1 //===- LoopInfo.cpp - Natural Loop Calculator -----------------------------===// 2 // 3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 4 // See https://llvm.org/LICENSE.txt for license information. 5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 6 // 7 //===----------------------------------------------------------------------===// 8 // 9 // This file defines the LoopInfo class that is used to identify natural loops 10 // and determine the loop depth of various nodes of the CFG. Note that the 11 // loops identified may actually be several natural loops that share the same 12 // header node... not just a single natural loop. 13 // 14 //===----------------------------------------------------------------------===// 15 16 #include "llvm/Analysis/LoopInfo.h" 17 #include "llvm/ADT/DepthFirstIterator.h" 18 #include "llvm/ADT/ScopeExit.h" 19 #include "llvm/ADT/SmallPtrSet.h" 20 #include "llvm/Analysis/IVDescriptors.h" 21 #include "llvm/Analysis/LoopInfoImpl.h" 22 #include "llvm/Analysis/LoopIterator.h" 23 #include "llvm/Analysis/LoopNestAnalysis.h" 24 #include "llvm/Analysis/MemorySSA.h" 25 #include "llvm/Analysis/MemorySSAUpdater.h" 26 #include "llvm/Analysis/ScalarEvolutionExpressions.h" 27 #include "llvm/Analysis/ValueTracking.h" 28 #include "llvm/Config/llvm-config.h" 29 #include "llvm/IR/CFG.h" 30 #include "llvm/IR/Constants.h" 31 #include "llvm/IR/DebugLoc.h" 32 #include "llvm/IR/Dominators.h" 33 #include "llvm/IR/IRPrintingPasses.h" 34 #include "llvm/IR/Instructions.h" 35 #include "llvm/IR/LLVMContext.h" 36 #include "llvm/IR/Metadata.h" 37 #include "llvm/IR/PassManager.h" 38 #include "llvm/IR/PrintPasses.h" 39 #include "llvm/InitializePasses.h" 40 #include "llvm/Support/CommandLine.h" 41 #include "llvm/Support/Debug.h" 42 #include "llvm/Support/raw_ostream.h" 43 #include <algorithm> 44 using namespace llvm; 45 46 // Explicitly instantiate methods in LoopInfoImpl.h for IR-level Loops. 47 template class llvm::LoopBase<BasicBlock, Loop>; 48 template class llvm::LoopInfoBase<BasicBlock, Loop>; 49 50 // Always verify loopinfo if expensive checking is enabled. 51 #ifdef EXPENSIVE_CHECKS 52 bool llvm::VerifyLoopInfo = true; 53 #else 54 bool llvm::VerifyLoopInfo = false; 55 #endif 56 static cl::opt<bool, true> 57 VerifyLoopInfoX("verify-loop-info", cl::location(VerifyLoopInfo), 58 cl::Hidden, cl::desc("Verify loop info (time consuming)")); 59 60 //===----------------------------------------------------------------------===// 61 // Loop implementation 62 // 63 64 bool Loop::isLoopInvariant(const Value *V) const { 65 if (const Instruction *I = dyn_cast<Instruction>(V)) 66 return !contains(I); 67 return true; // All non-instructions are loop invariant 68 } 69 70 bool Loop::hasLoopInvariantOperands(const Instruction *I) const { 71 return all_of(I->operands(), [this](Value *V) { return isLoopInvariant(V); }); 72 } 73 74 bool Loop::makeLoopInvariant(Value *V, bool &Changed, Instruction *InsertPt, 75 MemorySSAUpdater *MSSAU) const { 76 if (Instruction *I = dyn_cast<Instruction>(V)) 77 return makeLoopInvariant(I, Changed, InsertPt, MSSAU); 78 return true; // All non-instructions are loop-invariant. 79 } 80 81 bool Loop::makeLoopInvariant(Instruction *I, bool &Changed, 82 Instruction *InsertPt, 83 MemorySSAUpdater *MSSAU) const { 84 // Test if the value is already loop-invariant. 85 if (isLoopInvariant(I)) 86 return true; 87 if (!isSafeToSpeculativelyExecute(I)) 88 return false; 89 if (I->mayReadFromMemory()) 90 return false; 91 // EH block instructions are immobile. 92 if (I->isEHPad()) 93 return false; 94 // Determine the insertion point, unless one was given. 95 if (!InsertPt) { 96 BasicBlock *Preheader = getLoopPreheader(); 97 // Without a preheader, hoisting is not feasible. 98 if (!Preheader) 99 return false; 100 InsertPt = Preheader->getTerminator(); 101 } 102 // Don't hoist instructions with loop-variant operands. 103 for (Value *Operand : I->operands()) 104 if (!makeLoopInvariant(Operand, Changed, InsertPt, MSSAU)) 105 return false; 106 107 // Hoist. 108 I->moveBefore(InsertPt); 109 if (MSSAU) 110 if (auto *MUD = MSSAU->getMemorySSA()->getMemoryAccess(I)) 111 MSSAU->moveToPlace(MUD, InsertPt->getParent(), 112 MemorySSA::BeforeTerminator); 113 114 // There is possibility of hoisting this instruction above some arbitrary 115 // condition. Any metadata defined on it can be control dependent on this 116 // condition. Conservatively strip it here so that we don't give any wrong 117 // information to the optimizer. 118 I->dropUnknownNonDebugMetadata(); 119 120 Changed = true; 121 return true; 122 } 123 124 bool Loop::getIncomingAndBackEdge(BasicBlock *&Incoming, 125 BasicBlock *&Backedge) const { 126 BasicBlock *H = getHeader(); 127 128 Incoming = nullptr; 129 Backedge = nullptr; 130 pred_iterator PI = pred_begin(H); 131 assert(PI != pred_end(H) && "Loop must have at least one backedge!"); 132 Backedge = *PI++; 133 if (PI == pred_end(H)) 134 return false; // dead loop 135 Incoming = *PI++; 136 if (PI != pred_end(H)) 137 return false; // multiple backedges? 