BasicAliasAnalysis.cpp revision 895ace08e01578b5490ed9d064df6d89acf5420a
1//===- BasicAliasAnalysis.cpp - Stateless Alias Analysis Impl -------------===// 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 defines the primary stateless implementation of the 11// Alias Analysis interface that implements identities (two different 12// globals cannot alias, etc), but does no stateful analysis. 13// 14//===----------------------------------------------------------------------===// 15 16#include "llvm/Analysis/AliasAnalysis.h" 17#include "llvm/Analysis/Passes.h" 18#include "llvm/Constants.h" 19#include "llvm/DerivedTypes.h" 20#include "llvm/Function.h" 21#include "llvm/GlobalAlias.h" 22#include "llvm/GlobalVariable.h" 23#include "llvm/Instructions.h" 24#include "llvm/IntrinsicInst.h" 25#include "llvm/LLVMContext.h" 26#include "llvm/Operator.h" 27#include "llvm/Pass.h" 28#include "llvm/Analysis/CaptureTracking.h" 29#include "llvm/Analysis/MemoryBuiltins.h" 30#include "llvm/Analysis/InstructionSimplify.h" 31#include "llvm/Analysis/ValueTracking.h" 32#include "llvm/Target/TargetData.h" 33#include "llvm/ADT/SmallPtrSet.h" 34#include "llvm/ADT/SmallVector.h" 35#include "llvm/Support/ErrorHandling.h" 36#include "llvm/Support/GetElementPtrTypeIterator.h" 37#include <algorithm> 38using namespace llvm; 39 40//===----------------------------------------------------------------------===// 41// Useful predicates 42//===----------------------------------------------------------------------===// 43 44/// isKnownNonNull - Return true if we know that the specified value is never 45/// null. 46static bool isKnownNonNull(const Value *V) { 47 // Alloca never returns null, malloc might. 48 if (isa<AllocaInst>(V)) return true; 49 50 // A byval argument is never null. 51 if (const Argument *A = dyn_cast<Argument>(V)) 52 return A->hasByValAttr(); 53 54 // Global values are not null unless extern weak. 55 if (const GlobalValue *GV = dyn_cast<GlobalValue>(V)) 56 return !GV->hasExternalWeakLinkage(); 57 return false; 58} 59 60/// isNonEscapingLocalObject - Return true if the pointer is to a function-local 61/// object that never escapes from the function. 62static bool isNonEscapingLocalObject(const Value *V) { 63 // If this is a local allocation, check to see if it escapes. 64 if (isa<AllocaInst>(V) || isNoAliasCall(V)) 65 // Set StoreCaptures to True so that we can assume in our callers that the 66 // pointer is not the result of a load instruction. Currently 67 // PointerMayBeCaptured doesn't have any special analysis for the 68 // StoreCaptures=false case; if it did, our callers could be refined to be 69 // more precise. 70 return !PointerMayBeCaptured(V, false, /*StoreCaptures=*/true); 71 72 // If this is an argument that corresponds to a byval or noalias argument, 73 // then it has not escaped before entering the function. Check if it escapes 74 // inside the function. 75 if (const Argument *A = dyn_cast<Argument>(V)) 76 if (A->hasByValAttr() || A->hasNoAliasAttr()) { 77 // Don't bother analyzing arguments already known not to escape. 78 if (A->hasNoCaptureAttr()) 79 return true; 80 return !PointerMayBeCaptured(V, false, /*StoreCaptures=*/true); 81 } 82 return false; 83} 84 85/// isEscapeSource - Return true if the pointer is one which would have 86/// been considered an escape by isNonEscapingLocalObject. 87static bool isEscapeSource(const Value *V) { 88 if (isa<CallInst>(V) || isa<InvokeInst>(V) || isa<Argument>(V)) 89 return true; 90 91 // The load case works because isNonEscapingLocalObject considers all 92 // stores to be escapes (it passes true for the StoreCaptures argument 93 // to PointerMayBeCaptured). 94 if (isa<LoadInst>(V)) 95 return true; 96 97 return false; 98} 99 100/// isObjectSmallerThan - Return true if we can prove that the object specified 101/// by V is smaller than Size. 102static bool isObjectSmallerThan(const Value *V, uint64_t Size, 103 const TargetData &TD) { 104 const Type *AccessTy; 105 if (const GlobalVariable *GV = dyn_cast<GlobalVariable>(V)) { 106 if (!GV->hasDefinitiveInitializer()) 107 return false; 108 AccessTy = GV->getType()->getElementType(); 109 } else if (const AllocaInst *AI = dyn_cast<AllocaInst>(V)) { 110 if (!AI->isArrayAllocation()) 111 AccessTy = AI->getType()->getElementType(); 112 else 113 return false; 114 } else if (const CallInst* CI = extractMallocCall(V)) { 115 if (!isArrayMalloc(V, &TD)) 116 // The size is the argument to the malloc call. 117 if (const ConstantInt* C = dyn_cast<ConstantInt>(CI->getArgOperand(0))) 118 return (C->getZExtValue() < Size); 119 return false; 120 } else if (const Argument *A = dyn_cast<Argument>(V)) { 121 if (A->hasByValAttr()) 122 AccessTy = cast<PointerType>(A->getType())->getElementType(); 123 else 124 return false; 125 } else { 126 return false; 127 } 128 129 if (AccessTy->isSized()) 130 return TD.getTypeAllocSize(AccessTy) < Size; 131 return false; 132} 133 134//===----------------------------------------------------------------------===// 135// GetElementPtr Instruction Decomposition and Analysis 136//===----------------------------------------------------------------------===// 137 138namespace { 139 enum ExtensionKind { 140 EK_NotExtended, 141 EK_SignExt, 142 EK_ZeroExt 143 }; 144 145 struct VariableGEPIndex { 146 const Value *V; 147 ExtensionKind Extension; 148 int64_t Scale; 149 }; 150} 151 152 153/// GetLinearExpression - Analyze the specified value as a linear expression: 154/// "A*V + B", where A and B are constant integers. Return the scale and offset 155/// values as APInts and return V as a Value*, and return whether we looked 156/// through any sign or zero extends. The incoming Value is known to have 157/// IntegerType and it may already be sign or zero extended. 