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1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
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 #include "llvm/Analysis/ScalarEvolution.h"
62 #include "llvm/ADT/Optional.h"
63 #include "llvm/ADT/STLExtras.h"
64 #include "llvm/ADT/SmallPtrSet.h"
65 #include "llvm/ADT/Statistic.h"
66 #include "llvm/Analysis/AssumptionCache.h"
67 #include "llvm/Analysis/ConstantFolding.h"
68 #include "llvm/Analysis/InstructionSimplify.h"
69 #include "llvm/Analysis/LoopInfo.h"
70 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
71 #include "llvm/Analysis/TargetLibraryInfo.h"
72 #include "llvm/Analysis/ValueTracking.h"
73 #include "llvm/IR/ConstantRange.h"
74 #include "llvm/IR/Constants.h"
75 #include "llvm/IR/DataLayout.h"
76 #include "llvm/IR/DerivedTypes.h"
77 #include "llvm/IR/Dominators.h"
78 #include "llvm/IR/GetElementPtrTypeIterator.h"
79 #include "llvm/IR/GlobalAlias.h"
80 #include "llvm/IR/GlobalVariable.h"
81 #include "llvm/IR/InstIterator.h"
82 #include "llvm/IR/Instructions.h"
83 #include "llvm/IR/LLVMContext.h"
84 #include "llvm/IR/Metadata.h"
85 #include "llvm/IR/Operator.h"
86 #include "llvm/IR/PatternMatch.h"
87 #include "llvm/Support/CommandLine.h"
88 #include "llvm/Support/Debug.h"
89 #include "llvm/Support/ErrorHandling.h"
90 #include "llvm/Support/MathExtras.h"
91 #include "llvm/Support/raw_ostream.h"
92 #include "llvm/Support/SaveAndRestore.h"
93 #include <algorithm>
94 using namespace llvm;
95 
96 #define DEBUG_TYPE "scalar-evolution"
97 
98 STATISTIC(NumArrayLenItCounts,
99           "Number of trip counts computed with array length");
100 STATISTIC(NumTripCountsComputed,
101           "Number of loops with predictable loop counts");
102 STATISTIC(NumTripCountsNotComputed,
103           "Number of loops without predictable loop counts");
104 STATISTIC(NumBruteForceTripCountsComputed,
105           "Number of loops with trip counts computed by force");
106 
107 static cl::opt<unsigned>
108 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
109                         cl::desc("Maximum number of iterations SCEV will "
110                                  "symbolically execute a constant "
111                                  "derived loop"),
112                         cl::init(100));
113 
114 // FIXME: Enable this with EXPENSIVE_CHECKS when the test suite is clean.
115 static cl::opt<bool>
116 VerifySCEV("verify-scev",
117            cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
118 static cl::opt<bool>
119     VerifySCEVMap("verify-scev-maps",
120                   cl::desc("Verify no dangling value in ScalarEvolution's "
121                            "ExprValueMap (slow)"));
122 
123 //===----------------------------------------------------------------------===//
124 //                           SCEV class definitions
125 //===----------------------------------------------------------------------===//
126 
127 //===----------------------------------------------------------------------===//
128 // Implementation of the SCEV class.
129 //
130 
131 LLVM_DUMP_METHOD
dump() const132 void SCEV::dump() const {
133   print(dbgs());
134   dbgs() << '\n';
135 }
136 
print(raw_ostream & OS) const137 void SCEV::print(raw_ostream &OS) const {
138   switch (static_cast<SCEVTypes>(getSCEVType())) {
139   case scConstant:
140     cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
141     return;
142   case scTruncate: {
143     const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
144     const SCEV *Op = Trunc->getOperand();
145     OS << "(trunc " << *Op->getType() << " " << *Op << " to "
146        << *Trunc->getType() << ")";
147     return;
148   }
149   case scZeroExtend: {
150     const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
151     const SCEV *Op = ZExt->getOperand();
152     OS << "(zext " << *Op->getType() << " " << *Op << " to "
153        << *ZExt->getType() << ")";
154     return;
155   }
156   case scSignExtend: {
157     const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
158     const SCEV *Op = SExt->getOperand();
159     OS << "(sext " << *Op->getType() << " " << *Op << " to "
160        << *SExt->getType() << ")";
161     return;
162   }
163   case scAddRecExpr: {
164     const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
165     OS << "{" << *AR->getOperand(0);
166     for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
167       OS << ",+," << *AR->getOperand(i);
168     OS << "}<";
169     if (AR->hasNoUnsignedWrap())
170       OS << "nuw><";
171     if (AR->hasNoSignedWrap())
172       OS << "nsw><";
173     if (AR->hasNoSelfWrap() &&
174         !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
175       OS << "nw><";
176     AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
177     OS << ">";
178     return;
179   }
180   case scAddExpr:
181   case scMulExpr:
182   case scUMaxExpr:
183   case scSMaxExpr: {
184     const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
185     const char *OpStr = nullptr;
186     switch (NAry->getSCEVType()) {
187     case scAddExpr: OpStr = " + "; break;
188     case scMulExpr: OpStr = " * "; break;
189     case scUMaxExpr: OpStr = " umax "; break;
190     case scSMaxExpr: OpStr = " smax "; break;
191     }
192     OS << "(";
193     for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
194          I != E; ++I) {
195       OS << **I;
196       if (std::next(I) != E)
197         OS << OpStr;
198     }
199     OS << ")";
200     switch (NAry->getSCEVType()) {
201     case scAddExpr:
202     case scMulExpr:
203       if (NAry->hasNoUnsignedWrap())
204         OS << "<nuw>";
205       if (NAry->hasNoSignedWrap())
206         OS << "<nsw>";
207     }
208     return;
209   }
210   case scUDivExpr: {
211     const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
212     OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
213     return;
214   }
215   case scUnknown: {
216     const SCEVUnknown *U = cast<SCEVUnknown>(this);
217     Type *AllocTy;
218     if (U->isSizeOf(AllocTy)) {
219       OS << "sizeof(" << *AllocTy << ")";
220       return;
221     }
222     if (U->isAlignOf(AllocTy)) {
223       OS << "alignof(" << *AllocTy << ")";
224       return;
225     }
226 
227     Type *CTy;
228     Constant *FieldNo;
229     if (U->isOffsetOf(CTy, FieldNo)) {
230       OS << "offsetof(" << *CTy << ", ";
231       FieldNo->printAsOperand(OS, false);
232       OS << ")";
233       return;
234     }
235 
236     // Otherwise just print it normally.
237     U->getValue()->printAsOperand(OS, false);
238     return;
239   }
240   case scCouldNotCompute:
241     OS << "***COULDNOTCOMPUTE***";
242     return;
243   }
244   llvm_unreachable("Unknown SCEV kind!");
245 }
246 
getType() const247 Type *SCEV::getType() const {
248   switch (static_cast<SCEVTypes>(getSCEVType())) {
249   case scConstant:
250     return cast<SCEVConstant>(this)->getType();
251   case scTruncate:
252   case scZeroExtend:
253   case scSignExtend:
254     return cast<SCEVCastExpr>(this)->getType();
255   case scAddRecExpr:
256   case scMulExpr:
257   case scUMaxExpr:
258   case scSMaxExpr:
259     return cast<SCEVNAryExpr>(this)->getType();
260   case scAddExpr:
261     return cast<SCEVAddExpr>(this)->getType();
262   case scUDivExpr:
263     return cast<SCEVUDivExpr>(this)->getType();
264   case scUnknown:
265     return cast<SCEVUnknown>(this)->getType();
266   case scCouldNotCompute:
267     llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
268   }
269   llvm_unreachable("Unknown SCEV kind!");
270 }
271 
isZero() const272 bool SCEV::isZero() const {
273   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
274     return SC->getValue()->isZero();
275   return false;
276 }
277 
isOne() const278 bool SCEV::isOne() const {
279   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
280     return SC->getValue()->isOne();
281   return false;
282 }
283 
isAllOnesValue() const284 bool SCEV::isAllOnesValue() const {
285   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
286     return SC->getValue()->isAllOnesValue();
287   return false;
288 }
289 
isNonConstantNegative() const290 bool SCEV::isNonConstantNegative() const {
291   const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
292   if (!Mul) return false;
293 
294   // If there is a constant factor, it will be first.
295   const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
296   if (!SC) return false;
297 
298   // Return true if the value is negative, this matches things like (-42 * V).
299   return SC->getAPInt().isNegative();
300 }
301 
SCEVCouldNotCompute()302 SCEVCouldNotCompute::SCEVCouldNotCompute() :
303   SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
304 
classof(const SCEV * S)305 bool SCEVCouldNotCompute::classof(const SCEV *S) {
306   return S->getSCEVType() == scCouldNotCompute;
307 }
308 
getConstant(ConstantInt * V)309 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
310   FoldingSetNodeID ID;
311   ID.AddInteger(scConstant);
312   ID.AddPointer(V);
313   void *IP = nullptr;
314   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
315   SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
316   UniqueSCEVs.InsertNode(S, IP);
317   return S;
318 }
319 
getConstant(const APInt & Val)320 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
321   return getConstant(ConstantInt::get(getContext(), Val));
322 }
323 
324 const SCEV *
getConstant(Type * Ty,uint64_t V,bool isSigned)325 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
326   IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
327   return getConstant(ConstantInt::get(ITy, V, isSigned));
328 }
329 
SCEVCastExpr(const FoldingSetNodeIDRef ID,unsigned SCEVTy,const SCEV * op,Type * ty)330 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
331                            unsigned SCEVTy, const SCEV *op, Type *ty)
332   : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
333 
SCEVTruncateExpr(const FoldingSetNodeIDRef ID,const SCEV * op,Type * ty)334 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
335                                    const SCEV *op, Type *ty)
336   : SCEVCastExpr(ID, scTruncate, op, ty) {
337   assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
338          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
339          "Cannot truncate non-integer value!");
340 }
341 
SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,const SCEV * op,Type * ty)342 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
343                                        const SCEV *op, Type *ty)
344   : SCEVCastExpr(ID, scZeroExtend, op, ty) {
345   assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
346          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
347          "Cannot zero extend non-integer value!");
348 }
349 
SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,const SCEV * op,Type * ty)350 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
351                                        const SCEV *op, Type *ty)
352   : SCEVCastExpr(ID, scSignExtend, op, ty) {
353   assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
354          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
355          "Cannot sign extend non-integer value!");
356 }
357 
deleted()358 void SCEVUnknown::deleted() {
359   // Clear this SCEVUnknown from various maps.
360   SE->forgetMemoizedResults(this);
361 
362   // Remove this SCEVUnknown from the uniquing map.
363   SE->UniqueSCEVs.RemoveNode(this);
364 
365   // Release the value.
366   setValPtr(nullptr);
367 }
368 
allUsesReplacedWith(Value * New)369 void SCEVUnknown::allUsesReplacedWith(Value *New) {
370   // Clear this SCEVUnknown from various maps.
371   SE->forgetMemoizedResults(this);
372 
373   // Remove this SCEVUnknown from the uniquing map.
374   SE->UniqueSCEVs.RemoveNode(this);
375 
376   // Update this SCEVUnknown to point to the new value. This is needed
377   // because there may still be outstanding SCEVs which still point to
378   // this SCEVUnknown.
379   setValPtr(New);
380 }
381 
isSizeOf(Type * & AllocTy) const382 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
383   if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
384     if (VCE->getOpcode() == Instruction::PtrToInt)
385       if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
386         if (CE->getOpcode() == Instruction::GetElementPtr &&
387             CE->getOperand(0)->isNullValue() &&
388             CE->getNumOperands() == 2)
389           if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
390             if (CI->isOne()) {
391               AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
392                                  ->getElementType();
393               return true;
394             }
395 
396   return false;
397 }
398 
isAlignOf(Type * & AllocTy) const399 bool SCEVUnknown::isAlignOf(Type *&AllocTy) 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->getOperand(0)->isNullValue()) {
405           Type *Ty =
406             cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
407           if (StructType *STy = dyn_cast<StructType>(Ty))
408             if (!STy->isPacked() &&
409                 CE->getNumOperands() == 3 &&
410                 CE->getOperand(1)->isNullValue()) {
411               if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
412                 if (CI->isOne() &&
413                     STy->getNumElements() == 2 &&
414                     STy->getElementType(0)->isIntegerTy(1)) {
415                   AllocTy = STy->getElementType(1);
416                   return true;
417                 }
418             }
419         }
420 
421   return false;
422 }
423 
isOffsetOf(Type * & CTy,Constant * & FieldNo) const424 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
425   if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
426     if (VCE->getOpcode() == Instruction::PtrToInt)
427       if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
428         if (CE->getOpcode() == Instruction::GetElementPtr &&
429             CE->getNumOperands() == 3 &&
430             CE->getOperand(0)->isNullValue() &&
431             CE->getOperand(1)->isNullValue()) {
432           Type *Ty =
433             cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
434           // Ignore vector types here so that ScalarEvolutionExpander doesn't
435           // emit getelementptrs that index into vectors.
436           if (Ty->isStructTy() || Ty->isArrayTy()) {
437             CTy = Ty;
438             FieldNo = CE->getOperand(2);
439             return true;
440           }
441         }
442 
443   return false;
444 }
445 
446 //===----------------------------------------------------------------------===//
447 //                               SCEV Utilities
448 //===----------------------------------------------------------------------===//
449 
450 namespace {
451 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
452 /// than the complexity of the RHS.  This comparator is used to canonicalize
453 /// expressions.
454 class SCEVComplexityCompare {
455   const LoopInfo *const LI;
456 public:
SCEVComplexityCompare(const LoopInfo * li)457   explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
458 
459   // Return true or false if LHS is less than, or at least RHS, respectively.
operator ()(const SCEV * LHS,const SCEV * RHS) const460   bool operator()(const SCEV *LHS, const SCEV *RHS) const {
461     return compare(LHS, RHS) < 0;
462   }
463 
464   // Return negative, zero, or positive, if LHS is less than, equal to, or
465   // greater than RHS, respectively. A three-way result allows recursive
466   // comparisons to be more efficient.
compare(const SCEV * LHS,const SCEV * RHS) const467   int compare(const SCEV *LHS, const SCEV *RHS) const {
468     // Fast-path: SCEVs are uniqued so we can do a quick equality check.
469     if (LHS == RHS)
470       return 0;
471 
472     // Primarily, sort the SCEVs by their getSCEVType().
473     unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
474     if (LType != RType)
475       return (int)LType - (int)RType;
476 
477     // Aside from the getSCEVType() ordering, the particular ordering
478     // isn't very important except that it's beneficial to be consistent,
479     // so that (a + b) and (b + a) don't end up as different expressions.
480     switch (static_cast<SCEVTypes>(LType)) {
481     case scUnknown: {
482       const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
483       const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
484 
485       // Sort SCEVUnknown values with some loose heuristics. TODO: This is
486       // not as complete as it could be.
487       const Value *LV = LU->getValue(), *RV = RU->getValue();
488 
489       // Order pointer values after integer values. This helps SCEVExpander
490       // form GEPs.
491       bool LIsPointer = LV->getType()->isPointerTy(),
492         RIsPointer = RV->getType()->isPointerTy();
493       if (LIsPointer != RIsPointer)
494         return (int)LIsPointer - (int)RIsPointer;
495 
496       // Compare getValueID values.
497       unsigned LID = LV->getValueID(),
498         RID = RV->getValueID();
499       if (LID != RID)
500         return (int)LID - (int)RID;
501 
502       // Sort arguments by their position.
503       if (const Argument *LA = dyn_cast<Argument>(LV)) {
504         const Argument *RA = cast<Argument>(RV);
505         unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
506         return (int)LArgNo - (int)RArgNo;
507       }
508 
509       // For instructions, compare their loop depth, and their operand
510       // count.  This is pretty loose.
511       if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
512         const Instruction *RInst = cast<Instruction>(RV);
513 
514         // Compare loop depths.
515         const BasicBlock *LParent = LInst->getParent(),
516           *RParent = RInst->getParent();
517         if (LParent != RParent) {
518           unsigned LDepth = LI->getLoopDepth(LParent),
519             RDepth = LI->getLoopDepth(RParent);
520           if (LDepth != RDepth)
521             return (int)LDepth - (int)RDepth;
522         }
523 
524         // Compare the number of operands.
525         unsigned LNumOps = LInst->getNumOperands(),
526           RNumOps = RInst->getNumOperands();
527         return (int)LNumOps - (int)RNumOps;
528       }
529 
530       return 0;
531     }
532 
533     case scConstant: {
534       const SCEVConstant *LC = cast<SCEVConstant>(LHS);
535       const SCEVConstant *RC = cast<SCEVConstant>(RHS);
536 
537       // Compare constant values.
538       const APInt &LA = LC->getAPInt();
539       const APInt &RA = RC->getAPInt();
540       unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
541       if (LBitWidth != RBitWidth)
542         return (int)LBitWidth - (int)RBitWidth;
543       return LA.ult(RA) ? -1 : 1;
544     }
545 
546     case scAddRecExpr: {
547       const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
548       const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
549 
550       // Compare addrec loop depths.
551       const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
552       if (LLoop != RLoop) {
553         unsigned LDepth = LLoop->getLoopDepth(),
554           RDepth = RLoop->getLoopDepth();
555         if (LDepth != RDepth)
556           return (int)LDepth - (int)RDepth;
557       }
558 
559       // Addrec complexity grows with operand count.
560       unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
561       if (LNumOps != RNumOps)
562         return (int)LNumOps - (int)RNumOps;
563 
564       // Lexicographically compare.
565       for (unsigned i = 0; i != LNumOps; ++i) {
566         long X = compare(LA->getOperand(i), RA->getOperand(i));
567         if (X != 0)
568           return X;
569       }
570 
571       return 0;
572     }
573 
574     case scAddExpr:
575     case scMulExpr:
576     case scSMaxExpr:
577     case scUMaxExpr: {
578       const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
579       const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
580 
581       // Lexicographically compare n-ary expressions.
582       unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
583       if (LNumOps != RNumOps)
584         return (int)LNumOps - (int)RNumOps;
585 
586       for (unsigned i = 0; i != LNumOps; ++i) {
587         if (i >= RNumOps)
588           return 1;
589         long X = compare(LC->getOperand(i), RC->getOperand(i));
590         if (X != 0)
591           return X;
592       }
593       return (int)LNumOps - (int)RNumOps;
594     }
595 
596     case scUDivExpr: {
597       const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
598       const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
599 
600       // Lexicographically compare udiv expressions.
601       long X = compare(LC->getLHS(), RC->getLHS());
602       if (X != 0)
603         return X;
604       return compare(LC->getRHS(), RC->getRHS());
605     }
606 
607     case scTruncate:
608     case scZeroExtend:
609     case scSignExtend: {
610       const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
611       const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
612 
613       // Compare cast expressions by operand.
614       return compare(LC->getOperand(), RC->getOperand());
615     }
616 
617     case scCouldNotCompute:
618       llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
619     }
620     llvm_unreachable("Unknown SCEV kind!");
621   }
622 };
623 }  // end anonymous namespace
624 
625 /// Given a list of SCEV objects, order them by their complexity, and group
626 /// objects of the same complexity together by value.  When this routine is
627 /// finished, we know that any duplicates in the vector are consecutive and that
628 /// complexity is monotonically increasing.
629 ///
630 /// Note that we go take special precautions to ensure that we get deterministic
631 /// results from this routine.  In other words, we don't want the results of
632 /// this to depend on where the addresses of various SCEV objects happened to
633 /// land in memory.
634 ///
GroupByComplexity(SmallVectorImpl<const SCEV * > & Ops,LoopInfo * LI)635 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
636                               LoopInfo *LI) {
637   if (Ops.size() < 2) return;  // Noop
638   if (Ops.size() == 2) {
639     // This is the common case, which also happens to be trivially simple.
640     // Special case it.
641     const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
642     if (SCEVComplexityCompare(LI)(RHS, LHS))
643       std::swap(LHS, RHS);
644     return;
645   }
646 
647   // Do the rough sort by complexity.
648   std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
649 
650   // Now that we are sorted by complexity, group elements of the same
651   // complexity.  Note that this is, at worst, N^2, but the vector is likely to
652   // be extremely short in practice.  Note that we take this approach because we
653   // do not want to depend on the addresses of the objects we are grouping.
654   for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
655     const SCEV *S = Ops[i];
656     unsigned Complexity = S->getSCEVType();
657 
658     // If there are any objects of the same complexity and same value as this
659     // one, group them.
660     for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
661       if (Ops[j] == S) { // Found a duplicate.
662         // Move it to immediately after i'th element.
663         std::swap(Ops[i+1], Ops[j]);
664         ++i;   // no need to rescan it.
665         if (i == e-2) return;  // Done!
666       }
667     }
668   }
669 }
670 
671 // Returns the size of the SCEV S.
sizeOfSCEV(const SCEV * S)672 static inline int sizeOfSCEV(const SCEV *S) {
673   struct FindSCEVSize {
674     int Size;
675     FindSCEVSize() : Size(0) {}
676 
677     bool follow(const SCEV *S) {
678       ++Size;
679       // Keep looking at all operands of S.
680       return true;
681     }
682     bool isDone() const {
683       return false;
684     }
685   };
686 
687   FindSCEVSize F;
688   SCEVTraversal<FindSCEVSize> ST(F);
689   ST.visitAll(S);
690   return F.Size;
691 }
692 
693 namespace {
694 
695 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
696 public:
697   // Computes the Quotient and Remainder of the division of Numerator by
698   // Denominator.
divide__anon6eb5a8bf0211::SCEVDivision699   static void divide(ScalarEvolution &SE, const SCEV *Numerator,
700                      const SCEV *Denominator, const SCEV **Quotient,
701                      const SCEV **Remainder) {
702     assert(Numerator && Denominator && "Uninitialized SCEV");
703 
704     SCEVDivision D(SE, Numerator, Denominator);
705 
706     // Check for the trivial case here to avoid having to check for it in the
707     // rest of the code.
708     if (Numerator == Denominator) {
709       *Quotient = D.One;
710       *Remainder = D.Zero;
711       return;
712     }
713 
714     if (Numerator->isZero()) {
715       *Quotient = D.Zero;
716       *Remainder = D.Zero;
717       return;
718     }
719 
720     // A simple case when N/1. The quotient is N.
721     if (Denominator->isOne()) {
722       *Quotient = Numerator;
723       *Remainder = D.Zero;
724       return;
725     }
726 
727     // Split the Denominator when it is a product.
728     if (const SCEVMulExpr *T = dyn_cast<SCEVMulExpr>(Denominator)) {
729       const SCEV *Q, *R;
730       *Quotient = Numerator;
731       for (const SCEV *Op : T->operands()) {
732         divide(SE, *Quotient, Op, &Q, &R);
733         *Quotient = Q;
734 
735         // Bail out when the Numerator is not divisible by one of the terms of
736         // the Denominator.
737         if (!R->isZero()) {
738           *Quotient = D.Zero;
739           *Remainder = Numerator;
740           return;
741         }
742       }
743       *Remainder = D.Zero;
744       return;
745     }
746 
747     D.visit(Numerator);
748     *Quotient = D.Quotient;
749     *Remainder = D.Remainder;
750   }
751 
752   // Except in the trivial case described above, we do not know how to divide
753   // Expr by Denominator for the following functions with empty implementation.
visitTruncateExpr__anon6eb5a8bf0211::SCEVDivision754   void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
visitZeroExtendExpr__anon6eb5a8bf0211::SCEVDivision755   void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
visitSignExtendExpr__anon6eb5a8bf0211::SCEVDivision756   void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
visitUDivExpr__anon6eb5a8bf0211::SCEVDivision757   void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
visitSMaxExpr__anon6eb5a8bf0211::SCEVDivision758   void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
visitUMaxExpr__anon6eb5a8bf0211::SCEVDivision759   void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
visitUnknown__anon6eb5a8bf0211::SCEVDivision760   void visitUnknown(const SCEVUnknown *Numerator) {}
visitCouldNotCompute__anon6eb5a8bf0211::SCEVDivision761   void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
762 
visitConstant__anon6eb5a8bf0211::SCEVDivision763   void visitConstant(const SCEVConstant *Numerator) {
764     if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
765       APInt NumeratorVal = Numerator->getAPInt();
766       APInt DenominatorVal = D->getAPInt();
767       uint32_t NumeratorBW = NumeratorVal.getBitWidth();
768       uint32_t DenominatorBW = DenominatorVal.getBitWidth();
769 
770       if (NumeratorBW > DenominatorBW)
771         DenominatorVal = DenominatorVal.sext(NumeratorBW);
772       else if (NumeratorBW < DenominatorBW)
773         NumeratorVal = NumeratorVal.sext(DenominatorBW);
774 
775       APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
776       APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
777       APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
778       Quotient = SE.getConstant(QuotientVal);
779       Remainder = SE.getConstant(RemainderVal);
780       return;
781     }
782   }
783 
visitAddRecExpr__anon6eb5a8bf0211::SCEVDivision784   void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
785     const SCEV *StartQ, *StartR, *StepQ, *StepR;
786     if (!Numerator->isAffine())
787       return cannotDivide(Numerator);
788     divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
789     divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
790     // Bail out if the types do not match.
791     Type *Ty = Denominator->getType();
792     if (Ty != StartQ->getType() || Ty != StartR->getType() ||
793         Ty != StepQ->getType() || Ty != StepR->getType())
794       return cannotDivide(Numerator);
795     Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
796                                 Numerator->getNoWrapFlags());
797     Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
798                                  Numerator->getNoWrapFlags());
799   }
800 
visitAddExpr__anon6eb5a8bf0211::SCEVDivision801   void visitAddExpr(const SCEVAddExpr *Numerator) {
802     SmallVector<const SCEV *, 2> Qs, Rs;
803     Type *Ty = Denominator->getType();
804 
805     for (const SCEV *Op : Numerator->operands()) {
806       const SCEV *Q, *R;
807       divide(SE, Op, Denominator, &Q, &R);
808 
809       // Bail out if types do not match.
810       if (Ty != Q->getType() || Ty != R->getType())
811         return cannotDivide(Numerator);
812 
813       Qs.push_back(Q);
814       Rs.push_back(R);
815     }
816 
817     if (Qs.size() == 1) {
818       Quotient = Qs[0];
819       Remainder = Rs[0];
820       return;
821     }
822 
823     Quotient = SE.getAddExpr(Qs);
824     Remainder = SE.getAddExpr(Rs);
825   }
826 
visitMulExpr__anon6eb5a8bf0211::SCEVDivision827   void visitMulExpr(const SCEVMulExpr *Numerator) {
828     SmallVector<const SCEV *, 2> Qs;
829     Type *Ty = Denominator->getType();
830 
831     bool FoundDenominatorTerm = false;
832     for (const SCEV *Op : Numerator->operands()) {
833       // Bail out if types do not match.
834       if (Ty != Op->getType())
835         return cannotDivide(Numerator);
836 
837       if (FoundDenominatorTerm) {
838         Qs.push_back(Op);
839         continue;
840       }
841 
842       // Check whether Denominator divides one of the product operands.
843       const SCEV *Q, *R;
844       divide(SE, Op, Denominator, &Q, &R);
845       if (!R->isZero()) {
846         Qs.push_back(Op);
847         continue;
848       }
849 
850       // Bail out if types do not match.
851       if (Ty != Q->getType())
852         return cannotDivide(Numerator);
853 
854       FoundDenominatorTerm = true;
855       Qs.push_back(Q);
856     }
857 
858     if (FoundDenominatorTerm) {
859       Remainder = Zero;
860       if (Qs.size() == 1)
861         Quotient = Qs[0];
862       else
863         Quotient = SE.getMulExpr(Qs);
864       return;
865     }
866 
867     if (!isa<SCEVUnknown>(Denominator))
868       return cannotDivide(Numerator);
869 
870     // The Remainder is obtained by replacing Denominator by 0 in Numerator.
871     ValueToValueMap RewriteMap;
872     RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
873         cast<SCEVConstant>(Zero)->getValue();
874     Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
875 
876     if (Remainder->isZero()) {
877       // The Quotient is obtained by replacing Denominator by 1 in Numerator.
878       RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
879           cast<SCEVConstant>(One)->getValue();
880       Quotient =
881           SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
882       return;
883     }
884 
885     // Quotient is (Numerator - Remainder) divided by Denominator.
886     const SCEV *Q, *R;
887     const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
888     // This SCEV does not seem to simplify: fail the division here.
889     if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator))
890       return cannotDivide(Numerator);
891     divide(SE, Diff, Denominator, &Q, &R);
892     if (R != Zero)
893       return cannotDivide(Numerator);
894     Quotient = Q;
895   }
896 
897 private:
SCEVDivision__anon6eb5a8bf0211::SCEVDivision898   SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
899                const SCEV *Denominator)
900       : SE(S), Denominator(Denominator) {
901     Zero = SE.getZero(Denominator->getType());
902     One = SE.getOne(Denominator->getType());
903 
904     // We generally do not know how to divide Expr by Denominator. We
905     // initialize the division to a "cannot divide" state to simplify the rest
906     // of the code.
907     cannotDivide(Numerator);
908   }
909 
910   // Convenience function for giving up on the division. We set the quotient to
911   // be equal to zero and the remainder to be equal to the numerator.
cannotDivide__anon6eb5a8bf0211::SCEVDivision912   void cannotDivide(const SCEV *Numerator) {
913     Quotient = Zero;
914     Remainder = Numerator;
915   }
916 
917   ScalarEvolution &SE;
918   const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
919 };
920 
921 }
922 
923 //===----------------------------------------------------------------------===//
924 //                      Simple SCEV method implementations
925 //===----------------------------------------------------------------------===//
926 
927 /// Compute BC(It, K).  The result has width W.  Assume, K > 0.
BinomialCoefficient(const SCEV * It,unsigned K,ScalarEvolution & SE,Type * ResultTy)928 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
929                                        ScalarEvolution &SE,
930                                        Type *ResultTy) {
931   // Handle the simplest case efficiently.
932   if (K == 1)
933     return SE.getTruncateOrZeroExtend(It, ResultTy);
934 
935   // We are using the following formula for BC(It, K):
936   //
937   //   BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
938   //
939   // Suppose, W is the bitwidth of the return value.  We must be prepared for
940   // overflow.  Hence, we must assure that the result of our computation is
941   // equal to the accurate one modulo 2^W.  Unfortunately, division isn't
942   // safe in modular arithmetic.
943   //
944   // However, this code doesn't use exactly that formula; the formula it uses
945   // is something like the following, where T is the number of factors of 2 in
946   // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
947   // exponentiation:
948   //
949   //   BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
950   //
951   // This formula is trivially equivalent to the previous formula.  However,
952   // this formula can be implemented much more efficiently.  The trick is that
953   // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
954   // arithmetic.  To do exact division in modular arithmetic, all we have
955   // to do is multiply by the inverse.  Therefore, this step can be done at
956   // width W.
957   //
958   // The next issue is how to safely do the division by 2^T.  The way this
959   // is done is by doing the multiplication step at a width of at least W + T
960   // bits.  This way, the bottom W+T bits of the product are accurate. Then,
961   // when we perform the division by 2^T (which is equivalent to a right shift
962   // by T), the bottom W bits are accurate.  Extra bits are okay; they'll get
963   // truncated out after the division by 2^T.
964   //
965   // In comparison to just directly using the first formula, this technique
966   // is much more efficient; using the first formula requires W * K bits,
967   // but this formula less than W + K bits. Also, the first formula requires
968   // a division step, whereas this formula only requires multiplies and shifts.
969   //
970   // It doesn't matter whether the subtraction step is done in the calculation
971   // width or the input iteration count's width; if the subtraction overflows,
972   // the result must be zero anyway.  We prefer here to do it in the width of
973   // the induction variable because it helps a lot for certain cases; CodeGen
974   // isn't smart enough to ignore the overflow, which leads to much less
975   // efficient code if the width of the subtraction is wider than the native
976   // register width.
977   //
978   // (It's possible to not widen at all by pulling out factors of 2 before
979   // the multiplication; for example, K=2 can be calculated as
980   // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
981   // extra arithmetic, so it's not an obvious win, and it gets
982   // much more complicated for K > 3.)
983 
984   // Protection from insane SCEVs; this bound is conservative,
985   // but it probably doesn't matter.
986   if (K > 1000)
987     return SE.getCouldNotCompute();
988 
989   unsigned W = SE.getTypeSizeInBits(ResultTy);
990 
991   // Calculate K! / 2^T and T; we divide out the factors of two before
992   // multiplying for calculating K! / 2^T to avoid overflow.
993   // Other overflow doesn't matter because we only care about the bottom
994   // W bits of the result.
995   APInt OddFactorial(W, 1);
996   unsigned T = 1;
997   for (unsigned i = 3; i <= K; ++i) {
998     APInt Mult(W, i);
999     unsigned TwoFactors = Mult.countTrailingZeros();
1000     T += TwoFactors;
1001     Mult = Mult.lshr(TwoFactors);
1002     OddFactorial *= Mult;
1003   }
1004 
1005   // We need at least W + T bits for the multiplication step
1006   unsigned CalculationBits = W + T;
1007 
1008   // Calculate 2^T, at width T+W.
1009   APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1010 
1011   // Calculate the multiplicative inverse of K! / 2^T;
1012   // this multiplication factor will perform the exact division by
1013   // K! / 2^T.
1014   APInt Mod = APInt::getSignedMinValue(W+1);
1015   APInt MultiplyFactor = OddFactorial.zext(W+1);
1016   MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1017   MultiplyFactor = MultiplyFactor.trunc(W);
1018 
1019   // Calculate the product, at width T+W
1020   IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1021                                                       CalculationBits);
1022   const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1023   for (unsigned i = 1; i != K; ++i) {
1024     const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1025     Dividend = SE.getMulExpr(Dividend,
1026                              SE.getTruncateOrZeroExtend(S, CalculationTy));
1027   }
1028 
1029   // Divide by 2^T
1030   const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1031 
1032   // Truncate the result, and divide by K! / 2^T.
1033 
1034   return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1035                        SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1036 }
1037 
1038 /// Return the value of this chain of recurrences at the specified iteration
1039 /// number.  We can evaluate this recurrence by multiplying each element in the
1040 /// chain by the binomial coefficient corresponding to it.  In other words, we
1041 /// can evaluate {A,+,B,+,C,+,D} as:
1042 ///
1043 ///   A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1044 ///
1045 /// where BC(It, k) stands for binomial coefficient.
1046 ///
evaluateAtIteration(const SCEV * It,ScalarEvolution & SE) const1047 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1048                                                 ScalarEvolution &SE) const {
1049   const SCEV *Result = getStart();
1050   for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1051     // The computation is correct in the face of overflow provided that the
1052     // multiplication is performed _after_ the evaluation of the binomial
1053     // coefficient.
1054     const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1055     if (isa<SCEVCouldNotCompute>(Coeff))
1056       return Coeff;
1057 
1058     Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1059   }
1060   return Result;
1061 }
1062 
1063 //===----------------------------------------------------------------------===//
1064 //                    SCEV Expression folder implementations
1065 //===----------------------------------------------------------------------===//
1066 
getTruncateExpr(const SCEV * Op,Type * Ty)1067 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
1068                                              Type *Ty) {
1069   assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1070          "This is not a truncating conversion!");
1071   assert(isSCEVable(Ty) &&
1072          "This is not a conversion to a SCEVable type!");
1073   Ty = getEffectiveSCEVType(Ty);
1074 
1075   FoldingSetNodeID ID;
1076   ID.AddInteger(scTruncate);
1077   ID.AddPointer(Op);
1078   ID.AddPointer(Ty);
1079   void *IP = nullptr;
1080   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1081 
1082   // Fold if the operand is constant.
1083   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1084     return getConstant(
1085       cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1086 
1087   // trunc(trunc(x)) --> trunc(x)
1088   if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1089     return getTruncateExpr(ST->getOperand(), Ty);
1090 
1091   // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1092   if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1093     return getTruncateOrSignExtend(SS->getOperand(), Ty);
1094 
1095   // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1096   if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1097     return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1098 
1099   // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
1100   // eliminate all the truncates, or we replace other casts with truncates.
1101   if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
1102     SmallVector<const SCEV *, 4> Operands;
1103     bool hasTrunc = false;
1104     for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
1105       const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
1106       if (!isa<SCEVCastExpr>(SA->getOperand(i)))
1107         hasTrunc = isa<SCEVTruncateExpr>(S);
1108       Operands.push_back(S);
1109     }
1110     if (!hasTrunc)
1111       return getAddExpr(Operands);
1112     UniqueSCEVs.FindNodeOrInsertPos(ID, IP);  // Mutates IP, returns NULL.
1113   }
1114 
1115   // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
1116   // eliminate all the truncates, or we replace other casts with truncates.
1117   if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
1118     SmallVector<const SCEV *, 4> Operands;
1119     bool hasTrunc = false;
1120     for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
1121       const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
1122       if (!isa<SCEVCastExpr>(SM->getOperand(i)))
1123         hasTrunc = isa<SCEVTruncateExpr>(S);
1124       Operands.push_back(S);
1125     }
1126     if (!hasTrunc)
1127       return getMulExpr(Operands);
1128     UniqueSCEVs.FindNodeOrInsertPos(ID, IP);  // Mutates IP, returns NULL.
1129   }
1130 
1131   // If the input value is a chrec scev, truncate the chrec's operands.
1132   if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1133     SmallVector<const SCEV *, 4> Operands;
1134     for (const SCEV *Op : AddRec->operands())
1135       Operands.push_back(getTruncateExpr(Op, Ty));
1136     return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1137   }
1138 
1139   // The cast wasn't folded; create an explicit cast node. We can reuse
1140   // the existing insert position since if we get here, we won't have
1141   // made any changes which would invalidate it.
1142   SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1143                                                  Op, Ty);
1144   UniqueSCEVs.InsertNode(S, IP);
1145   return S;
1146 }
1147 
1148 // Get the limit of a recurrence such that incrementing by Step cannot cause
1149 // signed overflow as long as the value of the recurrence within the
1150 // loop does not exceed this limit before incrementing.
getSignedOverflowLimitForStep(const SCEV * Step,ICmpInst::Predicate * Pred,ScalarEvolution * SE)1151 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1152                                                  ICmpInst::Predicate *Pred,
1153                                                  ScalarEvolution *SE) {
1154   unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1155   if (SE->isKnownPositive(Step)) {
1156     *Pred = ICmpInst::ICMP_SLT;
1157     return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1158                            SE->getSignedRange(Step).getSignedMax());
1159   }
1160   if (SE->isKnownNegative(Step)) {
1161     *Pred = ICmpInst::ICMP_SGT;
1162     return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1163                            SE->getSignedRange(Step).getSignedMin());
1164   }
1165   return nullptr;
1166 }
1167 
1168 // Get the limit of a recurrence such that incrementing by Step cannot cause
1169 // unsigned overflow as long as the value of the recurrence within the loop does
1170 // not exceed this limit before incrementing.
getUnsignedOverflowLimitForStep(const SCEV * Step,ICmpInst::Predicate * Pred,ScalarEvolution * SE)1171 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1172                                                    ICmpInst::Predicate *Pred,
1173                                                    ScalarEvolution *SE) {
1174   unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1175   *Pred = ICmpInst::ICMP_ULT;
1176 
1177   return SE->getConstant(APInt::getMinValue(BitWidth) -
1178                          SE->getUnsignedRange(Step).getUnsignedMax());
1179 }
1180 
1181 namespace {
1182 
1183 struct ExtendOpTraitsBase {
1184   typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *);
1185 };
1186 
1187 // Used to make code generic over signed and unsigned overflow.
1188 template <typename ExtendOp> struct ExtendOpTraits {
1189   // Members present:
1190   //
1191   // static const SCEV::NoWrapFlags WrapType;
1192   //
1193   // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1194   //
1195   // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1196   //                                           ICmpInst::Predicate *Pred,
1197   //                                           ScalarEvolution *SE);
1198 };
1199 
1200 template <>
1201 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1202   static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1203 
1204   static const GetExtendExprTy GetExtendExpr;
1205 
getOverflowLimitForStep__anon6eb5a8bf0311::ExtendOpTraits1206   static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1207                                              ICmpInst::Predicate *Pred,
1208                                              ScalarEvolution *SE) {
1209     return getSignedOverflowLimitForStep(Step, Pred, SE);
1210   }
1211 };
1212 
1213 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1214     SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1215 
1216 template <>
1217 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1218   static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1219 
1220   static const GetExtendExprTy GetExtendExpr;
1221 
getOverflowLimitForStep__anon6eb5a8bf0311::ExtendOpTraits1222   static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1223                                              ICmpInst::Predicate *Pred,
1224                                              ScalarEvolution *SE) {
1225     return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1226   }
1227 };
1228 
1229 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1230     SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1231 }
1232 
1233 // The recurrence AR has been shown to have no signed/unsigned wrap or something
1234 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1235 // easily prove NSW/NUW for its preincrement or postincrement sibling. This
1236 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1237 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1238 // expression "Step + sext/zext(PreIncAR)" is congruent with
1239 // "sext/zext(PostIncAR)"
1240 template <typename ExtendOpTy>
getPreStartForExtend(const SCEVAddRecExpr * AR,Type * Ty,ScalarEvolution * SE)1241 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1242                                         ScalarEvolution *SE) {
1243   auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1244   auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1245 
1246   const Loop *L = AR->getLoop();
1247   const SCEV *Start = AR->getStart();
1248   const SCEV *Step = AR->getStepRecurrence(*SE);
1249 
1250   // Check for a simple looking step prior to loop entry.
1251   const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1252   if (!SA)
1253     return nullptr;
1254 
1255   // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1256   // subtraction is expensive. For this purpose, perform a quick and dirty
1257   // difference, by checking for Step in the operand list.
1258   SmallVector<const SCEV *, 4> DiffOps;
1259   for (const SCEV *Op : SA->operands())
1260     if (Op != Step)
1261       DiffOps.push_back(Op);
1262 
1263   if (DiffOps.size() == SA->getNumOperands())
1264     return nullptr;
1265 
1266   // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1267   // `Step`:
1268 
1269   // 1. NSW/NUW flags on the step increment.
1270   auto PreStartFlags =
1271     ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
1272   const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
1273   const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1274       SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1275 
1276   // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1277   // "S+X does not sign/unsign-overflow".
1278   //
1279 
1280   const SCEV *BECount = SE->getBackedgeTakenCount(L);
1281   if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1282       !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1283     return PreStart;
1284 
1285   // 2. Direct overflow check on the step operation's expression.
1286   unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1287   Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1288   const SCEV *OperandExtendedStart =
1289       SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy),
1290                      (SE->*GetExtendExpr)(Step, WideTy));
1291   if ((SE->*GetExtendExpr)(Start, WideTy) == OperandExtendedStart) {
1292     if (PreAR && AR->getNoWrapFlags(WrapType)) {
1293       // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1294       // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1295       // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`.  Cache this fact.
1296       const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1297     }
1298     return PreStart;
1299   }
1300 
1301   // 3. Loop precondition.
1302   ICmpInst::Predicate Pred;
1303   const SCEV *OverflowLimit =
1304       ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1305 
1306   if (OverflowLimit &&
1307       SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
1308     return PreStart;
1309 
1310   return nullptr;
1311 }
1312 
1313 // Get the normalized zero or sign extended expression for this AddRec's Start.
1314 template <typename ExtendOpTy>
getExtendAddRecStart(const SCEVAddRecExpr * AR,Type * Ty,ScalarEvolution * SE)1315 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1316                                         ScalarEvolution *SE) {
1317   auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1318 
1319   const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE);
1320   if (!PreStart)
1321     return (SE->*GetExtendExpr)(AR->getStart(), Ty);
1322 
1323   return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty),
1324                         (SE->*GetExtendExpr)(PreStart, Ty));
1325 }
1326 
1327 // Try to prove away overflow by looking at "nearby" add recurrences.  A
1328 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1329 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1330 //
1331 // Formally:
1332 //
1333 //     {S,+,X} == {S-T,+,X} + T
1334 //  => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1335 //
1336 // If ({S-T,+,X} + T) does not overflow  ... (1)
1337 //
1338 //  RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1339 //
1340 // If {S-T,+,X} does not overflow  ... (2)
1341 //
1342 //  RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1343 //      == {Ext(S-T)+Ext(T),+,Ext(X)}
1344 //
1345 // If (S-T)+T does not overflow  ... (3)
1346 //
1347 //  RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1348 //      == {Ext(S),+,Ext(X)} == LHS
1349 //
1350 // Thus, if (1), (2) and (3) are true for some T, then
1351 //   Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1352 //
1353 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1354 // does not overflow" restricted to the 0th iteration.  Therefore we only need
1355 // to check for (1) and (2).
1356 //
1357 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1358 // is `Delta` (defined below).
1359 //
1360 template <typename ExtendOpTy>
proveNoWrapByVaryingStart(const SCEV * Start,const SCEV * Step,const Loop * L)1361 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1362                                                 const SCEV *Step,
1363                                                 const Loop *L) {
1364   auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1365 
1366   // We restrict `Start` to a constant to prevent SCEV from spending too much
1367   // time here.  It is correct (but more expensive) to continue with a
1368   // non-constant `Start` and do a general SCEV subtraction to compute
1369   // `PreStart` below.
1370   //
1371   const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1372   if (!StartC)
1373     return false;
1374 
1375   APInt StartAI = StartC->getAPInt();
1376 
1377   for (unsigned Delta : {-2, -1, 1, 2}) {
1378     const SCEV *PreStart = getConstant(StartAI - Delta);
1379 
1380     FoldingSetNodeID ID;
1381     ID.AddInteger(scAddRecExpr);
1382     ID.AddPointer(PreStart);
1383     ID.AddPointer(Step);
1384     ID.AddPointer(L);
1385     void *IP = nullptr;
1386     const auto *PreAR =
1387       static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1388 
1389     // Give up if we don't already have the add recurrence we need because
1390     // actually constructing an add recurrence is relatively expensive.
1391     if (PreAR && PreAR->getNoWrapFlags(WrapType)) {  // proves (2)
1392       const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1393       ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1394       const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1395           DeltaS, &Pred, this);
1396       if (Limit && isKnownPredicate(Pred, PreAR, Limit))  // proves (1)
1397         return true;
1398     }
1399   }
1400 
1401   return false;
1402 }
1403 
getZeroExtendExpr(const SCEV * Op,Type * Ty)1404 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
1405                                                Type *Ty) {
1406   assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1407          "This is not an extending conversion!");
1408   assert(isSCEVable(Ty) &&
1409          "This is not a conversion to a SCEVable type!");
1410   Ty = getEffectiveSCEVType(Ty);
1411 
1412   // Fold if the operand is constant.
1413   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1414     return getConstant(
1415       cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1416 
1417   // zext(zext(x)) --> zext(x)
1418   if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1419     return getZeroExtendExpr(SZ->getOperand(), Ty);
1420 
1421   // Before doing any expensive analysis, check to see if we've already
1422   // computed a SCEV for this Op and Ty.
1423   FoldingSetNodeID ID;
1424   ID.AddInteger(scZeroExtend);
1425   ID.AddPointer(Op);
1426   ID.AddPointer(Ty);
1427   void *IP = nullptr;
1428   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1429 
1430   // zext(trunc(x)) --> zext(x) or x or trunc(x)
1431   if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1432     // It's possible the bits taken off by the truncate were all zero bits. If
1433     // so, we should be able to simplify this further.
1434     const SCEV *X = ST->getOperand();
1435     ConstantRange CR = getUnsignedRange(X);
1436     unsigned TruncBits = getTypeSizeInBits(ST->getType());
1437     unsigned NewBits = getTypeSizeInBits(Ty);
1438     if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1439             CR.zextOrTrunc(NewBits)))
1440       return getTruncateOrZeroExtend(X, Ty);
1441   }
1442 
1443   // If the input value is a chrec scev, and we can prove that the value
1444   // did not overflow the old, smaller, value, we can zero extend all of the
1445   // operands (often constants).  This allows analysis of something like
1446   // this:  for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1447   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1448     if (AR->isAffine()) {
1449       const SCEV *Start = AR->getStart();
1450       const SCEV *Step = AR->getStepRecurrence(*this);
1451       unsigned BitWidth = getTypeSizeInBits(AR->getType());
1452       const Loop *L = AR->getLoop();
1453 
1454       if (!AR->hasNoUnsignedWrap()) {
1455         auto NewFlags = proveNoWrapViaConstantRanges(AR);
1456         const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1457       }
1458 
1459       // If we have special knowledge that this addrec won't overflow,
1460       // we don't need to do any further analysis.
