1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===// 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 contains the implementation of the scalar evolution analysis 11 // engine, which is used primarily to analyze expressions involving induction 12 // variables in loops. 13 // 14 // There are several aspects to this library. First is the representation of 15 // scalar expressions, which are represented as subclasses of the SCEV class. 16 // These classes are used to represent certain types of subexpressions that we 17 // can handle. We only create one SCEV of a particular shape, so 18 // pointer-comparisons for equality are legal. 19 // 20 // One important aspect of the SCEV objects is that they are never cyclic, even 21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If 22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial 23 // recurrence) then we represent it directly as a recurrence node, otherwise we 24 // represent it as a SCEVUnknown node. 25 // 26 // In addition to being able to represent expressions of various types, we also 27 // have folders that are used to build the *canonical* representation for a 28 // particular expression. These folders are capable of using a variety of 29 // rewrite rules to simplify the expressions. 30 // 31 // Once the folders are defined, we can implement the more interesting 32 // higher-level code, such as the code that recognizes PHI nodes of various 33 // types, computes the execution count of a loop, etc. 34 // 35 // TODO: We should use these routines and value representations to implement 36 // dependence analysis! 37 // 38 //===----------------------------------------------------------------------===// 39 // 40 // There are several good references for the techniques used in this analysis. 41 // 42 // Chains of recurrences -- a method to expedite the evaluation 43 // of closed-form functions 44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima 45 // 46 // On computational properties of chains of recurrences 47 // Eugene V. Zima 48 // 49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization 50 // Robert A. van Engelen 51 // 52 // Efficient Symbolic Analysis for Optimizing Compilers 53 // Robert A. van Engelen 54 // 55 // Using the chains of recurrences algebra for data dependence testing and 56 // induction variable substitution 57 // MS Thesis, Johnie Birch 58 // 59 //===----------------------------------------------------------------------===// 60 61 #include "llvm/Analysis/ScalarEvolution.h" 62 #include "llvm/ADT/APInt.h" 63 #include "llvm/ADT/ArrayRef.h" 64 #include "llvm/ADT/DenseMap.h" 65 #include "llvm/ADT/DepthFirstIterator.h" 66 #include "llvm/ADT/EquivalenceClasses.h" 67 #include "llvm/ADT/FoldingSet.h" 68 #include "llvm/ADT/None.h" 69 #include "llvm/ADT/Optional.h" 70 #include "llvm/ADT/STLExtras.h" 71 #include "llvm/ADT/ScopeExit.h" 72 #include "llvm/ADT/Sequence.h" 73 #include "llvm/ADT/SetVector.h" 74 #include "llvm/ADT/SmallPtrSet.h" 75 #include "llvm/ADT/SmallSet.h" 76 #include "llvm/ADT/SmallVector.h" 77 #include "llvm/ADT/Statistic.h" 78 #include "llvm/ADT/StringRef.h" 79 #include "llvm/Analysis/AssumptionCache.h" 80 #include "llvm/Analysis/ConstantFolding.h" 81 #include "llvm/Analysis/InstructionSimplify.h" 82 #include "llvm/Analysis/LoopInfo.h" 83 #include "llvm/Analysis/ScalarEvolutionExpressions.h" 84 #include "llvm/Analysis/TargetLibraryInfo.h" 85 #include "llvm/Analysis/ValueTracking.h" 86 #include "llvm/IR/Argument.h" 87 #include "llvm/IR/BasicBlock.h" 88 #include "llvm/IR/CFG.h" 89 #include "llvm/IR/CallSite.h" 90 #include "llvm/IR/Constant.h" 91 #include "llvm/IR/ConstantRange.h" 92 #include "llvm/IR/Constants.h" 93 #include "llvm/IR/DataLayout.h" 94 #include "llvm/IR/DerivedTypes.h" 95 #include "llvm/IR/Dominators.h" 96 #include "llvm/IR/Function.h" 97 #include "llvm/IR/GlobalAlias.h" 98 #include "llvm/IR/GlobalValue.h" 99 #include "llvm/IR/GlobalVariable.h" 100 #include "llvm/IR/InstIterator.h" 101 #include "llvm/IR/InstrTypes.h" 102 #include "llvm/IR/Instruction.h" 103 #include "llvm/IR/Instructions.h" 104 #include "llvm/IR/IntrinsicInst.h" 105 #include "llvm/IR/Intrinsics.h" 106 #include "llvm/IR/LLVMContext.h" 107 #include "llvm/IR/Metadata.h" 108 #include "llvm/IR/Operator.h" 109 #include "llvm/IR/PatternMatch.h" 110 #include "llvm/IR/Type.h" 111 #include "llvm/IR/Use.h" 112 #include "llvm/IR/User.h" 113 #include "llvm/IR/Value.h" 114 #include "llvm/Pass.h" 115 #include "llvm/Support/Casting.h" 116 #include "llvm/Support/CommandLine.h" 117 #include "llvm/Support/Compiler.h" 118 #include "llvm/Support/Debug.h" 119 #include "llvm/Support/ErrorHandling.h" 120 #include "llvm/Support/KnownBits.h" 121 #include "llvm/Support/SaveAndRestore.h" 122 #include "llvm/Support/raw_ostream.h" 123 #include <algorithm> 124 #include <cassert> 125 #include <climits> 126 #include <cstddef> 127 #include <cstdint> 128 #include <cstdlib> 129 #include <map> 130 #include <memory> 131 #include <tuple> 132 #include <utility> 133 #include <vector> 134 135 using namespace llvm; 136 137 #define DEBUG_TYPE "scalar-evolution" 138 139 STATISTIC(NumArrayLenItCounts, 140 "Number of trip counts computed with array length"); 141 STATISTIC(NumTripCountsComputed, 142 "Number of loops with predictable loop counts"); 143 STATISTIC(NumTripCountsNotComputed, 144 "Number of loops without predictable loop counts"); 145 STATISTIC(NumBruteForceTripCountsComputed, 146 "Number of loops with trip counts computed by force"); 147 148 static cl::opt<unsigned> 149 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 150 cl::desc("Maximum number of iterations SCEV will " 151 "symbolically execute a constant " 152 "derived loop"), 153 cl::init(100)); 154 155 // FIXME: Enable this with EXPENSIVE_CHECKS when the test suite is clean. 156 static cl::opt<bool> VerifySCEV( 157 "verify-scev", cl::Hidden, 158 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)")); 159 static cl::opt<bool> 160 VerifySCEVMap("verify-scev-maps", cl::Hidden, 161 cl::desc("Verify no dangling value in ScalarEvolution's " 162 "ExprValueMap (slow)")); 163 164 static cl::opt<unsigned> MulOpsInlineThreshold( 165 "scev-mulops-inline-threshold", cl::Hidden, 166 cl::desc("Threshold for inlining multiplication operands into a SCEV"), 167 cl::init(32)); 168 169 static cl::opt<unsigned> AddOpsInlineThreshold( 170 "scev-addops-inline-threshold", cl::Hidden, 171 cl::desc("Threshold for inlining addition operands into a SCEV"), 172 cl::init(500)); 173 174 static cl::opt<unsigned> MaxSCEVCompareDepth( 175 "scalar-evolution-max-scev-compare-depth", cl::Hidden, 176 cl::desc("Maximum depth of recursive SCEV complexity comparisons"), 177 cl::init(32)); 178 179 static cl::opt<unsigned> MaxSCEVOperationsImplicationDepth( 180 "scalar-evolution-max-scev-operations-implication-depth", cl::Hidden, 181 cl::desc("Maximum depth of recursive SCEV operations implication analysis"), 182 cl::init(2)); 183 184 static cl::opt<unsigned> MaxValueCompareDepth( 185 "scalar-evolution-max-value-compare-depth", cl::Hidden, 186 cl::desc("Maximum depth of recursive value complexity comparisons"), 187 cl::init(2)); 188 189 static cl::opt<unsigned> 190 MaxArithDepth("scalar-evolution-max-arith-depth", cl::Hidden, 191 cl::desc("Maximum depth of recursive arithmetics"), 192 cl::init(32)); 193 194 static cl::opt<unsigned> MaxConstantEvolvingDepth( 195 "scalar-evolution-max-constant-evolving-depth", cl::Hidden, 196 cl::desc("Maximum depth of recursive constant evolving"), cl::init(32)); 197 198 static cl::opt<unsigned> 199 MaxExtDepth("scalar-evolution-max-ext-depth", cl::Hidden, 200 cl::desc("Maximum depth of recursive SExt/ZExt"), 201 cl::init(8)); 202 203 static cl::opt<unsigned> 204 MaxAddRecSize("scalar-evolution-max-add-rec-size", cl::Hidden, 205 cl::desc("Max coefficients in AddRec during evolving"), 206 cl::init(16)); 207 208 //===----------------------------------------------------------------------===// 209 // SCEV class definitions 210 //===----------------------------------------------------------------------===// 211 212 //===----------------------------------------------------------------------===// 213 // Implementation of the SCEV class. 214 // 215 216 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP) 217 LLVM_DUMP_METHOD void SCEV::dump() const { 218 print(dbgs()); 219 dbgs() << '\n'; 220 } 221 #endif 222 223 void SCEV::print(raw_ostream &OS) const { 224 switch (static_cast<SCEVTypes>(getSCEVType())) { 225 case scConstant: 226 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false); 227 return; 228 case scTruncate: { 229 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this); 230 const SCEV *Op = Trunc->getOperand(); 231 OS << "(trunc " << *Op->getType() << " " << *Op << " to " 232 << *Trunc->getType() << ")"; 233 return; 234 } 235 case scZeroExtend: { 236 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this); 237 const SCEV *Op = ZExt->getOperand(); 238 OS << "(zext " << *Op->getType() << " " << *Op << " to " 239 << *ZExt->getType() << ")"; 240 return; 241 } 242 case scSignExtend: { 243 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this); 244 const SCEV *Op = SExt->getOperand(); 245 OS << "(sext " << *Op->getType() << " " << *Op << " to " 246 << *SExt->getType() << ")"; 247 return; 248 } 249 case scAddRecExpr: { 250 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this); 251 OS << "{" << *AR->getOperand(0); 252 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i) 253 OS << ",+," << *AR->getOperand(i); 254 OS << "}<"; 255 if (AR->hasNoUnsignedWrap()) 256 OS << "nuw><"; 257 if (AR->hasNoSignedWrap()) 258 OS << "nsw><"; 259 if (AR->hasNoSelfWrap() && 260 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW))) 261 OS << "nw><"; 262 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false); 263 OS << ">"; 264 return; 265 } 266 case scAddExpr: 267 case scMulExpr: 268 case scUMaxExpr: 269 case scSMaxExpr: { 270 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this); 271 const char *OpStr = nullptr; 272 switch (NAry->getSCEVType()) { 273 case scAddExpr: OpStr = " + "; break; 274 case scMulExpr: OpStr = " * "; break; 275 case scUMaxExpr: OpStr = " umax "; break; 276 case scSMaxExpr: OpStr = " smax "; break; 277 } 278 OS << "("; 279 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 280 I != E; ++I) { 281 OS << **I; 282 if (std::next(I) != E) 283 OS << OpStr; 284 } 285 OS << ")"; 286 switch (NAry->getSCEVType()) { 287 case scAddExpr: 288 case scMulExpr: 289 if (NAry->hasNoUnsignedWrap()) 290 OS << "<nuw>"; 291 if (NAry->hasNoSignedWrap()) 292 OS << "<nsw>"; 293 } 294 return; 295 } 296 case scUDivExpr: { 297 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this); 298 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")"; 299 return; 300 } 301 case scUnknown: { 302 const SCEVUnknown *U = cast<SCEVUnknown>(this); 303 Type *AllocTy; 304 if (U->isSizeOf(AllocTy)) { 305 OS << "sizeof(" << *AllocTy << ")"; 306 return; 307 } 308 if (U->isAlignOf(AllocTy)) { 309 OS << "alignof(" << *AllocTy << ")"; 310 return; 311 } 312 313 Type *CTy; 314 Constant *FieldNo; 315 if (U->isOffsetOf(CTy, FieldNo)) { 316 OS << "offsetof(" << *CTy << ", "; 317 FieldNo->printAsOperand(OS, false); 318 OS << ")"; 319 return; 320 } 321 322 // Otherwise just print it normally. 323 U->getValue()->printAsOperand(OS, false); 324 return; 325 } 326 case scCouldNotCompute: 327 OS << "***COULDNOTCOMPUTE***"; 328 return; 329 } 330 llvm_unreachable("Unknown SCEV kind!"); 331 } 332 333 Type *SCEV::getType() const { 334 switch (static_cast<SCEVTypes>(getSCEVType())) { 335 case scConstant: 336 return cast<SCEVConstant>(this)->getType(); 337 case scTruncate: 338 case scZeroExtend: 339 case scSignExtend: 340 return cast<SCEVCastExpr>(this)->getType(); 341 case scAddRecExpr: 342 case scMulExpr: 343 case scUMaxExpr: 344 case scSMaxExpr: 345 return cast<SCEVNAryExpr>(this)->getType(); 346 case scAddExpr: 347 return cast<SCEVAddExpr>(this)->getType(); 348 case scUDivExpr: 349 return cast<SCEVUDivExpr>(this)->getType(); 350 case scUnknown: 351 return cast<SCEVUnknown>(this)->getType(); 352 case scCouldNotCompute: 353 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 354 } 355 llvm_unreachable("Unknown SCEV kind!"); 356 } 357 358 bool SCEV::isZero() const { 359 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 360 return SC->getValue()->isZero(); 361 return false; 362 } 363 364 bool SCEV::isOne() const { 365 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 366 return SC->getValue()->isOne(); 367 return false; 368 } 369 370 bool SCEV::isAllOnesValue() const { 371 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 372 return SC->getValue()->isMinusOne(); 373 return false; 374 } 375 376 bool SCEV::isNonConstantNegative() const { 377 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this); 378 if (!Mul) return false; 379 380 // If there is a constant factor, it will be first. 381 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0)); 382 if (!SC) return false; 383 384 // Return true if the value is negative, this matches things like (-42 * V). 385 return SC->getAPInt().isNegative(); 386 } 387 388 SCEVCouldNotCompute::SCEVCouldNotCompute() : 389 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {} 390 391 bool SCEVCouldNotCompute::classof(const SCEV *S) { 392 return S->getSCEVType() == scCouldNotCompute; 393 } 394 395 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 396 FoldingSetNodeID ID; 397 ID.AddInteger(scConstant); 398 ID.AddPointer(V); 399 void *IP = nullptr; 400 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 401 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V); 402 UniqueSCEVs.InsertNode(S, IP); 403 return S; 404 } 405 406 const SCEV *ScalarEvolution::getConstant(const APInt &Val) { 407 return getConstant(ConstantInt::get(getContext(), Val)); 408 } 409 410 const SCEV * 411 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) { 412 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 413 return getConstant(ConstantInt::get(ITy, V, isSigned)); 414 } 415 416 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, 417 unsigned SCEVTy, const SCEV *op, Type *ty) 418 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 419 420 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, 421 const SCEV *op, Type *ty) 422 : SCEVCastExpr(ID, scTruncate, op, ty) { 423 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 424 (Ty->isIntegerTy() || Ty->isPointerTy()) && 425 "Cannot truncate non-integer value!"); 426 } 427 428 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, 429 const SCEV *op, Type *ty) 430 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 431 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 432 (Ty->isIntegerTy() || Ty->isPointerTy()) && 433 "Cannot zero extend non-integer value!"); 434 } 435 436 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, 437 const SCEV *op, Type *ty) 438 : SCEVCastExpr(ID, scSignExtend, op, ty) { 439 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 440 (Ty->isIntegerTy() || Ty->isPointerTy()) && 441 "Cannot sign extend non-integer value!"); 442 } 443 444 void SCEVUnknown::deleted() { 445 // Clear this SCEVUnknown from various maps. 446 SE->forgetMemoizedResults(this); 447 448 // Remove this SCEVUnknown from the uniquing map. 449 SE->UniqueSCEVs.RemoveNode(this); 450 451 // Release the value. 452 setValPtr(nullptr); 453 } 454 455 void SCEVUnknown::allUsesReplacedWith(Value *New) { 456 // Remove this SCEVUnknown from the uniquing map. 457 SE->UniqueSCEVs.RemoveNode(this); 458 459 // Update this SCEVUnknown to point to the new value. This is needed 460 // because there may still be outstanding SCEVs which still point to 461 // this SCEVUnknown. 462 setValPtr(New); 463 } 464 465 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const { 466 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 467 if (VCE->getOpcode() == Instruction::PtrToInt) 468 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 469 if (CE->getOpcode() == Instruction::GetElementPtr && 470 CE->getOperand(0)->isNullValue() && 471 CE->getNumOperands() == 2) 472 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 473 if (CI->isOne()) { 474 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 475 ->getElementType(); 476 return true; 477 } 478 479 return false; 480 } 481 482 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const { 483 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 484 if (VCE->getOpcode() == Instruction::PtrToInt) 485 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 486 if (CE->getOpcode() == Instruction::GetElementPtr && 487 CE->getOperand(0)->isNullValue()) { 488 Type *Ty = 489 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 490 if (StructType *STy = dyn_cast<StructType>(Ty)) 491 if (!STy->isPacked() && 492 CE->getNumOperands() == 3 && 493 CE->getOperand(1)->isNullValue()) { 494 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 495 if (CI->isOne() && 496 STy->getNumElements() == 2 && 497 STy->getElementType(0)->isIntegerTy(1)) { 498 AllocTy = STy->getElementType(1); 499 return true; 500 } 501 } 502 } 503 504 return false; 505 } 506 507 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const { 508 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 509 if (VCE->getOpcode() == Instruction::PtrToInt) 510 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 511 if (CE->getOpcode() == Instruction::GetElementPtr && 512 CE->getNumOperands() == 3 && 513 CE->getOperand(0)->isNullValue() && 514 CE->getOperand(1)->isNullValue()) { 515 Type *Ty = 516 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 517 // Ignore vector types here so that ScalarEvolutionExpander doesn't 518 // emit getelementptrs that index into vectors. 519 if (Ty->isStructTy() || Ty->isArrayTy()) { 520 CTy = Ty; 521 FieldNo = CE->getOperand(2); 522 return true; 523 } 524 } 525 526 return false; 527 } 528 529 //===----------------------------------------------------------------------===// 530 // SCEV Utilities 531 //===----------------------------------------------------------------------===// 532 533 /// Compare the two values \p LV and \p RV in terms of their "complexity" where 534 /// "complexity" is a partial (and somewhat ad-hoc) relation used to order 535 /// operands in SCEV expressions. \p EqCache is a set of pairs of values that 536 /// have been previously deemed to be "equally complex" by this routine. It is 537 /// intended to avoid exponential time complexity in cases like: 538 /// 539 /// %a = f(%x, %y) 540 /// %b = f(%a, %a) 541 /// %c = f(%b, %b) 542 /// 543 /// %d = f(%x, %y) 544 /// %e = f(%d, %d) 545 /// %f = f(%e, %e) 546 /// 547 /// CompareValueComplexity(%f, %c) 548 /// 549 /// Since we do not continue running this routine on expression trees once we 550 /// have seen unequal values, there is no need to track them in the cache. 551 static int 552 CompareValueComplexity(EquivalenceClasses<const Value *> &EqCacheValue, 553 const LoopInfo *const LI, Value *LV, Value *RV, 554 unsigned Depth) { 555 if (Depth > MaxValueCompareDepth || EqCacheValue.isEquivalent(LV, RV)) 556 return 0; 557 558 // Order pointer values after integer values. This helps SCEVExpander form 559 // GEPs. 560 bool LIsPointer = LV->getType()->isPointerTy(), 561 RIsPointer = RV->getType()->isPointerTy(); 562 if (LIsPointer != RIsPointer) 563 return (int)LIsPointer - (int)RIsPointer; 564 565 // Compare getValueID values. 566 unsigned LID = LV->getValueID(), RID = RV->getValueID(); 567 if (LID != RID) 568 return (int)LID - (int)RID; 569 570 // Sort arguments by their position. 571 if (const auto *LA = dyn_cast<Argument>(LV)) { 572 const auto *RA = cast<Argument>(RV); 573 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo(); 574 return (int)LArgNo - (int)RArgNo; 575 } 576 577 if (const auto *LGV = dyn_cast<GlobalValue>(LV)) { 578 const auto *RGV = cast<GlobalValue>(RV); 579 580 const auto IsGVNameSemantic = [&](const GlobalValue *GV) { 581 auto LT = GV->getLinkage(); 582 return !(GlobalValue::isPrivateLinkage(LT) || 583 GlobalValue::isInternalLinkage(LT)); 584 }; 585 586 // Use the names to distinguish the two values, but only if the 587 // names are semantically important. 588 if (IsGVNameSemantic(LGV) && IsGVNameSemantic(RGV)) 589 return LGV->getName().compare(RGV->getName()); 590 } 591 592 // For instructions, compare their loop depth, and their operand count. This 593 // is pretty loose. 594 if (const auto *LInst = dyn_cast<Instruction>(LV)) { 595 const auto *RInst = cast<Instruction>(RV); 596 597 // Compare loop depths. 598 const BasicBlock *LParent = LInst->getParent(), 599 *RParent = RInst->getParent(); 600 if (LParent != RParent) { 601 unsigned LDepth = LI->getLoopDepth(LParent), 602 RDepth = LI->getLoopDepth(RParent); 603 if (LDepth != RDepth) 604 return (int)LDepth - (int)RDepth; 605 } 606 607 // Compare the number of operands. 608 unsigned LNumOps = LInst->getNumOperands(), 609 RNumOps = RInst->getNumOperands(); 610 if (LNumOps != RNumOps) 611 return (int)LNumOps - (int)RNumOps; 612 613 for (unsigned Idx : seq(0u, LNumOps)) { 614 int Result = 615 CompareValueComplexity(EqCacheValue, LI, LInst->getOperand(Idx), 616 RInst->getOperand(Idx), Depth + 1); 617 if (Result != 0) 618 return Result; 619 } 620 } 621 622 EqCacheValue.unionSets(LV, RV); 623 return 0; 624 } 625 626 // Return negative, zero, or positive, if LHS is less than, equal to, or greater 627 // than RHS, respectively. A three-way result allows recursive comparisons to be 628 // more efficient. 629 static int CompareSCEVComplexity( 630 EquivalenceClasses<const SCEV *> &EqCacheSCEV, 631 EquivalenceClasses<const Value *> &EqCacheValue, 632 const LoopInfo *const LI, const SCEV *LHS, const SCEV *RHS, 633 DominatorTree &DT, unsigned Depth = 0) { 634 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 635 if (LHS == RHS) 636 return 0; 637 638 // Primarily, sort the SCEVs by their getSCEVType(). 639 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); 640 if (LType != RType) 641 return (int)LType - (int)RType; 642 643 if (Depth > MaxSCEVCompareDepth || EqCacheSCEV.isEquivalent(LHS, RHS)) 644 return 0; 645 // Aside from the getSCEVType() ordering, the particular ordering 646 // isn't very important except that it's beneficial to be consistent, 647 // so that (a + b) and (b + a) don't end up as different expressions. 648 switch (static_cast<SCEVTypes>(LType)) { 649 case scUnknown: { 650 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS); 651 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 652 653 int X = CompareValueComplexity(EqCacheValue, LI, LU->getValue(), 654 RU->getValue(), Depth + 1); 655 if (X == 0) 656 EqCacheSCEV.unionSets(LHS, RHS); 657 return X; 658 } 659 660 case scConstant: { 661 const SCEVConstant *LC = cast<SCEVConstant>(LHS); 662 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 663 664 // Compare constant values. 665 const APInt &LA = LC->getAPInt(); 666 const APInt &RA = RC->getAPInt(); 667 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth(); 668 if (LBitWidth != RBitWidth) 669 return (int)LBitWidth - (int)RBitWidth; 670 return LA.ult(RA) ? -1 : 1; 671 } 672 673 case scAddRecExpr: { 674 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS); 675 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 676 677 // There is always a dominance between two recs that are used by one SCEV, 678 // so we can safely sort recs by loop header dominance. We require such 679 // order in getAddExpr. 680 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop(); 681 if (LLoop != RLoop) { 682 const BasicBlock *LHead = LLoop->getHeader(), *RHead = RLoop->getHeader(); 683 assert(LHead != RHead && "Two loops share the same header?"); 684 if (DT.dominates(LHead, RHead)) 685 return 1; 686 else 687 assert(DT.dominates(RHead, LHead) && 688 "No dominance between recurrences used by one SCEV?"); 689 return -1; 690 } 691 692 // Addrec complexity grows with operand count. 693 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands(); 694 if (LNumOps != RNumOps) 695 return (int)LNumOps - (int)RNumOps; 696 697 // Compare NoWrap flags. 698 if (LA->getNoWrapFlags() != RA->getNoWrapFlags()) 699 return (int)LA->getNoWrapFlags() - (int)RA->getNoWrapFlags(); 700 701 // Lexicographically compare. 702 for (unsigned i = 0; i != LNumOps; ++i) { 703 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, 704 LA->getOperand(i), RA->getOperand(i), DT, 705 Depth + 1); 706 if (X != 0) 707 return X; 708 } 709 EqCacheSCEV.unionSets(LHS, RHS); 710 return 0; 711 } 712 713 case scAddExpr: 714 case scMulExpr: 715 case scSMaxExpr: 716 case scUMaxExpr: { 717 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS); 718 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 719 720 // Lexicographically compare n-ary expressions. 721 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands(); 722 if (LNumOps != RNumOps) 723 return (int)LNumOps - (int)RNumOps; 724 725 // Compare NoWrap flags. 726 if (LC->getNoWrapFlags() != RC->getNoWrapFlags()) 727 return (int)LC->getNoWrapFlags() - (int)RC->getNoWrapFlags(); 728 729 for (unsigned i = 0; i != LNumOps; ++i) { 730 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, 731 LC->getOperand(i), RC->getOperand(i), DT, 732 Depth + 1); 733 if (X != 0) 734 return X; 735 } 736 EqCacheSCEV.unionSets(LHS, RHS); 737 return 0; 738 } 739 740 case scUDivExpr: { 741 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS); 742 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 743 744 // Lexicographically compare udiv expressions. 745 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getLHS(), 746 RC->getLHS(), DT, Depth + 1); 747 if (X != 0) 748 return X; 749 X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getRHS(), 750 RC->getRHS(), DT, Depth + 1); 751 if (X == 0) 752 EqCacheSCEV.unionSets(LHS, RHS); 753 return X; 754 } 755 756 case scTruncate: 757 case scZeroExtend: 758 case scSignExtend: { 759 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS); 760 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 761 762 // Compare cast expressions by operand. 763 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, 764 LC->getOperand(), RC->getOperand(), DT, 765 Depth + 1); 766 if (X == 0) 767 EqCacheSCEV.unionSets(LHS, RHS); 768 return X; 769 } 770 771 case scCouldNotCompute: 772 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 773 } 774 llvm_unreachable("Unknown SCEV kind!"); 775 } 776 777 /// Given a list of SCEV objects, order them by their complexity, and group 778 /// objects of the same complexity together by value. When this routine is 779 /// finished, we know that any duplicates in the vector are consecutive and that 780 /// complexity is monotonically increasing. 781 /// 782 /// Note that we go take special precautions to ensure that we get deterministic 783 /// results from this routine. In other words, we don't want the results of 784 /// this to depend on where the addresses of various SCEV objects happened to 785 /// land in memory. 786 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 787 LoopInfo *LI, DominatorTree &DT) { 788 if (Ops.size() < 2) return; // Noop 789 790 EquivalenceClasses<const SCEV *> EqCacheSCEV; 791 EquivalenceClasses<const Value *> EqCacheValue; 792 if (Ops.size() == 2) { 793 // This is the common case, which also happens to be trivially simple. 794 // Special case it. 795 const SCEV *&LHS = Ops[0], *&RHS = Ops[1]; 796 if (CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, RHS, LHS, DT) < 0) 797 std::swap(LHS, RHS); 798 return; 799 } 800 801 // Do the rough sort by complexity. 802 std::stable_sort(Ops.begin(), Ops.end(), 803 [&](const SCEV *LHS, const SCEV *RHS) { 804 return CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, 805 LHS, RHS, DT) < 0; 806 }); 807 808 // Now that we are sorted by complexity, group elements of the same 809 // complexity. Note that this is, at worst, N^2, but the vector is likely to 810 // be extremely short in practice. Note that we take this approach because we 811 // do not want to depend on the addresses of the objects we are grouping. 812 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 813 const SCEV *S = Ops[i]; 814 unsigned Complexity = S->getSCEVType(); 815 816 // If there are any objects of the same complexity and same value as this 817 // one, group them. 818 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 819 if (Ops[j] == S) { // Found a duplicate. 820 // Move it to immediately after i'th element. 821 std::swap(Ops[i+1], Ops[j]); 822 ++i; // no need to rescan it. 823 if (i == e-2) return; // Done! 824 } 825 } 826 } 827 } 828 829 // Returns the size of the SCEV S. 830 static inline int sizeOfSCEV(const SCEV *S) { 831 struct FindSCEVSize { 832 int Size = 0; 833 834 FindSCEVSize() = default; 835 836 bool follow(const SCEV *S) { 837 ++Size; 838 // Keep looking at all operands of S. 839 return true; 840 } 841 842 bool isDone() const { 843 return false; 844 } 845 }; 846 847 FindSCEVSize F; 848 SCEVTraversal<FindSCEVSize> ST(F); 849 ST.visitAll(S); 850 return F.Size; 851 } 852 853 namespace { 854 855 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> { 856 public: 857 // Computes the Quotient and Remainder of the division of Numerator by 858 // Denominator. 859 static void divide(ScalarEvolution &SE, const SCEV *Numerator, 860 const SCEV *Denominator, const SCEV **Quotient, 861 const SCEV **Remainder) { 862 assert(Numerator && Denominator && "Uninitialized SCEV"); 863 864 SCEVDivision D(SE, Numerator, Denominator); 865 866 // Check for the trivial case here to avoid having to check for it in the 867 // rest of the code. 868 if (Numerator == Denominator) { 869 *Quotient = D.One; 870 *Remainder = D.Zero; 871 return; 872 } 873 874 if (Numerator->isZero()) { 875 *Quotient = D.Zero; 876 *Remainder = D.Zero; 877 return; 878 } 879 880 // A simple case when N/1. The quotient is N. 881 if (Denominator->isOne()) { 882 *Quotient = Numerator; 883 *Remainder = D.Zero; 884 return; 885 } 886 887 // Split the Denominator when it is a product. 888 if (const SCEVMulExpr *T = dyn_cast<SCEVMulExpr>(Denominator)) { 889 const SCEV *Q, *R; 890 *Quotient = Numerator; 891 for (const SCEV *Op : T->operands()) { 892 divide(SE, *Quotient, Op, &Q, &R); 893 *Quotient = Q; 894 895 // Bail out when the Numerator is not divisible by one of the terms of 896 // the Denominator. 897 if (!R->isZero()) { 898 *Quotient = D.Zero; 899 *Remainder = Numerator; 900 return; 901 } 902 } 903 *Remainder = D.Zero; 904 return; 905 } 906 907 D.visit(Numerator); 908 *Quotient = D.Quotient; 909 *Remainder = D.Remainder; 910 } 911 912 // Except in the trivial case described above, we do not know how to divide 913 // Expr by Denominator for the following functions with empty implementation. 914 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {} 915 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {} 916 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {} 917 void visitUDivExpr(const SCEVUDivExpr *Numerator) {} 918 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {} 919 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {} 920 void visitUnknown(const SCEVUnknown *Numerator) {} 921 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {} 922 923 void visitConstant(const SCEVConstant *Numerator) { 924 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) { 925 APInt NumeratorVal = Numerator->getAPInt(); 926 APInt DenominatorVal = D->getAPInt(); 927 uint32_t NumeratorBW = NumeratorVal.getBitWidth(); 928 uint32_t DenominatorBW = DenominatorVal.getBitWidth(); 929 930 if (NumeratorBW > DenominatorBW) 931 DenominatorVal = DenominatorVal.sext(NumeratorBW); 932 else if (NumeratorBW < DenominatorBW) 933 NumeratorVal = NumeratorVal.sext(DenominatorBW); 934 935 APInt QuotientVal(NumeratorVal.getBitWidth(), 0); 936 APInt RemainderVal(NumeratorVal.getBitWidth(), 0); 937 APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal); 938 Quotient = SE.getConstant(QuotientVal); 939 Remainder = SE.getConstant(RemainderVal); 940 return; 941 } 942 } 943 944 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) { 945 const SCEV *StartQ, *StartR, *StepQ, *StepR; 946 if (!Numerator->isAffine()) 947 return cannotDivide(Numerator); 948 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR); 949 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR); 950 // Bail out if the types do not match. 951 Type *Ty = Denominator->getType(); 952 if (Ty != StartQ->getType() || Ty != StartR->getType() || 953 Ty != StepQ->getType() || Ty != StepR->getType()) 954 return cannotDivide(Numerator); 955 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(), 956 Numerator->getNoWrapFlags()); 957 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(), 958 Numerator->getNoWrapFlags()); 959 } 960 961 void visitAddExpr(const SCEVAddExpr *Numerator) { 962 SmallVector<const SCEV *, 2> Qs, Rs; 963 Type *Ty = Denominator->getType(); 964 965 for (const SCEV *Op : Numerator->operands()) { 966 const SCEV *Q, *R; 967 divide(SE, Op, Denominator, &Q, &R); 968 969 // Bail out if types do not match. 970 if (Ty != Q->getType() || Ty != R->getType()) 971 return cannotDivide(Numerator); 972 973 Qs.push_back(Q); 974 Rs.push_back(R); 975 } 976 977 if (Qs.size() == 1) { 978 Quotient = Qs[0]; 979 Remainder = Rs[0]; 980 return; 981 } 982 983 Quotient = SE.getAddExpr(Qs); 984 Remainder = SE.getAddExpr(Rs); 985 } 986 987 void visitMulExpr(const SCEVMulExpr *Numerator) { 988 SmallVector<const SCEV *, 2> Qs; 989 Type *Ty = Denominator->getType(); 990 991 bool FoundDenominatorTerm = false; 992 for (const SCEV *Op : Numerator->operands()) { 993 // Bail out if types do not match. 994 if (Ty != Op->getType()) 995 return cannotDivide(Numerator); 996 997 if (FoundDenominatorTerm) { 998 Qs.push_back(Op); 999 continue; 1000 } 1001 1002 // Check whether Denominator divides one of the product operands. 1003 const SCEV *Q, *R; 1004 divide(SE, Op, Denominator, &Q, &R); 1005 if (!R->isZero()) { 1006 Qs.push_back(Op); 1007 continue; 1008 } 1009 1010 // Bail out if types do not match. 1011 if (Ty != Q->getType()) 1012 return cannotDivide(Numerator); 1013 1014 FoundDenominatorTerm = true; 1015 Qs.push_back(Q); 1016 } 1017 1018 if (FoundDenominatorTerm) { 1019 Remainder = Zero; 1020 if (Qs.size() == 1) 1021 Quotient = Qs[0]; 1022 else 1023 Quotient = SE.getMulExpr(Qs); 1024 return; 1025 } 1026 1027 if (!isa<SCEVUnknown>(Denominator)) 1028 return cannotDivide(Numerator); 1029 1030 // The Remainder is obtained by replacing Denominator by 0 in Numerator. 1031 ValueToValueMap RewriteMap; 1032 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] = 1033 cast<SCEVConstant>(Zero)->getValue(); 1034 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true); 1035 1036 if (Remainder->isZero()) { 1037 // The Quotient is obtained by replacing Denominator by 1 in Numerator. 1038 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] = 1039 cast<SCEVConstant>(One)->getValue(); 1040 Quotient = 1041 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true); 1042 return; 1043 } 1044 1045 // Quotient is (Numerator - Remainder) divided by Denominator. 1046 const SCEV *Q, *R; 1047 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder); 1048 // This SCEV does not seem to simplify: fail the division here. 1049 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator)) 1050 return cannotDivide(Numerator); 1051 divide(SE, Diff, Denominator, &Q, &R); 1052 if (R != Zero) 1053 return cannotDivide(Numerator); 1054 Quotient = Q; 1055 } 1056 1057 private: 1058 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator, 1059 const SCEV *Denominator) 1060 : SE(S), Denominator(Denominator) { 1061 Zero = SE.getZero(Denominator->getType()); 1062 One = SE.getOne(Denominator->getType()); 1063 1064 // We generally do not know how to divide Expr by Denominator. We 1065 // initialize the division to a "cannot divide" state to simplify the rest 1066 // of the code. 1067 cannotDivide(Numerator); 1068 } 1069 1070 // Convenience function for giving up on the division. We set the quotient to 1071 // be equal to zero and the remainder to be equal to the numerator. 1072 void cannotDivide(const SCEV *Numerator) { 1073 Quotient = Zero; 1074 Remainder = Numerator; 1075 } 1076 1077 ScalarEvolution &SE; 1078 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One; 1079 }; 1080 1081 } // end anonymous namespace 1082 1083 //===----------------------------------------------------------------------===// 1084 // Simple SCEV method implementations 1085 //===----------------------------------------------------------------------===// 1086 1087 /// Compute BC(It, K). The result has width W. Assume, K > 0. 1088 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 1089 ScalarEvolution &SE, 1090 Type *ResultTy) { 1091 // Handle the simplest case efficiently. 1092 if (K == 1) 1093 return SE.getTruncateOrZeroExtend(It, ResultTy); 1094 1095 // We are using the following formula for BC(It, K): 1096 // 1097 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 1098 // 1099 // Suppose, W is the bitwidth of the return value. We must be prepared for 1100 // overflow. Hence, we must assure that the result of our computation is 1101 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 1102 // safe in modular arithmetic. 1103 // 1104 // However, this code doesn't use exactly that formula; the formula it uses 1105 // is something like the following, where T is the number of factors of 2 in 1106 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 1107 // exponentiation: 1108 // 1109 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 1110 // 1111 // This formula is trivially equivalent to the previous formula. However, 1112 // this formula can be implemented much more efficiently. The trick is that 1113 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 1114 // arithmetic. To do exact division in modular arithmetic, all we have 1115 // to do is multiply by the inverse. Therefore, this step can be done at 1116 // width W. 1117 // 1118 // The next issue is how to safely do the division by 2^T. The way this 1119 // is done is by doing the multiplication step at a width of at least W + T 1120 // bits. This way, the bottom W+T bits of the product are accurate. Then, 1121 // when we perform the division by 2^T (which is equivalent to a right shift 1122 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 1123 // truncated out after the division by 2^T. 1124 // 1125 // In comparison to just directly using the first formula, this technique 1126 // is much more efficient; using the first formula requires W * K bits, 1127 // but this formula less than W + K bits. Also, the first formula requires 1128 // a division step, whereas this formula only requires multiplies and shifts. 1129 // 1130 // It doesn't matter whether the subtraction step is done in the calculation 1131 // width or the input iteration count's width; if the subtraction overflows, 1132 // the result must be zero anyway. We prefer here to do it in the width of 1133 // the induction variable because it helps a lot for certain cases; CodeGen 1134 // isn't smart enough to ignore the overflow, which leads to much less 1135 // efficient code if the width of the subtraction is wider than the native 1136 // register width. 1137 // 1138 // (It's possible to not widen at all by pulling out factors of 2 before 1139 // the multiplication; for example, K=2 can be calculated as 1140 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 1141 // extra arithmetic, so it's not an obvious win, and it gets 1142 // much more complicated for K > 3.) 1143 1144 // Protection from insane SCEVs; this bound is conservative, 1145 // but it probably doesn't matter. 1146 if (K > 1000) 1147 return SE.getCouldNotCompute(); 1148 1149 unsigned W = SE.getTypeSizeInBits(ResultTy); 1150 1151 // Calculate K! / 2^T and T; we divide out the factors of two before 1152 // multiplying for calculating K! / 2^T to avoid overflow. 1153 // Other overflow doesn't matter because we only care about the bottom 1154 // W bits of the result. 1155 APInt OddFactorial(W, 1); 1156 unsigned T = 1; 1157 for (unsigned i = 3; i <= K; ++i) { 1158 APInt Mult(W, i); 1159 unsigned TwoFactors = Mult.countTrailingZeros(); 1160 T += TwoFactors; 1161 Mult.lshrInPlace(TwoFactors); 1162 OddFactorial *= Mult; 1163 } 1164 1165 // We need at least W + T bits for the multiplication step 1166 unsigned CalculationBits = W + T; 1167 1168 // Calculate 2^T, at width T+W. 1169 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T); 1170 1171 // Calculate the multiplicative inverse of K! / 2^T; 1172 // this multiplication factor will perform the exact division by 1173 // K! / 2^T. 1174 APInt Mod = APInt::getSignedMinValue(W+1); 1175 APInt MultiplyFactor = OddFactorial.zext(W+1); 1176 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 1177 MultiplyFactor = MultiplyFactor.trunc(W); 1178 1179 // Calculate the product, at width T+W 1180 IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 1181 CalculationBits); 1182 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 1183 for (unsigned i = 1; i != K; ++i) { 1184 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); 1185 Dividend = SE.getMulExpr(Dividend, 1186 SE.getTruncateOrZeroExtend(S, CalculationTy)); 1187 } 1188 1189 // Divide by 2^T 1190 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 1191 1192 // Truncate the result, and divide by K! / 2^T. 1193 1194 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 1195 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 1196 } 1197 1198 /// Return the value of this chain of recurrences at the specified iteration 1199 /// number. We can evaluate this recurrence by multiplying each element in the 1200 /// chain by the binomial coefficient corresponding to it. In other words, we 1201 /// can evaluate {A,+,B,+,C,+,D} as: 1202 /// 1203 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 1204 /// 1205 /// where BC(It, k) stands for binomial coefficient. 1206 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 1207 ScalarEvolution &SE) const { 1208 const SCEV *Result = getStart(); 1209 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 1210 // The computation is correct in the face of overflow provided that the 1211 // multiplication is performed _after_ the evaluation of the binomial 1212 // coefficient. 1213 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 1214 if (isa<SCEVCouldNotCompute>(Coeff)) 1215 return Coeff; 1216 1217 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 1218 } 1219 return Result; 1220 } 1221 1222 //===----------------------------------------------------------------------===// 1223 // SCEV Expression folder implementations 1224 //===----------------------------------------------------------------------===// 1225 1226 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 1227 Type *Ty) { 1228 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 1229 "This is not a truncating conversion!"); 1230 assert(isSCEVable(Ty) && 1231 "This is not a conversion to a SCEVable type!"); 1232 Ty = getEffectiveSCEVType(Ty); 1233 1234 FoldingSetNodeID ID; 1235 ID.AddInteger(scTruncate); 1236 ID.AddPointer(Op); 1237 ID.AddPointer(Ty); 1238 void *IP = nullptr; 1239 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1240 1241 // Fold if the operand is constant. 1242 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1243 return getConstant( 1244 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty))); 1245 1246 // trunc(trunc(x)) --> trunc(x) 1247 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 1248 return getTruncateExpr(ST->getOperand(), Ty); 1249 1250 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 1251 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1252 return getTruncateOrSignExtend(SS->getOperand(), Ty); 1253 1254 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 1255 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 1256 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 1257 1258 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can 1259 // eliminate all the truncates, or we replace other casts with truncates. 1260 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) { 1261 SmallVector<const SCEV *, 4> Operands; 1262 bool hasTrunc = false; 1263 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) { 1264 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty); 1265 if (!isa<SCEVCastExpr>(SA->getOperand(i))) 1266 hasTrunc = isa<SCEVTruncateExpr>(S); 1267 Operands.push_back(S); 1268 } 1269 if (!hasTrunc) 1270 return getAddExpr(Operands); 1271 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL. 1272 } 1273 1274 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can 1275 // eliminate all the truncates, or we replace other casts with truncates. 1276 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) { 1277 SmallVector<const SCEV *, 4> Operands; 1278 bool hasTrunc = false; 1279 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) { 1280 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty); 1281 if (!isa<SCEVCastExpr>(SM->getOperand(i))) 1282 hasTrunc = isa<SCEVTruncateExpr>(S); 1283 Operands.push_back(S); 1284 } 1285 if (!hasTrunc) 1286 return getMulExpr(Operands); 1287 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL. 1288 } 1289 1290 // If the input value is a chrec scev, truncate the chrec's operands. 1291 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 1292 SmallVector<const SCEV *, 4> Operands; 1293 for (const SCEV *Op : AddRec->operands()) 1294 Operands.push_back(getTruncateExpr(Op, Ty)); 1295 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap); 1296 } 1297 1298 // The cast wasn't folded; create an explicit cast node. We can reuse 1299 // the existing insert position since if we get here, we won't have 1300 // made any changes which would invalidate it. 1301 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 1302 Op, Ty); 1303 UniqueSCEVs.InsertNode(S, IP); 1304 addToLoopUseLists(S); 1305 return S; 1306 } 1307 1308 // Get the limit of a recurrence such that incrementing by Step cannot cause 1309 // signed overflow as long as the value of the recurrence within the 1310 // loop does not exceed this limit before incrementing. 1311 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step, 1312 ICmpInst::Predicate *Pred, 1313 ScalarEvolution *SE) { 1314 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType()); 1315 if (SE->isKnownPositive(Step)) { 1316 *Pred = ICmpInst::ICMP_SLT; 1317 return SE->getConstant(APInt::getSignedMinValue(BitWidth) - 1318 SE->getSignedRangeMax(Step)); 1319 } 1320 if (SE->isKnownNegative(Step)) { 1321 *Pred = ICmpInst::ICMP_SGT; 1322 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) - 1323 SE->getSignedRangeMin(Step)); 1324 } 1325 return nullptr; 1326 } 1327 1328 // Get the limit of a recurrence such that incrementing by Step cannot cause 1329 // unsigned overflow as long as the value of the recurrence within the loop does 1330 // not exceed this limit before incrementing. 1331 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step, 1332 ICmpInst::Predicate *Pred, 1333 ScalarEvolution *SE) { 1334 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType()); 1335 *Pred = ICmpInst::ICMP_ULT; 1336 1337 return SE->getConstant(APInt::getMinValue(BitWidth) - 1338 SE->getUnsignedRangeMax(Step)); 1339 } 1340 1341 namespace { 1342 1343 struct ExtendOpTraitsBase { 1344 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *, 1345 unsigned); 1346 }; 1347 1348 // Used to make code generic over signed and unsigned overflow. 1349 template <typename ExtendOp> struct ExtendOpTraits { 1350 // Members present: 1351 // 1352 // static const SCEV::NoWrapFlags WrapType; 1353 // 1354 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr; 1355 // 1356 // static const SCEV *getOverflowLimitForStep(const SCEV *Step, 1357 // ICmpInst::Predicate *Pred, 1358 // ScalarEvolution *SE); 1359 }; 1360 1361 template <> 1362 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase { 1363 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW; 1364 1365 static const GetExtendExprTy GetExtendExpr; 1366 1367 static const SCEV *getOverflowLimitForStep(const SCEV *Step, 1368 ICmpInst::Predicate *Pred, 1369 ScalarEvolution *SE) { 1370 return getSignedOverflowLimitForStep(Step, Pred, SE); 1371 } 1372 }; 1373 1374 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits< 1375 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr; 1376 1377 template <> 1378 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase { 1379 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW; 1380 1381 static const GetExtendExprTy GetExtendExpr; 1382 1383 static const SCEV *getOverflowLimitForStep(const SCEV *Step, 1384 ICmpInst::Predicate *Pred, 1385 ScalarEvolution *SE) { 1386 return getUnsignedOverflowLimitForStep(Step, Pred, SE); 1387 } 1388 }; 1389 1390 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits< 1391 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr; 1392 1393 } // end anonymous namespace 1394 1395 // The recurrence AR has been shown to have no signed/unsigned wrap or something 1396 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as 1397 // easily prove NSW/NUW for its preincrement or postincrement sibling. This 1398 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step + 1399 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the 1400 // expression "Step + sext/zext(PreIncAR)" is congruent with 1401 // "sext/zext(PostIncAR)" 1402 template <typename ExtendOpTy> 1403 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty, 1404 ScalarEvolution *SE, unsigned Depth) { 1405 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType; 1406 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr; 1407 1408 const Loop *L = AR->getLoop(); 1409 const SCEV *Start = AR->getStart(); 1410 const SCEV *Step = AR->getStepRecurrence(*SE); 1411 1412 // Check for a simple looking step prior to loop entry. 1413 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start); 1414 if (!SA) 1415 return nullptr; 1416 1417 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV 1418 // subtraction is expensive. For this purpose, perform a quick and dirty 1419 // difference, by checking for Step in the operand list. 1420 SmallVector<const SCEV *, 4> DiffOps; 1421 for (const SCEV *Op : SA->operands()) 1422 if (Op != Step) 1423 DiffOps.push_back(Op); 1424 1425 if (DiffOps.size() == SA->getNumOperands()) 1426 return nullptr; 1427 1428 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` + 1429 // `Step`: 1430 1431 // 1. NSW/NUW flags on the step increment. 1432 auto PreStartFlags = 1433 ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW); 1434 const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags); 1435 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>( 1436 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap)); 1437 1438 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies 1439 // "S+X does not sign/unsign-overflow". 1440 // 1441 1442 const SCEV *BECount = SE->getBackedgeTakenCount(L); 1443 if (PreAR && PreAR->getNoWrapFlags(WrapType) && 1444 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount)) 1445 return PreStart; 1446 1447 // 2. Direct overflow check on the step operation's expression. 1448 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType()); 1449 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2); 1450 const SCEV *OperandExtendedStart = 1451 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy, Depth), 1452 (SE->*GetExtendExpr)(Step, WideTy, Depth)); 1453 if ((SE->*GetExtendExpr)(Start, WideTy, Depth) == OperandExtendedStart) { 1454 if (PreAR && AR->getNoWrapFlags(WrapType)) { 1455 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW 1456 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then 1457 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact. 1458 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType); 1459 } 1460 return PreStart; 1461 } 1462 1463 // 3. Loop precondition. 1464 ICmpInst::Predicate Pred; 1465 const SCEV *OverflowLimit = 1466 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE); 1467 1468 if (OverflowLimit && 1469 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) 1470 return PreStart; 1471 1472 return nullptr; 1473 } 1474 1475 // Get the normalized zero or sign extended expression for this AddRec's Start. 1476 template <typename ExtendOpTy> 1477 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty, 1478 ScalarEvolution *SE, 1479 unsigned Depth) { 1480 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr; 1481 1482 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE, Depth); 1483 if (!PreStart) 1484 return (SE->*GetExtendExpr)(AR->getStart(), Ty, Depth); 1485 1486 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty, 1487 Depth), 1488 (SE->*GetExtendExpr)(PreStart, Ty, Depth)); 1489 } 1490 1491 // Try to prove away overflow by looking at "nearby" add recurrences. A 1492 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it 1493 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`. 1494 // 1495 // Formally: 1496 // 1497 // {S,+,X} == {S-T,+,X} + T 1498 // => Ext({S,+,X}) == Ext({S-T,+,X} + T) 1499 // 1500 // If ({S-T,+,X} + T) does not overflow ... (1) 1501 // 1502 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T) 1503 // 1504 // If {S-T,+,X} does not overflow ... (2) 1505 // 1506 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T) 1507 // == {Ext(S-T)+Ext(T),+,Ext(X)} 1508 // 1509 // If (S-T)+T does not overflow ... (3) 1510 // 1511 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)} 1512 // == {Ext(S),+,Ext(X)} == LHS 1513 // 1514 // Thus, if (1), (2) and (3) are true for some T, then 1515 // Ext({S,+,X}) == {Ext(S),+,Ext(X)} 1516 // 1517 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T) 1518 // does not overflow" restricted to the 0th iteration. Therefore we only need 1519 // to check for (1) and (2). 1520 // 1521 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T 1522 // is `Delta` (defined below). 1523 template <typename ExtendOpTy> 1524 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start, 1525 const SCEV *Step, 1526 const Loop *L) { 1527 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType; 1528 1529 // We restrict `Start` to a constant to prevent SCEV from spending too much 1530 // time here. It is correct (but more expensive) to continue with a 1531 // non-constant `Start` and do a general SCEV subtraction to compute 1532 // `PreStart` below. 1533 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start); 1534 if (!StartC) 1535 return false; 1536 1537 APInt StartAI = StartC->getAPInt(); 1538 1539 for (unsigned Delta : {-2, -1, 1, 2}) { 1540 const SCEV *PreStart = getConstant(StartAI - Delta); 1541 1542 FoldingSetNodeID ID; 1543 ID.AddInteger(scAddRecExpr); 1544 ID.AddPointer(PreStart); 1545 ID.AddPointer(Step); 1546 ID.AddPointer(L); 1547 void *IP = nullptr; 1548 const auto *PreAR = 1549 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1550 1551 // Give up if we don't already have the add recurrence we need because 1552 // actually constructing an add recurrence is relatively expensive. 