xref: /llvm-project/llvm/lib/Analysis/ScalarEvolution.cpp (revision 013a4ac4aa5da577fff807c44846eb6cfd6d32f4)
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
132 void SCEV::dump() const {
133   print(dbgs());
134   dbgs() << '\n';
135 }
136 
137 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 
247 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 
272 bool SCEV::isZero() const {
273   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
274     return SC->getValue()->isZero();
275   return false;
276 }
277 
278 bool SCEV::isOne() const {
279   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
280     return SC->getValue()->isOne();
281   return false;
282 }
283 
284 bool SCEV::isAllOnesValue() const {
285   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
286     return SC->getValue()->isAllOnesValue();
287   return false;
288 }
289 
290 /// isNonConstantNegative - Return true if the specified scev is negated, but
291 /// not a constant.
292 bool SCEV::isNonConstantNegative() const {
293   const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
294   if (!Mul) return false;
295 
296   // If there is a constant factor, it will be first.
297   const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
298   if (!SC) return false;
299 
300   // Return true if the value is negative, this matches things like (-42 * V).
301   return SC->getAPInt().isNegative();
302 }
303 
304 SCEVCouldNotCompute::SCEVCouldNotCompute() :
305   SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
306 
307 bool SCEVCouldNotCompute::classof(const SCEV *S) {
308   return S->getSCEVType() == scCouldNotCompute;
309 }
310 
311 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
312   FoldingSetNodeID ID;
313   ID.AddInteger(scConstant);
314   ID.AddPointer(V);
315   void *IP = nullptr;
316   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
317   SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
318   UniqueSCEVs.InsertNode(S, IP);
319   return S;
320 }
321 
322 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
323   return getConstant(ConstantInt::get(getContext(), Val));
324 }
325 
326 const SCEV *
327 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
328   IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
329   return getConstant(ConstantInt::get(ITy, V, isSigned));
330 }
331 
332 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
333                            unsigned SCEVTy, const SCEV *op, Type *ty)
334   : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
335 
336 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
337                                    const SCEV *op, Type *ty)
338   : SCEVCastExpr(ID, scTruncate, op, ty) {
339   assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
340          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
341          "Cannot truncate non-integer value!");
342 }
343 
344 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
345                                        const SCEV *op, Type *ty)
346   : SCEVCastExpr(ID, scZeroExtend, op, ty) {
347   assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
348          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
349          "Cannot zero extend non-integer value!");
350 }
351 
352 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
353                                        const SCEV *op, Type *ty)
354   : SCEVCastExpr(ID, scSignExtend, op, ty) {
355   assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
356          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
357          "Cannot sign extend non-integer value!");
358 }
359 
360 void SCEVUnknown::deleted() {
361   // Clear this SCEVUnknown from various maps.
362   SE->forgetMemoizedResults(this);
363 
364   // Remove this SCEVUnknown from the uniquing map.
365   SE->UniqueSCEVs.RemoveNode(this);
366 
367   // Release the value.
368   setValPtr(nullptr);
369 }
370 
371 void SCEVUnknown::allUsesReplacedWith(Value *New) {
372   // Clear this SCEVUnknown from various maps.
373   SE->forgetMemoizedResults(this);
374 
375   // Remove this SCEVUnknown from the uniquing map.
376   SE->UniqueSCEVs.RemoveNode(this);
377 
378   // Update this SCEVUnknown to point to the new value. This is needed
379   // because there may still be outstanding SCEVs which still point to
380   // this SCEVUnknown.
381   setValPtr(New);
382 }
383 
384 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
385   if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
386     if (VCE->getOpcode() == Instruction::PtrToInt)
387       if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
388         if (CE->getOpcode() == Instruction::GetElementPtr &&
389             CE->getOperand(0)->isNullValue() &&
390             CE->getNumOperands() == 2)
391           if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
392             if (CI->isOne()) {
393               AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
394                                  ->getElementType();
395               return true;
396             }
397 
398   return false;
399 }
400 
401 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
402   if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
403     if (VCE->getOpcode() == Instruction::PtrToInt)
404       if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
405         if (CE->getOpcode() == Instruction::GetElementPtr &&
406             CE->getOperand(0)->isNullValue()) {
407           Type *Ty =
408             cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
409           if (StructType *STy = dyn_cast<StructType>(Ty))
410             if (!STy->isPacked() &&
411                 CE->getNumOperands() == 3 &&
412                 CE->getOperand(1)->isNullValue()) {
413               if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
414                 if (CI->isOne() &&
415                     STy->getNumElements() == 2 &&
416                     STy->getElementType(0)->isIntegerTy(1)) {
417                   AllocTy = STy->getElementType(1);
418                   return true;
419                 }
420             }
421         }
422 
423   return false;
424 }
425 
426 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
427   if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
428     if (VCE->getOpcode() == Instruction::PtrToInt)
429       if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
430         if (CE->getOpcode() == Instruction::GetElementPtr &&
431             CE->getNumOperands() == 3 &&
432             CE->getOperand(0)->isNullValue() &&
433             CE->getOperand(1)->isNullValue()) {
434           Type *Ty =
435             cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
436           // Ignore vector types here so that ScalarEvolutionExpander doesn't
437           // emit getelementptrs that index into vectors.
438           if (Ty->isStructTy() || Ty->isArrayTy()) {
439             CTy = Ty;
440             FieldNo = CE->getOperand(2);
441             return true;
442           }
443         }
444 
445   return false;
446 }
447 
448 //===----------------------------------------------------------------------===//
449 //                               SCEV Utilities
450 //===----------------------------------------------------------------------===//
451 
452 namespace {
453 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
454 /// than the complexity of the RHS.  This comparator is used to canonicalize
455 /// expressions.
456 class SCEVComplexityCompare {
457   const LoopInfo *const LI;
458 public:
459   explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
460 
461   // Return true or false if LHS is less than, or at least RHS, respectively.
462   bool operator()(const SCEV *LHS, const SCEV *RHS) const {
463     return compare(LHS, RHS) < 0;
464   }
465 
466   // Return negative, zero, or positive, if LHS is less than, equal to, or
467   // greater than RHS, respectively. A three-way result allows recursive
468   // comparisons to be more efficient.
469   int compare(const SCEV *LHS, const SCEV *RHS) const {
470     // Fast-path: SCEVs are uniqued so we can do a quick equality check.
471     if (LHS == RHS)
472       return 0;
473 
474     // Primarily, sort the SCEVs by their getSCEVType().
475     unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
476     if (LType != RType)
477       return (int)LType - (int)RType;
478 
479     // Aside from the getSCEVType() ordering, the particular ordering
480     // isn't very important except that it's beneficial to be consistent,
481     // so that (a + b) and (b + a) don't end up as different expressions.
482     switch (static_cast<SCEVTypes>(LType)) {
483     case scUnknown: {
484       const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
485       const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
486 
487       // Sort SCEVUnknown values with some loose heuristics. TODO: This is
488       // not as complete as it could be.
489       const Value *LV = LU->getValue(), *RV = RU->getValue();
490 
491       // Order pointer values after integer values. This helps SCEVExpander
492       // form GEPs.
493       bool LIsPointer = LV->getType()->isPointerTy(),
494         RIsPointer = RV->getType()->isPointerTy();
495       if (LIsPointer != RIsPointer)
496         return (int)LIsPointer - (int)RIsPointer;
497 
498       // Compare getValueID values.
499       unsigned LID = LV->getValueID(),
500         RID = RV->getValueID();
501       if (LID != RID)
502         return (int)LID - (int)RID;
503 
504       // Sort arguments by their position.
505       if (const Argument *LA = dyn_cast<Argument>(LV)) {
506         const Argument *RA = cast<Argument>(RV);
507         unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
508         return (int)LArgNo - (int)RArgNo;
509       }
510 
511       // For instructions, compare their loop depth, and their operand
512       // count.  This is pretty loose.
513       if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
514         const Instruction *RInst = cast<Instruction>(RV);
515 
516         // Compare loop depths.
517         const BasicBlock *LParent = LInst->getParent(),
518           *RParent = RInst->getParent();
519         if (LParent != RParent) {
520           unsigned LDepth = LI->getLoopDepth(LParent),
521             RDepth = LI->getLoopDepth(RParent);
522           if (LDepth != RDepth)
523             return (int)LDepth - (int)RDepth;
524         }
525 
526         // Compare the number of operands.
527         unsigned LNumOps = LInst->getNumOperands(),
528           RNumOps = RInst->getNumOperands();
529         return (int)LNumOps - (int)RNumOps;
530       }
531 
532       return 0;
533     }
534 
535     case scConstant: {
536       const SCEVConstant *LC = cast<SCEVConstant>(LHS);
537       const SCEVConstant *RC = cast<SCEVConstant>(RHS);
538 
539       // Compare constant values.
540       const APInt &LA = LC->getAPInt();
541       const APInt &RA = RC->getAPInt();
542       unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
543       if (LBitWidth != RBitWidth)
544         return (int)LBitWidth - (int)RBitWidth;
545       return LA.ult(RA) ? -1 : 1;
546     }
547 
548     case scAddRecExpr: {
549       const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
550       const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
551 
552       // Compare addrec loop depths.
553       const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
554       if (LLoop != RLoop) {
555         unsigned LDepth = LLoop->getLoopDepth(),
556           RDepth = RLoop->getLoopDepth();
557         if (LDepth != RDepth)
558           return (int)LDepth - (int)RDepth;
559       }
560 
561       // Addrec complexity grows with operand count.
562       unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
563       if (LNumOps != RNumOps)
564         return (int)LNumOps - (int)RNumOps;
565 
566       // Lexicographically compare.
567       for (unsigned i = 0; i != LNumOps; ++i) {
568         long X = compare(LA->getOperand(i), RA->getOperand(i));
569         if (X != 0)
570           return X;
571       }
572 
573       return 0;
574     }
575 
576     case scAddExpr:
577     case scMulExpr:
578     case scSMaxExpr:
579     case scUMaxExpr: {
580       const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
581       const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
582 
583       // Lexicographically compare n-ary expressions.
584       unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
585       if (LNumOps != RNumOps)
586         return (int)LNumOps - (int)RNumOps;
587 
588       for (unsigned i = 0; i != LNumOps; ++i) {
589         if (i >= RNumOps)
590           return 1;
591         long X = compare(LC->getOperand(i), RC->getOperand(i));
592         if (X != 0)
593           return X;
594       }
595       return (int)LNumOps - (int)RNumOps;
596     }
597 
598     case scUDivExpr: {
599       const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
600       const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
601 
602       // Lexicographically compare udiv expressions.
603       long X = compare(LC->getLHS(), RC->getLHS());
604       if (X != 0)
605         return X;
606       return compare(LC->getRHS(), RC->getRHS());
607     }
608 
609     case scTruncate:
610     case scZeroExtend:
611     case scSignExtend: {
612       const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
613       const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
614 
615       // Compare cast expressions by operand.
616       return compare(LC->getOperand(), RC->getOperand());
617     }
618 
619     case scCouldNotCompute:
620       llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
621     }
622     llvm_unreachable("Unknown SCEV kind!");
623   }
624 };
625 }  // end anonymous namespace
626 
627 /// GroupByComplexity - Given a list of SCEV objects, order them by their
628 /// complexity, and group objects of the same complexity together by value.
629 /// When this routine is finished, we know that any duplicates in the vector are
630 /// consecutive and that complexity is monotonically increasing.
631 ///
632 /// Note that we go take special precautions to ensure that we get deterministic
633 /// results from this routine.  In other words, we don't want the results of
634 /// this to depend on where the addresses of various SCEV objects happened to
635 /// land in memory.
636 ///
637 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
638                               LoopInfo *LI) {
639   if (Ops.size() < 2) return;  // Noop
640   if (Ops.size() == 2) {
641     // This is the common case, which also happens to be trivially simple.
642     // Special case it.
643     const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
644     if (SCEVComplexityCompare(LI)(RHS, LHS))
645       std::swap(LHS, RHS);
646     return;
647   }
648 
649   // Do the rough sort by complexity.
650   std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
651 
652   // Now that we are sorted by complexity, group elements of the same
653   // complexity.  Note that this is, at worst, N^2, but the vector is likely to
654   // be extremely short in practice.  Note that we take this approach because we
655   // do not want to depend on the addresses of the objects we are grouping.
656   for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
657     const SCEV *S = Ops[i];
658     unsigned Complexity = S->getSCEVType();
659 
660     // If there are any objects of the same complexity and same value as this
661     // one, group them.
662     for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
663       if (Ops[j] == S) { // Found a duplicate.
664         // Move it to immediately after i'th element.
665         std::swap(Ops[i+1], Ops[j]);
666         ++i;   // no need to rescan it.
667         if (i == e-2) return;  // Done!
668       }
669     }
670   }
671 }
672 
673 // Returns the size of the SCEV S.
674 static inline int sizeOfSCEV(const SCEV *S) {
675   struct FindSCEVSize {
676     int Size;
677     FindSCEVSize() : Size(0) {}
678 
679     bool follow(const SCEV *S) {
680       ++Size;
681       // Keep looking at all operands of S.
682       return true;
683     }
684     bool isDone() const {
685       return false;
686     }
687   };
688 
689   FindSCEVSize F;
690   SCEVTraversal<FindSCEVSize> ST(F);
691   ST.visitAll(S);
692   return F.Size;
693 }
694 
695 namespace {
696 
697 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
698 public:
699   // Computes the Quotient and Remainder of the division of Numerator by
700   // Denominator.
701   static void divide(ScalarEvolution &SE, const SCEV *Numerator,
702                      const SCEV *Denominator, const SCEV **Quotient,
703                      const SCEV **Remainder) {
704     assert(Numerator && Denominator && "Uninitialized SCEV");
705 
706     SCEVDivision D(SE, Numerator, Denominator);
707 
708     // Check for the trivial case here to avoid having to check for it in the
709     // rest of the code.
710     if (Numerator == Denominator) {
711       *Quotient = D.One;
712       *Remainder = D.Zero;
713       return;
714     }
715 
716     if (Numerator->isZero()) {
717       *Quotient = D.Zero;
718       *Remainder = D.Zero;
719       return;
720     }
721 
722     // A simple case when N/1. The quotient is N.
723     if (Denominator->isOne()) {
724       *Quotient = Numerator;
725       *Remainder = D.Zero;
726       return;
727     }
728 
729     // Split the Denominator when it is a product.
730     if (const SCEVMulExpr *T = dyn_cast<const SCEVMulExpr>(Denominator)) {
731       const SCEV *Q, *R;
732       *Quotient = Numerator;
733       for (const SCEV *Op : T->operands()) {
734         divide(SE, *Quotient, Op, &Q, &R);
735         *Quotient = Q;
736 
737         // Bail out when the Numerator is not divisible by one of the terms of
738         // the Denominator.
739         if (!R->isZero()) {
740           *Quotient = D.Zero;
741           *Remainder = Numerator;
742           return;
743         }
744       }
745       *Remainder = D.Zero;
746       return;
747     }
748 
749     D.visit(Numerator);
750     *Quotient = D.Quotient;
751     *Remainder = D.Remainder;
752   }
753 
754   // Except in the trivial case described above, we do not know how to divide
755   // Expr by Denominator for the following functions with empty implementation.
756   void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
757   void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
758   void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
759   void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
760   void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
761   void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
762   void visitUnknown(const SCEVUnknown *Numerator) {}
763   void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
764 
765   void visitConstant(const SCEVConstant *Numerator) {
766     if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
767       APInt NumeratorVal = Numerator->getAPInt();
768       APInt DenominatorVal = D->getAPInt();
769       uint32_t NumeratorBW = NumeratorVal.getBitWidth();
770       uint32_t DenominatorBW = DenominatorVal.getBitWidth();
771 
772       if (NumeratorBW > DenominatorBW)
773         DenominatorVal = DenominatorVal.sext(NumeratorBW);
774       else if (NumeratorBW < DenominatorBW)
775         NumeratorVal = NumeratorVal.sext(DenominatorBW);
776 
777       APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
778       APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
779       APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
780       Quotient = SE.getConstant(QuotientVal);
781       Remainder = SE.getConstant(RemainderVal);
782       return;
783     }
784   }
785 
786   void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
787     const SCEV *StartQ, *StartR, *StepQ, *StepR;
788     if (!Numerator->isAffine())
789       return cannotDivide(Numerator);
790     divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
791     divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
792     // Bail out if the types do not match.
793     Type *Ty = Denominator->getType();
794     if (Ty != StartQ->getType() || Ty != StartR->getType() ||
795         Ty != StepQ->getType() || Ty != StepR->getType())
796       return cannotDivide(Numerator);
797     Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
798                                 Numerator->getNoWrapFlags());
799     Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
800                                  Numerator->getNoWrapFlags());
801   }
802 
803   void visitAddExpr(const SCEVAddExpr *Numerator) {
804     SmallVector<const SCEV *, 2> Qs, Rs;
805     Type *Ty = Denominator->getType();
806 
807     for (const SCEV *Op : Numerator->operands()) {
808       const SCEV *Q, *R;
809       divide(SE, Op, Denominator, &Q, &R);
810 
811       // Bail out if types do not match.
812       if (Ty != Q->getType() || Ty != R->getType())
813         return cannotDivide(Numerator);
814 
815       Qs.push_back(Q);
816       Rs.push_back(R);
817     }
818 
819     if (Qs.size() == 1) {
820       Quotient = Qs[0];
821       Remainder = Rs[0];
822       return;
823     }
824 
825     Quotient = SE.getAddExpr(Qs);
826     Remainder = SE.getAddExpr(Rs);
827   }
828 
829   void visitMulExpr(const SCEVMulExpr *Numerator) {
830     SmallVector<const SCEV *, 2> Qs;
831     Type *Ty = Denominator->getType();
832 
833     bool FoundDenominatorTerm = false;
834     for (const SCEV *Op : Numerator->operands()) {
835       // Bail out if types do not match.
836       if (Ty != Op->getType())
837         return cannotDivide(Numerator);
838 
839       if (FoundDenominatorTerm) {
840         Qs.push_back(Op);
841         continue;
842       }
843 
844       // Check whether Denominator divides one of the product operands.
845       const SCEV *Q, *R;
846       divide(SE, Op, Denominator, &Q, &R);
847       if (!R->isZero()) {
848         Qs.push_back(Op);
849         continue;
850       }
851 
852       // Bail out if types do not match.
853       if (Ty != Q->getType())
854         return cannotDivide(Numerator);
855 
856       FoundDenominatorTerm = true;
857       Qs.push_back(Q);
858     }
859 
860     if (FoundDenominatorTerm) {
861       Remainder = Zero;
862       if (Qs.size() == 1)
863         Quotient = Qs[0];
864       else
865         Quotient = SE.getMulExpr(Qs);
866       return;
867     }
868 
869     if (!isa<SCEVUnknown>(Denominator))
870       return cannotDivide(Numerator);
871 
872     // The Remainder is obtained by replacing Denominator by 0 in Numerator.
873     ValueToValueMap RewriteMap;
874     RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
875         cast<SCEVConstant>(Zero)->getValue();
876     Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
877 
878     if (Remainder->isZero()) {
879       // The Quotient is obtained by replacing Denominator by 1 in Numerator.
880       RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
881           cast<SCEVConstant>(One)->getValue();
882       Quotient =
883           SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
884       return;
885     }
886 
887     // Quotient is (Numerator - Remainder) divided by Denominator.
888     const SCEV *Q, *R;
889     const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
890     // This SCEV does not seem to simplify: fail the division here.
891     if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator))
892       return cannotDivide(Numerator);
893     divide(SE, Diff, Denominator, &Q, &R);
894     if (R != Zero)
895       return cannotDivide(Numerator);
896     Quotient = Q;
897   }
898 
899 private:
900   SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
901                const SCEV *Denominator)
902       : SE(S), Denominator(Denominator) {
903     Zero = SE.getZero(Denominator->getType());
904     One = SE.getOne(Denominator->getType());
905 
906     // We generally do not know how to divide Expr by Denominator. We
907     // initialize the division to a "cannot divide" state to simplify the rest
908     // of the code.
909     cannotDivide(Numerator);
910   }
911 
912   // Convenience function for giving up on the division. We set the quotient to
913   // be equal to zero and the remainder to be equal to the numerator.
914   void cannotDivide(const SCEV *Numerator) {
915     Quotient = Zero;
916     Remainder = Numerator;
917   }
918 
919   ScalarEvolution &SE;
920   const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
921 };
922 
923 }
924 
925 //===----------------------------------------------------------------------===//
926 //                      Simple SCEV method implementations
927 //===----------------------------------------------------------------------===//
928 
929 /// BinomialCoefficient - Compute BC(It, K).  The result has width W.
930 /// Assume, K > 0.
931 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
932                                        ScalarEvolution &SE,
933                                        Type *ResultTy) {
934   // Handle the simplest case efficiently.
935   if (K == 1)
936     return SE.getTruncateOrZeroExtend(It, ResultTy);
937 
938   // We are using the following formula for BC(It, K):
939   //
940   //   BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
941   //
942   // Suppose, W is the bitwidth of the return value.  We must be prepared for
943   // overflow.  Hence, we must assure that the result of our computation is
944   // equal to the accurate one modulo 2^W.  Unfortunately, division isn't
945   // safe in modular arithmetic.
946   //
947   // However, this code doesn't use exactly that formula; the formula it uses
948   // is something like the following, where T is the number of factors of 2 in
949   // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
950   // exponentiation:
951   //
952   //   BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
953   //
954   // This formula is trivially equivalent to the previous formula.  However,
955   // this formula can be implemented much more efficiently.  The trick is that
956   // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
957   // arithmetic.  To do exact division in modular arithmetic, all we have
958   // to do is multiply by the inverse.  Therefore, this step can be done at
959   // width W.
960   //
961   // The next issue is how to safely do the division by 2^T.  The way this
962   // is done is by doing the multiplication step at a width of at least W + T
963   // bits.  This way, the bottom W+T bits of the product are accurate. Then,
964   // when we perform the division by 2^T (which is equivalent to a right shift
965   // by T), the bottom W bits are accurate.  Extra bits are okay; they'll get
966   // truncated out after the division by 2^T.
967   //
968   // In comparison to just directly using the first formula, this technique
969   // is much more efficient; using the first formula requires W * K bits,
970   // but this formula less than W + K bits. Also, the first formula requires
971   // a division step, whereas this formula only requires multiplies and shifts.
972   //
973   // It doesn't matter whether the subtraction step is done in the calculation
974   // width or the input iteration count's width; if the subtraction overflows,
975   // the result must be zero anyway.  We prefer here to do it in the width of
976   // the induction variable because it helps a lot for certain cases; CodeGen
977   // isn't smart enough to ignore the overflow, which leads to much less
978   // efficient code if the width of the subtraction is wider than the native
979   // register width.
980   //
981   // (It's possible to not widen at all by pulling out factors of 2 before
982   // the multiplication; for example, K=2 can be calculated as
983   // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
984   // extra arithmetic, so it's not an obvious win, and it gets
985   // much more complicated for K > 3.)
986 
987   // Protection from insane SCEVs; this bound is conservative,
988   // but it probably doesn't matter.
989   if (K > 1000)
990     return SE.getCouldNotCompute();
991 
992   unsigned W = SE.getTypeSizeInBits(ResultTy);
993 
994   // Calculate K! / 2^T and T; we divide out the factors of two before
995   // multiplying for calculating K! / 2^T to avoid overflow.
996   // Other overflow doesn't matter because we only care about the bottom
997   // W bits of the result.
998   APInt OddFactorial(W, 1);
999   unsigned T = 1;
1000   for (unsigned i = 3; i <= K; ++i) {
1001     APInt Mult(W, i);
1002     unsigned TwoFactors = Mult.countTrailingZeros();
1003     T += TwoFactors;
1004     Mult = Mult.lshr(TwoFactors);
1005     OddFactorial *= Mult;
1006   }
1007 
1008   // We need at least W + T bits for the multiplication step
1009   unsigned CalculationBits = W + T;
1010 
1011   // Calculate 2^T, at width T+W.
1012   APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1013 
1014   // Calculate the multiplicative inverse of K! / 2^T;
1015   // this multiplication factor will perform the exact division by
1016   // K! / 2^T.
1017   APInt Mod = APInt::getSignedMinValue(W+1);
1018   APInt MultiplyFactor = OddFactorial.zext(W+1);
1019   MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1020   MultiplyFactor = MultiplyFactor.trunc(W);
1021 
1022   // Calculate the product, at width T+W
1023   IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1024                                                       CalculationBits);
1025   const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1026   for (unsigned i = 1; i != K; ++i) {
1027     const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1028     Dividend = SE.getMulExpr(Dividend,
1029                              SE.getTruncateOrZeroExtend(S, CalculationTy));
1030   }
1031 
1032   // Divide by 2^T
1033   const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1034 
1035   // Truncate the result, and divide by K! / 2^T.
1036 
1037   return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1038                        SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1039 }
1040 
1041 /// evaluateAtIteration - Return the value of this chain of recurrences at
1042 /// the specified iteration number.  We can evaluate this recurrence by
1043 /// multiplying each element in the chain by the binomial coefficient
1044 /// corresponding to it.  In other words, we can evaluate {A,+,B,+,C,+,D} as:
1045 ///
1046 ///   A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1047 ///
1048 /// where BC(It, k) stands for binomial coefficient.
1049 ///
1050 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1051                                                 ScalarEvolution &SE) const {
1052   const SCEV *Result = getStart();
1053   for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1054     // The computation is correct in the face of overflow provided that the
1055     // multiplication is performed _after_ the evaluation of the binomial
1056     // coefficient.
1057     const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1058     if (isa<SCEVCouldNotCompute>(Coeff))
1059       return Coeff;
1060 
1061     Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1062   }
1063   return Result;
1064 }
1065 
1066 //===----------------------------------------------------------------------===//
1067 //                    SCEV Expression folder implementations
1068 //===----------------------------------------------------------------------===//
1069 
1070 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
1071                                              Type *Ty) {
1072   assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1073          "This is not a truncating conversion!");
1074   assert(isSCEVable(Ty) &&
1075          "This is not a conversion to a SCEVable type!");
1076   Ty = getEffectiveSCEVType(Ty);
1077 
1078   FoldingSetNodeID ID;
1079   ID.AddInteger(scTruncate);
1080   ID.AddPointer(Op);
1081   ID.AddPointer(Ty);
1082   void *IP = nullptr;
1083   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1084 
1085   // Fold if the operand is constant.
1086   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1087     return getConstant(
1088       cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1089 
1090   // trunc(trunc(x)) --> trunc(x)
1091   if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1092     return getTruncateExpr(ST->getOperand(), Ty);
1093 
1094   // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1095   if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1096     return getTruncateOrSignExtend(SS->getOperand(), Ty);
1097 
1098   // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1099   if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1100     return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1101 
1102   // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
1103   // eliminate all the truncates, or we replace other casts with truncates.
1104   if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
1105     SmallVector<const SCEV *, 4> Operands;
1106     bool hasTrunc = false;
1107     for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
1108       const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
1109       if (!isa<SCEVCastExpr>(SA->getOperand(i)))
1110         hasTrunc = isa<SCEVTruncateExpr>(S);
1111       Operands.push_back(S);
1112     }
1113     if (!hasTrunc)
1114       return getAddExpr(Operands);
1115     UniqueSCEVs.FindNodeOrInsertPos(ID, IP);  // Mutates IP, returns NULL.
1116   }
1117 
1118   // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
1119   // eliminate all the truncates, or we replace other casts with truncates.
1120   if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
1121     SmallVector<const SCEV *, 4> Operands;
1122     bool hasTrunc = false;
1123     for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
1124       const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
1125       if (!isa<SCEVCastExpr>(SM->getOperand(i)))
1126         hasTrunc = isa<SCEVTruncateExpr>(S);
1127       Operands.push_back(S);
1128     }
1129     if (!hasTrunc)
1130       return getMulExpr(Operands);
1131     UniqueSCEVs.FindNodeOrInsertPos(ID, IP);  // Mutates IP, returns NULL.
1132   }
1133 
1134   // If the input value is a chrec scev, truncate the chrec's operands.
1135   if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1136     SmallVector<const SCEV *, 4> Operands;
1137     for (const SCEV *Op : AddRec->operands())
1138       Operands.push_back(getTruncateExpr(Op, Ty));
1139     return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1140   }
1141 
1142   // The cast wasn't folded; create an explicit cast node. We can reuse
1143   // the existing insert position since if we get here, we won't have
1144   // made any changes which would invalidate it.
1145   SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1146                                                  Op, Ty);
1147   UniqueSCEVs.InsertNode(S, IP);
1148   return S;
1149 }
1150 
1151 // Get the limit of a recurrence such that incrementing by Step cannot cause
1152 // signed overflow as long as the value of the recurrence within the
1153 // loop does not exceed this limit before incrementing.
1154 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1155                                                  ICmpInst::Predicate *Pred,
1156                                                  ScalarEvolution *SE) {
1157   unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1158   if (SE->isKnownPositive(Step)) {
1159     *Pred = ICmpInst::ICMP_SLT;
1160     return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1161                            SE->getSignedRange(Step).getSignedMax());
1162   }
1163   if (SE->isKnownNegative(Step)) {
1164     *Pred = ICmpInst::ICMP_SGT;
1165     return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1166                            SE->getSignedRange(Step).getSignedMin());
1167   }
1168   return nullptr;
1169 }
1170 
1171 // Get the limit of a recurrence such that incrementing by Step cannot cause
1172 // unsigned overflow as long as the value of the recurrence within the loop does
1173 // not exceed this limit before incrementing.
1174 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1175                                                    ICmpInst::Predicate *Pred,
1176                                                    ScalarEvolution *SE) {
1177   unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1178   *Pred = ICmpInst::ICMP_ULT;
1179 
1180   return SE->getConstant(APInt::getMinValue(BitWidth) -
1181                          SE->getUnsignedRange(Step).getUnsignedMax());
1182 }
1183 
1184 namespace {
1185 
1186 struct ExtendOpTraitsBase {
1187   typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *);
1188 };
1189 
1190 // Used to make code generic over signed and unsigned overflow.
1191 template <typename ExtendOp> struct ExtendOpTraits {
1192   // Members present:
1193   //
1194   // static const SCEV::NoWrapFlags WrapType;
1195   //
1196   // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1197   //
1198   // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1199   //                                           ICmpInst::Predicate *Pred,
1200   //                                           ScalarEvolution *SE);
1201 };
1202 
1203 template <>
1204 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1205   static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1206 
1207   static const GetExtendExprTy GetExtendExpr;
1208 
1209   static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1210                                              ICmpInst::Predicate *Pred,
1211                                              ScalarEvolution *SE) {
1212     return getSignedOverflowLimitForStep(Step, Pred, SE);
1213   }
1214 };
1215 
1216 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1217     SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1218 
1219 template <>
1220 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1221   static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1222 
1223   static const GetExtendExprTy GetExtendExpr;
1224 
1225   static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1226                                              ICmpInst::Predicate *Pred,
1227                                              ScalarEvolution *SE) {
1228     return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1229   }
1230 };
1231 
1232 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1233     SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1234 }
1235 
1236 // The recurrence AR has been shown to have no signed/unsigned wrap or something
1237 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1238 // easily prove NSW/NUW for its preincrement or postincrement sibling. This
1239 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1240 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1241 // expression "Step + sext/zext(PreIncAR)" is congruent with
1242 // "sext/zext(PostIncAR)"
1243 template <typename ExtendOpTy>
1244 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1245                                         ScalarEvolution *SE) {
1246   auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1247   auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1248 
1249   const Loop *L = AR->getLoop();
1250   const SCEV *Start = AR->getStart();
1251   const SCEV *Step = AR->getStepRecurrence(*SE);
1252 
1253   // Check for a simple looking step prior to loop entry.
1254   const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1255   if (!SA)
1256     return nullptr;
1257 
1258   // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1259   // subtraction is expensive. For this purpose, perform a quick and dirty
1260   // difference, by checking for Step in the operand list.
1261   SmallVector<const SCEV *, 4> DiffOps;
1262   for (const SCEV *Op : SA->operands())
1263     if (Op != Step)
1264       DiffOps.push_back(Op);
1265 
1266   if (DiffOps.size() == SA->getNumOperands())
1267     return nullptr;
1268 
1269   // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1270   // `Step`:
1271 
1272   // 1. NSW/NUW flags on the step increment.
1273   auto PreStartFlags =
1274     ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
1275   const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
1276   const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1277       SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1278 
1279   // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1280   // "S+X does not sign/unsign-overflow".
1281   //
1282 
1283   const SCEV *BECount = SE->getBackedgeTakenCount(L);
1284   if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1285       !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1286     return PreStart;
1287 
1288   // 2. Direct overflow check on the step operation's expression.
1289   unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1290   Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1291   const SCEV *OperandExtendedStart =
1292       SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy),
1293                      (SE->*GetExtendExpr)(Step, WideTy));
1294   if ((SE->*GetExtendExpr)(Start, WideTy) == OperandExtendedStart) {
1295     if (PreAR && AR->getNoWrapFlags(WrapType)) {
1296       // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1297       // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1298       // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`.  Cache this fact.
1299       const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1300     }
1301     return PreStart;
1302   }
1303 
1304   // 3. Loop precondition.
1305   ICmpInst::Predicate Pred;
1306   const SCEV *OverflowLimit =
1307       ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1308 
1309   if (OverflowLimit &&
1310       SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
1311     return PreStart;
1312 
1313   return nullptr;
1314 }
1315 
1316 // Get the normalized zero or sign extended expression for this AddRec's Start.
1317 template <typename ExtendOpTy>
1318 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1319                                         ScalarEvolution *SE) {
1320   auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1321 
1322   const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE);
1323   if (!PreStart)
1324     return (SE->*GetExtendExpr)(AR->getStart(), Ty);
1325 
1326   return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty),
1327                         (SE->*GetExtendExpr)(PreStart, Ty));
1328 }
1329 
1330 // Try to prove away overflow by looking at "nearby" add recurrences.  A
1331 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1332 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1333 //
1334 // Formally:
1335 //
1336 //     {S,+,X} == {S-T,+,X} + T
1337 //  => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1338 //
1339 // If ({S-T,+,X} + T) does not overflow  ... (1)
1340 //
1341 //  RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1342 //
1343 // If {S-T,+,X} does not overflow  ... (2)
1344 //
1345 //  RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1346 //      == {Ext(S-T)+Ext(T),+,Ext(X)}
1347 //
1348 // If (S-T)+T does not overflow  ... (3)
1349 //
1350 //  RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1351 //      == {Ext(S),+,Ext(X)} == LHS
1352 //
1353 // Thus, if (1), (2) and (3) are true for some T, then
1354 //   Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1355 //
1356 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1357 // does not overflow" restricted to the 0th iteration.  Therefore we only need
1358 // to check for (1) and (2).
1359 //
1360 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1361 // is `Delta` (defined below).
1362 //
1363 template <typename ExtendOpTy>
1364 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1365                                                 const SCEV *Step,
1366                                                 const Loop *L) {
1367   auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1368 
1369   // We restrict `Start` to a constant to prevent SCEV from spending too much
1370   // time here.  It is correct (but more expensive) to continue with a
1371   // non-constant `Start` and do a general SCEV subtraction to compute
1372   // `PreStart` below.
1373   //
1374   const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1375   if (!StartC)
1376     return false;
1377 
1378   APInt StartAI = StartC->getAPInt();
1379 
1380   for (unsigned Delta : {-2, -1, 1, 2}) {
1381     const SCEV *PreStart = getConstant(StartAI - Delta);
1382 
1383     FoldingSetNodeID ID;
1384     ID.AddInteger(scAddRecExpr);
1385     ID.AddPointer(PreStart);
1386     ID.AddPointer(Step);
1387     ID.AddPointer(L);
1388     void *IP = nullptr;
1389     const auto *PreAR =
1390       static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1391 
1392     // Give up if we don't already have the add recurrence we need because
1393     // actually constructing an add recurrence is relatively expensive.
1394     if (PreAR && PreAR->getNoWrapFlags(WrapType)) {  // proves (2)
1395       const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1396       ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1397       const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1398           DeltaS, &Pred, this);
1399       if (Limit && isKnownPredicate(Pred, PreAR, Limit))  // proves (1)
1400         return true;
1401     }
1402   }
1403 
1404   return false;
1405 }
1406 
1407 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
1408                                                Type *Ty) {
1409   assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1410          "This is not an extending conversion!");
1411   assert(isSCEVable(Ty) &&
1412          "This is not a conversion to a SCEVable type!");
1413   Ty = getEffectiveSCEVType(Ty);
1414 
1415   // Fold if the operand is constant.
1416   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1417     return getConstant(
1418       cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1419 
1420   // zext(zext(x)) --> zext(x)
1421   if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1422     return getZeroExtendExpr(SZ->getOperand(), Ty);
1423 
1424   // Before doing any expensive analysis, check to see if we've already
1425   // computed a SCEV for this Op and Ty.
1426   FoldingSetNodeID ID;
1427   ID.AddInteger(scZeroExtend);
1428   ID.AddPointer(Op);
1429   ID.AddPointer(Ty);
1430   void *IP = nullptr;
1431   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1432 
1433   // zext(trunc(x)) --> zext(x) or x or trunc(x)
1434   if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1435     // It's possible the bits taken off by the truncate were all zero bits. If
1436     // so, we should be able to simplify this further.
1437     const SCEV *X = ST->getOperand();
1438     ConstantRange CR = getUnsignedRange(X);
1439     unsigned TruncBits = getTypeSizeInBits(ST->getType());
1440     unsigned NewBits = getTypeSizeInBits(Ty);
1441     if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1442             CR.zextOrTrunc(NewBits)))
1443       return getTruncateOrZeroExtend(X, Ty);
1444   }
1445 
1446   // If the input value is a chrec scev, and we can prove that the value
1447   // did not overflow the old, smaller, value, we can zero extend all of the
1448   // operands (often constants).  This allows analysis of something like
1449   // this:  for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1450   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1451     if (AR->isAffine()) {
1452       const SCEV *Start = AR->getStart();
1453       const SCEV *Step = AR->getStepRecurrence(*this);
1454       unsigned BitWidth = getTypeSizeInBits(AR->getType());
1455       const Loop *L = AR->getLoop();
1456 
1457       if (!AR->hasNoUnsignedWrap()) {
1458         auto NewFlags = proveNoWrapViaConstantRanges(AR);
1459         const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1460       }
1461 
1462       // If we have special knowledge that this addrec won't overflow,
1463       // we don't need to do any further analysis.
1464       if (AR->hasNoUnsignedWrap())
1465         return getAddRecExpr(
1466             getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1467             getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1468 
1469       // Check whether the backedge-taken count is SCEVCouldNotCompute.
1470       // Note that this serves two purposes: It filters out loops that are
1471       // simply not analyzable, and it covers the case where this code is
1472       // being called from within backedge-taken count analysis, such that
1473       // attempting to ask for the backedge-taken count would likely result
1474       // in infinite recursion. In the later case, the analysis code will
1475       // cope with a conservative value, and it will take care to purge
1476       // that value once it has finished.
1477       const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1478       if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1479         // Manually compute the final value for AR, checking for
1480         // overflow.
1481 
1482         // Check whether the backedge-taken count can be losslessly casted to
1483         // the addrec's type. The count is always unsigned.
1484         const SCEV *CastedMaxBECount =
1485           getTruncateOrZeroExtend(MaxBECount, Start->getType());
1486         const SCEV *RecastedMaxBECount =
1487           getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1488         if (MaxBECount == RecastedMaxBECount) {
1489           Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1490           // Check whether Start+Step*MaxBECount has no unsigned overflow.
1491           const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1492           const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1493           const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1494           const SCEV *WideMaxBECount =
1495             getZeroExtendExpr(CastedMaxBECount, WideTy);
1496           const SCEV *OperandExtendedAdd =
1497             getAddExpr(WideStart,
1498                        getMulExpr(WideMaxBECount,
1499                                   getZeroExtendExpr(Step, WideTy)));
1500           if (ZAdd == OperandExtendedAdd) {
1501             // Cache knowledge of AR NUW, which is propagated to this AddRec.
1502             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1503             // Return the expression with the addrec on the outside.
1504             return getAddRecExpr(
1505                 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1506                 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1507           }
1508           // Similar to above, only this time treat the step value as signed.
1509           // This covers loops that count down.
1510           OperandExtendedAdd =
1511             getAddExpr(WideStart,
1512                        getMulExpr(WideMaxBECount,
1513                                   getSignExtendExpr(Step, WideTy)));
1514           if (ZAdd == OperandExtendedAdd) {
1515             // Cache knowledge of AR NW, which is propagated to this AddRec.
1516             // Negative step causes unsigned wrap, but it still can't self-wrap.
1517             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1518             // Return the expression with the addrec on the outside.
1519             return getAddRecExpr(
1520                 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1521                 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1522           }
1523         }
1524 
1525         // If the backedge is guarded by a comparison with the pre-inc value
1526         // the addrec is safe. Also, if the entry is guarded by a comparison
1527         // with the start value and the backedge is guarded by a comparison
1528         // with the post-inc value, the addrec is safe.
1529         if (isKnownPositive(Step)) {
1530           const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1531                                       getUnsignedRange(Step).getUnsignedMax());
1532           if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1533               (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1534                isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1535                                            AR->getPostIncExpr(*this), N))) {
1536             // Cache knowledge of AR NUW, which is propagated to this AddRec.
1537             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1538             // Return the expression with the addrec on the outside.
1539             return getAddRecExpr(
1540                 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1541                 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1542           }
1543         } else if (isKnownNegative(Step)) {
1544           const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1545                                       getSignedRange(Step).getSignedMin());
1546           if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1547               (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1548                isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1549                                            AR->getPostIncExpr(*this), N))) {
1550             // Cache knowledge of AR NW, which is propagated to this AddRec.
1551             // Negative step causes unsigned wrap, but it still can't self-wrap.
1552             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1553             // Return the expression with the addrec on the outside.
1554             return getAddRecExpr(
1555                 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1556                 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1557           }
1558         }
1559       }
1560 
1561       if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1562         const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1563         return getAddRecExpr(
1564             getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1565             getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1566       }
1567     }
1568 
1569   if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1570     // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
1571     if (SA->hasNoUnsignedWrap()) {
1572       // If the addition does not unsign overflow then we can, by definition,
1573       // commute the zero extension with the addition operation.
1574       SmallVector<const SCEV *, 4> Ops;
1575       for (const auto *Op : SA->operands())
1576         Ops.push_back(getZeroExtendExpr(Op, Ty));
1577       return getAddExpr(Ops, SCEV::FlagNUW);
1578     }
1579   }
1580 
1581   // The cast wasn't folded; create an explicit cast node.
1582   // Recompute the insert position, as it may have been invalidated.
1583   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1584   SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1585                                                    Op, Ty);
1586   UniqueSCEVs.InsertNode(S, IP);
1587   return S;
1588 }
1589 
1590 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1591                                                Type *Ty) {
1592   assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1593          "This is not an extending conversion!");
1594   assert(isSCEVable(Ty) &&
1595          "This is not a conversion to a SCEVable type!");
1596   Ty = getEffectiveSCEVType(Ty);
1597 
1598   // Fold if the operand is constant.
1599   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1600     return getConstant(
1601       cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1602 
1603   // sext(sext(x)) --> sext(x)
1604   if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1605     return getSignExtendExpr(SS->getOperand(), Ty);
1606 
1607   // sext(zext(x)) --> zext(x)
1608   if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1609     return getZeroExtendExpr(SZ->getOperand(), Ty);
1610 
1611   // Before doing any expensive analysis, check to see if we've already
1612   // computed a SCEV for this Op and Ty.
1613   FoldingSetNodeID ID;
1614   ID.AddInteger(scSignExtend);
1615   ID.AddPointer(Op);
1616   ID.AddPointer(Ty);
1617   void *IP = nullptr;
1618   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1619 
1620   // sext(trunc(x)) --> sext(x) or x or trunc(x)
1621   if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1622     // It's possible the bits taken off by the truncate were all sign bits. If
1623     // so, we should be able to simplify this further.
