LCOV - code coverage report
Current view: top level - lib/Analysis - ScalarEvolution.cpp (source / functions) Hit Total Coverage
Test: llvm-toolchain.info Lines: 4069 4459 91.3 %
Date: 2018-10-20 13:21:21 Functions: 323 368 87.8 %
Legend: Lines: hit not hit

          Line data    Source code
       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/APInt.h"
      63             : #include "llvm/ADT/ArrayRef.h"
      64             : #include "llvm/ADT/DenseMap.h"
      65             : #include "llvm/ADT/DepthFirstIterator.h"
      66             : #include "llvm/ADT/EquivalenceClasses.h"
      67             : #include "llvm/ADT/FoldingSet.h"
      68             : #include "llvm/ADT/None.h"
      69             : #include "llvm/ADT/Optional.h"
      70             : #include "llvm/ADT/STLExtras.h"
      71             : #include "llvm/ADT/ScopeExit.h"
      72             : #include "llvm/ADT/Sequence.h"
      73             : #include "llvm/ADT/SetVector.h"
      74             : #include "llvm/ADT/SmallPtrSet.h"
      75             : #include "llvm/ADT/SmallSet.h"
      76             : #include "llvm/ADT/SmallVector.h"
      77             : #include "llvm/ADT/Statistic.h"
      78             : #include "llvm/ADT/StringRef.h"
      79             : #include "llvm/Analysis/AssumptionCache.h"
      80             : #include "llvm/Analysis/ConstantFolding.h"
      81             : #include "llvm/Analysis/InstructionSimplify.h"
      82             : #include "llvm/Analysis/LoopInfo.h"
      83             : #include "llvm/Analysis/ScalarEvolutionExpressions.h"
      84             : #include "llvm/Analysis/TargetLibraryInfo.h"
      85             : #include "llvm/Analysis/ValueTracking.h"
      86             : #include "llvm/Config/llvm-config.h"
      87             : #include "llvm/IR/Argument.h"
      88             : #include "llvm/IR/BasicBlock.h"
      89             : #include "llvm/IR/CFG.h"
      90             : #include "llvm/IR/CallSite.h"
      91             : #include "llvm/IR/Constant.h"
      92             : #include "llvm/IR/ConstantRange.h"
      93             : #include "llvm/IR/Constants.h"
      94             : #include "llvm/IR/DataLayout.h"
      95             : #include "llvm/IR/DerivedTypes.h"
      96             : #include "llvm/IR/Dominators.h"
      97             : #include "llvm/IR/Function.h"
      98             : #include "llvm/IR/GlobalAlias.h"
      99             : #include "llvm/IR/GlobalValue.h"
     100             : #include "llvm/IR/GlobalVariable.h"
     101             : #include "llvm/IR/InstIterator.h"
     102             : #include "llvm/IR/InstrTypes.h"
     103             : #include "llvm/IR/Instruction.h"
     104             : #include "llvm/IR/Instructions.h"
     105             : #include "llvm/IR/IntrinsicInst.h"
     106             : #include "llvm/IR/Intrinsics.h"
     107             : #include "llvm/IR/LLVMContext.h"
     108             : #include "llvm/IR/Metadata.h"
     109             : #include "llvm/IR/Operator.h"
     110             : #include "llvm/IR/PatternMatch.h"
     111             : #include "llvm/IR/Type.h"
     112             : #include "llvm/IR/Use.h"
     113             : #include "llvm/IR/User.h"
     114             : #include "llvm/IR/Value.h"
     115             : #include "llvm/Pass.h"
     116             : #include "llvm/Support/Casting.h"
     117             : #include "llvm/Support/CommandLine.h"
     118             : #include "llvm/Support/Compiler.h"
     119             : #include "llvm/Support/Debug.h"
     120             : #include "llvm/Support/ErrorHandling.h"
     121             : #include "llvm/Support/KnownBits.h"
     122             : #include "llvm/Support/SaveAndRestore.h"
     123             : #include "llvm/Support/raw_ostream.h"
     124             : #include <algorithm>
     125             : #include <cassert>
     126             : #include <climits>
     127             : #include <cstddef>
     128             : #include <cstdint>
     129             : #include <cstdlib>
     130             : #include <map>
     131             : #include <memory>
     132             : #include <tuple>
     133             : #include <utility>
     134             : #include <vector>
     135             : 
     136             : using namespace llvm;
     137             : 
     138             : #define DEBUG_TYPE "scalar-evolution"
     139             : 
     140             : STATISTIC(NumArrayLenItCounts,
     141             :           "Number of trip counts computed with array length");
     142             : STATISTIC(NumTripCountsComputed,
     143             :           "Number of loops with predictable loop counts");
     144             : STATISTIC(NumTripCountsNotComputed,
     145             :           "Number of loops without predictable loop counts");
     146             : STATISTIC(NumBruteForceTripCountsComputed,
     147             :           "Number of loops with trip counts computed by force");
     148             : 
     149             : static cl::opt<unsigned>
     150             : MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
     151             :                         cl::desc("Maximum number of iterations SCEV will "
     152             :                                  "symbolically execute a constant "
     153             :                                  "derived loop"),
     154             :                         cl::init(100));
     155             : 
     156             : // FIXME: Enable this with EXPENSIVE_CHECKS when the test suite is clean.
     157             : static cl::opt<bool> VerifySCEV(
     158             :     "verify-scev", cl::Hidden,
     159             :     cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
     160             : static cl::opt<bool>
     161             :     VerifySCEVMap("verify-scev-maps", cl::Hidden,
     162             :                   cl::desc("Verify no dangling value in ScalarEvolution's "
     163             :                            "ExprValueMap (slow)"));
     164             : 
     165             : static cl::opt<unsigned> MulOpsInlineThreshold(
     166             :     "scev-mulops-inline-threshold", cl::Hidden,
     167             :     cl::desc("Threshold for inlining multiplication operands into a SCEV"),
     168             :     cl::init(32));
     169             : 
     170             : static cl::opt<unsigned> AddOpsInlineThreshold(
     171             :     "scev-addops-inline-threshold", cl::Hidden,
     172             :     cl::desc("Threshold for inlining addition operands into a SCEV"),
     173             :     cl::init(500));
     174             : 
     175             : static cl::opt<unsigned> MaxSCEVCompareDepth(
     176             :     "scalar-evolution-max-scev-compare-depth", cl::Hidden,
     177             :     cl::desc("Maximum depth of recursive SCEV complexity comparisons"),
     178             :     cl::init(32));
     179             : 
     180             : static cl::opt<unsigned> MaxSCEVOperationsImplicationDepth(
     181             :     "scalar-evolution-max-scev-operations-implication-depth", cl::Hidden,
     182             :     cl::desc("Maximum depth of recursive SCEV operations implication analysis"),
     183             :     cl::init(2));
     184             : 
     185             : static cl::opt<unsigned> MaxValueCompareDepth(
     186             :     "scalar-evolution-max-value-compare-depth", cl::Hidden,
     187             :     cl::desc("Maximum depth of recursive value complexity comparisons"),
     188             :     cl::init(2));
     189             : 
     190             : static cl::opt<unsigned>
     191             :     MaxArithDepth("scalar-evolution-max-arith-depth", cl::Hidden,
     192             :                   cl::desc("Maximum depth of recursive arithmetics"),
     193             :                   cl::init(32));
     194             : 
     195             : static cl::opt<unsigned> MaxConstantEvolvingDepth(
     196             :     "scalar-evolution-max-constant-evolving-depth", cl::Hidden,
     197             :     cl::desc("Maximum depth of recursive constant evolving"), cl::init(32));
     198             : 
     199             : static cl::opt<unsigned>
     200             :     MaxExtDepth("scalar-evolution-max-ext-depth", cl::Hidden,
     201             :                 cl::desc("Maximum depth of recursive SExt/ZExt"),
     202             :                 cl::init(8));
     203             : 
     204             : static cl::opt<unsigned>
     205             :     MaxAddRecSize("scalar-evolution-max-add-rec-size", cl::Hidden,
     206             :                   cl::desc("Max coefficients in AddRec during evolving"),
     207             :                   cl::init(8));
     208             : 
     209             : //===----------------------------------------------------------------------===//
     210             : //                           SCEV class definitions
     211             : //===----------------------------------------------------------------------===//
     212             : 
     213             : //===----------------------------------------------------------------------===//
     214             : // Implementation of the SCEV class.
     215             : //
     216             : 
     217             : #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
     218             : LLVM_DUMP_METHOD void SCEV::dump() const {
     219             :   print(dbgs());
     220             :   dbgs() << '\n';
     221             : }
     222             : #endif
     223             : 
     224       60436 : void SCEV::print(raw_ostream &OS) const {
     225      120872 :   switch (static_cast<SCEVTypes>(getSCEVType())) {
     226             :   case scConstant:
     227       21013 :     cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
     228       21013 :     return;
     229             :   case scTruncate: {
     230             :     const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
     231        1253 :     const SCEV *Op = Trunc->getOperand();
     232        2506 :     OS << "(trunc " << *Op->getType() << " " << *Op << " to "
     233        1253 :        << *Trunc->getType() << ")";
     234        1253 :     return;
     235             :   }
     236             :   case scZeroExtend: {
     237             :     const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
     238        2560 :     const SCEV *Op = ZExt->getOperand();
     239        5120 :     OS << "(zext " << *Op->getType() << " " << *Op << " to "
     240        2560 :        << *ZExt->getType() << ")";
     241        2560 :     return;
     242             :   }
     243             :   case scSignExtend: {
     244             :     const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
     245         459 :     const SCEV *Op = SExt->getOperand();
     246         918 :     OS << "(sext " << *Op->getType() << " " << *Op << " to "
     247         459 :        << *SExt->getType() << ")";
     248         459 :     return;
     249             :   }
     250             :   case scAddRecExpr: {
     251             :     const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
     252        3602 :     OS << "{" << *AR->getOperand(0);
     253        7731 :     for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
     254        4129 :       OS << ",+," << *AR->getOperand(i);
     255        3602 :     OS << "}<";
     256        3602 :     if (AR->hasNoUnsignedWrap())
     257         480 :       OS << "nuw><";
     258        3602 :     if (AR->hasNoSignedWrap())
     259         648 :       OS << "nsw><";
     260        3602 :     if (AR->hasNoSelfWrap() &&
     261             :         !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
     262         174 :       OS << "nw><";
     263        7204 :     AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
     264        3602 :     OS << ">";
     265        3602 :     return;
     266             :   }
     267             :   case scAddExpr:
     268             :   case scMulExpr:
     269             :   case scUMaxExpr:
     270             :   case scSMaxExpr: {
     271             :     const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
     272             :     const char *OpStr = nullptr;
     273             :     switch (NAry->getSCEVType()) {
     274        7249 :     case scAddExpr: OpStr = " + "; break;
     275        7905 :     case scMulExpr: OpStr = " * "; break;
     276        2727 :     case scUMaxExpr: OpStr = " umax "; break;
     277         306 :     case scSMaxExpr: OpStr = " smax "; break;
     278             :     }
     279       18187 :     OS << "(";
     280       18187 :     for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
     281       58431 :          I != E; ++I) {
     282       40244 :       OS << **I;
     283       40244 :       if (std::next(I) != E)
     284       22057 :         OS << OpStr;
     285             :     }
     286       18187 :     OS << ")";
     287       18187 :     switch (NAry->getSCEVType()) {
     288             :     case scAddExpr:
     289             :     case scMulExpr:
     290       15154 :       if (NAry->hasNoUnsignedWrap())
     291         458 :         OS << "<nuw>";
     292       15154 :       if (NAry->hasNoSignedWrap())
     293        4681 :         OS << "<nsw>";
     294             :     }
     295             :     return;
     296             :   }
     297             :   case scUDivExpr: {
     298             :     const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
     299         467 :     OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
     300         467 :     return;
     301             :   }
     302             :   case scUnknown: {
     303             :     const SCEVUnknown *U = cast<SCEVUnknown>(this);
     304             :     Type *AllocTy;
     305       12895 :     if (U->isSizeOf(AllocTy)) {
     306           4 :       OS << "sizeof(" << *AllocTy << ")";
     307           4 :       return;
     308             :     }
     309       12891 :     if (U->isAlignOf(AllocTy)) {
     310           3 :       OS << "alignof(" << *AllocTy << ")";
     311           3 :       return;
     312             :     }
     313             : 
     314             :     Type *CTy;
     315             :     Constant *FieldNo;
     316       12888 :     if (U->isOffsetOf(CTy, FieldNo)) {
     317           1 :       OS << "offsetof(" << *CTy << ", ";
     318           1 :       FieldNo->printAsOperand(OS, false);
     319           1 :       OS << ")";
     320           1 :       return;
     321             :     }
     322             : 
     323             :     // Otherwise just print it normally.
     324       12887 :     U->getValue()->printAsOperand(OS, false);
     325       12887 :     return;
     326             :   }
     327           0 :   case scCouldNotCompute:
     328           0 :     OS << "***COULDNOTCOMPUTE***";
     329           0 :     return;
     330             :   }
     331           0 :   llvm_unreachable("Unknown SCEV kind!");
     332             : }
     333             : 
     334     8983730 : Type *SCEV::getType() const {
     335     9061350 :   switch (static_cast<SCEVTypes>(getSCEVType())) {
     336             :   case scConstant:
     337     7167722 :     return cast<SCEVConstant>(this)->getType();
     338             :   case scTruncate:
     339             :   case scZeroExtend:
     340             :   case scSignExtend:
     341      209377 :     return cast<SCEVCastExpr>(this)->getType();
     342             :   case scAddRecExpr:
     343             :   case scMulExpr:
     344             :   case scUMaxExpr:
     345             :   case scSMaxExpr:
     346     1812052 :     return cast<SCEVNAryExpr>(this)->getType();
     347             :   case scAddExpr:
     348     1041278 :     return cast<SCEVAddExpr>(this)->getType();
     349             :   case scUDivExpr:
     350       77620 :     return cast<SCEVUDivExpr>(this)->getType();
     351             :   case scUnknown:
     352     2337162 :     return cast<SCEVUnknown>(this)->getType();
     353             :   case scCouldNotCompute:
     354             :     llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
     355             :   }
     356           0 :   llvm_unreachable("Unknown SCEV kind!");
     357             : }
     358             : 
     359     1501626 : bool SCEV::isZero() const {
     360             :   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
     361      968255 :     return SC->getValue()->isZero();
     362             :   return false;
     363             : }
     364             : 
     365       49140 : bool SCEV::isOne() const {
     366             :   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
     367       33347 :     return SC->getValue()->isOne();
     368             :   return false;
     369             : }
     370             : 
     371      684666 : bool SCEV::isAllOnesValue() const {
     372             :   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
     373      680741 :     return SC->getValue()->isMinusOne();
     374             :   return false;
     375             : }
     376             : 
     377       23334 : bool SCEV::isNonConstantNegative() const {
     378             :   const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
     379             :   if (!Mul) return false;
     380             : 
     381             :   // If there is a constant factor, it will be first.
     382        4863 :   const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
     383             :   if (!SC) return false;
     384             : 
     385             :   // Return true if the value is negative, this matches things like (-42 * V).
     386        4181 :   return SC->getAPInt().isNegative();
     387             : }
     388             : 
     389      557960 : SCEVCouldNotCompute::SCEVCouldNotCompute() :
     390      557960 :   SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
     391             : 
     392      663509 : bool SCEVCouldNotCompute::classof(const SCEV *S) {
     393      663509 :   return S->getSCEVType() == scCouldNotCompute;
     394             : }
     395             : 
     396     5965399 : const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
     397             :   FoldingSetNodeID ID;
     398     5965399 :   ID.AddInteger(scConstant);
     399     5965399 :   ID.AddPointer(V);
     400     5965399 :   void *IP = nullptr;
     401     5965399 :   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
     402      413480 :   SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
     403      413480 :   UniqueSCEVs.InsertNode(S, IP);
     404      413480 :   return S;
     405             : }
     406             : 
     407     2376486 : const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
     408     2376486 :   return getConstant(ConstantInt::get(getContext(), Val));
     409             : }
     410             : 
     411             : const SCEV *
     412     1361765 : ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
     413     1361765 :   IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
     414     1361765 :   return getConstant(ConstantInt::get(ITy, V, isSigned));
     415             : }
     416             : 
     417       75732 : SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
     418       75732 :                            unsigned SCEVTy, const SCEV *op, Type *ty)
     419       75732 :   : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
     420             : 
     421        5155 : SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
     422        5155 :                                    const SCEV *op, Type *ty)
     423        5155 :   : SCEVCastExpr(ID, scTruncate, op, ty) {
     424             :   assert(Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
     425             :          "Cannot truncate non-integer value!");
     426        5155 : }
     427             : 
     428       44742 : SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
     429       44742 :                                        const SCEV *op, Type *ty)
     430       44742 :   : SCEVCastExpr(ID, scZeroExtend, op, ty) {
     431             :   assert(Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
     432             :          "Cannot zero extend non-integer value!");
     433       44742 : }
     434             : 
     435       25835 : SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
     436       25835 :                                        const SCEV *op, Type *ty)
     437       25835 :   : SCEVCastExpr(ID, scSignExtend, op, ty) {
     438             :   assert(Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
     439             :          "Cannot sign extend non-integer value!");
     440       25835 : }
     441             : 
     442        1464 : void SCEVUnknown::deleted() {
     443             :   // Clear this SCEVUnknown from various maps.
     444        1464 :   SE->forgetMemoizedResults(this);
     445             : 
     446             :   // Remove this SCEVUnknown from the uniquing map.
     447        1464 :   SE->UniqueSCEVs.RemoveNode(this);
     448             : 
     449             :   // Release the value.
     450             :   setValPtr(nullptr);
     451        1464 : }
     452             : 
     453        2014 : void SCEVUnknown::allUsesReplacedWith(Value *New) {
     454             :   // Remove this SCEVUnknown from the uniquing map.
     455        2014 :   SE->UniqueSCEVs.RemoveNode(this);
     456             : 
     457             :   // Update this SCEVUnknown to point to the new value. This is needed
     458             :   // because there may still be outstanding SCEVs which still point to
     459             :   // this SCEVUnknown.
     460             :   setValPtr(New);
     461        2014 : }
     462             : 
     463       12895 : bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
     464             :   if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
     465          13 :     if (VCE->getOpcode() == Instruction::PtrToInt)
     466             :       if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
     467           8 :         if (CE->getOpcode() == Instruction::GetElementPtr &&
     468          24 :             CE->getOperand(0)->isNullValue() &&
     469             :             CE->getNumOperands() == 2)
     470             :           if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
     471           4 :             if (CI->isOne()) {
     472           4 :               AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
     473           4 :                                  ->getElementType();
     474           4 :               return true;
     475             :             }
     476             : 
     477             :   return false;
     478             : }
     479             : 
     480       12891 : bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
     481             :   if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
     482           9 :     if (VCE->getOpcode() == Instruction::PtrToInt)
     483             :       if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
     484           8 :         if (CE->getOpcode() == Instruction::GetElementPtr &&
     485           4 :             CE->getOperand(0)->isNullValue()) {
     486             :           Type *Ty =
     487           4 :             cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
     488             :           if (StructType *STy = dyn_cast<StructType>(Ty))
     489           4 :             if (!STy->isPacked() &&
     490           8 :                 CE->getNumOperands() == 3 &&
     491           4 :                 CE->getOperand(1)->isNullValue()) {
     492             :               if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
     493           3 :                 if (CI->isOne() &&
     494           7 :                     STy->getNumElements() == 2 &&
     495           6 :                     STy->getElementType(0)->isIntegerTy(1)) {
     496           3 :                   AllocTy = STy->getElementType(1);
     497           3 :                   return true;
     498             :                 }
     499             :             }
     500             :         }
     501             : 
     502             :   return false;
     503             : }
     504             : 
     505       12888 : bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
     506             :   if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
     507           6 :     if (VCE->getOpcode() == Instruction::PtrToInt)
     508             :       if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
     509           1 :         if (CE->getOpcode() == Instruction::GetElementPtr &&
     510           1 :             CE->getNumOperands() == 3 &&
     511           3 :             CE->getOperand(0)->isNullValue() &&
     512           1 :             CE->getOperand(1)->isNullValue()) {
     513             :           Type *Ty =
     514           1 :             cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
     515             :           // Ignore vector types here so that ScalarEvolutionExpander doesn't
     516             :           // emit getelementptrs that index into vectors.
     517           1 :           if (Ty->isStructTy() || Ty->isArrayTy()) {
     518           1 :             CTy = Ty;
     519           1 :             FieldNo = CE->getOperand(2);
     520           1 :             return true;
     521             :           }
     522             :         }
     523             : 
     524             :   return false;
     525             : }
     526             : 
     527             : //===----------------------------------------------------------------------===//
     528             : //                               SCEV Utilities
     529             : //===----------------------------------------------------------------------===//
     530             : 
     531             : /// Compare the two values \p LV and \p RV in terms of their "complexity" where
     532             : /// "complexity" is a partial (and somewhat ad-hoc) relation used to order
     533             : /// operands in SCEV expressions.  \p EqCache is a set of pairs of values that
     534             : /// have been previously deemed to be "equally complex" by this routine.  It is
     535             : /// intended to avoid exponential time complexity in cases like:
     536             : ///
     537             : ///   %a = f(%x, %y)
     538             : ///   %b = f(%a, %a)
     539             : ///   %c = f(%b, %b)
     540             : ///
     541             : ///   %d = f(%x, %y)
     542             : ///   %e = f(%d, %d)
     543             : ///   %f = f(%e, %e)
     544             : ///
     545             : ///   CompareValueComplexity(%f, %c)
     546             : ///
     547             : /// Since we do not continue running this routine on expression trees once we
     548             : /// have seen unequal values, there is no need to track them in the cache.
     549             : static int
     550     4136317 : CompareValueComplexity(EquivalenceClasses<const Value *> &EqCacheValue,
     551             :                        const LoopInfo *const LI, Value *LV, Value *RV,
     552             :                        unsigned Depth) {
     553     4136317 :   if (Depth > MaxValueCompareDepth || EqCacheValue.isEquivalent(LV, RV))
     554     2034519 :     return 0;
     555             : 
     556             :   // Order pointer values after integer values. This helps SCEVExpander form
     557             :   // GEPs.
     558     2101798 :   bool LIsPointer = LV->getType()->isPointerTy(),
     559     2101798 :        RIsPointer = RV->getType()->isPointerTy();
     560     2101798 :   if (LIsPointer != RIsPointer)
     561       20538 :     return (int)LIsPointer - (int)RIsPointer;
     562             : 
     563             :   // Compare getValueID values.
     564     2081260 :   unsigned LID = LV->getValueID(), RID = RV->getValueID();
     565     2081260 :   if (LID != RID)
     566      699798 :     return (int)LID - (int)RID;
     567             : 
     568             :   // Sort arguments by their position.
     569             :   if (const auto *LA = dyn_cast<Argument>(LV)) {
     570             :     const auto *RA = cast<Argument>(RV);
     571       10670 :     unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
     572       10670 :     return (int)LArgNo - (int)RArgNo;
     573             :   }
     574             : 
     575             :   if (const auto *LGV = dyn_cast<GlobalValue>(LV)) {
     576             :     const auto *RGV = cast<GlobalValue>(RV);
     577             : 
     578             :     const auto IsGVNameSemantic = [&](const GlobalValue *GV) {
     579             :       auto LT = GV->getLinkage();
     580        5682 :       return !(GlobalValue::isPrivateLinkage(LT) ||
     581             :                GlobalValue::isInternalLinkage(LT));
     582             :     };
     583             : 
     584             :     // Use the names to distinguish the two values, but only if the
     585             :     // names are semantically important.
     586             :     if (IsGVNameSemantic(LGV) && IsGVNameSemantic(RGV))
     587       11364 :       return LGV->getName().compare(RGV->getName());
     588             :   }
     589             : 
     590             :   // For instructions, compare their loop depth, and their operand count.  This
     591             :   // is pretty loose.
     592             :   if (const auto *LInst = dyn_cast<Instruction>(LV)) {
     593             :     const auto *RInst = cast<Instruction>(RV);
     594             : 
     595             :     // Compare loop depths.
     596     1361661 :     const BasicBlock *LParent = LInst->getParent(),
     597     1361661 :                      *RParent = RInst->getParent();
     598     1361661 :     if (LParent != RParent) {
     599      937121 :       unsigned LDepth = LI->getLoopDepth(LParent),
     600      937121 :                RDepth = LI->getLoopDepth(RParent);
     601      937121 :       if (LDepth != RDepth)
     602         415 :         return (int)LDepth - (int)RDepth;
     603             :     }
     604             : 
     605             :     // Compare the number of operands.
     606             :     unsigned LNumOps = LInst->getNumOperands(),
     607             :              RNumOps = RInst->getNumOperands();
     608     1361246 :     if (LNumOps != RNumOps)
     609         169 :       return (int)LNumOps - (int)RNumOps;
     610             : 
     611     4139251 :     for (unsigned Idx : seq(0u, LNumOps)) {
     612             :       int Result =
     613     8534064 :           CompareValueComplexity(EqCacheValue, LI, LInst->getOperand(Idx),
     614             :                                  RInst->getOperand(Idx), Depth + 1);
     615     2844688 :       if (Result != 0)
     616             :         return Result;
     617             :     }
     618             :   }
     619             : 
     620     1298012 :   EqCacheValue.unionSets(LV, RV);
     621     1298012 :   return 0;
     622             : }
     623             : 
     624             : // Return negative, zero, or positive, if LHS is less than, equal to, or greater
     625             : // than RHS, respectively. A three-way result allows recursive comparisons to be
     626             : // more efficient.
     627     8999173 : static int CompareSCEVComplexity(
     628             :     EquivalenceClasses<const SCEV *> &EqCacheSCEV,
     629             :     EquivalenceClasses<const Value *> &EqCacheValue,
     630             :     const LoopInfo *const LI, const SCEV *LHS, const SCEV *RHS,
     631             :     DominatorTree &DT, unsigned Depth = 0) {
     632             :   // Fast-path: SCEVs are uniqued so we can do a quick equality check.
     633     8999173 :   if (LHS == RHS)
     634             :     return 0;
     635             : 
     636             :   // Primarily, sort the SCEVs by their getSCEVType().
     637     8012228 :   unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
     638     8012228 :   if (LType != RType)
     639     3324573 :     return (int)LType - (int)RType;
     640             : 
     641     4687655 :   if (Depth > MaxSCEVCompareDepth || EqCacheSCEV.isEquivalent(LHS, RHS))
     642      954058 :     return 0;
     643             :   // Aside from the getSCEVType() ordering, the particular ordering
     644             :   // isn't very important except that it's beneficial to be consistent,
     645             :   // so that (a + b) and (b + a) don't end up as different expressions.
     646     3733597 :   switch (static_cast<SCEVTypes>(LType)) {
     647     1291629 :   case scUnknown: {
     648     1291629 :     const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
     649     1291629 :     const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
     650             : 
     651     2583258 :     int X = CompareValueComplexity(EqCacheValue, LI, LU->getValue(),
     652             :                                    RU->getValue(), Depth + 1);
     653     1291629 :     if (X == 0)
     654      554357 :       EqCacheSCEV.unionSets(LHS, RHS);
     655             :     return X;
     656             :   }
     657             : 
     658     1615757 :   case scConstant: {
     659     1615757 :     const SCEVConstant *LC = cast<SCEVConstant>(LHS);
     660     1615757 :     const SCEVConstant *RC = cast<SCEVConstant>(RHS);
     661             : 
     662             :     // Compare constant values.
     663             :     const APInt &LA = LC->getAPInt();
     664             :     const APInt &RA = RC->getAPInt();
     665     1615757 :     unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
     666     1615757 :     if (LBitWidth != RBitWidth)
     667           1 :       return (int)LBitWidth - (int)RBitWidth;
     668     1615756 :     return LA.ult(RA) ? -1 : 1;
     669             :   }
     670             : 
     671       21815 :   case scAddRecExpr: {
     672       21815 :     const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
     673       21815 :     const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
     674             : 
     675             :     // There is always a dominance between two recs that are used by one SCEV,
     676             :     // so we can safely sort recs by loop header dominance. We require such
     677             :     // order in getAddExpr.
     678       21815 :     const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
     679       21815 :     if (LLoop != RLoop) {
     680             :       const BasicBlock *LHead = LLoop->getHeader(), *RHead = RLoop->getHeader();
     681             :       assert(LHead != RHead && "Two loops share the same header?");
     682        4480 :       if (DT.dominates(LHead, RHead))
     683             :         return 1;
     684             :       else
     685             :         assert(DT.dominates(RHead, LHead) &&
     686             :                "No dominance between recurrences used by one SCEV?");
     687        2355 :       return -1;
     688             :     }
     689             : 
     690             :     // Addrec complexity grows with operand count.
     691       17335 :     unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
     692       17335 :     if (LNumOps != RNumOps)
     693        3248 :       return (int)LNumOps - (int)RNumOps;
     694             : 
     695             :     // Lexicographically compare.
     696       14317 :     for (unsigned i = 0; i != LNumOps; ++i) {
     697       42951 :       int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
     698             :                                     LA->getOperand(i), RA->getOperand(i), DT,
     699             :                                     Depth + 1);
     700       14317 :       if (X != 0)
     701       14087 :         return X;
     702             :     }
     703           0 :     EqCacheSCEV.unionSets(LHS, RHS);
     704           0 :     return 0;
     705             :   }
     706             : 
     707      780517 :   case scAddExpr:
     708             :   case scMulExpr:
     709             :   case scSMaxExpr:
     710             :   case scUMaxExpr: {
     711      780517 :     const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
     712      780517 :     const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
     713             : 
     714             :     // Lexicographically compare n-ary expressions.
     715      780517 :     unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
     716      780517 :     if (LNumOps != RNumOps)
     717       91950 :       return (int)LNumOps - (int)RNumOps;
     718             : 
     719     1496671 :     for (unsigned i = 0; i != LNumOps; ++i) {
     720     3689853 :       int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
     721             :                                     LC->getOperand(i), RC->getOperand(i), DT,
     722             :                                     Depth + 1);
     723     1229951 :       if (X != 0)
     724      421847 :         return X;
     725             :     }
     726      266720 :     EqCacheSCEV.unionSets(LHS, RHS);
     727      266720 :     return 0;
     728             :   }
     729             : 
     730        4314 :   case scUDivExpr: {
     731        4314 :     const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
     732        4314 :     const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
     733             : 
     734             :     // Lexicographically compare udiv expressions.
     735        4314 :     int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getLHS(),
     736             :                                   RC->getLHS(), DT, Depth + 1);
     737        4314 :     if (X != 0)
     738             :       return X;
     739         580 :     X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getRHS(),
     740             :                               RC->getRHS(), DT, Depth + 1);
     741         580 :     if (X == 0)
     742         349 :       EqCacheSCEV.unionSets(LHS, RHS);
     743             :     return X;
     744             :   }
     745             : 
     746       19565 :   case scTruncate:
     747             :   case scZeroExtend:
     748             :   case scSignExtend: {
     749       19565 :     const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
     750       19565 :     const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
     751             : 
     752             :     // Compare cast expressions by operand.
     753       19565 :     int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
     754             :                                   LC->getOperand(), RC->getOperand(), DT,
     755             :                                   Depth + 1);
     756       19565 :     if (X == 0)
     757       10885 :       EqCacheSCEV.unionSets(LHS, RHS);
     758             :     return X;
     759             :   }
     760             : 
     761             :   case scCouldNotCompute:
     762             :     llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
     763             :   }
     764           0 :   llvm_unreachable("Unknown SCEV kind!");
     765             : }
     766             : 
     767             : /// Given a list of SCEV objects, order them by their complexity, and group
     768             : /// objects of the same complexity together by value.  When this routine is
     769             : /// finished, we know that any duplicates in the vector are consecutive and that
     770             : /// complexity is monotonically increasing.
     771             : ///
     772             : /// Note that we go take special precautions to ensure that we get deterministic
     773             : /// results from this routine.  In other words, we don't want the results of
     774             : /// this to depend on where the addresses of various SCEV objects happened to
     775             : /// land in memory.
     776     4344134 : static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
     777             :                               LoopInfo *LI, DominatorTree &DT) {
     778    12566038 :   if (Ops.size() < 2) return;  // Noop
     779             : 
     780             :   EquivalenceClasses<const SCEV *> EqCacheSCEV;
     781             :   EquivalenceClasses<const Value *> EqCacheValue;
     782     4344134 :   if (Ops.size() == 2) {
     783             :     // This is the common case, which also happens to be trivially simple.
     784             :     // Special case it.
     785             :     const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
     786     3828103 :     if (CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, RHS, LHS, DT) < 0)
     787             :       std::swap(LHS, RHS);
     788     3828103 :     return;
     789             :   }
     790             : 
     791             :   // Do the rough sort by complexity.
     792             :   std::stable_sort(Ops.begin(), Ops.end(),
     793             :                    [&](const SCEV *LHS, const SCEV *RHS) {
     794             :                      return CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
     795             :                                                   LHS, RHS, DT) < 0;
     796             :                    });
     797             : 
     798             :   // Now that we are sorted by complexity, group elements of the same
     799             :   // complexity.  Note that this is, at worst, N^2, but the vector is likely to
     800             :   // be extremely short in practice.  Note that we take this approach because we
     801             :   // do not want to depend on the addresses of the objects we are grouping.
     802     1655060 :   for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
     803     1188696 :     const SCEV *S = Ops[i];
     804     1188696 :     unsigned Complexity = S->getSCEVType();
     805             : 
     806             :     // If there are any objects of the same complexity and same value as this
     807             :     // one, group them.
     808    13570706 :     for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
     809    12431677 :       if (Ops[j] == S) { // Found a duplicate.
     810             :         // Move it to immediately after i'th element.
     811       82420 :         std::swap(Ops[i+1], Ops[j]);
     812             :         ++i;   // no need to rescan it.
     813       82420 :         if (i == e-2) return;  // Done!
     814             :       }
     815             :     }
     816             :   }
     817             : }
     818             : 
     819             : // Returns the size of the SCEV S.
     820          72 : static inline int sizeOfSCEV(const SCEV *S) {
     821             :   struct FindSCEVSize {
     822             :     int Size = 0;
     823             : 
     824             :     FindSCEVSize() = default;
     825             : 
     826           0 :     bool follow(const SCEV *S) {
     827         209 :       ++Size;
     828             :       // Keep looking at all operands of S.
     829           0 :       return true;
     830             :     }
     831             : 
     832           0 :     bool isDone() const {
     833           0 :       return false;
     834             :     }
     835             :   };
     836             : 
     837          72 :   FindSCEVSize F;
     838          72 :   SCEVTraversal<FindSCEVSize> ST(F);
     839          72 :   ST.visitAll(S);
     840          72 :   return F.Size;
     841             : }
     842             : 
     843             : namespace {
     844             : 
     845             : struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
     846             : public:
     847             :   // Computes the Quotient and Remainder of the division of Numerator by
     848             :   // Denominator.
     849       37763 :   static void divide(ScalarEvolution &SE, const SCEV *Numerator,
     850             :                      const SCEV *Denominator, const SCEV **Quotient,
     851             :                      const SCEV **Remainder) {
     852             :     assert(Numerator && Denominator && "Uninitialized SCEV");
     853             : 
     854       37763 :     SCEVDivision D(SE, Numerator, Denominator);
     855             : 
     856             :     // Check for the trivial case here to avoid having to check for it in the
     857             :     // rest of the code.
     858       37763 :     if (Numerator == Denominator) {
     859       11068 :       *Quotient = D.One;
     860       11068 :       *Remainder = D.Zero;
     861       13752 :       return;
     862             :     }
     863             : 
     864       26695 :     if (Numerator->isZero()) {
     865        2630 :       *Quotient = D.Zero;
     866        2630 :       *Remainder = D.Zero;
     867        2630 :       return;
     868             :     }
     869             : 
     870             :     // A simple case when N/1. The quotient is N.
     871       24065 :     if (Denominator->isOne()) {
     872          44 :       *Quotient = Numerator;
     873          44 :       *Remainder = D.Zero;
     874          44 :       return;
     875             :     }
     876             : 
     877             :     // Split the Denominator when it is a product.
     878             :     if (const SCEVMulExpr *T = dyn_cast<SCEVMulExpr>(Denominator)) {
     879             :       const SCEV *Q, *R;
     880          10 :       *Quotient = Numerator;
     881          14 :       for (const SCEV *Op : T->operands()) {
     882          12 :         divide(SE, *Quotient, Op, &Q, &R);
     883          12 :         *Quotient = Q;
     884             : 
     885             :         // Bail out when the Numerator is not divisible by one of the terms of
     886             :         // the Denominator.
     887          12 :         if (!R->isZero()) {
     888           8 :           *Quotient = D.Zero;
     889           8 :           *Remainder = Numerator;
     890           8 :           return;
     891             :         }
     892             :       }
     893           2 :       *Remainder = D.Zero;
     894           2 :       return;
     895             :     }
     896             : 
     897       24011 :     D.visit(Numerator);
     898       24011 :     *Quotient = D.Quotient;
     899       24011 :     *Remainder = D.Remainder;
     900             :   }
     901             : 
     902             :   // Except in the trivial case described above, we do not know how to divide
     903             :   // Expr by Denominator for the following functions with empty implementation.
     904           0 :   void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
     905           0 :   void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
     906           0 :   void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
     907           0 :   void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
     908           0 :   void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
     909           0 :   void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
     910           0 :   void visitUnknown(const SCEVUnknown *Numerator) {}
     911           0 :   void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
     912             : 
     913        3560 :   void visitConstant(const SCEVConstant *Numerator) {
     914        3560 :     if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
     915             :       APInt NumeratorVal = Numerator->getAPInt();
     916             :       APInt DenominatorVal = D->getAPInt();
     917         384 :       uint32_t NumeratorBW = NumeratorVal.getBitWidth();
     918         384 :       uint32_t DenominatorBW = DenominatorVal.getBitWidth();
     919             : 
     920         384 :       if (NumeratorBW > DenominatorBW)
     921           0 :         DenominatorVal = DenominatorVal.sext(NumeratorBW);
     922         384 :       else if (NumeratorBW < DenominatorBW)
     923           0 :         NumeratorVal = NumeratorVal.sext(DenominatorBW);
     924             : 
     925         384 :       APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
     926         384 :       APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
     927         384 :       APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
     928         384 :       Quotient = SE.getConstant(QuotientVal);
     929         384 :       Remainder = SE.getConstant(RemainderVal);
     930             :       return;
     931             :     }
     932             :   }
     933             : 
     934        9328 :   void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
     935             :     const SCEV *StartQ, *StartR, *StepQ, *StepR;
     936        9328 :     if (!Numerator->isAffine())
     937          13 :       return cannotDivide(Numerator);
     938       18654 :     divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
     939        9327 :     divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
     940             :     // Bail out if the types do not match.
     941        9327 :     Type *Ty = Denominator->getType();
     942       27969 :     if (Ty != StartQ->getType() || Ty != StartR->getType() ||
     943       27957 :         Ty != StepQ->getType() || Ty != StepR->getType())
     944          12 :       return cannotDivide(Numerator);
     945       18630 :     Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
     946             :                                 Numerator->getNoWrapFlags());
     947       18630 :     Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
     948             :                                  Numerator->getNoWrapFlags());
     949             :   }
     950             : 
     951        1079 :   void visitAddExpr(const SCEVAddExpr *Numerator) {
     952             :     SmallVector<const SCEV *, 2> Qs, Rs;
     953        1079 :     Type *Ty = Denominator->getType();
     954             : 
     955        3270 :     for (const SCEV *Op : Numerator->operands()) {
     956             :       const SCEV *Q, *R;
     957        2191 :       divide(SE, Op, Denominator, &Q, &R);
     958             : 
     959             :       // Bail out if types do not match.
     960        2191 :       if (Ty != Q->getType() || Ty != R->getType())
     961           0 :         return cannotDivide(Numerator);
     962             : 
     963        2191 :       Qs.push_back(Q);
     964        2191 :       Rs.push_back(R);
     965             :     }
     966             : 
     967        1079 :     if (Qs.size() == 1) {
     968           0 :       Quotient = Qs[0];
     969           0 :       Remainder = Rs[0];
     970           0 :       return;
     971             :     }
     972             : 
     973        1079 :     Quotient = SE.getAddExpr(Qs);
     974        1079 :     Remainder = SE.getAddExpr(Rs);
     975             :   }
     976             : 
     977        6996 :   void visitMulExpr(const SCEVMulExpr *Numerator) {
     978             :     SmallVector<const SCEV *, 2> Qs;
     979        6996 :     Type *Ty = Denominator->getType();
     980             : 
     981             :     bool FoundDenominatorTerm = false;
     982       24236 :     for (const SCEV *Op : Numerator->operands()) {
     983             :       // Bail out if types do not match.
     984       17240 :       if (Ty != Op->getType())
     985           0 :         return cannotDivide(Numerator);
     986             : 
     987       17240 :       if (FoundDenominatorTerm) {
     988        7174 :         Qs.push_back(Op);
     989       10304 :         continue;
     990             :       }
     991             : 
     992             :       // Check whether Denominator divides one of the product operands.
     993             :       const SCEV *Q, *R;
     994       10066 :       divide(SE, Op, Denominator, &Q, &R);
     995       10066 :       if (!R->isZero()) {
     996        3130 :         Qs.push_back(Op);
     997        3130 :         continue;
     998             :       }
     999             : 
    1000             :       // Bail out if types do not match.
    1001        6936 :       if (Ty != Q->getType())
    1002           0 :         return cannotDivide(Numerator);
    1003             : 
    1004             :       FoundDenominatorTerm = true;
    1005        6936 :       Qs.push_back(Q);
    1006             :     }
    1007             : 
    1008        6996 :     if (FoundDenominatorTerm) {
    1009        6936 :       Remainder = Zero;
    1010        6936 :       if (Qs.size() == 1)
    1011           0 :         Quotient = Qs[0];
    1012             :       else
    1013        6936 :         Quotient = SE.getMulExpr(Qs);
    1014        6936 :       return;
    1015             :     }
    1016             : 
    1017          60 :     if (!isa<SCEVUnknown>(Denominator))
    1018          24 :       return cannotDivide(Numerator);
    1019             : 
    1020             :     // The Remainder is obtained by replacing Denominator by 0 in Numerator.
    1021             :     ValueToValueMap RewriteMap;
    1022          36 :     RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
    1023          36 :         cast<SCEVConstant>(Zero)->getValue();
    1024          36 :     Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
    1025             : 
    1026          36 :     if (Remainder->isZero()) {
    1027             :       // The Quotient is obtained by replacing Denominator by 1 in Numerator.
    1028           0 :       RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
    1029           0 :           cast<SCEVConstant>(One)->getValue();
    1030           0 :       Quotient =
    1031           0 :           SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
    1032           0 :       return;
    1033             :     }
    1034             : 
    1035             :     // Quotient is (Numerator - Remainder) divided by Denominator.
    1036             :     const SCEV *Q, *R;
    1037          36 :     const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
    1038             :     // This SCEV does not seem to simplify: fail the division here.
    1039          36 :     if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator))
    1040           0 :       return cannotDivide(Numerator);
    1041          36 :     divide(SE, Diff, Denominator, &Q, &R);
    1042          36 :     if (R != Zero)
    1043           0 :       return cannotDivide(Numerator);
    1044          36 :     Quotient = Q;
    1045             :   }
    1046             : 
    1047             : private:
    1048       37763 :   SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
    1049             :                const SCEV *Denominator)
    1050       37763 :       : SE(S), Denominator(Denominator) {
    1051       37763 :     Zero = SE.getZero(Denominator->getType());
    1052       37763 :     One = SE.getOne(Denominator->getType());
    1053             : 
    1054             :     // We generally do not know how to divide Expr by Denominator. We
    1055             :     // initialize the division to a "cannot divide" state to simplify the rest
    1056             :     // of the code.
    1057             :     cannotDivide(Numerator);
    1058       37763 :   }
    1059             : 
    1060             :   // Convenience function for giving up on the division. We set the quotient to
    1061             :   // be equal to zero and the remainder to be equal to the numerator.
    1062             :   void cannotDivide(const SCEV *Numerator) {
    1063       37800 :     Quotient = Zero;
    1064          37 :     Remainder = Numerator;
    1065             :   }
    1066             : 
    1067             :   ScalarEvolution &SE;
    1068             :   const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
    1069             : };
    1070             : 
    1071             : } // end anonymous namespace
    1072             : 
    1073             : //===----------------------------------------------------------------------===//
    1074             : //                      Simple SCEV method implementations
    1075             : //===----------------------------------------------------------------------===//
    1076             : 
    1077             : /// Compute BC(It, K).  The result has width W.  Assume, K > 0.
    1078       30456 : static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
    1079             :                                        ScalarEvolution &SE,
    1080             :                                        Type *ResultTy) {
    1081             :   // Handle the simplest case efficiently.
    1082       30456 :   if (K == 1)
    1083       27995 :     return SE.getTruncateOrZeroExtend(It, ResultTy);
    1084             : 
    1085             :   // We are using the following formula for BC(It, K):
    1086             :   //
    1087             :   //   BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
    1088             :   //
    1089             :   // Suppose, W is the bitwidth of the return value.  We must be prepared for
    1090             :   // overflow.  Hence, we must assure that the result of our computation is
    1091             :   // equal to the accurate one modulo 2^W.  Unfortunately, division isn't
    1092             :   // safe in modular arithmetic.
    1093             :   //
    1094             :   // However, this code doesn't use exactly that formula; the formula it uses
    1095             :   // is something like the following, where T is the number of factors of 2 in
    1096             :   // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
    1097             :   // exponentiation:
    1098             :   //
    1099             :   //   BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
    1100             :   //
    1101             :   // This formula is trivially equivalent to the previous formula.  However,
    1102             :   // this formula can be implemented much more efficiently.  The trick is that
    1103             :   // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
    1104             :   // arithmetic.  To do exact division in modular arithmetic, all we have
    1105             :   // to do is multiply by the inverse.  Therefore, this step can be done at
    1106             :   // width W.
    1107             :   //
    1108             :   // The next issue is how to safely do the division by 2^T.  The way this
    1109             :   // is done is by doing the multiplication step at a width of at least W + T
    1110             :   // bits.  This way, the bottom W+T bits of the product are accurate. Then,
    1111             :   // when we perform the division by 2^T (which is equivalent to a right shift
    1112             :   // by T), the bottom W bits are accurate.  Extra bits are okay; they'll get
    1113             :   // truncated out after the division by 2^T.
    1114             :   //
    1115             :   // In comparison to just directly using the first formula, this technique
    1116             :   // is much more efficient; using the first formula requires W * K bits,
    1117             :   // but this formula less than W + K bits. Also, the first formula requires
    1118             :   // a division step, whereas this formula only requires multiplies and shifts.
    1119             :   //
    1120             :   // It doesn't matter whether the subtraction step is done in the calculation
    1121             :   // width or the input iteration count's width; if the subtraction overflows,
    1122             :   // the result must be zero anyway.  We prefer here to do it in the width of
    1123             :   // the induction variable because it helps a lot for certain cases; CodeGen
    1124             :   // isn't smart enough to ignore the overflow, which leads to much less
    1125             :   // efficient code if the width of the subtraction is wider than the native
    1126             :   // register width.
    1127             :   //
    1128             :   // (It's possible to not widen at all by pulling out factors of 2 before
    1129             :   // the multiplication; for example, K=2 can be calculated as
    1130             :   // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
    1131             :   // extra arithmetic, so it's not an obvious win, and it gets
    1132             :   // much more complicated for K > 3.)
    1133             : 
    1134             :   // Protection from insane SCEVs; this bound is conservative,
    1135             :   // but it probably doesn't matter.
    1136        2461 :   if (K > 1000)
    1137           0 :     return SE.getCouldNotCompute();
    1138             : 
    1139        2461 :   unsigned W = SE.getTypeSizeInBits(ResultTy);
    1140             : 
    1141             :   // Calculate K! / 2^T and T; we divide out the factors of two before
    1142             :   // multiplying for calculating K! / 2^T to avoid overflow.
    1143             :   // Other overflow doesn't matter because we only care about the bottom
    1144             :   // W bits of the result.
    1145             :   APInt OddFactorial(W, 1);
    1146             :   unsigned T = 1;
    1147        4195 :   for (unsigned i = 3; i <= K; ++i) {
    1148        1734 :     APInt Mult(W, i);
    1149        1734 :     unsigned TwoFactors = Mult.countTrailingZeros();
    1150        1734 :     T += TwoFactors;
    1151             :     Mult.lshrInPlace(TwoFactors);
    1152        1734 :     OddFactorial *= Mult;
    1153             :   }
    1154             : 
    1155             :   // We need at least W + T bits for the multiplication step
    1156        2461 :   unsigned CalculationBits = W + T;
    1157             : 
    1158             :   // Calculate 2^T, at width T+W.
    1159        2461 :   APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
    1160             : 
    1161             :   // Calculate the multiplicative inverse of K! / 2^T;
    1162             :   // this multiplication factor will perform the exact division by
    1163             :   // K! / 2^T.
    1164        2461 :   APInt Mod = APInt::getSignedMinValue(W+1);
    1165        2461 :   APInt MultiplyFactor = OddFactorial.zext(W+1);
    1166        2461 :   MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
    1167        2461 :   MultiplyFactor = MultiplyFactor.trunc(W);
    1168             : 
    1169             :   // Calculate the product, at width T+W
    1170        2461 :   IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
    1171             :                                                       CalculationBits);
    1172        2461 :   const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
    1173        6656 :   for (unsigned i = 1; i != K; ++i) {
    1174        4195 :     const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
    1175        4195 :     Dividend = SE.getMulExpr(Dividend,
    1176             :                              SE.getTruncateOrZeroExtend(S, CalculationTy));
    1177             :   }
    1178             : 
    1179             :   // Divide by 2^T
    1180        2461 :   const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
    1181             : 
    1182             :   // Truncate the result, and divide by K! / 2^T.
    1183             : 
    1184        2461 :   return SE.getMulExpr(SE.getConstant(MultiplyFactor),
    1185             :                        SE.getTruncateOrZeroExtend(DivResult, ResultTy));
    1186             : }
    1187             : 
    1188             : /// Return the value of this chain of recurrences at the specified iteration
    1189             : /// number.  We can evaluate this recurrence by multiplying each element in the
    1190             : /// chain by the binomial coefficient corresponding to it.  In other words, we
    1191             : /// can evaluate {A,+,B,+,C,+,D} as:
    1192             : ///
    1193             : ///   A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
    1194             : ///
    1195             : /// where BC(It, k) stands for binomial coefficient.
    1196       27995 : const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
    1197             :                                                 ScalarEvolution &SE) const {
    1198       27995 :   const SCEV *Result = getStart();
    1199       58451 :   for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
    1200             :     // The computation is correct in the face of overflow provided that the
    1201             :     // multiplication is performed _after_ the evaluation of the binomial
    1202             :     // coefficient.
    1203       30456 :     const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
    1204       30456 :     if (isa<SCEVCouldNotCompute>(Coeff))
    1205             :       return Coeff;
    1206             : 
    1207       60912 :     Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
    1208             :   }
    1209             :   return Result;
    1210             : }
    1211             : 
    1212             : //===----------------------------------------------------------------------===//
    1213             : //                    SCEV Expression folder implementations
    1214             : //===----------------------------------------------------------------------===//
    1215             : 
    1216       32650 : const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
    1217             :                                              Type *Ty) {
    1218             :   assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
    1219             :          "This is not a truncating conversion!");
    1220             :   assert(isSCEVable(Ty) &&
    1221             :          "This is not a conversion to a SCEVable type!");
    1222       32650 :   Ty = getEffectiveSCEVType(Ty);
    1223             : 
    1224             :   FoldingSetNodeID ID;
    1225       32650 :   ID.AddInteger(scTruncate);
    1226       32650 :   ID.AddPointer(Op);
    1227       32650 :   ID.AddPointer(Ty);
    1228       32650 :   void *IP = nullptr;
    1229       32650 :   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
    1230             : 
    1231             :   // Fold if the operand is constant.
    1232             :   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
    1233       14993 :     return getConstant(
    1234       29986 :       cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
    1235             : 
    1236             :   // trunc(trunc(x)) --> trunc(x)
    1237             :   if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
    1238          21 :     return getTruncateExpr(ST->getOperand(), Ty);
    1239             : 
    1240             :   // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
    1241             :   if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
    1242         279 :     return getTruncateOrSignExtend(SS->getOperand(), Ty);
    1243             : 
    1244             :   // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
    1245             :   if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
    1246        3133 :     return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
    1247             : 
    1248             :   // trunc(x1 + ... + xN) --> trunc(x1) + ... + trunc(xN) and
    1249             :   // trunc(x1 * ... * xN) --> trunc(x1) * ... * trunc(xN),
    1250             :   // if after transforming we have at most one truncate, not counting truncates
    1251             :   // that replace other casts.
    1252       11387 :   if (isa<SCEVAddExpr>(Op) || isa<SCEVMulExpr>(Op)) {
    1253             :     auto *CommOp = cast<SCEVCommutativeExpr>(Op);
    1254             :     SmallVector<const SCEV *, 4> Operands;
    1255             :     unsigned numTruncs = 0;
    1256        9204 :     for (unsigned i = 0, e = CommOp->getNumOperands(); i != e && numTruncs < 2;
    1257             :          ++i) {
    1258       12340 :       const SCEV *S = getTruncateExpr(CommOp->getOperand(i), Ty);
    1259        9102 :       if (!isa<SCEVCastExpr>(CommOp->getOperand(i)) && isa<SCEVTruncateExpr>(S))
    1260        1309 :         numTruncs++;
    1261        6170 :       Operands.push_back(S);
    1262             :     }
    1263        3034 :     if (numTruncs < 2) {
    1264        2878 :       if (isa<SCEVAddExpr>(Op))
    1265        1773 :         return getAddExpr(Operands);
    1266        1105 :       else if (isa<SCEVMulExpr>(Op))
    1267        1105 :         return getMulExpr(Operands);
    1268             :       else
    1269           0 :         llvm_unreachable("Unexpected SCEV type for Op.");
    1270             :     }
    1271             :     // Although we checked in the beginning that ID is not in the cache, it is
    1272             :     // possible that during recursion and different modification ID was inserted
    1273             :     // into the cache. So if we find it, just return it.
    1274         156 :     if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
    1275             :       return S;
    1276             :   }
    1277             : 
    1278             :   // If the input value is a chrec scev, truncate the chrec's operands.
    1279             :   if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
    1280             :     SmallVector<const SCEV *, 4> Operands;
    1281       10078 :     for (const SCEV *Op : AddRec->operands())
    1282        6724 :       Operands.push_back(getTruncateExpr(Op, Ty));
    1283        3354 :     return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
    1284             :   }
    1285             : 
    1286             :   // The cast wasn't folded; create an explicit cast node. We can reuse
    1287             :   // the existing insert position since if we get here, we won't have
    1288             :   // made any changes which would invalidate it.
    1289        5155 :   SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
    1290        5155 :                                                  Op, Ty);
    1291        5155 :   UniqueSCEVs.InsertNode(S, IP);
    1292        5155 :   addToLoopUseLists(S);
    1293        5155 :   return S;
    1294             : }
    1295             : 
    1296             : // Get the limit of a recurrence such that incrementing by Step cannot cause
    1297             : // signed overflow as long as the value of the recurrence within the
    1298             : // loop does not exceed this limit before incrementing.
    1299        6357 : static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
    1300             :                                                  ICmpInst::Predicate *Pred,
    1301             :                                                  ScalarEvolution *SE) {
    1302        6357 :   unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
    1303        6357 :   if (SE->isKnownPositive(Step)) {
    1304        4075 :     *Pred = ICmpInst::ICMP_SLT;
    1305        8154 :     return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
    1306        4075 :                            SE->getSignedRangeMax(Step));
    1307             :   }
    1308        2282 :   if (SE->isKnownNegative(Step)) {
    1309        2156 :     *Pred = ICmpInst::ICMP_SGT;
    1310        4312 :     return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
    1311        2156 :                            SE->getSignedRangeMin(Step));
    1312             :   }
    1313             :   return nullptr;
    1314             : }
    1315             : 
    1316             : // Get the limit of a recurrence such that incrementing by Step cannot cause
    1317             : // unsigned overflow as long as the value of the recurrence within the loop does
    1318             : // not exceed this limit before incrementing.
    1319         547 : static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
    1320             :                                                    ICmpInst::Predicate *Pred,
    1321             :                                                    ScalarEvolution *SE) {
    1322         547 :   unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
    1323         547 :   *Pred = ICmpInst::ICMP_ULT;
    1324             : 
    1325        1094 :   return SE->getConstant(APInt::getMinValue(BitWidth) -
    1326         547 :                          SE->getUnsignedRangeMax(Step));
    1327             : }
    1328             : 
    1329             : namespace {
    1330             : 
    1331             : struct ExtendOpTraitsBase {
    1332             :   typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *,
    1333             :                                                           unsigned);
    1334             : };
    1335             : 
    1336             : // Used to make code generic over signed and unsigned overflow.
    1337             : template <typename ExtendOp> struct ExtendOpTraits {
    1338             :   // Members present:
    1339             :   //
    1340             :   // static const SCEV::NoWrapFlags WrapType;
    1341             :   //
    1342             :   // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
    1343             :   //
    1344             :   // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
    1345             :   //                                           ICmpInst::Predicate *Pred,
    1346             :   //                                           ScalarEvolution *SE);
    1347             : };
    1348             : 
    1349             : template <>
    1350             : struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
    1351             :   static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
    1352             : 
    1353             :   static const GetExtendExprTy GetExtendExpr;
    1354             : 
    1355         133 :   static const SCEV *getOverflowLimitForStep(const SCEV *Step,
    1356             :                                              ICmpInst::Predicate *Pred,
    1357             :                                              ScalarEvolution *SE) {
    1358         133 :     return getSignedOverflowLimitForStep(Step, Pred, SE);
    1359             :   }
    1360             : };
    1361             : 
    1362             : const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
    1363             :     SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
    1364             : 
    1365             : template <>
    1366             : struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
    1367             :   static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
    1368             : 
    1369             :   static const GetExtendExprTy GetExtendExpr;
    1370             : 
    1371         201 :   static const SCEV *getOverflowLimitForStep(const SCEV *Step,
    1372             :                                              ICmpInst::Predicate *Pred,
    1373             :                                              ScalarEvolution *SE) {
    1374         201 :     return getUnsignedOverflowLimitForStep(Step, Pred, SE);
    1375             :   }
    1376             : };
    1377             : 
    1378             : const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
    1379             :     SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
    1380             : 
    1381             : } // end anonymous namespace
    1382             : 
    1383             : // The recurrence AR has been shown to have no signed/unsigned wrap or something
    1384             : // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
    1385             : // easily prove NSW/NUW for its preincrement or postincrement sibling. This
    1386             : // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
    1387             : // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
    1388             : // expression "Step + sext/zext(PreIncAR)" is congruent with
    1389             : // "sext/zext(PostIncAR)"
    1390             : template <typename ExtendOpTy>
    1391           0 : static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
    1392             :                                         ScalarEvolution *SE, unsigned Depth) {
    1393             :   auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
    1394             :   auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
    1395             : 
    1396           0 :   const Loop *L = AR->getLoop();
    1397           0 :   const SCEV *Start = AR->getStart();
    1398           0 :   const SCEV *Step = AR->getStepRecurrence(*SE);
    1399             : 
    1400             :   // Check for a simple looking step prior to loop entry.
    1401             :   const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
    1402             :   if (!SA)
    1403           0 :     return nullptr;
    1404             : 
    1405             :   // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
    1406             :   // subtraction is expensive. For this purpose, perform a quick and dirty
    1407             :   // difference, by checking for Step in the operand list.
    1408             :   SmallVector<const SCEV *, 4> DiffOps;
    1409           0 :   for (const SCEV *Op : SA->operands())
    1410           0 :     if (Op != Step)
    1411           0 :       DiffOps.push_back(Op);
    1412             : 
    1413           0 :   if (DiffOps.size() == SA->getNumOperands())
    1414           0 :     return nullptr;
    1415             : 
    1416             :   // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
    1417             :   // `Step`:
    1418             : 
    1419             :   // 1. NSW/NUW flags on the step increment.
