lib/Transforms/Scalar/LoopRotation.cpp

   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 #define DEBUG_TYPE "loop-rotate"
  15 #include "llvm/Transforms/Scalar.h"
  16 #include "llvm/Function.h"
  17 #include "llvm/IntrinsicInst.h"
  18 #include "llvm/Analysis/LoopInfo.h"
  19 #include "llvm/Analysis/LoopPass.h"
  20 #include "llvm/Analysis/Dominators.h"
  21 #include "llvm/Analysis/ScalarEvolution.h"
  22 #include "llvm/Transforms/Utils/Local.h"
  23 #include "llvm/Transforms/Utils/BasicBlockUtils.h"
  24 #include "llvm/Support/CommandLine.h"
  25 #include "llvm/Support/Debug.h"
  26 #include "llvm/ADT/Statistic.h"
  27 #include "llvm/ADT/SmallVector.h"
  28 using namespace llvm;
  29
  30 #define MAX_HEADER_SIZE 16
  31
  32 STATISTIC(NumRotated, "Number of loops rotated");
  33 namespace {
  34
  35   class RenameData {
  36   public:
  37     RenameData(Instruction *O, Value *P, Instruction *H)
  38       : Original(O), PreHeader(P), Header(H) { }
  39   public:
  40     Instruction *Original; // Original instruction
  41     Value *PreHeader; // Original pre-header replacement
  42     Instruction *Header; // New header replacement
  43   };
  44
  45   class LoopRotate : public LoopPass {
  46   public:
  47     static char ID; // Pass ID, replacement for typeid
  48     LoopRotate() : LoopPass(&ID) {}
  49
  50     // Rotate Loop L as many times as possible. Return true if
  51     // loop is rotated at least once.
  52     bool runOnLoop(Loop *L, LPPassManager &LPM);
  53
  54     // LCSSA form makes instruction renaming easier.
  55     virtual void getAnalysisUsage(AnalysisUsage &AU) const {
  56       AU.addRequiredID(LoopSimplifyID);
  57       AU.addPreservedID(LoopSimplifyID);
  58       AU.addRequiredID(LCSSAID);
  59       AU.addPreservedID(LCSSAID);
  60       AU.addPreserved<ScalarEvolution>();
  61       AU.addPreserved<LoopInfo>();
  62       AU.addPreserved<DominatorTree>();
  63       AU.addPreserved<DominanceFrontier>();
  64     }
  65
  66     // Helper functions
  67
  68     /// Do actual work
  69     bool rotateLoop(Loop *L, LPPassManager &LPM);
  70
  71     /// Initialize local data
  72     void initialize();
  73
  74     /// Make sure all Exit block PHINodes have required incoming values.
  75     /// If incoming value is constant or defined outside the loop then
  76     /// PHINode may not have an entry for original pre-header.
  77     void  updateExitBlock();
  78
  79     /// Return true if this instruction is used outside original header.
  80     bool usedOutsideOriginalHeader(Instruction *In);
  81
  82     /// Find Replacement information for instruction. Return NULL if it is
  83     /// not available.
  84     const RenameData *findReplacementData(Instruction *I);
  85
  86     /// After loop rotation, loop pre-header has multiple sucessors.
  87     /// Insert one forwarding basic block to ensure that loop pre-header
  88     /// has only one successor.
  89     void preserveCanonicalLoopForm(LPPassManager &LPM);
  90
  91   private:
  92
  93     Loop *L;
  94     BasicBlock *OrigHeader;
  95     BasicBlock *OrigPreHeader;
  96     BasicBlock *OrigLatch;
  97     BasicBlock *NewHeader;
  98     BasicBlock *Exit;
  99     LPPassManager *LPM_Ptr;
 100     SmallVector<RenameData, MAX_HEADER_SIZE> LoopHeaderInfo;
 101   };
 102 }
 103
 104 char LoopRotate::ID = 0;
 105 static RegisterPass<LoopRotate> X("loop-rotate", "Rotate Loops");
 106
 107 Pass *llvm::createLoopRotatePass() { return new LoopRotate(); }
 108
 109 /// Rotate Loop L as many times as possible. Return true if
 110 /// the loop is rotated at least once.
