911     ConstantRange CR = getUnsignedRange(X);
912     unsigned TruncBits = getTypeSizeInBits(ST->getType());
913     unsigned NewBits = getTypeSizeInBits(Ty);
914     if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
915             CR.zextOrTrunc(NewBits)))
916       return getTruncateOrZeroExtend(X, Ty);
917   }
918 
919   // If the input value is a chrec scev, and we can prove that the value
920   // did not overflow the old, smaller, value, we can zero extend all of the
921   // operands (often constants).  This allows analysis of something like
922   // this:  for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
923   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
924     if (AR->isAffine()) {
925       const SCEV *Start = AR->getStart();
926       const SCEV *Step = AR->getStepRecurrence(*this);
927       unsigned BitWidth = getTypeSizeInBits(AR->getType());
928       const Loop *L = AR->getLoop();
929 
930       // If we have special knowledge that this addrec won't overflow,
931       // we don't need to do any further analysis.
932       if (AR->getNoWrapFlags(SCEV::FlagNUW))
933         return getAddRecExpr(getZeroExtendExpr(Start, Ty),
934                              getZeroExtendExpr(Step, Ty),
935                              L, AR->getNoWrapFlags());
936 
937       // Check whether the backedge-taken count is SCEVCouldNotCompute.
938       // Note that this serves two purposes: It filters out loops that are
939       // simply not analyzable, and it covers the case where this code is
940       // being called from within backedge-taken count analysis, such that
941       // attempting to ask for the backedge-taken count would likely result
942       // in infinite recursion. In the later case, the analysis code will
943       // cope with a conservative value, and it will take care to purge
944       // that value once it has finished.
945       const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
946       if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
947         // Manually compute the final value for AR, checking for
948         // overflow.
949 
950         // Check whether the backedge-taken count can be losslessly casted to
951         // the addrec's type. The count is always unsigned.
952         const SCEV *CastedMaxBECount =
953           getTruncateOrZeroExtend(MaxBECount, Start->getType());
954         const SCEV *RecastedMaxBECount =
955           getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
956         if (MaxBECount == RecastedMaxBECount) {
957           Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
958           // Check whether Start+Step*MaxBECount has no unsigned overflow.
959           const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
960           const SCEV *Add = getAddExpr(Start, ZMul);
961           const SCEV *OperandExtendedAdd =
962             getAddExpr(getZeroExtendExpr(Start, WideTy),
963                        getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
964                                   getZeroExtendExpr(Step, WideTy)));
965           if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) {
966             // Cache knowledge of AR NUW, which is propagated to this AddRec.
967             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
968             // Return the expression with the addrec on the outside.
969             return getAddRecExpr(getZeroExtendExpr(Start, Ty),
970                                  getZeroExtendExpr(Step, Ty),
971                                  L, AR->getNoWrapFlags());
972           }
973           // Similar to above, only this time treat the step value as signed.
974           // This covers loops that count down.
975           const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
976           Add = getAddExpr(Start, SMul);
977           OperandExtendedAdd =
978             getAddExpr(getZeroExtendExpr(Start, WideTy),
979                        getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
980                                   getSignExtendExpr(Step, WideTy)));
981           if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) {
982             // Cache knowledge of AR NW, which is propagated to this AddRec.
983             // Negative step causes unsigned wrap, but it still can't self-wrap.
984             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
985             // Return the expression with the addrec on the outside.
986             return getAddRecExpr(getZeroExtendExpr(Start, Ty),
987                                  getSignExtendExpr(Step, Ty),
988                                  L, AR->getNoWrapFlags());
989           }
990         }
991 
992         // If the backedge is guarded by a comparison with the pre-inc value
993         // the addrec is safe. Also, if the entry is guarded by a comparison
994         // with the start value and the backedge is guarded by a comparison
995         // with the post-inc value, the addrec is safe.
996         if (isKnownPositive(Step)) {
997           const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
998                                       getUnsignedRange(Step).getUnsignedMax());
999           if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1000               (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1001                isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1002                                            AR->getPostIncExpr(*this), N))) {
1003             // Cache knowledge of AR NUW, which is propagated to this AddRec.
1004             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1005             // Return the expression with the addrec on the outside.
1006             return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1007                                  getZeroExtendExpr(Step, Ty),
1008                                  L, AR->getNoWrapFlags());
1009           }
1010         } else if (isKnownNegative(Step)) {
1011           const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1012                                       getSignedRange(Step).getSignedMin());
1013           if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1014               (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1015                isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1016                                            AR->getPostIncExpr(*this), N))) {
1017             // Cache knowledge of AR NW, which is propagated to this AddRec.
1018             // Negative step causes unsigned wrap, but it still can't self-wrap.
1019             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1020             // Return the expression with the addrec on the outside.
1021             return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1022                                  getSignExtendExpr(Step, Ty),
1023                                  L, AR->getNoWrapFlags());
1024           }
1025         }
1026       }
1027     }
1028 
1029   // The cast wasn't folded; create an explicit cast node.
1030   // Recompute the insert position, as it may have been invalidated.
1031   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1032   SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1033                                                    Op, Ty);
1034   UniqueSCEVs.InsertNode(S, IP);
1035   return S;
1036 }
1037 
1038 // Get the limit of a recurrence such that incrementing by Step cannot cause
1039 // signed overflow as long as the value of the recurrence within the loop does
1040 // not exceed this limit before incrementing.
getOverflowLimitForStep(const SCEV * Step,ICmpInst::Predicate * Pred,ScalarEvolution * SE)1041 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1042                                            ICmpInst::Predicate *Pred,
1043                                            ScalarEvolution *SE) {
1044   unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1045   if (SE->isKnownPositive(Step)) {
1046     *Pred = ICmpInst::ICMP_SLT;
1047     return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1048                            SE->getSignedRange(Step).getSignedMax());
1049   }
1050   if (SE->isKnownNegative(Step)) {
1051     *Pred = ICmpInst::ICMP_SGT;
1052     return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1053                        SE->getSignedRange(Step).getSignedMin());
1054   }
1055   return 0;
1056 }
1057 
1058 // The recurrence AR has been shown to have no signed wrap. Typically, if we can
1059 // prove NSW for AR, then we can just as easily prove NSW for its preincrement
1060 // or postincrement sibling. This allows normalizing a sign extended AddRec as
1061 // such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a
1062 // result, the expression "Step + sext(PreIncAR)" is congruent with
1063 // "sext(PostIncAR)"
getPreStartForSignExtend(const SCEVAddRecExpr * AR,Type * Ty,ScalarEvolution * SE)1064 static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR,
1065                                             Type *Ty,
1066                                             ScalarEvolution *SE) {
1067   const Loop *L = AR->getLoop();
1068   const SCEV *Start = AR->getStart();
1069   const SCEV *Step = AR->getStepRecurrence(*SE);
1070 
1071   // Check for a simple looking step prior to loop entry.
1072   const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1073   if (!SA)
1074     return 0;
1075 
1076   // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1077   // subtraction is expensive. For this purpose, perform a quick and dirty
1078   // difference, by checking for Step in the operand list.
1079   SmallVector<const SCEV *, 4> DiffOps;
1080   for (SCEVAddExpr::op_iterator I = SA->op_begin(), E = SA->op_end();
1081        I != E; ++I) {
1082     if (*I != Step)
1083       DiffOps.push_back(*I);
1084   }
1085   if (DiffOps.size() == SA->getNumOperands())
1086     return 0;
1087 
1088   // This is a postinc AR. Check for overflow on the preinc recurrence using the
1089   // same three conditions that getSignExtendedExpr checks.
1090 
1091   // 1. NSW flags on the step increment.
1092   const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1093   const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1094     SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1095 
1096   if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW))
1097     return PreStart;
1098 
1099   // 2. Direct overflow check on the step operation's expression.
1100   unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1101   Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1102   const SCEV *OperandExtendedStart =
1103     SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1104                    SE->getSignExtendExpr(Step, WideTy));
1105   if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1106     // Cache knowledge of PreAR NSW.
1107     if (PreAR)
1108       const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1109     // FIXME: this optimization needs a unit test
1110     DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1111     return PreStart;
1112   }
1113 
1114   // 3. Loop precondition.
1115   ICmpInst::Predicate Pred;
1116   const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1117 
1118   if (OverflowLimit &&
1119       SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1120     return PreStart;
1121   }
1122   return 0;
1123 }
1124 
1125 // Get the normalized sign-extended expression for this AddRec's Start.
getSignExtendAddRecStart(const SCEVAddRecExpr * AR,Type * Ty,ScalarEvolution * SE)1126 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1127                                             Type *Ty,
1128                                             ScalarEvolution *SE) {
1129   const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1130   if (!PreStart)
1131     return SE->getSignExtendExpr(AR->getStart(), Ty);
1132 
1133   return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1134                         SE->getSignExtendExpr(PreStart, Ty));
1135 }
1136 
getSignExtendExpr(const SCEV * Op,Type * Ty)1137 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1138                                                Type *Ty) {
1139   assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1140          "This is not an extending conversion!");
1141   assert(isSCEVable(Ty) &&
1142          "This is not a conversion to a SCEVable type!");
1143   Ty = getEffectiveSCEVType(Ty);
1144 
1145   // Fold if the operand is constant.
1146   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1147     return getConstant(
1148       cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(),
1149                                               getEffectiveSCEVType(Ty))));
1150 
1151   // sext(sext(x)) --> sext(x)
1152   if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1153     return getSignExtendExpr(SS->getOperand(), Ty);
1154 
1155   // sext(zext(x)) --> zext(x)
1156   if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1157     return getZeroExtendExpr(SZ->getOperand(), Ty);
1158 
1159   // Before doing any expensive analysis, check to see if we've already
1160   // computed a SCEV for this Op and Ty.
1161   FoldingSetNodeID ID;
1162   ID.AddInteger(scSignExtend);
1163   ID.AddPointer(Op);
1164   ID.AddPointer(Ty);
1165   void *IP = 0;
1166   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1167 
1168   // If the input value is provably positive, build a zext instead.
1169   if (isKnownNonNegative(Op))
1170     return getZeroExtendExpr(Op, Ty);
1171 
1172   // sext(trunc(x)) --> sext(x) or x or trunc(x)
1173   if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1174     // It's possible the bits taken off by the truncate were all sign bits. If
1175     // so, we should be able to simplify this further.
1176     const SCEV *X = ST->getOperand();
1177     ConstantRange CR = getSignedRange(X);
1178     unsigned TruncBits = getTypeSizeInBits(ST->getType());
1179     unsigned NewBits = getTypeSizeInBits(Ty);
1180     if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1181             CR.sextOrTrunc(NewBits)))
1182       return getTruncateOrSignExtend(X, Ty);
1183   }
1184 
1185   // If the input value is a chrec scev, and we can prove that the value
1186   // did not overflow the old, smaller, value, we can sign extend all of the
1187   // operands (often constants).  This allows analysis of something like
1188   // this:  for (signed char X = 0; X < 100; ++X) { int Y = X; }
1189   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1190     if (AR->isAffine()) {
1191       const SCEV *Start = AR->getStart();
1192       const SCEV *Step = AR->getStepRecurrence(*this);
1193       unsigned BitWidth = getTypeSizeInBits(AR->getType());
1194       const Loop *L = AR->getLoop();
1195 
1196       // If we have special knowledge that this addrec won't overflow,
1197       // we don't need to do any further analysis.
1198       if (AR->getNoWrapFlags(SCEV::FlagNSW))
1199         return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1200                              getSignExtendExpr(Step, Ty),
1201                              L, SCEV::FlagNSW);
1202 
1203       // Check whether the backedge-taken count is SCEVCouldNotCompute.
1204       // Note that this serves two purposes: It filters out loops that are
1205       // simply not analyzable, and it covers the case where this code is
1206       // being called from within backedge-taken count analysis, such that
1207       // attempting to ask for the backedge-taken count would likely result
1208       // in infinite recursion. In the later case, the analysis code will
1209       // cope with a conservative value, and it will take care to purge
1210       // that value once it has finished.
1211       const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1212       if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1213         // Manually compute the final value for AR, checking for
1214         // overflow.
1215 
1216         // Check whether the backedge-taken count can be losslessly casted to
1217         // the addrec's type. The count is always unsigned.
1218         const SCEV *CastedMaxBECount =
1219           getTruncateOrZeroExtend(MaxBECount, Start->getType());
1220         const SCEV *RecastedMaxBECount =
1221           getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1222         if (MaxBECount == RecastedMaxBECount) {
1223           Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1224           // Check whether Start+Step*MaxBECount has no signed overflow.
1225           const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1226           const SCEV *Add = getAddExpr(Start, SMul);
1227           const SCEV *OperandExtendedAdd =
1228             getAddExpr(getSignExtendExpr(Start, WideTy),
1229                        getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1230                                   getSignExtendExpr(Step, WideTy)));
1231           if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) {
1232             // Cache knowledge of AR NSW, which is propagated to this AddRec.
1233             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1234             // Return the expression with the addrec on the outside.
1235             return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1236                                  getSignExtendExpr(Step, Ty),
1237                                  L, AR->getNoWrapFlags());
1238           }
1239           // Similar to above, only this time treat the step value as unsigned.
1240           // This covers loops that count up with an unsigned step.
1241           const SCEV *UMul = getMulExpr(CastedMaxBECount, Step);
1242           Add = getAddExpr(Start, UMul);
1243           OperandExtendedAdd =
1244             getAddExpr(getSignExtendExpr(Start, WideTy),
1245                        getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1246                                   getZeroExtendExpr(Step, WideTy)));
1247           if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) {
1248             // Cache knowledge of AR NSW, which is propagated to this AddRec.
1249             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1250             // Return the expression with the addrec on the outside.
1251             return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1252                                  getZeroExtendExpr(Step, Ty),
1253                                  L, AR->getNoWrapFlags());
1254           }
1255         }
1256 
1257         // If the backedge is guarded by a comparison with the pre-inc value
1258         // the addrec is safe. Also, if the entry is guarded by a comparison
1259         // with the start value and the backedge is guarded by a comparison
1260         // with the post-inc value, the addrec is safe.
1261         ICmpInst::Predicate Pred;
1262         const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1263         if (OverflowLimit &&
1264             (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1265              (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1266               isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1267                                           OverflowLimit)))) {
1268           // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1269           const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1270           return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1271                                getSignExtendExpr(Step, Ty),
1272                                L, AR->getNoWrapFlags());
1273         }
1274       }
1275     }
1276 
1277   // The cast wasn't folded; create an explicit cast node.
1278   // Recompute the insert position, as it may have been invalidated.
1279   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1280   SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1281                                                    Op, Ty);
1282   UniqueSCEVs.InsertNode(S, IP);
1283   return S;
1284 }
1285 
1286 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1287 /// unspecified bits out to the given type.
1288 ///
getAnyExtendExpr(const SCEV * Op,Type * Ty)1289 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1290                                               Type *Ty) {
1291   assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1292          "This is not an extending conversion!");
1293   assert(isSCEVable(Ty) &&
1294          "This is not a conversion to a SCEVable type!");
1295   Ty = getEffectiveSCEVType(Ty);
1296 
1297   // Sign-extend negative constants.
1298   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1299     if (SC->getValue()->getValue().isNegative())
1300       return getSignExtendExpr(Op, Ty);
1301 
1302   // Peel off a truncate cast.
1303   if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1304     const SCEV *NewOp = T->getOperand();
1305     if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1306       return getAnyExtendExpr(NewOp, Ty);
1307     return getTruncateOrNoop(NewOp, Ty);
1308   }
1309 
1310   // Next try a zext cast. If the cast is folded, use it.
1311   const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1312   if (!isa<SCEVZeroExtendExpr>(ZExt))
1313     return ZExt;
1314 
1315   // Next try a sext cast. If the cast is folded, use it.
1316   const SCEV *SExt = getSignExtendExpr(Op, Ty);
1317   if (!isa<SCEVSignExtendExpr>(SExt))
1318     return SExt;
1319 
1320   // Force the cast to be folded into the operands of an addrec.
1321   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1322     SmallVector<const SCEV *, 4> Ops;
1323     for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1324          I != E; ++I)
1325       Ops.push_back(getAnyExtendExpr(*I, Ty));
1326     return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1327   }
1328 
1329   // As a special case, fold anyext(undef) to undef. We don't want to
1330   // know too much about SCEVUnknowns, but this special case is handy
1331   // and harmless.
1332   if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
1333     if (isa<UndefValue>(U->getValue()))
1334       return getSCEV(UndefValue::get(Ty));
1335 
1336   // If the expression is obviously signed, use the sext cast value.
1337   if (isa<SCEVSMaxExpr>(Op))
1338     return SExt;
1339 
1340   // Absent any other information, use the zext cast value.
1341   return ZExt;
1342 }
1343 
1344 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1345 /// a list of operands to be added under the given scale, update the given
1346 /// map. This is a helper function for getAddRecExpr. As an example of
1347 /// what it does, given a sequence of operands that would form an add
1348 /// expression like this:
1349 ///
1350 ///    m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1351 ///
1352 /// where A and B are constants, update the map with these values:
1353 ///
1354 ///    (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1355 ///
1356 /// and add 13 + A*B*29 to AccumulatedConstant.
1357 /// This will allow getAddRecExpr to produce this:
1358 ///
1359 ///    13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1360 ///
1361 /// This form often exposes folding opportunities that are hidden in
1362 /// the original operand list.
1363 ///
1364 /// Return true iff it appears that any interesting folding opportunities
1365 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1366 /// the common case where no interesting opportunities are present, and
1367 /// is also used as a check to avoid infinite recursion.
1368 ///
1369 static bool
CollectAddOperandsWithScales(DenseMap<const SCEV *,APInt> & M,SmallVector<const SCEV *,8> & NewOps,APInt & AccumulatedConstant,const SCEV * const * Ops,size_t NumOperands,const APInt & Scale,ScalarEvolution & SE)1370 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1371                              SmallVector<const SCEV *, 8> &NewOps,
1372                              APInt &AccumulatedConstant,
1373                              const SCEV *const *Ops, size_t NumOperands,
1374                              const APInt &Scale,
1375                              ScalarEvolution &SE) {
1376   bool Interesting = false;
1377 
1378   // Iterate over the add operands. They are sorted, with constants first.
1379   unsigned i = 0;
1380   while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1381     ++i;
1382     // Pull a buried constant out to the outside.
1383     if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1384       Interesting = true;
1385     AccumulatedConstant += Scale * C->getValue()->getValue();
1386   }
1387 
1388   // Next comes everything else. We're especially interested in multiplies
1389   // here, but they're in the middle, so just visit the rest with one loop.
1390   for (; i != NumOperands; ++i) {
1391     const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1392     if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1393       APInt NewScale =
1394         Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1395       if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1396         // A multiplication of a constant with another add; recurse.
1397         const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1398         Interesting |=
1399           CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1400                                        Add->op_begin(), Add->getNumOperands(),
1401                                        NewScale, SE);
1402       } else {
1403         // A multiplication of a constant with some other value. Update
1404         // the map.
1405         SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1406         const SCEV *Key = SE.getMulExpr(MulOps);
1407         std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1408           M.insert(std::make_pair(Key, NewScale));
1409         if (Pair.second) {
1410           NewOps.push_back(Pair.first->first);
1411         } else {
1412           Pair.first->second += NewScale;
1413           // The map already had an entry for this value, which may indicate
1414           // a folding opportunity.
1415           Interesting = true;
1416         }
1417       }
1418     } else {
1419       // An ordinary operand. Update the map.
1420       std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1421         M.insert(std::make_pair(Ops[i], Scale));
1422       if (Pair.second) {
1423         NewOps.push_back(Pair.first->first);
1424       } else {
1425         Pair.first->second += Scale;
1426         // The map already had an entry for this value, which may indicate
1427         // a folding opportunity.
1428         Interesting = true;
1429       }
1430     }
1431   }
1432 
1433   return Interesting;
1434 }
1435 
1436 namespace {
1437   struct APIntCompare {
operator ()__anon07d303b50211::APIntCompare1438     bool operator()(const APInt &LHS, const APInt &RHS) const {
1439       return LHS.ult(RHS);
1440     }
1441   };
1442 }
1443 
1444 /// getAddExpr - Get a canonical add expression, or something simpler if
1445 /// possible.
getAddExpr(SmallVectorImpl<const SCEV * > & Ops,SCEV::NoWrapFlags Flags)1446 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1447                                         SCEV::NoWrapFlags Flags) {
1448   assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1449          "only nuw or nsw allowed");
1450   assert(!Ops.empty() && "Cannot get empty add!");
1451   if (Ops.size() == 1) return Ops[0];
1452 #ifndef NDEBUG
1453   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1454   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1455     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1456            "SCEVAddExpr operand types don't match!");
1457 #endif
1458 
1459   // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1460   // And vice-versa.
1461   int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1462   SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1463   if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1464     bool All = true;
1465     for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1466          E = Ops.end(); I != E; ++I)
1467       if (!isKnownNonNegative(*I)) {
1468         All = false;
1469         break;
1470       }
1471     if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1472   }
1473 
1474   // Sort by complexity, this groups all similar expression types together.
1475   GroupByComplexity(Ops, LI);
1476 
1477   // If there are any constants, fold them together.
1478   unsigned Idx = 0;
1479   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1480     ++Idx;
1481     assert(Idx < Ops.size());
1482     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1483       // We found two constants, fold them together!
1484       Ops[0] = getConstant(LHSC->getValue()->getValue() +
1485                            RHSC->getValue()->getValue());
1486       if (Ops.size() == 2) return Ops[0];
1487       Ops.erase(Ops.begin()+1);  // Erase the folded element
1488       LHSC = cast<SCEVConstant>(Ops[0]);
1489     }
1490 
1491     // If we are left with a constant zero being added, strip it off.
1492     if (LHSC->getValue()->isZero()) {
1493       Ops.erase(Ops.begin());
1494       --Idx;
1495     }
1496 
1497     if (Ops.size() == 1) return Ops[0];
1498   }
1499 
1500   // Okay, check to see if the same value occurs in the operand list more than
1501   // once.  If so, merge them together into an multiply expression.  Since we
1502   // sorted the list, these values are required to be adjacent.
1503   Type *Ty = Ops[0]->getType();
1504   bool FoundMatch = false;
1505   for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1506     if (Ops[i] == Ops[i+1]) {      //  X + Y + Y  -->  X + Y*2
1507       // Scan ahead to count how many equal operands there are.
1508       unsigned Count = 2;
1509       while (i+Count != e && Ops[i+Count] == Ops[i])
1510         ++Count;
1511       // Merge the values into a multiply.
1512       const SCEV *Scale = getConstant(Ty, Count);
1513       const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1514       if (Ops.size() == Count)
1515         return Mul;
1516       Ops[i] = Mul;
1517       Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1518       --i; e -= Count - 1;
1519       FoundMatch = true;
1520     }
1521   if (FoundMatch)
1522     return getAddExpr(Ops, Flags);
1523 
1524   // Check for truncates. If all the operands are truncated from the same
1525   // type, see if factoring out the truncate would permit the result to be
1526   // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1527   // if the contents of the resulting outer trunc fold to something simple.
1528   for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1529     const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1530     Type *DstType = Trunc->getType();
1531     Type *SrcType = Trunc->getOperand()->getType();
1532     SmallVector<const SCEV *, 8> LargeOps;
1533     bool Ok = true;
1534     // Check all the operands to see if they can be represented in the
1535     // source type of the truncate.
1536     for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1537       if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1538         if (T->getOperand()->getType() != SrcType) {
1539           Ok = false;
1540           break;
1541         }
1542         LargeOps.push_back(T->getOperand());
1543       } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1544         LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1545       } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1546         SmallVector<const SCEV *, 8> LargeMulOps;
1547         for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1548           if (const SCEVTruncateExpr *T =
1549                 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1550             if (T->getOperand()->getType() != SrcType) {
1551               Ok = false;
1552               break;
1553             }
1554             LargeMulOps.push_back(T->getOperand());
1555           } else if (const SCEVConstant *C =
1556                        dyn_cast<SCEVConstant>(M->getOperand(j))) {
1557             LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1558           } else {
1559             Ok = false;
1560             break;
1561           }
1562         }
1563         if (Ok)
1564           LargeOps.push_back(getMulExpr(LargeMulOps));
1565       } else {
1566         Ok = false;
1567         break;
1568       }
1569     }
1570     if (Ok) {
1571       // Evaluate the expression in the larger type.
1572       const SCEV *Fold = getAddExpr(LargeOps, Flags);
1573       // If it folds to something simple, use it. Otherwise, don't.
1574       if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1575         return getTruncateExpr(Fold, DstType);
1576     }
1577   }
1578 
1579   // Skip past any other cast SCEVs.
1580   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1581     ++Idx;
1582 
1583   // If there are add operands they would be next.
1584   if (Idx < Ops.size()) {
1585     bool DeletedAdd = false;
1586     while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1587       // If we have an add, expand the add operands onto the end of the operands
1588       // list.
1589       Ops.erase(Ops.begin()+Idx);
1590       Ops.append(Add->op_begin(), Add->op_end());
1591       DeletedAdd = true;
1592     }
1593 
1594     // If we deleted at least one add, we added operands to the end of the list,
1595     // and they are not necessarily sorted.  Recurse to resort and resimplify
1596     // any operands we just acquired.
1597     if (DeletedAdd)
1598       return getAddExpr(Ops);
1599   }
1600 
1601   // Skip over the add expression until we get to a multiply.
1602   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1603     ++Idx;
1604 
1605   // Check to see if there are any folding opportunities present with
1606   // operands multiplied by constant values.
1607   if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1608     uint64_t BitWidth = getTypeSizeInBits(Ty);
1609     DenseMap<const SCEV *, APInt> M;
1610     SmallVector<const SCEV *, 8> NewOps;
1611     APInt AccumulatedConstant(BitWidth, 0);
1612     if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1613                                      Ops.data(), Ops.size(),
1614                                      APInt(BitWidth, 1), *this)) {
1615       // Some interesting folding opportunity is present, so its worthwhile to
1616       // re-generate the operands list. Group the operands by constant scale,
1617       // to avoid multiplying by the same constant scale multiple times.
1618       std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1619       for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(),
1620            E = NewOps.end(); I != E; ++I)
1621         MulOpLists[M.find(*I)->second].push_back(*I);
1622       // Re-generate the operands list.