158/// 159/// Note that this looks through extends, so the high bits may not be 160/// represented in the result. 161static Value *GetLinearExpression(Value *V, APInt &Scale, APInt &Offset, 162 ExtensionKind &Extension, 163 const TargetData &TD, unsigned Depth) { 164 assert(V->getType()->isIntegerTy() && "Not an integer value"); 165 166 // Limit our recursion depth. 167 if (Depth == 6) { 168 Scale = 1; 169 Offset = 0; 170 return V; 171 } 172 173 if (BinaryOperator *BOp = dyn_cast<BinaryOperator>(V)) { 174 if (ConstantInt *RHSC = dyn_cast<ConstantInt>(BOp->getOperand(1))) { 175 switch (BOp->getOpcode()) { 176 default: break; 177 case Instruction::Or: 178 // X|C == X+C if all the bits in C are unset in X. Otherwise we can't 179 // analyze it. 180 if (!MaskedValueIsZero(BOp->getOperand(0), RHSC->getValue(), &TD)) 181 break; 182 // FALL THROUGH. 183 case Instruction::Add: 184 V = GetLinearExpression(BOp->getOperand(0), Scale, Offset, Extension, 185 TD, Depth+1); 186 Offset += RHSC->getValue(); 187 return V; 188 case Instruction::Mul: 189 V = GetLinearExpression(BOp->getOperand(0), Scale, Offset, Extension, 190 TD, Depth+1); 191 Offset *= RHSC->getValue(); 192 Scale *= RHSC->getValue(); 193 return V; 194 case Instruction::Shl: 195 V = GetLinearExpression(BOp->getOperand(0), Scale, Offset, Extension, 196 TD, Depth+1); 197 Offset <<= RHSC->getValue().getLimitedValue(); 198 Scale <<= RHSC->getValue().getLimitedValue(); 199 return V; 200 } 201 } 202 } 203 204 // Since GEP indices are sign extended anyway, we don't care about the high 205 // bits of a sign or zero extended value - just scales and offsets. The 206 // extensions have to be consistent though. 207 if ((isa<SExtInst>(V) && Extension != EK_ZeroExt) || 208 (isa<ZExtInst>(V) && Extension != EK_SignExt)) { 209 Value *CastOp = cast<CastInst>(V)->getOperand(0); 210 unsigned OldWidth = Scale.getBitWidth(); 211 unsigned SmallWidth = CastOp->getType()->getPrimitiveSizeInBits(); 212 Scale = Scale.trunc(SmallWidth); 213 Offset = Offset.trunc(SmallWidth); 214 Extension = isa<SExtInst>(V) ? EK_SignExt : EK_ZeroExt; 215 216 Value *Result = GetLinearExpression(CastOp, Scale, Offset, Extension, 217 TD, Depth+1); 218 Scale = Scale.zext(OldWidth); 219 Offset = Offset.zext(OldWidth); 220 221 return Result; 222 } 223 224 Scale = 1; 225 Offset = 0; 226 return V; 227} 228 229/// DecomposeGEPExpression - If V is a symbolic pointer expression, decompose it 230/// into a base pointer with a constant offset and a number of scaled symbolic 231/// offsets. 232/// 233/// The scaled symbolic offsets (represented by pairs of a Value* and a scale in 234/// the VarIndices vector) are Value*'s that are known to be scaled by the 235/// specified amount, but which may have other unrepresented high bits. As such, 236/// the gep cannot necessarily be reconstructed from its decomposed form. 237/// 238/// When TargetData is around, this function is capable of analyzing everything 239/// that GetUnderlyingObject can look through. When not, it just looks 240/// through pointer casts. 241/// 242static const Value * 243DecomposeGEPExpression(const Value *V, int64_t &BaseOffs, 244 SmallVectorImpl<VariableGEPIndex> &VarIndices, 245 const TargetData *TD) { 246 // Limit recursion depth to limit compile time in crazy cases. 247 unsigned MaxLookup = 6; 248 249 BaseOffs = 0; 250 do { 251 // See if this is a bitcast or GEP. 252 const Operator *Op = dyn_cast<Operator>(V); 253 if (Op == 0) { 254 // The only non-operator case we can handle are GlobalAliases. 255 if (const GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) { 256 if (!GA->mayBeOverridden()) { 257 V = GA->getAliasee(); 258 continue; 259 } 260 } 261 return V; 262 } 263 264 if (Op->getOpcode() == Instruction::BitCast) { 265 V = Op->getOperand(0); 266 continue; 267 } 268 269 if (const Instruction *I = dyn_cast<Instruction>(V)) 270 // TODO: Get a DominatorTree and use it here. 271 if (const Value *Simplified = 272 SimplifyInstruction(const_cast<Instruction *>(I), TD)) { 273 V = Simplified; 274 continue; 275 } 276 277 const GEPOperator *GEPOp = dyn_cast<GEPOperator>(Op); 278 if (GEPOp == 0) 279 return V; 280 281 // Don't attempt to analyze GEPs over unsized objects. 282 if (!cast<PointerType>(GEPOp->getOperand(0)->getType()) 283 ->getElementType()->isSized()) 284 return V; 285 286 // If we are lacking TargetData information, we can't compute the offets of 287 // elements computed by GEPs. However, we can handle bitcast equivalent 288 // GEPs. 289 if (TD == 0) { 290 if (!GEPOp->hasAllZeroIndices()) 291 return V; 292 V = GEPOp->getOperand(0); 293 continue; 294 } 295 296 // Walk the indices of the GEP, accumulating them into BaseOff/VarIndices. 297 gep_type_iterator GTI = gep_type_begin(GEPOp); 298 for (User::const_op_iterator I = GEPOp->op_begin()+1, 299 E = GEPOp->op_end(); I != E; ++I) { 300 Value *Index = *I; 301 // Compute the (potentially symbolic) offset in bytes for this index. 302 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 303 // For a struct, add the member offset. 