1624     const SCEV *X = ST->getOperand();
1625     ConstantRange CR = getSignedRange(X);
1626     unsigned TruncBits = getTypeSizeInBits(ST->getType());
1627     unsigned NewBits = getTypeSizeInBits(Ty);
1628     if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1629             CR.sextOrTrunc(NewBits)))
1630       return getTruncateOrSignExtend(X, Ty);
1631   }
1632 
1633   // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1634   if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1635     if (SA->getNumOperands() == 2) {
1636       auto *SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1637       auto *SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1638       if (SMul && SC1) {
1639         if (auto *SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1640           const APInt &C1 = SC1->getAPInt();
1641           const APInt &C2 = SC2->getAPInt();
1642           if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1643               C2.ugt(C1) && C2.isPowerOf2())
1644             return getAddExpr(getSignExtendExpr(SC1, Ty),
1645                               getSignExtendExpr(SMul, Ty));
1646         }
1647       }
1648     }
1649 
1650     // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
1651     if (SA->hasNoSignedWrap()) {
1652       // If the addition does not sign overflow then we can, by definition,
1653       // commute the sign extension with the addition operation.
1654       SmallVector<const SCEV *, 4> Ops;
1655       for (const auto *Op : SA->operands())
1656         Ops.push_back(getSignExtendExpr(Op, Ty));
1657       return getAddExpr(Ops, SCEV::FlagNSW);
1658     }
1659   }
1660   // If the input value is a chrec scev, and we can prove that the value
1661   // did not overflow the old, smaller, value, we can sign extend all of the
1662   // operands (often constants).  This allows analysis of something like
1663   // this:  for (signed char X = 0; X < 100; ++X) { int Y = X; }
1664   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1665     if (AR->isAffine()) {
1666       const SCEV *Start = AR->getStart();
1667       const SCEV *Step = AR->getStepRecurrence(*this);
1668       unsigned BitWidth = getTypeSizeInBits(AR->getType());
1669       const Loop *L = AR->getLoop();
1670 
1671       if (!AR->hasNoSignedWrap()) {
1672         auto NewFlags = proveNoWrapViaConstantRanges(AR);
1673         const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1674       }
1675 
1676       // If we have special knowledge that this addrec won't overflow,
1677       // we don't need to do any further analysis.
1678       if (AR->hasNoSignedWrap())
1679         return getAddRecExpr(
1680             getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1681             getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW);
1682 
1683       // Check whether the backedge-taken count is SCEVCouldNotCompute.
1684       // Note that this serves two purposes: It filters out loops that are
1685       // simply not analyzable, and it covers the case where this code is
1686       // being called from within backedge-taken count analysis, such that
1687       // attempting to ask for the backedge-taken count would likely result
1688       // in infinite recursion. In the later case, the analysis code will
1689       // cope with a conservative value, and it will take care to purge
1690       // that value once it has finished.
1691       const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1692       if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1693         // Manually compute the final value for AR, checking for
1694         // overflow.
1695 
1696         // Check whether the backedge-taken count can be losslessly casted to
1697         // the addrec's type. The count is always unsigned.
1698         const SCEV *CastedMaxBECount =
1699           getTruncateOrZeroExtend(MaxBECount, Start->getType());
1700         const SCEV *RecastedMaxBECount =
1701           getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1702         if (MaxBECount == RecastedMaxBECount) {
1703           Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1704           // Check whether Start+Step*MaxBECount has no signed overflow.
1705           const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1706           const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1707           const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1708           const SCEV *WideMaxBECount =
1709             getZeroExtendExpr(CastedMaxBECount, WideTy);
1710           const SCEV *OperandExtendedAdd =
1711             getAddExpr(WideStart,
1712                        getMulExpr(WideMaxBECount,
1713                                   getSignExtendExpr(Step, WideTy)));
1714           if (SAdd == OperandExtendedAdd) {
1715             // Cache knowledge of AR NSW, which is propagated to this AddRec.
1716             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1717             // Return the expression with the addrec on the outside.
1718             return getAddRecExpr(
1719                 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1720                 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1721           }
1722           // Similar to above, only this time treat the step value as unsigned.
1723           // This covers loops that count up with an unsigned step.
1724           OperandExtendedAdd =
1725             getAddExpr(WideStart,
1726                        getMulExpr(WideMaxBECount,
1727                                   getZeroExtendExpr(Step, WideTy)));
1728           if (SAdd == OperandExtendedAdd) {
1729             // If AR wraps around then
1730             //
1731             //    abs(Step) * MaxBECount > unsigned-max(AR->getType())
1732             // => SAdd != OperandExtendedAdd
1733             //
1734             // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1735             // (SAdd == OperandExtendedAdd => AR is NW)
1736 
1737             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1738 
1739             // Return the expression with the addrec on the outside.
1740             return getAddRecExpr(
1741                 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1742                 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1743           }
1744         }
1745 
1746         // If the backedge is guarded by a comparison with the pre-inc value
1747         // the addrec is safe. Also, if the entry is guarded by a comparison
1748         // with the start value and the backedge is guarded by a comparison
1749         // with the post-inc value, the addrec is safe.
1750         ICmpInst::Predicate Pred;
1751         const SCEV *OverflowLimit =
1752             getSignedOverflowLimitForStep(Step, &Pred, this);
1753         if (OverflowLimit &&
1754             (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1755              (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1756               isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1757                                           OverflowLimit)))) {
1758           // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1759           const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1760           return getAddRecExpr(
1761               getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1762               getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1763         }
1764       }
1765       // If Start and Step are constants, check if we can apply this
1766       // transformation:
1767       // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1768       auto *SC1 = dyn_cast<SCEVConstant>(Start);
1769       auto *SC2 = dyn_cast<SCEVConstant>(Step);
1770       if (SC1 && SC2) {
1771         const APInt &C1 = SC1->getAPInt();
1772         const APInt &C2 = SC2->getAPInt();
1773         if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1774             C2.isPowerOf2()) {
1775           Start = getSignExtendExpr(Start, Ty);
1776           const SCEV *NewAR = getAddRecExpr(getZero(AR->getType()), Step, L,
1777                                             AR->getNoWrapFlags());
1778           return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1779         }
1780       }
1781 
1782       if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
1783         const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1784         return getAddRecExpr(
1785             getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1786             getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1787       }
1788     }
1789 
1790   // If the input value is provably positive and we could not simplify
1791   // away the sext build a zext instead.
1792   if (isKnownNonNegative(Op))
1793     return getZeroExtendExpr(Op, Ty);
1794 
1795   // The cast wasn't folded; create an explicit cast node.
1796   // Recompute the insert position, as it may have been invalidated.
1797   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1798   SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1799                                                    Op, Ty);
1800   UniqueSCEVs.InsertNode(S, IP);
1801   return S;
1802 }
1803 
1804 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1805 /// unspecified bits out to the given type.
1806 ///
1807 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1808                                               Type *Ty) {
1809   assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1810          "This is not an extending conversion!");
1811   assert(isSCEVable(Ty) &&
1812          "This is not a conversion to a SCEVable type!");
1813   Ty = getEffectiveSCEVType(Ty);
1814 
1815   // Sign-extend negative constants.
1816   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1817     if (SC->getAPInt().isNegative())
1818       return getSignExtendExpr(Op, Ty);
1819 
1820   // Peel off a truncate cast.
1821   if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1822     const SCEV *NewOp = T->getOperand();
1823     if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1824       return getAnyExtendExpr(NewOp, Ty);
1825     return getTruncateOrNoop(NewOp, Ty);
1826   }
1827 
1828   // Next try a zext cast. If the cast is folded, use it.
1829   const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1830   if (!isa<SCEVZeroExtendExpr>(ZExt))
1831     return ZExt;
1832 
1833   // Next try a sext cast. If the cast is folded, use it.
1834   const SCEV *SExt = getSignExtendExpr(Op, Ty);
1835   if (!isa<SCEVSignExtendExpr>(SExt))
1836     return SExt;
1837 
1838   // Force the cast to be folded into the operands of an addrec.
1839   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1840     SmallVector<const SCEV *, 4> Ops;
1841     for (const SCEV *Op : AR->operands())
1842       Ops.push_back(getAnyExtendExpr(Op, Ty));
1843     return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1844   }
1845 
1846   // If the expression is obviously signed, use the sext cast value.
1847   if (isa<SCEVSMaxExpr>(Op))
1848     return SExt;
1849 
1850   // Absent any other information, use the zext cast value.
1851   return ZExt;
1852 }
1853 
1854 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1855 /// a list of operands to be added under the given scale, update the given
1856 /// map. This is a helper function for getAddRecExpr. As an example of
1857 /// what it does, given a sequence of operands that would form an add
1858 /// expression like this:
1859 ///
1860 ///    m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1861 ///
1862 /// where A and B are constants, update the map with these values:
1863 ///
1864 ///    (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1865 ///
1866 /// and add 13 + A*B*29 to AccumulatedConstant.
1867 /// This will allow getAddRecExpr to produce this:
1868 ///
1869 ///    13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1870 ///
1871 /// This form often exposes folding opportunities that are hidden in
1872 /// the original operand list.
1873 ///
1874 /// Return true iff it appears that any interesting folding opportunities
1875 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1876 /// the common case where no interesting opportunities are present, and
1877 /// is also used as a check to avoid infinite recursion.
1878 ///
1879 static bool
1880 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1881                              SmallVectorImpl<const SCEV *> &NewOps,
1882                              APInt &AccumulatedConstant,
1883                              const SCEV *const *Ops, size_t NumOperands,
1884                              const APInt &Scale,
1885                              ScalarEvolution &SE) {
1886   bool Interesting = false;
1887 
1888   // Iterate over the add operands. They are sorted, with constants first.
1889   unsigned i = 0;
1890   while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1891     ++i;
1892     // Pull a buried constant out to the outside.
1893     if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1894       Interesting = true;
1895     AccumulatedConstant += Scale * C->getAPInt();
1896   }
1897 
1898   // Next comes everything else. We're especially interested in multiplies
1899   // here, but they're in the middle, so just visit the rest with one loop.
1900   for (; i != NumOperands; ++i) {
1901     const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1902     if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1903       APInt NewScale =
1904           Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
1905       if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1906         // A multiplication of a constant with another add; recurse.
1907         const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1908         Interesting |=
1909           CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1910                                        Add->op_begin(), Add->getNumOperands(),
1911                                        NewScale, SE);
1912       } else {
1913         // A multiplication of a constant with some other value. Update
1914         // the map.
1915         SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1916         const SCEV *Key = SE.getMulExpr(MulOps);
1917         auto Pair = M.insert({Key, NewScale});
1918         if (Pair.second) {
1919           NewOps.push_back(Pair.first->first);
1920         } else {
1921           Pair.first->second += NewScale;
1922           // The map already had an entry for this value, which may indicate
1923           // a folding opportunity.
1924           Interesting = true;
1925         }
1926       }
1927     } else {
1928       // An ordinary operand. Update the map.
1929       std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1930           M.insert({Ops[i], Scale});
1931       if (Pair.second) {
1932         NewOps.push_back(Pair.first->first);
1933       } else {
1934         Pair.first->second += Scale;
1935         // The map already had an entry for this value, which may indicate
1936         // a folding opportunity.
1937         Interesting = true;
1938       }
1939     }
1940   }
1941 
1942   return Interesting;
1943 }
1944 
1945 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1946 // `OldFlags' as can't-wrap behavior.  Infer a more aggressive set of
1947 // can't-overflow flags for the operation if possible.
1948 static SCEV::NoWrapFlags
1949 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1950                       const SmallVectorImpl<const SCEV *> &Ops,
1951                       SCEV::NoWrapFlags Flags) {
1952   using namespace std::placeholders;
1953   typedef OverflowingBinaryOperator OBO;
1954 
1955   bool CanAnalyze =
1956       Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1957   (void)CanAnalyze;
1958   assert(CanAnalyze && "don't call from other places!");
1959 
1960   int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1961   SCEV::NoWrapFlags SignOrUnsignWrap =
1962       ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
1963 
1964   // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1965   auto IsKnownNonNegative = [&](const SCEV *S) {
1966     return SE->isKnownNonNegative(S);
1967   };
1968 
1969   if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
1970     Flags =
1971         ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1972 
1973   SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
1974 
1975   if (SignOrUnsignWrap != SignOrUnsignMask && Type == scAddExpr &&
1976       Ops.size() == 2 && isa<SCEVConstant>(Ops[0])) {
1977 
1978     // (A + C) --> (A + C)<nsw> if the addition does not sign overflow
1979     // (A + C) --> (A + C)<nuw> if the addition does not unsign overflow
1980 
1981     const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
1982     if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
1983       auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
1984           Instruction::Add, C, OBO::NoSignedWrap);
1985       if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
1986         Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
1987     }
1988     if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
1989       auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
1990           Instruction::Add, C, OBO::NoUnsignedWrap);
1991       if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
1992         Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
1993     }
1994   }
1995 
1996   return Flags;
1997 }
1998 
1999 /// getAddExpr - Get a canonical add expression, or something simpler if
2000 /// possible.
2001 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
2002                                         SCEV::NoWrapFlags Flags) {
2003   assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
2004          "only nuw or nsw allowed");
2005   assert(!Ops.empty() && "Cannot get empty add!");
2006   if (Ops.size() == 1) return Ops[0];
2007 #ifndef NDEBUG
2008   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2009   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2010     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2011            "SCEVAddExpr operand types don't match!");
2012 #endif
2013 
2014   // Sort by complexity, this groups all similar expression types together.
2015   GroupByComplexity(Ops, &LI);
2016 
2017   Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
2018 
2019   // If there are any constants, fold them together.
2020   unsigned Idx = 0;
2021   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2022     ++Idx;
2023     assert(Idx < Ops.size());
2024     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2025       // We found two constants, fold them together!
2026       Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt());
2027       if (Ops.size() == 2) return Ops[0];
2028       Ops.erase(Ops.begin()+1);  // Erase the folded element
2029       LHSC = cast<SCEVConstant>(Ops[0]);
2030     }
2031 
2032     // If we are left with a constant zero being added, strip it off.
2033     if (LHSC->getValue()->isZero()) {
2034       Ops.erase(Ops.begin());
2035       --Idx;
2036     }
2037 
2038     if (Ops.size() == 1) return Ops[0];
2039   }
2040 
2041   // Okay, check to see if the same value occurs in the operand list more than
2042   // once.  If so, merge them together into an multiply expression.  Since we
2043   // sorted the list, these values are required to be adjacent.
2044   Type *Ty = Ops[0]->getType();
2045   bool FoundMatch = false;
2046   for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2047     if (Ops[i] == Ops[i+1]) {      //  X + Y + Y  -->  X + Y*2
2048       // Scan ahead to count how many equal operands there are.
2049       unsigned Count = 2;
2050       while (i+Count != e && Ops[i+Count] == Ops[i])
2051         ++Count;
2052       // Merge the values into a multiply.
2053       const SCEV *Scale = getConstant(Ty, Count);
2054       const SCEV *Mul = getMulExpr(Scale, Ops[i]);
2055       if (Ops.size() == Count)
2056         return Mul;
2057       Ops[i] = Mul;
2058       Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2059       --i; e -= Count - 1;
2060       FoundMatch = true;
2061     }
2062   if (FoundMatch)
2063     return getAddExpr(Ops, Flags);
2064 
2065   // Check for truncates. If all the operands are truncated from the same
2066   // type, see if factoring out the truncate would permit the result to be
2067   // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
2068   // if the contents of the resulting outer trunc fold to something simple.
2069   for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
2070     const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
2071     Type *DstType = Trunc->getType();
2072     Type *SrcType = Trunc->getOperand()->getType();
2073     SmallVector<const SCEV *, 8> LargeOps;
2074     bool Ok = true;
2075     // Check all the operands to see if they can be represented in the
2076     // source type of the truncate.
2077     for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2078       if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2079         if (T->getOperand()->getType() != SrcType) {
2080           Ok = false;
2081           break;
2082         }
2083         LargeOps.push_back(T->getOperand());
2084       } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2085         LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2086       } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2087         SmallVector<const SCEV *, 8> LargeMulOps;
2088         for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2089           if (const SCEVTruncateExpr *T =
2090                 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2091             if (T->getOperand()->getType() != SrcType) {
2092               Ok = false;
2093               break;
2094             }
2095             LargeMulOps.push_back(T->getOperand());
2096           } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
2097             LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2098           } else {
2099             Ok = false;
2100             break;
2101           }
2102         }
2103         if (Ok)
2104           LargeOps.push_back(getMulExpr(LargeMulOps));
2105       } else {
2106         Ok = false;
2107         break;
2108       }
2109     }
2110     if (Ok) {
2111       // Evaluate the expression in the larger type.
2112       const SCEV *Fold = getAddExpr(LargeOps, Flags);
2113       // If it folds to something simple, use it. Otherwise, don't.
2114       if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2115         return getTruncateExpr(Fold, DstType);
2116     }
2117   }
2118 
2119   // Skip past any other cast SCEVs.
2120   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2121     ++Idx;
2122 
2123   // If there are add operands they would be next.
2124   if (Idx < Ops.size()) {
2125     bool DeletedAdd = false;
2126     while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2127       // If we have an add, expand the add operands onto the end of the operands
2128       // list.
2129       Ops.erase(Ops.begin()+Idx);
2130       Ops.append(Add->op_begin(), Add->op_end());
2131       DeletedAdd = true;
2132     }
2133 
2134     // If we deleted at least one add, we added operands to the end of the list,
2135     // and they are not necessarily sorted.  Recurse to resort and resimplify
2136     // any operands we just acquired.
2137     if (DeletedAdd)
2138       return getAddExpr(Ops);
2139   }
2140 
2141   // Skip over the add expression until we get to a multiply.
2142   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2143     ++Idx;
2144 
2145   // Check to see if there are any folding opportunities present with
2146   // operands multiplied by constant values.
2147   if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2148     uint64_t BitWidth = getTypeSizeInBits(Ty);
2149     DenseMap<const SCEV *, APInt> M;
2150     SmallVector<const SCEV *, 8> NewOps;
2151     APInt AccumulatedConstant(BitWidth, 0);
2152     if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2153                                      Ops.data(), Ops.size(),
2154                                      APInt(BitWidth, 1), *this)) {
2155       struct APIntCompare {
2156         bool operator()(const APInt &LHS, const APInt &RHS) const {
2157           return LHS.ult(RHS);
2158         }
2159       };
2160 
2161       // Some interesting folding opportunity is present, so its worthwhile to
2162       // re-generate the operands list. Group the operands by constant scale,
2163       // to avoid multiplying by the same constant scale multiple times.
2164       std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2165       for (const SCEV *NewOp : NewOps)
2166         MulOpLists[M.find(NewOp)->second].push_back(NewOp);
2167       // Re-generate the operands list.
2168       Ops.clear();
2169       if (AccumulatedConstant != 0)
2170         Ops.push_back(getConstant(AccumulatedConstant));
2171       for (auto &MulOp : MulOpLists)
2172         if (MulOp.first != 0)
2173           Ops.push_back(getMulExpr(getConstant(MulOp.first),
2174                                    getAddExpr(MulOp.second)));
2175       if (Ops.empty())
2176         return getZero(Ty);
2177       if (Ops.size() == 1)
2178         return Ops[0];
2179       return getAddExpr(Ops);
2180     }
2181   }
2182 
2183   // If we are adding something to a multiply expression, make sure the
2184   // something is not already an operand of the multiply.  If so, merge it into
2185   // the multiply.
2186   for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2187     const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2188     for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2189       const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2190       if (isa<SCEVConstant>(MulOpSCEV))
2191         continue;
2192       for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2193         if (MulOpSCEV == Ops[AddOp]) {
2194           // Fold W + X + (X * Y * Z)  -->  W + (X * ((Y*Z)+1))
2195           const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2196           if (Mul->getNumOperands() != 2) {
2197             // If the multiply has more than two operands, we must get the
2198             // Y*Z term.
2199             SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2200                                                 Mul->op_begin()+MulOp);
2201             MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2202             InnerMul = getMulExpr(MulOps);
2203           }
2204           const SCEV *One = getOne(Ty);
2205           const SCEV *AddOne = getAddExpr(One, InnerMul);
2206           const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2207           if (Ops.size() == 2) return OuterMul;
2208           if (AddOp < Idx) {
2209             Ops.erase(Ops.begin()+AddOp);
2210             Ops.erase(Ops.begin()+Idx-1);
2211           } else {
2212             Ops.erase(Ops.begin()+Idx);
2213             Ops.erase(Ops.begin()+AddOp-1);
2214           }
2215           Ops.push_back(OuterMul);
2216           return getAddExpr(Ops);
2217         }
2218 
2219       // Check this multiply against other multiplies being added together.
2220       for (unsigned OtherMulIdx = Idx+1;
2221            OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2222            ++OtherMulIdx) {
2223         const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2224         // If MulOp occurs in OtherMul, we can fold the two multiplies
2225         // together.
2226         for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2227              OMulOp != e; ++OMulOp)
2228           if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2229             // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2230             const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2231             if (Mul->getNumOperands() != 2) {
2232               SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2233                                                   Mul->op_begin()+MulOp);
2234               MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2235               InnerMul1 = getMulExpr(MulOps);
2236             }
2237             const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2238             if (OtherMul->getNumOperands() != 2) {
2239               SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2240                                                   OtherMul->op_begin()+OMulOp);
2241               MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2242               InnerMul2 = getMulExpr(MulOps);
2243             }
2244             const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2245             const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2246             if (Ops.size() == 2) return OuterMul;
2247             Ops.erase(Ops.begin()+Idx);
2248             Ops.erase(Ops.begin()+OtherMulIdx-1);
2249             Ops.push_back(OuterMul);
2250             return getAddExpr(Ops);
2251           }
2252       }
2253     }
2254   }
2255 
2256   // If there are any add recurrences in the operands list, see if any other
2257   // added values are loop invariant.  If so, we can fold them into the
2258   // recurrence.
2259   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2260     ++Idx;
2261 
2262   // Scan over all recurrences, trying to fold loop invariants into them.
2263   for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2264     // Scan all of the other operands to this add and add them to the vector if
2265     // they are loop invariant w.r.t. the recurrence.
2266     SmallVector<const SCEV *, 8> LIOps;
2267     const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2268     const Loop *AddRecLoop = AddRec->getLoop();
2269     for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2270       if (isLoopInvariant(Ops[i], AddRecLoop)) {
2271         LIOps.push_back(Ops[i]);
2272         Ops.erase(Ops.begin()+i);
2273         --i; --e;
2274       }
2275 
2276     // If we found some loop invariants, fold them into the recurrence.
2277     if (!LIOps.empty()) {
2278       //  NLI + LI + {Start,+,Step}  -->  NLI + {LI+Start,+,Step}
2279       LIOps.push_back(AddRec->getStart());
2280 
2281       SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2282                                              AddRec->op_end());
2283       AddRecOps[0] = getAddExpr(LIOps);
2284 
2285       // Build the new addrec. Propagate the NUW and NSW flags if both the
2286       // outer add and the inner addrec are guaranteed to have no overflow.
2287       // Always propagate NW.
2288       Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2289       const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2290 
2291       // If all of the other operands were loop invariant, we are done.
2292       if (Ops.size() == 1) return NewRec;
2293 
2294       // Otherwise, add the folded AddRec by the non-invariant parts.
2295       for (unsigned i = 0;; ++i)
2296         if (Ops[i] == AddRec) {
2297           Ops[i] = NewRec;
2298           break;
2299         }
2300       return getAddExpr(Ops);
2301     }
2302 
2303     // Okay, if there weren't any loop invariants to be folded, check to see if
2304     // there are multiple AddRec's with the same loop induction variable being
2305     // added together.  If so, we can fold them.
2306     for (unsigned OtherIdx = Idx+1;
2307          OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2308          ++OtherIdx)
2309       if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2310         // Other + {A,+,B}<L> + {C,+,D}<L>  -->  Other + {A+C,+,B+D}<L>
2311         SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2312                                                AddRec->op_end());
2313         for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2314              ++OtherIdx)
2315           if (const auto *OtherAddRec = dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2316             if (OtherAddRec->getLoop() == AddRecLoop) {
2317               for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2318                    i != e; ++i) {
2319                 if (i >= AddRecOps.size()) {
2320                   AddRecOps.append(OtherAddRec->op_begin()+i,
2321                                    OtherAddRec->op_end());
2322                   break;
2323                 }
2324                 AddRecOps[i] = getAddExpr(AddRecOps[i],
2325                                           OtherAddRec->getOperand(i));
2326               }
2327               Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2328             }
2329         // Step size has changed, so we cannot guarantee no self-wraparound.
2330         Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2331         return getAddExpr(Ops);
2332       }
2333 
2334     // Otherwise couldn't fold anything into this recurrence.  Move onto the
2335     // next one.
2336   }
2337 
2338   // Okay, it looks like we really DO need an add expr.  Check to see if we
2339   // already have one, otherwise create a new one.
2340   FoldingSetNodeID ID;
2341   ID.AddInteger(scAddExpr);
2342   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2343     ID.AddPointer(Ops[i]);
2344   void *IP = nullptr;
2345   SCEVAddExpr *S =
2346     static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2347   if (!S) {
2348     const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2349     std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2350     S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2351                                         O, Ops.size());
2352     UniqueSCEVs.InsertNode(S, IP);
2353   }
2354   S->setNoWrapFlags(Flags);
2355   return S;
2356 }
2357 
2358 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2359   uint64_t k = i*j;
2360   if (j > 1 && k / j != i) Overflow = true;
2361   return k;
2362 }
2363 
2364 /// Compute the result of "n choose k", the binomial coefficient.  If an
2365 /// intermediate computation overflows, Overflow will be set and the return will
2366 /// be garbage. Overflow is not cleared on absence of overflow.
2367 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2368   // We use the multiplicative formula:
2369   //     n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2370   // At each iteration, we take the n-th term of the numeral and divide by the
2371   // (k-n)th term of the denominator.  This division will always produce an
2372   // integral result, and helps reduce the chance of overflow in the
2373   // intermediate computations. However, we can still overflow even when the
2374   // final result would fit.
2375 
2376   if (n == 0 || n == k) return 1;
2377   if (k > n) return 0;
2378 
2379   if (k > n/2)
2380     k = n-k;
2381 
2382   uint64_t r = 1;
2383   for (uint64_t i = 1; i <= k; ++i) {
2384     r = umul_ov(r, n-(i-1), Overflow);
2385     r /= i;
2386   }
2387   return r;
2388 }
2389 
2390 /// Determine if any of the operands in this SCEV are a constant or if
2391 /// any of the add or multiply expressions in this SCEV contain a constant.
2392 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2393   SmallVector<const SCEV *, 4> Ops;
2394   Ops.push_back(StartExpr);
2395   while (!Ops.empty()) {
2396     const SCEV *CurrentExpr = Ops.pop_back_val();
2397     if (isa<SCEVConstant>(*CurrentExpr))
2398       return true;
2399 
2400     if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2401       const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2402       Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2403     }
2404   }
2405   return false;
2406 }
2407 
2408 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2409 /// possible.
2410 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2411                                         SCEV::NoWrapFlags Flags) {
2412   assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2413          "only nuw or nsw allowed");
2414   assert(!Ops.empty() && "Cannot get empty mul!");
2415   if (Ops.size() == 1) return Ops[0];
2416 #ifndef NDEBUG
2417   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2418   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2419     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2420            "SCEVMulExpr operand types don't match!");
2421 #endif
2422 
2423   // Sort by complexity, this groups all similar expression types together.
2424   GroupByComplexity(Ops, &LI);
2425 
2426   Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2427 
2428   // If there are any constants, fold them together.
2429   unsigned Idx = 0;
2430   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2431 
2432     // C1*(C2+V) -> C1*C2 + C1*V
2433     if (Ops.size() == 2)
2434         if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2435           // If any of Add's ops are Adds or Muls with a constant,
2436           // apply this transformation as well.
2437           if (Add->getNumOperands() == 2)
2438             if (containsConstantSomewhere(Add))
2439               return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2440                                 getMulExpr(LHSC, Add->getOperand(1)));
2441 
2442     ++Idx;
2443     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2444       // We found two constants, fold them together!
2445       ConstantInt *Fold =
2446           ConstantInt::get(getContext(), LHSC->getAPInt() * RHSC->getAPInt());
2447       Ops[0] = getConstant(Fold);
2448       Ops.erase(Ops.begin()+1);  // Erase the folded element
2449       if (Ops.size() == 1) return Ops[0];
2450       LHSC = cast<SCEVConstant>(Ops[0]);
2451     }
2452 
2453     // If we are left with a constant one being multiplied, strip it off.
2454     if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2455       Ops.erase(Ops.begin());
2456       --Idx;
2457     } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2458       // If we have a multiply of zero, it will always be zero.
2459       return Ops[0];
2460     } else if (Ops[0]->isAllOnesValue()) {
2461       // If we have a mul by -1 of an add, try distributing the -1 among the
2462       // add operands.
2463       if (Ops.size() == 2) {
2464         if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2465           SmallVector<const SCEV *, 4> NewOps;
2466           bool AnyFolded = false;
2467           for (const SCEV *AddOp : Add->operands()) {
2468             const SCEV *Mul = getMulExpr(Ops[0], AddOp);
2469             if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2470             NewOps.push_back(Mul);
2471           }
2472           if (AnyFolded)
2473             return getAddExpr(NewOps);
2474         } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2475           // Negation preserves a recurrence's no self-wrap property.
2476           SmallVector<const SCEV *, 4> Operands;
2477           for (const SCEV *AddRecOp : AddRec->operands())
2478             Operands.push_back(getMulExpr(Ops[0], AddRecOp));
2479 
2480           return getAddRecExpr(Operands, AddRec->getLoop(),
2481                                AddRec->getNoWrapFlags(SCEV::FlagNW));
2482         }
2483       }
2484     }
2485 
2486     if (Ops.size() == 1)
2487       return Ops[0];
2488   }
2489 
2490   // Skip over the add expression until we get to a multiply.
2491   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2492     ++Idx;
2493 
2494   // If there are mul operands inline them all into this expression.
2495   if (Idx < Ops.size()) {
2496     bool DeletedMul = false;
2497     while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2498       // If we have an mul, expand the mul operands onto the end of the operands
2499       // list.
2500       Ops.erase(Ops.begin()+Idx);
2501       Ops.append(Mul->op_begin(), Mul->op_end());
2502       DeletedMul = true;
2503     }
2504 
2505     // If we deleted at least one mul, we added operands to the end of the list,
2506     // and they are not necessarily sorted.  Recurse to resort and resimplify
2507     // any operands we just acquired.
2508     if (DeletedMul)
2509       return getMulExpr(Ops);
2510   }
2511 
2512   // If there are any add recurrences in the operands list, see if any other
2513   // added values are loop invariant.  If so, we can fold them into the
2514   // recurrence.
2515   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2516     ++Idx;
2517 
2518   // Scan over all recurrences, trying to fold loop invariants into them.
2519   for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2520     // Scan all of the other operands to this mul and add them to the vector if
2521     // they are loop invariant w.r.t. the recurrence.
2522     SmallVector<const SCEV *, 8> LIOps;
2523     const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2524     const Loop *AddRecLoop = AddRec->getLoop();
2525     for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2526       if (isLoopInvariant(Ops[i], AddRecLoop)) {
2527         LIOps.push_back(Ops[i]);
2528         Ops.erase(Ops.begin()+i);
2529         --i; --e;
2530       }
2531 
2532     // If we found some loop invariants, fold them into the recurrence.
2533     if (!LIOps.empty()) {
2534       //  NLI * LI * {Start,+,Step}  -->  NLI * {LI*Start,+,LI*Step}
2535       SmallVector<const SCEV *, 4> NewOps;
2536       NewOps.reserve(AddRec->getNumOperands());
2537       const SCEV *Scale = getMulExpr(LIOps);
2538       for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2539         NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2540 
2541       // Build the new addrec. Propagate the NUW and NSW flags if both the
2542       // outer mul and the inner addrec are guaranteed to have no overflow.
2543       //
2544       // No self-wrap cannot be guaranteed after changing the step size, but
2545       // will be inferred if either NUW or NSW is true.
2546       Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2547       const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2548 
2549       // If all of the other operands were loop invariant, we are done.
2550       if (Ops.size() == 1) return NewRec;
2551 
2552       // Otherwise, multiply the folded AddRec by the non-invariant parts.
2553       for (unsigned i = 0;; ++i)
2554         if (Ops[i] == AddRec) {
2555           Ops[i] = NewRec;
2556           break;
2557         }
2558       return getMulExpr(Ops);
2559     }
2560 
2561     // Okay, if there weren't any loop invariants to be folded, check to see if
2562     // there are multiple AddRec's with the same loop induction variable being
2563     // multiplied together.  If so, we can fold them.
2564 
2565     // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2566     // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2567     //       choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2568     //   ]]],+,...up to x=2n}.
2569     // Note that the arguments to choose() are always integers with values
2570     // known at compile time, never SCEV objects.
2571     //
2572     // The implementation avoids pointless extra computations when the two
2573     // addrec's are of different length (mathematically, it's equivalent to
2574     // an infinite stream of zeros on the right).
2575     bool OpsModified = false;
2576     for (unsigned OtherIdx = Idx+1;
2577          OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2578          ++OtherIdx) {
2579       const SCEVAddRecExpr *OtherAddRec =
2580         dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2581       if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2582         continue;
2583 
2584       bool Overflow = false;
2585       Type *Ty = AddRec->getType();
2586       bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2587       SmallVector<const SCEV*, 7> AddRecOps;
2588       for (int x = 0, xe = AddRec->getNumOperands() +
2589              OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2590         const SCEV *Term = getZero(Ty);
2591         for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2592           uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2593           for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2594                  ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2595                z < ze && !Overflow; ++z) {
2596             uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2597             uint64_t Coeff;
2598             if (LargerThan64Bits)
2599               Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2600             else
2601               Coeff = Coeff1*Coeff2;
2602             const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2603             const SCEV *Term1 = AddRec->getOperand(y-z);
2604             const SCEV *Term2 = OtherAddRec->getOperand(z);
2605             Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2606           }
2607         }
2608         AddRecOps.push_back(Term);
2609       }
2610       if (!Overflow) {
2611         const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2612                                               SCEV::FlagAnyWrap);
2613         if (Ops.size() == 2) return NewAddRec;
2614         Ops[Idx] = NewAddRec;
2615         Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2616         OpsModified = true;
2617         AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2618         if (!AddRec)
2619           break;
2620       }
2621     }
2622     if (OpsModified)
2623       return getMulExpr(Ops);
2624 
2625     // Otherwise couldn't fold anything into this recurrence.  Move onto the
2626     // next one.
2627   }
2628 
2629   // Okay, it looks like we really DO need an mul expr.  Check to see if we
2630   // already have one, otherwise create a new one.
2631   FoldingSetNodeID ID;
2632   ID.AddInteger(scMulExpr);
2633   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2634     ID.AddPointer(Ops[i]);
2635   void *IP = nullptr;
2636   SCEVMulExpr *S =
2637     static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2638   if (!S) {
2639     const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2640     std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2641     S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2642                                         O, Ops.size());
2643     UniqueSCEVs.InsertNode(S, IP);
2644   }
2645   S->setNoWrapFlags(Flags);
2646   return S;
2647 }
2648 
2649 /// getUDivExpr - Get a canonical unsigned division expression, or something
2650 /// simpler if possible.
2651 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2652                                          const SCEV *RHS) {
2653   assert(getEffectiveSCEVType(LHS->getType()) ==
2654          getEffectiveSCEVType(RHS->getType()) &&
2655          "SCEVUDivExpr operand types don't match!");
2656 
2657   if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2658     if (RHSC->getValue()->equalsInt(1))
2659       return LHS;                               // X udiv 1 --> x
2660     // If the denominator is zero, the result of the udiv is undefined. Don't
2661     // try to analyze it, because the resolution chosen here may differ from
2662     // the resolution chosen in other parts of the compiler.
2663     if (!RHSC->getValue()->isZero()) {
2664       // Determine if the division can be folded into the operands of
2665       // its operands.
2666       // TODO: Generalize this to non-constants by using known-bits information.
2667       Type *Ty = LHS->getType();
2668       unsigned LZ = RHSC->getAPInt().countLeadingZeros();
2669       unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2670       // For non-power-of-two values, effectively round the value up to the
2671       // nearest power of two.
2672       if (!RHSC->getAPInt().isPowerOf2())
2673         ++MaxShiftAmt;
2674       IntegerType *ExtTy =
2675         IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2676       if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2677         if (const SCEVConstant *Step =
2678             dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2679           // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2680           const APInt &StepInt = Step->getAPInt();
2681           const APInt &DivInt = RHSC->getAPInt();
2682           if (!StepInt.urem(DivInt) &&
2683               getZeroExtendExpr(AR, ExtTy) ==
2684               getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2685                             getZeroExtendExpr(Step, ExtTy),
2686                             AR->getLoop(), SCEV::FlagAnyWrap)) {
2687             SmallVector<const SCEV *, 4> Operands;
2688             for (const SCEV *Op : AR->operands())
2689               Operands.push_back(getUDivExpr(Op, RHS));
2690             return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
2691           }
2692           /// Get a canonical UDivExpr for a recurrence.
2693           /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2694           // We can currently only fold X%N if X is constant.
2695           const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2696           if (StartC && !DivInt.urem(StepInt) &&
2697               getZeroExtendExpr(AR, ExtTy) ==
2698               getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2699                             getZeroExtendExpr(Step, ExtTy),
2700                             AR->getLoop(), SCEV::FlagAnyWrap)) {
2701             const APInt &StartInt = StartC->getAPInt();
2702             const APInt &StartRem = StartInt.urem(StepInt);
2703             if (StartRem != 0)
2704               LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2705                                   AR->getLoop(), SCEV::FlagNW);
2706           }
2707         }
2708       // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2709       if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2710         SmallVector<const SCEV *, 4> Operands;
2711         for (const SCEV *Op : M->operands())
2712           Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2713         if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2714           // Find an operand that's safely divisible.
2715           for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2716             const SCEV *Op = M->getOperand(i);
2717             const SCEV *Div = getUDivExpr(Op, RHSC);
2718             if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2719               Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2720                                                       M->op_end());
2721               Operands[i] = Div;
2722               return getMulExpr(Operands);
2723             }
2724           }
2725       }
2726       // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2727       if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2728         SmallVector<const SCEV *, 4> Operands;
2729         for (const SCEV *Op : A->operands())
2730           Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2731         if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2732           Operands.clear();
2733           for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2734             const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2735             if (isa<SCEVUDivExpr>(Op) ||
2736                 getMulExpr(Op, RHS) != A->getOperand(i))
2737               break;
2738             Operands.push_back(Op);
2739           }
2740           if (Operands.size() == A->getNumOperands())
2741             return getAddExpr(Operands);
2742         }
2743       }
2744 
2745       // Fold if both operands are constant.
2746       if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2747         Constant *LHSCV = LHSC->getValue();
2748         Constant *RHSCV = RHSC->getValue();
2749         return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2750                                                                    RHSCV)));
2751       }
2752     }
2753   }
2754 
2755   FoldingSetNodeID ID;
2756   ID.AddInteger(scUDivExpr);
2757   ID.AddPointer(LHS);
2758   ID.AddPointer(RHS);
2759   void *IP = nullptr;
2760   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2761   SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2762                                              LHS, RHS);
2763   UniqueSCEVs.InsertNode(S, IP);
2764   return S;
2765 }
2766 
2767 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2768   APInt A = C1->getAPInt().abs();
2769   APInt B = C2->getAPInt().abs();
2770   uint32_t ABW = A.getBitWidth();
2771   uint32_t BBW = B.getBitWidth();
2772 
2773   if (ABW > BBW)
2774     B = B.zext(ABW);
2775   else if (ABW < BBW)
2776     A = A.zext(BBW);
2777 
2778   return APIntOps::GreatestCommonDivisor(A, B);
2779 }
2780 
2781 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2782 /// something simpler if possible. There is no representation for an exact udiv
2783 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2784 /// We can't do this when it's not exact because the udiv may be clearing bits.
2785 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2786                                               const SCEV *RHS) {
2787   // TODO: we could try to find factors in all sorts of things, but for now we
2788   // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2789   // end of this file for inspiration.
2790 
2791   const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2792   if (!Mul)
2793     return getUDivExpr(LHS, RHS);
2794 
2795   if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2796     // If the mulexpr multiplies by a constant, then that constant must be the
2797     // first element of the mulexpr.
2798     if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2799       if (LHSCst == RHSCst) {
2800         SmallVector<const SCEV *, 2> Operands;
2801         Operands.append(Mul->op_begin() + 1, Mul->op_end());
2802         return getMulExpr(Operands);
2803       }
2804 
2805       // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2806       // that there's a factor provided by one of the other terms. We need to
2807       // check.
2808       APInt Factor = gcd(LHSCst, RHSCst);
2809       if (!Factor.isIntN(1)) {
2810         LHSCst =
2811             cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor)));
2812         RHSCst =
2813             cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor)));
2814         SmallVector<const SCEV *, 2> Operands;
2815         Operands.push_back(LHSCst);
2816         Operands.append(Mul->op_begin() + 1, Mul->op_end());
2817         LHS = getMulExpr(Operands);
2818         RHS = RHSCst;
2819         Mul = dyn_cast<SCEVMulExpr>(LHS);
2820         if (!Mul)
2821           return getUDivExactExpr(LHS, RHS);
2822       }
2823     }
2824   }
2825 
2826   for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2827     if (Mul->getOperand(i) == RHS) {
2828       SmallVector<const SCEV *, 2> Operands;
2829       Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2830       Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2831       return getMulExpr(Operands);
2832     }
2833   }
2834 
2835   return getUDivExpr(LHS, RHS);
2836 }
2837 
2838 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2839 /// Simplify the expression as much as possible.
2840 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2841                                            const Loop *L,
2842                                            SCEV::NoWrapFlags Flags) {
2843   SmallVector<const SCEV *, 4> Operands;
2844   Operands.push_back(Start);
2845   if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2846     if (StepChrec->getLoop() == L) {
2847       Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2848       return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2849     }
2850 
2851   Operands.push_back(Step);
2852   return getAddRecExpr(Operands, L, Flags);
2853 }
2854 
2855 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2856 /// Simplify the expression as much as possible.
2857 const SCEV *
2858 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2859                                const Loop *L, SCEV::NoWrapFlags Flags) {
2860   if (Operands.size() == 1) return Operands[0];
2861 #ifndef NDEBUG
2862   Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2863   for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2864     assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2865            "SCEVAddRecExpr operand types don't match!");
2866   for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2867     assert(isLoopInvariant(Operands[i], L) &&
2868            "SCEVAddRecExpr operand is not loop-invariant!");
2869 #endif
2870 
2871   if (Operands.back()->isZero()) {
2872     Operands.pop_back();
2873     return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0}  -->  X
2874   }
2875 
2876   // It's tempting to want to call getMaxBackedgeTakenCount count here and
2877   // use that information to infer NUW and NSW flags. However, computing a
2878   // BE count requires calling getAddRecExpr, so we may not yet have a
2879   // meaningful BE count at this point (and if we don't, we'd be stuck
2880   // with a SCEVCouldNotCompute as the cached BE count).
2881 
2882   Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2883 
2884   // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2885   if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2886     const Loop *NestedLoop = NestedAR->getLoop();
2887     if (L->contains(NestedLoop)
2888             ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
2889             : (!NestedLoop->contains(L) &&
2890                DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
2891       SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2892                                                   NestedAR->op_end());
2893       Operands[0] = NestedAR->getStart();
2894       // AddRecs require their operands be loop-invariant with respect to their
2895       // loops. Don't perform this transformation if it would break this
2896       // requirement.
2897       bool AllInvariant = all_of(
2898           Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
2899 
2900       if (AllInvariant) {
2901         // Create a recurrence for the outer loop with the same step size.
2902         //
2903         // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2904         // inner recurrence has the same property.
2905         SCEV::NoWrapFlags OuterFlags =
2906           maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2907 
2908         NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2909         AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
2910           return isLoopInvariant(Op, NestedLoop);
2911         });
2912 
2913         if (AllInvariant) {
2914           // Ok, both add recurrences are valid after the transformation.
2915           //
2916           // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2917           // the outer recurrence has the same property.
2918           SCEV::NoWrapFlags InnerFlags =
2919             maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2920           return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2921         }
2922       }
2923       // Reset Operands to its original state.
2924       Operands[0] = NestedAR;
2925     }
2926   }
2927 
2928   // Okay, it looks like we really DO need an addrec expr.  Check to see if we
2929   // already have one, otherwise create a new one.
2930   FoldingSetNodeID ID;
2931   ID.AddInteger(scAddRecExpr);
2932   for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2933     ID.AddPointer(Operands[i]);
2934   ID.AddPointer(L);
2935   void *IP = nullptr;
2936   SCEVAddRecExpr *S =
2937     static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2938   if (!S) {
2939     const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2940     std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2941     S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2942                                            O, Operands.size(), L);
2943     UniqueSCEVs.InsertNode(S, IP);
2944   }
2945   S->setNoWrapFlags(Flags);
2946   return S;
2947 }
2948 
2949 const SCEV *
2950 ScalarEvolution::getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
2951                             const SmallVectorImpl<const SCEV *> &IndexExprs,
2952                             bool InBounds) {
2953   // getSCEV(Base)->getType() has the same address space as Base->getType()
2954   // because SCEV::getType() preserves the address space.