1623       Ops.clear();
1624       if (AccumulatedConstant != 0)
1625         Ops.push_back(getConstant(AccumulatedConstant));
1626       for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1627            I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1628         if (I->first != 0)
1629           Ops.push_back(getMulExpr(getConstant(I->first),
1630                                    getAddExpr(I->second)));
1631       if (Ops.empty())
1632         return getConstant(Ty, 0);
1633       if (Ops.size() == 1)
1634         return Ops[0];
1635       return getAddExpr(Ops);
1636     }
1637   }
1638 
1639   // If we are adding something to a multiply expression, make sure the
1640   // something is not already an operand of the multiply.  If so, merge it into
1641   // the multiply.
1642   for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1643     const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1644     for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1645       const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1646       if (isa<SCEVConstant>(MulOpSCEV))
1647         continue;
1648       for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1649         if (MulOpSCEV == Ops[AddOp]) {
1650           // Fold W + X + (X * Y * Z)  -->  W + (X * ((Y*Z)+1))
1651           const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1652           if (Mul->getNumOperands() != 2) {
1653             // If the multiply has more than two operands, we must get the
1654             // Y*Z term.
1655             SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1656                                                 Mul->op_begin()+MulOp);
1657             MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1658             InnerMul = getMulExpr(MulOps);
1659           }
1660           const SCEV *One = getConstant(Ty, 1);
1661           const SCEV *AddOne = getAddExpr(One, InnerMul);
1662           const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1663           if (Ops.size() == 2) return OuterMul;
1664           if (AddOp < Idx) {
1665             Ops.erase(Ops.begin()+AddOp);
1666             Ops.erase(Ops.begin()+Idx-1);
1667           } else {
1668             Ops.erase(Ops.begin()+Idx);
1669             Ops.erase(Ops.begin()+AddOp-1);
1670           }
1671           Ops.push_back(OuterMul);
1672           return getAddExpr(Ops);
1673         }
1674 
1675       // Check this multiply against other multiplies being added together.
1676       for (unsigned OtherMulIdx = Idx+1;
1677            OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1678            ++OtherMulIdx) {
1679         const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1680         // If MulOp occurs in OtherMul, we can fold the two multiplies
1681         // together.
1682         for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1683              OMulOp != e; ++OMulOp)
1684           if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1685             // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1686             const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1687             if (Mul->getNumOperands() != 2) {
1688               SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1689                                                   Mul->op_begin()+MulOp);
1690               MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1691               InnerMul1 = getMulExpr(MulOps);
1692             }
1693             const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1694             if (OtherMul->getNumOperands() != 2) {
1695               SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1696                                                   OtherMul->op_begin()+OMulOp);
1697               MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1698               InnerMul2 = getMulExpr(MulOps);
1699             }
1700             const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1701             const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1702             if (Ops.size() == 2) return OuterMul;
1703             Ops.erase(Ops.begin()+Idx);
1704             Ops.erase(Ops.begin()+OtherMulIdx-1);
1705             Ops.push_back(OuterMul);
1706             return getAddExpr(Ops);
1707           }
1708       }
1709     }
1710   }
1711 
1712   // If there are any add recurrences in the operands list, see if any other
1713   // added values are loop invariant.  If so, we can fold them into the
1714   // recurrence.
1715   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1716     ++Idx;
1717 
1718   // Scan over all recurrences, trying to fold loop invariants into them.
1719   for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1720     // Scan all of the other operands to this add and add them to the vector if
1721     // they are loop invariant w.r.t. the recurrence.
1722     SmallVector<const SCEV *, 8> LIOps;
1723     const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1724     const Loop *AddRecLoop = AddRec->getLoop();
1725     for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1726       if (isLoopInvariant(Ops[i], AddRecLoop)) {
1727         LIOps.push_back(Ops[i]);
1728         Ops.erase(Ops.begin()+i);
1729         --i; --e;
1730       }
1731 
1732     // If we found some loop invariants, fold them into the recurrence.
1733     if (!LIOps.empty()) {
1734       //  NLI + LI + {Start,+,Step}  -->  NLI + {LI+Start,+,Step}
1735       LIOps.push_back(AddRec->getStart());
1736 
1737       SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1738                                              AddRec->op_end());
1739       AddRecOps[0] = getAddExpr(LIOps);
1740 
1741       // Build the new addrec. Propagate the NUW and NSW flags if both the
1742       // outer add and the inner addrec are guaranteed to have no overflow.
1743       // Always propagate NW.
1744       Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
1745       const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
1746 
1747       // If all of the other operands were loop invariant, we are done.
1748       if (Ops.size() == 1) return NewRec;
1749 
1750       // Otherwise, add the folded AddRec by the non-invariant parts.
1751       for (unsigned i = 0;; ++i)
1752         if (Ops[i] == AddRec) {
1753           Ops[i] = NewRec;
1754           break;
1755         }
1756       return getAddExpr(Ops);
1757     }
1758 
1759     // Okay, if there weren't any loop invariants to be folded, check to see if
1760     // there are multiple AddRec's with the same loop induction variable being
1761     // added together.  If so, we can fold them.
1762     for (unsigned OtherIdx = Idx+1;
1763          OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1764          ++OtherIdx)
1765       if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1766         // Other + {A,+,B}<L> + {C,+,D}<L>  -->  Other + {A+C,+,B+D}<L>
1767         SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1768                                                AddRec->op_end());
1769         for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1770              ++OtherIdx)
1771           if (const SCEVAddRecExpr *OtherAddRec =
1772                 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1773             if (OtherAddRec->getLoop() == AddRecLoop) {
1774               for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1775                    i != e; ++i) {
1776                 if (i >= AddRecOps.size()) {
1777                   AddRecOps.append(OtherAddRec->op_begin()+i,
1778                                    OtherAddRec->op_end());
1779                   break;
1780                 }
1781                 AddRecOps[i] = getAddExpr(AddRecOps[i],
1782                                           OtherAddRec->getOperand(i));
1783               }
1784               Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1785             }
1786         // Step size has changed, so we cannot guarantee no self-wraparound.
1787         Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
1788         return getAddExpr(Ops);
1789       }
1790 
1791     // Otherwise couldn't fold anything into this recurrence.  Move onto the
1792     // next one.
1793   }
1794 
1795   // Okay, it looks like we really DO need an add expr.  Check to see if we
1796   // already have one, otherwise create a new one.
1797   FoldingSetNodeID ID;
1798   ID.AddInteger(scAddExpr);
1799   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1800     ID.AddPointer(Ops[i]);
1801   void *IP = 0;
1802   SCEVAddExpr *S =
1803     static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1804   if (!S) {
1805     const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1806     std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1807     S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1808                                         O, Ops.size());
1809     UniqueSCEVs.InsertNode(S, IP);
1810   }
1811   S->setNoWrapFlags(Flags);
1812   return S;
1813 }
1814 
umul_ov(uint64_t i,uint64_t j,bool & Overflow)1815 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
1816   uint64_t k = i*j;
1817   if (j > 1 && k / j != i) Overflow = true;
1818   return k;
1819 }
1820 
1821 /// Compute the result of "n choose k", the binomial coefficient.  If an
1822 /// intermediate computation overflows, Overflow will be set and the return will
1823 /// be garbage. Overflow is not cleared on absense of overflow.
Choose(uint64_t n,uint64_t k,bool & Overflow)1824 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
1825   // We use the multiplicative formula:
1826   //     n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
1827   // At each iteration, we take the n-th term of the numeral and divide by the
1828   // (k-n)th term of the denominator.  This division will always produce an
1829   // integral result, and helps reduce the chance of overflow in the
1830   // intermediate computations. However, we can still overflow even when the
1831   // final result would fit.
1832 
1833   if (n == 0 || n == k) return 1;
1834   if (k > n) return 0;
1835 
1836   if (k > n/2)
1837     k = n-k;
1838 
1839   uint64_t r = 1;
1840   for (uint64_t i = 1; i <= k; ++i) {
1841     r = umul_ov(r, n-(i-1), Overflow);
1842     r /= i;
1843   }
1844   return r;
1845 }
1846 
1847 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1848 /// possible.
getMulExpr(SmallVectorImpl<const SCEV * > & Ops,SCEV::NoWrapFlags Flags)1849 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1850                                         SCEV::NoWrapFlags Flags) {
1851   assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
1852          "only nuw or nsw allowed");
1853   assert(!Ops.empty() && "Cannot get empty mul!");
1854   if (Ops.size() == 1) return Ops[0];
1855 #ifndef NDEBUG
1856   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1857   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1858     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1859            "SCEVMulExpr operand types don't match!");
1860 #endif
1861 
1862   // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1863   // And vice-versa.
1864   int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1865   SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1866   if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1867     bool All = true;
1868     for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1869          E = Ops.end(); I != E; ++I)
1870       if (!isKnownNonNegative(*I)) {
1871         All = false;
1872         break;
1873       }
1874     if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1875   }
1876 
1877   // Sort by complexity, this groups all similar expression types together.
1878   GroupByComplexity(Ops, LI);
1879 
1880   // If there are any constants, fold them together.
1881   unsigned Idx = 0;
1882   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1883 
1884     // C1*(C2+V) -> C1*C2 + C1*V
1885     if (Ops.size() == 2)
1886       if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1887         if (Add->getNumOperands() == 2 &&
1888             isa<SCEVConstant>(Add->getOperand(0)))
1889           return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1890                             getMulExpr(LHSC, Add->getOperand(1)));
1891 
1892     ++Idx;
1893     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1894       // We found two constants, fold them together!
1895       ConstantInt *Fold = ConstantInt::get(getContext(),
1896                                            LHSC->getValue()->getValue() *
1897                                            RHSC->getValue()->getValue());
1898       Ops[0] = getConstant(Fold);
1899       Ops.erase(Ops.begin()+1);  // Erase the folded element
1900       if (Ops.size() == 1) return Ops[0];
1901       LHSC = cast<SCEVConstant>(Ops[0]);
1902     }
1903 
1904     // If we are left with a constant one being multiplied, strip it off.
1905     if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1906       Ops.erase(Ops.begin());
1907       --Idx;
1908     } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1909       // If we have a multiply of zero, it will always be zero.
1910       return Ops[0];
1911     } else if (Ops[0]->isAllOnesValue()) {
1912       // If we have a mul by -1 of an add, try distributing the -1 among the
1913       // add operands.
1914       if (Ops.size() == 2) {
1915         if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1916           SmallVector<const SCEV *, 4> NewOps;
1917           bool AnyFolded = false;
1918           for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
1919                  E = Add->op_end(); I != E; ++I) {
1920             const SCEV *Mul = getMulExpr(Ops[0], *I);
1921             if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1922             NewOps.push_back(Mul);
1923           }
1924           if (AnyFolded)
1925             return getAddExpr(NewOps);
1926         }
1927         else if (const SCEVAddRecExpr *
1928                  AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
1929           // Negation preserves a recurrence's no self-wrap property.
1930           SmallVector<const SCEV *, 4> Operands;
1931           for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
1932                  E = AddRec->op_end(); I != E; ++I) {
1933             Operands.push_back(getMulExpr(Ops[0], *I));
1934           }
1935           return getAddRecExpr(Operands, AddRec->getLoop(),
1936                                AddRec->getNoWrapFlags(SCEV::FlagNW));
1937         }
1938       }
1939     }
1940 
1941     if (Ops.size() == 1)
1942       return Ops[0];
1943   }
1944 
1945   // Skip over the add expression until we get to a multiply.
1946   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1947     ++Idx;
1948 
1949   // If there are mul operands inline them all into this expression.
1950   if (Idx < Ops.size()) {
1951     bool DeletedMul = false;
1952     while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1953       // If we have an mul, expand the mul operands onto the end of the operands
1954       // list.
1955       Ops.erase(Ops.begin()+Idx);
1956       Ops.append(Mul->op_begin(), Mul->op_end());
1957       DeletedMul = true;
1958     }
1959 
1960     // If we deleted at least one mul, we added operands to the end of the list,
1961     // and they are not necessarily sorted.  Recurse to resort and resimplify
1962     // any operands we just acquired.
1963     if (DeletedMul)
1964       return getMulExpr(Ops);
1965   }
1966 
1967   // If there are any add recurrences in the operands list, see if any other
1968   // added values are loop invariant.  If so, we can fold them into the
1969   // recurrence.
1970   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1971     ++Idx;
1972 
1973   // Scan over all recurrences, trying to fold loop invariants into them.
1974   for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1975     // Scan all of the other operands to this mul and add them to the vector if
1976     // they are loop invariant w.r.t. the recurrence.
1977     SmallVector<const SCEV *, 8> LIOps;
1978     const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1979     const Loop *AddRecLoop = AddRec->getLoop();
1980     for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1981       if (isLoopInvariant(Ops[i], AddRecLoop)) {
1982         LIOps.push_back(Ops[i]);
1983         Ops.erase(Ops.begin()+i);
1984         --i; --e;
1985       }
1986 
1987     // If we found some loop invariants, fold them into the recurrence.
1988     if (!LIOps.empty()) {
1989       //  NLI * LI * {Start,+,Step}  -->  NLI * {LI*Start,+,LI*Step}
1990       SmallVector<const SCEV *, 4> NewOps;
1991       NewOps.reserve(AddRec->getNumOperands());
1992       const SCEV *Scale = getMulExpr(LIOps);
1993       for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1994         NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1995 
1996       // Build the new addrec. Propagate the NUW and NSW flags if both the
1997       // outer mul and the inner addrec are guaranteed to have no overflow.
1998       //
1999       // No self-wrap cannot be guaranteed after changing the step size, but
2000       // will be inferred if either NUW or NSW is true.
2001       Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2002       const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2003 
2004       // If all of the other operands were loop invariant, we are done.
2005       if (Ops.size() == 1) return NewRec;
2006 
2007       // Otherwise, multiply the folded AddRec by the non-invariant parts.
2008       for (unsigned i = 0;; ++i)
2009         if (Ops[i] == AddRec) {
2010           Ops[i] = NewRec;
2011           break;
2012         }
2013       return getMulExpr(Ops);
2014     }
2015 
2016     // Okay, if there weren't any loop invariants to be folded, check to see if
2017     // there are multiple AddRec's with the same loop induction variable being
2018     // multiplied together.  If so, we can fold them.
2019     for (unsigned OtherIdx = Idx+1;
2020          OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2021          ++OtherIdx) {
2022       if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2023         // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2024         // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2025         //       choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2026         //   ]]],+,...up to x=2n}.
2027         // Note that the arguments to choose() are always integers with values
2028         // known at compile time, never SCEV objects.
2029         //
2030         // The implementation avoids pointless extra computations when the two
2031         // addrec's are of different length (mathematically, it's equivalent to
2032         // an infinite stream of zeros on the right).
2033         bool OpsModified = false;
2034         for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2035              ++OtherIdx)
2036           if (const SCEVAddRecExpr *OtherAddRec =
2037                 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2038             if (OtherAddRec->getLoop() == AddRecLoop) {
2039               bool Overflow = false;
2040               Type *Ty = AddRec->getType();
2041               bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2042               SmallVector<const SCEV*, 7> AddRecOps;
2043               for (int x = 0, xe = AddRec->getNumOperands() +
2044                      OtherAddRec->getNumOperands() - 1;
2045                    x != xe && !Overflow; ++x) {
2046                 const SCEV *Term = getConstant(Ty, 0);
2047                 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2048                   uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2049                   for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2050                          ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2051                        z < ze && !Overflow; ++z) {
2052                     uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2053                     uint64_t Coeff;
2054                     if (LargerThan64Bits)
2055                       Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2056                     else
2057                       Coeff = Coeff1*Coeff2;
2058                     const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2059                     const SCEV *Term1 = AddRec->getOperand(y-z);
2060                     const SCEV *Term2 = OtherAddRec->getOperand(z);
2061                     Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2062                   }
2063                 }
2064                 AddRecOps.push_back(Term);
2065               }
2066               if (!Overflow) {
2067                 const SCEV *NewAddRec = getAddRecExpr(AddRecOps,
2068                                                       AddRec->getLoop(),
2069                                                       SCEV::FlagAnyWrap);
2070                 if (Ops.size() == 2) return NewAddRec;
2071                 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec);
2072                 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2073                 OpsModified = true;
2074               }
2075             }
2076         if (OpsModified)
2077           return getMulExpr(Ops);
2078       }
2079     }
2080 
2081     // Otherwise couldn't fold anything into this recurrence.  Move onto the
2082     // next one.
2083   }
2084 
2085   // Okay, it looks like we really DO need an mul expr.  Check to see if we
2086   // already have one, otherwise create a new one.
2087   FoldingSetNodeID ID;
2088   ID.AddInteger(scMulExpr);
2089   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2090     ID.AddPointer(Ops[i]);
2091   void *IP = 0;
2092   SCEVMulExpr *S =
2093     static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2094   if (!S) {
2095     const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2096     std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2097     S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2098                                         O, Ops.size());
2099     UniqueSCEVs.InsertNode(S, IP);
2100   }
2101   S->setNoWrapFlags(Flags);
2102   return S;
2103 }
2104 
2105 /// getUDivExpr - Get a canonical unsigned division expression, or something
2106 /// simpler if possible.
getUDivExpr(const SCEV * LHS,const SCEV * RHS)2107 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2108                                          const SCEV *RHS) {
2109   assert(getEffectiveSCEVType(LHS->getType()) ==
2110          getEffectiveSCEVType(RHS->getType()) &&
2111          "SCEVUDivExpr operand types don't match!");
2112 
2113   if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2114     if (RHSC->getValue()->equalsInt(1))
2115       return LHS;                               // X udiv 1 --> x
2116     // If the denominator is zero, the result of the udiv is undefined. Don't
2117     // try to analyze it, because the resolution chosen here may differ from
2118     // the resolution chosen in other parts of the compiler.
2119     if (!RHSC->getValue()->isZero()) {
2120       // Determine if the division can be folded into the operands of
2121       // its operands.
2122       // TODO: Generalize this to non-constants by using known-bits information.
2123       Type *Ty = LHS->getType();
2124       unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2125       unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2126       // For non-power-of-two values, effectively round the value up to the
2127       // nearest power of two.
2128       if (!RHSC->getValue()->getValue().isPowerOf2())
2129         ++MaxShiftAmt;
2130       IntegerType *ExtTy =
2131         IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2132       if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2133         if (const SCEVConstant *Step =
2134             dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2135           // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2136           const APInt &StepInt = Step->getValue()->getValue();
2137           const APInt &DivInt = RHSC->getValue()->getValue();
2138           if (!StepInt.urem(DivInt) &&
2139               getZeroExtendExpr(AR, ExtTy) ==
2140               getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2141                             getZeroExtendExpr(Step, ExtTy),
2142                             AR->getLoop(), SCEV::FlagAnyWrap)) {
2143             SmallVector<const SCEV *, 4> Operands;
2144             for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2145               Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2146             return getAddRecExpr(Operands, AR->getLoop(),
2147                                  SCEV::FlagNW);
2148           }
2149           /// Get a canonical UDivExpr for a recurrence.
2150           /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2151           // We can currently only fold X%N if X is constant.
2152           const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2153           if (StartC && !DivInt.urem(StepInt) &&
2154               getZeroExtendExpr(AR, ExtTy) ==
2155               getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2156                             getZeroExtendExpr(Step, ExtTy),
2157                             AR->getLoop(), SCEV::FlagAnyWrap)) {
2158             const APInt &StartInt = StartC->getValue()->getValue();
2159             const APInt &StartRem = StartInt.urem(StepInt);
2160             if (StartRem != 0)
2161               LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2162                                   AR->getLoop(), SCEV::FlagNW);
2163           }
2164         }
2165       // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2166       if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2167         SmallVector<const SCEV *, 4> Operands;
2168         for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2169           Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2170         if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2171           // Find an operand that's safely divisible.
2172           for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2173             const SCEV *Op = M->getOperand(i);
2174             const SCEV *Div = getUDivExpr(Op, RHSC);
2175             if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2176               Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2177                                                       M->op_end());
2178               Operands[i] = Div;
2179               return getMulExpr(Operands);
2180             }
2181           }
2182       }
2183       // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2184       if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2185         SmallVector<const SCEV *, 4> Operands;
2186         for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2187           Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2188         if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2189           Operands.clear();
2190           for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2191             const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2192             if (isa<SCEVUDivExpr>(Op) ||
2193                 getMulExpr(Op, RHS) != A->getOperand(i))
2194               break;
2195             Operands.push_back(Op);
2196           }
2197           if (Operands.size() == A->getNumOperands())
2198             return getAddExpr(Operands);
2199         }
2200       }
2201 
2202       // Fold if both operands are constant.
2203       if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2204         Constant *LHSCV = LHSC->getValue();
2205         Constant *RHSCV = RHSC->getValue();
2206         return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2207                                                                    RHSCV)));
2208       }
2209     }
2210   }
2211 
2212   FoldingSetNodeID ID;
2213   ID.AddInteger(scUDivExpr);
2214   ID.AddPointer(LHS);
2215   ID.AddPointer(RHS);
2216   void *IP = 0;
2217   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2218   SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2219                                              LHS, RHS);
2220   UniqueSCEVs.InsertNode(S, IP);
2221   return S;
2222 }
2223 
2224 
2225 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2226 /// Simplify the expression as much as possible.
getAddRecExpr(const SCEV * Start,const SCEV * Step,const Loop * L,SCEV::NoWrapFlags Flags)2227 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2228                                            const Loop *L,
2229                                            SCEV::NoWrapFlags Flags) {
2230   SmallVector<const SCEV *, 4> Operands;
2231   Operands.push_back(Start);
2232   if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2233     if (StepChrec->getLoop() == L) {
2234       Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2235       return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2236     }
2237 
2238   Operands.push_back(Step);
2239   return getAddRecExpr(Operands, L, Flags);
2240 }
2241 
2242 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2243 /// Simplify the expression as much as possible.
2244 const SCEV *
getAddRecExpr(SmallVectorImpl<const SCEV * > & Operands,const Loop * L,SCEV::NoWrapFlags Flags)2245 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2246                                const Loop *L, SCEV::NoWrapFlags Flags) {
2247   if (Operands.size() == 1) return Operands[0];
2248 #ifndef NDEBUG
2249   Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2250   for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2251     assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2252            "SCEVAddRecExpr operand types don't match!");
2253   for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2254     assert(isLoopInvariant(Operands[i], L) &&
2255            "SCEVAddRecExpr operand is not loop-invariant!");
2256 #endif
2257 
2258   if (Operands.back()->isZero()) {
2259     Operands.pop_back();
2260     return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0}  -->  X
2261   }
2262 
2263   // It's tempting to want to call getMaxBackedgeTakenCount count here and
2264   // use that information to infer NUW and NSW flags. However, computing a
2265   // BE count requires calling getAddRecExpr, so we may not yet have a
2266   // meaningful BE count at this point (and if we don't, we'd be stuck
2267   // with a SCEVCouldNotCompute as the cached BE count).
2268 
2269   // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2270   // And vice-versa.
2271   int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2272   SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2273   if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2274     bool All = true;
2275     for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2276          E = Operands.end(); I != E; ++I)
2277       if (!isKnownNonNegative(*I)) {
2278         All = false;
2279         break;
2280       }
2281     if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2282   }
2283 
2284   // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2285   if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2286     const Loop *NestedLoop = NestedAR->getLoop();
2287     if (L->contains(NestedLoop) ?
2288         (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2289         (!NestedLoop->contains(L) &&
2290          DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2291       SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2292                                                   NestedAR->op_end());
2293       Operands[0] = NestedAR->getStart();
2294       // AddRecs require their operands be loop-invariant with respect to their
2295       // loops. Don't perform this transformation if it would break this
2296       // requirement.
2297       bool AllInvariant = true;
2298       for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2299         if (!isLoopInvariant(Operands[i], L)) {
2300           AllInvariant = false;
2301           break;
2302         }
2303       if (AllInvariant) {
2304         // Create a recurrence for the outer loop with the same step size.
2305         //
2306         // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2307         // inner recurrence has the same property.
2308         SCEV::NoWrapFlags OuterFlags =
2309           maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2310 
2311         NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2312         AllInvariant = true;
2313         for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2314           if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2315             AllInvariant = false;
2316             break;
2317           }
2318         if (AllInvariant) {
2319           // Ok, both add recurrences are valid after the transformation.
2320           //
2321           // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2322           // the outer recurrence has the same property.
2323           SCEV::NoWrapFlags InnerFlags =
2324             maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2325           return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2326         }
2327       }
2328       // Reset Operands to its original state.
2329       Operands[0] = NestedAR;
2330     }
2331   }
2332 
2333   // Okay, it looks like we really DO need an addrec expr.  Check to see if we
2334   // already have one, otherwise create a new one.
2335   FoldingSetNodeID ID;
2336   ID.AddInteger(scAddRecExpr);
2337   for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2338     ID.AddPointer(Operands[i]);
2339   ID.AddPointer(L);
2340   void *IP = 0;
2341   SCEVAddRecExpr *S =
2342     static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2343   if (!S) {
2344     const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2345     std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2346     S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2347                                            O, Operands.size(), L);
2348     UniqueSCEVs.InsertNode(S, IP);
2349   }
2350   S->setNoWrapFlags(Flags);
2351   return S;
2352 }
2353 
getSMaxExpr(const SCEV * LHS,const SCEV * RHS)2354 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2355                                          const SCEV *RHS) {
2356   SmallVector<const SCEV *, 2> Ops;
2357   Ops.push_back(LHS);
2358   Ops.push_back(RHS);
2359   return getSMaxExpr(Ops);
2360 }
2361 
2362 const SCEV *
getSMaxExpr(SmallVectorImpl<const SCEV * > & Ops)2363 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2364   assert(!Ops.empty() && "Cannot get empty smax!");
2365   if (Ops.size() == 1) return Ops[0];
2366 #ifndef NDEBUG
2367   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2368   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2369     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2370            "SCEVSMaxExpr operand types don't match!");
2371 #endif
2372 
2373   // Sort by complexity, this groups all similar expression types together.
2374   GroupByComplexity(Ops, LI);
2375 
2376   // If there are any constants, fold them together.
2377   unsigned Idx = 0;
2378   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2379     ++Idx;
2380     assert(Idx < Ops.size());
2381     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2382       // We found two constants, fold them together!
2383       ConstantInt *Fold = ConstantInt::get(getContext(),
2384                               APIntOps::smax(LHSC->getValue()->getValue(),
2385                                              RHSC->getValue()->getValue()));
2386       Ops[0] = getConstant(Fold);
2387       Ops.erase(Ops.begin()+1);  // Erase the folded element
2388       if (Ops.size() == 1) return Ops[0];
2389       LHSC = cast<SCEVConstant>(Ops[0]);
2390     }
2391 
2392     // If we are left with a constant minimum-int, strip it off.
