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/Optional.h" 63 #include "llvm/ADT/STLExtras.h" 64 #include "llvm/ADT/SmallPtrSet.h" 65 #include "llvm/ADT/Statistic.h" 66 #include "llvm/Analysis/AssumptionCache.h" 67 #include "llvm/Analysis/ConstantFolding.h" 68 #include "llvm/Analysis/InstructionSimplify.h" 69 #include "llvm/Analysis/LoopInfo.h" 70 #include "llvm/Analysis/ScalarEvolutionExpressions.h" 71 #include "llvm/Analysis/TargetLibraryInfo.h" 72 #include "llvm/Analysis/ValueTracking.h" 73 #include "llvm/IR/ConstantRange.h" 74 #include "llvm/IR/Constants.h" 75 #include "llvm/IR/DataLayout.h" 76 #include "llvm/IR/DerivedTypes.h" 77 #include "llvm/IR/Dominators.h" 78 #include "llvm/IR/GetElementPtrTypeIterator.h" 79 #include "llvm/IR/GlobalAlias.h" 80 #include "llvm/IR/GlobalVariable.h" 81 #include "llvm/IR/InstIterator.h" 82 #include "llvm/IR/Instructions.h" 83 #include "llvm/IR/LLVMContext.h" 84 #include "llvm/IR/Metadata.h" 85 #include "llvm/IR/Operator.h" 86 #include "llvm/Support/CommandLine.h" 87 #include "llvm/Support/Debug.h" 88 #include "llvm/Support/ErrorHandling.h" 89 #include "llvm/Support/MathExtras.h" 90 #include "llvm/Support/raw_ostream.h" 91 #include <algorithm> 92 using namespace llvm; 93 94 #define DEBUG_TYPE "scalar-evolution" 95 96 STATISTIC(NumArrayLenItCounts, 97 "Number of trip counts computed with array length"); 98 STATISTIC(NumTripCountsComputed, 99 "Number of loops with predictable loop counts"); 100 STATISTIC(NumTripCountsNotComputed, 101 "Number of loops without predictable loop counts"); 102 STATISTIC(NumBruteForceTripCountsComputed, 103 "Number of loops with trip counts computed by force"); 104 105 static cl::opt<unsigned> 106 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 107 cl::desc("Maximum number of iterations SCEV will " 108 "symbolically execute a constant " 109 "derived loop"), 110 cl::init(100)); 111 112 // FIXME: Enable this with XDEBUG when the test suite is clean. 113 static cl::opt<bool> 114 VerifySCEV("verify-scev", 115 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)")); 116 117 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution", 118 "Scalar Evolution Analysis", false, true) 119 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker) 120 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass) 121 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass) 122 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass) 123 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution", 124 "Scalar Evolution Analysis", false, true) 125 char ScalarEvolution::ID = 0; 126 127 //===----------------------------------------------------------------------===// 128 // SCEV class definitions 129 //===----------------------------------------------------------------------===// 130 131 //===----------------------------------------------------------------------===// 132 // Implementation of the SCEV class. 133 // 134 135 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP) 136 void SCEV::dump() const { 137 print(dbgs()); 138 dbgs() << '\n'; 139 } 140 #endif 141 142 void SCEV::print(raw_ostream &OS) const { 143 switch (static_cast<SCEVTypes>(getSCEVType())) { 144 case scConstant: 145 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false); 146 return; 147 case scTruncate: { 148 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this); 149 const SCEV *Op = Trunc->getOperand(); 150 OS << "(trunc " << *Op->getType() << " " << *Op << " to " 151 << *Trunc->getType() << ")"; 152 return; 153 } 154 case scZeroExtend: { 155 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this); 156 const SCEV *Op = ZExt->getOperand(); 157 OS << "(zext " << *Op->getType() << " " << *Op << " to " 158 << *ZExt->getType() << ")"; 159 return; 160 } 161 case scSignExtend: { 162 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this); 163 const SCEV *Op = SExt->getOperand(); 164 OS << "(sext " << *Op->getType() << " " << *Op << " to " 165 << *SExt->getType() << ")"; 166 return; 167 } 168 case scAddRecExpr: { 169 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this); 170 OS << "{" << *AR->getOperand(0); 171 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i) 172 OS << ",+," << *AR->getOperand(i); 173 OS << "}<"; 174 if (AR->getNoWrapFlags(FlagNUW)) 175 OS << "nuw><"; 176 if (AR->getNoWrapFlags(FlagNSW)) 177 OS << "nsw><"; 178 if (AR->getNoWrapFlags(FlagNW) && 179 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW))) 180 OS << "nw><"; 181 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false); 182 OS << ">"; 183 return; 184 } 185 case scAddExpr: 186 case scMulExpr: 187 case scUMaxExpr: 188 case scSMaxExpr: { 189 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this); 190 const char *OpStr = nullptr; 191 switch (NAry->getSCEVType()) { 192 case scAddExpr: OpStr = " + "; break; 193 case scMulExpr: OpStr = " * "; break; 194 case scUMaxExpr: OpStr = " umax "; break; 195 case scSMaxExpr: OpStr = " smax "; break; 196 } 197 OS << "("; 198 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 199 I != E; ++I) { 200 OS << **I; 201 if (std::next(I) != E) 202 OS << OpStr; 203 } 204 OS << ")"; 205 switch (NAry->getSCEVType()) { 206 case scAddExpr: 207 case scMulExpr: 208 if (NAry->getNoWrapFlags(FlagNUW)) 209 OS << "<nuw>"; 210 if (NAry->getNoWrapFlags(FlagNSW)) 211 OS << "<nsw>"; 212 } 213 return; 214 } 215 case scUDivExpr: { 216 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this); 217 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")"; 218 return; 219 } 220 case scUnknown: { 221 const SCEVUnknown *U = cast<SCEVUnknown>(this); 222 Type *AllocTy; 223 if (U->isSizeOf(AllocTy)) { 224 OS << "sizeof(" << *AllocTy << ")"; 225 return; 226 } 227 if (U->isAlignOf(AllocTy)) { 228 OS << "alignof(" << *AllocTy << ")"; 229 return; 230 } 231 232 Type *CTy; 233 Constant *FieldNo; 234 if (U->isOffsetOf(CTy, FieldNo)) { 235 OS << "offsetof(" << *CTy << ", "; 236 FieldNo->printAsOperand(OS, false); 237 OS << ")"; 238 return; 239 } 240 241 // Otherwise just print it normally. 242 U->getValue()->printAsOperand(OS, false); 243 return; 244 } 245 case scCouldNotCompute: 246 OS << "***COULDNOTCOMPUTE***"; 247 return; 248 } 249 llvm_unreachable("Unknown SCEV kind!"); 250 } 251 252 Type *SCEV::getType() const { 253 switch (static_cast<SCEVTypes>(getSCEVType())) { 254 case scConstant: 255 return cast<SCEVConstant>(this)->getType(); 256 case scTruncate: 257 case scZeroExtend: 258 case scSignExtend: 259 return cast<SCEVCastExpr>(this)->getType(); 260 case scAddRecExpr: 261 case scMulExpr: 262 case scUMaxExpr: 263 case scSMaxExpr: 264 return cast<SCEVNAryExpr>(this)->getType(); 265 case scAddExpr: 266 return cast<SCEVAddExpr>(this)->getType(); 267 case scUDivExpr: 268 return cast<SCEVUDivExpr>(this)->getType(); 269 case scUnknown: 270 return cast<SCEVUnknown>(this)->getType(); 271 case scCouldNotCompute: 272 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 273 } 274 llvm_unreachable("Unknown SCEV kind!"); 275 } 276 277 bool SCEV::isZero() const { 278 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 279 return SC->getValue()->isZero(); 280 return false; 281 } 282 283 bool SCEV::isOne() const { 284 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 285 return SC->getValue()->isOne(); 286 return false; 287 } 288 289 bool SCEV::isAllOnesValue() const { 290 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 291 return SC->getValue()->isAllOnesValue(); 292 return false; 293 } 294 295 /// isNonConstantNegative - Return true if the specified scev is negated, but 296 /// not a constant. 297 bool SCEV::isNonConstantNegative() const { 298 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this); 299 if (!Mul) return false; 300 301 // If there is a constant factor, it will be first. 302 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0)); 303 if (!SC) return false; 304 305 // Return true if the value is negative, this matches things like (-42 * V). 306 return SC->getValue()->getValue().isNegative(); 307 } 308 309 SCEVCouldNotCompute::SCEVCouldNotCompute() : 310 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {} 311 312 bool SCEVCouldNotCompute::classof(const SCEV *S) { 313 return S->getSCEVType() == scCouldNotCompute; 314 } 315 316 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 317 FoldingSetNodeID ID; 318 ID.AddInteger(scConstant); 319 ID.AddPointer(V); 320 void *IP = nullptr; 321 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 322 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V); 323 UniqueSCEVs.InsertNode(S, IP); 324 return S; 325 } 326 327 const SCEV *ScalarEvolution::getConstant(const APInt &Val) { 328 return getConstant(ConstantInt::get(getContext(), Val)); 329 } 330 331 const SCEV * 332 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) { 333 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 334 return getConstant(ConstantInt::get(ITy, V, isSigned)); 335 } 336 337 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, 338 unsigned SCEVTy, const SCEV *op, Type *ty) 339 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 340 341 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, 342 const SCEV *op, Type *ty) 343 : SCEVCastExpr(ID, scTruncate, op, ty) { 344 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 345 (Ty->isIntegerTy() || Ty->isPointerTy()) && 346 "Cannot truncate non-integer value!"); 347 } 348 349 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, 350 const SCEV *op, Type *ty) 351 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 352 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 353 (Ty->isIntegerTy() || Ty->isPointerTy()) && 354 "Cannot zero extend non-integer value!"); 355 } 356 357 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, 358 const SCEV *op, Type *ty) 359 : SCEVCastExpr(ID, scSignExtend, op, ty) { 360 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 361 (Ty->isIntegerTy() || Ty->isPointerTy()) && 362 "Cannot sign extend non-integer value!"); 363 } 364 365 void SCEVUnknown::deleted() { 366 // Clear this SCEVUnknown from various maps. 367 SE->forgetMemoizedResults(this); 368 369 // Remove this SCEVUnknown from the uniquing map. 370 SE->UniqueSCEVs.RemoveNode(this); 371 372 // Release the value. 373 setValPtr(nullptr); 374 } 375 376 void SCEVUnknown::allUsesReplacedWith(Value *New) { 377 // Clear this SCEVUnknown from various maps. 378 SE->forgetMemoizedResults(this); 379 380 // Remove this SCEVUnknown from the uniquing map. 381 SE->UniqueSCEVs.RemoveNode(this); 382 383 // Update this SCEVUnknown to point to the new value. This is needed 384 // because there may still be outstanding SCEVs which still point to 385 // this SCEVUnknown. 386 setValPtr(New); 387 } 388 389 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const { 390 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 391 if (VCE->getOpcode() == Instruction::PtrToInt) 392 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 393 if (CE->getOpcode() == Instruction::GetElementPtr && 394 CE->getOperand(0)->isNullValue() && 395 CE->getNumOperands() == 2) 396 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 397 if (CI->isOne()) { 398 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 399 ->getElementType(); 400 return true; 401 } 402 403 return false; 404 } 405 406 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const { 407 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 408 if (VCE->getOpcode() == Instruction::PtrToInt) 409 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 410 if (CE->getOpcode() == Instruction::GetElementPtr && 411 CE->getOperand(0)->isNullValue()) { 412 Type *Ty = 413 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 414 if (StructType *STy = dyn_cast<StructType>(Ty)) 415 if (!STy->isPacked() && 416 CE->getNumOperands() == 3 && 417 CE->getOperand(1)->isNullValue()) { 418 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 419 if (CI->isOne() && 420 STy->getNumElements() == 2 && 421 STy->getElementType(0)->isIntegerTy(1)) { 422 AllocTy = STy->getElementType(1); 423 return true; 424 } 425 } 426 } 427 428 return false; 429 } 430 431 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const { 432 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 433 if (VCE->getOpcode() == Instruction::PtrToInt) 434 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 435 if (CE->getOpcode() == Instruction::GetElementPtr && 436 CE->getNumOperands() == 3 && 437 CE->getOperand(0)->isNullValue() && 438 CE->getOperand(1)->isNullValue()) { 439 Type *Ty = 440 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 441 // Ignore vector types here so that ScalarEvolutionExpander doesn't 442 // emit getelementptrs that index into vectors. 443 if (Ty->isStructTy() || Ty->isArrayTy()) { 444 CTy = Ty; 445 FieldNo = CE->getOperand(2); 446 return true; 447 } 448 } 449 450 return false; 451 } 452 453 //===----------------------------------------------------------------------===// 454 // SCEV Utilities 455 //===----------------------------------------------------------------------===// 456 457 namespace { 458 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 459 /// than the complexity of the RHS. This comparator is used to canonicalize 460 /// expressions. 461 class SCEVComplexityCompare { 462 const LoopInfo *const LI; 463 public: 464 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {} 465 466 // Return true or false if LHS is less than, or at least RHS, respectively. 467 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 468 return compare(LHS, RHS) < 0; 469 } 470 471 // Return negative, zero, or positive, if LHS is less than, equal to, or 472 // greater than RHS, respectively. A three-way result allows recursive 473 // comparisons to be more efficient. 474 int compare(const SCEV *LHS, const SCEV *RHS) const { 475 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 476 if (LHS == RHS) 477 return 0; 478 479 // Primarily, sort the SCEVs by their getSCEVType(). 480 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); 481 if (LType != RType) 482 return (int)LType - (int)RType; 483 484 // Aside from the getSCEVType() ordering, the particular ordering 485 // isn't very important except that it's beneficial to be consistent, 486 // so that (a + b) and (b + a) don't end up as different expressions. 487 switch (static_cast<SCEVTypes>(LType)) { 488 case scUnknown: { 489 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS); 490 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 491 492 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 493 // not as complete as it could be. 494 const Value *LV = LU->getValue(), *RV = RU->getValue(); 495 496 // Order pointer values after integer values. This helps SCEVExpander 497 // form GEPs. 498 bool LIsPointer = LV->getType()->isPointerTy(), 499 RIsPointer = RV->getType()->isPointerTy(); 500 if (LIsPointer != RIsPointer) 501 return (int)LIsPointer - (int)RIsPointer; 502 503 // Compare getValueID values. 504 unsigned LID = LV->getValueID(), 505 RID = RV->getValueID(); 506 if (LID != RID) 507 return (int)LID - (int)RID; 508 509 // Sort arguments by their position. 510 if (const Argument *LA = dyn_cast<Argument>(LV)) { 511 const Argument *RA = cast<Argument>(RV); 512 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo(); 513 return (int)LArgNo - (int)RArgNo; 514 } 515 516 // For instructions, compare their loop depth, and their operand 517 // count. This is pretty loose. 518 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) { 519 const Instruction *RInst = cast<Instruction>(RV); 520 521 // Compare loop depths. 522 const BasicBlock *LParent = LInst->getParent(), 523 *RParent = RInst->getParent(); 524 if (LParent != RParent) { 525 unsigned LDepth = LI->getLoopDepth(LParent), 526 RDepth = LI->getLoopDepth(RParent); 527 if (LDepth != RDepth) 528 return (int)LDepth - (int)RDepth; 529 } 530 531 // Compare the number of operands. 532 unsigned LNumOps = LInst->getNumOperands(), 533 RNumOps = RInst->getNumOperands(); 534 return (int)LNumOps - (int)RNumOps; 535 } 536 537 return 0; 538 } 539 540 case scConstant: { 541 const SCEVConstant *LC = cast<SCEVConstant>(LHS); 542 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 543 544 // Compare constant values. 545 const APInt &LA = LC->getValue()->getValue(); 546 const APInt &RA = RC->getValue()->getValue(); 547 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth(); 548 if (LBitWidth != RBitWidth) 549 return (int)LBitWidth - (int)RBitWidth; 550 return LA.ult(RA) ? -1 : 1; 551 } 552 553 case scAddRecExpr: { 554 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS); 555 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 556 557 // Compare addrec loop depths. 558 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop(); 559 if (LLoop != RLoop) { 560 unsigned LDepth = LLoop->getLoopDepth(), 561 RDepth = RLoop->getLoopDepth(); 562 if (LDepth != RDepth) 563 return (int)LDepth - (int)RDepth; 564 } 565 566 // Addrec complexity grows with operand count. 567 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands(); 568 if (LNumOps != RNumOps) 569 return (int)LNumOps - (int)RNumOps; 570 571 // Lexicographically compare. 572 for (unsigned i = 0; i != LNumOps; ++i) { 573 long X = compare(LA->getOperand(i), RA->getOperand(i)); 574 if (X != 0) 575 return X; 576 } 577 578 return 0; 579 } 580 581 case scAddExpr: 582 case scMulExpr: 583 case scSMaxExpr: 584 case scUMaxExpr: { 585 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS); 586 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 587 588 // Lexicographically compare n-ary expressions. 589 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands(); 590 if (LNumOps != RNumOps) 591 return (int)LNumOps - (int)RNumOps; 592 593 for (unsigned i = 0; i != LNumOps; ++i) { 594 if (i >= RNumOps) 595 return 1; 596 long X = compare(LC->getOperand(i), RC->getOperand(i)); 597 if (X != 0) 598 return X; 599 } 600 return (int)LNumOps - (int)RNumOps; 601 } 602 603 case scUDivExpr: { 604 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS); 605 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 606 607 // Lexicographically compare udiv expressions. 608 long X = compare(LC->getLHS(), RC->getLHS()); 609 if (X != 0) 610 return X; 611 return compare(LC->getRHS(), RC->getRHS()); 612 } 613 614 case scTruncate: 615 case scZeroExtend: 616 case scSignExtend: { 617 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS); 618 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 619 620 // Compare cast expressions by operand. 621 return compare(LC->getOperand(), RC->getOperand()); 622 } 623 624 case scCouldNotCompute: 625 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 626 } 627 llvm_unreachable("Unknown SCEV kind!"); 628 } 629 }; 630 } 631 632 /// GroupByComplexity - Given a list of SCEV objects, order them by their 633 /// complexity, and group objects of the same complexity together by value. 634 /// When this routine is finished, we know that any duplicates in the vector are 635 /// consecutive and that complexity is monotonically increasing. 636 /// 637 /// Note that we go take special precautions to ensure that we get deterministic 638 /// results from this routine. In other words, we don't want the results of 639 /// this to depend on where the addresses of various SCEV objects happened to 640 /// land in memory. 641 /// 642 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 643 LoopInfo *LI) { 644 if (Ops.size() < 2) return; // Noop 645 if (Ops.size() == 2) { 646 // This is the common case, which also happens to be trivially simple. 647 // Special case it. 648 const SCEV *&LHS = Ops[0], *&RHS = Ops[1]; 649 if (SCEVComplexityCompare(LI)(RHS, LHS)) 650 std::swap(LHS, RHS); 651 return; 652 } 653 654 // Do the rough sort by complexity. 655 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 656 657 // Now that we are sorted by complexity, group elements of the same 658 // complexity. Note that this is, at worst, N^2, but the vector is likely to 659 // be extremely short in practice. Note that we take this approach because we 660 // do not want to depend on the addresses of the objects we are grouping. 661 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 662 const SCEV *S = Ops[i]; 663 unsigned Complexity = S->getSCEVType(); 664 665 // If there are any objects of the same complexity and same value as this 666 // one, group them. 667 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 668 if (Ops[j] == S) { // Found a duplicate. 669 // Move it to immediately after i'th element. 670 std::swap(Ops[i+1], Ops[j]); 671 ++i; // no need to rescan it. 672 if (i == e-2) return; // Done! 673 } 674 } 675 } 676 } 677 678 namespace { 679 struct FindSCEVSize { 680 int Size; 681 FindSCEVSize() : Size(0) {} 682 683 bool follow(const SCEV *S) { 684 ++Size; 685 // Keep looking at all operands of S. 686 return true; 687 } 688 bool isDone() const { 689 return false; 690 } 691 }; 692 } 693 694 // Returns the size of the SCEV S. 695 static inline int sizeOfSCEV(const SCEV *S) { 696 FindSCEVSize F; 697 SCEVTraversal<FindSCEVSize> ST(F); 698 ST.visitAll(S); 699 return F.Size; 700 } 701 702 namespace { 703 704 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> { 705 public: 706 // Computes the Quotient and Remainder of the division of Numerator by 707 // Denominator. 708 static void divide(ScalarEvolution &SE, const SCEV *Numerator, 709 const SCEV *Denominator, const SCEV **Quotient, 710 const SCEV **Remainder) { 711 assert(Numerator && Denominator && "Uninitialized SCEV"); 712 713 SCEVDivision D(SE, Numerator, Denominator); 714 715 // Check for the trivial case here to avoid having to check for it in the 716 // rest of the code. 717 if (Numerator == Denominator) { 718 *Quotient = D.One; 719 *Remainder = D.Zero; 720 return; 721 } 722 723 if (Numerator->isZero()) { 724 *Quotient = D.Zero; 725 *Remainder = D.Zero; 726 return; 727 } 728 729 // Split the Denominator when it is a product. 730 if (const SCEVMulExpr *T = dyn_cast<const SCEVMulExpr>(Denominator)) { 731 const SCEV *Q, *R; 732 *Quotient = Numerator; 733 for (const SCEV *Op : T->operands()) { 734 divide(SE, *Quotient, Op, &Q, &R); 735 *Quotient = Q; 736 737 // Bail out when the Numerator is not divisible by one of the terms of 738 // the Denominator. 739 if (!R->isZero()) { 740 *Quotient = D.Zero; 741 *Remainder = Numerator; 742 return; 743 } 744 } 745 *Remainder = D.Zero; 746 return; 747 } 748 749 D.visit(Numerator); 750 *Quotient = D.Quotient; 751 *Remainder = D.Remainder; 752 } 753 754 // Except in the trivial case described above, we do not know how to divide 755 // Expr by Denominator for the following functions with empty implementation. 756 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {} 757 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {} 758 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {} 759 void visitUDivExpr(const SCEVUDivExpr *Numerator) {} 760 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {} 761 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {} 762 void visitUnknown(const SCEVUnknown *Numerator) {} 763 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {} 764 765 void visitConstant(const SCEVConstant *Numerator) { 766 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) { 767 APInt NumeratorVal = Numerator->getValue()->getValue(); 768 APInt DenominatorVal = D->getValue()->getValue(); 769 uint32_t NumeratorBW = NumeratorVal.getBitWidth(); 770 uint32_t DenominatorBW = DenominatorVal.getBitWidth(); 771 772 if (NumeratorBW > DenominatorBW) 773 DenominatorVal = DenominatorVal.sext(NumeratorBW); 774 else if (NumeratorBW < DenominatorBW) 775 NumeratorVal = NumeratorVal.sext(DenominatorBW); 776 777 APInt QuotientVal(NumeratorVal.getBitWidth(), 0); 778 APInt RemainderVal(NumeratorVal.getBitWidth(), 0); 779 APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal); 780 Quotient = SE.getConstant(QuotientVal); 781 Remainder = SE.getConstant(RemainderVal); 782 return; 783 } 784 } 785 786 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) { 787 const SCEV *StartQ, *StartR, *StepQ, *StepR; 788 assert(Numerator->isAffine() && "Numerator should be affine"); 789 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR); 790 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR); 791 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(), 792 Numerator->getNoWrapFlags()); 793 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(), 794 Numerator->getNoWrapFlags()); 795 } 796 797 void visitAddExpr(const SCEVAddExpr *Numerator) { 798 SmallVector<const SCEV *, 2> Qs, Rs; 799 Type *Ty = Denominator->getType(); 800 801 for (const SCEV *Op : Numerator->operands()) { 802 const SCEV *Q, *R; 803 divide(SE, Op, Denominator, &Q, &R); 804 805 // Bail out if types do not match. 806 if (Ty != Q->getType() || Ty != R->getType()) { 807 Quotient = Zero; 808 Remainder = Numerator; 809 return; 810 } 811 812 Qs.push_back(Q); 813 Rs.push_back(R); 814 } 815 816 if (Qs.size() == 1) { 817 Quotient = Qs[0]; 818 Remainder = Rs[0]; 819 return; 820 } 821 822 Quotient = SE.getAddExpr(Qs); 823 Remainder = SE.getAddExpr(Rs); 824 } 825 826 void visitMulExpr(const SCEVMulExpr *Numerator) { 827 SmallVector<const SCEV *, 2> Qs; 828 Type *Ty = Denominator->getType(); 829 830 bool FoundDenominatorTerm = false; 831 for (const SCEV *Op : Numerator->operands()) { 832 // Bail out if types do not match. 833 if (Ty != Op->getType()) { 834 Quotient = Zero; 835 Remainder = Numerator; 836 return; 837 } 838 839 if (FoundDenominatorTerm) { 840 Qs.push_back(Op); 841 continue; 842 } 843 844 // Check whether Denominator divides one of the product operands. 845 const SCEV *Q, *R; 846 divide(SE, Op, Denominator, &Q, &R); 847 if (!R->isZero()) { 848 Qs.push_back(Op); 849 continue; 850 } 851 852 // Bail out if types do not match. 853 if (Ty != Q->getType()) { 854 Quotient = Zero; 855 Remainder = Numerator; 856 return; 857 } 858 859 FoundDenominatorTerm = true; 860 Qs.push_back(Q); 861 } 862 863 if (FoundDenominatorTerm) { 864 Remainder = Zero; 865 if (Qs.size() == 1) 866 Quotient = Qs[0]; 867 else 868 Quotient = SE.getMulExpr(Qs); 869 return; 870 } 871 872 if (!isa<SCEVUnknown>(Denominator)) { 873 Quotient = Zero; 874 Remainder = Numerator; 875 return; 876 } 877 878 // The Remainder is obtained by replacing Denominator by 0 in Numerator. 879 ValueToValueMap RewriteMap; 880 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] = 881 cast<SCEVConstant>(Zero)->getValue(); 882 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true); 883 884 if (Remainder->isZero()) { 885 // The Quotient is obtained by replacing Denominator by 1 in Numerator. 886 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] = 887 cast<SCEVConstant>(One)->getValue(); 888 Quotient = 889 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true); 890 return; 891 } 892 893 // Quotient is (Numerator - Remainder) divided by Denominator. 894 const SCEV *Q, *R; 895 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder); 896 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator)) { 897 // This SCEV does not seem to simplify: fail the division here. 898 Quotient = Zero; 899 Remainder = Numerator; 900 return; 901 } 902 divide(SE, Diff, Denominator, &Q, &R); 903 assert(R == Zero && 904 "(Numerator - Remainder) should evenly divide Denominator"); 905 Quotient = Q; 906 } 907 908 private: 909 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator, 910 const SCEV *Denominator) 911 : SE(S), Denominator(Denominator) { 912 Zero = SE.getConstant(Denominator->getType(), 0); 913 One = SE.getConstant(Denominator->getType(), 1); 914 915 // By default, we don't know how to divide Expr by Denominator. 916 // Providing the default here simplifies the rest of the code. 917 Quotient = Zero; 918 Remainder = Numerator; 919 } 920 921 ScalarEvolution &SE; 922 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One; 923 }; 924 925 } 926 927 //===----------------------------------------------------------------------===// 928 // Simple SCEV method implementations 929 //===----------------------------------------------------------------------===// 930 931 /// BinomialCoefficient - Compute BC(It, K). The result has width W. 932 /// Assume, K > 0. 933 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 934 ScalarEvolution &SE, 935 Type *ResultTy) { 936 // Handle the simplest case efficiently. 937 if (K == 1) 938 return SE.getTruncateOrZeroExtend(It, ResultTy); 939 940 // We are using the following formula for BC(It, K): 941 // 942 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 943 // 944 // Suppose, W is the bitwidth of the return value. We must be prepared for 945 // overflow. Hence, we must assure that the result of our computation is 946 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 947 // safe in modular arithmetic. 948 // 949 // However, this code doesn't use exactly that formula; the formula it uses 950 // is something like the following, where T is the number of factors of 2 in 951 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 952 // exponentiation: 953 // 954 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 955 // 956 // This formula is trivially equivalent to the previous formula. However, 957 // this formula can be implemented much more efficiently. The trick is that 958 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 959 // arithmetic. To do exact division in modular arithmetic, all we have 960 // to do is multiply by the inverse. Therefore, this step can be done at 961 // width W. 962 // 963 // The next issue is how to safely do the division by 2^T. The way this 964 // is done is by doing the multiplication step at a width of at least W + T 965 // bits. This way, the bottom W+T bits of the product are accurate. Then, 966 // when we perform the division by 2^T (which is equivalent to a right shift 967 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 968 // truncated out after the division by 2^T. 969 // 970 // In comparison to just directly using the first formula, this technique 971 // is much more efficient; using the first formula requires W * K bits, 972 // but this formula less than W + K bits. Also, the first formula requires 973 // a division step, whereas this formula only requires multiplies and shifts. 974 // 975 // It doesn't matter whether the subtraction step is done in the calculation 976 // width or the input iteration count's width; if the subtraction overflows, 977 // the result must be zero anyway. We prefer here to do it in the width of 978 // the induction variable because it helps a lot for certain cases; CodeGen 979 // isn't smart enough to ignore the overflow, which leads to much less 980 // efficient code if the width of the subtraction is wider than the native 981 // register width. 982 // 983 // (It's possible to not widen at all by pulling out factors of 2 before 984 // the multiplication; for example, K=2 can be calculated as 985 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 986 // extra arithmetic, so it's not an obvious win, and it gets 987 // much more complicated for K > 3.) 988 989 // Protection from insane SCEVs; this bound is conservative, 990 // but it probably doesn't matter. 991 if (K > 1000) 992 return SE.getCouldNotCompute(); 993 994 unsigned W = SE.getTypeSizeInBits(ResultTy); 995 996 // Calculate K! / 2^T and T; we divide out the factors of two before 997 // multiplying for calculating K! / 2^T to avoid overflow. 998 // Other overflow doesn't matter because we only care about the bottom 999 // W bits of the result. 1000 APInt OddFactorial(W, 1); 1001 unsigned T = 1; 1002 for (unsigned i = 3; i <= K; ++i) { 1003 APInt Mult(W, i); 1004 unsigned TwoFactors = Mult.countTrailingZeros(); 1005 T += TwoFactors; 1006 Mult = Mult.lshr(TwoFactors); 1007 OddFactorial *= Mult; 1008 } 1009 1010 // We need at least W + T bits for the multiplication step 1011 unsigned CalculationBits = W + T; 1012 1013 // Calculate 2^T, at width T+W. 1014 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T); 1015 1016 // Calculate the multiplicative inverse of K! / 2^T; 1017 // this multiplication factor will perform the exact division by 1018 // K! / 2^T. 1019 APInt Mod = APInt::getSignedMinValue(W+1); 1020 APInt MultiplyFactor = OddFactorial.zext(W+1); 1021 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 1022 MultiplyFactor = MultiplyFactor.trunc(W); 1023 1024 // Calculate the product, at width T+W 1025 IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 1026 CalculationBits); 1027 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 1028 for (unsigned i = 1; i != K; ++i) { 1029 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); 1030 Dividend = SE.getMulExpr(Dividend, 1031 SE.getTruncateOrZeroExtend(S, CalculationTy)); 1032 } 1033 1034 // Divide by 2^T 1035 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 1036 1037 // Truncate the result, and divide by K! / 2^T. 1038 1039 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 1040 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 1041 } 1042 1043 /// evaluateAtIteration - Return the value of this chain of recurrences at 1044 /// the specified iteration number. We can evaluate this recurrence by 1045 /// multiplying each element in the chain by the binomial coefficient 1046 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 1047 /// 1048 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 1049 /// 1050 /// where BC(It, k) stands for binomial coefficient. 1051 /// 1052 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 1053 ScalarEvolution &SE) const { 1054 const SCEV *Result = getStart(); 1055 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 1056 // The computation is correct in the face of overflow provided that the 1057 // multiplication is performed _after_ the evaluation of the binomial 1058 // coefficient. 1059 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 1060 if (isa<SCEVCouldNotCompute>(Coeff)) 1061 return Coeff; 1062 1063 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 1064 } 1065 return Result; 1066 } 1067 1068 //===----------------------------------------------------------------------===// 1069 // SCEV Expression folder implementations 1070 //===----------------------------------------------------------------------===// 1071 1072 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 1073 Type *Ty) { 1074 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 1075 "This is not a truncating conversion!"); 1076 assert(isSCEVable(Ty) && 1077 "This is not a conversion to a SCEVable type!"); 1078 Ty = getEffectiveSCEVType(Ty); 1079 1080 FoldingSetNodeID ID; 1081 ID.AddInteger(scTruncate); 1082 ID.AddPointer(Op); 1083 ID.AddPointer(Ty); 1084 void *IP = nullptr; 1085 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1086 1087 // Fold if the operand is constant. 1088 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1089 return getConstant( 1090 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty))); 1091 1092 // trunc(trunc(x)) --> trunc(x) 1093 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 1094 return getTruncateExpr(ST->getOperand(), Ty); 1095 1096 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 1097 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1098 return getTruncateOrSignExtend(SS->getOperand(), Ty); 1099 1100 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 1101 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 1102 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 1103 1104 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can 1105 // eliminate all the truncates, or we replace other casts with truncates. 1106 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) { 1107 SmallVector<const SCEV *, 4> Operands; 1108 bool hasTrunc = false; 1109 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) { 1110 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty); 1111 if (!isa<SCEVCastExpr>(SA->getOperand(i))) 1112 hasTrunc = isa<SCEVTruncateExpr>(S); 1113 Operands.push_back(S); 1114 } 1115 if (!hasTrunc) 1116 return getAddExpr(Operands); 1117 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL. 1118 } 1119 1120 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can 1121 // eliminate all the truncates, or we replace other casts with truncates. 1122 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) { 1123 SmallVector<const SCEV *, 4> Operands; 1124 bool hasTrunc = false; 1125 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) { 1126 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty); 1127 if (!isa<SCEVCastExpr>(SM->getOperand(i))) 1128 hasTrunc = isa<SCEVTruncateExpr>(S); 1129 Operands.push_back(S); 1130 } 1131 if (!hasTrunc) 1132 return getMulExpr(Operands); 1133 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL. 1134 } 1135 1136 // If the input value is a chrec scev, truncate the chrec's operands. 1137 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 1138 SmallVector<const SCEV *, 4> Operands; 1139 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1140 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 1141 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap); 1142 } 1143 1144 // The cast wasn't folded; create an explicit cast node. We can reuse 1145 // the existing insert position since if we get here, we won't have 1146 // made any changes which would invalidate it. 1147 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 1148 Op, Ty); 1149 UniqueSCEVs.InsertNode(S, IP); 1150 return S; 1151 } 1152 1153 // Get the limit of a recurrence such that incrementing by Step cannot cause 1154 // signed overflow as long as the value of the recurrence within the 1155 // loop does not exceed this limit before incrementing. 1156 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step, 1157 ICmpInst::Predicate *Pred, 1158 ScalarEvolution *SE) { 1159 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType()); 1160 if (SE->isKnownPositive(Step)) { 1161 *Pred = ICmpInst::ICMP_SLT; 1162 return SE->getConstant(APInt::getSignedMinValue(BitWidth) - 1163 SE->getSignedRange(Step).getSignedMax()); 1164 } 1165 if (SE->isKnownNegative(Step)) { 1166 *Pred = ICmpInst::ICMP_SGT; 1167 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) - 1168 SE->getSignedRange(Step).getSignedMin()); 1169 } 1170 return nullptr; 1171 } 1172 1173 // Get the limit of a recurrence such that incrementing by Step cannot cause 1174 // unsigned overflow as long as the value of the recurrence within the loop does 1175 // not exceed this limit before incrementing. 1176 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step, 1177 ICmpInst::Predicate *Pred, 1178 ScalarEvolution *SE) { 1179 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType()); 1180 *Pred = ICmpInst::ICMP_ULT; 1181 1182 return SE->getConstant(APInt::getMinValue(BitWidth) - 1183 SE->getUnsignedRange(Step).getUnsignedMax()); 1184 } 1185 1186 namespace { 1187 1188 struct ExtendOpTraitsBase { 1189 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *); 1190 }; 1191 1192 // Used to make code generic over signed and unsigned overflow. 