2955   Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
2956   // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
2957   // instruction to its SCEV, because the Instruction may be guarded by control
2958   // flow and the no-overflow bits may not be valid for the expression in any
2959   // context. This can be fixed similarly to how these flags are handled for
2960   // adds.
2961   SCEV::NoWrapFlags Wrap = InBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
2962 
2963   const SCEV *TotalOffset = getZero(IntPtrTy);
2964   // The address space is unimportant. The first thing we do on CurTy is getting
2965   // its element type.
2966   Type *CurTy = PointerType::getUnqual(PointeeType);
2967   for (const SCEV *IndexExpr : IndexExprs) {
2968     // Compute the (potentially symbolic) offset in bytes for this index.
2969     if (StructType *STy = dyn_cast<StructType>(CurTy)) {
2970       // For a struct, add the member offset.
2971       ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
2972       unsigned FieldNo = Index->getZExtValue();
2973       const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
2974 
2975       // Add the field offset to the running total offset.
2976       TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2977 
2978       // Update CurTy to the type of the field at Index.
2979       CurTy = STy->getTypeAtIndex(Index);
2980     } else {
2981       // Update CurTy to its element type.
2982       CurTy = cast<SequentialType>(CurTy)->getElementType();
2983       // For an array, add the element offset, explicitly scaled.
2984       const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
2985       // Getelementptr indices are signed.
2986       IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
2987 
2988       // Multiply the index by the element size to compute the element offset.
2989       const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
2990 
2991       // Add the element offset to the running total offset.
2992       TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2993     }
2994   }
2995 
2996   // Add the total offset from all the GEP indices to the base.
2997   return getAddExpr(BaseExpr, TotalOffset, Wrap);
2998 }
2999 
3000 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
3001                                          const SCEV *RHS) {
3002   SmallVector<const SCEV *, 2> Ops;
3003   Ops.push_back(LHS);
3004   Ops.push_back(RHS);
3005   return getSMaxExpr(Ops);
3006 }
3007 
3008 const SCEV *
3009 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3010   assert(!Ops.empty() && "Cannot get empty smax!");
3011   if (Ops.size() == 1) return Ops[0];
3012 #ifndef NDEBUG
3013   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3014   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3015     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3016            "SCEVSMaxExpr operand types don't match!");
3017 #endif
3018 
3019   // Sort by complexity, this groups all similar expression types together.
3020   GroupByComplexity(Ops, &LI);
3021 
3022   // If there are any constants, fold them together.
3023   unsigned Idx = 0;
3024   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3025     ++Idx;
3026     assert(Idx < Ops.size());
3027     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3028       // We found two constants, fold them together!
3029       ConstantInt *Fold = ConstantInt::get(
3030           getContext(), APIntOps::smax(LHSC->getAPInt(), RHSC->getAPInt()));
3031       Ops[0] = getConstant(Fold);
3032       Ops.erase(Ops.begin()+1);  // Erase the folded element
3033       if (Ops.size() == 1) return Ops[0];
3034       LHSC = cast<SCEVConstant>(Ops[0]);
3035     }
3036 
3037     // If we are left with a constant minimum-int, strip it off.
3038     if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3039       Ops.erase(Ops.begin());
3040       --Idx;
3041     } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3042       // If we have an smax with a constant maximum-int, it will always be
3043       // maximum-int.
3044       return Ops[0];
3045     }
3046 
3047     if (Ops.size() == 1) return Ops[0];
3048   }
3049 
3050   // Find the first SMax
3051   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3052     ++Idx;
3053 
3054   // Check to see if one of the operands is an SMax. If so, expand its operands
3055   // onto our operand list, and recurse to simplify.
3056   if (Idx < Ops.size()) {
3057     bool DeletedSMax = false;
3058     while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3059       Ops.erase(Ops.begin()+Idx);
3060       Ops.append(SMax->op_begin(), SMax->op_end());
3061       DeletedSMax = true;
3062     }
3063 
3064     if (DeletedSMax)
3065       return getSMaxExpr(Ops);
3066   }
3067 
3068   // Okay, check to see if the same value occurs in the operand list twice.  If
3069   // so, delete one.  Since we sorted the list, these values are required to
3070   // be adjacent.
3071   for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3072     //  X smax Y smax Y  -->  X smax Y
3073     //  X smax Y         -->  X, if X is always greater than Y
3074     if (Ops[i] == Ops[i+1] ||
3075         isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3076       Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3077       --i; --e;
3078     } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3079       Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3080       --i; --e;
3081     }
3082 
3083   if (Ops.size() == 1) return Ops[0];
3084 
3085   assert(!Ops.empty() && "Reduced smax down to nothing!");
3086 
3087   // Okay, it looks like we really DO need an smax expr.  Check to see if we
3088   // already have one, otherwise create a new one.
3089   FoldingSetNodeID ID;
3090   ID.AddInteger(scSMaxExpr);
3091   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3092     ID.AddPointer(Ops[i]);
3093   void *IP = nullptr;
3094   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3095   const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3096   std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3097   SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3098                                              O, Ops.size());
3099   UniqueSCEVs.InsertNode(S, IP);
3100   return S;
3101 }
3102 
3103 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3104                                          const SCEV *RHS) {
3105   SmallVector<const SCEV *, 2> Ops;
3106   Ops.push_back(LHS);
3107   Ops.push_back(RHS);
3108   return getUMaxExpr(Ops);
3109 }
3110 
3111 const SCEV *
3112 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3113   assert(!Ops.empty() && "Cannot get empty umax!");
3114   if (Ops.size() == 1) return Ops[0];
3115 #ifndef NDEBUG
3116   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3117   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3118     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3119            "SCEVUMaxExpr operand types don't match!");
3120 #endif
3121 
3122   // Sort by complexity, this groups all similar expression types together.
3123   GroupByComplexity(Ops, &LI);
3124 
3125   // If there are any constants, fold them together.
3126   unsigned Idx = 0;
3127   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3128     ++Idx;
3129     assert(Idx < Ops.size());
3130     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3131       // We found two constants, fold them together!
3132       ConstantInt *Fold = ConstantInt::get(
3133           getContext(), APIntOps::umax(LHSC->getAPInt(), RHSC->getAPInt()));
3134       Ops[0] = getConstant(Fold);
3135       Ops.erase(Ops.begin()+1);  // Erase the folded element
3136       if (Ops.size() == 1) return Ops[0];
3137       LHSC = cast<SCEVConstant>(Ops[0]);
3138     }
3139 
3140     // If we are left with a constant minimum-int, strip it off.
3141     if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3142       Ops.erase(Ops.begin());
3143       --Idx;
3144     } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3145       // If we have an umax with a constant maximum-int, it will always be
3146       // maximum-int.
3147       return Ops[0];
3148     }
3149 
3150     if (Ops.size() == 1) return Ops[0];
3151   }
3152 
3153   // Find the first UMax
3154   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3155     ++Idx;
3156 
3157   // Check to see if one of the operands is a UMax. If so, expand its operands
3158   // onto our operand list, and recurse to simplify.
3159   if (Idx < Ops.size()) {
3160     bool DeletedUMax = false;
3161     while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3162       Ops.erase(Ops.begin()+Idx);
3163       Ops.append(UMax->op_begin(), UMax->op_end());
3164       DeletedUMax = true;
3165     }
3166 
3167     if (DeletedUMax)
3168       return getUMaxExpr(Ops);
3169   }
3170 
3171   // Okay, check to see if the same value occurs in the operand list twice.  If
3172   // so, delete one.  Since we sorted the list, these values are required to
3173   // be adjacent.
3174   for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3175     //  X umax Y umax Y  -->  X umax Y
3176     //  X umax Y         -->  X, if X is always greater than Y
3177     if (Ops[i] == Ops[i+1] ||
3178         isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3179       Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3180       --i; --e;
3181     } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3182       Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3183       --i; --e;
3184     }
3185 
3186   if (Ops.size() == 1) return Ops[0];
3187 
3188   assert(!Ops.empty() && "Reduced umax down to nothing!");
3189 
3190   // Okay, it looks like we really DO need a umax expr.  Check to see if we
3191   // already have one, otherwise create a new one.
3192   FoldingSetNodeID ID;
3193   ID.AddInteger(scUMaxExpr);
3194   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3195     ID.AddPointer(Ops[i]);
3196   void *IP = nullptr;
3197   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3198   const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3199   std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3200   SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3201                                              O, Ops.size());
3202   UniqueSCEVs.InsertNode(S, IP);
3203   return S;
3204 }
3205 
3206 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3207                                          const SCEV *RHS) {
3208   // ~smax(~x, ~y) == smin(x, y).
3209   return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3210 }
3211 
3212 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3213                                          const SCEV *RHS) {
3214   // ~umax(~x, ~y) == umin(x, y)
3215   return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3216 }
3217 
3218 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3219   // We can bypass creating a target-independent
3220   // constant expression and then folding it back into a ConstantInt.
3221   // This is just a compile-time optimization.
3222   return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
3223 }
3224 
3225 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3226                                              StructType *STy,
3227                                              unsigned FieldNo) {
3228   // We can bypass creating a target-independent
3229   // constant expression and then folding it back into a ConstantInt.
3230   // This is just a compile-time optimization.
3231   return getConstant(
3232       IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
3233 }
3234 
3235 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3236   // Don't attempt to do anything other than create a SCEVUnknown object
3237   // here.  createSCEV only calls getUnknown after checking for all other
3238   // interesting possibilities, and any other code that calls getUnknown
3239   // is doing so in order to hide a value from SCEV canonicalization.
3240 
3241   FoldingSetNodeID ID;
3242   ID.AddInteger(scUnknown);
3243   ID.AddPointer(V);
3244   void *IP = nullptr;
3245   if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3246     assert(cast<SCEVUnknown>(S)->getValue() == V &&
3247            "Stale SCEVUnknown in uniquing map!");
3248     return S;
3249   }
3250   SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3251                                             FirstUnknown);
3252   FirstUnknown = cast<SCEVUnknown>(S);
3253   UniqueSCEVs.InsertNode(S, IP);
3254   return S;
3255 }
3256 
3257 //===----------------------------------------------------------------------===//
3258 //            Basic SCEV Analysis and PHI Idiom Recognition Code
3259 //
3260 
3261 /// isSCEVable - Test if values of the given type are analyzable within
3262 /// the SCEV framework. This primarily includes integer types, and it
3263 /// can optionally include pointer types if the ScalarEvolution class
3264 /// has access to target-specific information.
3265 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3266   // Integers and pointers are always SCEVable.
3267   return Ty->isIntegerTy() || Ty->isPointerTy();
3268 }
3269 
3270 /// getTypeSizeInBits - Return the size in bits of the specified type,
3271 /// for which isSCEVable must return true.
3272 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3273   assert(isSCEVable(Ty) && "Type is not SCEVable!");
3274   return getDataLayout().getTypeSizeInBits(Ty);
3275 }
3276 
3277 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3278 /// the given type and which represents how SCEV will treat the given
3279 /// type, for which isSCEVable must return true. For pointer types,
3280 /// this is the pointer-sized integer type.
3281 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3282   assert(isSCEVable(Ty) && "Type is not SCEVable!");
3283 
3284   if (Ty->isIntegerTy())
3285     return Ty;
3286 
3287   // The only other support type is pointer.
3288   assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3289   return getDataLayout().getIntPtrType(Ty);
3290 }
3291 
3292 const SCEV *ScalarEvolution::getCouldNotCompute() {
3293   return CouldNotCompute.get();
3294 }
3295 
3296 
3297 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3298   // Helper class working with SCEVTraversal to figure out if a SCEV contains
3299   // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3300   // is set iff if find such SCEVUnknown.
3301   //
3302   struct FindInvalidSCEVUnknown {
3303     bool FindOne;
3304     FindInvalidSCEVUnknown() { FindOne = false; }
3305     bool follow(const SCEV *S) {
3306       switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3307       case scConstant:
3308         return false;
3309       case scUnknown:
3310         if (!cast<SCEVUnknown>(S)->getValue())
3311           FindOne = true;
3312         return false;
3313       default:
3314         return true;
3315       }
3316     }
3317     bool isDone() const { return FindOne; }
3318   };
3319 
3320   FindInvalidSCEVUnknown F;
3321   SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3322   ST.visitAll(S);
3323 
3324   return !F.FindOne;
3325 }
3326 
3327 namespace {
3328 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3329 // a sub SCEV of scAddRecExpr type.  FindInvalidSCEVUnknown::FoundOne is set
3330 // iff if such sub scAddRecExpr type SCEV is found.
3331 struct FindAddRecurrence {
3332   bool FoundOne;
3333   FindAddRecurrence() : FoundOne(false) {}
3334 
3335   bool follow(const SCEV *S) {
3336     switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3337     case scAddRecExpr:
3338       FoundOne = true;
3339     case scConstant:
3340     case scUnknown:
3341     case scCouldNotCompute:
3342       return false;
3343     default:
3344       return true;
3345     }
3346   }
3347   bool isDone() const { return FoundOne; }
3348 };
3349 }
3350 
3351 bool ScalarEvolution::containsAddRecurrence(const SCEV *S) {
3352   HasRecMapType::iterator I = HasRecMap.find_as(S);
3353   if (I != HasRecMap.end())
3354     return I->second;
3355 
3356   FindAddRecurrence F;
3357   SCEVTraversal<FindAddRecurrence> ST(F);
3358   ST.visitAll(S);
3359   HasRecMap.insert({S, F.FoundOne});
3360   return F.FoundOne;
3361 }
3362 
3363 /// getSCEVValues - Return the Value set from S.
3364 SetVector<Value *> *ScalarEvolution::getSCEVValues(const SCEV *S) {
3365   ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
3366   if (SI == ExprValueMap.end())
3367     return nullptr;
3368 #ifndef NDEBUG
3369   if (VerifySCEVMap) {
3370     // Check there is no dangling Value in the set returned.
3371     for (const auto &VE : SI->second)
3372       assert(ValueExprMap.count(VE));
3373   }
3374 #endif
3375   return &SI->second;
3376 }
3377 
3378 /// eraseValueFromMap - Erase Value from ValueExprMap and ExprValueMap.
3379 /// If ValueExprMap.erase(V) is not used together with forgetMemoizedResults(S),
3380 /// eraseValueFromMap should be used instead to ensure whenever V->S is removed
3381 /// from ValueExprMap, V is also removed from the set of ExprValueMap[S].
3382 void ScalarEvolution::eraseValueFromMap(Value *V) {
3383   ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3384   if (I != ValueExprMap.end()) {
3385     const SCEV *S = I->second;
3386     SetVector<Value *> *SV = getSCEVValues(S);
3387     // Remove V from the set of ExprValueMap[S]
3388     if (SV)
3389       SV->remove(V);
3390     ValueExprMap.erase(V);
3391   }
3392 }
3393 
3394 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3395 /// expression and create a new one.
3396 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3397   assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3398 
3399   const SCEV *S = getExistingSCEV(V);
3400   if (S == nullptr) {
3401     S = createSCEV(V);
3402     // During PHI resolution, it is possible to create two SCEVs for the same
3403     // V, so it is needed to double check whether V->S is inserted into
3404     // ValueExprMap before insert S->V into ExprValueMap.
3405     std::pair<ValueExprMapType::iterator, bool> Pair =
3406         ValueExprMap.insert({SCEVCallbackVH(V, this), S});
3407     if (Pair.second)
3408       ExprValueMap[S].insert(V);
3409   }
3410   return S;
3411 }
3412 
3413 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3414   assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3415 
3416   ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3417   if (I != ValueExprMap.end()) {
3418     const SCEV *S = I->second;
3419     if (checkValidity(S))
3420       return S;
3421     forgetMemoizedResults(S);
3422     ValueExprMap.erase(I);
3423   }
3424   return nullptr;
3425 }
3426 
3427 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3428 ///
3429 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
3430                                              SCEV::NoWrapFlags Flags) {
3431   if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3432     return getConstant(
3433                cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3434 
3435   Type *Ty = V->getType();
3436   Ty = getEffectiveSCEVType(Ty);
3437   return getMulExpr(
3438       V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3439 }
3440 
3441 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3442 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3443   if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3444     return getConstant(
3445                 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3446 
3447   Type *Ty = V->getType();
3448   Ty = getEffectiveSCEVType(Ty);
3449   const SCEV *AllOnes =
3450                    getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3451   return getMinusSCEV(AllOnes, V);
3452 }
3453 
3454 /// getMinusSCEV - Return LHS-RHS.  Minus is represented in SCEV as A+B*-1.
3455 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3456                                           SCEV::NoWrapFlags Flags) {
3457   // Fast path: X - X --> 0.
3458   if (LHS == RHS)
3459     return getZero(LHS->getType());
3460 
3461   // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
3462   // makes it so that we cannot make much use of NUW.
3463   auto AddFlags = SCEV::FlagAnyWrap;
3464   const bool RHSIsNotMinSigned =
3465       !getSignedRange(RHS).getSignedMin().isMinSignedValue();
3466   if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
3467     // Let M be the minimum representable signed value. Then (-1)*RHS
3468     // signed-wraps if and only if RHS is M. That can happen even for
3469     // a NSW subtraction because e.g. (-1)*M signed-wraps even though
3470     // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
3471     // (-1)*RHS, we need to prove that RHS != M.
3472     //
3473     // If LHS is non-negative and we know that LHS - RHS does not
3474     // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
3475     // either by proving that RHS > M or that LHS >= 0.
3476     if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
3477       AddFlags = SCEV::FlagNSW;
3478     }
3479   }
3480 
3481   // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
3482   // RHS is NSW and LHS >= 0.
3483   //
3484   // The difficulty here is that the NSW flag may have been proven
3485   // relative to a loop that is to be found in a recurrence in LHS and
3486   // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
3487   // larger scope than intended.
3488   auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3489 
3490   return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags);
3491 }
3492 
3493 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3494 /// input value to the specified type.  If the type must be extended, it is zero
3495 /// extended.
3496 const SCEV *
3497 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3498   Type *SrcTy = V->getType();
3499   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3500          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3501          "Cannot truncate or zero extend with non-integer arguments!");
3502   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3503     return V;  // No conversion
3504   if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3505     return getTruncateExpr(V, Ty);
3506   return getZeroExtendExpr(V, Ty);
3507 }
3508 
3509 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3510 /// input value to the specified type.  If the type must be extended, it is sign
3511 /// extended.
3512 const SCEV *
3513 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3514                                          Type *Ty) {
3515   Type *SrcTy = V->getType();
3516   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3517          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3518          "Cannot truncate or zero extend with non-integer arguments!");
3519   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3520     return V;  // No conversion
3521   if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3522     return getTruncateExpr(V, Ty);
3523   return getSignExtendExpr(V, Ty);
3524 }
3525 
3526 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3527 /// input value to the specified type.  If the type must be extended, it is zero
3528 /// extended.  The conversion must not be narrowing.
3529 const SCEV *
3530 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3531   Type *SrcTy = V->getType();
3532   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3533          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3534          "Cannot noop or zero extend with non-integer arguments!");
3535   assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3536          "getNoopOrZeroExtend cannot truncate!");
3537   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3538     return V;  // No conversion
3539   return getZeroExtendExpr(V, Ty);
3540 }
3541 
3542 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3543 /// input value to the specified type.  If the type must be extended, it is sign
3544 /// extended.  The conversion must not be narrowing.
3545 const SCEV *
3546 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3547   Type *SrcTy = V->getType();
3548   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3549          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3550          "Cannot noop or sign extend with non-integer arguments!");
3551   assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3552          "getNoopOrSignExtend cannot truncate!");
3553   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3554     return V;  // No conversion
3555   return getSignExtendExpr(V, Ty);
3556 }
3557 
3558 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3559 /// the input value to the specified type. If the type must be extended,
3560 /// it is extended with unspecified bits. The conversion must not be
3561 /// narrowing.
3562 const SCEV *
3563 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3564   Type *SrcTy = V->getType();
3565   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3566          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3567          "Cannot noop or any extend with non-integer arguments!");
3568   assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3569          "getNoopOrAnyExtend cannot truncate!");
3570   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3571     return V;  // No conversion
3572   return getAnyExtendExpr(V, Ty);
3573 }
3574 
3575 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3576 /// input value to the specified type.  The conversion must not be widening.
3577 const SCEV *
3578 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3579   Type *SrcTy = V->getType();
3580   assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3581          (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3582          "Cannot truncate or noop with non-integer arguments!");
3583   assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3584          "getTruncateOrNoop cannot extend!");
3585   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3586     return V;  // No conversion
3587   return getTruncateExpr(V, Ty);
3588 }
3589 
3590 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3591 /// the types using zero-extension, and then perform a umax operation
3592 /// with them.
3593 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3594                                                         const SCEV *RHS) {
3595   const SCEV *PromotedLHS = LHS;
3596   const SCEV *PromotedRHS = RHS;
3597 
3598   if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3599     PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3600   else
3601     PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3602 
3603   return getUMaxExpr(PromotedLHS, PromotedRHS);
3604 }
3605 
3606 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3607 /// the types using zero-extension, and then perform a umin operation
3608 /// with them.
3609 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3610                                                         const SCEV *RHS) {
3611   const SCEV *PromotedLHS = LHS;
3612   const SCEV *PromotedRHS = RHS;
3613 
3614   if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3615     PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3616   else
3617     PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3618 
3619   return getUMinExpr(PromotedLHS, PromotedRHS);
3620 }
3621 
3622 /// getPointerBase - Transitively follow the chain of pointer-type operands
3623 /// until reaching a SCEV that does not have a single pointer operand. This
3624 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3625 /// but corner cases do exist.
3626 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3627   // A pointer operand may evaluate to a nonpointer expression, such as null.
3628   if (!V->getType()->isPointerTy())
3629     return V;
3630 
3631   if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3632     return getPointerBase(Cast->getOperand());
3633   } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3634     const SCEV *PtrOp = nullptr;
3635     for (const SCEV *NAryOp : NAry->operands()) {
3636       if (NAryOp->getType()->isPointerTy()) {
3637         // Cannot find the base of an expression with multiple pointer operands.
3638         if (PtrOp)
3639           return V;
3640         PtrOp = NAryOp;
3641       }
3642     }
3643     if (!PtrOp)
3644       return V;
3645     return getPointerBase(PtrOp);
3646   }
3647   return V;
3648 }
3649 
3650 /// PushDefUseChildren - Push users of the given Instruction
3651 /// onto the given Worklist.
3652 static void
3653 PushDefUseChildren(Instruction *I,
3654                    SmallVectorImpl<Instruction *> &Worklist) {
3655   // Push the def-use children onto the Worklist stack.
3656   for (User *U : I->users())
3657     Worklist.push_back(cast<Instruction>(U));
3658 }
3659 
3660 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3661 /// instructions that depend on the given instruction and removes them from
3662 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3663 /// resolution.
3664 void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3665   SmallVector<Instruction *, 16> Worklist;
3666   PushDefUseChildren(PN, Worklist);
3667 
3668   SmallPtrSet<Instruction *, 8> Visited;
3669   Visited.insert(PN);
3670   while (!Worklist.empty()) {
3671     Instruction *I = Worklist.pop_back_val();
3672     if (!Visited.insert(I).second)
3673       continue;
3674 
3675     auto It = ValueExprMap.find_as(static_cast<Value *>(I));
3676     if (It != ValueExprMap.end()) {
3677       const SCEV *Old = It->second;
3678 
3679       // Short-circuit the def-use traversal if the symbolic name
3680       // ceases to appear in expressions.
3681       if (Old != SymName && !hasOperand(Old, SymName))
3682         continue;
3683 
3684       // SCEVUnknown for a PHI either means that it has an unrecognized
3685       // structure, it's a PHI that's in the progress of being computed
3686       // by createNodeForPHI, or it's a single-value PHI. In the first case,
3687       // additional loop trip count information isn't going to change anything.
3688       // In the second case, createNodeForPHI will perform the necessary
3689       // updates on its own when it gets to that point. In the third, we do
3690       // want to forget the SCEVUnknown.
3691       if (!isa<PHINode>(I) ||
3692           !isa<SCEVUnknown>(Old) ||
3693           (I != PN && Old == SymName)) {
3694         forgetMemoizedResults(Old);
3695         ValueExprMap.erase(It);
3696       }
3697     }
3698 
3699     PushDefUseChildren(I, Worklist);
3700   }
3701 }
3702 
3703 namespace {
3704 class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
3705 public:
3706   static const SCEV *rewrite(const SCEV *S, const Loop *L,
3707                              ScalarEvolution &SE) {
3708     SCEVInitRewriter Rewriter(L, SE);
3709     const SCEV *Result = Rewriter.visit(S);
3710     return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
3711   }
3712 
3713   SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
3714       : SCEVRewriteVisitor(SE), L(L), Valid(true) {}
3715 
3716   const SCEV *visitUnknown(const SCEVUnknown *Expr) {
3717     if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
3718       Valid = false;
3719     return Expr;
3720   }
3721 
3722   const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
3723     // Only allow AddRecExprs for this loop.
3724     if (Expr->getLoop() == L)
3725       return Expr->getStart();
3726     Valid = false;
3727     return Expr;
3728   }
3729 
3730   bool isValid() { return Valid; }
3731 
3732 private:
3733   const Loop *L;
3734   bool Valid;
3735 };
3736 
3737 class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
3738 public:
3739   static const SCEV *rewrite(const SCEV *S, const Loop *L,
3740                              ScalarEvolution &SE) {
3741     SCEVShiftRewriter Rewriter(L, SE);
3742     const SCEV *Result = Rewriter.visit(S);
3743     return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
3744   }
3745 
3746   SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
3747       : SCEVRewriteVisitor(SE), L(L), Valid(true) {}
3748 
3749   const SCEV *visitUnknown(const SCEVUnknown *Expr) {
3750     // Only allow AddRecExprs for this loop.
3751     if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
3752       Valid = false;
3753     return Expr;
3754   }
3755 
3756   const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
3757     if (Expr->getLoop() == L && Expr->isAffine())
3758       return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
3759     Valid = false;
3760     return Expr;
3761   }
3762   bool isValid() { return Valid; }
3763 
3764 private:
3765   const Loop *L;
3766   bool Valid;
3767 };
3768 } // end anonymous namespace
3769 
3770 SCEV::NoWrapFlags
3771 ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
3772   if (!AR->isAffine())
3773     return SCEV::FlagAnyWrap;
3774 
3775   typedef OverflowingBinaryOperator OBO;
3776   SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap;
3777 
3778   if (!AR->hasNoSignedWrap()) {
3779     ConstantRange AddRecRange = getSignedRange(AR);
3780     ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this));
3781 
3782     auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
3783         Instruction::Add, IncRange, OBO::NoSignedWrap);
3784     if (NSWRegion.contains(AddRecRange))
3785       Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW);
3786   }
3787 
3788   if (!AR->hasNoUnsignedWrap()) {
3789     ConstantRange AddRecRange = getUnsignedRange(AR);
3790     ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this));
3791 
3792     auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
3793         Instruction::Add, IncRange, OBO::NoUnsignedWrap);
3794     if (NUWRegion.contains(AddRecRange))
3795       Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW);
3796   }
3797 
3798   return Result;
3799 }
3800 
3801 namespace {
3802 /// Represents an abstract binary operation.  This may exist as a
3803 /// normal instruction or constant expression, or may have been
3804 /// derived from an expression tree.
3805 struct BinaryOp {
3806   unsigned Opcode;
3807   Value *LHS;
3808   Value *RHS;
3809   bool IsNSW;
3810   bool IsNUW;
3811 
3812   /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
3813   /// constant expression.
3814   Operator *Op;
3815 
3816   explicit BinaryOp(Operator *Op)
3817       : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
3818         IsNSW(false), IsNUW(false), Op(Op) {
3819     if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
3820       IsNSW = OBO->hasNoSignedWrap();
3821       IsNUW = OBO->hasNoUnsignedWrap();
3822     }
3823   }
3824 
3825   explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
3826                     bool IsNUW = false)
3827       : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW),
3828         Op(nullptr) {}
3829 };
3830 }
3831 
3832 
3833 /// Try to map \p V into a BinaryOp, and return \c None on failure.
3834 static Optional<BinaryOp> MatchBinaryOp(Value *V) {
3835   auto *Op = dyn_cast<Operator>(V);
3836   if (!Op)
3837     return None;
3838 
3839   // Implementation detail: all the cleverness here should happen without
3840   // creating new SCEV expressions -- our caller knowns tricks to avoid creating
3841   // SCEV expressions when possible, and we should not break that.
3842 
3843   switch (Op->getOpcode()) {
3844   case Instruction::Add:
3845   case Instruction::Sub:
3846   case Instruction::Mul:
3847   case Instruction::UDiv:
3848   case Instruction::And:
3849   case Instruction::Or:
3850   case Instruction::AShr:
3851   case Instruction::Shl:
3852     return BinaryOp(Op);
3853 
3854   case Instruction::Xor:
3855     if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
3856       // If the RHS of the xor is a signbit, then this is just an add.
3857       // Instcombine turns add of signbit into xor as a strength reduction step.
3858       if (RHSC->getValue().isSignBit())
3859         return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
3860     return BinaryOp(Op);
3861 
3862   case Instruction::LShr:
3863     // Turn logical shift right of a constant into a unsigned divide.
3864     if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
3865       uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();
3866 
3867       // If the shift count is not less than the bitwidth, the result of
3868       // the shift is undefined. Don't try to analyze it, because the
3869       // resolution chosen here may differ from the resolution chosen in
3870       // other parts of the compiler.
3871       if (SA->getValue().ult(BitWidth)) {
3872         Constant *X =
3873             ConstantInt::get(SA->getContext(),
3874                              APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3875         return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
3876       }
3877     }
3878     return BinaryOp(Op);
3879 
3880   default:
3881     break;
3882   }
3883 
3884   return None;
3885 }
3886 
3887 const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
3888   const Loop *L = LI.getLoopFor(PN->getParent());
3889   if (!L || L->getHeader() != PN->getParent())
3890     return nullptr;
3891 
3892   // The loop may have multiple entrances or multiple exits; we can analyze
3893   // this phi as an addrec if it has a unique entry value and a unique
3894   // backedge value.
3895   Value *BEValueV = nullptr, *StartValueV = nullptr;
3896   for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3897     Value *V = PN->getIncomingValue(i);
3898     if (L->contains(PN->getIncomingBlock(i))) {
3899       if (!BEValueV) {
3900         BEValueV = V;
3901       } else if (BEValueV != V) {
3902         BEValueV = nullptr;
3903         break;
3904       }
3905     } else if (!StartValueV) {
3906       StartValueV = V;
3907     } else if (StartValueV != V) {
3908       StartValueV = nullptr;
3909       break;
3910     }
3911   }
3912   if (BEValueV && StartValueV) {
3913     // While we are analyzing this PHI node, handle its value symbolically.
3914     const SCEV *SymbolicName = getUnknown(PN);
3915     assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3916            "PHI node already processed?");
3917     ValueExprMap.insert({SCEVCallbackVH(PN, this), SymbolicName});
3918 
3919     // Using this symbolic name for the PHI, analyze the value coming around
3920     // the back-edge.
3921     const SCEV *BEValue = getSCEV(BEValueV);
3922 
3923     // NOTE: If BEValue is loop invariant, we know that the PHI node just
3924     // has a special value for the first iteration of the loop.
3925 
3926     // If the value coming around the backedge is an add with the symbolic
3927     // value we just inserted, then we found a simple induction variable!
3928     if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3929       // If there is a single occurrence of the symbolic value, replace it
3930       // with a recurrence.
3931       unsigned FoundIndex = Add->getNumOperands();
3932       for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3933         if (Add->getOperand(i) == SymbolicName)
3934           if (FoundIndex == e) {
3935             FoundIndex = i;
3936             break;
3937           }
3938 
3939       if (FoundIndex != Add->getNumOperands()) {
3940         // Create an add with everything but the specified operand.
3941         SmallVector<const SCEV *, 8> Ops;
3942         for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3943           if (i != FoundIndex)
3944             Ops.push_back(Add->getOperand(i));
3945         const SCEV *Accum = getAddExpr(Ops);
3946 
3947         // This is not a valid addrec if the step amount is varying each
3948         // loop iteration, but is not itself an addrec in this loop.
3949         if (isLoopInvariant(Accum, L) ||
3950             (isa<SCEVAddRecExpr>(Accum) &&
3951              cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3952           SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3953 
3954           // If the increment doesn't overflow, then neither the addrec nor
3955           // the post-increment will overflow.
3956           if (auto BO = MatchBinaryOp(BEValueV)) {
3957             if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
3958               if (BO->IsNUW)
3959                 Flags = setFlags(Flags, SCEV::FlagNUW);
3960               if (BO->IsNSW)
3961                 Flags = setFlags(Flags, SCEV::FlagNSW);
3962             }
3963           } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3964             // If the increment is an inbounds GEP, then we know the address
3965             // space cannot be wrapped around. We cannot make any guarantee
3966             // about signed or unsigned overflow because pointers are
3967             // unsigned but we may have a negative index from the base
3968             // pointer. We can guarantee that no unsigned wrap occurs if the
3969             // indices form a positive value.
3970             if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
3971               Flags = setFlags(Flags, SCEV::FlagNW);
3972 
3973               const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3974               if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3975                 Flags = setFlags(Flags, SCEV::FlagNUW);
3976             }
3977 
3978             // We cannot transfer nuw and nsw flags from subtraction
3979             // operations -- sub nuw X, Y is not the same as add nuw X, -Y
3980             // for instance.
3981           }
3982 
3983           const SCEV *StartVal = getSCEV(StartValueV);
3984           const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3985 
3986           // Since the no-wrap flags are on the increment, they apply to the
3987           // post-incremented value as well.
3988           if (isLoopInvariant(Accum, L))
3989             (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
3990 
3991           // Okay, for the entire analysis of this edge we assumed the PHI
3992           // to be symbolic.  We now need to go back and purge all of the
3993           // entries for the scalars that use the symbolic expression.
3994           forgetSymbolicName(PN, SymbolicName);
3995           ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3996           return PHISCEV;
3997         }
3998       }
3999     } else {
4000       // Otherwise, this could be a loop like this:
4001       //     i = 0;  for (j = 1; ..; ++j) { ....  i = j; }
4002       // In this case, j = {1,+,1}  and BEValue is j.
4003       // Because the other in-value of i (0) fits the evolution of BEValue
4004       // i really is an addrec evolution.
4005       //
4006       // We can generalize this saying that i is the shifted value of BEValue
4007       // by one iteration:
4008       //   PHI(f(0), f({1,+,1})) --> f({0,+,1})
4009       const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
4010       const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this);
4011       if (Shifted != getCouldNotCompute() &&
4012           Start != getCouldNotCompute()) {
4013         const SCEV *StartVal = getSCEV(StartValueV);
4014         if (Start == StartVal) {
4015           // Okay, for the entire analysis of this edge we assumed the PHI
4016           // to be symbolic.  We now need to go back and purge all of the
4017           // entries for the scalars that use the symbolic expression.
4018           forgetSymbolicName(PN, SymbolicName);
4019           ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
4020           return Shifted;
4021         }
4022       }
4023     }
4024 
4025     // Remove the temporary PHI node SCEV that has been inserted while intending
4026     // to create an AddRecExpr for this PHI node. We can not keep this temporary
4027     // as it will prevent later (possibly simpler) SCEV expressions to be added
4028     // to the ValueExprMap.
4029     ValueExprMap.erase(PN);
4030   }
4031 
4032   return nullptr;
4033 }
4034 
4035 // Checks if the SCEV S is available at BB.  S is considered available at BB
4036 // if S can be materialized at BB without introducing a fault.
4037 static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
4038                                BasicBlock *BB) {
4039   struct CheckAvailable {
4040     bool TraversalDone = false;
4041     bool Available = true;
4042 
4043     const Loop *L = nullptr;  // The loop BB is in (can be nullptr)
4044     BasicBlock *BB = nullptr;
4045     DominatorTree &DT;
4046 
4047     CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
4048       : L(L), BB(BB), DT(DT) {}
4049 
4050     bool setUnavailable() {
4051       TraversalDone = true;
4052       Available = false;
4053       return false;
4054     }
4055 
4056     bool follow(const SCEV *S) {
4057       switch (S->getSCEVType()) {
4058       case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
4059       case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
4060         // These expressions are available if their operand(s) is/are.
4061         return true;
4062 
4063       case scAddRecExpr: {
4064         // We allow add recurrences that are on the loop BB is in, or some
4065         // outer loop.  This guarantees availability because the value of the
4066         // add recurrence at BB is simply the "current" value of the induction
4067         // variable.  We can relax this in the future; for instance an add
4068         // recurrence on a sibling dominating loop is also available at BB.
4069         const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
4070         if (L && (ARLoop == L || ARLoop->contains(L)))
4071           return true;
4072 
4073         return setUnavailable();
4074       }
4075 
4076       case scUnknown: {
4077         // For SCEVUnknown, we check for simple dominance.
4078         const auto *SU = cast<SCEVUnknown>(S);
4079         Value *V = SU->getValue();
4080 
4081         if (isa<Argument>(V))
4082           return false;
4083 
4084         if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
4085           return false;
4086 
4087         return setUnavailable();
4088       }
4089 
4090       case scUDivExpr:
4091       case scCouldNotCompute:
4092         // We do not try to smart about these at all.
4093         return setUnavailable();
4094       }
4095       llvm_unreachable("switch should be fully covered!");
4096     }
4097 
4098     bool isDone() { return TraversalDone; }
4099   };
4100 
4101   CheckAvailable CA(L, BB, DT);
4102   SCEVTraversal<CheckAvailable> ST(CA);
4103 
4104   ST.visitAll(S);
4105   return CA.Available;
4106 }
4107 
4108 // Try to match a control flow sequence that branches out at BI and merges back
4109 // at Merge into a "C ? LHS : RHS" select pattern.  Return true on a successful
4110 // match.
4111 static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
4112                           Value *&C, Value *&LHS, Value *&RHS) {
4113   C = BI->getCondition();
4114 
4115   BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
4116   BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
4117 
4118   if (!LeftEdge.isSingleEdge())
4119     return false;
4120 
4121   assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
4122 
4123   Use &LeftUse = Merge->getOperandUse(0);
4124   Use &RightUse = Merge->getOperandUse(1);
4125 
4126   if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
4127     LHS = LeftUse;
4128     RHS = RightUse;
4129     return true;
4130   }
4131 
4132   if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
4133     LHS = RightUse;
4134     RHS = LeftUse;
4135     return true;
4136   }
4137 
4138   return false;
4139 }
4140 
4141 const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
4142   if (PN->getNumIncomingValues() == 2) {
4143     const Loop *L = LI.getLoopFor(PN->getParent());
4144 
4145     // We don't want to break LCSSA, even in a SCEV expression tree.
4146     for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
4147       if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
4148         return nullptr;
4149 
4150     // Try to match
4151     //
4152     //  br %cond, label %left, label %right
4153     // left:
4154     //  br label %merge
4155     // right:
4156     //  br label %merge
4157     // merge:
4158     //  V = phi [ %x, %left ], [ %y, %right ]
4159     //
4160     // as "select %cond, %x, %y"
4161 
4162     BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
4163     assert(IDom && "At least the entry block should dominate PN");
4164 
4165     auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
4166     Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
4167 
4168     if (BI && BI->isConditional() &&
4169         BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
4170         IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
4171         IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
4172       return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
4173   }
4174 
4175   return nullptr;
4176 }
4177 
4178 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
4179   if (const SCEV *S = createAddRecFromPHI(PN))
4180     return S;
4181 
4182   if (const SCEV *S = createNodeFromSelectLikePHI(PN))
4183     return S;
4184 
4185   // If the PHI has a single incoming value, follow that value, unless the
4186   // PHI's incoming blocks are in a different loop, in which case doing so
4187   // risks breaking LCSSA form. Instcombine would normally zap these, but
4188   // it doesn't have DominatorTree information, so it may miss cases.
4189   if (Value *V = SimplifyInstruction(PN, getDataLayout(), &TLI, &DT, &AC))
4190     if (LI.replacementPreservesLCSSAForm(PN, V))
4191       return getSCEV(V);
4192 
4193   // If it's not a loop phi, we can't handle it yet.
4194   return getUnknown(PN);
4195 }
4196 
4197 const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
4198                                                       Value *Cond,
4199                                                       Value *TrueVal,
4200                                                       Value *FalseVal) {
4201   // Handle "constant" branch or select. This can occur for instance when a
4202   // loop pass transforms an inner loop and moves on to process the outer loop.
4203   if (auto *CI = dyn_cast<ConstantInt>(Cond))
4204     return getSCEV(CI->isOne() ? TrueVal : FalseVal);
4205 
4206   // Try to match some simple smax or umax patterns.
4207   auto *ICI = dyn_cast<ICmpInst>(Cond);
4208   if (!ICI)
4209     return getUnknown(I);
4210 
4211   Value *LHS = ICI->getOperand(0);
4212   Value *RHS = ICI->getOperand(1);
4213 
4214   switch (ICI->getPredicate()) {
4215   case ICmpInst::ICMP_SLT:
4216   case ICmpInst::ICMP_SLE:
4217     std::swap(LHS, RHS);
4218   // fall through
4219   case ICmpInst::ICMP_SGT:
4220   case ICmpInst::ICMP_SGE:
4221     // a >s b ? a+x : b+x  ->  smax(a, b)+x
4222     // a >s b ? b+x : a+x  ->  smin(a, b)+x
4223     if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
4224       const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
4225       const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
4226       const SCEV *LA = getSCEV(TrueVal);
4227       const SCEV *RA = getSCEV(FalseVal);
4228       const SCEV *LDiff = getMinusSCEV(LA, LS);
4229       const SCEV *RDiff = getMinusSCEV(RA, RS);
4230       if (LDiff == RDiff)
4231         return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4232       LDiff = getMinusSCEV(LA, RS);
4233       RDiff = getMinusSCEV(RA, LS);
4234       if (LDiff == RDiff)
4235         return getAddExpr(getSMinExpr(LS, RS), LDiff);
4236     }
4237     break;
4238   case ICmpInst::ICMP_ULT:
4239   case ICmpInst::ICMP_ULE:
4240     std::swap(LHS, RHS);
4241   // fall through
4242   case ICmpInst::ICMP_UGT:
4243   case ICmpInst::ICMP_UGE:
4244     // a >u b ? a+x : b+x  ->  umax(a, b)+x
4245     // a >u b ? b+x : a+x  ->  umin(a, b)+x
4246     if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
4247       const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4248       const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
4249       const SCEV *LA = getSCEV(TrueVal);
4250       const SCEV *RA = getSCEV(FalseVal);
4251       const SCEV *LDiff = getMinusSCEV(LA, LS);
4252       const SCEV *RDiff = getMinusSCEV(RA, RS);
4253       if (LDiff == RDiff)
4254         return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4255       LDiff = getMinusSCEV(LA, RS);
4256       RDiff = getMinusSCEV(RA, LS);
4257       if (LDiff == RDiff)
4258         return getAddExpr(getUMinExpr(LS, RS), LDiff);
4259     }
4260     break;
4261   case ICmpInst::ICMP_NE:
4262     // n != 0 ? n+x : 1+x  ->  umax(n, 1)+x
4263     if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
4264         isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4265       const SCEV *One = getOne(I->getType());
4266       const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4267       const SCEV *LA = getSCEV(TrueVal);
4268       const SCEV *RA = getSCEV(FalseVal);
4269       const SCEV *LDiff = getMinusSCEV(LA, LS);
4270       const SCEV *RDiff = getMinusSCEV(RA, One);
4271       if (LDiff == RDiff)
4272         return getAddExpr(getUMaxExpr(One, LS), LDiff);
4273     }
4274     break;
4275   case ICmpInst::ICMP_EQ:
4276     // n == 0 ? 1+x : n+x  ->  umax(n, 1)+x
4277     if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
4278         isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4279       const SCEV *One = getOne(I->getType());
4280       const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4281       const SCEV *LA = getSCEV(TrueVal);
4282       const SCEV *RA = getSCEV(FalseVal);
4283       const SCEV *LDiff = getMinusSCEV(LA, One);
4284       const SCEV *RDiff = getMinusSCEV(RA, LS);
4285       if (LDiff == RDiff)
4286         return getAddExpr(getUMaxExpr(One, LS), LDiff);
4287     }
4288     break;
4289   default:
4290     break;
4291   }
4292 
4293   return getUnknown(I);
4294 }
4295 
4296 /// createNodeForGEP - Expand GEP instructions into add and multiply
4297 /// operations. This allows them to be analyzed by regular SCEV code.
