1 //===- LoopIndexSplit.cpp - Loop Index Splitting Pass ---------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file was developed by Devang Patel and is distributed under
6 // the University of Illinois Open Source License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file implements Loop Index Splitting Pass.
12 //===----------------------------------------------------------------------===//
14 #define DEBUG_TYPE "loop-index-split"
16 #include "llvm/Transforms/Scalar.h"
17 #include "llvm/Function.h"
18 #include "llvm/Analysis/LoopPass.h"
19 #include "llvm/Analysis/ScalarEvolutionExpander.h"
20 #include "llvm/Analysis/Dominators.h"
21 #include "llvm/Transforms/Utils/BasicBlockUtils.h"
22 #include "llvm/Transforms/Utils/Cloning.h"
23 #include "llvm/Support/Compiler.h"
24 #include "llvm/ADT/Statistic.h"
28 STATISTIC(NumIndexSplit, "Number of loops index split");
32 class VISIBILITY_HIDDEN LoopIndexSplit : public LoopPass {
35 static char ID; // Pass ID, replacement for typeid
36 LoopIndexSplit() : LoopPass((intptr_t)&ID) {}
38 // Index split Loop L. Return true if loop is split.
39 bool runOnLoop(Loop *L, LPPassManager &LPM);
41 void getAnalysisUsage(AnalysisUsage &AU) const {
42 AU.addRequired<ScalarEvolution>();
43 AU.addPreserved<ScalarEvolution>();
44 AU.addRequiredID(LCSSAID);
45 AU.addPreservedID(LCSSAID);
46 AU.addRequired<LoopInfo>();
47 AU.addPreserved<LoopInfo>();
48 AU.addRequiredID(LoopSimplifyID);
49 AU.addPreservedID(LoopSimplifyID);
50 AU.addRequired<DominatorTree>();
51 AU.addPreserved<DominatorTree>();
52 AU.addPreserved<DominanceFrontier>();
59 SplitInfo() : SplitValue(NULL), SplitCondition(NULL) {}
61 // Induction variable's range is split at this value.
64 // This compare instruction compares IndVar against SplitValue.
65 ICmpInst *SplitCondition;
70 SplitCondition = NULL;
76 /// Find condition inside a loop that is suitable candidate for index split.
77 void findSplitCondition();
79 /// Find loop's exit condition.
80 void findLoopConditionals();
82 /// Return induction variable associated with value V.
83 void findIndVar(Value *V, Loop *L);
85 /// processOneIterationLoop - Current loop L contains compare instruction
86 /// that compares induction variable, IndVar, agains loop invariant. If
87 /// entire (i.e. meaningful) loop body is dominated by this compare
88 /// instruction then loop body is executed only for one iteration. In
89 /// such case eliminate loop structure surrounding this loop body. For
90 bool processOneIterationLoop(SplitInfo &SD);
92 /// If loop header includes loop variant instruction operands then
93 /// this loop may not be eliminated.
94 bool safeHeader(SplitInfo &SD, BasicBlock *BB);
96 /// If Exit block includes loop variant instructions then this
97 /// loop may not be eliminated.
98 bool safeExitBlock(SplitInfo &SD, BasicBlock *BB);
100 /// removeBlocks - Remove basic block DeadBB and all blocks dominated by DeadBB.
101 /// This routine is used to remove split condition's dead branch, dominated by
102 /// DeadBB. LiveBB dominates split conidition's other branch.
103 void removeBlocks(BasicBlock *DeadBB, Loop *LP, BasicBlock *LiveBB);
105 /// Find cost of spliting loop L.
106 unsigned findSplitCost(Loop *L, SplitInfo &SD);
107 bool splitLoop(SplitInfo &SD);
111 IndVarIncrement = NULL;
112 ExitCondition = NULL;
126 DominanceFrontier *DF;
127 SmallVector<SplitInfo, 4> SplitData;
129 // Induction variable whose range is being split by this transformation.
131 Instruction *IndVarIncrement;
133 // Loop exit condition.
134 ICmpInst *ExitCondition;
136 // Induction variable's initial value.
139 // Induction variable's final loop exit value operand number in exit condition..