2393     if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2394       Ops.erase(Ops.begin());
2395       --Idx;
2396     } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2397       // If we have an smax with a constant maximum-int, it will always be
2398       // maximum-int.
2399       return Ops[0];
2400     }
2401 
2402     if (Ops.size() == 1) return Ops[0];
2403   }
2404 
2405   // Find the first SMax
2406   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2407     ++Idx;
2408 
2409   // Check to see if one of the operands is an SMax. If so, expand its operands
2410   // onto our operand list, and recurse to simplify.
2411   if (Idx < Ops.size()) {
2412     bool DeletedSMax = false;
2413     while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2414       Ops.erase(Ops.begin()+Idx);
2415       Ops.append(SMax->op_begin(), SMax->op_end());
2416       DeletedSMax = true;
2417     }
2418 
2419     if (DeletedSMax)
2420       return getSMaxExpr(Ops);
2421   }
2422 
2423   // Okay, check to see if the same value occurs in the operand list twice.  If
2424   // so, delete one.  Since we sorted the list, these values are required to
2425   // be adjacent.
2426   for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2427     //  X smax Y smax Y  -->  X smax Y
2428     //  X smax Y         -->  X, if X is always greater than Y
2429     if (Ops[i] == Ops[i+1] ||
2430         isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2431       Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2432       --i; --e;
2433     } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2434       Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2435       --i; --e;
2436     }
2437 
2438   if (Ops.size() == 1) return Ops[0];
2439 
2440   assert(!Ops.empty() && "Reduced smax down to nothing!");
2441 
2442   // Okay, it looks like we really DO need an smax expr.  Check to see if we
2443   // already have one, otherwise create a new one.
2444   FoldingSetNodeID ID;
2445   ID.AddInteger(scSMaxExpr);
2446   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2447     ID.AddPointer(Ops[i]);
2448   void *IP = 0;
2449   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2450   const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2451   std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2452   SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2453                                              O, Ops.size());
2454   UniqueSCEVs.InsertNode(S, IP);
2455   return S;
2456 }
2457 
getUMaxExpr(const SCEV * LHS,const SCEV * RHS)2458 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2459                                          const SCEV *RHS) {
2460   SmallVector<const SCEV *, 2> Ops;
2461   Ops.push_back(LHS);
2462   Ops.push_back(RHS);
2463   return getUMaxExpr(Ops);
2464 }
2465 
2466 const SCEV *
getUMaxExpr(SmallVectorImpl<const SCEV * > & Ops)2467 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2468   assert(!Ops.empty() && "Cannot get empty umax!");
2469   if (Ops.size() == 1) return Ops[0];
2470 #ifndef NDEBUG
2471   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2472   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2473     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2474            "SCEVUMaxExpr operand types don't match!");
2475 #endif
2476 
2477   // Sort by complexity, this groups all similar expression types together.
2478   GroupByComplexity(Ops, LI);
2479 
2480   // If there are any constants, fold them together.
2481   unsigned Idx = 0;
2482   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2483     ++Idx;
2484     assert(Idx < Ops.size());
2485     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2486       // We found two constants, fold them together!
2487       ConstantInt *Fold = ConstantInt::get(getContext(),
2488                               APIntOps::umax(LHSC->getValue()->getValue(),
2489                                              RHSC->getValue()->getValue()));
2490       Ops[0] = getConstant(Fold);
2491       Ops.erase(Ops.begin()+1);  // Erase the folded element
2492       if (Ops.size() == 1) return Ops[0];
2493       LHSC = cast<SCEVConstant>(Ops[0]);
2494     }
2495 
2496     // If we are left with a constant minimum-int, strip it off.
2497     if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2498       Ops.erase(Ops.begin());
2499       --Idx;
2500     } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2501       // If we have an umax with a constant maximum-int, it will always be
2502       // maximum-int.
2503       return Ops[0];
2504     }
2505 
2506     if (Ops.size() == 1) return Ops[0];
2507   }
2508 
2509   // Find the first UMax
2510   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2511     ++Idx;
2512 
2513   // Check to see if one of the operands is a UMax. If so, expand its operands
2514   // onto our operand list, and recurse to simplify.
2515   if (Idx < Ops.size()) {
2516     bool DeletedUMax = false;
2517     while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2518       Ops.erase(Ops.begin()+Idx);
2519       Ops.append(UMax->op_begin(), UMax->op_end());
2520       DeletedUMax = true;
2521     }
2522 
2523     if (DeletedUMax)
2524       return getUMaxExpr(Ops);
2525   }
2526 
2527   // Okay, check to see if the same value occurs in the operand list twice.  If
2528   // so, delete one.  Since we sorted the list, these values are required to
2529   // be adjacent.
2530   for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2531     //  X umax Y umax Y  -->  X umax Y
2532     //  X umax Y         -->  X, if X is always greater than Y
2533     if (Ops[i] == Ops[i+1] ||
2534         isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2535       Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2536       --i; --e;
2537     } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2538       Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2539       --i; --e;
2540     }
2541 
2542   if (Ops.size() == 1) return Ops[0];
2543 
2544   assert(!Ops.empty() && "Reduced umax down to nothing!");
2545 
2546   // Okay, it looks like we really DO need a umax expr.  Check to see if we
2547   // already have one, otherwise create a new one.
2548   FoldingSetNodeID ID;
2549   ID.AddInteger(scUMaxExpr);
2550   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2551     ID.AddPointer(Ops[i]);
2552   void *IP = 0;
2553   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2554   const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2555   std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2556   SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2557                                              O, Ops.size());
2558   UniqueSCEVs.InsertNode(S, IP);
2559   return S;
2560 }
2561 
getSMinExpr(const SCEV * LHS,const SCEV * RHS)2562 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2563                                          const SCEV *RHS) {
2564   // ~smax(~x, ~y) == smin(x, y).
2565   return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2566 }
2567 
getUMinExpr(const SCEV * LHS,const SCEV * RHS)2568 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2569                                          const SCEV *RHS) {
2570   // ~umax(~x, ~y) == umin(x, y)
2571   return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2572 }
2573 
getSizeOfExpr(Type * AllocTy)2574 const SCEV *ScalarEvolution::getSizeOfExpr(Type *AllocTy) {
2575   // If we have TargetData, we can bypass creating a target-independent
2576   // constant expression and then folding it back into a ConstantInt.
2577   // This is just a compile-time optimization.
2578   if (TD)
2579     return getConstant(TD->getIntPtrType(getContext()),
2580                        TD->getTypeAllocSize(AllocTy));
2581 
2582   Constant *C = ConstantExpr::getSizeOf(AllocTy);
2583   if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2584     if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2585       C = Folded;
2586   Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2587   return getTruncateOrZeroExtend(getSCEV(C), Ty);
2588 }
2589 
getAlignOfExpr(Type * AllocTy)2590 const SCEV *ScalarEvolution::getAlignOfExpr(Type *AllocTy) {
2591   Constant *C = ConstantExpr::getAlignOf(AllocTy);
2592   if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2593     if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2594       C = Folded;
2595   Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2596   return getTruncateOrZeroExtend(getSCEV(C), Ty);
2597 }
2598 
getOffsetOfExpr(StructType * STy,unsigned FieldNo)2599 const SCEV *ScalarEvolution::getOffsetOfExpr(StructType *STy,
2600                                              unsigned FieldNo) {
2601   // If we have TargetData, we can bypass creating a target-independent
2602   // constant expression and then folding it back into a ConstantInt.
2603   // This is just a compile-time optimization.
2604   if (TD)
2605     return getConstant(TD->getIntPtrType(getContext()),
2606                        TD->getStructLayout(STy)->getElementOffset(FieldNo));
2607 
2608   Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2609   if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2610     if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2611       C = Folded;
2612   Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2613   return getTruncateOrZeroExtend(getSCEV(C), Ty);
2614 }
2615 
getOffsetOfExpr(Type * CTy,Constant * FieldNo)2616 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *CTy,
2617                                              Constant *FieldNo) {
2618   Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2619   if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2620     if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2621       C = Folded;
2622   Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2623   return getTruncateOrZeroExtend(getSCEV(C), Ty);
2624 }
2625 
getUnknown(Value * V)2626 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2627   // Don't attempt to do anything other than create a SCEVUnknown object
2628   // here.  createSCEV only calls getUnknown after checking for all other
2629   // interesting possibilities, and any other code that calls getUnknown
2630   // is doing so in order to hide a value from SCEV canonicalization.
2631 
2632   FoldingSetNodeID ID;
2633   ID.AddInteger(scUnknown);
2634   ID.AddPointer(V);
2635   void *IP = 0;
2636   if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2637     assert(cast<SCEVUnknown>(S)->getValue() == V &&
2638            "Stale SCEVUnknown in uniquing map!");
2639     return S;
2640   }
2641   SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2642                                             FirstUnknown);
2643   FirstUnknown = cast<SCEVUnknown>(S);
2644   UniqueSCEVs.InsertNode(S, IP);
2645   return S;
2646 }
2647 
2648 //===----------------------------------------------------------------------===//
2649 //            Basic SCEV Analysis and PHI Idiom Recognition Code
2650 //
2651 
2652 /// isSCEVable - Test if values of the given type are analyzable within
2653 /// the SCEV framework. This primarily includes integer types, and it
2654 /// can optionally include pointer types if the ScalarEvolution class
2655 /// has access to target-specific information.
isSCEVable(Type * Ty) const2656 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2657   // Integers and pointers are always SCEVable.
2658   return Ty->isIntegerTy() || Ty->isPointerTy();
2659 }
2660 
2661 /// getTypeSizeInBits - Return the size in bits of the specified type,
2662 /// for which isSCEVable must return true.
getTypeSizeInBits(Type * Ty) const2663 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2664   assert(isSCEVable(Ty) && "Type is not SCEVable!");
2665 
2666   // If we have a TargetData, use it!
2667   if (TD)
2668     return TD->getTypeSizeInBits(Ty);
2669 
2670   // Integer types have fixed sizes.
2671   if (Ty->isIntegerTy())
2672     return Ty->getPrimitiveSizeInBits();
2673 
2674   // The only other support type is pointer. Without TargetData, conservatively
2675   // assume pointers are 64-bit.
2676   assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2677   return 64;
2678 }
2679 
2680 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2681 /// the given type and which represents how SCEV will treat the given
2682 /// type, for which isSCEVable must return true. For pointer types,
2683 /// this is the pointer-sized integer type.
getEffectiveSCEVType(Type * Ty) const2684 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2685   assert(isSCEVable(Ty) && "Type is not SCEVable!");
2686 
2687   if (Ty->isIntegerTy())
2688     return Ty;
2689 
2690   // The only other support type is pointer.
2691   assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2692   if (TD) return TD->getIntPtrType(getContext());
2693 
2694   // Without TargetData, conservatively assume pointers are 64-bit.
2695   return Type::getInt64Ty(getContext());
2696 }
2697 
getCouldNotCompute()2698 const SCEV *ScalarEvolution::getCouldNotCompute() {
2699   return &CouldNotCompute;
2700 }
2701 
2702 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2703 /// expression and create a new one.
getSCEV(Value * V)2704 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2705   assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2706 
2707   ValueExprMapType::const_iterator I = ValueExprMap.find(V);
2708   if (I != ValueExprMap.end()) return I->second;
2709   const SCEV *S = createSCEV(V);
2710 
2711   // The process of creating a SCEV for V may have caused other SCEVs
2712   // to have been created, so it's necessary to insert the new entry
2713   // from scratch, rather than trying to remember the insert position
2714   // above.
2715   ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2716   return S;
2717 }
2718 
2719 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2720 ///
getNegativeSCEV(const SCEV * V)2721 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2722   if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2723     return getConstant(
2724                cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2725 
2726   Type *Ty = V->getType();
2727   Ty = getEffectiveSCEVType(Ty);
2728   return getMulExpr(V,
2729                   getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2730 }
2731 
2732 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
getNotSCEV(const SCEV * V)2733 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2734   if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2735     return getConstant(
2736                 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2737 
2738   Type *Ty = V->getType();
2739   Ty = getEffectiveSCEVType(Ty);
2740   const SCEV *AllOnes =
2741                    getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2742   return getMinusSCEV(AllOnes, V);
2743 }
2744 
2745 /// getMinusSCEV - Return LHS-RHS.  Minus is represented in SCEV as A+B*-1.
getMinusSCEV(const SCEV * LHS,const SCEV * RHS,SCEV::NoWrapFlags Flags)2746 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2747                                           SCEV::NoWrapFlags Flags) {
2748   assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2749 
2750   // Fast path: X - X --> 0.
2751   if (LHS == RHS)
2752     return getConstant(LHS->getType(), 0);
2753 
2754   // X - Y --> X + -Y
2755   return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2756 }
2757 
2758 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2759 /// input value to the specified type.  If the type must be extended, it is zero
2760 /// extended.
2761 const SCEV *
getTruncateOrZeroExtend(const SCEV * V,Type * Ty)2762 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2763   Type *SrcTy = V->getType();
2764   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2765          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2766          "Cannot truncate or zero extend with non-integer arguments!");
2767   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2768     return V;  // No conversion
2769   if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2770     return getTruncateExpr(V, Ty);
2771   return getZeroExtendExpr(V, Ty);
2772 }
2773 
2774 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2775 /// input value to the specified type.  If the type must be extended, it is sign
2776 /// extended.
2777 const SCEV *
getTruncateOrSignExtend(const SCEV * V,Type * Ty)2778 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2779                                          Type *Ty) {
2780   Type *SrcTy = V->getType();
2781   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2782          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2783          "Cannot truncate or zero extend with non-integer arguments!");
2784   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2785     return V;  // No conversion
2786   if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2787     return getTruncateExpr(V, Ty);
2788   return getSignExtendExpr(V, Ty);
2789 }
2790 
2791 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2792 /// input value to the specified type.  If the type must be extended, it is zero
2793 /// extended.  The conversion must not be narrowing.
2794 const SCEV *
getNoopOrZeroExtend(const SCEV * V,Type * Ty)2795 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2796   Type *SrcTy = V->getType();
2797   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2798          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2799          "Cannot noop or zero extend with non-integer arguments!");
2800   assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2801          "getNoopOrZeroExtend cannot truncate!");
2802   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2803     return V;  // No conversion
2804   return getZeroExtendExpr(V, Ty);
2805 }
2806 
2807 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2808 /// input value to the specified type.  If the type must be extended, it is sign
2809 /// extended.  The conversion must not be narrowing.
2810 const SCEV *
getNoopOrSignExtend(const SCEV * V,Type * Ty)2811 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2812   Type *SrcTy = V->getType();
2813   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2814          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2815          "Cannot noop or sign extend with non-integer arguments!");
2816   assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2817          "getNoopOrSignExtend cannot truncate!");
2818   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2819     return V;  // No conversion
2820   return getSignExtendExpr(V, Ty);
2821 }
2822 
2823 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2824 /// the input value to the specified type. If the type must be extended,
2825 /// it is extended with unspecified bits. The conversion must not be
2826 /// narrowing.
2827 const SCEV *
getNoopOrAnyExtend(const SCEV * V,Type * Ty)2828 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2829   Type *SrcTy = V->getType();
2830   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2831          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2832          "Cannot noop or any extend with non-integer arguments!");
2833   assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2834          "getNoopOrAnyExtend cannot truncate!");
2835   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2836     return V;  // No conversion
2837   return getAnyExtendExpr(V, Ty);
2838 }
2839 
2840 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2841 /// input value to the specified type.  The conversion must not be widening.
2842 const SCEV *
getTruncateOrNoop(const SCEV * V,Type * Ty)2843 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2844   Type *SrcTy = V->getType();
2845   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2846          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2847          "Cannot truncate or noop with non-integer arguments!");
2848   assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2849          "getTruncateOrNoop cannot extend!");
2850   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2851     return V;  // No conversion
2852   return getTruncateExpr(V, Ty);
2853 }
2854 
2855 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2856 /// the types using zero-extension, and then perform a umax operation
2857 /// with them.
getUMaxFromMismatchedTypes(const SCEV * LHS,const SCEV * RHS)2858 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2859                                                         const SCEV *RHS) {
2860   const SCEV *PromotedLHS = LHS;
2861   const SCEV *PromotedRHS = RHS;
2862 
2863   if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2864     PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2865   else
2866     PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2867 
2868   return getUMaxExpr(PromotedLHS, PromotedRHS);
2869 }
2870 
2871 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2872 /// the types using zero-extension, and then perform a umin operation
2873 /// with them.
getUMinFromMismatchedTypes(const SCEV * LHS,const SCEV * RHS)2874 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2875                                                         const SCEV *RHS) {
2876   const SCEV *PromotedLHS = LHS;
2877   const SCEV *PromotedRHS = RHS;
2878 
2879   if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2880     PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2881   else
2882     PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2883 
2884   return getUMinExpr(PromotedLHS, PromotedRHS);
2885 }
2886 
2887 /// getPointerBase - Transitively follow the chain of pointer-type operands
2888 /// until reaching a SCEV that does not have a single pointer operand. This
2889 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
2890 /// but corner cases do exist.
getPointerBase(const SCEV * V)2891 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
2892   // A pointer operand may evaluate to a nonpointer expression, such as null.
2893   if (!V->getType()->isPointerTy())
2894     return V;
2895 
2896   if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
2897     return getPointerBase(Cast->getOperand());
2898   }
2899   else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
2900     const SCEV *PtrOp = 0;
2901     for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
2902          I != E; ++I) {
2903       if ((*I)->getType()->isPointerTy()) {
2904         // Cannot find the base of an expression with multiple pointer operands.
2905         if (PtrOp)
2906           return V;
2907         PtrOp = *I;
2908       }
2909     }
2910     if (!PtrOp)
2911       return V;
2912     return getPointerBase(PtrOp);
2913   }
2914   return V;
2915 }
2916 
2917 /// PushDefUseChildren - Push users of the given Instruction
2918 /// onto the given Worklist.
2919 static void
PushDefUseChildren(Instruction * I,SmallVectorImpl<Instruction * > & Worklist)2920 PushDefUseChildren(Instruction *I,
2921                    SmallVectorImpl<Instruction *> &Worklist) {
2922   // Push the def-use children onto the Worklist stack.
2923   for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2924        UI != UE; ++UI)
2925     Worklist.push_back(cast<Instruction>(*UI));
2926 }
2927 
2928 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2929 /// instructions that depend on the given instruction and removes them from
2930 /// the ValueExprMapType map if they reference SymName. This is used during PHI
2931 /// resolution.
2932 void
ForgetSymbolicName(Instruction * PN,const SCEV * SymName)2933 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2934   SmallVector<Instruction *, 16> Worklist;
2935   PushDefUseChildren(PN, Worklist);
2936 
2937   SmallPtrSet<Instruction *, 8> Visited;
2938   Visited.insert(PN);
2939   while (!Worklist.empty()) {
2940     Instruction *I = Worklist.pop_back_val();
2941     if (!Visited.insert(I)) continue;
2942 
2943     ValueExprMapType::iterator It =
2944       ValueExprMap.find(static_cast<Value *>(I));
2945     if (It != ValueExprMap.end()) {
2946       const SCEV *Old = It->second;
2947 
2948       // Short-circuit the def-use traversal if the symbolic name
2949       // ceases to appear in expressions.
2950       if (Old != SymName && !hasOperand(Old, SymName))
2951         continue;
2952 
2953       // SCEVUnknown for a PHI either means that it has an unrecognized
2954       // structure, it's a PHI that's in the progress of being computed
2955       // by createNodeForPHI, or it's a single-value PHI. In the first case,
2956       // additional loop trip count information isn't going to change anything.
2957       // In the second case, createNodeForPHI will perform the necessary
2958       // updates on its own when it gets to that point. In the third, we do
2959       // want to forget the SCEVUnknown.
2960       if (!isa<PHINode>(I) ||
2961           !isa<SCEVUnknown>(Old) ||
2962           (I != PN && Old == SymName)) {
2963         forgetMemoizedResults(Old);
2964         ValueExprMap.erase(It);
2965       }
2966     }
2967 
2968     PushDefUseChildren(I, Worklist);
2969   }
2970 }
2971 
2972 /// createNodeForPHI - PHI nodes have two cases.  Either the PHI node exists in
2973 /// a loop header, making it a potential recurrence, or it doesn't.
2974 ///
createNodeForPHI(PHINode * PN)2975 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2976   if (const Loop *L = LI->getLoopFor(PN->getParent()))
2977     if (L->getHeader() == PN->getParent()) {
2978       // The loop may have multiple entrances or multiple exits; we can analyze
2979       // this phi as an addrec if it has a unique entry value and a unique
2980       // backedge value.
2981       Value *BEValueV = 0, *StartValueV = 0;
2982       for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2983         Value *V = PN->getIncomingValue(i);
2984         if (L->contains(PN->getIncomingBlock(i))) {
2985           if (!BEValueV) {
2986             BEValueV = V;
2987           } else if (BEValueV != V) {
2988             BEValueV = 0;
2989             break;
2990           }
2991         } else if (!StartValueV) {
2992           StartValueV = V;
2993         } else if (StartValueV != V) {
2994           StartValueV = 0;
2995           break;
2996         }
2997       }
2998       if (BEValueV && StartValueV) {
2999         // While we are analyzing this PHI node, handle its value symbolically.
3000         const SCEV *SymbolicName = getUnknown(PN);
3001         assert(ValueExprMap.find(PN) == ValueExprMap.end() &&
3002                "PHI node already processed?");
3003         ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3004 
3005         // Using this symbolic name for the PHI, analyze the value coming around
3006         // the back-edge.
3007         const SCEV *BEValue = getSCEV(BEValueV);
3008 
3009         // NOTE: If BEValue is loop invariant, we know that the PHI node just
3010         // has a special value for the first iteration of the loop.
3011 
3012         // If the value coming around the backedge is an add with the symbolic
3013         // value we just inserted, then we found a simple induction variable!
3014         if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3015           // If there is a single occurrence of the symbolic value, replace it
3016           // with a recurrence.
3017           unsigned FoundIndex = Add->getNumOperands();
3018           for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3019             if (Add->getOperand(i) == SymbolicName)
3020               if (FoundIndex == e) {
3021                 FoundIndex = i;
3022                 break;
3023               }
3024 
3025           if (FoundIndex != Add->getNumOperands()) {
3026             // Create an add with everything but the specified operand.
3027             SmallVector<const SCEV *, 8> Ops;
3028             for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3029               if (i != FoundIndex)
3030                 Ops.push_back(Add->getOperand(i));
3031             const SCEV *Accum = getAddExpr(Ops);
3032 
3033             // This is not a valid addrec if the step amount is varying each
3034             // loop iteration, but is not itself an addrec in this loop.
3035             if (isLoopInvariant(Accum, L) ||
3036                 (isa<SCEVAddRecExpr>(Accum) &&
3037                  cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3038               SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3039 
3040               // If the increment doesn't overflow, then neither the addrec nor
3041               // the post-increment will overflow.
3042               if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3043                 if (OBO->hasNoUnsignedWrap())
3044                   Flags = setFlags(Flags, SCEV::FlagNUW);
3045                 if (OBO->hasNoSignedWrap())
3046                   Flags = setFlags(Flags, SCEV::FlagNSW);
3047               } else if (const GEPOperator *GEP =
3048                          dyn_cast<GEPOperator>(BEValueV)) {
3049                 // If the increment is an inbounds GEP, then we know the address
3050                 // space cannot be wrapped around. We cannot make any guarantee
3051                 // about signed or unsigned overflow because pointers are
3052                 // unsigned but we may have a negative index from the base
3053                 // pointer.
3054                 if (GEP->isInBounds())
3055                   Flags = setFlags(Flags, SCEV::FlagNW);
3056               }
3057 
3058               const SCEV *StartVal = getSCEV(StartValueV);
3059               const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3060 
3061               // Since the no-wrap flags are on the increment, they apply to the
3062               // post-incremented value as well.
3063               if (isLoopInvariant(Accum, L))
3064                 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3065                                     Accum, L, Flags);
3066 
3067               // Okay, for the entire analysis of this edge we assumed the PHI
3068               // to be symbolic.  We now need to go back and purge all of the
3069               // entries for the scalars that use the symbolic expression.
3070               ForgetSymbolicName(PN, SymbolicName);
3071               ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3072               return PHISCEV;
3073             }
3074           }
3075         } else if (const SCEVAddRecExpr *AddRec =
3076                      dyn_cast<SCEVAddRecExpr>(BEValue)) {
3077           // Otherwise, this could be a loop like this:
3078           //     i = 0;  for (j = 1; ..; ++j) { ....  i = j; }
3079           // In this case, j = {1,+,1}  and BEValue is j.
3080           // Because the other in-value of i (0) fits the evolution of BEValue
3081           // i really is an addrec evolution.
3082           if (AddRec->getLoop() == L && AddRec->isAffine()) {
3083             const SCEV *StartVal = getSCEV(StartValueV);
3084 
3085             // If StartVal = j.start - j.stride, we can use StartVal as the
3086             // initial step of the addrec evolution.
3087             if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3088                                          AddRec->getOperand(1))) {
3089               // FIXME: For constant StartVal, we should be able to infer
3090               // no-wrap flags.
3091               const SCEV *PHISCEV =
3092                 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3093                               SCEV::FlagAnyWrap);
3094 
3095               // Okay, for the entire analysis of this edge we assumed the PHI
3096               // to be symbolic.  We now need to go back and purge all of the
3097               // entries for the scalars that use the symbolic expression.
3098               ForgetSymbolicName(PN, SymbolicName);
3099               ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3100               return PHISCEV;
3101             }
3102           }
3103         }
3104       }
3105     }
3106 
3107   // If the PHI has a single incoming value, follow that value, unless the
3108   // PHI's incoming blocks are in a different loop, in which case doing so
3109   // risks breaking LCSSA form. Instcombine would normally zap these, but
3110   // it doesn't have DominatorTree information, so it may miss cases.
3111   if (Value *V = SimplifyInstruction(PN, TD, DT))
3112     if (LI->replacementPreservesLCSSAForm(PN, V))
3113       return getSCEV(V);
3114 
3115   // If it's not a loop phi, we can't handle it yet.
3116   return getUnknown(PN);
3117 }
3118 
3119 /// createNodeForGEP - Expand GEP instructions into add and multiply
3120 /// operations. This allows them to be analyzed by regular SCEV code.
