1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===// 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 #define DEBUG_TYPE "scalar-evolution" 62 #include "llvm/Analysis/ScalarEvolutionExpressions.h" 63 #include "llvm/Constants.h" 64 #include "llvm/DerivedTypes.h" 65 #include "llvm/GlobalVariable.h" 66 #include "llvm/GlobalAlias.h" 67 #include "llvm/Instructions.h" 68 #include "llvm/LLVMContext.h" 69 #include "llvm/Operator.h" 70 #include "llvm/Analysis/ConstantFolding.h" 71 #include "llvm/Analysis/Dominators.h" 72 #include "llvm/Analysis/InstructionSimplify.h" 73 #include "llvm/Analysis/LoopInfo.h" 74 #include "llvm/Analysis/ValueTracking.h" 75 #include "llvm/Assembly/Writer.h" 76 #include "llvm/Target/TargetData.h" 77 #include "llvm/Target/TargetLibraryInfo.h" 78 #include "llvm/Support/CommandLine.h" 79 #include "llvm/Support/ConstantRange.h" 80 #include "llvm/Support/Debug.h" 81 #include "llvm/Support/ErrorHandling.h" 82 #include "llvm/Support/GetElementPtrTypeIterator.h" 83 #include "llvm/Support/InstIterator.h" 84 #include "llvm/Support/MathExtras.h" 85 #include "llvm/Support/raw_ostream.h" 86 #include "llvm/ADT/Statistic.h" 87 #include "llvm/ADT/STLExtras.h" 88 #include "llvm/ADT/SmallPtrSet.h" 89 #include <algorithm> 90 using namespace llvm; 91 92 STATISTIC(NumArrayLenItCounts, 93 "Number of trip counts computed with array length"); 94 STATISTIC(NumTripCountsComputed, 95 "Number of loops with predictable loop counts"); 96 STATISTIC(NumTripCountsNotComputed, 97 "Number of loops without predictable loop counts"); 98 STATISTIC(NumBruteForceTripCountsComputed, 99 "Number of loops with trip counts computed by force"); 100 101 static cl::opt<unsigned> 102 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 103 cl::desc("Maximum number of iterations SCEV will " 104 "symbolically execute a constant " 105 "derived loop"), 106 cl::init(100)); 107 108 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution", 109 "Scalar Evolution Analysis", false, true) 110 INITIALIZE_PASS_DEPENDENCY(LoopInfo) 111 INITIALIZE_PASS_DEPENDENCY(DominatorTree) 112 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfo) 113 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution", 114 "Scalar Evolution Analysis", false, true) 115 char ScalarEvolution::ID = 0; 116 117 //===----------------------------------------------------------------------===// 118 // SCEV class definitions 119 //===----------------------------------------------------------------------===// 120 121 //===----------------------------------------------------------------------===// 122 // Implementation of the SCEV class. 123 // 124 125 #ifndef NDEBUG 126 void SCEV::dump() const { 127 print(dbgs()); 128 dbgs() << '\n'; 129 } 130 #endif 131 132 void SCEV::print(raw_ostream &OS) const { 133 switch (getSCEVType()) { 134 case scConstant: 135 WriteAsOperand(OS, cast<SCEVConstant>(this)->getValue(), false); 136 return; 137 case scTruncate: { 138 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this); 139 const SCEV *Op = Trunc->getOperand(); 140 OS << "(trunc " << *Op->getType() << " " << *Op << " to " 141 << *Trunc->getType() << ")"; 142 return; 143 } 144 case scZeroExtend: { 145 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this); 146 const SCEV *Op = ZExt->getOperand(); 147 OS << "(zext " << *Op->getType() << " " << *Op << " to " 148 << *ZExt->getType() << ")"; 149 return; 150 } 151 case scSignExtend: { 152 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this); 153 const SCEV *Op = SExt->getOperand(); 154 OS << "(sext " << *Op->getType() << " " << *Op << " to " 155 << *SExt->getType() << ")"; 156 return; 157 } 158 case scAddRecExpr: { 159 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this); 160 OS << "{" << *AR->getOperand(0); 161 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i) 162 OS << ",+," << *AR->getOperand(i); 163 OS << "}<"; 164 if (AR->getNoWrapFlags(FlagNUW)) 165 OS << "nuw><"; 166 if (AR->getNoWrapFlags(FlagNSW)) 167 OS << "nsw><"; 168 if (AR->getNoWrapFlags(FlagNW) && 169 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW))) 170 OS << "nw><"; 171 WriteAsOperand(OS, AR->getLoop()->getHeader(), /*PrintType=*/false); 172 OS << ">"; 173 return; 174 } 175 case scAddExpr: 176 case scMulExpr: 177 case scUMaxExpr: 178 case scSMaxExpr: { 179 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this); 180 const char *OpStr = 0; 181 switch (NAry->getSCEVType()) { 182 case scAddExpr: OpStr = " + "; break; 183 case scMulExpr: OpStr = " * "; break; 184 case scUMaxExpr: OpStr = " umax "; break; 185 case scSMaxExpr: OpStr = " smax "; break; 186 } 187 OS << "("; 188 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 189 I != E; ++I) { 190 OS << **I; 191 if (llvm::next(I) != E) 192 OS << OpStr; 193 } 194 OS << ")"; 195 switch (NAry->getSCEVType()) { 196 case scAddExpr: 197 case scMulExpr: 198 if (NAry->getNoWrapFlags(FlagNUW)) 199 OS << "<nuw>"; 200 if (NAry->getNoWrapFlags(FlagNSW)) 201 OS << "<nsw>"; 202 } 203 return; 204 } 205 case scUDivExpr: { 206 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this); 207 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")"; 208 return; 209 } 210 case scUnknown: { 211 const SCEVUnknown *U = cast<SCEVUnknown>(this); 212 Type *AllocTy; 213 if (U->isSizeOf(AllocTy)) { 214 OS << "sizeof(" << *AllocTy << ")"; 215 return; 216 } 217 if (U->isAlignOf(AllocTy)) { 218 OS << "alignof(" << *AllocTy << ")"; 219 return; 220 } 221 222 Type *CTy; 223 Constant *FieldNo; 224 if (U->isOffsetOf(CTy, FieldNo)) { 225 OS << "offsetof(" << *CTy << ", "; 226 WriteAsOperand(OS, FieldNo, false); 227 OS << ")"; 228 return; 229 } 230 231 // Otherwise just print it normally. 232 WriteAsOperand(OS, U->getValue(), false); 233 return; 234 } 235 case scCouldNotCompute: 236 OS << "***COULDNOTCOMPUTE***"; 237 return; 238 default: break; 239 } 240 llvm_unreachable("Unknown SCEV kind!"); 241 } 242 243 Type *SCEV::getType() const { 244 switch (getSCEVType()) { 245 case scConstant: 246 return cast<SCEVConstant>(this)->getType(); 247 case scTruncate: 248 case scZeroExtend: 249 case scSignExtend: 250 return cast<SCEVCastExpr>(this)->getType(); 251 case scAddRecExpr: 252 case scMulExpr: 253 case scUMaxExpr: 254 case scSMaxExpr: 255 return cast<SCEVNAryExpr>(this)->getType(); 256 case scAddExpr: 257 return cast<SCEVAddExpr>(this)->getType(); 258 case scUDivExpr: 259 return cast<SCEVUDivExpr>(this)->getType(); 260 case scUnknown: 261 return cast<SCEVUnknown>(this)->getType(); 262 case scCouldNotCompute: 263 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 264 default: 265 llvm_unreachable("Unknown SCEV kind!"); 266 } 267 } 268 269 bool SCEV::isZero() const { 270 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 271 return SC->getValue()->isZero(); 272 return false; 273 } 274 275 bool SCEV::isOne() const { 276 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 277 return SC->getValue()->isOne(); 278 return false; 279 } 280 281 bool SCEV::isAllOnesValue() const { 282 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 283 return SC->getValue()->isAllOnesValue(); 284 return false; 285 } 286 287 /// isNonConstantNegative - Return true if the specified scev is negated, but 288 /// not a constant. 289 bool SCEV::isNonConstantNegative() const { 290 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this); 291 if (!Mul) return false; 292 293 // If there is a constant factor, it will be first. 294 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0)); 295 if (!SC) return false; 296 297 // Return true if the value is negative, this matches things like (-42 * V). 298 return SC->getValue()->getValue().isNegative(); 299 } 300 301 SCEVCouldNotCompute::SCEVCouldNotCompute() : 302 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {} 303 304 bool SCEVCouldNotCompute::classof(const SCEV *S) { 305 return S->getSCEVType() == scCouldNotCompute; 306 } 307 308 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 309 FoldingSetNodeID ID; 310 ID.AddInteger(scConstant); 311 ID.AddPointer(V); 312 void *IP = 0; 313 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 314 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V); 315 UniqueSCEVs.InsertNode(S, IP); 316 return S; 317 } 318 319 const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 320 return getConstant(ConstantInt::get(getContext(), Val)); 321 } 322 323 const SCEV * 324 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) { 325 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 326 return getConstant(ConstantInt::get(ITy, V, isSigned)); 327 } 328 329 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, 330 unsigned SCEVTy, const SCEV *op, Type *ty) 331 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 332 333 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, 334 const SCEV *op, Type *ty) 335 : SCEVCastExpr(ID, scTruncate, op, ty) { 336 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 337 (Ty->isIntegerTy() || Ty->isPointerTy()) && 338 "Cannot truncate non-integer value!"); 339 } 340 341 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, 342 const SCEV *op, Type *ty) 343 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 344 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 345 (Ty->isIntegerTy() || Ty->isPointerTy()) && 346 "Cannot zero extend non-integer value!"); 347 } 348 349 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, 350 const SCEV *op, Type *ty) 351 : SCEVCastExpr(ID, scSignExtend, op, ty) { 352 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 353 (Ty->isIntegerTy() || Ty->isPointerTy()) && 354 "Cannot sign extend non-integer value!"); 355 } 356 357 void SCEVUnknown::deleted() { 358 // Clear this SCEVUnknown from various maps. 359 SE->forgetMemoizedResults(this); 360 361 // Remove this SCEVUnknown from the uniquing map. 362 SE->UniqueSCEVs.RemoveNode(this); 363 364 // Release the value. 365 setValPtr(0); 366 } 367 368 void SCEVUnknown::allUsesReplacedWith(Value *New) { 369 // Clear this SCEVUnknown from various maps. 370 SE->forgetMemoizedResults(this); 371 372 // Remove this SCEVUnknown from the uniquing map. 373 SE->UniqueSCEVs.RemoveNode(this); 374 375 // Update this SCEVUnknown to point to the new value. This is needed 376 // because there may still be outstanding SCEVs which still point to 377 // this SCEVUnknown. 378 setValPtr(New); 379 } 380 381 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const { 382 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 383 if (VCE->getOpcode() == Instruction::PtrToInt) 384 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 385 if (CE->getOpcode() == Instruction::GetElementPtr && 386 CE->getOperand(0)->isNullValue() && 387 CE->getNumOperands() == 2) 388 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 389 if (CI->isOne()) { 390 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 391 ->getElementType(); 392 return true; 393 } 394 395 return false; 396 } 397 398 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const { 399 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 400 if (VCE->getOpcode() == Instruction::PtrToInt) 401 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 402 if (CE->getOpcode() == Instruction::GetElementPtr && 403 CE->getOperand(0)->isNullValue()) { 404 Type *Ty = 405 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 406 if (StructType *STy = dyn_cast<StructType>(Ty)) 407 if (!STy->isPacked() && 408 CE->getNumOperands() == 3 && 409 CE->getOperand(1)->isNullValue()) { 410 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 411 if (CI->isOne() && 412 STy->getNumElements() == 2 && 413 STy->getElementType(0)->isIntegerTy(1)) { 414 AllocTy = STy->getElementType(1); 415 return true; 416 } 417 } 418 } 419 420 return false; 421 } 422 423 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const { 424 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 425 if (VCE->getOpcode() == Instruction::PtrToInt) 426 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 427 if (CE->getOpcode() == Instruction::GetElementPtr && 428 CE->getNumOperands() == 3 && 429 CE->getOperand(0)->isNullValue() && 430 CE->getOperand(1)->isNullValue()) { 431 Type *Ty = 432 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 433 // Ignore vector types here so that ScalarEvolutionExpander doesn't 434 // emit getelementptrs that index into vectors. 435 if (Ty->isStructTy() || Ty->isArrayTy()) { 436 CTy = Ty; 437 FieldNo = CE->getOperand(2); 438 return true; 439 } 440 } 441 442 return false; 443 } 444 445 //===----------------------------------------------------------------------===// 446 // SCEV Utilities 447 //===----------------------------------------------------------------------===// 448 449 namespace { 450 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 451 /// than the complexity of the RHS. This comparator is used to canonicalize 452 /// expressions. 453 class SCEVComplexityCompare { 454 const LoopInfo *const LI; 455 public: 456 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {} 457 458 // Return true or false if LHS is less than, or at least RHS, respectively. 459 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 460 return compare(LHS, RHS) < 0; 461 } 462 463 // Return negative, zero, or positive, if LHS is less than, equal to, or 464 // greater than RHS, respectively. A three-way result allows recursive 465 // comparisons to be more efficient. 466 int compare(const SCEV *LHS, const SCEV *RHS) const { 467 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 468 if (LHS == RHS) 469 return 0; 470 471 // Primarily, sort the SCEVs by their getSCEVType(). 472 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); 473 if (LType != RType) 474 return (int)LType - (int)RType; 475 476 // Aside from the getSCEVType() ordering, the particular ordering 477 // isn't very important except that it's beneficial to be consistent, 478 // so that (a + b) and (b + a) don't end up as different expressions. 479 switch (LType) { 480 case scUnknown: { 481 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS); 482 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 483 484 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 485 // not as complete as it could be. 486 const Value *LV = LU->getValue(), *RV = RU->getValue(); 487 488 // Order pointer values after integer values. This helps SCEVExpander 489 // form GEPs. 490 bool LIsPointer = LV->getType()->isPointerTy(), 491 RIsPointer = RV->getType()->isPointerTy(); 492 if (LIsPointer != RIsPointer) 493 return (int)LIsPointer - (int)RIsPointer; 494 495 // Compare getValueID values. 496 unsigned LID = LV->getValueID(), 497 RID = RV->getValueID(); 498 if (LID != RID) 499 return (int)LID - (int)RID; 500 501 // Sort arguments by their position. 502 if (const Argument *LA = dyn_cast<Argument>(LV)) { 503 const Argument *RA = cast<Argument>(RV); 504 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo(); 505 return (int)LArgNo - (int)RArgNo; 506 } 507 508 // For instructions, compare their loop depth, and their operand 509 // count. This is pretty loose. 510 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) { 511 const Instruction *RInst = cast<Instruction>(RV); 512 513 // Compare loop depths. 514 const BasicBlock *LParent = LInst->getParent(), 515 *RParent = RInst->getParent(); 516 if (LParent != RParent) { 517 unsigned LDepth = LI->getLoopDepth(LParent), 518 RDepth = LI->getLoopDepth(RParent); 519 if (LDepth != RDepth) 520 return (int)LDepth - (int)RDepth; 521 } 522 523 // Compare the number of operands. 524 unsigned LNumOps = LInst->getNumOperands(), 525 RNumOps = RInst->getNumOperands(); 526 return (int)LNumOps - (int)RNumOps; 527 } 528 529 return 0; 530 } 531 532 case scConstant: { 533 const SCEVConstant *LC = cast<SCEVConstant>(LHS); 534 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 535 536 // Compare constant values. 537 const APInt &LA = LC->getValue()->getValue(); 538 const APInt &RA = RC->getValue()->getValue(); 539 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth(); 540 if (LBitWidth != RBitWidth) 541 return (int)LBitWidth - (int)RBitWidth; 542 return LA.ult(RA) ? -1 : 1; 543 } 544 545 case scAddRecExpr: { 546 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS); 547 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 548 549 // Compare addrec loop depths. 550 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop(); 551 if (LLoop != RLoop) { 552 unsigned LDepth = LLoop->getLoopDepth(), 553 RDepth = RLoop->getLoopDepth(); 554 if (LDepth != RDepth) 555 return (int)LDepth - (int)RDepth; 556 } 557 558 // Addrec complexity grows with operand count. 559 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands(); 560 if (LNumOps != RNumOps) 561 return (int)LNumOps - (int)RNumOps; 562 563 // Lexicographically compare. 564 for (unsigned i = 0; i != LNumOps; ++i) { 565 long X = compare(LA->getOperand(i), RA->getOperand(i)); 566 if (X != 0) 567 return X; 568 } 569 570 return 0; 571 } 572 573 case scAddExpr: 574 case scMulExpr: 575 case scSMaxExpr: 576 case scUMaxExpr: { 577 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS); 578 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 579 580 // Lexicographically compare n-ary expressions. 581 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands(); 582 for (unsigned i = 0; i != LNumOps; ++i) { 583 if (i >= RNumOps) 584 return 1; 585 long X = compare(LC->getOperand(i), RC->getOperand(i)); 586 if (X != 0) 587 return X; 588 } 589 return (int)LNumOps - (int)RNumOps; 590 } 591 592 case scUDivExpr: { 593 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS); 594 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 595 596 // Lexicographically compare udiv expressions. 597 long X = compare(LC->getLHS(), RC->getLHS()); 598 if (X != 0) 599 return X; 600 return compare(LC->getRHS(), RC->getRHS()); 601 } 602 603 case scTruncate: 604 case scZeroExtend: 605 case scSignExtend: { 606 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS); 607 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 608 609 // Compare cast expressions by operand. 610 return compare(LC->getOperand(), RC->getOperand()); 611 } 612 613 default: 614 llvm_unreachable("Unknown SCEV kind!"); 615 } 616 } 617 }; 618 } 619 620 /// GroupByComplexity - Given a list of SCEV objects, order them by their 621 /// complexity, and group objects of the same complexity together by value. 622 /// When this routine is finished, we know that any duplicates in the vector are 623 /// consecutive and that complexity is monotonically increasing. 624 /// 625 /// Note that we go take special precautions to ensure that we get deterministic 626 /// results from this routine. In other words, we don't want the results of 627 /// this to depend on where the addresses of various SCEV objects happened to 628 /// land in memory. 629 /// 630 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 631 LoopInfo *LI) { 632 if (Ops.size() < 2) return; // Noop 633 if (Ops.size() == 2) { 634 // This is the common case, which also happens to be trivially simple. 635 // Special case it. 636 const SCEV *&LHS = Ops[0], *&RHS = Ops[1]; 637 if (SCEVComplexityCompare(LI)(RHS, LHS)) 638 std::swap(LHS, RHS); 639 return; 640 } 641 642 // Do the rough sort by complexity. 643 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 644 645 // Now that we are sorted by complexity, group elements of the same 646 // complexity. Note that this is, at worst, N^2, but the vector is likely to 647 // be extremely short in practice. Note that we take this approach because we 648 // do not want to depend on the addresses of the objects we are grouping. 649 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 650 const SCEV *S = Ops[i]; 651 unsigned Complexity = S->getSCEVType(); 652 653 // If there are any objects of the same complexity and same value as this 654 // one, group them. 655 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 656 if (Ops[j] == S) { // Found a duplicate. 657 // Move it to immediately after i'th element. 658 std::swap(Ops[i+1], Ops[j]); 659 ++i; // no need to rescan it. 660 if (i == e-2) return; // Done! 661 } 662 } 663 } 664 } 665 666 667 668 //===----------------------------------------------------------------------===// 669 // Simple SCEV method implementations 670 //===----------------------------------------------------------------------===// 671 672 /// BinomialCoefficient - Compute BC(It, K). The result has width W. 673 /// Assume, K > 0. 674 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 675 ScalarEvolution &SE, 676 Type *ResultTy) { 677 // Handle the simplest case efficiently. 678 if (K == 1) 679 return SE.getTruncateOrZeroExtend(It, ResultTy); 680 681 // We are using the following formula for BC(It, K): 682 // 683 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 684 // 685 // Suppose, W is the bitwidth of the return value. We must be prepared for 686 // overflow. Hence, we must assure that the result of our computation is 687 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 688 // safe in modular arithmetic. 689 // 690 // However, this code doesn't use exactly that formula; the formula it uses 691 // is something like the following, where T is the number of factors of 2 in 692 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 693 // exponentiation: 694 // 695 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 696 // 697 // This formula is trivially equivalent to the previous formula. However, 698 // this formula can be implemented much more efficiently. The trick is that 699 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 700 // arithmetic. To do exact division in modular arithmetic, all we have 701 // to do is multiply by the inverse. Therefore, this step can be done at 702 // width W. 703 // 704 // The next issue is how to safely do the division by 2^T. The way this 705 // is done is by doing the multiplication step at a width of at least W + T 706 // bits. This way, the bottom W+T bits of the product are accurate. Then, 707 // when we perform the division by 2^T (which is equivalent to a right shift 708 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 709 // truncated out after the division by 2^T. 710 // 711 // In comparison to just directly using the first formula, this technique 712 // is much more efficient; using the first formula requires W * K bits, 713 // but this formula less than W + K bits. Also, the first formula requires 714 // a division step, whereas this formula only requires multiplies and shifts. 715 // 716 // It doesn't matter whether the subtraction step is done in the calculation 717 // width or the input iteration count's width; if the subtraction overflows, 718 // the result must be zero anyway. We prefer here to do it in the width of 719 // the induction variable because it helps a lot for certain cases; CodeGen 720 // isn't smart enough to ignore the overflow, which leads to much less 721 // efficient code if the width of the subtraction is wider than the native 722 // register width. 723 // 724 // (It's possible to not widen at all by pulling out factors of 2 before 725 // the multiplication; for example, K=2 can be calculated as 726 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 727 // extra arithmetic, so it's not an obvious win, and it gets 728 // much more complicated for K > 3.) 729 730 // Protection from insane SCEVs; this bound is conservative, 731 // but it probably doesn't matter. 732 if (K > 1000) 733 return SE.getCouldNotCompute(); 734 735 unsigned W = SE.getTypeSizeInBits(ResultTy); 736 737 // Calculate K! / 2^T and T; we divide out the factors of two before 738 // multiplying for calculating K! / 2^T to avoid overflow. 739 // Other overflow doesn't matter because we only care about the bottom 740 // W bits of the result. 741 APInt OddFactorial(W, 1); 742 unsigned T = 1; 743 for (unsigned i = 3; i <= K; ++i) { 744 APInt Mult(W, i); 745 unsigned TwoFactors = Mult.countTrailingZeros(); 746 T += TwoFactors; 747 Mult = Mult.lshr(TwoFactors); 748 OddFactorial *= Mult; 749 } 750 751 // We need at least W + T bits for the multiplication step 752 unsigned CalculationBits = W + T; 753 754 // Calculate 2^T, at width T+W. 755 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 756 757 // Calculate the multiplicative inverse of K! / 2^T; 758 // this multiplication factor will perform the exact division by 759 // K! / 2^T. 760 APInt Mod = APInt::getSignedMinValue(W+1); 761 APInt MultiplyFactor = OddFactorial.zext(W+1); 762 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 763 MultiplyFactor = MultiplyFactor.trunc(W); 764 765 // Calculate the product, at width T+W 766 IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 767 CalculationBits); 768 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 769 for (unsigned i = 1; i != K; ++i) { 770 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); 771 Dividend = SE.getMulExpr(Dividend, 772 SE.getTruncateOrZeroExtend(S, CalculationTy)); 773 } 774 775 // Divide by 2^T 776 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 777 778 // Truncate the result, and divide by K! / 2^T. 779 780 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 781 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 782 } 783 784 /// evaluateAtIteration - Return the value of this chain of recurrences at 785 /// the specified iteration number. We can evaluate this recurrence by 786 /// multiplying each element in the chain by the binomial coefficient 787 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 788 /// 789 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 790 /// 791 /// where BC(It, k) stands for binomial coefficient. 792 /// 793 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 794 ScalarEvolution &SE) const { 795 const SCEV *Result = getStart(); 796 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 797 // The computation is correct in the face of overflow provided that the 798 // multiplication is performed _after_ the evaluation of the binomial 799 // coefficient. 800 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 801 if (isa<SCEVCouldNotCompute>(Coeff)) 802 return Coeff; 803 804 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 805 } 806 return Result; 807 } 808 809 //===----------------------------------------------------------------------===// 810 // SCEV Expression folder implementations 811 //===----------------------------------------------------------------------===// 812 813 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 814 Type *Ty) { 815 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 816 "This is not a truncating conversion!"); 817 assert(isSCEVable(Ty) && 818 "This is not a conversion to a SCEVable type!"); 819 Ty = getEffectiveSCEVType(Ty); 820 821 FoldingSetNodeID ID; 822 ID.AddInteger(scTruncate); 823 ID.AddPointer(Op); 824 ID.AddPointer(Ty); 825 void *IP = 0; 826 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 827 828 // Fold if the operand is constant. 829 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 830 return getConstant( 831 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty))); 832 833 // trunc(trunc(x)) --> trunc(x) 834 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 835 return getTruncateExpr(ST->getOperand(), Ty); 836 837 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 838 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 839 return getTruncateOrSignExtend(SS->getOperand(), Ty); 840 841 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 842 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 843 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 844 845 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can 846 // eliminate all the truncates. 847 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) { 848 SmallVector<const SCEV *, 4> Operands; 849 bool hasTrunc = false; 850 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) { 851 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty); 852 hasTrunc = isa<SCEVTruncateExpr>(S); 853 Operands.push_back(S); 854 } 855 if (!hasTrunc) 856 return getAddExpr(Operands); 857 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL. 858 } 859 860 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can 861 // eliminate all the truncates. 862 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) { 863 SmallVector<const SCEV *, 4> Operands; 864 bool hasTrunc = false; 865 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) { 866 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty); 867 hasTrunc = isa<SCEVTruncateExpr>(S); 868 Operands.push_back(S); 869 } 870 if (!hasTrunc) 871 return getMulExpr(Operands); 872 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL. 873 } 874 875 // If the input value is a chrec scev, truncate the chrec's operands. 876 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 877 SmallVector<const SCEV *, 4> Operands; 878 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 879 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 880 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap); 881 } 882 883 // The cast wasn't folded; create an explicit cast node. We can reuse 884 // the existing insert position since if we get here, we won't have 885 // made any changes which would invalidate it. 886 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 887 Op, Ty); 888 UniqueSCEVs.InsertNode(S, IP); 889 return S; 890 } 891 892 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 893 Type *Ty) { 894 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 895 "This is not an extending conversion!"); 896 assert(isSCEVable(Ty) && 897 "This is not a conversion to a SCEVable type!"); 898 Ty = getEffectiveSCEVType(Ty); 899 900 // Fold if the operand is constant. 901 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 902 return getConstant( 903 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty))); 904 905 // zext(zext(x)) --> zext(x) 906 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 907 return getZeroExtendExpr(SZ->getOperand(), Ty); 908 909 // Before doing any expensive analysis, check to see if we've already 910 // computed a SCEV for this Op and Ty. 911 FoldingSetNodeID ID; 912 ID.AddInteger(scZeroExtend); 913 ID.AddPointer(Op); 914 ID.AddPointer(Ty); 915 void *IP = 0; 916 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 917 918 // zext(trunc(x)) --> zext(x) or x or trunc(x) 919 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 920 // It's possible the bits taken off by the truncate were all zero bits. If 921 // so, we should be able to simplify this further. 922 const SCEV *X = ST->getOperand(); 923 ConstantRange CR = getUnsignedRange(X); 924 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 925 unsigned NewBits = getTypeSizeInBits(Ty); 926 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains( 927 CR.zextOrTrunc(NewBits))) 928 return getTruncateOrZeroExtend(X, Ty); 929 } 930 931 // If the input value is a chrec scev, and we can prove that the value 932 // did not overflow the old, smaller, value, we can zero extend all of the 933 // operands (often constants). This allows analysis of something like 934 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 935 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 936 if (AR->isAffine()) { 937 const SCEV *Start = AR->getStart(); 938 const SCEV *Step = AR->getStepRecurrence(*this); 939 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 940 const Loop *L = AR->getLoop(); 941 942 // If we have special knowledge that this addrec won't overflow, 943 // we don't need to do any further analysis. 944 if (AR->getNoWrapFlags(SCEV::FlagNUW)) 945 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 946 getZeroExtendExpr(Step, Ty), 947 L, AR->getNoWrapFlags()); 948 949 // Check whether the backedge-taken count is SCEVCouldNotCompute. 950 // Note that this serves two purposes: It filters out loops that are 951 // simply not analyzable, and it covers the case where this code is 952 // being called from within backedge-taken count analysis, such that 953 // attempting to ask for the backedge-taken count would likely result 954 // in infinite recursion. In the later case, the analysis code will 955 // cope with a conservative value, and it will take care to purge 956 // that value once it has finished. 957 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 958 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 959 // Manually compute the final value for AR, checking for 960 // overflow. 961 962 // Check whether the backedge-taken count can be losslessly casted to 963 // the addrec's type. The count is always unsigned. 964 const SCEV *CastedMaxBECount = 965 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 966 const SCEV *RecastedMaxBECount = 967 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 968 if (MaxBECount == RecastedMaxBECount) { 969 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 970 // Check whether Start+Step*MaxBECount has no unsigned overflow. 