140 unsigned ExitValueNum;
143 char LoopIndexSplit::ID = 0;
144 RegisterPass<LoopIndexSplit> X ("loop-index-split", "Index Split Loops");
147 LoopPass *llvm::createLoopIndexSplitPass() {
148 return new LoopIndexSplit();
151 // Index split Loop L. Return true if loop is split.
152 bool LoopIndexSplit::runOnLoop(Loop *IncomingLoop, LPPassManager &LPM_Ref) {
153 bool Changed = false;
157 // FIXME - Nested loops makes dominator info updates tricky.
158 if (!L->getSubLoops().empty())
161 SE = &getAnalysis<ScalarEvolution>();
162 DT = &getAnalysis<DominatorTree>();
163 LI = &getAnalysis<LoopInfo>();
164 DF = getAnalysisToUpdate<DominanceFrontier>();
168 findLoopConditionals();
173 findSplitCondition();
175 if (SplitData.empty())
178 // First see if it is possible to eliminate loop itself or not.
179 for (SmallVector<SplitInfo, 4>::iterator SI = SplitData.begin(),
180 E = SplitData.end(); SI != E; ++SI) {
182 if (SD.SplitCondition->getPredicate() == ICmpInst::ICMP_EQ) {
183 Changed = processOneIterationLoop(SD);
186 // If is loop is eliminated then nothing else to do here.
192 unsigned MaxCost = 99;
194 unsigned MostProfitableSDIndex = 0;
195 for (SmallVector<SplitInfo, 4>::iterator SI = SplitData.begin(),
196 E = SplitData.end(); SI != E; ++SI, ++Index) {
199 // ICM_EQs are already handled above.
200 if (SD.SplitCondition->getPredicate() == ICmpInst::ICMP_EQ)
203 unsigned Cost = findSplitCost(L, SD);
205 MostProfitableSDIndex = Index;
208 // Split most profitiable condition.
209 Changed = splitLoop(SplitData[MostProfitableSDIndex]);
217 /// Return true if V is a induction variable or induction variable's
218 /// increment for loop L.
219 void LoopIndexSplit::findIndVar(Value *V, Loop *L) {
221 Instruction *I = dyn_cast<Instruction>(V);
225 // Check if I is a phi node from loop header or not.
226 if (PHINode *PN = dyn_cast<PHINode>(V)) {
227 if (PN->getParent() == L->getHeader()) {
233 // Check if I is a add instruction whose one operand is
234 // phi node from loop header and second operand is constant.
235 if (I->getOpcode() != Instruction::Add)
238 Value *Op0 = I->getOperand(0);
239 Value *Op1 = I->getOperand(1);
241 if (PHINode *PN = dyn_cast<PHINode>(Op0)) {
242 if (PN->getParent() == L->getHeader()
243 && isa<ConstantInt>(Op1)) {
250 if (PHINode *PN = dyn_cast<PHINode>(Op1)) {
251 if (PN->getParent() == L->getHeader()
252 && isa<ConstantInt>(Op0)) {
262 // Find loop's exit condition and associated induction variable.
263 void LoopIndexSplit::findLoopConditionals() {
265 BasicBlock *ExitBlock = NULL;
267 for (Loop::block_iterator I = L->block_begin(), E = L->block_end();
270 if (!L->isLoopExit(BB))
280 // If exit block's terminator is conditional branch inst then we have found
282 BranchInst *BR = dyn_cast<BranchInst>(ExitBlock->getTerminator());
283 if (!BR || BR->isUnconditional())
286 ICmpInst *CI = dyn_cast<ICmpInst>(BR->getCondition());
292 // Exit condition's one operand is loop invariant exit value and second
293 // operand is SCEVAddRecExpr based on induction variable.
294 Value *V0 = CI->getOperand(0);
295 Value *V1 = CI->getOperand(1);
297 SCEVHandle SH0 = SE->getSCEV(V0);
298 SCEVHandle SH1 = SE->getSCEV(V1);
300 if (SH0->isLoopInvariant(L) && isa<SCEVAddRecExpr>(SH1)) {
304 else if (SH1->isLoopInvariant(L) && isa<SCEVAddRecExpr>(SH0)) {
310 ExitCondition = NULL;
312 BasicBlock *Preheader = L->getLoopPreheader();
313 StartValue = IndVar->getIncomingValueForBlock(Preheader);
317 /// Find condition inside a loop that is suitable candidate for index split.