1461       if (AR->hasNoUnsignedWrap())
1462         return getAddRecExpr(
1463             getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1464             getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1465 
1466       // Check whether the backedge-taken count is SCEVCouldNotCompute.
1467       // Note that this serves two purposes: It filters out loops that are
1468       // simply not analyzable, and it covers the case where this code is
1469       // being called from within backedge-taken count analysis, such that
1470       // attempting to ask for the backedge-taken count would likely result
1471       // in infinite recursion. In the later case, the analysis code will
1472       // cope with a conservative value, and it will take care to purge
1473       // that value once it has finished.
1474       const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1475       if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1476         // Manually compute the final value for AR, checking for
1477         // overflow.
1478 
1479         // Check whether the backedge-taken count can be losslessly casted to
1480         // the addrec's type. The count is always unsigned.
1481         const SCEV *CastedMaxBECount =
1482           getTruncateOrZeroExtend(MaxBECount, Start->getType());
1483         const SCEV *RecastedMaxBECount =
1484           getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1485         if (MaxBECount == RecastedMaxBECount) {
1486           Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1487           // Check whether Start+Step*MaxBECount has no unsigned overflow.
1488           const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1489           const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1490           const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1491           const SCEV *WideMaxBECount =
1492             getZeroExtendExpr(CastedMaxBECount, WideTy);
1493           const SCEV *OperandExtendedAdd =
1494             getAddExpr(WideStart,
1495                        getMulExpr(WideMaxBECount,
1496                                   getZeroExtendExpr(Step, WideTy)));
1497           if (ZAdd == OperandExtendedAdd) {
1498             // Cache knowledge of AR NUW, which is propagated to this AddRec.
1499             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1500             // Return the expression with the addrec on the outside.
1501             return getAddRecExpr(
1502                 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1503                 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1504           }
1505           // Similar to above, only this time treat the step value as signed.
1506           // This covers loops that count down.
1507           OperandExtendedAdd =
1508             getAddExpr(WideStart,
1509                        getMulExpr(WideMaxBECount,
1510                                   getSignExtendExpr(Step, WideTy)));
1511           if (ZAdd == OperandExtendedAdd) {
1512             // Cache knowledge of AR NW, which is propagated to this AddRec.
1513             // Negative step causes unsigned wrap, but it still can't self-wrap.
1514             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1515             // Return the expression with the addrec on the outside.
1516             return getAddRecExpr(
1517                 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1518                 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1519           }
1520         }
1521       }
1522 
1523       // Normally, in the cases we can prove no-overflow via a
1524       // backedge guarding condition, we can also compute a backedge
1525       // taken count for the loop.  The exceptions are assumptions and
1526       // guards present in the loop -- SCEV is not great at exploiting
1527       // these to compute max backedge taken counts, but can still use
1528       // these to prove lack of overflow.  Use this fact to avoid
1529       // doing extra work that may not pay off.
1530       if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1531           !AC.assumptions().empty()) {
1532         // If the backedge is guarded by a comparison with the pre-inc
1533         // value the addrec is safe. Also, if the entry is guarded by
1534         // a comparison with the start value and the backedge is
1535         // guarded by a comparison with the post-inc value, the addrec
1536         // is safe.
1537         if (isKnownPositive(Step)) {
1538           const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1539                                       getUnsignedRange(Step).getUnsignedMax());
1540           if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1541               (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1542                isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1543                                            AR->getPostIncExpr(*this), N))) {
1544             // Cache knowledge of AR NUW, which is propagated to this
1545             // AddRec.
1546             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1547             // Return the expression with the addrec on the outside.
1548             return getAddRecExpr(
1549                 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1550                 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1551           }
1552         } else if (isKnownNegative(Step)) {
1553           const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1554                                       getSignedRange(Step).getSignedMin());
1555           if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1556               (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1557                isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1558                                            AR->getPostIncExpr(*this), N))) {
1559             // Cache knowledge of AR NW, which is propagated to this
1560             // AddRec.  Negative step causes unsigned wrap, but it
1561             // still can't self-wrap.
1562             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1563             // Return the expression with the addrec on the outside.
1564             return getAddRecExpr(
1565                 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1566                 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1567           }
1568         }
1569       }
1570 
1571       if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1572         const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1573         return getAddRecExpr(
1574             getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1575             getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1576       }
1577     }
1578 
1579   if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1580     // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
1581     if (SA->hasNoUnsignedWrap()) {
1582       // If the addition does not unsign overflow then we can, by definition,
1583       // commute the zero extension with the addition operation.
1584       SmallVector<const SCEV *, 4> Ops;
1585       for (const auto *Op : SA->operands())
1586         Ops.push_back(getZeroExtendExpr(Op, Ty));
1587       return getAddExpr(Ops, SCEV::FlagNUW);
1588     }
1589   }
1590 
1591   // The cast wasn't folded; create an explicit cast node.
1592   // Recompute the insert position, as it may have been invalidated.
1593   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1594   SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1595                                                    Op, Ty);
1596   UniqueSCEVs.InsertNode(S, IP);
1597   return S;
1598 }
1599 
getSignExtendExpr(const SCEV * Op,Type * Ty)1600 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1601                                                Type *Ty) {
1602   assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1603          "This is not an extending conversion!");
1604   assert(isSCEVable(Ty) &&
1605          "This is not a conversion to a SCEVable type!");
1606   Ty = getEffectiveSCEVType(Ty);
1607 
1608   // Fold if the operand is constant.
1609   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1610     return getConstant(
1611       cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1612 
1613   // sext(sext(x)) --> sext(x)
1614   if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1615     return getSignExtendExpr(SS->getOperand(), Ty);
1616 
1617   // sext(zext(x)) --> zext(x)
1618   if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1619     return getZeroExtendExpr(SZ->getOperand(), Ty);
1620 
1621   // Before doing any expensive analysis, check to see if we've already
1622   // computed a SCEV for this Op and Ty.
1623   FoldingSetNodeID ID;
1624   ID.AddInteger(scSignExtend);
1625   ID.AddPointer(Op);
1626   ID.AddPointer(Ty);
1627   void *IP = nullptr;
1628   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1629 
1630   // sext(trunc(x)) --> sext(x) or x or trunc(x)
1631   if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1632     // It's possible the bits taken off by the truncate were all sign bits. If
1633     // so, we should be able to simplify this further.
1634     const SCEV *X = ST->getOperand();
1635     ConstantRange CR = getSignedRange(X);
1636     unsigned TruncBits = getTypeSizeInBits(ST->getType());
1637     unsigned NewBits = getTypeSizeInBits(Ty);
1638     if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1639             CR.sextOrTrunc(NewBits)))
1640       return getTruncateOrSignExtend(X, Ty);
1641   }
1642 
1643   // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1644   if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1645     if (SA->getNumOperands() == 2) {
1646       auto *SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1647       auto *SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1648       if (SMul && SC1) {
1649         if (auto *SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1650           const APInt &C1 = SC1->getAPInt();
1651           const APInt &C2 = SC2->getAPInt();
1652           if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1653               C2.ugt(C1) && C2.isPowerOf2())
1654             return getAddExpr(getSignExtendExpr(SC1, Ty),
1655                               getSignExtendExpr(SMul, Ty));
1656         }
1657       }
1658     }
1659 
1660     // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
1661     if (SA->hasNoSignedWrap()) {
1662       // If the addition does not sign overflow then we can, by definition,
1663       // commute the sign extension with the addition operation.
1664       SmallVector<const SCEV *, 4> Ops;
1665       for (const auto *Op : SA->operands())
1666         Ops.push_back(getSignExtendExpr(Op, Ty));
1667       return getAddExpr(Ops, SCEV::FlagNSW);
1668     }
1669   }
1670   // If the input value is a chrec scev, and we can prove that the value
1671   // did not overflow the old, smaller, value, we can sign extend all of the
1672   // operands (often constants).  This allows analysis of something like
1673   // this:  for (signed char X = 0; X < 100; ++X) { int Y = X; }
1674   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1675     if (AR->isAffine()) {
1676       const SCEV *Start = AR->getStart();
1677       const SCEV *Step = AR->getStepRecurrence(*this);
1678       unsigned BitWidth = getTypeSizeInBits(AR->getType());
1679       const Loop *L = AR->getLoop();
1680 
1681       if (!AR->hasNoSignedWrap()) {
1682         auto NewFlags = proveNoWrapViaConstantRanges(AR);
1683         const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1684       }
1685 
1686       // If we have special knowledge that this addrec won't overflow,
1687       // we don't need to do any further analysis.
1688       if (AR->hasNoSignedWrap())
1689         return getAddRecExpr(
1690             getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1691             getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW);
1692 
1693       // Check whether the backedge-taken count is SCEVCouldNotCompute.
1694       // Note that this serves two purposes: It filters out loops that are
1695       // simply not analyzable, and it covers the case where this code is
1696       // being called from within backedge-taken count analysis, such that
1697       // attempting to ask for the backedge-taken count would likely result
1698       // in infinite recursion. In the later case, the analysis code will
1699       // cope with a conservative value, and it will take care to purge
1700       // that value once it has finished.
1701       const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1702       if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1703         // Manually compute the final value for AR, checking for
1704         // overflow.
1705 
1706         // Check whether the backedge-taken count can be losslessly casted to
1707         // the addrec's type. The count is always unsigned.
1708         const SCEV *CastedMaxBECount =
1709           getTruncateOrZeroExtend(MaxBECount, Start->getType());
1710         const SCEV *RecastedMaxBECount =
1711           getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1712         if (MaxBECount == RecastedMaxBECount) {
1713           Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1714           // Check whether Start+Step*MaxBECount has no signed overflow.
1715           const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1716           const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1717           const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1718           const SCEV *WideMaxBECount =
1719             getZeroExtendExpr(CastedMaxBECount, WideTy);
1720           const SCEV *OperandExtendedAdd =
1721             getAddExpr(WideStart,
1722                        getMulExpr(WideMaxBECount,
1723                                   getSignExtendExpr(Step, WideTy)));
1724           if (SAdd == OperandExtendedAdd) {
1725             // Cache knowledge of AR NSW, which is propagated to this AddRec.
1726             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1727             // Return the expression with the addrec on the outside.
1728             return getAddRecExpr(
1729                 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1730                 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1731           }
1732           // Similar to above, only this time treat the step value as unsigned.
1733           // This covers loops that count up with an unsigned step.
1734           OperandExtendedAdd =
1735             getAddExpr(WideStart,
1736                        getMulExpr(WideMaxBECount,
1737                                   getZeroExtendExpr(Step, WideTy)));
1738           if (SAdd == OperandExtendedAdd) {
1739             // If AR wraps around then
1740             //
1741             //    abs(Step) * MaxBECount > unsigned-max(AR->getType())
1742             // => SAdd != OperandExtendedAdd
1743             //
1744             // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1745             // (SAdd == OperandExtendedAdd => AR is NW)
1746 
1747             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1748 
1749             // Return the expression with the addrec on the outside.
1750             return getAddRecExpr(
1751                 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1752                 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1753           }
1754         }
1755       }
1756 
1757       // Normally, in the cases we can prove no-overflow via a
1758       // backedge guarding condition, we can also compute a backedge
1759       // taken count for the loop.  The exceptions are assumptions and
1760       // guards present in the loop -- SCEV is not great at exploiting
1761       // these to compute max backedge taken counts, but can still use
1762       // these to prove lack of overflow.  Use this fact to avoid
1763       // doing extra work that may not pay off.
1764 
1765       if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1766           !AC.assumptions().empty()) {
1767         // If the backedge is guarded by a comparison with the pre-inc
1768         // value the addrec is safe. Also, if the entry is guarded by
1769         // a comparison with the start value and the backedge is
1770         // guarded by a comparison with the post-inc value, the addrec
1771         // is safe.
1772         ICmpInst::Predicate Pred;
1773         const SCEV *OverflowLimit =
1774             getSignedOverflowLimitForStep(Step, &Pred, this);
1775         if (OverflowLimit &&
1776             (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1777              (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1778               isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1779                                           OverflowLimit)))) {
1780           // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1781           const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1782           return getAddRecExpr(
1783               getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1784               getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1785         }
1786       }
1787 
1788       // If Start and Step are constants, check if we can apply this
1789       // transformation:
1790       // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1791       auto *SC1 = dyn_cast<SCEVConstant>(Start);
1792       auto *SC2 = dyn_cast<SCEVConstant>(Step);
1793       if (SC1 && SC2) {
1794         const APInt &C1 = SC1->getAPInt();
1795         const APInt &C2 = SC2->getAPInt();
1796         if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1797             C2.isPowerOf2()) {
1798           Start = getSignExtendExpr(Start, Ty);
1799           const SCEV *NewAR = getAddRecExpr(getZero(AR->getType()), Step, L,
1800                                             AR->getNoWrapFlags());
1801           return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1802         }
1803       }
1804 
1805       if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
1806         const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1807         return getAddRecExpr(
1808             getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1809             getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1810       }
1811     }
1812 
1813   // If the input value is provably positive and we could not simplify
1814   // away the sext build a zext instead.
1815   if (isKnownNonNegative(Op))
1816     return getZeroExtendExpr(Op, Ty);
1817 
1818   // The cast wasn't folded; create an explicit cast node.
1819   // Recompute the insert position, as it may have been invalidated.
1820   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1821   SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1822                                                    Op, Ty);
1823   UniqueSCEVs.InsertNode(S, IP);
1824   return S;
1825 }
1826 
1827 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1828 /// unspecified bits out to the given type.
1829 ///
getAnyExtendExpr(const SCEV * Op,Type * Ty)1830 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1831                                               Type *Ty) {
1832   assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1833          "This is not an extending conversion!");
1834   assert(isSCEVable(Ty) &&
1835          "This is not a conversion to a SCEVable type!");
1836   Ty = getEffectiveSCEVType(Ty);
1837 
1838   // Sign-extend negative constants.
1839   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1840     if (SC->getAPInt().isNegative())
1841       return getSignExtendExpr(Op, Ty);
1842 
1843   // Peel off a truncate cast.
1844   if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1845     const SCEV *NewOp = T->getOperand();
1846     if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1847       return getAnyExtendExpr(NewOp, Ty);
1848     return getTruncateOrNoop(NewOp, Ty);
1849   }
1850 
1851   // Next try a zext cast. If the cast is folded, use it.
1852   const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1853   if (!isa<SCEVZeroExtendExpr>(ZExt))
1854     return ZExt;
1855 
1856   // Next try a sext cast. If the cast is folded, use it.
1857   const SCEV *SExt = getSignExtendExpr(Op, Ty);
1858   if (!isa<SCEVSignExtendExpr>(SExt))
1859     return SExt;
1860 
1861   // Force the cast to be folded into the operands of an addrec.
1862   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1863     SmallVector<const SCEV *, 4> Ops;
1864     for (const SCEV *Op : AR->operands())
1865       Ops.push_back(getAnyExtendExpr(Op, Ty));
1866     return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1867   }
1868 
1869   // If the expression is obviously signed, use the sext cast value.
1870   if (isa<SCEVSMaxExpr>(Op))
1871     return SExt;
1872 
1873   // Absent any other information, use the zext cast value.
1874   return ZExt;
1875 }
1876 
1877 /// Process the given Ops list, which is a list of operands to be added under
1878 /// the given scale, update the given map. This is a helper function for
1879 /// getAddRecExpr. As an example of what it does, given a sequence of operands
1880 /// that would form an add expression like this:
1881 ///
1882 ///    m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1883 ///
1884 /// where A and B are constants, update the map with these values:
1885 ///
1886 ///    (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1887 ///
1888 /// and add 13 + A*B*29 to AccumulatedConstant.
1889 /// This will allow getAddRecExpr to produce this:
1890 ///
1891 ///    13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1892 ///
1893 /// This form often exposes folding opportunities that are hidden in
1894 /// the original operand list.
1895 ///
1896 /// Return true iff it appears that any interesting folding opportunities
1897 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1898 /// the common case where no interesting opportunities are present, and
1899 /// is also used as a check to avoid infinite recursion.
1900 ///
1901 static bool
CollectAddOperandsWithScales(DenseMap<const SCEV *,APInt> & M,SmallVectorImpl<const SCEV * > & NewOps,APInt & AccumulatedConstant,const SCEV * const * Ops,size_t NumOperands,const APInt & Scale,ScalarEvolution & SE)1902 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1903                              SmallVectorImpl<const SCEV *> &NewOps,
1904                              APInt &AccumulatedConstant,
1905                              const SCEV *const *Ops, size_t NumOperands,
1906                              const APInt &Scale,
1907                              ScalarEvolution &SE) {
1908   bool Interesting = false;
1909 
1910   // Iterate over the add operands. They are sorted, with constants first.
1911   unsigned i = 0;
1912   while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1913     ++i;
1914     // Pull a buried constant out to the outside.
1915     if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1916       Interesting = true;
1917     AccumulatedConstant += Scale * C->getAPInt();
1918   }
1919 
1920   // Next comes everything else. We're especially interested in multiplies
1921   // here, but they're in the middle, so just visit the rest with one loop.
1922   for (; i != NumOperands; ++i) {
1923     const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1924     if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1925       APInt NewScale =
1926           Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
1927       if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1928         // A multiplication of a constant with another add; recurse.
1929         const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1930         Interesting |=
1931           CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1932                                        Add->op_begin(), Add->getNumOperands(),
1933                                        NewScale, SE);
1934       } else {
1935         // A multiplication of a constant with some other value. Update
1936         // the map.
1937         SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1938         const SCEV *Key = SE.getMulExpr(MulOps);
1939         auto Pair = M.insert({Key, NewScale});
1940         if (Pair.second) {
1941           NewOps.push_back(Pair.first->first);
1942         } else {
1943           Pair.first->second += NewScale;
1944           // The map already had an entry for this value, which may indicate
1945           // a folding opportunity.
1946           Interesting = true;
1947         }
1948       }
1949     } else {
1950       // An ordinary operand. Update the map.
1951       std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1952           M.insert({Ops[i], Scale});
1953       if (Pair.second) {
1954         NewOps.push_back(Pair.first->first);
1955       } else {
1956         Pair.first->second += Scale;
1957         // The map already had an entry for this value, which may indicate
1958         // a folding opportunity.
1959         Interesting = true;
1960       }
1961     }
1962   }
1963 
1964   return Interesting;
1965 }
1966 
1967 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1968 // `OldFlags' as can't-wrap behavior.  Infer a more aggressive set of
1969 // can't-overflow flags for the operation if possible.
1970 static SCEV::NoWrapFlags
StrengthenNoWrapFlags(ScalarEvolution * SE,SCEVTypes Type,const SmallVectorImpl<const SCEV * > & Ops,SCEV::NoWrapFlags Flags)1971 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1972                       const SmallVectorImpl<const SCEV *> &Ops,
1973                       SCEV::NoWrapFlags Flags) {
1974   using namespace std::placeholders;
1975   typedef OverflowingBinaryOperator OBO;
1976 
1977   bool CanAnalyze =
1978       Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1979   (void)CanAnalyze;
1980   assert(CanAnalyze && "don't call from other places!");
1981 
1982   int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1983   SCEV::NoWrapFlags SignOrUnsignWrap =
1984       ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
1985 
1986   // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1987   auto IsKnownNonNegative = [&](const SCEV *S) {
1988     return SE->isKnownNonNegative(S);
1989   };
1990 
1991   if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
1992     Flags =
1993         ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1994 
1995   SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
1996 
1997   if (SignOrUnsignWrap != SignOrUnsignMask && Type == scAddExpr &&
1998       Ops.size() == 2 && isa<SCEVConstant>(Ops[0])) {
1999 
2000     // (A + C) --> (A + C)<nsw> if the addition does not sign overflow
2001     // (A + C) --> (A + C)<nuw> if the addition does not unsign overflow
2002 
2003     const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
2004     if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
2005       auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2006           Instruction::Add, C, OBO::NoSignedWrap);
2007       if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
2008         Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
2009     }
2010     if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
2011       auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2012           Instruction::Add, C, OBO::NoUnsignedWrap);
2013       if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
2014         Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
2015     }
2016   }
2017 
2018   return Flags;
2019 }
2020 
2021 /// Get a canonical add expression, or something simpler if possible.
getAddExpr(SmallVectorImpl<const SCEV * > & Ops,SCEV::NoWrapFlags Flags)2022 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
2023                                         SCEV::NoWrapFlags Flags) {
2024   assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
2025          "only nuw or nsw allowed");
2026   assert(!Ops.empty() && "Cannot get empty add!");
2027   if (Ops.size() == 1) return Ops[0];
2028 #ifndef NDEBUG
2029   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2030   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2031     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2032            "SCEVAddExpr operand types don't match!");
2033 #endif
2034 
2035   // Sort by complexity, this groups all similar expression types together.
2036   GroupByComplexity(Ops, &LI);
2037 
2038   Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
2039 
2040   // If there are any constants, fold them together.
2041   unsigned Idx = 0;
2042   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2043     ++Idx;
2044     assert(Idx < Ops.size());
2045     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2046       // We found two constants, fold them together!
2047       Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt());
2048       if (Ops.size() == 2) return Ops[0];
2049       Ops.erase(Ops.begin()+1);  // Erase the folded element
2050       LHSC = cast<SCEVConstant>(Ops[0]);
2051     }
2052 
2053     // If we are left with a constant zero being added, strip it off.
2054     if (LHSC->getValue()->isZero()) {
2055       Ops.erase(Ops.begin());
2056       --Idx;
2057     }
2058 
2059     if (Ops.size() == 1) return Ops[0];
2060   }
2061 
2062   // Okay, check to see if the same value occurs in the operand list more than
2063   // once.  If so, merge them together into an multiply expression.  Since we
2064   // sorted the list, these values are required to be adjacent.
2065   Type *Ty = Ops[0]->getType();
2066   bool FoundMatch = false;
2067   for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2068     if (Ops[i] == Ops[i+1]) {      //  X + Y + Y  -->  X + Y*2
2069       // Scan ahead to count how many equal operands there are.
2070       unsigned Count = 2;
2071       while (i+Count != e && Ops[i+Count] == Ops[i])
2072         ++Count;
2073       // Merge the values into a multiply.
2074       const SCEV *Scale = getConstant(Ty, Count);
2075       const SCEV *Mul = getMulExpr(Scale, Ops[i]);
2076       if (Ops.size() == Count)
2077         return Mul;
2078       Ops[i] = Mul;
2079       Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2080       --i; e -= Count - 1;
2081       FoundMatch = true;
2082     }
2083   if (FoundMatch)
2084     return getAddExpr(Ops, Flags);
2085 
2086   // Check for truncates. If all the operands are truncated from the same
2087   // type, see if factoring out the truncate would permit the result to be
2088   // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
2089   // if the contents of the resulting outer trunc fold to something simple.
2090   for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
2091     const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
2092     Type *DstType = Trunc->getType();
2093     Type *SrcType = Trunc->getOperand()->getType();
2094     SmallVector<const SCEV *, 8> LargeOps;
2095     bool Ok = true;
2096     // Check all the operands to see if they can be represented in the
2097     // source type of the truncate.
2098     for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2099       if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2100         if (T->getOperand()->getType() != SrcType) {
2101           Ok = false;
2102           break;
2103         }
2104         LargeOps.push_back(T->getOperand());
2105       } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2106         LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2107       } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2108         SmallVector<const SCEV *, 8> LargeMulOps;
2109         for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2110           if (const SCEVTruncateExpr *T =
2111                 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2112             if (T->getOperand()->getType() != SrcType) {
2113               Ok = false;
2114               break;
2115             }
2116             LargeMulOps.push_back(T->getOperand());
2117           } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
2118             LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2119           } else {
2120             Ok = false;
2121             break;
2122           }
2123         }
2124         if (Ok)
2125           LargeOps.push_back(getMulExpr(LargeMulOps));
2126       } else {
2127         Ok = false;
2128         break;
2129       }
2130     }
2131     if (Ok) {
2132       // Evaluate the expression in the larger type.
2133       const SCEV *Fold = getAddExpr(LargeOps, Flags);
2134       // If it folds to something simple, use it. Otherwise, don't.
2135       if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2136         return getTruncateExpr(Fold, DstType);
2137     }
2138   }
2139 
2140   // Skip past any other cast SCEVs.
2141   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2142     ++Idx;
2143 
2144   // If there are add operands they would be next.
2145   if (Idx < Ops.size()) {
2146     bool DeletedAdd = false;
2147     while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2148       // If we have an add, expand the add operands onto the end of the operands
2149       // list.
2150       Ops.erase(Ops.begin()+Idx);
2151       Ops.append(Add->op_begin(), Add->op_end());
2152       DeletedAdd = true;
2153     }
2154 
2155     // If we deleted at least one add, we added operands to the end of the list,
2156     // and they are not necessarily sorted.  Recurse to resort and resimplify
2157     // any operands we just acquired.
2158     if (DeletedAdd)
2159       return getAddExpr(Ops);
2160   }
2161 
2162   // Skip over the add expression until we get to a multiply.
2163   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2164     ++Idx;
2165 
2166   // Check to see if there are any folding opportunities present with
2167   // operands multiplied by constant values.
2168   if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2169     uint64_t BitWidth = getTypeSizeInBits(Ty);
2170     DenseMap<const SCEV *, APInt> M;
2171     SmallVector<const SCEV *, 8> NewOps;
2172     APInt AccumulatedConstant(BitWidth, 0);
2173     if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2174                                      Ops.data(), Ops.size(),
2175                                      APInt(BitWidth, 1), *this)) {
2176       struct APIntCompare {
2177         bool operator()(const APInt &LHS, const APInt &RHS) const {
2178           return LHS.ult(RHS);
2179         }
2180       };
2181 
2182       // Some interesting folding opportunity is present, so its worthwhile to
2183       // re-generate the operands list. Group the operands by constant scale,
2184       // to avoid multiplying by the same constant scale multiple times.
2185       std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2186       for (const SCEV *NewOp : NewOps)
2187         MulOpLists[M.find(NewOp)->second].push_back(NewOp);
2188       // Re-generate the operands list.
2189       Ops.clear();
2190       if (AccumulatedConstant != 0)
2191         Ops.push_back(getConstant(AccumulatedConstant));
2192       for (auto &MulOp : MulOpLists)
2193         if (MulOp.first != 0)
2194           Ops.push_back(getMulExpr(getConstant(MulOp.first),
2195                                    getAddExpr(MulOp.second)));
2196       if (Ops.empty())
2197         return getZero(Ty);
2198       if (Ops.size() == 1)
2199         return Ops[0];
2200       return getAddExpr(Ops);
2201     }
2202   }
2203 
2204   // If we are adding something to a multiply expression, make sure the
2205   // something is not already an operand of the multiply.  If so, merge it into
2206   // the multiply.
2207   for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2208     const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2209     for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2210       const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2211       if (isa<SCEVConstant>(MulOpSCEV))
2212         continue;
2213       for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2214         if (MulOpSCEV == Ops[AddOp]) {
2215           // Fold W + X + (X * Y * Z)  -->  W + (X * ((Y*Z)+1))
2216           const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2217           if (Mul->getNumOperands() != 2) {
2218             // If the multiply has more than two operands, we must get the
2219             // Y*Z term.
2220             SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2221                                                 Mul->op_begin()+MulOp);
2222             MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2223             InnerMul = getMulExpr(MulOps);
2224           }
2225           const SCEV *One = getOne(Ty);
2226           const SCEV *AddOne = getAddExpr(One, InnerMul);
2227           const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2228           if (Ops.size() == 2) return OuterMul;
2229           if (AddOp < Idx) {
2230             Ops.erase(Ops.begin()+AddOp);
2231             Ops.erase(Ops.begin()+Idx-1);
2232           } else {
2233             Ops.erase(Ops.begin()+Idx);
2234             Ops.erase(Ops.begin()+AddOp-1);
2235           }
2236           Ops.push_back(OuterMul);
2237           return getAddExpr(Ops);
2238         }
2239 
2240       // Check this multiply against other multiplies being added together.
2241       for (unsigned OtherMulIdx = Idx+1;
2242            OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2243            ++OtherMulIdx) {
2244         const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2245         // If MulOp occurs in OtherMul, we can fold the two multiplies
2246         // together.
2247         for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2248              OMulOp != e; ++OMulOp)
2249           if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2250             // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2251             const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2252             if (Mul->getNumOperands() != 2) {
2253               SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2254                                                   Mul->op_begin()+MulOp);
2255               MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2256               InnerMul1 = getMulExpr(MulOps);
2257             }
2258             const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2259             if (OtherMul->getNumOperands() != 2) {
2260               SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2261                                                   OtherMul->op_begin()+OMulOp);
2262               MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2263               InnerMul2 = getMulExpr(MulOps);
2264             }
2265             const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2266             const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2267             if (Ops.size() == 2) return OuterMul;
2268             Ops.erase(Ops.begin()+Idx);
2269             Ops.erase(Ops.begin()+OtherMulIdx-1);
2270             Ops.push_back(OuterMul);
2271             return getAddExpr(Ops);
2272           }
2273       }
2274     }
2275   }
2276 
2277   // If there are any add recurrences in the operands list, see if any other
2278   // added values are loop invariant.  If so, we can fold them into the
2279   // recurrence.
2280   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2281     ++Idx;
2282 
2283   // Scan over all recurrences, trying to fold loop invariants into them.
2284   for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2285     // Scan all of the other operands to this add and add them to the vector if
2286     // they are loop invariant w.r.t. the recurrence.
2287     SmallVector<const SCEV *, 8> LIOps;
2288     const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2289     const Loop *AddRecLoop = AddRec->getLoop();
2290     for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2291       if (isLoopInvariant(Ops[i], AddRecLoop)) {
2292         LIOps.push_back(Ops[i]);
2293         Ops.erase(Ops.begin()+i);
2294         --i; --e;
2295       }
2296 
2297     // If we found some loop invariants, fold them into the recurrence.
2298     if (!LIOps.empty()) {
2299       //  NLI + LI + {Start,+,Step}  -->  NLI + {LI+Start,+,Step}
2300       LIOps.push_back(AddRec->getStart());
2301 
2302       SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2303                                              AddRec->op_end());
2304       // This follows from the fact that the no-wrap flags on the outer add
2305       // expression are applicable on the 0th iteration, when the add recurrence
2306       // will be equal to its start value.
2307       AddRecOps[0] = getAddExpr(LIOps, Flags);
2308 
2309       // Build the new addrec. Propagate the NUW and NSW flags if both the
2310       // outer add and the inner addrec are guaranteed to have no overflow.
2311       // Always propagate NW.
2312       Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2313       const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2314 
2315       // If all of the other operands were loop invariant, we are done.
2316       if (Ops.size() == 1) return NewRec;
2317 
2318       // Otherwise, add the folded AddRec by the non-invariant parts.
2319       for (unsigned i = 0;; ++i)
2320         if (Ops[i] == AddRec) {
2321           Ops[i] = NewRec;
2322           break;
2323         }
2324       return getAddExpr(Ops);
2325     }
2326 
2327     // Okay, if there weren't any loop invariants to be folded, check to see if
2328     // there are multiple AddRec's with the same loop induction variable being
2329     // added together.  If so, we can fold them.
2330     for (unsigned OtherIdx = Idx+1;
2331          OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2332          ++OtherIdx)
2333       if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2334         // Other + {A,+,B}<L> + {C,+,D}<L>  -->  Other + {A+C,+,B+D}<L>
2335         SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2336                                                AddRec->op_end());
2337         for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2338              ++OtherIdx)
2339           if (const auto *OtherAddRec = dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2340             if (OtherAddRec->getLoop() == AddRecLoop) {
2341               for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2342                    i != e; ++i) {
2343                 if (i >= AddRecOps.size()) {
2344                   AddRecOps.append(OtherAddRec->op_begin()+i,
2345                                    OtherAddRec->op_end());
2346                   break;
2347                 }
2348                 AddRecOps[i] = getAddExpr(AddRecOps[i],
2349                                           OtherAddRec->getOperand(i));
2350               }
2351               Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2352             }
2353         // Step size has changed, so we cannot guarantee no self-wraparound.
2354         Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2355         return getAddExpr(Ops);
2356       }
2357 
2358     // Otherwise couldn't fold anything into this recurrence.  Move onto the
2359     // next one.
2360   }
2361 
2362   // Okay, it looks like we really DO need an add expr.  Check to see if we
2363   // already have one, otherwise create a new one.
2364   FoldingSetNodeID ID;
2365   ID.AddInteger(scAddExpr);
2366   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2367     ID.AddPointer(Ops[i]);
2368   void *IP = nullptr;
2369   SCEVAddExpr *S =
2370     static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2371   if (!S) {
2372     const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2373     std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2374     S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2375                                         O, Ops.size());
2376     UniqueSCEVs.InsertNode(S, IP);
2377   }
2378   S->setNoWrapFlags(Flags);
2379   return S;
2380 }
2381 
umul_ov(uint64_t i,uint64_t j,bool & Overflow)2382 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2383   uint64_t k = i*j;
2384   if (j > 1 && k / j != i) Overflow = true;
2385   return k;
2386 }
2387 
2388 /// Compute the result of "n choose k", the binomial coefficient.  If an
2389 /// intermediate computation overflows, Overflow will be set and the return will
2390 /// be garbage. Overflow is not cleared on absence of overflow.
Choose(uint64_t n,uint64_t k,bool & Overflow)2391 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2392   // We use the multiplicative formula:
2393   //     n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2394   // At each iteration, we take the n-th term of the numeral and divide by the
2395   // (k-n)th term of the denominator.  This division will always produce an
2396   // integral result, and helps reduce the chance of overflow in the
2397   // intermediate computations. However, we can still overflow even when the
2398   // final result would fit.
2399 
2400   if (n == 0 || n == k) return 1;
2401   if (k > n) return 0;
2402 
2403   if (k > n/2)
2404     k = n-k;
2405 
2406   uint64_t r = 1;
2407   for (uint64_t i = 1; i <= k; ++i) {
2408     r = umul_ov(r, n-(i-1), Overflow);
2409     r /= i;
2410   }
2411   return r;
2412 }
2413 
2414 /// Determine if any of the operands in this SCEV are a constant or if
2415 /// any of the add or multiply expressions in this SCEV contain a constant.
containsConstantSomewhere(const SCEV * StartExpr)2416 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2417   SmallVector<const SCEV *, 4> Ops;
2418   Ops.push_back(StartExpr);
2419   while (!Ops.empty()) {
2420     const SCEV *CurrentExpr = Ops.pop_back_val();
2421     if (isa<SCEVConstant>(*CurrentExpr))
2422       return true;
2423 
2424     if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2425       const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2426       Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2427     }
2428   }
2429   return false;
2430 }
2431 
2432 /// Get a canonical multiply expression, or something simpler if possible.
getMulExpr(SmallVectorImpl<const SCEV * > & Ops,SCEV::NoWrapFlags Flags)2433 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2434                                         SCEV::NoWrapFlags Flags) {
2435   assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2436          "only nuw or nsw allowed");
2437   assert(!Ops.empty() && "Cannot get empty mul!");
2438   if (Ops.size() == 1) return Ops[0];
2439 #ifndef NDEBUG
2440   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2441   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2442     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2443            "SCEVMulExpr operand types don't match!");
2444 #endif
2445 
2446   // Sort by complexity, this groups all similar expression types together.
2447   GroupByComplexity(Ops, &LI);
2448 
2449   Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2450 
2451   // If there are any constants, fold them together.
2452   unsigned Idx = 0;
2453   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2454 
2455     // C1*(C2+V) -> C1*C2 + C1*V
2456     if (Ops.size() == 2)
2457         if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2458           // If any of Add's ops are Adds or Muls with a constant,
2459           // apply this transformation as well.
2460           if (Add->getNumOperands() == 2)
2461             if (containsConstantSomewhere(Add))
2462               return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2463                                 getMulExpr(LHSC, Add->getOperand(1)));
2464 
2465     ++Idx;
2466     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2467       // We found two constants, fold them together!
2468       ConstantInt *Fold =
2469           ConstantInt::get(getContext(), LHSC->getAPInt() * RHSC->getAPInt());
2470       Ops[0] = getConstant(Fold);
2471       Ops.erase(Ops.begin()+1);  // Erase the folded element
2472       if (Ops.size() == 1) return Ops[0];
2473       LHSC = cast<SCEVConstant>(Ops[0]);
2474     }
2475 
2476     // If we are left with a constant one being multiplied, strip it off.
2477     if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2478       Ops.erase(Ops.begin());
2479       --Idx;
2480     } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2481       // If we have a multiply of zero, it will always be zero.
2482       return Ops[0];
2483     } else if (Ops[0]->isAllOnesValue()) {
2484       // If we have a mul by -1 of an add, try distributing the -1 among the
2485       // add operands.
2486       if (Ops.size() == 2) {
2487         if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2488           SmallVector<const SCEV *, 4> NewOps;
2489           bool AnyFolded = false;
2490           for (const SCEV *AddOp : Add->operands()) {
2491             const SCEV *Mul = getMulExpr(Ops[0], AddOp);
2492             if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2493             NewOps.push_back(Mul);
2494           }
2495           if (AnyFolded)
2496             return getAddExpr(NewOps);
2497         } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2498           // Negation preserves a recurrence's no self-wrap property.
2499           SmallVector<const SCEV *, 4> Operands;
2500           for (const SCEV *AddRecOp : AddRec->operands())
2501             Operands.push_back(getMulExpr(Ops[0], AddRecOp));
2502 
2503           return getAddRecExpr(Operands, AddRec->getLoop(),
2504                                AddRec->getNoWrapFlags(SCEV::FlagNW));
2505         }
2506       }
2507     }
2508 
2509     if (Ops.size() == 1)
2510       return Ops[0];
2511   }
2512 
2513   // Skip over the add expression until we get to a multiply.
2514   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2515     ++Idx;
2516 
2517   // If there are mul operands inline them all into this expression.
2518   if (Idx < Ops.size()) {
2519     bool DeletedMul = false;
2520     while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2521       // If we have an mul, expand the mul operands onto the end of the operands
2522       // list.
2523       Ops.erase(Ops.begin()+Idx);
2524       Ops.append(Mul->op_begin(), Mul->op_end());
2525       DeletedMul = true;
2526     }
2527 
2528     // If we deleted at least one mul, we added operands to the end of the list,
2529     // and they are not necessarily sorted.  Recurse to resort and resimplify
2530     // any operands we just acquired.
2531     if (DeletedMul)
2532       return getMulExpr(Ops);
2533   }
2534 
2535   // If there are any add recurrences in the operands list, see if any other
2536   // added values are loop invariant.  If so, we can fold them into the
2537   // recurrence.
2538   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2539     ++Idx;
2540 
2541   // Scan over all recurrences, trying to fold loop invariants into them.
2542   for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2543     // Scan all of the other operands to this mul and add them to the vector if
2544     // they are loop invariant w.r.t. the recurrence.
2545     SmallVector<const SCEV *, 8> LIOps;
2546     const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2547     const Loop *AddRecLoop = AddRec->getLoop();
2548     for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2549       if (isLoopInvariant(Ops[i], AddRecLoop)) {
2550         LIOps.push_back(Ops[i]);
2551         Ops.erase(Ops.begin()+i);
2552         --i; --e;
2553       }
2554 
2555     // If we found some loop invariants, fold them into the recurrence.
2556     if (!LIOps.empty()) {
2557       //  NLI * LI * {Start,+,Step}  -->  NLI * {LI*Start,+,LI*Step}
2558       SmallVector<const SCEV *, 4> NewOps;
2559       NewOps.reserve(AddRec->getNumOperands());
2560       const SCEV *Scale = getMulExpr(LIOps);
2561       for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2562         NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2563 
2564       // Build the new addrec. Propagate the NUW and NSW flags if both the
2565       // outer mul and the inner addrec are guaranteed to have no overflow.
2566       //
2567       // No self-wrap cannot be guaranteed after changing the step size, but
2568       // will be inferred if either NUW or NSW is true.
2569       Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2570       const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2571 
2572       // If all of the other operands were loop invariant, we are done.
2573       if (Ops.size() == 1) return NewRec;
2574 
2575       // Otherwise, multiply the folded AddRec by the non-invariant parts.
2576       for (unsigned i = 0;; ++i)
2577         if (Ops[i] == AddRec) {
2578           Ops[i] = NewRec;
2579           break;
2580         }
2581       return getMulExpr(Ops);
2582     }
2583 
2584     // Okay, if there weren't any loop invariants to be folded, check to see if
2585     // there are multiple AddRec's with the same loop induction variable being
2586     // multiplied together.  If so, we can fold them.
2587 
2588     // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2589     // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2590     //       choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2591     //   ]]],+,...up to x=2n}.
2592     // Note that the arguments to choose() are always integers with values
2593     // known at compile time, never SCEV objects.
2594     //
2595     // The implementation avoids pointless extra computations when the two
2596     // addrec's are of different length (mathematically, it's equivalent to
2597     // an infinite stream of zeros on the right).
2598     bool OpsModified = false;
2599     for (unsigned OtherIdx = Idx+1;
2600          OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2601          ++OtherIdx) {
2602       const SCEVAddRecExpr *OtherAddRec =
2603         dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2604       if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2605         continue;
2606 
2607       bool Overflow = false;
2608       Type *Ty = AddRec->getType();
2609       bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2610       SmallVector<const SCEV*, 7> AddRecOps;
2611       for (int x = 0, xe = AddRec->getNumOperands() +
2612              OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2613         const SCEV *Term = getZero(Ty);
2614         for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2615           uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2616           for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2617                  ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2618                z < ze && !Overflow; ++z) {
2619             uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2620             uint64_t Coeff;
2621             if (LargerThan64Bits)
2622               Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2623             else
2624               Coeff = Coeff1*Coeff2;
2625             const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2626             const SCEV *Term1 = AddRec->getOperand(y-z);
2627             const SCEV *Term2 = OtherAddRec->getOperand(z);
2628             Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2629           }
2630         }
2631         AddRecOps.push_back(Term);
2632       }
2633       if (!Overflow) {
2634         const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2635                                               SCEV::FlagAnyWrap);
2636         if (Ops.size() == 2) return NewAddRec;
2637         Ops[Idx] = NewAddRec;
2638         Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2639         OpsModified = true;
2640         AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2641         if (!AddRec)
2642           break;
2643       }
2644     }
2645     if (OpsModified)
2646       return getMulExpr(Ops);
2647 
2648     // Otherwise couldn't fold anything into this recurrence.  Move onto the
2649     // next one.
2650   }
2651 
2652   // Okay, it looks like we really DO need an mul expr.  Check to see if we
2653   // already have one, otherwise create a new one.
2654   FoldingSetNodeID ID;
2655   ID.AddInteger(scMulExpr);
2656   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2657     ID.AddPointer(Ops[i]);
2658   void *IP = nullptr;
2659   SCEVMulExpr *S =
2660     static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2661   if (!S) {
2662     const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2663     std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2664     S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2665                                         O, Ops.size());
2666     UniqueSCEVs.InsertNode(S, IP);
2667   }
2668   S->setNoWrapFlags(Flags);
2669   return S;
2670 }
2671 
2672 /// Get a canonical unsigned division expression, or something simpler if
2673 /// possible.
getUDivExpr(const SCEV * LHS,const SCEV * RHS)2674 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2675                                          const SCEV *RHS) {
2676   assert(getEffectiveSCEVType(LHS->getType()) ==
2677          getEffectiveSCEVType(RHS->getType()) &&
2678          "SCEVUDivExpr operand types don't match!");
2679 
2680   if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2681     if (RHSC->getValue()->equalsInt(1))
2682       return LHS;                               // X udiv 1 --> x
2683     // If the denominator is zero, the result of the udiv is undefined. Don't
2684     // try to analyze it, because the resolution chosen here may differ from
2685     // the resolution chosen in other parts of the compiler.
2686     if (!RHSC->getValue()->isZero()) {
2687       // Determine if the division can be folded into the operands of
2688       // its operands.
2689       // TODO: Generalize this to non-constants by using known-bits information.
2690       Type *Ty = LHS->getType();
2691       unsigned LZ = RHSC->getAPInt().countLeadingZeros();
2692       unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2693       // For non-power-of-two values, effectively round the value up to the
2694       // nearest power of two.
2695       if (!RHSC->getAPInt().isPowerOf2())
2696         ++MaxShiftAmt;
2697       IntegerType *ExtTy =
2698         IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2699       if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2700         if (const SCEVConstant *Step =
2701             dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2702           // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2703           const APInt &StepInt = Step->getAPInt();
2704           const APInt &DivInt = RHSC->getAPInt();
2705           if (!StepInt.urem(DivInt) &&
2706               getZeroExtendExpr(AR, ExtTy) ==
2707               getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2708                             getZeroExtendExpr(Step, ExtTy),
2709                             AR->getLoop(), SCEV::FlagAnyWrap)) {
2710             SmallVector<const SCEV *, 4> Operands;
2711             for (const SCEV *Op : AR->operands())
2712               Operands.push_back(getUDivExpr(Op, RHS));
2713             return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
2714           }
2715           /// Get a canonical UDivExpr for a recurrence.
2716           /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2717           // We can currently only fold X%N if X is constant.
2718           const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2719           if (StartC && !DivInt.urem(StepInt) &&
2720               getZeroExtendExpr(AR, ExtTy) ==
2721               getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2722                             getZeroExtendExpr(Step, ExtTy),
2723                             AR->getLoop(), SCEV::FlagAnyWrap)) {
2724             const APInt &StartInt = StartC->getAPInt();
2725             const APInt &StartRem = StartInt.urem(StepInt);
2726             if (StartRem != 0)
2727               LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2728                                   AR->getLoop(), SCEV::FlagNW);
2729           }
2730         }
2731       // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2732       if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2733         SmallVector<const SCEV *, 4> Operands;
2734         for (const SCEV *Op : M->operands())
2735           Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2736         if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2737           // Find an operand that's safely divisible.
2738           for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2739             const SCEV *Op = M->getOperand(i);
2740             const SCEV *Div = getUDivExpr(Op, RHSC);
2741             if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2742               Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2743                                                       M->op_end());
2744               Operands[i] = Div;
2745               return getMulExpr(Operands);
2746             }
2747           }
2748       }
2749       // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2750       if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2751         SmallVector<const SCEV *, 4> Operands;
2752         for (const SCEV *Op : A->operands())
2753           Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2754         if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2755           Operands.clear();
2756           for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2757             const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2758             if (isa<SCEVUDivExpr>(Op) ||
2759                 getMulExpr(Op, RHS) != A->getOperand(i))
2760               break;
2761             Operands.push_back(Op);
2762           }
2763           if (Operands.size() == A->getNumOperands())
2764             return getAddExpr(Operands);
2765         }
2766       }
2767 
2768       // Fold if both operands are constant.
2769       if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2770         Constant *LHSCV = LHSC->getValue();
2771         Constant *RHSCV = RHSC->getValue();
2772         return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2773                                                                    RHSCV)));
2774       }
2775     }
2776   }
2777 
2778   FoldingSetNodeID ID;
2779   ID.AddInteger(scUDivExpr);
2780   ID.AddPointer(LHS);
2781   ID.AddPointer(RHS);
2782   void *IP = nullptr;
2783   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2784   SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2785                                              LHS, RHS);
2786   UniqueSCEVs.InsertNode(S, IP);
2787   return S;
2788 }
2789 
gcd(const SCEVConstant * C1,const SCEVConstant * C2)2790 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2791   APInt A = C1->getAPInt().abs();
2792   APInt B = C2->getAPInt().abs();
2793   uint32_t ABW = A.getBitWidth();
2794   uint32_t BBW = B.getBitWidth();
2795 
2796   if (ABW > BBW)
2797     B = B.zext(ABW);
2798   else if (ABW < BBW)
2799     A = A.zext(BBW);
2800 
2801   return APIntOps::GreatestCommonDivisor(A, B);
2802 }
2803 
2804 /// Get a canonical unsigned division expression, or something simpler if
2805 /// possible. There is no representation for an exact udiv in SCEV IR, but we
2806 /// can attempt to remove factors from the LHS and RHS.  We can't do this when
2807 /// it's not exact because the udiv may be clearing bits.
getUDivExactExpr(const SCEV * LHS,const SCEV * RHS)2808 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2809                                               const SCEV *RHS) {
2810   // TODO: we could try to find factors in all sorts of things, but for now we
2811   // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2812   // end of this file for inspiration.