971 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); 972 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy); 973 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy); 974 const SCEV *WideMaxBECount = 975 getZeroExtendExpr(CastedMaxBECount, WideTy); 976 const SCEV *OperandExtendedAdd = 977 getAddExpr(WideStart, 978 getMulExpr(WideMaxBECount, 979 getZeroExtendExpr(Step, WideTy))); 980 if (ZAdd == OperandExtendedAdd) { 981 // Cache knowledge of AR NUW, which is propagated to this AddRec. 982 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); 983 // Return the expression with the addrec on the outside. 984 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 985 getZeroExtendExpr(Step, Ty), 986 L, AR->getNoWrapFlags()); 987 } 988 // Similar to above, only this time treat the step value as signed. 989 // This covers loops that count down. 990 OperandExtendedAdd = 991 getAddExpr(WideStart, 992 getMulExpr(WideMaxBECount, 993 getSignExtendExpr(Step, WideTy))); 994 if (ZAdd == OperandExtendedAdd) { 995 // Cache knowledge of AR NW, which is propagated to this AddRec. 996 // Negative step causes unsigned wrap, but it still can't self-wrap. 997 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); 998 // Return the expression with the addrec on the outside. 999 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1000 getSignExtendExpr(Step, Ty), 1001 L, AR->getNoWrapFlags()); 1002 } 1003 } 1004 1005 // If the backedge is guarded by a comparison with the pre-inc value 1006 // the addrec is safe. Also, if the entry is guarded by a comparison 1007 // with the start value and the backedge is guarded by a comparison 1008 // with the post-inc value, the addrec is safe. 1009 if (isKnownPositive(Step)) { 1010 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 1011 getUnsignedRange(Step).getUnsignedMax()); 1012 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 1013 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 1014 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 1015 AR->getPostIncExpr(*this), N))) { 1016 // Cache knowledge of AR NUW, which is propagated to this AddRec. 1017 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); 1018 // Return the expression with the addrec on the outside. 1019 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1020 getZeroExtendExpr(Step, Ty), 1021 L, AR->getNoWrapFlags()); 1022 } 1023 } else if (isKnownNegative(Step)) { 1024 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 1025 getSignedRange(Step).getSignedMin()); 1026 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || 1027 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) && 1028 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 1029 AR->getPostIncExpr(*this), N))) { 1030 // Cache knowledge of AR NW, which is propagated to this AddRec. 1031 // Negative step causes unsigned wrap, but it still can't self-wrap. 1032 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); 1033 // Return the expression with the addrec on the outside. 1034 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1035 getSignExtendExpr(Step, Ty), 1036 L, AR->getNoWrapFlags()); 1037 } 1038 } 1039 } 1040 } 1041 1042 // The cast wasn't folded; create an explicit cast node. 1043 // Recompute the insert position, as it may have been invalidated. 1044 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1045 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 1046 Op, Ty); 1047 UniqueSCEVs.InsertNode(S, IP); 1048 return S; 1049 } 1050 1051 // Get the limit of a recurrence such that incrementing by Step cannot cause 1052 // signed overflow as long as the value of the recurrence within the loop does 1053 // not exceed this limit before incrementing. 1054 static const SCEV *getOverflowLimitForStep(const SCEV *Step, 1055 ICmpInst::Predicate *Pred, 1056 ScalarEvolution *SE) { 1057 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType()); 1058 if (SE->isKnownPositive(Step)) { 1059 *Pred = ICmpInst::ICMP_SLT; 1060 return SE->getConstant(APInt::getSignedMinValue(BitWidth) - 1061 SE->getSignedRange(Step).getSignedMax()); 1062 } 1063 if (SE->isKnownNegative(Step)) { 1064 *Pred = ICmpInst::ICMP_SGT; 1065 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) - 1066 SE->getSignedRange(Step).getSignedMin()); 1067 } 1068 return 0; 1069 } 1070 1071 // The recurrence AR has been shown to have no signed wrap. Typically, if we can 1072 // prove NSW for AR, then we can just as easily prove NSW for its preincrement 1073 // or postincrement sibling. This allows normalizing a sign extended AddRec as 1074 // such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a 1075 // result, the expression "Step + sext(PreIncAR)" is congruent with 1076 // "sext(PostIncAR)" 1077 static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR, 1078 Type *Ty, 1079 ScalarEvolution *SE) { 1080 const Loop *L = AR->getLoop(); 1081 const SCEV *Start = AR->getStart(); 1082 const SCEV *Step = AR->getStepRecurrence(*SE); 1083 1084 // Check for a simple looking step prior to loop entry. 1085 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start); 1086 if (!SA) 1087 return 0; 1088 1089 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV 1090 // subtraction is expensive. For this purpose, perform a quick and dirty 1091 // difference, by checking for Step in the operand list. 1092 SmallVector<const SCEV *, 4> DiffOps; 1093 for (SCEVAddExpr::op_iterator I = SA->op_begin(), E = SA->op_end(); 1094 I != E; ++I) { 1095 if (*I != Step) 1096 DiffOps.push_back(*I); 1097 } 1098 if (DiffOps.size() == SA->getNumOperands()) 1099 return 0; 1100 1101 // This is a postinc AR. Check for overflow on the preinc recurrence using the 1102 // same three conditions that getSignExtendedExpr checks. 1103 1104 // 1. NSW flags on the step increment. 1105 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags()); 1106 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>( 1107 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap)); 1108 1109 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW)) 1110 return PreStart; 1111 1112 // 2. Direct overflow check on the step operation's expression. 1113 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType()); 1114 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2); 1115 const SCEV *OperandExtendedStart = 1116 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy), 1117 SE->getSignExtendExpr(Step, WideTy)); 1118 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) { 1119 // Cache knowledge of PreAR NSW. 1120 if (PreAR) 1121 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW); 1122 // FIXME: this optimization needs a unit test 1123 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n"); 1124 return PreStart; 1125 } 1126 1127 // 3. Loop precondition. 1128 ICmpInst::Predicate Pred; 1129 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE); 1130 1131 if (OverflowLimit && 1132 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) { 1133 return PreStart; 1134 } 1135 return 0; 1136 } 1137 1138 // Get the normalized sign-extended expression for this AddRec's Start. 1139 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR, 1140 Type *Ty, 1141 ScalarEvolution *SE) { 1142 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE); 1143 if (!PreStart) 1144 return SE->getSignExtendExpr(AR->getStart(), Ty); 1145 1146 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty), 1147 SE->getSignExtendExpr(PreStart, Ty)); 1148 } 1149 1150 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 1151 Type *Ty) { 1152 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1153 "This is not an extending conversion!"); 1154 assert(isSCEVable(Ty) && 1155 "This is not a conversion to a SCEVable type!"); 1156 Ty = getEffectiveSCEVType(Ty); 1157 1158 // Fold if the operand is constant. 1159 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1160 return getConstant( 1161 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty))); 1162 1163 // sext(sext(x)) --> sext(x) 1164 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1165 return getSignExtendExpr(SS->getOperand(), Ty); 1166 1167 // sext(zext(x)) --> zext(x) 1168 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 1169 return getZeroExtendExpr(SZ->getOperand(), Ty); 1170 1171 // Before doing any expensive analysis, check to see if we've already 1172 // computed a SCEV for this Op and Ty. 1173 FoldingSetNodeID ID; 1174 ID.AddInteger(scSignExtend); 1175 ID.AddPointer(Op); 1176 ID.AddPointer(Ty); 1177 void *IP = 0; 1178 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1179 1180 // If the input value is provably positive, build a zext instead. 1181 if (isKnownNonNegative(Op)) 1182 return getZeroExtendExpr(Op, Ty); 1183 1184 // sext(trunc(x)) --> sext(x) or x or trunc(x) 1185 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 1186 // It's possible the bits taken off by the truncate were all sign bits. If 1187 // so, we should be able to simplify this further. 1188 const SCEV *X = ST->getOperand(); 1189 ConstantRange CR = getSignedRange(X); 1190 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 1191 unsigned NewBits = getTypeSizeInBits(Ty); 1192 if (CR.truncate(TruncBits).signExtend(NewBits).contains( 1193 CR.sextOrTrunc(NewBits))) 1194 return getTruncateOrSignExtend(X, Ty); 1195 } 1196 1197 // If the input value is a chrec scev, and we can prove that the value 1198 // did not overflow the old, smaller, value, we can sign extend all of the 1199 // operands (often constants). This allows analysis of something like 1200 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1201 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1202 if (AR->isAffine()) { 1203 const SCEV *Start = AR->getStart(); 1204 const SCEV *Step = AR->getStepRecurrence(*this); 1205 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1206 const Loop *L = AR->getLoop(); 1207 1208 // If we have special knowledge that this addrec won't overflow, 1209 // we don't need to do any further analysis. 1210 if (AR->getNoWrapFlags(SCEV::FlagNSW)) 1211 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1212 getSignExtendExpr(Step, Ty), 1213 L, SCEV::FlagNSW); 1214 1215 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1216 // Note that this serves two purposes: It filters out loops that are 1217 // simply not analyzable, and it covers the case where this code is 1218 // being called from within backedge-taken count analysis, such that 1219 // attempting to ask for the backedge-taken count would likely result 1220 // in infinite recursion. In the later case, the analysis code will 1221 // cope with a conservative value, and it will take care to purge 1222 // that value once it has finished. 1223 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1224 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1225 // Manually compute the final value for AR, checking for 1226 // overflow. 1227 1228 // Check whether the backedge-taken count can be losslessly casted to 1229 // the addrec's type. The count is always unsigned. 1230 const SCEV *CastedMaxBECount = 1231 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1232 const SCEV *RecastedMaxBECount = 1233 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1234 if (MaxBECount == RecastedMaxBECount) { 1235 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1236 // Check whether Start+Step*MaxBECount has no signed overflow. 1237 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1238 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy); 1239 const SCEV *WideStart = getSignExtendExpr(Start, WideTy); 1240 const SCEV *WideMaxBECount = 1241 getZeroExtendExpr(CastedMaxBECount, WideTy); 1242 const SCEV *OperandExtendedAdd = 1243 getAddExpr(WideStart, 1244 getMulExpr(WideMaxBECount, 1245 getSignExtendExpr(Step, WideTy))); 1246 if (SAdd == OperandExtendedAdd) { 1247 // Cache knowledge of AR NSW, which is propagated to this AddRec. 1248 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1249 // Return the expression with the addrec on the outside. 1250 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1251 getSignExtendExpr(Step, Ty), 1252 L, AR->getNoWrapFlags()); 1253 } 1254 // Similar to above, only this time treat the step value as unsigned. 1255 // This covers loops that count up with an unsigned step. 1256 OperandExtendedAdd = 1257 getAddExpr(WideStart, 1258 getMulExpr(WideMaxBECount, 1259 getZeroExtendExpr(Step, WideTy))); 1260 if (SAdd == OperandExtendedAdd) { 1261 // Cache knowledge of AR NSW, which is propagated to this AddRec. 1262 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1263 // Return the expression with the addrec on the outside. 1264 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1265 getZeroExtendExpr(Step, Ty), 1266 L, AR->getNoWrapFlags()); 1267 } 1268 } 1269 1270 // If the backedge is guarded by a comparison with the pre-inc value 1271 // the addrec is safe. Also, if the entry is guarded by a comparison 1272 // with the start value and the backedge is guarded by a comparison 1273 // with the post-inc value, the addrec is safe. 1274 ICmpInst::Predicate Pred; 1275 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this); 1276 if (OverflowLimit && 1277 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) || 1278 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) && 1279 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this), 1280 OverflowLimit)))) { 1281 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec. 1282 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1283 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1284 getSignExtendExpr(Step, Ty), 1285 L, AR->getNoWrapFlags()); 1286 } 1287 } 1288 } 1289 1290 // The cast wasn't folded; create an explicit cast node. 1291 // Recompute the insert position, as it may have been invalidated. 1292 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1293 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1294 Op, Ty); 1295 UniqueSCEVs.InsertNode(S, IP); 1296 return S; 1297 } 1298 1299 /// getAnyExtendExpr - Return a SCEV for the given operand extended with 1300 /// unspecified bits out to the given type. 1301 /// 1302 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1303 Type *Ty) { 1304 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1305 "This is not an extending conversion!"); 1306 assert(isSCEVable(Ty) && 1307 "This is not a conversion to a SCEVable type!"); 1308 Ty = getEffectiveSCEVType(Ty); 1309 1310 // Sign-extend negative constants. 1311 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1312 if (SC->getValue()->getValue().isNegative()) 1313 return getSignExtendExpr(Op, Ty); 1314 1315 // Peel off a truncate cast. 1316 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1317 const SCEV *NewOp = T->getOperand(); 1318 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1319 return getAnyExtendExpr(NewOp, Ty); 1320 return getTruncateOrNoop(NewOp, Ty); 1321 } 1322 1323 // Next try a zext cast. If the cast is folded, use it. 1324 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1325 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1326 return ZExt; 1327 1328 // Next try a sext cast. If the cast is folded, use it. 1329 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1330 if (!isa<SCEVSignExtendExpr>(SExt)) 1331 return SExt; 1332 1333 // Force the cast to be folded into the operands of an addrec. 1334 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1335 SmallVector<const SCEV *, 4> Ops; 1336 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1337 I != E; ++I) 1338 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1339 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW); 1340 } 1341 1342 // If the expression is obviously signed, use the sext cast value. 1343 if (isa<SCEVSMaxExpr>(Op)) 1344 return SExt; 1345 1346 // Absent any other information, use the zext cast value. 1347 return ZExt; 1348 } 1349 1350 /// CollectAddOperandsWithScales - Process the given Ops list, which is 1351 /// a list of operands to be added under the given scale, update the given 1352 /// map. This is a helper function for getAddRecExpr. As an example of 1353 /// what it does, given a sequence of operands that would form an add 1354 /// expression like this: 1355 /// 1356 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1357 /// 1358 /// where A and B are constants, update the map with these values: 1359 /// 1360 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1361 /// 1362 /// and add 13 + A*B*29 to AccumulatedConstant. 1363 /// This will allow getAddRecExpr to produce this: 1364 /// 1365 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1366 /// 1367 /// This form often exposes folding opportunities that are hidden in 1368 /// the original operand list. 1369 /// 1370 /// Return true iff it appears that any interesting folding opportunities 1371 /// may be exposed. This helps getAddRecExpr short-circuit extra work in 1372 /// the common case where no interesting opportunities are present, and 1373 /// is also used as a check to avoid infinite recursion. 1374 /// 1375 static bool 1376 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1377 SmallVector<const SCEV *, 8> &NewOps, 1378 APInt &AccumulatedConstant, 1379 const SCEV *const *Ops, size_t NumOperands, 1380 const APInt &Scale, 1381 ScalarEvolution &SE) { 1382 bool Interesting = false; 1383 1384 // Iterate over the add operands. They are sorted, with constants first. 1385 unsigned i = 0; 1386 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1387 ++i; 1388 // Pull a buried constant out to the outside. 1389 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 1390 Interesting = true; 1391 AccumulatedConstant += Scale * C->getValue()->getValue(); 1392 } 1393 1394 // Next comes everything else. We're especially interested in multiplies 1395 // here, but they're in the middle, so just visit the rest with one loop. 1396 for (; i != NumOperands; ++i) { 1397 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1398 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1399 APInt NewScale = 1400 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1401 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1402 // A multiplication of a constant with another add; recurse. 1403 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1404 Interesting |= 1405 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1406 Add->op_begin(), Add->getNumOperands(), 1407 NewScale, SE); 1408 } else { 1409 // A multiplication of a constant with some other value. Update 1410 // the map. 1411 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1412 const SCEV *Key = SE.getMulExpr(MulOps); 1413 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1414 M.insert(std::make_pair(Key, NewScale)); 1415 if (Pair.second) { 1416 NewOps.push_back(Pair.first->first); 1417 } else { 1418 Pair.first->second += NewScale; 1419 // The map already had an entry for this value, which may indicate 1420 // a folding opportunity. 1421 Interesting = true; 1422 } 1423 } 1424 } else { 1425 // An ordinary operand. Update the map. 1426 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1427 M.insert(std::make_pair(Ops[i], Scale)); 1428 if (Pair.second) { 1429 NewOps.push_back(Pair.first->first); 1430 } else { 1431 Pair.first->second += Scale; 1432 // The map already had an entry for this value, which may indicate 1433 // a folding opportunity. 1434 Interesting = true; 1435 } 1436 } 1437 } 1438 1439 return Interesting; 1440 } 1441 1442 namespace { 1443 struct APIntCompare { 1444 bool operator()(const APInt &LHS, const APInt &RHS) const { 1445 return LHS.ult(RHS); 1446 } 1447 }; 1448 } 1449 1450 /// getAddExpr - Get a canonical add expression, or something simpler if 1451 /// possible. 1452 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1453 SCEV::NoWrapFlags Flags) { 1454 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && 1455 "only nuw or nsw allowed"); 1456 assert(!Ops.empty() && "Cannot get empty add!"); 1457 if (Ops.size() == 1) return Ops[0]; 1458 #ifndef NDEBUG 1459 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1460 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1461 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1462 "SCEVAddExpr operand types don't match!"); 1463 #endif 1464 1465 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 1466 // And vice-versa. 1467 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 1468 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 1469 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 1470 bool All = true; 1471 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1472 E = Ops.end(); I != E; ++I) 1473 if (!isKnownNonNegative(*I)) { 1474 All = false; 1475 break; 1476 } 1477 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 1478 } 1479 1480 // Sort by complexity, this groups all similar expression types together. 1481 GroupByComplexity(Ops, LI); 1482 1483 // If there are any constants, fold them together. 1484 unsigned Idx = 0; 1485 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1486 ++Idx; 1487 assert(Idx < Ops.size()); 1488 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1489 // We found two constants, fold them together! 1490 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1491 RHSC->getValue()->getValue()); 1492 if (Ops.size() == 2) return Ops[0]; 1493 Ops.erase(Ops.begin()+1); // Erase the folded element 1494 LHSC = cast<SCEVConstant>(Ops[0]); 1495 } 1496 1497 // If we are left with a constant zero being added, strip it off. 1498 if (LHSC->getValue()->isZero()) { 1499 Ops.erase(Ops.begin()); 1500 --Idx; 1501 } 1502 1503 if (Ops.size() == 1) return Ops[0]; 1504 } 1505 1506 // Okay, check to see if the same value occurs in the operand list more than 1507 // once. If so, merge them together into an multiply expression. Since we 1508 // sorted the list, these values are required to be adjacent. 1509 Type *Ty = Ops[0]->getType(); 1510 bool FoundMatch = false; 1511 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i) 1512 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1513 // Scan ahead to count how many equal operands there are. 1514 unsigned Count = 2; 1515 while (i+Count != e && Ops[i+Count] == Ops[i]) 1516 ++Count; 1517 // Merge the values into a multiply. 1518 const SCEV *Scale = getConstant(Ty, Count); 1519 const SCEV *Mul = getMulExpr(Scale, Ops[i]); 1520 if (Ops.size() == Count) 1521 return Mul; 1522 Ops[i] = Mul; 1523 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count); 1524 --i; e -= Count - 1; 1525 FoundMatch = true; 1526 } 1527 if (FoundMatch) 1528 return getAddExpr(Ops, Flags); 1529 1530 // Check for truncates. If all the operands are truncated from the same 1531 // type, see if factoring out the truncate would permit the result to be 1532 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1533 // if the contents of the resulting outer trunc fold to something simple. 1534 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1535 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1536 Type *DstType = Trunc->getType(); 1537 Type *SrcType = Trunc->getOperand()->getType(); 1538 SmallVector<const SCEV *, 8> LargeOps; 1539 bool Ok = true; 1540 // Check all the operands to see if they can be represented in the 1541 // source type of the truncate. 1542 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1543 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1544 if (T->getOperand()->getType() != SrcType) { 1545 Ok = false; 1546 break; 1547 } 1548 LargeOps.push_back(T->getOperand()); 1549 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1550 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 1551 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1552 SmallVector<const SCEV *, 8> LargeMulOps; 1553 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1554 if (const SCEVTruncateExpr *T = 1555 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1556 if (T->getOperand()->getType() != SrcType) { 1557 Ok = false; 1558 break; 1559 } 1560 LargeMulOps.push_back(T->getOperand()); 1561 } else if (const SCEVConstant *C = 1562 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1563 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 1564 } else { 1565 Ok = false; 1566 break; 1567 } 1568 } 1569 if (Ok) 1570 LargeOps.push_back(getMulExpr(LargeMulOps)); 1571 } else { 1572 Ok = false; 1573 break; 1574 } 1575 } 1576 if (Ok) { 1577 // Evaluate the expression in the larger type. 1578 const SCEV *Fold = getAddExpr(LargeOps, Flags); 1579 // If it folds to something simple, use it. Otherwise, don't. 1580 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1581 return getTruncateExpr(Fold, DstType); 1582 } 1583 } 1584 1585 // Skip past any other cast SCEVs. 1586 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1587 ++Idx; 1588 1589 // If there are add operands they would be next. 1590 if (Idx < Ops.size()) { 1591 bool DeletedAdd = false; 1592 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1593 // If we have an add, expand the add operands onto the end of the operands 1594 // list. 1595 Ops.erase(Ops.begin()+Idx); 1596 Ops.append(Add->op_begin(), Add->op_end()); 1597 DeletedAdd = true; 1598 } 1599 1600 // If we deleted at least one add, we added operands to the end of the list, 1601 // and they are not necessarily sorted. Recurse to resort and resimplify 1602 // any operands we just acquired. 1603 if (DeletedAdd) 1604 return getAddExpr(Ops); 1605 } 1606 1607 // Skip over the add expression until we get to a multiply. 1608 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1609 ++Idx; 1610 1611 // Check to see if there are any folding opportunities present with 1612 // operands multiplied by constant values. 1613 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1614 uint64_t BitWidth = getTypeSizeInBits(Ty); 1615 DenseMap<const SCEV *, APInt> M; 1616 SmallVector<const SCEV *, 8> NewOps; 1617 APInt AccumulatedConstant(BitWidth, 0); 1618 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1619 Ops.data(), Ops.size(), 1620 APInt(BitWidth, 1), *this)) { 1621 // Some interesting folding opportunity is present, so its worthwhile to 1622 // re-generate the operands list. Group the operands by constant scale, 1623 // to avoid multiplying by the same constant scale multiple times. 1624 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1625 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(), 1626 E = NewOps.end(); I != E; ++I) 1627 MulOpLists[M.find(*I)->second].push_back(*I); 1628 // Re-generate the operands list. 1629 Ops.clear(); 1630 if (AccumulatedConstant != 0) 1631 Ops.push_back(getConstant(AccumulatedConstant)); 1632 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1633 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1634 if (I->first != 0) 1635 Ops.push_back(getMulExpr(getConstant(I->first), 1636 getAddExpr(I->second))); 1637 if (Ops.empty()) 1638 return getConstant(Ty, 0); 1639 if (Ops.size() == 1) 1640 return Ops[0]; 1641 return getAddExpr(Ops); 1642 } 1643 } 1644 1645 // If we are adding something to a multiply expression, make sure the 1646 // something is not already an operand of the multiply. If so, merge it into 1647 // the multiply. 1648 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1649 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1650 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1651 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1652 if (isa<SCEVConstant>(MulOpSCEV)) 1653 continue; 1654 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1655 if (MulOpSCEV == Ops[AddOp]) { 1656 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1657 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1658 if (Mul->getNumOperands() != 2) { 1659 // If the multiply has more than two operands, we must get the 1660 // Y*Z term. 1661 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1662 Mul->op_begin()+MulOp); 1663 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1664 InnerMul = getMulExpr(MulOps); 1665 } 1666 const SCEV *One = getConstant(Ty, 1); 1667 const SCEV *AddOne = getAddExpr(One, InnerMul); 1668 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV); 1669 if (Ops.size() == 2) return OuterMul; 1670 if (AddOp < Idx) { 1671 Ops.erase(Ops.begin()+AddOp); 1672 Ops.erase(Ops.begin()+Idx-1); 1673 } else { 1674 Ops.erase(Ops.begin()+Idx); 1675 Ops.erase(Ops.begin()+AddOp-1); 1676 } 1677 Ops.push_back(OuterMul); 1678 return getAddExpr(Ops); 1679 } 1680 1681 // Check this multiply against other multiplies being added together. 1682 for (unsigned OtherMulIdx = Idx+1; 1683 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1684 ++OtherMulIdx) { 1685 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1686 // If MulOp occurs in OtherMul, we can fold the two multiplies 1687 // together. 1688 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1689 OMulOp != e; ++OMulOp) 1690 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1691 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1692 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1693 if (Mul->getNumOperands() != 2) { 1694 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1695 Mul->op_begin()+MulOp); 1696 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1697 InnerMul1 = getMulExpr(MulOps); 1698 } 1699 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1700 if (OtherMul->getNumOperands() != 2) { 1701 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1702 OtherMul->op_begin()+OMulOp); 1703 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end()); 1704 InnerMul2 = getMulExpr(MulOps); 1705 } 1706 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1707 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1708 if (Ops.size() == 2) return OuterMul; 1709 Ops.erase(Ops.begin()+Idx); 1710 Ops.erase(Ops.begin()+OtherMulIdx-1); 1711 Ops.push_back(OuterMul); 1712 return getAddExpr(Ops); 1713 } 1714 } 1715 } 1716 } 1717 1718 // If there are any add recurrences in the operands list, see if any other 1719 // added values are loop invariant. If so, we can fold them into the 1720 // recurrence. 1721 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1722 ++Idx; 1723 1724 // Scan over all recurrences, trying to fold loop invariants into them. 1725 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1726 // Scan all of the other operands to this add and add them to the vector if 1727 // they are loop invariant w.r.t. the recurrence. 1728 SmallVector<const SCEV *, 8> LIOps; 1729 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1730 const Loop *AddRecLoop = AddRec->getLoop(); 1731 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1732 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1733 LIOps.push_back(Ops[i]); 1734 Ops.erase(Ops.begin()+i); 1735 --i; --e; 1736 } 1737 1738 // If we found some loop invariants, fold them into the recurrence. 1739 if (!LIOps.empty()) { 1740 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1741 LIOps.push_back(AddRec->getStart()); 1742 1743 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1744 AddRec->op_end()); 1745 AddRecOps[0] = getAddExpr(LIOps); 1746 1747 // Build the new addrec. Propagate the NUW and NSW flags if both the 1748 // outer add and the inner addrec are guaranteed to have no overflow. 1749 // Always propagate NW. 1750 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW)); 1751 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags); 1752 1753 // If all of the other operands were loop invariant, we are done. 1754 if (Ops.size() == 1) return NewRec; 1755 1756 // Otherwise, add the folded AddRec by the non-invariant parts. 1757 for (unsigned i = 0;; ++i) 1758 if (Ops[i] == AddRec) { 1759 Ops[i] = NewRec; 1760 break; 1761 } 1762 return getAddExpr(Ops); 1763 } 1764 1765 // Okay, if there weren't any loop invariants to be folded, check to see if 1766 // there are multiple AddRec's with the same loop induction variable being 1767 // added together. If so, we can fold them. 1768 for (unsigned OtherIdx = Idx+1; 1769 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1770 ++OtherIdx) 1771 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1772 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L> 1773 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1774 AddRec->op_end()); 1775 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1776 ++OtherIdx) 1777 if (const SCEVAddRecExpr *OtherAddRec = 1778 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1779 if (OtherAddRec->getLoop() == AddRecLoop) { 1780 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); 1781 i != e; ++i) { 1782 if (i >= AddRecOps.size()) { 1783 AddRecOps.append(OtherAddRec->op_begin()+i, 1784 OtherAddRec->op_end()); 1785 break; 1786 } 1787 AddRecOps[i] = getAddExpr(AddRecOps[i], 1788 OtherAddRec->getOperand(i)); 1789 } 1790 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1791 } 1792 // Step size has changed, so we cannot guarantee no self-wraparound. 