4298 ///
4299 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
4300   // Don't attempt to analyze GEPs over unsized objects.
4301   if (!GEP->getSourceElementType()->isSized())
4302     return getUnknown(GEP);
4303 
4304   SmallVector<const SCEV *, 4> IndexExprs;
4305   for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
4306     IndexExprs.push_back(getSCEV(*Index));
4307   return getGEPExpr(GEP->getSourceElementType(),
4308                     getSCEV(GEP->getPointerOperand()),
4309                     IndexExprs, GEP->isInBounds());
4310 }
4311 
4312 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
4313 /// guaranteed to end in (at every loop iteration).  It is, at the same time,
4314 /// the minimum number of times S is divisible by 2.  For example, given {4,+,8}
4315 /// it returns 2.  If S is guaranteed to be 0, it returns the bitwidth of S.
4316 uint32_t
4317 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
4318   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4319     return C->getAPInt().countTrailingZeros();
4320 
4321   if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
4322     return std::min(GetMinTrailingZeros(T->getOperand()),
4323                     (uint32_t)getTypeSizeInBits(T->getType()));
4324 
4325   if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
4326     uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4327     return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4328              getTypeSizeInBits(E->getType()) : OpRes;
4329   }
4330 
4331   if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
4332     uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4333     return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4334              getTypeSizeInBits(E->getType()) : OpRes;
4335   }
4336 
4337   if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
4338     // The result is the min of all operands results.
4339     uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4340     for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4341       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4342     return MinOpRes;
4343   }
4344 
4345   if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
4346     // The result is the sum of all operands results.
4347     uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
4348     uint32_t BitWidth = getTypeSizeInBits(M->getType());
4349     for (unsigned i = 1, e = M->getNumOperands();
4350          SumOpRes != BitWidth && i != e; ++i)
4351       SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
4352                           BitWidth);
4353     return SumOpRes;
4354   }
4355 
4356   if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
4357     // The result is the min of all operands results.
4358     uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4359     for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4360       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4361     return MinOpRes;
4362   }
4363 
4364   if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
4365     // The result is the min of all operands results.
4366     uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4367     for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4368       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4369     return MinOpRes;
4370   }
4371 
4372   if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
4373     // The result is the min of all operands results.
4374     uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4375     for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4376       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4377     return MinOpRes;
4378   }
4379 
4380   if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4381     // For a SCEVUnknown, ask ValueTracking.
4382     unsigned BitWidth = getTypeSizeInBits(U->getType());
4383     APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4384     computeKnownBits(U->getValue(), Zeros, Ones, getDataLayout(), 0, &AC,
4385                      nullptr, &DT);
4386     return Zeros.countTrailingOnes();
4387   }
4388 
4389   // SCEVUDivExpr
4390   return 0;
4391 }
4392 
4393 /// GetRangeFromMetadata - Helper method to assign a range to V from
4394 /// metadata present in the IR.
4395 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
4396   if (Instruction *I = dyn_cast<Instruction>(V))
4397     if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
4398       return getConstantRangeFromMetadata(*MD);
4399 
4400   return None;
4401 }
4402 
4403 /// getRange - Determine the range for a particular SCEV.  If SignHint is
4404 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
4405 /// with a "cleaner" unsigned (resp. signed) representation.
4406 ///
4407 ConstantRange
4408 ScalarEvolution::getRange(const SCEV *S,
4409                           ScalarEvolution::RangeSignHint SignHint) {
4410   DenseMap<const SCEV *, ConstantRange> &Cache =
4411       SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
4412                                                        : SignedRanges;
4413 
4414   // See if we've computed this range already.
4415   DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
4416   if (I != Cache.end())
4417     return I->second;
4418 
4419   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4420     return setRange(C, SignHint, ConstantRange(C->getAPInt()));
4421 
4422   unsigned BitWidth = getTypeSizeInBits(S->getType());
4423   ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
4424 
4425   // If the value has known zeros, the maximum value will have those known zeros
4426   // as well.
4427   uint32_t TZ = GetMinTrailingZeros(S);
4428   if (TZ != 0) {
4429     if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
4430       ConservativeResult =
4431           ConstantRange(APInt::getMinValue(BitWidth),
4432                         APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
4433     else
4434       ConservativeResult = ConstantRange(
4435           APInt::getSignedMinValue(BitWidth),
4436           APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
4437   }
4438 
4439   if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
4440     ConstantRange X = getRange(Add->getOperand(0), SignHint);
4441     for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
4442       X = X.add(getRange(Add->getOperand(i), SignHint));
4443     return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
4444   }
4445 
4446   if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
4447     ConstantRange X = getRange(Mul->getOperand(0), SignHint);
4448     for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
4449       X = X.multiply(getRange(Mul->getOperand(i), SignHint));
4450     return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
4451   }
4452 
4453   if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
4454     ConstantRange X = getRange(SMax->getOperand(0), SignHint);
4455     for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
4456       X = X.smax(getRange(SMax->getOperand(i), SignHint));
4457     return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
4458   }
4459 
4460   if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
4461     ConstantRange X = getRange(UMax->getOperand(0), SignHint);
4462     for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
4463       X = X.umax(getRange(UMax->getOperand(i), SignHint));
4464     return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
4465   }
4466 
4467   if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
4468     ConstantRange X = getRange(UDiv->getLHS(), SignHint);
4469     ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
4470     return setRange(UDiv, SignHint,
4471                     ConservativeResult.intersectWith(X.udiv(Y)));
4472   }
4473 
4474   if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
4475     ConstantRange X = getRange(ZExt->getOperand(), SignHint);
4476     return setRange(ZExt, SignHint,
4477                     ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
4478   }
4479 
4480   if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
4481     ConstantRange X = getRange(SExt->getOperand(), SignHint);
4482     return setRange(SExt, SignHint,
4483                     ConservativeResult.intersectWith(X.signExtend(BitWidth)));
4484   }
4485 
4486   if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
4487     ConstantRange X = getRange(Trunc->getOperand(), SignHint);
4488     return setRange(Trunc, SignHint,
4489                     ConservativeResult.intersectWith(X.truncate(BitWidth)));
4490   }
4491 
4492   if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
4493     // If there's no unsigned wrap, the value will never be less than its
4494     // initial value.
4495     if (AddRec->hasNoUnsignedWrap())
4496       if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
4497         if (!C->getValue()->isZero())
4498           ConservativeResult = ConservativeResult.intersectWith(
4499               ConstantRange(C->getAPInt(), APInt(BitWidth, 0)));
4500 
4501     // If there's no signed wrap, and all the operands have the same sign or
4502     // zero, the value won't ever change sign.
4503     if (AddRec->hasNoSignedWrap()) {
4504       bool AllNonNeg = true;
4505       bool AllNonPos = true;
4506       for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4507         if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
4508         if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
4509       }
4510       if (AllNonNeg)
4511         ConservativeResult = ConservativeResult.intersectWith(
4512           ConstantRange(APInt(BitWidth, 0),
4513                         APInt::getSignedMinValue(BitWidth)));
4514       else if (AllNonPos)
4515         ConservativeResult = ConservativeResult.intersectWith(
4516           ConstantRange(APInt::getSignedMinValue(BitWidth),
4517                         APInt(BitWidth, 1)));
4518     }
4519 
4520     // TODO: non-affine addrec
4521     if (AddRec->isAffine()) {
4522       const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
4523       if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
4524           getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
4525         auto RangeFromAffine = getRangeForAffineAR(
4526             AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
4527             BitWidth);
4528         if (!RangeFromAffine.isFullSet())
4529           ConservativeResult =
4530               ConservativeResult.intersectWith(RangeFromAffine);
4531 
4532         auto RangeFromFactoring = getRangeViaFactoring(
4533             AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
4534             BitWidth);
4535         if (!RangeFromFactoring.isFullSet())
4536           ConservativeResult =
4537               ConservativeResult.intersectWith(RangeFromFactoring);
4538       }
4539     }
4540 
4541     return setRange(AddRec, SignHint, ConservativeResult);
4542   }
4543 
4544   if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4545     // Check if the IR explicitly contains !range metadata.
4546     Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4547     if (MDRange.hasValue())
4548       ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4549 
4550     // Split here to avoid paying the compile-time cost of calling both
4551     // computeKnownBits and ComputeNumSignBits.  This restriction can be lifted
4552     // if needed.
4553     const DataLayout &DL = getDataLayout();
4554     if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
4555       // For a SCEVUnknown, ask ValueTracking.
4556       APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4557       computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, &AC, nullptr, &DT);
4558       if (Ones != ~Zeros + 1)
4559         ConservativeResult =
4560             ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
4561     } else {
4562       assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
4563              "generalize as needed!");
4564       unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
4565       if (NS > 1)
4566         ConservativeResult = ConservativeResult.intersectWith(
4567             ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4568                           APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
4569     }
4570 
4571     return setRange(U, SignHint, ConservativeResult);
4572   }
4573 
4574   return setRange(S, SignHint, ConservativeResult);
4575 }
4576 
4577 ConstantRange ScalarEvolution::getRangeForAffineAR(const SCEV *Start,
4578                                                    const SCEV *Step,
4579                                                    const SCEV *MaxBECount,
4580                                                    unsigned BitWidth) {
4581   assert(!isa<SCEVCouldNotCompute>(MaxBECount) &&
4582          getTypeSizeInBits(MaxBECount->getType()) <= BitWidth &&
4583          "Precondition!");
4584 
4585   ConstantRange Result(BitWidth, /* isFullSet = */ true);
4586 
4587   // Check for overflow.  This must be done with ConstantRange arithmetic
4588   // because we could be called from within the ScalarEvolution overflow
4589   // checking code.
4590 
4591   MaxBECount = getNoopOrZeroExtend(MaxBECount, Start->getType());
4592   ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4593   ConstantRange ZExtMaxBECountRange =
4594       MaxBECountRange.zextOrTrunc(BitWidth * 2 + 1);
4595 
4596   ConstantRange StepSRange = getSignedRange(Step);
4597   ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2 + 1);
4598 
4599   ConstantRange StartURange = getUnsignedRange(Start);
4600   ConstantRange EndURange =
4601       StartURange.add(MaxBECountRange.multiply(StepSRange));
4602 
4603   // Check for unsigned overflow.
4604   ConstantRange ZExtStartURange = StartURange.zextOrTrunc(BitWidth * 2 + 1);
4605   ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2 + 1);
4606   if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4607       ZExtEndURange) {
4608     APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
4609                                EndURange.getUnsignedMin());
4610     APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
4611                                EndURange.getUnsignedMax());
4612     bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
4613     if (!IsFullRange)
4614       Result =
4615           Result.intersectWith(ConstantRange(Min, Max + 1));
4616   }
4617 
4618   ConstantRange StartSRange = getSignedRange(Start);
4619   ConstantRange EndSRange =
4620       StartSRange.add(MaxBECountRange.multiply(StepSRange));
4621 
4622   // Check for signed overflow. This must be done with ConstantRange
4623   // arithmetic because we could be called from within the ScalarEvolution
4624   // overflow checking code.
4625   ConstantRange SExtStartSRange = StartSRange.sextOrTrunc(BitWidth * 2 + 1);
4626   ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2 + 1);
4627   if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4628       SExtEndSRange) {
4629     APInt Min =
4630         APIntOps::smin(StartSRange.getSignedMin(), EndSRange.getSignedMin());
4631     APInt Max =
4632         APIntOps::smax(StartSRange.getSignedMax(), EndSRange.getSignedMax());
4633     bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
4634     if (!IsFullRange)
4635       Result =
4636           Result.intersectWith(ConstantRange(Min, Max + 1));
4637   }
4638 
4639   return Result;
4640 }
4641 
4642 ConstantRange ScalarEvolution::getRangeViaFactoring(const SCEV *Start,
4643                                                     const SCEV *Step,
4644                                                     const SCEV *MaxBECount,
4645                                                     unsigned BitWidth) {
4646   //    RangeOf({C?A:B,+,C?P:Q}) == RangeOf(C?{A,+,P}:{B,+,Q})
4647   // == RangeOf({A,+,P}) union RangeOf({B,+,Q})
4648 
4649   struct SelectPattern {
4650     Value *Condition = nullptr;
4651     APInt TrueValue;
4652     APInt FalseValue;
4653 
4654     explicit SelectPattern(ScalarEvolution &SE, unsigned BitWidth,
4655                            const SCEV *S) {
4656       Optional<unsigned> CastOp;
4657       APInt Offset(BitWidth, 0);
4658 
4659       assert(SE.getTypeSizeInBits(S->getType()) == BitWidth &&
4660              "Should be!");
4661 
4662       // Peel off a constant offset:
4663       if (auto *SA = dyn_cast<SCEVAddExpr>(S)) {
4664         // In the future we could consider being smarter here and handle
4665         // {Start+Step,+,Step} too.
4666         if (SA->getNumOperands() != 2 || !isa<SCEVConstant>(SA->getOperand(0)))
4667           return;
4668 
4669         Offset = cast<SCEVConstant>(SA->getOperand(0))->getAPInt();
4670         S = SA->getOperand(1);
4671       }
4672 
4673       // Peel off a cast operation
4674       if (auto *SCast = dyn_cast<SCEVCastExpr>(S)) {
4675         CastOp = SCast->getSCEVType();
4676         S = SCast->getOperand();
4677       }
4678 
4679       using namespace llvm::PatternMatch;
4680 
4681       auto *SU = dyn_cast<SCEVUnknown>(S);
4682       const APInt *TrueVal, *FalseVal;
4683       if (!SU ||
4684           !match(SU->getValue(), m_Select(m_Value(Condition), m_APInt(TrueVal),
4685                                           m_APInt(FalseVal)))) {
4686         Condition = nullptr;
4687         return;
4688       }
4689 
4690       TrueValue = *TrueVal;
4691       FalseValue = *FalseVal;
4692 
4693       // Re-apply the cast we peeled off earlier
4694       if (CastOp.hasValue())
4695         switch (*CastOp) {
4696         default:
4697           llvm_unreachable("Unknown SCEV cast type!");
4698 
4699         case scTruncate:
4700           TrueValue = TrueValue.trunc(BitWidth);
4701           FalseValue = FalseValue.trunc(BitWidth);
4702           break;
4703         case scZeroExtend:
4704           TrueValue = TrueValue.zext(BitWidth);
4705           FalseValue = FalseValue.zext(BitWidth);
4706           break;
4707         case scSignExtend:
4708           TrueValue = TrueValue.sext(BitWidth);
4709           FalseValue = FalseValue.sext(BitWidth);
4710           break;
4711         }
4712 
4713       // Re-apply the constant offset we peeled off earlier
4714       TrueValue += Offset;
4715       FalseValue += Offset;
4716     }
4717 
4718     bool isRecognized() { return Condition != nullptr; }
4719   };
4720 
4721   SelectPattern StartPattern(*this, BitWidth, Start);
4722   if (!StartPattern.isRecognized())
4723     return ConstantRange(BitWidth, /* isFullSet = */ true);
4724 
4725   SelectPattern StepPattern(*this, BitWidth, Step);
4726   if (!StepPattern.isRecognized())
4727     return ConstantRange(BitWidth, /* isFullSet = */ true);
4728 
4729   if (StartPattern.Condition != StepPattern.Condition) {
4730     // We don't handle this case today; but we could, by considering four
4731     // possibilities below instead of two. I'm not sure if there are cases where
4732     // that will help over what getRange already does, though.
4733     return ConstantRange(BitWidth, /* isFullSet = */ true);
4734   }
4735 
4736   // NB! Calling ScalarEvolution::getConstant is fine, but we should not try to
4737   // construct arbitrary general SCEV expressions here.  This function is called
4738   // from deep in the call stack, and calling getSCEV (on a sext instruction,
4739   // say) can end up caching a suboptimal value.
4740 
4741   // FIXME: without the explicit `this` receiver below, MSVC errors out with
4742   // C2352 and C2512 (otherwise it isn't needed).
4743 
4744   const SCEV *TrueStart = this->getConstant(StartPattern.TrueValue);
4745   const SCEV *TrueStep = this->getConstant(StepPattern.TrueValue);
4746   const SCEV *FalseStart = this->getConstant(StartPattern.FalseValue);
4747   const SCEV *FalseStep = this->getConstant(StepPattern.FalseValue);
4748 
4749   ConstantRange TrueRange =
4750       this->getRangeForAffineAR(TrueStart, TrueStep, MaxBECount, BitWidth);
4751   ConstantRange FalseRange =
4752       this->getRangeForAffineAR(FalseStart, FalseStep, MaxBECount, BitWidth);
4753 
4754   return TrueRange.unionWith(FalseRange);
4755 }
4756 
4757 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
4758   if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
4759   const BinaryOperator *BinOp = cast<BinaryOperator>(V);
4760 
4761   // Return early if there are no flags to propagate to the SCEV.
4762   SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4763   if (BinOp->hasNoUnsignedWrap())
4764     Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
4765   if (BinOp->hasNoSignedWrap())
4766     Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
4767   if (Flags == SCEV::FlagAnyWrap)
4768     return SCEV::FlagAnyWrap;
4769 
4770   return isSCEVExprNeverPoison(BinOp) ? Flags : SCEV::FlagAnyWrap;
4771 }
4772 
4773 bool ScalarEvolution::isSCEVExprNeverPoison(const Instruction *I) {
4774   // Here we check that I is in the header of the innermost loop containing I,
4775   // since we only deal with instructions in the loop header. The actual loop we
4776   // need to check later will come from an add recurrence, but getting that
4777   // requires computing the SCEV of the operands, which can be expensive. This
4778   // check we can do cheaply to rule out some cases early.
4779   Loop *InnermostContainingLoop = LI.getLoopFor(I->getParent());
4780   if (InnermostContainingLoop == nullptr ||
4781       InnermostContainingLoop->getHeader() != I->getParent())
4782     return false;
4783 
4784   // Only proceed if we can prove that I does not yield poison.
4785   if (!isKnownNotFullPoison(I)) return false;
4786 
4787   // At this point we know that if I is executed, then it does not wrap
4788   // according to at least one of NSW or NUW. If I is not executed, then we do
4789   // not know if the calculation that I represents would wrap. Multiple
4790   // instructions can map to the same SCEV. If we apply NSW or NUW from I to
4791   // the SCEV, we must guarantee no wrapping for that SCEV also when it is
4792   // derived from other instructions that map to the same SCEV. We cannot make
4793   // that guarantee for cases where I is not executed. So we need to find the
4794   // loop that I is considered in relation to and prove that I is executed for
4795   // every iteration of that loop. That implies that the value that I
4796   // calculates does not wrap anywhere in the loop, so then we can apply the
4797   // flags to the SCEV.
4798   //
4799   // We check isLoopInvariant to disambiguate in case we are adding recurrences
4800   // from different loops, so that we know which loop to prove that I is
4801   // executed in.
4802   for (unsigned OpIndex = 0; OpIndex < I->getNumOperands(); ++OpIndex) {
4803     const SCEV *Op = getSCEV(I->getOperand(OpIndex));
4804     if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
4805       bool AllOtherOpsLoopInvariant = true;
4806       for (unsigned OtherOpIndex = 0; OtherOpIndex < I->getNumOperands();
4807            ++OtherOpIndex) {
4808         if (OtherOpIndex != OpIndex) {
4809           const SCEV *OtherOp = getSCEV(I->getOperand(OtherOpIndex));
4810           if (!isLoopInvariant(OtherOp, AddRec->getLoop())) {
4811             AllOtherOpsLoopInvariant = false;
4812             break;
4813           }
4814         }
4815       }
4816       if (AllOtherOpsLoopInvariant &&
4817           isGuaranteedToExecuteForEveryIteration(I, AddRec->getLoop()))
4818         return true;
4819     }
4820   }
4821   return false;
4822 }
4823 
4824 /// createSCEV - We know that there is no SCEV for the specified value.  Analyze
4825 /// the expression.
4826 ///
4827 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4828   if (!isSCEVable(V->getType()))
4829     return getUnknown(V);
4830 
4831   if (Instruction *I = dyn_cast<Instruction>(V)) {
4832     // Don't attempt to analyze instructions in blocks that aren't
4833     // reachable. Such instructions don't matter, and they aren't required
4834     // to obey basic rules for definitions dominating uses which this
4835     // analysis depends on.
4836     if (!DT.isReachableFromEntry(I->getParent()))
4837       return getUnknown(V);
4838   } else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4839     return getConstant(CI);
4840   else if (isa<ConstantPointerNull>(V))
4841     return getZero(V->getType());
4842   else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4843     return GA->isInterposable() ? getUnknown(V) : getSCEV(GA->getAliasee());
4844   else if (!isa<ConstantExpr>(V))
4845     return getUnknown(V);
4846 
4847   Operator *U = cast<Operator>(V);
4848   if (auto BO = MatchBinaryOp(U)) {
4849     switch (BO->Opcode) {
4850     case Instruction::Add: {
4851       // The simple thing to do would be to just call getSCEV on both operands
4852       // and call getAddExpr with the result. However if we're looking at a
4853       // bunch of things all added together, this can be quite inefficient,
4854       // because it leads to N-1 getAddExpr calls for N ultimate operands.
4855       // Instead, gather up all the operands and make a single getAddExpr call.
4856       // LLVM IR canonical form means we need only traverse the left operands.
4857       SmallVector<const SCEV *, 4> AddOps;
4858       do {
4859         if (BO->Op) {
4860           if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
4861             AddOps.push_back(OpSCEV);
4862             break;
4863           }
4864 
4865           // If a NUW or NSW flag can be applied to the SCEV for this
4866           // addition, then compute the SCEV for this addition by itself
4867           // with a separate call to getAddExpr. We need to do that
4868           // instead of pushing the operands of the addition onto AddOps,
4869           // since the flags are only known to apply to this particular
4870           // addition - they may not apply to other additions that can be
4871           // formed with operands from AddOps.
4872           const SCEV *RHS = getSCEV(BO->RHS);
4873           SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
4874           if (Flags != SCEV::FlagAnyWrap) {
4875             const SCEV *LHS = getSCEV(BO->LHS);
4876             if (BO->Opcode == Instruction::Sub)
4877               AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
4878             else
4879               AddOps.push_back(getAddExpr(LHS, RHS, Flags));
4880             break;
4881           }
4882         }
4883 
4884         if (BO->Opcode == Instruction::Sub)
4885           AddOps.push_back(getNegativeSCEV(getSCEV(BO->RHS)));
4886         else
4887           AddOps.push_back(getSCEV(BO->RHS));
4888 
4889         auto NewBO = MatchBinaryOp(BO->LHS);
4890         if (!NewBO || (NewBO->Opcode != Instruction::Add &&
4891                        NewBO->Opcode != Instruction::Sub)) {
4892           AddOps.push_back(getSCEV(BO->LHS));
4893           break;
4894         }
4895         BO = NewBO;
4896       } while (true);
4897 
4898       return getAddExpr(AddOps);
4899     }
4900 
4901     case Instruction::Mul: {
4902       SmallVector<const SCEV *, 4> MulOps;
4903       do {
4904         if (BO->Op) {
4905           if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
4906             MulOps.push_back(OpSCEV);
4907             break;
4908           }
4909 
4910           SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
4911           if (Flags != SCEV::FlagAnyWrap) {
4912             MulOps.push_back(
4913                 getMulExpr(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags));
4914             break;
4915           }
4916         }
4917 
4918         MulOps.push_back(getSCEV(BO->RHS));
4919         auto NewBO = MatchBinaryOp(BO->LHS);
4920         if (!NewBO || NewBO->Opcode != Instruction::Mul) {
4921           MulOps.push_back(getSCEV(BO->LHS));
4922           break;
4923         }
4924 	BO = NewBO;
4925       } while (true);
4926 
4927       return getMulExpr(MulOps);
4928     }
4929     case Instruction::UDiv:
4930       return getUDivExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
4931     case Instruction::Sub: {
4932       SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4933       if (BO->Op)
4934         Flags = getNoWrapFlagsFromUB(BO->Op);
4935       return getMinusSCEV(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags);
4936     }
4937     case Instruction::And:
4938       // For an expression like x&255 that merely masks off the high bits,
4939       // use zext(trunc(x)) as the SCEV expression.
4940       if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
4941         if (CI->isNullValue())
4942           return getSCEV(BO->RHS);
4943         if (CI->isAllOnesValue())
4944           return getSCEV(BO->LHS);
4945         const APInt &A = CI->getValue();
4946 
4947         // Instcombine's ShrinkDemandedConstant may strip bits out of
4948         // constants, obscuring what would otherwise be a low-bits mask.
4949         // Use computeKnownBits to compute what ShrinkDemandedConstant
4950         // knew about to reconstruct a low-bits mask value.
4951         unsigned LZ = A.countLeadingZeros();
4952         unsigned TZ = A.countTrailingZeros();
4953         unsigned BitWidth = A.getBitWidth();
4954         APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4955         computeKnownBits(BO->LHS, KnownZero, KnownOne, getDataLayout(),
4956                          0, &AC, nullptr, &DT);
4957 
4958         APInt EffectiveMask =
4959             APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4960         if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4961           const SCEV *MulCount = getConstant(ConstantInt::get(
4962               getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4963           return getMulExpr(
4964               getZeroExtendExpr(
4965                   getTruncateExpr(
4966                       getUDivExactExpr(getSCEV(BO->LHS), MulCount),
4967                       IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4968                   BO->LHS->getType()),
4969               MulCount);
4970         }
4971       }
4972       break;
4973 
4974     case Instruction::Or:
4975       // If the RHS of the Or is a constant, we may have something like:
4976       // X*4+1 which got turned into X*4|1.  Handle this as an Add so loop
4977       // optimizations will transparently handle this case.
4978       //
4979       // In order for this transformation to be safe, the LHS must be of the
4980       // form X*(2^n) and the Or constant must be less than 2^n.
4981       if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
4982         const SCEV *LHS = getSCEV(BO->LHS);
4983         const APInt &CIVal = CI->getValue();
4984         if (GetMinTrailingZeros(LHS) >=
4985             (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4986           // Build a plain add SCEV.
4987           const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4988           // If the LHS of the add was an addrec and it has no-wrap flags,
4989           // transfer the no-wrap flags, since an or won't introduce a wrap.
4990           if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4991             const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4992             const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4993                 OldAR->getNoWrapFlags());
4994           }
4995           return S;
4996         }
4997       }
4998       break;
4999 
5000     case Instruction::Xor:
5001       if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
5002         // If the RHS of xor is -1, then this is a not operation.
5003         if (CI->isAllOnesValue())
5004           return getNotSCEV(getSCEV(BO->LHS));
5005 
5006         // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
5007         // This is a variant of the check for xor with -1, and it handles
5008         // the case where instcombine has trimmed non-demanded bits out
5009         // of an xor with -1.
5010         if (auto *LBO = dyn_cast<BinaryOperator>(BO->LHS))
5011           if (ConstantInt *LCI = dyn_cast<ConstantInt>(LBO->getOperand(1)))
5012             if (LBO->getOpcode() == Instruction::And &&
5013                 LCI->getValue() == CI->getValue())
5014               if (const SCEVZeroExtendExpr *Z =
5015                       dyn_cast<SCEVZeroExtendExpr>(getSCEV(BO->LHS))) {
5016                 Type *UTy = BO->LHS->getType();
5017                 const SCEV *Z0 = Z->getOperand();
5018                 Type *Z0Ty = Z0->getType();
5019                 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
5020 
5021                 // If C is a low-bits mask, the zero extend is serving to
5022                 // mask off the high bits. Complement the operand and
5023                 // re-apply the zext.
5024                 if (APIntOps::isMask(Z0TySize, CI->getValue()))
5025                   return getZeroExtendExpr(getNotSCEV(Z0), UTy);
5026 
5027                 // If C is a single bit, it may be in the sign-bit position
5028                 // before the zero-extend. In this case, represent the xor
5029                 // using an add, which is equivalent, and re-apply the zext.
5030                 APInt Trunc = CI->getValue().trunc(Z0TySize);
5031                 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
5032                     Trunc.isSignBit())
5033                   return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
5034                                            UTy);
5035               }
5036       }
5037       break;
5038 
5039   case Instruction::Shl:
5040     // Turn shift left of a constant amount into a multiply.
5041     if (ConstantInt *SA = dyn_cast<ConstantInt>(BO->RHS)) {
5042       uint32_t BitWidth = cast<IntegerType>(SA->getType())->getBitWidth();
5043 
5044       // If the shift count is not less than the bitwidth, the result of
5045       // the shift is undefined. Don't try to analyze it, because the
5046       // resolution chosen here may differ from the resolution chosen in
5047       // other parts of the compiler.
5048       if (SA->getValue().uge(BitWidth))
5049         break;
5050 
5051       // It is currently not resolved how to interpret NSW for left
5052       // shift by BitWidth - 1, so we avoid applying flags in that
5053       // case. Remove this check (or this comment) once the situation
5054       // is resolved. See
5055       // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
5056       // and http://reviews.llvm.org/D8890 .
5057       auto Flags = SCEV::FlagAnyWrap;
5058       if (BO->Op && SA->getValue().ult(BitWidth - 1))
5059         Flags = getNoWrapFlagsFromUB(BO->Op);
5060 
5061       Constant *X = ConstantInt::get(getContext(),
5062         APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
5063       return getMulExpr(getSCEV(BO->LHS), getSCEV(X), Flags);
5064     }
5065     break;
5066 
5067     case Instruction::AShr:
5068       // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
5069       if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS))
5070         if (Operator *L = dyn_cast<Operator>(BO->LHS))
5071           if (L->getOpcode() == Instruction::Shl &&
5072               L->getOperand(1) == BO->RHS) {
5073             uint64_t BitWidth = getTypeSizeInBits(BO->LHS->getType());
5074 
5075             // If the shift count is not less than the bitwidth, the result of
5076             // the shift is undefined. Don't try to analyze it, because the
5077             // resolution chosen here may differ from the resolution chosen in
5078             // other parts of the compiler.
5079             if (CI->getValue().uge(BitWidth))
5080               break;
5081 
5082             uint64_t Amt = BitWidth - CI->getZExtValue();
5083             if (Amt == BitWidth)
5084               return getSCEV(L->getOperand(0)); // shift by zero --> noop
5085             return getSignExtendExpr(
5086                 getTruncateExpr(getSCEV(L->getOperand(0)),
5087                                 IntegerType::get(getContext(), Amt)),
5088                 BO->LHS->getType());
5089           }
5090       break;
5091     }
5092   }
5093 
5094   switch (U->getOpcode()) {
5095   case Instruction::Trunc:
5096     return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
5097 
5098   case Instruction::ZExt:
5099     return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
5100 
5101   case Instruction::SExt:
5102     return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
5103 
5104   case Instruction::BitCast:
5105     // BitCasts are no-op casts so we just eliminate the cast.
5106     if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
5107       return getSCEV(U->getOperand(0));
5108     break;
5109 
5110   // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
5111   // lead to pointer expressions which cannot safely be expanded to GEPs,
5112   // because ScalarEvolution doesn't respect the GEP aliasing rules when
5113   // simplifying integer expressions.
5114 
5115   case Instruction::GetElementPtr:
5116     return createNodeForGEP(cast<GEPOperator>(U));
5117 
5118   case Instruction::PHI:
5119     return createNodeForPHI(cast<PHINode>(U));
5120 
5121   case Instruction::Select:
5122     // U can also be a select constant expr, which let fall through.  Since
5123     // createNodeForSelect only works for a condition that is an `ICmpInst`, and
5124     // constant expressions cannot have instructions as operands, we'd have
5125     // returned getUnknown for a select constant expressions anyway.
5126     if (isa<Instruction>(U))
5127       return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
5128                                       U->getOperand(1), U->getOperand(2));
5129   }
5130 
5131   return getUnknown(V);
5132 }
5133 
5134 
5135 
5136 //===----------------------------------------------------------------------===//
5137 //                   Iteration Count Computation Code
5138 //
5139 
5140 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
5141   if (BasicBlock *ExitingBB = L->getExitingBlock())
5142     return getSmallConstantTripCount(L, ExitingBB);
5143 
5144   // No trip count information for multiple exits.
5145   return 0;
5146 }
5147 
5148 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
5149 /// normal unsigned value. Returns 0 if the trip count is unknown or not
5150 /// constant. Will also return 0 if the maximum trip count is very large (>=
5151 /// 2^32).
5152 ///
5153 /// This "trip count" assumes that control exits via ExitingBlock. More
5154 /// precisely, it is the number of times that control may reach ExitingBlock
5155 /// before taking the branch. For loops with multiple exits, it may not be the
5156 /// number times that the loop header executes because the loop may exit
5157 /// prematurely via another branch.
5158 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
5159                                                     BasicBlock *ExitingBlock) {
5160   assert(ExitingBlock && "Must pass a non-null exiting block!");
5161   assert(L->isLoopExiting(ExitingBlock) &&
5162          "Exiting block must actually branch out of the loop!");
5163   const SCEVConstant *ExitCount =
5164       dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
5165   if (!ExitCount)
5166     return 0;
5167 
5168   ConstantInt *ExitConst = ExitCount->getValue();
5169 
5170   // Guard against huge trip counts.
5171   if (ExitConst->getValue().getActiveBits() > 32)
5172     return 0;
5173 
5174   // In case of integer overflow, this returns 0, which is correct.
5175   return ((unsigned)ExitConst->getZExtValue()) + 1;
5176 }
5177 
5178 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
5179   if (BasicBlock *ExitingBB = L->getExitingBlock())
5180     return getSmallConstantTripMultiple(L, ExitingBB);
5181 
5182   // No trip multiple information for multiple exits.
5183   return 0;
5184 }
5185 
5186 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
5187 /// trip count of this loop as a normal unsigned value, if possible. This
5188 /// means that the actual trip count is always a multiple of the returned
5189 /// value (don't forget the trip count could very well be zero as well!).
5190 ///
5191 /// Returns 1 if the trip count is unknown or not guaranteed to be the
5192 /// multiple of a constant (which is also the case if the trip count is simply
5193 /// constant, use getSmallConstantTripCount for that case), Will also return 1
5194 /// if the trip count is very large (>= 2^32).
5195 ///
5196 /// As explained in the comments for getSmallConstantTripCount, this assumes
5197 /// that control exits the loop via ExitingBlock.
5198 unsigned
5199 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
5200                                               BasicBlock *ExitingBlock) {
5201   assert(ExitingBlock && "Must pass a non-null exiting block!");
5202   assert(L->isLoopExiting(ExitingBlock) &&
5203          "Exiting block must actually branch out of the loop!");
5204   const SCEV *ExitCount = getExitCount(L, ExitingBlock);
5205   if (ExitCount == getCouldNotCompute())
5206     return 1;
5207 
5208   // Get the trip count from the BE count by adding 1.
5209   const SCEV *TCMul = getAddExpr(ExitCount, getOne(ExitCount->getType()));
5210   // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
5211   // to factor simple cases.
5212   if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
5213     TCMul = Mul->getOperand(0);
5214 
5215   const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
5216   if (!MulC)
5217     return 1;
5218 
5219   ConstantInt *Result = MulC->getValue();
5220 
5221   // Guard against huge trip counts (this requires checking
5222   // for zero to handle the case where the trip count == -1 and the
5223   // addition wraps).
5224   if (!Result || Result->getValue().getActiveBits() > 32 ||
5225       Result->getValue().getActiveBits() == 0)
5226     return 1;
5227 
5228   return (unsigned)Result->getZExtValue();
5229 }
5230 
5231 // getExitCount - Get the expression for the number of loop iterations for which
5232 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
5233 // SCEVCouldNotCompute.
5234 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
5235   return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
5236 }
5237 
5238 const SCEV *
5239 ScalarEvolution::getPredicatedBackedgeTakenCount(const Loop *L,
5240                                                  SCEVUnionPredicate &Preds) {
5241   return getPredicatedBackedgeTakenInfo(L).getExact(this, &Preds);
5242 }
5243 
5244 /// getBackedgeTakenCount - If the specified loop has a predictable
5245 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
5246 /// object. The backedge-taken count is the number of times the loop header
5247 /// will be branched to from within the loop. This is one less than the
5248 /// trip count of the loop, since it doesn't count the first iteration,
5249 /// when the header is branched to from outside the loop.
5250 ///
5251 /// Note that it is not valid to call this method on a loop without a
5252 /// loop-invariant backedge-taken count (see
5253 /// hasLoopInvariantBackedgeTakenCount).
5254 ///
5255 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
5256   return getBackedgeTakenInfo(L).getExact(this);
5257 }
5258 
5259 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
5260 /// return the least SCEV value that is known never to be less than the
5261 /// actual backedge taken count.
5262 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
5263   return getBackedgeTakenInfo(L).getMax(this);
5264 }
5265 
5266 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
5267 /// onto the given Worklist.
5268 static void
5269 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
5270   BasicBlock *Header = L->getHeader();
5271 
5272   // Push all Loop-header PHIs onto the Worklist stack.
5273   for (BasicBlock::iterator I = Header->begin();
5274        PHINode *PN = dyn_cast<PHINode>(I); ++I)
5275     Worklist.push_back(PN);
5276 }
5277 
5278 const ScalarEvolution::BackedgeTakenInfo &
5279 ScalarEvolution::getPredicatedBackedgeTakenInfo(const Loop *L) {
5280   auto &BTI = getBackedgeTakenInfo(L);
5281   if (BTI.hasFullInfo())
5282     return BTI;
5283 
5284   auto Pair = PredicatedBackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
5285 
5286   if (!Pair.second)
5287     return Pair.first->second;
5288 
5289   BackedgeTakenInfo Result =
5290       computeBackedgeTakenCount(L, /*AllowPredicates=*/true);
5291 
5292   return PredicatedBackedgeTakenCounts.find(L)->second = Result;
5293 }
5294 
5295 const ScalarEvolution::BackedgeTakenInfo &
5296 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
5297   // Initially insert an invalid entry for this loop. If the insertion
5298   // succeeds, proceed to actually compute a backedge-taken count and
5299   // update the value. The temporary CouldNotCompute value tells SCEV
5300   // code elsewhere that it shouldn't attempt to request a new
5301   // backedge-taken count, which could result in infinite recursion.
5302   std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
5303       BackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
5304   if (!Pair.second)
5305     return Pair.first->second;
5306 
5307   // computeBackedgeTakenCount may allocate memory for its result. Inserting it
5308   // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
5309   // must be cleared in this scope.
5310   BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
5311 
5312   if (Result.getExact(this) != getCouldNotCompute()) {
5313     assert(isLoopInvariant(Result.getExact(this), L) &&
5314            isLoopInvariant(Result.getMax(this), L) &&
5315            "Computed backedge-taken count isn't loop invariant for loop!");
5316     ++NumTripCountsComputed;
5317   }
5318   else if (Result.getMax(this) == getCouldNotCompute() &&
5319            isa<PHINode>(L->getHeader()->begin())) {
5320     // Only count loops that have phi nodes as not being computable.
5321     ++NumTripCountsNotComputed;
5322   }
5323 
5324   // Now that we know more about the trip count for this loop, forget any
5325   // existing SCEV values for PHI nodes in this loop since they are only
5326   // conservative estimates made without the benefit of trip count
5327   // information. This is similar to the code in forgetLoop, except that
5328   // it handles SCEVUnknown PHI nodes specially.
5329   if (Result.hasAnyInfo()) {
5330     SmallVector<Instruction *, 16> Worklist;
5331     PushLoopPHIs(L, Worklist);
5332 
5333     SmallPtrSet<Instruction *, 8> Visited;
5334     while (!Worklist.empty()) {
5335       Instruction *I = Worklist.pop_back_val();
5336       if (!Visited.insert(I).second)
5337         continue;
5338 
5339       ValueExprMapType::iterator It =
5340         ValueExprMap.find_as(static_cast<Value *>(I));
5341       if (It != ValueExprMap.end()) {
5342         const SCEV *Old = It->second;
5343 
5344         // SCEVUnknown for a PHI either means that it has an unrecognized
5345         // structure, or it's a PHI that's in the progress of being computed
5346         // by createNodeForPHI.  In the former case, additional loop trip
5347         // count information isn't going to change anything. In the later
5348         // case, createNodeForPHI will perform the necessary updates on its
5349         // own when it gets to that point.
5350         if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
5351           forgetMemoizedResults(Old);
5352           ValueExprMap.erase(It);
5353         }
5354         if (PHINode *PN = dyn_cast<PHINode>(I))
5355           ConstantEvolutionLoopExitValue.erase(PN);
5356       }
5357 
5358       PushDefUseChildren(I, Worklist);
5359     }
5360   }
5361 
5362   // Re-lookup the insert position, since the call to
5363   // computeBackedgeTakenCount above could result in a
5364   // recusive call to getBackedgeTakenInfo (on a different
5365   // loop), which would invalidate the iterator computed
5366   // earlier.
5367   return BackedgeTakenCounts.find(L)->second = Result;
5368 }
5369 
5370 /// forgetLoop - This method should be called by the client when it has
5371 /// changed a loop in a way that may effect ScalarEvolution's ability to
5372 /// compute a trip count, or if the loop is deleted.
5373 void ScalarEvolution::forgetLoop(const Loop *L) {
5374   // Drop any stored trip count value.
5375   auto RemoveLoopFromBackedgeMap =
5376       [L](DenseMap<const Loop *, BackedgeTakenInfo> &Map) {
5377         auto BTCPos = Map.find(L);
5378         if (BTCPos != Map.end()) {
5379           BTCPos->second.clear();
5380           Map.erase(BTCPos);
5381         }
5382       };
5383 
5384   RemoveLoopFromBackedgeMap(BackedgeTakenCounts);
5385   RemoveLoopFromBackedgeMap(PredicatedBackedgeTakenCounts);
5386 
5387   // Drop information about expressions based on loop-header PHIs.
5388   SmallVector<Instruction *, 16> Worklist;
5389   PushLoopPHIs(L, Worklist);
5390 
5391   SmallPtrSet<Instruction *, 8> Visited;
5392   while (!Worklist.empty()) {
5393     Instruction *I = Worklist.pop_back_val();
5394     if (!Visited.insert(I).second)
5395       continue;
5396 
5397     ValueExprMapType::iterator It =
5398       ValueExprMap.find_as(static_cast<Value *>(I));
5399     if (It != ValueExprMap.end()) {
5400       forgetMemoizedResults(It->second);
5401       ValueExprMap.erase(It);
5402       if (PHINode *PN = dyn_cast<PHINode>(I))
5403         ConstantEvolutionLoopExitValue.erase(PN);
5404     }
5405 
5406     PushDefUseChildren(I, Worklist);
5407   }
5408 
5409   // Forget all contained loops too, to avoid dangling entries in the
5410   // ValuesAtScopes map.
5411   for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5412     forgetLoop(*I);
5413 }
5414 
5415 /// forgetValue - This method should be called by the client when it has
5416 /// changed a value in a way that may effect its value, or which may
5417 /// disconnect it from a def-use chain linking it to a loop.
5418 void ScalarEvolution::forgetValue(Value *V) {
5419   Instruction *I = dyn_cast<Instruction>(V);
5420   if (!I) return;
5421 
5422   // Drop information about expressions based on loop-header PHIs.
5423   SmallVector<Instruction *, 16> Worklist;
5424   Worklist.push_back(I);
5425 
5426   SmallPtrSet<Instruction *, 8> Visited;
5427   while (!Worklist.empty()) {
5428     I = Worklist.pop_back_val();
5429     if (!Visited.insert(I).second)
5430       continue;
5431 
5432     ValueExprMapType::iterator It =
5433       ValueExprMap.find_as(static_cast<Value *>(I));
5434     if (It != ValueExprMap.end()) {
5435       forgetMemoizedResults(It->second);
5436       ValueExprMap.erase(It);
5437       if (PHINode *PN = dyn_cast<PHINode>(I))
5438         ConstantEvolutionLoopExitValue.erase(PN);
5439     }
5440 
5441     PushDefUseChildren(I, Worklist);
5442   }
5443 }
5444 
5445 /// getExact - Get the exact loop backedge taken count considering all loop
5446 /// exits. A computable result can only be returned for loops with a single
5447 /// exit.  Returning the minimum taken count among all exits is incorrect
5448 /// because one of the loop's exit limit's may have been skipped. HowFarToZero
5449 /// assumes that the limit of each loop test is never skipped. This is a valid
5450 /// assumption as long as the loop exits via that test. For precise results, it
5451 /// is the caller's responsibility to specify the relevant loop exit using
5452 /// getExact(ExitingBlock, SE).