2813 
2814   const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2815   if (!Mul)
2816     return getUDivExpr(LHS, RHS);
2817 
2818   if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2819     // If the mulexpr multiplies by a constant, then that constant must be the
2820     // first element of the mulexpr.
2821     if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2822       if (LHSCst == RHSCst) {
2823         SmallVector<const SCEV *, 2> Operands;
2824         Operands.append(Mul->op_begin() + 1, Mul->op_end());
2825         return getMulExpr(Operands);
2826       }
2827 
2828       // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2829       // that there's a factor provided by one of the other terms. We need to
2830       // check.
2831       APInt Factor = gcd(LHSCst, RHSCst);
2832       if (!Factor.isIntN(1)) {
2833         LHSCst =
2834             cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor)));
2835         RHSCst =
2836             cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor)));
2837         SmallVector<const SCEV *, 2> Operands;
2838         Operands.push_back(LHSCst);
2839         Operands.append(Mul->op_begin() + 1, Mul->op_end());
2840         LHS = getMulExpr(Operands);
2841         RHS = RHSCst;
2842         Mul = dyn_cast<SCEVMulExpr>(LHS);
2843         if (!Mul)
2844           return getUDivExactExpr(LHS, RHS);
2845       }
2846     }
2847   }
2848 
2849   for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2850     if (Mul->getOperand(i) == RHS) {
2851       SmallVector<const SCEV *, 2> Operands;
2852       Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2853       Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2854       return getMulExpr(Operands);
2855     }
2856   }
2857 
2858   return getUDivExpr(LHS, RHS);
2859 }
2860 
2861 /// Get an add recurrence expression for the specified loop.  Simplify the
2862 /// expression as much as possible.
getAddRecExpr(const SCEV * Start,const SCEV * Step,const Loop * L,SCEV::NoWrapFlags Flags)2863 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2864                                            const Loop *L,
2865                                            SCEV::NoWrapFlags Flags) {
2866   SmallVector<const SCEV *, 4> Operands;
2867   Operands.push_back(Start);
2868   if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2869     if (StepChrec->getLoop() == L) {
2870       Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2871       return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2872     }
2873 
2874   Operands.push_back(Step);
2875   return getAddRecExpr(Operands, L, Flags);
2876 }
2877 
2878 /// Get an add recurrence expression for the specified loop.  Simplify the
2879 /// expression as much as possible.
2880 const SCEV *
getAddRecExpr(SmallVectorImpl<const SCEV * > & Operands,const Loop * L,SCEV::NoWrapFlags Flags)2881 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2882                                const Loop *L, SCEV::NoWrapFlags Flags) {
2883   if (Operands.size() == 1) return Operands[0];
2884 #ifndef NDEBUG
2885   Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2886   for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2887     assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2888            "SCEVAddRecExpr operand types don't match!");
2889   for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2890     assert(isLoopInvariant(Operands[i], L) &&
2891            "SCEVAddRecExpr operand is not loop-invariant!");
2892 #endif
2893 
2894   if (Operands.back()->isZero()) {
2895     Operands.pop_back();
2896     return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0}  -->  X
2897   }
2898 
2899   // It's tempting to want to call getMaxBackedgeTakenCount count here and
2900   // use that information to infer NUW and NSW flags. However, computing a
2901   // BE count requires calling getAddRecExpr, so we may not yet have a
2902   // meaningful BE count at this point (and if we don't, we'd be stuck
2903   // with a SCEVCouldNotCompute as the cached BE count).
2904 
2905   Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2906 
2907   // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2908   if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2909     const Loop *NestedLoop = NestedAR->getLoop();
2910     if (L->contains(NestedLoop)
2911             ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
2912             : (!NestedLoop->contains(L) &&
2913                DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
2914       SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2915                                                   NestedAR->op_end());
2916       Operands[0] = NestedAR->getStart();
2917       // AddRecs require their operands be loop-invariant with respect to their
2918       // loops. Don't perform this transformation if it would break this
2919       // requirement.
2920       bool AllInvariant = all_of(
2921           Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
2922 
2923       if (AllInvariant) {
2924         // Create a recurrence for the outer loop with the same step size.
2925         //
2926         // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2927         // inner recurrence has the same property.
2928         SCEV::NoWrapFlags OuterFlags =
2929           maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2930 
2931         NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2932         AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
2933           return isLoopInvariant(Op, NestedLoop);
2934         });
2935 
2936         if (AllInvariant) {
2937           // Ok, both add recurrences are valid after the transformation.
2938           //
2939           // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2940           // the outer recurrence has the same property.
2941           SCEV::NoWrapFlags InnerFlags =
2942             maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2943           return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2944         }
2945       }
2946       // Reset Operands to its original state.
2947       Operands[0] = NestedAR;
2948     }
2949   }
2950 
2951   // Okay, it looks like we really DO need an addrec expr.  Check to see if we
2952   // already have one, otherwise create a new one.
2953   FoldingSetNodeID ID;
2954   ID.AddInteger(scAddRecExpr);
2955   for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2956     ID.AddPointer(Operands[i]);
2957   ID.AddPointer(L);
2958   void *IP = nullptr;
2959   SCEVAddRecExpr *S =
2960     static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2961   if (!S) {
2962     const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2963     std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2964     S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2965                                            O, Operands.size(), L);
2966     UniqueSCEVs.InsertNode(S, IP);
2967   }
2968   S->setNoWrapFlags(Flags);
2969   return S;
2970 }
2971 
2972 const SCEV *
getGEPExpr(Type * PointeeType,const SCEV * BaseExpr,const SmallVectorImpl<const SCEV * > & IndexExprs,bool InBounds)2973 ScalarEvolution::getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
2974                             const SmallVectorImpl<const SCEV *> &IndexExprs,
2975                             bool InBounds) {
2976   // getSCEV(Base)->getType() has the same address space as Base->getType()
2977   // because SCEV::getType() preserves the address space.
2978   Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
2979   // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
2980   // instruction to its SCEV, because the Instruction may be guarded by control
2981   // flow and the no-overflow bits may not be valid for the expression in any
2982   // context. This can be fixed similarly to how these flags are handled for
2983   // adds.
2984   SCEV::NoWrapFlags Wrap = InBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
2985 
2986   const SCEV *TotalOffset = getZero(IntPtrTy);
2987   // The address space is unimportant. The first thing we do on CurTy is getting
2988   // its element type.
2989   Type *CurTy = PointerType::getUnqual(PointeeType);
2990   for (const SCEV *IndexExpr : IndexExprs) {
2991     // Compute the (potentially symbolic) offset in bytes for this index.
2992     if (StructType *STy = dyn_cast<StructType>(CurTy)) {
2993       // For a struct, add the member offset.
2994       ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
2995       unsigned FieldNo = Index->getZExtValue();
2996       const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
2997 
2998       // Add the field offset to the running total offset.
2999       TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3000 
3001       // Update CurTy to the type of the field at Index.
3002       CurTy = STy->getTypeAtIndex(Index);
3003     } else {
3004       // Update CurTy to its element type.
3005       CurTy = cast<SequentialType>(CurTy)->getElementType();
3006       // For an array, add the element offset, explicitly scaled.
3007       const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
3008       // Getelementptr indices are signed.
3009       IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
3010 
3011       // Multiply the index by the element size to compute the element offset.
3012       const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
3013 
3014       // Add the element offset to the running total offset.
3015       TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3016     }
3017   }
3018 
3019   // Add the total offset from all the GEP indices to the base.
3020   return getAddExpr(BaseExpr, TotalOffset, Wrap);
3021 }
3022 
getSMaxExpr(const SCEV * LHS,const SCEV * RHS)3023 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
3024                                          const SCEV *RHS) {
3025   SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3026   return getSMaxExpr(Ops);
3027 }
3028 
3029 const SCEV *
getSMaxExpr(SmallVectorImpl<const SCEV * > & Ops)3030 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3031   assert(!Ops.empty() && "Cannot get empty smax!");
3032   if (Ops.size() == 1) return Ops[0];
3033 #ifndef NDEBUG
3034   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3035   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3036     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3037            "SCEVSMaxExpr operand types don't match!");
3038 #endif
3039 
3040   // Sort by complexity, this groups all similar expression types together.
3041   GroupByComplexity(Ops, &LI);
3042 
3043   // If there are any constants, fold them together.
3044   unsigned Idx = 0;
3045   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3046     ++Idx;
3047     assert(Idx < Ops.size());
3048     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3049       // We found two constants, fold them together!
3050       ConstantInt *Fold = ConstantInt::get(
3051           getContext(), APIntOps::smax(LHSC->getAPInt(), RHSC->getAPInt()));
3052       Ops[0] = getConstant(Fold);
3053       Ops.erase(Ops.begin()+1);  // Erase the folded element
3054       if (Ops.size() == 1) return Ops[0];
3055       LHSC = cast<SCEVConstant>(Ops[0]);
3056     }
3057 
3058     // If we are left with a constant minimum-int, strip it off.
3059     if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3060       Ops.erase(Ops.begin());
3061       --Idx;
3062     } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3063       // If we have an smax with a constant maximum-int, it will always be
3064       // maximum-int.
3065       return Ops[0];
3066     }
3067 
3068     if (Ops.size() == 1) return Ops[0];
3069   }
3070 
3071   // Find the first SMax
3072   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3073     ++Idx;
3074 
3075   // Check to see if one of the operands is an SMax. If so, expand its operands
3076   // onto our operand list, and recurse to simplify.
3077   if (Idx < Ops.size()) {
3078     bool DeletedSMax = false;
3079     while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3080       Ops.erase(Ops.begin()+Idx);
3081       Ops.append(SMax->op_begin(), SMax->op_end());
3082       DeletedSMax = true;
3083     }
3084 
3085     if (DeletedSMax)
3086       return getSMaxExpr(Ops);
3087   }
3088 
3089   // Okay, check to see if the same value occurs in the operand list twice.  If
3090   // so, delete one.  Since we sorted the list, these values are required to
3091   // be adjacent.
3092   for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3093     //  X smax Y smax Y  -->  X smax Y
3094     //  X smax Y         -->  X, if X is always greater than Y
3095     if (Ops[i] == Ops[i+1] ||
3096         isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3097       Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3098       --i; --e;
3099     } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3100       Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3101       --i; --e;
3102     }
3103 
3104   if (Ops.size() == 1) return Ops[0];
3105 
3106   assert(!Ops.empty() && "Reduced smax down to nothing!");
3107 
3108   // Okay, it looks like we really DO need an smax expr.  Check to see if we
3109   // already have one, otherwise create a new one.
3110   FoldingSetNodeID ID;
3111   ID.AddInteger(scSMaxExpr);
3112   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3113     ID.AddPointer(Ops[i]);
3114   void *IP = nullptr;
3115   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3116   const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3117   std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3118   SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3119                                              O, Ops.size());
3120   UniqueSCEVs.InsertNode(S, IP);
3121   return S;
3122 }
3123 
getUMaxExpr(const SCEV * LHS,const SCEV * RHS)3124 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3125                                          const SCEV *RHS) {
3126   SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3127   return getUMaxExpr(Ops);
3128 }
3129 
3130 const SCEV *
getUMaxExpr(SmallVectorImpl<const SCEV * > & Ops)3131 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3132   assert(!Ops.empty() && "Cannot get empty umax!");
3133   if (Ops.size() == 1) return Ops[0];
3134 #ifndef NDEBUG
3135   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3136   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3137     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3138            "SCEVUMaxExpr operand types don't match!");
3139 #endif
3140 
3141   // Sort by complexity, this groups all similar expression types together.
3142   GroupByComplexity(Ops, &LI);
3143 
3144   // If there are any constants, fold them together.
3145   unsigned Idx = 0;
3146   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3147     ++Idx;
3148     assert(Idx < Ops.size());
3149     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3150       // We found two constants, fold them together!
3151       ConstantInt *Fold = ConstantInt::get(
3152           getContext(), APIntOps::umax(LHSC->getAPInt(), RHSC->getAPInt()));
3153       Ops[0] = getConstant(Fold);
3154       Ops.erase(Ops.begin()+1);  // Erase the folded element
3155       if (Ops.size() == 1) return Ops[0];
3156       LHSC = cast<SCEVConstant>(Ops[0]);
3157     }
3158 
3159     // If we are left with a constant minimum-int, strip it off.
3160     if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3161       Ops.erase(Ops.begin());
3162       --Idx;
3163     } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3164       // If we have an umax with a constant maximum-int, it will always be
3165       // maximum-int.
3166       return Ops[0];
3167     }
3168 
3169     if (Ops.size() == 1) return Ops[0];
3170   }
3171 
3172   // Find the first UMax
3173   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3174     ++Idx;
3175 
3176   // Check to see if one of the operands is a UMax. If so, expand its operands
3177   // onto our operand list, and recurse to simplify.
3178   if (Idx < Ops.size()) {
3179     bool DeletedUMax = false;
3180     while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3181       Ops.erase(Ops.begin()+Idx);
3182       Ops.append(UMax->op_begin(), UMax->op_end());
3183       DeletedUMax = true;
3184     }
3185 
3186     if (DeletedUMax)
3187       return getUMaxExpr(Ops);
3188   }
3189 
3190   // Okay, check to see if the same value occurs in the operand list twice.  If
3191   // so, delete one.  Since we sorted the list, these values are required to
3192   // be adjacent.
3193   for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3194     //  X umax Y umax Y  -->  X umax Y
3195     //  X umax Y         -->  X, if X is always greater than Y
3196     if (Ops[i] == Ops[i+1] ||
3197         isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3198       Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3199       --i; --e;
3200     } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3201       Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3202       --i; --e;
3203     }
3204 
3205   if (Ops.size() == 1) return Ops[0];
3206 
3207   assert(!Ops.empty() && "Reduced umax down to nothing!");
3208 
3209   // Okay, it looks like we really DO need a umax expr.  Check to see if we
3210   // already have one, otherwise create a new one.
3211   FoldingSetNodeID ID;
3212   ID.AddInteger(scUMaxExpr);
3213   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3214     ID.AddPointer(Ops[i]);
3215   void *IP = nullptr;
3216   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3217   const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3218   std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3219   SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3220                                              O, Ops.size());
3221   UniqueSCEVs.InsertNode(S, IP);
3222   return S;
3223 }
3224 
getSMinExpr(const SCEV * LHS,const SCEV * RHS)3225 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3226                                          const SCEV *RHS) {
3227   // ~smax(~x, ~y) == smin(x, y).
3228   return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3229 }
3230 
getUMinExpr(const SCEV * LHS,const SCEV * RHS)3231 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3232                                          const SCEV *RHS) {
3233   // ~umax(~x, ~y) == umin(x, y)
3234   return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3235 }
3236 
getSizeOfExpr(Type * IntTy,Type * AllocTy)3237 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3238   // We can bypass creating a target-independent
3239   // constant expression and then folding it back into a ConstantInt.
3240   // This is just a compile-time optimization.
3241   return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
3242 }
3243 
getOffsetOfExpr(Type * IntTy,StructType * STy,unsigned FieldNo)3244 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3245                                              StructType *STy,
3246                                              unsigned FieldNo) {
3247   // We can bypass creating a target-independent
3248   // constant expression and then folding it back into a ConstantInt.
3249   // This is just a compile-time optimization.
3250   return getConstant(
3251       IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
3252 }
3253 
getUnknown(Value * V)3254 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3255   // Don't attempt to do anything other than create a SCEVUnknown object
3256   // here.  createSCEV only calls getUnknown after checking for all other
3257   // interesting possibilities, and any other code that calls getUnknown
3258   // is doing so in order to hide a value from SCEV canonicalization.
3259 
3260   FoldingSetNodeID ID;
3261   ID.AddInteger(scUnknown);
3262   ID.AddPointer(V);
3263   void *IP = nullptr;
3264   if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3265     assert(cast<SCEVUnknown>(S)->getValue() == V &&
3266            "Stale SCEVUnknown in uniquing map!");
3267     return S;
3268   }
3269   SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3270                                             FirstUnknown);
3271   FirstUnknown = cast<SCEVUnknown>(S);
3272   UniqueSCEVs.InsertNode(S, IP);
3273   return S;
3274 }
3275 
3276 //===----------------------------------------------------------------------===//
3277 //            Basic SCEV Analysis and PHI Idiom Recognition Code
3278 //
3279 
3280 /// Test if values of the given type are analyzable within the SCEV
3281 /// framework. This primarily includes integer types, and it can optionally
3282 /// include pointer types if the ScalarEvolution class has access to
3283 /// target-specific information.
isSCEVable(Type * Ty) const3284 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3285   // Integers and pointers are always SCEVable.
3286   return Ty->isIntegerTy() || Ty->isPointerTy();
3287 }
3288 
3289 /// Return the size in bits of the specified type, for which isSCEVable must
3290 /// return true.
getTypeSizeInBits(Type * Ty) const3291 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3292   assert(isSCEVable(Ty) && "Type is not SCEVable!");
3293   return getDataLayout().getTypeSizeInBits(Ty);
3294 }
3295 
3296 /// Return a type with the same bitwidth as the given type and which represents
3297 /// how SCEV will treat the given type, for which isSCEVable must return
3298 /// true. For pointer types, this is the pointer-sized integer type.
getEffectiveSCEVType(Type * Ty) const3299 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3300   assert(isSCEVable(Ty) && "Type is not SCEVable!");
3301 
3302   if (Ty->isIntegerTy())
3303     return Ty;
3304 
3305   // The only other support type is pointer.
3306   assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3307   return getDataLayout().getIntPtrType(Ty);
3308 }
3309 
getCouldNotCompute()3310 const SCEV *ScalarEvolution::getCouldNotCompute() {
3311   return CouldNotCompute.get();
3312 }
3313 
3314 
checkValidity(const SCEV * S) const3315 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3316   // Helper class working with SCEVTraversal to figure out if a SCEV contains
3317   // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3318   // is set iff if find such SCEVUnknown.
3319   //
3320   struct FindInvalidSCEVUnknown {
3321     bool FindOne;
3322     FindInvalidSCEVUnknown() { FindOne = false; }
3323     bool follow(const SCEV *S) {
3324       switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3325       case scConstant:
3326         return false;
3327       case scUnknown:
3328         if (!cast<SCEVUnknown>(S)->getValue())
3329           FindOne = true;
3330         return false;
3331       default:
3332         return true;
3333       }
3334     }
3335     bool isDone() const { return FindOne; }
3336   };
3337 
3338   FindInvalidSCEVUnknown F;
3339   SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3340   ST.visitAll(S);
3341 
3342   return !F.FindOne;
3343 }
3344 
3345 namespace {
3346 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3347 // a sub SCEV of scAddRecExpr type.  FindInvalidSCEVUnknown::FoundOne is set
3348 // iff if such sub scAddRecExpr type SCEV is found.
3349 struct FindAddRecurrence {
3350   bool FoundOne;
FindAddRecurrence__anon6eb5a8bf0711::FindAddRecurrence3351   FindAddRecurrence() : FoundOne(false) {}
3352 
follow__anon6eb5a8bf0711::FindAddRecurrence3353   bool follow(const SCEV *S) {
3354     switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3355     case scAddRecExpr:
3356       FoundOne = true;
3357     case scConstant:
3358     case scUnknown:
3359     case scCouldNotCompute:
3360       return false;
3361     default:
3362       return true;
3363     }
3364   }
isDone__anon6eb5a8bf0711::FindAddRecurrence3365   bool isDone() const { return FoundOne; }
3366 };
3367 }
3368 
containsAddRecurrence(const SCEV * S)3369 bool ScalarEvolution::containsAddRecurrence(const SCEV *S) {
3370   HasRecMapType::iterator I = HasRecMap.find_as(S);
3371   if (I != HasRecMap.end())
3372     return I->second;
3373 
3374   FindAddRecurrence F;
3375   SCEVTraversal<FindAddRecurrence> ST(F);
3376   ST.visitAll(S);
3377   HasRecMap.insert({S, F.FoundOne});
3378   return F.FoundOne;
3379 }
3380 
3381 /// Return the Value set from S.
getSCEVValues(const SCEV * S)3382 SetVector<Value *> *ScalarEvolution::getSCEVValues(const SCEV *S) {
3383   ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
3384   if (SI == ExprValueMap.end())
3385     return nullptr;
3386 #ifndef NDEBUG
3387   if (VerifySCEVMap) {
3388     // Check there is no dangling Value in the set returned.
3389     for (const auto &VE : SI->second)
3390       assert(ValueExprMap.count(VE));
3391   }
3392 #endif
3393   return &SI->second;
3394 }
3395 
3396 /// Erase Value from ValueExprMap and ExprValueMap.  If ValueExprMap.erase(V) is
3397 /// not used together with forgetMemoizedResults(S), eraseValueFromMap should be
3398 /// used instead to ensure whenever V->S is removed from ValueExprMap, V is also
3399 /// removed from the set of ExprValueMap[S].
eraseValueFromMap(Value * V)3400 void ScalarEvolution::eraseValueFromMap(Value *V) {
3401   ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3402   if (I != ValueExprMap.end()) {
3403     const SCEV *S = I->second;
3404     SetVector<Value *> *SV = getSCEVValues(S);
3405     // Remove V from the set of ExprValueMap[S]
3406     if (SV)
3407       SV->remove(V);
3408     ValueExprMap.erase(V);
3409   }
3410 }
3411 
3412 /// Return an existing SCEV if it exists, otherwise analyze the expression and
3413 /// create a new one.
getSCEV(Value * V)3414 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3415   assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3416 
3417   const SCEV *S = getExistingSCEV(V);
3418   if (S == nullptr) {
3419     S = createSCEV(V);
3420     // During PHI resolution, it is possible to create two SCEVs for the same
3421     // V, so it is needed to double check whether V->S is inserted into
3422     // ValueExprMap before insert S->V into ExprValueMap.
3423     std::pair<ValueExprMapType::iterator, bool> Pair =
3424         ValueExprMap.insert({SCEVCallbackVH(V, this), S});
3425     if (Pair.second)
3426       ExprValueMap[S].insert(V);
3427   }
3428   return S;
3429 }
3430 
getExistingSCEV(Value * V)3431 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3432   assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3433 
3434   ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3435   if (I != ValueExprMap.end()) {
3436     const SCEV *S = I->second;
3437     if (checkValidity(S))
3438       return S;
3439     forgetMemoizedResults(S);
3440     ValueExprMap.erase(I);
3441   }
3442   return nullptr;
3443 }
3444 
3445 /// Return a SCEV corresponding to -V = -1*V
3446 ///
getNegativeSCEV(const SCEV * V,SCEV::NoWrapFlags Flags)3447 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
3448                                              SCEV::NoWrapFlags Flags) {
3449   if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3450     return getConstant(
3451                cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3452 
3453   Type *Ty = V->getType();
3454   Ty = getEffectiveSCEVType(Ty);
3455   return getMulExpr(
3456       V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3457 }
3458 
3459 /// Return a SCEV corresponding to ~V = -1-V
getNotSCEV(const SCEV * V)3460 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3461   if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3462     return getConstant(
3463                 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3464 
3465   Type *Ty = V->getType();
3466   Ty = getEffectiveSCEVType(Ty);
3467   const SCEV *AllOnes =
3468                    getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3469   return getMinusSCEV(AllOnes, V);
3470 }
3471 
getMinusSCEV(const SCEV * LHS,const SCEV * RHS,SCEV::NoWrapFlags Flags)3472 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3473                                           SCEV::NoWrapFlags Flags) {
3474   // Fast path: X - X --> 0.
3475   if (LHS == RHS)
3476     return getZero(LHS->getType());
3477 
3478   // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
3479   // makes it so that we cannot make much use of NUW.
3480   auto AddFlags = SCEV::FlagAnyWrap;
3481   const bool RHSIsNotMinSigned =
3482       !getSignedRange(RHS).getSignedMin().isMinSignedValue();
3483   if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
3484     // Let M be the minimum representable signed value. Then (-1)*RHS
3485     // signed-wraps if and only if RHS is M. That can happen even for
3486     // a NSW subtraction because e.g. (-1)*M signed-wraps even though
3487     // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
3488     // (-1)*RHS, we need to prove that RHS != M.
3489     //
3490     // If LHS is non-negative and we know that LHS - RHS does not
3491     // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
3492     // either by proving that RHS > M or that LHS >= 0.
3493     if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
3494       AddFlags = SCEV::FlagNSW;
3495     }
3496   }
3497 
3498   // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
3499   // RHS is NSW and LHS >= 0.
3500   //
3501   // The difficulty here is that the NSW flag may have been proven
3502   // relative to a loop that is to be found in a recurrence in LHS and
3503   // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
3504   // larger scope than intended.
3505   auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3506 
3507   return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags);
3508 }
3509 
3510 const SCEV *
getTruncateOrZeroExtend(const SCEV * V,Type * Ty)3511 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3512   Type *SrcTy = V->getType();
3513   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3514          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3515          "Cannot truncate or zero extend with non-integer arguments!");
3516   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3517     return V;  // No conversion
3518   if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3519     return getTruncateExpr(V, Ty);
3520   return getZeroExtendExpr(V, Ty);
3521 }
3522 
3523 const SCEV *
getTruncateOrSignExtend(const SCEV * V,Type * Ty)3524 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3525                                          Type *Ty) {
3526   Type *SrcTy = V->getType();
3527   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3528          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3529          "Cannot truncate or zero extend with non-integer arguments!");
3530   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3531     return V;  // No conversion
3532   if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3533     return getTruncateExpr(V, Ty);
3534   return getSignExtendExpr(V, Ty);
3535 }
3536 
3537 const SCEV *
getNoopOrZeroExtend(const SCEV * V,Type * Ty)3538 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3539   Type *SrcTy = V->getType();
3540   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3541          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3542          "Cannot noop or zero extend with non-integer arguments!");
3543   assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3544          "getNoopOrZeroExtend cannot truncate!");
3545   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3546     return V;  // No conversion
3547   return getZeroExtendExpr(V, Ty);
3548 }
3549 
3550 const SCEV *
getNoopOrSignExtend(const SCEV * V,Type * Ty)3551 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3552   Type *SrcTy = V->getType();
3553   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3554          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3555          "Cannot noop or sign extend with non-integer arguments!");
3556   assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3557          "getNoopOrSignExtend cannot truncate!");
3558   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3559     return V;  // No conversion
3560   return getSignExtendExpr(V, Ty);
3561 }
3562 
3563 const SCEV *
getNoopOrAnyExtend(const SCEV * V,Type * Ty)3564 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3565   Type *SrcTy = V->getType();
3566   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3567          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3568          "Cannot noop or any extend with non-integer arguments!");
3569   assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3570          "getNoopOrAnyExtend cannot truncate!");
3571   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3572     return V;  // No conversion
3573   return getAnyExtendExpr(V, Ty);
3574 }
3575 
3576 const SCEV *
getTruncateOrNoop(const SCEV * V,Type * Ty)3577 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3578   Type *SrcTy = V->getType();
3579   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3580          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3581          "Cannot truncate or noop with non-integer arguments!");
3582   assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3583          "getTruncateOrNoop cannot extend!");
3584   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3585     return V;  // No conversion
3586   return getTruncateExpr(V, Ty);
3587 }
3588 
getUMaxFromMismatchedTypes(const SCEV * LHS,const SCEV * RHS)3589 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3590                                                         const SCEV *RHS) {
3591   const SCEV *PromotedLHS = LHS;
3592   const SCEV *PromotedRHS = RHS;
3593 
3594   if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3595     PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3596   else
3597     PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3598 
3599   return getUMaxExpr(PromotedLHS, PromotedRHS);
3600 }
3601 
getUMinFromMismatchedTypes(const SCEV * LHS,const SCEV * RHS)3602 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3603                                                         const SCEV *RHS) {
3604   const SCEV *PromotedLHS = LHS;
3605   const SCEV *PromotedRHS = RHS;
3606 
3607   if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3608     PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3609   else
3610     PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3611 
3612   return getUMinExpr(PromotedLHS, PromotedRHS);
3613 }
3614 
getPointerBase(const SCEV * V)3615 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3616   // A pointer operand may evaluate to a nonpointer expression, such as null.
3617   if (!V->getType()->isPointerTy())
3618     return V;
3619 
3620   if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3621     return getPointerBase(Cast->getOperand());
3622   } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3623     const SCEV *PtrOp = nullptr;
3624     for (const SCEV *NAryOp : NAry->operands()) {
3625       if (NAryOp->getType()->isPointerTy()) {
3626         // Cannot find the base of an expression with multiple pointer operands.
3627         if (PtrOp)
3628           return V;
3629         PtrOp = NAryOp;
3630       }
3631     }
3632     if (!PtrOp)
3633       return V;
3634     return getPointerBase(PtrOp);
3635   }
3636   return V;
3637 }
3638 
3639 /// Push users of the given Instruction onto the given Worklist.
3640 static void
PushDefUseChildren(Instruction * I,SmallVectorImpl<Instruction * > & Worklist)3641 PushDefUseChildren(Instruction *I,
3642                    SmallVectorImpl<Instruction *> &Worklist) {
3643   // Push the def-use children onto the Worklist stack.
3644   for (User *U : I->users())
3645     Worklist.push_back(cast<Instruction>(U));
3646 }
3647 
forgetSymbolicName(Instruction * PN,const SCEV * SymName)3648 void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3649   SmallVector<Instruction *, 16> Worklist;
3650   PushDefUseChildren(PN, Worklist);
3651 
3652   SmallPtrSet<Instruction *, 8> Visited;
3653   Visited.insert(PN);
3654   while (!Worklist.empty()) {
3655     Instruction *I = Worklist.pop_back_val();
3656     if (!Visited.insert(I).second)
3657       continue;
3658 
3659     auto It = ValueExprMap.find_as(static_cast<Value *>(I));
3660     if (It != ValueExprMap.end()) {
3661       const SCEV *Old = It->second;
3662 
3663       // Short-circuit the def-use traversal if the symbolic name
3664       // ceases to appear in expressions.
3665       if (Old != SymName && !hasOperand(Old, SymName))
3666         continue;
3667 
3668       // SCEVUnknown for a PHI either means that it has an unrecognized
3669       // structure, it's a PHI that's in the progress of being computed
3670       // by createNodeForPHI, or it's a single-value PHI. In the first case,
3671       // additional loop trip count information isn't going to change anything.
3672       // In the second case, createNodeForPHI will perform the necessary
3673       // updates on its own when it gets to that point. In the third, we do
3674       // want to forget the SCEVUnknown.
3675       if (!isa<PHINode>(I) ||
3676           !isa<SCEVUnknown>(Old) ||
3677           (I != PN && Old == SymName)) {
3678         forgetMemoizedResults(Old);
3679         ValueExprMap.erase(It);
3680       }
3681     }
3682 
3683     PushDefUseChildren(I, Worklist);
3684   }
3685 }
3686 
3687 namespace {
3688 class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
3689 public:
rewrite(const SCEV * S,const Loop * L,ScalarEvolution & SE)3690   static const SCEV *rewrite(const SCEV *S, const Loop *L,
3691                              ScalarEvolution &SE) {
3692     SCEVInitRewriter Rewriter(L, SE);
3693     const SCEV *Result = Rewriter.visit(S);
3694     return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
3695   }
3696 
SCEVInitRewriter(const Loop * L,ScalarEvolution & SE)3697   SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
3698       : SCEVRewriteVisitor(SE), L(L), Valid(true) {}
3699 
visitUnknown(const SCEVUnknown * Expr)3700   const SCEV *visitUnknown(const SCEVUnknown *Expr) {
3701     if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
3702       Valid = false;
3703     return Expr;
3704   }
3705 
visitAddRecExpr(const SCEVAddRecExpr * Expr)3706   const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
3707     // Only allow AddRecExprs for this loop.
3708     if (Expr->getLoop() == L)
3709       return Expr->getStart();
3710     Valid = false;
3711     return Expr;
3712   }
3713 
isValid()3714   bool isValid() { return Valid; }
3715 
3716 private:
3717   const Loop *L;
3718   bool Valid;
3719 };
3720 
3721 class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
3722 public:
rewrite(const SCEV * S,const Loop * L,ScalarEvolution & SE)3723   static const SCEV *rewrite(const SCEV *S, const Loop *L,
3724                              ScalarEvolution &SE) {
3725     SCEVShiftRewriter Rewriter(L, SE);
3726     const SCEV *Result = Rewriter.visit(S);
3727     return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
3728   }
3729 
SCEVShiftRewriter(const Loop * L,ScalarEvolution & SE)3730   SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
3731       : SCEVRewriteVisitor(SE), L(L), Valid(true) {}
3732 
visitUnknown(const SCEVUnknown * Expr)3733   const SCEV *visitUnknown(const SCEVUnknown *Expr) {
3734     // Only allow AddRecExprs for this loop.
3735     if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
3736       Valid = false;
3737     return Expr;
3738   }
3739 
visitAddRecExpr(const SCEVAddRecExpr * Expr)3740   const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
3741     if (Expr->getLoop() == L && Expr->isAffine())
3742       return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
3743     Valid = false;
3744     return Expr;
3745   }
isValid()3746   bool isValid() { return Valid; }
3747 
3748 private:
3749   const Loop *L;
3750   bool Valid;
3751 };
3752 } // end anonymous namespace
3753 
3754 SCEV::NoWrapFlags
proveNoWrapViaConstantRanges(const SCEVAddRecExpr * AR)3755 ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
3756   if (!AR->isAffine())
3757     return SCEV::FlagAnyWrap;
3758 
3759   typedef OverflowingBinaryOperator OBO;
3760   SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap;
3761 
3762   if (!AR->hasNoSignedWrap()) {
3763     ConstantRange AddRecRange = getSignedRange(AR);
3764     ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this));
3765 
3766     auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
3767         Instruction::Add, IncRange, OBO::NoSignedWrap);
3768     if (NSWRegion.contains(AddRecRange))
3769       Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW);
3770   }
3771 
3772   if (!AR->hasNoUnsignedWrap()) {
3773     ConstantRange AddRecRange = getUnsignedRange(AR);
3774     ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this));
3775 
3776     auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
3777         Instruction::Add, IncRange, OBO::NoUnsignedWrap);
3778     if (NUWRegion.contains(AddRecRange))
3779       Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW);
3780   }
3781 
3782   return Result;
3783 }
3784 
3785 namespace {
3786 /// Represents an abstract binary operation.  This may exist as a
3787 /// normal instruction or constant expression, or may have been
3788 /// derived from an expression tree.
3789 struct BinaryOp {
3790   unsigned Opcode;
3791   Value *LHS;
3792   Value *RHS;
3793   bool IsNSW;
3794   bool IsNUW;
3795 
3796   /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
3797   /// constant expression.
3798   Operator *Op;
3799 
BinaryOp__anon6eb5a8bf0911::BinaryOp3800   explicit BinaryOp(Operator *Op)
3801       : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
3802         IsNSW(false), IsNUW(false), Op(Op) {
3803     if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
3804       IsNSW = OBO->hasNoSignedWrap();
3805       IsNUW = OBO->hasNoUnsignedWrap();
3806     }
3807   }
3808 
BinaryOp__anon6eb5a8bf0911::BinaryOp3809   explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
3810                     bool IsNUW = false)
3811       : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW),
3812         Op(nullptr) {}
3813 };
3814 }
3815 
3816 
3817 /// Try to map \p V into a BinaryOp, and return \c None on failure.
MatchBinaryOp(Value * V,DominatorTree & DT)3818 static Optional<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) {
3819   auto *Op = dyn_cast<Operator>(V);
3820   if (!Op)
3821     return None;
3822 
3823   // Implementation detail: all the cleverness here should happen without
3824   // creating new SCEV expressions -- our caller knowns tricks to avoid creating
3825   // SCEV expressions when possible, and we should not break that.
3826 
3827   switch (Op->getOpcode()) {
3828   case Instruction::Add:
3829   case Instruction::Sub:
3830   case Instruction::Mul:
3831   case Instruction::UDiv:
3832   case Instruction::And:
3833   case Instruction::Or:
3834   case Instruction::AShr:
3835   case Instruction::Shl:
3836     return BinaryOp(Op);
3837 
3838   case Instruction::Xor:
3839     if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
3840       // If the RHS of the xor is a signbit, then this is just an add.
3841       // Instcombine turns add of signbit into xor as a strength reduction step.
3842       if (RHSC->getValue().isSignBit())
3843         return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
3844     return BinaryOp(Op);
3845 
3846   case Instruction::LShr:
3847     // Turn logical shift right of a constant into a unsigned divide.
3848     if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
3849       uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();
3850 
3851       // If the shift count is not less than the bitwidth, the result of
3852       // the shift is undefined. Don't try to analyze it, because the
3853       // resolution chosen here may differ from the resolution chosen in
3854       // other parts of the compiler.
3855       if (SA->getValue().ult(BitWidth)) {
3856         Constant *X =
3857             ConstantInt::get(SA->getContext(),
3858                              APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3859         return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
3860       }
3861     }
3862     return BinaryOp(Op);
3863 
3864   case Instruction::ExtractValue: {
3865     auto *EVI = cast<ExtractValueInst>(Op);
3866     if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
3867       break;
3868 
3869     auto *CI = dyn_cast<CallInst>(EVI->getAggregateOperand());
3870     if (!CI)
3871       break;
3872 
3873     if (auto *F = CI->getCalledFunction())
3874       switch (F->getIntrinsicID()) {
3875       case Intrinsic::sadd_with_overflow:
3876       case Intrinsic::uadd_with_overflow: {
3877         if (!isOverflowIntrinsicNoWrap(cast<IntrinsicInst>(CI), DT))
3878           return BinaryOp(Instruction::Add, CI->getArgOperand(0),
3879                           CI->getArgOperand(1));
3880 
3881         // Now that we know that all uses of the arithmetic-result component of
3882         // CI are guarded by the overflow check, we can go ahead and pretend
3883         // that the arithmetic is non-overflowing.
3884         if (F->getIntrinsicID() == Intrinsic::sadd_with_overflow)
3885           return BinaryOp(Instruction::Add, CI->getArgOperand(0),
3886                           CI->getArgOperand(1), /* IsNSW = */ true,
3887                           /* IsNUW = */ false);
3888         else
3889           return BinaryOp(Instruction::Add, CI->getArgOperand(0),
3890                           CI->getArgOperand(1), /* IsNSW = */ false,
3891                           /* IsNUW*/ true);
3892       }
3893 
3894       case Intrinsic::ssub_with_overflow:
3895       case Intrinsic::usub_with_overflow:
3896         return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
3897                         CI->getArgOperand(1));
3898 
3899       case Intrinsic::smul_with_overflow:
3900       case Intrinsic::umul_with_overflow:
3901         return BinaryOp(Instruction::Mul, CI->getArgOperand(0),
3902                         CI->getArgOperand(1));
3903       default:
3904         break;
3905       }
3906   }
3907 
3908   default:
3909     break;
3910   }
3911 
3912   return None;
3913 }
3914 
createAddRecFromPHI(PHINode * PN)3915 const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
3916   const Loop *L = LI.getLoopFor(PN->getParent());
3917   if (!L || L->getHeader() != PN->getParent())
3918     return nullptr;
3919 
3920   // The loop may have multiple entrances or multiple exits; we can analyze
3921   // this phi as an addrec if it has a unique entry value and a unique
3922   // backedge value.
3923   Value *BEValueV = nullptr, *StartValueV = nullptr;
3924   for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3925     Value *V = PN->getIncomingValue(i);
3926     if (L->contains(PN->getIncomingBlock(i))) {
3927       if (!BEValueV) {
3928         BEValueV = V;
3929       } else if (BEValueV != V) {
3930         BEValueV = nullptr;
3931         break;
3932       }
3933     } else if (!StartValueV) {
3934       StartValueV = V;
3935     } else if (StartValueV != V) {
3936       StartValueV = nullptr;
3937       break;
3938     }
3939   }
3940   if (BEValueV && StartValueV) {
3941     // While we are analyzing this PHI node, handle its value symbolically.
3942     const SCEV *SymbolicName = getUnknown(PN);
3943     assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3944            "PHI node already processed?");
3945     ValueExprMap.insert({SCEVCallbackVH(PN, this), SymbolicName});
3946 
3947     // Using this symbolic name for the PHI, analyze the value coming around
3948     // the back-edge.
3949     const SCEV *BEValue = getSCEV(BEValueV);
3950 
3951     // NOTE: If BEValue is loop invariant, we know that the PHI node just
3952     // has a special value for the first iteration of the loop.
3953 
3954     // If the value coming around the backedge is an add with the symbolic
3955     // value we just inserted, then we found a simple induction variable!
3956     if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3957       // If there is a single occurrence of the symbolic value, replace it
3958       // with a recurrence.
3959       unsigned FoundIndex = Add->getNumOperands();
3960       for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3961         if (Add->getOperand(i) == SymbolicName)
3962           if (FoundIndex == e) {
3963             FoundIndex = i;
3964             break;
3965           }
3966 
3967       if (FoundIndex != Add->getNumOperands()) {
3968         // Create an add with everything but the specified operand.
3969         SmallVector<const SCEV *, 8> Ops;
3970         for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3971           if (i != FoundIndex)
3972             Ops.push_back(Add->getOperand(i));
3973         const SCEV *Accum = getAddExpr(Ops);
3974 
3975         // This is not a valid addrec if the step amount is varying each
3976         // loop iteration, but is not itself an addrec in this loop.
3977         if (isLoopInvariant(Accum, L) ||
3978             (isa<SCEVAddRecExpr>(Accum) &&
3979              cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3980           SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3981 
3982           if (auto BO = MatchBinaryOp(BEValueV, DT)) {
3983             if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
3984               if (BO->IsNUW)
3985                 Flags = setFlags(Flags, SCEV::FlagNUW);
3986               if (BO->IsNSW)
3987                 Flags = setFlags(Flags, SCEV::FlagNSW);
3988             }
3989           } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3990             // If the increment is an inbounds GEP, then we know the address
3991             // space cannot be wrapped around. We cannot make any guarantee
3992             // about signed or unsigned overflow because pointers are
3993             // unsigned but we may have a negative index from the base
3994             // pointer. We can guarantee that no unsigned wrap occurs if the
3995             // indices form a positive value.
3996             if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
3997               Flags = setFlags(Flags, SCEV::FlagNW);
3998 
3999               const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
4000               if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
4001                 Flags = setFlags(Flags, SCEV::FlagNUW);
4002             }
4003 
4004             // We cannot transfer nuw and nsw flags from subtraction
4005             // operations -- sub nuw X, Y is not the same as add nuw X, -Y
4006             // for instance.
4007           }
4008 
4009           const SCEV *StartVal = getSCEV(StartValueV);
4010           const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
4011 
4012           // Okay, for the entire analysis of this edge we assumed the PHI
4013           // to be symbolic.  We now need to go back and purge all of the
4014           // entries for the scalars that use the symbolic expression.
4015           forgetSymbolicName(PN, SymbolicName);
4016           ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
4017 
4018           // We can add Flags to the post-inc expression only if we
4019           // know that it us *undefined behavior* for BEValueV to
4020           // overflow.
4021           if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
4022             if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
4023               (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
4024 
4025           return PHISCEV;
4026         }
4027       }
4028     } else {
4029       // Otherwise, this could be a loop like this:
4030       //     i = 0;  for (j = 1; ..; ++j) { ....  i = j; }
4031       // In this case, j = {1,+,1}  and BEValue is j.
4032       // Because the other in-value of i (0) fits the evolution of BEValue
4033       // i really is an addrec evolution.
4034       //
4035       // We can generalize this saying that i is the shifted value of BEValue
4036       // by one iteration:
4037       //   PHI(f(0), f({1,+,1})) --> f({0,+,1})
4038       const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
4039       const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this);
4040       if (Shifted != getCouldNotCompute() &&
4041           Start != getCouldNotCompute()) {
4042         const SCEV *StartVal = getSCEV(StartValueV);
4043         if (Start == StartVal) {
4044           // Okay, for the entire analysis of this edge we assumed the PHI
4045           // to be symbolic.  We now need to go back and purge all of the
4046           // entries for the scalars that use the symbolic expression.
4047           forgetSymbolicName(PN, SymbolicName);
4048           ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
4049           return Shifted;
4050         }
4051       }
4052     }
4053 
4054     // Remove the temporary PHI node SCEV that has been inserted while intending
4055     // to create an AddRecExpr for this PHI node. We can not keep this temporary
4056     // as it will prevent later (possibly simpler) SCEV expressions to be added
4057     // to the ValueExprMap.
4058     ValueExprMap.erase(PN);
4059   }
4060 
4061   return nullptr;
4062 }
4063 
4064 // Checks if the SCEV S is available at BB.  S is considered available at BB
4065 // if S can be materialized at BB without introducing a fault.
IsAvailableOnEntry(const Loop * L,DominatorTree & DT,const SCEV * S,BasicBlock * BB)4066 static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
4067                                BasicBlock *BB) {
4068   struct CheckAvailable {
4069     bool TraversalDone = false;
4070     bool Available = true;
4071 
4072     const Loop *L = nullptr;  // The loop BB is in (can be nullptr)
4073     BasicBlock *BB = nullptr;
4074     DominatorTree &DT;
4075 
4076     CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
4077       : L(L), BB(BB), DT(DT) {}
4078 
4079     bool setUnavailable() {
4080       TraversalDone = true;
4081       Available = false;
4082       return false;
4083     }
4084 
4085     bool follow(const SCEV *S) {
4086       switch (S->getSCEVType()) {
4087       case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
4088       case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
4089         // These expressions are available if their operand(s) is/are.
4090         return true;
4091 
4092       case scAddRecExpr: {
4093         // We allow add recurrences that are on the loop BB is in, or some
4094         // outer loop.  This guarantees availability because the value of the
4095         // add recurrence at BB is simply the "current" value of the induction
4096         // variable.  We can relax this in the future; for instance an add
4097         // recurrence on a sibling dominating loop is also available at BB.
4098         const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
4099         if (L && (ARLoop == L || ARLoop->contains(L)))
4100           return true;
4101 
4102         return setUnavailable();
4103       }
4104 
4105       case scUnknown: {
4106         // For SCEVUnknown, we check for simple dominance.
4107         const auto *SU = cast<SCEVUnknown>(S);
4108         Value *V = SU->getValue();
4109 
4110         if (isa<Argument>(V))
4111           return false;
4112 
4113         if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
4114           return false;
4115 
4116         return setUnavailable();
4117       }
4118 
4119       case scUDivExpr:
4120       case scCouldNotCompute:
4121         // We do not try to smart about these at all.
4122         return setUnavailable();
4123       }
4124       llvm_unreachable("switch should be fully covered!");
4125     }
4126 
4127     bool isDone() { return TraversalDone; }
4128   };
4129 
4130   CheckAvailable CA(L, BB, DT);
4131   SCEVTraversal<CheckAvailable> ST(CA);
4132 
4133   ST.visitAll(S);
4134   return CA.Available;
4135 }
4136 
4137 // Try to match a control flow sequence that branches out at BI and merges back
4138 // at Merge into a "C ? LHS : RHS" select pattern.  Return true on a successful
4139 // match.
BrPHIToSelect(DominatorTree & DT,BranchInst * BI,PHINode * Merge,Value * & C,Value * & LHS,Value * & RHS)4140 static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
4141                           Value *&C, Value *&LHS, Value *&RHS) {
4142   C = BI->getCondition();
4143 
4144   BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
4145   BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
4146 
4147   if (!LeftEdge.isSingleEdge())
4148     return false;
4149 
4150   assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
4151 
4152   Use &LeftUse = Merge->getOperandUse(0);
4153   Use &RightUse = Merge->getOperandUse(1);
4154 
4155   if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
4156     LHS = LeftUse;
4157     RHS = RightUse;
4158     return true;
4159   }
4160 
4161   if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
4162     LHS = RightUse;
4163     RHS = LeftUse;
4164     return true;
4165   }
4166 
4167   return false;
4168 }
4169 
createNodeFromSelectLikePHI(PHINode * PN)4170 const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
4171   if (PN->getNumIncomingValues() == 2) {
4172     const Loop *L = LI.getLoopFor(PN->getParent());
4173 
4174     // We don't want to break LCSSA, even in a SCEV expression tree.
