lib/Transforms/Scalar/NaryReassociate.cpp - platform/external/spirv-llvm - Git at Google

 //===- NaryReassociate.cpp - Reassociate n-ary expressions ----------------===//
 //
 //                     The LLVM Compiler Infrastructure
 //
 // This file is distributed under the University of Illinois Open Source
 // License. See LICENSE.TXT for details.
 //
 //===----------------------------------------------------------------------===//
 //
 // This pass reassociates n-ary add expressions and eliminates the redundancy
 // exposed by the reassociation.
 //
 // A motivating example:
 //
 //   void foo(int a, int b) {
 //     bar(a + b);
 //     bar((a + 2) + b);
 //   }
 //
 // An ideal compiler should reassociate (a + 2) + b to (a + b) + 2 and simplify
 // the above code to
 //
 //   int t = a + b;
 //   bar(t);
 //   bar(t + 2);
 //
 // However, the Reassociate pass is unable to do that because it processes each
 // instruction individually and believes (a + 2) + b is the best form according
 // to its rank system.
 //
 // To address this limitation, NaryReassociate reassociates an expression in a
 // form that reuses existing instructions. As a result, NaryReassociate can
 // reassociate (a + 2) + b in the example to (a + b) + 2 because it detects that
 // (a + b) is computed before.
 //
 // NaryReassociate works as follows. For every instruction in the form of (a +
 // b) + c, it checks whether a + c or b + c is already computed by a dominating
 // instruction. If so, it then reassociates (a + b) + c into (a + c) + b or (b +
 // c) + a and removes the redundancy accordingly. To efficiently look up whether
 // an expression is computed before, we store each instruction seen and its SCEV
 // into an SCEV-to-instruction map.
 //
 // Although the algorithm pattern-matches only ternary additions, it
 // automatically handles many >3-ary expressions by walking through the function
 // in the depth-first order. For example, given
 //
 //   (a + c) + d
 //   ((a + b) + c) + d
 //
 // NaryReassociate first rewrites (a + b) + c to (a + c) + b, and then rewrites
 // ((a + c) + b) + d into ((a + c) + d) + b.
 //
 // Finally, the above dominator-based algorithm may need to be run multiple
 // iterations before emitting optimal code. One source of this need is that we
 // only split an operand when it is used only once. The above algorithm can
 // eliminate an instruction and decrease the usage count of its operands. As a
 // result, an instruction that previously had multiple uses may become a
 // single-use instruction and thus eligible for split consideration. For
 // example,
 //
 //   ac = a + c
 //   ab = a + b
 //   abc = ab + c
 //   ab2 = ab + b
 //   ab2c = ab2 + c
 //
 // In the first iteration, we cannot reassociate abc to ac+b because ab is used
 // twice. However, we can reassociate ab2c to abc+b in the first iteration. As a
 // result, ab2 becomes dead and ab will be used only once in the second
 // iteration.
 //
 // Limitations and TODO items:
 //
 // 1) We only considers n-ary adds and muls for now. This should be extended
 // and generalized.
 //
 //===----------------------------------------------------------------------===//

 #include "llvm/Analysis/AssumptionCache.h"
 #include "llvm/Analysis/ScalarEvolution.h"
 #include "llvm/Analysis/TargetLibraryInfo.h"
 #include "llvm/Analysis/TargetTransformInfo.h"
 #include "llvm/Analysis/ValueTracking.h"
 #include "llvm/IR/Dominators.h"
 #include "llvm/IR/Module.h"
 #include "llvm/IR/PatternMatch.h"
 #include "llvm/Support/Debug.h"
 #include "llvm/Support/raw_ostream.h"
 #include "llvm/Transforms/Scalar.h"
 #include "llvm/Transforms/Utils/Local.h"
 using namespace llvm;
 using namespace PatternMatch;

 #define DEBUG_TYPE "nary-reassociate"

 namespace {
 class NaryReassociate : public FunctionPass {
 public:
   static char ID;

   NaryReassociate(): FunctionPass(ID) {
     initializeNaryReassociatePass(*PassRegistry::getPassRegistry());
   }

   bool doInitialization(Module &M) override {
     DL = &M.getDataLayout();
     return false;
   }
   bool runOnFunction(Function &F) override;

   void getAnalysisUsage(AnalysisUsage &AU) const override {
     AU.addPreserved<DominatorTreeWrapperPass>();
     AU.addPreserved<ScalarEvolutionWrapperPass>();
     AU.addPreserved<TargetLibraryInfoWrapperPass>();
     AU.addRequired<AssumptionCacheTracker>();
     AU.addRequired<DominatorTreeWrapperPass>();
     AU.addRequired<ScalarEvolutionWrapperPass>();
     AU.addRequired<TargetLibraryInfoWrapperPass>();
     AU.addRequired<TargetTransformInfoWrapperPass>();
     AU.setPreservesCFG();
   }

 private:
   // Runs only one iteration of the dominator-based algorithm. See the header
   // comments for why we need multiple iterations.
   bool doOneIteration(Function &F);

   // Reassociates I for better CSE.
   Instruction *tryReassociate(Instruction *I);

   // Reassociate GEP for better CSE.
   Instruction *tryReassociateGEP(GetElementPtrInst *GEP);
   // Try splitting GEP at the I-th index and see whether either part can be
   // CSE'ed. This is a helper function for tryReassociateGEP.
   //
   // \p IndexedType The element type indexed by GEP's I-th index. This is
   //                equivalent to
   //                  GEP->getIndexedType(GEP->getPointerOperand(), 0-th index,
   //                                      ..., i-th index).
   GetElementPtrInst *tryReassociateGEPAtIndex(GetElementPtrInst *GEP,
                                               unsigned I, Type *IndexedType);
   // Given GEP's I-th index = LHS + RHS, see whether &Base[..][LHS][..] or
   // &Base[..][RHS][..] can be CSE'ed and rewrite GEP accordingly.
   GetElementPtrInst *tryReassociateGEPAtIndex(GetElementPtrInst *GEP,
                                               unsigned I, Value *LHS,
                                               Value *RHS, Type *IndexedType);