304 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 305 if (FieldNo == 0) continue; 306 307 BaseOffs += TD->getStructLayout(STy)->getElementOffset(FieldNo); 308 continue; 309 } 310 311 // For an array/pointer, add the element offset, explicitly scaled. 312 if (ConstantInt *CIdx = dyn_cast<ConstantInt>(Index)) { 313 if (CIdx->isZero()) continue; 314 BaseOffs += TD->getTypeAllocSize(*GTI)*CIdx->getSExtValue(); 315 continue; 316 } 317 318 uint64_t Scale = TD->getTypeAllocSize(*GTI); 319 ExtensionKind Extension = EK_NotExtended; 320 321 // If the integer type is smaller than the pointer size, it is implicitly 322 // sign extended to pointer size. 323 unsigned Width = cast<IntegerType>(Index->getType())->getBitWidth(); 324 if (TD->getPointerSizeInBits() > Width) 325 Extension = EK_SignExt; 326 327 // Use GetLinearExpression to decompose the index into a C1*V+C2 form. 328 APInt IndexScale(Width, 0), IndexOffset(Width, 0); 329 Index = GetLinearExpression(Index, IndexScale, IndexOffset, Extension, 330 *TD, 0); 331 332 // The GEP index scale ("Scale") scales C1*V+C2, yielding (C1*V+C2)*Scale. 333 // This gives us an aggregate computation of (C1*Scale)*V + C2*Scale. 334 BaseOffs += IndexOffset.getSExtValue()*Scale; 335 Scale *= IndexScale.getSExtValue(); 336 337 338 // If we already had an occurrance of this index variable, merge this 339 // scale into it. For example, we want to handle: 340 // A[x][x] -> x*16 + x*4 -> x*20 341 // This also ensures that 'x' only appears in the index list once. 342 for (unsigned i = 0, e = VarIndices.size(); i != e; ++i) { 343 if (VarIndices[i].V == Index && 344 VarIndices[i].Extension == Extension) { 345 Scale += VarIndices[i].Scale; 346 VarIndices.erase(VarIndices.begin()+i); 347 break; 348 } 349 } 350 351 // Make sure that we have a scale that makes sense for this target's 352 // pointer size. 353 if (unsigned ShiftBits = 64-TD->getPointerSizeInBits()) { 354 Scale <<= ShiftBits; 355 Scale = (int64_t)Scale >> ShiftBits; 356 } 357 358 if (Scale) { 359 VariableGEPIndex Entry = {Index, Extension, Scale}; 360 VarIndices.push_back(Entry); 361 } 362 } 363 364 // Analyze the base pointer next. 365 V = GEPOp->getOperand(0); 366 } while (--MaxLookup); 367 368 // If the chain of expressions is too deep, just return early. 369 return V; 370} 371 372/// GetIndexDifference - Dest and Src are the variable indices from two 373/// decomposed GetElementPtr instructions GEP1 and GEP2 which have common base 374/// pointers. Subtract the GEP2 indices from GEP1 to find the symbolic 375/// difference between the two pointers. 376static void GetIndexDifference(SmallVectorImpl<VariableGEPIndex> &Dest, 377 const SmallVectorImpl<VariableGEPIndex> &Src) { 378 if (Src.empty()) return; 379 380 for (unsigned i = 0, e = Src.size(); i != e; ++i) { 381 const Value *V = Src[i].V; 382 ExtensionKind Extension = Src[i].Extension; 383 int64_t Scale = Src[i].Scale; 384 385 // Find V in Dest. This is N^2, but pointer indices almost never have more 386 // than a few variable indexes. 387 for (unsigned j = 0, e = Dest.size(); j != e; ++j) { 388 if (Dest[j].V != V || Dest[j].Extension != Extension) continue; 389 390 // If we found it, subtract off Scale V's from the entry in Dest. If it 391 // goes to zero, remove the entry. 392 if (Dest[j].Scale != Scale) 393 Dest[j].Scale -= Scale; 394 else 395 Dest.erase(Dest.begin()+j); 396 Scale = 0; 397 break; 398 } 399 400 // If we didn't consume this entry, add it to the end of the Dest list. 401 if (Scale) { 402 VariableGEPIndex Entry = { V, Extension, -Scale }; 403 Dest.push_back(Entry); 404 } 405 } 406} 407 408//===----------------------------------------------------------------------===// 409// BasicAliasAnalysis Pass 410//===----------------------------------------------------------------------===// 411 412#ifndef NDEBUG 413static const Function *getParent(const Value *V) { 414 if (const Instruction *inst = dyn_cast<Instruction>(V)) 415 return inst->getParent()->getParent(); 416 417 if (const Argument *arg = dyn_cast<Argument>(V)) 418 return arg->getParent(); 419 420 return NULL; 421} 422 423static bool notDifferentParent(const Value *O1, const Value *O2) { 424 425 const Function *F1 = getParent(O1); 426 const Function *F2 = getParent(O2); 427 428 return !F1 || !F2 || F1 == F2; 429} 430#endif 431 432namespace { 433 /// BasicAliasAnalysis - This is the primary alias analysis implementation. 434 struct BasicAliasAnalysis : public ImmutablePass, public AliasAnalysis { 435 static char ID; // Class identification, replacement for typeinfo 436 BasicAliasAnalysis() : ImmutablePass(ID) { 437 initializeBasicAliasAnalysisPass(*PassRegistry::getPassRegistry()); 438 } 439 440 virtual void initializePass() { 441 InitializeAliasAnalysis(this); 442 } 443 444 virtual void getAnalysisUsage(AnalysisUsage &AU) const { 445 AU.addRequired<AliasAnalysis>(); 446 } 447 448 virtual AliasResult alias(const Location &LocA, 449 const Location &LocB) { 450 assert(Visited.empty() && "Visited must be cleared after use!"); 451 assert(notDifferentParent(LocA.Ptr, LocB.Ptr) && 452 "BasicAliasAnalysis doesn't support interprocedural queries."); 453 AliasResult Alias = aliasCheck(LocA.Ptr, LocA.Size, LocA.TBAATag, 454 LocB.Ptr, LocB.Size, LocB.TBAATag); 455 Visited.clear(); 456 return Alias; 457 } 458 459 virtual ModRefResult getModRefInfo(ImmutableCallSite CS, 460 const Location &Loc); 461 462 virtual ModRefResult getModRefInfo(ImmutableCallSite CS1, 463 ImmutableCallSite CS2) { 464 // The AliasAnalysis base class has some smarts, lets use them. 465 return AliasAnalysis::getModRefInfo(CS1, CS2); 466 } 467 468 /// pointsToConstantMemory - Chase pointers until we find a (constant 469 /// global) or not. 470 virtual bool pointsToConstantMemory(const Location &Loc, bool OrLocal); 471 472 /// getModRefBehavior - Return the behavior when calling the given 473 /// call site. 474 virtual ModRefBehavior getModRefBehavior(ImmutableCallSite CS); 475 476 /// getModRefBehavior - Return the behavior when calling the given function. 