1193 template <typename ExtendOp> struct ExtendOpTraits { 1194 // Members present: 1195 // 1196 // static const SCEV::NoWrapFlags WrapType; 1197 // 1198 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr; 1199 // 1200 // static const SCEV *getOverflowLimitForStep(const SCEV *Step, 1201 // ICmpInst::Predicate *Pred, 1202 // ScalarEvolution *SE); 1203 }; 1204 1205 template <> 1206 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase { 1207 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW; 1208 1209 static const GetExtendExprTy GetExtendExpr; 1210 1211 static const SCEV *getOverflowLimitForStep(const SCEV *Step, 1212 ICmpInst::Predicate *Pred, 1213 ScalarEvolution *SE) { 1214 return getSignedOverflowLimitForStep(Step, Pred, SE); 1215 } 1216 }; 1217 1218 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits< 1219 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr; 1220 1221 template <> 1222 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase { 1223 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW; 1224 1225 static const GetExtendExprTy GetExtendExpr; 1226 1227 static const SCEV *getOverflowLimitForStep(const SCEV *Step, 1228 ICmpInst::Predicate *Pred, 1229 ScalarEvolution *SE) { 1230 return getUnsignedOverflowLimitForStep(Step, Pred, SE); 1231 } 1232 }; 1233 1234 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits< 1235 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr; 1236 } 1237 1238 // The recurrence AR has been shown to have no signed/unsigned wrap or something 1239 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as 1240 // easily prove NSW/NUW for its preincrement or postincrement sibling. This 1241 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step + 1242 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the 1243 // expression "Step + sext/zext(PreIncAR)" is congruent with 1244 // "sext/zext(PostIncAR)" 1245 template <typename ExtendOpTy> 1246 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty, 1247 ScalarEvolution *SE) { 1248 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType; 1249 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr; 1250 1251 const Loop *L = AR->getLoop(); 1252 const SCEV *Start = AR->getStart(); 1253 const SCEV *Step = AR->getStepRecurrence(*SE); 1254 1255 // Check for a simple looking step prior to loop entry. 1256 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start); 1257 if (!SA) 1258 return nullptr; 1259 1260 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV 1261 // subtraction is expensive. For this purpose, perform a quick and dirty 1262 // difference, by checking for Step in the operand list. 1263 SmallVector<const SCEV *, 4> DiffOps; 1264 for (const SCEV *Op : SA->operands()) 1265 if (Op != Step) 1266 DiffOps.push_back(Op); 1267 1268 if (DiffOps.size() == SA->getNumOperands()) 1269 return nullptr; 1270 1271 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` + 1272 // `Step`: 1273 1274 // 1. NSW/NUW flags on the step increment. 1275 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags()); 1276 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>( 1277 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap)); 1278 1279 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies 1280 // "S+X does not sign/unsign-overflow". 1281 // 1282 1283 const SCEV *BECount = SE->getBackedgeTakenCount(L); 1284 if (PreAR && PreAR->getNoWrapFlags(WrapType) && 1285 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount)) 1286 return PreStart; 1287 1288 // 2. Direct overflow check on the step operation's expression. 1289 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType()); 1290 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2); 1291 const SCEV *OperandExtendedStart = 1292 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy), 1293 (SE->*GetExtendExpr)(Step, WideTy)); 1294 if ((SE->*GetExtendExpr)(Start, WideTy) == OperandExtendedStart) { 1295 if (PreAR && AR->getNoWrapFlags(WrapType)) { 1296 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW 1297 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then 1298 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact. 1299 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType); 1300 } 1301 return PreStart; 1302 } 1303 1304 // 3. Loop precondition. 1305 ICmpInst::Predicate Pred; 1306 const SCEV *OverflowLimit = 1307 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE); 1308 1309 if (OverflowLimit && 1310 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) { 1311 return PreStart; 1312 } 1313 return nullptr; 1314 } 1315 1316 // Get the normalized zero or sign extended expression for this AddRec's Start. 1317 template <typename ExtendOpTy> 1318 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty, 1319 ScalarEvolution *SE) { 1320 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr; 1321 1322 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE); 1323 if (!PreStart) 1324 return (SE->*GetExtendExpr)(AR->getStart(), Ty); 1325 1326 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty), 1327 (SE->*GetExtendExpr)(PreStart, Ty)); 1328 } 1329 1330 // Try to prove away overflow by looking at "nearby" add recurrences. A 1331 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it 1332 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`. 1333 // 1334 // Formally: 1335 // 1336 // {S,+,X} == {S-T,+,X} + T 1337 // => Ext({S,+,X}) == Ext({S-T,+,X} + T) 1338 // 1339 // If ({S-T,+,X} + T) does not overflow ... (1) 1340 // 1341 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T) 1342 // 1343 // If {S-T,+,X} does not overflow ... (2) 1344 // 1345 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T) 1346 // == {Ext(S-T)+Ext(T),+,Ext(X)} 1347 // 1348 // If (S-T)+T does not overflow ... (3) 1349 // 1350 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)} 1351 // == {Ext(S),+,Ext(X)} == LHS 1352 // 1353 // Thus, if (1), (2) and (3) are true for some T, then 1354 // Ext({S,+,X}) == {Ext(S),+,Ext(X)} 1355 // 1356 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T) 1357 // does not overflow" restricted to the 0th iteration. Therefore we only need 1358 // to check for (1) and (2). 1359 // 1360 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T 1361 // is `Delta` (defined below). 1362 // 1363 template <typename ExtendOpTy> 1364 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start, 1365 const SCEV *Step, 1366 const Loop *L) { 1367 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType; 1368 1369 // We restrict `Start` to a constant to prevent SCEV from spending too much 1370 // time here. It is correct (but more expensive) to continue with a 1371 // non-constant `Start` and do a general SCEV subtraction to compute 1372 // `PreStart` below. 1373 // 1374 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start); 1375 if (!StartC) 1376 return false; 1377 1378 APInt StartAI = StartC->getValue()->getValue(); 1379 1380 for (unsigned Delta : {-2, -1, 1, 2}) { 1381 const SCEV *PreStart = getConstant(StartAI - Delta); 1382 1383 // Give up if we don't already have the add recurrence we need because 1384 // actually constructing an add recurrence is relatively expensive. 1385 const SCEVAddRecExpr *PreAR = [&]() { 1386 FoldingSetNodeID ID; 1387 ID.AddInteger(scAddRecExpr); 1388 ID.AddPointer(PreStart); 1389 ID.AddPointer(Step); 1390 ID.AddPointer(L); 1391 void *IP = nullptr; 1392 return static_cast<SCEVAddRecExpr *>( 1393 this->UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1394 }(); 1395 1396 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2) 1397 const SCEV *DeltaS = getConstant(StartC->getType(), Delta); 1398 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE; 1399 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep( 1400 DeltaS, &Pred, this); 1401 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1) 1402 return true; 1403 } 1404 } 1405 1406 return false; 1407 } 1408 1409 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 1410 Type *Ty) { 1411 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1412 "This is not an extending conversion!"); 1413 assert(isSCEVable(Ty) && 1414 "This is not a conversion to a SCEVable type!"); 1415 Ty = getEffectiveSCEVType(Ty); 1416 1417 // Fold if the operand is constant. 1418 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1419 return getConstant( 1420 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty))); 1421 1422 // zext(zext(x)) --> zext(x) 1423 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 1424 return getZeroExtendExpr(SZ->getOperand(), Ty); 1425 1426 // Before doing any expensive analysis, check to see if we've already 1427 // computed a SCEV for this Op and Ty. 1428 FoldingSetNodeID ID; 1429 ID.AddInteger(scZeroExtend); 1430 ID.AddPointer(Op); 1431 ID.AddPointer(Ty); 1432 void *IP = nullptr; 1433 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1434 1435 // zext(trunc(x)) --> zext(x) or x or trunc(x) 1436 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 1437 // It's possible the bits taken off by the truncate were all zero bits. If 1438 // so, we should be able to simplify this further. 1439 const SCEV *X = ST->getOperand(); 1440 ConstantRange CR = getUnsignedRange(X); 1441 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 1442 unsigned NewBits = getTypeSizeInBits(Ty); 1443 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains( 1444 CR.zextOrTrunc(NewBits))) 1445 return getTruncateOrZeroExtend(X, Ty); 1446 } 1447 1448 // If the input value is a chrec scev, and we can prove that the value 1449 // did not overflow the old, smaller, value, we can zero extend all of the 1450 // operands (often constants). This allows analysis of something like 1451 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 1452 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1453 if (AR->isAffine()) { 1454 const SCEV *Start = AR->getStart(); 1455 const SCEV *Step = AR->getStepRecurrence(*this); 1456 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1457 const Loop *L = AR->getLoop(); 1458 1459 // If we have special knowledge that this addrec won't overflow, 1460 // we don't need to do any further analysis. 1461 if (AR->getNoWrapFlags(SCEV::FlagNUW)) 1462 return getAddRecExpr( 1463 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this), 1464 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); 1465 1466 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1467 // Note that this serves two purposes: It filters out loops that are 1468 // simply not analyzable, and it covers the case where this code is 1469 // being called from within backedge-taken count analysis, such that 1470 // attempting to ask for the backedge-taken count would likely result 1471 // in infinite recursion. In the later case, the analysis code will 1472 // cope with a conservative value, and it will take care to purge 1473 // that value once it has finished. 1474 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1475 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1476 // Manually compute the final value for AR, checking for 1477 // overflow. 1478 1479 // Check whether the backedge-taken count can be losslessly casted to 1480 // the addrec's type. The count is always unsigned. 1481 const SCEV *CastedMaxBECount = 1482 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1483 const SCEV *RecastedMaxBECount = 1484 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1485 if (MaxBECount == RecastedMaxBECount) { 1486 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1487 // Check whether Start+Step*MaxBECount has no unsigned overflow. 1488 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); 1489 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy); 1490 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy); 1491 const SCEV *WideMaxBECount = 1492 getZeroExtendExpr(CastedMaxBECount, WideTy); 1493 const SCEV *OperandExtendedAdd = 1494 getAddExpr(WideStart, 1495 getMulExpr(WideMaxBECount, 1496 getZeroExtendExpr(Step, WideTy))); 1497 if (ZAdd == OperandExtendedAdd) { 1498 // Cache knowledge of AR NUW, which is propagated to this AddRec. 1499 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); 1500 // Return the expression with the addrec on the outside. 1501 return getAddRecExpr( 1502 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this), 1503 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); 1504 } 1505 // Similar to above, only this time treat the step value as signed. 1506 // This covers loops that count down. 1507 OperandExtendedAdd = 1508 getAddExpr(WideStart, 1509 getMulExpr(WideMaxBECount, 1510 getSignExtendExpr(Step, WideTy))); 1511 if (ZAdd == OperandExtendedAdd) { 1512 // Cache knowledge of AR NW, which is propagated to this AddRec. 1513 // Negative step causes unsigned wrap, but it still can't self-wrap. 1514 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); 1515 // Return the expression with the addrec on the outside. 1516 return getAddRecExpr( 1517 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this), 1518 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); 1519 } 1520 } 1521 1522 // If the backedge is guarded by a comparison with the pre-inc value 1523 // the addrec is safe. Also, if the entry is guarded by a comparison 1524 // with the start value and the backedge is guarded by a comparison 1525 // with the post-inc value, the addrec is safe. 1526 if (isKnownPositive(Step)) { 1527 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 1528 getUnsignedRange(Step).getUnsignedMax()); 1529 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 1530 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 1531 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 1532 AR->getPostIncExpr(*this), N))) { 1533 // Cache knowledge of AR NUW, which is propagated to this AddRec. 1534 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); 1535 // Return the expression with the addrec on the outside. 1536 return getAddRecExpr( 1537 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this), 1538 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); 1539 } 1540 } else if (isKnownNegative(Step)) { 1541 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 1542 getSignedRange(Step).getSignedMin()); 1543 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || 1544 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) && 1545 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 1546 AR->getPostIncExpr(*this), N))) { 1547 // Cache knowledge of AR NW, which is propagated to this AddRec. 1548 // Negative step causes unsigned wrap, but it still can't self-wrap. 1549 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); 1550 // Return the expression with the addrec on the outside. 1551 return getAddRecExpr( 1552 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this), 1553 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); 1554 } 1555 } 1556 } 1557 1558 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) { 1559 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); 1560 return getAddRecExpr( 1561 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this), 1562 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); 1563 } 1564 } 1565 1566 // The cast wasn't folded; create an explicit cast node. 1567 // Recompute the insert position, as it may have been invalidated. 1568 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1569 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 1570 Op, Ty); 1571 UniqueSCEVs.InsertNode(S, IP); 1572 return S; 1573 } 1574 1575 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 1576 Type *Ty) { 1577 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1578 "This is not an extending conversion!"); 1579 assert(isSCEVable(Ty) && 1580 "This is not a conversion to a SCEVable type!"); 1581 Ty = getEffectiveSCEVType(Ty); 1582 1583 // Fold if the operand is constant. 1584 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1585 return getConstant( 1586 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty))); 1587 1588 // sext(sext(x)) --> sext(x) 1589 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1590 return getSignExtendExpr(SS->getOperand(), Ty); 1591 1592 // sext(zext(x)) --> zext(x) 1593 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 1594 return getZeroExtendExpr(SZ->getOperand(), Ty); 1595 1596 // Before doing any expensive analysis, check to see if we've already 1597 // computed a SCEV for this Op and Ty. 1598 FoldingSetNodeID ID; 1599 ID.AddInteger(scSignExtend); 1600 ID.AddPointer(Op); 1601 ID.AddPointer(Ty); 1602 void *IP = nullptr; 1603 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1604 1605 // If the input value is provably positive, build a zext instead. 1606 if (isKnownNonNegative(Op)) 1607 return getZeroExtendExpr(Op, Ty); 1608 1609 // sext(trunc(x)) --> sext(x) or x or trunc(x) 1610 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 1611 // It's possible the bits taken off by the truncate were all sign bits. If 1612 // so, we should be able to simplify this further. 1613 const SCEV *X = ST->getOperand(); 1614 ConstantRange CR = getSignedRange(X); 1615 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 1616 unsigned NewBits = getTypeSizeInBits(Ty); 1617 if (CR.truncate(TruncBits).signExtend(NewBits).contains( 1618 CR.sextOrTrunc(NewBits))) 1619 return getTruncateOrSignExtend(X, Ty); 1620 } 1621 1622 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2 1623 if (auto SA = dyn_cast<SCEVAddExpr>(Op)) { 1624 if (SA->getNumOperands() == 2) { 1625 auto SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0)); 1626 auto SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1)); 1627 if (SMul && SC1) { 1628 if (auto SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) { 1629 const APInt &C1 = SC1->getValue()->getValue(); 1630 const APInt &C2 = SC2->getValue()->getValue(); 1631 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && 1632 C2.ugt(C1) && C2.isPowerOf2()) 1633 return getAddExpr(getSignExtendExpr(SC1, Ty), 1634 getSignExtendExpr(SMul, Ty)); 1635 } 1636 } 1637 } 1638 } 1639 // If the input value is a chrec scev, and we can prove that the value 1640 // did not overflow the old, smaller, value, we can sign extend all of the 1641 // operands (often constants). This allows analysis of something like 1642 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1643 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1644 if (AR->isAffine()) { 1645 const SCEV *Start = AR->getStart(); 1646 const SCEV *Step = AR->getStepRecurrence(*this); 1647 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1648 const Loop *L = AR->getLoop(); 1649 1650 // If we have special knowledge that this addrec won't overflow, 1651 // we don't need to do any further analysis. 1652 if (AR->getNoWrapFlags(SCEV::FlagNSW)) 1653 return getAddRecExpr( 1654 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this), 1655 getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW); 1656 1657 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1658 // Note that this serves two purposes: It filters out loops that are 1659 // simply not analyzable, and it covers the case where this code is 1660 // being called from within backedge-taken count analysis, such that 1661 // attempting to ask for the backedge-taken count would likely result 1662 // in infinite recursion. In the later case, the analysis code will 1663 // cope with a conservative value, and it will take care to purge 1664 // that value once it has finished. 1665 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1666 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1667 // Manually compute the final value for AR, checking for 1668 // overflow. 1669 1670 // Check whether the backedge-taken count can be losslessly casted to 1671 // the addrec's type. The count is always unsigned. 1672 const SCEV *CastedMaxBECount = 1673 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1674 const SCEV *RecastedMaxBECount = 1675 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1676 if (MaxBECount == RecastedMaxBECount) { 1677 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1678 // Check whether Start+Step*MaxBECount has no signed overflow. 1679 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1680 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy); 1681 const SCEV *WideStart = getSignExtendExpr(Start, WideTy); 1682 const SCEV *WideMaxBECount = 1683 getZeroExtendExpr(CastedMaxBECount, WideTy); 1684 const SCEV *OperandExtendedAdd = 1685 getAddExpr(WideStart, 1686 getMulExpr(WideMaxBECount, 1687 getSignExtendExpr(Step, WideTy))); 1688 if (SAdd == OperandExtendedAdd) { 1689 // Cache knowledge of AR NSW, which is propagated to this AddRec. 1690 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1691 // Return the expression with the addrec on the outside. 1692 return getAddRecExpr( 1693 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this), 1694 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); 1695 } 1696 // Similar to above, only this time treat the step value as unsigned. 1697 // This covers loops that count up with an unsigned step. 1698 OperandExtendedAdd = 1699 getAddExpr(WideStart, 1700 getMulExpr(WideMaxBECount, 1701 getZeroExtendExpr(Step, WideTy))); 1702 if (SAdd == OperandExtendedAdd) { 1703 // If AR wraps around then 1704 // 1705 // abs(Step) * MaxBECount > unsigned-max(AR->getType()) 1706 // => SAdd != OperandExtendedAdd 1707 // 1708 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=> 1709 // (SAdd == OperandExtendedAdd => AR is NW) 1710 1711 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); 1712 1713 // Return the expression with the addrec on the outside. 1714 return getAddRecExpr( 1715 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this), 1716 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); 1717 } 1718 } 1719 1720 // If the backedge is guarded by a comparison with the pre-inc value 1721 // the addrec is safe. Also, if the entry is guarded by a comparison 1722 // with the start value and the backedge is guarded by a comparison 1723 // with the post-inc value, the addrec is safe. 1724 ICmpInst::Predicate Pred; 1725 const SCEV *OverflowLimit = 1726 getSignedOverflowLimitForStep(Step, &Pred, this); 1727 if (OverflowLimit && 1728 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) || 1729 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) && 1730 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this), 1731 OverflowLimit)))) { 1732 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec. 1733 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1734 return getAddRecExpr( 1735 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this), 1736 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); 1737 } 1738 } 1739 // If Start and Step are constants, check if we can apply this 1740 // transformation: 1741 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2 1742 auto SC1 = dyn_cast<SCEVConstant>(Start); 1743 auto SC2 = dyn_cast<SCEVConstant>(Step); 1744 if (SC1 && SC2) { 1745 const APInt &C1 = SC1->getValue()->getValue(); 1746 const APInt &C2 = SC2->getValue()->getValue(); 1747 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) && 1748 C2.isPowerOf2()) { 1749 Start = getSignExtendExpr(Start, Ty); 1750 const SCEV *NewAR = getAddRecExpr(getConstant(AR->getType(), 0), Step, 1751 L, AR->getNoWrapFlags()); 1752 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty)); 1753 } 1754 } 1755 1756 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) { 1757 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1758 return getAddRecExpr( 1759 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this), 1760 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); 1761 } 1762 } 1763 1764 // The cast wasn't folded; create an explicit cast node. 1765 // Recompute the insert position, as it may have been invalidated. 1766 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1767 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1768 Op, Ty); 1769 UniqueSCEVs.InsertNode(S, IP); 1770 return S; 1771 } 1772 1773 /// getAnyExtendExpr - Return a SCEV for the given operand extended with 1774 /// unspecified bits out to the given type. 1775 /// 1776 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1777 Type *Ty) { 1778 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1779 "This is not an extending conversion!"); 1780 assert(isSCEVable(Ty) && 1781 "This is not a conversion to a SCEVable type!"); 1782 Ty = getEffectiveSCEVType(Ty); 1783 1784 // Sign-extend negative constants. 1785 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1786 if (SC->getValue()->getValue().isNegative()) 1787 return getSignExtendExpr(Op, Ty); 1788 1789 // Peel off a truncate cast. 1790 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1791 const SCEV *NewOp = T->getOperand(); 1792 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1793 return getAnyExtendExpr(NewOp, Ty); 1794 return getTruncateOrNoop(NewOp, Ty); 1795 } 1796 1797 // Next try a zext cast. If the cast is folded, use it. 1798 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1799 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1800 return ZExt; 1801 1802 // Next try a sext cast. If the cast is folded, use it. 1803 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1804 if (!isa<SCEVSignExtendExpr>(SExt)) 1805 return SExt; 1806 1807 // Force the cast to be folded into the operands of an addrec. 1808 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1809 SmallVector<const SCEV *, 4> Ops; 1810 for (const SCEV *Op : AR->operands()) 1811 Ops.push_back(getAnyExtendExpr(Op, Ty)); 1812 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW); 1813 } 1814 1815 // If the expression is obviously signed, use the sext cast value. 1816 if (isa<SCEVSMaxExpr>(Op)) 1817 return SExt; 1818 1819 // Absent any other information, use the zext cast value. 1820 return ZExt; 1821 } 1822 1823 /// CollectAddOperandsWithScales - Process the given Ops list, which is 1824 /// a list of operands to be added under the given scale, update the given 1825 /// map. This is a helper function for getAddRecExpr. As an example of 1826 /// what it does, given a sequence of operands that would form an add 1827 /// expression like this: 1828 /// 1829 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r) 1830 /// 1831 /// where A and B are constants, update the map with these values: 1832 /// 1833 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1834 /// 1835 /// and add 13 + A*B*29 to AccumulatedConstant. 1836 /// This will allow getAddRecExpr to produce this: 1837 /// 1838 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1839 /// 1840 /// This form often exposes folding opportunities that are hidden in 1841 /// the original operand list. 1842 /// 1843 /// Return true iff it appears that any interesting folding opportunities 1844 /// may be exposed. This helps getAddRecExpr short-circuit extra work in 1845 /// the common case where no interesting opportunities are present, and 1846 /// is also used as a check to avoid infinite recursion. 1847 /// 1848 static bool 1849 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1850 SmallVectorImpl<const SCEV *> &NewOps, 1851 APInt &AccumulatedConstant, 1852 const SCEV *const *Ops, size_t NumOperands, 1853 const APInt &Scale, 1854 ScalarEvolution &SE) { 1855 bool Interesting = false; 1856 1857 // Iterate over the add operands. They are sorted, with constants first. 1858 unsigned i = 0; 1859 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1860 ++i; 1861 // Pull a buried constant out to the outside. 1862 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 1863 Interesting = true; 1864 AccumulatedConstant += Scale * C->getValue()->getValue(); 1865 } 1866 1867 // Next comes everything else. We're especially interested in multiplies 1868 // here, but they're in the middle, so just visit the rest with one loop. 1869 for (; i != NumOperands; ++i) { 1870 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1871 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1872 APInt NewScale = 1873 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1874 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1875 // A multiplication of a constant with another add; recurse. 1876 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1877 Interesting |= 1878 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1879 Add->op_begin(), Add->getNumOperands(), 1880 NewScale, SE); 1881 } else { 1882 // A multiplication of a constant with some other value. Update 1883 // the map. 1884 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1885 const SCEV *Key = SE.getMulExpr(MulOps); 1886 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1887 M.insert(std::make_pair(Key, NewScale)); 1888 if (Pair.second) { 1889 NewOps.push_back(Pair.first->first); 1890 } else { 1891 Pair.first->second += NewScale; 1892 // The map already had an entry for this value, which may indicate 1893 // a folding opportunity. 1894 Interesting = true; 1895 } 1896 } 1897 } else { 1898 // An ordinary operand. Update the map. 1899 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1900 M.insert(std::make_pair(Ops[i], Scale)); 1901 if (Pair.second) { 1902 NewOps.push_back(Pair.first->first); 1903 } else { 1904 Pair.first->second += Scale; 1905 // The map already had an entry for this value, which may indicate 1906 // a folding opportunity. 1907 Interesting = true; 1908 } 1909 } 1910 } 1911 1912 return Interesting; 1913 } 1914 1915 namespace { 1916 struct APIntCompare { 1917 bool operator()(const APInt &LHS, const APInt &RHS) const { 1918 return LHS.ult(RHS); 1919 } 1920 }; 1921 } 1922 1923 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and 1924 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of 1925 // can't-overflow flags for the operation if possible. 1926 static SCEV::NoWrapFlags 1927 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type, 1928 const SmallVectorImpl<const SCEV *> &Ops, 1929 SCEV::NoWrapFlags OldFlags) { 1930 using namespace std::placeholders; 1931 1932 bool CanAnalyze = 1933 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr; 1934 (void)CanAnalyze; 1935 assert(CanAnalyze && "don't call from other places!"); 1936 1937 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 1938 SCEV::NoWrapFlags SignOrUnsignWrap = 1939 ScalarEvolution::maskFlags(OldFlags, SignOrUnsignMask); 1940 1941 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 1942 auto IsKnownNonNegative = 1943 std::bind(std::mem_fn(&ScalarEvolution::isKnownNonNegative), SE, _1); 1944 1945 if (SignOrUnsignWrap == SCEV::FlagNSW && 1946 std::all_of(Ops.begin(), Ops.end(), IsKnownNonNegative)) 1947 return ScalarEvolution::setFlags(OldFlags, 1948 (SCEV::NoWrapFlags)SignOrUnsignMask); 1949 1950 return OldFlags; 1951 } 1952 1953 /// getAddExpr - Get a canonical add expression, or something simpler if 1954 /// possible. 1955 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1956 SCEV::NoWrapFlags Flags) { 1957 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && 1958 "only nuw or nsw allowed"); 1959 assert(!Ops.empty() && "Cannot get empty add!"); 1960 if (Ops.size() == 1) return Ops[0]; 1961 #ifndef NDEBUG 1962 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1963 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1964 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1965 "SCEVAddExpr operand types don't match!"); 1966 #endif 1967 1968 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags); 1969 1970 // Sort by complexity, this groups all similar expression types together. 1971 GroupByComplexity(Ops, LI); 1972 1973 // If there are any constants, fold them together. 1974 unsigned Idx = 0; 1975 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1976 ++Idx; 1977 assert(Idx < Ops.size()); 1978 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1979 // We found two constants, fold them together! 1980 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1981 RHSC->getValue()->getValue()); 1982 if (Ops.size() == 2) return Ops[0]; 1983 Ops.erase(Ops.begin()+1); // Erase the folded element 1984 LHSC = cast<SCEVConstant>(Ops[0]); 1985 } 1986 1987 // If we are left with a constant zero being added, strip it off. 1988 if (LHSC->getValue()->isZero()) { 1989 Ops.erase(Ops.begin()); 1990 --Idx; 1991 } 1992 1993 if (Ops.size() == 1) return Ops[0]; 1994 } 1995 1996 // Okay, check to see if the same value occurs in the operand list more than 1997 // once. If so, merge them together into an multiply expression. Since we 1998 // sorted the list, these values are required to be adjacent. 1999 Type *Ty = Ops[0]->getType(); 2000 bool FoundMatch = false; 2001 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i) 2002 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 2003 // Scan ahead to count how many equal operands there are. 2004 unsigned Count = 2; 2005 while (i+Count != e && Ops[i+Count] == Ops[i]) 2006 ++Count; 2007 // Merge the values into a multiply. 2008 const SCEV *Scale = getConstant(Ty, Count); 2009 const SCEV *Mul = getMulExpr(Scale, Ops[i]); 2010 if (Ops.size() == Count) 2011 return Mul; 2012 Ops[i] = Mul; 2013 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count); 2014 --i; e -= Count - 1; 2015 FoundMatch = true; 2016 } 2017 if (FoundMatch) 2018 return getAddExpr(Ops, Flags); 2019 2020 // Check for truncates. If all the operands are truncated from the same 2021 // type, see if factoring out the truncate would permit the result to be 2022 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 2023 // if the contents of the resulting outer trunc fold to something simple. 2024 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 2025 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 2026 Type *DstType = Trunc->getType(); 2027 Type *SrcType = Trunc->getOperand()->getType(); 2028 SmallVector<const SCEV *, 8> LargeOps; 2029 bool Ok = true; 2030 // Check all the operands to see if they can be represented in the 2031 // source type of the truncate. 2032 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 2033 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 2034 if (T->getOperand()->getType() != SrcType) { 2035 Ok = false; 2036 break; 2037 } 2038 LargeOps.push_back(T->getOperand()); 2039 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 2040 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 2041 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 2042 SmallVector<const SCEV *, 8> LargeMulOps; 2043 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 2044 if (const SCEVTruncateExpr *T = 2045 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 2046 if (T->getOperand()->getType() != SrcType) { 2047 Ok = false; 2048 break; 2049 } 2050 LargeMulOps.push_back(T->getOperand()); 2051 } else if (const SCEVConstant *C = 2052 dyn_cast<SCEVConstant>(M->getOperand(j))) { 2053 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 2054 } else { 2055 Ok = false; 2056 break; 2057 } 2058 } 2059 if (Ok) 2060 LargeOps.push_back(getMulExpr(LargeMulOps)); 2061 } else { 2062 Ok = false; 2063 break; 2064 } 2065 } 2066 if (Ok) { 2067 // Evaluate the expression in the larger type. 2068 const SCEV *Fold = getAddExpr(LargeOps, Flags); 2069 // If it folds to something simple, use it. Otherwise, don't. 2070 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 2071 return getTruncateExpr(Fold, DstType); 2072 } 2073 } 2074 2075 // Skip past any other cast SCEVs. 2076 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 2077 ++Idx; 2078 2079 // If there are add operands they would be next. 2080 if (Idx < Ops.size()) { 2081 bool DeletedAdd = false; 2082 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 2083 // If we have an add, expand the add operands onto the end of the operands 2084 // list. 2085 Ops.erase(Ops.begin()+Idx); 2086 Ops.append(Add->op_begin(), Add->op_end()); 2087 DeletedAdd = true; 2088 } 2089 2090 // If we deleted at least one add, we added operands to the end of the list, 2091 // and they are not necessarily sorted. Recurse to resort and resimplify 2092 // any operands we just acquired. 2093 if (DeletedAdd) 2094 return getAddExpr(Ops); 2095 } 2096 2097 // Skip over the add expression until we get to a multiply. 2098 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 2099 ++Idx; 2100 2101 // Check to see if there are any folding opportunities present with 2102 // operands multiplied by constant values. 2103 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 2104 uint64_t BitWidth = getTypeSizeInBits(Ty); 2105 DenseMap<const SCEV *, APInt> M; 2106 SmallVector<const SCEV *, 8> NewOps; 2107 APInt AccumulatedConstant(BitWidth, 0); 2108 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 2109 Ops.data(), Ops.size(), 2110 APInt(BitWidth, 1), *this)) { 2111 // Some interesting folding opportunity is present, so its worthwhile to 2112 // re-generate the operands list. Group the operands by constant scale, 2113 // to avoid multiplying by the same constant scale multiple times. 2114 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 2115 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(), 2116 E = NewOps.end(); I != E; ++I) 2117 MulOpLists[M.find(*I)->second].push_back(*I); 2118 // Re-generate the operands list. 2119 Ops.clear(); 2120 if (AccumulatedConstant != 0) 2121 Ops.push_back(getConstant(AccumulatedConstant)); 2122 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 2123 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 2124 if (I->first != 0) 2125 Ops.push_back(getMulExpr(getConstant(I->first), 2126 getAddExpr(I->second))); 2127 if (Ops.empty()) 2128 return getConstant(Ty, 0); 2129 if (Ops.size() == 1) 2130 return Ops[0]; 2131 return getAddExpr(Ops); 2132 } 2133 } 2134 2135 // If we are adding something to a multiply expression, make sure the 2136 // something is not already an operand of the multiply. If so, merge it into 2137 // the multiply. 2138 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 2139 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 2140 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 2141 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 2142 if (isa<SCEVConstant>(MulOpSCEV)) 2143 continue; 2144 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 2145 if (MulOpSCEV == Ops[AddOp]) { 2146 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 2147 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 2148 if (Mul->getNumOperands() != 2) { 2149 // If the multiply has more than two operands, we must get the 2150 // Y*Z term. 2151 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 2152 Mul->op_begin()+MulOp); 2153 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 2154 InnerMul = getMulExpr(MulOps); 2155 } 2156 const SCEV *One = getConstant(Ty, 1); 2157 const SCEV *AddOne = getAddExpr(One, InnerMul); 2158 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV); 2159 if (Ops.size() == 2) return OuterMul; 2160 if (AddOp < Idx) { 2161 Ops.erase(Ops.begin()+AddOp); 2162 Ops.erase(Ops.begin()+Idx-1); 2163 } else { 2164 Ops.erase(Ops.begin()+Idx); 2165 Ops.erase(Ops.begin()+AddOp-1); 2166 } 2167 Ops.push_back(OuterMul); 2168 return getAddExpr(Ops); 2169 } 2170 2171 // Check this multiply against other multiplies being added together. 2172 for (unsigned OtherMulIdx = Idx+1; 2173 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 2174 ++OtherMulIdx) { 2175 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 2176 // If MulOp occurs in OtherMul, we can fold the two multiplies 2177 // together. 