   // Reassociate binary operators for better CSE.
   Instruction *tryReassociateBinaryOp(BinaryOperator *I);

   // A helper function for tryReassociateBinaryOp. LHS and RHS are explicitly
   // passed.
   Instruction *tryReassociateBinaryOp(Value *LHS, Value *RHS,
                                       BinaryOperator *I);
   // Rewrites I to (LHS op RHS) if LHS is computed already.
   Instruction *tryReassociatedBinaryOp(const SCEV *LHS, Value *RHS,
                                        BinaryOperator *I);

   // Tries to match Op1 and Op2 by using V.
   bool matchTernaryOp(BinaryOperator *I, Value *V, Value *&Op1, Value *&Op2);

   // Gets SCEV for (LHS op RHS).
   const SCEV *getBinarySCEV(BinaryOperator *I, const SCEV *LHS,
                             const SCEV *RHS);

   // Returns the closest dominator of \c Dominatee that computes
   // \c CandidateExpr. Returns null if not found.
   Instruction *findClosestMatchingDominator(const SCEV *CandidateExpr,
                                             Instruction *Dominatee);
   // GetElementPtrInst implicitly sign-extends an index if the index is shorter
   // than the pointer size. This function returns whether Index is shorter than
   // GEP's pointer size, i.e., whether Index needs to be sign-extended in order
   // to be an index of GEP.
   bool requiresSignExtension(Value *Index, GetElementPtrInst *GEP);

   AssumptionCache *AC;
   const DataLayout *DL;
   DominatorTree *DT;
   ScalarEvolution *SE;
   TargetLibraryInfo *TLI;
   TargetTransformInfo *TTI;
   // A lookup table quickly telling which instructions compute the given SCEV.
   // Note that there can be multiple instructions at different locations
   // computing to the same SCEV, so we map a SCEV to an instruction list.  For
   // example,
   //
   //   if (p1)
   //     foo(a + b);
   //   if (p2)
   //     bar(a + b);
   DenseMap<const SCEV *, SmallVector<WeakVH, 2>> SeenExprs;
 };
 } // anonymous namespace

 char NaryReassociate::ID = 0;
 INITIALIZE_PASS_BEGIN(NaryReassociate, "nary-reassociate", "Nary reassociation",
                       false, false)
 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
 INITIALIZE_PASS_DEPENDENCY(ScalarEvolutionWrapperPass)
 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
 INITIALIZE_PASS_DEPENDENCY(TargetTransformInfoWrapperPass)
 INITIALIZE_PASS_END(NaryReassociate, "nary-reassociate", "Nary reassociation",
                     false, false)

 FunctionPass *llvm::createNaryReassociatePass() {
   return new NaryReassociate();
 }

 bool NaryReassociate::runOnFunction(Function &F) {
   if (skipOptnoneFunction(F))
     return false;

   AC = &getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F);
   DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
   SE = &getAnalysis<ScalarEvolutionWrapperPass>().getSE();
   TLI = &getAnalysis<TargetLibraryInfoWrapperPass>().getTLI();
   TTI = &getAnalysis<TargetTransformInfoWrapperPass>().getTTI(F);

   bool Changed = false, ChangedInThisIteration;
   do {
     ChangedInThisIteration = doOneIteration(F);
     Changed |= ChangedInThisIteration;
   } while (ChangedInThisIteration);
   return Changed;
 }

 // Whitelist the instruction types NaryReassociate handles for now.
 static bool isPotentiallyNaryReassociable(Instruction *I) {
   switch (I->getOpcode()) {
   case Instruction::Add:
   case Instruction::GetElementPtr:
   case Instruction::Mul:
     return true;
   default:
     return false;
   }
 }

 bool NaryReassociate::doOneIteration(Function &F) {
   bool Changed = false;
   SeenExprs.clear();
   // Process the basic blocks in pre-order of the dominator tree. This order
   // ensures that all bases of a candidate are in Candidates when we process it.
   for (auto Node = GraphTraits<DominatorTree *>::nodes_begin(DT);
        Node != GraphTraits<DominatorTree *>::nodes_end(DT); ++Node) {
     BasicBlock *BB = Node->getBlock();
     for (auto I = BB->begin(); I != BB->end(); ++I) {
       if (SE->isSCEVable(I->getType()) && isPotentiallyNaryReassociable(&*I)) {
         const SCEV *OldSCEV = SE->getSCEV(&*I);
         if (Instruction *NewI = tryReassociate(&*I)) {
           Changed = true;
           SE->forgetValue(&*I);
           I->replaceAllUsesWith(NewI);
           // If SeenExprs constains I's WeakVH, that entry will be replaced with
           // nullptr.
           RecursivelyDeleteTriviallyDeadInstructions(&*I, TLI);
           I = NewI->getIterator();
         }
         // Add the rewritten instruction to SeenExprs; the original instruction
         // is deleted.
         const SCEV *NewSCEV = SE->getSCEV(&*I);
         SeenExprs[NewSCEV].push_back(WeakVH(&*I));
         // Ideally, NewSCEV should equal OldSCEV because tryReassociate(I)
         // is equivalent to I. However, ScalarEvolution::getSCEV may
         // weaken nsw causing NewSCEV not to equal OldSCEV. For example, suppose
         // we reassociate
         //   I = &a[sext(i +nsw j)] // assuming sizeof(a[0]) = 4
         // to
         //   NewI = &a[sext(i)] + sext(j).
         //
         // ScalarEvolution computes
         //   getSCEV(I)    = a + 4 * sext(i + j)
         //   getSCEV(newI) = a + 4 * sext(i) + 4 * sext(j)
         // which are different SCEVs.
         //
         // To alleviate this issue of ScalarEvolution not always capturing
         // equivalence, we add I to SeenExprs[OldSCEV] as well so that we can
         // map both SCEV before and after tryReassociate(I) to I.
         //
         // This improvement is exercised in @reassociate_gep_nsw in nary-gep.ll.
         if (NewSCEV != OldSCEV)
           SeenExprs[OldSCEV].push_back(WeakVH(&*I));
       }
     }
   }
   return Changed;
 }

