// 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 respectively. To efficiently look up whether an expression is
-// computed before, we store each instruction seen and its SCEV into an
-// SCEV-to-instruction map.
+// 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
// 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/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;
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<AssumptionCacheTracker>();
AU.addRequired<DominatorTreeWrapperPass>();
- // TODO: can we preserve ScalarEvolution?
AU.addRequired<ScalarEvolution>();
+ AU.addRequired<TargetLibraryInfoWrapperPass>();
+ AU.addRequired<TargetTransformInfoWrapperPass>();
AU.setPreservesCFG();
}
private:
- // Reasssociates I to a better form.
- Instruction *tryReassociateAdd(Instruction *I);
+ // 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);
+ // Returns whether V is known to be non-negative at context \c Ctxt.
+ bool isKnownNonNegative(Value *V, Instruction *Ctxt);
+ // Returns whether AO may sign overflow at context \c Ctxt. It computes a
+ // conservative result -- it answers true when not sure.
+ bool maySignOverflow(AddOperator *AO, Instruction *Ctxt);
+
+ 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. For example,
+ // computing to the same SCEV, so we map a SCEV to an instruction list. For
+ // example,
+ //
// if (p1)
// foo(a + b);
// if (p2)
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(ScalarEvolution)
+INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
+INITIALIZE_PASS_DEPENDENCY(TargetTransformInfoWrapperPass)
INITIALIZE_PASS_END(NaryReassociate, "nary-reassociate", "Nary reassociation",
false, false)
if (skipOptnoneFunction(F))
return false;
+ AC = &getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F);
DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
SE = &getAnalysis<ScalarEvolution>();
+ TLI = &getAnalysis<TargetLibraryInfoWrapperPass>().getTLI();
+ TTI = &getAnalysis<TargetTransformInfoWrapperPass>().getTTI(F);
- // Traverse the dominator tree in the depth-first order. This order makes sure
- // all bases of a candidate are in Candidates when we process it.
+ 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 (I->getOpcode() == Instruction::Add) {
- if (Instruction *NewI = tryReassociateAdd(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);
- I->eraseFromParent();
+ RecursivelyDeleteTriviallyDeadInstructions(I, TLI);
I = NewI;
}
- // We should add the rewritten instruction because tryReassociateAdd may
- // have invalidated the original one.
- SeenExprs[SE->getSCEV(I)].push_back(I);
+ // 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::tryReassociateAdd(Instruction *I) {
+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;
+}
+
+bool NaryReassociate::isKnownNonNegative(Value *V, Instruction *Ctxt) {
+ bool NonNegative, Negative;
+ // TODO: ComputeSignBits is expensive. Consider caching the results.
+ ComputeSignBit(V, NonNegative, Negative, *DL, 0, AC, Ctxt, DT);
+ return NonNegative;
+}
+
+bool NaryReassociate::maySignOverflow(AddOperator *AO, Instruction *Ctxt) {
+ if (AO->hasNoSignedWrap())
+ return false;
+
+ Value *LHS = AO->getOperand(0), *RHS = AO->getOperand(1);
+ // If LHS or RHS has the same sign as the sum, AO doesn't sign overflow.
+ // TODO: handle the negative case as well.
+ if (isKnownNonNegative(AO, Ctxt) &&
+ (isKnownNonNegative(LHS, Ctxt) || isKnownNonNegative(RHS, Ctxt)))
+ return false;
+
+ return true;
+}
+
+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), GEP))
+ 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) && maySignOverflow(AO, GEP))
+ 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, GEP) &&
+ 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());
+
+ 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;
// = (A + RHS) + B or (B + RHS) + A
const SCEV *AExpr = SE->getSCEV(A), *BExpr = SE->getSCEV(B);
const SCEV *RHSExpr = SE->getSCEV(RHS);
- if (auto *NewI = tryReassociatedAdd(SE->getAddExpr(AExpr, RHSExpr), B, I))
- return NewI;
- if (auto *NewI = tryReassociatedAdd(SE->getAddExpr(BExpr, RHSExpr), A, I))
- return NewI;
+ 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.
+ // 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 &LHSCandidates = Pos->second;
- unsigned NumIterations = 0;
- // Search at most 10 items to avoid running quadratically.
- static const unsigned MaxNumIterations = 10;
- for (auto LHS = LHSCandidates.rbegin();
- LHS != LHSCandidates.rend() && NumIterations < MaxNumIterations;
- ++LHS, ++NumIterations) {
- if (DT->dominates(*LHS, I)) {
- Instruction *NewI = BinaryOperator::CreateAdd(*LHS, RHS, "", I);
- NewI->takeName(I);
- return NewI;
- }
+ 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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