1793 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap); 1794 return getAddExpr(Ops); 1795 } 1796 1797 // Otherwise couldn't fold anything into this recurrence. Move onto the 1798 // next one. 1799 } 1800 1801 // Okay, it looks like we really DO need an add expr. Check to see if we 1802 // already have one, otherwise create a new one. 1803 FoldingSetNodeID ID; 1804 ID.AddInteger(scAddExpr); 1805 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1806 ID.AddPointer(Ops[i]); 1807 void *IP = 0; 1808 SCEVAddExpr *S = 1809 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1810 if (!S) { 1811 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1812 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1813 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), 1814 O, Ops.size()); 1815 UniqueSCEVs.InsertNode(S, IP); 1816 } 1817 S->setNoWrapFlags(Flags); 1818 return S; 1819 } 1820 1821 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) { 1822 uint64_t k = i*j; 1823 if (j > 1 && k / j != i) Overflow = true; 1824 return k; 1825 } 1826 1827 /// Compute the result of "n choose k", the binomial coefficient. If an 1828 /// intermediate computation overflows, Overflow will be set and the return will 1829 /// be garbage. Overflow is not cleared on absence of overflow. 1830 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) { 1831 // We use the multiplicative formula: 1832 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 . 1833 // At each iteration, we take the n-th term of the numeral and divide by the 1834 // (k-n)th term of the denominator. This division will always produce an 1835 // integral result, and helps reduce the chance of overflow in the 1836 // intermediate computations. However, we can still overflow even when the 1837 // final result would fit. 1838 1839 if (n == 0 || n == k) return 1; 1840 if (k > n) return 0; 1841 1842 if (k > n/2) 1843 k = n-k; 1844 1845 uint64_t r = 1; 1846 for (uint64_t i = 1; i <= k; ++i) { 1847 r = umul_ov(r, n-(i-1), Overflow); 1848 r /= i; 1849 } 1850 return r; 1851 } 1852 1853 /// getMulExpr - Get a canonical multiply expression, or something simpler if 1854 /// possible. 1855 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1856 SCEV::NoWrapFlags Flags) { 1857 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) && 1858 "only nuw or nsw allowed"); 1859 assert(!Ops.empty() && "Cannot get empty mul!"); 1860 if (Ops.size() == 1) return Ops[0]; 1861 #ifndef NDEBUG 1862 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1863 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1864 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1865 "SCEVMulExpr operand types don't match!"); 1866 #endif 1867 1868 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 1869 // And vice-versa. 1870 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 1871 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 1872 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 1873 bool All = true; 1874 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1875 E = Ops.end(); I != E; ++I) 1876 if (!isKnownNonNegative(*I)) { 1877 All = false; 1878 break; 1879 } 1880 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 1881 } 1882 1883 // Sort by complexity, this groups all similar expression types together. 1884 GroupByComplexity(Ops, LI); 1885 1886 // If there are any constants, fold them together. 1887 unsigned Idx = 0; 1888 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1889 1890 // C1*(C2+V) -> C1*C2 + C1*V 1891 if (Ops.size() == 2) 1892 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1893 if (Add->getNumOperands() == 2 && 1894 isa<SCEVConstant>(Add->getOperand(0))) 1895 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1896 getMulExpr(LHSC, Add->getOperand(1))); 1897 1898 ++Idx; 1899 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1900 // We found two constants, fold them together! 1901 ConstantInt *Fold = ConstantInt::get(getContext(), 1902 LHSC->getValue()->getValue() * 1903 RHSC->getValue()->getValue()); 1904 Ops[0] = getConstant(Fold); 1905 Ops.erase(Ops.begin()+1); // Erase the folded element 1906 if (Ops.size() == 1) return Ops[0]; 1907 LHSC = cast<SCEVConstant>(Ops[0]); 1908 } 1909 1910 // If we are left with a constant one being multiplied, strip it off. 1911 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1912 Ops.erase(Ops.begin()); 1913 --Idx; 1914 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1915 // If we have a multiply of zero, it will always be zero. 1916 return Ops[0]; 1917 } else if (Ops[0]->isAllOnesValue()) { 1918 // If we have a mul by -1 of an add, try distributing the -1 among the 1919 // add operands. 1920 if (Ops.size() == 2) { 1921 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1922 SmallVector<const SCEV *, 4> NewOps; 1923 bool AnyFolded = false; 1924 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), 1925 E = Add->op_end(); I != E; ++I) { 1926 const SCEV *Mul = getMulExpr(Ops[0], *I); 1927 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1928 NewOps.push_back(Mul); 1929 } 1930 if (AnyFolded) 1931 return getAddExpr(NewOps); 1932 } 1933 else if (const SCEVAddRecExpr * 1934 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) { 1935 // Negation preserves a recurrence's no self-wrap property. 1936 SmallVector<const SCEV *, 4> Operands; 1937 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(), 1938 E = AddRec->op_end(); I != E; ++I) { 1939 Operands.push_back(getMulExpr(Ops[0], *I)); 1940 } 1941 return getAddRecExpr(Operands, AddRec->getLoop(), 1942 AddRec->getNoWrapFlags(SCEV::FlagNW)); 1943 } 1944 } 1945 } 1946 1947 if (Ops.size() == 1) 1948 return Ops[0]; 1949 } 1950 1951 // Skip over the add expression until we get to a multiply. 1952 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1953 ++Idx; 1954 1955 // If there are mul operands inline them all into this expression. 1956 if (Idx < Ops.size()) { 1957 bool DeletedMul = false; 1958 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1959 // If we have an mul, expand the mul operands onto the end of the operands 1960 // list. 1961 Ops.erase(Ops.begin()+Idx); 1962 Ops.append(Mul->op_begin(), Mul->op_end()); 1963 DeletedMul = true; 1964 } 1965 1966 // If we deleted at least one mul, we added operands to the end of the list, 1967 // and they are not necessarily sorted. Recurse to resort and resimplify 1968 // any operands we just acquired. 1969 if (DeletedMul) 1970 return getMulExpr(Ops); 1971 } 1972 1973 // If there are any add recurrences in the operands list, see if any other 1974 // added values are loop invariant. If so, we can fold them into the 1975 // recurrence. 1976 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1977 ++Idx; 1978 1979 // Scan over all recurrences, trying to fold loop invariants into them. 1980 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1981 // Scan all of the other operands to this mul and add them to the vector if 1982 // they are loop invariant w.r.t. the recurrence. 1983 SmallVector<const SCEV *, 8> LIOps; 1984 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1985 const Loop *AddRecLoop = AddRec->getLoop(); 1986 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1987 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1988 LIOps.push_back(Ops[i]); 1989 Ops.erase(Ops.begin()+i); 1990 --i; --e; 1991 } 1992 1993 // If we found some loop invariants, fold them into the recurrence. 1994 if (!LIOps.empty()) { 1995 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1996 SmallVector<const SCEV *, 4> NewOps; 1997 NewOps.reserve(AddRec->getNumOperands()); 1998 const SCEV *Scale = getMulExpr(LIOps); 1999 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 2000 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 2001 2002 // Build the new addrec. Propagate the NUW and NSW flags if both the 2003 // outer mul and the inner addrec are guaranteed to have no overflow. 2004 // 2005 // No self-wrap cannot be guaranteed after changing the step size, but 2006 // will be inferred if either NUW or NSW is true. 2007 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW)); 2008 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags); 2009 2010 // If all of the other operands were loop invariant, we are done. 2011 if (Ops.size() == 1) return NewRec; 2012 2013 // Otherwise, multiply the folded AddRec by the non-invariant parts. 2014 for (unsigned i = 0;; ++i) 2015 if (Ops[i] == AddRec) { 2016 Ops[i] = NewRec; 2017 break; 2018 } 2019 return getMulExpr(Ops); 2020 } 2021 2022 // Okay, if there weren't any loop invariants to be folded, check to see if 2023 // there are multiple AddRec's with the same loop induction variable being 2024 // multiplied together. If so, we can fold them. 2025 for (unsigned OtherIdx = Idx+1; 2026 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 2027 ++OtherIdx) { 2028 if (AddRecLoop != cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) 2029 continue; 2030 2031 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L> 2032 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [ 2033 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z 2034 // ]]],+,...up to x=2n}. 2035 // Note that the arguments to choose() are always integers with values 2036 // known at compile time, never SCEV objects. 2037 // 2038 // The implementation avoids pointless extra computations when the two 2039 // addrec's are of different length (mathematically, it's equivalent to 2040 // an infinite stream of zeros on the right). 2041 bool OpsModified = false; 2042 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 2043 ++OtherIdx) { 2044 const SCEVAddRecExpr *OtherAddRec = 2045 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]); 2046 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop) 2047 continue; 2048 2049 bool Overflow = false; 2050 Type *Ty = AddRec->getType(); 2051 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64; 2052 SmallVector<const SCEV*, 7> AddRecOps; 2053 for (int x = 0, xe = AddRec->getNumOperands() + 2054 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) { 2055 const SCEV *Term = getConstant(Ty, 0); 2056 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) { 2057 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow); 2058 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1), 2059 ze = std::min(x+1, (int)OtherAddRec->getNumOperands()); 2060 z < ze && !Overflow; ++z) { 2061 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow); 2062 uint64_t Coeff; 2063 if (LargerThan64Bits) 2064 Coeff = umul_ov(Coeff1, Coeff2, Overflow); 2065 else 2066 Coeff = Coeff1*Coeff2; 2067 const SCEV *CoeffTerm = getConstant(Ty, Coeff); 2068 const SCEV *Term1 = AddRec->getOperand(y-z); 2069 const SCEV *Term2 = OtherAddRec->getOperand(z); 2070 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2)); 2071 } 2072 } 2073 AddRecOps.push_back(Term); 2074 } 2075 if (!Overflow) { 2076 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(), 2077 SCEV::FlagAnyWrap); 2078 if (Ops.size() == 2) return NewAddRec; 2079 Ops[Idx] = NewAddRec; 2080 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 2081 OpsModified = true; 2082 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec); 2083 if (!AddRec) 2084 break; 2085 } 2086 } 2087 if (OpsModified) 2088 return getMulExpr(Ops); 2089 } 2090 2091 // Otherwise couldn't fold anything into this recurrence. Move onto the 2092 // next one. 2093 } 2094 2095 // Okay, it looks like we really DO need an mul expr. Check to see if we 2096 // already have one, otherwise create a new one. 2097 FoldingSetNodeID ID; 2098 ID.AddInteger(scMulExpr); 2099 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2100 ID.AddPointer(Ops[i]); 2101 void *IP = 0; 2102 SCEVMulExpr *S = 2103 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2104 if (!S) { 2105 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2106 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2107 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 2108 O, Ops.size()); 2109 UniqueSCEVs.InsertNode(S, IP); 2110 } 2111 S->setNoWrapFlags(Flags); 2112 return S; 2113 } 2114 2115 /// getUDivExpr - Get a canonical unsigned division expression, or something 2116 /// simpler if possible. 2117 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 2118 const SCEV *RHS) { 2119 assert(getEffectiveSCEVType(LHS->getType()) == 2120 getEffectiveSCEVType(RHS->getType()) && 2121 "SCEVUDivExpr operand types don't match!"); 2122 2123 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 2124 if (RHSC->getValue()->equalsInt(1)) 2125 return LHS; // X udiv 1 --> x 2126 // If the denominator is zero, the result of the udiv is undefined. Don't 2127 // try to analyze it, because the resolution chosen here may differ from 2128 // the resolution chosen in other parts of the compiler. 2129 if (!RHSC->getValue()->isZero()) { 2130 // Determine if the division can be folded into the operands of 2131 // its operands. 2132 // TODO: Generalize this to non-constants by using known-bits information. 2133 Type *Ty = LHS->getType(); 2134 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 2135 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; 2136 // For non-power-of-two values, effectively round the value up to the 2137 // nearest power of two. 2138 if (!RHSC->getValue()->getValue().isPowerOf2()) 2139 ++MaxShiftAmt; 2140 IntegerType *ExtTy = 2141 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 2142 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 2143 if (const SCEVConstant *Step = 2144 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) { 2145 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 2146 const APInt &StepInt = Step->getValue()->getValue(); 2147 const APInt &DivInt = RHSC->getValue()->getValue(); 2148 if (!StepInt.urem(DivInt) && 2149 getZeroExtendExpr(AR, ExtTy) == 2150 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 2151 getZeroExtendExpr(Step, ExtTy), 2152 AR->getLoop(), SCEV::FlagAnyWrap)) { 2153 SmallVector<const SCEV *, 4> Operands; 2154 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 2155 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 2156 return getAddRecExpr(Operands, AR->getLoop(), 2157 SCEV::FlagNW); 2158 } 2159 /// Get a canonical UDivExpr for a recurrence. 2160 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0. 2161 // We can currently only fold X%N if X is constant. 2162 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart()); 2163 if (StartC && !DivInt.urem(StepInt) && 2164 getZeroExtendExpr(AR, ExtTy) == 2165 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 2166 getZeroExtendExpr(Step, ExtTy), 2167 AR->getLoop(), SCEV::FlagAnyWrap)) { 2168 const APInt &StartInt = StartC->getValue()->getValue(); 2169 const APInt &StartRem = StartInt.urem(StepInt); 2170 if (StartRem != 0) 2171 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step, 2172 AR->getLoop(), SCEV::FlagNW); 2173 } 2174 } 2175 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 2176 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 2177 SmallVector<const SCEV *, 4> Operands; 2178 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 2179 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 2180 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 2181 // Find an operand that's safely divisible. 2182 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 2183 const SCEV *Op = M->getOperand(i); 2184 const SCEV *Div = getUDivExpr(Op, RHSC); 2185 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 2186 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 2187 M->op_end()); 2188 Operands[i] = Div; 2189 return getMulExpr(Operands); 2190 } 2191 } 2192 } 2193 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 2194 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) { 2195 SmallVector<const SCEV *, 4> Operands; 2196 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 2197 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 2198 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 2199 Operands.clear(); 2200 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 2201 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 2202 if (isa<SCEVUDivExpr>(Op) || 2203 getMulExpr(Op, RHS) != A->getOperand(i)) 2204 break; 2205 Operands.push_back(Op); 2206 } 2207 if (Operands.size() == A->getNumOperands()) 2208 return getAddExpr(Operands); 2209 } 2210 } 2211 2212 // Fold if both operands are constant. 2213 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 2214 Constant *LHSCV = LHSC->getValue(); 2215 Constant *RHSCV = RHSC->getValue(); 2216 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 2217 RHSCV))); 2218 } 2219 } 2220 } 2221 2222 FoldingSetNodeID ID; 2223 ID.AddInteger(scUDivExpr); 2224 ID.AddPointer(LHS); 2225 ID.AddPointer(RHS); 2226 void *IP = 0; 2227 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2228 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 2229 LHS, RHS); 2230 UniqueSCEVs.InsertNode(S, IP); 2231 return S; 2232 } 2233 2234 2235 /// getAddRecExpr - Get an add recurrence expression for the specified loop. 2236 /// Simplify the expression as much as possible. 2237 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step, 2238 const Loop *L, 2239 SCEV::NoWrapFlags Flags) { 2240 SmallVector<const SCEV *, 4> Operands; 2241 Operands.push_back(Start); 2242 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 2243 if (StepChrec->getLoop() == L) { 2244 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 2245 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW)); 2246 } 2247 2248 Operands.push_back(Step); 2249 return getAddRecExpr(Operands, L, Flags); 2250 } 2251 2252 /// getAddRecExpr - Get an add recurrence expression for the specified loop. 2253 /// Simplify the expression as much as possible. 2254 const SCEV * 2255 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 2256 const Loop *L, SCEV::NoWrapFlags Flags) { 2257 if (Operands.size() == 1) return Operands[0]; 2258 #ifndef NDEBUG 2259 Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); 2260 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 2261 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && 2262 "SCEVAddRecExpr operand types don't match!"); 2263 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2264 assert(isLoopInvariant(Operands[i], L) && 2265 "SCEVAddRecExpr operand is not loop-invariant!"); 2266 #endif 2267 2268 if (Operands.back()->isZero()) { 2269 Operands.pop_back(); 2270 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X 2271 } 2272 2273 // It's tempting to want to call getMaxBackedgeTakenCount count here and 2274 // use that information to infer NUW and NSW flags. However, computing a 2275 // BE count requires calling getAddRecExpr, so we may not yet have a 2276 // meaningful BE count at this point (and if we don't, we'd be stuck 2277 // with a SCEVCouldNotCompute as the cached BE count). 2278 2279 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 2280 // And vice-versa. 2281 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 2282 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 2283 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 2284 bool All = true; 2285 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(), 2286 E = Operands.end(); I != E; ++I) 2287 if (!isKnownNonNegative(*I)) { 2288 All = false; 2289 break; 2290 } 2291 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 2292 } 2293 2294 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 2295 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 2296 const Loop *NestedLoop = NestedAR->getLoop(); 2297 if (L->contains(NestedLoop) ? 2298 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 2299 (!NestedLoop->contains(L) && 2300 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 2301 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 2302 NestedAR->op_end()); 2303 Operands[0] = NestedAR->getStart(); 2304 // AddRecs require their operands be loop-invariant with respect to their 2305 // loops. Don't perform this transformation if it would break this 2306 // requirement. 2307 bool AllInvariant = true; 2308 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2309 if (!isLoopInvariant(Operands[i], L)) { 2310 AllInvariant = false; 2311 break; 2312 } 2313 if (AllInvariant) { 2314 // Create a recurrence for the outer loop with the same step size. 2315 // 2316 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the 2317 // inner recurrence has the same property. 2318 SCEV::NoWrapFlags OuterFlags = 2319 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags()); 2320 2321 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags); 2322 AllInvariant = true; 2323 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2324 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) { 2325 AllInvariant = false; 2326 break; 2327 } 2328 if (AllInvariant) { 2329 // Ok, both add recurrences are valid after the transformation. 2330 // 2331 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if 2332 // the outer recurrence has the same property. 2333 SCEV::NoWrapFlags InnerFlags = 2334 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags); 2335 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags); 2336 } 2337 } 2338 // Reset Operands to its original state. 2339 Operands[0] = NestedAR; 2340 } 2341 } 2342 2343 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2344 // already have one, otherwise create a new one. 2345 FoldingSetNodeID ID; 2346 ID.AddInteger(scAddRecExpr); 2347 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2348 ID.AddPointer(Operands[i]); 2349 ID.AddPointer(L); 2350 void *IP = 0; 2351 SCEVAddRecExpr *S = 2352 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2353 if (!S) { 2354 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2355 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2356 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2357 O, Operands.size(), L); 2358 UniqueSCEVs.InsertNode(S, IP); 2359 } 2360 S->setNoWrapFlags(Flags); 2361 return S; 2362 } 2363 2364 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2365 const SCEV *RHS) { 2366 SmallVector<const SCEV *, 2> Ops; 2367 Ops.push_back(LHS); 2368 Ops.push_back(RHS); 2369 return getSMaxExpr(Ops); 2370 } 2371 2372 const SCEV * 2373 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2374 assert(!Ops.empty() && "Cannot get empty smax!"); 2375 if (Ops.size() == 1) return Ops[0]; 2376 #ifndef NDEBUG 2377 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2378 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2379 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2380 "SCEVSMaxExpr operand types don't match!"); 2381 #endif 2382 2383 // Sort by complexity, this groups all similar expression types together. 2384 GroupByComplexity(Ops, LI); 2385 2386 // If there are any constants, fold them together. 2387 unsigned Idx = 0; 2388 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2389 ++Idx; 2390 assert(Idx < Ops.size()); 2391 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2392 // We found two constants, fold them together! 2393 ConstantInt *Fold = ConstantInt::get(getContext(), 2394 APIntOps::smax(LHSC->getValue()->getValue(), 2395 RHSC->getValue()->getValue())); 2396 Ops[0] = getConstant(Fold); 2397 Ops.erase(Ops.begin()+1); // Erase the folded element 2398 if (Ops.size() == 1) return Ops[0]; 2399 LHSC = cast<SCEVConstant>(Ops[0]); 2400 } 2401 2402 // If we are left with a constant minimum-int, strip it off. 2403 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2404 Ops.erase(Ops.begin()); 2405 --Idx; 2406 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2407 // If we have an smax with a constant maximum-int, it will always be 2408 // maximum-int. 2409 return Ops[0]; 2410 } 2411 2412 if (Ops.size() == 1) return Ops[0]; 2413 } 2414 2415 // Find the first SMax 2416 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2417 ++Idx; 2418 2419 // Check to see if one of the operands is an SMax. If so, expand its operands 2420 // onto our operand list, and recurse to simplify. 2421 if (Idx < Ops.size()) { 2422 bool DeletedSMax = false; 2423 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2424 Ops.erase(Ops.begin()+Idx); 2425 Ops.append(SMax->op_begin(), SMax->op_end()); 2426 DeletedSMax = true; 2427 } 2428 2429 if (DeletedSMax) 2430 return getSMaxExpr(Ops); 2431 } 2432 2433 // Okay, check to see if the same value occurs in the operand list twice. If 2434 // so, delete one. Since we sorted the list, these values are required to 2435 // be adjacent. 2436 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2437 // X smax Y smax Y --> X smax Y 2438 // X smax Y --> X, if X is always greater than Y 2439 if (Ops[i] == Ops[i+1] || 2440 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 2441 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2442 --i; --e; 2443 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 2444 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2445 --i; --e; 2446 } 2447 2448 if (Ops.size() == 1) return Ops[0]; 2449 2450 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2451 2452 // Okay, it looks like we really DO need an smax expr. Check to see if we 2453 // already have one, otherwise create a new one. 2454 FoldingSetNodeID ID; 2455 ID.AddInteger(scSMaxExpr); 2456 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2457 ID.AddPointer(Ops[i]); 2458 void *IP = 0; 2459 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2460 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2461 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2462 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 2463 O, Ops.size()); 2464 UniqueSCEVs.InsertNode(S, IP); 2465 return S; 2466 } 2467 2468 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2469 const SCEV *RHS) { 2470 SmallVector<const SCEV *, 2> Ops; 2471 Ops.push_back(LHS); 2472 Ops.push_back(RHS); 2473 return getUMaxExpr(Ops); 2474 } 2475 2476 const SCEV * 2477 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2478 assert(!Ops.empty() && "Cannot get empty umax!"); 2479 if (Ops.size() == 1) return Ops[0]; 2480 #ifndef NDEBUG 2481 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2482 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2483 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2484 "SCEVUMaxExpr operand types don't match!"); 2485 #endif 2486 2487 // Sort by complexity, this groups all similar expression types together. 2488 GroupByComplexity(Ops, LI); 2489 2490 // If there are any constants, fold them together. 2491 unsigned Idx = 0; 2492 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2493 ++Idx; 2494 assert(Idx < Ops.size()); 2495 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2496 // We found two constants, fold them together! 2497 ConstantInt *Fold = ConstantInt::get(getContext(), 2498 APIntOps::umax(LHSC->getValue()->getValue(), 2499 RHSC->getValue()->getValue())); 2500 Ops[0] = getConstant(Fold); 2501 Ops.erase(Ops.begin()+1); // Erase the folded element 2502 if (Ops.size() == 1) return Ops[0]; 2503 LHSC = cast<SCEVConstant>(Ops[0]); 2504 } 2505 2506 // If we are left with a constant minimum-int, strip it off. 2507 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2508 Ops.erase(Ops.begin()); 2509 --Idx; 2510 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2511 // If we have an umax with a constant maximum-int, it will always be 2512 // maximum-int. 2513 return Ops[0]; 2514 } 2515 2516 if (Ops.size() == 1) return Ops[0]; 2517 } 2518 2519 // Find the first UMax 2520 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2521 ++Idx; 2522 2523 // Check to see if one of the operands is a UMax. If so, expand its operands 2524 // onto our operand list, and recurse to simplify. 2525 if (Idx < Ops.size()) { 2526 bool DeletedUMax = false; 2527 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2528 Ops.erase(Ops.begin()+Idx); 2529 Ops.append(UMax->op_begin(), UMax->op_end()); 2530 DeletedUMax = true; 2531 } 2532 2533 if (DeletedUMax) 2534 return getUMaxExpr(Ops); 2535 } 2536 2537 // Okay, check to see if the same value occurs in the operand list twice. If 2538 // so, delete one. Since we sorted the list, these values are required to 2539 // be adjacent. 2540 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2541 // X umax Y umax Y --> X umax Y 2542 // X umax Y --> X, if X is always greater than Y 2543 if (Ops[i] == Ops[i+1] || 2544 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 2545 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2546 --i; --e; 2547 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 2548 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2549 --i; --e; 2550 } 2551 2552 if (Ops.size() == 1) return Ops[0]; 2553 2554 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2555 2556 // Okay, it looks like we really DO need a umax expr. Check to see if we 2557 // already have one, otherwise create a new one. 2558 FoldingSetNodeID ID; 2559 ID.AddInteger(scUMaxExpr); 2560 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2561 ID.AddPointer(Ops[i]); 2562 void *IP = 0; 2563 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2564 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2565 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2566 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 2567 O, Ops.size()); 2568 UniqueSCEVs.InsertNode(S, IP); 2569 return S; 2570 } 2571 2572 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2573 const SCEV *RHS) { 2574 // ~smax(~x, ~y) == smin(x, y). 2575 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2576 } 2577 2578 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2579 const SCEV *RHS) { 2580 // ~umax(~x, ~y) == umin(x, y) 2581 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2582 } 2583 2584 const SCEV *ScalarEvolution::getSizeOfExpr(Type *AllocTy) { 2585 // If we have TargetData, we can bypass creating a target-independent 2586 // constant expression and then folding it back into a ConstantInt. 2587 // This is just a compile-time optimization. 2588 if (TD) 2589 return getConstant(TD->getIntPtrType(getContext()), 2590 TD->getTypeAllocSize(AllocTy)); 2591 2592 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2593 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2594 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI)) 2595 C = Folded; 2596 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2597 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2598 } 2599 2600 const SCEV *ScalarEvolution::getAlignOfExpr(Type *AllocTy) { 2601 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2602 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2603 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI)) 2604 C = Folded; 2605 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2606 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2607 } 2608 2609 const SCEV *ScalarEvolution::getOffsetOfExpr(StructType *STy, 2610 unsigned FieldNo) { 2611 // If we have TargetData, we can bypass creating a target-independent 2612 // constant expression and then folding it back into a ConstantInt. 2613 // This is just a compile-time optimization. 2614 if (TD) 2615 return getConstant(TD->getIntPtrType(getContext()), 2616 TD->getStructLayout(STy)->getElementOffset(FieldNo)); 2617 2618 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2619 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2620 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI)) 2621 C = Folded; 2622 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2623 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2624 } 2625 2626 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *CTy, 2627 Constant *FieldNo) { 2628 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2629 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2630 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI)) 2631 C = Folded; 2632 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2633 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2634 } 2635 2636 const SCEV *ScalarEvolution::getUnknown(Value *V) { 2637 // Don't attempt to do anything other than create a SCEVUnknown object 2638 // here. createSCEV only calls getUnknown after checking for all other 2639 // interesting possibilities, and any other code that calls getUnknown 2640 // is doing so in order to hide a value from SCEV canonicalization. 