 Instruction *NaryReassociate::tryReassociate(Instruction *I) {
   switch (I->getOpcode()) {
   case Instruction::Add:
   case Instruction::Mul:
     return tryReassociateBinaryOp(cast<BinaryOperator>(I));
   case Instruction::GetElementPtr:
     return tryReassociateGEP(cast<GetElementPtrInst>(I));
   default:
     llvm_unreachable("should be filtered out by isPotentiallyNaryReassociable");
   }
 }

 // FIXME: extract this method into TTI->getGEPCost.
 static bool isGEPFoldable(GetElementPtrInst *GEP,
                           const TargetTransformInfo *TTI,
                           const DataLayout *DL) {
   GlobalVariable *BaseGV = nullptr;
   int64_t BaseOffset = 0;
   bool HasBaseReg = false;
   int64_t Scale = 0;

   if (GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getPointerOperand()))
     BaseGV = GV;
   else
     HasBaseReg = true;

   gep_type_iterator GTI = gep_type_begin(GEP);
   for (auto I = GEP->idx_begin(); I != GEP->idx_end(); ++I, ++GTI) {
     if (isa<SequentialType>(*GTI)) {
       int64_t ElementSize = DL->getTypeAllocSize(GTI.getIndexedType());
       if (ConstantInt *ConstIdx = dyn_cast<ConstantInt>(*I)) {
         BaseOffset += ConstIdx->getSExtValue() * ElementSize;
       } else {
         // Needs scale register.
         if (Scale != 0) {
           // No addressing mode takes two scale registers.
           return false;
         }
         Scale = ElementSize;
       }
     } else {
       StructType *STy = cast<StructType>(*GTI);
       uint64_t Field = cast<ConstantInt>(*I)->getZExtValue();
       BaseOffset += DL->getStructLayout(STy)->getElementOffset(Field);
     }
   }

   unsigned AddrSpace = GEP->getPointerAddressSpace();
   return TTI->isLegalAddressingMode(GEP->getType()->getElementType(), BaseGV,
                                     BaseOffset, HasBaseReg, Scale, AddrSpace);
 }

 Instruction *NaryReassociate::tryReassociateGEP(GetElementPtrInst *GEP) {
   // Not worth reassociating GEP if it is foldable.
   if (isGEPFoldable(GEP, TTI, DL))
     return nullptr;

   gep_type_iterator GTI = gep_type_begin(*GEP);
   for (unsigned I = 1, E = GEP->getNumOperands(); I != E; ++I) {
     if (isa<SequentialType>(*GTI++)) {
       if (auto *NewGEP = tryReassociateGEPAtIndex(GEP, I - 1, *GTI)) {
         return NewGEP;
       }
     }
   }
   return nullptr;
 }

 bool NaryReassociate::requiresSignExtension(Value *Index,
                                             GetElementPtrInst *GEP) {
   unsigned PointerSizeInBits =
       DL->getPointerSizeInBits(GEP->getType()->getPointerAddressSpace());
   return cast<IntegerType>(Index->getType())->getBitWidth() < PointerSizeInBits;
 }

 GetElementPtrInst *
 NaryReassociate::tryReassociateGEPAtIndex(GetElementPtrInst *GEP, unsigned I,
                                           Type *IndexedType) {
   Value *IndexToSplit = GEP->getOperand(I + 1);
   if (SExtInst *SExt = dyn_cast<SExtInst>(IndexToSplit)) {
     IndexToSplit = SExt->getOperand(0);
   } else if (ZExtInst *ZExt = dyn_cast<ZExtInst>(IndexToSplit)) {
     // zext can be treated as sext if the source is non-negative.
     if (isKnownNonNegative(ZExt->getOperand(0), *DL, 0, AC, GEP, DT))
       IndexToSplit = ZExt->getOperand(0);
   }

   if (AddOperator *AO = dyn_cast<AddOperator>(IndexToSplit)) {
     // If the I-th index needs sext and the underlying add is not equipped with
     // nsw, we cannot split the add because
     //   sext(LHS + RHS) != sext(LHS) + sext(RHS).
     if (requiresSignExtension(IndexToSplit, GEP) &&
         computeOverflowForSignedAdd(AO, *DL, AC, GEP, DT) !=
             OverflowResult::NeverOverflows)
       return nullptr;

     Value *LHS = AO->getOperand(0), *RHS = AO->getOperand(1);
     // IndexToSplit = LHS + RHS.
     if (auto *NewGEP = tryReassociateGEPAtIndex(GEP, I, LHS, RHS, IndexedType))
       return NewGEP;
     // Symmetrically, try IndexToSplit = RHS + LHS.
     if (LHS != RHS) {
       if (auto *NewGEP =
               tryReassociateGEPAtIndex(GEP, I, RHS, LHS, IndexedType))
         return NewGEP;
     }
   }
   return nullptr;
 }

 GetElementPtrInst *NaryReassociate::tryReassociateGEPAtIndex(
     GetElementPtrInst *GEP, unsigned I, Value *LHS, Value *RHS,
     Type *IndexedType) {
   // Look for GEP's closest dominator that has the same SCEV as GEP except that
   // the I-th index is replaced with LHS.
   SmallVector<const SCEV *, 4> IndexExprs;
   for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
     IndexExprs.push_back(SE->getSCEV(*Index));
   // Replace the I-th index with LHS.
   IndexExprs[I] = SE->getSCEV(LHS);
   if (isKnownNonNegative(LHS, *DL, 0, AC, GEP, DT) &&
       DL->getTypeSizeInBits(LHS->getType()) <
           DL->getTypeSizeInBits(GEP->getOperand(I)->getType())) {
     // Zero-extend LHS if it is non-negative. InstCombine canonicalizes sext to
     // zext if the source operand is proved non-negative. We should do that
     // consistently so that CandidateExpr more likely appears before. See
     // @reassociate_gep_assume for an example of this canonicalization.
     IndexExprs[I] =
         SE->getZeroExtendExpr(IndexExprs[I], GEP->getOperand(I)->getType());
   }
   const SCEV *CandidateExpr = SE->getGEPExpr(
       GEP->getSourceElementType(), SE->getSCEV(GEP->getPointerOperand()),
       IndexExprs, GEP->isInBounds());