3121 ///
createNodeForGEP(GEPOperator * GEP)3122 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3123 
3124   // Don't blindly transfer the inbounds flag from the GEP instruction to the
3125   // Add expression, because the Instruction may be guarded by control flow
3126   // and the no-overflow bits may not be valid for the expression in any
3127   // context.
3128   bool isInBounds = GEP->isInBounds();
3129 
3130   Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3131   Value *Base = GEP->getOperand(0);
3132   // Don't attempt to analyze GEPs over unsized objects.
3133   if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
3134     return getUnknown(GEP);
3135   const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3136   gep_type_iterator GTI = gep_type_begin(GEP);
3137   for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
3138                                       E = GEP->op_end();
3139        I != E; ++I) {
3140     Value *Index = *I;
3141     // Compute the (potentially symbolic) offset in bytes for this index.
3142     if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3143       // For a struct, add the member offset.
3144       unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3145       const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
3146 
3147       // Add the field offset to the running total offset.
3148       TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3149     } else {
3150       // For an array, add the element offset, explicitly scaled.
3151       const SCEV *ElementSize = getSizeOfExpr(*GTI);
3152       const SCEV *IndexS = getSCEV(Index);
3153       // Getelementptr indices are signed.
3154       IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3155 
3156       // Multiply the index by the element size to compute the element offset.
3157       const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize,
3158                                            isInBounds ? SCEV::FlagNSW :
3159                                            SCEV::FlagAnyWrap);
3160 
3161       // Add the element offset to the running total offset.
3162       TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3163     }
3164   }
3165 
3166   // Get the SCEV for the GEP base.
3167   const SCEV *BaseS = getSCEV(Base);
3168 
3169   // Add the total offset from all the GEP indices to the base.
3170   return getAddExpr(BaseS, TotalOffset,
3171                     isInBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap);
3172 }
3173 
3174 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3175 /// guaranteed to end in (at every loop iteration).  It is, at the same time,
3176 /// the minimum number of times S is divisible by 2.  For example, given {4,+,8}
3177 /// it returns 2.  If S is guaranteed to be 0, it returns the bitwidth of S.
3178 uint32_t
GetMinTrailingZeros(const SCEV * S)3179 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3180   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3181     return C->getValue()->getValue().countTrailingZeros();
3182 
3183   if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3184     return std::min(GetMinTrailingZeros(T->getOperand()),
3185                     (uint32_t)getTypeSizeInBits(T->getType()));
3186 
3187   if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3188     uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3189     return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3190              getTypeSizeInBits(E->getType()) : OpRes;
3191   }
3192 
3193   if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3194     uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3195     return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3196              getTypeSizeInBits(E->getType()) : OpRes;
3197   }
3198 
3199   if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3200     // The result is the min of all operands results.
3201     uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3202     for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3203       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3204     return MinOpRes;
3205   }
3206 
3207   if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3208     // The result is the sum of all operands results.
3209     uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3210     uint32_t BitWidth = getTypeSizeInBits(M->getType());
3211     for (unsigned i = 1, e = M->getNumOperands();
3212          SumOpRes != BitWidth && i != e; ++i)
3213       SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3214                           BitWidth);
3215     return SumOpRes;
3216   }
3217 
3218   if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3219     // The result is the min of all operands results.
3220     uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3221     for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3222       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3223     return MinOpRes;
3224   }
3225 
3226   if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3227     // The result is the min of all operands results.
3228     uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3229     for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3230       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3231     return MinOpRes;
3232   }
3233 
3234   if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3235     // The result is the min of all operands results.
3236     uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3237     for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3238       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3239     return MinOpRes;
3240   }
3241 
3242   if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3243     // For a SCEVUnknown, ask ValueTracking.
3244     unsigned BitWidth = getTypeSizeInBits(U->getType());
3245     APInt Mask = APInt::getAllOnesValue(BitWidth);
3246     APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3247     ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
3248     return Zeros.countTrailingOnes();
3249   }
3250 
3251   // SCEVUDivExpr
3252   return 0;
3253 }
3254 
3255 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3256 ///
3257 ConstantRange
getUnsignedRange(const SCEV * S)3258 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3259   // See if we've computed this range already.
3260   DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3261   if (I != UnsignedRanges.end())
3262     return I->second;
3263 
3264   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3265     return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3266 
3267   unsigned BitWidth = getTypeSizeInBits(S->getType());
3268   ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3269 
3270   // If the value has known zeros, the maximum unsigned value will have those
3271   // known zeros as well.
3272   uint32_t TZ = GetMinTrailingZeros(S);
3273   if (TZ != 0)
3274     ConservativeResult =
3275       ConstantRange(APInt::getMinValue(BitWidth),
3276                     APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3277 
3278   if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3279     ConstantRange X = getUnsignedRange(Add->getOperand(0));
3280     for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3281       X = X.add(getUnsignedRange(Add->getOperand(i)));
3282     return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3283   }
3284 
3285   if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3286     ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3287     for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3288       X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3289     return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3290   }
3291 
3292   if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3293     ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3294     for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3295       X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3296     return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3297   }
3298 
3299   if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3300     ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3301     for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3302       X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3303     return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3304   }
3305 
3306   if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3307     ConstantRange X = getUnsignedRange(UDiv->getLHS());
3308     ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3309     return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3310   }
3311 
3312   if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3313     ConstantRange X = getUnsignedRange(ZExt->getOperand());
3314     return setUnsignedRange(ZExt,
3315       ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3316   }
3317 
3318   if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3319     ConstantRange X = getUnsignedRange(SExt->getOperand());
3320     return setUnsignedRange(SExt,
3321       ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3322   }
3323 
3324   if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3325     ConstantRange X = getUnsignedRange(Trunc->getOperand());
3326     return setUnsignedRange(Trunc,
3327       ConservativeResult.intersectWith(X.truncate(BitWidth)));
3328   }
3329 
3330   if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3331     // If there's no unsigned wrap, the value will never be less than its
3332     // initial value.
3333     if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3334       if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3335         if (!C->getValue()->isZero())
3336           ConservativeResult =
3337             ConservativeResult.intersectWith(
3338               ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3339 
3340     // TODO: non-affine addrec
3341     if (AddRec->isAffine()) {
3342       Type *Ty = AddRec->getType();
3343       const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3344       if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3345           getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3346         MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3347 
3348         const SCEV *Start = AddRec->getStart();
3349         const SCEV *Step = AddRec->getStepRecurrence(*this);
3350 
3351         ConstantRange StartRange = getUnsignedRange(Start);
3352         ConstantRange StepRange = getSignedRange(Step);
3353         ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3354         ConstantRange EndRange =
3355           StartRange.add(MaxBECountRange.multiply(StepRange));
3356 
3357         // Check for overflow. This must be done with ConstantRange arithmetic
3358         // because we could be called from within the ScalarEvolution overflow
3359         // checking code.
3360         ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3361         ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3362         ConstantRange ExtMaxBECountRange =
3363           MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3364         ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3365         if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3366             ExtEndRange)
3367           return setUnsignedRange(AddRec, ConservativeResult);
3368 
3369         APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3370                                    EndRange.getUnsignedMin());
3371         APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3372                                    EndRange.getUnsignedMax());
3373         if (Min.isMinValue() && Max.isMaxValue())
3374           return setUnsignedRange(AddRec, ConservativeResult);
3375         return setUnsignedRange(AddRec,
3376           ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3377       }
3378     }
3379 
3380     return setUnsignedRange(AddRec, ConservativeResult);
3381   }
3382 
3383   if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3384     // For a SCEVUnknown, ask ValueTracking.
3385     APInt Mask = APInt::getAllOnesValue(BitWidth);
3386     APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3387     ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
3388     if (Ones == ~Zeros + 1)
3389       return setUnsignedRange(U, ConservativeResult);
3390     return setUnsignedRange(U,
3391       ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3392   }
3393 
3394   return setUnsignedRange(S, ConservativeResult);
3395 }
3396 
3397 /// getSignedRange - Determine the signed range for a particular SCEV.
3398 ///
3399 ConstantRange
getSignedRange(const SCEV * S)3400 ScalarEvolution::getSignedRange(const SCEV *S) {
3401   // See if we've computed this range already.
3402   DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3403   if (I != SignedRanges.end())
3404     return I->second;
3405 
3406   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3407     return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3408 
3409   unsigned BitWidth = getTypeSizeInBits(S->getType());
3410   ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3411 
3412   // If the value has known zeros, the maximum signed value will have those
3413   // known zeros as well.
3414   uint32_t TZ = GetMinTrailingZeros(S);
3415   if (TZ != 0)
3416     ConservativeResult =
3417       ConstantRange(APInt::getSignedMinValue(BitWidth),
3418                     APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3419 
3420   if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3421     ConstantRange X = getSignedRange(Add->getOperand(0));
3422     for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3423       X = X.add(getSignedRange(Add->getOperand(i)));
3424     return setSignedRange(Add, ConservativeResult.intersectWith(X));
3425   }
3426 
3427   if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3428     ConstantRange X = getSignedRange(Mul->getOperand(0));
3429     for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3430       X = X.multiply(getSignedRange(Mul->getOperand(i)));
3431     return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3432   }
3433 
3434   if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3435     ConstantRange X = getSignedRange(SMax->getOperand(0));
3436     for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3437       X = X.smax(getSignedRange(SMax->getOperand(i)));
3438     return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3439   }
3440 
3441   if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3442     ConstantRange X = getSignedRange(UMax->getOperand(0));
3443     for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3444       X = X.umax(getSignedRange(UMax->getOperand(i)));
3445     return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3446   }
3447 
3448   if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3449     ConstantRange X = getSignedRange(UDiv->getLHS());
3450     ConstantRange Y = getSignedRange(UDiv->getRHS());
3451     return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3452   }
3453 
3454   if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3455     ConstantRange X = getSignedRange(ZExt->getOperand());
3456     return setSignedRange(ZExt,
3457       ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3458   }
3459 
3460   if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3461     ConstantRange X = getSignedRange(SExt->getOperand());
3462     return setSignedRange(SExt,
3463       ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3464   }
3465 
3466   if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3467     ConstantRange X = getSignedRange(Trunc->getOperand());
3468     return setSignedRange(Trunc,
3469       ConservativeResult.intersectWith(X.truncate(BitWidth)));
3470   }
3471 
3472   if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3473     // If there's no signed wrap, and all the operands have the same sign or
3474     // zero, the value won't ever change sign.
3475     if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3476       bool AllNonNeg = true;
3477       bool AllNonPos = true;
3478       for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3479         if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3480         if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3481       }
3482       if (AllNonNeg)
3483         ConservativeResult = ConservativeResult.intersectWith(
3484           ConstantRange(APInt(BitWidth, 0),
3485                         APInt::getSignedMinValue(BitWidth)));
3486       else if (AllNonPos)
3487         ConservativeResult = ConservativeResult.intersectWith(
3488           ConstantRange(APInt::getSignedMinValue(BitWidth),
3489                         APInt(BitWidth, 1)));
3490     }
3491 
3492     // TODO: non-affine addrec
3493     if (AddRec->isAffine()) {
3494       Type *Ty = AddRec->getType();
3495       const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3496       if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3497           getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3498         MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3499 
3500         const SCEV *Start = AddRec->getStart();
3501         const SCEV *Step = AddRec->getStepRecurrence(*this);
3502 
3503         ConstantRange StartRange = getSignedRange(Start);
3504         ConstantRange StepRange = getSignedRange(Step);
3505         ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3506         ConstantRange EndRange =
3507           StartRange.add(MaxBECountRange.multiply(StepRange));
3508 
3509         // Check for overflow. This must be done with ConstantRange arithmetic
3510         // because we could be called from within the ScalarEvolution overflow
3511         // checking code.
3512         ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3513         ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3514         ConstantRange ExtMaxBECountRange =
3515           MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3516         ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3517         if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3518             ExtEndRange)
3519           return setSignedRange(AddRec, ConservativeResult);
3520 
3521         APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3522                                    EndRange.getSignedMin());
3523         APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3524                                    EndRange.getSignedMax());
3525         if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3526           return setSignedRange(AddRec, ConservativeResult);
3527         return setSignedRange(AddRec,
3528           ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3529       }
3530     }
3531 
3532     return setSignedRange(AddRec, ConservativeResult);
3533   }
3534 
3535   if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3536     // For a SCEVUnknown, ask ValueTracking.
3537     if (!U->getValue()->getType()->isIntegerTy() && !TD)
3538       return setSignedRange(U, ConservativeResult);
3539     unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3540     if (NS == 1)
3541       return setSignedRange(U, ConservativeResult);
3542     return setSignedRange(U, ConservativeResult.intersectWith(
3543       ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3544                     APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3545   }
3546 
3547   return setSignedRange(S, ConservativeResult);
3548 }
3549 
3550 /// createSCEV - We know that there is no SCEV for the specified value.
3551 /// Analyze the expression.
3552 ///
createSCEV(Value * V)3553 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3554   if (!isSCEVable(V->getType()))
3555     return getUnknown(V);
3556 
3557   unsigned Opcode = Instruction::UserOp1;
3558   if (Instruction *I = dyn_cast<Instruction>(V)) {
3559     Opcode = I->getOpcode();
3560 
3561     // Don't attempt to analyze instructions in blocks that aren't
3562     // reachable. Such instructions don't matter, and they aren't required
3563     // to obey basic rules for definitions dominating uses which this
3564     // analysis depends on.
3565     if (!DT->isReachableFromEntry(I->getParent()))
3566       return getUnknown(V);
3567   } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3568     Opcode = CE->getOpcode();
3569   else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3570     return getConstant(CI);
3571   else if (isa<ConstantPointerNull>(V))
3572     return getConstant(V->getType(), 0);
3573   else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3574     return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3575   else
3576     return getUnknown(V);
3577 
3578   Operator *U = cast<Operator>(V);
3579   switch (Opcode) {
3580   case Instruction::Add: {
3581     // The simple thing to do would be to just call getSCEV on both operands
3582     // and call getAddExpr with the result. However if we're looking at a
3583     // bunch of things all added together, this can be quite inefficient,
3584     // because it leads to N-1 getAddExpr calls for N ultimate operands.
3585     // Instead, gather up all the operands and make a single getAddExpr call.
3586     // LLVM IR canonical form means we need only traverse the left operands.
3587     SmallVector<const SCEV *, 4> AddOps;
3588     AddOps.push_back(getSCEV(U->getOperand(1)));
3589     for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3590       unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3591       if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3592         break;
3593       U = cast<Operator>(Op);
3594       const SCEV *Op1 = getSCEV(U->getOperand(1));
3595       if (Opcode == Instruction::Sub)
3596         AddOps.push_back(getNegativeSCEV(Op1));
3597       else
3598         AddOps.push_back(Op1);
3599     }
3600     AddOps.push_back(getSCEV(U->getOperand(0)));
3601     SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3602     OverflowingBinaryOperator *OBO = cast<OverflowingBinaryOperator>(V);
3603     if (OBO->hasNoSignedWrap())
3604       setFlags(Flags, SCEV::FlagNSW);
3605     if (OBO->hasNoUnsignedWrap())
3606       setFlags(Flags, SCEV::FlagNUW);
3607     return getAddExpr(AddOps, Flags);
3608   }
3609   case Instruction::Mul: {
3610     // See the Add code above.
3611     SmallVector<const SCEV *, 4> MulOps;
3612     MulOps.push_back(getSCEV(U->getOperand(1)));
3613     for (Value *Op = U->getOperand(0);
3614          Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3615          Op = U->getOperand(0)) {
3616       U = cast<Operator>(Op);
3617       MulOps.push_back(getSCEV(U->getOperand(1)));
3618     }
3619     MulOps.push_back(getSCEV(U->getOperand(0)));
3620     return getMulExpr(MulOps);
3621   }
3622   case Instruction::UDiv:
3623     return getUDivExpr(getSCEV(U->getOperand(0)),
3624                        getSCEV(U->getOperand(1)));
3625   case Instruction::Sub:
3626     return getMinusSCEV(getSCEV(U->getOperand(0)),
3627                         getSCEV(U->getOperand(1)));
3628   case Instruction::And:
3629     // For an expression like x&255 that merely masks off the high bits,
3630     // use zext(trunc(x)) as the SCEV expression.
3631     if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3632       if (CI->isNullValue())
3633         return getSCEV(U->getOperand(1));
3634       if (CI->isAllOnesValue())
3635         return getSCEV(U->getOperand(0));
3636       const APInt &A = CI->getValue();
3637 
3638       // Instcombine's ShrinkDemandedConstant may strip bits out of
3639       // constants, obscuring what would otherwise be a low-bits mask.
3640       // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3641       // knew about to reconstruct a low-bits mask value.
3642       unsigned LZ = A.countLeadingZeros();
3643       unsigned BitWidth = A.getBitWidth();
3644       APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3645       APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3646       ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3647 
3648       APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3649 
3650       if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3651         return
3652           getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3653                                 IntegerType::get(getContext(), BitWidth - LZ)),
3654                             U->getType());
3655     }
3656     break;
3657 
3658   case Instruction::Or:
3659     // If the RHS of the Or is a constant, we may have something like:
3660     // X*4+1 which got turned into X*4|1.  Handle this as an Add so loop
3661     // optimizations will transparently handle this case.
3662     //
3663     // In order for this transformation to be safe, the LHS must be of the
3664     // form X*(2^n) and the Or constant must be less than 2^n.
3665     if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3666       const SCEV *LHS = getSCEV(U->getOperand(0));
3667       const APInt &CIVal = CI->getValue();
3668       if (GetMinTrailingZeros(LHS) >=
3669           (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3670         // Build a plain add SCEV.
3671         const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3672         // If the LHS of the add was an addrec and it has no-wrap flags,
3673         // transfer the no-wrap flags, since an or won't introduce a wrap.
3674         if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3675           const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3676           const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3677             OldAR->getNoWrapFlags());
3678         }
3679         return S;
3680       }
3681     }
3682     break;
3683   case Instruction::Xor:
3684     if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3685       // If the RHS of the xor is a signbit, then this is just an add.
3686       // Instcombine turns add of signbit into xor as a strength reduction step.
3687       if (CI->getValue().isSignBit())
3688         return getAddExpr(getSCEV(U->getOperand(0)),
3689                           getSCEV(U->getOperand(1)));
3690 
3691       // If the RHS of xor is -1, then this is a not operation.
3692       if (CI->isAllOnesValue())
3693         return getNotSCEV(getSCEV(U->getOperand(0)));
3694 
3695       // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3696       // This is a variant of the check for xor with -1, and it handles
3697       // the case where instcombine has trimmed non-demanded bits out
3698       // of an xor with -1.
3699       if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3700         if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3701           if (BO->getOpcode() == Instruction::And &&
3702               LCI->getValue() == CI->getValue())
3703             if (const SCEVZeroExtendExpr *Z =
3704                   dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3705               Type *UTy = U->getType();
3706               const SCEV *Z0 = Z->getOperand();
3707               Type *Z0Ty = Z0->getType();
3708               unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3709 
3710               // If C is a low-bits mask, the zero extend is serving to
3711               // mask off the high bits. Complement the operand and
3712               // re-apply the zext.
3713               if (APIntOps::isMask(Z0TySize, CI->getValue()))
3714                 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3715 
3716               // If C is a single bit, it may be in the sign-bit position
3717               // before the zero-extend. In this case, represent the xor
3718               // using an add, which is equivalent, and re-apply the zext.
3719               APInt Trunc = CI->getValue().trunc(Z0TySize);
3720               if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3721                   Trunc.isSignBit())
3722                 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3723                                          UTy);
3724             }
3725     }
3726     break;
3727 
3728   case Instruction::Shl:
3729     // Turn shift left of a constant amount into a multiply.
3730     if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3731       uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3732 
3733       // If the shift count is not less than the bitwidth, the result of
3734       // the shift is undefined. Don't try to analyze it, because the
3735       // resolution chosen here may differ from the resolution chosen in
3736       // other parts of the compiler.
3737       if (SA->getValue().uge(BitWidth))
3738         break;
3739 
3740       Constant *X = ConstantInt::get(getContext(),
3741         APInt(BitWidth, 1).shl(SA->getZExtValue()));
3742       return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3743     }
3744     break;
3745 
3746   case Instruction::LShr:
3747     // Turn logical shift right of a constant into a unsigned divide.
3748     if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3749       uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3750 
3751       // If the shift count is not less than the bitwidth, the result of
3752       // the shift is undefined. Don't try to analyze it, because the
3753       // resolution chosen here may differ from the resolution chosen in
3754       // other parts of the compiler.
3755       if (SA->getValue().uge(BitWidth))
3756         break;
3757 
3758       Constant *X = ConstantInt::get(getContext(),
3759         APInt(BitWidth, 1).shl(SA->getZExtValue()));
3760       return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3761     }
3762     break;
3763 
3764   case Instruction::AShr:
3765     // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3766     if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3767       if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3768         if (L->getOpcode() == Instruction::Shl &&
3769             L->getOperand(1) == U->getOperand(1)) {
3770           uint64_t BitWidth = getTypeSizeInBits(U->getType());
3771 
3772           // If the shift count is not less than the bitwidth, the result of
3773           // the shift is undefined. Don't try to analyze it, because the
3774           // resolution chosen here may differ from the resolution chosen in
3775           // other parts of the compiler.
3776           if (CI->getValue().uge(BitWidth))
3777             break;
3778 
3779           uint64_t Amt = BitWidth - CI->getZExtValue();
3780           if (Amt == BitWidth)
3781             return getSCEV(L->getOperand(0));       // shift by zero --> noop
3782           return
3783             getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3784                                               IntegerType::get(getContext(),
3785                                                                Amt)),
3786                               U->getType());
3787         }
3788     break;
3789 
3790   case Instruction::Trunc:
3791     return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3792 
3793   case Instruction::ZExt:
3794     return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3795 
3796   case Instruction::SExt:
3797     return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3798 
3799   case Instruction::BitCast:
3800     // BitCasts are no-op casts so we just eliminate the cast.
3801     if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3802       return getSCEV(U->getOperand(0));
3803     break;
3804 
3805   // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3806   // lead to pointer expressions which cannot safely be expanded to GEPs,
3807   // because ScalarEvolution doesn't respect the GEP aliasing rules when
3808   // simplifying integer expressions.
3809 
3810   case Instruction::GetElementPtr:
3811     return createNodeForGEP(cast<GEPOperator>(U));
3812 
3813   case Instruction::PHI:
3814     return createNodeForPHI(cast<PHINode>(U));
3815 
3816   case Instruction::Select:
3817     // This could be a smax or umax that was lowered earlier.
3818     // Try to recover it.
3819     if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3820       Value *LHS = ICI->getOperand(0);
3821       Value *RHS = ICI->getOperand(1);
3822       switch (ICI->getPredicate()) {
3823       case ICmpInst::ICMP_SLT:
3824       case ICmpInst::ICMP_SLE:
3825         std::swap(LHS, RHS);
3826         // fall through
3827       case ICmpInst::ICMP_SGT:
3828       case ICmpInst::ICMP_SGE:
3829         // a >s b ? a+x : b+x  ->  smax(a, b)+x
3830         // a >s b ? b+x : a+x  ->  smin(a, b)+x
3831         if (LHS->getType() == U->getType()) {
3832           const SCEV *LS = getSCEV(LHS);
3833           const SCEV *RS = getSCEV(RHS);
3834           const SCEV *LA = getSCEV(U->getOperand(1));
3835           const SCEV *RA = getSCEV(U->getOperand(2));
3836           const SCEV *LDiff = getMinusSCEV(LA, LS);
3837           const SCEV *RDiff = getMinusSCEV(RA, RS);
3838           if (LDiff == RDiff)
3839             return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3840           LDiff = getMinusSCEV(LA, RS);
3841           RDiff = getMinusSCEV(RA, LS);
3842           if (LDiff == RDiff)
3843             return getAddExpr(getSMinExpr(LS, RS), LDiff);
3844         }
3845         break;
3846       case ICmpInst::ICMP_ULT:
3847       case ICmpInst::ICMP_ULE:
3848         std::swap(LHS, RHS);
3849         // fall through
3850       case ICmpInst::ICMP_UGT:
3851       case ICmpInst::ICMP_UGE:
3852         // a >u b ? a+x : b+x  ->  umax(a, b)+x
3853         // a >u b ? b+x : a+x  ->  umin(a, b)+x
3854         if (LHS->getType() == U->getType()) {
3855           const SCEV *LS = getSCEV(LHS);
3856           const SCEV *RS = getSCEV(RHS);
3857           const SCEV *LA = getSCEV(U->getOperand(1));
3858           const SCEV *RA = getSCEV(U->getOperand(2));
3859           const SCEV *LDiff = getMinusSCEV(LA, LS);
3860           const SCEV *RDiff = getMinusSCEV(RA, RS);
3861           if (LDiff == RDiff)
3862             return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3863           LDiff = getMinusSCEV(LA, RS);
3864           RDiff = getMinusSCEV(RA, LS);
3865           if (LDiff == RDiff)
3866             return getAddExpr(getUMinExpr(LS, RS), LDiff);
3867         }
3868         break;
3869       case ICmpInst::ICMP_NE:
3870         // n != 0 ? n+x : 1+x  ->  umax(n, 1)+x
3871         if (LHS->getType() == U->getType() &&
3872             isa<ConstantInt>(RHS) &&
3873             cast<ConstantInt>(RHS)->isZero()) {
3874           const SCEV *One = getConstant(LHS->getType(), 1);
3875           const SCEV *LS = getSCEV(LHS);
3876           const SCEV *LA = getSCEV(U->getOperand(1));
3877           const SCEV *RA = getSCEV(U->getOperand(2));
3878           const SCEV *LDiff = getMinusSCEV(LA, LS);
3879           const SCEV *RDiff = getMinusSCEV(RA, One);
3880           if (LDiff == RDiff)
3881             return getAddExpr(getUMaxExpr(One, LS), LDiff);
3882         }
3883         break;
3884       case ICmpInst::ICMP_EQ:
3885         // n == 0 ? 1+x : n+x  ->  umax(n, 1)+x
3886         if (LHS->getType() == U->getType() &&
3887             isa<ConstantInt>(RHS) &&
3888             cast<ConstantInt>(RHS)->isZero()) {
3889           const SCEV *One = getConstant(LHS->getType(), 1);
3890           const SCEV *LS = getSCEV(LHS);
3891           const SCEV *LA = getSCEV(U->getOperand(1));
3892           const SCEV *RA = getSCEV(U->getOperand(2));
3893           const SCEV *LDiff = getMinusSCEV(LA, One);
3894           const SCEV *RDiff = getMinusSCEV(RA, LS);
3895           if (LDiff == RDiff)
3896             return getAddExpr(getUMaxExpr(One, LS), LDiff);
3897         }
3898         break;
3899       default:
3900         break;
3901       }
3902     }
3903 
3904   default: // We cannot analyze this expression.