477 /// For use when the call site is not known. 478 virtual ModRefBehavior getModRefBehavior(const Function *F); 479 480 /// getAdjustedAnalysisPointer - This method is used when a pass implements 481 /// an analysis interface through multiple inheritance. If needed, it 482 /// should override this to adjust the this pointer as needed for the 483 /// specified pass info. 484 virtual void *getAdjustedAnalysisPointer(const void *ID) { 485 if (ID == &AliasAnalysis::ID) 486 return (AliasAnalysis*)this; 487 return this; 488 } 489 490 private: 491 // Visited - Track instructions visited by a aliasPHI, aliasSelect(), and aliasGEP(). 492 SmallPtrSet<const Value*, 16> Visited; 493 494 // aliasGEP - Provide a bunch of ad-hoc rules to disambiguate a GEP 495 // instruction against another. 496 AliasResult aliasGEP(const GEPOperator *V1, uint64_t V1Size, 497 const Value *V2, uint64_t V2Size, 498 const MDNode *V2TBAAInfo, 499 const Value *UnderlyingV1, const Value *UnderlyingV2); 500 501 // aliasPHI - Provide a bunch of ad-hoc rules to disambiguate a PHI 502 // instruction against another. 503 AliasResult aliasPHI(const PHINode *PN, uint64_t PNSize, 504 const MDNode *PNTBAAInfo, 505 const Value *V2, uint64_t V2Size, 506 const MDNode *V2TBAAInfo); 507 508 /// aliasSelect - Disambiguate a Select instruction against another value. 509 AliasResult aliasSelect(const SelectInst *SI, uint64_t SISize, 510 const MDNode *SITBAAInfo, 511 const Value *V2, uint64_t V2Size, 512 const MDNode *V2TBAAInfo); 513 514 AliasResult aliasCheck(const Value *V1, uint64_t V1Size, 515 const MDNode *V1TBAATag, 516 const Value *V2, uint64_t V2Size, 517 const MDNode *V2TBAATag); 518 }; 519} // End of anonymous namespace 520 521// Register this pass... 522char BasicAliasAnalysis::ID = 0; 523INITIALIZE_AG_PASS(BasicAliasAnalysis, AliasAnalysis, "basicaa", 524 "Basic Alias Analysis (stateless AA impl)", 525 false, true, false) 526 527ImmutablePass *llvm::createBasicAliasAnalysisPass() { 528 return new BasicAliasAnalysis(); 529} 530 531/// pointsToConstantMemory - Returns whether the given pointer value 532/// points to memory that is local to the function, with global constants being 533/// considered local to all functions. 534bool 535BasicAliasAnalysis::pointsToConstantMemory(const Location &Loc, bool OrLocal) { 536 assert(Visited.empty() && "Visited must be cleared after use!"); 537 538 unsigned MaxLookup = 8; 539 SmallVector<const Value *, 16> Worklist; 540 Worklist.push_back(Loc.Ptr); 541 do { 542 const Value *V = GetUnderlyingObject(Worklist.pop_back_val()); 543 if (!Visited.insert(V)) { 544 Visited.clear(); 545 return AliasAnalysis::pointsToConstantMemory(Loc, OrLocal); 546 } 547 548 // An alloca instruction defines local memory. 549 if (OrLocal && isa<AllocaInst>(V)) 550 continue; 551 552 // A global constant counts as local memory for our purposes. 553 if (const GlobalVariable *GV = dyn_cast<GlobalVariable>(V)) { 554 // Note: this doesn't require GV to be "ODR" because it isn't legal for a 555 // global to be marked constant in some modules and non-constant in 556 // others. GV may even be a declaration, not a definition. 557 if (!GV->isConstant()) { 558 Visited.clear(); 559 return AliasAnalysis::pointsToConstantMemory(Loc, OrLocal); 560 } 561 continue; 562 } 563 564 // If both select values point to local memory, then so does the select. 565 if (const SelectInst *SI = dyn_cast<SelectInst>(V)) { 566 Worklist.push_back(SI->getTrueValue()); 567 Worklist.push_back(SI->getFalseValue()); 568 continue; 569 } 570 571 // If all values incoming to a phi node point to local memory, then so does 572 // the phi. 573 if (const PHINode *PN = dyn_cast<PHINode>(V)) { 574 // Don't bother inspecting phi nodes with many operands. 575 if (PN->getNumIncomingValues() > MaxLookup) { 576 Visited.clear(); 577 return AliasAnalysis::pointsToConstantMemory(Loc, OrLocal); 578 } 579 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) 580 Worklist.push_back(PN->getIncomingValue(i)); 581 continue; 582 } 583 584 // Otherwise be conservative. 585 Visited.clear(); 586 return AliasAnalysis::pointsToConstantMemory(Loc, OrLocal); 587 588 } while (!Worklist.empty() && --MaxLookup); 589 590 Visited.clear(); 591 return Worklist.empty(); 592} 593 594/// getModRefBehavior - Return the behavior when calling the given call site. 595AliasAnalysis::ModRefBehavior 596BasicAliasAnalysis::getModRefBehavior(ImmutableCallSite CS) { 597 if (CS.doesNotAccessMemory()) 598 // Can't do better than this. 599 return DoesNotAccessMemory; 600 601 ModRefBehavior Min = UnknownModRefBehavior; 602 603 // If the callsite knows it only reads memory, don't return worse 604 // than that. 605 if (CS.onlyReadsMemory()) 606 Min = OnlyReadsMemory; 607 608 // The AliasAnalysis base class has some smarts, lets use them. 609 return ModRefBehavior(AliasAnalysis::getModRefBehavior(CS) & Min); 610} 611 612/// getModRefBehavior - Return the behavior when calling the given function. 