 111 bool LoopRotate::runOnLoop(Loop *Lp, LPPassManager &LPM) {
 112
 113   bool RotatedOneLoop = false;
 114   initialize();
 115   LPM_Ptr = &LPM;
 116
 117   // One loop can be rotated multiple times.
 118   while (rotateLoop(Lp,LPM)) {
 119     RotatedOneLoop = true;
 120     initialize();
 121   }
 122
 123   return RotatedOneLoop;
 124 }
 125
 126 /// Rotate loop LP. Return true if the loop is rotated.
 127 bool LoopRotate::rotateLoop(Loop *Lp, LPPassManager &LPM) {
 128   L = Lp;
 129
 130   OrigHeader =  L->getHeader();
 131   OrigPreHeader = L->getLoopPreheader();
 132   OrigLatch = L->getLoopLatch();
 133
 134   // If the loop has only one block then there is not much to rotate.
 135   if (L->getBlocks().size() == 1)
 136     return false;
 137
 138   assert(OrigHeader && OrigLatch && OrigPreHeader &&
 139          "Loop is not in canonical form");
 140
 141   // If the loop header is not one of the loop exiting blocks then
 142   // either this loop is already rotated or it is not
 143   // suitable for loop rotation transformations.
 144   if (!L->isLoopExit(OrigHeader))
 145     return false;
 146
 147   BranchInst *BI = dyn_cast<BranchInst>(OrigHeader->getTerminator());
 148   if (!BI)
 149     return false;
 150   assert(BI->isConditional() && "Branch Instruction is not conditional");
 151
 152   // Updating PHInodes in loops with multiple exits adds complexity.
 153   // Keep it simple, and restrict loop rotation to loops with one exit only.
 154   // In future, lift this restriction and support for multiple exits if
 155   // required.
 156   SmallVector<BasicBlock*, 8> ExitBlocks;
 157   L->getExitBlocks(ExitBlocks);
 158   if (ExitBlocks.size() > 1)
 159     return false;
 160
 161   // Check size of original header and reject
 162   // loop if it is very big.
 163   unsigned Size = 0;
 164
 165   // FIXME: Use common api to estimate size.
 166   for (BasicBlock::const_iterator OI = OrigHeader->begin(),
 167          OE = OrigHeader->end(); OI != OE; ++OI) {
 168       if (isa<PHINode>(OI))
 169         continue;           // PHI nodes don't count.
 170       if (isa<DbgInfoIntrinsic>(OI))
 171         continue;  // Debug intrinsics don't count as size.
 172       Size++;
 173   }
 174
 175   if (Size > MAX_HEADER_SIZE)
 176     return false;
 177
 178   // Now, this loop is suitable for rotation.
 179
 180   // Find new Loop header. NewHeader is a Header's one and only successor
 181   // that is inside loop.  Header's other successor is outside the
 182   // loop.  Otherwise loop is not suitable for rotation.
 183   Exit = BI->getSuccessor(0);
 184   NewHeader = BI->getSuccessor(1);
 185   if (L->contains(Exit))
 186     std::swap(Exit, NewHeader);
 187   assert(NewHeader && "Unable to determine new loop header");
 188   assert(L->contains(NewHeader) && !L->contains(Exit) &&
 189          "Unable to determine loop header and exit blocks");
 190
 191   // This code assumes that the new header has exactly one predecessor.
 192   // Remove any single-entry PHI nodes in it.
 193   assert(NewHeader->getSinglePredecessor() &&
 194          "New header doesn't have one pred!");
 195   FoldSingleEntryPHINodes(NewHeader);
 196
 197   // Copy PHI nodes and other instructions from the original header
 198   // into the original pre-header. Unlike the original header, the original
 199   // pre-header is not a member of the loop.
 200   //
 201   // The new loop header is the one and only successor of original header that
 202   // is inside the loop. All other original header successors are outside
 203   // the loop. Copy PHI Nodes from the original header into the new loop header.
 204   // Add second incoming value, from original loop pre-header into these phi
 205   // nodes. If a value defined in original header is used outside original
 206   // header then new loop header will need new phi nodes with two incoming
 207   // values, one definition from original header and second definition is
 208   // from original loop pre-header.
 209
 210   // Remove terminator from Original pre-header. Original pre-header will
 211   // receive a clone of original header terminator as a new terminator.