   Value *Candidate = findClosestMatchingDominator(CandidateExpr, GEP);
   if (Candidate == nullptr)
     return nullptr;

   IRBuilder<> Builder(GEP);
   // Candidate does not necessarily have the same pointer type as GEP. Use
   // bitcast or pointer cast to make sure they have the same type, so that the
   // later RAUW doesn't complain.
   Candidate = Builder.CreateBitOrPointerCast(Candidate, GEP->getType());
   assert(Candidate->getType() == GEP->getType());

   // NewGEP = (char *)Candidate + RHS * sizeof(IndexedType)
   uint64_t IndexedSize = DL->getTypeAllocSize(IndexedType);
   Type *ElementType = GEP->getType()->getElementType();
   uint64_t ElementSize = DL->getTypeAllocSize(ElementType);
   // Another less rare case: because I is not necessarily the last index of the
   // GEP, the size of the type at the I-th index (IndexedSize) is not
   // necessarily divisible by ElementSize. For example,
   //
   // #pragma pack(1)
   // struct S {
   //   int a[3];
   //   int64 b[8];
   // };
   // #pragma pack()
   //
   // sizeof(S) = 100 is indivisible by sizeof(int64) = 8.
   //
   // TODO: bail out on this case for now. We could emit uglygep.
   if (IndexedSize % ElementSize != 0)
     return nullptr;

   // NewGEP = &Candidate[RHS * (sizeof(IndexedType) / sizeof(Candidate[0])));
   Type *IntPtrTy = DL->getIntPtrType(GEP->getType());
   if (RHS->getType() != IntPtrTy)
     RHS = Builder.CreateSExtOrTrunc(RHS, IntPtrTy);
   if (IndexedSize != ElementSize) {
     RHS = Builder.CreateMul(
         RHS, ConstantInt::get(IntPtrTy, IndexedSize / ElementSize));
   }
   GetElementPtrInst *NewGEP =
       cast<GetElementPtrInst>(Builder.CreateGEP(Candidate, RHS));
   NewGEP->setIsInBounds(GEP->isInBounds());
   NewGEP->takeName(GEP);
   return NewGEP;
 }

 Instruction *NaryReassociate::tryReassociateBinaryOp(BinaryOperator *I) {
   Value *LHS = I->getOperand(0), *RHS = I->getOperand(1);
   if (auto *NewI = tryReassociateBinaryOp(LHS, RHS, I))
     return NewI;
   if (auto *NewI = tryReassociateBinaryOp(RHS, LHS, I))
     return NewI;
   return nullptr;
 }

 Instruction *NaryReassociate::tryReassociateBinaryOp(Value *LHS, Value *RHS,
                                                      BinaryOperator *I) {
   Value *A = nullptr, *B = nullptr;
   // To be conservative, we reassociate I only when it is the only user of (A op
   // B).
   if (LHS->hasOneUse() && matchTernaryOp(I, LHS, A, B)) {
     // I = (A op B) op RHS
     //   = (A op RHS) op B or (B op RHS) op A
     const SCEV *AExpr = SE->getSCEV(A), *BExpr = SE->getSCEV(B);
     const SCEV *RHSExpr = SE->getSCEV(RHS);
     if (BExpr != RHSExpr) {
       if (auto *NewI =
               tryReassociatedBinaryOp(getBinarySCEV(I, AExpr, RHSExpr), B, I))
         return NewI;
     }
     if (AExpr != RHSExpr) {
       if (auto *NewI =
               tryReassociatedBinaryOp(getBinarySCEV(I, BExpr, RHSExpr), A, I))
         return NewI;
     }
   }
   return nullptr;
 }

 Instruction *NaryReassociate::tryReassociatedBinaryOp(const SCEV *LHSExpr,
                                                       Value *RHS,
                                                       BinaryOperator *I) {
   // Look for the closest dominator LHS of I that computes LHSExpr, and replace
   // I with LHS op RHS.
   auto *LHS = findClosestMatchingDominator(LHSExpr, I);
   if (LHS == nullptr)
     return nullptr;

   Instruction *NewI = nullptr;
   switch (I->getOpcode()) {
   case Instruction::Add:
     NewI = BinaryOperator::CreateAdd(LHS, RHS, "", I);
     break;
   case Instruction::Mul:
     NewI = BinaryOperator::CreateMul(LHS, RHS, "", I);
     break;
   default:
     llvm_unreachable("Unexpected instruction.");
   }
   NewI->takeName(I);
   return NewI;
 }

 bool NaryReassociate::matchTernaryOp(BinaryOperator *I, Value *V, Value *&Op1,
                                      Value *&Op2) {
   switch (I->getOpcode()) {
   case Instruction::Add:
     return match(V, m_Add(m_Value(Op1), m_Value(Op2)));
   case Instruction::Mul:
     return match(V, m_Mul(m_Value(Op1), m_Value(Op2)));
   default:
     llvm_unreachable("Unexpected instruction.");
   }
   return false;
 }

 const SCEV *NaryReassociate::getBinarySCEV(BinaryOperator *I, const SCEV *LHS,
                                            const SCEV *RHS) {
   switch (I->getOpcode()) {
   case Instruction::Add:
     return SE->getAddExpr(LHS, RHS);
   case Instruction::Mul:
     return SE->getMulExpr(LHS, RHS);
   default:
     llvm_unreachable("Unexpected instruction.");
   }
   return nullptr;
 }