318 void LoopIndexSplit::findSplitCondition() {
321 // Check all basic block's terminators.
323 for (Loop::block_iterator I = L->block_begin(), E = L->block_end();
327 // If this basic block does not terminate in a conditional branch
328 // then terminator is not a suitable split condition.
329 BranchInst *BR = dyn_cast<BranchInst>(BB->getTerminator());
333 if (BR->isUnconditional())
336 ICmpInst *CI = dyn_cast<ICmpInst>(BR->getCondition());
337 if (!CI || CI == ExitCondition)
340 // If one operand is loop invariant and second operand is SCEVAddRecExpr
341 // based on induction variable then CI is a candidate split condition.
342 Value *V0 = CI->getOperand(0);
343 Value *V1 = CI->getOperand(1);
345 SCEVHandle SH0 = SE->getSCEV(V0);
346 SCEVHandle SH1 = SE->getSCEV(V1);
348 if (SH0->isLoopInvariant(L) && isa<SCEVAddRecExpr>(SH1)) {
350 SD.SplitCondition = CI;
351 if (PHINode *PN = dyn_cast<PHINode>(V1)) {
353 SplitData.push_back(SD);
355 else if (Instruction *Insn = dyn_cast<Instruction>(V1)) {
356 if (IndVarIncrement && IndVarIncrement == Insn)
357 SplitData.push_back(SD);
360 else if (SH1->isLoopInvariant(L) && isa<SCEVAddRecExpr>(SH0)) {
362 SD.SplitCondition = CI;
363 if (PHINode *PN = dyn_cast<PHINode>(V0)) {
365 SplitData.push_back(SD);
367 else if (Instruction *Insn = dyn_cast<Instruction>(V0)) {
368 if (IndVarIncrement && IndVarIncrement == Insn)
369 SplitData.push_back(SD);
375 /// processOneIterationLoop - Current loop L contains compare instruction
376 /// that compares induction variable, IndVar, against loop invariant. If
377 /// entire (i.e. meaningful) loop body is dominated by this compare
378 /// instruction then loop body is executed only once. In such case eliminate
379 /// loop structure surrounding this loop body. For example,
380 /// for (int i = start; i < end; ++i) {
381 /// if ( i == somevalue) {
385 /// can be transformed into
386 /// if (somevalue >= start && somevalue < end) {
390 bool LoopIndexSplit::processOneIterationLoop(SplitInfo &SD) {
392 BasicBlock *Header = L->getHeader();
394 // First of all, check if SplitCondition dominates entire loop body
397 // If SplitCondition is not in loop header then this loop is not suitable
398 // for this transformation.
399 if (SD.SplitCondition->getParent() != Header)
402 // If loop header includes loop variant instruction operands then
403 // this loop may not be eliminated.
404 if (!safeHeader(SD, Header))
407 // If Exit block includes loop variant instructions then this
408 // loop may not be eliminated.
409 if (!safeExitBlock(SD, ExitCondition->getParent()))
414 // As a first step to break this loop, remove Latch to Header edge.
415 BasicBlock *Latch = L->getLoopLatch();
416 BasicBlock *LatchSucc = NULL;
417 BranchInst *BR = dyn_cast<BranchInst>(Latch->getTerminator());
420 Header->removePredecessor(Latch);
421 for (succ_iterator SI = succ_begin(Latch), E = succ_end(Latch);
426 BR->setUnconditionalDest(LatchSucc);
428 Instruction *Terminator = Header->getTerminator();
429 Value *ExitValue = ExitCondition->getOperand(ExitValueNum);
431 // Replace split condition in header.
433 // SplitCondition : icmp eq i32 IndVar, SplitValue
435 // c1 = icmp uge i32 SplitValue, StartValue
436 // c2 = icmp ult i32 vSplitValue, ExitValue
438 bool SignedPredicate = ExitCondition->isSignedPredicate();
439 Instruction *C1 = new ICmpInst(SignedPredicate ?
440 ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE,
441 SD.SplitValue, StartValue, "lisplit",
443 Instruction *C2 = new ICmpInst(SignedPredicate ?
444 ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
445 SD.SplitValue, ExitValue, "lisplit",
447 Instruction *NSplitCond = BinaryOperator::createAnd(C1, C2, "lisplit",
449 SD.SplitCondition->replaceAllUsesWith(NSplitCond);
450 SD.SplitCondition->eraseFromParent();
452 // Now, clear latch block. Remove instructions that are responsible
453 // to increment induction variable.
