ScalarEvolution.cpp revision 71c4144076d35bd45f8a5103357532f958de6757
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/LoopInfo.h" 73#include "llvm/Analysis/ValueTracking.h" 74#include "llvm/Assembly/Writer.h" 75#include "llvm/Target/TargetData.h" 76#include "llvm/Support/CommandLine.h" 77#include "llvm/Support/ConstantRange.h" 78#include "llvm/Support/Debug.h" 79#include "llvm/Support/ErrorHandling.h" 80#include "llvm/Support/GetElementPtrTypeIterator.h" 81#include "llvm/Support/InstIterator.h" 82#include "llvm/Support/MathExtras.h" 83#include "llvm/Support/raw_ostream.h" 84#include "llvm/ADT/Statistic.h" 85#include "llvm/ADT/STLExtras.h" 86#include "llvm/ADT/SmallPtrSet.h" 87#include <algorithm> 88using namespace llvm; 89 90STATISTIC(NumArrayLenItCounts, 91 "Number of trip counts computed with array length"); 92STATISTIC(NumTripCountsComputed, 93 "Number of loops with predictable loop counts"); 94STATISTIC(NumTripCountsNotComputed, 95 "Number of loops without predictable loop counts"); 96STATISTIC(NumBruteForceTripCountsComputed, 97 "Number of loops with trip counts computed by force"); 98 99static cl::opt<unsigned> 100MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 101 cl::desc("Maximum number of iterations SCEV will " 102 "symbolically execute a constant " 103 "derived loop"), 104 cl::init(100)); 105 106INITIALIZE_PASS(ScalarEvolution, "scalar-evolution", 107 "Scalar Evolution Analysis", false, true); 108char ScalarEvolution::ID = 0; 109 110//===----------------------------------------------------------------------===// 111// SCEV class definitions 112//===----------------------------------------------------------------------===// 113 114//===----------------------------------------------------------------------===// 115// Implementation of the SCEV class. 116// 117 118SCEV::~SCEV() {} 119 120void SCEV::dump() const { 121 print(dbgs()); 122 dbgs() << '\n'; 123} 124 125bool SCEV::isZero() const { 126 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 127 return SC->getValue()->isZero(); 128 return false; 129} 130 131bool SCEV::isOne() const { 132 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 133 return SC->getValue()->isOne(); 134 return false; 135} 136 137bool SCEV::isAllOnesValue() const { 138 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 139 return SC->getValue()->isAllOnesValue(); 140 return false; 141} 142 143SCEVCouldNotCompute::SCEVCouldNotCompute() : 144 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {} 145 146bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 147 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 148 return false; 149} 150 151const Type *SCEVCouldNotCompute::getType() const { 152 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 153 return 0; 154} 155 156bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 157 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 158 return false; 159} 160 161bool SCEVCouldNotCompute::hasOperand(const SCEV *) const { 162 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 163 return false; 164} 165 166void SCEVCouldNotCompute::print(raw_ostream &OS) const { 167 OS << "***COULDNOTCOMPUTE***"; 168} 169 170bool SCEVCouldNotCompute::classof(const SCEV *S) { 171 return S->getSCEVType() == scCouldNotCompute; 172} 173 174const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 175 FoldingSetNodeID ID; 176 ID.AddInteger(scConstant); 177 ID.AddPointer(V); 178 void *IP = 0; 179 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 180 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V); 181 UniqueSCEVs.InsertNode(S, IP); 182 return S; 183} 184 185const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 186 return getConstant(ConstantInt::get(getContext(), Val)); 187} 188 189const SCEV * 190ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) { 191 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 192 return getConstant(ConstantInt::get(ITy, V, isSigned)); 193} 194 195const Type *SCEVConstant::getType() const { return V->getType(); } 196 197void SCEVConstant::print(raw_ostream &OS) const { 198 WriteAsOperand(OS, V, false); 199} 200 201SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, 202 unsigned SCEVTy, const SCEV *op, const Type *ty) 203 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 204 205bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 206 return Op->dominates(BB, DT); 207} 208 209bool SCEVCastExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 210 return Op->properlyDominates(BB, DT); 211} 212 213SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, 214 const SCEV *op, const Type *ty) 215 : SCEVCastExpr(ID, scTruncate, op, ty) { 216 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 217 (Ty->isIntegerTy() || Ty->isPointerTy()) && 218 "Cannot truncate non-integer value!"); 219} 220 221void SCEVTruncateExpr::print(raw_ostream &OS) const { 222 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 223} 224 225SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, 226 const SCEV *op, const Type *ty) 227 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 228 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 229 (Ty->isIntegerTy() || Ty->isPointerTy()) && 230 "Cannot zero extend non-integer value!"); 231} 232 233void SCEVZeroExtendExpr::print(raw_ostream &OS) const { 234 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 235} 236 237SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, 238 const SCEV *op, const Type *ty) 239 : SCEVCastExpr(ID, scSignExtend, op, ty) { 240 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 241 (Ty->isIntegerTy() || Ty->isPointerTy()) && 242 "Cannot sign extend non-integer value!"); 243} 244 245void SCEVSignExtendExpr::print(raw_ostream &OS) const { 246 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 247} 248 249void SCEVCommutativeExpr::print(raw_ostream &OS) const { 250 const char *OpStr = getOperationStr(); 251 OS << "("; 252 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) { 253 OS << **I; 254 if (llvm::next(I) != E) 255 OS << OpStr; 256 } 257 OS << ")"; 258} 259 260bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 261 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 262 if (!getOperand(i)->dominates(BB, DT)) 263 return false; 264 } 265 return true; 266} 267 268bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 269 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 270 if (!getOperand(i)->properlyDominates(BB, DT)) 271 return false; 272 } 273 return true; 274} 275 276bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 277 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 278} 279 280bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 281 return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT); 282} 283 284void SCEVUDivExpr::print(raw_ostream &OS) const { 285 OS << "(" << *LHS << " /u " << *RHS << ")"; 286} 287 288const Type *SCEVUDivExpr::getType() const { 289 // In most cases the types of LHS and RHS will be the same, but in some 290 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't 291 // depend on the type for correctness, but handling types carefully can 292 // avoid extra casts in the SCEVExpander. The LHS is more likely to be 293 // a pointer type than the RHS, so use the RHS' type here. 294 return RHS->getType(); 295} 296 297bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 298 // Add recurrences are never invariant in the function-body (null loop). 299 if (!QueryLoop) 300 return false; 301 302 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L. 303 if (QueryLoop->contains(L)) 304 return false; 305 306 // This recurrence is invariant w.r.t. QueryLoop if L contains QueryLoop. 307 if (L->contains(QueryLoop)) 308 return true; 309 310 // This recurrence is variant w.r.t. QueryLoop if any of its operands 311 // are variant. 312 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 313 if (!getOperand(i)->isLoopInvariant(QueryLoop)) 314 return false; 315 316 // Otherwise it's loop-invariant. 317 return true; 318} 319 320bool 321SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 322 return DT->dominates(L->getHeader(), BB) && 323 SCEVNAryExpr::dominates(BB, DT); 324} 325 326bool 327SCEVAddRecExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 328 // This uses a "dominates" query instead of "properly dominates" query because 329 // the instruction which produces the addrec's value is a PHI, and a PHI 330 // effectively properly dominates its entire containing block. 331 return DT->dominates(L->getHeader(), BB) && 332 SCEVNAryExpr::properlyDominates(BB, DT); 333} 334 335void SCEVAddRecExpr::print(raw_ostream &OS) const { 336 OS << "{" << *Operands[0]; 337 for (unsigned i = 1, e = NumOperands; i != e; ++i) 338 OS << ",+," << *Operands[i]; 339 OS << "}<"; 340 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 341 OS << ">"; 342} 343 344void SCEVUnknown::deleted() { 345 // Clear this SCEVUnknown from ValuesAtScopes. 346 SE->ValuesAtScopes.erase(this); 347 348 // Remove this SCEVUnknown from the uniquing map. 349 SE->UniqueSCEVs.RemoveNode(this); 350 351 // Release the value. 352 setValPtr(0); 353} 354 355void SCEVUnknown::allUsesReplacedWith(Value *New) { 356 // Clear this SCEVUnknown from ValuesAtScopes. 357 SE->ValuesAtScopes.erase(this); 358 359 // Remove this SCEVUnknown from the uniquing map. 360 SE->UniqueSCEVs.RemoveNode(this); 361 362 // Update this SCEVUnknown to point to the new value. This is needed 363 // because there may still be outstanding SCEVs which still point to 364 // this SCEVUnknown. 365 setValPtr(New); 366} 367 368bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 369 // All non-instruction values are loop invariant. All instructions are loop 370 // invariant if they are not contained in the specified loop. 371 // Instructions are never considered invariant in the function body 372 // (null loop) because they are defined within the "loop". 373 if (Instruction *I = dyn_cast<Instruction>(getValue())) 374 return L && !L->contains(I); 375 return true; 376} 377 378bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 379 if (Instruction *I = dyn_cast<Instruction>(getValue())) 380 return DT->dominates(I->getParent(), BB); 381 return true; 382} 383 384bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 385 if (Instruction *I = dyn_cast<Instruction>(getValue())) 386 return DT->properlyDominates(I->getParent(), BB); 387 return true; 388} 389 390const Type *SCEVUnknown::getType() const { 391 return getValue()->getType(); 392} 393 394bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const { 395 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 396 if (VCE->getOpcode() == Instruction::PtrToInt) 397 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 398 if (CE->getOpcode() == Instruction::GetElementPtr && 399 CE->getOperand(0)->isNullValue() && 400 CE->getNumOperands() == 2) 401 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 402 if (CI->isOne()) { 403 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 404 ->getElementType(); 405 return true; 406 } 407 408 return false; 409} 410 411bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const { 412 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 413 if (VCE->getOpcode() == Instruction::PtrToInt) 414 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 415 if (CE->getOpcode() == Instruction::GetElementPtr && 416 CE->getOperand(0)->isNullValue()) { 417 const Type *Ty = 418 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 419 if (const StructType *STy = dyn_cast<StructType>(Ty)) 420 if (!STy->isPacked() && 421 CE->getNumOperands() == 3 && 422 CE->getOperand(1)->isNullValue()) { 423 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 424 if (CI->isOne() && 425 STy->getNumElements() == 2 && 426 STy->getElementType(0)->isIntegerTy(1)) { 427 AllocTy = STy->getElementType(1); 428 return true; 429 } 430 } 431 } 432 433 return false; 434} 435 436bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const { 437 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 438 if (VCE->getOpcode() == Instruction::PtrToInt) 439 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 440 if (CE->getOpcode() == Instruction::GetElementPtr && 441 CE->getNumOperands() == 3 && 442 CE->getOperand(0)->isNullValue() && 443 CE->getOperand(1)->isNullValue()) { 444 const Type *Ty = 445 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 446 // Ignore vector types here so that ScalarEvolutionExpander doesn't 447 // emit getelementptrs that index into vectors. 448 if (Ty->isStructTy() || Ty->isArrayTy()) { 449 CTy = Ty; 450 FieldNo = CE->getOperand(2); 451 return true; 452 } 453 } 454 455 return false; 456} 457 458void SCEVUnknown::print(raw_ostream &OS) const { 459 const Type *AllocTy; 460 if (isSizeOf(AllocTy)) { 461 OS << "sizeof(" << *AllocTy << ")"; 462 return; 463 } 464 if (isAlignOf(AllocTy)) { 465 OS << "alignof(" << *AllocTy << ")"; 466 return; 467 } 468 469 const Type *CTy; 470 Constant *FieldNo; 471 if (isOffsetOf(CTy, FieldNo)) { 472 OS << "offsetof(" << *CTy << ", "; 473 WriteAsOperand(OS, FieldNo, false); 474 OS << ")"; 475 return; 476 } 477 478 // Otherwise just print it normally. 479 WriteAsOperand(OS, getValue(), false); 480} 481 482//===----------------------------------------------------------------------===// 483// SCEV Utilities 484//===----------------------------------------------------------------------===// 485 486static bool CompareTypes(const Type *A, const Type *B) { 487 if (A->getTypeID() != B->getTypeID()) 488 return A->getTypeID() < B->getTypeID(); 489 if (const IntegerType *AI = dyn_cast<IntegerType>(A)) { 490 const IntegerType *BI = cast<IntegerType>(B); 491 return AI->getBitWidth() < BI->getBitWidth(); 492 } 493 if (const PointerType *AI = dyn_cast<PointerType>(A)) { 494 const PointerType *BI = cast<PointerType>(B); 495 return CompareTypes(AI->getElementType(), BI->getElementType()); 496 } 497 if (const ArrayType *AI = dyn_cast<ArrayType>(A)) { 498 const ArrayType *BI = cast<ArrayType>(B); 499 if (AI->getNumElements() != BI->getNumElements()) 500 return AI->getNumElements() < BI->getNumElements(); 501 return CompareTypes(AI->getElementType(), BI->getElementType()); 502 } 503 if (const VectorType *AI = dyn_cast<VectorType>(A)) { 504 const VectorType *BI = cast<VectorType>(B); 505 if (AI->getNumElements() != BI->getNumElements()) 506 return AI->getNumElements() < BI->getNumElements(); 507 return CompareTypes(AI->getElementType(), BI->getElementType()); 508 } 509 if (const StructType *AI = dyn_cast<StructType>(A)) { 510 const StructType *BI = cast<StructType>(B); 511 if (AI->getNumElements() != BI->getNumElements()) 512 return AI->getNumElements() < BI->getNumElements(); 513 for (unsigned i = 0, e = AI->getNumElements(); i != e; ++i) 514 if (CompareTypes(AI->getElementType(i), BI->getElementType(i)) || 515 CompareTypes(BI->getElementType(i), AI->getElementType(i))) 516 return CompareTypes(AI->getElementType(i), BI->getElementType(i)); 517 } 518 return false; 519} 520 521namespace { 522 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 523 /// than the complexity of the RHS. This comparator is used to canonicalize 524 /// expressions. 525 class SCEVComplexityCompare { 526 const LoopInfo *LI; 527 public: 528 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {} 529 530 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 531 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 532 if (LHS == RHS) 533 return false; 534 535 // Primarily, sort the SCEVs by their getSCEVType(). 536 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); 537 if (LType != RType) 538 return LType < RType; 539 540 // Aside from the getSCEVType() ordering, the particular ordering 541 // isn't very important except that it's beneficial to be consistent, 542 // so that (a + b) and (b + a) don't end up as different expressions. 543 544 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 545 // not as complete as it could be. 546 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) { 547 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 548 549 // Order pointer values after integer values. This helps SCEVExpander 550 // form GEPs. 551 bool LIsPointer = LU->getType()->isPointerTy(), 552 RIsPointer = RU->getType()->isPointerTy(); 553 if (LIsPointer != RIsPointer) 554 return RIsPointer; 555 556 // Compare getValueID values. 557 unsigned LID = LU->getValue()->getValueID(), 558 RID = RU->getValue()->getValueID(); 559 if (LID != RID) 560 return LID < RID; 561 562 // Sort arguments by their position. 563 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) { 564 const Argument *RA = cast<Argument>(RU->getValue()); 565 return LA->getArgNo() < RA->getArgNo(); 566 } 567 568 // For instructions, compare their loop depth, and their opcode. 569 // This is pretty loose. 570 if (const Instruction *LV = dyn_cast<Instruction>(LU->getValue())) { 571 const Instruction *RV = cast<Instruction>(RU->getValue()); 572 573 // Compare loop depths. 574 unsigned LDepth = LI->getLoopDepth(LV->getParent()), 575 RDepth = LI->getLoopDepth(RV->getParent()); 576 if (LDepth != RDepth) 577 return LDepth < RDepth; 578 579 // Compare the number of operands. 580 unsigned LNumOps = LV->getNumOperands(), 581 RNumOps = RV->getNumOperands(); 582 if (LNumOps != RNumOps) 583 return LNumOps < RNumOps; 584 } 585 586 return false; 587 } 588 589 // Compare constant values. 590 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) { 591 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 592 const ConstantInt *LCC = LC->getValue(); 593 const ConstantInt *RCC = RC->getValue(); 594 unsigned LBitWidth = LCC->getBitWidth(), RBitWidth = RCC->getBitWidth(); 595 if (LBitWidth != RBitWidth) 596 return LBitWidth < RBitWidth; 597 return LCC->getValue().ult(RCC->getValue()); 598 } 599 600 // Compare addrec loop depths. 601 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) { 602 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 603 unsigned LDepth = LA->getLoop()->getLoopDepth(), 604 RDepth = RA->getLoop()->getLoopDepth(); 605 if (LDepth != RDepth) 606 return LDepth < RDepth; 607 } 608 609 // Lexicographically compare n-ary expressions. 610 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) { 611 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 612 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands(); 613 for (unsigned i = 0; i != LNumOps; ++i) { 614 if (i >= RNumOps) 615 return false; 616 const SCEV *LOp = LC->getOperand(i), *ROp = RC->getOperand(i); 617 if (operator()(LOp, ROp)) 618 return true; 619 if (operator()(ROp, LOp)) 620 return false; 621 } 622 return LNumOps < RNumOps; 623 } 624 625 // Lexicographically compare udiv expressions. 626 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) { 627 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 628 const SCEV *LL = LC->getLHS(), *LR = LC->getRHS(), 629 *RL = RC->getLHS(), *RR = RC->getRHS(); 630 if (operator()(LL, RL)) 631 return true; 632 if (operator()(RL, LL)) 633 return false; 634 if (operator()(LR, RR)) 635 return true; 636 if (operator()(RR, LR)) 637 return false; 638 return false; 639 } 640 641 // Compare cast expressions by operand. 642 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) { 643 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 644 return operator()(LC->getOperand(), RC->getOperand()); 645 } 646 647 llvm_unreachable("Unknown SCEV kind!"); 648 return false; 649 } 650 }; 651} 652 653/// GroupByComplexity - Given a list of SCEV objects, order them by their 654/// complexity, and group objects of the same complexity together by value. 655/// When this routine is finished, we know that any duplicates in the vector are 656/// consecutive and that complexity is monotonically increasing. 657/// 658/// Note that we go take special precautions to ensure that we get deterministic 659/// results from this routine. In other words, we don't want the results of 660/// this to depend on where the addresses of various SCEV objects happened to 661/// land in memory. 662/// 663static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 664 LoopInfo *LI) { 665 if (Ops.size() < 2) return; // Noop 666 if (Ops.size() == 2) { 667 // This is the common case, which also happens to be trivially simple. 668 // Special case it. 669 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0])) 670 std::swap(Ops[0], Ops[1]); 671 return; 672 } 673 674 // Do the rough sort by complexity. 675 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 676 677 // Now that we are sorted by complexity, group elements of the same 678 // complexity. Note that this is, at worst, N^2, but the vector is likely to 679 // be extremely short in practice. Note that we take this approach because we 680 // do not want to depend on the addresses of the objects we are grouping. 681 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 682 const SCEV *S = Ops[i]; 683 unsigned Complexity = S->getSCEVType(); 684 685 // If there are any objects of the same complexity and same value as this 686 // one, group them. 687 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 688 if (Ops[j] == S) { // Found a duplicate. 689 // Move it to immediately after i'th element. 690 std::swap(Ops[i+1], Ops[j]); 691 ++i; // no need to rescan it. 692 if (i == e-2) return; // Done! 693 } 694 } 695 } 696} 697 698 699 700//===----------------------------------------------------------------------===// 701// Simple SCEV method implementations 702//===----------------------------------------------------------------------===// 703 704/// BinomialCoefficient - Compute BC(It, K). The result has width W. 705/// Assume, K > 0. 706static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 707 ScalarEvolution &SE, 708 const Type* ResultTy) { 709 // Handle the simplest case efficiently. 710 if (K == 1) 711 return SE.getTruncateOrZeroExtend(It, ResultTy); 712 713 // We are using the following formula for BC(It, K): 714 // 715 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 716 // 717 // Suppose, W is the bitwidth of the return value. We must be prepared for 718 // overflow. Hence, we must assure that the result of our computation is 719 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 720 // safe in modular arithmetic. 721 // 722 // However, this code doesn't use exactly that formula; the formula it uses 723 // is something like the following, where T is the number of factors of 2 in 724 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 725 // exponentiation: 726 // 727 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 728 // 729 // This formula is trivially equivalent to the previous formula. However, 730 // this formula can be implemented much more efficiently. The trick is that 731 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 732 // arithmetic. To do exact division in modular arithmetic, all we have 733 // to do is multiply by the inverse. Therefore, this step can be done at 734 // width W. 735 // 736 // The next issue is how to safely do the division by 2^T. The way this 737 // is done is by doing the multiplication step at a width of at least W + T 738 // bits. This way, the bottom W+T bits of the product are accurate. Then, 739 // when we perform the division by 2^T (which is equivalent to a right shift 740 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 741 // truncated out after the division by 2^T. 742 // 743 // In comparison to just directly using the first formula, this technique 744 // is much more efficient; using the first formula requires W * K bits, 745 // but this formula less than W + K bits. Also, the first formula requires 746 // a division step, whereas this formula only requires multiplies and shifts. 747 // 748 // It doesn't matter whether the subtraction step is done in the calculation 749 // width or the input iteration count's width; if the subtraction overflows, 750 // the result must be zero anyway. We prefer here to do it in the width of 751 // the induction variable because it helps a lot for certain cases; CodeGen 752 // isn't smart enough to ignore the overflow, which leads to much less 753 // efficient code if the width of the subtraction is wider than the native 754 // register width. 