5453 const SCEV *
5454 ScalarEvolution::BackedgeTakenInfo::getExact(
5455     ScalarEvolution *SE, SCEVUnionPredicate *Preds) const {
5456   // If any exits were not computable, the loop is not computable.
5457   if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
5458 
5459   // We need exactly one computable exit.
5460   if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
5461   assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
5462 
5463   const SCEV *BECount = nullptr;
5464   for (auto &ENT : ExitNotTaken) {
5465     assert(ENT.ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
5466 
5467     if (!BECount)
5468       BECount = ENT.ExactNotTaken;
5469     else if (BECount != ENT.ExactNotTaken)
5470       return SE->getCouldNotCompute();
5471     if (Preds && ENT.getPred())
5472       Preds->add(ENT.getPred());
5473 
5474     assert((Preds || ENT.hasAlwaysTruePred()) &&
5475            "Predicate should be always true!");
5476   }
5477 
5478   assert(BECount && "Invalid not taken count for loop exit");
5479   return BECount;
5480 }
5481 
5482 /// getExact - Get the exact not taken count for this loop exit.
5483 const SCEV *
5484 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
5485                                              ScalarEvolution *SE) const {
5486   for (auto &ENT : ExitNotTaken)
5487     if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePred())
5488       return ENT.ExactNotTaken;
5489 
5490   return SE->getCouldNotCompute();
5491 }
5492 
5493 /// getMax - Get the max backedge taken count for the loop.
5494 const SCEV *
5495 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
5496   for (auto &ENT : ExitNotTaken)
5497     if (!ENT.hasAlwaysTruePred())
5498       return SE->getCouldNotCompute();
5499 
5500   return Max ? Max : SE->getCouldNotCompute();
5501 }
5502 
5503 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
5504                                                     ScalarEvolution *SE) const {
5505   if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
5506     return true;
5507 
5508   if (!ExitNotTaken.ExitingBlock)
5509     return false;
5510 
5511   for (auto &ENT : ExitNotTaken)
5512     if (ENT.ExactNotTaken != SE->getCouldNotCompute() &&
5513         SE->hasOperand(ENT.ExactNotTaken, S))
5514       return true;
5515 
5516   return false;
5517 }
5518 
5519 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
5520 /// computable exit into a persistent ExitNotTakenInfo array.
5521 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
5522     SmallVectorImpl<EdgeInfo> &ExitCounts, bool Complete, const SCEV *MaxCount)
5523     : Max(MaxCount) {
5524 
5525   if (!Complete)
5526     ExitNotTaken.setIncomplete();
5527 
5528   unsigned NumExits = ExitCounts.size();
5529   if (NumExits == 0) return;
5530 
5531   ExitNotTaken.ExitingBlock = ExitCounts[0].ExitBlock;
5532   ExitNotTaken.ExactNotTaken = ExitCounts[0].Taken;
5533 
5534   // Determine the number of ExitNotTakenExtras structures that we need.
5535   unsigned ExtraInfoSize = 0;
5536   if (NumExits > 1)
5537     ExtraInfoSize = 1 + std::count_if(std::next(ExitCounts.begin()),
5538                                       ExitCounts.end(), [](EdgeInfo &Entry) {
5539                                         return !Entry.Pred.isAlwaysTrue();
5540                                       });
5541   else if (!ExitCounts[0].Pred.isAlwaysTrue())
5542     ExtraInfoSize = 1;
5543 
5544   ExitNotTakenExtras *ENT = nullptr;
5545 
5546   // Allocate the ExitNotTakenExtras structures and initialize the first
5547   // element (ExitNotTaken).
5548   if (ExtraInfoSize > 0) {
5549     ENT = new ExitNotTakenExtras[ExtraInfoSize];
5550     ExitNotTaken.ExtraInfo = &ENT[0];
5551     *ExitNotTaken.getPred() = std::move(ExitCounts[0].Pred);
5552   }
5553 
5554   if (NumExits == 1)
5555     return;
5556 
5557   auto &Exits = ExitNotTaken.ExtraInfo->Exits;
5558 
5559   // Handle the rare case of multiple computable exits.
5560   for (unsigned i = 1, PredPos = 1; i < NumExits; ++i) {
5561     ExitNotTakenExtras *Ptr = nullptr;
5562     if (!ExitCounts[i].Pred.isAlwaysTrue()) {
5563       Ptr = &ENT[PredPos++];
5564       Ptr->Pred = std::move(ExitCounts[i].Pred);
5565     }
5566 
5567     Exits.emplace_back(ExitCounts[i].ExitBlock, ExitCounts[i].Taken, Ptr);
5568   }
5569 }
5570 
5571 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
5572 void ScalarEvolution::BackedgeTakenInfo::clear() {
5573   ExitNotTaken.ExitingBlock = nullptr;
5574   ExitNotTaken.ExactNotTaken = nullptr;
5575   delete[] ExitNotTaken.ExtraInfo;
5576 }
5577 
5578 /// computeBackedgeTakenCount - Compute the number of times the backedge
5579 /// of the specified loop will execute.
5580 ScalarEvolution::BackedgeTakenInfo
5581 ScalarEvolution::computeBackedgeTakenCount(const Loop *L,
5582                                            bool AllowPredicates) {
5583   SmallVector<BasicBlock *, 8> ExitingBlocks;
5584   L->getExitingBlocks(ExitingBlocks);
5585 
5586   SmallVector<EdgeInfo, 4> ExitCounts;
5587   bool CouldComputeBECount = true;
5588   BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
5589   const SCEV *MustExitMaxBECount = nullptr;
5590   const SCEV *MayExitMaxBECount = nullptr;
5591 
5592   // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
5593   // and compute maxBECount.
5594   // Do a union of all the predicates here.
5595   for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
5596     BasicBlock *ExitBB = ExitingBlocks[i];
5597     ExitLimit EL = computeExitLimit(L, ExitBB, AllowPredicates);
5598 
5599     assert((AllowPredicates || EL.Pred.isAlwaysTrue()) &&
5600            "Predicated exit limit when predicates are not allowed!");
5601 
5602     // 1. For each exit that can be computed, add an entry to ExitCounts.
5603     // CouldComputeBECount is true only if all exits can be computed.
5604     if (EL.Exact == getCouldNotCompute())
5605       // We couldn't compute an exact value for this exit, so
5606       // we won't be able to compute an exact value for the loop.
5607       CouldComputeBECount = false;
5608     else
5609       ExitCounts.emplace_back(EdgeInfo(ExitBB, EL.Exact, EL.Pred));
5610 
5611     // 2. Derive the loop's MaxBECount from each exit's max number of
5612     // non-exiting iterations. Partition the loop exits into two kinds:
5613     // LoopMustExits and LoopMayExits.
5614     //
5615     // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
5616     // is a LoopMayExit.  If any computable LoopMustExit is found, then
5617     // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
5618     // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
5619     // considered greater than any computable EL.Max.
5620     if (EL.Max != getCouldNotCompute() && Latch &&
5621         DT.dominates(ExitBB, Latch)) {
5622       if (!MustExitMaxBECount)
5623         MustExitMaxBECount = EL.Max;
5624       else {
5625         MustExitMaxBECount =
5626           getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
5627       }
5628     } else if (MayExitMaxBECount != getCouldNotCompute()) {
5629       if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
5630         MayExitMaxBECount = EL.Max;
5631       else {
5632         MayExitMaxBECount =
5633           getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
5634       }
5635     }
5636   }
5637   const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
5638     (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
5639   return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
5640 }
5641 
5642 ScalarEvolution::ExitLimit
5643 ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
5644                                   bool AllowPredicates) {
5645 
5646   // Okay, we've chosen an exiting block.  See what condition causes us to exit
5647   // at this block and remember the exit block and whether all other targets
5648   // lead to the loop header.
5649   bool MustExecuteLoopHeader = true;
5650   BasicBlock *Exit = nullptr;
5651   for (auto *SBB : successors(ExitingBlock))
5652     if (!L->contains(SBB)) {
5653       if (Exit) // Multiple exit successors.
5654         return getCouldNotCompute();
5655       Exit = SBB;
5656     } else if (SBB != L->getHeader()) {
5657       MustExecuteLoopHeader = false;
5658     }
5659 
5660   // At this point, we know we have a conditional branch that determines whether
5661   // the loop is exited.  However, we don't know if the branch is executed each
5662   // time through the loop.  If not, then the execution count of the branch will
5663   // not be equal to the trip count of the loop.
5664   //
5665   // Currently we check for this by checking to see if the Exit branch goes to
5666   // the loop header.  If so, we know it will always execute the same number of
5667   // times as the loop.  We also handle the case where the exit block *is* the
5668   // loop header.  This is common for un-rotated loops.
5669   //
5670   // If both of those tests fail, walk up the unique predecessor chain to the
5671   // header, stopping if there is an edge that doesn't exit the loop. If the
5672   // header is reached, the execution count of the branch will be equal to the
5673   // trip count of the loop.
5674   //
5675   //  More extensive analysis could be done to handle more cases here.
5676   //
5677   if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
5678     // The simple checks failed, try climbing the unique predecessor chain
5679     // up to the header.
5680     bool Ok = false;
5681     for (BasicBlock *BB = ExitingBlock; BB; ) {
5682       BasicBlock *Pred = BB->getUniquePredecessor();
5683       if (!Pred)
5684         return getCouldNotCompute();
5685       TerminatorInst *PredTerm = Pred->getTerminator();
5686       for (const BasicBlock *PredSucc : PredTerm->successors()) {
5687         if (PredSucc == BB)
5688           continue;
5689         // If the predecessor has a successor that isn't BB and isn't
5690         // outside the loop, assume the worst.
5691         if (L->contains(PredSucc))
5692           return getCouldNotCompute();
5693       }
5694       if (Pred == L->getHeader()) {
5695         Ok = true;
5696         break;
5697       }
5698       BB = Pred;
5699     }
5700     if (!Ok)
5701       return getCouldNotCompute();
5702   }
5703 
5704   bool IsOnlyExit = (L->getExitingBlock() != nullptr);
5705   TerminatorInst *Term = ExitingBlock->getTerminator();
5706   if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
5707     assert(BI->isConditional() && "If unconditional, it can't be in loop!");
5708     // Proceed to the next level to examine the exit condition expression.
5709     return computeExitLimitFromCond(
5710         L, BI->getCondition(), BI->getSuccessor(0), BI->getSuccessor(1),
5711         /*ControlsExit=*/IsOnlyExit, AllowPredicates);
5712   }
5713 
5714   if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
5715     return computeExitLimitFromSingleExitSwitch(L, SI, Exit,
5716                                                 /*ControlsExit=*/IsOnlyExit);
5717 
5718   return getCouldNotCompute();
5719 }
5720 
5721 /// computeExitLimitFromCond - Compute the number of times the
5722 /// backedge of the specified loop will execute if its exit condition
5723 /// were a conditional branch of ExitCond, TBB, and FBB.
5724 ///
5725 /// @param ControlsExit is true if ExitCond directly controls the exit
5726 /// branch. In this case, we can assume that the loop exits only if the
5727 /// condition is true and can infer that failing to meet the condition prior to
5728 /// integer wraparound results in undefined behavior.
5729 ScalarEvolution::ExitLimit
5730 ScalarEvolution::computeExitLimitFromCond(const Loop *L,
5731                                           Value *ExitCond,
5732                                           BasicBlock *TBB,
5733                                           BasicBlock *FBB,
5734                                           bool ControlsExit,
5735                                           bool AllowPredicates) {
5736   // Check if the controlling expression for this loop is an And or Or.
5737   if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
5738     if (BO->getOpcode() == Instruction::And) {
5739       // Recurse on the operands of the and.
5740       bool EitherMayExit = L->contains(TBB);
5741       ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5742                                                ControlsExit && !EitherMayExit,
5743                                                AllowPredicates);
5744       ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5745                                                ControlsExit && !EitherMayExit,
5746                                                AllowPredicates);
5747       const SCEV *BECount = getCouldNotCompute();
5748       const SCEV *MaxBECount = getCouldNotCompute();
5749       if (EitherMayExit) {
5750         // Both conditions must be true for the loop to continue executing.
5751         // Choose the less conservative count.
5752         if (EL0.Exact == getCouldNotCompute() ||
5753             EL1.Exact == getCouldNotCompute())
5754           BECount = getCouldNotCompute();
5755         else
5756           BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5757         if (EL0.Max == getCouldNotCompute())
5758           MaxBECount = EL1.Max;
5759         else if (EL1.Max == getCouldNotCompute())
5760           MaxBECount = EL0.Max;
5761         else
5762           MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5763       } else {
5764         // Both conditions must be true at the same time for the loop to exit.
5765         // For now, be conservative.
5766         assert(L->contains(FBB) && "Loop block has no successor in loop!");
5767         if (EL0.Max == EL1.Max)
5768           MaxBECount = EL0.Max;
5769         if (EL0.Exact == EL1.Exact)
5770           BECount = EL0.Exact;
5771       }
5772 
5773       SCEVUnionPredicate NP;
5774       NP.add(&EL0.Pred);
5775       NP.add(&EL1.Pred);
5776       // There are cases (e.g. PR26207) where computeExitLimitFromCond is able
5777       // to be more aggressive when computing BECount than when computing
5778       // MaxBECount.  In these cases it is possible for EL0.Exact and EL1.Exact
5779       // to match, but for EL0.Max and EL1.Max to not.
5780       if (isa<SCEVCouldNotCompute>(MaxBECount) &&
5781           !isa<SCEVCouldNotCompute>(BECount))
5782         MaxBECount = BECount;
5783 
5784       return ExitLimit(BECount, MaxBECount, NP);
5785     }
5786     if (BO->getOpcode() == Instruction::Or) {
5787       // Recurse on the operands of the or.
5788       bool EitherMayExit = L->contains(FBB);
5789       ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5790                                                ControlsExit && !EitherMayExit,
5791                                                AllowPredicates);
5792       ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5793                                                ControlsExit && !EitherMayExit,
5794                                                AllowPredicates);
5795       const SCEV *BECount = getCouldNotCompute();
5796       const SCEV *MaxBECount = getCouldNotCompute();
5797       if (EitherMayExit) {
5798         // Both conditions must be false for the loop to continue executing.
5799         // Choose the less conservative count.
5800         if (EL0.Exact == getCouldNotCompute() ||
5801             EL1.Exact == getCouldNotCompute())
5802           BECount = getCouldNotCompute();
5803         else
5804           BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5805         if (EL0.Max == getCouldNotCompute())
5806           MaxBECount = EL1.Max;
5807         else if (EL1.Max == getCouldNotCompute())
5808           MaxBECount = EL0.Max;
5809         else
5810           MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5811       } else {
5812         // Both conditions must be false at the same time for the loop to exit.
5813         // For now, be conservative.
5814         assert(L->contains(TBB) && "Loop block has no successor in loop!");
5815         if (EL0.Max == EL1.Max)
5816           MaxBECount = EL0.Max;
5817         if (EL0.Exact == EL1.Exact)
5818           BECount = EL0.Exact;
5819       }
5820 
5821       SCEVUnionPredicate NP;
5822       NP.add(&EL0.Pred);
5823       NP.add(&EL1.Pred);
5824       return ExitLimit(BECount, MaxBECount, NP);
5825     }
5826   }
5827 
5828   // With an icmp, it may be feasible to compute an exact backedge-taken count.
5829   // Proceed to the next level to examine the icmp.
5830   if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) {
5831     ExitLimit EL =
5832         computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5833     if (EL.hasFullInfo() || !AllowPredicates)
5834       return EL;
5835 
5836     // Try again, but use SCEV predicates this time.
5837     return computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit,
5838                                     /*AllowPredicates=*/true);
5839   }
5840 
5841   // Check for a constant condition. These are normally stripped out by
5842   // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5843   // preserve the CFG and is temporarily leaving constant conditions
5844   // in place.
5845   if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5846     if (L->contains(FBB) == !CI->getZExtValue())
5847       // The backedge is always taken.
5848       return getCouldNotCompute();
5849     else
5850       // The backedge is never taken.
5851       return getZero(CI->getType());
5852   }
5853 
5854   // If it's not an integer or pointer comparison then compute it the hard way.
5855   return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5856 }
5857 
5858 ScalarEvolution::ExitLimit
5859 ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
5860                                           ICmpInst *ExitCond,
5861                                           BasicBlock *TBB,
5862                                           BasicBlock *FBB,
5863                                           bool ControlsExit,
5864                                           bool AllowPredicates) {
5865 
5866   // If the condition was exit on true, convert the condition to exit on false
5867   ICmpInst::Predicate Cond;
5868   if (!L->contains(FBB))
5869     Cond = ExitCond->getPredicate();
5870   else
5871     Cond = ExitCond->getInversePredicate();
5872 
5873   // Handle common loops like: for (X = "string"; *X; ++X)
5874   if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5875     if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5876       ExitLimit ItCnt =
5877         computeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5878       if (ItCnt.hasAnyInfo())
5879         return ItCnt;
5880     }
5881 
5882   ExitLimit ShiftEL = computeShiftCompareExitLimit(
5883       ExitCond->getOperand(0), ExitCond->getOperand(1), L, Cond);
5884   if (ShiftEL.hasAnyInfo())
5885     return ShiftEL;
5886 
5887   const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5888   const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5889 
5890   // Try to evaluate any dependencies out of the loop.
5891   LHS = getSCEVAtScope(LHS, L);
5892   RHS = getSCEVAtScope(RHS, L);
5893 
5894   // At this point, we would like to compute how many iterations of the
5895   // loop the predicate will return true for these inputs.
5896   if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5897     // If there is a loop-invariant, force it into the RHS.
5898     std::swap(LHS, RHS);
5899     Cond = ICmpInst::getSwappedPredicate(Cond);
5900   }
5901 
5902   // Simplify the operands before analyzing them.
5903   (void)SimplifyICmpOperands(Cond, LHS, RHS);
5904 
5905   // If we have a comparison of a chrec against a constant, try to use value
5906   // ranges to answer this query.
5907   if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5908     if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5909       if (AddRec->getLoop() == L) {
5910         // Form the constant range.
5911         ConstantRange CompRange(
5912             ICmpInst::makeConstantRange(Cond, RHSC->getAPInt()));
5913 
5914         const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5915         if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5916       }
5917 
5918   switch (Cond) {
5919   case ICmpInst::ICMP_NE: {                     // while (X != Y)
5920     // Convert to: while (X-Y != 0)
5921     ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit,
5922                                 AllowPredicates);
5923     if (EL.hasAnyInfo()) return EL;
5924     break;
5925   }
5926   case ICmpInst::ICMP_EQ: {                     // while (X == Y)
5927     // Convert to: while (X-Y == 0)
5928     ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5929     if (EL.hasAnyInfo()) return EL;
5930     break;
5931   }
5932   case ICmpInst::ICMP_SLT:
5933   case ICmpInst::ICMP_ULT: {                    // while (X < Y)
5934     bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5935     ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit,
5936                                     AllowPredicates);
5937     if (EL.hasAnyInfo()) return EL;
5938     break;
5939   }
5940   case ICmpInst::ICMP_SGT:
5941   case ICmpInst::ICMP_UGT: {                    // while (X > Y)
5942     bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5943     ExitLimit EL =
5944         HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit,
5945                             AllowPredicates);
5946     if (EL.hasAnyInfo()) return EL;
5947     break;
5948   }
5949   default:
5950     break;
5951   }
5952   return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5953 }
5954 
5955 ScalarEvolution::ExitLimit
5956 ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
5957                                                       SwitchInst *Switch,
5958                                                       BasicBlock *ExitingBlock,
5959                                                       bool ControlsExit) {
5960   assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5961 
5962   // Give up if the exit is the default dest of a switch.
5963   if (Switch->getDefaultDest() == ExitingBlock)
5964     return getCouldNotCompute();
5965 
5966   assert(L->contains(Switch->getDefaultDest()) &&
5967          "Default case must not exit the loop!");
5968   const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5969   const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5970 
5971   // while (X != Y) --> while (X-Y != 0)
5972   ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5973   if (EL.hasAnyInfo())
5974     return EL;
5975 
5976   return getCouldNotCompute();
5977 }
5978 
5979 static ConstantInt *
5980 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5981                                 ScalarEvolution &SE) {
5982   const SCEV *InVal = SE.getConstant(C);
5983   const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5984   assert(isa<SCEVConstant>(Val) &&
5985          "Evaluation of SCEV at constant didn't fold correctly?");
5986   return cast<SCEVConstant>(Val)->getValue();
5987 }
5988 
5989 /// computeLoadConstantCompareExitLimit - Given an exit condition of
5990 /// 'icmp op load X, cst', try to see if we can compute the backedge
5991 /// execution count.
5992 ScalarEvolution::ExitLimit
5993 ScalarEvolution::computeLoadConstantCompareExitLimit(
5994   LoadInst *LI,
5995   Constant *RHS,
5996   const Loop *L,
5997   ICmpInst::Predicate predicate) {
5998 
5999   if (LI->isVolatile()) return getCouldNotCompute();
6000 
6001   // Check to see if the loaded pointer is a getelementptr of a global.
6002   // TODO: Use SCEV instead of manually grubbing with GEPs.
6003   GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
6004   if (!GEP) return getCouldNotCompute();
6005 
6006   // Make sure that it is really a constant global we are gepping, with an
6007   // initializer, and make sure the first IDX is really 0.
6008   GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
6009   if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
6010       GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
6011       !cast<Constant>(GEP->getOperand(1))->isNullValue())
6012     return getCouldNotCompute();
6013 
6014   // Okay, we allow one non-constant index into the GEP instruction.
6015   Value *VarIdx = nullptr;
6016   std::vector<Constant*> Indexes;
6017   unsigned VarIdxNum = 0;
6018   for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
6019     if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
6020       Indexes.push_back(CI);
6021     } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
6022       if (VarIdx) return getCouldNotCompute();  // Multiple non-constant idx's.
6023       VarIdx = GEP->getOperand(i);
6024       VarIdxNum = i-2;
6025       Indexes.push_back(nullptr);
6026     }
6027 
6028   // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
6029   if (!VarIdx)
6030     return getCouldNotCompute();
6031 
6032   // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
6033   // Check to see if X is a loop variant variable value now.
6034   const SCEV *Idx = getSCEV(VarIdx);
6035   Idx = getSCEVAtScope(Idx, L);
6036 
6037   // We can only recognize very limited forms of loop index expressions, in
6038   // particular, only affine AddRec's like {C1,+,C2}.
6039   const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
6040   if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
6041       !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
6042       !isa<SCEVConstant>(IdxExpr->getOperand(1)))
6043     return getCouldNotCompute();
6044 
6045   unsigned MaxSteps = MaxBruteForceIterations;
6046   for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
6047     ConstantInt *ItCst = ConstantInt::get(
6048                            cast<IntegerType>(IdxExpr->getType()), IterationNum);
6049     ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
6050 
6051     // Form the GEP offset.
6052     Indexes[VarIdxNum] = Val;
6053 
6054     Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
6055                                                          Indexes);
6056     if (!Result) break;  // Cannot compute!
6057 
6058     // Evaluate the condition for this iteration.
6059     Result = ConstantExpr::getICmp(predicate, Result, RHS);
6060     if (!isa<ConstantInt>(Result)) break;  // Couldn't decide for sure
6061     if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
6062       ++NumArrayLenItCounts;
6063       return getConstant(ItCst);   // Found terminating iteration!
6064     }
6065   }
6066   return getCouldNotCompute();
6067 }
6068 
6069 ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit(
6070     Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) {
6071   ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV);
6072   if (!RHS)
6073     return getCouldNotCompute();
6074 
6075   const BasicBlock *Latch = L->getLoopLatch();
6076   if (!Latch)
6077     return getCouldNotCompute();
6078 
6079   const BasicBlock *Predecessor = L->getLoopPredecessor();
6080   if (!Predecessor)
6081     return getCouldNotCompute();
6082 
6083   // Return true if V is of the form "LHS `shift_op` <positive constant>".
6084   // Return LHS in OutLHS and shift_opt in OutOpCode.
6085   auto MatchPositiveShift =
6086       [](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) {
6087 
6088     using namespace PatternMatch;
6089 
6090     ConstantInt *ShiftAmt;
6091     if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
6092       OutOpCode = Instruction::LShr;
6093     else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
6094       OutOpCode = Instruction::AShr;
6095     else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
6096       OutOpCode = Instruction::Shl;
6097     else
6098       return false;
6099 
6100     return ShiftAmt->getValue().isStrictlyPositive();
6101   };
6102 
6103   // Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in
6104   //
6105   // loop:
6106   //   %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ]
6107   //   %iv.shifted = lshr i32 %iv, <positive constant>
6108   //
6109   // Return true on a succesful match.  Return the corresponding PHI node (%iv
6110   // above) in PNOut and the opcode of the shift operation in OpCodeOut.
6111   auto MatchShiftRecurrence =
6112       [&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) {
6113     Optional<Instruction::BinaryOps> PostShiftOpCode;
6114 
6115     {
6116       Instruction::BinaryOps OpC;
6117       Value *V;
6118 
6119       // If we encounter a shift instruction, "peel off" the shift operation,
6120       // and remember that we did so.  Later when we inspect %iv's backedge
6121       // value, we will make sure that the backedge value uses the same
6122       // operation.
6123       //
6124       // Note: the peeled shift operation does not have to be the same
6125       // instruction as the one feeding into the PHI's backedge value.  We only
6126       // really care about it being the same *kind* of shift instruction --
6127       // that's all that is required for our later inferences to hold.
6128       if (MatchPositiveShift(LHS, V, OpC)) {
6129         PostShiftOpCode = OpC;
6130         LHS = V;
6131       }
6132     }
6133 
6134     PNOut = dyn_cast<PHINode>(LHS);
6135     if (!PNOut || PNOut->getParent() != L->getHeader())
6136       return false;
6137 
6138     Value *BEValue = PNOut->getIncomingValueForBlock(Latch);
6139     Value *OpLHS;
6140 
6141     return
6142         // The backedge value for the PHI node must be a shift by a positive
6143         // amount
6144         MatchPositiveShift(BEValue, OpLHS, OpCodeOut) &&
6145 
6146         // of the PHI node itself
6147         OpLHS == PNOut &&
6148 
6149         // and the kind of shift should be match the kind of shift we peeled
6150         // off, if any.
6151         (!PostShiftOpCode.hasValue() || *PostShiftOpCode == OpCodeOut);
6152   };
6153 
6154   PHINode *PN;
6155   Instruction::BinaryOps OpCode;
6156   if (!MatchShiftRecurrence(LHS, PN, OpCode))
6157     return getCouldNotCompute();
6158 
6159   const DataLayout &DL = getDataLayout();
6160 
6161   // The key rationale for this optimization is that for some kinds of shift
6162   // recurrences, the value of the recurrence "stabilizes" to either 0 or -1
6163   // within a finite number of iterations.  If the condition guarding the
6164   // backedge (in the sense that the backedge is taken if the condition is true)
6165   // is false for the value the shift recurrence stabilizes to, then we know
6166   // that the backedge is taken only a finite number of times.
6167 
6168   ConstantInt *StableValue = nullptr;
6169   switch (OpCode) {
6170   default:
6171     llvm_unreachable("Impossible case!");
6172 
6173   case Instruction::AShr: {
6174     // {K,ashr,<positive-constant>} stabilizes to signum(K) in at most
6175     // bitwidth(K) iterations.
6176     Value *FirstValue = PN->getIncomingValueForBlock(Predecessor);
6177     bool KnownZero, KnownOne;
6178     ComputeSignBit(FirstValue, KnownZero, KnownOne, DL, 0, nullptr,
6179                    Predecessor->getTerminator(), &DT);
6180     auto *Ty = cast<IntegerType>(RHS->getType());
6181     if (KnownZero)
6182       StableValue = ConstantInt::get(Ty, 0);
6183     else if (KnownOne)
6184       StableValue = ConstantInt::get(Ty, -1, true);
6185     else
6186       return getCouldNotCompute();
6187 
6188     break;
6189   }
6190   case Instruction::LShr:
6191   case Instruction::Shl:
6192     // Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>}
6193     // stabilize to 0 in at most bitwidth(K) iterations.
6194     StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0);
6195     break;
6196   }
6197 
6198   auto *Result =
6199       ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI);
6200   assert(Result->getType()->isIntegerTy(1) &&
6201          "Otherwise cannot be an operand to a branch instruction");
6202 
6203   if (Result->isZeroValue()) {
6204     unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6205     const SCEV *UpperBound =
6206         getConstant(getEffectiveSCEVType(RHS->getType()), BitWidth);
6207     SCEVUnionPredicate P;
6208     return ExitLimit(getCouldNotCompute(), UpperBound, P);
6209   }
6210 
6211   return getCouldNotCompute();
6212 }
6213 
6214 /// CanConstantFold - Return true if we can constant fold an instruction of the
6215 /// specified type, assuming that all operands were constants.
6216 static bool CanConstantFold(const Instruction *I) {
6217   if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
6218       isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
6219       isa<LoadInst>(I))
6220     return true;
6221 
6222   if (const CallInst *CI = dyn_cast<CallInst>(I))
6223     if (const Function *F = CI->getCalledFunction())
6224       return canConstantFoldCallTo(F);
6225   return false;
6226 }
6227 
6228 /// Determine whether this instruction can constant evolve within this loop
6229 /// assuming its operands can all constant evolve.
6230 static bool canConstantEvolve(Instruction *I, const Loop *L) {
6231   // An instruction outside of the loop can't be derived from a loop PHI.
6232   if (!L->contains(I)) return false;
6233 
6234   if (isa<PHINode>(I)) {
6235     // We don't currently keep track of the control flow needed to evaluate
6236     // PHIs, so we cannot handle PHIs inside of loops.
6237     return L->getHeader() == I->getParent();
6238   }
6239 
6240   // If we won't be able to constant fold this expression even if the operands
6241   // are constants, bail early.
6242   return CanConstantFold(I);
6243 }
6244 
6245 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
6246 /// recursing through each instruction operand until reaching a loop header phi.
6247 static PHINode *
6248 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
6249                                DenseMap<Instruction *, PHINode *> &PHIMap) {
6250 
6251   // Otherwise, we can evaluate this instruction if all of its operands are
6252   // constant or derived from a PHI node themselves.
6253   PHINode *PHI = nullptr;
6254   for (Value *Op : UseInst->operands()) {
6255     if (isa<Constant>(Op)) continue;
6256 
6257     Instruction *OpInst = dyn_cast<Instruction>(Op);
6258     if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
6259 
6260     PHINode *P = dyn_cast<PHINode>(OpInst);
6261     if (!P)
6262       // If this operand is already visited, reuse the prior result.
6263       // We may have P != PHI if this is the deepest point at which the
6264       // inconsistent paths meet.
6265       P = PHIMap.lookup(OpInst);
6266     if (!P) {
6267       // Recurse and memoize the results, whether a phi is found or not.
6268       // This recursive call invalidates pointers into PHIMap.
6269       P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
6270       PHIMap[OpInst] = P;
6271     }
6272     if (!P)
6273       return nullptr;  // Not evolving from PHI
6274     if (PHI && PHI != P)
6275       return nullptr;  // Evolving from multiple different PHIs.
6276     PHI = P;
6277   }
6278   // This is a expression evolving from a constant PHI!
6279   return PHI;
6280 }
6281 
6282 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
6283 /// in the loop that V is derived from.  We allow arbitrary operations along the
6284 /// way, but the operands of an operation must either be constants or a value
6285 /// derived from a constant PHI.  If this expression does not fit with these
6286 /// constraints, return null.
6287 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
6288   Instruction *I = dyn_cast<Instruction>(V);
6289   if (!I || !canConstantEvolve(I, L)) return nullptr;
6290 
6291   if (PHINode *PN = dyn_cast<PHINode>(I))
6292     return PN;
6293 
6294   // Record non-constant instructions contained by the loop.
6295   DenseMap<Instruction *, PHINode *> PHIMap;
6296   return getConstantEvolvingPHIOperands(I, L, PHIMap);
6297 }
6298 
6299 /// EvaluateExpression - Given an expression that passes the
6300 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
6301 /// in the loop has the value PHIVal.  If we can't fold this expression for some
6302 /// reason, return null.
6303 static Constant *EvaluateExpression(Value *V, const Loop *L,
6304                                     DenseMap<Instruction *, Constant *> &Vals,
6305                                     const DataLayout &DL,
6306                                     const TargetLibraryInfo *TLI) {
6307   // Convenient constant check, but redundant for recursive calls.
6308   if (Constant *C = dyn_cast<Constant>(V)) return C;
6309   Instruction *I = dyn_cast<Instruction>(V);
6310   if (!I) return nullptr;
6311 
6312   if (Constant *C = Vals.lookup(I)) return C;
6313 
6314   // An instruction inside the loop depends on a value outside the loop that we
6315   // weren't given a mapping for, or a value such as a call inside the loop.
6316   if (!canConstantEvolve(I, L)) return nullptr;
6317 
6318   // An unmapped PHI can be due to a branch or another loop inside this loop,
6319   // or due to this not being the initial iteration through a loop where we
6320   // couldn't compute the evolution of this particular PHI last time.
6321   if (isa<PHINode>(I)) return nullptr;
6322 
6323   std::vector<Constant*> Operands(I->getNumOperands());
6324 
6325   for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
6326     Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
6327     if (!Operand) {
6328       Operands[i] = dyn_cast<Constant>(I->getOperand(i));
6329       if (!Operands[i]) return nullptr;
6330       continue;
6331     }
6332     Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
6333     Vals[Operand] = C;
6334     if (!C) return nullptr;
6335     Operands[i] = C;
6336   }
6337 
6338   if (CmpInst *CI = dyn_cast<CmpInst>(I))
6339     return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
6340                                            Operands[1], DL, TLI);
6341   if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
6342     if (!LI->isVolatile())
6343       return ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
6344   }
6345   return ConstantFoldInstOperands(I, Operands, DL, TLI);
6346 }
6347 
6348 
6349 // If every incoming value to PN except the one for BB is a specific Constant,
6350 // return that, else return nullptr.
6351 static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) {
6352   Constant *IncomingVal = nullptr;
6353 
6354   for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
6355     if (PN->getIncomingBlock(i) == BB)
6356       continue;
6357 
6358     auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i));
6359     if (!CurrentVal)
6360       return nullptr;
6361 
6362     if (IncomingVal != CurrentVal) {
6363       if (IncomingVal)
6364         return nullptr;
6365       IncomingVal = CurrentVal;
6366     }
6367   }
6368 
6369   return IncomingVal;
6370 }
6371 
6372 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
6373 /// in the header of its containing loop, we know the loop executes a
6374 /// constant number of times, and the PHI node is just a recurrence
6375 /// involving constants, fold it.
6376 Constant *
6377 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
6378                                                    const APInt &BEs,
6379                                                    const Loop *L) {
6380   auto I = ConstantEvolutionLoopExitValue.find(PN);
6381   if (I != ConstantEvolutionLoopExitValue.end())
6382     return I->second;
6383 
6384   if (BEs.ugt(MaxBruteForceIterations))
6385     return ConstantEvolutionLoopExitValue[PN] = nullptr;  // Not going to evaluate it.
6386 
6387   Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
6388 
6389   DenseMap<Instruction *, Constant *> CurrentIterVals;
6390   BasicBlock *Header = L->getHeader();
6391   assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
6392 
6393   BasicBlock *Latch = L->getLoopLatch();
6394   if (!Latch)
6395     return nullptr;
6396 
6397   for (auto &I : *Header) {
6398     PHINode *PHI = dyn_cast<PHINode>(&I);
6399     if (!PHI) break;
6400     auto *StartCST = getOtherIncomingValue(PHI, Latch);
6401     if (!StartCST) continue;
6402     CurrentIterVals[PHI] = StartCST;
6403   }
6404   if (!CurrentIterVals.count(PN))
6405     return RetVal = nullptr;
6406 
6407   Value *BEValue = PN->getIncomingValueForBlock(Latch);
6408 
6409   // Execute the loop symbolically to determine the exit value.
6410   if (BEs.getActiveBits() >= 32)
6411     return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
6412 
6413   unsigned NumIterations = BEs.getZExtValue(); // must be in range
6414   unsigned IterationNum = 0;
6415   const DataLayout &DL = getDataLayout();
6416   for (; ; ++IterationNum) {
6417     if (IterationNum == NumIterations)
6418       return RetVal = CurrentIterVals[PN];  // Got exit value!
6419 
6420     // Compute the value of the PHIs for the next iteration.
6421     // EvaluateExpression adds non-phi values to the CurrentIterVals map.
6422     DenseMap<Instruction *, Constant *> NextIterVals;
6423     Constant *NextPHI =
6424         EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6425     if (!NextPHI)
6426       return nullptr;        // Couldn't evaluate!
6427     NextIterVals[PN] = NextPHI;
6428 
6429     bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
6430 
6431     // Also evaluate the other PHI nodes.  However, we don't get to stop if we
6432     // cease to be able to evaluate one of them or if they stop evolving,
6433     // because that doesn't necessarily prevent us from computing PN.
6434     SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
6435     for (const auto &I : CurrentIterVals) {
6436       PHINode *PHI = dyn_cast<PHINode>(I.first);
6437       if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
6438       PHIsToCompute.emplace_back(PHI, I.second);
6439     }
6440     // We use two distinct loops because EvaluateExpression may invalidate any
6441     // iterators into CurrentIterVals.
6442     for (const auto &I : PHIsToCompute) {
6443       PHINode *PHI = I.first;
6444       Constant *&NextPHI = NextIterVals[PHI];
6445       if (!NextPHI) {   // Not already computed.
6446         Value *BEValue = PHI->getIncomingValueForBlock(Latch);
6447         NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6448       }
6449       if (NextPHI != I.second)
6450         StoppedEvolving = false;
6451     }
6452 
6453     // If all entries in CurrentIterVals == NextIterVals then we can stop
6454     // iterating, the loop can't continue to change.
6455     if (StoppedEvolving)
6456       return RetVal = CurrentIterVals[PN];
6457 
6458     CurrentIterVals.swap(NextIterVals);
6459   }
6460 }
6461 
6462 const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
6463                                                           Value *Cond,
6464                                                           bool ExitWhen) {
6465   PHINode *PN = getConstantEvolvingPHI(Cond, L);
6466   if (!PN) return getCouldNotCompute();
6467 
6468   // If the loop is canonicalized, the PHI will have exactly two entries.
6469   // That's the only form we support here.
6470   if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
6471 
6472   DenseMap<Instruction *, Constant *> CurrentIterVals;
6473   BasicBlock *Header = L->getHeader();
6474   assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
6475 
6476   BasicBlock *Latch = L->getLoopLatch();
6477   assert(Latch && "Should follow from NumIncomingValues == 2!");
6478 
6479   for (auto &I : *Header) {
6480     PHINode *PHI = dyn_cast<PHINode>(&I);
6481     if (!PHI)
6482       break;
6483     auto *StartCST = getOtherIncomingValue(PHI, Latch);
6484     if (!StartCST) continue;
6485     CurrentIterVals[PHI] = StartCST;
6486   }
6487   if (!CurrentIterVals.count(PN))
6488     return getCouldNotCompute();
6489 
6490   // Okay, we find a PHI node that defines the trip count of this loop.  Execute
6491   // the loop symbolically to determine when the condition gets a value of
6492   // "ExitWhen".
6493   unsigned MaxIterations = MaxBruteForceIterations;   // Limit analysis.
6494   const DataLayout &DL = getDataLayout();
6495   for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
6496     auto *CondVal = dyn_cast_or_null<ConstantInt>(
6497         EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
6498 
6499     // Couldn't symbolically evaluate.
6500     if (!CondVal) return getCouldNotCompute();
6501 
6502     if (CondVal->getValue() == uint64_t(ExitWhen)) {
6503       ++NumBruteForceTripCountsComputed;
6504       return getConstant(Type::getInt32Ty(getContext()), IterationNum);
6505     }
6506 
6507     // Update all the PHI nodes for the next iteration.
6508     DenseMap<Instruction *, Constant *> NextIterVals;
6509 
6510     // Create a list of which PHIs we need to compute. We want to do this before
6511     // calling EvaluateExpression on them because that may invalidate iterators
6512     // into CurrentIterVals.
6513     SmallVector<PHINode *, 8> PHIsToCompute;
6514     for (const auto &I : CurrentIterVals) {
6515       PHINode *PHI = dyn_cast<PHINode>(I.first);
6516       if (!PHI || PHI->getParent() != Header) continue;
6517       PHIsToCompute.push_back(PHI);
6518     }
6519     for (PHINode *PHI : PHIsToCompute) {
6520       Constant *&NextPHI = NextIterVals[PHI];
6521       if (NextPHI) continue;    // Already computed!
6522 
6523       Value *BEValue = PHI->getIncomingValueForBlock(Latch);
6524       NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6525     }
6526     CurrentIterVals.swap(NextIterVals);
6527   }
6528 
6529   // Too many iterations were needed to evaluate.
6530   return getCouldNotCompute();
6531 }
6532 
6533 /// getSCEVAtScope - Return a SCEV expression for the specified value
6534 /// at the specified scope in the program.  The L value specifies a loop
6535 /// nest to evaluate the expression at, where null is the top-level or a
6536 /// specified loop is immediately inside of the loop.
6537 ///
6538 /// This method can be used to compute the exit value for a variable defined
6539 /// in a loop by querying what the value will hold in the parent loop.
6540 ///
6541 /// In the case that a relevant loop exit value cannot be computed, the
6542 /// original value V is returned.
6543 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
6544   SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values =
6545       ValuesAtScopes[V];
6546   // Check to see if we've folded this expression at this loop before.
6547   for (auto &LS : Values)
6548     if (LS.first == L)
6549       return LS.second ? LS.second : V;
6550 
6551   Values.emplace_back(L, nullptr);
6552 
6553   // Otherwise compute it.
6554   const SCEV *C = computeSCEVAtScope(V, L);
6555   for (auto &LS : reverse(ValuesAtScopes[V]))
6556     if (LS.first == L) {
6557       LS.second = C;
6558       break;
6559     }
6560   return C;
6561 }
6562 
6563 /// This builds up a Constant using the ConstantExpr interface.  That way, we
6564 /// will return Constants for objects which aren't represented by a
6565 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
6566 /// Returns NULL if the SCEV isn't representable as a Constant.
6567 static Constant *BuildConstantFromSCEV(const SCEV *V) {
6568   switch (static_cast<SCEVTypes>(V->getSCEVType())) {
6569     case scCouldNotCompute:
6570     case scAddRecExpr:
6571       break;
6572     case scConstant:
6573       return cast<SCEVConstant>(V)->getValue();
6574     case scUnknown:
6575       return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
6576     case scSignExtend: {
6577       const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
6578       if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
6579         return ConstantExpr::getSExt(CastOp, SS->getType());
6580       break;
6581     }
6582     case scZeroExtend: {
6583       const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
6584       if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
6585         return ConstantExpr::getZExt(CastOp, SZ->getType());
6586       break;
6587     }
6588     case scTruncate: {
6589       const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
6590       if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
6591         return ConstantExpr::getTrunc(CastOp, ST->getType());
6592       break;
6593     }
6594     case scAddExpr: {
6595       const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
6596       if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
6597         if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
6598           unsigned AS = PTy->getAddressSpace();
6599           Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
6600           C = ConstantExpr::getBitCast(C, DestPtrTy);
6601         }
6602         for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
6603           Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
6604           if (!C2) return nullptr;
6605 
6606           // First pointer!
6607           if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
6608             unsigned AS = C2->getType()->getPointerAddressSpace();
6609             std::swap(C, C2);
6610             Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
6611             // The offsets have been converted to bytes.  We can add bytes to an
6612             // i8* by GEP with the byte count in the first index.
6613             C = ConstantExpr::getBitCast(C, DestPtrTy);
6614           }
6615 
6616           // Don't bother trying to sum two pointers. We probably can't
6617           // statically compute a load that results from it anyway.
6618           if (C2->getType()->isPointerTy())
6619             return nullptr;
6620 
6621           if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
6622             if (PTy->getElementType()->isStructTy())
6623               C2 = ConstantExpr::getIntegerCast(
6624                   C2, Type::getInt32Ty(C->getContext()), true);
6625             C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
6626           } else
6627             C = ConstantExpr::getAdd(C, C2);
6628         }
6629         return C;
6630       }
6631       break;
6632     }
6633     case scMulExpr: {
6634       const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
6635       if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
6636         // Don't bother with pointers at all.