4175     for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
4176       if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
4177         return nullptr;
4178 
4179     // Try to match
4180     //
4181     //  br %cond, label %left, label %right
4182     // left:
4183     //  br label %merge
4184     // right:
4185     //  br label %merge
4186     // merge:
4187     //  V = phi [ %x, %left ], [ %y, %right ]
4188     //
4189     // as "select %cond, %x, %y"
4190 
4191     BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
4192     assert(IDom && "At least the entry block should dominate PN");
4193 
4194     auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
4195     Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
4196 
4197     if (BI && BI->isConditional() &&
4198         BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
4199         IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
4200         IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
4201       return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
4202   }
4203 
4204   return nullptr;
4205 }
4206 
createNodeForPHI(PHINode * PN)4207 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
4208   if (const SCEV *S = createAddRecFromPHI(PN))
4209     return S;
4210 
4211   if (const SCEV *S = createNodeFromSelectLikePHI(PN))
4212     return S;
4213 
4214   // If the PHI has a single incoming value, follow that value, unless the
4215   // PHI's incoming blocks are in a different loop, in which case doing so
4216   // risks breaking LCSSA form. Instcombine would normally zap these, but
4217   // it doesn't have DominatorTree information, so it may miss cases.
4218   if (Value *V = SimplifyInstruction(PN, getDataLayout(), &TLI, &DT, &AC))
4219     if (LI.replacementPreservesLCSSAForm(PN, V))
4220       return getSCEV(V);
4221 
4222   // If it's not a loop phi, we can't handle it yet.
4223   return getUnknown(PN);
4224 }
4225 
createNodeForSelectOrPHI(Instruction * I,Value * Cond,Value * TrueVal,Value * FalseVal)4226 const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
4227                                                       Value *Cond,
4228                                                       Value *TrueVal,
4229                                                       Value *FalseVal) {
4230   // Handle "constant" branch or select. This can occur for instance when a
4231   // loop pass transforms an inner loop and moves on to process the outer loop.
4232   if (auto *CI = dyn_cast<ConstantInt>(Cond))
4233     return getSCEV(CI->isOne() ? TrueVal : FalseVal);
4234 
4235   // Try to match some simple smax or umax patterns.
4236   auto *ICI = dyn_cast<ICmpInst>(Cond);
4237   if (!ICI)
4238     return getUnknown(I);
4239 
4240   Value *LHS = ICI->getOperand(0);
4241   Value *RHS = ICI->getOperand(1);
4242 
4243   switch (ICI->getPredicate()) {
4244   case ICmpInst::ICMP_SLT:
4245   case ICmpInst::ICMP_SLE:
4246     std::swap(LHS, RHS);
4247   // fall through
4248   case ICmpInst::ICMP_SGT:
4249   case ICmpInst::ICMP_SGE:
4250     // a >s b ? a+x : b+x  ->  smax(a, b)+x
4251     // a >s b ? b+x : a+x  ->  smin(a, b)+x
4252     if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
4253       const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
4254       const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
4255       const SCEV *LA = getSCEV(TrueVal);
4256       const SCEV *RA = getSCEV(FalseVal);
4257       const SCEV *LDiff = getMinusSCEV(LA, LS);
4258       const SCEV *RDiff = getMinusSCEV(RA, RS);
4259       if (LDiff == RDiff)
4260         return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4261       LDiff = getMinusSCEV(LA, RS);
4262       RDiff = getMinusSCEV(RA, LS);
4263       if (LDiff == RDiff)
4264         return getAddExpr(getSMinExpr(LS, RS), LDiff);
4265     }
4266     break;
4267   case ICmpInst::ICMP_ULT:
4268   case ICmpInst::ICMP_ULE:
4269     std::swap(LHS, RHS);
4270   // fall through
4271   case ICmpInst::ICMP_UGT:
4272   case ICmpInst::ICMP_UGE:
4273     // a >u b ? a+x : b+x  ->  umax(a, b)+x
4274     // a >u b ? b+x : a+x  ->  umin(a, b)+x
4275     if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
4276       const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4277       const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
4278       const SCEV *LA = getSCEV(TrueVal);
4279       const SCEV *RA = getSCEV(FalseVal);
4280       const SCEV *LDiff = getMinusSCEV(LA, LS);
4281       const SCEV *RDiff = getMinusSCEV(RA, RS);
4282       if (LDiff == RDiff)
4283         return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4284       LDiff = getMinusSCEV(LA, RS);
4285       RDiff = getMinusSCEV(RA, LS);
4286       if (LDiff == RDiff)
4287         return getAddExpr(getUMinExpr(LS, RS), LDiff);
4288     }
4289     break;
4290   case ICmpInst::ICMP_NE:
4291     // n != 0 ? n+x : 1+x  ->  umax(n, 1)+x
4292     if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
4293         isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4294       const SCEV *One = getOne(I->getType());
4295       const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4296       const SCEV *LA = getSCEV(TrueVal);
4297       const SCEV *RA = getSCEV(FalseVal);
4298       const SCEV *LDiff = getMinusSCEV(LA, LS);
4299       const SCEV *RDiff = getMinusSCEV(RA, One);
4300       if (LDiff == RDiff)
4301         return getAddExpr(getUMaxExpr(One, LS), LDiff);
4302     }
4303     break;
4304   case ICmpInst::ICMP_EQ:
4305     // n == 0 ? 1+x : n+x  ->  umax(n, 1)+x
4306     if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
4307         isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4308       const SCEV *One = getOne(I->getType());
4309       const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4310       const SCEV *LA = getSCEV(TrueVal);
4311       const SCEV *RA = getSCEV(FalseVal);
4312       const SCEV *LDiff = getMinusSCEV(LA, One);
4313       const SCEV *RDiff = getMinusSCEV(RA, LS);
4314       if (LDiff == RDiff)
4315         return getAddExpr(getUMaxExpr(One, LS), LDiff);
4316     }
4317     break;
4318   default:
4319     break;
4320   }
4321 
4322   return getUnknown(I);
4323 }
4324 
4325 /// Expand GEP instructions into add and multiply operations. This allows them
4326 /// to be analyzed by regular SCEV code.
createNodeForGEP(GEPOperator * GEP)4327 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
4328   // Don't attempt to analyze GEPs over unsized objects.
4329   if (!GEP->getSourceElementType()->isSized())
4330     return getUnknown(GEP);
4331 
4332   SmallVector<const SCEV *, 4> IndexExprs;
4333   for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
4334     IndexExprs.push_back(getSCEV(*Index));
4335   return getGEPExpr(GEP->getSourceElementType(),
4336                     getSCEV(GEP->getPointerOperand()),
4337                     IndexExprs, GEP->isInBounds());
4338 }
4339 
4340 uint32_t
GetMinTrailingZeros(const SCEV * S)4341 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
4342   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4343     return C->getAPInt().countTrailingZeros();
4344 
4345   if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
4346     return std::min(GetMinTrailingZeros(T->getOperand()),
4347                     (uint32_t)getTypeSizeInBits(T->getType()));
4348 
4349   if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
4350     uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4351     return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4352              getTypeSizeInBits(E->getType()) : OpRes;
4353   }
4354 
4355   if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
4356     uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4357     return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4358              getTypeSizeInBits(E->getType()) : OpRes;
4359   }
4360 
4361   if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
4362     // The result is the min of all operands results.
4363     uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4364     for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4365       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4366     return MinOpRes;
4367   }
4368 
4369   if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
4370     // The result is the sum of all operands results.
4371     uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
4372     uint32_t BitWidth = getTypeSizeInBits(M->getType());
4373     for (unsigned i = 1, e = M->getNumOperands();
4374          SumOpRes != BitWidth && i != e; ++i)
4375       SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
4376                           BitWidth);
4377     return SumOpRes;
4378   }
4379 
4380   if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
4381     // The result is the min of all operands results.
4382     uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4383     for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4384       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4385     return MinOpRes;
4386   }
4387 
4388   if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
4389     // The result is the min of all operands results.
4390     uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4391     for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4392       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4393     return MinOpRes;
4394   }
4395 
4396   if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
4397     // The result is the min of all operands results.
4398     uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4399     for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4400       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4401     return MinOpRes;
4402   }
4403 
4404   if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4405     // For a SCEVUnknown, ask ValueTracking.
4406     unsigned BitWidth = getTypeSizeInBits(U->getType());
4407     APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4408     computeKnownBits(U->getValue(), Zeros, Ones, getDataLayout(), 0, &AC,
4409                      nullptr, &DT);
4410     return Zeros.countTrailingOnes();
4411   }
4412 
4413   // SCEVUDivExpr
4414   return 0;
4415 }
4416 
4417 /// Helper method to assign a range to V from metadata present in the IR.
GetRangeFromMetadata(Value * V)4418 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
4419   if (Instruction *I = dyn_cast<Instruction>(V))
4420     if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
4421       return getConstantRangeFromMetadata(*MD);
4422 
4423   return None;
4424 }
4425 
4426 /// Determine the range for a particular SCEV.  If SignHint is
4427 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
4428 /// with a "cleaner" unsigned (resp. signed) representation.
4429 ConstantRange
getRange(const SCEV * S,ScalarEvolution::RangeSignHint SignHint)4430 ScalarEvolution::getRange(const SCEV *S,
4431                           ScalarEvolution::RangeSignHint SignHint) {
4432   DenseMap<const SCEV *, ConstantRange> &Cache =
4433       SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
4434                                                        : SignedRanges;
4435 
4436   // See if we've computed this range already.
4437   DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
4438   if (I != Cache.end())
4439     return I->second;
4440 
4441   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4442     return setRange(C, SignHint, ConstantRange(C->getAPInt()));
4443 
4444   unsigned BitWidth = getTypeSizeInBits(S->getType());
4445   ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
4446 
4447   // If the value has known zeros, the maximum value will have those known zeros
4448   // as well.
4449   uint32_t TZ = GetMinTrailingZeros(S);
4450   if (TZ != 0) {
4451     if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
4452       ConservativeResult =
4453           ConstantRange(APInt::getMinValue(BitWidth),
4454                         APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
4455     else
4456       ConservativeResult = ConstantRange(
4457           APInt::getSignedMinValue(BitWidth),
4458           APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
4459   }
4460 
4461   if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
4462     ConstantRange X = getRange(Add->getOperand(0), SignHint);
4463     for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
4464       X = X.add(getRange(Add->getOperand(i), SignHint));
4465     return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
4466   }
4467 
4468   if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
4469     ConstantRange X = getRange(Mul->getOperand(0), SignHint);
4470     for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
4471       X = X.multiply(getRange(Mul->getOperand(i), SignHint));
4472     return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
4473   }
4474 
4475   if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
4476     ConstantRange X = getRange(SMax->getOperand(0), SignHint);
4477     for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
4478       X = X.smax(getRange(SMax->getOperand(i), SignHint));
4479     return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
4480   }
4481 
4482   if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
4483     ConstantRange X = getRange(UMax->getOperand(0), SignHint);
4484     for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
4485       X = X.umax(getRange(UMax->getOperand(i), SignHint));
4486     return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
4487   }
4488 
4489   if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
4490     ConstantRange X = getRange(UDiv->getLHS(), SignHint);
4491     ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
4492     return setRange(UDiv, SignHint,
4493                     ConservativeResult.intersectWith(X.udiv(Y)));
4494   }
4495 
4496   if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
4497     ConstantRange X = getRange(ZExt->getOperand(), SignHint);
4498     return setRange(ZExt, SignHint,
4499                     ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
4500   }
4501 
4502   if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
4503     ConstantRange X = getRange(SExt->getOperand(), SignHint);
4504     return setRange(SExt, SignHint,
4505                     ConservativeResult.intersectWith(X.signExtend(BitWidth)));
4506   }
4507 
4508   if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
4509     ConstantRange X = getRange(Trunc->getOperand(), SignHint);
4510     return setRange(Trunc, SignHint,
4511                     ConservativeResult.intersectWith(X.truncate(BitWidth)));
4512   }
4513 
4514   if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
4515     // If there's no unsigned wrap, the value will never be less than its
4516     // initial value.
4517     if (AddRec->hasNoUnsignedWrap())
4518       if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
4519         if (!C->getValue()->isZero())
4520           ConservativeResult = ConservativeResult.intersectWith(
4521               ConstantRange(C->getAPInt(), APInt(BitWidth, 0)));
4522 
4523     // If there's no signed wrap, and all the operands have the same sign or
4524     // zero, the value won't ever change sign.
4525     if (AddRec->hasNoSignedWrap()) {
4526       bool AllNonNeg = true;
4527       bool AllNonPos = true;
4528       for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4529         if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
4530         if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
4531       }
4532       if (AllNonNeg)
4533         ConservativeResult = ConservativeResult.intersectWith(
4534           ConstantRange(APInt(BitWidth, 0),
4535                         APInt::getSignedMinValue(BitWidth)));
4536       else if (AllNonPos)
4537         ConservativeResult = ConservativeResult.intersectWith(
4538           ConstantRange(APInt::getSignedMinValue(BitWidth),
4539                         APInt(BitWidth, 1)));
4540     }
4541 
4542     // TODO: non-affine addrec
4543     if (AddRec->isAffine()) {
4544       const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
4545       if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
4546           getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
4547         auto RangeFromAffine = getRangeForAffineAR(
4548             AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
4549             BitWidth);
4550         if (!RangeFromAffine.isFullSet())
4551           ConservativeResult =
4552               ConservativeResult.intersectWith(RangeFromAffine);
4553 
4554         auto RangeFromFactoring = getRangeViaFactoring(
4555             AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
4556             BitWidth);
4557         if (!RangeFromFactoring.isFullSet())
4558           ConservativeResult =
4559               ConservativeResult.intersectWith(RangeFromFactoring);
4560       }
4561     }
4562 
4563     return setRange(AddRec, SignHint, ConservativeResult);
4564   }
4565 
4566   if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4567     // Check if the IR explicitly contains !range metadata.
4568     Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4569     if (MDRange.hasValue())
4570       ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4571 
4572     // Split here to avoid paying the compile-time cost of calling both
4573     // computeKnownBits and ComputeNumSignBits.  This restriction can be lifted
4574     // if needed.
4575     const DataLayout &DL = getDataLayout();
4576     if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
4577       // For a SCEVUnknown, ask ValueTracking.
4578       APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4579       computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, &AC, nullptr, &DT);
4580       if (Ones != ~Zeros + 1)
4581         ConservativeResult =
4582             ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
4583     } else {
4584       assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
4585              "generalize as needed!");
4586       unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
4587       if (NS > 1)
4588         ConservativeResult = ConservativeResult.intersectWith(
4589             ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4590                           APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
4591     }
4592 
4593     return setRange(U, SignHint, ConservativeResult);
4594   }
4595 
4596   return setRange(S, SignHint, ConservativeResult);
4597 }
4598 
getRangeForAffineAR(const SCEV * Start,const SCEV * Step,const SCEV * MaxBECount,unsigned BitWidth)4599 ConstantRange ScalarEvolution::getRangeForAffineAR(const SCEV *Start,
4600                                                    const SCEV *Step,
4601                                                    const SCEV *MaxBECount,
4602                                                    unsigned BitWidth) {
4603   assert(!isa<SCEVCouldNotCompute>(MaxBECount) &&
4604          getTypeSizeInBits(MaxBECount->getType()) <= BitWidth &&
4605          "Precondition!");
4606 
4607   ConstantRange Result(BitWidth, /* isFullSet = */ true);
4608 
4609   // Check for overflow.  This must be done with ConstantRange arithmetic
4610   // because we could be called from within the ScalarEvolution overflow
4611   // checking code.
4612 
4613   MaxBECount = getNoopOrZeroExtend(MaxBECount, Start->getType());
4614   ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4615   ConstantRange ZExtMaxBECountRange =
4616       MaxBECountRange.zextOrTrunc(BitWidth * 2 + 1);
4617 
4618   ConstantRange StepSRange = getSignedRange(Step);
4619   ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2 + 1);
4620 
4621   ConstantRange StartURange = getUnsignedRange(Start);
4622   ConstantRange EndURange =
4623       StartURange.add(MaxBECountRange.multiply(StepSRange));
4624 
4625   // Check for unsigned overflow.
4626   ConstantRange ZExtStartURange = StartURange.zextOrTrunc(BitWidth * 2 + 1);
4627   ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2 + 1);
4628   if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4629       ZExtEndURange) {
4630     APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
4631                                EndURange.getUnsignedMin());
4632     APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
4633                                EndURange.getUnsignedMax());
4634     bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
4635     if (!IsFullRange)
4636       Result =
4637           Result.intersectWith(ConstantRange(Min, Max + 1));
4638   }
4639 
4640   ConstantRange StartSRange = getSignedRange(Start);
4641   ConstantRange EndSRange =
4642       StartSRange.add(MaxBECountRange.multiply(StepSRange));
4643 
4644   // Check for signed overflow. This must be done with ConstantRange
4645   // arithmetic because we could be called from within the ScalarEvolution
4646   // overflow checking code.
4647   ConstantRange SExtStartSRange = StartSRange.sextOrTrunc(BitWidth * 2 + 1);
4648   ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2 + 1);
4649   if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4650       SExtEndSRange) {
4651     APInt Min =
4652         APIntOps::smin(StartSRange.getSignedMin(), EndSRange.getSignedMin());
4653     APInt Max =
4654         APIntOps::smax(StartSRange.getSignedMax(), EndSRange.getSignedMax());
4655     bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
4656     if (!IsFullRange)
4657       Result =
4658           Result.intersectWith(ConstantRange(Min, Max + 1));
4659   }
4660 
4661   return Result;
4662 }
4663 
getRangeViaFactoring(const SCEV * Start,const SCEV * Step,const SCEV * MaxBECount,unsigned BitWidth)4664 ConstantRange ScalarEvolution::getRangeViaFactoring(const SCEV *Start,
4665                                                     const SCEV *Step,
4666                                                     const SCEV *MaxBECount,
4667                                                     unsigned BitWidth) {
4668   //    RangeOf({C?A:B,+,C?P:Q}) == RangeOf(C?{A,+,P}:{B,+,Q})
4669   // == RangeOf({A,+,P}) union RangeOf({B,+,Q})
4670 
4671   struct SelectPattern {
4672     Value *Condition = nullptr;
4673     APInt TrueValue;
4674     APInt FalseValue;
4675 
4676     explicit SelectPattern(ScalarEvolution &SE, unsigned BitWidth,
4677                            const SCEV *S) {
4678       Optional<unsigned> CastOp;
4679       APInt Offset(BitWidth, 0);
4680 
4681       assert(SE.getTypeSizeInBits(S->getType()) == BitWidth &&
4682              "Should be!");
4683 
4684       // Peel off a constant offset:
4685       if (auto *SA = dyn_cast<SCEVAddExpr>(S)) {
4686         // In the future we could consider being smarter here and handle
4687         // {Start+Step,+,Step} too.
4688         if (SA->getNumOperands() != 2 || !isa<SCEVConstant>(SA->getOperand(0)))
4689           return;
4690 
4691         Offset = cast<SCEVConstant>(SA->getOperand(0))->getAPInt();
4692         S = SA->getOperand(1);
4693       }
4694 
4695       // Peel off a cast operation
4696       if (auto *SCast = dyn_cast<SCEVCastExpr>(S)) {
4697         CastOp = SCast->getSCEVType();
4698         S = SCast->getOperand();
4699       }
4700 
4701       using namespace llvm::PatternMatch;
4702 
4703       auto *SU = dyn_cast<SCEVUnknown>(S);
4704       const APInt *TrueVal, *FalseVal;
4705       if (!SU ||
4706           !match(SU->getValue(), m_Select(m_Value(Condition), m_APInt(TrueVal),
4707                                           m_APInt(FalseVal)))) {
4708         Condition = nullptr;
4709         return;
4710       }
4711 
4712       TrueValue = *TrueVal;
4713       FalseValue = *FalseVal;
4714 
4715       // Re-apply the cast we peeled off earlier
4716       if (CastOp.hasValue())
4717         switch (*CastOp) {
4718         default:
4719           llvm_unreachable("Unknown SCEV cast type!");
4720 
4721         case scTruncate:
4722           TrueValue = TrueValue.trunc(BitWidth);
4723           FalseValue = FalseValue.trunc(BitWidth);
4724           break;
4725         case scZeroExtend:
4726           TrueValue = TrueValue.zext(BitWidth);
4727           FalseValue = FalseValue.zext(BitWidth);
4728           break;
4729         case scSignExtend:
4730           TrueValue = TrueValue.sext(BitWidth);
4731           FalseValue = FalseValue.sext(BitWidth);
4732           break;
4733         }
4734 
4735       // Re-apply the constant offset we peeled off earlier
4736       TrueValue += Offset;
4737       FalseValue += Offset;
4738     }
4739 
4740     bool isRecognized() { return Condition != nullptr; }
4741   };
4742 
4743   SelectPattern StartPattern(*this, BitWidth, Start);
4744   if (!StartPattern.isRecognized())
4745     return ConstantRange(BitWidth, /* isFullSet = */ true);
4746 
4747   SelectPattern StepPattern(*this, BitWidth, Step);
4748   if (!StepPattern.isRecognized())
4749     return ConstantRange(BitWidth, /* isFullSet = */ true);
4750 
4751   if (StartPattern.Condition != StepPattern.Condition) {
4752     // We don't handle this case today; but we could, by considering four
4753     // possibilities below instead of two. I'm not sure if there are cases where
4754     // that will help over what getRange already does, though.
4755     return ConstantRange(BitWidth, /* isFullSet = */ true);
4756   }
4757 
4758   // NB! Calling ScalarEvolution::getConstant is fine, but we should not try to
4759   // construct arbitrary general SCEV expressions here.  This function is called
4760   // from deep in the call stack, and calling getSCEV (on a sext instruction,
4761   // say) can end up caching a suboptimal value.
4762 
4763   // FIXME: without the explicit `this` receiver below, MSVC errors out with
4764   // C2352 and C2512 (otherwise it isn't needed).
4765 
4766   const SCEV *TrueStart = this->getConstant(StartPattern.TrueValue);
4767   const SCEV *TrueStep = this->getConstant(StepPattern.TrueValue);
4768   const SCEV *FalseStart = this->getConstant(StartPattern.FalseValue);
4769   const SCEV *FalseStep = this->getConstant(StepPattern.FalseValue);
4770 
4771   ConstantRange TrueRange =
4772       this->getRangeForAffineAR(TrueStart, TrueStep, MaxBECount, BitWidth);
4773   ConstantRange FalseRange =
4774       this->getRangeForAffineAR(FalseStart, FalseStep, MaxBECount, BitWidth);
4775 
4776   return TrueRange.unionWith(FalseRange);
4777 }
4778 
getNoWrapFlagsFromUB(const Value * V)4779 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
4780   if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
4781   const BinaryOperator *BinOp = cast<BinaryOperator>(V);
4782 
4783   // Return early if there are no flags to propagate to the SCEV.
4784   SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4785   if (BinOp->hasNoUnsignedWrap())
4786     Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
4787   if (BinOp->hasNoSignedWrap())
4788     Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
4789   if (Flags == SCEV::FlagAnyWrap)
4790     return SCEV::FlagAnyWrap;
4791 
4792   return isSCEVExprNeverPoison(BinOp) ? Flags : SCEV::FlagAnyWrap;
4793 }
4794 
isSCEVExprNeverPoison(const Instruction * I)4795 bool ScalarEvolution::isSCEVExprNeverPoison(const Instruction *I) {
4796   // Here we check that I is in the header of the innermost loop containing I,
4797   // since we only deal with instructions in the loop header. The actual loop we
4798   // need to check later will come from an add recurrence, but getting that
4799   // requires computing the SCEV of the operands, which can be expensive. This
4800   // check we can do cheaply to rule out some cases early.
4801   Loop *InnermostContainingLoop = LI.getLoopFor(I->getParent());
4802   if (InnermostContainingLoop == nullptr ||
4803       InnermostContainingLoop->getHeader() != I->getParent())
4804     return false;
4805 
4806   // Only proceed if we can prove that I does not yield poison.
4807   if (!isKnownNotFullPoison(I)) return false;
4808 
4809   // At this point we know that if I is executed, then it does not wrap
4810   // according to at least one of NSW or NUW. If I is not executed, then we do
4811   // not know if the calculation that I represents would wrap. Multiple
4812   // instructions can map to the same SCEV. If we apply NSW or NUW from I to
4813   // the SCEV, we must guarantee no wrapping for that SCEV also when it is
4814   // derived from other instructions that map to the same SCEV. We cannot make
4815   // that guarantee for cases where I is not executed. So we need to find the
4816   // loop that I is considered in relation to and prove that I is executed for
4817   // every iteration of that loop. That implies that the value that I
4818   // calculates does not wrap anywhere in the loop, so then we can apply the
4819   // flags to the SCEV.
4820   //
4821   // We check isLoopInvariant to disambiguate in case we are adding recurrences
4822   // from different loops, so that we know which loop to prove that I is
4823   // executed in.
4824   for (unsigned OpIndex = 0; OpIndex < I->getNumOperands(); ++OpIndex) {
4825     const SCEV *Op = getSCEV(I->getOperand(OpIndex));
4826     if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
4827       bool AllOtherOpsLoopInvariant = true;
4828       for (unsigned OtherOpIndex = 0; OtherOpIndex < I->getNumOperands();
4829            ++OtherOpIndex) {
4830         if (OtherOpIndex != OpIndex) {
4831           const SCEV *OtherOp = getSCEV(I->getOperand(OtherOpIndex));
4832           if (!isLoopInvariant(OtherOp, AddRec->getLoop())) {
4833             AllOtherOpsLoopInvariant = false;
4834             break;
4835           }
4836         }
4837       }
4838       if (AllOtherOpsLoopInvariant &&
4839           isGuaranteedToExecuteForEveryIteration(I, AddRec->getLoop()))
4840         return true;
4841     }
4842   }
4843   return false;
4844 }
4845 
isAddRecNeverPoison(const Instruction * I,const Loop * L)4846 bool ScalarEvolution::isAddRecNeverPoison(const Instruction *I, const Loop *L) {
4847   // If we know that \c I can never be poison period, then that's enough.
4848   if (isSCEVExprNeverPoison(I))
4849     return true;
4850 
4851   // For an add recurrence specifically, we assume that infinite loops without
4852   // side effects are undefined behavior, and then reason as follows:
4853   //
4854   // If the add recurrence is poison in any iteration, it is poison on all
4855   // future iterations (since incrementing poison yields poison). If the result
4856   // of the add recurrence is fed into the loop latch condition and the loop
4857   // does not contain any throws or exiting blocks other than the latch, we now
4858   // have the ability to "choose" whether the backedge is taken or not (by
4859   // choosing a sufficiently evil value for the poison feeding into the branch)
4860   // for every iteration including and after the one in which \p I first became
4861   // poison.  There are two possibilities (let's call the iteration in which \p
4862   // I first became poison as K):
4863   //
4864   //  1. In the set of iterations including and after K, the loop body executes
4865   //     no side effects.  In this case executing the backege an infinte number
4866   //     of times will yield undefined behavior.
4867   //
4868   //  2. In the set of iterations including and after K, the loop body executes
4869   //     at least one side effect.  In this case, that specific instance of side
4870   //     effect is control dependent on poison, which also yields undefined
4871   //     behavior.
4872 
4873   auto *ExitingBB = L->getExitingBlock();
4874   auto *LatchBB = L->getLoopLatch();
4875   if (!ExitingBB || !LatchBB || ExitingBB != LatchBB)
4876     return false;
4877 
4878   SmallPtrSet<const Instruction *, 16> Pushed;
4879   SmallVector<const Instruction *, 8> PoisonStack;
4880 
4881   // We start by assuming \c I, the post-inc add recurrence, is poison.  Only
4882   // things that are known to be fully poison under that assumption go on the
4883   // PoisonStack.
4884   Pushed.insert(I);
4885   PoisonStack.push_back(I);
4886 
4887   bool LatchControlDependentOnPoison = false;
4888   while (!PoisonStack.empty() && !LatchControlDependentOnPoison) {
4889     const Instruction *Poison = PoisonStack.pop_back_val();
4890 
4891     for (auto *PoisonUser : Poison->users()) {
4892       if (propagatesFullPoison(cast<Instruction>(PoisonUser))) {
4893         if (Pushed.insert(cast<Instruction>(PoisonUser)).second)
4894           PoisonStack.push_back(cast<Instruction>(PoisonUser));
4895       } else if (auto *BI = dyn_cast<BranchInst>(PoisonUser)) {
4896         assert(BI->isConditional() && "Only possibility!");
4897         if (BI->getParent() == LatchBB) {
4898           LatchControlDependentOnPoison = true;
4899           break;
4900         }
4901       }
4902     }
4903   }
4904 
4905   return LatchControlDependentOnPoison && loopHasNoAbnormalExits(L);
4906 }
4907 
loopHasNoAbnormalExits(const Loop * L)4908 bool ScalarEvolution::loopHasNoAbnormalExits(const Loop *L) {
4909   auto Itr = LoopHasNoAbnormalExits.find(L);
4910   if (Itr == LoopHasNoAbnormalExits.end()) {
4911     auto NoAbnormalExitInBB = [&](BasicBlock *BB) {
4912       return all_of(*BB, [](Instruction &I) {
4913         return isGuaranteedToTransferExecutionToSuccessor(&I);
4914       });
4915     };
4916 
4917     auto InsertPair = LoopHasNoAbnormalExits.insert(
4918         {L, all_of(L->getBlocks(), NoAbnormalExitInBB)});
4919     assert(InsertPair.second && "We just checked!");
4920     Itr = InsertPair.first;
4921   }
4922 
4923   return Itr->second;
4924 }
4925 
createSCEV(Value * V)4926 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4927   if (!isSCEVable(V->getType()))
4928     return getUnknown(V);
4929 
4930   if (Instruction *I = dyn_cast<Instruction>(V)) {
4931     // Don't attempt to analyze instructions in blocks that aren't
4932     // reachable. Such instructions don't matter, and they aren't required
4933     // to obey basic rules for definitions dominating uses which this
4934     // analysis depends on.
4935     if (!DT.isReachableFromEntry(I->getParent()))
4936       return getUnknown(V);
4937   } else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4938     return getConstant(CI);
4939   else if (isa<ConstantPointerNull>(V))
4940     return getZero(V->getType());
4941   else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4942     return GA->isInterposable() ? getUnknown(V) : getSCEV(GA->getAliasee());
4943   else if (!isa<ConstantExpr>(V))
4944     return getUnknown(V);
4945 
4946   Operator *U = cast<Operator>(V);
4947   if (auto BO = MatchBinaryOp(U, DT)) {
4948     switch (BO->Opcode) {
4949     case Instruction::Add: {
4950       // The simple thing to do would be to just call getSCEV on both operands
4951       // and call getAddExpr with the result. However if we're looking at a
4952       // bunch of things all added together, this can be quite inefficient,
4953       // because it leads to N-1 getAddExpr calls for N ultimate operands.
4954       // Instead, gather up all the operands and make a single getAddExpr call.
4955       // LLVM IR canonical form means we need only traverse the left operands.
4956       SmallVector<const SCEV *, 4> AddOps;
4957       do {
4958         if (BO->Op) {
4959           if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
4960             AddOps.push_back(OpSCEV);
4961             break;
4962           }
4963 
4964           // If a NUW or NSW flag can be applied to the SCEV for this
4965           // addition, then compute the SCEV for this addition by itself
4966           // with a separate call to getAddExpr. We need to do that
4967           // instead of pushing the operands of the addition onto AddOps,
4968           // since the flags are only known to apply to this particular
4969           // addition - they may not apply to other additions that can be
4970           // formed with operands from AddOps.
4971           const SCEV *RHS = getSCEV(BO->RHS);
4972           SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
4973           if (Flags != SCEV::FlagAnyWrap) {
4974             const SCEV *LHS = getSCEV(BO->LHS);
4975             if (BO->Opcode == Instruction::Sub)
4976               AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
4977             else
4978               AddOps.push_back(getAddExpr(LHS, RHS, Flags));
4979             break;
4980           }
4981         }
4982 
4983         if (BO->Opcode == Instruction::Sub)
4984           AddOps.push_back(getNegativeSCEV(getSCEV(BO->RHS)));
4985         else
4986           AddOps.push_back(getSCEV(BO->RHS));
4987 
4988         auto NewBO = MatchBinaryOp(BO->LHS, DT);
4989         if (!NewBO || (NewBO->Opcode != Instruction::Add &&
4990                        NewBO->Opcode != Instruction::Sub)) {
4991           AddOps.push_back(getSCEV(BO->LHS));
4992           break;
4993         }
4994         BO = NewBO;
4995       } while (true);
4996 
4997       return getAddExpr(AddOps);
4998     }
4999 
5000     case Instruction::Mul: {
5001       SmallVector<const SCEV *, 4> MulOps;
5002       do {
5003         if (BO->Op) {
5004           if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
5005             MulOps.push_back(OpSCEV);
5006             break;
5007           }
5008 
5009           SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
5010           if (Flags != SCEV::FlagAnyWrap) {
5011             MulOps.push_back(
5012                 getMulExpr(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags));
5013             break;
5014           }
5015         }
5016 
5017         MulOps.push_back(getSCEV(BO->RHS));
5018         auto NewBO = MatchBinaryOp(BO->LHS, DT);
5019         if (!NewBO || NewBO->Opcode != Instruction::Mul) {
5020           MulOps.push_back(getSCEV(BO->LHS));
5021           break;
5022         }
5023         BO = NewBO;
5024       } while (true);
5025 
5026       return getMulExpr(MulOps);
5027     }
5028     case Instruction::UDiv:
5029       return getUDivExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
5030     case Instruction::Sub: {
5031       SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
5032       if (BO->Op)
5033         Flags = getNoWrapFlagsFromUB(BO->Op);
5034       return getMinusSCEV(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags);
5035     }
5036     case Instruction::And:
5037       // For an expression like x&255 that merely masks off the high bits,
5038       // use zext(trunc(x)) as the SCEV expression.
5039       if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
5040         if (CI->isNullValue())
5041           return getSCEV(BO->RHS);
5042         if (CI->isAllOnesValue())
5043           return getSCEV(BO->LHS);
5044         const APInt &A = CI->getValue();
5045 
5046         // Instcombine's ShrinkDemandedConstant may strip bits out of
5047         // constants, obscuring what would otherwise be a low-bits mask.
5048         // Use computeKnownBits to compute what ShrinkDemandedConstant
5049         // knew about to reconstruct a low-bits mask value.
5050         unsigned LZ = A.countLeadingZeros();
5051         unsigned TZ = A.countTrailingZeros();
5052         unsigned BitWidth = A.getBitWidth();
5053         APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
5054         computeKnownBits(BO->LHS, KnownZero, KnownOne, getDataLayout(),
5055                          0, &AC, nullptr, &DT);
5056 
5057         APInt EffectiveMask =
5058             APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
5059         if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
5060           const SCEV *MulCount = getConstant(ConstantInt::get(
5061               getContext(), APInt::getOneBitSet(BitWidth, TZ)));
5062           return getMulExpr(
5063               getZeroExtendExpr(
5064                   getTruncateExpr(
5065                       getUDivExactExpr(getSCEV(BO->LHS), MulCount),
5066                       IntegerType::get(getContext(), BitWidth - LZ - TZ)),
5067                   BO->LHS->getType()),
5068               MulCount);
5069         }
5070       }
5071       break;
5072 
5073     case Instruction::Or:
5074       // If the RHS of the Or is a constant, we may have something like:
5075       // X*4+1 which got turned into X*4|1.  Handle this as an Add so loop
5076       // optimizations will transparently handle this case.
5077       //
5078       // In order for this transformation to be safe, the LHS must be of the
5079       // form X*(2^n) and the Or constant must be less than 2^n.
5080       if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
5081         const SCEV *LHS = getSCEV(BO->LHS);
5082         const APInt &CIVal = CI->getValue();
5083         if (GetMinTrailingZeros(LHS) >=
5084             (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
5085           // Build a plain add SCEV.
5086           const SCEV *S = getAddExpr(LHS, getSCEV(CI));
5087           // If the LHS of the add was an addrec and it has no-wrap flags,
5088           // transfer the no-wrap flags, since an or won't introduce a wrap.
5089           if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
5090             const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
5091             const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
5092                 OldAR->getNoWrapFlags());
5093           }
5094           return S;
5095         }
5096       }
5097       break;
5098 
5099     case Instruction::Xor:
5100       if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
5101         // If the RHS of xor is -1, then this is a not operation.
5102         if (CI->isAllOnesValue())
5103           return getNotSCEV(getSCEV(BO->LHS));
5104 
5105         // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
5106         // This is a variant of the check for xor with -1, and it handles
5107         // the case where instcombine has trimmed non-demanded bits out
5108         // of an xor with -1.
5109         if (auto *LBO = dyn_cast<BinaryOperator>(BO->LHS))
5110           if (ConstantInt *LCI = dyn_cast<ConstantInt>(LBO->getOperand(1)))
5111             if (LBO->getOpcode() == Instruction::And &&
5112                 LCI->getValue() == CI->getValue())
5113               if (const SCEVZeroExtendExpr *Z =
5114                       dyn_cast<SCEVZeroExtendExpr>(getSCEV(BO->LHS))) {
5115                 Type *UTy = BO->LHS->getType();
5116                 const SCEV *Z0 = Z->getOperand();
5117                 Type *Z0Ty = Z0->getType();
5118                 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
5119 
5120                 // If C is a low-bits mask, the zero extend is serving to
5121                 // mask off the high bits. Complement the operand and
5122                 // re-apply the zext.
5123                 if (APIntOps::isMask(Z0TySize, CI->getValue()))
5124                   return getZeroExtendExpr(getNotSCEV(Z0), UTy);
5125 
5126                 // If C is a single bit, it may be in the sign-bit position
5127                 // before the zero-extend. In this case, represent the xor
5128                 // using an add, which is equivalent, and re-apply the zext.
5129                 APInt Trunc = CI->getValue().trunc(Z0TySize);
5130                 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
5131                     Trunc.isSignBit())
5132                   return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
5133                                            UTy);
5134               }
5135       }
5136       break;
5137 
5138   case Instruction::Shl:
5139     // Turn shift left of a constant amount into a multiply.
5140     if (ConstantInt *SA = dyn_cast<ConstantInt>(BO->RHS)) {
5141       uint32_t BitWidth = cast<IntegerType>(SA->getType())->getBitWidth();
5142 
5143       // If the shift count is not less than the bitwidth, the result of
5144       // the shift is undefined. Don't try to analyze it, because the
5145       // resolution chosen here may differ from the resolution chosen in
5146       // other parts of the compiler.
5147       if (SA->getValue().uge(BitWidth))
5148         break;
5149 
5150       // It is currently not resolved how to interpret NSW for left
5151       // shift by BitWidth - 1, so we avoid applying flags in that
5152       // case. Remove this check (or this comment) once the situation
5153       // is resolved. See
5154       // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
5155       // and http://reviews.llvm.org/D8890 .
5156       auto Flags = SCEV::FlagAnyWrap;
5157       if (BO->Op && SA->getValue().ult(BitWidth - 1))
5158         Flags = getNoWrapFlagsFromUB(BO->Op);
5159 
5160       Constant *X = ConstantInt::get(getContext(),
5161         APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
5162       return getMulExpr(getSCEV(BO->LHS), getSCEV(X), Flags);
5163     }
5164     break;
5165 
5166     case Instruction::AShr:
5167       // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
5168       if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS))
5169         if (Operator *L = dyn_cast<Operator>(BO->LHS))
5170           if (L->getOpcode() == Instruction::Shl &&
5171               L->getOperand(1) == BO->RHS) {
5172             uint64_t BitWidth = getTypeSizeInBits(BO->LHS->getType());
5173 
5174             // If the shift count is not less than the bitwidth, the result of
5175             // the shift is undefined. Don't try to analyze it, because the
5176             // resolution chosen here may differ from the resolution chosen in
5177             // other parts of the compiler.
5178             if (CI->getValue().uge(BitWidth))
5179               break;
5180 
5181             uint64_t Amt = BitWidth - CI->getZExtValue();
5182             if (Amt == BitWidth)
5183               return getSCEV(L->getOperand(0)); // shift by zero --> noop
5184             return getSignExtendExpr(
5185                 getTruncateExpr(getSCEV(L->getOperand(0)),
5186                                 IntegerType::get(getContext(), Amt)),
5187                 BO->LHS->getType());
5188           }
5189       break;
5190     }
5191   }
5192 
5193   switch (U->getOpcode()) {
5194   case Instruction::Trunc:
5195     return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
5196 
5197   case Instruction::ZExt:
5198     return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
5199 
5200   case Instruction::SExt:
5201     return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
5202 
5203   case Instruction::BitCast:
5204     // BitCasts are no-op casts so we just eliminate the cast.
5205     if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
5206       return getSCEV(U->getOperand(0));
5207     break;
5208 
5209   // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
5210   // lead to pointer expressions which cannot safely be expanded to GEPs,
5211   // because ScalarEvolution doesn't respect the GEP aliasing rules when
5212   // simplifying integer expressions.
5213 
5214   case Instruction::GetElementPtr:
5215     return createNodeForGEP(cast<GEPOperator>(U));
5216 
5217   case Instruction::PHI:
5218     return createNodeForPHI(cast<PHINode>(U));
5219 
5220   case Instruction::Select:
5221     // U can also be a select constant expr, which let fall through.  Since
5222     // createNodeForSelect only works for a condition that is an `ICmpInst`, and
5223     // constant expressions cannot have instructions as operands, we'd have
5224     // returned getUnknown for a select constant expressions anyway.
5225     if (isa<Instruction>(U))
5226       return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
5227                                       U->getOperand(1), U->getOperand(2));
5228     break;
5229 
5230   case Instruction::Call:
5231   case Instruction::Invoke:
5232     if (Value *RV = CallSite(U).getReturnedArgOperand())
5233       return getSCEV(RV);
5234     break;
5235   }
5236 
5237   return getUnknown(V);
5238 }
5239 
5240 
5241 
5242 //===----------------------------------------------------------------------===//
5243 //                   Iteration Count Computation Code
5244 //
5245 
getSmallConstantTripCount(Loop * L)5246 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
5247   if (BasicBlock *ExitingBB = L->getExitingBlock())
5248     return getSmallConstantTripCount(L, ExitingBB);
5249 
5250   // No trip count information for multiple exits.
5251   return 0;
5252 }
5253 
getSmallConstantTripCount(Loop * L,BasicBlock * ExitingBlock)5254 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
5255                                                     BasicBlock *ExitingBlock) {
5256   assert(ExitingBlock && "Must pass a non-null exiting block!");
5257   assert(L->isLoopExiting(ExitingBlock) &&
5258          "Exiting block must actually branch out of the loop!");
5259   const SCEVConstant *ExitCount =
5260       dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
5261   if (!ExitCount)
5262     return 0;
5263 
5264   ConstantInt *ExitConst = ExitCount->getValue();
5265 
5266   // Guard against huge trip counts.
5267   if (ExitConst->getValue().getActiveBits() > 32)
5268     return 0;
5269 
5270   // In case of integer overflow, this returns 0, which is correct.
5271   return ((unsigned)ExitConst->getZExtValue()) + 1;
5272 }
5273 
getSmallConstantTripMultiple(Loop * L)5274 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
5275   if (BasicBlock *ExitingBB = L->getExitingBlock())
5276     return getSmallConstantTripMultiple(L, ExitingBB);
5277 
5278   // No trip multiple information for multiple exits.
5279   return 0;
5280 }
5281 
5282 /// Returns the largest constant divisor of the trip count of this loop as a
5283 /// normal unsigned value, if possible. This means that the actual trip count is
5284 /// always a multiple of the returned value (don't forget the trip count could
5285 /// very well be zero as well!).
5286 ///
5287 /// Returns 1 if the trip count is unknown or not guaranteed to be the
5288 /// multiple of a constant (which is also the case if the trip count is simply
5289 /// constant, use getSmallConstantTripCount for that case), Will also return 1
5290 /// if the trip count is very large (>= 2^32).
5291 ///
5292 /// As explained in the comments for getSmallConstantTripCount, this assumes
5293 /// that control exits the loop via ExitingBlock.
5294 unsigned
getSmallConstantTripMultiple(Loop * L,BasicBlock * ExitingBlock)5295 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
5296                                               BasicBlock *ExitingBlock) {
5297   assert(ExitingBlock && "Must pass a non-null exiting block!");
5298   assert(L->isLoopExiting(ExitingBlock) &&
5299          "Exiting block must actually branch out of the loop!");
5300   const SCEV *ExitCount = getExitCount(L, ExitingBlock);
5301   if (ExitCount == getCouldNotCompute())
5302     return 1;
5303 
5304   // Get the trip count from the BE count by adding 1.
5305   const SCEV *TCMul = getAddExpr(ExitCount, getOne(ExitCount->getType()));
5306   // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
5307   // to factor simple cases.
5308   if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
5309     TCMul = Mul->getOperand(0);
5310 
5311   const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
5312   if (!MulC)
5313     return 1;
5314 
5315   ConstantInt *Result = MulC->getValue();
5316 
5317   // Guard against huge trip counts (this requires checking
5318   // for zero to handle the case where the trip count == -1 and the
5319   // addition wraps).
5320   if (!Result || Result->getValue().getActiveBits() > 32 ||
5321       Result->getValue().getActiveBits() == 0)
5322     return 1;
5323 
5324   return (unsigned)Result->getZExtValue();
5325 }
5326 
5327 /// Get the expression for the number of loop iterations for which this loop is
5328 /// guaranteed not to exit via ExitingBlock. Otherwise return
5329 /// SCEVCouldNotCompute.
getExitCount(Loop * L,BasicBlock * ExitingBlock)5330 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
5331   return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
5332 }
5333 
5334 const SCEV *
getPredicatedBackedgeTakenCount(const Loop * L,SCEVUnionPredicate & Preds)5335 ScalarEvolution::getPredicatedBackedgeTakenCount(const Loop *L,
5336                                                  SCEVUnionPredicate &Preds) {
5337   return getPredicatedBackedgeTakenInfo(L).getExact(this, &Preds);
5338 }
5339 
getBackedgeTakenCount(const Loop * L)5340 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
5341   return getBackedgeTakenInfo(L).getExact(this);
5342 }
5343 
5344 /// Similar to getBackedgeTakenCount, except return the least SCEV value that is
5345 /// known never to be less than the actual backedge taken count.
getMaxBackedgeTakenCount(const Loop * L)5346 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
5347   return getBackedgeTakenInfo(L).getMax(this);
5348 }
5349 
5350 /// Push PHI nodes in the header of the given loop onto the given Worklist.
5351 static void
PushLoopPHIs(const Loop * L,SmallVectorImpl<Instruction * > & Worklist)5352 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
5353   BasicBlock *Header = L->getHeader();
5354 
5355   // Push all Loop-header PHIs onto the Worklist stack.
5356   for (BasicBlock::iterator I = Header->begin();
5357        PHINode *PN = dyn_cast<PHINode>(I); ++I)
5358     Worklist.push_back(PN);
5359 }
5360 
5361 const ScalarEvolution::BackedgeTakenInfo &
getPredicatedBackedgeTakenInfo(const Loop * L)5362 ScalarEvolution::getPredicatedBackedgeTakenInfo(const Loop *L) {
5363   auto &BTI = getBackedgeTakenInfo(L);
5364   if (BTI.hasFullInfo())
5365     return BTI;
5366 
5367   auto Pair = PredicatedBackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
5368 
5369   if (!Pair.second)
5370     return Pair.first->second;
5371 
5372   BackedgeTakenInfo Result =
5373       computeBackedgeTakenCount(L, /*AllowPredicates=*/true);
5374 
5375   return PredicatedBackedgeTakenCounts.find(L)->second = Result;
5376 }
5377 
5378 const ScalarEvolution::BackedgeTakenInfo &
getBackedgeTakenInfo(const Loop * L)5379 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
5380   // Initially insert an invalid entry for this loop. If the insertion
5381   // succeeds, proceed to actually compute a backedge-taken count and
5382   // update the value. The temporary CouldNotCompute value tells SCEV
5383   // code elsewhere that it shouldn't attempt to request a new
5384   // backedge-taken count, which could result in infinite recursion.
5385   std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
5386       BackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
5387   if (!Pair.second)
5388     return Pair.first->second;
5389 
5390   // computeBackedgeTakenCount may allocate memory for its result. Inserting it
5391   // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
5392   // must be cleared in this scope.