755 // 756 // (It's possible to not widen at all by pulling out factors of 2 before 757 // the multiplication; for example, K=2 can be calculated as 758 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 759 // extra arithmetic, so it's not an obvious win, and it gets 760 // much more complicated for K > 3.) 761 762 // Protection from insane SCEVs; this bound is conservative, 763 // but it probably doesn't matter. 764 if (K > 1000) 765 return SE.getCouldNotCompute(); 766 767 unsigned W = SE.getTypeSizeInBits(ResultTy); 768 769 // Calculate K! / 2^T and T; we divide out the factors of two before 770 // multiplying for calculating K! / 2^T to avoid overflow. 771 // Other overflow doesn't matter because we only care about the bottom 772 // W bits of the result. 773 APInt OddFactorial(W, 1); 774 unsigned T = 1; 775 for (unsigned i = 3; i <= K; ++i) { 776 APInt Mult(W, i); 777 unsigned TwoFactors = Mult.countTrailingZeros(); 778 T += TwoFactors; 779 Mult = Mult.lshr(TwoFactors); 780 OddFactorial *= Mult; 781 } 782 783 // We need at least W + T bits for the multiplication step 784 unsigned CalculationBits = W + T; 785 786 // Calculate 2^T, at width T+W. 787 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 788 789 // Calculate the multiplicative inverse of K! / 2^T; 790 // this multiplication factor will perform the exact division by 791 // K! / 2^T. 792 APInt Mod = APInt::getSignedMinValue(W+1); 793 APInt MultiplyFactor = OddFactorial.zext(W+1); 794 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 795 MultiplyFactor = MultiplyFactor.trunc(W); 796 797 // Calculate the product, at width T+W 798 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 799 CalculationBits); 800 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 801 for (unsigned i = 1; i != K; ++i) { 802 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); 803 Dividend = SE.getMulExpr(Dividend, 804 SE.getTruncateOrZeroExtend(S, CalculationTy)); 805 } 806 807 // Divide by 2^T 808 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 809 810 // Truncate the result, and divide by K! / 2^T. 811 812 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 813 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 814} 815 816/// evaluateAtIteration - Return the value of this chain of recurrences at 817/// the specified iteration number. We can evaluate this recurrence by 818/// multiplying each element in the chain by the binomial coefficient 819/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 820/// 821/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 822/// 823/// where BC(It, k) stands for binomial coefficient. 824/// 825const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 826 ScalarEvolution &SE) const { 827 const SCEV *Result = getStart(); 828 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 829 // The computation is correct in the face of overflow provided that the 830 // multiplication is performed _after_ the evaluation of the binomial 831 // coefficient. 832 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 833 if (isa<SCEVCouldNotCompute>(Coeff)) 834 return Coeff; 835 836 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 837 } 838 return Result; 839} 840 841//===----------------------------------------------------------------------===// 842// SCEV Expression folder implementations 843//===----------------------------------------------------------------------===// 844 845const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 846 const Type *Ty) { 847 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 848 "This is not a truncating conversion!"); 849 assert(isSCEVable(Ty) && 850 "This is not a conversion to a SCEVable type!"); 851 Ty = getEffectiveSCEVType(Ty); 852 853 FoldingSetNodeID ID; 854 ID.AddInteger(scTruncate); 855 ID.AddPointer(Op); 856 ID.AddPointer(Ty); 857 void *IP = 0; 858 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 859 860 // Fold if the operand is constant. 861 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 862 return getConstant( 863 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), 864 getEffectiveSCEVType(Ty)))); 865 866 // trunc(trunc(x)) --> trunc(x) 867 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 868 return getTruncateExpr(ST->getOperand(), Ty); 869 870 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 871 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 872 return getTruncateOrSignExtend(SS->getOperand(), Ty); 873 874 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 875 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 876 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 877 878 // If the input value is a chrec scev, truncate the chrec's operands. 879 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 880 SmallVector<const SCEV *, 4> Operands; 881 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 882 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 883 return getAddRecExpr(Operands, AddRec->getLoop()); 884 } 885 886 // As a special case, fold trunc(undef) to undef. We don't want to 887 // know too much about SCEVUnknowns, but this special case is handy 888 // and harmless. 889 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 890 if (isa<UndefValue>(U->getValue())) 891 return getSCEV(UndefValue::get(Ty)); 892 893 // The cast wasn't folded; create an explicit cast node. We can reuse 894 // the existing insert position since if we get here, we won't have 895 // made any changes which would invalidate it. 896 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 897 Op, Ty); 898 UniqueSCEVs.InsertNode(S, IP); 899 return S; 900} 901 902const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 903 const Type *Ty) { 904 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 905 "This is not an extending conversion!"); 906 assert(isSCEVable(Ty) && 907 "This is not a conversion to a SCEVable type!"); 908 Ty = getEffectiveSCEVType(Ty); 909 910 // Fold if the operand is constant. 911 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 912 return getConstant( 913 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), 914 getEffectiveSCEVType(Ty)))); 915 916 // zext(zext(x)) --> zext(x) 917 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 918 return getZeroExtendExpr(SZ->getOperand(), Ty); 919 920 // Before doing any expensive analysis, check to see if we've already 921 // computed a SCEV for this Op and Ty. 922 FoldingSetNodeID ID; 923 ID.AddInteger(scZeroExtend); 924 ID.AddPointer(Op); 925 ID.AddPointer(Ty); 926 void *IP = 0; 927 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 928 929 // If the input value is a chrec scev, and we can prove that the value 930 // did not overflow the old, smaller, value, we can zero extend all of the 931 // operands (often constants). This allows analysis of something like 932 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 933 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 934 if (AR->isAffine()) { 935 const SCEV *Start = AR->getStart(); 936 const SCEV *Step = AR->getStepRecurrence(*this); 937 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 938 const Loop *L = AR->getLoop(); 939 940 // If we have special knowledge that this addrec won't overflow, 941 // we don't need to do any further analysis. 942 if (AR->hasNoUnsignedWrap()) 943 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 944 getZeroExtendExpr(Step, Ty), 945 L); 946 947 // Check whether the backedge-taken count is SCEVCouldNotCompute. 948 // Note that this serves two purposes: It filters out loops that are 949 // simply not analyzable, and it covers the case where this code is 950 // being called from within backedge-taken count analysis, such that 951 // attempting to ask for the backedge-taken count would likely result 952 // in infinite recursion. In the later case, the analysis code will 953 // cope with a conservative value, and it will take care to purge 954 // that value once it has finished. 955 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 956 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 957 // Manually compute the final value for AR, checking for 958 // overflow. 959 960 // Check whether the backedge-taken count can be losslessly casted to 961 // the addrec's type. The count is always unsigned. 962 const SCEV *CastedMaxBECount = 963 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 964 const SCEV *RecastedMaxBECount = 965 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 966 if (MaxBECount == RecastedMaxBECount) { 967 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 968 // Check whether Start+Step*MaxBECount has no unsigned overflow. 969 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); 970 const SCEV *Add = getAddExpr(Start, ZMul); 971 const SCEV *OperandExtendedAdd = 972 getAddExpr(getZeroExtendExpr(Start, WideTy), 973 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 974 getZeroExtendExpr(Step, WideTy))); 975 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 976 // Return the expression with the addrec on the outside. 977 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 978 getZeroExtendExpr(Step, Ty), 979 L); 980 981 // Similar to above, only this time treat the step value as signed. 982 // This covers loops that count down. 983 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 984 Add = getAddExpr(Start, SMul); 985 OperandExtendedAdd = 986 getAddExpr(getZeroExtendExpr(Start, WideTy), 987 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 988 getSignExtendExpr(Step, WideTy))); 989 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 990 // Return the expression with the addrec on the outside. 991 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 992 getSignExtendExpr(Step, Ty), 993 L); 994 } 995 996 // If the backedge is guarded by a comparison with the pre-inc value 997 // the addrec is safe. Also, if the entry is guarded by a comparison 998 // with the start value and the backedge is guarded by a comparison 999 // with the post-inc value, the addrec is safe. 1000 if (isKnownPositive(Step)) { 1001 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 1002 getUnsignedRange(Step).getUnsignedMax()); 1003 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 1004 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 1005 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 1006 AR->getPostIncExpr(*this), N))) 1007 // Return the expression with the addrec on the outside. 1008 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1009 getZeroExtendExpr(Step, Ty), 1010 L); 1011 } else if (isKnownNegative(Step)) { 1012 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 1013 getSignedRange(Step).getSignedMin()); 1014 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || 1015 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) && 1016 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 1017 AR->getPostIncExpr(*this), N))) 1018 // Return the expression with the addrec on the outside. 1019 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1020 getSignExtendExpr(Step, Ty), 1021 L); 1022 } 1023 } 1024 } 1025 1026 // The cast wasn't folded; create an explicit cast node. 1027 // Recompute the insert position, as it may have been invalidated. 1028 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1029 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 1030 Op, Ty); 1031 UniqueSCEVs.InsertNode(S, IP); 1032 return S; 1033} 1034 1035const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 1036 const Type *Ty) { 1037 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1038 "This is not an extending conversion!"); 1039 assert(isSCEVable(Ty) && 1040 "This is not a conversion to a SCEVable type!"); 1041 Ty = getEffectiveSCEVType(Ty); 1042 1043 // Fold if the operand is constant. 1044 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1045 return getConstant( 1046 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), 1047 getEffectiveSCEVType(Ty)))); 1048 1049 // sext(sext(x)) --> sext(x) 1050 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1051 return getSignExtendExpr(SS->getOperand(), Ty); 1052 1053 // Before doing any expensive analysis, check to see if we've already 1054 // computed a SCEV for this Op and Ty. 1055 FoldingSetNodeID ID; 1056 ID.AddInteger(scSignExtend); 1057 ID.AddPointer(Op); 1058 ID.AddPointer(Ty); 1059 void *IP = 0; 1060 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1061 1062 // If the input value is a chrec scev, and we can prove that the value 1063 // did not overflow the old, smaller, value, we can sign extend all of the 1064 // operands (often constants). This allows analysis of something like 1065 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1066 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1067 if (AR->isAffine()) { 1068 const SCEV *Start = AR->getStart(); 1069 const SCEV *Step = AR->getStepRecurrence(*this); 1070 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1071 const Loop *L = AR->getLoop(); 1072 1073 // If we have special knowledge that this addrec won't overflow, 1074 // we don't need to do any further analysis. 1075 if (AR->hasNoSignedWrap()) 1076 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1077 getSignExtendExpr(Step, Ty), 1078 L); 1079 1080 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1081 // Note that this serves two purposes: It filters out loops that are 1082 // simply not analyzable, and it covers the case where this code is 1083 // being called from within backedge-taken count analysis, such that 1084 // attempting to ask for the backedge-taken count would likely result 1085 // in infinite recursion. In the later case, the analysis code will 1086 // cope with a conservative value, and it will take care to purge 1087 // that value once it has finished. 1088 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1089 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1090 // Manually compute the final value for AR, checking for 1091 // overflow. 1092 1093 // Check whether the backedge-taken count can be losslessly casted to 1094 // the addrec's type. The count is always unsigned. 1095 const SCEV *CastedMaxBECount = 1096 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1097 const SCEV *RecastedMaxBECount = 1098 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1099 if (MaxBECount == RecastedMaxBECount) { 1100 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1101 // Check whether Start+Step*MaxBECount has no signed overflow. 1102 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1103 const SCEV *Add = getAddExpr(Start, SMul); 1104 const SCEV *OperandExtendedAdd = 1105 getAddExpr(getSignExtendExpr(Start, WideTy), 1106 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1107 getSignExtendExpr(Step, WideTy))); 1108 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1109 // Return the expression with the addrec on the outside. 1110 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1111 getSignExtendExpr(Step, Ty), 1112 L); 1113 1114 // Similar to above, only this time treat the step value as unsigned. 1115 // This covers loops that count up with an unsigned step. 1116 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step); 1117 Add = getAddExpr(Start, UMul); 1118 OperandExtendedAdd = 1119 getAddExpr(getSignExtendExpr(Start, WideTy), 1120 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1121 getZeroExtendExpr(Step, WideTy))); 1122 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1123 // Return the expression with the addrec on the outside. 1124 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1125 getZeroExtendExpr(Step, Ty), 1126 L); 1127 } 1128 1129 // If the backedge is guarded by a comparison with the pre-inc value 1130 // the addrec is safe. Also, if the entry is guarded by a comparison 1131 // with the start value and the backedge is guarded by a comparison 1132 // with the post-inc value, the addrec is safe. 1133 if (isKnownPositive(Step)) { 1134 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 1135 getSignedRange(Step).getSignedMax()); 1136 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 1137 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 1138 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 1139 AR->getPostIncExpr(*this), N))) 1140 // Return the expression with the addrec on the outside. 1141 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1142 getSignExtendExpr(Step, Ty), 1143 L); 1144 } else if (isKnownNegative(Step)) { 1145 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 1146 getSignedRange(Step).getSignedMin()); 1147 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 1148 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 1149 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 1150 AR->getPostIncExpr(*this), N))) 1151 // Return the expression with the addrec on the outside. 1152 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1153 getSignExtendExpr(Step, Ty), 1154 L); 1155 } 1156 } 1157 } 1158 1159 // The cast wasn't folded; create an explicit cast node. 1160 // Recompute the insert position, as it may have been invalidated. 1161 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1162 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1163 Op, Ty); 1164 UniqueSCEVs.InsertNode(S, IP); 1165 return S; 1166} 1167 1168/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1169/// unspecified bits out to the given type. 1170/// 1171const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1172 const Type *Ty) { 1173 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1174 "This is not an extending conversion!"); 1175 assert(isSCEVable(Ty) && 1176 "This is not a conversion to a SCEVable type!"); 1177 Ty = getEffectiveSCEVType(Ty); 1178 1179 // Sign-extend negative constants. 1180 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1181 if (SC->getValue()->getValue().isNegative()) 1182 return getSignExtendExpr(Op, Ty); 1183 1184 // Peel off a truncate cast. 1185 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1186 const SCEV *NewOp = T->getOperand(); 1187 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1188 return getAnyExtendExpr(NewOp, Ty); 1189 return getTruncateOrNoop(NewOp, Ty); 1190 } 1191 1192 // Next try a zext cast. If the cast is folded, use it. 1193 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1194 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1195 return ZExt; 1196 1197 // Next try a sext cast. If the cast is folded, use it. 1198 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1199 if (!isa<SCEVSignExtendExpr>(SExt)) 1200 return SExt; 1201 1202 // Force the cast to be folded into the operands of an addrec. 1203 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1204 SmallVector<const SCEV *, 4> Ops; 1205 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1206 I != E; ++I) 1207 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1208 return getAddRecExpr(Ops, AR->getLoop()); 1209 } 1210 1211 // As a special case, fold anyext(undef) to undef. We don't want to 1212 // know too much about SCEVUnknowns, but this special case is handy 1213 // and harmless. 1214 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 1215 if (isa<UndefValue>(U->getValue())) 1216 return getSCEV(UndefValue::get(Ty)); 1217 1218 // If the expression is obviously signed, use the sext cast value. 1219 if (isa<SCEVSMaxExpr>(Op)) 1220 return SExt; 1221 1222 // Absent any other information, use the zext cast value. 1223 return ZExt; 1224} 1225 1226/// CollectAddOperandsWithScales - Process the given Ops list, which is 1227/// a list of operands to be added under the given scale, update the given 1228/// map. This is a helper function for getAddRecExpr. As an example of 1229/// what it does, given a sequence of operands that would form an add 1230/// expression like this: 1231/// 1232/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1233/// 1234/// where A and B are constants, update the map with these values: 1235/// 1236/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1237/// 1238/// and add 13 + A*B*29 to AccumulatedConstant. 1239/// This will allow getAddRecExpr to produce this: 1240/// 1241/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1242/// 1243/// This form often exposes folding opportunities that are hidden in 1244/// the original operand list. 1245/// 1246/// Return true iff it appears that any interesting folding opportunities 1247/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1248/// the common case where no interesting opportunities are present, and 1249/// is also used as a check to avoid infinite recursion. 1250/// 1251static bool 1252CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1253 SmallVector<const SCEV *, 8> &NewOps, 1254 APInt &AccumulatedConstant, 1255 const SCEV *const *Ops, size_t NumOperands, 1256 const APInt &Scale, 1257 ScalarEvolution &SE) { 1258 bool Interesting = false; 1259 1260 // Iterate over the add operands. They are sorted, with constants first. 1261 unsigned i = 0; 1262 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1263 ++i; 1264 // Pull a buried constant out to the outside. 1265 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 1266 Interesting = true; 1267 AccumulatedConstant += Scale * C->getValue()->getValue(); 1268 } 1269 1270 // Next comes everything else. We're especially interested in multiplies 1271 // here, but they're in the middle, so just visit the rest with one loop. 1272 for (; i != NumOperands; ++i) { 1273 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1274 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1275 APInt NewScale = 1276 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1277 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1278 // A multiplication of a constant with another add; recurse. 1279 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1280 Interesting |= 1281 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1282 Add->op_begin(), Add->getNumOperands(), 1283 NewScale, SE); 1284 } else { 1285 // A multiplication of a constant with some other value. Update 1286 // the map. 1287 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1288 const SCEV *Key = SE.getMulExpr(MulOps); 1289 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1290 M.insert(std::make_pair(Key, NewScale)); 1291 if (Pair.second) { 1292 NewOps.push_back(Pair.first->first); 1293 } else { 1294 Pair.first->second += NewScale; 1295 // The map already had an entry for this value, which may indicate 1296 // a folding opportunity. 1297 Interesting = true; 1298 } 1299 } 1300 } else { 1301 // An ordinary operand. Update the map. 1302 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1303 M.insert(std::make_pair(Ops[i], Scale)); 1304 if (Pair.second) { 1305 NewOps.push_back(Pair.first->first); 1306 } else { 1307 Pair.first->second += Scale; 1308 // The map already had an entry for this value, which may indicate 1309 // a folding opportunity. 1310 Interesting = true; 1311 } 1312 } 1313 } 1314 1315 return Interesting; 1316} 1317 1318namespace { 1319 struct APIntCompare { 1320 bool operator()(const APInt &LHS, const APInt &RHS) const { 1321 return LHS.ult(RHS); 1322 } 1323 }; 1324} 1325 1326/// getAddExpr - Get a canonical add expression, or something simpler if 1327/// possible. 1328const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1329 bool HasNUW, bool HasNSW) { 1330 assert(!Ops.empty() && "Cannot get empty add!"); 1331 if (Ops.size() == 1) return Ops[0]; 1332#ifndef NDEBUG 1333 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1334 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1335 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1336 "SCEVAddExpr operand types don't match!"); 1337#endif 1338 1339 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1340 if (!HasNUW && HasNSW) { 1341 bool All = true; 1342 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1343 if (!isKnownNonNegative(Ops[i])) { 1344 All = false; 1345 break; 1346 } 1347 if (All) HasNUW = true; 1348 } 1349 1350 // Sort by complexity, this groups all similar expression types together. 