2178 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 2179 OMulOp != e; ++OMulOp) 2180 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 2181 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 2182 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 2183 if (Mul->getNumOperands() != 2) { 2184 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 2185 Mul->op_begin()+MulOp); 2186 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 2187 InnerMul1 = getMulExpr(MulOps); 2188 } 2189 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 2190 if (OtherMul->getNumOperands() != 2) { 2191 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 2192 OtherMul->op_begin()+OMulOp); 2193 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end()); 2194 InnerMul2 = getMulExpr(MulOps); 2195 } 2196 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 2197 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 2198 if (Ops.size() == 2) return OuterMul; 2199 Ops.erase(Ops.begin()+Idx); 2200 Ops.erase(Ops.begin()+OtherMulIdx-1); 2201 Ops.push_back(OuterMul); 2202 return getAddExpr(Ops); 2203 } 2204 } 2205 } 2206 } 2207 2208 // If there are any add recurrences in the operands list, see if any other 2209 // added values are loop invariant. If so, we can fold them into the 2210 // recurrence. 2211 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 2212 ++Idx; 2213 2214 // Scan over all recurrences, trying to fold loop invariants into them. 2215 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 2216 // Scan all of the other operands to this add and add them to the vector if 2217 // they are loop invariant w.r.t. the recurrence. 2218 SmallVector<const SCEV *, 8> LIOps; 2219 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 2220 const Loop *AddRecLoop = AddRec->getLoop(); 2221 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2222 if (isLoopInvariant(Ops[i], AddRecLoop)) { 2223 LIOps.push_back(Ops[i]); 2224 Ops.erase(Ops.begin()+i); 2225 --i; --e; 2226 } 2227 2228 // If we found some loop invariants, fold them into the recurrence. 2229 if (!LIOps.empty()) { 2230 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 2231 LIOps.push_back(AddRec->getStart()); 2232 2233 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 2234 AddRec->op_end()); 2235 AddRecOps[0] = getAddExpr(LIOps); 2236 2237 // Build the new addrec. Propagate the NUW and NSW flags if both the 2238 // outer add and the inner addrec are guaranteed to have no overflow. 2239 // Always propagate NW. 2240 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW)); 2241 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags); 2242 2243 // If all of the other operands were loop invariant, we are done. 2244 if (Ops.size() == 1) return NewRec; 2245 2246 // Otherwise, add the folded AddRec by the non-invariant parts. 2247 for (unsigned i = 0;; ++i) 2248 if (Ops[i] == AddRec) { 2249 Ops[i] = NewRec; 2250 break; 2251 } 2252 return getAddExpr(Ops); 2253 } 2254 2255 // Okay, if there weren't any loop invariants to be folded, check to see if 2256 // there are multiple AddRec's with the same loop induction variable being 2257 // added together. If so, we can fold them. 2258 for (unsigned OtherIdx = Idx+1; 2259 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 2260 ++OtherIdx) 2261 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 2262 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L> 2263 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 2264 AddRec->op_end()); 2265 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 2266 ++OtherIdx) 2267 if (const SCEVAddRecExpr *OtherAddRec = 2268 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 2269 if (OtherAddRec->getLoop() == AddRecLoop) { 2270 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); 2271 i != e; ++i) { 2272 if (i >= AddRecOps.size()) { 2273 AddRecOps.append(OtherAddRec->op_begin()+i, 2274 OtherAddRec->op_end()); 2275 break; 2276 } 2277 AddRecOps[i] = getAddExpr(AddRecOps[i], 2278 OtherAddRec->getOperand(i)); 2279 } 2280 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 2281 } 2282 // Step size has changed, so we cannot guarantee no self-wraparound. 2283 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap); 2284 return getAddExpr(Ops); 2285 } 2286 2287 // Otherwise couldn't fold anything into this recurrence. Move onto the 2288 // next one. 2289 } 2290 2291 // Okay, it looks like we really DO need an add expr. Check to see if we 2292 // already have one, otherwise create a new one. 2293 FoldingSetNodeID ID; 2294 ID.AddInteger(scAddExpr); 2295 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2296 ID.AddPointer(Ops[i]); 2297 void *IP = nullptr; 2298 SCEVAddExpr *S = 2299 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2300 if (!S) { 2301 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2302 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2303 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), 2304 O, Ops.size()); 2305 UniqueSCEVs.InsertNode(S, IP); 2306 } 2307 S->setNoWrapFlags(Flags); 2308 return S; 2309 } 2310 2311 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) { 2312 uint64_t k = i*j; 2313 if (j > 1 && k / j != i) Overflow = true; 2314 return k; 2315 } 2316 2317 /// Compute the result of "n choose k", the binomial coefficient. If an 2318 /// intermediate computation overflows, Overflow will be set and the return will 2319 /// be garbage. Overflow is not cleared on absence of overflow. 2320 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) { 2321 // We use the multiplicative formula: 2322 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 . 2323 // At each iteration, we take the n-th term of the numeral and divide by the 2324 // (k-n)th term of the denominator. This division will always produce an 2325 // integral result, and helps reduce the chance of overflow in the 2326 // intermediate computations. However, we can still overflow even when the 2327 // final result would fit. 2328 2329 if (n == 0 || n == k) return 1; 2330 if (k > n) return 0; 2331 2332 if (k > n/2) 2333 k = n-k; 2334 2335 uint64_t r = 1; 2336 for (uint64_t i = 1; i <= k; ++i) { 2337 r = umul_ov(r, n-(i-1), Overflow); 2338 r /= i; 2339 } 2340 return r; 2341 } 2342 2343 /// Determine if any of the operands in this SCEV are a constant or if 2344 /// any of the add or multiply expressions in this SCEV contain a constant. 2345 static bool containsConstantSomewhere(const SCEV *StartExpr) { 2346 SmallVector<const SCEV *, 4> Ops; 2347 Ops.push_back(StartExpr); 2348 while (!Ops.empty()) { 2349 const SCEV *CurrentExpr = Ops.pop_back_val(); 2350 if (isa<SCEVConstant>(*CurrentExpr)) 2351 return true; 2352 2353 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) { 2354 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr); 2355 Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end()); 2356 } 2357 } 2358 return false; 2359 } 2360 2361 /// getMulExpr - Get a canonical multiply expression, or something simpler if 2362 /// possible. 2363 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 2364 SCEV::NoWrapFlags Flags) { 2365 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) && 2366 "only nuw or nsw allowed"); 2367 assert(!Ops.empty() && "Cannot get empty mul!"); 2368 if (Ops.size() == 1) return Ops[0]; 2369 #ifndef NDEBUG 2370 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2371 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2372 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2373 "SCEVMulExpr operand types don't match!"); 2374 #endif 2375 2376 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags); 2377 2378 // Sort by complexity, this groups all similar expression types together. 2379 GroupByComplexity(Ops, LI); 2380 2381 // If there are any constants, fold them together. 2382 unsigned Idx = 0; 2383 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2384 2385 // C1*(C2+V) -> C1*C2 + C1*V 2386 if (Ops.size() == 2) 2387 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 2388 // If any of Add's ops are Adds or Muls with a constant, 2389 // apply this transformation as well. 2390 if (Add->getNumOperands() == 2) 2391 if (containsConstantSomewhere(Add)) 2392 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 2393 getMulExpr(LHSC, Add->getOperand(1))); 2394 2395 ++Idx; 2396 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2397 // We found two constants, fold them together! 2398 ConstantInt *Fold = ConstantInt::get(getContext(), 2399 LHSC->getValue()->getValue() * 2400 RHSC->getValue()->getValue()); 2401 Ops[0] = getConstant(Fold); 2402 Ops.erase(Ops.begin()+1); // Erase the folded element 2403 if (Ops.size() == 1) return Ops[0]; 2404 LHSC = cast<SCEVConstant>(Ops[0]); 2405 } 2406 2407 // If we are left with a constant one being multiplied, strip it off. 2408 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 2409 Ops.erase(Ops.begin()); 2410 --Idx; 2411 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 2412 // If we have a multiply of zero, it will always be zero. 2413 return Ops[0]; 2414 } else if (Ops[0]->isAllOnesValue()) { 2415 // If we have a mul by -1 of an add, try distributing the -1 among the 2416 // add operands. 2417 if (Ops.size() == 2) { 2418 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 2419 SmallVector<const SCEV *, 4> NewOps; 2420 bool AnyFolded = false; 2421 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), 2422 E = Add->op_end(); I != E; ++I) { 2423 const SCEV *Mul = getMulExpr(Ops[0], *I); 2424 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 2425 NewOps.push_back(Mul); 2426 } 2427 if (AnyFolded) 2428 return getAddExpr(NewOps); 2429 } 2430 else if (const SCEVAddRecExpr * 2431 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) { 2432 // Negation preserves a recurrence's no self-wrap property. 2433 SmallVector<const SCEV *, 4> Operands; 2434 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(), 2435 E = AddRec->op_end(); I != E; ++I) { 2436 Operands.push_back(getMulExpr(Ops[0], *I)); 2437 } 2438 return getAddRecExpr(Operands, AddRec->getLoop(), 2439 AddRec->getNoWrapFlags(SCEV::FlagNW)); 2440 } 2441 } 2442 } 2443 2444 if (Ops.size() == 1) 2445 return Ops[0]; 2446 } 2447 2448 // Skip over the add expression until we get to a multiply. 2449 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 2450 ++Idx; 2451 2452 // If there are mul operands inline them all into this expression. 2453 if (Idx < Ops.size()) { 2454 bool DeletedMul = false; 2455 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 2456 // If we have an mul, expand the mul operands onto the end of the operands 2457 // list. 2458 Ops.erase(Ops.begin()+Idx); 2459 Ops.append(Mul->op_begin(), Mul->op_end()); 2460 DeletedMul = true; 2461 } 2462 2463 // If we deleted at least one mul, we added operands to the end of the list, 2464 // and they are not necessarily sorted. Recurse to resort and resimplify 2465 // any operands we just acquired. 2466 if (DeletedMul) 2467 return getMulExpr(Ops); 2468 } 2469 2470 // If there are any add recurrences in the operands list, see if any other 2471 // added values are loop invariant. If so, we can fold them into the 2472 // recurrence. 2473 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 2474 ++Idx; 2475 2476 // Scan over all recurrences, trying to fold loop invariants into them. 2477 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 2478 // Scan all of the other operands to this mul and add them to the vector if 2479 // they are loop invariant w.r.t. the recurrence. 2480 SmallVector<const SCEV *, 8> LIOps; 2481 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 2482 const Loop *AddRecLoop = AddRec->getLoop(); 2483 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2484 if (isLoopInvariant(Ops[i], AddRecLoop)) { 2485 LIOps.push_back(Ops[i]); 2486 Ops.erase(Ops.begin()+i); 2487 --i; --e; 2488 } 2489 2490 // If we found some loop invariants, fold them into the recurrence. 2491 if (!LIOps.empty()) { 2492 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 2493 SmallVector<const SCEV *, 4> NewOps; 2494 NewOps.reserve(AddRec->getNumOperands()); 2495 const SCEV *Scale = getMulExpr(LIOps); 2496 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 2497 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 2498 2499 // Build the new addrec. Propagate the NUW and NSW flags if both the 2500 // outer mul and the inner addrec are guaranteed to have no overflow. 2501 // 2502 // No self-wrap cannot be guaranteed after changing the step size, but 2503 // will be inferred if either NUW or NSW is true. 2504 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW)); 2505 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags); 2506 2507 // If all of the other operands were loop invariant, we are done. 2508 if (Ops.size() == 1) return NewRec; 2509 2510 // Otherwise, multiply the folded AddRec by the non-invariant parts. 2511 for (unsigned i = 0;; ++i) 2512 if (Ops[i] == AddRec) { 2513 Ops[i] = NewRec; 2514 break; 2515 } 2516 return getMulExpr(Ops); 2517 } 2518 2519 // Okay, if there weren't any loop invariants to be folded, check to see if 2520 // there are multiple AddRec's with the same loop induction variable being 2521 // multiplied together. If so, we can fold them. 2522 2523 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L> 2524 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [ 2525 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z 2526 // ]]],+,...up to x=2n}. 2527 // Note that the arguments to choose() are always integers with values 2528 // known at compile time, never SCEV objects. 2529 // 2530 // The implementation avoids pointless extra computations when the two 2531 // addrec's are of different length (mathematically, it's equivalent to 2532 // an infinite stream of zeros on the right). 2533 bool OpsModified = false; 2534 for (unsigned OtherIdx = Idx+1; 2535 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 2536 ++OtherIdx) { 2537 const SCEVAddRecExpr *OtherAddRec = 2538 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]); 2539 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop) 2540 continue; 2541 2542 bool Overflow = false; 2543 Type *Ty = AddRec->getType(); 2544 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64; 2545 SmallVector<const SCEV*, 7> AddRecOps; 2546 for (int x = 0, xe = AddRec->getNumOperands() + 2547 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) { 2548 const SCEV *Term = getConstant(Ty, 0); 2549 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) { 2550 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow); 2551 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1), 2552 ze = std::min(x+1, (int)OtherAddRec->getNumOperands()); 2553 z < ze && !Overflow; ++z) { 2554 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow); 2555 uint64_t Coeff; 2556 if (LargerThan64Bits) 2557 Coeff = umul_ov(Coeff1, Coeff2, Overflow); 2558 else 2559 Coeff = Coeff1*Coeff2; 2560 const SCEV *CoeffTerm = getConstant(Ty, Coeff); 2561 const SCEV *Term1 = AddRec->getOperand(y-z); 2562 const SCEV *Term2 = OtherAddRec->getOperand(z); 2563 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2)); 2564 } 2565 } 2566 AddRecOps.push_back(Term); 2567 } 2568 if (!Overflow) { 2569 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(), 2570 SCEV::FlagAnyWrap); 2571 if (Ops.size() == 2) return NewAddRec; 2572 Ops[Idx] = NewAddRec; 2573 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 2574 OpsModified = true; 2575 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec); 2576 if (!AddRec) 2577 break; 2578 } 2579 } 2580 if (OpsModified) 2581 return getMulExpr(Ops); 2582 2583 // Otherwise couldn't fold anything into this recurrence. Move onto the 2584 // next one. 2585 } 2586 2587 // Okay, it looks like we really DO need an mul expr. Check to see if we 2588 // already have one, otherwise create a new one. 2589 FoldingSetNodeID ID; 2590 ID.AddInteger(scMulExpr); 2591 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2592 ID.AddPointer(Ops[i]); 2593 void *IP = nullptr; 2594 SCEVMulExpr *S = 2595 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2596 if (!S) { 2597 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2598 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2599 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 2600 O, Ops.size()); 2601 UniqueSCEVs.InsertNode(S, IP); 2602 } 2603 S->setNoWrapFlags(Flags); 2604 return S; 2605 } 2606 2607 /// getUDivExpr - Get a canonical unsigned division expression, or something 2608 /// simpler if possible. 2609 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 2610 const SCEV *RHS) { 2611 assert(getEffectiveSCEVType(LHS->getType()) == 2612 getEffectiveSCEVType(RHS->getType()) && 2613 "SCEVUDivExpr operand types don't match!"); 2614 2615 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 2616 if (RHSC->getValue()->equalsInt(1)) 2617 return LHS; // X udiv 1 --> x 2618 // If the denominator is zero, the result of the udiv is undefined. Don't 2619 // try to analyze it, because the resolution chosen here may differ from 2620 // the resolution chosen in other parts of the compiler. 2621 if (!RHSC->getValue()->isZero()) { 2622 // Determine if the division can be folded into the operands of 2623 // its operands. 2624 // TODO: Generalize this to non-constants by using known-bits information. 2625 Type *Ty = LHS->getType(); 2626 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 2627 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; 2628 // For non-power-of-two values, effectively round the value up to the 2629 // nearest power of two. 2630 if (!RHSC->getValue()->getValue().isPowerOf2()) 2631 ++MaxShiftAmt; 2632 IntegerType *ExtTy = 2633 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 2634 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 2635 if (const SCEVConstant *Step = 2636 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) { 2637 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 2638 const APInt &StepInt = Step->getValue()->getValue(); 2639 const APInt &DivInt = RHSC->getValue()->getValue(); 2640 if (!StepInt.urem(DivInt) && 2641 getZeroExtendExpr(AR, ExtTy) == 2642 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 2643 getZeroExtendExpr(Step, ExtTy), 2644 AR->getLoop(), SCEV::FlagAnyWrap)) { 2645 SmallVector<const SCEV *, 4> Operands; 2646 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 2647 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 2648 return getAddRecExpr(Operands, AR->getLoop(), 2649 SCEV::FlagNW); 2650 } 2651 /// Get a canonical UDivExpr for a recurrence. 2652 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0. 2653 // We can currently only fold X%N if X is constant. 2654 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart()); 2655 if (StartC && !DivInt.urem(StepInt) && 2656 getZeroExtendExpr(AR, ExtTy) == 2657 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 2658 getZeroExtendExpr(Step, ExtTy), 2659 AR->getLoop(), SCEV::FlagAnyWrap)) { 2660 const APInt &StartInt = StartC->getValue()->getValue(); 2661 const APInt &StartRem = StartInt.urem(StepInt); 2662 if (StartRem != 0) 2663 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step, 2664 AR->getLoop(), SCEV::FlagNW); 2665 } 2666 } 2667 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 2668 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 2669 SmallVector<const SCEV *, 4> Operands; 2670 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 2671 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 2672 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 2673 // Find an operand that's safely divisible. 2674 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 2675 const SCEV *Op = M->getOperand(i); 2676 const SCEV *Div = getUDivExpr(Op, RHSC); 2677 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 2678 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 2679 M->op_end()); 2680 Operands[i] = Div; 2681 return getMulExpr(Operands); 2682 } 2683 } 2684 } 2685 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 2686 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) { 2687 SmallVector<const SCEV *, 4> Operands; 2688 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 2689 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 2690 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 2691 Operands.clear(); 2692 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 2693 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 2694 if (isa<SCEVUDivExpr>(Op) || 2695 getMulExpr(Op, RHS) != A->getOperand(i)) 2696 break; 2697 Operands.push_back(Op); 2698 } 2699 if (Operands.size() == A->getNumOperands()) 2700 return getAddExpr(Operands); 2701 } 2702 } 2703 2704 // Fold if both operands are constant. 2705 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 2706 Constant *LHSCV = LHSC->getValue(); 2707 Constant *RHSCV = RHSC->getValue(); 2708 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 2709 RHSCV))); 2710 } 2711 } 2712 } 2713 2714 FoldingSetNodeID ID; 2715 ID.AddInteger(scUDivExpr); 2716 ID.AddPointer(LHS); 2717 ID.AddPointer(RHS); 2718 void *IP = nullptr; 2719 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2720 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 2721 LHS, RHS); 2722 UniqueSCEVs.InsertNode(S, IP); 2723 return S; 2724 } 2725 2726 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) { 2727 APInt A = C1->getValue()->getValue().abs(); 2728 APInt B = C2->getValue()->getValue().abs(); 2729 uint32_t ABW = A.getBitWidth(); 2730 uint32_t BBW = B.getBitWidth(); 2731 2732 if (ABW > BBW) 2733 B = B.zext(ABW); 2734 else if (ABW < BBW) 2735 A = A.zext(BBW); 2736 2737 return APIntOps::GreatestCommonDivisor(A, B); 2738 } 2739 2740 /// getUDivExactExpr - Get a canonical unsigned division expression, or 2741 /// something simpler if possible. There is no representation for an exact udiv 2742 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS. 2743 /// We can't do this when it's not exact because the udiv may be clearing bits. 2744 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS, 2745 const SCEV *RHS) { 2746 // TODO: we could try to find factors in all sorts of things, but for now we 2747 // just deal with u/exact (multiply, constant). See SCEVDivision towards the 2748 // end of this file for inspiration. 2749 2750 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS); 2751 if (!Mul) 2752 return getUDivExpr(LHS, RHS); 2753 2754 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) { 2755 // If the mulexpr multiplies by a constant, then that constant must be the 2756 // first element of the mulexpr. 2757 if (const SCEVConstant *LHSCst = 2758 dyn_cast<SCEVConstant>(Mul->getOperand(0))) { 2759 if (LHSCst == RHSCst) { 2760 SmallVector<const SCEV *, 2> Operands; 2761 Operands.append(Mul->op_begin() + 1, Mul->op_end()); 2762 return getMulExpr(Operands); 2763 } 2764 2765 // We can't just assume that LHSCst divides RHSCst cleanly, it could be 2766 // that there's a factor provided by one of the other terms. We need to 2767 // check. 2768 APInt Factor = gcd(LHSCst, RHSCst); 2769 if (!Factor.isIntN(1)) { 2770 LHSCst = cast<SCEVConstant>( 2771 getConstant(LHSCst->getValue()->getValue().udiv(Factor))); 2772 RHSCst = cast<SCEVConstant>( 2773 getConstant(RHSCst->getValue()->getValue().udiv(Factor))); 2774 SmallVector<const SCEV *, 2> Operands; 2775 Operands.push_back(LHSCst); 2776 Operands.append(Mul->op_begin() + 1, Mul->op_end()); 2777 LHS = getMulExpr(Operands); 2778 RHS = RHSCst; 2779 Mul = dyn_cast<SCEVMulExpr>(LHS); 2780 if (!Mul) 2781 return getUDivExactExpr(LHS, RHS); 2782 } 2783 } 2784 } 2785 2786 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) { 2787 if (Mul->getOperand(i) == RHS) { 2788 SmallVector<const SCEV *, 2> Operands; 2789 Operands.append(Mul->op_begin(), Mul->op_begin() + i); 2790 Operands.append(Mul->op_begin() + i + 1, Mul->op_end()); 2791 return getMulExpr(Operands); 2792 } 2793 } 2794 2795 return getUDivExpr(LHS, RHS); 2796 } 2797 2798 /// getAddRecExpr - Get an add recurrence expression for the specified loop. 2799 /// Simplify the expression as much as possible. 2800 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step, 2801 const Loop *L, 2802 SCEV::NoWrapFlags Flags) { 2803 SmallVector<const SCEV *, 4> Operands; 2804 Operands.push_back(Start); 2805 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 2806 if (StepChrec->getLoop() == L) { 2807 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 2808 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW)); 2809 } 2810 2811 Operands.push_back(Step); 2812 return getAddRecExpr(Operands, L, Flags); 2813 } 2814 2815 /// getAddRecExpr - Get an add recurrence expression for the specified loop. 2816 /// Simplify the expression as much as possible. 2817 const SCEV * 2818 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 2819 const Loop *L, SCEV::NoWrapFlags Flags) { 2820 if (Operands.size() == 1) return Operands[0]; 2821 #ifndef NDEBUG 2822 Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); 2823 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 2824 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && 2825 "SCEVAddRecExpr operand types don't match!"); 2826 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2827 assert(isLoopInvariant(Operands[i], L) && 2828 "SCEVAddRecExpr operand is not loop-invariant!"); 2829 #endif 2830 2831 if (Operands.back()->isZero()) { 2832 Operands.pop_back(); 2833 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X 2834 } 2835 2836 // It's tempting to want to call getMaxBackedgeTakenCount count here and 2837 // use that information to infer NUW and NSW flags. However, computing a 2838 // BE count requires calling getAddRecExpr, so we may not yet have a 2839 // meaningful BE count at this point (and if we don't, we'd be stuck 2840 // with a SCEVCouldNotCompute as the cached BE count). 2841 2842 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags); 2843 2844 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 2845 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 2846 const Loop *NestedLoop = NestedAR->getLoop(); 2847 if (L->contains(NestedLoop) ? 2848 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 2849 (!NestedLoop->contains(L) && 2850 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 2851 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 2852 NestedAR->op_end()); 2853 Operands[0] = NestedAR->getStart(); 2854 // AddRecs require their operands be loop-invariant with respect to their 2855 // loops. Don't perform this transformation if it would break this 2856 // requirement. 2857 bool AllInvariant = true; 2858 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2859 if (!isLoopInvariant(Operands[i], L)) { 2860 AllInvariant = false; 2861 break; 2862 } 2863 if (AllInvariant) { 2864 // Create a recurrence for the outer loop with the same step size. 2865 // 2866 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the 2867 // inner recurrence has the same property. 2868 SCEV::NoWrapFlags OuterFlags = 2869 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags()); 2870 2871 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags); 2872 AllInvariant = true; 2873 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2874 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) { 2875 AllInvariant = false; 2876 break; 2877 } 2878 if (AllInvariant) { 2879 // Ok, both add recurrences are valid after the transformation. 2880 // 2881 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if 2882 // the outer recurrence has the same property. 2883 SCEV::NoWrapFlags InnerFlags = 2884 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags); 2885 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags); 2886 } 2887 } 2888 // Reset Operands to its original state. 2889 Operands[0] = NestedAR; 2890 } 2891 } 2892 2893 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2894 // already have one, otherwise create a new one. 2895 FoldingSetNodeID ID; 2896 ID.AddInteger(scAddRecExpr); 2897 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2898 ID.AddPointer(Operands[i]); 2899 ID.AddPointer(L); 2900 void *IP = nullptr; 2901 SCEVAddRecExpr *S = 2902 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2903 if (!S) { 2904 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2905 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2906 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2907 O, Operands.size(), L); 2908 UniqueSCEVs.InsertNode(S, IP); 2909 } 2910 S->setNoWrapFlags(Flags); 2911 return S; 2912 } 2913 2914 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2915 const SCEV *RHS) { 2916 SmallVector<const SCEV *, 2> Ops; 2917 Ops.push_back(LHS); 2918 Ops.push_back(RHS); 2919 return getSMaxExpr(Ops); 2920 } 2921 2922 const SCEV * 2923 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2924 assert(!Ops.empty() && "Cannot get empty smax!"); 2925 if (Ops.size() == 1) return Ops[0]; 2926 #ifndef NDEBUG 2927 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2928 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2929 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2930 "SCEVSMaxExpr operand types don't match!"); 2931 #endif 2932 2933 // Sort by complexity, this groups all similar expression types together. 2934 GroupByComplexity(Ops, LI); 2935 2936 // If there are any constants, fold them together. 2937 unsigned Idx = 0; 2938 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2939 ++Idx; 2940 assert(Idx < Ops.size()); 2941 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2942 // We found two constants, fold them together! 2943 ConstantInt *Fold = ConstantInt::get(getContext(), 2944 APIntOps::smax(LHSC->getValue()->getValue(), 2945 RHSC->getValue()->getValue())); 2946 Ops[0] = getConstant(Fold); 2947 Ops.erase(Ops.begin()+1); // Erase the folded element 2948 if (Ops.size() == 1) return Ops[0]; 2949 LHSC = cast<SCEVConstant>(Ops[0]); 2950 } 2951 2952 // If we are left with a constant minimum-int, strip it off. 2953 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2954 Ops.erase(Ops.begin()); 2955 --Idx; 2956 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2957 // If we have an smax with a constant maximum-int, it will always be 2958 // maximum-int. 2959 return Ops[0]; 2960 } 2961 2962 if (Ops.size() == 1) return Ops[0]; 2963 } 2964 2965 // Find the first SMax 2966 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2967 ++Idx; 2968 2969 // Check to see if one of the operands is an SMax. If so, expand its operands 2970 // onto our operand list, and recurse to simplify. 2971 if (Idx < Ops.size()) { 2972 bool DeletedSMax = false; 2973 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2974 Ops.erase(Ops.begin()+Idx); 2975 Ops.append(SMax->op_begin(), SMax->op_end()); 2976 DeletedSMax = true; 2977 } 2978 2979 if (DeletedSMax) 2980 return getSMaxExpr(Ops); 2981 } 2982 2983 // Okay, check to see if the same value occurs in the operand list twice. If 2984 // so, delete one. Since we sorted the list, these values are required to 2985 // be adjacent. 2986 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2987 // X smax Y smax Y --> X smax Y 2988 // X smax Y --> X, if X is always greater than Y 2989 if (Ops[i] == Ops[i+1] || 2990 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 2991 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2992 --i; --e; 2993 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 2994 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2995 --i; --e; 2996 } 2997 2998 if (Ops.size() == 1) return Ops[0]; 2999 3000 assert(!Ops.empty() && "Reduced smax down to nothing!"); 3001 3002 // Okay, it looks like we really DO need an smax expr. Check to see if we 3003 // already have one, otherwise create a new one. 3004 FoldingSetNodeID ID; 3005 ID.AddInteger(scSMaxExpr); 3006 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 3007 ID.AddPointer(Ops[i]); 3008 void *IP = nullptr; 3009 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 3010 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 3011 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 3012 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 3013 O, Ops.size()); 3014 UniqueSCEVs.InsertNode(S, IP); 3015 return S; 3016 } 3017 3018 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 3019 const SCEV *RHS) { 3020 SmallVector<const SCEV *, 2> Ops; 3021 Ops.push_back(LHS); 3022 Ops.push_back(RHS); 3023 return getUMaxExpr(Ops); 3024 } 3025 3026 const SCEV * 3027 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 3028 assert(!Ops.empty() && "Cannot get empty umax!"); 3029 if (Ops.size() == 1) return Ops[0]; 3030 #ifndef NDEBUG 3031 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 3032 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 3033 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 3034 "SCEVUMaxExpr operand types don't match!"); 3035 #endif 3036 3037 // Sort by complexity, this groups all similar expression types together. 3038 GroupByComplexity(Ops, LI); 3039 3040 // If there are any constants, fold them together. 3041 unsigned Idx = 0; 3042 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 3043 ++Idx; 3044 assert(Idx < Ops.size()); 3045 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 3046 // We found two constants, fold them together! 3047 ConstantInt *Fold = ConstantInt::get(getContext(), 3048 APIntOps::umax(LHSC->getValue()->getValue(), 3049 RHSC->getValue()->getValue())); 3050 Ops[0] = getConstant(Fold); 3051 Ops.erase(Ops.begin()+1); // Erase the folded element 3052 if (Ops.size() == 1) return Ops[0]; 3053 LHSC = cast<SCEVConstant>(Ops[0]); 3054 } 3055 3056 // If we are left with a constant minimum-int, strip it off. 3057 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 3058 Ops.erase(Ops.begin()); 3059 --Idx; 3060 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 3061 // If we have an umax with a constant maximum-int, it will always be 3062 // maximum-int. 3063 return Ops[0]; 3064 } 3065 3066 if (Ops.size() == 1) return Ops[0]; 3067 } 3068 3069 // Find the first UMax 3070 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 3071 ++Idx; 3072 3073 // Check to see if one of the operands is a UMax. If so, expand its operands 3074 // onto our operand list, and recurse to simplify. 3075 if (Idx < Ops.size()) { 3076 bool DeletedUMax = false; 3077 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 3078 Ops.erase(Ops.begin()+Idx); 3079 Ops.append(UMax->op_begin(), UMax->op_end()); 3080 DeletedUMax = true; 3081 } 3082 3083 if (DeletedUMax) 3084 return getUMaxExpr(Ops); 3085 } 3086 3087 // Okay, check to see if the same value occurs in the operand list twice. If 3088 // so, delete one. Since we sorted the list, these values are required to 3089 // be adjacent. 3090 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 3091 // X umax Y umax Y --> X umax Y 3092 // X umax Y --> X, if X is always greater than Y 3093 if (Ops[i] == Ops[i+1] || 3094 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 3095 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 3096 --i; --e; 3097 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 3098 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 3099 --i; --e; 3100 } 3101 3102 if (Ops.size() == 1) return Ops[0]; 3103 3104 assert(!Ops.empty() && "Reduced umax down to nothing!"); 3105 3106 // Okay, it looks like we really DO need a umax expr. Check to see if we 3107 // already have one, otherwise create a new one. 3108 FoldingSetNodeID ID; 3109 ID.AddInteger(scUMaxExpr); 3110 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 3111 ID.AddPointer(Ops[i]); 3112 void *IP = nullptr; 3113 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 3114 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 3115 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 3116 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 3117 O, Ops.size()); 3118 UniqueSCEVs.InsertNode(S, IP); 3119 return S; 3120 } 3121 3122 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 3123 const SCEV *RHS) { 3124 // ~smax(~x, ~y) == smin(x, y). 3125 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 3126 } 3127 3128 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 3129 const SCEV *RHS) { 3130 // ~umax(~x, ~y) == umin(x, y) 3131 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 3132 } 3133 3134 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) { 3135 // We can bypass creating a target-independent 3136 // constant expression and then folding it back into a ConstantInt. 3137 // This is just a compile-time optimization. 3138 return getConstant(IntTy, 3139 F->getParent()->getDataLayout().getTypeAllocSize(AllocTy)); 3140 } 3141 3142 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy, 3143 StructType *STy, 3144 unsigned FieldNo) { 3145 // We can bypass creating a target-independent 3146 // constant expression and then folding it back into a ConstantInt. 3147 // This is just a compile-time optimization. 3148 return getConstant( 3149 IntTy, 3150 F->getParent()->getDataLayout().getStructLayout(STy)->getElementOffset( 3151 FieldNo)); 3152 } 3153 3154 const SCEV *ScalarEvolution::getUnknown(Value *V) { 3155 // Don't attempt to do anything other than create a SCEVUnknown object 3156 // here. createSCEV only calls getUnknown after checking for all other 3157 // interesting possibilities, and any other code that calls getUnknown 3158 // is doing so in order to hide a value from SCEV canonicalization. 3159 3160 FoldingSetNodeID ID; 3161 ID.AddInteger(scUnknown); 3162 ID.AddPointer(V); 3163 void *IP = nullptr; 3164 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { 3165 assert(cast<SCEVUnknown>(S)->getValue() == V && 3166 "Stale SCEVUnknown in uniquing map!"); 3167 return S; 3168 } 3169 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, 3170 FirstUnknown); 3171 FirstUnknown = cast<SCEVUnknown>(S); 3172 UniqueSCEVs.InsertNode(S, IP); 3173 return S; 3174 } 3175 3176 //===----------------------------------------------------------------------===// 3177 // Basic SCEV Analysis and PHI Idiom Recognition Code 3178 // 3179 3180 /// isSCEVable - Test if values of the given type are analyzable within 3181 /// the SCEV framework. This primarily includes integer types, and it 3182 /// can optionally include pointer types if the ScalarEvolution class 3183 /// has access to target-specific information. 3184 bool ScalarEvolution::isSCEVable(Type *Ty) const { 3185 // Integers and pointers are always SCEVable. 3186 return Ty->isIntegerTy() || Ty->isPointerTy(); 3187 } 3188 3189 /// getTypeSizeInBits - Return the size in bits of the specified type, 3190 /// for which isSCEVable must return true. 3191 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const { 3192 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 3193 return F->getParent()->getDataLayout().getTypeSizeInBits(Ty); 3194 } 3195 3196 /// getEffectiveSCEVType - Return a type with the same bitwidth as 3197 /// the given type and which represents how SCEV will treat the given 3198 /// type, for which isSCEVable must return true. For pointer types, 3199 /// this is the pointer-sized integer type. 3200 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const { 3201 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 3202 3203 if (Ty->isIntegerTy()) { 3204 return Ty; 3205 } 3206 3207 // The only other support type is pointer. 3208 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 3209 return F->getParent()->getDataLayout().getIntPtrType(Ty); 3210 } 3211 3212 const SCEV *ScalarEvolution::getCouldNotCompute() { 3213 return &CouldNotCompute; 3214 } 3215 3216 namespace { 3217 // Helper class working with SCEVTraversal to figure out if a SCEV contains 3218 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne 3219 // is set iff if find such SCEVUnknown. 