6637         if (C->getType()->isPointerTy()) return nullptr;
6638         for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
6639           Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
6640           if (!C2 || C2->getType()->isPointerTy()) return nullptr;
6641           C = ConstantExpr::getMul(C, C2);
6642         }
6643         return C;
6644       }
6645       break;
6646     }
6647     case scUDivExpr: {
6648       const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
6649       if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
6650         if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
6651           if (LHS->getType() == RHS->getType())
6652             return ConstantExpr::getUDiv(LHS, RHS);
6653       break;
6654     }
6655     case scSMaxExpr:
6656     case scUMaxExpr:
6657       break; // TODO: smax, umax.
6658   }
6659   return nullptr;
6660 }
6661 
6662 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
6663   if (isa<SCEVConstant>(V)) return V;
6664 
6665   // If this instruction is evolved from a constant-evolving PHI, compute the
6666   // exit value from the loop without using SCEVs.
6667   if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
6668     if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
6669       const Loop *LI = this->LI[I->getParent()];
6670       if (LI && LI->getParentLoop() == L)  // Looking for loop exit value.
6671         if (PHINode *PN = dyn_cast<PHINode>(I))
6672           if (PN->getParent() == LI->getHeader()) {
6673             // Okay, there is no closed form solution for the PHI node.  Check
6674             // to see if the loop that contains it has a known backedge-taken
6675             // count.  If so, we may be able to force computation of the exit
6676             // value.
6677             const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
6678             if (const SCEVConstant *BTCC =
6679                   dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
6680               // Okay, we know how many times the containing loop executes.  If
6681               // this is a constant evolving PHI node, get the final value at
6682               // the specified iteration number.
6683               Constant *RV =
6684                   getConstantEvolutionLoopExitValue(PN, BTCC->getAPInt(), LI);
6685               if (RV) return getSCEV(RV);
6686             }
6687           }
6688 
6689       // Okay, this is an expression that we cannot symbolically evaluate
6690       // into a SCEV.  Check to see if it's possible to symbolically evaluate
6691       // the arguments into constants, and if so, try to constant propagate the
6692       // result.  This is particularly useful for computing loop exit values.
6693       if (CanConstantFold(I)) {
6694         SmallVector<Constant *, 4> Operands;
6695         bool MadeImprovement = false;
6696         for (Value *Op : I->operands()) {
6697           if (Constant *C = dyn_cast<Constant>(Op)) {
6698             Operands.push_back(C);
6699             continue;
6700           }
6701 
6702           // If any of the operands is non-constant and if they are
6703           // non-integer and non-pointer, don't even try to analyze them
6704           // with scev techniques.
6705           if (!isSCEVable(Op->getType()))
6706             return V;
6707 
6708           const SCEV *OrigV = getSCEV(Op);
6709           const SCEV *OpV = getSCEVAtScope(OrigV, L);
6710           MadeImprovement |= OrigV != OpV;
6711 
6712           Constant *C = BuildConstantFromSCEV(OpV);
6713           if (!C) return V;
6714           if (C->getType() != Op->getType())
6715             C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
6716                                                               Op->getType(),
6717                                                               false),
6718                                       C, Op->getType());
6719           Operands.push_back(C);
6720         }
6721 
6722         // Check to see if getSCEVAtScope actually made an improvement.
6723         if (MadeImprovement) {
6724           Constant *C = nullptr;
6725           const DataLayout &DL = getDataLayout();
6726           if (const CmpInst *CI = dyn_cast<CmpInst>(I))
6727             C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
6728                                                 Operands[1], DL, &TLI);
6729           else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
6730             if (!LI->isVolatile())
6731               C = ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
6732           } else
6733             C = ConstantFoldInstOperands(I, Operands, DL, &TLI);
6734           if (!C) return V;
6735           return getSCEV(C);
6736         }
6737       }
6738     }
6739 
6740     // This is some other type of SCEVUnknown, just return it.
6741     return V;
6742   }
6743 
6744   if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
6745     // Avoid performing the look-up in the common case where the specified
6746     // expression has no loop-variant portions.
6747     for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
6748       const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6749       if (OpAtScope != Comm->getOperand(i)) {
6750         // Okay, at least one of these operands is loop variant but might be
6751         // foldable.  Build a new instance of the folded commutative expression.
6752         SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
6753                                             Comm->op_begin()+i);
6754         NewOps.push_back(OpAtScope);
6755 
6756         for (++i; i != e; ++i) {
6757           OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6758           NewOps.push_back(OpAtScope);
6759         }
6760         if (isa<SCEVAddExpr>(Comm))
6761           return getAddExpr(NewOps);
6762         if (isa<SCEVMulExpr>(Comm))
6763           return getMulExpr(NewOps);
6764         if (isa<SCEVSMaxExpr>(Comm))
6765           return getSMaxExpr(NewOps);
6766         if (isa<SCEVUMaxExpr>(Comm))
6767           return getUMaxExpr(NewOps);
6768         llvm_unreachable("Unknown commutative SCEV type!");
6769       }
6770     }
6771     // If we got here, all operands are loop invariant.
6772     return Comm;
6773   }
6774 
6775   if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
6776     const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
6777     const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
6778     if (LHS == Div->getLHS() && RHS == Div->getRHS())
6779       return Div;   // must be loop invariant
6780     return getUDivExpr(LHS, RHS);
6781   }
6782 
6783   // If this is a loop recurrence for a loop that does not contain L, then we
6784   // are dealing with the final value computed by the loop.
6785   if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
6786     // First, attempt to evaluate each operand.
6787     // Avoid performing the look-up in the common case where the specified
6788     // expression has no loop-variant portions.
6789     for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
6790       const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
6791       if (OpAtScope == AddRec->getOperand(i))
6792         continue;
6793 
6794       // Okay, at least one of these operands is loop variant but might be
6795       // foldable.  Build a new instance of the folded commutative expression.
6796       SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
6797                                           AddRec->op_begin()+i);
6798       NewOps.push_back(OpAtScope);
6799       for (++i; i != e; ++i)
6800         NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
6801 
6802       const SCEV *FoldedRec =
6803         getAddRecExpr(NewOps, AddRec->getLoop(),
6804                       AddRec->getNoWrapFlags(SCEV::FlagNW));
6805       AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
6806       // The addrec may be folded to a nonrecurrence, for example, if the
6807       // induction variable is multiplied by zero after constant folding. Go
6808       // ahead and return the folded value.
6809       if (!AddRec)
6810         return FoldedRec;
6811       break;
6812     }
6813 
6814     // If the scope is outside the addrec's loop, evaluate it by using the
6815     // loop exit value of the addrec.
6816     if (!AddRec->getLoop()->contains(L)) {
6817       // To evaluate this recurrence, we need to know how many times the AddRec
6818       // loop iterates.  Compute this now.
6819       const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
6820       if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
6821 
6822       // Then, evaluate the AddRec.
6823       return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
6824     }
6825 
6826     return AddRec;
6827   }
6828 
6829   if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
6830     const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6831     if (Op == Cast->getOperand())
6832       return Cast;  // must be loop invariant
6833     return getZeroExtendExpr(Op, Cast->getType());
6834   }
6835 
6836   if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
6837     const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6838     if (Op == Cast->getOperand())
6839       return Cast;  // must be loop invariant
6840     return getSignExtendExpr(Op, Cast->getType());
6841   }
6842 
6843   if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
6844     const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6845     if (Op == Cast->getOperand())
6846       return Cast;  // must be loop invariant
6847     return getTruncateExpr(Op, Cast->getType());
6848   }
6849 
6850   llvm_unreachable("Unknown SCEV type!");
6851 }
6852 
6853 /// getSCEVAtScope - This is a convenience function which does
6854 /// getSCEVAtScope(getSCEV(V), L).
6855 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
6856   return getSCEVAtScope(getSCEV(V), L);
6857 }
6858 
6859 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
6860 /// following equation:
6861 ///
6862 ///     A * X = B (mod N)
6863 ///
6864 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
6865 /// A and B isn't important.
6866 ///
6867 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
6868 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
6869                                                ScalarEvolution &SE) {
6870   uint32_t BW = A.getBitWidth();
6871   assert(BW == B.getBitWidth() && "Bit widths must be the same.");
6872   assert(A != 0 && "A must be non-zero.");
6873 
6874   // 1. D = gcd(A, N)
6875   //
6876   // The gcd of A and N may have only one prime factor: 2. The number of
6877   // trailing zeros in A is its multiplicity
6878   uint32_t Mult2 = A.countTrailingZeros();
6879   // D = 2^Mult2
6880 
6881   // 2. Check if B is divisible by D.
6882   //
6883   // B is divisible by D if and only if the multiplicity of prime factor 2 for B
6884   // is not less than multiplicity of this prime factor for D.
6885   if (B.countTrailingZeros() < Mult2)
6886     return SE.getCouldNotCompute();
6887 
6888   // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
6889   // modulo (N / D).
6890   //
6891   // (N / D) may need BW+1 bits in its representation.  Hence, we'll use this
6892   // bit width during computations.
6893   APInt AD = A.lshr(Mult2).zext(BW + 1);  // AD = A / D
6894   APInt Mod(BW + 1, 0);
6895   Mod.setBit(BW - Mult2);  // Mod = N / D
6896   APInt I = AD.multiplicativeInverse(Mod);
6897 
6898   // 4. Compute the minimum unsigned root of the equation:
6899   // I * (B / D) mod (N / D)
6900   APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
6901 
6902   // The result is guaranteed to be less than 2^BW so we may truncate it to BW
6903   // bits.
6904   return SE.getConstant(Result.trunc(BW));
6905 }
6906 
6907 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
6908 /// given quadratic chrec {L,+,M,+,N}.  This returns either the two roots (which
6909 /// might be the same) or two SCEVCouldNotCompute objects.
6910 ///
6911 static std::pair<const SCEV *,const SCEV *>
6912 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
6913   assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
6914   const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
6915   const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
6916   const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
6917 
6918   // We currently can only solve this if the coefficients are constants.
6919   if (!LC || !MC || !NC) {
6920     const SCEV *CNC = SE.getCouldNotCompute();
6921     return {CNC, CNC};
6922   }
6923 
6924   uint32_t BitWidth = LC->getAPInt().getBitWidth();
6925   const APInt &L = LC->getAPInt();
6926   const APInt &M = MC->getAPInt();
6927   const APInt &N = NC->getAPInt();
6928   APInt Two(BitWidth, 2);
6929   APInt Four(BitWidth, 4);
6930 
6931   {
6932     using namespace APIntOps;
6933     const APInt& C = L;
6934     // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
6935     // The B coefficient is M-N/2
6936     APInt B(M);
6937     B -= sdiv(N,Two);
6938 
6939     // The A coefficient is N/2
6940     APInt A(N.sdiv(Two));
6941 
6942     // Compute the B^2-4ac term.
6943     APInt SqrtTerm(B);
6944     SqrtTerm *= B;
6945     SqrtTerm -= Four * (A * C);
6946 
6947     if (SqrtTerm.isNegative()) {
6948       // The loop is provably infinite.
6949       const SCEV *CNC = SE.getCouldNotCompute();
6950       return {CNC, CNC};
6951     }
6952 
6953     // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
6954     // integer value or else APInt::sqrt() will assert.
6955     APInt SqrtVal(SqrtTerm.sqrt());
6956 
6957     // Compute the two solutions for the quadratic formula.
6958     // The divisions must be performed as signed divisions.
6959     APInt NegB(-B);
6960     APInt TwoA(A << 1);
6961     if (TwoA.isMinValue()) {
6962       const SCEV *CNC = SE.getCouldNotCompute();
6963       return {CNC, CNC};
6964     }
6965 
6966     LLVMContext &Context = SE.getContext();
6967 
6968     ConstantInt *Solution1 =
6969       ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
6970     ConstantInt *Solution2 =
6971       ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
6972 
6973     return {SE.getConstant(Solution1), SE.getConstant(Solution2)};
6974   } // end APIntOps namespace
6975 }
6976 
6977 /// HowFarToZero - Return the number of times a backedge comparing the specified
6978 /// value to zero will execute.  If not computable, return CouldNotCompute.
6979 ///
6980 /// This is only used for loops with a "x != y" exit test. The exit condition is
6981 /// now expressed as a single expression, V = x-y. So the exit test is
6982 /// effectively V != 0.  We know and take advantage of the fact that this
6983 /// expression only being used in a comparison by zero context.
6984 ScalarEvolution::ExitLimit
6985 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit,
6986                               bool AllowPredicates) {
6987   SCEVUnionPredicate P;
6988   // If the value is a constant
6989   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6990     // If the value is already zero, the branch will execute zero times.
6991     if (C->getValue()->isZero()) return C;
6992     return getCouldNotCompute();  // Otherwise it will loop infinitely.
6993   }
6994 
6995   const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6996   if (!AddRec && AllowPredicates)
6997     // Try to make this an AddRec using runtime tests, in the first X
6998     // iterations of this loop, where X is the SCEV expression found by the
6999     // algorithm below.
7000     AddRec = convertSCEVToAddRecWithPredicates(V, L, P);
7001 
7002   if (!AddRec || AddRec->getLoop() != L)
7003     return getCouldNotCompute();
7004 
7005   // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
7006   // the quadratic equation to solve it.
7007   if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
7008     std::pair<const SCEV *,const SCEV *> Roots =
7009       SolveQuadraticEquation(AddRec, *this);
7010     const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
7011     const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
7012     if (R1 && R2) {
7013       // Pick the smallest positive root value.
7014       if (ConstantInt *CB =
7015           dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
7016                                                       R1->getValue(),
7017                                                       R2->getValue()))) {
7018         if (!CB->getZExtValue())
7019           std::swap(R1, R2);   // R1 is the minimum root now.
7020 
7021         // We can only use this value if the chrec ends up with an exact zero
7022         // value at this index.  When solving for "X*X != 5", for example, we
7023         // should not accept a root of 2.
7024         const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
7025         if (Val->isZero())
7026           return ExitLimit(R1, R1, P); // We found a quadratic root!
7027       }
7028     }
7029     return getCouldNotCompute();
7030   }
7031 
7032   // Otherwise we can only handle this if it is affine.
7033   if (!AddRec->isAffine())
7034     return getCouldNotCompute();
7035 
7036   // If this is an affine expression, the execution count of this branch is
7037   // the minimum unsigned root of the following equation:
7038   //
7039   //     Start + Step*N = 0 (mod 2^BW)
7040   //
7041   // equivalent to:
7042   //
7043   //             Step*N = -Start (mod 2^BW)
7044   //
7045   // where BW is the common bit width of Start and Step.
7046 
7047   // Get the initial value for the loop.
7048   const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
7049   const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
7050 
7051   // For now we handle only constant steps.
7052   //
7053   // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
7054   // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
7055   // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
7056   // We have not yet seen any such cases.
7057   const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
7058   if (!StepC || StepC->getValue()->equalsInt(0))
7059     return getCouldNotCompute();
7060 
7061   // For positive steps (counting up until unsigned overflow):
7062   //   N = -Start/Step (as unsigned)
7063   // For negative steps (counting down to zero):
7064   //   N = Start/-Step
7065   // First compute the unsigned distance from zero in the direction of Step.
7066   bool CountDown = StepC->getAPInt().isNegative();
7067   const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
7068 
7069   // Handle unitary steps, which cannot wraparound.
7070   // 1*N = -Start; -1*N = Start (mod 2^BW), so:
7071   //   N = Distance (as unsigned)
7072   if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
7073     ConstantRange CR = getUnsignedRange(Start);
7074     const SCEV *MaxBECount;
7075     if (!CountDown && CR.getUnsignedMin().isMinValue())
7076       // When counting up, the worst starting value is 1, not 0.
7077       MaxBECount = CR.getUnsignedMax().isMinValue()
7078         ? getConstant(APInt::getMinValue(CR.getBitWidth()))
7079         : getConstant(APInt::getMaxValue(CR.getBitWidth()));
7080     else
7081       MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
7082                                          : -CR.getUnsignedMin());
7083     return ExitLimit(Distance, MaxBECount, P);
7084   }
7085 
7086   // As a special case, handle the instance where Step is a positive power of
7087   // two. In this case, determining whether Step divides Distance evenly can be
7088   // done by counting and comparing the number of trailing zeros of Step and
7089   // Distance.
7090   if (!CountDown) {
7091     const APInt &StepV = StepC->getAPInt();
7092     // StepV.isPowerOf2() returns true if StepV is an positive power of two.  It
7093     // also returns true if StepV is maximally negative (eg, INT_MIN), but that
7094     // case is not handled as this code is guarded by !CountDown.
7095     if (StepV.isPowerOf2() &&
7096         GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) {
7097       // Here we've constrained the equation to be of the form
7098       //
7099       //   2^(N + k) * Distance' = (StepV == 2^N) * X (mod 2^W)  ... (0)
7100       //
7101       // where we're operating on a W bit wide integer domain and k is
7102       // non-negative.  The smallest unsigned solution for X is the trip count.
7103       //
7104       // (0) is equivalent to:
7105       //
7106       //      2^(N + k) * Distance' - 2^N * X = L * 2^W
7107       // <=>  2^N(2^k * Distance' - X) = L * 2^(W - N) * 2^N
7108       // <=>  2^k * Distance' - X = L * 2^(W - N)
7109       // <=>  2^k * Distance'     = L * 2^(W - N) + X    ... (1)
7110       //
7111       // The smallest X satisfying (1) is unsigned remainder of dividing the LHS
7112       // by 2^(W - N).
7113       //
7114       // <=>  X = 2^k * Distance' URem 2^(W - N)   ... (2)
7115       //
7116       // E.g. say we're solving
7117       //
7118       //   2 * Val = 2 * X  (in i8)   ... (3)
7119       //
7120       // then from (2), we get X = Val URem i8 128 (k = 0 in this case).
7121       //
7122       // Note: It is tempting to solve (3) by setting X = Val, but Val is not
7123       // necessarily the smallest unsigned value of X that satisfies (3).
7124       // E.g. if Val is i8 -127 then the smallest value of X that satisfies (3)
7125       // is i8 1, not i8 -127
7126 
7127       const auto *ModuloResult = getUDivExactExpr(Distance, Step);
7128 
7129       // Since SCEV does not have a URem node, we construct one using a truncate
7130       // and a zero extend.
7131 
7132       unsigned NarrowWidth = StepV.getBitWidth() - StepV.countTrailingZeros();
7133       auto *NarrowTy = IntegerType::get(getContext(), NarrowWidth);
7134       auto *WideTy = Distance->getType();
7135 
7136       const SCEV *Limit =
7137           getZeroExtendExpr(getTruncateExpr(ModuloResult, NarrowTy), WideTy);
7138       return ExitLimit(Limit, Limit, P);
7139     }
7140   }
7141 
7142   // If the condition controls loop exit (the loop exits only if the expression
7143   // is true) and the addition is no-wrap we can use unsigned divide to
7144   // compute the backedge count.  In this case, the step may not divide the
7145   // distance, but we don't care because if the condition is "missed" the loop
7146   // will have undefined behavior due to wrapping.
7147   if (ControlsExit && AddRec->hasNoSelfWrap()) {
7148     const SCEV *Exact =
7149         getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
7150     return ExitLimit(Exact, Exact, P);
7151   }
7152 
7153   // Then, try to solve the above equation provided that Start is constant.
7154   if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
7155     const SCEV *E = SolveLinEquationWithOverflow(
7156         StepC->getValue()->getValue(), -StartC->getValue()->getValue(), *this);
7157     return ExitLimit(E, E, P);
7158   }
7159   return getCouldNotCompute();
7160 }
7161 
7162 /// HowFarToNonZero - Return the number of times a backedge checking the
7163 /// specified value for nonzero will execute.  If not computable, return
7164 /// CouldNotCompute
7165 ScalarEvolution::ExitLimit
7166 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
7167   // Loops that look like: while (X == 0) are very strange indeed.  We don't
7168   // handle them yet except for the trivial case.  This could be expanded in the
7169   // future as needed.
7170 
7171   // If the value is a constant, check to see if it is known to be non-zero
7172   // already.  If so, the backedge will execute zero times.
7173   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
7174     if (!C->getValue()->isNullValue())
7175       return getZero(C->getType());
7176     return getCouldNotCompute();  // Otherwise it will loop infinitely.
7177   }
7178 
7179   // We could implement others, but I really doubt anyone writes loops like
7180   // this, and if they did, they would already be constant folded.
7181   return getCouldNotCompute();
7182 }
7183 
7184 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
7185 /// (which may not be an immediate predecessor) which has exactly one
7186 /// successor from which BB is reachable, or null if no such block is
7187 /// found.
7188 ///
7189 std::pair<BasicBlock *, BasicBlock *>
7190 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
7191   // If the block has a unique predecessor, then there is no path from the
7192   // predecessor to the block that does not go through the direct edge
7193   // from the predecessor to the block.
7194   if (BasicBlock *Pred = BB->getSinglePredecessor())
7195     return {Pred, BB};
7196 
7197   // A loop's header is defined to be a block that dominates the loop.
7198   // If the header has a unique predecessor outside the loop, it must be
7199   // a block that has exactly one successor that can reach the loop.
7200   if (Loop *L = LI.getLoopFor(BB))
7201     return {L->getLoopPredecessor(), L->getHeader()};
7202 
7203   return {nullptr, nullptr};
7204 }
7205 
7206 /// HasSameValue - SCEV structural equivalence is usually sufficient for
7207 /// testing whether two expressions are equal, however for the purposes of
7208 /// looking for a condition guarding a loop, it can be useful to be a little
7209 /// more general, since a front-end may have replicated the controlling
7210 /// expression.
7211 ///
7212 static bool HasSameValue(const SCEV *A, const SCEV *B) {
7213   // Quick check to see if they are the same SCEV.
7214   if (A == B) return true;
7215 
7216   auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
7217     // Not all instructions that are "identical" compute the same value.  For
7218     // instance, two distinct alloca instructions allocating the same type are
7219     // identical and do not read memory; but compute distinct values.
7220     return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
7221   };
7222 
7223   // Otherwise, if they're both SCEVUnknown, it's possible that they hold
7224   // two different instructions with the same value. Check for this case.
7225   if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
7226     if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
7227       if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
7228         if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
7229           if (ComputesEqualValues(AI, BI))
7230             return true;
7231 
7232   // Otherwise assume they may have a different value.
7233   return false;
7234 }
7235 
7236 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
7237 /// predicate Pred. Return true iff any changes were made.
7238 ///
7239 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
7240                                            const SCEV *&LHS, const SCEV *&RHS,
7241                                            unsigned Depth) {
7242   bool Changed = false;
7243 
7244   // If we hit the max recursion limit bail out.
7245   if (Depth >= 3)
7246     return false;
7247 
7248   // Canonicalize a constant to the right side.
7249   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
7250     // Check for both operands constant.
7251     if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
7252       if (ConstantExpr::getICmp(Pred,
7253                                 LHSC->getValue(),
7254                                 RHSC->getValue())->isNullValue())
7255         goto trivially_false;
7256       else
7257         goto trivially_true;
7258     }
7259     // Otherwise swap the operands to put the constant on the right.
7260     std::swap(LHS, RHS);
7261     Pred = ICmpInst::getSwappedPredicate(Pred);
7262     Changed = true;
7263   }
7264 
7265   // If we're comparing an addrec with a value which is loop-invariant in the
7266   // addrec's loop, put the addrec on the left. Also make a dominance check,
7267   // as both operands could be addrecs loop-invariant in each other's loop.
7268   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
7269     const Loop *L = AR->getLoop();
7270     if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
7271       std::swap(LHS, RHS);
7272       Pred = ICmpInst::getSwappedPredicate(Pred);
7273       Changed = true;
7274     }
7275   }
7276 
7277   // If there's a constant operand, canonicalize comparisons with boundary
7278   // cases, and canonicalize *-or-equal comparisons to regular comparisons.
7279   if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
7280     const APInt &RA = RC->getAPInt();
7281     switch (Pred) {
7282     default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7283     case ICmpInst::ICMP_EQ:
7284     case ICmpInst::ICMP_NE:
7285       // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
7286       if (!RA)
7287         if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
7288           if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
7289             if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
7290                 ME->getOperand(0)->isAllOnesValue()) {
7291               RHS = AE->getOperand(1);
7292               LHS = ME->getOperand(1);
7293               Changed = true;
7294             }
7295       break;
7296     case ICmpInst::ICMP_UGE:
7297       if ((RA - 1).isMinValue()) {
7298         Pred = ICmpInst::ICMP_NE;
7299         RHS = getConstant(RA - 1);
7300         Changed = true;
7301         break;
7302       }
7303       if (RA.isMaxValue()) {
7304         Pred = ICmpInst::ICMP_EQ;
7305         Changed = true;
7306         break;
7307       }
7308       if (RA.isMinValue()) goto trivially_true;
7309 
7310       Pred = ICmpInst::ICMP_UGT;
7311       RHS = getConstant(RA - 1);
7312       Changed = true;
7313       break;
7314     case ICmpInst::ICMP_ULE:
7315       if ((RA + 1).isMaxValue()) {
7316         Pred = ICmpInst::ICMP_NE;
7317         RHS = getConstant(RA + 1);
7318         Changed = true;
7319         break;
7320       }
7321       if (RA.isMinValue()) {
7322         Pred = ICmpInst::ICMP_EQ;
7323         Changed = true;
7324         break;
7325       }
7326       if (RA.isMaxValue()) goto trivially_true;
7327 
7328       Pred = ICmpInst::ICMP_ULT;
7329       RHS = getConstant(RA + 1);
7330       Changed = true;
7331       break;
7332     case ICmpInst::ICMP_SGE:
7333       if ((RA - 1).isMinSignedValue()) {
7334         Pred = ICmpInst::ICMP_NE;
7335         RHS = getConstant(RA - 1);
7336         Changed = true;
7337         break;
7338       }
7339       if (RA.isMaxSignedValue()) {
7340         Pred = ICmpInst::ICMP_EQ;
7341         Changed = true;
7342         break;
7343       }
7344       if (RA.isMinSignedValue()) goto trivially_true;
7345 
7346       Pred = ICmpInst::ICMP_SGT;
7347       RHS = getConstant(RA - 1);
7348       Changed = true;
7349       break;
7350     case ICmpInst::ICMP_SLE:
7351       if ((RA + 1).isMaxSignedValue()) {
7352         Pred = ICmpInst::ICMP_NE;
7353         RHS = getConstant(RA + 1);
7354         Changed = true;
7355         break;
7356       }
7357       if (RA.isMinSignedValue()) {
7358         Pred = ICmpInst::ICMP_EQ;
7359         Changed = true;
7360         break;
7361       }
7362       if (RA.isMaxSignedValue()) goto trivially_true;
7363 
7364       Pred = ICmpInst::ICMP_SLT;
7365       RHS = getConstant(RA + 1);
7366       Changed = true;
7367       break;
7368     case ICmpInst::ICMP_UGT:
7369       if (RA.isMinValue()) {
7370         Pred = ICmpInst::ICMP_NE;
7371         Changed = true;
7372         break;
7373       }
7374       if ((RA + 1).isMaxValue()) {
7375         Pred = ICmpInst::ICMP_EQ;
7376         RHS = getConstant(RA + 1);
7377         Changed = true;
7378         break;
7379       }
7380       if (RA.isMaxValue()) goto trivially_false;
7381       break;
7382     case ICmpInst::ICMP_ULT:
7383       if (RA.isMaxValue()) {
7384         Pred = ICmpInst::ICMP_NE;
7385         Changed = true;
7386         break;
7387       }
7388       if ((RA - 1).isMinValue()) {
7389         Pred = ICmpInst::ICMP_EQ;
7390         RHS = getConstant(RA - 1);
7391         Changed = true;
7392         break;
7393       }
7394       if (RA.isMinValue()) goto trivially_false;
7395       break;
7396     case ICmpInst::ICMP_SGT:
7397       if (RA.isMinSignedValue()) {
7398         Pred = ICmpInst::ICMP_NE;
7399         Changed = true;
7400         break;
7401       }
7402       if ((RA + 1).isMaxSignedValue()) {
7403         Pred = ICmpInst::ICMP_EQ;
7404         RHS = getConstant(RA + 1);
7405         Changed = true;
7406         break;
7407       }
7408       if (RA.isMaxSignedValue()) goto trivially_false;
7409       break;
7410     case ICmpInst::ICMP_SLT:
7411       if (RA.isMaxSignedValue()) {
7412         Pred = ICmpInst::ICMP_NE;
7413         Changed = true;
7414         break;
7415       }
7416       if ((RA - 1).isMinSignedValue()) {
7417        Pred = ICmpInst::ICMP_EQ;
7418        RHS = getConstant(RA - 1);
7419         Changed = true;
7420        break;
7421       }
7422       if (RA.isMinSignedValue()) goto trivially_false;
7423       break;
7424     }
7425   }
7426 
7427   // Check for obvious equality.
7428   if (HasSameValue(LHS, RHS)) {
7429     if (ICmpInst::isTrueWhenEqual(Pred))
7430       goto trivially_true;
7431     if (ICmpInst::isFalseWhenEqual(Pred))
7432       goto trivially_false;
7433   }
7434 
7435   // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
7436   // adding or subtracting 1 from one of the operands.
7437   switch (Pred) {
7438   case ICmpInst::ICMP_SLE:
7439     if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
7440       RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
7441                        SCEV::FlagNSW);
7442       Pred = ICmpInst::ICMP_SLT;
7443       Changed = true;
7444     } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
7445       LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
7446                        SCEV::FlagNSW);
7447       Pred = ICmpInst::ICMP_SLT;
7448       Changed = true;
7449     }
7450     break;
7451   case ICmpInst::ICMP_SGE:
7452     if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
7453       RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
7454                        SCEV::FlagNSW);
7455       Pred = ICmpInst::ICMP_SGT;
7456       Changed = true;
7457     } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
7458       LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
7459                        SCEV::FlagNSW);
7460       Pred = ICmpInst::ICMP_SGT;
7461       Changed = true;
7462     }
7463     break;
7464   case ICmpInst::ICMP_ULE:
7465     if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
7466       RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
7467                        SCEV::FlagNUW);
7468       Pred = ICmpInst::ICMP_ULT;
7469       Changed = true;
7470     } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
7471       LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS);
7472       Pred = ICmpInst::ICMP_ULT;
7473       Changed = true;
7474     }
7475     break;
7476   case ICmpInst::ICMP_UGE:
7477     if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
7478       RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
7479       Pred = ICmpInst::ICMP_UGT;
7480       Changed = true;
7481     } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
7482       LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
7483                        SCEV::FlagNUW);
7484       Pred = ICmpInst::ICMP_UGT;
7485       Changed = true;
7486     }
7487     break;
7488   default:
7489     break;
7490   }
7491 
7492   // TODO: More simplifications are possible here.
7493 
7494   // Recursively simplify until we either hit a recursion limit or nothing
7495   // changes.
7496   if (Changed)
7497     return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
7498 
7499   return Changed;
7500 
7501 trivially_true:
7502   // Return 0 == 0.
7503   LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
7504   Pred = ICmpInst::ICMP_EQ;
7505   return true;
7506 
7507 trivially_false:
7508   // Return 0 != 0.
7509   LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
7510   Pred = ICmpInst::ICMP_NE;
7511   return true;
7512 }
7513 
7514 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
7515   return getSignedRange(S).getSignedMax().isNegative();
7516 }
7517 
7518 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
7519   return getSignedRange(S).getSignedMin().isStrictlyPositive();
7520 }
7521 
7522 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
7523   return !getSignedRange(S).getSignedMin().isNegative();
7524 }
7525 
7526 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
7527   return !getSignedRange(S).getSignedMax().isStrictlyPositive();
7528 }
7529 
7530 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
7531   return isKnownNegative(S) || isKnownPositive(S);
7532 }
7533 
7534 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
7535                                        const SCEV *LHS, const SCEV *RHS) {
7536   // Canonicalize the inputs first.
7537   (void)SimplifyICmpOperands(Pred, LHS, RHS);
7538 
7539   // If LHS or RHS is an addrec, check to see if the condition is true in
7540   // every iteration of the loop.
7541   // If LHS and RHS are both addrec, both conditions must be true in
7542   // every iteration of the loop.
7543   const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
7544   const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
7545   bool LeftGuarded = false;
7546   bool RightGuarded = false;
7547   if (LAR) {
7548     const Loop *L = LAR->getLoop();
7549     if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
7550         isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
7551       if (!RAR) return true;
7552       LeftGuarded = true;
7553     }
7554   }
7555   if (RAR) {
7556     const Loop *L = RAR->getLoop();
7557     if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
7558         isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
7559       if (!LAR) return true;
7560       RightGuarded = true;
7561     }
7562   }
7563   if (LeftGuarded && RightGuarded)
7564     return true;
7565 
7566   if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
7567     return true;
7568 
7569   // Otherwise see what can be done with known constant ranges.
7570   return isKnownPredicateViaConstantRanges(Pred, LHS, RHS);
7571 }
7572 
7573 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
7574                                            ICmpInst::Predicate Pred,
7575                                            bool &Increasing) {
7576   bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
7577 
7578 #ifndef NDEBUG
7579   // Verify an invariant: inverting the predicate should turn a monotonically
7580   // increasing change to a monotonically decreasing one, and vice versa.
7581   bool IncreasingSwapped;
7582   bool ResultSwapped = isMonotonicPredicateImpl(
7583       LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
7584 
7585   assert(Result == ResultSwapped && "should be able to analyze both!");
7586   if (ResultSwapped)
7587     assert(Increasing == !IncreasingSwapped &&
7588            "monotonicity should flip as we flip the predicate");
7589 #endif
7590 
7591   return Result;
7592 }
7593 
7594 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
7595                                                ICmpInst::Predicate Pred,
7596                                                bool &Increasing) {
7597 
7598   // A zero step value for LHS means the induction variable is essentially a
7599   // loop invariant value. We don't really depend on the predicate actually
7600   // flipping from false to true (for increasing predicates, and the other way
7601   // around for decreasing predicates), all we care about is that *if* the
7602   // predicate changes then it only changes from false to true.
7603   //
7604   // A zero step value in itself is not very useful, but there may be places
7605   // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
7606   // as general as possible.
7607 
7608   switch (Pred) {
7609   default:
7610     return false; // Conservative answer
7611 
7612   case ICmpInst::ICMP_UGT:
7613   case ICmpInst::ICMP_UGE:
7614   case ICmpInst::ICMP_ULT:
7615   case ICmpInst::ICMP_ULE:
7616     if (!LHS->hasNoUnsignedWrap())
7617       return false;
7618 
7619     Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
7620     return true;
7621 
7622   case ICmpInst::ICMP_SGT:
7623   case ICmpInst::ICMP_SGE:
7624   case ICmpInst::ICMP_SLT:
7625   case ICmpInst::ICMP_SLE: {
7626     if (!LHS->hasNoSignedWrap())
7627       return false;
7628 
7629     const SCEV *Step = LHS->getStepRecurrence(*this);
7630 
7631     if (isKnownNonNegative(Step)) {
7632       Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
7633       return true;
7634     }
7635 
7636     if (isKnownNonPositive(Step)) {
7637       Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
7638       return true;
7639     }
7640 
7641     return false;
7642   }
7643 
7644   }
7645 
7646   llvm_unreachable("switch has default clause!");
7647 }
7648 
7649 bool ScalarEvolution::isLoopInvariantPredicate(
7650     ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
7651     ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
7652     const SCEV *&InvariantRHS) {
7653 
7654   // If there is a loop-invariant, force it into the RHS, otherwise bail out.
7655   if (!isLoopInvariant(RHS, L)) {
7656     if (!isLoopInvariant(LHS, L))
7657       return false;
7658 
7659     std::swap(LHS, RHS);
7660     Pred = ICmpInst::getSwappedPredicate(Pred);
7661   }
7662 
7663   const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
7664   if (!ArLHS || ArLHS->getLoop() != L)
7665     return false;
7666 
7667   bool Increasing;
7668   if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
7669     return false;
7670 
7671   // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
7672   // true as the loop iterates, and the backedge is control dependent on
7673   // "ArLHS `Pred` RHS" == true then we can reason as follows:
7674   //
7675   //   * if the predicate was false in the first iteration then the predicate
7676   //     is never evaluated again, since the loop exits without taking the
7677   //     backedge.
7678   //   * if the predicate was true in the first iteration then it will
7679   //     continue to be true for all future iterations since it is
7680   //     monotonically increasing.
7681   //
7682   // For both the above possibilities, we can replace the loop varying
7683   // predicate with its value on the first iteration of the loop (which is
7684   // loop invariant).
7685   //
7686   // A similar reasoning applies for a monotonically decreasing predicate, by
7687   // replacing true with false and false with true in the above two bullets.
7688 
7689   auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
7690 
7691   if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
7692     return false;
7693 
7694   InvariantPred = Pred;
7695   InvariantLHS = ArLHS->getStart();
7696   InvariantRHS = RHS;
7697   return true;
7698 }
7699 
7700 bool ScalarEvolution::isKnownPredicateViaConstantRanges(
7701     ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
7702   if (HasSameValue(LHS, RHS))
7703     return ICmpInst::isTrueWhenEqual(Pred);
7704 
7705   // This code is split out from isKnownPredicate because it is called from
7706   // within isLoopEntryGuardedByCond.
7707 
7708   auto CheckRanges =
7709       [&](const ConstantRange &RangeLHS, const ConstantRange &RangeRHS) {
7710     return ConstantRange::makeSatisfyingICmpRegion(Pred, RangeRHS)
7711         .contains(RangeLHS);
7712   };
7713 
7714   // The check at the top of the function catches the case where the values are
7715   // known to be equal.
7716   if (Pred == CmpInst::ICMP_EQ)
7717     return false;
7718 
7719   if (Pred == CmpInst::ICMP_NE)
7720     return CheckRanges(getSignedRange(LHS), getSignedRange(RHS)) ||
7721            CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS)) ||
7722            isKnownNonZero(getMinusSCEV(LHS, RHS));
7723 
7724   if (CmpInst::isSigned(Pred))
7725     return CheckRanges(getSignedRange(LHS), getSignedRange(RHS));
7726 
7727   return CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS));
7728 }
7729 
7730 bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
7731                                                     const SCEV *LHS,
7732                                                     const SCEV *RHS) {
7733 
7734   // Match Result to (X + Y)<ExpectedFlags> where Y is a constant integer.
7735   // Return Y via OutY.
7736   auto MatchBinaryAddToConst =
7737       [this](const SCEV *Result, const SCEV *X, APInt &OutY,
7738              SCEV::NoWrapFlags ExpectedFlags) {
7739     const SCEV *NonConstOp, *ConstOp;
7740     SCEV::NoWrapFlags FlagsPresent;
7741 
7742     if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) ||
7743         !isa<SCEVConstant>(ConstOp) || NonConstOp != X)
7744       return false;
7745 
7746     OutY = cast<SCEVConstant>(ConstOp)->getAPInt();
7747     return (FlagsPresent & ExpectedFlags) == ExpectedFlags;
7748   };
7749 
7750   APInt C;
7751 
7752   switch (Pred) {
7753   default:
7754     break;
7755 
7756   case ICmpInst::ICMP_SGE:
7757     std::swap(LHS, RHS);
7758   case ICmpInst::ICMP_SLE:
7759     // X s<= (X + C)<nsw> if C >= 0
7760     if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative())
7761       return true;
7762 
7763     // (X + C)<nsw> s<= X if C <= 0
7764     if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) &&
7765         !C.isStrictlyPositive())
7766       return true;
7767     break;
7768 
7769   case ICmpInst::ICMP_SGT:
7770     std::swap(LHS, RHS);
7771   case ICmpInst::ICMP_SLT:
7772     // X s< (X + C)<nsw> if C > 0
7773     if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) &&
7774         C.isStrictlyPositive())
7775       return true;
7776 
7777     // (X + C)<nsw> s< X if C < 0
7778     if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative())
7779       return true;
7780     break;
7781   }
7782 
7783   return false;
7784 }
7785 
7786 bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
7787                                                    const SCEV *LHS,
7788                                                    const SCEV *RHS) {
7789   if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
7790     return false;
7791 
7792   // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
7793   // the stack can result in exponential time complexity.
7794   SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
7795 
7796   // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
7797   //
7798   // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
7799   // isKnownPredicate.  isKnownPredicate is more powerful, but also more
7800   // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
7801   // interesting cases seen in practice.  We can consider "upgrading" L >= 0 to
7802   // use isKnownPredicate later if needed.
7803   return isKnownNonNegative(RHS) &&
7804          isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
7805          isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS);
7806 }
7807 
7808 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
7809 /// protected by a conditional between LHS and RHS.  This is used to
7810 /// to eliminate casts.
7811 bool
7812 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
7813                                              ICmpInst::Predicate Pred,
7814                                              const SCEV *LHS, const SCEV *RHS) {
7815   // Interpret a null as meaning no loop, where there is obviously no guard
7816   // (interprocedural conditions notwithstanding).
7817   if (!L) return true;
7818 
7819   if (isKnownPredicateViaConstantRanges(Pred, LHS, RHS))
7820     return true;
7821 
7822   BasicBlock *Latch = L->getLoopLatch();
7823   if (!Latch)
7824     return false;
7825 
7826   BranchInst *LoopContinuePredicate =
7827     dyn_cast<BranchInst>(Latch->getTerminator());
7828   if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
7829       isImpliedCond(Pred, LHS, RHS,
7830                     LoopContinuePredicate->getCondition(),
7831                     LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
7832     return true;
7833 
7834   // We don't want more than one activation of the following loops on the stack
7835   // -- that can lead to O(n!) time complexity.
7836   if (WalkingBEDominatingConds)
7837     return false;
7838 
7839   SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
7840 
7841   // See if we can exploit a trip count to prove the predicate.
7842   const auto &BETakenInfo = getBackedgeTakenInfo(L);
7843   const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
7844   if (LatchBECount != getCouldNotCompute()) {
7845     // We know that Latch branches back to the loop header exactly
7846     // LatchBECount times.  This means the backdege condition at Latch is
7847     // equivalent to  "{0,+,1} u< LatchBECount".
7848     Type *Ty = LatchBECount->getType();
7849     auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
7850     const SCEV *LoopCounter =
7851       getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
7852     if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
7853                       LatchBECount))
7854       return true;
7855   }
7856 
7857   // Check conditions due to any @llvm.assume intrinsics.
7858   for (auto &AssumeVH : AC.assumptions()) {
7859     if (!AssumeVH)
7860       continue;
7861     auto *CI = cast<CallInst>(AssumeVH);
7862     if (!DT.dominates(CI, Latch->getTerminator()))
7863       continue;
7864 
7865     if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7866       return true;
7867   }
7868 
7869   // If the loop is not reachable from the entry block, we risk running into an
7870   // infinite loop as we walk up into the dom tree.  These loops do not matter
7871   // anyway, so we just return a conservative answer when we see them.
7872   if (!DT.isReachableFromEntry(L->getHeader()))
7873     return false;
7874 
7875   for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
7876        DTN != HeaderDTN; DTN = DTN->getIDom()) {
7877 
7878     assert(DTN && "should reach the loop header before reaching the root!");
7879 
7880     BasicBlock *BB = DTN->getBlock();
7881     BasicBlock *PBB = BB->getSinglePredecessor();
7882     if (!PBB)
7883       continue;
7884 
7885     BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
7886     if (!ContinuePredicate || !ContinuePredicate->isConditional())
7887       continue;
7888 
7889     Value *Condition = ContinuePredicate->getCondition();
7890 
7891     // If we have an edge `E` within the loop body that dominates the only
7892     // latch, the condition guarding `E` also guards the backedge.  This
7893     // reasoning works only for loops with a single latch.
7894 
7895     BasicBlockEdge DominatingEdge(PBB, BB);
7896     if (DominatingEdge.isSingleEdge()) {
7897       // We're constructively (and conservatively) enumerating edges within the
7898       // loop body that dominate the latch.  The dominator tree better agree
7899       // with us on this:
7900       assert(DT.dominates(DominatingEdge, Latch) && "should be!");
7901 
7902       if (isImpliedCond(Pred, LHS, RHS, Condition,
7903                         BB != ContinuePredicate->getSuccessor(0)))
7904         return true;
7905     }
7906   }
7907 
7908   return false;
7909 }
7910 
7911 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
7912 /// by a conditional between LHS and RHS.  This is used to help avoid max
7913 /// expressions in loop trip counts, and to eliminate casts.
