1 //===- LoopRotation.cpp - Loop Rotation Pass ------------------------------===// 2 // 3 // The LLVM Compiler Infrastructure 4 // 5 // This file is distributed under the University of Illinois Open Source 6 // License. See LICENSE.TXT for details. 7 // 8 //===----------------------------------------------------------------------===// 9 // 10 // This file implements Loop Rotation Pass. 11 // 12 //===----------------------------------------------------------------------===// 13 14 #include "llvm/Transforms/Scalar.h" 15 #include "llvm/ADT/Statistic.h" 16 #include "llvm/Analysis/CodeMetrics.h" 17 #include "llvm/Analysis/InstructionSimplify.h" 18 #include "llvm/Analysis/LoopPass.h" 19 #include "llvm/Analysis/ScalarEvolution.h" 20 #include "llvm/Analysis/TargetTransformInfo.h" 21 #include "llvm/Analysis/ValueTracking.h" 22 #include "llvm/IR/CFG.h" 23 #include "llvm/IR/Dominators.h" 24 #include "llvm/IR/Function.h" 25 #include "llvm/IR/IntrinsicInst.h" 26 #include "llvm/Support/Debug.h" 27 #include "llvm/Transforms/Utils/BasicBlockUtils.h" 28 #include "llvm/Transforms/Utils/Local.h" 29 #include "llvm/Transforms/Utils/SSAUpdater.h" 30 #include "llvm/Transforms/Utils/ValueMapper.h" 31 using namespace llvm; 32 33 #define DEBUG_TYPE "loop-rotate" 34 35 #define MAX_HEADER_SIZE 16 36 37 STATISTIC(NumRotated, "Number of loops rotated"); 38 namespace { 39 40 class LoopRotate : public LoopPass { 41 public: 42 static char ID; // Pass ID, replacement for typeid 43 LoopRotate() : LoopPass(ID) { 44 initializeLoopRotatePass(*PassRegistry::getPassRegistry()); 45 } 46 47 // LCSSA form makes instruction renaming easier. 48 void getAnalysisUsage(AnalysisUsage &AU) const override { 49 AU.addPreserved<DominatorTreeWrapperPass>(); 50 AU.addRequired<LoopInfo>(); 51 AU.addPreserved<LoopInfo>(); 52 AU.addRequiredID(LoopSimplifyID); 53 AU.addPreservedID(LoopSimplifyID); 54 AU.addRequiredID(LCSSAID); 55 AU.addPreservedID(LCSSAID); 56 AU.addPreserved<ScalarEvolution>(); 57 AU.addRequired<TargetTransformInfo>(); 58 } 59 60 bool runOnLoop(Loop *L, LPPassManager &LPM) override; 61 bool simplifyLoopLatch(Loop *L); 62 bool rotateLoop(Loop *L, bool SimplifiedLatch); 63 64 private: 65 LoopInfo *LI; 66 const TargetTransformInfo *TTI; 67 }; 68 } 69 70 char LoopRotate::ID = 0; 71 INITIALIZE_PASS_BEGIN(LoopRotate, "loop-rotate", "Rotate Loops", false, false) 72 INITIALIZE_AG_DEPENDENCY(TargetTransformInfo) 73 INITIALIZE_PASS_DEPENDENCY(LoopInfo) 74 INITIALIZE_PASS_DEPENDENCY(LoopSimplify) 75 INITIALIZE_PASS_DEPENDENCY(LCSSA) 76 INITIALIZE_PASS_END(LoopRotate, "loop-rotate", "Rotate Loops", false, false) 77 78 Pass *llvm::createLoopRotatePass() { return new LoopRotate(); } 79 80 /// Rotate Loop L as many times as possible. Return true if 81 /// the loop is rotated at least once. 82 bool LoopRotate::runOnLoop(Loop *L, LPPassManager &LPM) { 83 if (skipOptnoneFunction(L)) 84 return false; 85 86 // Save the loop metadata. 87 MDNode *LoopMD = L->getLoopID(); 88 89 LI = &getAnalysis<LoopInfo>(); 90 TTI = &getAnalysis<TargetTransformInfo>(); 91 92 // Simplify the loop latch before attempting to rotate the header 93 // upward. Rotation may not be needed if the loop tail can be folded into the 94 // loop exit. 95 bool SimplifiedLatch = simplifyLoopLatch(L); 96 97 // One loop can be rotated multiple times. 98 bool MadeChange = false; 99 while (rotateLoop(L, SimplifiedLatch)) { 100 MadeChange = true; 101 SimplifiedLatch = false; 102 } 103 104 // Restore the loop metadata. 105 // NB! We presume LoopRotation DOESN'T ADD its own metadata. 