3220 // 3221 struct FindInvalidSCEVUnknown { 3222 bool FindOne; 3223 FindInvalidSCEVUnknown() { FindOne = false; } 3224 bool follow(const SCEV *S) { 3225 switch (static_cast<SCEVTypes>(S->getSCEVType())) { 3226 case scConstant: 3227 return false; 3228 case scUnknown: 3229 if (!cast<SCEVUnknown>(S)->getValue()) 3230 FindOne = true; 3231 return false; 3232 default: 3233 return true; 3234 } 3235 } 3236 bool isDone() const { return FindOne; } 3237 }; 3238 } 3239 3240 bool ScalarEvolution::checkValidity(const SCEV *S) const { 3241 FindInvalidSCEVUnknown F; 3242 SCEVTraversal<FindInvalidSCEVUnknown> ST(F); 3243 ST.visitAll(S); 3244 3245 return !F.FindOne; 3246 } 3247 3248 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 3249 /// expression and create a new one. 3250 const SCEV *ScalarEvolution::getSCEV(Value *V) { 3251 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 3252 3253 ValueExprMapType::iterator I = ValueExprMap.find_as(V); 3254 if (I != ValueExprMap.end()) { 3255 const SCEV *S = I->second; 3256 if (checkValidity(S)) 3257 return S; 3258 else 3259 ValueExprMap.erase(I); 3260 } 3261 const SCEV *S = createSCEV(V); 3262 3263 // The process of creating a SCEV for V may have caused other SCEVs 3264 // to have been created, so it's necessary to insert the new entry 3265 // from scratch, rather than trying to remember the insert position 3266 // above. 3267 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 3268 return S; 3269 } 3270 3271 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 3272 /// 3273 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 3274 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 3275 return getConstant( 3276 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 3277 3278 Type *Ty = V->getType(); 3279 Ty = getEffectiveSCEVType(Ty); 3280 return getMulExpr(V, 3281 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 3282 } 3283 3284 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 3285 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 3286 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 3287 return getConstant( 3288 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 3289 3290 Type *Ty = V->getType(); 3291 Ty = getEffectiveSCEVType(Ty); 3292 const SCEV *AllOnes = 3293 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 3294 return getMinusSCEV(AllOnes, V); 3295 } 3296 3297 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1. 3298 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS, 3299 SCEV::NoWrapFlags Flags) { 3300 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW"); 3301 3302 // Fast path: X - X --> 0. 3303 if (LHS == RHS) 3304 return getConstant(LHS->getType(), 0); 3305 3306 // X - Y --> X + -Y. 3307 // X -(nsw || nuw) Y --> X + -Y. 3308 return getAddExpr(LHS, getNegativeSCEV(RHS)); 3309 } 3310 3311 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 3312 /// input value to the specified type. If the type must be extended, it is zero 3313 /// extended. 3314 const SCEV * 3315 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) { 3316 Type *SrcTy = V->getType(); 3317 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 3318 (Ty->isIntegerTy() || Ty->isPointerTy()) && 3319 "Cannot truncate or zero extend with non-integer arguments!"); 3320 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 3321 return V; // No conversion 3322 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 3323 return getTruncateExpr(V, Ty); 3324 return getZeroExtendExpr(V, Ty); 3325 } 3326 3327 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 3328 /// input value to the specified type. If the type must be extended, it is sign 3329 /// extended. 3330 const SCEV * 3331 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 3332 Type *Ty) { 3333 Type *SrcTy = V->getType(); 3334 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 3335 (Ty->isIntegerTy() || Ty->isPointerTy()) && 3336 "Cannot truncate or zero extend with non-integer arguments!"); 3337 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 3338 return V; // No conversion 3339 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 3340 return getTruncateExpr(V, Ty); 3341 return getSignExtendExpr(V, Ty); 3342 } 3343 3344 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 3345 /// input value to the specified type. If the type must be extended, it is zero 3346 /// extended. The conversion must not be narrowing. 3347 const SCEV * 3348 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) { 3349 Type *SrcTy = V->getType(); 3350 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 3351 (Ty->isIntegerTy() || Ty->isPointerTy()) && 3352 "Cannot noop or zero extend with non-integer arguments!"); 3353 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 3354 "getNoopOrZeroExtend cannot truncate!"); 3355 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 3356 return V; // No conversion 3357 return getZeroExtendExpr(V, Ty); 3358 } 3359 3360 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 3361 /// input value to the specified type. If the type must be extended, it is sign 3362 /// extended. The conversion must not be narrowing. 3363 const SCEV * 3364 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) { 3365 Type *SrcTy = V->getType(); 3366 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 3367 (Ty->isIntegerTy() || Ty->isPointerTy()) && 3368 "Cannot noop or sign extend with non-integer arguments!"); 3369 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 3370 "getNoopOrSignExtend cannot truncate!"); 3371 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 3372 return V; // No conversion 3373 return getSignExtendExpr(V, Ty); 3374 } 3375 3376 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 3377 /// the input value to the specified type. If the type must be extended, 3378 /// it is extended with unspecified bits. The conversion must not be 3379 /// narrowing. 3380 const SCEV * 3381 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) { 3382 Type *SrcTy = V->getType(); 3383 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 3384 (Ty->isIntegerTy() || Ty->isPointerTy()) && 3385 "Cannot noop or any extend with non-integer arguments!"); 3386 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 3387 "getNoopOrAnyExtend cannot truncate!"); 3388 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 3389 return V; // No conversion 3390 return getAnyExtendExpr(V, Ty); 3391 } 3392 3393 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 3394 /// input value to the specified type. The conversion must not be widening. 3395 const SCEV * 3396 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) { 3397 Type *SrcTy = V->getType(); 3398 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 3399 (Ty->isIntegerTy() || Ty->isPointerTy()) && 3400 "Cannot truncate or noop with non-integer arguments!"); 3401 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 3402 "getTruncateOrNoop cannot extend!"); 3403 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 3404 return V; // No conversion 3405 return getTruncateExpr(V, Ty); 3406 } 3407 3408 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of 3409 /// the types using zero-extension, and then perform a umax operation 3410 /// with them. 3411 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 3412 const SCEV *RHS) { 3413 const SCEV *PromotedLHS = LHS; 3414 const SCEV *PromotedRHS = RHS; 3415 3416 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 3417 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 3418 else 3419 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 3420 3421 return getUMaxExpr(PromotedLHS, PromotedRHS); 3422 } 3423 3424 /// getUMinFromMismatchedTypes - Promote the operands to the wider of 3425 /// the types using zero-extension, and then perform a umin operation 3426 /// with them. 3427 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 3428 const SCEV *RHS) { 3429 const SCEV *PromotedLHS = LHS; 3430 const SCEV *PromotedRHS = RHS; 3431 3432 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 3433 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 3434 else 3435 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 3436 3437 return getUMinExpr(PromotedLHS, PromotedRHS); 3438 } 3439 3440 /// getPointerBase - Transitively follow the chain of pointer-type operands 3441 /// until reaching a SCEV that does not have a single pointer operand. This 3442 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions, 3443 /// but corner cases do exist. 3444 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) { 3445 // A pointer operand may evaluate to a nonpointer expression, such as null. 3446 if (!V->getType()->isPointerTy()) 3447 return V; 3448 3449 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) { 3450 return getPointerBase(Cast->getOperand()); 3451 } 3452 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) { 3453 const SCEV *PtrOp = nullptr; 3454 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 3455 I != E; ++I) { 3456 if ((*I)->getType()->isPointerTy()) { 3457 // Cannot find the base of an expression with multiple pointer operands. 3458 if (PtrOp) 3459 return V; 3460 PtrOp = *I; 3461 } 3462 } 3463 if (!PtrOp) 3464 return V; 3465 return getPointerBase(PtrOp); 3466 } 3467 return V; 3468 } 3469 3470 /// PushDefUseChildren - Push users of the given Instruction 3471 /// onto the given Worklist. 3472 static void 3473 PushDefUseChildren(Instruction *I, 3474 SmallVectorImpl<Instruction *> &Worklist) { 3475 // Push the def-use children onto the Worklist stack. 3476 for (User *U : I->users()) 3477 Worklist.push_back(cast<Instruction>(U)); 3478 } 3479 3480 /// ForgetSymbolicValue - This looks up computed SCEV values for all 3481 /// instructions that depend on the given instruction and removes them from 3482 /// the ValueExprMapType map if they reference SymName. This is used during PHI 3483 /// resolution. 3484 void 3485 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 3486 SmallVector<Instruction *, 16> Worklist; 3487 PushDefUseChildren(PN, Worklist); 3488 3489 SmallPtrSet<Instruction *, 8> Visited; 3490 Visited.insert(PN); 3491 while (!Worklist.empty()) { 3492 Instruction *I = Worklist.pop_back_val(); 3493 if (!Visited.insert(I).second) 3494 continue; 3495 3496 ValueExprMapType::iterator It = 3497 ValueExprMap.find_as(static_cast<Value *>(I)); 3498 if (It != ValueExprMap.end()) { 3499 const SCEV *Old = It->second; 3500 3501 // Short-circuit the def-use traversal if the symbolic name 3502 // ceases to appear in expressions. 3503 if (Old != SymName && !hasOperand(Old, SymName)) 3504 continue; 3505 3506 // SCEVUnknown for a PHI either means that it has an unrecognized 3507 // structure, it's a PHI that's in the progress of being computed 3508 // by createNodeForPHI, or it's a single-value PHI. In the first case, 3509 // additional loop trip count information isn't going to change anything. 3510 // In the second case, createNodeForPHI will perform the necessary 3511 // updates on its own when it gets to that point. In the third, we do 3512 // want to forget the SCEVUnknown. 3513 if (!isa<PHINode>(I) || 3514 !isa<SCEVUnknown>(Old) || 3515 (I != PN && Old == SymName)) { 3516 forgetMemoizedResults(Old); 3517 ValueExprMap.erase(It); 3518 } 3519 } 3520 3521 PushDefUseChildren(I, Worklist); 3522 } 3523 } 3524 3525 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 3526 /// a loop header, making it a potential recurrence, or it doesn't. 3527 /// 3528 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 3529 if (const Loop *L = LI->getLoopFor(PN->getParent())) 3530 if (L->getHeader() == PN->getParent()) { 3531 // The loop may have multiple entrances or multiple exits; we can analyze 3532 // this phi as an addrec if it has a unique entry value and a unique 3533 // backedge value. 3534 Value *BEValueV = nullptr, *StartValueV = nullptr; 3535 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 3536 Value *V = PN->getIncomingValue(i); 3537 if (L->contains(PN->getIncomingBlock(i))) { 3538 if (!BEValueV) { 3539 BEValueV = V; 3540 } else if (BEValueV != V) { 3541 BEValueV = nullptr; 3542 break; 3543 } 3544 } else if (!StartValueV) { 3545 StartValueV = V; 3546 } else if (StartValueV != V) { 3547 StartValueV = nullptr; 3548 break; 3549 } 3550 } 3551 if (BEValueV && StartValueV) { 3552 // While we are analyzing this PHI node, handle its value symbolically. 3553 const SCEV *SymbolicName = getUnknown(PN); 3554 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() && 3555 "PHI node already processed?"); 3556 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 3557 3558 // Using this symbolic name for the PHI, analyze the value coming around 3559 // the back-edge. 3560 const SCEV *BEValue = getSCEV(BEValueV); 3561 3562 // NOTE: If BEValue is loop invariant, we know that the PHI node just 3563 // has a special value for the first iteration of the loop. 3564 3565 // If the value coming around the backedge is an add with the symbolic 3566 // value we just inserted, then we found a simple induction variable! 3567 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 3568 // If there is a single occurrence of the symbolic value, replace it 3569 // with a recurrence. 3570 unsigned FoundIndex = Add->getNumOperands(); 3571 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 3572 if (Add->getOperand(i) == SymbolicName) 3573 if (FoundIndex == e) { 3574 FoundIndex = i; 3575 break; 3576 } 3577 3578 if (FoundIndex != Add->getNumOperands()) { 3579 // Create an add with everything but the specified operand. 3580 SmallVector<const SCEV *, 8> Ops; 3581 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 3582 if (i != FoundIndex) 3583 Ops.push_back(Add->getOperand(i)); 3584 const SCEV *Accum = getAddExpr(Ops); 3585 3586 // This is not a valid addrec if the step amount is varying each 3587 // loop iteration, but is not itself an addrec in this loop. 3588 if (isLoopInvariant(Accum, L) || 3589 (isa<SCEVAddRecExpr>(Accum) && 3590 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 3591 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; 3592 3593 // If the increment doesn't overflow, then neither the addrec nor 3594 // the post-increment will overflow. 3595 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 3596 if (OBO->getOperand(0) == PN) { 3597 if (OBO->hasNoUnsignedWrap()) 3598 Flags = setFlags(Flags, SCEV::FlagNUW); 3599 if (OBO->hasNoSignedWrap()) 3600 Flags = setFlags(Flags, SCEV::FlagNSW); 3601 } 3602 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) { 3603 // If the increment is an inbounds GEP, then we know the address 3604 // space cannot be wrapped around. We cannot make any guarantee 3605 // about signed or unsigned overflow because pointers are 3606 // unsigned but we may have a negative index from the base 3607 // pointer. We can guarantee that no unsigned wrap occurs if the 3608 // indices form a positive value. 3609 if (GEP->isInBounds() && GEP->getOperand(0) == PN) { 3610 Flags = setFlags(Flags, SCEV::FlagNW); 3611 3612 const SCEV *Ptr = getSCEV(GEP->getPointerOperand()); 3613 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr))) 3614 Flags = setFlags(Flags, SCEV::FlagNUW); 3615 } 3616 3617 // We cannot transfer nuw and nsw flags from subtraction 3618 // operations -- sub nuw X, Y is not the same as add nuw X, -Y 3619 // for instance. 3620 } 3621 3622 const SCEV *StartVal = getSCEV(StartValueV); 3623 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags); 3624 3625 // Since the no-wrap flags are on the increment, they apply to the 3626 // post-incremented value as well. 3627 if (isLoopInvariant(Accum, L)) 3628 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 3629 Accum, L, Flags); 3630 3631 // Okay, for the entire analysis of this edge we assumed the PHI 3632 // to be symbolic. We now need to go back and purge all of the 3633 // entries for the scalars that use the symbolic expression. 3634 ForgetSymbolicName(PN, SymbolicName); 3635 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 3636 return PHISCEV; 3637 } 3638 } 3639 } else if (const SCEVAddRecExpr *AddRec = 3640 dyn_cast<SCEVAddRecExpr>(BEValue)) { 3641 // Otherwise, this could be a loop like this: 3642 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 3643 // In this case, j = {1,+,1} and BEValue is j. 3644 // Because the other in-value of i (0) fits the evolution of BEValue 3645 // i really is an addrec evolution. 3646 if (AddRec->getLoop() == L && AddRec->isAffine()) { 3647 const SCEV *StartVal = getSCEV(StartValueV); 3648 3649 // If StartVal = j.start - j.stride, we can use StartVal as the 3650 // initial step of the addrec evolution. 3651 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 3652 AddRec->getOperand(1))) { 3653 // FIXME: For constant StartVal, we should be able to infer 3654 // no-wrap flags. 3655 const SCEV *PHISCEV = 3656 getAddRecExpr(StartVal, AddRec->getOperand(1), L, 3657 SCEV::FlagAnyWrap); 3658 3659 // Okay, for the entire analysis of this edge we assumed the PHI 3660 // to be symbolic. We now need to go back and purge all of the 3661 // entries for the scalars that use the symbolic expression. 3662 ForgetSymbolicName(PN, SymbolicName); 3663 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 3664 return PHISCEV; 3665 } 3666 } 3667 } 3668 } 3669 } 3670 3671 // If the PHI has a single incoming value, follow that value, unless the 3672 // PHI's incoming blocks are in a different loop, in which case doing so 3673 // risks breaking LCSSA form. Instcombine would normally zap these, but 3674 // it doesn't have DominatorTree information, so it may miss cases. 3675 if (Value *V = 3676 SimplifyInstruction(PN, F->getParent()->getDataLayout(), TLI, DT, AC)) 3677 if (LI->replacementPreservesLCSSAForm(PN, V)) 3678 return getSCEV(V); 3679 3680 // If it's not a loop phi, we can't handle it yet. 3681 return getUnknown(PN); 3682 } 3683 3684 /// createNodeForGEP - Expand GEP instructions into add and multiply 3685 /// operations. This allows them to be analyzed by regular SCEV code. 3686 /// 3687 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 3688 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 3689 Value *Base = GEP->getOperand(0); 3690 // Don't attempt to analyze GEPs over unsized objects. 3691 if (!Base->getType()->getPointerElementType()->isSized()) 3692 return getUnknown(GEP); 3693 3694 // Don't blindly transfer the inbounds flag from the GEP instruction to the 3695 // Add expression, because the Instruction may be guarded by control flow 3696 // and the no-overflow bits may not be valid for the expression in any 3697 // context. 3698 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap; 3699 3700 const SCEV *TotalOffset = getConstant(IntPtrTy, 0); 3701 gep_type_iterator GTI = gep_type_begin(GEP); 3702 for (GetElementPtrInst::op_iterator I = std::next(GEP->op_begin()), 3703 E = GEP->op_end(); 3704 I != E; ++I) { 3705 Value *Index = *I; 3706 // Compute the (potentially symbolic) offset in bytes for this index. 3707 if (StructType *STy = dyn_cast<StructType>(*GTI++)) { 3708 // For a struct, add the member offset. 3709 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 3710 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo); 3711 3712 // Add the field offset to the running total offset. 3713 TotalOffset = getAddExpr(TotalOffset, FieldOffset); 3714 } else { 3715 // For an array, add the element offset, explicitly scaled. 3716 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI); 3717 const SCEV *IndexS = getSCEV(Index); 3718 // Getelementptr indices are signed. 3719 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy); 3720 3721 // Multiply the index by the element size to compute the element offset. 3722 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap); 3723 3724 // Add the element offset to the running total offset. 3725 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 3726 } 3727 } 3728 3729 // Get the SCEV for the GEP base. 3730 const SCEV *BaseS = getSCEV(Base); 3731 3732 // Add the total offset from all the GEP indices to the base. 3733 return getAddExpr(BaseS, TotalOffset, Wrap); 3734 } 3735 3736 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 3737 /// guaranteed to end in (at every loop iteration). It is, at the same time, 3738 /// the minimum number of times S is divisible by 2. For example, given {4,+,8} 3739 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 3740 uint32_t 3741 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 3742 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3743 return C->getValue()->getValue().countTrailingZeros(); 3744 3745 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 3746 return std::min(GetMinTrailingZeros(T->getOperand()), 3747 (uint32_t)getTypeSizeInBits(T->getType())); 3748 3749 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 3750 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 3751 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 3752 getTypeSizeInBits(E->getType()) : OpRes; 3753 } 3754 3755 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 3756 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 3757 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 3758 getTypeSizeInBits(E->getType()) : OpRes; 3759 } 3760 3761 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 3762 // The result is the min of all operands results. 3763 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 3764 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 3765 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 3766 return MinOpRes; 3767 } 3768 3769 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 3770 // The result is the sum of all operands results. 3771 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 3772 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 3773 for (unsigned i = 1, e = M->getNumOperands(); 3774 SumOpRes != BitWidth && i != e; ++i) 3775 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 3776 BitWidth); 3777 return SumOpRes; 3778 } 3779 3780 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 3781 // The result is the min of all operands results. 3782 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 3783 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 3784 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 3785 return MinOpRes; 3786 } 3787 3788 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 3789 // The result is the min of all operands results. 3790 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 3791 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 3792 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 3793 return MinOpRes; 3794 } 3795 3796 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 3797 // The result is the min of all operands results. 3798 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 3799 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 3800 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 3801 return MinOpRes; 3802 } 3803 3804 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3805 // For a SCEVUnknown, ask ValueTracking. 3806 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3807 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3808 computeKnownBits(U->getValue(), Zeros, Ones, 3809 F->getParent()->getDataLayout(), 0, AC, nullptr, DT); 3810 return Zeros.countTrailingOnes(); 3811 } 3812 3813 // SCEVUDivExpr 3814 return 0; 3815 } 3816 3817 /// GetRangeFromMetadata - Helper method to assign a range to V from 3818 /// metadata present in the IR. 3819 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) { 3820 if (Instruction *I = dyn_cast<Instruction>(V)) { 3821 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) { 3822 ConstantRange TotalRange( 3823 cast<IntegerType>(I->getType())->getBitWidth(), false); 3824 3825 unsigned NumRanges = MD->getNumOperands() / 2; 3826 assert(NumRanges >= 1); 3827 3828 for (unsigned i = 0; i < NumRanges; ++i) { 3829 ConstantInt *Lower = 3830 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 0)); 3831 ConstantInt *Upper = 3832 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 1)); 3833 ConstantRange Range(Lower->getValue(), Upper->getValue()); 3834 TotalRange = TotalRange.unionWith(Range); 3835 } 3836 3837 return TotalRange; 3838 } 3839 } 3840 3841 return None; 3842 } 3843 3844 /// getRange - Determine the range for a particular SCEV. If SignHint is 3845 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges 3846 /// with a "cleaner" unsigned (resp. signed) representation. 3847 /// 3848 ConstantRange 3849 ScalarEvolution::getRange(const SCEV *S, 3850 ScalarEvolution::RangeSignHint SignHint) { 3851 DenseMap<const SCEV *, ConstantRange> &Cache = 3852 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges 3853 : SignedRanges; 3854 3855 // See if we've computed this range already. 3856 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S); 3857 if (I != Cache.end()) 3858 return I->second; 3859 3860 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3861 return setRange(C, SignHint, ConstantRange(C->getValue()->getValue())); 3862 3863 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3864 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3865 3866 // If the value has known zeros, the maximum value will have those known zeros 3867 // as well. 3868 uint32_t TZ = GetMinTrailingZeros(S); 3869 if (TZ != 0) { 3870 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) 3871 ConservativeResult = 3872 ConstantRange(APInt::getMinValue(BitWidth), 3873 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 3874 else 3875 ConservativeResult = ConstantRange( 3876 APInt::getSignedMinValue(BitWidth), 3877 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 3878 } 3879 3880 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3881 ConstantRange X = getRange(Add->getOperand(0), SignHint); 3882 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3883 X = X.add(getRange(Add->getOperand(i), SignHint)); 3884 return setRange(Add, SignHint, ConservativeResult.intersectWith(X)); 3885 } 3886 3887 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3888 ConstantRange X = getRange(Mul->getOperand(0), SignHint); 3889 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3890 X = X.multiply(getRange(Mul->getOperand(i), SignHint)); 3891 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X)); 3892 } 3893 3894 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3895 ConstantRange X = getRange(SMax->getOperand(0), SignHint); 3896 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3897 X = X.smax(getRange(SMax->getOperand(i), SignHint)); 3898 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X)); 3899 } 3900 3901 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3902 ConstantRange X = getRange(UMax->getOperand(0), SignHint); 3903 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3904 X = X.umax(getRange(UMax->getOperand(i), SignHint)); 3905 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X)); 3906 } 3907 3908 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3909 ConstantRange X = getRange(UDiv->getLHS(), SignHint); 3910 ConstantRange Y = getRange(UDiv->getRHS(), SignHint); 3911 return setRange(UDiv, SignHint, 3912 ConservativeResult.intersectWith(X.udiv(Y))); 3913 } 3914 3915 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3916 ConstantRange X = getRange(ZExt->getOperand(), SignHint); 3917 return setRange(ZExt, SignHint, 3918 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3919 } 3920 3921 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3922 ConstantRange X = getRange(SExt->getOperand(), SignHint); 3923 return setRange(SExt, SignHint, 3924 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3925 } 3926 3927 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3928 ConstantRange X = getRange(Trunc->getOperand(), SignHint); 3929 return setRange(Trunc, SignHint, 3930 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3931 } 3932 3933 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3934 // If there's no unsigned wrap, the value will never be less than its 3935 // initial value. 3936 if (AddRec->getNoWrapFlags(SCEV::FlagNUW)) 3937 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 3938 if (!C->getValue()->isZero()) 3939 ConservativeResult = 3940 ConservativeResult.intersectWith( 3941 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0))); 3942 3943 // If there's no signed wrap, and all the operands have the same sign or 3944 // zero, the value won't ever change sign. 3945 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) { 3946 bool AllNonNeg = true; 3947 bool AllNonPos = true; 3948 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3949 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3950 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3951 } 3952 if (AllNonNeg) 3953 ConservativeResult = ConservativeResult.intersectWith( 3954 ConstantRange(APInt(BitWidth, 0), 3955 APInt::getSignedMinValue(BitWidth))); 3956 else if (AllNonPos) 3957 ConservativeResult = ConservativeResult.intersectWith( 3958 ConstantRange(APInt::getSignedMinValue(BitWidth), 3959 APInt(BitWidth, 1))); 3960 } 3961 3962 // TODO: non-affine addrec 3963 if (AddRec->isAffine()) { 3964 Type *Ty = AddRec->getType(); 3965 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3966 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3967 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3968 3969 // Check for overflow. This must be done with ConstantRange arithmetic 3970 // because we could be called from within the ScalarEvolution overflow 3971 // checking code. 3972 3973 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3974 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3975 ConstantRange ZExtMaxBECountRange = 3976 MaxBECountRange.zextOrTrunc(BitWidth * 2 + 1); 3977 3978 const SCEV *Start = AddRec->getStart(); 3979 const SCEV *Step = AddRec->getStepRecurrence(*this); 3980 ConstantRange StepSRange = getSignedRange(Step); 3981 ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2 + 1); 3982 3983 ConstantRange StartURange = getUnsignedRange(Start); 3984 ConstantRange EndURange = 3985 StartURange.add(MaxBECountRange.multiply(StepSRange)); 3986 3987 // Check for unsigned overflow. 3988 ConstantRange ZExtStartURange = 3989 StartURange.zextOrTrunc(BitWidth * 2 + 1); 3990 ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2 + 1); 3991 if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) == 3992 ZExtEndURange) { 3993 APInt Min = APIntOps::umin(StartURange.getUnsignedMin(), 3994 EndURange.getUnsignedMin()); 3995 APInt Max = APIntOps::umax(StartURange.getUnsignedMax(), 3996 EndURange.getUnsignedMax()); 3997 bool IsFullRange = Min.isMinValue() && Max.isMaxValue(); 3998 if (!IsFullRange) 3999 ConservativeResult = 4000 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1)); 4001 } 4002 4003 ConstantRange StartSRange = getSignedRange(Start); 4004 ConstantRange EndSRange = 4005 StartSRange.add(MaxBECountRange.multiply(StepSRange)); 4006 4007 // Check for signed overflow. This must be done with ConstantRange 4008 // arithmetic because we could be called from within the ScalarEvolution 4009 // overflow checking code. 4010 ConstantRange SExtStartSRange = 4011 StartSRange.sextOrTrunc(BitWidth * 2 + 1); 4012 ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2 + 1); 4013 if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) == 4014 SExtEndSRange) { 4015 APInt Min = APIntOps::smin(StartSRange.getSignedMin(), 4016 EndSRange.getSignedMin()); 4017 APInt Max = APIntOps::smax(StartSRange.getSignedMax(), 4018 EndSRange.getSignedMax()); 4019 bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue(); 4020 if (!IsFullRange) 4021 ConservativeResult = 4022 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1)); 4023 } 4024 } 4025 } 4026 4027 return setRange(AddRec, SignHint, ConservativeResult); 4028 } 4029 4030 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 4031 // Check if the IR explicitly contains !range metadata. 4032 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue()); 4033 if (MDRange.hasValue()) 4034 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue()); 4035 4036 // Split here to avoid paying the compile-time cost of calling both 4037 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted 4038 // if needed. 4039 const DataLayout &DL = F->getParent()->getDataLayout(); 4040 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) { 4041 // For a SCEVUnknown, ask ValueTracking. 4042 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 4043 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT); 4044 if (Ones != ~Zeros + 1) 4045 ConservativeResult = 4046 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)); 4047 } else { 4048 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED && 4049 "generalize as needed!"); 4050 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, AC, nullptr, DT); 4051 if (NS > 1) 4052 ConservativeResult = ConservativeResult.intersectWith( 4053 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 4054 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1)); 4055 } 4056 4057 return setRange(U, SignHint, ConservativeResult); 4058 } 4059 4060 return setRange(S, SignHint, ConservativeResult); 4061 } 4062 4063 /// createSCEV - We know that there is no SCEV for the specified value. 4064 /// Analyze the expression. 4065 /// 4066 const SCEV *ScalarEvolution::createSCEV(Value *V) { 4067 if (!isSCEVable(V->getType())) 4068 return getUnknown(V); 4069 4070 unsigned Opcode = Instruction::UserOp1; 4071 if (Instruction *I = dyn_cast<Instruction>(V)) { 4072 Opcode = I->getOpcode(); 4073 4074 // Don't attempt to analyze instructions in blocks that aren't 4075 // reachable. Such instructions don't matter, and they aren't required 4076 // to obey basic rules for definitions dominating uses which this 4077 // analysis depends on. 4078 if (!DT->isReachableFromEntry(I->getParent())) 4079 return getUnknown(V); 4080 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 4081 Opcode = CE->getOpcode(); 4082 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 4083 return getConstant(CI); 4084 else if (isa<ConstantPointerNull>(V)) 4085 return getConstant(V->getType(), 0); 4086 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 4087 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 4088 else 4089 return getUnknown(V); 4090 4091 Operator *U = cast<Operator>(V); 4092 switch (Opcode) { 4093 case Instruction::Add: { 4094 // The simple thing to do would be to just call getSCEV on both operands 4095 // and call getAddExpr with the result. However if we're looking at a 4096 // bunch of things all added together, this can be quite inefficient, 4097 // because it leads to N-1 getAddExpr calls for N ultimate operands. 4098 // Instead, gather up all the operands and make a single getAddExpr call. 4099 // LLVM IR canonical form means we need only traverse the left operands. 4100 // 4101 // Don't apply this instruction's NSW or NUW flags to the new 4102 // expression. The instruction may be guarded by control flow that the 4103 // no-wrap behavior depends on. Non-control-equivalent instructions can be 4104 // mapped to the same SCEV expression, and it would be incorrect to transfer 4105 // NSW/NUW semantics to those operations. 4106 SmallVector<const SCEV *, 4> AddOps; 4107 AddOps.push_back(getSCEV(U->getOperand(1))); 4108 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) { 4109 unsigned Opcode = Op->getValueID() - Value::InstructionVal; 4110 if (Opcode != Instruction::Add && Opcode != Instruction::Sub) 4111 break; 4112 U = cast<Operator>(Op); 4113 const SCEV *Op1 = getSCEV(U->getOperand(1)); 4114 if (Opcode == Instruction::Sub) 4115 AddOps.push_back(getNegativeSCEV(Op1)); 4116 else 4117 AddOps.push_back(Op1); 4118 } 4119 AddOps.push_back(getSCEV(U->getOperand(0))); 4120 return getAddExpr(AddOps); 4121 } 4122 case Instruction::Mul: { 4123 // Don't transfer NSW/NUW for the same reason as AddExpr. 4124 SmallVector<const SCEV *, 4> MulOps; 4125 MulOps.push_back(getSCEV(U->getOperand(1))); 4126 for (Value *Op = U->getOperand(0); 4127 Op->getValueID() == Instruction::Mul + Value::InstructionVal; 4128 Op = U->getOperand(0)) { 4129 U = cast<Operator>(Op); 4130 MulOps.push_back(getSCEV(U->getOperand(1))); 4131 } 4132 MulOps.push_back(getSCEV(U->getOperand(0))); 4133 return getMulExpr(MulOps); 4134 } 4135 case Instruction::UDiv: 4136 return getUDivExpr(getSCEV(U->getOperand(0)), 4137 getSCEV(U->getOperand(1))); 4138 case Instruction::Sub: 4139 return getMinusSCEV(getSCEV(U->getOperand(0)), 4140 getSCEV(U->getOperand(1))); 4141 case Instruction::And: 4142 // For an expression like x&255 that merely masks off the high bits, 4143 // use zext(trunc(x)) as the SCEV expression. 4144 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 4145 if (CI->isNullValue()) 4146 return getSCEV(U->getOperand(1)); 4147 if (CI->isAllOnesValue()) 4148 return getSCEV(U->getOperand(0)); 4149 const APInt &A = CI->getValue(); 4150 4151 // Instcombine's ShrinkDemandedConstant may strip bits out of 4152 // constants, obscuring what would otherwise be a low-bits mask. 4153 // Use computeKnownBits to compute what ShrinkDemandedConstant 4154 // knew about to reconstruct a low-bits mask value. 4155 unsigned LZ = A.countLeadingZeros(); 4156 unsigned TZ = A.countTrailingZeros(); 4157 unsigned BitWidth = A.getBitWidth(); 4158 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 4159 computeKnownBits(U->getOperand(0), KnownZero, KnownOne, 4160 F->getParent()->getDataLayout(), 0, AC, nullptr, DT); 4161 4162 APInt EffectiveMask = 4163 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ); 4164 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) { 4165 const SCEV *MulCount = getConstant( 4166 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ))); 4167 return getMulExpr( 4168 getZeroExtendExpr( 4169 getTruncateExpr( 4170 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount), 4171 IntegerType::get(getContext(), BitWidth - LZ - TZ)), 4172 U->getType()), 4173 MulCount); 4174 } 4175 } 4176 break; 4177 4178 case Instruction::Or: 4179 // If the RHS of the Or is a constant, we may have something like: 4180 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 4181 // optimizations will transparently handle this case. 4182 // 4183 // In order for this transformation to be safe, the LHS must be of the 4184 // form X*(2^n) and the Or constant must be less than 2^n. 4185 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 4186 const SCEV *LHS = getSCEV(U->getOperand(0)); 4187 const APInt &CIVal = CI->getValue(); 4188 if (GetMinTrailingZeros(LHS) >= 4189 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 4190 // Build a plain add SCEV. 4191 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 4192 // If the LHS of the add was an addrec and it has no-wrap flags, 4193 // transfer the no-wrap flags, since an or won't introduce a wrap. 4194 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 4195 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 4196 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags( 4197 OldAR->getNoWrapFlags()); 4198 } 4199 return S; 4200 } 4201 } 4202 break; 4203 case Instruction::Xor: 4204 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 4205 // If the RHS of the xor is a signbit, then this is just an add. 4206 // Instcombine turns add of signbit into xor as a strength reduction step. 4207 if (CI->getValue().isSignBit()) 4208 return getAddExpr(getSCEV(U->getOperand(0)), 4209 getSCEV(U->getOperand(1))); 4210 4211 // If the RHS of xor is -1, then this is a not operation. 