454 Instruction *LTerminator = Latch->getTerminator();
455 for (BasicBlock::iterator LB = Latch->begin(), LE = Latch->end();
459 if (isa<PHINode>(I) || I == LTerminator)
462 if (I == IndVarIncrement)
463 I->replaceAllUsesWith(ExitValue);
465 I->replaceAllUsesWith(UndefValue::get(I->getType()));
466 I->eraseFromParent();
469 LPM->deleteLoopFromQueue(L);
471 // Update Dominator Info.
472 // Only CFG change done is to remove Latch to Header edge. This
473 // does not change dominator tree because Latch did not dominate
476 DominanceFrontier::iterator HeaderDF = DF->find(Header);
477 if (HeaderDF != DF->end())
478 DF->removeFromFrontier(HeaderDF, Header);
480 DominanceFrontier::iterator LatchDF = DF->find(Latch);
481 if (LatchDF != DF->end())
482 DF->removeFromFrontier(LatchDF, Header);
487 // If loop header includes loop variant instruction operands then
488 // this loop can not be eliminated. This is used by processOneIterationLoop().
489 bool LoopIndexSplit::safeHeader(SplitInfo &SD, BasicBlock *Header) {
491 Instruction *Terminator = Header->getTerminator();
492 for(BasicBlock::iterator BI = Header->begin(), BE = Header->end();
500 // SplitCondition itself is OK.
501 if (I == SD.SplitCondition)
504 // Induction variable is OK.
508 // Induction variable increment is OK.
509 if (I == IndVarIncrement)
512 // Terminator is also harmless.
516 // Otherwise we have a instruction that may not be safe.
523 // If Exit block includes loop variant instructions then this
524 // loop may not be eliminated. This is used by processOneIterationLoop().
525 bool LoopIndexSplit::safeExitBlock(SplitInfo &SD, BasicBlock *ExitBlock) {
527 for (BasicBlock::iterator BI = ExitBlock->begin(), BE = ExitBlock->end();
535 // Induction variable increment is OK.
536 if (IndVarIncrement && IndVarIncrement == I)
539 // Check if I is induction variable increment instruction.
540 if (!IndVarIncrement && I->getOpcode() == Instruction::Add) {
542 Value *Op0 = I->getOperand(0);
543 Value *Op1 = I->getOperand(1);
545 ConstantInt *CI = NULL;
547 if ((PN = dyn_cast<PHINode>(Op0))) {
548 if ((CI = dyn_cast<ConstantInt>(Op1)))
551 if ((PN = dyn_cast<PHINode>(Op1))) {
552 if ((CI = dyn_cast<ConstantInt>(Op0)))
556 if (IndVarIncrement && PN == IndVar && CI->isOne())
560 // I is an Exit condition if next instruction is block terminator.
561 // Exit condition is OK if it compares loop invariant exit value,
562 // which is checked below.
563 else if (ICmpInst *EC = dyn_cast<ICmpInst>(I)) {
564 if (EC == ExitCondition)
568 if (I == ExitBlock->getTerminator())
571 // Otherwise we have instruction that may not be safe.
575 // We could not find any reason to consider ExitBlock unsafe.
579 /// Find cost of spliting loop L. Cost is measured in terms of size growth.
580 /// Size is growth is calculated based on amount of code duplicated in second
582 unsigned LoopIndexSplit::findSplitCost(Loop *L, SplitInfo &SD) {
585 BasicBlock *SDBlock = SD.SplitCondition->getParent();
586 for (Loop::block_iterator I = L->block_begin(), E = L->block_end();
589 // If a block is not dominated by split condition block then
590 // it must be duplicated in both loops.
591 if (!DT->dominates(SDBlock, BB))
598 /// removeBlocks - Remove basic block DeadBB and all blocks dominated by DeadBB.
599 /// This routine is used to remove split condition's dead branch, dominated by
600 /// DeadBB. LiveBB dominates split conidition's other branch.
