//===- LoopInfo.cpp - Natural Loop Calculator -----------------------------===// // // The LLVM Compiler Infrastructure // // This file is distributed under the University of Illinois Open Source // License. See LICENSE.TXT for details. // //===----------------------------------------------------------------------===// // // This file defines the LoopInfo class that is used to identify natural loops // and determine the loop depth of various nodes of the CFG. Note that the // loops identified may actually be several natural loops that share the same // header node... not just a single natural loop. // //===----------------------------------------------------------------------===// #include "llvm/Analysis/LoopInfo.h" #include "llvm/ADT/DepthFirstIterator.h" #include "llvm/ADT/SmallPtrSet.h" #include "llvm/Analysis/Dominators.h" #include "llvm/Analysis/LoopInfoImpl.h" #include "llvm/Analysis/LoopIterator.h" #include "llvm/Analysis/ValueTracking.h" #include "llvm/Assembly/Writer.h" #include "llvm/IR/Constants.h" #include "llvm/IR/Instructions.h" #include "llvm/IR/Metadata.h" #include "llvm/Support/CFG.h" #include "llvm/Support/CommandLine.h" #include "llvm/Support/Debug.h" #include <algorithm> using namespace llvm; // Explicitly instantiate methods in LoopInfoImpl.h for IR-level Loops. template class llvm::LoopBase<BasicBlock, Loop>; template class llvm::LoopInfoBase<BasicBlock, Loop>; // Always verify loopinfo if expensive checking is enabled. #ifdef XDEBUG static bool VerifyLoopInfo = true; #else static bool VerifyLoopInfo = false; #endif static cl::opt<bool,true> VerifyLoopInfoX("verify-loop-info", cl::location(VerifyLoopInfo), cl::desc("Verify loop info (time consuming)")); char LoopInfo::ID = 0; INITIALIZE_PASS_BEGIN(LoopInfo, "loops", "Natural Loop Information", true, true) INITIALIZE_PASS_DEPENDENCY(DominatorTree) INITIALIZE_PASS_END(LoopInfo, "loops", "Natural Loop Information", true, true) // Loop identifier metadata name. static const char *const LoopMDName = "llvm.loop"; //===----------------------------------------------------------------------===// // Loop implementation // /// isLoopInvariant - Return true if the specified value is loop invariant /// bool Loop::isLoopInvariant(Value *V) const { if (Instruction *I = dyn_cast<Instruction>(V)) return !contains(I); return true; // All non-instructions are loop invariant } /// hasLoopInvariantOperands - Return true if all the operands of the /// specified instruction are loop invariant. bool Loop::hasLoopInvariantOperands(Instruction *I) const { for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) if (!isLoopInvariant(I->getOperand(i))) return false; return true; } /// makeLoopInvariant - If the given value is an instruciton inside of the /// loop and it can be hoisted, do so to make it trivially loop-invariant. /// Return true if the value after any hoisting is loop invariant. This /// function can be used as a slightly more aggressive replacement for /// isLoopInvariant. /// /// If InsertPt is specified, it is the point to hoist instructions to. /// If null, the terminator of the loop preheader is used. /// bool Loop::makeLoopInvariant(Value *V, bool &Changed, Instruction *InsertPt) const { if (Instruction *I = dyn_cast<Instruction>(V)) return makeLoopInvariant(I, Changed, InsertPt); return true; // All non-instructions are loop-invariant. } /// makeLoopInvariant - If the given instruction is inside of the /// loop and it can be hoisted, do so to make it trivially loop-invariant. /// Return true if the instruction after any hoisting is loop invariant. This /// function can be used as a slightly more aggressive replacement for /// isLoopInvariant. /// /// If InsertPt is specified, it is the point to hoist instructions to. /// If null, the terminator of the loop preheader is used. /// bool Loop::makeLoopInvariant(Instruction *I, bool &Changed, Instruction *InsertPt) const { // Test if the value is already loop-invariant. if (isLoopInvariant(I)) return true; if (!isSafeToSpeculativelyExecute(I)) return false; if (I->mayReadFromMemory()) return false; // The landingpad instruction is immobile. if (isa<LandingPadInst>(I)) return false; // Determine the insertion point, unless one was given. if (!InsertPt) { BasicBlock *Preheader = getLoopPreheader(); // Without a preheader, hoisting is not feasible. if (!Preheader) return false; InsertPt = Preheader->getTerminator(); } // Don't hoist instructions with loop-variant operands. for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) if (!makeLoopInvariant(I->getOperand(i), Changed, InsertPt)) return false; // Hoist. I->moveBefore(InsertPt); Changed = true; return true; } /// getCanonicalInductionVariable - Check to see if the loop has a canonical /// induction variable: an integer recurrence that starts at 0 and increments /// by one each time through the loop. If so, return the phi node that /// corresponds to it. /// /// The IndVarSimplify pass transforms loops to have a canonical induction /// variable. /// PHINode *Loop::getCanonicalInductionVariable() const { BasicBlock *H = getHeader(); BasicBlock *Incoming = 0, *Backedge = 0; pred_iterator PI = pred_begin(H); assert(PI != pred_end(H) && "Loop must have at least one backedge!"); Backedge = *PI++; if (PI == pred_end(H)) return 0; // dead loop Incoming = *PI++; if (PI != pred_end(H)) return 0; // multiple backedges? if (contains(Incoming)) { if (contains(Backedge)) return 0; std::swap(Incoming, Backedge); } else if (!contains(Backedge)) return 0; // Loop over all of the PHI nodes, looking for a canonical indvar. for (BasicBlock::iterator I = H->begin(); isa<PHINode>(I); ++I) { PHINode *PN = cast<PHINode>(I); if (ConstantInt *CI = dyn_cast<ConstantInt>(PN->getIncomingValueForBlock(Incoming))) if (CI->isNullValue()) if (Instruction *Inc = dyn_cast<Instruction>(PN->getIncomingValueForBlock(Backedge))) if (Inc->getOpcode() == Instruction::Add && Inc->getOperand(0) == PN) if (ConstantInt *CI = dyn_cast<ConstantInt>(Inc->getOperand(1))) if (CI->equalsInt(1)) return PN; } return 0; } /// isLCSSAForm - Return true if the Loop is in LCSSA form bool Loop::isLCSSAForm(DominatorTree &DT) const { // Sort the blocks vector so that we can use binary search to do quick // lookups. SmallPtrSet<BasicBlock*, 16> LoopBBs(block_begin(), block_end()); for (block_iterator BI = block_begin(), E = block_end(); BI != E; ++BI) { BasicBlock *BB = *BI; for (BasicBlock::iterator I = BB->begin(), E = BB->end(); I != E;++I) for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); UI != E; ++UI) { User *U = *UI; BasicBlock *UserBB = cast<Instruction>(U)->getParent(); if (PHINode *P = dyn_cast<PHINode>(U)) UserBB = P->getIncomingBlock(UI); // Check the current block, as a fast-path, before checking whether // the use is anywhere in the loop. Most values are used in the same // block they are defined in. Also, blocks not reachable from the // entry are special; uses in them don't need to go through PHIs. if (UserBB != BB && !LoopBBs.count(UserBB) && DT.isReachableFromEntry(UserBB)) return false; } } return true; } /// isLoopSimplifyForm - Return true if the Loop is in the form that /// the LoopSimplify form transforms loops to, which is sometimes called /// normal form. bool Loop::isLoopSimplifyForm() const { // Normal-form loops have a preheader, a single backedge, and all of their // exits have all their predecessors inside the loop. return getLoopPreheader() && getLoopLatch() && hasDedicatedExits(); } /// isSafeToClone - Return true if the loop body is safe to clone in practice. /// Routines that reform the loop CFG and split edges often fail on indirectbr. bool Loop::isSafeToClone() const { // Return false if any loop blocks contain indirectbrs, or there are any calls // to noduplicate functions. for (Loop::block_iterator I = block_begin(), E = block_end(); I != E; ++I) { if (isa<IndirectBrInst>((*I)->getTerminator())) { return false; } else if (const InvokeInst *II = dyn_cast<InvokeInst>((*I)->getTerminator())) { if (II->hasFnAttr(Attribute::NoDuplicate)) return false; } for (BasicBlock::iterator BI = (*I)->begin(), BE = (*I)->end(); BI != BE; ++BI) { if (const CallInst *CI = dyn_cast<CallInst>(BI)) { if (CI->hasFnAttr(Attribute::NoDuplicate)) return false; } } } return true; } MDNode *Loop::getLoopID() const { MDNode *LoopID = 0; if (isLoopSimplifyForm()) { LoopID = getLoopLatch()->getTerminator()->getMetadata(LoopMDName); } else { // Go through each predecessor of the loop header and check the // terminator for the metadata. BasicBlock *H = getHeader(); for (block_iterator I = block_begin(), IE = block_end(); I != IE; ++I) { TerminatorInst *TI = (*I)->getTerminator(); MDNode *MD = 0; // Check if this terminator branches to the loop header. for (unsigned i = 0, ie = TI->getNumSuccessors(); i != ie; ++i) { if (TI->getSuccessor(i) == H) { MD = TI->getMetadata(LoopMDName); break; } } if (!MD) return 0; if (!LoopID) LoopID = MD; else if (MD != LoopID) return 0; } } if (!LoopID || LoopID->getNumOperands() == 0 || LoopID->getOperand(0) != LoopID) return 0; return LoopID; } void Loop::setLoopID(MDNode *LoopID) const { assert(LoopID && "Loop ID should not be null"); assert(LoopID->getNumOperands() > 0 && "Loop ID needs at least one operand"); assert(LoopID->getOperand(0) == LoopID && "Loop ID should refer to itself"); if (isLoopSimplifyForm()) { getLoopLatch()->getTerminator()->setMetadata(LoopMDName, LoopID); return; } BasicBlock *H = getHeader(); for (block_iterator I = block_begin(), IE = block_end(); I != IE; ++I) { TerminatorInst *TI = (*I)->getTerminator(); for (unsigned i = 0, ie = TI->getNumSuccessors(); i != ie; ++i) { if (TI->getSuccessor(i) == H) TI->setMetadata(LoopMDName, LoopID); } } } bool Loop::isAnnotatedParallel() const { MDNode *desiredLoopIdMetadata = getLoopID(); if (!desiredLoopIdMetadata) return false; // The loop branch contains the parallel loop metadata. In order to ensure // that any parallel-loop-unaware optimization pass hasn't added loop-carried // dependencies (thus converted the loop back to a sequential loop), check // that all the memory instructions in the loop contain parallelism metadata // that point to the same unique "loop id metadata" the loop branch does. for (block_iterator BB = block_begin(), BE = block_end(); BB != BE; ++BB) { for (BasicBlock::iterator II = (*BB)->begin(), EE = (*BB)->end(); II != EE; II++) { if (!II->mayReadOrWriteMemory()) continue; if (!II->getMetadata("llvm.mem.parallel_loop_access")) return false; // The memory instruction can refer to the loop identifier metadata // directly or indirectly through another list metadata (in case of // nested parallel loops). The loop identifier metadata refers to // itself so we can check both cases with the same routine. MDNode *loopIdMD = dyn_cast<MDNode>(II->getMetadata("llvm.mem.parallel_loop_access")); bool loopIdMDFound = false; for (unsigned i = 0, e = loopIdMD->getNumOperands(); i < e; ++i) { if (loopIdMD->getOperand(i) == desiredLoopIdMetadata) { loopIdMDFound = true; break; } } if (!loopIdMDFound) return false; } } return true; } /// hasDedicatedExits - Return true if no exit block for the loop /// has a predecessor that is outside the loop. bool Loop::hasDedicatedExits() const { // Sort the blocks vector so that we can use binary search to do quick // lookups. SmallPtrSet<BasicBlock *, 16> LoopBBs(block_begin(), block_end()); // Each predecessor of each exit block of a normal loop is contained // within the loop. SmallVector<BasicBlock *, 4> ExitBlocks; getExitBlocks(ExitBlocks); for (unsigned i = 0, e = ExitBlocks.size(); i != e; ++i) for (pred_iterator PI = pred_begin(ExitBlocks[i]), PE = pred_end(ExitBlocks[i]); PI != PE; ++PI) if (!LoopBBs.count(*PI)) return false; // All the requirements are met. return true; } /// getUniqueExitBlocks - Return all unique successor blocks of this loop. /// These are the blocks _outside of the current loop_ which are branched to. /// This assumes that loop exits are in canonical form. /// void