4212 if (CI->isAllOnesValue()) 4213 return getNotSCEV(getSCEV(U->getOperand(0))); 4214 4215 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 4216 // This is a variant of the check for xor with -1, and it handles 4217 // the case where instcombine has trimmed non-demanded bits out 4218 // of an xor with -1. 4219 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 4220 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 4221 if (BO->getOpcode() == Instruction::And && 4222 LCI->getValue() == CI->getValue()) 4223 if (const SCEVZeroExtendExpr *Z = 4224 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 4225 Type *UTy = U->getType(); 4226 const SCEV *Z0 = Z->getOperand(); 4227 Type *Z0Ty = Z0->getType(); 4228 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 4229 4230 // If C is a low-bits mask, the zero extend is serving to 4231 // mask off the high bits. Complement the operand and 4232 // re-apply the zext. 4233 if (APIntOps::isMask(Z0TySize, CI->getValue())) 4234 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 4235 4236 // If C is a single bit, it may be in the sign-bit position 4237 // before the zero-extend. In this case, represent the xor 4238 // using an add, which is equivalent, and re-apply the zext. 4239 APInt Trunc = CI->getValue().trunc(Z0TySize); 4240 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() && 4241 Trunc.isSignBit()) 4242 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 4243 UTy); 4244 } 4245 } 4246 break; 4247 4248 case Instruction::Shl: 4249 // Turn shift left of a constant amount into a multiply. 4250 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 4251 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 4252 4253 // If the shift count is not less than the bitwidth, the result of 4254 // the shift is undefined. Don't try to analyze it, because the 4255 // resolution chosen here may differ from the resolution chosen in 4256 // other parts of the compiler. 4257 if (SA->getValue().uge(BitWidth)) 4258 break; 4259 4260 Constant *X = ConstantInt::get(getContext(), 4261 APInt::getOneBitSet(BitWidth, SA->getZExtValue())); 4262 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 4263 } 4264 break; 4265 4266 case Instruction::LShr: 4267 // Turn logical shift right of a constant into a unsigned divide. 4268 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 4269 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 4270 4271 // If the shift count is not less than the bitwidth, the result of 4272 // the shift is undefined. Don't try to analyze it, because the 4273 // resolution chosen here may differ from the resolution chosen in 4274 // other parts of the compiler. 4275 if (SA->getValue().uge(BitWidth)) 4276 break; 4277 4278 Constant *X = ConstantInt::get(getContext(), 4279 APInt::getOneBitSet(BitWidth, SA->getZExtValue())); 4280 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 4281 } 4282 break; 4283 4284 case Instruction::AShr: 4285 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 4286 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 4287 if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) 4288 if (L->getOpcode() == Instruction::Shl && 4289 L->getOperand(1) == U->getOperand(1)) { 4290 uint64_t BitWidth = getTypeSizeInBits(U->getType()); 4291 4292 // If the shift count is not less than the bitwidth, the result of 4293 // the shift is undefined. Don't try to analyze it, because the 4294 // resolution chosen here may differ from the resolution chosen in 4295 // other parts of the compiler. 4296 if (CI->getValue().uge(BitWidth)) 4297 break; 4298 4299 uint64_t Amt = BitWidth - CI->getZExtValue(); 4300 if (Amt == BitWidth) 4301 return getSCEV(L->getOperand(0)); // shift by zero --> noop 4302 return 4303 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 4304 IntegerType::get(getContext(), 4305 Amt)), 4306 U->getType()); 4307 } 4308 break; 4309 4310 case Instruction::Trunc: 4311 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 4312 4313 case Instruction::ZExt: 4314 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 4315 4316 case Instruction::SExt: 4317 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 4318 4319 case Instruction::BitCast: 4320 // BitCasts are no-op casts so we just eliminate the cast. 4321 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 4322 return getSCEV(U->getOperand(0)); 4323 break; 4324 4325 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 4326 // lead to pointer expressions which cannot safely be expanded to GEPs, 4327 // because ScalarEvolution doesn't respect the GEP aliasing rules when 4328 // simplifying integer expressions. 4329 4330 case Instruction::GetElementPtr: 4331 return createNodeForGEP(cast<GEPOperator>(U)); 4332 4333 case Instruction::PHI: 4334 return createNodeForPHI(cast<PHINode>(U)); 4335 4336 case Instruction::Select: 4337 // This could be a smax or umax that was lowered earlier. 4338 // Try to recover it. 4339 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 4340 Value *LHS = ICI->getOperand(0); 4341 Value *RHS = ICI->getOperand(1); 4342 switch (ICI->getPredicate()) { 4343 case ICmpInst::ICMP_SLT: 4344 case ICmpInst::ICMP_SLE: 4345 std::swap(LHS, RHS); 4346 // fall through 4347 case ICmpInst::ICMP_SGT: 4348 case ICmpInst::ICMP_SGE: 4349 // a >s b ? a+x : b+x -> smax(a, b)+x 4350 // a >s b ? b+x : a+x -> smin(a, b)+x 4351 if (getTypeSizeInBits(LHS->getType()) <= 4352 getTypeSizeInBits(U->getType())) { 4353 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), U->getType()); 4354 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), U->getType()); 4355 const SCEV *LA = getSCEV(U->getOperand(1)); 4356 const SCEV *RA = getSCEV(U->getOperand(2)); 4357 const SCEV *LDiff = getMinusSCEV(LA, LS); 4358 const SCEV *RDiff = getMinusSCEV(RA, RS); 4359 if (LDiff == RDiff) 4360 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 4361 LDiff = getMinusSCEV(LA, RS); 4362 RDiff = getMinusSCEV(RA, LS); 4363 if (LDiff == RDiff) 4364 return getAddExpr(getSMinExpr(LS, RS), LDiff); 4365 } 4366 break; 4367 case ICmpInst::ICMP_ULT: 4368 case ICmpInst::ICMP_ULE: 4369 std::swap(LHS, RHS); 4370 // fall through 4371 case ICmpInst::ICMP_UGT: 4372 case ICmpInst::ICMP_UGE: 4373 // a >u b ? a+x : b+x -> umax(a, b)+x 4374 // a >u b ? b+x : a+x -> umin(a, b)+x 4375 if (getTypeSizeInBits(LHS->getType()) <= 4376 getTypeSizeInBits(U->getType())) { 4377 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType()); 4378 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), U->getType()); 4379 const SCEV *LA = getSCEV(U->getOperand(1)); 4380 const SCEV *RA = getSCEV(U->getOperand(2)); 4381 const SCEV *LDiff = getMinusSCEV(LA, LS); 4382 const SCEV *RDiff = getMinusSCEV(RA, RS); 4383 if (LDiff == RDiff) 4384 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 4385 LDiff = getMinusSCEV(LA, RS); 4386 RDiff = getMinusSCEV(RA, LS); 4387 if (LDiff == RDiff) 4388 return getAddExpr(getUMinExpr(LS, RS), LDiff); 4389 } 4390 break; 4391 case ICmpInst::ICMP_NE: 4392 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 4393 if (getTypeSizeInBits(LHS->getType()) <= 4394 getTypeSizeInBits(U->getType()) && 4395 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) { 4396 const SCEV *One = getConstant(U->getType(), 1); 4397 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType()); 4398 const SCEV *LA = getSCEV(U->getOperand(1)); 4399 const SCEV *RA = getSCEV(U->getOperand(2)); 4400 const SCEV *LDiff = getMinusSCEV(LA, LS); 4401 const SCEV *RDiff = getMinusSCEV(RA, One); 4402 if (LDiff == RDiff) 4403 return getAddExpr(getUMaxExpr(One, LS), LDiff); 4404 } 4405 break; 4406 case ICmpInst::ICMP_EQ: 4407 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 4408 if (getTypeSizeInBits(LHS->getType()) <= 4409 getTypeSizeInBits(U->getType()) && 4410 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) { 4411 const SCEV *One = getConstant(U->getType(), 1); 4412 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType()); 4413 const SCEV *LA = getSCEV(U->getOperand(1)); 4414 const SCEV *RA = getSCEV(U->getOperand(2)); 4415 const SCEV *LDiff = getMinusSCEV(LA, One); 4416 const SCEV *RDiff = getMinusSCEV(RA, LS); 4417 if (LDiff == RDiff) 4418 return getAddExpr(getUMaxExpr(One, LS), LDiff); 4419 } 4420 break; 4421 default: 4422 break; 4423 } 4424 } 4425 4426 default: // We cannot analyze this expression. 4427 break; 4428 } 4429 4430 return getUnknown(V); 4431 } 4432 4433 4434 4435 //===----------------------------------------------------------------------===// 4436 // Iteration Count Computation Code 4437 // 4438 4439 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) { 4440 if (BasicBlock *ExitingBB = L->getExitingBlock()) 4441 return getSmallConstantTripCount(L, ExitingBB); 4442 4443 // No trip count information for multiple exits. 4444 return 0; 4445 } 4446 4447 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a 4448 /// normal unsigned value. Returns 0 if the trip count is unknown or not 4449 /// constant. Will also return 0 if the maximum trip count is very large (>= 4450 /// 2^32). 4451 /// 4452 /// This "trip count" assumes that control exits via ExitingBlock. More 4453 /// precisely, it is the number of times that control may reach ExitingBlock 4454 /// before taking the branch. For loops with multiple exits, it may not be the 4455 /// number times that the loop header executes because the loop may exit 4456 /// prematurely via another branch. 4457 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L, 4458 BasicBlock *ExitingBlock) { 4459 assert(ExitingBlock && "Must pass a non-null exiting block!"); 4460 assert(L->isLoopExiting(ExitingBlock) && 4461 "Exiting block must actually branch out of the loop!"); 4462 const SCEVConstant *ExitCount = 4463 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock)); 4464 if (!ExitCount) 4465 return 0; 4466 4467 ConstantInt *ExitConst = ExitCount->getValue(); 4468 4469 // Guard against huge trip counts. 4470 if (ExitConst->getValue().getActiveBits() > 32) 4471 return 0; 4472 4473 // In case of integer overflow, this returns 0, which is correct. 4474 return ((unsigned)ExitConst->getZExtValue()) + 1; 4475 } 4476 4477 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) { 4478 if (BasicBlock *ExitingBB = L->getExitingBlock()) 4479 return getSmallConstantTripMultiple(L, ExitingBB); 4480 4481 // No trip multiple information for multiple exits. 4482 return 0; 4483 } 4484 4485 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the 4486 /// trip count of this loop as a normal unsigned value, if possible. This 4487 /// means that the actual trip count is always a multiple of the returned 4488 /// value (don't forget the trip count could very well be zero as well!). 4489 /// 4490 /// Returns 1 if the trip count is unknown or not guaranteed to be the 4491 /// multiple of a constant (which is also the case if the trip count is simply 4492 /// constant, use getSmallConstantTripCount for that case), Will also return 1 4493 /// if the trip count is very large (>= 2^32). 4494 /// 4495 /// As explained in the comments for getSmallConstantTripCount, this assumes 4496 /// that control exits the loop via ExitingBlock. 4497 unsigned 4498 ScalarEvolution::getSmallConstantTripMultiple(Loop *L, 4499 BasicBlock *ExitingBlock) { 4500 assert(ExitingBlock && "Must pass a non-null exiting block!"); 4501 assert(L->isLoopExiting(ExitingBlock) && 4502 "Exiting block must actually branch out of the loop!"); 4503 const SCEV *ExitCount = getExitCount(L, ExitingBlock); 4504 if (ExitCount == getCouldNotCompute()) 4505 return 1; 4506 4507 // Get the trip count from the BE count by adding 1. 4508 const SCEV *TCMul = getAddExpr(ExitCount, 4509 getConstant(ExitCount->getType(), 1)); 4510 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt 4511 // to factor simple cases. 4512 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul)) 4513 TCMul = Mul->getOperand(0); 4514 4515 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul); 4516 if (!MulC) 4517 return 1; 4518 4519 ConstantInt *Result = MulC->getValue(); 4520 4521 // Guard against huge trip counts (this requires checking 4522 // for zero to handle the case where the trip count == -1 and the 4523 // addition wraps). 4524 if (!Result || Result->getValue().getActiveBits() > 32 || 4525 Result->getValue().getActiveBits() == 0) 4526 return 1; 4527 4528 return (unsigned)Result->getZExtValue(); 4529 } 4530 4531 // getExitCount - Get the expression for the number of loop iterations for which 4532 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return 4533 // SCEVCouldNotCompute. 4534 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) { 4535 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this); 4536 } 4537 4538 /// getBackedgeTakenCount - If the specified loop has a predictable 4539 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 4540 /// object. The backedge-taken count is the number of times the loop header 4541 /// will be branched to from within the loop. This is one less than the 4542 /// trip count of the loop, since it doesn't count the first iteration, 4543 /// when the header is branched to from outside the loop. 4544 /// 4545 /// Note that it is not valid to call this method on a loop without a 4546 /// loop-invariant backedge-taken count (see 4547 /// hasLoopInvariantBackedgeTakenCount). 4548 /// 4549 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 4550 return getBackedgeTakenInfo(L).getExact(this); 4551 } 4552 4553 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 4554 /// return the least SCEV value that is known never to be less than the 4555 /// actual backedge taken count. 4556 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 4557 return getBackedgeTakenInfo(L).getMax(this); 4558 } 4559 4560 /// PushLoopPHIs - Push PHI nodes in the header of the given loop 4561 /// onto the given Worklist. 4562 static void 4563 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 4564 BasicBlock *Header = L->getHeader(); 4565 4566 // Push all Loop-header PHIs onto the Worklist stack. 4567 for (BasicBlock::iterator I = Header->begin(); 4568 PHINode *PN = dyn_cast<PHINode>(I); ++I) 4569 Worklist.push_back(PN); 4570 } 4571 4572 const ScalarEvolution::BackedgeTakenInfo & 4573 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 4574 // Initially insert an invalid entry for this loop. If the insertion 4575 // succeeds, proceed to actually compute a backedge-taken count and 4576 // update the value. The temporary CouldNotCompute value tells SCEV 4577 // code elsewhere that it shouldn't attempt to request a new 4578 // backedge-taken count, which could result in infinite recursion. 4579 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 4580 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo())); 4581 if (!Pair.second) 4582 return Pair.first->second; 4583 4584 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it 4585 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result 4586 // must be cleared in this scope. 4587 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L); 4588 4589 if (Result.getExact(this) != getCouldNotCompute()) { 4590 assert(isLoopInvariant(Result.getExact(this), L) && 4591 isLoopInvariant(Result.getMax(this), L) && 4592 "Computed backedge-taken count isn't loop invariant for loop!"); 4593 ++NumTripCountsComputed; 4594 } 4595 else if (Result.getMax(this) == getCouldNotCompute() && 4596 isa<PHINode>(L->getHeader()->begin())) { 4597 // Only count loops that have phi nodes as not being computable. 4598 ++NumTripCountsNotComputed; 4599 } 4600 4601 // Now that we know more about the trip count for this loop, forget any 4602 // existing SCEV values for PHI nodes in this loop since they are only 4603 // conservative estimates made without the benefit of trip count 4604 // information. This is similar to the code in forgetLoop, except that 4605 // it handles SCEVUnknown PHI nodes specially. 4606 if (Result.hasAnyInfo()) { 4607 SmallVector<Instruction *, 16> Worklist; 4608 PushLoopPHIs(L, Worklist); 4609 4610 SmallPtrSet<Instruction *, 8> Visited; 4611 while (!Worklist.empty()) { 4612 Instruction *I = Worklist.pop_back_val(); 4613 if (!Visited.insert(I).second) 4614 continue; 4615 4616 ValueExprMapType::iterator It = 4617 ValueExprMap.find_as(static_cast<Value *>(I)); 4618 if (It != ValueExprMap.end()) { 4619 const SCEV *Old = It->second; 4620 4621 // SCEVUnknown for a PHI either means that it has an unrecognized 4622 // structure, or it's a PHI that's in the progress of being computed 4623 // by createNodeForPHI. In the former case, additional loop trip 4624 // count information isn't going to change anything. In the later 4625 // case, createNodeForPHI will perform the necessary updates on its 4626 // own when it gets to that point. 4627 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) { 4628 forgetMemoizedResults(Old); 4629 ValueExprMap.erase(It); 4630 } 4631 if (PHINode *PN = dyn_cast<PHINode>(I)) 4632 ConstantEvolutionLoopExitValue.erase(PN); 4633 } 4634 4635 PushDefUseChildren(I, Worklist); 4636 } 4637 } 4638 4639 // Re-lookup the insert position, since the call to 4640 // ComputeBackedgeTakenCount above could result in a 4641 // recusive call to getBackedgeTakenInfo (on a different 4642 // loop), which would invalidate the iterator computed 4643 // earlier. 4644 return BackedgeTakenCounts.find(L)->second = Result; 4645 } 4646 4647 /// forgetLoop - This method should be called by the client when it has 4648 /// changed a loop in a way that may effect ScalarEvolution's ability to 4649 /// compute a trip count, or if the loop is deleted. 4650 void ScalarEvolution::forgetLoop(const Loop *L) { 4651 // Drop any stored trip count value. 4652 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos = 4653 BackedgeTakenCounts.find(L); 4654 if (BTCPos != BackedgeTakenCounts.end()) { 4655 BTCPos->second.clear(); 4656 BackedgeTakenCounts.erase(BTCPos); 4657 } 4658 4659 // Drop information about expressions based on loop-header PHIs. 4660 SmallVector<Instruction *, 16> Worklist; 4661 PushLoopPHIs(L, Worklist); 4662 4663 SmallPtrSet<Instruction *, 8> Visited; 4664 while (!Worklist.empty()) { 4665 Instruction *I = Worklist.pop_back_val(); 4666 if (!Visited.insert(I).second) 4667 continue; 4668 4669 ValueExprMapType::iterator It = 4670 ValueExprMap.find_as(static_cast<Value *>(I)); 4671 if (It != ValueExprMap.end()) { 4672 forgetMemoizedResults(It->second); 4673 ValueExprMap.erase(It); 4674 if (PHINode *PN = dyn_cast<PHINode>(I)) 4675 ConstantEvolutionLoopExitValue.erase(PN); 4676 } 4677 4678 PushDefUseChildren(I, Worklist); 4679 } 4680 4681 // Forget all contained loops too, to avoid dangling entries in the 4682 // ValuesAtScopes map. 4683 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 4684 forgetLoop(*I); 4685 } 4686 4687 /// forgetValue - This method should be called by the client when it has 4688 /// changed a value in a way that may effect its value, or which may 4689 /// disconnect it from a def-use chain linking it to a loop. 4690 void ScalarEvolution::forgetValue(Value *V) { 4691 Instruction *I = dyn_cast<Instruction>(V); 4692 if (!I) return; 4693 4694 // Drop information about expressions based on loop-header PHIs. 4695 SmallVector<Instruction *, 16> Worklist; 4696 Worklist.push_back(I); 4697 4698 SmallPtrSet<Instruction *, 8> Visited; 4699 while (!Worklist.empty()) { 4700 I = Worklist.pop_back_val(); 4701 if (!Visited.insert(I).second) 4702 continue; 4703 4704 ValueExprMapType::iterator It = 4705 ValueExprMap.find_as(static_cast<Value *>(I)); 4706 if (It != ValueExprMap.end()) { 4707 forgetMemoizedResults(It->second); 4708 ValueExprMap.erase(It); 4709 if (PHINode *PN = dyn_cast<PHINode>(I)) 4710 ConstantEvolutionLoopExitValue.erase(PN); 4711 } 4712 4713 PushDefUseChildren(I, Worklist); 4714 } 4715 } 4716 4717 /// getExact - Get the exact loop backedge taken count considering all loop 4718 /// exits. A computable result can only be return for loops with a single exit. 4719 /// Returning the minimum taken count among all exits is incorrect because one 4720 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that 4721 /// the limit of each loop test is never skipped. This is a valid assumption as 4722 /// long as the loop exits via that test. For precise results, it is the 4723 /// caller's responsibility to specify the relevant loop exit using 4724 /// getExact(ExitingBlock, SE). 4725 const SCEV * 4726 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const { 4727 // If any exits were not computable, the loop is not computable. 4728 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute(); 4729 4730 // We need exactly one computable exit. 4731 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute(); 4732 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info"); 4733 4734 const SCEV *BECount = nullptr; 4735 for (const ExitNotTakenInfo *ENT = &ExitNotTaken; 4736 ENT != nullptr; ENT = ENT->getNextExit()) { 4737 4738 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV"); 4739 4740 if (!BECount) 4741 BECount = ENT->ExactNotTaken; 4742 else if (BECount != ENT->ExactNotTaken) 4743 return SE->getCouldNotCompute(); 4744 } 4745 assert(BECount && "Invalid not taken count for loop exit"); 4746 return BECount; 4747 } 4748 4749 /// getExact - Get the exact not taken count for this loop exit. 4750 const SCEV * 4751 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock, 4752 ScalarEvolution *SE) const { 4753 for (const ExitNotTakenInfo *ENT = &ExitNotTaken; 4754 ENT != nullptr; ENT = ENT->getNextExit()) { 4755 4756 if (ENT->ExitingBlock == ExitingBlock) 4757 return ENT->ExactNotTaken; 4758 } 4759 return SE->getCouldNotCompute(); 4760 } 4761 4762 /// getMax - Get the max backedge taken count for the loop. 4763 const SCEV * 4764 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const { 4765 return Max ? Max : SE->getCouldNotCompute(); 4766 } 4767 4768 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S, 4769 ScalarEvolution *SE) const { 4770 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S)) 4771 return true; 4772 4773 if (!ExitNotTaken.ExitingBlock) 4774 return false; 4775 4776 for (const ExitNotTakenInfo *ENT = &ExitNotTaken; 4777 ENT != nullptr; ENT = ENT->getNextExit()) { 4778 4779 if (ENT->ExactNotTaken != SE->getCouldNotCompute() 4780 && SE->hasOperand(ENT->ExactNotTaken, S)) { 4781 return true; 4782 } 4783 } 4784 return false; 4785 } 4786 4787 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each 4788 /// computable exit into a persistent ExitNotTakenInfo array. 4789 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo( 4790 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts, 4791 bool Complete, const SCEV *MaxCount) : Max(MaxCount) { 4792 4793 if (!Complete) 4794 ExitNotTaken.setIncomplete(); 4795 4796 unsigned NumExits = ExitCounts.size(); 4797 if (NumExits == 0) return; 4798 4799 ExitNotTaken.ExitingBlock = ExitCounts[0].first; 4800 ExitNotTaken.ExactNotTaken = ExitCounts[0].second; 4801 if (NumExits == 1) return; 4802 4803 // Handle the rare case of multiple computable exits. 4804 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1]; 4805 4806 ExitNotTakenInfo *PrevENT = &ExitNotTaken; 4807 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) { 4808 PrevENT->setNextExit(ENT); 4809 ENT->ExitingBlock = ExitCounts[i].first; 4810 ENT->ExactNotTaken = ExitCounts[i].second; 4811 } 4812 } 4813 4814 /// clear - Invalidate this result and free the ExitNotTakenInfo array. 4815 void ScalarEvolution::BackedgeTakenInfo::clear() { 4816 ExitNotTaken.ExitingBlock = nullptr; 4817 ExitNotTaken.ExactNotTaken = nullptr; 4818 delete[] ExitNotTaken.getNextExit(); 4819 } 4820 4821 /// ComputeBackedgeTakenCount - Compute the number of times the backedge 4822 /// of the specified loop will execute. 4823 ScalarEvolution::BackedgeTakenInfo 4824 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 4825 SmallVector<BasicBlock *, 8> ExitingBlocks; 4826 L->getExitingBlocks(ExitingBlocks); 4827 4828 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts; 4829 bool CouldComputeBECount = true; 4830 BasicBlock *Latch = L->getLoopLatch(); // may be NULL. 4831 const SCEV *MustExitMaxBECount = nullptr; 4832 const SCEV *MayExitMaxBECount = nullptr; 4833 4834 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts 4835 // and compute maxBECount. 4836 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 4837 BasicBlock *ExitBB = ExitingBlocks[i]; 4838 ExitLimit EL = ComputeExitLimit(L, ExitBB); 4839 4840 // 1. For each exit that can be computed, add an entry to ExitCounts. 4841 // CouldComputeBECount is true only if all exits can be computed. 4842 if (EL.Exact == getCouldNotCompute()) 4843 // We couldn't compute an exact value for this exit, so 4844 // we won't be able to compute an exact value for the loop. 4845 CouldComputeBECount = false; 4846 else 4847 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact)); 4848 4849 // 2. Derive the loop's MaxBECount from each exit's max number of 4850 // non-exiting iterations. Partition the loop exits into two kinds: 4851 // LoopMustExits and LoopMayExits. 4852 // 4853 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it 4854 // is a LoopMayExit. If any computable LoopMustExit is found, then 4855 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise, 4856 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is 4857 // considered greater than any computable EL.Max. 4858 if (EL.Max != getCouldNotCompute() && Latch && 4859 DT->dominates(ExitBB, Latch)) { 4860 if (!MustExitMaxBECount) 4861 MustExitMaxBECount = EL.Max; 4862 else { 4863 MustExitMaxBECount = 4864 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max); 4865 } 4866 } else if (MayExitMaxBECount != getCouldNotCompute()) { 4867 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute()) 4868 MayExitMaxBECount = EL.Max; 4869 else { 4870 MayExitMaxBECount = 4871 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max); 4872 } 4873 } 4874 } 4875 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount : 4876 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute()); 4877 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount); 4878 } 4879 4880 /// ComputeExitLimit - Compute the number of times the backedge of the specified 4881 /// loop will execute if it exits via the specified block. 4882 ScalarEvolution::ExitLimit 4883 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) { 4884 4885 // Okay, we've chosen an exiting block. See what condition causes us to 4886 // exit at this block and remember the exit block and whether all other targets 4887 // lead to the loop header. 4888 bool MustExecuteLoopHeader = true; 4889 BasicBlock *Exit = nullptr; 4890 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock); 4891 SI != SE; ++SI) 4892 if (!L->contains(*SI)) { 4893 if (Exit) // Multiple exit successors. 4894 return getCouldNotCompute(); 4895 Exit = *SI; 4896 } else if (*SI != L->getHeader()) { 4897 MustExecuteLoopHeader = false; 4898 } 4899 4900 // At this point, we know we have a conditional branch that determines whether 4901 // the loop is exited. However, we don't know if the branch is executed each 4902 // time through the loop. If not, then the execution count of the branch will 4903 // not be equal to the trip count of the loop. 4904 // 4905 // Currently we check for this by checking to see if the Exit branch goes to 4906 // the loop header. If so, we know it will always execute the same number of 4907 // times as the loop. We also handle the case where the exit block *is* the 4908 // loop header. This is common for un-rotated loops. 4909 // 4910 // If both of those tests fail, walk up the unique predecessor chain to the 4911 // header, stopping if there is an edge that doesn't exit the loop. If the 4912 // header is reached, the execution count of the branch will be equal to the 4913 // trip count of the loop. 4914 // 4915 // More extensive analysis could be done to handle more cases here. 4916 // 4917 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) { 4918 // The simple checks failed, try climbing the unique predecessor chain 4919 // up to the header. 4920 bool Ok = false; 4921 for (BasicBlock *BB = ExitingBlock; BB; ) { 4922 BasicBlock *Pred = BB->getUniquePredecessor(); 4923 if (!Pred) 4924 return getCouldNotCompute(); 4925 TerminatorInst *PredTerm = Pred->getTerminator(); 4926 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 4927 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 4928 if (PredSucc == BB) 4929 continue; 4930 // If the predecessor has a successor that isn't BB and isn't 4931 // outside the loop, assume the worst. 4932 if (L->contains(PredSucc)) 4933 return getCouldNotCompute(); 4934 } 4935 if (Pred == L->getHeader()) { 4936 Ok = true; 4937 break; 4938 } 4939 BB = Pred; 4940 } 4941 if (!Ok) 4942 return getCouldNotCompute(); 4943 } 4944 4945 bool IsOnlyExit = (L->getExitingBlock() != nullptr); 4946 TerminatorInst *Term = ExitingBlock->getTerminator(); 4947 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) { 4948 assert(BI->isConditional() && "If unconditional, it can't be in loop!"); 4949 // Proceed to the next level to examine the exit condition expression. 4950 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0), 4951 BI->getSuccessor(1), 4952 /*ControlsExit=*/IsOnlyExit); 4953 } 4954 4955 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term)) 4956 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit, 4957 /*ControlsExit=*/IsOnlyExit); 4958 4959 return getCouldNotCompute(); 4960 } 4961 4962 /// ComputeExitLimitFromCond - Compute the number of times the 4963 /// backedge of the specified loop will execute if its exit condition 4964 /// were a conditional branch of ExitCond, TBB, and FBB. 4965 /// 4966 /// @param ControlsExit is true if ExitCond directly controls the exit 4967 /// branch. In this case, we can assume that the loop exits only if the 4968 /// condition is true and can infer that failing to meet the condition prior to 4969 /// integer wraparound results in undefined behavior. 4970 ScalarEvolution::ExitLimit 4971 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L, 4972 Value *ExitCond, 4973 BasicBlock *TBB, 4974 BasicBlock *FBB, 4975 bool ControlsExit) { 4976 // Check if the controlling expression for this loop is an And or Or. 4977 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 4978 if (BO->getOpcode() == Instruction::And) { 4979 // Recurse on the operands of the and. 4980 bool EitherMayExit = L->contains(TBB); 4981 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB, 4982 ControlsExit && !EitherMayExit); 4983 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB, 4984 ControlsExit && !EitherMayExit); 4985 const SCEV *BECount = getCouldNotCompute(); 4986 const SCEV *MaxBECount = getCouldNotCompute(); 4987 if (EitherMayExit) { 4988 // Both conditions must be true for the loop to continue executing. 4989 // Choose the less conservative count. 4990 if (EL0.Exact == getCouldNotCompute() || 4991 EL1.Exact == getCouldNotCompute()) 4992 BECount = getCouldNotCompute(); 4993 else 4994 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact); 4995 if (EL0.Max == getCouldNotCompute()) 4996 MaxBECount = EL1.Max; 4997 else if (EL1.Max == getCouldNotCompute()) 4998 MaxBECount = EL0.Max; 4999 else 5000 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max); 5001 } else { 5002 // Both conditions must be true at the same time for the loop to exit. 5003 // For now, be conservative. 5004 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 5005 if (EL0.Max == EL1.Max) 5006 MaxBECount = EL0.Max; 5007 if (EL0.Exact == EL1.Exact) 5008 BECount = EL0.Exact; 5009 } 5010 5011 return ExitLimit(BECount, MaxBECount); 5012 } 5013 if (BO->getOpcode() == Instruction::Or) { 5014 // Recurse on the operands of the or. 5015 bool EitherMayExit = L->contains(FBB); 5016 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB, 5017 ControlsExit && !EitherMayExit); 5018 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB, 5019 ControlsExit && !EitherMayExit); 5020 const SCEV *BECount = getCouldNotCompute(); 5021 const SCEV *MaxBECount = getCouldNotCompute(); 5022 if (EitherMayExit) { 5023 // Both conditions must be false for the loop to continue executing. 5024 // Choose the less conservative count. 5025 if (EL0.Exact == getCouldNotCompute() || 5026 EL1.Exact == getCouldNotCompute()) 5027 BECount = getCouldNotCompute(); 5028 else 5029 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact); 5030 if (EL0.Max == getCouldNotCompute()) 5031 MaxBECount = EL1.Max; 5032 else if (EL1.Max == getCouldNotCompute()) 5033 MaxBECount = EL0.Max; 5034 else 5035 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max); 5036 } else { 5037 // Both conditions must be false at the same time for the loop to exit. 5038 // For now, be conservative. 5039 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 5040 if (EL0.Max == EL1.Max) 5041 MaxBECount = EL0.Max; 5042 if (EL0.Exact == EL1.Exact) 5043 BECount = EL0.Exact; 5044 } 5045 5046 return ExitLimit(BECount, MaxBECount); 5047 } 5048 } 5049 5050 // With an icmp, it may be feasible to compute an exact backedge-taken count. 5051 // Proceed to the next level to examine the icmp. 5052 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 5053 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit); 5054 5055 // Check for a constant condition. These are normally stripped out by 5056 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 5057 // preserve the CFG and is temporarily leaving constant conditions 5058 // in place. 5059 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 5060 if (L->contains(FBB) == !CI->getZExtValue()) 5061 // The backedge is always taken. 5062 return getCouldNotCompute(); 5063 else 5064 // The backedge is never taken. 5065 return getConstant(CI->getType(), 0); 5066 } 5067 5068 // If it's not an integer or pointer comparison then compute it the hard way. 5069 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB)); 5070 } 5071 5072 /// ComputeExitLimitFromICmp - Compute the number of times the 5073 /// backedge of the specified loop will execute if its exit condition 5074 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 5075 ScalarEvolution::ExitLimit 5076 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L, 5077 ICmpInst *ExitCond, 5078 BasicBlock *TBB, 5079 BasicBlock *FBB, 5080 bool ControlsExit) { 5081 5082 // If the condition was exit on true, convert the condition to exit on false 5083 ICmpInst::Predicate Cond; 5084 if (!L->contains(FBB)) 5085 Cond = ExitCond->getPredicate(); 5086 else 5087 Cond = ExitCond->getInversePredicate(); 5088 5089 // Handle common loops like: for (X = "string"; *X; ++X) 5090 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 5091 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 5092 ExitLimit ItCnt = 5093 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond); 5094 if (ItCnt.hasAnyInfo()) 5095 return ItCnt; 5096 } 5097 5098 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 5099 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 5100 5101 // Try to evaluate any dependencies out of the loop. 5102 LHS = getSCEVAtScope(LHS, L); 5103 RHS = getSCEVAtScope(RHS, L); 5104 5105 // At this point, we would like to compute how many iterations of the 5106 // loop the predicate will return true for these inputs. 5107 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) { 5108 // If there is a loop-invariant, force it into the RHS. 5109 std::swap(LHS, RHS); 5110 Cond = ICmpInst::getSwappedPredicate(Cond); 5111 } 5112 5113 // Simplify the operands before analyzing them. 5114 (void)SimplifyICmpOperands(Cond, LHS, RHS); 5115 5116 // If we have a comparison of a chrec against a constant, try to use value 5117 // ranges to answer this query. 5118 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 5119 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 5120 if (AddRec->getLoop() == L) { 5121 // Form the constant range. 5122 ConstantRange CompRange( 5123 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 5124 5125 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 5126 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 5127 } 5128 5129 switch (Cond) { 5130 case ICmpInst::ICMP_NE: { // while (X != Y) 5131 // Convert to: while (X-Y != 0) 5132 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit); 5133 if (EL.hasAnyInfo()) return EL; 5134 break; 5135 } 5136 case ICmpInst::ICMP_EQ: { // while (X == Y) 5137 // Convert to: while (X-Y == 0) 5138 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 5139 if (EL.hasAnyInfo()) return EL; 5140 break; 5141 } 5142 case ICmpInst::ICMP_SLT: 5143 case ICmpInst::ICMP_ULT: { // while (X < Y) 5144 bool IsSigned = Cond == ICmpInst::ICMP_SLT; 5145 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit); 5146 if (EL.hasAnyInfo()) return EL; 5147 break; 5148 } 5149 case ICmpInst::ICMP_SGT: 5150 case ICmpInst::ICMP_UGT: { // while (X > Y) 5151 bool IsSigned = Cond == ICmpInst::ICMP_SGT; 5152 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit); 5153 if (EL.hasAnyInfo()) return EL; 5154 break; 5155 } 5156 default: 5157 #if 0 5158 dbgs() << "ComputeBackedgeTakenCount "; 5159 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 5160 dbgs() << "[unsigned] "; 5161 dbgs() << *LHS << " " 5162 << Instruction::getOpcodeName(Instruction::ICmp) 5163 << " " << *RHS << "\n"; 5164 #endif 5165 break; 5166 } 5167 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB)); 5168 } 5169 5170 ScalarEvolution::ExitLimit 5171 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L, 5172 SwitchInst *Switch, 5173 BasicBlock *ExitingBlock, 5174 bool ControlsExit) { 5175 assert(!L->contains(ExitingBlock) && "Not an exiting block!"); 5176 5177 // Give up if the exit is the default dest of a switch. 5178 if (Switch->getDefaultDest() == ExitingBlock) 5179 return getCouldNotCompute(); 5180 5181 assert(L->contains(Switch->getDefaultDest()) && 5182 "Default case must not exit the loop!"); 5183 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L); 5184 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock)); 5185 5186 // while (X != Y) --> while (X-Y != 0) 5187 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit); 5188 if (EL.hasAnyInfo()) 5189 return EL; 5190 5191 return getCouldNotCompute(); 5192 } 5193 5194 static ConstantInt * 5195 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 5196 ScalarEvolution &SE) { 5197 const SCEV *InVal = SE.getConstant(C); 5198 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 5199 assert(isa<SCEVConstant>(Val) && 5200 "Evaluation of SCEV at constant didn't fold correctly?"); 5201 return cast<SCEVConstant>(Val)->getValue(); 5202 } 5203 5204 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of 5205 /// 'icmp op load X, cst', try to see if we can compute the backedge 5206 /// execution count. 5207 ScalarEvolution::ExitLimit 5208 ScalarEvolution::ComputeLoadConstantCompareExitLimit( 5209 LoadInst *LI, 5210 Constant *RHS, 5211 const Loop *L, 5212 ICmpInst::Predicate predicate) { 5213 5214 if (LI->isVolatile()) return getCouldNotCompute(); 5215 5216 // Check to see if the loaded pointer is a getelementptr of a global. 