    1420             :   auto PreStartFlags =
    1421           0 :     ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
    1422           0 :   const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
    1423           0 :   const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
    1424             :       SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
    1425             : 
    1426             :   // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
    1427             :   // "S+X does not sign/unsign-overflow".
    1428             :   //
    1429             : 
    1430           0 :   const SCEV *BECount = SE->getBackedgeTakenCount(L);
    1431           0 :   if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
    1432           0 :       !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
    1433           0 :     return PreStart;
    1434             : 
    1435             :   // 2. Direct overflow check on the step operation's expression.
    1436           0 :   unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
    1437           0 :   Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
    1438           0 :   const SCEV *OperandExtendedStart =
    1439             :       SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy, Depth),
    1440             :                      (SE->*GetExtendExpr)(Step, WideTy, Depth));
    1441           0 :   if ((SE->*GetExtendExpr)(Start, WideTy, Depth) == OperandExtendedStart) {
    1442           0 :     if (PreAR && AR->getNoWrapFlags(WrapType)) {
    1443             :       // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
    1444             :       // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
    1445             :       // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`.  Cache this fact.
    1446             :       const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
    1447             :     }
    1448           0 :     return PreStart;
    1449             :   }
    1450             : 
    1451             :   // 3. Loop precondition.
    1452             :   ICmpInst::Predicate Pred;
    1453             :   const SCEV *OverflowLimit =
    1454           0 :       ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
    1455             : 
    1456           0 :   if (OverflowLimit &&
    1457           0 :       SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
    1458           0 :     return PreStart;
    1459             : 
    1460             :   return nullptr;
    1461             : }
    1462           0 : 
    1463             : // Get the normalized zero or sign extended expression for this AddRec's Start.
    1464             : template <typename ExtendOpTy>
    1465             : static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
    1466             :                                         ScalarEvolution *SE,
    1467           0 :                                         unsigned Depth) {
    1468           0 :   auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
    1469           0 : 
    1470             :   const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE, Depth);
    1471             :   if (!PreStart)
    1472             :     return (SE->*GetExtendExpr)(AR->getStart(), Ty, Depth);
    1473             : 
    1474           0 :   return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty,
    1475             :                                              Depth),
    1476             :                         (SE->*GetExtendExpr)(PreStart, Ty, Depth));
    1477             : }
    1478             : 
    1479             : // Try to prove away overflow by looking at "nearby" add recurrences.  A
    1480           0 : // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
    1481           0 : // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
    1482           0 : //
    1483             : // Formally:
    1484           0 : //
    1485           0 : //     {S,+,X} == {S-T,+,X} + T
    1486             : //  => Ext({S,+,X}) == Ext({S-T,+,X} + T)
    1487             : //
    1488             : // If ({S-T,+,X} + T) does not overflow  ... (1)
    1489             : //
    1490             : //  RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
    1491             : //
    1492           0 : // If {S-T,+,X} does not overflow  ... (2)
    1493           0 : //
    1494           0 : //  RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
    1495             : //      == {Ext(S-T)+Ext(T),+,Ext(X)}
    1496             : //
    1497             : // If (S-T)+T does not overflow  ... (3)
    1498             : //
    1499             : //  RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
    1500             : //      == {Ext(S),+,Ext(X)} == LHS
    1501           0 : //
    1502           0 : // Thus, if (1), (2) and (3) are true for some T, then
    1503           0 : //   Ext({S,+,X}) == {Ext(S),+,Ext(X)}
    1504           0 : //
    1505             : // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
    1506             : // does not overflow" restricted to the 0th iteration.  Therefore we only need
    1507           0 : // to check for (1) and (2).
    1508           0 : //
    1509           0 : // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
    1510             : // is `Delta` (defined below).
    1511             : template <typename ExtendOpTy>
    1512           0 : bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
    1513           0 :                                                 const SCEV *Step,
    1514             :                                                 const Loop *L) {
    1515             :   auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
    1516             : 
    1517             :   // We restrict `Start` to a constant to prevent SCEV from spending too much
    1518             :   // time here.  It is correct (but more expensive) to continue with a
    1519           0 :   // non-constant `Start` and do a general SCEV subtraction to compute
    1520             :   // `PreStart` below.
    1521             :   const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
    1522             :   if (!StartC)
    1523             :     return false;
    1524             : 
    1525           0 :   APInt StartAI = StartC->getAPInt();
    1526             : 
    1527           0 :   for (unsigned Delta : {-2, -1, 1, 2}) {
    1528           0 :     const SCEV *PreStart = getConstant(StartAI - Delta);
    1529           0 : 
    1530             :     FoldingSetNodeID ID;
    1531             :     ID.AddInteger(scAddRecExpr);
    1532             :     ID.AddPointer(PreStart);
    1533           0 :     ID.AddPointer(Step);
    1534             :     ID.AddPointer(L);
    1535             :     void *IP = nullptr;
    1536             :     const auto *PreAR =
    1537             :       static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
    1538           0 : 
    1539           0 :     // Give up if we don't already have the add recurrence we need because
    1540           0 :     // actually constructing an add recurrence is relatively expensive.
    1541             :     if (PreAR && PreAR->getNoWrapFlags(WrapType)) {  // proves (2)
    1542             :       const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
    1543             :       ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
    1544             :       const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
    1545           0 :           DeltaS, &Pred, this);
    1546             :       if (Limit && isKnownPredicate(Pred, PreAR, Limit))  // proves (1)
    1547             :         return true;
    1548             :     }
    1549             :   }
    1550             : 
    1551           0 :   return false;
    1552           0 : }
    1553           0 : 
    1554             : // Finds an integer D for an expression (C + x + y + ...) such that the top
    1555           0 : // level addition in (D + (C - D + x + y + ...)) would not wrap (signed or
    1556           0 : // unsigned) and the number of trailing zeros of (C - D + x + y + ...) is
    1557             : // maximized, where C is the \p ConstantTerm, x, y, ... are arbitrary SCEVs, and
    1558             : // the (C + x + y + ...) expression is \p WholeAddExpr.
    1559             : static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
    1560             :                                             const SCEVConstant *ConstantTerm,
    1561             :                                             const SCEVAddExpr *WholeAddExpr) {
    1562             :   const APInt C = ConstantTerm->getAPInt();
    1563           0 :   const unsigned BitWidth = C.getBitWidth();
    1564           0 :   // Find number of trailing zeros of (x + y + ...) w/o the C first:
    1565           0 :   uint32_t TZ = BitWidth;
    1566             :   for (unsigned I = 1, E = WholeAddExpr->getNumOperands(); I < E && TZ; ++I)
    1567             :     TZ = std::min(TZ, SE.GetMinTrailingZeros(WholeAddExpr->getOperand(I)));
    1568             :   if (TZ) {
    1569             :     // Set D to be as many least significant bits of C as possible while still
    1570             :     // guaranteeing that adding D to (C - D + x + y + ...) won't cause a wrap:
    1571             :     return TZ < BitWidth ? C.trunc(TZ).zext(BitWidth) : C;
    1572           0 :   }
    1573           0 :   return APInt(BitWidth, 0);
    1574           0 : }
    1575           0 : 
    1576             : // Finds an integer D for an affine AddRec expression {C,+,x} such that the top
    1577             : // level addition in (D + {C-D,+,x}) would not wrap (signed or unsigned) and the
    1578           0 : // number of trailing zeros of (C - D + x * n) is maximized, where C is the \p
    1579           0 : // ConstantStart, x is an arbitrary \p Step, and n is the loop trip count.
    1580           0 : static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
    1581             :                                             const APInt &ConstantStart,
    1582             :                                             const SCEV *Step) {
    1583           0 :   const unsigned BitWidth = ConstantStart.getBitWidth();
    1584           0 :   const uint32_t TZ = SE.GetMinTrailingZeros(Step);
    1585             :   if (TZ)
    1586             :     return TZ < BitWidth ? ConstantStart.trunc(TZ).zext(BitWidth)
    1587             :                          : ConstantStart;
    1588             :   return APInt(BitWidth, 0);
    1589             : }
    1590           0 : 
    1591             : const SCEV *
    1592             : ScalarEvolution::getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
    1593             :   assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
    1594             :          "This is not an extending conversion!");
    1595             :   assert(isSCEVable(Ty) &&
    1596             :          "This is not a conversion to a SCEVable type!");
    1597             :   Ty = getEffectiveSCEVType(Ty);
    1598           0 : 
    1599           0 :   // Fold if the operand is constant.
    1600           0 :   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
    1601             :     return getConstant(
    1602             :       cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
    1603             : 
    1604             :   // zext(zext(x)) --> zext(x)
    1605             :   if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
    1606             :     return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
    1607       33222 : 
    1608             :   // Before doing any expensive analysis, check to see if we've already
    1609             :   // computed a SCEV for this Op and Ty.
    1610             :   FoldingSetNodeID ID;
    1611             :   ID.AddInteger(scZeroExtend);
    1612       33222 :   ID.AddPointer(Op);
    1613       33222 :   ID.AddPointer(Ty);
    1614       65726 :   void *IP = nullptr;
    1615             :   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
    1616             :   if (Depth > MaxExtDepth) {
    1617             :     SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
    1618         359 :                                                      Op, Ty);
    1619             :     UniqueSCEVs.InsertNode(S, IP);
    1620       11231 :     addToLoopUseLists(S);
    1621             :     return S;
    1622             :   }
    1623             : 
    1624             :   // zext(trunc(x)) --> zext(x) or x or trunc(x)
    1625       11231 :   if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
    1626       11231 :     // It's possible the bits taken off by the truncate were all zero bits. If
    1627       21866 :     // so, we should be able to simplify this further.
    1628             :     const SCEV *X = ST->getOperand();
    1629             :     ConstantRange CR = getUnsignedRange(X);
    1630             :     unsigned TruncBits = getTypeSizeInBits(ST->getType());
    1631         298 :     unsigned NewBits = getTypeSizeInBits(Ty);
    1632             :     if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
    1633       21991 :             CR.zextOrTrunc(NewBits)))
    1634             :       return getTruncateOrZeroExtend(X, Ty);
    1635             :   }
    1636             : 
    1637             :   // If the input value is a chrec scev, and we can prove that the value
    1638       21991 :   // did not overflow the old, smaller, value, we can zero extend all of the
    1639       21991 :   // operands (often constants).  This allows analysis of something like
    1640       43860 :   // this:  for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
    1641             :   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
    1642             :     if (AR->isAffine()) {
    1643             :       const SCEV *Start = AR->getStart();
    1644          61 :       const SCEV *Step = AR->getStepRecurrence(*this);
    1645             :       unsigned BitWidth = getTypeSizeInBits(AR->getType());
    1646             :       const Loop *L = AR->getLoop();
    1647             : 
    1648             :       if (!AR->hasNoUnsignedWrap()) {
    1649             :         auto NewFlags = proveNoWrapViaConstantRanges(AR);
    1650             :         const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
    1651             :       }
    1652             : 
    1653             :       // If we have special knowledge that this addrec won't overflow,
    1654             :       // we don't need to do any further analysis.
    1655             :       if (AR->hasNoUnsignedWrap())
    1656             :         return getAddRecExpr(
    1657             :             getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
    1658             :             getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
    1659             : 
    1660             :       // Check whether the backedge-taken count is SCEVCouldNotCompute.
    1661             :       // Note that this serves two purposes: It filters out loops that are
    1662             :       // simply not analyzable, and it covers the case where this code is
    1663             :       // being called from within backedge-taken count analysis, such that
    1664             :       // attempting to ask for the backedge-taken count would likely result
    1665             :       // in infinite recursion. In the later case, the analysis code will
    1666             :       // cope with a conservative value, and it will take care to purge
    1667             :       // that value once it has finished.
    1668             :       const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
    1669             :       if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
    1670             :         // Manually compute the final value for AR, checking for
    1671             :         // overflow.
    1672             : 
    1673             :         // Check whether the backedge-taken count can be losslessly casted to
    1674             :         // the addrec's type. The count is always unsigned.
    1675             :         const SCEV *CastedMaxBECount =
    1676             :           getTruncateOrZeroExtend(MaxBECount, Start->getType());
    1677             :         const SCEV *RecastedMaxBECount =
    1678             :           getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
    1679             :         if (MaxBECount == RecastedMaxBECount) {
    1680       19590 :           Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
    1681             :           // Check whether Start+Step*MaxBECount has no unsigned overflow.
    1682             :           const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step,
    1683             :                                         SCEV::FlagAnyWrap, Depth + 1);
    1684             :           const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul,
    1685             :                                                           SCEV::FlagAnyWrap,
    1686             :                                                           Depth + 1),
    1687             :                                                WideTy, Depth + 1);
    1688             :           const SCEV *WideStart = getZeroExtendExpr(Start, WideTy, Depth + 1);
    1689             :           const SCEV *WideMaxBECount =
    1690             :             getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
    1691             :           const SCEV *OperandExtendedAdd =
    1692             :             getAddExpr(WideStart,
    1693             :                        getMulExpr(WideMaxBECount,
    1694             :                                   getZeroExtendExpr(Step, WideTy, Depth + 1),
    1695       32359 :                                   SCEV::FlagAnyWrap, Depth + 1),
    1696       77664 :                        SCEV::FlagAnyWrap, Depth + 1);
    1697             :           if (ZAdd == OperandExtendedAdd) {
    1698             :             // Cache knowledge of AR NUW, which is propagated to this AddRec.
    1699       25888 :             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
    1700       25888 :             // Return the expression with the addrec on the outside.
    1701       25888 :             return getAddRecExpr(
    1702       25888 :                 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
    1703       25888 :                                                          Depth + 1),
    1704             :                 getZeroExtendExpr(Step, Ty, Depth + 1), L,
    1705             :                 AR->getNoWrapFlags());
    1706             :           }
    1707             :           // Similar to above, only this time treat the step value as signed.
    1708             :           // This covers loops that count down.
    1709       25888 :           OperandExtendedAdd =
    1710         460 :             getAddExpr(WideStart,
    1711         230 :                        getMulExpr(WideMaxBECount,
    1712         201 :                                   getSignExtendExpr(Step, WideTy, Depth + 1),
    1713             :                                   SCEV::FlagAnyWrap, Depth + 1),
    1714         230 :                        SCEV::FlagAnyWrap, Depth + 1);
    1715           1 :           if (ZAdd == OperandExtendedAdd) {
    1716             :             // Cache knowledge of AR NW, which is propagated to this AddRec.
    1717             :             // Negative step causes unsigned wrap, but it still can't self-wrap.
    1718             :             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
    1719             :             // Return the expression with the addrec on the outside.
    1720             :             return getAddRecExpr(
    1721       10653 :                 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
    1722             :                                                          Depth + 1),
    1723             :                 getSignExtendExpr(Step, Ty, Depth + 1), L,
    1724             :                 AR->getNoWrapFlags());
    1725             :           }
    1726             :         }
    1727             :       }
    1728             : 
    1729             :       // Normally, in the cases we can prove no-overflow via a
    1730             :       // backedge guarding condition, we can also compute a backedge
    1731             :       // taken count for the loop.  The exceptions are assumptions and
    1732             :       // guards present in the loop -- SCEV is not great at exploiting
    1733             :       // these to compute max backedge taken counts, but can still use
    1734             :       // these to prove lack of overflow.  Use this fact to avoid
    1735             :       // doing extra work that may not pay off.
    1736       16555 :       if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
    1737       39732 :           !AC.assumptions().empty()) {
    1738             :         // If the backedge is guarded by a comparison with the pre-inc
    1739             :         // value the addrec is safe. Also, if the entry is guarded by
    1740       13244 :         // a comparison with the start value and the backedge is
    1741       13244 :         // guarded by a comparison with the post-inc value, the addrec
    1742       13244 :         // is safe.
    1743       13244 :         if (isKnownPositive(Step)) {
    1744       13244 :           const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
    1745             :                                       getUnsignedRangeMax(Step));
    1746             :           if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
    1747             :               isKnownOnEveryIteration(ICmpInst::ICMP_ULT, AR, N)) {
    1748             :             // Cache knowledge of AR NUW, which is propagated to this
    1749             :             // AddRec.
    1750       13244 :             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
    1751          58 :             // Return the expression with the addrec on the outside.
    1752          29 :             return getAddRecExpr(
    1753             :                 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
    1754             :                                                          Depth + 1),
    1755          29 :                 getZeroExtendExpr(Step, Ty, Depth + 1), L,
    1756           0 :                 AR->getNoWrapFlags());
    1757             :           }
    1758             :         } else if (isKnownNegative(Step)) {
    1759             :           const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
    1760             :                                       getSignedRangeMin(Step));
    1761             :           if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
    1762        8937 :               isKnownOnEveryIteration(ICmpInst::ICMP_UGT, AR, N)) {
    1763             :             // Cache knowledge of AR NW, which is propagated to this
    1764             :             // AddRec.  Negative step causes unsigned wrap, but it
    1765             :             // still can't self-wrap.
    1766             :             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
    1767             :             // Return the expression with the addrec on the outside.
    1768             :             return getAddRecExpr(
    1769             :                 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
    1770             :                                                          Depth + 1),
    1771             :                 getSignExtendExpr(Step, Ty, Depth + 1), L,
    1772             :                 AR->getNoWrapFlags());
    1773             :           }
    1774             :         }
    1775             :       }
    1776             : 
    1777       15804 :       // zext({C,+,Step}) --> (zext(D) + zext({C-D,+,Step}))<nuw><nsw>
    1778       37932 :       // if D + (C - D + Step * n) could be proven to not unsigned wrap
    1779             :       // where D maximizes the number of trailing zeros of (C - D + Step * n)
    1780             :       if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
    1781       12644 :         const APInt &C = SC->getAPInt();
    1782       12644 :         const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
    1783       12644 :         if (D != 0) {
    1784       12644 :           const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
    1785       12644 :           const SCEV *SResidual =
    1786             :               getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
    1787             :           const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
    1788             :           return getAddExpr(SZExtD, SZExtR,
    1789             :                             (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
    1790             :                             Depth + 1);
    1791       12644 :         }
    1792         402 :       }
    1793         201 : 
    1794         201 :       if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
    1795             :         const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
    1796         201 :         return getAddRecExpr(
    1797           1 :             getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
    1798             :             getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
    1799             :       }
    1800             :     }
    1801             : 
    1802             :   // zext(A % B) --> zext(A) % zext(B)
    1803             :   {
    1804             :     const SCEV *LHS;
    1805             :     const SCEV *RHS;
    1806             :     if (matchURem(Op, LHS, RHS))
    1807             :       return getURemExpr(getZeroExtendExpr(LHS, Ty, Depth + 1),
    1808             :                          getZeroExtendExpr(RHS, Ty, Depth + 1));
    1809       13695 :   }
    1810             : 
    1811             :   // zext(A / B) --> zext(A) / zext(B).
    1812             :   if (auto *Div = dyn_cast<SCEVUDivExpr>(Op))
    1813       13695 :     return getUDivExpr(getZeroExtendExpr(Div->getLHS(), Ty, Depth + 1),
    1814             :                        getZeroExtendExpr(Div->getRHS(), Ty, Depth + 1));
    1815       13695 : 
    1816       27820 :   if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
    1817       42165 :     // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
    1818       13695 :     if (SA->hasNoUnsignedWrap()) {
    1819             :       // If the addition does not unsign overflow then we can, by definition,
    1820             :       // commute the zero extension with the addition operation.
    1821        5052 :       SmallVector<const SCEV *, 4> Ops;
    1822             :       for (const auto *Op : SA->operands())
    1823             :         Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
    1824             :       return getAddExpr(Ops, SCEV::FlagNUW, Depth + 1);
    1825             :     }
    1826             : 
    1827             :     // zext(C + x + y + ...) --> (zext(D) + zext((C - D) + x + y + ...))
    1828             :     // if D + (C - D + x + y + ...) could be proven to not unsigned wrap
    1829             :     // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
    1830        9342 :     //
    1831             :     // Often address arithmetics contain expressions like
    1832             :     // (zext (add (shl X, C1), C2)), for instance, (zext (5 + (4 * X))).
    1833        9342 :     // This transformation is useful while proving that such expressions are
    1834        9342 :     // equal or differ by a small constant amount, see LoadStoreVectorizer pass.
    1835        9342 :     if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
    1836       10234 :       const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
    1837       10234 :       if (D != 0) {
    1838             :         const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
    1839             :         const SCEV *SResidual =
    1840             :             getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
    1841             :         const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
    1842      289751 :         return getAddExpr(SZExtD, SZExtR,
    1843             :                           (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
    1844             :                           Depth + 1);
    1845             :       }
    1846             :     }
    1847      289751 :   }
    1848             : 
    1849             :   if (auto *SM = dyn_cast<SCEVMulExpr>(Op)) {
    1850             :     // zext((A * B * ...)<nuw>) --> (zext(A) * zext(B) * ...)<nuw>
    1851      143850 :     if (SM->hasNoUnsignedWrap()) {
    1852      287700 :       // If the multiply does not unsign overflow then we can, by definition,
    1853             :       // commute the zero extension with the multiply operation.
    1854             :       SmallVector<const SCEV *, 4> Ops;
    1855             :       for (const auto *Op : SM->operands())
    1856        8878 :         Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
    1857             :       return getMulExpr(Ops, SCEV::FlagNUW, Depth + 1);
    1858             :     }
    1859             : 
    1860             :     // zext(2^K * (trunc X to iN)) to iM ->
    1861      137023 :     // 2^K * (zext(trunc X to i{N-K}) to iM)<nuw>
    1862      137023 :     //
    1863      137023 :     // Proof:
    1864      137023 :     //
    1865      137023 :     //     zext(2^K * (trunc X to iN)) to iM
    1866       78755 :     //   = zext((trunc X to iN) << K) to iM
    1867          12 :     //   = zext((trunc X to i{N-K}) << K)<nuw> to iM
    1868          12 :     //     (because shl removes the top K bits)
    1869          12 :     //   = zext((2^K * (trunc X to i{N-K}))<nuw>) to iM
    1870          12 :     //   = (2^K * (zext(trunc X to i{N-K}) to iM))<nuw>.
    1871          12 :     //
    1872             :     if (SM->getNumOperands() == 2)
    1873             :       if (auto *MulLHS = dyn_cast<SCEVConstant>(SM->getOperand(0)))
    1874             :         if (MulLHS->getAPInt().isPowerOf2())
    1875             :           if (auto *TruncRHS = dyn_cast<SCEVTruncateExpr>(SM->getOperand(1))) {
    1876             :             int NewTruncBits = getTypeSizeInBits(TruncRHS->getType()) -
    1877             :                                MulLHS->getAPInt().logBase2();
    1878        2527 :             Type *NewTruncTy = IntegerType::get(getContext(), NewTruncBits);
    1879        4650 :             return getMulExpr(
    1880        2527 :                 getZeroExtendExpr(MulLHS, Ty),
    1881        2527 :                 getZeroExtendExpr(
    1882        7581 :                     getTruncateExpr(TruncRHS->getOperand(), NewTruncTy), Ty),
    1883        5054 :                 SCEV::FlagNUW, Depth + 1);
    1884         404 :           }
    1885             :   }
    1886             : 
    1887             :   // The cast wasn't folded; create an explicit cast node.
    1888             :   // Recompute the insert position, as it may have been invalidated.
    1889             :   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
    1890             :   SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
    1891             :                                                    Op, Ty);
    1892       32596 :   UniqueSCEVs.InsertNode(S, IP);
    1893       32517 :   addToLoopUseLists(S);
    1894       32517 :   return S;
    1895       32517 : }
    1896       32517 : 
    1897             : const SCEV *
    1898       32517 : ScalarEvolution::getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
    1899       25399 :   assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
    1900             :          "This is not an extending conversion!");
    1901             :   assert(isSCEVable(Ty) &&
    1902             :          "This is not a conversion to a SCEVable type!");
    1903             :   Ty = getEffectiveSCEVType(Ty);
    1904             : 
    1905       32517 :   // Fold if the operand is constant.
    1906        9545 :   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
    1907             :     return getConstant(
    1908        9545 :       cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
    1909             : 
    1910             :   // sext(sext(x)) --> sext(x)
    1911             :   if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
    1912             :     return getSignExtendExpr(SS->getOperand(), Ty, Depth + 1);
    1913             : 
    1914             :   // sext(zext(x)) --> zext(x)
    1915             :   if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
    1916             :     return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
    1917             : 
    1918       22972 :   // Before doing any expensive analysis, check to see if we've already
    1919       22972 :   // computed a SCEV for this Op and Ty.
    1920             :   FoldingSetNodeID ID;
    1921             :   ID.AddInteger(scSignExtend);
    1922             :   ID.AddPointer(Op);
    1923             :   ID.AddPointer(Ty);
    1924             :   void *IP = nullptr;
    1925             :   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
    1926       18510 :   // Limit recursion depth.
    1927             :   if (Depth > MaxExtDepth) {
    1928       18510 :     SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
    1929       18510 :                                                      Op, Ty);
    1930       17396 :     UniqueSCEVs.InsertNode(S, IP);
    1931             :     addToLoopUseLists(S);
    1932       17396 :     return S;
    1933             :   }
    1934       17396 : 
    1935             :   // sext(trunc(x)) --> sext(x) or x or trunc(x)
    1936             :   if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
    1937             :     // It's possible the bits taken off by the truncate were all sign bits. If
    1938       17396 :     // so, we should be able to simplify this further.
    1939             :     const SCEV *X = ST->getOperand();
    1940       17396 :     ConstantRange CR = getSignedRange(X);
    1941             :     unsigned TruncBits = getTypeSizeInBits(ST->getType());
    1942       17396 :     unsigned NewBits = getTypeSizeInBits(Ty);
    1943             :     if (CR.truncate(TruncBits).signExtend(NewBits).contains(
    1944             :             CR.sextOrTrunc(NewBits)))
    1945             :       return getTruncateOrSignExtend(X, Ty);
    1946             :   }
    1947       17396 : 
    1948             :   if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
    1949             :     // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
    1950             :     if (SA->hasNoSignedWrap()) {
    1951         906 :       // If the addition does not sign overflow then we can, by definition,
    1952             :       // commute the sign extension with the addition operation.
    1953             :       SmallVector<const SCEV *, 4> Ops;
    1954             :       for (const auto *Op : SA->operands())
    1955         906 :         Ops.push_back(getSignExtendExpr(Op, Ty, Depth + 1));
    1956             :       return getAddExpr(Ops, SCEV::FlagNSW, Depth + 1);
    1957             :     }
    1958             : 
    1959             :     // sext(C + x + y + ...) --> (sext(D) + sext((C - D) + x + y + ...))
    1960       16490 :     // if D + (C - D + x + y + ...) could be proven to not signed wrap
    1961             :     // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
    1962             :     //
    1963             :     // For instance, this will bring two seemingly different expressions:
    1964             :     //     1 + sext(5 + 20 * %x + 24 * %y)  and
    1965       16490 :     //         sext(6 + 20 * %x + 24 * %y)
    1966             :     // to the same form:
    1967             :     //     2 + sext(4 + 20 * %x + 24 * %y)
    1968             :     if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
    1969             :       const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
    1970        1083 :       if (D != 0) {
    1971             :         const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
    1972             :         const SCEV *SResidual =
    1973             :             getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
    1974        1083 :         const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
    1975             :         return getAddExpr(SSExtD, SSExtR,
    1976             :                           (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
    1977             :                           Depth + 1);
    1978             :       }
    1979             :     }
    1980             :   }
    1981             :   // If the input value is a chrec scev, and we can prove that the value
    1982             :   // did not overflow the old, smaller, value, we can sign extend all of the
    1983             :   // operands (often constants).  This allows analysis of something like
    1984             :   // this:  for (signed char X = 0; X < 100; ++X) { int Y = X; }
    1985             :   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
    1986       25436 :     if (AR->isAffine()) {
    1987        4453 :       const SCEV *Start = AR->getStart();
    1988             :       const SCEV *Step = AR->getStepRecurrence(*this);
    1989             :       unsigned BitWidth = getTypeSizeInBits(AR->getType());
    1990             :       const Loop *L = AR->getLoop();
    1991             : 
    1992             :       if (!AR->hasNoSignedWrap()) {
    1993       16563 :         auto NewFlags = proveNoWrapViaConstantRanges(AR);
    1994        6946 :         const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
    1995        3473 :       }
    1996        6900 : 
    1997        3427 :       // If we have special knowledge that this addrec won't overflow,
    1998             :       // we don't need to do any further analysis.
    1999             :       if (AR->hasNoSignedWrap())
    2000             :         return getAddRecExpr(
    2001             :             getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
    2002          82 :             getSignExtendExpr(Step, Ty, Depth + 1), L, SCEV::FlagNSW);
    2003             : 
    2004             :       // Check whether the backedge-taken count is SCEVCouldNotCompute.
    2005             :       // Note that this serves two purposes: It filters out loops that are
    2006          82 :       // simply not analyzable, and it covers the case where this code is
    2007             :       // being called from within backedge-taken count analysis, such that
    2008       13090 :       // attempting to ask for the backedge-taken count would likely result
    2009       25872 :       // in infinite recursion. In the later case, the analysis code will
    2010       12936 :       // cope with a conservative value, and it will take care to purge
    2011       15659 :       // that value once it has finished.
    2012        2723 :       const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
    2013             :       if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
    2014             :         // Manually compute the final value for AR, checking for
    2015             :         // overflow.
    2016             : 
    2017             :         // Check whether the backedge-taken count can be losslessly casted to
    2018       10374 :         // the addrec's type. The count is always unsigned.
    2019             :         const SCEV *CastedMaxBECount =
    2020             :           getTruncateOrZeroExtend(MaxBECount, Start->getType());
    2021             :         const SCEV *RecastedMaxBECount =
    2022       10374 :           getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
    2023             :         if (MaxBECount == RecastedMaxBECount) {
    2024             :           Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
    2025             :           // Check whether Start+Step*MaxBECount has no signed overflow.
    2026             :           const SCEV *SMul = getMulExpr(CastedMaxBECount, Step,
    2027             :                                         SCEV::FlagAnyWrap, Depth + 1);
    2028             :           const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul,
    2029             :                                                           SCEV::FlagAnyWrap,
    2030             :                                                           Depth + 1),
    2031             :                                                WideTy, Depth + 1);
    2032        4751 :           const SCEV *WideStart = getSignExtendExpr(Start, WideTy, Depth + 1);
    2033        4751 :           const SCEV *WideMaxBECount =
    2034        1590 :             getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
    2035             :           const SCEV *OperandExtendedAdd =
    2036        4770 :             getAddExpr(WideStart,
    2037        1590 :                        getMulExpr(WideMaxBECount,
    2038        1590 :                                   getSignExtendExpr(Step, WideTy, Depth + 1),
    2039             :                                   SCEV::FlagAnyWrap, Depth + 1),
    2040             :                        SCEV::FlagAnyWrap, Depth + 1);
    2041             :           if (SAdd == OperandExtendedAdd) {
    2042             :             // Cache knowledge of AR NSW, which is propagated to this AddRec.
    2043             :             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
    2044        8937 :             // Return the expression with the addrec on the outside.
    2045             :             return getAddRecExpr(
    2046           1 :                 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
    2047             :                                                          Depth + 1),
    2048           1 :                 getSignExtendExpr(Step, Ty, Depth + 1), L,
    2049             :                 AR->getNoWrapFlags());
    2050             :           }
    2051             :           // Similar to above, only this time treat the step value as unsigned.
    2052             :           // This covers loops that count up with an unsigned step.
    2053             :           OperandExtendedAdd =
    2054             :             getAddExpr(WideStart,
    2055             :                        getMulExpr(WideMaxBECount,
    2056       54758 :                                   getZeroExtendExpr(Step, WideTy, Depth + 1),
    2057          41 :                                   SCEV::FlagAnyWrap, Depth + 1),
    2058          41 :                        SCEV::FlagAnyWrap, Depth + 1);
    2059             :           if (SAdd == OperandExtendedAdd) {
    2060             :             // If AR wraps around then
    2061             :             //
    2062             :             //    abs(Step) * MaxBECount > unsigned-max(AR->getType())
    2063        6460 :             // => SAdd != OperandExtendedAdd
    2064        6460 :             //
    2065             :             // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
    2066             :             // (SAdd == OperandExtendedAdd => AR is NW)
    2067             : 
    2068       11436 :             const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
    2069             : 
    2070             :             // Return the expression with the addrec on the outside.
    2071             :             return getAddRecExpr(
    2072        2103 :                 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
    2073        1402 :                                                          Depth + 1),
    2074         701 :                 getZeroExtendExpr(Step, Ty, Depth + 1), L,
    2075             :                 AR->getNoWrapFlags());
    2076             :           }
    2077             :         }
    2078             :       }
    2079             : 
    2080             :       // Normally, in the cases we can prove no-overflow via a
    2081             :       // backedge guarding condition, we can also compute a backedge
    2082             :       // taken count for the loop.  The exceptions are assumptions and
    2083             :       // guards present in the loop -- SCEV is not great at exploiting
    2084             :       // these to compute max backedge taken counts, but can still use
    2085       10735 :       // these to prove lack of overflow.  Use this fact to avoid
    2086        8303 :       // doing extra work that may not pay off.
    2087        8303 : 
    2088         412 :       if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
    2089             :           !AC.assumptions().empty()) {
    2090         824 :         // If the backedge is guarded by a comparison with the pre-inc
    2091         412 :         // value the addrec is safe. Also, if the entry is guarded by
    2092         412 :         // a comparison with the start value and the backedge is
    2093             :         // guarded by a comparison with the post-inc value, the addrec
    2094             :         // is safe.
    2095             :         ICmpInst::Predicate Pred;
    2096             :         const SCEV *OverflowLimit =
    2097             :             getSignedOverflowLimitForStep(Step, &Pred, this);
    2098             :         if (OverflowLimit &&
    2099             :             (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
    2100             :              isKnownOnEveryIteration(Pred, AR, OverflowLimit))) {
    2101        6061 :           // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
    2102             :           const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
    2103             :           return getAddRecExpr(
    2104             :               getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
    2105        4563 :               getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
    2106        3042 :         }
    2107        1521 :       }
    2108             : 
    2109             :       // sext({C,+,Step}) --> (sext(D) + sext({C-D,+,Step}))<nuw><nsw>
    2110             :       // if D + (C - D + Step * n) could be proven to not signed wrap
    2111             :       // where D maximizes the number of trailing zeros of (C - D + Step * n)
    2112             :       if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
    2113             :         const APInt &C = SC->getAPInt();
    2114             :         const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
    2115             :         if (D != 0) {
    2116             :           const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
    2117             :           const SCEV *SResidual =
    2118             :               getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
    2119             :           const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
    2120             :           return getAddExpr(SSExtD, SSExtR,
    2121             :                             (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
    2122        4540 :                             Depth + 1);
    2123        4513 :         }
    2124        2973 :       }
    2125             : 
    2126          10 :       if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
    2127             :         const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
    2128          10 :         return getAddRecExpr(
    2129          10 :             getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
    2130             :             getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
    2131             :       }
    2132             :     }
    2133          10 : 
    2134             :   // If the input value is provably positive and we could not simplify
    2135             :   // away the sext build a zext instead.
    2136             :   if (isKnownNonNegative(Op))
    2137             :     return getZeroExtendExpr(Op, Ty, Depth + 1);
    2138             : 
    2139       45613 :   // The cast wasn't folded; create an explicit cast node.
    2140       44730 :   // Recompute the insert position, as it may have been invalidated.
    2141       44730 :   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
    2142       44730 :   SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
    2143       44730 :                                                    Op, Ty);
    2144       44730 :   UniqueSCEVs.InsertNode(S, IP);
    2145             :   addToLoopUseLists(S);
    2146             :   return S;
    2147             : }
    2148      168293 : 
    2149             : /// getAnyExtendExpr - Return a SCEV for the given operand extended with
    2150             : /// unspecified bits out to the given type.
    2151             : const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
    2152             :                                               Type *Ty) {
    2153      168293 :   assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
    2154             :          "This is not an extending conversion!");
    2155             :   assert(isSCEVable(Ty) &&
    2156             :          "This is not a conversion to a SCEVable type!");
    2157      103167 :   Ty = getEffectiveSCEVType(Ty);
    2158      206334 : 
    2159             :   // Sign-extend negative constants.
    2160             :   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
    2161             :     if (SC->getAPInt().isNegative())
    2162         278 :       return getSignExtendExpr(Op, Ty);
    2163             : 
    2164             :   // Peel off a truncate cast.
    2165             :   if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
    2166         250 :     const SCEV *NewOp = T->getOperand();
    2167             :     if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
    2168             :       return getAnyExtendExpr(NewOp, Ty);
    2169             :     return getTruncateOrNoop(NewOp, Ty);
    2170             :   }
    2171       64598 : 
    2172       64598 :   // Next try a zext cast. If the cast is folded, use it.
    2173       64598 :   const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
    2174       64598 :   if (!isa<SCEVZeroExtendExpr>(ZExt))
    2175       64598 :     return ZExt;
    2176             : 
    2177       48412 :   // Next try a sext cast. If the cast is folded, use it.
    2178           4 :   const SCEV *SExt = getSignExtendExpr(Op, Ty);
    2179           4 :   if (!isa<SCEVSignExtendExpr>(SExt))
    2180           4 :     return SExt;
    2181           4 : 
    2182           4 :   // Force the cast to be folded into the operands of an addrec.
    2183             :   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
    2184             :     SmallVector<const SCEV *, 4> Ops;
    2185             :     for (const SCEV *Op : AR->operands())
    2186             :       Ops.push_back(getAnyExtendExpr(Op, Ty));
    2187             :     return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
    2188             :   }
    2189         426 : 
    2190         847 :   // If the expression is obviously signed, use the sext cast value.
    2191         426 :   if (isa<SCEVSMaxExpr>(Op))
    2192         426 :     return SExt;
    2193        1278 : 
    2194         852 :   // Absent any other information, use the zext cast value.
    2195           5 :   return ZExt;
    2196             : }
    2197             : 
    2198             : /// Process the given Ops list, which is a list of operands to be added under
    2199             : /// the given scale, update the given map. This is a helper function for
    2200        7350 : /// getAddRecExpr. As an example of what it does, given a sequence of operands
    2201             : /// that would form an add expression like this:
    2202             : ///
    2203             : ///    m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
    2204        1983 : ///
    2205        1322 : /// where A and B are constants, update the map with these values:
    2206         661 : ///
    2207             : ///    (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
    2208             : ///
    2209             : /// and add 13 + A*B*29 to AccumulatedConstant.
    2210             : /// This will allow getAddRecExpr to produce this:
    2211             : ///
    2212             : ///    13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
    2213             : ///
    2214             : /// This form often exposes folding opportunities that are hidden in
    2215             : /// the original operand list.
    2216             : ///
    2217             : /// Return true iff it appears that any interesting folding opportunities
    2218        6689 : /// may be exposed. This helps getAddRecExpr short-circuit extra work in
    2219        5392 : /// the common case where no interesting opportunities are present, and
    2220        5392 : /// is also used as a check to avoid infinite recursion.
    2221         197 : static bool
    2222             : CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
    2223         394 :                              SmallVectorImpl<const SCEV *> &NewOps,
    2224         197 :                              APInt &AccumulatedConstant,
    2225         197 :                              const SCEV *const *Ops, size_t NumOperands,
    2226             :                              const APInt &Scale,
    2227             :                              ScalarEvolution &SE) {
    2228             :   bool Interesting = false;
    2229             : 
    2230             :   // Iterate over the add operands. They are sorted, with constants first.
    2231             :   unsigned i = 0;
    2232             :   while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
    2233             :     ++i;
    2234             :     // Pull a buried constant out to the outside.
    2235             :     if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
    2236       23225 :       Interesting = true;
    2237       23164 :     AccumulatedConstant += Scale * C->getAPInt();
    2238       23164 :   }
    2239       23164 : 
    2240       23164 :   // Next comes everything else. We're especially interested in multiplies
    2241             :   // here, but they're in the middle, so just visit the rest with one loop.
    2242       23164 :   for (; i != NumOperands; ++i) {
    2243       15153 :     const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
    2244             :     if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
    2245             :       APInt NewScale =
    2246             :           Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
    2247             :       if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
    2248             :         // A multiplication of a constant with another add; recurse.
    2249       23164 :         const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
    2250       10757 :         Interesting |=
    2251             :           CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
    2252       10757 :                                        Add->op_begin(), Add->getNumOperands(),
    2253             :                                        NewScale, SE);
    2254             :       } else {
    2255             :         // A multiplication of a constant with some other value. Update
    2256             :         // the map.
    2257             :         SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
    2258             :         const SCEV *Key = SE.getMulExpr(MulOps);
    2259             :         auto Pair = M.insert({Key, NewScale});
    2260             :         if (Pair.second) {
    2261             :           NewOps.push_back(Pair.first->first);
    2262       12407 :         } else {
    2263       12407 :           Pair.first->second += NewScale;
    2264             :           // The map already had an entry for this value, which may indicate
    2265             :           // a folding opportunity.
    2266             :           Interesting = true;
    2267             :         }
    2268             :       }
    2269             :     } else {
    2270        6505 :       // An ordinary operand. Update the map.
    2271             :       std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
    2272        6505 :           M.insert({Ops[i], Scale});
    2273        6505 :       if (Pair.second) {
    2274        5990 :         NewOps.push_back(Pair.first->first);
    2275             :       } else {
    2276        5990 :         Pair.first->second += Scale;
    2277             :         // The map already had an entry for this value, which may indicate
    2278        5990 :         // a folding opportunity.
    2279             :         Interesting = true;
    2280             :       }
    2281             :     }
    2282        5990 :   }
    2283             : 
    2284        5990 :   return Interesting;
    2285             : }
    2286        5990 : 
    2287             : // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
    2288             : // `OldFlags' as can't-wrap behavior.  Infer a more aggressive set of
    2289             : // can't-overflow flags for the operation if possible.
    2290             : static SCEV::NoWrapFlags
    2291        5990 : StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
    2292             :                       const SmallVectorImpl<const SCEV *> &Ops,
    2293             :                       SCEV::NoWrapFlags Flags) {
    2294             :   using namespace std::placeholders;
    2295         327 : 
    2296             :   using OBO = OverflowingBinaryOperator;
    2297             : 
    2298             :   bool CanAnalyze =
    2299         327 :       Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
    2300             :   (void)CanAnalyze;
    2301             :   assert(CanAnalyze && "don't call from other places!");
    2302             : 
    2303             :   int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
    2304        5663 :   SCEV::NoWrapFlags SignOrUnsignWrap =
    2305             :       ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
    2306             : 
    2307             :   // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
    2308             :   auto IsKnownNonNegative = [&](const SCEV *S) {
    2309        5663 :     return SE->isKnownNonNegative(S);
    2310             :   };
    2311             : 
    2312             :   if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
    2313             :     Flags =
    2314             :         ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
    2315             : 
    2316             :   SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
    2317             : 
    2318             :   if (SignOrUnsignWrap != SignOrUnsignMask &&
    2319             :       (Type == scAddExpr || Type == scMulExpr) && Ops.size() == 2 &&
    2320             :       isa<SCEVConstant>(Ops[0])) {
    2321           1 : 
    2322             :     auto Opcode = [&] {
    2323             :       switch (Type) {
    2324             :       case scAddExpr:
    2325           1 :         return Instruction::Add;
    2326             :       case scMulExpr:
    2327             :         return Instruction::Mul;
    2328             :       default:
    2329             :         llvm_unreachable("Unexpected SCEV op.");
    2330             :       }
    2331             :     }();
    2332             : 
    2333             :     const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
    2334             : 
    2335             :     // (A <opcode> C) --> (A <opcode> C)<nsw> if the op doesn't sign overflow.
    2336             :     if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
    2337             :       auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
    2338       17972 :           Opcode, C, OBO::NoSignedWrap);
    2339        5893 :       if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
    2340             :         Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
    2341             :     }
    2342             : 
    2343             :     // (A <opcode> C) --> (A <opcode> C)<nuw> if the op doesn't unsign overflow.
    2344             :     if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
    2345             :       auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
    2346             :           Opcode, C, OBO::NoUnsignedWrap);
    2347        6195 :       if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
    2348       12264 :         Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
    2349       12045 :     }
    2350        5976 :   }
    2351             : 
    2352             :   return Flags;
    2353         146 : }
    2354             : 
    2355         146 : bool ScalarEvolution::isAvailableAtLoopEntry(const SCEV *S, const Loop *L) {
    2356             :   return isLoopInvariant(S, L) && properlyDominates(S, L->getHeader());
    2357             : }
    2358             : 
    2359             : /// Get a canonical add expression, or something simpler if possible.
    2360             : const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
    2361             :                                         SCEV::NoWrapFlags Flags,
    2362             :                                         unsigned Depth) {
    2363             :   assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
    2364        4591 :          "only nuw or nsw allowed");
    2365        4591 :   assert(!Ops.empty() && "Cannot get empty add!");
    2366        1280 :   if (Ops.size() == 1) return Ops[0];
    2367             : #ifndef NDEBUG
    2368        3840 :   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
    2369        1280 :   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
    2370        1280 :     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
    2371             :            "SCEVAddExpr operand types don't match!");
    2372             : #endif
    2373             : 
    2374             :   // Sort by complexity, this groups all similar expression types together.
    2375             :   GroupByComplexity(Ops, &LI, DT);
    2376       10653 : 
    2377             :   Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
    2378           0 : 
    2379             :   // If there are any constants, fold them together.
    2380           0 :   unsigned Idx = 0;
    2381             :   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
    2382             :     ++Idx;
    2383             :     assert(Idx < Ops.size());
    2384             :     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
    2385             :       // We found two constants, fold them together!
    2386       35034 :       Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt());
    2387        8875 :       if (Ops.size() == 2) return Ops[0];
    2388             :       Ops.erase(Ops.begin()+1);  // Erase the folded element
    2389             :       LHSC = cast<SCEVConstant>(Ops[0]);
    2390             :     }
    2391       26159 : 
    2392       25831 :     // If we are left with a constant zero being added, strip it off.
    2393       25831 :     if (LHSC->getValue()->isZero()) {
    2394       25831 :       Ops.erase(Ops.begin());
    2395       25831 :       --Idx;
    2396       25831 :     }
    2397             : 
    2398             :     if (Ops.size() == 1) return Ops[0];
    2399             :   }
    2400             : 
    2401       11199 :   // Limit recursion calls depth.
    2402             :   if (Depth > MaxArithDepth)
    2403             :     return getOrCreateAddExpr(Ops, Flags);
    2404             : 
    2405             :   // Okay, check to see if the same value occurs in the operand list more than
    2406             :   // once.  If so, merge them together into an multiply expression.  Since we
    2407       11199 :   // sorted the list, these values are required to be adjacent.
    2408             :   Type *Ty = Ops[0]->getType();
    2409             :   bool FoundMatch = false;
    2410             :   for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
    2411        8171 :     if (Ops[i] == Ops[i+1]) {      //  X + Y + Y  -->  X + Y*2
    2412        5630 :       // Scan ahead to count how many equal operands there are.
    2413             :       unsigned Count = 2;
    2414             :       while (i+Count != e && Ops[i+Count] == Ops[i])
    2415             :         ++Count;
    2416         112 :       // Merge the values into a multiply.
    2417         112 :       const SCEV *Scale = getConstant(Ty, Count);
    2418           0 :       const SCEV *Mul = getMulExpr(Scale, Ops[i], SCEV::FlagAnyWrap, Depth + 1);
    2419         112 :       if (Ops.size() == Count)
    2420             :         return Mul;
    2421             :       Ops[i] = Mul;
    2422             :       Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
    2423        5457 :       --i; e -= Count - 1;
    2424        5457 :       FoundMatch = true;
    2425             :     }
    2426             :   if (FoundMatch)
    2427             :     return getAddExpr(Ops, Flags, Depth + 1);
    2428        2157 : 
    2429        2157 :   // Check for truncates. If all the operands are truncated from the same
    2430             :   // type, see if factoring out the truncate would permit the result to be
    2431             :   // folded. eg., n*trunc(x) + m*trunc(y) --> trunc(trunc(m)*x + trunc(n)*y)
    2432             :   // if the contents of the resulting outer trunc fold to something simple.
    2433             :   auto FindTruncSrcType = [&]() -> Type * {
    2434             :     // We're ultimately looking to fold an addrec of truncs and muls of only
    2435        2181 :     // constants and truncs, so if we find any other types of SCEV
    2436        1454 :     // as operands of the addrec then we bail and return nullptr here.
    2437         727 :     // Otherwise, we return the type of the operand of a trunc that we find.
    2438             :     if (auto *T = dyn_cast<SCEVTruncateExpr>(Ops[Idx]))
    2439             :       return T->getOperand()->getType();
    2440             :     if (const auto *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
    2441        1259 :       const auto *LastOp = Mul->getOperand(Mul->getNumOperands() - 1);
    2442           0 :       if (const auto *T = dyn_cast<SCEVTruncateExpr>(LastOp))
    2443             :         return T->getOperand()->getType();
    2444             :     }
    2445             :     return nullptr;
    2446             :   };
    2447             :   if (auto *SrcType = FindTruncSrcType()) {
    2448             :     SmallVector<const SCEV *, 8> LargeOps;
    2449             :     bool Ok = true;
    2450             :     // Check all the operands to see if they can be represented in the
    2451             :     // source type of the truncate.
    2452             :     for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
    2453             :       if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
    2454             :         if (T->getOperand()->getType() != SrcType) {
    2455             :           Ok = false;
    2456             :           break;
    2457             :         }
    2458             :         LargeOps.push_back(T->getOperand());
    2459             :       } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
    2460             :         LargeOps.push_back(getAnyExtendExpr(C, SrcType));
    2461             :       } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
    2462             :         SmallVector<const SCEV *, 8> LargeMulOps;
    2463             :         for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
    2464             :           if (const SCEVTruncateExpr *T =
    2465             :                 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
    2466             :             if (T->getOperand()->getType() != SrcType) {
    2467             :               Ok = false;
    2468             :               break;
    2469             :             }
    2470             :             LargeMulOps.push_back(T->getOperand());
    2471             :           } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
    2472      567368 :             LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
    2473             :           } else {
    2474             :             Ok = false;
    2475             :             break;
    2476             :           }
    2477             :         }
    2478             :         if (Ok)
    2479             :           LargeOps.push_back(getMulExpr(LargeMulOps, SCEV::FlagAnyWrap, Depth + 1));
    2480             :       } else {
    2481             :         Ok = false;
    2482      996198 :         break;
    2483      428830 :       }
    2484             :     }
    2485      857134 :     if (Ok) {
    2486             :       // Evaluate the expression in the larger type.
    2487      428830 :       const SCEV *Fold = getAddExpr(LargeOps, SCEV::FlagAnyWrap, Depth + 1);
    2488      428830 :       // If it folds to something simple, use it. Otherwise, don't.
    2489             :       if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
    2490             :         return getTruncateExpr(Fold, Ty);
    2491             :     }
    2492     2195228 :   }
    2493     1627860 : 
    2494     1794828 :   // Skip past any other cast SCEVs.
    2495             :   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
    2496      859883 :     ++Idx;
    2497      859883 : 
    2498             :   // If there are add operands they would be next.
    2499             :   if (Idx < Ops.size()) {
    2500        6093 :     bool DeletedAdd = false;
    2501        6093 :     while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
    2502             :       if (Ops.size() > AddOpsInlineThreshold ||
    2503             :           Add->getNumOperands() > AddOpsInlineThreshold)
    2504             :         break;
    2505             :       // If we have an add, expand the add operands onto the end of the operands
    2506             :       // list.
    2507     1707580 :       Ops.erase(Ops.begin()+Idx);
    2508      853790 :       Ops.append(Add->op_begin(), Add->op_end());
    2509      853790 :       DeletedAdd = true;
    2510      853790 :     }
    2511      850074 : 
    2512             :     // If we deleted at least one add, we added operands to the end of the list,
    2513        3716 :     // and they are not necessarily sorted.  Recurse to resort and resimplify
    2514             :     // any operands we just acquired.
    2515             :     if (DeletedAdd)
    2516             :       return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
    2517             :   }
    2518             : 
    2519             :   // Skip over the add expression until we get to a multiply.
    2520             :   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
    2521             :     ++Idx;
    2522      767977 : 
    2523      767977 :   // Check to see if there are any folding opportunities present with
    2524      490010 :   // operands multiplied by constant values.
    2525             :   if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
    2526      277967 :     uint64_t BitWidth = getTypeSizeInBits(Ty);
    2527             :     DenseMap<const SCEV *, APInt> M;
    2528             :     SmallVector<const SCEV *, 8> NewOps;
    2529             :     APInt AccumulatedConstant(BitWidth, 0);
    2530             :     if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
    2531             :                                      Ops.data(), Ops.size(),
    2532             :                                      APInt(BitWidth, 1), *this)) {
    2533             :       struct APIntCompare {
    2534      567368 :         bool operator()(const APInt &LHS, const APInt &RHS) const {
    2535             :           return LHS.ult(RHS);
    2536             :         }
    2537             :       };
    2538             : 
    2539             :       // Some interesting folding opportunity is present, so its worthwhile to
    2540             :       // re-generate the operands list. Group the operands by constant scale,
    2541     5093509 :       // to avoid multiplying by the same constant scale multiple times.
    2542             :       std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
    2543             :       for (const SCEV *NewOp : NewOps)
    2544             :         MulOpLists[M.find(NewOp)->second].push_back(NewOp);
    2545             :       // Re-generate the operands list.
    2546             :       Ops.clear();
    2547             :       if (AccumulatedConstant != 0)
    2548             :         Ops.push_back(getConstant(AccumulatedConstant));
    2549             :       for (auto &MulOp : MulOpLists)
    2550             :         if (MulOp.first != 0)
    2551             :           Ops.push_back(getMulExpr(
    2552             :               getConstant(MulOp.first),
    2553             :               getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1),
    2554             :               SCEV::FlagAnyWrap, Depth + 1));
    2555             :       if (Ops.empty())
    2556             :         return getZero(Ty);
    2557             :       if (Ops.size() == 1)
    2558             :         return Ops[0];
    2559           0 :       return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
    2560             :     }
    2561             :   }
    2562     5874390 : 
    2563             :   // If we are adding something to a multiply expression, make sure the
    2564             :   // something is not already an operand of the multiply.  If so, merge it into
    2565             :   // the multiply.
    2566             :   for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
    2567             :     const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
    2568     4684800 :     for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
    2569     5093509 :       const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
    2570     3479599 :       if (isa<SCEVConstant>(MulOpSCEV))
    2571             :         continue;
    2572             :       for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
    2573     2975552 :         if (MulOpSCEV == Ops[AddOp]) {
    2574             :           // Fold W + X + (X * Y * Z)  -->  W + (X * ((Y*Z)+1))
    2575             :           const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
    2576     1114788 :           if (Mul->getNumOperands() != 2) {
    2577             :             // If the multiply has more than two operands, we must get the
    2578           0 :             // Y*Z term.
    2579           0 :             SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
    2580             :                                                 Mul->op_begin()+MulOp);
    2581             :             MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
    2582             :             InnerMul = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
    2583             :           }
    2584             :           SmallVector<const SCEV *, 2> TwoOps = {getOne(Ty), InnerMul};
    2585             :           const SCEV *AddOne = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
    2586     2975552 :           const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV,
    2587             :                                             SCEV::FlagAnyWrap, Depth + 1);
    2588     7728312 :           if (Ops.size() == 2) return OuterMul;
    2589     7728312 :           if (AddOp < Idx) {
    2590             :             Ops.erase(Ops.begin()+AddOp);
    2591             :             Ops.erase(Ops.begin()+Idx-1);
    2592             :           } else {
    2593             :             Ops.erase(Ops.begin()+Idx);
    2594     2975552 :             Ops.erase(Ops.begin()+AddOp-1);
    2595             :           }
    2596     8876352 :           Ops.push_back(OuterMul);
    2597     8876352 :           return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
    2598             :         }
    2599             : 
    2600             :       // Check this multiply against other multiplies being added together.
    2601             :       for (unsigned OtherMulIdx = Idx+1;
    2602     5093509 :            OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
    2603             :            ++OtherMulIdx) {
    2604             :         const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
    2605      831735 :         // If MulOp occurs in OtherMul, we can fold the two multiplies
    2606      831735 :         // together.
    2607             :         for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
    2608             :              OMulOp != e; ++OMulOp)
    2609             :           if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
    2610     2919946 :             // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
    2611             :             const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
    2612             :             if (Mul->getNumOperands() != 2) {
    2613             :               SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
    2614             :                                                   Mul->op_begin()+MulOp);
    2615             :               MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
    2616     2919946 :               InnerMul1 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
    2617             :             }
    2618             :             const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
    2619             :             if (OtherMul->getNumOperands() != 2) {
    2620             :               SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
    2621             :                                                   OtherMul->op_begin()+OMulOp);
    2622             :               MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
    2623             :               InnerMul2 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
    2624             :             }
    2625     2785206 :             SmallVector<const SCEV *, 2> TwoOps = {InnerMul1, InnerMul2};
    2626             :             const SCEV *InnerMulSum =
    2627     2785206 :                 getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
    2628             :             const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum,
    2629             :                                               SCEV::FlagAnyWrap, Depth + 1);
    2630     2785206 :             if (Ops.size() == 2) return OuterMul;
    2631     2785206 :             Ops.erase(Ops.begin()+Idx);
    2632     2296136 :             Ops.erase(Ops.begin()+OtherMulIdx-1);
    2633             :             Ops.push_back(OuterMul);
    2634     4829216 :             return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
    2635             :           }
    2636     1095637 :       }
    2637     1086948 :     }
    2638      118472 :   }
    2639      118472 : 
    2640      118472 :   // If there are any add recurrences in the operands list, see if any other
    2641             :   // added values are loop invariant.  If so, we can fold them into the
    2642             :   // recurrence.
    2643     2655320 :   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
    2644      282936 :     ++Idx;
    2645      282936 : 
    2646             :   // Scan over all recurrences, trying to fold loop invariants into them.
    2647             :   for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
    2648     1327660 :     // Scan all of the other operands to this add and add them to the vector if
    2649             :     // they are loop invariant w.r.t. the recurrence.
    2650             :     SmallVector<const SCEV *, 8> LIOps;
    2651             :     const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
    2652     1543934 :     const Loop *AddRecLoop = AddRec->getLoop();
    2653        3169 :     for (unsigned i = 0, e = Ops.size(); i != e; ++i)
    2654             :       if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
    2655             :         LIOps.push_back(Ops[i]);
    2656             :         Ops.erase(Ops.begin()+i);
    2657             :         --i; --e;
    2658     1540765 :       }
    2659             : 
    2660     4019066 :     // If we found some loop invariants, fold them into the recurrence.
    2661     7436316 :     if (!LIOps.empty()) {
    2662             :       //  NLI + LI + {Start,+,Step}  -->  NLI + {LI+Start,+,Step}
    2663             :       LIOps.push_back(AddRec->getStart());
    2664        1427 : 
    2665         126 :       SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
    2666             :                                              AddRec->op_end());
    2667        1301 :       // This follows from the fact that the no-wrap flags on the outer add
    2668        2602 :       // expression are applicable on the 0th iteration, when the add recurrence
    2669        1301 :       // will be equal to its start value.
    2670         471 :       AddRecOps[0] = getAddExpr(LIOps, Flags, Depth + 1);
    2671         830 : 
    2672         830 :       // Build the new addrec. Propagate the NUW and NSW flags if both the
    2673         830 :       // outer add and the inner addrec are guaranteed to have no overflow.
    2674             :       // Always propagate NW.
    2675             :       Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
    2676     1540294 :       const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
    2677         761 : 
    2678             :       // If all of the other operands were loop invariant, we are done.
    2679             :       if (Ops.size() == 1) return NewRec;
    2680             : 
    2681             :       // Otherwise, add the folded AddRec by the non-invariant parts.
    2682             :       for (unsigned i = 0;; ++i)
    2683             :         if (Ops[i] == AddRec) {
    2684             :           Ops[i] = NewRec;
    2685             :           break;
    2686             :         }
    2687             :       return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
    2688             :     }
    2689             : 
    2690             :     // Okay, if there weren't any loop invariants to be folded, check to see if
    2691             :     // there are multiple AddRec's with the same loop induction variable being
    2692             :     // added together.  If so, we can fold them.