613/// For use when the call site is not known. 614AliasAnalysis::ModRefBehavior 615BasicAliasAnalysis::getModRefBehavior(const Function *F) { 616 // If the function declares it doesn't access memory, we can't do better. 617 if (F->doesNotAccessMemory()) 618 return DoesNotAccessMemory; 619 620 // For intrinsics, we can check the table. 621 if (unsigned iid = F->getIntrinsicID()) { 622#define GET_INTRINSIC_MODREF_BEHAVIOR 623#include "llvm/Intrinsics.gen" 624#undef GET_INTRINSIC_MODREF_BEHAVIOR 625 } 626 627 ModRefBehavior Min = UnknownModRefBehavior; 628 629 // If the function declares it only reads memory, go with that. 630 if (F->onlyReadsMemory()) 631 Min = OnlyReadsMemory; 632 633 // Otherwise be conservative. 634 return ModRefBehavior(AliasAnalysis::getModRefBehavior(F) & Min); 635} 636 637/// getModRefInfo - Check to see if the specified callsite can clobber the 638/// specified memory object. Since we only look at local properties of this 639/// function, we really can't say much about this query. We do, however, use 640/// simple "address taken" analysis on local objects. 641AliasAnalysis::ModRefResult 642BasicAliasAnalysis::getModRefInfo(ImmutableCallSite CS, 643 const Location &Loc) { 644 assert(notDifferentParent(CS.getInstruction(), Loc.Ptr) && 645 "AliasAnalysis query involving multiple functions!"); 646 647 const Value *Object = GetUnderlyingObject(Loc.Ptr); 648 649 // If this is a tail call and Loc.Ptr points to a stack location, we know that 650 // the tail call cannot access or modify the local stack. 651 // We cannot exclude byval arguments here; these belong to the caller of 652 // the current function not to the current function, and a tail callee 653 // may reference them. 654 if (isa<AllocaInst>(Object)) 655 if (const CallInst *CI = dyn_cast<CallInst>(CS.getInstruction())) 656 if (CI->isTailCall()) 657 return NoModRef; 658 659 // If the pointer is to a locally allocated object that does not escape, 660 // then the call can not mod/ref the pointer unless the call takes the pointer 661 // as an argument, and itself doesn't capture it. 662 if (!isa<Constant>(Object) && CS.getInstruction() != Object && 663 isNonEscapingLocalObject(Object)) { 664 bool PassedAsArg = false; 665 unsigned ArgNo = 0; 666 for (ImmutableCallSite::arg_iterator CI = CS.arg_begin(), CE = CS.arg_end(); 667 CI != CE; ++CI, ++ArgNo) { 668 // Only look at the no-capture pointer arguments. 669 if (!(*CI)->getType()->isPointerTy() || 670 !CS.paramHasAttr(ArgNo+1, Attribute::NoCapture)) 671 continue; 672 673 // If this is a no-capture pointer argument, see if we can tell that it 674 // is impossible to alias the pointer we're checking. If not, we have to 675 // assume that the call could touch the pointer, even though it doesn't 676 // escape. 677 if (!isNoAlias(Location(cast<Value>(CI)), Loc)) { 678 PassedAsArg = true; 679 break; 680 } 681 } 682 683 if (!PassedAsArg) 684 return NoModRef; 685 } 686 687 ModRefResult Min = ModRef; 688 689 // Finally, handle specific knowledge of intrinsics. 690 const IntrinsicInst *II = dyn_cast<IntrinsicInst>(CS.getInstruction()); 691 if (II != 0) 692 switch (II->getIntrinsicID()) { 693 default: break; 694 case Intrinsic::memcpy: 695 case Intrinsic::memmove: { 696 uint64_t Len = UnknownSize; 697 if (ConstantInt *LenCI = dyn_cast<ConstantInt>(II->getArgOperand(2))) 698 Len = LenCI->getZExtValue(); 699 Value *Dest = II->getArgOperand(0); 700 Value *Src = II->getArgOperand(1); 701 // If it can't overlap the source dest, then it doesn't modref the loc. 702 if (isNoAlias(Location(Dest, Len), Loc)) { 703 if (isNoAlias(Location(Src, Len), Loc)) 704 return NoModRef; 705 // If it can't overlap the dest, then worst case it reads the loc. 706 Min = Ref; 707 } else if (isNoAlias(Location(Src, Len), Loc)) { 708 // If it can't overlap the source, then worst case it mutates the loc. 709 Min = Mod; 710 } 711 break; 712 } 713 case Intrinsic::memset: 714 // Since memset is 'accesses arguments' only, the AliasAnalysis base class 715 // will handle it for the variable length case. 716 if (ConstantInt *LenCI = dyn_cast<ConstantInt>(II->getArgOperand(2))) { 717 uint64_t Len = LenCI->getZExtValue(); 718 Value *Dest = II->getArgOperand(0); 719 if (isNoAlias(Location(Dest, Len), Loc)) 720 return NoModRef; 721 } 722 // We know that memset doesn't load anything. 723 Min = Mod; 724 break; 725 case Intrinsic::atomic_cmp_swap: 726 case Intrinsic::atomic_swap: 727 case Intrinsic::atomic_load_add: 728 case Intrinsic::atomic_load_sub: 729 case Intrinsic::atomic_load_and: 730 case Intrinsic::atomic_load_nand: 731 case Intrinsic::atomic_load_or: 732 case Intrinsic::atomic_load_xor: 733 case Intrinsic::atomic_load_max: 734 case Intrinsic::atomic_load_min: 735 case Intrinsic::atomic_load_umax: 736 case Intrinsic::atomic_load_umin: 737 if (TD) { 738 Value *Op1 = II->getArgOperand(0); 739 uint64_t Op1Size = TD->getTypeStoreSize(Op1->getType()); 740 MDNode *Tag = II->getMetadata(LLVMContext::MD_tbaa); 741 if (isNoAlias(Location(Op1, Op1Size, Tag), Loc)) 742 return NoModRef; 743 } 744 break; 745 case Intrinsic::lifetime_start: 746 case Intrinsic::lifetime_end: 747 case Intrinsic::invariant_start: { 748 uint64_t PtrSize = 749 cast<ConstantInt>(II->getArgOperand(0))->getZExtValue(); 750 if (isNoAlias(Location(II->getArgOperand(1), 751 PtrSize, 752 II->getMetadata(LLVMContext::MD_tbaa)), 753 Loc)) 754 return NoModRef; 755 break; 756 } 757 case Intrinsic::invariant_end: { 758 uint64_t PtrSize = 759 cast<ConstantInt>(II->getArgOperand(1))->getZExtValue(); 760 if (isNoAlias(Location(II->getArgOperand(2), 761 PtrSize, 762 II->getMetadata(LLVMContext::MD_tbaa)), 763 Loc)) 764 return NoModRef; 765 break; 766 } 767 } 768 769 // The AliasAnalysis base class has some smarts, lets use them. 770 return ModRefResult(AliasAnalysis::getModRefInfo(CS, Loc) & Min); 771} 772 773/// aliasGEP - Provide a bunch of ad-hoc rules to disambiguate a GEP instruction 774/// against another pointer. We know that V1 is a GEP, but we don't know 775/// anything about V2. UnderlyingV1 is GetUnderlyingObject(GEP1), 776/// UnderlyingV2 is the same for V2. 