5217 // TODO: Use SCEV instead of manually grubbing with GEPs. 5218 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 5219 if (!GEP) return getCouldNotCompute(); 5220 5221 // Make sure that it is really a constant global we are gepping, with an 5222 // initializer, and make sure the first IDX is really 0. 5223 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 5224 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 5225 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 5226 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 5227 return getCouldNotCompute(); 5228 5229 // Okay, we allow one non-constant index into the GEP instruction. 5230 Value *VarIdx = nullptr; 5231 std::vector<Constant*> Indexes; 5232 unsigned VarIdxNum = 0; 5233 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 5234 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 5235 Indexes.push_back(CI); 5236 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 5237 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 5238 VarIdx = GEP->getOperand(i); 5239 VarIdxNum = i-2; 5240 Indexes.push_back(nullptr); 5241 } 5242 5243 // Loop-invariant loads may be a byproduct of loop optimization. Skip them. 5244 if (!VarIdx) 5245 return getCouldNotCompute(); 5246 5247 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 5248 // Check to see if X is a loop variant variable value now. 5249 const SCEV *Idx = getSCEV(VarIdx); 5250 Idx = getSCEVAtScope(Idx, L); 5251 5252 // We can only recognize very limited forms of loop index expressions, in 5253 // particular, only affine AddRec's like {C1,+,C2}. 5254 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 5255 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) || 5256 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 5257 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 5258 return getCouldNotCompute(); 5259 5260 unsigned MaxSteps = MaxBruteForceIterations; 5261 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 5262 ConstantInt *ItCst = ConstantInt::get( 5263 cast<IntegerType>(IdxExpr->getType()), IterationNum); 5264 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 5265 5266 // Form the GEP offset. 5267 Indexes[VarIdxNum] = Val; 5268 5269 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(), 5270 Indexes); 5271 if (!Result) break; // Cannot compute! 5272 5273 // Evaluate the condition for this iteration. 5274 Result = ConstantExpr::getICmp(predicate, Result, RHS); 5275 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 5276 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 5277 #if 0 5278 dbgs() << "\n***\n*** Computed loop count " << *ItCst 5279 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 5280 << "***\n"; 5281 #endif 5282 ++NumArrayLenItCounts; 5283 return getConstant(ItCst); // Found terminating iteration! 5284 } 5285 } 5286 return getCouldNotCompute(); 5287 } 5288 5289 5290 /// CanConstantFold - Return true if we can constant fold an instruction of the 5291 /// specified type, assuming that all operands were constants. 5292 static bool CanConstantFold(const Instruction *I) { 5293 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 5294 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) || 5295 isa<LoadInst>(I)) 5296 return true; 5297 5298 if (const CallInst *CI = dyn_cast<CallInst>(I)) 5299 if (const Function *F = CI->getCalledFunction()) 5300 return canConstantFoldCallTo(F); 5301 return false; 5302 } 5303 5304 /// Determine whether this instruction can constant evolve within this loop 5305 /// assuming its operands can all constant evolve. 5306 static bool canConstantEvolve(Instruction *I, const Loop *L) { 5307 // An instruction outside of the loop can't be derived from a loop PHI. 5308 if (!L->contains(I)) return false; 5309 5310 if (isa<PHINode>(I)) { 5311 // We don't currently keep track of the control flow needed to evaluate 5312 // PHIs, so we cannot handle PHIs inside of loops. 5313 return L->getHeader() == I->getParent(); 5314 } 5315 5316 // If we won't be able to constant fold this expression even if the operands 5317 // are constants, bail early. 5318 return CanConstantFold(I); 5319 } 5320 5321 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by 5322 /// recursing through each instruction operand until reaching a loop header phi. 5323 static PHINode * 5324 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L, 5325 DenseMap<Instruction *, PHINode *> &PHIMap) { 5326 5327 // Otherwise, we can evaluate this instruction if all of its operands are 5328 // constant or derived from a PHI node themselves. 5329 PHINode *PHI = nullptr; 5330 for (Instruction::op_iterator OpI = UseInst->op_begin(), 5331 OpE = UseInst->op_end(); OpI != OpE; ++OpI) { 5332 5333 if (isa<Constant>(*OpI)) continue; 5334 5335 Instruction *OpInst = dyn_cast<Instruction>(*OpI); 5336 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr; 5337 5338 PHINode *P = dyn_cast<PHINode>(OpInst); 5339 if (!P) 5340 // If this operand is already visited, reuse the prior result. 5341 // We may have P != PHI if this is the deepest point at which the 5342 // inconsistent paths meet. 5343 P = PHIMap.lookup(OpInst); 5344 if (!P) { 5345 // Recurse and memoize the results, whether a phi is found or not. 5346 // This recursive call invalidates pointers into PHIMap. 5347 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap); 5348 PHIMap[OpInst] = P; 5349 } 5350 if (!P) 5351 return nullptr; // Not evolving from PHI 5352 if (PHI && PHI != P) 5353 return nullptr; // Evolving from multiple different PHIs. 5354 PHI = P; 5355 } 5356 // This is a expression evolving from a constant PHI! 5357 return PHI; 5358 } 5359 5360 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 5361 /// in the loop that V is derived from. We allow arbitrary operations along the 5362 /// way, but the operands of an operation must either be constants or a value 5363 /// derived from a constant PHI. If this expression does not fit with these 5364 /// constraints, return null. 5365 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 5366 Instruction *I = dyn_cast<Instruction>(V); 5367 if (!I || !canConstantEvolve(I, L)) return nullptr; 5368 5369 if (PHINode *PN = dyn_cast<PHINode>(I)) { 5370 return PN; 5371 } 5372 5373 // Record non-constant instructions contained by the loop. 5374 DenseMap<Instruction *, PHINode *> PHIMap; 5375 return getConstantEvolvingPHIOperands(I, L, PHIMap); 5376 } 5377 5378 /// EvaluateExpression - Given an expression that passes the 5379 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 5380 /// in the loop has the value PHIVal. If we can't fold this expression for some 5381 /// reason, return null. 5382 static Constant *EvaluateExpression(Value *V, const Loop *L, 5383 DenseMap<Instruction *, Constant *> &Vals, 5384 const DataLayout &DL, 5385 const TargetLibraryInfo *TLI) { 5386 // Convenient constant check, but redundant for recursive calls. 5387 if (Constant *C = dyn_cast<Constant>(V)) return C; 5388 Instruction *I = dyn_cast<Instruction>(V); 5389 if (!I) return nullptr; 5390 5391 if (Constant *C = Vals.lookup(I)) return C; 5392 5393 // An instruction inside the loop depends on a value outside the loop that we 5394 // weren't given a mapping for, or a value such as a call inside the loop. 5395 if (!canConstantEvolve(I, L)) return nullptr; 5396 5397 // An unmapped PHI can be due to a branch or another loop inside this loop, 5398 // or due to this not being the initial iteration through a loop where we 5399 // couldn't compute the evolution of this particular PHI last time. 5400 if (isa<PHINode>(I)) return nullptr; 5401 5402 std::vector<Constant*> Operands(I->getNumOperands()); 5403 5404 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 5405 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i)); 5406 if (!Operand) { 5407 Operands[i] = dyn_cast<Constant>(I->getOperand(i)); 5408 if (!Operands[i]) return nullptr; 5409 continue; 5410 } 5411 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI); 5412 Vals[Operand] = C; 5413 if (!C) return nullptr; 5414 Operands[i] = C; 5415 } 5416 5417 if (CmpInst *CI = dyn_cast<CmpInst>(I)) 5418 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 5419 Operands[1], DL, TLI); 5420 if (LoadInst *LI = dyn_cast<LoadInst>(I)) { 5421 if (!LI->isVolatile()) 5422 return ConstantFoldLoadFromConstPtr(Operands[0], DL); 5423 } 5424 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL, 5425 TLI); 5426 } 5427 5428 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 5429 /// in the header of its containing loop, we know the loop executes a 5430 /// constant number of times, and the PHI node is just a recurrence 5431 /// involving constants, fold it. 5432 Constant * 5433 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 5434 const APInt &BEs, 5435 const Loop *L) { 5436 DenseMap<PHINode*, Constant*>::const_iterator I = 5437 ConstantEvolutionLoopExitValue.find(PN); 5438 if (I != ConstantEvolutionLoopExitValue.end()) 5439 return I->second; 5440 5441 if (BEs.ugt(MaxBruteForceIterations)) 5442 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it. 5443 5444 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 5445 5446 DenseMap<Instruction *, Constant *> CurrentIterVals; 5447 BasicBlock *Header = L->getHeader(); 5448 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!"); 5449 5450 // Since the loop is canonicalized, the PHI node must have two entries. One 5451 // entry must be a constant (coming in from outside of the loop), and the 5452 // second must be derived from the same PHI. 5453 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 5454 PHINode *PHI = nullptr; 5455 for (BasicBlock::iterator I = Header->begin(); 5456 (PHI = dyn_cast<PHINode>(I)); ++I) { 5457 Constant *StartCST = 5458 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge)); 5459 if (!StartCST) continue; 5460 CurrentIterVals[PHI] = StartCST; 5461 } 5462 if (!CurrentIterVals.count(PN)) 5463 return RetVal = nullptr; 5464 5465 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 5466 5467 // Execute the loop symbolically to determine the exit value. 5468 if (BEs.getActiveBits() >= 32) 5469 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it! 5470 5471 unsigned NumIterations = BEs.getZExtValue(); // must be in range 5472 unsigned IterationNum = 0; 5473 const DataLayout &DL = F->getParent()->getDataLayout(); 5474 for (; ; ++IterationNum) { 5475 if (IterationNum == NumIterations) 5476 return RetVal = CurrentIterVals[PN]; // Got exit value! 5477 5478 // Compute the value of the PHIs for the next iteration. 5479 // EvaluateExpression adds non-phi values to the CurrentIterVals map. 5480 DenseMap<Instruction *, Constant *> NextIterVals; 5481 Constant *NextPHI = 5482 EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI); 5483 if (!NextPHI) 5484 return nullptr; // Couldn't evaluate! 5485 NextIterVals[PN] = NextPHI; 5486 5487 bool StoppedEvolving = NextPHI == CurrentIterVals[PN]; 5488 5489 // Also evaluate the other PHI nodes. However, we don't get to stop if we 5490 // cease to be able to evaluate one of them or if they stop evolving, 5491 // because that doesn't necessarily prevent us from computing PN. 5492 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute; 5493 for (DenseMap<Instruction *, Constant *>::const_iterator 5494 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){ 5495 PHINode *PHI = dyn_cast<PHINode>(I->first); 5496 if (!PHI || PHI == PN || PHI->getParent() != Header) continue; 5497 PHIsToCompute.push_back(std::make_pair(PHI, I->second)); 5498 } 5499 // We use two distinct loops because EvaluateExpression may invalidate any 5500 // iterators into CurrentIterVals. 5501 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator 5502 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) { 5503 PHINode *PHI = I->first; 5504 Constant *&NextPHI = NextIterVals[PHI]; 5505 if (!NextPHI) { // Not already computed. 5506 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge); 5507 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI); 5508 } 5509 if (NextPHI != I->second) 5510 StoppedEvolving = false; 5511 } 5512 5513 // If all entries in CurrentIterVals == NextIterVals then we can stop 5514 // iterating, the loop can't continue to change. 5515 if (StoppedEvolving) 5516 return RetVal = CurrentIterVals[PN]; 5517 5518 CurrentIterVals.swap(NextIterVals); 5519 } 5520 } 5521 5522 /// ComputeExitCountExhaustively - If the loop is known to execute a 5523 /// constant number of times (the condition evolves only from constants), 5524 /// try to evaluate a few iterations of the loop until we get the exit 5525 /// condition gets a value of ExitWhen (true or false). If we cannot 5526 /// evaluate the trip count of the loop, return getCouldNotCompute(). 5527 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L, 5528 Value *Cond, 5529 bool ExitWhen) { 5530 PHINode *PN = getConstantEvolvingPHI(Cond, L); 5531 if (!PN) return getCouldNotCompute(); 5532 5533 // If the loop is canonicalized, the PHI will have exactly two entries. 5534 // That's the only form we support here. 5535 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 5536 5537 DenseMap<Instruction *, Constant *> CurrentIterVals; 5538 BasicBlock *Header = L->getHeader(); 5539 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!"); 5540 5541 // One entry must be a constant (coming in from outside of the loop), and the 5542 // second must be derived from the same PHI. 5543 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 5544 PHINode *PHI = nullptr; 5545 for (BasicBlock::iterator I = Header->begin(); 5546 (PHI = dyn_cast<PHINode>(I)); ++I) { 5547 Constant *StartCST = 5548 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge)); 5549 if (!StartCST) continue; 5550 CurrentIterVals[PHI] = StartCST; 5551 } 5552 if (!CurrentIterVals.count(PN)) 5553 return getCouldNotCompute(); 5554 5555 // Okay, we find a PHI node that defines the trip count of this loop. Execute 5556 // the loop symbolically to determine when the condition gets a value of 5557 // "ExitWhen". 5558 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 5559 const DataLayout &DL = F->getParent()->getDataLayout(); 5560 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){ 5561 ConstantInt *CondVal = dyn_cast_or_null<ConstantInt>( 5562 EvaluateExpression(Cond, L, CurrentIterVals, DL, TLI)); 5563 5564 // Couldn't symbolically evaluate. 5565 if (!CondVal) return getCouldNotCompute(); 5566 5567 if (CondVal->getValue() == uint64_t(ExitWhen)) { 5568 ++NumBruteForceTripCountsComputed; 5569 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 5570 } 5571 5572 // Update all the PHI nodes for the next iteration. 5573 DenseMap<Instruction *, Constant *> NextIterVals; 5574 5575 // Create a list of which PHIs we need to compute. We want to do this before 5576 // calling EvaluateExpression on them because that may invalidate iterators 5577 // into CurrentIterVals. 5578 SmallVector<PHINode *, 8> PHIsToCompute; 5579 for (DenseMap<Instruction *, Constant *>::const_iterator 5580 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){ 5581 PHINode *PHI = dyn_cast<PHINode>(I->first); 5582 if (!PHI || PHI->getParent() != Header) continue; 5583 PHIsToCompute.push_back(PHI); 5584 } 5585 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(), 5586 E = PHIsToCompute.end(); I != E; ++I) { 5587 PHINode *PHI = *I; 5588 Constant *&NextPHI = NextIterVals[PHI]; 5589 if (NextPHI) continue; // Already computed! 5590 5591 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge); 5592 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI); 5593 } 5594 CurrentIterVals.swap(NextIterVals); 5595 } 5596 5597 // Too many iterations were needed to evaluate. 5598 return getCouldNotCompute(); 5599 } 5600 5601 /// getSCEVAtScope - Return a SCEV expression for the specified value 5602 /// at the specified scope in the program. The L value specifies a loop 5603 /// nest to evaluate the expression at, where null is the top-level or a 5604 /// specified loop is immediately inside of the loop. 5605 /// 5606 /// This method can be used to compute the exit value for a variable defined 5607 /// in a loop by querying what the value will hold in the parent loop. 5608 /// 5609 /// In the case that a relevant loop exit value cannot be computed, the 5610 /// original value V is returned. 5611 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 5612 // Check to see if we've folded this expression at this loop before. 5613 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V]; 5614 for (unsigned u = 0; u < Values.size(); u++) { 5615 if (Values[u].first == L) 5616 return Values[u].second ? Values[u].second : V; 5617 } 5618 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr))); 5619 // Otherwise compute it. 5620 const SCEV *C = computeSCEVAtScope(V, L); 5621 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V]; 5622 for (unsigned u = Values2.size(); u > 0; u--) { 5623 if (Values2[u - 1].first == L) { 5624 Values2[u - 1].second = C; 5625 break; 5626 } 5627 } 5628 return C; 5629 } 5630 5631 /// This builds up a Constant using the ConstantExpr interface. That way, we 5632 /// will return Constants for objects which aren't represented by a 5633 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt. 5634 /// Returns NULL if the SCEV isn't representable as a Constant. 5635 static Constant *BuildConstantFromSCEV(const SCEV *V) { 5636 switch (static_cast<SCEVTypes>(V->getSCEVType())) { 5637 case scCouldNotCompute: 5638 case scAddRecExpr: 5639 break; 5640 case scConstant: 5641 return cast<SCEVConstant>(V)->getValue(); 5642 case scUnknown: 5643 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue()); 5644 case scSignExtend: { 5645 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V); 5646 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand())) 5647 return ConstantExpr::getSExt(CastOp, SS->getType()); 5648 break; 5649 } 5650 case scZeroExtend: { 5651 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V); 5652 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand())) 5653 return ConstantExpr::getZExt(CastOp, SZ->getType()); 5654 break; 5655 } 5656 case scTruncate: { 5657 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V); 5658 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand())) 5659 return ConstantExpr::getTrunc(CastOp, ST->getType()); 5660 break; 5661 } 5662 case scAddExpr: { 5663 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V); 5664 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) { 5665 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) { 5666 unsigned AS = PTy->getAddressSpace(); 5667 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS); 5668 C = ConstantExpr::getBitCast(C, DestPtrTy); 5669 } 5670 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) { 5671 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i)); 5672 if (!C2) return nullptr; 5673 5674 // First pointer! 5675 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) { 5676 unsigned AS = C2->getType()->getPointerAddressSpace(); 5677 std::swap(C, C2); 5678 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS); 5679 // The offsets have been converted to bytes. We can add bytes to an 5680 // i8* by GEP with the byte count in the first index. 5681 C = ConstantExpr::getBitCast(C, DestPtrTy); 5682 } 5683 5684 // Don't bother trying to sum two pointers. We probably can't 5685 // statically compute a load that results from it anyway. 5686 if (C2->getType()->isPointerTy()) 5687 return nullptr; 5688 5689 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) { 5690 if (PTy->getElementType()->isStructTy()) 5691 C2 = ConstantExpr::getIntegerCast( 5692 C2, Type::getInt32Ty(C->getContext()), true); 5693 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2); 5694 } else 5695 C = ConstantExpr::getAdd(C, C2); 5696 } 5697 return C; 5698 } 5699 break; 5700 } 5701 case scMulExpr: { 5702 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V); 5703 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) { 5704 // Don't bother with pointers at all. 5705 if (C->getType()->isPointerTy()) return nullptr; 5706 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) { 5707 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i)); 5708 if (!C2 || C2->getType()->isPointerTy()) return nullptr; 5709 C = ConstantExpr::getMul(C, C2); 5710 } 5711 return C; 5712 } 5713 break; 5714 } 5715 case scUDivExpr: { 5716 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V); 5717 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS())) 5718 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS())) 5719 if (LHS->getType() == RHS->getType()) 5720 return ConstantExpr::getUDiv(LHS, RHS); 5721 break; 5722 } 5723 case scSMaxExpr: 5724 case scUMaxExpr: 5725 break; // TODO: smax, umax. 5726 } 5727 return nullptr; 5728 } 5729 5730 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 5731 if (isa<SCEVConstant>(V)) return V; 5732 5733 // If this instruction is evolved from a constant-evolving PHI, compute the 5734 // exit value from the loop without using SCEVs. 5735 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 5736 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 5737 const Loop *LI = (*this->LI)[I->getParent()]; 5738 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 5739 if (PHINode *PN = dyn_cast<PHINode>(I)) 5740 if (PN->getParent() == LI->getHeader()) { 5741 // Okay, there is no closed form solution for the PHI node. Check 5742 // to see if the loop that contains it has a known backedge-taken 5743 // count. If so, we may be able to force computation of the exit 5744 // value. 5745 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 5746 if (const SCEVConstant *BTCC = 5747 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 5748 // Okay, we know how many times the containing loop executes. If 5749 // this is a constant evolving PHI node, get the final value at 5750 // the specified iteration number. 5751 Constant *RV = getConstantEvolutionLoopExitValue(PN, 5752 BTCC->getValue()->getValue(), 5753 LI); 5754 if (RV) return getSCEV(RV); 5755 } 5756 } 5757 5758 // Okay, this is an expression that we cannot symbolically evaluate 5759 // into a SCEV. Check to see if it's possible to symbolically evaluate 5760 // the arguments into constants, and if so, try to constant propagate the 5761 // result. This is particularly useful for computing loop exit values. 5762 if (CanConstantFold(I)) { 5763 SmallVector<Constant *, 4> Operands; 5764 bool MadeImprovement = false; 5765 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 5766 Value *Op = I->getOperand(i); 5767 if (Constant *C = dyn_cast<Constant>(Op)) { 5768 Operands.push_back(C); 5769 continue; 5770 } 5771 5772 // If any of the operands is non-constant and if they are 5773 // non-integer and non-pointer, don't even try to analyze them 5774 // with scev techniques. 5775 if (!isSCEVable(Op->getType())) 5776 return V; 5777 5778 const SCEV *OrigV = getSCEV(Op); 5779 const SCEV *OpV = getSCEVAtScope(OrigV, L); 5780 MadeImprovement |= OrigV != OpV; 5781 5782 Constant *C = BuildConstantFromSCEV(OpV); 5783 if (!C) return V; 5784 if (C->getType() != Op->getType()) 5785 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 5786 Op->getType(), 5787 false), 5788 C, Op->getType()); 5789 Operands.push_back(C); 5790 } 5791 5792 // Check to see if getSCEVAtScope actually made an improvement. 5793 if (MadeImprovement) { 5794 Constant *C = nullptr; 5795 const DataLayout &DL = F->getParent()->getDataLayout(); 5796 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 5797 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 5798 Operands[1], DL, TLI); 5799 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) { 5800 if (!LI->isVolatile()) 5801 C = ConstantFoldLoadFromConstPtr(Operands[0], DL); 5802 } else 5803 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, 5804 DL, TLI); 5805 if (!C) return V; 5806 return getSCEV(C); 5807 } 5808 } 5809 } 5810 5811 // This is some other type of SCEVUnknown, just return it. 5812 return V; 5813 } 5814 5815 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 5816 // Avoid performing the look-up in the common case where the specified 5817 // expression has no loop-variant portions. 5818 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 5819 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 5820 if (OpAtScope != Comm->getOperand(i)) { 5821 // Okay, at least one of these operands is loop variant but might be 5822 // foldable. Build a new instance of the folded commutative expression. 5823 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 5824 Comm->op_begin()+i); 5825 NewOps.push_back(OpAtScope); 5826 5827 for (++i; i != e; ++i) { 5828 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 5829 NewOps.push_back(OpAtScope); 5830 } 5831 if (isa<SCEVAddExpr>(Comm)) 5832 return getAddExpr(NewOps); 5833 if (isa<SCEVMulExpr>(Comm)) 5834 return getMulExpr(NewOps); 5835 if (isa<SCEVSMaxExpr>(Comm)) 5836 return getSMaxExpr(NewOps); 5837 if (isa<SCEVUMaxExpr>(Comm)) 5838 return getUMaxExpr(NewOps); 5839 llvm_unreachable("Unknown commutative SCEV type!"); 5840 } 5841 } 5842 // If we got here, all operands are loop invariant. 5843 return Comm; 5844 } 5845 5846 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 5847 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 5848 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 5849 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 5850 return Div; // must be loop invariant 5851 return getUDivExpr(LHS, RHS); 5852 } 5853 5854 // If this is a loop recurrence for a loop that does not contain L, then we 5855 // are dealing with the final value computed by the loop. 5856 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 5857 // First, attempt to evaluate each operand. 5858 // Avoid performing the look-up in the common case where the specified 5859 // expression has no loop-variant portions. 5860 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 5861 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); 5862 if (OpAtScope == AddRec->getOperand(i)) 5863 continue; 5864 5865 // Okay, at least one of these operands is loop variant but might be 5866 // foldable. Build a new instance of the folded commutative expression. 5867 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(), 5868 AddRec->op_begin()+i); 5869 NewOps.push_back(OpAtScope); 5870 for (++i; i != e; ++i) 5871 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); 5872 5873 const SCEV *FoldedRec = 5874 getAddRecExpr(NewOps, AddRec->getLoop(), 5875 AddRec->getNoWrapFlags(SCEV::FlagNW)); 5876 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec); 5877 // The addrec may be folded to a nonrecurrence, for example, if the 5878 // induction variable is multiplied by zero after constant folding. Go 5879 // ahead and return the folded value. 5880 if (!AddRec) 5881 return FoldedRec; 5882 break; 5883 } 5884 5885 // If the scope is outside the addrec's loop, evaluate it by using the 5886 // loop exit value of the addrec. 5887 if (!AddRec->getLoop()->contains(L)) { 5888 // To evaluate this recurrence, we need to know how many times the AddRec 5889 // loop iterates. Compute this now. 5890 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 5891 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 5892 5893 // Then, evaluate the AddRec. 5894 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 5895 } 5896 5897 return AddRec; 5898 } 5899 5900 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 5901 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 5902 if (Op == Cast->getOperand()) 5903 return Cast; // must be loop invariant 5904 return getZeroExtendExpr(Op, Cast->getType()); 5905 } 5906 5907 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 5908 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 5909 if (Op == Cast->getOperand()) 5910 return Cast; // must be loop invariant 5911 return getSignExtendExpr(Op, Cast->getType()); 5912 } 5913 5914 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 5915 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 5916 if (Op == Cast->getOperand()) 5917 return Cast; // must be loop invariant 5918 return getTruncateExpr(Op, Cast->getType()); 5919 } 5920 5921 llvm_unreachable("Unknown SCEV type!"); 5922 } 5923 5924 /// getSCEVAtScope - This is a convenience function which does 5925 /// getSCEVAtScope(getSCEV(V), L). 5926 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 5927 return getSCEVAtScope(getSCEV(V), L); 5928 } 5929 5930 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 5931 /// following equation: 5932 /// 5933 /// A * X = B (mod N) 5934 /// 5935 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of 5936 /// A and B isn't important. 5937 /// 5938 /// If the equation does not have a solution, SCEVCouldNotCompute is returned. 5939 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 5940 ScalarEvolution &SE) { 5941 uint32_t BW = A.getBitWidth(); 5942 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 5943 assert(A != 0 && "A must be non-zero."); 5944 5945 // 1. D = gcd(A, N) 5946 // 5947 // The gcd of A and N may have only one prime factor: 2. The number of 5948 // trailing zeros in A is its multiplicity 5949 uint32_t Mult2 = A.countTrailingZeros(); 5950 // D = 2^Mult2 5951 5952 // 2. Check if B is divisible by D. 5953 // 5954 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 5955 // is not less than multiplicity of this prime factor for D. 5956 if (B.countTrailingZeros() < Mult2) 5957 return SE.getCouldNotCompute(); 5958 5959 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 5960 // modulo (N / D). 5961 // 5962 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 5963 // bit width during computations. 5964 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 5965 APInt Mod(BW + 1, 0); 5966 Mod.setBit(BW - Mult2); // Mod = N / D 5967 APInt I = AD.multiplicativeInverse(Mod); 5968 5969 // 4. Compute the minimum unsigned root of the equation: 5970 // I * (B / D) mod (N / D) 5971 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 5972 5973 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 5974 // bits. 5975 return SE.getConstant(Result.trunc(BW)); 5976 } 5977 5978 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the 5979 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 5980 /// might be the same) or two SCEVCouldNotCompute objects. 5981 /// 5982 static std::pair<const SCEV *,const SCEV *> 5983 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 5984 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 5985 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 5986 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 5987 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 5988 5989 // We currently can only solve this if the coefficients are constants. 5990 if (!LC || !MC || !NC) { 5991 const SCEV *CNC = SE.getCouldNotCompute(); 5992 return std::make_pair(CNC, CNC); 5993 } 5994 5995 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 5996 const APInt &L = LC->getValue()->getValue(); 5997 const APInt &M = MC->getValue()->getValue(); 5998 const APInt &N = NC->getValue()->getValue(); 5999 APInt Two(BitWidth, 2); 6000 APInt Four(BitWidth, 4); 6001 6002 { 6003 using namespace APIntOps; 6004 const APInt& C = L; 6005 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 6006 // The B coefficient is M-N/2 6007 APInt B(M); 6008 B -= sdiv(N,Two); 6009 6010 // The A coefficient is N/2 6011 APInt A(N.sdiv(Two)); 6012 6013 // Compute the B^2-4ac term. 6014 APInt SqrtTerm(B); 6015 SqrtTerm *= B; 6016 SqrtTerm -= Four * (A * C); 6017 6018 if (SqrtTerm.isNegative()) { 6019 // The loop is provably infinite. 6020 const SCEV *CNC = SE.getCouldNotCompute(); 6021 return std::make_pair(CNC, CNC); 6022 } 6023 6024 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 6025 // integer value or else APInt::sqrt() will assert. 6026 APInt SqrtVal(SqrtTerm.sqrt()); 6027 6028 // Compute the two solutions for the quadratic formula. 6029 // The divisions must be performed as signed divisions. 6030 APInt NegB(-B); 6031 APInt TwoA(A << 1); 6032 if (TwoA.isMinValue()) { 6033 const SCEV *CNC = SE.getCouldNotCompute(); 6034 return std::make_pair(CNC, CNC); 6035 } 6036 6037 LLVMContext &Context = SE.getContext(); 6038 6039 ConstantInt *Solution1 = 6040 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 6041 ConstantInt *Solution2 = 6042 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 6043 6044 return std::make_pair(SE.getConstant(Solution1), 6045 SE.getConstant(Solution2)); 6046 } // end APIntOps namespace 6047 } 6048 6049 /// HowFarToZero - Return the number of times a backedge comparing the specified 6050 /// value to zero will execute. If not computable, return CouldNotCompute. 6051 /// 6052 /// This is only used for loops with a "x != y" exit test. The exit condition is 6053 /// now expressed as a single expression, V = x-y. So the exit test is 6054 /// effectively V != 0. We know and take advantage of the fact that this 6055 /// expression only being used in a comparison by zero context. 6056 ScalarEvolution::ExitLimit 6057 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) { 6058 // If the value is a constant 6059 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 6060 // If the value is already zero, the branch will execute zero times. 6061 if (C->getValue()->isZero()) return C; 6062 return getCouldNotCompute(); // Otherwise it will loop infinitely. 6063 } 6064 6065 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 6066 if (!AddRec || AddRec->getLoop() != L) 6067 return getCouldNotCompute(); 6068 6069 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 6070 // the quadratic equation to solve it. 6071 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 6072 std::pair<const SCEV *,const SCEV *> Roots = 6073 SolveQuadraticEquation(AddRec, *this); 6074 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 6075 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 6076 if (R1 && R2) { 6077 #if 0 6078 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 6079 << " sol#2: " << *R2 << "\n"; 6080 #endif 6081 // Pick the smallest positive root value. 6082 if (ConstantInt *CB = 6083 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT, 6084 R1->getValue(), 6085 R2->getValue()))) { 6086 if (!CB->getZExtValue()) 6087 std::swap(R1, R2); // R1 is the minimum root now. 6088 6089 // We can only use this value if the chrec ends up with an exact zero 6090 // value at this index. When solving for "X*X != 5", for example, we 6091 // should not accept a root of 2. 6092 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 6093 if (Val->isZero()) 6094 return R1; // We found a quadratic root! 6095 } 6096 } 6097 return getCouldNotCompute(); 6098 } 6099 6100 // Otherwise we can only handle this if it is affine. 6101 if (!AddRec->isAffine()) 6102 return getCouldNotCompute(); 6103 6104 // If this is an affine expression, the execution count of this branch is 6105 // the minimum unsigned root of the following equation: 6106 // 6107 // Start + Step*N = 0 (mod 2^BW) 6108 // 6109 // equivalent to: 6110 // 6111 // Step*N = -Start (mod 2^BW) 6112 // 6113 // where BW is the common bit width of Start and Step. 6114 6115 // Get the initial value for the loop. 6116 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 6117 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 6118 6119 // For now we handle only constant steps. 6120 // 6121 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the 6122 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap 6123 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step. 6124 // We have not yet seen any such cases. 6125 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step); 6126 if (!StepC || StepC->getValue()->equalsInt(0)) 6127 return getCouldNotCompute(); 6128 6129 // For positive steps (counting up until unsigned overflow): 6130 // N = -Start/Step (as unsigned) 6131 // For negative steps (counting down to zero): 6132 // N = Start/-Step 6133 // First compute the unsigned distance from zero in the direction of Step. 6134 bool CountDown = StepC->getValue()->getValue().isNegative(); 6135 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start); 6136 6137 // Handle unitary steps, which cannot wraparound. 6138 // 1*N = -Start; -1*N = Start (mod 2^BW), so: 6139 // N = Distance (as unsigned) 6140 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) { 6141 ConstantRange CR = getUnsignedRange(Start); 6142 const SCEV *MaxBECount; 6143 if (!CountDown && CR.getUnsignedMin().isMinValue()) 6144 // When counting up, the worst starting value is 1, not 0. 6145 MaxBECount = CR.getUnsignedMax().isMinValue() 6146 ? getConstant(APInt::getMinValue(CR.getBitWidth())) 6147 : getConstant(APInt::getMaxValue(CR.getBitWidth())); 6148 else 6149 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax() 6150 : -CR.getUnsignedMin()); 6151 return ExitLimit(Distance, MaxBECount); 6152 } 6153 6154 // As a special case, handle the instance where Step is a positive power of 6155 // two. In this case, determining whether Step divides Distance evenly can be 6156 // done by counting and comparing the number of trailing zeros of Step and 6157 // Distance. 6158 if (!CountDown) { 6159 const APInt &StepV = StepC->getValue()->getValue(); 6160 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It 6161 // also returns true if StepV is maximally negative (eg, INT_MIN), but that 6162 // case is not handled as this code is guarded by !CountDown. 6163 if (StepV.isPowerOf2() && 6164 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) 6165 return getUDivExactExpr(Distance, Step); 6166 } 6167 6168 // If the condition controls loop exit (the loop exits only if the expression 6169 // is true) and the addition is no-wrap we can use unsigned divide to 6170 // compute the backedge count. In this case, the step may not divide the 6171 // distance, but we don't care because if the condition is "missed" the loop 6172 // will have undefined behavior due to wrapping. 6173 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) { 6174 const SCEV *Exact = 6175 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step); 6176 return ExitLimit(Exact, Exact); 6177 } 6178 6179 // Then, try to solve the above equation provided that Start is constant. 6180 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 6181 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 6182 -StartC->getValue()->getValue(), 6183 *this); 6184 return getCouldNotCompute(); 6185 } 6186 6187 /// HowFarToNonZero - Return the number of times a backedge checking the 6188 /// specified value for nonzero will execute. If not computable, return 6189 /// CouldNotCompute 6190 ScalarEvolution::ExitLimit 6191 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 6192 // Loops that look like: while (X == 0) are very strange indeed. We don't 6193 // handle them yet except for the trivial case. This could be expanded in the 6194 // future as needed. 6195 6196 // If the value is a constant, check to see if it is known to be non-zero 6197 // already. If so, the backedge will execute zero times. 6198 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 6199 if (!C->getValue()->isNullValue()) 6200 return getConstant(C->getType(), 0); 6201 return getCouldNotCompute(); // Otherwise it will loop infinitely. 6202 } 6203 6204 // We could implement others, but I really doubt anyone writes loops like 6205 // this, and if they did, they would already be constant folded. 