2641 2642 FoldingSetNodeID ID; 2643 ID.AddInteger(scUnknown); 2644 ID.AddPointer(V); 2645 void *IP = 0; 2646 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { 2647 assert(cast<SCEVUnknown>(S)->getValue() == V && 2648 "Stale SCEVUnknown in uniquing map!"); 2649 return S; 2650 } 2651 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, 2652 FirstUnknown); 2653 FirstUnknown = cast<SCEVUnknown>(S); 2654 UniqueSCEVs.InsertNode(S, IP); 2655 return S; 2656 } 2657 2658 //===----------------------------------------------------------------------===// 2659 // Basic SCEV Analysis and PHI Idiom Recognition Code 2660 // 2661 2662 /// isSCEVable - Test if values of the given type are analyzable within 2663 /// the SCEV framework. This primarily includes integer types, and it 2664 /// can optionally include pointer types if the ScalarEvolution class 2665 /// has access to target-specific information. 2666 bool ScalarEvolution::isSCEVable(Type *Ty) const { 2667 // Integers and pointers are always SCEVable. 2668 return Ty->isIntegerTy() || Ty->isPointerTy(); 2669 } 2670 2671 /// getTypeSizeInBits - Return the size in bits of the specified type, 2672 /// for which isSCEVable must return true. 2673 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const { 2674 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2675 2676 // If we have a TargetData, use it! 2677 if (TD) 2678 return TD->getTypeSizeInBits(Ty); 2679 2680 // Integer types have fixed sizes. 2681 if (Ty->isIntegerTy()) 2682 return Ty->getPrimitiveSizeInBits(); 2683 2684 // The only other support type is pointer. Without TargetData, conservatively 2685 // assume pointers are 64-bit. 2686 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2687 return 64; 2688 } 2689 2690 /// getEffectiveSCEVType - Return a type with the same bitwidth as 2691 /// the given type and which represents how SCEV will treat the given 2692 /// type, for which isSCEVable must return true. For pointer types, 2693 /// this is the pointer-sized integer type. 2694 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const { 2695 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2696 2697 if (Ty->isIntegerTy()) 2698 return Ty; 2699 2700 // The only other support type is pointer. 2701 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2702 if (TD) return TD->getIntPtrType(getContext()); 2703 2704 // Without TargetData, conservatively assume pointers are 64-bit. 2705 return Type::getInt64Ty(getContext()); 2706 } 2707 2708 const SCEV *ScalarEvolution::getCouldNotCompute() { 2709 return &CouldNotCompute; 2710 } 2711 2712 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2713 /// expression and create a new one. 2714 const SCEV *ScalarEvolution::getSCEV(Value *V) { 2715 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2716 2717 ValueExprMapType::const_iterator I = ValueExprMap.find_as(V); 2718 if (I != ValueExprMap.end()) return I->second; 2719 const SCEV *S = createSCEV(V); 2720 2721 // The process of creating a SCEV for V may have caused other SCEVs 2722 // to have been created, so it's necessary to insert the new entry 2723 // from scratch, rather than trying to remember the insert position 2724 // above. 2725 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2726 return S; 2727 } 2728 2729 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2730 /// 2731 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2732 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2733 return getConstant( 2734 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2735 2736 Type *Ty = V->getType(); 2737 Ty = getEffectiveSCEVType(Ty); 2738 return getMulExpr(V, 2739 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2740 } 2741 2742 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2743 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2744 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2745 return getConstant( 2746 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2747 2748 Type *Ty = V->getType(); 2749 Ty = getEffectiveSCEVType(Ty); 2750 const SCEV *AllOnes = 2751 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2752 return getMinusSCEV(AllOnes, V); 2753 } 2754 2755 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1. 2756 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS, 2757 SCEV::NoWrapFlags Flags) { 2758 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW"); 2759 2760 // Fast path: X - X --> 0. 2761 if (LHS == RHS) 2762 return getConstant(LHS->getType(), 0); 2763 2764 // X - Y --> X + -Y 2765 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags); 2766 } 2767 2768 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2769 /// input value to the specified type. If the type must be extended, it is zero 2770 /// extended. 2771 const SCEV * 2772 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) { 2773 Type *SrcTy = V->getType(); 2774 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2775 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2776 "Cannot truncate or zero extend with non-integer arguments!"); 2777 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2778 return V; // No conversion 2779 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2780 return getTruncateExpr(V, Ty); 2781 return getZeroExtendExpr(V, Ty); 2782 } 2783 2784 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2785 /// input value to the specified type. If the type must be extended, it is sign 2786 /// extended. 2787 const SCEV * 2788 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2789 Type *Ty) { 2790 Type *SrcTy = V->getType(); 2791 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2792 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2793 "Cannot truncate or zero extend with non-integer arguments!"); 2794 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2795 return V; // No conversion 2796 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2797 return getTruncateExpr(V, Ty); 2798 return getSignExtendExpr(V, Ty); 2799 } 2800 2801 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2802 /// input value to the specified type. If the type must be extended, it is zero 2803 /// extended. The conversion must not be narrowing. 2804 const SCEV * 2805 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) { 2806 Type *SrcTy = V->getType(); 2807 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2808 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2809 "Cannot noop or zero extend with non-integer arguments!"); 2810 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2811 "getNoopOrZeroExtend cannot truncate!"); 2812 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2813 return V; // No conversion 2814 return getZeroExtendExpr(V, Ty); 2815 } 2816 2817 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2818 /// input value to the specified type. If the type must be extended, it is sign 2819 /// extended. The conversion must not be narrowing. 2820 const SCEV * 2821 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) { 2822 Type *SrcTy = V->getType(); 2823 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2824 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2825 "Cannot noop or sign extend with non-integer arguments!"); 2826 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2827 "getNoopOrSignExtend cannot truncate!"); 2828 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2829 return V; // No conversion 2830 return getSignExtendExpr(V, Ty); 2831 } 2832 2833 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2834 /// the input value to the specified type. If the type must be extended, 2835 /// it is extended with unspecified bits. The conversion must not be 2836 /// narrowing. 2837 const SCEV * 2838 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) { 2839 Type *SrcTy = V->getType(); 2840 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2841 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2842 "Cannot noop or any extend with non-integer arguments!"); 2843 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2844 "getNoopOrAnyExtend cannot truncate!"); 2845 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2846 return V; // No conversion 2847 return getAnyExtendExpr(V, Ty); 2848 } 2849 2850 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2851 /// input value to the specified type. The conversion must not be widening. 2852 const SCEV * 2853 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) { 2854 Type *SrcTy = V->getType(); 2855 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2856 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2857 "Cannot truncate or noop with non-integer arguments!"); 2858 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2859 "getTruncateOrNoop cannot extend!"); 2860 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2861 return V; // No conversion 2862 return getTruncateExpr(V, Ty); 2863 } 2864 2865 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2866 /// the types using zero-extension, and then perform a umax operation 2867 /// with them. 2868 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2869 const SCEV *RHS) { 2870 const SCEV *PromotedLHS = LHS; 2871 const SCEV *PromotedRHS = RHS; 2872 2873 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2874 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2875 else 2876 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2877 2878 return getUMaxExpr(PromotedLHS, PromotedRHS); 2879 } 2880 2881 /// getUMinFromMismatchedTypes - Promote the operands to the wider of 2882 /// the types using zero-extension, and then perform a umin operation 2883 /// with them. 2884 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2885 const SCEV *RHS) { 2886 const SCEV *PromotedLHS = LHS; 2887 const SCEV *PromotedRHS = RHS; 2888 2889 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2890 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2891 else 2892 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2893 2894 return getUMinExpr(PromotedLHS, PromotedRHS); 2895 } 2896 2897 /// getPointerBase - Transitively follow the chain of pointer-type operands 2898 /// until reaching a SCEV that does not have a single pointer operand. This 2899 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions, 2900 /// but corner cases do exist. 2901 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) { 2902 // A pointer operand may evaluate to a nonpointer expression, such as null. 2903 if (!V->getType()->isPointerTy()) 2904 return V; 2905 2906 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) { 2907 return getPointerBase(Cast->getOperand()); 2908 } 2909 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) { 2910 const SCEV *PtrOp = 0; 2911 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 2912 I != E; ++I) { 2913 if ((*I)->getType()->isPointerTy()) { 2914 // Cannot find the base of an expression with multiple pointer operands. 2915 if (PtrOp) 2916 return V; 2917 PtrOp = *I; 2918 } 2919 } 2920 if (!PtrOp) 2921 return V; 2922 return getPointerBase(PtrOp); 2923 } 2924 return V; 2925 } 2926 2927 /// PushDefUseChildren - Push users of the given Instruction 2928 /// onto the given Worklist. 2929 static void 2930 PushDefUseChildren(Instruction *I, 2931 SmallVectorImpl<Instruction *> &Worklist) { 2932 // Push the def-use children onto the Worklist stack. 2933 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2934 UI != UE; ++UI) 2935 Worklist.push_back(cast<Instruction>(*UI)); 2936 } 2937 2938 /// ForgetSymbolicValue - This looks up computed SCEV values for all 2939 /// instructions that depend on the given instruction and removes them from 2940 /// the ValueExprMapType map if they reference SymName. This is used during PHI 2941 /// resolution. 2942 void 2943 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2944 SmallVector<Instruction *, 16> Worklist; 2945 PushDefUseChildren(PN, Worklist); 2946 2947 SmallPtrSet<Instruction *, 8> Visited; 2948 Visited.insert(PN); 2949 while (!Worklist.empty()) { 2950 Instruction *I = Worklist.pop_back_val(); 2951 if (!Visited.insert(I)) continue; 2952 2953 ValueExprMapType::iterator It = 2954 ValueExprMap.find_as(static_cast<Value *>(I)); 2955 if (It != ValueExprMap.end()) { 2956 const SCEV *Old = It->second; 2957 2958 // Short-circuit the def-use traversal if the symbolic name 2959 // ceases to appear in expressions. 2960 if (Old != SymName && !hasOperand(Old, SymName)) 2961 continue; 2962 2963 // SCEVUnknown for a PHI either means that it has an unrecognized 2964 // structure, it's a PHI that's in the progress of being computed 2965 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2966 // additional loop trip count information isn't going to change anything. 2967 // In the second case, createNodeForPHI will perform the necessary 2968 // updates on its own when it gets to that point. In the third, we do 2969 // want to forget the SCEVUnknown. 2970 if (!isa<PHINode>(I) || 2971 !isa<SCEVUnknown>(Old) || 2972 (I != PN && Old == SymName)) { 2973 forgetMemoizedResults(Old); 2974 ValueExprMap.erase(It); 2975 } 2976 } 2977 2978 PushDefUseChildren(I, Worklist); 2979 } 2980 } 2981 2982 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2983 /// a loop header, making it a potential recurrence, or it doesn't. 2984 /// 2985 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2986 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2987 if (L->getHeader() == PN->getParent()) { 2988 // The loop may have multiple entrances or multiple exits; we can analyze 2989 // this phi as an addrec if it has a unique entry value and a unique 2990 // backedge value. 2991 Value *BEValueV = 0, *StartValueV = 0; 2992 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 2993 Value *V = PN->getIncomingValue(i); 2994 if (L->contains(PN->getIncomingBlock(i))) { 2995 if (!BEValueV) { 2996 BEValueV = V; 2997 } else if (BEValueV != V) { 2998 BEValueV = 0; 2999 break; 3000 } 3001 } else if (!StartValueV) { 3002 StartValueV = V; 3003 } else if (StartValueV != V) { 3004 StartValueV = 0; 3005 break; 3006 } 3007 } 3008 if (BEValueV && StartValueV) { 3009 // While we are analyzing this PHI node, handle its value symbolically. 3010 const SCEV *SymbolicName = getUnknown(PN); 3011 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() && 3012 "PHI node already processed?"); 3013 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 3014 3015 // Using this symbolic name for the PHI, analyze the value coming around 3016 // the back-edge. 3017 const SCEV *BEValue = getSCEV(BEValueV); 3018 3019 // NOTE: If BEValue is loop invariant, we know that the PHI node just 3020 // has a special value for the first iteration of the loop. 3021 3022 // If the value coming around the backedge is an add with the symbolic 3023 // value we just inserted, then we found a simple induction variable! 3024 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 3025 // If there is a single occurrence of the symbolic value, replace it 3026 // with a recurrence. 3027 unsigned FoundIndex = Add->getNumOperands(); 3028 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 3029 if (Add->getOperand(i) == SymbolicName) 3030 if (FoundIndex == e) { 3031 FoundIndex = i; 3032 break; 3033 } 3034 3035 if (FoundIndex != Add->getNumOperands()) { 3036 // Create an add with everything but the specified operand. 3037 SmallVector<const SCEV *, 8> Ops; 3038 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 3039 if (i != FoundIndex) 3040 Ops.push_back(Add->getOperand(i)); 3041 const SCEV *Accum = getAddExpr(Ops); 3042 3043 // This is not a valid addrec if the step amount is varying each 3044 // loop iteration, but is not itself an addrec in this loop. 3045 if (isLoopInvariant(Accum, L) || 3046 (isa<SCEVAddRecExpr>(Accum) && 3047 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 3048 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; 3049 3050 // If the increment doesn't overflow, then neither the addrec nor 3051 // the post-increment will overflow. 3052 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 3053 if (OBO->hasNoUnsignedWrap()) 3054 Flags = setFlags(Flags, SCEV::FlagNUW); 3055 if (OBO->hasNoSignedWrap()) 3056 Flags = setFlags(Flags, SCEV::FlagNSW); 3057 } else if (const GEPOperator *GEP = 3058 dyn_cast<GEPOperator>(BEValueV)) { 3059 // If the increment is an inbounds GEP, then we know the address 3060 // space cannot be wrapped around. We cannot make any guarantee 3061 // about signed or unsigned overflow because pointers are 3062 // unsigned but we may have a negative index from the base 3063 // pointer. 3064 if (GEP->isInBounds()) 3065 Flags = setFlags(Flags, SCEV::FlagNW); 3066 } 3067 3068 const SCEV *StartVal = getSCEV(StartValueV); 3069 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags); 3070 3071 // Since the no-wrap flags are on the increment, they apply to the 3072 // post-incremented value as well. 3073 if (isLoopInvariant(Accum, L)) 3074 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 3075 Accum, L, Flags); 3076 3077 // Okay, for the entire analysis of this edge we assumed the PHI 3078 // to be symbolic. We now need to go back and purge all of the 3079 // entries for the scalars that use the symbolic expression. 3080 ForgetSymbolicName(PN, SymbolicName); 3081 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 3082 return PHISCEV; 3083 } 3084 } 3085 } else if (const SCEVAddRecExpr *AddRec = 3086 dyn_cast<SCEVAddRecExpr>(BEValue)) { 3087 // Otherwise, this could be a loop like this: 3088 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 3089 // In this case, j = {1,+,1} and BEValue is j. 3090 // Because the other in-value of i (0) fits the evolution of BEValue 3091 // i really is an addrec evolution. 3092 if (AddRec->getLoop() == L && AddRec->isAffine()) { 3093 const SCEV *StartVal = getSCEV(StartValueV); 3094 3095 // If StartVal = j.start - j.stride, we can use StartVal as the 3096 // initial step of the addrec evolution. 3097 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 3098 AddRec->getOperand(1))) { 3099 // FIXME: For constant StartVal, we should be able to infer 3100 // no-wrap flags. 3101 const SCEV *PHISCEV = 3102 getAddRecExpr(StartVal, AddRec->getOperand(1), L, 3103 SCEV::FlagAnyWrap); 3104 3105 // Okay, for the entire analysis of this edge we assumed the PHI 3106 // to be symbolic. We now need to go back and purge all of the 3107 // entries for the scalars that use the symbolic expression. 3108 ForgetSymbolicName(PN, SymbolicName); 3109 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 3110 return PHISCEV; 3111 } 3112 } 3113 } 3114 } 3115 } 3116 3117 // If the PHI has a single incoming value, follow that value, unless the 3118 // PHI's incoming blocks are in a different loop, in which case doing so 3119 // risks breaking LCSSA form. Instcombine would normally zap these, but 3120 // it doesn't have DominatorTree information, so it may miss cases. 3121 if (Value *V = SimplifyInstruction(PN, TD, TLI, DT)) 3122 if (LI->replacementPreservesLCSSAForm(PN, V)) 3123 return getSCEV(V); 3124 3125 // If it's not a loop phi, we can't handle it yet. 3126 return getUnknown(PN); 3127 } 3128 3129 /// createNodeForGEP - Expand GEP instructions into add and multiply 3130 /// operations. This allows them to be analyzed by regular SCEV code. 3131 /// 3132 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 3133 3134 // Don't blindly transfer the inbounds flag from the GEP instruction to the 3135 // Add expression, because the Instruction may be guarded by control flow 3136 // and the no-overflow bits may not be valid for the expression in any 3137 // context. 3138 bool isInBounds = GEP->isInBounds(); 3139 3140 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 3141 Value *Base = GEP->getOperand(0); 3142 // Don't attempt to analyze GEPs over unsized objects. 3143 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 3144 return getUnknown(GEP); 3145 const SCEV *TotalOffset = getConstant(IntPtrTy, 0); 3146 gep_type_iterator GTI = gep_type_begin(GEP); 3147 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()), 3148 E = GEP->op_end(); 3149 I != E; ++I) { 3150 Value *Index = *I; 3151 // Compute the (potentially symbolic) offset in bytes for this index. 3152 if (StructType *STy = dyn_cast<StructType>(*GTI++)) { 3153 // For a struct, add the member offset. 3154 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 3155 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo); 3156 3157 // Add the field offset to the running total offset. 3158 TotalOffset = getAddExpr(TotalOffset, FieldOffset); 3159 } else { 3160 // For an array, add the element offset, explicitly scaled. 3161 const SCEV *ElementSize = getSizeOfExpr(*GTI); 3162 const SCEV *IndexS = getSCEV(Index); 3163 // Getelementptr indices are signed. 3164 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy); 3165 3166 // Multiply the index by the element size to compute the element offset. 3167 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, 3168 isInBounds ? SCEV::FlagNSW : 3169 SCEV::FlagAnyWrap); 3170 3171 // Add the element offset to the running total offset. 3172 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 3173 } 3174 } 3175 3176 // Get the SCEV for the GEP base. 3177 const SCEV *BaseS = getSCEV(Base); 3178 3179 // Add the total offset from all the GEP indices to the base. 3180 return getAddExpr(BaseS, TotalOffset, 3181 isInBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap); 3182 } 3183 3184 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 3185 /// guaranteed to end in (at every loop iteration). It is, at the same time, 3186 /// the minimum number of times S is divisible by 2. For example, given {4,+,8} 3187 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 3188 uint32_t 3189 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 3190 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3191 return C->getValue()->getValue().countTrailingZeros(); 3192 3193 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 3194 return std::min(GetMinTrailingZeros(T->getOperand()), 3195 (uint32_t)getTypeSizeInBits(T->getType())); 3196 3197 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 3198 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 3199 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 3200 getTypeSizeInBits(E->getType()) : OpRes; 3201 } 3202 3203 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 3204 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 3205 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 3206 getTypeSizeInBits(E->getType()) : OpRes; 3207 } 3208 3209 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 3210 // The result is the min of all operands results. 3211 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 3212 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 3213 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 3214 return MinOpRes; 3215 } 3216 3217 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 3218 // The result is the sum of all operands results. 3219 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 3220 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 3221 for (unsigned i = 1, e = M->getNumOperands(); 3222 SumOpRes != BitWidth && i != e; ++i) 3223 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 3224 BitWidth); 3225 return SumOpRes; 3226 } 3227 3228 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 3229 // The result is the min of all operands results. 3230 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 3231 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 3232 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 3233 return MinOpRes; 3234 } 3235 3236 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 3237 // The result is the min of all operands results. 3238 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 3239 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 3240 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 3241 return MinOpRes; 3242 } 3243 3244 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 3245 // The result is the min of all operands results. 3246 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 3247 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 3248 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 3249 return MinOpRes; 3250 } 3251 3252 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3253 // For a SCEVUnknown, ask ValueTracking. 3254 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3255 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3256 ComputeMaskedBits(U->getValue(), Zeros, Ones); 3257 return Zeros.countTrailingOnes(); 3258 } 3259 3260 // SCEVUDivExpr 3261 return 0; 3262 } 3263 3264 /// getUnsignedRange - Determine the unsigned range for a particular SCEV. 3265 /// 3266 ConstantRange 3267 ScalarEvolution::getUnsignedRange(const SCEV *S) { 3268 // See if we've computed this range already. 3269 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S); 3270 if (I != UnsignedRanges.end()) 3271 return I->second; 3272 3273 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3274 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue())); 3275 3276 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3277 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3278 3279 // If the value has known zeros, the maximum unsigned value will have those 3280 // known zeros as well. 3281 uint32_t TZ = GetMinTrailingZeros(S); 3282 if (TZ != 0) 3283 ConservativeResult = 3284 ConstantRange(APInt::getMinValue(BitWidth), 3285 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 3286 3287 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3288 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 3289 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3290 X = X.add(getUnsignedRange(Add->getOperand(i))); 3291 return setUnsignedRange(Add, ConservativeResult.intersectWith(X)); 3292 } 3293 3294 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3295 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 3296 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3297 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 3298 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X)); 3299 } 3300 3301 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3302 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 3303 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3304 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 3305 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X)); 3306 } 3307 3308 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3309 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 3310 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3311 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 3312 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X)); 3313 } 3314 3315 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3316 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 3317 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 3318 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 3319 } 3320 3321 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3322 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 3323 return setUnsignedRange(ZExt, 3324 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3325 } 3326 3327 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3328 ConstantRange X = getUnsignedRange(SExt->getOperand()); 3329 return setUnsignedRange(SExt, 3330 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3331 } 3332 3333 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3334 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 3335 return setUnsignedRange(Trunc, 3336 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3337 } 3338 3339 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3340 // If there's no unsigned wrap, the value will never be less than its 3341 // initial value. 3342 if (AddRec->getNoWrapFlags(SCEV::FlagNUW)) 3343 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 3344 if (!C->getValue()->isZero()) 3345 ConservativeResult = 3346 ConservativeResult.intersectWith( 3347 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0))); 3348 3349 // TODO: non-affine addrec 3350 if (AddRec->isAffine()) { 3351 Type *Ty = AddRec->getType(); 3352 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3353 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3354 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3355 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3356 3357 const SCEV *Start = AddRec->getStart(); 3358 const SCEV *Step = AddRec->getStepRecurrence(*this); 3359 3360 ConstantRange StartRange = getUnsignedRange(Start); 3361 ConstantRange StepRange = getSignedRange(Step); 3362 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3363 ConstantRange EndRange = 3364 StartRange.add(MaxBECountRange.multiply(StepRange)); 3365 3366 // Check for overflow. This must be done with ConstantRange arithmetic 3367 // because we could be called from within the ScalarEvolution overflow 3368 // checking code. 3369 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1); 3370 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3371 ConstantRange ExtMaxBECountRange = 3372 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3373 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1); 3374 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3375 ExtEndRange) 3376 return setUnsignedRange(AddRec, ConservativeResult); 3377 3378 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 3379 EndRange.getUnsignedMin()); 3380 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 3381 EndRange.getUnsignedMax()); 3382 if (Min.isMinValue() && Max.isMaxValue()) 3383 return setUnsignedRange(AddRec, ConservativeResult); 3384 return setUnsignedRange(AddRec, 3385 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3386 } 3387 } 3388 3389 return setUnsignedRange(AddRec, ConservativeResult); 3390 } 3391 3392 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3393 // For a SCEVUnknown, ask ValueTracking. 3394 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3395 ComputeMaskedBits(U->getValue(), Zeros, Ones, TD); 3396 if (Ones == ~Zeros + 1) 3397 return setUnsignedRange(U, ConservativeResult); 3398 return setUnsignedRange(U, 3399 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1))); 3400 } 3401 3402 return setUnsignedRange(S, ConservativeResult); 3403 } 3404 3405 /// getSignedRange - Determine the signed range for a particular SCEV. 3406 /// 3407 ConstantRange 3408 ScalarEvolution::getSignedRange(const SCEV *S) { 3409 // See if we've computed this range already. 