1351 GroupByComplexity(Ops, LI); 1352 1353 // If there are any constants, fold them together. 1354 unsigned Idx = 0; 1355 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1356 ++Idx; 1357 assert(Idx < Ops.size()); 1358 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1359 // We found two constants, fold them together! 1360 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1361 RHSC->getValue()->getValue()); 1362 if (Ops.size() == 2) return Ops[0]; 1363 Ops.erase(Ops.begin()+1); // Erase the folded element 1364 LHSC = cast<SCEVConstant>(Ops[0]); 1365 } 1366 1367 // If we are left with a constant zero being added, strip it off. 1368 if (LHSC->getValue()->isZero()) { 1369 Ops.erase(Ops.begin()); 1370 --Idx; 1371 } 1372 1373 if (Ops.size() == 1) return Ops[0]; 1374 } 1375 1376 // Okay, check to see if the same value occurs in the operand list twice. If 1377 // so, merge them together into an multiply expression. Since we sorted the 1378 // list, these values are required to be adjacent. 1379 const Type *Ty = Ops[0]->getType(); 1380 bool FoundMatch = false; 1381 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1382 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1383 // Found a match, merge the two values into a multiply, and add any 1384 // remaining values to the result. 1385 const SCEV *Two = getConstant(Ty, 2); 1386 const SCEV *Mul = getMulExpr(Ops[i], Two); 1387 if (Ops.size() == 2) 1388 return Mul; 1389 Ops[i] = Mul; 1390 Ops.erase(Ops.begin()+i+1); 1391 --i; --e; 1392 FoundMatch = true; 1393 } 1394 if (FoundMatch) 1395 return getAddExpr(Ops, HasNUW, HasNSW); 1396 1397 // Check for truncates. If all the operands are truncated from the same 1398 // type, see if factoring out the truncate would permit the result to be 1399 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1400 // if the contents of the resulting outer trunc fold to something simple. 1401 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1402 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1403 const Type *DstType = Trunc->getType(); 1404 const Type *SrcType = Trunc->getOperand()->getType(); 1405 SmallVector<const SCEV *, 8> LargeOps; 1406 bool Ok = true; 1407 // Check all the operands to see if they can be represented in the 1408 // source type of the truncate. 1409 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1410 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1411 if (T->getOperand()->getType() != SrcType) { 1412 Ok = false; 1413 break; 1414 } 1415 LargeOps.push_back(T->getOperand()); 1416 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1417 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 1418 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1419 SmallVector<const SCEV *, 8> LargeMulOps; 1420 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1421 if (const SCEVTruncateExpr *T = 1422 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1423 if (T->getOperand()->getType() != SrcType) { 1424 Ok = false; 1425 break; 1426 } 1427 LargeMulOps.push_back(T->getOperand()); 1428 } else if (const SCEVConstant *C = 1429 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1430 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 1431 } else { 1432 Ok = false; 1433 break; 1434 } 1435 } 1436 if (Ok) 1437 LargeOps.push_back(getMulExpr(LargeMulOps)); 1438 } else { 1439 Ok = false; 1440 break; 1441 } 1442 } 1443 if (Ok) { 1444 // Evaluate the expression in the larger type. 1445 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW); 1446 // If it folds to something simple, use it. Otherwise, don't. 1447 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1448 return getTruncateExpr(Fold, DstType); 1449 } 1450 } 1451 1452 // Skip past any other cast SCEVs. 1453 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1454 ++Idx; 1455 1456 // If there are add operands they would be next. 1457 if (Idx < Ops.size()) { 1458 bool DeletedAdd = false; 1459 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1460 // If we have an add, expand the add operands onto the end of the operands 1461 // list. 1462 Ops.erase(Ops.begin()+Idx); 1463 Ops.append(Add->op_begin(), Add->op_end()); 1464 DeletedAdd = true; 1465 } 1466 1467 // If we deleted at least one add, we added operands to the end of the list, 1468 // and they are not necessarily sorted. Recurse to resort and resimplify 1469 // any operands we just acquired. 1470 if (DeletedAdd) 1471 return getAddExpr(Ops); 1472 } 1473 1474 // Skip over the add expression until we get to a multiply. 1475 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1476 ++Idx; 1477 1478 // Check to see if there are any folding opportunities present with 1479 // operands multiplied by constant values. 1480 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1481 uint64_t BitWidth = getTypeSizeInBits(Ty); 1482 DenseMap<const SCEV *, APInt> M; 1483 SmallVector<const SCEV *, 8> NewOps; 1484 APInt AccumulatedConstant(BitWidth, 0); 1485 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1486 Ops.data(), Ops.size(), 1487 APInt(BitWidth, 1), *this)) { 1488 // Some interesting folding opportunity is present, so its worthwhile to 1489 // re-generate the operands list. Group the operands by constant scale, 1490 // to avoid multiplying by the same constant scale multiple times. 1491 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1492 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(), 1493 E = NewOps.end(); I != E; ++I) 1494 MulOpLists[M.find(*I)->second].push_back(*I); 1495 // Re-generate the operands list. 1496 Ops.clear(); 1497 if (AccumulatedConstant != 0) 1498 Ops.push_back(getConstant(AccumulatedConstant)); 1499 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1500 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1501 if (I->first != 0) 1502 Ops.push_back(getMulExpr(getConstant(I->first), 1503 getAddExpr(I->second))); 1504 if (Ops.empty()) 1505 return getConstant(Ty, 0); 1506 if (Ops.size() == 1) 1507 return Ops[0]; 1508 return getAddExpr(Ops); 1509 } 1510 } 1511 1512 // If we are adding something to a multiply expression, make sure the 1513 // something is not already an operand of the multiply. If so, merge it into 1514 // the multiply. 1515 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1516 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1517 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1518 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1519 if (isa<SCEVConstant>(MulOpSCEV)) 1520 continue; 1521 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1522 if (MulOpSCEV == Ops[AddOp]) { 1523 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1524 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1525 if (Mul->getNumOperands() != 2) { 1526 // If the multiply has more than two operands, we must get the 1527 // Y*Z term. 1528 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end()); 1529 MulOps.erase(MulOps.begin()+MulOp); 1530 InnerMul = getMulExpr(MulOps); 1531 } 1532 const SCEV *One = getConstant(Ty, 1); 1533 const SCEV *AddOne = getAddExpr(InnerMul, One); 1534 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV); 1535 if (Ops.size() == 2) return OuterMul; 1536 if (AddOp < Idx) { 1537 Ops.erase(Ops.begin()+AddOp); 1538 Ops.erase(Ops.begin()+Idx-1); 1539 } else { 1540 Ops.erase(Ops.begin()+Idx); 1541 Ops.erase(Ops.begin()+AddOp-1); 1542 } 1543 Ops.push_back(OuterMul); 1544 return getAddExpr(Ops); 1545 } 1546 1547 // Check this multiply against other multiplies being added together. 1548 bool AnyFold = false; 1549 for (unsigned OtherMulIdx = Idx+1; 1550 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1551 ++OtherMulIdx) { 1552 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1553 // If MulOp occurs in OtherMul, we can fold the two multiplies 1554 // together. 1555 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1556 OMulOp != e; ++OMulOp) 1557 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1558 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1559 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1560 if (Mul->getNumOperands() != 2) { 1561 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1562 Mul->op_end()); 1563 MulOps.erase(MulOps.begin()+MulOp); 1564 InnerMul1 = getMulExpr(MulOps); 1565 } 1566 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1567 if (OtherMul->getNumOperands() != 2) { 1568 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1569 OtherMul->op_end()); 1570 MulOps.erase(MulOps.begin()+OMulOp); 1571 InnerMul2 = getMulExpr(MulOps); 1572 } 1573 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1574 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1575 if (Ops.size() == 2) return OuterMul; 1576 Ops[Idx] = OuterMul; 1577 Ops.erase(Ops.begin()+OtherMulIdx); 1578 OtherMulIdx = Idx; 1579 AnyFold = true; 1580 } 1581 } 1582 if (AnyFold) 1583 return getAddExpr(Ops); 1584 } 1585 } 1586 1587 // If there are any add recurrences in the operands list, see if any other 1588 // added values are loop invariant. If so, we can fold them into the 1589 // recurrence. 1590 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1591 ++Idx; 1592 1593 // Scan over all recurrences, trying to fold loop invariants into them. 1594 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1595 // Scan all of the other operands to this add and add them to the vector if 1596 // they are loop invariant w.r.t. the recurrence. 1597 SmallVector<const SCEV *, 8> LIOps; 1598 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1599 const Loop *AddRecLoop = AddRec->getLoop(); 1600 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1601 if (Ops[i]->isLoopInvariant(AddRecLoop)) { 1602 LIOps.push_back(Ops[i]); 1603 Ops.erase(Ops.begin()+i); 1604 --i; --e; 1605 } 1606 1607 // If we found some loop invariants, fold them into the recurrence. 1608 if (!LIOps.empty()) { 1609 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1610 LIOps.push_back(AddRec->getStart()); 1611 1612 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1613 AddRec->op_end()); 1614 AddRecOps[0] = getAddExpr(LIOps); 1615 1616 // Build the new addrec. Propagate the NUW and NSW flags if both the 1617 // outer add and the inner addrec are guaranteed to have no overflow. 1618 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, 1619 HasNUW && AddRec->hasNoUnsignedWrap(), 1620 HasNSW && AddRec->hasNoSignedWrap()); 1621 1622 // If all of the other operands were loop invariant, we are done. 1623 if (Ops.size() == 1) return NewRec; 1624 1625 // Otherwise, add the folded AddRec by the non-liv parts. 1626 for (unsigned i = 0;; ++i) 1627 if (Ops[i] == AddRec) { 1628 Ops[i] = NewRec; 1629 break; 1630 } 1631 return getAddExpr(Ops); 1632 } 1633 1634 // Okay, if there weren't any loop invariants to be folded, check to see if 1635 // there are multiple AddRec's with the same loop induction variable being 1636 // added together. If so, we can fold them. 1637 for (unsigned OtherIdx = Idx+1; 1638 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1639 if (OtherIdx != Idx) { 1640 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1641 if (AddRecLoop == OtherAddRec->getLoop()) { 1642 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 1643 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(), 1644 AddRec->op_end()); 1645 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 1646 if (i >= NewOps.size()) { 1647 NewOps.append(OtherAddRec->op_begin()+i, 1648 OtherAddRec->op_end()); 1649 break; 1650 } 1651 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 1652 } 1653 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRecLoop); 1654 1655 if (Ops.size() == 2) return NewAddRec; 1656 1657 Ops.erase(Ops.begin()+Idx); 1658 Ops.erase(Ops.begin()+OtherIdx-1); 1659 Ops.push_back(NewAddRec); 1660 return getAddExpr(Ops); 1661 } 1662 } 1663 1664 // Otherwise couldn't fold anything into this recurrence. Move onto the 1665 // next one. 1666 } 1667 1668 // Okay, it looks like we really DO need an add expr. Check to see if we 1669 // already have one, otherwise create a new one. 1670 FoldingSetNodeID ID; 1671 ID.AddInteger(scAddExpr); 1672 ID.AddInteger(Ops.size()); 1673 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1674 ID.AddPointer(Ops[i]); 1675 void *IP = 0; 1676 SCEVAddExpr *S = 1677 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1678 if (!S) { 1679 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1680 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1681 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), 1682 O, Ops.size()); 1683 UniqueSCEVs.InsertNode(S, IP); 1684 } 1685 if (HasNUW) S->setHasNoUnsignedWrap(true); 1686 if (HasNSW) S->setHasNoSignedWrap(true); 1687 return S; 1688} 1689 1690/// getMulExpr - Get a canonical multiply expression, or something simpler if 1691/// possible. 1692const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1693 bool HasNUW, bool HasNSW) { 1694 assert(!Ops.empty() && "Cannot get empty mul!"); 1695 if (Ops.size() == 1) return Ops[0]; 1696#ifndef NDEBUG 1697 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1698 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1699 getEffectiveSCEVType(Ops[0]->getType()) && 1700 "SCEVMulExpr operand types don't match!"); 1701#endif 1702 1703 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1704 if (!HasNUW && HasNSW) { 1705 bool All = true; 1706 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1707 if (!isKnownNonNegative(Ops[i])) { 1708 All = false; 1709 break; 1710 } 1711 if (All) HasNUW = true; 1712 } 1713 1714 // Sort by complexity, this groups all similar expression types together. 1715 GroupByComplexity(Ops, LI); 1716 1717 // If there are any constants, fold them together. 1718 unsigned Idx = 0; 1719 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1720 1721 // C1*(C2+V) -> C1*C2 + C1*V 1722 if (Ops.size() == 2) 1723 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1724 if (Add->getNumOperands() == 2 && 1725 isa<SCEVConstant>(Add->getOperand(0))) 1726 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1727 getMulExpr(LHSC, Add->getOperand(1))); 1728 1729 ++Idx; 1730 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1731 // We found two constants, fold them together! 1732 ConstantInt *Fold = ConstantInt::get(getContext(), 1733 LHSC->getValue()->getValue() * 1734 RHSC->getValue()->getValue()); 1735 Ops[0] = getConstant(Fold); 1736 Ops.erase(Ops.begin()+1); // Erase the folded element 1737 if (Ops.size() == 1) return Ops[0]; 1738 LHSC = cast<SCEVConstant>(Ops[0]); 1739 } 1740 1741 // If we are left with a constant one being multiplied, strip it off. 1742 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1743 Ops.erase(Ops.begin()); 1744 --Idx; 1745 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1746 // If we have a multiply of zero, it will always be zero. 1747 return Ops[0]; 1748 } else if (Ops[0]->isAllOnesValue()) { 1749 // If we have a mul by -1 of an add, try distributing the -1 among the 1750 // add operands. 1751 if (Ops.size() == 2) 1752 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1753 SmallVector<const SCEV *, 4> NewOps; 1754 bool AnyFolded = false; 1755 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end(); 1756 I != E; ++I) { 1757 const SCEV *Mul = getMulExpr(Ops[0], *I); 1758 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1759 NewOps.push_back(Mul); 1760 } 1761 if (AnyFolded) 1762 return getAddExpr(NewOps); 1763 } 1764 } 1765 1766 if (Ops.size() == 1) 1767 return Ops[0]; 1768 } 1769 1770 // Skip over the add expression until we get to a multiply. 1771 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1772 ++Idx; 1773 1774 // If there are mul operands inline them all into this expression. 1775 if (Idx < Ops.size()) { 1776 bool DeletedMul = false; 1777 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1778 // If we have an mul, expand the mul operands onto the end of the operands 1779 // list. 1780 Ops.erase(Ops.begin()+Idx); 1781 Ops.append(Mul->op_begin(), Mul->op_end()); 1782 DeletedMul = true; 1783 } 1784 1785 // If we deleted at least one mul, we added operands to the end of the list, 1786 // and they are not necessarily sorted. Recurse to resort and resimplify 1787 // any operands we just acquired. 1788 if (DeletedMul) 1789 return getMulExpr(Ops); 1790 } 1791 1792 // If there are any add recurrences in the operands list, see if any other 1793 // added values are loop invariant. If so, we can fold them into the 1794 // recurrence. 1795 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1796 ++Idx; 1797 1798 // Scan over all recurrences, trying to fold loop invariants into them. 1799 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1800 // Scan all of the other operands to this mul and add them to the vector if 1801 // they are loop invariant w.r.t. the recurrence. 1802 SmallVector<const SCEV *, 8> LIOps; 1803 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1804 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1805 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1806 LIOps.push_back(Ops[i]); 1807 Ops.erase(Ops.begin()+i); 1808 --i; --e; 1809 } 1810 1811 // If we found some loop invariants, fold them into the recurrence. 1812 if (!LIOps.empty()) { 1813 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1814 SmallVector<const SCEV *, 4> NewOps; 1815 NewOps.reserve(AddRec->getNumOperands()); 1816 const SCEV *Scale = getMulExpr(LIOps); 1817 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1818 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1819 1820 // Build the new addrec. Propagate the NUW and NSW flags if both the 1821 // outer mul and the inner addrec are guaranteed to have no overflow. 1822 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(), 1823 HasNUW && AddRec->hasNoUnsignedWrap(), 1824 HasNSW && AddRec->hasNoSignedWrap()); 1825 1826 // If all of the other operands were loop invariant, we are done. 1827 if (Ops.size() == 1) return NewRec; 1828 1829 // Otherwise, multiply the folded AddRec by the non-liv parts. 1830 for (unsigned i = 0;; ++i) 1831 if (Ops[i] == AddRec) { 1832 Ops[i] = NewRec; 1833 break; 1834 } 1835 return getMulExpr(Ops); 1836 } 1837 1838 // Okay, if there weren't any loop invariants to be folded, check to see if 1839 // there are multiple AddRec's with the same loop induction variable being 1840 // multiplied together. If so, we can fold them. 1841 for (unsigned OtherIdx = Idx+1; 1842 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1843 if (OtherIdx != Idx) { 1844 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1845 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1846 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1847 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1848 const SCEV *NewStart = getMulExpr(F->getStart(), 1849 G->getStart()); 1850 const SCEV *B = F->getStepRecurrence(*this); 1851 const SCEV *D = G->getStepRecurrence(*this); 1852 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1853 getMulExpr(G, B), 1854 getMulExpr(B, D)); 1855 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1856 F->getLoop()); 1857 if (Ops.size() == 2) return NewAddRec; 1858 1859 Ops.erase(Ops.begin()+Idx); 1860 Ops.erase(Ops.begin()+OtherIdx-1); 1861 Ops.push_back(NewAddRec); 1862 return getMulExpr(Ops); 1863 } 1864 } 1865 1866 // Otherwise couldn't fold anything into this recurrence. Move onto the 1867 // next one. 1868 } 1869 1870 // Okay, it looks like we really DO need an mul expr. Check to see if we 1871 // already have one, otherwise create a new one. 1872 FoldingSetNodeID ID; 1873 ID.AddInteger(scMulExpr); 1874 ID.AddInteger(Ops.size()); 1875 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1876 ID.AddPointer(Ops[i]); 1877 void *IP = 0; 1878 SCEVMulExpr *S = 1879 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1880 if (!S) { 1881 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1882 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1883 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 1884 O, Ops.size()); 1885 UniqueSCEVs.InsertNode(S, IP); 1886 } 1887 if (HasNUW) S->setHasNoUnsignedWrap(true); 1888 if (HasNSW) S->setHasNoSignedWrap(true); 1889 return S; 1890} 1891 1892/// getUDivExpr - Get a canonical unsigned division expression, or something 1893/// simpler if possible. 1894const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1895 const SCEV *RHS) { 1896 assert(getEffectiveSCEVType(LHS->getType()) == 1897 getEffectiveSCEVType(RHS->getType()) && 1898 "SCEVUDivExpr operand types don't match!"); 1899 1900 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1901 if (RHSC->getValue()->equalsInt(1)) 1902 return LHS; // X udiv 1 --> x 1903 // If the denominator is zero, the result of the udiv is undefined. Don't 1904 // try to analyze it, because the resolution chosen here may differ from 1905 // the resolution chosen in other parts of the compiler. 1906 if (!RHSC->getValue()->isZero()) { 1907 // Determine if the division can be folded into the operands of 1908 // its operands. 1909 // TODO: Generalize this to non-constants by using known-bits information. 1910 const Type *Ty = LHS->getType(); 1911 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1912 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; 1913 // For non-power-of-two values, effectively round the value up to the 1914 // nearest power of two. 1915 if (!RHSC->getValue()->getValue().isPowerOf2()) 1916 ++MaxShiftAmt; 1917 const IntegerType *ExtTy = 1918 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 1919 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1920 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1921 if (const SCEVConstant *Step = 1922 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1923 if (!Step->getValue()->getValue() 1924 .urem(RHSC->getValue()->getValue()) && 1925 getZeroExtendExpr(AR, ExtTy) == 1926 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1927 getZeroExtendExpr(Step, ExtTy), 1928 AR->getLoop())) { 1929 SmallVector<const SCEV *, 4> Operands; 1930 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1931 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1932 return getAddRecExpr(Operands, AR->getLoop()); 1933 } 1934 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1935 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1936 SmallVector<const SCEV *, 4> Operands; 1937 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1938 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1939 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1940 // Find an operand that's safely divisible. 1941 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1942 const SCEV *Op = M->getOperand(i); 1943 const SCEV *Div = getUDivExpr(Op, RHSC); 1944 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1945 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 1946 M->op_end()); 1947 Operands[i] = Div; 1948 return getMulExpr(Operands); 1949 } 1950 } 1951 } 1952 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1953 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1954 SmallVector<const SCEV *, 4> Operands; 1955 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1956 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1957 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1958 Operands.clear(); 1959 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1960 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 1961 if (isa<SCEVUDivExpr>(Op) || 1962 getMulExpr(Op, RHS) != A->getOperand(i)) 1963 break; 1964 Operands.push_back(Op); 1965 } 1966 if (Operands.size() == A->getNumOperands()) 1967 return getAddExpr(Operands); 1968 } 1969 } 1970 1971 // Fold if both operands are constant. 1972 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1973 Constant *LHSCV = LHSC->getValue(); 1974 Constant *RHSCV = RHSC->getValue(); 1975 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 1976 RHSCV))); 1977 } 1978 } 1979 } 1980 1981 FoldingSetNodeID ID; 1982 ID.AddInteger(scUDivExpr); 1983 ID.AddPointer(LHS); 1984 ID.AddPointer(RHS); 1985 void *IP = 0; 1986 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1987 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 1988 LHS, RHS); 1989 UniqueSCEVs.InsertNode(S, IP); 1990 return S; 1991} 1992 1993 1994/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1995/// Simplify the expression as much as possible. 