 212   OrigPreHeader->getInstList().pop_back();
 213   BasicBlock::iterator I = OrigHeader->begin(), E = OrigHeader->end();
 214   PHINode *PN = 0;
 215   for (; (PN = dyn_cast<PHINode>(I)); ++I) {
 216     // PHI nodes are not copied into original pre-header. Instead their values
 217     // are directly propagated.
 218     Value *NPV = PN->getIncomingValueForBlock(OrigPreHeader);
 219
 220     // Create a new PHI node with two incoming values for NewHeader.
 221     // One incoming value is from OrigLatch (through OrigHeader) and the
 222     // second incoming value is from original pre-header.
 223     PHINode *NH = PHINode::Create(PN->getType(), PN->getName(),
 224                                   NewHeader->begin());
 225     NH->addIncoming(PN->getIncomingValueForBlock(OrigLatch), OrigHeader);
 226     NH->addIncoming(NPV, OrigPreHeader);
 227
 228     // "In" can be replaced by NH at various places.
 229     LoopHeaderInfo.push_back(RenameData(PN, NPV, NH));
 230   }
 231
 232   // Now, handle non-phi instructions.
 233   for (; I != E; ++I) {
 234     Instruction *In = I;
 235     assert(!isa<PHINode>(In) && "PHINode is not expected here");
 236
 237     // This is not a PHI instruction. Insert its clone into original pre-header.
 238     // If this instruction is using a value from same basic block then
 239     // update it to use value from cloned instruction.
 240     Instruction *C = In->clone(In->getContext());
 241     C->setName(In->getName());
 242     OrigPreHeader->getInstList().push_back(C);
 243
 244     for (unsigned opi = 0, e = In->getNumOperands(); opi != e; ++opi) {
 245       Instruction *OpInsn = dyn_cast<Instruction>(In->getOperand(opi));
 246       if (!OpInsn) continue;  // Ignore non-instruction values.
 247       if (const RenameData *D = findReplacementData(OpInsn))
 248         C->setOperand(opi, D->PreHeader);
 249     }
 250
 251     // If this instruction is used outside this basic block then
 252     // create new PHINode for this instruction.
 253     Instruction *NewHeaderReplacement = NULL;
 254     if (usedOutsideOriginalHeader(In)) {
 255       PHINode *PN = PHINode::Create(In->getType(), In->getName(),
 256                                     NewHeader->begin());
 257       PN->addIncoming(In, OrigHeader);
 258       PN->addIncoming(C, OrigPreHeader);
 259       NewHeaderReplacement = PN;
 260     }
 261     LoopHeaderInfo.push_back(RenameData(In, C, NewHeaderReplacement));
 262   }
 263
 264   // Rename uses of original header instructions to reflect their new
 265   // definitions (either from original pre-header node or from newly created
 266   // new header PHINodes.
 267   //
 268   // Original header instructions are used in
 269   // 1) Original header:
 270   //
 271   //    If instruction is used in non-phi instructions then it is using
 272   //    defintion from original heder iteself. Do not replace this use
 273   //    with definition from new header or original pre-header.
 274   //
 275   //    If instruction is used in phi node then it is an incoming
 276   //    value. Rename its use to reflect new definition from new-preheader
 277   //    or new header.
 278   //
 279   // 2) Inside loop but not in original header
 280   //
 281   //    Replace this use to reflect definition from new header.
 282   for (unsigned LHI = 0, LHI_E = LoopHeaderInfo.size(); LHI != LHI_E; ++LHI) {
 283     const RenameData &ILoopHeaderInfo = LoopHeaderInfo[LHI];
 284
 285     if (!ILoopHeaderInfo.Header)
 286       continue;
 287
 288     Instruction *OldPhi = ILoopHeaderInfo.Original;
 289     Instruction *NewPhi = ILoopHeaderInfo.Header;
 290
 291     // Before replacing uses, collect them first, so that iterator is
 292     // not invalidated.