3410 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S); 3411 if (I != SignedRanges.end()) 3412 return I->second; 3413 3414 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3415 return setSignedRange(C, ConstantRange(C->getValue()->getValue())); 3416 3417 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3418 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3419 3420 // If the value has known zeros, the maximum signed value will have those 3421 // known zeros as well. 3422 uint32_t TZ = GetMinTrailingZeros(S); 3423 if (TZ != 0) 3424 ConservativeResult = 3425 ConstantRange(APInt::getSignedMinValue(BitWidth), 3426 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 3427 3428 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3429 ConstantRange X = getSignedRange(Add->getOperand(0)); 3430 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3431 X = X.add(getSignedRange(Add->getOperand(i))); 3432 return setSignedRange(Add, ConservativeResult.intersectWith(X)); 3433 } 3434 3435 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3436 ConstantRange X = getSignedRange(Mul->getOperand(0)); 3437 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3438 X = X.multiply(getSignedRange(Mul->getOperand(i))); 3439 return setSignedRange(Mul, ConservativeResult.intersectWith(X)); 3440 } 3441 3442 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3443 ConstantRange X = getSignedRange(SMax->getOperand(0)); 3444 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3445 X = X.smax(getSignedRange(SMax->getOperand(i))); 3446 return setSignedRange(SMax, ConservativeResult.intersectWith(X)); 3447 } 3448 3449 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3450 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3451 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3452 X = X.umax(getSignedRange(UMax->getOperand(i))); 3453 return setSignedRange(UMax, ConservativeResult.intersectWith(X)); 3454 } 3455 3456 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3457 ConstantRange X = getSignedRange(UDiv->getLHS()); 3458 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3459 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 3460 } 3461 3462 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3463 ConstantRange X = getSignedRange(ZExt->getOperand()); 3464 return setSignedRange(ZExt, 3465 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3466 } 3467 3468 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3469 ConstantRange X = getSignedRange(SExt->getOperand()); 3470 return setSignedRange(SExt, 3471 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3472 } 3473 3474 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3475 ConstantRange X = getSignedRange(Trunc->getOperand()); 3476 return setSignedRange(Trunc, 3477 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3478 } 3479 3480 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3481 // If there's no signed wrap, and all the operands have the same sign or 3482 // zero, the value won't ever change sign. 3483 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) { 3484 bool AllNonNeg = true; 3485 bool AllNonPos = true; 3486 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3487 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3488 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3489 } 3490 if (AllNonNeg) 3491 ConservativeResult = ConservativeResult.intersectWith( 3492 ConstantRange(APInt(BitWidth, 0), 3493 APInt::getSignedMinValue(BitWidth))); 3494 else if (AllNonPos) 3495 ConservativeResult = ConservativeResult.intersectWith( 3496 ConstantRange(APInt::getSignedMinValue(BitWidth), 3497 APInt(BitWidth, 1))); 3498 } 3499 3500 // TODO: non-affine addrec 3501 if (AddRec->isAffine()) { 3502 Type *Ty = AddRec->getType(); 3503 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3504 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3505 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3506 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3507 3508 const SCEV *Start = AddRec->getStart(); 3509 const SCEV *Step = AddRec->getStepRecurrence(*this); 3510 3511 ConstantRange StartRange = getSignedRange(Start); 3512 ConstantRange StepRange = getSignedRange(Step); 3513 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3514 ConstantRange EndRange = 3515 StartRange.add(MaxBECountRange.multiply(StepRange)); 3516 3517 // Check for overflow. This must be done with ConstantRange arithmetic 3518 // because we could be called from within the ScalarEvolution overflow 3519 // checking code. 3520 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1); 3521 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3522 ConstantRange ExtMaxBECountRange = 3523 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3524 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1); 3525 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3526 ExtEndRange) 3527 return setSignedRange(AddRec, ConservativeResult); 3528 3529 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3530 EndRange.getSignedMin()); 3531 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3532 EndRange.getSignedMax()); 3533 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3534 return setSignedRange(AddRec, ConservativeResult); 3535 return setSignedRange(AddRec, 3536 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3537 } 3538 } 3539 3540 return setSignedRange(AddRec, ConservativeResult); 3541 } 3542 3543 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3544 // For a SCEVUnknown, ask ValueTracking. 3545 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3546 return setSignedRange(U, ConservativeResult); 3547 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3548 if (NS == 1) 3549 return setSignedRange(U, ConservativeResult); 3550 return setSignedRange(U, ConservativeResult.intersectWith( 3551 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3552 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1))); 3553 } 3554 3555 return setSignedRange(S, ConservativeResult); 3556 } 3557 3558 /// createSCEV - We know that there is no SCEV for the specified value. 3559 /// Analyze the expression. 3560 /// 3561 const SCEV *ScalarEvolution::createSCEV(Value *V) { 3562 if (!isSCEVable(V->getType())) 3563 return getUnknown(V); 3564 3565 unsigned Opcode = Instruction::UserOp1; 3566 if (Instruction *I = dyn_cast<Instruction>(V)) { 3567 Opcode = I->getOpcode(); 3568 3569 // Don't attempt to analyze instructions in blocks that aren't 3570 // reachable. Such instructions don't matter, and they aren't required 3571 // to obey basic rules for definitions dominating uses which this 3572 // analysis depends on. 3573 if (!DT->isReachableFromEntry(I->getParent())) 3574 return getUnknown(V); 3575 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3576 Opcode = CE->getOpcode(); 3577 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3578 return getConstant(CI); 3579 else if (isa<ConstantPointerNull>(V)) 3580 return getConstant(V->getType(), 0); 3581 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3582 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3583 else 3584 return getUnknown(V); 3585 3586 Operator *U = cast<Operator>(V); 3587 switch (Opcode) { 3588 case Instruction::Add: { 3589 // The simple thing to do would be to just call getSCEV on both operands 3590 // and call getAddExpr with the result. However if we're looking at a 3591 // bunch of things all added together, this can be quite inefficient, 3592 // because it leads to N-1 getAddExpr calls for N ultimate operands. 3593 // Instead, gather up all the operands and make a single getAddExpr call. 3594 // LLVM IR canonical form means we need only traverse the left operands. 3595 // 3596 // Don't apply this instruction's NSW or NUW flags to the new 3597 // expression. The instruction may be guarded by control flow that the 3598 // no-wrap behavior depends on. Non-control-equivalent instructions can be 3599 // mapped to the same SCEV expression, and it would be incorrect to transfer 3600 // NSW/NUW semantics to those operations. 3601 SmallVector<const SCEV *, 4> AddOps; 3602 AddOps.push_back(getSCEV(U->getOperand(1))); 3603 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) { 3604 unsigned Opcode = Op->getValueID() - Value::InstructionVal; 3605 if (Opcode != Instruction::Add && Opcode != Instruction::Sub) 3606 break; 3607 U = cast<Operator>(Op); 3608 const SCEV *Op1 = getSCEV(U->getOperand(1)); 3609 if (Opcode == Instruction::Sub) 3610 AddOps.push_back(getNegativeSCEV(Op1)); 3611 else 3612 AddOps.push_back(Op1); 3613 } 3614 AddOps.push_back(getSCEV(U->getOperand(0))); 3615 return getAddExpr(AddOps); 3616 } 3617 case Instruction::Mul: { 3618 // Don't transfer NSW/NUW for the same reason as AddExpr. 3619 SmallVector<const SCEV *, 4> MulOps; 3620 MulOps.push_back(getSCEV(U->getOperand(1))); 3621 for (Value *Op = U->getOperand(0); 3622 Op->getValueID() == Instruction::Mul + Value::InstructionVal; 3623 Op = U->getOperand(0)) { 3624 U = cast<Operator>(Op); 3625 MulOps.push_back(getSCEV(U->getOperand(1))); 3626 } 3627 MulOps.push_back(getSCEV(U->getOperand(0))); 3628 return getMulExpr(MulOps); 3629 } 3630 case Instruction::UDiv: 3631 return getUDivExpr(getSCEV(U->getOperand(0)), 3632 getSCEV(U->getOperand(1))); 3633 case Instruction::Sub: 3634 return getMinusSCEV(getSCEV(U->getOperand(0)), 3635 getSCEV(U->getOperand(1))); 3636 case Instruction::And: 3637 // For an expression like x&255 that merely masks off the high bits, 3638 // use zext(trunc(x)) as the SCEV expression. 3639 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3640 if (CI->isNullValue()) 3641 return getSCEV(U->getOperand(1)); 3642 if (CI->isAllOnesValue()) 3643 return getSCEV(U->getOperand(0)); 3644 const APInt &A = CI->getValue(); 3645 3646 // Instcombine's ShrinkDemandedConstant may strip bits out of 3647 // constants, obscuring what would otherwise be a low-bits mask. 3648 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3649 // knew about to reconstruct a low-bits mask value. 3650 unsigned LZ = A.countLeadingZeros(); 3651 unsigned BitWidth = A.getBitWidth(); 3652 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3653 ComputeMaskedBits(U->getOperand(0), KnownZero, KnownOne, TD); 3654 3655 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3656 3657 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3658 return 3659 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3660 IntegerType::get(getContext(), BitWidth - LZ)), 3661 U->getType()); 3662 } 3663 break; 3664 3665 case Instruction::Or: 3666 // If the RHS of the Or is a constant, we may have something like: 3667 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3668 // optimizations will transparently handle this case. 3669 // 3670 // In order for this transformation to be safe, the LHS must be of the 3671 // form X*(2^n) and the Or constant must be less than 2^n. 3672 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3673 const SCEV *LHS = getSCEV(U->getOperand(0)); 3674 const APInt &CIVal = CI->getValue(); 3675 if (GetMinTrailingZeros(LHS) >= 3676 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3677 // Build a plain add SCEV. 3678 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3679 // If the LHS of the add was an addrec and it has no-wrap flags, 3680 // transfer the no-wrap flags, since an or won't introduce a wrap. 3681 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3682 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3683 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags( 3684 OldAR->getNoWrapFlags()); 3685 } 3686 return S; 3687 } 3688 } 3689 break; 3690 case Instruction::Xor: 3691 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3692 // If the RHS of the xor is a signbit, then this is just an add. 3693 // Instcombine turns add of signbit into xor as a strength reduction step. 3694 if (CI->getValue().isSignBit()) 3695 return getAddExpr(getSCEV(U->getOperand(0)), 3696 getSCEV(U->getOperand(1))); 3697 3698 // If the RHS of xor is -1, then this is a not operation. 3699 if (CI->isAllOnesValue()) 3700 return getNotSCEV(getSCEV(U->getOperand(0))); 3701 3702 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3703 // This is a variant of the check for xor with -1, and it handles 3704 // the case where instcombine has trimmed non-demanded bits out 3705 // of an xor with -1. 3706 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3707 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3708 if (BO->getOpcode() == Instruction::And && 3709 LCI->getValue() == CI->getValue()) 3710 if (const SCEVZeroExtendExpr *Z = 3711 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3712 Type *UTy = U->getType(); 3713 const SCEV *Z0 = Z->getOperand(); 3714 Type *Z0Ty = Z0->getType(); 3715 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3716 3717 // If C is a low-bits mask, the zero extend is serving to 3718 // mask off the high bits. Complement the operand and 3719 // re-apply the zext. 3720 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3721 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3722 3723 // If C is a single bit, it may be in the sign-bit position 3724 // before the zero-extend. In this case, represent the xor 3725 // using an add, which is equivalent, and re-apply the zext. 3726 APInt Trunc = CI->getValue().trunc(Z0TySize); 3727 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3728 Trunc.isSignBit()) 3729 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3730 UTy); 3731 } 3732 } 3733 break; 3734 3735 case Instruction::Shl: 3736 // Turn shift left of a constant amount into a multiply. 3737 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3738 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3739 3740 // If the shift count is not less than the bitwidth, the result of 3741 // the shift is undefined. Don't try to analyze it, because the 3742 // resolution chosen here may differ from the resolution chosen in 3743 // other parts of the compiler. 3744 if (SA->getValue().uge(BitWidth)) 3745 break; 3746 3747 Constant *X = ConstantInt::get(getContext(), 3748 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3749 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3750 } 3751 break; 3752 3753 case Instruction::LShr: 3754 // Turn logical shift right of a constant into a unsigned divide. 3755 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3756 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3757 3758 // If the shift count is not less than the bitwidth, the result of 3759 // the shift is undefined. Don't try to analyze it, because the 3760 // resolution chosen here may differ from the resolution chosen in 3761 // other parts of the compiler. 3762 if (SA->getValue().uge(BitWidth)) 3763 break; 3764 3765 Constant *X = ConstantInt::get(getContext(), 3766 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3767 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3768 } 3769 break; 3770 3771 case Instruction::AShr: 3772 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3773 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3774 if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) 3775 if (L->getOpcode() == Instruction::Shl && 3776 L->getOperand(1) == U->getOperand(1)) { 3777 uint64_t BitWidth = getTypeSizeInBits(U->getType()); 3778 3779 // If the shift count is not less than the bitwidth, the result of 3780 // the shift is undefined. Don't try to analyze it, because the 3781 // resolution chosen here may differ from the resolution chosen in 3782 // other parts of the compiler. 3783 if (CI->getValue().uge(BitWidth)) 3784 break; 3785 3786 uint64_t Amt = BitWidth - CI->getZExtValue(); 3787 if (Amt == BitWidth) 3788 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3789 return 3790 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3791 IntegerType::get(getContext(), 3792 Amt)), 3793 U->getType()); 3794 } 3795 break; 3796 3797 case Instruction::Trunc: 3798 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3799 3800 case Instruction::ZExt: 3801 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3802 3803 case Instruction::SExt: 3804 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3805 3806 case Instruction::BitCast: 3807 // BitCasts are no-op casts so we just eliminate the cast. 3808 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3809 return getSCEV(U->getOperand(0)); 3810 break; 3811 3812 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3813 // lead to pointer expressions which cannot safely be expanded to GEPs, 3814 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3815 // simplifying integer expressions. 3816 3817 case Instruction::GetElementPtr: 3818 return createNodeForGEP(cast<GEPOperator>(U)); 3819 3820 case Instruction::PHI: 3821 return createNodeForPHI(cast<PHINode>(U)); 3822 3823 case Instruction::Select: 3824 // This could be a smax or umax that was lowered earlier. 3825 // Try to recover it. 3826 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3827 Value *LHS = ICI->getOperand(0); 3828 Value *RHS = ICI->getOperand(1); 3829 switch (ICI->getPredicate()) { 3830 case ICmpInst::ICMP_SLT: 3831 case ICmpInst::ICMP_SLE: 3832 std::swap(LHS, RHS); 3833 // fall through 3834 case ICmpInst::ICMP_SGT: 3835 case ICmpInst::ICMP_SGE: 3836 // a >s b ? a+x : b+x -> smax(a, b)+x 3837 // a >s b ? b+x : a+x -> smin(a, b)+x 3838 if (LHS->getType() == U->getType()) { 3839 const SCEV *LS = getSCEV(LHS); 3840 const SCEV *RS = getSCEV(RHS); 3841 const SCEV *LA = getSCEV(U->getOperand(1)); 3842 const SCEV *RA = getSCEV(U->getOperand(2)); 3843 const SCEV *LDiff = getMinusSCEV(LA, LS); 3844 const SCEV *RDiff = getMinusSCEV(RA, RS); 3845 if (LDiff == RDiff) 3846 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 3847 LDiff = getMinusSCEV(LA, RS); 3848 RDiff = getMinusSCEV(RA, LS); 3849 if (LDiff == RDiff) 3850 return getAddExpr(getSMinExpr(LS, RS), LDiff); 3851 } 3852 break; 3853 case ICmpInst::ICMP_ULT: 3854 case ICmpInst::ICMP_ULE: 3855 std::swap(LHS, RHS); 3856 // fall through 3857 case ICmpInst::ICMP_UGT: 3858 case ICmpInst::ICMP_UGE: 3859 // a >u b ? a+x : b+x -> umax(a, b)+x 3860 // a >u b ? b+x : a+x -> umin(a, b)+x 3861 if (LHS->getType() == U->getType()) { 3862 const SCEV *LS = getSCEV(LHS); 3863 const SCEV *RS = getSCEV(RHS); 3864 const SCEV *LA = getSCEV(U->getOperand(1)); 3865 const SCEV *RA = getSCEV(U->getOperand(2)); 3866 const SCEV *LDiff = getMinusSCEV(LA, LS); 3867 const SCEV *RDiff = getMinusSCEV(RA, RS); 3868 if (LDiff == RDiff) 3869 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 3870 LDiff = getMinusSCEV(LA, RS); 3871 RDiff = getMinusSCEV(RA, LS); 3872 if (LDiff == RDiff) 3873 return getAddExpr(getUMinExpr(LS, RS), LDiff); 3874 } 3875 break; 3876 case ICmpInst::ICMP_NE: 3877 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 3878 if (LHS->getType() == U->getType() && 3879 isa<ConstantInt>(RHS) && 3880 cast<ConstantInt>(RHS)->isZero()) { 3881 const SCEV *One = getConstant(LHS->getType(), 1); 3882 const SCEV *LS = getSCEV(LHS); 3883 const SCEV *LA = getSCEV(U->getOperand(1)); 3884 const SCEV *RA = getSCEV(U->getOperand(2)); 3885 const SCEV *LDiff = getMinusSCEV(LA, LS); 3886 const SCEV *RDiff = getMinusSCEV(RA, One); 3887 if (LDiff == RDiff) 3888 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3889 } 3890 break; 3891 case ICmpInst::ICMP_EQ: 3892 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 3893 if (LHS->getType() == U->getType() && 3894 isa<ConstantInt>(RHS) && 3895 cast<ConstantInt>(RHS)->isZero()) { 3896 const SCEV *One = getConstant(LHS->getType(), 1); 3897 const SCEV *LS = getSCEV(LHS); 3898 const SCEV *LA = getSCEV(U->getOperand(1)); 3899 const SCEV *RA = getSCEV(U->getOperand(2)); 3900 const SCEV *LDiff = getMinusSCEV(LA, One); 3901 const SCEV *RDiff = getMinusSCEV(RA, LS); 3902 if (LDiff == RDiff) 3903 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3904 } 3905 break; 3906 default: 3907 break; 3908 } 3909 } 3910 3911 default: // We cannot analyze this expression. 3912 break; 3913 } 3914 3915 return getUnknown(V); 3916 } 3917 3918 3919 3920 //===----------------------------------------------------------------------===// 3921 // Iteration Count Computation Code 3922 // 3923 3924 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a 3925 /// normal unsigned value. Returns 0 if the trip count is unknown or not 3926 /// constant. Will also return 0 if the maximum trip count is very large (>= 3927 /// 2^32). 3928 /// 3929 /// This "trip count" assumes that control exits via ExitingBlock. More 3930 /// precisely, it is the number of times that control may reach ExitingBlock 3931 /// before taking the branch. For loops with multiple exits, it may not be the 3932 /// number times that the loop header executes because the loop may exit 3933 /// prematurely via another branch. 3934 unsigned ScalarEvolution:: 3935 getSmallConstantTripCount(Loop *L, BasicBlock *ExitingBlock) { 3936 const SCEVConstant *ExitCount = 3937 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock)); 3938 if (!ExitCount) 3939 return 0; 3940 3941 ConstantInt *ExitConst = ExitCount->getValue(); 3942 3943 // Guard against huge trip counts. 3944 if (ExitConst->getValue().getActiveBits() > 32) 3945 return 0; 3946 3947 // In case of integer overflow, this returns 0, which is correct. 3948 return ((unsigned)ExitConst->getZExtValue()) + 1; 3949 } 3950 3951 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the 3952 /// trip count of this loop as a normal unsigned value, if possible. This 3953 /// means that the actual trip count is always a multiple of the returned 3954 /// value (don't forget the trip count could very well be zero as well!). 3955 /// 3956 /// Returns 1 if the trip count is unknown or not guaranteed to be the 3957 /// multiple of a constant (which is also the case if the trip count is simply 3958 /// constant, use getSmallConstantTripCount for that case), Will also return 1 3959 /// if the trip count is very large (>= 2^32). 3960 /// 3961 /// As explained in the comments for getSmallConstantTripCount, this assumes 3962 /// that control exits the loop via ExitingBlock. 3963 unsigned ScalarEvolution:: 3964 getSmallConstantTripMultiple(Loop *L, BasicBlock *ExitingBlock) { 3965 const SCEV *ExitCount = getExitCount(L, ExitingBlock); 3966 if (ExitCount == getCouldNotCompute()) 3967 return 1; 3968 3969 // Get the trip count from the BE count by adding 1. 3970 const SCEV *TCMul = getAddExpr(ExitCount, 3971 getConstant(ExitCount->getType(), 1)); 3972 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt 3973 // to factor simple cases. 3974 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul)) 3975 TCMul = Mul->getOperand(0); 3976 3977 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul); 3978 if (!MulC) 3979 return 1; 3980 3981 ConstantInt *Result = MulC->getValue(); 3982 3983 // Guard against huge trip counts. 3984 if (!Result || Result->getValue().getActiveBits() > 32) 3985 return 1; 3986 3987 return (unsigned)Result->getZExtValue(); 3988 } 3989 3990 // getExitCount - Get the expression for the number of loop iterations for which 3991 // this loop is guaranteed not to exit via ExitintBlock. Otherwise return 3992 // SCEVCouldNotCompute. 3993 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) { 3994 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this); 3995 } 3996 3997 /// getBackedgeTakenCount - If the specified loop has a predictable 3998 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3999 /// object. The backedge-taken count is the number of times the loop header 4000 /// will be branched to from within the loop. This is one less than the 4001 /// trip count of the loop, since it doesn't count the first iteration, 4002 /// when the header is branched to from outside the loop. 4003 /// 4004 /// Note that it is not valid to call this method on a loop without a 4005 /// loop-invariant backedge-taken count (see 4006 /// hasLoopInvariantBackedgeTakenCount). 4007 /// 4008 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 4009 return getBackedgeTakenInfo(L).getExact(this); 4010 } 4011 4012 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 4013 /// return the least SCEV value that is known never to be less than the 4014 /// actual backedge taken count. 4015 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 4016 return getBackedgeTakenInfo(L).getMax(this); 4017 } 4018 4019 /// PushLoopPHIs - Push PHI nodes in the header of the given loop 4020 /// onto the given Worklist. 4021 static void 4022 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 4023 BasicBlock *Header = L->getHeader(); 4024 4025 // Push all Loop-header PHIs onto the Worklist stack. 4026 for (BasicBlock::iterator I = Header->begin(); 4027 PHINode *PN = dyn_cast<PHINode>(I); ++I) 4028 Worklist.push_back(PN); 4029 } 4030 4031 const ScalarEvolution::BackedgeTakenInfo & 4032 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 4033 // Initially insert an invalid entry for this loop. If the insertion 4034 // succeeds, proceed to actually compute a backedge-taken count and 4035 // update the value. The temporary CouldNotCompute value tells SCEV 4036 // code elsewhere that it shouldn't attempt to request a new 4037 // backedge-taken count, which could result in infinite recursion. 4038 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 4039 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo())); 4040 if (!Pair.second) 4041 return Pair.first->second; 4042 4043 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it 4044 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result 4045 // must be cleared in this scope. 4046 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L); 4047 4048 if (Result.getExact(this) != getCouldNotCompute()) { 4049 assert(isLoopInvariant(Result.getExact(this), L) && 4050 isLoopInvariant(Result.getMax(this), L) && 4051 "Computed backedge-taken count isn't loop invariant for loop!"); 4052 ++NumTripCountsComputed; 4053 } 4054 else if (Result.getMax(this) == getCouldNotCompute() && 4055 isa<PHINode>(L->getHeader()->begin())) { 4056 // Only count loops that have phi nodes as not being computable. 4057 ++NumTripCountsNotComputed; 4058 } 4059 4060 // Now that we know more about the trip count for this loop, forget any 4061 // existing SCEV values for PHI nodes in this loop since they are only 4062 // conservative estimates made without the benefit of trip count 4063 // information. This is similar to the code in forgetLoop, except that 4064 // it handles SCEVUnknown PHI nodes specially. 4065 if (Result.hasAnyInfo()) { 4066 SmallVector<Instruction *, 16> Worklist; 4067 PushLoopPHIs(L, Worklist); 4068 4069 SmallPtrSet<Instruction *, 8> Visited; 4070 while (!Worklist.empty()) { 4071 Instruction *I = Worklist.pop_back_val(); 4072 if (!Visited.insert(I)) continue; 4073 4074 ValueExprMapType::iterator It = 4075 ValueExprMap.find_as(static_cast<Value *>(I)); 4076 if (It != ValueExprMap.end()) { 4077 const SCEV *Old = It->second; 4078 4079 // SCEVUnknown for a PHI either means that it has an unrecognized 4080 // structure, or it's a PHI that's in the progress of being computed 4081 // by createNodeForPHI. In the former case, additional loop trip 4082 // count information isn't going to change anything. In the later 4083 // case, createNodeForPHI will perform the necessary updates on its 4084 // own when it gets to that point. 4085 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) { 4086 forgetMemoizedResults(Old); 4087 ValueExprMap.erase(It); 4088 } 4089 if (PHINode *PN = dyn_cast<PHINode>(I)) 4090 ConstantEvolutionLoopExitValue.erase(PN); 4091 } 4092 4093 PushDefUseChildren(I, Worklist); 4094 } 4095 } 4096 4097 // Re-lookup the insert position, since the call to 4098 // ComputeBackedgeTakenCount above could result in a 4099 // recusive call to getBackedgeTakenInfo (on a different 4100 // loop), which would invalidate the iterator computed 4101 // earlier. 4102 return BackedgeTakenCounts.find(L)->second = Result; 4103 } 4104 4105 /// forgetLoop - This method should be called by the client when it has 4106 /// changed a loop in a way that may effect ScalarEvolution's ability to 4107 /// compute a trip count, or if the loop is deleted. 4108 void ScalarEvolution::forgetLoop(const Loop *L) { 4109 // Drop any stored trip count value. 4110 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos = 4111 BackedgeTakenCounts.find(L); 4112 if (BTCPos != BackedgeTakenCounts.end()) { 4113 BTCPos->second.clear(); 4114 BackedgeTakenCounts.erase(BTCPos); 4115 } 4116 4117 // Drop information about expressions based on loop-header PHIs. 4118 SmallVector<Instruction *, 16> Worklist; 4119 PushLoopPHIs(L, Worklist); 4120 4121 SmallPtrSet<Instruction *, 8> Visited; 4122 while (!Worklist.empty()) { 4123 Instruction *I = Worklist.pop_back_val(); 4124 if (!Visited.insert(I)) continue; 4125 4126 ValueExprMapType::iterator It = 4127 ValueExprMap.find_as(static_cast<Value *>(I)); 4128 if (It != ValueExprMap.end()) { 4129 forgetMemoizedResults(It->second); 4130 ValueExprMap.erase(It); 4131 if (PHINode *PN = dyn_cast<PHINode>(I)) 4132 ConstantEvolutionLoopExitValue.erase(PN); 4133 } 4134 4135 PushDefUseChildren(I, Worklist); 4136 } 4137 4138 // Forget all contained loops too, to avoid dangling entries in the 4139 // ValuesAtScopes map. 4140 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 4141 forgetLoop(*I); 4142 } 4143 4144 /// forgetValue - This method should be called by the client when it has 4145 /// changed a value in a way that may effect its value, or which may 4146 /// disconnect it from a def-use chain linking it to a loop. 4147 void ScalarEvolution::forgetValue(Value *V) { 4148 Instruction *I = dyn_cast<Instruction>(V); 4149 if (!I) return; 4150 4151 // Drop information about expressions based on loop-header PHIs. 4152 SmallVector<Instruction *, 16> Worklist; 4153 Worklist.push_back(I); 4154 4155 SmallPtrSet<Instruction *, 8> Visited; 4156 while (!Worklist.empty()) { 4157 I = Worklist.pop_back_val(); 4158 if (!Visited.insert(I)) continue; 4159 4160 ValueExprMapType::iterator It = 4161 ValueExprMap.find_as(static_cast<Value *>(I)); 4162 if (It != ValueExprMap.end()) { 4163 forgetMemoizedResults(It->second); 4164 ValueExprMap.erase(It); 4165 if (PHINode *PN = dyn_cast<PHINode>(I)) 4166 ConstantEvolutionLoopExitValue.erase(PN); 4167 } 4168 4169 PushDefUseChildren(I, Worklist); 4170 } 4171 } 4172 4173 /// getExact - Get the exact loop backedge taken count considering all loop 4174 /// exits. A computable result can only be return for loops with a single exit. 4175 /// Returning the minimum taken count among all exits is incorrect because one 4176 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that 4177 /// the limit of each loop test is never skipped. This is a valid assumption as 4178 /// long as the loop exits via that test. For precise results, it is the 4179 /// caller's responsibility to specify the relevant loop exit using 4180 /// getExact(ExitingBlock, SE). 4181 const SCEV * 4182 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const { 4183 // If any exits were not computable, the loop is not computable. 4184 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute(); 4185 4186 // We need exactly one computable exit. 4187 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute(); 4188 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info"); 4189 4190 const SCEV *BECount = 0; 4191 for (const ExitNotTakenInfo *ENT = &ExitNotTaken; 4192 ENT != 0; ENT = ENT->getNextExit()) { 4193 4194 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV"); 4195 4196 if (!BECount) 4197 BECount = ENT->ExactNotTaken; 4198 else if (BECount != ENT->ExactNotTaken) 4199 return SE->getCouldNotCompute(); 4200 } 4201 assert(BECount && "Invalid not taken count for loop exit"); 4202 return BECount; 4203 } 4204 4205 /// getExact - Get the exact not taken count for this loop exit. 4206 const SCEV * 4207 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock, 4208 ScalarEvolution *SE) const { 4209 for (const ExitNotTakenInfo *ENT = &ExitNotTaken; 4210 ENT != 0; ENT = ENT->getNextExit()) { 4211 4212 if (ENT->ExitingBlock == ExitingBlock) 4213 return ENT->ExactNotTaken; 4214 } 4215 return SE->getCouldNotCompute(); 4216 } 4217 4218 /// getMax - Get the max backedge taken count for the loop. 4219 const SCEV * 4220 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const { 4221 return Max ? Max : SE->getCouldNotCompute(); 4222 } 4223 4224 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each 4225 /// computable exit into a persistent ExitNotTakenInfo array. 4226 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo( 4227 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts, 4228 bool Complete, const SCEV *MaxCount) : Max(MaxCount) { 4229 4230 if (!Complete) 4231 ExitNotTaken.setIncomplete(); 4232 4233 unsigned NumExits = ExitCounts.size(); 4234 if (NumExits == 0) return; 4235 4236 ExitNotTaken.ExitingBlock = ExitCounts[0].first; 4237 ExitNotTaken.ExactNotTaken = ExitCounts[0].second; 4238 if (NumExits == 1) return; 4239 4240 // Handle the rare case of multiple computable exits. 4241 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1]; 4242 4243 ExitNotTakenInfo *PrevENT = &ExitNotTaken; 4244 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) { 4245 PrevENT->setNextExit(ENT); 4246 ENT->ExitingBlock = ExitCounts[i].first; 4247 ENT->ExactNotTaken = ExitCounts[i].second; 4248 } 4249 } 4250 4251 /// clear - Invalidate this result and free the ExitNotTakenInfo array. 4252 void ScalarEvolution::BackedgeTakenInfo::clear() { 4253 ExitNotTaken.ExitingBlock = 0; 4254 ExitNotTaken.ExactNotTaken = 0; 4255 delete[] ExitNotTaken.getNextExit(); 4256 } 4257 4258 /// ComputeBackedgeTakenCount - Compute the number of times the backedge 4259 /// of the specified loop will execute. 4260 ScalarEvolution::BackedgeTakenInfo 4261 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 4262 SmallVector<BasicBlock *, 8> ExitingBlocks; 4263 L->getExitingBlocks(ExitingBlocks); 4264 4265 // Examine all exits and pick the most conservative values. 4266 const SCEV *MaxBECount = getCouldNotCompute(); 4267 bool CouldComputeBECount = true; 4268 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts; 4269 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 4270 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]); 4271 if (EL.Exact == getCouldNotCompute()) 4272 // We couldn't compute an exact value for this exit, so 4273 // we won't be able to compute an exact value for the loop. 4274 CouldComputeBECount = false; 4275 else 4276 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact)); 4277 4278 if (MaxBECount == getCouldNotCompute()) 4279 MaxBECount = EL.Max; 4280 else if (EL.Max != getCouldNotCompute()) { 4281 // We cannot take the "min" MaxBECount, because non-unit stride loops may 4282 // skip some loop tests. Taking the max over the exits is sufficiently 4283 // conservative. TODO: We could do better taking into consideration 4284 // that (1) the loop has unit stride (2) the last loop test is 4285 // less-than/greater-than (3) any loop test is less-than/greater-than AND 4286 // falls-through some constant times less then the other tests. 4287 MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, EL.Max); 4288 } 4289 } 4290 4291 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount); 4292 } 4293 4294 /// ComputeExitLimit - Compute the number of times the backedge of the specified 4295 /// loop will execute if it exits via the specified block. 