3905     break;
3906   }
3907 
3908   return getUnknown(V);
3909 }
3910 
3911 
3912 
3913 //===----------------------------------------------------------------------===//
3914 //                   Iteration Count Computation Code
3915 //
3916 
3917 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
3918 /// normal unsigned value, if possible. Returns 0 if the trip count is unknown
3919 /// or not constant. Will also return 0 if the maximum trip count is very large
3920 /// (>= 2^32)
getSmallConstantTripCount(Loop * L,BasicBlock * ExitBlock)3921 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
3922                                                     BasicBlock *ExitBlock) {
3923   const SCEVConstant *ExitCount =
3924     dyn_cast<SCEVConstant>(getExitCount(L, ExitBlock));
3925   if (!ExitCount)
3926     return 0;
3927 
3928   ConstantInt *ExitConst = ExitCount->getValue();
3929 
3930   // Guard against huge trip counts.
3931   if (ExitConst->getValue().getActiveBits() > 32)
3932     return 0;
3933 
3934   // In case of integer overflow, this returns 0, which is correct.
3935   return ((unsigned)ExitConst->getZExtValue()) + 1;
3936 }
3937 
3938 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
3939 /// trip count of this loop as a normal unsigned value, if possible. This
3940 /// means that the actual trip count is always a multiple of the returned
3941 /// value (don't forget the trip count could very well be zero as well!).
3942 ///
3943 /// Returns 1 if the trip count is unknown or not guaranteed to be the
3944 /// multiple of a constant (which is also the case if the trip count is simply
3945 /// constant, use getSmallConstantTripCount for that case), Will also return 1
3946 /// if the trip count is very large (>= 2^32).
getSmallConstantTripMultiple(Loop * L,BasicBlock * ExitBlock)3947 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
3948                                                        BasicBlock *ExitBlock) {
3949   const SCEV *ExitCount = getExitCount(L, ExitBlock);
3950   if (ExitCount == getCouldNotCompute())
3951     return 1;
3952 
3953   // Get the trip count from the BE count by adding 1.
3954   const SCEV *TCMul = getAddExpr(ExitCount,
3955                                  getConstant(ExitCount->getType(), 1));
3956   // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
3957   // to factor simple cases.
3958   if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
3959     TCMul = Mul->getOperand(0);
3960 
3961   const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
3962   if (!MulC)
3963     return 1;
3964 
3965   ConstantInt *Result = MulC->getValue();
3966 
3967   // Guard against huge trip counts.
3968   if (!Result || Result->getValue().getActiveBits() > 32)
3969     return 1;
3970 
3971   return (unsigned)Result->getZExtValue();
3972 }
3973 
3974 // getExitCount - Get the expression for the number of loop iterations for which
3975 // this loop is guaranteed not to exit via ExitintBlock. Otherwise return
3976 // SCEVCouldNotCompute.
getExitCount(Loop * L,BasicBlock * ExitingBlock)3977 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
3978   return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
3979 }
3980 
3981 /// getBackedgeTakenCount - If the specified loop has a predictable
3982 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3983 /// object. The backedge-taken count is the number of times the loop header
3984 /// will be branched to from within the loop. This is one less than the
3985 /// trip count of the loop, since it doesn't count the first iteration,
3986 /// when the header is branched to from outside the loop.
3987 ///
3988 /// Note that it is not valid to call this method on a loop without a
3989 /// loop-invariant backedge-taken count (see
3990 /// hasLoopInvariantBackedgeTakenCount).
3991 ///
getBackedgeTakenCount(const Loop * L)3992 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3993   return getBackedgeTakenInfo(L).getExact(this);
3994 }
3995 
3996 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3997 /// return the least SCEV value that is known never to be less than the
3998 /// actual backedge taken count.
getMaxBackedgeTakenCount(const Loop * L)3999 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4000   return getBackedgeTakenInfo(L).getMax(this);
4001 }
4002 
4003 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4004 /// onto the given Worklist.
4005 static void
PushLoopPHIs(const Loop * L,SmallVectorImpl<Instruction * > & Worklist)4006 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4007   BasicBlock *Header = L->getHeader();
4008 
4009   // Push all Loop-header PHIs onto the Worklist stack.
4010   for (BasicBlock::iterator I = Header->begin();
4011        PHINode *PN = dyn_cast<PHINode>(I); ++I)
4012     Worklist.push_back(PN);
4013 }
4014 
4015 const ScalarEvolution::BackedgeTakenInfo &
getBackedgeTakenInfo(const Loop * L)4016 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4017   // Initially insert an invalid entry for this loop. If the insertion
4018   // succeeds, proceed to actually compute a backedge-taken count and
4019   // update the value. The temporary CouldNotCompute value tells SCEV
4020   // code elsewhere that it shouldn't attempt to request a new
4021   // backedge-taken count, which could result in infinite recursion.
4022   std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4023     BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4024   if (!Pair.second)
4025     return Pair.first->second;
4026 
4027   // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4028   // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4029   // must be cleared in this scope.
4030   BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4031 
4032   if (Result.getExact(this) != getCouldNotCompute()) {
4033     assert(isLoopInvariant(Result.getExact(this), L) &&
4034            isLoopInvariant(Result.getMax(this), L) &&
4035            "Computed backedge-taken count isn't loop invariant for loop!");
4036     ++NumTripCountsComputed;
4037   }
4038   else if (Result.getMax(this) == getCouldNotCompute() &&
4039            isa<PHINode>(L->getHeader()->begin())) {
4040     // Only count loops that have phi nodes as not being computable.
4041     ++NumTripCountsNotComputed;
4042   }
4043 
4044   // Now that we know more about the trip count for this loop, forget any
4045   // existing SCEV values for PHI nodes in this loop since they are only
4046   // conservative estimates made without the benefit of trip count
4047   // information. This is similar to the code in forgetLoop, except that
4048   // it handles SCEVUnknown PHI nodes specially.
4049   if (Result.hasAnyInfo()) {
4050     SmallVector<Instruction *, 16> Worklist;
4051     PushLoopPHIs(L, Worklist);
4052 
4053     SmallPtrSet<Instruction *, 8> Visited;
4054     while (!Worklist.empty()) {
4055       Instruction *I = Worklist.pop_back_val();
4056       if (!Visited.insert(I)) continue;
4057 
4058       ValueExprMapType::iterator It =
4059         ValueExprMap.find(static_cast<Value *>(I));
4060       if (It != ValueExprMap.end()) {
4061         const SCEV *Old = It->second;
4062 
4063         // SCEVUnknown for a PHI either means that it has an unrecognized
4064         // structure, or it's a PHI that's in the progress of being computed
4065         // by createNodeForPHI.  In the former case, additional loop trip
4066         // count information isn't going to change anything. In the later
4067         // case, createNodeForPHI will perform the necessary updates on its
4068         // own when it gets to that point.
4069         if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4070           forgetMemoizedResults(Old);
4071           ValueExprMap.erase(It);
4072         }
4073         if (PHINode *PN = dyn_cast<PHINode>(I))
4074           ConstantEvolutionLoopExitValue.erase(PN);
4075       }
4076 
4077       PushDefUseChildren(I, Worklist);
4078     }
4079   }
4080 
4081   // Re-lookup the insert position, since the call to
4082   // ComputeBackedgeTakenCount above could result in a
4083   // recusive call to getBackedgeTakenInfo (on a different
4084   // loop), which would invalidate the iterator computed
4085   // earlier.
4086   return BackedgeTakenCounts.find(L)->second = Result;
4087 }
4088 
4089 /// forgetLoop - This method should be called by the client when it has
4090 /// changed a loop in a way that may effect ScalarEvolution's ability to
4091 /// compute a trip count, or if the loop is deleted.
forgetLoop(const Loop * L)4092 void ScalarEvolution::forgetLoop(const Loop *L) {
4093   // Drop any stored trip count value.
4094   DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4095     BackedgeTakenCounts.find(L);
4096   if (BTCPos != BackedgeTakenCounts.end()) {
4097     BTCPos->second.clear();
4098     BackedgeTakenCounts.erase(BTCPos);
4099   }
4100 
4101   // Drop information about expressions based on loop-header PHIs.
4102   SmallVector<Instruction *, 16> Worklist;
4103   PushLoopPHIs(L, Worklist);
4104 
4105   SmallPtrSet<Instruction *, 8> Visited;
4106   while (!Worklist.empty()) {
4107     Instruction *I = Worklist.pop_back_val();
4108     if (!Visited.insert(I)) continue;
4109 
4110     ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
4111     if (It != ValueExprMap.end()) {
4112       forgetMemoizedResults(It->second);
4113       ValueExprMap.erase(It);
4114       if (PHINode *PN = dyn_cast<PHINode>(I))
4115         ConstantEvolutionLoopExitValue.erase(PN);
4116     }
4117 
4118     PushDefUseChildren(I, Worklist);
4119   }
4120 
4121   // Forget all contained loops too, to avoid dangling entries in the
4122   // ValuesAtScopes map.
4123   for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4124     forgetLoop(*I);
4125 }
4126 
4127 /// forgetValue - This method should be called by the client when it has
4128 /// changed a value in a way that may effect its value, or which may
4129 /// disconnect it from a def-use chain linking it to a loop.
forgetValue(Value * V)4130 void ScalarEvolution::forgetValue(Value *V) {
4131   Instruction *I = dyn_cast<Instruction>(V);
4132   if (!I) return;
4133 
4134   // Drop information about expressions based on loop-header PHIs.
4135   SmallVector<Instruction *, 16> Worklist;
4136   Worklist.push_back(I);
4137 
4138   SmallPtrSet<Instruction *, 8> Visited;
4139   while (!Worklist.empty()) {
4140     I = Worklist.pop_back_val();
4141     if (!Visited.insert(I)) continue;
4142 
4143     ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
4144     if (It != ValueExprMap.end()) {
4145       forgetMemoizedResults(It->second);
4146       ValueExprMap.erase(It);
4147       if (PHINode *PN = dyn_cast<PHINode>(I))
4148         ConstantEvolutionLoopExitValue.erase(PN);
4149     }
4150 
4151     PushDefUseChildren(I, Worklist);
4152   }
4153 }
4154 
4155 /// getExact - Get the exact loop backedge taken count considering all loop
4156 /// exits. If all exits are computable, this is the minimum computed count.
4157 const SCEV *
getExact(ScalarEvolution * SE) const4158 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4159   // If any exits were not computable, the loop is not computable.
4160   if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4161 
4162   // We need at least one computable exit.
4163   if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4164   assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4165 
4166   const SCEV *BECount = 0;
4167   for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4168        ENT != 0; ENT = ENT->getNextExit()) {
4169 
4170     assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4171 
4172     if (!BECount)
4173       BECount = ENT->ExactNotTaken;
4174     else
4175       BECount = SE->getUMinFromMismatchedTypes(BECount, ENT->ExactNotTaken);
4176   }
4177   assert(BECount && "Invalid not taken count for loop exit");
4178   return BECount;
4179 }
4180 
4181 /// getExact - Get the exact not taken count for this loop exit.
4182 const SCEV *
getExact(BasicBlock * ExitingBlock,ScalarEvolution * SE) const4183 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4184                                              ScalarEvolution *SE) const {
4185   for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4186        ENT != 0; ENT = ENT->getNextExit()) {
4187 
4188     if (ENT->ExitingBlock == ExitingBlock)
4189       return ENT->ExactNotTaken;
4190   }
4191   return SE->getCouldNotCompute();
4192 }
4193 
4194 /// getMax - Get the max backedge taken count for the loop.
4195 const SCEV *
getMax(ScalarEvolution * SE) const4196 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4197   return Max ? Max : SE->getCouldNotCompute();
4198 }
4199 
4200 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4201 /// computable exit into a persistent ExitNotTakenInfo array.
BackedgeTakenInfo(SmallVectorImpl<std::pair<BasicBlock *,const SCEV * >> & ExitCounts,bool Complete,const SCEV * MaxCount)4202 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4203   SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4204   bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4205 
4206   if (!Complete)
4207     ExitNotTaken.setIncomplete();
4208 
4209   unsigned NumExits = ExitCounts.size();
4210   if (NumExits == 0) return;
4211 
4212   ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4213   ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4214   if (NumExits == 1) return;
4215 
4216   // Handle the rare case of multiple computable exits.
4217   ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4218 
4219   ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4220   for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4221     PrevENT->setNextExit(ENT);
4222     ENT->ExitingBlock = ExitCounts[i].first;
4223     ENT->ExactNotTaken = ExitCounts[i].second;
4224   }
4225 }
4226 
4227 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
clear()4228 void ScalarEvolution::BackedgeTakenInfo::clear() {
4229   ExitNotTaken.ExitingBlock = 0;
4230   ExitNotTaken.ExactNotTaken = 0;
4231   delete[] ExitNotTaken.getNextExit();
4232 }
4233 
4234 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4235 /// of the specified loop will execute.
4236 ScalarEvolution::BackedgeTakenInfo
ComputeBackedgeTakenCount(const Loop * L)4237 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4238   SmallVector<BasicBlock *, 8> ExitingBlocks;
4239   L->getExitingBlocks(ExitingBlocks);
4240 
4241   // Examine all exits and pick the most conservative values.
4242   const SCEV *MaxBECount = getCouldNotCompute();
4243   bool CouldComputeBECount = true;
4244   SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4245   for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4246     ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]);
4247     if (EL.Exact == getCouldNotCompute())
4248       // We couldn't compute an exact value for this exit, so
4249       // we won't be able to compute an exact value for the loop.
4250       CouldComputeBECount = false;
4251     else
4252       ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact));
4253 
4254     if (MaxBECount == getCouldNotCompute())
4255       MaxBECount = EL.Max;
4256     else if (EL.Max != getCouldNotCompute())
4257       MaxBECount = getUMinFromMismatchedTypes(MaxBECount, EL.Max);
4258   }
4259 
4260   return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4261 }
4262 
4263 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4264 /// loop will execute if it exits via the specified block.
4265 ScalarEvolution::ExitLimit
ComputeExitLimit(const Loop * L,BasicBlock * ExitingBlock)4266 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4267 
4268   // Okay, we've chosen an exiting block.  See what condition causes us to
4269   // exit at this block.
4270   //
4271   // FIXME: we should be able to handle switch instructions (with a single exit)
4272   BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
4273   if (ExitBr == 0) return getCouldNotCompute();
4274   assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
4275 
4276   // At this point, we know we have a conditional branch that determines whether
4277   // the loop is exited.  However, we don't know if the branch is executed each
4278   // time through the loop.  If not, then the execution count of the branch will
4279   // not be equal to the trip count of the loop.
4280   //
4281   // Currently we check for this by checking to see if the Exit branch goes to
4282   // the loop header.  If so, we know it will always execute the same number of
4283   // times as the loop.  We also handle the case where the exit block *is* the
4284   // loop header.  This is common for un-rotated loops.
4285   //
4286   // If both of those tests fail, walk up the unique predecessor chain to the
4287   // header, stopping if there is an edge that doesn't exit the loop. If the
4288   // header is reached, the execution count of the branch will be equal to the
4289   // trip count of the loop.
4290   //
4291   //  More extensive analysis could be done to handle more cases here.
4292   //
4293   if (ExitBr->getSuccessor(0) != L->getHeader() &&
4294       ExitBr->getSuccessor(1) != L->getHeader() &&
4295       ExitBr->getParent() != L->getHeader()) {
4296     // The simple checks failed, try climbing the unique predecessor chain
4297     // up to the header.
4298     bool Ok = false;
4299     for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
4300       BasicBlock *Pred = BB->getUniquePredecessor();
4301       if (!Pred)
4302         return getCouldNotCompute();
4303       TerminatorInst *PredTerm = Pred->getTerminator();
4304       for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4305         BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4306         if (PredSucc == BB)
4307           continue;
4308         // If the predecessor has a successor that isn't BB and isn't
4309         // outside the loop, assume the worst.
4310         if (L->contains(PredSucc))
4311           return getCouldNotCompute();
4312       }
4313       if (Pred == L->getHeader()) {
4314         Ok = true;
4315         break;
4316       }
4317       BB = Pred;
4318     }
4319     if (!Ok)
4320       return getCouldNotCompute();
4321   }
4322 
4323   // Proceed to the next level to examine the exit condition expression.
4324   return ComputeExitLimitFromCond(L, ExitBr->getCondition(),
4325                                   ExitBr->getSuccessor(0),
4326                                   ExitBr->getSuccessor(1));
4327 }
4328 
4329 /// ComputeExitLimitFromCond - Compute the number of times the
4330 /// backedge of the specified loop will execute if its exit condition
4331 /// were a conditional branch of ExitCond, TBB, and FBB.
4332 ScalarEvolution::ExitLimit
ComputeExitLimitFromCond(const Loop * L,Value * ExitCond,BasicBlock * TBB,BasicBlock * FBB)4333 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4334                                           Value *ExitCond,
4335                                           BasicBlock *TBB,
4336                                           BasicBlock *FBB) {
4337   // Check if the controlling expression for this loop is an And or Or.
4338   if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4339     if (BO->getOpcode() == Instruction::And) {
4340       // Recurse on the operands of the and.
4341       ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4342       ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4343       const SCEV *BECount = getCouldNotCompute();
4344       const SCEV *MaxBECount = getCouldNotCompute();
4345       if (L->contains(TBB)) {
4346         // Both conditions must be true for the loop to continue executing.
4347         // Choose the less conservative count.
4348         if (EL0.Exact == getCouldNotCompute() ||
4349             EL1.Exact == getCouldNotCompute())
4350           BECount = getCouldNotCompute();
4351         else
4352           BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4353         if (EL0.Max == getCouldNotCompute())
4354           MaxBECount = EL1.Max;
4355         else if (EL1.Max == getCouldNotCompute())
4356           MaxBECount = EL0.Max;
4357         else
4358           MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4359       } else {
4360         // Both conditions must be true at the same time for the loop to exit.
4361         // For now, be conservative.
4362         assert(L->contains(FBB) && "Loop block has no successor in loop!");
4363         if (EL0.Max == EL1.Max)
4364           MaxBECount = EL0.Max;
4365         if (EL0.Exact == EL1.Exact)
4366           BECount = EL0.Exact;
4367       }
4368 
4369       return ExitLimit(BECount, MaxBECount);
4370     }
4371     if (BO->getOpcode() == Instruction::Or) {
4372       // Recurse on the operands of the or.
4373       ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4374       ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4375       const SCEV *BECount = getCouldNotCompute();
4376       const SCEV *MaxBECount = getCouldNotCompute();
4377       if (L->contains(FBB)) {
4378         // Both conditions must be false for the loop to continue executing.
4379         // Choose the less conservative count.
4380         if (EL0.Exact == getCouldNotCompute() ||
4381             EL1.Exact == getCouldNotCompute())
4382           BECount = getCouldNotCompute();
4383         else
4384           BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4385         if (EL0.Max == getCouldNotCompute())
4386           MaxBECount = EL1.Max;
4387         else if (EL1.Max == getCouldNotCompute())
4388           MaxBECount = EL0.Max;
4389         else
4390           MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4391       } else {
4392         // Both conditions must be false at the same time for the loop to exit.
4393         // For now, be conservative.
4394         assert(L->contains(TBB) && "Loop block has no successor in loop!");
4395         if (EL0.Max == EL1.Max)
4396           MaxBECount = EL0.Max;
4397         if (EL0.Exact == EL1.Exact)
4398           BECount = EL0.Exact;
4399       }
4400 
4401       return ExitLimit(BECount, MaxBECount);
4402     }
4403   }
4404 
4405   // With an icmp, it may be feasible to compute an exact backedge-taken count.
4406   // Proceed to the next level to examine the icmp.
4407   if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4408     return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB);
4409 
4410   // Check for a constant condition. These are normally stripped out by
4411   // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4412   // preserve the CFG and is temporarily leaving constant conditions
4413   // in place.
4414   if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4415     if (L->contains(FBB) == !CI->getZExtValue())
4416       // The backedge is always taken.
4417       return getCouldNotCompute();
4418     else
4419       // The backedge is never taken.
4420       return getConstant(CI->getType(), 0);
4421   }
4422 
4423   // If it's not an integer or pointer comparison then compute it the hard way.
4424   return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4425 }
4426 
4427 /// ComputeExitLimitFromICmp - Compute the number of times the
4428 /// backedge of the specified loop will execute if its exit condition
4429 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4430 ScalarEvolution::ExitLimit
ComputeExitLimitFromICmp(const Loop * L,ICmpInst * ExitCond,BasicBlock * TBB,BasicBlock * FBB)4431 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4432                                           ICmpInst *ExitCond,
4433                                           BasicBlock *TBB,
4434                                           BasicBlock *FBB) {
4435 
4436   // If the condition was exit on true, convert the condition to exit on false
4437   ICmpInst::Predicate Cond;
4438   if (!L->contains(FBB))
4439     Cond = ExitCond->getPredicate();
4440   else
4441     Cond = ExitCond->getInversePredicate();
4442 
4443   // Handle common loops like: for (X = "string"; *X; ++X)
4444   if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4445     if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4446       ExitLimit ItCnt =
4447         ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4448       if (ItCnt.hasAnyInfo())
4449         return ItCnt;
4450     }
4451 
4452   const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4453   const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4454 
4455   // Try to evaluate any dependencies out of the loop.
4456   LHS = getSCEVAtScope(LHS, L);
4457   RHS = getSCEVAtScope(RHS, L);
4458 
4459   // At this point, we would like to compute how many iterations of the
4460   // loop the predicate will return true for these inputs.
4461   if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4462     // If there is a loop-invariant, force it into the RHS.
4463     std::swap(LHS, RHS);
4464     Cond = ICmpInst::getSwappedPredicate(Cond);
4465   }
4466 
4467   // Simplify the operands before analyzing them.
4468   (void)SimplifyICmpOperands(Cond, LHS, RHS);
4469 
4470   // If we have a comparison of a chrec against a constant, try to use value
4471   // ranges to answer this query.
4472   if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4473     if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4474       if (AddRec->getLoop() == L) {
4475         // Form the constant range.
4476         ConstantRange CompRange(
4477             ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4478 
4479         const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4480         if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4481       }
4482 
4483   switch (Cond) {
4484   case ICmpInst::ICMP_NE: {                     // while (X != Y)
4485     // Convert to: while (X-Y != 0)
4486     ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L);
4487     if (EL.hasAnyInfo()) return EL;
4488     break;
4489   }
4490   case ICmpInst::ICMP_EQ: {                     // while (X == Y)
4491     // Convert to: while (X-Y == 0)
4492     ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4493     if (EL.hasAnyInfo()) return EL;
4494     break;
4495   }
4496   case ICmpInst::ICMP_SLT: {
4497     ExitLimit EL = HowManyLessThans(LHS, RHS, L, true);
4498     if (EL.hasAnyInfo()) return EL;
4499     break;
4500   }
4501   case ICmpInst::ICMP_SGT: {
4502     ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4503                                              getNotSCEV(RHS), L, true);
4504     if (EL.hasAnyInfo()) return EL;
4505     break;
4506   }
4507   case ICmpInst::ICMP_ULT: {
4508     ExitLimit EL = HowManyLessThans(LHS, RHS, L, false);
4509     if (EL.hasAnyInfo()) return EL;
4510     break;
4511   }
4512   case ICmpInst::ICMP_UGT: {
4513     ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4514                                              getNotSCEV(RHS), L, false);
4515     if (EL.hasAnyInfo()) return EL;
4516     break;
4517   }
4518   default:
4519 #if 0
4520     dbgs() << "ComputeBackedgeTakenCount ";
4521     if (ExitCond->getOperand(0)->getType()->isUnsigned())
4522       dbgs() << "[unsigned] ";
4523     dbgs() << *LHS << "   "
4524          << Instruction::getOpcodeName(Instruction::ICmp)
4525          << "   " << *RHS << "\n";
4526 #endif
4527     break;
4528   }
4529   return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4530 }
4531 
4532 static ConstantInt *
EvaluateConstantChrecAtConstant(const SCEVAddRecExpr * AddRec,ConstantInt * C,ScalarEvolution & SE)4533 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4534                                 ScalarEvolution &SE) {
4535   const SCEV *InVal = SE.getConstant(C);
4536   const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4537   assert(isa<SCEVConstant>(Val) &&
4538          "Evaluation of SCEV at constant didn't fold correctly?");
4539   return cast<SCEVConstant>(Val)->getValue();
4540 }
4541 
4542 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
4543 /// and a GEP expression (missing the pointer index) indexing into it, return
4544 /// the addressed element of the initializer or null if the index expression is
4545 /// invalid.
4546 static Constant *
GetAddressedElementFromGlobal(GlobalVariable * GV,const std::vector<ConstantInt * > & Indices)4547 GetAddressedElementFromGlobal(GlobalVariable *GV,
4548                               const std::vector<ConstantInt*> &Indices) {
4549   Constant *Init = GV->getInitializer();
4550   for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
4551     uint64_t Idx = Indices[i]->getZExtValue();
4552     if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
4553       assert(Idx < CS->getNumOperands() && "Bad struct index!");
4554       Init = cast<Constant>(CS->getOperand(Idx));
4555     } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
4556       if (Idx >= CA->getNumOperands()) return 0;  // Bogus program
4557       Init = cast<Constant>(CA->getOperand(Idx));
4558     } else if (isa<ConstantAggregateZero>(Init)) {
4559       if (StructType *STy = dyn_cast<StructType>(Init->getType())) {
4560         assert(Idx < STy->getNumElements() && "Bad struct index!");
4561         Init = Constant::getNullValue(STy->getElementType(Idx));
4562       } else if (ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
4563         if (Idx >= ATy->getNumElements()) return 0;  // Bogus program
4564         Init = Constant::getNullValue(ATy->getElementType());
4565       } else {
4566         llvm_unreachable("Unknown constant aggregate type!");
4567       }
4568       return 0;
4569     } else {
4570       return 0; // Unknown initializer type
4571     }
4572   }
4573   return Init;
4574 }
4575 
4576 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4577 /// 'icmp op load X, cst', try to see if we can compute the backedge
4578 /// execution count.