777/// 778AliasAnalysis::AliasResult 779BasicAliasAnalysis::aliasGEP(const GEPOperator *GEP1, uint64_t V1Size, 780 const Value *V2, uint64_t V2Size, 781 const MDNode *V2TBAAInfo, 782 const Value *UnderlyingV1, 783 const Value *UnderlyingV2) { 784 // If this GEP has been visited before, we're on a use-def cycle. 785 // Such cycles are only valid when PHI nodes are involved or in unreachable 786 // code. The visitPHI function catches cycles containing PHIs, but there 787 // could still be a cycle without PHIs in unreachable code. 788 if (!Visited.insert(GEP1)) 789 return MayAlias; 790 791 int64_t GEP1BaseOffset; 792 SmallVector<VariableGEPIndex, 4> GEP1VariableIndices; 793 794 // If we have two gep instructions with must-alias'ing base pointers, figure 795 // out if the indexes to the GEP tell us anything about the derived pointer. 796 if (const GEPOperator *GEP2 = dyn_cast<GEPOperator>(V2)) { 797 // Do the base pointers alias? 798 AliasResult BaseAlias = aliasCheck(UnderlyingV1, UnknownSize, 0, 799 UnderlyingV2, UnknownSize, 0); 800 801 // If we get a No or May, then return it immediately, no amount of analysis 802 // will improve this situation. 803 if (BaseAlias != MustAlias) return BaseAlias; 804 805 // Otherwise, we have a MustAlias. Since the base pointers alias each other 806 // exactly, see if the computed offset from the common pointer tells us 807 // about the relation of the resulting pointer. 808 const Value *GEP1BasePtr = 809 DecomposeGEPExpression(GEP1, GEP1BaseOffset, GEP1VariableIndices, TD); 810 811 int64_t GEP2BaseOffset; 812 SmallVector<VariableGEPIndex, 4> GEP2VariableIndices; 813 const Value *GEP2BasePtr = 814 DecomposeGEPExpression(GEP2, GEP2BaseOffset, GEP2VariableIndices, TD); 815 816 // If DecomposeGEPExpression isn't able to look all the way through the 817 // addressing operation, we must not have TD and this is too complex for us 818 // to handle without it. 819 if (GEP1BasePtr != UnderlyingV1 || GEP2BasePtr != UnderlyingV2) { 820 assert(TD == 0 && 821 "DecomposeGEPExpression and GetUnderlyingObject disagree!"); 822 return MayAlias; 823 } 824 825 // Subtract the GEP2 pointer from the GEP1 pointer to find out their 826 // symbolic difference. 827 GEP1BaseOffset -= GEP2BaseOffset; 828 GetIndexDifference(GEP1VariableIndices, GEP2VariableIndices); 829 830 } else { 831 // Check to see if these two pointers are related by the getelementptr 832 // instruction. If one pointer is a GEP with a non-zero index of the other 833 // pointer, we know they cannot alias. 834 835 // If both accesses are unknown size, we can't do anything useful here. 836 if (V1Size == UnknownSize && V2Size == UnknownSize) 837 return MayAlias; 838 839 AliasResult R = aliasCheck(UnderlyingV1, UnknownSize, 0, 840 V2, V2Size, V2TBAAInfo); 841 if (R != MustAlias) 842 // If V2 may alias GEP base pointer, conservatively returns MayAlias. 843 // If V2 is known not to alias GEP base pointer, then the two values 844 // cannot alias per GEP semantics: "A pointer value formed from a 845 // getelementptr instruction is associated with the addresses associated 846 // with the first operand of the getelementptr". 847 return R; 848 849 const Value *GEP1BasePtr = 850 DecomposeGEPExpression(GEP1, GEP1BaseOffset, GEP1VariableIndices, TD); 851 852 // If DecomposeGEPExpression isn't able to look all the way through the 853 // addressing operation, we must not have TD and this is too complex for us 854 // to handle without it. 855 if (GEP1BasePtr != UnderlyingV1) { 856 assert(TD == 0 && 857 "DecomposeGEPExpression and GetUnderlyingObject disagree!"); 858 return MayAlias; 859 } 860 } 861 862 // In the two GEP Case, if there is no difference in the offsets of the 863 // computed pointers, the resultant pointers are a must alias. This 864 // hapens when we have two lexically identical GEP's (for example). 865 // 866 // In the other case, if we have getelementptr <ptr>, 0, 0, 0, 0, ... and V2 867 // must aliases the GEP, the end result is a must alias also. 868 if (GEP1BaseOffset == 0 && GEP1VariableIndices.empty()) 869 return MustAlias; 870 871 // If there is a difference betwen the pointers, but the difference is 872 // less than the size of the associated memory object, then we know 873 // that the objects are partially overlapping. 874 if (GEP1BaseOffset != 0 && GEP1VariableIndices.empty()) { 875 if (GEP1BaseOffset >= 0 ? 