    2693             :     for (unsigned OtherIdx = Idx+1;
    2694             :          OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
    2695             :          ++OtherIdx) {
    2696             :       // We expect the AddRecExpr's to be sorted in reverse dominance order,
    2697     1539533 :       // so that the 1st found AddRecExpr is dominated by all others.
    2698             :       assert(DT.dominates(
    2699             :            cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(),
    2700             :            AddRec->getLoop()->getHeader()) &&
    2701             :         "AddRecExprs are not sorted in reverse dominance order?");
    2702       15680 :       if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
    2703       24870 :         // Other + {A,+,B}<L> + {C,+,D}<L>  -->  Other + {A+C,+,B+D}<L>
    2704        2864 :         SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
    2705             :                                                AddRec->op_end());
    2706             :         for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
    2707             :              ++OtherIdx) {
    2708        2843 :           const auto *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
    2709             :           if (OtherAddRec->getLoop() == AddRecLoop) {
    2710        3019 :             for (unsigned i = 0, e = OtherAddRec->getNumOperands();
    2711             :                  i != e; ++i) {
    2712             :               if (i >= AddRecOps.size()) {
    2713       12134 :                 AddRecOps.append(OtherAddRec->op_begin()+i,
    2714             :                                  OtherAddRec->op_end());
    2715        8497 :                 break;
    2716        3608 :               }
    2717             :               SmallVector<const SCEV *, 2> TwoOps = {
    2718             :                   AddRecOps[i], OtherAddRec->getOperand(i)};
    2719             :               AddRecOps[i] = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
    2720        3602 :             }
    2721             :             Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
    2722        3978 :           }
    2723             :         }
    2724             :         // Step size has changed, so we cannot guarantee no self-wraparound.
    2725             :         Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
    2726             :         return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
    2727             :       }
    2728        4554 :     }
    2729        3514 : 
    2730             :     // Otherwise couldn't fold anything into this recurrence.  Move onto the
    2731             :     // next one.
    2732             :   }
    2733             : 
    2734             :   // Okay, it looks like we really DO need an add expr.  Check to see if we
    2735        5264 :   // already have one, otherwise create a new one.
    2736             :   return getOrCreateAddExpr(Ops, Flags);
    2737        2383 : }
    2738             : 
    2739        2383 : const SCEV *
    2740           7 : ScalarEvolution::getOrCreateAddExpr(SmallVectorImpl<const SCEV *> &Ops,
    2741             :                                     SCEV::NoWrapFlags Flags) {
    2742             :   FoldingSetNodeID ID;
    2743             :   ID.AddInteger(scAddExpr);
    2744             :   for (const SCEV *Op : Ops)
    2745     1615679 :     ID.AddPointer(Op);
    2746       76153 :   void *IP = nullptr;
    2747             :   SCEVAddExpr *S =
    2748             :       static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
    2749     1539526 :   if (!S) {
    2750             :     const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
    2751     3784474 :     std::uninitialized_copy(Ops.begin(), Ops.end(), O);
    2752      825086 :     S = new (SCEVAllocator)
    2753      412542 :         SCEVAddExpr(ID.Intern(SCEVAllocator), O, Ops.size());
    2754             :     UniqueSCEVs.InsertNode(S, IP);
    2755             :     addToLoopUseLists(S);
    2756             :   }
    2757      412542 :   S->setNoWrapFlags(Flags);
    2758      825084 :   return S;
    2759             : }
    2760      412542 : 
    2761             : const SCEV *
    2762             : ScalarEvolution::getOrCreateAddRecExpr(SmallVectorImpl<const SCEV *> &Ops,
    2763             :                                        const Loop *L, SCEV::NoWrapFlags Flags) {
    2764             :   FoldingSetNodeID ID;
    2765     1479695 :   ID.AddInteger(scAddRecExpr);
    2766      375137 :   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
    2767             :     ID.AddPointer(Ops[i]);
    2768             :   ID.AddPointer(L);
    2769             :   void *IP = nullptr;
    2770     1164390 :   SCEVAddRecExpr *S =
    2771           1 :       static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
    2772             :   if (!S) {
    2773             :     const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
    2774             :     std::uninitialized_copy(Ops.begin(), Ops.end(), O);
    2775     1164389 :     S = new (SCEVAllocator)
    2776      561275 :         SCEVAddRecExpr(ID.Intern(SCEVAllocator), O, Ops.size(), L);
    2777             :     UniqueSCEVs.InsertNode(S, IP);
    2778             :     addToLoopUseLists(S);
    2779      561275 :   }
    2780      561275 :   S->setNoWrapFlags(Flags);
    2781      561275 :   return S;
    2782      561275 : }
    2783             : 
    2784           0 : const SCEV *
    2785           0 : ScalarEvolution::getOrCreateMulExpr(SmallVectorImpl<const SCEV *> &Ops,
    2786             :                                     SCEV::NoWrapFlags Flags) {
    2787             :   FoldingSetNodeID ID;
    2788             :   ID.AddInteger(scMulExpr);
    2789             :   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
    2790             :     ID.AddPointer(Ops[i]);
    2791             :   void *IP = nullptr;
    2792             :   SCEVMulExpr *S =
    2793      572569 :     static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
    2794      292987 :   if (!S) {
    2795             :     const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
    2796             :     std::uninitialized_copy(Ops.begin(), Ops.end(), O);
    2797      279582 :     S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
    2798      259385 :                                         O, Ops.size());
    2799      569361 :     UniqueSCEVs.InsertNode(S, IP);
    2800      579558 :     addToLoopUseLists(S);
    2801       12135 :   }
    2802             :   S->setNoWrapFlags(Flags);
    2803             :   return S;
    2804             : }
    2805      279582 : 
    2806       12971 : static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
    2807      266611 :   uint64_t k = i*j;
    2808      262796 :   if (j > 1 && k / j != i) Overflow = true;
    2809        3815 :   return k;
    2810             : }
    2811             : 
    2812             : /// Compute the result of "n choose k", the binomial coefficient.  If an
    2813             : /// intermediate computation overflows, Overflow will be set and the return will
    2814             : /// be garbage. Overflow is not cleared on absence of overflow.
    2815             : static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
    2816     1471944 :   // We use the multiplicative formula:
    2817             :   //     n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
    2818     1800788 :   // At each iteration, we take the n-th term of the numeral and divide by the
    2819     1213651 :   // (k-n)th term of the denominator.  This division will always produce an
    2820     1213651 :   // integral result, and helps reduce the chance of overflow in the
    2821             :   // intermediate computations. However, we can still overflow even when the
    2822    25024862 :   // final result would fit.
    2823    48746246 : 
    2824             :   if (n == 0 || n == k) return 1;
    2825         219 :   if (k > n) return 0;
    2826         219 : 
    2827             :   if (k > n/2)
    2828             :     k = n-k;
    2829             : 
    2830             :   uint64_t r = 1;
    2831         200 :   for (uint64_t i = 1; i <= k; ++i) {
    2832         100 :     r = umul_ov(r, n-(i-1), Overflow);
    2833             :     r /= i;
    2834         219 :   }
    2835         219 :   return r;
    2836         219 : }
    2837         219 : 
    2838         219 : /// Determine if any of the operands in this SCEV are a constant or if
    2839         138 : /// any of the add or multiply expressions in this SCEV contain a constant.
    2840           4 : static bool containsConstantInAddMulChain(const SCEV *StartExpr) {
    2841           4 :   struct FindConstantInAddMulChain {
    2842             :     bool FoundConstant = false;
    2843         134 : 
    2844         134 :     bool follow(const SCEV *S) {
    2845             :       FoundConstant |= isa<SCEVConstant>(S);
    2846         138 :       return isa<SCEVAddExpr>(S) || isa<SCEVMulExpr>(S);
    2847         138 :     }
    2848             : 
    2849             :     bool isDone() const {
    2850             :       return FoundConstant;
    2851     6267781 :     }
    2852     6267781 :   };
    2853             : 
    2854             :   FindConstantInAddMulChain F;
    2855             :   SCEVTraversal<FindConstantInAddMulChain> ST(F);
    2856             :   ST.visitAll(StartExpr);
    2857    16934389 :   return F.FoundConstant;
    2858    16934389 : }
    2859    22636694 : 
    2860             : /// Get a canonical multiply expression, or something simpler if possible.
    2861        5710 : const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
    2862        5710 :                                         SCEV::NoWrapFlags Flags,
    2863             :                                         unsigned Depth) {
    2864             :   assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
    2865        6476 :          "only nuw or nsw allowed");
    2866        3238 :   assert(!Ops.empty() && "Cannot get empty mul!");
    2867             :   if (Ops.size() == 1) return Ops[0];
    2868        5710 : #ifndef NDEBUG
    2869        5710 :   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
    2870             :   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
    2871        5114 :     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
    2872       10228 :            "SCEVMulExpr operand types don't match!");
    2873        5114 : #endif
    2874             : 
    2875        5710 :   // Sort by complexity, this groups all similar expression types together.
    2876             :   GroupByComplexity(Ops, &LI, DT);
    2877        5710 : 
    2878        5710 :   Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
    2879        5710 : 
    2880        5710 :   // Limit recursion calls depth.
    2881        1981 :   if (Depth > MaxArithDepth)
    2882        1981 :     return getOrCreateMulExpr(Ops, Flags);
    2883        1981 : 
    2884        1981 :   // If there are any constants, fold them together.
    2885             :   unsigned Idx = 0;
    2886             :   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
    2887             : 
    2888             :     if (Ops.size() == 2)
    2889             :       // C1*(C2+V) -> C1*C2 + C1*V
    2890             :       if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
    2891             :         // If any of Add's ops are Adds or Muls with a constant, apply this
    2892             :         // transformation as well.
    2893      891361 :         //
    2894       12483 :         // TODO: There are some cases where this transformation is not
    2895             :         // profitable; for example, Add = (C0 + X) * Y + Z.  Maybe the scope of
    2896             :         // this transformation should be narrowed down.
    2897      884685 :         if (Add->getNumOperands() == 2 && containsConstantInAddMulChain(Add))
    2898             :           return getAddExpr(getMulExpr(LHSC, Add->getOperand(0),
    2899             :                                        SCEV::FlagAnyWrap, Depth + 1),
    2900             :                             getMulExpr(LHSC, Add->getOperand(1),
    2901      353998 :                                        SCEV::FlagAnyWrap, Depth + 1),
    2902      353998 :                             SCEV::FlagAnyWrap, Depth + 1);
    2903     1073791 : 
    2904     1439586 :     ++Idx;
    2905      346732 :     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
    2906      346732 :       // We found two constants, fold them together!
    2907      346732 :       ConstantInt *Fold =
    2908             :           ConstantInt::get(getContext(), LHSC->getAPInt() * RHSC->getAPInt());
    2909             :       Ops[0] = getConstant(Fold);
    2910             :       Ops.erase(Ops.begin()+1);  // Erase the folded element
    2911      353998 :       if (Ops.size() == 1) return Ops[0];
    2912             :       LHSC = cast<SCEVConstant>(Ops[0]);
    2913      675846 :     }
    2914             : 
    2915             :     // If we are left with a constant one being multiplied, strip it off.
    2916      337923 :     if (cast<SCEVConstant>(Ops[0])->getValue()->isOne()) {
    2917             :       Ops.erase(Ops.begin());
    2918             :       --Idx;
    2919             :     } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
    2920      675846 :       // If we have a multiply of zero, it will always be zero.
    2921             :       return Ops[0];
    2922             :     } else if (Ops[0]->isAllOnesValue()) {
    2923             :       // If we have a mul by -1 of an add, try distributing the -1 among the
    2924             :       // add operands.
    2925      337923 :       if (Ops.size() == 2) {
    2926      337923 :         if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
    2927             :           SmallVector<const SCEV *, 4> NewOps;
    2928             :           bool AnyFolded = false;
    2929      337923 :           for (const SCEV *AddOp : Add->operands()) {
    2930             :             const SCEV *Mul = getMulExpr(Ops[0], AddOp, SCEV::FlagAnyWrap,
    2931             :                                          Depth + 1);
    2932         911 :             if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
    2933        3185 :             NewOps.push_back(Mul);
    2934        1137 :           }
    2935             :           if (AnyFolded)
    2936             :             return getAddExpr(NewOps, SCEV::FlagAnyWrap, Depth + 1);
    2937        1137 :         } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
    2938             :           // Negation preserves a recurrence's no self-wrap property.
    2939             :           SmallVector<const SCEV *, 4> Operands;
    2940             :           for (const SCEV *AddRecOp : AddRec->operands())
    2941             :             Operands.push_back(getMulExpr(Ops[0], AddRecOp, SCEV::FlagAnyWrap,
    2942             :                                           Depth + 1));
    2943       16075 : 
    2944       16075 :           return getAddRecExpr(Operands, AddRec->getLoop(),
    2945             :                                AddRec->getNoWrapFlags(SCEV::FlagNW));
    2946             :         }
    2947             :       }
    2948             :     }
    2949             : 
    2950             :     if (Ops.size() == 1)
    2951             :       return Ops[0];
    2952       10268 :   }
    2953             : 
    2954             :   // Skip over the add expression until we get to a multiply.
    2955       10268 :   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
    2956       20541 :     ++Idx;
    2957             : 
    2958             :   // If there are mul operands inline them all into this expression.
    2959       10273 :   if (Idx < Ops.size()) {
    2960       31706 :     bool DeletedMul = false;
    2961       31706 :     while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
    2962       21827 :       if (Ops.size() > MulOpsInlineThreshold)
    2963         788 :         break;
    2964             :       // If we have an mul, expand the mul operands onto the end of the
    2965         394 :       // operands list.
    2966             :       Ops.erase(Ops.begin()+Idx);
    2967             :       Ops.append(Mul->op_begin(), Mul->op_end());
    2968       42866 :       DeletedMul = true;
    2969       42866 :     }
    2970             : 
    2971       10273 :     // If we deleted at least one mul, we added operands to the end of the
    2972             :     // list, and they are not necessarily sorted.  Recurse to resort and
    2973             :     // resimplify any operands we just acquired.
    2974             :     if (DeletedMul)
    2975       20536 :       return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
    2976       10268 :   }
    2977             : 
    2978             :   // If there are any add recurrences in the operands list, see if any other
    2979             :   // added values are loop invariant.  If so, we can fold them into the
    2980             :   // recurrence.
    2981             :   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
    2982             :     ++Idx;
    2983             : 
    2984             :   // Scan over all recurrences, trying to fold loop invariants into them.
    2985             :   for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
    2986      530687 :     // Scan all of the other operands to this mul and add them to the vector
    2987             :     // if they are loop invariant w.r.t. the recurrence.
    2988             :     SmallVector<const SCEV *, 8> LIOps;
    2989             :     const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
    2990      533856 :     const Loop *AddRecLoop = AddRec->getLoop();
    2991             :     for (unsigned i = 0, e = Ops.size(); i != e; ++i)
    2992             :       if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
    2993      533856 :         LIOps.push_back(Ops[i]);
    2994     2249139 :         Ops.erase(Ops.begin()+i);
    2995     1715283 :         --i; --e;
    2996      533856 :       }
    2997             : 
    2998             :     // If we found some loop invariants, fold them into the recurrence.
    2999      533856 :     if (!LIOps.empty()) {
    3000      286037 :       //  NLI * LI * {Start,+,Step}  -->  NLI * {LI*Start,+,LI*Step}
    3001             :       SmallVector<const SCEV *, 4> NewOps;
    3002             :       NewOps.reserve(AddRec->getNumOperands());
    3003      286037 :       const SCEV *Scale = getMulExpr(LIOps, SCEV::FlagAnyWrap, Depth + 1);
    3004      286037 :       for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
    3005      286037 :         NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i),
    3006             :                                     SCEV::FlagAnyWrap, Depth + 1));
    3007             : 
    3008      533856 :       // Build the new addrec. Propagate the NUW and NSW flags if both the
    3009             :       // outer mul and the inner addrec are guaranteed to have no overflow.
    3010             :       //
    3011             :       // No self-wrap cannot be guaranteed after changing the step size, but
    3012      773795 :       // will be inferred if either NUW or NSW is true.
    3013             :       Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
    3014             :       const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
    3015      773795 : 
    3016     2335318 :       // If all of the other operands were loop invariant, we are done.
    3017     3123046 :       if (Ops.size() == 1) return NewRec;
    3018      773795 : 
    3019      773795 :       // Otherwise, multiply the folded AddRec by the non-invariant parts.
    3020             :       for (unsigned i = 0;; ++i)
    3021             :         if (Ops[i] == AddRec) {
    3022      773795 :           Ops[i] = NewRec;
    3023      190206 :           break;
    3024             :         }
    3025             :       return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
    3026      190206 :     }
    3027      190206 : 
    3028      190206 :     // Okay, if there weren't any loop invariants to be folded, check to see
    3029             :     // if there are multiple AddRec's with the same loop induction variable
    3030             :     // being multiplied together.  If so, we can fold them.
    3031      773795 : 
    3032             :     // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
    3033             :     // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
    3034             :     //       choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
    3035      555244 :     //   ]]],+,...up to x=2n}.
    3036             :     // Note that the arguments to choose() are always integers with values
    3037             :     // known at compile time, never SCEV objects.
    3038      555244 :     //
    3039     1745500 :     // The implementation avoids pointless extra computations when the two
    3040     2380512 :     // addrec's are of different length (mathematically, it's equivalent to
    3041      555244 :     // an infinite stream of zeros on the right).
    3042             :     bool OpsModified = false;
    3043             :     for (unsigned OtherIdx = Idx+1;
    3044      555244 :          OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
    3045      128500 :          ++OtherIdx) {
    3046             :       const SCEVAddRecExpr *OtherAddRec =
    3047      128500 :         dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
    3048      128500 :       if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
    3049      128500 :         continue;
    3050      128500 : 
    3051             :       // Limit max number of arguments to avoid creation of unreasonably big
    3052             :       // SCEVAddRecs with very complex operands.
    3053      555244 :       if (AddRec->getNumOperands() + OtherAddRec->getNumOperands() - 1 >
    3054             :           MaxAddRecSize)
    3055             :         continue;
    3056             : 
    3057        3467 :       bool Overflow = false;
    3058        3467 :       Type *Ty = AddRec->getType();
    3059             :       bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
    3060             :       SmallVector<const SCEV*, 7> AddRecOps;
    3061             :       for (int x = 0, xe = AddRec->getNumOperands() +
    3062             :              OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
    3063             :         const SCEV *Term = getZero(Ty);
    3064             :         for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
    3065       11562 :           uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
    3066             :           for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
    3067             :                  ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
    3068             :                z < ze && !Overflow; ++z) {
    3069             :             uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
    3070             :             uint64_t Coeff;
    3071             :             if (LargerThan64Bits)
    3072             :               Coeff = umul_ov(Coeff1, Coeff2, Overflow);
    3073             :             else
    3074       11562 :               Coeff = Coeff1*Coeff2;
    3075        6702 :             const SCEV *CoeffTerm = getConstant(Ty, Coeff);
    3076             :             const SCEV *Term1 = AddRec->getOperand(y-z);
    3077        6702 :             const SCEV *Term2 = OtherAddRec->getOperand(z);
    3078         615 :             Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1, Term2,
    3079             :                                                SCEV::FlagAnyWrap, Depth + 1),
    3080             :                               SCEV::FlagAnyWrap, Depth + 1);
    3081       10164 :           }
    3082        3462 :         }
    3083        3462 :         AddRecOps.push_back(Term);
    3084             :       }
    3085             :       if (!Overflow) {
    3086             :         const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
    3087             :                                               SCEV::FlagAnyWrap);
    3088             :         if (Ops.size() == 2) return NewAddRec;
    3089             :         Ops[Idx] = NewAddRec;
    3090       80261 :         Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
    3091             :         OpsModified = true;
    3092             :         AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
    3093             :         if (!AddRec)
    3094           0 :           break;
    3095      272676 :       }
    3096      272676 :     }
    3097             :     if (OpsModified)
    3098             :       return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
    3099           0 : 
    3100           0 :     // Otherwise couldn't fold anything into this recurrence.  Move onto the
    3101             :     // next one.
    3102             :   }
    3103             : 
    3104       80261 :   // Okay, it looks like we really DO need an mul expr.  Check to see if we
    3105       80261 :   // already have one, otherwise create a new one.
    3106       80261 :   return getOrCreateMulExpr(Ops, Flags);
    3107       80261 : }
    3108             : 
    3109             : /// Represents an unsigned remainder expression based on unsigned division.
    3110             : const SCEV *ScalarEvolution::getURemExpr(const SCEV *LHS,
    3111     2396245 :                                          const SCEV *RHS) {
    3112             :   assert(getEffectiveSCEVType(LHS->getType()) ==
    3113             :          getEffectiveSCEVType(RHS->getType()) &&
    3114             :          "SCEVURemExpr operand types don't match!");
    3115             : 
    3116             :   // Short-circuit easy cases
    3117     2396245 :   if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
    3118             :     // If constant is one, the result is trivial
    3119             :     if (RHSC->getValue()->isOne())
    3120             :       return getZero(LHS->getType()); // X urem 1 --> 0
    3121             : 
    3122             :     // If constant is a power of two, fold into a zext(trunc(LHS)).
    3123             :     if (RHSC->getAPInt().isPowerOf2()) {
    3124             :       Type *FullTy = LHS->getType();
    3125             :       Type *TruncTy =
    3126     1534508 :           IntegerType::get(getContext(), RHSC->getAPInt().logBase2());
    3127             :       return getZeroExtendExpr(getTruncateExpr(LHS, TruncTy), FullTy);
    3128     1534508 :     }
    3129             :   }
    3130             : 
    3131     1534508 :   // Fallback to %a == %x urem %y == %x -<nuw> ((%x udiv %y) *<nuw> %y)
    3132       17274 :   const SCEV *UDiv = getUDivExpr(LHS, RHS);
    3133             :   const SCEV *Mult = getMulExpr(UDiv, RHS, SCEV::FlagNUW);
    3134             :   return getMinusSCEV(LHS, Mult, SCEV::FlagNUW);
    3135             : }
    3136     1517234 : 
    3137             : /// Get a canonical unsigned division expression, or something simpler if
    3138     1456652 : /// possible.
    3139             : const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
    3140     1376371 :                                          const SCEV *RHS) {
    3141             :   assert(getEffectiveSCEVType(LHS->getType()) ==
    3142             :          getEffectiveSCEVType(RHS->getType()) &&
    3143             :          "SCEVUDivExpr operand types don't match!");
    3144             : 
    3145             :   if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
    3146             :     if (RHSC->getValue()->isOne())
    3147       92851 :       return LHS;                               // X udiv 1 --> x
    3148      154436 :     // If the denominator is zero, the result of the udiv is undefined. Don't
    3149             :     // try to analyze it, because the resolution chosen here may differ from
    3150             :     // the resolution chosen in other parts of the compiler.
    3151             :     if (!RHSC->getValue()->isZero()) {
    3152       77218 :       // Determine if the division can be folded into the operands of
    3153             :       // its operands.
    3154             :       // TODO: Generalize this to non-constants by using known-bits information.
    3155     1437883 :       Type *Ty = LHS->getType();
    3156             :       unsigned LZ = RHSC->getAPInt().countLeadingZeros();
    3157             :       unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
    3158     1418558 :       // For non-power-of-two values, effectively round the value up to the
    3159      709279 :       // nearest power of two.
    3160      709279 :       if (!RHSC->getAPInt().isPowerOf2())
    3161      709279 :         ++MaxShiftAmt;
    3162       58449 :       IntegerType *ExtTy =
    3163       58449 :         IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
    3164             :       if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
    3165             :         if (const SCEVConstant *Step =
    3166     1457208 :             dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
    3167       57185 :           // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
    3168             :           const APInt &StepInt = Step->getAPInt();
    3169      671419 :           const APInt &DivInt = RHSC->getAPInt();
    3170             :           if (!StepInt.urem(DivInt) &&
    3171             :               getZeroExtendExpr(AR, ExtTy) ==
    3172      665438 :               getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
    3173             :                             getZeroExtendExpr(Step, ExtTy),
    3174             :                             AR->getLoop(), SCEV::FlagAnyWrap)) {
    3175      533488 :             SmallVector<const SCEV *, 4> Operands;
    3176      528057 :             for (const SCEV *Op : AR->operands())
    3177             :               Operands.push_back(getUDivExpr(Op, RHS));
    3178             :             return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
    3179       43779 :           }
    3180       65278 :           /// Get a canonical UDivExpr for a recurrence.
    3181       32639 :           /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
    3182       32639 :           // We can currently only fold X%N if X is constant.
    3183       32639 :           const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
    3184             :           if (StartC && !DivInt.urem(StepInt) &&
    3185       11140 :               getZeroExtendExpr(AR, ExtTy) ==
    3186        9138 :               getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
    3187             :                             getZeroExtendExpr(Step, ExtTy),
    3188             :                             AR->getLoop(), SCEV::FlagAnyWrap)) {
    3189             :             const APInt &StartInt = StartC->getAPInt();
    3190      254117 :             const APInt &StartRem = StartInt.urem(StepInt);
    3191      341774 :             if (StartRem != 0)
    3192             :               LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
    3193             :                                   AR->getLoop(), SCEV::FlagNW);
    3194      166460 :           }
    3195             :         }
    3196             :       // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
    3197             :       if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
    3198             :         SmallVector<const SCEV *, 4> Operands;
    3199             :         for (const SCEV *Op : M->operands())
    3200      630255 :           Operands.push_back(getZeroExtendExpr(Op, ExtTy));
    3201       50378 :         if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
    3202             :           // Find an operand that's safely divisible.
    3203             :           for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
    3204             :             const SCEV *Op = M->getOperand(i);
    3205      812214 :             const SCEV *Div = getUDivExpr(Op, RHSC);
    3206      171755 :             if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
    3207             :               Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
    3208             :                                                       M->op_end());
    3209      640459 :               Operands[i] = Div;
    3210             :               return getMulExpr(Operands);
    3211      634567 :             }
    3212      145152 :           }
    3213             :       }
    3214             : 
    3215             :       // (A/B)/C --> A/(B*C) if safe and B*C can be folded.
    3216       72208 :       if (const SCEVUDivExpr *OtherDiv = dyn_cast<SCEVUDivExpr>(LHS)) {
    3217      144416 :         if (auto *DivisorConstant =
    3218             :                 dyn_cast<SCEVConstant>(OtherDiv->getRHS())) {
    3219       72208 :           bool Overflow = false;
    3220             :           APInt NewRHS =
    3221             :               DivisorConstant->getAPInt().umul_ov(RHSC->getAPInt(), Overflow);
    3222             :           if (Overflow) {
    3223             :             return getConstant(RHSC->getType(), 0, false);
    3224      562359 :           }
    3225       70374 :           return getUDivExpr(OtherDiv->getLHS(), getConstant(NewRHS));
    3226             :         }
    3227             :       }
    3228             : 
    3229             :       // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
    3230             :       if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
    3231      617900 :         SmallVector<const SCEV *, 4> Operands;
    3232       47815 :         for (const SCEV *Op : A->operands())
    3233             :           Operands.push_back(getZeroExtendExpr(Op, ExtTy));
    3234             :         if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
    3235      573213 :           Operands.clear();
    3236             :           for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
    3237             :             const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
    3238             :             if (isa<SCEVUDivExpr>(Op) ||
    3239       35243 :                 getMulExpr(Op, RHS) != A->getOperand(i))
    3240       35243 :               break;
    3241      117758 :             Operands.push_back(Op);
    3242      165030 :           }
    3243       31800 :           if (Operands.size() == A->getNumOperands())
    3244       31800 :             return getAddExpr(Operands);
    3245       31800 :         }
    3246             :       }
    3247             : 
    3248             :       // Fold if both operands are constant.
    3249       35243 :       if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
    3250             :         Constant *LHSCV = LHSC->getValue();
    3251             :         Constant *RHSCV = RHSC->getValue();
    3252       31446 :         return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
    3253       31446 :                                                                    RHSCV)));
    3254       96491 :       }
    3255      130090 :     }
    3256             :   }
    3257             : 
    3258             :   FoldingSetNodeID ID;
    3259             :   ID.AddInteger(scUDivExpr);
    3260             :   ID.AddPointer(LHS);
    3261             :   ID.AddPointer(RHS);
    3262             :   void *IP = nullptr;
    3263       31446 :   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
    3264       31446 :   SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
    3265             :                                              LHS, RHS);
    3266             :   UniqueSCEVs.InsertNode(S, IP);
    3267       31446 :   addToLoopUseLists(S);
    3268             :   return S;
    3269             : }
    3270          73 : 
    3271        2507 : static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
    3272        1217 :   APInt A = C1->getAPInt().abs();
    3273             :   APInt B = C2->getAPInt().abs();
    3274             :   uint32_t ABW = A.getBitWidth();
    3275        1217 :   uint32_t BBW = B.getBitWidth();
    3276             : 
    3277             :   if (ABW > BBW)
    3278             :     B = B.zext(ABW);
    3279             :   else if (ABW < BBW)
    3280             :     A = A.zext(BBW);
    3281             : 
    3282             :   return APIntOps::GreatestCommonDivisor(std::move(A), std::move(B));
    3283             : }
    3284             : 
    3285             : /// Get a canonical unsigned division expression, or something simpler if
    3286             : /// possible. There is no representation for an exact udiv in SCEV IR, but we
    3287             : /// can attempt to remove factors from the LHS and RHS.  We can't do this when
    3288             : /// it's not exact because the udiv may be clearing bits.
    3289             : const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
    3290             :                                               const SCEV *RHS) {
    3291             :   // TODO: we could try to find factors in all sorts of things, but for now we
    3292             :   // just deal with u/exact (multiply, constant). See SCEVDivision towards the
    3293        6336 :   // end of this file for inspiration.
    3294        6336 : 
    3295             :   const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
    3296             :   if (!Mul || !Mul->hasNoUnsignedWrap())
    3297             :     return getUDivExpr(LHS, RHS);
    3298        3075 : 
    3299        2363 :   if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
    3300             :     // If the mulexpr multiplies by a constant, then that constant must be the
    3301             :     // first element of the mulexpr.
    3302             :     if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
    3303        3075 :       if (LHSCst == RHSCst) {
    3304        3075 :         SmallVector<const SCEV *, 2> Operands;
    3305             :         Operands.append(Mul->op_begin() + 1, Mul->op_end());
    3306             :         return getMulExpr(Operands);
    3307         712 :       }
    3308             : 
    3309         712 :       // We can't just assume that LHSCst divides RHSCst cleanly, it could be
    3310             :       // that there's a factor provided by one of the other terms. We need to
    3311        2621 :       // check.
    3312        3333 :       APInt Factor = gcd(LHSCst, RHSCst);
    3313        2621 :       if (!Factor.isIntN(1)) {
    3314        9033 :         LHSCst =
    3315        6412 :             cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor)));
    3316        6412 :         RHSCst =
    3317        9198 :             cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor)));
    3318       11562 :         SmallVector<const SCEV *, 2> Operands;
    3319        5150 :         Operands.push_back(LHSCst);
    3320             :         Operands.append(Mul->op_begin() + 1, Mul->op_end());
    3321        5150 :         LHS = getMulExpr(Operands);
    3322             :         RHS = RHSCst;
    3323             :         Mul = dyn_cast<SCEVMulExpr>(LHS);
    3324        5145 :         if (!Mul)
    3325        5150 :           return getUDivExactExpr(LHS, RHS);
    3326        5150 :       }
    3327        5150 :     }
    3328        5150 :   }
    3329             : 
    3330             :   for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
    3331             :     if (Mul->getOperand(i) == RHS) {
    3332             :       SmallVector<const SCEV *, 2> Operands;
    3333        2621 :       Operands.append(Mul->op_begin(), Mul->op_begin() + i);
    3334             :       Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
    3335         712 :       return getMulExpr(Operands);
    3336         712 :     }
    3337             :   }
    3338         712 : 
    3339         179 :   return getUDivExpr(LHS, RHS);
    3340         179 : }
    3341             : 
    3342             : /// Get an add recurrence expression for the specified loop.  Simplify the
    3343             : /// expression as much as possible.
    3344             : const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
    3345             :                                            const Loop *L,
    3346             :                                            SCEV::NoWrapFlags Flags) {
    3347        3261 :   SmallVector<const SCEV *, 4> Operands;
    3348         136 :   Operands.push_back(Start);
    3349             :   if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
    3350             :     if (StepChrec->getLoop() == L) {
    3351             :       Operands.append(StepChrec->op_begin(), StepChrec->op_end());
    3352             :       return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
    3353             :     }
    3354             : 
    3355             :   Operands.push_back(Step);
    3356      537970 :   return getAddRecExpr(Operands, L, Flags);
    3357             : }
    3358             : 
    3359             : /// Get an add recurrence expression for the specified loop.  Simplify the
    3360        5471 : /// expression as much as possible.
    3361             : const SCEV *
    3362             : ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
    3363             :                                const Loop *L, SCEV::NoWrapFlags Flags) {
    3364             :   if (Operands.size() == 1) return Operands[0];
    3365             : #ifndef NDEBUG
    3366             :   Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
    3367             :   for (unsigned i = 1, e = Operands.size(); i != e; ++i)
    3368             :     assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
    3369        5002 :            "SCEVAddRecExpr operand types don't match!");
    3370        1852 :   for (unsigned i = 0, e = Operands.size(); i != e; ++i)
    3371             :     assert(isLoopInvariant(Operands[i], L) &&
    3372             :            "SCEVAddRecExpr operand is not loop-invariant!");
    3373        1575 : #endif
    3374         181 : 
    3375             :   if (Operands.back()->isZero()) {
    3376         181 :     Operands.pop_back();
    3377         181 :     return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0}  -->  X
    3378             :   }
    3379             : 
    3380             :   // It's tempting to want to call getMaxBackedgeTakenCount count here and
    3381             :   // use that information to infer NUW and NSW flags. However, computing a
    3382        4364 :   // BE count requires calling getAddRecExpr, so we may not yet have a
    3383        4364 :   // meaningful BE count at this point (and if we don't, we'd be stuck
    3384        4364 :   // with a SCEVCouldNotCompute as the cached BE count).
    3385             : 
    3386             :   Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
    3387             : 
    3388             :   // Canonicalize nested AddRecs in by nesting them in order of loop depth.
    3389       42008 :   if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
    3390             :     const Loop *NestedLoop = NestedAR->getLoop();
    3391             :     if (L->contains(NestedLoop)
    3392             :             ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
    3393             :             : (!NestedLoop->contains(L) &&
    3394             :                DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
    3395             :       SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
    3396       76920 :                                                   NestedAR->op_end());
    3397             :       Operands[0] = NestedAR->getStart();
    3398             :       // AddRecs require their operands be loop-invariant with respect to their
    3399             :       // loops. Don't perform this transformation if it would break this
    3400             :       // requirement.
    3401       26814 :       bool AllInvariant = all_of(
    3402             :           Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
    3403             : 
    3404             :       if (AllInvariant) {
    3405       26813 :         // Create a recurrence for the outer loop with the same step size.
    3406       26813 :         //
    3407       26813 :         // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
    3408             :         // inner recurrence has the same property.
    3409             :         SCEV::NoWrapFlags OuterFlags =
    3410       26813 :           maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
    3411             : 
    3412             :         NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
    3413       26813 :         AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
    3414             :           return isLoopInvariant(Op, NestedLoop);
    3415             :         });
    3416         721 : 
    3417             :         if (AllInvariant) {
    3418             :           // Ok, both add recurrences are valid after the transformation.
    3419             :           //
    3420        2158 :           // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
    3421         103 :           // the outer recurrence has the same property.
    3422         103 :           SCEV::NoWrapFlags InnerFlags =
    3423             :             maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
    3424             :           return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
    3425             :         }
    3426          60 :       }
    3427          40 :       // Reset Operands to its original state.
    3428          20 :       Operands[0] = NestedAR;
    3429             :     }
    3430             :   }
    3431             : 
    3432             :   // Okay, it looks like we really DO need an addrec expr.  Check to see if we
    3433         665 :   // already have one, otherwise create a new one.
    3434        2439 :   return getOrCreateAddRecExpr(Operands, L, Flags);
    3435         526 : }
    3436         526 : 
    3437             : const SCEV *
    3438             : ScalarEvolution::getGEPExpr(GEPOperator *GEP,
    3439             :                             const SmallVectorImpl<const SCEV *> &IndexExprs) {
    3440         323 :   const SCEV *BaseExpr = getSCEV(GEP->getPointerOperand());
    3441         323 :   // getSCEV(Base)->getType() has the same address space as Base->getType()
    3442          36 :   // because SCEV::getType() preserves the address space.
    3443             :   Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
    3444             :   // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
    3445             :   // instruction to its SCEV, because the Instruction may be guarded by control
    3446             :   // flow and the no-overflow bits may not be valid for the expression in any
    3447             :   // context. This can be fixed similarly to how these flags are handled for
    3448             :   // adds.
    3449       10616 :   SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW
    3450        7202 :                                              : SCEV::FlagAnyWrap;
    3451        3414 : 
    3452             :   const SCEV *TotalOffset = getZero(IntPtrTy);
    3453           4 :   // The array size is unimportant. The first thing we do on CurTy is getting
    3454           4 :   // its element type.
    3455           4 :   Type *CurTy = ArrayType::get(GEP->getSourceElementType(), 0);
    3456           4 :   for (const SCEV *IndexExpr : IndexExprs) {
    3457           8 :     // Compute the (potentially symbolic) offset in bytes for this index.
    3458             :     if (StructType *STy = dyn_cast<StructType>(CurTy)) {
    3459           4 :       // For a struct, add the member offset.
    3460           4 :       ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
    3461             :       unsigned FieldNo = Index->getZExtValue();
    3462             :       const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
    3463             : 
    3464             :       // Add the field offset to the running total offset.
    3465             :       TotalOffset = getAddExpr(TotalOffset, FieldOffset);
    3466             : 
    3467             :       // Update CurTy to the type of the field at Index.
    3468          21 :       CurTy = STy->getTypeAtIndex(Index);
    3469          21 :     } else {
    3470             :       // Update CurTy to its element type.
    3471          21 :       CurTy = cast<SequentialType>(CurTy)->getElementType();
    3472          21 :       // For an array, add the element offset, explicitly scaled.
    3473           6 :       const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
    3474             :       // Getelementptr indices are signed.
    3475          18 :       IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
    3476             : 
    3477             :       // Multiply the index by the element size to compute the element offset.
    3478             :       const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
    3479             : 
    3480             :       // Add the element offset to the running total offset.
    3481             :       TotalOffset = getAddExpr(TotalOffset, LocalOffset);
    3482        9930 :     }
    3483        6916 :   }
    3484        3014 : 
    3485             :   // Add the total offset from all the GEP indices to the base.
    3486         273 :   return getAddExpr(BaseExpr, TotalOffset, Wrap);
    3487         546 : }
    3488         545 : 
    3489         272 : const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
    3490             :                                          const SCEV *RHS) {
    3491           1 :   SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
    3492             :   return getSMaxExpr(Ops);
    3493         544 : }
    3494           0 : 
    3495             : const SCEV *
    3496             : ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
    3497             :   assert(!Ops.empty() && "Cannot get empty smax!");
    3498             :   if (Ops.size() == 1) return Ops[0];
    3499             : #ifndef NDEBUG
    3500       10266 :   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
    3501       10266 :   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
    3502       10266 :     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
    3503       10266 :            "SCEVSMaxExpr operand types don't match!");
    3504             : #endif
    3505             : 
    3506             :   // Sort by complexity, this groups all similar expression types together.
    3507             :   GroupByComplexity(Ops, &LI, DT);
    3508             : 
    3509       20051 :   // If there are any constants, fold them together.
    3510       20051 :   unsigned Idx = 0;
    3511       20051 :   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
    3512       20051 :     ++Idx;
    3513       20051 :     assert(Idx < Ops.size());
    3514       11464 :     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
    3515             :       // We found two constants, fold them together!
    3516       11464 :       ConstantInt *Fold = ConstantInt::get(
    3517       11464 :           getContext(), APIntOps::smax(LHSC->getAPInt(), RHSC->getAPInt()));
    3518       11464 :       Ops[0] = getConstant(Fold);
    3519             :       Ops.erase(Ops.begin()+1);  // Erase the folded element
    3520             :       if (Ops.size() == 1) return Ops[0];
    3521           0 :       LHSC = cast<SCEVConstant>(Ops[0]);
    3522           0 :     }
    3523           0 : 
    3524           0 :     // If we are left with a constant minimum-int, strip it off.
    3525           0 :     if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
    3526             :       Ops.erase(Ops.begin());
    3527           0 :       --Idx;
    3528           0 :     } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
    3529           0 :       // If we have an smax with a constant maximum-int, it will always be
    3530           0 :       // maximum-int.
    3531             :       return Ops[0];
    3532           0 :     }
    3533             : 
    3534             :     if (Ops.size() == 1) return Ops[0];
    3535             :   }
    3536             : 
    3537             :   // Find the first SMax
    3538             :   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
    3539         488 :     ++Idx;
    3540             : 
    3541             :   // Check to see if one of the operands is an SMax. If so, expand its operands
    3542             :   // onto our operand list, and recurse to simplify.
    3543             :   if (Idx < Ops.size()) {
    3544             :     bool DeletedSMax = false;
    3545             :     while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
    3546          32 :       Ops.erase(Ops.begin()+Idx);
    3547         488 :       Ops.append(SMax->op_begin(), SMax->op_end());
    3548             :       DeletedSMax = true;
    3549             :     }
    3550             : 
    3551             :     if (DeletedSMax)
    3552           0 :       return getSMaxExpr(Ops);
    3553           0 :   }
    3554             : 
    3555           0 :   // Okay, check to see if the same value occurs in the operand list twice.  If
    3556           0 :   // so, delete one.  Since we sorted the list, these values are required to
    3557             :   // be adjacent.
    3558             :   for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
    3559             :     //  X smax Y smax Y  -->  X smax Y
    3560             :     //  X smax Y         -->  X, if X is always greater than Y
    3561             :     if (Ops[i] == Ops[i+1] ||
    3562           0 :         isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
    3563           0 :       Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
    3564             :       --i; --e;
    3565           0 :     } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
    3566             :       Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
    3567           0 :       --i; --e;
    3568             :     }
    3569           0 : 
    3570           0 :   if (Ops.size() == 1) return Ops[0];
    3571           0 : 
    3572             :   assert(!Ops.empty() && "Reduced smax down to nothing!");
    3573             : 
    3574             :   // Okay, it looks like we really DO need an smax expr.  Check to see if we
    3575           0 :   // already have one, otherwise create a new one.
    3576             :   FoldingSetNodeID ID;
    3577             :   ID.AddInteger(scSMaxExpr);
    3578             :   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
    3579             :     ID.AddPointer(Ops[i]);
    3580           0 :   void *IP = nullptr;
    3581           0 :   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
    3582             :   const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
    3583           0 :   std::uninitialized_copy(Ops.begin(), Ops.end(), O);
    3584           0 :   SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
    3585           0 :                                              O, Ops.size());
    3586             :   UniqueSCEVs.InsertNode(S, IP);
    3587             :   addToLoopUseLists(S);
    3588             :   return S;
    3589           0 : }
    3590             : 
    3591             : const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
    3592             :                                          const SCEV *RHS) {
    3593             :   SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
    3594      178554 :   return getUMaxExpr(Ops);
    3595             : }
    3596             : 
    3597             : const SCEV *
    3598      178554 : ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
    3599      178554 :   assert(!Ops.empty() && "Cannot get empty umax!");
    3600         222 :   if (Ops.size() == 1) return Ops[0];
    3601         162 : #ifndef NDEBUG
    3602          81 :   Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
    3603             :   for (unsigned i = 1, e = Ops.size(); i != e; ++i)
    3604             :     assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
    3605      178473 :            "SCEVUMaxExpr operand types don't match!");
    3606      178473 : #endif
    3607             : 
    3608             :   // Sort by complexity, this groups all similar expression types together.
    3609             :   GroupByComplexity(Ops, &LI, DT);
    3610             : 
    3611             :   // If there are any constants, fold them together.
    3612      815329 :   unsigned Idx = 0;
    3613             :   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
    3614     1630658 :     ++Idx;
    3615             :     assert(Idx < Ops.size());
    3616             :     while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
    3617             :       // We found two constants, fold them together!
    3618             :       ConstantInt *Fold = ConstantInt::get(
    3619             :           getContext(), APIntOps::umax(LHSC->getAPInt(), RHSC->getAPInt()));
    3620             :       Ops[0] = getConstant(Fold);
    3621             :       Ops.erase(Ops.begin()+1);  // Erase the folded element
    3622             :       if (Ops.size() == 1) return Ops[0];
    3623             :       LHSC = cast<SCEVConstant>(Ops[0]);
    3624             :     }
    3625      795592 : 
    3626             :     // If we are left with a constant minimum-int, strip it off.
    3627       21797 :     if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
    3628             :       Ops.erase(Ops.begin());
    3629             :       --Idx;
    3630             :     } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
    3631             :       // If we have an umax with a constant maximum-int, it will always be
    3632             :       // maximum-int.
    3633             :       return Ops[0];
    3634             :     }
    3635             : 
    3636      773795 :     if (Ops.size() == 1) return Ops[0];
    3637             :   }
    3638             : 
    3639      773795 :   // Find the first UMax
    3640      142129 :   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
    3641      142129 :     ++Idx;
    3642      142129 : 
    3643      404071 :   // Check to see if one of the operands is a UMax. If so, expand its operands
    3644      239626 :   // onto our operand list, and recurse to simplify.
    3645             :   if (Idx < Ops.size()) {
    3646           0 :     bool DeletedUMax = false;
    3647           0 :     while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
    3648             :       Ops.erase(Ops.begin()+Idx);
    3649             :       Ops.append(UMax->op_begin(), UMax->op_end());
    3650             :       DeletedUMax = true;
    3651             :     }
    3652           0 : 
    3653             :     if (DeletedUMax)
    3654           0 :       return getUMaxExpr(Ops);
    3655             :   }
    3656             : 
    3657             :   // Okay, check to see if the same value occurs in the operand list twice.  If
    3658             :   // so, delete one.  Since we sorted the list, these values are required to
    3659             :   // be adjacent.
    3660           0 :   for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
    3661             :     //  X umax Y umax Y  -->  X umax Y
    3662           0 :     //  X umax Y         -->  X, if X is always greater than Y
    3663             :     if (Ops[i] == Ops[i + 1] || isKnownViaNonRecursiveReasoning(
    3664           0 :                                     ICmpInst::ICMP_UGE, Ops[i], Ops[i + 1])) {
    3665             :       Ops.erase(Ops.begin() + i + 1, Ops.begin() + i + 2);
    3666             :       --i; --e;
    3667           0 :     } else if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, Ops[i],
    3668             :                                                Ops[i + 1])) {
    3669             :       Ops.erase(Ops.begin() + i, Ops.begin() + i + 1);
    3670             :       --i; --e;
    3671             :     }
    3672             : 
    3673           0 :   if (Ops.size() == 1) return Ops[0];
    3674           0 : 
    3675             :   assert(!Ops.empty() && "Reduced umax down to nothing!");
    3676             : 
    3677             :   // Okay, it looks like we really DO need a umax expr.  Check to see if we
    3678           0 :   // already have one, otherwise create a new one.
    3679             :   FoldingSetNodeID ID;
    3680             :   ID.AddInteger(scUMaxExpr);
    3681             :   for (unsigned i = 0, e = Ops.size(); i != e; ++i)
    3682             :     ID.AddPointer(Ops[i]);
    3683             :   void *IP = nullptr;
    3684      773795 :   if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
    3685             :   const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
    3686             :   std::uninitialized_copy(Ops.begin(), Ops.end(), O);
    3687             :   SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
    3688      207966 :                                              O, Ops.size());
    3689             :   UniqueSCEVs.InsertNode(S, IP);
    3690      207966 :   addToLoopUseLists(S);
    3691             :   return S;
    3692             : }
    3693      207966 : 
    3694             : const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
    3695             :                                          const SCEV *RHS) {
    3696             :   SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
    3697             :   return getSMinExpr(Ops);
    3698             : }
    3699      207966 : 
    3700             : const SCEV *ScalarEvolution::getSMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
    3701             :   // ~smax(~x, ~y, ~z) == smin(x, y, z).
    3702             :   SmallVector<const SCEV *, 2> NotOps;
    3703             :   for (auto *S : Ops)
    3704             :     NotOps.push_back(getNotSCEV(S));
    3705      207966 :   return getNotSCEV(getSMaxExpr(NotOps));
    3706      570829 : }
    3707             : 
    3708             : const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
    3709             :                                          const SCEV *RHS) {
    3710       37646 :   SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
    3711       37646 :   return getUMinExpr(Ops);
    3712       37646 : }
    3713             : 
    3714             : const SCEV *ScalarEvolution::getUMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
    3715       37646 :   assert(!Ops.empty() && "At least one operand must be!");
    3716             :   // Trivial case.
    3717             :   if (Ops.size() == 1)
    3718       37646 :     return Ops[0];
    3719             : 
    3720             :   // ~umax(~x, ~y, ~z) == umin(x, y, z).
    3721      325217 :   SmallVector<const SCEV *, 2> NotOps;
    3722             :   for (auto *S : Ops)
    3723      325217 :     NotOps.push_back(getNotSCEV(S));
    3724             :   return getNotSCEV(getUMaxExpr(NotOps));
    3725      325217 : }
    3726             : 
    3727             : const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
    3728      325217 :   // We can bypass creating a target-independent
    3729             :   // constant expression and then folding it back into a ConstantInt.
    3730             :   // This is just a compile-time optimization.
    3731      325217 :   return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
    3732             : }
    3733             : 
    3734             : const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
    3735             :                                              StructType *STy,
    3736      207966 :                                              unsigned FieldNo) {
    3737             :   // We can bypass creating a target-independent
    3738             :   // constant expression and then folding it back into a ConstantInt.
    3739        4749 :   // This is just a compile-time optimization.
    3740             :   return getConstant(
    3741        4749 :       IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
    3742        4749 : }
    3743             : 
    3744             : const SCEV *ScalarEvolution::getUnknown(Value *V) {
    3745             :   // Don't attempt to do anything other than create a SCEVUnknown object
    3746       22358 :   // here.  createSCEV only calls getUnknown after checking for all other
    3747             :   // interesting possibilities, and any other code that calls getUnknown
    3748       22358 :   // is doing so in order to hide a value from SCEV canonicalization.
    3749             : 
    3750             :   FoldingSetNodeID ID;
    3751             :   ID.AddInteger(scUnknown);
    3752             :   ID.AddPointer(V);
    3753             :   void *IP = nullptr;
    3754             :   if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
    3755             :     assert(cast<SCEVUnknown>(S)->getValue() == V &&
    3756             :            "Stale SCEVUnknown in uniquing map!");
    3757       22358 :     return S;
    3758             :   }
    3759             :   SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
    3760             :                                             FirstUnknown);
    3761       22358 :   FirstUnknown = cast<SCEVUnknown>(S);
    3762             :   UniqueSCEVs.InsertNode(S, IP);
    3763             :   return S;
    3764       21769 : }
    3765             : 
    3766       19226 : //===----------------------------------------------------------------------===//
    3767             : //            Basic SCEV Analysis and PHI Idiom Recognition Code
    3768       19226 : //
    3769       19226 : 
    3770       19226 : /// Test if values of the given type are analyzable within the SCEV
    3771           2 : /// framework. This primarily includes integer types, and it can optionally
    3772           2 : /// include pointer types if the ScalarEvolution class has access to
    3773             : /// target-specific information.
    3774             : bool ScalarEvolution::isSCEVable(Type *Ty) const {
    3775        2543 :   // Integers and pointers are always SCEVable.
    3776          11 :   return Ty->isIntOrPtrTy();
    3777             : }
    3778        2532 : 
    3779             : /// Return the size in bits of the specified type, for which isSCEVable must
    3780             : /// return true.
    3781             : uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
    3782             :   assert(isSCEVable(Ty) && "Type is not SCEVable!");
    3783             :   if (Ty->isPointerTy())
    3784        2539 :     return getDataLayout().getIndexTypeSizeInBits(Ty);
    3785             :   return getDataLayout().getTypeSizeInBits(Ty);
    3786             : }
    3787             : 
    3788        5541 : /// Return a type with the same bitwidth as the given type and which represents
    3789        2422 : /// how SCEV will treat the given type, for which isSCEVable must return
    3790             : /// true. For pointer types, this is the pointer-sized integer type.
    3791             : Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
    3792             :   assert(isSCEVable(Ty) && "Type is not SCEVable!");
    3793        3119 : 
    3794             :   if (Ty->isIntegerTy())
    3795        1318 :     return Ty;
    3796          92 : 
    3797         184 :   // The only other support type is pointer.
    3798             :   assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
    3799          92 :   return getDataLayout().getIntPtrType(Ty);
    3800             : }
    3801        1226 : 
    3802          92 : Type *ScalarEvolution::getWiderType(Type *T1, Type *T2) const {
    3803             :   return  getTypeSizeInBits(T1) >= getTypeSizeInBits(T2) ? T1 : T2;
    3804             : }
    3805             : 
    3806             : const SCEV *ScalarEvolution::getCouldNotCompute() {
    3807             :   return CouldNotCompute.get();
    3808        6486 : }
    3809             : 
    3810             : bool ScalarEvolution::checkValidity(const SCEV *S) const {
    3811       13831 :   bool ContainsNulls = SCEVExprContains(S, [](const SCEV *S) {
    3812        3454 :     auto *SU = dyn_cast<SCEVUnknown>(S);
    3813         136 :     return SU && SU->getValue() == nullptr;
    3814         136 :   });
    3815        6646 : 
    3816          48 :   return !ContainsNulls;
    3817          48 : }
    3818             : 
    3819             : bool ScalarEvolution::containsAddRecurrence(const SCEV *S) {
    3820        3027 :   HasRecMapType::iterator I = HasRecMap.find(S);
    3821             :   if (I != HasRecMap.end())
    3822             :     return I->second;
    3823             : 
    3824             :   bool FoundAddRec = SCEVExprContains(S, isa<SCEVAddRecExpr, const SCEV *>);
    3825             :   HasRecMap.insert({S, FoundAddRec});
    3826             :   return FoundAddRec;
    3827        2843 : }
    3828        8961 : 
    3829       12236 : /// Try to split a SCEVAddExpr into a pair of {SCEV, ConstantInt}.
    3830        2843 : /// If \p S is a SCEVAddExpr and is composed of a sub SCEV S' and an
    3831        2843 : /// offset I, then return {S', I}, else return {\p S, nullptr}.
    3832        2382 : static std::pair<const SCEV *, ConstantInt *> splitAddExpr(const SCEV *S) {
    3833             :   const auto *Add = dyn_cast<SCEVAddExpr>(S);
    3834        2382 :   if (!Add)
    3835        2382 :     return {S, nullptr};
    3836        2382 : 
    3837        2382 :   if (Add->getNumOperands() != 2)
    3838        2382 :     return {S, nullptr};
    3839             : 
    3840             :   auto *ConstOp = dyn_cast<SCEVConstant>(Add->getOperand(0));
    3841         932 :   if (!ConstOp)
    3842             :     return {S, nullptr};
    3843         932 : 
    3844         932 :   return {Add->getOperand(1), ConstOp->getValue()};
    3845             : }
    3846             : 
    3847             : /// Return the ValueOffsetPair set for \p S. \p S can be represented
    3848        2062 : /// by the value and offset from any ValueOffsetPair in the set.
    3849             : SetVector<ScalarEvolution::ValueOffsetPair> *
    3850        2062 : ScalarEvolution::getSCEVValues(const SCEV *S) {
    3851             :   ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
    3852             :   if (SI == ExprValueMap.end())
    3853             :     return nullptr;
    3854             : #ifndef NDEBUG
    3855             :   if (VerifySCEVMap) {
    3856             :     // Check there is no dangling Value in the set returned.
    3857             :     for (const auto &VE : SI->second)
    3858             :       assert(ValueExprMap.count(VE.first));
    3859        2062 :   }
    3860             : #endif
    3861             :   return &SI->second;
    3862             : }
    3863        2062 : 
    3864             : /// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V)
    3865             : /// cannot be used separately. eraseValueFromMap should be used to remove
    3866        1389 : /// V from ValueExprMap and ExprValueMap at the same time.
    3867             : void ScalarEvolution::eraseValueFromMap(Value *V) {
    3868         562 :   ValueExprMapType::iterator I = ValueExprMap.find_as(V);
    3869             :   if (I != ValueExprMap.end()) {
    3870         562 :     const SCEV *S = I->second;
    3871         562 :     // Remove {V, 0} from the set of ExprValueMap[S]
    3872         562 :     if (SetVector<ValueOffsetPair> *SV = getSCEVValues(S))
    3873          25 :       SV->remove({V, nullptr});
    3874          25 : 
    3875             :     // Remove {V, Offset} from the set of ExprValueMap[Stripped]
    3876             :     const SCEV *Stripped;
    3877         827 :     ConstantInt *Offset;
    3878         146 :     std::tie(Stripped, Offset) = splitAddExpr(S);
    3879             :     if (Offset != nullptr) {
    3880         681 :       if (SetVector<ValueOffsetPair> *SV = getSCEVValues(Stripped))
    3881             :         SV->remove({V, Offset});
    3882             :     }
    3883             :     ValueExprMap.erase(V);
    3884             :   }
    3885             : }
    3886         802 : 
    3887             : /// Check whether value has nuw/nsw/exact set but SCEV does not.
    3888             : /// TODO: In reality it is better to check the poison recursevely
    3889             : /// but this is better than nothing.
    3890        2804 : static bool SCEVLostPoisonFlags(const SCEV *S, const Value *V) {
    3891        1450 :   if (auto *I = dyn_cast<Instruction>(V)) {
    3892             :     if (isa<OverflowingBinaryOperator>(I)) {
    3893             :       if (auto *NS = dyn_cast<SCEVNAryExpr>(S)) {
    3894             :         if (I->hasNoSignedWrap() && !NS->hasNoSignedWrap())
    3895        1354 :           return true;
    3896             :         if (I->hasNoUnsignedWrap() && !NS->hasNoUnsignedWrap())
    3897         582 :           return true;
    3898          30 :       }
    3899          60 :     } else if (isa<PossiblyExactOperator>(I) && I->isExact())
    3900             :       return true;
    3901          30 :   }
    3902             :   return false;
    3903         552 : }
    3904          30 : 
    3905             : /// Return an existing SCEV if it exists, otherwise analyze the expression and
    3906             : /// create a new one.
    3907             : const SCEV *ScalarEvolution::getSCEV(Value *V) {
    3908             :   assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
    3909             : 
    3910        2702 :   const SCEV *S = getExistingSCEV(V);
    3911             :   if (S == nullptr) {
    3912             :     S = createSCEV(V);
    3913        4134 :     // During PHI resolution, it is possible to create two SCEVs for the same
    3914             :     // V, so it is needed to double check whether V->S is inserted into
    3915          24 :     // ValueExprMap before insert S->{V, 0} into ExprValueMap.
    3916          24 :     std::pair<ValueExprMapType::iterator, bool> Pair =
    3917        2708 :         ValueExprMap.insert({SCEVCallbackVH(V, this), S});
    3918             :     if (Pair.second && !SCEVLostPoisonFlags(S, V)) {
    3919          41 :       ExprValueMap[S].insert({V, nullptr});
    3920          41 : 
    3921             :       // If S == Stripped + Offset, add Stripped -> {V, Offset} into
    3922             :       // ExprValueMap.
    3923        1324 :       const SCEV *Stripped = S;
    3924             :       ConstantInt *Offset = nullptr;
    3925             :       std::tie(Stripped, Offset) = splitAddExpr(S);
    3926             :       // If stripped is SCEVUnknown, don't bother to save
    3927             :       // Stripped -> {V, offset}. It doesn't simplify and sometimes even
    3928             :       // increase the complexity of the expansion code.
    3929             :       // If V is GetElementPtrInst, don't save Stripped -> {V, offset}
    3930        1261 :       // because it may generate add/sub instead of GEP in SCEV expansion.