1996const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 1997 const SCEV *Step, const Loop *L, 1998 bool HasNUW, bool HasNSW) { 1999 SmallVector<const SCEV *, 4> Operands; 2000 Operands.push_back(Start); 2001 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 2002 if (StepChrec->getLoop() == L) { 2003 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 2004 return getAddRecExpr(Operands, L); 2005 } 2006 2007 Operands.push_back(Step); 2008 return getAddRecExpr(Operands, L, HasNUW, HasNSW); 2009} 2010 2011/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2012/// Simplify the expression as much as possible. 2013const SCEV * 2014ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 2015 const Loop *L, 2016 bool HasNUW, bool HasNSW) { 2017 if (Operands.size() == 1) return Operands[0]; 2018#ifndef NDEBUG 2019 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 2020 assert(getEffectiveSCEVType(Operands[i]->getType()) == 2021 getEffectiveSCEVType(Operands[0]->getType()) && 2022 "SCEVAddRecExpr operand types don't match!"); 2023#endif 2024 2025 if (Operands.back()->isZero()) { 2026 Operands.pop_back(); 2027 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X 2028 } 2029 2030 // It's tempting to want to call getMaxBackedgeTakenCount count here and 2031 // use that information to infer NUW and NSW flags. However, computing a 2032 // BE count requires calling getAddRecExpr, so we may not yet have a 2033 // meaningful BE count at this point (and if we don't, we'd be stuck 2034 // with a SCEVCouldNotCompute as the cached BE count). 2035 2036 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 2037 if (!HasNUW && HasNSW) { 2038 bool All = true; 2039 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2040 if (!isKnownNonNegative(Operands[i])) { 2041 All = false; 2042 break; 2043 } 2044 if (All) HasNUW = true; 2045 } 2046 2047 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 2048 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 2049 const Loop *NestedLoop = NestedAR->getLoop(); 2050 if (L->contains(NestedLoop->getHeader()) ? 2051 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 2052 (!NestedLoop->contains(L->getHeader()) && 2053 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 2054 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 2055 NestedAR->op_end()); 2056 Operands[0] = NestedAR->getStart(); 2057 // AddRecs require their operands be loop-invariant with respect to their 2058 // loops. Don't perform this transformation if it would break this 2059 // requirement. 2060 bool AllInvariant = true; 2061 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2062 if (!Operands[i]->isLoopInvariant(L)) { 2063 AllInvariant = false; 2064 break; 2065 } 2066 if (AllInvariant) { 2067 NestedOperands[0] = getAddRecExpr(Operands, L); 2068 AllInvariant = true; 2069 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2070 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 2071 AllInvariant = false; 2072 break; 2073 } 2074 if (AllInvariant) 2075 // Ok, both add recurrences are valid after the transformation. 2076 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW); 2077 } 2078 // Reset Operands to its original state. 2079 Operands[0] = NestedAR; 2080 } 2081 } 2082 2083 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2084 // already have one, otherwise create a new one. 2085 FoldingSetNodeID ID; 2086 ID.AddInteger(scAddRecExpr); 2087 ID.AddInteger(Operands.size()); 2088 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2089 ID.AddPointer(Operands[i]); 2090 ID.AddPointer(L); 2091 void *IP = 0; 2092 SCEVAddRecExpr *S = 2093 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2094 if (!S) { 2095 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2096 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2097 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2098 O, Operands.size(), L); 2099 UniqueSCEVs.InsertNode(S, IP); 2100 } 2101 if (HasNUW) S->setHasNoUnsignedWrap(true); 2102 if (HasNSW) S->setHasNoSignedWrap(true); 2103 return S; 2104} 2105 2106const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2107 const SCEV *RHS) { 2108 SmallVector<const SCEV *, 2> Ops; 2109 Ops.push_back(LHS); 2110 Ops.push_back(RHS); 2111 return getSMaxExpr(Ops); 2112} 2113 2114const SCEV * 2115ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2116 assert(!Ops.empty() && "Cannot get empty smax!"); 2117 if (Ops.size() == 1) return Ops[0]; 2118#ifndef NDEBUG 2119 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2120 assert(getEffectiveSCEVType(Ops[i]->getType()) == 2121 getEffectiveSCEVType(Ops[0]->getType()) && 2122 "SCEVSMaxExpr operand types don't match!"); 2123#endif 2124 2125 // Sort by complexity, this groups all similar expression types together. 2126 GroupByComplexity(Ops, LI); 2127 2128 // If there are any constants, fold them together. 2129 unsigned Idx = 0; 2130 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2131 ++Idx; 2132 assert(Idx < Ops.size()); 2133 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2134 // We found two constants, fold them together! 2135 ConstantInt *Fold = ConstantInt::get(getContext(), 2136 APIntOps::smax(LHSC->getValue()->getValue(), 2137 RHSC->getValue()->getValue())); 2138 Ops[0] = getConstant(Fold); 2139 Ops.erase(Ops.begin()+1); // Erase the folded element 2140 if (Ops.size() == 1) return Ops[0]; 2141 LHSC = cast<SCEVConstant>(Ops[0]); 2142 } 2143 2144 // If we are left with a constant minimum-int, strip it off. 2145 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2146 Ops.erase(Ops.begin()); 2147 --Idx; 2148 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2149 // If we have an smax with a constant maximum-int, it will always be 2150 // maximum-int. 2151 return Ops[0]; 2152 } 2153 2154 if (Ops.size() == 1) return Ops[0]; 2155 } 2156 2157 // Find the first SMax 2158 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2159 ++Idx; 2160 2161 // Check to see if one of the operands is an SMax. If so, expand its operands 2162 // onto our operand list, and recurse to simplify. 2163 if (Idx < Ops.size()) { 2164 bool DeletedSMax = false; 2165 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2166 Ops.erase(Ops.begin()+Idx); 2167 Ops.append(SMax->op_begin(), SMax->op_end()); 2168 DeletedSMax = true; 2169 } 2170 2171 if (DeletedSMax) 2172 return getSMaxExpr(Ops); 2173 } 2174 2175 // Okay, check to see if the same value occurs in the operand list twice. If 2176 // so, delete one. Since we sorted the list, these values are required to 2177 // be adjacent. 2178 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2179 // X smax Y smax Y --> X smax Y 2180 // X smax Y --> X, if X is always greater than Y 2181 if (Ops[i] == Ops[i+1] || 2182 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 2183 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2184 --i; --e; 2185 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 2186 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2187 --i; --e; 2188 } 2189 2190 if (Ops.size() == 1) return Ops[0]; 2191 2192 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2193 2194 // Okay, it looks like we really DO need an smax expr. Check to see if we 2195 // already have one, otherwise create a new one. 2196 FoldingSetNodeID ID; 2197 ID.AddInteger(scSMaxExpr); 2198 ID.AddInteger(Ops.size()); 2199 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2200 ID.AddPointer(Ops[i]); 2201 void *IP = 0; 2202 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2203 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2204 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2205 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 2206 O, Ops.size()); 2207 UniqueSCEVs.InsertNode(S, IP); 2208 return S; 2209} 2210 2211const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2212 const SCEV *RHS) { 2213 SmallVector<const SCEV *, 2> Ops; 2214 Ops.push_back(LHS); 2215 Ops.push_back(RHS); 2216 return getUMaxExpr(Ops); 2217} 2218 2219const SCEV * 2220ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2221 assert(!Ops.empty() && "Cannot get empty umax!"); 2222 if (Ops.size() == 1) return Ops[0]; 2223#ifndef NDEBUG 2224 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2225 assert(getEffectiveSCEVType(Ops[i]->getType()) == 2226 getEffectiveSCEVType(Ops[0]->getType()) && 2227 "SCEVUMaxExpr operand types don't match!"); 2228#endif 2229 2230 // Sort by complexity, this groups all similar expression types together. 2231 GroupByComplexity(Ops, LI); 2232 2233 // If there are any constants, fold them together. 2234 unsigned Idx = 0; 2235 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2236 ++Idx; 2237 assert(Idx < Ops.size()); 2238 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2239 // We found two constants, fold them together! 2240 ConstantInt *Fold = ConstantInt::get(getContext(), 2241 APIntOps::umax(LHSC->getValue()->getValue(), 2242 RHSC->getValue()->getValue())); 2243 Ops[0] = getConstant(Fold); 2244 Ops.erase(Ops.begin()+1); // Erase the folded element 2245 if (Ops.size() == 1) return Ops[0]; 2246 LHSC = cast<SCEVConstant>(Ops[0]); 2247 } 2248 2249 // If we are left with a constant minimum-int, strip it off. 2250 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2251 Ops.erase(Ops.begin()); 2252 --Idx; 2253 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2254 // If we have an umax with a constant maximum-int, it will always be 2255 // maximum-int. 2256 return Ops[0]; 2257 } 2258 2259 if (Ops.size() == 1) return Ops[0]; 2260 } 2261 2262 // Find the first UMax 2263 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2264 ++Idx; 2265 2266 // Check to see if one of the operands is a UMax. If so, expand its operands 2267 // onto our operand list, and recurse to simplify. 2268 if (Idx < Ops.size()) { 2269 bool DeletedUMax = false; 2270 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2271 Ops.erase(Ops.begin()+Idx); 2272 Ops.append(UMax->op_begin(), UMax->op_end()); 2273 DeletedUMax = true; 2274 } 2275 2276 if (DeletedUMax) 2277 return getUMaxExpr(Ops); 2278 } 2279 2280 // Okay, check to see if the same value occurs in the operand list twice. If 2281 // so, delete one. Since we sorted the list, these values are required to 2282 // be adjacent. 2283 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2284 // X umax Y umax Y --> X umax Y 2285 // X umax Y --> X, if X is always greater than Y 2286 if (Ops[i] == Ops[i+1] || 2287 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 2288 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2289 --i; --e; 2290 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 2291 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2292 --i; --e; 2293 } 2294 2295 if (Ops.size() == 1) return Ops[0]; 2296 2297 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2298 2299 // Okay, it looks like we really DO need a umax expr. Check to see if we 2300 // already have one, otherwise create a new one. 2301 FoldingSetNodeID ID; 2302 ID.AddInteger(scUMaxExpr); 2303 ID.AddInteger(Ops.size()); 2304 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2305 ID.AddPointer(Ops[i]); 2306 void *IP = 0; 2307 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2308 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2309 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2310 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 2311 O, Ops.size()); 2312 UniqueSCEVs.InsertNode(S, IP); 2313 return S; 2314} 2315 2316const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2317 const SCEV *RHS) { 2318 // ~smax(~x, ~y) == smin(x, y). 2319 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2320} 2321 2322const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2323 const SCEV *RHS) { 2324 // ~umax(~x, ~y) == umin(x, y) 2325 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2326} 2327 2328const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) { 2329 // If we have TargetData, we can bypass creating a target-independent 2330 // constant expression and then folding it back into a ConstantInt. 2331 // This is just a compile-time optimization. 2332 if (TD) 2333 return getConstant(TD->getIntPtrType(getContext()), 2334 TD->getTypeAllocSize(AllocTy)); 2335 2336 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2337 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2338 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2339 C = Folded; 2340 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2341 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2342} 2343 2344const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) { 2345 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2346 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2347 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2348 C = Folded; 2349 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2350 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2351} 2352 2353const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy, 2354 unsigned FieldNo) { 2355 // If we have TargetData, we can bypass creating a target-independent 2356 // constant expression and then folding it back into a ConstantInt. 2357 // This is just a compile-time optimization. 2358 if (TD) 2359 return getConstant(TD->getIntPtrType(getContext()), 2360 TD->getStructLayout(STy)->getElementOffset(FieldNo)); 2361 2362 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2363 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2364 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2365 C = Folded; 2366 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2367 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2368} 2369 2370const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy, 2371 Constant *FieldNo) { 2372 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2373 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2374 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2375 C = Folded; 2376 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2377 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2378} 2379 2380const SCEV *ScalarEvolution::getUnknown(Value *V) { 2381 // Don't attempt to do anything other than create a SCEVUnknown object 2382 // here. createSCEV only calls getUnknown after checking for all other 2383 // interesting possibilities, and any other code that calls getUnknown 2384 // is doing so in order to hide a value from SCEV canonicalization. 2385 2386 FoldingSetNodeID ID; 2387 ID.AddInteger(scUnknown); 2388 ID.AddPointer(V); 2389 void *IP = 0; 2390 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { 2391 assert(cast<SCEVUnknown>(S)->getValue() == V && 2392 "Stale SCEVUnknown in uniquing map!"); 2393 return S; 2394 } 2395 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, 2396 FirstUnknown); 2397 FirstUnknown = cast<SCEVUnknown>(S); 2398 UniqueSCEVs.InsertNode(S, IP); 2399 return S; 2400} 2401 2402//===----------------------------------------------------------------------===// 2403// Basic SCEV Analysis and PHI Idiom Recognition Code 2404// 2405 2406/// isSCEVable - Test if values of the given type are analyzable within 2407/// the SCEV framework. This primarily includes integer types, and it 2408/// can optionally include pointer types if the ScalarEvolution class 2409/// has access to target-specific information. 2410bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2411 // Integers and pointers are always SCEVable. 2412 return Ty->isIntegerTy() || Ty->isPointerTy(); 2413} 2414 2415/// getTypeSizeInBits - Return the size in bits of the specified type, 2416/// for which isSCEVable must return true. 2417uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2418 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2419 2420 // If we have a TargetData, use it! 2421 if (TD) 2422 return TD->getTypeSizeInBits(Ty); 2423 2424 // Integer types have fixed sizes. 2425 if (Ty->isIntegerTy()) 2426 return Ty->getPrimitiveSizeInBits(); 2427 2428 // The only other support type is pointer. Without TargetData, conservatively 2429 // assume pointers are 64-bit. 2430 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2431 return 64; 2432} 2433 2434/// getEffectiveSCEVType - Return a type with the same bitwidth as 2435/// the given type and which represents how SCEV will treat the given 2436/// type, for which isSCEVable must return true. For pointer types, 2437/// this is the pointer-sized integer type. 2438const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2439 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2440 2441 if (Ty->isIntegerTy()) 2442 return Ty; 2443 2444 // The only other support type is pointer. 2445 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2446 if (TD) return TD->getIntPtrType(getContext()); 2447 2448 // Without TargetData, conservatively assume pointers are 64-bit. 2449 return Type::getInt64Ty(getContext()); 2450} 2451 2452const SCEV *ScalarEvolution::getCouldNotCompute() { 2453 return &CouldNotCompute; 2454} 2455 2456/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2457/// expression and create a new one. 2458const SCEV *ScalarEvolution::getSCEV(Value *V) { 2459 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2460 2461 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V); 2462 if (I != Scalars.end()) return I->second; 2463 const SCEV *S = createSCEV(V); 2464 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2465 return S; 2466} 2467 2468/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2469/// 2470const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2471 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2472 return getConstant( 2473 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2474 2475 const Type *Ty = V->getType(); 2476 Ty = getEffectiveSCEVType(Ty); 2477 return getMulExpr(V, 2478 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2479} 2480 2481/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2482const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2483 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2484 return getConstant( 2485 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2486 2487 const Type *Ty = V->getType(); 2488 Ty = getEffectiveSCEVType(Ty); 2489 const SCEV *AllOnes = 2490 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2491 return getMinusSCEV(AllOnes, V); 2492} 2493 2494/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2495/// 2496const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2497 const SCEV *RHS) { 2498 // Fast path: X - X --> 0. 2499 if (LHS == RHS) 2500 return getConstant(LHS->getType(), 0); 2501 2502 // X - Y --> X + -Y 2503 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2504} 2505 2506/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2507/// input value to the specified type. If the type must be extended, it is zero 2508/// extended. 2509const SCEV * 2510ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2511 const Type *Ty) { 2512 const Type *SrcTy = V->getType(); 2513 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2514 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2515 "Cannot truncate or zero extend with non-integer arguments!"); 2516 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2517 return V; // No conversion 2518 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2519 return getTruncateExpr(V, Ty); 2520 return getZeroExtendExpr(V, Ty); 2521} 2522 2523/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2524/// input value to the specified type. If the type must be extended, it is sign 2525/// extended. 2526const SCEV * 2527ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2528 const Type *Ty) { 2529 const Type *SrcTy = V->getType(); 2530 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2531 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2532 "Cannot truncate or zero extend with non-integer arguments!"); 2533 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2534 return V; // No conversion 2535 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2536 return getTruncateExpr(V, Ty); 2537 return getSignExtendExpr(V, Ty); 2538} 2539 2540/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2541/// input value to the specified type. If the type must be extended, it is zero 2542/// extended. The conversion must not be narrowing. 2543const SCEV * 2544ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2545 const Type *SrcTy = V->getType(); 2546 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2547 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2548 "Cannot noop or zero extend with non-integer arguments!"); 2549 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2550 "getNoopOrZeroExtend cannot truncate!"); 2551 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2552 return V; // No conversion 2553 return getZeroExtendExpr(V, Ty); 2554} 2555 2556/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2557/// input value to the specified type. If the type must be extended, it is sign 2558/// extended. The conversion must not be narrowing. 2559const SCEV * 2560ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2561 const Type *SrcTy = V->getType(); 2562 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2563 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2564 "Cannot noop or sign extend with non-integer arguments!"); 2565 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2566 "getNoopOrSignExtend cannot truncate!"); 2567 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2568 return V; // No conversion 2569 return getSignExtendExpr(V, Ty); 2570} 2571 2572/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2573/// the input value to the specified type. If the type must be extended, 2574/// it is extended with unspecified bits. The conversion must not be 2575/// narrowing. 2576const SCEV * 2577ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2578 const Type *SrcTy = V->getType(); 2579 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2580 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2581 "Cannot noop or any extend with non-integer arguments!"); 2582 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2583 "getNoopOrAnyExtend cannot truncate!"); 2584 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2585 return V; // No conversion 2586 return getAnyExtendExpr(V, Ty); 2587} 2588 2589/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2590/// input value to the specified type. The conversion must not be widening. 2591const SCEV * 2592ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2593 const Type *SrcTy = V->getType(); 2594 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2595 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2596 "Cannot truncate or noop with non-integer arguments!"); 2597 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2598 "getTruncateOrNoop cannot extend!"); 2599 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2600 return V; // No conversion 2601 return getTruncateExpr(V, Ty); 2602} 2603 2604/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2605/// the types using zero-extension, and then perform a umax operation 2606/// with them. 2607const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2608 const SCEV *RHS) { 2609 const SCEV *PromotedLHS = LHS; 2610 const SCEV *PromotedRHS = RHS; 2611 2612 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2613 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2614 else 2615 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2616 2617 return getUMaxExpr(PromotedLHS, PromotedRHS); 2618} 2619 2620/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2621/// the types using zero-extension, and then perform a umin operation 2622/// with them. 2623const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2624 const SCEV *RHS) { 2625 const SCEV *PromotedLHS = LHS; 2626 const SCEV *PromotedRHS = RHS; 2627 2628 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2629 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2630 else 2631 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2632 2633 return getUMinExpr(PromotedLHS, PromotedRHS); 2634} 2635 2636/// PushDefUseChildren - Push users of the given Instruction 2637/// onto the given Worklist. 