1553 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2) 1554 const SCEV *DeltaS = getConstant(StartC->getType(), Delta); 1555 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE; 1556 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep( 1557 DeltaS, &Pred, this); 1558 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1) 1559 return true; 1560 } 1561 } 1562 1563 return false; 1564 } 1565 1566 const SCEV * 1567 ScalarEvolution::getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) { 1568 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1569 "This is not an extending conversion!"); 1570 assert(isSCEVable(Ty) && 1571 "This is not a conversion to a SCEVable type!"); 1572 Ty = getEffectiveSCEVType(Ty); 1573 1574 // Fold if the operand is constant. 1575 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1576 return getConstant( 1577 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty))); 1578 1579 // zext(zext(x)) --> zext(x) 1580 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 1581 return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1); 1582 1583 // Before doing any expensive analysis, check to see if we've already 1584 // computed a SCEV for this Op and Ty. 1585 FoldingSetNodeID ID; 1586 ID.AddInteger(scZeroExtend); 1587 ID.AddPointer(Op); 1588 ID.AddPointer(Ty); 1589 void *IP = nullptr; 1590 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1591 if (Depth > MaxExtDepth) { 1592 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 1593 Op, Ty); 1594 UniqueSCEVs.InsertNode(S, IP); 1595 addToLoopUseLists(S); 1596 return S; 1597 } 1598 1599 // zext(trunc(x)) --> zext(x) or x or trunc(x) 1600 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 1601 // It's possible the bits taken off by the truncate were all zero bits. If 1602 // so, we should be able to simplify this further. 1603 const SCEV *X = ST->getOperand(); 1604 ConstantRange CR = getUnsignedRange(X); 1605 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 1606 unsigned NewBits = getTypeSizeInBits(Ty); 1607 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains( 1608 CR.zextOrTrunc(NewBits))) 1609 return getTruncateOrZeroExtend(X, Ty); 1610 } 1611 1612 // If the input value is a chrec scev, and we can prove that the value 1613 // did not overflow the old, smaller, value, we can zero extend all of the 1614 // operands (often constants). This allows analysis of something like 1615 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 1616 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1617 if (AR->isAffine()) { 1618 const SCEV *Start = AR->getStart(); 1619 const SCEV *Step = AR->getStepRecurrence(*this); 1620 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1621 const Loop *L = AR->getLoop(); 1622 1623 if (!AR->hasNoUnsignedWrap()) { 1624 auto NewFlags = proveNoWrapViaConstantRanges(AR); 1625 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags); 1626 } 1627 1628 // If we have special knowledge that this addrec won't overflow, 1629 // we don't need to do any further analysis. 1630 if (AR->hasNoUnsignedWrap()) 1631 return getAddRecExpr( 1632 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1), 1633 getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags()); 1634 1635 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1636 // Note that this serves two purposes: It filters out loops that are 1637 // simply not analyzable, and it covers the case where this code is 1638 // being called from within backedge-taken count analysis, such that 1639 // attempting to ask for the backedge-taken count would likely result 1640 // in infinite recursion. In the later case, the analysis code will 1641 // cope with a conservative value, and it will take care to purge 1642 // that value once it has finished. 1643 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1644 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1645 // Manually compute the final value for AR, checking for 1646 // overflow. 1647 1648 // Check whether the backedge-taken count can be losslessly casted to 1649 // the addrec's type. The count is always unsigned. 1650 const SCEV *CastedMaxBECount = 1651 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1652 const SCEV *RecastedMaxBECount = 1653 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1654 if (MaxBECount == RecastedMaxBECount) { 1655 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1656 // Check whether Start+Step*MaxBECount has no unsigned overflow. 1657 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step, 1658 SCEV::FlagAnyWrap, Depth + 1); 1659 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul, 1660 SCEV::FlagAnyWrap, 1661 Depth + 1), 1662 WideTy, Depth + 1); 1663 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy, Depth + 1); 1664 const SCEV *WideMaxBECount = 1665 getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1); 1666 const SCEV *OperandExtendedAdd = 1667 getAddExpr(WideStart, 1668 getMulExpr(WideMaxBECount, 1669 getZeroExtendExpr(Step, WideTy, Depth + 1), 1670 SCEV::FlagAnyWrap, Depth + 1), 1671 SCEV::FlagAnyWrap, Depth + 1); 1672 if (ZAdd == OperandExtendedAdd) { 1673 // Cache knowledge of AR NUW, which is propagated to this AddRec. 1674 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); 1675 // Return the expression with the addrec on the outside. 1676 return getAddRecExpr( 1677 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, 1678 Depth + 1), 1679 getZeroExtendExpr(Step, Ty, Depth + 1), L, 1680 AR->getNoWrapFlags()); 1681 } 1682 // Similar to above, only this time treat the step value as signed. 1683 // This covers loops that count down. 1684 OperandExtendedAdd = 1685 getAddExpr(WideStart, 1686 getMulExpr(WideMaxBECount, 1687 getSignExtendExpr(Step, WideTy, Depth + 1), 1688 SCEV::FlagAnyWrap, Depth + 1), 1689 SCEV::FlagAnyWrap, Depth + 1); 1690 if (ZAdd == OperandExtendedAdd) { 1691 // Cache knowledge of AR NW, which is propagated to this AddRec. 1692 // Negative step causes unsigned wrap, but it still can't self-wrap. 1693 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); 1694 // Return the expression with the addrec on the outside. 1695 return getAddRecExpr( 1696 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, 1697 Depth + 1), 1698 getSignExtendExpr(Step, Ty, Depth + 1), L, 1699 AR->getNoWrapFlags()); 1700 } 1701 } 1702 } 1703 1704 // Normally, in the cases we can prove no-overflow via a 1705 // backedge guarding condition, we can also compute a backedge 1706 // taken count for the loop. The exceptions are assumptions and 1707 // guards present in the loop -- SCEV is not great at exploiting 1708 // these to compute max backedge taken counts, but can still use 1709 // these to prove lack of overflow. Use this fact to avoid 1710 // doing extra work that may not pay off. 1711 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards || 1712 !AC.assumptions().empty()) { 1713 // If the backedge is guarded by a comparison with the pre-inc 1714 // value the addrec is safe. Also, if the entry is guarded by 1715 // a comparison with the start value and the backedge is 1716 // guarded by a comparison with the post-inc value, the addrec 1717 // is safe. 1718 if (isKnownPositive(Step)) { 1719 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 1720 getUnsignedRangeMax(Step)); 1721 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 1722 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 1723 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 1724 AR->getPostIncExpr(*this), N))) { 1725 // Cache knowledge of AR NUW, which is propagated to this 1726 // AddRec. 1727 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); 1728 // Return the expression with the addrec on the outside. 1729 return getAddRecExpr( 1730 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, 1731 Depth + 1), 1732 getZeroExtendExpr(Step, Ty, Depth + 1), L, 1733 AR->getNoWrapFlags()); 1734 } 1735 } else if (isKnownNegative(Step)) { 1736 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 1737 getSignedRangeMin(Step)); 1738 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || 1739 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) && 1740 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 1741 AR->getPostIncExpr(*this), N))) { 1742 // Cache knowledge of AR NW, which is propagated to this 1743 // AddRec. Negative step causes unsigned wrap, but it 1744 // still can't self-wrap. 1745 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); 1746 // Return the expression with the addrec on the outside. 1747 return getAddRecExpr( 1748 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, 1749 Depth + 1), 1750 getSignExtendExpr(Step, Ty, Depth + 1), L, 1751 AR->getNoWrapFlags()); 1752 } 1753 } 1754 } 1755 1756 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) { 1757 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); 1758 return getAddRecExpr( 1759 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1), 1760 getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags()); 1761 } 1762 } 1763 1764 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) { 1765 // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw> 1766 if (SA->hasNoUnsignedWrap()) { 1767 // If the addition does not unsign overflow then we can, by definition, 1768 // commute the zero extension with the addition operation. 1769 SmallVector<const SCEV *, 4> Ops; 1770 for (const auto *Op : SA->operands()) 1771 Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1)); 1772 return getAddExpr(Ops, SCEV::FlagNUW, Depth + 1); 1773 } 1774 } 1775 1776 // The cast wasn't folded; create an explicit cast node. 1777 // Recompute the insert position, as it may have been invalidated. 1778 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1779 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 1780 Op, Ty); 1781 UniqueSCEVs.InsertNode(S, IP); 1782 addToLoopUseLists(S); 1783 return S; 1784 } 1785 1786 const SCEV * 1787 ScalarEvolution::getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) { 1788 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1789 "This is not an extending conversion!"); 1790 assert(isSCEVable(Ty) && 1791 "This is not a conversion to a SCEVable type!"); 1792 Ty = getEffectiveSCEVType(Ty); 1793 1794 // Fold if the operand is constant. 1795 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1796 return getConstant( 1797 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty))); 1798 1799 // sext(sext(x)) --> sext(x) 1800 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1801 return getSignExtendExpr(SS->getOperand(), Ty, Depth + 1); 1802 1803 // sext(zext(x)) --> zext(x) 1804 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 1805 return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1); 1806 1807 // Before doing any expensive analysis, check to see if we've already 1808 // computed a SCEV for this Op and Ty. 1809 FoldingSetNodeID ID; 1810 ID.AddInteger(scSignExtend); 1811 ID.AddPointer(Op); 1812 ID.AddPointer(Ty); 1813 void *IP = nullptr; 1814 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1815 // Limit recursion depth. 1816 if (Depth > MaxExtDepth) { 1817 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1818 Op, Ty); 1819 UniqueSCEVs.InsertNode(S, IP); 1820 addToLoopUseLists(S); 1821 return S; 1822 } 1823 1824 // sext(trunc(x)) --> sext(x) or x or trunc(x) 1825 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 1826 // It's possible the bits taken off by the truncate were all sign bits. If 1827 // so, we should be able to simplify this further. 1828 const SCEV *X = ST->getOperand(); 1829 ConstantRange CR = getSignedRange(X); 1830 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 1831 unsigned NewBits = getTypeSizeInBits(Ty); 1832 if (CR.truncate(TruncBits).signExtend(NewBits).contains( 1833 CR.sextOrTrunc(NewBits))) 1834 return getTruncateOrSignExtend(X, Ty); 1835 } 1836 1837 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2 1838 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) { 1839 if (SA->getNumOperands() == 2) { 1840 auto *SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0)); 1841 auto *SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1)); 1842 if (SMul && SC1) { 1843 if (auto *SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) { 1844 const APInt &C1 = SC1->getAPInt(); 1845 const APInt &C2 = SC2->getAPInt(); 1846 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && 1847 C2.ugt(C1) && C2.isPowerOf2()) 1848 return getAddExpr(getSignExtendExpr(SC1, Ty, Depth + 1), 1849 getSignExtendExpr(SMul, Ty, Depth + 1), 1850 SCEV::FlagAnyWrap, Depth + 1); 1851 } 1852 } 1853 } 1854 1855 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw> 1856 if (SA->hasNoSignedWrap()) { 1857 // If the addition does not sign overflow then we can, by definition, 1858 // commute the sign extension with the addition operation. 1859 SmallVector<const SCEV *, 4> Ops; 1860 for (const auto *Op : SA->operands()) 1861 Ops.push_back(getSignExtendExpr(Op, Ty, Depth + 1)); 1862 return getAddExpr(Ops, SCEV::FlagNSW, Depth + 1); 1863 } 1864 } 1865 // If the input value is a chrec scev, and we can prove that the value 1866 // did not overflow the old, smaller, value, we can sign extend all of the 1867 // operands (often constants). This allows analysis of something like 1868 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1869 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1870 if (AR->isAffine()) { 1871 const SCEV *Start = AR->getStart(); 1872 const SCEV *Step = AR->getStepRecurrence(*this); 1873 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1874 const Loop *L = AR->getLoop(); 1875 1876 if (!AR->hasNoSignedWrap()) { 1877 auto NewFlags = proveNoWrapViaConstantRanges(AR); 1878 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags); 1879 } 1880 1881 // If we have special knowledge that this addrec won't overflow, 1882 // we don't need to do any further analysis. 1883 if (AR->hasNoSignedWrap()) 1884 return getAddRecExpr( 1885 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1), 1886 getSignExtendExpr(Step, Ty, Depth + 1), L, SCEV::FlagNSW); 1887 1888 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1889 // Note that this serves two purposes: It filters out loops that are 1890 // simply not analyzable, and it covers the case where this code is 1891 // being called from within backedge-taken count analysis, such that 1892 // attempting to ask for the backedge-taken count would likely result 1893 // in infinite recursion. In the later case, the analysis code will 1894 // cope with a conservative value, and it will take care to purge 1895 // that value once it has finished. 1896 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1897 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1898 // Manually compute the final value for AR, checking for 1899 // overflow. 1900 1901 // Check whether the backedge-taken count can be losslessly casted to 1902 // the addrec's type. The count is always unsigned. 1903 const SCEV *CastedMaxBECount = 1904 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1905 const SCEV *RecastedMaxBECount = 1906 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1907 if (MaxBECount == RecastedMaxBECount) { 1908 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1909 // Check whether Start+Step*MaxBECount has no signed overflow. 1910 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step, 1911 SCEV::FlagAnyWrap, Depth + 1); 1912 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul, 1913 SCEV::FlagAnyWrap, 1914 Depth + 1), 1915 WideTy, Depth + 1); 1916 const SCEV *WideStart = getSignExtendExpr(Start, WideTy, Depth + 1); 1917 const SCEV *WideMaxBECount = 1918 getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1); 1919 const SCEV *OperandExtendedAdd = 1920 getAddExpr(WideStart, 1921 getMulExpr(WideMaxBECount, 1922 getSignExtendExpr(Step, WideTy, Depth + 1), 1923 SCEV::FlagAnyWrap, Depth + 1), 1924 SCEV::FlagAnyWrap, Depth + 1); 1925 if (SAdd == OperandExtendedAdd) { 1926 // Cache knowledge of AR NSW, which is propagated to this AddRec. 1927 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1928 // Return the expression with the addrec on the outside. 1929 return getAddRecExpr( 1930 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, 1931 Depth + 1), 1932 getSignExtendExpr(Step, Ty, Depth + 1), L, 1933 AR->getNoWrapFlags()); 1934 } 1935 // Similar to above, only this time treat the step value as unsigned. 1936 // This covers loops that count up with an unsigned step. 1937 OperandExtendedAdd = 1938 getAddExpr(WideStart, 1939 getMulExpr(WideMaxBECount, 1940 getZeroExtendExpr(Step, WideTy, Depth + 1), 1941 SCEV::FlagAnyWrap, Depth + 1), 1942 SCEV::FlagAnyWrap, Depth + 1); 1943 if (SAdd == OperandExtendedAdd) { 1944 // If AR wraps around then 1945 // 1946 // abs(Step) * MaxBECount > unsigned-max(AR->getType()) 1947 // => SAdd != OperandExtendedAdd 1948 // 1949 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=> 1950 // (SAdd == OperandExtendedAdd => AR is NW) 1951 1952 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); 1953 1954 // Return the expression with the addrec on the outside. 1955 return getAddRecExpr( 1956 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, 1957 Depth + 1), 1958 getZeroExtendExpr(Step, Ty, Depth + 1), L, 1959 AR->getNoWrapFlags()); 1960 } 1961 } 1962 } 1963 1964 // Normally, in the cases we can prove no-overflow via a 1965 // backedge guarding condition, we can also compute a backedge 1966 // taken count for the loop. The exceptions are assumptions and 1967 // guards present in the loop -- SCEV is not great at exploiting 1968 // these to compute max backedge taken counts, but can still use 1969 // these to prove lack of overflow. Use this fact to avoid 1970 // doing extra work that may not pay off. 1971 1972 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards || 1973 !AC.assumptions().empty()) { 1974 // If the backedge is guarded by a comparison with the pre-inc 1975 // value the addrec is safe. Also, if the entry is guarded by 1976 // a comparison with the start value and the backedge is 1977 // guarded by a comparison with the post-inc value, the addrec 1978 // is safe. 1979 ICmpInst::Predicate Pred; 1980 const SCEV *OverflowLimit = 1981 getSignedOverflowLimitForStep(Step, &Pred, this); 1982 if (OverflowLimit && 1983 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) || 1984 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) && 1985 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this), 1986 OverflowLimit)))) { 1987 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec. 1988 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1989 return getAddRecExpr( 1990 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1), 1991 getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags()); 1992 } 1993 } 1994 1995 // If Start and Step are constants, check if we can apply this 1996 // transformation: 1997 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2 1998 auto *SC1 = dyn_cast<SCEVConstant>(Start); 1999 auto *SC2 = dyn_cast<SCEVConstant>(Step); 2000 if (SC1 && SC2) { 2001 const APInt &C1 = SC1->getAPInt(); 2002 const APInt &C2 = SC2->getAPInt(); 2003 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) && 2004 C2.isPowerOf2()) { 2005 Start = getSignExtendExpr(Start, Ty, Depth + 1); 2006 const SCEV *NewAR = getAddRecExpr(getZero(AR->getType()), Step, L, 2007 AR->getNoWrapFlags()); 2008 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty, Depth + 1), 2009 SCEV::FlagAnyWrap, Depth + 1); 2010 } 2011 } 2012 2013 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) { 2014 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 2015 return getAddRecExpr( 2016 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1), 2017 getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags()); 2018 } 2019 } 2020 2021 // If the input value is provably positive and we could not simplify 2022 // away the sext build a zext instead. 2023 if (isKnownNonNegative(Op)) 2024 return getZeroExtendExpr(Op, Ty, Depth + 1); 2025 2026 // The cast wasn't folded; create an explicit cast node. 2027 // Recompute the insert position, as it may have been invalidated. 2028 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2029 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 2030 Op, Ty); 2031 UniqueSCEVs.InsertNode(S, IP); 2032 addToLoopUseLists(S); 2033 return S; 2034 } 2035 2036 /// getAnyExtendExpr - Return a SCEV for the given operand extended with 2037 /// unspecified bits out to the given type. 2038 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 2039 Type *Ty) { 2040 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 2041 "This is not an extending conversion!"); 2042 assert(isSCEVable(Ty) && 2043 "This is not a conversion to a SCEVable type!"); 2044 Ty = getEffectiveSCEVType(Ty); 2045 2046 // Sign-extend negative constants. 2047 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 2048 if (SC->getAPInt().isNegative()) 2049 return getSignExtendExpr(Op, Ty); 2050 2051 // Peel off a truncate cast. 2052 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 2053 const SCEV *NewOp = T->getOperand(); 2054 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 2055 return getAnyExtendExpr(NewOp, Ty); 2056 return getTruncateOrNoop(NewOp, Ty); 2057 } 2058 2059 // Next try a zext cast. If the cast is folded, use it. 2060 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 2061 if (!isa<SCEVZeroExtendExpr>(ZExt)) 2062 return ZExt; 2063 2064 // Next try a sext cast. If the cast is folded, use it. 2065 const SCEV *SExt = getSignExtendExpr(Op, Ty); 2066 if (!isa<SCEVSignExtendExpr>(SExt)) 2067 return SExt; 2068 2069 // Force the cast to be folded into the operands of an addrec. 2070 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 2071 SmallVector<const SCEV *, 4> Ops; 2072 for (const SCEV *Op : AR->operands()) 2073 Ops.push_back(getAnyExtendExpr(Op, Ty)); 2074 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW); 2075 } 2076 2077 // If the expression is obviously signed, use the sext cast value. 2078 if (isa<SCEVSMaxExpr>(Op)) 2079 return SExt; 2080 2081 // Absent any other information, use the zext cast value. 2082 return ZExt; 2083 } 2084 2085 /// Process the given Ops list, which is a list of operands to be added under 2086 /// the given scale, update the given map. This is a helper function for 2087 /// getAddRecExpr. As an example of what it does, given a sequence of operands 2088 /// that would form an add expression like this: 2089 /// 2090 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r) 2091 /// 2092 /// where A and B are constants, update the map with these values: 2093 /// 2094 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 2095 /// 2096 /// and add 13 + A*B*29 to AccumulatedConstant. 2097 /// This will allow getAddRecExpr to produce this: 2098 /// 2099 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 2100 /// 2101 /// This form often exposes folding opportunities that are hidden in 2102 /// the original operand list. 2103 /// 2104 /// Return true iff it appears that any interesting folding opportunities 2105 /// may be exposed. This helps getAddRecExpr short-circuit extra work in 2106 /// the common case where no interesting opportunities are present, and 2107 /// is also used as a check to avoid infinite recursion. 2108 static bool 2109 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 2110 SmallVectorImpl<const SCEV *> &NewOps, 2111 APInt &AccumulatedConstant, 2112 const SCEV *const *Ops, size_t NumOperands, 2113 const APInt &Scale, 2114 ScalarEvolution &SE) { 2115 bool Interesting = false; 2116 2117 // Iterate over the add operands. They are sorted, with constants first. 2118 unsigned i = 0; 2119 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 2120 ++i; 2121 // Pull a buried constant out to the outside. 2122 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 2123 Interesting = true; 2124 AccumulatedConstant += Scale * C->getAPInt(); 2125 } 2126 2127 // Next comes everything else. We're especially interested in multiplies 2128 // here, but they're in the middle, so just visit the rest with one loop. 2129 for (; i != NumOperands; ++i) { 2130 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 2131 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 2132 APInt NewScale = 2133 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt(); 2134 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 2135 // A multiplication of a constant with another add; recurse. 2136 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 2137 Interesting |= 2138 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 2139 Add->op_begin(), Add->getNumOperands(), 2140 NewScale, SE); 2141 } else { 2142 // A multiplication of a constant with some other value. Update 2143 // the map. 2144 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 2145 const SCEV *Key = SE.getMulExpr(MulOps); 2146 auto Pair = M.insert({Key, NewScale}); 2147 if (Pair.second) { 2148 NewOps.push_back(Pair.first->first); 2149 } else { 2150 Pair.first->second += NewScale; 2151 // The map already had an entry for this value, which may indicate 2152 // a folding opportunity. 2153 Interesting = true; 2154 } 2155 } 2156 } else { 2157 // An ordinary operand. Update the map. 2158 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 2159 M.insert({Ops[i], Scale}); 2160 if (Pair.second) { 2161 NewOps.push_back(Pair.first->first); 2162 } else { 2163 Pair.first->second += Scale; 2164 // The map already had an entry for this value, which may indicate 2165 // a folding opportunity. 2166 Interesting = true; 2167 } 2168 } 2169 } 2170 2171 return Interesting; 2172 } 2173 2174 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and 2175 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of 2176 // can't-overflow flags for the operation if possible. 2177 static SCEV::NoWrapFlags 2178 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type, 2179 const SmallVectorImpl<const SCEV *> &Ops, 2180 SCEV::NoWrapFlags Flags) { 2181 using namespace std::placeholders; 2182 2183 using OBO = OverflowingBinaryOperator; 2184 2185 bool CanAnalyze = 2186 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr; 2187 (void)CanAnalyze; 2188 assert(CanAnalyze && "don't call from other places!"); 2189 2190 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 2191 SCEV::NoWrapFlags SignOrUnsignWrap = 2192 ScalarEvolution::maskFlags(Flags, SignOrUnsignMask); 2193 2194 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 2195 auto IsKnownNonNegative = [&](const SCEV *S) { 2196 return SE->isKnownNonNegative(S); 2197 }; 2198 2199 if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative)) 2200 Flags = 2201 ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 2202 2203 SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask); 2204 2205 if (SignOrUnsignWrap != SignOrUnsignMask && Type == scAddExpr && 2206 Ops.size() == 2 && isa<SCEVConstant>(Ops[0])) { 2207 2208 // (A + C) --> (A + C)<nsw> if the addition does not sign overflow 2209 // (A + C) --> (A + C)<nuw> if the addition does not unsign overflow 2210 2211 const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt(); 2212 if (!(SignOrUnsignWrap & SCEV::FlagNSW)) { 2213 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion( 2214 Instruction::Add, C, OBO::NoSignedWrap); 2215 if (NSWRegion.contains(SE->getSignedRange(Ops[1]))) 2216 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW); 2217 } 2218 if (!(SignOrUnsignWrap & SCEV::FlagNUW)) { 2219 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion( 2220 Instruction::Add, C, OBO::NoUnsignedWrap); 2221 if (NUWRegion.contains(SE->getUnsignedRange(Ops[1]))) 2222 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW); 2223 } 2224 } 2225 2226 return Flags; 2227 } 2228 2229 bool ScalarEvolution::isAvailableAtLoopEntry(const SCEV *S, const Loop *L) { 2230 if (!isLoopInvariant(S, L)) 2231 return false; 2232 // If a value depends on a SCEVUnknown which is defined after the loop, we 2233 // conservatively assume that we cannot calculate it at the loop's entry. 2234 struct FindDominatedSCEVUnknown { 2235 bool Found = false; 2236 const Loop *L; 2237 DominatorTree &DT; 2238 LoopInfo &LI; 2239 2240 FindDominatedSCEVUnknown(const Loop *L, DominatorTree &DT, LoopInfo &LI) 2241 : L(L), DT(DT), LI(LI) {} 2242 2243 bool checkSCEVUnknown(const SCEVUnknown *SU) { 2244 if (auto *I = dyn_cast<Instruction>(SU->getValue())) { 2245 if (DT.dominates(L->getHeader(), I->getParent())) 2246 Found = true; 2247 else 2248 assert(DT.dominates(I->getParent(), L->getHeader()) && 2249 "No dominance relationship between SCEV and loop?"); 2250 } 2251 return false; 2252 } 2253 2254 bool follow(const SCEV *S) { 2255 switch (static_cast<SCEVTypes>(S->getSCEVType())) { 2256 case scConstant: 2257 return false; 2258 case scAddRecExpr: 2259 case scTruncate: 2260 case scZeroExtend: 2261 case scSignExtend: 2262 case scAddExpr: 2263 case scMulExpr: 2264 case scUMaxExpr: 2265 case scSMaxExpr: 2266 case scUDivExpr: 2267 return true; 2268 case scUnknown: 2269 return checkSCEVUnknown(cast<SCEVUnknown>(S)); 2270 case scCouldNotCompute: 2271 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 2272 } 2273 return false; 2274 } 2275 2276 bool isDone() { return Found; } 2277 }; 2278 2279 FindDominatedSCEVUnknown FSU(L, DT, LI); 2280 SCEVTraversal<FindDominatedSCEVUnknown> ST(FSU); 2281 ST.visitAll(S); 2282 return !FSU.Found; 2283 } 2284 2285 /// Get a canonical add expression, or something simpler if possible. 2286 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 2287 SCEV::NoWrapFlags Flags, 2288 unsigned Depth) { 2289 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && 2290 "only nuw or nsw allowed"); 2291 assert(!Ops.empty() && "Cannot get empty add!"); 2292 if (Ops.size() == 1) return Ops[0]; 2293 #ifndef NDEBUG 2294 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2295 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2296 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2297 "SCEVAddExpr operand types don't match!"); 2298 #endif 2299 2300 // Sort by complexity, this groups all similar expression types together. 2301 GroupByComplexity(Ops, &LI, DT); 2302 2303 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags); 2304 2305 // If there are any constants, fold them together. 2306 unsigned Idx = 0; 2307 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2308 ++Idx; 2309 assert(Idx < Ops.size()); 2310 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2311 // We found two constants, fold them together! 2312 Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt()); 2313 if (Ops.size() == 2) return Ops[0]; 2314 Ops.erase(Ops.begin()+1); // Erase the folded element 2315 LHSC = cast<SCEVConstant>(Ops[0]); 2316 } 2317 2318 // If we are left with a constant zero being added, strip it off. 2319 if (LHSC->getValue()->isZero()) { 2320 Ops.erase(Ops.begin()); 2321 --Idx; 2322 } 2323 2324 if (Ops.size() == 1) return Ops[0]; 2325 } 2326 2327 // Limit recursion calls depth. 2328 if (Depth > MaxArithDepth) 2329 return getOrCreateAddExpr(Ops, Flags); 2330 2331 // Okay, check to see if the same value occurs in the operand list more than 2332 // once. If so, merge them together into an multiply expression. Since we 2333 // sorted the list, these values are required to be adjacent. 2334 Type *Ty = Ops[0]->getType(); 2335 bool FoundMatch = false; 2336 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i) 2337 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 2338 // Scan ahead to count how many equal operands there are. 2339 unsigned Count = 2; 2340 while (i+Count != e && Ops[i+Count] == Ops[i]) 2341 ++Count; 2342 // Merge the values into a multiply. 2343 const SCEV *Scale = getConstant(Ty, Count); 2344 const SCEV *Mul = getMulExpr(Scale, Ops[i], SCEV::FlagAnyWrap, Depth + 1); 2345 if (Ops.size() == Count) 2346 return Mul; 2347 Ops[i] = Mul; 2348 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count); 2349 --i; e -= Count - 1; 2350 FoundMatch = true; 2351 } 2352 if (FoundMatch) 2353 return getAddExpr(Ops, Flags); 2354 2355 // Check for truncates. If all the operands are truncated from the same 2356 // type, see if factoring out the truncate would permit the result to be 2357 // folded. eg., n*trunc(x) + m*trunc(y) --> trunc(trunc(m)*x + trunc(n)*y) 2358 // if the contents of the resulting outer trunc fold to something simple. 2359 auto FindTruncSrcType = [&]() -> Type * { 2360 // We're ultimately looking to fold an addrec of truncs and muls of only 2361 // constants and truncs, so if we find any other types of SCEV 2362 // as operands of the addrec then we bail and return nullptr here. 2363 // Otherwise, we return the type of the operand of a trunc that we find. 2364 if (auto *T = dyn_cast<SCEVTruncateExpr>(Ops[Idx])) 2365 return T->getOperand()->getType(); 2366 if (const auto *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 2367 const auto *LastOp = Mul->getOperand(Mul->getNumOperands() - 1); 2368 if (const auto *T = dyn_cast<SCEVTruncateExpr>(LastOp)) 2369 return T->getOperand()->getType(); 2370 } 2371 return nullptr; 2372 }; 2373 if (auto *SrcType = FindTruncSrcType()) { 2374 SmallVector<const SCEV *, 8> LargeOps; 2375 bool Ok = true; 2376 // Check all the operands to see if they can be represented in the 2377 // source type of the truncate. 2378 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 2379 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 2380 if (T->getOperand()->getType() != SrcType) { 2381 Ok = false; 2382 break; 2383 } 2384 LargeOps.push_back(T->getOperand()); 2385 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 2386 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 2387 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 2388 SmallVector<const SCEV *, 8> LargeMulOps; 2389 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 2390 if (const SCEVTruncateExpr *T = 2391 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 2392 if (T->getOperand()->getType() != SrcType) { 2393 Ok = false; 2394 break; 2395 } 2396 LargeMulOps.push_back(T->getOperand()); 2397 } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) { 2398 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 2399 } else { 2400 Ok = false; 2401 break; 2402 } 2403 } 2404 if (Ok) 2405 LargeOps.push_back(getMulExpr(LargeMulOps, SCEV::FlagAnyWrap, Depth + 1)); 2406 } else { 2407 Ok = false; 2408 break; 2409 } 2410 } 2411 if (Ok) { 2412 // Evaluate the expression in the larger type. 2413 const SCEV *Fold = getAddExpr(LargeOps, Flags, Depth + 1); 2414 // If it folds to something simple, use it. Otherwise, don't. 2415 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 2416 return getTruncateExpr(Fold, Ty); 2417 } 2418 } 2419 2420 // Skip past any other cast SCEVs. 2421 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 2422 ++Idx; 2423 2424 // If there are add operands they would be next. 2425 if (Idx < Ops.size()) { 2426 bool DeletedAdd = false; 2427 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 2428 if (Ops.size() > AddOpsInlineThreshold || 2429 Add->getNumOperands() > AddOpsInlineThreshold) 2430 break; 2431 // If we have an add, expand the add operands onto the end of the operands 2432 // list. 2433 Ops.erase(Ops.begin()+Idx); 2434 Ops.append(Add->op_begin(), Add->op_end()); 2435 DeletedAdd = true; 2436 } 2437 2438 // If we deleted at least one add, we added operands to the end of the list, 2439 // and they are not necessarily sorted. Recurse to resort and resimplify 2440 // any operands we just acquired. 2441 if (DeletedAdd) 2442 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1); 2443 } 2444 2445 // Skip over the add expression until we get to a multiply. 2446 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 2447 ++Idx; 2448 2449 // Check to see if there are any folding opportunities present with 2450 // operands multiplied by constant values. 2451 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 2452 uint64_t BitWidth = getTypeSizeInBits(Ty); 2453 DenseMap<const SCEV *, APInt> M; 2454 SmallVector<const SCEV *, 8> NewOps; 2455 APInt AccumulatedConstant(BitWidth, 0); 2456 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 2457 Ops.data(), Ops.size(), 2458 APInt(BitWidth, 1), *this)) { 2459 struct APIntCompare { 2460 bool operator()(const APInt &LHS, const APInt &RHS) const { 2461 return LHS.ult(RHS); 2462 } 2463 }; 2464 2465 // Some interesting folding opportunity is present, so its worthwhile to 2466 // re-generate the operands list. Group the operands by constant scale, 2467 // to avoid multiplying by the same constant scale multiple times. 2468 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 2469 for (const SCEV *NewOp : NewOps) 2470 MulOpLists[M.find(NewOp)->second].push_back(NewOp); 2471 // Re-generate the operands list. 2472 Ops.clear(); 2473 if (AccumulatedConstant != 0) 2474 Ops.push_back(getConstant(AccumulatedConstant)); 2475 for (auto &MulOp : MulOpLists) 2476 if (MulOp.first != 0) 2477 Ops.push_back(getMulExpr( 2478 getConstant(MulOp.first), 2479 getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1), 2480 SCEV::FlagAnyWrap, Depth + 1)); 2481 if (Ops.empty()) 2482 return getZero(Ty); 2483 if (Ops.size() == 1) 2484 return Ops[0]; 2485 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1); 2486 } 2487 } 2488 2489 // If we are adding something to a multiply expression, make sure the 2490 // something is not already an operand of the multiply. If so, merge it into 2491 // the multiply. 2492 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 2493 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 2494 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 2495 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 2496 if (isa<SCEVConstant>(MulOpSCEV)) 2497 continue; 2498 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 2499 if (MulOpSCEV == Ops[AddOp]) { 2500 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 2501 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 2502 if (Mul->getNumOperands() != 2) { 2503 // If the multiply has more than two operands, we must get the 2504 // Y*Z term. 2505 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 2506 Mul->op_begin()+MulOp); 2507 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 2508 InnerMul = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1); 2509 } 2510 SmallVector<const SCEV *, 2> TwoOps = {getOne(Ty), InnerMul}; 2511 const SCEV *AddOne = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1); 2512 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV, 2513 SCEV::FlagAnyWrap, Depth + 1); 2514 if (Ops.size() == 2) return OuterMul; 2515 if (AddOp < Idx) { 2516 Ops.erase(Ops.begin()+AddOp); 2517 Ops.erase(Ops.begin()+Idx-1); 2518 } else { 2519 Ops.erase(Ops.begin()+Idx); 2520 Ops.erase(Ops.begin()+AddOp-1); 2521 } 2522 Ops.push_back(OuterMul); 2523 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1); 2524 } 2525 2526 // Check this multiply against other multiplies being added together. 2527 for (unsigned OtherMulIdx = Idx+1; 2528 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 2529 ++OtherMulIdx) { 2530 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 2531 // If MulOp occurs in OtherMul, we can fold the two multiplies 2532 // together. 2533 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 2534 OMulOp != e; ++OMulOp) 2535 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 2536 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 2537 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 2538 if (Mul->getNumOperands() != 2) { 2539 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 2540 Mul->op_begin()+MulOp); 2541 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 2542 InnerMul1 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1); 2543 } 2544 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 2545 if (OtherMul->getNumOperands() != 2) { 2546 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 2547 OtherMul->op_begin()+OMulOp); 2548 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end()); 2549 InnerMul2 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1); 2550 } 2551 SmallVector<const SCEV *, 2> TwoOps = {InnerMul1, InnerMul2}; 2552 const SCEV *InnerMulSum = 2553 getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1); 2554 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum, 2555 SCEV::FlagAnyWrap, Depth + 1); 2556 if (Ops.size() == 2) return OuterMul; 2557 Ops.erase(Ops.begin()+Idx); 2558 Ops.erase(Ops.begin()+OtherMulIdx-1); 2559 Ops.push_back(OuterMul); 2560 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1); 2561 } 2562 } 2563 } 2564 } 2565 2566 // If there are any add recurrences in the operands list, see if any other 2567 // added values are loop invariant. If so, we can fold them into the 2568 // recurrence. 2569 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 2570 ++Idx; 2571 2572 // Scan over all recurrences, trying to fold loop invariants into them. 2573 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 2574 // Scan all of the other operands to this add and add them to the vector if 2575 // they are loop invariant w.r.t. the recurrence. 2576 SmallVector<const SCEV *, 8> LIOps; 2577 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 2578 const Loop *AddRecLoop = AddRec->getLoop(); 2579 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2580 if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) { 2581 LIOps.push_back(Ops[i]); 2582 Ops.erase(Ops.begin()+i); 2583 --i; --e; 2584 } 2585 2586 // If we found some loop invariants, fold them into the recurrence. 2587 if (!LIOps.empty()) { 2588 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 2589 LIOps.push_back(AddRec->getStart()); 2590 2591 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 2592 AddRec->op_end()); 2593 // This follows from the fact that the no-wrap flags on the outer add 2594 // expression are applicable on the 0th iteration, when the add recurrence 2595 // will be equal to its start value. 2596 AddRecOps[0] = getAddExpr(LIOps, Flags, Depth + 1); 2597 2598 // Build the new addrec. Propagate the NUW and NSW flags if both the 2599 // outer add and the inner addrec are guaranteed to have no overflow. 2600 // Always propagate NW. 2601 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW)); 2602 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags); 2603 2604 // If all of the other operands were loop invariant, we are done. 2605 if (Ops.size() == 1) return NewRec; 2606 2607 // Otherwise, add the folded AddRec by the non-invariant parts. 2608 for (unsigned i = 0;; ++i) 2609 if (Ops[i] == AddRec) { 2610 Ops[i] = NewRec; 2611 break; 2612 } 2613 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1); 2614 } 2615 2616 // Okay, if there weren't any loop invariants to be folded, check to see if 2617 // there are multiple AddRec's with the same loop induction variable being 2618 // added together. If so, we can fold them. 2619 for (unsigned OtherIdx = Idx+1; 2620 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 2621 ++OtherIdx) { 2622 // We expect the AddRecExpr's to be sorted in reverse dominance order, 2623 // so that the 1st found AddRecExpr is dominated by all others. 2624 assert(DT.dominates( 2625 cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(), 2626 AddRec->getLoop()->getHeader()) && 2627 "AddRecExprs are not sorted in reverse dominance order?"); 2628 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 2629 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L> 2630 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 2631 AddRec->op_end()); 2632 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 2633 ++OtherIdx) { 2634 const auto *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 2635 if (OtherAddRec->getLoop() == AddRecLoop) { 2636 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); 2637 i != e; ++i) { 2638 if (i >= AddRecOps.size()) { 2639 AddRecOps.append(OtherAddRec->op_begin()+i, 2640 OtherAddRec->op_end()); 2641 break; 2642 } 2643 SmallVector<const SCEV *, 2> TwoOps = { 2644 AddRecOps[i], OtherAddRec->getOperand(i)}; 2645 AddRecOps[i] = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1); 2646 } 2647 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 2648 } 2649 } 2650 // Step size has changed, so we cannot guarantee no self-wraparound. 2651 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap); 2652 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1); 2653 } 2654 } 2655 2656 // Otherwise couldn't fold anything into this recurrence. Move onto the 2657 // next one. 2658 } 2659 2660 // Okay, it looks like we really DO need an add expr. Check to see if we 2661 // already have one, otherwise create a new one. 2662 return getOrCreateAddExpr(Ops, Flags); 2663 } 2664 2665 const SCEV * 2666 ScalarEvolution::getOrCreateAddExpr(SmallVectorImpl<const SCEV *> &Ops, 2667 SCEV::NoWrapFlags Flags) { 2668 FoldingSetNodeID ID; 2669 ID.AddInteger(scAddExpr); 2670 for (const SCEV *Op : Ops) 2671 ID.AddPointer(Op); 2672 void *IP = nullptr; 2673 SCEVAddExpr *S = 2674 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2675 if (!S) { 2676 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2677 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2678 S = new (SCEVAllocator) 2679 SCEVAddExpr(ID.Intern(SCEVAllocator), O, Ops.size()); 2680 UniqueSCEVs.InsertNode(S, IP); 2681 addToLoopUseLists(S); 2682 } 2683 S->setNoWrapFlags(Flags); 2684 return S; 2685 } 2686 2687 const SCEV * 2688 ScalarEvolution::getOrCreateMulExpr(SmallVectorImpl<const SCEV *> &Ops, 2689 SCEV::NoWrapFlags Flags) { 2690 FoldingSetNodeID ID; 2691 ID.AddInteger(scMulExpr); 2692 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2693 ID.AddPointer(Ops[i]); 2694 void *IP = nullptr; 2695 SCEVMulExpr *S = 2696 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2697 if (!S) { 2698 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2699 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2700 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 2701 O, Ops.size()); 2702 UniqueSCEVs.InsertNode(S, IP); 2703 addToLoopUseLists(S); 2704 } 2705 S->setNoWrapFlags(Flags); 2706 return S; 2707 } 2708 2709 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) { 2710 uint64_t k = i*j; 2711 if (j > 1 && k / j != i) Overflow = true; 2712 return k; 2713 } 2714 2715 /// Compute the result of "n choose k", the binomial coefficient. If an 2716 /// intermediate computation overflows, Overflow will be set and the return will 2717 /// be garbage. Overflow is not cleared on absence of overflow. 2718 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) { 2719 // We use the multiplicative formula: 2720 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 . 2721 // At each iteration, we take the n-th term of the numeral and divide by the 2722 // (k-n)th term of the denominator. This division will always produce an 2723 // integral result, and helps reduce the chance of overflow in the 2724 // intermediate computations. However, we can still overflow even when the 2725 // final result would fit. 2726 2727 if (n == 0 || n == k) return 1; 2728 if (k > n) return 0; 2729 2730 if (k > n/2) 2731 k = n-k; 2732 2733 uint64_t r = 1; 2734 for (uint64_t i = 1; i <= k; ++i) { 2735 r = umul_ov(r, n-(i-1), Overflow); 2736 r /= i; 2737 } 2738 return r; 2739 } 2740 2741 /// Determine if any of the operands in this SCEV are a constant or if 2742 /// any of the add or multiply expressions in this SCEV contain a constant. 2743 static bool containsConstantInAddMulChain(const SCEV *StartExpr) { 2744 struct FindConstantInAddMulChain { 2745 bool FoundConstant = false; 2746 2747 bool follow(const SCEV *S) { 2748 FoundConstant |= isa<SCEVConstant>(S); 2749 return isa<SCEVAddExpr>(S) || isa<SCEVMulExpr>(S); 2750 } 2751 2752 bool isDone() const { 2753 return FoundConstant; 2754 } 2755 }; 2756 2757 FindConstantInAddMulChain F; 2758 SCEVTraversal<FindConstantInAddMulChain> ST(F); 2759 ST.visitAll(StartExpr); 2760 return F.FoundConstant; 2761 } 2762 2763 /// Get a canonical multiply expression, or something simpler if possible. 2764 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 2765 SCEV::NoWrapFlags Flags, 2766 unsigned Depth) { 2767 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) && 2768 "only nuw or nsw allowed"); 2769 assert(!Ops.empty() && "Cannot get empty mul!"); 2770 if (Ops.size() == 1) return Ops[0]; 2771 #ifndef NDEBUG 2772 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2773 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2774 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2775 "SCEVMulExpr operand types don't match!"); 2776 #endif 2777 2778 // Sort by complexity, this groups all similar expression types together. 2779 GroupByComplexity(Ops, &LI, DT); 2780 2781 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags); 2782 2783 // Limit recursion calls depth. 2784 if (Depth > MaxArithDepth) 2785 return getOrCreateMulExpr(Ops, Flags); 2786 2787 // If there are any constants, fold them together. 2788 unsigned Idx = 0; 2789 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2790 2791 // C1*(C2+V) -> C1*C2 + C1*V 2792 if (Ops.size() == 2) 2793 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 2794 // If any of Add's ops are Adds or Muls with a constant, 2795 // apply this transformation as well. 2796 if (Add->getNumOperands() == 2) 2797 // TODO: There are some cases where this transformation is not 2798 // profitable, for example: 2799 // Add = (C0 + X) * Y + Z. 2800 // Maybe the scope of this transformation should be narrowed down. 2801 if (containsConstantInAddMulChain(Add)) 2802 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0), 2803 SCEV::FlagAnyWrap, Depth + 1), 2804 getMulExpr(LHSC, Add->getOperand(1), 2805 SCEV::FlagAnyWrap, Depth + 1), 2806 SCEV::FlagAnyWrap, Depth + 1); 2807 2808 ++Idx; 2809 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2810 // We found two constants, fold them together! 2811 ConstantInt *Fold = 2812 ConstantInt::get(getContext(), LHSC->getAPInt() * RHSC->getAPInt()); 2813 Ops[0] = getConstant(Fold); 2814 Ops.erase(Ops.begin()+1); // Erase the folded element 2815 if (Ops.size() == 1) return Ops[0]; 2816 LHSC = cast<SCEVConstant>(Ops[0]); 2817 } 2818 2819 // If we are left with a constant one being multiplied, strip it off. 2820 if (cast<SCEVConstant>(Ops[0])->getValue()->isOne()) { 2821 Ops.erase(Ops.begin()); 2822 --Idx; 2823 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 2824 // If we have a multiply of zero, it will always be zero. 2825 return Ops[0]; 2826 } else if (Ops[0]->isAllOnesValue()) { 2827 // If we have a mul by -1 of an add, try distributing the -1 among the 2828 // add operands. 2829 if (Ops.size() == 2) { 2830 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 2831 SmallVector<const SCEV *, 4> NewOps; 2832 bool AnyFolded = false; 2833 for (const SCEV *AddOp : Add->operands()) { 2834 const SCEV *Mul = getMulExpr(Ops[0], AddOp, SCEV::FlagAnyWrap, 2835 Depth + 1); 2836 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 2837 NewOps.push_back(Mul); 2838 } 2839 if (AnyFolded) 2840 return getAddExpr(NewOps, SCEV::FlagAnyWrap, Depth + 1); 2841 } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) { 2842 // Negation preserves a recurrence's no self-wrap property. 2843 SmallVector<const SCEV *, 4> Operands; 2844 for (const SCEV *AddRecOp : AddRec->operands()) 2845 Operands.push_back(getMulExpr(Ops[0], AddRecOp, SCEV::FlagAnyWrap, 2846 Depth + 1)); 2847 2848 return getAddRecExpr(Operands, AddRec->getLoop(), 2849 AddRec->getNoWrapFlags(SCEV::FlagNW)); 2850 } 2851 } 2852 } 2853 2854 if (Ops.size() == 1) 2855 return Ops[0]; 2856 } 2857 2858 // Skip over the add expression until we get to a multiply. 2859 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 2860 ++Idx; 2861 2862 // If there are mul operands inline them all into this expression. 2863 if (Idx < Ops.size()) { 2864 bool DeletedMul = false; 2865 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 2866 if (Ops.size() > MulOpsInlineThreshold) 2867 break; 2868 // If we have an mul, expand the mul operands onto the end of the 2869 // operands list. 2870 Ops.erase(Ops.begin()+Idx); 2871 Ops.append(Mul->op_begin(), Mul->op_end()); 2872 DeletedMul = true; 2873 } 2874 2875 // If we deleted at least one mul, we added operands to the end of the 2876 // list, and they are not necessarily sorted. Recurse to resort and 2877 // resimplify any operands we just acquired. 2878 if (DeletedMul) 2879 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1); 2880 } 2881 2882 // If there are any add recurrences in the operands list, see if any other 2883 // added values are loop invariant. If so, we can fold them into the 2884 // recurrence. 2885 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 2886 ++Idx; 2887 2888 // Scan over all recurrences, trying to fold loop invariants into them. 2889 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 2890 // Scan all of the other operands to this mul and add them to the vector 2891 // if they are loop invariant w.r.t. the recurrence. 2892 SmallVector<const SCEV *, 8> LIOps; 2893 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 2894 const Loop *AddRecLoop = AddRec->getLoop(); 2895 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2896 if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) { 2897 LIOps.push_back(Ops[i]); 2898 Ops.erase(Ops.begin()+i); 2899 --i; --e; 2900 } 2901 2902 // If we found some loop invariants, fold them into the recurrence. 2903 if (!LIOps.empty()) { 2904 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 2905 SmallVector<const SCEV *, 4> NewOps; 2906 NewOps.reserve(AddRec->getNumOperands()); 2907 const SCEV *Scale = getMulExpr(LIOps, SCEV::FlagAnyWrap, Depth + 1); 2908 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 2909 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i), 2910 SCEV::FlagAnyWrap, Depth + 1)); 2911 2912 // Build the new addrec. Propagate the NUW and NSW flags if both the 2913 // outer mul and the inner addrec are guaranteed to have no overflow. 2914 // 2915 // No self-wrap cannot be guaranteed after changing the step size, but 2916 // will be inferred if either NUW or NSW is true. 2917 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW)); 2918 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags); 2919 2920 // If all of the other operands were loop invariant, we are done. 2921 if (Ops.size() == 1) return NewRec; 2922 2923 // Otherwise, multiply the folded AddRec by the non-invariant parts. 2924 for (unsigned i = 0;; ++i) 2925 if (Ops[i] == AddRec) { 2926 Ops[i] = NewRec; 2927 break; 2928 } 2929 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1); 2930 } 2931 2932 // Okay, if there weren't any loop invariants to be folded, check to see 2933 // if there are multiple AddRec's with the same loop induction variable 2934 // being multiplied together. If so, we can fold them. 2935 2936 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L> 2937 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [ 2938 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z 2939 // ]]],+,...up to x=2n}. 2940 // Note that the arguments to choose() are always integers with values 2941 // known at compile time, never SCEV objects. 2942 // 2943 // The implementation avoids pointless extra computations when the two 2944 // addrec's are of different length (mathematically, it's equivalent to 2945 // an infinite stream of zeros on the right). 