    3931        3835 :       if (Offset != nullptr && !isa<SCEVUnknown>(Stripped) &&
    3932        5148 :           !isa<GetElementPtrInst>(V))
    3933        1261 :         ExprValueMap[Stripped].insert({V, Offset});
    3934        1261 :     }
    3935         956 :   }
    3936             :   return S;
    3937         956 : }
    3938         956 : 
    3939         956 : const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
    3940         956 :   assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
    3941         956 : 
    3942             :   ValueExprMapType::iterator I = ValueExprMap.find_as(V);
    3943             :   if (I != ValueExprMap.end()) {
    3944       17322 :     const SCEV *S = I->second;
    3945             :     if (checkValidity(S))
    3946       17322 :       return S;
    3947       17322 :     eraseValueFromMap(V);
    3948             :     forgetMemoizedResults(S);
    3949             :   }
    3950       17322 :   return nullptr;
    3951             : }
    3952             : 
    3953       51966 : /// Return a SCEV corresponding to -V = -1*V
    3954       34644 : const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
    3955       17322 :                                              SCEV::NoWrapFlags Flags) {
    3956             :   if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
    3957             :     return getConstant(
    3958         358 :                cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
    3959             : 
    3960         358 :   Type *Ty = V->getType();
    3961         358 :   Ty = getEffectiveSCEVType(Ty);
    3962             :   return getMulExpr(
    3963             :       V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
    3964        1091 : }
    3965             : 
    3966             : /// Return a SCEV corresponding to ~V = -1-V
    3967        2182 : const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
    3968           0 :   if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
    3969             :     return getConstant(
    3970             :                 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
    3971             : 
    3972        3298 :   Type *Ty = V->getType();
    3973        2207 :   Ty = getEffectiveSCEVType(Ty);
    3974        1091 :   const SCEV *AllOnes =
    3975             :                    getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
    3976             :   return getMinusSCEV(AllOnes, V);
    3977      369278 : }
    3978             : 
    3979             : const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
    3980             :                                           SCEV::NoWrapFlags Flags,
    3981      369278 :                                           unsigned Depth) {
    3982             :   // Fast path: X - X --> 0.
    3983             :   if (LHS == RHS)
    3984       37646 :     return getZero(LHS->getType());
    3985             : 
    3986             :   // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
    3987             :   // makes it so that we cannot make much use of NUW.
    3988             :   auto AddFlags = SCEV::FlagAnyWrap;
    3989             :   const bool RHSIsNotMinSigned =
    3990       37646 :       !getSignedRangeMin(RHS).isMinSignedValue();
    3991       37646 :   if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
    3992             :     // Let M be the minimum representable signed value. Then (-1)*RHS
    3993             :     // signed-wraps if and only if RHS is M. That can happen even for
    3994      282622 :     // a NSW subtraction because e.g. (-1)*M signed-wraps even though
    3995             :     // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
    3996             :     // (-1)*RHS, we need to prove that RHS != M.
    3997             :     //
    3998             :     // If LHS is non-negative and we know that LHS - RHS does not
    3999             :     // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
    4000             :     // either by proving that RHS > M or that LHS >= 0.
    4001      282622 :     if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
    4002      282622 :       AddFlags = SCEV::FlagNSW;
    4003      282622 :     }
    4004      282622 :   }
    4005             : 
    4006             :   // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
    4007             :   // RHS is NSW and LHS >= 0.
    4008             :   //
    4009      227236 :   // The difficulty here is that the NSW flag may have been proven
    4010      227236 :   // relative to a loop that is to be found in a recurrence in LHS and
    4011      227236 :   // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
    4012      227236 :   // larger scope than intended.
    4013      227236 :   auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
    4014             : 
    4015             :   return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags, Depth);
    4016             : }
    4017             : 
    4018             : const SCEV *
    4019             : ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
    4020             :   Type *SrcTy = V->getType();
    4021             :   assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
    4022             :          "Cannot truncate or zero extend with non-integer arguments!");
    4023             :   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
    4024     1632233 :     return V;  // No conversion
    4025             :   if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
    4026     1632233 :     return getTruncateExpr(V, Ty);
    4027             :   return getZeroExtendExpr(V, Ty);
    4028             : }
    4029             : 
    4030             : const SCEV *
    4031     3702970 : ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
    4032             :                                          Type *Ty) {
    4033     3702970 :   Type *SrcTy = V->getType();
    4034      410570 :   assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
    4035     3292400 :          "Cannot truncate or zero extend with non-integer arguments!");
    4036             :   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
    4037             :     return V;  // No conversion
    4038             :   if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
    4039             :     return getTruncateExpr(V, Ty);
    4040             :   return getSignExtendExpr(V, Ty);
    4041     2835674 : }
    4042             : 
    4043             : const SCEV *
    4044     2835674 : ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
    4045             :   Type *SrcTy = V->getType();
    4046             :   assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
    4047             :          "Cannot noop or zero extend with non-integer arguments!");
    4048             :   assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
    4049      829844 :          "getNoopOrZeroExtend cannot truncate!");
    4050             :   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
    4051             :     return V;  // No conversion
    4052         841 :   return getZeroExtendExpr(V, Ty);
    4053         841 : }
    4054             : 
    4055             : const SCEV *
    4056      658341 : ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
    4057      658341 :   Type *SrcTy = V->getType();
    4058             :   assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
    4059             :          "Cannot noop or sign extend with non-integer arguments!");
    4060     2016965 :   assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
    4061             :          "getNoopOrSignExtend cannot truncate!");
    4062             :   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
    4063     1405841 :     return V;  // No conversion
    4064             :   return getSignExtendExpr(V, Ty);
    4065             : }
    4066     2016965 : 
    4067             : const SCEV *
    4068             : ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
    4069       78043 :   Type *SrcTy = V->getType();
    4070       78043 :   assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
    4071       78043 :          "Cannot noop or any extend with non-integer arguments!");
    4072       17392 :   assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
    4073             :          "getNoopOrAnyExtend cannot truncate!");
    4074             :   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
    4075       60651 :     return V;  // No conversion
    4076       60651 :   return getAnyExtendExpr(V, Ty);
    4077             : }
    4078             : 
    4079             : const SCEV *
    4080             : ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
    4081             :   Type *SrcTy = V->getType();
    4082      738514 :   assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
    4083             :          "Cannot truncate or noop with non-integer arguments!");
    4084             :   assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
    4085      583616 :          "getTruncateOrNoop cannot extend!");
    4086             :   if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
    4087      154898 :     return V;  // No conversion
    4088        8995 :   return getTruncateExpr(V, Ty);
    4089             : }
    4090      145903 : 
    4091             : const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
    4092       23924 :                                                         const SCEV *RHS) {
    4093             :   const SCEV *PromotedLHS = LHS;
    4094      121979 :   const SCEV *PromotedRHS = RHS;
    4095             : 
    4096             :   if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
    4097             :     PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
    4098             :   else
    4099             :     PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
    4100      240805 : 
    4101      240805 :   return getUMaxExpr(PromotedLHS, PromotedRHS);
    4102      240805 : }
    4103             : 
    4104             : const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
    4105             :                                                         const SCEV *RHS) {
    4106             :   SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
    4107             :   return getUMinFromMismatchedTypes(Ops);
    4108             : }
    4109             : 
    4110             : const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(
    4111       99447 :     SmallVectorImpl<const SCEV *> &Ops) {
    4112             :   assert(!Ops.empty() && "At least one operand must be!");
    4113             :   // Trivial case.
    4114             :   if (Ops.size() == 1)
    4115             :     return Ops[0];
    4116             : 
    4117      134807 :   // Find the max type first.
    4118      134807 :   Type *MaxType = nullptr;
    4119      134807 :   for (auto *S : Ops)
    4120      122909 :     if (MaxType)
    4121             :       MaxType = getWiderType(MaxType, S->getType());
    4122      122909 :     else
    4123       69611 :       MaxType = S->getType();
    4124             : 
    4125             :   // Extend all ops to max type.
    4126             :   SmallVector<const SCEV *, 2> PromotedOps;
    4127             :   for (auto *S : Ops)
    4128      122909 :     PromotedOps.push_back(getNoopOrZeroExtend(S, MaxType));
    4129      122909 : 
    4130       17556 :   // Generate umin.
    4131         977 :   return getUMinExpr(PromotedOps);
    4132             : }
    4133      245818 : 
    4134             : const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
    4135      134807 :   // A pointer operand may evaluate to a nonpointer expression, such as null.
    4136             :   if (!V->getType()->isPointerTy())
    4137             :     return V;
    4138             : 
    4139             :   if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
    4140      637589 :     return getPointerBase(Cast->getOperand());
    4141             :   } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
    4142             :     const SCEV *PtrOp = nullptr;
    4143             :     for (const SCEV *NAryOp : NAry->operands()) {
    4144       78343 :       if (NAryOp->getType()->isPointerTy()) {
    4145             :         // Cannot find the base of an expression with multiple pointer operands.
    4146       60226 :         if (PtrOp)
    4147        2150 :           return V;
    4148             :         PtrOp = NAryOp;
    4149        7343 :       }
    4150        1717 :     }
    4151             :     if (!PtrOp)
    4152             :       return V;
    4153             :     return getPointerBase(PtrOp);
    4154             :   }
    4155             :   return V;
    4156             : }
    4157     2711046 : 
    4158             : /// Push users of the given Instruction onto the given Worklist.
    4159             : static void
    4160     2711046 : PushDefUseChildren(Instruction *I,
    4161     2711046 :                    SmallVectorImpl<Instruction *> &Worklist) {
    4162      701261 :   // Push the def-use children onto the Worklist stack.
    4163             :   for (User *U : I->users())
    4164             :     Worklist.push_back(cast<Instruction>(U));
    4165             : }
    4166             : 
    4167     1402522 : void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) {
    4168      701261 :   SmallVector<Instruction *, 16> Worklist;
    4169      615605 :   PushDefUseChildren(PN, Worklist);
    4170             : 
    4171             :   SmallPtrSet<Instruction *, 8> Visited;
    4172             :   Visited.insert(PN);
    4173      615605 :   while (!Worklist.empty()) {
    4174             :     Instruction *I = Worklist.pop_back_val();
    4175      615605 :     if (!Visited.insert(I).second)
    4176             :       continue;
    4177             : 
    4178             :     auto It = ValueExprMap.find_as(static_cast<Value *>(I));
    4179             :     if (It != ValueExprMap.end()) {
    4180             :       const SCEV *Old = It->second;
    4181      615605 : 
    4182             :       // Short-circuit the def-use traversal if the symbolic name
    4183        3442 :       // ceases to appear in expressions.
    4184             :       if (Old != SymName && !hasOperand(Old, SymName))
    4185             :         continue;
    4186     2711046 : 
    4187             :       // SCEVUnknown for a PHI either means that it has an unrecognized
    4188             :       // structure, it's a PHI that's in the progress of being computed
    4189     2802907 :       // by createNodeForPHI, or it's a single-value PHI. In the first case,
    4190             :       // additional loop trip count information isn't going to change anything.
    4191             :       // In the second case, createNodeForPHI will perform the necessary
    4192     2802907 :       // updates on its own when it gets to that point. In the third, we do
    4193     2802907 :       // want to forget the SCEVUnknown.
    4194     2016965 :       if (!isa<PHINode>(I) ||
    4195     2016965 :           !isa<SCEVUnknown>(Old) ||
    4196             :           (I != PN && Old == SymName)) {
    4197           0 :         eraseValueFromMap(It->first);
    4198           0 :         forgetMemoizedResults(Old);
    4199             :       }
    4200             :     }
    4201             : 
    4202             :     PushDefUseChildren(I, Worklist);
    4203             :   }
    4204      894892 : }
    4205             : 
    4206             : namespace {
    4207      487301 : 
    4208      974602 : /// Takes SCEV S and Loop L. For each AddRec sub-expression, use its start
    4209             : /// expression in case its Loop is L. If it is not L then
    4210      407591 : /// if IgnoreOtherLoops is true then use AddRec itself
    4211      407591 : /// otherwise rewrite cannot be done.
    4212      407591 : /// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
    4213      407591 : class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
    4214             : public:
    4215             :   static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
    4216             :                              bool IgnoreOtherLoops = true) {
    4217      170709 :     SCEVInitRewriter Rewriter(L, SE);
    4218             :     const SCEV *Result = Rewriter.visit(S);
    4219       87407 :     if (Rewriter.hasSeenLoopVariantSCEVUnknown())
    4220      174814 :       return SE.getCouldNotCompute();
    4221             :     return Rewriter.hasSeenOtherLoops() && !IgnoreOtherLoops
    4222       83302 :                ? SE.getCouldNotCompute()
    4223       83302 :                : Result;
    4224             :   }
    4225       83302 : 
    4226       83302 :   const SCEV *visitUnknown(const SCEVUnknown *Expr) {
    4227             :     if (!SE.isLoopInvariant(Expr, L))
    4228             :       SeenLoopVariantSCEVUnknown = true;
    4229     1028559 :     return Expr;
    4230             :   }
    4231             : 
    4232             :   const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
    4233     1028559 :     // Only re-write AddRecExprs for this loop.
    4234      304478 :     if (Expr->getLoop() == L)
    4235             :       return Expr->getStart();
    4236             :     SeenOtherLoops = true;
    4237             :     return Expr;
    4238             :   }
    4239             : 
    4240      877629 :   bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
    4241      876320 : 
    4242             :   bool hasSeenOtherLoops() { return SeenOtherLoops; }
    4243             : 
    4244             : private:
    4245             :   explicit SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
    4246             :       : SCEVRewriteVisitor(SE), L(L) {}
    4247             : 
    4248             :   const Loop *L;
    4249             :   bool SeenLoopVariantSCEVUnknown = false;
    4250             :   bool SeenOtherLoops = false;
    4251         317 : };
    4252             : 
    4253             : /// Takes SCEV S and Loop L. For each AddRec sub-expression, use its post
    4254             : /// increment expression in case its Loop is L. If it is not L then
    4255             : /// use AddRec itself.
    4256             : /// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
    4257             : class SCEVPostIncRewriter : public SCEVRewriteVisitor<SCEVPostIncRewriter> {
    4258             : public:
    4259             :   static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE) {
    4260             :     SCEVPostIncRewriter Rewriter(L, SE);
    4261             :     const SCEV *Result = Rewriter.visit(S);
    4262             :     return Rewriter.hasSeenLoopVariantSCEVUnknown()
    4263      876320 :         ? SE.getCouldNotCompute()
    4264             :         : Result;
    4265      876320 :   }
    4266             : 
    4267             :   const SCEV *visitUnknown(const SCEVUnknown *Expr) {
    4268             :     if (!SE.isLoopInvariant(Expr, L))
    4269       93333 :       SeenLoopVariantSCEVUnknown = true;
    4270       93333 :     return Expr;
    4271             :   }
    4272             : 
    4273       93333 :   const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
    4274             :     // Only re-write AddRecExprs for this loop.
    4275       19243 :     if (Expr->getLoop() == L)
    4276        9405 :       return Expr->getPostIncExpr(SE);
    4277        9838 :     SeenOtherLoops = true;
    4278             :     return Expr;
    4279             :   }
    4280             : 
    4281      325501 :   bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
    4282             : 
    4283      325501 :   bool hasSeenOtherLoops() { return SeenOtherLoops; }
    4284             : 
    4285             : private:
    4286      325501 :   explicit SCEVPostIncRewriter(const Loop *L, ScalarEvolution &SE)
    4287             :       : SCEVRewriteVisitor(SE), L(L) {}
    4288       23113 : 
    4289         646 :   const Loop *L;
    4290       22467 :   bool SeenLoopVariantSCEVUnknown = false;
    4291             :   bool SeenOtherLoops = false;
    4292             : };
    4293             : 
    4294      180126 : /// This class evaluates the compare condition by matching it against the
    4295      180126 : /// condition of loop latch. If there is a match we assume a true value
    4296             : /// for the condition while building SCEV nodes.
    4297             : class SCEVBackedgeConditionFolder
    4298             :     : public SCEVRewriteVisitor<SCEVBackedgeConditionFolder> {
    4299             : public:
    4300      180126 :   static const SCEV *rewrite(const SCEV *S, const Loop *L,
    4301             :                              ScalarEvolution &SE) {
    4302       22956 :     bool IsPosBECond = false;
    4303             :     Value *BECond = nullptr;
    4304             :     if (BasicBlock *Latch = L->getLoopLatch()) {
    4305             :       BranchInst *BI = dyn_cast<BranchInst>(Latch->getTerminator());
    4306        3978 :       if (BI && BI->isConditional()) {
    4307        3978 :         assert(BI->getSuccessor(0) != BI->getSuccessor(1) &&
    4308             :                "Both outgoing branches should not target same header!");
    4309             :         BECond = BI->getCondition();
    4310             :         IsPosBECond = BI->getSuccessor(0) == L->getHeader();
    4311             :       } else {
    4312        3978 :         return S;
    4313             :       }
    4314         520 :     }
    4315             :     SCEVBackedgeConditionFolder Rewriter(L, BECond, IsPosBECond, SE);
    4316             :     return Rewriter.visit(S);
    4317             :   }
    4318          84 : 
    4319          84 :   const SCEV *visitUnknown(const SCEVUnknown *Expr) {
    4320             :     const SCEV *Result = Expr;
    4321             :     bool InvariantF = SE.isLoopInvariant(Expr, L);
    4322             : 
    4323             :     if (!InvariantF) {
    4324          84 :       Instruction *I = cast<Instruction>(Expr->getValue());
    4325             :       switch (I->getOpcode()) {
    4326           0 :       case Instruction::Select: {
    4327             :         SelectInst *SI = cast<SelectInst>(I);
    4328             :         Optional<const SCEV *> Res =
    4329             :             compareWithBackedgeCondition(SI->getCondition());
    4330         277 :         if (Res.hasValue()) {
    4331         277 :           bool IsOne = cast<SCEVConstant>(Res.getValue())->getValue()->isOne();
    4332             :           Result = SE.getSCEV(IsOne ? SI->getTrueValue() : SI->getFalseValue());
    4333             :         }
    4334             :         break;
    4335             :       }
    4336         277 :       default: {
    4337             :         Optional<const SCEV *> Res = compareWithBackedgeCondition(I);
    4338          24 :         if (Res.hasValue())
    4339             :           Result = Res.getValue();
    4340             :         break;
    4341           0 :       }
    4342             :       }
    4343             :     }
    4344             :     return Result;
    4345             :   }
    4346           0 : 
    4347           0 : private:
    4348             :   explicit SCEVBackedgeConditionFolder(const Loop *L, Value *BECond,
    4349           0 :                                        bool IsPosBECond, ScalarEvolution &SE)
    4350             :       : SCEVRewriteVisitor(SE), L(L), BackedgeCond(BECond),
    4351           0 :         IsPositiveBECond(IsPosBECond) {}
    4352             : 
    4353             :   Optional<const SCEV *> compareWithBackedgeCondition(Value *IC);
    4354         419 : 
    4355             :   const Loop *L;
    4356         419 :   /// Loop back condition.
    4357         419 :   Value *BackedgeCond = nullptr;
    4358             :   /// Set to true if loop back is on positive branch condition.
    4359             :   bool IsPositiveBECond;
    4360       33779 : };
    4361             : 
    4362             : Optional<const SCEV *>
    4363             : SCEVBackedgeConditionFolder::compareWithBackedgeCondition(Value *IC) {
    4364       67558 : 
    4365       33046 :   // If value matches the backedge condition for loop latch,
    4366             :   // then return a constant evolution node based on loopback
    4367             :   // branch taken.
    4368             :   if (BackedgeCond == IC)
    4369        2224 :     return IsPositiveBECond ? SE.getOne(Type::getInt1Ty(SE.getContext()))
    4370        1491 :                             : SE.getZero(Type::getInt1Ty(SE.getContext()));
    4371         758 :   return None;
    4372             : }
    4373         733 : 
    4374             : class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
    4375             : public:
    4376             :   static const SCEV *rewrite(const SCEV *S, const Loop *L,
    4377        2224 :                              ScalarEvolution &SE) {
    4378        1491 :     SCEVShiftRewriter Rewriter(L, SE);
    4379             :     const SCEV *Result = Rewriter.visit(S);
    4380             :     return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
    4381         733 :   }
    4382             : 
    4383             :   const SCEV *visitUnknown(const SCEVUnknown *Expr) {
    4384       56377 :     // Only allow AddRecExprs for this loop.
    4385             :     if (!SE.isLoopInvariant(Expr, L))
    4386      110471 :       Valid = false;
    4387             :     return Expr;
    4388             :   }
    4389             : 
    4390           0 :   const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
    4391             :     if (Expr->getLoop() == L && Expr->isAffine())
    4392             :       return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
    4393      163728 :     Valid = false;
    4394      109634 :     return Expr;
    4395             :   }
    4396       54094 : 
    4397             :   bool isValid() { return Valid; }
    4398             : 
    4399             : private:
    4400             :   explicit SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
    4401       54094 :       : SCEVRewriteVisitor(SE), L(L) {}
    4402             : 
    4403             :   const Loop *L;
    4404             :   bool Valid = true;
    4405             : };
    4406             : 
    4407             : } // end anonymous namespace
    4408             : 
    4409             : SCEV::NoWrapFlags
    4410      537992 : ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
    4411             :   if (!AR->isAffine())
    4412             :     return SCEV::FlagAnyWrap;
    4413     1146803 : 
    4414      608811 :   using OBO = OverflowingBinaryOperator;
    4415      537992 : 
    4416             :   SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap;
    4417       12837 : 
    4418             :   if (!AR->hasNoSignedWrap()) {
    4419       12837 :     ConstantRange AddRecRange = getSignedRange(AR);
    4420             :     ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this));
    4421             : 
    4422       12837 :     auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
    4423      282945 :         Instruction::Add, IncRange, OBO::NoSignedWrap);
    4424             :     if (NSWRegion.contains(AddRecRange))
    4425      270108 :       Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW);
    4426       45826 :   }
    4427             : 
    4428      230398 :   if (!AR->hasNoUnsignedWrap()) {
    4429      230398 :     ConstantRange AddRecRange = getUnsignedRange(AR);
    4430       22714 :     ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this));
    4431             : 
    4432             :     auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
    4433             :         Instruction::Add, IncRange, OBO::NoUnsignedWrap);
    4434       22714 :     if (NUWRegion.contains(AddRecRange))
    4435             :       Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW);
    4436             :   }
    4437             : 
    4438             :   return Result;
    4439             : }
    4440             : 
    4441             : namespace {
    4442             : 
    4443             : /// Represents an abstract binary operation.  This may exist as a
    4444          18 : /// normal instruction or constant expression, or may have been
    4445       16603 : /// derived from an expression tree.
    4446           5 : struct BinaryOp {
    4447       16598 :   unsigned Opcode;
    4448       16598 :   Value *LHS;
    4449             :   Value *RHS;
    4450             :   bool IsNSW = false;
    4451             :   bool IsNUW = false;
    4452      224282 : 
    4453             :   /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
    4454       12837 :   /// constant expression.
    4455             :   Operator *Op = nullptr;
    4456             : 
    4457             :   explicit BinaryOp(Operator *Op)
    4458             :       : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
    4459             :         Op(Op) {
    4460             :     if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
    4461             :       IsNSW = OBO->hasNoSignedWrap();
    4462             :       IsNUW = OBO->hasNoUnsignedWrap();
    4463             :     }
    4464             :   }
    4465       39118 : 
    4466             :   explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
    4467             :                     bool IsNUW = false)
    4468       39118 :       : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW) {}
    4469       39118 : };
    4470        1241 : 
    4471         244 : } // end anonymous namespace
    4472       37877 : 
    4473             : /// Try to map \p V into a BinaryOp, and return \c None on failure.
    4474             : static Optional<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) {
    4475             :   auto *Op = dyn_cast<Operator>(V);
    4476             :   if (!Op)
    4477        6532 :     return None;
    4478        1273 : 
    4479             :   // Implementation detail: all the cleverness here should happen without
    4480             :   // creating new SCEV expressions -- our caller knowns tricks to avoid creating
    4481             :   // SCEV expressions when possible, and we should not break that.
    4482           0 : 
    4483             :   switch (Op->getOpcode()) {
    4484       16877 :   case Instruction::Add:
    4485       16629 :   case Instruction::Sub:
    4486         248 :   case Instruction::Mul:
    4487           0 :   case Instruction::UDiv:
    4488             :   case Instruction::URem:
    4489             :   case Instruction::And:
    4490           0 :   case Instruction::Or:
    4491             :   case Instruction::AShr:
    4492           0 :   case Instruction::Shl:
    4493             :     return BinaryOp(Op);
    4494             : 
    4495             :   case Instruction::Xor:
    4496       39118 :     if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
    4497             :       // If the RHS of the xor is a signmask, then this is just an add.
    4498             :       // Instcombine turns add of signmask into xor as a strength reduction step.
    4499             :       if (RHSC->getValue().isSignMask())
    4500             :         return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
    4501             :     return BinaryOp(Op);
    4502             : 
    4503             :   case Instruction::LShr:
    4504             :     // Turn logical shift right of a constant into a unsigned divide.
    4505             :     if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
    4506             :       uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();
    4507             : 
    4508             :       // If the shift count is not less than the bitwidth, the result of
    4509       29965 :       // the shift is undefined. Don't try to analyze it, because the
    4510             :       // resolution chosen here may differ from the resolution chosen in
    4511       29965 :       // other parts of the compiler.
    4512       29965 :       if (SA->getValue().ult(BitWidth)) {
    4513       29965 :         Constant *X =
    4514       29965 :             ConstantInt::get(SA->getContext(),
    4515             :                              APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
    4516             :         return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
    4517             :       }
    4518        5108 :     }
    4519           0 :     return BinaryOp(Op);
    4520             : 
    4521             :   case Instruction::ExtractValue: {
    4522             :     auto *EVI = cast<ExtractValueInst>(Op);
    4523       15877 :     if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
    4524             :       break;
    4525       15877 : 
    4526       15633 :     auto *CI = dyn_cast<CallInst>(EVI->getAggregateOperand());
    4527         244 :     if (!CI)
    4528         244 :       break;
    4529             : 
    4530             :     if (auto *F = CI->getCalledFunction())
    4531           0 :       switch (F->getIntrinsicID()) {
    4532             :       case Intrinsic::sadd_with_overflow:
    4533             :       case Intrinsic::uadd_with_overflow:
    4534             :         if (!isOverflowIntrinsicNoWrap(cast<IntrinsicInst>(CI), DT))
    4535             :           return BinaryOp(Instruction::Add, CI->getArgOperand(0),
    4536             :                           CI->getArgOperand(1));
    4537       29965 : 
    4538             :         // Now that we know that all uses of the arithmetic-result component of
    4539             :         // CI are guarded by the overflow check, we can go ahead and pretend
    4540             :         // that the arithmetic is non-overflowing.
    4541             :         if (F->getIntrinsicID() == Intrinsic::sadd_with_overflow)
    4542             :           return BinaryOp(Instruction::Add, CI->getArgOperand(0),
    4543             :                           CI->getArgOperand(1), /* IsNSW = */ true,
    4544             :                           /* IsNUW = */ false);
    4545             :         else
    4546             :           return BinaryOp(Instruction::Add, CI->getArgOperand(0),
    4547             :                           CI->getArgOperand(1), /* IsNSW = */ false,
    4548             :                           /* IsNUW*/ true);
    4549             :       case Intrinsic::ssub_with_overflow:
    4550       13532 :       case Intrinsic::usub_with_overflow:
    4551             :         if (!isOverflowIntrinsicNoWrap(cast<IntrinsicInst>(CI), DT))
    4552             :           return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
    4553             :                           CI->getArgOperand(1));
    4554       13532 : 
    4555             :         // The same reasoning as sadd/uadd above.
    4556       13466 :         if (F->getIntrinsicID() == Intrinsic::ssub_with_overflow)
    4557             :           return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
    4558             :                           CI->getArgOperand(1), /* IsNSW = */ true,
    4559             :                           /* IsNUW = */ false);
    4560       12628 :         else
    4561             :           return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
    4562             :                           CI->getArgOperand(1), /* IsNSW = */ false,
    4563             :                           /* IsNUW = */ true);
    4564             :       case Intrinsic::smul_with_overflow:
    4565             :       case Intrinsic::umul_with_overflow:
    4566       12639 :         return BinaryOp(Instruction::Mul, CI->getArgOperand(0),
    4567             :                         CI->getArgOperand(1));
    4568             :       default:
    4569        2115 :         break;
    4570        2115 :       }
    4571        2115 :     break;
    4572             :   }
    4573        2115 : 
    4574             :   default:
    4575        1748 :     break;
    4576             :   }
    4577             : 
    4578             :   return None;
    4579         114 : }
    4580         114 : 
    4581           5 : /// Helper function to createAddRecFromPHIWithCasts. We have a phi
    4582          10 : /// node whose symbolic (unknown) SCEV is \p SymbolicPHI, which is updated via
    4583             : /// the loop backedge by a SCEVAddExpr, possibly also with a few casts on the
    4584             : /// way. This function checks if \p Op, an operand of this SCEVAddExpr,
    4585             : /// follows one of the following patterns:
    4586        1634 : /// Op == (SExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
    4587        1634 : /// Op == (ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
    4588        1634 : /// If the SCEV expression of \p Op conforms with one of the expected patterns
    4589           4 : /// we return the type of the truncation operation, and indicate whether the
    4590             : /// truncated type should be treated as signed/unsigned by setting
    4591             : /// \p Signed to true/false, respectively.
    4592             : static Type *isSimpleCastedPHI(const SCEV *Op, const SCEVUnknown *SymbolicPHI,
    4593             :                                bool &Signed, ScalarEvolution &SE) {
    4594        2115 :   // The case where Op == SymbolicPHI (that is, with no type conversions on
    4595             :   // the way) is handled by the regular add recurrence creating logic and
    4596             :   // would have already been triggered in createAddRecForPHI. Reaching it here
    4597             :   // means that createAddRecFromPHI had failed for this PHI before (e.g.,
    4598             :   // because one of the other operands of the SCEVAddExpr updating this PHI is
    4599             :   // not invariant).
    4600       12639 :   //
    4601       12639 :   // Here we look for the case where Op = (ext(trunc(SymbolicPHI))), and in
    4602             :   // this case predicates that allow us to prove that Op == SymbolicPHI will
    4603             :   // be added.
    4604             :   if (Op == SymbolicPHI)
    4605             :     return nullptr;
    4606             : 
    4607             :   unsigned SourceBits = SE.getTypeSizeInBits(SymbolicPHI->getType());
    4608             :   unsigned NewBits = SE.getTypeSizeInBits(Op->getType());
    4609             :   if (SourceBits != NewBits)
    4610             :     return nullptr;
    4611             : 
    4612             :   const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(Op);
    4613        1748 :   const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(Op);
    4614             :   if (!SExt && !ZExt)
    4615             :     return nullptr;
    4616             :   const SCEVTruncateExpr *Trunc =
    4617             :       SExt ? dyn_cast<SCEVTruncateExpr>(SExt->getOperand())
    4618        1748 :            : dyn_cast<SCEVTruncateExpr>(ZExt->getOperand());
    4619           9 :   if (!Trunc)
    4620           1 :     return nullptr;
    4621             :   const SCEV *X = Trunc->getOperand();
    4622             :   if (X != SymbolicPHI)
    4623             :     return nullptr;
    4624             :   Signed = SExt != nullptr;
    4625             :   return Trunc->getType();
    4626        7912 : }
    4627             : 
    4628             : static const Loop *isIntegerLoopHeaderPHI(const PHINode *PN, LoopInfo &LI) {
    4629        7912 :   if (!PN->getType()->isIntegerTy())
    4630        7912 :     return nullptr;
    4631             :   const Loop *L = LI.getLoopFor(PN->getParent());
    4632             :   if (!L || L->getHeader() != PN->getParent())
    4633             :     return nullptr;
    4634             :   return L;
    4635        6881 : }
    4636        6755 : 
    4637             : // Analyze \p SymbolicPHI, a SCEV expression of a phi node, and check if the
    4638             : // computation that updates the phi follows the following pattern:
    4639             : //   (SExt/ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) + InvariantAccum
    4640        1105 : // which correspond to a phi->trunc->sext/zext->add->phi update chain.
    4641        1105 : // If so, try to see if it can be rewritten as an AddRecExpr under some
    4642        1027 : // Predicates. If successful, return them as a pair. Also cache the results
    4643          78 : // of the analysis.
    4644          78 : //
    4645             : // Example usage scenario:
    4646             : //    Say the Rewriter is called for the following SCEV:
    4647           0 : //         8 * ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
    4648             : //    where:
    4649             : //         %X = phi i64 (%Start, %BEValue)
    4650             : //    It will visitMul->visitAdd->visitSExt->visitTrunc->visitUnknown(%X),
    4651        7912 : //    and call this function with %SymbolicPHI = %X.
    4652             : //
    4653             : //    The analysis will find that the value coming around the backedge has
    4654             : //    the following SCEV:
    4655             : //         BEValue = ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
    4656             : //    Upon concluding that this matches the desired pattern, the function
    4657             : //    will return the pair {NewAddRec, SmallPredsVec} where:
    4658             : //         NewAddRec = {%Start,+,%Step}
    4659             : //         SmallPredsVec = {P1, P2, P3} as follows:
    4660       40552 : //           P1(WrapPred): AR: {trunc(%Start),+,(trunc %Step)}<nsw> Flags: <nssw>
    4661       40552 : //           P2(EqualPred): %Start == (sext i32 (trunc i64 %Start to i32) to i64)
    4662             : //           P3(EqualPred): %Step == (sext i32 (trunc i64 %Step to i32) to i64)
    4663             : //    The returned pair means that SymbolicPHI can be rewritten into NewAddRec
    4664             : //    under the predicates {P1,P2,P3}.
    4665             : //    This predicated rewrite will be cached in PredicatedSCEVRewrites:
    4666             : //         PredicatedSCEVRewrites[{%X,L}] = {NewAddRec, {P1,P2,P3)}
    4667             : //
    4668       40552 : // TODO's:
    4669       29097 : //
    4670       58194 : // 1) Extend the Induction descriptor to also support inductions that involve
    4671             : //    casts: When needed (namely, when we are called in the context of the
    4672             : //    vectorizer induction analysis), a Set of cast instructions will be
    4673       58194 : //    populated by this method, and provided back to isInductionPHI. This is
    4674       29097 : //    needed to allow the vectorizer to properly record them to be ignored by
    4675             : //    the cost model and to avoid vectorizing them (otherwise these casts,
    4676             : //    which are redundant under the runtime overflow checks, will be
    4677             : //    vectorized, which can be costly).
    4678       40552 : //
    4679       38989 : // 2) Support additional induction/PHISCEV patterns: We also want to support
    4680       77978 : //    inductions where the sext-trunc / zext-trunc operations (partly) occur
    4681             : //    after the induction update operation (the induction increment):
    4682             : //
    4683       77978 : //      (Trunc iy (SExt/ZExt ix (%SymbolicPHI + InvariantAccum) to iy) to ix)
    4684       38989 : //    which correspond to a phi->add->trunc->sext/zext->phi update chain.
    4685             : //
    4686             : //      (Trunc iy ((SExt/ZExt ix (%SymbolicPhi) to iy) + InvariantAccum) to ix)
    4687             : //    which correspond to a phi->trunc->add->sext/zext->phi update chain.
    4688             : //
    4689             : // 3) Outline common code with createAddRecFromPHI to avoid duplication.
    4690             : Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
    4691             : ScalarEvolution::createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI) {
    4692             :   SmallVector<const SCEVPredicate *, 3> Predicates;
    4693             : 
    4694             :   // *** Part1: Analyze if we have a phi-with-cast pattern for which we can
    4695             :   // return an AddRec expression under some predicate.
    4696             : 
    4697             :   auto *PN = cast<PHINode>(SymbolicPHI->getValue());
    4698             :   const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
    4699             :   assert(L && "Expecting an integer loop header phi");
    4700             : 
    4701             :   // The loop may have multiple entrances or multiple exits; we can analyze
    4702             :   // this phi as an addrec if it has a unique entry value and a unique
    4703             :   // backedge value.
    4704             :   Value *BEValueV = nullptr, *StartValueV = nullptr;
    4705             :   for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
    4706             :     Value *V = PN->getIncomingValue(i);
    4707      162486 :     if (L->contains(PN->getIncomingBlock(i))) {
    4708      162486 :       if (!BEValueV) {
    4709      487458 :         BEValueV = V;
    4710             :       } else if (BEValueV != V) {
    4711      152234 :         BEValueV = nullptr;
    4712      152234 :         break;
    4713             :       }
    4714      162486 :     } else if (!StartValueV) {
    4715             :       StartValueV = V;
    4716             :     } else if (StartValueV != V) {
    4717             :       StartValueV = nullptr;
    4718             :       break;
    4719             :     }
    4720             :   }
    4721             :   if (!BEValueV || !StartValueV)
    4722             :     return None;
    4723             : 
    4724      648645 :   const SCEV *BEValue = getSCEV(BEValueV);
    4725             : 
    4726             :   // If the value coming around the backedge is an add with the symbolic
    4727             :   // value we just inserted, possibly with casts that we can ignore under
    4728             :   // an appropriate runtime guard, then we found a simple induction variable!
    4729             :   const auto *Add = dyn_cast<SCEVAddExpr>(BEValue);
    4730             :   if (!Add)
    4731             :     return None;
    4732             : 
    4733      644643 :   // If there is a single occurrence of the symbolic value, possibly
    4734      161154 :   // casted, replace it with a recurrence.
    4735             :   unsigned FoundIndex = Add->getNumOperands();
    4736             :   Type *TruncTy = nullptr;
    4737             :   bool Signed;
    4738             :   for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
    4739             :     if ((TruncTy =
    4740             :              isSimpleCastedPHI(Add->getOperand(i), SymbolicPHI, Signed, *this)))
    4741             :       if (FoundIndex == e) {
    4742             :         FoundIndex = i;
    4743      161154 :         break;
    4744             :       }
    4745        1055 : 
    4746        1055 :   if (FoundIndex == Add->getNumOperands())
    4747             :     return None;
    4748             : 
    4749         445 :   // Create an add with everything but the specified operand.
    4750             :   SmallVector<const SCEV *, 8> Ops;
    4751        1023 :   for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
    4752             :     if (i != FoundIndex)
    4753        6075 :       Ops.push_back(Add->getOperand(i));
    4754             :   const SCEV *Accum = getAddExpr(Ops);
    4755        6075 : 
    4756        5768 :   // The runtime checks will not be valid if the step amount is
    4757             :   // varying inside the loop.
    4758             :   if (!isLoopInvariant(Accum, L))
    4759             :     return None;
    4760             : 
    4761             :   // *** Part2: Create the predicates
    4762        5768 : 
    4763             :   // Analysis was successful: we have a phi-with-cast pattern for which we
    4764        5766 :   // can return an AddRec expression under the following predicates:
    4765       11532 :   //
    4766             :   // P1: A Wrap predicate that guarantees that Trunc(Start) + i*Trunc(Accum)
    4767             :   //     fits within the truncated type (does not overflow) for i = 0 to n-1.
    4768             :   // P2: An Equal predicate that guarantees that
    4769         309 :   //     Start = (Ext ix (Trunc iy (Start) to ix) to iy)
    4770             :   // P3: An Equal predicate that guarantees that
    4771             :   //     Accum = (Ext ix (Trunc iy (Accum) to ix) to iy)
    4772             :   //
    4773        1025 :   // As we next prove, the above predicates guarantee that:
    4774             :   //     Start + i*Accum = (Ext ix (Trunc iy ( Start + i*Accum ) to ix) to iy)
    4775             :   //
    4776             :   //
    4777             :   // More formally, we want to prove that:
    4778             :   //     Expr(i+1) = Start + (i+1) * Accum
    4779             :   //               = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
    4780             :   //
    4781         189 :   // Given that:
    4782             :   // 1) Expr(0) = Start
    4783             :   // 2) Expr(1) = Start + Accum
    4784          93 :   //            = (Ext ix (Trunc iy (Start) to ix) to iy) + Accum :: from P2
    4785          30 :   // 3) Induction hypothesis (step i):
    4786             :   //    Expr(i) = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum
    4787             :   //
    4788             :   // Proof:
    4789             :   //  Expr(i+1) =
    4790             :   //   = Start + (i+1)*Accum
    4791          63 :   //   = (Start + i*Accum) + Accum
    4792          56 :   //   = Expr(i) + Accum
    4793             :   //   = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum + Accum
    4794             :   //                                                             :: from step i
    4795             :   //
    4796           7 :   //   = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) + Accum + Accum
    4797             :   //
    4798             :   //   = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy)
    4799             :   //     + (Ext ix (Trunc iy (Accum) to ix) to iy)
    4800             :   //     + Accum                                                     :: from P3
    4801          61 :   //
    4802          22 :   //   = (Ext ix (Trunc iy ((Start + (i-1)*Accum) + Accum) to ix) to iy)
    4803             :   //     + Accum                            :: from P1: Ext(x)+Ext(y)=>Ext(x+y)
    4804             :   //
    4805             :   //   = (Ext ix (Trunc iy (Start + i*Accum) to ix) to iy) + Accum
    4806          39 :   //   = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
    4807          21 :   //
    4808             :   // By induction, the same applies to all iterations 1<=i<n:
    4809             :   //
    4810             : 
    4811          18 :   // Create a truncated addrec for which we will add a no overflow check (P1).
    4812             :   const SCEV *StartVal = getSCEV(StartValueV);
    4813             :   const SCEV *PHISCEV =
    4814           9 :       getAddRecExpr(getTruncateExpr(StartVal, TruncTy),
    4815             :                     getTruncateExpr(Accum, TruncTy), L, SCEV::FlagAnyWrap);
    4816           9 : 
    4817             :   // PHISCEV can be either a SCEVConstant or a SCEVAddRecExpr.
    4818             :   // ex: If truncated Accum is 0 and StartVal is a constant, then PHISCEV
    4819             :   // will be constant.
    4820             :   //
    4821             :   //  If PHISCEV is a constant, then P1 degenerates into P2 or P3, so we don't
    4822             :   // add P1.
    4823             :   if (const auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV)) {
    4824             :     SCEVWrapPredicate::IncrementWrapFlags AddedFlags =
    4825             :         Signed ? SCEVWrapPredicate::IncrementNSSW
    4826             :                : SCEVWrapPredicate::IncrementNUSW;
    4827             :     const SCEVPredicate *AddRecPred = getWrapPredicate(AR, AddedFlags);
    4828             :     Predicates.push_back(AddRecPred);
    4829             :   }
    4830             : 
    4831             :   // Create the Equal Predicates P2,P3:
    4832             : 
    4833             :   // It is possible that the predicates P2 and/or P3 are computable at
    4834             :   // compile time due to StartVal and/or Accum being constants.
    4835             :   // If either one is, then we can check that now and escape if either P2
    4836             :   // or P3 is false.
    4837             : 
    4838             :   // Construct the extended SCEV: (Ext ix (Trunc iy (Expr) to ix) to iy)
    4839             :   // for each of StartVal and Accum
    4840             :   auto getExtendedExpr = [&](const SCEV *Expr,
    4841             :                              bool CreateSignExtend) -> const SCEV * {
    4842         116 :     assert(isLoopInvariant(Expr, L) && "Expr is expected to be invariant");
    4843             :     const SCEV *TruncatedExpr = getTruncateExpr(Expr, TruncTy);
    4844             :     const SCEV *ExtendedExpr =
    4845             :         CreateSignExtend ? getSignExtendExpr(TruncatedExpr, Expr->getType())
    4846             :                          : getZeroExtendExpr(TruncatedExpr, Expr->getType());
    4847             :     return ExtendedExpr;
    4848             :   };
    4849             : 
    4850             :   // Given:
    4851             :   //  ExtendedExpr = (Ext ix (Trunc iy (Expr) to ix) to iy
    4852             :   //               = getExtendedExpr(Expr)
    4853             :   // Determine whether the predicate P: Expr == ExtendedExpr
    4854         116 :   // is known to be false at compile time
    4855             :   auto PredIsKnownFalse = [&](const SCEV *Expr,
    4856             :                               const SCEV *ExtendedExpr) -> bool {
    4857          96 :     return Expr != ExtendedExpr &&
    4858          96 :            isKnownPredicate(ICmpInst::ICMP_NE, Expr, ExtendedExpr);
    4859          96 :   };
    4860             : 
    4861             :   const SCEV *StartExtended = getExtendedExpr(StartVal, Signed);
    4862             :   if (PredIsKnownFalse(StartVal, StartExtended)) {
    4863             :     LLVM_DEBUG(dbgs() << "P2 is compile-time false\n";);
    4864          96 :     return None;
    4865             :   }
    4866             : 
    4867          23 :   // The Step is always Signed (because the overflow checks are either
    4868          12 :   // NSSW or NUSW)
    4869          19 :   const SCEV *AccumExtended = getExtendedExpr(Accum, /*CreateSignExtend=*/true);
    4870             :   if (PredIsKnownFalse(Accum, AccumExtended)) {
    4871          19 :     LLVM_DEBUG(dbgs() << "P3 is compile-time false\n";);
    4872          19 :     return None;
    4873             :   }
    4874          19 : 
    4875          19 :   auto AppendPredicate = [&](const SCEV *Expr,
    4876             :                              const SCEV *ExtendedExpr) -> void {
    4877             :     if (Expr != ExtendedExpr &&
    4878        1932 :         !isKnownPredicate(ICmpInst::ICMP_EQ, Expr, ExtendedExpr)) {
    4879        3864 :       const SCEVPredicate *Pred = getEqualPredicate(Expr, ExtendedExpr);
    4880             :       LLVM_DEBUG(dbgs() << "Added Predicate: " << *Pred);
    4881        1093 :       Predicates.push_back(Pred);
    4882         995 :     }
    4883         135 :   };
    4884             : 
    4885             :   AppendPredicate(StartVal, StartExtended);
    4886             :   AppendPredicate(Accum, AccumExtended);
    4887             : 
    4888             :   // *** Part3: Predicates are ready. Now go ahead and create the new addrec in
    4889             :   // which the casts had been folded away. The caller can rewrite SymbolicPHI
    4890             :   // into NewAR if it will also add the runtime overflow checks specified in
    4891             :   // Predicates.
    4892             :   auto *NewAR = getAddRecExpr(StartVal, Accum, L, SCEV::FlagAnyWrap);
    4893             : 
    4894             :   std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> PredRewrite =
    4895             :       std::make_pair(NewAR, Predicates);
    4896             :   // Remember the result of the analysis for this SCEV at this locayyytion.
    4897             :   PredicatedSCEVRewrites[{SymbolicPHI, L}] = PredRewrite;
    4898             :   return PredRewrite;
    4899             : }
    4900             : 
    4901             : Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
    4902             : ScalarEvolution::createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI) {
    4903             :   auto *PN = cast<PHINode>(SymbolicPHI->getValue());
    4904             :   const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
    4905             :   if (!L)
    4906             :     return None;
    4907             : 
    4908             :   // Check to see if we already analyzed this PHI.
    4909             :   auto I = PredicatedSCEVRewrites.find({SymbolicPHI, L});
    4910             :   if (I != PredicatedSCEVRewrites.end()) {
    4911             :     std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> Rewrite =
    4912             :         I->second;
    4913             :     // Analysis was done before and failed to create an AddRec:
    4914             :     if (Rewrite.first == SymbolicPHI)
    4915             :       return None;
    4916             :     // Analysis was done before and succeeded to create an AddRec under
    4917             :     // a predicate:
    4918             :     assert(isa<SCEVAddRecExpr>(Rewrite.first) && "Expected an AddRec");
    4919             :     assert(!(Rewrite.second).empty() && "Expected to find Predicates");
    4920             :     return Rewrite;
    4921             :   }
    4922             : 
    4923             :   Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
    4924             :     Rewrite = createAddRecFromPHIWithCastsImpl(SymbolicPHI);
    4925             : 
    4926             :   // Record in the cache that the analysis failed
    4927             :   if (!Rewrite) {
    4928             :     SmallVector<const SCEVPredicate *, 3> Predicates;
    4929             :     PredicatedSCEVRewrites[{SymbolicPHI, L}] = {SymbolicPHI, Predicates};
    4930             :     return None;
    4931             :   }
    4932             : 
    4933             :   return Rewrite;
    4934             : }
    4935             : 
    4936             : // FIXME: This utility is currently required because the Rewriter currently
    4937             : // does not rewrite this expression:
    4938             : // {0, +, (sext ix (trunc iy to ix) to iy)}
    4939             : // into {0, +, %step},
    4940             : // even when the following Equal predicate exists:
    4941         330 : // "%step == (sext ix (trunc iy to ix) to iy)".
    4942             : bool PredicatedScalarEvolution::areAddRecsEqualWithPreds(
    4943             :     const SCEVAddRecExpr *AR1, const SCEVAddRecExpr *AR2) const {
    4944             :   if (AR1 == AR2)
    4945             :     return true;
    4946             : 
    4947             :   auto areExprsEqual = [&](const SCEV *Expr1, const SCEV *Expr2) -> bool {
    4948         330 :     if (Expr1 != Expr2 && !Preds.implies(SE.getEqualPredicate(Expr1, Expr2)) &&
    4949             :         !Preds.implies(SE.getEqualPredicate(Expr2, Expr1)))
    4950             :       return false;
    4951             :     return true;
    4952             :   };
    4953             : 
    4954             :   if (!areExprsEqual(AR1->getStart(), AR2->getStart()) ||
    4955         990 :       !areExprsEqual(AR1->getStepRecurrence(SE), AR2->getStepRecurrence(SE)))
    4956             :     return false;
    4957         661 :   return true;
    4958         330 : }
    4959             : 
    4960           0 : /// A helper function for createAddRecFromPHI to handle simple cases.
    4961             : ///
    4962             : /// This function tries to find an AddRec expression for the simplest (yet most
    4963             : /// common) cases: PN = PHI(Start, OP(Self, LoopInvariant)).
    4964         331 : /// If it fails, createAddRecFromPHI will use a more general, but slow,
    4965             : /// technique for finding the AddRec expression.
    4966           1 : const SCEV *ScalarEvolution::createSimpleAffineAddRec(PHINode *PN,
    4967             :                                                       Value *BEValueV,
    4968             :                                                       Value *StartValueV) {
    4969             :   const Loop *L = LI.getLoopFor(PN->getParent());
    4970             :   assert(L && L->getHeader() == PN->getParent());
    4971         330 :   assert(BEValueV && StartValueV);
    4972             : 
    4973             :   auto BO = MatchBinaryOp(BEValueV, DT);
    4974         329 :   if (!BO)
    4975             :     return nullptr;
    4976             : 
    4977             :   if (BO->Opcode != Instruction::Add)
    4978             :     return nullptr;
    4979             : 
    4980             :   const SCEV *Accum = nullptr;
    4981             :   if (BO->LHS == PN && L->isLoopInvariant(BO->RHS))
    4982             :     Accum = getSCEV(BO->RHS);
    4983             :   else if (BO->RHS == PN && L->isLoopInvariant(BO->LHS))
    4984             :     Accum = getSCEV(BO->LHS);
    4985          56 : 
    4986          56 :   if (!Accum)
    4987             :     return nullptr;
    4988         153 : 
    4989         116 :   SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
    4990         232 :   if (BO->IsNUW)
    4991             :     Flags = setFlags(Flags, SCEV::FlagNUW);
    4992             :   if (BO->IsNSW)
    4993             :     Flags = setFlags(Flags, SCEV::FlagNSW);
    4994             : 
    4995             :   const SCEV *StartVal = getSCEV(StartValueV);
    4996          56 :   const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
    4997             : 
    4998             :   ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
    4999             : 
    5000             :   // We can add Flags to the post-inc expression only if we
    5001          57 :   // know that it is *undefined behavior* for BEValueV to
    5002          38 :   // overflow.
    5003          38 :   if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
    5004          19 :     if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
    5005             :       (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
    5006             : 
    5007             :   return PHISCEV;
    5008          19 : }
    5009             : 
    5010             : const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
    5011             :   const Loop *L = LI.getLoopFor(PN->getParent());
    5012             :   if (!L || L->getHeader() != PN->getParent())
    5013             :     return nullptr;
    5014             : 
    5015             :   // The loop may have multiple entrances or multiple exits; we can analyze
    5016             :   // this phi as an addrec if it has a unique entry value and a unique
    5017             :   // backedge value.
    5018             :   Value *BEValueV = nullptr, *StartValueV = nullptr;
    5019             :   for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
    5020             :     Value *V = PN->getIncomingValue(i);
    5021             :     if (L->contains(PN->getIncomingBlock(i))) {
    5022             :       if (!BEValueV) {
    5023             :         BEValueV = V;
    5024             :       } else if (BEValueV != V) {
    5025             :         BEValueV = nullptr;
    5026             :         break;
    5027             :       }
    5028             :     } else if (!StartValueV) {
    5029             :       StartValueV = V;
    5030             :     } else if (StartValueV != V) {
    5031             :       StartValueV = nullptr;
    5032             :       break;
    5033             :     }
    5034             :   }
    5035             :   if (!BEValueV || !StartValueV)
    5036             :     return nullptr;
    5037             : 
    5038             :   assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
    5039             :          "PHI node already processed?");
    5040             : 
    5041             :   // First, try to find AddRec expression without creating a fictituos symbolic
    5042             :   // value for PN.
    5043             :   if (auto *S = createSimpleAffineAddRec(PN, BEValueV, StartValueV))
    5044             :     return S;
    5045             : 
    5046             :   // Handle PHI node value symbolically.
    5047             :   const SCEV *SymbolicName = getUnknown(PN);
    5048             :   ValueExprMap.insert({SCEVCallbackVH(PN, this), SymbolicName});
    5049             : 
    5050             :   // Using this symbolic name for the PHI, analyze the value coming around
    5051             :   // the back-edge.
    5052             :   const SCEV *BEValue = getSCEV(BEValueV);
    5053             : 
    5054             :   // NOTE: If BEValue is loop invariant, we know that the PHI node just
    5055             :   // has a special value for the first iteration of the loop.
    5056             : 
    5057             :   // If the value coming around the backedge is an add with the symbolic
    5058             :   // value we just inserted, then we found a simple induction variable!
    5059             :   if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
    5060             :     // If there is a single occurrence of the symbolic value, replace it
    5061             :     // with a recurrence.
    5062          18 :     unsigned FoundIndex = Add->getNumOperands();
    5063             :     for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
    5064          18 :       if (Add->getOperand(i) == SymbolicName)
    5065             :         if (FoundIndex == e) {
    5066             :           FoundIndex = i;
    5067             :           break;
    5068             :         }
    5069             : 
    5070             :     if (FoundIndex != Add->getNumOperands()) {
    5071             :       // Create an add with everything but the specified operand.
    5072             :       SmallVector<const SCEV *, 8> Ops;
    5073             :       for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
    5074             :         if (i != FoundIndex)
    5075          16 :           Ops.push_back(SCEVBackedgeConditionFolder::rewrite(Add->getOperand(i),
    5076             :                                                              L, *this));
    5077          16 :       const SCEV *Accum = getAddExpr(Ops);
    5078          16 : 
    5079             :       // This is not a valid addrec if the step amount is varying each
    5080             :       // loop iteration, but is not itself an addrec in this loop.
    5081             :       if (isLoopInvariant(Accum, L) ||
    5082             :           (isa<SCEVAddRecExpr>(Accum) &&
    5083             :            cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
    5084             :         SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
    5085             : 
    5086             :         if (auto BO = MatchBinaryOp(BEValueV, DT)) {
    5087             :           if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
    5088             :             if (BO->IsNUW)
    5089             :               Flags = setFlags(Flags, SCEV::FlagNUW);
    5090             :             if (BO->IsNSW)
    5091             :               Flags = setFlags(Flags, SCEV::FlagNSW);
    5092             :           }
    5093             :         } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
    5094             :           // If the increment is an inbounds GEP, then we know the address
    5095             :           // space cannot be wrapped around. We cannot make any guarantee
    5096             :           // about signed or unsigned overflow because pointers are
    5097             :           // unsigned but we may have a negative index from the base
    5098          18 :           // pointer. We can guarantee that no unsigned wrap occurs if the
    5099             :           // indices form a positive value.
    5100             :           if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
    5101             :             Flags = setFlags(Flags, SCEV::FlagNW);
    5102             : 
    5103             :             const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
    5104             :             if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
    5105             :               Flags = setFlags(Flags, SCEV::FlagNUW);
    5106             :           }
    5107          53 : 
    5108          18 :           // We cannot transfer nuw and nsw flags from subtraction
    5109             :           // operations -- sub nuw X, Y is not the same as add nuw X, -Y
    5110             :           // for instance.
    5111          18 :         }
    5112             : 
    5113             :         const SCEV *StartVal = getSCEV(StartValueV);
    5114             :         const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
    5115             : 
    5116             :         // Okay, for the entire analysis of this edge we assumed the PHI
    5117             :         // to be symbolic.  We now need to go back and purge all of the
    5118             :         // entries for the scalars that use the symbolic expression.
    5119          17 :         forgetSymbolicName(PN, SymbolicName);
    5120             :         ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
    5121             : 
    5122             :         // We can add Flags to the post-inc expression only if we
    5123             :         // know that it is *undefined behavior* for BEValueV to
    5124             :         // overflow.
    5125             :         if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
    5126             :           if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
    5127             :             (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
    5128             : 
    5129             :         return PHISCEV;
    5130             :       }
    5131             :     }
    5132             :   } else {
    5133          13 :     // Otherwise, this could be a loop like this:
    5134             :     //     i = 0;  for (j = 1; ..; ++j) { ....  i = j; }
    5135          13 :     // In this case, j = {1,+,1}  and BEValue is j.
    5136          13 :     // Because the other in-value of i (0) fits the evolution of BEValue
    5137             :     // i really is an addrec evolution.
    5138             :     //
    5139             :     // We can generalize this saying that i is the shifted value of BEValue
    5140             :     // by one iteration:
    5141             :     //   PHI(f(0), f({1,+,1})) --> f({0,+,1})
    5142          13 :     const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
    5143             :     const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this, false);
    5144             :     if (Shifted != getCouldNotCompute() &&
    5145             :         Start != getCouldNotCompute()) {
    5146             :       const SCEV *StartVal = getSCEV(StartValueV);
    5147          26 :       if (Start == StartVal) {
    5148             :         // Okay, for the entire analysis of this edge we assumed the PHI
    5149             :         // to be symbolic.  We now need to go back and purge all of the
    5150             :         // entries for the scalars that use the symbolic expression.
    5151             :         forgetSymbolicName(PN, SymbolicName);
    5152        1602 :         ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
    5153             :         return Shifted;
    5154        1602 :       }
    5155        1602 :     }
    5156             :   }
    5157             : 
    5158             :   // Remove the temporary PHI node SCEV that has been inserted while intending
    5159        1256 :   // to create an AddRecExpr for this PHI node. We can not keep this temporary
    5160         628 :   // as it will prevent later (possibly simpler) SCEV expressions to be added
    5161             :   // to the ValueExprMap.
    5162             :   eraseValueFromMap(PN);
    5163             : 
    5164         298 :   return nullptr;
    5165             : }
    5166             : 
    5167             : // Checks if the SCEV S is available at BB.  S is considered available at BB
    5168             : // if S can be materialized at BB without introducing a fault.
    5169             : static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
    5170             :                                BasicBlock *BB) {
    5171             :   struct CheckAvailable {
    5172             :     bool TraversalDone = false;
    5173             :     bool Available = true;
    5174         330 : 
    5175             :     const Loop *L = nullptr;  // The loop BB is in (can be nullptr)
    5176             :     BasicBlock *BB = nullptr;
    5177         330 :     DominatorTree &DT;
    5178             : 
    5179         317 :     CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
    5180             :       : L(L), BB(BB), DT(DT) {}
    5181             : 
    5182             :     bool setUnavailable() {
    5183             :       TraversalDone = true;
    5184             :       Available = false;
    5185             :       return false;
    5186             :     }
    5187             : 
    5188             :     bool follow(const SCEV *S) {
    5189             :       switch (S->getSCEVType()) {
    5190             :       case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
    5191             :       case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
    5192          28 :         // These expressions are available if their operand(s) is/are.