4296 ScalarEvolution::ExitLimit 4297 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) { 4298 4299 // Okay, we've chosen an exiting block. See what condition causes us to 4300 // exit at this block. 4301 // 4302 // FIXME: we should be able to handle switch instructions (with a single exit) 4303 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 4304 if (ExitBr == 0) return getCouldNotCompute(); 4305 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 4306 4307 // At this point, we know we have a conditional branch that determines whether 4308 // the loop is exited. However, we don't know if the branch is executed each 4309 // time through the loop. If not, then the execution count of the branch will 4310 // not be equal to the trip count of the loop. 4311 // 4312 // Currently we check for this by checking to see if the Exit branch goes to 4313 // the loop header. If so, we know it will always execute the same number of 4314 // times as the loop. We also handle the case where the exit block *is* the 4315 // loop header. This is common for un-rotated loops. 4316 // 4317 // If both of those tests fail, walk up the unique predecessor chain to the 4318 // header, stopping if there is an edge that doesn't exit the loop. If the 4319 // header is reached, the execution count of the branch will be equal to the 4320 // trip count of the loop. 4321 // 4322 // More extensive analysis could be done to handle more cases here. 4323 // 4324 if (ExitBr->getSuccessor(0) != L->getHeader() && 4325 ExitBr->getSuccessor(1) != L->getHeader() && 4326 ExitBr->getParent() != L->getHeader()) { 4327 // The simple checks failed, try climbing the unique predecessor chain 4328 // up to the header. 4329 bool Ok = false; 4330 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 4331 BasicBlock *Pred = BB->getUniquePredecessor(); 4332 if (!Pred) 4333 return getCouldNotCompute(); 4334 TerminatorInst *PredTerm = Pred->getTerminator(); 4335 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 4336 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 4337 if (PredSucc == BB) 4338 continue; 4339 // If the predecessor has a successor that isn't BB and isn't 4340 // outside the loop, assume the worst. 4341 if (L->contains(PredSucc)) 4342 return getCouldNotCompute(); 4343 } 4344 if (Pred == L->getHeader()) { 4345 Ok = true; 4346 break; 4347 } 4348 BB = Pred; 4349 } 4350 if (!Ok) 4351 return getCouldNotCompute(); 4352 } 4353 4354 // Proceed to the next level to examine the exit condition expression. 4355 return ComputeExitLimitFromCond(L, ExitBr->getCondition(), 4356 ExitBr->getSuccessor(0), 4357 ExitBr->getSuccessor(1)); 4358 } 4359 4360 /// ComputeExitLimitFromCond - Compute the number of times the 4361 /// backedge of the specified loop will execute if its exit condition 4362 /// were a conditional branch of ExitCond, TBB, and FBB. 4363 ScalarEvolution::ExitLimit 4364 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L, 4365 Value *ExitCond, 4366 BasicBlock *TBB, 4367 BasicBlock *FBB) { 4368 // Check if the controlling expression for this loop is an And or Or. 4369 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 4370 if (BO->getOpcode() == Instruction::And) { 4371 // Recurse on the operands of the and. 4372 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB); 4373 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB); 4374 const SCEV *BECount = getCouldNotCompute(); 4375 const SCEV *MaxBECount = getCouldNotCompute(); 4376 if (L->contains(TBB)) { 4377 // Both conditions must be true for the loop to continue executing. 4378 // Choose the less conservative count. 4379 if (EL0.Exact == getCouldNotCompute() || 4380 EL1.Exact == getCouldNotCompute()) 4381 BECount = getCouldNotCompute(); 4382 else 4383 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact); 4384 if (EL0.Max == getCouldNotCompute()) 4385 MaxBECount = EL1.Max; 4386 else if (EL1.Max == getCouldNotCompute()) 4387 MaxBECount = EL0.Max; 4388 else 4389 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max); 4390 } else { 4391 // Both conditions must be true at the same time for the loop to exit. 4392 // For now, be conservative. 4393 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 4394 if (EL0.Max == EL1.Max) 4395 MaxBECount = EL0.Max; 4396 if (EL0.Exact == EL1.Exact) 4397 BECount = EL0.Exact; 4398 } 4399 4400 return ExitLimit(BECount, MaxBECount); 4401 } 4402 if (BO->getOpcode() == Instruction::Or) { 4403 // Recurse on the operands of the or. 4404 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB); 4405 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB); 4406 const SCEV *BECount = getCouldNotCompute(); 4407 const SCEV *MaxBECount = getCouldNotCompute(); 4408 if (L->contains(FBB)) { 4409 // Both conditions must be false for the loop to continue executing. 4410 // Choose the less conservative count. 4411 if (EL0.Exact == getCouldNotCompute() || 4412 EL1.Exact == getCouldNotCompute()) 4413 BECount = getCouldNotCompute(); 4414 else 4415 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact); 4416 if (EL0.Max == getCouldNotCompute()) 4417 MaxBECount = EL1.Max; 4418 else if (EL1.Max == getCouldNotCompute()) 4419 MaxBECount = EL0.Max; 4420 else 4421 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max); 4422 } else { 4423 // Both conditions must be false at the same time for the loop to exit. 4424 // For now, be conservative. 4425 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 4426 if (EL0.Max == EL1.Max) 4427 MaxBECount = EL0.Max; 4428 if (EL0.Exact == EL1.Exact) 4429 BECount = EL0.Exact; 4430 } 4431 4432 return ExitLimit(BECount, MaxBECount); 4433 } 4434 } 4435 4436 // With an icmp, it may be feasible to compute an exact backedge-taken count. 4437 // Proceed to the next level to examine the icmp. 4438 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 4439 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB); 4440 4441 // Check for a constant condition. These are normally stripped out by 4442 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 4443 // preserve the CFG and is temporarily leaving constant conditions 4444 // in place. 4445 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 4446 if (L->contains(FBB) == !CI->getZExtValue()) 4447 // The backedge is always taken. 4448 return getCouldNotCompute(); 4449 else 4450 // The backedge is never taken. 4451 return getConstant(CI->getType(), 0); 4452 } 4453 4454 // If it's not an integer or pointer comparison then compute it the hard way. 4455 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB)); 4456 } 4457 4458 /// ComputeExitLimitFromICmp - Compute the number of times the 4459 /// backedge of the specified loop will execute if its exit condition 4460 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 4461 ScalarEvolution::ExitLimit 4462 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L, 4463 ICmpInst *ExitCond, 4464 BasicBlock *TBB, 4465 BasicBlock *FBB) { 4466 4467 // If the condition was exit on true, convert the condition to exit on false 4468 ICmpInst::Predicate Cond; 4469 if (!L->contains(FBB)) 4470 Cond = ExitCond->getPredicate(); 4471 else 4472 Cond = ExitCond->getInversePredicate(); 4473 4474 // Handle common loops like: for (X = "string"; *X; ++X) 4475 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 4476 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 4477 ExitLimit ItCnt = 4478 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond); 4479 if (ItCnt.hasAnyInfo()) 4480 return ItCnt; 4481 } 4482 4483 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 4484 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 4485 4486 // Try to evaluate any dependencies out of the loop. 4487 LHS = getSCEVAtScope(LHS, L); 4488 RHS = getSCEVAtScope(RHS, L); 4489 4490 // At this point, we would like to compute how many iterations of the 4491 // loop the predicate will return true for these inputs. 4492 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) { 4493 // If there is a loop-invariant, force it into the RHS. 4494 std::swap(LHS, RHS); 4495 Cond = ICmpInst::getSwappedPredicate(Cond); 4496 } 4497 4498 // Simplify the operands before analyzing them. 4499 (void)SimplifyICmpOperands(Cond, LHS, RHS); 4500 4501 // If we have a comparison of a chrec against a constant, try to use value 4502 // ranges to answer this query. 4503 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 4504 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 4505 if (AddRec->getLoop() == L) { 4506 // Form the constant range. 4507 ConstantRange CompRange( 4508 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 4509 4510 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 4511 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 4512 } 4513 4514 switch (Cond) { 4515 case ICmpInst::ICMP_NE: { // while (X != Y) 4516 // Convert to: while (X-Y != 0) 4517 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L); 4518 if (EL.hasAnyInfo()) return EL; 4519 break; 4520 } 4521 case ICmpInst::ICMP_EQ: { // while (X == Y) 4522 // Convert to: while (X-Y == 0) 4523 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 4524 if (EL.hasAnyInfo()) return EL; 4525 break; 4526 } 4527 case ICmpInst::ICMP_SLT: { 4528 ExitLimit EL = HowManyLessThans(LHS, RHS, L, true); 4529 if (EL.hasAnyInfo()) return EL; 4530 break; 4531 } 4532 case ICmpInst::ICMP_SGT: { 4533 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS), 4534 getNotSCEV(RHS), L, true); 4535 if (EL.hasAnyInfo()) return EL; 4536 break; 4537 } 4538 case ICmpInst::ICMP_ULT: { 4539 ExitLimit EL = HowManyLessThans(LHS, RHS, L, false); 4540 if (EL.hasAnyInfo()) return EL; 4541 break; 4542 } 4543 case ICmpInst::ICMP_UGT: { 4544 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS), 4545 getNotSCEV(RHS), L, false); 4546 if (EL.hasAnyInfo()) return EL; 4547 break; 4548 } 4549 default: 4550 #if 0 4551 dbgs() << "ComputeBackedgeTakenCount "; 4552 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 4553 dbgs() << "[unsigned] "; 4554 dbgs() << *LHS << " " 4555 << Instruction::getOpcodeName(Instruction::ICmp) 4556 << " " << *RHS << "\n"; 4557 #endif 4558 break; 4559 } 4560 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB)); 4561 } 4562 4563 static ConstantInt * 4564 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 4565 ScalarEvolution &SE) { 4566 const SCEV *InVal = SE.getConstant(C); 4567 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 4568 assert(isa<SCEVConstant>(Val) && 4569 "Evaluation of SCEV at constant didn't fold correctly?"); 4570 return cast<SCEVConstant>(Val)->getValue(); 4571 } 4572 4573 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of 4574 /// 'icmp op load X, cst', try to see if we can compute the backedge 4575 /// execution count. 4576 ScalarEvolution::ExitLimit 4577 ScalarEvolution::ComputeLoadConstantCompareExitLimit( 4578 LoadInst *LI, 4579 Constant *RHS, 4580 const Loop *L, 4581 ICmpInst::Predicate predicate) { 4582 4583 if (LI->isVolatile()) return getCouldNotCompute(); 4584 4585 // Check to see if the loaded pointer is a getelementptr of a global. 4586 // TODO: Use SCEV instead of manually grubbing with GEPs. 4587 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 4588 if (!GEP) return getCouldNotCompute(); 4589 4590 // Make sure that it is really a constant global we are gepping, with an 4591 // initializer, and make sure the first IDX is really 0. 4592 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 4593 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 4594 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 4595 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 4596 return getCouldNotCompute(); 4597 4598 // Okay, we allow one non-constant index into the GEP instruction. 4599 Value *VarIdx = 0; 4600 std::vector<Constant*> Indexes; 4601 unsigned VarIdxNum = 0; 4602 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 4603 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 4604 Indexes.push_back(CI); 4605 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 4606 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 4607 VarIdx = GEP->getOperand(i); 4608 VarIdxNum = i-2; 4609 Indexes.push_back(0); 4610 } 4611 4612 // Loop-invariant loads may be a byproduct of loop optimization. Skip them. 4613 if (!VarIdx) 4614 return getCouldNotCompute(); 4615 4616 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 4617 // Check to see if X is a loop variant variable value now. 4618 const SCEV *Idx = getSCEV(VarIdx); 4619 Idx = getSCEVAtScope(Idx, L); 4620 4621 // We can only recognize very limited forms of loop index expressions, in 4622 // particular, only affine AddRec's like {C1,+,C2}. 4623 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 4624 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) || 4625 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 4626 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 4627 return getCouldNotCompute(); 4628 4629 unsigned MaxSteps = MaxBruteForceIterations; 4630 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 4631 ConstantInt *ItCst = ConstantInt::get( 4632 cast<IntegerType>(IdxExpr->getType()), IterationNum); 4633 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 4634 4635 // Form the GEP offset. 4636 Indexes[VarIdxNum] = Val; 4637 4638 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(), 4639 Indexes); 4640 if (Result == 0) break; // Cannot compute! 4641 4642 // Evaluate the condition for this iteration. 4643 Result = ConstantExpr::getICmp(predicate, Result, RHS); 4644 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 4645 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 4646 #if 0 4647 dbgs() << "\n***\n*** Computed loop count " << *ItCst 4648 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 4649 << "***\n"; 4650 #endif 4651 ++NumArrayLenItCounts; 4652 return getConstant(ItCst); // Found terminating iteration! 4653 } 4654 } 4655 return getCouldNotCompute(); 4656 } 4657 4658 4659 /// CanConstantFold - Return true if we can constant fold an instruction of the 4660 /// specified type, assuming that all operands were constants. 4661 static bool CanConstantFold(const Instruction *I) { 4662 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 4663 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) || 4664 isa<LoadInst>(I)) 4665 return true; 4666 4667 if (const CallInst *CI = dyn_cast<CallInst>(I)) 4668 if (const Function *F = CI->getCalledFunction()) 4669 return canConstantFoldCallTo(F); 4670 return false; 4671 } 4672 4673 /// Determine whether this instruction can constant evolve within this loop 4674 /// assuming its operands can all constant evolve. 4675 static bool canConstantEvolve(Instruction *I, const Loop *L) { 4676 // An instruction outside of the loop can't be derived from a loop PHI. 4677 if (!L->contains(I)) return false; 4678 4679 if (isa<PHINode>(I)) { 4680 if (L->getHeader() == I->getParent()) 4681 return true; 4682 else 4683 // We don't currently keep track of the control flow needed to evaluate 4684 // PHIs, so we cannot handle PHIs inside of loops. 4685 return false; 4686 } 4687 4688 // If we won't be able to constant fold this expression even if the operands 4689 // are constants, bail early. 4690 return CanConstantFold(I); 4691 } 4692 4693 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by 4694 /// recursing through each instruction operand until reaching a loop header phi. 4695 static PHINode * 4696 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L, 4697 DenseMap<Instruction *, PHINode *> &PHIMap) { 4698 4699 // Otherwise, we can evaluate this instruction if all of its operands are 4700 // constant or derived from a PHI node themselves. 4701 PHINode *PHI = 0; 4702 for (Instruction::op_iterator OpI = UseInst->op_begin(), 4703 OpE = UseInst->op_end(); OpI != OpE; ++OpI) { 4704 4705 if (isa<Constant>(*OpI)) continue; 4706 4707 Instruction *OpInst = dyn_cast<Instruction>(*OpI); 4708 if (!OpInst || !canConstantEvolve(OpInst, L)) return 0; 4709 4710 PHINode *P = dyn_cast<PHINode>(OpInst); 4711 if (!P) 4712 // If this operand is already visited, reuse the prior result. 4713 // We may have P != PHI if this is the deepest point at which the 4714 // inconsistent paths meet. 4715 P = PHIMap.lookup(OpInst); 4716 if (!P) { 4717 // Recurse and memoize the results, whether a phi is found or not. 4718 // This recursive call invalidates pointers into PHIMap. 4719 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap); 4720 PHIMap[OpInst] = P; 4721 } 4722 if (P == 0) return 0; // Not evolving from PHI 4723 if (PHI && PHI != P) return 0; // Evolving from multiple different PHIs. 4724 PHI = P; 4725 } 4726 // This is a expression evolving from a constant PHI! 4727 return PHI; 4728 } 4729 4730 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 4731 /// in the loop that V is derived from. We allow arbitrary operations along the 4732 /// way, but the operands of an operation must either be constants or a value 4733 /// derived from a constant PHI. If this expression does not fit with these 4734 /// constraints, return null. 4735 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 4736 Instruction *I = dyn_cast<Instruction>(V); 4737 if (I == 0 || !canConstantEvolve(I, L)) return 0; 4738 4739 if (PHINode *PN = dyn_cast<PHINode>(I)) { 4740 return PN; 4741 } 4742 4743 // Record non-constant instructions contained by the loop. 4744 DenseMap<Instruction *, PHINode *> PHIMap; 4745 return getConstantEvolvingPHIOperands(I, L, PHIMap); 4746 } 4747 4748 /// EvaluateExpression - Given an expression that passes the 4749 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4750 /// in the loop has the value PHIVal. If we can't fold this expression for some 4751 /// reason, return null. 4752 static Constant *EvaluateExpression(Value *V, const Loop *L, 4753 DenseMap<Instruction *, Constant *> &Vals, 4754 const TargetData *TD, 4755 const TargetLibraryInfo *TLI) { 4756 // Convenient constant check, but redundant for recursive calls. 4757 if (Constant *C = dyn_cast<Constant>(V)) return C; 4758 Instruction *I = dyn_cast<Instruction>(V); 4759 if (!I) return 0; 4760 4761 if (Constant *C = Vals.lookup(I)) return C; 4762 4763 // An instruction inside the loop depends on a value outside the loop that we 4764 // weren't given a mapping for, or a value such as a call inside the loop. 4765 if (!canConstantEvolve(I, L)) return 0; 4766 4767 // An unmapped PHI can be due to a branch or another loop inside this loop, 4768 // or due to this not being the initial iteration through a loop where we 4769 // couldn't compute the evolution of this particular PHI last time. 4770 if (isa<PHINode>(I)) return 0; 4771 4772 std::vector<Constant*> Operands(I->getNumOperands()); 4773 4774 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4775 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i)); 4776 if (!Operand) { 4777 Operands[i] = dyn_cast<Constant>(I->getOperand(i)); 4778 if (!Operands[i]) return 0; 4779 continue; 4780 } 4781 Constant *C = EvaluateExpression(Operand, L, Vals, TD, TLI); 4782 Vals[Operand] = C; 4783 if (!C) return 0; 4784 Operands[i] = C; 4785 } 4786 4787 if (CmpInst *CI = dyn_cast<CmpInst>(I)) 4788 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4789 Operands[1], TD, TLI); 4790 if (LoadInst *LI = dyn_cast<LoadInst>(I)) { 4791 if (!LI->isVolatile()) 4792 return ConstantFoldLoadFromConstPtr(Operands[0], TD); 4793 } 4794 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD, 4795 TLI); 4796 } 4797 4798 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4799 /// in the header of its containing loop, we know the loop executes a 4800 /// constant number of times, and the PHI node is just a recurrence 4801 /// involving constants, fold it. 4802 Constant * 4803 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4804 const APInt &BEs, 4805 const Loop *L) { 4806 DenseMap<PHINode*, Constant*>::const_iterator I = 4807 ConstantEvolutionLoopExitValue.find(PN); 4808 if (I != ConstantEvolutionLoopExitValue.end()) 4809 return I->second; 4810 4811 if (BEs.ugt(MaxBruteForceIterations)) 4812 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4813 4814 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4815 4816 DenseMap<Instruction *, Constant *> CurrentIterVals; 4817 BasicBlock *Header = L->getHeader(); 4818 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!"); 4819 4820 // Since the loop is canonicalized, the PHI node must have two entries. One 4821 // entry must be a constant (coming in from outside of the loop), and the 4822 // second must be derived from the same PHI. 4823 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4824 PHINode *PHI = 0; 4825 for (BasicBlock::iterator I = Header->begin(); 4826 (PHI = dyn_cast<PHINode>(I)); ++I) { 4827 Constant *StartCST = 4828 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge)); 4829 if (StartCST == 0) continue; 4830 CurrentIterVals[PHI] = StartCST; 4831 } 4832 if (!CurrentIterVals.count(PN)) 4833 return RetVal = 0; 4834 4835 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4836 4837 // Execute the loop symbolically to determine the exit value. 4838 if (BEs.getActiveBits() >= 32) 4839 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4840 4841 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4842 unsigned IterationNum = 0; 4843 for (; ; ++IterationNum) { 4844 if (IterationNum == NumIterations) 4845 return RetVal = CurrentIterVals[PN]; // Got exit value! 4846 4847 // Compute the value of the PHIs for the next iteration. 4848 // EvaluateExpression adds non-phi values to the CurrentIterVals map. 4849 DenseMap<Instruction *, Constant *> NextIterVals; 4850 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, 4851 TLI); 4852 if (NextPHI == 0) 4853 return 0; // Couldn't evaluate! 4854 NextIterVals[PN] = NextPHI; 4855 4856 bool StoppedEvolving = NextPHI == CurrentIterVals[PN]; 4857 4858 // Also evaluate the other PHI nodes. However, we don't get to stop if we 4859 // cease to be able to evaluate one of them or if they stop evolving, 4860 // because that doesn't necessarily prevent us from computing PN. 4861 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute; 4862 for (DenseMap<Instruction *, Constant *>::const_iterator 4863 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){ 4864 PHINode *PHI = dyn_cast<PHINode>(I->first); 4865 if (!PHI || PHI == PN || PHI->getParent() != Header) continue; 4866 PHIsToCompute.push_back(std::make_pair(PHI, I->second)); 4867 } 4868 // We use two distinct loops because EvaluateExpression may invalidate any 4869 // iterators into CurrentIterVals. 4870 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator 4871 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) { 4872 PHINode *PHI = I->first; 4873 Constant *&NextPHI = NextIterVals[PHI]; 4874 if (!NextPHI) { // Not already computed. 4875 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge); 4876 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI); 4877 } 4878 if (NextPHI != I->second) 4879 StoppedEvolving = false; 4880 } 4881 4882 // If all entries in CurrentIterVals == NextIterVals then we can stop 4883 // iterating, the loop can't continue to change. 4884 if (StoppedEvolving) 4885 return RetVal = CurrentIterVals[PN]; 4886 4887 CurrentIterVals.swap(NextIterVals); 4888 } 4889 } 4890 4891 /// ComputeExitCountExhaustively - If the loop is known to execute a 4892 /// constant number of times (the condition evolves only from constants), 4893 /// try to evaluate a few iterations of the loop until we get the exit 4894 /// condition gets a value of ExitWhen (true or false). If we cannot 4895 /// evaluate the trip count of the loop, return getCouldNotCompute(). 4896 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L, 4897 Value *Cond, 4898 bool ExitWhen) { 4899 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4900 if (PN == 0) return getCouldNotCompute(); 4901 4902 // If the loop is canonicalized, the PHI will have exactly two entries. 4903 // That's the only form we support here. 4904 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 4905 4906 DenseMap<Instruction *, Constant *> CurrentIterVals; 4907 BasicBlock *Header = L->getHeader(); 4908 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!"); 4909 4910 // One entry must be a constant (coming in from outside of the loop), and the 4911 // second must be derived from the same PHI. 4912 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4913 PHINode *PHI = 0; 4914 for (BasicBlock::iterator I = Header->begin(); 4915 (PHI = dyn_cast<PHINode>(I)); ++I) { 4916 Constant *StartCST = 4917 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge)); 4918 if (StartCST == 0) continue; 4919 CurrentIterVals[PHI] = StartCST; 4920 } 4921 if (!CurrentIterVals.count(PN)) 4922 return getCouldNotCompute(); 4923 4924 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4925 // the loop symbolically to determine when the condition gets a value of 4926 // "ExitWhen". 4927 4928 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4929 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){ 4930 ConstantInt *CondVal = 4931 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals, 4932 TD, TLI)); 4933 4934 // Couldn't symbolically evaluate. 4935 if (!CondVal) return getCouldNotCompute(); 4936 4937 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4938 ++NumBruteForceTripCountsComputed; 4939 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4940 } 4941 4942 // Update all the PHI nodes for the next iteration. 4943 DenseMap<Instruction *, Constant *> NextIterVals; 4944 4945 // Create a list of which PHIs we need to compute. We want to do this before 4946 // calling EvaluateExpression on them because that may invalidate iterators 4947 // into CurrentIterVals. 4948 SmallVector<PHINode *, 8> PHIsToCompute; 4949 for (DenseMap<Instruction *, Constant *>::const_iterator 4950 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){ 4951 PHINode *PHI = dyn_cast<PHINode>(I->first); 4952 if (!PHI || PHI->getParent() != Header) continue; 4953 PHIsToCompute.push_back(PHI); 4954 } 4955 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(), 4956 E = PHIsToCompute.end(); I != E; ++I) { 4957 PHINode *PHI = *I; 4958 Constant *&NextPHI = NextIterVals[PHI]; 4959 if (NextPHI) continue; // Already computed! 4960 4961 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge); 4962 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI); 4963 } 4964 CurrentIterVals.swap(NextIterVals); 4965 } 4966 4967 // Too many iterations were needed to evaluate. 4968 return getCouldNotCompute(); 4969 } 4970 4971 /// getSCEVAtScope - Return a SCEV expression for the specified value 4972 /// at the specified scope in the program. The L value specifies a loop 4973 /// nest to evaluate the expression at, where null is the top-level or a 4974 /// specified loop is immediately inside of the loop. 4975 /// 4976 /// This method can be used to compute the exit value for a variable defined 4977 /// in a loop by querying what the value will hold in the parent loop. 4978 /// 4979 /// In the case that a relevant loop exit value cannot be computed, the 4980 /// original value V is returned. 4981 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4982 // Check to see if we've folded this expression at this loop before. 4983 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4984 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4985 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4986 if (!Pair.second) 4987 return Pair.first->second ? Pair.first->second : V; 4988 4989 // Otherwise compute it. 4990 const SCEV *C = computeSCEVAtScope(V, L); 4991 ValuesAtScopes[V][L] = C; 4992 return C; 4993 } 4994 4995 /// This builds up a Constant using the ConstantExpr interface. That way, we 4996 /// will return Constants for objects which aren't represented by a 4997 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt. 4998 /// Returns NULL if the SCEV isn't representable as a Constant. 4999 static Constant *BuildConstantFromSCEV(const SCEV *V) { 5000 switch (V->getSCEVType()) { 5001 default: // TODO: smax, umax. 5002 case scCouldNotCompute: 5003 case scAddRecExpr: 5004 break; 5005 case scConstant: 5006 return cast<SCEVConstant>(V)->getValue(); 5007 case scUnknown: 5008 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue()); 5009 case scSignExtend: { 5010 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V); 5011 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand())) 5012 return ConstantExpr::getSExt(CastOp, SS->getType()); 5013 break; 5014 } 5015 case scZeroExtend: { 5016 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V); 5017 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand())) 5018 return ConstantExpr::getZExt(CastOp, SZ->getType()); 5019 break; 5020 } 5021 case scTruncate: { 5022 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V); 5023 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand())) 5024 return ConstantExpr::getTrunc(CastOp, ST->getType()); 5025 break; 5026 } 5027 case scAddExpr: { 5028 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V); 5029 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) { 5030 if (C->getType()->isPointerTy()) 5031 C = ConstantExpr::getBitCast(C, Type::getInt8PtrTy(C->getContext())); 5032 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) { 5033 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i)); 5034 if (!C2) return 0; 5035 5036 // First pointer! 5037 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) { 5038 std::swap(C, C2); 5039 // The offsets have been converted to bytes. We can add bytes to an 5040 // i8* by GEP with the byte count in the first index. 5041 C = ConstantExpr::getBitCast(C,Type::getInt8PtrTy(C->getContext())); 5042 } 5043 5044 // Don't bother trying to sum two pointers. We probably can't 5045 // statically compute a load that results from it anyway. 5046 if (C2->getType()->isPointerTy()) 5047 return 0; 5048 5049 if (C->getType()->isPointerTy()) { 5050 if (cast<PointerType>(C->getType())->getElementType()->isStructTy()) 5051 C2 = ConstantExpr::getIntegerCast( 5052 C2, Type::getInt32Ty(C->getContext()), true); 5053 C = ConstantExpr::getGetElementPtr(C, C2); 5054 } else 5055 C = ConstantExpr::getAdd(C, C2); 5056 } 5057 return C; 5058 } 5059 break; 5060 } 5061 case scMulExpr: { 5062 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V); 5063 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) { 5064 // Don't bother with pointers at all. 5065 if (C->getType()->isPointerTy()) return 0; 5066 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) { 5067 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i)); 5068 if (!C2 || C2->getType()->isPointerTy()) return 0; 5069 C = ConstantExpr::getMul(C, C2); 5070 } 5071 return C; 5072 } 5073 break; 5074 } 5075 case scUDivExpr: { 5076 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V); 5077 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS())) 5078 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS())) 5079 if (LHS->getType() == RHS->getType()) 5080 return ConstantExpr::getUDiv(LHS, RHS); 5081 break; 5082 } 5083 } 5084 return 0; 5085 } 5086 5087 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 5088 if (isa<SCEVConstant>(V)) return V; 5089 5090 // If this instruction is evolved from a constant-evolving PHI, compute the 5091 // exit value from the loop without using SCEVs. 5092 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 5093 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 5094 const Loop *LI = (*this->LI)[I->getParent()]; 5095 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 5096 if (PHINode *PN = dyn_cast<PHINode>(I)) 5097 if (PN->getParent() == LI->getHeader()) { 5098 // Okay, there is no closed form solution for the PHI node. Check 5099 // to see if the loop that contains it has a known backedge-taken 5100 // count. If so, we may be able to force computation of the exit 5101 // value. 5102 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 5103 if (const SCEVConstant *BTCC = 5104 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 5105 // Okay, we know how many times the containing loop executes. If 5106 // this is a constant evolving PHI node, get the final value at 5107 // the specified iteration number. 5108 Constant *RV = getConstantEvolutionLoopExitValue(PN, 5109 BTCC->getValue()->getValue(), 5110 LI); 5111 if (RV) return getSCEV(RV); 5112 } 5113 } 5114 5115 // Okay, this is an expression that we cannot symbolically evaluate 5116 // into a SCEV. Check to see if it's possible to symbolically evaluate 5117 // the arguments into constants, and if so, try to constant propagate the 5118 // result. This is particularly useful for computing loop exit values. 