138 139 if (contains(Incoming)) { 140 if (contains(Backedge)) 141 return false; 142 std::swap(Incoming, Backedge); 143 } else if (!contains(Backedge)) 144 return false; 145 146 assert(Incoming && Backedge && "expected non-null incoming and backedges"); 147 return true; 148 } 149 150 PHINode *Loop::getCanonicalInductionVariable() const { 151 BasicBlock *H = getHeader(); 152 153 BasicBlock *Incoming = nullptr, *Backedge = nullptr; 154 if (!getIncomingAndBackEdge(Incoming, Backedge)) 155 return nullptr; 156 157 // Loop over all of the PHI nodes, looking for a canonical indvar. 158 for (BasicBlock::iterator I = H->begin(); isa<PHINode>(I); ++I) { 159 PHINode *PN = cast<PHINode>(I); 160 if (ConstantInt *CI = 161 dyn_cast<ConstantInt>(PN->getIncomingValueForBlock(Incoming))) 162 if (CI->isZero()) 163 if (Instruction *Inc = 164 dyn_cast<Instruction>(PN->getIncomingValueForBlock(Backedge))) 165 if (Inc->getOpcode() == Instruction::Add && Inc->getOperand(0) == PN) 166 if (ConstantInt *CI = dyn_cast<ConstantInt>(Inc->getOperand(1))) 167 if (CI->isOne()) 168 return PN; 169 } 170 return nullptr; 171 } 172 173 /// Get the latch condition instruction. 174 ICmpInst *Loop::getLatchCmpInst() const { 175 if (BasicBlock *Latch = getLoopLatch()) 176 if (BranchInst *BI = dyn_cast_or_null<BranchInst>(Latch->getTerminator())) 177 if (BI->isConditional()) 178 return dyn_cast<ICmpInst>(BI->getCondition()); 179 180 return nullptr; 181 } 182 183 /// Return the final value of the loop induction variable if found. 184 static Value *findFinalIVValue(const Loop &L, const PHINode &IndVar, 185 const Instruction &StepInst) { 186 ICmpInst *LatchCmpInst = L.getLatchCmpInst(); 187 if (!LatchCmpInst) 188 return nullptr; 189 190 Value *Op0 = LatchCmpInst->getOperand(0); 191 Value *Op1 = LatchCmpInst->getOperand(1); 192 if (Op0 == &IndVar || Op0 == &StepInst) 193 return Op1; 194 195 if (Op1 == &IndVar || Op1 == &StepInst) 196 return Op0; 197 198 return nullptr; 199 } 200 201 Optional<Loop::LoopBounds> Loop::LoopBounds::getBounds(const Loop &L, 202 PHINode &IndVar, 203 ScalarEvolution &SE) { 204 InductionDescriptor IndDesc; 205 if (!InductionDescriptor::isInductionPHI(&IndVar, &L, &SE, IndDesc)) 206 return None; 207 208 Value *InitialIVValue = IndDesc.getStartValue(); 209 Instruction *StepInst = IndDesc.getInductionBinOp(); 210 if (!InitialIVValue || !StepInst) 211 return None; 212 213 const SCEV *Step = IndDesc.getStep(); 214 Value *StepInstOp1 = StepInst->getOperand(1); 215 Value *StepInstOp0 = StepInst->getOperand(0); 216 Value *StepValue = nullptr; 217 if (SE.getSCEV(StepInstOp1) == Step) 218 StepValue = StepInstOp1; 219 else if (SE.getSCEV(StepInstOp0) == Step) 220 StepValue = StepInstOp0; 221 222 Value *FinalIVValue = findFinalIVValue(L, IndVar, *StepInst); 223 if (!FinalIVValue) 224 return None; 225 226 return LoopBounds(L, *InitialIVValue, *StepInst, StepValue, *FinalIVValue, 227 SE); 228 } 229 230 using Direction = Loop::LoopBounds::Direction; 231 232 ICmpInst::Predicate Loop::LoopBounds::getCanonicalPredicate() const { 233 BasicBlock *Latch = L.getLoopLatch(); 234 assert(Latch && "Expecting valid latch"); 235 236 BranchInst *BI = dyn_cast_or_null<BranchInst>(Latch->getTerminator()); 237 assert(BI && BI->isConditional() && "Expecting conditional latch branch"); 238 239 ICmpInst *LatchCmpInst = dyn_cast<ICmpInst>(BI->getCondition()); 240 assert(LatchCmpInst && 241 "Expecting the latch compare instruction to be a CmpInst"); 242 243 // Need to inverse the predicate when first successor is not the loop 244 // header 245 ICmpInst::Predicate Pred = (BI->getSuccessor(0) == L.getHeader()) 246 ? LatchCmpInst->getPredicate() 247 : LatchCmpInst->getInversePredicate(); 248 249 if (LatchCmpInst->getOperand(0) == &getFinalIVValue()) 250 Pred = ICmpInst::getSwappedPredicate(Pred); 251 252 // Need to flip strictness of the predicate when the latch compare instruction 253 // is not using StepInst 254 if (LatchCmpInst->getOperand(0) == &getStepInst() || 255 LatchCmpInst->getOperand(1) == &getStepInst()) 256 return Pred; 257 258 // Cannot flip strictness of NE and EQ 259 if (Pred != ICmpInst::ICMP_NE && Pred != ICmpInst::ICMP_EQ) 260 return ICmpInst::getFlippedStrictnessPredicate(Pred); 261 262 Direction D = getDirection(); 263 if (D == Direction::Increasing) 264 return ICmpInst::ICMP_SLT; 265 266 if (D == Direction::Decreasing) 267 return ICmpInst::ICMP_SGT; 268 269 // If cannot determine the direction, then unable to find the canonical 270 // predicate 271 return ICmpInst::BAD_ICMP_PREDICATE; 272 } 273 274 Direction Loop::LoopBounds::getDirection() const { 275 if (const SCEVAddRecExpr *StepAddRecExpr = 276 dyn_cast<SCEVAddRecExpr>(SE.getSCEV(&getStepInst()))) 277 if (const SCEV *StepRecur = StepAddRecExpr->getStepRecurrence(SE)) { 278 if (SE.isKnownPositive(StepRecur)) 279 return Direction::Increasing; 280 if (SE.isKnownNegative(StepRecur)) 281 return Direction::Decreasing; 282 } 283 284 return Direction::Unknown; 285 } 286 287 Optional<Loop::LoopBounds> Loop::getBounds(ScalarEvolution &SE) const { 288 if (PHINode *IndVar = getInductionVariable(SE)) 289 return LoopBounds::getBounds(*this, *IndVar, SE); 290 291 return None; 292 } 293 294 PHINode *Loop::getInductionVariable(ScalarEvolution &SE) const { 295 if (!isLoopSimplifyForm()) 296 return nullptr; 297 298 BasicBlock *Header = getHeader(); 299 assert(Header && "Expected a valid loop header"); 300 ICmpInst *CmpInst = getLatchCmpInst(); 301 if (!CmpInst) 302 return nullptr; 303 304 Value *LatchCmpOp0 = CmpInst->getOperand(0); 