    5193             :         return true;
    5194          28 : 
    5195             :       case scAddRecExpr: {
    5196             :         // We allow add recurrences that are on the loop BB is in, or some
    5197             :         // outer loop.  This guarantees availability because the value of the
    5198             :         // add recurrence at BB is simply the "current" value of the induction
    5199             :         // variable.  We can relax this in the future; for instance an add
    5200             :         // recurrence on a sibling dominating loop is also available at BB.
    5201             :         const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
    5202          25 :         if (L && (ARLoop == L || ARLoop->contains(L)))
    5203             :           return true;
    5204          89 : 
    5205          14 :         return setUnavailable();
    5206          17 :       }
    5207             : 
    5208             :       case scUnknown: {
    5209             :         // For SCEVUnknown, we check for simple dominance.
    5210             :         const auto *SU = cast<SCEVUnknown>(S);
    5211             :         Value *V = SU->getValue();
    5212             : 
    5213             :         if (isa<Argument>(V))
    5214             :           return false;
    5215             : 
    5216       60314 :         if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
    5217             :           return false;
    5218             : 
    5219       60314 :         return setUnavailable();
    5220             :       }
    5221             : 
    5222             :       case scUDivExpr:
    5223       60314 :       case scCouldNotCompute:
    5224       60314 :         // We do not try to smart about these at all.
    5225             :         return setUnavailable();
    5226             :       }
    5227       42223 :       llvm_unreachable("switch should be fully covered!");
    5228             :     }
    5229             : 
    5230             :     bool isDone() { return TraversalDone; }
    5231       41115 :   };
    5232       38069 : 
    5233        3046 :   CheckAvailable CA(L, BB, DT);
    5234          57 :   SCEVTraversal<CheckAvailable> ST(CA);
    5235             : 
    5236       38126 :   ST.visitAll(S);
    5237        2989 :   return CA.Available;
    5238             : }
    5239             : 
    5240       38126 : // Try to match a control flow sequence that branches out at BI and merges back
    5241             : // at Merge into a "C ? LHS : RHS" select pattern.  Return true on a successful
    5242       38126 : // match.
    5243             : static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
    5244             :                           Value *&C, Value *&LHS, Value *&RHS) {
    5245       38126 :   C = BI->getCondition();
    5246       38126 : 
    5247             :   BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
    5248       76252 :   BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
    5249             : 
    5250             :   if (!LeftEdge.isSingleEdge())
    5251             :     return false;
    5252             : 
    5253             :   assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
    5254       38126 : 
    5255       16012 :   Use &LeftUse = Merge->getOperandUse(0);
    5256             :   Use &RightUse = Merge->getOperandUse(1);
    5257             : 
    5258             :   if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
    5259             :     LHS = LeftUse;
    5260       72000 :     RHS = RightUse;
    5261       72000 :     return true;
    5262       67983 :   }
    5263       11627 : 
    5264             :   if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
    5265             :     LHS = RightUse;
    5266             :     RHS = LeftUse;
    5267             :     return true;
    5268             :   }
    5269      181244 : 
    5270             :   return false;
    5271      120930 : }
    5272       60536 : 
    5273             : const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
    5274         163 :   auto IsReachable =
    5275             :       [&](BasicBlock *BB) { return DT.isReachableFromEntry(BB); };
    5276             :   if (PN->getNumIncomingValues() == 2 && all_of(PN->blocks(), IsReachable)) {
    5277             :     const Loop *L = LI.getLoopFor(PN->getParent());
    5278       60394 : 
    5279             :     // We don't want to break LCSSA, even in a SCEV expression tree.
    5280          28 :     for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
    5281             :       if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
    5282             :         return nullptr;
    5283             : 
    5284             :     // Try to match
    5285       60373 :     //
    5286             :     //  br %cond, label %left, label %right
    5287             :     // left:
    5288             :     //  br label %merge
    5289             :     // right:
    5290             :     //  br label %merge
    5291             :     // merge:
    5292             :     //  V = phi [ %x, %left ], [ %y, %right ]
    5293       60314 :     //
    5294             :     // as "select %cond, %x, %y"
    5295             : 
    5296             :     BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
    5297       22188 :     assert(IDom && "At least the entry block should dominate PN");
    5298       66564 : 
    5299             :     auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
    5300             :     Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
    5301             : 
    5302       22188 :     if (BI && BI->isConditional() &&
    5303             :         BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
    5304             :         IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
    5305             :         IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
    5306             :       return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
    5307             :   }
    5308             : 
    5309             :   return nullptr;
    5310             : }
    5311             : 
    5312       14276 : const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
    5313       30633 :   if (const SCEV *S = createAddRecFromPHI(PN))
    5314       58272 :     return S;
    5315             : 
    5316             :   if (const SCEV *S = createNodeFromSelectLikePHI(PN))
    5317             :     return S;
    5318             : 
    5319             :   // If the PHI has a single incoming value, follow that value, unless the
    5320       14276 :   // PHI's incoming blocks are in a different loop, in which case doing so
    5321             :   // risks breaking LCSSA form. Instcombine would normally zap these, but
    5322             :   // it doesn't have DominatorTree information, so it may miss cases.
    5323       39090 :   if (Value *V = SimplifyInstruction(PN, {getDataLayout(), &TLI, &DT, &AC}))
    5324       26311 :     if (LI.replacementPreservesLCSSAForm(PN, V))
    5325       27064 :       return getSCEV(V);
    5326             : 
    5327       12779 :   // If it's not a loop phi, we can't handle it yet.
    5328             :   return getUnknown(PN);
    5329             : }
    5330             : 
    5331       12779 : const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
    5332          81 :                                                       Value *Cond,
    5333          81 :                                                       Value *TrueVal,
    5334             :                                                       Value *FalseVal) {
    5335             :   // Handle "constant" branch or select. This can occur for instance when a
    5336       11868 :   // loop pass transforms an inner loop and moves on to process the outer loop.
    5337        2102 :   if (auto *CI = dyn_cast<ConstantInt>(Cond))
    5338          58 :     return getSCEV(CI->isOne() ? TrueVal : FalseVal);
    5339             : 
    5340          58 :   // Try to match some simple smax or umax patterns.
    5341             :   auto *ICI = dyn_cast<ICmpInst>(Cond);
    5342             :   if (!ICI)
    5343             :     return getUnknown(I);
    5344             : 
    5345             :   Value *LHS = ICI->getOperand(0);
    5346             :   Value *RHS = ICI->getOperand(1);
    5347             : 
    5348             :   switch (ICI->getPredicate()) {
    5349             :   case ICmpInst::ICMP_SLT:
    5350       17630 :   case ICmpInst::ICMP_SLE:
    5351             :     std::swap(LHS, RHS);
    5352             :     LLVM_FALLTHROUGH;
    5353        8184 :   case ICmpInst::ICMP_SGT:
    5354        8184 :   case ICmpInst::ICMP_SGE:
    5355             :     // a >s b ? a+x : b+x  ->  smax(a, b)+x
    5356             :     // a >s b ? b+x : a+x  ->  smin(a, b)+x
    5357             :     if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
    5358             :       const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
    5359             :       const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
    5360             :       const SCEV *LA = getSCEV(TrueVal);
    5361             :       const SCEV *RA = getSCEV(FalseVal);
    5362             :       const SCEV *LDiff = getMinusSCEV(LA, LS);
    5363       11868 :       const SCEV *RDiff = getMinusSCEV(RA, RS);
    5364       11868 :       if (LDiff == RDiff)
    5365             :         return getAddExpr(getSMaxExpr(LS, RS), LDiff);
    5366             :       LDiff = getMinusSCEV(LA, RS);
    5367             :       RDiff = getMinusSCEV(RA, LS);
    5368             :       if (LDiff == RDiff)
    5369       11868 :         return getAddExpr(getSMinExpr(LS, RS), LDiff);
    5370       35604 :     }
    5371             :     break;
    5372             :   case ICmpInst::ICMP_ULT:
    5373             :   case ICmpInst::ICMP_ULE:
    5374             :     std::swap(LHS, RHS);
    5375             :     LLVM_FALLTHROUGH;
    5376       11868 :   case ICmpInst::ICMP_UGT:
    5377        3530 :   case ICmpInst::ICMP_UGE:
    5378             :     // a >u b ? a+x : b+x  ->  umax(a, b)+x
    5379             :     // a >u b ? b+x : a+x  ->  umin(a, b)+x
    5380             :     if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
    5381             :       const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
    5382             :       const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
    5383             :       const SCEV *LA = getSCEV(TrueVal);
    5384             :       const SCEV *RA = getSCEV(FalseVal);
    5385             :       const SCEV *LDiff = getMinusSCEV(LA, LS);
    5386             :       const SCEV *RDiff = getMinusSCEV(RA, RS);
    5387             :       if (LDiff == RDiff)
    5388             :         return getAddExpr(getUMaxExpr(LS, RS), LDiff);
    5389             :       LDiff = getMinusSCEV(LA, RS);
    5390             :       RDiff = getMinusSCEV(RA, LS);
    5391             :       if (LDiff == RDiff)
    5392        7912 :         return getAddExpr(getUMinExpr(LS, RS), LDiff);
    5393        7912 :     }
    5394        9127 :     break;
    5395        1215 :   case ICmpInst::ICMP_NE:
    5396        1215 :     // n != 0 ? n+x : 1+x  ->  umax(n, 1)+x
    5397        1215 :     if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
    5398             :         isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
    5399             :       const SCEV *One = getOne(I->getType());
    5400             :       const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
    5401         969 :       const SCEV *LA = getSCEV(TrueVal);
    5402        1938 :       const SCEV *RA = getSCEV(FalseVal);
    5403         969 :       const SCEV *LDiff = getMinusSCEV(LA, LS);
    5404             :       const SCEV *RDiff = getMinusSCEV(RA, One);
    5405             :       if (LDiff == RDiff)
    5406             :         return getAddExpr(getUMaxExpr(One, LS), LDiff);
    5407             :     }
    5408             :     break;
    5409             :   case ICmpInst::ICMP_EQ:
    5410             :     // n == 0 ? 1+x : n+x  ->  umax(n, 1)+x
    5411             :     if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
    5412        9351 :         isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
    5413             :       const SCEV *One = getOne(I->getType());
    5414        9351 :       const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
    5415             :       const SCEV *LA = getSCEV(TrueVal);
    5416             :       const SCEV *RA = getSCEV(FalseVal);
    5417             :       const SCEV *LDiff = getMinusSCEV(LA, One);
    5418             :       const SCEV *RDiff = getMinusSCEV(RA, LS);
    5419       12111 :       if (LDiff == RDiff)
    5420             :         return getAddExpr(getUMaxExpr(One, LS), LDiff);
    5421             :     }
    5422             :     break;
    5423             :   default:
    5424             :     break;
    5425             :   }
    5426             : 
    5427             :   return getUnknown(I);
    5428             : }
    5429             : 
    5430       12111 : /// Expand GEP instructions into add and multiply operations. This allows them
    5431             : /// to be analyzed by regular SCEV code.
    5432           0 : const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
    5433        4782 :   // Don't attempt to analyze GEPs over unsized objects.
    5434        4782 :   if (!GEP->getSourceElementType()->isSized())
    5435           0 :     return getUnknown(GEP);
    5436             : 
    5437             :   SmallVector<const SCEV *, 4> IndexExprs;
    5438       22396 :   for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
    5439       44792 :     IndexExprs.push_back(getSCEV(*Index));
    5440             :   return getGEPExpr(GEP, IndexExprs);
    5441             : }
    5442             : 
    5443             : uint32_t ScalarEvolution::GetMinTrailingZerosImpl(const SCEV *S) {
    5444             :   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
    5445             :     return C->getAPInt().countTrailingZeros();
    5446             : 
    5447             :   if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
    5448             :     return std::min(GetMinTrailingZeros(T->getOperand()),
    5449             :                     (uint32_t)getTypeSizeInBits(T->getType()));
    5450             : 
    5451         583 :   if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
    5452         677 :     uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
    5453             :     return OpRes == getTypeSizeInBits(E->getOperand()->getType())
    5454             :                ? getTypeSizeInBits(E->getType())
    5455         400 :                : OpRes;
    5456             :   }
    5457             : 
    5458             :   if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
    5459             :     uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
    5460             :     return OpRes == getTypeSizeInBits(E->getOperand()->getType())
    5461             :                ? getTypeSizeInBits(E->getType())
    5462             :                : OpRes;
    5463        9600 :   }
    5464             : 
    5465             :   if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
    5466        8726 :     // The result is the min of all operands results.
    5467             :     uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
    5468             :     for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
    5469        3165 :       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
    5470             :     return MinOpRes;
    5471             :   }
    5472        1217 : 
    5473             :   if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
    5474             :     // The result is the sum of all operands results.
    5475        1217 :     uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
    5476             :     uint32_t BitWidth = getTypeSizeInBits(M->getType());
    5477           0 :     for (unsigned i = 1, e = M->getNumOperands();
    5478             :          SumOpRes != BitWidth && i != e; ++i)
    5479             :       SumOpRes =
    5480           0 :           std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), BitWidth);
    5481             :     return SumOpRes;
    5482             :   }
    5483             : 
    5484       12111 :   if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
    5485             :     // The result is the min of all operands results.
    5486       12111 :     uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
    5487       12111 :     for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
    5488             :       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
    5489             :     return MinOpRes;
    5490             :   }
    5491             : 
    5492             :   if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
    5493        7584 :     // The result is the min of all operands results.
    5494             :     uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
    5495        7584 :     for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
    5496             :       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
    5497        7584 :     return MinOpRes;
    5498             :   }
    5499             : 
    5500        7584 :   if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
    5501             :     // The result is the min of all operands results.
    5502             :     uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
    5503             :     for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
    5504             :       MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
    5505        7584 :     return MinOpRes;
    5506             :   }
    5507             : 
    5508        7584 :   if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
    5509        3304 :     // For a SCEVUnknown, ask ValueTracking.
    5510        3304 :     KnownBits Known = computeKnownBits(U->getValue(), getDataLayout(), 0, &AC, nullptr, &DT);
    5511        3304 :     return Known.countMinTrailingZeros();
    5512             :   }
    5513             : 
    5514        4280 :   // SCEVUDivExpr
    5515        3896 :   return 0;
    5516        3896 : }
    5517        3896 : 
    5518             : uint32_t ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
    5519             :   auto I = MinTrailingZerosCache.find(S);
    5520             :   if (I != MinTrailingZerosCache.end())
    5521             :     return I->second;
    5522             : 
    5523       21037 :   uint32_t Result = GetMinTrailingZerosImpl(S);
    5524             :   auto InsertPair = MinTrailingZerosCache.insert({S, Result});
    5525           0 :   assert(InsertPair.second && "Should insert a new key");
    5526       38253 :   return InsertPair.first->second;
    5527       17215 : }
    5528             : 
    5529             : /// Helper method to assign a range to V from metadata present in the IR.
    5530       36780 : static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
    5531       58216 :   if (Instruction *I = dyn_cast<Instruction>(V))
    5532       11967 :     if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
    5533             :       return getConstantRangeFromMetadata(*MD);
    5534             : 
    5535             :   return None;
    5536             : }
    5537             : 
    5538             : /// Determine the range for a particular SCEV.  If SignHint is
    5539             : /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
    5540             : /// with a "cleaner" unsigned (resp. signed) representation.
    5541             : const ConstantRange &
    5542             : ScalarEvolution::getRangeRef(const SCEV *S,
    5543             :                              ScalarEvolution::RangeSignHint SignHint) {
    5544             :   DenseMap<const SCEV *, ConstantRange> &Cache =
    5545             :       SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
    5546       15344 :                                                        : SignedRanges;
    5547             : 
    5548             :   // See if we've computed this range already.
    5549             :   DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
    5550        7672 :   if (I != Cache.end())
    5551             :     return I->second;
    5552       15168 : 
    5553       14784 :   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
    5554       19783 :     return setRange(C, SignHint, ConstantRange(C->getAPInt()));
    5555        4911 : 
    5556        2424 :   unsigned BitWidth = getTypeSizeInBits(S->getType());
    5557             :   ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
    5558             : 
    5559             :   // If the value has known zeros, the maximum value will have those known zeros
    5560             :   // as well.
    5561             :   uint32_t TZ = GetMinTrailingZeros(S);
    5562       72000 :   if (TZ != 0) {
    5563       72000 :     if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
    5564             :       ConservativeResult =
    5565             :           ConstantRange(APInt::getMinValue(BitWidth),
    5566       21037 :                         APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
    5567             :     else
    5568             :       ConservativeResult = ConstantRange(
    5569             :           APInt::getSignedMinValue(BitWidth),
    5570             :           APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
    5571             :   }
    5572             : 
    5573       18613 :   if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
    5574        1579 :     ConstantRange X = getRangeRef(Add->getOperand(0), SignHint);
    5575         154 :     for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
    5576             :       X = X.add(getRangeRef(Add->getOperand(i), SignHint));
    5577             :     return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
    5578       18459 :   }
    5579             : 
    5580             :   if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
    5581        5989 :     ConstantRange X = getRangeRef(Mul->getOperand(0), SignHint);
    5582             :     for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
    5583             :       X = X.multiply(getRangeRef(Mul->getOperand(i), SignHint));
    5584             :     return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
    5585             :   }
    5586             : 
    5587             :   if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
    5588         171 :     ConstantRange X = getRangeRef(SMax->getOperand(0), SignHint);
    5589             :     for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
    5590             :       X = X.smax(getRangeRef(SMax->getOperand(i), SignHint));
    5591             :     return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
    5592             :   }
    5593         467 : 
    5594             :   if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
    5595             :     ConstantRange X = getRangeRef(UMax->getOperand(0), SignHint);
    5596             :     for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
    5597             :       X = X.umax(getRangeRef(UMax->getOperand(i), SignHint));
    5598        5431 :     return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
    5599             :   }
    5600             : 
    5601             :   if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
    5602             :     ConstantRange X = getRangeRef(UDiv->getLHS(), SignHint);
    5603        1053 :     ConstantRange Y = getRangeRef(UDiv->getRHS(), SignHint);
    5604             :     return setRange(UDiv, SignHint,
    5605             :                     ConservativeResult.intersectWith(X.udiv(Y)));
    5606             :   }
    5607        1053 : 
    5608        1022 :   if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
    5609        1022 :     ConstantRange X = getRangeRef(ZExt->getOperand(), SignHint);
    5610        1022 :     return setRange(ZExt, SignHint,
    5611        1022 :                     ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
    5612        1022 :   }
    5613        1022 : 
    5614        1022 :   if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
    5615         422 :     ConstantRange X = getRangeRef(SExt->getOperand(), SignHint);
    5616         600 :     return setRange(SExt, SignHint,
    5617         600 :                     ConservativeResult.intersectWith(X.signExtend(BitWidth)));
    5618         600 :   }
    5619         181 : 
    5620             :   if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
    5621             :     ConstantRange X = getRangeRef(Trunc->getOperand(), SignHint);
    5622             :     return setRange(Trunc, SignHint,
    5623             :                     ConservativeResult.intersectWith(X.truncate(BitWidth)));
    5624             :   }
    5625             : 
    5626        1595 :   if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
    5627             :     // If there's no unsigned wrap, the value will never be less than its
    5628             :     // initial value.
    5629             :     if (AddRec->hasNoUnsignedWrap())
    5630        1595 :       if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
    5631        1549 :         if (!C->getValue()->isZero())
    5632        1549 :           ConservativeResult = ConservativeResult.intersectWith(
    5633        1549 :               ConstantRange(C->getAPInt(), APInt(BitWidth, 0)));
    5634        1549 : 
    5635        1549 :     // If there's no signed wrap, and all the operands have the same sign or
    5636        1549 :     // zero, the value won't ever change sign.
    5637        1549 :     if (AddRec->hasNoSignedWrap()) {
    5638         262 :       bool AllNonNeg = true;
    5639        1287 :       bool AllNonPos = true;
    5640        1287 :       for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
    5641        1287 :         if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
    5642         250 :         if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
    5643             :       }
    5644             :       if (AllNonNeg)
    5645          52 :         ConservativeResult = ConservativeResult.intersectWith(
    5646             :           ConstantRange(APInt(BitWidth, 0),
    5647         102 :                         APInt::getSignedMinValue(BitWidth)));
    5648          98 :       else if (AllNonPos)
    5649          46 :         ConservativeResult = ConservativeResult.intersectWith(
    5650          46 :           ConstantRange(APInt::getSignedMinValue(BitWidth),
    5651          46 :                         APInt(BitWidth, 1)));
    5652          46 :     }
    5653          46 : 
    5654          46 :     // TODO: non-affine addrec
    5655          46 :     if (AddRec->isAffine()) {
    5656           1 :       const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
    5657             :       if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
    5658             :           getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
    5659        2731 :         auto RangeFromAffine = getRangeForAffineAR(
    5660             :             AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
    5661        5169 :             BitWidth);
    5662        4848 :         if (!RangeFromAffine.isFullSet())
    5663        1748 :           ConservativeResult =
    5664        1748 :               ConservativeResult.intersectWith(RangeFromAffine);
    5665        1748 : 
    5666        1748 :         auto RangeFromFactoring = getRangeViaFactoring(
    5667        1748 :             AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
    5668        1748 :             BitWidth);
    5669        1748 :         if (!RangeFromFactoring.isFullSet())
    5670          54 :           ConservativeResult =
    5671             :               ConservativeResult.intersectWith(RangeFromFactoring);
    5672             :       }
    5673             :     }
    5674             : 
    5675             :     return setRange(AddRec, SignHint, std::move(ConservativeResult));
    5676             :   }
    5677        4261 : 
    5678             :   if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
    5679             :     // Check if the IR explicitly contains !range metadata.
    5680             :     Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
    5681             :     if (MDRange.hasValue())
    5682      191606 :       ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
    5683             : 
    5684      191606 :     // Split here to avoid paying the compile-time cost of calling both
    5685           0 :     // computeKnownBits and ComputeNumSignBits.  This restriction can be lifted
    5686             :     // if needed.
    5687             :     const DataLayout &DL = getDataLayout();
    5688      533704 :     if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
    5689      342098 :       // For a SCEVUnknown, ask ValueTracking.
    5690      191606 :       KnownBits Known = computeKnownBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
    5691             :       if (Known.One != ~Known.Zero + 1)
    5692             :         ConservativeResult =
    5693      602449 :             ConservativeResult.intersectWith(ConstantRange(Known.One,
    5694             :                                                            ~Known.Zero + 1));
    5695      108988 :     } else {
    5696             :       assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
    5697             :              "generalize as needed!");
    5698        3860 :       unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
    5699        7720 :       if (NS > 1)
    5700             :         ConservativeResult = ConservativeResult.intersectWith(
    5701             :             ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
    5702       20330 :                           APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
    5703       20330 :     }
    5704           0 : 
    5705       20330 :     // A range of Phi is a subset of union of all ranges of its input.
    5706             :     if (const PHINode *Phi = dyn_cast<PHINode>(U->getValue())) {
    5707             :       // Make sure that we do not run over cycled Phis.
    5708             :       if (PendingPhiRanges.insert(Phi).second) {
    5709       10987 :         ConstantRange RangeFromOps(BitWidth, /*isFullSet=*/false);
    5710       10987 :         for (auto &Op : Phi->operands()) {
    5711           0 :           auto OpRange = getRangeRef(getSCEV(Op), SignHint);
    5712       10987 :           RangeFromOps = RangeFromOps.unionWith(OpRange);
    5713             :           // No point to continue if we already have a full set.
    5714             :           if (RangeFromOps.isFullSet())
    5715             :             break;
    5716             :         }
    5717      206220 :         ConservativeResult = ConservativeResult.intersectWith(RangeFromOps);
    5718      164445 :         bool Erased = PendingPhiRanges.erase(Phi);
    5719      162862 :         assert(Erased && "Failed to erase Phi properly?");
    5720             :         (void) Erased;
    5721             :       }
    5722             :     }
    5723             : 
    5724             :     return setRange(U, SignHint, std::move(ConservativeResult));
    5725      117434 :   }
    5726       58717 : 
    5727       58717 :   return setRange(S, SignHint, std::move(ConservativeResult));
    5728      125732 : }
    5729       67015 : 
    5730      136866 : // Given a StartRange, Step and MaxBECount for an expression compute a range of
    5731             : // values that the expression can take. Initially, the expression has a value
    5732             : // from StartRange and then is changed by Step up to MaxBECount times. Signed
    5733             : // argument defines if we treat Step as signed or unsigned.
    5734             : static ConstantRange getRangeForAffineARHelper(APInt Step,
    5735             :                                                const ConstantRange &StartRange,
    5736      278782 :                                                const APInt &MaxBECount,
    5737      219406 :                                                unsigned BitWidth, bool Signed) {
    5738      220023 :   // If either Step or MaxBECount is 0, then the expression won't change, and we
    5739             :   // just need to return the initial range.
    5740             :   if (Step == 0 || MaxBECount == 0)
    5741             :     return StartRange;
    5742             : 
    5743             :   // If we don't know anything about the initial value (i.e. StartRange is
    5744        4622 :   // FullRange), then we don't know anything about the final range either.
    5745        3443 :   // Return FullRange.
    5746        3388 :   if (StartRange.isFullSet())
    5747             :     return ConstantRange(BitWidth, /* isFullSet = */ true);
    5748             : 
    5749             :   // If Step is signed and negative, then we use its absolute value, but we also
    5750             :   // note that we're moving in the opposite direction.
    5751             :   bool Descending = Signed && Step.isNegative();
    5752        1906 : 
    5753        1028 :   if (Signed)
    5754         225 :     // This is correct even for INT_SMIN. Let's look at i8 to illustrate this:
    5755             :     // abs(INT_SMIN) = abs(-128) = abs(0x80) = -0x80 = 0x80 = 128.
    5756             :     // This equations hold true due to the well-defined wrap-around behavior of
    5757             :     // APInt.
    5758      144185 :     Step = Step.abs();
    5759             : 
    5760      288370 :   // Check if Offset is more than full span of BitWidth. If it is, the
    5761             :   // expression is guaranteed to overflow.
    5762             :   if (APInt::getMaxValue(StartRange.getBitWidth()).udiv(Step).ult(MaxBECount))
    5763             :     return ConstantRange(BitWidth, /* isFullSet = */ true);
    5764             : 
    5765             :   // Offset is by how much the expression can change. Checks above guarantee no
    5766             :   // overflow here.
    5767             :   APInt Offset = Step * MaxBECount;
    5768     1507251 : 
    5769     1507251 :   // Minimum value of the final range will match the minimal value of StartRange
    5770     1507251 :   // if the expression is increasing and will be decreased by Offset otherwise.
    5771      904802 :   // Maximum value of the final range will match the maximal value of StartRange
    5772             :   // if the expression is decreasing and will be increased by Offset otherwise.
    5773      602449 :   APInt StartLower = StartRange.getLower();
    5774      602449 :   APInt StartUpper = StartRange.getUpper() - 1;
    5775             :   APInt MovedBoundary = Descending ? (StartLower - std::move(Offset))
    5776      602449 :                                    : (StartUpper + std::move(Offset));
    5777             : 
    5778             :   // It's possible that the new minimum/maximum value will fall into the initial
    5779             :   // range (due to wrap around). This means that the expression can take any
    5780      288023 :   // value in this bitwidth, and we have to return full range.
    5781             :   if (StartRange.contains(MovedBoundary))
    5782       69218 :     return ConstantRange(BitWidth, /* isFullSet = */ true);
    5783       12270 : 
    5784             :   APInt NewLower =
    5785             :       Descending ? std::move(MovedBoundary) : std::move(StartLower);
    5786             :   APInt NewUpper =
    5787             :       Descending ? std::move(StartUpper) : std::move(MovedBoundary);
    5788             :   NewUpper += 1;
    5789             : 
    5790             :   // If we end up with full range, return a proper full range.
    5791             :   if (NewLower == NewUpper)
    5792    11108401 :     return ConstantRange(BitWidth, /* isFullSet = */ true);
    5793             : 
    5794    11108401 :   // No overflow detected, return [StartLower, StartUpper + Offset + 1) range.
    5795             :   return ConstantRange(std::move(NewLower), std::move(NewUpper));
    5796             : }
    5797             : 
    5798             : ConstantRange ScalarEvolution::getRangeForAffineAR(const SCEV *Start,
    5799    11108401 :                                                    const SCEV *Step,
    5800    11108401 :                                                    const SCEV *MaxBECount,
    5801     9645488 :                                                    unsigned BitWidth) {
    5802             :   assert(!isa<SCEVCouldNotCompute>(MaxBECount) &&
    5803             :          getTypeSizeInBits(MaxBECount->getType()) <= BitWidth &&
    5804      534337 :          "Precondition!");
    5805             : 
    5806      928576 :   MaxBECount = getNoopOrZeroExtend(MaxBECount, Start->getType());
    5807     1857152 :   APInt MaxBECountValue = getUnsignedRangeMax(MaxBECount);
    5808             : 
    5809             :   // First, consider step signed.
    5810             :   ConstantRange StartSRange = getSignedRange(Start);
    5811      928576 :   ConstantRange StepSRange = getSignedRange(Step);
    5812      928576 : 
    5813      253778 :   // If Step can be both positive and negative, we need to find ranges for the
    5814             :   // maximum absolute step values in both directions and union them.
    5815      244488 :   ConstantRange SR =
    5816      372662 :       getRangeForAffineARHelper(StepSRange.getSignedMin(), StartSRange,
    5817             :                                 MaxBECountValue, BitWidth, /* Signed = */ true);
    5818      263068 :   SR = SR.unionWith(getRangeForAffineARHelper(StepSRange.getSignedMax(),
    5819      263068 :                                               StartSRange, MaxBECountValue,
    5820      401114 :                                               BitWidth, /* Signed = */ true));
    5821             : 
    5822             :   // Next, consider step unsigned.
    5823             :   ConstantRange UR = getRangeForAffineARHelper(
    5824      349994 :       getUnsignedRangeMax(Step), getUnsignedRange(Start),
    5825      933355 :       MaxBECountValue, BitWidth, /* Signed = */ false);
    5826     1516716 : 
    5827      174997 :   // Finally, intersect signed and unsigned ranges.
    5828             :   return SR.intersectWith(UR);
    5829             : }
    5830             : 
    5831      222598 : ConstantRange ScalarEvolution::getRangeViaFactoring(const SCEV *Start,
    5832      243761 :                                                     const SCEV *Step,
    5833      264924 :                                                     const SCEV *MaxBECount,
    5834      111299 :                                                     unsigned BitWidth) {
    5835             :   //    RangeOf({C?A:B,+,C?P:Q}) == RangeOf(C?{A,+,P}:{B,+,Q})
    5836             :   // == RangeOf({A,+,P}) union RangeOf({B,+,Q})
    5837             : 
    5838        9244 :   struct SelectPattern {
    5839       10088 :     Value *Condition = nullptr;
    5840       10932 :     APInt TrueValue;
    5841        4622 :     APInt FalseValue;
    5842             : 
    5843             :     explicit SelectPattern(ScalarEvolution &SE, unsigned BitWidth,
    5844             :                            const SCEV *S) {
    5845        3812 :       Optional<unsigned> CastOp;
    5846        3868 :       APInt Offset(BitWidth, 0);
    5847        3924 : 
    5848        1906 :       assert(SE.getTypeSizeInBits(S->getType()) == BitWidth &&
    5849             :              "Should be!");
    5850             : 
    5851             :       // Peel off a constant offset:
    5852       38108 :       if (auto *SA = dyn_cast<SCEVAddExpr>(S)) {
    5853       19054 :         // In the future we could consider being smarter here and handle
    5854             :         // {Start+Step,+,Step} too.
    5855       19054 :         if (SA->getNumOperands() != 2 || !isa<SCEVConstant>(SA->getOperand(0)))
    5856             :           return;
    5857             : 
    5858             :         Offset = cast<SCEVConstant>(SA->getOperand(0))->getAPInt();
    5859       39816 :         S = SA->getOperand(1);
    5860             :       }
    5861       39816 : 
    5862             :       // Peel off a cast operation
    5863             :       if (auto *SCast = dyn_cast<SCEVCastExpr>(S)) {
    5864             :         CastOp = SCast->getSCEVType();
    5865       21489 :         S = SCast->getOperand();
    5866             :       }
    5867       21489 : 
    5868             :       using namespace llvm::PatternMatch;
    5869             : 
    5870             :       auto *SU = dyn_cast<SCEVUnknown>(S);
    5871        7359 :       const APInt *TrueVal, *FalseVal;
    5872             :       if (!SU ||
    5873        7359 :           !match(SU->getValue(), m_Select(m_Value(Condition), m_APInt(TrueVal),
    5874             :                                           m_APInt(FalseVal)))) {
    5875             :         Condition = nullptr;
    5876             :         return;
    5877             :       }
    5878             : 
    5879      260011 :       TrueValue = *TrueVal;
    5880       82735 :       FalseValue = *FalseVal;
    5881      135626 : 
    5882       40432 :       // Re-apply the cast we peeled off earlier
    5883       60648 :       if (CastOp.hasValue())
    5884             :         switch (*CastOp) {
    5885             :         default:
    5886             :           llvm_unreachable("Unknown SCEV cast type!");
    5887      260011 : 
    5888             :         case scTruncate:
    5889             :           TrueValue = TrueValue.trunc(BitWidth);
    5890      220815 :           FalseValue = FalseValue.trunc(BitWidth);
    5891      294420 :           break;
    5892      294420 :         case scZeroExtend:
    5893             :           TrueValue = TrueValue.zext(BitWidth);
    5894       73605 :           FalseValue = FalseValue.zext(BitWidth);
    5895      116852 :           break;
    5896      116852 :         case scSignExtend:
    5897      175278 :           TrueValue = TrueValue.sext(BitWidth);
    5898       15179 :           FalseValue = FalseValue.sext(BitWidth);
    5899         810 :           break;
    5900         810 :         }
    5901         810 : 
    5902             :       // Re-apply the constant offset we peeled off earlier
    5903             :       TrueValue += Offset;
    5904             :       FalseValue += Offset;
    5905      260011 :     }
    5906      258061 : 
    5907      434593 :     bool isRecognized() { return Condition != nullptr; }
    5908      176532 :   };
    5909             : 
    5910             :   SelectPattern StartPattern(*this, BitWidth, Start);
    5911      345422 :   if (!StartPattern.isRecognized())
    5912      172711 :     return ConstantRange(BitWidth, /* isFullSet = */ true);
    5913             : 
    5914      114932 :   SelectPattern StepPattern(*this, BitWidth, Step);
    5915             :   if (!StepPattern.isRecognized())
    5916             :     return ConstantRange(BitWidth, /* isFullSet = */ true);
    5917             : 
    5918      345422 :   if (StartPattern.Condition != StepPattern.Condition) {
    5919      172711 :     // We don't handle this case today; but we could, by considering four
    5920             :     // possibilities below instead of two. I'm not sure if there are cases where
    5921          62 :     // that will help over what getRange already does, though.
    5922             :     return ConstantRange(BitWidth, /* isFullSet = */ true);
    5923             :   }
    5924             : 
    5925      260011 :   // NB! Calling ScalarEvolution::getConstant is fine, but we should not try to
    5926             :   // construct arbitrary general SCEV expressions here.  This function is called
    5927             :   // from deep in the call stack, and calling getSCEV (on a sext instruction,
    5928      288023 :   // say) can end up caching a suboptimal value.
    5929             : 
    5930      288023 :   // FIXME: without the explicit `this` receiver below, MSVC errors out with
    5931      288023 :   // C2352 and C2512 (otherwise it isn't needed).
    5932       12270 : 
    5933             :   const SCEV *TrueStart = this->getConstant(StartPattern.TrueValue);
    5934             :   const SCEV *TrueStep = this->getConstant(StepPattern.TrueValue);
    5935             :   const SCEV *FalseStart = this->getConstant(StartPattern.FalseValue);
    5936             :   const SCEV *FalseStep = this->getConstant(StepPattern.FalseValue);
    5937      288023 : 
    5938      288023 :   ConstantRange TrueRange =
    5939             :       this->getRangeForAffineAR(TrueStart, TrueStep, MaxBECount, BitWidth);
    5940      412584 :   ConstantRange FalseRange =
    5941      137528 :       this->getRangeForAffineAR(FalseStart, FalseStep, MaxBECount, BitWidth);
    5942             : 
    5943      105244 :   return TrueRange.unionWith(FalseRange);
    5944      105244 : }
    5945             : 
    5946             : SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
    5947             :   if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
    5948      300990 :   const BinaryOperator *BinOp = cast<BinaryOperator>(V);
    5949      150495 : 
    5950       18724 :   // Return early if there are no flags to propagate to the SCEV.
    5951       18728 :   SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
    5952       28090 :   if (BinOp->hasNoUnsignedWrap())
    5953             :     Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
    5954             :   if (BinOp->hasNoSignedWrap())
    5955             :     Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
    5956             :   if (Flags == SCEV::FlagAnyWrap)
    5957             :     return SCEV::FlagAnyWrap;
    5958       47673 : 
    5959       64046 :   return isSCEVExprNeverPoison(BinOp) ? Flags : SCEV::FlagAnyWrap;
    5960       74775 : }
    5961       50040 : 
    5962       39311 : bool ScalarEvolution::isSCEVExprNeverPoison(const Instruction *I) {
    5963             :   // Here we check that I is in the header of the innermost loop containing I,
    5964       39311 :   // since we only deal with instructions in the loop header. The actual loop we
    5965             :   // need to check later will come from an add recurrence, but getting that
    5966             :   // requires computing the SCEV of the operands, which can be expensive. This
    5967       32023 :   // check we can do cheaply to rule out some cases early.
    5968             :   Loop *InnermostContainingLoop = LI.getLoopFor(I->getParent());
    5969             :   if (InnermostContainingLoop == nullptr ||
    5970             :       InnermostContainingLoop->getHeader() != I->getParent())
    5971             :     return false;
    5972             : 
    5973             :   // Only proceed if we can prove that I does not yield poison.
    5974      288023 :   if (!programUndefinedIfFullPoison(I))
    5975             :     return false;
    5976             : 
    5977           0 :   // At this point we know that if I is executed, then it does not wrap
    5978             :   // according to at least one of NSW or NUW. If I is not executed, then we do
    5979             :   // not know if the calculation that I represents would wrap. Multiple
    5980             :   // instructions can map to the same SCEV. If we apply NSW or NUW from I to
    5981             :   // the SCEV, we must guarantee no wrapping for that SCEV also when it is
    5982             :   // derived from other instructions that map to the same SCEV. We cannot make
    5983             :   // that guarantee for cases where I is not executed. So we need to find the
    5984      518505 :   // loop that I is considered in relation to and prove that I is executed for
    5985             :   // every iteration of that loop. That implies that the value that I
    5986             :   // calculates does not wrap anywhere in the loop, so then we can apply the
    5987             :   // flags to the SCEV.
    5988             :   //
    5989             :   // We check isLoopInvariant to disambiguate in case we are adding recurrences
    5990      518505 :   // from different loops, so that we know which loop to prove that I is
    5991       12208 :   // executed in.
    5992             :   for (unsigned OpIndex = 0; OpIndex < I->getNumOperands(); ++OpIndex) {
    5993             :     // I could be an extractvalue from a call to an overflow intrinsic.
    5994             :     // TODO: We can do better here in some cases.
    5995             :     if (!isSCEVable(I->getOperand(OpIndex)->getType()))
    5996      506297 :       return false;
    5997      106016 :     const SCEV *Op = getSCEV(I->getOperand(OpIndex));
    5998             :     if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
    5999             :       bool AllOtherOpsLoopInvariant = true;
    6000             :       for (unsigned OtherOpIndex = 0; OtherOpIndex < I->getNumOperands();
    6001      409127 :            ++OtherOpIndex) {
    6002             :         if (OtherOpIndex != OpIndex) {
    6003      400281 :           const SCEV *OtherOp = getSCEV(I->getOperand(OtherOpIndex));
    6004             :           if (!isLoopInvariant(OtherOp, AddRec->getLoop())) {
    6005             :             AllOtherOpsLoopInvariant = false;
    6006             :             break;
    6007             :           }
    6008      534212 :         }
    6009             :       }
    6010             :       if (AllOtherOpsLoopInvariant &&
    6011             :           isGuaranteedToExecuteForEveryIteration(I, AddRec->getLoop()))
    6012      813831 :         return true;
    6013       65694 :     }
    6014             :   }
    6015             :   return false;
    6016             : }
    6017      334587 : 
    6018             : bool ScalarEvolution::isAddRecNeverPoison(const Instruction *I, const Loop *L) {
    6019             :   // If we know that \c I can never be poison period, then that's enough.
    6020             :   if (isSCEVExprNeverPoison(I))
    6021             :     return true;
    6022             : 
    6023             :   // For an add recurrence specifically, we assume that infinite loops without
    6024      334587 :   // side effects are undefined behavior, and then reason as follows:
    6025             :   //
    6026      334587 :   // If the add recurrence is poison in any iteration, it is poison on all
    6027             :   // future iterations (since incrementing poison yields poison). If the result
    6028             :   // of the add recurrence is fed into the loop latch condition and the loop
    6029             :   // does not contain any throws or exiting blocks other than the latch, we now
    6030             :   // have the ability to "choose" whether the backedge is taken or not (by
    6031      334587 :   // choosing a sufficiently evil value for the poison feeding into the branch)
    6032       16124 :   // for every iteration including and after the one in which \p I first became
    6033             :   // poison.  There are two possibilities (let's call the iteration in which \p
    6034             :   // I first became poison as K):
    6035      318463 :   //
    6036             :   //  1. In the set of iterations including and after K, the loop body executes
    6037      318463 :   //     no side effects.  In this case executing the backege an infinte number
    6038      318463 :   //     of times will yield undefined behavior.
    6039             :   //
    6040             :   //  2. In the set of iterations including and after K, the loop body executes
    6041      318463 :   //     at least one side effect.  In this case, that specific instance of side
    6042       13002 :   //     effect is control dependent on poison, which also yields undefined
    6043             :   //     behavior.
    6044             : 
    6045      610922 :   auto *ExitingBB = L->getExitingBlock();
    6046             :   auto *LatchBB = L->getLoopLatch();
    6047             :   if (!ExitingBB || !LatchBB || ExitingBB != LatchBB)
    6048      172835 :     return false;
    6049             : 
    6050             :   SmallPtrSet<const Instruction *, 16> Pushed;
    6051             :   SmallVector<const Instruction *, 8> PoisonStack;
    6052             : 
    6053             :   // We start by assuming \c I, the post-inc add recurrence, is poison.  Only
    6054             :   // things that are known to be fully poison under that assumption go on the
    6055             :   // PoisonStack.
    6056      172835 :   Pushed.insert(I);
    6057             :   PoisonStack.push_back(I);
    6058             : 
    6059             :   bool LatchControlDependentOnPoison = false;
    6060      172835 :   while (!PoisonStack.empty() && !LatchControlDependentOnPoison) {
    6061      172835 :     const Instruction *Poison = PoisonStack.pop_back_val();
    6062             : 
    6063             :     for (auto *PoisonUser : Poison->users()) {
    6064             :       if (propagatesFullPoison(cast<Instruction>(PoisonUser))) {
    6065             :         if (Pushed.insert(cast<Instruction>(PoisonUser)).second)
    6066      172835 :           PoisonStack.push_back(cast<Instruction>(PoisonUser));
    6067      345670 :       } else if (auto *BI = dyn_cast<BranchInst>(PoisonUser)) {
    6068      350231 :         assert(BI->isConditional() && "Only possibility!");
    6069             :         if (BI->getParent() == LatchBB) {
    6070      172835 :           LatchControlDependentOnPoison = true;
    6071             :           break;
    6072             :         }
    6073             :       }
    6074      172835 :     }
    6075      345670 :   }
    6076             : 
    6077             :   return LatchControlDependentOnPoison && loopHasNoAbnormalExits(L);
    6078      172835 : }
    6079             : 
    6080             : ScalarEvolution::LoopProperties
    6081      172711 : ScalarEvolution::getLoopProperties(const Loop *L) {
    6082             :   using LoopProperties = ScalarEvolution::LoopProperties;
    6083             : 
    6084             :   auto Itr = LoopPropertiesCache.find(L);
    6085             :   if (Itr == LoopPropertiesCache.end()) {
    6086             :     auto HasSideEffects = [](Instruction *I) {
    6087             :       if (auto *SI = dyn_cast<StoreInst>(I))
    6088             :         return !SI->isSimple();
    6089             : 
    6090             :       return I->mayHaveSideEffects();
    6091             :     };
    6092             : 
    6093           0 :     LoopProperties LP = {/* HasNoAbnormalExits */ true,
    6094           0 :                          /*HasNoSideEffects*/ true};
    6095             : 
    6096             :     for (auto *BB : L->getBlocks())
    6097             :       for (auto &I : *BB) {
    6098             :         if (!isGuaranteedToTransferExecutionToSuccessor(&I))
    6099             :           LP.HasNoAbnormalExits = false;
    6100             :         if (HasSideEffects(&I))
    6101             :           LP.HasNoSideEffects = false;
    6102             :         if (!LP.HasNoAbnormalExits && !LP.HasNoSideEffects)
    6103             :           break; // We're already as pessimistic as we can get.
    6104             :       }
    6105           0 : 
    6106           0 :     auto InsertPair = LoopPropertiesCache.insert({L, LP});
    6107             :     assert(InsertPair.second && "We just checked!");
    6108           0 :     Itr = InsertPair.first;
    6109           0 :   }
    6110             : 
    6111             :   return Itr->second;
    6112             : }
    6113             : 
    6114             : const SCEV *ScalarEvolution::createSCEV(Value *V) {
    6115           0 :   if (!isSCEVable(V->getType()))
    6116             :     return getUnknown(V);
    6117             : 
    6118             :   if (Instruction *I = dyn_cast<Instruction>(V)) {
    6119             :     // Don't attempt to analyze instructions in blocks that aren't
    6120             :     // reachable. Such instructions don't matter, and they aren't required
    6121             :     // to obey basic rules for definitions dominating uses which this
    6122           0 :     // analysis depends on.
    6123           0 :     if (!DT.isReachableFromEntry(I->getParent()))
    6124             :       return getUnknown(V);
    6125           0 :   } else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
    6126           0 :     return getConstant(CI);
    6127             :   else if (isa<ConstantPointerNull>(V))
    6128             :     return getZero(V->getType());
    6129           0 :   else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
    6130           0 :     return GA->isInterposable() ? getUnknown(V) : getSCEV(GA->getAliasee());
    6131             :   else if (!isa<ConstantExpr>(V))
    6132             :     return getUnknown(V);
    6133           0 : 
    6134           0 :   Operator *U = cast<Operator>(V);
    6135           0 :   if (auto BO = MatchBinaryOp(U, DT)) {
    6136           0 :     switch (BO->Opcode) {
    6137             :     case Instruction::Add: {
    6138           0 :       // The simple thing to do would be to just call getSCEV on both operands
    6139           0 :       // and call getAddExpr with the result. However if we're looking at a
    6140           0 :       // bunch of things all added together, this can be quite inefficient,
    6141           0 :       // because it leads to N-1 getAddExpr calls for N ultimate operands.
    6142           0 :       // Instead, gather up all the operands and make a single getAddExpr call.
    6143           0 :       // LLVM IR canonical form means we need only traverse the left operands.
    6144           0 :       SmallVector<const SCEV *, 4> AddOps;
    6145           0 :       do {
    6146           0 :         if (BO->Op) {
    6147           0 :           if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
    6148           0 :             AddOps.push_back(OpSCEV);
    6149           0 :             break;
    6150             :           }
    6151             : 
    6152             :           // If a NUW or NSW flag can be applied to the SCEV for this
    6153           0 :           // addition, then compute the SCEV for this addition by itself
    6154           0 :           // with a separate call to getAddExpr. We need to do that
    6155             :           // instead of pushing the operands of the addition onto AddOps,
    6156             :           // since the flags are only known to apply to this particular
    6157           0 :           // addition - they may not apply to other additions that can be
    6158             :           // formed with operands from AddOps.
    6159             :           const SCEV *RHS = getSCEV(BO->RHS);
    6160      345422 :           SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
    6161      172711 :           if (Flags != SCEV::FlagAnyWrap) {
    6162      172644 :             const SCEV *LHS = getSCEV(BO->LHS);
    6163             :             if (BO->Opcode == Instruction::Sub)
    6164         134 :               AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
    6165          67 :             else
    6166           5 :               AddOps.push_back(getAddExpr(LHS, RHS, Flags));
    6167             :             break;
    6168          62 :           }
    6169             :         }
    6170             : 
    6171             :         if (BO->Opcode == Instruction::Sub)
    6172           0 :           AddOps.push_back(getNegativeSCEV(getSCEV(BO->RHS)));
    6173             :         else
    6174             :           AddOps.push_back(getSCEV(BO->RHS));
    6175             : 
    6176             :         auto NewBO = MatchBinaryOp(BO->LHS, DT);
    6177             :         if (!NewBO || (NewBO->Opcode != Instruction::Add &&
    6178             :                        NewBO->Opcode != Instruction::Sub)) {
    6179             :           AddOps.push_back(getSCEV(BO->LHS));
    6180             :           break;
    6181             :         }
    6182             :         BO = NewBO;
    6183          62 :       } while (true);
    6184          62 : 
    6185          62 :       return getAddExpr(AddOps);
    6186          62 :     }
    6187             : 
    6188             :     case Instruction::Mul: {
    6189         124 :       SmallVector<const SCEV *, 4> MulOps;
    6190             :       do {
    6191         124 :         if (BO->Op) {
    6192             :           if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
    6193          62 :             MulOps.push_back(OpSCEV);
    6194             :             break;
    6195             :           }
    6196       95879 : 
    6197       95879 :           SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
    6198             :           if (Flags != SCEV::FlagAnyWrap) {
    6199             :             MulOps.push_back(
    6200             :                 getMulExpr(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags));
    6201             :             break;
    6202       95876 :           }
    6203             :         }
    6204       95876 : 
    6205             :         MulOps.push_back(getSCEV(BO->RHS));
    6206       95876 :         auto NewBO = MatchBinaryOp(BO->LHS, DT);
    6207             :         if (!NewBO || NewBO->Opcode != Instruction::Mul) {
    6208             :           MulOps.push_back(getSCEV(BO->LHS));
    6209       49070 :           break;
    6210             :         }
    6211             :         BO = NewBO;
    6212       98983 :       } while (true);
    6213             : 
    6214             :       return getMulExpr(MulOps);
    6215             :     }
    6216             :     case Instruction::UDiv:
    6217             :       return getUDivExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
    6218       98983 :     case Instruction::URem:
    6219       94818 :       return getURemExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
    6220       94818 :     case Instruction::Sub: {
    6221       44252 :       SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
    6222             :       if (BO->Op)
    6223             :         Flags = getNoWrapFlagsFromUB(BO->Op);
    6224       54731 :       return getMinusSCEV(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags);
    6225             :     }
    6226             :     case Instruction::And:
    6227             :       // For an expression like x&255 that merely masks off the high bits,
    6228             :       // use zext(trunc(x)) as the SCEV expression.
    6229             :       if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
    6230             :         if (CI->isZero())
    6231             :           return getSCEV(BO->RHS);
    6232             :         if (CI->isMinusOne())
    6233             :           return getSCEV(BO->LHS);
    6234             :         const APInt &A = CI->getValue();
    6235             : 
    6236             :         // Instcombine's ShrinkDemandedConstant may strip bits out of
    6237             :         // constants, obscuring what would otherwise be a low-bits mask.
    6238             :         // Use computeKnownBits to compute what ShrinkDemandedConstant
    6239             :         // knew about to reconstruct a low-bits mask value.
    6240             :         unsigned LZ = A.countLeadingZeros();
    6241             :         unsigned TZ = A.countTrailingZeros();
    6242       21317 :         unsigned BitWidth = A.getBitWidth();
    6243             :         KnownBits Known(BitWidth);
    6244             :         computeKnownBits(BO->LHS, Known, getDataLayout(),
    6245       32928 :                          0, &AC, nullptr, &DT);
    6246             : 
    6247       16463 :         APInt EffectiveMask =
    6248             :             APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
    6249             :         if ((LZ != 0 || TZ != 0) && !((~A & ~Known.Zero) & EffectiveMask)) {
    6250       21316 :           const SCEV *MulCount = getConstant(APInt::getOneBitSet(BitWidth, TZ));
    6251             :           const SCEV *LHS = getSCEV(BO->LHS);
    6252       14383 :           const SCEV *ShiftedLHS = nullptr;
    6253        7228 :           if (auto *LHSMul = dyn_cast<SCEVMulExpr>(LHS)) {
    6254        7228 :             if (auto *OpC = dyn_cast<SCEVConstant>(LHSMul->getOperand(0))) {
    6255             :               // For an expression like (x * 8) & 8, simplify the multiply.
    6256             :               unsigned MulZeros = OpC->getAPInt().countTrailingZeros();
    6257             :               unsigned GCD = std::min(MulZeros, TZ);
    6258             :               APInt DivAmt = APInt::getOneBitSet(BitWidth, TZ - GCD);
    6259             :               SmallVector<const SCEV*, 4> MulOps;
    6260       14161 :               MulOps.push_back(getConstant(OpC->getAPInt().lshr(GCD)));
    6261        6933 :               MulOps.append(LHSMul->op_begin() + 1, LHSMul->op_end());
    6262             :               auto *NewMul = getMulExpr(MulOps, LHSMul->getNoWrapFlags());
    6263             :               ShiftedLHS = getUDivExpr(NewMul, getConstant(DivAmt));
    6264             :             }
    6265             :           }
    6266             :           if (!ShiftedLHS)
    6267             :             ShiftedLHS = getUDivExpr(LHS, MulCount);
    6268       49913 :           return getMulExpr(
    6269             :               getZeroExtendExpr(
    6270       49913 :                   getTruncateExpr(ShiftedLHS,
    6271             :                       IntegerType::get(getContext(), BitWidth - LZ - TZ)),
    6272             :                   BO->LHS->getType()),
    6273             :               MulCount);
    6274             :         }
    6275             :       }
    6276             :       break;
    6277             : 
    6278             :     case Instruction::Or:
    6279             :       // If the RHS of the Or is a constant, we may have something like:
    6280             :       // X*4+1 which got turned into X*4|1.  Handle this as an Add so loop
    6281             :       // optimizations will transparently handle this case.
    6282             :       //
    6283             :       // In order for this transformation to be safe, the LHS must be of the
    6284             :       // form X*(2^n) and the Or constant must be less than 2^n.
    6285             :       if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
    6286             :         const SCEV *LHS = getSCEV(BO->LHS);
    6287             :         const APInt &CIVal = CI->getValue();
    6288             :         if (GetMinTrailingZeros(LHS) >=
    6289             :             (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
    6290             :           // Build a plain add SCEV.
    6291             :           const SCEV *S = getAddExpr(LHS, getSCEV(CI));
    6292             :           // If the LHS of the add was an addrec and it has no-wrap flags,
    6293             :           // transfer the no-wrap flags, since an or won't introduce a wrap.
    6294             :           if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
    6295       48405 :             const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
    6296       48405 :             const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
    6297       48405 :                 OldAR->getNoWrapFlags());
    6298             :           }
    6299             :           return S;
    6300             :         }
    6301             :       }
    6302             :       break;
    6303             : 
    6304             :     case Instruction::Xor:
    6305             :       if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
    6306       31644 :         // If the RHS of xor is -1, then this is a not operation.
    6307       31644 :         if (CI->isMinusOne())
    6308             :           return getNotSCEV(getSCEV(BO->LHS));
    6309             : 
    6310       89144 :         // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
    6311             :         // This is a variant of the check for xor with -1, and it handles
    6312             :         // the case where instcombine has trimmed non-demanded bits out
    6313      119327 :         // of an xor with -1.
    6314       84423 :         if (auto *LBO = dyn_cast<BinaryOperator>(BO->LHS))
    6315       25887 :           if (ConstantInt *LCI = dyn_cast<ConstantInt>(LBO->getOperand(1)))
    6316       25883 :             if (LBO->getOpcode() == Instruction::And &&
    6317             :                 LCI->getValue() == CI->getValue())
    6318             :               if (const SCEVZeroExtendExpr *Z =
    6319       22669 :                       dyn_cast<SCEVZeroExtendExpr>(getSCEV(BO->LHS))) {
    6320             :                 Type *UTy = BO->LHS->getType();
    6321             :                 const SCEV *Z0 = Z->getOperand();
    6322             :                 Type *Z0Ty = Z0->getType();
    6323             :                 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
    6324             : 
    6325             :                 // If C is a low-bits mask, the zero extend is serving to
    6326             :                 // mask off the high bits. Complement the operand and
    6327       54240 :                 // re-apply the zext.
    6328             :                 if (CI->getValue().isMask(Z0TySize))
    6329             :                   return getZeroExtendExpr(getNotSCEV(Z0), UTy);
    6330             : 
    6331       24391 :                 // If C is a single bit, it may be in the sign-bit position
    6332             :                 // before the zero-extend. In this case, represent the xor
    6333             :                 // using an add, which is equivalent, and re-apply the zext.
    6334       24391 :                 APInt Trunc = CI->getValue().trunc(Z0TySize);
    6335       24391 :                 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
    6336             :                     Trunc.isSignMask())
    6337             :                   return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
    6338             :                                            UTy);
    6339             :               }
    6340             :       }
    6341             :       break;
    6342             : 
    6343             :     case Instruction::Shl:
    6344             :       // Turn shift left of a constant amount into a multiply.
    6345             :       if (ConstantInt *SA = dyn_cast<ConstantInt>(BO->RHS)) {
    6346       39237 :         uint32_t BitWidth = cast<IntegerType>(SA->getType())->getBitWidth();
    6347      293854 : 
    6348      273480 :         // If the shift count is not less than the bitwidth, the result of
    6349             :         // the shift is undefined. Don't try to analyze it, because the
    6350      273480 :         // resolution chosen here may differ from the resolution chosen in
    6351             :         // other parts of the compiler.
    6352      273480 :         if (SA->getValue().uge(BitWidth))
    6353             :           break;
    6354             : 
    6355             :         // It is currently not resolved how to interpret NSW for left
    6356       12435 :         // shift by BitWidth - 1, so we avoid applying flags in that
    6357             :         // case. Remove this check (or this comment) once the situation
    6358       12435 :         // is resolved. See
    6359             :         // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
    6360             :         // and http://reviews.llvm.org/D8890 .
    6361       24391 :         auto Flags = SCEV::FlagAnyWrap;
    6362             :         if (BO->Op && SA->getValue().ult(BitWidth - 1))
    6363             :           Flags = getNoWrapFlagsFromUB(BO->Op);
    6364      701261 : 
    6365      701261 :         Constant *X = ConstantInt::get(
    6366           0 :             getContext(), APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
    6367             :         return getMulExpr(getSCEV(BO->LHS), getSCEV(X), Flags);
    6368             :       }
    6369             :       break;
    6370             : 
    6371             :     case Instruction::AShr: {
    6372             :       // AShr X, C, where C is a constant.
    6373      386475 :       ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS);
    6374           1 :       if (!CI)
    6375             :         break;
    6376      127730 : 
    6377      187056 :       Type *OuterTy = BO->LHS->getType();
    6378        1193 :       uint64_t BitWidth = getTypeSizeInBits(OuterTy);
    6379             :       // If the shift count is not less than the bitwidth, the result of
    6380           0 :       // the shift is undefined. Don't try to analyze it, because the
    6381      185863 :       // resolution chosen here may differ from the resolution chosen in
    6382       86986 :       // other parts of the compiler.
    6383             :       if (CI->getValue().uge(BitWidth))
    6384             :         break;
    6385      485351 : 
    6386       96232 :       if (CI->isZero())
    6387             :         return getSCEV(BO->LHS); // shift by zero --> noop
    6388             : 
    6389             :       uint64_t AShrAmt = CI->getZExtValue();
    6390             :       Type *TruncTy = IntegerType::get(getContext(), BitWidth - AShrAmt);
    6391             : 
    6392             :       Operator *L = dyn_cast<Operator>(BO->LHS);
    6393             :       if (L && L->getOpcode() == Instruction::Shl) {
    6394             :         // X = Shl A, n
    6395             :         // Y = AShr X, m
    6396       81350 :         // Both n and m are constant.