 293     SmallVector<Instruction *, 16> AllUses;
 294     for (Value::use_iterator UI = OldPhi->use_begin(), UE = OldPhi->use_end();
 295          UI != UE; ++UI)
 296       AllUses.push_back(cast<Instruction>(UI));
 297
 298     for (SmallVector<Instruction *, 16>::iterator UI = AllUses.begin(),
 299            UE = AllUses.end(); UI != UE; ++UI) {
 300       Instruction *U = *UI;
 301       BasicBlock *Parent = U->getParent();
 302
 303       // Used inside original header
 304       if (Parent == OrigHeader) {
 305         // Do not rename uses inside original header non-phi instructions.
 306         PHINode *PU = dyn_cast<PHINode>(U);
 307         if (!PU)
 308           continue;
 309
 310         // Do not rename uses inside original header phi nodes, if the
 311         // incoming value is for new header.
 312         if (PU->getBasicBlockIndex(NewHeader) != -1
 313             && PU->getIncomingValueForBlock(NewHeader) == U)
 314           continue;
 315
 316        U->replaceUsesOfWith(OldPhi, NewPhi);
 317        continue;
 318       }
 319
 320       // Used inside loop, but not in original header.
 321       if (L->contains(U->getParent())) {
 322         if (U != NewPhi)
 323           U->replaceUsesOfWith(OldPhi, NewPhi);
 324         continue;
 325       }
 326
 327       // Used inside Exit Block. Since we are in LCSSA form, U must be PHINode.
 328       if (U->getParent() == Exit) {
 329         assert(isa<PHINode>(U) && "Use in Exit Block that is not PHINode");
 330
 331         PHINode *UPhi = cast<PHINode>(U);
 332         // UPhi already has one incoming argument from original header.
 333         // Add second incoming argument from new Pre header.
 334         UPhi->addIncoming(ILoopHeaderInfo.PreHeader, OrigPreHeader);
 335       } else {
 336         // Used outside Exit block. Create a new PHI node in the exit block
 337         // to receive the value from the new header and pre-header.
 338         PHINode *PN = PHINode::Create(U->getType(), U->getName(),
 339                                       Exit->begin());
 340         PN->addIncoming(ILoopHeaderInfo.PreHeader, OrigPreHeader);
 341         PN->addIncoming(OldPhi, OrigHeader);
 342         U->replaceUsesOfWith(OldPhi, PN);
 343       }
 344     }
 345   }
 346
 347   /// Make sure all Exit block PHINodes have required incoming values.
 348   updateExitBlock();
 349
 350   // Update CFG
 351
 352   // Removing incoming branch from loop preheader to original header.
 353   // Now original header is inside the loop.
 354   for (BasicBlock::iterator I = OrigHeader->begin();
 355        (PN = dyn_cast<PHINode>(I)); ++I)
 356     PN->removeIncomingValue(OrigPreHeader);
 357
 358   // Make NewHeader as the new header for the loop.
 359   L->moveToHeader(NewHeader);
 360
 361   preserveCanonicalLoopForm(LPM);
 362
 363   NumRotated++;
 364   return true;
 365 }
 366
 367 /// Make sure all Exit block PHINodes have required incoming values.
 368 /// If an incoming value is constant or defined outside the loop then
 369 /// PHINode may not have an entry for the original pre-header.
 370 void LoopRotate::updateExitBlock() {
 371
 372   PHINode *PN;
 373   for (BasicBlock::iterator I = Exit->begin();
 374        (PN = dyn_cast<PHINode>(I)); ++I) {
 375
 376     // There is already one incoming value from original pre-header block.
 377     if (PN->getBasicBlockIndex(OrigPreHeader) != -1)
 378       continue;
 379
 380     const RenameData *ILoopHeaderInfo;
 381     Value *V = PN->getIncomingValueForBlock(OrigHeader);
 382     if (isa<Instruction>(V) &&
 383         (ILoopHeaderInfo = findReplacementData(cast<Instruction>(V)))) {
 384       assert(ILoopHeaderInfo->PreHeader && "Missing New Preheader Instruction");
 385       PN->addIncoming(ILoopHeaderInfo->PreHeader, OrigPreHeader);
 386     } else {
 387       PN->addIncoming(V, OrigPreHeader);
 388     }
 389   }
 390 }
 391
 392 /// Initialize local data
 393 void LoopRotate::initialize() {
 394   L = NULL;
 395   OrigHeader = NULL;
 396   OrigPreHeader = NULL;
 397   NewHeader = NULL;
 398   Exit = NULL;
 399
 400   LoopHeaderInfo.clear();
 401 }
 402
 403 /// Return true if this instruction is used by any instructions in the loop that
 404 /// aren't in original header.
