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+//===- 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 for now. This should be extended and
+// generalized.
+//
+// 2) Besides arithmetic operations, similar reassociation can be applied to
+// GEPs. For example, if
+// X = &arr[a]
+// dominates
+// Y = &arr[a + b]
+// we may rewrite Y into X + b.
+//
+//===----------------------------------------------------------------------===//
+
+#include "llvm/Analysis/ScalarEvolution.h"
+#include "llvm/Analysis/TargetLibraryInfo.h"
+#include "llvm/Analysis/TargetTransformInfo.h"
+#include "llvm/IR/Dominators.h"
+#include "llvm/IR/Module.h"
+#include "llvm/IR/PatternMatch.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<ScalarEvolution>();
+ AU.addPreserved<TargetLibraryInfoWrapperPass>();
+ AU.addRequired<DominatorTreeWrapperPass>();
+ AU.addRequired<ScalarEvolution>();
+ 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 Add for better CSE.
+ Instruction *tryReassociateAdd(BinaryOperator *I);
+ // A helper function for tryReassociateAdd. LHS and RHS are explicitly passed.
+ Instruction *tryReassociateAdd(Value *LHS, Value *RHS, Instruction *I);
+ // Rewrites I to LHS + RHS if LHS is computed already.
+ Instruction *tryReassociatedAdd(const SCEV *LHS, Value *RHS, Instruction *I);
+
+ // 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);
+
+ DominatorTree *DT;
+ ScalarEvolution *SE;
+ TargetLibraryInfo *TLI;
+ TargetTransformInfo *TTI;
+ const DataLayout *DL;
+ // 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<Instruction *, 2>> SeenExprs;
+};
+} // anonymous namespace
+
+char NaryReassociate::ID = 0;
+INITIALIZE_PASS_BEGIN(NaryReassociate, "nary-reassociate", "Nary reassociation",
+ false, false)
+INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
+INITIALIZE_PASS_DEPENDENCY(ScalarEvolution)
+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;
+
+ DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
+ SE = &getAnalysis<ScalarEvolution>();
+ 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:
+ 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);
+ RecursivelyDeleteTriviallyDeadInstructions(I, TLI);
+ I = NewI;
+ }
+ // Add the rewritten instruction to SeenExprs; the original instruction
+ // is deleted.
+ const SCEV *NewSCEV = SE->getSCEV(I);
+ SeenExprs[NewSCEV].push_back(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(I);
+ }
+ }
+ }
+ return Changed;
+}
+
+Instruction *NaryReassociate::tryReassociate(Instruction *I) {
+ switch (I->getOpcode()) {
+ case Instruction::Add:
+ return tryReassociateAdd(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);
+
+ 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) && !AO->hasNoSignedWrap())
+ 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);
+ const SCEV *CandidateExpr = SE->getGEPExpr(
+ GEP->getSourceElementType(), SE->getSCEV(GEP->getPointerOperand()),
+ IndexExprs, GEP->isInBounds());
+
+ auto *Candidate = findClosestMatchingDominator(CandidateExpr, GEP);
+ if (Candidate == nullptr)
+ return nullptr;
+
+ PointerType *TypeOfCandidate = dyn_cast<PointerType>(Candidate->getType());
+ // Pretty rare but theoretically possible when a numeric value happens to
+ // share CandidateExpr.
+ if (TypeOfCandidate == nullptr)
+ return nullptr;
+
+ // NewGEP = (char *)Candidate + RHS * sizeof(IndexedType)
+ uint64_t IndexedSize = DL->getTypeAllocSize(IndexedType);
+ Type *ElementType = TypeOfCandidate->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])));
+ IRBuilder<> Builder(GEP);
+ Type *IntPtrTy = DL->getIntPtrType(TypeOfCandidate);
+ 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::tryReassociateAdd(BinaryOperator *I) {
+ Value *LHS = I->getOperand(0), *RHS = I->getOperand(1);
+ if (auto *NewI = tryReassociateAdd(LHS, RHS, I))
+ return NewI;
+ if (auto *NewI = tryReassociateAdd(RHS, LHS, I))
+ return NewI;
+ return nullptr;
+}
+
+Instruction *NaryReassociate::tryReassociateAdd(Value *LHS, Value *RHS,
+ Instruction *I) {
+ Value *A = nullptr, *B = nullptr;
+ // To be conservative, we reassociate I only when it is the only user of A+B.
+ if (LHS->hasOneUse() && match(LHS, m_Add(m_Value(A), m_Value(B)))) {
+ // I = (A + B) + RHS
+ // = (A + RHS) + B or (B + RHS) + A
+ const SCEV *AExpr = SE->getSCEV(A), *BExpr = SE->getSCEV(B);
+ const SCEV *RHSExpr = SE->getSCEV(RHS);
+ if (BExpr != RHSExpr) {
+ if (auto *NewI = tryReassociatedAdd(SE->getAddExpr(AExpr, RHSExpr), B, I))
+ return NewI;
+ }
+ if (AExpr != RHSExpr) {
+ if (auto *NewI = tryReassociatedAdd(SE->getAddExpr(BExpr, RHSExpr), A, I))
+ return NewI;
+ }
+ }
+ return nullptr;
+}
+
+Instruction *NaryReassociate::tryReassociatedAdd(const SCEV *LHSExpr,
+ Value *RHS, Instruction *I) {
+ auto Pos = SeenExprs.find(LHSExpr);
+ // Bail out if LHSExpr is not previously seen.
+ if (Pos == SeenExprs.end())
+ return nullptr;
+
+ // Look for the closest dominator LHS of I that computes LHSExpr, and replace
+ // I with LHS + RHS.
+ auto *LHS = findClosestMatchingDominator(LHSExpr, I);
+ if (LHS == nullptr)
+ return nullptr;
+
+ Instruction *NewI = BinaryOperator::CreateAdd(LHS, RHS, "", I);
+ NewI->takeName(I);
+ return NewI;
+}
+
+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()) {
+ Instruction *Candidate = Candidates.back();
+ if (DT->dominates(Candidate, Dominatee))
+ return Candidate;
+ Candidates.pop_back();
+ }
+ return nullptr;
+}
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