305 Value *LatchCmpOp1 = CmpInst->getOperand(1); 306 307 for (PHINode &IndVar : Header->phis()) { 308 InductionDescriptor IndDesc; 309 if (!InductionDescriptor::isInductionPHI(&IndVar, this, &SE, IndDesc)) 310 continue; 311 312 BasicBlock *Latch = getLoopLatch(); 313 Value *StepInst = IndVar.getIncomingValueForBlock(Latch); 314 315 // case 1: 316 // IndVar = phi[{InitialValue, preheader}, {StepInst, latch}] 317 // StepInst = IndVar + step 318 // cmp = StepInst < FinalValue 319 if (StepInst == LatchCmpOp0 || StepInst == LatchCmpOp1) 320 return &IndVar; 321 322 // case 2: 323 // IndVar = phi[{InitialValue, preheader}, {StepInst, latch}] 324 // StepInst = IndVar + step 325 // cmp = IndVar < FinalValue 326 if (&IndVar == LatchCmpOp0 || &IndVar == LatchCmpOp1) 327 return &IndVar; 328 } 329 330 return nullptr; 331 } 332 333 bool Loop::getInductionDescriptor(ScalarEvolution &SE, 334 InductionDescriptor &IndDesc) const { 335 if (PHINode *IndVar = getInductionVariable(SE)) 336 return InductionDescriptor::isInductionPHI(IndVar, this, &SE, IndDesc); 337 338 return false; 339 } 340 341 bool Loop::isAuxiliaryInductionVariable(PHINode &AuxIndVar, 342 ScalarEvolution &SE) const { 343 // Located in the loop header 344 BasicBlock *Header = getHeader(); 345 if (AuxIndVar.getParent() != Header) 346 return false; 347 348 // No uses outside of the loop 349 for (User *U : AuxIndVar.users()) 350 if (const Instruction *I = dyn_cast<Instruction>(U)) 351 if (!contains(I)) 352 return false; 353 354 InductionDescriptor IndDesc; 355 if (!InductionDescriptor::isInductionPHI(&AuxIndVar, this, &SE, IndDesc)) 356 return false; 357 358 // The step instruction opcode should be add or sub. 359 if (IndDesc.getInductionOpcode() != Instruction::Add && 360 IndDesc.getInductionOpcode() != Instruction::Sub) 361 return false; 362 363 // Incremented by a loop invariant step for each loop iteration 364 return SE.isLoopInvariant(IndDesc.getStep(), this); 365 } 366 367 BranchInst *Loop::getLoopGuardBranch() const { 368 if (!isLoopSimplifyForm()) 369 return nullptr; 370 371 BasicBlock *Preheader = getLoopPreheader(); 372 assert(Preheader && getLoopLatch() && 373 "Expecting a loop with valid preheader and latch"); 374 375 // Loop should be in rotate form. 376 if (!isRotatedForm()) 377 return nullptr; 378 379 // Disallow loops with more than one unique exit block, as we do not verify 380 // that GuardOtherSucc post dominates all exit blocks. 381 BasicBlock *ExitFromLatch = getUniqueExitBlock(); 382 if (!ExitFromLatch) 383 return nullptr; 384 385 BasicBlock *GuardBB = Preheader->getUniquePredecessor(); 386 if (!GuardBB) 387 return nullptr; 388 389 assert(GuardBB->getTerminator() && "Expecting valid guard terminator"); 390 391 BranchInst *GuardBI = dyn_cast<BranchInst>(GuardBB->getTerminator()); 392 if (!GuardBI || GuardBI->isUnconditional()) 393 return nullptr; 394 395 BasicBlock *GuardOtherSucc = (GuardBI->getSuccessor(0) == Preheader) 396 ? GuardBI->getSuccessor(1) 397 : GuardBI->getSuccessor(0); 398 399 // Check if ExitFromLatch (or any BasicBlock which is an empty unique 400 // successor of ExitFromLatch) is equal to GuardOtherSucc. If 401 // skipEmptyBlockUntil returns GuardOtherSucc, then the guard branch for the 402 // loop is GuardBI (return GuardBI), otherwise return nullptr. 403 if (&LoopNest::skipEmptyBlockUntil(ExitFromLatch, GuardOtherSucc, 404 /*CheckUniquePred=*/true) == 405 GuardOtherSucc) 406 return GuardBI; 407 else 408 return nullptr; 409 } 410 411 bool Loop::isCanonical(ScalarEvolution &SE) const { 412 InductionDescriptor IndDesc; 413 if (!getInductionDescriptor(SE, IndDesc)) 414 return false; 415 416 ConstantInt *Init = dyn_cast_or_null<ConstantInt>(IndDesc.getStartValue()); 417 if (!Init || !Init->isZero()) 418 return false; 419 420 if (IndDesc.getInductionOpcode() != Instruction::Add) 421 return false; 422 423 ConstantInt *Step = IndDesc.getConstIntStepValue(); 424 if (!Step || !Step->isOne()) 425 return false; 426 427 return true; 428 } 429 430 // Check that 'BB' doesn't have any uses outside of the 'L' 431 static bool isBlockInLCSSAForm(const Loop &L, const BasicBlock &BB, 432 const DominatorTree &DT) { 433 for (const Instruction &I : BB) { 434 // Tokens can't be used in PHI nodes and live-out tokens prevent loop 435 // optimizations, so for the purposes of considered LCSSA form, we 436 // can ignore them. 437 if (I.getType()->isTokenTy()) 438 continue; 439 440 for (const Use &U : I.uses()) { 441 const Instruction *UI = cast<Instruction>(U.getUser()); 442 const BasicBlock *UserBB = UI->getParent(); 443 444 // For practical purposes, we consider that the use in a PHI 445 // occurs in the respective predecessor block. For more info, 446 // see the `phi` doc in LangRef and the LCSSA doc. 447 if (const PHINode *P = dyn_cast<PHINode>(UI)) 448 UserBB = P->getIncomingBlock(U); 449 450 // Check the current block, as a fast-path, before checking whether 451 // the use is anywhere in the loop. Most values are used in the same 452 // block they are defined in. Also, blocks not reachable from the 453 // entry are special; uses in them don't need to go through PHIs. 454 if (UserBB != &BB && !L.contains(UserBB) && 455 DT.isReachableFromEntry(UserBB)) 456 return false; 457 } 458 } 459 return true; 460 } 461 462 bool Loop::isLCSSAForm(const