4579 ScalarEvolution::ExitLimit
ComputeLoadConstantCompareExitLimit(LoadInst * LI,Constant * RHS,const Loop * L,ICmpInst::Predicate predicate)4580 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4581   LoadInst *LI,
4582   Constant *RHS,
4583   const Loop *L,
4584   ICmpInst::Predicate predicate) {
4585 
4586   if (LI->isVolatile()) return getCouldNotCompute();
4587 
4588   // Check to see if the loaded pointer is a getelementptr of a global.
4589   // TODO: Use SCEV instead of manually grubbing with GEPs.
4590   GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4591   if (!GEP) return getCouldNotCompute();
4592 
4593   // Make sure that it is really a constant global we are gepping, with an
4594   // initializer, and make sure the first IDX is really 0.
4595   GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4596   if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4597       GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4598       !cast<Constant>(GEP->getOperand(1))->isNullValue())
4599     return getCouldNotCompute();
4600 
4601   // Okay, we allow one non-constant index into the GEP instruction.
4602   Value *VarIdx = 0;
4603   std::vector<ConstantInt*> Indexes;
4604   unsigned VarIdxNum = 0;
4605   for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4606     if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4607       Indexes.push_back(CI);
4608     } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4609       if (VarIdx) return getCouldNotCompute();  // Multiple non-constant idx's.
4610       VarIdx = GEP->getOperand(i);
4611       VarIdxNum = i-2;
4612       Indexes.push_back(0);
4613     }
4614 
4615   // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4616   // Check to see if X is a loop variant variable value now.
4617   const SCEV *Idx = getSCEV(VarIdx);
4618   Idx = getSCEVAtScope(Idx, L);
4619 
4620   // We can only recognize very limited forms of loop index expressions, in
4621   // particular, only affine AddRec's like {C1,+,C2}.
4622   const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4623   if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4624       !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4625       !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4626     return getCouldNotCompute();
4627 
4628   unsigned MaxSteps = MaxBruteForceIterations;
4629   for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4630     ConstantInt *ItCst = ConstantInt::get(
4631                            cast<IntegerType>(IdxExpr->getType()), IterationNum);
4632     ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4633 
4634     // Form the GEP offset.
4635     Indexes[VarIdxNum] = Val;
4636 
4637     Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
4638     if (Result == 0) break;  // Cannot compute!
4639 
4640     // Evaluate the condition for this iteration.
4641     Result = ConstantExpr::getICmp(predicate, Result, RHS);
4642     if (!isa<ConstantInt>(Result)) break;  // Couldn't decide for sure
4643     if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4644 #if 0
4645       dbgs() << "\n***\n*** Computed loop count " << *ItCst
4646              << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4647              << "***\n";
4648 #endif
4649       ++NumArrayLenItCounts;
4650       return getConstant(ItCst);   // Found terminating iteration!
4651     }
4652   }
4653   return getCouldNotCompute();
4654 }
4655 
4656 
4657 /// CanConstantFold - Return true if we can constant fold an instruction of the
4658 /// specified type, assuming that all operands were constants.
CanConstantFold(const Instruction * I)4659 static bool CanConstantFold(const Instruction *I) {
4660   if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4661       isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
4662     return true;
4663 
4664   if (const CallInst *CI = dyn_cast<CallInst>(I))
4665     if (const Function *F = CI->getCalledFunction())
4666       return canConstantFoldCallTo(F);
4667   return false;
4668 }
4669 
4670 /// Determine whether this instruction can constant evolve within this loop
4671 /// assuming its operands can all constant evolve.
canConstantEvolve(Instruction * I,const Loop * L)4672 static bool canConstantEvolve(Instruction *I, const Loop *L) {
4673   // An instruction outside of the loop can't be derived from a loop PHI.
4674   if (!L->contains(I)) return false;
4675 
4676   if (isa<PHINode>(I)) {
4677     if (L->getHeader() == I->getParent())
4678       return true;
4679     else
4680       // We don't currently keep track of the control flow needed to evaluate
4681       // PHIs, so we cannot handle PHIs inside of loops.
4682       return false;
4683   }
4684 
4685   // If we won't be able to constant fold this expression even if the operands
4686   // are constants, bail early.
4687   return CanConstantFold(I);
4688 }
4689 
4690 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
4691 /// recursing through each instruction operand until reaching a loop header phi.
4692 static PHINode *
getConstantEvolvingPHIOperands(Instruction * UseInst,const Loop * L,DenseMap<Instruction *,PHINode * > & PHIMap)4693 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
4694                                DenseMap<Instruction *, PHINode *> &PHIMap) {
4695 
4696   // Otherwise, we can evaluate this instruction if all of its operands are
4697   // constant or derived from a PHI node themselves.
4698   PHINode *PHI = 0;
4699   for (Instruction::op_iterator OpI = UseInst->op_begin(),
4700          OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
4701 
4702     if (isa<Constant>(*OpI)) continue;
4703 
4704     Instruction *OpInst = dyn_cast<Instruction>(*OpI);
4705     if (!OpInst || !canConstantEvolve(OpInst, L)) return 0;
4706 
4707     PHINode *P = dyn_cast<PHINode>(OpInst);
4708     if (!P)
4709       // If this operand is already visited, reuse the prior result.
4710       // We may have P != PHI if this is the deepest point at which the
4711       // inconsistent paths meet.
4712       P = PHIMap.lookup(OpInst);
4713     if (!P) {
4714       // Recurse and memoize the results, whether a phi is found or not.
4715       // This recursive call invalidates pointers into PHIMap.
4716       P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
4717       PHIMap[OpInst] = P;
4718     }
4719     if (P == 0) return 0;        // Not evolving from PHI
4720     if (PHI && PHI != P) return 0;  // Evolving from multiple different PHIs.
4721     PHI = P;
4722   }
4723   // This is a expression evolving from a constant PHI!
4724   return PHI;
4725 }
4726 
4727 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4728 /// in the loop that V is derived from.  We allow arbitrary operations along the
4729 /// way, but the operands of an operation must either be constants or a value
4730 /// derived from a constant PHI.  If this expression does not fit with these
4731 /// constraints, return null.
getConstantEvolvingPHI(Value * V,const Loop * L)4732 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4733   Instruction *I = dyn_cast<Instruction>(V);
4734   if (I == 0 || !canConstantEvolve(I, L)) return 0;
4735 
4736   if (PHINode *PN = dyn_cast<PHINode>(I)) {
4737     return PN;
4738   }
4739 
4740   // Record non-constant instructions contained by the loop.
4741   DenseMap<Instruction *, PHINode *> PHIMap;
4742   return getConstantEvolvingPHIOperands(I, L, PHIMap);
4743 }
4744 
4745 /// EvaluateExpression - Given an expression that passes the
4746 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4747 /// in the loop has the value PHIVal.  If we can't fold this expression for some
4748 /// reason, return null.
EvaluateExpression(Value * V,const Loop * L,DenseMap<Instruction *,Constant * > & Vals,const TargetData * TD)4749 static Constant *EvaluateExpression(Value *V, const Loop *L,
4750                                     DenseMap<Instruction *, Constant *> &Vals,
4751                                     const TargetData *TD) {
4752   // Convenient constant check, but redundant for recursive calls.
4753   if (Constant *C = dyn_cast<Constant>(V)) return C;
4754 
4755   Instruction *I = cast<Instruction>(V);
4756   if (Constant *C = Vals.lookup(I)) return C;
4757 
4758   assert(!isa<PHINode>(I) && "loop header phis should be mapped to constant");
4759   assert(canConstantEvolve(I, L) && "cannot evaluate expression in this loop");
4760   (void)L;
4761 
4762   std::vector<Constant*> Operands(I->getNumOperands());
4763 
4764   for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4765     Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
4766     if (!Operand) {
4767       Operands[i] = dyn_cast<Constant>(I->getOperand(i));
4768       if (!Operands[i]) return 0;
4769       continue;
4770     }
4771     Constant *C = EvaluateExpression(Operand, L, Vals, TD);
4772     Vals[Operand] = C;
4773     if (!C) return 0;
4774     Operands[i] = C;
4775   }
4776 
4777   if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4778     return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4779                                            Operands[1], TD);
4780   return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD);
4781 }
4782 
4783 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4784 /// in the header of its containing loop, we know the loop executes a
4785 /// constant number of times, and the PHI node is just a recurrence
4786 /// involving constants, fold it.
4787 Constant *
getConstantEvolutionLoopExitValue(PHINode * PN,const APInt & BEs,const Loop * L)4788 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4789                                                    const APInt &BEs,
4790                                                    const Loop *L) {
4791   DenseMap<PHINode*, Constant*>::const_iterator I =
4792     ConstantEvolutionLoopExitValue.find(PN);
4793   if (I != ConstantEvolutionLoopExitValue.end())
4794     return I->second;
4795 
4796   if (BEs.ugt(MaxBruteForceIterations))
4797     return ConstantEvolutionLoopExitValue[PN] = 0;  // Not going to evaluate it.
4798 
4799   Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4800 
4801   // FIXME: Nick's fix for PR11034 will seed constants for multiple header phis.
4802   DenseMap<Instruction *, Constant *> CurrentIterVals;
4803 
4804   // Since the loop is canonicalized, the PHI node must have two entries.  One
4805   // entry must be a constant (coming in from outside of the loop), and the
4806   // second must be derived from the same PHI.
4807   bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4808   Constant *StartCST =
4809     dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4810   if (StartCST == 0)
4811     return RetVal = 0;  // Must be a constant.
4812   CurrentIterVals[PN] = StartCST;
4813 
4814   Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4815   if (getConstantEvolvingPHI(BEValue, L) != PN &&
4816       !isa<Constant>(BEValue))
4817     return RetVal = 0;  // Not derived from same PHI.
4818 
4819   // Execute the loop symbolically to determine the exit value.
4820   if (BEs.getActiveBits() >= 32)
4821     return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4822 
4823   unsigned NumIterations = BEs.getZExtValue(); // must be in range
4824   unsigned IterationNum = 0;
4825   for (; ; ++IterationNum) {
4826     if (IterationNum == NumIterations)
4827       return RetVal = CurrentIterVals[PN];  // Got exit value!
4828 
4829     // Compute the value of the PHI node for the next iteration.
4830     // EvaluateExpression adds non-phi values to the CurrentIterVals map.
4831     Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD);
4832     if (NextPHI == CurrentIterVals[PN])
4833       return RetVal = NextPHI;  // Stopped evolving!
4834     if (NextPHI == 0)
4835       return 0;        // Couldn't evaluate!
4836     DenseMap<Instruction *, Constant *> NextIterVals;
4837     NextIterVals[PN] = NextPHI;
4838     CurrentIterVals.swap(NextIterVals);
4839   }
4840 }
4841 
4842 /// ComputeExitCountExhaustively - If the loop is known to execute a
4843 /// constant number of times (the condition evolves only from constants),
4844 /// try to evaluate a few iterations of the loop until we get the exit
4845 /// condition gets a value of ExitWhen (true or false).  If we cannot
4846 /// evaluate the trip count of the loop, return getCouldNotCompute().
ComputeExitCountExhaustively(const Loop * L,Value * Cond,bool ExitWhen)4847 const SCEV * ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
4848                                                            Value *Cond,
4849                                                            bool ExitWhen) {
4850   PHINode *PN = getConstantEvolvingPHI(Cond, L);
4851   if (PN == 0) return getCouldNotCompute();
4852 
4853   // If the loop is canonicalized, the PHI will have exactly two entries.
4854   // That's the only form we support here.
4855   if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4856 
4857   // One entry must be a constant (coming in from outside of the loop), and the
4858   // second must be derived from the same PHI.
4859   bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4860   Constant *StartCST =
4861     dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4862   if (StartCST == 0) return getCouldNotCompute();  // Must be a constant.
4863 
4864   Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4865   if (getConstantEvolvingPHI(BEValue, L) != PN &&
4866       !isa<Constant>(BEValue))
4867     return getCouldNotCompute();  // Not derived from same PHI.
4868 
4869   // Okay, we find a PHI node that defines the trip count of this loop.  Execute
4870   // the loop symbolically to determine when the condition gets a value of
4871   // "ExitWhen".
4872   unsigned IterationNum = 0;
4873   unsigned MaxIterations = MaxBruteForceIterations;   // Limit analysis.
4874   for (Constant *PHIVal = StartCST;
4875        IterationNum != MaxIterations; ++IterationNum) {
4876     DenseMap<Instruction *, Constant *> PHIValMap;
4877     PHIValMap[PN] = PHIVal;
4878     ConstantInt *CondVal =
4879       dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, PHIValMap, TD));
4880 
4881     // Couldn't symbolically evaluate.
4882     if (!CondVal) return getCouldNotCompute();
4883 
4884     if (CondVal->getValue() == uint64_t(ExitWhen)) {
4885       ++NumBruteForceTripCountsComputed;
4886       return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4887     }
4888 
4889     // Compute the value of the PHI node for the next iteration.
4890     Constant *NextPHI = EvaluateExpression(BEValue, L, PHIValMap, TD);
4891     if (NextPHI == 0 || NextPHI == PHIVal)
4892       return getCouldNotCompute();// Couldn't evaluate or not making progress...
4893     PHIVal = NextPHI;
4894   }
4895 
4896   // Too many iterations were needed to evaluate.
4897   return getCouldNotCompute();
4898 }
4899 
4900 /// getSCEVAtScope - Return a SCEV expression for the specified value
4901 /// at the specified scope in the program.  The L value specifies a loop
4902 /// nest to evaluate the expression at, where null is the top-level or a
4903 /// specified loop is immediately inside of the loop.
4904 ///
4905 /// This method can be used to compute the exit value for a variable defined
4906 /// in a loop by querying what the value will hold in the parent loop.
4907 ///
4908 /// In the case that a relevant loop exit value cannot be computed, the
4909 /// original value V is returned.
getSCEVAtScope(const SCEV * V,const Loop * L)4910 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4911   // Check to see if we've folded this expression at this loop before.
4912   std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4913   std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4914     Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4915   if (!Pair.second)
4916     return Pair.first->second ? Pair.first->second : V;
4917 
4918   // Otherwise compute it.
4919   const SCEV *C = computeSCEVAtScope(V, L);
4920   ValuesAtScopes[V][L] = C;
4921   return C;
4922 }
4923 
computeSCEVAtScope(const SCEV * V,const Loop * L)4924 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
4925   if (isa<SCEVConstant>(V)) return V;
4926 
4927   // If this instruction is evolved from a constant-evolving PHI, compute the
4928   // exit value from the loop without using SCEVs.
4929   if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
4930     if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
4931       const Loop *LI = (*this->LI)[I->getParent()];
4932       if (LI && LI->getParentLoop() == L)  // Looking for loop exit value.
4933         if (PHINode *PN = dyn_cast<PHINode>(I))
4934           if (PN->getParent() == LI->getHeader()) {
4935             // Okay, there is no closed form solution for the PHI node.  Check
4936             // to see if the loop that contains it has a known backedge-taken
4937             // count.  If so, we may be able to force computation of the exit
4938             // value.
4939             const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
4940             if (const SCEVConstant *BTCC =
4941                   dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
4942               // Okay, we know how many times the containing loop executes.  If
4943               // this is a constant evolving PHI node, get the final value at
4944               // the specified iteration number.
4945               Constant *RV = getConstantEvolutionLoopExitValue(PN,
4946                                                    BTCC->getValue()->getValue(),
4947                                                                LI);
4948               if (RV) return getSCEV(RV);
4949             }
4950           }
4951 
4952       // Okay, this is an expression that we cannot symbolically evaluate
4953       // into a SCEV.  Check to see if it's possible to symbolically evaluate
4954       // the arguments into constants, and if so, try to constant propagate the
4955       // result.  This is particularly useful for computing loop exit values.
4956       if (CanConstantFold(I)) {
4957         SmallVector<Constant *, 4> Operands;
4958         bool MadeImprovement = false;
4959         for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4960           Value *Op = I->getOperand(i);
4961           if (Constant *C = dyn_cast<Constant>(Op)) {
4962             Operands.push_back(C);
4963             continue;
4964           }
4965 
4966           // If any of the operands is non-constant and if they are
4967           // non-integer and non-pointer, don't even try to analyze them
4968           // with scev techniques.
4969           if (!isSCEVable(Op->getType()))
4970             return V;
4971 
4972           const SCEV *OrigV = getSCEV(Op);
4973           const SCEV *OpV = getSCEVAtScope(OrigV, L);
4974           MadeImprovement |= OrigV != OpV;
4975 
4976           Constant *C = 0;
4977           if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
4978             C = SC->getValue();
4979           if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV))
4980             C = dyn_cast<Constant>(SU->getValue());
4981           if (!C) return V;
4982           if (C->getType() != Op->getType())
4983             C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4984                                                               Op->getType(),
4985                                                               false),
4986                                       C, Op->getType());
4987           Operands.push_back(C);
4988         }
4989 
4990         // Check to see if getSCEVAtScope actually made an improvement.
4991         if (MadeImprovement) {
4992           Constant *C = 0;
4993           if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4994             C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4995                                                 Operands[0], Operands[1], TD);
4996           else
4997             C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4998                                          Operands, TD);
4999           if (!C) return V;
5000           return getSCEV(C);
5001         }
5002       }
5003     }
5004 
5005     // This is some other type of SCEVUnknown, just return it.
5006     return V;
5007   }
5008 
5009   if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5010     // Avoid performing the look-up in the common case where the specified
5011     // expression has no loop-variant portions.
5012     for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5013       const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5014       if (OpAtScope != Comm->getOperand(i)) {
5015         // Okay, at least one of these operands is loop variant but might be
5016         // foldable.  Build a new instance of the folded commutative expression.
5017         SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5018                                             Comm->op_begin()+i);
5019         NewOps.push_back(OpAtScope);
5020 
5021         for (++i; i != e; ++i) {
5022           OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5023           NewOps.push_back(OpAtScope);
5024         }
5025         if (isa<SCEVAddExpr>(Comm))
5026           return getAddExpr(NewOps);
5027         if (isa<SCEVMulExpr>(Comm))
5028           return getMulExpr(NewOps);
5029         if (isa<SCEVSMaxExpr>(Comm))
5030           return getSMaxExpr(NewOps);
5031         if (isa<SCEVUMaxExpr>(Comm))
5032           return getUMaxExpr(NewOps);
5033         llvm_unreachable("Unknown commutative SCEV type!");
5034       }
5035     }
5036     // If we got here, all operands are loop invariant.
5037     return Comm;
5038   }
5039 
5040   if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5041     const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5042     const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5043     if (LHS == Div->getLHS() && RHS == Div->getRHS())
5044       return Div;   // must be loop invariant
5045     return getUDivExpr(LHS, RHS);
5046   }
5047 
5048   // If this is a loop recurrence for a loop that does not contain L, then we
5049   // are dealing with the final value computed by the loop.
5050   if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5051     // First, attempt to evaluate each operand.
5052     // Avoid performing the look-up in the common case where the specified
5053     // expression has no loop-variant portions.
5054     for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5055       const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5056       if (OpAtScope == AddRec->getOperand(i))
5057         continue;
5058 
5059       // Okay, at least one of these operands is loop variant but might be
5060       // foldable.  Build a new instance of the folded commutative expression.
5061       SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5062                                           AddRec->op_begin()+i);
5063       NewOps.push_back(OpAtScope);
5064       for (++i; i != e; ++i)
5065         NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5066 
5067       const SCEV *FoldedRec =
5068         getAddRecExpr(NewOps, AddRec->getLoop(),
5069                       AddRec->getNoWrapFlags(SCEV::FlagNW));
5070       AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5071       // The addrec may be folded to a nonrecurrence, for example, if the
5072       // induction variable is multiplied by zero after constant folding. Go
5073       // ahead and return the folded value.
5074       if (!AddRec)
5075         return FoldedRec;
5076       break;
5077     }
5078 
5079     // If the scope is outside the addrec's loop, evaluate it by using the
5080     // loop exit value of the addrec.
5081     if (!AddRec->getLoop()->contains(L)) {
5082       // To evaluate this recurrence, we need to know how many times the AddRec
5083       // loop iterates.  Compute this now.
5084       const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5085       if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5086 
5087       // Then, evaluate the AddRec.
5088       return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5089     }
5090 
5091     return AddRec;
5092   }
5093 
5094   if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5095     const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5096     if (Op == Cast->getOperand())
5097       return Cast;  // must be loop invariant
5098     return getZeroExtendExpr(Op, Cast->getType());
5099   }
5100 
5101   if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5102     const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5103     if (Op == Cast->getOperand())
5104       return Cast;  // must be loop invariant
5105     return getSignExtendExpr(Op, Cast->getType());
5106   }
5107 
5108   if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5109     const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5110     if (Op == Cast->getOperand())
5111       return Cast;  // must be loop invariant
5112     return getTruncateExpr(Op, Cast->getType());
5113   }
5114 
5115   llvm_unreachable("Unknown SCEV type!");
5116   return 0;
5117 }
5118 
5119 /// getSCEVAtScope - This is a convenience function which does
5120 /// getSCEVAtScope(getSCEV(V), L).
getSCEVAtScope(Value * V,const Loop * L)5121 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5122   return getSCEVAtScope(getSCEV(V), L);
5123 }
5124 
5125 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5126 /// following equation:
5127 ///
5128 ///     A * X = B (mod N)
5129 ///
5130 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5131 /// A and B isn't important.
5132 ///
5133 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
SolveLinEquationWithOverflow(const APInt & A,const APInt & B,ScalarEvolution & SE)5134 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5135                                                ScalarEvolution &SE) {
5136   uint32_t BW = A.getBitWidth();
5137   assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5138   assert(A != 0 && "A must be non-zero.");
5139 
5140   // 1. D = gcd(A, N)
5141   //
5142   // The gcd of A and N may have only one prime factor: 2. The number of
5143   // trailing zeros in A is its multiplicity
5144   uint32_t Mult2 = A.countTrailingZeros();
5145   // D = 2^Mult2
5146 
5147   // 2. Check if B is divisible by D.
5148   //
5149   // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5150   // is not less than multiplicity of this prime factor for D.
5151   if (B.countTrailingZeros() < Mult2)
5152     return SE.getCouldNotCompute();
5153 
5154   // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5155   // modulo (N / D).
5156   //
5157   // (N / D) may need BW+1 bits in its representation.  Hence, we'll use this
5158   // bit width during computations.
5159   APInt AD = A.lshr(Mult2).zext(BW + 1);  // AD = A / D
5160   APInt Mod(BW + 1, 0);
5161   Mod.setBit(BW - Mult2);  // Mod = N / D
5162   APInt I = AD.multiplicativeInverse(Mod);
5163 
5164   // 4. Compute the minimum unsigned root of the equation:
5165   // I * (B / D) mod (N / D)
5166   APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5167 
5168   // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5169   // bits.
5170   return SE.getConstant(Result.trunc(BW));
5171 }
5172 
5173 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5174 /// given quadratic chrec {L,+,M,+,N}.  This returns either the two roots (which
5175 /// might be the same) or two SCEVCouldNotCompute objects.
5176 ///
5177 static std::pair<const SCEV *,const SCEV *>
SolveQuadraticEquation(const SCEVAddRecExpr * AddRec,ScalarEvolution & SE)5178 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5179   assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5180   const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5181   const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5182   const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5183 
5184   // We currently can only solve this if the coefficients are constants.
5185   if (!LC || !MC || !NC) {
5186     const SCEV *CNC = SE.getCouldNotCompute();
5187     return std::make_pair(CNC, CNC);
5188   }
5189 
5190   uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5191   const APInt &L = LC->getValue()->getValue();
5192   const APInt &M = MC->getValue()->getValue();
5193   const APInt &N = NC->getValue()->getValue();
5194   APInt Two(BitWidth, 2);
5195   APInt Four(BitWidth, 4);
5196 
5197   {
5198     using namespace APIntOps;
5199     const APInt& C = L;
5200     // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5201     // The B coefficient is M-N/2
5202     APInt B(M);
5203     B -= sdiv(N,Two);
5204 
5205     // The A coefficient is N/2
5206     APInt A(N.sdiv(Two));
5207 
5208     // Compute the B^2-4ac term.
5209     APInt SqrtTerm(B);
5210     SqrtTerm *= B;
5211     SqrtTerm -= Four * (A * C);
5212 
5213     // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5214     // integer value or else APInt::sqrt() will assert.
5215     APInt SqrtVal(SqrtTerm.sqrt());
5216 
5217     // Compute the two solutions for the quadratic formula.
5218     // The divisions must be performed as signed divisions.
5219     APInt NegB(-B);
5220     APInt TwoA(A << 1);
5221     if (TwoA.isMinValue()) {
5222       const SCEV *CNC = SE.getCouldNotCompute();
5223       return std::make_pair(CNC, CNC);
5224     }
5225 
5226     LLVMContext &Context = SE.getContext();
5227 
5228     ConstantInt *Solution1 =
5229       ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5230     ConstantInt *Solution2 =
5231       ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5232 
5233     return std::make_pair(SE.getConstant(Solution1),
5234                           SE.getConstant(Solution2));
5235   } // end APIntOps namespace
5236 }
5237 
5238 /// HowFarToZero - Return the number of times a backedge comparing the specified
5239 /// value to zero will execute.  If not computable, return CouldNotCompute.
5240 ///
5241 /// This is only used for loops with a "x != y" exit test. The exit condition is
5242 /// now expressed as a single expression, V = x-y. So the exit test is
5243 /// effectively V != 0.  We know and take advantage of the fact that this
5244 /// expression only being used in a comparison by zero context.
5245 ScalarEvolution::ExitLimit
HowFarToZero(const SCEV * V,const Loop * L)5246 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
5247   // If the value is a constant
5248   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5249     // If the value is already zero, the branch will execute zero times.
5250     if (C->getValue()->isZero()) return C;
5251     return getCouldNotCompute();  // Otherwise it will loop infinitely.
5252   }
5253 
5254   const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5255   if (!AddRec || AddRec->getLoop() != L)
5256     return getCouldNotCompute();
5257 
5258   // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5259   // the quadratic equation to solve it.
5260   if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5261     std::pair<const SCEV *,const SCEV *> Roots =
5262       SolveQuadraticEquation(AddRec, *this);
5263     const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5264     const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5265     if (R1 && R2) {
5266 #if 0
5267       dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5268              << "  sol#2: " << *R2 << "\n";
5269 #endif
5270       // Pick the smallest positive root value.