106 if ((MadeChange || SimplifiedLatch) && LoopMD) 107 L->setLoopID(LoopMD); 108 109 return MadeChange; 110 } 111 112 /// RewriteUsesOfClonedInstructions - We just cloned the instructions from the 113 /// old header into the preheader. If there were uses of the values produced by 114 /// these instruction that were outside of the loop, we have to insert PHI nodes 115 /// to merge the two values. Do this now. 116 static void RewriteUsesOfClonedInstructions(BasicBlock *OrigHeader, 117 BasicBlock *OrigPreheader, 118 ValueToValueMapTy &ValueMap) { 119 // Remove PHI node entries that are no longer live. 120 BasicBlock::iterator I, E = OrigHeader->end(); 121 for (I = OrigHeader->begin(); PHINode *PN = dyn_cast<PHINode>(I); ++I) 122 PN->removeIncomingValue(PN->getBasicBlockIndex(OrigPreheader)); 123 124 // Now fix up users of the instructions in OrigHeader, inserting PHI nodes 125 // as necessary. 126 SSAUpdater SSA; 127 for (I = OrigHeader->begin(); I != E; ++I) { 128 Value *OrigHeaderVal = I; 129 130 // If there are no uses of the value (e.g. because it returns void), there 131 // is nothing to rewrite. 132 if (OrigHeaderVal->use_empty()) 133 continue; 134 135 Value *OrigPreHeaderVal = ValueMap[OrigHeaderVal]; 136 137 // The value now exits in two versions: the initial value in the preheader 138 // and the loop "next" value in the original header. 139 SSA.Initialize(OrigHeaderVal->getType(), OrigHeaderVal->getName()); 140 SSA.AddAvailableValue(OrigHeader, OrigHeaderVal); 141 SSA.AddAvailableValue(OrigPreheader, OrigPreHeaderVal); 142 143 // Visit each use of the OrigHeader instruction. 144 for (Value::use_iterator UI = OrigHeaderVal->use_begin(), 145 UE = OrigHeaderVal->use_end(); UI != UE; ) { 146 // Grab the use before incrementing the iterator. 147 Use &U = *UI; 148 149 // Increment the iterator before removing the use from the list. 150 ++UI; 151 152 // SSAUpdater can't handle a non-PHI use in the same block as an 153 // earlier def. We can easily handle those cases manually. 154 Instruction *UserInst = cast<Instruction>(U.getUser()); 155 if (!isa<PHINode>(UserInst)) { 156 BasicBlock *UserBB = UserInst->getParent(); 157 158 // The original users in the OrigHeader are already using the 159 // original definitions. 160 if (UserBB == OrigHeader) 161 continue; 162 163 // Users in the OrigPreHeader need to use the value to which the 164 // original definitions are mapped. 165 if (UserBB == OrigPreheader) { 166 U = OrigPreHeaderVal; 167 continue; 168 } 169 } 170 171 // Anything else can be handled by SSAUpdater. 172 SSA.RewriteUse(U); 173 } 174 } 175 } 176 177 /// Determine whether the instructions in this range my be safely and cheaply 178 /// speculated. This is not an important enough situation to develop complex 179 /// heuristics. We handle a single arithmetic instruction along with any type 180 /// conversions. 181 static bool shouldSpeculateInstrs(BasicBlock::iterator Begin, 182 BasicBlock::iterator End) { 183 bool seenIncrement = false; 184 for (BasicBlock::iterator I = Begin; I != End; ++I) { 185 186 if (!isSafeToSpeculativelyExecute(I)) 187 return false; 188 189 if (isa<DbgInfoIntrinsic>(I)) 190 continue; 191 192 switch (I->getOpcode()) { 193 default: 194 return false; 195 case Instruction::GetElementPtr: 196 // GEPs are cheap if all indices are constant. 