    6397       81254 : 
    6398        6329 :         const SCEV *ShlOp0SCEV = getSCEV(L->getOperand(0));
    6399        6329 :         if (L->getOperand(1) == BO->RHS)
    6400             :           // For a two-shift sext-inreg, i.e. n = m,
    6401             :           // use sext(trunc(x)) as the SCEV expression.
    6402             :           return getSignExtendExpr(
    6403             :               getTruncateExpr(ShlOp0SCEV, TruncTy), OuterTy);
    6404             : 
    6405             :         ConstantInt *ShlAmtCI = dyn_cast<ConstantInt>(L->getOperand(1));
    6406             :         if (ShlAmtCI && ShlAmtCI->getValue().ult(BitWidth)) {
    6407             :           uint64_t ShlAmt = ShlAmtCI->getZExtValue();
    6408             :           if (ShlAmt > AShrAmt) {
    6409       74925 :             // When n > m, use sext(mul(trunc(x), 2^(n-m)))) as the SCEV
    6410       74925 :             // expression. We already checked that ShlAmt < BitWidth, so
    6411       74925 :             // the multiplier, 1 << (ShlAmt - AShrAmt), fits into TruncTy as
    6412        4692 :             // ShlAmt - AShrAmt < Amt.
    6413        4692 :             APInt Mul = APInt::getOneBitSet(BitWidth - AShrAmt,
    6414           2 :                                             ShlAmt - AShrAmt);
    6415             :             return getSignExtendExpr(
    6416        4690 :                 getMulExpr(getTruncateExpr(ShlOp0SCEV, TruncTy),
    6417             :                 getConstant(Mul)), OuterTy);
    6418             :           }
    6419             :         }
    6420             :       }
    6421       70329 :       break;
    6422         346 :     }
    6423             :     }
    6424       69983 :   }
    6425             : 
    6426       70329 :   switch (U->getOpcode()) {
    6427       70329 :   case Instruction::Trunc:
    6428             :     return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
    6429       51243 : 
    6430             :   case Instruction::ZExt:
    6431             :     return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
    6432             : 
    6433             :   case Instruction::SExt:
    6434             :     if (auto BO = MatchBinaryOp(U->getOperand(0), DT)) {
    6435       62264 :       // The NSW flag of a subtract does not always survive the conversion to
    6436             :       // A + (-1)*B.  By pushing sign extension onto its operands we are much
    6437             :       // more likely to preserve NSW and allow later AddRec optimisations.
    6438             :       //
    6439             :       // NOTE: This is effectively duplicating this logic from getSignExtend:
    6440             :       //   sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
    6441       10169 :       // but by that point the NSW information has potentially been lost.
    6442       10163 :       if (BO->Opcode == Instruction::Sub && BO->IsNSW) {
    6443         407 :         Type *Ty = U->getType();
    6444         407 :         auto *V1 = getSignExtendExpr(getSCEV(BO->LHS), Ty);
    6445             :         auto *V2 = getSignExtendExpr(getSCEV(BO->RHS), Ty);
    6446             :         return getMinusSCEV(V1, V2, SCEV::FlagNSW);
    6447        9756 :       }
    6448        9756 :     }
    6449         133 :     return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
    6450         133 : 
    6451         133 :   case Instruction::BitCast:
    6452             :     // BitCasts are no-op casts so we just eliminate the cast.
    6453             :     if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
    6454             :       return getSCEV(U->getOperand(0));
    6455        9629 :     break;
    6456        9629 : 
    6457        9629 :   // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
    6458        8812 :   // lead to pointer expressions which cannot safely be expanded to GEPs,
    6459             :   // because ScalarEvolution doesn't respect the GEP aliasing rules when
    6460             :   // simplifying integer expressions.
    6461             : 
    6462             :   case Instruction::GetElementPtr:
    6463             :     return createNodeForGEP(cast<GEPOperator>(U));
    6464        9352 : 
    6465             :   case Instruction::PHI:
    6466             :     return createNodeForPHI(cast<PHINode>(U));
    6467        4934 : 
    6468             :   case Instruction::Select:
    6469         476 :     // U can also be a select constant expr, which let fall through.  Since
    6470        8810 :     // createNodeForSelect only works for a condition that is an `ICmpInst`, and
    6471             :     // constant expressions cannot have instructions as operands, we'd have
    6472        8810 :     // returned getUnknown for a select constant expressions anyway.
    6473        8777 :     if (isa<Instruction>(U))
    6474        8810 :       return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
    6475             :                                       U->getOperand(1), U->getOperand(2));
    6476             :     break;
    6477             : 
    6478             :   case Instruction::Call:
    6479        3108 :   case Instruction::Invoke:
    6480        2777 :     if (Value *RV = CallSite(U).getReturnedArgOperand())
    6481        2708 :       return getSCEV(RV);
    6482        2775 :     break;
    6483           0 :   }
    6484             : 
    6485             :   return getUnknown(V);
    6486             : }
    6487             : 
    6488             : //===----------------------------------------------------------------------===//
    6489             : //                   Iteration Count Computation Code
    6490        2775 : //
    6491        2775 : 
    6492             : static unsigned getConstantTripCount(const SCEVConstant *ExitCount) {
    6493        2844 :   if (!ExitCount)
    6494        2775 :     return 0;
    6495        2775 : 
    6496             :   ConstantInt *ExitConst = ExitCount->getValue();
    6497             : 
    6498        2775 :   // Guard against huge trip counts.
    6499       22269 :   if (ExitConst->getValue().getActiveBits() > 32)
    6500        2706 :     return 0;
    6501        2706 : 
    6502             :   // In case of integer overflow, this returns 0, which is correct.
    6503             :   return ((unsigned)ExitConst->getZExtValue()) + 1;
    6504          67 : }
    6505             : 
    6506          66 : unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L) {
    6507          66 :   if (BasicBlock *ExitingBB = L->getExitingBlock())
    6508          66 :     return getSmallConstantTripCount(L, ExitingBB);
    6509             : 
    6510          66 :   // No trip count information for multiple exits.
    6511         132 :   return 0;
    6512         132 : }
    6513          66 : 
    6514             : unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L,
    6515             :                                                     BasicBlock *ExitingBlock) {
    6516          66 :   assert(ExitingBlock && "Must pass a non-null exiting block!");
    6517        2640 :   assert(L->isLoopExiting(ExitingBlock) &&
    6518        2706 :          "Exiting block must actually branch out of the loop!");
    6519             :   const SCEVConstant *ExitCount =
    6520             :       dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
    6521        2706 :   return getConstantTripCount(ExitCount);
    6522        2706 : }
    6523             : 
    6524             : unsigned ScalarEvolution::getSmallConstantMaxTripCount(const Loop *L) {
    6525             :   const auto *MaxExitCount =
    6526             :       dyn_cast<SCEVConstant>(getMaxBackedgeTakenCount(L));
    6527             :   return getConstantTripCount(MaxExitCount);
    6528             : }
    6529             : 
    6530             : unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L) {
    6531             :   if (BasicBlock *ExitingBB = L->getExitingBlock())
    6532             :     return getSmallConstantTripMultiple(L, ExitingBB);
    6533             : 
    6534             :   // No trip multiple information for multiple exits.
    6535        1570 :   return 0;
    6536        1041 : }
    6537             : 
    6538        1041 : /// Returns the largest constant divisor of the trip count of this loop as a
    6539        1041 : /// normal unsigned value, if possible. This means that the actual trip count is
    6540             : /// always a multiple of the returned value (don't forget the trip count could
    6541        1005 : /// very well be zero as well!).
    6542             : ///
    6543             : /// Returns 1 if the trip count is unknown or not guaranteed to be the
    6544             : /// multiple of a constant (which is also the case if the trip count is simply
    6545             : /// constant, use getSmallConstantTripCount for that case), Will also return 1
    6546         680 : /// if the trip count is very large (>= 2^32).
    6547             : ///
    6548             : /// As explained in the comments for getSmallConstantTripCount, this assumes
    6549        1005 : /// that control exits the loop via ExitingBlock.
    6550             : unsigned
    6551             : ScalarEvolution::getSmallConstantTripMultiple(const Loop *L,
    6552             :                                               BasicBlock *ExitingBlock) {
    6553             :   assert(ExitingBlock && "Must pass a non-null exiting block!");
    6554             :   assert(L->isLoopExiting(ExitingBlock) &&
    6555         875 :          "Exiting block must actually branch out of the loop!");
    6556             :   const SCEV *ExitCount = getExitCount(L, ExitingBlock);
    6557         382 :   if (ExitCount == getCouldNotCompute())
    6558         338 :     return 1;
    6559             : 
    6560             :   // Get the trip count from the BE count by adding 1.
    6561             :   const SCEV *TCExpr = getAddExpr(ExitCount, getOne(ExitCount->getType()));
    6562             : 
    6563             :   const SCEVConstant *TC = dyn_cast<SCEVConstant>(TCExpr);
    6564          44 :   if (!TC)
    6565             :     // Attempt to factor more general cases. Returns the greatest power of
    6566          10 :     // two divisor. If overflow happens, the trip count expression is still
    6567             :     // divisible by the greatest power of 2 divisor returned.
    6568             :     return 1U << std::min((uint32_t)31, GetMinTrailingZeros(TCExpr));
    6569           4 : 
    6570           2 :   ConstantInt *Result = TC->getValue();
    6571           2 : 
    6572           2 :   // Guard against huge trip counts (this requires checking
    6573           2 :   // for zero to handle the case where the trip count == -1 and the
    6574             :   // addition wraps).
    6575             :   if (!Result || Result->getValue().getActiveBits() > 32 ||
    6576             :       Result->getValue().getActiveBits() == 0)
    6577             :     return 1;
    6578           2 : 
    6579           2 :   return (unsigned)Result->getZExtValue();
    6580             : }
    6581             : 
    6582             : /// Get the expression for the number of loop iterations for which this loop is
    6583             : /// guaranteed not to exit via ExitingBlock. Otherwise return
    6584           0 : /// SCEVCouldNotCompute.
    6585           0 : const SCEV *ScalarEvolution::getExitCount(const Loop *L,
    6586             :                                           BasicBlock *ExitingBlock) {
    6587           0 :   return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
    6588             : }
    6589             : 
    6590             : const SCEV *
    6591             : ScalarEvolution::getPredicatedBackedgeTakenCount(const Loop *L,
    6592             :                                                  SCEVUnionPredicate &Preds) {
    6593             :   return getPredicatedBackedgeTakenInfo(L).getExact(L, this, &Preds);
    6594             : }
    6595        2789 : 
    6596             : const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
    6597             :   return getBackedgeTakenInfo(L).getExact(L, this);
    6598             : }
    6599             : 
    6600             : /// Similar to getBackedgeTakenCount, except return the least SCEV value that is
    6601             : /// known never to be less than the actual backedge taken count.
    6602        4852 : const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
    6603             :   return getBackedgeTakenInfo(L).getMax(this);
    6604             : }
    6605             : 
    6606             : bool ScalarEvolution::isBackedgeTakenCountMaxOrZero(const Loop *L) {
    6607             :   return getBackedgeTakenInfo(L).isMaxOrZero(this);
    6608             : }
    6609             : 
    6610             : /// Push PHI nodes in the header of the given loop onto the given Worklist.
    6611             : static void
    6612        2422 : PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
    6613        2421 :   BasicBlock *Header = L->getHeader();
    6614             : 
    6615        2422 :   // Push all Loop-header PHIs onto the Worklist stack.
    6616        2422 :   for (PHINode &PN : Header->phis())
    6617        2422 :     Worklist.push_back(&PN);
    6618             : }
    6619             : 
    6620             : const ScalarEvolution::BackedgeTakenInfo &
    6621             : ScalarEvolution::getPredicatedBackedgeTakenInfo(const Loop *L) {
    6622             :   auto &BTI = getBackedgeTakenInfo(L);
    6623        1755 :   if (BTI.hasFullInfo())
    6624             :     return BTI;
    6625             : 
    6626             :   auto Pair = PredicatedBackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
    6627        1751 : 
    6628        1751 :   if (!Pair.second)
    6629             :     return Pair.first->second;
    6630             : 
    6631             :   BackedgeTakenInfo Result =
    6632             :       computeBackedgeTakenCount(L, /*AllowPredicates=*/true);
    6633        1751 : 
    6634             :   return PredicatedBackedgeTakenCounts.find(L)->second = std::move(Result);
    6635             : }
    6636        1747 : 
    6637           1 : const ScalarEvolution::BackedgeTakenInfo &
    6638             : ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
    6639             :   // Initially insert an invalid entry for this loop. If the insertion
    6640        1746 :   // succeeds, proceed to actually compute a backedge-taken count and
    6641             :   // update the value. The temporary CouldNotCompute value tells SCEV
    6642        1746 :   // code elsewhere that it shouldn't attempt to request a new
    6643        1674 :   // backedge-taken count, which could result in infinite recursion.
    6644             :   std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
    6645             :       BackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
    6646             :   if (!Pair.second)
    6647             :     return Pair.first->second;
    6648         842 : 
    6649         421 :   // computeBackedgeTakenCount may allocate memory for its result. Inserting it
    6650             :   // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
    6651             :   // must be cleared in this scope.
    6652         395 :   BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
    6653         395 : 
    6654             :   // In product build, there are no usage of statistic.
    6655             :   (void)NumTripCountsComputed;
    6656          26 :   (void)NumTripCountsNotComputed;
    6657             : #if LLVM_ENABLE_STATS || !defined(NDEBUG)
    6658          26 :   const SCEV *BEExact = Result.getExact(L, this);
    6659             :   if (BEExact != getCouldNotCompute()) {
    6660             :     assert(isLoopInvariant(BEExact, L) &&
    6661             :            isLoopInvariant(Result.getMax(this), L) &&
    6662             :            "Computed backedge-taken count isn't loop invariant for loop!");
    6663             :     ++NumTripCountsComputed;
    6664           2 :   }
    6665           2 :   else if (Result.getMax(this) == getCouldNotCompute() &&
    6666             :            isa<PHINode>(L->getHeader()->begin())) {
    6667             :     // Only count loops that have phi nodes as not being computable.
    6668             :     ++NumTripCountsNotComputed;
    6669             :   }
    6670             : #endif // LLVM_ENABLE_STATS || !defined(NDEBUG)
    6671             : 
    6672             :   // Now that we know more about the trip count for this loop, forget any
    6673             :   // existing SCEV values for PHI nodes in this loop since they are only
    6674             :   // conservative estimates made without the benefit of trip count
    6675             :   // information. This is similar to the code in forgetLoop, except that
    6676      392642 :   // it handles SCEVUnknown PHI nodes specially.
    6677        5362 :   if (Result.hasAnyInfo()) {
    6678       10724 :     SmallVector<Instruction *, 16> Worklist;
    6679             :     PushLoopPHIs(L, Worklist);
    6680        9320 : 
    6681       18640 :     SmallPtrSet<Instruction *, 8> Discovered;
    6682             :     while (!Worklist.empty()) {
    6683       11154 :       Instruction *I = Worklist.pop_back_val();
    6684       22308 : 
    6685             :       ValueExprMapType::iterator It =
    6686             :         ValueExprMap.find_as(static_cast<Value *>(I));
    6687             :       if (It != ValueExprMap.end()) {
    6688             :         const SCEV *Old = It->second;
    6689             : 
    6690             :         // SCEVUnknown for a PHI either means that it has an unrecognized
    6691             :         // structure, or it's a PHI that's in the progress of being computed
    6692         737 :         // by createNodeForPHI.  In the former case, additional loop trip
    6693          18 :         // count information isn't going to change anything. In the later
    6694          18 :         // case, createNodeForPHI will perform the necessary updates on its
    6695          18 :         // own when it gets to that point.
    6696          18 :         if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
    6697             :           eraseValueFromMap(It->first);
    6698          18 :           forgetMemoizedResults(Old);
    6699       22272 :         }
    6700             :         if (PHINode *PN = dyn_cast<PHINode>(I))
    6701       16020 :           ConstantEvolutionLoopExitValue.erase(PN);
    6702             :       }
    6703       32040 : 
    6704       15841 :       // Since we don't need to invalidate anything for correctness and we're
    6705             :       // only invalidating to make SCEV's results more precise, we get to stop
    6706             :       // early to avoid invalidating too much.  This is especially important in
    6707             :       // cases like:
    6708             :       //
    6709             :       //   %v = f(pn0, pn1) // pn0 and pn1 used through some other phi node
    6710             :       // loop0:
    6711             :       //   %pn0 = phi
    6712      191606 :       //   ...
    6713      191606 :       // loop1:
    6714             :       //   %pn1 = phi
    6715       72000 :       //   ...
    6716       72000 :       //
    6717             :       // where both loop0 and loop1's backedge taken count uses the SCEV
    6718        3567 :       // expression for %v.  If we don't have the early stop below then in cases
    6719             :       // like the above, getBackedgeTakenInfo(loop1) will clear out the trip
    6720             :       // count for loop0 and getBackedgeTakenInfo(loop0) will clear out the trip
    6721             :       // count for loop1, effectively nullifying SCEV's trip count cache.
    6722             :       for (auto *U : I->users())
    6723        3567 :         if (auto *I = dyn_cast<Instruction>(U)) {
    6724        7130 :           auto *LoopForUser = LI.getLoopFor(I->getParent());
    6725        3565 :           if (LoopForUser && L->contains(LoopForUser) &&
    6726             :               Discovered.insert(I).second)
    6727             :             Worklist.push_back(I);
    6728       11857 :         }
    6729             :     }
    6730       11857 :   }
    6731       11857 : 
    6732             :   // Re-lookup the insert position, since the call to
    6733             :   // computeBackedgeTakenCount above could result in a
    6734             :   // recusive call to getBackedgeTakenInfo (on a different
    6735       83787 :   // loop), which would invalidate the iterator computed
    6736             :   // earlier.
    6737             :   return BackedgeTakenCounts.find(L)->second = std::move(Result);
    6738             : }
    6739             : 
    6740             : void ScalarEvolution::forgetLoop(const Loop *L) {
    6741             :   // Drop any stored trip count value.
    6742       17501 :   auto RemoveLoopFromBackedgeMap =
    6743       17501 :       [](DenseMap<const Loop *, BackedgeTakenInfo> &Map, const Loop *L) {
    6744             :         auto BTCPos = Map.find(L);
    6745             :         if (BTCPos != Map.end()) {
    6746        6691 :           BTCPos->second.clear();
    6747             :           Map.erase(BTCPos);
    6748             :         }
    6749        6691 :       };
    6750             : 
    6751             :   SmallVector<const Loop *, 16> LoopWorklist(1, L);
    6752             :   SmallVector<Instruction *, 32> Worklist;
    6753        4476 :   SmallPtrSet<Instruction *, 16> Visited;
    6754             : 
    6755             :   // Iterate over all the loops and sub-loops to drop SCEV information.
    6756        2295 :   while (!LoopWorklist.empty()) {
    6757        2295 :     auto *CurrL = LoopWorklist.pop_back_val();
    6758        2230 : 
    6759             :     RemoveLoopFromBackedgeMap(BackedgeTakenCounts, CurrL);
    6760             :     RemoveLoopFromBackedgeMap(PredicatedBackedgeTakenCounts, CurrL);
    6761             : 
    6762             :     // Drop information about predicated SCEV rewrites for this loop.
    6763             :     for (auto I = PredicatedSCEVRewrites.begin();
    6764       10352 :          I != PredicatedSCEVRewrites.end();) {
    6765             :       std::pair<const SCEV *, const Loop *> Entry = I->first;
    6766             :       if (Entry.second == CurrL)
    6767             :         PredicatedSCEVRewrites.erase(I++);
    6768             :       else
    6769             :         ++I;
    6770       10352 :     }
    6771       10352 : 
    6772             :     auto LoopUsersItr = LoopUsers.find(CurrL);
    6773             :     if (LoopUsersItr != LoopUsers.end()) {
    6774        7149 :       for (auto *S : LoopUsersItr->second)
    6775             :         forgetMemoizedResults(S);
    6776        7149 :       LoopUsers.erase(LoopUsersItr);
    6777        7149 :     }
    6778             : 
    6779             :     // Drop information about expressions based on loop-header PHIs.
    6780         264 :     PushLoopPHIs(CurrL, Worklist);
    6781         264 : 
    6782         254 :     while (!Worklist.empty()) {
    6783             :       Instruction *I = Worklist.pop_back_val();
    6784             :       if (!Visited.insert(I).second)
    6785             :         continue;
    6786             : 
    6787             :       ValueExprMapType::iterator It =
    6788             :           ValueExprMap.find_as(static_cast<Value *>(I));
    6789             :       if (It != ValueExprMap.end()) {
    6790             :         eraseValueFromMap(It->first);
    6791             :         forgetMemoizedResults(It->second);
    6792             :         if (PHINode *PN = dyn_cast<PHINode>(I))
    6793             :           ConstantEvolutionLoopExitValue.erase(PN);
    6794             :       }
    6795             : 
    6796             :       PushDefUseChildren(I, Worklist);
    6797             :     }
    6798             : 
    6799             :     LoopPropertiesCache.erase(CurrL);
    6800             :     // Forget all contained loops too, to avoid dangling entries in the
    6801        8340 :     // ValuesAtScopes map.
    6802             :     LoopWorklist.append(CurrL->begin(), CurrL->end());
    6803             :   }
    6804             : }
    6805             : 
    6806        8340 : void ScalarEvolution::forgetTopmostLoop(const Loop *L) {
    6807        8340 :   while (Loop *Parent = L->getParentLoop())
    6808             :     L = Parent;
    6809             :   forgetLoop(L);
    6810             : }
    6811        9220 : 
    6812             : void ScalarEvolution::forgetValue(Value *V) {
    6813             :   Instruction *I = dyn_cast<Instruction>(V);
    6814             :   if (!I) return;
    6815             : 
    6816             :   // Drop information about expressions based on loop-header PHIs.
    6817             :   SmallVector<Instruction *, 16> Worklist;
    6818        4520 :   Worklist.push_back(I);
    6819             : 
    6820        2350 :   SmallPtrSet<Instruction *, 8> Visited;
    6821             :   while (!Worklist.empty()) {
    6822             :     I = Worklist.pop_back_val();
    6823             :     if (!Visited.insert(I).second)
    6824             :       continue;
    6825        2350 : 
    6826             :     ValueExprMapType::iterator It =
    6827             :       ValueExprMap.find_as(static_cast<Value *>(I));
    6828             :     if (It != ValueExprMap.end()) {
    6829        2348 :       eraseValueFromMap(It->first);
    6830             :       forgetMemoizedResults(It->second);
    6831             :       if (PHINode *PN = dyn_cast<PHINode>(I))
    6832             :         ConstantEvolutionLoopExitValue.erase(PN);
    6833             :     }
    6834             : 
    6835       19884 :     PushDefUseChildren(I, Worklist);
    6836             :   }
    6837       19884 : }
    6838             : 
    6839             : /// Get the exact loop backedge taken count considering all loop exits. A
    6840             : /// computable result can only be returned for loops with all exiting blocks
    6841        4774 : /// dominating the latch. howFarToZero assumes that the limit of each loop test
    6842             : /// is never skipped. This is a valid assumption as long as the loop exits via
    6843        4774 : /// that test. For precise results, it is the caller's responsibility to specify
    6844             : /// the relevant loop exiting block using getExact(ExitingBlock, SE).
    6845             : const SCEV *
    6846       45398 : ScalarEvolution::BackedgeTakenInfo::getExact(const Loop *L, ScalarEvolution *SE,
    6847       45398 :                                              SCEVUnionPredicate *Preds) const {
    6848             :   // If any exits were not computable, the loop is not computable.
    6849             :   if (!isComplete() || ExitNotTaken.empty())
    6850             :     return SE->getCouldNotCompute();
    6851             : 
    6852      301549 :   const BasicBlock *Latch = L->getLoopLatch();
    6853      301549 :   // All exiting blocks we have collected must dominate the only backedge.
    6854             :   if (!Latch)
    6855             :     return SE->getCouldNotCompute();
    6856        6840 : 
    6857        6840 :   // All exiting blocks we have gathered dominate loop's latch, so exact trip
    6858             :   // count is simply a minimum out of all these calculated exit counts.
    6859             :   SmallVector<const SCEV *, 2> Ops;
    6860             :   for (auto &ENT : ExitNotTaken) {
    6861             :     const SCEV *BECount = ENT.ExactNotTaken;
    6862       28551 :     assert(BECount != SE->getCouldNotCompute() && "Bad exit SCEV!");
    6863             :     assert(SE->DT.dominates(ENT.ExitingBlock, Latch) &&
    6864             :            "We should only have known counts for exiting blocks that dominate "
    6865             :            "latch!");
    6866      101097 : 
    6867       43995 :     Ops.push_back(BECount);
    6868       28551 : 
    6869             :     if (Preds && !ENT.hasAlwaysTruePredicate())
    6870             :       Preds->add(ENT.Predicate.get());
    6871        4774 : 
    6872        4774 :     assert((Preds || ENT.hasAlwaysTruePredicate()) &&
    6873        4774 :            "Predicate should be always true!");
    6874             :   }
    6875             : 
    6876        2494 :   return SE->getUMinFromMismatchedTypes(Ops);
    6877             : }
    6878        1247 : 
    6879          12 : /// Get the exact not taken count for this loop exit.
    6880             : const SCEV *
    6881             : ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
    6882        1235 :                                              ScalarEvolution *SE) const {
    6883             :   for (auto &ENT : ExitNotTaken)
    6884        1235 :     if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate())
    6885             :       return ENT.ExactNotTaken;
    6886             : 
    6887             :   return SE->getCouldNotCompute();
    6888      397606 : }
    6889             : 
    6890             : /// getMax - Get the max backedge taken count for the loop.
    6891             : const SCEV *
    6892             : ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
    6893             :   auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
    6894             :     return !ENT.hasAlwaysTruePredicate();
    6895      795212 :   };
    6896      397606 : 
    6897      372151 :   if (any_of(ExitNotTaken, PredicateNotAlwaysTrue) || !getMax())
    6898             :     return SE->getCouldNotCompute();
    6899             : 
    6900             :   assert((isa<SCEVCouldNotCompute>(getMax()) || isa<SCEVConstant>(getMax())) &&
    6901             :          "No point in having a non-constant max backedge taken count!");
    6902       25455 :   return getMax();
    6903             : }
    6904             : 
    6905             : bool ScalarEvolution::BackedgeTakenInfo::isMaxOrZero(ScalarEvolution *SE) const {
    6906             :   auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
    6907             :     return !ENT.hasAlwaysTruePredicate();
    6908             :   };
    6909             :   return MaxOrZero && !any_of(ExitNotTaken, PredicateNotAlwaysTrue);
    6910             : }
    6911             : 
    6912             : bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
    6913             :                                                     ScalarEvolution *SE) const {
    6914             :   if (getMax() && getMax() != SE->getCouldNotCompute() &&
    6915             :       SE->hasOperand(getMax(), S))
    6916             :     return true;
    6917             : 
    6918             :   for (auto &ENT : ExitNotTaken)
    6919             :     if (ENT.ExactNotTaken != SE->getCouldNotCompute() &&
    6920             :         SE->hasOperand(ENT.ExactNotTaken, S))
    6921             :       return true;
    6922             : 
    6923             :   return false;
    6924             : }
    6925             : 
    6926             : ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E)
    6927             :     : ExactNotTaken(E), MaxNotTaken(E) {
    6928             :   assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
    6929       18350 :           isa<SCEVConstant>(MaxNotTaken)) &&
    6930             :          "No point in having a non-constant max backedge taken count!");
    6931             : }
    6932      308741 : 
    6933             : ScalarEvolution::ExitLimit::ExitLimit(
    6934             :     const SCEV *E, const SCEV *M, bool MaxOrZero,
    6935             :     ArrayRef<const SmallPtrSetImpl<const SCEVPredicate *> *> PredSetList)
    6936      290391 :     : ExactNotTaken(E), MaxNotTaken(M), MaxOrZero(MaxOrZero) {
    6937      290391 :   assert((isa<SCEVCouldNotCompute>(ExactNotTaken) ||
    6938       47476 :           !isa<SCEVCouldNotCompute>(MaxNotTaken)) &&
    6939             :          "Exact is not allowed to be less precise than Max");
    6940             :   assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
    6941             :           isa<SCEVConstant>(MaxNotTaken)) &&
    6942             :          "No point in having a non-constant max backedge taken count!");
    6943             :   for (auto *PredSet : PredSetList)
    6944             :     for (auto *P : *PredSet)
    6945             :       addPredicate(P);
    6946       47476 : }
    6947       44302 : 
    6948       44302 : ScalarEvolution::ExitLimit::ExitLimit(
    6949             :     const SCEV *E, const SCEV *M, bool MaxOrZero,
    6950       47476 :     const SmallPtrSetImpl<const SCEVPredicate *> &PredSet)
    6951       22664 :     : ExitLimit(E, M, MaxOrZero, {&PredSet}) {
    6952             :   assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
    6953             :           isa<SCEVConstant>(MaxNotTaken)) &&
    6954             :          "No point in having a non-constant max backedge taken count!");
    6955             : }
    6956             : 
    6957             : ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E, const SCEV *M,
    6958             :                                       bool MaxOrZero)
    6959             :     : ExitLimit(E, M, MaxOrZero, None) {
    6960             :   assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
    6961             :           isa<SCEVConstant>(MaxNotTaken)) &&
    6962             :          "No point in having a non-constant max backedge taken count!");
    6963             : }
    6964             : 
    6965             : /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
    6966             : /// computable exit into a persistent ExitNotTakenInfo array.
    6967             : ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
    6968             :     SmallVectorImpl<ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo>
    6969             :         &&ExitCounts,
    6970             :     bool Complete, const SCEV *MaxCount, bool MaxOrZero)
    6971             :     : MaxAndComplete(MaxCount, Complete), MaxOrZero(MaxOrZero) {
    6972      669458 :   using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;
    6973      379067 : 
    6974      379067 :   ExitNotTaken.reserve(ExitCounts.size());
    6975      737132 :   std::transform(
    6976      379067 :       ExitCounts.begin(), ExitCounts.end(), std::back_inserter(ExitNotTaken),
    6977      262528 :       [&](const EdgeExitInfo &EEI) {
    6978             :         BasicBlock *ExitBB = EEI.first;
    6979             :         const ExitLimit &EL = EEI.second;
    6980             :         if (EL.Predicates.empty())
    6981             :           return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, nullptr);
    6982             : 
    6983             :         std::unique_ptr<SCEVUnionPredicate> Predicate(new SCEVUnionPredicate);
    6984             :         for (auto *Pred : EL.Predicates)
    6985             :           Predicate->add(Pred);
    6986             : 
    6987       25455 :         return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, std::move(Predicate));
    6988             :       });
    6989             :   assert((isa<SCEVCouldNotCompute>(MaxCount) || isa<SCEVConstant>(MaxCount)) &&
    6990        6682 :          "No point in having a non-constant max backedge taken count!");
    6991             : }
    6992             : 
    6993             : /// Invalidate this result and free the ExitNotTakenInfo array.
    6994             : void ScalarEvolution::BackedgeTakenInfo::clear() {
    6995             :   ExitNotTaken.clear();
    6996             : }
    6997             : 
    6998             : /// Compute the number of times the backedge of the specified loop will execute.
    6999             : ScalarEvolution::BackedgeTakenInfo
    7000             : ScalarEvolution::computeBackedgeTakenCount(const Loop *L,
    7001             :                                            bool AllowPredicates) {
    7002             :   SmallVector<BasicBlock *, 8> ExitingBlocks;
    7003             :   L->getExitingBlocks(ExitingBlocks);
    7004             : 
    7005             :   using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;
    7006       16883 : 
    7007       10201 :   SmallVector<EdgeExitInfo, 4> ExitCounts;
    7008             :   bool CouldComputeBECount = true;
    7009       10201 :   BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
    7010       10201 :   const SCEV *MustExitMaxBECount = nullptr;
    7011             :   const SCEV *MayExitMaxBECount = nullptr;
    7012             :   bool MustExitMaxOrZero = false;
    7013       10282 : 
    7014       10282 :   // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
    7015             :   // and compute maxBECount.
    7016          81 :   // Do a union of all the predicates here.
    7017             :   for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
    7018             :     BasicBlock *ExitBB = ExitingBlocks[i];
    7019          12 :     ExitLimit EL = computeExitLimit(L, ExitBB, AllowPredicates);
    7020             : 
    7021             :     assert((AllowPredicates || EL.Predicates.empty()) &&
    7022       10201 :            "Predicated exit limit when predicates are not allowed!");
    7023       10201 : 
    7024       17601 :     // 1. For each exit that can be computed, add an entry to ExitCounts.
    7025       15269 :     // CouldComputeBECount is true only if all exits can be computed.
    7026             :     if (EL.ExactNotTaken == getCouldNotCompute())
    7027             :       // We couldn't compute an exact value for this exit, so
    7028             :       // we won't be able to compute an exact value for the loop.
    7029             :       CouldComputeBECount = false;
    7030       10201 :     else
    7031             :       ExitCounts.emplace_back(ExitBB, EL);
    7032      212233 : 
    7033             :     // 2. Derive the loop's MaxBECount from each exit's max number of
    7034      202032 :     // non-exiting iterations. Partition the loop exits into two kinds:
    7035       43348 :     // LoopMustExits and LoopMayExits.
    7036             :     //
    7037             :     // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
    7038      158684 :     // is a LoopMayExit.  If any computable LoopMustExit is found, then
    7039      158684 :     // MaxBECount is the minimum EL.MaxNotTaken of computable
    7040        7145 :     // LoopMustExits. Otherwise, MaxBECount is conservatively the maximum
    7041        7145 :     // EL.MaxNotTaken, where CouldNotCompute is considered greater than any
    7042        7145 :     // computable EL.MaxNotTaken.
    7043        2436 :     if (EL.MaxNotTaken != getCouldNotCompute() && Latch &&
    7044             :         DT.dominates(ExitBB, Latch)) {
    7045             :       if (!MustExitMaxBECount) {
    7046      158684 :         MustExitMaxBECount = EL.MaxNotTaken;
    7047             :         MustExitMaxOrZero = EL.MaxOrZero;
    7048             :       } else {
    7049       10201 :         MustExitMaxBECount =
    7050             :             getUMinFromMismatchedTypes(MustExitMaxBECount, EL.MaxNotTaken);
    7051             :       }
    7052       20402 :     } else if (MayExitMaxBECount != getCouldNotCompute()) {
    7053             :       if (!MayExitMaxBECount || EL.MaxNotTaken == getCouldNotCompute())
    7054        6682 :         MayExitMaxBECount = EL.MaxNotTaken;
    7055             :       else {
    7056        4864 :         MayExitMaxBECount =
    7057        5760 :             getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.MaxNotTaken);
    7058             :       }
    7059        4864 :     }
    7060        4864 :   }
    7061             :   const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
    7062       12360 :     (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
    7063       12360 :   // The loop backedge will be taken the maximum or zero times if there's
    7064       12360 :   // a single exit that must be taken the maximum or zero times.
    7065             :   bool MaxOrZero = (MustExitMaxOrZero && ExitingBlocks.size() == 1);
    7066             :   return BackedgeTakenInfo(std::move(ExitCounts), CouldComputeBECount,
    7067             :                            MaxBECount, MaxOrZero);
    7068       12360 : }
    7069             : 
    7070             : ScalarEvolution::ExitLimit
    7071      177523 : ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
    7072      165163 :                                       bool AllowPredicates) {
    7073      165163 :   assert(L->contains(ExitingBlock) && "Exit count for non-loop block?");
    7074       22974 :   // If our exiting block does not dominate the latch, then its connection with
    7075             :   // loop's exit limit may be far from trivial.
    7076             :   const BasicBlock *Latch = L->getLoopLatch();
    7077      142189 :   if (!Latch || !DT.dominates(ExitingBlock, Latch))
    7078      142189 :     return getCouldNotCompute();
    7079       20209 : 
    7080       20209 :   bool IsOnlyExit = (L->getExitingBlock() != nullptr);
    7081       35652 :   Instruction *Term = ExitingBlock->getTerminator();
    7082        4766 :   if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
    7083             :     assert(BI->isConditional() && "If unconditional, it can't be in loop!");
    7084             :     bool ExitIfTrue = !L->contains(BI->getSuccessor(0));
    7085      142189 :     assert(ExitIfTrue == L->contains(BI->getSuccessor(1)) &&
    7086             :            "It should have one successor in loop and one exit block!");
    7087             :     // Proceed to the next level to examine the exit condition expression.
    7088             :     return computeExitLimitFromCond(
    7089             :         L, BI->getCondition(), ExitIfTrue,
    7090             :         /*ControlsExit=*/IsOnlyExit, AllowPredicates);
    7091             :   }
    7092             : 
    7093             :   if (SwitchInst *SI = dyn_cast<SwitchInst>(Term)) {
    7094             :     // For switch, make sure that there is a single exit from the loop.
    7095             :     BasicBlock *Exit = nullptr;
    7096       50172 :     for (auto *SBB : successors(ExitingBlock))
    7097             :       if (!L->contains(SBB)) {
    7098             :         if (Exit) // Multiple exit successors.
    7099       50172 :           return getCouldNotCompute();
    7100       16812 :         Exit = SBB;
    7101             :       }
    7102       33360 :     assert(Exit && "Exiting block must have at least one exit");
    7103             :     return computeExitLimitFromSingleExitSwitch(L, SI, Exit,
    7104       33360 :                                                 /*ControlsExit=*/IsOnlyExit);
    7105           0 :   }
    7106             : 
    7107             :   return getCouldNotCompute();
    7108             : }
    7109             : 
    7110       67059 : ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCond(
    7111       33699 :     const Loop *L, Value *ExitCond, bool ExitIfTrue,
    7112             :     bool ControlsExit, bool AllowPredicates) {
    7113             :   ScalarEvolution::ExitLimitCacheTy Cache(L, ExitIfTrue, AllowPredicates);
    7114             :   return computeExitLimitFromCondCached(Cache, L, ExitCond, ExitIfTrue,
    7115             :                                         ControlsExit, AllowPredicates);
    7116             : }
    7117       33699 : 
    7118             : Optional<ScalarEvolution::ExitLimit>
    7119       33699 : ScalarEvolution::ExitLimitCache::find(const Loop *L, Value *ExitCond,
    7120          24 :                                       bool ExitIfTrue, bool ControlsExit,
    7121             :                                       bool AllowPredicates) {
    7122             :   (void)this->L;
    7123             :   (void)this->ExitIfTrue;
    7124             :   (void)this->AllowPredicates;
    7125             : 
    7126       33360 :   assert(this->L == L && this->ExitIfTrue == ExitIfTrue &&
    7127             :          this->AllowPredicates == AllowPredicates &&
    7128             :          "Variance in assumed invariant key components!");
    7129             :   auto Itr = TripCountMap.find({ExitCond, ControlsExit});
    7130             :   if (Itr == TripCountMap.end())
    7131       39045 :     return None;
    7132             :   return Itr->second;
    7133       41918 : }
    7134       30980 : 
    7135       28107 : void ScalarEvolution::ExitLimitCache::insert(const Loop *L, Value *ExitCond,
    7136             :                                              bool ExitIfTrue,
    7137       10938 :                                              bool ControlsExit,
    7138             :                                              bool AllowPredicates,
    7139             :                                              const ExitLimit &EL) {
    7140             :   assert(this->L == L && this->ExitIfTrue == ExitIfTrue &&
    7141             :          this->AllowPredicates == AllowPredicates &&
    7142      301549 :          "Variance in assumed invariant key components!");
    7143             : 
    7144           0 :   auto InsertResult = TripCountMap.insert({{ExitCond, ControlsExit}, EL});
    7145             :   assert(InsertResult.second && "Expected successful insertion!");
    7146             :   (void)InsertResult;
    7147      301549 :   (void)ExitIfTrue;
    7148       41472 : }
    7149             : 
    7150             : ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondCached(
    7151             :     ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
    7152             :     bool ControlsExit, bool AllowPredicates) {
    7153             : 
    7154             :   if (auto MaybeEL =
    7155        6840 :           Cache.find(L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates))
    7156             :     return *MaybeEL;
    7157           0 : 
    7158             :   ExitLimit EL = computeExitLimitFromCondImpl(Cache, L, ExitCond, ExitIfTrue,
    7159        6858 :                                               ControlsExit, AllowPredicates);
    7160             :   Cache.insert(L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates, EL);
    7161             :   return EL;
    7162      193796 : }
    7163             : 
    7164      290975 : ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondImpl(
    7165       97179 :     ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
    7166             :     bool ControlsExit, bool AllowPredicates) {
    7167             :   // Check if the controlling expression for this loop is an And or Or.
    7168      286124 :   if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
    7169      184876 :     if (BO->getOpcode() == Instruction::And) {
    7170       92438 :       // Recurse on the operands of the and.
    7171             :       bool EitherMayExit = !ExitIfTrue;
    7172             :       ExitLimit EL0 = computeExitLimitFromCondCached(
    7173             :           Cache, L, BO->getOperand(0), ExitIfTrue,
    7174             :           ControlsExit && !EitherMayExit, AllowPredicates);
    7175             :       ExitLimit EL1 = computeExitLimitFromCondCached(
    7176       63194 :           Cache, L, BO->getOperand(1), ExitIfTrue,
    7177       63194 :           ControlsExit && !EitherMayExit, AllowPredicates);
    7178             :       const SCEV *BECount = getCouldNotCompute();
    7179             :       const SCEV *MaxBECount = getCouldNotCompute();
    7180             :       if (EitherMayExit) {
    7181       63194 :         // Both conditions must be true for the loop to continue executing.
    7182             :         // Choose the less conservative count.
    7183       12911 :         if (EL0.ExactNotTaken == getCouldNotCompute() ||
    7184             :             EL1.ExactNotTaken == getCouldNotCompute())
    7185       12911 :           BECount = getCouldNotCompute();
    7186       12911 :         else
    7187             :           BECount =
    7188             :               getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken);
    7189             :         if (EL0.MaxNotTaken == getCouldNotCompute())
    7190             :           MaxBECount = EL1.MaxNotTaken;
    7191             :         else if (EL1.MaxNotTaken == getCouldNotCompute())
    7192             :           MaxBECount = EL0.MaxNotTaken;
    7193       26188 :         else
    7194       13290 :           MaxBECount =
    7195             :               getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken);
    7196       12911 :       } else {
    7197             :         // Both conditions must be true at the same time for the loop to exit.
    7198       12447 :         // For now, be conservative.
    7199             :         if (EL0.MaxNotTaken == EL1.MaxNotTaken)
    7200       12447 :           MaxBECount = EL0.MaxNotTaken;
    7201       24894 :         if (EL0.ExactNotTaken == EL1.ExactNotTaken)
    7202             :           BECount = EL0.ExactNotTaken;
    7203             :       }
    7204             : 
    7205       12447 :       // There are cases (e.g. PR26207) where computeExitLimitFromCond is able
    7206             :       // to be more aggressive when computing BECount than when computing
    7207          49 :       // MaxBECount.  In these cases it is possible for EL0.ExactNotTaken and
    7208          49 :       // EL1.ExactNotTaken to match, but for EL0.MaxNotTaken and EL1.MaxNotTaken
    7209          49 :       // to not.
    7210             :       if (isa<SCEVCouldNotCompute>(MaxBECount) &&
    7211             :           !isa<SCEVCouldNotCompute>(BECount))
    7212             :         MaxBECount = getConstant(getUnsignedRangeMax(BECount));
    7213          49 : 
    7214             :       return ExitLimit(BECount, MaxBECount, false,
    7215             :                        {&EL0.Predicates, &EL1.Predicates});
    7216             :     }
    7217       26690 :     if (BO->getOpcode() == Instruction::Or) {
    7218             :       // Recurse on the operands of the or.
    7219             :       bool EitherMayExit = ExitIfTrue;
    7220       26690 :       ExitLimit EL0 = computeExitLimitFromCondCached(
    7221       26690 :           Cache, L, BO->getOperand(0), ExitIfTrue,
    7222             :           ControlsExit && !EitherMayExit, AllowPredicates);
    7223             :       ExitLimit EL1 = computeExitLimitFromCondCached(
    7224       26690 :           Cache, L, BO->getOperand(1), ExitIfTrue,
    7225             :           ControlsExit && !EitherMayExit, AllowPredicates);
    7226             :       const SCEV *BECount = getCouldNotCompute();
    7227             :       const SCEV *MaxBECount = getCouldNotCompute();
    7228             :       if (EitherMayExit) {
    7229             :         // Both conditions must be false for the loop to continue executing.
    7230             :         // Choose the less conservative count.
    7231             :         if (EL0.ExactNotTaken == getCouldNotCompute() ||
    7232             :             EL1.ExactNotTaken == getCouldNotCompute())
    7233             :           BECount = getCouldNotCompute();
    7234             :         else
    7235             :           BECount =
    7236             :               getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken);
    7237             :         if (EL0.MaxNotTaken == getCouldNotCompute())
    7238       26690 :           MaxBECount = EL1.MaxNotTaken;
    7239             :         else if (EL1.MaxNotTaken == getCouldNotCompute())
    7240             :           MaxBECount = EL0.MaxNotTaken;
    7241       26690 :         else
    7242             :           MaxBECount =
    7243             :               getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken);
    7244       26594 :       } else {
    7245             :         // Both conditions must be false at the same time for the loop to exit.
    7246       26594 :         // For now, be conservative.
    7247             :         if (EL0.MaxNotTaken == EL1.MaxNotTaken)
    7248             :           MaxBECount = EL0.MaxNotTaken;
    7249             :         if (EL0.ExactNotTaken == EL1.ExactNotTaken)
    7250       26690 :           BECount = EL0.ExactNotTaken;
    7251             :       }
    7252             : 
    7253       26690 :       return ExitLimit(BECount, MaxBECount, false,
    7254             :                        {&EL0.Predicates, &EL1.Predicates});
    7255             :     }
    7256             :   }
    7257       26690 : 
    7258             :   // With an icmp, it may be feasible to compute an exact backedge-taken count.
    7259       26690 :   // Proceed to the next level to examine the icmp.
    7260             :   if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) {
    7261             :     ExitLimit EL =
    7262             :         computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue, ControlsExit);
    7263             :     if (EL.hasFullInfo() || !AllowPredicates)
    7264             :       return EL;
    7265             : 
    7266             :     // Try again, but use SCEV predicates this time.
    7267       86750 :     return computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue, ControlsExit,
    7268       60060 :                                     /*AllowPredicates=*/true);
    7269       60060 :   }
    7270             : 
    7271             :   // Check for a constant condition. These are normally stripped out by
    7272             :   // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
    7273             :   // preserve the CFG and is temporarily leaving constant conditions
    7274             :   // in place.
    7275             :   if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
    7276       60060 :     if (ExitIfTrue == !CI->getZExtValue())
    7277             :       // The backedge is always taken.
    7278             :       return getCouldNotCompute();
    7279             :     else
    7280             :       // The backedge is never taken.
    7281       17813 :       return getZero(CI->getType());
    7282             :   }
    7283             : 
    7284             :   // If it's not an integer or pointer comparison then compute it the hard way.
    7285             :   return computeExitCountExhaustively(L, ExitCond, ExitIfTrue);
    7286             : }
    7287             : 
    7288             : ScalarEvolution::ExitLimit
    7289             : ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
    7290             :                                           ICmpInst *ExitCond,
    7291             :                                           bool ExitIfTrue,
    7292             :                                           bool ControlsExit,
    7293       78939 :                                           bool AllowPredicates) {
    7294       18879 :   // If the condition was exit on true, convert the condition to exit on false
    7295       18879 :   ICmpInst::Predicate Pred;
    7296       18502 :   if (!ExitIfTrue)
    7297       18502 :     Pred = ExitCond->getPredicate();
    7298             :   else
    7299             :     Pred = ExitCond->getInversePredicate();
    7300         377 :   const ICmpInst::Predicate OriginalPred = Pred;
    7301             : 
    7302       41181 :   // Handle common loops like: for (X = "string"; *X; ++X)
    7303       12001 :   if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
    7304       12001 :     if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
    7305             :       ExitLimit ItCnt =
    7306             :         computeLoadConstantCompareExitLimit(LI, RHS, L, Pred);
    7307           0 :       if (ItCnt.hasAnyInfo())
    7308             :         return ItCnt;
    7309             :     }
    7310             : 
    7311       26690 :   const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
    7312        8188 :   const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
    7313             : 
    7314             :   // Try to evaluate any dependencies out of the loop.
    7315       26690 :   LHS = getSCEVAtScope(LHS, L);
    7316             :   RHS = getSCEVAtScope(RHS, L);
    7317       26690 : 
    7318             :   // At this point, we would like to compute how many iterations of the
    7319             :   // loop the predicate will return true for these inputs.
    7320             :   if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
    7321       60060 :     // If there is a loop-invariant, force it into the RHS.
    7322             :     std::swap(LHS, RHS);
    7323             :     Pred = ICmpInst::getSwappedPredicate(Pred);
    7324             :   }
    7325             : 
    7326       60060 :   // Simplify the operands before analyzing them.
    7327       60060 :   (void)SimplifyICmpOperands(Pred, LHS, RHS);
    7328       21445 : 
    7329             :   // If we have a comparison of a chrec against a constant, try to use value
    7330       38615 :   // ranges to answer this query.
    7331             :   if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
    7332             :     if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
    7333             :       if (AddRec->getLoop() == L) {
    7334       31158 :         // Form the constant range.
    7335             :         ConstantRange CompRange =
    7336             :             ConstantRange::makeExactICmpRegion(Pred, RHSC->getAPInt());
    7337             : 
    7338             :         const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
    7339             :         if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
    7340       62316 :       }
    7341             : 
    7342             :   switch (Pred) {
    7343             :   case ICmpInst::ICMP_NE: {                     // while (X != Y)
    7344             :     // Convert to: while (X-Y != 0)
    7345             :     ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit,
    7346        1109 :                                 AllowPredicates);
    7347         783 :     if (EL.hasAnyInfo()) return EL;
    7348         415 :     break;
    7349         168 :   }
    7350             :   case ICmpInst::ICMP_EQ: {                     // while (X == Y)
    7351             :     // Convert to: while (X-Y == 0)
    7352             :     ExitLimit EL = howFarToNonZero(getMinusSCEV(LHS, RHS), L);
    7353             :     if (EL.hasAnyInfo()) return EL;
    7354          79 :     break;
    7355             :   }
    7356             :   case ICmpInst::ICMP_SLT:
    7357        7210 :   case ICmpInst::ICMP_ULT: {                    // while (X < Y)
    7358             :     bool IsSigned = Pred == ICmpInst::ICMP_SLT;
    7359             :     ExitLimit EL = howManyLessThans(LHS, RHS, L, IsSigned, ControlsExit,
    7360       31158 :                                     AllowPredicates);
    7361             :     if (EL.hasAnyInfo()) return EL;
    7362             :     break;
    7363       31158 :   }
    7364             :   case ICmpInst::ICMP_SGT:
    7365       31158 :   case ICmpInst::ICMP_UGT: {                    // while (X > Y)
    7366             :     bool IsSigned = Pred == ICmpInst::ICMP_SGT;
    7367             :     ExitLimit EL =
    7368             :         howManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit,
    7369       31988 :                             AllowPredicates);
    7370             :     if (EL.hasAnyInfo()) return EL;
    7371             :     break;
    7372             :   }
    7373             :   default:
    7374             :     break;
    7375             :   }
    7376             : 
    7377             :   auto *ExhaustiveCount =
    7378             :       computeExitCountExhaustively(L, ExitCond, ExitIfTrue);
    7379       63976 : 
    7380       31988 :   if (!isa<SCEVCouldNotCompute>(ExhaustiveCount))
    7381             :     return ExhaustiveCount;
    7382             : 
    7383             :   return computeShiftCompareExitLimit(ExitCond->getOperand(0),
    7384             :                                       ExitCond->getOperand(1), L, OriginalPred);
    7385       31928 : }
    7386             : 
    7387             : ScalarEvolution::ExitLimit
    7388             : ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
    7389             :                                                       SwitchInst *Switch,
    7390             :                                                       BasicBlock *ExitingBlock,
    7391             :                                                       bool ControlsExit) {
    7392             :   assert(!L->contains(ExitingBlock) && "Not an exiting block!");
    7393             : 
    7394       31928 :   // Give up if the exit is the default dest of a switch.
    7395             :   if (Switch->getDefaultDest() == ExitingBlock)
    7396             :     return getCouldNotCompute();
    7397             : 
    7398       31928 :   assert(L->contains(Switch->getDefaultDest()) &&
    7399             :          "Default case must not exit the loop!");
    7400       31988 :   const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
    7401             :   const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
    7402             : 
    7403             :   // while (X != Y) --> while (X-Y != 0)
    7404       31988 :   ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
    7405       31988 :   if (EL.hasAnyInfo())
    7406             :     return EL;
    7407             : 
    7408             :   return getCouldNotCompute();
    7409       31928 : }
    7410       31928 : 
    7411             : static ConstantInt *
    7412             : EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
    7413             :                                 ScalarEvolution &SE) {
    7414       31928 :   const SCEV *InVal = SE.getConstant(C);
    7415             :   const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
    7416             :   assert(isa<SCEVConstant>(Val) &&
    7417             :          "Evaluation of SCEV at constant didn't fold correctly?");
    7418             :   return cast<SCEVConstant>(Val)->getValue();
    7419         444 : }
    7420             : 
    7421             : /// Given an exit condition of 'icmp op load X, cst', try to see if we can
    7422             : /// compute the backedge execution count.
    7423             : ScalarEvolution::ExitLimit
    7424         301 : ScalarEvolution::computeLoadConstantCompareExitLimit(
    7425             :   LoadInst *LI,
    7426             :   Constant *RHS,
    7427         301 :   const Loop *L,
    7428         301 :   ICmpInst::Predicate predicate) {
    7429         301 :   if (LI->isVolatile()) return getCouldNotCompute();
    7430         301 : 
    7431             :   // Check to see if the loaded pointer is a getelementptr of a global.
    7432             :   // TODO: Use SCEV instead of manually grubbing with GEPs.
    7433         336 :   GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
    7434         107 :   if (!GEP) return getCouldNotCompute();
    7435         211 : 
    7436             :   // Make sure that it is really a constant global we are gepping, with an
    7437             :   // initializer, and make sure the first IDX is really 0.
    7438          18 :   GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
    7439         229 :   if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
    7440         122 :       GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
    7441         107 :       !cast<Constant>(GEP->getOperand(1))->isNullValue())
    7442          89 :     return getCouldNotCompute();
    7443             : 
    7444             :   // Okay, we allow one non-constant index into the GEP instruction.
    7445          18 :   Value *VarIdx = nullptr;
    7446             :   std::vector<Constant*> Indexes;
    7447             :   unsigned VarIdxNum = 0;
    7448             :   for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
    7449          72 :     if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
    7450             :       Indexes.push_back(CI);
    7451          72 :     } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
    7452             :       if (VarIdx) return getCouldNotCompute();  // Multiple non-constant idx's.
    7453             :       VarIdx = GEP->getOperand(i);
    7454             :       VarIdxNum = i-2;
    7455             :       Indexes.push_back(nullptr);
    7456             :     }
    7457             : 
    7458             :   // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
    7459             :   if (!VarIdx)
    7460         393 :     return getCouldNotCompute();
    7461             : 
    7462           2 :   // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
    7463             :   // Check to see if X is a loop variant variable value now.
    7464             :   const SCEV *Idx = getSCEV(VarIdx);
    7465         602 :   Idx = getSCEVAtScope(Idx, L);
    7466             : 
    7467         143 :   // We can only recognize very limited forms of loop index expressions, in
    7468             :   // particular, only affine AddRec's like {C1,+,C2}.
    7469             :   const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
    7470             :   if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
    7471             :       !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
    7472         114 :       !isa<SCEVConstant>(IdxExpr->getOperand(1)))
    7473             :     return getCouldNotCompute();
    7474             : 
    7475         114 :   unsigned MaxSteps = MaxBruteForceIterations;
    7476         114 :   for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
    7477         114 :     ConstantInt *ItCst = ConstantInt::get(
    7478         114 :                            cast<IntegerType>(IdxExpr->getType()), IterationNum);
    7479             :     ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
    7480             : 
    7481          81 :     // Form the GEP offset.
    7482           7 :     Indexes[VarIdxNum] = Val;
    7483          71 : 
    7484             :     Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
    7485             :                                                          Indexes);
    7486           3 :     if (!Result) break;  // Cannot compute!
    7487          74 : 
    7488          67 :     // Evaluate the condition for this iteration.
    7489           7 :     Result = ConstantExpr::getICmp(predicate, Result, RHS);
    7490           4 :     if (!isa<ConstantInt>(Result)) break;  // Couldn't decide for sure
    7491             :     if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
    7492             :       ++NumArrayLenItCounts;
    7493           3 :       return getConstant(ItCst);   // Found terminating iteration!
    7494             :     }
    7495             :   }
    7496             :   return getCouldNotCompute();
    7497          40 : }
    7498             : 
    7499          40 : ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit(
    7500             :     Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) {
    7501             :   ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV);
    7502             :   if (!RHS)
    7503             :     return getCouldNotCompute();
    7504         228 : 
    7505             :   const BasicBlock *Latch = L->getLoopLatch();
    7506             :   if (!Latch)
    7507             :     return getCouldNotCompute();
    7508             : 
    7509             :   const BasicBlock *Predecessor = L->getLoopPredecessor();
    7510             :   if (!Predecessor)
    7511             :     return getCouldNotCompute();
    7512       29897 : 
    7513       29897 :   // Return true if V is of the form "LHS `shift_op` <positive constant>".
    7514             :   // Return LHS in OutLHS and shift_opt in OutOpCode.
    7515             :   auto MatchPositiveShift =
    7516             :       [](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) {
    7517             : 
    7518        1144 :     using namespace PatternMatch;
    7519             : 
    7520             :     ConstantInt *ShiftAmt;
    7521             :     if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
    7522             :       OutOpCode = Instruction::LShr;
    7523             :     else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
    7524             :       OutOpCode = Instruction::AShr;
    7525             :     else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
    7526         682 :       OutOpCode = Instruction::Shl;
    7527             :     else
    7528         142 :       return false;
    7529             : 
    7530             :     return ShiftAmt->getValue().isStrictlyPositive();
    7531         540 :   };
    7532             : 
    7533             :   // Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in
    7534             :   //
    7535         934 :   // loop:
    7536             :   //   %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ]
    7537             :   //   %iv.shifted = lshr i32 %iv, <positive constant>
    7538             :   //
    7539       31041 :   // Return true on a successful match.  Return the corresponding PHI node (%iv
    7540             :   // above) in PNOut and the opcode of the shift operation in OpCodeOut.
    7541             :   auto MatchShiftRecurrence =
    7542             :       [&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) {
    7543             :     Optional<Instruction::BinaryOps> PostShiftOpCode;
    7544             : 
    7545             :     {
    7546       31041 :       Instruction::BinaryOps OpC;
    7547       15487 :       Value *V;
    7548             : 
    7549       15554 :       // If we encounter a shift instruction, "peel off" the shift operation,
    7550       31041 :       // and remember that we did so.  Later when we inspect %iv's backedge
    7551             :       // value, we will make sure that the backedge value uses the same
    7552             :       // operation.
    7553             :       //
    7554             :       // Note: the peeled shift operation does not have to be the same
    7555             :       // instruction as the one feeding into the PHI's backedge value.  We only
    7556        2450 :       // really care about it being the same *kind* of shift instruction --
    7557        2450 :       // that's all that is required for our later inferences to hold.