2638static void 2639PushDefUseChildren(Instruction *I, 2640 SmallVectorImpl<Instruction *> &Worklist) { 2641 // Push the def-use children onto the Worklist stack. 2642 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2643 UI != UE; ++UI) 2644 Worklist.push_back(cast<Instruction>(*UI)); 2645} 2646 2647/// ForgetSymbolicValue - This looks up computed SCEV values for all 2648/// instructions that depend on the given instruction and removes them from 2649/// the Scalars map if they reference SymName. This is used during PHI 2650/// resolution. 2651void 2652ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2653 SmallVector<Instruction *, 16> Worklist; 2654 PushDefUseChildren(PN, Worklist); 2655 2656 SmallPtrSet<Instruction *, 8> Visited; 2657 Visited.insert(PN); 2658 while (!Worklist.empty()) { 2659 Instruction *I = Worklist.pop_back_val(); 2660 if (!Visited.insert(I)) continue; 2661 2662 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 2663 Scalars.find(static_cast<Value *>(I)); 2664 if (It != Scalars.end()) { 2665 // Short-circuit the def-use traversal if the symbolic name 2666 // ceases to appear in expressions. 2667 if (It->second != SymName && !It->second->hasOperand(SymName)) 2668 continue; 2669 2670 // SCEVUnknown for a PHI either means that it has an unrecognized 2671 // structure, it's a PHI that's in the progress of being computed 2672 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2673 // additional loop trip count information isn't going to change anything. 2674 // In the second case, createNodeForPHI will perform the necessary 2675 // updates on its own when it gets to that point. In the third, we do 2676 // want to forget the SCEVUnknown. 2677 if (!isa<PHINode>(I) || 2678 !isa<SCEVUnknown>(It->second) || 2679 (I != PN && It->second == SymName)) { 2680 ValuesAtScopes.erase(It->second); 2681 Scalars.erase(It); 2682 } 2683 } 2684 2685 PushDefUseChildren(I, Worklist); 2686 } 2687} 2688 2689/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2690/// a loop header, making it a potential recurrence, or it doesn't. 2691/// 2692const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2693 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2694 if (L->getHeader() == PN->getParent()) { 2695 // The loop may have multiple entrances or multiple exits; we can analyze 2696 // this phi as an addrec if it has a unique entry value and a unique 2697 // backedge value. 2698 Value *BEValueV = 0, *StartValueV = 0; 2699 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 2700 Value *V = PN->getIncomingValue(i); 2701 if (L->contains(PN->getIncomingBlock(i))) { 2702 if (!BEValueV) { 2703 BEValueV = V; 2704 } else if (BEValueV != V) { 2705 BEValueV = 0; 2706 break; 2707 } 2708 } else if (!StartValueV) { 2709 StartValueV = V; 2710 } else if (StartValueV != V) { 2711 StartValueV = 0; 2712 break; 2713 } 2714 } 2715 if (BEValueV && StartValueV) { 2716 // While we are analyzing this PHI node, handle its value symbolically. 2717 const SCEV *SymbolicName = getUnknown(PN); 2718 assert(Scalars.find(PN) == Scalars.end() && 2719 "PHI node already processed?"); 2720 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2721 2722 // Using this symbolic name for the PHI, analyze the value coming around 2723 // the back-edge. 2724 const SCEV *BEValue = getSCEV(BEValueV); 2725 2726 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2727 // has a special value for the first iteration of the loop. 2728 2729 // If the value coming around the backedge is an add with the symbolic 2730 // value we just inserted, then we found a simple induction variable! 2731 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2732 // If there is a single occurrence of the symbolic value, replace it 2733 // with a recurrence. 2734 unsigned FoundIndex = Add->getNumOperands(); 2735 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2736 if (Add->getOperand(i) == SymbolicName) 2737 if (FoundIndex == e) { 2738 FoundIndex = i; 2739 break; 2740 } 2741 2742 if (FoundIndex != Add->getNumOperands()) { 2743 // Create an add with everything but the specified operand. 2744 SmallVector<const SCEV *, 8> Ops; 2745 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2746 if (i != FoundIndex) 2747 Ops.push_back(Add->getOperand(i)); 2748 const SCEV *Accum = getAddExpr(Ops); 2749 2750 // This is not a valid addrec if the step amount is varying each 2751 // loop iteration, but is not itself an addrec in this loop. 2752 if (Accum->isLoopInvariant(L) || 2753 (isa<SCEVAddRecExpr>(Accum) && 2754 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2755 bool HasNUW = false; 2756 bool HasNSW = false; 2757 2758 // If the increment doesn't overflow, then neither the addrec nor 2759 // the post-increment will overflow. 2760 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 2761 if (OBO->hasNoUnsignedWrap()) 2762 HasNUW = true; 2763 if (OBO->hasNoSignedWrap()) 2764 HasNSW = true; 2765 } 2766 2767 const SCEV *StartVal = getSCEV(StartValueV); 2768 const SCEV *PHISCEV = 2769 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW); 2770 2771 // Since the no-wrap flags are on the increment, they apply to the 2772 // post-incremented value as well. 2773 if (Accum->isLoopInvariant(L)) 2774 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 2775 Accum, L, HasNUW, HasNSW); 2776 2777 // Okay, for the entire analysis of this edge we assumed the PHI 2778 // to be symbolic. We now need to go back and purge all of the 2779 // entries for the scalars that use the symbolic expression. 2780 ForgetSymbolicName(PN, SymbolicName); 2781 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2782 return PHISCEV; 2783 } 2784 } 2785 } else if (const SCEVAddRecExpr *AddRec = 2786 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2787 // Otherwise, this could be a loop like this: 2788 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2789 // In this case, j = {1,+,1} and BEValue is j. 2790 // Because the other in-value of i (0) fits the evolution of BEValue 2791 // i really is an addrec evolution. 2792 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2793 const SCEV *StartVal = getSCEV(StartValueV); 2794 2795 // If StartVal = j.start - j.stride, we can use StartVal as the 2796 // initial step of the addrec evolution. 2797 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2798 AddRec->getOperand(1))) { 2799 const SCEV *PHISCEV = 2800 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2801 2802 // Okay, for the entire analysis of this edge we assumed the PHI 2803 // to be symbolic. We now need to go back and purge all of the 2804 // entries for the scalars that use the symbolic expression. 2805 ForgetSymbolicName(PN, SymbolicName); 2806 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2807 return PHISCEV; 2808 } 2809 } 2810 } 2811 } 2812 } 2813 2814 // If the PHI has a single incoming value, follow that value, unless the 2815 // PHI's incoming blocks are in a different loop, in which case doing so 2816 // risks breaking LCSSA form. Instcombine would normally zap these, but 2817 // it doesn't have DominatorTree information, so it may miss cases. 2818 if (Value *V = PN->hasConstantValue(DT)) { 2819 bool AllSameLoop = true; 2820 Loop *PNLoop = LI->getLoopFor(PN->getParent()); 2821 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i) 2822 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) { 2823 AllSameLoop = false; 2824 break; 2825 } 2826 if (AllSameLoop) 2827 return getSCEV(V); 2828 } 2829 2830 // If it's not a loop phi, we can't handle it yet. 2831 return getUnknown(PN); 2832} 2833 2834/// createNodeForGEP - Expand GEP instructions into add and multiply 2835/// operations. This allows them to be analyzed by regular SCEV code. 2836/// 2837const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 2838 2839 // Don't blindly transfer the inbounds flag from the GEP instruction to the 2840 // Add expression, because the Instruction may be guarded by control flow 2841 // and the no-overflow bits may not be valid for the expression in any 2842 // context. 2843 2844 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 2845 Value *Base = GEP->getOperand(0); 2846 // Don't attempt to analyze GEPs over unsized objects. 2847 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2848 return getUnknown(GEP); 2849 const SCEV *TotalOffset = getConstant(IntPtrTy, 0); 2850 gep_type_iterator GTI = gep_type_begin(GEP); 2851 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()), 2852 E = GEP->op_end(); 2853 I != E; ++I) { 2854 Value *Index = *I; 2855 // Compute the (potentially symbolic) offset in bytes for this index. 2856 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2857 // For a struct, add the member offset. 2858 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2859 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo); 2860 2861 // Add the field offset to the running total offset. 2862 TotalOffset = getAddExpr(TotalOffset, FieldOffset); 2863 } else { 2864 // For an array, add the element offset, explicitly scaled. 2865 const SCEV *ElementSize = getSizeOfExpr(*GTI); 2866 const SCEV *IndexS = getSCEV(Index); 2867 // Getelementptr indices are signed. 2868 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy); 2869 2870 // Multiply the index by the element size to compute the element offset. 2871 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize); 2872 2873 // Add the element offset to the running total offset. 2874 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2875 } 2876 } 2877 2878 // Get the SCEV for the GEP base. 2879 const SCEV *BaseS = getSCEV(Base); 2880 2881 // Add the total offset from all the GEP indices to the base. 2882 return getAddExpr(BaseS, TotalOffset); 2883} 2884 2885/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2886/// guaranteed to end in (at every loop iteration). It is, at the same time, 2887/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2888/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2889uint32_t 2890ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2891 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2892 return C->getValue()->getValue().countTrailingZeros(); 2893 2894 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2895 return std::min(GetMinTrailingZeros(T->getOperand()), 2896 (uint32_t)getTypeSizeInBits(T->getType())); 2897 2898 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2899 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2900 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2901 getTypeSizeInBits(E->getType()) : OpRes; 2902 } 2903 2904 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2905 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2906 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2907 getTypeSizeInBits(E->getType()) : OpRes; 2908 } 2909 2910 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2911 // The result is the min of all operands results. 2912 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2913 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2914 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2915 return MinOpRes; 2916 } 2917 2918 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2919 // The result is the sum of all operands results. 2920 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2921 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2922 for (unsigned i = 1, e = M->getNumOperands(); 2923 SumOpRes != BitWidth && i != e; ++i) 2924 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2925 BitWidth); 2926 return SumOpRes; 2927 } 2928 2929 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2930 // The result is the min of all operands results. 2931 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2932 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2933 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2934 return MinOpRes; 2935 } 2936 2937 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2938 // The result is the min of all operands results. 2939 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2940 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2941 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2942 return MinOpRes; 2943 } 2944 2945 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2946 // The result is the min of all operands results. 2947 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2948 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2949 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2950 return MinOpRes; 2951 } 2952 2953 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2954 // For a SCEVUnknown, ask ValueTracking. 2955 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2956 APInt Mask = APInt::getAllOnesValue(BitWidth); 2957 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2958 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2959 return Zeros.countTrailingOnes(); 2960 } 2961 2962 // SCEVUDivExpr 2963 return 0; 2964} 2965 2966/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 2967/// 2968ConstantRange 2969ScalarEvolution::getUnsignedRange(const SCEV *S) { 2970 2971 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2972 return ConstantRange(C->getValue()->getValue()); 2973 2974 unsigned BitWidth = getTypeSizeInBits(S->getType()); 2975 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 2976 2977 // If the value has known zeros, the maximum unsigned value will have those 2978 // known zeros as well. 2979 uint32_t TZ = GetMinTrailingZeros(S); 2980 if (TZ != 0) 2981 ConservativeResult = 2982 ConstantRange(APInt::getMinValue(BitWidth), 2983 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 2984 2985 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2986 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 2987 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2988 X = X.add(getUnsignedRange(Add->getOperand(i))); 2989 return ConservativeResult.intersectWith(X); 2990 } 2991 2992 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2993 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 2994 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2995 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 2996 return ConservativeResult.intersectWith(X); 2997 } 2998 2999 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3000 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 3001 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3002 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 3003 return ConservativeResult.intersectWith(X); 3004 } 3005 3006 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3007 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 3008 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3009 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 3010 return ConservativeResult.intersectWith(X); 3011 } 3012 3013 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3014 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 3015 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 3016 return ConservativeResult.intersectWith(X.udiv(Y)); 3017 } 3018 3019 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3020 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 3021 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 3022 } 3023 3024 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3025 ConstantRange X = getUnsignedRange(SExt->getOperand()); 3026 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 3027 } 3028 3029 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3030 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 3031 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 3032 } 3033 3034 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3035 // If there's no unsigned wrap, the value will never be less than its 3036 // initial value. 3037 if (AddRec->hasNoUnsignedWrap()) 3038 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 3039 if (!C->getValue()->isZero()) 3040 ConservativeResult = 3041 ConservativeResult.intersectWith( 3042 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0))); 3043 3044 // TODO: non-affine addrec 3045 if (AddRec->isAffine()) { 3046 const Type *Ty = AddRec->getType(); 3047 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3048 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3049 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3050 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3051 3052 const SCEV *Start = AddRec->getStart(); 3053 const SCEV *Step = AddRec->getStepRecurrence(*this); 3054 3055 ConstantRange StartRange = getUnsignedRange(Start); 3056 ConstantRange StepRange = getSignedRange(Step); 3057 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3058 ConstantRange EndRange = 3059 StartRange.add(MaxBECountRange.multiply(StepRange)); 3060 3061 // Check for overflow. This must be done with ConstantRange arithmetic 3062 // because we could be called from within the ScalarEvolution overflow 3063 // checking code. 3064 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1); 3065 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3066 ConstantRange ExtMaxBECountRange = 3067 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3068 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1); 3069 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3070 ExtEndRange) 3071 return ConservativeResult; 3072 3073 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 3074 EndRange.getUnsignedMin()); 3075 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 3076 EndRange.getUnsignedMax()); 3077 if (Min.isMinValue() && Max.isMaxValue()) 3078 return ConservativeResult; 3079 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 3080 } 3081 } 3082 3083 return ConservativeResult; 3084 } 3085 3086 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3087 // For a SCEVUnknown, ask ValueTracking. 3088 APInt Mask = APInt::getAllOnesValue(BitWidth); 3089 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3090 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 3091 if (Ones == ~Zeros + 1) 3092 return ConservativeResult; 3093 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)); 3094 } 3095 3096 return ConservativeResult; 3097} 3098 3099/// getSignedRange - Determine the signed range for a particular SCEV. 3100/// 3101ConstantRange 3102ScalarEvolution::getSignedRange(const SCEV *S) { 3103 3104 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3105 return ConstantRange(C->getValue()->getValue()); 3106 3107 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3108 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3109 3110 // If the value has known zeros, the maximum signed value will have those 3111 // known zeros as well. 3112 uint32_t TZ = GetMinTrailingZeros(S); 3113 if (TZ != 0) 3114 ConservativeResult = 3115 ConstantRange(APInt::getSignedMinValue(BitWidth), 3116 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 3117 3118 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3119 ConstantRange X = getSignedRange(Add->getOperand(0)); 3120 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3121 X = X.add(getSignedRange(Add->getOperand(i))); 3122 return ConservativeResult.intersectWith(X); 3123 } 3124 3125 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3126 ConstantRange X = getSignedRange(Mul->getOperand(0)); 3127 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3128 X = X.multiply(getSignedRange(Mul->getOperand(i))); 3129 return ConservativeResult.intersectWith(X); 3130 } 3131 3132 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3133 ConstantRange X = getSignedRange(SMax->getOperand(0)); 3134 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3135 X = X.smax(getSignedRange(SMax->getOperand(i))); 3136 return ConservativeResult.intersectWith(X); 3137 } 3138 3139 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3140 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3141 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3142 X = X.umax(getSignedRange(UMax->getOperand(i))); 3143 return ConservativeResult.intersectWith(X); 3144 } 3145 3146 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3147 ConstantRange X = getSignedRange(UDiv->getLHS()); 3148 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3149 return ConservativeResult.intersectWith(X.udiv(Y)); 3150 } 3151 3152 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3153 ConstantRange X = getSignedRange(ZExt->getOperand()); 3154 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 3155 } 3156 3157 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3158 ConstantRange X = getSignedRange(SExt->getOperand()); 3159 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 3160 } 3161 3162 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3163 ConstantRange X = getSignedRange(Trunc->getOperand()); 3164 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 3165 } 3166 3167 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3168 // If there's no signed wrap, and all the operands have the same sign or 3169 // zero, the value won't ever change sign. 3170 if (AddRec->hasNoSignedWrap()) { 3171 bool AllNonNeg = true; 3172 bool AllNonPos = true; 3173 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3174 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3175 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3176 } 3177 if (AllNonNeg) 3178 ConservativeResult = ConservativeResult.intersectWith( 3179 ConstantRange(APInt(BitWidth, 0), 3180 APInt::getSignedMinValue(BitWidth))); 3181 else if (AllNonPos) 3182 ConservativeResult = ConservativeResult.intersectWith( 3183 ConstantRange(APInt::getSignedMinValue(BitWidth), 3184 APInt(BitWidth, 1))); 3185 } 3186 3187 // TODO: non-affine addrec 3188 if (AddRec->isAffine()) { 3189 const Type *Ty = AddRec->getType(); 3190 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3191 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3192 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3193 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3194 3195 const SCEV *Start = AddRec->getStart(); 3196 const SCEV *Step = AddRec->getStepRecurrence(*this); 3197 3198 ConstantRange StartRange = getSignedRange(Start); 3199 ConstantRange StepRange = getSignedRange(Step); 3200 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3201 ConstantRange EndRange = 3202 StartRange.add(MaxBECountRange.multiply(StepRange)); 3203 3204 // Check for overflow. This must be done with ConstantRange arithmetic 3205 // because we could be called from within the ScalarEvolution overflow 3206 // checking code. 3207 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1); 3208 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3209 ConstantRange ExtMaxBECountRange = 3210 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3211 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1); 3212 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3213 ExtEndRange) 3214 return ConservativeResult; 3215 3216 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3217 EndRange.getSignedMin()); 3218 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3219 EndRange.getSignedMax()); 3220 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3221 return ConservativeResult; 3222 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 3223 } 3224 } 3225 3226 return ConservativeResult; 3227 } 3228 3229 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3230 // For a SCEVUnknown, ask ValueTracking. 3231 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3232 return ConservativeResult; 3233 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3234 if (NS == 1) 3235 return ConservativeResult; 3236 return ConservativeResult.intersectWith( 3237 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3238 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)); 3239 } 3240 3241 return ConservativeResult; 3242} 3243 3244/// createSCEV - We know that there is no SCEV for the specified value. 