DominatorTree &DT) const { 463 // For each block we check that it doesn't have any uses outside of this loop. 464 return all_of(this->blocks(), [&](const BasicBlock *BB) { 465 return isBlockInLCSSAForm(*this, *BB, DT); 466 }); 467 } 468 469 bool Loop::isRecursivelyLCSSAForm(const DominatorTree &DT, 470 const LoopInfo &LI) const { 471 // For each block we check that it doesn't have any uses outside of its 472 // innermost loop. This process will transitively guarantee that the current 473 // loop and all of the nested loops are in LCSSA form. 474 return all_of(this->blocks(), [&](const BasicBlock *BB) { 475 return isBlockInLCSSAForm(*LI.getLoopFor(BB), *BB, DT); 476 }); 477 } 478 479 bool Loop::isLoopSimplifyForm() const { 480 // Normal-form loops have a preheader, a single backedge, and all of their 481 // exits have all their predecessors inside the loop. 482 return getLoopPreheader() && getLoopLatch() && hasDedicatedExits(); 483 } 484 485 // Routines that reform the loop CFG and split edges often fail on indirectbr. 486 bool Loop::isSafeToClone() const { 487 // Return false if any loop blocks contain indirectbrs, or there are any calls 488 // to noduplicate functions. 489 // FIXME: it should be ok to clone CallBrInst's if we correctly update the 490 // operand list to reflect the newly cloned labels. 491 for (BasicBlock *BB : this->blocks()) { 492 if (isa<IndirectBrInst>(BB->getTerminator()) || 493 isa<CallBrInst>(BB->getTerminator())) 494 return false; 495 496 for (Instruction &I : *BB) 497 if (auto *CB = dyn_cast<CallBase>(&I)) 498 if (CB->cannotDuplicate()) 499 return false; 500 } 501 return true; 502 } 503 504 MDNode *Loop::getLoopID() const { 505 MDNode *LoopID = nullptr; 506 507 // Go through the latch blocks and check the terminator for the metadata. 508 SmallVector<BasicBlock *, 4> LatchesBlocks; 509 getLoopLatches(LatchesBlocks); 510 for (BasicBlock *BB : LatchesBlocks) { 511 Instruction *TI = BB->getTerminator(); 512 MDNode *MD = TI->getMetadata(LLVMContext::MD_loop); 513 514 if (!MD) 515 return nullptr; 516 517 if (!LoopID) 518 LoopID = MD; 519 else if (MD != LoopID) 520 return nullptr; 521 } 522 if (!LoopID || LoopID->getNumOperands() == 0 || 523 LoopID->getOperand(0) != LoopID) 524 return nullptr; 525 return LoopID; 526 } 527 528 void Loop::setLoopID(MDNode *LoopID) const { 529 assert((!LoopID || LoopID->getNumOperands() > 0) && 530 "Loop ID needs at least one operand"); 531 assert((!LoopID || LoopID->getOperand(0) == LoopID) && 532 "Loop ID should refer to itself"); 533 534 SmallVector<BasicBlock *, 4> LoopLatches; 535 getLoopLatches(LoopLatches); 536 for (BasicBlock *BB : LoopLatches) 537 BB->getTerminator()->setMetadata(LLVMContext::MD_loop, LoopID); 538 } 539 540 void Loop::setLoopAlreadyUnrolled() { 541 LLVMContext &Context = getHeader()->getContext(); 542 543 MDNode *DisableUnrollMD = 544 MDNode::get(Context, MDString::get(Context, "llvm.loop.unroll.disable")); 545 MDNode *LoopID = getLoopID(); 546 MDNode *NewLoopID = makePostTransformationMetadata( 547 Context, LoopID, {"llvm.loop.unroll."}, {DisableUnrollMD}); 548 setLoopID(NewLoopID); 549 } 550 551 void Loop::setLoopMustProgress() { 552 LLVMContext &Context = getHeader()->getContext(); 553 554 MDNode *MustProgress = findOptionMDForLoop(this, "llvm.loop.mustprogress"); 555 556 if (MustProgress) 557 return; 558 559 MDNode *MustProgressMD = 560 MDNode::get(Context, MDString::get(Context, "llvm.loop.mustprogress")); 561 MDNode *LoopID = getLoopID(); 562 MDNode *NewLoopID = 563 makePostTransformationMetadata(Context, LoopID, {}, {MustProgressMD}); 564 setLoopID(NewLoopID); 565 } 566 567 bool Loop::isAnnotatedParallel() const { 568 MDNode *DesiredLoopIdMetadata = getLoopID(); 569 570 if (!DesiredLoopIdMetadata) 571 return false; 572 573 MDNode *ParallelAccesses = 574 findOptionMDForLoop(this, "llvm.loop.parallel_accesses"); 575 SmallPtrSet<MDNode *, 4> 576 ParallelAccessGroups; // For scalable 'contains' check. 577 if (ParallelAccesses) { 578 for (const MDOperand &MD : drop_begin(ParallelAccesses->operands())) { 579 MDNode *AccGroup = cast<MDNode>(MD.get()); 580 assert(isValidAsAccessGroup(AccGroup) && 581 "List item must be an access group"); 582 ParallelAccessGroups.insert(AccGroup); 583 } 584 } 585 586 // The loop branch contains the parallel loop metadata. In order to ensure 587 // that any parallel-loop-unaware optimization pass hasn't added loop-carried 588 // dependencies (thus converted the loop back to a sequential loop), check 589 // that all the memory instructions in the loop belong to an access group that 590 // is parallel to this loop. 591 for (BasicBlock *BB : this->blocks()) { 592 for (Instruction &I : *BB) { 593 if (!I.mayReadOrWriteMemory()) 594 continue; 595 596 if (MDNode *AccessGroup = I.getMetadata(LLVMContext::MD_access_group)) { 597 auto ContainsAccessGroup = [&ParallelAccessGroups](MDNode *AG) -> bool { 598 if (AG->getNumOperands() == 0) { 599 assert(isValidAsAccessGroup(AG) && "Item must be an access group"); 600 return ParallelAccessGroups.count(AG); 601 } 602 603 for (const MDOperand &AccessListItem : AG->operands()) { 604 MDNode *AccGroup = cast<MDNode>(AccessListItem.get()); 605 assert(isValidAsAccessGroup(AccGroup) && 606 "List item must be an access group"); 607 if (ParallelAccessGroups.count(AccGroup)) 608 return true; 609 } 610 return false; 611 }; 612 613 if (ContainsAccessGroup(AccessGroup)) 614 continue; 615 } 616 617 // The memory instruction can refer to the loop identifier metadata 618 // directly or indirectly through another list metadata (in case of 619 // nested parallel loops). The loop identifier metadata refers to 620 // itself so we can check both cases with the same routine. 