Loop::getUniqueExitBlocks(SmallVectorImpl<BasicBlock *> &ExitBlocks) const { assert(hasDedicatedExits() && "getUniqueExitBlocks assumes the loop has canonical form exits!"); // Sort the blocks vector so that we can use binary search to do quick // lookups. SmallVector<BasicBlock *, 128> LoopBBs(block_begin(), block_end()); std::sort(LoopBBs.begin(), LoopBBs.end()); SmallVector<BasicBlock *, 32> switchExitBlocks; for (block_iterator BI = block_begin(), BE = block_end(); BI != BE; ++BI) { BasicBlock *current = *BI; switchExitBlocks.clear(); for (succ_iterator I = succ_begin(*BI), E = succ_end(*BI); I != E; ++I) { // If block is inside the loop then it is not a exit block. if (std::binary_search(LoopBBs.begin(), LoopBBs.end(), *I)) continue; pred_iterator PI = pred_begin(*I); BasicBlock *firstPred = *PI; // If current basic block is this exit block's first predecessor // then only insert exit block in to the output ExitBlocks vector. // This ensures that same exit block is not inserted twice into // ExitBlocks vector. if (current != firstPred) continue; // If a terminator has more then two successors, for example SwitchInst, // then it is possible that there are multiple edges from current block // to one exit block. if (std::distance(succ_begin(current), succ_end(current)) <= 2) { ExitBlocks.push_back(*I); continue; } // In case of multiple edges from current block to exit block, collect // only one edge in ExitBlocks. Use switchExitBlocks to keep track of // duplicate edges. if (std::find(switchExitBlocks.begin(), switchExitBlocks.end(), *I) == switchExitBlocks.end()) { switchExitBlocks.push_back(*I); ExitBlocks.push_back(*I); } } } } /// getUniqueExitBlock - If getUniqueExitBlocks would return exactly one /// block, return that block. Otherwise return null. BasicBlock *Loop::getUniqueExitBlock() const { SmallVector<BasicBlock *, 8> UniqueExitBlocks; getUniqueExitBlocks(UniqueExitBlocks); if (UniqueExitBlocks.size() == 1) return UniqueExitBlocks[0]; return 0; } #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP) void Loop::dump() const { print(dbgs()); } #endif //===----------------------------------------------------------------------===// // UnloopUpdater implementation // namespace { /// Find the new parent loop for all blocks within the "unloop" whose last /// backedges has just been removed. class UnloopUpdater { Loop *Unloop; LoopInfo *LI; LoopBlocksDFS DFS; // Map unloop's immediate subloops to their nearest reachable parents. Nested // loops within these subloops will not change parents. However, an immediate // subloop's new parent will be the nearest loop reachable from either its own // exits *or* any of its nested loop's exits. DenseMap<Loop*, Loop*> SubloopParents; // Flag the presence of an irreducible backedge whose destination is a block // directly contained by the original unloop. bool FoundIB; public: UnloopUpdater(Loop *UL, LoopInfo *LInfo) : Unloop(UL), LI(LInfo), DFS(UL), FoundIB(false) {} void updateBlockParents(); void removeBlocksFromAncestors(); void updateSubloopParents(); protected: Loop *getNearestLoop(BasicBlock *BB, Loop *BBLoop); }; } // end anonymous namespace /// updateBlockParents - Update the parent loop for all blocks that are directly /// contained within the original "unloop". void UnloopUpdater::updateBlockParents() { if (Unloop->getNumBlocks()) { // Perform a post order CFG traversal of all blocks within this loop, // propagating the nearest loop from sucessors to predecessors. LoopBlocksTraversal Traversal(DFS, LI); for (LoopBlocksTraversal::POTIterator POI = Traversal.begin(), POE = Traversal.end(); POI != POE; ++POI) { Loop *L = LI->getLoopFor(*POI); Loop *NL = getNearestLoop(*POI, L); if (NL != L) { // For reducible loops, NL is now an ancestor of Unloop. assert((NL != Unloop && (!NL || NL->contains(Unloop))) && "uninitialized successor"); LI->changeLoopFor(*POI, NL); } else { // Or the current block is part of a subloop, in which case its parent // is unchanged. assert((FoundIB || Unloop->contains(L)) && "uninitialized