876 (V2Size != UnknownSize && (uint64_t)GEP1BaseOffset < V2Size) : 877 (V1Size != UnknownSize && -(uint64_t)GEP1BaseOffset < V1Size && 878 GEP1BaseOffset != INT64_MIN)) 879 return PartialAlias; 880 } 881 882 // If we have a known constant offset, see if this offset is larger than the 883 // access size being queried. If so, and if no variable indices can remove 884 // pieces of this constant, then we know we have a no-alias. For example, 885 // &A[100] != &A. 886 887 // In order to handle cases like &A[100][i] where i is an out of range 888 // subscript, we have to ignore all constant offset pieces that are a multiple 889 // of a scaled index. Do this by removing constant offsets that are a 890 // multiple of any of our variable indices. This allows us to transform 891 // things like &A[i][1] because i has a stride of (e.g.) 8 bytes but the 1 892 // provides an offset of 4 bytes (assuming a <= 4 byte access). 893 for (unsigned i = 0, e = GEP1VariableIndices.size(); 894 i != e && GEP1BaseOffset;++i) 895 if (int64_t RemovedOffset = GEP1BaseOffset/GEP1VariableIndices[i].Scale) 896 GEP1BaseOffset -= RemovedOffset*GEP1VariableIndices[i].Scale; 897 898 // If our known offset is bigger than the access size, we know we don't have 899 // an alias. 900 if (GEP1BaseOffset) { 901 if (GEP1BaseOffset >= 0 ? 902 (V2Size != UnknownSize && (uint64_t)GEP1BaseOffset >= V2Size) : 903 (V1Size != UnknownSize && -(uint64_t)GEP1BaseOffset >= V1Size && 904 GEP1BaseOffset != INT64_MIN)) 905 return NoAlias; 906 } 907 908 return MayAlias; 909} 910 911/// aliasSelect - Provide a bunch of ad-hoc rules to disambiguate a Select 912/// instruction against another. 913AliasAnalysis::AliasResult 914BasicAliasAnalysis::aliasSelect(const SelectInst *SI, uint64_t SISize, 915 const MDNode *SITBAAInfo, 916 const Value *V2, uint64_t V2Size, 917 const MDNode *V2TBAAInfo) { 918 // If this select has been visited before, we're on a use-def cycle. 919 // Such cycles are only valid when PHI nodes are involved or in unreachable 920 // code. The visitPHI function catches cycles containing PHIs, but there 921 // could still be a cycle without PHIs in unreachable code. 922 if (!Visited.insert(SI)) 923 return MayAlias; 924 925 // If the values are Selects with the same condition, we can do a more precise 926 // check: just check for aliases between the values on corresponding arms. 927 if (const SelectInst *SI2 = dyn_cast<SelectInst>(V2)) 928 if (SI->getCondition() == SI2->getCondition()) { 929 AliasResult Alias = 930 aliasCheck(SI->getTrueValue(), SISize, SITBAAInfo, 931 SI2->getTrueValue(), V2Size, V2TBAAInfo); 932 if (Alias == MayAlias) 933 return MayAlias; 934 AliasResult ThisAlias = 935 aliasCheck(SI->getFalseValue(), SISize, SITBAAInfo, 936 SI2->getFalseValue(), V2Size, V2TBAAInfo); 937 if (ThisAlias != Alias) 938 return MayAlias; 939 return Alias; 940 } 941 942 // If both arms of the Select node NoAlias or MustAlias V2, then returns 943 // NoAlias / MustAlias. Otherwise, returns MayAlias. 944 AliasResult Alias = 945 aliasCheck(V2, V2Size, V2TBAAInfo, SI->getTrueValue(), SISize, SITBAAInfo); 946 if (Alias == MayAlias) 947 return MayAlias; 948 949 // If V2 is visited, the recursive case will have been caught in the 950 // above aliasCheck call, so these subsequent calls to aliasCheck 951 // don't need to assume that V2 is being visited recursively. 952 Visited.erase(V2); 953 954 AliasResult ThisAlias = 955 aliasCheck(V2, V2Size, V2TBAAInfo, SI->getFalseValue(), SISize, SITBAAInfo); 956 if (ThisAlias != Alias) 957 return MayAlias; 958 return Alias; 959} 960 961// aliasPHI - Provide a bunch of ad-hoc rules to disambiguate a PHI instruction 962// against another. 963AliasAnalysis::AliasResult 964BasicAliasAnalysis::aliasPHI(const PHINode *PN, uint64_t PNSize, 965 const MDNode *PNTBAAInfo, 966 const Value *V2, uint64_t V2Size, 967 const MDNode *V2TBAAInfo) { 968 // The PHI node has already been visited, avoid recursion any further. 969 if (!Visited.insert(PN)) 970 return MayAlias; 971 972 // If the values are PHIs in the same block, we can do a more precise 973 // as well as efficient check: just check for aliases between the values 974 // on corresponding edges. 975 if (const PHINode *PN2 = dyn_cast<PHINode>(V2)) 976 if (PN2->getParent() == PN->getParent()) { 977 AliasResult Alias = 978 aliasCheck(PN->getIncomingValue(0), PNSize, PNTBAAInfo, 979 PN2->getIncomingValueForBlock(PN->getIncomingBlock(0)), 980 V2Size, V2TBAAInfo); 981 if (Alias == MayAlias) 982 return MayAlias; 983 for (unsigned i = 1, e = PN->getNumIncomingValues(); i != e; ++i) { 984 AliasResult ThisAlias = 985 aliasCheck(PN->getIncomingValue(i), PNSize, PNTBAAInfo, 986 PN2->getIncomingValueForBlock(PN->getIncomingBlock(i)), 987 V2Size, V2TBAAInfo); 988 if (ThisAlias != Alias) 989 return MayAlias; 990 } 991 return Alias; 992 } 993 994 SmallPtrSet<Value*, 4> UniqueSrc; 995 SmallVector<Value*, 4> V1Srcs; 996 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 997 Value *PV1 = PN->getIncomingValue(i); 998 if (isa<PHINode>(PV1)) 999 // If any of the source itself is a PHI, return MayAlias conservatively 1000 // to avoid compile time explosion. The worst possible case is if both 1001 // sides are PHI nodes. In which case, this is O(m x n) time where 'm' 1002 // and 'n' are the number of PHI sources. 1003 return MayAlias; 1004 if (UniqueSrc.insert(PV1)) 1005 V1Srcs.push_back(PV1); 1006 } 1007 1008 AliasResult Alias = aliasCheck(V2, V2Size, V2TBAAInfo, 1009 V1Srcs[0], PNSize, PNTBAAInfo); 1010 // Early exit if the check of the first PHI source against V2 is MayAlias. 1011 // Other results are not possible. 