197 if (!cast<GEPOperator>(I)->hasAllConstantIndices()) 198 return false; 199 // fall-thru to increment case 200 case Instruction::Add: 201 case Instruction::Sub: 202 case Instruction::And: 203 case Instruction::Or: 204 case Instruction::Xor: 205 case Instruction::Shl: 206 case Instruction::LShr: 207 case Instruction::AShr: 208 if (seenIncrement) 209 return false; 210 seenIncrement = true; 211 break; 212 case Instruction::Trunc: 213 case Instruction::ZExt: 214 case Instruction::SExt: 215 // ignore type conversions 216 break; 217 } 218 } 219 return true; 220 } 221 222 /// Fold the loop tail into the loop exit by speculating the loop tail 223 /// instructions. Typically, this is a single post-increment. In the case of a 224 /// simple 2-block loop, hoisting the increment can be much better than 225 /// duplicating the entire loop header. In the cast of loops with early exits, 226 /// rotation will not work anyway, but simplifyLoopLatch will put the loop in 227 /// canonical form so downstream passes can handle it. 228 /// 229 /// I don't believe this invalidates SCEV. 230 bool LoopRotate::simplifyLoopLatch(Loop *L) { 231 BasicBlock *Latch = L->getLoopLatch(); 232 if (!Latch || Latch->hasAddressTaken()) 233 return false; 234 235 BranchInst *Jmp = dyn_cast<BranchInst>(Latch->getTerminator()); 236 if (!Jmp || !Jmp->isUnconditional()) 237 return false; 238 239 BasicBlock *LastExit = Latch->getSinglePredecessor(); 240 if (!LastExit || !L->isLoopExiting(LastExit)) 241 return false; 242 243 BranchInst *BI = dyn_cast<BranchInst>(LastExit->getTerminator()); 244 if (!BI) 245 return false; 246 247 if (!shouldSpeculateInstrs(Latch->begin(), Jmp)) 248 return false; 249 250 DEBUG(dbgs() << "Folding loop latch " << Latch->getName() << " into " 251 << LastExit->getName() << "\n"); 252 253 // Hoist the instructions from Latch into LastExit. 254 LastExit->getInstList().splice(BI, Latch->getInstList(), Latch->begin(), Jmp); 255 256 unsigned FallThruPath = BI->getSuccessor(0) == Latch ? 0 : 1; 257 BasicBlock *Header = Jmp->getSuccessor(0); 258 assert(Header == L->getHeader() && "expected a backward branch"); 259 260 // Remove Latch from the CFG so that LastExit becomes the new Latch. 261 BI->setSuccessor(FallThruPath, Header); 262 Latch->replaceSuccessorsPhiUsesWith(LastExit); 263 Jmp->eraseFromParent(); 264 265 // Nuke the Latch block. 266 assert(Latch->empty() && "unable to evacuate Latch"); 267 LI->removeBlock(Latch); 268 if (DominatorTreeWrapperPass *DTWP = 269 getAnalysisIfAvailable<DominatorTreeWrapperPass>()) 270 DTWP->getDomTree().eraseNode(Latch); 271 Latch->eraseFromParent(); 272 return true; 273 } 274 275 /// Rotate loop LP. Return true if the loop is rotated. 276 /// 277 /// \param SimplifiedLatch is true if the latch was just folded into the final 278 /// loop exit. In this case we may want to rotate even though the new latch is 279 /// now an exiting branch. This rotation would have happened had the latch not 280 /// been simplified. However, if SimplifiedLatch is false, then we avoid 281 /// rotating loops in which the latch exits to avoid excessive or endless 282 /// rotation. LoopRotate should be repeatable and converge to a canonical 283 /// form. This property is satisfied because simplifying the loop latch can only 284 /// happen once across multiple invocations of the LoopRotate pass. 285 bool LoopRotate::rotateLoop(Loop *L, bool SimplifiedLatch) { 286 // If the loop has only one block then there is not much to rotate. 287 if (L->getBlocks().size() == 1) 288 return false; 289 290 BasicBlock *OrigHeader = L->getHeader(); 291 BasicBlock *OrigLatch = L->getLoopLatch(); 292 293 BranchInst *BI = dyn_cast<BranchInst>(OrigHeader->getTerminator()); 294 if (!BI || BI->isUnconditional()) 295 return false; 296 297 // If the loop header is not one of the loop exiting blocks then 298 // either this loop is already rotated or it is not 299 // suitable for loop rotation transformations. 300 if (!L->isLoopExiting(OrigHeader)) 301 return false; 302 303 // If the loop latch already contains a branch that leaves the loop then the 304 // loop is already rotated. 305 if (!OrigLatch) 306 return false; 307 308 // Rotate if either the loop latch does *not* exit the loop, or if the loop 309 // latch was just simplified. 