 Instruction *
 NaryReassociate::findClosestMatchingDominator(const SCEV *CandidateExpr,
                                               Instruction *Dominatee) {
   auto Pos = SeenExprs.find(CandidateExpr);
   if (Pos == SeenExprs.end())
     return nullptr;

   auto &Candidates = Pos->second;
   // Because we process the basic blocks in pre-order of the dominator tree, a
   // candidate that doesn't dominate the current instruction won't dominate any
   // future instruction either. Therefore, we pop it out of the stack. This
   // optimization makes the algorithm O(n).
   while (!Candidates.empty()) {
     // Candidates stores WeakVHs, so a candidate can be nullptr if it's removed
     // during rewriting.
     if (Value *Candidate = Candidates.back()) {
       Instruction *CandidateInstruction = cast<Instruction>(Candidate);
       if (DT->dominates(CandidateInstruction, Dominatee))
         return CandidateInstruction;
     }
     Candidates.pop_back();
   }
   return nullptr;
 }
	//===- NaryReassociate.cpp - Reassociate n-ary expressions ----------------===//
	//
	// The LLVM Compiler Infrastructure
	//
	// This file is distributed under the University of Illinois Open Source
	// License. See LICENSE.TXT for details.
	//
	//===----------------------------------------------------------------------===//
	//
	// This pass reassociates n-ary add expressions and eliminates the redundancy
	// exposed by the reassociation.
	//
	// A motivating example:
	//
	// void foo(int a, int b) {
	// bar(a + b);
	// bar((a + 2) + b);
	// }
	//
	// An ideal compiler should reassociate (a + 2) + b to (a + b) + 2 and simplify
	// the above code to
	//
	// int t = a + b;
	// bar(t);
	// bar(t + 2);
	//
	// However, the Reassociate pass is unable to do that because it processes each
	// instruction individually and believes (a + 2) + b is the best form according
	// to its rank system.
	//
	// To address this limitation, NaryReassociate reassociates an expression in a
	// form that reuses existing instructions. As a result, NaryReassociate can
	// reassociate (a + 2) + b in the example to (a + b) + 2 because it detects that
	// (a + b) is computed before.
	//
	// NaryReassociate works as follows. For every instruction in the form of (a +
	// b) + c, it checks whether a + c or b + c is already computed by a dominating
	// instruction. If so, it then reassociates (a + b) + c into (a + c) + b or (b +
	// c) + a and removes the redundancy accordingly. To efficiently look up whether
	// an expression is computed before, we store each instruction seen and its SCEV
	// into an SCEV-to-instruction map.
	//
	// Although the algorithm pattern-matches only ternary additions, it
	// automatically handles many >3-ary expressions by walking through the function
	// in the depth-first order. For example, given
	//
	// (a + c) + d
	// ((a + b) + c) + d
	//
	// NaryReassociate first rewrites (a + b) + c to (a + c) + b, and then rewrites
	// ((a + c) + b) + d into ((a + c) + d) + b.
	//
	// Finally, the above dominator-based algorithm may need to be run multiple
	// iterations before emitting optimal code. One source of this need is that we
	// only split an operand when it is used only once. The above algorithm can
	// eliminate an instruction and decrease the usage count of its operands. As a
	// result, an instruction that previously had multiple uses may become a
	// single-use instruction and thus eligible for split consideration. For
	// example,
	//
	// ac = a + c
	// ab = a + b
	// abc = ab + c
	// ab2 = ab + b
	// ab2c = ab2 + c
	//
	// In the first iteration, we cannot reassociate abc to ac+b because ab is used
	// twice. However, we can reassociate ab2c to abc+b in the first iteration. As a
	// result, ab2 becomes dead and ab will be used only once in the second
	// iteration.
	//
	// Limitations and TODO items:
	//
	// 1) We only considers n-ary adds and muls for now. This should be extended
	// and generalized.
	//
	//===----------------------------------------------------------------------===//

	#include "llvm/Analysis/AssumptionCache.h"
	#include "llvm/Analysis/ScalarEvolution.h"
	#include "llvm/Analysis/TargetLibraryInfo.h"
	#include "llvm/Analysis/TargetTransformInfo.h"
	#include "llvm/Analysis/ValueTracking.h"
	#include "llvm/IR/Dominators.h"
	#include "llvm/IR/Module.h"
	#include "llvm/IR/PatternMatch.h"
	#include "llvm/Support/Debug.h"
	#include "llvm/Support/raw_ostream.h"
	#include "llvm/Transforms/Scalar.h"
	#include "llvm/Transforms/Utils/Local.h"
	using namespace llvm;
	using namespace PatternMatch;

	#define DEBUG_TYPE "nary-reassociate"

	namespace {
	class NaryReassociate : public FunctionPass {
	public:
	static char ID;

	NaryReassociate(): FunctionPass(ID) {
	initializeNaryReassociatePass(*PassRegistry::getPassRegistry());
	}

	bool doInitialization(Module &M) override {
	DL = &M.getDataLayout();
	return false;
	}
	bool runOnFunction(Function &F) override;

	void getAnalysisUsage(AnalysisUsage &AU) const override {
	AU.addPreserved<DominatorTreeWrapperPass>();
	AU.addPreserved<ScalarEvolutionWrapperPass>();
	AU.addPreserved<TargetLibraryInfoWrapperPass>();
	AU.addRequired<AssumptionCacheTracker>();
	AU.addRequired<DominatorTreeWrapperPass>();
	AU.addRequired<ScalarEvolutionWrapperPass>();
	AU.addRequired<TargetLibraryInfoWrapperPass>();
	AU.addRequired<TargetTransformInfoWrapperPass>();
	AU.setPreservesCFG();
	}

	private:
	// Runs only one iteration of the dominator-based algorithm. See the header
	// comments for why we need multiple iterations.
	bool doOneIteration(Function &F);

	// Reassociates I for better CSE.
	Instruction tryReassociate(Instruction I);

	// Reassociate GEP for better CSE.
	Instruction tryReassociateGEP(GetElementPtrInst GEP);
	// Try splitting GEP at the I-th index and see whether either part can be
	// CSE'ed. This is a helper function for tryReassociateGEP.
	//
	// \p IndexedType The element type indexed by GEP's I-th index. This is
	// equivalent to
	// GEP->getIndexedType(GEP->getPointerOperand(), 0-th index,
	// ..., i-th index).
	GetElementPtrInst tryReassociateGEPAtIndex(GetElementPtrInst GEP,
	unsigned I, Type *IndexedType);
	// Given GEP's I-th index = LHS + RHS, see whether &Base[..][LHS][..] or
	// &Base[..][RHS][..] can be CSE'ed and rewrite GEP accordingly.
	GetElementPtrInst tryReassociateGEPAtIndex(GetElementPtrInst GEP,
	unsigned I, Value *LHS,
	Value RHS, Type IndexedType);