7914 bool
7915 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
7916                                           ICmpInst::Predicate Pred,
7917                                           const SCEV *LHS, const SCEV *RHS) {
7918   // Interpret a null as meaning no loop, where there is obviously no guard
7919   // (interprocedural conditions notwithstanding).
7920   if (!L) return false;
7921 
7922   if (isKnownPredicateViaConstantRanges(Pred, LHS, RHS))
7923     return true;
7924 
7925   // Starting at the loop predecessor, climb up the predecessor chain, as long
7926   // as there are predecessors that can be found that have unique successors
7927   // leading to the original header.
7928   for (std::pair<BasicBlock *, BasicBlock *>
7929          Pair(L->getLoopPredecessor(), L->getHeader());
7930        Pair.first;
7931        Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
7932 
7933     BranchInst *LoopEntryPredicate =
7934       dyn_cast<BranchInst>(Pair.first->getTerminator());
7935     if (!LoopEntryPredicate ||
7936         LoopEntryPredicate->isUnconditional())
7937       continue;
7938 
7939     if (isImpliedCond(Pred, LHS, RHS,
7940                       LoopEntryPredicate->getCondition(),
7941                       LoopEntryPredicate->getSuccessor(0) != Pair.second))
7942       return true;
7943   }
7944 
7945   // Check conditions due to any @llvm.assume intrinsics.
7946   for (auto &AssumeVH : AC.assumptions()) {
7947     if (!AssumeVH)
7948       continue;
7949     auto *CI = cast<CallInst>(AssumeVH);
7950     if (!DT.dominates(CI, L->getHeader()))
7951       continue;
7952 
7953     if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7954       return true;
7955   }
7956 
7957   return false;
7958 }
7959 
7960 namespace {
7961 /// RAII wrapper to prevent recursive application of isImpliedCond.
7962 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
7963 /// currently evaluating isImpliedCond.
7964 struct MarkPendingLoopPredicate {
7965   Value *Cond;
7966   DenseSet<Value*> &LoopPreds;
7967   bool Pending;
7968 
7969   MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
7970     : Cond(C), LoopPreds(LP) {
7971     Pending = !LoopPreds.insert(Cond).second;
7972   }
7973   ~MarkPendingLoopPredicate() {
7974     if (!Pending)
7975       LoopPreds.erase(Cond);
7976   }
7977 };
7978 } // end anonymous namespace
7979 
7980 /// isImpliedCond - Test whether the condition described by Pred, LHS,
7981 /// and RHS is true whenever the given Cond value evaluates to true.
7982 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
7983                                     const SCEV *LHS, const SCEV *RHS,
7984                                     Value *FoundCondValue,
7985                                     bool Inverse) {
7986   MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
7987   if (Mark.Pending)
7988     return false;
7989 
7990   // Recursively handle And and Or conditions.
7991   if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
7992     if (BO->getOpcode() == Instruction::And) {
7993       if (!Inverse)
7994         return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7995                isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7996     } else if (BO->getOpcode() == Instruction::Or) {
7997       if (Inverse)
7998         return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7999                isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
8000     }
8001   }
8002 
8003   ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
8004   if (!ICI) return false;
8005 
8006   // Now that we found a conditional branch that dominates the loop or controls
8007   // the loop latch. Check to see if it is the comparison we are looking for.
8008   ICmpInst::Predicate FoundPred;
8009   if (Inverse)
8010     FoundPred = ICI->getInversePredicate();
8011   else
8012     FoundPred = ICI->getPredicate();
8013 
8014   const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
8015   const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
8016 
8017   return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS);
8018 }
8019 
8020 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
8021                                     const SCEV *RHS,
8022                                     ICmpInst::Predicate FoundPred,
8023                                     const SCEV *FoundLHS,
8024                                     const SCEV *FoundRHS) {
8025   // Balance the types.
8026   if (getTypeSizeInBits(LHS->getType()) <
8027       getTypeSizeInBits(FoundLHS->getType())) {
8028     if (CmpInst::isSigned(Pred)) {
8029       LHS = getSignExtendExpr(LHS, FoundLHS->getType());
8030       RHS = getSignExtendExpr(RHS, FoundLHS->getType());
8031     } else {
8032       LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
8033       RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
8034     }
8035   } else if (getTypeSizeInBits(LHS->getType()) >
8036       getTypeSizeInBits(FoundLHS->getType())) {
8037     if (CmpInst::isSigned(FoundPred)) {
8038       FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
8039       FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
8040     } else {
8041       FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
8042       FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
8043     }
8044   }
8045 
8046   // Canonicalize the query to match the way instcombine will have
8047   // canonicalized the comparison.
8048   if (SimplifyICmpOperands(Pred, LHS, RHS))
8049     if (LHS == RHS)
8050       return CmpInst::isTrueWhenEqual(Pred);
8051   if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
8052     if (FoundLHS == FoundRHS)
8053       return CmpInst::isFalseWhenEqual(FoundPred);
8054 
8055   // Check to see if we can make the LHS or RHS match.
8056   if (LHS == FoundRHS || RHS == FoundLHS) {
8057     if (isa<SCEVConstant>(RHS)) {
8058       std::swap(FoundLHS, FoundRHS);
8059       FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
8060     } else {
8061       std::swap(LHS, RHS);
8062       Pred = ICmpInst::getSwappedPredicate(Pred);
8063     }
8064   }
8065 
8066   // Check whether the found predicate is the same as the desired predicate.
8067   if (FoundPred == Pred)
8068     return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
8069 
8070   // Check whether swapping the found predicate makes it the same as the
8071   // desired predicate.
8072   if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
8073     if (isa<SCEVConstant>(RHS))
8074       return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
8075     else
8076       return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
8077                                    RHS, LHS, FoundLHS, FoundRHS);
8078   }
8079 
8080   // Unsigned comparison is the same as signed comparison when both the operands
8081   // are non-negative.
8082   if (CmpInst::isUnsigned(FoundPred) &&
8083       CmpInst::getSignedPredicate(FoundPred) == Pred &&
8084       isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS))
8085     return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
8086 
8087   // Check if we can make progress by sharpening ranges.
8088   if (FoundPred == ICmpInst::ICMP_NE &&
8089       (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
8090 
8091     const SCEVConstant *C = nullptr;
8092     const SCEV *V = nullptr;
8093 
8094     if (isa<SCEVConstant>(FoundLHS)) {
8095       C = cast<SCEVConstant>(FoundLHS);
8096       V = FoundRHS;
8097     } else {
8098       C = cast<SCEVConstant>(FoundRHS);
8099       V = FoundLHS;
8100     }
8101 
8102     // The guarding predicate tells us that C != V. If the known range
8103     // of V is [C, t), we can sharpen the range to [C + 1, t).  The
8104     // range we consider has to correspond to same signedness as the
8105     // predicate we're interested in folding.
8106 
8107     APInt Min = ICmpInst::isSigned(Pred) ?
8108         getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
8109 
8110     if (Min == C->getAPInt()) {
8111       // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
8112       // This is true even if (Min + 1) wraps around -- in case of
8113       // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
8114 
8115       APInt SharperMin = Min + 1;
8116 
8117       switch (Pred) {
8118         case ICmpInst::ICMP_SGE:
8119         case ICmpInst::ICMP_UGE:
8120           // We know V `Pred` SharperMin.  If this implies LHS `Pred`
8121           // RHS, we're done.
8122           if (isImpliedCondOperands(Pred, LHS, RHS, V,
8123                                     getConstant(SharperMin)))
8124             return true;
8125 
8126         case ICmpInst::ICMP_SGT:
8127         case ICmpInst::ICMP_UGT:
8128           // We know from the range information that (V `Pred` Min ||
8129           // V == Min).  We know from the guarding condition that !(V
8130           // == Min).  This gives us
8131           //
8132           //       V `Pred` Min || V == Min && !(V == Min)
8133           //   =>  V `Pred` Min
8134           //
8135           // If V `Pred` Min implies LHS `Pred` RHS, we're done.
8136 
8137           if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
8138             return true;
8139 
8140         default:
8141           // No change
8142           break;
8143       }
8144     }
8145   }
8146 
8147   // Check whether the actual condition is beyond sufficient.
8148   if (FoundPred == ICmpInst::ICMP_EQ)
8149     if (ICmpInst::isTrueWhenEqual(Pred))
8150       if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
8151         return true;
8152   if (Pred == ICmpInst::ICMP_NE)
8153     if (!ICmpInst::isTrueWhenEqual(FoundPred))
8154       if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
8155         return true;
8156 
8157   // Otherwise assume the worst.
8158   return false;
8159 }
8160 
8161 bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr,
8162                                      const SCEV *&L, const SCEV *&R,
8163                                      SCEV::NoWrapFlags &Flags) {
8164   const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
8165   if (!AE || AE->getNumOperands() != 2)
8166     return false;
8167 
8168   L = AE->getOperand(0);
8169   R = AE->getOperand(1);
8170   Flags = AE->getNoWrapFlags();
8171   return true;
8172 }
8173 
8174 bool ScalarEvolution::computeConstantDifference(const SCEV *Less,
8175                                                 const SCEV *More,
8176                                                 APInt &C) {
8177   // We avoid subtracting expressions here because this function is usually
8178   // fairly deep in the call stack (i.e. is called many times).
8179 
8180   if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
8181     const auto *LAR = cast<SCEVAddRecExpr>(Less);
8182     const auto *MAR = cast<SCEVAddRecExpr>(More);
8183 
8184     if (LAR->getLoop() != MAR->getLoop())
8185       return false;
8186 
8187     // We look at affine expressions only; not for correctness but to keep
8188     // getStepRecurrence cheap.
8189     if (!LAR->isAffine() || !MAR->isAffine())
8190       return false;
8191 
8192     if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
8193       return false;
8194 
8195     Less = LAR->getStart();
8196     More = MAR->getStart();
8197 
8198     // fall through
8199   }
8200 
8201   if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
8202     const auto &M = cast<SCEVConstant>(More)->getAPInt();
8203     const auto &L = cast<SCEVConstant>(Less)->getAPInt();
8204     C = M - L;
8205     return true;
8206   }
8207 
8208   const SCEV *L, *R;
8209   SCEV::NoWrapFlags Flags;
8210   if (splitBinaryAdd(Less, L, R, Flags))
8211     if (const auto *LC = dyn_cast<SCEVConstant>(L))
8212       if (R == More) {
8213         C = -(LC->getAPInt());
8214         return true;
8215       }
8216 
8217   if (splitBinaryAdd(More, L, R, Flags))
8218     if (const auto *LC = dyn_cast<SCEVConstant>(L))
8219       if (R == Less) {
8220         C = LC->getAPInt();
8221         return true;
8222       }
8223 
8224   return false;
8225 }
8226 
8227 bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
8228     ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
8229     const SCEV *FoundLHS, const SCEV *FoundRHS) {
8230   if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
8231     return false;
8232 
8233   const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
8234   if (!AddRecLHS)
8235     return false;
8236 
8237   const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
8238   if (!AddRecFoundLHS)
8239     return false;
8240 
8241   // We'd like to let SCEV reason about control dependencies, so we constrain
8242   // both the inequalities to be about add recurrences on the same loop.  This
8243   // way we can use isLoopEntryGuardedByCond later.
8244 
8245   const Loop *L = AddRecFoundLHS->getLoop();
8246   if (L != AddRecLHS->getLoop())
8247     return false;
8248 
8249   //  FoundLHS u< FoundRHS u< -C =>  (FoundLHS + C) u< (FoundRHS + C) ... (1)
8250   //
8251   //  FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
8252   //                                                                  ... (2)
8253   //
8254   // Informal proof for (2), assuming (1) [*]:
8255   //
8256   // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
8257   //
8258   // Then
8259   //
8260   //       FoundLHS s< FoundRHS s< INT_MIN - C
8261   // <=>  (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C   [ using (3) ]
8262   // <=>  (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
8263   // <=>  (FoundLHS + INT_MIN + C + INT_MIN) s<
8264   //                        (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
8265   // <=>  FoundLHS + C s< FoundRHS + C
8266   //
8267   // [*]: (1) can be proved by ruling out overflow.
8268   //
8269   // [**]: This can be proved by analyzing all the four possibilities:
8270   //    (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
8271   //    (A s>= 0, B s>= 0).
8272   //
8273   // Note:
8274   // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
8275   // will not sign underflow.  For instance, say FoundLHS = (i8 -128), FoundRHS
8276   // = (i8 -127) and C = (i8 -100).  Then INT_MIN - C = (i8 -28), and FoundRHS
8277   // s< (INT_MIN - C).  Lack of sign overflow / underflow in "FoundRHS + C" is
8278   // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
8279   // C)".
8280 
8281   APInt LDiff, RDiff;
8282   if (!computeConstantDifference(FoundLHS, LHS, LDiff) ||
8283       !computeConstantDifference(FoundRHS, RHS, RDiff) ||
8284       LDiff != RDiff)
8285     return false;
8286 
8287   if (LDiff == 0)
8288     return true;
8289 
8290   APInt FoundRHSLimit;
8291 
8292   if (Pred == CmpInst::ICMP_ULT) {
8293     FoundRHSLimit = -RDiff;
8294   } else {
8295     assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
8296     FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - RDiff;
8297   }
8298 
8299   // Try to prove (1) or (2), as needed.
8300   return isLoopEntryGuardedByCond(L, Pred, FoundRHS,
8301                                   getConstant(FoundRHSLimit));
8302 }
8303 
8304 /// isImpliedCondOperands - Test whether the condition described by Pred,
8305 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
8306 /// and FoundRHS is true.
8307 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
8308                                             const SCEV *LHS, const SCEV *RHS,
8309                                             const SCEV *FoundLHS,
8310                                             const SCEV *FoundRHS) {
8311   if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
8312     return true;
8313 
8314   if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
8315     return true;
8316 
8317   return isImpliedCondOperandsHelper(Pred, LHS, RHS,
8318                                      FoundLHS, FoundRHS) ||
8319          // ~x < ~y --> x > y
8320          isImpliedCondOperandsHelper(Pred, LHS, RHS,
8321                                      getNotSCEV(FoundRHS),
8322                                      getNotSCEV(FoundLHS));
8323 }
8324 
8325 
8326 /// If Expr computes ~A, return A else return nullptr
8327 static const SCEV *MatchNotExpr(const SCEV *Expr) {
8328   const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
8329   if (!Add || Add->getNumOperands() != 2 ||
8330       !Add->getOperand(0)->isAllOnesValue())
8331     return nullptr;
8332 
8333   const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
8334   if (!AddRHS || AddRHS->getNumOperands() != 2 ||
8335       !AddRHS->getOperand(0)->isAllOnesValue())
8336     return nullptr;
8337 
8338   return AddRHS->getOperand(1);
8339 }
8340 
8341 
8342 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
8343 template<typename MaxExprType>
8344 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
8345                               const SCEV *Candidate) {
8346   const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
8347   if (!MaxExpr) return false;
8348 
8349   return find(MaxExpr->operands(), Candidate) != MaxExpr->op_end();
8350 }
8351 
8352 
8353 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
8354 template<typename MaxExprType>
8355 static bool IsMinConsistingOf(ScalarEvolution &SE,
8356                               const SCEV *MaybeMinExpr,
8357                               const SCEV *Candidate) {
8358   const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
8359   if (!MaybeMaxExpr)
8360     return false;
8361 
8362   return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
8363 }
8364 
8365 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
8366                                            ICmpInst::Predicate Pred,
8367                                            const SCEV *LHS, const SCEV *RHS) {
8368 
8369   // If both sides are affine addrecs for the same loop, with equal
8370   // steps, and we know the recurrences don't wrap, then we only
8371   // need to check the predicate on the starting values.
8372 
8373   if (!ICmpInst::isRelational(Pred))
8374     return false;
8375 
8376   const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
8377   if (!LAR)
8378     return false;
8379   const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
8380   if (!RAR)
8381     return false;
8382   if (LAR->getLoop() != RAR->getLoop())
8383     return false;
8384   if (!LAR->isAffine() || !RAR->isAffine())
8385     return false;
8386 
8387   if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
8388     return false;
8389 
8390   SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
8391                          SCEV::FlagNSW : SCEV::FlagNUW;
8392   if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
8393     return false;
8394 
8395   return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
8396 }
8397 
8398 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
8399 /// expression?
8400 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
8401                                         ICmpInst::Predicate Pred,
8402                                         const SCEV *LHS, const SCEV *RHS) {
8403   switch (Pred) {
8404   default:
8405     return false;
8406 
8407   case ICmpInst::ICMP_SGE:
8408     std::swap(LHS, RHS);
8409     // fall through
8410   case ICmpInst::ICMP_SLE:
8411     return
8412       // min(A, ...) <= A
8413       IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
8414       // A <= max(A, ...)
8415       IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
8416 
8417   case ICmpInst::ICMP_UGE:
8418     std::swap(LHS, RHS);
8419     // fall through
8420   case ICmpInst::ICMP_ULE:
8421     return
8422       // min(A, ...) <= A
8423       IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
8424       // A <= max(A, ...)
8425       IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
8426   }
8427 
8428   llvm_unreachable("covered switch fell through?!");
8429 }
8430 
8431 /// isImpliedCondOperandsHelper - Test whether the condition described by
8432 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
8433 /// FoundLHS, and FoundRHS is true.
8434 bool
8435 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
8436                                              const SCEV *LHS, const SCEV *RHS,
8437                                              const SCEV *FoundLHS,
8438                                              const SCEV *FoundRHS) {
8439   auto IsKnownPredicateFull =
8440       [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
8441     return isKnownPredicateViaConstantRanges(Pred, LHS, RHS) ||
8442            IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
8443            IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
8444            isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
8445   };
8446 
8447   switch (Pred) {
8448   default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
8449   case ICmpInst::ICMP_EQ:
8450   case ICmpInst::ICMP_NE:
8451     if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
8452       return true;
8453     break;
8454   case ICmpInst::ICMP_SLT:
8455   case ICmpInst::ICMP_SLE:
8456     if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
8457         IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
8458       return true;
8459     break;
8460   case ICmpInst::ICMP_SGT:
8461   case ICmpInst::ICMP_SGE:
8462     if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
8463         IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
8464       return true;
8465     break;
8466   case ICmpInst::ICMP_ULT:
8467   case ICmpInst::ICMP_ULE:
8468     if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
8469         IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
8470       return true;
8471     break;
8472   case ICmpInst::ICMP_UGT:
8473   case ICmpInst::ICMP_UGE:
8474     if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
8475         IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
8476       return true;
8477     break;
8478   }
8479 
8480   return false;
8481 }
8482 
8483 /// isImpliedCondOperandsViaRanges - helper function for isImpliedCondOperands.
8484 /// Tries to get cases like "X `sgt` 0 => X - 1 `sgt` -1".
8485 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
8486                                                      const SCEV *LHS,
8487                                                      const SCEV *RHS,
8488                                                      const SCEV *FoundLHS,
8489                                                      const SCEV *FoundRHS) {
8490   if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
8491     // The restriction on `FoundRHS` be lifted easily -- it exists only to
8492     // reduce the compile time impact of this optimization.
8493     return false;
8494 
8495   const SCEVAddExpr *AddLHS = dyn_cast<SCEVAddExpr>(LHS);
8496   if (!AddLHS || AddLHS->getOperand(1) != FoundLHS ||
8497       !isa<SCEVConstant>(AddLHS->getOperand(0)))
8498     return false;
8499 
8500   APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getAPInt();
8501 
8502   // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
8503   // antecedent "`FoundLHS` `Pred` `FoundRHS`".
8504   ConstantRange FoundLHSRange =
8505       ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
8506 
8507   // Since `LHS` is `FoundLHS` + `AddLHS->getOperand(0)`, we can compute a range
8508   // for `LHS`:
8509   APInt Addend = cast<SCEVConstant>(AddLHS->getOperand(0))->getAPInt();
8510   ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(Addend));
8511 
8512   // We can also compute the range of values for `LHS` that satisfy the
8513   // consequent, "`LHS` `Pred` `RHS`":
8514   APInt ConstRHS = cast<SCEVConstant>(RHS)->getAPInt();
8515   ConstantRange SatisfyingLHSRange =
8516       ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
8517 
8518   // The antecedent implies the consequent if every value of `LHS` that
8519   // satisfies the antecedent also satisfies the consequent.
8520   return SatisfyingLHSRange.contains(LHSRange);
8521 }
8522 
8523 // Verify if an linear IV with positive stride can overflow when in a
8524 // less-than comparison, knowing the invariant term of the comparison, the
8525 // stride and the knowledge of NSW/NUW flags on the recurrence.
8526 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
8527                                          bool IsSigned, bool NoWrap) {
8528   if (NoWrap) return false;
8529 
8530   unsigned BitWidth = getTypeSizeInBits(RHS->getType());
8531   const SCEV *One = getOne(Stride->getType());
8532 
8533   if (IsSigned) {
8534     APInt MaxRHS = getSignedRange(RHS).getSignedMax();
8535     APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
8536     APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
8537                                 .getSignedMax();
8538 
8539     // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
8540     return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
8541   }
8542 
8543   APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
8544   APInt MaxValue = APInt::getMaxValue(BitWidth);
8545   APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
8546                               .getUnsignedMax();
8547 
8548   // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
8549   return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
8550 }
8551 
8552 // Verify if an linear IV with negative stride can overflow when in a
8553 // greater-than comparison, knowing the invariant term of the comparison,
8554 // the stride and the knowledge of NSW/NUW flags on the recurrence.
8555 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
8556                                          bool IsSigned, bool NoWrap) {
8557   if (NoWrap) return false;
8558 
8559   unsigned BitWidth = getTypeSizeInBits(RHS->getType());
8560   const SCEV *One = getOne(Stride->getType());
8561 
8562   if (IsSigned) {
8563     APInt MinRHS = getSignedRange(RHS).getSignedMin();
8564     APInt MinValue = APInt::getSignedMinValue(BitWidth);
8565     APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
8566                                .getSignedMax();
8567 
8568     // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
8569     return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
8570   }
8571 
8572   APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
8573   APInt MinValue = APInt::getMinValue(BitWidth);
8574   APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
8575                             .getUnsignedMax();
8576 
8577   // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
8578   return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
8579 }
8580 
8581 // Compute the backedge taken count knowing the interval difference, the
8582 // stride and presence of the equality in the comparison.
8583 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
8584                                             bool Equality) {
8585   const SCEV *One = getOne(Step->getType());
8586   Delta = Equality ? getAddExpr(Delta, Step)
8587                    : getAddExpr(Delta, getMinusSCEV(Step, One));
8588   return getUDivExpr(Delta, Step);
8589 }
8590 
8591 /// HowManyLessThans - Return the number of times a backedge containing the
8592 /// specified less-than comparison will execute.  If not computable, return
8593 /// CouldNotCompute.
8594 ///
8595 /// @param ControlsExit is true when the LHS < RHS condition directly controls
8596 /// the branch (loops exits only if condition is true). In this case, we can use
8597 /// NoWrapFlags to skip overflow checks.
8598 ScalarEvolution::ExitLimit
8599 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
8600                                   const Loop *L, bool IsSigned,
8601                                   bool ControlsExit, bool AllowPredicates) {
8602   SCEVUnionPredicate P;
8603   // We handle only IV < Invariant
8604   if (!isLoopInvariant(RHS, L))
8605     return getCouldNotCompute();
8606 
8607   const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8608   if (!IV && AllowPredicates)
8609     // Try to make this an AddRec using runtime tests, in the first X
8610     // iterations of this loop, where X is the SCEV expression found by the
8611     // algorithm below.
8612     IV = convertSCEVToAddRecWithPredicates(LHS, L, P);
8613 
8614   // Avoid weird loops
8615   if (!IV || IV->getLoop() != L || !IV->isAffine())
8616     return getCouldNotCompute();
8617 
8618   bool NoWrap = ControlsExit &&
8619                 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8620 
8621   const SCEV *Stride = IV->getStepRecurrence(*this);
8622 
8623   // Avoid negative or zero stride values
8624   if (!isKnownPositive(Stride))
8625     return getCouldNotCompute();
8626 
8627   // Avoid proven overflow cases: this will ensure that the backedge taken count
8628   // will not generate any unsigned overflow. Relaxed no-overflow conditions
8629   // exploit NoWrapFlags, allowing to optimize in presence of undefined
8630   // behaviors like the case of C language.
8631   if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
8632     return getCouldNotCompute();
8633 
8634   ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
8635                                       : ICmpInst::ICMP_ULT;
8636   const SCEV *Start = IV->getStart();
8637   const SCEV *End = RHS;
8638   if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
8639     const SCEV *Diff = getMinusSCEV(RHS, Start);
8640     // If we have NoWrap set, then we can assume that the increment won't
8641     // overflow, in which case if RHS - Start is a constant, we don't need to
8642     // do a max operation since we can just figure it out statically
8643     if (NoWrap && isa<SCEVConstant>(Diff)) {
8644       APInt D = dyn_cast<const SCEVConstant>(Diff)->getAPInt();
8645       if (D.isNegative())
8646         End = Start;
8647     } else
8648       End = IsSigned ? getSMaxExpr(RHS, Start)
8649                      : getUMaxExpr(RHS, Start);
8650   }
8651 
8652   const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
8653 
8654   APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
8655                             : getUnsignedRange(Start).getUnsignedMin();
8656 
8657   APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8658                              : getUnsignedRange(Stride).getUnsignedMin();
8659 
8660   unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8661   APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
8662                          : APInt::getMaxValue(BitWidth) - (MinStride - 1);
8663 
8664   // Although End can be a MAX expression we estimate MaxEnd considering only
8665   // the case End = RHS. This is safe because in the other case (End - Start)
8666   // is zero, leading to a zero maximum backedge taken count.
8667   APInt MaxEnd =
8668     IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
8669              : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
8670 
8671   const SCEV *MaxBECount;
8672   if (isa<SCEVConstant>(BECount))
8673     MaxBECount = BECount;
8674   else
8675     MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
8676                                 getConstant(MinStride), false);
8677 
8678   if (isa<SCEVCouldNotCompute>(MaxBECount))
8679     MaxBECount = BECount;
8680 
8681   return ExitLimit(BECount, MaxBECount, P);
8682 }
8683 
8684 ScalarEvolution::ExitLimit
8685 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
8686                                      const Loop *L, bool IsSigned,
8687                                      bool ControlsExit, bool AllowPredicates) {
8688   SCEVUnionPredicate P;
8689   // We handle only IV > Invariant
8690   if (!isLoopInvariant(RHS, L))
8691     return getCouldNotCompute();
8692 
8693   const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8694   if (!IV && AllowPredicates)
8695     // Try to make this an AddRec using runtime tests, in the first X
8696     // iterations of this loop, where X is the SCEV expression found by the
8697     // algorithm below.
8698     IV = convertSCEVToAddRecWithPredicates(LHS, L, P);
8699 
8700   // Avoid weird loops
8701   if (!IV || IV->getLoop() != L || !IV->isAffine())
8702     return getCouldNotCompute();
8703 
8704   bool NoWrap = ControlsExit &&
8705                 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8706 
8707   const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
8708 
8709   // Avoid negative or zero stride values
8710   if (!isKnownPositive(Stride))
8711     return getCouldNotCompute();
8712 
8713   // Avoid proven overflow cases: this will ensure that the backedge taken count
8714   // will not generate any unsigned overflow. Relaxed no-overflow conditions
8715   // exploit NoWrapFlags, allowing to optimize in presence of undefined
8716   // behaviors like the case of C language.
8717   if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
8718     return getCouldNotCompute();
8719 
8720   ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
8721                                       : ICmpInst::ICMP_UGT;
8722 
8723   const SCEV *Start = IV->getStart();
8724   const SCEV *End = RHS;
8725   if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
8726     const SCEV *Diff = getMinusSCEV(RHS, Start);
8727     // If we have NoWrap set, then we can assume that the increment won't
8728     // overflow, in which case if RHS - Start is a constant, we don't need to
8729     // do a max operation since we can just figure it out statically
8730     if (NoWrap && isa<SCEVConstant>(Diff)) {
8731       APInt D = dyn_cast<const SCEVConstant>(Diff)->getAPInt();
8732       if (!D.isNegative())
8733         End = Start;
8734     } else
8735       End = IsSigned ? getSMinExpr(RHS, Start)
8736                      : getUMinExpr(RHS, Start);
8737   }
8738 
8739   const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
8740 
8741   APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
8742                             : getUnsignedRange(Start).getUnsignedMax();
8743 
8744   APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8745                              : getUnsignedRange(Stride).getUnsignedMin();
8746 
8747   unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8748   APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
8749                          : APInt::getMinValue(BitWidth) + (MinStride - 1);
8750 
8751   // Although End can be a MIN expression we estimate MinEnd considering only
8752   // the case End = RHS. This is safe because in the other case (Start - End)
8753   // is zero, leading to a zero maximum backedge taken count.
8754   APInt MinEnd =
8755     IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
8756              : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
8757 
8758 
8759   const SCEV *MaxBECount = getCouldNotCompute();
8760   if (isa<SCEVConstant>(BECount))
8761     MaxBECount = BECount;
8762   else
8763     MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
8764                                 getConstant(MinStride), false);
8765 
8766   if (isa<SCEVCouldNotCompute>(MaxBECount))
8767     MaxBECount = BECount;
8768 
8769   return ExitLimit(BECount, MaxBECount, P);
8770 }
8771 
8772 /// getNumIterationsInRange - Return the number of iterations of this loop that
8773 /// produce values in the specified constant range.  Another way of looking at
8774 /// this is that it returns the first iteration number where the value is not in
8775 /// the condition, thus computing the exit count. If the iteration count can't
8776 /// be computed, an instance of SCEVCouldNotCompute is returned.
8777 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
8778                                                     ScalarEvolution &SE) const {
8779   if (Range.isFullSet())  // Infinite loop.
8780     return SE.getCouldNotCompute();
8781 
8782   // If the start is a non-zero constant, shift the range to simplify things.
8783   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
8784     if (!SC->getValue()->isZero()) {
8785       SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
8786       Operands[0] = SE.getZero(SC->getType());
8787       const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
8788                                              getNoWrapFlags(FlagNW));
8789       if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
8790         return ShiftedAddRec->getNumIterationsInRange(
8791             Range.subtract(SC->getAPInt()), SE);
8792       // This is strange and shouldn't happen.
8793       return SE.getCouldNotCompute();
8794     }
8795 
8796   // The only time we can solve this is when we have all constant indices.
8797   // Otherwise, we cannot determine the overflow conditions.
8798   if (any_of(operands(), [](const SCEV *Op) { return !isa<SCEVConstant>(Op); }))
8799     return SE.getCouldNotCompute();
8800 
8801   // Okay at this point we know that all elements of the chrec are constants and
8802   // that the start element is zero.
8803 
8804   // First check to see if the range contains zero.  If not, the first
8805   // iteration exits.
8806   unsigned BitWidth = SE.getTypeSizeInBits(getType());
8807   if (!Range.contains(APInt(BitWidth, 0)))
8808     return SE.getZero(getType());
8809 
8810   if (isAffine()) {
8811     // If this is an affine expression then we have this situation:
8812     //   Solve {0,+,A} in Range  ===  Ax in Range
8813 
8814     // We know that zero is in the range.  If A is positive then we know that
8815     // the upper value of the range must be the first possible exit value.
8816     // If A is negative then the lower of the range is the last possible loop
8817     // value.  Also note that we already checked for a full range.
8818     APInt One(BitWidth,1);
8819     APInt A = cast<SCEVConstant>(getOperand(1))->getAPInt();
8820     APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
8821 
8822     // The exit value should be (End+A)/A.
8823     APInt ExitVal = (End + A).udiv(A);
8824     ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
8825 
8826     // Evaluate at the exit value.  If we really did fall out of the valid
8827     // range, then we computed our trip count, otherwise wrap around or other
8828     // things must have happened.
8829     ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
8830     if (Range.contains(Val->getValue()))
8831       return SE.getCouldNotCompute();  // Something strange happened
8832 
8833     // Ensure that the previous value is in the range.  This is a sanity check.
8834     assert(Range.contains(
8835            EvaluateConstantChrecAtConstant(this,
8836            ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
8837            "Linear scev computation is off in a bad way!");
8838     return SE.getConstant(ExitValue);
8839   } else if (isQuadratic()) {
8840     // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
8841     // quadratic equation to solve it.  To do this, we must frame our problem in
8842     // terms of figuring out when zero is crossed, instead of when
8843     // Range.getUpper() is crossed.
8844     SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
8845     NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
8846     const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
8847                                              // getNoWrapFlags(FlagNW)
8848                                              FlagAnyWrap);
8849 
8850     // Next, solve the constructed addrec
8851     auto Roots = SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
8852     const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
8853     const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
8854     if (R1) {
8855       // Pick the smallest positive root value.
8856       if (ConstantInt *CB = dyn_cast<ConstantInt>(ConstantExpr::getICmp(
8857               ICmpInst::ICMP_ULT, R1->getValue(), R2->getValue()))) {
8858         if (!CB->getZExtValue())
8859           std::swap(R1, R2);   // R1 is the minimum root now.
8860 
8861         // Make sure the root is not off by one.  The returned iteration should
8862         // not be in the range, but the previous one should be.  When solving
8863         // for "X*X < 5", for example, we should not return a root of 2.
8864         ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
8865                                                              R1->getValue(),
8866                                                              SE);
8867         if (Range.contains(R1Val->getValue())) {
8868           // The next iteration must be out of the range...
8869           ConstantInt *NextVal =
8870               ConstantInt::get(SE.getContext(), R1->getAPInt() + 1);
8871 
8872           R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8873           if (!Range.contains(R1Val->getValue()))
8874             return SE.getConstant(NextVal);
8875           return SE.getCouldNotCompute();  // Something strange happened
8876         }
8877 
8878         // If R1 was not in the range, then it is a good return value.  Make
8879         // sure that R1-1 WAS in the range though, just in case.
8880         ConstantInt *NextVal =
8881             ConstantInt::get(SE.getContext(), R1->getAPInt() - 1);
8882         R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8883         if (Range.contains(R1Val->getValue()))
8884           return R1;
8885         return SE.getCouldNotCompute();  // Something strange happened
8886       }
8887     }
8888   }
8889 
8890   return SE.getCouldNotCompute();
8891 }
8892 
8893 namespace {
8894 struct FindUndefs {
8895   bool Found;
8896   FindUndefs() : Found(false) {}
8897 
8898   bool follow(const SCEV *S) {
8899     if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
8900       if (isa<UndefValue>(C->getValue()))
8901         Found = true;
8902     } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
8903       if (isa<UndefValue>(C->getValue()))
8904         Found = true;
8905     }
8906 
8907     // Keep looking if we haven't found it yet.
8908     return !Found;
8909   }
8910   bool isDone() const {
8911     // Stop recursion if we have found an undef.
8912     return Found;
8913   }
8914 };
8915 }
8916 
8917 // Return true when S contains at least an undef value.
8918 static inline bool
8919 containsUndefs(const SCEV *S) {
8920   FindUndefs F;
8921   SCEVTraversal<FindUndefs> ST(F);
8922   ST.visitAll(S);
8923 
8924   return F.Found;
8925 }
8926 
8927 namespace {
8928 // Collect all steps of SCEV expressions.
8929 struct SCEVCollectStrides {
8930   ScalarEvolution &SE;
8931   SmallVectorImpl<const SCEV *> &Strides;
8932 
8933   SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
8934       : SE(SE), Strides(S) {}
8935 
8936   bool follow(const SCEV *S) {
8937     if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
8938       Strides.push_back(AR->getStepRecurrence(SE));
8939     return true;
8940   }
8941   bool isDone() const { return false; }
8942 };
8943 
8944 // Collect all SCEVUnknown and SCEVMulExpr expressions.
8945 struct SCEVCollectTerms {
8946   SmallVectorImpl<const SCEV *> &Terms;
8947 
8948   SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
8949       : Terms(T) {}
8950 
8951   bool follow(const SCEV *S) {
8952     if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
8953       if (!containsUndefs(S))
8954         Terms.push_back(S);
8955 
8956       // Stop recursion: once we collected a term, do not walk its operands.
8957       return false;
8958     }
8959 
8960     // Keep looking.
8961     return true;
8962   }
8963   bool isDone() const { return false; }
8964 };
8965 
8966 // Check if a SCEV contains an AddRecExpr.
8967 struct SCEVHasAddRec {
8968   bool &ContainsAddRec;
8969 
8970   SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) {
8971    ContainsAddRec = false;
8972   }
8973 
8974   bool follow(const SCEV *S) {
8975     if (isa<SCEVAddRecExpr>(S)) {
8976       ContainsAddRec = true;
8977 
8978       // Stop recursion: once we collected a term, do not walk its operands.
8979       return false;
8980     }
8981 
8982     // Keep looking.
8983     return true;
8984   }
8985   bool isDone() const { return false; }
8986 };
8987 
8988 // Find factors that are multiplied with an expression that (possibly as a
8989 // subexpression) contains an AddRecExpr. In the expression:
8990 //
8991 //  8 * (100 +  %p * %q * (%a + {0, +, 1}_loop))
8992 //
8993 // "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)"
8994 // that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size
8995 // parameters as they form a product with an induction variable.
8996 //
8997 // This collector expects all array size parameters to be in the same MulExpr.
8998 // It might be necessary to later add support for collecting parameters that are
8999 // spread over different nested MulExpr.
9000 struct SCEVCollectAddRecMultiplies {
9001   SmallVectorImpl<const SCEV *> &Terms;
9002   ScalarEvolution &SE;
9003 
9004   SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE)
9005       : Terms(T), SE(SE) {}
9006 
9007   bool follow(const SCEV *S) {
9008     if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) {
9009       bool HasAddRec = false;
9010       SmallVector<const SCEV *, 0> Operands;
9011       for (auto Op : Mul->operands()) {
9012         if (isa<SCEVUnknown>(Op)) {
9013           Operands.push_back(Op);
9014         } else {
9015           bool ContainsAddRec;
9016           SCEVHasAddRec ContiansAddRec(ContainsAddRec);
9017           visitAll(Op, ContiansAddRec);
9018           HasAddRec |= ContainsAddRec;
9019         }
9020       }
9021       if (Operands.size() == 0)
9022         return true;
9023 
9024       if (!HasAddRec)
9025         return false;
9026 
9027       Terms.push_back(SE.getMulExpr(Operands));
9028       // Stop recursion: once we collected a term, do not walk its operands.
9029       return false;
9030     }
9031 
9032     // Keep looking.
9033     return true;
9034   }
9035   bool isDone() const { return false; }
9036 };
9037 }
9038 
9039 /// Find parametric terms in this SCEVAddRecExpr. We first for parameters in
9040 /// two places:
9041 ///   1) The strides of AddRec expressions.
9042 ///   2) Unknowns that are multiplied with AddRec expressions.
9043 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
9044     SmallVectorImpl<const SCEV *> &Terms) {
9045   SmallVector<const SCEV *, 4> Strides;
9046   SCEVCollectStrides StrideCollector(*this, Strides);
9047   visitAll(Expr, StrideCollector);
9048 
9049   DEBUG({
9050       dbgs() << "Strides:\n";
9051       for (const SCEV *S : Strides)
9052         dbgs() << *S << "\n";
9053     });
9054 
9055   for (const SCEV *S : Strides) {
9056     SCEVCollectTerms TermCollector(Terms);
9057     visitAll(S, TermCollector);
9058   }
9059 
9060   DEBUG({
9061       dbgs() << "Terms:\n";
9062       for (const SCEV *T : Terms)
9063         dbgs() << *T << "\n";
9064     });
9065 
9066   SCEVCollectAddRecMultiplies MulCollector(Terms, *this);
9067   visitAll(Expr, MulCollector);
9068 }
9069 
9070 static bool findArrayDimensionsRec(ScalarEvolution &SE,
9071                                    SmallVectorImpl<const SCEV *> &Terms,
9072                                    SmallVectorImpl<const SCEV *> &Sizes) {
9073   int Last = Terms.size() - 1;
9074   const SCEV *Step = Terms[Last];
9075 
9076   // End of recursion.
9077   if (Last == 0) {
9078     if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
9079       SmallVector<const SCEV *, 2> Qs;
9080       for (const SCEV *Op : M->operands())
9081         if (!isa<SCEVConstant>(Op))
9082           Qs.push_back(Op);
9083 
9084       Step = SE.getMulExpr(Qs);
9085     }
9086 
9087     Sizes.push_back(Step);
9088     return true;
9089   }
9090 
9091   for (const SCEV *&Term : Terms) {
9092     // Normalize the terms before the next call to findArrayDimensionsRec.
9093     const SCEV *Q, *R;
9094     SCEVDivision::divide(SE, Term, Step, &Q, &R);
9095 
9096     // Bail out when GCD does not evenly divide one of the terms.
9097     if (!R->isZero())
9098       return false;
9099 
9100     Term = Q;
9101   }
9102 
9103   // Remove all SCEVConstants.
9104   Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
9105                 return isa<SCEVConstant>(E);
9106               }),
9107               Terms.end());
9108 
9109   if (Terms.size() > 0)
9110     if (!findArrayDimensionsRec(SE, Terms, Sizes))
9111       return false;
9112 
9113   Sizes.push_back(Step);
9114   return true;
9115 }
9116 
9117 // Returns true when S contains at least a SCEVUnknown parameter.
9118 static inline bool
9119 containsParameters(const SCEV *S) {
9120   struct FindParameter {
9121     bool FoundParameter;
9122     FindParameter() : FoundParameter(false) {}
9123 
9124     bool follow(const SCEV *S) {
9125       if (isa<SCEVUnknown>(S)) {
9126         FoundParameter = true;
9127         // Stop recursion: we found a parameter.
9128         return false;
9129       }
9130       // Keep looking.
9131       return true;
9132     }
9133     bool isDone() const {
9134       // Stop recursion if we have found a parameter.
9135       return FoundParameter;
9136     }
9137   };
9138 
9139   FindParameter F;
9140   SCEVTraversal<FindParameter> ST(F);
9141   ST.visitAll(S);
9142 
9143   return F.FoundParameter;
9144 }
9145 
9146 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
9147 static inline bool
9148 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
9149   for (const SCEV *T : Terms)
9150     if (containsParameters(T))
9151       return true;
9152   return false;
9153 }
9154 
9155 // Return the number of product terms in S.
9156 static inline int numberOfTerms(const SCEV *S) {
9157   if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
9158     return Expr->getNumOperands();
9159   return 1;
9160 }
9161 
9162 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
9163   if (isa<SCEVConstant>(T))
9164     return nullptr;
9165 
9166   if (isa<SCEVUnknown>(T))
9167     return T;
9168 
9169   if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
9170     SmallVector<const SCEV *, 2> Factors;
9171     for (const SCEV *Op : M->operands())
9172       if (!isa<SCEVConstant>(Op))
9173         Factors.push_back(Op);
9174 
9175     return SE.getMulExpr(Factors);
9176   }
9177 
9178   return T;
9179 }
9180 
9181 /// Return the size of an element read or written by Inst.
9182 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
9183   Type *Ty;
9184   if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
9185     Ty = Store->getValueOperand()->getType();
9186   else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
9187     Ty = Load->getType();
9188   else
9189     return nullptr;
9190 
9191   Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
9192   return getSizeOfExpr(ETy, Ty);
9193 }
9194 
9195 /// Second step of delinearization: compute the array dimensions Sizes from the
9196 /// set of Terms extracted from the memory access function of this SCEVAddRec.
9197 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
9198                                           SmallVectorImpl<const SCEV *> &Sizes,
9199                                           const SCEV *ElementSize) const {
9200 
9201   if (Terms.size() < 1 || !ElementSize)
9202     return;
9203 
9204   // Early return when Terms do not contain parameters: we do not delinearize
9205   // non parametric SCEVs.
9206   if (!containsParameters(Terms))
9207     return;
9208 
9209   DEBUG({
9210       dbgs() << "Terms:\n";
9211       for (const SCEV *T : Terms)
9212         dbgs() << *T << "\n";
9213     });
9214 
9215   // Remove duplicates.
9216   std::sort(Terms.begin(), Terms.end());
9217   Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
9218 
9219   // Put larger terms first.
9220   std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
9221     return numberOfTerms(LHS) > numberOfTerms(RHS);
9222   });
9223 
9224   ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9225 
9226   // Try to divide all terms by the element size. If term is not divisible by
9227   // element size, proceed with the original term.
9228   for (const SCEV *&Term : Terms) {
9229     const SCEV *Q, *R;
9230     SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
9231     if (!Q->isZero())
9232       Term = Q;
9233   }
9234 
9235   SmallVector<const SCEV *, 4> NewTerms;
9236 
9237   // Remove constant factors.