6206 return getCouldNotCompute(); 6207 } 6208 6209 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 6210 /// (which may not be an immediate predecessor) which has exactly one 6211 /// successor from which BB is reachable, or null if no such block is 6212 /// found. 6213 /// 6214 std::pair<BasicBlock *, BasicBlock *> 6215 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 6216 // If the block has a unique predecessor, then there is no path from the 6217 // predecessor to the block that does not go through the direct edge 6218 // from the predecessor to the block. 6219 if (BasicBlock *Pred = BB->getSinglePredecessor()) 6220 return std::make_pair(Pred, BB); 6221 6222 // A loop's header is defined to be a block that dominates the loop. 6223 // If the header has a unique predecessor outside the loop, it must be 6224 // a block that has exactly one successor that can reach the loop. 6225 if (Loop *L = LI->getLoopFor(BB)) 6226 return std::make_pair(L->getLoopPredecessor(), L->getHeader()); 6227 6228 return std::pair<BasicBlock *, BasicBlock *>(); 6229 } 6230 6231 /// HasSameValue - SCEV structural equivalence is usually sufficient for 6232 /// testing whether two expressions are equal, however for the purposes of 6233 /// looking for a condition guarding a loop, it can be useful to be a little 6234 /// more general, since a front-end may have replicated the controlling 6235 /// expression. 6236 /// 6237 static bool HasSameValue(const SCEV *A, const SCEV *B) { 6238 // Quick check to see if they are the same SCEV. 6239 if (A == B) return true; 6240 6241 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 6242 // two different instructions with the same value. Check for this case. 6243 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 6244 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 6245 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 6246 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 6247 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 6248 return true; 6249 6250 // Otherwise assume they may have a different value. 6251 return false; 6252 } 6253 6254 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with 6255 /// predicate Pred. Return true iff any changes were made. 6256 /// 6257 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 6258 const SCEV *&LHS, const SCEV *&RHS, 6259 unsigned Depth) { 6260 bool Changed = false; 6261 6262 // If we hit the max recursion limit bail out. 6263 if (Depth >= 3) 6264 return false; 6265 6266 // Canonicalize a constant to the right side. 6267 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 6268 // Check for both operands constant. 6269 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 6270 if (ConstantExpr::getICmp(Pred, 6271 LHSC->getValue(), 6272 RHSC->getValue())->isNullValue()) 6273 goto trivially_false; 6274 else 6275 goto trivially_true; 6276 } 6277 // Otherwise swap the operands to put the constant on the right. 6278 std::swap(LHS, RHS); 6279 Pred = ICmpInst::getSwappedPredicate(Pred); 6280 Changed = true; 6281 } 6282 6283 // If we're comparing an addrec with a value which is loop-invariant in the 6284 // addrec's loop, put the addrec on the left. Also make a dominance check, 6285 // as both operands could be addrecs loop-invariant in each other's loop. 6286 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 6287 const Loop *L = AR->getLoop(); 6288 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) { 6289 std::swap(LHS, RHS); 6290 Pred = ICmpInst::getSwappedPredicate(Pred); 6291 Changed = true; 6292 } 6293 } 6294 6295 // If there's a constant operand, canonicalize comparisons with boundary 6296 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 6297 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 6298 const APInt &RA = RC->getValue()->getValue(); 6299 switch (Pred) { 6300 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 6301 case ICmpInst::ICMP_EQ: 6302 case ICmpInst::ICMP_NE: 6303 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b. 6304 if (!RA) 6305 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS)) 6306 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0))) 6307 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 && 6308 ME->getOperand(0)->isAllOnesValue()) { 6309 RHS = AE->getOperand(1); 6310 LHS = ME->getOperand(1); 6311 Changed = true; 6312 } 6313 break; 6314 case ICmpInst::ICMP_UGE: 6315 if ((RA - 1).isMinValue()) { 6316 Pred = ICmpInst::ICMP_NE; 6317 RHS = getConstant(RA - 1); 6318 Changed = true; 6319 break; 6320 } 6321 if (RA.isMaxValue()) { 6322 Pred = ICmpInst::ICMP_EQ; 6323 Changed = true; 6324 break; 6325 } 6326 if (RA.isMinValue()) goto trivially_true; 6327 6328 Pred = ICmpInst::ICMP_UGT; 6329 RHS = getConstant(RA - 1); 6330 Changed = true; 6331 break; 6332 case ICmpInst::ICMP_ULE: 6333 if ((RA + 1).isMaxValue()) { 6334 Pred = ICmpInst::ICMP_NE; 6335 RHS = getConstant(RA + 1); 6336 Changed = true; 6337 break; 6338 } 6339 if (RA.isMinValue()) { 6340 Pred = ICmpInst::ICMP_EQ; 6341 Changed = true; 6342 break; 6343 } 6344 if (RA.isMaxValue()) goto trivially_true; 6345 6346 Pred = ICmpInst::ICMP_ULT; 6347 RHS = getConstant(RA + 1); 6348 Changed = true; 6349 break; 6350 case ICmpInst::ICMP_SGE: 6351 if ((RA - 1).isMinSignedValue()) { 6352 Pred = ICmpInst::ICMP_NE; 6353 RHS = getConstant(RA - 1); 6354 Changed = true; 6355 break; 6356 } 6357 if (RA.isMaxSignedValue()) { 6358 Pred = ICmpInst::ICMP_EQ; 6359 Changed = true; 6360 break; 6361 } 6362 if (RA.isMinSignedValue()) goto trivially_true; 6363 6364 Pred = ICmpInst::ICMP_SGT; 6365 RHS = getConstant(RA - 1); 6366 Changed = true; 6367 break; 6368 case ICmpInst::ICMP_SLE: 6369 if ((RA + 1).isMaxSignedValue()) { 6370 Pred = ICmpInst::ICMP_NE; 6371 RHS = getConstant(RA + 1); 6372 Changed = true; 6373 break; 6374 } 6375 if (RA.isMinSignedValue()) { 6376 Pred = ICmpInst::ICMP_EQ; 6377 Changed = true; 6378 break; 6379 } 6380 if (RA.isMaxSignedValue()) goto trivially_true; 6381 6382 Pred = ICmpInst::ICMP_SLT; 6383 RHS = getConstant(RA + 1); 6384 Changed = true; 6385 break; 6386 case ICmpInst::ICMP_UGT: 6387 if (RA.isMinValue()) { 6388 Pred = ICmpInst::ICMP_NE; 6389 Changed = true; 6390 break; 6391 } 6392 if ((RA + 1).isMaxValue()) { 6393 Pred = ICmpInst::ICMP_EQ; 6394 RHS = getConstant(RA + 1); 6395 Changed = true; 6396 break; 6397 } 6398 if (RA.isMaxValue()) goto trivially_false; 6399 break; 6400 case ICmpInst::ICMP_ULT: 6401 if (RA.isMaxValue()) { 6402 Pred = ICmpInst::ICMP_NE; 6403 Changed = true; 6404 break; 6405 } 6406 if ((RA - 1).isMinValue()) { 6407 Pred = ICmpInst::ICMP_EQ; 6408 RHS = getConstant(RA - 1); 6409 Changed = true; 6410 break; 6411 } 6412 if (RA.isMinValue()) goto trivially_false; 6413 break; 6414 case ICmpInst::ICMP_SGT: 6415 if (RA.isMinSignedValue()) { 6416 Pred = ICmpInst::ICMP_NE; 6417 Changed = true; 6418 break; 6419 } 6420 if ((RA + 1).isMaxSignedValue()) { 6421 Pred = ICmpInst::ICMP_EQ; 6422 RHS = getConstant(RA + 1); 6423 Changed = true; 6424 break; 6425 } 6426 if (RA.isMaxSignedValue()) goto trivially_false; 6427 break; 6428 case ICmpInst::ICMP_SLT: 6429 if (RA.isMaxSignedValue()) { 6430 Pred = ICmpInst::ICMP_NE; 6431 Changed = true; 6432 break; 6433 } 6434 if ((RA - 1).isMinSignedValue()) { 6435 Pred = ICmpInst::ICMP_EQ; 6436 RHS = getConstant(RA - 1); 6437 Changed = true; 6438 break; 6439 } 6440 if (RA.isMinSignedValue()) goto trivially_false; 6441 break; 6442 } 6443 } 6444 6445 // Check for obvious equality. 6446 if (HasSameValue(LHS, RHS)) { 6447 if (ICmpInst::isTrueWhenEqual(Pred)) 6448 goto trivially_true; 6449 if (ICmpInst::isFalseWhenEqual(Pred)) 6450 goto trivially_false; 6451 } 6452 6453 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 6454 // adding or subtracting 1 from one of the operands. 6455 switch (Pred) { 6456 case ICmpInst::ICMP_SLE: 6457 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { 6458 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 6459 SCEV::FlagNSW); 6460 Pred = ICmpInst::ICMP_SLT; 6461 Changed = true; 6462 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { 6463 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 6464 SCEV::FlagNSW); 6465 Pred = ICmpInst::ICMP_SLT; 6466 Changed = true; 6467 } 6468 break; 6469 case ICmpInst::ICMP_SGE: 6470 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { 6471 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 6472 SCEV::FlagNSW); 6473 Pred = ICmpInst::ICMP_SGT; 6474 Changed = true; 6475 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { 6476 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 6477 SCEV::FlagNSW); 6478 Pred = ICmpInst::ICMP_SGT; 6479 Changed = true; 6480 } 6481 break; 6482 case ICmpInst::ICMP_ULE: 6483 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { 6484 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 6485 SCEV::FlagNUW); 6486 Pred = ICmpInst::ICMP_ULT; 6487 Changed = true; 6488 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { 6489 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 6490 SCEV::FlagNUW); 6491 Pred = ICmpInst::ICMP_ULT; 6492 Changed = true; 6493 } 6494 break; 6495 case ICmpInst::ICMP_UGE: 6496 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { 6497 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 6498 SCEV::FlagNUW); 6499 Pred = ICmpInst::ICMP_UGT; 6500 Changed = true; 6501 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { 6502 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 6503 SCEV::FlagNUW); 6504 Pred = ICmpInst::ICMP_UGT; 6505 Changed = true; 6506 } 6507 break; 6508 default: 6509 break; 6510 } 6511 6512 // TODO: More simplifications are possible here. 6513 6514 // Recursively simplify until we either hit a recursion limit or nothing 6515 // changes. 6516 if (Changed) 6517 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1); 6518 6519 return Changed; 6520 6521 trivially_true: 6522 // Return 0 == 0. 6523 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 6524 Pred = ICmpInst::ICMP_EQ; 6525 return true; 6526 6527 trivially_false: 6528 // Return 0 != 0. 6529 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 6530 Pred = ICmpInst::ICMP_NE; 6531 return true; 6532 } 6533 6534 bool ScalarEvolution::isKnownNegative(const SCEV *S) { 6535 return getSignedRange(S).getSignedMax().isNegative(); 6536 } 6537 6538 bool ScalarEvolution::isKnownPositive(const SCEV *S) { 6539 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 6540 } 6541 6542 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 6543 return !getSignedRange(S).getSignedMin().isNegative(); 6544 } 6545 6546 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 6547 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 6548 } 6549 6550 bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 6551 return isKnownNegative(S) || isKnownPositive(S); 6552 } 6553 6554 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 6555 const SCEV *LHS, const SCEV *RHS) { 6556 // Canonicalize the inputs first. 6557 (void)SimplifyICmpOperands(Pred, LHS, RHS); 6558 6559 // If LHS or RHS is an addrec, check to see if the condition is true in 6560 // every iteration of the loop. 6561 // If LHS and RHS are both addrec, both conditions must be true in 6562 // every iteration of the loop. 6563 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS); 6564 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS); 6565 bool LeftGuarded = false; 6566 bool RightGuarded = false; 6567 if (LAR) { 6568 const Loop *L = LAR->getLoop(); 6569 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) && 6570 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) { 6571 if (!RAR) return true; 6572 LeftGuarded = true; 6573 } 6574 } 6575 if (RAR) { 6576 const Loop *L = RAR->getLoop(); 6577 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) && 6578 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) { 6579 if (!LAR) return true; 6580 RightGuarded = true; 6581 } 6582 } 6583 if (LeftGuarded && RightGuarded) 6584 return true; 6585 6586 // Otherwise see what can be done with known constant ranges. 6587 return isKnownPredicateWithRanges(Pred, LHS, RHS); 6588 } 6589 6590 bool 6591 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, 6592 const SCEV *LHS, const SCEV *RHS) { 6593 if (HasSameValue(LHS, RHS)) 6594 return ICmpInst::isTrueWhenEqual(Pred); 6595 6596 // This code is split out from isKnownPredicate because it is called from 6597 // within isLoopEntryGuardedByCond. 6598 switch (Pred) { 6599 default: 6600 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 6601 case ICmpInst::ICMP_SGT: 6602 std::swap(LHS, RHS); 6603 case ICmpInst::ICMP_SLT: { 6604 ConstantRange LHSRange = getSignedRange(LHS); 6605 ConstantRange RHSRange = getSignedRange(RHS); 6606 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 6607 return true; 6608 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 6609 return false; 6610 break; 6611 } 6612 case ICmpInst::ICMP_SGE: 6613 std::swap(LHS, RHS); 6614 case ICmpInst::ICMP_SLE: { 6615 ConstantRange LHSRange = getSignedRange(LHS); 6616 ConstantRange RHSRange = getSignedRange(RHS); 6617 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 6618 return true; 6619 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 6620 return false; 6621 break; 6622 } 6623 case ICmpInst::ICMP_UGT: 6624 std::swap(LHS, RHS); 6625 case ICmpInst::ICMP_ULT: { 6626 ConstantRange LHSRange = getUnsignedRange(LHS); 6627 ConstantRange RHSRange = getUnsignedRange(RHS); 6628 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 6629 return true; 6630 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 6631 return false; 6632 break; 6633 } 6634 case ICmpInst::ICMP_UGE: 6635 std::swap(LHS, RHS); 6636 case ICmpInst::ICMP_ULE: { 6637 ConstantRange LHSRange = getUnsignedRange(LHS); 6638 ConstantRange RHSRange = getUnsignedRange(RHS); 6639 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 6640 return true; 6641 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 6642 return false; 6643 break; 6644 } 6645 case ICmpInst::ICMP_NE: { 6646 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 6647 return true; 6648 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 6649 return true; 6650 6651 const SCEV *Diff = getMinusSCEV(LHS, RHS); 6652 if (isKnownNonZero(Diff)) 6653 return true; 6654 break; 6655 } 6656 case ICmpInst::ICMP_EQ: 6657 // The check at the top of the function catches the case where 6658 // the values are known to be equal. 6659 break; 6660 } 6661 return false; 6662 } 6663 6664 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 6665 /// protected by a conditional between LHS and RHS. This is used to 6666 /// to eliminate casts. 6667 bool 6668 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 6669 ICmpInst::Predicate Pred, 6670 const SCEV *LHS, const SCEV *RHS) { 6671 // Interpret a null as meaning no loop, where there is obviously no guard 6672 // (interprocedural conditions notwithstanding). 6673 if (!L) return true; 6674 6675 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true; 6676 6677 BasicBlock *Latch = L->getLoopLatch(); 6678 if (!Latch) 6679 return false; 6680 6681 BranchInst *LoopContinuePredicate = 6682 dyn_cast<BranchInst>(Latch->getTerminator()); 6683 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() && 6684 isImpliedCond(Pred, LHS, RHS, 6685 LoopContinuePredicate->getCondition(), 6686 LoopContinuePredicate->getSuccessor(0) != L->getHeader())) 6687 return true; 6688 6689 // Check conditions due to any @llvm.assume intrinsics. 6690 for (auto &AssumeVH : AC->assumptions()) { 6691 if (!AssumeVH) 6692 continue; 6693 auto *CI = cast<CallInst>(AssumeVH); 6694 if (!DT->dominates(CI, Latch->getTerminator())) 6695 continue; 6696 6697 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false)) 6698 return true; 6699 } 6700 6701 struct ClearWalkingBEDominatingCondsOnExit { 6702 ScalarEvolution &SE; 6703 6704 explicit ClearWalkingBEDominatingCondsOnExit(ScalarEvolution &SE) 6705 : SE(SE){}; 6706 6707 ~ClearWalkingBEDominatingCondsOnExit() { 6708 SE.WalkingBEDominatingConds = false; 6709 } 6710 }; 6711 6712 // We don't want more than one activation of the following loop on the stack 6713 // -- that can lead to O(n!) time complexity. 6714 if (WalkingBEDominatingConds) 6715 return false; 6716 6717 WalkingBEDominatingConds = true; 6718 ClearWalkingBEDominatingCondsOnExit ClearOnExit(*this); 6719 6720 // If the loop is not reachable from the entry block, we risk running into an 6721 // infinite loop as we walk up into the dom tree. These loops do not matter 6722 // anyway, so we just return a conservative answer when we see them. 6723 if (!DT->isReachableFromEntry(L->getHeader())) 6724 return false; 6725 6726 for (DomTreeNode *DTN = (*DT)[Latch], *HeaderDTN = (*DT)[L->getHeader()]; 6727 DTN != HeaderDTN; 6728 DTN = DTN->getIDom()) { 6729 6730 assert(DTN && "should reach the loop header before reaching the root!"); 6731 6732 BasicBlock *BB = DTN->getBlock(); 6733 BasicBlock *PBB = BB->getSinglePredecessor(); 6734 if (!PBB) 6735 continue; 6736 6737 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator()); 6738 if (!ContinuePredicate || !ContinuePredicate->isConditional()) 6739 continue; 6740 6741 Value *Condition = ContinuePredicate->getCondition(); 6742 6743 // If we have an edge `E` within the loop body that dominates the only 6744 // latch, the condition guarding `E` also guards the backedge. This 6745 // reasoning works only for loops with a single latch. 6746 6747 BasicBlockEdge DominatingEdge(PBB, BB); 6748 if (DominatingEdge.isSingleEdge()) { 6749 // We're constructively (and conservatively) enumerating edges within the 6750 // loop body that dominate the latch. The dominator tree better agree 6751 // with us on this: 6752 assert(DT->dominates(DominatingEdge, Latch) && "should be!"); 6753 6754 if (isImpliedCond(Pred, LHS, RHS, Condition, 6755 BB != ContinuePredicate->getSuccessor(0))) 6756 return true; 6757 } 6758 } 6759 6760 return false; 6761 } 6762 6763 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected 6764 /// by a conditional between LHS and RHS. This is used to help avoid max 6765 /// expressions in loop trip counts, and to eliminate casts. 6766 bool 6767 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 6768 ICmpInst::Predicate Pred, 6769 const SCEV *LHS, const SCEV *RHS) { 6770 // Interpret a null as meaning no loop, where there is obviously no guard 6771 // (interprocedural conditions notwithstanding). 6772 if (!L) return false; 6773 6774 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true; 6775 6776 // Starting at the loop predecessor, climb up the predecessor chain, as long 6777 // as there are predecessors that can be found that have unique successors 6778 // leading to the original header. 6779 for (std::pair<BasicBlock *, BasicBlock *> 6780 Pair(L->getLoopPredecessor(), L->getHeader()); 6781 Pair.first; 6782 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 6783 6784 BranchInst *LoopEntryPredicate = 6785 dyn_cast<BranchInst>(Pair.first->getTerminator()); 6786 if (!LoopEntryPredicate || 6787 LoopEntryPredicate->isUnconditional()) 6788 continue; 6789 6790 if (isImpliedCond(Pred, LHS, RHS, 6791 LoopEntryPredicate->getCondition(), 6792 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 6793 return true; 6794 } 6795 6796 // Check conditions due to any @llvm.assume intrinsics. 6797 for (auto &AssumeVH : AC->assumptions()) { 6798 if (!AssumeVH) 6799 continue; 6800 auto *CI = cast<CallInst>(AssumeVH); 6801 if (!DT->dominates(CI, L->getHeader())) 6802 continue; 6803 6804 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false)) 6805 return true; 6806 } 6807 6808 return false; 6809 } 6810 6811 /// RAII wrapper to prevent recursive application of isImpliedCond. 6812 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are 6813 /// currently evaluating isImpliedCond. 6814 struct MarkPendingLoopPredicate { 6815 Value *Cond; 6816 DenseSet<Value*> &LoopPreds; 6817 bool Pending; 6818 6819 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP) 6820 : Cond(C), LoopPreds(LP) { 6821 Pending = !LoopPreds.insert(Cond).second; 6822 } 6823 ~MarkPendingLoopPredicate() { 6824 if (!Pending) 6825 LoopPreds.erase(Cond); 6826 } 6827 }; 6828 6829 /// isImpliedCond - Test whether the condition described by Pred, LHS, 6830 /// and RHS is true whenever the given Cond value evaluates to true. 6831 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, 6832 const SCEV *LHS, const SCEV *RHS, 6833 Value *FoundCondValue, 6834 bool Inverse) { 6835 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates); 6836 if (Mark.Pending) 6837 return false; 6838 6839 // Recursively handle And and Or conditions. 6840 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) { 6841 if (BO->getOpcode() == Instruction::And) { 6842 if (!Inverse) 6843 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 6844 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 6845 } else if (BO->getOpcode() == Instruction::Or) { 6846 if (Inverse) 6847 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 6848 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 6849 } 6850 } 6851 6852 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue); 6853 if (!ICI) return false; 6854 6855 // Now that we found a conditional branch that dominates the loop or controls 6856 // the loop latch. Check to see if it is the comparison we are looking for. 6857 ICmpInst::Predicate FoundPred; 6858 if (Inverse) 6859 FoundPred = ICI->getInversePredicate(); 6860 else 6861 FoundPred = ICI->getPredicate(); 6862 6863 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 6864 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 6865 6866 // Balance the types. 6867 if (getTypeSizeInBits(LHS->getType()) < 6868 getTypeSizeInBits(FoundLHS->getType())) { 6869 if (CmpInst::isSigned(Pred)) { 6870 LHS = getSignExtendExpr(LHS, FoundLHS->getType()); 6871 RHS = getSignExtendExpr(RHS, FoundLHS->getType()); 6872 } else { 6873 LHS = getZeroExtendExpr(LHS, FoundLHS->getType()); 6874 RHS = getZeroExtendExpr(RHS, FoundLHS->getType()); 6875 } 6876 } else if (getTypeSizeInBits(LHS->getType()) > 6877 getTypeSizeInBits(FoundLHS->getType())) { 6878 if (CmpInst::isSigned(FoundPred)) { 6879 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 6880 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 6881 } else { 6882 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 6883 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 6884 } 6885 } 6886 6887 // Canonicalize the query to match the way instcombine will have 6888 // canonicalized the comparison. 6889 if (SimplifyICmpOperands(Pred, LHS, RHS)) 6890 if (LHS == RHS) 6891 return CmpInst::isTrueWhenEqual(Pred); 6892 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 6893 if (FoundLHS == FoundRHS) 6894 return CmpInst::isFalseWhenEqual(FoundPred); 6895 6896 // Check to see if we can make the LHS or RHS match. 6897 if (LHS == FoundRHS || RHS == FoundLHS) { 6898 if (isa<SCEVConstant>(RHS)) { 6899 std::swap(FoundLHS, FoundRHS); 6900 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 6901 } else { 6902 std::swap(LHS, RHS); 6903 Pred = ICmpInst::getSwappedPredicate(Pred); 6904 } 6905 } 6906 6907 // Check whether the found predicate is the same as the desired predicate. 6908 if (FoundPred == Pred) 6909 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 6910 6911 // Check whether swapping the found predicate makes it the same as the 6912 // desired predicate. 6913 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 6914 if (isa<SCEVConstant>(RHS)) 6915 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 6916 else 6917 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 6918 RHS, LHS, FoundLHS, FoundRHS); 6919 } 6920 6921 // Check if we can make progress by sharpening ranges. 6922 if (FoundPred == ICmpInst::ICMP_NE && 6923 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) { 6924 6925 const SCEVConstant *C = nullptr; 6926 const SCEV *V = nullptr; 6927 6928 if (isa<SCEVConstant>(FoundLHS)) { 6929 C = cast<SCEVConstant>(FoundLHS); 6930 V = FoundRHS; 6931 } else { 6932 C = cast<SCEVConstant>(FoundRHS); 6933 V = FoundLHS; 6934 } 6935 6936 // The guarding predicate tells us that C != V. If the known range 6937 // of V is [C, t), we can sharpen the range to [C + 1, t). The 6938 // range we consider has to correspond to same signedness as the 6939 // predicate we're interested in folding. 6940 6941 APInt Min = ICmpInst::isSigned(Pred) ? 6942 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin(); 6943 6944 if (Min == C->getValue()->getValue()) { 6945 // Given (V >= Min && V != Min) we conclude V >= (Min + 1). 6946 // This is true even if (Min + 1) wraps around -- in case of 6947 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)). 6948 6949 APInt SharperMin = Min + 1; 6950 6951 switch (Pred) { 6952 case ICmpInst::ICMP_SGE: 6953 case ICmpInst::ICMP_UGE: 6954 // We know V `Pred` SharperMin. If this implies LHS `Pred` 6955 // RHS, we're done. 6956 if (isImpliedCondOperands(Pred, LHS, RHS, V, 6957 getConstant(SharperMin))) 6958 return true; 6959 6960 case ICmpInst::ICMP_SGT: 6961 case ICmpInst::ICMP_UGT: 6962 // We know from the range information that (V `Pred` Min || 6963 // V == Min). We know from the guarding condition that !(V 6964 // == Min). This gives us 6965 // 6966 // V `Pred` Min || V == Min && !(V == Min) 6967 // => V `Pred` Min 6968 // 6969 // If V `Pred` Min implies LHS `Pred` RHS, we're done. 6970 6971 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min))) 6972 return true; 6973 6974 default: 6975 // No change 6976 break; 6977 } 6978 } 6979 } 6980 6981 // Check whether the actual condition is beyond sufficient. 6982 if (FoundPred == ICmpInst::ICMP_EQ) 6983 if (ICmpInst::isTrueWhenEqual(Pred)) 6984 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 6985 return true; 6986 if (Pred == ICmpInst::ICMP_NE) 6987 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 6988 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 6989 return true; 6990 6991 // Otherwise assume the worst. 6992 return false; 6993 } 6994 6995 /// isImpliedCondOperands - Test whether the condition described by Pred, 6996 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 6997 /// and FoundRHS is true. 6998 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 6999 const SCEV *LHS, const SCEV *RHS, 7000 const SCEV *FoundLHS, 7001 const SCEV *FoundRHS) { 7002 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS)) 7003 return true; 7004 7005 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 7006 FoundLHS, FoundRHS) || 7007 // ~x < ~y --> x > y 7008 isImpliedCondOperandsHelper(Pred, LHS, RHS, 7009 getNotSCEV(FoundRHS), 7010 getNotSCEV(FoundLHS)); 7011 } 7012 7013 7014 /// If Expr computes ~A, return A else return nullptr 7015 static const SCEV *MatchNotExpr(const SCEV *Expr) { 7016 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr); 7017 if (!Add || Add->getNumOperands() != 2) return nullptr; 7018 7019 const SCEVConstant *AddLHS = dyn_cast<SCEVConstant>(Add->getOperand(0)); 7020 if (!(AddLHS && AddLHS->getValue()->getValue().isAllOnesValue())) 7021 return nullptr; 7022 7023 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1)); 7024 if (!AddRHS || AddRHS->getNumOperands() != 2) return nullptr; 7025 7026 const SCEVConstant *MulLHS = dyn_cast<SCEVConstant>(AddRHS->getOperand(0)); 7027 if (!(MulLHS && MulLHS->getValue()->getValue().isAllOnesValue())) 7028 return nullptr; 7029 7030 return AddRHS->getOperand(1); 7031 } 7032 7033 7034 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values? 7035 template<typename MaxExprType> 7036 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr, 7037 const SCEV *Candidate) { 7038 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr); 7039 if (!MaxExpr) return false; 7040 7041 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate); 7042 return It != MaxExpr->op_end(); 7043 } 7044 7045 7046 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values? 7047 template<typename MaxExprType> 7048 static bool IsMinConsistingOf(ScalarEvolution &SE, 7049 const SCEV *MaybeMinExpr, 7050 const SCEV *Candidate) { 7051 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr); 7052 if (!MaybeMaxExpr) 7053 return false; 7054 7055 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate)); 7056 } 7057 7058 7059 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max 7060 /// expression? 7061 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE, 7062 ICmpInst::Predicate Pred, 7063 const SCEV *LHS, const SCEV *RHS) { 7064 switch (Pred) { 7065 default: 7066 return false; 7067 7068 case ICmpInst::ICMP_SGE: 7069 std::swap(LHS, RHS); 7070 // fall through 7071 case ICmpInst::ICMP_SLE: 7072 return 7073 // min(A, ...) <= A 7074 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) || 7075 // A <= max(A, ...) 7076 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS); 7077 7078 case ICmpInst::ICMP_UGE: 7079 std::swap(LHS, RHS); 7080 // fall through 7081 case ICmpInst::ICMP_ULE: 7082 return 7083 // min(A, ...) <= A 7084 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) || 7085 // A <= max(A, ...) 7086 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS); 7087 } 7088 7089 llvm_unreachable("covered switch fell through?!"); 7090 } 7091 7092 /// isImpliedCondOperandsHelper - Test whether the condition described by 7093 /// Pred, LHS, and RHS is true whenever the condition described by Pred, 7094 /// FoundLHS, and FoundRHS is true. 7095 bool 7096 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 7097 const SCEV *LHS, const SCEV *RHS, 7098 const SCEV *FoundLHS, 7099 const SCEV *FoundRHS) { 7100 auto IsKnownPredicateFull = 7101 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) { 7102 return isKnownPredicateWithRanges(Pred, LHS, RHS) || 7103 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS); 7104 }; 7105 7106 switch (Pred) { 7107 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 7108 case ICmpInst::ICMP_EQ: 7109 case ICmpInst::ICMP_NE: 7110 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 7111 return true; 7112 break; 7113 case ICmpInst::ICMP_SLT: 7114 case ICmpInst::ICMP_SLE: 7115 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 7116 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 7117 return true; 7118 break; 7119 case ICmpInst::ICMP_SGT: 7120 case ICmpInst::ICMP_SGE: 7121 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 7122 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 7123 return true; 7124 break; 7125 case ICmpInst::ICMP_ULT: 7126 case ICmpInst::ICMP_ULE: 7127 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 7128 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 7129 return true; 7130 break; 7131 case ICmpInst::ICMP_UGT: 7132 case ICmpInst::ICMP_UGE: 7133 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 7134 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 7135 return true; 7136 break; 7137 } 7138 7139 return false; 7140 } 7141 7142 /// isImpliedCondOperandsViaRanges - helper function for isImpliedCondOperands. 7143 /// Tries to get cases like "X `sgt` 0 => X - 1 `sgt` -1". 7144 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred, 7145 const SCEV *LHS, 7146 const SCEV *RHS, 7147 const SCEV *FoundLHS, 7148 const SCEV *FoundRHS) { 7149 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS)) 7150 // The restriction on `FoundRHS` be lifted easily -- it exists only to 7151 // reduce the compile time impact of this optimization. 7152 return false; 7153 7154 const SCEVAddExpr *AddLHS = dyn_cast<SCEVAddExpr>(LHS); 7155 if (!AddLHS || AddLHS->getOperand(1) != FoundLHS || 7156 !isa<SCEVConstant>(AddLHS->getOperand(0))) 7157 return false; 7158 7159 APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getValue()->getValue(); 7160 7161 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the 7162 // antecedent "`FoundLHS` `Pred` `FoundRHS`". 7163 ConstantRange FoundLHSRange = 7164 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS); 7165 7166 // Since `LHS` is `FoundLHS` + `AddLHS->getOperand(0)`, we can compute a range 7167 // for `LHS`: 7168 APInt Addend = 7169 cast<SCEVConstant>(AddLHS->getOperand(0))->getValue()->getValue(); 7170 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(Addend)); 7171 7172 // We can also compute the range of values for `LHS` that satisfy the 7173 // consequent, "`LHS` `Pred` `RHS`": 7174 APInt ConstRHS = cast<SCEVConstant>(RHS)->getValue()->getValue(); 7175 ConstantRange SatisfyingLHSRange = 7176 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS); 7177 7178 // The antecedent implies the consequent if every value of `LHS` that 7179 // satisfies the antecedent also satisfies the consequent. 7180 return SatisfyingLHSRange.contains(LHSRange); 7181 } 7182 7183 // Verify if an linear IV with positive stride can overflow when in a 7184 // less-than comparison, knowing the invariant term of the comparison, the 7185 // stride and the knowledge of NSW/NUW flags on the recurrence. 7186 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride, 7187 bool IsSigned, bool NoWrap) { 7188 if (NoWrap) return false; 7189 7190 unsigned BitWidth = getTypeSizeInBits(RHS->getType()); 7191 const SCEV *One = getConstant(Stride->getType(), 1); 7192 7193 if (IsSigned) { 7194 APInt MaxRHS = getSignedRange(RHS).getSignedMax(); 7195 APInt MaxValue = APInt::getSignedMaxValue(BitWidth); 7196 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One)) 7197 .getSignedMax(); 7198 7199 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow! 7200 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS); 7201 } 7202 7203 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax(); 7204 APInt MaxValue = APInt::getMaxValue(BitWidth); 7205 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One)) 7206 .getUnsignedMax(); 7207 7208 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow! 7209 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS); 7210 } 7211 7212 // Verify if an linear IV with negative stride can overflow when in a 7213 // greater-than comparison, knowing the invariant term of the comparison, 7214 // the stride and the knowledge of NSW/NUW flags on the recurrence. 7215 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride, 7216 bool IsSigned, bool NoWrap) { 7217 if (NoWrap) return false; 7218 7219 unsigned BitWidth = getTypeSizeInBits(RHS->getType()); 7220 const SCEV *One = getConstant(Stride->getType(), 1); 7221 7222 if (IsSigned) { 7223 APInt MinRHS = getSignedRange(RHS).getSignedMin(); 7224 APInt MinValue = APInt::getSignedMinValue(BitWidth); 7225 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One)) 7226 .getSignedMax(); 7227 7228 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow! 7229 return (MinValue + MaxStrideMinusOne).sgt(MinRHS); 7230 } 7231 7232 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin(); 7233 APInt MinValue = APInt::getMinValue(BitWidth); 7234 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One)) 7235 .getUnsignedMax(); 7236 7237 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow! 7238 return (MinValue + MaxStrideMinusOne).ugt(MinRHS); 7239 } 7240 7241 // Compute the backedge taken count knowing the interval difference, the 7242 // stride and presence of the equality in the comparison. 7243 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step, 7244 bool Equality) { 7245 const SCEV *One = getConstant(Step->getType(), 1); 7246 Delta = Equality ? getAddExpr(Delta, Step) 7247 : getAddExpr(Delta, getMinusSCEV(Step, One)); 7248 return getUDivExpr(Delta, Step); 7249 } 7250 7251 /// HowManyLessThans - Return the number of times a backedge containing the 7252 /// specified less-than comparison will execute. If not computable, return 7253 /// CouldNotCompute. 7254 /// 7255 /// @param ControlsExit is true when the LHS < RHS condition directly controls 7256 /// the branch (loops exits only if condition is true). In this case, we can use 7257 /// NoWrapFlags to skip overflow checks. 7258 ScalarEvolution::ExitLimit 7259 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 7260 const Loop *L, bool IsSigned, 7261 bool ControlsExit) { 7262 // We handle only IV < Invariant 7263 if (!isLoopInvariant(RHS, L)) 7264 return getCouldNotCompute(); 7265 7266 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS); 7267 7268 // Avoid weird loops 7269 if (!IV || IV->getLoop() != L || !IV->isAffine()) 7270 return getCouldNotCompute(); 7271 7272 bool NoWrap = ControlsExit && 7273 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW); 7274 7275 const SCEV *Stride = IV->getStepRecurrence(*this); 7276 7277 // Avoid negative or zero stride values 7278 if (!isKnownPositive(Stride)) 7279 return getCouldNotCompute(); 7280 7281 // Avoid proven overflow cases: this will ensure that the backedge taken count 7282 // will not generate any unsigned overflow. Relaxed no-overflow conditions 7283 // exploit NoWrapFlags, allowing to optimize in presence of undefined 7284 // behaviors like the case of C language. 7285 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap)) 7286 return getCouldNotCompute(); 7287 7288 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT 7289 : ICmpInst::ICMP_ULT; 7290 const SCEV *Start = IV->getStart(); 7291 const SCEV *End = RHS; 7292 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) { 7293 const SCEV *Diff = getMinusSCEV(RHS, Start); 7294 // If we have NoWrap set, then we can assume that the increment won't 7295 // overflow, in which case if RHS - Start is a constant, we don't need to 7296 // do a max operation since we can just figure it out statically 7297 if (NoWrap && isa<SCEVConstant>(Diff)) { 7298 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue(); 7299 if (D.isNegative()) 7300 End = Start; 7301 } else 7302 End = IsSigned ? getSMaxExpr(RHS, Start) 7303 : getUMaxExpr(RHS, Start); 7304 } 7305 7306 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false); 7307 7308 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin() 7309 : getUnsignedRange(Start).getUnsignedMin(); 7310 7311 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin() 7312 : getUnsignedRange(Stride).getUnsignedMin(); 7313 7314 unsigned BitWidth = getTypeSizeInBits(LHS->getType()); 7315 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1) 7316 : APInt::getMaxValue(BitWidth) - (MinStride - 1); 7317 7318 // Although End can be a MAX expression we estimate MaxEnd considering only 7319 // the case End = RHS. This is safe because in the other case (End - Start) 7320 // is zero, leading to a zero maximum backedge taken count. 7321 APInt MaxEnd = 7322 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit) 7323 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit); 7324 7325 const SCEV *MaxBECount; 7326 if (isa<SCEVConstant>(BECount)) 7327 MaxBECount = BECount; 7328 else 7329 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart), 7330 getConstant(MinStride), false); 7331 7332 if (isa<SCEVCouldNotCompute>(MaxBECount)) 7333 MaxBECount = BECount; 7334 7335 return ExitLimit(BECount, MaxBECount); 7336 } 7337 7338 ScalarEvolution::ExitLimit 7339 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS, 7340 const Loop *L, bool IsSigned, 7341 bool ControlsExit) { 7342 // We handle only IV > Invariant 7343 if (!isLoopInvariant(RHS, L)) 7344 return getCouldNotCompute(); 7345 7346 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS); 7347 7348 // Avoid weird loops 7349 if (!IV || IV->getLoop() != L || !IV->isAffine()) 7350 return getCouldNotCompute(); 7351 7352 bool NoWrap = ControlsExit && 7353 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW); 7354 7355 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this)); 7356 7357 // Avoid negative or zero stride values 7358 if (!isKnownPositive(Stride)) 7359 return getCouldNotCompute(); 7360 7361 // Avoid proven overflow cases: this will ensure that the backedge taken count 7362 // will not generate any unsigned overflow. Relaxed no-overflow conditions 7363 // exploit NoWrapFlags, allowing to optimize in presence of undefined 7364 // behaviors like the case of C language. 