5119 if (CanConstantFold(I)) { 5120 SmallVector<Constant *, 4> Operands; 5121 bool MadeImprovement = false; 5122 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 5123 Value *Op = I->getOperand(i); 5124 if (Constant *C = dyn_cast<Constant>(Op)) { 5125 Operands.push_back(C); 5126 continue; 5127 } 5128 5129 // If any of the operands is non-constant and if they are 5130 // non-integer and non-pointer, don't even try to analyze them 5131 // with scev techniques. 5132 if (!isSCEVable(Op->getType())) 5133 return V; 5134 5135 const SCEV *OrigV = getSCEV(Op); 5136 const SCEV *OpV = getSCEVAtScope(OrigV, L); 5137 MadeImprovement |= OrigV != OpV; 5138 5139 Constant *C = BuildConstantFromSCEV(OpV); 5140 if (!C) return V; 5141 if (C->getType() != Op->getType()) 5142 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 5143 Op->getType(), 5144 false), 5145 C, Op->getType()); 5146 Operands.push_back(C); 5147 } 5148 5149 // Check to see if getSCEVAtScope actually made an improvement. 5150 if (MadeImprovement) { 5151 Constant *C = 0; 5152 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 5153 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 5154 Operands[0], Operands[1], TD, 5155 TLI); 5156 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) { 5157 if (!LI->isVolatile()) 5158 C = ConstantFoldLoadFromConstPtr(Operands[0], TD); 5159 } else 5160 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 5161 Operands, TD, TLI); 5162 if (!C) return V; 5163 return getSCEV(C); 5164 } 5165 } 5166 } 5167 5168 // This is some other type of SCEVUnknown, just return it. 5169 return V; 5170 } 5171 5172 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 5173 // Avoid performing the look-up in the common case where the specified 5174 // expression has no loop-variant portions. 5175 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 5176 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 5177 if (OpAtScope != Comm->getOperand(i)) { 5178 // Okay, at least one of these operands is loop variant but might be 5179 // foldable. Build a new instance of the folded commutative expression. 5180 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 5181 Comm->op_begin()+i); 5182 NewOps.push_back(OpAtScope); 5183 5184 for (++i; i != e; ++i) { 5185 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 5186 NewOps.push_back(OpAtScope); 5187 } 5188 if (isa<SCEVAddExpr>(Comm)) 5189 return getAddExpr(NewOps); 5190 if (isa<SCEVMulExpr>(Comm)) 5191 return getMulExpr(NewOps); 5192 if (isa<SCEVSMaxExpr>(Comm)) 5193 return getSMaxExpr(NewOps); 5194 if (isa<SCEVUMaxExpr>(Comm)) 5195 return getUMaxExpr(NewOps); 5196 llvm_unreachable("Unknown commutative SCEV type!"); 5197 } 5198 } 5199 // If we got here, all operands are loop invariant. 5200 return Comm; 5201 } 5202 5203 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 5204 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 5205 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 5206 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 5207 return Div; // must be loop invariant 5208 return getUDivExpr(LHS, RHS); 5209 } 5210 5211 // If this is a loop recurrence for a loop that does not contain L, then we 5212 // are dealing with the final value computed by the loop. 5213 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 5214 // First, attempt to evaluate each operand. 5215 // Avoid performing the look-up in the common case where the specified 5216 // expression has no loop-variant portions. 5217 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 5218 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); 5219 if (OpAtScope == AddRec->getOperand(i)) 5220 continue; 5221 5222 // Okay, at least one of these operands is loop variant but might be 5223 // foldable. Build a new instance of the folded commutative expression. 5224 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(), 5225 AddRec->op_begin()+i); 5226 NewOps.push_back(OpAtScope); 5227 for (++i; i != e; ++i) 5228 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); 5229 5230 const SCEV *FoldedRec = 5231 getAddRecExpr(NewOps, AddRec->getLoop(), 5232 AddRec->getNoWrapFlags(SCEV::FlagNW)); 5233 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec); 5234 // The addrec may be folded to a nonrecurrence, for example, if the 5235 // induction variable is multiplied by zero after constant folding. Go 5236 // ahead and return the folded value. 5237 if (!AddRec) 5238 return FoldedRec; 5239 break; 5240 } 5241 5242 // If the scope is outside the addrec's loop, evaluate it by using the 5243 // loop exit value of the addrec. 5244 if (!AddRec->getLoop()->contains(L)) { 5245 // To evaluate this recurrence, we need to know how many times the AddRec 5246 // loop iterates. Compute this now. 5247 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 5248 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 5249 5250 // Then, evaluate the AddRec. 5251 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 5252 } 5253 5254 return AddRec; 5255 } 5256 5257 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 5258 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 5259 if (Op == Cast->getOperand()) 5260 return Cast; // must be loop invariant 5261 return getZeroExtendExpr(Op, Cast->getType()); 5262 } 5263 5264 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 5265 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 5266 if (Op == Cast->getOperand()) 5267 return Cast; // must be loop invariant 5268 return getSignExtendExpr(Op, Cast->getType()); 5269 } 5270 5271 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 5272 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 5273 if (Op == Cast->getOperand()) 5274 return Cast; // must be loop invariant 5275 return getTruncateExpr(Op, Cast->getType()); 5276 } 5277 5278 llvm_unreachable("Unknown SCEV type!"); 5279 } 5280 5281 /// getSCEVAtScope - This is a convenience function which does 5282 /// getSCEVAtScope(getSCEV(V), L). 5283 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 5284 return getSCEVAtScope(getSCEV(V), L); 5285 } 5286 5287 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 5288 /// following equation: 5289 /// 5290 /// A * X = B (mod N) 5291 /// 5292 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of 5293 /// A and B isn't important. 5294 /// 5295 /// If the equation does not have a solution, SCEVCouldNotCompute is returned. 5296 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 5297 ScalarEvolution &SE) { 5298 uint32_t BW = A.getBitWidth(); 5299 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 5300 assert(A != 0 && "A must be non-zero."); 5301 5302 // 1. D = gcd(A, N) 5303 // 5304 // The gcd of A and N may have only one prime factor: 2. The number of 5305 // trailing zeros in A is its multiplicity 5306 uint32_t Mult2 = A.countTrailingZeros(); 5307 // D = 2^Mult2 5308 5309 // 2. Check if B is divisible by D. 5310 // 5311 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 5312 // is not less than multiplicity of this prime factor for D. 5313 if (B.countTrailingZeros() < Mult2) 5314 return SE.getCouldNotCompute(); 5315 5316 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 5317 // modulo (N / D). 5318 // 5319 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 5320 // bit width during computations. 5321 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 5322 APInt Mod(BW + 1, 0); 5323 Mod.setBit(BW - Mult2); // Mod = N / D 5324 APInt I = AD.multiplicativeInverse(Mod); 5325 5326 // 4. Compute the minimum unsigned root of the equation: 5327 // I * (B / D) mod (N / D) 5328 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 5329 5330 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 5331 // bits. 5332 return SE.getConstant(Result.trunc(BW)); 5333 } 5334 5335 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the 5336 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 5337 /// might be the same) or two SCEVCouldNotCompute objects. 5338 /// 5339 static std::pair<const SCEV *,const SCEV *> 5340 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 5341 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 5342 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 5343 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 5344 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 5345 5346 // We currently can only solve this if the coefficients are constants. 5347 if (!LC || !MC || !NC) { 5348 const SCEV *CNC = SE.getCouldNotCompute(); 5349 return std::make_pair(CNC, CNC); 5350 } 5351 5352 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 5353 const APInt &L = LC->getValue()->getValue(); 5354 const APInt &M = MC->getValue()->getValue(); 5355 const APInt &N = NC->getValue()->getValue(); 5356 APInt Two(BitWidth, 2); 5357 APInt Four(BitWidth, 4); 5358 5359 { 5360 using namespace APIntOps; 5361 const APInt& C = L; 5362 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 5363 // The B coefficient is M-N/2 5364 APInt B(M); 5365 B -= sdiv(N,Two); 5366 5367 // The A coefficient is N/2 5368 APInt A(N.sdiv(Two)); 5369 5370 // Compute the B^2-4ac term. 5371 APInt SqrtTerm(B); 5372 SqrtTerm *= B; 5373 SqrtTerm -= Four * (A * C); 5374 5375 if (SqrtTerm.isNegative()) { 5376 // The loop is provably infinite. 5377 const SCEV *CNC = SE.getCouldNotCompute(); 5378 return std::make_pair(CNC, CNC); 5379 } 5380 5381 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 5382 // integer value or else APInt::sqrt() will assert. 5383 APInt SqrtVal(SqrtTerm.sqrt()); 5384 5385 // Compute the two solutions for the quadratic formula. 5386 // The divisions must be performed as signed divisions. 5387 APInt NegB(-B); 5388 APInt TwoA(A << 1); 5389 if (TwoA.isMinValue()) { 5390 const SCEV *CNC = SE.getCouldNotCompute(); 5391 return std::make_pair(CNC, CNC); 5392 } 5393 5394 LLVMContext &Context = SE.getContext(); 5395 5396 ConstantInt *Solution1 = 5397 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 5398 ConstantInt *Solution2 = 5399 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 5400 5401 return std::make_pair(SE.getConstant(Solution1), 5402 SE.getConstant(Solution2)); 5403 } // end APIntOps namespace 5404 } 5405 5406 /// HowFarToZero - Return the number of times a backedge comparing the specified 5407 /// value to zero will execute. If not computable, return CouldNotCompute. 5408 /// 5409 /// This is only used for loops with a "x != y" exit test. The exit condition is 5410 /// now expressed as a single expression, V = x-y. So the exit test is 5411 /// effectively V != 0. We know and take advantage of the fact that this 5412 /// expression only being used in a comparison by zero context. 5413 ScalarEvolution::ExitLimit 5414 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 5415 // If the value is a constant 5416 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 5417 // If the value is already zero, the branch will execute zero times. 5418 if (C->getValue()->isZero()) return C; 5419 return getCouldNotCompute(); // Otherwise it will loop infinitely. 5420 } 5421 5422 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 5423 if (!AddRec || AddRec->getLoop() != L) 5424 return getCouldNotCompute(); 5425 5426 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 5427 // the quadratic equation to solve it. 5428 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 5429 std::pair<const SCEV *,const SCEV *> Roots = 5430 SolveQuadraticEquation(AddRec, *this); 5431 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5432 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5433 if (R1 && R2) { 5434 #if 0 5435 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 5436 << " sol#2: " << *R2 << "\n"; 5437 #endif 5438 // Pick the smallest positive root value. 5439 if (ConstantInt *CB = 5440 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT, 5441 R1->getValue(), 5442 R2->getValue()))) { 5443 if (CB->getZExtValue() == false) 5444 std::swap(R1, R2); // R1 is the minimum root now. 5445 5446 // We can only use this value if the chrec ends up with an exact zero 5447 // value at this index. When solving for "X*X != 5", for example, we 5448 // should not accept a root of 2. 5449 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 5450 if (Val->isZero()) 5451 return R1; // We found a quadratic root! 5452 } 5453 } 5454 return getCouldNotCompute(); 5455 } 5456 5457 // Otherwise we can only handle this if it is affine. 5458 if (!AddRec->isAffine()) 5459 return getCouldNotCompute(); 5460 5461 // If this is an affine expression, the execution count of this branch is 5462 // the minimum unsigned root of the following equation: 5463 // 5464 // Start + Step*N = 0 (mod 2^BW) 5465 // 5466 // equivalent to: 5467 // 5468 // Step*N = -Start (mod 2^BW) 5469 // 5470 // where BW is the common bit width of Start and Step. 5471 5472 // Get the initial value for the loop. 5473 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 5474 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 5475 5476 // For now we handle only constant steps. 5477 // 5478 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the 5479 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap 5480 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step. 5481 // We have not yet seen any such cases. 5482 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step); 5483 if (StepC == 0 || StepC->getValue()->equalsInt(0)) 5484 return getCouldNotCompute(); 5485 5486 // For positive steps (counting up until unsigned overflow): 5487 // N = -Start/Step (as unsigned) 5488 // For negative steps (counting down to zero): 5489 // N = Start/-Step 5490 // First compute the unsigned distance from zero in the direction of Step. 5491 bool CountDown = StepC->getValue()->getValue().isNegative(); 5492 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start); 5493 5494 // Handle unitary steps, which cannot wraparound. 5495 // 1*N = -Start; -1*N = Start (mod 2^BW), so: 5496 // N = Distance (as unsigned) 5497 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) { 5498 ConstantRange CR = getUnsignedRange(Start); 5499 const SCEV *MaxBECount; 5500 if (!CountDown && CR.getUnsignedMin().isMinValue()) 5501 // When counting up, the worst starting value is 1, not 0. 5502 MaxBECount = CR.getUnsignedMax().isMinValue() 5503 ? getConstant(APInt::getMinValue(CR.getBitWidth())) 5504 : getConstant(APInt::getMaxValue(CR.getBitWidth())); 5505 else 5506 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax() 5507 : -CR.getUnsignedMin()); 5508 return ExitLimit(Distance, MaxBECount); 5509 } 5510 5511 // If the recurrence is known not to wraparound, unsigned divide computes the 5512 // back edge count. We know that the value will either become zero (and thus 5513 // the loop terminates), that the loop will terminate through some other exit 5514 // condition first, or that the loop has undefined behavior. This means 5515 // we can't "miss" the exit value, even with nonunit stride. 5516 // 5517 // FIXME: Prove that loops always exhibits *acceptable* undefined 5518 // behavior. Loops must exhibit defined behavior until a wrapped value is 5519 // actually used. So the trip count computed by udiv could be smaller than the 5520 // number of well-defined iterations. 5521 if (AddRec->getNoWrapFlags(SCEV::FlagNW)) { 5522 // FIXME: We really want an "isexact" bit for udiv. 5523 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step); 5524 } 5525 // Then, try to solve the above equation provided that Start is constant. 5526 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 5527 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 5528 -StartC->getValue()->getValue(), 5529 *this); 5530 return getCouldNotCompute(); 5531 } 5532 5533 /// HowFarToNonZero - Return the number of times a backedge checking the 5534 /// specified value for nonzero will execute. If not computable, return 5535 /// CouldNotCompute 5536 ScalarEvolution::ExitLimit 5537 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 5538 // Loops that look like: while (X == 0) are very strange indeed. We don't 5539 // handle them yet except for the trivial case. This could be expanded in the 5540 // future as needed. 5541 5542 // If the value is a constant, check to see if it is known to be non-zero 5543 // already. If so, the backedge will execute zero times. 5544 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 5545 if (!C->getValue()->isNullValue()) 5546 return getConstant(C->getType(), 0); 5547 return getCouldNotCompute(); // Otherwise it will loop infinitely. 5548 } 5549 5550 // We could implement others, but I really doubt anyone writes loops like 5551 // this, and if they did, they would already be constant folded. 5552 return getCouldNotCompute(); 5553 } 5554 5555 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 5556 /// (which may not be an immediate predecessor) which has exactly one 5557 /// successor from which BB is reachable, or null if no such block is 5558 /// found. 5559 /// 5560 std::pair<BasicBlock *, BasicBlock *> 5561 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 5562 // If the block has a unique predecessor, then there is no path from the 5563 // predecessor to the block that does not go through the direct edge 5564 // from the predecessor to the block. 5565 if (BasicBlock *Pred = BB->getSinglePredecessor()) 5566 return std::make_pair(Pred, BB); 5567 5568 // A loop's header is defined to be a block that dominates the loop. 5569 // If the header has a unique predecessor outside the loop, it must be 5570 // a block that has exactly one successor that can reach the loop. 5571 if (Loop *L = LI->getLoopFor(BB)) 5572 return std::make_pair(L->getLoopPredecessor(), L->getHeader()); 5573 5574 return std::pair<BasicBlock *, BasicBlock *>(); 5575 } 5576 5577 /// HasSameValue - SCEV structural equivalence is usually sufficient for 5578 /// testing whether two expressions are equal, however for the purposes of 5579 /// looking for a condition guarding a loop, it can be useful to be a little 5580 /// more general, since a front-end may have replicated the controlling 5581 /// expression. 5582 /// 5583 static bool HasSameValue(const SCEV *A, const SCEV *B) { 5584 // Quick check to see if they are the same SCEV. 5585 if (A == B) return true; 5586 5587 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 5588 // two different instructions with the same value. Check for this case. 5589 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 5590 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 5591 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 5592 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 5593 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 5594 return true; 5595 5596 // Otherwise assume they may have a different value. 5597 return false; 5598 } 5599 5600 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with 5601 /// predicate Pred. Return true iff any changes were made. 5602 /// 5603 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 5604 const SCEV *&LHS, const SCEV *&RHS, 5605 unsigned Depth) { 5606 bool Changed = false; 5607 5608 // If we hit the max recursion limit bail out. 5609 if (Depth >= 3) 5610 return false; 5611 5612 // Canonicalize a constant to the right side. 5613 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 5614 // Check for both operands constant. 5615 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 5616 if (ConstantExpr::getICmp(Pred, 5617 LHSC->getValue(), 5618 RHSC->getValue())->isNullValue()) 5619 goto trivially_false; 5620 else 5621 goto trivially_true; 5622 } 5623 // Otherwise swap the operands to put the constant on the right. 5624 std::swap(LHS, RHS); 5625 Pred = ICmpInst::getSwappedPredicate(Pred); 5626 Changed = true; 5627 } 5628 5629 // If we're comparing an addrec with a value which is loop-invariant in the 5630 // addrec's loop, put the addrec on the left. Also make a dominance check, 5631 // as both operands could be addrecs loop-invariant in each other's loop. 5632 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 5633 const Loop *L = AR->getLoop(); 5634 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) { 5635 std::swap(LHS, RHS); 5636 Pred = ICmpInst::getSwappedPredicate(Pred); 5637 Changed = true; 5638 } 5639 } 5640 5641 // If there's a constant operand, canonicalize comparisons with boundary 5642 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 5643 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 5644 const APInt &RA = RC->getValue()->getValue(); 5645 switch (Pred) { 5646 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5647 case ICmpInst::ICMP_EQ: 5648 case ICmpInst::ICMP_NE: 5649 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b. 5650 if (!RA) 5651 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS)) 5652 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0))) 5653 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 && 5654 ME->getOperand(0)->isAllOnesValue()) { 5655 RHS = AE->getOperand(1); 5656 LHS = ME->getOperand(1); 5657 Changed = true; 5658 } 5659 break; 5660 case ICmpInst::ICMP_UGE: 5661 if ((RA - 1).isMinValue()) { 5662 Pred = ICmpInst::ICMP_NE; 5663 RHS = getConstant(RA - 1); 5664 Changed = true; 5665 break; 5666 } 5667 if (RA.isMaxValue()) { 5668 Pred = ICmpInst::ICMP_EQ; 5669 Changed = true; 5670 break; 5671 } 5672 if (RA.isMinValue()) goto trivially_true; 5673 5674 Pred = ICmpInst::ICMP_UGT; 5675 RHS = getConstant(RA - 1); 5676 Changed = true; 5677 break; 5678 case ICmpInst::ICMP_ULE: 5679 if ((RA + 1).isMaxValue()) { 5680 Pred = ICmpInst::ICMP_NE; 5681 RHS = getConstant(RA + 1); 5682 Changed = true; 5683 break; 5684 } 5685 if (RA.isMinValue()) { 5686 Pred = ICmpInst::ICMP_EQ; 5687 Changed = true; 5688 break; 5689 } 5690 if (RA.isMaxValue()) goto trivially_true; 5691 5692 Pred = ICmpInst::ICMP_ULT; 5693 RHS = getConstant(RA + 1); 5694 Changed = true; 5695 break; 5696 case ICmpInst::ICMP_SGE: 5697 if ((RA - 1).isMinSignedValue()) { 5698 Pred = ICmpInst::ICMP_NE; 5699 RHS = getConstant(RA - 1); 5700 Changed = true; 5701 break; 5702 } 5703 if (RA.isMaxSignedValue()) { 5704 Pred = ICmpInst::ICMP_EQ; 5705 Changed = true; 5706 break; 5707 } 5708 if (RA.isMinSignedValue()) goto trivially_true; 5709 5710 Pred = ICmpInst::ICMP_SGT; 5711 RHS = getConstant(RA - 1); 5712 Changed = true; 5713 break; 5714 case ICmpInst::ICMP_SLE: 5715 if ((RA + 1).isMaxSignedValue()) { 5716 Pred = ICmpInst::ICMP_NE; 5717 RHS = getConstant(RA + 1); 5718 Changed = true; 5719 break; 5720 } 5721 if (RA.isMinSignedValue()) { 5722 Pred = ICmpInst::ICMP_EQ; 5723 Changed = true; 5724 break; 5725 } 5726 if (RA.isMaxSignedValue()) goto trivially_true; 5727 5728 Pred = ICmpInst::ICMP_SLT; 5729 RHS = getConstant(RA + 1); 5730 Changed = true; 5731 break; 5732 case ICmpInst::ICMP_UGT: 5733 if (RA.isMinValue()) { 5734 Pred = ICmpInst::ICMP_NE; 5735 Changed = true; 5736 break; 5737 } 5738 if ((RA + 1).isMaxValue()) { 5739 Pred = ICmpInst::ICMP_EQ; 5740 RHS = getConstant(RA + 1); 5741 Changed = true; 5742 break; 5743 } 5744 if (RA.isMaxValue()) goto trivially_false; 5745 break; 5746 case ICmpInst::ICMP_ULT: 5747 if (RA.isMaxValue()) { 5748 Pred = ICmpInst::ICMP_NE; 5749 Changed = true; 5750 break; 5751 } 5752 if ((RA - 1).isMinValue()) { 5753 Pred = ICmpInst::ICMP_EQ; 5754 RHS = getConstant(RA - 1); 5755 Changed = true; 5756 break; 5757 } 5758 if (RA.isMinValue()) goto trivially_false; 5759 break; 5760 case ICmpInst::ICMP_SGT: 5761 if (RA.isMinSignedValue()) { 5762 Pred = ICmpInst::ICMP_NE; 5763 Changed = true; 5764 break; 5765 } 5766 if ((RA + 1).isMaxSignedValue()) { 5767 Pred = ICmpInst::ICMP_EQ; 5768 RHS = getConstant(RA + 1); 5769 Changed = true; 5770 break; 5771 } 5772 if (RA.isMaxSignedValue()) goto trivially_false; 5773 break; 5774 case ICmpInst::ICMP_SLT: 5775 if (RA.isMaxSignedValue()) { 5776 Pred = ICmpInst::ICMP_NE; 5777 Changed = true; 5778 break; 5779 } 5780 if ((RA - 1).isMinSignedValue()) { 5781 Pred = ICmpInst::ICMP_EQ; 5782 RHS = getConstant(RA - 1); 5783 Changed = true; 5784 break; 5785 } 5786 if (RA.isMinSignedValue()) goto trivially_false; 5787 break; 5788 } 5789 } 5790 5791 // Check for obvious equality. 5792 if (HasSameValue(LHS, RHS)) { 5793 if (ICmpInst::isTrueWhenEqual(Pred)) 5794 goto trivially_true; 5795 if (ICmpInst::isFalseWhenEqual(Pred)) 5796 goto trivially_false; 5797 } 5798 5799 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 5800 // adding or subtracting 1 from one of the operands. 5801 switch (Pred) { 5802 case ICmpInst::ICMP_SLE: 5803 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { 5804 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5805 SCEV::FlagNSW); 5806 Pred = ICmpInst::ICMP_SLT; 5807 Changed = true; 5808 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { 5809 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5810 SCEV::FlagNSW); 5811 Pred = ICmpInst::ICMP_SLT; 5812 Changed = true; 5813 } 5814 break; 5815 case ICmpInst::ICMP_SGE: 5816 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { 5817 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5818 SCEV::FlagNSW); 5819 Pred = ICmpInst::ICMP_SGT; 5820 Changed = true; 5821 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { 5822 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5823 SCEV::FlagNSW); 5824 Pred = ICmpInst::ICMP_SGT; 5825 Changed = true; 5826 } 5827 break; 5828 case ICmpInst::ICMP_ULE: 5829 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { 5830 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5831 SCEV::FlagNUW); 5832 Pred = ICmpInst::ICMP_ULT; 5833 Changed = true; 5834 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { 5835 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5836 SCEV::FlagNUW); 5837 Pred = ICmpInst::ICMP_ULT; 5838 Changed = true; 5839 } 5840 break; 5841 case ICmpInst::ICMP_UGE: 5842 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { 5843 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5844 SCEV::FlagNUW); 5845 Pred = ICmpInst::ICMP_UGT; 5846 Changed = true; 5847 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { 5848 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5849 SCEV::FlagNUW); 5850 Pred = ICmpInst::ICMP_UGT; 5851 Changed = true; 5852 } 5853 break; 5854 default: 5855 break; 5856 } 5857 5858 // TODO: More simplifications are possible here. 5859 5860 // Recursively simplify until we either hit a recursion limit or nothing 5861 // changes. 5862 if (Changed) 5863 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1); 5864 5865 return Changed; 5866 5867 trivially_true: 5868 // Return 0 == 0. 5869 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5870 Pred = ICmpInst::ICMP_EQ; 5871 return true; 5872 5873 trivially_false: 5874 // Return 0 != 0. 5875 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5876 Pred = ICmpInst::ICMP_NE; 5877 return true; 5878 } 5879 5880 bool ScalarEvolution::isKnownNegative(const SCEV *S) { 5881 return getSignedRange(S).getSignedMax().isNegative(); 5882 } 5883 5884 bool ScalarEvolution::isKnownPositive(const SCEV *S) { 5885 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 5886 } 5887 5888 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 5889 return !getSignedRange(S).getSignedMin().isNegative(); 5890 } 5891 5892 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 5893 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 5894 } 5895 5896 bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 5897 return isKnownNegative(S) || isKnownPositive(S); 5898 } 5899 5900 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 5901 const SCEV *LHS, const SCEV *RHS) { 5902 // Canonicalize the inputs first. 5903 (void)SimplifyICmpOperands(Pred, LHS, RHS); 5904 5905 // If LHS or RHS is an addrec, check to see if the condition is true in 5906 // every iteration of the loop. 5907 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 5908 if (isLoopEntryGuardedByCond( 5909 AR->getLoop(), Pred, AR->getStart(), RHS) && 5910 isLoopBackedgeGuardedByCond( 5911 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS)) 5912 return true; 5913 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) 5914 if (isLoopEntryGuardedByCond( 5915 AR->getLoop(), Pred, LHS, AR->getStart()) && 5916 isLoopBackedgeGuardedByCond( 5917 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this))) 5918 return true; 5919 5920 // Otherwise see what can be done with known constant ranges. 5921 return isKnownPredicateWithRanges(Pred, LHS, RHS); 5922 } 5923 5924 bool 5925 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, 5926 const SCEV *LHS, const SCEV *RHS) { 5927 if (HasSameValue(LHS, RHS)) 5928 return ICmpInst::isTrueWhenEqual(Pred); 5929 5930 // This code is split out from isKnownPredicate because it is called from 5931 // within isLoopEntryGuardedByCond. 5932 switch (Pred) { 5933 default: 5934 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5935 case ICmpInst::ICMP_SGT: 5936 Pred = ICmpInst::ICMP_SLT; 5937 std::swap(LHS, RHS); 5938 case ICmpInst::ICMP_SLT: { 5939 ConstantRange LHSRange = getSignedRange(LHS); 5940 ConstantRange RHSRange = getSignedRange(RHS); 5941 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 5942 return true; 5943 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 5944 return false; 5945 break; 5946 } 5947 case ICmpInst::ICMP_SGE: 5948 Pred = ICmpInst::ICMP_SLE; 5949 std::swap(LHS, RHS); 5950 case ICmpInst::ICMP_SLE: { 5951 ConstantRange LHSRange = getSignedRange(LHS); 5952 ConstantRange RHSRange = getSignedRange(RHS); 5953 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 5954 return true; 5955 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 5956 return false; 5957 break; 5958 } 5959 case ICmpInst::ICMP_UGT: 5960 Pred = ICmpInst::ICMP_ULT; 5961 std::swap(LHS, RHS); 5962 case ICmpInst::ICMP_ULT: { 5963 ConstantRange LHSRange = getUnsignedRange(LHS); 5964 ConstantRange RHSRange = getUnsignedRange(RHS); 5965 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 5966 return true; 5967 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 5968 return false; 5969 break; 5970 } 5971 case ICmpInst::ICMP_UGE: 5972 Pred = ICmpInst::ICMP_ULE; 5973 std::swap(LHS, RHS); 5974 case ICmpInst::ICMP_ULE: { 5975 ConstantRange LHSRange = getUnsignedRange(LHS); 5976 ConstantRange RHSRange = getUnsignedRange(RHS); 5977 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 5978 return true; 5979 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 5980 return false; 5981 break; 5982 } 5983 case ICmpInst::ICMP_NE: { 5984 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 5985 return true; 5986 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 5987 return true; 5988 5989 const SCEV *Diff = getMinusSCEV(LHS, RHS); 5990 if (isKnownNonZero(Diff)) 5991 return true; 5992 break; 5993 } 5994 case ICmpInst::ICMP_EQ: 5995 // The check at the top of the function catches the case where 5996 // the values are known to be equal. 5997 break; 5998 } 5999 return false; 6000 } 6001 6002 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 6003 /// protected by a conditional between LHS and RHS. This is used to 6004 /// to eliminate casts. 6005 bool 6006 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 6007 ICmpInst::Predicate Pred, 6008 const SCEV *LHS, const SCEV *RHS) { 6009 // Interpret a null as meaning no loop, where there is obviously no guard 6010 // (interprocedural conditions notwithstanding). 6011 if (!L) return true; 6012 6013 BasicBlock *Latch = L->getLoopLatch(); 6014 if (!Latch) 6015 return false; 6016 6017 BranchInst *LoopContinuePredicate = 6018 dyn_cast<BranchInst>(Latch->getTerminator()); 6019 if (!LoopContinuePredicate || 6020 LoopContinuePredicate->isUnconditional()) 6021 return false; 6022 6023 return isImpliedCond(Pred, LHS, RHS, 6024 LoopContinuePredicate->getCondition(), 6025 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 6026 } 6027 6028 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected 6029 /// by a conditional between LHS and RHS. This is used to help avoid max 6030 /// expressions in loop trip counts, and to eliminate casts. 6031 bool 6032 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 6033 ICmpInst::Predicate Pred, 6034 const SCEV *LHS, const SCEV *RHS) { 6035 // Interpret a null as meaning no loop, where there is obviously no guard 6036 // (interprocedural conditions notwithstanding). 6037 if (!L) return false; 6038 6039 // Starting at the loop predecessor, climb up the predecessor chain, as long 6040 // as there are predecessors that can be found that have unique successors 6041 // leading to the original header. 6042 for (std::pair<BasicBlock *, BasicBlock *> 6043 Pair(L->getLoopPredecessor(), L->getHeader()); 6044 Pair.first; 6045 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 6046 6047 BranchInst *LoopEntryPredicate = 6048 dyn_cast<BranchInst>(Pair.first->getTerminator()); 6049 if (!LoopEntryPredicate || 6050 LoopEntryPredicate->isUnconditional()) 6051 continue; 6052 6053 if (isImpliedCond(Pred, LHS, RHS, 6054 LoopEntryPredicate->getCondition(), 6055 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 6056 return true; 6057 } 6058 6059 return false; 6060 } 6061 6062 /// RAII wrapper to prevent recursive application of isImpliedCond. 