2946 bool OpsModified = false; 2947 for (unsigned OtherIdx = Idx+1; 2948 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 2949 ++OtherIdx) { 2950 const SCEVAddRecExpr *OtherAddRec = 2951 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]); 2952 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop) 2953 continue; 2954 2955 // Limit max number of arguments to avoid creation of unreasonably big 2956 // SCEVAddRecs with very complex operands. 2957 if (AddRec->getNumOperands() + OtherAddRec->getNumOperands() - 1 > 2958 MaxAddRecSize) 2959 continue; 2960 2961 bool Overflow = false; 2962 Type *Ty = AddRec->getType(); 2963 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64; 2964 SmallVector<const SCEV*, 7> AddRecOps; 2965 for (int x = 0, xe = AddRec->getNumOperands() + 2966 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) { 2967 const SCEV *Term = getZero(Ty); 2968 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) { 2969 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow); 2970 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1), 2971 ze = std::min(x+1, (int)OtherAddRec->getNumOperands()); 2972 z < ze && !Overflow; ++z) { 2973 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow); 2974 uint64_t Coeff; 2975 if (LargerThan64Bits) 2976 Coeff = umul_ov(Coeff1, Coeff2, Overflow); 2977 else 2978 Coeff = Coeff1*Coeff2; 2979 const SCEV *CoeffTerm = getConstant(Ty, Coeff); 2980 const SCEV *Term1 = AddRec->getOperand(y-z); 2981 const SCEV *Term2 = OtherAddRec->getOperand(z); 2982 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1, Term2, 2983 SCEV::FlagAnyWrap, Depth + 1), 2984 SCEV::FlagAnyWrap, Depth + 1); 2985 } 2986 } 2987 AddRecOps.push_back(Term); 2988 } 2989 if (!Overflow) { 2990 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(), 2991 SCEV::FlagAnyWrap); 2992 if (Ops.size() == 2) return NewAddRec; 2993 Ops[Idx] = NewAddRec; 2994 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 2995 OpsModified = true; 2996 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec); 2997 if (!AddRec) 2998 break; 2999 } 3000 } 3001 if (OpsModified) 3002 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1); 3003 3004 // Otherwise couldn't fold anything into this recurrence. Move onto the 3005 // next one. 3006 } 3007 3008 // Okay, it looks like we really DO need an mul expr. Check to see if we 3009 // already have one, otherwise create a new one. 3010 return getOrCreateMulExpr(Ops, Flags); 3011 } 3012 3013 /// Represents an unsigned remainder expression based on unsigned division. 3014 const SCEV *ScalarEvolution::getURemExpr(const SCEV *LHS, 3015 const SCEV *RHS) { 3016 assert(getEffectiveSCEVType(LHS->getType()) == 3017 getEffectiveSCEVType(RHS->getType()) && 3018 "SCEVURemExpr operand types don't match!"); 3019 3020 // Short-circuit easy cases 3021 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 3022 // If constant is one, the result is trivial 3023 if (RHSC->getValue()->isOne()) 3024 return getZero(LHS->getType()); // X urem 1 --> 0 3025 3026 // If constant is a power of two, fold into a zext(trunc(LHS)). 3027 if (RHSC->getAPInt().isPowerOf2()) { 3028 Type *FullTy = LHS->getType(); 3029 Type *TruncTy = 3030 IntegerType::get(getContext(), RHSC->getAPInt().logBase2()); 3031 return getZeroExtendExpr(getTruncateExpr(LHS, TruncTy), FullTy); 3032 } 3033 } 3034 3035 // Fallback to %a == %x urem %y == %x -<nuw> ((%x udiv %y) *<nuw> %y) 3036 const SCEV *UDiv = getUDivExpr(LHS, RHS); 3037 const SCEV *Mult = getMulExpr(UDiv, RHS, SCEV::FlagNUW); 3038 return getMinusSCEV(LHS, Mult, SCEV::FlagNUW); 3039 } 3040 3041 /// Get a canonical unsigned division expression, or something simpler if 3042 /// possible. 3043 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 3044 const SCEV *RHS) { 3045 assert(getEffectiveSCEVType(LHS->getType()) == 3046 getEffectiveSCEVType(RHS->getType()) && 3047 "SCEVUDivExpr operand types don't match!"); 3048 3049 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 3050 if (RHSC->getValue()->isOne()) 3051 return LHS; // X udiv 1 --> x 3052 // If the denominator is zero, the result of the udiv is undefined. Don't 3053 // try to analyze it, because the resolution chosen here may differ from 3054 // the resolution chosen in other parts of the compiler. 3055 if (!RHSC->getValue()->isZero()) { 3056 // Determine if the division can be folded into the operands of 3057 // its operands. 3058 // TODO: Generalize this to non-constants by using known-bits information. 3059 Type *Ty = LHS->getType(); 3060 unsigned LZ = RHSC->getAPInt().countLeadingZeros(); 3061 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; 3062 // For non-power-of-two values, effectively round the value up to the 3063 // nearest power of two. 3064 if (!RHSC->getAPInt().isPowerOf2()) 3065 ++MaxShiftAmt; 3066 IntegerType *ExtTy = 3067 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 3068 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 3069 if (const SCEVConstant *Step = 3070 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) { 3071 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 3072 const APInt &StepInt = Step->getAPInt(); 3073 const APInt &DivInt = RHSC->getAPInt(); 3074 if (!StepInt.urem(DivInt) && 3075 getZeroExtendExpr(AR, ExtTy) == 3076 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 3077 getZeroExtendExpr(Step, ExtTy), 3078 AR->getLoop(), SCEV::FlagAnyWrap)) { 3079 SmallVector<const SCEV *, 4> Operands; 3080 for (const SCEV *Op : AR->operands()) 3081 Operands.push_back(getUDivExpr(Op, RHS)); 3082 return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW); 3083 } 3084 /// Get a canonical UDivExpr for a recurrence. 3085 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0. 3086 // We can currently only fold X%N if X is constant. 3087 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart()); 3088 if (StartC && !DivInt.urem(StepInt) && 3089 getZeroExtendExpr(AR, ExtTy) == 3090 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 3091 getZeroExtendExpr(Step, ExtTy), 3092 AR->getLoop(), SCEV::FlagAnyWrap)) { 3093 const APInt &StartInt = StartC->getAPInt(); 3094 const APInt &StartRem = StartInt.urem(StepInt); 3095 if (StartRem != 0) 3096 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step, 3097 AR->getLoop(), SCEV::FlagNW); 3098 } 3099 } 3100 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 3101 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 3102 SmallVector<const SCEV *, 4> Operands; 3103 for (const SCEV *Op : M->operands()) 3104 Operands.push_back(getZeroExtendExpr(Op, ExtTy)); 3105 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 3106 // Find an operand that's safely divisible. 3107 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 3108 const SCEV *Op = M->getOperand(i); 3109 const SCEV *Div = getUDivExpr(Op, RHSC); 3110 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 3111 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 3112 M->op_end()); 3113 Operands[i] = Div; 3114 return getMulExpr(Operands); 3115 } 3116 } 3117 } 3118 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 3119 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) { 3120 SmallVector<const SCEV *, 4> Operands; 3121 for (const SCEV *Op : A->operands()) 3122 Operands.push_back(getZeroExtendExpr(Op, ExtTy)); 3123 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 3124 Operands.clear(); 3125 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 3126 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 3127 if (isa<SCEVUDivExpr>(Op) || 3128 getMulExpr(Op, RHS) != A->getOperand(i)) 3129 break; 3130 Operands.push_back(Op); 3131 } 3132 if (Operands.size() == A->getNumOperands()) 3133 return getAddExpr(Operands); 3134 } 3135 } 3136 3137 // Fold if both operands are constant. 3138 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 3139 Constant *LHSCV = LHSC->getValue(); 3140 Constant *RHSCV = RHSC->getValue(); 3141 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 3142 RHSCV))); 3143 } 3144 } 3145 } 3146 3147 FoldingSetNodeID ID; 3148 ID.AddInteger(scUDivExpr); 3149 ID.AddPointer(LHS); 3150 ID.AddPointer(RHS); 3151 void *IP = nullptr; 3152 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 3153 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 3154 LHS, RHS); 3155 UniqueSCEVs.InsertNode(S, IP); 3156 addToLoopUseLists(S); 3157 return S; 3158 } 3159 3160 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) { 3161 APInt A = C1->getAPInt().abs(); 3162 APInt B = C2->getAPInt().abs(); 3163 uint32_t ABW = A.getBitWidth(); 3164 uint32_t BBW = B.getBitWidth(); 3165 3166 if (ABW > BBW) 3167 B = B.zext(ABW); 3168 else if (ABW < BBW) 3169 A = A.zext(BBW); 3170 3171 return APIntOps::GreatestCommonDivisor(std::move(A), std::move(B)); 3172 } 3173 3174 /// Get a canonical unsigned division expression, or something simpler if 3175 /// possible. There is no representation for an exact udiv in SCEV IR, but we 3176 /// can attempt to remove factors from the LHS and RHS. We can't do this when 3177 /// it's not exact because the udiv may be clearing bits. 3178 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS, 3179 const SCEV *RHS) { 3180 // TODO: we could try to find factors in all sorts of things, but for now we 3181 // just deal with u/exact (multiply, constant). See SCEVDivision towards the 3182 // end of this file for inspiration. 3183 3184 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS); 3185 if (!Mul || !Mul->hasNoUnsignedWrap()) 3186 return getUDivExpr(LHS, RHS); 3187 3188 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) { 3189 // If the mulexpr multiplies by a constant, then that constant must be the 3190 // first element of the mulexpr. 3191 if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) { 3192 if (LHSCst == RHSCst) { 3193 SmallVector<const SCEV *, 2> Operands; 3194 Operands.append(Mul->op_begin() + 1, Mul->op_end()); 3195 return getMulExpr(Operands); 3196 } 3197 3198 // We can't just assume that LHSCst divides RHSCst cleanly, it could be 3199 // that there's a factor provided by one of the other terms. We need to 3200 // check. 3201 APInt Factor = gcd(LHSCst, RHSCst); 3202 if (!Factor.isIntN(1)) { 3203 LHSCst = 3204 cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor))); 3205 RHSCst = 3206 cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor))); 3207 SmallVector<const SCEV *, 2> Operands; 3208 Operands.push_back(LHSCst); 3209 Operands.append(Mul->op_begin() + 1, Mul->op_end()); 3210 LHS = getMulExpr(Operands); 3211 RHS = RHSCst; 3212 Mul = dyn_cast<SCEVMulExpr>(LHS); 3213 if (!Mul) 3214 return getUDivExactExpr(LHS, RHS); 3215 } 3216 } 3217 } 3218 3219 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) { 3220 if (Mul->getOperand(i) == RHS) { 3221 SmallVector<const SCEV *, 2> Operands; 3222 Operands.append(Mul->op_begin(), Mul->op_begin() + i); 3223 Operands.append(Mul->op_begin() + i + 1, Mul->op_end()); 3224 return getMulExpr(Operands); 3225 } 3226 } 3227 3228 return getUDivExpr(LHS, RHS); 3229 } 3230 3231 /// Get an add recurrence expression for the specified loop. Simplify the 3232 /// expression as much as possible. 3233 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step, 3234 const Loop *L, 3235 SCEV::NoWrapFlags Flags) { 3236 SmallVector<const SCEV *, 4> Operands; 3237 Operands.push_back(Start); 3238 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 3239 if (StepChrec->getLoop() == L) { 3240 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 3241 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW)); 3242 } 3243 3244 Operands.push_back(Step); 3245 return getAddRecExpr(Operands, L, Flags); 3246 } 3247 3248 /// Get an add recurrence expression for the specified loop. Simplify the 3249 /// expression as much as possible. 3250 const SCEV * 3251 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 3252 const Loop *L, SCEV::NoWrapFlags Flags) { 3253 if (Operands.size() == 1) return Operands[0]; 3254 #ifndef NDEBUG 3255 Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); 3256 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 3257 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && 3258 "SCEVAddRecExpr operand types don't match!"); 3259 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 3260 assert(isLoopInvariant(Operands[i], L) && 3261 "SCEVAddRecExpr operand is not loop-invariant!"); 3262 #endif 3263 3264 if (Operands.back()->isZero()) { 3265 Operands.pop_back(); 3266 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X 3267 } 3268 3269 // It's tempting to want to call getMaxBackedgeTakenCount count here and 3270 // use that information to infer NUW and NSW flags. However, computing a 3271 // BE count requires calling getAddRecExpr, so we may not yet have a 3272 // meaningful BE count at this point (and if we don't, we'd be stuck 3273 // with a SCEVCouldNotCompute as the cached BE count). 3274 3275 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags); 3276 3277 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 3278 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 3279 const Loop *NestedLoop = NestedAR->getLoop(); 3280 if (L->contains(NestedLoop) 3281 ? (L->getLoopDepth() < NestedLoop->getLoopDepth()) 3282 : (!NestedLoop->contains(L) && 3283 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) { 3284 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 3285 NestedAR->op_end()); 3286 Operands[0] = NestedAR->getStart(); 3287 // AddRecs require their operands be loop-invariant with respect to their 3288 // loops. Don't perform this transformation if it would break this 3289 // requirement. 3290 bool AllInvariant = all_of( 3291 Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); }); 3292 3293 if (AllInvariant) { 3294 // Create a recurrence for the outer loop with the same step size. 3295 // 3296 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the 3297 // inner recurrence has the same property. 3298 SCEV::NoWrapFlags OuterFlags = 3299 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags()); 3300 3301 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags); 3302 AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) { 3303 return isLoopInvariant(Op, NestedLoop); 3304 }); 3305 3306 if (AllInvariant) { 3307 // Ok, both add recurrences are valid after the transformation. 3308 // 3309 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if 3310 // the outer recurrence has the same property. 3311 SCEV::NoWrapFlags InnerFlags = 3312 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags); 3313 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags); 3314 } 3315 } 3316 // Reset Operands to its original state. 3317 Operands[0] = NestedAR; 3318 } 3319 } 3320 3321 // Okay, it looks like we really DO need an addrec expr. Check to see if we 3322 // already have one, otherwise create a new one. 3323 FoldingSetNodeID ID; 3324 ID.AddInteger(scAddRecExpr); 3325 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 3326 ID.AddPointer(Operands[i]); 3327 ID.AddPointer(L); 3328 void *IP = nullptr; 3329 SCEVAddRecExpr *S = 3330 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 3331 if (!S) { 3332 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 3333 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 3334 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 3335 O, Operands.size(), L); 3336 UniqueSCEVs.InsertNode(S, IP); 3337 addToLoopUseLists(S); 3338 } 3339 S->setNoWrapFlags(Flags); 3340 return S; 3341 } 3342 3343 const SCEV * 3344 ScalarEvolution::getGEPExpr(GEPOperator *GEP, 3345 const SmallVectorImpl<const SCEV *> &IndexExprs) { 3346 const SCEV *BaseExpr = getSCEV(GEP->getPointerOperand()); 3347 // getSCEV(Base)->getType() has the same address space as Base->getType() 3348 // because SCEV::getType() preserves the address space. 3349 Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType()); 3350 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP 3351 // instruction to its SCEV, because the Instruction may be guarded by control 3352 // flow and the no-overflow bits may not be valid for the expression in any 3353 // context. This can be fixed similarly to how these flags are handled for 3354 // adds. 3355 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW 3356 : SCEV::FlagAnyWrap; 3357 3358 const SCEV *TotalOffset = getZero(IntPtrTy); 3359 // The array size is unimportant. The first thing we do on CurTy is getting 3360 // its element type. 3361 Type *CurTy = ArrayType::get(GEP->getSourceElementType(), 0); 3362 for (const SCEV *IndexExpr : IndexExprs) { 3363 // Compute the (potentially symbolic) offset in bytes for this index. 3364 if (StructType *STy = dyn_cast<StructType>(CurTy)) { 3365 // For a struct, add the member offset. 3366 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue(); 3367 unsigned FieldNo = Index->getZExtValue(); 3368 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo); 3369 3370 // Add the field offset to the running total offset. 3371 TotalOffset = getAddExpr(TotalOffset, FieldOffset); 3372 3373 // Update CurTy to the type of the field at Index. 3374 CurTy = STy->getTypeAtIndex(Index); 3375 } else { 3376 // Update CurTy to its element type. 3377 CurTy = cast<SequentialType>(CurTy)->getElementType(); 3378 // For an array, add the element offset, explicitly scaled. 3379 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy); 3380 // Getelementptr indices are signed. 3381 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy); 3382 3383 // Multiply the index by the element size to compute the element offset. 3384 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap); 3385 3386 // Add the element offset to the running total offset. 3387 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 3388 } 3389 } 3390 3391 // Add the total offset from all the GEP indices to the base. 3392 return getAddExpr(BaseExpr, TotalOffset, Wrap); 3393 } 3394 3395 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 3396 const SCEV *RHS) { 3397 SmallVector<const SCEV *, 2> Ops = {LHS, RHS}; 3398 return getSMaxExpr(Ops); 3399 } 3400 3401 const SCEV * 3402 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 3403 assert(!Ops.empty() && "Cannot get empty smax!"); 3404 if (Ops.size() == 1) return Ops[0]; 3405 #ifndef NDEBUG 3406 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 3407 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 3408 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 3409 "SCEVSMaxExpr operand types don't match!"); 3410 #endif 3411 3412 // Sort by complexity, this groups all similar expression types together. 3413 GroupByComplexity(Ops, &LI, DT); 3414 3415 // If there are any constants, fold them together. 3416 unsigned Idx = 0; 3417 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 3418 ++Idx; 3419 assert(Idx < Ops.size()); 3420 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 3421 // We found two constants, fold them together! 3422 ConstantInt *Fold = ConstantInt::get( 3423 getContext(), APIntOps::smax(LHSC->getAPInt(), RHSC->getAPInt())); 3424 Ops[0] = getConstant(Fold); 3425 Ops.erase(Ops.begin()+1); // Erase the folded element 3426 if (Ops.size() == 1) return Ops[0]; 3427 LHSC = cast<SCEVConstant>(Ops[0]); 3428 } 3429 3430 // If we are left with a constant minimum-int, strip it off. 3431 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 3432 Ops.erase(Ops.begin()); 3433 --Idx; 3434 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 3435 // If we have an smax with a constant maximum-int, it will always be 3436 // maximum-int. 3437 return Ops[0]; 3438 } 3439 3440 if (Ops.size() == 1) return Ops[0]; 3441 } 3442 3443 // Find the first SMax 3444 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 3445 ++Idx; 3446 3447 // Check to see if one of the operands is an SMax. If so, expand its operands 3448 // onto our operand list, and recurse to simplify. 3449 if (Idx < Ops.size()) { 3450 bool DeletedSMax = false; 3451 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 3452 Ops.erase(Ops.begin()+Idx); 3453 Ops.append(SMax->op_begin(), SMax->op_end()); 3454 DeletedSMax = true; 3455 } 3456 3457 if (DeletedSMax) 3458 return getSMaxExpr(Ops); 3459 } 3460 3461 // Okay, check to see if the same value occurs in the operand list twice. If 3462 // so, delete one. Since we sorted the list, these values are required to 3463 // be adjacent. 3464 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 3465 // X smax Y smax Y --> X smax Y 3466 // X smax Y --> X, if X is always greater than Y 3467 if (Ops[i] == Ops[i+1] || 3468 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 3469 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 3470 --i; --e; 3471 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 3472 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 3473 --i; --e; 3474 } 3475 3476 if (Ops.size() == 1) return Ops[0]; 3477 3478 assert(!Ops.empty() && "Reduced smax down to nothing!"); 3479 3480 // Okay, it looks like we really DO need an smax expr. Check to see if we 3481 // already have one, otherwise create a new one. 3482 FoldingSetNodeID ID; 3483 ID.AddInteger(scSMaxExpr); 3484 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 3485 ID.AddPointer(Ops[i]); 3486 void *IP = nullptr; 3487 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 3488 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 3489 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 3490 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 3491 O, Ops.size()); 3492 UniqueSCEVs.InsertNode(S, IP); 3493 addToLoopUseLists(S); 3494 return S; 3495 } 3496 3497 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 3498 const SCEV *RHS) { 3499 SmallVector<const SCEV *, 2> Ops = {LHS, RHS}; 3500 return getUMaxExpr(Ops); 3501 } 3502 3503 const SCEV * 3504 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 3505 assert(!Ops.empty() && "Cannot get empty umax!"); 3506 if (Ops.size() == 1) return Ops[0]; 3507 #ifndef NDEBUG 3508 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 3509 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 3510 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 3511 "SCEVUMaxExpr operand types don't match!"); 3512 #endif 3513 3514 // Sort by complexity, this groups all similar expression types together. 3515 GroupByComplexity(Ops, &LI, DT); 3516 3517 // If there are any constants, fold them together. 3518 unsigned Idx = 0; 3519 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 3520 ++Idx; 3521 assert(Idx < Ops.size()); 3522 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 3523 // We found two constants, fold them together! 3524 ConstantInt *Fold = ConstantInt::get( 3525 getContext(), APIntOps::umax(LHSC->getAPInt(), RHSC->getAPInt())); 3526 Ops[0] = getConstant(Fold); 3527 Ops.erase(Ops.begin()+1); // Erase the folded element 3528 if (Ops.size() == 1) return Ops[0]; 3529 LHSC = cast<SCEVConstant>(Ops[0]); 3530 } 3531 3532 // If we are left with a constant minimum-int, strip it off. 3533 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 3534 Ops.erase(Ops.begin()); 3535 --Idx; 3536 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 3537 // If we have an umax with a constant maximum-int, it will always be 3538 // maximum-int. 3539 return Ops[0]; 3540 } 3541 3542 if (Ops.size() == 1) return Ops[0]; 3543 } 3544 3545 // Find the first UMax 3546 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 3547 ++Idx; 3548 3549 // Check to see if one of the operands is a UMax. If so, expand its operands 3550 // onto our operand list, and recurse to simplify. 3551 if (Idx < Ops.size()) { 3552 bool DeletedUMax = false; 3553 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 3554 Ops.erase(Ops.begin()+Idx); 3555 Ops.append(UMax->op_begin(), UMax->op_end()); 3556 DeletedUMax = true; 3557 } 3558 3559 if (DeletedUMax) 3560 return getUMaxExpr(Ops); 3561 } 3562 3563 // Okay, check to see if the same value occurs in the operand list twice. If 3564 // so, delete one. Since we sorted the list, these values are required to 3565 // be adjacent. 3566 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 3567 // X umax Y umax Y --> X umax Y 3568 // X umax Y --> X, if X is always greater than Y 3569 if (Ops[i] == Ops[i+1] || 3570 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 3571 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 3572 --i; --e; 3573 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 3574 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 3575 --i; --e; 3576 } 3577 3578 if (Ops.size() == 1) return Ops[0]; 3579 3580 assert(!Ops.empty() && "Reduced umax down to nothing!"); 3581 3582 // Okay, it looks like we really DO need a umax expr. Check to see if we 3583 // already have one, otherwise create a new one. 3584 FoldingSetNodeID ID; 3585 ID.AddInteger(scUMaxExpr); 3586 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 3587 ID.AddPointer(Ops[i]); 3588 void *IP = nullptr; 3589 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 3590 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 3591 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 3592 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 3593 O, Ops.size()); 3594 UniqueSCEVs.InsertNode(S, IP); 3595 addToLoopUseLists(S); 3596 return S; 3597 } 3598 3599 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 3600 const SCEV *RHS) { 3601 // ~smax(~x, ~y) == smin(x, y). 3602 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 3603 } 3604 3605 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 3606 const SCEV *RHS) { 3607 // ~umax(~x, ~y) == umin(x, y) 3608 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 3609 } 3610 3611 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) { 3612 // We can bypass creating a target-independent 3613 // constant expression and then folding it back into a ConstantInt. 3614 // This is just a compile-time optimization. 3615 return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy)); 3616 } 3617 3618 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy, 3619 StructType *STy, 3620 unsigned FieldNo) { 3621 // We can bypass creating a target-independent 3622 // constant expression and then folding it back into a ConstantInt. 3623 // This is just a compile-time optimization. 3624 return getConstant( 3625 IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo)); 3626 } 3627 3628 const SCEV *ScalarEvolution::getUnknown(Value *V) { 3629 // Don't attempt to do anything other than create a SCEVUnknown object 3630 // here. createSCEV only calls getUnknown after checking for all other 3631 // interesting possibilities, and any other code that calls getUnknown 3632 // is doing so in order to hide a value from SCEV canonicalization. 3633 3634 FoldingSetNodeID ID; 3635 ID.AddInteger(scUnknown); 3636 ID.AddPointer(V); 3637 void *IP = nullptr; 3638 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { 3639 assert(cast<SCEVUnknown>(S)->getValue() == V && 3640 "Stale SCEVUnknown in uniquing map!"); 3641 return S; 3642 } 3643 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, 3644 FirstUnknown); 3645 FirstUnknown = cast<SCEVUnknown>(S); 3646 UniqueSCEVs.InsertNode(S, IP); 3647 return S; 3648 } 3649 3650 //===----------------------------------------------------------------------===// 3651 // Basic SCEV Analysis and PHI Idiom Recognition Code 3652 // 3653 3654 /// Test if values of the given type are analyzable within the SCEV 3655 /// framework. This primarily includes integer types, and it can optionally 3656 /// include pointer types if the ScalarEvolution class has access to 3657 /// target-specific information. 3658 bool ScalarEvolution::isSCEVable(Type *Ty) const { 3659 // Integers and pointers are always SCEVable. 3660 return Ty->isIntegerTy() || Ty->isPointerTy(); 3661 } 3662 3663 /// Return the size in bits of the specified type, for which isSCEVable must 3664 /// return true. 3665 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const { 3666 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 3667 return getDataLayout().getTypeSizeInBits(Ty); 3668 } 3669 3670 /// Return a type with the same bitwidth as the given type and which represents 3671 /// how SCEV will treat the given type, for which isSCEVable must return 3672 /// true. For pointer types, this is the pointer-sized integer type. 3673 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const { 3674 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 3675 3676 if (Ty->isIntegerTy()) 3677 return Ty; 3678 3679 // The only other support type is pointer. 3680 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 3681 return getDataLayout().getIntPtrType(Ty); 3682 } 3683 3684 Type *ScalarEvolution::getWiderType(Type *T1, Type *T2) const { 3685 return getTypeSizeInBits(T1) >= getTypeSizeInBits(T2) ? T1 : T2; 3686 } 3687 3688 const SCEV *ScalarEvolution::getCouldNotCompute() { 3689 return CouldNotCompute.get(); 3690 } 3691 3692 bool ScalarEvolution::checkValidity(const SCEV *S) const { 3693 bool ContainsNulls = SCEVExprContains(S, [](const SCEV *S) { 3694 auto *SU = dyn_cast<SCEVUnknown>(S); 3695 return SU && SU->getValue() == nullptr; 3696 }); 3697 3698 return !ContainsNulls; 3699 } 3700 3701 bool ScalarEvolution::containsAddRecurrence(const SCEV *S) { 3702 HasRecMapType::iterator I = HasRecMap.find(S); 3703 if (I != HasRecMap.end()) 3704 return I->second; 3705 3706 bool FoundAddRec = SCEVExprContains(S, isa<SCEVAddRecExpr, const SCEV *>); 3707 HasRecMap.insert({S, FoundAddRec}); 3708 return FoundAddRec; 3709 } 3710 3711 /// Try to split a SCEVAddExpr into a pair of {SCEV, ConstantInt}. 3712 /// If \p S is a SCEVAddExpr and is composed of a sub SCEV S' and an 3713 /// offset I, then return {S', I}, else return {\p S, nullptr}. 3714 static std::pair<const SCEV *, ConstantInt *> splitAddExpr(const SCEV *S) { 3715 const auto *Add = dyn_cast<SCEVAddExpr>(S); 3716 if (!Add) 3717 return {S, nullptr}; 3718 3719 if (Add->getNumOperands() != 2) 3720 return {S, nullptr}; 3721 3722 auto *ConstOp = dyn_cast<SCEVConstant>(Add->getOperand(0)); 3723 if (!ConstOp) 3724 return {S, nullptr}; 3725 3726 return {Add->getOperand(1), ConstOp->getValue()}; 3727 } 3728 3729 /// Return the ValueOffsetPair set for \p S. \p S can be represented 3730 /// by the value and offset from any ValueOffsetPair in the set. 3731 SetVector<ScalarEvolution::ValueOffsetPair> * 3732 ScalarEvolution::getSCEVValues(const SCEV *S) { 3733 ExprValueMapType::iterator SI = ExprValueMap.find_as(S); 3734 if (SI == ExprValueMap.end()) 3735 return nullptr; 3736 #ifndef NDEBUG 3737 if (VerifySCEVMap) { 3738 // Check there is no dangling Value in the set returned. 3739 for (const auto &VE : SI->second) 3740 assert(ValueExprMap.count(VE.first)); 3741 } 3742 #endif 3743 return &SI->second; 3744 } 3745 3746 /// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V) 3747 /// cannot be used separately. eraseValueFromMap should be used to remove 3748 /// V from ValueExprMap and ExprValueMap at the same time. 3749 void ScalarEvolution::eraseValueFromMap(Value *V) { 3750 ValueExprMapType::iterator I = ValueExprMap.find_as(V); 3751 if (I != ValueExprMap.end()) { 3752 const SCEV *S = I->second; 3753 // Remove {V, 0} from the set of ExprValueMap[S] 3754 if (SetVector<ValueOffsetPair> *SV = getSCEVValues(S)) 3755 SV->remove({V, nullptr}); 3756 3757 // Remove {V, Offset} from the set of ExprValueMap[Stripped] 3758 const SCEV *Stripped; 3759 ConstantInt *Offset; 3760 std::tie(Stripped, Offset) = splitAddExpr(S); 3761 if (Offset != nullptr) { 3762 if (SetVector<ValueOffsetPair> *SV = getSCEVValues(Stripped)) 3763 SV->remove({V, Offset}); 3764 } 3765 ValueExprMap.erase(V); 3766 } 3767 } 3768 3769 /// Return an existing SCEV if it exists, otherwise analyze the expression and 3770 /// create a new one. 3771 const SCEV *ScalarEvolution::getSCEV(Value *V) { 3772 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 3773 3774 const SCEV *S = getExistingSCEV(V); 3775 if (S == nullptr) { 3776 S = createSCEV(V); 3777 // During PHI resolution, it is possible to create two SCEVs for the same 3778 // V, so it is needed to double check whether V->S is inserted into 3779 // ValueExprMap before insert S->{V, 0} into ExprValueMap. 3780 std::pair<ValueExprMapType::iterator, bool> Pair = 3781 ValueExprMap.insert({SCEVCallbackVH(V, this), S}); 3782 if (Pair.second) { 3783 ExprValueMap[S].insert({V, nullptr}); 3784 3785 // If S == Stripped + Offset, add Stripped -> {V, Offset} into 3786 // ExprValueMap. 3787 const SCEV *Stripped = S; 3788 ConstantInt *Offset = nullptr; 3789 std::tie(Stripped, Offset) = splitAddExpr(S); 3790 // If stripped is SCEVUnknown, don't bother to save 3791 // Stripped -> {V, offset}. It doesn't simplify and sometimes even 3792 // increase the complexity of the expansion code. 3793 // If V is GetElementPtrInst, don't save Stripped -> {V, offset} 3794 // because it may generate add/sub instead of GEP in SCEV expansion. 3795 if (Offset != nullptr && !isa<SCEVUnknown>(Stripped) && 3796 !isa<GetElementPtrInst>(V)) 3797 ExprValueMap[Stripped].insert({V, Offset}); 3798 } 3799 } 3800 return S; 3801 } 3802 3803 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) { 3804 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 3805 3806 ValueExprMapType::iterator I = ValueExprMap.find_as(V); 3807 if (I != ValueExprMap.end()) { 3808 const SCEV *S = I->second; 3809 if (checkValidity(S)) 3810 return S; 3811 eraseValueFromMap(V); 3812 forgetMemoizedResults(S); 3813 } 3814 return nullptr; 3815 } 3816 3817 /// Return a SCEV corresponding to -V = -1*V 3818 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V, 3819 SCEV::NoWrapFlags Flags) { 3820 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 3821 return getConstant( 3822 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 3823 3824 Type *Ty = V->getType(); 3825 Ty = getEffectiveSCEVType(Ty); 3826 return getMulExpr( 3827 V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags); 3828 } 3829 3830 /// Return a SCEV corresponding to ~V = -1-V 3831 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 3832 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 3833 return getConstant( 3834 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 3835 3836 Type *Ty = V->getType(); 3837 Ty = getEffectiveSCEVType(Ty); 3838 const SCEV *AllOnes = 3839 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 3840 return getMinusSCEV(AllOnes, V); 3841 } 3842 3843 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS, 3844 SCEV::NoWrapFlags Flags, 3845 unsigned Depth) { 3846 // Fast path: X - X --> 0. 3847 if (LHS == RHS) 3848 return getZero(LHS->getType()); 3849 3850 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation 3851 // makes it so that we cannot make much use of NUW. 3852 auto AddFlags = SCEV::FlagAnyWrap; 3853 const bool RHSIsNotMinSigned = 3854 !getSignedRangeMin(RHS).isMinSignedValue(); 3855 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) { 3856 // Let M be the minimum representable signed value. Then (-1)*RHS 3857 // signed-wraps if and only if RHS is M. That can happen even for 3858 // a NSW subtraction because e.g. (-1)*M signed-wraps even though 3859 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS + 3860 // (-1)*RHS, we need to prove that RHS != M. 3861 // 3862 // If LHS is non-negative and we know that LHS - RHS does not 3863 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap 3864 // either by proving that RHS > M or that LHS >= 0. 3865 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) { 3866 AddFlags = SCEV::FlagNSW; 3867 } 3868 } 3869 3870 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS - 3871 // RHS is NSW and LHS >= 0. 3872 // 3873 // The difficulty here is that the NSW flag may have been proven 3874 // relative to a loop that is to be found in a recurrence in LHS and 3875 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a 3876 // larger scope than intended. 3877 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap; 3878 3879 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags, Depth); 3880 } 3881 3882 const SCEV * 3883 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) { 3884 Type *SrcTy = V->getType(); 3885 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 3886 (Ty->isIntegerTy() || Ty->isPointerTy()) && 3887 "Cannot truncate or zero extend with non-integer arguments!"); 3888 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 3889 return V; // No conversion 3890 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 3891 return getTruncateExpr(V, Ty); 3892 return getZeroExtendExpr(V, Ty); 3893 } 3894 3895 const SCEV * 3896 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 3897 Type *Ty) { 3898 Type *SrcTy = V->getType(); 3899 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 3900 (Ty->isIntegerTy() || Ty->isPointerTy()) && 3901 "Cannot truncate or zero extend with non-integer arguments!"); 3902 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 3903 return V; // No conversion 3904 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 3905 return getTruncateExpr(V, Ty); 3906 return getSignExtendExpr(V, Ty); 3907 } 3908 3909 const SCEV * 3910 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) { 3911 Type *SrcTy = V->getType(); 3912 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 3913 (Ty->isIntegerTy() || Ty->isPointerTy()) && 3914 "Cannot noop or zero extend with non-integer arguments!"); 3915 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 3916 "getNoopOrZeroExtend cannot truncate!"); 3917 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 3918 return V; // No conversion 3919 return getZeroExtendExpr(V, Ty); 3920 } 3921 3922 const SCEV * 3923 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) { 3924 Type *SrcTy = V->getType(); 3925 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 3926 (Ty->isIntegerTy() || Ty->isPointerTy()) && 3927 "Cannot noop or sign extend with non-integer arguments!"); 3928 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 3929 "getNoopOrSignExtend cannot truncate!"); 3930 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 3931 return V; // No conversion 3932 return getSignExtendExpr(V, Ty); 3933 } 3934 3935 const SCEV * 3936 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) { 3937 Type *SrcTy = V->getType(); 3938 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 3939 (Ty->isIntegerTy() || Ty->isPointerTy()) && 3940 "Cannot noop or any extend with non-integer arguments!"); 3941 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 3942 "getNoopOrAnyExtend cannot truncate!"); 3943 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 3944 return V; // No conversion 3945 return getAnyExtendExpr(V, Ty); 3946 } 3947 3948 const SCEV * 3949 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) { 3950 Type *SrcTy = V->getType(); 3951 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 3952 (Ty->isIntegerTy() || Ty->isPointerTy()) && 3953 "Cannot truncate or noop with non-integer arguments!"); 3954 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 3955 "getTruncateOrNoop cannot extend!"); 3956 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 3957 return V; // No conversion 3958 return getTruncateExpr(V, Ty); 3959 } 3960 3961 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 3962 const SCEV *RHS) { 3963 const SCEV *PromotedLHS = LHS; 3964 const SCEV *PromotedRHS = RHS; 3965 3966 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 3967 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 3968 else 3969 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 3970 3971 return getUMaxExpr(PromotedLHS, PromotedRHS); 3972 } 3973 3974 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 3975 const SCEV *RHS) { 3976 const SCEV *PromotedLHS = LHS; 3977 const SCEV *PromotedRHS = RHS; 3978 3979 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 3980 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 3981 else 3982 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 3983 3984 return getUMinExpr(PromotedLHS, PromotedRHS); 3985 } 3986 3987 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) { 3988 // A pointer operand may evaluate to a nonpointer expression, such as null. 3989 if (!V->getType()->isPointerTy()) 3990 return V; 3991 3992 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) { 3993 return getPointerBase(Cast->getOperand()); 3994 } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) { 3995 const SCEV *PtrOp = nullptr; 3996 for (const SCEV *NAryOp : NAry->operands()) { 3997 if (NAryOp->getType()->isPointerTy()) { 3998 // Cannot find the base of an expression with multiple pointer operands. 3999 if (PtrOp) 4000 return V; 4001 PtrOp = NAryOp; 4002 } 4003 } 4004 if (!PtrOp) 4005 return V; 4006 return getPointerBase(PtrOp); 4007 } 4008 return V; 4009 } 4010 4011 /// Push users of the given Instruction onto the given Worklist. 4012 static void 4013 PushDefUseChildren(Instruction *I, 4014 SmallVectorImpl<Instruction *> &Worklist) { 4015 // Push the def-use children onto the Worklist stack. 4016 for (User *U : I->users()) 4017 Worklist.push_back(cast<Instruction>(U)); 4018 } 4019 4020 void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) { 4021 SmallVector<Instruction *, 16> Worklist; 4022 PushDefUseChildren(PN, Worklist); 4023 4024 SmallPtrSet<Instruction *, 8> Visited; 4025 Visited.insert(PN); 4026 while (!Worklist.empty()) { 4027 Instruction *I = Worklist.pop_back_val(); 4028 if (!Visited.insert(I).second) 4029 continue; 4030 4031 auto It = ValueExprMap.find_as(static_cast<Value *>(I)); 4032 if (It != ValueExprMap.end()) { 4033 const SCEV *Old = It->second; 4034 4035 // Short-circuit the def-use traversal if the symbolic name 4036 // ceases to appear in expressions. 4037 if (Old != SymName && !hasOperand(Old, SymName)) 4038 continue; 4039 4040 // SCEVUnknown for a PHI either means that it has an unrecognized 4041 // structure, it's a PHI that's in the progress of being computed 4042 // by createNodeForPHI, or it's a single-value PHI. In the first case, 4043 // additional loop trip count information isn't going to change anything. 4044 // In the second case, createNodeForPHI will perform the necessary 4045 // updates on its own when it gets to that point. In the third, we do 4046 // want to forget the SCEVUnknown. 4047 if (!isa<PHINode>(I) || 4048 !isa<SCEVUnknown>(Old) || 4049 (I != PN && Old == SymName)) { 4050 eraseValueFromMap(It->first); 4051 forgetMemoizedResults(Old); 4052 } 4053 } 4054 4055 PushDefUseChildren(I, Worklist); 4056 } 4057 } 4058 4059 namespace { 4060 4061 class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> { 4062 public: 4063 static const SCEV *rewrite(const SCEV *S, const Loop *L, 4064 ScalarEvolution &SE) { 4065 SCEVInitRewriter Rewriter(L, SE); 4066 const SCEV *Result = Rewriter.visit(S); 4067 return Rewriter.isValid() ? Result : SE.getCouldNotCompute(); 4068 } 4069 4070 const SCEV *visitUnknown(const SCEVUnknown *Expr) { 4071 if (!SE.isLoopInvariant(Expr, L)) 4072 Valid = false; 4073 return Expr; 4074 } 4075 4076 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) { 4077 // Only allow AddRecExprs for this loop. 4078 if (Expr->getLoop() == L) 4079 return Expr->getStart(); 4080 Valid = false; 4081 return Expr; 4082 } 4083 4084 bool isValid() { return Valid; } 4085 4086 private: 4087 explicit SCEVInitRewriter(const Loop *L, ScalarEvolution &SE) 4088 : SCEVRewriteVisitor(SE), L(L) {} 4089 4090 const Loop *L; 4091 bool Valid = true; 4092 }; 4093 4094 /// This class evaluates the compare condition by matching it against the 4095 /// condition of loop latch. If there is a match we assume a true value 4096 /// for the condition while building SCEV nodes. 4097 class SCEVBackedgeConditionFolder 4098 : public SCEVRewriteVisitor<SCEVBackedgeConditionFolder> { 4099 public: 4100 static const SCEV *rewrite(const SCEV *S, const Loop *L, 4101 ScalarEvolution &SE) { 4102 bool IsPosBECond = false; 4103 Value *BECond = nullptr; 4104 if (BasicBlock *Latch = L->getLoopLatch()) { 4105 BranchInst *BI = dyn_cast<BranchInst>(Latch->getTerminator()); 4106 if (BI && BI->isConditional()) { 4107 assert(BI->getSuccessor(0) != BI->getSuccessor(1) && 4108 "Both outgoing branches should not target same header!"); 4109 BECond = BI->getCondition(); 4110 IsPosBECond = BI->getSuccessor(0) == L->getHeader(); 4111 } else { 4112 return S; 4113 } 4114 } 4115 SCEVBackedgeConditionFolder Rewriter(L, BECond, IsPosBECond, SE); 4116 return Rewriter.visit(S); 4117 } 4118 4119 const SCEV *visitUnknown(const SCEVUnknown *Expr) { 4120 const SCEV *Result = Expr; 4121 bool InvariantF = SE.isLoopInvariant(Expr, L); 4122 4123 if (!InvariantF) { 4124 Instruction *I = cast<Instruction>(Expr->getValue()); 4125 switch (I->getOpcode()) { 4126 case Instruction::Select: { 4127 SelectInst *SI = cast<SelectInst>(I); 4128 Optional<const SCEV *> Res = 4129 compareWithBackedgeCondition(SI->getCondition()); 4130 if (Res.hasValue()) { 4131 bool IsOne = cast<SCEVConstant>(Res.getValue())->getValue()->isOne(); 4132 Result = SE.getSCEV(IsOne ? SI->getTrueValue() : SI->getFalseValue()); 4133 } 4134 break; 4135 } 4136 default: { 4137 Optional<const SCEV *> Res = compareWithBackedgeCondition(I); 4138 if (Res.hasValue()) 4139 Result = Res.getValue(); 4140 break; 4141 } 4142 } 4143 } 4144 return Result; 4145 } 4146 4147 private: 4148 explicit SCEVBackedgeConditionFolder(const Loop *L, Value *BECond, 4149 bool IsPosBECond, ScalarEvolution &SE) 4150 : SCEVRewriteVisitor(SE), L(L), BackedgeCond(BECond), 4151 IsPositiveBECond(IsPosBECond) {} 4152 4153 Optional<const SCEV *> compareWithBackedgeCondition(Value *IC); 4154 4155 const Loop *L; 4156 /// Loop back condition. 4157 Value *BackedgeCond = nullptr; 4158 /// Set to true if loop back is on positive branch condition. 4159 bool IsPositiveBECond; 4160 }; 4161 4162 Optional<const SCEV *> 4163 SCEVBackedgeConditionFolder::compareWithBackedgeCondition(Value *IC) { 4164 4165 // If value matches the backedge condition for loop latch, 4166 // then return a constant evolution node based on loopback 4167 // branch taken. 4168 if (BackedgeCond == IC) 4169 return IsPositiveBECond ? SE.getOne(Type::getInt1Ty(SE.getContext())) 4170 : SE.getZero(Type::getInt1Ty(SE.getContext())); 4171 return None; 4172 } 4173 4174 class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> { 4175 public: 4176 static const SCEV *rewrite(const SCEV *S, const Loop *L, 4177 ScalarEvolution &SE) { 4178 SCEVShiftRewriter Rewriter(L, SE); 4179 const SCEV *Result = Rewriter.visit(S); 4180 return Rewriter.isValid() ? Result : SE.getCouldNotCompute(); 4181 } 4182 4183 const SCEV *visitUnknown(const SCEVUnknown *Expr) { 4184 // Only allow AddRecExprs for this loop. 4185 if (!SE.isLoopInvariant(Expr, L)) 4186 Valid = false; 4187 return Expr; 4188 } 4189 4190 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) { 4191 if (Expr->getLoop() == L && Expr->isAffine()) 4192 return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE)); 4193 Valid = false; 4194 return Expr; 4195 } 4196 4197 bool isValid() { return Valid; } 4198 4199 private: 4200 explicit SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE) 4201 : SCEVRewriteVisitor(SE), L(L) {} 4202 4203 const Loop *L; 4204 bool Valid = true; 4205 }; 4206 4207 } // end anonymous namespace 4208 4209 SCEV::NoWrapFlags 4210 ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) { 4211 if (!AR->isAffine()) 4212 return SCEV::FlagAnyWrap; 4213 4214 using OBO = OverflowingBinaryOperator; 4215 4216 SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap; 4217 4218 if (!AR->hasNoSignedWrap()) { 4219 ConstantRange AddRecRange = getSignedRange(AR); 4220 ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this)); 4221 4222 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion( 4223 Instruction::Add, IncRange, OBO::NoSignedWrap); 4224 if (NSWRegion.contains(AddRecRange)) 4225 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW); 4226 } 4227 4228 if (!AR->hasNoUnsignedWrap()) { 4229 ConstantRange AddRecRange = getUnsignedRange(AR); 4230 ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this)); 4231 4232 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion( 4233 Instruction::Add, IncRange, OBO::NoUnsignedWrap); 4234 if (NUWRegion.contains(AddRecRange)) 4235 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW); 4236 } 4237 4238 return Result; 4239 } 4240 4241 namespace { 4242 4243 /// Represents an abstract binary operation. This may exist as a 4244 /// normal instruction or constant expression, or may have been 4245 /// derived from an expression tree. 4246 struct BinaryOp { 4247 unsigned Opcode; 4248 Value *LHS; 4249 Value *RHS; 4250 bool IsNSW = false; 4251 bool IsNUW = false; 4252 4253 /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or 4254 /// constant expression. 4255 Operator *Op = nullptr; 4256 4257 explicit BinaryOp(Operator *Op) 4258 : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)), 4259 Op(Op) { 4260 if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) { 4261 IsNSW = OBO->hasNoSignedWrap(); 4262 IsNUW = OBO->hasNoUnsignedWrap(); 4263 } 4264 } 4265 4266 explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false, 4267 bool IsNUW = false) 4268 : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW) {} 4269 }; 4270 4271 } // end anonymous namespace 4272 4273 /// Try to map \p V into a BinaryOp, and return \c None on failure. 4274 static Optional<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) { 4275 auto *Op = dyn_cast<Operator>(V); 4276 if (!Op) 4277 return None; 4278 4279 // Implementation detail: all the cleverness here should happen without 4280 // creating new SCEV expressions -- our caller knowns tricks to avoid creating 4281 // SCEV expressions when possible, and we should not break that. 4282 4283 switch (Op->getOpcode()) { 4284 case Instruction::Add: 4285 case Instruction::Sub: 4286 case Instruction::Mul: 4287 case Instruction::UDiv: 4288 case Instruction::URem: 4289 case Instruction::And: 4290 case Instruction::Or: 4291 case Instruction::AShr: 4292 case Instruction::Shl: 4293 return BinaryOp(Op); 4294 4295 case Instruction::Xor: 4296 if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1))) 4297 // If the RHS of the xor is a signmask, then this is just an add. 4298 // Instcombine turns add of signmask into xor as a strength reduction step. 4299 if (RHSC->getValue().isSignMask()) 4300 return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1)); 4301 return BinaryOp(Op); 4302 4303 case Instruction::LShr: 4304 // Turn logical shift right of a constant into a unsigned divide. 4305 if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) { 4306 uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth(); 4307 4308 // If the shift count is not less than the bitwidth, the result of 4309 // the shift is undefined. Don't try to analyze it, because the 4310 // resolution chosen here may differ from the resolution chosen in 4311 // other parts of the compiler. 4312 if (SA->getValue().ult(BitWidth)) { 4313 Constant *X = 4314 ConstantInt::get(SA->getContext(), 4315 APInt::getOneBitSet(BitWidth, SA->getZExtValue())); 4316 return BinaryOp(Instruction::UDiv, Op->getOperand(0), X); 4317 } 4318 } 4319 return BinaryOp(Op); 4320 4321 case Instruction::ExtractValue: { 4322 auto *EVI = cast<ExtractValueInst>(Op); 4323 if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0) 4324 break; 4325 4326 auto *CI = dyn_cast<CallInst>(EVI->getAggregateOperand()); 4327 if (!CI) 4328 break; 4329 4330 if (auto *F = CI->getCalledFunction()) 4331 switch (F->getIntrinsicID()) { 4332 case Intrinsic::sadd_with_overflow: 4333 case Intrinsic::uadd_with_overflow: 4334 if (!isOverflowIntrinsicNoWrap(cast<IntrinsicInst>(CI), DT)) 4335 return BinaryOp(Instruction::Add, CI->getArgOperand(0), 4336 CI->getArgOperand(1)); 4337 4338 // Now that we know that all uses of the arithmetic-result component of 4339 // CI are guarded by the overflow check, we can go ahead and pretend 4340 // that the arithmetic is non-overflowing. 4341 if (F->getIntrinsicID() == Intrinsic::sadd_with_overflow) 4342 return BinaryOp(Instruction::Add, CI->getArgOperand(0), 4343 CI->getArgOperand(1), /* IsNSW = */ true, 4344 /* IsNUW = */ false); 4345 else 4346 return BinaryOp(Instruction::Add, CI->getArgOperand(0), 4347 CI->getArgOperand(1), /* IsNSW = */ false, 4348 /* IsNUW*/ true); 4349 case Intrinsic::ssub_with_overflow: 4350 case Intrinsic::usub_with_overflow: 4351 if (!isOverflowIntrinsicNoWrap(cast<IntrinsicInst>(CI), DT)) 4352 return BinaryOp(Instruction::Sub, CI->getArgOperand(0), 4353 CI->getArgOperand(1)); 4354 4355 // The same reasoning as sadd/uadd above. 4356 if (F->getIntrinsicID() == Intrinsic::ssub_with_overflow) 4357 return BinaryOp(Instruction::Sub, CI->getArgOperand(0), 4358 CI->getArgOperand(1), /* IsNSW = */ true, 4359 /* IsNUW = */ false); 4360 else 4361 return BinaryOp(Instruction::Sub, CI->getArgOperand(0), 4362 CI->getArgOperand(1), /* IsNSW = */ false, 4363 /* IsNUW = */ true); 4364 case Intrinsic::smul_with_overflow: 4365 case Intrinsic::umul_with_overflow: 4366 return BinaryOp(Instruction::Mul, CI->getArgOperand(0), 4367 CI->getArgOperand(1)); 4368 default: 4369 break; 4370 } 4371 } 4372 4373 default: 4374 break; 4375 } 4376 4377 return None; 4378 } 4379 4380 /// Helper function to createAddRecFromPHIWithCasts. We have a phi 4381 /// node whose symbolic (unknown) SCEV is \p SymbolicPHI, which is updated via 4382 /// the loop backedge by a SCEVAddExpr, possibly also with a few casts on the 4383 /// way. This function checks if \p Op, an operand of this SCEVAddExpr, 4384 /// follows one of the following patterns: 4385 /// Op == (SExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) 4386 /// Op == (ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) 4387 /// If the SCEV expression of \p Op conforms with one of the expected patterns 4388 /// we return the type of the truncation operation, and indicate whether the 4389 /// truncated type should be treated as signed/unsigned by setting 4390 /// \p Signed to true/false, respectively. 4391 static Type *isSimpleCastedPHI(const SCEV *Op, const SCEVUnknown *SymbolicPHI, 4392 bool &Signed, ScalarEvolution &SE) { 4393 // The case where Op == SymbolicPHI (that is, with no type conversions on 4394 // the way) is handled by the regular add recurrence creating logic and 4395 // would have already been triggered in createAddRecForPHI. Reaching it here 4396 // means that createAddRecFromPHI had failed for this PHI before (e.g., 4397 // because one of the other operands of the SCEVAddExpr updating this PHI is 4398 // not invariant). 4399 // 4400 // Here we look for the case where Op = (ext(trunc(SymbolicPHI))), and in 4401 // this case predicates that allow us to prove that Op == SymbolicPHI will 4402 // be added. 