310 if (L->isLoopExiting(OrigLatch) && !SimplifiedLatch) 311 return false; 312 313 // Check size of original header and reject loop if it is very big or we can't 314 // duplicate blocks inside it. 315 { 316 CodeMetrics Metrics; 317 Metrics.analyzeBasicBlock(OrigHeader, *TTI); 318 if (Metrics.notDuplicatable) { 319 DEBUG(dbgs() << "LoopRotation: NOT rotating - contains non-duplicatable" 320 << " instructions: "; L->dump()); 321 return false; 322 } 323 if (Metrics.NumInsts > MAX_HEADER_SIZE) 324 return false; 325 } 326 327 // Now, this loop is suitable for rotation. 328 BasicBlock *OrigPreheader = L->getLoopPreheader(); 329 330 // If the loop could not be converted to canonical form, it must have an 331 // indirectbr in it, just give up. 332 if (!OrigPreheader) 333 return false; 334 335 // Anything ScalarEvolution may know about this loop or the PHI nodes 336 // in its header will soon be invalidated. 337 if (ScalarEvolution *SE = getAnalysisIfAvailable<ScalarEvolution>()) 338 SE->forgetLoop(L); 339 340 DEBUG(dbgs() << "LoopRotation: rotating "; L->dump()); 341 342 // Find new Loop header. NewHeader is a Header's one and only successor 343 // that is inside loop. Header's other successor is outside the 344 // loop. Otherwise loop is not suitable for rotation. 345 BasicBlock *Exit = BI->getSuccessor(0); 346 BasicBlock *NewHeader = BI->getSuccessor(1); 347 if (L->contains(Exit)) 348 std::swap(Exit, NewHeader); 349 assert(NewHeader && "Unable to determine new loop header"); 350 assert(L->contains(NewHeader) && !L->contains(Exit) && 351 "Unable to determine loop header and exit blocks"); 352 353 // This code assumes that the new header has exactly one predecessor. 354 // Remove any single-entry PHI nodes in it. 355 assert(NewHeader->getSinglePredecessor() && 356 "New header doesn't have one pred!"); 357 FoldSingleEntryPHINodes(NewHeader); 358 359 // Begin by walking OrigHeader and populating ValueMap with an entry for 360 // each Instruction. 361 BasicBlock::iterator I = OrigHeader->begin(), E = OrigHeader->end(); 362 ValueToValueMapTy ValueMap; 363 364 // For PHI nodes, the value available in OldPreHeader is just the 365 // incoming value from OldPreHeader. 366 for (; PHINode *PN = dyn_cast<PHINode>(I); ++I) 367 ValueMap[PN] = PN->getIncomingValueForBlock(OrigPreheader); 368 369 // For the rest of the instructions, either hoist to the OrigPreheader if 370 // possible or create a clone in the OldPreHeader if not. 371 TerminatorInst *LoopEntryBranch = OrigPreheader->getTerminator(); 372 while (I != E) { 373 Instruction *Inst = I++; 374 375 // If the instruction's operands are invariant and it doesn't read or write 376 // memory, then it is safe to hoist. Doing this doesn't change the order of 377 // execution in the preheader, but does prevent the instruction from 378 // executing in each iteration of the loop. This means it is safe to hoist 379 // something that might trap, but isn't safe to hoist something that reads 380 // memory (without proving that the loop doesn't write). 381 if (L->hasLoopInvariantOperands(Inst) && 382 !Inst->mayReadFromMemory() && !Inst->mayWriteToMemory() && 383 !isa<TerminatorInst>(Inst) && !isa<DbgInfoIntrinsic>(Inst) && 384 !isa<AllocaInst>(Inst)) { 385 Inst->moveBefore(LoopEntryBranch); 386 continue; 387 } 388 389 // Otherwise, create a duplicate of the instruction. 390 Instruction *C = Inst->clone(); 391 392 // Eagerly remap the operands of the instruction. 