7365 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap)) 7366 return getCouldNotCompute(); 7367 7368 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT 7369 : ICmpInst::ICMP_UGT; 7370 7371 const SCEV *Start = IV->getStart(); 7372 const SCEV *End = RHS; 7373 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) { 7374 const SCEV *Diff = getMinusSCEV(RHS, Start); 7375 // If we have NoWrap set, then we can assume that the increment won't 7376 // overflow, in which case if RHS - Start is a constant, we don't need to 7377 // do a max operation since we can just figure it out statically 7378 if (NoWrap && isa<SCEVConstant>(Diff)) { 7379 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue(); 7380 if (!D.isNegative()) 7381 End = Start; 7382 } else 7383 End = IsSigned ? getSMinExpr(RHS, Start) 7384 : getUMinExpr(RHS, Start); 7385 } 7386 7387 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false); 7388 7389 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax() 7390 : getUnsignedRange(Start).getUnsignedMax(); 7391 7392 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin() 7393 : getUnsignedRange(Stride).getUnsignedMin(); 7394 7395 unsigned BitWidth = getTypeSizeInBits(LHS->getType()); 7396 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1) 7397 : APInt::getMinValue(BitWidth) + (MinStride - 1); 7398 7399 // Although End can be a MIN expression we estimate MinEnd considering only 7400 // the case End = RHS. This is safe because in the other case (Start - End) 7401 // is zero, leading to a zero maximum backedge taken count. 7402 APInt MinEnd = 7403 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit) 7404 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit); 7405 7406 7407 const SCEV *MaxBECount = getCouldNotCompute(); 7408 if (isa<SCEVConstant>(BECount)) 7409 MaxBECount = BECount; 7410 else 7411 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd), 7412 getConstant(MinStride), false); 7413 7414 if (isa<SCEVCouldNotCompute>(MaxBECount)) 7415 MaxBECount = BECount; 7416 7417 return ExitLimit(BECount, MaxBECount); 7418 } 7419 7420 /// getNumIterationsInRange - Return the number of iterations of this loop that 7421 /// produce values in the specified constant range. Another way of looking at 7422 /// this is that it returns the first iteration number where the value is not in 7423 /// the condition, thus computing the exit count. If the iteration count can't 7424 /// be computed, an instance of SCEVCouldNotCompute is returned. 7425 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 7426 ScalarEvolution &SE) const { 7427 if (Range.isFullSet()) // Infinite loop. 7428 return SE.getCouldNotCompute(); 7429 7430 // If the start is a non-zero constant, shift the range to simplify things. 7431 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 7432 if (!SC->getValue()->isZero()) { 7433 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 7434 Operands[0] = SE.getConstant(SC->getType(), 0); 7435 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(), 7436 getNoWrapFlags(FlagNW)); 7437 if (const SCEVAddRecExpr *ShiftedAddRec = 7438 dyn_cast<SCEVAddRecExpr>(Shifted)) 7439 return ShiftedAddRec->getNumIterationsInRange( 7440 Range.subtract(SC->getValue()->getValue()), SE); 7441 // This is strange and shouldn't happen. 7442 return SE.getCouldNotCompute(); 7443 } 7444 7445 // The only time we can solve this is when we have all constant indices. 7446 // Otherwise, we cannot determine the overflow conditions. 7447 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 7448 if (!isa<SCEVConstant>(getOperand(i))) 7449 return SE.getCouldNotCompute(); 7450 7451 7452 // Okay at this point we know that all elements of the chrec are constants and 7453 // that the start element is zero. 7454 7455 // First check to see if the range contains zero. If not, the first 7456 // iteration exits. 7457 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 7458 if (!Range.contains(APInt(BitWidth, 0))) 7459 return SE.getConstant(getType(), 0); 7460 7461 if (isAffine()) { 7462 // If this is an affine expression then we have this situation: 7463 // Solve {0,+,A} in Range === Ax in Range 7464 7465 // We know that zero is in the range. If A is positive then we know that 7466 // the upper value of the range must be the first possible exit value. 7467 // If A is negative then the lower of the range is the last possible loop 7468 // value. Also note that we already checked for a full range. 7469 APInt One(BitWidth,1); 7470 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 7471 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 7472 7473 // The exit value should be (End+A)/A. 7474 APInt ExitVal = (End + A).udiv(A); 7475 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 7476 7477 // Evaluate at the exit value. If we really did fall out of the valid 7478 // range, then we computed our trip count, otherwise wrap around or other 7479 // things must have happened. 7480 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 7481 if (Range.contains(Val->getValue())) 7482 return SE.getCouldNotCompute(); // Something strange happened 7483 7484 // Ensure that the previous value is in the range. This is a sanity check. 7485 assert(Range.contains( 7486 EvaluateConstantChrecAtConstant(this, 7487 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 7488 "Linear scev computation is off in a bad way!"); 7489 return SE.getConstant(ExitValue); 7490 } else if (isQuadratic()) { 7491 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 7492 // quadratic equation to solve it. To do this, we must frame our problem in 7493 // terms of figuring out when zero is crossed, instead of when 7494 // Range.getUpper() is crossed. 7495 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 7496 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 7497 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(), 7498 // getNoWrapFlags(FlagNW) 7499 FlagAnyWrap); 7500 7501 // Next, solve the constructed addrec 7502 std::pair<const SCEV *,const SCEV *> Roots = 7503 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 7504 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 7505 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 7506 if (R1) { 7507 // Pick the smallest positive root value. 7508 if (ConstantInt *CB = 7509 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 7510 R1->getValue(), R2->getValue()))) { 7511 if (!CB->getZExtValue()) 7512 std::swap(R1, R2); // R1 is the minimum root now. 7513 7514 // Make sure the root is not off by one. The returned iteration should 7515 // not be in the range, but the previous one should be. When solving 7516 // for "X*X < 5", for example, we should not return a root of 2. 7517 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 7518 R1->getValue(), 7519 SE); 7520 if (Range.contains(R1Val->getValue())) { 7521 // The next iteration must be out of the range... 7522 ConstantInt *NextVal = 7523 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 7524 7525 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 7526 if (!Range.contains(R1Val->getValue())) 7527 return SE.getConstant(NextVal); 7528 return SE.getCouldNotCompute(); // Something strange happened 7529 } 7530 7531 // If R1 was not in the range, then it is a good return value. Make 7532 // sure that R1-1 WAS in the range though, just in case. 7533 ConstantInt *NextVal = 7534 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 7535 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 7536 if (Range.contains(R1Val->getValue())) 7537 return R1; 7538 return SE.getCouldNotCompute(); // Something strange happened 7539 } 7540 } 7541 } 7542 7543 return SE.getCouldNotCompute(); 7544 } 7545 7546 namespace { 7547 struct FindUndefs { 7548 bool Found; 7549 FindUndefs() : Found(false) {} 7550 7551 bool follow(const SCEV *S) { 7552 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) { 7553 if (isa<UndefValue>(C->getValue())) 7554 Found = true; 7555 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) { 7556 if (isa<UndefValue>(C->getValue())) 7557 Found = true; 7558 } 7559 7560 // Keep looking if we haven't found it yet. 7561 return !Found; 7562 } 7563 bool isDone() const { 7564 // Stop recursion if we have found an undef. 7565 return Found; 7566 } 7567 }; 7568 } 7569 7570 // Return true when S contains at least an undef value. 7571 static inline bool 7572 containsUndefs(const SCEV *S) { 7573 FindUndefs F; 7574 SCEVTraversal<FindUndefs> ST(F); 7575 ST.visitAll(S); 7576 7577 return F.Found; 7578 } 7579 7580 namespace { 7581 // Collect all steps of SCEV expressions. 7582 struct SCEVCollectStrides { 7583 ScalarEvolution &SE; 7584 SmallVectorImpl<const SCEV *> &Strides; 7585 7586 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S) 7587 : SE(SE), Strides(S) {} 7588 7589 bool follow(const SCEV *S) { 7590 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S)) 7591 Strides.push_back(AR->getStepRecurrence(SE)); 7592 return true; 7593 } 7594 bool isDone() const { return false; } 7595 }; 7596 7597 // Collect all SCEVUnknown and SCEVMulExpr expressions. 7598 struct SCEVCollectTerms { 7599 SmallVectorImpl<const SCEV *> &Terms; 7600 7601 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T) 7602 : Terms(T) {} 7603 7604 bool follow(const SCEV *S) { 7605 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) { 7606 if (!containsUndefs(S)) 7607 Terms.push_back(S); 7608 7609 // Stop recursion: once we collected a term, do not walk its operands. 7610 return false; 7611 } 7612 7613 // Keep looking. 7614 return true; 7615 } 7616 bool isDone() const { return false; } 7617 }; 7618 } 7619 7620 /// Find parametric terms in this SCEVAddRecExpr. 7621 void SCEVAddRecExpr::collectParametricTerms( 7622 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Terms) const { 7623 SmallVector<const SCEV *, 4> Strides; 7624 SCEVCollectStrides StrideCollector(SE, Strides); 7625 visitAll(this, StrideCollector); 7626 7627 DEBUG({ 7628 dbgs() << "Strides:\n"; 7629 for (const SCEV *S : Strides) 7630 dbgs() << *S << "\n"; 7631 }); 7632 7633 for (const SCEV *S : Strides) { 7634 SCEVCollectTerms TermCollector(Terms); 7635 visitAll(S, TermCollector); 7636 } 7637 7638 DEBUG({ 7639 dbgs() << "Terms:\n"; 7640 for (const SCEV *T : Terms) 7641 dbgs() << *T << "\n"; 7642 }); 7643 } 7644 7645 static bool findArrayDimensionsRec(ScalarEvolution &SE, 7646 SmallVectorImpl<const SCEV *> &Terms, 7647 SmallVectorImpl<const SCEV *> &Sizes) { 7648 int Last = Terms.size() - 1; 7649 const SCEV *Step = Terms[Last]; 7650 7651 // End of recursion. 7652 if (Last == 0) { 7653 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) { 7654 SmallVector<const SCEV *, 2> Qs; 7655 for (const SCEV *Op : M->operands()) 7656 if (!isa<SCEVConstant>(Op)) 7657 Qs.push_back(Op); 7658 7659 Step = SE.getMulExpr(Qs); 7660 } 7661 7662 Sizes.push_back(Step); 7663 return true; 7664 } 7665 7666 for (const SCEV *&Term : Terms) { 7667 // Normalize the terms before the next call to findArrayDimensionsRec. 7668 const SCEV *Q, *R; 7669 SCEVDivision::divide(SE, Term, Step, &Q, &R); 7670 7671 // Bail out when GCD does not evenly divide one of the terms. 7672 if (!R->isZero()) 7673 return false; 7674 7675 Term = Q; 7676 } 7677 7678 // Remove all SCEVConstants. 7679 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) { 7680 return isa<SCEVConstant>(E); 7681 }), 7682 Terms.end()); 7683 7684 if (Terms.size() > 0) 7685 if (!findArrayDimensionsRec(SE, Terms, Sizes)) 7686 return false; 7687 7688 Sizes.push_back(Step); 7689 return true; 7690 } 7691 7692 namespace { 7693 struct FindParameter { 7694 bool FoundParameter; 7695 FindParameter() : FoundParameter(false) {} 7696 7697 bool follow(const SCEV *S) { 7698 if (isa<SCEVUnknown>(S)) { 7699 FoundParameter = true; 7700 // Stop recursion: we found a parameter. 7701 return false; 7702 } 7703 // Keep looking. 7704 return true; 7705 } 7706 bool isDone() const { 7707 // Stop recursion if we have found a parameter. 7708 return FoundParameter; 7709 } 7710 }; 7711 } 7712 7713 // Returns true when S contains at least a SCEVUnknown parameter. 7714 static inline bool 7715 containsParameters(const SCEV *S) { 7716 FindParameter F; 7717 SCEVTraversal<FindParameter> ST(F); 7718 ST.visitAll(S); 7719 7720 return F.FoundParameter; 7721 } 7722 7723 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter. 7724 static inline bool 7725 containsParameters(SmallVectorImpl<const SCEV *> &Terms) { 7726 for (const SCEV *T : Terms) 7727 if (containsParameters(T)) 7728 return true; 7729 return false; 7730 } 7731 7732 // Return the number of product terms in S. 7733 static inline int numberOfTerms(const SCEV *S) { 7734 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S)) 7735 return Expr->getNumOperands(); 7736 return 1; 7737 } 7738 7739 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) { 7740 if (isa<SCEVConstant>(T)) 7741 return nullptr; 7742 7743 if (isa<SCEVUnknown>(T)) 7744 return T; 7745 7746 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) { 7747 SmallVector<const SCEV *, 2> Factors; 7748 for (const SCEV *Op : M->operands()) 7749 if (!isa<SCEVConstant>(Op)) 7750 Factors.push_back(Op); 7751 7752 return SE.getMulExpr(Factors); 7753 } 7754 7755 return T; 7756 } 7757 7758 /// Return the size of an element read or written by Inst. 7759 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) { 7760 Type *Ty; 7761 if (StoreInst *Store = dyn_cast<StoreInst>(Inst)) 7762 Ty = Store->getValueOperand()->getType(); 7763 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst)) 7764 Ty = Load->getType(); 7765 else 7766 return nullptr; 7767 7768 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty)); 7769 return getSizeOfExpr(ETy, Ty); 7770 } 7771 7772 /// Second step of delinearization: compute the array dimensions Sizes from the 7773 /// set of Terms extracted from the memory access function of this SCEVAddRec. 7774 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms, 7775 SmallVectorImpl<const SCEV *> &Sizes, 7776 const SCEV *ElementSize) const { 7777 7778 if (Terms.size() < 1 || !ElementSize) 7779 return; 7780 7781 // Early return when Terms do not contain parameters: we do not delinearize 7782 // non parametric SCEVs. 7783 if (!containsParameters(Terms)) 7784 return; 7785 7786 DEBUG({ 7787 dbgs() << "Terms:\n"; 7788 for (const SCEV *T : Terms) 7789 dbgs() << *T << "\n"; 7790 }); 7791 7792 // Remove duplicates. 7793 std::sort(Terms.begin(), Terms.end()); 7794 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end()); 7795 7796 // Put larger terms first. 7797 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) { 7798 return numberOfTerms(LHS) > numberOfTerms(RHS); 7799 }); 7800 7801 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 7802 7803 // Divide all terms by the element size. 7804 for (const SCEV *&Term : Terms) { 7805 const SCEV *Q, *R; 7806 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R); 7807 Term = Q; 7808 } 7809 7810 SmallVector<const SCEV *, 4> NewTerms; 7811 7812 // Remove constant factors. 7813 for (const SCEV *T : Terms) 7814 if (const SCEV *NewT = removeConstantFactors(SE, T)) 7815 NewTerms.push_back(NewT); 7816 7817 DEBUG({ 7818 dbgs() << "Terms after sorting:\n"; 7819 for (const SCEV *T : NewTerms) 7820 dbgs() << *T << "\n"; 7821 }); 7822 7823 if (NewTerms.empty() || 7824 !findArrayDimensionsRec(SE, NewTerms, Sizes)) { 7825 Sizes.clear(); 7826 return; 7827 } 7828 7829 // The last element to be pushed into Sizes is the size of an element. 7830 Sizes.push_back(ElementSize); 7831 7832 DEBUG({ 7833 dbgs() << "Sizes:\n"; 7834 for (const SCEV *S : Sizes) 7835 dbgs() << *S << "\n"; 7836 }); 7837 } 7838 7839 /// Third step of delinearization: compute the access functions for the 7840 /// Subscripts based on the dimensions in Sizes. 7841 void SCEVAddRecExpr::computeAccessFunctions( 7842 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Subscripts, 7843 SmallVectorImpl<const SCEV *> &Sizes) const { 7844 7845 // Early exit in case this SCEV is not an affine multivariate function. 7846 if (Sizes.empty() || !this->isAffine()) 7847 return; 7848 7849 const SCEV *Res = this; 7850 int Last = Sizes.size() - 1; 7851 for (int i = Last; i >= 0; i--) { 7852 const SCEV *Q, *R; 7853 SCEVDivision::divide(SE, Res, Sizes[i], &Q, &R); 7854 7855 DEBUG({ 7856 dbgs() << "Res: " << *Res << "\n"; 7857 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n"; 7858 dbgs() << "Res divided by Sizes[i]:\n"; 7859 dbgs() << "Quotient: " << *Q << "\n"; 7860 dbgs() << "Remainder: " << *R << "\n"; 7861 }); 7862 7863 Res = Q; 7864 7865 // Do not record the last subscript corresponding to the size of elements in 7866 // the array. 7867 if (i == Last) { 7868 7869 // Bail out if the remainder is too complex. 7870 if (isa<SCEVAddRecExpr>(R)) { 7871 Subscripts.clear(); 7872 Sizes.clear(); 7873 return; 7874 } 7875 7876 continue; 7877 } 7878 7879 // Record the access function for the current subscript. 7880 Subscripts.push_back(R); 7881 } 7882 7883 // Also push in last position the remainder of the last division: it will be 7884 // the access function of the innermost dimension. 7885 Subscripts.push_back(Res); 7886 7887 std::reverse(Subscripts.begin(), Subscripts.end()); 7888 7889 DEBUG({ 7890 dbgs() << "Subscripts:\n"; 7891 for (const SCEV *S : Subscripts) 7892 dbgs() << *S << "\n"; 7893 }); 7894 } 7895 7896 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and 7897 /// sizes of an array access. Returns the remainder of the delinearization that 7898 /// is the offset start of the array. The SCEV->delinearize algorithm computes 7899 /// the multiples of SCEV coefficients: that is a pattern matching of sub 7900 /// expressions in the stride and base of a SCEV corresponding to the 7901 /// computation of a GCD (greatest common divisor) of base and stride. When 7902 /// SCEV->delinearize fails, it returns the SCEV unchanged. 7903 /// 7904 /// For example: when analyzing the memory access A[i][j][k] in this loop nest 7905 /// 7906 /// void foo(long n, long m, long o, double A[n][m][o]) { 7907 /// 7908 /// for (long i = 0; i < n; i++) 7909 /// for (long j = 0; j < m; j++) 7910 /// for (long k = 0; k < o; k++) 7911 /// A[i][j][k] = 1.0; 7912 /// } 7913 /// 7914 /// the delinearization input is the following AddRec SCEV: 7915 /// 7916 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k> 7917 /// 7918 /// From this SCEV, we are able to say that the base offset of the access is %A 7919 /// because it appears as an offset that does not divide any of the strides in 7920 /// the loops: 7921 /// 7922 /// CHECK: Base offset: %A 7923 /// 7924 /// and then SCEV->delinearize determines the size of some of the dimensions of 7925 /// the array as these are the multiples by which the strides are happening: 7926 /// 7927 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes. 7928 /// 7929 /// Note that the outermost dimension remains of UnknownSize because there are 7930 /// no strides that would help identifying the size of the last dimension: when 7931 /// the array has been statically allocated, one could compute the size of that 7932 /// dimension by dividing the overall size of the array by the size of the known 7933 /// dimensions: %m * %o * 8. 7934 /// 7935 /// Finally delinearize provides the access functions for the array reference 7936 /// that does correspond to A[i][j][k] of the above C testcase: 7937 /// 7938 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>] 7939 /// 7940 /// The testcases are checking the output of a function pass: 7941 /// DelinearizationPass that walks through all loads and stores of a function 7942 /// asking for the SCEV of the memory access with respect to all enclosing 7943 /// loops, calling SCEV->delinearize on that and printing the results. 7944 7945 void SCEVAddRecExpr::delinearize(ScalarEvolution &SE, 7946 SmallVectorImpl<const SCEV *> &Subscripts, 7947 SmallVectorImpl<const SCEV *> &Sizes, 7948 const SCEV *ElementSize) const { 7949 // First step: collect parametric terms. 7950 SmallVector<const SCEV *, 4> Terms; 7951 collectParametricTerms(SE, Terms); 7952 7953 if (Terms.empty()) 7954 return; 7955 7956 // Second step: find subscript sizes. 7957 SE.findArrayDimensions(Terms, Sizes, ElementSize); 7958 7959 if (Sizes.empty()) 7960 return; 7961 7962 // Third step: compute the access functions for each subscript. 7963 computeAccessFunctions(SE, Subscripts, Sizes); 7964 7965 if (Subscripts.empty()) 7966 return; 7967 7968 DEBUG({ 7969 dbgs() << "succeeded to delinearize " << *this << "\n"; 7970 dbgs() << "ArrayDecl[UnknownSize]"; 7971 for (const SCEV *S : Sizes) 7972 dbgs() << "[" << *S << "]"; 7973 7974 dbgs() << "\nArrayRef"; 7975 for (const SCEV *S : Subscripts) 7976 dbgs() << "[" << *S << "]"; 7977 dbgs() << "\n"; 7978 }); 7979 } 7980 7981 //===----------------------------------------------------------------------===// 7982 // SCEVCallbackVH Class Implementation 7983 //===----------------------------------------------------------------------===// 7984 7985 void ScalarEvolution::SCEVCallbackVH::deleted() { 7986 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 7987 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 7988 SE->ConstantEvolutionLoopExitValue.erase(PN); 7989 SE->ValueExprMap.erase(getValPtr()); 7990 // this now dangles! 7991 } 7992 7993 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 7994 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 7995 7996 // Forget all the expressions associated with users of the old value, 7997 // so that future queries will recompute the expressions using the new 7998 // value. 7999 Value *Old = getValPtr(); 8000 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end()); 8001 SmallPtrSet<User *, 8> Visited; 8002 while (!Worklist.empty()) { 8003 User *U = Worklist.pop_back_val(); 8004 // Deleting the Old value will cause this to dangle. Postpone 8005 // that until everything else is done. 8006 if (U == Old) 8007 continue; 8008 if (!Visited.insert(U).second) 8009 continue; 8010 if (PHINode *PN = dyn_cast<PHINode>(U)) 8011 SE->ConstantEvolutionLoopExitValue.erase(PN); 8012 SE->ValueExprMap.erase(U); 8013 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end()); 8014 } 8015 // Delete the Old value. 8016 if (PHINode *PN = dyn_cast<PHINode>(Old)) 8017 SE->ConstantEvolutionLoopExitValue.erase(PN); 8018 SE->ValueExprMap.erase(Old); 8019 // this now dangles! 8020 } 8021 8022 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 8023 : CallbackVH(V), SE(se) {} 8024 8025 //===----------------------------------------------------------------------===// 8026 // ScalarEvolution Class Implementation 8027 //===----------------------------------------------------------------------===// 8028 8029 ScalarEvolution::ScalarEvolution() 8030 : FunctionPass(ID), WalkingBEDominatingConds(false), ValuesAtScopes(64), 8031 LoopDispositions(64), BlockDispositions(64), FirstUnknown(nullptr) { 8032 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry()); 8033 } 8034 8035 bool ScalarEvolution::runOnFunction(Function &F) { 8036 this->F = &F; 8037 AC = &getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F); 8038 LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo(); 8039 TLI = &getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(); 8040 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree(); 8041 return false; 8042 } 8043 8044 void ScalarEvolution::releaseMemory() { 8045 // Iterate through all the SCEVUnknown instances and call their 8046 // destructors, so that they release their references to their values. 8047 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next) 8048 U->~SCEVUnknown(); 8049 FirstUnknown = nullptr; 8050 8051 ValueExprMap.clear(); 8052 8053 // Free any extra memory created for ExitNotTakenInfo in the unlikely event 8054 // that a loop had multiple computable exits. 8055 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I = 8056 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); 8057 I != E; ++I) { 8058 I->second.clear(); 8059 } 8060 8061 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage"); 8062 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!"); 8063 8064 BackedgeTakenCounts.clear(); 8065 ConstantEvolutionLoopExitValue.clear(); 8066 ValuesAtScopes.clear(); 8067 LoopDispositions.clear(); 8068 BlockDispositions.clear(); 8069 UnsignedRanges.clear(); 8070 SignedRanges.clear(); 8071 UniqueSCEVs.clear(); 8072 SCEVAllocator.Reset(); 8073 } 8074 8075 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 8076 AU.setPreservesAll(); 8077 AU.addRequired<AssumptionCacheTracker>(); 8078 AU.addRequiredTransitive<LoopInfoWrapperPass>(); 8079 AU.addRequiredTransitive<DominatorTreeWrapperPass>(); 8080 AU.addRequired<TargetLibraryInfoWrapperPass>(); 8081 } 8082 8083 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 8084 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 8085 } 8086 8087 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 8088 const Loop *L) { 8089 // Print all inner loops first 8090 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 8091 PrintLoopInfo(OS, SE, *I); 8092 8093 OS << "Loop "; 8094 L->getHeader()->printAsOperand(OS, /*PrintType=*/false); 8095 OS << ": "; 8096 8097 SmallVector<BasicBlock *, 8> ExitBlocks; 8098 L->getExitBlocks(ExitBlocks); 8099 if (ExitBlocks.size() != 1) 8100 OS << "<multiple exits> "; 8101 8102 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 8103 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 8104 } else { 8105 OS << "Unpredictable backedge-taken count. "; 8106 } 8107 8108 OS << "\n" 8109 "Loop "; 8110 L->getHeader()->printAsOperand(OS, /*PrintType=*/false); 8111 OS << ": "; 8112 8113 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 8114 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 8115 } else { 8116 OS << "Unpredictable max backedge-taken count. "; 8117 } 8118 8119 OS << "\n"; 8120 } 8121 8122 void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 8123 // ScalarEvolution's implementation of the print method is to print 8124 // out SCEV values of all instructions that are interesting. Doing 8125 // this potentially causes it to create new SCEV objects though, 8126 // which technically conflicts with the const qualifier. This isn't 8127 // observable from outside the class though, so casting away the 8128 // const isn't dangerous. 8129 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 8130 8131 OS << "Classifying expressions for: "; 8132 F->printAsOperand(OS, /*PrintType=*/false); 8133 OS << "\n"; 8134 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 8135 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { 8136 OS << *I << '\n'; 8137 OS << " --> "; 8138 const SCEV *SV = SE.getSCEV(&*I); 8139 SV->print(OS); 8140 if (!isa<SCEVCouldNotCompute>(SV)) { 8141 OS << " U: "; 8142 SE.getUnsignedRange(SV).print(OS); 8143 OS << " S: "; 8144 SE.getSignedRange(SV).print(OS); 8145 } 8146 8147 const Loop *L = LI->getLoopFor((*I).getParent()); 8148 8149 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 8150 if (AtUse != SV) { 8151 OS << " --> "; 8152 AtUse->print(OS); 8153 if (!isa<SCEVCouldNotCompute>(AtUse)) { 8154 OS << " U: "; 8155 SE.getUnsignedRange(AtUse).print(OS); 8156 OS << " S: "; 8157 SE.getSignedRange(AtUse).print(OS); 8158 } 8159 } 8160 8161 if (L) { 8162 OS << "\t\t" "Exits: "; 8163 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 8164 if (!SE.isLoopInvariant(ExitValue, L)) { 8165 OS << "<<Unknown>>"; 8166 } else { 8167 OS << *ExitValue; 8168 } 8169 } 8170 8171 OS << "\n"; 8172 } 8173 8174 OS << "Determining loop execution counts for: "; 8175 F->printAsOperand(OS, /*PrintType=*/false); 8176 OS << "\n"; 8177 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 8178 PrintLoopInfo(OS, &SE, *I); 8179 } 8180 8181 ScalarEvolution::LoopDisposition 8182 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) { 8183 auto &Values = LoopDispositions[S]; 8184 for (auto &V : Values) { 8185 if (V.getPointer() == L) 8186 return V.getInt(); 8187 } 8188 Values.emplace_back(L, LoopVariant); 8189 LoopDisposition D = computeLoopDisposition(S, L); 8190 auto &Values2 = LoopDispositions[S]; 8191 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) { 8192 if (V.getPointer() == L) { 8193 V.setInt(D); 8194 break; 8195 } 8196 } 8197 return D; 8198 } 8199 8200 ScalarEvolution::LoopDisposition 8201 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) { 8202 switch (static_cast<SCEVTypes>(S->getSCEVType())) { 8203 case scConstant: 8204 return LoopInvariant; 8205 case scTruncate: 8206 case scZeroExtend: 8207 case scSignExtend: 8208 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L); 8209 case scAddRecExpr: { 8210 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 8211 8212 // If L is the addrec's loop, it's computable. 8213 if (AR->getLoop() == L) 8214 return LoopComputable; 8215 8216 // Add recurrences are never invariant in the function-body (null loop). 8217 if (!L) 8218 return LoopVariant; 8219 8220 // This recurrence is variant w.r.t. L if L contains AR's loop. 8221 if (L->contains(AR->getLoop())) 8222 return LoopVariant; 8223 8224 // This recurrence is invariant w.r.t. L if AR's loop contains L. 8225 if (AR->getLoop()->contains(L)) 8226 return LoopInvariant; 8227 8228 // This recurrence is variant w.r.t. L if any of its operands 8229 // are variant. 8230 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 8231 I != E; ++I) 8232 if (!isLoopInvariant(*I, L)) 8233 return LoopVariant; 8234 8235 // Otherwise it's loop-invariant. 8236 return LoopInvariant; 8237 } 8238 case scAddExpr: 8239 case scMulExpr: 8240 case scUMaxExpr: 8241 case scSMaxExpr: { 8242 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 8243 bool HasVarying = false; 8244 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 8245 I != E; ++I) { 8246 LoopDisposition D = getLoopDisposition(*I, L); 8247 if (D == LoopVariant) 8248 return LoopVariant; 8249 if (D == LoopComputable) 8250 HasVarying = true; 8251 } 8252 return HasVarying ? LoopComputable : LoopInvariant; 8253 } 8254 case scUDivExpr: { 8255 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 8256 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L); 8257 if (LD == LoopVariant) 8258 return LoopVariant; 8259 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L); 8260 if (RD == LoopVariant) 8261 return LoopVariant; 8262 return (LD == LoopInvariant && RD == LoopInvariant) ? 8263 LoopInvariant : LoopComputable; 8264 } 8265 case scUnknown: 8266 // All non-instruction values are loop invariant. All instructions are loop 8267 // invariant if they are not contained in the specified loop. 8268 // Instructions are never considered invariant in the function body 8269 // (null loop) because they are defined within the "loop". 8270 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) 8271 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant; 8272 return LoopInvariant; 8273 case scCouldNotCompute: 8274 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 8275 } 8276 llvm_unreachable("Unknown SCEV kind!"); 8277 } 8278 8279 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) { 8280 return getLoopDisposition(S, L) == LoopInvariant; 8281 } 8282 8283 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) { 8284 return getLoopDisposition(S, L) == LoopComputable; 8285 } 8286 8287 ScalarEvolution::BlockDisposition 8288 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) { 8289 auto &Values = BlockDispositions[S]; 8290 for (auto &V : Values) { 8291 if (V.getPointer() == BB) 8292 return V.getInt(); 8293 } 8294 Values.emplace_back(BB, DoesNotDominateBlock); 8295 BlockDisposition D = computeBlockDisposition(S, BB); 8296 auto &Values2 = BlockDispositions[S]; 8297 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) { 8298 if (V.getPointer() == BB) { 8299 V.setInt(D); 8300 break; 8301 } 8302 } 8303 return D; 8304 } 8305 8306 ScalarEvolution::BlockDisposition 8307 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) { 8308 switch (static_cast<SCEVTypes>(S->getSCEVType())) { 8309 case scConstant: 8310 return ProperlyDominatesBlock; 8311 case scTruncate: 8312 case scZeroExtend: 8313 case scSignExtend: 8314 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB); 8315 case scAddRecExpr: { 8316 // This uses a "dominates" query instead of "properly dominates" query 8317 // to test for proper dominance too, because the instruction which 8318 // produces the addrec's value is a PHI, and a PHI effectively properly 8319 // dominates its entire containing block. 8320 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 8321 if (!DT->dominates(AR->getLoop()->getHeader(), BB)) 8322 return DoesNotDominateBlock; 8323 } 8324 // FALL THROUGH into SCEVNAryExpr handling. 8325 case scAddExpr: 8326 case scMulExpr: 8327 case scUMaxExpr: 8328 case scSMaxExpr: { 8329 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 8330 bool Proper = true; 8331 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 8332 I != E; ++I) { 8333 BlockDisposition D = getBlockDisposition(*I, BB); 8334 if (D == DoesNotDominateBlock) 8335 return DoesNotDominateBlock; 8336 if (D == DominatesBlock) 8337 Proper = false; 8338 } 8339 return Proper ? ProperlyDominatesBlock : DominatesBlock; 8340 } 8341 case scUDivExpr: { 8342 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 8343 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 8344 BlockDisposition LD = getBlockDisposition(LHS, BB); 8345 if (LD == DoesNotDominateBlock) 8346 return DoesNotDominateBlock; 8347 BlockDisposition RD = getBlockDisposition(RHS, BB); 8348 if (RD == DoesNotDominateBlock) 8349 return DoesNotDominateBlock; 8350 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ? 8351 ProperlyDominatesBlock : DominatesBlock; 8352 } 8353 case scUnknown: 8354 if (Instruction *I = 8355 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) { 8356 if (I->getParent() == BB) 8357 return DominatesBlock; 8358 if (DT->properlyDominates(I->getParent(), BB)) 8359 return ProperlyDominatesBlock; 8360 return DoesNotDominateBlock; 8361 } 8362 return ProperlyDominatesBlock; 8363 case scCouldNotCompute: 8364 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 8365 } 8366 llvm_unreachable("Unknown SCEV kind!"); 8367 } 8368 8369 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) { 8370 return getBlockDisposition(S, BB) >= DominatesBlock; 8371 } 8372 8373 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) { 8374 return getBlockDisposition(S, BB) == ProperlyDominatesBlock; 8375 } 8376 8377 namespace { 8378 // Search for a SCEV expression node within an expression tree. 8379 // Implements SCEVTraversal::Visitor. 8380 struct SCEVSearch { 8381 const SCEV *Node; 8382 bool IsFound; 8383 8384 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {} 8385 8386 bool follow(const SCEV *S) { 8387 IsFound |= (S == Node); 8388 return !IsFound; 8389 } 8390 bool isDone() const { return IsFound; } 8391 }; 8392 } 8393 8394 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const { 8395 SCEVSearch Search(Op); 8396 visitAll(S, Search); 8397 return Search.IsFound; 8398 } 8399 8400 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) { 8401 ValuesAtScopes.erase(S); 8402 LoopDispositions.erase(S); 8403 BlockDispositions.erase(S); 8404 UnsignedRanges.erase(S); 8405 SignedRanges.erase(S); 8406 8407 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I = 8408 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) { 8409 BackedgeTakenInfo &BEInfo = I->second; 8410 if (BEInfo.hasOperand(S, this)) { 8411 BEInfo.clear(); 8412 BackedgeTakenCounts.erase(I++); 8413 } 8414 else 8415 ++I; 8416 } 8417 } 8418 8419 typedef DenseMap<const Loop *, std::string> VerifyMap; 8420 8421 /// replaceSubString - Replaces all occurrences of From in Str with To. 8422 static void replaceSubString(std::string &Str, StringRef From, StringRef To) { 8423 size_t Pos = 0; 8424 while ((Pos = Str.find(From, Pos)) != std::string::npos) { 8425 Str.replace(Pos, From.size(), To.data(), To.size()); 8426 Pos += To.size(); 8427 } 8428 } 8429 8430 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis. 8431 static void 8432 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) { 8433 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) { 8434 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse. 8435 8436 std::string &S = Map[L]; 8437 if (S.empty()) { 8438 raw_string_ostream OS(S); 8439 SE.getBackedgeTakenCount(L)->print(OS); 8440 8441 // false and 0 are semantically equivalent. This can happen in dead loops. 8442 replaceSubString(OS.str(), "false", "0"); 8443 // Remove wrap flags, their use in SCEV is highly fragile. 8444 // FIXME: Remove this when SCEV gets smarter about them. 8445 replaceSubString(OS.str(), "<nw>", ""); 8446 replaceSubString(OS.str(), "<nsw>", ""); 8447 replaceSubString(OS.str(), "<nuw>", ""); 8448 } 8449 } 8450 } 8451 8452 void ScalarEvolution::verifyAnalysis() const { 8453 if (!VerifySCEV) 8454 return; 8455 8456 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 8457 8458 // Gather stringified backedge taken counts for all loops using SCEV's caches. 8459 // FIXME: It would be much better to store actual values instead of strings, 8460 // but SCEV pointers will change if we drop the caches. 8461 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew; 8462 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I) 8463 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE); 8464 8465 // Gather stringified backedge taken counts for all loops without using 8466 // SCEV's caches. 8467 SE.releaseMemory(); 8468 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I) 8469 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE); 8470 8471 // Now compare whether they're the same with and without caches. This allows 8472 // verifying that no pass changed the cache. 8473 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() && 8474 "New loops suddenly appeared!"); 8475 8476 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(), 8477 OldE = BackedgeDumpsOld.end(), 8478 NewI = BackedgeDumpsNew.begin(); 8479 OldI != OldE; ++OldI, ++NewI) { 8480 assert(OldI->first == NewI->first && "Loop order changed!"); 8481 8482 // Compare the stringified SCEVs. We don't care if undef backedgetaken count 8483 // changes. 8484 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This 8485 // means that a pass is buggy or SCEV has to learn a new pattern but is 8486 // usually not harmful. 8487 if (OldI->second != NewI->second && 8488 OldI->second.find("undef") == std::string::npos && 8489 NewI->second.find("undef") == std::string::npos && 8490 OldI->second != "***COULDNOTCOMPUTE***" && 8491 NewI->second != "***COULDNOTCOMPUTE***") { 8492 dbgs() << "SCEVValidator: SCEV for loop '" 8493 << OldI->first->getHeader()->getName() 8494 << "' changed from '" << OldI->second 8495 << "' to '" << NewI->second << "'!\n"; 8496 std::abort(); 8497 } 8498 } 8499 8500 // TODO: Verify more things. 8501 } 8502