6063 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are 6064 /// currently evaluating isImpliedCond. 6065 struct MarkPendingLoopPredicate { 6066 Value *Cond; 6067 DenseSet<Value*> &LoopPreds; 6068 bool Pending; 6069 6070 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP) 6071 : Cond(C), LoopPreds(LP) { 6072 Pending = !LoopPreds.insert(Cond).second; 6073 } 6074 ~MarkPendingLoopPredicate() { 6075 if (!Pending) 6076 LoopPreds.erase(Cond); 6077 } 6078 }; 6079 6080 /// isImpliedCond - Test whether the condition described by Pred, LHS, 6081 /// and RHS is true whenever the given Cond value evaluates to true. 6082 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, 6083 const SCEV *LHS, const SCEV *RHS, 6084 Value *FoundCondValue, 6085 bool Inverse) { 6086 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates); 6087 if (Mark.Pending) 6088 return false; 6089 6090 // Recursively handle And and Or conditions. 6091 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) { 6092 if (BO->getOpcode() == Instruction::And) { 6093 if (!Inverse) 6094 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 6095 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 6096 } else if (BO->getOpcode() == Instruction::Or) { 6097 if (Inverse) 6098 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 6099 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 6100 } 6101 } 6102 6103 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue); 6104 if (!ICI) return false; 6105 6106 // Bail if the ICmp's operands' types are wider than the needed type 6107 // before attempting to call getSCEV on them. This avoids infinite 6108 // recursion, since the analysis of widening casts can require loop 6109 // exit condition information for overflow checking, which would 6110 // lead back here. 6111 if (getTypeSizeInBits(LHS->getType()) < 6112 getTypeSizeInBits(ICI->getOperand(0)->getType())) 6113 return false; 6114 6115 // Now that we found a conditional branch that dominates the loop, check to 6116 // see if it is the comparison we are looking for. 6117 ICmpInst::Predicate FoundPred; 6118 if (Inverse) 6119 FoundPred = ICI->getInversePredicate(); 6120 else 6121 FoundPred = ICI->getPredicate(); 6122 6123 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 6124 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 6125 6126 // Balance the types. The case where FoundLHS' type is wider than 6127 // LHS' type is checked for above. 6128 if (getTypeSizeInBits(LHS->getType()) > 6129 getTypeSizeInBits(FoundLHS->getType())) { 6130 if (CmpInst::isSigned(Pred)) { 6131 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 6132 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 6133 } else { 6134 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 6135 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 6136 } 6137 } 6138 6139 // Canonicalize the query to match the way instcombine will have 6140 // canonicalized the comparison. 6141 if (SimplifyICmpOperands(Pred, LHS, RHS)) 6142 if (LHS == RHS) 6143 return CmpInst::isTrueWhenEqual(Pred); 6144 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 6145 if (FoundLHS == FoundRHS) 6146 return CmpInst::isFalseWhenEqual(Pred); 6147 6148 // Check to see if we can make the LHS or RHS match. 6149 if (LHS == FoundRHS || RHS == FoundLHS) { 6150 if (isa<SCEVConstant>(RHS)) { 6151 std::swap(FoundLHS, FoundRHS); 6152 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 6153 } else { 6154 std::swap(LHS, RHS); 6155 Pred = ICmpInst::getSwappedPredicate(Pred); 6156 } 6157 } 6158 6159 // Check whether the found predicate is the same as the desired predicate. 6160 if (FoundPred == Pred) 6161 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 6162 6163 // Check whether swapping the found predicate makes it the same as the 6164 // desired predicate. 6165 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 6166 if (isa<SCEVConstant>(RHS)) 6167 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 6168 else 6169 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 6170 RHS, LHS, FoundLHS, FoundRHS); 6171 } 6172 6173 // Check whether the actual condition is beyond sufficient. 6174 if (FoundPred == ICmpInst::ICMP_EQ) 6175 if (ICmpInst::isTrueWhenEqual(Pred)) 6176 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 6177 return true; 6178 if (Pred == ICmpInst::ICMP_NE) 6179 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 6180 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 6181 return true; 6182 6183 // Otherwise assume the worst. 6184 return false; 6185 } 6186 6187 /// isImpliedCondOperands - Test whether the condition described by Pred, 6188 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 6189 /// and FoundRHS is true. 6190 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 6191 const SCEV *LHS, const SCEV *RHS, 6192 const SCEV *FoundLHS, 6193 const SCEV *FoundRHS) { 6194 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 6195 FoundLHS, FoundRHS) || 6196 // ~x < ~y --> x > y 6197 isImpliedCondOperandsHelper(Pred, LHS, RHS, 6198 getNotSCEV(FoundRHS), 6199 getNotSCEV(FoundLHS)); 6200 } 6201 6202 /// isImpliedCondOperandsHelper - Test whether the condition described by 6203 /// Pred, LHS, and RHS is true whenever the condition described by Pred, 6204 /// FoundLHS, and FoundRHS is true. 6205 bool 6206 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 6207 const SCEV *LHS, const SCEV *RHS, 6208 const SCEV *FoundLHS, 6209 const SCEV *FoundRHS) { 6210 switch (Pred) { 6211 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 6212 case ICmpInst::ICMP_EQ: 6213 case ICmpInst::ICMP_NE: 6214 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 6215 return true; 6216 break; 6217 case ICmpInst::ICMP_SLT: 6218 case ICmpInst::ICMP_SLE: 6219 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 6220 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 6221 return true; 6222 break; 6223 case ICmpInst::ICMP_SGT: 6224 case ICmpInst::ICMP_SGE: 6225 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 6226 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 6227 return true; 6228 break; 6229 case ICmpInst::ICMP_ULT: 6230 case ICmpInst::ICMP_ULE: 6231 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 6232 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 6233 return true; 6234 break; 6235 case ICmpInst::ICMP_UGT: 6236 case ICmpInst::ICMP_UGE: 6237 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 6238 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 6239 return true; 6240 break; 6241 } 6242 6243 return false; 6244 } 6245 6246 /// getBECount - Subtract the end and start values and divide by the step, 6247 /// rounding up, to get the number of times the backedge is executed. Return 6248 /// CouldNotCompute if an intermediate computation overflows. 6249 const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 6250 const SCEV *End, 6251 const SCEV *Step, 6252 bool NoWrap) { 6253 assert(!isKnownNegative(Step) && 6254 "This code doesn't handle negative strides yet!"); 6255 6256 Type *Ty = Start->getType(); 6257 6258 // When Start == End, we have an exact BECount == 0. Short-circuit this case 6259 // here because SCEV may not be able to determine that the unsigned division 6260 // after rounding is zero. 6261 if (Start == End) 6262 return getConstant(Ty, 0); 6263 6264 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1); 6265 const SCEV *Diff = getMinusSCEV(End, Start); 6266 const SCEV *RoundUp = getAddExpr(Step, NegOne); 6267 6268 // Add an adjustment to the difference between End and Start so that 6269 // the division will effectively round up. 6270 const SCEV *Add = getAddExpr(Diff, RoundUp); 6271 6272 if (!NoWrap) { 6273 // Check Add for unsigned overflow. 6274 // TODO: More sophisticated things could be done here. 6275 Type *WideTy = IntegerType::get(getContext(), 6276 getTypeSizeInBits(Ty) + 1); 6277 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 6278 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 6279 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 6280 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 6281 return getCouldNotCompute(); 6282 } 6283 6284 return getUDivExpr(Add, Step); 6285 } 6286 6287 /// HowManyLessThans - Return the number of times a backedge containing the 6288 /// specified less-than comparison will execute. If not computable, return 6289 /// CouldNotCompute. 6290 ScalarEvolution::ExitLimit 6291 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 6292 const Loop *L, bool isSigned) { 6293 // Only handle: "ADDREC < LoopInvariant". 6294 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute(); 6295 6296 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 6297 if (!AddRec || AddRec->getLoop() != L) 6298 return getCouldNotCompute(); 6299 6300 // Check to see if we have a flag which makes analysis easy. 6301 bool NoWrap = isSigned ? 6302 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNW)) : 6303 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNUW | SCEV::FlagNW)); 6304 6305 if (AddRec->isAffine()) { 6306 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 6307 const SCEV *Step = AddRec->getStepRecurrence(*this); 6308 6309 if (Step->isZero()) 6310 return getCouldNotCompute(); 6311 if (Step->isOne()) { 6312 // With unit stride, the iteration never steps past the limit value. 6313 } else if (isKnownPositive(Step)) { 6314 // Test whether a positive iteration can step past the limit 6315 // value and past the maximum value for its type in a single step. 6316 // Note that it's not sufficient to check NoWrap here, because even 6317 // though the value after a wrap is undefined, it's not undefined 6318 // behavior, so if wrap does occur, the loop could either terminate or 6319 // loop infinitely, but in either case, the loop is guaranteed to 6320 // iterate at least until the iteration where the wrapping occurs. 6321 const SCEV *One = getConstant(Step->getType(), 1); 6322 if (isSigned) { 6323 APInt Max = APInt::getSignedMaxValue(BitWidth); 6324 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 6325 .slt(getSignedRange(RHS).getSignedMax())) 6326 return getCouldNotCompute(); 6327 } else { 6328 APInt Max = APInt::getMaxValue(BitWidth); 6329 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 6330 .ult(getUnsignedRange(RHS).getUnsignedMax())) 6331 return getCouldNotCompute(); 6332 } 6333 } else 6334 // TODO: Handle negative strides here and below. 6335 return getCouldNotCompute(); 6336 6337 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 6338 // m. So, we count the number of iterations in which {n,+,s} < m is true. 6339 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 6340 // treat m-n as signed nor unsigned due to overflow possibility. 6341 6342 // First, we get the value of the LHS in the first iteration: n 6343 const SCEV *Start = AddRec->getOperand(0); 6344 6345 // Determine the minimum constant start value. 6346 const SCEV *MinStart = getConstant(isSigned ? 6347 getSignedRange(Start).getSignedMin() : 6348 getUnsignedRange(Start).getUnsignedMin()); 6349 6350 // If we know that the condition is true in order to enter the loop, 6351 // then we know that it will run exactly (m-n)/s times. Otherwise, we 6352 // only know that it will execute (max(m,n)-n)/s times. In both cases, 6353 // the division must round up. 6354 const SCEV *End = RHS; 6355 if (!isLoopEntryGuardedByCond(L, 6356 isSigned ? ICmpInst::ICMP_SLT : 6357 ICmpInst::ICMP_ULT, 6358 getMinusSCEV(Start, Step), RHS)) 6359 End = isSigned ? getSMaxExpr(RHS, Start) 6360 : getUMaxExpr(RHS, Start); 6361 6362 // Determine the maximum constant end value. 6363 const SCEV *MaxEnd = getConstant(isSigned ? 6364 getSignedRange(End).getSignedMax() : 6365 getUnsignedRange(End).getUnsignedMax()); 6366 6367 // If MaxEnd is within a step of the maximum integer value in its type, 6368 // adjust it down to the minimum value which would produce the same effect. 6369 // This allows the subsequent ceiling division of (N+(step-1))/step to 6370 // compute the correct value. 6371 const SCEV *StepMinusOne = getMinusSCEV(Step, 6372 getConstant(Step->getType(), 1)); 6373 MaxEnd = isSigned ? 6374 getSMinExpr(MaxEnd, 6375 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 6376 StepMinusOne)) : 6377 getUMinExpr(MaxEnd, 6378 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 6379 StepMinusOne)); 6380 6381 // Finally, we subtract these two values and divide, rounding up, to get 6382 // the number of times the backedge is executed. 6383 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 6384 6385 // The maximum backedge count is similar, except using the minimum start 6386 // value and the maximum end value. 6387 // If we already have an exact constant BECount, use it instead. 6388 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount 6389 : getBECount(MinStart, MaxEnd, Step, NoWrap); 6390 6391 // If the stride is nonconstant, and NoWrap == true, then 6392 // getBECount(MinStart, MaxEnd) may not compute. This would result in an 6393 // exact BECount and invalid MaxBECount, which should be avoided to catch 6394 // more optimization opportunities. 6395 if (isa<SCEVCouldNotCompute>(MaxBECount)) 6396 MaxBECount = BECount; 6397 6398 return ExitLimit(BECount, MaxBECount); 6399 } 6400 6401 return getCouldNotCompute(); 6402 } 6403 6404 /// getNumIterationsInRange - Return the number of iterations of this loop that 6405 /// produce values in the specified constant range. Another way of looking at 6406 /// this is that it returns the first iteration number where the value is not in 6407 /// the condition, thus computing the exit count. If the iteration count can't 6408 /// be computed, an instance of SCEVCouldNotCompute is returned. 6409 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 6410 ScalarEvolution &SE) const { 6411 if (Range.isFullSet()) // Infinite loop. 6412 return SE.getCouldNotCompute(); 6413 6414 // If the start is a non-zero constant, shift the range to simplify things. 6415 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 6416 if (!SC->getValue()->isZero()) { 6417 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 6418 Operands[0] = SE.getConstant(SC->getType(), 0); 6419 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(), 6420 getNoWrapFlags(FlagNW)); 6421 if (const SCEVAddRecExpr *ShiftedAddRec = 6422 dyn_cast<SCEVAddRecExpr>(Shifted)) 6423 return ShiftedAddRec->getNumIterationsInRange( 6424 Range.subtract(SC->getValue()->getValue()), SE); 6425 // This is strange and shouldn't happen. 6426 return SE.getCouldNotCompute(); 6427 } 6428 6429 // The only time we can solve this is when we have all constant indices. 6430 // Otherwise, we cannot determine the overflow conditions. 6431 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 6432 if (!isa<SCEVConstant>(getOperand(i))) 6433 return SE.getCouldNotCompute(); 6434 6435 6436 // Okay at this point we know that all elements of the chrec are constants and 6437 // that the start element is zero. 6438 6439 // First check to see if the range contains zero. If not, the first 6440 // iteration exits. 6441 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 6442 if (!Range.contains(APInt(BitWidth, 0))) 6443 return SE.getConstant(getType(), 0); 6444 6445 if (isAffine()) { 6446 // If this is an affine expression then we have this situation: 6447 // Solve {0,+,A} in Range === Ax in Range 6448 6449 // We know that zero is in the range. If A is positive then we know that 6450 // the upper value of the range must be the first possible exit value. 6451 // If A is negative then the lower of the range is the last possible loop 6452 // value. Also note that we already checked for a full range. 6453 APInt One(BitWidth,1); 6454 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 6455 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 6456 6457 // The exit value should be (End+A)/A. 6458 APInt ExitVal = (End + A).udiv(A); 6459 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 6460 6461 // Evaluate at the exit value. If we really did fall out of the valid 6462 // range, then we computed our trip count, otherwise wrap around or other 6463 // things must have happened. 6464 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 6465 if (Range.contains(Val->getValue())) 6466 return SE.getCouldNotCompute(); // Something strange happened 6467 6468 // Ensure that the previous value is in the range. This is a sanity check. 6469 assert(Range.contains( 6470 EvaluateConstantChrecAtConstant(this, 6471 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 6472 "Linear scev computation is off in a bad way!"); 6473 return SE.getConstant(ExitValue); 6474 } else if (isQuadratic()) { 6475 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 6476 // quadratic equation to solve it. To do this, we must frame our problem in 6477 // terms of figuring out when zero is crossed, instead of when 6478 // Range.getUpper() is crossed. 6479 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 6480 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 6481 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(), 6482 // getNoWrapFlags(FlagNW) 6483 FlagAnyWrap); 6484 6485 // Next, solve the constructed addrec 6486 std::pair<const SCEV *,const SCEV *> Roots = 6487 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 6488 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 6489 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 6490 if (R1) { 6491 // Pick the smallest positive root value. 6492 if (ConstantInt *CB = 6493 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 6494 R1->getValue(), R2->getValue()))) { 6495 if (CB->getZExtValue() == false) 6496 std::swap(R1, R2); // R1 is the minimum root now. 6497 6498 // Make sure the root is not off by one. The returned iteration should 6499 // not be in the range, but the previous one should be. When solving 6500 // for "X*X < 5", for example, we should not return a root of 2. 6501 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 6502 R1->getValue(), 6503 SE); 6504 if (Range.contains(R1Val->getValue())) { 6505 // The next iteration must be out of the range... 6506 ConstantInt *NextVal = 6507 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 6508 6509 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 6510 if (!Range.contains(R1Val->getValue())) 6511 return SE.getConstant(NextVal); 6512 return SE.getCouldNotCompute(); // Something strange happened 6513 } 6514 6515 // If R1 was not in the range, then it is a good return value. Make 6516 // sure that R1-1 WAS in the range though, just in case. 6517 ConstantInt *NextVal = 6518 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 6519 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 6520 if (Range.contains(R1Val->getValue())) 6521 return R1; 6522 return SE.getCouldNotCompute(); // Something strange happened 6523 } 6524 } 6525 } 6526 6527 return SE.getCouldNotCompute(); 6528 } 6529 6530 6531 6532 //===----------------------------------------------------------------------===// 6533 // SCEVCallbackVH Class Implementation 6534 //===----------------------------------------------------------------------===// 6535 6536 void ScalarEvolution::SCEVCallbackVH::deleted() { 6537 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 6538 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 6539 SE->ConstantEvolutionLoopExitValue.erase(PN); 6540 SE->ValueExprMap.erase(getValPtr()); 6541 // this now dangles! 6542 } 6543 6544 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 6545 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 6546 6547 // Forget all the expressions associated with users of the old value, 6548 // so that future queries will recompute the expressions using the new 6549 // value. 6550 Value *Old = getValPtr(); 6551 SmallVector<User *, 16> Worklist; 6552 SmallPtrSet<User *, 8> Visited; 6553 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 6554 UI != UE; ++UI) 6555 Worklist.push_back(*UI); 6556 while (!Worklist.empty()) { 6557 User *U = Worklist.pop_back_val(); 6558 // Deleting the Old value will cause this to dangle. Postpone 6559 // that until everything else is done. 6560 if (U == Old) 6561 continue; 6562 if (!Visited.insert(U)) 6563 continue; 6564 if (PHINode *PN = dyn_cast<PHINode>(U)) 6565 SE->ConstantEvolutionLoopExitValue.erase(PN); 6566 SE->ValueExprMap.erase(U); 6567 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 6568 UI != UE; ++UI) 6569 Worklist.push_back(*UI); 6570 } 6571 // Delete the Old value. 6572 if (PHINode *PN = dyn_cast<PHINode>(Old)) 6573 SE->ConstantEvolutionLoopExitValue.erase(PN); 6574 SE->ValueExprMap.erase(Old); 6575 // this now dangles! 6576 } 6577 6578 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 6579 : CallbackVH(V), SE(se) {} 6580 6581 //===----------------------------------------------------------------------===// 6582 // ScalarEvolution Class Implementation 6583 //===----------------------------------------------------------------------===// 6584 6585 ScalarEvolution::ScalarEvolution() 6586 : FunctionPass(ID), FirstUnknown(0) { 6587 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry()); 6588 } 6589 6590 bool ScalarEvolution::runOnFunction(Function &F) { 6591 this->F = &F; 6592 LI = &getAnalysis<LoopInfo>(); 6593 TD = getAnalysisIfAvailable<TargetData>(); 6594 TLI = &getAnalysis<TargetLibraryInfo>(); 6595 DT = &getAnalysis<DominatorTree>(); 6596 return false; 6597 } 6598 6599 void ScalarEvolution::releaseMemory() { 6600 // Iterate through all the SCEVUnknown instances and call their 6601 // destructors, so that they release their references to their values. 6602 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next) 6603 U->~SCEVUnknown(); 6604 FirstUnknown = 0; 6605 6606 ValueExprMap.clear(); 6607 6608 // Free any extra memory created for ExitNotTakenInfo in the unlikely event 6609 // that a loop had multiple computable exits. 6610 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I = 6611 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); 6612 I != E; ++I) { 6613 I->second.clear(); 6614 } 6615 6616 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage"); 6617 6618 BackedgeTakenCounts.clear(); 6619 ConstantEvolutionLoopExitValue.clear(); 6620 ValuesAtScopes.clear(); 6621 LoopDispositions.clear(); 6622 BlockDispositions.clear(); 6623 UnsignedRanges.clear(); 6624 SignedRanges.clear(); 6625 UniqueSCEVs.clear(); 6626 SCEVAllocator.Reset(); 6627 } 6628 6629 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 6630 AU.setPreservesAll(); 6631 AU.addRequiredTransitive<LoopInfo>(); 6632 AU.addRequiredTransitive<DominatorTree>(); 6633 AU.addRequired<TargetLibraryInfo>(); 6634 } 6635 6636 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 6637 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 6638 } 6639 6640 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 6641 const Loop *L) { 6642 // Print all inner loops first 6643 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 6644 PrintLoopInfo(OS, SE, *I); 6645 6646 OS << "Loop "; 6647 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 6648 OS << ": "; 6649 6650 SmallVector<BasicBlock *, 8> ExitBlocks; 6651 L->getExitBlocks(ExitBlocks); 6652 if (ExitBlocks.size() != 1) 6653 OS << "<multiple exits> "; 6654 6655 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 6656 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 6657 } else { 6658 OS << "Unpredictable backedge-taken count. "; 6659 } 6660 6661 OS << "\n" 6662 "Loop "; 6663 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 6664 OS << ": "; 6665 6666 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 6667 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 6668 } else { 6669 OS << "Unpredictable max backedge-taken count. "; 6670 } 6671 6672 OS << "\n"; 6673 } 6674 6675 void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 6676 // ScalarEvolution's implementation of the print method is to print 6677 // out SCEV values of all instructions that are interesting. Doing 6678 // this potentially causes it to create new SCEV objects though, 6679 // which technically conflicts with the const qualifier. This isn't 6680 // observable from outside the class though, so casting away the 6681 // const isn't dangerous. 6682 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 6683 6684 OS << "Classifying expressions for: "; 6685 WriteAsOperand(OS, F, /*PrintType=*/false); 6686 OS << "\n"; 6687 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 6688 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { 6689 OS << *I << '\n'; 6690 OS << " --> "; 6691 const SCEV *SV = SE.getSCEV(&*I); 6692 SV->print(OS); 6693 6694 const Loop *L = LI->getLoopFor((*I).getParent()); 6695 6696 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 6697 if (AtUse != SV) { 6698 OS << " --> "; 6699 AtUse->print(OS); 6700 } 6701 6702 if (L) { 6703 OS << "\t\t" "Exits: "; 6704 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 6705 if (!SE.isLoopInvariant(ExitValue, L)) { 6706 OS << "<<Unknown>>"; 6707 } else { 6708 OS << *ExitValue; 6709 } 6710 } 6711 6712 OS << "\n"; 6713 } 6714 6715 OS << "Determining loop execution counts for: "; 6716 WriteAsOperand(OS, F, /*PrintType=*/false); 6717 OS << "\n"; 6718 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 6719 PrintLoopInfo(OS, &SE, *I); 6720 } 6721 6722 ScalarEvolution::LoopDisposition 6723 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) { 6724 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S]; 6725 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair = 6726 Values.insert(std::make_pair(L, LoopVariant)); 6727 if (!Pair.second) 6728 return Pair.first->second; 6729 6730 LoopDisposition D = computeLoopDisposition(S, L); 6731 return LoopDispositions[S][L] = D; 6732 } 6733 6734 ScalarEvolution::LoopDisposition 6735 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) { 6736 switch (S->getSCEVType()) { 6737 case scConstant: 6738 return LoopInvariant; 6739 case scTruncate: 6740 case scZeroExtend: 6741 case scSignExtend: 6742 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L); 6743 case scAddRecExpr: { 6744 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6745 6746 // If L is the addrec's loop, it's computable. 6747 if (AR->getLoop() == L) 6748 return LoopComputable; 6749 6750 // Add recurrences are never invariant in the function-body (null loop). 6751 if (!L) 6752 return LoopVariant; 6753 6754 // This recurrence is variant w.r.t. L if L contains AR's loop. 6755 if (L->contains(AR->getLoop())) 6756 return LoopVariant; 6757 6758 // This recurrence is invariant w.r.t. L if AR's loop contains L. 6759 if (AR->getLoop()->contains(L)) 6760 return LoopInvariant; 6761 6762 // This recurrence is variant w.r.t. L if any of its operands 6763 // are variant. 6764 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 6765 I != E; ++I) 6766 if (!isLoopInvariant(*I, L)) 6767 return LoopVariant; 6768 6769 // Otherwise it's loop-invariant. 6770 return LoopInvariant; 6771 } 6772 case scAddExpr: 6773 case scMulExpr: 6774 case scUMaxExpr: 6775 case scSMaxExpr: { 6776 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6777 bool HasVarying = false; 6778 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6779 I != E; ++I) { 6780 LoopDisposition D = getLoopDisposition(*I, L); 6781 if (D == LoopVariant) 6782 return LoopVariant; 6783 if (D == LoopComputable) 6784 HasVarying = true; 6785 } 6786 return HasVarying ? LoopComputable : LoopInvariant; 6787 } 6788 case scUDivExpr: { 6789 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6790 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L); 6791 if (LD == LoopVariant) 6792 return LoopVariant; 6793 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L); 6794 if (RD == LoopVariant) 6795 return LoopVariant; 6796 return (LD == LoopInvariant && RD == LoopInvariant) ? 6797 LoopInvariant : LoopComputable; 6798 } 6799 case scUnknown: 6800 // All non-instruction values are loop invariant. All instructions are loop 6801 // invariant if they are not contained in the specified loop. 6802 // Instructions are never considered invariant in the function body 6803 // (null loop) because they are defined within the "loop". 6804 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) 6805 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant; 6806 return LoopInvariant; 6807 case scCouldNotCompute: 6808 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6809 default: llvm_unreachable("Unknown SCEV kind!"); 6810 } 6811 } 6812 6813 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) { 6814 return getLoopDisposition(S, L) == LoopInvariant; 6815 } 6816 6817 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) { 6818 return getLoopDisposition(S, L) == LoopComputable; 6819 } 6820 6821 ScalarEvolution::BlockDisposition 6822 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6823 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S]; 6824 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool> 6825 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock)); 6826 if (!Pair.second) 6827 return Pair.first->second; 6828 6829 BlockDisposition D = computeBlockDisposition(S, BB); 6830 return BlockDispositions[S][BB] = D; 6831 } 6832 6833 ScalarEvolution::BlockDisposition 6834 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6835 switch (S->getSCEVType()) { 6836 case scConstant: 6837 return ProperlyDominatesBlock; 6838 case scTruncate: 6839 case scZeroExtend: 6840 case scSignExtend: 6841 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB); 6842 case scAddRecExpr: { 6843 // This uses a "dominates" query instead of "properly dominates" query 6844 // to test for proper dominance too, because the instruction which 6845 // produces the addrec's value is a PHI, and a PHI effectively properly 6846 // dominates its entire containing block. 6847 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6848 if (!DT->dominates(AR->getLoop()->getHeader(), BB)) 6849 return DoesNotDominateBlock; 6850 } 6851 // FALL THROUGH into SCEVNAryExpr handling. 6852 case scAddExpr: 6853 case scMulExpr: 6854 case scUMaxExpr: 6855 case scSMaxExpr: { 6856 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6857 bool Proper = true; 6858 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6859 I != E; ++I) { 6860 BlockDisposition D = getBlockDisposition(*I, BB); 6861 if (D == DoesNotDominateBlock) 6862 return DoesNotDominateBlock; 6863 if (D == DominatesBlock) 6864 Proper = false; 6865 } 6866 return Proper ? ProperlyDominatesBlock : DominatesBlock; 6867 } 6868 case scUDivExpr: { 6869 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6870 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 6871 BlockDisposition LD = getBlockDisposition(LHS, BB); 6872 if (LD == DoesNotDominateBlock) 6873 return DoesNotDominateBlock; 6874 BlockDisposition RD = getBlockDisposition(RHS, BB); 6875 if (RD == DoesNotDominateBlock) 6876 return DoesNotDominateBlock; 6877 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ? 6878 ProperlyDominatesBlock : DominatesBlock; 6879 } 6880 case scUnknown: 6881 if (Instruction *I = 6882 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) { 6883 if (I->getParent() == BB) 6884 return DominatesBlock; 6885 if (DT->properlyDominates(I->getParent(), BB)) 6886 return ProperlyDominatesBlock; 6887 return DoesNotDominateBlock; 6888 } 6889 return ProperlyDominatesBlock; 6890 case scCouldNotCompute: 6891 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6892 default: 6893 llvm_unreachable("Unknown SCEV kind!"); 6894 } 6895 } 6896 6897 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) { 6898 return getBlockDisposition(S, BB) >= DominatesBlock; 6899 } 6900 6901 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) { 6902 return getBlockDisposition(S, BB) == ProperlyDominatesBlock; 6903 } 6904 6905 namespace { 6906 // Search for a SCEV expression node within an expression tree. 6907 // Implements SCEVTraversal::Visitor. 6908 struct SCEVSearch { 6909 const SCEV *Node; 6910 bool IsFound; 6911 6912 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {} 6913 6914 bool follow(const SCEV *S) { 6915 IsFound |= (S == Node); 6916 return !IsFound; 6917 } 6918 bool isDone() const { return IsFound; } 6919 }; 6920 } 6921 6922 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const { 6923 SCEVSearch Search(Op); 6924 visitAll(S, Search); 6925 return Search.IsFound; 6926 } 6927 6928 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) { 6929 ValuesAtScopes.erase(S); 6930 LoopDispositions.erase(S); 6931 BlockDispositions.erase(S); 6932 UnsignedRanges.erase(S); 6933 SignedRanges.erase(S); 6934 } 6935