393 RemapInstruction(C, ValueMap, 394 RF_NoModuleLevelChanges|RF_IgnoreMissingEntries); 395 396 // With the operands remapped, see if the instruction constant folds or is 397 // otherwise simplifyable. This commonly occurs because the entry from PHI 398 // nodes allows icmps and other instructions to fold. 399 Value *V = SimplifyInstruction(C); 400 if (V && LI->replacementPreservesLCSSAForm(C, V)) { 401 // If so, then delete the temporary instruction and stick the folded value 402 // in the map. 403 delete C; 404 ValueMap[Inst] = V; 405 } else { 406 // Otherwise, stick the new instruction into the new block! 407 C->setName(Inst->getName()); 408 C->insertBefore(LoopEntryBranch); 409 ValueMap[Inst] = C; 410 } 411 } 412 413 // Along with all the other instructions, we just cloned OrigHeader's 414 // terminator into OrigPreHeader. Fix up the PHI nodes in each of OrigHeader's 415 // successors by duplicating their incoming values for OrigHeader. 416 TerminatorInst *TI = OrigHeader->getTerminator(); 417 for (unsigned i = 0, e = TI->getNumSuccessors(); i != e; ++i) 418 for (BasicBlock::iterator BI = TI->getSuccessor(i)->begin(); 419 PHINode *PN = dyn_cast<PHINode>(BI); ++BI) 420 PN->addIncoming(PN->getIncomingValueForBlock(OrigHeader), OrigPreheader); 421 422 // Now that OrigPreHeader has a clone of OrigHeader's terminator, remove 423 // OrigPreHeader's old terminator (the original branch into the loop), and 424 // remove the corresponding incoming values from the PHI nodes in OrigHeader. 425 LoopEntryBranch->eraseFromParent(); 426 427 // If there were any uses of instructions in the duplicated block outside the 428 // loop, update them, inserting PHI nodes as required 429 RewriteUsesOfClonedInstructions(OrigHeader, OrigPreheader, ValueMap); 430 431 // NewHeader is now the header of the loop. 432 L->moveToHeader(NewHeader); 433 assert(L->getHeader() == NewHeader && "Latch block is our new header"); 434 435 436 // At this point, we've finished our major CFG changes. As part of cloning 437 // the loop into the preheader we've simplified instructions and the 438 // duplicated conditional branch may now be branching on a constant. If it is 439 // branching on a constant and if that constant means that we enter the loop, 440 // then we fold away the cond branch to an uncond branch. This simplifies the 441 // loop in cases important for nested loops, and it also means we don't have 442 // to split as many edges. 443 BranchInst *PHBI = cast<BranchInst>(OrigPreheader->getTerminator()); 444 assert(PHBI->isConditional() && "Should be clone of BI condbr!"); 445 if (!isa<ConstantInt>(PHBI->getCondition()) || 446 PHBI->getSuccessor(cast<ConstantInt>(PHBI->getCondition())->isZero()) 447 != NewHeader) { 448 // The conditional branch can't be folded, handle the general case. 449 // Update DominatorTree to reflect the CFG change we just made. Then split 450 // edges as necessary to preserve LoopSimplify form. 451 if (DominatorTreeWrapperPass *DTWP = 452 getAnalysisIfAvailable<DominatorTreeWrapperPass>()) { 453 DominatorTree &DT = DTWP->getDomTree(); 454 // Everything that was dominated by the old loop header is now dominated 455 // by the original loop preheader. Conceptually the header was merged 456 // into the preheader, even though we reuse the actual block as a new 457 // loop latch. 458 DomTreeNode *OrigHeaderNode = DT.getNode(OrigHeader); 459 SmallVector<DomTreeNode *, 8> HeaderChildren(OrigHeaderNode->begin(), 460 OrigHeaderNode->end()); 461 DomTreeNode *OrigPreheaderNode = DT.getNode(OrigPreheader); 462 for (unsigned I = 0, E = HeaderChildren.size(); I != E; ++I) 463 DT.changeImmediateDominator(HeaderChildren[I], OrigPreheaderNode); 464 465 assert(DT.getNode(Exit)->getIDom() == OrigPreheaderNode); 466 assert(DT.getNode(NewHeader)->getIDom() == OrigPreheaderNode); 467 468 // Update OrigHeader to be dominated by the new header block. 