4403 if (Op == SymbolicPHI) 4404 return nullptr; 4405 4406 unsigned SourceBits = SE.getTypeSizeInBits(SymbolicPHI->getType()); 4407 unsigned NewBits = SE.getTypeSizeInBits(Op->getType()); 4408 if (SourceBits != NewBits) 4409 return nullptr; 4410 4411 const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(Op); 4412 const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(Op); 4413 if (!SExt && !ZExt) 4414 return nullptr; 4415 const SCEVTruncateExpr *Trunc = 4416 SExt ? dyn_cast<SCEVTruncateExpr>(SExt->getOperand()) 4417 : dyn_cast<SCEVTruncateExpr>(ZExt->getOperand()); 4418 if (!Trunc) 4419 return nullptr; 4420 const SCEV *X = Trunc->getOperand(); 4421 if (X != SymbolicPHI) 4422 return nullptr; 4423 Signed = SExt != nullptr; 4424 return Trunc->getType(); 4425 } 4426 4427 static const Loop *isIntegerLoopHeaderPHI(const PHINode *PN, LoopInfo &LI) { 4428 if (!PN->getType()->isIntegerTy()) 4429 return nullptr; 4430 const Loop *L = LI.getLoopFor(PN->getParent()); 4431 if (!L || L->getHeader() != PN->getParent()) 4432 return nullptr; 4433 return L; 4434 } 4435 4436 // Analyze \p SymbolicPHI, a SCEV expression of a phi node, and check if the 4437 // computation that updates the phi follows the following pattern: 4438 // (SExt/ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) + InvariantAccum 4439 // which correspond to a phi->trunc->sext/zext->add->phi update chain. 4440 // If so, try to see if it can be rewritten as an AddRecExpr under some 4441 // Predicates. If successful, return them as a pair. Also cache the results 4442 // of the analysis. 4443 // 4444 // Example usage scenario: 4445 // Say the Rewriter is called for the following SCEV: 4446 // 8 * ((sext i32 (trunc i64 %X to i32) to i64) + %Step) 4447 // where: 4448 // %X = phi i64 (%Start, %BEValue) 4449 // It will visitMul->visitAdd->visitSExt->visitTrunc->visitUnknown(%X), 4450 // and call this function with %SymbolicPHI = %X. 4451 // 4452 // The analysis will find that the value coming around the backedge has 4453 // the following SCEV: 4454 // BEValue = ((sext i32 (trunc i64 %X to i32) to i64) + %Step) 4455 // Upon concluding that this matches the desired pattern, the function 4456 // will return the pair {NewAddRec, SmallPredsVec} where: 4457 // NewAddRec = {%Start,+,%Step} 4458 // SmallPredsVec = {P1, P2, P3} as follows: 4459 // P1(WrapPred): AR: {trunc(%Start),+,(trunc %Step)}<nsw> Flags: <nssw> 4460 // P2(EqualPred): %Start == (sext i32 (trunc i64 %Start to i32) to i64) 4461 // P3(EqualPred): %Step == (sext i32 (trunc i64 %Step to i32) to i64) 4462 // The returned pair means that SymbolicPHI can be rewritten into NewAddRec 4463 // under the predicates {P1,P2,P3}. 4464 // This predicated rewrite will be cached in PredicatedSCEVRewrites: 4465 // PredicatedSCEVRewrites[{%X,L}] = {NewAddRec, {P1,P2,P3)} 4466 // 4467 // TODO's: 4468 // 4469 // 1) Extend the Induction descriptor to also support inductions that involve 4470 // casts: When needed (namely, when we are called in the context of the 4471 // vectorizer induction analysis), a Set of cast instructions will be 4472 // populated by this method, and provided back to isInductionPHI. This is 4473 // needed to allow the vectorizer to properly record them to be ignored by 4474 // the cost model and to avoid vectorizing them (otherwise these casts, 4475 // which are redundant under the runtime overflow checks, will be 4476 // vectorized, which can be costly). 4477 // 4478 // 2) Support additional induction/PHISCEV patterns: We also want to support 4479 // inductions where the sext-trunc / zext-trunc operations (partly) occur 4480 // after the induction update operation (the induction increment): 4481 // 4482 // (Trunc iy (SExt/ZExt ix (%SymbolicPHI + InvariantAccum) to iy) to ix) 4483 // which correspond to a phi->add->trunc->sext/zext->phi update chain. 4484 // 4485 // (Trunc iy ((SExt/ZExt ix (%SymbolicPhi) to iy) + InvariantAccum) to ix) 4486 // which correspond to a phi->trunc->add->sext/zext->phi update chain. 4487 // 4488 // 3) Outline common code with createAddRecFromPHI to avoid duplication. 4489 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>> 4490 ScalarEvolution::createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI) { 4491 SmallVector<const SCEVPredicate *, 3> Predicates; 4492 4493 // *** Part1: Analyze if we have a phi-with-cast pattern for which we can 4494 // return an AddRec expression under some predicate. 4495 4496 auto *PN = cast<PHINode>(SymbolicPHI->getValue()); 4497 const Loop *L = isIntegerLoopHeaderPHI(PN, LI); 4498 assert(L && "Expecting an integer loop header phi"); 4499 4500 // The loop may have multiple entrances or multiple exits; we can analyze 4501 // this phi as an addrec if it has a unique entry value and a unique 4502 // backedge value. 4503 Value *BEValueV = nullptr, *StartValueV = nullptr; 4504 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 4505 Value *V = PN->getIncomingValue(i); 4506 if (L->contains(PN->getIncomingBlock(i))) { 4507 if (!BEValueV) { 4508 BEValueV = V; 4509 } else if (BEValueV != V) { 4510 BEValueV = nullptr; 4511 break; 4512 } 4513 } else if (!StartValueV) { 4514 StartValueV = V; 4515 } else if (StartValueV != V) { 4516 StartValueV = nullptr; 4517 break; 4518 } 4519 } 4520 if (!BEValueV || !StartValueV) 4521 return None; 4522 4523 const SCEV *BEValue = getSCEV(BEValueV); 4524 4525 // If the value coming around the backedge is an add with the symbolic 4526 // value we just inserted, possibly with casts that we can ignore under 4527 // an appropriate runtime guard, then we found a simple induction variable! 4528 const auto *Add = dyn_cast<SCEVAddExpr>(BEValue); 4529 if (!Add) 4530 return None; 4531 4532 // If there is a single occurrence of the symbolic value, possibly 4533 // casted, replace it with a recurrence. 4534 unsigned FoundIndex = Add->getNumOperands(); 4535 Type *TruncTy = nullptr; 4536 bool Signed; 4537 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 4538 if ((TruncTy = 4539 isSimpleCastedPHI(Add->getOperand(i), SymbolicPHI, Signed, *this))) 4540 if (FoundIndex == e) { 4541 FoundIndex = i; 4542 break; 4543 } 4544 4545 if (FoundIndex == Add->getNumOperands()) 4546 return None; 4547 4548 // Create an add with everything but the specified operand. 4549 SmallVector<const SCEV *, 8> Ops; 4550 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 4551 if (i != FoundIndex) 4552 Ops.push_back(Add->getOperand(i)); 4553 const SCEV *Accum = getAddExpr(Ops); 4554 4555 // The runtime checks will not be valid if the step amount is 4556 // varying inside the loop. 4557 if (!isLoopInvariant(Accum, L)) 4558 return None; 4559 4560 // *** Part2: Create the predicates 4561 4562 // Analysis was successful: we have a phi-with-cast pattern for which we 4563 // can return an AddRec expression under the following predicates: 4564 // 4565 // P1: A Wrap predicate that guarantees that Trunc(Start) + i*Trunc(Accum) 4566 // fits within the truncated type (does not overflow) for i = 0 to n-1. 4567 // P2: An Equal predicate that guarantees that 4568 // Start = (Ext ix (Trunc iy (Start) to ix) to iy) 4569 // P3: An Equal predicate that guarantees that 4570 // Accum = (Ext ix (Trunc iy (Accum) to ix) to iy) 4571 // 4572 // As we next prove, the above predicates guarantee that: 4573 // Start + i*Accum = (Ext ix (Trunc iy ( Start + i*Accum ) to ix) to iy) 4574 // 4575 // 4576 // More formally, we want to prove that: 4577 // Expr(i+1) = Start + (i+1) * Accum 4578 // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum 4579 // 4580 // Given that: 4581 // 1) Expr(0) = Start 4582 // 2) Expr(1) = Start + Accum 4583 // = (Ext ix (Trunc iy (Start) to ix) to iy) + Accum :: from P2 4584 // 3) Induction hypothesis (step i): 4585 // Expr(i) = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum 4586 // 4587 // Proof: 4588 // Expr(i+1) = 4589 // = Start + (i+1)*Accum 4590 // = (Start + i*Accum) + Accum 4591 // = Expr(i) + Accum 4592 // = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum + Accum 4593 // :: from step i 4594 // 4595 // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) + Accum + Accum 4596 // 4597 // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) 4598 // + (Ext ix (Trunc iy (Accum) to ix) to iy) 4599 // + Accum :: from P3 4600 // 4601 // = (Ext ix (Trunc iy ((Start + (i-1)*Accum) + Accum) to ix) to iy) 4602 // + Accum :: from P1: Ext(x)+Ext(y)=>Ext(x+y) 4603 // 4604 // = (Ext ix (Trunc iy (Start + i*Accum) to ix) to iy) + Accum 4605 // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum 4606 // 4607 // By induction, the same applies to all iterations 1<=i<n: 4608 // 4609 4610 // Create a truncated addrec for which we will add a no overflow check (P1). 4611 const SCEV *StartVal = getSCEV(StartValueV); 4612 const SCEV *PHISCEV = 4613 getAddRecExpr(getTruncateExpr(StartVal, TruncTy), 4614 getTruncateExpr(Accum, TruncTy), L, SCEV::FlagAnyWrap); 4615 4616 // PHISCEV can be either a SCEVConstant or a SCEVAddRecExpr. 4617 // ex: If truncated Accum is 0 and StartVal is a constant, then PHISCEV 4618 // will be constant. 4619 // 4620 // If PHISCEV is a constant, then P1 degenerates into P2 or P3, so we don't 4621 // add P1. 4622 if (const auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV)) { 4623 SCEVWrapPredicate::IncrementWrapFlags AddedFlags = 4624 Signed ? SCEVWrapPredicate::IncrementNSSW 4625 : SCEVWrapPredicate::IncrementNUSW; 4626 const SCEVPredicate *AddRecPred = getWrapPredicate(AR, AddedFlags); 4627 Predicates.push_back(AddRecPred); 4628 } 4629 4630 // Create the Equal Predicates P2,P3: 4631 4632 // It is possible that the predicates P2 and/or P3 are computable at 4633 // compile time due to StartVal and/or Accum being constants. 4634 // If either one is, then we can check that now and escape if either P2 4635 // or P3 is false. 4636 4637 // Construct the extended SCEV: (Ext ix (Trunc iy (Expr) to ix) to iy) 4638 // for each of StartVal and Accum 4639 auto GetExtendedExpr = [&](const SCEV *Expr) -> const SCEV * { 4640 assert(isLoopInvariant(Expr, L) && "Expr is expected to be invariant"); 4641 const SCEV *TruncatedExpr = getTruncateExpr(Expr, TruncTy); 4642 const SCEV *ExtendedExpr = 4643 Signed ? getSignExtendExpr(TruncatedExpr, Expr->getType()) 4644 : getZeroExtendExpr(TruncatedExpr, Expr->getType()); 4645 return ExtendedExpr; 4646 }; 4647 4648 // Given: 4649 // ExtendedExpr = (Ext ix (Trunc iy (Expr) to ix) to iy 4650 // = GetExtendedExpr(Expr) 4651 // Determine whether the predicate P: Expr == ExtendedExpr 4652 // is known to be false at compile time 4653 auto PredIsKnownFalse = [&](const SCEV *Expr, 4654 const SCEV *ExtendedExpr) -> bool { 4655 return Expr != ExtendedExpr && 4656 isKnownPredicate(ICmpInst::ICMP_NE, Expr, ExtendedExpr); 4657 }; 4658 4659 const SCEV *StartExtended = GetExtendedExpr(StartVal); 4660 if (PredIsKnownFalse(StartVal, StartExtended)) { 4661 DEBUG(dbgs() << "P2 is compile-time false\n";); 4662 return None; 4663 } 4664 4665 const SCEV *AccumExtended = GetExtendedExpr(Accum); 4666 if (PredIsKnownFalse(Accum, AccumExtended)) { 4667 DEBUG(dbgs() << "P3 is compile-time false\n";); 4668 return None; 4669 } 4670 4671 auto AppendPredicate = [&](const SCEV *Expr, 4672 const SCEV *ExtendedExpr) -> void { 4673 if (Expr != ExtendedExpr && 4674 !isKnownPredicate(ICmpInst::ICMP_EQ, Expr, ExtendedExpr)) { 4675 const SCEVPredicate *Pred = getEqualPredicate(Expr, ExtendedExpr); 4676 DEBUG (dbgs() << "Added Predicate: " << *Pred); 4677 Predicates.push_back(Pred); 4678 } 4679 }; 4680 4681 AppendPredicate(StartVal, StartExtended); 4682 AppendPredicate(Accum, AccumExtended); 4683 4684 // *** Part3: Predicates are ready. Now go ahead and create the new addrec in 4685 // which the casts had been folded away. The caller can rewrite SymbolicPHI 4686 // into NewAR if it will also add the runtime overflow checks specified in 4687 // Predicates. 4688 auto *NewAR = getAddRecExpr(StartVal, Accum, L, SCEV::FlagAnyWrap); 4689 4690 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> PredRewrite = 4691 std::make_pair(NewAR, Predicates); 4692 // Remember the result of the analysis for this SCEV at this locayyytion. 4693 PredicatedSCEVRewrites[{SymbolicPHI, L}] = PredRewrite; 4694 return PredRewrite; 4695 } 4696 4697 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>> 4698 ScalarEvolution::createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI) { 4699 auto *PN = cast<PHINode>(SymbolicPHI->getValue()); 4700 const Loop *L = isIntegerLoopHeaderPHI(PN, LI); 4701 if (!L) 4702 return None; 4703 4704 // Check to see if we already analyzed this PHI. 4705 auto I = PredicatedSCEVRewrites.find({SymbolicPHI, L}); 4706 if (I != PredicatedSCEVRewrites.end()) { 4707 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> Rewrite = 4708 I->second; 4709 // Analysis was done before and failed to create an AddRec: 4710 if (Rewrite.first == SymbolicPHI) 4711 return None; 4712 // Analysis was done before and succeeded to create an AddRec under 4713 // a predicate: 4714 assert(isa<SCEVAddRecExpr>(Rewrite.first) && "Expected an AddRec"); 4715 assert(!(Rewrite.second).empty() && "Expected to find Predicates"); 4716 return Rewrite; 4717 } 4718 4719 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>> 4720 Rewrite = createAddRecFromPHIWithCastsImpl(SymbolicPHI); 4721 4722 // Record in the cache that the analysis failed 4723 if (!Rewrite) { 4724 SmallVector<const SCEVPredicate *, 3> Predicates; 4725 PredicatedSCEVRewrites[{SymbolicPHI, L}] = {SymbolicPHI, Predicates}; 4726 return None; 4727 } 4728 4729 return Rewrite; 4730 } 4731 4732 /// A helper function for createAddRecFromPHI to handle simple cases. 4733 /// 4734 /// This function tries to find an AddRec expression for the simplest (yet most 4735 /// common) cases: PN = PHI(Start, OP(Self, LoopInvariant)). 4736 /// If it fails, createAddRecFromPHI will use a more general, but slow, 4737 /// technique for finding the AddRec expression. 4738 const SCEV *ScalarEvolution::createSimpleAffineAddRec(PHINode *PN, 4739 Value *BEValueV, 4740 Value *StartValueV) { 4741 const Loop *L = LI.getLoopFor(PN->getParent()); 4742 assert(L && L->getHeader() == PN->getParent()); 4743 assert(BEValueV && StartValueV); 4744 4745 auto BO = MatchBinaryOp(BEValueV, DT); 4746 if (!BO) 4747 return nullptr; 4748 4749 if (BO->Opcode != Instruction::Add) 4750 return nullptr; 4751 4752 const SCEV *Accum = nullptr; 4753 if (BO->LHS == PN && L->isLoopInvariant(BO->RHS)) 4754 Accum = getSCEV(BO->RHS); 4755 else if (BO->RHS == PN && L->isLoopInvariant(BO->LHS)) 4756 Accum = getSCEV(BO->LHS); 4757 4758 if (!Accum) 4759 return nullptr; 4760 4761 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; 4762 if (BO->IsNUW) 4763 Flags = setFlags(Flags, SCEV::FlagNUW); 4764 if (BO->IsNSW) 4765 Flags = setFlags(Flags, SCEV::FlagNSW); 4766 4767 const SCEV *StartVal = getSCEV(StartValueV); 4768 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags); 4769 4770 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 4771 4772 // We can add Flags to the post-inc expression only if we 4773 // know that it is *undefined behavior* for BEValueV to 4774 // overflow. 4775 if (auto *BEInst = dyn_cast<Instruction>(BEValueV)) 4776 if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L)) 4777 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags); 4778 4779 return PHISCEV; 4780 } 4781 4782 const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) { 4783 const Loop *L = LI.getLoopFor(PN->getParent()); 4784 if (!L || L->getHeader() != PN->getParent()) 4785 return nullptr; 4786 4787 // The loop may have multiple entrances or multiple exits; we can analyze 4788 // this phi as an addrec if it has a unique entry value and a unique 4789 // backedge value. 4790 Value *BEValueV = nullptr, *StartValueV = nullptr; 4791 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 4792 Value *V = PN->getIncomingValue(i); 4793 if (L->contains(PN->getIncomingBlock(i))) { 4794 if (!BEValueV) { 4795 BEValueV = V; 4796 } else if (BEValueV != V) { 4797 BEValueV = nullptr; 4798 break; 4799 } 4800 } else if (!StartValueV) { 4801 StartValueV = V; 4802 } else if (StartValueV != V) { 4803 StartValueV = nullptr; 4804 break; 4805 } 4806 } 4807 if (!BEValueV || !StartValueV) 4808 return nullptr; 4809 4810 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() && 4811 "PHI node already processed?"); 4812 4813 // First, try to find AddRec expression without creating a fictituos symbolic 4814 // value for PN. 4815 if (auto *S = createSimpleAffineAddRec(PN, BEValueV, StartValueV)) 4816 return S; 4817 4818 // Handle PHI node value symbolically. 4819 const SCEV *SymbolicName = getUnknown(PN); 4820 ValueExprMap.insert({SCEVCallbackVH(PN, this), SymbolicName}); 4821 4822 // Using this symbolic name for the PHI, analyze the value coming around 4823 // the back-edge. 4824 const SCEV *BEValue = getSCEV(BEValueV); 4825 4826 // NOTE: If BEValue is loop invariant, we know that the PHI node just 4827 // has a special value for the first iteration of the loop. 4828 4829 // If the value coming around the backedge is an add with the symbolic 4830 // value we just inserted, then we found a simple induction variable! 4831 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 4832 // If there is a single occurrence of the symbolic value, replace it 4833 // with a recurrence. 4834 unsigned FoundIndex = Add->getNumOperands(); 4835 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 4836 if (Add->getOperand(i) == SymbolicName) 4837 if (FoundIndex == e) { 4838 FoundIndex = i; 4839 break; 4840 } 4841 4842 if (FoundIndex != Add->getNumOperands()) { 4843 // Create an add with everything but the specified operand. 4844 SmallVector<const SCEV *, 8> Ops; 4845 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 4846 if (i != FoundIndex) 4847 Ops.push_back(SCEVBackedgeConditionFolder::rewrite(Add->getOperand(i), 4848 L, *this)); 4849 const SCEV *Accum = getAddExpr(Ops); 4850 4851 // This is not a valid addrec if the step amount is varying each 4852 // loop iteration, but is not itself an addrec in this loop. 4853 if (isLoopInvariant(Accum, L) || 4854 (isa<SCEVAddRecExpr>(Accum) && 4855 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 4856 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; 4857 4858 if (auto BO = MatchBinaryOp(BEValueV, DT)) { 4859 if (BO->Opcode == Instruction::Add && BO->LHS == PN) { 4860 if (BO->IsNUW) 4861 Flags = setFlags(Flags, SCEV::FlagNUW); 4862 if (BO->IsNSW) 4863 Flags = setFlags(Flags, SCEV::FlagNSW); 4864 } 4865 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) { 4866 // If the increment is an inbounds GEP, then we know the address 4867 // space cannot be wrapped around. We cannot make any guarantee 4868 // about signed or unsigned overflow because pointers are 4869 // unsigned but we may have a negative index from the base 4870 // pointer. We can guarantee that no unsigned wrap occurs if the 4871 // indices form a positive value. 4872 if (GEP->isInBounds() && GEP->getOperand(0) == PN) { 4873 Flags = setFlags(Flags, SCEV::FlagNW); 4874 4875 const SCEV *Ptr = getSCEV(GEP->getPointerOperand()); 4876 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr))) 4877 Flags = setFlags(Flags, SCEV::FlagNUW); 4878 } 4879 4880 // We cannot transfer nuw and nsw flags from subtraction 4881 // operations -- sub nuw X, Y is not the same as add nuw X, -Y 4882 // for instance. 4883 } 4884 4885 const SCEV *StartVal = getSCEV(StartValueV); 4886 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags); 4887 4888 // Okay, for the entire analysis of this edge we assumed the PHI 4889 // to be symbolic. We now need to go back and purge all of the 4890 // entries for the scalars that use the symbolic expression. 4891 forgetSymbolicName(PN, SymbolicName); 4892 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 4893 4894 // We can add Flags to the post-inc expression only if we 4895 // know that it is *undefined behavior* for BEValueV to 4896 // overflow. 4897 if (auto *BEInst = dyn_cast<Instruction>(BEValueV)) 4898 if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L)) 4899 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags); 4900 4901 return PHISCEV; 4902 } 4903 } 4904 } else { 4905 // Otherwise, this could be a loop like this: 4906 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 4907 // In this case, j = {1,+,1} and BEValue is j. 4908 // Because the other in-value of i (0) fits the evolution of BEValue 4909 // i really is an addrec evolution. 4910 // 4911 // We can generalize this saying that i is the shifted value of BEValue 4912 // by one iteration: 4913 // PHI(f(0), f({1,+,1})) --> f({0,+,1}) 4914 const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this); 4915 const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this); 4916 if (Shifted != getCouldNotCompute() && 4917 Start != getCouldNotCompute()) { 4918 const SCEV *StartVal = getSCEV(StartValueV); 4919 if (Start == StartVal) { 4920 // Okay, for the entire analysis of this edge we assumed the PHI 4921 // to be symbolic. We now need to go back and purge all of the 4922 // entries for the scalars that use the symbolic expression. 4923 forgetSymbolicName(PN, SymbolicName); 4924 ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted; 4925 return Shifted; 4926 } 4927 } 4928 } 4929 4930 // Remove the temporary PHI node SCEV that has been inserted while intending 4931 // to create an AddRecExpr for this PHI node. We can not keep this temporary 4932 // as it will prevent later (possibly simpler) SCEV expressions to be added 4933 // to the ValueExprMap. 4934 eraseValueFromMap(PN); 4935 4936 return nullptr; 4937 } 4938 4939 // Checks if the SCEV S is available at BB. S is considered available at BB 4940 // if S can be materialized at BB without introducing a fault. 4941 static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S, 4942 BasicBlock *BB) { 4943 struct CheckAvailable { 4944 bool TraversalDone = false; 4945 bool Available = true; 4946 4947 const Loop *L = nullptr; // The loop BB is in (can be nullptr) 4948 BasicBlock *BB = nullptr; 4949 DominatorTree &DT; 4950 4951 CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT) 4952 : L(L), BB(BB), DT(DT) {} 4953 4954 bool setUnavailable() { 4955 TraversalDone = true; 4956 Available = false; 4957 return false; 4958 } 4959 4960 bool follow(const SCEV *S) { 4961 switch (S->getSCEVType()) { 4962 case scConstant: case scTruncate: case scZeroExtend: case scSignExtend: 4963 case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr: 4964 // These expressions are available if their operand(s) is/are. 4965 return true; 4966 4967 case scAddRecExpr: { 4968 // We allow add recurrences that are on the loop BB is in, or some 4969 // outer loop. This guarantees availability because the value of the 4970 // add recurrence at BB is simply the "current" value of the induction 4971 // variable. We can relax this in the future; for instance an add 4972 // recurrence on a sibling dominating loop is also available at BB. 4973 const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop(); 4974 if (L && (ARLoop == L || ARLoop->contains(L))) 4975 return true; 4976 4977 return setUnavailable(); 4978 } 4979 4980 case scUnknown: { 4981 // For SCEVUnknown, we check for simple dominance. 4982 const auto *SU = cast<SCEVUnknown>(S); 4983 Value *V = SU->getValue(); 4984 4985 if (isa<Argument>(V)) 4986 return false; 4987 4988 if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB)) 4989 return false; 4990 4991 return setUnavailable(); 4992 } 4993 4994 case scUDivExpr: 4995 case scCouldNotCompute: 4996 // We do not try to smart about these at all. 4997 return setUnavailable(); 4998 } 4999 llvm_unreachable("switch should be fully covered!"); 5000 } 5001 5002 bool isDone() { return TraversalDone; } 5003 }; 5004 5005 CheckAvailable CA(L, BB, DT); 5006 SCEVTraversal<CheckAvailable> ST(CA); 5007 5008 ST.visitAll(S); 5009 return CA.Available; 5010 } 5011 5012 // Try to match a control flow sequence that branches out at BI and merges back 5013 // at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful 5014 // match. 5015 static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge, 5016 Value *&C, Value *&LHS, Value *&RHS) { 5017 C = BI->getCondition(); 5018 5019 BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0)); 5020 BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1)); 5021 5022 if (!LeftEdge.isSingleEdge()) 5023 return false; 5024 5025 assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()"); 5026 5027 Use &LeftUse = Merge->getOperandUse(0); 5028 Use &RightUse = Merge->getOperandUse(1); 5029 5030 if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) { 5031 LHS = LeftUse; 5032 RHS = RightUse; 5033 return true; 5034 } 5035 5036 if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) { 5037 LHS = RightUse; 5038 RHS = LeftUse; 5039 return true; 5040 } 5041 5042 return false; 5043 } 5044 5045 const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) { 5046 auto IsReachable = 5047 [&](BasicBlock *BB) { return DT.isReachableFromEntry(BB); }; 5048 if (PN->getNumIncomingValues() == 2 && all_of(PN->blocks(), IsReachable)) { 5049 const Loop *L = LI.getLoopFor(PN->getParent()); 5050 5051 // We don't want to break LCSSA, even in a SCEV expression tree. 5052 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) 5053 if (LI.getLoopFor(PN->getIncomingBlock(i)) != L) 5054 return nullptr; 5055 5056 // Try to match 5057 // 5058 // br %cond, label %left, label %right 5059 // left: 5060 // br label %merge 5061 // right: 5062 // br label %merge 5063 // merge: 5064 // V = phi [ %x, %left ], [ %y, %right ] 5065 // 5066 // as "select %cond, %x, %y" 5067 5068 BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock(); 5069 assert(IDom && "At least the entry block should dominate PN"); 5070 5071 auto *BI = dyn_cast<BranchInst>(IDom->getTerminator()); 5072 Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr; 5073 5074 if (BI && BI->isConditional() && 5075 BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) && 5076 IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) && 5077 IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent())) 5078 return createNodeForSelectOrPHI(PN, Cond, LHS, RHS); 5079 } 5080 5081 return nullptr; 5082 } 5083 5084 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 5085 if (const SCEV *S = createAddRecFromPHI(PN)) 5086 return S; 5087 5088 if (const SCEV *S = createNodeFromSelectLikePHI(PN)) 5089 return S; 5090 5091 // If the PHI has a single incoming value, follow that value, unless the 5092 // PHI's incoming blocks are in a different loop, in which case doing so 5093 // risks breaking LCSSA form. Instcombine would normally zap these, but 5094 // it doesn't have DominatorTree information, so it may miss cases. 5095 if (Value *V = SimplifyInstruction(PN, {getDataLayout(), &TLI, &DT, &AC})) 5096 if (LI.replacementPreservesLCSSAForm(PN, V)) 5097 return getSCEV(V); 5098 5099 // If it's not a loop phi, we can't handle it yet. 5100 return getUnknown(PN); 5101 } 5102 5103 const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I, 5104 Value *Cond, 5105 Value *TrueVal, 5106 Value *FalseVal) { 5107 // Handle "constant" branch or select. This can occur for instance when a 5108 // loop pass transforms an inner loop and moves on to process the outer loop. 5109 if (auto *CI = dyn_cast<ConstantInt>(Cond)) 5110 return getSCEV(CI->isOne() ? TrueVal : FalseVal); 5111 5112 // Try to match some simple smax or umax patterns. 5113 auto *ICI = dyn_cast<ICmpInst>(Cond); 5114 if (!ICI) 5115 return getUnknown(I); 5116 5117 Value *LHS = ICI->getOperand(0); 5118 Value *RHS = ICI->getOperand(1); 5119 5120 switch (ICI->getPredicate()) { 5121 case ICmpInst::ICMP_SLT: 5122 case ICmpInst::ICMP_SLE: 5123 std::swap(LHS, RHS); 5124 LLVM_FALLTHROUGH; 5125 case ICmpInst::ICMP_SGT: 5126 case ICmpInst::ICMP_SGE: 5127 // a >s b ? a+x : b+x -> smax(a, b)+x 5128 // a >s b ? b+x : a+x -> smin(a, b)+x 5129 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) { 5130 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType()); 5131 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType()); 5132 const SCEV *LA = getSCEV(TrueVal); 5133 const SCEV *RA = getSCEV(FalseVal); 5134 const SCEV *LDiff = getMinusSCEV(LA, LS); 5135 const SCEV *RDiff = getMinusSCEV(RA, RS); 5136 if (LDiff == RDiff) 5137 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 5138 LDiff = getMinusSCEV(LA, RS); 5139 RDiff = getMinusSCEV(RA, LS); 5140 if (LDiff == RDiff) 5141 return getAddExpr(getSMinExpr(LS, RS), LDiff); 5142 } 5143 break; 5144 case ICmpInst::ICMP_ULT: 5145 case ICmpInst::ICMP_ULE: 5146 std::swap(LHS, RHS); 5147 LLVM_FALLTHROUGH; 5148 case ICmpInst::ICMP_UGT: 5149 case ICmpInst::ICMP_UGE: 5150 // a >u b ? a+x : b+x -> umax(a, b)+x 5151 // a >u b ? b+x : a+x -> umin(a, b)+x 5152 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) { 5153 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType()); 5154 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType()); 5155 const SCEV *LA = getSCEV(TrueVal); 5156 const SCEV *RA = getSCEV(FalseVal); 5157 const SCEV *LDiff = getMinusSCEV(LA, LS); 5158 const SCEV *RDiff = getMinusSCEV(RA, RS); 5159 if (LDiff == RDiff) 5160 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 5161 LDiff = getMinusSCEV(LA, RS); 5162 RDiff = getMinusSCEV(RA, LS); 5163 if (LDiff == RDiff) 5164 return getAddExpr(getUMinExpr(LS, RS), LDiff); 5165 } 5166 break; 5167 case ICmpInst::ICMP_NE: 5168 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 5169 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) && 5170 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) { 5171 const SCEV *One = getOne(I->getType()); 5172 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType()); 5173 const SCEV *LA = getSCEV(TrueVal); 5174 const SCEV *RA = getSCEV(FalseVal); 5175 const SCEV *LDiff = getMinusSCEV(LA, LS); 5176 const SCEV *RDiff = getMinusSCEV(RA, One); 5177 if (LDiff == RDiff) 5178 return getAddExpr(getUMaxExpr(One, LS), LDiff); 5179 } 5180 break; 5181 case ICmpInst::ICMP_EQ: 5182 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 5183 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) && 5184 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) { 5185 const SCEV *One = getOne(I->getType()); 5186 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType()); 5187 const SCEV *LA = getSCEV(TrueVal); 5188 const SCEV *RA = getSCEV(FalseVal); 5189 const SCEV *LDiff = getMinusSCEV(LA, One); 5190 const SCEV *RDiff = getMinusSCEV(RA, LS); 5191 if (LDiff == RDiff) 5192 return getAddExpr(getUMaxExpr(One, LS), LDiff); 5193 } 5194 break; 5195 default: 5196 break; 5197 } 5198 5199 return getUnknown(I); 5200 } 5201 5202 /// Expand GEP instructions into add and multiply operations. This allows them 5203 /// to be analyzed by regular SCEV code. 5204 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 5205 // Don't attempt to analyze GEPs over unsized objects. 5206 if (!GEP->getSourceElementType()->isSized()) 5207 return getUnknown(GEP); 5208 5209 SmallVector<const SCEV *, 4> IndexExprs; 5210 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index) 5211 IndexExprs.push_back(getSCEV(*Index)); 5212 return getGEPExpr(GEP, IndexExprs); 5213 } 5214 5215 uint32_t ScalarEvolution::GetMinTrailingZerosImpl(const SCEV *S) { 5216 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 5217 return C->getAPInt().countTrailingZeros(); 5218 5219 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 5220 return std::min(GetMinTrailingZeros(T->getOperand()), 5221 (uint32_t)getTypeSizeInBits(T->getType())); 5222 5223 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 5224 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 5225 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) 5226 ? getTypeSizeInBits(E->getType()) 5227 : OpRes; 5228 } 5229 5230 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 5231 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 5232 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) 5233 ? getTypeSizeInBits(E->getType()) 5234 : OpRes; 5235 } 5236 5237 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 5238 // The result is the min of all operands results. 5239 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 5240 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 5241 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 5242 return MinOpRes; 5243 } 5244 5245 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 5246 // The result is the sum of all operands results. 5247 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 5248 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 5249 for (unsigned i = 1, e = M->getNumOperands(); 5250 SumOpRes != BitWidth && i != e; ++i) 5251 SumOpRes = 5252 std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), BitWidth); 5253 return SumOpRes; 5254 } 5255 5256 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 5257 // The result is the min of all operands results. 5258 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 5259 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 5260 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 5261 return MinOpRes; 5262 } 5263 5264 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 5265 // The result is the min of all operands results. 5266 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 5267 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 5268 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 5269 return MinOpRes; 5270 } 5271 5272 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 5273 // The result is the min of all operands results. 5274 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 5275 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 5276 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 5277 return MinOpRes; 5278 } 5279 5280 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 5281 // For a SCEVUnknown, ask ValueTracking. 5282 KnownBits Known = computeKnownBits(U->getValue(), getDataLayout(), 0, &AC, nullptr, &DT); 5283 return Known.countMinTrailingZeros(); 5284 } 5285 5286 // SCEVUDivExpr 5287 return 0; 5288 } 5289 5290 uint32_t ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 5291 auto I = MinTrailingZerosCache.find(S); 5292 if (I != MinTrailingZerosCache.end()) 5293 return I->second; 5294 5295 uint32_t Result = GetMinTrailingZerosImpl(S); 5296 auto InsertPair = MinTrailingZerosCache.insert({S, Result}); 5297 assert(InsertPair.second && "Should insert a new key"); 5298 return InsertPair.first->second; 5299 } 5300 5301 /// Helper method to assign a range to V from metadata present in the IR. 5302 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) { 5303 if (Instruction *I = dyn_cast<Instruction>(V)) 5304 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) 5305 return getConstantRangeFromMetadata(*MD); 5306 5307 return None; 5308 } 5309 5310 /// Determine the range for a particular SCEV. If SignHint is 5311 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges 5312 /// with a "cleaner" unsigned (resp. signed) representation. 5313 const ConstantRange & 5314 ScalarEvolution::getRangeRef(const SCEV *S, 5315 ScalarEvolution::RangeSignHint SignHint) { 5316 DenseMap<const SCEV *, ConstantRange> &Cache = 5317 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges 5318 : SignedRanges; 5319 5320 // See if we've computed this range already. 5321 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S); 5322 if (I != Cache.end()) 5323 return I->second; 5324 5325 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 5326 return setRange(C, SignHint, ConstantRange(C->getAPInt())); 5327 5328 unsigned BitWidth = getTypeSizeInBits(S->getType()); 5329 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 5330 5331 // If the value has known zeros, the maximum value will have those known zeros 5332 // as well. 5333 uint32_t TZ = GetMinTrailingZeros(S); 5334 if (TZ != 0) { 5335 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) 5336 ConservativeResult = 5337 ConstantRange(APInt::getMinValue(BitWidth), 5338 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 5339 else 5340 ConservativeResult = ConstantRange( 5341 APInt::getSignedMinValue(BitWidth), 5342 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 5343 } 5344 5345 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 5346 ConstantRange X = getRangeRef(Add->getOperand(0), SignHint); 5347 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 5348 X = X.add(getRangeRef(Add->getOperand(i), SignHint)); 5349 return setRange(Add, SignHint, ConservativeResult.intersectWith(X)); 5350 } 5351 5352 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 5353 ConstantRange X = getRangeRef(Mul->getOperand(0), SignHint); 5354 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 5355 X = X.multiply(getRangeRef(Mul->getOperand(i), SignHint)); 5356 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X)); 5357 } 5358 5359 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 5360 ConstantRange X = getRangeRef(SMax->getOperand(0), SignHint); 5361 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 5362 X = X.smax(getRangeRef(SMax->getOperand(i), SignHint)); 5363 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X)); 5364 } 5365 5366 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 5367 ConstantRange X = getRangeRef(UMax->getOperand(0), SignHint); 5368 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 5369 X = X.umax(getRangeRef(UMax->getOperand(i), SignHint)); 5370 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X)); 5371 } 5372 5373 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 5374 ConstantRange X = getRangeRef(UDiv->getLHS(), SignHint); 5375 ConstantRange Y = getRangeRef(UDiv->getRHS(), SignHint); 5376 return setRange(UDiv, SignHint, 5377 ConservativeResult.intersectWith(X.udiv(Y))); 5378 } 5379 5380 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 5381 ConstantRange X = getRangeRef(ZExt->getOperand(), SignHint); 5382 return setRange(ZExt, SignHint, 5383 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 5384 } 5385 5386 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 5387 ConstantRange X = getRangeRef(SExt->getOperand(), SignHint); 5388 return setRange(SExt, SignHint, 5389 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 5390 } 5391 5392 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 5393 ConstantRange X = getRangeRef(Trunc->getOperand(), SignHint); 5394 return setRange(Trunc, SignHint, 5395 ConservativeResult.intersectWith(X.truncate(BitWidth))); 5396 } 5397 5398 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 5399 // If there's no unsigned wrap, the value will never be less than its 5400 // initial value. 5401 if (AddRec->hasNoUnsignedWrap()) 5402 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 5403 if (!C->getValue()->isZero()) 5404 ConservativeResult = ConservativeResult.intersectWith( 5405 ConstantRange(C->getAPInt(), APInt(BitWidth, 0))); 5406 5407 // If there's no signed wrap, and all the operands have the same sign or 5408 // zero, the value won't ever change sign. 5409 if (AddRec->hasNoSignedWrap()) { 5410 bool AllNonNeg = true; 5411 bool AllNonPos = true; 5412 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 5413 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 5414 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 5415 } 5416 if (AllNonNeg) 5417 ConservativeResult = ConservativeResult.intersectWith( 5418 ConstantRange(APInt(BitWidth, 0), 5419 APInt::getSignedMinValue(BitWidth))); 5420 else if (AllNonPos) 5421 ConservativeResult = ConservativeResult.intersectWith( 5422 ConstantRange(APInt::getSignedMinValue(BitWidth), 5423 APInt(BitWidth, 1))); 5424 } 5425 5426 // TODO: non-affine addrec 5427 if (AddRec->isAffine()) { 5428 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 5429 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 5430 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 5431 auto RangeFromAffine = getRangeForAffineAR( 5432 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount, 5433 BitWidth); 5434 if (!RangeFromAffine.isFullSet()) 5435 ConservativeResult = 5436 ConservativeResult.intersectWith(RangeFromAffine); 5437 5438 auto RangeFromFactoring = getRangeViaFactoring( 5439 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount, 5440 BitWidth); 5441 if (!RangeFromFactoring.isFullSet()) 5442 ConservativeResult = 5443 ConservativeResult.intersectWith(RangeFromFactoring); 5444 } 5445 } 5446 5447 return setRange(AddRec, SignHint, std::move(ConservativeResult)); 5448 } 5449 5450 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 5451 // Check if the IR explicitly contains !range metadata. 5452 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue()); 5453 if (MDRange.hasValue()) 5454 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue()); 5455 5456 // Split here to avoid paying the compile-time cost of calling both 5457 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted 5458 // if needed. 5459 const DataLayout &DL = getDataLayout(); 5460 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) { 5461 // For a SCEVUnknown, ask ValueTracking. 5462 KnownBits Known = computeKnownBits(U->getValue(), DL, 0, &AC, nullptr, &DT); 5463 if (Known.One != ~Known.Zero + 1) 5464 ConservativeResult = 5465 ConservativeResult.intersectWith(ConstantRange(Known.One, 5466 ~Known.Zero + 1)); 5467 } else { 5468 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED && 5469 "generalize as needed!"); 5470 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT); 5471 if (NS > 1) 5472 ConservativeResult = ConservativeResult.intersectWith( 5473 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 5474 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1)); 5475 } 5476 5477 return setRange(U, SignHint, std::move(ConservativeResult)); 5478 } 5479 5480 return setRange(S, SignHint, std::move(ConservativeResult)); 5481 } 5482 5483 // Given a StartRange, Step and MaxBECount for an expression compute a range of 5484 // values that the expression can take. Initially, the expression has a value 5485 // from StartRange and then is changed by Step up to MaxBECount times. Signed 5486 // argument defines if we treat Step as signed or unsigned. 5487 static ConstantRange getRangeForAffineARHelper(APInt Step, 5488 const ConstantRange &StartRange, 5489 const APInt &MaxBECount, 5490 unsigned BitWidth, bool Signed) { 5491 // If either Step or MaxBECount is 0, then the expression won't change, and we 5492 // just need to return the initial range. 5493 if (Step == 0 || MaxBECount == 0) 5494 return StartRange; 5495 5496 // If we don't know anything about the initial value (i.e. StartRange is 5497 // FullRange), then we don't know anything about the final range either. 5498 // Return FullRange. 5499 if (StartRange.isFullSet()) 5500 return ConstantRange(BitWidth, /* isFullSet = */ true); 5501 5502 // If Step is signed and negative, then we use its absolute value, but we also 5503 // note that we're moving in the opposite direction. 5504 bool Descending = Signed && Step.isNegative(); 5505 5506 if (Signed) 5507 // This is correct even for INT_SMIN. Let's look at i8 to illustrate this: 5508 // abs(INT_SMIN) = abs(-128) = abs(0x80) = -0x80 = 0x80 = 128. 5509 // This equations hold true due to the well-defined wrap-around behavior of 5510 // APInt. 5511 Step = Step.abs(); 5512 5513 // Check if Offset is more than full span of BitWidth. If it is, the 5514 // expression is guaranteed to overflow. 5515 if (APInt::getMaxValue(StartRange.getBitWidth()).udiv(Step).ult(MaxBECount)) 5516 return ConstantRange(BitWidth, /* isFullSet = */ true); 5517 5518 // Offset is by how much the expression can change. Checks above guarantee no 5519 // overflow here. 5520 APInt Offset = Step * MaxBECount; 5521 5522 // Minimum value of the final range will match the minimal value of StartRange 5523 // if the expression is increasing and will be decreased by Offset otherwise. 5524 // Maximum value of the final range will match the maximal value of StartRange 5525 // if the expression is decreasing and will be increased by Offset otherwise. 5526 APInt StartLower = StartRange.getLower(); 5527 APInt StartUpper = StartRange.getUpper() - 1; 5528 APInt MovedBoundary = Descending ? (StartLower - std::move(Offset)) 5529 : (StartUpper + std::move(Offset)); 5530 5531 // It's possible that the new minimum/maximum value will fall into the initial 5532 // range (due to wrap around). This means that the expression can take any 5533 // value in this bitwidth, and we have to return full range. 5534 if (StartRange.contains(MovedBoundary)) 5535 return ConstantRange(BitWidth, /* isFullSet = */ true); 5536 5537 APInt NewLower = 5538 Descending ? std::move(MovedBoundary) : std::move(StartLower); 5539 APInt NewUpper = 5540 Descending ? std::move(StartUpper) : std::move(MovedBoundary); 5541 NewUpper += 1; 5542 5543 // If we end up with full range, return a proper full range. 5544 if (NewLower == NewUpper) 5545 return ConstantRange(BitWidth, /* isFullSet = */ true); 5546 5547 // No overflow detected, return [StartLower, StartUpper + Offset + 1) range. 5548 return ConstantRange(std::move(NewLower), std::move(NewUpper)); 5549 } 5550 5551 ConstantRange ScalarEvolution::getRangeForAffineAR(const SCEV *Start, 5552 const SCEV *Step, 5553 const SCEV *MaxBECount, 5554 unsigned BitWidth) { 5555 assert(!isa<SCEVCouldNotCompute>(MaxBECount) && 5556 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth && 5557 "Precondition!"); 5558 5559 MaxBECount = getNoopOrZeroExtend(MaxBECount, Start->getType()); 5560 APInt MaxBECountValue = getUnsignedRangeMax(MaxBECount); 5561 5562 // First, consider step signed. 5563 ConstantRange StartSRange = getSignedRange(Start); 5564 ConstantRange StepSRange = getSignedRange(Step); 5565 5566 // If Step can be both positive and negative, we need to find ranges for the 5567 // maximum absolute step values in both directions and union them. 5568 ConstantRange SR = 5569 getRangeForAffineARHelper(StepSRange.getSignedMin(), StartSRange, 5570 MaxBECountValue, BitWidth, /* Signed = */ true); 5571 SR = SR.unionWith(getRangeForAffineARHelper(StepSRange.getSignedMax(), 5572 StartSRange, MaxBECountValue, 5573 BitWidth, /* Signed = */ true)); 5574 5575 // Next, consider step unsigned. 5576 ConstantRange UR = getRangeForAffineARHelper( 5577 getUnsignedRangeMax(Step), getUnsignedRange(Start), 5578 MaxBECountValue, BitWidth, /* Signed = */ false); 5579 5580 // Finally, intersect signed and unsigned ranges. 5581 return SR.intersectWith(UR); 5582 } 5583 5584 ConstantRange ScalarEvolution::getRangeViaFactoring(const SCEV *Start, 5585 const SCEV *Step, 5586 const SCEV *MaxBECount, 5587 unsigned BitWidth) { 5588 // RangeOf({C?A:B,+,C?P:Q}) == RangeOf(C?{A,+,P}:{B,+,Q}) 5589 // == RangeOf({A,+,P}) union RangeOf({B,+,Q}) 5590 5591 struct SelectPattern { 5592 Value *Condition = nullptr; 5593 APInt TrueValue; 5594 APInt FalseValue; 5595 5596 explicit SelectPattern(ScalarEvolution &SE, unsigned BitWidth, 5597 const SCEV *S) { 5598 Optional<unsigned> CastOp; 5599 APInt Offset(BitWidth, 0); 5600 5601 assert(SE.getTypeSizeInBits(S->getType()) == BitWidth && 5602 "Should be!"); 5603 5604 // Peel off a constant offset: 5605 if (auto *SA = dyn_cast<SCEVAddExpr>(S)) { 5606 // In the future we could consider being smarter here and handle 5607 // {Start+Step,+,Step} too. 5608 if (SA->getNumOperands() != 2 || !isa<SCEVConstant>(SA->getOperand(0))) 5609 return; 5610 5611 Offset = cast<SCEVConstant>(SA->getOperand(0))->getAPInt(); 5612 S = SA->getOperand(1); 5613 } 5614 5615 // Peel off a cast operation 5616 if (auto *SCast = dyn_cast<SCEVCastExpr>(S)) { 5617 CastOp = SCast->getSCEVType(); 5618 S = SCast->getOperand(); 5619 } 5620 5621 using namespace llvm::PatternMatch; 5622 5623 auto *SU = dyn_cast<SCEVUnknown>(S); 5624 const APInt *TrueVal, *FalseVal; 5625 if (!SU || 5626 !match(SU->getValue(), m_Select(m_Value(Condition), m_APInt(TrueVal), 5627 m_APInt(FalseVal)))) { 5628 Condition = nullptr; 5629 return; 5630 } 5631 5632 TrueValue = *TrueVal; 5633 FalseValue = *FalseVal; 5634 5635 // Re-apply the cast we peeled off earlier 5636 if (CastOp.hasValue()) 5637 switch (*CastOp) { 5638 default: 5639 llvm_unreachable("Unknown SCEV cast type!"); 5640 5641 case scTruncate: 5642 TrueValue = TrueValue.trunc(BitWidth); 5643 FalseValue = FalseValue.trunc(BitWidth); 5644 break; 5645 case scZeroExtend: 5646 TrueValue = TrueValue.zext(BitWidth); 5647 FalseValue = FalseValue.zext(BitWidth); 5648 break; 5649 case scSignExtend: 5650 TrueValue = TrueValue.sext(BitWidth); 5651 FalseValue = FalseValue.sext(BitWidth); 5652 break; 5653 } 5654 5655 // Re-apply the constant offset we peeled off earlier 5656 TrueValue += Offset; 5657 FalseValue += Offset; 5658 } 5659 5660 bool isRecognized() { return Condition != nullptr; } 5661 }; 5662 5663 SelectPattern StartPattern(*this, BitWidth, Start); 5664 if (!StartPattern.isRecognized()) 5665 return ConstantRange(BitWidth, /* isFullSet = */ true); 5666 5667 SelectPattern StepPattern(*this, BitWidth, Step); 5668 if (!StepPattern.isRecognized()) 5669 return ConstantRange(BitWidth, /* isFullSet = */ true); 5670 5671 if (StartPattern.Condition != StepPattern.Condition) { 5672 // We don't handle this case today; but we could, by considering four 5673 // possibilities below instead of two. I'm not sure if there are cases where 5674 // that will help over what getRange already does, though. 5675 return ConstantRange(BitWidth, /* isFullSet = */ true); 5676 } 5677 5678 // NB! Calling ScalarEvolution::getConstant is fine, but we should not try to 5679 // construct arbitrary general SCEV expressions here. This function is called 5680 // from deep in the call stack, and calling getSCEV (on a sext instruction, 5681 // say) can end up caching a suboptimal value. 5682 5683 // FIXME: without the explicit `this` receiver below, MSVC errors out with 5684 // C2352 and C2512 (otherwise it isn't needed). 5685 5686 const SCEV *TrueStart = this->getConstant(StartPattern.TrueValue); 5687 const SCEV *TrueStep = this->getConstant(StepPattern.TrueValue); 5688 const SCEV *FalseStart = this->getConstant(StartPattern.FalseValue); 5689 const SCEV *FalseStep = this->getConstant(StepPattern.FalseValue); 5690 5691 ConstantRange TrueRange = 5692 this->getRangeForAffineAR(TrueStart, TrueStep, MaxBECount, BitWidth); 5693 ConstantRange FalseRange = 5694 this->getRangeForAffineAR(FalseStart, FalseStep, MaxBECount, BitWidth); 5695 5696 return TrueRange.unionWith(FalseRange); 5697 } 5698 5699 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) { 5700 if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap; 5701 const BinaryOperator *BinOp = cast<BinaryOperator>(V); 5702 5703 // Return early if there are no flags to propagate to the SCEV. 5704 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; 5705 if (BinOp->hasNoUnsignedWrap()) 5706 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW); 5707 if (BinOp->hasNoSignedWrap()) 5708 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW); 5709 if (Flags == SCEV::FlagAnyWrap) 5710 return SCEV::FlagAnyWrap; 5711 5712 return isSCEVExprNeverPoison(BinOp) ? Flags : SCEV::FlagAnyWrap; 5713 } 5714 5715 bool ScalarEvolution::isSCEVExprNeverPoison(const Instruction *I) { 5716 // Here we check that I is in the header of the innermost loop containing I, 5717 // since we only deal with instructions in the loop header. The actual loop we 5718 // need to check later will come from an add recurrence, but getting that 5719 // requires computing the SCEV of the operands, which can be expensive. This 5720 // check we can do cheaply to rule out some cases early. 5721 Loop *InnermostContainingLoop = LI.getLoopFor(I->getParent()); 5722 if (InnermostContainingLoop == nullptr || 5723 InnermostContainingLoop->getHeader() != I->getParent()) 5724 return false; 5725 5726 // Only proceed if we can prove that I does not yield poison. 5727 if (!programUndefinedIfFullPoison(I)) 5728 return false; 5729 5730 // At this point we know that if I is executed, then it does not wrap 5731 // according to at least one of NSW or NUW. If I is not executed, then we do 5732 // not know if the calculation that I represents would wrap. Multiple 5733 // instructions can map to the same SCEV. If we apply NSW or NUW from I to 5734 // the SCEV, we must guarantee no wrapping for that SCEV also when it is 5735 // derived from other instructions that map to the same SCEV. We cannot make 5736 // that guarantee for cases where I is not executed. So we need to find the 5737 // loop that I is considered in relation to and prove that I is executed for 5738 // every iteration of that loop. That implies that the value that I 5739 // calculates does not wrap anywhere in the loop, so then we can apply the 5740 // flags to the SCEV. 5741 // 5742 // We check isLoopInvariant to disambiguate in case we are adding recurrences 5743 // from different loops, so that we know which loop to prove that I is 5744 // executed in. 5745 for (unsigned OpIndex = 0; OpIndex < I->getNumOperands(); ++OpIndex) { 5746 // I could be an extractvalue from a call to an overflow intrinsic. 5747 // TODO: We can do better here in some cases. 5748 if (!isSCEVable(I->getOperand(OpIndex)->getType())) 5749 return false; 5750 const SCEV *Op = getSCEV(I->getOperand(OpIndex)); 5751 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 5752 bool AllOtherOpsLoopInvariant = true; 5753 for (unsigned OtherOpIndex = 0; OtherOpIndex < I->getNumOperands(); 5754 ++OtherOpIndex) { 5755 if (OtherOpIndex != OpIndex) { 5756 const SCEV *OtherOp = getSCEV(I->getOperand(OtherOpIndex)); 5757 if (!isLoopInvariant(OtherOp, AddRec->getLoop())) { 5758 AllOtherOpsLoopInvariant = false; 5759 break; 5760 } 5761 } 5762 } 5763 if (AllOtherOpsLoopInvariant && 5764 isGuaranteedToExecuteForEveryIteration(I, AddRec->getLoop())) 5765 return true; 5766 } 5767 } 5768 return false; 5769 } 5770 5771 bool ScalarEvolution::isAddRecNeverPoison(const Instruction *I, const Loop *L) { 5772 // If we know that \c I can never be poison period, then that's enough. 5773 if (isSCEVExprNeverPoison(I)) 5774 return true; 5775 5776 // For an add recurrence specifically, we assume that infinite loops without 5777 // side effects are undefined behavior, and then reason as follows: 5778 // 5779 // If the add recurrence is poison in any iteration, it is poison on all 5780 // future iterations (since incrementing poison yields poison). If the result 5781 // of the add recurrence is fed into the loop latch condition and the loop 5782 // does not contain any throws or exiting blocks other than the latch, we now 5783 // have the ability to "choose" whether the backedge is taken or not (by 5784 // choosing a sufficiently evil value for the poison feeding into the branch) 5785 // for every iteration including and after the one in which \p I first became 5786 // poison. There are two possibilities (let's call the iteration in which \p 5787 // I first became poison as K): 5788 // 5789 // 1. In the set of iterations including and after K, the loop body executes 5790 // no side effects. In this case executing the backege an infinte number 5791 // of times will yield undefined behavior. 5792 // 5793 // 2. In the set of iterations including and after K, the loop body executes 5794 // at least one side effect. In this case, that specific instance of side 5795 // effect is control dependent on poison, which also yields undefined 5796 // behavior. 5797 5798 auto *ExitingBB = L->getExitingBlock(); 5799 auto *LatchBB = L->getLoopLatch(); 5800 if (!ExitingBB || !LatchBB || ExitingBB != LatchBB) 5801 return false; 5802 5803 SmallPtrSet<const Instruction *, 16> Pushed; 5804 SmallVector<const Instruction *, 8> PoisonStack; 5805 5806 // We start by assuming \c I, the post-inc add recurrence, is poison. Only 5807 // things that are known to be fully poison under that assumption go on the 5808 // PoisonStack. 