	// Reassociate binary operators for better CSE.
	Instruction tryReassociateBinaryOp(BinaryOperator I);

	// A helper function for tryReassociateBinaryOp. LHS and RHS are explicitly
	// passed.
	Instruction tryReassociateBinaryOp(Value LHS, Value *RHS,
	BinaryOperator *I);
	// Rewrites I to (LHS op RHS) if LHS is computed already.
	Instruction tryReassociatedBinaryOp(const SCEV LHS, Value *RHS,
	BinaryOperator *I);

	// Tries to match Op1 and Op2 by using V.
	bool matchTernaryOp(BinaryOperator I, Value V, Value &Op1, Value &Op2);

	// Gets SCEV for (LHS op RHS).
	const SCEV getBinarySCEV(BinaryOperator I, const SCEV *LHS,
	const SCEV *RHS);

	// Returns the closest dominator of \c Dominatee that computes
	// \c CandidateExpr. Returns null if not found.
	Instruction findClosestMatchingDominator(const SCEV CandidateExpr,
	Instruction *Dominatee);
	// GetElementPtrInst implicitly sign-extends an index if the index is shorter
	// than the pointer size. This function returns whether Index is shorter than
	// GEP's pointer size, i.e., whether Index needs to be sign-extended in order
	// to be an index of GEP.
	bool requiresSignExtension(Value Index, GetElementPtrInst GEP);

	AssumptionCache *AC;
	const DataLayout *DL;
	DominatorTree *DT;
	ScalarEvolution *SE;
	TargetLibraryInfo *TLI;
	TargetTransformInfo *TTI;
	// A lookup table quickly telling which instructions compute the given SCEV.
	// Note that there can be multiple instructions at different locations
	// computing to the same SCEV, so we map a SCEV to an instruction list. For
	// example,
	//
	// if (p1)
	// foo(a + b);
	// if (p2)
	// bar(a + b);
	DenseMap<const SCEV *, SmallVector<WeakVH, 2>> SeenExprs;
	};
	} // anonymous namespace

	char NaryReassociate::ID = 0;
	INITIALIZE_PASS_BEGIN(NaryReassociate, "nary-reassociate", "Nary reassociation",
	false, false)
	INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
	INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
	INITIALIZE_PASS_DEPENDENCY(ScalarEvolutionWrapperPass)
	INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
	INITIALIZE_PASS_DEPENDENCY(TargetTransformInfoWrapperPass)
	INITIALIZE_PASS_END(NaryReassociate, "nary-reassociate", "Nary reassociation",
	false, false)

	FunctionPass *llvm::createNaryReassociatePass() {
	return new NaryReassociate();
	}

	bool NaryReassociate::runOnFunction(Function &F) {
	if (skipOptnoneFunction(F))
	return false;

	AC = &getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F);
	DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
	SE = &getAnalysis<ScalarEvolutionWrapperPass>().getSE();
	TLI = &getAnalysis<TargetLibraryInfoWrapperPass>().getTLI();
	TTI = &getAnalysis<TargetTransformInfoWrapperPass>().getTTI(F);

	bool Changed = false, ChangedInThisIteration;
	do {
	ChangedInThisIteration = doOneIteration(F);
	Changed \|= ChangedInThisIteration;
	} while (ChangedInThisIteration);
	return Changed;
	}

	// Whitelist the instruction types NaryReassociate handles for now.
	static bool isPotentiallyNaryReassociable(Instruction *I) {
	switch (I->getOpcode()) {
	case Instruction::Add:
	case Instruction::GetElementPtr:
	case Instruction::Mul:
	return true;
	default:
	return false;
	}
	}

	bool NaryReassociate::doOneIteration(Function &F) {
	bool Changed = false;
	SeenExprs.clear();
	// Process the basic blocks in pre-order of the dominator tree. This order
	// ensures that all bases of a candidate are in Candidates when we process it.
	for (auto Node = GraphTraits<DominatorTree *>::nodes_begin(DT);
	Node != GraphTraits<DominatorTree *>::nodes_end(DT); ++Node) {
	BasicBlock *BB = Node->getBlock();
	for (auto I = BB->begin(); I != BB->end(); ++I) {
	if (SE->isSCEVable(I->getType()) && isPotentiallyNaryReassociable(&*I)) {
	const SCEV OldSCEV = SE->getSCEV(&I);
	if (Instruction NewI = tryReassociate(&I)) {
	Changed = true;
	SE->forgetValue(&*I);
	I->replaceAllUsesWith(NewI);
	// If SeenExprs constains I's WeakVH, that entry will be replaced with
	// nullptr.
	RecursivelyDeleteTriviallyDeadInstructions(&*I, TLI);
	I = NewI->getIterator();
	}
	// Add the rewritten instruction to SeenExprs; the original instruction
	// is deleted.
	const SCEV NewSCEV = SE->getSCEV(&I);
	SeenExprs[NewSCEV].push_back(WeakVH(&*I));
	// Ideally, NewSCEV should equal OldSCEV because tryReassociate(I)
	// is equivalent to I. However, ScalarEvolution::getSCEV may
	// weaken nsw causing NewSCEV not to equal OldSCEV. For example, suppose
	// we reassociate
	// I = &a[sext(i +nsw j)] // assuming sizeof(a[0]) = 4
	// to
	// NewI = &a[sext(i)] + sext(j).
	//
	// ScalarEvolution computes
	// getSCEV(I) = a + 4 * sext(i + j)
	// getSCEV(newI) = a + 4 * sext(i) + 4 * sext(j)
	// which are different SCEVs.
	//
	// To alleviate this issue of ScalarEvolution not always capturing
	// equivalence, we add I to SeenExprs[OldSCEV] as well so that we can
	// map both SCEV before and after tryReassociate(I) to I.
	//
	// This improvement is exercised in @reassociate_gep_nsw in nary-gep.ll.
	if (NewSCEV != OldSCEV)
	SeenExprs[OldSCEV].push_back(WeakVH(&*I));
	}
	}
	}
	return Changed;
	}