469 DT.changeImmediateDominator(OrigHeader, OrigLatch); 470 } 471 472 // Right now OrigPreHeader has two successors, NewHeader and ExitBlock, and 473 // thus is not a preheader anymore. 474 // Split the edge to form a real preheader. 475 BasicBlock *NewPH = SplitCriticalEdge(OrigPreheader, NewHeader, this); 476 NewPH->setName(NewHeader->getName() + ".lr.ph"); 477 478 // Preserve canonical loop form, which means that 'Exit' should have only 479 // one predecessor. Note that Exit could be an exit block for multiple 480 // nested loops, causing both of the edges to now be critical and need to 481 // be split. 482 SmallVector<BasicBlock *, 4> ExitPreds(pred_begin(Exit), pred_end(Exit)); 483 bool SplitLatchEdge = false; 484 for (SmallVectorImpl<BasicBlock *>::iterator PI = ExitPreds.begin(), 485 PE = ExitPreds.end(); 486 PI != PE; ++PI) { 487 // We only need to split loop exit edges. 488 Loop *PredLoop = LI->getLoopFor(*PI); 489 if (!PredLoop || PredLoop->contains(Exit)) 490 continue; 491 SplitLatchEdge |= L->getLoopLatch() == *PI; 492 BasicBlock *ExitSplit = SplitCriticalEdge(*PI, Exit, this); 493 ExitSplit->moveBefore(Exit); 494 } 495 assert(SplitLatchEdge && 496 "Despite splitting all preds, failed to split latch exit?"); 497 } else { 498 // We can fold the conditional branch in the preheader, this makes things 499 // simpler. The first step is to remove the extra edge to the Exit block. 500 Exit->removePredecessor(OrigPreheader, true /*preserve LCSSA*/); 501 BranchInst *NewBI = BranchInst::Create(NewHeader, PHBI); 502 NewBI->setDebugLoc(PHBI->getDebugLoc()); 503 PHBI->eraseFromParent(); 504 505 // With our CFG finalized, update DomTree if it is available. 506 if (DominatorTreeWrapperPass *DTWP = 507 getAnalysisIfAvailable<DominatorTreeWrapperPass>()) { 508 DominatorTree &DT = DTWP->getDomTree(); 509 // Update OrigHeader to be dominated by the new header block. 510 DT.changeImmediateDominator(NewHeader, OrigPreheader); 511 DT.changeImmediateDominator(OrigHeader, OrigLatch); 512 513 // Brute force incremental dominator tree update. Call 514 // findNearestCommonDominator on all CFG predecessors of each child of the 515 // original header. 516 DomTreeNode *OrigHeaderNode = DT.getNode(OrigHeader); 517 SmallVector<DomTreeNode *, 8> HeaderChildren(OrigHeaderNode->begin(), 518 OrigHeaderNode->end()); 519 bool Changed; 520 do { 521 Changed = false; 522 for (unsigned I = 0, E = HeaderChildren.size(); I != E; ++I) { 523 DomTreeNode *Node = HeaderChildren[I]; 524 BasicBlock *BB = Node->getBlock(); 525 526 pred_iterator PI = pred_begin(BB); 527 BasicBlock *NearestDom = *PI; 528 for (pred_iterator PE = pred_end(BB); PI != PE; ++PI) 529 NearestDom = DT.findNearestCommonDominator(NearestDom, *PI); 530 531 // Remember if this changes the DomTree. 532 if (Node->getIDom()->getBlock() != NearestDom) { 533 DT.changeImmediateDominator(BB, NearestDom); 534 Changed = true; 535 } 536 } 537 538 // If the dominator changed, this may have an effect on other 539 // predecessors, continue until we reach a fixpoint. 540 } while (Changed); 541 } 542 } 543 544 assert(L->getLoopPreheader() && "Invalid loop preheader after loop rotation"); 545 assert(L->getLoopLatch() && "Invalid loop latch after loop rotation"); 546 547 // Now that the CFG and DomTree are in a consistent state again, try to merge 548 // the OrigHeader block into OrigLatch. This will succeed if they are 549 // connected by an unconditional branch. This is just a cleanup so the 550 // emitted code isn't too gross in this common case. 551 MergeBlockIntoPredecessor(OrigHeader, this); 552 553 DEBUG(dbgs() << "LoopRotation: into "; L->dump()); 554 555 ++NumRotated; 556 return true; 557 } 558