5393   BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
5394 
5395   if (Result.getExact(this) != getCouldNotCompute()) {
5396     assert(isLoopInvariant(Result.getExact(this), L) &&
5397            isLoopInvariant(Result.getMax(this), L) &&
5398            "Computed backedge-taken count isn't loop invariant for loop!");
5399     ++NumTripCountsComputed;
5400   }
5401   else if (Result.getMax(this) == getCouldNotCompute() &&
5402            isa<PHINode>(L->getHeader()->begin())) {
5403     // Only count loops that have phi nodes as not being computable.
5404     ++NumTripCountsNotComputed;
5405   }
5406 
5407   // Now that we know more about the trip count for this loop, forget any
5408   // existing SCEV values for PHI nodes in this loop since they are only
5409   // conservative estimates made without the benefit of trip count
5410   // information. This is similar to the code in forgetLoop, except that
5411   // it handles SCEVUnknown PHI nodes specially.
5412   if (Result.hasAnyInfo()) {
5413     SmallVector<Instruction *, 16> Worklist;
5414     PushLoopPHIs(L, Worklist);
5415 
5416     SmallPtrSet<Instruction *, 8> Visited;
5417     while (!Worklist.empty()) {
5418       Instruction *I = Worklist.pop_back_val();
5419       if (!Visited.insert(I).second)
5420         continue;
5421 
5422       ValueExprMapType::iterator It =
5423         ValueExprMap.find_as(static_cast<Value *>(I));
5424       if (It != ValueExprMap.end()) {
5425         const SCEV *Old = It->second;
5426 
5427         // SCEVUnknown for a PHI either means that it has an unrecognized
5428         // structure, or it's a PHI that's in the progress of being computed
5429         // by createNodeForPHI.  In the former case, additional loop trip
5430         // count information isn't going to change anything. In the later
5431         // case, createNodeForPHI will perform the necessary updates on its
5432         // own when it gets to that point.
5433         if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
5434           forgetMemoizedResults(Old);
5435           ValueExprMap.erase(It);
5436         }
5437         if (PHINode *PN = dyn_cast<PHINode>(I))
5438           ConstantEvolutionLoopExitValue.erase(PN);
5439       }
5440 
5441       PushDefUseChildren(I, Worklist);
5442     }
5443   }
5444 
5445   // Re-lookup the insert position, since the call to
5446   // computeBackedgeTakenCount above could result in a
5447   // recusive call to getBackedgeTakenInfo (on a different
5448   // loop), which would invalidate the iterator computed
5449   // earlier.
5450   return BackedgeTakenCounts.find(L)->second = Result;
5451 }
5452 
forgetLoop(const Loop * L)5453 void ScalarEvolution::forgetLoop(const Loop *L) {
5454   // Drop any stored trip count value.
5455   auto RemoveLoopFromBackedgeMap =
5456       [L](DenseMap<const Loop *, BackedgeTakenInfo> &Map) {
5457         auto BTCPos = Map.find(L);
5458         if (BTCPos != Map.end()) {
5459           BTCPos->second.clear();
5460           Map.erase(BTCPos);
5461         }
5462       };
5463 
5464   RemoveLoopFromBackedgeMap(BackedgeTakenCounts);
5465   RemoveLoopFromBackedgeMap(PredicatedBackedgeTakenCounts);
5466 
5467   // Drop information about expressions based on loop-header PHIs.
5468   SmallVector<Instruction *, 16> Worklist;
5469   PushLoopPHIs(L, Worklist);
5470 
5471   SmallPtrSet<Instruction *, 8> Visited;
5472   while (!Worklist.empty()) {
5473     Instruction *I = Worklist.pop_back_val();
5474     if (!Visited.insert(I).second)
5475       continue;
5476 
5477     ValueExprMapType::iterator It =
5478       ValueExprMap.find_as(static_cast<Value *>(I));
5479     if (It != ValueExprMap.end()) {
5480       forgetMemoizedResults(It->second);
5481       ValueExprMap.erase(It);
5482       if (PHINode *PN = dyn_cast<PHINode>(I))
5483         ConstantEvolutionLoopExitValue.erase(PN);
5484     }
5485 
5486     PushDefUseChildren(I, Worklist);
5487   }
5488 
5489   // Forget all contained loops too, to avoid dangling entries in the
5490   // ValuesAtScopes map.
5491   for (Loop *I : *L)
5492     forgetLoop(I);
5493 
5494   LoopHasNoAbnormalExits.erase(L);
5495 }
5496 
forgetValue(Value * V)5497 void ScalarEvolution::forgetValue(Value *V) {
5498   Instruction *I = dyn_cast<Instruction>(V);
5499   if (!I) return;
5500 
5501   // Drop information about expressions based on loop-header PHIs.
5502   SmallVector<Instruction *, 16> Worklist;
5503   Worklist.push_back(I);
5504 
5505   SmallPtrSet<Instruction *, 8> Visited;
5506   while (!Worklist.empty()) {
5507     I = Worklist.pop_back_val();
5508     if (!Visited.insert(I).second)
5509       continue;
5510 
5511     ValueExprMapType::iterator It =
5512       ValueExprMap.find_as(static_cast<Value *>(I));
5513     if (It != ValueExprMap.end()) {
5514       forgetMemoizedResults(It->second);
5515       ValueExprMap.erase(It);
5516       if (PHINode *PN = dyn_cast<PHINode>(I))
5517         ConstantEvolutionLoopExitValue.erase(PN);
5518     }
5519 
5520     PushDefUseChildren(I, Worklist);
5521   }
5522 }
5523 
5524 /// Get the exact loop backedge taken count considering all loop exits. A
5525 /// computable result can only be returned for loops with a single exit.
5526 /// Returning the minimum taken count among all exits is incorrect because one
5527 /// of the loop's exit limit's may have been skipped. howFarToZero assumes that
5528 /// the limit of each loop test is never skipped. This is a valid assumption as
5529 /// long as the loop exits via that test. For precise results, it is the
5530 /// caller's responsibility to specify the relevant loop exit using
5531 /// getExact(ExitingBlock, SE).
5532 const SCEV *
getExact(ScalarEvolution * SE,SCEVUnionPredicate * Preds) const5533 ScalarEvolution::BackedgeTakenInfo::getExact(
5534     ScalarEvolution *SE, SCEVUnionPredicate *Preds) const {
5535   // If any exits were not computable, the loop is not computable.
5536   if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
5537 
5538   // We need exactly one computable exit.
5539   if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
5540   assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
5541 
5542   const SCEV *BECount = nullptr;
5543   for (auto &ENT : ExitNotTaken) {
5544     assert(ENT.ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
5545 
5546     if (!BECount)
5547       BECount = ENT.ExactNotTaken;
5548     else if (BECount != ENT.ExactNotTaken)
5549       return SE->getCouldNotCompute();
5550     if (Preds && ENT.getPred())
5551       Preds->add(ENT.getPred());
5552 
5553     assert((Preds || ENT.hasAlwaysTruePred()) &&
5554            "Predicate should be always true!");
5555   }
5556 
5557   assert(BECount && "Invalid not taken count for loop exit");
5558   return BECount;
5559 }
5560 
5561 /// Get the exact not taken count for this loop exit.
5562 const SCEV *
getExact(BasicBlock * ExitingBlock,ScalarEvolution * SE) const5563 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
5564                                              ScalarEvolution *SE) const {
5565   for (auto &ENT : ExitNotTaken)
5566     if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePred())
5567       return ENT.ExactNotTaken;
5568 
5569   return SE->getCouldNotCompute();
5570 }
5571 
5572 /// getMax - Get the max backedge taken count for the loop.
5573 const SCEV *
getMax(ScalarEvolution * SE) const5574 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
5575   for (auto &ENT : ExitNotTaken)
5576     if (!ENT.hasAlwaysTruePred())
5577       return SE->getCouldNotCompute();
5578 
5579   return Max ? Max : SE->getCouldNotCompute();
5580 }
5581 
hasOperand(const SCEV * S,ScalarEvolution * SE) const5582 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
5583                                                     ScalarEvolution *SE) const {
5584   if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
5585     return true;
5586 
5587   if (!ExitNotTaken.ExitingBlock)
5588     return false;
5589 
5590   for (auto &ENT : ExitNotTaken)
5591     if (ENT.ExactNotTaken != SE->getCouldNotCompute() &&
5592         SE->hasOperand(ENT.ExactNotTaken, S))
5593       return true;
5594 
5595   return false;
5596 }
5597 
5598 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
5599 /// computable exit into a persistent ExitNotTakenInfo array.
BackedgeTakenInfo(SmallVectorImpl<EdgeInfo> & ExitCounts,bool Complete,const SCEV * MaxCount)5600 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
5601     SmallVectorImpl<EdgeInfo> &ExitCounts, bool Complete, const SCEV *MaxCount)
5602     : Max(MaxCount) {
5603 
5604   if (!Complete)
5605     ExitNotTaken.setIncomplete();
5606 
5607   unsigned NumExits = ExitCounts.size();
5608   if (NumExits == 0) return;
5609 
5610   ExitNotTaken.ExitingBlock = ExitCounts[0].ExitBlock;
5611   ExitNotTaken.ExactNotTaken = ExitCounts[0].Taken;
5612 
5613   // Determine the number of ExitNotTakenExtras structures that we need.
5614   unsigned ExtraInfoSize = 0;
5615   if (NumExits > 1)
5616     ExtraInfoSize = 1 + std::count_if(std::next(ExitCounts.begin()),
5617                                       ExitCounts.end(), [](EdgeInfo &Entry) {
5618                                         return !Entry.Pred.isAlwaysTrue();
5619                                       });
5620   else if (!ExitCounts[0].Pred.isAlwaysTrue())
5621     ExtraInfoSize = 1;
5622 
5623   ExitNotTakenExtras *ENT = nullptr;
5624 
5625   // Allocate the ExitNotTakenExtras structures and initialize the first
5626   // element (ExitNotTaken).
5627   if (ExtraInfoSize > 0) {
5628     ENT = new ExitNotTakenExtras[ExtraInfoSize];
5629     ExitNotTaken.ExtraInfo = &ENT[0];
5630     *ExitNotTaken.getPred() = std::move(ExitCounts[0].Pred);
5631   }
5632 
5633   if (NumExits == 1)
5634     return;
5635 
5636   assert(ENT && "ExitNotTakenExtras is NULL while having more than one exit");
5637 
5638   auto &Exits = ExitNotTaken.ExtraInfo->Exits;
5639 
5640   // Handle the rare case of multiple computable exits.
5641   for (unsigned i = 1, PredPos = 1; i < NumExits; ++i) {
5642     ExitNotTakenExtras *Ptr = nullptr;
5643     if (!ExitCounts[i].Pred.isAlwaysTrue()) {
5644       Ptr = &ENT[PredPos++];
5645       Ptr->Pred = std::move(ExitCounts[i].Pred);
5646     }
5647 
5648     Exits.emplace_back(ExitCounts[i].ExitBlock, ExitCounts[i].Taken, Ptr);
5649   }
5650 }
5651 
5652 /// Invalidate this result and free the ExitNotTakenInfo array.
clear()5653 void ScalarEvolution::BackedgeTakenInfo::clear() {
5654   ExitNotTaken.ExitingBlock = nullptr;
5655   ExitNotTaken.ExactNotTaken = nullptr;
5656   delete[] ExitNotTaken.ExtraInfo;
5657 }
5658 
5659 /// Compute the number of times the backedge of the specified loop will execute.
5660 ScalarEvolution::BackedgeTakenInfo
computeBackedgeTakenCount(const Loop * L,bool AllowPredicates)5661 ScalarEvolution::computeBackedgeTakenCount(const Loop *L,
5662                                            bool AllowPredicates) {
5663   SmallVector<BasicBlock *, 8> ExitingBlocks;
5664   L->getExitingBlocks(ExitingBlocks);
5665 
5666   SmallVector<EdgeInfo, 4> ExitCounts;
5667   bool CouldComputeBECount = true;
5668   BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
5669   const SCEV *MustExitMaxBECount = nullptr;
5670   const SCEV *MayExitMaxBECount = nullptr;
5671 
5672   // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
5673   // and compute maxBECount.
5674   // Do a union of all the predicates here.
5675   for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
5676     BasicBlock *ExitBB = ExitingBlocks[i];
5677     ExitLimit EL = computeExitLimit(L, ExitBB, AllowPredicates);
5678 
5679     assert((AllowPredicates || EL.Pred.isAlwaysTrue()) &&
5680            "Predicated exit limit when predicates are not allowed!");
5681 
5682     // 1. For each exit that can be computed, add an entry to ExitCounts.
5683     // CouldComputeBECount is true only if all exits can be computed.
5684     if (EL.Exact == getCouldNotCompute())
5685       // We couldn't compute an exact value for this exit, so
5686       // we won't be able to compute an exact value for the loop.
5687       CouldComputeBECount = false;
5688     else
5689       ExitCounts.emplace_back(EdgeInfo(ExitBB, EL.Exact, EL.Pred));
5690 
5691     // 2. Derive the loop's MaxBECount from each exit's max number of
5692     // non-exiting iterations. Partition the loop exits into two kinds:
5693     // LoopMustExits and LoopMayExits.
5694     //
5695     // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
5696     // is a LoopMayExit.  If any computable LoopMustExit is found, then
5697     // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
5698     // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
5699     // considered greater than any computable EL.Max.
5700     if (EL.Max != getCouldNotCompute() && Latch &&
5701         DT.dominates(ExitBB, Latch)) {
5702       if (!MustExitMaxBECount)
5703         MustExitMaxBECount = EL.Max;
5704       else {
5705         MustExitMaxBECount =
5706           getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
5707       }
5708     } else if (MayExitMaxBECount != getCouldNotCompute()) {
5709       if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
5710         MayExitMaxBECount = EL.Max;
5711       else {
5712         MayExitMaxBECount =
5713           getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
5714       }
5715     }
5716   }
5717   const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
5718     (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
5719   return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
5720 }
5721 
5722 ScalarEvolution::ExitLimit
computeExitLimit(const Loop * L,BasicBlock * ExitingBlock,bool AllowPredicates)5723 ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
5724                                   bool AllowPredicates) {
5725 
5726   // Okay, we've chosen an exiting block.  See what condition causes us to exit
5727   // at this block and remember the exit block and whether all other targets
5728   // lead to the loop header.
5729   bool MustExecuteLoopHeader = true;
5730   BasicBlock *Exit = nullptr;
5731   for (auto *SBB : successors(ExitingBlock))
5732     if (!L->contains(SBB)) {
5733       if (Exit) // Multiple exit successors.
5734         return getCouldNotCompute();
5735       Exit = SBB;
5736     } else if (SBB != L->getHeader()) {
5737       MustExecuteLoopHeader = false;
5738     }
5739 
5740   // At this point, we know we have a conditional branch that determines whether
5741   // the loop is exited.  However, we don't know if the branch is executed each
5742   // time through the loop.  If not, then the execution count of the branch will
5743   // not be equal to the trip count of the loop.
5744   //
5745   // Currently we check for this by checking to see if the Exit branch goes to
5746   // the loop header.  If so, we know it will always execute the same number of
5747   // times as the loop.  We also handle the case where the exit block *is* the
5748   // loop header.  This is common for un-rotated loops.
5749   //
5750   // If both of those tests fail, walk up the unique predecessor chain to the
5751   // header, stopping if there is an edge that doesn't exit the loop. If the
5752   // header is reached, the execution count of the branch will be equal to the
5753   // trip count of the loop.
5754   //
5755   //  More extensive analysis could be done to handle more cases here.
5756   //
5757   if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
5758     // The simple checks failed, try climbing the unique predecessor chain
5759     // up to the header.
5760     bool Ok = false;
5761     for (BasicBlock *BB = ExitingBlock; BB; ) {
5762       BasicBlock *Pred = BB->getUniquePredecessor();
5763       if (!Pred)
5764         return getCouldNotCompute();
5765       TerminatorInst *PredTerm = Pred->getTerminator();
5766       for (const BasicBlock *PredSucc : PredTerm->successors()) {
5767         if (PredSucc == BB)
5768           continue;
5769         // If the predecessor has a successor that isn't BB and isn't
5770         // outside the loop, assume the worst.
5771         if (L->contains(PredSucc))
5772           return getCouldNotCompute();
5773       }
5774       if (Pred == L->getHeader()) {
5775         Ok = true;
5776         break;
5777       }
5778       BB = Pred;
5779     }
5780     if (!Ok)
5781       return getCouldNotCompute();
5782   }
5783 
5784   bool IsOnlyExit = (L->getExitingBlock() != nullptr);
5785   TerminatorInst *Term = ExitingBlock->getTerminator();
5786   if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
5787     assert(BI->isConditional() && "If unconditional, it can't be in loop!");
5788     // Proceed to the next level to examine the exit condition expression.
5789     return computeExitLimitFromCond(
5790         L, BI->getCondition(), BI->getSuccessor(0), BI->getSuccessor(1),
5791         /*ControlsExit=*/IsOnlyExit, AllowPredicates);
5792   }
5793 
5794   if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
5795     return computeExitLimitFromSingleExitSwitch(L, SI, Exit,
5796                                                 /*ControlsExit=*/IsOnlyExit);
5797 
5798   return getCouldNotCompute();
5799 }
5800 
5801 ScalarEvolution::ExitLimit
computeExitLimitFromCond(const Loop * L,Value * ExitCond,BasicBlock * TBB,BasicBlock * FBB,bool ControlsExit,bool AllowPredicates)5802 ScalarEvolution::computeExitLimitFromCond(const Loop *L,
5803                                           Value *ExitCond,
5804                                           BasicBlock *TBB,
5805                                           BasicBlock *FBB,
5806                                           bool ControlsExit,
5807                                           bool AllowPredicates) {
5808   // Check if the controlling expression for this loop is an And or Or.
5809   if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
5810     if (BO->getOpcode() == Instruction::And) {
5811       // Recurse on the operands of the and.
5812       bool EitherMayExit = L->contains(TBB);
5813       ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5814                                                ControlsExit && !EitherMayExit,
5815                                                AllowPredicates);
5816       ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5817                                                ControlsExit && !EitherMayExit,
5818                                                AllowPredicates);
5819       const SCEV *BECount = getCouldNotCompute();
5820       const SCEV *MaxBECount = getCouldNotCompute();
5821       if (EitherMayExit) {
5822         // Both conditions must be true for the loop to continue executing.
5823         // Choose the less conservative count.
5824         if (EL0.Exact == getCouldNotCompute() ||
5825             EL1.Exact == getCouldNotCompute())
5826           BECount = getCouldNotCompute();
5827         else
5828           BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5829         if (EL0.Max == getCouldNotCompute())
5830           MaxBECount = EL1.Max;
5831         else if (EL1.Max == getCouldNotCompute())
5832           MaxBECount = EL0.Max;
5833         else
5834           MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5835       } else {
5836         // Both conditions must be true at the same time for the loop to exit.
5837         // For now, be conservative.
5838         assert(L->contains(FBB) && "Loop block has no successor in loop!");
5839         if (EL0.Max == EL1.Max)
5840           MaxBECount = EL0.Max;
5841         if (EL0.Exact == EL1.Exact)
5842           BECount = EL0.Exact;
5843       }
5844 
5845       SCEVUnionPredicate NP;
5846       NP.add(&EL0.Pred);
5847       NP.add(&EL1.Pred);
5848       // There are cases (e.g. PR26207) where computeExitLimitFromCond is able
5849       // to be more aggressive when computing BECount than when computing
5850       // MaxBECount.  In these cases it is possible for EL0.Exact and EL1.Exact
5851       // to match, but for EL0.Max and EL1.Max to not.
5852       if (isa<SCEVCouldNotCompute>(MaxBECount) &&
5853           !isa<SCEVCouldNotCompute>(BECount))
5854         MaxBECount = BECount;
5855 
5856       return ExitLimit(BECount, MaxBECount, NP);
5857     }
5858     if (BO->getOpcode() == Instruction::Or) {
5859       // Recurse on the operands of the or.
5860       bool EitherMayExit = L->contains(FBB);
5861       ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5862                                                ControlsExit && !EitherMayExit,
5863                                                AllowPredicates);
5864       ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5865                                                ControlsExit && !EitherMayExit,
5866                                                AllowPredicates);
5867       const SCEV *BECount = getCouldNotCompute();
5868       const SCEV *MaxBECount = getCouldNotCompute();
5869       if (EitherMayExit) {
5870         // Both conditions must be false for the loop to continue executing.
5871         // Choose the less conservative count.
5872         if (EL0.Exact == getCouldNotCompute() ||
5873             EL1.Exact == getCouldNotCompute())
5874           BECount = getCouldNotCompute();
5875         else
5876           BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5877         if (EL0.Max == getCouldNotCompute())
5878           MaxBECount = EL1.Max;
5879         else if (EL1.Max == getCouldNotCompute())
5880           MaxBECount = EL0.Max;
5881         else
5882           MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5883       } else {
5884         // Both conditions must be false at the same time for the loop to exit.
5885         // For now, be conservative.
5886         assert(L->contains(TBB) && "Loop block has no successor in loop!");
5887         if (EL0.Max == EL1.Max)
5888           MaxBECount = EL0.Max;
5889         if (EL0.Exact == EL1.Exact)
5890           BECount = EL0.Exact;
5891       }
5892 
5893       SCEVUnionPredicate NP;
5894       NP.add(&EL0.Pred);
5895       NP.add(&EL1.Pred);
5896       return ExitLimit(BECount, MaxBECount, NP);
5897     }
5898   }
5899 
5900   // With an icmp, it may be feasible to compute an exact backedge-taken count.
5901   // Proceed to the next level to examine the icmp.
5902   if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) {
5903     ExitLimit EL =
5904         computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5905     if (EL.hasFullInfo() || !AllowPredicates)
5906       return EL;
5907 
5908     // Try again, but use SCEV predicates this time.
5909     return computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit,
5910                                     /*AllowPredicates=*/true);
5911   }
5912 
5913   // Check for a constant condition. These are normally stripped out by
5914   // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5915   // preserve the CFG and is temporarily leaving constant conditions
5916   // in place.
5917   if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5918     if (L->contains(FBB) == !CI->getZExtValue())
5919       // The backedge is always taken.
5920       return getCouldNotCompute();
5921     else
5922       // The backedge is never taken.
5923       return getZero(CI->getType());
5924   }
5925 
5926   // If it's not an integer or pointer comparison then compute it the hard way.
5927   return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5928 }
5929 
5930 ScalarEvolution::ExitLimit
computeExitLimitFromICmp(const Loop * L,ICmpInst * ExitCond,BasicBlock * TBB,BasicBlock * FBB,bool ControlsExit,bool AllowPredicates)5931 ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
5932                                           ICmpInst *ExitCond,
5933                                           BasicBlock *TBB,
5934                                           BasicBlock *FBB,
5935                                           bool ControlsExit,
5936                                           bool AllowPredicates) {
5937 
5938   // If the condition was exit on true, convert the condition to exit on false
5939   ICmpInst::Predicate Cond;
5940   if (!L->contains(FBB))
5941     Cond = ExitCond->getPredicate();
5942   else
5943     Cond = ExitCond->getInversePredicate();
5944 
5945   // Handle common loops like: for (X = "string"; *X; ++X)
5946   if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5947     if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5948       ExitLimit ItCnt =
5949         computeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5950       if (ItCnt.hasAnyInfo())
5951         return ItCnt;
5952     }
5953 
5954   const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5955   const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5956 
5957   // Try to evaluate any dependencies out of the loop.
5958   LHS = getSCEVAtScope(LHS, L);
5959   RHS = getSCEVAtScope(RHS, L);
5960 
5961   // At this point, we would like to compute how many iterations of the
5962   // loop the predicate will return true for these inputs.
5963   if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5964     // If there is a loop-invariant, force it into the RHS.
5965     std::swap(LHS, RHS);
5966     Cond = ICmpInst::getSwappedPredicate(Cond);
5967   }
5968 
5969   // Simplify the operands before analyzing them.
5970   (void)SimplifyICmpOperands(Cond, LHS, RHS);
5971 
5972   // If we have a comparison of a chrec against a constant, try to use value
5973   // ranges to answer this query.
5974   if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5975     if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5976       if (AddRec->getLoop() == L) {
5977         // Form the constant range.
5978         ConstantRange CompRange(
5979             ICmpInst::makeConstantRange(Cond, RHSC->getAPInt()));
5980 
5981         const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5982         if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5983       }
5984 
5985   switch (Cond) {
5986   case ICmpInst::ICMP_NE: {                     // while (X != Y)
5987     // Convert to: while (X-Y != 0)
5988     ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit,
5989                                 AllowPredicates);
5990     if (EL.hasAnyInfo()) return EL;
5991     break;
5992   }
5993   case ICmpInst::ICMP_EQ: {                     // while (X == Y)
5994     // Convert to: while (X-Y == 0)
5995     ExitLimit EL = howFarToNonZero(getMinusSCEV(LHS, RHS), L);
5996     if (EL.hasAnyInfo()) return EL;
5997     break;
5998   }
5999   case ICmpInst::ICMP_SLT:
6000   case ICmpInst::ICMP_ULT: {                    // while (X < Y)
6001     bool IsSigned = Cond == ICmpInst::ICMP_SLT;
6002     ExitLimit EL = howManyLessThans(LHS, RHS, L, IsSigned, ControlsExit,
6003                                     AllowPredicates);
6004     if (EL.hasAnyInfo()) return EL;
6005     break;
6006   }
6007   case ICmpInst::ICMP_SGT:
6008   case ICmpInst::ICMP_UGT: {                    // while (X > Y)
6009     bool IsSigned = Cond == ICmpInst::ICMP_SGT;
6010     ExitLimit EL =
6011         howManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit,
6012                             AllowPredicates);
6013     if (EL.hasAnyInfo()) return EL;
6014     break;
6015   }
6016   default:
6017     break;
6018   }
6019 
6020   auto *ExhaustiveCount =
6021       computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
6022 
6023   if (!isa<SCEVCouldNotCompute>(ExhaustiveCount))
6024     return ExhaustiveCount;
6025 
6026   return computeShiftCompareExitLimit(ExitCond->getOperand(0),
6027                                       ExitCond->getOperand(1), L, Cond);
6028 }
6029 
6030 ScalarEvolution::ExitLimit
computeExitLimitFromSingleExitSwitch(const Loop * L,SwitchInst * Switch,BasicBlock * ExitingBlock,bool ControlsExit)6031 ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
6032                                                       SwitchInst *Switch,
6033                                                       BasicBlock *ExitingBlock,
6034                                                       bool ControlsExit) {
6035   assert(!L->contains(ExitingBlock) && "Not an exiting block!");
6036 
6037   // Give up if the exit is the default dest of a switch.
6038   if (Switch->getDefaultDest() == ExitingBlock)
6039     return getCouldNotCompute();
6040 
6041   assert(L->contains(Switch->getDefaultDest()) &&
6042          "Default case must not exit the loop!");
6043   const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
6044   const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
6045 
6046   // while (X != Y) --> while (X-Y != 0)
6047   ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
6048   if (EL.hasAnyInfo())
6049     return EL;
6050 
6051   return getCouldNotCompute();
6052 }
6053 
6054 static ConstantInt *
EvaluateConstantChrecAtConstant(const SCEVAddRecExpr * AddRec,ConstantInt * C,ScalarEvolution & SE)6055 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
6056                                 ScalarEvolution &SE) {
6057   const SCEV *InVal = SE.getConstant(C);
6058   const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
6059   assert(isa<SCEVConstant>(Val) &&
6060          "Evaluation of SCEV at constant didn't fold correctly?");
6061   return cast<SCEVConstant>(Val)->getValue();
6062 }
6063 
6064 /// Given an exit condition of 'icmp op load X, cst', try to see if we can
6065 /// compute the backedge execution count.
6066 ScalarEvolution::ExitLimit
computeLoadConstantCompareExitLimit(LoadInst * LI,Constant * RHS,const Loop * L,ICmpInst::Predicate predicate)6067 ScalarEvolution::computeLoadConstantCompareExitLimit(
6068   LoadInst *LI,
6069   Constant *RHS,
6070   const Loop *L,
6071   ICmpInst::Predicate predicate) {
6072 
6073   if (LI->isVolatile()) return getCouldNotCompute();
6074 
6075   // Check to see if the loaded pointer is a getelementptr of a global.
6076   // TODO: Use SCEV instead of manually grubbing with GEPs.
6077   GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
6078   if (!GEP) return getCouldNotCompute();
6079 
6080   // Make sure that it is really a constant global we are gepping, with an
6081   // initializer, and make sure the first IDX is really 0.
6082   GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
6083   if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
6084       GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
6085       !cast<Constant>(GEP->getOperand(1))->isNullValue())
6086     return getCouldNotCompute();
6087 
6088   // Okay, we allow one non-constant index into the GEP instruction.
6089   Value *VarIdx = nullptr;
6090   std::vector<Constant*> Indexes;
6091   unsigned VarIdxNum = 0;
6092   for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
6093     if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
6094       Indexes.push_back(CI);
6095     } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
6096       if (VarIdx) return getCouldNotCompute();  // Multiple non-constant idx's.
6097       VarIdx = GEP->getOperand(i);
6098       VarIdxNum = i-2;
6099       Indexes.push_back(nullptr);
6100     }
6101 
6102   // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
6103   if (!VarIdx)
6104     return getCouldNotCompute();
6105 
6106   // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
6107   // Check to see if X is a loop variant variable value now.
6108   const SCEV *Idx = getSCEV(VarIdx);
6109   Idx = getSCEVAtScope(Idx, L);
6110 
6111   // We can only recognize very limited forms of loop index expressions, in
6112   // particular, only affine AddRec's like {C1,+,C2}.
6113   const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
6114   if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
6115       !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
6116       !isa<SCEVConstant>(IdxExpr->getOperand(1)))
6117     return getCouldNotCompute();
6118 
6119   unsigned MaxSteps = MaxBruteForceIterations;
6120   for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
6121     ConstantInt *ItCst = ConstantInt::get(
6122                            cast<IntegerType>(IdxExpr->getType()), IterationNum);
6123     ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
6124 
6125     // Form the GEP offset.
6126     Indexes[VarIdxNum] = Val;
6127 
6128     Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
6129                                                          Indexes);
6130     if (!Result) break;  // Cannot compute!
6131 
6132     // Evaluate the condition for this iteration.
6133     Result = ConstantExpr::getICmp(predicate, Result, RHS);
6134     if (!isa<ConstantInt>(Result)) break;  // Couldn't decide for sure
6135     if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
6136       ++NumArrayLenItCounts;
6137       return getConstant(ItCst);   // Found terminating iteration!
6138     }
6139   }
6140   return getCouldNotCompute();
6141 }
6142 
computeShiftCompareExitLimit(Value * LHS,Value * RHSV,const Loop * L,ICmpInst::Predicate Pred)6143 ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit(
6144     Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) {
6145   ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV);
6146   if (!RHS)
6147     return getCouldNotCompute();
6148 
6149   const BasicBlock *Latch = L->getLoopLatch();
6150   if (!Latch)
6151     return getCouldNotCompute();
6152 
6153   const BasicBlock *Predecessor = L->getLoopPredecessor();
6154   if (!Predecessor)
6155     return getCouldNotCompute();
6156 
6157   // Return true if V is of the form "LHS `shift_op` <positive constant>".
6158   // Return LHS in OutLHS and shift_opt in OutOpCode.
6159   auto MatchPositiveShift =
6160       [](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) {
6161 
6162     using namespace PatternMatch;
6163 
6164     ConstantInt *ShiftAmt;
6165     if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
6166       OutOpCode = Instruction::LShr;
6167     else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
6168       OutOpCode = Instruction::AShr;
6169     else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
6170       OutOpCode = Instruction::Shl;
6171     else
6172       return false;
6173 
6174     return ShiftAmt->getValue().isStrictlyPositive();
6175   };
6176 
6177   // Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in
6178   //
6179   // loop:
6180   //   %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ]
6181   //   %iv.shifted = lshr i32 %iv, <positive constant>
6182   //
6183   // Return true on a succesful match.  Return the corresponding PHI node (%iv
6184   // above) in PNOut and the opcode of the shift operation in OpCodeOut.
6185   auto MatchShiftRecurrence =
6186       [&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) {
6187     Optional<Instruction::BinaryOps> PostShiftOpCode;
6188 
6189     {
6190       Instruction::BinaryOps OpC;
6191       Value *V;
6192 
6193       // If we encounter a shift instruction, "peel off" the shift operation,
6194       // and remember that we did so.  Later when we inspect %iv's backedge
6195       // value, we will make sure that the backedge value uses the same
6196       // operation.
6197       //
6198       // Note: the peeled shift operation does not have to be the same
6199       // instruction as the one feeding into the PHI's backedge value.  We only
6200       // really care about it being the same *kind* of shift instruction --
6201       // that's all that is required for our later inferences to hold.
6202       if (MatchPositiveShift(LHS, V, OpC)) {
6203         PostShiftOpCode = OpC;
6204         LHS = V;
6205       }
6206     }
6207 
6208     PNOut = dyn_cast<PHINode>(LHS);
6209     if (!PNOut || PNOut->getParent() != L->getHeader())
6210       return false;
6211 
6212     Value *BEValue = PNOut->getIncomingValueForBlock(Latch);
6213     Value *OpLHS;
6214 
6215     return
6216         // The backedge value for the PHI node must be a shift by a positive
6217         // amount
6218         MatchPositiveShift(BEValue, OpLHS, OpCodeOut) &&
6219 
6220         // of the PHI node itself
6221         OpLHS == PNOut &&
6222 
6223         // and the kind of shift should be match the kind of shift we peeled
6224         // off, if any.
6225         (!PostShiftOpCode.hasValue() || *PostShiftOpCode == OpCodeOut);
6226   };
6227 
6228   PHINode *PN;
6229   Instruction::BinaryOps OpCode;
6230   if (!MatchShiftRecurrence(LHS, PN, OpCode))
6231     return getCouldNotCompute();
6232 
6233   const DataLayout &DL = getDataLayout();
6234 
6235   // The key rationale for this optimization is that for some kinds of shift
6236   // recurrences, the value of the recurrence "stabilizes" to either 0 or -1
6237   // within a finite number of iterations.  If the condition guarding the
6238   // backedge (in the sense that the backedge is taken if the condition is true)
6239   // is false for the value the shift recurrence stabilizes to, then we know
6240   // that the backedge is taken only a finite number of times.
6241 
6242   ConstantInt *StableValue = nullptr;
6243   switch (OpCode) {
6244   default:
6245     llvm_unreachable("Impossible case!");
6246 
6247   case Instruction::AShr: {
6248     // {K,ashr,<positive-constant>} stabilizes to signum(K) in at most
6249     // bitwidth(K) iterations.
6250     Value *FirstValue = PN->getIncomingValueForBlock(Predecessor);
6251     bool KnownZero, KnownOne;
6252     ComputeSignBit(FirstValue, KnownZero, KnownOne, DL, 0, nullptr,
6253                    Predecessor->getTerminator(), &DT);
6254     auto *Ty = cast<IntegerType>(RHS->getType());
6255     if (KnownZero)
6256       StableValue = ConstantInt::get(Ty, 0);
6257     else if (KnownOne)
6258       StableValue = ConstantInt::get(Ty, -1, true);
6259     else
6260       return getCouldNotCompute();
6261 
6262     break;
6263   }
6264   case Instruction::LShr:
6265   case Instruction::Shl:
6266     // Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>}
6267     // stabilize to 0 in at most bitwidth(K) iterations.
6268     StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0);
6269     break;
6270   }
6271 
6272   auto *Result =
6273       ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI);
6274   assert(Result->getType()->isIntegerTy(1) &&
6275          "Otherwise cannot be an operand to a branch instruction");
6276 
6277   if (Result->isZeroValue()) {
6278     unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6279     const SCEV *UpperBound =
6280         getConstant(getEffectiveSCEVType(RHS->getType()), BitWidth);
6281     SCEVUnionPredicate P;
6282     return ExitLimit(getCouldNotCompute(), UpperBound, P);
6283   }
6284 
6285   return getCouldNotCompute();
6286 }
6287 
6288 /// Return true if we can constant fold an instruction of the specified type,
6289 /// assuming that all operands were constants.
CanConstantFold(const Instruction * I)6290 static bool CanConstantFold(const Instruction *I) {
6291   if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
6292       isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
6293       isa<LoadInst>(I))
6294     return true;
6295 
6296   if (const CallInst *CI = dyn_cast<CallInst>(I))
6297     if (const Function *F = CI->getCalledFunction())
6298       return canConstantFoldCallTo(F);
6299   return false;
6300 }
6301 
6302 /// Determine whether this instruction can constant evolve within this loop
6303 /// assuming its operands can all constant evolve.
canConstantEvolve(Instruction * I,const Loop * L)6304 static bool canConstantEvolve(Instruction *I, const Loop *L) {
6305   // An instruction outside of the loop can't be derived from a loop PHI.
6306   if (!L->contains(I)) return false;
6307 
6308   if (isa<PHINode>(I)) {
6309     // We don't currently keep track of the control flow needed to evaluate
6310     // PHIs, so we cannot handle PHIs inside of loops.
6311     return L->getHeader() == I->getParent();
6312   }
6313 
6314   // If we won't be able to constant fold this expression even if the operands
6315   // are constants, bail early.
6316   return CanConstantFold(I);
6317 }
6318 
6319 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
6320 /// recursing through each instruction operand until reaching a loop header phi.
6321 static PHINode *
getConstantEvolvingPHIOperands(Instruction * UseInst,const Loop * L,DenseMap<Instruction *,PHINode * > & PHIMap)6322 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
6323                                DenseMap<Instruction *, PHINode *> &PHIMap) {
6324 
6325   // Otherwise, we can evaluate this instruction if all of its operands are
6326   // constant or derived from a PHI node themselves.
6327   PHINode *PHI = nullptr;
6328   for (Value *Op : UseInst->operands()) {
6329     if (isa<Constant>(Op)) continue;
6330 
6331     Instruction *OpInst = dyn_cast<Instruction>(Op);
6332     if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
6333 
6334     PHINode *P = dyn_cast<PHINode>(OpInst);
6335     if (!P)
6336       // If this operand is already visited, reuse the prior result.
6337       // We may have P != PHI if this is the deepest point at which the
6338       // inconsistent paths meet.
6339       P = PHIMap.lookup(OpInst);
6340     if (!P) {
6341       // Recurse and memoize the results, whether a phi is found or not.
6342       // This recursive call invalidates pointers into PHIMap.
6343       P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
6344       PHIMap[OpInst] = P;
6345     }
6346     if (!P)
6347       return nullptr;  // Not evolving from PHI
6348     if (PHI && PHI != P)
6349       return nullptr;  // Evolving from multiple different PHIs.
6350     PHI = P;
6351   }
6352   // This is a expression evolving from a constant PHI!
6353   return PHI;
6354 }
6355 
6356 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
6357 /// in the loop that V is derived from.  We allow arbitrary operations along the
6358 /// way, but the operands of an operation must either be constants or a value
6359 /// derived from a constant PHI.  If this expression does not fit with these
6360 /// constraints, return null.
getConstantEvolvingPHI(Value * V,const Loop * L)6361 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
6362   Instruction *I = dyn_cast<Instruction>(V);
6363   if (!I || !canConstantEvolve(I, L)) return nullptr;
6364 
6365   if (PHINode *PN = dyn_cast<PHINode>(I))
6366     return PN;
6367 
6368   // Record non-constant instructions contained by the loop.
6369   DenseMap<Instruction *, PHINode *> PHIMap;
6370   return getConstantEvolvingPHIOperands(I, L, PHIMap);
6371 }
6372 
6373 /// EvaluateExpression - Given an expression that passes the
6374 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
6375 /// in the loop has the value PHIVal.  If we can't fold this expression for some
6376 /// reason, return null.
EvaluateExpression(Value * V,const Loop * L,DenseMap<Instruction *,Constant * > & Vals,const DataLayout & DL,const TargetLibraryInfo * TLI)6377 static Constant *EvaluateExpression(Value *V, const Loop *L,
6378                                     DenseMap<Instruction *, Constant *> &Vals,
6379                                     const DataLayout &DL,
6380                                     const TargetLibraryInfo *TLI) {
6381   // Convenient constant check, but redundant for recursive calls.
6382   if (Constant *C = dyn_cast<Constant>(V)) return C;
6383   Instruction *I = dyn_cast<Instruction>(V);
6384   if (!I) return nullptr;
6385 
6386   if (Constant *C = Vals.lookup(I)) return C;
6387 
6388   // An instruction inside the loop depends on a value outside the loop that we
6389   // weren't given a mapping for, or a value such as a call inside the loop.
6390   if (!canConstantEvolve(I, L)) return nullptr;
6391 
6392   // An unmapped PHI can be due to a branch or another loop inside this loop,
6393   // or due to this not being the initial iteration through a loop where we
6394   // couldn't compute the evolution of this particular PHI last time.
6395   if (isa<PHINode>(I)) return nullptr;
6396 
6397   std::vector<Constant*> Operands(I->getNumOperands());
6398 
6399   for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
6400     Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
6401     if (!Operand) {
6402       Operands[i] = dyn_cast<Constant>(I->getOperand(i));
6403       if (!Operands[i]) return nullptr;
6404       continue;
6405     }
6406     Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
6407     Vals[Operand] = C;
6408     if (!C) return nullptr;
6409     Operands[i] = C;
6410   }
6411 
6412   if (CmpInst *CI = dyn_cast<CmpInst>(I))
6413     return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
6414                                            Operands[1], DL, TLI);
6415   if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
6416     if (!LI->isVolatile())
6417       return ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
6418   }
6419   return ConstantFoldInstOperands(I, Operands, DL, TLI);
6420 }
6421 
6422 
6423 // If every incoming value to PN except the one for BB is a specific Constant,
6424 // return that, else return nullptr.
getOtherIncomingValue(PHINode * PN,BasicBlock * BB)6425 static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) {
6426   Constant *IncomingVal = nullptr;
6427 
6428   for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
6429     if (PN->getIncomingBlock(i) == BB)
6430       continue;
6431 
6432     auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i));
6433     if (!CurrentVal)
6434       return nullptr;
6435 
6436     if (IncomingVal != CurrentVal) {
6437       if (IncomingVal)
6438         return nullptr;
6439       IncomingVal = CurrentVal;
6440     }
6441   }
6442 
6443   return IncomingVal;
6444 }
6445 
6446 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
6447 /// in the header of its containing loop, we know the loop executes a
6448 /// constant number of times, and the PHI node is just a recurrence
6449 /// involving constants, fold it.
6450 Constant *
getConstantEvolutionLoopExitValue(PHINode * PN,const APInt & BEs,const Loop * L)6451 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
6452                                                    const APInt &BEs,
6453                                                    const Loop *L) {
6454   auto I = ConstantEvolutionLoopExitValue.find(PN);
6455   if (I != ConstantEvolutionLoopExitValue.end())
6456     return I->second;
6457 
6458   if (BEs.ugt(MaxBruteForceIterations))
6459     return ConstantEvolutionLoopExitValue[PN] = nullptr;  // Not going to evaluate it.
6460 
6461   Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
6462 
6463   DenseMap<Instruction *, Constant *> CurrentIterVals;
6464   BasicBlock *Header = L->getHeader();
6465   assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
6466 
6467   BasicBlock *Latch = L->getLoopLatch();
6468   if (!Latch)
6469     return nullptr;
6470 
6471   for (auto &I : *Header) {
6472     PHINode *PHI = dyn_cast<PHINode>(&I);
6473     if (!PHI) break;
6474     auto *StartCST = getOtherIncomingValue(PHI, Latch);
6475     if (!StartCST) continue;
6476     CurrentIterVals[PHI] = StartCST;
6477   }
6478   if (!CurrentIterVals.count(PN))
6479     return RetVal = nullptr;
6480 
6481   Value *BEValue = PN->getIncomingValueForBlock(Latch);
6482 
6483   // Execute the loop symbolically to determine the exit value.
6484   if (BEs.getActiveBits() >= 32)
6485     return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
6486 
6487   unsigned NumIterations = BEs.getZExtValue(); // must be in range
6488   unsigned IterationNum = 0;
6489   const DataLayout &DL = getDataLayout();
6490   for (; ; ++IterationNum) {
6491     if (IterationNum == NumIterations)
6492       return RetVal = CurrentIterVals[PN];  // Got exit value!
6493 
6494     // Compute the value of the PHIs for the next iteration.
6495     // EvaluateExpression adds non-phi values to the CurrentIterVals map.
6496     DenseMap<Instruction *, Constant *> NextIterVals;
6497     Constant *NextPHI =
6498         EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6499     if (!NextPHI)
6500       return nullptr;        // Couldn't evaluate!
6501     NextIterVals[PN] = NextPHI;
6502 
6503     bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
6504 
6505     // Also evaluate the other PHI nodes.  However, we don't get to stop if we
6506     // cease to be able to evaluate one of them or if they stop evolving,
6507     // because that doesn't necessarily prevent us from computing PN.
6508     SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
6509     for (const auto &I : CurrentIterVals) {
6510       PHINode *PHI = dyn_cast<PHINode>(I.first);
6511       if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
6512       PHIsToCompute.emplace_back(PHI, I.second);
6513     }
6514     // We use two distinct loops because EvaluateExpression may invalidate any
6515     // iterators into CurrentIterVals.
6516     for (const auto &I : PHIsToCompute) {
6517       PHINode *PHI = I.first;
6518       Constant *&NextPHI = NextIterVals[PHI];
6519       if (!NextPHI) {   // Not already computed.
6520         Value *BEValue = PHI->getIncomingValueForBlock(Latch);
6521         NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6522       }
6523       if (NextPHI != I.second)
6524         StoppedEvolving = false;
6525     }
6526 
6527     // If all entries in CurrentIterVals == NextIterVals then we can stop
6528     // iterating, the loop can't continue to change.
6529     if (StoppedEvolving)
6530       return RetVal = CurrentIterVals[PN];
6531 
6532     CurrentIterVals.swap(NextIterVals);
6533   }
6534 }
6535 
computeExitCountExhaustively(const Loop * L,Value * Cond,bool ExitWhen)6536 const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
6537                                                           Value *Cond,
6538                                                           bool ExitWhen) {
6539   PHINode *PN = getConstantEvolvingPHI(Cond, L);
6540   if (!PN) return getCouldNotCompute();
6541 
6542   // If the loop is canonicalized, the PHI will have exactly two entries.
6543   // That's the only form we support here.
6544   if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
6545 
6546   DenseMap<Instruction *, Constant *> CurrentIterVals;
6547   BasicBlock *Header = L->getHeader();
6548   assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
6549 
6550   BasicBlock *Latch = L->getLoopLatch();
6551   assert(Latch && "Should follow from NumIncomingValues == 2!");
6552 
6553   for (auto &I : *Header) {
6554     PHINode *PHI = dyn_cast<PHINode>(&I);
6555     if (!PHI)
6556       break;
6557     auto *StartCST = getOtherIncomingValue(PHI, Latch);
6558     if (!StartCST) continue;
6559     CurrentIterVals[PHI] = StartCST;
6560   }
6561   if (!CurrentIterVals.count(PN))
6562     return getCouldNotCompute();
6563 
6564   // Okay, we find a PHI node that defines the trip count of this loop.  Execute
6565   // the loop symbolically to determine when the condition gets a value of
6566   // "ExitWhen".
6567   unsigned MaxIterations = MaxBruteForceIterations;   // Limit analysis.
6568   const DataLayout &DL = getDataLayout();
6569   for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
6570     auto *CondVal = dyn_cast_or_null<ConstantInt>(
6571         EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
6572 
6573     // Couldn't symbolically evaluate.
6574     if (!CondVal) return getCouldNotCompute();
6575 
6576     if (CondVal->getValue() == uint64_t(ExitWhen)) {
6577       ++NumBruteForceTripCountsComputed;
6578       return getConstant(Type::getInt32Ty(getContext()), IterationNum);
6579     }
6580 
6581     // Update all the PHI nodes for the next iteration.
6582     DenseMap<Instruction *, Constant *> NextIterVals;
6583 
6584     // Create a list of which PHIs we need to compute. We want to do this before
6585     // calling EvaluateExpression on them because that may invalidate iterators
6586     // into CurrentIterVals.