5271       if (ConstantInt *CB =
5272           dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5273                                                       R1->getValue(),
5274                                                       R2->getValue()))) {
5275         if (CB->getZExtValue() == false)
5276           std::swap(R1, R2);   // R1 is the minimum root now.
5277 
5278         // We can only use this value if the chrec ends up with an exact zero
5279         // value at this index.  When solving for "X*X != 5", for example, we
5280         // should not accept a root of 2.
5281         const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5282         if (Val->isZero())
5283           return R1;  // We found a quadratic root!
5284       }
5285     }
5286     return getCouldNotCompute();
5287   }
5288 
5289   // Otherwise we can only handle this if it is affine.
5290   if (!AddRec->isAffine())
5291     return getCouldNotCompute();
5292 
5293   // If this is an affine expression, the execution count of this branch is
5294   // the minimum unsigned root of the following equation:
5295   //
5296   //     Start + Step*N = 0 (mod 2^BW)
5297   //
5298   // equivalent to:
5299   //
5300   //             Step*N = -Start (mod 2^BW)
5301   //
5302   // where BW is the common bit width of Start and Step.
5303 
5304   // Get the initial value for the loop.
5305   const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5306   const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5307 
5308   // For now we handle only constant steps.
5309   //
5310   // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5311   // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5312   // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5313   // We have not yet seen any such cases.
5314   const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5315   if (StepC == 0)
5316     return getCouldNotCompute();
5317 
5318   // For positive steps (counting up until unsigned overflow):
5319   //   N = -Start/Step (as unsigned)
5320   // For negative steps (counting down to zero):
5321   //   N = Start/-Step
5322   // First compute the unsigned distance from zero in the direction of Step.
5323   bool CountDown = StepC->getValue()->getValue().isNegative();
5324   const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5325 
5326   // Handle unitary steps, which cannot wraparound.
5327   // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5328   //   N = Distance (as unsigned)
5329   if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
5330     ConstantRange CR = getUnsignedRange(Start);
5331     const SCEV *MaxBECount;
5332     if (!CountDown && CR.getUnsignedMin().isMinValue())
5333       // When counting up, the worst starting value is 1, not 0.
5334       MaxBECount = CR.getUnsignedMax().isMinValue()
5335         ? getConstant(APInt::getMinValue(CR.getBitWidth()))
5336         : getConstant(APInt::getMaxValue(CR.getBitWidth()));
5337     else
5338       MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
5339                                          : -CR.getUnsignedMin());
5340     return ExitLimit(Distance, MaxBECount);
5341   }
5342 
5343   // If the recurrence is known not to wraparound, unsigned divide computes the
5344   // back edge count. We know that the value will either become zero (and thus
5345   // the loop terminates), that the loop will terminate through some other exit
5346   // condition first, or that the loop has undefined behavior.  This means
5347   // we can't "miss" the exit value, even with nonunit stride.
5348   //
5349   // FIXME: Prove that loops always exhibits *acceptable* undefined
5350   // behavior. Loops must exhibit defined behavior until a wrapped value is
5351   // actually used. So the trip count computed by udiv could be smaller than the
5352   // number of well-defined iterations.
5353   if (AddRec->getNoWrapFlags(SCEV::FlagNW))
5354     // FIXME: We really want an "isexact" bit for udiv.
5355     return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5356 
5357   // Then, try to solve the above equation provided that Start is constant.
5358   if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5359     return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5360                                         -StartC->getValue()->getValue(),
5361                                         *this);
5362   return getCouldNotCompute();
5363 }
5364 
5365 /// HowFarToNonZero - Return the number of times a backedge checking the
5366 /// specified value for nonzero will execute.  If not computable, return
5367 /// CouldNotCompute
5368 ScalarEvolution::ExitLimit
HowFarToNonZero(const SCEV * V,const Loop * L)5369 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5370   // Loops that look like: while (X == 0) are very strange indeed.  We don't
5371   // handle them yet except for the trivial case.  This could be expanded in the
5372   // future as needed.
5373 
5374   // If the value is a constant, check to see if it is known to be non-zero
5375   // already.  If so, the backedge will execute zero times.
5376   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5377     if (!C->getValue()->isNullValue())
5378       return getConstant(C->getType(), 0);
5379     return getCouldNotCompute();  // Otherwise it will loop infinitely.
5380   }
5381 
5382   // We could implement others, but I really doubt anyone writes loops like
5383   // this, and if they did, they would already be constant folded.
5384   return getCouldNotCompute();
5385 }
5386 
5387 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5388 /// (which may not be an immediate predecessor) which has exactly one
5389 /// successor from which BB is reachable, or null if no such block is
5390 /// found.
5391 ///
5392 std::pair<BasicBlock *, BasicBlock *>
getPredecessorWithUniqueSuccessorForBB(BasicBlock * BB)5393 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5394   // If the block has a unique predecessor, then there is no path from the
5395   // predecessor to the block that does not go through the direct edge
5396   // from the predecessor to the block.
5397   if (BasicBlock *Pred = BB->getSinglePredecessor())
5398     return std::make_pair(Pred, BB);
5399 
5400   // A loop's header is defined to be a block that dominates the loop.
5401   // If the header has a unique predecessor outside the loop, it must be
5402   // a block that has exactly one successor that can reach the loop.
5403   if (Loop *L = LI->getLoopFor(BB))
5404     return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5405 
5406   return std::pair<BasicBlock *, BasicBlock *>();
5407 }
5408 
5409 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5410 /// testing whether two expressions are equal, however for the purposes of
5411 /// looking for a condition guarding a loop, it can be useful to be a little
5412 /// more general, since a front-end may have replicated the controlling
5413 /// expression.
5414 ///
HasSameValue(const SCEV * A,const SCEV * B)5415 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5416   // Quick check to see if they are the same SCEV.
5417   if (A == B) return true;
5418 
5419   // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5420   // two different instructions with the same value. Check for this case.
5421   if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5422     if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5423       if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5424         if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5425           if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5426             return true;
5427 
5428   // Otherwise assume they may have a different value.
5429   return false;
5430 }
5431 
5432 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5433 /// predicate Pred. Return true iff any changes were made.
5434 ///
SimplifyICmpOperands(ICmpInst::Predicate & Pred,const SCEV * & LHS,const SCEV * & RHS)5435 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5436                                            const SCEV *&LHS, const SCEV *&RHS) {
5437   bool Changed = false;
5438 
5439   // Canonicalize a constant to the right side.
5440   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5441     // Check for both operands constant.
5442     if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5443       if (ConstantExpr::getICmp(Pred,
5444                                 LHSC->getValue(),
5445                                 RHSC->getValue())->isNullValue())
5446         goto trivially_false;
5447       else
5448         goto trivially_true;
5449     }
5450     // Otherwise swap the operands to put the constant on the right.
5451     std::swap(LHS, RHS);
5452     Pred = ICmpInst::getSwappedPredicate(Pred);
5453     Changed = true;
5454   }
5455 
5456   // If we're comparing an addrec with a value which is loop-invariant in the
5457   // addrec's loop, put the addrec on the left. Also make a dominance check,
5458   // as both operands could be addrecs loop-invariant in each other's loop.
5459   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5460     const Loop *L = AR->getLoop();
5461     if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5462       std::swap(LHS, RHS);
5463       Pred = ICmpInst::getSwappedPredicate(Pred);
5464       Changed = true;
5465     }
5466   }
5467 
5468   // If there's a constant operand, canonicalize comparisons with boundary
5469   // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5470   if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5471     const APInt &RA = RC->getValue()->getValue();
5472     switch (Pred) {
5473     default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5474     case ICmpInst::ICMP_EQ:
5475     case ICmpInst::ICMP_NE:
5476       break;
5477     case ICmpInst::ICMP_UGE:
5478       if ((RA - 1).isMinValue()) {
5479         Pred = ICmpInst::ICMP_NE;
5480         RHS = getConstant(RA - 1);
5481         Changed = true;
5482         break;
5483       }
5484       if (RA.isMaxValue()) {
5485         Pred = ICmpInst::ICMP_EQ;
5486         Changed = true;
5487         break;
5488       }
5489       if (RA.isMinValue()) goto trivially_true;
5490 
5491       Pred = ICmpInst::ICMP_UGT;
5492       RHS = getConstant(RA - 1);
5493       Changed = true;
5494       break;
5495     case ICmpInst::ICMP_ULE:
5496       if ((RA + 1).isMaxValue()) {
5497         Pred = ICmpInst::ICMP_NE;
5498         RHS = getConstant(RA + 1);
5499         Changed = true;
5500         break;
5501       }
5502       if (RA.isMinValue()) {
5503         Pred = ICmpInst::ICMP_EQ;
5504         Changed = true;
5505         break;
5506       }
5507       if (RA.isMaxValue()) goto trivially_true;
5508 
5509       Pred = ICmpInst::ICMP_ULT;
5510       RHS = getConstant(RA + 1);
5511       Changed = true;
5512       break;
5513     case ICmpInst::ICMP_SGE:
5514       if ((RA - 1).isMinSignedValue()) {
5515         Pred = ICmpInst::ICMP_NE;
5516         RHS = getConstant(RA - 1);
5517         Changed = true;
5518         break;
5519       }
5520       if (RA.isMaxSignedValue()) {
5521         Pred = ICmpInst::ICMP_EQ;
5522         Changed = true;
5523         break;
5524       }
5525       if (RA.isMinSignedValue()) goto trivially_true;
5526 
5527       Pred = ICmpInst::ICMP_SGT;
5528       RHS = getConstant(RA - 1);
5529       Changed = true;
5530       break;
5531     case ICmpInst::ICMP_SLE:
5532       if ((RA + 1).isMaxSignedValue()) {
5533         Pred = ICmpInst::ICMP_NE;
5534         RHS = getConstant(RA + 1);
5535         Changed = true;
5536         break;
5537       }
5538       if (RA.isMinSignedValue()) {
5539         Pred = ICmpInst::ICMP_EQ;
5540         Changed = true;
5541         break;
5542       }
5543       if (RA.isMaxSignedValue()) goto trivially_true;
5544 
5545       Pred = ICmpInst::ICMP_SLT;
5546       RHS = getConstant(RA + 1);
5547       Changed = true;
5548       break;
5549     case ICmpInst::ICMP_UGT:
5550       if (RA.isMinValue()) {
5551         Pred = ICmpInst::ICMP_NE;
5552         Changed = true;
5553         break;
5554       }
5555       if ((RA + 1).isMaxValue()) {
5556         Pred = ICmpInst::ICMP_EQ;
5557         RHS = getConstant(RA + 1);
5558         Changed = true;
5559         break;
5560       }
5561       if (RA.isMaxValue()) goto trivially_false;
5562       break;
5563     case ICmpInst::ICMP_ULT:
5564       if (RA.isMaxValue()) {
5565         Pred = ICmpInst::ICMP_NE;
5566         Changed = true;
5567         break;
5568       }
5569       if ((RA - 1).isMinValue()) {
5570         Pred = ICmpInst::ICMP_EQ;
5571         RHS = getConstant(RA - 1);
5572         Changed = true;
5573         break;
5574       }
5575       if (RA.isMinValue()) goto trivially_false;
5576       break;
5577     case ICmpInst::ICMP_SGT:
5578       if (RA.isMinSignedValue()) {
5579         Pred = ICmpInst::ICMP_NE;
5580         Changed = true;
5581         break;
5582       }
5583       if ((RA + 1).isMaxSignedValue()) {
5584         Pred = ICmpInst::ICMP_EQ;
5585         RHS = getConstant(RA + 1);
5586         Changed = true;
5587         break;
5588       }
5589       if (RA.isMaxSignedValue()) goto trivially_false;
5590       break;
5591     case ICmpInst::ICMP_SLT:
5592       if (RA.isMaxSignedValue()) {
5593         Pred = ICmpInst::ICMP_NE;
5594         Changed = true;
5595         break;
5596       }
5597       if ((RA - 1).isMinSignedValue()) {
5598        Pred = ICmpInst::ICMP_EQ;
5599        RHS = getConstant(RA - 1);
5600         Changed = true;
5601        break;
5602       }
5603       if (RA.isMinSignedValue()) goto trivially_false;
5604       break;
5605     }
5606   }
5607 
5608   // Check for obvious equality.
5609   if (HasSameValue(LHS, RHS)) {
5610     if (ICmpInst::isTrueWhenEqual(Pred))
5611       goto trivially_true;
5612     if (ICmpInst::isFalseWhenEqual(Pred))
5613       goto trivially_false;
5614   }
5615 
5616   // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5617   // adding or subtracting 1 from one of the operands.
5618   switch (Pred) {
5619   case ICmpInst::ICMP_SLE:
5620     if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5621       RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5622                        SCEV::FlagNSW);
5623       Pred = ICmpInst::ICMP_SLT;
5624       Changed = true;
5625     } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5626       LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5627                        SCEV::FlagNSW);
5628       Pred = ICmpInst::ICMP_SLT;
5629       Changed = true;
5630     }
5631     break;
5632   case ICmpInst::ICMP_SGE:
5633     if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5634       RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5635                        SCEV::FlagNSW);
5636       Pred = ICmpInst::ICMP_SGT;
5637       Changed = true;
5638     } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5639       LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5640                        SCEV::FlagNSW);
5641       Pred = ICmpInst::ICMP_SGT;
5642       Changed = true;
5643     }
5644     break;
5645   case ICmpInst::ICMP_ULE:
5646     if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5647       RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5648                        SCEV::FlagNUW);
5649       Pred = ICmpInst::ICMP_ULT;
5650       Changed = true;
5651     } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5652       LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5653                        SCEV::FlagNUW);
5654       Pred = ICmpInst::ICMP_ULT;
5655       Changed = true;
5656     }
5657     break;
5658   case ICmpInst::ICMP_UGE:
5659     if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5660       RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5661                        SCEV::FlagNUW);
5662       Pred = ICmpInst::ICMP_UGT;
5663       Changed = true;
5664     } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5665       LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5666                        SCEV::FlagNUW);
5667       Pred = ICmpInst::ICMP_UGT;
5668       Changed = true;
5669     }
5670     break;
5671   default:
5672     break;
5673   }
5674 
5675   // TODO: More simplifications are possible here.
5676 
5677   return Changed;
5678 
5679 trivially_true:
5680   // Return 0 == 0.
5681   LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5682   Pred = ICmpInst::ICMP_EQ;
5683   return true;
5684 
5685 trivially_false:
5686   // Return 0 != 0.
5687   LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5688   Pred = ICmpInst::ICMP_NE;
5689   return true;
5690 }
5691 
isKnownNegative(const SCEV * S)5692 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5693   return getSignedRange(S).getSignedMax().isNegative();
5694 }
5695 
isKnownPositive(const SCEV * S)5696 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5697   return getSignedRange(S).getSignedMin().isStrictlyPositive();
5698 }
5699 
isKnownNonNegative(const SCEV * S)5700 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5701   return !getSignedRange(S).getSignedMin().isNegative();
5702 }
5703 
isKnownNonPositive(const SCEV * S)5704 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5705   return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5706 }
5707 
isKnownNonZero(const SCEV * S)5708 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5709   return isKnownNegative(S) || isKnownPositive(S);
5710 }
5711 
isKnownPredicate(ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS)5712 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5713                                        const SCEV *LHS, const SCEV *RHS) {
5714   // Canonicalize the inputs first.
5715   (void)SimplifyICmpOperands(Pred, LHS, RHS);
5716 
5717   // If LHS or RHS is an addrec, check to see if the condition is true in
5718   // every iteration of the loop.
5719   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5720     if (isLoopEntryGuardedByCond(
5721           AR->getLoop(), Pred, AR->getStart(), RHS) &&
5722         isLoopBackedgeGuardedByCond(
5723           AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5724       return true;
5725   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5726     if (isLoopEntryGuardedByCond(
5727           AR->getLoop(), Pred, LHS, AR->getStart()) &&
5728         isLoopBackedgeGuardedByCond(
5729           AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5730       return true;
5731 
5732   // Otherwise see what can be done with known constant ranges.
5733   return isKnownPredicateWithRanges(Pred, LHS, RHS);
5734 }
5735 
5736 bool
isKnownPredicateWithRanges(ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS)5737 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5738                                             const SCEV *LHS, const SCEV *RHS) {
5739   if (HasSameValue(LHS, RHS))
5740     return ICmpInst::isTrueWhenEqual(Pred);
5741 
5742   // This code is split out from isKnownPredicate because it is called from
5743   // within isLoopEntryGuardedByCond.
5744   switch (Pred) {
5745   default:
5746     llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5747     break;
5748   case ICmpInst::ICMP_SGT:
5749     Pred = ICmpInst::ICMP_SLT;
5750     std::swap(LHS, RHS);
5751   case ICmpInst::ICMP_SLT: {
5752     ConstantRange LHSRange = getSignedRange(LHS);
5753     ConstantRange RHSRange = getSignedRange(RHS);
5754     if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5755       return true;
5756     if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5757       return false;
5758     break;
5759   }
5760   case ICmpInst::ICMP_SGE:
5761     Pred = ICmpInst::ICMP_SLE;
5762     std::swap(LHS, RHS);
5763   case ICmpInst::ICMP_SLE: {
5764     ConstantRange LHSRange = getSignedRange(LHS);
5765     ConstantRange RHSRange = getSignedRange(RHS);
5766     if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5767       return true;
5768     if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5769       return false;
5770     break;
5771   }
5772   case ICmpInst::ICMP_UGT:
5773     Pred = ICmpInst::ICMP_ULT;
5774     std::swap(LHS, RHS);
5775   case ICmpInst::ICMP_ULT: {
5776     ConstantRange LHSRange = getUnsignedRange(LHS);
5777     ConstantRange RHSRange = getUnsignedRange(RHS);
5778     if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5779       return true;
5780     if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5781       return false;
5782     break;
5783   }
5784   case ICmpInst::ICMP_UGE:
5785     Pred = ICmpInst::ICMP_ULE;
5786     std::swap(LHS, RHS);
5787   case ICmpInst::ICMP_ULE: {
5788     ConstantRange LHSRange = getUnsignedRange(LHS);
5789     ConstantRange RHSRange = getUnsignedRange(RHS);
5790     if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5791       return true;
5792     if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5793       return false;
5794     break;
5795   }
5796   case ICmpInst::ICMP_NE: {
5797     if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5798       return true;
5799     if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5800       return true;
5801 
5802     const SCEV *Diff = getMinusSCEV(LHS, RHS);
5803     if (isKnownNonZero(Diff))
5804       return true;
5805     break;
5806   }
5807   case ICmpInst::ICMP_EQ:
5808     // The check at the top of the function catches the case where
5809     // the values are known to be equal.
5810     break;
5811   }
5812   return false;
5813 }
5814 
5815 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
5816 /// protected by a conditional between LHS and RHS.  This is used to
5817 /// to eliminate casts.
5818 bool
isLoopBackedgeGuardedByCond(const Loop * L,ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS)5819 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
5820                                              ICmpInst::Predicate Pred,
5821                                              const SCEV *LHS, const SCEV *RHS) {
5822   // Interpret a null as meaning no loop, where there is obviously no guard
5823   // (interprocedural conditions notwithstanding).
5824   if (!L) return true;
5825 
5826   BasicBlock *Latch = L->getLoopLatch();
5827   if (!Latch)
5828     return false;
5829 
5830   BranchInst *LoopContinuePredicate =
5831     dyn_cast<BranchInst>(Latch->getTerminator());
5832   if (!LoopContinuePredicate ||
5833       LoopContinuePredicate->isUnconditional())
5834     return false;
5835 
5836   return isImpliedCond(Pred, LHS, RHS,
5837                        LoopContinuePredicate->getCondition(),
5838                        LoopContinuePredicate->getSuccessor(0) != L->getHeader());
5839 }
5840 
5841 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
5842 /// by a conditional between LHS and RHS.  This is used to help avoid max
5843 /// expressions in loop trip counts, and to eliminate casts.
5844 bool
isLoopEntryGuardedByCond(const Loop * L,ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS)5845 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
5846                                           ICmpInst::Predicate Pred,
5847                                           const SCEV *LHS, const SCEV *RHS) {
5848   // Interpret a null as meaning no loop, where there is obviously no guard
5849   // (interprocedural conditions notwithstanding).
5850   if (!L) return false;
5851 
5852   // Starting at the loop predecessor, climb up the predecessor chain, as long
5853   // as there are predecessors that can be found that have unique successors
5854   // leading to the original header.
5855   for (std::pair<BasicBlock *, BasicBlock *>
5856          Pair(L->getLoopPredecessor(), L->getHeader());
5857        Pair.first;
5858        Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
5859 
5860     BranchInst *LoopEntryPredicate =
5861       dyn_cast<BranchInst>(Pair.first->getTerminator());
5862     if (!LoopEntryPredicate ||
5863         LoopEntryPredicate->isUnconditional())
5864       continue;
5865 
5866     if (isImpliedCond(Pred, LHS, RHS,
5867                       LoopEntryPredicate->getCondition(),
5868                       LoopEntryPredicate->getSuccessor(0) != Pair.second))
5869       return true;
5870   }
5871 
5872   return false;
5873 }
5874 
5875 /// isImpliedCond - Test whether the condition described by Pred, LHS,
5876 /// and RHS is true whenever the given Cond value evaluates to true.
isImpliedCond(ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS,Value * FoundCondValue,bool Inverse)5877 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
5878                                     const SCEV *LHS, const SCEV *RHS,
5879                                     Value *FoundCondValue,
5880                                     bool Inverse) {
5881   // Recursively handle And and Or conditions.
5882   if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
5883     if (BO->getOpcode() == Instruction::And) {
5884       if (!Inverse)
5885         return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5886                isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5887     } else if (BO->getOpcode() == Instruction::Or) {
5888       if (Inverse)
5889         return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5890                isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5891     }
5892   }
5893 
5894   ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
5895   if (!ICI) return false;
5896 
5897   // Bail if the ICmp's operands' types are wider than the needed type
5898   // before attempting to call getSCEV on them. This avoids infinite
5899   // recursion, since the analysis of widening casts can require loop
5900   // exit condition information for overflow checking, which would
5901   // lead back here.
5902   if (getTypeSizeInBits(LHS->getType()) <
5903       getTypeSizeInBits(ICI->getOperand(0)->getType()))
5904     return false;
5905 
5906   // Now that we found a conditional branch that dominates the loop, check to
5907   // see if it is the comparison we are looking for.
5908   ICmpInst::Predicate FoundPred;
5909   if (Inverse)
5910     FoundPred = ICI->getInversePredicate();
5911   else
5912     FoundPred = ICI->getPredicate();
5913 
5914   const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
5915   const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
5916 
5917   // Balance the types. The case where FoundLHS' type is wider than
5918   // LHS' type is checked for above.
5919   if (getTypeSizeInBits(LHS->getType()) >
5920       getTypeSizeInBits(FoundLHS->getType())) {
5921     if (CmpInst::isSigned(Pred)) {
5922       FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
5923       FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
5924     } else {
5925       FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
5926       FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
5927     }
5928   }
5929 
5930   // Canonicalize the query to match the way instcombine will have
5931   // canonicalized the comparison.
5932   if (SimplifyICmpOperands(Pred, LHS, RHS))
5933     if (LHS == RHS)
5934       return CmpInst::isTrueWhenEqual(Pred);
5935   if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
5936     if (FoundLHS == FoundRHS)
5937       return CmpInst::isFalseWhenEqual(Pred);
5938 
5939   // Check to see if we can make the LHS or RHS match.
5940   if (LHS == FoundRHS || RHS == FoundLHS) {
5941     if (isa<SCEVConstant>(RHS)) {
5942       std::swap(FoundLHS, FoundRHS);
5943       FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
5944     } else {
5945       std::swap(LHS, RHS);
5946       Pred = ICmpInst::getSwappedPredicate(Pred);
5947     }
5948   }
5949 
5950   // Check whether the found predicate is the same as the desired predicate.
5951   if (FoundPred == Pred)
5952     return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
5953 
5954   // Check whether swapping the found predicate makes it the same as the
5955   // desired predicate.
5956   if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
5957     if (isa<SCEVConstant>(RHS))
5958       return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
5959     else
5960       return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
5961                                    RHS, LHS, FoundLHS, FoundRHS);
5962   }
5963 
5964   // Check whether the actual condition is beyond sufficient.
5965   if (FoundPred == ICmpInst::ICMP_EQ)
5966     if (ICmpInst::isTrueWhenEqual(Pred))
5967       if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
5968         return true;
5969   if (Pred == ICmpInst::ICMP_NE)
5970     if (!ICmpInst::isTrueWhenEqual(FoundPred))
5971       if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
5972         return true;
5973 
5974   // Otherwise assume the worst.
5975   return false;
5976 }
5977 
5978 /// isImpliedCondOperands - Test whether the condition described by Pred,
5979 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
5980 /// and FoundRHS is true.
isImpliedCondOperands(ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS,const SCEV * FoundLHS,const SCEV * FoundRHS)5981 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
5982                                             const SCEV *LHS, const SCEV *RHS,
5983                                             const SCEV *FoundLHS,
5984                                             const SCEV *FoundRHS) {
5985   return isImpliedCondOperandsHelper(Pred, LHS, RHS,
5986                                      FoundLHS, FoundRHS) ||
5987          // ~x < ~y --> x > y
5988          isImpliedCondOperandsHelper(Pred, LHS, RHS,
5989                                      getNotSCEV(FoundRHS),
5990                                      getNotSCEV(FoundLHS));
5991 }
5992 
5993 /// isImpliedCondOperandsHelper - Test whether the condition described by
5994 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
5995 /// FoundLHS, and FoundRHS is true.