9238   for (const SCEV *T : Terms)
9239     if (const SCEV *NewT = removeConstantFactors(SE, T))
9240       NewTerms.push_back(NewT);
9241 
9242   DEBUG({
9243       dbgs() << "Terms after sorting:\n";
9244       for (const SCEV *T : NewTerms)
9245         dbgs() << *T << "\n";
9246     });
9247 
9248   if (NewTerms.empty() ||
9249       !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
9250     Sizes.clear();
9251     return;
9252   }
9253 
9254   // The last element to be pushed into Sizes is the size of an element.
9255   Sizes.push_back(ElementSize);
9256 
9257   DEBUG({
9258       dbgs() << "Sizes:\n";
9259       for (const SCEV *S : Sizes)
9260         dbgs() << *S << "\n";
9261     });
9262 }
9263 
9264 /// Third step of delinearization: compute the access functions for the
9265 /// Subscripts based on the dimensions in Sizes.
9266 void ScalarEvolution::computeAccessFunctions(
9267     const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
9268     SmallVectorImpl<const SCEV *> &Sizes) {
9269 
9270   // Early exit in case this SCEV is not an affine multivariate function.
9271   if (Sizes.empty())
9272     return;
9273 
9274   if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr))
9275     if (!AR->isAffine())
9276       return;
9277 
9278   const SCEV *Res = Expr;
9279   int Last = Sizes.size() - 1;
9280   for (int i = Last; i >= 0; i--) {
9281     const SCEV *Q, *R;
9282     SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
9283 
9284     DEBUG({
9285         dbgs() << "Res: " << *Res << "\n";
9286         dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
9287         dbgs() << "Res divided by Sizes[i]:\n";
9288         dbgs() << "Quotient: " << *Q << "\n";
9289         dbgs() << "Remainder: " << *R << "\n";
9290       });
9291 
9292     Res = Q;
9293 
9294     // Do not record the last subscript corresponding to the size of elements in
9295     // the array.
9296     if (i == Last) {
9297 
9298       // Bail out if the remainder is too complex.
9299       if (isa<SCEVAddRecExpr>(R)) {
9300         Subscripts.clear();
9301         Sizes.clear();
9302         return;
9303       }
9304 
9305       continue;
9306     }
9307 
9308     // Record the access function for the current subscript.
9309     Subscripts.push_back(R);
9310   }
9311 
9312   // Also push in last position the remainder of the last division: it will be
9313   // the access function of the innermost dimension.
9314   Subscripts.push_back(Res);
9315 
9316   std::reverse(Subscripts.begin(), Subscripts.end());
9317 
9318   DEBUG({
9319       dbgs() << "Subscripts:\n";
9320       for (const SCEV *S : Subscripts)
9321         dbgs() << *S << "\n";
9322     });
9323 }
9324 
9325 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
9326 /// sizes of an array access. Returns the remainder of the delinearization that
9327 /// is the offset start of the array.  The SCEV->delinearize algorithm computes
9328 /// the multiples of SCEV coefficients: that is a pattern matching of sub
9329 /// expressions in the stride and base of a SCEV corresponding to the
9330 /// computation of a GCD (greatest common divisor) of base and stride.  When
9331 /// SCEV->delinearize fails, it returns the SCEV unchanged.
9332 ///
9333 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
9334 ///
9335 ///  void foo(long n, long m, long o, double A[n][m][o]) {
9336 ///
9337 ///    for (long i = 0; i < n; i++)
9338 ///      for (long j = 0; j < m; j++)
9339 ///        for (long k = 0; k < o; k++)
9340 ///          A[i][j][k] = 1.0;
9341 ///  }
9342 ///
9343 /// the delinearization input is the following AddRec SCEV:
9344 ///
9345 ///  AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
9346 ///
9347 /// From this SCEV, we are able to say that the base offset of the access is %A
9348 /// because it appears as an offset that does not divide any of the strides in
9349 /// the loops:
9350 ///
9351 ///  CHECK: Base offset: %A
9352 ///
9353 /// and then SCEV->delinearize determines the size of some of the dimensions of
9354 /// the array as these are the multiples by which the strides are happening:
9355 ///
9356 ///  CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
9357 ///
9358 /// Note that the outermost dimension remains of UnknownSize because there are
9359 /// no strides that would help identifying the size of the last dimension: when
9360 /// the array has been statically allocated, one could compute the size of that
9361 /// dimension by dividing the overall size of the array by the size of the known
9362 /// dimensions: %m * %o * 8.
9363 ///
9364 /// Finally delinearize provides the access functions for the array reference
9365 /// that does correspond to A[i][j][k] of the above C testcase:
9366 ///
9367 ///  CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
9368 ///
9369 /// The testcases are checking the output of a function pass:
9370 /// DelinearizationPass that walks through all loads and stores of a function
9371 /// asking for the SCEV of the memory access with respect to all enclosing
9372 /// loops, calling SCEV->delinearize on that and printing the results.
9373 
9374 void ScalarEvolution::delinearize(const SCEV *Expr,
9375                                  SmallVectorImpl<const SCEV *> &Subscripts,
9376                                  SmallVectorImpl<const SCEV *> &Sizes,
9377                                  const SCEV *ElementSize) {
9378   // First step: collect parametric terms.
9379   SmallVector<const SCEV *, 4> Terms;
9380   collectParametricTerms(Expr, Terms);
9381 
9382   if (Terms.empty())
9383     return;
9384 
9385   // Second step: find subscript sizes.
9386   findArrayDimensions(Terms, Sizes, ElementSize);
9387 
9388   if (Sizes.empty())
9389     return;
9390 
9391   // Third step: compute the access functions for each subscript.
9392   computeAccessFunctions(Expr, Subscripts, Sizes);
9393 
9394   if (Subscripts.empty())
9395     return;
9396 
9397   DEBUG({
9398       dbgs() << "succeeded to delinearize " << *Expr << "\n";
9399       dbgs() << "ArrayDecl[UnknownSize]";
9400       for (const SCEV *S : Sizes)
9401         dbgs() << "[" << *S << "]";
9402 
9403       dbgs() << "\nArrayRef";
9404       for (const SCEV *S : Subscripts)
9405         dbgs() << "[" << *S << "]";
9406       dbgs() << "\n";
9407     });
9408 }
9409 
9410 //===----------------------------------------------------------------------===//
9411 //                   SCEVCallbackVH Class Implementation
9412 //===----------------------------------------------------------------------===//
9413 
9414 void ScalarEvolution::SCEVCallbackVH::deleted() {
9415   assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
9416   if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
9417     SE->ConstantEvolutionLoopExitValue.erase(PN);
9418   SE->eraseValueFromMap(getValPtr());
9419   // this now dangles!
9420 }
9421 
9422 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
9423   assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
9424 
9425   // Forget all the expressions associated with users of the old value,
9426   // so that future queries will recompute the expressions using the new
9427   // value.
9428   Value *Old = getValPtr();
9429   SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
9430   SmallPtrSet<User *, 8> Visited;
9431   while (!Worklist.empty()) {
9432     User *U = Worklist.pop_back_val();
9433     // Deleting the Old value will cause this to dangle. Postpone
9434     // that until everything else is done.
9435     if (U == Old)
9436       continue;
9437     if (!Visited.insert(U).second)
9438       continue;
9439     if (PHINode *PN = dyn_cast<PHINode>(U))
9440       SE->ConstantEvolutionLoopExitValue.erase(PN);
9441     SE->eraseValueFromMap(U);
9442     Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
9443   }
9444   // Delete the Old value.
9445   if (PHINode *PN = dyn_cast<PHINode>(Old))
9446     SE->ConstantEvolutionLoopExitValue.erase(PN);
9447   SE->eraseValueFromMap(Old);
9448   // this now dangles!
9449 }
9450 
9451 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
9452   : CallbackVH(V), SE(se) {}
9453 
9454 //===----------------------------------------------------------------------===//
9455 //                   ScalarEvolution Class Implementation
9456 //===----------------------------------------------------------------------===//
9457 
9458 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
9459                                  AssumptionCache &AC, DominatorTree &DT,
9460                                  LoopInfo &LI)
9461     : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
9462       CouldNotCompute(new SCEVCouldNotCompute()),
9463       WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
9464       ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64),
9465       FirstUnknown(nullptr) {}
9466 
9467 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
9468     : F(Arg.F), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT), LI(Arg.LI),
9469       CouldNotCompute(std::move(Arg.CouldNotCompute)),
9470       ValueExprMap(std::move(Arg.ValueExprMap)),
9471       WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
9472       BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
9473       PredicatedBackedgeTakenCounts(
9474           std::move(Arg.PredicatedBackedgeTakenCounts)),
9475       ConstantEvolutionLoopExitValue(
9476           std::move(Arg.ConstantEvolutionLoopExitValue)),
9477       ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
9478       LoopDispositions(std::move(Arg.LoopDispositions)),
9479       BlockDispositions(std::move(Arg.BlockDispositions)),
9480       UnsignedRanges(std::move(Arg.UnsignedRanges)),
9481       SignedRanges(std::move(Arg.SignedRanges)),
9482       UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
9483       UniquePreds(std::move(Arg.UniquePreds)),
9484       SCEVAllocator(std::move(Arg.SCEVAllocator)),
9485       FirstUnknown(Arg.FirstUnknown) {
9486   Arg.FirstUnknown = nullptr;
9487 }
9488 
9489 ScalarEvolution::~ScalarEvolution() {
9490   // Iterate through all the SCEVUnknown instances and call their
9491   // destructors, so that they release their references to their values.
9492   for (SCEVUnknown *U = FirstUnknown; U;) {
9493     SCEVUnknown *Tmp = U;
9494     U = U->Next;
9495     Tmp->~SCEVUnknown();
9496   }
9497   FirstUnknown = nullptr;
9498 
9499   ExprValueMap.clear();
9500   ValueExprMap.clear();
9501   HasRecMap.clear();
9502 
9503   // Free any extra memory created for ExitNotTakenInfo in the unlikely event
9504   // that a loop had multiple computable exits.
9505   for (auto &BTCI : BackedgeTakenCounts)
9506     BTCI.second.clear();
9507   for (auto &BTCI : PredicatedBackedgeTakenCounts)
9508     BTCI.second.clear();
9509 
9510   assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
9511   assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
9512   assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
9513 }
9514 
9515 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
9516   return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
9517 }
9518 
9519 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
9520                           const Loop *L) {
9521   // Print all inner loops first
9522   for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
9523     PrintLoopInfo(OS, SE, *I);
9524 
9525   OS << "Loop ";
9526   L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9527   OS << ": ";
9528 
9529   SmallVector<BasicBlock *, 8> ExitBlocks;
9530   L->getExitBlocks(ExitBlocks);
9531   if (ExitBlocks.size() != 1)
9532     OS << "<multiple exits> ";
9533 
9534   if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
9535     OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
9536   } else {
9537     OS << "Unpredictable backedge-taken count. ";
9538   }
9539 
9540   OS << "\n"
9541         "Loop ";
9542   L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9543   OS << ": ";
9544 
9545   if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
9546     OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
9547   } else {
9548     OS << "Unpredictable max backedge-taken count. ";
9549   }
9550 
9551   OS << "\n"
9552         "Loop ";
9553   L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9554   OS << ": ";
9555 
9556   SCEVUnionPredicate Pred;
9557   auto PBT = SE->getPredicatedBackedgeTakenCount(L, Pred);
9558   if (!isa<SCEVCouldNotCompute>(PBT)) {
9559     OS << "Predicated backedge-taken count is " << *PBT << "\n";
9560     OS << " Predicates:\n";
9561     Pred.print(OS, 4);
9562   } else {
9563     OS << "Unpredictable predicated backedge-taken count. ";
9564   }
9565   OS << "\n";
9566 }
9567 
9568 static StringRef loopDispositionToStr(ScalarEvolution::LoopDisposition LD) {
9569   switch (LD) {
9570   case ScalarEvolution::LoopVariant:
9571     return "Variant";
9572   case ScalarEvolution::LoopInvariant:
9573     return "Invariant";
9574   case ScalarEvolution::LoopComputable:
9575     return "Computable";
9576   }
9577   llvm_unreachable("Unknown ScalarEvolution::LoopDisposition kind!");
9578 }
9579 
9580 void ScalarEvolution::print(raw_ostream &OS) const {
9581   // ScalarEvolution's implementation of the print method is to print
9582   // out SCEV values of all instructions that are interesting. Doing
9583   // this potentially causes it to create new SCEV objects though,
9584   // which technically conflicts with the const qualifier. This isn't
9585   // observable from outside the class though, so casting away the
9586   // const isn't dangerous.
9587   ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9588 
9589   OS << "Classifying expressions for: ";
9590   F.printAsOperand(OS, /*PrintType=*/false);
9591   OS << "\n";
9592   for (Instruction &I : instructions(F))
9593     if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) {
9594       OS << I << '\n';
9595       OS << "  -->  ";
9596       const SCEV *SV = SE.getSCEV(&I);
9597       SV->print(OS);
9598       if (!isa<SCEVCouldNotCompute>(SV)) {
9599         OS << " U: ";
9600         SE.getUnsignedRange(SV).print(OS);
9601         OS << " S: ";
9602         SE.getSignedRange(SV).print(OS);
9603       }
9604 
9605       const Loop *L = LI.getLoopFor(I.getParent());
9606 
9607       const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
9608       if (AtUse != SV) {
9609         OS << "  -->  ";
9610         AtUse->print(OS);
9611         if (!isa<SCEVCouldNotCompute>(AtUse)) {
9612           OS << " U: ";
9613           SE.getUnsignedRange(AtUse).print(OS);
9614           OS << " S: ";
9615           SE.getSignedRange(AtUse).print(OS);
9616         }
9617       }
9618 
9619       if (L) {
9620         OS << "\t\t" "Exits: ";
9621         const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
9622         if (!SE.isLoopInvariant(ExitValue, L)) {
9623           OS << "<<Unknown>>";
9624         } else {
9625           OS << *ExitValue;
9626         }
9627 
9628         bool First = true;
9629         for (auto *Iter = L; Iter; Iter = Iter->getParentLoop()) {
9630           if (First) {
9631             OS << "\t\t" "LoopDispositions: { ";
9632             First = false;
9633           } else {
9634             OS << ", ";
9635           }
9636 
9637           Iter->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9638           OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, Iter));
9639         }
9640 
9641         for (auto *InnerL : depth_first(L)) {
9642           if (InnerL == L)
9643             continue;
9644           if (First) {
9645             OS << "\t\t" "LoopDispositions: { ";
9646             First = false;
9647           } else {
9648             OS << ", ";
9649           }
9650 
9651           InnerL->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9652           OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, InnerL));
9653         }
9654 
9655         OS << " }";
9656       }
9657 
9658       OS << "\n";
9659     }
9660 
9661   OS << "Determining loop execution counts for: ";
9662   F.printAsOperand(OS, /*PrintType=*/false);
9663   OS << "\n";
9664   for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
9665     PrintLoopInfo(OS, &SE, *I);
9666 }
9667 
9668 ScalarEvolution::LoopDisposition
9669 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
9670   auto &Values = LoopDispositions[S];
9671   for (auto &V : Values) {
9672     if (V.getPointer() == L)
9673       return V.getInt();
9674   }
9675   Values.emplace_back(L, LoopVariant);
9676   LoopDisposition D = computeLoopDisposition(S, L);
9677   auto &Values2 = LoopDispositions[S];
9678   for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9679     if (V.getPointer() == L) {
9680       V.setInt(D);
9681       break;
9682     }
9683   }
9684   return D;
9685 }
9686 
9687 ScalarEvolution::LoopDisposition
9688 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
9689   switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9690   case scConstant:
9691     return LoopInvariant;
9692   case scTruncate:
9693   case scZeroExtend:
9694   case scSignExtend:
9695     return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
9696   case scAddRecExpr: {
9697     const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9698 
9699     // If L is the addrec's loop, it's computable.
9700     if (AR->getLoop() == L)
9701       return LoopComputable;
9702 
9703     // Add recurrences are never invariant in the function-body (null loop).
9704     if (!L)
9705       return LoopVariant;
9706 
9707     // This recurrence is variant w.r.t. L if L contains AR's loop.
9708     if (L->contains(AR->getLoop()))
9709       return LoopVariant;
9710 
9711     // This recurrence is invariant w.r.t. L if AR's loop contains L.
9712     if (AR->getLoop()->contains(L))
9713       return LoopInvariant;
9714 
9715     // This recurrence is variant w.r.t. L if any of its operands
9716     // are variant.
9717     for (auto *Op : AR->operands())
9718       if (!isLoopInvariant(Op, L))
9719         return LoopVariant;
9720 
9721     // Otherwise it's loop-invariant.
9722     return LoopInvariant;
9723   }
9724   case scAddExpr:
9725   case scMulExpr:
9726   case scUMaxExpr:
9727   case scSMaxExpr: {
9728     bool HasVarying = false;
9729     for (auto *Op : cast<SCEVNAryExpr>(S)->operands()) {
9730       LoopDisposition D = getLoopDisposition(Op, L);
9731       if (D == LoopVariant)
9732         return LoopVariant;
9733       if (D == LoopComputable)
9734         HasVarying = true;
9735     }
9736     return HasVarying ? LoopComputable : LoopInvariant;
9737   }
9738   case scUDivExpr: {
9739     const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9740     LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
9741     if (LD == LoopVariant)
9742       return LoopVariant;
9743     LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
9744     if (RD == LoopVariant)
9745       return LoopVariant;
9746     return (LD == LoopInvariant && RD == LoopInvariant) ?
9747            LoopInvariant : LoopComputable;
9748   }
9749   case scUnknown:
9750     // All non-instruction values are loop invariant.  All instructions are loop
9751     // invariant if they are not contained in the specified loop.
9752     // Instructions are never considered invariant in the function body
9753     // (null loop) because they are defined within the "loop".
9754     if (auto *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
9755       return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
9756     return LoopInvariant;
9757   case scCouldNotCompute:
9758     llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9759   }
9760   llvm_unreachable("Unknown SCEV kind!");
9761 }
9762 
9763 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
9764   return getLoopDisposition(S, L) == LoopInvariant;
9765 }
9766 
9767 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
9768   return getLoopDisposition(S, L) == LoopComputable;
9769 }
9770 
9771 ScalarEvolution::BlockDisposition
9772 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9773   auto &Values = BlockDispositions[S];
9774   for (auto &V : Values) {
9775     if (V.getPointer() == BB)
9776       return V.getInt();
9777   }
9778   Values.emplace_back(BB, DoesNotDominateBlock);
9779   BlockDisposition D = computeBlockDisposition(S, BB);
9780   auto &Values2 = BlockDispositions[S];
9781   for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9782     if (V.getPointer() == BB) {
9783       V.setInt(D);
9784       break;
9785     }
9786   }
9787   return D;
9788 }
9789 
9790 ScalarEvolution::BlockDisposition
9791 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9792   switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9793   case scConstant:
9794     return ProperlyDominatesBlock;
9795   case scTruncate:
9796   case scZeroExtend:
9797   case scSignExtend:
9798     return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
9799   case scAddRecExpr: {
9800     // This uses a "dominates" query instead of "properly dominates" query
9801     // to test for proper dominance too, because the instruction which
9802     // produces the addrec's value is a PHI, and a PHI effectively properly
9803     // dominates its entire containing block.
9804     const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9805     if (!DT.dominates(AR->getLoop()->getHeader(), BB))
9806       return DoesNotDominateBlock;
9807   }
9808   // FALL THROUGH into SCEVNAryExpr handling.
9809   case scAddExpr:
9810   case scMulExpr:
9811   case scUMaxExpr:
9812   case scSMaxExpr: {
9813     const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
9814     bool Proper = true;
9815     for (const SCEV *NAryOp : NAry->operands()) {
9816       BlockDisposition D = getBlockDisposition(NAryOp, BB);
9817       if (D == DoesNotDominateBlock)
9818         return DoesNotDominateBlock;
9819       if (D == DominatesBlock)
9820         Proper = false;
9821     }
9822     return Proper ? ProperlyDominatesBlock : DominatesBlock;
9823   }
9824   case scUDivExpr: {
9825     const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9826     const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
9827     BlockDisposition LD = getBlockDisposition(LHS, BB);
9828     if (LD == DoesNotDominateBlock)
9829       return DoesNotDominateBlock;
9830     BlockDisposition RD = getBlockDisposition(RHS, BB);
9831     if (RD == DoesNotDominateBlock)
9832       return DoesNotDominateBlock;
9833     return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
9834       ProperlyDominatesBlock : DominatesBlock;
9835   }
9836   case scUnknown:
9837     if (Instruction *I =
9838           dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
9839       if (I->getParent() == BB)
9840         return DominatesBlock;
9841       if (DT.properlyDominates(I->getParent(), BB))
9842         return ProperlyDominatesBlock;
9843       return DoesNotDominateBlock;
9844     }
9845     return ProperlyDominatesBlock;
9846   case scCouldNotCompute:
9847     llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9848   }
9849   llvm_unreachable("Unknown SCEV kind!");
9850 }
9851 
9852 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
9853   return getBlockDisposition(S, BB) >= DominatesBlock;
9854 }
9855 
9856 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
9857   return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
9858 }
9859 
9860 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
9861   // Search for a SCEV expression node within an expression tree.
9862   // Implements SCEVTraversal::Visitor.
9863   struct SCEVSearch {
9864     const SCEV *Node;
9865     bool IsFound;
9866 
9867     SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
9868 
9869     bool follow(const SCEV *S) {
9870       IsFound |= (S == Node);
9871       return !IsFound;
9872     }
9873     bool isDone() const { return IsFound; }
9874   };
9875 
9876   SCEVSearch Search(Op);
9877   visitAll(S, Search);
9878   return Search.IsFound;
9879 }
9880 
9881 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
9882   ValuesAtScopes.erase(S);
9883   LoopDispositions.erase(S);
9884   BlockDispositions.erase(S);
9885   UnsignedRanges.erase(S);
9886   SignedRanges.erase(S);
9887   ExprValueMap.erase(S);
9888   HasRecMap.erase(S);
9889 
9890   auto RemoveSCEVFromBackedgeMap =
9891       [S, this](DenseMap<const Loop *, BackedgeTakenInfo> &Map) {
9892         for (auto I = Map.begin(), E = Map.end(); I != E;) {
9893           BackedgeTakenInfo &BEInfo = I->second;
9894           if (BEInfo.hasOperand(S, this)) {
9895             BEInfo.clear();
9896             Map.erase(I++);
9897           } else
9898             ++I;
9899         }
9900       };
9901 
9902   RemoveSCEVFromBackedgeMap(BackedgeTakenCounts);
9903   RemoveSCEVFromBackedgeMap(PredicatedBackedgeTakenCounts);
9904 }
9905 
9906 typedef DenseMap<const Loop *, std::string> VerifyMap;
9907 
9908 /// replaceSubString - Replaces all occurrences of From in Str with To.
9909 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
9910   size_t Pos = 0;
9911   while ((Pos = Str.find(From, Pos)) != std::string::npos) {
9912     Str.replace(Pos, From.size(), To.data(), To.size());
9913     Pos += To.size();
9914   }
9915 }
9916 
9917 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
9918 static void
9919 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
9920   std::string &S = Map[L];
9921   if (S.empty()) {
9922     raw_string_ostream OS(S);
9923     SE.getBackedgeTakenCount(L)->print(OS);
9924 
9925     // false and 0 are semantically equivalent. This can happen in dead loops.
9926     replaceSubString(OS.str(), "false", "0");
9927     // Remove wrap flags, their use in SCEV is highly fragile.
9928     // FIXME: Remove this when SCEV gets smarter about them.
9929     replaceSubString(OS.str(), "<nw>", "");
9930     replaceSubString(OS.str(), "<nsw>", "");
9931     replaceSubString(OS.str(), "<nuw>", "");
9932   }
9933 
9934   for (auto *R : reverse(*L))
9935     getLoopBackedgeTakenCounts(R, Map, SE); // recurse.
9936 }
9937 
9938 void ScalarEvolution::verify() const {
9939   ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9940 
9941   // Gather stringified backedge taken counts for all loops using SCEV's caches.
9942   // FIXME: It would be much better to store actual values instead of strings,
9943   //        but SCEV pointers will change if we drop the caches.
9944   VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
9945   for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9946     getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
9947 
9948   // Gather stringified backedge taken counts for all loops using a fresh
9949   // ScalarEvolution object.
9950   ScalarEvolution SE2(F, TLI, AC, DT, LI);
9951   for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9952     getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE2);
9953 
9954   // Now compare whether they're the same with and without caches. This allows
9955   // verifying that no pass changed the cache.
9956   assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
9957          "New loops suddenly appeared!");
9958 
9959   for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
9960                            OldE = BackedgeDumpsOld.end(),
9961                            NewI = BackedgeDumpsNew.begin();
9962        OldI != OldE; ++OldI, ++NewI) {
9963     assert(OldI->first == NewI->first && "Loop order changed!");
9964 
9965     // Compare the stringified SCEVs. We don't care if undef backedgetaken count
9966     // changes.
9967     // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
9968     // means that a pass is buggy or SCEV has to learn a new pattern but is
9969     // usually not harmful.
9970     if (OldI->second != NewI->second &&
9971         OldI->second.find("undef") == std::string::npos &&
9972         NewI->second.find("undef") == std::string::npos &&
9973         OldI->second != "***COULDNOTCOMPUTE***" &&
9974         NewI->second != "***COULDNOTCOMPUTE***") {
9975       dbgs() << "SCEVValidator: SCEV for loop '"
9976              << OldI->first->getHeader()->getName()
9977              << "' changed from '" << OldI->second
9978              << "' to '" << NewI->second << "'!\n";
9979       std::abort();
9980     }
9981   }
9982 
9983   // TODO: Verify more things.
9984 }
9985 
9986 char ScalarEvolutionAnalysis::PassID;
9987 
9988 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
9989                                              AnalysisManager<Function> &AM) {
9990   return ScalarEvolution(F, AM.getResult<TargetLibraryAnalysis>(F),
9991                          AM.getResult<AssumptionAnalysis>(F),
9992                          AM.getResult<DominatorTreeAnalysis>(F),
9993                          AM.getResult<LoopAnalysis>(F));
9994 }
9995 
9996 PreservedAnalyses
9997 ScalarEvolutionPrinterPass::run(Function &F, AnalysisManager<Function> &AM) {
9998   AM.getResult<ScalarEvolutionAnalysis>(F).print(OS);
9999   return PreservedAnalyses::all();
10000 }
10001 
10002 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
10003                       "Scalar Evolution Analysis", false, true)
10004 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
10005 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
10006 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
10007 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
10008 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
10009                     "Scalar Evolution Analysis", false, true)
10010 char ScalarEvolutionWrapperPass::ID = 0;
10011 
10012 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
10013   initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
10014 }
10015 
10016 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
10017   SE.reset(new ScalarEvolution(
10018       F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(),
10019       getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
10020       getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
10021       getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
10022   return false;
10023 }
10024 
10025 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
10026 
10027 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
10028   SE->print(OS);
10029 }
10030 
10031 void ScalarEvolutionWrapperPass::verifyAnalysis() const {
10032   if (!VerifySCEV)
10033     return;
10034 
10035   SE->verify();
10036 }
10037 
10038 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
10039   AU.setPreservesAll();
10040   AU.addRequiredTransitive<AssumptionCacheTracker>();
10041   AU.addRequiredTransitive<LoopInfoWrapperPass>();
10042   AU.addRequiredTransitive<DominatorTreeWrapperPass>();
10043   AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
10044 }
10045 
10046 const SCEVPredicate *
10047 ScalarEvolution::getEqualPredicate(const SCEVUnknown *LHS,
10048                                    const SCEVConstant *RHS) {
10049   FoldingSetNodeID ID;
10050   // Unique this node based on the arguments
10051   ID.AddInteger(SCEVPredicate::P_Equal);
10052   ID.AddPointer(LHS);
10053   ID.AddPointer(RHS);
10054   void *IP = nullptr;
10055   if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
10056     return S;
10057   SCEVEqualPredicate *Eq = new (SCEVAllocator)
10058       SCEVEqualPredicate(ID.Intern(SCEVAllocator), LHS, RHS);
10059   UniquePreds.InsertNode(Eq, IP);
10060   return Eq;
10061 }
10062 
10063 const SCEVPredicate *ScalarEvolution::getWrapPredicate(
10064     const SCEVAddRecExpr *AR,
10065     SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
10066   FoldingSetNodeID ID;
10067   // Unique this node based on the arguments
10068   ID.AddInteger(SCEVPredicate::P_Wrap);
10069   ID.AddPointer(AR);
10070   ID.AddInteger(AddedFlags);
10071   void *IP = nullptr;
10072   if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
10073     return S;
10074   auto *OF = new (SCEVAllocator)
10075       SCEVWrapPredicate(ID.Intern(SCEVAllocator), AR, AddedFlags);
10076   UniquePreds.InsertNode(OF, IP);
10077   return OF;
10078 }
10079 
10080 namespace {
10081 
10082 class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> {
10083 public:
10084   // Rewrites \p S in the context of a loop L and the predicate A.
10085   // If Assume is true, rewrite is free to add further predicates to A
10086   // such that the result will be an AddRecExpr.
10087   static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
10088                              SCEVUnionPredicate &A, bool Assume) {
10089     SCEVPredicateRewriter Rewriter(L, SE, A, Assume);
10090     return Rewriter.visit(S);
10091   }
10092 
10093   SCEVPredicateRewriter(const Loop *L, ScalarEvolution &SE,
10094                         SCEVUnionPredicate &P, bool Assume)
10095       : SCEVRewriteVisitor(SE), P(P), L(L), Assume(Assume) {}
10096 
10097   const SCEV *visitUnknown(const SCEVUnknown *Expr) {
10098     auto ExprPreds = P.getPredicatesForExpr(Expr);
10099     for (auto *Pred : ExprPreds)
10100       if (const auto *IPred = dyn_cast<const SCEVEqualPredicate>(Pred))
10101         if (IPred->getLHS() == Expr)
10102           return IPred->getRHS();
10103 
10104     return Expr;
10105   }
10106 
10107   const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
10108     const SCEV *Operand = visit(Expr->getOperand());
10109     const SCEVAddRecExpr *AR = dyn_cast<const SCEVAddRecExpr>(Operand);
10110     if (AR && AR->getLoop() == L && AR->isAffine()) {
10111       // This couldn't be folded because the operand didn't have the nuw
10112       // flag. Add the nusw flag as an assumption that we could make.
10113       const SCEV *Step = AR->getStepRecurrence(SE);
10114       Type *Ty = Expr->getType();
10115       if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNUSW))
10116         return SE.getAddRecExpr(SE.getZeroExtendExpr(AR->getStart(), Ty),
10117                                 SE.getSignExtendExpr(Step, Ty), L,
10118                                 AR->getNoWrapFlags());
10119     }
10120     return SE.getZeroExtendExpr(Operand, Expr->getType());
10121   }
10122 
10123   const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
10124     const SCEV *Operand = visit(Expr->getOperand());
10125     const SCEVAddRecExpr *AR = dyn_cast<const SCEVAddRecExpr>(Operand);
10126     if (AR && AR->getLoop() == L && AR->isAffine()) {
10127       // This couldn't be folded because the operand didn't have the nsw
10128       // flag. Add the nssw flag as an assumption that we could make.
10129       const SCEV *Step = AR->getStepRecurrence(SE);
10130       Type *Ty = Expr->getType();
10131       if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNSSW))
10132         return SE.getAddRecExpr(SE.getSignExtendExpr(AR->getStart(), Ty),
10133                                 SE.getSignExtendExpr(Step, Ty), L,
10134                                 AR->getNoWrapFlags());
10135     }
10136     return SE.getSignExtendExpr(Operand, Expr->getType());
10137   }
10138 
10139 private:
10140   bool addOverflowAssumption(const SCEVAddRecExpr *AR,
10141                              SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
10142     auto *A = SE.getWrapPredicate(AR, AddedFlags);
10143     if (!Assume) {
10144       // Check if we've already made this assumption.
10145       if (P.implies(A))
10146         return true;
10147       return false;
10148     }
10149     P.add(A);
10150     return true;
10151   }
10152 
10153   SCEVUnionPredicate &P;
10154   const Loop *L;
10155   bool Assume;
10156 };
10157 } // end anonymous namespace
10158 
10159 const SCEV *ScalarEvolution::rewriteUsingPredicate(const SCEV *S, const Loop *L,
10160                                                    SCEVUnionPredicate &Preds) {
10161   return SCEVPredicateRewriter::rewrite(S, L, *this, Preds, false);
10162 }
10163 
10164 const SCEVAddRecExpr *
10165 ScalarEvolution::convertSCEVToAddRecWithPredicates(const SCEV *S, const Loop *L,
10166                                                    SCEVUnionPredicate &Preds) {
10167   SCEVUnionPredicate TransformPreds;
10168   S = SCEVPredicateRewriter::rewrite(S, L, *this, TransformPreds, true);
10169   auto *AddRec = dyn_cast<SCEVAddRecExpr>(S);
10170 
10171   if (!AddRec)
10172     return nullptr;
10173 
10174   // Since the transformation was successful, we can now transfer the SCEV
10175   // predicates.
10176   Preds.add(&TransformPreds);
10177   return AddRec;
10178 }
10179 
10180 /// SCEV predicates
10181 SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID,
10182                              SCEVPredicateKind Kind)
10183     : FastID(ID), Kind(Kind) {}
10184 
10185 SCEVEqualPredicate::SCEVEqualPredicate(const FoldingSetNodeIDRef ID,
10186                                        const SCEVUnknown *LHS,
10187                                        const SCEVConstant *RHS)
10188     : SCEVPredicate(ID, P_Equal), LHS(LHS), RHS(RHS) {}
10189 
10190 bool SCEVEqualPredicate::implies(const SCEVPredicate *N) const {
10191   const auto *Op = dyn_cast<const SCEVEqualPredicate>(N);
10192 
10193   if (!Op)
10194     return false;
10195 
10196   return Op->LHS == LHS && Op->RHS == RHS;
10197 }
10198 
10199 bool SCEVEqualPredicate::isAlwaysTrue() const { return false; }
10200 
10201 const SCEV *SCEVEqualPredicate::getExpr() const { return LHS; }
10202 
10203 void SCEVEqualPredicate::print(raw_ostream &OS, unsigned Depth) const {
10204   OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n";
10205 }
10206 
10207 SCEVWrapPredicate::SCEVWrapPredicate(const FoldingSetNodeIDRef ID,
10208                                      const SCEVAddRecExpr *AR,
10209                                      IncrementWrapFlags Flags)
10210     : SCEVPredicate(ID, P_Wrap), AR(AR), Flags(Flags) {}
10211 
10212 const SCEV *SCEVWrapPredicate::getExpr() const { return AR; }
10213 
10214 bool SCEVWrapPredicate::implies(const SCEVPredicate *N) const {
10215   const auto *Op = dyn_cast<SCEVWrapPredicate>(N);
10216 
10217   return Op && Op->AR == AR && setFlags(Flags, Op->Flags) == Flags;
10218 }
10219 
10220 bool SCEVWrapPredicate::isAlwaysTrue() const {
10221   SCEV::NoWrapFlags ScevFlags = AR->getNoWrapFlags();
10222   IncrementWrapFlags IFlags = Flags;
10223 
10224   if (ScalarEvolution::setFlags(ScevFlags, SCEV::FlagNSW) == ScevFlags)
10225     IFlags = clearFlags(IFlags, IncrementNSSW);
10226 
10227   return IFlags == IncrementAnyWrap;
10228 }
10229 
10230 void SCEVWrapPredicate::print(raw_ostream &OS, unsigned Depth) const {
10231   OS.indent(Depth) << *getExpr() << " Added Flags: ";
10232   if (SCEVWrapPredicate::IncrementNUSW & getFlags())
10233     OS << "<nusw>";
10234   if (SCEVWrapPredicate::IncrementNSSW & getFlags())
10235     OS << "<nssw>";
10236   OS << "\n";
10237 }
10238 
10239 SCEVWrapPredicate::IncrementWrapFlags
10240 SCEVWrapPredicate::getImpliedFlags(const SCEVAddRecExpr *AR,
10241                                    ScalarEvolution &SE) {
10242   IncrementWrapFlags ImpliedFlags = IncrementAnyWrap;
10243   SCEV::NoWrapFlags StaticFlags = AR->getNoWrapFlags();
10244 
10245   // We can safely transfer the NSW flag as NSSW.
10246   if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNSW) == StaticFlags)
10247     ImpliedFlags = IncrementNSSW;
10248 
10249   if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNUW) == StaticFlags) {
10250     // If the increment is positive, the SCEV NUW flag will also imply the
10251     // WrapPredicate NUSW flag.
10252     if (const auto *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(SE)))
10253       if (Step->getValue()->getValue().isNonNegative())
10254         ImpliedFlags = setFlags(ImpliedFlags, IncrementNUSW);
10255   }
10256 
10257   return ImpliedFlags;
10258 }
10259 
10260 /// Union predicates don't get cached so create a dummy set ID for it.
10261 SCEVUnionPredicate::SCEVUnionPredicate()
10262     : SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {}
10263 
10264 bool SCEVUnionPredicate::isAlwaysTrue() const {
10265   return all_of(Preds,
10266                 [](const SCEVPredicate *I) { return I->isAlwaysTrue(); });
10267 }
10268 
10269 ArrayRef<const SCEVPredicate *>
10270 SCEVUnionPredicate::getPredicatesForExpr(const SCEV *Expr) {
10271   auto I = SCEVToPreds.find(Expr);
10272   if (I == SCEVToPreds.end())
10273     return ArrayRef<const SCEVPredicate *>();
10274   return I->second;
10275 }
10276 
10277 bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const {
10278   if (const auto *Set = dyn_cast<const SCEVUnionPredicate>(N))
10279     return all_of(Set->Preds,
10280                   [this](const SCEVPredicate *I) { return this->implies(I); });
10281 
10282   auto ScevPredsIt = SCEVToPreds.find(N->getExpr());
10283   if (ScevPredsIt == SCEVToPreds.end())
10284     return false;
10285   auto &SCEVPreds = ScevPredsIt->second;
10286 
10287   return any_of(SCEVPreds,
10288                 [N](const SCEVPredicate *I) { return I->implies(N); });
10289 }
10290 
10291 const SCEV *SCEVUnionPredicate::getExpr() const { return nullptr; }
10292 
10293 void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const {
10294   for (auto Pred : Preds)
10295     Pred->print(OS, Depth);
10296 }
10297 
10298 void SCEVUnionPredicate::add(const SCEVPredicate *N) {
10299   if (const auto *Set = dyn_cast<const SCEVUnionPredicate>(N)) {
10300     for (auto Pred : Set->Preds)
10301       add(Pred);
10302     return;
10303   }
10304 
10305   if (implies(N))
10306     return;
10307 
10308   const SCEV *Key = N->getExpr();
10309   assert(Key && "Only SCEVUnionPredicate doesn't have an "
10310                 " associated expression!");
10311 
10312   SCEVToPreds[Key].push_back(N);
10313   Preds.push_back(N);
10314 }
10315 
10316 PredicatedScalarEvolution::PredicatedScalarEvolution(ScalarEvolution &SE,
10317                                                      Loop &L)
10318     : SE(SE), L(L), Generation(0), BackedgeCount(nullptr) {}
10319 
10320 const SCEV *PredicatedScalarEvolution::getSCEV(Value *V) {
10321   const SCEV *Expr = SE.getSCEV(V);
10322   RewriteEntry &Entry = RewriteMap[Expr];
10323 
10324   // If we already have an entry and the version matches, return it.
10325   if (Entry.second && Generation == Entry.first)
10326     return Entry.second;
10327 
10328   // We found an entry but it's stale. Rewrite the stale entry
10329   // acording to the current predicate.
10330   if (Entry.second)
10331     Expr = Entry.second;
10332 
10333   const SCEV *NewSCEV = SE.rewriteUsingPredicate(Expr, &L, Preds);
10334   Entry = {Generation, NewSCEV};
10335 
10336   return NewSCEV;
10337 }
10338 
10339 const SCEV *PredicatedScalarEvolution::getBackedgeTakenCount() {
10340   if (!BackedgeCount) {
10341     SCEVUnionPredicate BackedgePred;
10342     BackedgeCount = SE.getPredicatedBackedgeTakenCount(&L, BackedgePred);
10343     addPredicate(BackedgePred);
10344   }
10345   return BackedgeCount;
10346 }
10347 
10348 void PredicatedScalarEvolution::addPredicate(const SCEVPredicate &Pred) {
10349   if (Preds.implies(&Pred))
10350     return;
10351   Preds.add(&Pred);
10352   updateGeneration();
10353 }
10354 
10355 const SCEVUnionPredicate &PredicatedScalarEvolution::getUnionPredicate() const {
10356   return Preds;
10357 }
10358 
10359 void PredicatedScalarEvolution::updateGeneration() {
10360   // If the generation number wrapped recompute everything.
10361   if (++Generation == 0) {
10362     for (auto &II : RewriteMap) {
10363       const SCEV *Rewritten = II.second.second;
10364       II.second = {Generation, SE.rewriteUsingPredicate(Rewritten, &L, Preds)};
10365     }
10366   }
10367 }
10368 
10369 void PredicatedScalarEvolution::setNoOverflow(
10370     Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
10371   const SCEV *Expr = getSCEV(V);
10372   const auto *AR = cast<SCEVAddRecExpr>(Expr);
10373 
10374   auto ImpliedFlags = SCEVWrapPredicate::getImpliedFlags(AR, SE);
10375 
10376   // Clear the statically implied flags.
10377   Flags = SCEVWrapPredicate::clearFlags(Flags, ImpliedFlags);
10378   addPredicate(*SE.getWrapPredicate(AR, Flags));
10379 
10380   auto II = FlagsMap.insert({V, Flags});
10381   if (!II.second)
10382     II.first->second = SCEVWrapPredicate::setFlags(Flags, II.first->second);
10383 }
10384 
10385 bool PredicatedScalarEvolution::hasNoOverflow(
10386     Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
10387   const SCEV *Expr = getSCEV(V);
10388   const auto *AR = cast<SCEVAddRecExpr>(Expr);
10389 
10390   Flags = SCEVWrapPredicate::clearFlags(
10391       Flags, SCEVWrapPredicate::getImpliedFlags(AR, SE));
10392 
10393   auto II = FlagsMap.find(V);
10394 
10395   if (II != FlagsMap.end())
10396     Flags = SCEVWrapPredicate::clearFlags(Flags, II->second);
10397 
10398   return Flags == SCEVWrapPredicate::IncrementAnyWrap;
10399 }
10400 
10401 const SCEVAddRecExpr *PredicatedScalarEvolution::getAsAddRec(Value *V) {
10402   const SCEV *Expr = this->getSCEV(V);
10403   auto *New = SE.convertSCEVToAddRecWithPredicates(Expr, &L, Preds);
10404 
10405   if (!New)
10406     return nullptr;
10407 
10408   updateGeneration();
10409   RewriteMap[SE.getSCEV(V)] = {Generation, New};
10410   return New;
10411 }
10412 
10413 PredicatedScalarEvolution::PredicatedScalarEvolution(
10414     const PredicatedScalarEvolution &Init)
10415     : RewriteMap(Init.RewriteMap), SE(Init.SE), L(Init.L), Preds(Init.Preds),
10416       Generation(Init.Generation), BackedgeCount(Init.BackedgeCount) {
10417   for (auto I = Init.FlagsMap.begin(), E = Init.FlagsMap.end(); I != E; ++I)
10418     FlagsMap.insert(*I);
10419 }
10420 
10421 void PredicatedScalarEvolution::print(raw_ostream &OS, unsigned Depth) const {
10422   // For each block.
10423   for (auto *BB : L.getBlocks())
10424     for (auto &I : *BB) {
10425       if (!SE.isSCEVable(I.getType()))
10426         continue;
10427 
10428       auto *Expr = SE.getSCEV(&I);
10429       auto II = RewriteMap.find(Expr);
10430 
10431       if (II == RewriteMap.end())
10432         continue;
10433 
10434       // Don't print things that are not interesting.
10435       if (II->second.second == Expr)
10436         continue;
10437 
10438       OS.indent(Depth) << "[PSE]" << I << ":\n";
10439       OS.indent(Depth + 2) << *Expr << "\n";
10440       OS.indent(Depth + 2) << "--> " << *II->second.second << "\n";
10441     }
10442 }
10443