5809 Pushed.insert(I); 5810 PoisonStack.push_back(I); 5811 5812 bool LatchControlDependentOnPoison = false; 5813 while (!PoisonStack.empty() && !LatchControlDependentOnPoison) { 5814 const Instruction *Poison = PoisonStack.pop_back_val(); 5815 5816 for (auto *PoisonUser : Poison->users()) { 5817 if (propagatesFullPoison(cast<Instruction>(PoisonUser))) { 5818 if (Pushed.insert(cast<Instruction>(PoisonUser)).second) 5819 PoisonStack.push_back(cast<Instruction>(PoisonUser)); 5820 } else if (auto *BI = dyn_cast<BranchInst>(PoisonUser)) { 5821 assert(BI->isConditional() && "Only possibility!"); 5822 if (BI->getParent() == LatchBB) { 5823 LatchControlDependentOnPoison = true; 5824 break; 5825 } 5826 } 5827 } 5828 } 5829 5830 return LatchControlDependentOnPoison && loopHasNoAbnormalExits(L); 5831 } 5832 5833 ScalarEvolution::LoopProperties 5834 ScalarEvolution::getLoopProperties(const Loop *L) { 5835 using LoopProperties = ScalarEvolution::LoopProperties; 5836 5837 auto Itr = LoopPropertiesCache.find(L); 5838 if (Itr == LoopPropertiesCache.end()) { 5839 auto HasSideEffects = [](Instruction *I) { 5840 if (auto *SI = dyn_cast<StoreInst>(I)) 5841 return !SI->isSimple(); 5842 5843 return I->mayHaveSideEffects(); 5844 }; 5845 5846 LoopProperties LP = {/* HasNoAbnormalExits */ true, 5847 /*HasNoSideEffects*/ true}; 5848 5849 for (auto *BB : L->getBlocks()) 5850 for (auto &I : *BB) { 5851 if (!isGuaranteedToTransferExecutionToSuccessor(&I)) 5852 LP.HasNoAbnormalExits = false; 5853 if (HasSideEffects(&I)) 5854 LP.HasNoSideEffects = false; 5855 if (!LP.HasNoAbnormalExits && !LP.HasNoSideEffects) 5856 break; // We're already as pessimistic as we can get. 5857 } 5858 5859 auto InsertPair = LoopPropertiesCache.insert({L, LP}); 5860 assert(InsertPair.second && "We just checked!"); 5861 Itr = InsertPair.first; 5862 } 5863 5864 return Itr->second; 5865 } 5866 5867 const SCEV *ScalarEvolution::createSCEV(Value *V) { 5868 if (!isSCEVable(V->getType())) 5869 return getUnknown(V); 5870 5871 if (Instruction *I = dyn_cast<Instruction>(V)) { 5872 // Don't attempt to analyze instructions in blocks that aren't 5873 // reachable. Such instructions don't matter, and they aren't required 5874 // to obey basic rules for definitions dominating uses which this 5875 // analysis depends on. 5876 if (!DT.isReachableFromEntry(I->getParent())) 5877 return getUnknown(V); 5878 } else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 5879 return getConstant(CI); 5880 else if (isa<ConstantPointerNull>(V)) 5881 return getZero(V->getType()); 5882 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 5883 return GA->isInterposable() ? getUnknown(V) : getSCEV(GA->getAliasee()); 5884 else if (!isa<ConstantExpr>(V)) 5885 return getUnknown(V); 5886 5887 Operator *U = cast<Operator>(V); 5888 if (auto BO = MatchBinaryOp(U, DT)) { 5889 switch (BO->Opcode) { 5890 case Instruction::Add: { 5891 // The simple thing to do would be to just call getSCEV on both operands 5892 // and call getAddExpr with the result. However if we're looking at a 5893 // bunch of things all added together, this can be quite inefficient, 5894 // because it leads to N-1 getAddExpr calls for N ultimate operands. 5895 // Instead, gather up all the operands and make a single getAddExpr call. 5896 // LLVM IR canonical form means we need only traverse the left operands. 5897 SmallVector<const SCEV *, 4> AddOps; 5898 do { 5899 if (BO->Op) { 5900 if (auto *OpSCEV = getExistingSCEV(BO->Op)) { 5901 AddOps.push_back(OpSCEV); 5902 break; 5903 } 5904 5905 // If a NUW or NSW flag can be applied to the SCEV for this 5906 // addition, then compute the SCEV for this addition by itself 5907 // with a separate call to getAddExpr. We need to do that 5908 // instead of pushing the operands of the addition onto AddOps, 5909 // since the flags are only known to apply to this particular 5910 // addition - they may not apply to other additions that can be 5911 // formed with operands from AddOps. 5912 const SCEV *RHS = getSCEV(BO->RHS); 5913 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op); 5914 if (Flags != SCEV::FlagAnyWrap) { 5915 const SCEV *LHS = getSCEV(BO->LHS); 5916 if (BO->Opcode == Instruction::Sub) 5917 AddOps.push_back(getMinusSCEV(LHS, RHS, Flags)); 5918 else 5919 AddOps.push_back(getAddExpr(LHS, RHS, Flags)); 5920 break; 5921 } 5922 } 5923 5924 if (BO->Opcode == Instruction::Sub) 5925 AddOps.push_back(getNegativeSCEV(getSCEV(BO->RHS))); 5926 else 5927 AddOps.push_back(getSCEV(BO->RHS)); 5928 5929 auto NewBO = MatchBinaryOp(BO->LHS, DT); 5930 if (!NewBO || (NewBO->Opcode != Instruction::Add && 5931 NewBO->Opcode != Instruction::Sub)) { 5932 AddOps.push_back(getSCEV(BO->LHS)); 5933 break; 5934 } 5935 BO = NewBO; 5936 } while (true); 5937 5938 return getAddExpr(AddOps); 5939 } 5940 5941 case Instruction::Mul: { 5942 SmallVector<const SCEV *, 4> MulOps; 5943 do { 5944 if (BO->Op) { 5945 if (auto *OpSCEV = getExistingSCEV(BO->Op)) { 5946 MulOps.push_back(OpSCEV); 5947 break; 5948 } 5949 5950 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op); 5951 if (Flags != SCEV::FlagAnyWrap) { 5952 MulOps.push_back( 5953 getMulExpr(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags)); 5954 break; 5955 } 5956 } 5957 5958 MulOps.push_back(getSCEV(BO->RHS)); 5959 auto NewBO = MatchBinaryOp(BO->LHS, DT); 5960 if (!NewBO || NewBO->Opcode != Instruction::Mul) { 5961 MulOps.push_back(getSCEV(BO->LHS)); 5962 break; 5963 } 5964 BO = NewBO; 5965 } while (true); 5966 5967 return getMulExpr(MulOps); 5968 } 5969 case Instruction::UDiv: 5970 return getUDivExpr(getSCEV(BO->LHS), getSCEV(BO->RHS)); 5971 case Instruction::URem: 5972 return getURemExpr(getSCEV(BO->LHS), getSCEV(BO->RHS)); 5973 case Instruction::Sub: { 5974 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; 5975 if (BO->Op) 5976 Flags = getNoWrapFlagsFromUB(BO->Op); 5977 return getMinusSCEV(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags); 5978 } 5979 case Instruction::And: 5980 // For an expression like x&255 that merely masks off the high bits, 5981 // use zext(trunc(x)) as the SCEV expression. 5982 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) { 5983 if (CI->isZero()) 5984 return getSCEV(BO->RHS); 5985 if (CI->isMinusOne()) 5986 return getSCEV(BO->LHS); 5987 const APInt &A = CI->getValue(); 5988 5989 // Instcombine's ShrinkDemandedConstant may strip bits out of 5990 // constants, obscuring what would otherwise be a low-bits mask. 5991 // Use computeKnownBits to compute what ShrinkDemandedConstant 5992 // knew about to reconstruct a low-bits mask value. 5993 unsigned LZ = A.countLeadingZeros(); 5994 unsigned TZ = A.countTrailingZeros(); 5995 unsigned BitWidth = A.getBitWidth(); 5996 KnownBits Known(BitWidth); 5997 computeKnownBits(BO->LHS, Known, getDataLayout(), 5998 0, &AC, nullptr, &DT); 5999 6000 APInt EffectiveMask = 6001 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ); 6002 if ((LZ != 0 || TZ != 0) && !((~A & ~Known.Zero) & EffectiveMask)) { 6003 const SCEV *MulCount = getConstant(APInt::getOneBitSet(BitWidth, TZ)); 6004 const SCEV *LHS = getSCEV(BO->LHS); 6005 const SCEV *ShiftedLHS = nullptr; 6006 if (auto *LHSMul = dyn_cast<SCEVMulExpr>(LHS)) { 6007 if (auto *OpC = dyn_cast<SCEVConstant>(LHSMul->getOperand(0))) { 6008 // For an expression like (x * 8) & 8, simplify the multiply. 6009 unsigned MulZeros = OpC->getAPInt().countTrailingZeros(); 6010 unsigned GCD = std::min(MulZeros, TZ); 6011 APInt DivAmt = APInt::getOneBitSet(BitWidth, TZ - GCD); 6012 SmallVector<const SCEV*, 4> MulOps; 6013 MulOps.push_back(getConstant(OpC->getAPInt().lshr(GCD))); 6014 MulOps.append(LHSMul->op_begin() + 1, LHSMul->op_end()); 6015 auto *NewMul = getMulExpr(MulOps, LHSMul->getNoWrapFlags()); 6016 ShiftedLHS = getUDivExpr(NewMul, getConstant(DivAmt)); 6017 } 6018 } 6019 if (!ShiftedLHS) 6020 ShiftedLHS = getUDivExpr(LHS, MulCount); 6021 return getMulExpr( 6022 getZeroExtendExpr( 6023 getTruncateExpr(ShiftedLHS, 6024 IntegerType::get(getContext(), BitWidth - LZ - TZ)), 6025 BO->LHS->getType()), 6026 MulCount); 6027 } 6028 } 6029 break; 6030 6031 case Instruction::Or: 6032 // If the RHS of the Or is a constant, we may have something like: 6033 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 6034 // optimizations will transparently handle this case. 6035 // 6036 // In order for this transformation to be safe, the LHS must be of the 6037 // form X*(2^n) and the Or constant must be less than 2^n. 6038 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) { 6039 const SCEV *LHS = getSCEV(BO->LHS); 6040 const APInt &CIVal = CI->getValue(); 6041 if (GetMinTrailingZeros(LHS) >= 6042 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 6043 // Build a plain add SCEV. 6044 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 6045 // If the LHS of the add was an addrec and it has no-wrap flags, 6046 // transfer the no-wrap flags, since an or won't introduce a wrap. 6047 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 6048 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 6049 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags( 6050 OldAR->getNoWrapFlags()); 6051 } 6052 return S; 6053 } 6054 } 6055 break; 6056 6057 case Instruction::Xor: 6058 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) { 6059 // If the RHS of xor is -1, then this is a not operation. 6060 if (CI->isMinusOne()) 6061 return getNotSCEV(getSCEV(BO->LHS)); 6062 6063 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 6064 // This is a variant of the check for xor with -1, and it handles 6065 // the case where instcombine has trimmed non-demanded bits out 6066 // of an xor with -1. 6067 if (auto *LBO = dyn_cast<BinaryOperator>(BO->LHS)) 6068 if (ConstantInt *LCI = dyn_cast<ConstantInt>(LBO->getOperand(1))) 6069 if (LBO->getOpcode() == Instruction::And && 6070 LCI->getValue() == CI->getValue()) 6071 if (const SCEVZeroExtendExpr *Z = 6072 dyn_cast<SCEVZeroExtendExpr>(getSCEV(BO->LHS))) { 6073 Type *UTy = BO->LHS->getType(); 6074 const SCEV *Z0 = Z->getOperand(); 6075 Type *Z0Ty = Z0->getType(); 6076 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 6077 6078 // If C is a low-bits mask, the zero extend is serving to 6079 // mask off the high bits. Complement the operand and 6080 // re-apply the zext. 6081 if (CI->getValue().isMask(Z0TySize)) 6082 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 6083 6084 // If C is a single bit, it may be in the sign-bit position 6085 // before the zero-extend. In this case, represent the xor 6086 // using an add, which is equivalent, and re-apply the zext. 6087 APInt Trunc = CI->getValue().trunc(Z0TySize); 6088 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() && 6089 Trunc.isSignMask()) 6090 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 6091 UTy); 6092 } 6093 } 6094 break; 6095 6096 case Instruction::Shl: 6097 // Turn shift left of a constant amount into a multiply. 6098 if (ConstantInt *SA = dyn_cast<ConstantInt>(BO->RHS)) { 6099 uint32_t BitWidth = cast<IntegerType>(SA->getType())->getBitWidth(); 6100 6101 // If the shift count is not less than the bitwidth, the result of 6102 // the shift is undefined. Don't try to analyze it, because the 6103 // resolution chosen here may differ from the resolution chosen in 6104 // other parts of the compiler. 6105 if (SA->getValue().uge(BitWidth)) 6106 break; 6107 6108 // It is currently not resolved how to interpret NSW for left 6109 // shift by BitWidth - 1, so we avoid applying flags in that 6110 // case. Remove this check (or this comment) once the situation 6111 // is resolved. See 6112 // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html 6113 // and http://reviews.llvm.org/D8890 . 6114 auto Flags = SCEV::FlagAnyWrap; 6115 if (BO->Op && SA->getValue().ult(BitWidth - 1)) 6116 Flags = getNoWrapFlagsFromUB(BO->Op); 6117 6118 Constant *X = ConstantInt::get(getContext(), 6119 APInt::getOneBitSet(BitWidth, SA->getZExtValue())); 6120 return getMulExpr(getSCEV(BO->LHS), getSCEV(X), Flags); 6121 } 6122 break; 6123 6124 case Instruction::AShr: { 6125 // AShr X, C, where C is a constant. 6126 ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS); 6127 if (!CI) 6128 break; 6129 6130 Type *OuterTy = BO->LHS->getType(); 6131 uint64_t BitWidth = getTypeSizeInBits(OuterTy); 6132 // If the shift count is not less than the bitwidth, the result of 6133 // the shift is undefined. Don't try to analyze it, because the 6134 // resolution chosen here may differ from the resolution chosen in 6135 // other parts of the compiler. 6136 if (CI->getValue().uge(BitWidth)) 6137 break; 6138 6139 if (CI->isZero()) 6140 return getSCEV(BO->LHS); // shift by zero --> noop 6141 6142 uint64_t AShrAmt = CI->getZExtValue(); 6143 Type *TruncTy = IntegerType::get(getContext(), BitWidth - AShrAmt); 6144 6145 Operator *L = dyn_cast<Operator>(BO->LHS); 6146 if (L && L->getOpcode() == Instruction::Shl) { 6147 // X = Shl A, n 6148 // Y = AShr X, m 6149 // Both n and m are constant. 6150 6151 const SCEV *ShlOp0SCEV = getSCEV(L->getOperand(0)); 6152 if (L->getOperand(1) == BO->RHS) 6153 // For a two-shift sext-inreg, i.e. n = m, 6154 // use sext(trunc(x)) as the SCEV expression. 6155 return getSignExtendExpr( 6156 getTruncateExpr(ShlOp0SCEV, TruncTy), OuterTy); 6157 6158 ConstantInt *ShlAmtCI = dyn_cast<ConstantInt>(L->getOperand(1)); 6159 if (ShlAmtCI && ShlAmtCI->getValue().ult(BitWidth)) { 6160 uint64_t ShlAmt = ShlAmtCI->getZExtValue(); 6161 if (ShlAmt > AShrAmt) { 6162 // When n > m, use sext(mul(trunc(x), 2^(n-m)))) as the SCEV 6163 // expression. We already checked that ShlAmt < BitWidth, so 6164 // the multiplier, 1 << (ShlAmt - AShrAmt), fits into TruncTy as 6165 // ShlAmt - AShrAmt < Amt. 6166 APInt Mul = APInt::getOneBitSet(BitWidth - AShrAmt, 6167 ShlAmt - AShrAmt); 6168 return getSignExtendExpr( 6169 getMulExpr(getTruncateExpr(ShlOp0SCEV, TruncTy), 6170 getConstant(Mul)), OuterTy); 6171 } 6172 } 6173 } 6174 break; 6175 } 6176 } 6177 } 6178 6179 switch (U->getOpcode()) { 6180 case Instruction::Trunc: 6181 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 6182 6183 case Instruction::ZExt: 6184 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 6185 6186 case Instruction::SExt: 6187 if (auto BO = MatchBinaryOp(U->getOperand(0), DT)) { 6188 // The NSW flag of a subtract does not always survive the conversion to 6189 // A + (-1)*B. By pushing sign extension onto its operands we are much 6190 // more likely to preserve NSW and allow later AddRec optimisations. 6191 // 6192 // NOTE: This is effectively duplicating this logic from getSignExtend: 6193 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw> 6194 // but by that point the NSW information has potentially been lost. 6195 if (BO->Opcode == Instruction::Sub && BO->IsNSW) { 6196 Type *Ty = U->getType(); 6197 auto *V1 = getSignExtendExpr(getSCEV(BO->LHS), Ty); 6198 auto *V2 = getSignExtendExpr(getSCEV(BO->RHS), Ty); 6199 return getMinusSCEV(V1, V2, SCEV::FlagNSW); 6200 } 6201 } 6202 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 6203 6204 case Instruction::BitCast: 6205 // BitCasts are no-op casts so we just eliminate the cast. 6206 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 6207 return getSCEV(U->getOperand(0)); 6208 break; 6209 6210 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 6211 // lead to pointer expressions which cannot safely be expanded to GEPs, 6212 // because ScalarEvolution doesn't respect the GEP aliasing rules when 6213 // simplifying integer expressions. 6214 6215 case Instruction::GetElementPtr: 6216 return createNodeForGEP(cast<GEPOperator>(U)); 6217 6218 case Instruction::PHI: 6219 return createNodeForPHI(cast<PHINode>(U)); 6220 6221 case Instruction::Select: 6222 // U can also be a select constant expr, which let fall through. Since 6223 // createNodeForSelect only works for a condition that is an `ICmpInst`, and 6224 // constant expressions cannot have instructions as operands, we'd have 6225 // returned getUnknown for a select constant expressions anyway. 6226 if (isa<Instruction>(U)) 6227 return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0), 6228 U->getOperand(1), U->getOperand(2)); 6229 break; 6230 6231 case Instruction::Call: 6232 case Instruction::Invoke: 6233 if (Value *RV = CallSite(U).getReturnedArgOperand()) 6234 return getSCEV(RV); 6235 break; 6236 } 6237 6238 return getUnknown(V); 6239 } 6240 6241 //===----------------------------------------------------------------------===// 6242 // Iteration Count Computation Code 6243 // 6244 6245 static unsigned getConstantTripCount(const SCEVConstant *ExitCount) { 6246 if (!ExitCount) 6247 return 0; 6248 6249 ConstantInt *ExitConst = ExitCount->getValue(); 6250 6251 // Guard against huge trip counts. 6252 if (ExitConst->getValue().getActiveBits() > 32) 6253 return 0; 6254 6255 // In case of integer overflow, this returns 0, which is correct. 6256 return ((unsigned)ExitConst->getZExtValue()) + 1; 6257 } 6258 6259 unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L) { 6260 if (BasicBlock *ExitingBB = L->getExitingBlock()) 6261 return getSmallConstantTripCount(L, ExitingBB); 6262 6263 // No trip count information for multiple exits. 6264 return 0; 6265 } 6266 6267 unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L, 6268 BasicBlock *ExitingBlock) { 6269 assert(ExitingBlock && "Must pass a non-null exiting block!"); 6270 assert(L->isLoopExiting(ExitingBlock) && 6271 "Exiting block must actually branch out of the loop!"); 6272 const SCEVConstant *ExitCount = 6273 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock)); 6274 return getConstantTripCount(ExitCount); 6275 } 6276 6277 unsigned ScalarEvolution::getSmallConstantMaxTripCount(const Loop *L) { 6278 const auto *MaxExitCount = 6279 dyn_cast<SCEVConstant>(getMaxBackedgeTakenCount(L)); 6280 return getConstantTripCount(MaxExitCount); 6281 } 6282 6283 unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L) { 6284 if (BasicBlock *ExitingBB = L->getExitingBlock()) 6285 return getSmallConstantTripMultiple(L, ExitingBB); 6286 6287 // No trip multiple information for multiple exits. 6288 return 0; 6289 } 6290 6291 /// Returns the largest constant divisor of the trip count of this loop as a 6292 /// normal unsigned value, if possible. This means that the actual trip count is 6293 /// always a multiple of the returned value (don't forget the trip count could 6294 /// very well be zero as well!). 6295 /// 6296 /// Returns 1 if the trip count is unknown or not guaranteed to be the 6297 /// multiple of a constant (which is also the case if the trip count is simply 6298 /// constant, use getSmallConstantTripCount for that case), Will also return 1 6299 /// if the trip count is very large (>= 2^32). 6300 /// 6301 /// As explained in the comments for getSmallConstantTripCount, this assumes 6302 /// that control exits the loop via ExitingBlock. 6303 unsigned 6304 ScalarEvolution::getSmallConstantTripMultiple(const Loop *L, 6305 BasicBlock *ExitingBlock) { 6306 assert(ExitingBlock && "Must pass a non-null exiting block!"); 6307 assert(L->isLoopExiting(ExitingBlock) && 6308 "Exiting block must actually branch out of the loop!"); 6309 const SCEV *ExitCount = getExitCount(L, ExitingBlock); 6310 if (ExitCount == getCouldNotCompute()) 6311 return 1; 6312 6313 // Get the trip count from the BE count by adding 1. 6314 const SCEV *TCExpr = getAddExpr(ExitCount, getOne(ExitCount->getType())); 6315 6316 const SCEVConstant *TC = dyn_cast<SCEVConstant>(TCExpr); 6317 if (!TC) 6318 // Attempt to factor more general cases. Returns the greatest power of 6319 // two divisor. If overflow happens, the trip count expression is still 6320 // divisible by the greatest power of 2 divisor returned. 6321 return 1U << std::min((uint32_t)31, GetMinTrailingZeros(TCExpr)); 6322 6323 ConstantInt *Result = TC->getValue(); 6324 6325 // Guard against huge trip counts (this requires checking 6326 // for zero to handle the case where the trip count == -1 and the 6327 // addition wraps). 6328 if (!Result || Result->getValue().getActiveBits() > 32 || 6329 Result->getValue().getActiveBits() == 0) 6330 return 1; 6331 6332 return (unsigned)Result->getZExtValue(); 6333 } 6334 6335 /// Get the expression for the number of loop iterations for which this loop is 6336 /// guaranteed not to exit via ExitingBlock. Otherwise return 6337 /// SCEVCouldNotCompute. 6338 const SCEV *ScalarEvolution::getExitCount(const Loop *L, 6339 BasicBlock *ExitingBlock) { 6340 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this); 6341 } 6342 6343 const SCEV * 6344 ScalarEvolution::getPredicatedBackedgeTakenCount(const Loop *L, 6345 SCEVUnionPredicate &Preds) { 6346 return getPredicatedBackedgeTakenInfo(L).getExact(this, &Preds); 6347 } 6348 6349 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 6350 return getBackedgeTakenInfo(L).getExact(this); 6351 } 6352 6353 /// Similar to getBackedgeTakenCount, except return the least SCEV value that is 6354 /// known never to be less than the actual backedge taken count. 6355 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 6356 return getBackedgeTakenInfo(L).getMax(this); 6357 } 6358 6359 bool ScalarEvolution::isBackedgeTakenCountMaxOrZero(const Loop *L) { 6360 return getBackedgeTakenInfo(L).isMaxOrZero(this); 6361 } 6362 6363 /// Push PHI nodes in the header of the given loop onto the given Worklist. 6364 static void 6365 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 6366 BasicBlock *Header = L->getHeader(); 6367 6368 // Push all Loop-header PHIs onto the Worklist stack. 6369 for (BasicBlock::iterator I = Header->begin(); 6370 PHINode *PN = dyn_cast<PHINode>(I); ++I) 6371 Worklist.push_back(PN); 6372 } 6373 6374 const ScalarEvolution::BackedgeTakenInfo & 6375 ScalarEvolution::getPredicatedBackedgeTakenInfo(const Loop *L) { 6376 auto &BTI = getBackedgeTakenInfo(L); 6377 if (BTI.hasFullInfo()) 6378 return BTI; 6379 6380 auto Pair = PredicatedBackedgeTakenCounts.insert({L, BackedgeTakenInfo()}); 6381 6382 if (!Pair.second) 6383 return Pair.first->second; 6384 6385 BackedgeTakenInfo Result = 6386 computeBackedgeTakenCount(L, /*AllowPredicates=*/true); 6387 6388 return PredicatedBackedgeTakenCounts.find(L)->second = std::move(Result); 6389 } 6390 6391 const ScalarEvolution::BackedgeTakenInfo & 6392 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 6393 // Initially insert an invalid entry for this loop. If the insertion 6394 // succeeds, proceed to actually compute a backedge-taken count and 6395 // update the value. The temporary CouldNotCompute value tells SCEV 6396 // code elsewhere that it shouldn't attempt to request a new 6397 // backedge-taken count, which could result in infinite recursion. 6398 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 6399 BackedgeTakenCounts.insert({L, BackedgeTakenInfo()}); 6400 if (!Pair.second) 6401 return Pair.first->second; 6402 6403 // computeBackedgeTakenCount may allocate memory for its result. Inserting it 6404 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result 6405 // must be cleared in this scope. 6406 BackedgeTakenInfo Result = computeBackedgeTakenCount(L); 6407 6408 if (Result.getExact(this) != getCouldNotCompute()) { 6409 assert(isLoopInvariant(Result.getExact(this), L) && 6410 isLoopInvariant(Result.getMax(this), L) && 6411 "Computed backedge-taken count isn't loop invariant for loop!"); 6412 ++NumTripCountsComputed; 6413 } 6414 else if (Result.getMax(this) == getCouldNotCompute() && 6415 isa<PHINode>(L->getHeader()->begin())) { 6416 // Only count loops that have phi nodes as not being computable. 6417 ++NumTripCountsNotComputed; 6418 } 6419 6420 // Now that we know more about the trip count for this loop, forget any 6421 // existing SCEV values for PHI nodes in this loop since they are only 6422 // conservative estimates made without the benefit of trip count 6423 // information. This is similar to the code in forgetLoop, except that 6424 // it handles SCEVUnknown PHI nodes specially. 6425 if (Result.hasAnyInfo()) { 6426 SmallVector<Instruction *, 16> Worklist; 6427 PushLoopPHIs(L, Worklist); 6428 6429 SmallPtrSet<Instruction *, 8> Discovered; 6430 while (!Worklist.empty()) { 6431 Instruction *I = Worklist.pop_back_val(); 6432 6433 ValueExprMapType::iterator It = 6434 ValueExprMap.find_as(static_cast<Value *>(I)); 6435 if (It != ValueExprMap.end()) { 6436 const SCEV *Old = It->second; 6437 6438 // SCEVUnknown for a PHI either means that it has an unrecognized 6439 // structure, or it's a PHI that's in the progress of being computed 6440 // by createNodeForPHI. In the former case, additional loop trip 6441 // count information isn't going to change anything. In the later 6442 // case, createNodeForPHI will perform the necessary updates on its 6443 // own when it gets to that point. 6444 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) { 6445 eraseValueFromMap(It->first); 6446 forgetMemoizedResults(Old); 6447 } 6448 if (PHINode *PN = dyn_cast<PHINode>(I)) 6449 ConstantEvolutionLoopExitValue.erase(PN); 6450 } 6451 6452 // Since we don't need to invalidate anything for correctness and we're 6453 // only invalidating to make SCEV's results more precise, we get to stop 6454 // early to avoid invalidating too much. This is especially important in 6455 // cases like: 6456 // 6457 // %v = f(pn0, pn1) // pn0 and pn1 used through some other phi node 6458 // loop0: 6459 // %pn0 = phi 6460 // ... 6461 // loop1: 6462 // %pn1 = phi 6463 // ... 6464 // 6465 // where both loop0 and loop1's backedge taken count uses the SCEV 6466 // expression for %v. If we don't have the early stop below then in cases 6467 // like the above, getBackedgeTakenInfo(loop1) will clear out the trip 6468 // count for loop0 and getBackedgeTakenInfo(loop0) will clear out the trip 6469 // count for loop1, effectively nullifying SCEV's trip count cache. 6470 for (auto *U : I->users()) 6471 if (auto *I = dyn_cast<Instruction>(U)) { 6472 auto *LoopForUser = LI.getLoopFor(I->getParent()); 6473 if (LoopForUser && L->contains(LoopForUser) && 6474 Discovered.insert(I).second) 6475 Worklist.push_back(I); 6476 } 6477 } 6478 } 6479 6480 // Re-lookup the insert position, since the call to 6481 // computeBackedgeTakenCount above could result in a 6482 // recusive call to getBackedgeTakenInfo (on a different 6483 // loop), which would invalidate the iterator computed 6484 // earlier. 6485 return BackedgeTakenCounts.find(L)->second = std::move(Result); 6486 } 6487 6488 void ScalarEvolution::forgetLoop(const Loop *L) { 6489 // Drop any stored trip count value. 6490 auto RemoveLoopFromBackedgeMap = 6491 [](DenseMap<const Loop *, BackedgeTakenInfo> &Map, const Loop *L) { 6492 auto BTCPos = Map.find(L); 6493 if (BTCPos != Map.end()) { 6494 BTCPos->second.clear(); 6495 Map.erase(BTCPos); 6496 } 6497 }; 6498 6499 SmallVector<const Loop *, 16> LoopWorklist(1, L); 6500 SmallVector<Instruction *, 32> Worklist; 6501 SmallPtrSet<Instruction *, 16> Visited; 6502 6503 // Iterate over all the loops and sub-loops to drop SCEV information. 6504 while (!LoopWorklist.empty()) { 6505 auto *CurrL = LoopWorklist.pop_back_val(); 6506 6507 RemoveLoopFromBackedgeMap(BackedgeTakenCounts, CurrL); 6508 RemoveLoopFromBackedgeMap(PredicatedBackedgeTakenCounts, CurrL); 6509 6510 // Drop information about predicated SCEV rewrites for this loop. 6511 for (auto I = PredicatedSCEVRewrites.begin(); 6512 I != PredicatedSCEVRewrites.end();) { 6513 std::pair<const SCEV *, const Loop *> Entry = I->first; 6514 if (Entry.second == CurrL) 6515 PredicatedSCEVRewrites.erase(I++); 6516 else 6517 ++I; 6518 } 6519 6520 auto LoopUsersItr = LoopUsers.find(CurrL); 6521 if (LoopUsersItr != LoopUsers.end()) { 6522 for (auto *S : LoopUsersItr->second) 6523 forgetMemoizedResults(S); 6524 LoopUsers.erase(LoopUsersItr); 6525 } 6526 6527 // Drop information about expressions based on loop-header PHIs. 6528 PushLoopPHIs(CurrL, Worklist); 6529 6530 while (!Worklist.empty()) { 6531 Instruction *I = Worklist.pop_back_val(); 6532 if (!Visited.insert(I).second) 6533 continue; 6534 6535 ValueExprMapType::iterator It = 6536 ValueExprMap.find_as(static_cast<Value *>(I)); 6537 if (It != ValueExprMap.end()) { 6538 eraseValueFromMap(It->first); 6539 forgetMemoizedResults(It->second); 6540 if (PHINode *PN = dyn_cast<PHINode>(I)) 6541 ConstantEvolutionLoopExitValue.erase(PN); 6542 } 6543 6544 PushDefUseChildren(I, Worklist); 6545 } 6546 6547 LoopPropertiesCache.erase(CurrL); 6548 // Forget all contained loops too, to avoid dangling entries in the 6549 // ValuesAtScopes map. 6550 LoopWorklist.append(CurrL->begin(), CurrL->end()); 6551 } 6552 } 6553 6554 void ScalarEvolution::forgetValue(Value *V) { 6555 Instruction *I = dyn_cast<Instruction>(V); 6556 if (!I) return; 6557 6558 // Drop information about expressions based on loop-header PHIs. 6559 SmallVector<Instruction *, 16> Worklist; 6560 Worklist.push_back(I); 6561 6562 SmallPtrSet<Instruction *, 8> Visited; 6563 while (!Worklist.empty()) { 6564 I = Worklist.pop_back_val(); 6565 if (!Visited.insert(I).second) 6566 continue; 6567 6568 ValueExprMapType::iterator It = 6569 ValueExprMap.find_as(static_cast<Value *>(I)); 6570 if (It != ValueExprMap.end()) { 6571 eraseValueFromMap(It->first); 6572 forgetMemoizedResults(It->second); 6573 if (PHINode *PN = dyn_cast<PHINode>(I)) 6574 ConstantEvolutionLoopExitValue.erase(PN); 6575 } 6576 6577 PushDefUseChildren(I, Worklist); 6578 } 6579 } 6580 6581 /// Get the exact loop backedge taken count considering all loop exits. A 6582 /// computable result can only be returned for loops with a single exit. 6583 /// Returning the minimum taken count among all exits is incorrect because one 6584 /// of the loop's exit limit's may have been skipped. howFarToZero assumes that 6585 /// the limit of each loop test is never skipped. This is a valid assumption as 6586 /// long as the loop exits via that test. For precise results, it is the 6587 /// caller's responsibility to specify the relevant loop exit using 6588 /// getExact(ExitingBlock, SE). 6589 const SCEV * 6590 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE, 6591 SCEVUnionPredicate *Preds) const { 6592 // If any exits were not computable, the loop is not computable. 6593 if (!isComplete() || ExitNotTaken.empty()) 6594 return SE->getCouldNotCompute(); 6595 6596 const SCEV *BECount = nullptr; 6597 for (auto &ENT : ExitNotTaken) { 6598 assert(ENT.ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV"); 6599 6600 if (!BECount) 6601 BECount = ENT.ExactNotTaken; 6602 else if (BECount != ENT.ExactNotTaken) 6603 return SE->getCouldNotCompute(); 6604 if (Preds && !ENT.hasAlwaysTruePredicate()) 6605 Preds->add(ENT.Predicate.get()); 6606 6607 assert((Preds || ENT.hasAlwaysTruePredicate()) && 6608 "Predicate should be always true!"); 6609 } 6610 6611 assert(BECount && "Invalid not taken count for loop exit"); 6612 return BECount; 6613 } 6614 6615 /// Get the exact not taken count for this loop exit. 6616 const SCEV * 6617 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock, 6618 ScalarEvolution *SE) const { 6619 for (auto &ENT : ExitNotTaken) 6620 if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate()) 6621 return ENT.ExactNotTaken; 6622 6623 return SE->getCouldNotCompute(); 6624 } 6625 6626 /// getMax - Get the max backedge taken count for the loop. 6627 const SCEV * 6628 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const { 6629 auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) { 6630 return !ENT.hasAlwaysTruePredicate(); 6631 }; 6632 6633 if (any_of(ExitNotTaken, PredicateNotAlwaysTrue) || !getMax()) 6634 return SE->getCouldNotCompute(); 6635 6636 assert((isa<SCEVCouldNotCompute>(getMax()) || isa<SCEVConstant>(getMax())) && 6637 "No point in having a non-constant max backedge taken count!"); 6638 return getMax(); 6639 } 6640 6641 bool ScalarEvolution::BackedgeTakenInfo::isMaxOrZero(ScalarEvolution *SE) const { 6642 auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) { 6643 return !ENT.hasAlwaysTruePredicate(); 6644 }; 6645 return MaxOrZero && !any_of(ExitNotTaken, PredicateNotAlwaysTrue); 6646 } 6647 6648 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S, 6649 ScalarEvolution *SE) const { 6650 if (getMax() && getMax() != SE->getCouldNotCompute() && 6651 SE->hasOperand(getMax(), S)) 6652 return true; 6653 6654 for (auto &ENT : ExitNotTaken) 6655 if (ENT.ExactNotTaken != SE->getCouldNotCompute() && 6656 SE->hasOperand(ENT.ExactNotTaken, S)) 6657 return true; 6658 6659 return false; 6660 } 6661 6662 ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E) 6663 : ExactNotTaken(E), MaxNotTaken(E) { 6664 assert((isa<SCEVCouldNotCompute>(MaxNotTaken) || 6665 isa<SCEVConstant>(MaxNotTaken)) && 6666 "No point in having a non-constant max backedge taken count!"); 6667 } 6668 6669 ScalarEvolution::ExitLimit::ExitLimit( 6670 const SCEV *E, const SCEV *M, bool MaxOrZero, 6671 ArrayRef<const SmallPtrSetImpl<const SCEVPredicate *> *> PredSetList) 6672 : ExactNotTaken(E), MaxNotTaken(M), MaxOrZero(MaxOrZero) { 6673 assert((isa<SCEVCouldNotCompute>(ExactNotTaken) || 6674 !isa<SCEVCouldNotCompute>(MaxNotTaken)) && 6675 "Exact is not allowed to be less precise than Max"); 6676 assert((isa<SCEVCouldNotCompute>(MaxNotTaken) || 6677 isa<SCEVConstant>(MaxNotTaken)) && 6678 "No point in having a non-constant max backedge taken count!"); 6679 for (auto *PredSet : PredSetList) 6680 for (auto *P : *PredSet) 6681 addPredicate(P); 6682 } 6683 6684 ScalarEvolution::ExitLimit::ExitLimit( 6685 const SCEV *E, const SCEV *M, bool MaxOrZero, 6686 const SmallPtrSetImpl<const SCEVPredicate *> &PredSet) 6687 : ExitLimit(E, M, MaxOrZero, {&PredSet}) { 6688 assert((isa<SCEVCouldNotCompute>(MaxNotTaken) || 6689 isa<SCEVConstant>(MaxNotTaken)) && 6690 "No point in having a non-constant max backedge taken count!"); 6691 } 6692 6693 ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E, const SCEV *M, 6694 bool MaxOrZero) 6695 : ExitLimit(E, M, MaxOrZero, None) { 6696 assert((isa<SCEVCouldNotCompute>(MaxNotTaken) || 6697 isa<SCEVConstant>(MaxNotTaken)) && 6698 "No point in having a non-constant max backedge taken count!"); 6699 } 6700 6701 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each 6702 /// computable exit into a persistent ExitNotTakenInfo array. 6703 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo( 6704 SmallVectorImpl<ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo> 6705 &&ExitCounts, 6706 bool Complete, const SCEV *MaxCount, bool MaxOrZero) 6707 : MaxAndComplete(MaxCount, Complete), MaxOrZero(MaxOrZero) { 6708 using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo; 6709 6710 ExitNotTaken.reserve(ExitCounts.size()); 6711 std::transform( 6712 ExitCounts.begin(), ExitCounts.end(), std::back_inserter(ExitNotTaken), 6713 [&](const EdgeExitInfo &EEI) { 6714 BasicBlock *ExitBB = EEI.first; 6715 const ExitLimit &EL = EEI.second; 6716 if (EL.Predicates.empty()) 6717 return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, nullptr); 6718 6719 std::unique_ptr<SCEVUnionPredicate> Predicate(new SCEVUnionPredicate); 6720 for (auto *Pred : EL.Predicates) 6721 Predicate->add(Pred); 6722 6723 return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, std::move(Predicate)); 6724 }); 6725 assert((isa<SCEVCouldNotCompute>(MaxCount) || isa<SCEVConstant>(MaxCount)) && 6726 "No point in having a non-constant max backedge taken count!"); 6727 } 6728 6729 /// Invalidate this result and free the ExitNotTakenInfo array. 6730 void ScalarEvolution::BackedgeTakenInfo::clear() { 6731 ExitNotTaken.clear(); 6732 } 6733 6734 /// Compute the number of times the backedge of the specified loop will execute. 6735 ScalarEvolution::BackedgeTakenInfo 6736 ScalarEvolution::computeBackedgeTakenCount(const Loop *L, 6737 bool AllowPredicates) { 6738 SmallVector<BasicBlock *, 8> ExitingBlocks; 6739 L->getExitingBlocks(ExitingBlocks); 6740 6741 using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo; 6742 6743 SmallVector<EdgeExitInfo, 4> ExitCounts; 6744 bool CouldComputeBECount = true; 6745 BasicBlock *Latch = L->getLoopLatch(); // may be NULL. 6746 const SCEV *MustExitMaxBECount = nullptr; 6747 const SCEV *MayExitMaxBECount = nullptr; 6748 bool MustExitMaxOrZero = false; 6749 6750 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts 6751 // and compute maxBECount. 6752 // Do a union of all the predicates here. 6753 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 6754 BasicBlock *ExitBB = ExitingBlocks[i]; 6755 ExitLimit EL = computeExitLimit(L, ExitBB, AllowPredicates); 6756 6757 assert((AllowPredicates || EL.Predicates.empty()) && 6758 "Predicated exit limit when predicates are not allowed!"); 6759 6760 // 1. For each exit that can be computed, add an entry to ExitCounts. 6761 // CouldComputeBECount is true only if all exits can be computed. 6762 if (EL.ExactNotTaken == getCouldNotCompute()) 6763 // We couldn't compute an exact value for this exit, so 6764 // we won't be able to compute an exact value for the loop. 6765 CouldComputeBECount = false; 6766 else 6767 ExitCounts.emplace_back(ExitBB, EL); 6768 6769 // 2. Derive the loop's MaxBECount from each exit's max number of 6770 // non-exiting iterations. Partition the loop exits into two kinds: 6771 // LoopMustExits and LoopMayExits. 6772 // 6773 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it 6774 // is a LoopMayExit. If any computable LoopMustExit is found, then 6775 // MaxBECount is the minimum EL.MaxNotTaken of computable 6776 // LoopMustExits. Otherwise, MaxBECount is conservatively the maximum 6777 // EL.MaxNotTaken, where CouldNotCompute is considered greater than any 6778 // computable EL.MaxNotTaken. 6779 if (EL.MaxNotTaken != getCouldNotCompute() && Latch && 6780 DT.dominates(ExitBB, Latch)) { 6781 if (!MustExitMaxBECount) { 6782 MustExitMaxBECount = EL.MaxNotTaken; 6783 MustExitMaxOrZero = EL.MaxOrZero; 6784 } else { 6785 MustExitMaxBECount = 6786 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.MaxNotTaken); 6787 } 6788 } else if (MayExitMaxBECount != getCouldNotCompute()) { 6789 if (!MayExitMaxBECount || EL.MaxNotTaken == getCouldNotCompute()) 6790 MayExitMaxBECount = EL.MaxNotTaken; 6791 else { 6792 MayExitMaxBECount = 6793 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.MaxNotTaken); 6794 } 6795 } 6796 } 6797 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount : 6798 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute()); 6799 // The loop backedge will be taken the maximum or zero times if there's 6800 // a single exit that must be taken the maximum or zero times. 6801 bool MaxOrZero = (MustExitMaxOrZero && ExitingBlocks.size() == 1); 6802 return BackedgeTakenInfo(std::move(ExitCounts), CouldComputeBECount, 6803 MaxBECount, MaxOrZero); 6804 } 6805 6806 ScalarEvolution::ExitLimit 6807 ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock, 6808 bool AllowPredicates) { 6809 // Okay, we've chosen an exiting block. See what condition causes us to exit 6810 // at this block and remember the exit block and whether all other targets 6811 // lead to the loop header. 6812 bool MustExecuteLoopHeader = true; 6813 BasicBlock *Exit = nullptr; 6814 for (auto *SBB : successors(ExitingBlock)) 6815 if (!L->contains(SBB)) { 6816 if (Exit) // Multiple exit successors. 6817 return getCouldNotCompute(); 6818 Exit = SBB; 6819 } else if (SBB != L->getHeader()) { 6820 MustExecuteLoopHeader = false; 6821 } 6822 6823 // At this point, we know we have a conditional branch that determines whether 6824 // the loop is exited. However, we don't know if the branch is executed each 6825 // time through the loop. If not, then the execution count of the branch will 6826 // not be equal to the trip count of the loop. 6827 // 6828 // Currently we check for this by checking to see if the Exit branch goes to 6829 // the loop header. If so, we know it will always execute the same number of 6830 // times as the loop. We also handle the case where the exit block *is* the 6831 // loop header. This is common for un-rotated loops. 6832 // 6833 // If both of those tests fail, walk up the unique predecessor chain to the 6834 // header, stopping if there is an edge that doesn't exit the loop. If the 6835 // header is reached, the execution count of the branch will be equal to the 6836 // trip count of the loop. 6837 // 6838 // More extensive analysis could be done to handle more cases here. 6839 // 6840 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) { 6841 // The simple checks failed, try climbing the unique predecessor chain 6842 // up to the header. 6843 bool Ok = false; 6844 for (BasicBlock *BB = ExitingBlock; BB; ) { 6845 BasicBlock *Pred = BB->getUniquePredecessor(); 6846 if (!Pred) 6847 return getCouldNotCompute(); 6848 TerminatorInst *PredTerm = Pred->getTerminator(); 6849 for (const BasicBlock *PredSucc : PredTerm->successors()) { 6850 if (PredSucc == BB) 6851 continue; 6852 // If the predecessor has a successor that isn't BB and isn't 6853 // outside the loop, assume the worst. 6854 if (L->contains(PredSucc)) 6855 return getCouldNotCompute(); 6856 } 6857 if (Pred == L->getHeader()) { 6858 Ok = true; 6859 break; 6860 } 6861 BB = Pred; 6862 } 6863 if (!Ok) 6864 return getCouldNotCompute(); 6865 } 6866 6867 bool IsOnlyExit = (L->getExitingBlock() != nullptr); 6868 TerminatorInst *Term = ExitingBlock->getTerminator(); 6869 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) { 6870 assert(BI->isConditional() && "If unconditional, it can't be in loop!"); 6871 // Proceed to the next level to examine the exit condition expression. 6872 return computeExitLimitFromCond( 6873 L, BI->getCondition(), BI->getSuccessor(0), BI->getSuccessor(1), 6874 /*ControlsExit=*/IsOnlyExit, AllowPredicates); 6875 } 6876 6877 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term)) 6878 return computeExitLimitFromSingleExitSwitch(L, SI, Exit, 6879 /*ControlsExit=*/IsOnlyExit); 6880 6881 return getCouldNotCompute(); 6882 } 6883 6884 ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCond( 6885 const Loop *L, Value *ExitCond, BasicBlock *TBB, BasicBlock *FBB, 6886 bool ControlsExit, bool AllowPredicates) { 6887 ScalarEvolution::ExitLimitCacheTy Cache(L, TBB, FBB, AllowPredicates); 6888 return computeExitLimitFromCondCached(Cache, L, ExitCond, TBB, FBB, 6889 ControlsExit, AllowPredicates); 6890 } 6891 6892 Optional<ScalarEvolution::ExitLimit> 6893 ScalarEvolution::ExitLimitCache::find(const Loop *L, Value *ExitCond, 6894 BasicBlock *TBB, BasicBlock *FBB, 6895 bool ControlsExit, bool AllowPredicates) { 6896 (void)this->L; 6897 (void)this->TBB; 6898 (void)this->FBB; 6899 (void)this->AllowPredicates; 6900 6901 assert(this->L == L && this->TBB == TBB && this->FBB == FBB && 6902 this->AllowPredicates == AllowPredicates && 6903 "Variance in assumed invariant key components!"); 6904 auto Itr = TripCountMap.find({ExitCond, ControlsExit}); 6905 if (Itr == TripCountMap.end()) 6906 return None; 6907 return Itr->second; 6908 } 6909 6910 void ScalarEvolution::ExitLimitCache::insert(const Loop *L, Value *ExitCond, 6911 BasicBlock *TBB, BasicBlock *FBB, 6912 bool ControlsExit, 6913 bool AllowPredicates, 6914 const ExitLimit &EL) { 6915 assert(this->L == L && this->TBB == TBB && this->FBB == FBB && 6916 this->AllowPredicates == AllowPredicates && 6917 "Variance in assumed invariant key components!"); 6918 6919 auto InsertResult = TripCountMap.insert({{ExitCond, ControlsExit}, EL}); 6920 assert(InsertResult.second && "Expected successful insertion!"); 6921 (void)InsertResult; 6922 } 6923 6924 ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondCached( 6925 ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, BasicBlock *TBB, 6926 BasicBlock *FBB, bool ControlsExit, bool AllowPredicates) { 6927 6928 if (auto MaybeEL = 6929 Cache.find(L, ExitCond, TBB, FBB, ControlsExit, AllowPredicates)) 6930 return *MaybeEL; 6931 6932 ExitLimit EL = computeExitLimitFromCondImpl(Cache, L, ExitCond, TBB, FBB, 6933 ControlsExit, AllowPredicates); 6934 Cache.insert(L, ExitCond, TBB, FBB, ControlsExit, AllowPredicates, EL); 6935 return EL; 6936 } 6937 6938 ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondImpl( 6939 ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, BasicBlock *TBB, 6940 BasicBlock *FBB, bool ControlsExit, bool AllowPredicates) { 6941 // Check if the controlling expression for this loop is an And or Or. 6942 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 6943 if (BO->getOpcode() == Instruction::And) { 6944 // Recurse on the operands of the and. 6945 bool EitherMayExit = L->contains(TBB); 6946 ExitLimit EL0 = computeExitLimitFromCondCached( 6947 Cache, L, BO->getOperand(0), TBB, FBB, ControlsExit && !EitherMayExit, 6948 AllowPredicates); 6949 ExitLimit EL1 = computeExitLimitFromCondCached( 6950 Cache, L, BO->getOperand(1), TBB, FBB, ControlsExit && !EitherMayExit, 6951 AllowPredicates); 6952 const SCEV *BECount = getCouldNotCompute(); 6953 const SCEV *MaxBECount = getCouldNotCompute(); 6954 if (EitherMayExit) { 6955 // Both conditions must be true for the loop to continue executing. 6956 // Choose the less conservative count. 6957 if (EL0.ExactNotTaken == getCouldNotCompute() || 6958 EL1.ExactNotTaken == getCouldNotCompute()) 6959 BECount = getCouldNotCompute(); 6960 else 6961 BECount = 6962 getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken); 6963 if (EL0.MaxNotTaken == getCouldNotCompute()) 6964 MaxBECount = EL1.MaxNotTaken; 6965 else if (EL1.MaxNotTaken == getCouldNotCompute()) 6966 MaxBECount = EL0.MaxNotTaken; 6967 else 6968 MaxBECount = 6969 getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken); 6970 } else { 6971 // Both conditions must be true at the same time for the loop to exit. 6972 // For now, be conservative. 6973 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 6974 if (EL0.MaxNotTaken == EL1.MaxNotTaken) 6975 MaxBECount = EL0.MaxNotTaken; 6976 if (EL0.ExactNotTaken == EL1.ExactNotTaken) 6977 BECount = EL0.ExactNotTaken; 6978 } 6979 6980 // There are cases (e.g. PR26207) where computeExitLimitFromCond is able 6981 // to be more aggressive when computing BECount than when computing 6982 // MaxBECount. In these cases it is possible for EL0.ExactNotTaken and 6983 // EL1.ExactNotTaken to match, but for EL0.MaxNotTaken and EL1.MaxNotTaken 6984 // to not. 6985 if (isa<SCEVCouldNotCompute>(MaxBECount) && 6986 !isa<SCEVCouldNotCompute>(BECount)) 6987 MaxBECount = getConstant(getUnsignedRangeMax(BECount)); 6988 6989 return ExitLimit(BECount, MaxBECount, false, 6990 {&EL0.Predicates, &EL1.Predicates}); 6991 } 6992 if (BO->getOpcode() == Instruction::Or) { 6993 // Recurse on the operands of the or. 6994 bool EitherMayExit = L->contains(FBB); 6995 ExitLimit EL0 = computeExitLimitFromCondCached( 6996 Cache, L, BO->getOperand(0), TBB, FBB, ControlsExit && !EitherMayExit, 6997 AllowPredicates); 6998 ExitLimit EL1 = computeExitLimitFromCondCached( 6999 Cache, L, BO->getOperand(1), TBB, FBB, ControlsExit && !EitherMayExit, 7000 AllowPredicates); 7001 const SCEV *BECount = getCouldNotCompute(); 7002 const SCEV *MaxBECount = getCouldNotCompute(); 7003 if (EitherMayExit) { 7004 // Both conditions must be false for the loop to continue executing. 7005 // Choose the less conservative count. 7006 if (EL0.ExactNotTaken == getCouldNotCompute() || 7007 EL1.ExactNotTaken == getCouldNotCompute()) 7008 BECount = getCouldNotCompute(); 7009 else 7010 BECount = 7011 getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken); 7012 if (EL0.MaxNotTaken == getCouldNotCompute()) 7013 MaxBECount = EL1.MaxNotTaken; 7014 else if (EL1.MaxNotTaken == getCouldNotCompute()) 7015 MaxBECount = EL0.MaxNotTaken; 7016 else 7017 MaxBECount = 7018 getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken); 7019 } else { 7020 // Both conditions must be false at the same time for the loop to exit. 7021 // For now, be conservative. 7022 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 7023 if (EL0.MaxNotTaken == EL1.MaxNotTaken) 7024 MaxBECount = EL0.MaxNotTaken; 7025 if (EL0.ExactNotTaken == EL1.ExactNotTaken) 7026 BECount = EL0.ExactNotTaken; 7027 } 7028 7029 return ExitLimit(BECount, MaxBECount, false, 7030 {&EL0.Predicates, &EL1.Predicates}); 7031 } 7032 } 7033 7034 // With an icmp, it may be feasible to compute an exact backedge-taken count. 7035 // Proceed to the next level to examine the icmp. 7036 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) { 7037 ExitLimit EL = 7038 computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit); 7039 if (EL.hasFullInfo() || !AllowPredicates) 7040 return EL; 7041 7042 // Try again, but use SCEV predicates this time. 7043 return computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit, 7044 /*AllowPredicates=*/true); 7045 } 7046 7047 // Check for a constant condition. These are normally stripped out by 7048 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 7049 // preserve the CFG and is temporarily leaving constant conditions 7050 // in place. 7051 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 7052 if (L->contains(FBB) == !CI->getZExtValue()) 7053 // The backedge is always taken. 7054 return getCouldNotCompute(); 7055 else 7056 // The backedge is never taken. 7057 return getZero(CI->getType()); 7058 } 7059 7060 // If it's not an integer or pointer comparison then compute it the hard way. 7061 return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB)); 7062 } 7063 7064 ScalarEvolution::ExitLimit 7065 ScalarEvolution::computeExitLimitFromICmp(const Loop *L, 7066 ICmpInst *ExitCond, 7067 BasicBlock *TBB, 7068 BasicBlock *FBB, 7069 bool ControlsExit, 7070 bool AllowPredicates) { 7071 // If the condition was exit on true, convert the condition to exit on false 7072 ICmpInst::Predicate Pred; 7073 if (!L->contains(FBB)) 7074 Pred = ExitCond->getPredicate(); 7075 else 7076 Pred = ExitCond->getInversePredicate(); 7077 const ICmpInst::Predicate OriginalPred = Pred; 7078 7079 // Handle common loops like: for (X = "string"; *X; ++X) 7080 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 7081 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 7082 ExitLimit ItCnt = 7083 computeLoadConstantCompareExitLimit(LI, RHS, L, Pred); 7084 if (ItCnt.hasAnyInfo()) 7085 return ItCnt; 7086 } 7087 7088 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 7089 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 7090 7091 // Try to evaluate any dependencies out of the loop. 7092 LHS = getSCEVAtScope(LHS, L); 7093 RHS = getSCEVAtScope(RHS, L); 7094 7095 // At this point, we would like to compute how many iterations of the 7096 // loop the predicate will return true for these inputs. 7097 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) { 7098 // If there is a loop-invariant, force it into the RHS. 7099 std::swap(LHS, RHS); 7100 Pred = ICmpInst::getSwappedPredicate(Pred); 7101 } 7102 7103 // Simplify the operands before analyzing them. 7104 (void)SimplifyICmpOperands(Pred, LHS, RHS); 7105 7106 // If we have a comparison of a chrec against a constant, try to use value 7107 // ranges to answer this query. 7108 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 7109 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 7110 if (AddRec->getLoop() == L) { 7111 // Form the constant range. 7112 ConstantRange CompRange = 7113 ConstantRange::makeExactICmpRegion(Pred, RHSC->getAPInt()); 7114 7115 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 7116 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 7117 } 7118 7119 switch (Pred) { 7120 case ICmpInst::ICMP_NE: { // while (X != Y) 7121 // Convert to: while (X-Y != 0) 7122 ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit, 7123 AllowPredicates); 7124 if (EL.hasAnyInfo()) return EL; 7125 break; 7126 } 7127 case ICmpInst::ICMP_EQ: { // while (X == Y) 7128 // Convert to: while (X-Y == 0) 7129 ExitLimit EL = howFarToNonZero(getMinusSCEV(LHS, RHS), L); 7130 if (EL.hasAnyInfo()) return EL; 7131 break; 7132 } 7133 case ICmpInst::ICMP_SLT: 7134 case ICmpInst::ICMP_ULT: { // while (X < Y) 7135 bool IsSigned = Pred == ICmpInst::ICMP_SLT; 7136 ExitLimit EL = howManyLessThans(LHS, RHS, L, IsSigned, ControlsExit, 7137 AllowPredicates); 7138 if (EL.hasAnyInfo()) return EL; 7139 break; 7140 } 7141 case ICmpInst::ICMP_SGT: 7142 case ICmpInst::ICMP_UGT: { // while (X > Y) 7143 bool IsSigned = Pred == ICmpInst::ICMP_SGT; 7144 ExitLimit EL = 7145 howManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit, 7146 AllowPredicates); 7147 if (EL.hasAnyInfo()) return EL; 7148 break; 7149 } 7150 default: 7151 break; 7152 } 7153 7154 auto *ExhaustiveCount = 7155 computeExitCountExhaustively(L, ExitCond, !L->contains(TBB)); 7156 7157 if (!isa<SCEVCouldNotCompute>(ExhaustiveCount)) 7158 return ExhaustiveCount; 7159 7160 return computeShiftCompareExitLimit(ExitCond->getOperand(0), 7161 ExitCond->getOperand(1), L, OriginalPred); 7162 } 7163 7164 ScalarEvolution::ExitLimit 7165 ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L, 7166 SwitchInst *Switch, 7167 BasicBlock *ExitingBlock, 7168 bool ControlsExit) { 7169 assert(!L->contains(ExitingBlock) && "Not an exiting block!"); 7170 7171 // Give up if the exit is the default dest of a switch. 7172 if (Switch->getDefaultDest() == ExitingBlock) 7173 return getCouldNotCompute(); 7174 7175 assert(L->contains(Switch->getDefaultDest()) && 7176 "Default case must not exit the loop!"); 7177 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L); 7178 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock)); 7179 7180 // while (X != Y) --> while (X-Y != 0) 7181 ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit); 7182 if (EL.hasAnyInfo()) 7183 return EL; 7184 7185 return getCouldNotCompute(); 7186 } 7187 7188 static ConstantInt * 7189 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 7190 ScalarEvolution &SE) { 7191 const SCEV *InVal = SE.getConstant(C); 7192 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 7193 assert(isa<SCEVConstant>(Val) && 7194 "Evaluation of SCEV at constant didn't fold correctly?"); 7195 return cast<SCEVConstant>(Val)->getValue(); 7196 } 7197 7198 /// Given an exit condition of 'icmp op load X, cst', try to see if we can 7199 /// compute the backedge execution count. 7200 ScalarEvolution::ExitLimit 7201 ScalarEvolution::computeLoadConstantCompareExitLimit( 7202 LoadInst *LI, 7203 Constant *RHS, 7204 const Loop *L, 7205 ICmpInst::Predicate predicate) { 7206 if (LI->isVolatile()) return getCouldNotCompute(); 7207 7208 // Check to see if the loaded pointer is a getelementptr of a global. 7209 // TODO: Use SCEV instead of manually grubbing with GEPs. 7210 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 7211 if (!GEP) return getCouldNotCompute(); 7212 7213 // Make sure that it is really a constant global we are gepping, with an 7214 // initializer, and make sure the first IDX is really 0. 7215 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 7216 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 7217 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 7218 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 7219 return getCouldNotCompute(); 7220 7221 // Okay, we allow one non-constant index into the GEP instruction. 