3245/// Analyze the expression. 3246/// 3247const SCEV *ScalarEvolution::createSCEV(Value *V) { 3248 if (!isSCEVable(V->getType())) 3249 return getUnknown(V); 3250 3251 unsigned Opcode = Instruction::UserOp1; 3252 if (Instruction *I = dyn_cast<Instruction>(V)) { 3253 Opcode = I->getOpcode(); 3254 3255 // Don't attempt to analyze instructions in blocks that aren't 3256 // reachable. Such instructions don't matter, and they aren't required 3257 // to obey basic rules for definitions dominating uses which this 3258 // analysis depends on. 3259 if (!DT->isReachableFromEntry(I->getParent())) 3260 return getUnknown(V); 3261 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3262 Opcode = CE->getOpcode(); 3263 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3264 return getConstant(CI); 3265 else if (isa<ConstantPointerNull>(V)) 3266 return getConstant(V->getType(), 0); 3267 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3268 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3269 else 3270 return getUnknown(V); 3271 3272 Operator *U = cast<Operator>(V); 3273 switch (Opcode) { 3274 case Instruction::Add: 3275 return getAddExpr(getSCEV(U->getOperand(0)), 3276 getSCEV(U->getOperand(1))); 3277 case Instruction::Mul: 3278 return getMulExpr(getSCEV(U->getOperand(0)), 3279 getSCEV(U->getOperand(1))); 3280 case Instruction::UDiv: 3281 return getUDivExpr(getSCEV(U->getOperand(0)), 3282 getSCEV(U->getOperand(1))); 3283 case Instruction::Sub: 3284 return getMinusSCEV(getSCEV(U->getOperand(0)), 3285 getSCEV(U->getOperand(1))); 3286 case Instruction::And: 3287 // For an expression like x&255 that merely masks off the high bits, 3288 // use zext(trunc(x)) as the SCEV expression. 3289 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3290 if (CI->isNullValue()) 3291 return getSCEV(U->getOperand(1)); 3292 if (CI->isAllOnesValue()) 3293 return getSCEV(U->getOperand(0)); 3294 const APInt &A = CI->getValue(); 3295 3296 // Instcombine's ShrinkDemandedConstant may strip bits out of 3297 // constants, obscuring what would otherwise be a low-bits mask. 3298 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3299 // knew about to reconstruct a low-bits mask value. 3300 unsigned LZ = A.countLeadingZeros(); 3301 unsigned BitWidth = A.getBitWidth(); 3302 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3303 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3304 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3305 3306 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3307 3308 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3309 return 3310 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3311 IntegerType::get(getContext(), BitWidth - LZ)), 3312 U->getType()); 3313 } 3314 break; 3315 3316 case Instruction::Or: 3317 // If the RHS of the Or is a constant, we may have something like: 3318 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3319 // optimizations will transparently handle this case. 3320 // 3321 // In order for this transformation to be safe, the LHS must be of the 3322 // form X*(2^n) and the Or constant must be less than 2^n. 3323 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3324 const SCEV *LHS = getSCEV(U->getOperand(0)); 3325 const APInt &CIVal = CI->getValue(); 3326 if (GetMinTrailingZeros(LHS) >= 3327 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3328 // Build a plain add SCEV. 3329 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3330 // If the LHS of the add was an addrec and it has no-wrap flags, 3331 // transfer the no-wrap flags, since an or won't introduce a wrap. 3332 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3333 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3334 if (OldAR->hasNoUnsignedWrap()) 3335 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true); 3336 if (OldAR->hasNoSignedWrap()) 3337 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true); 3338 } 3339 return S; 3340 } 3341 } 3342 break; 3343 case Instruction::Xor: 3344 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3345 // If the RHS of the xor is a signbit, then this is just an add. 3346 // Instcombine turns add of signbit into xor as a strength reduction step. 3347 if (CI->getValue().isSignBit()) 3348 return getAddExpr(getSCEV(U->getOperand(0)), 3349 getSCEV(U->getOperand(1))); 3350 3351 // If the RHS of xor is -1, then this is a not operation. 3352 if (CI->isAllOnesValue()) 3353 return getNotSCEV(getSCEV(U->getOperand(0))); 3354 3355 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3356 // This is a variant of the check for xor with -1, and it handles 3357 // the case where instcombine has trimmed non-demanded bits out 3358 // of an xor with -1. 3359 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3360 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3361 if (BO->getOpcode() == Instruction::And && 3362 LCI->getValue() == CI->getValue()) 3363 if (const SCEVZeroExtendExpr *Z = 3364 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3365 const Type *UTy = U->getType(); 3366 const SCEV *Z0 = Z->getOperand(); 3367 const Type *Z0Ty = Z0->getType(); 3368 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3369 3370 // If C is a low-bits mask, the zero extend is serving to 3371 // mask off the high bits. Complement the operand and 3372 // re-apply the zext. 3373 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3374 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3375 3376 // If C is a single bit, it may be in the sign-bit position 3377 // before the zero-extend. In this case, represent the xor 3378 // using an add, which is equivalent, and re-apply the zext. 3379 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 3380 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3381 Trunc.isSignBit()) 3382 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3383 UTy); 3384 } 3385 } 3386 break; 3387 3388 case Instruction::Shl: 3389 // Turn shift left of a constant amount into a multiply. 3390 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3391 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3392 3393 // If the shift count is not less than the bitwidth, the result of 3394 // the shift is undefined. Don't try to analyze it, because the 3395 // resolution chosen here may differ from the resolution chosen in 3396 // other parts of the compiler. 3397 if (SA->getValue().uge(BitWidth)) 3398 break; 3399 3400 Constant *X = ConstantInt::get(getContext(), 3401 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3402 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3403 } 3404 break; 3405 3406 case Instruction::LShr: 3407 // Turn logical shift right of a constant into a unsigned divide. 3408 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3409 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3410 3411 // If the shift count is not less than the bitwidth, the result of 3412 // the shift is undefined. Don't try to analyze it, because the 3413 // resolution chosen here may differ from the resolution chosen in 3414 // other parts of the compiler. 3415 if (SA->getValue().uge(BitWidth)) 3416 break; 3417 3418 Constant *X = ConstantInt::get(getContext(), 3419 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3420 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3421 } 3422 break; 3423 3424 case Instruction::AShr: 3425 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3426 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3427 if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) 3428 if (L->getOpcode() == Instruction::Shl && 3429 L->getOperand(1) == U->getOperand(1)) { 3430 uint64_t BitWidth = getTypeSizeInBits(U->getType()); 3431 3432 // If the shift count is not less than the bitwidth, the result of 3433 // the shift is undefined. Don't try to analyze it, because the 3434 // resolution chosen here may differ from the resolution chosen in 3435 // other parts of the compiler. 3436 if (CI->getValue().uge(BitWidth)) 3437 break; 3438 3439 uint64_t Amt = BitWidth - CI->getZExtValue(); 3440 if (Amt == BitWidth) 3441 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3442 return 3443 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3444 IntegerType::get(getContext(), 3445 Amt)), 3446 U->getType()); 3447 } 3448 break; 3449 3450 case Instruction::Trunc: 3451 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3452 3453 case Instruction::ZExt: 3454 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3455 3456 case Instruction::SExt: 3457 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3458 3459 case Instruction::BitCast: 3460 // BitCasts are no-op casts so we just eliminate the cast. 3461 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3462 return getSCEV(U->getOperand(0)); 3463 break; 3464 3465 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3466 // lead to pointer expressions which cannot safely be expanded to GEPs, 3467 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3468 // simplifying integer expressions. 3469 3470 case Instruction::GetElementPtr: 3471 return createNodeForGEP(cast<GEPOperator>(U)); 3472 3473 case Instruction::PHI: 3474 return createNodeForPHI(cast<PHINode>(U)); 3475 3476 case Instruction::Select: 3477 // This could be a smax or umax that was lowered earlier. 3478 // Try to recover it. 3479 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3480 Value *LHS = ICI->getOperand(0); 3481 Value *RHS = ICI->getOperand(1); 3482 switch (ICI->getPredicate()) { 3483 case ICmpInst::ICMP_SLT: 3484 case ICmpInst::ICMP_SLE: 3485 std::swap(LHS, RHS); 3486 // fall through 3487 case ICmpInst::ICMP_SGT: 3488 case ICmpInst::ICMP_SGE: 3489 // a >s b ? a+x : b+x -> smax(a, b)+x 3490 // a >s b ? b+x : a+x -> smin(a, b)+x 3491 if (LHS->getType() == U->getType()) { 3492 const SCEV *LS = getSCEV(LHS); 3493 const SCEV *RS = getSCEV(RHS); 3494 const SCEV *LA = getSCEV(U->getOperand(1)); 3495 const SCEV *RA = getSCEV(U->getOperand(2)); 3496 const SCEV *LDiff = getMinusSCEV(LA, LS); 3497 const SCEV *RDiff = getMinusSCEV(RA, RS); 3498 if (LDiff == RDiff) 3499 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 3500 LDiff = getMinusSCEV(LA, RS); 3501 RDiff = getMinusSCEV(RA, LS); 3502 if (LDiff == RDiff) 3503 return getAddExpr(getSMinExpr(LS, RS), LDiff); 3504 } 3505 break; 3506 case ICmpInst::ICMP_ULT: 3507 case ICmpInst::ICMP_ULE: 3508 std::swap(LHS, RHS); 3509 // fall through 3510 case ICmpInst::ICMP_UGT: 3511 case ICmpInst::ICMP_UGE: 3512 // a >u b ? a+x : b+x -> umax(a, b)+x 3513 // a >u b ? b+x : a+x -> umin(a, b)+x 3514 if (LHS->getType() == U->getType()) { 3515 const SCEV *LS = getSCEV(LHS); 3516 const SCEV *RS = getSCEV(RHS); 3517 const SCEV *LA = getSCEV(U->getOperand(1)); 3518 const SCEV *RA = getSCEV(U->getOperand(2)); 3519 const SCEV *LDiff = getMinusSCEV(LA, LS); 3520 const SCEV *RDiff = getMinusSCEV(RA, RS); 3521 if (LDiff == RDiff) 3522 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 3523 LDiff = getMinusSCEV(LA, RS); 3524 RDiff = getMinusSCEV(RA, LS); 3525 if (LDiff == RDiff) 3526 return getAddExpr(getUMinExpr(LS, RS), LDiff); 3527 } 3528 break; 3529 case ICmpInst::ICMP_NE: 3530 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 3531 if (LHS->getType() == U->getType() && 3532 isa<ConstantInt>(RHS) && 3533 cast<ConstantInt>(RHS)->isZero()) { 3534 const SCEV *One = getConstant(LHS->getType(), 1); 3535 const SCEV *LS = getSCEV(LHS); 3536 const SCEV *LA = getSCEV(U->getOperand(1)); 3537 const SCEV *RA = getSCEV(U->getOperand(2)); 3538 const SCEV *LDiff = getMinusSCEV(LA, LS); 3539 const SCEV *RDiff = getMinusSCEV(RA, One); 3540 if (LDiff == RDiff) 3541 return getAddExpr(getUMaxExpr(LS, One), LDiff); 3542 } 3543 break; 3544 case ICmpInst::ICMP_EQ: 3545 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 3546 if (LHS->getType() == U->getType() && 3547 isa<ConstantInt>(RHS) && 3548 cast<ConstantInt>(RHS)->isZero()) { 3549 const SCEV *One = getConstant(LHS->getType(), 1); 3550 const SCEV *LS = getSCEV(LHS); 3551 const SCEV *LA = getSCEV(U->getOperand(1)); 3552 const SCEV *RA = getSCEV(U->getOperand(2)); 3553 const SCEV *LDiff = getMinusSCEV(LA, One); 3554 const SCEV *RDiff = getMinusSCEV(RA, LS); 3555 if (LDiff == RDiff) 3556 return getAddExpr(getUMaxExpr(LS, One), LDiff); 3557 } 3558 break; 3559 default: 3560 break; 3561 } 3562 } 3563 3564 default: // We cannot analyze this expression. 3565 break; 3566 } 3567 3568 return getUnknown(V); 3569} 3570 3571 3572 3573//===----------------------------------------------------------------------===// 3574// Iteration Count Computation Code 3575// 3576 3577/// getBackedgeTakenCount - If the specified loop has a predictable 3578/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3579/// object. The backedge-taken count is the number of times the loop header 3580/// will be branched to from within the loop. This is one less than the 3581/// trip count of the loop, since it doesn't count the first iteration, 3582/// when the header is branched to from outside the loop. 3583/// 3584/// Note that it is not valid to call this method on a loop without a 3585/// loop-invariant backedge-taken count (see 3586/// hasLoopInvariantBackedgeTakenCount). 3587/// 3588const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3589 return getBackedgeTakenInfo(L).Exact; 3590} 3591 3592/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3593/// return the least SCEV value that is known never to be less than the 3594/// actual backedge taken count. 3595const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3596 return getBackedgeTakenInfo(L).Max; 3597} 3598 3599/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3600/// onto the given Worklist. 3601static void 3602PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3603 BasicBlock *Header = L->getHeader(); 3604 3605 // Push all Loop-header PHIs onto the Worklist stack. 3606 for (BasicBlock::iterator I = Header->begin(); 3607 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3608 Worklist.push_back(PN); 3609} 3610 3611const ScalarEvolution::BackedgeTakenInfo & 3612ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3613 // Initially insert a CouldNotCompute for this loop. If the insertion 3614 // succeeds, proceed to actually compute a backedge-taken count and 3615 // update the value. The temporary CouldNotCompute value tells SCEV 3616 // code elsewhere that it shouldn't attempt to request a new 3617 // backedge-taken count, which could result in infinite recursion. 3618 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3619 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3620 if (Pair.second) { 3621 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L); 3622 if (BECount.Exact != getCouldNotCompute()) { 3623 assert(BECount.Exact->isLoopInvariant(L) && 3624 BECount.Max->isLoopInvariant(L) && 3625 "Computed backedge-taken count isn't loop invariant for loop!"); 3626 ++NumTripCountsComputed; 3627 3628 // Update the value in the map. 3629 Pair.first->second = BECount; 3630 } else { 3631 if (BECount.Max != getCouldNotCompute()) 3632 // Update the value in the map. 3633 Pair.first->second = BECount; 3634 if (isa<PHINode>(L->getHeader()->begin())) 3635 // Only count loops that have phi nodes as not being computable. 3636 ++NumTripCountsNotComputed; 3637 } 3638 3639 // Now that we know more about the trip count for this loop, forget any 3640 // existing SCEV values for PHI nodes in this loop since they are only 3641 // conservative estimates made without the benefit of trip count 3642 // information. This is similar to the code in forgetLoop, except that 3643 // it handles SCEVUnknown PHI nodes specially. 3644 if (BECount.hasAnyInfo()) { 3645 SmallVector<Instruction *, 16> Worklist; 3646 PushLoopPHIs(L, Worklist); 3647 3648 SmallPtrSet<Instruction *, 8> Visited; 3649 while (!Worklist.empty()) { 3650 Instruction *I = Worklist.pop_back_val(); 3651 if (!Visited.insert(I)) continue; 3652 3653 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3654 Scalars.find(static_cast<Value *>(I)); 3655 if (It != Scalars.end()) { 3656 // SCEVUnknown for a PHI either means that it has an unrecognized 3657 // structure, or it's a PHI that's in the progress of being computed 3658 // by createNodeForPHI. In the former case, additional loop trip 3659 // count information isn't going to change anything. In the later 3660 // case, createNodeForPHI will perform the necessary updates on its 3661 // own when it gets to that point. 3662 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 3663 ValuesAtScopes.erase(It->second); 3664 Scalars.erase(It); 3665 } 3666 if (PHINode *PN = dyn_cast<PHINode>(I)) 3667 ConstantEvolutionLoopExitValue.erase(PN); 3668 } 3669 3670 PushDefUseChildren(I, Worklist); 3671 } 3672 } 3673 } 3674 return Pair.first->second; 3675} 3676 3677/// forgetLoop - This method should be called by the client when it has 3678/// changed a loop in a way that may effect ScalarEvolution's ability to 3679/// compute a trip count, or if the loop is deleted. 3680void ScalarEvolution::forgetLoop(const Loop *L) { 3681 // Drop any stored trip count value. 3682 BackedgeTakenCounts.erase(L); 3683 3684 // Drop information about expressions based on loop-header PHIs. 3685 SmallVector<Instruction *, 16> Worklist; 3686 PushLoopPHIs(L, Worklist); 3687 3688 SmallPtrSet<Instruction *, 8> Visited; 3689 while (!Worklist.empty()) { 3690 Instruction *I = Worklist.pop_back_val(); 3691 if (!Visited.insert(I)) continue; 3692 3693 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3694 Scalars.find(static_cast<Value *>(I)); 3695 if (It != Scalars.end()) { 3696 ValuesAtScopes.erase(It->second); 3697 Scalars.erase(It); 3698 if (PHINode *PN = dyn_cast<PHINode>(I)) 3699 ConstantEvolutionLoopExitValue.erase(PN); 3700 } 3701 3702 PushDefUseChildren(I, Worklist); 3703 } 3704} 3705 3706/// forgetValue - This method should be called by the client when it has 3707/// changed a value in a way that may effect its value, or which may 3708/// disconnect it from a def-use chain linking it to a loop. 3709void ScalarEvolution::forgetValue(Value *V) { 3710 Instruction *I = dyn_cast<Instruction>(V); 3711 if (!I) return; 3712 3713 // Drop information about expressions based on loop-header PHIs. 3714 SmallVector<Instruction *, 16> Worklist; 3715 Worklist.push_back(I); 3716 3717 SmallPtrSet<Instruction *, 8> Visited; 3718 while (!Worklist.empty()) { 3719 I = Worklist.pop_back_val(); 3720 if (!Visited.insert(I)) continue; 3721 3722 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3723 Scalars.find(static_cast<Value *>(I)); 3724 if (It != Scalars.end()) { 3725 ValuesAtScopes.erase(It->second); 3726 Scalars.erase(It); 3727 if (PHINode *PN = dyn_cast<PHINode>(I)) 3728 ConstantEvolutionLoopExitValue.erase(PN); 3729 } 3730 3731 PushDefUseChildren(I, Worklist); 3732 } 3733} 3734 3735/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3736/// of the specified loop will execute. 3737ScalarEvolution::BackedgeTakenInfo 3738ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3739 SmallVector<BasicBlock *, 8> ExitingBlocks; 3740 L->getExitingBlocks(ExitingBlocks); 3741 3742 // Examine all exits and pick the most conservative values. 3743 const SCEV *BECount = getCouldNotCompute(); 3744 const SCEV *MaxBECount = getCouldNotCompute(); 3745 bool CouldNotComputeBECount = false; 3746 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3747 BackedgeTakenInfo NewBTI = 3748 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3749 3750 if (NewBTI.Exact == getCouldNotCompute()) { 3751 // We couldn't compute an exact value for this exit, so 3752 // we won't be able to compute an exact value for the loop. 3753 CouldNotComputeBECount = true; 3754 BECount = getCouldNotCompute(); 3755 } else if (!CouldNotComputeBECount) { 3756 if (BECount == getCouldNotCompute()) 3757 BECount = NewBTI.Exact; 3758 else 3759 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3760 } 3761 if (MaxBECount == getCouldNotCompute()) 3762 MaxBECount = NewBTI.Max; 3763 else if (NewBTI.Max != getCouldNotCompute()) 3764 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3765 } 3766 3767 return BackedgeTakenInfo(BECount, MaxBECount); 3768} 3769 3770/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3771/// of the specified loop will execute if it exits via the specified block. 3772ScalarEvolution::BackedgeTakenInfo 3773ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3774 BasicBlock *ExitingBlock) { 3775 3776 // Okay, we've chosen an exiting block. See what condition causes us to 3777 // exit at this block. 3778 // 3779 // FIXME: we should be able to handle switch instructions (with a single exit) 3780 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3781 if (ExitBr == 0) return getCouldNotCompute(); 3782 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3783 3784 // At this point, we know we have a conditional branch that determines whether 3785 // the loop is exited. However, we don't know if the branch is executed each 3786 // time through the loop. If not, then the execution count of the branch will 3787 // not be equal to the trip count of the loop. 3788 // 3789 // Currently we check for this by checking to see if the Exit branch goes to 3790 // the loop header. If so, we know it will always execute the same number of 3791 // times as the loop. We also handle the case where the exit block *is* the 3792 // loop header. This is common for un-rotated loops. 3793 // 3794 // If both of those tests fail, walk up the unique predecessor chain to the 3795 // header, stopping if there is an edge that doesn't exit the loop. If the 3796 // header is reached, the execution count of the branch will be equal to the 3797 // trip count of the loop. 3798 // 3799 // More extensive analysis could be done to handle more cases here. 3800 // 3801 if (ExitBr->getSuccessor(0) != L->getHeader() && 3802 ExitBr->getSuccessor(1) != L->getHeader() && 3803 ExitBr->getParent() != L->getHeader()) { 3804 // The simple checks failed, try climbing the unique predecessor chain 3805 // up to the header. 3806 bool Ok = false; 3807 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3808 BasicBlock *Pred = BB->getUniquePredecessor(); 3809 if (!Pred) 3810 return getCouldNotCompute(); 3811 TerminatorInst *PredTerm = Pred->getTerminator(); 3812 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3813 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3814 if (PredSucc == BB) 3815 continue; 3816 // If the predecessor has a successor that isn't BB and isn't 3817 // outside the loop, assume the worst. 3818 if (L->contains(PredSucc)) 3819 return getCouldNotCompute(); 3820 } 3821 if (Pred == L->getHeader()) { 3822 Ok = true; 3823 break; 3824 } 3825 BB = Pred; 3826 } 3827 if (!Ok) 3828 return getCouldNotCompute(); 3829 } 3830 3831 // Proceed to the next level to examine the exit condition expression. 3832 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3833 ExitBr->getSuccessor(0), 3834 ExitBr->getSuccessor(1)); 3835} 3836 3837/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3838/// backedge of the specified loop will execute if its exit condition 3839/// were a conditional branch of ExitCond, TBB, and FBB. 3840ScalarEvolution::BackedgeTakenInfo 3841ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3842 Value *ExitCond, 3843 BasicBlock *TBB, 3844 BasicBlock *FBB) { 3845 // Check if the controlling expression for this loop is an And or Or. 3846 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3847 if (BO->getOpcode() == Instruction::And) { 3848 // Recurse on the operands of the and. 3849 BackedgeTakenInfo BTI0 = 3850 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3851 BackedgeTakenInfo BTI1 = 3852 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3853 const SCEV *BECount = getCouldNotCompute(); 3854 const SCEV *MaxBECount = getCouldNotCompute(); 3855 if (L->contains(TBB)) { 3856 // Both conditions must be true for the loop to continue executing. 3857 // Choose the less conservative count. 