621 MDNode *LoopIdMD = 622 I.getMetadata(LLVMContext::MD_mem_parallel_loop_access); 623 624 if (!LoopIdMD) 625 return false; 626 627 if (!llvm::is_contained(LoopIdMD->operands(), DesiredLoopIdMetadata)) 628 return false; 629 } 630 } 631 return true; 632 } 633 634 DebugLoc Loop::getStartLoc() const { return getLocRange().getStart(); } 635 636 Loop::LocRange Loop::getLocRange() const { 637 // If we have a debug location in the loop ID, then use it. 638 if (MDNode *LoopID = getLoopID()) { 639 DebugLoc Start; 640 // We use the first DebugLoc in the header as the start location of the loop 641 // and if there is a second DebugLoc in the header we use it as end location 642 // of the loop. 643 for (unsigned i = 1, ie = LoopID->getNumOperands(); i < ie; ++i) { 644 if (DILocation *L = dyn_cast<DILocation>(LoopID->getOperand(i))) { 645 if (!Start) 646 Start = DebugLoc(L); 647 else 648 return LocRange(Start, DebugLoc(L)); 649 } 650 } 651 652 if (Start) 653 return LocRange(Start); 654 } 655 656 // Try the pre-header first. 657 if (BasicBlock *PHeadBB = getLoopPreheader()) 658 if (DebugLoc DL = PHeadBB->getTerminator()->getDebugLoc()) 659 return LocRange(DL); 660 661 // If we have no pre-header or there are no instructions with debug 662 // info in it, try the header. 663 if (BasicBlock *HeadBB = getHeader()) 664 return LocRange(HeadBB->getTerminator()->getDebugLoc()); 665 666 return LocRange(); 667 } 668 669 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP) 670 LLVM_DUMP_METHOD void Loop::dump() const { print(dbgs()); } 671 672 LLVM_DUMP_METHOD void Loop::dumpVerbose() const { 673 print(dbgs(), /*Verbose=*/true); 674 } 675 #endif 676 677 //===----------------------------------------------------------------------===// 678 // UnloopUpdater implementation 679 // 680 681 namespace { 682 /// Find the new parent loop for all blocks within the "unloop" whose last 683 /// backedges has just been removed. 684 class UnloopUpdater { 685 Loop &Unloop; 686 LoopInfo *LI; 687 688 LoopBlocksDFS DFS; 689 690 // Map unloop's immediate subloops to their nearest reachable parents. Nested 691 // loops within these subloops will not change parents. However, an immediate 692 // subloop's new parent will be the nearest loop reachable from either its own 693 // exits *or* any of its nested loop's exits. 694 DenseMap<Loop *, Loop *> SubloopParents; 695 696 // Flag the presence of an irreducible backedge whose destination is a block 697 // directly contained by the original unloop. 698 bool FoundIB; 699 700 public: 701 UnloopUpdater(Loop *UL, LoopInfo *LInfo) 702 : Unloop(*UL), LI(LInfo), DFS(UL), FoundIB(false) {} 703 704 void updateBlockParents(); 705 706 void removeBlocksFromAncestors(); 707 708 void updateSubloopParents(); 709 710 protected: 711 Loop *getNearestLoop(BasicBlock *BB, Loop *BBLoop); 712 }; 713 } // end anonymous namespace 714 715 /// Update the parent loop for all blocks that are directly contained within the 716 /// original "unloop". 717 void UnloopUpdater::updateBlockParents() { 718 if (Unloop.getNumBlocks()) { 719 // Perform a post order CFG traversal of all blocks within this loop, 720 // propagating the nearest loop from successors to predecessors. 721 LoopBlocksTraversal Traversal(DFS, LI); 722 for (BasicBlock *POI : Traversal) { 723 724 Loop *L = LI->getLoopFor(POI); 725 Loop *NL = getNearestLoop(POI, L); 726 727 if (NL != L) { 728 // For reducible loops, NL is now an ancestor of Unloop. 729 assert((NL != &Unloop && (!NL || NL->contains(&Unloop))) && 730 "uninitialized successor"); 731 LI->changeLoopFor(POI, NL); 732 } else { 733 // Or the current block is part of a subloop, in which case its parent 734 // is unchanged. 735 assert((FoundIB || Unloop.contains(L)) && "uninitialized successor"); 736 } 737 } 738 } 739 // Each irreducible loop within the unloop induces a round of iteration using 740 // the DFS result cached by Traversal. 741 bool Changed = FoundIB; 742 for (unsigned NIters = 0; Changed; ++NIters) { 743 assert(NIters < Unloop.getNumBlocks() && "runaway iterative algorithm"); 744 745 // Iterate over the postorder list of blocks, propagating the nearest loop 746 // from successors to predecessors as before. 747 Changed = false; 748 for (LoopBlocksDFS::POIterator POI = DFS.beginPostorder(), 749 POE = DFS.endPostorder(); 750 POI != POE; ++POI) { 751 752 Loop *L = LI->getLoopFor(*POI); 753 Loop *NL = getNearestLoop(*POI, L); 754 if (NL != L) { 755 assert(NL != &Unloop && (!NL || NL->contains(&Unloop)) && 756 "uninitialized successor"); 757 LI->changeLoopFor(*POI, NL); 758 Changed = true; 759 } 760 } 761 } 762 } 763 764 /// Remove unloop's blocks from all ancestors below their new parents. 