7222 Value *VarIdx = nullptr; 7223 std::vector<Constant*> Indexes; 7224 unsigned VarIdxNum = 0; 7225 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 7226 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 7227 Indexes.push_back(CI); 7228 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 7229 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 7230 VarIdx = GEP->getOperand(i); 7231 VarIdxNum = i-2; 7232 Indexes.push_back(nullptr); 7233 } 7234 7235 // Loop-invariant loads may be a byproduct of loop optimization. Skip them. 7236 if (!VarIdx) 7237 return getCouldNotCompute(); 7238 7239 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 7240 // Check to see if X is a loop variant variable value now. 7241 const SCEV *Idx = getSCEV(VarIdx); 7242 Idx = getSCEVAtScope(Idx, L); 7243 7244 // We can only recognize very limited forms of loop index expressions, in 7245 // particular, only affine AddRec's like {C1,+,C2}. 7246 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 7247 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) || 7248 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 7249 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 7250 return getCouldNotCompute(); 7251 7252 unsigned MaxSteps = MaxBruteForceIterations; 7253 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 7254 ConstantInt *ItCst = ConstantInt::get( 7255 cast<IntegerType>(IdxExpr->getType()), IterationNum); 7256 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 7257 7258 // Form the GEP offset. 7259 Indexes[VarIdxNum] = Val; 7260 7261 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(), 7262 Indexes); 7263 if (!Result) break; // Cannot compute! 7264 7265 // Evaluate the condition for this iteration. 7266 Result = ConstantExpr::getICmp(predicate, Result, RHS); 7267 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 7268 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 7269 ++NumArrayLenItCounts; 7270 return getConstant(ItCst); // Found terminating iteration! 7271 } 7272 } 7273 return getCouldNotCompute(); 7274 } 7275 7276 ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit( 7277 Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) { 7278 ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV); 7279 if (!RHS) 7280 return getCouldNotCompute(); 7281 7282 const BasicBlock *Latch = L->getLoopLatch(); 7283 if (!Latch) 7284 return getCouldNotCompute(); 7285 7286 const BasicBlock *Predecessor = L->getLoopPredecessor(); 7287 if (!Predecessor) 7288 return getCouldNotCompute(); 7289 7290 // Return true if V is of the form "LHS `shift_op` <positive constant>". 7291 // Return LHS in OutLHS and shift_opt in OutOpCode. 7292 auto MatchPositiveShift = 7293 [](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) { 7294 7295 using namespace PatternMatch; 7296 7297 ConstantInt *ShiftAmt; 7298 if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt)))) 7299 OutOpCode = Instruction::LShr; 7300 else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt)))) 7301 OutOpCode = Instruction::AShr; 7302 else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt)))) 7303 OutOpCode = Instruction::Shl; 7304 else 7305 return false; 7306 7307 return ShiftAmt->getValue().isStrictlyPositive(); 7308 }; 7309 7310 // Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in 7311 // 7312 // loop: 7313 // %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ] 7314 // %iv.shifted = lshr i32 %iv, <positive constant> 7315 // 7316 // Return true on a successful match. Return the corresponding PHI node (%iv 7317 // above) in PNOut and the opcode of the shift operation in OpCodeOut. 7318 auto MatchShiftRecurrence = 7319 [&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) { 7320 Optional<Instruction::BinaryOps> PostShiftOpCode; 7321 7322 { 7323 Instruction::BinaryOps OpC; 7324 Value *V; 7325 7326 // If we encounter a shift instruction, "peel off" the shift operation, 7327 // and remember that we did so. Later when we inspect %iv's backedge 7328 // value, we will make sure that the backedge value uses the same 7329 // operation. 7330 // 7331 // Note: the peeled shift operation does not have to be the same 7332 // instruction as the one feeding into the PHI's backedge value. We only 7333 // really care about it being the same *kind* of shift instruction -- 7334 // that's all that is required for our later inferences to hold. 7335 if (MatchPositiveShift(LHS, V, OpC)) { 7336 PostShiftOpCode = OpC; 7337 LHS = V; 7338 } 7339 } 7340 7341 PNOut = dyn_cast<PHINode>(LHS); 7342 if (!PNOut || PNOut->getParent() != L->getHeader()) 7343 return false; 7344 7345 Value *BEValue = PNOut->getIncomingValueForBlock(Latch); 7346 Value *OpLHS; 7347 7348 return 7349 // The backedge value for the PHI node must be a shift by a positive 7350 // amount 7351 MatchPositiveShift(BEValue, OpLHS, OpCodeOut) && 7352 7353 // of the PHI node itself 7354 OpLHS == PNOut && 7355 7356 // and the kind of shift should be match the kind of shift we peeled 7357 // off, if any. 7358 (!PostShiftOpCode.hasValue() || *PostShiftOpCode == OpCodeOut); 7359 }; 7360 7361 PHINode *PN; 7362 Instruction::BinaryOps OpCode; 7363 if (!MatchShiftRecurrence(LHS, PN, OpCode)) 7364 return getCouldNotCompute(); 7365 7366 const DataLayout &DL = getDataLayout(); 7367 7368 // The key rationale for this optimization is that for some kinds of shift 7369 // recurrences, the value of the recurrence "stabilizes" to either 0 or -1 7370 // within a finite number of iterations. If the condition guarding the 7371 // backedge (in the sense that the backedge is taken if the condition is true) 7372 // is false for the value the shift recurrence stabilizes to, then we know 7373 // that the backedge is taken only a finite number of times. 7374 7375 ConstantInt *StableValue = nullptr; 7376 switch (OpCode) { 7377 default: 7378 llvm_unreachable("Impossible case!"); 7379 7380 case Instruction::AShr: { 7381 // {K,ashr,<positive-constant>} stabilizes to signum(K) in at most 7382 // bitwidth(K) iterations. 7383 Value *FirstValue = PN->getIncomingValueForBlock(Predecessor); 7384 KnownBits Known = computeKnownBits(FirstValue, DL, 0, nullptr, 7385 Predecessor->getTerminator(), &DT); 7386 auto *Ty = cast<IntegerType>(RHS->getType()); 7387 if (Known.isNonNegative()) 7388 StableValue = ConstantInt::get(Ty, 0); 7389 else if (Known.isNegative()) 7390 StableValue = ConstantInt::get(Ty, -1, true); 7391 else 7392 return getCouldNotCompute(); 7393 7394 break; 7395 } 7396 case Instruction::LShr: 7397 case Instruction::Shl: 7398 // Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>} 7399 // stabilize to 0 in at most bitwidth(K) iterations. 7400 StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0); 7401 break; 7402 } 7403 7404 auto *Result = 7405 ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI); 7406 assert(Result->getType()->isIntegerTy(1) && 7407 "Otherwise cannot be an operand to a branch instruction"); 7408 7409 if (Result->isZeroValue()) { 7410 unsigned BitWidth = getTypeSizeInBits(RHS->getType()); 7411 const SCEV *UpperBound = 7412 getConstant(getEffectiveSCEVType(RHS->getType()), BitWidth); 7413 return ExitLimit(getCouldNotCompute(), UpperBound, false); 7414 } 7415 7416 return getCouldNotCompute(); 7417 } 7418 7419 /// Return true if we can constant fold an instruction of the specified type, 7420 /// assuming that all operands were constants. 7421 static bool CanConstantFold(const Instruction *I) { 7422 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 7423 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) || 7424 isa<LoadInst>(I)) 7425 return true; 7426 7427 if (const CallInst *CI = dyn_cast<CallInst>(I)) 7428 if (const Function *F = CI->getCalledFunction()) 7429 return canConstantFoldCallTo(CI, F); 7430 return false; 7431 } 7432 7433 /// Determine whether this instruction can constant evolve within this loop 7434 /// assuming its operands can all constant evolve. 7435 static bool canConstantEvolve(Instruction *I, const Loop *L) { 7436 // An instruction outside of the loop can't be derived from a loop PHI. 7437 if (!L->contains(I)) return false; 7438 7439 if (isa<PHINode>(I)) { 7440 // We don't currently keep track of the control flow needed to evaluate 7441 // PHIs, so we cannot handle PHIs inside of loops. 7442 return L->getHeader() == I->getParent(); 7443 } 7444 7445 // If we won't be able to constant fold this expression even if the operands 7446 // are constants, bail early. 7447 return CanConstantFold(I); 7448 } 7449 7450 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by 7451 /// recursing through each instruction operand until reaching a loop header phi. 7452 static PHINode * 7453 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L, 7454 DenseMap<Instruction *, PHINode *> &PHIMap, 7455 unsigned Depth) { 7456 if (Depth > MaxConstantEvolvingDepth) 7457 return nullptr; 7458 7459 // Otherwise, we can evaluate this instruction if all of its operands are 7460 // constant or derived from a PHI node themselves. 7461 PHINode *PHI = nullptr; 7462 for (Value *Op : UseInst->operands()) { 7463 if (isa<Constant>(Op)) continue; 7464 7465 Instruction *OpInst = dyn_cast<Instruction>(Op); 7466 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr; 7467 7468 PHINode *P = dyn_cast<PHINode>(OpInst); 7469 if (!P) 7470 // If this operand is already visited, reuse the prior result. 7471 // We may have P != PHI if this is the deepest point at which the 7472 // inconsistent paths meet. 7473 P = PHIMap.lookup(OpInst); 7474 if (!P) { 7475 // Recurse and memoize the results, whether a phi is found or not. 7476 // This recursive call invalidates pointers into PHIMap. 7477 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap, Depth + 1); 7478 PHIMap[OpInst] = P; 7479 } 7480 if (!P) 7481 return nullptr; // Not evolving from PHI 7482 if (PHI && PHI != P) 7483 return nullptr; // Evolving from multiple different PHIs. 7484 PHI = P; 7485 } 7486 // This is a expression evolving from a constant PHI! 7487 return PHI; 7488 } 7489 7490 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 7491 /// in the loop that V is derived from. We allow arbitrary operations along the 7492 /// way, but the operands of an operation must either be constants or a value 7493 /// derived from a constant PHI. If this expression does not fit with these 7494 /// constraints, return null. 7495 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 7496 Instruction *I = dyn_cast<Instruction>(V); 7497 if (!I || !canConstantEvolve(I, L)) return nullptr; 7498 7499 if (PHINode *PN = dyn_cast<PHINode>(I)) 7500 return PN; 7501 7502 // Record non-constant instructions contained by the loop. 7503 DenseMap<Instruction *, PHINode *> PHIMap; 7504 return getConstantEvolvingPHIOperands(I, L, PHIMap, 0); 7505 } 7506 7507 /// EvaluateExpression - Given an expression that passes the 7508 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 7509 /// in the loop has the value PHIVal. If we can't fold this expression for some 7510 /// reason, return null. 7511 static Constant *EvaluateExpression(Value *V, const Loop *L, 7512 DenseMap<Instruction *, Constant *> &Vals, 7513 const DataLayout &DL, 7514 const TargetLibraryInfo *TLI) { 7515 // Convenient constant check, but redundant for recursive calls. 7516 if (Constant *C = dyn_cast<Constant>(V)) return C; 7517 Instruction *I = dyn_cast<Instruction>(V); 7518 if (!I) return nullptr; 7519 7520 if (Constant *C = Vals.lookup(I)) return C; 7521 7522 // An instruction inside the loop depends on a value outside the loop that we 7523 // weren't given a mapping for, or a value such as a call inside the loop. 7524 if (!canConstantEvolve(I, L)) return nullptr; 7525 7526 // An unmapped PHI can be due to a branch or another loop inside this loop, 7527 // or due to this not being the initial iteration through a loop where we 7528 // couldn't compute the evolution of this particular PHI last time. 7529 if (isa<PHINode>(I)) return nullptr; 7530 7531 std::vector<Constant*> Operands(I->getNumOperands()); 7532 7533 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 7534 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i)); 7535 if (!Operand) { 7536 Operands[i] = dyn_cast<Constant>(I->getOperand(i)); 7537 if (!Operands[i]) return nullptr; 7538 continue; 7539 } 7540 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI); 7541 Vals[Operand] = C; 7542 if (!C) return nullptr; 7543 Operands[i] = C; 7544 } 7545 7546 if (CmpInst *CI = dyn_cast<CmpInst>(I)) 7547 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 7548 Operands[1], DL, TLI); 7549 if (LoadInst *LI = dyn_cast<LoadInst>(I)) { 7550 if (!LI->isVolatile()) 7551 return ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL); 7552 } 7553 return ConstantFoldInstOperands(I, Operands, DL, TLI); 7554 } 7555 7556 7557 // If every incoming value to PN except the one for BB is a specific Constant, 7558 // return that, else return nullptr. 7559 static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) { 7560 Constant *IncomingVal = nullptr; 7561 7562 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 7563 if (PN->getIncomingBlock(i) == BB) 7564 continue; 7565 7566 auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i)); 7567 if (!CurrentVal) 7568 return nullptr; 7569 7570 if (IncomingVal != CurrentVal) { 7571 if (IncomingVal) 7572 return nullptr; 7573 IncomingVal = CurrentVal; 7574 } 7575 } 7576 7577 return IncomingVal; 7578 } 7579 7580 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 7581 /// in the header of its containing loop, we know the loop executes a 7582 /// constant number of times, and the PHI node is just a recurrence 7583 /// involving constants, fold it. 7584 Constant * 7585 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 7586 const APInt &BEs, 7587 const Loop *L) { 7588 auto I = ConstantEvolutionLoopExitValue.find(PN); 7589 if (I != ConstantEvolutionLoopExitValue.end()) 7590 return I->second; 7591 7592 if (BEs.ugt(MaxBruteForceIterations)) 7593 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it. 7594 7595 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 7596 7597 DenseMap<Instruction *, Constant *> CurrentIterVals; 7598 BasicBlock *Header = L->getHeader(); 7599 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!"); 7600 7601 BasicBlock *Latch = L->getLoopLatch(); 7602 if (!Latch) 7603 return nullptr; 7604 7605 for (auto &I : *Header) { 7606 PHINode *PHI = dyn_cast<PHINode>(&I); 7607 if (!PHI) break; 7608 auto *StartCST = getOtherIncomingValue(PHI, Latch); 7609 if (!StartCST) continue; 7610 CurrentIterVals[PHI] = StartCST; 7611 } 7612 if (!CurrentIterVals.count(PN)) 7613 return RetVal = nullptr; 7614 7615 Value *BEValue = PN->getIncomingValueForBlock(Latch); 7616 7617 // Execute the loop symbolically to determine the exit value. 7618 assert(BEs.getActiveBits() < CHAR_BIT * sizeof(unsigned) && 7619 "BEs is <= MaxBruteForceIterations which is an 'unsigned'!"); 7620 7621 unsigned NumIterations = BEs.getZExtValue(); // must be in range 7622 unsigned IterationNum = 0; 7623 const DataLayout &DL = getDataLayout(); 7624 for (; ; ++IterationNum) { 7625 if (IterationNum == NumIterations) 7626 return RetVal = CurrentIterVals[PN]; // Got exit value! 7627 7628 // Compute the value of the PHIs for the next iteration. 7629 // EvaluateExpression adds non-phi values to the CurrentIterVals map. 7630 DenseMap<Instruction *, Constant *> NextIterVals; 7631 Constant *NextPHI = 7632 EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI); 7633 if (!NextPHI) 7634 return nullptr; // Couldn't evaluate! 7635 NextIterVals[PN] = NextPHI; 7636 7637 bool StoppedEvolving = NextPHI == CurrentIterVals[PN]; 7638 7639 // Also evaluate the other PHI nodes. However, we don't get to stop if we 7640 // cease to be able to evaluate one of them or if they stop evolving, 7641 // because that doesn't necessarily prevent us from computing PN. 7642 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute; 7643 for (const auto &I : CurrentIterVals) { 7644 PHINode *PHI = dyn_cast<PHINode>(I.first); 7645 if (!PHI || PHI == PN || PHI->getParent() != Header) continue; 7646 PHIsToCompute.emplace_back(PHI, I.second); 7647 } 7648 // We use two distinct loops because EvaluateExpression may invalidate any 7649 // iterators into CurrentIterVals. 7650 for (const auto &I : PHIsToCompute) { 7651 PHINode *PHI = I.first; 7652 Constant *&NextPHI = NextIterVals[PHI]; 7653 if (!NextPHI) { // Not already computed. 7654 Value *BEValue = PHI->getIncomingValueForBlock(Latch); 7655 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI); 7656 } 7657 if (NextPHI != I.second) 7658 StoppedEvolving = false; 7659 } 7660 7661 // If all entries in CurrentIterVals == NextIterVals then we can stop 7662 // iterating, the loop can't continue to change. 7663 if (StoppedEvolving) 7664 return RetVal = CurrentIterVals[PN]; 7665 7666 CurrentIterVals.swap(NextIterVals); 7667 } 7668 } 7669 7670 const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L, 7671 Value *Cond, 7672 bool ExitWhen) { 7673 PHINode *PN = getConstantEvolvingPHI(Cond, L); 7674 if (!PN) return getCouldNotCompute(); 7675 7676 // If the loop is canonicalized, the PHI will have exactly two entries. 7677 // That's the only form we support here. 7678 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 7679 7680 DenseMap<Instruction *, Constant *> CurrentIterVals; 7681 BasicBlock *Header = L->getHeader(); 7682 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!"); 7683 7684 BasicBlock *Latch = L->getLoopLatch(); 7685 assert(Latch && "Should follow from NumIncomingValues == 2!"); 7686 7687 for (auto &I : *Header) { 7688 PHINode *PHI = dyn_cast<PHINode>(&I); 7689 if (!PHI) 7690 break; 7691 auto *StartCST = getOtherIncomingValue(PHI, Latch); 7692 if (!StartCST) continue; 7693 CurrentIterVals[PHI] = StartCST; 7694 } 7695 if (!CurrentIterVals.count(PN)) 7696 return getCouldNotCompute(); 7697 7698 // Okay, we find a PHI node that defines the trip count of this loop. Execute 7699 // the loop symbolically to determine when the condition gets a value of 7700 // "ExitWhen". 7701 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 7702 const DataLayout &DL = getDataLayout(); 7703 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){ 7704 auto *CondVal = dyn_cast_or_null<ConstantInt>( 7705 EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI)); 7706 7707 // Couldn't symbolically evaluate. 7708 if (!CondVal) return getCouldNotCompute(); 7709 7710 if (CondVal->getValue() == uint64_t(ExitWhen)) { 7711 ++NumBruteForceTripCountsComputed; 7712 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 7713 } 7714 7715 // Update all the PHI nodes for the next iteration. 7716 DenseMap<Instruction *, Constant *> NextIterVals; 7717 7718 // Create a list of which PHIs we need to compute. We want to do this before 7719 // calling EvaluateExpression on them because that may invalidate iterators 7720 // into CurrentIterVals. 7721 SmallVector<PHINode *, 8> PHIsToCompute; 7722 for (const auto &I : CurrentIterVals) { 7723 PHINode *PHI = dyn_cast<PHINode>(I.first); 7724 if (!PHI || PHI->getParent() != Header) continue; 7725 PHIsToCompute.push_back(PHI); 7726 } 7727 for (PHINode *PHI : PHIsToCompute) { 7728 Constant *&NextPHI = NextIterVals[PHI]; 7729 if (NextPHI) continue; // Already computed! 7730 7731 Value *BEValue = PHI->getIncomingValueForBlock(Latch); 7732 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI); 7733 } 7734 CurrentIterVals.swap(NextIterVals); 7735 } 7736 7737 // Too many iterations were needed to evaluate. 7738 return getCouldNotCompute(); 7739 } 7740 7741 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 7742 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = 7743 ValuesAtScopes[V]; 7744 // Check to see if we've folded this expression at this loop before. 7745 for (auto &LS : Values) 7746 if (LS.first == L) 7747 return LS.second ? LS.second : V; 7748 7749 Values.emplace_back(L, nullptr); 7750 7751 // Otherwise compute it. 7752 const SCEV *C = computeSCEVAtScope(V, L); 7753 for (auto &LS : reverse(ValuesAtScopes[V])) 7754 if (LS.first == L) { 7755 LS.second = C; 7756 break; 7757 } 7758 return C; 7759 } 7760 7761 /// This builds up a Constant using the ConstantExpr interface. That way, we 7762 /// will return Constants for objects which aren't represented by a 7763 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt. 7764 /// Returns NULL if the SCEV isn't representable as a Constant. 7765 static Constant *BuildConstantFromSCEV(const SCEV *V) { 7766 switch (static_cast<SCEVTypes>(V->getSCEVType())) { 7767 case scCouldNotCompute: 7768 case scAddRecExpr: 7769 break; 7770 case scConstant: 7771 return cast<SCEVConstant>(V)->getValue(); 7772 case scUnknown: 7773 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue()); 7774 case scSignExtend: { 7775 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V); 7776 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand())) 7777 return ConstantExpr::getSExt(CastOp, SS->getType()); 7778 break; 7779 } 7780 case scZeroExtend: { 7781 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V); 7782 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand())) 7783 return ConstantExpr::getZExt(CastOp, SZ->getType()); 7784 break; 7785 } 7786 case scTruncate: { 7787 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V); 7788 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand())) 7789 return ConstantExpr::getTrunc(CastOp, ST->getType()); 7790 break; 7791 } 7792 case scAddExpr: { 7793 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V); 7794 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) { 7795 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) { 7796 unsigned AS = PTy->getAddressSpace(); 7797 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS); 7798 C = ConstantExpr::getBitCast(C, DestPtrTy); 7799 } 7800 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) { 7801 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i)); 7802 if (!C2) return nullptr; 7803 7804 // First pointer! 7805 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) { 7806 unsigned AS = C2->getType()->getPointerAddressSpace(); 7807 std::swap(C, C2); 7808 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS); 7809 // The offsets have been converted to bytes. We can add bytes to an 7810 // i8* by GEP with the byte count in the first index. 7811 C = ConstantExpr::getBitCast(C, DestPtrTy); 7812 } 7813 7814 // Don't bother trying to sum two pointers. We probably can't 7815 // statically compute a load that results from it anyway. 7816 if (C2->getType()->isPointerTy()) 7817 return nullptr; 7818 7819 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) { 7820 if (PTy->getElementType()->isStructTy()) 7821 C2 = ConstantExpr::getIntegerCast( 7822 C2, Type::getInt32Ty(C->getContext()), true); 7823 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2); 7824 } else 7825 C = ConstantExpr::getAdd(C, C2); 7826 } 7827 return C; 7828 } 7829 break; 7830 } 7831 case scMulExpr: { 7832 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V); 7833 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) { 7834 // Don't bother with pointers at all. 7835 if (C->getType()->isPointerTy()) return nullptr; 7836 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) { 7837 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i)); 7838 if (!C2 || C2->getType()->isPointerTy()) return nullptr; 7839 C = ConstantExpr::getMul(C, C2); 7840 } 7841 return C; 7842 } 7843 break; 7844 } 7845 case scUDivExpr: { 7846 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V); 7847 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS())) 7848 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS())) 7849 if (LHS->getType() == RHS->getType()) 7850 return ConstantExpr::getUDiv(LHS, RHS); 7851 break; 7852 } 7853 case scSMaxExpr: 7854 case scUMaxExpr: 7855 break; // TODO: smax, umax. 7856 } 7857 return nullptr; 7858 } 7859 7860 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 7861 if (isa<SCEVConstant>(V)) return V; 7862 7863 // If this instruction is evolved from a constant-evolving PHI, compute the 7864 // exit value from the loop without using SCEVs. 7865 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 7866 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 7867 const Loop *LI = this->LI[I->getParent()]; 7868 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 7869 if (PHINode *PN = dyn_cast<PHINode>(I)) 7870 if (PN->getParent() == LI->getHeader()) { 7871 // Okay, there is no closed form solution for the PHI node. Check 7872 // to see if the loop that contains it has a known backedge-taken 7873 // count. If so, we may be able to force computation of the exit 7874 // value. 7875 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 7876 if (const SCEVConstant *BTCC = 7877 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 7878 7879 // This trivial case can show up in some degenerate cases where 7880 // the incoming IR has not yet been fully simplified. 7881 if (BTCC->getValue()->isZero()) { 7882 Value *InitValue = nullptr; 7883 bool MultipleInitValues = false; 7884 for (unsigned i = 0; i < PN->getNumIncomingValues(); i++) { 7885 if (!LI->contains(PN->getIncomingBlock(i))) { 7886 if (!InitValue) 7887 InitValue = PN->getIncomingValue(i); 7888 else if (InitValue != PN->getIncomingValue(i)) { 7889 MultipleInitValues = true; 7890 break; 7891 } 7892 } 7893 if (!MultipleInitValues && InitValue) 7894 return getSCEV(InitValue); 7895 } 7896 } 7897 // Okay, we know how many times the containing loop executes. If 7898 // this is a constant evolving PHI node, get the final value at 7899 // the specified iteration number. 7900 Constant *RV = 7901 getConstantEvolutionLoopExitValue(PN, BTCC->getAPInt(), LI); 7902 if (RV) return getSCEV(RV); 7903 } 7904 } 7905 7906 // Okay, this is an expression that we cannot symbolically evaluate 7907 // into a SCEV. Check to see if it's possible to symbolically evaluate 7908 // the arguments into constants, and if so, try to constant propagate the 7909 // result. This is particularly useful for computing loop exit values. 7910 if (CanConstantFold(I)) { 7911 SmallVector<Constant *, 4> Operands; 7912 bool MadeImprovement = false; 7913 for (Value *Op : I->operands()) { 7914 if (Constant *C = dyn_cast<Constant>(Op)) { 7915 Operands.push_back(C); 7916 continue; 7917 } 7918 7919 // If any of the operands is non-constant and if they are 7920 // non-integer and non-pointer, don't even try to analyze them 7921 // with scev techniques. 7922 if (!isSCEVable(Op->getType())) 7923 return V; 7924 7925 const SCEV *OrigV = getSCEV(Op); 7926 const SCEV *OpV = getSCEVAtScope(OrigV, L); 7927 MadeImprovement |= OrigV != OpV; 7928 7929 Constant *C = BuildConstantFromSCEV(OpV); 7930 if (!C) return V; 7931 if (C->getType() != Op->getType()) 7932 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 7933 Op->getType(), 7934 false), 7935 C, Op->getType()); 7936 Operands.push_back(C); 7937 } 7938 7939 // Check to see if getSCEVAtScope actually made an improvement. 7940 if (MadeImprovement) { 7941 Constant *C = nullptr; 7942 const DataLayout &DL = getDataLayout(); 7943 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 7944 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 7945 Operands[1], DL, &TLI); 7946 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) { 7947 if (!LI->isVolatile()) 7948 C = ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL); 7949 } else 7950 C = ConstantFoldInstOperands(I, Operands, DL, &TLI); 7951 if (!C) return V; 7952 return getSCEV(C); 7953 } 7954 } 7955 } 7956 7957 // This is some other type of SCEVUnknown, just return it. 7958 return V; 7959 } 7960 7961 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 7962 // Avoid performing the look-up in the common case where the specified 7963 // expression has no loop-variant portions. 7964 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 7965 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 7966 if (OpAtScope != Comm->getOperand(i)) { 7967 // Okay, at least one of these operands is loop variant but might be 7968 // foldable. Build a new instance of the folded commutative expression. 7969 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 7970 Comm->op_begin()+i); 7971 NewOps.push_back(OpAtScope); 7972 7973 for (++i; i != e; ++i) { 7974 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 7975 NewOps.push_back(OpAtScope); 7976 } 7977 if (isa<SCEVAddExpr>(Comm)) 7978 return getAddExpr(NewOps); 7979 if (isa<SCEVMulExpr>(Comm)) 7980 return getMulExpr(NewOps); 7981 if (isa<SCEVSMaxExpr>(Comm)) 7982 return getSMaxExpr(NewOps); 7983 if (isa<SCEVUMaxExpr>(Comm)) 7984 return getUMaxExpr(NewOps); 7985 llvm_unreachable("Unknown commutative SCEV type!"); 7986 } 7987 } 7988 // If we got here, all operands are loop invariant. 7989 return Comm; 7990 } 7991 7992 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 7993 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 7994 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 7995 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 7996 return Div; // must be loop invariant 7997 return getUDivExpr(LHS, RHS); 7998 } 7999 8000 // If this is a loop recurrence for a loop that does not contain L, then we 8001 // are dealing with the final value computed by the loop. 8002 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 8003 // First, attempt to evaluate each operand. 8004 // Avoid performing the look-up in the common case where the specified 8005 // expression has no loop-variant portions. 8006 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 8007 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); 8008 if (OpAtScope == AddRec->getOperand(i)) 8009 continue; 8010 8011 // Okay, at least one of these operands is loop variant but might be 8012 // foldable. Build a new instance of the folded commutative expression. 8013 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(), 8014 AddRec->op_begin()+i); 8015 NewOps.push_back(OpAtScope); 8016 for (++i; i != e; ++i) 8017 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); 8018 8019 const SCEV *FoldedRec = 8020 getAddRecExpr(NewOps, AddRec->getLoop(), 8021 AddRec->getNoWrapFlags(SCEV::FlagNW)); 8022 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec); 8023 // The addrec may be folded to a nonrecurrence, for example, if the 8024 // induction variable is multiplied by zero after constant folding. Go 8025 // ahead and return the folded value. 8026 if (!AddRec) 8027 return FoldedRec; 8028 break; 8029 } 8030 8031 // If the scope is outside the addrec's loop, evaluate it by using the 8032 // loop exit value of the addrec. 8033 if (!AddRec->getLoop()->contains(L)) { 8034 // To evaluate this recurrence, we need to know how many times the AddRec 8035 // loop iterates. Compute this now. 8036 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 8037 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 8038 8039 // Then, evaluate the AddRec. 8040 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 8041 } 8042 8043 return AddRec; 8044 } 8045 8046 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 8047 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 8048 if (Op == Cast->getOperand()) 8049 return Cast; // must be loop invariant 8050 return getZeroExtendExpr(Op, Cast->getType()); 8051 } 8052 8053 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 8054 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 8055 if (Op == Cast->getOperand()) 8056 return Cast; // must be loop invariant 8057 return getSignExtendExpr(Op, Cast->getType()); 8058 } 8059 8060 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 8061 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 8062 if (Op == Cast->getOperand()) 8063 return Cast; // must be loop invariant 8064 return getTruncateExpr(Op, Cast->getType()); 8065 } 8066 8067 llvm_unreachable("Unknown SCEV type!"); 8068 } 8069 8070 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 8071 return getSCEVAtScope(getSCEV(V), L); 8072 } 8073 8074 /// Finds the minimum unsigned root of the following equation: 8075 /// 8076 /// A * X = B (mod N) 8077 /// 8078 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of 8079 /// A and B isn't important. 8080 /// 8081 /// If the equation does not have a solution, SCEVCouldNotCompute is returned. 8082 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const SCEV *B, 8083 ScalarEvolution &SE) { 8084 uint32_t BW = A.getBitWidth(); 8085 assert(BW == SE.getTypeSizeInBits(B->getType())); 8086 assert(A != 0 && "A must be non-zero."); 8087 8088 // 1. D = gcd(A, N) 8089 // 8090 // The gcd of A and N may have only one prime factor: 2. The number of 8091 // trailing zeros in A is its multiplicity 8092 uint32_t Mult2 = A.countTrailingZeros(); 8093 // D = 2^Mult2 8094 8095 // 2. Check if B is divisible by D. 8096 // 8097 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 8098 // is not less than multiplicity of this prime factor for D. 8099 if (SE.GetMinTrailingZeros(B) < Mult2) 8100 return SE.getCouldNotCompute(); 8101 8102 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 8103 // modulo (N / D). 8104 // 8105 // If D == 1, (N / D) == N == 2^BW, so we need one extra bit to represent 8106 // (N / D) in general. The inverse itself always fits into BW bits, though, 8107 // so we immediately truncate it. 8108 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 8109 APInt Mod(BW + 1, 0); 8110 Mod.setBit(BW - Mult2); // Mod = N / D 8111 APInt I = AD.multiplicativeInverse(Mod).trunc(BW); 8112 8113 // 4. Compute the minimum unsigned root of the equation: 8114 // I * (B / D) mod (N / D) 8115 // To simplify the computation, we factor out the divide by D: 8116 // (I * B mod N) / D 8117 const SCEV *D = SE.getConstant(APInt::getOneBitSet(BW, Mult2)); 8118 return SE.getUDivExactExpr(SE.getMulExpr(B, SE.getConstant(I)), D); 8119 } 8120 8121 /// Find the roots of the quadratic equation for the given quadratic chrec 8122 /// {L,+,M,+,N}. This returns either the two roots (which might be the same) or 8123 /// two SCEVCouldNotCompute objects. 8124 static Optional<std::pair<const SCEVConstant *,const SCEVConstant *>> 8125 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 8126 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 8127 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 8128 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 8129 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 8130 8131 // We currently can only solve this if the coefficients are constants. 8132 if (!LC || !MC || !NC) 8133 return None; 8134 8135 uint32_t BitWidth = LC->getAPInt().getBitWidth(); 8136 const APInt &L = LC->getAPInt(); 8137 const APInt &M = MC->getAPInt(); 8138 const APInt &N = NC->getAPInt(); 8139 APInt Two(BitWidth, 2); 8140 8141 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 8142 8143 // The A coefficient is N/2 8144 APInt A = N.sdiv(Two); 8145 8146 // The B coefficient is M-N/2 8147 APInt B = M; 8148 B -= A; // A is the same as N/2. 8149 8150 // The C coefficient is L. 8151 const APInt& C = L; 8152 8153 // Compute the B^2-4ac term. 8154 APInt SqrtTerm = B; 8155 SqrtTerm *= B; 8156 SqrtTerm -= 4 * (A * C); 8157 8158 if (SqrtTerm.isNegative()) { 8159 // The loop is provably infinite. 8160 return None; 8161 } 8162 8163 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 8164 // integer value or else APInt::sqrt() will assert. 8165 APInt SqrtVal = SqrtTerm.sqrt(); 8166 8167 // Compute the two solutions for the quadratic formula. 8168 // The divisions must be performed as signed divisions. 8169 APInt NegB = -std::move(B); 8170 APInt TwoA = std::move(A); 8171 TwoA <<= 1; 8172 if (TwoA.isNullValue()) 8173 return None; 8174 8175 LLVMContext &Context = SE.getContext(); 8176 8177 ConstantInt *Solution1 = 8178 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 8179 ConstantInt *Solution2 = 8180 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 8181 8182 return std::make_pair(cast<SCEVConstant>(SE.getConstant(Solution1)), 8183 cast<SCEVConstant>(SE.getConstant(Solution2))); 8184 } 8185 8186 ScalarEvolution::ExitLimit 8187 ScalarEvolution::howFarToZero(const SCEV *V, const Loop *L, bool ControlsExit, 8188 bool AllowPredicates) { 8189 8190 // This is only used for loops with a "x != y" exit test. The exit condition 8191 // is now expressed as a single expression, V = x-y. So the exit test is 8192 // effectively V != 0. We know and take advantage of the fact that this 8193 // expression only being used in a comparison by zero context. 8194 8195 SmallPtrSet<const SCEVPredicate *, 4> Predicates; 8196 // If the value is a constant 8197 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 8198 // If the value is already zero, the branch will execute zero times. 8199 if (C->getValue()->isZero()) return C; 8200 return getCouldNotCompute(); // Otherwise it will loop infinitely. 8201 } 8202 8203 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 8204 if (!AddRec && AllowPredicates) 8205 // Try to make this an AddRec using runtime tests, in the first X 8206 // iterations of this loop, where X is the SCEV expression found by the 8207 // algorithm below. 8208 AddRec = convertSCEVToAddRecWithPredicates(V, L, Predicates); 8209 8210 if (!AddRec || AddRec->getLoop() != L) 8211 return getCouldNotCompute(); 8212 8213 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 8214 // the quadratic equation to solve it. 8215 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 8216 if (auto Roots = SolveQuadraticEquation(AddRec, *this)) { 8217 const SCEVConstant *R1 = Roots->first; 8218 const SCEVConstant *R2 = Roots->second; 8219 // Pick the smallest positive root value. 8220 if (ConstantInt *CB = dyn_cast<ConstantInt>(ConstantExpr::getICmp( 8221 CmpInst::ICMP_ULT, R1->getValue(), R2->getValue()))) { 8222 if (!CB->getZExtValue()) 8223 std::swap(R1, R2); // R1 is the minimum root now. 8224 8225 // We can only use this value if the chrec ends up with an exact zero 8226 // value at this index. When solving for "X*X != 5", for example, we 8227 // should not accept a root of 2. 8228 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 8229 if (Val->isZero()) 8230 // We found a quadratic root! 8231 return ExitLimit(R1, R1, false, Predicates); 8232 } 8233 } 8234 return getCouldNotCompute(); 8235 } 8236 8237 // Otherwise we can only handle this if it is affine. 8238 if (!AddRec->isAffine()) 8239 return getCouldNotCompute(); 8240 8241 // If this is an affine expression, the execution count of this branch is 8242 // the minimum unsigned root of the following equation: 8243 // 8244 // Start + Step*N = 0 (mod 2^BW) 8245 // 8246 // equivalent to: 8247 // 8248 // Step*N = -Start (mod 2^BW) 8249 // 8250 // where BW is the common bit width of Start and Step. 8251 8252 // Get the initial value for the loop. 8253 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 8254 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 8255 8256 // For now we handle only constant steps. 8257 // 8258 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the 8259 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap 8260 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step. 8261 // We have not yet seen any such cases. 8262 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step); 8263 if (!StepC || StepC->getValue()->isZero()) 8264 return getCouldNotCompute(); 8265 8266 // For positive steps (counting up until unsigned overflow): 8267 // N = -Start/Step (as unsigned) 8268 // For negative steps (counting down to zero): 8269 // N = Start/-Step 8270 // First compute the unsigned distance from zero in the direction of Step. 8271 bool CountDown = StepC->getAPInt().isNegative(); 8272 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start); 8273 8274 // Handle unitary steps, which cannot wraparound. 8275 // 1*N = -Start; -1*N = Start (mod 2^BW), so: 8276 // N = Distance (as unsigned) 8277 if (StepC->getValue()->isOne() || StepC->getValue()->isMinusOne()) { 8278 APInt MaxBECount = getUnsignedRangeMax(Distance); 8279 8280 // When a loop like "for (int i = 0; i != n; ++i) { /* body */ }" is rotated, 8281 // we end up with a loop whose backedge-taken count is n - 1. Detect this 8282 // case, and see if we can improve the bound. 8283 // 8284 // Explicitly handling this here is necessary because getUnsignedRange 8285 // isn't context-sensitive; it doesn't know that we only care about the 8286 // range inside the loop. 8287 const SCEV *Zero = getZero(Distance->getType()); 8288 const SCEV *One = getOne(Distance->getType()); 8289 const SCEV *DistancePlusOne = getAddExpr(Distance, One); 8290 if (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, DistancePlusOne, Zero)) { 8291 // If Distance + 1 doesn't overflow, we can compute the maximum distance 8292 // as "unsigned_max(Distance + 1) - 1". 8293 ConstantRange CR = getUnsignedRange(DistancePlusOne); 8294 MaxBECount = APIntOps::umin(MaxBECount, CR.getUnsignedMax() - 1); 8295 } 8296 return ExitLimit(Distance, getConstant(MaxBECount), false, Predicates); 8297 } 8298 8299 // If the condition controls loop exit (the loop exits only if the expression 8300 // is true) and the addition is no-wrap we can use unsigned divide to 8301 // compute the backedge count. In this case, the step may not divide the 8302 // distance, but we don't care because if the condition is "missed" the loop 8303 // will have undefined behavior due to wrapping. 8304 if (ControlsExit && AddRec->hasNoSelfWrap() && 8305 loopHasNoAbnormalExits(AddRec->getLoop())) { 8306 const SCEV *Exact = 8307 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step); 8308 const SCEV *Max = 8309 Exact == getCouldNotCompute() 8310 ? Exact 8311 : getConstant(getUnsignedRangeMax(Exact)); 8312 return ExitLimit(Exact, Max, false, Predicates); 8313 } 8314 8315 // Solve the general equation. 8316 const SCEV *E = SolveLinEquationWithOverflow(StepC->getAPInt(), 8317 getNegativeSCEV(Start), *this); 8318 const SCEV *M = E == getCouldNotCompute() 8319 ? E 8320 : getConstant(getUnsignedRangeMax(E)); 8321 return ExitLimit(E, M, false, Predicates); 8322 } 8323 8324 ScalarEvolution::ExitLimit 8325 ScalarEvolution::howFarToNonZero(const SCEV *V, const Loop *L) { 8326 // Loops that look like: while (X == 0) are very strange indeed. We don't 8327 // handle them yet except for the trivial case. This could be expanded in the 8328 // future as needed. 8329 8330 // If the value is a constant, check to see if it is known to be non-zero 8331 // already. If so, the backedge will execute zero times. 8332 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 8333 if (!C->getValue()->isZero()) 8334 return getZero(C->getType()); 8335 return getCouldNotCompute(); // Otherwise it will loop infinitely. 8336 } 8337 8338 // We could implement others, but I really doubt anyone writes loops like 8339 // this, and if they did, they would already be constant folded. 8340 return getCouldNotCompute(); 8341 } 8342 8343 std::pair<BasicBlock *, BasicBlock *> 8344 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 8345 // If the block has a unique predecessor, then there is no path from the 8346 // predecessor to the block that does not go through the direct edge 8347 // from the predecessor to the block. 8348 if (BasicBlock *Pred = BB->getSinglePredecessor()) 8349 return {Pred, BB}; 8350 8351 // A loop's header is defined to be a block that dominates the loop. 8352 // If the header has a unique predecessor outside the loop, it must be 8353 // a block that has exactly one successor that can reach the loop. 8354 if (Loop *L = LI.getLoopFor(BB)) 8355 return {L->getLoopPredecessor(), L->getHeader()}; 8356 8357 return {nullptr, nullptr}; 8358 } 8359 8360 /// SCEV structural equivalence is usually sufficient for testing whether two 8361 /// expressions are equal, however for the purposes of looking for a condition 8362 /// guarding a loop, it can be useful to be a little more general, since a 8363 /// front-end may have replicated the controlling expression. 8364 static bool HasSameValue(const SCEV *A, const SCEV *B) { 8365 // Quick check to see if they are the same SCEV. 8366 if (A == B) return true; 8367 8368 auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) { 8369 // Not all instructions that are "identical" compute the same value. For 8370 // instance, two distinct alloca instructions allocating the same type are 8371 // identical and do not read memory; but compute distinct values. 8372 return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A)); 8373 }; 8374 8375 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 8376 // two different instructions with the same value. Check for this case. 8377 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 8378 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 8379 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 8380 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 8381 if (ComputesEqualValues(AI, BI)) 8382 return true; 8383 8384 // Otherwise assume they may have a different value. 8385 return false; 8386 } 8387 8388 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 8389 const SCEV *&LHS, const SCEV *&RHS, 8390 unsigned Depth) { 8391 bool Changed = false; 8392 8393 // If we hit the max recursion limit bail out. 8394 if (Depth >= 3) 8395 return false; 8396 8397 // Canonicalize a constant to the right side. 8398 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 8399 // Check for both operands constant. 8400 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 8401 if (ConstantExpr::getICmp(Pred, 8402 LHSC->getValue(), 8403 RHSC->getValue())->isNullValue()) 8404 goto trivially_false; 8405 else 8406 goto trivially_true; 8407 } 8408 // Otherwise swap the operands to put the constant on the right. 8409 std::swap(LHS, RHS); 8410 Pred = ICmpInst::getSwappedPredicate(Pred); 8411 Changed = true; 8412 } 8413 8414 // If we're comparing an addrec with a value which is loop-invariant in the 8415 // addrec's loop, put the addrec on the left. Also make a dominance check, 8416 // as both operands could be addrecs loop-invariant in each other's loop. 8417 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 8418 const Loop *L = AR->getLoop(); 8419 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) { 8420 std::swap(LHS, RHS); 8421 Pred = ICmpInst::getSwappedPredicate(Pred); 8422 Changed = true; 8423 } 8424 } 8425 8426 // If there's a constant operand, canonicalize comparisons with boundary 8427 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 8428 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 8429 const APInt &RA = RC->getAPInt(); 8430 8431 bool SimplifiedByConstantRange = false; 8432 8433 if (!ICmpInst::isEquality(Pred)) { 8434 ConstantRange ExactCR = ConstantRange::makeExactICmpRegion(Pred, RA); 8435 if (ExactCR.isFullSet()) 8436 goto trivially_true; 8437 else if (ExactCR.isEmptySet()) 8438 goto trivially_false; 8439 8440 APInt NewRHS; 8441 CmpInst::Predicate NewPred; 8442 if (ExactCR.getEquivalentICmp(NewPred, NewRHS) && 8443 ICmpInst::isEquality(NewPred)) { 8444 // We were able to convert an inequality to an equality. 8445 Pred = NewPred; 8446 RHS = getConstant(NewRHS); 8447 Changed = SimplifiedByConstantRange = true; 8448 } 8449 } 8450 8451 if (!SimplifiedByConstantRange) { 8452 switch (Pred) { 8453 default: 8454 break; 8455 case ICmpInst::ICMP_EQ: 8456 case ICmpInst::ICMP_NE: 8457 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b. 8458 if (!RA) 8459 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS)) 8460 if (const SCEVMulExpr *ME = 8461 dyn_cast<SCEVMulExpr>(AE->getOperand(0))) 8462 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 && 8463 ME->getOperand(0)->isAllOnesValue()) { 8464 RHS = AE->getOperand(1); 8465 LHS = ME->getOperand(1); 8466 Changed = true; 8467 } 8468 break; 8469 8470 8471 // The "Should have been caught earlier!" messages refer to the fact 8472 // that the ExactCR.isFullSet() or ExactCR.isEmptySet() check above 8473 // should have fired on the corresponding cases, and canonicalized the 8474 // check to trivially_true or trivially_false. 8475 8476 case ICmpInst::ICMP_UGE: 8477 assert(!RA.isMinValue() && "Should have been caught earlier!"); 8478 Pred = ICmpInst::ICMP_UGT; 8479 RHS = getConstant(RA - 1); 8480 Changed = true; 8481 break; 8482 case ICmpInst::ICMP_ULE: 8483 assert(!RA.isMaxValue() && "Should have been caught earlier!"); 8484 Pred = ICmpInst::ICMP_ULT; 8485 RHS = getConstant(RA + 1); 8486 Changed = true; 8487 break; 8488 case ICmpInst::ICMP_SGE: 8489 assert(!RA.isMinSignedValue() && "Should have been caught earlier!"); 8490 Pred = ICmpInst::ICMP_SGT; 8491 RHS = getConstant(RA - 1); 8492 Changed = true; 8493 break; 8494 case ICmpInst::ICMP_SLE: 8495 assert(!RA.isMaxSignedValue() && "Should have been caught earlier!"); 8496 Pred = ICmpInst::ICMP_SLT; 8497 RHS = getConstant(RA + 1); 8498 Changed = true; 8499 break; 8500 } 8501 } 8502 } 8503 8504 // Check for obvious equality. 8505 if (HasSameValue(LHS, RHS)) { 8506 if (ICmpInst::isTrueWhenEqual(Pred)) 8507 goto trivially_true; 8508 if (ICmpInst::isFalseWhenEqual(Pred)) 8509 goto trivially_false; 8510 } 8511 8512 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 8513 // adding or subtracting 1 from one of the operands. 8514 switch (Pred) { 8515 case ICmpInst::ICMP_SLE: 8516 if (!getSignedRangeMax(RHS).isMaxSignedValue()) { 8517 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 8518 SCEV::FlagNSW); 8519 Pred = ICmpInst::ICMP_SLT; 8520 Changed = true; 8521 } else if (!getSignedRangeMin(LHS).isMinSignedValue()) { 8522 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 8523 SCEV::FlagNSW); 8524 Pred = ICmpInst::ICMP_SLT; 8525 Changed = true; 8526 } 8527 break; 8528 case ICmpInst::ICMP_SGE: 8529 if (!getSignedRangeMin(RHS).isMinSignedValue()) { 8530 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 8531 SCEV::FlagNSW); 8532 Pred = ICmpInst::ICMP_SGT; 8533 Changed = true; 8534 } else if (!getSignedRangeMax(LHS).isMaxSignedValue()) { 8535 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 8536 SCEV::FlagNSW); 8537 Pred = ICmpInst::ICMP_SGT; 8538 Changed = true; 8539 } 8540 break; 8541 case ICmpInst::ICMP_ULE: 8542 if (!getUnsignedRangeMax(RHS).isMaxValue()) { 8543 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 8544 SCEV::FlagNUW); 8545 Pred = ICmpInst::ICMP_ULT; 8546 Changed = true; 8547 } else if (!getUnsignedRangeMin(LHS).isMinValue()) { 8548 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS); 8549 Pred = ICmpInst::ICMP_ULT; 8550 Changed = true; 8551 } 8552 break; 8553 case ICmpInst::ICMP_UGE: 8554 if (!getUnsignedRangeMin(RHS).isMinValue()) { 8555 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS); 8556 Pred = ICmpInst::ICMP_UGT; 8557 Changed = true; 8558 } else if (!getUnsignedRangeMax(LHS).isMaxValue()) { 8559 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 8560 SCEV::FlagNUW); 8561 Pred = ICmpInst::ICMP_UGT; 8562 Changed = true; 8563 } 8564 break; 8565 default: 8566 break; 8567 } 8568 8569 // TODO: More simplifications are possible here. 8570 8571 // Recursively simplify until we either hit a recursion limit or nothing 8572 // changes. 8573 if (Changed) 8574 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1); 8575 8576 return Changed; 8577 8578 trivially_true: 8579 // Return 0 == 0. 8580 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 8581 Pred = ICmpInst::ICMP_EQ; 8582 return true; 8583 8584 trivially_false: 8585 // Return 0 != 0. 8586 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 8587 Pred = ICmpInst::ICMP_NE; 8588 return true; 8589 } 8590 8591 bool ScalarEvolution::isKnownNegative(const SCEV *S) { 8592 return getSignedRangeMax(S).isNegative(); 8593 } 8594 8595 bool ScalarEvolution::isKnownPositive(const SCEV *S) { 8596 return getSignedRangeMin(S).isStrictlyPositive(); 8597 } 8598 8599 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 8600 return !getSignedRangeMin(S).isNegative(); 8601 } 8602 8603 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 8604 return !getSignedRangeMax(S).isStrictlyPositive(); 8605 } 8606 8607 bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 8608 return isKnownNegative(S) || isKnownPositive(S); 8609 } 8610 8611 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 8612 const SCEV *LHS, const SCEV *RHS) { 8613 // Canonicalize the inputs first. 8614 (void)SimplifyICmpOperands(Pred, LHS, RHS); 8615 8616 // If LHS or RHS is an addrec, check to see if the condition is true in 8617 // every iteration of the loop. 8618 // If LHS and RHS are both addrec, both conditions must be true in 8619 // every iteration of the loop. 8620 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS); 8621 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS); 8622 bool LeftGuarded = false; 8623 bool RightGuarded = false; 8624 if (LAR) { 8625 const Loop *L = LAR->getLoop(); 8626 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) && 8627 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) { 8628 if (!RAR) return true; 8629 LeftGuarded = true; 8630 } 8631 } 8632 if (RAR) { 8633 const Loop *L = RAR->getLoop(); 8634 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) && 8635 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) { 8636 if (!LAR) return true; 8637 RightGuarded = true; 8638 } 8639 } 8640 if (LeftGuarded && RightGuarded) 8641 return true; 8642 8643 if (isKnownPredicateViaSplitting(Pred, LHS, RHS)) 8644 return true; 8645 8646 // Otherwise see what can be done with known constant ranges. 8647 return isKnownPredicateViaConstantRanges(Pred, LHS, RHS); 8648 } 8649 8650 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS, 8651 ICmpInst::Predicate Pred, 8652 bool &Increasing) { 8653 bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing); 8654 8655 #ifndef NDEBUG 8656 // Verify an invariant: inverting the predicate should turn a monotonically 8657 // increasing change to a monotonically decreasing one, and vice versa. 8658 bool IncreasingSwapped; 8659 bool ResultSwapped = isMonotonicPredicateImpl( 8660 LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped); 8661 8662 assert(Result == ResultSwapped && "should be able to analyze both!"); 8663 if (ResultSwapped) 8664 assert(Increasing == !IncreasingSwapped && 8665 "monotonicity should flip as we flip the predicate"); 8666 #endif 8667 8668 return Result; 8669 } 8670 8671 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS, 8672 ICmpInst::Predicate Pred, 8673 bool &Increasing) { 8674 8675 // A zero step value for LHS means the induction variable is essentially a 8676 // loop invariant value. We don't really depend on the predicate actually 8677 // flipping from false to true (for increasing predicates, and the other way 8678 // around for decreasing predicates), all we care about is that *if* the 8679 // predicate changes then it only changes from false to true. 8680 // 8681 // A zero step value in itself is not very useful, but there may be places 8682 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be 8683 // as general as possible. 