    7558             :       if (MatchPositiveShift(LHS, V, OpC)) {
    7559             :         PostShiftOpCode = OpC;
    7560             :         LHS = V;
    7561       31041 :       }
    7562       31041 :     }
    7563             : 
    7564             :     PNOut = dyn_cast<PHINode>(LHS);
    7565       31041 :     if (!PNOut || PNOut->getParent() != L->getHeader())
    7566       31041 :       return false;
    7567             : 
    7568             :     Value *BEValue = PNOut->getIncomingValueForBlock(Latch);
    7569             :     Value *OpLHS;
    7570       31041 : 
    7571             :     return
    7572             :         // The backedge value for the PHI node must be a shift by a positive
    7573         978 :         // amount
    7574             :         MatchPositiveShift(BEValue, OpLHS, OpCodeOut) &&
    7575             : 
    7576             :         // of the PHI node itself
    7577       31041 :         OpLHS == PNOut &&
    7578             : 
    7579             :         // and the kind of shift should be match the kind of shift we peeled
    7580             :         // off, if any.
    7581       31041 :         (!PostShiftOpCode.hasValue() || *PostShiftOpCode == OpCodeOut);
    7582       16230 :   };
    7583       10545 : 
    7584             :   PHINode *PN;
    7585             :   Instruction::BinaryOps OpCode;
    7586       12991 :   if (!MatchShiftRecurrence(LHS, PN, OpCode))
    7587             :     return getCouldNotCompute();
    7588       10531 : 
    7589       10531 :   const DataLayout &DL = getDataLayout();
    7590             : 
    7591             :   // The key rationale for this optimization is that for some kinds of shift
    7592       22970 :   // recurrences, the value of the recurrence "stabilizes" to either 0 or -1
    7593       12641 :   // within a finite number of iterations.  If the condition guarding the
    7594             :   // backedge (in the sense that the backedge is taken if the condition is true)
    7595             :   // is false for the value the shift recurrence stabilizes to, then we know
    7596       12641 :   // that the backedge is taken only a finite number of times.
    7597       12641 : 
    7598             :   ConstantInt *StableValue = nullptr;
    7599             :   switch (OpCode) {
    7600        1568 :   default:
    7601             :     llvm_unreachable("Impossible case!");
    7602        1568 : 
    7603        1568 :   case Instruction::AShr: {
    7604             :     // {K,ashr,<positive-constant>} stabilizes to signum(K) in at most
    7605             :     // bitwidth(K) iterations.
    7606        5958 :     Value *FirstValue = PN->getIncomingValueForBlock(Predecessor);
    7607             :     KnownBits Known = computeKnownBits(FirstValue, DL, 0, nullptr,
    7608        5958 :                                        Predecessor->getTerminator(), &DT);
    7609             :     auto *Ty = cast<IntegerType>(RHS->getType());
    7610        5958 :     if (Known.isNonNegative())
    7611        5958 :       StableValue = ConstantInt::get(Ty, 0);
    7612             :     else if (Known.isNegative())
    7613             :       StableValue = ConstantInt::get(Ty, -1, true);
    7614        1757 :     else
    7615             :       return getCouldNotCompute();
    7616        1757 : 
    7617             :     break;
    7618             :   }
    7619        1757 :   case Instruction::LShr:
    7620        1757 :   case Instruction::Shl:
    7621             :     // Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>}
    7622             :     // stabilize to 0 in at most bitwidth(K) iterations.
    7623             :     StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0);
    7624             :     break;
    7625             :   }
    7626             : 
    7627             :   auto *Result =
    7628       12696 :       ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI);
    7629             :   assert(Result->getType()->isIntegerTy(1) &&
    7630       12696 :          "Otherwise cannot be an operand to a branch instruction");
    7631          61 : 
    7632             :   if (Result->isZeroValue()) {
    7633             :     unsigned BitWidth = getTypeSizeInBits(RHS->getType());
    7634       12635 :     const SCEV *UpperBound =
    7635             :         getConstant(getEffectiveSCEVType(RHS->getType()), BitWidth);
    7636             :     return ExitLimit(getCouldNotCompute(), UpperBound, false);
    7637             :   }
    7638          79 : 
    7639             :   return getCouldNotCompute();
    7640             : }
    7641             : 
    7642             : /// Return true if we can constant fold an instruction of the specified type,
    7643             : /// assuming that all operands were constants.
    7644             : static bool CanConstantFold(const Instruction *I) {
    7645          79 :   if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
    7646          47 :       isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
    7647             :       isa<LoadInst>(I))
    7648             :     return true;
    7649             : 
    7650          32 :   if (const CallInst *CI = dyn_cast<CallInst>(I))
    7651          32 :     if (const Function *F = CI->getCalledFunction())
    7652             :       return canConstantFoldCallTo(CI, F);
    7653             :   return false;
    7654          32 : }
    7655          32 : 
    7656             : /// Determine whether this instruction can constant evolve within this loop
    7657             : /// assuming its operands can all constant evolve.
    7658          31 : static bool canConstantEvolve(Instruction *I, const Loop *L) {
    7659             :   // An instruction outside of the loop can't be derived from a loop PHI.
    7660             :   if (!L->contains(I)) return false;
    7661             : 
    7662        8348 :   if (isa<PHINode>(I)) {
    7663             :     // We don't currently keep track of the control flow needed to evaluate
    7664        8348 :     // PHIs, so we cannot handle PHIs inside of loops.
    7665        8348 :     return L->getHeader() == I->getParent();
    7666             :   }
    7667             : 
    7668        8348 :   // If we won't be able to constant fold this expression even if the operands
    7669             :   // are constants, bail early.
    7670             :   return CanConstantFold(I);
    7671             : }
    7672             : 
    7673             : /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
    7674        2450 : /// recursing through each instruction operand until reaching a loop header phi.
    7675             : static PHINode *
    7676             : getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
    7677             :                                DenseMap<Instruction *, PHINode *> &PHIMap,
    7678             :                                unsigned Depth) {
    7679        2450 :   if (Depth > MaxConstantEvolvingDepth)
    7680             :     return nullptr;
    7681             : 
    7682             :   // Otherwise, we can evaluate this instruction if all of its operands are
    7683             :   // constant or derived from a PHI node themselves.
    7684         937 :   PHINode *PHI = nullptr;
    7685             :   for (Value *Op : UseInst->operands()) {
    7686             :     if (isa<Constant>(Op)) continue;
    7687             : 
    7688             :     Instruction *OpInst = dyn_cast<Instruction>(Op);
    7689          18 :     if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
    7690           0 : 
    7691           0 :     PHINode *P = dyn_cast<PHINode>(OpInst);
    7692        1449 :     if (!P)
    7693             :       // If this operand is already visited, reuse the prior result.
    7694             :       // We may have P != PHI if this is the deepest point at which the
    7695             :       // inconsistent paths meet.
    7696             :       P = PHIMap.lookup(OpInst);
    7697             :     if (!P) {
    7698           0 :       // Recurse and memoize the results, whether a phi is found or not.
    7699             :       // This recursive call invalidates pointers into PHIMap.
    7700           0 :       P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap, Depth + 1);
    7701           0 :       PHIMap[OpInst] = P;
    7702           0 :     }
    7703             :     if (!P)
    7704           0 :       return nullptr;  // Not evolving from PHI
    7705           0 :     if (PHI && PHI != P)
    7706             :       return nullptr;  // Evolving from multiple different PHIs.
    7707             :     PHI = P;
    7708             :   }
    7709           0 :   // This is a expression evolving from a constant PHI!
    7710           0 :   return PHI;
    7711             : }
    7712             : 
    7713             : /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
    7714           0 : /// in the loop that V is derived from.  We allow arbitrary operations along the
    7715           0 : /// way, but the operands of an operation must either be constants or a value
    7716             : /// derived from a constant PHI.  If this expression does not fit with these
    7717             : /// constraints, return null.
    7718             : static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
    7719             :   Instruction *I = dyn_cast<Instruction>(V);
    7720           0 :   if (!I || !canConstantEvolve(I, L)) return nullptr;
    7721           0 : 
    7722             :   if (PHINode *PN = dyn_cast<PHINode>(I))
    7723           0 :     return PN;
    7724             : 
    7725             :   // Record non-constant instructions contained by the loop.
    7726           0 :   DenseMap<Instruction *, PHINode *> PHIMap;
    7727           0 :   return getConstantEvolvingPHIOperands(I, L, PHIMap, 0);
    7728             : }
    7729           0 : 
    7730             : /// EvaluateExpression - Given an expression that passes the
    7731             : /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
    7732           0 : /// in the loop has the value PHIVal.  If we can't fold this expression for some
    7733             : /// reason, return null.
    7734           0 : static Constant *EvaluateExpression(Value *V, const Loop *L,
    7735             :                                     DenseMap<Instruction *, Constant *> &Vals,
    7736           0 :                                     const DataLayout &DL,
    7737             :                                     const TargetLibraryInfo *TLI) {
    7738             :   // Convenient constant check, but redundant for recursive calls.
    7739           0 :   if (Constant *C = dyn_cast<Constant>(V)) return C;
    7740           0 :   Instruction *I = dyn_cast<Instruction>(V);
    7741           0 :   if (!I) return nullptr;
    7742             : 
    7743           0 :   if (Constant *C = Vals.lookup(I)) return C;
    7744             : 
    7745             :   // An instruction inside the loop depends on a value outside the loop that we
    7746           0 :   // weren't given a mapping for, or a value such as a call inside the loop.
    7747             :   if (!canConstantEvolve(I, L)) return nullptr;
    7748             : 
    7749       12635 :   // An unmapped PHI can be due to a branch or another loop inside this loop,
    7750             :   // or due to this not being the initial iteration through a loop where we
    7751             :   // couldn't compute the evolution of this particular PHI last time.
    7752             :   if (isa<PHINode>(I)) return nullptr;
    7753        7395 : 
    7754             :   std::vector<Constant*> Operands(I->getNumOperands());
    7755        5240 : 
    7756        5240 :   for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
    7757           0 :     Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
    7758             :     if (!Operand) {
    7759        5240 :       Operands[i] = dyn_cast<Constant>(I->getOperand(i));
    7760        5240 :       if (!Operands[i]) return nullptr;
    7761           3 :       continue;
    7762             :     }
    7763             :     Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
    7764             :     Vals[Operand] = C;
    7765             :     if (!C) return nullptr;
    7766             :     Operands[i] = C;
    7767             :   }
    7768             : 
    7769             :   if (CmpInst *CI = dyn_cast<CmpInst>(I))
    7770             :     return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
    7771             :                                            Operands[1], DL, TLI);
    7772             :   if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
    7773             :     if (!LI->isVolatile())
    7774             :       return ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
    7775             :   }
    7776             :   return ConstantFoldInstOperands(I, Operands, DL, TLI);
    7777             : }
    7778             : 
    7779             : 
    7780             : // If every incoming value to PN except the one for BB is a specific Constant,
    7781             : // return that, else return nullptr.
    7782             : static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) {
    7783             :   Constant *IncomingVal = nullptr;
    7784             : 
    7785             :   for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
    7786             :     if (PN->getIncomingBlock(i) == BB)
    7787             :       continue;
    7788             : 
    7789             :     auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i));
    7790             :     if (!CurrentVal)
    7791             :       return nullptr;
    7792             : 
    7793             :     if (IncomingVal != CurrentVal) {
    7794             :       if (IncomingVal)
    7795             :         return nullptr;
    7796             :       IncomingVal = CurrentVal;
    7797             :     }
    7798             :   }
    7799             : 
    7800             :   return IncomingVal;
    7801             : }
    7802             : 
    7803             : /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
    7804             : /// in the header of its containing loop, we know the loop executes a
    7805             : /// constant number of times, and the PHI node is just a recurrence
    7806             : /// involving constants, fold it.
    7807             : Constant *
    7808             : ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
    7809             :                                                    const APInt &BEs,
    7810             :                                                    const Loop *L) {
    7811             :   auto I = ConstantEvolutionLoopExitValue.find(PN);
    7812             :   if (I != ConstantEvolutionLoopExitValue.end())
    7813             :     return I->second;
    7814             : 
    7815             :   if (BEs.ugt(MaxBruteForceIterations))
    7816             :     return ConstantEvolutionLoopExitValue[PN] = nullptr;  // Not going to evaluate it.
    7817             : 
    7818             :   Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
    7819             : 
    7820             :   DenseMap<Instruction *, Constant *> CurrentIterVals;
    7821             :   BasicBlock *Header = L->getHeader();
    7822             :   assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
    7823             : 
    7824             :   BasicBlock *Latch = L->getLoopLatch();
    7825             :   if (!Latch)
    7826             :     return nullptr;
    7827             : 
    7828             :   for (PHINode &PHI : Header->phis()) {
    7829             :     if (auto *StartCST = getOtherIncomingValue(&PHI, Latch))
    7830             :       CurrentIterVals[&PHI] = StartCST;
    7831             :   }
    7832        5237 :   if (!CurrentIterVals.count(PN))
    7833             :     return RetVal = nullptr;
    7834             : 
    7835             :   Value *BEValue = PN->getIncomingValueForBlock(Latch);
    7836        5237 : 
    7837        5177 :   // Execute the loop symbolically to determine the exit value.
    7838             :   assert(BEs.getActiveBits() < CHAR_BIT * sizeof(unsigned) &&
    7839          60 :          "BEs is <= MaxBruteForceIterations which is an 'unsigned'!");
    7840             : 
    7841             :   unsigned NumIterations = BEs.getZExtValue(); // must be in range
    7842             :   unsigned IterationNum = 0;
    7843             :   const DataLayout &DL = getDataLayout();
    7844             :   for (; ; ++IterationNum) {
    7845             :     if (IterationNum == NumIterations)
    7846             :       return RetVal = CurrentIterVals[PN];  // Got exit value!
    7847             : 
    7848             :     // Compute the value of the PHIs for the next iteration.
    7849          60 :     // EvaluateExpression adds non-phi values to the CurrentIterVals map.
    7850           0 :     DenseMap<Instruction *, Constant *> NextIterVals;
    7851           0 :     Constant *NextPHI =
    7852             :         EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
    7853          37 :     if (!NextPHI)
    7854             :       return nullptr;        // Couldn't evaluate!
    7855             :     NextIterVals[PN] = NextPHI;
    7856          37 : 
    7857             :     bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
    7858          37 : 
    7859             :     // Also evaluate the other PHI nodes.  However, we don't get to stop if we
    7860          37 :     // cease to be able to evaluate one of them or if they stop evolving,
    7861          23 :     // because that doesn't necessarily prevent us from computing PN.
    7862          14 :     SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
    7863           9 :     for (const auto &I : CurrentIterVals) {
    7864             :       PHINode *PHI = dyn_cast<PHINode>(I.first);
    7865           5 :       if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
    7866             :       PHIsToCompute.emplace_back(PHI, I.second);
    7867          32 :     }
    7868             :     // We use two distinct loops because EvaluateExpression may invalidate any
    7869             :     // iterators into CurrentIterVals.
    7870             :     for (const auto &I : PHIsToCompute) {
    7871             :       PHINode *PHI = I.first;
    7872             :       Constant *&NextPHI = NextIterVals[PHI];
    7873          23 :       if (!NextPHI) {   // Not already computed.
    7874          23 :         Value *BEValue = PHI->getIncomingValueForBlock(Latch);
    7875             :         NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
    7876             :       }
    7877             :       if (NextPHI != I.second)
    7878          55 :         StoppedEvolving = false;
    7879             :     }
    7880             : 
    7881             :     // If all entries in CurrentIterVals == NextIterVals then we can stop
    7882          55 :     // iterating, the loop can't continue to change.
    7883          49 :     if (StoppedEvolving)
    7884             :       return RetVal = CurrentIterVals[PN];
    7885          49 : 
    7886          49 :     CurrentIterVals.swap(NextIterVals);
    7887             :   }
    7888             : }
    7889           6 : 
    7890             : const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
    7891             :                                                           Value *Cond,
    7892             :                                                           bool ExitWhen) {
    7893             :   PHINode *PN = getConstantEvolvingPHI(Cond, L);
    7894      105427 :   if (!PN) return getCouldNotCompute();
    7895       52777 : 
    7896      156306 :   // If the loop is canonicalized, the PHI will have exactly two entries.
    7897             :   // That's the only form we support here.
    7898             :   if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
    7899             : 
    7900             :   DenseMap<Instruction *, Constant *> CurrentIterVals;
    7901             :   BasicBlock *Header = L->getHeader();
    7902        3918 :   assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
    7903             : 
    7904             :   BasicBlock *Latch = L->getLoopLatch();
    7905             :   assert(Latch && "Should follow from NumIncomingValues == 2!");
    7906             : 
    7907             :   for (PHINode &PHI : Header->phis()) {
    7908       75135 :     if (auto *StartCST = getOtherIncomingValue(&PHI, Latch))
    7909             :       CurrentIterVals[&PHI] = StartCST;
    7910       75135 :   }
    7911             :   if (!CurrentIterVals.count(PN))
    7912       69667 :     return getCouldNotCompute();
    7913             : 
    7914             :   // Okay, we find a PHI node that defines the trip count of this loop.  Execute
    7915        7867 :   // the loop symbolically to determine when the condition gets a value of
    7916             :   // "ExitWhen".
    7917             :   unsigned MaxIterations = MaxBruteForceIterations;   // Limit analysis.
    7918             :   const DataLayout &DL = getDataLayout();
    7919             :   for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
    7920       61800 :     auto *CondVal = dyn_cast_or_null<ConstantInt>(
    7921             :         EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
    7922             : 
    7923             :     // Couldn't symbolically evaluate.
    7924             :     if (!CondVal) return getCouldNotCompute();
    7925             : 
    7926       30190 :     if (CondVal->getValue() == uint64_t(ExitWhen)) {
    7927             :       ++NumBruteForceTripCountsComputed;
    7928             :       return getConstant(Type::getInt32Ty(getContext()), IterationNum);
    7929       30190 :     }
    7930             : 
    7931             :     // Update all the PHI nodes for the next iteration.
    7932             :     DenseMap<Instruction *, Constant *> NextIterVals;
    7933             : 
    7934             :     // Create a list of which PHIs we need to compute. We want to do this before
    7935       85130 :     // calling EvaluateExpression on them because that may invalidate iterators
    7936       43643 :     // into CurrentIterVals.
    7937             :     SmallVector<PHINode *, 8> PHIsToCompute;
    7938       34703 :     for (const auto &I : CurrentIterVals) {
    7939       42913 :       PHINode *PHI = dyn_cast<PHINode>(I.first);
    7940             :       if (!PHI || PHI->getParent() != Header) continue;
    7941       24036 :       PHIsToCompute.push_back(PHI);
    7942             :     }
    7943             :     for (PHINode *PHI : PHIsToCompute) {
    7944             :       Constant *&NextPHI = NextIterVals[PHI];
    7945             :       if (NextPHI) continue;    // Already computed!
    7946       17692 : 
    7947        6676 :       Value *BEValue = PHI->getIncomingValueForBlock(Latch);
    7948             :       NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
    7949             :     }
    7950       17360 :     CurrentIterVals.swap(NextIterVals);
    7951       17360 :   }
    7952             : 
    7953       24036 :   // Too many iterations were needed to evaluate.
    7954             :   return getCouldNotCompute();
    7955       16104 : }
    7956             : 
    7957             : const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
    7958             :   SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values =
    7959             :       ValuesAtScopes[V];
    7960             :   // Check to see if we've folded this expression at this loop before.
    7961             :   for (auto &LS : Values)
    7962             :     if (LS.first == L)
    7963             :       return LS.second ? LS.second : V;
    7964             : 
    7965             :   Values.emplace_back(L, nullptr);
    7966             : 
    7967             :   // Otherwise compute it.
    7968       13630 :   const SCEV *C = computeSCEVAtScope(V, L);
    7969             :   for (auto &LS : reverse(ValuesAtScopes[V]))
    7970       13630 :     if (LS.first == L) {
    7971             :       LS.second = C;
    7972             :       break;
    7973             :     }
    7974             :   return C;
    7975             : }
    7976             : 
    7977       12830 : /// This builds up a Constant using the ConstantExpr interface.  That way, we
    7978             : /// will return Constants for objects which aren't represented by a
    7979             : /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
    7980             : /// Returns NULL if the SCEV isn't representable as a Constant.
    7981             : static Constant *BuildConstantFromSCEV(const SCEV *V) {
    7982             :   switch (static_cast<SCEVTypes>(V->getSCEVType())) {
    7983             :     case scCouldNotCompute:
    7984       54794 :     case scAddRecExpr:
    7985             :       break;
    7986             :     case scConstant:
    7987             :       return cast<SCEVConstant>(V)->getValue();
    7988             :     case scUnknown:
    7989             :       return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
    7990             :     case scSignExtend: {
    7991             :       const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
    7992             :       if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
    7993       54685 :         return ConstantExpr::getSExt(CastOp, SS->getType());
    7994             :       break;
    7995             :     }
    7996             :     case scZeroExtend: {
    7997       28811 :       const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
    7998             :       if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
    7999             :         return ConstantExpr::getZExt(CastOp, SZ->getType());
    8000             :       break;
    8001             :     }
    8002       28782 :     case scTruncate: {
    8003             :       const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
    8004       28742 :       if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
    8005             :         return ConstantExpr::getTrunc(CastOp, ST->getType());
    8006       85685 :       break;
    8007       57100 :     }
    8008       57100 :     case scAddExpr: {
    8009       17734 :       const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
    8010       17886 :       if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
    8011       17729 :         if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
    8012             :           unsigned AS = PTy->getAddressSpace();
    8013       39366 :           Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
    8014       39366 :           C = ConstantExpr::getBitCast(C, DestPtrTy);
    8015       39366 :         }
    8016       78428 :         for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
    8017             :           Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
    8018             :           if (!C2) return nullptr;
    8019             : 
    8020        7417 :           // First pointer!
    8021        7417 :           if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
    8022             :             unsigned AS = C2->getType()->getPointerAddressSpace();
    8023         202 :             std::swap(C, C2);
    8024         202 :             Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
    8025             :             // The offsets have been converted to bytes.  We can add bytes to an
    8026       20966 :             // i8* by GEP with the byte count in the first index.
    8027             :             C = ConstantExpr::getBitCast(C, DestPtrTy);
    8028             :           }
    8029             : 
    8030             :           // Don't bother trying to sum two pointers. We probably can't
    8031             :           // statically compute a load that results from it anyway.
    8032        3854 :           if (C2->getType()->isPointerTy())
    8033             :             return nullptr;
    8034             : 
    8035        7698 :           if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
    8036        6481 :             if (PTy->getElementType()->isStructTy())
    8037             :               C2 = ConstantExpr::getIntegerCast(
    8038             :                   C2, Type::getInt32Ty(C->getContext()), true);
    8039             :             C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
    8040             :           } else
    8041             :             C = ConstantExpr::getAdd(C, C2);
    8042             :         }
    8043        1219 :         return C;
    8044        1217 :       }
    8045             :       break;
    8046             :     }
    8047             :     case scMulExpr: {
    8048             :       const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
    8049             :       if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
    8050             :         // Don't bother with pointers at all.
    8051             :         if (C->getType()->isPointerTy()) return nullptr;
    8052             :         for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
    8053             :           Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
    8054             :           if (!C2 || C2->getType()->isPointerTy()) return nullptr;
    8055             :           C = ConstantExpr::getMul(C, C2);
    8056             :         }
    8057             :         return C;
    8058         123 :       }
    8059             :       break;
    8060             :     }
    8061         123 :     case scUDivExpr: {
    8062         123 :       const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
    8063           0 :       if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
    8064             :         if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
    8065         123 :           if (LHS->getType() == RHS->getType())
    8066          11 :             return ConstantExpr::getUDiv(LHS, RHS);
    8067             :       break;
    8068             :     }
    8069             :     case scSMaxExpr:
    8070             :     case scUMaxExpr:
    8071             :       break; // TODO: smax, umax.
    8072             :   }
    8073             :   return nullptr;
    8074         112 : }
    8075         112 : 
    8076             : const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
    8077             :   if (isa<SCEVConstant>(V)) return V;
    8078         592 : 
    8079         368 :   // If this instruction is evolved from a constant-evolving PHI, compute the
    8080         217 :   // exit value from the loop without using SCEVs.
    8081             :   if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
    8082         112 :     if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
    8083          19 :       const Loop *LI = this->LI[I->getParent()];
    8084             :       if (LI && LI->getParentLoop() == L)  // Looking for loop exit value.
    8085          93 :         if (PHINode *PN = dyn_cast<PHINode>(I))
    8086             :           if (PN->getParent() == LI->getHeader()) {
    8087             :             // Okay, there is no closed form solution for the PHI node.  Check
    8088             :             // to see if the loop that contains it has a known backedge-taken
    8089             :             // count.  If so, we may be able to force computation of the exit
    8090             :             // value.
    8091          93 :             const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
    8092             :             if (const SCEVConstant *BTCC =
    8093          93 :                   dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
    8094         443 : 
    8095         536 :               // This trivial case can show up in some degenerate cases where
    8096          65 :               // the incoming IR has not yet been fully simplified.
    8097             :               if (BTCC->getValue()->isZero()) {
    8098             :                 Value *InitValue = nullptr;
    8099             :                 bool MultipleInitValues = false;
    8100             :                 for (unsigned i = 0; i < PN->getNumIncomingValues(); i++) {
    8101             :                   if (!LI->contains(PN->getIncomingBlock(i))) {
    8102         471 :                     if (!InitValue)
    8103         471 :                       InitValue = PN->getIncomingValue(i);
    8104             :                     else if (InitValue != PN->getIncomingValue(i)) {
    8105         443 :                       MultipleInitValues = true;
    8106             :                       break;
    8107         443 :                     }
    8108             :                   }
    8109             :                   if (!MultipleInitValues && InitValue)
    8110             :                     return getSCEV(InitValue);
    8111             :                 }
    8112             :               }
    8113        2109 :               // Okay, we know how many times the containing loop executes.  If
    8114        1666 :               // this is a constant evolving PHI node, get the final value at
    8115        1666 :               // the specified iteration number.
    8116         383 :               Constant *RV =
    8117             :                   getConstantEvolutionLoopExitValue(PN, BTCC->getAPInt(), LI);
    8118             :               if (RV) return getSCEV(RV);
    8119             :             }
    8120         826 :           }
    8121         383 : 
    8122         383 :       // Okay, this is an expression that we cannot symbolically evaluate
    8123         383 :       // into a SCEV.  Check to see if it's possible to symbolically evaluate
    8124         383 :       // the arguments into constants, and if so, try to constant propagate the
    8125         383 :       // result.  This is particularly useful for computing loop exit values.
    8126             :       if (CanConstantFold(I)) {
    8127         383 :         SmallVector<Constant *, 4> Operands;
    8128             :         bool MadeImprovement = false;
    8129             :         for (Value *Op : I->operands()) {
    8130             :           if (Constant *C = dyn_cast<Constant>(Op)) {
    8131             :             Operands.push_back(C);
    8132             :             continue;
    8133         443 :           }
    8134           0 : 
    8135             :           // If any of the operands is non-constant and if they are
    8136             :           // non-integer and non-pointer, don't even try to analyze them
    8137         443 :           // with scev techniques.
    8138             :           if (!isSCEVable(Op->getType()))
    8139             :             return V;
    8140       13630 : 
    8141             :           const SCEV *OrigV = getSCEV(Op);
    8142             :           const SCEV *OpV = getSCEVAtScope(OrigV, L);
    8143       13630 :           MadeImprovement |= OrigV != OpV;
    8144       13630 : 
    8145             :           Constant *C = BuildConstantFromSCEV(OpV);
    8146             :           if (!C) return V;
    8147             :           if (C->getType() != Op->getType())
    8148        1782 :             C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
    8149             :                                                               Op->getType(),
    8150             :                                                               false),
    8151             :                                       C, Op->getType());
    8152             :           Operands.push_back(C);
    8153             :         }
    8154        1779 : 
    8155             :         // Check to see if getSCEVAtScope actually made an improvement.
    8156             :         if (MadeImprovement) {
    8157        7044 :           Constant *C = nullptr;
    8158        3486 :           const DataLayout &DL = getDataLayout();
    8159        1000 :           if (const CmpInst *CI = dyn_cast<CmpInst>(I))
    8160             :             C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
    8161         182 :                                                 Operands[1], DL, &TLI);
    8162        1597 :           else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
    8163             :             if (!LI->isVolatile())
    8164             :               C = ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
    8165             :           } else
    8166             :             C = ConstantFoldInstOperands(I, Operands, DL, &TLI);
    8167             :           if (!C) return V;
    8168         182 :           return getSCEV(C);
    8169        6692 :         }
    8170        6631 :       }
    8171        6631 :     }
    8172             : 
    8173             :     // This is some other type of SCEVUnknown, just return it.
    8174         121 :     return V;
    8175             :   }
    8176       13152 : 
    8177             :   if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
    8178          66 :     // Avoid performing the look-up in the common case where the specified
    8179             :     // expression has no loop-variant portions.
    8180             :     for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
    8181             :       const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
    8182             :       if (OpAtScope != Comm->getOperand(i)) {
    8183             :         // Okay, at least one of these operands is loop variant but might be
    8184             :         // foldable.  Build a new instance of the folded commutative expression.
    8185             :         SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
    8186             :                                             Comm->op_begin()+i);
    8187             :         NewOps.push_back(OpAtScope);
    8188       30126 : 
    8189       23616 :         for (++i; i != e; ++i) {
    8190       23616 :           OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
    8191        7943 :           NewOps.push_back(OpAtScope);
    8192             :         }
    8193       14453 :         if (isa<SCEVAddExpr>(Comm))
    8194        7943 :           return getAddExpr(NewOps);
    8195        7943 :         if (isa<SCEVMulExpr>(Comm))
    8196             :           return getMulExpr(NewOps);
    8197        7943 :         if (isa<SCEVSMaxExpr>(Comm))
    8198        7943 :           return getSMaxExpr(NewOps);
    8199             :         if (isa<SCEVUMaxExpr>(Comm))
    8200             :           return getUMaxExpr(NewOps);
    8201             :         llvm_unreachable("Unknown commutative SCEV type!");
    8202             :       }
    8203             :     }
    8204          61 :     // If we got here, all operands are loop invariant.
    8205             :     return Comm;
    8206             :   }
    8207      605174 : 
    8208             :   if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
    8209      605174 :     const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
    8210             :     const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
    8211     1204891 :     if (LHS == Div->getLHS() && RHS == Div->getRHS())
    8212      924548 :       return Div;   // must be loop invariant
    8213      324831 :     return getUDivExpr(LHS, RHS);
    8214             :   }
    8215      280343 : 
    8216             :   // If this is a loop recurrence for a loop that does not contain L, then we
    8217             :   // are dealing with the final value computed by the loop.
    8218      280343 :   if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
    8219      280500 :     // First, attempt to evaluate each operand.
    8220      279665 :     // Avoid performing the look-up in the common case where the specified
    8221      279508 :     // expression has no loop-variant portions.
    8222      279508 :     for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
    8223             :       const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
    8224             :       if (OpAtScope == AddRec->getOperand(i))
    8225             :         continue;
    8226             : 
    8227             :       // Okay, at least one of these operands is loop variant but might be
    8228             :       // foldable.  Build a new instance of the folded commutative expression.
    8229             :       SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
    8230             :                                           AddRec->op_begin()+i);
    8231       52606 :       NewOps.push_back(OpAtScope);
    8232       52606 :       for (++i; i != e; ++i)
    8233             :         NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
    8234             : 
    8235             :       const SCEV *FoldedRec =
    8236             :         getAddRecExpr(NewOps, AddRec->getLoop(),
    8237        9963 :                       AddRec->getNoWrapFlags(SCEV::FlagNW));
    8238             :       AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
    8239             :       // The addrec may be folded to a nonrecurrence, for example, if the
    8240             :       // induction variable is multiplied by zero after constant folding. Go
    8241             :       // ahead and return the folded value.
    8242         409 :       if (!AddRec)
    8243           0 :         return FoldedRec;
    8244             :       break;
    8245             :     }
    8246             : 
    8247             :     // If the scope is outside the addrec's loop, evaluate it by using the
    8248         598 :     // loop exit value of the addrec.
    8249           5 :     if (!AddRec->getLoop()->contains(L)) {
    8250             :       // To evaluate this recurrence, we need to know how many times the AddRec
    8251             :       // loop iterates.  Compute this now.
    8252             :       const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
    8253             :       if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
    8254         339 : 
    8255           2 :       // Then, evaluate the AddRec.
    8256             :       return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
    8257             :     }
    8258             : 
    8259             :     return AddRec;
    8260       19386 :   }
    8261        7560 : 
    8262             :   if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
    8263           0 :     const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
    8264           0 :     if (Op == Cast->getOperand())
    8265             :       return Cast;  // must be loop invariant
    8266        7578 :     return getZeroExtendExpr(Op, Cast->getType());
    8267       15122 :   }
    8268        7561 : 
    8269             :   if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
    8270             :     const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
    8271          36 :     if (Op == Cast->getOperand())
    8272             :       return Cast;  // must be loop invariant
    8273             :     return getSignExtendExpr(Op, Cast->getType());
    8274          15 :   }
    8275             : 
    8276             :   if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
    8277          15 :     const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
    8278             :     if (Op == Cast->getOperand())
    8279             :       return Cast;  // must be loop invariant
    8280             :     return getTruncateExpr(Op, Cast->getType());
    8281             :   }
    8282          36 : 
    8283             :   llvm_unreachable("Unknown SCEV type!");
    8284             : }
    8285          18 : 
    8286          30 : const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
    8287           0 :   return getSCEVAtScope(getSCEV(V), L);
    8288           0 : }
    8289          15 : 
    8290             : const SCEV *ScalarEvolution::stripInjectiveFunctions(const SCEV *S) const {
    8291           3 :   if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S))
    8292             :     return stripInjectiveFunctions(ZExt->getOperand());
    8293          17 :   if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S))
    8294             :     return stripInjectiveFunctions(SExt->getOperand());
    8295             :   return S;
    8296             : }
    8297             : 
    8298             : /// Finds the minimum unsigned root of the following equation:
    8299        4706 : ///
    8300             : ///     A * X = B (mod N)
    8301        4642 : ///
    8302        2324 : /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
    8303        4642 : /// A and B isn't important.
    8304        2321 : ///
    8305           3 : /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
    8306             : static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const SCEV *B,
    8307           3 :                                                ScalarEvolution &SE) {
    8308             :   uint32_t BW = A.getBitWidth();
    8309             :   assert(BW == SE.getTypeSizeInBits(B->getType()));
    8310             :   assert(A != 0 && "A must be non-zero.");
    8311             : 
    8312             :   // 1. D = gcd(A, N)
    8313         342 :   //
    8314           8 :   // The gcd of A and N may have only one prime factor: 2. The number of
    8315           2 :   // trailing zeros in A is its multiplicity
    8316           2 :   uint32_t Mult2 = A.countTrailingZeros();
    8317             :   // D = 2^Mult2
    8318             : 
    8319             :   // 2. Check if B is divisible by D.
    8320             :   //
    8321             :   // B is divisible by D if and only if the multiplicity of prime factor 2 for B
    8322             :   // is not less than multiplicity of this prime factor for D.
    8323             :   if (SE.GetMinTrailingZeros(B) < Mult2)
    8324             :     return SE.getCouldNotCompute();
    8325             : 
    8326      280343 :   // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
    8327      280343 :   // modulo (N / D).
    8328             :   //
    8329             :   // If D == 1, (N / D) == N == 2^BW, so we need one extra bit to represent
    8330             :   // (N / D) in general. The inverse itself always fits into BW bits, though,
    8331       69181 :   // so we immediately truncate it.
    8332             :   APInt AD = A.lshr(Mult2).zext(BW + 1);  // AD = A / D
    8333       43718 :   APInt Mod(BW + 1, 0);
    8334       25413 :   Mod.setBit(BW - Mult2);  // Mod = N / D
    8335             :   APInt I = AD.multiplicativeInverse(Mod).trunc(BW);
    8336         930 : 
    8337             :   // 4. Compute the minimum unsigned root of the equation:
    8338             :   // I * (B / D) mod (N / D)
    8339             :   // To simplify the computation, we factor out the divide by D:
    8340             :   // (I * B mod N) / D
    8341         365 :   const SCEV *D = SE.getConstant(APInt::getOneBitSet(BW, Mult2));
    8342             :   return SE.getUDivExactExpr(SE.getMulExpr(B, SE.getConstant(I)), D);
    8343             : }
    8344             : 
    8345             : /// For a given quadratic addrec, generate coefficients of the corresponding
    8346             : /// quadratic equation, multiplied by a common value to ensure that they are
    8347         298 : /// integers.
    8348             : /// The returned value is a tuple { A, B, C, M, BitWidth }, where
    8349             : /// Ax^2 + Bx + C is the quadratic function, M is the value that A, B and C
    8350          46 : /// were multiplied by, and BitWidth is the bit width of the original addrec
    8351          46 : /// coefficients.
    8352          26 : /// This function returns None if the addrec coefficients are not compile-
    8353             : /// time constants.
    8354           0 : static Optional<std::tuple<APInt, APInt, APInt, APInt, unsigned>>
    8355             : GetQuadraticEquation(const SCEVAddRecExpr *AddRec) {
    8356             :   assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
    8357             :   const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
    8358             :   const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
    8359          46 :   const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
    8360          26 :   LLVM_DEBUG(dbgs() << __func__ << ": analyzing quadratic addrec: "
    8361             :                     << *AddRec << '\n');
    8362             : 
    8363             :   // We currently can only solve this if the coefficients are constants.
    8364             :   if (!LC || !MC || !NC) {
    8365             :     LLVM_DEBUG(dbgs() << __func__ << ": coefficients are not constant\n");
    8366             :     return None;
    8367         123 :   }
    8368         123 : 
    8369             :   APInt L = LC->getAPInt();
    8370             :   APInt M = MC->getAPInt();
    8371             :   APInt N = NC->getAPInt();
    8372             :   assert(!N.isNullValue() && "This is not a quadratic addrec");
    8373             : 
    8374             :   unsigned BitWidth = LC->getAPInt().getBitWidth();
    8375             :   unsigned NewWidth = BitWidth + 1;
    8376       43627 :   LLVM_DEBUG(dbgs() << __func__ << ": addrec coeff bw: "
    8377             :                     << BitWidth << '\n');
    8378             :   // The sign-extension (as opposed to a zero-extension) here matches the
    8379       61658 :   // extension used in SolveQuadraticEquationWrap (with the same motivation).
    8380       30459 :   N = N.sext(NewWidth);
    8381        1339 :   M = M.sext(NewWidth);
    8382        1339 :   L = L.sext(NewWidth);
    8383             : 
    8384             :   // The increments are M, M+N, M+2N, ..., so the accumulated values are
    8385             :   //   L+M, (L+M)+(M+N), (L+M)+(M+N)+(M+2N), ..., that is,
    8386             :   //   L+M, L+2M+N, L+3M+3N, ...
    8387             :   // After n iterations the accumulated value Acc is L + nM + n(n-1)/2 N.
    8388       29120 :   //
    8389       29003 :   // The equation Acc = 0 is then
    8390             :   //   L + nM + n(n-1)/2 N = 0,  or  2L + 2M n + n(n-1) N = 0.
    8391       28982 :   // In a quadratic form it becomes:
    8392       28982 :   //   N n^2 + (2M-N) n + 2L = 0.
    8393       28982 : 
    8394             :   APInt A = N;
    8395       28982 :   APInt B = 2 * M - A;
    8396       28982 :   APInt C = 2 * L;
    8397         117 :   APInt T = APInt(NewWidth, 2);
    8398          25 :   LLVM_DEBUG(dbgs() << __func__ << ": equation " << A << "x^2 + " << B
    8399             :                     << "x + " << C << ", coeff bw: " << NewWidth
    8400             :                     << ", multiplied by " << T << '\n');
    8401             :   return std::make_tuple(A, B, C, T, BitWidth);
    8402         117 : }
    8403             : 
    8404             : /// Helper function to compare optional APInts:
    8405             : /// (a) if X and Y both exist, return min(X, Y),
    8406        1098 : /// (b) if neither X nor Y exist, return None,
    8407             : /// (c) if exactly one of X and Y exists, return that value.
    8408          39 : static Optional<APInt> MinOptional(Optional<APInt> X, Optional<APInt> Y) {
    8409             :   if (X.hasValue() && Y.hasValue()) {
    8410          26 :     unsigned W = std::max(X->getBitWidth(), Y->getBitWidth());
    8411          13 :     APInt XW = X->sextOrSelf(W);
    8412             :     APInt YW = Y->sextOrSelf(W);
    8413          14 :     return XW.slt(YW) ? *X : *Y;
    8414          28 :   }
    8415             :   if (!X.hasValue() && !Y.hasValue())
    8416          24 :     return None;
    8417          39 :   return X.hasValue() ? *X : *Y;
    8418          31 : }
    8419             : 
    8420             : /// Helper function to truncate an optional APInt to a given BitWidth.
    8421             : /// When solving addrec-related equations, it is preferable to return a value
    8422             : /// that has the same bit width as the original addrec's coefficients. If the
    8423             : /// solution fits in the original bit width, truncate it (except for i1).
    8424       40048 : /// Returning a value of a different bit width may inhibit some optimizations.
    8425             : ///
    8426             : /// In general, a solution to a quadratic equation generated from an addrec
    8427             : /// may require BW+1 bits, where BW is the bit width of the addrec's
    8428             : /// coefficients. The reason is that the coefficients of the quadratic
    8429             : /// equation are BW+1 bits wide (to avoid truncation when converting from
    8430      193555 : /// the addrec to the equation).
    8431      286524 : static Optional<APInt> TruncIfPossible(Optional<APInt> X, unsigned BitWidth) {
    8432      286524 :   if (!X.hasValue())
    8433             :     return None;
    8434             :   unsigned W = X->getBitWidth();
    8435             :   if (BitWidth > 1 && BitWidth < W && X->isIntN(BitWidth))
    8436             :     return X->trunc(BitWidth);
    8437       18400 :   return X;
    8438             : }
    8439       31329 : 
    8440       25858 : /// Let c(n) be the value of the quadratic chrec {L,+,M,+,N} after n
    8441       12929 : /// iterations. The values L, M, N are assumed to be signed, and they
    8442             : /// should all have the same bit widths.
    8443       18400 : /// Find the least n >= 0 such that c(n) = 0 in the arithmetic modulo 2^BW,
    8444        4248 : /// where BW is the bit width of the addrec's coefficients.
    8445       14152 : /// If the calculated value is a BW-bit integer (for BW > 1), it will be
    8446       14145 : /// returned as such, otherwise the bit width of the returned value may
    8447           7 : /// be greater than BW.
    8448           4 : ///
    8449           3 : /// This function returns None if
    8450           3 : /// (a) the addrec coefficients are not constant, or
    8451           0 : /// (b) SolveQuadraticEquationWrap was unable to find a solution. For cases
    8452             : ///     like x^2 = 5, no integer solutions exist, in other cases an integer
    8453             : ///     solution may exist, but SolveQuadraticEquationWrap may fail to find it.
    8454             : static Optional<APInt>
    8455             : SolveQuadraticAddRecExact(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
    8456             :   APInt A, B, C, M;
    8457             :   unsigned BitWidth;
    8458             :   auto T = GetQuadraticEquation(AddRec);
    8459        3196 :   if (!T.hasValue())
    8460        3196 :     return None;
    8461        3196 : 
    8462             :   std::tie(A, B, C, M, BitWidth) = *T;
    8463           8 :   LLVM_DEBUG(dbgs() << __func__ << ": solving for unsigned overflow\n");
    8464             :   Optional<APInt> X = APIntOps::SolveQuadraticEquationWrap(A, B, C, BitWidth+1);
    8465             :   if (!X.hasValue())
    8466             :     return None;
    8467             : 
    8468             :   ConstantInt *CX = ConstantInt::get(SE.getContext(), *X);
    8469             :   ConstantInt *V = EvaluateConstantChrecAtConstant(AddRec, CX, SE);
    8470             :   if (!V->isZero())
    8471             :     return None;
    8472      149155 : 
    8473      201828 :   return TruncIfPossible(X, BitWidth);
    8474      201828 : }
    8475       97534 : 
    8476             : /// Let c(n) be the value of the quadratic chrec {0,+,M,+,N} after n
    8477             : /// iterations. The values M, N are assumed to be signed, and they
    8478             : /// should all have the same bit widths.
    8479             : /// Find the least n such that c(n) does not belong to the given range,
    8480             : /// while c(n-1) does.
    8481        3380 : ///
    8482       10232 : /// This function returns None if
    8483       13704 : /// (a) the addrec coefficients are not constant, or
    8484             : /// (b) SolveQuadraticEquationWrap was unable to find a solution for the
    8485             : ///     bounds of the range.
    8486        6760 : static Optional<APInt>
    8487             : SolveQuadraticAddRecRange(const SCEVAddRecExpr *AddRec,
    8488             :                           const ConstantRange &Range, ScalarEvolution &SE) {
    8489             :   assert(AddRec->getOperand(0)->isZero() &&
    8490             :          "Starting value of addrec should be 0");
    8491             :   LLVM_DEBUG(dbgs() << __func__ << ": solving boundary crossing for range "
    8492             :                     << Range << ", addrec " << *AddRec << '\n');
    8493             :   // This case is handled in getNumIterationsInRange. Here we can assume that
    8494             :   // we start in the range.
    8495             :   assert(Range.contains(APInt(SE.getTypeSizeInBits(AddRec->getType()), 0)) &&
    8496             :          "Addrec's initial value should be in range");
    8497             : 
    8498             :   APInt A, B, C, M;
    8499      101222 :   unsigned BitWidth;
    8500             :   auto T = GetQuadraticEquation(AddRec);
    8501             :   if (!T.hasValue())
    8502        4693 :     return None;
    8503        4693 : 
    8504             :   // Be careful about the return value: there can be two reasons for not
    8505             :   // returning an actual number. First, if no solutions to the equations
    8506        4060 :   // were found, and second, if the solutions don't leave the given range.
    8507             :   // The first case means that the actual solution is "unknown", the second
    8508             :   // means that it's known, but not valid. If the solution is unknown, we
    8509             :   // cannot make any conclusions.
    8510             :   // Return a pair: the optional solution and a flag indicating if the
    8511             :   // solution was found.
    8512             :   auto SolveForBoundary = [&](APInt Bound) -> std::pair<Optional<APInt>,bool> {
    8513        3208 :     // Solve for signed overflow and unsigned overflow, pick the lower
    8514        3208 :     // solution.
    8515             :     LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: checking boundary "
    8516          20 :                       << Bound << " (before multiplying by " << M << ")\n");
    8517             :     Bound *= M; // The quadratic equation multiplier.
    8518             : 
    8519             :     Optional<APInt> SO = None;
    8520        2135 :     if (BitWidth > 1) {
    8521        2135 :       LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for "
    8522             :                            "signed overflow\n");
    8523          44 :       SO = APIntOps::SolveQuadraticEquationWrap(A, B, -Bound, BitWidth);
    8524             :     }
    8525             :     LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for "
    8526             :                          "unsigned overflow\n");
    8527        2278 :     Optional<APInt> UO = APIntOps::SolveQuadraticEquationWrap(A, B, -Bound,
    8528        2278 :                                                               BitWidth+1);
    8529             : 
    8530           9 :     auto LeavesRange = [&] (const APInt &X) {
    8531             :       ConstantInt *C0 = ConstantInt::get(SE.getContext(), X);
    8532             :       ConstantInt *V0 = EvaluateConstantChrecAtConstant(AddRec, C0, SE);
    8533           0 :       if (Range.contains(V0->getValue()))
    8534             :         return false;
    8535             :       // X should be at least 1, so X-1 is non-negative.
    8536      216416 :       ConstantInt *C1 = ConstantInt::get(SE.getContext(), X-1);
    8537      216416 :       ConstantInt *V1 = EvaluateConstantChrecAtConstant(AddRec, C1, SE);
    8538             :       if (Range.contains(V1->getValue()))
    8539             :         return true;
    8540       12657 :       return false;
    8541             :     };
    8542          62 : 
    8543             :     // If SolveQuadraticEquationWrap returns None, it means that there can
    8544           0 :     // be a solution, but the function failed to find it. We cannot treat it
    8545             :     // as "no solution".
    8546             :     if (!SO.hasValue() || !UO.hasValue())
    8547             :       return { None, false };
    8548             : 
    8549             :     // Check the smaller value first to see if it leaves the range.
    8550             :     // At this point, both SO and UO must have values.
    8551             :     Optional<APInt> Min = MinOptional(SO, UO);
    8552             :     if (LeavesRange(*Min))
    8553             :       return { Min, true };
    8554             :     Optional<APInt> Max = Min == SO ? UO : SO;
    8555             :     if (LeavesRange(*Max))
    8556        2676 :       return { Max, true };
    8557             : 
    8558        2676 :     // Solutions were found, but were eliminated, hence the "true".
    8559             :     return { None, true };
    8560             :   };
    8561             : 
    8562             :   std::tie(A, B, C, M, BitWidth) = *T;
    8563             :   // Lower bound is inclusive, subtract 1 to represent the exiting value.
    8564             :   APInt Lower = Range.getLower().sextOrSelf(A.getBitWidth()) - 1;
    8565             :   APInt Upper = Range.getUpper().sextOrSelf(A.getBitWidth());
    8566        2676 :   auto SL = SolveForBoundary(Lower);
    8567             :   auto SU = SolveForBoundary(Upper);
    8568             :   // If any of the solutions was unknown, no meaninigful conclusions can
    8569             :   // be made.
    8570             :   if (!SL.second || !SU.second)
    8571             :     return None;
    8572             : 
    8573        2676 :   // Claim: The correct solution is not some value between Min and Max.
    8574        2188 :   //
    8575             :   // Justification: Assuming that Min and Max are different values, one of
    8576             :   // them is when the first signed overflow happens, the other is when the
    8577             :   // first unsigned overflow happens. Crossing the range boundary is only
    8578             :   // possible via an overflow (treating 0 as a special case of it, modeling
    8579             :   // an overflow as crossing k*2^W for some k).
    8580             :   //
    8581             :   // The interesting case here is when Min was eliminated as an invalid
    8582         976 :   // solution, but Max was not. The argument is that if there was another
    8583             :   // overflow between Min and Max, it would also have been eliminated if
    8584         488 :   // it was considered.
    8585         488 :   //
    8586             :   // For a given boundary, it is possible to have two overflows of the same
    8587             :   // type (signed/unsigned) without having the other type in between: this
    8588             :   // can happen when the vertex of the parabola is between the iterations
    8589             :   // corresponding to the overflows. This is only possible when the two
    8590             :   // overflows cross k*2^W for the same k. In such case, if the second one
    8591         488 :   // left the range (and was the first one to do so), the first overflow
    8592         488 :   // would have to enter the range, which would mean that either we had left
    8593             :   // the range before or that we started outside of it. Both of these cases
    8594             :   // are contradictions.
    8595             :   //
    8596             :   // Claim: In the case where SolveForBoundary returns None, the correct
    8597             :   // solution is not some value between the Max for this boundary and the
    8598             :   // Min of the other boundary.
    8599             :   //
    8600             :   // Justification: Assume that we had such Max_A and Min_B corresponding
    8601             :   // to range boundaries A and B and such that Max_A < Min_B. If there was
    8602             :   // a solution between Max_A and Min_B, it would have to be caused by an
    8603             :   // overflow corresponding to either A or B. It cannot correspond to B,
    8604             :   // since Min_B is the first occurrence of such an overflow. If it
    8605          25 :   // corresponded to A, it would have to be either a signed or an unsigned
    8606             :   // overflow that is larger than both eliminated overflows for A. But
    8607          25 :   // between the eliminated overflows and this overflow, the values would
    8608             :   // cover the entire value space, thus crossing the other boundary, which
    8609             :   // is a contradiction.
    8610             : 
    8611             :   return TruncIfPossible(MinOptional(SL.first, SU.first), BitWidth);
    8612             : }
    8613             : 
    8614          25 : ScalarEvolution::ExitLimit
    8615             : ScalarEvolution::howFarToZero(const SCEV *V, const Loop *L, bool ControlsExit,
    8616             :                               bool AllowPredicates) {
    8617             : 
    8618             :   // This is only used for loops with a "x != y" exit test. The exit condition
    8619             :   // is now expressed as a single expression, V = x-y. So the exit test is
    8620             :   // effectively V != 0.  We know and take advantage of the fact that this
    8621             :   // expression only being used in a comparison by zero context.
    8622             : 
    8623             :   SmallPtrSet<const SCEVPredicate *, 4> Predicates;
    8624          25 :   // If the value is a constant
    8625          25 :   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
    8626             :     // If the value is already zero, the branch will execute zero times.
    8627             :     if (C->getValue()->isZero()) return C;
    8628             :     return getCouldNotCompute();  // Otherwise it will loop infinitely.
    8629             :   }
    8630          25 : 
    8631          25 :   const SCEVAddRecExpr *AddRec =
    8632          50 :       dyn_cast<SCEVAddRecExpr>(stripInjectiveFunctions(V));
    8633             : 
    8634             :   if (!AddRec && AllowPredicates)
    8635             :     // Try to make this an AddRec using runtime tests, in the first X
    8636             :     // iterations of this loop, where X is the SCEV expression found by the
    8637             :     // algorithm below.
    8638             :     AddRec = convertSCEVToAddRecWithPredicates(V, L, Predicates);
    8639             : 
    8640             :   if (!AddRec || AddRec->getLoop() != L)
    8641             :     return getCouldNotCompute();
    8642             : 
    8643             :   // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
    8644             :   // the quadratic equation to solve it.
    8645          25 :   if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
    8646          25 :     // We can only use this value if the chrec ends up with an exact zero
    8647             :     // value at this index.  When solving for "X*X != 5", for example, we
    8648             :     // should not accept a root of 2.
    8649             :     if (auto S = SolveQuadraticAddRecExact(AddRec, *this)) {
    8650             :       const auto *R = cast<SCEVConstant>(getConstant(S.getValue()));
    8651          25 :       return ExitLimit(R, R, false, Predicates);
    8652             :     }
    8653             :     return getCouldNotCompute();
    8654             :   }
    8655             : 
    8656             :   // Otherwise we can only handle this if it is affine.
    8657             :   if (!AddRec->isAffine())
    8658          42 :     return getCouldNotCompute();
    8659          42 : 
    8660          30 :   // If this is an affine expression, the execution count of this branch is
    8661          30 :   // the minimum unsigned root of the following equation:
    8662          30 :   //
    8663          30 :   //     Start + Step*N = 0 (mod 2^BW)
    8664             :   //
    8665          12 :   // equivalent to:
    8666             :   //
    8667           6 :   //             Step*N = -Start (mod 2^BW)
    8668             :   //
    8669             :   // where BW is the common bit width of Start and Step.
    8670             : 
    8671             :   // Get the initial value for the loop.
    8672             :   const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
    8673             :   const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
    8674             : 
    8675             :   // For now we handle only constant steps.
    8676             :   //
    8677             :   // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
    8678             :   // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
    8679             :   // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
    8680             :   // We have not yet seen any such cases.
    8681          16 :   const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
    8682          16 :   if (!StepC || StepC->getValue()->isZero())
    8683             :     return getCouldNotCompute();
    8684          10 : 
    8685          10 :   // For positive steps (counting up until unsigned overflow):
    8686           8 :   //   N = -Start/Step (as unsigned)
    8687             :   // For negative steps (counting down to zero):
    8688             :   //   N = Start/-Step
    8689             :   // First compute the unsigned distance from zero in the direction of Step.
    8690             :   bool CountDown = StepC->getAPInt().isNegative();
    8691             :   const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
    8692             : 
    8693             :   // Handle unitary steps, which cannot wraparound.
    8694             :   // 1*N = -Start; -1*N = Start (mod 2^BW), so:
    8695             :   //   N = Distance (as unsigned)
    8696             :   if (StepC->getValue()->isOne() || StepC->getValue()->isMinusOne()) {
    8697             :     APInt MaxBECount = getUnsignedRangeMax(Distance);
    8698             : 
    8699             :     // When a loop like "for (int i = 0; i != n; ++i) { /* body */ }" is rotated,
    8700             :     // we end up with a loop whose backedge-taken count is n - 1.  Detect this
    8701             :     // case, and see if we can improve the bound.
    8702             :     //
    8703             :     // Explicitly handling this here is necessary because getUnsignedRange
    8704             :     // isn't context-sensitive; it doesn't know that we only care about the
    8705          11 :     // range inside the loop.
    8706             :     const SCEV *Zero = getZero(Distance->getType());
    8707             :     const SCEV *One = getOne(Distance->getType());
    8708          11 :     const SCEV *DistancePlusOne = getAddExpr(Distance, One);
    8709          11 :     if (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, DistancePlusOne, Zero)) {
    8710             :       // If Distance + 1 doesn't overflow, we can compute the maximum distance
    8711             :       // as "unsigned_max(Distance + 1) - 1".
    8712          11 :       ConstantRange CR = getUnsignedRange(DistancePlusOne);
    8713             :       MaxBECount = APIntOps::umin(MaxBECount, CR.getUnsignedMax() - 1);
    8714          42 :     }
    8715          11 :     return ExitLimit(Distance, getConstant(MaxBECount), false, Predicates);
    8716             :   }
    8717             : 
    8718          11 :   // If the condition controls loop exit (the loop exits only if the expression
    8719          11 :   // is true) and the addition is no-wrap we can use unsigned divide to
    8720          11 :   // compute the backedge count.  In this case, the step may not divide the
    8721             :   // distance, but we don't care because if the condition is "missed" the loop
    8722             :   // will have undefined behavior due to wrapping.
    8723           6 :   if (ControlsExit && AddRec->hasNoSelfWrap() &&
    8724             :       loopHasNoAbnormalExits(AddRec->getLoop())) {
    8725             :     const SCEV *Exact =
    8726             :         getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
    8727             :     const SCEV *Max =
    8728             :         Exact == getCouldNotCompute()
    8729             :             ? Exact
    8730             :             : getConstant(getUnsignedRangeMax(Exact));
    8731             :     return ExitLimit(Exact, Max, false, Predicates);
    8732             :   }
    8733             : 
    8734             :   // Solve the general equation.
    8735             :   const SCEV *E = SolveLinEquationWithOverflow(StepC->getAPInt(),
    8736             :                                                getNegativeSCEV(Start), *this);
    8737          14 :   const SCEV *M = E == getCouldNotCompute()
    8738             :                       ? E
    8739             :                       : getConstant(getUnsignedRangeMax(E));
    8740             :   return ExitLimit(E, M, false, Predicates);
    8741             : }
    8742             : 
    8743             : ScalarEvolution::ExitLimit
    8744             : ScalarEvolution::howFarToNonZero(const SCEV *V, const Loop *L) {
    8745             :   // Loops that look like: while (X == 0) are very strange indeed.  We don't
    8746             :   // handle them yet except for the trivial case.  This could be expanded in the
    8747             :   // future as needed.
    8748             : 
    8749             :   // If the value is a constant, check to see if it is known to be non-zero
    8750          14 :   // already.  If so, the backedge will execute zero times.
    8751          14 :   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
    8752             :     if (!C->getValue()->isZero())
    8753             :       return getZero(C->getType());
    8754             :     return getCouldNotCompute();  // Otherwise it will loop infinitely.
    8755             :   }
    8756             : 
    8757             :   // We could implement others, but I really doubt anyone writes loops like
    8758             :   // this, and if they did, they would already be constant folded.
    8759             :   return getCouldNotCompute();
    8760             : }
    8761             : 
    8762             : std::pair<BasicBlock *, BasicBlock *>
    8763             : ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
    8764             :   // If the block has a unique predecessor, then there is no path from the
    8765             :   // predecessor to the block that does not go through the direct edge
    8766             :   // from the predecessor to the block.
    8767             :   if (BasicBlock *Pred = BB->getSinglePredecessor())
    8768             :     return {Pred, BB};
    8769             : 
    8770             :   // A loop's header is defined to be a block that dominates the loop.
    8771             :   // If the header has a unique predecessor outside the loop, it must be
    8772             :   // a block that has exactly one successor that can reach the loop.
    8773             :   if (Loop *L = LI.getLoopFor(BB))
    8774             :     return {L->getLoopPredecessor(), L->getHeader()};
    8775             : 
    8776             :   return {nullptr, nullptr};
    8777             : }
    8778             : 
    8779             : /// SCEV structural equivalence is usually sufficient for testing whether two
    8780             : /// expressions are equal, however for the purposes of looking for a condition
    8781             : /// guarding a loop, it can be useful to be a little more general, since a
    8782             : /// front-end may have replicated the controlling expression.