6587     SmallVector<PHINode *, 8> PHIsToCompute;
6588     for (const auto &I : CurrentIterVals) {
6589       PHINode *PHI = dyn_cast<PHINode>(I.first);
6590       if (!PHI || PHI->getParent() != Header) continue;
6591       PHIsToCompute.push_back(PHI);
6592     }
6593     for (PHINode *PHI : PHIsToCompute) {
6594       Constant *&NextPHI = NextIterVals[PHI];
6595       if (NextPHI) continue;    // Already computed!
6596 
6597       Value *BEValue = PHI->getIncomingValueForBlock(Latch);
6598       NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6599     }
6600     CurrentIterVals.swap(NextIterVals);
6601   }
6602 
6603   // Too many iterations were needed to evaluate.
6604   return getCouldNotCompute();
6605 }
6606 
getSCEVAtScope(const SCEV * V,const Loop * L)6607 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
6608   SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values =
6609       ValuesAtScopes[V];
6610   // Check to see if we've folded this expression at this loop before.
6611   for (auto &LS : Values)
6612     if (LS.first == L)
6613       return LS.second ? LS.second : V;
6614 
6615   Values.emplace_back(L, nullptr);
6616 
6617   // Otherwise compute it.
6618   const SCEV *C = computeSCEVAtScope(V, L);
6619   for (auto &LS : reverse(ValuesAtScopes[V]))
6620     if (LS.first == L) {
6621       LS.second = C;
6622       break;
6623     }
6624   return C;
6625 }
6626 
6627 /// This builds up a Constant using the ConstantExpr interface.  That way, we
6628 /// will return Constants for objects which aren't represented by a
6629 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
6630 /// Returns NULL if the SCEV isn't representable as a Constant.
BuildConstantFromSCEV(const SCEV * V)6631 static Constant *BuildConstantFromSCEV(const SCEV *V) {
6632   switch (static_cast<SCEVTypes>(V->getSCEVType())) {
6633     case scCouldNotCompute:
6634     case scAddRecExpr:
6635       break;
6636     case scConstant:
6637       return cast<SCEVConstant>(V)->getValue();
6638     case scUnknown:
6639       return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
6640     case scSignExtend: {
6641       const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
6642       if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
6643         return ConstantExpr::getSExt(CastOp, SS->getType());
6644       break;
6645     }
6646     case scZeroExtend: {
6647       const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
6648       if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
6649         return ConstantExpr::getZExt(CastOp, SZ->getType());
6650       break;
6651     }
6652     case scTruncate: {
6653       const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
6654       if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
6655         return ConstantExpr::getTrunc(CastOp, ST->getType());
6656       break;
6657     }
6658     case scAddExpr: {
6659       const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
6660       if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
6661         if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
6662           unsigned AS = PTy->getAddressSpace();
6663           Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
6664           C = ConstantExpr::getBitCast(C, DestPtrTy);
6665         }
6666         for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
6667           Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
6668           if (!C2) return nullptr;
6669 
6670           // First pointer!
6671           if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
6672             unsigned AS = C2->getType()->getPointerAddressSpace();
6673             std::swap(C, C2);
6674             Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
6675             // The offsets have been converted to bytes.  We can add bytes to an
6676             // i8* by GEP with the byte count in the first index.
6677             C = ConstantExpr::getBitCast(C, DestPtrTy);
6678           }
6679 
6680           // Don't bother trying to sum two pointers. We probably can't
6681           // statically compute a load that results from it anyway.
6682           if (C2->getType()->isPointerTy())
6683             return nullptr;
6684 
6685           if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
6686             if (PTy->getElementType()->isStructTy())
6687               C2 = ConstantExpr::getIntegerCast(
6688                   C2, Type::getInt32Ty(C->getContext()), true);
6689             C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
6690           } else
6691             C = ConstantExpr::getAdd(C, C2);
6692         }
6693         return C;
6694       }
6695       break;
6696     }
6697     case scMulExpr: {
6698       const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
6699       if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
6700         // Don't bother with pointers at all.
6701         if (C->getType()->isPointerTy()) return nullptr;
6702         for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
6703           Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
6704           if (!C2 || C2->getType()->isPointerTy()) return nullptr;
6705           C = ConstantExpr::getMul(C, C2);
6706         }
6707         return C;
6708       }
6709       break;
6710     }
6711     case scUDivExpr: {
6712       const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
6713       if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
6714         if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
6715           if (LHS->getType() == RHS->getType())
6716             return ConstantExpr::getUDiv(LHS, RHS);
6717       break;
6718     }
6719     case scSMaxExpr:
6720     case scUMaxExpr:
6721       break; // TODO: smax, umax.
6722   }
6723   return nullptr;
6724 }
6725 
computeSCEVAtScope(const SCEV * V,const Loop * L)6726 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
6727   if (isa<SCEVConstant>(V)) return V;
6728 
6729   // If this instruction is evolved from a constant-evolving PHI, compute the
6730   // exit value from the loop without using SCEVs.
6731   if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
6732     if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
6733       const Loop *LI = this->LI[I->getParent()];
6734       if (LI && LI->getParentLoop() == L)  // Looking for loop exit value.
6735         if (PHINode *PN = dyn_cast<PHINode>(I))
6736           if (PN->getParent() == LI->getHeader()) {
6737             // Okay, there is no closed form solution for the PHI node.  Check
6738             // to see if the loop that contains it has a known backedge-taken
6739             // count.  If so, we may be able to force computation of the exit
6740             // value.
6741             const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
6742             if (const SCEVConstant *BTCC =
6743                   dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
6744               // Okay, we know how many times the containing loop executes.  If
6745               // this is a constant evolving PHI node, get the final value at
6746               // the specified iteration number.
6747               Constant *RV =
6748                   getConstantEvolutionLoopExitValue(PN, BTCC->getAPInt(), LI);
6749               if (RV) return getSCEV(RV);
6750             }
6751           }
6752 
6753       // Okay, this is an expression that we cannot symbolically evaluate
6754       // into a SCEV.  Check to see if it's possible to symbolically evaluate
6755       // the arguments into constants, and if so, try to constant propagate the
6756       // result.  This is particularly useful for computing loop exit values.
6757       if (CanConstantFold(I)) {
6758         SmallVector<Constant *, 4> Operands;
6759         bool MadeImprovement = false;
6760         for (Value *Op : I->operands()) {
6761           if (Constant *C = dyn_cast<Constant>(Op)) {
6762             Operands.push_back(C);
6763             continue;
6764           }
6765 
6766           // If any of the operands is non-constant and if they are
6767           // non-integer and non-pointer, don't even try to analyze them
6768           // with scev techniques.
6769           if (!isSCEVable(Op->getType()))
6770             return V;
6771 
6772           const SCEV *OrigV = getSCEV(Op);
6773           const SCEV *OpV = getSCEVAtScope(OrigV, L);
6774           MadeImprovement |= OrigV != OpV;
6775 
6776           Constant *C = BuildConstantFromSCEV(OpV);
6777           if (!C) return V;
6778           if (C->getType() != Op->getType())
6779             C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
6780                                                               Op->getType(),
6781                                                               false),
6782                                       C, Op->getType());
6783           Operands.push_back(C);
6784         }
6785 
6786         // Check to see if getSCEVAtScope actually made an improvement.
6787         if (MadeImprovement) {
6788           Constant *C = nullptr;
6789           const DataLayout &DL = getDataLayout();
6790           if (const CmpInst *CI = dyn_cast<CmpInst>(I))
6791             C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
6792                                                 Operands[1], DL, &TLI);
6793           else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
6794             if (!LI->isVolatile())
6795               C = ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
6796           } else
6797             C = ConstantFoldInstOperands(I, Operands, DL, &TLI);
6798           if (!C) return V;
6799           return getSCEV(C);
6800         }
6801       }
6802     }
6803 
6804     // This is some other type of SCEVUnknown, just return it.
6805     return V;
6806   }
6807 
6808   if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
6809     // Avoid performing the look-up in the common case where the specified
6810     // expression has no loop-variant portions.
6811     for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
6812       const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6813       if (OpAtScope != Comm->getOperand(i)) {
6814         // Okay, at least one of these operands is loop variant but might be
6815         // foldable.  Build a new instance of the folded commutative expression.
6816         SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
6817                                             Comm->op_begin()+i);
6818         NewOps.push_back(OpAtScope);
6819 
6820         for (++i; i != e; ++i) {
6821           OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6822           NewOps.push_back(OpAtScope);
6823         }
6824         if (isa<SCEVAddExpr>(Comm))
6825           return getAddExpr(NewOps);
6826         if (isa<SCEVMulExpr>(Comm))
6827           return getMulExpr(NewOps);
6828         if (isa<SCEVSMaxExpr>(Comm))
6829           return getSMaxExpr(NewOps);
6830         if (isa<SCEVUMaxExpr>(Comm))
6831           return getUMaxExpr(NewOps);
6832         llvm_unreachable("Unknown commutative SCEV type!");
6833       }
6834     }
6835     // If we got here, all operands are loop invariant.
6836     return Comm;
6837   }
6838 
6839   if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
6840     const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
6841     const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
6842     if (LHS == Div->getLHS() && RHS == Div->getRHS())
6843       return Div;   // must be loop invariant
6844     return getUDivExpr(LHS, RHS);
6845   }
6846 
6847   // If this is a loop recurrence for a loop that does not contain L, then we
6848   // are dealing with the final value computed by the loop.
6849   if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
6850     // First, attempt to evaluate each operand.
6851     // Avoid performing the look-up in the common case where the specified
6852     // expression has no loop-variant portions.
6853     for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
6854       const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
6855       if (OpAtScope == AddRec->getOperand(i))
6856         continue;
6857 
6858       // Okay, at least one of these operands is loop variant but might be
6859       // foldable.  Build a new instance of the folded commutative expression.
6860       SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
6861                                           AddRec->op_begin()+i);
6862       NewOps.push_back(OpAtScope);
6863       for (++i; i != e; ++i)
6864         NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
6865 
6866       const SCEV *FoldedRec =
6867         getAddRecExpr(NewOps, AddRec->getLoop(),
6868                       AddRec->getNoWrapFlags(SCEV::FlagNW));
6869       AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
6870       // The addrec may be folded to a nonrecurrence, for example, if the
6871       // induction variable is multiplied by zero after constant folding. Go
6872       // ahead and return the folded value.
6873       if (!AddRec)
6874         return FoldedRec;
6875       break;
6876     }
6877 
6878     // If the scope is outside the addrec's loop, evaluate it by using the
6879     // loop exit value of the addrec.
6880     if (!AddRec->getLoop()->contains(L)) {
6881       // To evaluate this recurrence, we need to know how many times the AddRec
6882       // loop iterates.  Compute this now.
6883       const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
6884       if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
6885 
6886       // Then, evaluate the AddRec.
6887       return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
6888     }
6889 
6890     return AddRec;
6891   }
6892 
6893   if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
6894     const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6895     if (Op == Cast->getOperand())
6896       return Cast;  // must be loop invariant
6897     return getZeroExtendExpr(Op, Cast->getType());
6898   }
6899 
6900   if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
6901     const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6902     if (Op == Cast->getOperand())
6903       return Cast;  // must be loop invariant
6904     return getSignExtendExpr(Op, Cast->getType());
6905   }
6906 
6907   if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
6908     const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6909     if (Op == Cast->getOperand())
6910       return Cast;  // must be loop invariant
6911     return getTruncateExpr(Op, Cast->getType());
6912   }
6913 
6914   llvm_unreachable("Unknown SCEV type!");
6915 }
6916 
getSCEVAtScope(Value * V,const Loop * L)6917 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
6918   return getSCEVAtScope(getSCEV(V), L);
6919 }
6920 
6921 /// Finds the minimum unsigned root of the following equation:
6922 ///
6923 ///     A * X = B (mod N)
6924 ///
6925 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
6926 /// A and B isn't important.
6927 ///
6928 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
SolveLinEquationWithOverflow(const APInt & A,const APInt & B,ScalarEvolution & SE)6929 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
6930                                                ScalarEvolution &SE) {
6931   uint32_t BW = A.getBitWidth();
6932   assert(BW == B.getBitWidth() && "Bit widths must be the same.");
6933   assert(A != 0 && "A must be non-zero.");
6934 
6935   // 1. D = gcd(A, N)
6936   //
6937   // The gcd of A and N may have only one prime factor: 2. The number of
6938   // trailing zeros in A is its multiplicity
6939   uint32_t Mult2 = A.countTrailingZeros();
6940   // D = 2^Mult2
6941 
6942   // 2. Check if B is divisible by D.
6943   //
6944   // B is divisible by D if and only if the multiplicity of prime factor 2 for B
6945   // is not less than multiplicity of this prime factor for D.
6946   if (B.countTrailingZeros() < Mult2)
6947     return SE.getCouldNotCompute();
6948 
6949   // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
6950   // modulo (N / D).
6951   //
6952   // (N / D) may need BW+1 bits in its representation.  Hence, we'll use this
6953   // bit width during computations.
6954   APInt AD = A.lshr(Mult2).zext(BW + 1);  // AD = A / D
6955   APInt Mod(BW + 1, 0);
6956   Mod.setBit(BW - Mult2);  // Mod = N / D
6957   APInt I = AD.multiplicativeInverse(Mod);
6958 
6959   // 4. Compute the minimum unsigned root of the equation:
6960   // I * (B / D) mod (N / D)
6961   APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
6962 
6963   // The result is guaranteed to be less than 2^BW so we may truncate it to BW
6964   // bits.
6965   return SE.getConstant(Result.trunc(BW));
6966 }
6967 
6968 /// Find the roots of the quadratic equation for the given quadratic chrec
6969 /// {L,+,M,+,N}.  This returns either the two roots (which might be the same) or
6970 /// two SCEVCouldNotCompute objects.
6971 ///
6972 static Optional<std::pair<const SCEVConstant *,const SCEVConstant *>>
SolveQuadraticEquation(const SCEVAddRecExpr * AddRec,ScalarEvolution & SE)6973 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
6974   assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
6975   const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
6976   const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
6977   const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
6978 
6979   // We currently can only solve this if the coefficients are constants.
6980   if (!LC || !MC || !NC)
6981     return None;
6982 
6983   uint32_t BitWidth = LC->getAPInt().getBitWidth();
6984   const APInt &L = LC->getAPInt();
6985   const APInt &M = MC->getAPInt();
6986   const APInt &N = NC->getAPInt();
6987   APInt Two(BitWidth, 2);
6988   APInt Four(BitWidth, 4);
6989 
6990   {
6991     using namespace APIntOps;
6992     const APInt& C = L;
6993     // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
6994     // The B coefficient is M-N/2
6995     APInt B(M);
6996     B -= sdiv(N,Two);
6997 
6998     // The A coefficient is N/2
6999     APInt A(N.sdiv(Two));
7000 
7001     // Compute the B^2-4ac term.
7002     APInt SqrtTerm(B);
7003     SqrtTerm *= B;
7004     SqrtTerm -= Four * (A * C);
7005 
7006     if (SqrtTerm.isNegative()) {
7007       // The loop is provably infinite.
7008       return None;
7009     }
7010 
7011     // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
7012     // integer value or else APInt::sqrt() will assert.
7013     APInt SqrtVal(SqrtTerm.sqrt());
7014 
7015     // Compute the two solutions for the quadratic formula.
7016     // The divisions must be performed as signed divisions.
7017     APInt NegB(-B);
7018     APInt TwoA(A << 1);
7019     if (TwoA.isMinValue())
7020       return None;
7021 
7022     LLVMContext &Context = SE.getContext();
7023 
7024     ConstantInt *Solution1 =
7025       ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
7026     ConstantInt *Solution2 =
7027       ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
7028 
7029     return std::make_pair(cast<SCEVConstant>(SE.getConstant(Solution1)),
7030                           cast<SCEVConstant>(SE.getConstant(Solution2)));
7031   } // end APIntOps namespace
7032 }
7033 
7034 ScalarEvolution::ExitLimit
howFarToZero(const SCEV * V,const Loop * L,bool ControlsExit,bool AllowPredicates)7035 ScalarEvolution::howFarToZero(const SCEV *V, const Loop *L, bool ControlsExit,
7036                               bool AllowPredicates) {
7037 
7038   // This is only used for loops with a "x != y" exit test. The exit condition
7039   // is now expressed as a single expression, V = x-y. So the exit test is
7040   // effectively V != 0.  We know and take advantage of the fact that this
7041   // expression only being used in a comparison by zero context.
7042 
7043   SCEVUnionPredicate P;
7044   // If the value is a constant
7045   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
7046     // If the value is already zero, the branch will execute zero times.
7047     if (C->getValue()->isZero()) return C;
7048     return getCouldNotCompute();  // Otherwise it will loop infinitely.
7049   }
7050 
7051   const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
7052   if (!AddRec && AllowPredicates)
7053     // Try to make this an AddRec using runtime tests, in the first X
7054     // iterations of this loop, where X is the SCEV expression found by the
7055     // algorithm below.
7056     AddRec = convertSCEVToAddRecWithPredicates(V, L, P);
7057 
7058   if (!AddRec || AddRec->getLoop() != L)
7059     return getCouldNotCompute();
7060 
7061   // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
7062   // the quadratic equation to solve it.
7063   if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
7064     if (auto Roots = SolveQuadraticEquation(AddRec, *this)) {
7065       const SCEVConstant *R1 = Roots->first;
7066       const SCEVConstant *R2 = Roots->second;
7067       // Pick the smallest positive root value.
7068       if (ConstantInt *CB = dyn_cast<ConstantInt>(ConstantExpr::getICmp(
7069               CmpInst::ICMP_ULT, R1->getValue(), R2->getValue()))) {
7070         if (!CB->getZExtValue())
7071           std::swap(R1, R2); // R1 is the minimum root now.
7072 
7073         // We can only use this value if the chrec ends up with an exact zero
7074         // value at this index.  When solving for "X*X != 5", for example, we
7075         // should not accept a root of 2.
7076         const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
7077         if (Val->isZero())
7078           return ExitLimit(R1, R1, P); // We found a quadratic root!
7079       }
7080     }
7081     return getCouldNotCompute();
7082   }
7083 
7084   // Otherwise we can only handle this if it is affine.
7085   if (!AddRec->isAffine())
7086     return getCouldNotCompute();
7087 
7088   // If this is an affine expression, the execution count of this branch is
7089   // the minimum unsigned root of the following equation:
7090   //
7091   //     Start + Step*N = 0 (mod 2^BW)
7092   //
7093   // equivalent to:
7094   //
7095   //             Step*N = -Start (mod 2^BW)
7096   //
7097   // where BW is the common bit width of Start and Step.
7098 
7099   // Get the initial value for the loop.
7100   const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
7101   const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
7102 
7103   // For now we handle only constant steps.
7104   //
7105   // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
7106   // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
7107   // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
7108   // We have not yet seen any such cases.
7109   const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
7110   if (!StepC || StepC->getValue()->equalsInt(0))
7111     return getCouldNotCompute();
7112 
7113   // For positive steps (counting up until unsigned overflow):
7114   //   N = -Start/Step (as unsigned)
7115   // For negative steps (counting down to zero):
7116   //   N = Start/-Step
7117   // First compute the unsigned distance from zero in the direction of Step.
7118   bool CountDown = StepC->getAPInt().isNegative();
7119   const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
7120 
7121   // Handle unitary steps, which cannot wraparound.
7122   // 1*N = -Start; -1*N = Start (mod 2^BW), so:
7123   //   N = Distance (as unsigned)
7124   if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
7125     ConstantRange CR = getUnsignedRange(Start);
7126     const SCEV *MaxBECount;
7127     if (!CountDown && CR.getUnsignedMin().isMinValue())
7128       // When counting up, the worst starting value is 1, not 0.
7129       MaxBECount = CR.getUnsignedMax().isMinValue()
7130         ? getConstant(APInt::getMinValue(CR.getBitWidth()))
7131         : getConstant(APInt::getMaxValue(CR.getBitWidth()));
7132     else
7133       MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
7134                                          : -CR.getUnsignedMin());
7135     return ExitLimit(Distance, MaxBECount, P);
7136   }
7137 
7138   // As a special case, handle the instance where Step is a positive power of
7139   // two. In this case, determining whether Step divides Distance evenly can be
7140   // done by counting and comparing the number of trailing zeros of Step and
7141   // Distance.
7142   if (!CountDown) {
7143     const APInt &StepV = StepC->getAPInt();
7144     // StepV.isPowerOf2() returns true if StepV is an positive power of two.  It
7145     // also returns true if StepV is maximally negative (eg, INT_MIN), but that
7146     // case is not handled as this code is guarded by !CountDown.
7147     if (StepV.isPowerOf2() &&
7148         GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) {
7149       // Here we've constrained the equation to be of the form
7150       //
7151       //   2^(N + k) * Distance' = (StepV == 2^N) * X (mod 2^W)  ... (0)
7152       //
7153       // where we're operating on a W bit wide integer domain and k is
7154       // non-negative.  The smallest unsigned solution for X is the trip count.
7155       //
7156       // (0) is equivalent to:
7157       //
7158       //      2^(N + k) * Distance' - 2^N * X = L * 2^W
7159       // <=>  2^N(2^k * Distance' - X) = L * 2^(W - N) * 2^N
7160       // <=>  2^k * Distance' - X = L * 2^(W - N)
7161       // <=>  2^k * Distance'     = L * 2^(W - N) + X    ... (1)
7162       //
7163       // The smallest X satisfying (1) is unsigned remainder of dividing the LHS
7164       // by 2^(W - N).
7165       //
7166       // <=>  X = 2^k * Distance' URem 2^(W - N)   ... (2)
7167       //
7168       // E.g. say we're solving
7169       //
7170       //   2 * Val = 2 * X  (in i8)   ... (3)
7171       //
7172       // then from (2), we get X = Val URem i8 128 (k = 0 in this case).
7173       //
7174       // Note: It is tempting to solve (3) by setting X = Val, but Val is not
7175       // necessarily the smallest unsigned value of X that satisfies (3).
7176       // E.g. if Val is i8 -127 then the smallest value of X that satisfies (3)
7177       // is i8 1, not i8 -127
7178 
7179       const auto *ModuloResult = getUDivExactExpr(Distance, Step);
7180 
7181       // Since SCEV does not have a URem node, we construct one using a truncate
7182       // and a zero extend.
7183 
7184       unsigned NarrowWidth = StepV.getBitWidth() - StepV.countTrailingZeros();
7185       auto *NarrowTy = IntegerType::get(getContext(), NarrowWidth);
7186       auto *WideTy = Distance->getType();
7187 
7188       const SCEV *Limit =
7189           getZeroExtendExpr(getTruncateExpr(ModuloResult, NarrowTy), WideTy);
7190       return ExitLimit(Limit, Limit, P);
7191     }
7192   }
7193 
7194   // If the condition controls loop exit (the loop exits only if the expression
7195   // is true) and the addition is no-wrap we can use unsigned divide to
7196   // compute the backedge count.  In this case, the step may not divide the
7197   // distance, but we don't care because if the condition is "missed" the loop
7198   // will have undefined behavior due to wrapping.
7199   if (ControlsExit && AddRec->hasNoSelfWrap() &&
7200       loopHasNoAbnormalExits(AddRec->getLoop())) {
7201     const SCEV *Exact =
7202         getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
7203     return ExitLimit(Exact, Exact, P);
7204   }
7205 
7206   // Then, try to solve the above equation provided that Start is constant.
7207   if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
7208     const SCEV *E = SolveLinEquationWithOverflow(
7209         StepC->getValue()->getValue(), -StartC->getValue()->getValue(), *this);
7210     return ExitLimit(E, E, P);
7211   }
7212   return getCouldNotCompute();
7213 }
7214 
7215 ScalarEvolution::ExitLimit
howFarToNonZero(const SCEV * V,const Loop * L)7216 ScalarEvolution::howFarToNonZero(const SCEV *V, const Loop *L) {
7217   // Loops that look like: while (X == 0) are very strange indeed.  We don't
7218   // handle them yet except for the trivial case.  This could be expanded in the
7219   // future as needed.
7220 
7221   // If the value is a constant, check to see if it is known to be non-zero
7222   // already.  If so, the backedge will execute zero times.
7223   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
7224     if (!C->getValue()->isNullValue())
7225       return getZero(C->getType());
7226     return getCouldNotCompute();  // Otherwise it will loop infinitely.
7227   }
7228 
7229   // We could implement others, but I really doubt anyone writes loops like
7230   // this, and if they did, they would already be constant folded.
7231   return getCouldNotCompute();
7232 }
7233 
7234 std::pair<BasicBlock *, BasicBlock *>
getPredecessorWithUniqueSuccessorForBB(BasicBlock * BB)7235 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
7236   // If the block has a unique predecessor, then there is no path from the
7237   // predecessor to the block that does not go through the direct edge
7238   // from the predecessor to the block.
7239   if (BasicBlock *Pred = BB->getSinglePredecessor())
7240     return {Pred, BB};
7241 
7242   // A loop's header is defined to be a block that dominates the loop.
7243   // If the header has a unique predecessor outside the loop, it must be
7244   // a block that has exactly one successor that can reach the loop.
7245   if (Loop *L = LI.getLoopFor(BB))
7246     return {L->getLoopPredecessor(), L->getHeader()};
7247 
7248   return {nullptr, nullptr};
7249 }
7250 
7251 /// SCEV structural equivalence is usually sufficient for testing whether two
7252 /// expressions are equal, however for the purposes of looking for a condition
7253 /// guarding a loop, it can be useful to be a little more general, since a
7254 /// front-end may have replicated the controlling expression.
7255 ///
HasSameValue(const SCEV * A,const SCEV * B)7256 static bool HasSameValue(const SCEV *A, const SCEV *B) {
7257   // Quick check to see if they are the same SCEV.
7258   if (A == B) return true;
7259 
7260   auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
7261     // Not all instructions that are "identical" compute the same value.  For
7262     // instance, two distinct alloca instructions allocating the same type are
7263     // identical and do not read memory; but compute distinct values.
7264     return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
7265   };
7266 
7267   // Otherwise, if they're both SCEVUnknown, it's possible that they hold
7268   // two different instructions with the same value. Check for this case.
7269   if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
7270     if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
7271       if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
7272         if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
7273           if (ComputesEqualValues(AI, BI))
7274             return true;
7275 
7276   // Otherwise assume they may have a different value.
7277   return false;
7278 }
7279 
SimplifyICmpOperands(ICmpInst::Predicate & Pred,const SCEV * & LHS,const SCEV * & RHS,unsigned Depth)7280 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
7281                                            const SCEV *&LHS, const SCEV *&RHS,
7282                                            unsigned Depth) {
7283   bool Changed = false;
7284 
7285   // If we hit the max recursion limit bail out.
7286   if (Depth >= 3)
7287     return false;
7288 
7289   // Canonicalize a constant to the right side.
7290   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
7291     // Check for both operands constant.
7292     if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
7293       if (ConstantExpr::getICmp(Pred,
7294                                 LHSC->getValue(),
7295                                 RHSC->getValue())->isNullValue())
7296         goto trivially_false;
7297       else
7298         goto trivially_true;
7299     }
7300     // Otherwise swap the operands to put the constant on the right.
7301     std::swap(LHS, RHS);
7302     Pred = ICmpInst::getSwappedPredicate(Pred);
7303     Changed = true;
7304   }
7305 
7306   // If we're comparing an addrec with a value which is loop-invariant in the
7307   // addrec's loop, put the addrec on the left. Also make a dominance check,
7308   // as both operands could be addrecs loop-invariant in each other's loop.
7309   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
7310     const Loop *L = AR->getLoop();
7311     if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
7312       std::swap(LHS, RHS);
7313       Pred = ICmpInst::getSwappedPredicate(Pred);
7314       Changed = true;
7315     }
7316   }
7317 
7318   // If there's a constant operand, canonicalize comparisons with boundary
7319   // cases, and canonicalize *-or-equal comparisons to regular comparisons.
7320   if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
7321     const APInt &RA = RC->getAPInt();
7322     switch (Pred) {
7323     default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7324     case ICmpInst::ICMP_EQ:
7325     case ICmpInst::ICMP_NE:
7326       // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
7327       if (!RA)
7328         if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
7329           if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
7330             if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
7331                 ME->getOperand(0)->isAllOnesValue()) {
7332               RHS = AE->getOperand(1);
7333               LHS = ME->getOperand(1);
7334               Changed = true;
7335             }
7336       break;
7337     case ICmpInst::ICMP_UGE:
7338       if ((RA - 1).isMinValue()) {
7339         Pred = ICmpInst::ICMP_NE;
7340         RHS = getConstant(RA - 1);
7341         Changed = true;
7342         break;
7343       }
7344       if (RA.isMaxValue()) {
7345         Pred = ICmpInst::ICMP_EQ;
7346         Changed = true;
7347         break;
7348       }
7349       if (RA.isMinValue()) goto trivially_true;
7350 
7351       Pred = ICmpInst::ICMP_UGT;
7352       RHS = getConstant(RA - 1);
7353       Changed = true;
7354       break;
7355     case ICmpInst::ICMP_ULE:
7356       if ((RA + 1).isMaxValue()) {
7357         Pred = ICmpInst::ICMP_NE;
7358         RHS = getConstant(RA + 1);
7359         Changed = true;
7360         break;
7361       }
7362       if (RA.isMinValue()) {
7363         Pred = ICmpInst::ICMP_EQ;
7364         Changed = true;
7365         break;
7366       }
7367       if (RA.isMaxValue()) goto trivially_true;
7368 
7369       Pred = ICmpInst::ICMP_ULT;
7370       RHS = getConstant(RA + 1);
7371       Changed = true;
7372       break;
7373     case ICmpInst::ICMP_SGE:
7374       if ((RA - 1).isMinSignedValue()) {
7375         Pred = ICmpInst::ICMP_NE;
7376         RHS = getConstant(RA - 1);
7377         Changed = true;
7378         break;
7379       }
7380       if (RA.isMaxSignedValue()) {
7381         Pred = ICmpInst::ICMP_EQ;
7382         Changed = true;
7383         break;
7384       }
7385       if (RA.isMinSignedValue()) goto trivially_true;
7386 
7387       Pred = ICmpInst::ICMP_SGT;
7388       RHS = getConstant(RA - 1);
7389       Changed = true;
7390       break;
7391     case ICmpInst::ICMP_SLE:
7392       if ((RA + 1).isMaxSignedValue()) {
7393         Pred = ICmpInst::ICMP_NE;
7394         RHS = getConstant(RA + 1);
7395         Changed = true;
7396         break;
7397       }
7398       if (RA.isMinSignedValue()) {
7399         Pred = ICmpInst::ICMP_EQ;
7400         Changed = true;
7401         break;
7402       }
7403       if (RA.isMaxSignedValue()) goto trivially_true;
7404 
7405       Pred = ICmpInst::ICMP_SLT;
7406       RHS = getConstant(RA + 1);
7407       Changed = true;
7408       break;
7409     case ICmpInst::ICMP_UGT:
7410       if (RA.isMinValue()) {
7411         Pred = ICmpInst::ICMP_NE;
7412         Changed = true;
7413         break;
7414       }
7415       if ((RA + 1).isMaxValue()) {
7416         Pred = ICmpInst::ICMP_EQ;
7417         RHS = getConstant(RA + 1);
7418         Changed = true;
7419         break;
7420       }
7421       if (RA.isMaxValue()) goto trivially_false;
7422       break;
7423     case ICmpInst::ICMP_ULT:
7424       if (RA.isMaxValue()) {
7425         Pred = ICmpInst::ICMP_NE;
7426         Changed = true;
7427         break;
7428       }
7429       if ((RA - 1).isMinValue()) {
7430         Pred = ICmpInst::ICMP_EQ;
7431         RHS = getConstant(RA - 1);
7432         Changed = true;
7433         break;
7434       }
7435       if (RA.isMinValue()) goto trivially_false;
7436       break;
7437     case ICmpInst::ICMP_SGT:
7438       if (RA.isMinSignedValue()) {
7439         Pred = ICmpInst::ICMP_NE;
7440         Changed = true;
7441         break;
7442       }
7443       if ((RA + 1).isMaxSignedValue()) {
7444         Pred = ICmpInst::ICMP_EQ;
7445         RHS = getConstant(RA + 1);
7446         Changed = true;
7447         break;
7448       }
7449       if (RA.isMaxSignedValue()) goto trivially_false;
7450       break;
7451     case ICmpInst::ICMP_SLT:
7452       if (RA.isMaxSignedValue()) {
7453         Pred = ICmpInst::ICMP_NE;
7454         Changed = true;
7455         break;
7456       }
7457       if ((RA - 1).isMinSignedValue()) {
7458        Pred = ICmpInst::ICMP_EQ;
7459        RHS = getConstant(RA - 1);
7460         Changed = true;
7461        break;
7462       }
7463       if (RA.isMinSignedValue()) goto trivially_false;
7464       break;
7465     }
7466   }
7467 
7468   // Check for obvious equality.
7469   if (HasSameValue(LHS, RHS)) {
7470     if (ICmpInst::isTrueWhenEqual(Pred))
7471       goto trivially_true;
7472     if (ICmpInst::isFalseWhenEqual(Pred))
7473       goto trivially_false;
7474   }
7475 
7476   // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
7477   // adding or subtracting 1 from one of the operands.
7478   switch (Pred) {
7479   case ICmpInst::ICMP_SLE:
7480     if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
7481       RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
7482                        SCEV::FlagNSW);
7483       Pred = ICmpInst::ICMP_SLT;
7484       Changed = true;
7485     } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
7486       LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
7487                        SCEV::FlagNSW);
7488       Pred = ICmpInst::ICMP_SLT;
7489       Changed = true;
7490     }
7491     break;
7492   case ICmpInst::ICMP_SGE:
7493     if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
7494       RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
7495                        SCEV::FlagNSW);
7496       Pred = ICmpInst::ICMP_SGT;
7497       Changed = true;
7498     } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
7499       LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
7500                        SCEV::FlagNSW);
7501       Pred = ICmpInst::ICMP_SGT;
7502       Changed = true;
7503     }
7504     break;
7505   case ICmpInst::ICMP_ULE:
7506     if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
7507       RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
7508                        SCEV::FlagNUW);
7509       Pred = ICmpInst::ICMP_ULT;
7510       Changed = true;
7511     } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
7512       LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS);
7513       Pred = ICmpInst::ICMP_ULT;
7514       Changed = true;
7515     }
7516     break;
7517   case ICmpInst::ICMP_UGE:
7518     if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
7519       RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
7520       Pred = ICmpInst::ICMP_UGT;
7521       Changed = true;
7522     } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
7523       LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
7524                        SCEV::FlagNUW);
7525       Pred = ICmpInst::ICMP_UGT;
7526       Changed = true;
7527     }
7528     break;
7529   default:
7530     break;
7531   }
7532 
7533   // TODO: More simplifications are possible here.
7534 
7535   // Recursively simplify until we either hit a recursion limit or nothing
7536   // changes.
7537   if (Changed)
7538     return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
7539 
7540   return Changed;
7541 
7542 trivially_true:
7543   // Return 0 == 0.
7544   LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
7545   Pred = ICmpInst::ICMP_EQ;
7546   return true;
7547 
7548 trivially_false:
7549   // Return 0 != 0.
7550   LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
7551   Pred = ICmpInst::ICMP_NE;
7552   return true;
7553 }
7554 
isKnownNegative(const SCEV * S)7555 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
7556   return getSignedRange(S).getSignedMax().isNegative();
7557 }
7558 
isKnownPositive(const SCEV * S)7559 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
7560   return getSignedRange(S).getSignedMin().isStrictlyPositive();
7561 }
7562 
isKnownNonNegative(const SCEV * S)7563 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
7564   return !getSignedRange(S).getSignedMin().isNegative();
7565 }
7566 
isKnownNonPositive(const SCEV * S)7567 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
7568   return !getSignedRange(S).getSignedMax().isStrictlyPositive();
7569 }
7570 
isKnownNonZero(const SCEV * S)7571 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
7572   return isKnownNegative(S) || isKnownPositive(S);
7573 }
7574 
isKnownPredicate(ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS)7575 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
7576                                        const SCEV *LHS, const SCEV *RHS) {
7577   // Canonicalize the inputs first.
7578   (void)SimplifyICmpOperands(Pred, LHS, RHS);
7579 
7580   // If LHS or RHS is an addrec, check to see if the condition is true in
7581   // every iteration of the loop.
7582   // If LHS and RHS are both addrec, both conditions must be true in
7583   // every iteration of the loop.
7584   const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
7585   const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
7586   bool LeftGuarded = false;
7587   bool RightGuarded = false;
7588   if (LAR) {
7589     const Loop *L = LAR->getLoop();
7590     if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
7591         isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
7592       if (!RAR) return true;
7593       LeftGuarded = true;
7594     }
7595   }
7596   if (RAR) {
7597     const Loop *L = RAR->getLoop();
7598     if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
7599         isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
7600       if (!LAR) return true;
7601       RightGuarded = true;
7602     }
7603   }
7604   if (LeftGuarded && RightGuarded)
7605     return true;
7606 
7607   if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
7608     return true;
7609 
7610   // Otherwise see what can be done with known constant ranges.
7611   return isKnownPredicateViaConstantRanges(Pred, LHS, RHS);
7612 }
7613 
isMonotonicPredicate(const SCEVAddRecExpr * LHS,ICmpInst::Predicate Pred,bool & Increasing)7614 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
7615                                            ICmpInst::Predicate Pred,
7616                                            bool &Increasing) {
7617   bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
7618 
7619 #ifndef NDEBUG
7620   // Verify an invariant: inverting the predicate should turn a monotonically
7621   // increasing change to a monotonically decreasing one, and vice versa.
7622   bool IncreasingSwapped;
7623   bool ResultSwapped = isMonotonicPredicateImpl(
7624       LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
7625 
7626   assert(Result == ResultSwapped && "should be able to analyze both!");
7627   if (ResultSwapped)
7628     assert(Increasing == !IncreasingSwapped &&
7629            "monotonicity should flip as we flip the predicate");
7630 #endif
7631 
7632   return Result;
7633 }
7634 
isMonotonicPredicateImpl(const SCEVAddRecExpr * LHS,ICmpInst::Predicate Pred,bool & Increasing)7635 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
7636                                                ICmpInst::Predicate Pred,
7637                                                bool &Increasing) {
7638 
7639   // A zero step value for LHS means the induction variable is essentially a
7640   // loop invariant value. We don't really depend on the predicate actually
7641   // flipping from false to true (for increasing predicates, and the other way
7642   // around for decreasing predicates), all we care about is that *if* the
7643   // predicate changes then it only changes from false to true.
7644   //
7645   // A zero step value in itself is not very useful, but there may be places
7646   // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
7647   // as general as possible.
7648 
7649   switch (Pred) {
7650   default:
7651     return false; // Conservative answer
7652 
7653   case ICmpInst::ICMP_UGT:
7654   case ICmpInst::ICMP_UGE:
7655   case ICmpInst::ICMP_ULT:
7656   case ICmpInst::ICMP_ULE:
7657     if (!LHS->hasNoUnsignedWrap())
7658       return false;
7659 
7660     Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
7661     return true;
7662 
7663   case ICmpInst::ICMP_SGT:
7664   case ICmpInst::ICMP_SGE:
7665   case ICmpInst::ICMP_SLT:
7666   case ICmpInst::ICMP_SLE: {
7667     if (!LHS->hasNoSignedWrap())
7668       return false;
7669 
7670     const SCEV *Step = LHS->getStepRecurrence(*this);
7671 
7672     if (isKnownNonNegative(Step)) {
7673       Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
7674       return true;
7675     }
7676 
7677     if (isKnownNonPositive(Step)) {
7678       Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
7679       return true;
7680     }
7681 
7682     return false;
7683   }
7684 
7685   }
7686 
7687   llvm_unreachable("switch has default clause!");
7688 }
7689 
isLoopInvariantPredicate(ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS,const Loop * L,ICmpInst::Predicate & InvariantPred,const SCEV * & InvariantLHS,const SCEV * & InvariantRHS)7690 bool ScalarEvolution::isLoopInvariantPredicate(
7691     ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
7692     ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
7693     const SCEV *&InvariantRHS) {
7694 
7695   // If there is a loop-invariant, force it into the RHS, otherwise bail out.
7696   if (!isLoopInvariant(RHS, L)) {
7697     if (!isLoopInvariant(LHS, L))
7698       return false;
7699 
7700     std::swap(LHS, RHS);
7701     Pred = ICmpInst::getSwappedPredicate(Pred);
7702   }
7703 
7704   const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
7705   if (!ArLHS || ArLHS->getLoop() != L)
7706     return false;
7707 
7708   bool Increasing;
7709   if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
7710     return false;
7711 
7712   // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
7713   // true as the loop iterates, and the backedge is control dependent on
7714   // "ArLHS `Pred` RHS" == true then we can reason as follows:
7715   //
7716   //   * if the predicate was false in the first iteration then the predicate
7717   //     is never evaluated again, since the loop exits without taking the
7718   //     backedge.
7719   //   * if the predicate was true in the first iteration then it will
7720   //     continue to be true for all future iterations since it is
7721   //     monotonically increasing.
7722   //
7723   // For both the above possibilities, we can replace the loop varying
7724   // predicate with its value on the first iteration of the loop (which is
7725   // loop invariant).
7726   //
7727   // A similar reasoning applies for a monotonically decreasing predicate, by
7728   // replacing true with false and false with true in the above two bullets.
7729 
7730   auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
7731 
7732   if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
7733     return false;
7734 
7735   InvariantPred = Pred;
7736   InvariantLHS = ArLHS->getStart();
7737   InvariantRHS = RHS;
7738   return true;
7739 }
7740 
isKnownPredicateViaConstantRanges(ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS)7741 bool ScalarEvolution::isKnownPredicateViaConstantRanges(
7742     ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
7743   if (HasSameValue(LHS, RHS))
7744     return ICmpInst::isTrueWhenEqual(Pred);
7745 
7746   // This code is split out from isKnownPredicate because it is called from
7747   // within isLoopEntryGuardedByCond.
7748 
7749   auto CheckRanges =
7750       [&](const ConstantRange &RangeLHS, const ConstantRange &RangeRHS) {
7751     return ConstantRange::makeSatisfyingICmpRegion(Pred, RangeRHS)
7752         .contains(RangeLHS);
7753   };
7754 
7755   // The check at the top of the function catches the case where the values are
7756   // known to be equal.
7757   if (Pred == CmpInst::ICMP_EQ)
7758     return false;
7759 
7760   if (Pred == CmpInst::ICMP_NE)
7761     return CheckRanges(getSignedRange(LHS), getSignedRange(RHS)) ||
7762            CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS)) ||
7763            isKnownNonZero(getMinusSCEV(LHS, RHS));
7764 
7765   if (CmpInst::isSigned(Pred))
7766     return CheckRanges(getSignedRange(LHS), getSignedRange(RHS));
7767 
7768   return CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS));
7769 }
7770 
isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS)7771 bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
7772                                                     const SCEV *LHS,
7773                                                     const SCEV *RHS) {
7774 
7775   // Match Result to (X + Y)<ExpectedFlags> where Y is a constant integer.
7776   // Return Y via OutY.
7777   auto MatchBinaryAddToConst =
7778       [this](const SCEV *Result, const SCEV *X, APInt &OutY,
7779              SCEV::NoWrapFlags ExpectedFlags) {
7780     const SCEV *NonConstOp, *ConstOp;
7781     SCEV::NoWrapFlags FlagsPresent;
7782 
7783     if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) ||
7784         !isa<SCEVConstant>(ConstOp) || NonConstOp != X)
7785       return false;
7786 
7787     OutY = cast<SCEVConstant>(ConstOp)->getAPInt();
7788     return (FlagsPresent & ExpectedFlags) == ExpectedFlags;
7789   };
7790 
7791   APInt C;
7792 
7793   switch (Pred) {
7794   default:
7795     break;
7796 
7797   case ICmpInst::ICMP_SGE:
7798     std::swap(LHS, RHS);
7799   case ICmpInst::ICMP_SLE:
7800     // X s<= (X + C)<nsw> if C >= 0
7801     if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative())
7802       return true;
7803 
7804     // (X + C)<nsw> s<= X if C <= 0
7805     if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) &&
7806         !C.isStrictlyPositive())
7807       return true;
7808     break;
7809 
7810   case ICmpInst::ICMP_SGT:
7811     std::swap(LHS, RHS);
7812   case ICmpInst::ICMP_SLT:
7813     // X s< (X + C)<nsw> if C > 0
7814     if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) &&
7815         C.isStrictlyPositive())
7816       return true;
7817 
7818     // (X + C)<nsw> s< X if C < 0
7819     if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative())
7820       return true;
7821     break;
7822   }
7823 
7824   return false;
7825 }
7826 
isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS)7827 bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
7828                                                    const SCEV *LHS,
7829                                                    const SCEV *RHS) {
7830   if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
7831     return false;
7832 
7833   // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
7834   // the stack can result in exponential time complexity.
7835   SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
7836 
7837   // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
7838   //
7839   // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
7840   // isKnownPredicate.  isKnownPredicate is more powerful, but also more
7841   // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
7842   // interesting cases seen in practice.  We can consider "upgrading" L >= 0 to
7843   // use isKnownPredicate later if needed.
7844   return isKnownNonNegative(RHS) &&
7845          isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
7846          isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS);
7847 }
7848 
isImpliedViaGuard(BasicBlock * BB,ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS)7849 bool ScalarEvolution::isImpliedViaGuard(BasicBlock *BB,
7850                                         ICmpInst::Predicate Pred,
7851                                         const SCEV *LHS, const SCEV *RHS) {
7852   // No need to even try if we know the module has no guards.
7853   if (!HasGuards)
7854     return false;
7855 
7856   return any_of(*BB, [&](Instruction &I) {
7857     using namespace llvm::PatternMatch;
7858 
7859     Value *Condition;
7860     return match(&I, m_Intrinsic<Intrinsic::experimental_guard>(
7861                          m_Value(Condition))) &&
7862            isImpliedCond(Pred, LHS, RHS, Condition, false);
7863   });
7864 }
7865 
7866 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
7867 /// protected by a conditional between LHS and RHS.  This is used to
7868 /// to eliminate casts.
7869 bool
isLoopBackedgeGuardedByCond(const Loop * L,ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS)7870 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
7871                                              ICmpInst::Predicate Pred,
7872                                              const SCEV *LHS, const SCEV *RHS) {
7873   // Interpret a null as meaning no loop, where there is obviously no guard
7874   // (interprocedural conditions notwithstanding).
7875   if (!L) return true;
7876 
7877   if (isKnownPredicateViaConstantRanges(Pred, LHS, RHS))
7878     return true;
7879 
7880   BasicBlock *Latch = L->getLoopLatch();
7881   if (!Latch)
7882     return false;
7883 
7884   BranchInst *LoopContinuePredicate =
7885     dyn_cast<BranchInst>(Latch->getTerminator());
7886   if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
7887       isImpliedCond(Pred, LHS, RHS,
7888                     LoopContinuePredicate->getCondition(),
7889                     LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
7890     return true;
7891 
7892   // We don't want more than one activation of the following loops on the stack
7893   // -- that can lead to O(n!) time complexity.
7894   if (WalkingBEDominatingConds)
7895     return false;
7896 
7897   SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
7898 
7899   // See if we can exploit a trip count to prove the predicate.
7900   const auto &BETakenInfo = getBackedgeTakenInfo(L);
7901   const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
7902   if (LatchBECount != getCouldNotCompute()) {
7903     // We know that Latch branches back to the loop header exactly
7904     // LatchBECount times.  This means the backdege condition at Latch is
7905     // equivalent to  "{0,+,1} u< LatchBECount".
7906     Type *Ty = LatchBECount->getType();
7907     auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
7908     const SCEV *LoopCounter =
7909       getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
7910     if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
7911                       LatchBECount))
7912       return true;
7913   }
7914 
7915   // Check conditions due to any @llvm.assume intrinsics.
7916   for (auto &AssumeVH : AC.assumptions()) {
7917     if (!AssumeVH)
7918       continue;
7919     auto *CI = cast<CallInst>(AssumeVH);
7920     if (!DT.dominates(CI, Latch->getTerminator()))
7921       continue;
7922 
7923     if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7924       return true;
7925   }
7926 
7927   // If the loop is not reachable from the entry block, we risk running into an
7928   // infinite loop as we walk up into the dom tree.  These loops do not matter
7929   // anyway, so we just return a conservative answer when we see them.