601 void LoopIndexSplit::removeBlocks(BasicBlock *DeadBB, Loop *LP,
602 BasicBlock *LiveBB) {
604 SmallVector<std::pair<BasicBlock *, succ_iterator>, 8> WorkList;
605 WorkList.push_back(std::make_pair(DeadBB, succ_begin(DeadBB)));
606 while (!WorkList.empty()) {
607 BasicBlock *BB = WorkList.back(). first;
608 succ_iterator SIter =WorkList.back().second;
610 // If all successor's are processed then remove this block.
611 if (SIter == succ_end(BB)) {
613 for(BasicBlock::iterator BBI = BB->begin(), BBE = BB->end();
615 Instruction *I = BBI;
616 I->replaceAllUsesWith(UndefValue::get(I->getType()));
617 I->eraseFromParent();
619 LPM->deleteSimpleAnalysisValue(BB, LP);
623 BB->eraseFromParent();
625 BasicBlock *SuccBB = *SIter;
626 ++WorkList.back().second;
628 if (DT->dominates(BB, SuccBB)) {
629 WorkList.push_back(std::make_pair(SuccBB, succ_begin(SuccBB)));
632 // If SuccBB is not dominated by BB then it is not removed, however remove
633 // any PHI incoming edge from BB.
634 for(BasicBlock::iterator SBI = SuccBB->begin(), SBE = SuccBB->end();
636 if (PHINode *PN = dyn_cast<PHINode>(SBI))
637 PN->removeIncomingValue(BB);
642 DT->changeImmediateDominator(SuccBB, LiveBB);
644 // If BB is not dominating SuccBB then SuccBB is in BB's dominance
646 DominanceFrontier::iterator BBDF = DF->find(BB);
647 DF->removeFromFrontier(BBDF, SuccBB);
649 // LiveBB is now dominating SuccBB. Which means SuccBB's dominance
650 // frontier is member of LiveBB's dominance frontier. However, SuccBB
651 // itself is not member of LiveBB's dominance frontier.
652 DominanceFrontier::iterator LiveDF = DF->find(LiveBB);
653 DominanceFrontier::iterator SuccDF = DF->find(SuccBB);
654 DominanceFrontier::DomSetType SuccBBSet = SuccDF->second;
655 for (DominanceFrontier::DomSetType::iterator SuccBBSetI = SuccBBSet.begin(),
656 SuccBBSetE = SuccBBSet.end(); SuccBBSetI != SuccBBSetE; ++SuccBBSetI) {
657 BasicBlock *DFMember = *SuccBBSetI;
658 // Insert only if LiveBB dominates DFMember.
659 if (!DT->dominates(LiveBB, DFMember))
660 LiveDF->second.insert(DFMember);
662 DF->removeFromFrontier(LiveDF, SuccBB);
669 bool LoopIndexSplit::splitLoop(SplitInfo &SD) {
671 BasicBlock *Preheader = L->getLoopPreheader();
673 // True loop is original loop. False loop is cloned loop.
675 bool SignedPredicate = ExitCondition->isSignedPredicate();
676 //[*] Calculate True loop's new Exit Value in loop preheader.
677 // TLExitValue = min(SplitValue, ExitValue)
678 //[*] Calculate False loop's new Start Value in loop preheader.
679 // FLStartValue = min(SplitValue, TrueLoop.StartValue)
680 Value *TLExitValue = NULL;
681 Value *FLStartValue = NULL;
682 if (isa<ConstantInt>(SD.SplitValue)) {
683 TLExitValue = SD.SplitValue;
684 FLStartValue = SD.SplitValue;
687 Value *C1 = new ICmpInst(SignedPredicate ?
688 ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
690 ExitCondition->getOperand(ExitValueNum),
692 Preheader->getTerminator());
693 TLExitValue = new SelectInst(C1, SD.SplitValue,
694 ExitCondition->getOperand(ExitValueNum),
695 "lsplit.ev", Preheader->getTerminator());
697 Value *C2 = new ICmpInst(SignedPredicate ?
698 ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
699 SD.SplitValue, StartValue, "lsplit.sv",
700 Preheader->getTerminator());
701 FLStartValue = new SelectInst(C2, SD.SplitValue, StartValue,
702 "lsplit.sv", Preheader->getTerminator());
705 //[*] Clone loop. Avoid true destination of split condition and
706 // the blocks dominated by true destination.