    8783             : static bool HasSameValue(const SCEV *A, const SCEV *B) {
    8784             :   // Quick check to see if they are the same SCEV.
    8785             :   if (A == B) return true;
    8786             : 
    8787             :   auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
    8788             :     // Not all instructions that are "identical" compute the same value.  For
    8789             :     // instance, two distinct alloca instructions allocating the same type are
    8790             :     // identical and do not read memory; but compute distinct values.
    8791             :     return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
    8792             :   };
    8793             : 
    8794             :   // Otherwise, if they're both SCEVUnknown, it's possible that they hold
    8795             :   // two different instructions with the same value. Check for this case.
    8796             :   if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
    8797             :     if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
    8798             :       if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
    8799             :         if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
    8800             :           if (ComputesEqualValues(AI, BI))
    8801             :             return true;
    8802             : 
    8803             :   // Otherwise assume they may have a different value.
    8804             :   return false;
    8805             : }
    8806             : 
    8807             : bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
    8808             :                                            const SCEV *&LHS, const SCEV *&RHS,
    8809             :                                            unsigned Depth) {
    8810          14 :   bool Changed = false;
    8811             :   // Simplifies ICMP to trivial true or false by turning it into '0 == 0' or
    8812          14 :   // '0 != 0'.
    8813             :   auto TrivialCase = [&](bool TriviallyTrue) {
    8814          28 :     LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
    8815          14 :     Pred = TriviallyTrue ? ICmpInst::ICMP_EQ : ICmpInst::ICMP_NE;
    8816          28 :     return true;
    8817          14 :   };
    8818             :   // If we hit the max recursion limit bail out.
    8819             :   if (Depth >= 3)
    8820          14 :     return false;
    8821             : 
    8822             :   // Canonicalize a constant to the right side.
    8823             :   if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
    8824             :     // Check for both operands constant.
    8825             :     if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
    8826             :       if (ConstantExpr::getICmp(Pred,
    8827             :                                 LHSC->getValue(),
    8828             :                                 RHSC->getValue())->isNullValue())
    8829             :         return TrivialCase(false);
    8830             :       else
    8831             :         return TrivialCase(true);
    8832             :     }
    8833             :     // Otherwise swap the operands to put the constant on the right.
    8834             :     std::swap(LHS, RHS);
    8835             :     Pred = ICmpInst::getSwappedPredicate(Pred);
    8836             :     Changed = true;
    8837             :   }
    8838             : 
    8839             :   // If we're comparing an addrec with a value which is loop-invariant in the
    8840             :   // addrec's loop, put the addrec on the left. Also make a dominance check,
    8841             :   // as both operands could be addrecs loop-invariant in each other's loop.
    8842             :   if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
    8843             :     const Loop *L = AR->getLoop();
    8844             :     if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
    8845             :       std::swap(LHS, RHS);
    8846             :       Pred = ICmpInst::getSwappedPredicate(Pred);
    8847             :       Changed = true;
    8848             :     }
    8849             :   }
    8850             : 
    8851             :   // If there's a constant operand, canonicalize comparisons with boundary
    8852             :   // cases, and canonicalize *-or-equal comparisons to regular comparisons.
    8853             :   if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
    8854             :     const APInt &RA = RC->getAPInt();
    8855             : 
    8856             :     bool SimplifiedByConstantRange = false;
    8857             : 
    8858             :     if (!ICmpInst::isEquality(Pred)) {
    8859             :       ConstantRange ExactCR = ConstantRange::makeExactICmpRegion(Pred, RA);
    8860             :       if (ExactCR.isFullSet())
    8861          42 :         return TrivialCase(true);
    8862             :       else if (ExactCR.isEmptySet())
    8863             :         return TrivialCase(false);
    8864             : 
    8865       12673 :       APInt NewRHS;
    8866             :       CmpInst::Predicate NewPred;
    8867             :       if (ExactCR.getEquivalentICmp(NewPred, NewRHS) &&
    8868             :           ICmpInst::isEquality(NewPred)) {
    8869             :         // We were able to convert an inequality to an equality.
    8870             :         Pred = NewPred;
    8871             :         RHS = getConstant(NewRHS);
    8872             :         Changed = SimplifiedByConstantRange = true;
    8873             :       }
    8874             :     }
    8875             : 
    8876             :     if (!SimplifiedByConstantRange) {
    8877          32 :       switch (Pred) {
    8878           0 :       default:
    8879             :         break;
    8880             :       case ICmpInst::ICMP_EQ:
    8881             :       case ICmpInst::ICMP_NE:
    8882       12657 :         // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
    8883             :         if (!RA)
    8884       12657 :           if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
    8885             :             if (const SCEVMulExpr *ME =
    8886             :                     dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
    8887             :               if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
    8888         480 :                   ME->getOperand(0)->isAllOnesValue()) {
    8889             :                 RHS = AE->getOperand(1);
    8890       12657 :                 LHS = ME->getOperand(1);
    8891        4905 :                 Changed = true;
    8892             :               }
    8893             :         break;
    8894             : 
    8895        7769 : 
    8896             :         // The "Should have been caught earlier!" messages refer to the fact
    8897             :         // that the ExactCR.isFullSet() or ExactCR.isEmptySet() check above
    8898             :         // should have fired on the corresponding cases, and canonicalized the
    8899          11 :         // check to trivial case.
    8900           2 : 
    8901           2 :       case ICmpInst::ICMP_UGE:
    8902             :         assert(!RA.isMinValue() && "Should have been caught earlier!");
    8903           9 :         Pred = ICmpInst::ICMP_UGT;
    8904             :         RHS = getConstant(RA - 1);
    8905             :         Changed = true;
    8906             :         break;
    8907        7741 :       case ICmpInst::ICMP_ULE:
    8908           6 :         assert(!RA.isMaxValue() && "Should have been caught earlier!");
    8909             :         Pred = ICmpInst::ICMP_ULT;
    8910             :         RHS = getConstant(RA + 1);
    8911             :         Changed = true;
    8912             :         break;
    8913             :       case ICmpInst::ICMP_SGE:
    8914             :         assert(!RA.isMinSignedValue() && "Should have been caught earlier!");
    8915             :         Pred = ICmpInst::ICMP_SGT;
    8916             :         RHS = getConstant(RA - 1);
    8917             :         Changed = true;
    8918             :         break;
    8919             :       case ICmpInst::ICMP_SLE:
    8920             :         assert(!RA.isMaxSignedValue() && "Should have been caught earlier!");
    8921             :         Pred = ICmpInst::ICMP_SLT;
    8922       15470 :         RHS = getConstant(RA + 1);
    8923       15470 :         Changed = true;
    8924             :         break;
    8925             :       }
    8926             :     }
    8927             :   }
    8928             : 
    8929             :   // Check for obvious equality.
    8930             :   if (HasSameValue(LHS, RHS)) {
    8931             :     if (ICmpInst::isTrueWhenEqual(Pred))
    8932       15338 :       return TrivialCase(true);
    8933          69 :     if (ICmpInst::isFalseWhenEqual(Pred))
    8934             :       return TrivialCase(false);
    8935             :   }
    8936             : 
    8937             :   // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
    8938             :   // adding or subtracting 1 from one of the operands.
    8939             :   switch (Pred) {
    8940        7666 :   case ICmpInst::ICMP_SLE:
    8941        7666 :     if (!getSignedRangeMax(RHS).isMaxSignedValue()) {
    8942             :       RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
    8943             :                        SCEV::FlagNSW);
    8944             :       Pred = ICmpInst::ICMP_SLT;
    8945             :       Changed = true;
    8946       19882 :     } else if (!getSignedRangeMin(LHS).isMinSignedValue()) {
    8947             :       LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
    8948             :                        SCEV::FlagNSW);
    8949             :       Pred = ICmpInst::ICMP_SLT;
    8950             :       Changed = true;
    8951             :     }
    8952             :     break;
    8953             :   case ICmpInst::ICMP_SGE:
    8954             :     if (!getSignedRangeMin(RHS).isMinSignedValue()) {
    8955             :       RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
    8956        4182 :                        SCEV::FlagNSW);
    8957        4182 :       Pred = ICmpInst::ICMP_SGT;
    8958        4182 :       Changed = true;
    8959        4182 :     } else if (!getSignedRangeMax(LHS).isMaxSignedValue()) {
    8960             :       LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
    8961             :                        SCEV::FlagNSW);
    8962        2611 :       Pred = ICmpInst::ICMP_SGT;
    8963        7833 :       Changed = true;
    8964             :     }
    8965        4182 :     break;
    8966             :   case ICmpInst::ICMP_ULE:
    8967             :     if (!getUnsignedRangeMax(RHS).isMaxValue()) {
    8968             :       RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
    8969             :                        SCEV::FlagNUW);
    8970             :       Pred = ICmpInst::ICMP_ULT;
    8971             :       Changed = true;
    8972             :     } else if (!getUnsignedRangeMin(LHS).isMinValue()) {
    8973        5272 :       LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS);
    8974        1788 :       Pred = ICmpInst::ICMP_ULT;
    8975             :       Changed = true;
    8976         808 :     }
    8977             :     break;
    8978         808 :   case ICmpInst::ICMP_UGE:
    8979         808 :     if (!getUnsignedRangeMin(RHS).isMinValue()) {
    8980         808 :       RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
    8981         808 :       Pred = ICmpInst::ICMP_UGT;
    8982             :       Changed = true;
    8983             :     } else if (!getUnsignedRangeMax(LHS).isMaxValue()) {
    8984             :       LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
    8985        2676 :                        SCEV::FlagNUW);
    8986             :       Pred = ICmpInst::ICMP_UGT;
    8987        2676 :       Changed = true;
    8988        2676 :     }
    8989         488 :     break;
    8990        2676 :   default:
    8991             :     break;
    8992             :   }
    8993             : 
    8994        1568 :   // TODO: More simplifications are possible here.
    8995             : 
    8996             :   // Recursively simplify until we either hit a recursion limit or nothing
    8997             :   // changes.
    8998             :   if (Changed)
    8999             :     return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
    9000             : 
    9001             :   return Changed;
    9002          44 : }
    9003           0 : 
    9004          22 : bool ScalarEvolution::isKnownNegative(const SCEV *S) {
    9005             :   return getSignedRangeMax(S).isNegative();
    9006             : }
    9007             : 
    9008             : bool ScalarEvolution::isKnownPositive(const SCEV *S) {
    9009        1546 :   return getSignedRangeMin(S).isStrictlyPositive();
    9010             : }
    9011             : 
    9012             : bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
    9013       63133 :   return !getSignedRangeMin(S).isNegative();
    9014             : }
    9015             : 
    9016             : bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
    9017       63133 :   return !getSignedRangeMax(S).isStrictlyPositive();
    9018       33390 : }
    9019             : 
    9020             : bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
    9021             :   return isKnownNegative(S) || isKnownPositive(S);
    9022             : }
    9023       40042 : 
    9024       10299 : std::pair<const SCEV *, const SCEV *>
    9025             : ScalarEvolution::SplitIntoInitAndPostInc(const Loop *L, const SCEV *S) {
    9026       19444 :   // Compute SCEV on entry of loop L.
    9027             :   const SCEV *Start = SCEVInitRewriter::rewrite(S, L, *this);
    9028             :   if (Start == getCouldNotCompute())
    9029             :     return { Start, Start };
    9030             :   // Compute post increment SCEV for loop L.
    9031             :   const SCEV *PostInc = SCEVPostIncRewriter::rewrite(S, L, *this);
    9032             :   assert(PostInc != getCouldNotCompute() && "Unexpected could not compute");
    9033      581302 :   return { Start, PostInc };
    9034             : }
    9035      581302 : 
    9036             : bool ScalarEvolution::isKnownViaInduction(ICmpInst::Predicate Pred,
    9037             :                                           const SCEV *LHS, const SCEV *RHS) {
    9038             :   // First collect all loops.
    9039             :   SmallPtrSet<const Loop *, 8> LoopsUsed;
    9040             :   getUsedLoops(LHS, LoopsUsed);
    9041             :   getUsedLoops(RHS, LoopsUsed);
    9042             : 
    9043             :   if (LoopsUsed.empty())
    9044             :     return false;
    9045             : 
    9046       88029 :   // Domination relationship must be a linear order on collected loops.
    9047       17234 : #ifndef NDEBUG
    9048             :   for (auto *L1 : LoopsUsed)
    9049             :     for (auto *L2 : LoopsUsed)
    9050       10609 :       assert((DT.dominates(L1->getHeader(), L2->getHeader()) ||
    9051           4 :               DT.dominates(L2->getHeader(), L1->getHeader())) &&
    9052             :              "Domination relationship is not a linear order");
    9053             : #endif
    9054             : 
    9055             :   const Loop *MDL =
    9056             :       *std::max_element(LoopsUsed.begin(), LoopsUsed.end(),
    9057      313243 :                         [&](const Loop *L1, const Loop *L2) {
    9058             :          return DT.properlyDominates(L1->getHeader(), L2->getHeader());
    9059             :        });
    9060             : 
    9061             :   // Get init and post increment value for LHS.
    9062             :   auto SplitLHS = SplitIntoInitAndPostInc(MDL, LHS);
    9063             :   // if LHS contains unknown non-invariant SCEV then bail out.
    9064             :   if (SplitLHS.first == getCouldNotCompute())
    9065             :     return false;
    9066             :   assert (SplitLHS.second != getCouldNotCompute() && "Unexpected CNC");
    9067      313243 :   // Get init and post increment value for RHS.
    9068             :   auto SplitRHS = SplitIntoInitAndPostInc(MDL, RHS);
    9069      313243 :   // if RHS contains unknown non-invariant SCEV then bail out.
    9070             :   if (SplitRHS.first == getCouldNotCompute())
    9071             :     return false;
    9072             :   assert (SplitRHS.second != getCouldNotCompute() && "Unexpected CNC");
    9073      313243 :   // It is possible that init SCEV contains an invariant load but it does
    9074             :   // not dominate MDL and is not available at MDL loop entry, so we should
    9075       27121 :   // check it here.
    9076       10396 :   if (!isAvailableAtLoopEntry(SplitLHS.first, MDL) ||
    9077       10396 :       !isAvailableAtLoopEntry(SplitRHS.first, MDL))
    9078       10396 :     return false;
    9079        8307 : 
    9080             :   return isLoopEntryGuardedByCond(MDL, Pred, SplitLHS.first, SplitRHS.first) &&
    9081        2089 :          isLoopBackedgeGuardedByCond(MDL, Pred, SplitLHS.second,
    9082             :                                      SplitRHS.second);
    9083             : }
    9084             : 
    9085       16725 : bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
    9086             :                                        const SCEV *LHS, const SCEV *RHS) {
    9087             :   // Canonicalize the inputs first.
    9088             :   (void)SimplifyICmpOperands(Pred, LHS, RHS);
    9089             : 
    9090             :   if (isKnownViaInduction(Pred, LHS, RHS))
    9091             :     return true;
    9092      302847 : 
    9093        2178 :   if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
    9094        2178 :     return true;
    9095             : 
    9096         361 :   // Otherwise see what can be done with some simple reasoning.
    9097             :   return isKnownViaNonRecursiveReasoning(Pred, LHS, RHS);
    9098             : }
    9099             : 
    9100             : bool ScalarEvolution::isKnownOnEveryIteration(ICmpInst::Predicate Pred,
    9101             :                                               const SCEVAddRecExpr *LHS,
    9102             :                                               const SCEV *RHS) {
    9103      302847 :   const Loop *L = LHS->getLoop();
    9104             :   return isLoopEntryGuardedByCond(L, Pred, LHS->getStart(), RHS) &&
    9105             :          isLoopBackedgeGuardedByCond(L, Pred, LHS->getPostIncExpr(*this), RHS);
    9106             : }
    9107             : 
    9108      468202 : bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
    9109      285592 :                                            ICmpInst::Predicate Pred,
    9110      142848 :                                            bool &Increasing) {
    9111         104 :   bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
    9112      142839 : 
    9113          95 : #ifndef NDEBUG
    9114             :   // Verify an invariant: inverting the predicate should turn a monotonically
    9115             :   // increasing change to a monotonically decreasing one, and vice versa.
    9116             :   bool IncreasingSwapped;
    9117      142744 :   bool ResultSwapped = isMonotonicPredicateImpl(
    9118      142744 :       LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
    9119             : 
    9120       27440 :   assert(Result == ResultSwapped && "should be able to analyze both!");
    9121       27440 :   if (ResultSwapped)
    9122             :     assert(Increasing == !IncreasingSwapped &&
    9123             :            "monotonicity should flip as we flip the predicate");
    9124             : #endif
    9125             : 
    9126      233997 :   return Result;
    9127      206557 : }
    9128             : 
    9129             : bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
    9130             :                                                ICmpInst::Predicate Pred,
    9131             :                                                bool &Increasing) {
    9132             : 
    9133       91253 :   // A zero step value for LHS means the induction variable is essentially a
    9134       41223 :   // loop invariant value. We don't really depend on the predicate actually
    9135             :   // flipping from false to true (for increasing predicates, and the other way
    9136        6283 :   // around for decreasing predicates), all we care about is that *if* the
    9137        2603 :   // predicate changes then it only changes from false to true.
    9138        2458 :   //
    9139        1146 :   // A zero step value in itself is not very useful, but there may be places
    9140        2292 :   // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
    9141             :   // as general as possible.
    9142             : 
    9143             :   switch (Pred) {
    9144             :   default:
    9145             :     return false; // Conservative answer
    9146             : 
    9147             :   case ICmpInst::ICMP_UGT:
    9148             :   case ICmpInst::ICMP_UGE:
    9149             :   case ICmpInst::ICMP_ULT:
    9150             :   case ICmpInst::ICMP_ULE:
    9151        4522 :     if (!LHS->hasNoUnsignedWrap())
    9152             :       return false;
    9153        4522 : 
    9154        4522 :     Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
    9155             :     return true;
    9156        4522 : 
    9157        2320 :   case ICmpInst::ICMP_SGT:
    9158             :   case ICmpInst::ICMP_SGE:
    9159        2320 :   case ICmpInst::ICMP_SLT:
    9160        2320 :   case ICmpInst::ICMP_SLE: {
    9161             :     if (!LHS->hasNoSignedWrap())
    9162        2320 :       return false;
    9163       10923 : 
    9164             :     const SCEV *Step = LHS->getStepRecurrence(*this);
    9165       10923 : 
    9166       10923 :     if (isKnownNonNegative(Step)) {
    9167             :       Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
    9168       10923 :       return true;
    9169        5614 :     }
    9170             : 
    9171        5614 :     if (isKnownNonPositive(Step)) {
    9172        5614 :       Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
    9173             :       return true;
    9174        5614 :     }
    9175             : 
    9176             :     return false;
    9177             :   }
    9178             : 
    9179             :   }
    9180      302743 : 
    9181         226 :   llvm_unreachable("switch has default clause!");
    9182         198 : }
    9183          28 : 
    9184          28 : bool ScalarEvolution::isLoopInvariantPredicate(
    9185             :     ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
    9186             :     ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
    9187             :     const SCEV *&InvariantRHS) {
    9188             : 
    9189      302517 :   // If there is a loop-invariant, force it into the RHS, otherwise bail out.
    9190        1959 :   if (!isLoopInvariant(RHS, L)) {
    9191        3918 :     if (!isLoopInvariant(LHS, L))
    9192         423 :       return false;
    9193             : 
    9194         423 :     std::swap(LHS, RHS);
    9195             :     Pred = ICmpInst::getSwappedPredicate(Pred);
    9196        3072 :   }
    9197         134 : 
    9198             :   const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
    9199         134 :   if (!ArLHS || ArLHS->getLoop() != L)
    9200             :     return false;
    9201             : 
    9202             :   bool Increasing;
    9203        3445 :   if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
    9204        6890 :     return false;
    9205         850 : 
    9206             :   // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
    9207         850 :   // true as the loop iterates, and the backedge is control dependent on
    9208             :   // "ArLHS `Pred` RHS" == true then we can reason as follows:
    9209        5190 :   //
    9210         210 :   //   * if the predicate was false in the first iteration then the predicate
    9211             :   //     is never evaluated again, since the loop exits without taking the
    9212         210 :   //     backedge.
    9213             :   //   * if the predicate was true in the first iteration then it will
    9214             :   //     continue to be true for all future iterations since it is
    9215             :   //     monotonically increasing.
    9216        1702 :   //
    9217        3404 :   // For both the above possibilities, we can replace the loop varying
    9218         457 :   // predicate with its value on the first iteration of the loop (which is
    9219             :   // loop invariant).
    9220         457 :   //
    9221             :   // A similar reasoning applies for a monotonically decreasing predicate, by
    9222        2490 :   // replacing true with false and false with true in the above two bullets.
    9223          48 : 
    9224          48 :   auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
    9225             : 
    9226             :   if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
    9227             :     return false;
    9228        3385 : 
    9229        6770 :   InvariantPred = Pred;
    9230         194 :   InvariantLHS = ArLHS->getStart();
    9231         194 :   InvariantRHS = RHS;
    9232             :   return true;
    9233        6382 : }
    9234         891 : 
    9235             : bool ScalarEvolution::isKnownPredicateViaConstantRanges(
    9236         891 :     ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
    9237             :   if (HasSameValue(LHS, RHS))
    9238             :     return ICmpInst::isTrueWhenEqual(Pred);
    9239             : 
    9240             :   // This code is split out from isKnownPredicate because it is called from
    9241             :   // within isLoopEntryGuardedByCond.
    9242             : 
    9243             :   auto CheckRanges =
    9244             :       [&](const ConstantRange &RangeLHS, const ConstantRange &RangeRHS) {
    9245             :     return ConstantRange::makeSatisfyingICmpRegion(Pred, RangeRHS)
    9246             :         .contains(RangeLHS);
    9247             :   };
    9248      299310 : 
    9249       62905 :   // The check at the top of the function catches the case where the values are
    9250             :   // known to be equal.
    9251             :   if (Pred == CmpInst::ICMP_EQ)
    9252             :     return false;
    9253             : 
    9254       39390 :   if (Pred == CmpInst::ICMP_NE)
    9255       39390 :     return CheckRanges(getSignedRange(LHS), getSignedRange(RHS)) ||
    9256             :            CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS)) ||
    9257             :            isKnownNonZero(getMinusSCEV(LHS, RHS));
    9258       64863 : 
    9259       64863 :   if (CmpInst::isSigned(Pred))
    9260             :     return CheckRanges(getSignedRange(LHS), getSignedRange(RHS));
    9261             : 
    9262     1541314 :   return CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS));
    9263     1605557 : }
    9264             : 
    9265             : bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
    9266      147473 :                                                     const SCEV *LHS,
    9267      147473 :                                                     const SCEV *RHS) {
    9268             :   // Match Result to (X + Y)<ExpectedFlags> where Y is a constant integer.
    9269             :   // Return Y via OutY.
    9270       22755 :   auto MatchBinaryAddToConst =
    9271       22755 :       [this](const SCEV *Result, const SCEV *X, APInt &OutY,
    9272             :              SCEV::NoWrapFlags ExpectedFlags) {
    9273             :     const SCEV *NonConstOp, *ConstOp;
    9274             :     SCEV::NoWrapFlags FlagsPresent;
    9275       31206 : 
    9276             :     if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) ||
    9277       31206 :         !isa<SCEVConstant>(ConstOp) || NonConstOp != X)
    9278       31206 :       return false;
    9279        1241 : 
    9280             :     OutY = cast<SCEVConstant>(ConstOp)->getAPInt();
    9281       29965 :     return (FlagsPresent & ExpectedFlags) == ExpectedFlags;
    9282             :   };
    9283       29965 : 
    9284             :   APInt C;
    9285             : 
    9286       33486 :   switch (Pred) {
    9287             :   default:
    9288             :     break;
    9289             : 
    9290       33486 :   case ICmpInst::ICMP_SGE:
    9291       33486 :     std::swap(LHS, RHS);
    9292             :     LLVM_FALLTHROUGH;
    9293       33486 :   case ICmpInst::ICMP_SLE:
    9294             :     // X s<= (X + C)<nsw> if C >= 0
    9295             :     if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative())
    9296             :       return true;
    9297             : 
    9298             :     // (X + C)<nsw> s<= X if C <= 0
    9299             :     if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) &&
    9300             :         !C.isStrictlyPositive())
    9301             :       return true;
    9302             :     break;
    9303             : 
    9304             :   case ICmpInst::ICMP_SGT:
    9305             :     std::swap(LHS, RHS);
    9306             :     LLVM_FALLTHROUGH;
    9307             :   case ICmpInst::ICMP_SLT:
    9308           0 :     // X s< (X + C)<nsw> if C > 0
    9309       15701 :     if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) &&
    9310             :         C.isStrictlyPositive())
    9311             :       return true;
    9312       15701 : 
    9313             :     // (X + C)<nsw> s< X if C < 0
    9314       15701 :     if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative())
    9315             :       return true;
    9316             :     break;
    9317             :   }
    9318       15505 : 
    9319             :   return false;
    9320       15505 : }
    9321             : 
    9322             : bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
    9323             :                                                    const SCEV *LHS,
    9324             :                                                    const SCEV *RHS) {
    9325             :   if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
    9326       28920 :     return false;
    9327       14460 : 
    9328           0 :   // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
    9329             :   // the stack can result in exponential time complexity.
    9330       20206 :   SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
    9331        5746 : 
    9332             :   // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
    9333             :   //
    9334             :   // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
    9335       33486 :   // isKnownPredicate.  isKnownPredicate is more powerful, but also more
    9336             :   // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
    9337             :   // interesting cases seen in practice.  We can consider "upgrading" L >= 0 to
    9338       33486 :   // use isKnownPredicate later if needed.
    9339             :   return isKnownNonNegative(RHS) &&
    9340       33486 :          isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
    9341             :          isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS);
    9342             : }
    9343       31539 : 
    9344             : bool ScalarEvolution::isImpliedViaGuard(BasicBlock *BB,
    9345             :                                         ICmpInst::Predicate Pred,
    9346             :                                         const SCEV *LHS, const SCEV *RHS) {
    9347       31537 :   // No need to even try if we know the module has no guards.
    9348             :   if (!HasGuards)
    9349             :     return false;
    9350       12126 : 
    9351             :   return any_of(*BB, [&](Instruction &I) {
    9352             :     using namespace llvm::PatternMatch;
    9353       12126 : 
    9354       29882 :     Value *Condition;
    9355        5630 :     return match(&I, m_Intrinsic<Intrinsic::experimental_guard>(
    9356             :                          m_Value(Condition))) &&
    9357             :            isImpliedCond(Pred, LHS, RHS, Condition, false);
    9358         802 :   });
    9359             : }
    9360             : 
    9361         802 : /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
    9362             : /// protected by a conditional between LHS and RHS.  This is used to
    9363             : /// to eliminate casts.
    9364             : bool
    9365             : ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
    9366             :                                              ICmpInst::Predicate Pred,
    9367             :                                              const SCEV *LHS, const SCEV *RHS) {
    9368             :   // Interpret a null as meaning no loop, where there is obviously no guard
    9369             :   // (interprocedural conditions notwithstanding).
    9370             :   if (!L) return true;
    9371             : 
    9372             :   if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS))
    9373             :     return true;
    9374             : 
    9375             :   BasicBlock *Latch = L->getLoopLatch();
    9376         802 :   if (!Latch)
    9377             :     return false;
    9378             : 
    9379         802 :   BranchInst *LoopContinuePredicate =
    9380             :     dyn_cast<BranchInst>(Latch->getTerminator());
    9381             :   if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
    9382             :       isImpliedCond(Pred, LHS, RHS,
    9383             :                     LoopContinuePredicate->getCondition(),
    9384             :                     LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
    9385             :     return true;
    9386             : 
    9387             :   // We don't want more than one activation of the following loops on the stack
    9388             :   // -- that can lead to O(n!) time complexity.
    9389             :   if (WalkingBEDominatingConds)
    9390             :     return false;
    9391             : 
    9392             :   SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
    9393         802 : 
    9394             :   // See if we can exploit a trip count to prove the predicate.
    9395             :   const auto &BETakenInfo = getBackedgeTakenInfo(L);
    9396             :   const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
    9397         274 :   if (LatchBECount != getCouldNotCompute()) {
    9398             :     // We know that Latch branches back to the loop header exactly
    9399             :     // LatchBECount times.  This means the backdege condition at Latch is
    9400             :     // equivalent to  "{0,+,1} u< LatchBECount".
    9401         274 :     Type *Ty = LatchBECount->getType();
    9402             :     auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
    9403             :     const SCEV *LoopCounter =
    9404         181 :       getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
    9405         181 :     if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
    9406             :                       LatchBECount))
    9407         120 :       return true;
    9408             :   }
    9409             : 
    9410             :   // Check conditions due to any @llvm.assume intrinsics.
    9411         120 :   for (auto &AssumeVH : AC.assumptions()) {
    9412             :     if (!AssumeVH)
    9413             :       continue;
    9414         107 :     auto *CI = cast<CallInst>(AssumeVH);
    9415             :     if (!DT.dominates(CI, Latch->getTerminator()))
    9416         107 :       continue;
    9417          74 : 
    9418          74 :     if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
    9419             :       return true;
    9420             :   }
    9421          33 : 
    9422          31 :   // If the loop is not reachable from the entry block, we risk running into an
    9423          31 :   // infinite loop as we walk up into the dom tree.  These loops do not matter
    9424             :   // anyway, so we just return a conservative answer when we see them.
    9425             :   if (!DT.isReachableFromEntry(L->getHeader()))
    9426             :     return false;
    9427             : 
    9428             :   if (isImpliedViaGuard(Latch, Pred, LHS, RHS))
    9429             :     return true;
    9430             : 
    9431             :   for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
    9432             :        DTN != HeaderDTN; DTN = DTN->getIDom()) {
    9433             :     assert(DTN && "should reach the loop header before reaching the root!");
    9434        1541 : 
    9435             :     BasicBlock *BB = DTN->getBlock();
    9436             :     if (isImpliedViaGuard(BB, Pred, LHS, RHS))
    9437             :       return true;
    9438             : 
    9439             :     BasicBlock *PBB = BB->getSinglePredecessor();
    9440        1541 :     if (!PBB)
    9441         517 :       continue;
    9442             : 
    9443             :     BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
    9444             :     if (!ContinuePredicate || !ContinuePredicate->isConditional())
    9445           1 :       continue;
    9446             : 
    9447             :     Value *Condition = ContinuePredicate->getCondition();
    9448             : 
    9449         723 :     // If we have an edge `E` within the loop body that dominates the only
    9450             :     // latch, the condition guarding `E` also guards the backedge.  This
    9451             :     // reasoning works only for loops with a single latch.
    9452             : 
    9453         723 :     BasicBlockEdge DominatingEdge(PBB, BB);
    9454             :     if (DominatingEdge.isSingleEdge()) {
    9455             :       // We're constructively (and conservatively) enumerating edges within the
    9456             :       // loop body that dominate the latch.  The dominator tree better agree
    9457             :       // with us on this:
    9458             :       assert(DT.dominates(DominatingEdge, Latch) && "should be!");
    9459             : 
    9460             :       if (isImpliedCond(Pred, LHS, RHS, Condition,
    9461             :                         BB != ContinuePredicate->getSuccessor(0)))
    9462             :         return true;
    9463             :     }
    9464             :   }
    9465             : 
    9466             :   return false;
    9467             : }
    9468             : 
    9469             : bool
    9470             : ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
    9471             :                                           ICmpInst::Predicate Pred,
    9472             :                                           const SCEV *LHS, const SCEV *RHS) {
    9473             :   // Interpret a null as meaning no loop, where there is obviously no guard
    9474         272 :   // (interprocedural conditions notwithstanding).
    9475             :   if (!L) return false;
    9476         272 : 
    9477             :   // Both LHS and RHS must be available at loop entry.
    9478             :   assert(isAvailableAtLoopEntry(LHS, L) &&
    9479          11 :          "LHS is not available at Loop Entry");
    9480          11 :   assert(isAvailableAtLoopEntry(RHS, L) &&
    9481          11 :          "RHS is not available at Loop Entry");
    9482          11 : 
    9483             :   if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS))
    9484             :     return true;
    9485      241108 : 
    9486             :   // If we cannot prove strict comparison (e.g. a > b), maybe we can prove
    9487      241108 :   // the facts (a >= b && a != b) separately. A typical situation is when the
    9488       18095 :   // non-strict comparison is known from ranges and non-equality is known from
    9489             :   // dominating predicates. If we are proving strict comparison, we always try
    9490             :   // to prove non-equality and non-strict comparison separately.
    9491             :   auto NonStrictPredicate = ICmpInst::getNonStrictPredicate(Pred);
    9492             :   const bool ProvingStrictComparison = (Pred != NonStrictPredicate);
    9493             :   bool ProvedNonStrictComparison = false;
    9494             :   bool ProvedNonEquality = false;
    9495             : 
    9496             :   if (ProvingStrictComparison) {
    9497             :     ProvedNonStrictComparison =
    9498             :         isKnownViaNonRecursiveReasoning(NonStrictPredicate, LHS, RHS);
    9499             :     ProvedNonEquality =
    9500             :         isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_NE, LHS, RHS);
    9501      223013 :     if (ProvedNonStrictComparison && ProvedNonEquality)
    9502             :       return true;
    9503             :   }
    9504      217331 : 
    9505       74714 :   // Try to prove (Pred, LHS, RHS) using isImpliedViaGuard.
    9506       71799 :   auto ProveViaGuard = [&](BasicBlock *Block) {
    9507       22719 :     if (isImpliedViaGuard(Block, Pred, LHS, RHS))
    9508             :       return true;
    9509      191388 :     if (ProvingStrictComparison) {
    9510       92477 :       if (!ProvedNonStrictComparison)
    9511             :         ProvedNonStrictComparison =
    9512       98911 :             isImpliedViaGuard(Block, NonStrictPredicate, LHS, RHS);
    9513             :       if (!ProvedNonEquality)
    9514             :         ProvedNonEquality =
    9515      188975 :             isImpliedViaGuard(Block, ICmpInst::ICMP_NE, LHS, RHS);
    9516             :       if (ProvedNonStrictComparison && ProvedNonEquality)
    9517             :         return true;
    9518             :     }
    9519             :     return false;
    9520             :   };
    9521             : 
    9522             :   // Try to prove (Pred, LHS, RHS) using isImpliedCond.
    9523             :   auto ProveViaCond = [&](Value *Condition, bool Inverse) {
    9524             :     if (isImpliedCond(Pred, LHS, RHS, Condition, Inverse))
    9525             :       return true;
    9526             :     if (ProvingStrictComparison) {
    9527             :       if (!ProvedNonStrictComparison)
    9528             :         ProvedNonStrictComparison =
    9529             :             isImpliedCond(NonStrictPredicate, LHS, RHS, Condition, Inverse);
    9530             :       if (!ProvedNonEquality)
    9531             :         ProvedNonEquality =
    9532             :             isImpliedCond(ICmpInst::ICMP_NE, LHS, RHS, Condition, Inverse);
    9533             :       if (ProvedNonStrictComparison && ProvedNonEquality)
    9534             :         return true;
    9535             :     }
    9536      188975 :     return false;
    9537             :   };
    9538             : 
    9539             :   // Starting at the loop predecessor, climb up the predecessor chain, as long
    9540             :   // as there are predecessors that can be found that have unique successors
    9541             :   // leading to the original header.
    9542             :   for (std::pair<BasicBlock *, BasicBlock *>
    9543       41270 :          Pair(L->getLoopPredecessor(), L->getHeader());
    9544             :        Pair.first;
    9545       41482 :        Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
    9546             : 
    9547             :     if (ProveViaGuard(Pair.first))
    9548             :       return true;
    9549       41176 : 
    9550         166 :     BranchInst *LoopEntryPredicate =
    9551         106 :       dyn_cast<BranchInst>(Pair.first->getTerminator());
    9552             :     if (!LoopEntryPredicate ||
    9553             :         LoopEntryPredicate->isUnconditional())
    9554             :       continue;
    9555             : 
    9556             :     if (ProveViaCond(LoopEntryPredicate->getCondition(),
    9557       37706 :                      LoopEntryPredicate->getSuccessor(0) != Pair.second))
    9558             :       return true;
    9559       37706 :   }
    9560           2 : 
    9561             :   // Check conditions due to any @llvm.assume intrinsics.
    9562             :   for (auto &AssumeVH : AC.assumptions()) {
    9563             :     if (!AssumeVH)
    9564       37704 :       continue;
    9565           0 :     auto *CI = cast<CallInst>(AssumeVH);
    9566             :     if (!DT.dominates(CI, L->getHeader()))
    9567             :       continue;
    9568             : 
    9569             :     if (ProveViaCond(CI->getArgOperand(0), false))
    9570             :       return true;
    9571             :   }
    9572       31539 : 
    9573             :   return false;
    9574             : }
    9575       31539 : 
    9576             : bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
    9577             :                                     const SCEV *LHS, const SCEV *RHS,
    9578             :                                     Value *FoundCondValue,
    9579             :                                     bool Inverse) {
    9580        2259 :   if (!PendingLoopPredicates.insert(FoundCondValue).second)
    9581             :     return false;
    9582             : 
    9583             :   auto ClearOnExit =
    9584             :       make_scope_exit([&]() { PendingLoopPredicates.erase(FoundCondValue); });
    9585             : 
    9586             :   // Recursively handle And and Or conditions.
    9587             :   if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
    9588             :     if (BO->getOpcode() == Instruction::And) {
    9589        3768 :       if (!Inverse)
    9590        5115 :         return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
    9591        1347 :                isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
    9592             :     } else if (BO->getOpcode() == Instruction::Or) {
    9593             :       if (Inverse)
    9594      175344 :         return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
    9595             :                isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
    9596             :     }
    9597             :   }
    9598      175344 : 
    9599             :   ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
    9600             :   if (!ICI) return false;
    9601        1565 : 
    9602             :   // Now that we found a conditional branch that dominates the loop or controls
    9603             :   // the loop latch. Check to see if it is the comparison we are looking for.
    9604             :   ICmpInst::Predicate FoundPred;
    9605             :   if (Inverse)
    9606             :     FoundPred = ICI->getInversePredicate();
    9607             :   else
    9608        1565 :     FoundPred = ICI->getPredicate();
    9609             : 
    9610             :   const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
    9611             :   const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
    9612             : 
    9613             :   return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS);
    9614             : }
    9615       34126 : 
    9616             : bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
    9617             :                                     const SCEV *RHS,
    9618             :                                     ICmpInst::Predicate FoundPred,
    9619             :                                     const SCEV *FoundLHS,
    9620       34126 :                                     const SCEV *FoundRHS) {
    9621             :   // Balance the types.
    9622       34126 :   if (getTypeSizeInBits(LHS->getType()) <
    9623             :       getTypeSizeInBits(FoundLHS->getType())) {
    9624             :     if (CmpInst::isSigned(Pred)) {
    9625       22473 :       LHS = getSignExtendExpr(LHS, FoundLHS->getType());
    9626       22473 :       RHS = getSignExtendExpr(RHS, FoundLHS->getType());
    9627             :     } else {
    9628             :       LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
    9629             :       RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
    9630             :     }
    9631       43163 :   } else if (getTypeSizeInBits(LHS->getType()) >
    9632       41668 :       getTypeSizeInBits(FoundLHS->getType())) {
    9633             :     if (CmpInst::isSigned(FoundPred)) {
    9634             :       FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
    9635             :       FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
    9636             :     } else {
    9637             :       FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
    9638             :       FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
    9639       21689 :     }
    9640             :   }
    9641             : 
    9642       19161 :   // Canonicalize the query to match the way instcombine will have
    9643             :   // canonicalized the comparison.
    9644             :   if (SimplifyICmpOperands(Pred, LHS, RHS))
    9645       19161 :     if (LHS == RHS)
    9646       19161 :       return CmpInst::isTrueWhenEqual(Pred);
    9647       19161 :   if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
    9648             :     if (FoundLHS == FoundRHS)
    9649             :       return CmpInst::isFalseWhenEqual(FoundPred);
    9650             : 
    9651       16074 :   // Check to see if we can make the LHS or RHS match.
    9652             :   if (LHS == FoundRHS || RHS == FoundLHS) {
    9653             :     if (isa<SCEVConstant>(RHS)) {
    9654       16074 :       std::swap(FoundLHS, FoundRHS);
    9655       16074 :       FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
    9656             :     } else {
    9657             :       std::swap(LHS, RHS);
    9658             :       Pred = ICmpInst::getSwappedPredicate(Pred);
    9659             :     }
    9660             :   }
    9661       41739 : 
    9662        3479 :   // Check whether the found predicate is the same as the desired predicate.
    9663             :   if (FoundPred == Pred)
    9664             :     return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
    9665        6958 : 
    9666             :   // Check whether swapping the found predicate makes it the same as the
    9667             :   // desired predicate.
    9668        3479 :   if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
    9669             :     if (isa<SCEVConstant>(RHS))
    9670             :       return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
    9671             :     else
    9672             :       return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
    9673             :                                    RHS, LHS, FoundLHS, FoundRHS);
    9674             :   }
    9675       38258 : 
    9676             :   // Unsigned comparison is the same as signed comparison when both the operands
    9677             :   // are non-negative.
    9678       19129 :   if (CmpInst::isUnsigned(FoundPred) &&
    9679             :       CmpInst::getSignedPredicate(FoundPred) == Pred &&
    9680             :       isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS))
    9681       38232 :     return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
    9682       42443 : 
    9683             :   // Check if we can make progress by sharpening ranges.
    9684             :   if (FoundPred == ICmpInst::ICMP_NE &&
    9685       23405 :       (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
    9686       23405 : 
    9687          78 :     const SCEVConstant *C = nullptr;
    9688             :     const SCEV *V = nullptr;
    9689             : 
    9690       23405 :     if (isa<SCEVConstant>(FoundLHS)) {
    9691       17378 :       C = cast<SCEVConstant>(FoundLHS);
    9692             :       V = FoundRHS;
    9693             :     } else {
    9694        7073 :       C = cast<SCEVConstant>(FoundRHS);
    9695             :       V = FoundLHS;
    9696             :     }
    9697             : 
    9698             :     // The guarding predicate tells us that C != V. If the known range
    9699             :     // of V is [C, t), we can sharpen the range to [C + 1, t).  The
    9700             :     // range we consider has to correspond to same signedness as the
    9701             :     // predicate we're interested in folding.
    9702             : 
    9703             :     APInt Min = ICmpInst::isSigned(Pred) ?
    9704        6027 :         getSignedRangeMin(V) : getUnsignedRangeMin(V);
    9705             : 
    9706             :     if (Min == C->getAPInt()) {
    9707             :       // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
    9708             :       // This is true even if (Min + 1) wraps around -- in case of
    9709             :       // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
    9710        6027 : 
    9711             :       APInt SharperMin = Min + 1;
    9712             : 
    9713             :       switch (Pred) {
    9714             :         case ICmpInst::ICMP_SGE:
    9715             :         case ICmpInst::ICMP_UGE:
    9716             :           // We know V `Pred` SharperMin.  If this implies LHS `Pred`
    9717             :           // RHS, we're done.
    9718             :           if (isImpliedCondOperands(Pred, LHS, RHS, V,
    9719             :                                     getConstant(SharperMin)))
    9720       35774 :             return true;
    9721             :           LLVM_FALLTHROUGH;
    9722             : 
    9723             :         case ICmpInst::ICMP_SGT:
    9724             :         case ICmpInst::ICMP_UGT:
    9725       35774 :           // We know from the range information that (V `Pred` Min ||
    9726             :           // V == Min).  We know from the guarding condition that !(V
    9727             :           // == Min).  This gives us
    9728             :           //
    9729             :           //       V `Pred` Min || V == Min && !(V == Min)
    9730             :           //   =>  V `Pred` Min
    9731             :           //
    9732             :           // If V `Pred` Min implies LHS `Pred` RHS, we're done.
    9733       35774 : 
    9734             :           if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
    9735             :             return true;
    9736             :           LLVM_FALLTHROUGH;
    9737             : 
    9738             :         default:
    9739             :           // No change
    9740             :           break;
    9741       24281 :       }
    9742       24281 :     }
    9743       24281 :   }
    9744       24281 : 
    9745             :   // Check whether the actual condition is beyond sufficient.
    9746       24281 :   if (FoundPred == ICmpInst::ICMP_EQ)
    9747       15786 :     if (ICmpInst::isTrueWhenEqual(Pred))
    9748       15786 :       if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
    9749       15786 :         return true;
    9750       15786 :   if (Pred == ICmpInst::ICMP_NE)
    9751       15786 :     if (!ICmpInst::isTrueWhenEqual(FoundPred))
    9752             :       if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
    9753             :         return true;
    9754             : 
    9755             :   // Otherwise assume the worst.
    9756             :   return false;
    9757             : }
    9758             : 
    9759             : bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr,
    9760             :                                      const SCEV *&L, const SCEV *&R,
    9761             :                                      SCEV::NoWrapFlags &Flags) {
    9762             :   const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
    9763             :   if (!AE || AE->getNumOperands() != 2)
    9764             :     return false;
    9765             : 
    9766             :   L = AE->getOperand(0);
    9767             :   R = AE->getOperand(1);
    9768             :   Flags = AE->getNoWrapFlags();
    9769             :   return true;
    9770       24281 : }
    9771             : 
    9772             : Optional<APInt> ScalarEvolution::computeConstantDifference(const SCEV *More,
    9773             :                                                            const SCEV *Less) {
    9774             :   // We avoid subtracting expressions here because this function is usually
    9775             :   // fairly deep in the call stack (i.e. is called many times).
    9776             : 
    9777             :   if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
    9778             :     const auto *LAR = cast<SCEVAddRecExpr>(Less);
    9779             :     const auto *MAR = cast<SCEVAddRecExpr>(More);
    9780             : 
    9781             :     if (LAR->getLoop() != MAR->getLoop())
    9782             :       return None;
    9783             : 
    9784             :     // We look at affine expressions only; not for correctness but to keep
    9785             :     // getStepRecurrence cheap.
    9786             :     if (!LAR->isAffine() || !MAR->isAffine())
    9787       24281 :       return None;
    9788             : 
    9789             :     if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
    9790             :       return None;
    9791             : 
    9792       63133 :     Less = LAR->getStart();
    9793       24281 :     More = MAR->getStart();
    9794       87414 : 
    9795       63133 :     // fall through
    9796             :   }
    9797       67966 : 
    9798             :   if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
    9799             :     const auto &M = cast<SCEVConstant>(More)->getAPInt();
    9800             :     const auto &L = cast<SCEVConstant>(Less)->getAPInt();
    9801             :     return M - L;
    9802       64229 :   }
    9803             : 
    9804             :   SCEV::NoWrapFlags Flags;
    9805             :   const SCEV *LLess = nullptr, *RLess = nullptr;
    9806       59468 :   const SCEV *LMore = nullptr, *RMore = nullptr;
    9807             :   const SCEVConstant *C1 = nullptr, *C2 = nullptr;
    9808             :   // Compare (X + C1) vs X.
    9809             :   if (splitBinaryAdd(Less, LLess, RLess, Flags))
    9810             :     if ((C1 = dyn_cast<SCEVConstant>(LLess)))
    9811             :       if (RLess == More)
    9812       48681 :         return -(C1->getAPInt());
    9813        9794 : 
    9814             :   // Compare X vs (X + C2).
    9815             :   if (splitBinaryAdd(More, LMore, RMore, Flags))
    9816       19588 :     if ((C2 = dyn_cast<SCEVConstant>(LMore)))
    9817             :       if (RMore == Less)
    9818             :         return C2->getAPInt();
    9819          41 : 
    9820             :   // Compare (X + C1) vs (X + C2).
    9821             :   if (C1 && C2 && RLess == RMore)
    9822             :     return C2->getAPInt() - C1->getAPInt();
    9823             : 
    9824             :   return None;
    9825             : }
    9826       86543 : 
    9827             : bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
    9828             :     ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
    9829             :     const SCEV *FoundLHS, const SCEV *FoundRHS) {
    9830       86543 :   if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
    9831             :     return false;
    9832             : 
    9833             :   const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
    9834       83109 :   if (!AddRecLHS)
    9835             :     return false;
    9836             : 
    9837             :   const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
    9838        1866 :   if (!AddRecFoundLHS)
    9839        1339 :     return false;
    9840        2077 : 
    9841         950 :   // We'd like to let SCEV reason about control dependencies, so we constrain
    9842         527 :   // both the inequalities to be about add recurrences on the same loop.  This
    9843         483 :   // way we can use isLoopEntryGuardedByCond later.
    9844         547 : 
    9845         259 :   const Loop *L = AddRecFoundLHS->getLoop();
    9846             :   if (L != AddRecLHS->getLoop())
    9847             :     return false;
    9848             : 
    9849             :   //  FoundLHS u< FoundRHS u< -C =>  (FoundLHS + C) u< (FoundRHS + C) ... (1)
    9850             :   //
    9851             :   //  FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
    9852             :   //                                                                  ... (2)
    9853             :   //
    9854             :   // Informal proof for (2), assuming (1) [*]:
    9855       78709 :   //
    9856             :   // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
    9857             :   //
    9858             :   // Then
    9859             :   //
    9860       78709 :   //       FoundLHS s< FoundRHS s< INT_MIN - C
    9861       78709 :   // <=>  (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C   [ using (3) ]
    9862             :   // <=>  (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
    9863       78709 :   // <=>  (FoundLHS + INT_MIN + C + INT_MIN) s<
    9864             :   //                        (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
    9865             :   // <=>  FoundLHS + C s< FoundRHS + C
    9866       94783 :   //
    9867             :   // [*]: (1) can be proved by ruling out overflow.
    9868             :   //
    9869             :   // [**]: This can be proved by analyzing all the four possibilities:
    9870             :   //    (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
    9871             :   //    (A s>= 0, B s>= 0).
    9872      189566 :   //
    9873       94783 :   // Note:
    9874       11820 :   // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
    9875        2096 :   // will not sign underflow.  For instance, say FoundLHS = (i8 -128), FoundRHS
    9876        2096 :   // = (i8 -127) and C = (i8 -100).  Then INT_MIN - C = (i8 -28), and FoundRHS
    9877             :   // s< (INT_MIN - C).  Lack of sign overflow / underflow in "FoundRHS + C" is
    9878        9724 :   // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
    9879        9724 :   // C)".
    9880             : 
    9881      165926 :   Optional<APInt> LDiff = computeConstantDifference(LHS, FoundLHS);
    9882       82963 :   Optional<APInt> RDiff = computeConstantDifference(RHS, FoundRHS);
    9883       10540 :   if (!LDiff || !RDiff || *LDiff != *RDiff)
    9884        3702 :     return false;
    9885        3702 : 
    9886             :   if (LDiff->isMinValue())
    9887        6838 :     return true;
    9888        6838 : 
    9889             :   APInt FoundRHSLimit;
    9890             : 
    9891             :   if (Pred == CmpInst::ICMP_ULT) {
    9892             :     FoundRHSLimit = -(*RDiff);
    9893             :   } else {
    9894       94783 :     assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
    9895        3755 :     FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - *RDiff;
    9896        3755 :   }
    9897       91028 : 
    9898          52 :   // Try to prove (1) or (2), as needed.
    9899          52 :   return isAvailableAtLoopEntry(FoundRHS, L) &&
    9900             :          isLoopEntryGuardedByCond(L, Pred, FoundRHS,
    9901             :                                   getConstant(FoundRHSLimit));
    9902       90976 : }
    9903        1616 : 
    9904             : bool ScalarEvolution::isImpliedViaMerge(ICmpInst::Predicate Pred,
    9905         417 :                                         const SCEV *LHS, const SCEV *RHS,
    9906             :                                         const SCEV *FoundLHS,
    9907             :                                         const SCEV *FoundRHS, unsigned Depth) {
    9908         391 :   const PHINode *LPhi = nullptr, *RPhi = nullptr;
    9909             : 
    9910             :   auto ClearOnExit = make_scope_exit([&]() {
    9911             :     if (LPhi) {
    9912             :       bool Erased = PendingMerges.erase(LPhi);
    9913       90976 :       assert(Erased && "Failed to erase LPhi!");
    9914       28709 :       (void)Erased;
    9915             :     }
    9916             :     if (RPhi) {
    9917             :       bool Erased = PendingMerges.erase(RPhi);
    9918       62267 :       assert(Erased && "Failed to erase RPhi!");
    9919       10502 :       (void)Erased;
    9920        4898 :     }
    9921             :   });
    9922         353 : 
    9923         353 :   // Find respective Phis and check that they are not being pending.
    9924             :   if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS))
    9925             :     if (auto *Phi = dyn_cast<PHINode>(LU->getValue())) {
    9926             :       if (!PendingMerges.insert(Phi).second)
    9927             :         return false;
    9928       57016 :       LPhi = Phi;
    9929       29563 :     }
    9930       65579 :   if (const SCEVUnknown *RU = dyn_cast<SCEVUnknown>(RHS))
    9931        3173 :     if (auto *Phi = dyn_cast<PHINode>(RU->getValue())) {
    9932             :       // If we detect a loop of Phi nodes being processed by this method, for
    9933             :       // example:
    9934       53843 :       //
    9935       14325 :       //   %a = phi i32 [ %some1, %preheader ], [ %b, %latch ]
    9936             :       //   %b = phi i32 [ %some2, %preheader ], [ %a, %latch ]
    9937             :       //
    9938             :       // we don't want to deal with a case that complex, so return conservative
    9939             :       // answer false.
    9940       10062 :       if (!PendingMerges.insert(Phi).second)
    9941             :         return false;
    9942           0 :       RPhi = Phi;
    9943             :     }
    9944       10062 : 
    9945             :   // If none of LHS, RHS is a Phi, nothing to do here.
    9946             :   if (!LPhi && !RPhi)
    9947             :     return false;
    9948             : 
    9949             :   // If there is a SCEVUnknown Phi we are interested in, make it left.
    9950             :   if (!LPhi) {
    9951             :     std::swap(LHS, RHS);
    9952             :     std::swap(FoundLHS, FoundRHS);
    9953       10062 :     std::swap(LPhi, RPhi);
    9954       10062 :     Pred = ICmpInst::getSwappedPredicate(Pred);
    9955             :   }
    9956       10062 : 
    9957             :   assert(LPhi && "LPhi should definitely be a SCEVUnknown Phi!");
    9958             :   const BasicBlock *LBB = LPhi->getParent();
    9959             :   const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
    9960             : 
    9961        4092 :   auto ProvedEasily = [&](const SCEV *S1, const SCEV *S2) {
    9962             :     return isKnownViaNonRecursiveReasoning(Pred, S1, S2) ||
    9963        4092 :            isImpliedCondOperandsViaRanges(Pred, S1, S2, FoundLHS, FoundRHS) ||
    9964          52 :            isImpliedViaOperations(Pred, S1, S2, FoundLHS, FoundRHS, Depth);
    9965             :   };
    9966             : 
    9967             :   if (RPhi && RPhi->getParent() == LBB) {
    9968          52 :     // Case one: RHS is also a SCEVUnknown Phi from the same basic block.
    9969             :     // If we compare two Phis from the same block, and for each entry block
    9970             :     // the predicate is true for incoming values from this block, then the
    9971             :     // predicate is also true for the Phis.
    9972             :     for (const BasicBlock *IncBB : predecessors(LBB)) {
    9973             :       const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB));
    9974             :       const SCEV *R = getSCEV(RPhi->getIncomingValueForBlock(IncBB));
    9975             :       if (!ProvedEasily(L, R))
    9976             :         return false;
    9977             :     }
    9978             :   } else if (RAR && RAR->getLoop()->getHeader() == LBB) {
    9979             :     // Case two: RHS is also a Phi from the same basic block, and it is an
    9980             :     // AddRec. It means that there is a loop which has both AddRec and Unknown
    9981             :     // PHIs, for it we can compare incoming values of AddRec from above the loop
    9982             :     // and latch with their respective incoming values of LPhi.
    9983             :     // TODO: Generalize to handle loops with many inputs in a header.
    9984        1526 :     if (LPhi->getNumIncomingValues() != 2) return false;
    9985             : 
    9986             :     auto *RLoop = RAR->getLoop();
    9987             :     auto *Predecessor = RLoop->getLoopPredecessor();
    9988             :     assert(Predecessor && "Loop with AddRec with no predecessor?");
    9989             :     const SCEV *L1 = getSCEV(LPhi->getIncomingValueForBlock(Predecessor));
    9990             :     if (!ProvedEasily(L1, RAR->getStart()))
    9991             :       return false;
    9992             :     auto *Latch = RLoop->getLoopLatch();
    9993             :     assert(Latch && "Loop with AddRec with no latch?");
    9994             :     const SCEV *L2 = getSCEV(LPhi->getIncomingValueForBlock(Latch));
    9995             :     if (!ProvedEasily(L2, RAR->getPostIncExpr(*this)))
    9996       53782 :       return false;
    9997        7483 :   } else {
    9998          12 :     // In all other cases go over inputs of LHS and compare each of them to RHS,
    9999             :     // the predicate is true for (LHS, RHS) if it is true for all such pairs.
   10000       53782 :     // At this point RHS is either a non-Phi, or it is a Phi from some block
   10001       29402 :     // different from LBB.
   10002       23584 :     for (const BasicBlock *IncBB : predecessors(LBB)) {
   10003        1975 :       // Check that RHS is available in this block.
   10004             :       if (!dominates(RHS, IncBB))
   10005             :         return false;
   10006             :       const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB));
   10007             :       if (!ProvedEasily(L, RHS))
   10008             :         return false;
   10009      237559 :     }
   10010             :   }
   10011             :   return true;
   10012             : }
   10013       54702 : 
   10014             : bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
   10015             :                                             const SCEV *LHS, const SCEV *RHS,
   10016       92272 :                                             const SCEV *FoundLHS,
   10017       46136 :                                             const SCEV *FoundRHS) {
   10018       46136 :   if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
   10019       46136 :     return true;
   10020             : 
   10021             :   if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
   10022       71130 :     return true;
   10023             : 
   10024             :   return isImpliedCondOperandsHelper(Pred, LHS, RHS,
   10025             :                                      FoundLHS, FoundRHS) ||
   10026             :          // ~x < ~y --> x > y
   10027       71130 :          isImpliedCondOperandsHelper(Pred, LHS, RHS,
   10028             :                                      getNotSCEV(FoundRHS),
   10029             :                                      getNotSCEV(FoundLHS));
   10030             : }
   10031       30770 : 
   10032             : /// If Expr computes ~A, return A else return nullptr
   10033             : static const SCEV *MatchNotExpr(const SCEV *Expr) {
   10034             :   const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
   10035             :   if (!Add || Add->getNumOperands() != 2 ||
   10036       30682 :       !Add->getOperand(0)->isAllOnesValue())
   10037             :     return nullptr;
   10038             : 
   10039       30656 :   const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
   10040             :   if (!AddRHS || AddRHS->getNumOperands() != 2 ||
   10041             :       !AddRHS->getOperand(0)->isAllOnesValue())
   10042       24388 :     return nullptr;
   10043       24388 : 
   10044             :   return AddRHS->getOperand(1);
   10045             : }
   10046             : 
   10047             : /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
   10048       64748 : template<typename MaxExprType>
   10049             : static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
   10050             :                               const SCEV *Candidate) {
   10051       24489 :   const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
   10052             :   if (!MaxExpr) return false;
   10053             : 
   10054             :   return find(MaxExpr->operands(), Candidate) != MaxExpr->op_end();
   10055       40259 : }
   10056       40259 : 
   10057             : /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
   10058             : template<typename MaxExprType>
   10059       40259 : static bool IsMinConsistingOf(ScalarEvolution &SE,
   10060        9274 :                               const SCEV *MaybeMinExpr,
   10061        7374 :                               const SCEV *Candidate) {
   10062         815 :   const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
   10063             :   if (!MaybeMaxExpr)
   10064             :     return false;
   10065       39444 : 
   10066       11731 :   return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
   10067       11041 : }
   10068             : 
   10069             : static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
   10070             :                                            ICmpInst::Predicate Pred,
   10071       37284 :                                            const SCEV *LHS, const SCEV *RHS) {
   10072        1798 :   // If both sides are affine addrecs for the same loop, with equal
   10073