8684 8685 switch (Pred) { 8686 default: 8687 return false; // Conservative answer 8688 8689 case ICmpInst::ICMP_UGT: 8690 case ICmpInst::ICMP_UGE: 8691 case ICmpInst::ICMP_ULT: 8692 case ICmpInst::ICMP_ULE: 8693 if (!LHS->hasNoUnsignedWrap()) 8694 return false; 8695 8696 Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE; 8697 return true; 8698 8699 case ICmpInst::ICMP_SGT: 8700 case ICmpInst::ICMP_SGE: 8701 case ICmpInst::ICMP_SLT: 8702 case ICmpInst::ICMP_SLE: { 8703 if (!LHS->hasNoSignedWrap()) 8704 return false; 8705 8706 const SCEV *Step = LHS->getStepRecurrence(*this); 8707 8708 if (isKnownNonNegative(Step)) { 8709 Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE; 8710 return true; 8711 } 8712 8713 if (isKnownNonPositive(Step)) { 8714 Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE; 8715 return true; 8716 } 8717 8718 return false; 8719 } 8720 8721 } 8722 8723 llvm_unreachable("switch has default clause!"); 8724 } 8725 8726 bool ScalarEvolution::isLoopInvariantPredicate( 8727 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L, 8728 ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS, 8729 const SCEV *&InvariantRHS) { 8730 8731 // If there is a loop-invariant, force it into the RHS, otherwise bail out. 8732 if (!isLoopInvariant(RHS, L)) { 8733 if (!isLoopInvariant(LHS, L)) 8734 return false; 8735 8736 std::swap(LHS, RHS); 8737 Pred = ICmpInst::getSwappedPredicate(Pred); 8738 } 8739 8740 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS); 8741 if (!ArLHS || ArLHS->getLoop() != L) 8742 return false; 8743 8744 bool Increasing; 8745 if (!isMonotonicPredicate(ArLHS, Pred, Increasing)) 8746 return false; 8747 8748 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to 8749 // true as the loop iterates, and the backedge is control dependent on 8750 // "ArLHS `Pred` RHS" == true then we can reason as follows: 8751 // 8752 // * if the predicate was false in the first iteration then the predicate 8753 // is never evaluated again, since the loop exits without taking the 8754 // backedge. 8755 // * if the predicate was true in the first iteration then it will 8756 // continue to be true for all future iterations since it is 8757 // monotonically increasing. 8758 // 8759 // For both the above possibilities, we can replace the loop varying 8760 // predicate with its value on the first iteration of the loop (which is 8761 // loop invariant). 8762 // 8763 // A similar reasoning applies for a monotonically decreasing predicate, by 8764 // replacing true with false and false with true in the above two bullets. 8765 8766 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred); 8767 8768 if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS)) 8769 return false; 8770 8771 InvariantPred = Pred; 8772 InvariantLHS = ArLHS->getStart(); 8773 InvariantRHS = RHS; 8774 return true; 8775 } 8776 8777 bool ScalarEvolution::isKnownPredicateViaConstantRanges( 8778 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) { 8779 if (HasSameValue(LHS, RHS)) 8780 return ICmpInst::isTrueWhenEqual(Pred); 8781 8782 // This code is split out from isKnownPredicate because it is called from 8783 // within isLoopEntryGuardedByCond. 8784 8785 auto CheckRanges = 8786 [&](const ConstantRange &RangeLHS, const ConstantRange &RangeRHS) { 8787 return ConstantRange::makeSatisfyingICmpRegion(Pred, RangeRHS) 8788 .contains(RangeLHS); 8789 }; 8790 8791 // The check at the top of the function catches the case where the values are 8792 // known to be equal. 8793 if (Pred == CmpInst::ICMP_EQ) 8794 return false; 8795 8796 if (Pred == CmpInst::ICMP_NE) 8797 return CheckRanges(getSignedRange(LHS), getSignedRange(RHS)) || 8798 CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS)) || 8799 isKnownNonZero(getMinusSCEV(LHS, RHS)); 8800 8801 if (CmpInst::isSigned(Pred)) 8802 return CheckRanges(getSignedRange(LHS), getSignedRange(RHS)); 8803 8804 return CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS)); 8805 } 8806 8807 bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred, 8808 const SCEV *LHS, 8809 const SCEV *RHS) { 8810 // Match Result to (X + Y)<ExpectedFlags> where Y is a constant integer. 8811 // Return Y via OutY. 8812 auto MatchBinaryAddToConst = 8813 [this](const SCEV *Result, const SCEV *X, APInt &OutY, 8814 SCEV::NoWrapFlags ExpectedFlags) { 8815 const SCEV *NonConstOp, *ConstOp; 8816 SCEV::NoWrapFlags FlagsPresent; 8817 8818 if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) || 8819 !isa<SCEVConstant>(ConstOp) || NonConstOp != X) 8820 return false; 8821 8822 OutY = cast<SCEVConstant>(ConstOp)->getAPInt(); 8823 return (FlagsPresent & ExpectedFlags) == ExpectedFlags; 8824 }; 8825 8826 APInt C; 8827 8828 switch (Pred) { 8829 default: 8830 break; 8831 8832 case ICmpInst::ICMP_SGE: 8833 std::swap(LHS, RHS); 8834 LLVM_FALLTHROUGH; 8835 case ICmpInst::ICMP_SLE: 8836 // X s<= (X + C)<nsw> if C >= 0 8837 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative()) 8838 return true; 8839 8840 // (X + C)<nsw> s<= X if C <= 0 8841 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && 8842 !C.isStrictlyPositive()) 8843 return true; 8844 break; 8845 8846 case ICmpInst::ICMP_SGT: 8847 std::swap(LHS, RHS); 8848 LLVM_FALLTHROUGH; 8849 case ICmpInst::ICMP_SLT: 8850 // X s< (X + C)<nsw> if C > 0 8851 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && 8852 C.isStrictlyPositive()) 8853 return true; 8854 8855 // (X + C)<nsw> s< X if C < 0 8856 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative()) 8857 return true; 8858 break; 8859 } 8860 8861 return false; 8862 } 8863 8864 bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred, 8865 const SCEV *LHS, 8866 const SCEV *RHS) { 8867 if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate) 8868 return false; 8869 8870 // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on 8871 // the stack can result in exponential time complexity. 8872 SaveAndRestore<bool> Restore(ProvingSplitPredicate, true); 8873 8874 // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L 8875 // 8876 // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use 8877 // isKnownPredicate. isKnownPredicate is more powerful, but also more 8878 // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the 8879 // interesting cases seen in practice. We can consider "upgrading" L >= 0 to 8880 // use isKnownPredicate later if needed. 8881 return isKnownNonNegative(RHS) && 8882 isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) && 8883 isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS); 8884 } 8885 8886 bool ScalarEvolution::isImpliedViaGuard(BasicBlock *BB, 8887 ICmpInst::Predicate Pred, 8888 const SCEV *LHS, const SCEV *RHS) { 8889 // No need to even try if we know the module has no guards. 8890 if (!HasGuards) 8891 return false; 8892 8893 return any_of(*BB, [&](Instruction &I) { 8894 using namespace llvm::PatternMatch; 8895 8896 Value *Condition; 8897 return match(&I, m_Intrinsic<Intrinsic::experimental_guard>( 8898 m_Value(Condition))) && 8899 isImpliedCond(Pred, LHS, RHS, Condition, false); 8900 }); 8901 } 8902 8903 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 8904 /// protected by a conditional between LHS and RHS. This is used to 8905 /// to eliminate casts. 8906 bool 8907 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 8908 ICmpInst::Predicate Pred, 8909 const SCEV *LHS, const SCEV *RHS) { 8910 // Interpret a null as meaning no loop, where there is obviously no guard 8911 // (interprocedural conditions notwithstanding). 8912 if (!L) return true; 8913 8914 if (isKnownPredicateViaConstantRanges(Pred, LHS, RHS)) 8915 return true; 8916 8917 BasicBlock *Latch = L->getLoopLatch(); 8918 if (!Latch) 8919 return false; 8920 8921 BranchInst *LoopContinuePredicate = 8922 dyn_cast<BranchInst>(Latch->getTerminator()); 8923 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() && 8924 isImpliedCond(Pred, LHS, RHS, 8925 LoopContinuePredicate->getCondition(), 8926 LoopContinuePredicate->getSuccessor(0) != L->getHeader())) 8927 return true; 8928 8929 // We don't want more than one activation of the following loops on the stack 8930 // -- that can lead to O(n!) time complexity. 8931 if (WalkingBEDominatingConds) 8932 return false; 8933 8934 SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true); 8935 8936 // See if we can exploit a trip count to prove the predicate. 8937 const auto &BETakenInfo = getBackedgeTakenInfo(L); 8938 const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this); 8939 if (LatchBECount != getCouldNotCompute()) { 8940 // We know that Latch branches back to the loop header exactly 8941 // LatchBECount times. This means the backdege condition at Latch is 8942 // equivalent to "{0,+,1} u< LatchBECount". 8943 Type *Ty = LatchBECount->getType(); 8944 auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW); 8945 const SCEV *LoopCounter = 8946 getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags); 8947 if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter, 8948 LatchBECount)) 8949 return true; 8950 } 8951 8952 // Check conditions due to any @llvm.assume intrinsics. 8953 for (auto &AssumeVH : AC.assumptions()) { 8954 if (!AssumeVH) 8955 continue; 8956 auto *CI = cast<CallInst>(AssumeVH); 8957 if (!DT.dominates(CI, Latch->getTerminator())) 8958 continue; 8959 8960 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false)) 8961 return true; 8962 } 8963 8964 // If the loop is not reachable from the entry block, we risk running into an 8965 // infinite loop as we walk up into the dom tree. These loops do not matter 8966 // anyway, so we just return a conservative answer when we see them. 8967 if (!DT.isReachableFromEntry(L->getHeader())) 8968 return false; 8969 8970 if (isImpliedViaGuard(Latch, Pred, LHS, RHS)) 8971 return true; 8972 8973 for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()]; 8974 DTN != HeaderDTN; DTN = DTN->getIDom()) { 8975 assert(DTN && "should reach the loop header before reaching the root!"); 8976 8977 BasicBlock *BB = DTN->getBlock(); 8978 if (isImpliedViaGuard(BB, Pred, LHS, RHS)) 8979 return true; 8980 8981 BasicBlock *PBB = BB->getSinglePredecessor(); 8982 if (!PBB) 8983 continue; 8984 8985 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator()); 8986 if (!ContinuePredicate || !ContinuePredicate->isConditional()) 8987 continue; 8988 8989 Value *Condition = ContinuePredicate->getCondition(); 8990 8991 // If we have an edge `E` within the loop body that dominates the only 8992 // latch, the condition guarding `E` also guards the backedge. This 8993 // reasoning works only for loops with a single latch. 8994 8995 BasicBlockEdge DominatingEdge(PBB, BB); 8996 if (DominatingEdge.isSingleEdge()) { 8997 // We're constructively (and conservatively) enumerating edges within the 8998 // loop body that dominate the latch. The dominator tree better agree 8999 // with us on this: 9000 assert(DT.dominates(DominatingEdge, Latch) && "should be!"); 9001 9002 if (isImpliedCond(Pred, LHS, RHS, Condition, 9003 BB != ContinuePredicate->getSuccessor(0))) 9004 return true; 9005 } 9006 } 9007 9008 return false; 9009 } 9010 9011 bool 9012 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 9013 ICmpInst::Predicate Pred, 9014 const SCEV *LHS, const SCEV *RHS) { 9015 // Interpret a null as meaning no loop, where there is obviously no guard 9016 // (interprocedural conditions notwithstanding). 9017 if (!L) return false; 9018 9019 if (isKnownPredicateViaConstantRanges(Pred, LHS, RHS)) 9020 return true; 9021 9022 // Starting at the loop predecessor, climb up the predecessor chain, as long 9023 // as there are predecessors that can be found that have unique successors 9024 // leading to the original header. 9025 for (std::pair<BasicBlock *, BasicBlock *> 9026 Pair(L->getLoopPredecessor(), L->getHeader()); 9027 Pair.first; 9028 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 9029 9030 if (isImpliedViaGuard(Pair.first, Pred, LHS, RHS)) 9031 return true; 9032 9033 BranchInst *LoopEntryPredicate = 9034 dyn_cast<BranchInst>(Pair.first->getTerminator()); 9035 if (!LoopEntryPredicate || 9036 LoopEntryPredicate->isUnconditional()) 9037 continue; 9038 9039 if (isImpliedCond(Pred, LHS, RHS, 9040 LoopEntryPredicate->getCondition(), 9041 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 9042 return true; 9043 } 9044 9045 // Check conditions due to any @llvm.assume intrinsics. 9046 for (auto &AssumeVH : AC.assumptions()) { 9047 if (!AssumeVH) 9048 continue; 9049 auto *CI = cast<CallInst>(AssumeVH); 9050 if (!DT.dominates(CI, L->getHeader())) 9051 continue; 9052 9053 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false)) 9054 return true; 9055 } 9056 9057 return false; 9058 } 9059 9060 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, 9061 const SCEV *LHS, const SCEV *RHS, 9062 Value *FoundCondValue, 9063 bool Inverse) { 9064 if (!PendingLoopPredicates.insert(FoundCondValue).second) 9065 return false; 9066 9067 auto ClearOnExit = 9068 make_scope_exit([&]() { PendingLoopPredicates.erase(FoundCondValue); }); 9069 9070 // Recursively handle And and Or conditions. 9071 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) { 9072 if (BO->getOpcode() == Instruction::And) { 9073 if (!Inverse) 9074 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 9075 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 9076 } else if (BO->getOpcode() == Instruction::Or) { 9077 if (Inverse) 9078 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 9079 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 9080 } 9081 } 9082 9083 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue); 9084 if (!ICI) return false; 9085 9086 // Now that we found a conditional branch that dominates the loop or controls 9087 // the loop latch. Check to see if it is the comparison we are looking for. 9088 ICmpInst::Predicate FoundPred; 9089 if (Inverse) 9090 FoundPred = ICI->getInversePredicate(); 9091 else 9092 FoundPred = ICI->getPredicate(); 9093 9094 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 9095 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 9096 9097 return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS); 9098 } 9099 9100 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS, 9101 const SCEV *RHS, 9102 ICmpInst::Predicate FoundPred, 9103 const SCEV *FoundLHS, 9104 const SCEV *FoundRHS) { 9105 // Balance the types. 9106 if (getTypeSizeInBits(LHS->getType()) < 9107 getTypeSizeInBits(FoundLHS->getType())) { 9108 if (CmpInst::isSigned(Pred)) { 9109 LHS = getSignExtendExpr(LHS, FoundLHS->getType()); 9110 RHS = getSignExtendExpr(RHS, FoundLHS->getType()); 9111 } else { 9112 LHS = getZeroExtendExpr(LHS, FoundLHS->getType()); 9113 RHS = getZeroExtendExpr(RHS, FoundLHS->getType()); 9114 } 9115 } else if (getTypeSizeInBits(LHS->getType()) > 9116 getTypeSizeInBits(FoundLHS->getType())) { 9117 if (CmpInst::isSigned(FoundPred)) { 9118 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 9119 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 9120 } else { 9121 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 9122 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 9123 } 9124 } 9125 9126 // Canonicalize the query to match the way instcombine will have 9127 // canonicalized the comparison. 9128 if (SimplifyICmpOperands(Pred, LHS, RHS)) 9129 if (LHS == RHS) 9130 return CmpInst::isTrueWhenEqual(Pred); 9131 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 9132 if (FoundLHS == FoundRHS) 9133 return CmpInst::isFalseWhenEqual(FoundPred); 9134 9135 // Check to see if we can make the LHS or RHS match. 9136 if (LHS == FoundRHS || RHS == FoundLHS) { 9137 if (isa<SCEVConstant>(RHS)) { 9138 std::swap(FoundLHS, FoundRHS); 9139 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 9140 } else { 9141 std::swap(LHS, RHS); 9142 Pred = ICmpInst::getSwappedPredicate(Pred); 9143 } 9144 } 9145 9146 // Check whether the found predicate is the same as the desired predicate. 9147 if (FoundPred == Pred) 9148 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 9149 9150 // Check whether swapping the found predicate makes it the same as the 9151 // desired predicate. 9152 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 9153 if (isa<SCEVConstant>(RHS)) 9154 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 9155 else 9156 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 9157 RHS, LHS, FoundLHS, FoundRHS); 9158 } 9159 9160 // Unsigned comparison is the same as signed comparison when both the operands 9161 // are non-negative. 9162 if (CmpInst::isUnsigned(FoundPred) && 9163 CmpInst::getSignedPredicate(FoundPred) == Pred && 9164 isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS)) 9165 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 9166 9167 // Check if we can make progress by sharpening ranges. 9168 if (FoundPred == ICmpInst::ICMP_NE && 9169 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) { 9170 9171 const SCEVConstant *C = nullptr; 9172 const SCEV *V = nullptr; 9173 9174 if (isa<SCEVConstant>(FoundLHS)) { 9175 C = cast<SCEVConstant>(FoundLHS); 9176 V = FoundRHS; 9177 } else { 9178 C = cast<SCEVConstant>(FoundRHS); 9179 V = FoundLHS; 9180 } 9181 9182 // The guarding predicate tells us that C != V. If the known range 9183 // of V is [C, t), we can sharpen the range to [C + 1, t). The 9184 // range we consider has to correspond to same signedness as the 9185 // predicate we're interested in folding. 9186 9187 APInt Min = ICmpInst::isSigned(Pred) ? 9188 getSignedRangeMin(V) : getUnsignedRangeMin(V); 9189 9190 if (Min == C->getAPInt()) { 9191 // Given (V >= Min && V != Min) we conclude V >= (Min + 1). 9192 // This is true even if (Min + 1) wraps around -- in case of 9193 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)). 9194 9195 APInt SharperMin = Min + 1; 9196 9197 switch (Pred) { 9198 case ICmpInst::ICMP_SGE: 9199 case ICmpInst::ICMP_UGE: 9200 // We know V `Pred` SharperMin. If this implies LHS `Pred` 9201 // RHS, we're done. 9202 if (isImpliedCondOperands(Pred, LHS, RHS, V, 9203 getConstant(SharperMin))) 9204 return true; 9205 LLVM_FALLTHROUGH; 9206 9207 case ICmpInst::ICMP_SGT: 9208 case ICmpInst::ICMP_UGT: 9209 // We know from the range information that (V `Pred` Min || 9210 // V == Min). We know from the guarding condition that !(V 9211 // == Min). This gives us 9212 // 9213 // V `Pred` Min || V == Min && !(V == Min) 9214 // => V `Pred` Min 9215 // 9216 // If V `Pred` Min implies LHS `Pred` RHS, we're done. 9217 9218 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min))) 9219 return true; 9220 LLVM_FALLTHROUGH; 9221 9222 default: 9223 // No change 9224 break; 9225 } 9226 } 9227 } 9228 9229 // Check whether the actual condition is beyond sufficient. 9230 if (FoundPred == ICmpInst::ICMP_EQ) 9231 if (ICmpInst::isTrueWhenEqual(Pred)) 9232 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 9233 return true; 9234 if (Pred == ICmpInst::ICMP_NE) 9235 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 9236 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 9237 return true; 9238 9239 // Otherwise assume the worst. 9240 return false; 9241 } 9242 9243 bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr, 9244 const SCEV *&L, const SCEV *&R, 9245 SCEV::NoWrapFlags &Flags) { 9246 const auto *AE = dyn_cast<SCEVAddExpr>(Expr); 9247 if (!AE || AE->getNumOperands() != 2) 9248 return false; 9249 9250 L = AE->getOperand(0); 9251 R = AE->getOperand(1); 9252 Flags = AE->getNoWrapFlags(); 9253 return true; 9254 } 9255 9256 Optional<APInt> ScalarEvolution::computeConstantDifference(const SCEV *More, 9257 const SCEV *Less) { 9258 // We avoid subtracting expressions here because this function is usually 9259 // fairly deep in the call stack (i.e. is called many times). 9260 9261 if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) { 9262 const auto *LAR = cast<SCEVAddRecExpr>(Less); 9263 const auto *MAR = cast<SCEVAddRecExpr>(More); 9264 9265 if (LAR->getLoop() != MAR->getLoop()) 9266 return None; 9267 9268 // We look at affine expressions only; not for correctness but to keep 9269 // getStepRecurrence cheap. 9270 if (!LAR->isAffine() || !MAR->isAffine()) 9271 return None; 9272 9273 if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this)) 9274 return None; 9275 9276 Less = LAR->getStart(); 9277 More = MAR->getStart(); 9278 9279 // fall through 9280 } 9281 9282 if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) { 9283 const auto &M = cast<SCEVConstant>(More)->getAPInt(); 9284 const auto &L = cast<SCEVConstant>(Less)->getAPInt(); 9285 return M - L; 9286 } 9287 9288 const SCEV *L, *R; 9289 SCEV::NoWrapFlags Flags; 9290 if (splitBinaryAdd(Less, L, R, Flags)) 9291 if (const auto *LC = dyn_cast<SCEVConstant>(L)) 9292 if (R == More) 9293 return -(LC->getAPInt()); 9294 9295 if (splitBinaryAdd(More, L, R, Flags)) 9296 if (const auto *LC = dyn_cast<SCEVConstant>(L)) 9297 if (R == Less) 9298 return LC->getAPInt(); 9299 9300 return None; 9301 } 9302 9303 bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow( 9304 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, 9305 const SCEV *FoundLHS, const SCEV *FoundRHS) { 9306 if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT) 9307 return false; 9308 9309 const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS); 9310 if (!AddRecLHS) 9311 return false; 9312 9313 const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS); 9314 if (!AddRecFoundLHS) 9315 return false; 9316 9317 // We'd like to let SCEV reason about control dependencies, so we constrain 9318 // both the inequalities to be about add recurrences on the same loop. This 9319 // way we can use isLoopEntryGuardedByCond later. 9320 9321 const Loop *L = AddRecFoundLHS->getLoop(); 9322 if (L != AddRecLHS->getLoop()) 9323 return false; 9324 9325 // FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1) 9326 // 9327 // FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C) 9328 // ... (2) 9329 // 9330 // Informal proof for (2), assuming (1) [*]: 9331 // 9332 // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**] 9333 // 9334 // Then 9335 // 9336 // FoundLHS s< FoundRHS s< INT_MIN - C 9337 // <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ] 9338 // <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ] 9339 // <=> (FoundLHS + INT_MIN + C + INT_MIN) s< 9340 // (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ] 9341 // <=> FoundLHS + C s< FoundRHS + C 9342 // 9343 // [*]: (1) can be proved by ruling out overflow. 9344 // 9345 // [**]: This can be proved by analyzing all the four possibilities: 9346 // (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and 9347 // (A s>= 0, B s>= 0). 9348 // 9349 // Note: 9350 // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C" 9351 // will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS 9352 // = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS 9353 // s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is 9354 // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS + 9355 // C)". 9356 9357 Optional<APInt> LDiff = computeConstantDifference(LHS, FoundLHS); 9358 Optional<APInt> RDiff = computeConstantDifference(RHS, FoundRHS); 9359 if (!LDiff || !RDiff || *LDiff != *RDiff) 9360 return false; 9361 9362 if (LDiff->isMinValue()) 9363 return true; 9364 9365 APInt FoundRHSLimit; 9366 9367 if (Pred == CmpInst::ICMP_ULT) { 9368 FoundRHSLimit = -(*RDiff); 9369 } else { 9370 assert(Pred == CmpInst::ICMP_SLT && "Checked above!"); 9371 FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - *RDiff; 9372 } 9373 9374 // Try to prove (1) or (2), as needed. 9375 return isLoopEntryGuardedByCond(L, Pred, FoundRHS, 9376 getConstant(FoundRHSLimit)); 9377 } 9378 9379 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 9380 const SCEV *LHS, const SCEV *RHS, 9381 const SCEV *FoundLHS, 9382 const SCEV *FoundRHS) { 9383 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS)) 9384 return true; 9385 9386 if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS)) 9387 return true; 9388 9389 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 9390 FoundLHS, FoundRHS) || 9391 // ~x < ~y --> x > y 9392 isImpliedCondOperandsHelper(Pred, LHS, RHS, 9393 getNotSCEV(FoundRHS), 9394 getNotSCEV(FoundLHS)); 9395 } 9396 9397 /// If Expr computes ~A, return A else return nullptr 9398 static const SCEV *MatchNotExpr(const SCEV *Expr) { 9399 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr); 9400 if (!Add || Add->getNumOperands() != 2 || 9401 !Add->getOperand(0)->isAllOnesValue()) 9402 return nullptr; 9403 9404 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1)); 9405 if (!AddRHS || AddRHS->getNumOperands() != 2 || 9406 !AddRHS->getOperand(0)->isAllOnesValue()) 9407 return nullptr; 9408 9409 return AddRHS->getOperand(1); 9410 } 9411 9412 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values? 9413 template<typename MaxExprType> 9414 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr, 9415 const SCEV *Candidate) { 9416 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr); 9417 if (!MaxExpr) return false; 9418 9419 return find(MaxExpr->operands(), Candidate) != MaxExpr->op_end(); 9420 } 9421 9422 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values? 9423 template<typename MaxExprType> 9424 static bool IsMinConsistingOf(ScalarEvolution &SE, 9425 const SCEV *MaybeMinExpr, 9426 const SCEV *Candidate) { 9427 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr); 9428 if (!MaybeMaxExpr) 9429 return false; 9430 9431 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate)); 9432 } 9433 9434 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE, 9435 ICmpInst::Predicate Pred, 9436 const SCEV *LHS, const SCEV *RHS) { 9437 // If both sides are affine addrecs for the same loop, with equal 9438 // steps, and we know the recurrences don't wrap, then we only 9439 // need to check the predicate on the starting values. 9440 9441 if (!ICmpInst::isRelational(Pred)) 9442 return false; 9443 9444 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS); 9445 if (!LAR) 9446 return false; 9447 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS); 9448 if (!RAR) 9449 return false; 9450 if (LAR->getLoop() != RAR->getLoop()) 9451 return false; 9452 if (!LAR->isAffine() || !RAR->isAffine()) 9453 return false; 9454 9455 if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE)) 9456 return false; 9457 9458 SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ? 9459 SCEV::FlagNSW : SCEV::FlagNUW; 9460 if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW)) 9461 return false; 9462 9463 return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart()); 9464 } 9465 9466 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max 9467 /// expression? 9468 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE, 9469 ICmpInst::Predicate Pred, 9470 const SCEV *LHS, const SCEV *RHS) { 9471 switch (Pred) { 9472 default: 9473 return false; 9474 9475 case ICmpInst::ICMP_SGE: 9476 std::swap(LHS, RHS); 9477 LLVM_FALLTHROUGH; 9478 case ICmpInst::ICMP_SLE: 9479 return 9480 // min(A, ...) <= A 9481 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) || 9482 // A <= max(A, ...) 9483 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS); 9484 9485 case ICmpInst::ICMP_UGE: 9486 std::swap(LHS, RHS); 9487 LLVM_FALLTHROUGH; 9488 case ICmpInst::ICMP_ULE: 9489 return 9490 // min(A, ...) <= A 9491 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) || 9492 // A <= max(A, ...) 9493 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS); 9494 } 9495 9496 llvm_unreachable("covered switch fell through?!"); 9497 } 9498 9499 bool ScalarEvolution::isImpliedViaOperations(ICmpInst::Predicate Pred, 9500 const SCEV *LHS, const SCEV *RHS, 9501 const SCEV *FoundLHS, 9502 const SCEV *FoundRHS, 9503 unsigned Depth) { 9504 assert(getTypeSizeInBits(LHS->getType()) == 9505 getTypeSizeInBits(RHS->getType()) && 9506 "LHS and RHS have different sizes?"); 9507 assert(getTypeSizeInBits(FoundLHS->getType()) == 9508 getTypeSizeInBits(FoundRHS->getType()) && 9509 "FoundLHS and FoundRHS have different sizes?"); 9510 // We want to avoid hurting the compile time with analysis of too big trees. 9511 if (Depth > MaxSCEVOperationsImplicationDepth) 9512 return false; 9513 // We only want to work with ICMP_SGT comparison so far. 9514 // TODO: Extend to ICMP_UGT? 9515 if (Pred == ICmpInst::ICMP_SLT) { 9516 Pred = ICmpInst::ICMP_SGT; 9517 std::swap(LHS, RHS); 9518 std::swap(FoundLHS, FoundRHS); 9519 } 9520 if (Pred != ICmpInst::ICMP_SGT) 9521 return false; 9522 9523 auto GetOpFromSExt = [&](const SCEV *S) { 9524 if (auto *Ext = dyn_cast<SCEVSignExtendExpr>(S)) 9525 return Ext->getOperand(); 9526 // TODO: If S is a SCEVConstant then you can cheaply "strip" the sext off 9527 // the constant in some cases. 9528 return S; 9529 }; 9530 9531 // Acquire values from extensions. 9532 auto *OrigFoundLHS = FoundLHS; 9533 LHS = GetOpFromSExt(LHS); 9534 FoundLHS = GetOpFromSExt(FoundLHS); 9535 9536 // Is the SGT predicate can be proved trivially or using the found context. 9537 auto IsSGTViaContext = [&](const SCEV *S1, const SCEV *S2) { 9538 return isKnownViaSimpleReasoning(ICmpInst::ICMP_SGT, S1, S2) || 9539 isImpliedViaOperations(ICmpInst::ICMP_SGT, S1, S2, OrigFoundLHS, 9540 FoundRHS, Depth + 1); 9541 }; 9542 9543 if (auto *LHSAddExpr = dyn_cast<SCEVAddExpr>(LHS)) { 9544 // We want to avoid creation of any new non-constant SCEV. Since we are 9545 // going to compare the operands to RHS, we should be certain that we don't 9546 // need any size extensions for this. So let's decline all cases when the 9547 // sizes of types of LHS and RHS do not match. 9548 // TODO: Maybe try to get RHS from sext to catch more cases? 9549 if (getTypeSizeInBits(LHS->getType()) != getTypeSizeInBits(RHS->getType())) 9550 return false; 9551 9552 // Should not overflow. 9553 if (!LHSAddExpr->hasNoSignedWrap()) 9554 return false; 9555 9556 auto *LL = LHSAddExpr->getOperand(0); 9557 auto *LR = LHSAddExpr->getOperand(1); 9558 auto *MinusOne = getNegativeSCEV(getOne(RHS->getType())); 9559 9560 // Checks that S1 >= 0 && S2 > RHS, trivially or using the found context. 9561 auto IsSumGreaterThanRHS = [&](const SCEV *S1, const SCEV *S2) { 9562 return IsSGTViaContext(S1, MinusOne) && IsSGTViaContext(S2, RHS); 9563 }; 9564 // Try to prove the following rule: 9565 // (LHS = LL + LR) && (LL >= 0) && (LR > RHS) => (LHS > RHS). 9566 // (LHS = LL + LR) && (LR >= 0) && (LL > RHS) => (LHS > RHS). 9567 if (IsSumGreaterThanRHS(LL, LR) || IsSumGreaterThanRHS(LR, LL)) 9568 return true; 9569 } else if (auto *LHSUnknownExpr = dyn_cast<SCEVUnknown>(LHS)) { 9570 Value *LL, *LR; 9571 // FIXME: Once we have SDiv implemented, we can get rid of this matching. 9572 9573 using namespace llvm::PatternMatch; 9574 9575 if (match(LHSUnknownExpr->getValue(), m_SDiv(m_Value(LL), m_Value(LR)))) { 9576 // Rules for division. 9577 // We are going to perform some comparisons with Denominator and its 9578 // derivative expressions. In general case, creating a SCEV for it may 9579 // lead to a complex analysis of the entire graph, and in particular it 9580 // can request trip count recalculation for the same loop. This would 9581 // cache as SCEVCouldNotCompute to avoid the infinite recursion. To avoid 9582 // this, we only want to create SCEVs that are constants in this section. 9583 // So we bail if Denominator is not a constant. 9584 if (!isa<ConstantInt>(LR)) 9585 return false; 9586 9587 auto *Denominator = cast<SCEVConstant>(getSCEV(LR)); 9588 9589 // We want to make sure that LHS = FoundLHS / Denominator. If it is so, 9590 // then a SCEV for the numerator already exists and matches with FoundLHS. 9591 auto *Numerator = getExistingSCEV(LL); 9592 if (!Numerator || Numerator->getType() != FoundLHS->getType()) 9593 return false; 9594 9595 // Make sure that the numerator matches with FoundLHS and the denominator 9596 // is positive. 9597 if (!HasSameValue(Numerator, FoundLHS) || !isKnownPositive(Denominator)) 9598 return false; 9599 9600 auto *DTy = Denominator->getType(); 9601 auto *FRHSTy = FoundRHS->getType(); 9602 if (DTy->isPointerTy() != FRHSTy->isPointerTy()) 9603 // One of types is a pointer and another one is not. We cannot extend 9604 // them properly to a wider type, so let us just reject this case. 9605 // TODO: Usage of getEffectiveSCEVType for DTy, FRHSTy etc should help 9606 // to avoid this check. 9607 return false; 9608 9609 // Given that: 9610 // FoundLHS > FoundRHS, LHS = FoundLHS / Denominator, Denominator > 0. 9611 auto *WTy = getWiderType(DTy, FRHSTy); 9612 auto *DenominatorExt = getNoopOrSignExtend(Denominator, WTy); 9613 auto *FoundRHSExt = getNoopOrSignExtend(FoundRHS, WTy); 9614 9615 // Try to prove the following rule: 9616 // (FoundRHS > Denominator - 2) && (RHS <= 0) => (LHS > RHS). 9617 // For example, given that FoundLHS > 2. It means that FoundLHS is at 9618 // least 3. If we divide it by Denominator < 4, we will have at least 1. 9619 auto *DenomMinusTwo = getMinusSCEV(DenominatorExt, getConstant(WTy, 2)); 9620 if (isKnownNonPositive(RHS) && 9621 IsSGTViaContext(FoundRHSExt, DenomMinusTwo)) 9622 return true; 9623 9624 // Try to prove the following rule: 9625 // (FoundRHS > -1 - Denominator) && (RHS < 0) => (LHS > RHS). 9626 // For example, given that FoundLHS > -3. Then FoundLHS is at least -2. 9627 // If we divide it by Denominator > 2, then: 9628 // 1. If FoundLHS is negative, then the result is 0. 9629 // 2. If FoundLHS is non-negative, then the result is non-negative. 9630 // Anyways, the result is non-negative. 9631 auto *MinusOne = getNegativeSCEV(getOne(WTy)); 9632 auto *NegDenomMinusOne = getMinusSCEV(MinusOne, DenominatorExt); 9633 if (isKnownNegative(RHS) && 9634 IsSGTViaContext(FoundRHSExt, NegDenomMinusOne)) 9635 return true; 9636 } 9637 } 9638 9639 return false; 9640 } 9641 9642 bool 9643 ScalarEvolution::isKnownViaSimpleReasoning(ICmpInst::Predicate Pred, 9644 const SCEV *LHS, const SCEV *RHS) { 9645 return isKnownPredicateViaConstantRanges(Pred, LHS, RHS) || 9646 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) || 9647 IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) || 9648 isKnownPredicateViaNoOverflow(Pred, LHS, RHS); 9649 } 9650 9651 bool 9652 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 9653 const SCEV *LHS, const SCEV *RHS, 9654 const SCEV *FoundLHS, 9655 const SCEV *FoundRHS) { 9656 switch (Pred) { 9657 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 9658 case ICmpInst::ICMP_EQ: 9659 case ICmpInst::ICMP_NE: 9660 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 9661 return true; 9662 break; 9663 case ICmpInst::ICMP_SLT: 9664 case ICmpInst::ICMP_SLE: 9665 if (isKnownViaSimpleReasoning(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 9666 isKnownViaSimpleReasoning(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 9667 return true; 9668 break; 9669 case ICmpInst::ICMP_SGT: 9670 case ICmpInst::ICMP_SGE: 9671 if (isKnownViaSimpleReasoning(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 9672 isKnownViaSimpleReasoning(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 9673 return true; 9674 break; 9675 case ICmpInst::ICMP_ULT: 9676 case ICmpInst::ICMP_ULE: 9677 if (isKnownViaSimpleReasoning(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 9678 isKnownViaSimpleReasoning(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 9679 return true; 9680 break; 9681 case ICmpInst::ICMP_UGT: 9682 case ICmpInst::ICMP_UGE: 9683 if (isKnownViaSimpleReasoning(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 9684 isKnownViaSimpleReasoning(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 9685 return true; 9686 break; 9687 } 9688 9689 // Maybe it can be proved via operations? 9690 if (isImpliedViaOperations(Pred, LHS, RHS, FoundLHS, FoundRHS)) 9691 return true; 9692 9693 return false; 9694 } 9695 9696 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred, 9697 const SCEV *LHS, 9698 const SCEV *RHS, 9699 const SCEV *FoundLHS, 9700 const SCEV *FoundRHS) { 9701 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS)) 9702 // The restriction on `FoundRHS` be lifted easily -- it exists only to 9703 // reduce the compile time impact of this optimization. 9704 return false; 9705 9706 Optional<APInt> Addend = computeConstantDifference(LHS, FoundLHS); 9707 if (!Addend) 9708 return false; 9709 9710 const APInt &ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getAPInt(); 9711 9712 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the 9713 // antecedent "`FoundLHS` `Pred` `FoundRHS`". 9714 ConstantRange FoundLHSRange = 9715 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS); 9716 9717 // Since `LHS` is `FoundLHS` + `Addend`, we can compute a range for `LHS`: 9718 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(*Addend)); 9719 9720 // We can also compute the range of values for `LHS` that satisfy the 9721 // consequent, "`LHS` `Pred` `RHS`": 9722 const APInt &ConstRHS = cast<SCEVConstant>(RHS)->getAPInt(); 9723 ConstantRange SatisfyingLHSRange = 9724 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS); 9725 9726 // The antecedent implies the consequent if every value of `LHS` that 9727 // satisfies the antecedent also satisfies the consequent. 9728 return SatisfyingLHSRange.contains(LHSRange); 9729 } 9730 9731 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride, 9732 bool IsSigned, bool NoWrap) { 9733 assert(isKnownPositive(Stride) && "Positive stride expected!"); 9734 9735 if (NoWrap) return false; 9736 9737 unsigned BitWidth = getTypeSizeInBits(RHS->getType()); 9738 const SCEV *One = getOne(Stride->getType()); 9739 9740 if (IsSigned) { 9741 APInt MaxRHS = getSignedRangeMax(RHS); 9742 APInt MaxValue = APInt::getSignedMaxValue(BitWidth); 9743 APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One)); 9744 9745 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow! 9746 return (std::move(MaxValue) - MaxStrideMinusOne).slt(MaxRHS); 9747 } 9748 9749 APInt MaxRHS = getUnsignedRangeMax(RHS); 9750 APInt MaxValue = APInt::getMaxValue(BitWidth); 9751 APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One)); 9752 9753 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow! 9754 return (std::move(MaxValue) - MaxStrideMinusOne).ult(MaxRHS); 9755 } 9756 9757 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride, 9758 bool IsSigned, bool NoWrap) { 9759 if (NoWrap) return false; 9760 9761 unsigned BitWidth = getTypeSizeInBits(RHS->getType()); 9762 const SCEV *One = getOne(Stride->getType()); 9763 9764 if (IsSigned) { 9765 APInt MinRHS = getSignedRangeMin(RHS); 9766 APInt MinValue = APInt::getSignedMinValue(BitWidth); 9767 APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One)); 9768 9769 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow! 9770 return (std::move(MinValue) + MaxStrideMinusOne).sgt(MinRHS); 9771 } 9772 9773 APInt MinRHS = getUnsignedRangeMin(RHS); 9774 APInt MinValue = APInt::getMinValue(BitWidth); 9775 APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One)); 9776 9777 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow! 9778 return (std::move(MinValue) + MaxStrideMinusOne).ugt(MinRHS); 9779 } 9780 9781 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step, 9782 bool Equality) { 9783 const SCEV *One = getOne(Step->getType()); 9784 Delta = Equality ? getAddExpr(Delta, Step) 9785 : getAddExpr(Delta, getMinusSCEV(Step, One)); 9786 return getUDivExpr(Delta, Step); 9787 } 9788 9789 const SCEV *ScalarEvolution::computeMaxBECountForLT(const SCEV *Start, 9790 const SCEV *Stride, 9791 const SCEV *End, 9792 unsigned BitWidth, 9793 bool IsSigned) { 9794 9795 assert(!isKnownNonPositive(Stride) && 9796 "Stride is expected strictly positive!"); 9797 // Calculate the maximum backedge count based on the range of values 9798 // permitted by Start, End, and Stride. 9799 const SCEV *MaxBECount; 9800 APInt MinStart = 9801 IsSigned ? getSignedRangeMin(Start) : getUnsignedRangeMin(Start); 9802 9803 APInt StrideForMaxBECount = 9804 IsSigned ? getSignedRangeMin(Stride) : getUnsignedRangeMin(Stride); 9805 9806 // We already know that the stride is positive, so we paper over conservatism 9807 // in our range computation by forcing StrideForMaxBECount to be at least one. 9808 // In theory this is unnecessary, but we expect MaxBECount to be a 9809 // SCEVConstant, and (udiv <constant> 0) is not constant folded by SCEV (there 9810 // is nothing to constant fold it to). 9811 APInt One(BitWidth, 1, IsSigned); 9812 StrideForMaxBECount = APIntOps::smax(One, StrideForMaxBECount); 9813 9814 APInt MaxValue = IsSigned ? APInt::getSignedMaxValue(BitWidth) 9815 : APInt::getMaxValue(BitWidth); 9816 APInt Limit = MaxValue - (StrideForMaxBECount - 1); 9817 9818 // Although End can be a MAX expression we estimate MaxEnd considering only 9819 // the case End = RHS of the loop termination condition. This is safe because 9820 // in the other case (End - Start) is zero, leading to a zero maximum backedge 9821 // taken count. 9822 APInt MaxEnd = IsSigned ? APIntOps::smin(getSignedRangeMax(End), Limit) 9823 : APIntOps::umin(getUnsignedRangeMax(End), Limit); 9824 9825 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart) /* Delta */, 9826 getConstant(StrideForMaxBECount) /* Step */, 9827 false /* Equality */); 9828 9829 return MaxBECount; 9830 } 9831 9832 ScalarEvolution::ExitLimit 9833 ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS, 9834 const Loop *L, bool IsSigned, 9835 bool ControlsExit, bool AllowPredicates) { 9836 SmallPtrSet<const SCEVPredicate *, 4> Predicates; 9837 9838 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS); 9839 bool PredicatedIV = false; 9840 9841 if (!IV && AllowPredicates) { 9842 // Try to make this an AddRec using runtime tests, in the first X 9843 // iterations of this loop, where X is the SCEV expression found by the 9844 // algorithm below. 9845 IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates); 9846 PredicatedIV = true; 9847 } 9848 9849 // Avoid weird loops 9850 if (!IV || IV->getLoop() != L || !IV->isAffine()) 9851 return getCouldNotCompute(); 9852 9853 bool NoWrap = ControlsExit && 9854 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW); 9855 9856 const SCEV *Stride = IV->getStepRecurrence(*this); 9857 9858 bool PositiveStride = isKnownPositive(Stride); 9859 9860 // Avoid negative or zero stride values. 9861 if (!PositiveStride) { 9862 // We can compute the correct backedge taken count for loops with unknown 9863 // strides if we can prove that the loop is not an infinite loop with side 9864 // effects. Here's the loop structure we are trying to handle - 9865 // 9866 // i = start 9867 // do { 9868 // A[i] = i; 9869 // i += s; 9870 // } while (i < end); 9871 // 9872 // The backedge taken count for such loops is evaluated as - 9873 // (max(end, start + stride) - start - 1) /u stride 9874 // 9875 // The additional preconditions that we need to check to prove correctness 9876 // of the above formula is as follows - 9877 // 9878 // a) IV is either nuw or nsw depending upon signedness (indicated by the 9879 // NoWrap flag). 9880 // b) loop is single exit with no side effects. 9881 // 9882 // 9883 // Precondition a) implies that if the stride is negative, this is a single 9884 // trip loop. The backedge taken count formula reduces to zero in this case. 9885 // 9886 // Precondition b) implies that the unknown stride cannot be zero otherwise 9887 // we have UB. 9888 // 9889 // The positive stride case is the same as isKnownPositive(Stride) returning 9890 // true (original behavior of the function). 9891 // 9892 // We want to make sure that the stride is truly unknown as there are edge 9893 // cases where ScalarEvolution propagates no wrap flags to the 9894 // post-increment/decrement IV even though the increment/decrement operation 9895 // itself is wrapping. The computed backedge taken count may be wrong in 9896 // such cases. This is prevented by checking that the stride is not known to 9897 // be either positive or non-positive. For example, no wrap flags are 9898 // propagated to the post-increment IV of this loop with a trip count of 2 - 9899 // 9900 // unsigned char i; 9901 // for(i=127; i<128; i+=129) 9902 // A[i] = i; 9903 // 9904 if (PredicatedIV || !NoWrap || isKnownNonPositive(Stride) || 9905 !loopHasNoSideEffects(L)) 9906 return getCouldNotCompute(); 9907 } else if (!Stride->isOne() && 9908 doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap)) 9909 // Avoid proven overflow cases: this will ensure that the backedge taken 9910 // count will not generate any unsigned overflow. Relaxed no-overflow 9911 // conditions exploit NoWrapFlags, allowing to optimize in presence of 9912 // undefined behaviors like the case of C language. 9913 return getCouldNotCompute(); 9914 9915 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT 9916 : ICmpInst::ICMP_ULT; 9917 const SCEV *Start = IV->getStart(); 9918 const SCEV *End = RHS; 9919 // When the RHS is not invariant, we do not know the end bound of the loop and 9920 // cannot calculate the ExactBECount needed by ExitLimit. However, we can 9921 // calculate the MaxBECount, given the start, stride and max value for the end 9922 // bound of the loop (RHS), and the fact that IV does not overflow (which is 9923 // checked above). 9924 if (!isLoopInvariant(RHS, L)) { 9925 const SCEV *MaxBECount = computeMaxBECountForLT( 9926 Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned); 9927 return ExitLimit(getCouldNotCompute() /* ExactNotTaken */, MaxBECount, 9928 false /*MaxOrZero*/, Predicates); 9929 } 9930 // If the backedge is taken at least once, then it will be taken 9931 // (End-Start)/Stride times (rounded up to a multiple of Stride), where Start 9932 // is the LHS value of the less-than comparison the first time it is evaluated 9933 // and End is the RHS. 9934 const SCEV *BECountIfBackedgeTaken = 9935 computeBECount(getMinusSCEV(End, Start), Stride, false); 9936 // If the loop entry is guarded by the result of the backedge test of the 9937 // first loop iteration, then we know the backedge will be taken at least 9938 // once and so the backedge taken count is as above. If not then we use the 9939 // expression (max(End,Start)-Start)/Stride to describe the backedge count, 9940 // as if the backedge is taken at least once max(End,Start) is End and so the 9941 // result is as above, and if not max(End,Start) is Start so we get a backedge 9942 // count of zero. 9943 const SCEV *BECount; 9944 if (isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) 9945 BECount = BECountIfBackedgeTaken; 9946 else { 9947 End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start); 9948 BECount = computeBECount(getMinusSCEV(End, Start), Stride, false); 9949 } 9950 9951 const SCEV *MaxBECount; 9952 bool MaxOrZero = false; 9953 if (isa<SCEVConstant>(BECount)) 9954 MaxBECount = BECount; 9955 else if (isa<SCEVConstant>(BECountIfBackedgeTaken)) { 9956 // If we know exactly how many times the backedge will be taken if it's 9957 // taken at least once, then the backedge count will either be that or 9958 // zero. 9959 MaxBECount = BECountIfBackedgeTaken; 9960 MaxOrZero = true; 9961 } else { 9962 MaxBECount = computeMaxBECountForLT( 9963 Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned); 9964 } 9965 9966 if (isa<SCEVCouldNotCompute>(MaxBECount) && 9967 !isa<SCEVCouldNotCompute>(BECount)) 9968 MaxBECount = getConstant(getUnsignedRangeMax(BECount)); 9969 9970 return ExitLimit(BECount, MaxBECount, MaxOrZero, Predicates); 9971 } 9972 9973 ScalarEvolution::ExitLimit 9974 ScalarEvolution::howManyGreaterThans(const SCEV *LHS, const SCEV *RHS, 9975 const Loop *L, bool IsSigned, 9976 bool ControlsExit, bool AllowPredicates) { 9977 SmallPtrSet<const SCEVPredicate *, 4> Predicates; 9978 // We handle only IV > Invariant 9979 if (!isLoopInvariant(RHS, L)) 9980 return getCouldNotCompute(); 9981 9982 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS); 9983 if (!IV && AllowPredicates) 9984 // Try to make this an AddRec using runtime tests, in the first X 9985 // iterations of this loop, where X is the SCEV expression found by the 9986 // algorithm below. 9987 IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates); 9988 9989 // Avoid weird loops 9990 if (!IV || IV->getLoop() != L || !IV->isAffine()) 9991 return getCouldNotCompute(); 9992 9993 bool NoWrap = ControlsExit && 9994 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW); 9995 9996 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this)); 9997 9998 // Avoid negative or zero stride values 9999 if (!isKnownPositive(Stride)) 10000 return getCouldNotCompute(); 10001 10002 // Avoid proven overflow cases: this will ensure that the backedge taken count 10003 // will not generate any unsigned overflow. Relaxed no-overflow conditions 10004 // exploit NoWrapFlags, allowing to optimize in presence of undefined 10005 // behaviors like the case of C language. 10006 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap)) 10007 return getCouldNotCompute(); 10008 10009 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT 10010 : ICmpInst::ICMP_UGT; 10011 10012 const SCEV *Start = IV->getStart(); 10013 const SCEV *End = RHS; 10014 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) 10015 End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start); 10016 10017 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false); 10018 10019 APInt MaxStart = IsSigned ? getSignedRangeMax(Start) 10020 : getUnsignedRangeMax(Start); 10021 10022 APInt MinStride = IsSigned ? getSignedRangeMin(Stride) 10023 : getUnsignedRangeMin(Stride); 10024 10025 unsigned BitWidth = getTypeSizeInBits(LHS->getType()); 10026 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1) 10027 : APInt::getMinValue(BitWidth) + (MinStride - 1); 10028 10029 // Although End can be a MIN expression we estimate MinEnd considering only 10030 // the case End = RHS. This is safe because in the other case (Start - End) 10031 // is zero, leading to a zero maximum backedge taken count. 10032 APInt MinEnd = 10033 IsSigned ? APIntOps::smax(getSignedRangeMin(RHS), Limit) 10034 : APIntOps::umax(getUnsignedRangeMin(RHS), Limit); 10035 10036 10037 const SCEV *MaxBECount = getCouldNotCompute(); 10038 if (isa<SCEVConstant>(BECount)) 10039 MaxBECount = BECount; 10040 else 10041 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd), 10042 getConstant(MinStride), false); 10043 10044 if (isa<SCEVCouldNotCompute>(MaxBECount)) 10045 MaxBECount = BECount; 10046 10047 return ExitLimit(BECount, MaxBECount, false, Predicates); 10048 } 10049 10050 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(const ConstantRange &Range, 10051 ScalarEvolution &SE) const { 10052 if (Range.isFullSet()) // Infinite loop. 10053 return SE.getCouldNotCompute(); 10054 10055 // If the start is a non-zero constant, shift the range to simplify things. 10056 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 10057 if (!SC->getValue()->isZero()) { 10058 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 10059 Operands[0] = SE.getZero(SC->getType()); 10060 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(), 10061 getNoWrapFlags(FlagNW)); 10062 if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 10063 return ShiftedAddRec->getNumIterationsInRange( 10064 Range.subtract(SC->getAPInt()), SE); 10065 // This is strange and shouldn't happen. 10066 return SE.getCouldNotCompute(); 10067 } 10068 10069 // The only time we can solve this is when we have all constant indices. 10070 // Otherwise, we cannot determine the overflow conditions. 10071 if (any_of(operands(), [](const SCEV *Op) { return !isa<SCEVConstant>(Op); })) 10072 return SE.getCouldNotCompute(); 10073 10074 // Okay at this point we know that all elements of the chrec are constants and 10075 // that the start element is zero. 10076 10077 // First check to see if the range contains zero. If not, the first 10078 // iteration exits. 10079 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 10080 if (!Range.contains(APInt(BitWidth, 0))) 10081 return SE.getZero(getType()); 10082 10083 if (isAffine()) { 10084 // If this is an affine expression then we have this situation: 10085 // Solve {0,+,A} in Range === Ax in Range 10086 10087 // We know that zero is in the range. If A is positive then we know that 10088 // the upper value of the range must be the first possible exit value. 10089 // If A is negative then the lower of the range is the last possible loop 10090 // value. Also note that we already checked for a full range. 10091 APInt A = cast<SCEVConstant>(getOperand(1))->getAPInt(); 10092 APInt End = A.sge(1) ? (Range.getUpper() - 1) : Range.getLower(); 10093 10094 // The exit value should be (End+A)/A. 10095 APInt ExitVal = (End + A).udiv(A); 10096 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 10097 10098 // Evaluate at the exit value. If we really did fall out of the valid 10099 // range, then we computed our trip count, otherwise wrap around or other 10100 // things must have happened. 10101 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 10102 if (Range.contains(Val->getValue())) 10103 return SE.getCouldNotCompute(); // Something strange happened 10104 10105 // Ensure that the previous value is in the range. This is a sanity check. 10106 assert(Range.contains( 10107 EvaluateConstantChrecAtConstant(this, 10108 ConstantInt::get(SE.getContext(), ExitVal - 1), SE)->getValue()) && 10109 "Linear scev computation is off in a bad way!"); 10110 return SE.getConstant(ExitValue); 10111 } else if (isQuadratic()) { 10112 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 10113 // quadratic equation to solve it. To do this, we must frame our problem in 10114 // terms of figuring out when zero is crossed, instead of when 10115 // Range.getUpper() is crossed. 10116 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 10117 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 10118 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(), FlagAnyWrap); 10119 10120 // Next, solve the constructed addrec 10121 if (auto Roots = 10122 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE)) { 10123 const SCEVConstant *R1 = Roots->first; 10124 const SCEVConstant *R2 = Roots->second; 10125 // Pick the smallest positive root value. 10126 if (ConstantInt *CB = dyn_cast<ConstantInt>(ConstantExpr::getICmp( 10127 ICmpInst::ICMP_ULT, R1->getValue(), R2->getValue()))) { 10128 if (!CB->getZExtValue()) 10129 std::swap(R1, R2); // R1 is the minimum root now. 10130 10131 // Make sure the root is not off by one. The returned iteration should 10132 // not be in the range, but the previous one should be. When solving 10133 // for "X*X < 5", for example, we should not return a root of 2. 10134 ConstantInt *R1Val = 10135 EvaluateConstantChrecAtConstant(this, R1->getValue(), SE); 10136 if (Range.contains(R1Val->getValue())) { 10137 // The next iteration must be out of the range... 10138 ConstantInt *NextVal = 10139 ConstantInt::get(SE.getContext(), R1->getAPInt() + 1); 10140 10141 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 10142 if (!Range.contains(R1Val->getValue())) 10143 return SE.getConstant(NextVal); 10144 return SE.getCouldNotCompute(); // Something strange happened 10145 } 10146 10147 // If R1 was not in the range, then it is a good return value. Make 10148 // sure that R1-1 WAS in the range though, just in case. 10149 ConstantInt *NextVal = 10150 ConstantInt::get(SE.getContext(), R1->getAPInt() - 1); 10151 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 10152 if (Range.contains(R1Val->getValue())) 10153 return R1; 10154 return SE.getCouldNotCompute(); // Something strange happened 10155 } 10156 } 10157 } 10158 10159 return SE.getCouldNotCompute(); 10160 } 10161 10162 // Return true when S contains at least an undef value. 10163 static inline bool containsUndefs(const SCEV *S) { 10164 return SCEVExprContains(S, [](const SCEV *S) { 10165 if (const auto *SU = dyn_cast<SCEVUnknown>(S)) 10166 return isa<UndefValue>(SU->getValue()); 10167 else if (const auto *SC = dyn_cast<SCEVConstant>(S)) 10168 return isa<UndefValue>(SC->getValue()); 10169 return false; 10170 }); 10171 } 10172 10173 namespace { 10174 10175 // Collect all steps of SCEV expressions. 