	Instruction NaryReassociate::tryReassociate(Instruction I) {
	switch (I->getOpcode()) {
	case Instruction::Add:
	case Instruction::Mul:
	return tryReassociateBinaryOp(cast<BinaryOperator>(I));
	case Instruction::GetElementPtr:
	return tryReassociateGEP(cast<GetElementPtrInst>(I));
	default:
	llvm_unreachable("should be filtered out by isPotentiallyNaryReassociable");
	}
	}

	// FIXME: extract this method into TTI->getGEPCost.
	static bool isGEPFoldable(GetElementPtrInst *GEP,
	const TargetTransformInfo *TTI,
	const DataLayout *DL) {
	GlobalVariable *BaseGV = nullptr;
	int64_t BaseOffset = 0;
	bool HasBaseReg = false;
	int64_t Scale = 0;

	if (GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getPointerOperand()))
	BaseGV = GV;
	else
	HasBaseReg = true;

	gep_type_iterator GTI = gep_type_begin(GEP);
	for (auto I = GEP->idx_begin(); I != GEP->idx_end(); ++I, ++GTI) {
	if (isa<SequentialType>(*GTI)) {
	int64_t ElementSize = DL->getTypeAllocSize(GTI.getIndexedType());
	if (ConstantInt ConstIdx = dyn_cast<ConstantInt>(I)) {
	BaseOffset += ConstIdx->getSExtValue() * ElementSize;
	} else {
	// Needs scale register.
	if (Scale != 0) {
	// No addressing mode takes two scale registers.
	return false;
	}
	Scale = ElementSize;
	}
	} else {
	StructType STy = cast<StructType>(GTI);
	uint64_t Field = cast<ConstantInt>(*I)->getZExtValue();
	BaseOffset += DL->getStructLayout(STy)->getElementOffset(Field);
	}
	}

	unsigned AddrSpace = GEP->getPointerAddressSpace();
	return TTI->isLegalAddressingMode(GEP->getType()->getElementType(), BaseGV,
	BaseOffset, HasBaseReg, Scale, AddrSpace);
	}

	Instruction NaryReassociate::tryReassociateGEP(GetElementPtrInst GEP) {
	// Not worth reassociating GEP if it is foldable.
	if (isGEPFoldable(GEP, TTI, DL))
	return nullptr;

	gep_type_iterator GTI = gep_type_begin(*GEP);
	for (unsigned I = 1, E = GEP->getNumOperands(); I != E; ++I) {
	if (isa<SequentialType>(*GTI++)) {
	if (auto NewGEP = tryReassociateGEPAtIndex(GEP, I - 1, GTI)) {
	return NewGEP;
	}
	}
	}
	return nullptr;
	}

	bool NaryReassociate::requiresSignExtension(Value *Index,
	GetElementPtrInst *GEP) {
	unsigned PointerSizeInBits =
	DL->getPointerSizeInBits(GEP->getType()->getPointerAddressSpace());
	return cast<IntegerType>(Index->getType())->getBitWidth() < PointerSizeInBits;
	}

	GetElementPtrInst *
	NaryReassociate::tryReassociateGEPAtIndex(GetElementPtrInst *GEP, unsigned I,
	Type *IndexedType) {
	Value *IndexToSplit = GEP->getOperand(I + 1);
	if (SExtInst *SExt = dyn_cast<SExtInst>(IndexToSplit)) {
	IndexToSplit = SExt->getOperand(0);
	} else if (ZExtInst *ZExt = dyn_cast<ZExtInst>(IndexToSplit)) {
	// zext can be treated as sext if the source is non-negative.
	if (isKnownNonNegative(ZExt->getOperand(0), *DL, 0, AC, GEP, DT))
	IndexToSplit = ZExt->getOperand(0);
	}

	if (AddOperator *AO = dyn_cast<AddOperator>(IndexToSplit)) {
	// If the I-th index needs sext and the underlying add is not equipped with
	// nsw, we cannot split the add because
	// sext(LHS + RHS) != sext(LHS) + sext(RHS).
	if (requiresSignExtension(IndexToSplit, GEP) &&
	computeOverflowForSignedAdd(AO, *DL, AC, GEP, DT) !=
	OverflowResult::NeverOverflows)
	return nullptr;

	Value LHS = AO->getOperand(0), RHS = AO->getOperand(1);
	// IndexToSplit = LHS + RHS.
	if (auto *NewGEP = tryReassociateGEPAtIndex(GEP, I, LHS, RHS, IndexedType))
	return NewGEP;
	// Symmetrically, try IndexToSplit = RHS + LHS.
	if (LHS != RHS) {
	if (auto *NewGEP =
	tryReassociateGEPAtIndex(GEP, I, RHS, LHS, IndexedType))
	return NewGEP;
	}
	}
	return nullptr;
	}

	GetElementPtrInst *NaryReassociate::tryReassociateGEPAtIndex(
	GetElementPtrInst GEP, unsigned I, Value LHS, Value *RHS,
	Type *IndexedType) {
	// Look for GEP's closest dominator that has the same SCEV as GEP except that
	// the I-th index is replaced with LHS.
	SmallVector<const SCEV *, 4> IndexExprs;
	for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
	IndexExprs.push_back(SE->getSCEV(*Index));
	// Replace the I-th index with LHS.
	IndexExprs[I] = SE->getSCEV(LHS);
	if (isKnownNonNegative(LHS, *DL, 0, AC, GEP, DT) &&
	DL->getTypeSizeInBits(LHS->getType()) <
	DL->getTypeSizeInBits(GEP->getOperand(I)->getType())) {
	// Zero-extend LHS if it is non-negative. InstCombine canonicalizes sext to
	// zext if the source operand is proved non-negative. We should do that
	// consistently so that CandidateExpr more likely appears before. See
	// @reassociate_gep_assume for an example of this canonicalization.
	IndexExprs[I] =
	SE->getZeroExtendExpr(IndexExprs[I], GEP->getOperand(I)->getType());
	}
	const SCEV *CandidateExpr = SE->getGEPExpr(
	GEP->getSourceElementType(), SE->getSCEV(GEP->getPointerOperand()),
	IndexExprs, GEP->isInBounds());

	Value *Candidate = findClosestMatchingDominator(CandidateExpr, GEP);
	if (Candidate == nullptr)
	return nullptr;