successor"); } } } // Each irreducible loop within the unloop induces a round of iteration using // the DFS result cached by Traversal. bool Changed = FoundIB; for (unsigned NIters = 0; Changed; ++NIters) { assert(NIters < Unloop->getNumBlocks() && "runaway iterative algorithm"); // Iterate over the postorder list of blocks, propagating the nearest loop // from successors to predecessors as before. Changed = false; for (LoopBlocksDFS::POIterator POI = DFS.beginPostorder(), POE = DFS.endPostorder(); POI != POE; ++POI) { Loop *L = LI->getLoopFor(*POI); Loop *NL = getNearestLoop(*POI, L); if (NL != L) { assert(NL != Unloop && (!NL || NL->contains(Unloop)) && "uninitialized successor"); LI->changeLoopFor(*POI, NL); Changed = true; } } } } /// removeBlocksFromAncestors - Remove unloop's blocks from all ancestors below /// their new parents. void UnloopUpdater::removeBlocksFromAncestors() { // Remove all unloop's blocks (including those in nested subloops) from // ancestors below the new parent loop. for (Loop::block_iterator BI = Unloop->block_begin(), BE = Unloop->block_end(); BI != BE; ++BI) { Loop *OuterParent = LI->getLoopFor(*BI); if (Unloop->contains(OuterParent)) { while (OuterParent->getParentLoop() != Unloop) OuterParent = OuterParent->getParentLoop(); OuterParent = SubloopParents[OuterParent]; } // Remove blocks from former Ancestors except Unloop itself which will be // deleted. for (Loop *OldParent = Unloop->getParentLoop(); OldParent != OuterParent; OldParent = OldParent->getParentLoop()) { assert(OldParent && "new loop is not an ancestor of the original"); OldParent->removeBlockFromLoop(*BI); } } } /// updateSubloopParents - Update the parent loop for all subloops directly /// nested within unloop. void UnloopUpdater::updateSubloopParents() { while (!Unloop->empty()) { Loop *Subloop = *llvm::prior(Unloop->end()); Unloop->removeChildLoop(llvm::prior(Unloop->end())); assert(SubloopParents.count(Subloop) && "DFS failed to visit subloop"); if (Loop *Parent = SubloopParents[Subloop]) Parent->addChildLoop(Subloop); else LI->addTopLevelLoop(Subloop); } } /// getNearestLoop - Return the nearest parent loop among this block's /// successors. If a successor is a subloop header, consider its parent to be /// the nearest parent of the subloop's exits. /// /// For subloop blocks, simply update SubloopParents and return NULL. Loop *UnloopUpdater::getNearestLoop(BasicBlock *BB, Loop *BBLoop) { // Initially for blocks directly contained by Unloop, NearLoop == Unloop and // is considered uninitialized. Loop *NearLoop = BBLoop; Loop *Subloop = 0; if (NearLoop != Unloop && Unloop->contains(NearLoop)) { Subloop = NearLoop; // Find the subloop ancestor that is directly contained within Unloop. while (Subloop->getParentLoop() != Unloop) { Subloop = Subloop->getParentLoop(); assert(Subloop && "subloop is not an ancestor of the original loop"); } // Get the current nearest parent of the Subloop exits, initially Unloop. NearLoop = SubloopParents.insert(std::make_pair(Subloop, Unloop)).first->second; } succ_iterator I = succ_begin(BB), E = succ_end(BB); if (I == E) { assert(!Subloop && "subloop blocks must have a successor"); NearLoop = 0; // unloop blocks may now exit the function. } for (; I != E; ++I) { if (*I == BB) continue; // self loops are uninteresting Loop *L = LI->getLoopFor(*I); if (L == Unloop) { // This successor has not been processed. This path must lead to an // irreducible backedge. assert((FoundIB || !DFS.hasPostorder(*I)) && "should have seen IB"); FoundIB = true; } if (L != Unloop && Unloop->contains(L)) { // Successor is in a subloop. if (Subloop) continue; // Branching within subloops. Ignore it. // BB branches from the original into a subloop header. assert(L->getParentLoop() == Unloop && "cannot skip into nested loops"); // Get the current nearest parent of the Subloop's exits. L = SubloopParents[L]; // L could be Unloop if the only exit was an irreducible backedge. } if (L == Unloop) { continue; } // Handle