 405 bool LoopRotate::usedOutsideOriginalHeader(Instruction *In) {
 406   for (Value::use_iterator UI = In->use_begin(), UE = In->use_end();
 407        UI != UE; ++UI) {
 408     BasicBlock *UserBB = cast<Instruction>(UI)->getParent();
 409     if (UserBB != OrigHeader && L->contains(UserBB))
 410       return true;
 411   }
 412
 413   return false;
 414 }
 415
 416 /// Find Replacement information for instruction. Return NULL if it is
 417 /// not available.
 418 const RenameData *LoopRotate::findReplacementData(Instruction *In) {
 419
 420   // Since LoopHeaderInfo is small, linear walk is OK.
 421   for (unsigned LHI = 0, LHI_E = LoopHeaderInfo.size(); LHI != LHI_E; ++LHI) {
 422     const RenameData &ILoopHeaderInfo = LoopHeaderInfo[LHI];
 423     if (ILoopHeaderInfo.Original == In)
 424       return &ILoopHeaderInfo;
 425   }
 426   return NULL;
 427 }
 428
 429 /// After loop rotation, loop pre-header has multiple sucessors.
 430 /// Insert one forwarding basic block to ensure that loop pre-header
 431 /// has only one successor.
 432 void LoopRotate::preserveCanonicalLoopForm(LPPassManager &LPM) {
 433
 434   // Right now original pre-header has two successors, new header and
 435   // exit block. Insert new block between original pre-header and
 436   // new header such that loop's new pre-header has only one successor.
 437   BasicBlock *NewPreHeader = BasicBlock::Create(OrigHeader->getContext(),
 438                                                 "bb.nph",
 439                                                 OrigHeader->getParent(),
 440                                                 NewHeader);
 441   LoopInfo &LI = LPM.getAnalysis<LoopInfo>();
 442   if (Loop *PL = LI.getLoopFor(OrigPreHeader))
 443     PL->addBasicBlockToLoop(NewPreHeader, LI.getBase());
 444   BranchInst::Create(NewHeader, NewPreHeader);
 445
 446   BranchInst *OrigPH_BI = cast<BranchInst>(OrigPreHeader->getTerminator());
 447   if (OrigPH_BI->getSuccessor(0) == NewHeader)
 448     OrigPH_BI->setSuccessor(0, NewPreHeader);
 449   else {
 450     assert(OrigPH_BI->getSuccessor(1) == NewHeader &&
 451            "Unexpected original pre-header terminator");
 452     OrigPH_BI->setSuccessor(1, NewPreHeader);
 453   }
 454
 455   PHINode *PN;
 456   for (BasicBlock::iterator I = NewHeader->begin();
 457        (PN = dyn_cast<PHINode>(I)); ++I) {
 458     int index = PN->getBasicBlockIndex(OrigPreHeader);
 459     assert(index != -1 && "Expected incoming value from Original PreHeader");
 460     PN->setIncomingBlock(index, NewPreHeader);
 461     assert(PN->getBasicBlockIndex(OrigPreHeader) == -1 &&
 462            "Expected only one incoming value from Original PreHeader");
 463   }
 464
 465   if (DominatorTree *DT = getAnalysisIfAvailable<DominatorTree>()) {
 466     DT->addNewBlock(NewPreHeader, OrigPreHeader);
 467     DT->changeImmediateDominator(L->getHeader(), NewPreHeader);
 468     DT->changeImmediateDominator(Exit, OrigPreHeader);
 469     for (Loop::block_iterator BI = L->block_begin(), BE = L->block_end();
 470          BI != BE; ++BI) {
 471       BasicBlock *B = *BI;
 472       if (L->getHeader() != B) {
 473         DomTreeNode *Node = DT->getNode(B);
 474         if (Node && Node->getBlock() == OrigHeader)
 475           DT->changeImmediateDominator(*BI, L->getHeader());
 476       }
 477     }
 478     DT->changeImmediateDominator(OrigHeader, OrigLatch);
 479   }
 480
 481   if (DominanceFrontier *DF = getAnalysisIfAvailable<DominanceFrontier>()) {
 482     // New Preheader's dominance frontier is Exit block.