765 void UnloopUpdater::removeBlocksFromAncestors() { 766 // Remove all unloop's blocks (including those in nested subloops) from 767 // ancestors below the new parent loop. 768 for (BasicBlock *BB : Unloop.blocks()) { 769 Loop *OuterParent = LI->getLoopFor(BB); 770 if (Unloop.contains(OuterParent)) { 771 while (OuterParent->getParentLoop() != &Unloop) 772 OuterParent = OuterParent->getParentLoop(); 773 OuterParent = SubloopParents[OuterParent]; 774 } 775 // Remove blocks from former Ancestors except Unloop itself which will be 776 // deleted. 777 for (Loop *OldParent = Unloop.getParentLoop(); OldParent != OuterParent; 778 OldParent = OldParent->getParentLoop()) { 779 assert(OldParent && "new loop is not an ancestor of the original"); 780 OldParent->removeBlockFromLoop(BB); 781 } 782 } 783 } 784 785 /// Update the parent loop for all subloops directly nested within unloop. 786 void UnloopUpdater::updateSubloopParents() { 787 while (!Unloop.isInnermost()) { 788 Loop *Subloop = *std::prev(Unloop.end()); 789 Unloop.removeChildLoop(std::prev(Unloop.end())); 790 791 assert(SubloopParents.count(Subloop) && "DFS failed to visit subloop"); 792 if (Loop *Parent = SubloopParents[Subloop]) 793 Parent->addChildLoop(Subloop); 794 else 795 LI->addTopLevelLoop(Subloop); 796 } 797 } 798 799 /// Return the nearest parent loop among this block's successors. If a successor 800 /// is a subloop header, consider its parent to be the nearest parent of the 801 /// subloop's exits. 802 /// 803 /// For subloop blocks, simply update SubloopParents and return NULL. 804 Loop *UnloopUpdater::getNearestLoop(BasicBlock *BB, Loop *BBLoop) { 805 806 // Initially for blocks directly contained by Unloop, NearLoop == Unloop and 807 // is considered uninitialized. 808 Loop *NearLoop = BBLoop; 809 810 Loop *Subloop = nullptr; 811 if (NearLoop != &Unloop && Unloop.contains(NearLoop)) { 812 Subloop = NearLoop; 813 // Find the subloop ancestor that is directly contained within Unloop. 814 while (Subloop->getParentLoop() != &Unloop) { 815 Subloop = Subloop->getParentLoop(); 816 assert(Subloop && "subloop is not an ancestor of the original loop"); 817 } 818 // Get the current nearest parent of the Subloop exits, initially Unloop. 819 NearLoop = SubloopParents.insert({Subloop, &Unloop}).first->second; 820 } 821 822 succ_iterator I = succ_begin(BB), E = succ_end(BB); 823 if (I == E) { 824 assert(!Subloop && "subloop blocks must have a successor"); 825 NearLoop = nullptr; // unloop blocks may now exit the function. 826 } 827 for (; I != E; ++I) { 828 if (*I == BB) 829 continue; // self loops are uninteresting 830 831 Loop *L = LI->getLoopFor(*I); 832 if (L == &Unloop) { 833 // This successor has not been processed. This path must lead to an 834 // irreducible backedge. 835 assert((FoundIB || !DFS.hasPostorder(*I)) && "should have seen IB"); 836 FoundIB = true; 837 } 838 if (L != &Unloop && Unloop.contains(L)) { 839 // Successor is in a subloop. 840 if (Subloop) 841 continue; // Branching within subloops. Ignore it. 842 843 // BB branches from the original into a subloop header. 844 assert(L->getParentLoop() == &Unloop && "cannot skip into nested loops"); 845 846 // Get the current nearest parent of the Subloop's exits. 847 L = SubloopParents[L]; 848 // L could be Unloop if the only exit was an irreducible backedge. 849 } 850 if (L == &Unloop) { 851 continue; 852 } 853 // Handle critical edges from Unloop into a sibling loop. 854 if (L && !L->contains(&Unloop)) { 855 L = L->getParentLoop(); 856 } 857 // Remember the nearest parent loop among successors or subloop exits. 858 if (NearLoop == &Unloop || !NearLoop || NearLoop->contains(L)) 859 NearLoop = L; 860 } 861 if (Subloop) { 862 SubloopParents[Subloop] = NearLoop; 863 return BBLoop; 864 } 865 return NearLoop; 866 } 867 868 LoopInfo::LoopInfo(const DomTreeBase<BasicBlock> &DomTree) { analyze(DomTree); } 869 870 bool LoopInfo::invalidate(Function &F, const PreservedAnalyses &PA, 871 FunctionAnalysisManager::Invalidator &) { 872 // Check whether the analysis, all analyses on functions, or the function's 873 // CFG have been preserved. 874 auto PAC = PA.getChecker<LoopAnalysis>(); 875 return !(PAC.preserved() || PAC.preservedSet<AllAnalysesOn<Function>>() || 876 PAC.preservedSet<CFGAnalyses>()); 877 } 878 879 void LoopInfo::erase(Loop *Unloop) { 880 assert(!Unloop->isInvalid() && "Loop has already been erased!"); 881 882 auto InvalidateOnExit = make_scope_exit([&]() { destroy(Unloop); }); 883 884 // First handle the special case of no parent loop to simplify the algorithm. 885 if (Unloop->isOutermost()) { 886 // Since BBLoop had no parent, Unloop blocks are no longer in a loop. 887 for (BasicBlock *BB : Unloop->blocks()) { 888 // Don't reparent blocks in subloops. 889 if (getLoopFor(BB) != Unloop) 890 continue; 891 892 // Blocks no longer have a parent but are still referenced by Unloop until 893 // the Unloop object is deleted. 894 changeLoopFor(BB, nullptr); 895 } 896 897 // Remove the loop from the top-level LoopInfo object. 898 for (iterator I = begin();; ++I) { 899 assert(I != end() && "Couldn't find loop"); 900 if (*I == Unloop) { 901 removeLoop(I); 902 break; 903 } 904 } 905 906 // Move all of the subloops to the top-level. 907 while (!Unloop->isInnermost()) 908 addTopLevelLoop(Unloop->removeChildLoop(std::prev(Unloop->end()))); 909 910 return; 911 } 912 913 // Update the parent loop for all blocks within the loop. Blocks within 914 // subloops will not change parents. 