3858 if (BTI0.Exact == getCouldNotCompute() || 3859 BTI1.Exact == getCouldNotCompute()) 3860 BECount = getCouldNotCompute(); 3861 else 3862 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3863 if (BTI0.Max == getCouldNotCompute()) 3864 MaxBECount = BTI1.Max; 3865 else if (BTI1.Max == getCouldNotCompute()) 3866 MaxBECount = BTI0.Max; 3867 else 3868 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3869 } else { 3870 // Both conditions must be true at the same time for the loop to exit. 3871 // For now, be conservative. 3872 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3873 if (BTI0.Max == BTI1.Max) 3874 MaxBECount = BTI0.Max; 3875 if (BTI0.Exact == BTI1.Exact) 3876 BECount = BTI0.Exact; 3877 } 3878 3879 return BackedgeTakenInfo(BECount, MaxBECount); 3880 } 3881 if (BO->getOpcode() == Instruction::Or) { 3882 // Recurse on the operands of the or. 3883 BackedgeTakenInfo BTI0 = 3884 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3885 BackedgeTakenInfo BTI1 = 3886 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3887 const SCEV *BECount = getCouldNotCompute(); 3888 const SCEV *MaxBECount = getCouldNotCompute(); 3889 if (L->contains(FBB)) { 3890 // Both conditions must be false for the loop to continue executing. 3891 // Choose the less conservative count. 3892 if (BTI0.Exact == getCouldNotCompute() || 3893 BTI1.Exact == getCouldNotCompute()) 3894 BECount = getCouldNotCompute(); 3895 else 3896 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3897 if (BTI0.Max == getCouldNotCompute()) 3898 MaxBECount = BTI1.Max; 3899 else if (BTI1.Max == getCouldNotCompute()) 3900 MaxBECount = BTI0.Max; 3901 else 3902 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3903 } else { 3904 // Both conditions must be false at the same time for the loop to exit. 3905 // For now, be conservative. 3906 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3907 if (BTI0.Max == BTI1.Max) 3908 MaxBECount = BTI0.Max; 3909 if (BTI0.Exact == BTI1.Exact) 3910 BECount = BTI0.Exact; 3911 } 3912 3913 return BackedgeTakenInfo(BECount, MaxBECount); 3914 } 3915 } 3916 3917 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3918 // Proceed to the next level to examine the icmp. 3919 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3920 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3921 3922 // Check for a constant condition. These are normally stripped out by 3923 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 3924 // preserve the CFG and is temporarily leaving constant conditions 3925 // in place. 3926 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 3927 if (L->contains(FBB) == !CI->getZExtValue()) 3928 // The backedge is always taken. 3929 return getCouldNotCompute(); 3930 else 3931 // The backedge is never taken. 3932 return getConstant(CI->getType(), 0); 3933 } 3934 3935 // If it's not an integer or pointer comparison then compute it the hard way. 3936 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3937} 3938 3939/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 3940/// backedge of the specified loop will execute if its exit condition 3941/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 3942ScalarEvolution::BackedgeTakenInfo 3943ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 3944 ICmpInst *ExitCond, 3945 BasicBlock *TBB, 3946 BasicBlock *FBB) { 3947 3948 // If the condition was exit on true, convert the condition to exit on false 3949 ICmpInst::Predicate Cond; 3950 if (!L->contains(FBB)) 3951 Cond = ExitCond->getPredicate(); 3952 else 3953 Cond = ExitCond->getInversePredicate(); 3954 3955 // Handle common loops like: for (X = "string"; *X; ++X) 3956 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 3957 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 3958 BackedgeTakenInfo ItCnt = 3959 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 3960 if (ItCnt.hasAnyInfo()) 3961 return ItCnt; 3962 } 3963 3964 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 3965 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 3966 3967 // Try to evaluate any dependencies out of the loop. 3968 LHS = getSCEVAtScope(LHS, L); 3969 RHS = getSCEVAtScope(RHS, L); 3970 3971 // At this point, we would like to compute how many iterations of the 3972 // loop the predicate will return true for these inputs. 3973 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 3974 // If there is a loop-invariant, force it into the RHS. 3975 std::swap(LHS, RHS); 3976 Cond = ICmpInst::getSwappedPredicate(Cond); 3977 } 3978 3979 // Simplify the operands before analyzing them. 3980 (void)SimplifyICmpOperands(Cond, LHS, RHS); 3981 3982 // If we have a comparison of a chrec against a constant, try to use value 3983 // ranges to answer this query. 3984 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 3985 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 3986 if (AddRec->getLoop() == L) { 3987 // Form the constant range. 3988 ConstantRange CompRange( 3989 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 3990 3991 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 3992 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 3993 } 3994 3995 switch (Cond) { 3996 case ICmpInst::ICMP_NE: { // while (X != Y) 3997 // Convert to: while (X-Y != 0) 3998 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L); 3999 if (BTI.hasAnyInfo()) return BTI; 4000 break; 4001 } 4002 case ICmpInst::ICMP_EQ: { // while (X == Y) 4003 // Convert to: while (X-Y == 0) 4004 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 4005 if (BTI.hasAnyInfo()) return BTI; 4006 break; 4007 } 4008 case ICmpInst::ICMP_SLT: { 4009 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 4010 if (BTI.hasAnyInfo()) return BTI; 4011 break; 4012 } 4013 case ICmpInst::ICMP_SGT: { 4014 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4015 getNotSCEV(RHS), L, true); 4016 if (BTI.hasAnyInfo()) return BTI; 4017 break; 4018 } 4019 case ICmpInst::ICMP_ULT: { 4020 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 4021 if (BTI.hasAnyInfo()) return BTI; 4022 break; 4023 } 4024 case ICmpInst::ICMP_UGT: { 4025 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4026 getNotSCEV(RHS), L, false); 4027 if (BTI.hasAnyInfo()) return BTI; 4028 break; 4029 } 4030 default: 4031#if 0 4032 dbgs() << "ComputeBackedgeTakenCount "; 4033 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 4034 dbgs() << "[unsigned] "; 4035 dbgs() << *LHS << " " 4036 << Instruction::getOpcodeName(Instruction::ICmp) 4037 << " " << *RHS << "\n"; 4038#endif 4039 break; 4040 } 4041 return 4042 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 4043} 4044 4045static ConstantInt * 4046EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 4047 ScalarEvolution &SE) { 4048 const SCEV *InVal = SE.getConstant(C); 4049 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 4050 assert(isa<SCEVConstant>(Val) && 4051 "Evaluation of SCEV at constant didn't fold correctly?"); 4052 return cast<SCEVConstant>(Val)->getValue(); 4053} 4054 4055/// GetAddressedElementFromGlobal - Given a global variable with an initializer 4056/// and a GEP expression (missing the pointer index) indexing into it, return 4057/// the addressed element of the initializer or null if the index expression is 4058/// invalid. 4059static Constant * 4060GetAddressedElementFromGlobal(GlobalVariable *GV, 4061 const std::vector<ConstantInt*> &Indices) { 4062 Constant *Init = GV->getInitializer(); 4063 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 4064 uint64_t Idx = Indices[i]->getZExtValue(); 4065 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 4066 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 4067 Init = cast<Constant>(CS->getOperand(Idx)); 4068 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 4069 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 4070 Init = cast<Constant>(CA->getOperand(Idx)); 4071 } else if (isa<ConstantAggregateZero>(Init)) { 4072 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 4073 assert(Idx < STy->getNumElements() && "Bad struct index!"); 4074 Init = Constant::getNullValue(STy->getElementType(Idx)); 4075 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 4076 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 4077 Init = Constant::getNullValue(ATy->getElementType()); 4078 } else { 4079 llvm_unreachable("Unknown constant aggregate type!"); 4080 } 4081 return 0; 4082 } else { 4083 return 0; // Unknown initializer type 4084 } 4085 } 4086 return Init; 4087} 4088 4089/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 4090/// 'icmp op load X, cst', try to see if we can compute the backedge 4091/// execution count. 4092ScalarEvolution::BackedgeTakenInfo 4093ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 4094 LoadInst *LI, 4095 Constant *RHS, 4096 const Loop *L, 4097 ICmpInst::Predicate predicate) { 4098 if (LI->isVolatile()) return getCouldNotCompute(); 4099 4100 // Check to see if the loaded pointer is a getelementptr of a global. 4101 // TODO: Use SCEV instead of manually grubbing with GEPs. 4102 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 4103 if (!GEP) return getCouldNotCompute(); 4104 4105 // Make sure that it is really a constant global we are gepping, with an 4106 // initializer, and make sure the first IDX is really 0. 4107 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 4108 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 4109 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 4110 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 4111 return getCouldNotCompute(); 4112 4113 // Okay, we allow one non-constant index into the GEP instruction. 4114 Value *VarIdx = 0; 4115 std::vector<ConstantInt*> Indexes; 4116 unsigned VarIdxNum = 0; 4117 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 4118 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 4119 Indexes.push_back(CI); 4120 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 4121 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 4122 VarIdx = GEP->getOperand(i); 4123 VarIdxNum = i-2; 4124 Indexes.push_back(0); 4125 } 4126 4127 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 4128 // Check to see if X is a loop variant variable value now. 4129 const SCEV *Idx = getSCEV(VarIdx); 4130 Idx = getSCEVAtScope(Idx, L); 4131 4132 // We can only recognize very limited forms of loop index expressions, in 4133 // particular, only affine AddRec's like {C1,+,C2}. 4134 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 4135 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 4136 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 4137 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 4138 return getCouldNotCompute(); 4139 4140 unsigned MaxSteps = MaxBruteForceIterations; 4141 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 4142 ConstantInt *ItCst = ConstantInt::get( 4143 cast<IntegerType>(IdxExpr->getType()), IterationNum); 4144 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 4145 4146 // Form the GEP offset. 4147 Indexes[VarIdxNum] = Val; 4148 4149 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 4150 if (Result == 0) break; // Cannot compute! 4151 4152 // Evaluate the condition for this iteration. 4153 Result = ConstantExpr::getICmp(predicate, Result, RHS); 4154 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 4155 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 4156#if 0 4157 dbgs() << "\n***\n*** Computed loop count " << *ItCst 4158 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 4159 << "***\n"; 4160#endif 4161 ++NumArrayLenItCounts; 4162 return getConstant(ItCst); // Found terminating iteration! 4163 } 4164 } 4165 return getCouldNotCompute(); 4166} 4167 4168 4169/// CanConstantFold - Return true if we can constant fold an instruction of the 4170/// specified type, assuming that all operands were constants. 4171static bool CanConstantFold(const Instruction *I) { 4172 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 4173 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 4174 return true; 4175 4176 if (const CallInst *CI = dyn_cast<CallInst>(I)) 4177 if (const Function *F = CI->getCalledFunction()) 4178 return canConstantFoldCallTo(F); 4179 return false; 4180} 4181 4182/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 4183/// in the loop that V is derived from. We allow arbitrary operations along the 4184/// way, but the operands of an operation must either be constants or a value 4185/// derived from a constant PHI. If this expression does not fit with these 4186/// constraints, return null. 4187static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 4188 // If this is not an instruction, or if this is an instruction outside of the 4189 // loop, it can't be derived from a loop PHI. 4190 Instruction *I = dyn_cast<Instruction>(V); 4191 if (I == 0 || !L->contains(I)) return 0; 4192 4193 if (PHINode *PN = dyn_cast<PHINode>(I)) { 4194 if (L->getHeader() == I->getParent()) 4195 return PN; 4196 else 4197 // We don't currently keep track of the control flow needed to evaluate 4198 // PHIs, so we cannot handle PHIs inside of loops. 4199 return 0; 4200 } 4201 4202 // If we won't be able to constant fold this expression even if the operands 4203 // are constants, return early. 4204 if (!CanConstantFold(I)) return 0; 4205 4206 // Otherwise, we can evaluate this instruction if all of its operands are 4207 // constant or derived from a PHI node themselves. 4208 PHINode *PHI = 0; 4209 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 4210 if (!isa<Constant>(I->getOperand(Op))) { 4211 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 4212 if (P == 0) return 0; // Not evolving from PHI 4213 if (PHI == 0) 4214 PHI = P; 4215 else if (PHI != P) 4216 return 0; // Evolving from multiple different PHIs. 4217 } 4218 4219 // This is a expression evolving from a constant PHI! 4220 return PHI; 4221} 4222 4223/// EvaluateExpression - Given an expression that passes the 4224/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4225/// in the loop has the value PHIVal. If we can't fold this expression for some 4226/// reason, return null. 4227static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 4228 const TargetData *TD) { 4229 if (isa<PHINode>(V)) return PHIVal; 4230 if (Constant *C = dyn_cast<Constant>(V)) return C; 4231 Instruction *I = cast<Instruction>(V); 4232 4233 std::vector<Constant*> Operands(I->getNumOperands()); 4234 4235 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4236 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 4237 if (Operands[i] == 0) return 0; 4238 } 4239 4240 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4241 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4242 Operands[1], TD); 4243 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4244 &Operands[0], Operands.size(), TD); 4245} 4246 4247/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4248/// in the header of its containing loop, we know the loop executes a 4249/// constant number of times, and the PHI node is just a recurrence 4250/// involving constants, fold it. 4251Constant * 4252ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4253 const APInt &BEs, 4254 const Loop *L) { 4255 std::map<PHINode*, Constant*>::iterator I = 4256 ConstantEvolutionLoopExitValue.find(PN); 4257 if (I != ConstantEvolutionLoopExitValue.end()) 4258 return I->second; 4259 4260 if (BEs.ugt(MaxBruteForceIterations)) 4261 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4262 4263 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4264 4265 // Since the loop is canonicalized, the PHI node must have two entries. One 4266 // entry must be a constant (coming in from outside of the loop), and the 4267 // second must be derived from the same PHI. 4268 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4269 Constant *StartCST = 4270 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4271 if (StartCST == 0) 4272 return RetVal = 0; // Must be a constant. 4273 4274 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4275 if (getConstantEvolvingPHI(BEValue, L) != PN && 4276 !isa<Constant>(BEValue)) 4277 return RetVal = 0; // Not derived from same PHI. 4278 4279 // Execute the loop symbolically to determine the exit value. 4280 if (BEs.getActiveBits() >= 32) 4281 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4282 4283 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4284 unsigned IterationNum = 0; 4285 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4286 if (IterationNum == NumIterations) 4287 return RetVal = PHIVal; // Got exit value! 4288 4289 // Compute the value of the PHI node for the next iteration. 4290 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4291 if (NextPHI == PHIVal) 4292 return RetVal = NextPHI; // Stopped evolving! 4293 if (NextPHI == 0) 4294 return 0; // Couldn't evaluate! 4295 PHIVal = NextPHI; 4296 } 4297} 4298 4299/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a 4300/// constant number of times (the condition evolves only from constants), 4301/// try to evaluate a few iterations of the loop until we get the exit 4302/// condition gets a value of ExitWhen (true or false). If we cannot 4303/// evaluate the trip count of the loop, return getCouldNotCompute(). 4304const SCEV * 4305ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 4306 Value *Cond, 4307 bool ExitWhen) { 4308 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4309 if (PN == 0) return getCouldNotCompute(); 4310 4311 // If the loop is canonicalized, the PHI will have exactly two entries. 4312 // That's the only form we support here. 4313 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 4314 4315 // One entry must be a constant (coming in from outside of the loop), and the 4316 // second must be derived from the same PHI. 4317 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4318 Constant *StartCST = 4319 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4320 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4321 4322 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4323 if (getConstantEvolvingPHI(BEValue, L) != PN && 4324 !isa<Constant>(BEValue)) 4325 return getCouldNotCompute(); // Not derived from same PHI. 4326 4327 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4328 // the loop symbolically to determine when the condition gets a value of 4329 // "ExitWhen". 4330 unsigned IterationNum = 0; 4331 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4332 for (Constant *PHIVal = StartCST; 4333 IterationNum != MaxIterations; ++IterationNum) { 4334 ConstantInt *CondVal = 4335 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4336 4337 // Couldn't symbolically evaluate. 4338 if (!CondVal) return getCouldNotCompute(); 4339 4340 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4341 ++NumBruteForceTripCountsComputed; 4342 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4343 } 4344 4345 // Compute the value of the PHI node for the next iteration. 4346 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4347 if (NextPHI == 0 || NextPHI == PHIVal) 4348 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4349 PHIVal = NextPHI; 4350 } 4351 4352 // Too many iterations were needed to evaluate. 4353 return getCouldNotCompute(); 4354} 4355 4356/// getSCEVAtScope - Return a SCEV expression for the specified value 4357/// at the specified scope in the program. The L value specifies a loop 4358/// nest to evaluate the expression at, where null is the top-level or a 4359/// specified loop is immediately inside of the loop. 4360/// 4361/// This method can be used to compute the exit value for a variable defined 4362/// in a loop by querying what the value will hold in the parent loop. 4363/// 4364/// In the case that a relevant loop exit value cannot be computed, the 4365/// original value V is returned. 4366const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4367 // Check to see if we've folded this expression at this loop before. 4368 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4369 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4370 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4371 if (!Pair.second) 4372 return Pair.first->second ? Pair.first->second : V; 4373 4374 // Otherwise compute it. 4375 const SCEV *C = computeSCEVAtScope(V, L); 4376 ValuesAtScopes[V][L] = C; 4377 return C; 4378} 4379 4380const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4381 if (isa<SCEVConstant>(V)) return V; 4382 4383 // If this instruction is evolved from a constant-evolving PHI, compute the 4384 // exit value from the loop without using SCEVs. 4385 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4386 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4387 const Loop *LI = (*this->LI)[I->getParent()]; 4388 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4389 if (PHINode *PN = dyn_cast<PHINode>(I)) 4390 if (PN->getParent() == LI->getHeader()) { 4391 // Okay, there is no closed form solution for the PHI node. Check 4392 // to see if the loop that contains it has a known backedge-taken 4393 // count. If so, we may be able to force computation of the exit 4394 // value. 4395 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4396 if (const SCEVConstant *BTCC = 4397 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4398 // Okay, we know how many times the containing loop executes. If 4399 // this is a constant evolving PHI node, get the final value at 4400 // the specified iteration number. 4401 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4402 BTCC->getValue()->getValue(), 4403 LI); 4404 if (RV) return getSCEV(RV); 4405 } 4406 } 4407 4408 // Okay, this is an expression that we cannot symbolically evaluate 4409 // into a SCEV. Check to see if it's possible to symbolically evaluate 4410 // the arguments into constants, and if so, try to constant propagate the 4411 // result. This is particularly useful for computing loop exit values. 4412 if (CanConstantFold(I)) { 4413 SmallVector<Constant *, 4> Operands; 4414 bool MadeImprovement = false; 4415 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4416 Value *Op = I->getOperand(i); 4417 if (Constant *C = dyn_cast<Constant>(Op)) { 4418 Operands.push_back(C); 4419 continue; 4420 } 4421 4422 // If any of the operands is non-constant and if they are 4423 // non-integer and non-pointer, don't even try to analyze them 4424 // with scev techniques. 4425 if (!isSCEVable(Op->getType())) 4426 return V; 4427 4428 const SCEV *OrigV = getSCEV(Op); 4429 const SCEV *OpV = getSCEVAtScope(OrigV, L); 4430 MadeImprovement |= OrigV != OpV; 4431 4432 Constant *C = 0; 4433 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 4434 C = SC->getValue(); 4435 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) 4436 C = dyn_cast<Constant>(SU->getValue()); 4437 if (!C) return V; 4438 if (C->getType() != Op->getType()) 4439 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4440 Op->getType(), 4441 false), 4442 C, Op->getType()); 4443 Operands.push_back(C); 4444 } 4445 4446 // Check to see if getSCEVAtScope actually made an improvement. 4447 if (MadeImprovement) { 4448 Constant *C = 0; 4449 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4450 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4451 Operands[0], Operands[1], TD); 4452 else 4453 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4454 &Operands[0], Operands.size(), TD); 4455 if (!C) return V; 4456 return getSCEV(C); 4457 } 4458 } 4459 } 4460 4461 // This is some other type of SCEVUnknown, just return it. 4462 return V; 4463 } 4464 4465 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4466 // Avoid performing the look-up in the common case where the specified 4467 // expression has no loop-variant portions. 4468 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4469 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4470 if (OpAtScope != Comm->getOperand(i)) { 4471 // Okay, at least one of these operands is loop variant but might be 4472 // foldable. Build a new instance of the folded commutative expression. 