5996 bool
isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS,const SCEV * FoundLHS,const SCEV * FoundRHS)5997 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
5998                                              const SCEV *LHS, const SCEV *RHS,
5999                                              const SCEV *FoundLHS,
6000                                              const SCEV *FoundRHS) {
6001   switch (Pred) {
6002   default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6003   case ICmpInst::ICMP_EQ:
6004   case ICmpInst::ICMP_NE:
6005     if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6006       return true;
6007     break;
6008   case ICmpInst::ICMP_SLT:
6009   case ICmpInst::ICMP_SLE:
6010     if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6011         isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6012       return true;
6013     break;
6014   case ICmpInst::ICMP_SGT:
6015   case ICmpInst::ICMP_SGE:
6016     if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6017         isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6018       return true;
6019     break;
6020   case ICmpInst::ICMP_ULT:
6021   case ICmpInst::ICMP_ULE:
6022     if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6023         isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6024       return true;
6025     break;
6026   case ICmpInst::ICMP_UGT:
6027   case ICmpInst::ICMP_UGE:
6028     if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6029         isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6030       return true;
6031     break;
6032   }
6033 
6034   return false;
6035 }
6036 
6037 /// getBECount - Subtract the end and start values and divide by the step,
6038 /// rounding up, to get the number of times the backedge is executed. Return
6039 /// CouldNotCompute if an intermediate computation overflows.
getBECount(const SCEV * Start,const SCEV * End,const SCEV * Step,bool NoWrap)6040 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
6041                                         const SCEV *End,
6042                                         const SCEV *Step,
6043                                         bool NoWrap) {
6044   assert(!isKnownNegative(Step) &&
6045          "This code doesn't handle negative strides yet!");
6046 
6047   Type *Ty = Start->getType();
6048 
6049   // When Start == End, we have an exact BECount == 0. Short-circuit this case
6050   // here because SCEV may not be able to determine that the unsigned division
6051   // after rounding is zero.
6052   if (Start == End)
6053     return getConstant(Ty, 0);
6054 
6055   const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
6056   const SCEV *Diff = getMinusSCEV(End, Start);
6057   const SCEV *RoundUp = getAddExpr(Step, NegOne);
6058 
6059   // Add an adjustment to the difference between End and Start so that
6060   // the division will effectively round up.
6061   const SCEV *Add = getAddExpr(Diff, RoundUp);
6062 
6063   if (!NoWrap) {
6064     // Check Add for unsigned overflow.
6065     // TODO: More sophisticated things could be done here.
6066     Type *WideTy = IntegerType::get(getContext(),
6067                                           getTypeSizeInBits(Ty) + 1);
6068     const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
6069     const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
6070     const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
6071     if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
6072       return getCouldNotCompute();
6073   }
6074 
6075   return getUDivExpr(Add, Step);
6076 }
6077 
6078 /// HowManyLessThans - Return the number of times a backedge containing the
6079 /// specified less-than comparison will execute.  If not computable, return
6080 /// CouldNotCompute.
6081 ScalarEvolution::ExitLimit
HowManyLessThans(const SCEV * LHS,const SCEV * RHS,const Loop * L,bool isSigned)6082 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
6083                                   const Loop *L, bool isSigned) {
6084   // Only handle:  "ADDREC < LoopInvariant".
6085   if (!isLoopInvariant(RHS, L)) return getCouldNotCompute();
6086 
6087   const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
6088   if (!AddRec || AddRec->getLoop() != L)
6089     return getCouldNotCompute();
6090 
6091   // Check to see if we have a flag which makes analysis easy.
6092   bool NoWrap = isSigned ? AddRec->getNoWrapFlags(SCEV::FlagNSW) :
6093                            AddRec->getNoWrapFlags(SCEV::FlagNUW);
6094 
6095   if (AddRec->isAffine()) {
6096     unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
6097     const SCEV *Step = AddRec->getStepRecurrence(*this);
6098 
6099     if (Step->isZero())
6100       return getCouldNotCompute();
6101     if (Step->isOne()) {
6102       // With unit stride, the iteration never steps past the limit value.
6103     } else if (isKnownPositive(Step)) {
6104       // Test whether a positive iteration can step past the limit
6105       // value and past the maximum value for its type in a single step.
6106       // Note that it's not sufficient to check NoWrap here, because even
6107       // though the value after a wrap is undefined, it's not undefined
6108       // behavior, so if wrap does occur, the loop could either terminate or
6109       // loop infinitely, but in either case, the loop is guaranteed to
6110       // iterate at least until the iteration where the wrapping occurs.
6111       const SCEV *One = getConstant(Step->getType(), 1);
6112       if (isSigned) {
6113         APInt Max = APInt::getSignedMaxValue(BitWidth);
6114         if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
6115               .slt(getSignedRange(RHS).getSignedMax()))
6116           return getCouldNotCompute();
6117       } else {
6118         APInt Max = APInt::getMaxValue(BitWidth);
6119         if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
6120               .ult(getUnsignedRange(RHS).getUnsignedMax()))
6121           return getCouldNotCompute();
6122       }
6123     } else
6124       // TODO: Handle negative strides here and below.
6125       return getCouldNotCompute();
6126 
6127     // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
6128     // m.  So, we count the number of iterations in which {n,+,s} < m is true.
6129     // Note that we cannot simply return max(m-n,0)/s because it's not safe to
6130     // treat m-n as signed nor unsigned due to overflow possibility.
6131 
6132     // First, we get the value of the LHS in the first iteration: n
6133     const SCEV *Start = AddRec->getOperand(0);
6134 
6135     // Determine the minimum constant start value.
6136     const SCEV *MinStart = getConstant(isSigned ?
6137       getSignedRange(Start).getSignedMin() :
6138       getUnsignedRange(Start).getUnsignedMin());
6139 
6140     // If we know that the condition is true in order to enter the loop,
6141     // then we know that it will run exactly (m-n)/s times. Otherwise, we
6142     // only know that it will execute (max(m,n)-n)/s times. In both cases,
6143     // the division must round up.
6144     const SCEV *End = RHS;
6145     if (!isLoopEntryGuardedByCond(L,
6146                                   isSigned ? ICmpInst::ICMP_SLT :
6147                                              ICmpInst::ICMP_ULT,
6148                                   getMinusSCEV(Start, Step), RHS))
6149       End = isSigned ? getSMaxExpr(RHS, Start)
6150                      : getUMaxExpr(RHS, Start);
6151 
6152     // Determine the maximum constant end value.
6153     const SCEV *MaxEnd = getConstant(isSigned ?
6154       getSignedRange(End).getSignedMax() :
6155       getUnsignedRange(End).getUnsignedMax());
6156 
6157     // If MaxEnd is within a step of the maximum integer value in its type,
6158     // adjust it down to the minimum value which would produce the same effect.
6159     // This allows the subsequent ceiling division of (N+(step-1))/step to
6160     // compute the correct value.
6161     const SCEV *StepMinusOne = getMinusSCEV(Step,
6162                                             getConstant(Step->getType(), 1));
6163     MaxEnd = isSigned ?
6164       getSMinExpr(MaxEnd,
6165                   getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
6166                                StepMinusOne)) :
6167       getUMinExpr(MaxEnd,
6168                   getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
6169                                StepMinusOne));
6170 
6171     // Finally, we subtract these two values and divide, rounding up, to get
6172     // the number of times the backedge is executed.
6173     const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
6174 
6175     // The maximum backedge count is similar, except using the minimum start
6176     // value and the maximum end value.
6177     // If we already have an exact constant BECount, use it instead.
6178     const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount
6179       : getBECount(MinStart, MaxEnd, Step, NoWrap);
6180 
6181     // If the stride is nonconstant, and NoWrap == true, then
6182     // getBECount(MinStart, MaxEnd) may not compute. This would result in an
6183     // exact BECount and invalid MaxBECount, which should be avoided to catch
6184     // more optimization opportunities.
6185     if (isa<SCEVCouldNotCompute>(MaxBECount))
6186       MaxBECount = BECount;
6187 
6188     return ExitLimit(BECount, MaxBECount);
6189   }
6190 
6191   return getCouldNotCompute();
6192 }
6193 
6194 /// getNumIterationsInRange - Return the number of iterations of this loop that
6195 /// produce values in the specified constant range.  Another way of looking at
6196 /// this is that it returns the first iteration number where the value is not in
6197 /// the condition, thus computing the exit count. If the iteration count can't
6198 /// be computed, an instance of SCEVCouldNotCompute is returned.
getNumIterationsInRange(ConstantRange Range,ScalarEvolution & SE) const6199 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6200                                                     ScalarEvolution &SE) const {
6201   if (Range.isFullSet())  // Infinite loop.
6202     return SE.getCouldNotCompute();
6203 
6204   // If the start is a non-zero constant, shift the range to simplify things.
6205   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6206     if (!SC->getValue()->isZero()) {
6207       SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6208       Operands[0] = SE.getConstant(SC->getType(), 0);
6209       const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6210                                              getNoWrapFlags(FlagNW));
6211       if (const SCEVAddRecExpr *ShiftedAddRec =
6212             dyn_cast<SCEVAddRecExpr>(Shifted))
6213         return ShiftedAddRec->getNumIterationsInRange(
6214                            Range.subtract(SC->getValue()->getValue()), SE);
6215       // This is strange and shouldn't happen.
6216       return SE.getCouldNotCompute();
6217     }
6218 
6219   // The only time we can solve this is when we have all constant indices.
6220   // Otherwise, we cannot determine the overflow conditions.
6221   for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6222     if (!isa<SCEVConstant>(getOperand(i)))
6223       return SE.getCouldNotCompute();
6224 
6225 
6226   // Okay at this point we know that all elements of the chrec are constants and
6227   // that the start element is zero.
6228 
6229   // First check to see if the range contains zero.  If not, the first
6230   // iteration exits.
6231   unsigned BitWidth = SE.getTypeSizeInBits(getType());
6232   if (!Range.contains(APInt(BitWidth, 0)))
6233     return SE.getConstant(getType(), 0);
6234 
6235   if (isAffine()) {
6236     // If this is an affine expression then we have this situation:
6237     //   Solve {0,+,A} in Range  ===  Ax in Range
6238 
6239     // We know that zero is in the range.  If A is positive then we know that
6240     // the upper value of the range must be the first possible exit value.
6241     // If A is negative then the lower of the range is the last possible loop
6242     // value.  Also note that we already checked for a full range.
6243     APInt One(BitWidth,1);
6244     APInt A     = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6245     APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6246 
6247     // The exit value should be (End+A)/A.
6248     APInt ExitVal = (End + A).udiv(A);
6249     ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6250 
6251     // Evaluate at the exit value.  If we really did fall out of the valid
6252     // range, then we computed our trip count, otherwise wrap around or other
6253     // things must have happened.
6254     ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6255     if (Range.contains(Val->getValue()))
6256       return SE.getCouldNotCompute();  // Something strange happened
6257 
6258     // Ensure that the previous value is in the range.  This is a sanity check.
6259     assert(Range.contains(
6260            EvaluateConstantChrecAtConstant(this,
6261            ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6262            "Linear scev computation is off in a bad way!");
6263     return SE.getConstant(ExitValue);
6264   } else if (isQuadratic()) {
6265     // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6266     // quadratic equation to solve it.  To do this, we must frame our problem in
6267     // terms of figuring out when zero is crossed, instead of when
6268     // Range.getUpper() is crossed.
6269     SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6270     NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6271     const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6272                                              // getNoWrapFlags(FlagNW)
6273                                              FlagAnyWrap);
6274 
6275     // Next, solve the constructed addrec
6276     std::pair<const SCEV *,const SCEV *> Roots =
6277       SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6278     const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6279     const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6280     if (R1) {
6281       // Pick the smallest positive root value.
6282       if (ConstantInt *CB =
6283           dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6284                          R1->getValue(), R2->getValue()))) {
6285         if (CB->getZExtValue() == false)
6286           std::swap(R1, R2);   // R1 is the minimum root now.
6287 
6288         // Make sure the root is not off by one.  The returned iteration should
6289         // not be in the range, but the previous one should be.  When solving
6290         // for "X*X < 5", for example, we should not return a root of 2.
6291         ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6292                                                              R1->getValue(),
6293                                                              SE);
6294         if (Range.contains(R1Val->getValue())) {
6295           // The next iteration must be out of the range...
6296           ConstantInt *NextVal =
6297                 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6298 
6299           R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6300           if (!Range.contains(R1Val->getValue()))
6301             return SE.getConstant(NextVal);
6302           return SE.getCouldNotCompute();  // Something strange happened
6303         }
6304 
6305         // If R1 was not in the range, then it is a good return value.  Make
6306         // sure that R1-1 WAS in the range though, just in case.
6307         ConstantInt *NextVal =
6308                ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6309         R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6310         if (Range.contains(R1Val->getValue()))
6311           return R1;
6312         return SE.getCouldNotCompute();  // Something strange happened
6313       }
6314     }
6315   }
6316 
6317   return SE.getCouldNotCompute();
6318 }
6319 
6320 
6321 
6322 //===----------------------------------------------------------------------===//
6323 //                   SCEVCallbackVH Class Implementation
6324 //===----------------------------------------------------------------------===//
6325 
deleted()6326 void ScalarEvolution::SCEVCallbackVH::deleted() {
6327   assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6328   if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
6329     SE->ConstantEvolutionLoopExitValue.erase(PN);
6330   SE->ValueExprMap.erase(getValPtr());
6331   // this now dangles!
6332 }
6333 
allUsesReplacedWith(Value * V)6334 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
6335   assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6336 
6337   // Forget all the expressions associated with users of the old value,
6338   // so that future queries will recompute the expressions using the new
6339   // value.
6340   Value *Old = getValPtr();
6341   SmallVector<User *, 16> Worklist;
6342   SmallPtrSet<User *, 8> Visited;
6343   for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
6344        UI != UE; ++UI)
6345     Worklist.push_back(*UI);
6346   while (!Worklist.empty()) {
6347     User *U = Worklist.pop_back_val();
6348     // Deleting the Old value will cause this to dangle. Postpone
6349     // that until everything else is done.
6350     if (U == Old)
6351       continue;
6352     if (!Visited.insert(U))
6353       continue;
6354     if (PHINode *PN = dyn_cast<PHINode>(U))
6355       SE->ConstantEvolutionLoopExitValue.erase(PN);
6356     SE->ValueExprMap.erase(U);
6357     for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
6358          UI != UE; ++UI)
6359       Worklist.push_back(*UI);
6360   }
6361   // Delete the Old value.
6362   if (PHINode *PN = dyn_cast<PHINode>(Old))
6363     SE->ConstantEvolutionLoopExitValue.erase(PN);
6364   SE->ValueExprMap.erase(Old);
6365   // this now dangles!
6366 }
6367 
SCEVCallbackVH(Value * V,ScalarEvolution * se)6368 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
6369   : CallbackVH(V), SE(se) {}
6370 
6371 //===----------------------------------------------------------------------===//
6372 //                   ScalarEvolution Class Implementation
6373 //===----------------------------------------------------------------------===//
6374 
ScalarEvolution()6375 ScalarEvolution::ScalarEvolution()
6376   : FunctionPass(ID), FirstUnknown(0) {
6377   initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
6378 }
6379 
runOnFunction(Function & F)6380 bool ScalarEvolution::runOnFunction(Function &F) {
6381   this->F = &F;
6382   LI = &getAnalysis<LoopInfo>();
6383   TD = getAnalysisIfAvailable<TargetData>();
6384   DT = &getAnalysis<DominatorTree>();
6385   return false;
6386 }
6387 
releaseMemory()6388 void ScalarEvolution::releaseMemory() {
6389   // Iterate through all the SCEVUnknown instances and call their
6390   // destructors, so that they release their references to their values.
6391   for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
6392     U->~SCEVUnknown();
6393   FirstUnknown = 0;
6394 
6395   ValueExprMap.clear();
6396 
6397   // Free any extra memory created for ExitNotTakenInfo in the unlikely event
6398   // that a loop had multiple computable exits.
6399   for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
6400          BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
6401        I != E; ++I) {
6402     I->second.clear();
6403   }
6404 
6405   BackedgeTakenCounts.clear();
6406   ConstantEvolutionLoopExitValue.clear();
6407   ValuesAtScopes.clear();
6408   LoopDispositions.clear();
6409   BlockDispositions.clear();
6410   UnsignedRanges.clear();
6411   SignedRanges.clear();
6412   UniqueSCEVs.clear();
6413   SCEVAllocator.Reset();
6414 }
6415 
getAnalysisUsage(AnalysisUsage & AU) const6416 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
6417   AU.setPreservesAll();
6418   AU.addRequiredTransitive<LoopInfo>();
6419   AU.addRequiredTransitive<DominatorTree>();
6420 }
6421 
hasLoopInvariantBackedgeTakenCount(const Loop * L)6422 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
6423   return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
6424 }
6425 
PrintLoopInfo(raw_ostream & OS,ScalarEvolution * SE,const Loop * L)6426 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
6427                           const Loop *L) {
6428   // Print all inner loops first
6429   for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
6430     PrintLoopInfo(OS, SE, *I);
6431 
6432   OS << "Loop ";
6433   WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6434   OS << ": ";
6435 
6436   SmallVector<BasicBlock *, 8> ExitBlocks;
6437   L->getExitBlocks(ExitBlocks);
6438   if (ExitBlocks.size() != 1)
6439     OS << "<multiple exits> ";
6440 
6441   if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
6442     OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
6443   } else {
6444     OS << "Unpredictable backedge-taken count. ";
6445   }
6446 
6447   OS << "\n"
6448         "Loop ";
6449   WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6450   OS << ": ";
6451 
6452   if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
6453     OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
6454   } else {
6455     OS << "Unpredictable max backedge-taken count. ";
6456   }
6457 
6458   OS << "\n";
6459 }
6460 
print(raw_ostream & OS,const Module *) const6461 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
6462   // ScalarEvolution's implementation of the print method is to print
6463   // out SCEV values of all instructions that are interesting. Doing
6464   // this potentially causes it to create new SCEV objects though,
6465   // which technically conflicts with the const qualifier. This isn't
6466   // observable from outside the class though, so casting away the
6467   // const isn't dangerous.
6468   ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
6469 
6470   OS << "Classifying expressions for: ";
6471   WriteAsOperand(OS, F, /*PrintType=*/false);
6472   OS << "\n";
6473   for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
6474     if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
6475       OS << *I << '\n';
6476       OS << "  -->  ";
6477       const SCEV *SV = SE.getSCEV(&*I);
6478       SV->print(OS);
6479 
6480       const Loop *L = LI->getLoopFor((*I).getParent());
6481 
6482       const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
6483       if (AtUse != SV) {
6484         OS << "  -->  ";
6485         AtUse->print(OS);
6486       }
6487 
6488       if (L) {
6489         OS << "\t\t" "Exits: ";
6490         const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
6491         if (!SE.isLoopInvariant(ExitValue, L)) {
6492           OS << "<<Unknown>>";
6493         } else {
6494           OS << *ExitValue;
6495         }
6496       }
6497 
6498       OS << "\n";
6499     }
6500 
6501   OS << "Determining loop execution counts for: ";
6502   WriteAsOperand(OS, F, /*PrintType=*/false);
6503   OS << "\n";
6504   for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
6505     PrintLoopInfo(OS, &SE, *I);
6506 }
6507 
6508 ScalarEvolution::LoopDisposition
getLoopDisposition(const SCEV * S,const Loop * L)6509 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
6510   std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S];
6511   std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair =
6512     Values.insert(std::make_pair(L, LoopVariant));
6513   if (!Pair.second)
6514     return Pair.first->second;
6515 
6516   LoopDisposition D = computeLoopDisposition(S, L);
6517   return LoopDispositions[S][L] = D;
6518 }
6519 
6520 ScalarEvolution::LoopDisposition
computeLoopDisposition(const SCEV * S,const Loop * L)6521 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
6522   switch (S->getSCEVType()) {
6523   case scConstant:
6524     return LoopInvariant;
6525   case scTruncate:
6526   case scZeroExtend:
6527   case scSignExtend:
6528     return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
6529   case scAddRecExpr: {
6530     const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6531 
6532     // If L is the addrec's loop, it's computable.
6533     if (AR->getLoop() == L)
6534       return LoopComputable;
6535 
6536     // Add recurrences are never invariant in the function-body (null loop).
6537     if (!L)
6538       return LoopVariant;
6539 
6540     // This recurrence is variant w.r.t. L if L contains AR's loop.
6541     if (L->contains(AR->getLoop()))
6542       return LoopVariant;
6543 
6544     // This recurrence is invariant w.r.t. L if AR's loop contains L.
6545     if (AR->getLoop()->contains(L))
6546       return LoopInvariant;
6547 
6548     // This recurrence is variant w.r.t. L if any of its operands
6549     // are variant.
6550     for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
6551          I != E; ++I)
6552       if (!isLoopInvariant(*I, L))
6553         return LoopVariant;
6554 
6555     // Otherwise it's loop-invariant.
6556     return LoopInvariant;
6557   }
6558   case scAddExpr:
6559   case scMulExpr:
6560   case scUMaxExpr:
6561   case scSMaxExpr: {
6562     const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6563     bool HasVarying = false;
6564     for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6565          I != E; ++I) {
6566       LoopDisposition D = getLoopDisposition(*I, L);
6567       if (D == LoopVariant)
6568         return LoopVariant;
6569       if (D == LoopComputable)
6570         HasVarying = true;
6571     }
6572     return HasVarying ? LoopComputable : LoopInvariant;
6573   }
6574   case scUDivExpr: {
6575     const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6576     LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
6577     if (LD == LoopVariant)
6578       return LoopVariant;
6579     LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
6580     if (RD == LoopVariant)
6581       return LoopVariant;
6582     return (LD == LoopInvariant && RD == LoopInvariant) ?
6583            LoopInvariant : LoopComputable;
6584   }
6585   case scUnknown:
6586     // All non-instruction values are loop invariant.  All instructions are loop
6587     // invariant if they are not contained in the specified loop.
6588     // Instructions are never considered invariant in the function body
6589     // (null loop) because they are defined within the "loop".
6590     if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
6591       return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
6592     return LoopInvariant;
6593   case scCouldNotCompute:
6594     llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6595     return LoopVariant;
6596   default: break;
6597   }
6598   llvm_unreachable("Unknown SCEV kind!");
6599   return LoopVariant;
6600 }
6601 
isLoopInvariant(const SCEV * S,const Loop * L)6602 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
6603   return getLoopDisposition(S, L) == LoopInvariant;
6604 }
6605 
hasComputableLoopEvolution(const SCEV * S,const Loop * L)6606 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
6607   return getLoopDisposition(S, L) == LoopComputable;
6608 }
6609 
6610 ScalarEvolution::BlockDisposition
getBlockDisposition(const SCEV * S,const BasicBlock * BB)6611 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6612   std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S];
6613   std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool>
6614     Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock));
6615   if (!Pair.second)
6616     return Pair.first->second;
6617 
6618   BlockDisposition D = computeBlockDisposition(S, BB);
6619   return BlockDispositions[S][BB] = D;
6620 }
6621 
6622 ScalarEvolution::BlockDisposition
computeBlockDisposition(const SCEV * S,const BasicBlock * BB)6623 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6624   switch (S->getSCEVType()) {
6625   case scConstant:
6626     return ProperlyDominatesBlock;
6627   case scTruncate:
6628   case scZeroExtend:
6629   case scSignExtend:
6630     return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
6631   case scAddRecExpr: {
6632     // This uses a "dominates" query instead of "properly dominates" query
6633     // to test for proper dominance too, because the instruction which
6634     // produces the addrec's value is a PHI, and a PHI effectively properly
6635     // dominates its entire containing block.
6636     const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6637     if (!DT->dominates(AR->getLoop()->getHeader(), BB))
6638       return DoesNotDominateBlock;
6639   }
6640   // FALL THROUGH into SCEVNAryExpr handling.
6641   case scAddExpr:
6642   case scMulExpr:
6643   case scUMaxExpr:
6644   case scSMaxExpr: {
6645     const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6646     bool Proper = true;
6647     for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6648          I != E; ++I) {
6649       BlockDisposition D = getBlockDisposition(*I, BB);
6650       if (D == DoesNotDominateBlock)
6651         return DoesNotDominateBlock;
6652       if (D == DominatesBlock)
6653         Proper = false;
6654     }
6655     return Proper ? ProperlyDominatesBlock : DominatesBlock;
6656   }
6657   case scUDivExpr: {
6658     const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6659     const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6660     BlockDisposition LD = getBlockDisposition(LHS, BB);
6661     if (LD == DoesNotDominateBlock)
6662       return DoesNotDominateBlock;
6663     BlockDisposition RD = getBlockDisposition(RHS, BB);
6664     if (RD == DoesNotDominateBlock)
6665       return DoesNotDominateBlock;
6666     return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
6667       ProperlyDominatesBlock : DominatesBlock;
6668   }
6669   case scUnknown:
6670     if (Instruction *I =
6671           dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
6672       if (I->getParent() == BB)
6673         return DominatesBlock;
6674       if (DT->properlyDominates(I->getParent(), BB))
6675         return ProperlyDominatesBlock;
6676       return DoesNotDominateBlock;
6677     }
6678     return ProperlyDominatesBlock;
6679   case scCouldNotCompute:
6680     llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6681     return DoesNotDominateBlock;
6682   default: break;
6683   }
6684   llvm_unreachable("Unknown SCEV kind!");
6685   return DoesNotDominateBlock;
6686 }
6687 
dominates(const SCEV * S,const BasicBlock * BB)6688 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
6689   return getBlockDisposition(S, BB) >= DominatesBlock;
6690 }
6691 
properlyDominates(const SCEV * S,const BasicBlock * BB)6692 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
6693   return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
6694 }
6695 
hasOperand(const SCEV * S,const SCEV * Op) const6696 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
6697   switch (S->getSCEVType()) {
6698   case scConstant:
6699     return false;
6700   case scTruncate:
6701   case scZeroExtend:
6702   case scSignExtend: {
6703     const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S);
6704     const SCEV *CastOp = Cast->getOperand();
6705     return Op == CastOp || hasOperand(CastOp, Op);
6706   }
6707   case scAddRecExpr:
6708   case scAddExpr:
6709   case scMulExpr:
6710   case scUMaxExpr:
6711   case scSMaxExpr: {
6712     const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6713     for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6714          I != E; ++I) {
6715       const SCEV *NAryOp = *I;
6716       if (NAryOp == Op || hasOperand(NAryOp, Op))
6717         return true;
6718     }
6719     return false;
6720   }
6721   case scUDivExpr: {
6722     const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6723     const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6724     return LHS == Op || hasOperand(LHS, Op) ||
6725            RHS == Op || hasOperand(RHS, Op);
6726   }
6727   case scUnknown:
6728     return false;
6729   case scCouldNotCompute:
6730     llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6731     return false;
6732   default: break;
6733   }
6734   llvm_unreachable("Unknown SCEV kind!");
6735   return false;
6736 }
6737 
forgetMemoizedResults(const SCEV * S)6738 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
6739   ValuesAtScopes.erase(S);
6740   LoopDispositions.erase(S);
6741   BlockDispositions.erase(S);
6742   UnsignedRanges.erase(S);
6743   SignedRanges.erase(S);
6744 }
6745