915 UnloopUpdater Updater(Unloop, this); 916 Updater.updateBlockParents(); 917 918 // Remove blocks from former ancestor loops. 919 Updater.removeBlocksFromAncestors(); 920 921 // Add direct subloops as children in their new parent loop. 922 Updater.updateSubloopParents(); 923 924 // Remove unloop from its parent loop. 925 Loop *ParentLoop = Unloop->getParentLoop(); 926 for (Loop::iterator I = ParentLoop->begin();; ++I) { 927 assert(I != ParentLoop->end() && "Couldn't find loop"); 928 if (*I == Unloop) { 929 ParentLoop->removeChildLoop(I); 930 break; 931 } 932 } 933 } 934 935 bool 936 LoopInfo::wouldBeOutOfLoopUseRequiringLCSSA(const Value *V, 937 const BasicBlock *ExitBB) const { 938 if (V->getType()->isTokenTy()) 939 // We can't form PHIs of token type, so the definition of LCSSA excludes 940 // values of that type. 941 return false; 942 943 const Instruction *I = dyn_cast<Instruction>(V); 944 if (!I) 945 return false; 946 const Loop *L = getLoopFor(I->getParent()); 947 if (!L) 948 return false; 949 if (L->contains(ExitBB)) 950 // Could be an exit bb of a subloop and contained in defining loop 951 return false; 952 953 // We found a (new) out-of-loop use location, for a value defined in-loop. 954 // (Note that because of LCSSA, we don't have to account for values defined 955 // in sibling loops. Such values will have LCSSA phis of their own in the 956 // common parent loop.) 957 return true; 958 } 959 960 AnalysisKey LoopAnalysis::Key; 961 962 LoopInfo LoopAnalysis::run(Function &F, FunctionAnalysisManager &AM) { 963 // FIXME: Currently we create a LoopInfo from scratch for every function. 964 // This may prove to be too wasteful due to deallocating and re-allocating 965 // memory each time for the underlying map and vector datastructures. At some 966 // point it may prove worthwhile to use a freelist and recycle LoopInfo 967 // objects. I don't want to add that kind of complexity until the scope of 968 // the problem is better understood. 969 LoopInfo LI; 970 LI.analyze(AM.getResult<DominatorTreeAnalysis>(F)); 971 return LI; 972 } 973 974 PreservedAnalyses LoopPrinterPass::run(Function &F, 975 FunctionAnalysisManager &AM) { 976 AM.getResult<LoopAnalysis>(F).print(OS); 977 return PreservedAnalyses::all(); 978 } 979 980 void llvm::printLoop(Loop &L, raw_ostream &OS, const std::string &Banner) { 981 982 if (forcePrintModuleIR()) { 983 // handling -print-module-scope 984 OS << Banner << " (loop: "; 985 L.getHeader()->printAsOperand(OS, false); 986 OS << ")\n"; 987 988 // printing whole module 989 OS << *L.getHeader()->getModule(); 990 return; 991 } 992 993 OS << Banner; 994 995 auto *PreHeader = L.getLoopPreheader(); 996 if (PreHeader) { 997 OS << "\n; Preheader:"; 998 PreHeader->print(OS); 999 OS << "\n; Loop:"; 1000 } 1001 1002 for (auto *Block : L.blocks()) 1003 if (Block) 1004 Block->print(OS); 1005 else 1006 OS << "Printing <null> block"; 1007 1008 SmallVector<BasicBlock *, 8> ExitBlocks; 1009 L.getExitBlocks(ExitBlocks); 1010 if (!ExitBlocks.empty()) { 1011 OS << "\n; Exit blocks"; 1012 for (auto *Block : ExitBlocks) 1013 if (Block) 1014 Block->print(OS); 1015 else 1016 OS << "Printing <null> block"; 1017 } 1018 } 1019 1020 MDNode *llvm::findOptionMDForLoopID(MDNode *LoopID, StringRef Name) { 1021 // No loop metadata node, no loop properties. 1022 if (!LoopID) 1023 return nullptr; 1024 1025 // First operand should refer to the metadata node itself, for legacy reasons. 1026 assert(LoopID->getNumOperands() > 0 && "requires at least one operand"); 1027 assert(LoopID->getOperand(0) == LoopID && "invalid loop id"); 1028 1029 // Iterate over the metdata node operands and look for MDString metadata. 1030 for (unsigned i = 1, e = LoopID->getNumOperands(); i < e; ++i) { 1031 MDNode *MD = dyn_cast<MDNode>(LoopID->getOperand(i)); 1032 if (!MD || MD->getNumOperands() < 1) 1033 continue; 1034 MDString *S = dyn_cast<MDString>(MD->getOperand(0)); 1035 if (!S) 1036 continue; 1037 // Return the operand node if MDString holds expected metadata. 1038 if (Name.equals(S->getString())) 1039 return MD; 1040 } 1041 1042 // Loop property not found. 1043 return nullptr; 1044 } 1045 1046 MDNode *llvm::findOptionMDForLoop(const Loop *TheLoop, StringRef Name) { 1047 return findOptionMDForLoopID(TheLoop->getLoopID(), Name); 1048 } 1049 1050 /// Find string metadata for loop 1051 /// 1052 /// If it has a value (e.g. {"llvm.distribute", 1} return the value as an 1053 /// operand or null otherwise. If the string metadata is not found return 1054 /// Optional's not-a-value. 1055 Optional<const MDOperand *> llvm::findStringMetadataForLoop(const Loop *TheLoop, 1056 StringRef Name) { 1057 MDNode *MD = findOptionMDForLoop(TheLoop, Name); 1058 if (!MD) 1059 return None; 1060 switch (MD->getNumOperands()) { 1061 case 1: 1062 return nullptr; 1063 case 2: 1064 return &MD->getOperand(1); 1065 default: 1066 llvm_unreachable("loop metadata has 0 or 1 operand"); 1067 } 1068 } 1069 1070 Optional<bool> llvm::getOptionalBoolLoopAttribute(const Loop *TheLoop, 1071 StringRef Name) { 1072 MDNode *MD = findOptionMDForLoop(TheLoop, Name); 1073 if (!MD) 1074 return None; 1075 switch (MD->getNumOperands()) { 1076 case 1: 1077 // When the value is absent it is interpreted as 'attribute set'. 