7930   if (!DT.isReachableFromEntry(L->getHeader()))
7931     return false;
7932 
7933   if (isImpliedViaGuard(Latch, Pred, LHS, RHS))
7934     return true;
7935 
7936   for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
7937        DTN != HeaderDTN; DTN = DTN->getIDom()) {
7938 
7939     assert(DTN && "should reach the loop header before reaching the root!");
7940 
7941     BasicBlock *BB = DTN->getBlock();
7942     if (isImpliedViaGuard(BB, Pred, LHS, RHS))
7943       return true;
7944 
7945     BasicBlock *PBB = BB->getSinglePredecessor();
7946     if (!PBB)
7947       continue;
7948 
7949     BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
7950     if (!ContinuePredicate || !ContinuePredicate->isConditional())
7951       continue;
7952 
7953     Value *Condition = ContinuePredicate->getCondition();
7954 
7955     // If we have an edge `E` within the loop body that dominates the only
7956     // latch, the condition guarding `E` also guards the backedge.  This
7957     // reasoning works only for loops with a single latch.
7958 
7959     BasicBlockEdge DominatingEdge(PBB, BB);
7960     if (DominatingEdge.isSingleEdge()) {
7961       // We're constructively (and conservatively) enumerating edges within the
7962       // loop body that dominate the latch.  The dominator tree better agree
7963       // with us on this:
7964       assert(DT.dominates(DominatingEdge, Latch) && "should be!");
7965 
7966       if (isImpliedCond(Pred, LHS, RHS, Condition,
7967                         BB != ContinuePredicate->getSuccessor(0)))
7968         return true;
7969     }
7970   }
7971 
7972   return false;
7973 }
7974 
7975 bool
isLoopEntryGuardedByCond(const Loop * L,ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS)7976 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
7977                                           ICmpInst::Predicate Pred,
7978                                           const SCEV *LHS, const SCEV *RHS) {
7979   // Interpret a null as meaning no loop, where there is obviously no guard
7980   // (interprocedural conditions notwithstanding).
7981   if (!L) return false;
7982 
7983   if (isKnownPredicateViaConstantRanges(Pred, LHS, RHS))
7984     return true;
7985 
7986   // Starting at the loop predecessor, climb up the predecessor chain, as long
7987   // as there are predecessors that can be found that have unique successors
7988   // leading to the original header.
7989   for (std::pair<BasicBlock *, BasicBlock *>
7990          Pair(L->getLoopPredecessor(), L->getHeader());
7991        Pair.first;
7992        Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
7993 
7994     if (isImpliedViaGuard(Pair.first, Pred, LHS, RHS))
7995       return true;
7996 
7997     BranchInst *LoopEntryPredicate =
7998       dyn_cast<BranchInst>(Pair.first->getTerminator());
7999     if (!LoopEntryPredicate ||
8000         LoopEntryPredicate->isUnconditional())
8001       continue;
8002 
8003     if (isImpliedCond(Pred, LHS, RHS,
8004                       LoopEntryPredicate->getCondition(),
8005                       LoopEntryPredicate->getSuccessor(0) != Pair.second))
8006       return true;
8007   }
8008 
8009   // Check conditions due to any @llvm.assume intrinsics.
8010   for (auto &AssumeVH : AC.assumptions()) {
8011     if (!AssumeVH)
8012       continue;
8013     auto *CI = cast<CallInst>(AssumeVH);
8014     if (!DT.dominates(CI, L->getHeader()))
8015       continue;
8016 
8017     if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
8018       return true;
8019   }
8020 
8021   return false;
8022 }
8023 
8024 namespace {
8025 /// RAII wrapper to prevent recursive application of isImpliedCond.
8026 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
8027 /// currently evaluating isImpliedCond.
8028 struct MarkPendingLoopPredicate {
8029   Value *Cond;
8030   DenseSet<Value*> &LoopPreds;
8031   bool Pending;
8032 
MarkPendingLoopPredicate__anon6eb5a8bf1411::MarkPendingLoopPredicate8033   MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
8034     : Cond(C), LoopPreds(LP) {
8035     Pending = !LoopPreds.insert(Cond).second;
8036   }
~MarkPendingLoopPredicate__anon6eb5a8bf1411::MarkPendingLoopPredicate8037   ~MarkPendingLoopPredicate() {
8038     if (!Pending)
8039       LoopPreds.erase(Cond);
8040   }
8041 };
8042 } // end anonymous namespace
8043 
isImpliedCond(ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS,Value * FoundCondValue,bool Inverse)8044 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
8045                                     const SCEV *LHS, const SCEV *RHS,
8046                                     Value *FoundCondValue,
8047                                     bool Inverse) {
8048   MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
8049   if (Mark.Pending)
8050     return false;
8051 
8052   // Recursively handle And and Or conditions.
8053   if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
8054     if (BO->getOpcode() == Instruction::And) {
8055       if (!Inverse)
8056         return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
8057                isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
8058     } else if (BO->getOpcode() == Instruction::Or) {
8059       if (Inverse)
8060         return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
8061                isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
8062     }
8063   }
8064 
8065   ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
8066   if (!ICI) return false;
8067 
8068   // Now that we found a conditional branch that dominates the loop or controls
8069   // the loop latch. Check to see if it is the comparison we are looking for.
8070   ICmpInst::Predicate FoundPred;
8071   if (Inverse)
8072     FoundPred = ICI->getInversePredicate();
8073   else
8074     FoundPred = ICI->getPredicate();
8075 
8076   const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
8077   const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
8078 
8079   return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS);
8080 }
8081 
isImpliedCond(ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS,ICmpInst::Predicate FoundPred,const SCEV * FoundLHS,const SCEV * FoundRHS)8082 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
8083                                     const SCEV *RHS,
8084                                     ICmpInst::Predicate FoundPred,
8085                                     const SCEV *FoundLHS,
8086                                     const SCEV *FoundRHS) {
8087   // Balance the types.
8088   if (getTypeSizeInBits(LHS->getType()) <
8089       getTypeSizeInBits(FoundLHS->getType())) {
8090     if (CmpInst::isSigned(Pred)) {
8091       LHS = getSignExtendExpr(LHS, FoundLHS->getType());
8092       RHS = getSignExtendExpr(RHS, FoundLHS->getType());
8093     } else {
8094       LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
8095       RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
8096     }
8097   } else if (getTypeSizeInBits(LHS->getType()) >
8098       getTypeSizeInBits(FoundLHS->getType())) {
8099     if (CmpInst::isSigned(FoundPred)) {
8100       FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
8101       FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
8102     } else {
8103       FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
8104       FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
8105     }
8106   }
8107 
8108   // Canonicalize the query to match the way instcombine will have
8109   // canonicalized the comparison.
8110   if (SimplifyICmpOperands(Pred, LHS, RHS))
8111     if (LHS == RHS)
8112       return CmpInst::isTrueWhenEqual(Pred);
8113   if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
8114     if (FoundLHS == FoundRHS)
8115       return CmpInst::isFalseWhenEqual(FoundPred);
8116 
8117   // Check to see if we can make the LHS or RHS match.
8118   if (LHS == FoundRHS || RHS == FoundLHS) {
8119     if (isa<SCEVConstant>(RHS)) {
8120       std::swap(FoundLHS, FoundRHS);
8121       FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
8122     } else {
8123       std::swap(LHS, RHS);
8124       Pred = ICmpInst::getSwappedPredicate(Pred);
8125     }
8126   }
8127 
8128   // Check whether the found predicate is the same as the desired predicate.
8129   if (FoundPred == Pred)
8130     return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
8131 
8132   // Check whether swapping the found predicate makes it the same as the
8133   // desired predicate.
8134   if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
8135     if (isa<SCEVConstant>(RHS))
8136       return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
8137     else
8138       return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
8139                                    RHS, LHS, FoundLHS, FoundRHS);
8140   }
8141 
8142   // Unsigned comparison is the same as signed comparison when both the operands
8143   // are non-negative.
8144   if (CmpInst::isUnsigned(FoundPred) &&
8145       CmpInst::getSignedPredicate(FoundPred) == Pred &&
8146       isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS))
8147     return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
8148 
8149   // Check if we can make progress by sharpening ranges.
8150   if (FoundPred == ICmpInst::ICMP_NE &&
8151       (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
8152 
8153     const SCEVConstant *C = nullptr;
8154     const SCEV *V = nullptr;
8155 
8156     if (isa<SCEVConstant>(FoundLHS)) {
8157       C = cast<SCEVConstant>(FoundLHS);
8158       V = FoundRHS;
8159     } else {
8160       C = cast<SCEVConstant>(FoundRHS);
8161       V = FoundLHS;
8162     }
8163 
8164     // The guarding predicate tells us that C != V. If the known range
8165     // of V is [C, t), we can sharpen the range to [C + 1, t).  The
8166     // range we consider has to correspond to same signedness as the
8167     // predicate we're interested in folding.
8168 
8169     APInt Min = ICmpInst::isSigned(Pred) ?
8170         getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
8171 
8172     if (Min == C->getAPInt()) {
8173       // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
8174       // This is true even if (Min + 1) wraps around -- in case of
8175       // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
8176 
8177       APInt SharperMin = Min + 1;
8178 
8179       switch (Pred) {
8180         case ICmpInst::ICMP_SGE:
8181         case ICmpInst::ICMP_UGE:
8182           // We know V `Pred` SharperMin.  If this implies LHS `Pred`
8183           // RHS, we're done.
8184           if (isImpliedCondOperands(Pred, LHS, RHS, V,
8185                                     getConstant(SharperMin)))
8186             return true;
8187 
8188         case ICmpInst::ICMP_SGT:
8189         case ICmpInst::ICMP_UGT:
8190           // We know from the range information that (V `Pred` Min ||
8191           // V == Min).  We know from the guarding condition that !(V
8192           // == Min).  This gives us
8193           //
8194           //       V `Pred` Min || V == Min && !(V == Min)
8195           //   =>  V `Pred` Min
8196           //
8197           // If V `Pred` Min implies LHS `Pred` RHS, we're done.
8198 
8199           if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
8200             return true;
8201 
8202         default:
8203           // No change
8204           break;
8205       }
8206     }
8207   }
8208 
8209   // Check whether the actual condition is beyond sufficient.
8210   if (FoundPred == ICmpInst::ICMP_EQ)
8211     if (ICmpInst::isTrueWhenEqual(Pred))
8212       if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
8213         return true;
8214   if (Pred == ICmpInst::ICMP_NE)
8215     if (!ICmpInst::isTrueWhenEqual(FoundPred))
8216       if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
8217         return true;
8218 
8219   // Otherwise assume the worst.
8220   return false;
8221 }
8222 
splitBinaryAdd(const SCEV * Expr,const SCEV * & L,const SCEV * & R,SCEV::NoWrapFlags & Flags)8223 bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr,
8224                                      const SCEV *&L, const SCEV *&R,
8225                                      SCEV::NoWrapFlags &Flags) {
8226   const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
8227   if (!AE || AE->getNumOperands() != 2)
8228     return false;
8229 
8230   L = AE->getOperand(0);
8231   R = AE->getOperand(1);
8232   Flags = AE->getNoWrapFlags();
8233   return true;
8234 }
8235 
computeConstantDifference(const SCEV * Less,const SCEV * More,APInt & C)8236 bool ScalarEvolution::computeConstantDifference(const SCEV *Less,
8237                                                 const SCEV *More,
8238                                                 APInt &C) {
8239   // We avoid subtracting expressions here because this function is usually
8240   // fairly deep in the call stack (i.e. is called many times).
8241 
8242   if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
8243     const auto *LAR = cast<SCEVAddRecExpr>(Less);
8244     const auto *MAR = cast<SCEVAddRecExpr>(More);
8245 
8246     if (LAR->getLoop() != MAR->getLoop())
8247       return false;
8248 
8249     // We look at affine expressions only; not for correctness but to keep
8250     // getStepRecurrence cheap.
8251     if (!LAR->isAffine() || !MAR->isAffine())
8252       return false;
8253 
8254     if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
8255       return false;
8256 
8257     Less = LAR->getStart();
8258     More = MAR->getStart();
8259 
8260     // fall through
8261   }
8262 
8263   if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
8264     const auto &M = cast<SCEVConstant>(More)->getAPInt();
8265     const auto &L = cast<SCEVConstant>(Less)->getAPInt();
8266     C = M - L;
8267     return true;
8268   }
8269 
8270   const SCEV *L, *R;
8271   SCEV::NoWrapFlags Flags;
8272   if (splitBinaryAdd(Less, L, R, Flags))
8273     if (const auto *LC = dyn_cast<SCEVConstant>(L))
8274       if (R == More) {
8275         C = -(LC->getAPInt());
8276         return true;
8277       }
8278 
8279   if (splitBinaryAdd(More, L, R, Flags))
8280     if (const auto *LC = dyn_cast<SCEVConstant>(L))
8281       if (R == Less) {
8282         C = LC->getAPInt();
8283         return true;
8284       }
8285 
8286   return false;
8287 }
8288 
isImpliedCondOperandsViaNoOverflow(ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS,const SCEV * FoundLHS,const SCEV * FoundRHS)8289 bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
8290     ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
8291     const SCEV *FoundLHS, const SCEV *FoundRHS) {
8292   if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
8293     return false;
8294 
8295   const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
8296   if (!AddRecLHS)
8297     return false;
8298 
8299   const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
8300   if (!AddRecFoundLHS)
8301     return false;
8302 
8303   // We'd like to let SCEV reason about control dependencies, so we constrain
8304   // both the inequalities to be about add recurrences on the same loop.  This
8305   // way we can use isLoopEntryGuardedByCond later.
8306 
8307   const Loop *L = AddRecFoundLHS->getLoop();
8308   if (L != AddRecLHS->getLoop())
8309     return false;
8310 
8311   //  FoundLHS u< FoundRHS u< -C =>  (FoundLHS + C) u< (FoundRHS + C) ... (1)
8312   //
8313   //  FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
8314   //                                                                  ... (2)
8315   //
8316   // Informal proof for (2), assuming (1) [*]:
8317   //
8318   // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
8319   //
8320   // Then
8321   //
8322   //       FoundLHS s< FoundRHS s< INT_MIN - C
8323   // <=>  (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C   [ using (3) ]
8324   // <=>  (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
8325   // <=>  (FoundLHS + INT_MIN + C + INT_MIN) s<
8326   //                        (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
8327   // <=>  FoundLHS + C s< FoundRHS + C
8328   //
8329   // [*]: (1) can be proved by ruling out overflow.
8330   //
8331   // [**]: This can be proved by analyzing all the four possibilities:
8332   //    (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
8333   //    (A s>= 0, B s>= 0).
8334   //
8335   // Note:
8336   // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
8337   // will not sign underflow.  For instance, say FoundLHS = (i8 -128), FoundRHS
8338   // = (i8 -127) and C = (i8 -100).  Then INT_MIN - C = (i8 -28), and FoundRHS
8339   // s< (INT_MIN - C).  Lack of sign overflow / underflow in "FoundRHS + C" is
8340   // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
8341   // C)".
8342 
8343   APInt LDiff, RDiff;
8344   if (!computeConstantDifference(FoundLHS, LHS, LDiff) ||
8345       !computeConstantDifference(FoundRHS, RHS, RDiff) ||
8346       LDiff != RDiff)
8347     return false;
8348 
8349   if (LDiff == 0)
8350     return true;
8351 
8352   APInt FoundRHSLimit;
8353 
8354   if (Pred == CmpInst::ICMP_ULT) {
8355     FoundRHSLimit = -RDiff;
8356   } else {
8357     assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
8358     FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - RDiff;
8359   }
8360 
8361   // Try to prove (1) or (2), as needed.
8362   return isLoopEntryGuardedByCond(L, Pred, FoundRHS,
8363                                   getConstant(FoundRHSLimit));
8364 }
8365 
isImpliedCondOperands(ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS,const SCEV * FoundLHS,const SCEV * FoundRHS)8366 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
8367                                             const SCEV *LHS, const SCEV *RHS,
8368                                             const SCEV *FoundLHS,
8369                                             const SCEV *FoundRHS) {
8370   if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
8371     return true;
8372 
8373   if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
8374     return true;
8375 
8376   return isImpliedCondOperandsHelper(Pred, LHS, RHS,
8377                                      FoundLHS, FoundRHS) ||
8378          // ~x < ~y --> x > y
8379          isImpliedCondOperandsHelper(Pred, LHS, RHS,
8380                                      getNotSCEV(FoundRHS),
8381                                      getNotSCEV(FoundLHS));
8382 }
8383 
8384 
8385 /// If Expr computes ~A, return A else return nullptr
MatchNotExpr(const SCEV * Expr)8386 static const SCEV *MatchNotExpr(const SCEV *Expr) {
8387   const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
8388   if (!Add || Add->getNumOperands() != 2 ||
8389       !Add->getOperand(0)->isAllOnesValue())
8390     return nullptr;
8391 
8392   const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
8393   if (!AddRHS || AddRHS->getNumOperands() != 2 ||
8394       !AddRHS->getOperand(0)->isAllOnesValue())
8395     return nullptr;
8396 
8397   return AddRHS->getOperand(1);
8398 }
8399 
8400 
8401 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
8402 template<typename MaxExprType>
IsMaxConsistingOf(const SCEV * MaybeMaxExpr,const SCEV * Candidate)8403 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
8404                               const SCEV *Candidate) {
8405   const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
8406   if (!MaxExpr) return false;
8407 
8408   return find(MaxExpr->operands(), Candidate) != MaxExpr->op_end();
8409 }
8410 
8411 
8412 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
8413 template<typename MaxExprType>
IsMinConsistingOf(ScalarEvolution & SE,const SCEV * MaybeMinExpr,const SCEV * Candidate)8414 static bool IsMinConsistingOf(ScalarEvolution &SE,
8415                               const SCEV *MaybeMinExpr,
8416                               const SCEV *Candidate) {
8417   const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
8418   if (!MaybeMaxExpr)
8419     return false;
8420 
8421   return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
8422 }
8423 
IsKnownPredicateViaAddRecStart(ScalarEvolution & SE,ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS)8424 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
8425                                            ICmpInst::Predicate Pred,
8426                                            const SCEV *LHS, const SCEV *RHS) {
8427 
8428   // If both sides are affine addrecs for the same loop, with equal
8429   // steps, and we know the recurrences don't wrap, then we only
8430   // need to check the predicate on the starting values.
8431 
8432   if (!ICmpInst::isRelational(Pred))
8433     return false;
8434 
8435   const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
8436   if (!LAR)
8437     return false;
8438   const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
8439   if (!RAR)
8440     return false;
8441   if (LAR->getLoop() != RAR->getLoop())
8442     return false;
8443   if (!LAR->isAffine() || !RAR->isAffine())
8444     return false;
8445 
8446   if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
8447     return false;
8448 
8449   SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
8450                          SCEV::FlagNSW : SCEV::FlagNUW;
8451   if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
8452     return false;
8453 
8454   return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
8455 }
8456 
8457 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
8458 /// expression?
IsKnownPredicateViaMinOrMax(ScalarEvolution & SE,ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS)8459 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
8460                                         ICmpInst::Predicate Pred,
8461                                         const SCEV *LHS, const SCEV *RHS) {
8462   switch (Pred) {
8463   default:
8464     return false;
8465 
8466   case ICmpInst::ICMP_SGE:
8467     std::swap(LHS, RHS);
8468     // fall through
8469   case ICmpInst::ICMP_SLE:
8470     return
8471       // min(A, ...) <= A
8472       IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
8473       // A <= max(A, ...)
8474       IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
8475 
8476   case ICmpInst::ICMP_UGE:
8477     std::swap(LHS, RHS);
8478     // fall through
8479   case ICmpInst::ICMP_ULE:
8480     return
8481       // min(A, ...) <= A
8482       IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
8483       // A <= max(A, ...)
8484       IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
8485   }
8486 
8487   llvm_unreachable("covered switch fell through?!");
8488 }
8489 
8490 bool
isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS,const SCEV * FoundLHS,const SCEV * FoundRHS)8491 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
8492                                              const SCEV *LHS, const SCEV *RHS,
8493                                              const SCEV *FoundLHS,
8494                                              const SCEV *FoundRHS) {
8495   auto IsKnownPredicateFull =
8496       [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
8497     return isKnownPredicateViaConstantRanges(Pred, LHS, RHS) ||
8498            IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
8499            IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
8500            isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
8501   };
8502 
8503   switch (Pred) {
8504   default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
8505   case ICmpInst::ICMP_EQ:
8506   case ICmpInst::ICMP_NE:
8507     if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
8508       return true;
8509     break;
8510   case ICmpInst::ICMP_SLT:
8511   case ICmpInst::ICMP_SLE:
8512     if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
8513         IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
8514       return true;
8515     break;
8516   case ICmpInst::ICMP_SGT:
8517   case ICmpInst::ICMP_SGE:
8518     if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
8519         IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
8520       return true;
8521     break;
8522   case ICmpInst::ICMP_ULT:
8523   case ICmpInst::ICMP_ULE:
8524     if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
8525         IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
8526       return true;
8527     break;
8528   case ICmpInst::ICMP_UGT:
8529   case ICmpInst::ICMP_UGE:
8530     if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
8531         IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
8532       return true;
8533     break;
8534   }
8535 
8536   return false;
8537 }
8538 
isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,const SCEV * LHS,const SCEV * RHS,const SCEV * FoundLHS,const SCEV * FoundRHS)8539 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
8540                                                      const SCEV *LHS,
8541                                                      const SCEV *RHS,
8542                                                      const SCEV *FoundLHS,
8543                                                      const SCEV *FoundRHS) {
8544   if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
8545     // The restriction on `FoundRHS` be lifted easily -- it exists only to
8546     // reduce the compile time impact of this optimization.
8547     return false;
8548 
8549   const SCEVAddExpr *AddLHS = dyn_cast<SCEVAddExpr>(LHS);
8550   if (!AddLHS || AddLHS->getOperand(1) != FoundLHS ||
8551       !isa<SCEVConstant>(AddLHS->getOperand(0)))
8552     return false;
8553 
8554   APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getAPInt();
8555 
8556   // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
8557   // antecedent "`FoundLHS` `Pred` `FoundRHS`".
8558   ConstantRange FoundLHSRange =
8559       ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
8560 
8561   // Since `LHS` is `FoundLHS` + `AddLHS->getOperand(0)`, we can compute a range
8562   // for `LHS`:
8563   APInt Addend = cast<SCEVConstant>(AddLHS->getOperand(0))->getAPInt();
8564   ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(Addend));
8565 
8566   // We can also compute the range of values for `LHS` that satisfy the
8567   // consequent, "`LHS` `Pred` `RHS`":
8568   APInt ConstRHS = cast<SCEVConstant>(RHS)->getAPInt();
8569   ConstantRange SatisfyingLHSRange =
8570       ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
8571 
8572   // The antecedent implies the consequent if every value of `LHS` that
8573   // satisfies the antecedent also satisfies the consequent.
8574   return SatisfyingLHSRange.contains(LHSRange);
8575 }
8576 
doesIVOverflowOnLT(const SCEV * RHS,const SCEV * Stride,bool IsSigned,bool NoWrap)8577 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
8578                                          bool IsSigned, bool NoWrap) {
8579   if (NoWrap) return false;
8580 
8581   unsigned BitWidth = getTypeSizeInBits(RHS->getType());
8582   const SCEV *One = getOne(Stride->getType());
8583 
8584   if (IsSigned) {
8585     APInt MaxRHS = getSignedRange(RHS).getSignedMax();
8586     APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
8587     APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
8588                                 .getSignedMax();
8589 
8590     // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
8591     return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
8592   }
8593 
8594   APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
8595   APInt MaxValue = APInt::getMaxValue(BitWidth);
8596   APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
8597                               .getUnsignedMax();
8598 
8599   // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
8600   return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
8601 }
8602 
doesIVOverflowOnGT(const SCEV * RHS,const SCEV * Stride,bool IsSigned,bool NoWrap)8603 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
8604                                          bool IsSigned, bool NoWrap) {
8605   if (NoWrap) return false;
8606 
8607   unsigned BitWidth = getTypeSizeInBits(RHS->getType());
8608   const SCEV *One = getOne(Stride->getType());
8609 
8610   if (IsSigned) {
8611     APInt MinRHS = getSignedRange(RHS).getSignedMin();
8612     APInt MinValue = APInt::getSignedMinValue(BitWidth);
8613     APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
8614                                .getSignedMax();
8615 
8616     // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
8617     return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
8618   }
8619 
8620   APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
8621   APInt MinValue = APInt::getMinValue(BitWidth);
8622   APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
8623                             .getUnsignedMax();
8624 
8625   // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
8626   return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
8627 }
8628 
computeBECount(const SCEV * Delta,const SCEV * Step,bool Equality)8629 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
8630                                             bool Equality) {
8631   const SCEV *One = getOne(Step->getType());
8632   Delta = Equality ? getAddExpr(Delta, Step)
8633                    : getAddExpr(Delta, getMinusSCEV(Step, One));
8634   return getUDivExpr(Delta, Step);
8635 }
8636 
8637 ScalarEvolution::ExitLimit
howManyLessThans(const SCEV * LHS,const SCEV * RHS,const Loop * L,bool IsSigned,bool ControlsExit,bool AllowPredicates)8638 ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS,
8639                                   const Loop *L, bool IsSigned,
8640                                   bool ControlsExit, bool AllowPredicates) {
8641   SCEVUnionPredicate P;
8642   // We handle only IV < Invariant
8643   if (!isLoopInvariant(RHS, L))
8644     return getCouldNotCompute();
8645 
8646   const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8647   if (!IV && AllowPredicates)
8648     // Try to make this an AddRec using runtime tests, in the first X
8649     // iterations of this loop, where X is the SCEV expression found by the
8650     // algorithm below.
8651     IV = convertSCEVToAddRecWithPredicates(LHS, L, P);
8652 
8653   // Avoid weird loops
8654   if (!IV || IV->getLoop() != L || !IV->isAffine())
8655     return getCouldNotCompute();
8656 
8657   bool NoWrap = ControlsExit &&
8658                 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8659 
8660   const SCEV *Stride = IV->getStepRecurrence(*this);
8661 
8662   // Avoid negative or zero stride values
8663   if (!isKnownPositive(Stride))
8664     return getCouldNotCompute();
8665 
8666   // Avoid proven overflow cases: this will ensure that the backedge taken count
8667   // will not generate any unsigned overflow. Relaxed no-overflow conditions
8668   // exploit NoWrapFlags, allowing to optimize in presence of undefined
8669   // behaviors like the case of C language.
8670   if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
8671     return getCouldNotCompute();
8672 
8673   ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
8674                                       : ICmpInst::ICMP_ULT;
8675   const SCEV *Start = IV->getStart();
8676   const SCEV *End = RHS;
8677   if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
8678     End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start);
8679 
8680   const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
8681 
8682   APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
8683                             : getUnsignedRange(Start).getUnsignedMin();
8684 
8685   APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8686                              : getUnsignedRange(Stride).getUnsignedMin();
8687 
8688   unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8689   APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
8690                          : APInt::getMaxValue(BitWidth) - (MinStride - 1);
8691 
8692   // Although End can be a MAX expression we estimate MaxEnd considering only
8693   // the case End = RHS. This is safe because in the other case (End - Start)
8694   // is zero, leading to a zero maximum backedge taken count.
8695   APInt MaxEnd =
8696     IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
8697              : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
8698 
8699   const SCEV *MaxBECount;
8700   if (isa<SCEVConstant>(BECount))
8701     MaxBECount = BECount;
8702   else
8703     MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
8704                                 getConstant(MinStride), false);
8705 
8706   if (isa<SCEVCouldNotCompute>(MaxBECount))
8707     MaxBECount = BECount;
8708 
8709   return ExitLimit(BECount, MaxBECount, P);
8710 }
8711 
8712 ScalarEvolution::ExitLimit
howManyGreaterThans(const SCEV * LHS,const SCEV * RHS,const Loop * L,bool IsSigned,bool ControlsExit,bool AllowPredicates)8713 ScalarEvolution::howManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
8714                                      const Loop *L, bool IsSigned,
8715                                      bool ControlsExit, bool AllowPredicates) {
8716   SCEVUnionPredicate P;
8717   // We handle only IV > Invariant
8718   if (!isLoopInvariant(RHS, L))
8719     return getCouldNotCompute();
8720 
8721   const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8722   if (!IV && AllowPredicates)
8723     // Try to make this an AddRec using runtime tests, in the first X
8724     // iterations of this loop, where X is the SCEV expression found by the
8725     // algorithm below.
8726     IV = convertSCEVToAddRecWithPredicates(LHS, L, P);
8727 
8728   // Avoid weird loops
8729   if (!IV || IV->getLoop() != L || !IV->isAffine())
8730     return getCouldNotCompute();
8731 
8732   bool NoWrap = ControlsExit &&
8733                 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8734 
8735   const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
8736 
8737   // Avoid negative or zero stride values
8738   if (!isKnownPositive(Stride))
8739     return getCouldNotCompute();
8740 
8741   // Avoid proven overflow cases: this will ensure that the backedge taken count
8742   // will not generate any unsigned overflow. Relaxed no-overflow conditions
8743   // exploit NoWrapFlags, allowing to optimize in presence of undefined
8744   // behaviors like the case of C language.
8745   if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
8746     return getCouldNotCompute();
8747 
8748   ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
8749                                       : ICmpInst::ICMP_UGT;
8750 
8751   const SCEV *Start = IV->getStart();
8752   const SCEV *End = RHS;
8753   if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS))
8754     End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start);
8755 
8756   const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
8757 
8758   APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
8759                             : getUnsignedRange(Start).getUnsignedMax();
8760 
8761   APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8762                              : getUnsignedRange(Stride).getUnsignedMin();
8763 
8764   unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8765   APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
8766                          : APInt::getMinValue(BitWidth) + (MinStride - 1);
8767 
8768   // Although End can be a MIN expression we estimate MinEnd considering only
8769   // the case End = RHS. This is safe because in the other case (Start - End)
8770   // is zero, leading to a zero maximum backedge taken count.
8771   APInt MinEnd =
8772     IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
8773              : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
8774 
8775 
8776   const SCEV *MaxBECount = getCouldNotCompute();
8777   if (isa<SCEVConstant>(BECount))
8778     MaxBECount = BECount;
8779   else
8780     MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
8781                                 getConstant(MinStride), false);
8782 
8783   if (isa<SCEVCouldNotCompute>(MaxBECount))
8784     MaxBECount = BECount;
8785 
8786   return ExitLimit(BECount, MaxBECount, P);
8787 }
8788 
getNumIterationsInRange(const ConstantRange & Range,ScalarEvolution & SE) const8789 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(const ConstantRange &Range,
8790                                                     ScalarEvolution &SE) const {
8791   if (Range.isFullSet())  // Infinite loop.
8792     return SE.getCouldNotCompute();
8793 
8794   // If the start is a non-zero constant, shift the range to simplify things.
8795   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
8796     if (!SC->getValue()->isZero()) {
8797       SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
8798       Operands[0] = SE.getZero(SC->getType());
8799       const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
8800                                              getNoWrapFlags(FlagNW));
8801       if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
8802         return ShiftedAddRec->getNumIterationsInRange(
8803             Range.subtract(SC->getAPInt()), SE);
8804       // This is strange and shouldn't happen.
8805       return SE.getCouldNotCompute();
8806     }
8807 
8808   // The only time we can solve this is when we have all constant indices.
8809   // Otherwise, we cannot determine the overflow conditions.
8810   if (any_of(operands(), [](const SCEV *Op) { return !isa<SCEVConstant>(Op); }))
8811     return SE.getCouldNotCompute();
8812 
8813   // Okay at this point we know that all elements of the chrec are constants and
8814   // that the start element is zero.
8815 
8816   // First check to see if the range contains zero.  If not, the first
8817   // iteration exits.
8818   unsigned BitWidth = SE.getTypeSizeInBits(getType());
8819   if (!Range.contains(APInt(BitWidth, 0)))
8820     return SE.getZero(getType());
8821 
8822   if (isAffine()) {
8823     // If this is an affine expression then we have this situation:
8824     //   Solve {0,+,A} in Range  ===  Ax in Range
8825 
8826     // We know that zero is in the range.  If A is positive then we know that
8827     // the upper value of the range must be the first possible exit value.
8828     // If A is negative then the lower of the range is the last possible loop
8829     // value.  Also note that we already checked for a full range.
8830     APInt One(BitWidth,1);
8831     APInt A = cast<SCEVConstant>(getOperand(1))->getAPInt();
8832     APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
8833 
8834     // The exit value should be (End+A)/A.
8835     APInt ExitVal = (End + A).udiv(A);
8836     ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
8837 
8838     // Evaluate at the exit value.  If we really did fall out of the valid
8839     // range, then we computed our trip count, otherwise wrap around or other
8840     // things must have happened.
8841     ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
8842     if (Range.contains(Val->getValue()))
8843       return SE.getCouldNotCompute();  // Something strange happened
8844 
8845     // Ensure that the previous value is in the range.  This is a sanity check.
8846     assert(Range.contains(
8847            EvaluateConstantChrecAtConstant(this,
8848            ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
8849            "Linear scev computation is off in a bad way!");
8850     return SE.getConstant(ExitValue);
8851   } else if (isQuadratic()) {
8852     // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
8853     // quadratic equation to solve it.  To do this, we must frame our problem in
8854     // terms of figuring out when zero is crossed, instead of when
8855     // Range.getUpper() is crossed.
8856     SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
8857     NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
8858     const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
8859                                              // getNoWrapFlags(FlagNW)
8860                                              FlagAnyWrap);
8861 
8862     // Next, solve the constructed addrec
8863     if (auto Roots =
8864             SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE)) {
8865       const SCEVConstant *R1 = Roots->first;
8866       const SCEVConstant *R2 = Roots->second;
8867       // Pick the smallest positive root value.
8868       if (ConstantInt *CB = dyn_cast<ConstantInt>(ConstantExpr::getICmp(
8869               ICmpInst::ICMP_ULT, R1->getValue(), R2->getValue()))) {
8870         if (!CB->getZExtValue())
8871           std::swap(R1, R2); // R1 is the minimum root now.
8872 
8873         // Make sure the root is not off by one.  The returned iteration should
8874         // not be in the range, but the previous one should be.  When solving
8875         // for "X*X < 5", for example, we should not return a root of 2.
8876         ConstantInt *R1Val =
8877             EvaluateConstantChrecAtConstant(this, R1->getValue(), SE);
8878         if (Range.contains(R1Val->getValue())) {
8879           // The next iteration must be out of the range...
8880           ConstantInt *NextVal =
8881               ConstantInt::get(SE.getContext(), R1->getAPInt() + 1);
8882 
8883           R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8884           if (!Range.contains(R1Val->getValue()))
8885             return SE.getConstant(NextVal);
8886           return SE.getCouldNotCompute(); // Something strange happened
8887         }
8888 
8889         // If R1 was not in the range, then it is a good return value.  Make
8890         // sure that R1-1 WAS in the range though, just in case.
8891         ConstantInt *NextVal =
8892             ConstantInt::get(SE.getContext(), R1->getAPInt() - 1);
8893         R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8894         if (Range.contains(R1Val->getValue()))
8895           return R1;
8896         return SE.getCouldNotCompute(); // Something strange happened
8897       }
8898     }
8899   }
8900 
8901   return SE.getCouldNotCompute();
8902 }
8903 
8904 namespace {
8905 struct FindUndefs {
8906   bool Found;
FindUndefs__anon6eb5a8bf1711::FindUndefs8907   FindUndefs() : Found(false) {}
8908 
follow__anon6eb5a8bf1711::FindUndefs8909   bool follow(const SCEV *S) {
8910     if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
8911       if (isa<UndefValue>(C->getValue()))
8912         Found = true;
8913     } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
8914       if (isa<UndefValue>(C->getValue()))
8915         Found = true;
8916     }
8917 
8918     // Keep looking if we haven't found it yet.
8919     return !Found;
8920   }
isDone__anon6eb5a8bf1711::FindUndefs8921   bool isDone() const {
8922     // Stop recursion if we have found an undef.
8923     return Found;
8924   }
8925 };
8926 }
8927 
8928 // Return true when S contains at least an undef value.
8929 static inline bool
containsUndefs(const SCEV * S)8930 containsUndefs(const SCEV *S) {
8931   FindUndefs F;
8932   SCEVTraversal<FindUndefs> ST(F);
8933   ST.visitAll(S);
8934 
8935   return F.Found;
8936 }
8937 
8938 namespace {
8939 // Collect all steps of SCEV expressions.
8940 struct SCEVCollectStrides {
8941   ScalarEvolution &SE;
8942   SmallVectorImpl<const SCEV *> &Strides;
8943 
SCEVCollectStrides__anon6eb5a8bf1811::SCEVCollectStrides8944   SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
8945       : SE(SE), Strides(S) {}
8946 
follow__anon6eb5a8bf1811::SCEVCollectStrides8947   bool follow(const SCEV *S) {
8948     if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
8949       Strides.push_back(AR->getStepRecurrence(SE));
8950     return true;
8951   }
isDone__anon6eb5a8bf1811::SCEVCollectStrides8952   bool isDone() const { return false; }
8953 };
8954 
8955 // Collect all SCEVUnknown and SCEVMulExpr expressions.
8956 struct SCEVCollectTerms {
8957   SmallVectorImpl<const SCEV *> &Terms;
8958 
SCEVCollectTerms__anon6eb5a8bf1811::SCEVCollectTerms8959   SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
8960       : Terms(T) {}
8961 
follow__anon6eb5a8bf1811::SCEVCollectTerms8962   bool follow(const SCEV *S) {
8963     if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
8964       if (!containsUndefs(S))
8965         Terms.push_back(S);
8966 
8967       // Stop recursion: once we collected a term, do not walk its operands.
8968       return false;
8969     }
8970 
8971     // Keep looking.
8972     return true;
8973   }
isDone__anon6eb5a8bf1811::SCEVCollectTerms8974   bool isDone() const { return false; }
8975 };
8976 
8977 // Check if a SCEV contains an AddRecExpr.
8978 struct SCEVHasAddRec {
8979   bool &ContainsAddRec;
8980 
SCEVHasAddRec__anon6eb5a8bf1811::SCEVHasAddRec8981   SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) {
8982    ContainsAddRec = false;
8983   }
8984 
follow__anon6eb5a8bf1811::SCEVHasAddRec8985   bool follow(const SCEV *S) {
8986     if (isa<SCEVAddRecExpr>(S)) {
8987       ContainsAddRec = true;
8988 
8989       // Stop recursion: once we collected a term, do not walk its operands.
8990       return false;
8991     }
8992 
8993     // Keep looking.
8994     return true;
8995   }
isDone__anon6eb5a8bf1811::SCEVHasAddRec8996   bool isDone() const { return false; }
8997 };
8998 
8999 // Find factors that are multiplied with an expression that (possibly as a
9000 // subexpression) contains an AddRecExpr. In the expression:
9001 //
9002 //  8 * (100 +  %p * %q * (%a + {0, +, 1}_loop))
9003 //
9004 // "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)"
9005 // that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size
9006 // parameters as they form a product with an induction variable.
9007 //
9008 // This collector expects all array size parameters to be in the same MulExpr.
9009 // It might be necessary to later add support for collecting parameters that are
9010 // spread over different nested MulExpr.
9011 struct SCEVCollectAddRecMultiplies {
9012   SmallVectorImpl<const SCEV *> &Terms;
9013   ScalarEvolution &SE;
9014 
SCEVCollectAddRecMultiplies__anon6eb5a8bf1811::SCEVCollectAddRecMultiplies9015   SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE)
9016       : Terms(T), SE(SE) {}
9017 
follow__anon6eb5a8bf1811::SCEVCollectAddRecMultiplies9018   bool follow(const SCEV *S) {
9019     if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) {
9020       bool HasAddRec = false;
9021       SmallVector<const SCEV *, 0> Operands;
9022       for (auto Op : Mul->operands()) {
9023         if (isa<SCEVUnknown>(Op)) {
9024           Operands.push_back(Op);
9025         } else {
9026           bool ContainsAddRec;
9027           SCEVHasAddRec ContiansAddRec(ContainsAddRec);
9028           visitAll(Op, ContiansAddRec);
9029           HasAddRec |= ContainsAddRec;
9030         }
9031       }
9032       if (Operands.size() == 0)
9033         return true;
9034 
9035       if (!HasAddRec)
9036         return false;
9037 
9038       Terms.push_back(SE.getMulExpr(Operands));
9039       // Stop recursion: once we collected a term, do not walk its operands.
9040       return false;
9041     }
9042 
9043     // Keep looking.
9044     return true;
9045   }
isDone__anon6eb5a8bf1811::SCEVCollectAddRecMultiplies9046   bool isDone() const { return false; }
9047 };
9048 }
9049 
9050 /// Find parametric terms in this SCEVAddRecExpr. We first for parameters in
9051 /// two places:
9052 ///   1) The strides of AddRec expressions.
9053 ///   2) Unknowns that are multiplied with AddRec expressions.
collectParametricTerms(const SCEV * Expr,SmallVectorImpl<const SCEV * > & Terms)9054 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
9055     SmallVectorImpl<const SCEV *> &Terms) {
9056   SmallVector<const SCEV *, 4> Strides;
9057   SCEVCollectStrides StrideCollector(*this, Strides);
9058   visitAll(Expr, StrideCollector);
9059 
9060   DEBUG({
9061       dbgs() << "Strides:\n";
9062       for (const SCEV *S : Strides)
9063         dbgs() << *S << "\n";
9064     });
9065 
9066   for (const SCEV *S : Strides) {
9067     SCEVCollectTerms TermCollector(Terms);
9068     visitAll(S, TermCollector);
9069   }
9070 
9071   DEBUG({
9072       dbgs() << "Terms:\n";
9073       for (const SCEV *T : Terms)
9074         dbgs() << *T << "\n";
9075     });
9076 
9077   SCEVCollectAddRecMultiplies MulCollector(Terms, *this);
9078   visitAll(Expr, MulCollector);
9079 }
9080 
findArrayDimensionsRec(ScalarEvolution & SE,SmallVectorImpl<const SCEV * > & Terms,SmallVectorImpl<const SCEV * > & Sizes)9081 static bool findArrayDimensionsRec(ScalarEvolution &SE,
9082                                    SmallVectorImpl<const SCEV *> &Terms,
9083                                    SmallVectorImpl<const SCEV *> &Sizes) {
9084   int Last = Terms.size() - 1;
9085   const SCEV *Step = Terms[Last];
9086 
9087   // End of recursion.
9088   if (Last == 0) {
9089     if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
9090       SmallVector<const SCEV *, 2> Qs;
9091       for (const SCEV *Op : M->operands())
9092         if (!isa<SCEVConstant>(Op))
9093           Qs.push_back(Op);
9094 
9095       Step = SE.getMulExpr(Qs);
9096     }
9097 
9098     Sizes.push_back(Step);
9099     return true;
9100   }
9101 
9102   for (const SCEV *&Term : Terms) {
9103     // Normalize the terms before the next call to findArrayDimensionsRec.
9104     const SCEV *Q, *R;
9105     SCEVDivision::divide(SE, Term, Step, &Q, &R);
9106 
9107     // Bail out when GCD does not evenly divide one of the terms.
9108     if (!R->isZero())
9109       return false;
9110 
9111     Term = Q;
9112   }
9113 
9114   // Remove all SCEVConstants.
9115   Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
9116                 return isa<SCEVConstant>(E);
9117               }),
9118               Terms.end());
9119 
9120   if (Terms.size() > 0)
9121     if (!findArrayDimensionsRec(SE, Terms, Sizes))
9122       return false;
9123 
9124   Sizes.push_back(Step);
9125   return true;
9126 }
9127 
9128 // Returns true when S contains at least a SCEVUnknown parameter.
9129 static inline bool
containsParameters(const SCEV * S)9130 containsParameters(const SCEV *S) {
9131   struct FindParameter {
9132     bool FoundParameter;
9133     FindParameter() : FoundParameter(false) {}
9134 
9135     bool follow(const SCEV *S) {
9136       if (isa<SCEVUnknown>(S)) {
9137         FoundParameter = true;
9138         // Stop recursion: we found a parameter.
9139         return false;
9140       }
9141       // Keep looking.
9142       return true;
9143     }
9144     bool isDone() const {
9145       // Stop recursion if we have found a parameter.
9146       return FoundParameter;
9147     }
9148   };
9149 
9150   FindParameter F;
9151   SCEVTraversal<FindParameter> ST(F);
9152   ST.visitAll(S);
9153 
9154   return F.FoundParameter;
9155 }
9156 
9157 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
9158 static inline bool
containsParameters(SmallVectorImpl<const SCEV * > & Terms)9159 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
9160   for (const SCEV *T : Terms)
9161     if (containsParameters(T))
9162       return true;
9163   return false;
9164 }
9165 
9166 // Return the number of product terms in S.
numberOfTerms(const SCEV * S)9167 static inline int numberOfTerms(const SCEV *S) {
9168   if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
9169     return Expr->getNumOperands();
9170   return 1;
9171 }
9172 
removeConstantFactors(ScalarEvolution & SE,const SCEV * T)9173 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
9174   if (isa<SCEVConstant>(T))
9175     return nullptr;
9176 
9177   if (isa<SCEVUnknown>(T))
9178     return T;
9179 
9180   if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
9181     SmallVector<const SCEV *, 2> Factors;
9182     for (const SCEV *Op : M->operands())
9183       if (!isa<SCEVConstant>(Op))
9184         Factors.push_back(Op);
9185 
9186     return SE.getMulExpr(Factors);
9187   }
9188 
9189   return T;
9190 }
9191 
9192 /// Return the size of an element read or written by Inst.
getElementSize(Instruction * Inst)9193 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
9194   Type *Ty;
9195   if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
9196     Ty = Store->getValueOperand()->getType();
9197   else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
9198     Ty = Load->getType();
9199   else
9200     return nullptr;
9201 
9202   Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
9203   return getSizeOfExpr(ETy, Ty);
9204 }
9205 
findArrayDimensions(SmallVectorImpl<const SCEV * > & Terms,SmallVectorImpl<const SCEV * > & Sizes,const SCEV * ElementSize) const9206 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
9207                                           SmallVectorImpl<const SCEV *> &Sizes,
9208                                           const SCEV *ElementSize) const {
9209   if (Terms.size() < 1 || !ElementSize)
9210     return;
9211 
9212   // Early return when Terms do not contain parameters: we do not delinearize
9213   // non parametric SCEVs.
9214   if (!containsParameters(Terms))
9215     return;
9216 
9217   DEBUG({
9218       dbgs() << "Terms:\n";
9219       for (const SCEV *T : Terms)
9220         dbgs() << *T << "\n";
9221     });
9222 
9223   // Remove duplicates.
9224   std::sort(Terms.begin(), Terms.end());
9225   Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
9226 
9227   // Put larger terms first.
9228   std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
9229     return numberOfTerms(LHS) > numberOfTerms(RHS);
9230   });
9231 
9232   ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9233 
9234   // Try to divide all terms by the element size. If term is not divisible by
9235   // element size, proceed with the original term.
9236   for (const SCEV *&Term : Terms) {
9237     const SCEV *Q, *R;
9238     SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
9239     if (!Q->isZero())
9240       Term = Q;
9241   }
9242 
9243   SmallVector<const SCEV *, 4> NewTerms;
9244 
9245   // Remove constant factors.
9246   for (const SCEV *T : Terms)
9247     if (const SCEV *NewT = removeConstantFactors(SE, T))
9248       NewTerms.push_back(NewT);
9249 
9250   DEBUG({
9251       dbgs() << "Terms after sorting:\n";
9252       for (const SCEV *T : NewTerms)
9253         dbgs() << *T << "\n";
9254     });
9255 
9256   if (NewTerms.empty() ||
9257       !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
9258     Sizes.clear();
9259     return;
9260   }
9261 
9262   // The last element to be pushed into Sizes is the size of an element.
9263   Sizes.push_back(ElementSize);
9264 
9265   DEBUG({
9266       dbgs() << "Sizes:\n";
9267       for (const SCEV *S : Sizes)
9268         dbgs() << *S << "\n";
9269     });
9270 }
9271 
computeAccessFunctions(const SCEV * Expr,SmallVectorImpl<const SCEV * > & Subscripts,SmallVectorImpl<const SCEV * > & Sizes)9272 void ScalarEvolution::computeAccessFunctions(
9273     const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
9274     SmallVectorImpl<const SCEV *> &Sizes) {
9275 
9276   // Early exit in case this SCEV is not an affine multivariate function.