critical edges from Unloop into a sibling loop. if (L && !L->contains(Unloop)) { L = L->getParentLoop(); } // Remember the nearest parent loop among successors or subloop exits. if (NearLoop == Unloop || !NearLoop || NearLoop->contains(L)) NearLoop = L; } if (Subloop) { SubloopParents[Subloop] = NearLoop; return BBLoop; } return NearLoop; } //===----------------------------------------------------------------------===// // LoopInfo implementation // bool LoopInfo::runOnFunction(Function &) { releaseMemory(); LI.Analyze(getAnalysis<DominatorTree>().getBase()); return false; } /// updateUnloop - The last backedge has been removed from a loop--now the /// "unloop". Find a new parent for the blocks contained within unloop and /// update the loop tree. We don't necessarily have valid dominators at this /// point, but LoopInfo is still valid except for the removal of this loop. /// /// Note that Unloop may now be an empty loop. Calling Loop::getHeader without /// checking first is illegal. void LoopInfo::updateUnloop(Loop *Unloop) { // First handle the special case of no parent loop to simplify the algorithm. if (!Unloop->getParentLoop()) { // Since BBLoop had no parent, Unloop blocks are no longer in a loop. for (Loop::block_iterator I = Unloop->block_begin(), E = Unloop->block_end(); I != E; ++I) { // Don't reparent blocks in subloops. if (getLoopFor(*I) != Unloop) continue; // Blocks no longer have a parent but are still referenced by Unloop until // the Unloop object is deleted. LI.changeLoopFor(*I, 0); } // Remove the loop from the top-level LoopInfo object. for (LoopInfo::iterator I = LI.begin();; ++I) { assert(I != LI.end() && "Couldn't find loop"); if (*I == Unloop) { LI.removeLoop(I); break; } } // Move all of the subloops to the top-level. while (!Unloop->empty()) LI.addTopLevelLoop(Unloop->removeChildLoop(llvm::prior(Unloop->end()))); return; } // Update the parent loop for all blocks within the loop. Blocks within // subloops will not change parents. UnloopUpdater Updater(Unloop, this); Updater.updateBlockParents(); // Remove blocks from former ancestor loops. Updater.removeBlocksFromAncestors(); // Add direct subloops as children in their new parent loop. Updater.updateSubloopParents(); // Remove unloop from its parent loop. Loop *ParentLoop = Unloop->getParentLoop(); for (Loop::iterator I = ParentLoop->begin();; ++I) { assert(I != ParentLoop->end() && "Couldn't find loop"); if (*I == Unloop) { ParentLoop->removeChildLoop(I); break; } } } void LoopInfo::verifyAnalysis() const { // LoopInfo is a FunctionPass, but verifying every loop in the function // each time verifyAnalysis is called is very expensive. The // -verify-loop-info option can enable this. In order to perform some // checking by default, LoopPass has been taught to call verifyLoop // manually during loop pass sequences. if (!VerifyLoopInfo) return; DenseSet<const Loop*> Loops; for (iterator I = begin(), E = end(); I != E; ++I) { assert(!(*I)->getParentLoop() && "Top-level loop has a parent!"); (*I)->verifyLoopNest(&Loops); } // Verify that blocks are mapped to valid loops. for (DenseMap<BasicBlock*, Loop*>::const_iterator I = LI.BBMap.begin(), E = LI.BBMap.end(); I != E; ++I) { assert(Loops.count(I->second) && "orphaned loop"); assert(I->second->contains(I->first) && "orphaned block"); } } void LoopInfo::getAnalysisUsage(AnalysisUsage &AU) const { AU.setPreservesAll(); AU.addRequired<DominatorTree>(); } void LoopInfo::print(raw_ostream &OS, const Module*) const { LI.print(OS); } //===----------------------------------------------------------------------===// // LoopBlocksDFS implementation // /// Traverse the loop blocks and store the DFS result. /// Useful for clients that just want the final DFS result and don't need to /// visit blocks during the initial traversal. void LoopBlocksDFS::perform(LoopInfo *LI) { LoopBlocksTraversal Traversal(*this, LI); for (LoopBlocksTraversal::POTIterator POI = Traversal.begin(), POE = Traversal.end(); POI != POE; ++POI) ; }