 483     DominanceFrontier::DomSetType NewPHSet;
 484     NewPHSet.insert(Exit);
 485     DF->addBasicBlock(NewPreHeader, NewPHSet);
 486
 487     // New Header's dominance frontier now includes itself and Exit block
 488     DominanceFrontier::iterator HeadI = DF->find(L->getHeader());
 489     if (HeadI != DF->end()) {
 490       DominanceFrontier::DomSetType & HeaderSet = HeadI->second;
 491       HeaderSet.clear();
 492       HeaderSet.insert(L->getHeader());
 493       HeaderSet.insert(Exit);
 494     } else {
 495       DominanceFrontier::DomSetType HeaderSet;
 496       HeaderSet.insert(L->getHeader());
 497       HeaderSet.insert(Exit);
 498       DF->addBasicBlock(L->getHeader(), HeaderSet);
 499     }
 500
 501     // Original header (new Loop Latch)'s dominance frontier is Exit.
 502     DominanceFrontier::iterator LatchI = DF->find(L->getLoopLatch());
 503     if (LatchI != DF->end()) {
 504       DominanceFrontier::DomSetType &LatchSet = LatchI->second;
 505       LatchSet = LatchI->second;
 506       LatchSet.clear();
 507       LatchSet.insert(Exit);
 508     } else {
 509       DominanceFrontier::DomSetType LatchSet;
 510       LatchSet.insert(Exit);
 511       DF->addBasicBlock(L->getHeader(), LatchSet);
 512     }
 513
 514     // If a loop block dominates new loop latch then add to its frontiers
 515     // new header and Exit and remove new latch (which is equal to original
 516     // header).
 517     BasicBlock *NewLatch = L->getLoopLatch();
 518
 519     assert(NewLatch == OrigHeader && "NewLatch is inequal to OrigHeader");
 520
 521     if (DominatorTree *DT = getAnalysisIfAvailable<DominatorTree>()) {
 522       for (Loop::block_iterator BI = L->block_begin(), BE = L->block_end();
 523            BI != BE; ++BI) {
 524         BasicBlock *B = *BI;
 525         if (DT->dominates(B, NewLatch)) {
 526           DominanceFrontier::iterator BDFI = DF->find(B);
 527           if (BDFI != DF->end()) {
 528             DominanceFrontier::DomSetType &BSet = BDFI->second;
 529             BSet.erase(NewLatch);
 530             BSet.insert(L->getHeader());
 531             BSet.insert(Exit);
 532           } else {
 533             DominanceFrontier::DomSetType BSet;
 534             BSet.insert(L->getHeader());
 535             BSet.insert(Exit);
 536             DF->addBasicBlock(B, BSet);
 537           }
 538         }
 539       }
 540     }
 541   }
 542
 543   // Preserve canonical loop form, which means Exit block should
 544   // have only one predecessor.
 545   BasicBlock *NExit = SplitEdge(L->getLoopLatch(), Exit, this);
 546
 547   // Preserve LCSSA.
 548   for (BasicBlock::iterator I = Exit->begin();
 549        (PN = dyn_cast<PHINode>(I)); ++I) {
 550     unsigned N = PN->getNumIncomingValues();
 551     for (unsigned index = 0; index != N; ++index)
 552       if (PN->getIncomingBlock(index) == NExit) {
 553         PHINode *NewPN = PHINode::Create(PN->getType(), PN->getName(),
 554                                          NExit->begin());
 555         NewPN->addIncoming(PN->getIncomingValue(index), L->getLoopLatch());
 556         PN->setIncomingValue(index, NewPN);
 557         PN->setIncomingBlock(index, NExit);
 558         break;
 559       }
 560   }
 561
 562   assert(NewHeader && L->getHeader() == NewHeader &&
 563          "Invalid loop header after loop rotation");
 564   assert(NewPreHeader && L->getLoopPreheader() == NewPreHeader &&
 565          "Invalid loop preheader after loop rotation");
 566   assert(L->getLoopLatch() &&
 567          "Invalid loop latch after loop rotation");
 568 }