1078 return true; 1079 case 2: 1080 if (ConstantInt *IntMD = 1081 mdconst::extract_or_null<ConstantInt>(MD->getOperand(1).get())) 1082 return IntMD->getZExtValue(); 1083 return true; 1084 } 1085 llvm_unreachable("unexpected number of options"); 1086 } 1087 1088 bool llvm::getBooleanLoopAttribute(const Loop *TheLoop, StringRef Name) { 1089 return getOptionalBoolLoopAttribute(TheLoop, Name).getValueOr(false); 1090 } 1091 1092 llvm::Optional<int> llvm::getOptionalIntLoopAttribute(const Loop *TheLoop, 1093 StringRef Name) { 1094 const MDOperand *AttrMD = 1095 findStringMetadataForLoop(TheLoop, Name).getValueOr(nullptr); 1096 if (!AttrMD) 1097 return None; 1098 1099 ConstantInt *IntMD = mdconst::extract_or_null<ConstantInt>(AttrMD->get()); 1100 if (!IntMD) 1101 return None; 1102 1103 return IntMD->getSExtValue(); 1104 } 1105 1106 int llvm::getIntLoopAttribute(const Loop *TheLoop, StringRef Name, 1107 int Default) { 1108 return getOptionalIntLoopAttribute(TheLoop, Name).getValueOr(Default); 1109 } 1110 1111 static const char *LLVMLoopMustProgress = "llvm.loop.mustprogress"; 1112 1113 bool llvm::hasMustProgress(const Loop *L) { 1114 return getBooleanLoopAttribute(L, LLVMLoopMustProgress); 1115 } 1116 1117 bool llvm::isMustProgress(const Loop *L) { 1118 return L->getHeader()->getParent()->mustProgress() || hasMustProgress(L); 1119 } 1120 1121 bool llvm::isValidAsAccessGroup(MDNode *Node) { 1122 return Node->getNumOperands() == 0 && Node->isDistinct(); 1123 } 1124 1125 MDNode *llvm::makePostTransformationMetadata(LLVMContext &Context, 1126 MDNode *OrigLoopID, 1127 ArrayRef<StringRef> RemovePrefixes, 1128 ArrayRef<MDNode *> AddAttrs) { 1129 // First remove any existing loop metadata related to this transformation. 1130 SmallVector<Metadata *, 4> MDs; 1131 1132 // Reserve first location for self reference to the LoopID metadata node. 1133 MDs.push_back(nullptr); 1134 1135 // Remove metadata for the transformation that has been applied or that became 1136 // outdated. 1137 if (OrigLoopID) { 1138 for (unsigned i = 1, ie = OrigLoopID->getNumOperands(); i < ie; ++i) { 1139 bool IsVectorMetadata = false; 1140 Metadata *Op = OrigLoopID->getOperand(i); 1141 if (MDNode *MD = dyn_cast<MDNode>(Op)) { 1142 const MDString *S = dyn_cast<MDString>(MD->getOperand(0)); 1143 if (S) 1144 IsVectorMetadata = 1145 llvm::any_of(RemovePrefixes, [S](StringRef Prefix) -> bool { 1146 return S->getString().startswith(Prefix); 1147 }); 1148 } 1149 if (!IsVectorMetadata) 1150 MDs.push_back(Op); 1151 } 1152 } 1153 1154 // Add metadata to avoid reapplying a transformation, such as 1155 // llvm.loop.unroll.disable and llvm.loop.isvectorized. 1156 MDs.append(AddAttrs.begin(), AddAttrs.end()); 1157 1158 MDNode *NewLoopID = MDNode::getDistinct(Context, MDs); 1159 // Replace the temporary node with a self-reference. 1160 NewLoopID->replaceOperandWith(0, NewLoopID); 1161 return NewLoopID; 1162 } 1163 1164 //===----------------------------------------------------------------------===// 1165 // LoopInfo implementation 1166 // 1167 1168 LoopInfoWrapperPass::LoopInfoWrapperPass() : FunctionPass(ID) { 1169 initializeLoopInfoWrapperPassPass(*PassRegistry::getPassRegistry()); 1170 } 1171 1172 char LoopInfoWrapperPass::ID = 0; 1173 INITIALIZE_PASS_BEGIN(LoopInfoWrapperPass, "loops", "Natural Loop Information", 1174 true, true) 1175 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass) 1176 INITIALIZE_PASS_END(LoopInfoWrapperPass, "loops", "Natural Loop Information", 1177 true, true) 1178 1179 bool LoopInfoWrapperPass::runOnFunction(Function &) { 1180 releaseMemory(); 1181 LI.analyze(getAnalysis<DominatorTreeWrapperPass>().getDomTree()); 1182 return false; 1183 } 1184 1185 void LoopInfoWrapperPass::verifyAnalysis() const { 1186 // LoopInfoWrapperPass is a FunctionPass, but verifying every loop in the 1187 // function each time verifyAnalysis is called is very expensive. The 1188 // -verify-loop-info option can enable this. In order to perform some 1189 // checking by default, LoopPass has been taught to call verifyLoop manually 1190 // during loop pass sequences. 1191 if (VerifyLoopInfo) { 1192 auto &DT = getAnalysis<DominatorTreeWrapperPass>().getDomTree(); 1193 LI.verify(DT); 1194 } 1195 } 1196 1197 void LoopInfoWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const { 1198 AU.setPreservesAll(); 1199 AU.addRequiredTransitive<DominatorTreeWrapperPass>(); 1200 } 1201 1202 void LoopInfoWrapperPass::print(raw_ostream &OS, const Module *) const { 1203 LI.print(OS); 1204 } 1205 1206 PreservedAnalyses LoopVerifierPass::run(Function &F, 1207 FunctionAnalysisManager &AM) { 1208 LoopInfo &LI = AM.getResult<LoopAnalysis>(F); 1209 auto &DT = AM.getResult<DominatorTreeAnalysis>(F); 1210 LI.verify(DT); 1211 return PreservedAnalyses::all(); 1212 } 1213 1214 //===----------------------------------------------------------------------===// 1215 // LoopBlocksDFS implementation 1216 // 1217 1218 /// Traverse the loop blocks and store the DFS result. 1219 /// Useful for clients that just want the final DFS result and don't need to 1220 /// visit blocks during the initial traversal. 1221 void LoopBlocksDFS::perform(LoopInfo *LI) { 1222 LoopBlocksTraversal Traversal(*this, LI); 1223 for (LoopBlocksTraversal::POTIterator POI = Traversal.begin(), 1224 POE = Traversal.end(); 1225 POI != POE; ++POI) 1226 ; 1227 } 1228