707 DenseMap<const Value *, Value *> ValueMap;
708 Loop *FalseLoop = CloneLoop(L, LPM, LI, ValueMap, this);
709 BasicBlock *FalseHeader = FalseLoop->getHeader();
711 //[*] True loop's exit edge enters False loop.
712 PHINode *IndVarClone = cast<PHINode>(ValueMap[IndVar]);
713 BasicBlock *ExitBlock = ExitCondition->getParent();
714 BranchInst *ExitInsn = dyn_cast<BranchInst>(ExitBlock->getTerminator());
715 assert (ExitInsn && "Unable to find suitable loop exit branch");
716 BasicBlock *ExitDest = ExitInsn->getSuccessor(1);
718 if (L->contains(ExitDest)) {
719 ExitDest = ExitInsn->getSuccessor(0);
720 ExitInsn->setSuccessor(0, FalseHeader);
722 ExitInsn->setSuccessor(1, FalseHeader);
724 // Collect inverse map of Header PHINodes.
725 DenseMap<Value *, Value *> InverseMap;
726 for (BasicBlock::iterator BI = L->getHeader()->begin(),
727 BE = L->getHeader()->end(); BI != BE; ++BI) {
728 if (PHINode *PN = dyn_cast<PHINode>(BI)) {
729 PHINode *PNClone = cast<PHINode>(ValueMap[PN]);
730 InverseMap[PNClone] = PN;
735 // Update False loop's header
736 for (BasicBlock::iterator BI = FalseHeader->begin(), BE = FalseHeader->end();
738 if (PHINode *PN = dyn_cast<PHINode>(BI)) {
739 PN->removeIncomingValue(Preheader);
740 if (PN == IndVarClone)
741 PN->addIncoming(FLStartValue, ExitBlock);
743 PHINode *OrigPN = cast<PHINode>(InverseMap[PN]);
744 Value *V2 = OrigPN->getIncomingValueForBlock(ExitBlock);
745 PN->addIncoming(V2, ExitBlock);
751 // Update ExitDest. Now it's predecessor is False loop's exit block.
752 BasicBlock *ExitBlockClone = cast<BasicBlock>(ValueMap[ExitBlock]);
753 for (BasicBlock::iterator BI = ExitDest->begin(), BE = ExitDest->end();
755 if (PHINode *PN = dyn_cast<PHINode>(BI)) {
756 PN->addIncoming(ValueMap[PN->getIncomingValueForBlock(ExitBlock)], ExitBlockClone);
757 PN->removeIncomingValue(ExitBlock);
763 DT->changeImmediateDominator(FalseHeader, ExitBlock);
764 DT->changeImmediateDominator(ExitDest, cast<BasicBlock>(ValueMap[ExitBlock]));
767 assert (!L->contains(ExitDest) && " Unable to find exit edge destination");
769 //[*] Split Exit Edge.
770 SplitEdge(ExitBlock, FalseHeader, this);
772 //[*] Eliminate split condition's false branch from True loop.
773 BasicBlock *SplitBlock = SD.SplitCondition->getParent();
774 BranchInst *BR = cast<BranchInst>(SplitBlock->getTerminator());
775 BasicBlock *FBB = BR->getSuccessor(1);
776 BR->setUnconditionalDest(BR->getSuccessor(0));
777 removeBlocks(FBB, L, BR->getSuccessor(0));
779 //[*] Update True loop's exit value using new exit value.
780 ExitCondition->setOperand(ExitValueNum, TLExitValue);
782 //[*] Eliminate split condition's true branch in False loop CFG.
783 BasicBlock *FSplitBlock = cast<BasicBlock>(ValueMap[SplitBlock]);
784 BranchInst *FBR = cast<BranchInst>(FSplitBlock->getTerminator());
785 BasicBlock *TBB = FBR->getSuccessor(0);
786 FBR->setUnconditionalDest(FBR->getSuccessor(1));
787 removeBlocks(TBB, FalseLoop, cast<BasicBlock>(FBR->getSuccessor(0)));