	IRBuilder<> Builder(GEP);
	// Candidate does not necessarily have the same pointer type as GEP. Use
	// bitcast or pointer cast to make sure they have the same type, so that the
	// later RAUW doesn't complain.
	Candidate = Builder.CreateBitOrPointerCast(Candidate, GEP->getType());
	assert(Candidate->getType() == GEP->getType());

	// NewGEP = (char )Candidate + RHS sizeof(IndexedType)
	uint64_t IndexedSize = DL->getTypeAllocSize(IndexedType);
	Type *ElementType = GEP->getType()->getElementType();
	uint64_t ElementSize = DL->getTypeAllocSize(ElementType);
	// Another less rare case: because I is not necessarily the last index of the
	// GEP, the size of the type at the I-th index (IndexedSize) is not
	// necessarily divisible by ElementSize. For example,
	//
	// #pragma pack(1)
	// struct S {
	// int a[3];
	// int64 b[8];
	// };
	// #pragma pack()
	//
	// sizeof(S) = 100 is indivisible by sizeof(int64) = 8.
	//
	// TODO: bail out on this case for now. We could emit uglygep.
	if (IndexedSize % ElementSize != 0)
	return nullptr;

	// NewGEP = &Candidate[RHS * (sizeof(IndexedType) / sizeof(Candidate[0])));
	Type *IntPtrTy = DL->getIntPtrType(GEP->getType());
	if (RHS->getType() != IntPtrTy)
	RHS = Builder.CreateSExtOrTrunc(RHS, IntPtrTy);
	if (IndexedSize != ElementSize) {
	RHS = Builder.CreateMul(
	RHS, ConstantInt::get(IntPtrTy, IndexedSize / ElementSize));
	}
	GetElementPtrInst *NewGEP =
	cast<GetElementPtrInst>(Builder.CreateGEP(Candidate, RHS));
	NewGEP->setIsInBounds(GEP->isInBounds());
	NewGEP->takeName(GEP);
	return NewGEP;
	}

	Instruction NaryReassociate::tryReassociateBinaryOp(BinaryOperator I) {
	Value LHS = I->getOperand(0), RHS = I->getOperand(1);
	if (auto *NewI = tryReassociateBinaryOp(LHS, RHS, I))
	return NewI;
	if (auto *NewI = tryReassociateBinaryOp(RHS, LHS, I))
	return NewI;
	return nullptr;
	}

	Instruction NaryReassociate::tryReassociateBinaryOp(Value LHS, Value *RHS,
	BinaryOperator *I) {
	Value A = nullptr, B = nullptr;
	// To be conservative, we reassociate I only when it is the only user of (A op
	// B).
	if (LHS->hasOneUse() && matchTernaryOp(I, LHS, A, B)) {
	// I = (A op B) op RHS
	// = (A op RHS) op B or (B op RHS) op A
	const SCEV AExpr = SE->getSCEV(A), BExpr = SE->getSCEV(B);
	const SCEV *RHSExpr = SE->getSCEV(RHS);
	if (BExpr != RHSExpr) {
	if (auto *NewI =
	tryReassociatedBinaryOp(getBinarySCEV(I, AExpr, RHSExpr), B, I))
	return NewI;
	}
	if (AExpr != RHSExpr) {
	if (auto *NewI =
	tryReassociatedBinaryOp(getBinarySCEV(I, BExpr, RHSExpr), A, I))
	return NewI;
	}
	}
	return nullptr;
	}

	Instruction NaryReassociate::tryReassociatedBinaryOp(const SCEV LHSExpr,
	Value *RHS,
	BinaryOperator *I) {
	// Look for the closest dominator LHS of I that computes LHSExpr, and replace
	// I with LHS op RHS.
	auto *LHS = findClosestMatchingDominator(LHSExpr, I);
	if (LHS == nullptr)
	return nullptr;

	Instruction *NewI = nullptr;
	switch (I->getOpcode()) {
	case Instruction::Add:
	NewI = BinaryOperator::CreateAdd(LHS, RHS, "", I);
	break;
	case Instruction::Mul:
	NewI = BinaryOperator::CreateMul(LHS, RHS, "", I);
	break;
	default:
	llvm_unreachable("Unexpected instruction.");
	}
	NewI->takeName(I);
	return NewI;
	}

	bool NaryReassociate::matchTernaryOp(BinaryOperator I, Value V, Value *&Op1,
	Value *&Op2) {
	switch (I->getOpcode()) {
	case Instruction::Add:
	return match(V, m_Add(m_Value(Op1), m_Value(Op2)));
	case Instruction::Mul:
	return match(V, m_Mul(m_Value(Op1), m_Value(Op2)));
	default:
	llvm_unreachable("Unexpected instruction.");
	}
	return false;
	}

	const SCEV NaryReassociate::getBinarySCEV(BinaryOperator I, const SCEV *LHS,
	const SCEV *RHS) {
	switch (I->getOpcode()) {
	case Instruction::Add:
	return SE->getAddExpr(LHS, RHS);
	case Instruction::Mul:
	return SE->getMulExpr(LHS, RHS);
	default:
	llvm_unreachable("Unexpected instruction.");
	}
	return nullptr;
	}

	Instruction *
	NaryReassociate::findClosestMatchingDominator(const SCEV *CandidateExpr,
	Instruction *Dominatee) {
	auto Pos = SeenExprs.find(CandidateExpr);
	if (Pos == SeenExprs.end())
	return nullptr;

	auto &Candidates = Pos->second;
	// Because we process the basic blocks in pre-order of the dominator tree, a
	// candidate that doesn't dominate the current instruction won't dominate any
	// future instruction either. Therefore, we pop it out of the stack. This
	// optimization makes the algorithm O(n).
	while (!Candidates.empty()) {
	// Candidates stores WeakVHs, so a candidate can be nullptr if it's removed
	// during rewriting.
	if (Value *Candidate = Candidates.back()) {
	Instruction *CandidateInstruction = cast<Instruction>(Candidate);
	if (DT->dominates(CandidateInstruction, Dominatee))
	return CandidateInstruction;
	}
	Candidates.pop_back();
	}
	return nullptr;
	}