10176 struct SCEVCollectStrides { 10177 ScalarEvolution &SE; 10178 SmallVectorImpl<const SCEV *> &Strides; 10179 10180 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S) 10181 : SE(SE), Strides(S) {} 10182 10183 bool follow(const SCEV *S) { 10184 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S)) 10185 Strides.push_back(AR->getStepRecurrence(SE)); 10186 return true; 10187 } 10188 10189 bool isDone() const { return false; } 10190 }; 10191 10192 // Collect all SCEVUnknown and SCEVMulExpr expressions. 10193 struct SCEVCollectTerms { 10194 SmallVectorImpl<const SCEV *> &Terms; 10195 10196 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T) : Terms(T) {} 10197 10198 bool follow(const SCEV *S) { 10199 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S) || 10200 isa<SCEVSignExtendExpr>(S)) { 10201 if (!containsUndefs(S)) 10202 Terms.push_back(S); 10203 10204 // Stop recursion: once we collected a term, do not walk its operands. 10205 return false; 10206 } 10207 10208 // Keep looking. 10209 return true; 10210 } 10211 10212 bool isDone() const { return false; } 10213 }; 10214 10215 // Check if a SCEV contains an AddRecExpr. 10216 struct SCEVHasAddRec { 10217 bool &ContainsAddRec; 10218 10219 SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) { 10220 ContainsAddRec = false; 10221 } 10222 10223 bool follow(const SCEV *S) { 10224 if (isa<SCEVAddRecExpr>(S)) { 10225 ContainsAddRec = true; 10226 10227 // Stop recursion: once we collected a term, do not walk its operands. 10228 return false; 10229 } 10230 10231 // Keep looking. 10232 return true; 10233 } 10234 10235 bool isDone() const { return false; } 10236 }; 10237 10238 // Find factors that are multiplied with an expression that (possibly as a 10239 // subexpression) contains an AddRecExpr. In the expression: 10240 // 10241 // 8 * (100 + %p * %q * (%a + {0, +, 1}_loop)) 10242 // 10243 // "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)" 10244 // that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size 10245 // parameters as they form a product with an induction variable. 10246 // 10247 // This collector expects all array size parameters to be in the same MulExpr. 10248 // It might be necessary to later add support for collecting parameters that are 10249 // spread over different nested MulExpr. 10250 struct SCEVCollectAddRecMultiplies { 10251 SmallVectorImpl<const SCEV *> &Terms; 10252 ScalarEvolution &SE; 10253 10254 SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE) 10255 : Terms(T), SE(SE) {} 10256 10257 bool follow(const SCEV *S) { 10258 if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) { 10259 bool HasAddRec = false; 10260 SmallVector<const SCEV *, 0> Operands; 10261 for (auto Op : Mul->operands()) { 10262 const SCEVUnknown *Unknown = dyn_cast<SCEVUnknown>(Op); 10263 if (Unknown && !isa<CallInst>(Unknown->getValue())) { 10264 Operands.push_back(Op); 10265 } else if (Unknown) { 10266 HasAddRec = true; 10267 } else { 10268 bool ContainsAddRec; 10269 SCEVHasAddRec ContiansAddRec(ContainsAddRec); 10270 visitAll(Op, ContiansAddRec); 10271 HasAddRec |= ContainsAddRec; 10272 } 10273 } 10274 if (Operands.size() == 0) 10275 return true; 10276 10277 if (!HasAddRec) 10278 return false; 10279 10280 Terms.push_back(SE.getMulExpr(Operands)); 10281 // Stop recursion: once we collected a term, do not walk its operands. 10282 return false; 10283 } 10284 10285 // Keep looking. 10286 return true; 10287 } 10288 10289 bool isDone() const { return false; } 10290 }; 10291 10292 } // end anonymous namespace 10293 10294 /// Find parametric terms in this SCEVAddRecExpr. We first for parameters in 10295 /// two places: 10296 /// 1) The strides of AddRec expressions. 10297 /// 2) Unknowns that are multiplied with AddRec expressions. 10298 void ScalarEvolution::collectParametricTerms(const SCEV *Expr, 10299 SmallVectorImpl<const SCEV *> &Terms) { 10300 SmallVector<const SCEV *, 4> Strides; 10301 SCEVCollectStrides StrideCollector(*this, Strides); 10302 visitAll(Expr, StrideCollector); 10303 10304 DEBUG({ 10305 dbgs() << "Strides:\n"; 10306 for (const SCEV *S : Strides) 10307 dbgs() << *S << "\n"; 10308 }); 10309 10310 for (const SCEV *S : Strides) { 10311 SCEVCollectTerms TermCollector(Terms); 10312 visitAll(S, TermCollector); 10313 } 10314 10315 DEBUG({ 10316 dbgs() << "Terms:\n"; 10317 for (const SCEV *T : Terms) 10318 dbgs() << *T << "\n"; 10319 }); 10320 10321 SCEVCollectAddRecMultiplies MulCollector(Terms, *this); 10322 visitAll(Expr, MulCollector); 10323 } 10324 10325 static bool findArrayDimensionsRec(ScalarEvolution &SE, 10326 SmallVectorImpl<const SCEV *> &Terms, 10327 SmallVectorImpl<const SCEV *> &Sizes) { 10328 int Last = Terms.size() - 1; 10329 const SCEV *Step = Terms[Last]; 10330 10331 // End of recursion. 10332 if (Last == 0) { 10333 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) { 10334 SmallVector<const SCEV *, 2> Qs; 10335 for (const SCEV *Op : M->operands()) 10336 if (!isa<SCEVConstant>(Op)) 10337 Qs.push_back(Op); 10338 10339 Step = SE.getMulExpr(Qs); 10340 } 10341 10342 Sizes.push_back(Step); 10343 return true; 10344 } 10345 10346 for (const SCEV *&Term : Terms) { 10347 // Normalize the terms before the next call to findArrayDimensionsRec. 10348 const SCEV *Q, *R; 10349 SCEVDivision::divide(SE, Term, Step, &Q, &R); 10350 10351 // Bail out when GCD does not evenly divide one of the terms. 10352 if (!R->isZero()) 10353 return false; 10354 10355 Term = Q; 10356 } 10357 10358 // Remove all SCEVConstants. 10359 Terms.erase( 10360 remove_if(Terms, [](const SCEV *E) { return isa<SCEVConstant>(E); }), 10361 Terms.end()); 10362 10363 if (Terms.size() > 0) 10364 if (!findArrayDimensionsRec(SE, Terms, Sizes)) 10365 return false; 10366 10367 Sizes.push_back(Step); 10368 return true; 10369 } 10370 10371 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter. 10372 static inline bool containsParameters(SmallVectorImpl<const SCEV *> &Terms) { 10373 for (const SCEV *T : Terms) 10374 if (SCEVExprContains(T, isa<SCEVUnknown, const SCEV *>)) 10375 return true; 10376 return false; 10377 } 10378 10379 // Return the number of product terms in S. 10380 static inline int numberOfTerms(const SCEV *S) { 10381 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S)) 10382 return Expr->getNumOperands(); 10383 return 1; 10384 } 10385 10386 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) { 10387 if (isa<SCEVConstant>(T)) 10388 return nullptr; 10389 10390 if (isa<SCEVUnknown>(T)) 10391 return T; 10392 10393 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) { 10394 SmallVector<const SCEV *, 2> Factors; 10395 for (const SCEV *Op : M->operands()) 10396 if (!isa<SCEVConstant>(Op)) 10397 Factors.push_back(Op); 10398 10399 return SE.getMulExpr(Factors); 10400 } 10401 10402 return T; 10403 } 10404 10405 /// Return the size of an element read or written by Inst. 10406 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) { 10407 Type *Ty; 10408 if (StoreInst *Store = dyn_cast<StoreInst>(Inst)) 10409 Ty = Store->getValueOperand()->getType(); 10410 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst)) 10411 Ty = Load->getType(); 10412 else 10413 return nullptr; 10414 10415 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty)); 10416 return getSizeOfExpr(ETy, Ty); 10417 } 10418 10419 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms, 10420 SmallVectorImpl<const SCEV *> &Sizes, 10421 const SCEV *ElementSize) { 10422 if (Terms.size() < 1 || !ElementSize) 10423 return; 10424 10425 // Early return when Terms do not contain parameters: we do not delinearize 10426 // non parametric SCEVs. 10427 if (!containsParameters(Terms)) 10428 return; 10429 10430 DEBUG({ 10431 dbgs() << "Terms:\n"; 10432 for (const SCEV *T : Terms) 10433 dbgs() << *T << "\n"; 10434 }); 10435 10436 // Remove duplicates. 10437 array_pod_sort(Terms.begin(), Terms.end()); 10438 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end()); 10439 10440 // Put larger terms first. 10441 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) { 10442 return numberOfTerms(LHS) > numberOfTerms(RHS); 10443 }); 10444 10445 // Try to divide all terms by the element size. If term is not divisible by 10446 // element size, proceed with the original term. 10447 for (const SCEV *&Term : Terms) { 10448 const SCEV *Q, *R; 10449 SCEVDivision::divide(*this, Term, ElementSize, &Q, &R); 10450 if (!Q->isZero()) 10451 Term = Q; 10452 } 10453 10454 SmallVector<const SCEV *, 4> NewTerms; 10455 10456 // Remove constant factors. 10457 for (const SCEV *T : Terms) 10458 if (const SCEV *NewT = removeConstantFactors(*this, T)) 10459 NewTerms.push_back(NewT); 10460 10461 DEBUG({ 10462 dbgs() << "Terms after sorting:\n"; 10463 for (const SCEV *T : NewTerms) 10464 dbgs() << *T << "\n"; 10465 }); 10466 10467 if (NewTerms.empty() || !findArrayDimensionsRec(*this, NewTerms, Sizes)) { 10468 Sizes.clear(); 10469 return; 10470 } 10471 10472 // The last element to be pushed into Sizes is the size of an element. 10473 Sizes.push_back(ElementSize); 10474 10475 DEBUG({ 10476 dbgs() << "Sizes:\n"; 10477 for (const SCEV *S : Sizes) 10478 dbgs() << *S << "\n"; 10479 }); 10480 } 10481 10482 void ScalarEvolution::computeAccessFunctions( 10483 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts, 10484 SmallVectorImpl<const SCEV *> &Sizes) { 10485 // Early exit in case this SCEV is not an affine multivariate function. 10486 if (Sizes.empty()) 10487 return; 10488 10489 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr)) 10490 if (!AR->isAffine()) 10491 return; 10492 10493 const SCEV *Res = Expr; 10494 int Last = Sizes.size() - 1; 10495 for (int i = Last; i >= 0; i--) { 10496 const SCEV *Q, *R; 10497 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R); 10498 10499 DEBUG({ 10500 dbgs() << "Res: " << *Res << "\n"; 10501 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n"; 10502 dbgs() << "Res divided by Sizes[i]:\n"; 10503 dbgs() << "Quotient: " << *Q << "\n"; 10504 dbgs() << "Remainder: " << *R << "\n"; 10505 }); 10506 10507 Res = Q; 10508 10509 // Do not record the last subscript corresponding to the size of elements in 10510 // the array. 10511 if (i == Last) { 10512 10513 // Bail out if the remainder is too complex. 10514 if (isa<SCEVAddRecExpr>(R)) { 10515 Subscripts.clear(); 10516 Sizes.clear(); 10517 return; 10518 } 10519 10520 continue; 10521 } 10522 10523 // Record the access function for the current subscript. 10524 Subscripts.push_back(R); 10525 } 10526 10527 // Also push in last position the remainder of the last division: it will be 10528 // the access function of the innermost dimension. 10529 Subscripts.push_back(Res); 10530 10531 std::reverse(Subscripts.begin(), Subscripts.end()); 10532 10533 DEBUG({ 10534 dbgs() << "Subscripts:\n"; 10535 for (const SCEV *S : Subscripts) 10536 dbgs() << *S << "\n"; 10537 }); 10538 } 10539 10540 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and 10541 /// sizes of an array access. Returns the remainder of the delinearization that 10542 /// is the offset start of the array. The SCEV->delinearize algorithm computes 10543 /// the multiples of SCEV coefficients: that is a pattern matching of sub 10544 /// expressions in the stride and base of a SCEV corresponding to the 10545 /// computation of a GCD (greatest common divisor) of base and stride. When 10546 /// SCEV->delinearize fails, it returns the SCEV unchanged. 10547 /// 10548 /// For example: when analyzing the memory access A[i][j][k] in this loop nest 10549 /// 10550 /// void foo(long n, long m, long o, double A[n][m][o]) { 10551 /// 10552 /// for (long i = 0; i < n; i++) 10553 /// for (long j = 0; j < m; j++) 10554 /// for (long k = 0; k < o; k++) 10555 /// A[i][j][k] = 1.0; 10556 /// } 10557 /// 10558 /// the delinearization input is the following AddRec SCEV: 10559 /// 10560 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k> 10561 /// 10562 /// From this SCEV, we are able to say that the base offset of the access is %A 10563 /// because it appears as an offset that does not divide any of the strides in 10564 /// the loops: 10565 /// 10566 /// CHECK: Base offset: %A 10567 /// 10568 /// and then SCEV->delinearize determines the size of some of the dimensions of 10569 /// the array as these are the multiples by which the strides are happening: 10570 /// 10571 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes. 10572 /// 10573 /// Note that the outermost dimension remains of UnknownSize because there are 10574 /// no strides that would help identifying the size of the last dimension: when 10575 /// the array has been statically allocated, one could compute the size of that 10576 /// dimension by dividing the overall size of the array by the size of the known 10577 /// dimensions: %m * %o * 8. 10578 /// 10579 /// Finally delinearize provides the access functions for the array reference 10580 /// that does correspond to A[i][j][k] of the above C testcase: 10581 /// 10582 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>] 10583 /// 10584 /// The testcases are checking the output of a function pass: 10585 /// DelinearizationPass that walks through all loads and stores of a function 10586 /// asking for the SCEV of the memory access with respect to all enclosing 10587 /// loops, calling SCEV->delinearize on that and printing the results. 10588 void ScalarEvolution::delinearize(const SCEV *Expr, 10589 SmallVectorImpl<const SCEV *> &Subscripts, 10590 SmallVectorImpl<const SCEV *> &Sizes, 10591 const SCEV *ElementSize) { 10592 // First step: collect parametric terms. 10593 SmallVector<const SCEV *, 4> Terms; 10594 collectParametricTerms(Expr, Terms); 10595 10596 if (Terms.empty()) 10597 return; 10598 10599 // Second step: find subscript sizes. 10600 findArrayDimensions(Terms, Sizes, ElementSize); 10601 10602 if (Sizes.empty()) 10603 return; 10604 10605 // Third step: compute the access functions for each subscript. 10606 computeAccessFunctions(Expr, Subscripts, Sizes); 10607 10608 if (Subscripts.empty()) 10609 return; 10610 10611 DEBUG({ 10612 dbgs() << "succeeded to delinearize " << *Expr << "\n"; 10613 dbgs() << "ArrayDecl[UnknownSize]"; 10614 for (const SCEV *S : Sizes) 10615 dbgs() << "[" << *S << "]"; 10616 10617 dbgs() << "\nArrayRef"; 10618 for (const SCEV *S : Subscripts) 10619 dbgs() << "[" << *S << "]"; 10620 dbgs() << "\n"; 10621 }); 10622 } 10623 10624 //===----------------------------------------------------------------------===// 10625 // SCEVCallbackVH Class Implementation 10626 //===----------------------------------------------------------------------===// 10627 10628 void ScalarEvolution::SCEVCallbackVH::deleted() { 10629 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 10630 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 10631 SE->ConstantEvolutionLoopExitValue.erase(PN); 10632 SE->eraseValueFromMap(getValPtr()); 10633 // this now dangles! 10634 } 10635 10636 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 10637 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 10638 10639 // Forget all the expressions associated with users of the old value, 10640 // so that future queries will recompute the expressions using the new 10641 // value. 10642 Value *Old = getValPtr(); 10643 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end()); 10644 SmallPtrSet<User *, 8> Visited; 10645 while (!Worklist.empty()) { 10646 User *U = Worklist.pop_back_val(); 10647 // Deleting the Old value will cause this to dangle. Postpone 10648 // that until everything else is done. 10649 if (U == Old) 10650 continue; 10651 if (!Visited.insert(U).second) 10652 continue; 10653 if (PHINode *PN = dyn_cast<PHINode>(U)) 10654 SE->ConstantEvolutionLoopExitValue.erase(PN); 10655 SE->eraseValueFromMap(U); 10656 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end()); 10657 } 10658 // Delete the Old value. 10659 if (PHINode *PN = dyn_cast<PHINode>(Old)) 10660 SE->ConstantEvolutionLoopExitValue.erase(PN); 10661 SE->eraseValueFromMap(Old); 10662 // this now dangles! 10663 } 10664 10665 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 10666 : CallbackVH(V), SE(se) {} 10667 10668 //===----------------------------------------------------------------------===// 10669 // ScalarEvolution Class Implementation 10670 //===----------------------------------------------------------------------===// 10671 10672 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI, 10673 AssumptionCache &AC, DominatorTree &DT, 10674 LoopInfo &LI) 10675 : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI), 10676 CouldNotCompute(new SCEVCouldNotCompute()), ValuesAtScopes(64), 10677 LoopDispositions(64), BlockDispositions(64) { 10678 // To use guards for proving predicates, we need to scan every instruction in 10679 // relevant basic blocks, and not just terminators. Doing this is a waste of 10680 // time if the IR does not actually contain any calls to 10681 // @llvm.experimental.guard, so do a quick check and remember this beforehand. 10682 // 10683 // This pessimizes the case where a pass that preserves ScalarEvolution wants 10684 // to _add_ guards to the module when there weren't any before, and wants 10685 // ScalarEvolution to optimize based on those guards. For now we prefer to be 10686 // efficient in lieu of being smart in that rather obscure case. 10687 10688 auto *GuardDecl = F.getParent()->getFunction( 10689 Intrinsic::getName(Intrinsic::experimental_guard)); 10690 HasGuards = GuardDecl && !GuardDecl->use_empty(); 10691 } 10692 10693 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg) 10694 : F(Arg.F), HasGuards(Arg.HasGuards), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT), 10695 LI(Arg.LI), CouldNotCompute(std::move(Arg.CouldNotCompute)), 10696 ValueExprMap(std::move(Arg.ValueExprMap)), 10697 PendingLoopPredicates(std::move(Arg.PendingLoopPredicates)), 10698 MinTrailingZerosCache(std::move(Arg.MinTrailingZerosCache)), 10699 BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)), 10700 PredicatedBackedgeTakenCounts( 10701 std::move(Arg.PredicatedBackedgeTakenCounts)), 10702 ConstantEvolutionLoopExitValue( 10703 std::move(Arg.ConstantEvolutionLoopExitValue)), 10704 ValuesAtScopes(std::move(Arg.ValuesAtScopes)), 10705 LoopDispositions(std::move(Arg.LoopDispositions)), 10706 LoopPropertiesCache(std::move(Arg.LoopPropertiesCache)), 10707 BlockDispositions(std::move(Arg.BlockDispositions)), 10708 UnsignedRanges(std::move(Arg.UnsignedRanges)), 10709 SignedRanges(std::move(Arg.SignedRanges)), 10710 UniqueSCEVs(std::move(Arg.UniqueSCEVs)), 10711 UniquePreds(std::move(Arg.UniquePreds)), 10712 SCEVAllocator(std::move(Arg.SCEVAllocator)), 10713 LoopUsers(std::move(Arg.LoopUsers)), 10714 PredicatedSCEVRewrites(std::move(Arg.PredicatedSCEVRewrites)), 10715 FirstUnknown(Arg.FirstUnknown) { 10716 Arg.FirstUnknown = nullptr; 10717 } 10718 10719 ScalarEvolution::~ScalarEvolution() { 10720 // Iterate through all the SCEVUnknown instances and call their 10721 // destructors, so that they release their references to their values. 10722 for (SCEVUnknown *U = FirstUnknown; U;) { 10723 SCEVUnknown *Tmp = U; 10724 U = U->Next; 10725 Tmp->~SCEVUnknown(); 10726 } 10727 FirstUnknown = nullptr; 10728 10729 ExprValueMap.clear(); 10730 ValueExprMap.clear(); 10731 HasRecMap.clear(); 10732 10733 // Free any extra memory created for ExitNotTakenInfo in the unlikely event 10734 // that a loop had multiple computable exits. 10735 for (auto &BTCI : BackedgeTakenCounts) 10736 BTCI.second.clear(); 10737 for (auto &BTCI : PredicatedBackedgeTakenCounts) 10738 BTCI.second.clear(); 10739 10740 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage"); 10741 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!"); 10742 assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!"); 10743 } 10744 10745 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 10746 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 10747 } 10748 10749 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 10750 const Loop *L) { 10751 // Print all inner loops first 10752 for (Loop *I : *L) 10753 PrintLoopInfo(OS, SE, I); 10754 10755 OS << "Loop "; 10756 L->getHeader()->printAsOperand(OS, /*PrintType=*/false); 10757 OS << ": "; 10758 10759 SmallVector<BasicBlock *, 8> ExitBlocks; 10760 L->getExitBlocks(ExitBlocks); 10761 if (ExitBlocks.size() != 1) 10762 OS << "<multiple exits> "; 10763 10764 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 10765 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 10766 } else { 10767 OS << "Unpredictable backedge-taken count. "; 10768 } 10769 10770 OS << "\n" 10771 "Loop "; 10772 L->getHeader()->printAsOperand(OS, /*PrintType=*/false); 10773 OS << ": "; 10774 10775 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 10776 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 10777 if (SE->isBackedgeTakenCountMaxOrZero(L)) 10778 OS << ", actual taken count either this or zero."; 10779 } else { 10780 OS << "Unpredictable max backedge-taken count. "; 10781 } 10782 10783 OS << "\n" 10784 "Loop "; 10785 L->getHeader()->printAsOperand(OS, /*PrintType=*/false); 10786 OS << ": "; 10787 10788 SCEVUnionPredicate Pred; 10789 auto PBT = SE->getPredicatedBackedgeTakenCount(L, Pred); 10790 if (!isa<SCEVCouldNotCompute>(PBT)) { 10791 OS << "Predicated backedge-taken count is " << *PBT << "\n"; 10792 OS << " Predicates:\n"; 10793 Pred.print(OS, 4); 10794 } else { 10795 OS << "Unpredictable predicated backedge-taken count. "; 10796 } 10797 OS << "\n"; 10798 10799 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 10800 OS << "Loop "; 10801 L->getHeader()->printAsOperand(OS, /*PrintType=*/false); 10802 OS << ": "; 10803 OS << "Trip multiple is " << SE->getSmallConstantTripMultiple(L) << "\n"; 10804 } 10805 } 10806 10807 static StringRef loopDispositionToStr(ScalarEvolution::LoopDisposition LD) { 10808 switch (LD) { 10809 case ScalarEvolution::LoopVariant: 10810 return "Variant"; 10811 case ScalarEvolution::LoopInvariant: 10812 return "Invariant"; 10813 case ScalarEvolution::LoopComputable: 10814 return "Computable"; 10815 } 10816 llvm_unreachable("Unknown ScalarEvolution::LoopDisposition kind!"); 10817 } 10818 10819 void ScalarEvolution::print(raw_ostream &OS) const { 10820 // ScalarEvolution's implementation of the print method is to print 10821 // out SCEV values of all instructions that are interesting. Doing 10822 // this potentially causes it to create new SCEV objects though, 10823 // which technically conflicts with the const qualifier. This isn't 10824 // observable from outside the class though, so casting away the 10825 // const isn't dangerous. 10826 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 10827 10828 OS << "Classifying expressions for: "; 10829 F.printAsOperand(OS, /*PrintType=*/false); 10830 OS << "\n"; 10831 for (Instruction &I : instructions(F)) 10832 if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) { 10833 OS << I << '\n'; 10834 OS << " --> "; 10835 const SCEV *SV = SE.getSCEV(&I); 10836 SV->print(OS); 10837 if (!isa<SCEVCouldNotCompute>(SV)) { 10838 OS << " U: "; 10839 SE.getUnsignedRange(SV).print(OS); 10840 OS << " S: "; 10841 SE.getSignedRange(SV).print(OS); 10842 } 10843 10844 const Loop *L = LI.getLoopFor(I.getParent()); 10845 10846 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 10847 if (AtUse != SV) { 10848 OS << " --> "; 10849 AtUse->print(OS); 10850 if (!isa<SCEVCouldNotCompute>(AtUse)) { 10851 OS << " U: "; 10852 SE.getUnsignedRange(AtUse).print(OS); 10853 OS << " S: "; 10854 SE.getSignedRange(AtUse).print(OS); 10855 } 10856 } 10857 10858 if (L) { 10859 OS << "\t\t" "Exits: "; 10860 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 10861 if (!SE.isLoopInvariant(ExitValue, L)) { 10862 OS << "<<Unknown>>"; 10863 } else { 10864 OS << *ExitValue; 10865 } 10866 10867 bool First = true; 10868 for (auto *Iter = L; Iter; Iter = Iter->getParentLoop()) { 10869 if (First) { 10870 OS << "\t\t" "LoopDispositions: { "; 10871 First = false; 10872 } else { 10873 OS << ", "; 10874 } 10875 10876 Iter->getHeader()->printAsOperand(OS, /*PrintType=*/false); 10877 OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, Iter)); 10878 } 10879 10880 for (auto *InnerL : depth_first(L)) { 10881 if (InnerL == L) 10882 continue; 10883 if (First) { 10884 OS << "\t\t" "LoopDispositions: { "; 10885 First = false; 10886 } else { 10887 OS << ", "; 10888 } 10889 10890 InnerL->getHeader()->printAsOperand(OS, /*PrintType=*/false); 10891 OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, InnerL)); 10892 } 10893 10894 OS << " }"; 10895 } 10896 10897 OS << "\n"; 10898 } 10899 10900 OS << "Determining loop execution counts for: "; 10901 F.printAsOperand(OS, /*PrintType=*/false); 10902 OS << "\n"; 10903 for (Loop *I : LI) 10904 PrintLoopInfo(OS, &SE, I); 10905 } 10906 10907 ScalarEvolution::LoopDisposition 10908 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) { 10909 auto &Values = LoopDispositions[S]; 10910 for (auto &V : Values) { 10911 if (V.getPointer() == L) 10912 return V.getInt(); 10913 } 10914 Values.emplace_back(L, LoopVariant); 10915 LoopDisposition D = computeLoopDisposition(S, L); 10916 auto &Values2 = LoopDispositions[S]; 10917 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) { 10918 if (V.getPointer() == L) { 10919 V.setInt(D); 10920 break; 10921 } 10922 } 10923 return D; 10924 } 10925 10926 ScalarEvolution::LoopDisposition 10927 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) { 10928 switch (static_cast<SCEVTypes>(S->getSCEVType())) { 10929 case scConstant: 10930 return LoopInvariant; 10931 case scTruncate: 10932 case scZeroExtend: 10933 case scSignExtend: 10934 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L); 10935 case scAddRecExpr: { 10936 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 10937 10938 // If L is the addrec's loop, it's computable. 10939 if (AR->getLoop() == L) 10940 return LoopComputable; 10941 10942 // Add recurrences are never invariant in the function-body (null loop). 10943 if (!L) 10944 return LoopVariant; 10945 10946 // Everything that is not defined at loop entry is variant. 10947 if (DT.dominates(L->getHeader(), AR->getLoop()->getHeader())) 10948 return LoopVariant; 10949 assert(!L->contains(AR->getLoop()) && "Containing loop's header does not" 10950 " dominate the contained loop's header?"); 10951 10952 // This recurrence is invariant w.r.t. L if AR's loop contains L. 10953 if (AR->getLoop()->contains(L)) 10954 return LoopInvariant; 10955 10956 // This recurrence is variant w.r.t. L if any of its operands 10957 // are variant. 10958 for (auto *Op : AR->operands()) 10959 if (!isLoopInvariant(Op, L)) 10960 return LoopVariant; 10961 10962 // Otherwise it's loop-invariant. 10963 return LoopInvariant; 10964 } 10965 case scAddExpr: 10966 case scMulExpr: 10967 case scUMaxExpr: 10968 case scSMaxExpr: { 10969 bool HasVarying = false; 10970 for (auto *Op : cast<SCEVNAryExpr>(S)->operands()) { 10971 LoopDisposition D = getLoopDisposition(Op, L); 10972 if (D == LoopVariant) 10973 return LoopVariant; 10974 if (D == LoopComputable) 10975 HasVarying = true; 10976 } 10977 return HasVarying ? LoopComputable : LoopInvariant; 10978 } 10979 case scUDivExpr: { 10980 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 10981 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L); 10982 if (LD == LoopVariant) 10983 return LoopVariant; 10984 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L); 10985 if (RD == LoopVariant) 10986 return LoopVariant; 10987 return (LD == LoopInvariant && RD == LoopInvariant) ? 10988 LoopInvariant : LoopComputable; 10989 } 10990 case scUnknown: 10991 // All non-instruction values are loop invariant. All instructions are loop 10992 // invariant if they are not contained in the specified loop. 10993 // Instructions are never considered invariant in the function body 10994 // (null loop) because they are defined within the "loop". 10995 if (auto *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) 10996 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant; 10997 return LoopInvariant; 10998 case scCouldNotCompute: 10999 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 11000 } 11001 llvm_unreachable("Unknown SCEV kind!"); 11002 } 11003 11004 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) { 11005 return getLoopDisposition(S, L) == LoopInvariant; 11006 } 11007 11008 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) { 11009 return getLoopDisposition(S, L) == LoopComputable; 11010 } 11011 11012 ScalarEvolution::BlockDisposition 11013 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) { 11014 auto &Values = BlockDispositions[S]; 11015 for (auto &V : Values) { 11016 if (V.getPointer() == BB) 11017 return V.getInt(); 11018 } 11019 Values.emplace_back(BB, DoesNotDominateBlock); 11020 BlockDisposition D = computeBlockDisposition(S, BB); 11021 auto &Values2 = BlockDispositions[S]; 11022 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) { 11023 if (V.getPointer() == BB) { 11024 V.setInt(D); 11025 break; 11026 } 11027 } 11028 return D; 11029 } 11030 11031 ScalarEvolution::BlockDisposition 11032 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) { 11033 switch (static_cast<SCEVTypes>(S->getSCEVType())) { 11034 case scConstant: 11035 return ProperlyDominatesBlock; 11036 case scTruncate: 11037 case scZeroExtend: 11038 case scSignExtend: 11039 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB); 11040 case scAddRecExpr: { 11041 // This uses a "dominates" query instead of "properly dominates" query 11042 // to test for proper dominance too, because the instruction which 11043 // produces the addrec's value is a PHI, and a PHI effectively properly 11044 // dominates its entire containing block. 11045 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 11046 if (!DT.dominates(AR->getLoop()->getHeader(), BB)) 11047 return DoesNotDominateBlock; 11048 11049 // Fall through into SCEVNAryExpr handling. 11050 LLVM_FALLTHROUGH; 11051 } 11052 case scAddExpr: 11053 case scMulExpr: 11054 case scUMaxExpr: 11055 case scSMaxExpr: { 11056 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 11057 bool Proper = true; 11058 for (const SCEV *NAryOp : NAry->operands()) { 11059 BlockDisposition D = getBlockDisposition(NAryOp, BB); 11060 if (D == DoesNotDominateBlock) 11061 return DoesNotDominateBlock; 11062 if (D == DominatesBlock) 11063 Proper = false; 11064 } 11065 return Proper ? ProperlyDominatesBlock : DominatesBlock; 11066 } 11067 case scUDivExpr: { 11068 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 11069 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 11070 BlockDisposition LD = getBlockDisposition(LHS, BB); 11071 if (LD == DoesNotDominateBlock) 11072 return DoesNotDominateBlock; 11073 BlockDisposition RD = getBlockDisposition(RHS, BB); 11074 if (RD == DoesNotDominateBlock) 11075 return DoesNotDominateBlock; 11076 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ? 11077 ProperlyDominatesBlock : DominatesBlock; 11078 } 11079 case scUnknown: 11080 if (Instruction *I = 11081 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) { 11082 if (I->getParent() == BB) 11083 return DominatesBlock; 11084 if (DT.properlyDominates(I->getParent(), BB)) 11085 return ProperlyDominatesBlock; 11086 return DoesNotDominateBlock; 11087 } 11088 return ProperlyDominatesBlock; 11089 case scCouldNotCompute: 11090 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 11091 } 11092 llvm_unreachable("Unknown SCEV kind!"); 11093 } 11094 11095 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) { 11096 return getBlockDisposition(S, BB) >= DominatesBlock; 11097 } 11098 11099 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) { 11100 return getBlockDisposition(S, BB) == ProperlyDominatesBlock; 11101 } 11102 11103 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const { 11104 return SCEVExprContains(S, [&](const SCEV *Expr) { return Expr == Op; }); 11105 } 11106 11107 bool ScalarEvolution::ExitLimit::hasOperand(const SCEV *S) const { 11108 auto IsS = [&](const SCEV *X) { return S == X; }; 11109 auto ContainsS = [&](const SCEV *X) { 11110 return !isa<SCEVCouldNotCompute>(X) && SCEVExprContains(X, IsS); 11111 }; 11112 return ContainsS(ExactNotTaken) || ContainsS(MaxNotTaken); 11113 } 11114 11115 void 11116 ScalarEvolution::forgetMemoizedResults(const SCEV *S) { 11117 ValuesAtScopes.erase(S); 11118 LoopDispositions.erase(S); 11119 BlockDispositions.erase(S); 11120 UnsignedRanges.erase(S); 11121 SignedRanges.erase(S); 11122 ExprValueMap.erase(S); 11123 HasRecMap.erase(S); 11124 MinTrailingZerosCache.erase(S); 11125 11126 for (auto I = PredicatedSCEVRewrites.begin(); 11127 I != PredicatedSCEVRewrites.end();) { 11128 std::pair<const SCEV *, const Loop *> Entry = I->first; 11129 if (Entry.first == S) 11130 PredicatedSCEVRewrites.erase(I++); 11131 else 11132 ++I; 11133 } 11134 11135 auto RemoveSCEVFromBackedgeMap = 11136 [S, this](DenseMap<const Loop *, BackedgeTakenInfo> &Map) { 11137 for (auto I = Map.begin(), E = Map.end(); I != E;) { 11138 BackedgeTakenInfo &BEInfo = I->second; 11139 if (BEInfo.hasOperand(S, this)) { 11140 BEInfo.clear(); 11141 Map.erase(I++); 11142 } else 11143 ++I; 11144 } 11145 }; 11146 11147 RemoveSCEVFromBackedgeMap(BackedgeTakenCounts); 11148 RemoveSCEVFromBackedgeMap(PredicatedBackedgeTakenCounts); 11149 } 11150 11151 void ScalarEvolution::addToLoopUseLists(const SCEV *S) { 11152 struct FindUsedLoops { 11153 SmallPtrSet<const Loop *, 8> LoopsUsed; 11154 bool follow(const SCEV *S) { 11155 if (auto *AR = dyn_cast<SCEVAddRecExpr>(S)) 11156 LoopsUsed.insert(AR->getLoop()); 11157 return true; 11158 } 11159 11160 bool isDone() const { return false; } 11161 }; 11162 11163 FindUsedLoops F; 11164 SCEVTraversal<FindUsedLoops>(F).visitAll(S); 11165 11166 for (auto *L : F.LoopsUsed) 11167 LoopUsers[L].push_back(S); 11168 } 11169 11170 void ScalarEvolution::verify() const { 11171 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 11172 ScalarEvolution SE2(F, TLI, AC, DT, LI); 11173 11174 SmallVector<Loop *, 8> LoopStack(LI.begin(), LI.end()); 11175 11176 // Map's SCEV expressions from one ScalarEvolution "universe" to another. 11177 struct SCEVMapper : public SCEVRewriteVisitor<SCEVMapper> { 11178 SCEVMapper(ScalarEvolution &SE) : SCEVRewriteVisitor<SCEVMapper>(SE) {} 11179 11180 const SCEV *visitConstant(const SCEVConstant *Constant) { 11181 return SE.getConstant(Constant->getAPInt()); 11182 } 11183 11184 const SCEV *visitUnknown(const SCEVUnknown *Expr) { 11185 return SE.getUnknown(Expr->getValue()); 11186 } 11187 11188 const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) { 11189 return SE.getCouldNotCompute(); 11190 } 11191 }; 11192 11193 SCEVMapper SCM(SE2); 11194 11195 while (!LoopStack.empty()) { 11196 auto *L = LoopStack.pop_back_val(); 11197 LoopStack.insert(LoopStack.end(), L->begin(), L->end()); 11198 11199 auto *CurBECount = SCM.visit( 11200 const_cast<ScalarEvolution *>(this)->getBackedgeTakenCount(L)); 11201 auto *NewBECount = SE2.getBackedgeTakenCount(L); 11202 11203 if (CurBECount == SE2.getCouldNotCompute() || 11204 NewBECount == SE2.getCouldNotCompute()) { 11205 // NB! This situation is legal, but is very suspicious -- whatever pass 11206 // change the loop to make a trip count go from could not compute to 11207 // computable or vice-versa *should have* invalidated SCEV. However, we 11208 // choose not to assert here (for now) since we don't want false 11209 // positives. 11210 continue; 11211 } 11212 11213 if (containsUndefs(CurBECount) || containsUndefs(NewBECount)) { 11214 // SCEV treats "undef" as an unknown but consistent value (i.e. it does 11215 // not propagate undef aggressively). This means we can (and do) fail 11216 // verification in cases where a transform makes the trip count of a loop 11217 // go from "undef" to "undef+1" (say). The transform is fine, since in 11218 // both cases the loop iterates "undef" times, but SCEV thinks we 11219 // increased the trip count of the loop by 1 incorrectly. 11220 continue; 11221 } 11222 11223 if (SE.getTypeSizeInBits(CurBECount->getType()) > 11224 SE.getTypeSizeInBits(NewBECount->getType())) 11225 NewBECount = SE2.getZeroExtendExpr(NewBECount, CurBECount->getType()); 11226 else if (SE.getTypeSizeInBits(CurBECount->getType()) < 11227 SE.getTypeSizeInBits(NewBECount->getType())) 11228 CurBECount = SE2.getZeroExtendExpr(CurBECount, NewBECount->getType()); 11229 11230 auto *ConstantDelta = 11231 dyn_cast<SCEVConstant>(SE2.getMinusSCEV(CurBECount, NewBECount)); 11232 11233 if (ConstantDelta && ConstantDelta->getAPInt() != 0) { 11234 dbgs() << "Trip Count Changed!\n"; 11235 dbgs() << "Old: " << *CurBECount << "\n"; 11236 dbgs() << "New: " << *NewBECount << "\n"; 11237 dbgs() << "Delta: " << *ConstantDelta << "\n"; 11238 std::abort(); 11239 } 11240 } 11241 } 11242 11243 bool ScalarEvolution::invalidate( 11244 Function &F, const PreservedAnalyses &PA, 11245 FunctionAnalysisManager::Invalidator &Inv) { 11246 // Invalidate the ScalarEvolution object whenever it isn't preserved or one 11247 // of its dependencies is invalidated. 11248 auto PAC = PA.getChecker<ScalarEvolutionAnalysis>(); 11249 return !(PAC.preserved() || PAC.preservedSet<AllAnalysesOn<Function>>()) || 11250 Inv.invalidate<AssumptionAnalysis>(F, PA) || 11251 Inv.invalidate<DominatorTreeAnalysis>(F, PA) || 11252 Inv.invalidate<LoopAnalysis>(F, PA); 11253 } 11254 11255 AnalysisKey ScalarEvolutionAnalysis::Key; 11256 11257 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F, 11258 FunctionAnalysisManager &AM) { 11259 return ScalarEvolution(F, AM.getResult<TargetLibraryAnalysis>(F), 11260 AM.getResult<AssumptionAnalysis>(F), 11261 AM.getResult<DominatorTreeAnalysis>(F), 11262 AM.getResult<LoopAnalysis>(F)); 11263 } 11264 11265 PreservedAnalyses 11266 ScalarEvolutionPrinterPass::run(Function &F, FunctionAnalysisManager &AM) { 11267 AM.getResult<ScalarEvolutionAnalysis>(F).print(OS); 11268 return PreservedAnalyses::all(); 11269 } 11270 11271 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution", 11272 "Scalar Evolution Analysis", false, true) 11273 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker) 11274 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass) 11275 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass) 11276 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass) 11277 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution", 11278 "Scalar Evolution Analysis", false, true) 11279 11280 char ScalarEvolutionWrapperPass::ID = 0; 11281 11282 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) { 11283 initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry()); 11284 } 11285 11286 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) { 11287 SE.reset(new ScalarEvolution( 11288 F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(), 11289 getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F), 11290 getAnalysis<DominatorTreeWrapperPass>().getDomTree(), 11291 getAnalysis<LoopInfoWrapperPass>().getLoopInfo())); 11292 return false; 11293 } 11294 11295 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); } 11296 11297 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const { 11298 SE->print(OS); 11299 } 11300 11301 void ScalarEvolutionWrapperPass::verifyAnalysis() const { 11302 if (!VerifySCEV) 11303 return; 11304 11305 SE->verify(); 11306 } 11307 11308 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const { 11309 AU.setPreservesAll(); 11310 AU.addRequiredTransitive<AssumptionCacheTracker>(); 11311 AU.addRequiredTransitive<LoopInfoWrapperPass>(); 11312 AU.addRequiredTransitive<DominatorTreeWrapperPass>(); 11313 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>(); 11314 } 11315 11316 const SCEVPredicate *ScalarEvolution::getEqualPredicate(const SCEV *LHS, 11317 const SCEV *RHS) { 11318 FoldingSetNodeID ID; 11319 assert(LHS->getType() == RHS->getType() && 11320 "Type mismatch between LHS and RHS"); 11321 // Unique this node based on the arguments 11322 ID.AddInteger(SCEVPredicate::P_Equal); 11323 ID.AddPointer(LHS); 11324 ID.AddPointer(RHS); 11325 void *IP = nullptr; 11326 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP)) 11327 return S; 11328 SCEVEqualPredicate *Eq = new (SCEVAllocator) 11329 SCEVEqualPredicate(ID.Intern(SCEVAllocator), LHS, RHS); 11330 UniquePreds.InsertNode(Eq, IP); 11331 return Eq; 11332 } 11333 11334 const SCEVPredicate *ScalarEvolution::getWrapPredicate( 11335 const SCEVAddRecExpr *AR, 11336 SCEVWrapPredicate::IncrementWrapFlags AddedFlags) { 11337 FoldingSetNodeID ID; 11338 // Unique this node based on the arguments 11339 ID.AddInteger(SCEVPredicate::P_Wrap); 11340 ID.AddPointer(AR); 11341 ID.AddInteger(AddedFlags); 11342 void *IP = nullptr; 11343 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP)) 11344 return S; 11345 auto *OF = new (SCEVAllocator) 11346 SCEVWrapPredicate(ID.Intern(SCEVAllocator), AR, AddedFlags); 11347 UniquePreds.InsertNode(OF, IP); 11348 return OF; 11349 } 11350 11351 namespace { 11352 11353 class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> { 11354 public: 11355 11356 /// Rewrites \p S in the context of a loop L and the SCEV predication 11357 /// infrastructure. 11358 /// 11359 /// If \p Pred is non-null, the SCEV expression is rewritten to respect the 11360 /// equivalences present in \p Pred. 11361 /// 11362 /// If \p NewPreds is non-null, rewrite is free to add further predicates to 11363 /// \p NewPreds such that the result will be an AddRecExpr. 11364 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE, 11365 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds, 11366 SCEVUnionPredicate *Pred) { 11367 SCEVPredicateRewriter Rewriter(L, SE, NewPreds, Pred); 11368 return Rewriter.visit(S); 11369 } 11370 11371 const SCEV *visitUnknown(const SCEVUnknown *Expr) { 11372 if (Pred) { 11373 auto ExprPreds = Pred->getPredicatesForExpr(Expr); 11374 for (auto *Pred : ExprPreds) 11375 if (const auto *IPred = dyn_cast<SCEVEqualPredicate>(Pred)) 11376 if (IPred->getLHS() == Expr) 11377 return IPred->getRHS(); 11378 } 11379 return convertToAddRecWithPreds(Expr); 11380 } 11381 11382 const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) { 11383 const SCEV *Operand = visit(Expr->getOperand()); 11384 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand); 11385 if (AR && AR->getLoop() == L && AR->isAffine()) { 11386 // This couldn't be folded because the operand didn't have the nuw 11387 // flag. Add the nusw flag as an assumption that we could make. 11388 const SCEV *Step = AR->getStepRecurrence(SE); 11389 Type *Ty = Expr->getType(); 11390 if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNUSW)) 11391 return SE.getAddRecExpr(SE.getZeroExtendExpr(AR->getStart(), Ty), 11392 SE.getSignExtendExpr(Step, Ty), L, 11393 AR->getNoWrapFlags()); 11394 } 11395 return SE.getZeroExtendExpr(Operand, Expr->getType()); 11396 } 11397 11398 const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) { 11399 const SCEV *Operand = visit(Expr->getOperand()); 11400 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand); 11401 if (AR && AR->getLoop() == L && AR->isAffine()) { 11402 // This couldn't be folded because the operand didn't have the nsw 11403 // flag. Add the nssw flag as an assumption that we could make. 11404 const SCEV *Step = AR->getStepRecurrence(SE); 11405 Type *Ty = Expr->getType(); 11406 if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNSSW)) 11407 return SE.getAddRecExpr(SE.getSignExtendExpr(AR->getStart(), Ty), 11408 SE.getSignExtendExpr(Step, Ty), L, 11409 AR->getNoWrapFlags()); 11410 } 11411 return SE.getSignExtendExpr(Operand, Expr->getType()); 11412 } 11413 11414 private: 11415 explicit SCEVPredicateRewriter(const Loop *L, ScalarEvolution &SE, 11416 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds, 11417 SCEVUnionPredicate *Pred) 11418 : SCEVRewriteVisitor(SE), NewPreds(NewPreds), Pred(Pred), L(L) {} 11419 11420 bool addOverflowAssumption(const SCEVPredicate *P) { 11421 if (!NewPreds) { 11422 // Check if we've already made this assumption. 11423 return Pred && Pred->implies(P); 11424 } 11425 NewPreds->insert(P); 11426 return true; 11427 } 11428 11429 bool addOverflowAssumption(const SCEVAddRecExpr *AR, 11430 SCEVWrapPredicate::IncrementWrapFlags AddedFlags) { 11431 auto *A = SE.getWrapPredicate(AR, AddedFlags); 11432 return addOverflowAssumption(A); 11433 } 11434 11435 // If \p Expr represents a PHINode, we try to see if it can be represented 11436 // as an AddRec, possibly under a predicate (PHISCEVPred). If it is possible 11437 // to add this predicate as a runtime overflow check, we return the AddRec. 11438 // If \p Expr does not meet these conditions (is not a PHI node, or we 11439 // couldn't create an AddRec for it, or couldn't add the predicate), we just 11440 // return \p Expr. 11441 const SCEV *convertToAddRecWithPreds(const SCEVUnknown *Expr) { 11442 if (!isa<PHINode>(Expr->getValue())) 11443 return Expr; 11444 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>> 11445 PredicatedRewrite = SE.createAddRecFromPHIWithCasts(Expr); 11446 if (!PredicatedRewrite) 11447 return Expr; 11448 for (auto *P : PredicatedRewrite->second){ 11449 if (!addOverflowAssumption(P)) 11450 return Expr; 11451 } 11452 return PredicatedRewrite->first; 11453 } 11454 11455 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds; 11456 SCEVUnionPredicate *Pred; 11457 const Loop *L; 11458 }; 11459 11460 } // end anonymous namespace 11461 11462 const SCEV *ScalarEvolution::rewriteUsingPredicate(const SCEV *S, const Loop *L, 11463 SCEVUnionPredicate &Preds) { 11464 return SCEVPredicateRewriter::rewrite(S, L, *this, nullptr, &Preds); 11465 } 11466 11467 const SCEVAddRecExpr *ScalarEvolution::convertSCEVToAddRecWithPredicates( 11468 const SCEV *S, const Loop *L, 11469 SmallPtrSetImpl<const SCEVPredicate *> &Preds) { 11470 SmallPtrSet<const SCEVPredicate *, 4> TransformPreds; 11471 S = SCEVPredicateRewriter::rewrite(S, L, *this, &TransformPreds, nullptr); 11472 auto *AddRec = dyn_cast<SCEVAddRecExpr>(S); 11473 11474 if (!AddRec) 11475 return nullptr; 11476 11477 // Since the transformation was successful, we can now transfer the SCEV 11478 // predicates. 11479 for (auto *P : TransformPreds) 11480 Preds.insert(P); 11481 11482 return AddRec; 11483 } 11484 11485 /// SCEV predicates 11486 SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID, 11487 SCEVPredicateKind Kind) 11488 : FastID(ID), Kind(Kind) {} 11489 11490 SCEVEqualPredicate::SCEVEqualPredicate(const FoldingSetNodeIDRef ID, 11491 const SCEV *LHS, const SCEV *RHS) 11492 : SCEVPredicate(ID, P_Equal), LHS(LHS), RHS(RHS) { 11493 assert(LHS->getType() == RHS->getType() && "LHS and RHS types don't match"); 11494 assert(LHS != RHS && "LHS and RHS are the same SCEV"); 11495 } 11496 11497 bool SCEVEqualPredicate::implies(const SCEVPredicate *N) const { 11498 const auto *Op = dyn_cast<SCEVEqualPredicate>(N); 11499 11500 if (!Op) 11501 return false; 11502 11503 return Op->LHS == LHS && Op->RHS == RHS; 11504 } 11505 11506 bool SCEVEqualPredicate::isAlwaysTrue() const { return false; } 11507 11508 const SCEV *SCEVEqualPredicate::getExpr() const { return LHS; } 11509 11510 void SCEVEqualPredicate::print(raw_ostream &OS, unsigned Depth) const { 11511 OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n"; 11512 } 11513 11514 SCEVWrapPredicate::SCEVWrapPredicate(const FoldingSetNodeIDRef ID, 11515 const SCEVAddRecExpr *AR, 11516 IncrementWrapFlags Flags) 11517 : SCEVPredicate(ID, P_Wrap), AR(AR), Flags(Flags) {} 11518 11519 const SCEV *SCEVWrapPredicate::getExpr() const { return AR; } 11520 11521 bool SCEVWrapPredicate::implies(const SCEVPredicate *N) const { 11522 const auto *Op = dyn_cast<SCEVWrapPredicate>(N); 11523 11524 return Op && Op->AR == AR && setFlags(Flags, Op->Flags) == Flags; 11525 } 11526 11527 bool SCEVWrapPredicate::isAlwaysTrue() const { 11528 SCEV::NoWrapFlags ScevFlags = AR->getNoWrapFlags(); 11529 IncrementWrapFlags IFlags = Flags; 11530 11531 if (ScalarEvolution::setFlags(ScevFlags, SCEV::FlagNSW) == ScevFlags) 11532 IFlags = clearFlags(IFlags, IncrementNSSW); 11533 11534 return IFlags == IncrementAnyWrap; 11535 } 11536 11537 void SCEVWrapPredicate::print(raw_ostream &OS, unsigned Depth) const { 11538 OS.indent(Depth) << *getExpr() << " Added Flags: "; 11539 if (SCEVWrapPredicate::IncrementNUSW & getFlags()) 11540 OS << "<nusw>"; 11541 if (SCEVWrapPredicate::IncrementNSSW & getFlags()) 11542 OS << "<nssw>"; 11543 OS << "\n"; 11544 } 11545 11546 SCEVWrapPredicate::IncrementWrapFlags 11547 SCEVWrapPredicate::getImpliedFlags(const SCEVAddRecExpr *AR, 11548 ScalarEvolution &SE) { 11549 IncrementWrapFlags ImpliedFlags = IncrementAnyWrap; 11550 SCEV::NoWrapFlags StaticFlags = AR->getNoWrapFlags(); 11551 11552 // We can safely transfer the NSW flag as NSSW. 11553 if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNSW) == StaticFlags) 11554 ImpliedFlags = IncrementNSSW; 11555 11556 if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNUW) == StaticFlags) { 11557 // If the increment is positive, the SCEV NUW flag will also imply the 11558 // WrapPredicate NUSW flag. 11559 if (const auto *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(SE))) 11560 if (Step->getValue()->getValue().isNonNegative()) 11561 ImpliedFlags = setFlags(ImpliedFlags, IncrementNUSW); 11562 } 11563 11564 return ImpliedFlags; 11565 } 11566 11567 /// Union predicates don't get cached so create a dummy set ID for it. 11568 SCEVUnionPredicate::SCEVUnionPredicate() 11569 : SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {} 11570 11571 bool SCEVUnionPredicate::isAlwaysTrue() const { 11572 return all_of(Preds, 11573 [](const SCEVPredicate *I) { return I->isAlwaysTrue(); }); 11574 } 11575 11576 ArrayRef<const SCEVPredicate *> 11577 SCEVUnionPredicate::getPredicatesForExpr(const SCEV *Expr) { 11578 auto I = SCEVToPreds.find(Expr); 11579 if (I == SCEVToPreds.end()) 11580 return ArrayRef<const SCEVPredicate *>(); 11581 return I->second; 11582 } 11583 11584 bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const { 11585 if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N)) 11586 return all_of(Set->Preds, 11587 [this](const SCEVPredicate *I) { return this->implies(I); }); 11588 11589 auto ScevPredsIt = SCEVToPreds.find(N->getExpr()); 11590 if (ScevPredsIt == SCEVToPreds.end()) 11591 return false; 11592 auto &SCEVPreds = ScevPredsIt->second; 11593 11594 return any_of(SCEVPreds, 11595 [N](const SCEVPredicate *I) { return I->implies(N); }); 11596 } 11597 11598 const SCEV *SCEVUnionPredicate::getExpr() const { return nullptr; } 11599 11600 void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const { 11601 for (auto Pred : Preds) 11602 Pred->print(OS, Depth); 11603 } 11604 11605 void SCEVUnionPredicate::add(const SCEVPredicate *N) { 11606 if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N)) { 11607 for (auto Pred : Set->Preds) 11608 add(Pred); 11609 return; 11610 } 11611 11612 if (implies(N)) 11613 return; 11614 11615 const SCEV *Key = N->getExpr(); 11616 assert(Key && "Only SCEVUnionPredicate doesn't have an " 11617 " associated expression!"); 11618 11619 SCEVToPreds[Key].push_back(N); 11620 Preds.push_back(N); 11621 } 11622 11623 PredicatedScalarEvolution::PredicatedScalarEvolution(ScalarEvolution &SE, 11624 Loop &L) 11625 : SE(SE), L(L) {} 11626 11627 const SCEV *PredicatedScalarEvolution::getSCEV(Value *V) { 11628 const SCEV *Expr = SE.getSCEV(V); 11629 RewriteEntry &Entry = RewriteMap[Expr]; 11630 11631 // If we already have an entry and the version matches, return it. 11632 if (Entry.second && Generation == Entry.first) 11633 return Entry.second; 11634 11635 // We found an entry but it's stale. Rewrite the stale entry 11636 // according to the current predicate. 11637 if (Entry.second) 11638 Expr = Entry.second; 11639 11640 const SCEV *NewSCEV = SE.rewriteUsingPredicate(Expr, &L, Preds); 11641 Entry = {Generation, NewSCEV}; 11642 11643 return NewSCEV; 11644 } 11645 11646 const SCEV *PredicatedScalarEvolution::getBackedgeTakenCount() { 11647 if (!BackedgeCount) { 11648 SCEVUnionPredicate BackedgePred; 11649 BackedgeCount = SE.getPredicatedBackedgeTakenCount(&L, BackedgePred); 11650 addPredicate(BackedgePred); 11651 } 11652 return BackedgeCount; 11653 } 11654 11655 void PredicatedScalarEvolution::addPredicate(const SCEVPredicate &Pred) { 11656 if (Preds.implies(&Pred)) 11657 return; 11658 Preds.add(&Pred); 11659 updateGeneration(); 11660 } 11661 11662 const SCEVUnionPredicate &PredicatedScalarEvolution::getUnionPredicate() const { 11663 return Preds; 11664 } 11665 11666 void PredicatedScalarEvolution::updateGeneration() { 11667 // If the generation number wrapped recompute everything. 11668 if (++Generation == 0) { 11669 for (auto &II : RewriteMap) { 11670 const SCEV *Rewritten = II.second.second; 11671 II.second = {Generation, SE.rewriteUsingPredicate(Rewritten, &L, Preds)}; 11672 } 11673 } 11674 } 11675 11676 void PredicatedScalarEvolution::setNoOverflow( 11677 Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) { 11678 const SCEV *Expr = getSCEV(V); 11679 const auto *AR = cast<SCEVAddRecExpr>(Expr); 11680 11681 auto ImpliedFlags = SCEVWrapPredicate::getImpliedFlags(AR, SE); 11682 11683 // Clear the statically implied flags. 11684 Flags = SCEVWrapPredicate::clearFlags(Flags, ImpliedFlags); 11685 addPredicate(*SE.getWrapPredicate(AR, Flags)); 11686 11687 auto II = FlagsMap.insert({V, Flags}); 11688 if (!II.second) 11689 II.first->second = SCEVWrapPredicate::setFlags(Flags, II.first->second); 11690 } 11691 11692 bool PredicatedScalarEvolution::hasNoOverflow( 11693 Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) { 11694 const SCEV *Expr = getSCEV(V); 11695 const auto *AR = cast<SCEVAddRecExpr>(Expr); 11696 11697 Flags = SCEVWrapPredicate::clearFlags( 11698 Flags, SCEVWrapPredicate::getImpliedFlags(AR, SE)); 11699 11700 auto II = FlagsMap.find(V); 11701 11702 if (II != FlagsMap.end()) 11703 Flags = SCEVWrapPredicate::clearFlags(Flags, II->second); 11704 11705 return Flags == SCEVWrapPredicate::IncrementAnyWrap; 11706 } 11707 11708 const SCEVAddRecExpr *PredicatedScalarEvolution::getAsAddRec(Value *V) { 11709 const SCEV *Expr = this->getSCEV(V); 11710 SmallPtrSet<const SCEVPredicate *, 4> NewPreds; 11711 auto *New = SE.convertSCEVToAddRecWithPredicates(Expr, &L, NewPreds); 11712 11713 if (!New) 11714 return nullptr; 11715 11716 for (auto *P : NewPreds) 11717 Preds.add(P); 11718 11719 updateGeneration(); 11720 RewriteMap[SE.getSCEV(V)] = {Generation, New}; 11721 return New; 11722 } 11723 11724 PredicatedScalarEvolution::PredicatedScalarEvolution( 11725 const PredicatedScalarEvolution &Init) 11726 : RewriteMap(Init.RewriteMap), SE(Init.SE), L(Init.L), Preds(Init.Preds), 11727 Generation(Init.Generation), BackedgeCount(Init.BackedgeCount) { 11728 for (const auto &I : Init.FlagsMap) 11729 FlagsMap.insert(I); 11730 } 11731 11732 void PredicatedScalarEvolution::print(raw_ostream &OS, unsigned Depth) const { 11733 // For each block. 11734 for (auto *BB : L.getBlocks()) 11735 for (auto &I : *BB) { 11736 if (!SE.isSCEVable(I.getType())) 11737 continue; 11738 11739 auto *Expr = SE.getSCEV(&I); 11740 auto II = RewriteMap.find(Expr); 11741 11742 if (II == RewriteMap.end()) 11743 continue; 11744 11745 // Don't print things that are not interesting. 11746 if (II->second.second == Expr) 11747 continue; 11748 11749 OS.indent(Depth) << "[PSE]" << I << ":\n"; 11750 OS.indent(Depth + 2) << *Expr << "\n"; 11751 OS.indent(Depth + 2) << "--> " << *II->second.second << "\n"; 11752 } 11753 } 11754