1012 if (Alias == MayAlias) 1013 return MayAlias; 1014 1015 // If all sources of the PHI node NoAlias or MustAlias V2, then returns 1016 // NoAlias / MustAlias. Otherwise, returns MayAlias. 1017 for (unsigned i = 1, e = V1Srcs.size(); i != e; ++i) { 1018 Value *V = V1Srcs[i]; 1019 1020 // If V2 is visited, the recursive case will have been caught in the 1021 // above aliasCheck call, so these subsequent calls to aliasCheck 1022 // don't need to assume that V2 is being visited recursively. 1023 Visited.erase(V2); 1024 1025 AliasResult ThisAlias = aliasCheck(V2, V2Size, V2TBAAInfo, 1026 V, PNSize, PNTBAAInfo); 1027 if (ThisAlias != Alias || ThisAlias == MayAlias) 1028 return MayAlias; 1029 } 1030 1031 return Alias; 1032} 1033 1034// aliasCheck - Provide a bunch of ad-hoc rules to disambiguate in common cases, 1035// such as array references. 1036// 1037AliasAnalysis::AliasResult 1038BasicAliasAnalysis::aliasCheck(const Value *V1, uint64_t V1Size, 1039 const MDNode *V1TBAAInfo, 1040 const Value *V2, uint64_t V2Size, 1041 const MDNode *V2TBAAInfo) { 1042 // If either of the memory references is empty, it doesn't matter what the 1043 // pointer values are. 1044 if (V1Size == 0 || V2Size == 0) 1045 return NoAlias; 1046 1047 // Strip off any casts if they exist. 1048 V1 = V1->stripPointerCasts(); 1049 V2 = V2->stripPointerCasts(); 1050 1051 // Are we checking for alias of the same value? 1052 if (V1 == V2) return MustAlias; 1053 1054 if (!V1->getType()->isPointerTy() || !V2->getType()->isPointerTy()) 1055 return NoAlias; // Scalars cannot alias each other 1056 1057 // Figure out what objects these things are pointing to if we can. 1058 const Value *O1 = GetUnderlyingObject(V1); 1059 const Value *O2 = GetUnderlyingObject(V2); 1060 1061 // Null values in the default address space don't point to any object, so they 1062 // don't alias any other pointer. 1063 if (const ConstantPointerNull *CPN = dyn_cast<ConstantPointerNull>(O1)) 1064 if (CPN->getType()->getAddressSpace() == 0) 1065 return NoAlias; 1066 if (const ConstantPointerNull *CPN = dyn_cast<ConstantPointerNull>(O2)) 1067 if (CPN->getType()->getAddressSpace() == 0) 1068 return NoAlias; 1069 1070 if (O1 != O2) { 1071 // If V1/V2 point to two different objects we know that we have no alias. 1072 if (isIdentifiedObject(O1) && isIdentifiedObject(O2)) 1073 return NoAlias; 1074 1075 // Constant pointers can't alias with non-const isIdentifiedObject objects. 1076 if ((isa<Constant>(O1) && isIdentifiedObject(O2) && !isa<Constant>(O2)) || 1077 (isa<Constant>(O2) && isIdentifiedObject(O1) && !isa<Constant>(O1))) 1078 return NoAlias; 1079 1080 // Arguments can't alias with local allocations or noalias calls 1081 // in the same function. 1082 if (((isa<Argument>(O1) && (isa<AllocaInst>(O2) || isNoAliasCall(O2))) || 1083 (isa<Argument>(O2) && (isa<AllocaInst>(O1) || isNoAliasCall(O1))))) 1084 return NoAlias; 1085 1086 // Most objects can't alias null. 1087 if ((isa<ConstantPointerNull>(O2) && isKnownNonNull(O1)) || 1088 (isa<ConstantPointerNull>(O1) && isKnownNonNull(O2))) 1089 return NoAlias; 1090 1091 // If one pointer is the result of a call/invoke or load and the other is a 1092 // non-escaping local object within the same function, then we know the 1093 // object couldn't escape to a point where the call could return it. 1094 // 1095 // Note that if the pointers are in different functions, there are a 1096 // variety of complications. A call with a nocapture argument may still 1097 // temporary store the nocapture argument's value in a temporary memory 1098 // location if that memory location doesn't escape. Or it may pass a 1099 // nocapture value to other functions as long as they don't capture it. 1100 if (isEscapeSource(O1) && isNonEscapingLocalObject(O2)) 1101 return NoAlias; 1102 if (isEscapeSource(O2) && isNonEscapingLocalObject(O1)) 1103 return NoAlias; 1104 } 1105 1106 // If the size of one access is larger than the entire object on the other 1107 // side, then we know such behavior is undefined and can assume no alias. 1108 if (TD) 1109 if ((V1Size != UnknownSize && isObjectSmallerThan(O2, V1Size, *TD)) || 1110 (V2Size != UnknownSize && isObjectSmallerThan(O1, V2Size, *TD))) 1111 return NoAlias; 1112 1113 // FIXME: This isn't aggressively handling alias(GEP, PHI) for example: if the 1114 // GEP can't simplify, we don't even look at the PHI cases. 1115 if (!isa<GEPOperator>(V1) && isa<GEPOperator>(V2)) { 1116 std::swap(V1, V2); 1117 std::swap(V1Size, V2Size); 1118 std::swap(O1, O2); 1119 } 1120 if (const GEPOperator *GV1 = dyn_cast<GEPOperator>(V1)) { 1121 AliasResult Result = aliasGEP(GV1, V1Size, V2, V2Size, V2TBAAInfo, O1, O2); 1122 if (Result != MayAlias) return Result; 1123 } 1124 1125 if (isa<PHINode>(V2) && !isa<PHINode>(V1)) { 1126 std::swap(V1, V2); 1127 std::swap(V1Size, V2Size); 1128 } 1129 if (const PHINode *PN = dyn_cast<PHINode>(V1)) { 1130 AliasResult Result = aliasPHI(PN, V1Size, V1TBAAInfo, 1131 V2, V2Size, V2TBAAInfo); 1132 if (Result != MayAlias) return Result; 1133 } 1134 1135 if (isa<SelectInst>(V2) && !isa<SelectInst>(V1)) { 1136 std::swap(V1, V2); 1137 std::swap(V1Size, V2Size); 1138 } 1139 if (const SelectInst *S1 = dyn_cast<SelectInst>(V1)) { 1140 AliasResult Result = aliasSelect(S1, V1Size, V1TBAAInfo, 1141 V2, V2Size, V2TBAAInfo); 1142 if (Result != MayAlias) return Result; 1143 } 1144 1145 return AliasAnalysis::alias(Location(V1, V1Size, V1TBAAInfo), 1146 Location(V2, V2Size, V2TBAAInfo)); 1147} 1148