9277   if (Sizes.empty())
9278     return;
9279 
9280   if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr))
9281     if (!AR->isAffine())
9282       return;
9283 
9284   const SCEV *Res = Expr;
9285   int Last = Sizes.size() - 1;
9286   for (int i = Last; i >= 0; i--) {
9287     const SCEV *Q, *R;
9288     SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
9289 
9290     DEBUG({
9291         dbgs() << "Res: " << *Res << "\n";
9292         dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
9293         dbgs() << "Res divided by Sizes[i]:\n";
9294         dbgs() << "Quotient: " << *Q << "\n";
9295         dbgs() << "Remainder: " << *R << "\n";
9296       });
9297 
9298     Res = Q;
9299 
9300     // Do not record the last subscript corresponding to the size of elements in
9301     // the array.
9302     if (i == Last) {
9303 
9304       // Bail out if the remainder is too complex.
9305       if (isa<SCEVAddRecExpr>(R)) {
9306         Subscripts.clear();
9307         Sizes.clear();
9308         return;
9309       }
9310 
9311       continue;
9312     }
9313 
9314     // Record the access function for the current subscript.
9315     Subscripts.push_back(R);
9316   }
9317 
9318   // Also push in last position the remainder of the last division: it will be
9319   // the access function of the innermost dimension.
9320   Subscripts.push_back(Res);
9321 
9322   std::reverse(Subscripts.begin(), Subscripts.end());
9323 
9324   DEBUG({
9325       dbgs() << "Subscripts:\n";
9326       for (const SCEV *S : Subscripts)
9327         dbgs() << *S << "\n";
9328     });
9329 }
9330 
9331 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
9332 /// sizes of an array access. Returns the remainder of the delinearization that
9333 /// is the offset start of the array.  The SCEV->delinearize algorithm computes
9334 /// the multiples of SCEV coefficients: that is a pattern matching of sub
9335 /// expressions in the stride and base of a SCEV corresponding to the
9336 /// computation of a GCD (greatest common divisor) of base and stride.  When
9337 /// SCEV->delinearize fails, it returns the SCEV unchanged.
9338 ///
9339 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
9340 ///
9341 ///  void foo(long n, long m, long o, double A[n][m][o]) {
9342 ///
9343 ///    for (long i = 0; i < n; i++)
9344 ///      for (long j = 0; j < m; j++)
9345 ///        for (long k = 0; k < o; k++)
9346 ///          A[i][j][k] = 1.0;
9347 ///  }
9348 ///
9349 /// the delinearization input is the following AddRec SCEV:
9350 ///
9351 ///  AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
9352 ///
9353 /// From this SCEV, we are able to say that the base offset of the access is %A
9354 /// because it appears as an offset that does not divide any of the strides in
9355 /// the loops:
9356 ///
9357 ///  CHECK: Base offset: %A
9358 ///
9359 /// and then SCEV->delinearize determines the size of some of the dimensions of
9360 /// the array as these are the multiples by which the strides are happening:
9361 ///
9362 ///  CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
9363 ///
9364 /// Note that the outermost dimension remains of UnknownSize because there are
9365 /// no strides that would help identifying the size of the last dimension: when
9366 /// the array has been statically allocated, one could compute the size of that
9367 /// dimension by dividing the overall size of the array by the size of the known
9368 /// dimensions: %m * %o * 8.
9369 ///
9370 /// Finally delinearize provides the access functions for the array reference
9371 /// that does correspond to A[i][j][k] of the above C testcase:
9372 ///
9373 ///  CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
9374 ///
9375 /// The testcases are checking the output of a function pass:
9376 /// DelinearizationPass that walks through all loads and stores of a function
9377 /// asking for the SCEV of the memory access with respect to all enclosing
9378 /// loops, calling SCEV->delinearize on that and printing the results.
9379 
delinearize(const SCEV * Expr,SmallVectorImpl<const SCEV * > & Subscripts,SmallVectorImpl<const SCEV * > & Sizes,const SCEV * ElementSize)9380 void ScalarEvolution::delinearize(const SCEV *Expr,
9381                                  SmallVectorImpl<const SCEV *> &Subscripts,
9382                                  SmallVectorImpl<const SCEV *> &Sizes,
9383                                  const SCEV *ElementSize) {
9384   // First step: collect parametric terms.
9385   SmallVector<const SCEV *, 4> Terms;
9386   collectParametricTerms(Expr, Terms);
9387 
9388   if (Terms.empty())
9389     return;
9390 
9391   // Second step: find subscript sizes.
9392   findArrayDimensions(Terms, Sizes, ElementSize);
9393 
9394   if (Sizes.empty())
9395     return;
9396 
9397   // Third step: compute the access functions for each subscript.
9398   computeAccessFunctions(Expr, Subscripts, Sizes);
9399 
9400   if (Subscripts.empty())
9401     return;
9402 
9403   DEBUG({
9404       dbgs() << "succeeded to delinearize " << *Expr << "\n";
9405       dbgs() << "ArrayDecl[UnknownSize]";
9406       for (const SCEV *S : Sizes)
9407         dbgs() << "[" << *S << "]";
9408 
9409       dbgs() << "\nArrayRef";
9410       for (const SCEV *S : Subscripts)
9411         dbgs() << "[" << *S << "]";
9412       dbgs() << "\n";
9413     });
9414 }
9415 
9416 //===----------------------------------------------------------------------===//
9417 //                   SCEVCallbackVH Class Implementation
9418 //===----------------------------------------------------------------------===//
9419 
deleted()9420 void ScalarEvolution::SCEVCallbackVH::deleted() {
9421   assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
9422   if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
9423     SE->ConstantEvolutionLoopExitValue.erase(PN);
9424   SE->eraseValueFromMap(getValPtr());
9425   // this now dangles!
9426 }
9427 
allUsesReplacedWith(Value * V)9428 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
9429   assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
9430 
9431   // Forget all the expressions associated with users of the old value,
9432   // so that future queries will recompute the expressions using the new
9433   // value.
9434   Value *Old = getValPtr();
9435   SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
9436   SmallPtrSet<User *, 8> Visited;
9437   while (!Worklist.empty()) {
9438     User *U = Worklist.pop_back_val();
9439     // Deleting the Old value will cause this to dangle. Postpone
9440     // that until everything else is done.
9441     if (U == Old)
9442       continue;
9443     if (!Visited.insert(U).second)
9444       continue;
9445     if (PHINode *PN = dyn_cast<PHINode>(U))
9446       SE->ConstantEvolutionLoopExitValue.erase(PN);
9447     SE->eraseValueFromMap(U);
9448     Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
9449   }
9450   // Delete the Old value.
9451   if (PHINode *PN = dyn_cast<PHINode>(Old))
9452     SE->ConstantEvolutionLoopExitValue.erase(PN);
9453   SE->eraseValueFromMap(Old);
9454   // this now dangles!
9455 }
9456 
SCEVCallbackVH(Value * V,ScalarEvolution * se)9457 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
9458   : CallbackVH(V), SE(se) {}
9459 
9460 //===----------------------------------------------------------------------===//
9461 //                   ScalarEvolution Class Implementation
9462 //===----------------------------------------------------------------------===//
9463 
ScalarEvolution(Function & F,TargetLibraryInfo & TLI,AssumptionCache & AC,DominatorTree & DT,LoopInfo & LI)9464 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
9465                                  AssumptionCache &AC, DominatorTree &DT,
9466                                  LoopInfo &LI)
9467     : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
9468       CouldNotCompute(new SCEVCouldNotCompute()),
9469       WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
9470       ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64),
9471       FirstUnknown(nullptr) {
9472 
9473   // To use guards for proving predicates, we need to scan every instruction in
9474   // relevant basic blocks, and not just terminators.  Doing this is a waste of
9475   // time if the IR does not actually contain any calls to
9476   // @llvm.experimental.guard, so do a quick check and remember this beforehand.
9477   //
9478   // This pessimizes the case where a pass that preserves ScalarEvolution wants
9479   // to _add_ guards to the module when there weren't any before, and wants
9480   // ScalarEvolution to optimize based on those guards.  For now we prefer to be
9481   // efficient in lieu of being smart in that rather obscure case.
9482 
9483   auto *GuardDecl = F.getParent()->getFunction(
9484       Intrinsic::getName(Intrinsic::experimental_guard));
9485   HasGuards = GuardDecl && !GuardDecl->use_empty();
9486 }
9487 
ScalarEvolution(ScalarEvolution && Arg)9488 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
9489     : F(Arg.F), HasGuards(Arg.HasGuards), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT),
9490       LI(Arg.LI), CouldNotCompute(std::move(Arg.CouldNotCompute)),
9491       ValueExprMap(std::move(Arg.ValueExprMap)),
9492       WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
9493       BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
9494       PredicatedBackedgeTakenCounts(
9495           std::move(Arg.PredicatedBackedgeTakenCounts)),
9496       ConstantEvolutionLoopExitValue(
9497           std::move(Arg.ConstantEvolutionLoopExitValue)),
9498       ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
9499       LoopDispositions(std::move(Arg.LoopDispositions)),
9500       BlockDispositions(std::move(Arg.BlockDispositions)),
9501       UnsignedRanges(std::move(Arg.UnsignedRanges)),
9502       SignedRanges(std::move(Arg.SignedRanges)),
9503       UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
9504       UniquePreds(std::move(Arg.UniquePreds)),
9505       SCEVAllocator(std::move(Arg.SCEVAllocator)),
9506       FirstUnknown(Arg.FirstUnknown) {
9507   Arg.FirstUnknown = nullptr;
9508 }
9509 
~ScalarEvolution()9510 ScalarEvolution::~ScalarEvolution() {
9511   // Iterate through all the SCEVUnknown instances and call their
9512   // destructors, so that they release their references to their values.
9513   for (SCEVUnknown *U = FirstUnknown; U;) {
9514     SCEVUnknown *Tmp = U;
9515     U = U->Next;
9516     Tmp->~SCEVUnknown();
9517   }
9518   FirstUnknown = nullptr;
9519 
9520   ExprValueMap.clear();
9521   ValueExprMap.clear();
9522   HasRecMap.clear();
9523 
9524   // Free any extra memory created for ExitNotTakenInfo in the unlikely event
9525   // that a loop had multiple computable exits.
9526   for (auto &BTCI : BackedgeTakenCounts)
9527     BTCI.second.clear();
9528   for (auto &BTCI : PredicatedBackedgeTakenCounts)
9529     BTCI.second.clear();
9530 
9531   assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
9532   assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
9533   assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
9534 }
9535 
hasLoopInvariantBackedgeTakenCount(const Loop * L)9536 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
9537   return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
9538 }
9539 
PrintLoopInfo(raw_ostream & OS,ScalarEvolution * SE,const Loop * L)9540 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
9541                           const Loop *L) {
9542   // Print all inner loops first
9543   for (Loop *I : *L)
9544     PrintLoopInfo(OS, SE, I);
9545 
9546   OS << "Loop ";
9547   L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9548   OS << ": ";
9549 
9550   SmallVector<BasicBlock *, 8> ExitBlocks;
9551   L->getExitBlocks(ExitBlocks);
9552   if (ExitBlocks.size() != 1)
9553     OS << "<multiple exits> ";
9554 
9555   if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
9556     OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
9557   } else {
9558     OS << "Unpredictable backedge-taken count. ";
9559   }
9560 
9561   OS << "\n"
9562         "Loop ";
9563   L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9564   OS << ": ";
9565 
9566   if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
9567     OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
9568   } else {
9569     OS << "Unpredictable max backedge-taken count. ";
9570   }
9571 
9572   OS << "\n"
9573         "Loop ";
9574   L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9575   OS << ": ";
9576 
9577   SCEVUnionPredicate Pred;
9578   auto PBT = SE->getPredicatedBackedgeTakenCount(L, Pred);
9579   if (!isa<SCEVCouldNotCompute>(PBT)) {
9580     OS << "Predicated backedge-taken count is " << *PBT << "\n";
9581     OS << " Predicates:\n";
9582     Pred.print(OS, 4);
9583   } else {
9584     OS << "Unpredictable predicated backedge-taken count. ";
9585   }
9586   OS << "\n";
9587 }
9588 
loopDispositionToStr(ScalarEvolution::LoopDisposition LD)9589 static StringRef loopDispositionToStr(ScalarEvolution::LoopDisposition LD) {
9590   switch (LD) {
9591   case ScalarEvolution::LoopVariant:
9592     return "Variant";
9593   case ScalarEvolution::LoopInvariant:
9594     return "Invariant";
9595   case ScalarEvolution::LoopComputable:
9596     return "Computable";
9597   }
9598   llvm_unreachable("Unknown ScalarEvolution::LoopDisposition kind!");
9599 }
9600 
print(raw_ostream & OS) const9601 void ScalarEvolution::print(raw_ostream &OS) const {
9602   // ScalarEvolution's implementation of the print method is to print
9603   // out SCEV values of all instructions that are interesting. Doing
9604   // this potentially causes it to create new SCEV objects though,
9605   // which technically conflicts with the const qualifier. This isn't
9606   // observable from outside the class though, so casting away the
9607   // const isn't dangerous.
9608   ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9609 
9610   OS << "Classifying expressions for: ";
9611   F.printAsOperand(OS, /*PrintType=*/false);
9612   OS << "\n";
9613   for (Instruction &I : instructions(F))
9614     if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) {
9615       OS << I << '\n';
9616       OS << "  -->  ";
9617       const SCEV *SV = SE.getSCEV(&I);
9618       SV->print(OS);
9619       if (!isa<SCEVCouldNotCompute>(SV)) {
9620         OS << " U: ";
9621         SE.getUnsignedRange(SV).print(OS);
9622         OS << " S: ";
9623         SE.getSignedRange(SV).print(OS);
9624       }
9625 
9626       const Loop *L = LI.getLoopFor(I.getParent());
9627 
9628       const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
9629       if (AtUse != SV) {
9630         OS << "  -->  ";
9631         AtUse->print(OS);
9632         if (!isa<SCEVCouldNotCompute>(AtUse)) {
9633           OS << " U: ";
9634           SE.getUnsignedRange(AtUse).print(OS);
9635           OS << " S: ";
9636           SE.getSignedRange(AtUse).print(OS);
9637         }
9638       }
9639 
9640       if (L) {
9641         OS << "\t\t" "Exits: ";
9642         const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
9643         if (!SE.isLoopInvariant(ExitValue, L)) {
9644           OS << "<<Unknown>>";
9645         } else {
9646           OS << *ExitValue;
9647         }
9648 
9649         bool First = true;
9650         for (auto *Iter = L; Iter; Iter = Iter->getParentLoop()) {
9651           if (First) {
9652             OS << "\t\t" "LoopDispositions: { ";
9653             First = false;
9654           } else {
9655             OS << ", ";
9656           }
9657 
9658           Iter->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9659           OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, Iter));
9660         }
9661 
9662         for (auto *InnerL : depth_first(L)) {
9663           if (InnerL == L)
9664             continue;
9665           if (First) {
9666             OS << "\t\t" "LoopDispositions: { ";
9667             First = false;
9668           } else {
9669             OS << ", ";
9670           }
9671 
9672           InnerL->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9673           OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, InnerL));
9674         }
9675 
9676         OS << " }";
9677       }
9678 
9679       OS << "\n";
9680     }
9681 
9682   OS << "Determining loop execution counts for: ";
9683   F.printAsOperand(OS, /*PrintType=*/false);
9684   OS << "\n";
9685   for (Loop *I : LI)
9686     PrintLoopInfo(OS, &SE, I);
9687 }
9688 
9689 ScalarEvolution::LoopDisposition
getLoopDisposition(const SCEV * S,const Loop * L)9690 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
9691   auto &Values = LoopDispositions[S];
9692   for (auto &V : Values) {
9693     if (V.getPointer() == L)
9694       return V.getInt();
9695   }
9696   Values.emplace_back(L, LoopVariant);
9697   LoopDisposition D = computeLoopDisposition(S, L);
9698   auto &Values2 = LoopDispositions[S];
9699   for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9700     if (V.getPointer() == L) {
9701       V.setInt(D);
9702       break;
9703     }
9704   }
9705   return D;
9706 }
9707 
9708 ScalarEvolution::LoopDisposition
computeLoopDisposition(const SCEV * S,const Loop * L)9709 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
9710   switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9711   case scConstant:
9712     return LoopInvariant;
9713   case scTruncate:
9714   case scZeroExtend:
9715   case scSignExtend:
9716     return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
9717   case scAddRecExpr: {
9718     const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9719 
9720     // If L is the addrec's loop, it's computable.
9721     if (AR->getLoop() == L)
9722       return LoopComputable;
9723 
9724     // Add recurrences are never invariant in the function-body (null loop).
9725     if (!L)
9726       return LoopVariant;
9727 
9728     // This recurrence is variant w.r.t. L if L contains AR's loop.
9729     if (L->contains(AR->getLoop()))
9730       return LoopVariant;
9731 
9732     // This recurrence is invariant w.r.t. L if AR's loop contains L.
9733     if (AR->getLoop()->contains(L))
9734       return LoopInvariant;
9735 
9736     // This recurrence is variant w.r.t. L if any of its operands
9737     // are variant.
9738     for (auto *Op : AR->operands())
9739       if (!isLoopInvariant(Op, L))
9740         return LoopVariant;
9741 
9742     // Otherwise it's loop-invariant.
9743     return LoopInvariant;
9744   }
9745   case scAddExpr:
9746   case scMulExpr:
9747   case scUMaxExpr:
9748   case scSMaxExpr: {
9749     bool HasVarying = false;
9750     for (auto *Op : cast<SCEVNAryExpr>(S)->operands()) {
9751       LoopDisposition D = getLoopDisposition(Op, L);
9752       if (D == LoopVariant)
9753         return LoopVariant;
9754       if (D == LoopComputable)
9755         HasVarying = true;
9756     }
9757     return HasVarying ? LoopComputable : LoopInvariant;
9758   }
9759   case scUDivExpr: {
9760     const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9761     LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
9762     if (LD == LoopVariant)
9763       return LoopVariant;
9764     LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
9765     if (RD == LoopVariant)
9766       return LoopVariant;
9767     return (LD == LoopInvariant && RD == LoopInvariant) ?
9768            LoopInvariant : LoopComputable;
9769   }
9770   case scUnknown:
9771     // All non-instruction values are loop invariant.  All instructions are loop
9772     // invariant if they are not contained in the specified loop.
9773     // Instructions are never considered invariant in the function body
9774     // (null loop) because they are defined within the "loop".
9775     if (auto *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
9776       return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
9777     return LoopInvariant;
9778   case scCouldNotCompute:
9779     llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9780   }
9781   llvm_unreachable("Unknown SCEV kind!");
9782 }
9783 
isLoopInvariant(const SCEV * S,const Loop * L)9784 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
9785   return getLoopDisposition(S, L) == LoopInvariant;
9786 }
9787 
hasComputableLoopEvolution(const SCEV * S,const Loop * L)9788 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
9789   return getLoopDisposition(S, L) == LoopComputable;
9790 }
9791 
9792 ScalarEvolution::BlockDisposition
getBlockDisposition(const SCEV * S,const BasicBlock * BB)9793 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9794   auto &Values = BlockDispositions[S];
9795   for (auto &V : Values) {
9796     if (V.getPointer() == BB)
9797       return V.getInt();
9798   }
9799   Values.emplace_back(BB, DoesNotDominateBlock);
9800   BlockDisposition D = computeBlockDisposition(S, BB);
9801   auto &Values2 = BlockDispositions[S];
9802   for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9803     if (V.getPointer() == BB) {
9804       V.setInt(D);
9805       break;
9806     }
9807   }
9808   return D;
9809 }
9810 
9811 ScalarEvolution::BlockDisposition
computeBlockDisposition(const SCEV * S,const BasicBlock * BB)9812 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9813   switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9814   case scConstant:
9815     return ProperlyDominatesBlock;
9816   case scTruncate:
9817   case scZeroExtend:
9818   case scSignExtend:
9819     return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
9820   case scAddRecExpr: {
9821     // This uses a "dominates" query instead of "properly dominates" query
9822     // to test for proper dominance too, because the instruction which
9823     // produces the addrec's value is a PHI, and a PHI effectively properly
9824     // dominates its entire containing block.
9825     const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9826     if (!DT.dominates(AR->getLoop()->getHeader(), BB))
9827       return DoesNotDominateBlock;
9828   }
9829   // FALL THROUGH into SCEVNAryExpr handling.
9830   case scAddExpr:
9831   case scMulExpr:
9832   case scUMaxExpr:
9833   case scSMaxExpr: {
9834     const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
9835     bool Proper = true;
9836     for (const SCEV *NAryOp : NAry->operands()) {
9837       BlockDisposition D = getBlockDisposition(NAryOp, BB);
9838       if (D == DoesNotDominateBlock)
9839         return DoesNotDominateBlock;
9840       if (D == DominatesBlock)
9841         Proper = false;
9842     }
9843     return Proper ? ProperlyDominatesBlock : DominatesBlock;
9844   }
9845   case scUDivExpr: {
9846     const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9847     const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
9848     BlockDisposition LD = getBlockDisposition(LHS, BB);
9849     if (LD == DoesNotDominateBlock)
9850       return DoesNotDominateBlock;
9851     BlockDisposition RD = getBlockDisposition(RHS, BB);
9852     if (RD == DoesNotDominateBlock)
9853       return DoesNotDominateBlock;
9854     return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
9855       ProperlyDominatesBlock : DominatesBlock;
9856   }
9857   case scUnknown:
9858     if (Instruction *I =
9859           dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
9860       if (I->getParent() == BB)
9861         return DominatesBlock;
9862       if (DT.properlyDominates(I->getParent(), BB))
9863         return ProperlyDominatesBlock;
9864       return DoesNotDominateBlock;
9865     }
9866     return ProperlyDominatesBlock;
9867   case scCouldNotCompute:
9868     llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9869   }
9870   llvm_unreachable("Unknown SCEV kind!");
9871 }
9872 
dominates(const SCEV * S,const BasicBlock * BB)9873 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
9874   return getBlockDisposition(S, BB) >= DominatesBlock;
9875 }
9876 
properlyDominates(const SCEV * S,const BasicBlock * BB)9877 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
9878   return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
9879 }
9880 
hasOperand(const SCEV * S,const SCEV * Op) const9881 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
9882   // Search for a SCEV expression node within an expression tree.
9883   // Implements SCEVTraversal::Visitor.
9884   struct SCEVSearch {
9885     const SCEV *Node;
9886     bool IsFound;
9887 
9888     SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
9889 
9890     bool follow(const SCEV *S) {
9891       IsFound |= (S == Node);
9892       return !IsFound;
9893     }
9894     bool isDone() const { return IsFound; }
9895   };
9896 
9897   SCEVSearch Search(Op);
9898   visitAll(S, Search);
9899   return Search.IsFound;
9900 }
9901 
forgetMemoizedResults(const SCEV * S)9902 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
9903   ValuesAtScopes.erase(S);
9904   LoopDispositions.erase(S);
9905   BlockDispositions.erase(S);
9906   UnsignedRanges.erase(S);
9907   SignedRanges.erase(S);
9908   ExprValueMap.erase(S);
9909   HasRecMap.erase(S);
9910 
9911   auto RemoveSCEVFromBackedgeMap =
9912       [S, this](DenseMap<const Loop *, BackedgeTakenInfo> &Map) {
9913         for (auto I = Map.begin(), E = Map.end(); I != E;) {
9914           BackedgeTakenInfo &BEInfo = I->second;
9915           if (BEInfo.hasOperand(S, this)) {
9916             BEInfo.clear();
9917             Map.erase(I++);
9918           } else
9919             ++I;
9920         }
9921       };
9922 
9923   RemoveSCEVFromBackedgeMap(BackedgeTakenCounts);
9924   RemoveSCEVFromBackedgeMap(PredicatedBackedgeTakenCounts);
9925 }
9926 
9927 typedef DenseMap<const Loop *, std::string> VerifyMap;
9928 
9929 /// replaceSubString - Replaces all occurrences of From in Str with To.
replaceSubString(std::string & Str,StringRef From,StringRef To)9930 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
9931   size_t Pos = 0;
9932   while ((Pos = Str.find(From, Pos)) != std::string::npos) {
9933     Str.replace(Pos, From.size(), To.data(), To.size());
9934     Pos += To.size();
9935   }
9936 }
9937 
9938 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
9939 static void
getLoopBackedgeTakenCounts(Loop * L,VerifyMap & Map,ScalarEvolution & SE)9940 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
9941   std::string &S = Map[L];
9942   if (S.empty()) {
9943     raw_string_ostream OS(S);
9944     SE.getBackedgeTakenCount(L)->print(OS);
9945 
9946     // false and 0 are semantically equivalent. This can happen in dead loops.
9947     replaceSubString(OS.str(), "false", "0");
9948     // Remove wrap flags, their use in SCEV is highly fragile.
9949     // FIXME: Remove this when SCEV gets smarter about them.
9950     replaceSubString(OS.str(), "<nw>", "");
9951     replaceSubString(OS.str(), "<nsw>", "");
9952     replaceSubString(OS.str(), "<nuw>", "");
9953   }
9954 
9955   for (auto *R : reverse(*L))
9956     getLoopBackedgeTakenCounts(R, Map, SE); // recurse.
9957 }
9958 
verify() const9959 void ScalarEvolution::verify() const {
9960   ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9961 
9962   // Gather stringified backedge taken counts for all loops using SCEV's caches.
9963   // FIXME: It would be much better to store actual values instead of strings,
9964   //        but SCEV pointers will change if we drop the caches.
9965   VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
9966   for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9967     getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
9968 
9969   // Gather stringified backedge taken counts for all loops using a fresh
9970   // ScalarEvolution object.
9971   ScalarEvolution SE2(F, TLI, AC, DT, LI);
9972   for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9973     getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE2);
9974 
9975   // Now compare whether they're the same with and without caches. This allows
9976   // verifying that no pass changed the cache.
9977   assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
9978          "New loops suddenly appeared!");
9979 
9980   for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
9981                            OldE = BackedgeDumpsOld.end(),
9982                            NewI = BackedgeDumpsNew.begin();
9983        OldI != OldE; ++OldI, ++NewI) {
9984     assert(OldI->first == NewI->first && "Loop order changed!");
9985 
9986     // Compare the stringified SCEVs. We don't care if undef backedgetaken count
9987     // changes.
9988     // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
9989     // means that a pass is buggy or SCEV has to learn a new pattern but is
9990     // usually not harmful.
9991     if (OldI->second != NewI->second &&
9992         OldI->second.find("undef") == std::string::npos &&
9993         NewI->second.find("undef") == std::string::npos &&
9994         OldI->second != "***COULDNOTCOMPUTE***" &&
9995         NewI->second != "***COULDNOTCOMPUTE***") {
9996       dbgs() << "SCEVValidator: SCEV for loop '"
9997              << OldI->first->getHeader()->getName()
9998              << "' changed from '" << OldI->second
9999              << "' to '" << NewI->second << "'!\n";
10000       std::abort();
10001     }
10002   }
10003 
10004   // TODO: Verify more things.
10005 }
10006 
10007 char ScalarEvolutionAnalysis::PassID;
10008 
run(Function & F,AnalysisManager<Function> & AM)10009 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
10010                                              AnalysisManager<Function> &AM) {
10011   return ScalarEvolution(F, AM.getResult<TargetLibraryAnalysis>(F),
10012                          AM.getResult<AssumptionAnalysis>(F),
10013                          AM.getResult<DominatorTreeAnalysis>(F),
10014                          AM.getResult<LoopAnalysis>(F));
10015 }
10016 
10017 PreservedAnalyses
run(Function & F,AnalysisManager<Function> & AM)10018 ScalarEvolutionPrinterPass::run(Function &F, AnalysisManager<Function> &AM) {
10019   AM.getResult<ScalarEvolutionAnalysis>(F).print(OS);
10020   return PreservedAnalyses::all();
10021 }
10022 
10023 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
10024                       "Scalar Evolution Analysis", false, true)
10025 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
10026 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
10027 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
10028 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
10029 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
10030                     "Scalar Evolution Analysis", false, true)
10031 char ScalarEvolutionWrapperPass::ID = 0;
10032 
ScalarEvolutionWrapperPass()10033 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
10034   initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
10035 }
10036 
runOnFunction(Function & F)10037 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
10038   SE.reset(new ScalarEvolution(
10039       F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(),
10040       getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
10041       getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
10042       getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
10043   return false;
10044 }
10045 
releaseMemory()10046 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
10047 
print(raw_ostream & OS,const Module *) const10048 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
10049   SE->print(OS);
10050 }
10051 
verifyAnalysis() const10052 void ScalarEvolutionWrapperPass::verifyAnalysis() const {
10053   if (!VerifySCEV)
10054     return;
10055 
10056   SE->verify();
10057 }
10058 
getAnalysisUsage(AnalysisUsage & AU) const10059 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
10060   AU.setPreservesAll();
10061   AU.addRequiredTransitive<AssumptionCacheTracker>();
10062   AU.addRequiredTransitive<LoopInfoWrapperPass>();
10063   AU.addRequiredTransitive<DominatorTreeWrapperPass>();
10064   AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
10065 }
10066 
10067 const SCEVPredicate *
getEqualPredicate(const SCEVUnknown * LHS,const SCEVConstant * RHS)10068 ScalarEvolution::getEqualPredicate(const SCEVUnknown *LHS,
10069                                    const SCEVConstant *RHS) {
10070   FoldingSetNodeID ID;
10071   // Unique this node based on the arguments
10072   ID.AddInteger(SCEVPredicate::P_Equal);
10073   ID.AddPointer(LHS);
10074   ID.AddPointer(RHS);
10075   void *IP = nullptr;
10076   if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
10077     return S;
10078   SCEVEqualPredicate *Eq = new (SCEVAllocator)
10079       SCEVEqualPredicate(ID.Intern(SCEVAllocator), LHS, RHS);
10080   UniquePreds.InsertNode(Eq, IP);
10081   return Eq;
10082 }
10083 
getWrapPredicate(const SCEVAddRecExpr * AR,SCEVWrapPredicate::IncrementWrapFlags AddedFlags)10084 const SCEVPredicate *ScalarEvolution::getWrapPredicate(
10085     const SCEVAddRecExpr *AR,
10086     SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
10087   FoldingSetNodeID ID;
10088   // Unique this node based on the arguments
10089   ID.AddInteger(SCEVPredicate::P_Wrap);
10090   ID.AddPointer(AR);
10091   ID.AddInteger(AddedFlags);
10092   void *IP = nullptr;
10093   if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
10094     return S;
10095   auto *OF = new (SCEVAllocator)
10096       SCEVWrapPredicate(ID.Intern(SCEVAllocator), AR, AddedFlags);
10097   UniquePreds.InsertNode(OF, IP);
10098   return OF;
10099 }
10100 
10101 namespace {
10102 
10103 class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> {
10104 public:
10105   // Rewrites \p S in the context of a loop L and the predicate A.
10106   // If Assume is true, rewrite is free to add further predicates to A
10107   // such that the result will be an AddRecExpr.
rewrite(const SCEV * S,const Loop * L,ScalarEvolution & SE,SCEVUnionPredicate & A,bool Assume)10108   static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
10109                              SCEVUnionPredicate &A, bool Assume) {
10110     SCEVPredicateRewriter Rewriter(L, SE, A, Assume);
10111     return Rewriter.visit(S);
10112   }
10113 
SCEVPredicateRewriter(const Loop * L,ScalarEvolution & SE,SCEVUnionPredicate & P,bool Assume)10114   SCEVPredicateRewriter(const Loop *L, ScalarEvolution &SE,
10115                         SCEVUnionPredicate &P, bool Assume)
10116       : SCEVRewriteVisitor(SE), P(P), L(L), Assume(Assume) {}
10117 
visitUnknown(const SCEVUnknown * Expr)10118   const SCEV *visitUnknown(const SCEVUnknown *Expr) {
10119     auto ExprPreds = P.getPredicatesForExpr(Expr);
10120     for (auto *Pred : ExprPreds)
10121       if (const auto *IPred = dyn_cast<SCEVEqualPredicate>(Pred))
10122         if (IPred->getLHS() == Expr)
10123           return IPred->getRHS();
10124 
10125     return Expr;
10126   }
10127 
visitZeroExtendExpr(const SCEVZeroExtendExpr * Expr)10128   const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
10129     const SCEV *Operand = visit(Expr->getOperand());
10130     const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
10131     if (AR && AR->getLoop() == L && AR->isAffine()) {
10132       // This couldn't be folded because the operand didn't have the nuw
10133       // flag. Add the nusw flag as an assumption that we could make.
10134       const SCEV *Step = AR->getStepRecurrence(SE);
10135       Type *Ty = Expr->getType();
10136       if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNUSW))
10137         return SE.getAddRecExpr(SE.getZeroExtendExpr(AR->getStart(), Ty),
10138                                 SE.getSignExtendExpr(Step, Ty), L,
10139                                 AR->getNoWrapFlags());
10140     }
10141     return SE.getZeroExtendExpr(Operand, Expr->getType());
10142   }
10143 
visitSignExtendExpr(const SCEVSignExtendExpr * Expr)10144   const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
10145     const SCEV *Operand = visit(Expr->getOperand());
10146     const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
10147     if (AR && AR->getLoop() == L && AR->isAffine()) {
10148       // This couldn't be folded because the operand didn't have the nsw
10149       // flag. Add the nssw flag as an assumption that we could make.
10150       const SCEV *Step = AR->getStepRecurrence(SE);
10151       Type *Ty = Expr->getType();
10152       if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNSSW))
10153         return SE.getAddRecExpr(SE.getSignExtendExpr(AR->getStart(), Ty),
10154                                 SE.getSignExtendExpr(Step, Ty), L,
10155                                 AR->getNoWrapFlags());
10156     }
10157     return SE.getSignExtendExpr(Operand, Expr->getType());
10158   }
10159 
10160 private:
addOverflowAssumption(const SCEVAddRecExpr * AR,SCEVWrapPredicate::IncrementWrapFlags AddedFlags)10161   bool addOverflowAssumption(const SCEVAddRecExpr *AR,
10162                              SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
10163     auto *A = SE.getWrapPredicate(AR, AddedFlags);
10164     if (!Assume) {
10165       // Check if we've already made this assumption.
10166       if (P.implies(A))
10167         return true;
10168       return false;
10169     }
10170     P.add(A);
10171     return true;
10172   }
10173 
10174   SCEVUnionPredicate &P;
10175   const Loop *L;
10176   bool Assume;
10177 };
10178 } // end anonymous namespace
10179 
rewriteUsingPredicate(const SCEV * S,const Loop * L,SCEVUnionPredicate & Preds)10180 const SCEV *ScalarEvolution::rewriteUsingPredicate(const SCEV *S, const Loop *L,
10181                                                    SCEVUnionPredicate &Preds) {
10182   return SCEVPredicateRewriter::rewrite(S, L, *this, Preds, false);
10183 }
10184 
10185 const SCEVAddRecExpr *
convertSCEVToAddRecWithPredicates(const SCEV * S,const Loop * L,SCEVUnionPredicate & Preds)10186 ScalarEvolution::convertSCEVToAddRecWithPredicates(const SCEV *S, const Loop *L,
10187                                                    SCEVUnionPredicate &Preds) {
10188   SCEVUnionPredicate TransformPreds;
10189   S = SCEVPredicateRewriter::rewrite(S, L, *this, TransformPreds, true);
10190   auto *AddRec = dyn_cast<SCEVAddRecExpr>(S);
10191 
10192   if (!AddRec)
10193     return nullptr;
10194 
10195   // Since the transformation was successful, we can now transfer the SCEV
10196   // predicates.
10197   Preds.add(&TransformPreds);
10198   return AddRec;
10199 }
10200 
10201 /// SCEV predicates
SCEVPredicate(const FoldingSetNodeIDRef ID,SCEVPredicateKind Kind)10202 SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID,
10203                              SCEVPredicateKind Kind)
10204     : FastID(ID), Kind(Kind) {}
10205 
SCEVEqualPredicate(const FoldingSetNodeIDRef ID,const SCEVUnknown * LHS,const SCEVConstant * RHS)10206 SCEVEqualPredicate::SCEVEqualPredicate(const FoldingSetNodeIDRef ID,
10207                                        const SCEVUnknown *LHS,
10208                                        const SCEVConstant *RHS)
10209     : SCEVPredicate(ID, P_Equal), LHS(LHS), RHS(RHS) {}
10210 
implies(const SCEVPredicate * N) const10211 bool SCEVEqualPredicate::implies(const SCEVPredicate *N) const {
10212   const auto *Op = dyn_cast<SCEVEqualPredicate>(N);
10213 
10214   if (!Op)
10215     return false;
10216 
10217   return Op->LHS == LHS && Op->RHS == RHS;
10218 }
10219 
isAlwaysTrue() const10220 bool SCEVEqualPredicate::isAlwaysTrue() const { return false; }
10221 
getExpr() const10222 const SCEV *SCEVEqualPredicate::getExpr() const { return LHS; }
10223 
print(raw_ostream & OS,unsigned Depth) const10224 void SCEVEqualPredicate::print(raw_ostream &OS, unsigned Depth) const {
10225   OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n";
10226 }
10227 
SCEVWrapPredicate(const FoldingSetNodeIDRef ID,const SCEVAddRecExpr * AR,IncrementWrapFlags Flags)10228 SCEVWrapPredicate::SCEVWrapPredicate(const FoldingSetNodeIDRef ID,
10229                                      const SCEVAddRecExpr *AR,
10230                                      IncrementWrapFlags Flags)
10231     : SCEVPredicate(ID, P_Wrap), AR(AR), Flags(Flags) {}
10232 
getExpr() const10233 const SCEV *SCEVWrapPredicate::getExpr() const { return AR; }
10234 
implies(const SCEVPredicate * N) const10235 bool SCEVWrapPredicate::implies(const SCEVPredicate *N) const {
10236   const auto *Op = dyn_cast<SCEVWrapPredicate>(N);
10237 
10238   return Op && Op->AR == AR && setFlags(Flags, Op->Flags) == Flags;
10239 }
10240 
isAlwaysTrue() const10241 bool SCEVWrapPredicate::isAlwaysTrue() const {
10242   SCEV::NoWrapFlags ScevFlags = AR->getNoWrapFlags();
10243   IncrementWrapFlags IFlags = Flags;
10244 
10245   if (ScalarEvolution::setFlags(ScevFlags, SCEV::FlagNSW) == ScevFlags)
10246     IFlags = clearFlags(IFlags, IncrementNSSW);
10247 
10248   return IFlags == IncrementAnyWrap;
10249 }
10250 
print(raw_ostream & OS,unsigned Depth) const10251 void SCEVWrapPredicate::print(raw_ostream &OS, unsigned Depth) const {
10252   OS.indent(Depth) << *getExpr() << " Added Flags: ";
10253   if (SCEVWrapPredicate::IncrementNUSW & getFlags())
10254     OS << "<nusw>";
10255   if (SCEVWrapPredicate::IncrementNSSW & getFlags())
10256     OS << "<nssw>";
10257   OS << "\n";
10258 }
10259 
10260 SCEVWrapPredicate::IncrementWrapFlags
getImpliedFlags(const SCEVAddRecExpr * AR,ScalarEvolution & SE)10261 SCEVWrapPredicate::getImpliedFlags(const SCEVAddRecExpr *AR,
10262                                    ScalarEvolution &SE) {
10263   IncrementWrapFlags ImpliedFlags = IncrementAnyWrap;
10264   SCEV::NoWrapFlags StaticFlags = AR->getNoWrapFlags();
10265 
10266   // We can safely transfer the NSW flag as NSSW.
10267   if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNSW) == StaticFlags)
10268     ImpliedFlags = IncrementNSSW;
10269 
10270   if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNUW) == StaticFlags) {
10271     // If the increment is positive, the SCEV NUW flag will also imply the
10272     // WrapPredicate NUSW flag.
10273     if (const auto *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(SE)))
10274       if (Step->getValue()->getValue().isNonNegative())
10275         ImpliedFlags = setFlags(ImpliedFlags, IncrementNUSW);
10276   }
10277 
10278   return ImpliedFlags;
10279 }
10280 
10281 /// Union predicates don't get cached so create a dummy set ID for it.
SCEVUnionPredicate()10282 SCEVUnionPredicate::SCEVUnionPredicate()
10283     : SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {}
10284 
isAlwaysTrue() const10285 bool SCEVUnionPredicate::isAlwaysTrue() const {
10286   return all_of(Preds,
10287                 [](const SCEVPredicate *I) { return I->isAlwaysTrue(); });
10288 }
10289 
10290 ArrayRef<const SCEVPredicate *>
getPredicatesForExpr(const SCEV * Expr)10291 SCEVUnionPredicate::getPredicatesForExpr(const SCEV *Expr) {
10292   auto I = SCEVToPreds.find(Expr);
10293   if (I == SCEVToPreds.end())
10294     return ArrayRef<const SCEVPredicate *>();
10295   return I->second;
10296 }
10297 
implies(const SCEVPredicate * N) const10298 bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const {
10299   if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N))
10300     return all_of(Set->Preds,
10301                   [this](const SCEVPredicate *I) { return this->implies(I); });
10302 
10303   auto ScevPredsIt = SCEVToPreds.find(N->getExpr());
10304   if (ScevPredsIt == SCEVToPreds.end())
10305     return false;
10306   auto &SCEVPreds = ScevPredsIt->second;
10307 
10308   return any_of(SCEVPreds,
10309                 [N](const SCEVPredicate *I) { return I->implies(N); });
10310 }
10311 
getExpr() const10312 const SCEV *SCEVUnionPredicate::getExpr() const { return nullptr; }
10313 
print(raw_ostream & OS,unsigned Depth) const10314 void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const {
10315   for (auto Pred : Preds)
10316     Pred->print(OS, Depth);
10317 }
10318 
add(const SCEVPredicate * N)10319 void SCEVUnionPredicate::add(const SCEVPredicate *N) {
10320   if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N)) {
10321     for (auto Pred : Set->Preds)
10322       add(Pred);
10323     return;
10324   }
10325 
10326   if (implies(N))
10327     return;
10328 
10329   const SCEV *Key = N->getExpr();
10330   assert(Key && "Only SCEVUnionPredicate doesn't have an "
10331                 " associated expression!");
10332 
10333   SCEVToPreds[Key].push_back(N);
10334   Preds.push_back(N);
10335 }
10336 
PredicatedScalarEvolution(ScalarEvolution & SE,Loop & L)10337 PredicatedScalarEvolution::PredicatedScalarEvolution(ScalarEvolution &SE,
10338                                                      Loop &L)
10339     : SE(SE), L(L), Generation(0), BackedgeCount(nullptr) {}
10340 
getSCEV(Value * V)10341 const SCEV *PredicatedScalarEvolution::getSCEV(Value *V) {
10342   const SCEV *Expr = SE.getSCEV(V);
10343   RewriteEntry &Entry = RewriteMap[Expr];
10344 
10345   // If we already have an entry and the version matches, return it.
10346   if (Entry.second && Generation == Entry.first)
10347     return Entry.second;
10348 
10349   // We found an entry but it's stale. Rewrite the stale entry
10350   // acording to the current predicate.
10351   if (Entry.second)
10352     Expr = Entry.second;
10353 
10354   const SCEV *NewSCEV = SE.rewriteUsingPredicate(Expr, &L, Preds);
10355   Entry = {Generation, NewSCEV};
10356 
10357   return NewSCEV;
10358 }
10359 
getBackedgeTakenCount()10360 const SCEV *PredicatedScalarEvolution::getBackedgeTakenCount() {
10361   if (!BackedgeCount) {
10362     SCEVUnionPredicate BackedgePred;
10363     BackedgeCount = SE.getPredicatedBackedgeTakenCount(&L, BackedgePred);
10364     addPredicate(BackedgePred);
10365   }
10366   return BackedgeCount;
10367 }
10368 
addPredicate(const SCEVPredicate & Pred)10369 void PredicatedScalarEvolution::addPredicate(const SCEVPredicate &Pred) {
10370   if (Preds.implies(&Pred))
10371     return;
10372   Preds.add(&Pred);
10373   updateGeneration();
10374 }
10375 
getUnionPredicate() const10376 const SCEVUnionPredicate &PredicatedScalarEvolution::getUnionPredicate() const {
10377   return Preds;
10378 }
10379 
updateGeneration()10380 void PredicatedScalarEvolution::updateGeneration() {
10381   // If the generation number wrapped recompute everything.
10382   if (++Generation == 0) {
10383     for (auto &II : RewriteMap) {
10384       const SCEV *Rewritten = II.second.second;
10385       II.second = {Generation, SE.rewriteUsingPredicate(Rewritten, &L, Preds)};
10386     }
10387   }
10388 }
10389 
setNoOverflow(Value * V,SCEVWrapPredicate::IncrementWrapFlags Flags)10390 void PredicatedScalarEvolution::setNoOverflow(
10391     Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
10392   const SCEV *Expr = getSCEV(V);
10393   const auto *AR = cast<SCEVAddRecExpr>(Expr);
10394 
10395   auto ImpliedFlags = SCEVWrapPredicate::getImpliedFlags(AR, SE);
10396 
10397   // Clear the statically implied flags.
10398   Flags = SCEVWrapPredicate::clearFlags(Flags, ImpliedFlags);
10399   addPredicate(*SE.getWrapPredicate(AR, Flags));
10400 
10401   auto II = FlagsMap.insert({V, Flags});
10402   if (!II.second)
10403     II.first->second = SCEVWrapPredicate::setFlags(Flags, II.first->second);
10404 }
10405 
hasNoOverflow(Value * V,SCEVWrapPredicate::IncrementWrapFlags Flags)10406 bool PredicatedScalarEvolution::hasNoOverflow(
10407     Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
10408   const SCEV *Expr = getSCEV(V);
10409   const auto *AR = cast<SCEVAddRecExpr>(Expr);
10410 
10411   Flags = SCEVWrapPredicate::clearFlags(
10412       Flags, SCEVWrapPredicate::getImpliedFlags(AR, SE));
10413 
10414   auto II = FlagsMap.find(V);
10415 
10416   if (II != FlagsMap.end())
10417     Flags = SCEVWrapPredicate::clearFlags(Flags, II->second);
10418 
10419   return Flags == SCEVWrapPredicate::IncrementAnyWrap;
10420 }
10421 
getAsAddRec(Value * V)10422 const SCEVAddRecExpr *PredicatedScalarEvolution::getAsAddRec(Value *V) {
10423   const SCEV *Expr = this->getSCEV(V);
10424   auto *New = SE.convertSCEVToAddRecWithPredicates(Expr, &L, Preds);
10425 
10426   if (!New)
10427     return nullptr;
10428 
10429   updateGeneration();
10430   RewriteMap[SE.getSCEV(V)] = {Generation, New};
10431   return New;
10432 }
10433 
PredicatedScalarEvolution(const PredicatedScalarEvolution & Init)10434 PredicatedScalarEvolution::PredicatedScalarEvolution(
10435     const PredicatedScalarEvolution &Init)
10436     : RewriteMap(Init.RewriteMap), SE(Init.SE), L(Init.L), Preds(Init.Preds),
10437       Generation(Init.Generation), BackedgeCount(Init.BackedgeCount) {
10438   for (const auto &I : Init.FlagsMap)
10439     FlagsMap.insert(I);
10440 }
10441 
print(raw_ostream & OS,unsigned Depth) const10442 void PredicatedScalarEvolution::print(raw_ostream &OS, unsigned Depth) const {
10443   // For each block.
10444   for (auto *BB : L.getBlocks())
10445     for (auto &I : *BB) {
10446       if (!SE.isSCEVable(I.getType()))
10447         continue;
10448 
10449       auto *Expr = SE.getSCEV(&I);
10450       auto II = RewriteMap.find(Expr);
10451 
10452       if (II == RewriteMap.end())
10453         continue;
10454 
10455       // Don't print things that are not interesting.
10456       if (II->second.second == Expr)
10457         continue;
10458 
10459       OS.indent(Depth) << "[PSE]" << I << ":\n";
10460       OS.indent(Depth + 2) << *Expr << "\n";
10461       OS.indent(Depth + 2) << "--> " << *II->second.second << "\n";
10462     }
10463 }
10464