4473 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4474 Comm->op_begin()+i); 4475 NewOps.push_back(OpAtScope); 4476 4477 for (++i; i != e; ++i) { 4478 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4479 NewOps.push_back(OpAtScope); 4480 } 4481 if (isa<SCEVAddExpr>(Comm)) 4482 return getAddExpr(NewOps); 4483 if (isa<SCEVMulExpr>(Comm)) 4484 return getMulExpr(NewOps); 4485 if (isa<SCEVSMaxExpr>(Comm)) 4486 return getSMaxExpr(NewOps); 4487 if (isa<SCEVUMaxExpr>(Comm)) 4488 return getUMaxExpr(NewOps); 4489 llvm_unreachable("Unknown commutative SCEV type!"); 4490 } 4491 } 4492 // If we got here, all operands are loop invariant. 4493 return Comm; 4494 } 4495 4496 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4497 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4498 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4499 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4500 return Div; // must be loop invariant 4501 return getUDivExpr(LHS, RHS); 4502 } 4503 4504 // If this is a loop recurrence for a loop that does not contain L, then we 4505 // are dealing with the final value computed by the loop. 4506 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4507 // First, attempt to evaluate each operand. 4508 // Avoid performing the look-up in the common case where the specified 4509 // expression has no loop-variant portions. 4510 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 4511 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); 4512 if (OpAtScope == AddRec->getOperand(i)) 4513 continue; 4514 4515 // Okay, at least one of these operands is loop variant but might be 4516 // foldable. Build a new instance of the folded commutative expression. 4517 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(), 4518 AddRec->op_begin()+i); 4519 NewOps.push_back(OpAtScope); 4520 for (++i; i != e; ++i) 4521 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); 4522 4523 AddRec = cast<SCEVAddRecExpr>(getAddRecExpr(NewOps, AddRec->getLoop())); 4524 break; 4525 } 4526 4527 // If the scope is outside the addrec's loop, evaluate it by using the 4528 // loop exit value of the addrec. 4529 if (!AddRec->getLoop()->contains(L)) { 4530 // To evaluate this recurrence, we need to know how many times the AddRec 4531 // loop iterates. Compute this now. 4532 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4533 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4534 4535 // Then, evaluate the AddRec. 4536 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4537 } 4538 4539 return AddRec; 4540 } 4541 4542 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4543 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4544 if (Op == Cast->getOperand()) 4545 return Cast; // must be loop invariant 4546 return getZeroExtendExpr(Op, Cast->getType()); 4547 } 4548 4549 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4550 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4551 if (Op == Cast->getOperand()) 4552 return Cast; // must be loop invariant 4553 return getSignExtendExpr(Op, Cast->getType()); 4554 } 4555 4556 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4557 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4558 if (Op == Cast->getOperand()) 4559 return Cast; // must be loop invariant 4560 return getTruncateExpr(Op, Cast->getType()); 4561 } 4562 4563 llvm_unreachable("Unknown SCEV type!"); 4564 return 0; 4565} 4566 4567/// getSCEVAtScope - This is a convenience function which does 4568/// getSCEVAtScope(getSCEV(V), L). 4569const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4570 return getSCEVAtScope(getSCEV(V), L); 4571} 4572 4573/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4574/// following equation: 4575/// 4576/// A * X = B (mod N) 4577/// 4578/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4579/// A and B isn't important. 4580/// 4581/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4582static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4583 ScalarEvolution &SE) { 4584 uint32_t BW = A.getBitWidth(); 4585 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4586 assert(A != 0 && "A must be non-zero."); 4587 4588 // 1. D = gcd(A, N) 4589 // 4590 // The gcd of A and N may have only one prime factor: 2. The number of 4591 // trailing zeros in A is its multiplicity 4592 uint32_t Mult2 = A.countTrailingZeros(); 4593 // D = 2^Mult2 4594 4595 // 2. Check if B is divisible by D. 4596 // 4597 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4598 // is not less than multiplicity of this prime factor for D. 4599 if (B.countTrailingZeros() < Mult2) 4600 return SE.getCouldNotCompute(); 4601 4602 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4603 // modulo (N / D). 4604 // 4605 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4606 // bit width during computations. 4607 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4608 APInt Mod(BW + 1, 0); 4609 Mod.set(BW - Mult2); // Mod = N / D 4610 APInt I = AD.multiplicativeInverse(Mod); 4611 4612 // 4. Compute the minimum unsigned root of the equation: 4613 // I * (B / D) mod (N / D) 4614 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4615 4616 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4617 // bits. 4618 return SE.getConstant(Result.trunc(BW)); 4619} 4620 4621/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4622/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4623/// might be the same) or two SCEVCouldNotCompute objects. 4624/// 4625static std::pair<const SCEV *,const SCEV *> 4626SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4627 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4628 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4629 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4630 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4631 4632 // We currently can only solve this if the coefficients are constants. 4633 if (!LC || !MC || !NC) { 4634 const SCEV *CNC = SE.getCouldNotCompute(); 4635 return std::make_pair(CNC, CNC); 4636 } 4637 4638 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4639 const APInt &L = LC->getValue()->getValue(); 4640 const APInt &M = MC->getValue()->getValue(); 4641 const APInt &N = NC->getValue()->getValue(); 4642 APInt Two(BitWidth, 2); 4643 APInt Four(BitWidth, 4); 4644 4645 { 4646 using namespace APIntOps; 4647 const APInt& C = L; 4648 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4649 // The B coefficient is M-N/2 4650 APInt B(M); 4651 B -= sdiv(N,Two); 4652 4653 // The A coefficient is N/2 4654 APInt A(N.sdiv(Two)); 4655 4656 // Compute the B^2-4ac term. 4657 APInt SqrtTerm(B); 4658 SqrtTerm *= B; 4659 SqrtTerm -= Four * (A * C); 4660 4661 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4662 // integer value or else APInt::sqrt() will assert. 4663 APInt SqrtVal(SqrtTerm.sqrt()); 4664 4665 // Compute the two solutions for the quadratic formula. 4666 // The divisions must be performed as signed divisions. 4667 APInt NegB(-B); 4668 APInt TwoA( A << 1 ); 4669 if (TwoA.isMinValue()) { 4670 const SCEV *CNC = SE.getCouldNotCompute(); 4671 return std::make_pair(CNC, CNC); 4672 } 4673 4674 LLVMContext &Context = SE.getContext(); 4675 4676 ConstantInt *Solution1 = 4677 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4678 ConstantInt *Solution2 = 4679 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4680 4681 return std::make_pair(SE.getConstant(Solution1), 4682 SE.getConstant(Solution2)); 4683 } // end APIntOps namespace 4684} 4685 4686/// HowFarToZero - Return the number of times a backedge comparing the specified 4687/// value to zero will execute. If not computable, return CouldNotCompute. 4688ScalarEvolution::BackedgeTakenInfo 4689ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4690 // If the value is a constant 4691 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4692 // If the value is already zero, the branch will execute zero times. 4693 if (C->getValue()->isZero()) return C; 4694 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4695 } 4696 4697 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4698 if (!AddRec || AddRec->getLoop() != L) 4699 return getCouldNotCompute(); 4700 4701 if (AddRec->isAffine()) { 4702 // If this is an affine expression, the execution count of this branch is 4703 // the minimum unsigned root of the following equation: 4704 // 4705 // Start + Step*N = 0 (mod 2^BW) 4706 // 4707 // equivalent to: 4708 // 4709 // Step*N = -Start (mod 2^BW) 4710 // 4711 // where BW is the common bit width of Start and Step. 4712 4713 // Get the initial value for the loop. 4714 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4715 L->getParentLoop()); 4716 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4717 L->getParentLoop()); 4718 4719 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4720 // For now we handle only constant steps. 4721 4722 // First, handle unitary steps. 4723 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4724 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4725 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4726 return Start; // N = Start (as unsigned) 4727 4728 // Then, try to solve the above equation provided that Start is constant. 4729 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4730 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4731 -StartC->getValue()->getValue(), 4732 *this); 4733 } 4734 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 4735 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4736 // the quadratic equation to solve it. 4737 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4738 *this); 4739 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4740 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4741 if (R1) { 4742#if 0 4743 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 4744 << " sol#2: " << *R2 << "\n"; 4745#endif 4746 // Pick the smallest positive root value. 4747 if (ConstantInt *CB = 4748 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 4749 R1->getValue(), R2->getValue()))) { 4750 if (CB->getZExtValue() == false) 4751 std::swap(R1, R2); // R1 is the minimum root now. 4752 4753 // We can only use this value if the chrec ends up with an exact zero 4754 // value at this index. When solving for "X*X != 5", for example, we 4755 // should not accept a root of 2. 4756 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4757 if (Val->isZero()) 4758 return R1; // We found a quadratic root! 4759 } 4760 } 4761 } 4762 4763 return getCouldNotCompute(); 4764} 4765 4766/// HowFarToNonZero - Return the number of times a backedge checking the 4767/// specified value for nonzero will execute. If not computable, return 4768/// CouldNotCompute 4769ScalarEvolution::BackedgeTakenInfo 4770ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4771 // Loops that look like: while (X == 0) are very strange indeed. We don't 4772 // handle them yet except for the trivial case. This could be expanded in the 4773 // future as needed. 4774 4775 // If the value is a constant, check to see if it is known to be non-zero 4776 // already. If so, the backedge will execute zero times. 4777 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4778 if (!C->getValue()->isNullValue()) 4779 return getConstant(C->getType(), 0); 4780 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4781 } 4782 4783 // We could implement others, but I really doubt anyone writes loops like 4784 // this, and if they did, they would already be constant folded. 4785 return getCouldNotCompute(); 4786} 4787 4788/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4789/// (which may not be an immediate predecessor) which has exactly one 4790/// successor from which BB is reachable, or null if no such block is 4791/// found. 4792/// 4793std::pair<BasicBlock *, BasicBlock *> 4794ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4795 // If the block has a unique predecessor, then there is no path from the 4796 // predecessor to the block that does not go through the direct edge 4797 // from the predecessor to the block. 4798 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4799 return std::make_pair(Pred, BB); 4800 4801 // A loop's header is defined to be a block that dominates the loop. 4802 // If the header has a unique predecessor outside the loop, it must be 4803 // a block that has exactly one successor that can reach the loop. 4804 if (Loop *L = LI->getLoopFor(BB)) 4805 return std::make_pair(L->getLoopPredecessor(), L->getHeader()); 4806 4807 return std::pair<BasicBlock *, BasicBlock *>(); 4808} 4809 4810/// HasSameValue - SCEV structural equivalence is usually sufficient for 4811/// testing whether two expressions are equal, however for the purposes of 4812/// looking for a condition guarding a loop, it can be useful to be a little 4813/// more general, since a front-end may have replicated the controlling 4814/// expression. 4815/// 4816static bool HasSameValue(const SCEV *A, const SCEV *B) { 4817 // Quick check to see if they are the same SCEV. 4818 if (A == B) return true; 4819 4820 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4821 // two different instructions with the same value. Check for this case. 4822 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4823 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4824 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4825 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4826 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 4827 return true; 4828 4829 // Otherwise assume they may have a different value. 4830 return false; 4831} 4832 4833/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with 4834/// predicate Pred. Return true iff any changes were made. 4835/// 4836bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 4837 const SCEV *&LHS, const SCEV *&RHS) { 4838 bool Changed = false; 4839 4840 // Canonicalize a constant to the right side. 4841 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 4842 // Check for both operands constant. 4843 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 4844 if (ConstantExpr::getICmp(Pred, 4845 LHSC->getValue(), 4846 RHSC->getValue())->isNullValue()) 4847 goto trivially_false; 4848 else 4849 goto trivially_true; 4850 } 4851 // Otherwise swap the operands to put the constant on the right. 4852 std::swap(LHS, RHS); 4853 Pred = ICmpInst::getSwappedPredicate(Pred); 4854 Changed = true; 4855 } 4856 4857 // If we're comparing an addrec with a value which is loop-invariant in the 4858 // addrec's loop, put the addrec on the left. Also make a dominance check, 4859 // as both operands could be addrecs loop-invariant in each other's loop. 4860 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 4861 const Loop *L = AR->getLoop(); 4862 if (LHS->isLoopInvariant(L) && LHS->properlyDominates(L->getHeader(), DT)) { 4863 std::swap(LHS, RHS); 4864 Pred = ICmpInst::getSwappedPredicate(Pred); 4865 Changed = true; 4866 } 4867 } 4868 4869 // If there's a constant operand, canonicalize comparisons with boundary 4870 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 4871 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 4872 const APInt &RA = RC->getValue()->getValue(); 4873 switch (Pred) { 4874 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4875 case ICmpInst::ICMP_EQ: 4876 case ICmpInst::ICMP_NE: 4877 break; 4878 case ICmpInst::ICMP_UGE: 4879 if ((RA - 1).isMinValue()) { 4880 Pred = ICmpInst::ICMP_NE; 4881 RHS = getConstant(RA - 1); 4882 Changed = true; 4883 break; 4884 } 4885 if (RA.isMaxValue()) { 4886 Pred = ICmpInst::ICMP_EQ; 4887 Changed = true; 4888 break; 4889 } 4890 if (RA.isMinValue()) goto trivially_true; 4891 4892 Pred = ICmpInst::ICMP_UGT; 4893 RHS = getConstant(RA - 1); 4894 Changed = true; 4895 break; 4896 case ICmpInst::ICMP_ULE: 4897 if ((RA + 1).isMaxValue()) { 4898 Pred = ICmpInst::ICMP_NE; 4899 RHS = getConstant(RA + 1); 4900 Changed = true; 4901 break; 4902 } 4903 if (RA.isMinValue()) { 4904 Pred = ICmpInst::ICMP_EQ; 4905 Changed = true; 4906 break; 4907 } 4908 if (RA.isMaxValue()) goto trivially_true; 4909 4910 Pred = ICmpInst::ICMP_ULT; 4911 RHS = getConstant(RA + 1); 4912 Changed = true; 4913 break; 4914 case ICmpInst::ICMP_SGE: 4915 if ((RA - 1).isMinSignedValue()) { 4916 Pred = ICmpInst::ICMP_NE; 4917 RHS = getConstant(RA - 1); 4918 Changed = true; 4919 break; 4920 } 4921 if (RA.isMaxSignedValue()) { 4922 Pred = ICmpInst::ICMP_EQ; 4923 Changed = true; 4924 break; 4925 } 4926 if (RA.isMinSignedValue()) goto trivially_true; 4927 4928 Pred = ICmpInst::ICMP_SGT; 4929 RHS = getConstant(RA - 1); 4930 Changed = true; 4931 break; 4932 case ICmpInst::ICMP_SLE: 4933 if ((RA + 1).isMaxSignedValue()) { 4934 Pred = ICmpInst::ICMP_NE; 4935 RHS = getConstant(RA + 1); 4936 Changed = true; 4937 break; 4938 } 4939 if (RA.isMinSignedValue()) { 4940 Pred = ICmpInst::ICMP_EQ; 4941 Changed = true; 4942 break; 4943 } 4944 if (RA.isMaxSignedValue()) goto trivially_true; 4945 4946 Pred = ICmpInst::ICMP_SLT; 4947 RHS = getConstant(RA + 1); 4948 Changed = true; 4949 break; 4950 case ICmpInst::ICMP_UGT: 4951 if (RA.isMinValue()) { 4952 Pred = ICmpInst::ICMP_NE; 4953 Changed = true; 4954 break; 4955 } 4956 if ((RA + 1).isMaxValue()) { 4957 Pred = ICmpInst::ICMP_EQ; 4958 RHS = getConstant(RA + 1); 4959 Changed = true; 4960 break; 4961 } 4962 if (RA.isMaxValue()) goto trivially_false; 4963 break; 4964 case ICmpInst::ICMP_ULT: 4965 if (RA.isMaxValue()) { 4966 Pred = ICmpInst::ICMP_NE; 4967 Changed = true; 4968 break; 4969 } 4970 if ((RA - 1).isMinValue()) { 4971 Pred = ICmpInst::ICMP_EQ; 4972 RHS = getConstant(RA - 1); 4973 Changed = true; 4974 break; 4975 } 4976 if (RA.isMinValue()) goto trivially_false; 4977 break; 4978 case ICmpInst::ICMP_SGT: 4979 if (RA.isMinSignedValue()) { 4980 Pred = ICmpInst::ICMP_NE; 4981 Changed = true; 4982 break; 4983 } 4984 if ((RA + 1).isMaxSignedValue()) { 4985 Pred = ICmpInst::ICMP_EQ; 4986 RHS = getConstant(RA + 1); 4987 Changed = true; 4988 break; 4989 } 4990 if (RA.isMaxSignedValue()) goto trivially_false; 4991 break; 4992 case ICmpInst::ICMP_SLT: 4993 if (RA.isMaxSignedValue()) { 4994 Pred = ICmpInst::ICMP_NE; 4995 Changed = true; 4996 break; 4997 } 4998 if ((RA - 1).isMinSignedValue()) { 4999 Pred = ICmpInst::ICMP_EQ; 5000 RHS = getConstant(RA - 1); 5001 Changed = true; 5002 break; 5003 } 5004 if (RA.isMinSignedValue()) goto trivially_false; 5005 break; 5006 } 5007 } 5008 5009 // Check for obvious equality. 5010 if (HasSameValue(LHS, RHS)) { 5011 if (ICmpInst::isTrueWhenEqual(Pred)) 5012 goto trivially_true; 5013 if (ICmpInst::isFalseWhenEqual(Pred)) 5014 goto trivially_false; 5015 } 5016 5017 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 5018 // adding or subtracting 1 from one of the operands. 5019 switch (Pred) { 5020 case ICmpInst::ICMP_SLE: 5021 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { 5022 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5023 /*HasNUW=*/false, /*HasNSW=*/true); 5024 Pred = ICmpInst::ICMP_SLT; 5025 Changed = true; 5026 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { 5027 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5028 /*HasNUW=*/false, /*HasNSW=*/true); 5029 Pred = ICmpInst::ICMP_SLT; 5030 Changed = true; 5031 } 5032 break; 5033 case ICmpInst::ICMP_SGE: 5034 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { 5035 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5036 /*HasNUW=*/false, /*HasNSW=*/true); 5037 Pred = ICmpInst::ICMP_SGT; 5038 Changed = true; 5039 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { 5040 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5041 /*HasNUW=*/false, /*HasNSW=*/true); 5042 Pred = ICmpInst::ICMP_SGT; 5043 Changed = true; 5044 } 5045 break; 5046 case ICmpInst::ICMP_ULE: 5047 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { 5048 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5049 /*HasNUW=*/true, /*HasNSW=*/false); 5050 Pred = ICmpInst::ICMP_ULT; 5051 Changed = true; 5052 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { 5053 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5054 /*HasNUW=*/true, /*HasNSW=*/false); 5055 Pred = ICmpInst::ICMP_ULT; 5056 Changed = true; 5057 } 5058 break; 5059 case ICmpInst::ICMP_UGE: 5060 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { 5061 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5062 /*HasNUW=*/true, /*HasNSW=*/false); 5063 Pred = ICmpInst::ICMP_UGT; 5064 Changed = true; 5065 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { 5066 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5067 /*HasNUW=*/true, /*HasNSW=*/false); 5068 Pred = ICmpInst::ICMP_UGT; 5069 Changed = true; 5070 } 5071 break; 5072 default: 5073 break; 5074 } 5075 5076 // TODO: More simplifications are possible here. 5077 5078 return Changed; 5079 5080trivially_true: 5081 // Return 0 == 0. 5082 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0); 5083 Pred = ICmpInst::ICMP_EQ; 5084 return true; 5085 5086trivially_false: 5087 // Return 0 != 0. 5088 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0); 5089 Pred = ICmpInst::ICMP_NE; 5090 return true; 5091} 5092 5093bool ScalarEvolution::isKnownNegative(const SCEV *S) { 5094 return getSignedRange(S).getSignedMax().isNegative(); 5095} 5096 5097bool ScalarEvolution::isKnownPositive(const SCEV *S) { 5098 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 5099} 5100 5101bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 5102 return !getSignedRange(S).getSignedMin().isNegative(); 5103} 5104 5105bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 5106 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 5107} 5108 5109bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 5110 return isKnownNegative(S) || isKnownPositive(S); 5111} 5112 5113bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 5114 const SCEV *LHS, const SCEV *RHS) { 5115 // Canonicalize the inputs first. 5116 (void)SimplifyICmpOperands(Pred, LHS, RHS); 5117 5118 // If LHS or RHS is an addrec, check to see if the condition is true in 5119 // every iteration of the loop. 5120 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 5121 if (isLoopEntryGuardedByCond( 5122 AR->getLoop(), Pred, AR->getStart(), RHS) && 5123 isLoopBackedgeGuardedByCond( 5124 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS)) 5125 return true; 5126 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) 5127 if (isLoopEntryGuardedByCond( 5128 AR->getLoop(), Pred, LHS, AR->getStart()) && 5129 isLoopBackedgeGuardedByCond( 5130 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this))) 5131 return true; 5132 5133 // Otherwise see what can be done with known constant ranges. 5134 return isKnownPredicateWithRanges(Pred, LHS, RHS); 5135} 5136 5137bool 5138ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, 5139 const SCEV *LHS, const SCEV *RHS) { 5140 if (HasSameValue(LHS, RHS)) 5141 return ICmpInst::isTrueWhenEqual(Pred); 5142 5143 // This code is split out from isKnownPredicate because it is called from 5144 // within isLoopEntryGuardedByCond. 5145 switch (Pred) { 5146 default: 5147 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5148 break; 5149 case ICmpInst::ICMP_SGT: 5150 Pred = ICmpInst::ICMP_SLT; 5151 std::swap(LHS, RHS); 5152 case ICmpInst::ICMP_SLT: { 5153 ConstantRange LHSRange = getSignedRange(LHS); 5154 ConstantRange RHSRange = getSignedRange(RHS); 5155 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 5156 return true; 5157 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 5158 return false; 5159 break; 5160 } 5161 case ICmpInst::ICMP_SGE: 5162 Pred = ICmpInst::ICMP_SLE; 5163 std::swap(LHS, RHS); 5164 case ICmpInst::ICMP_SLE: { 5165 ConstantRange LHSRange = getSignedRange(LHS); 5166 ConstantRange RHSRange = getSignedRange(RHS); 5167 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 5168 return true; 5169 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 5170 return false; 5171 break; 5172 } 5173 case ICmpInst::ICMP_UGT: 5174 Pred = ICmpInst::ICMP_ULT; 5175 std::swap(LHS, RHS); 5176 case ICmpInst::ICMP_ULT: { 5177 ConstantRange LHSRange = getUnsignedRange(LHS); 5178 ConstantRange RHSRange = getUnsignedRange(RHS); 5179 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 5180 return true; 5181 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 5182 return false; 5183 break; 5184 } 5185 case ICmpInst::ICMP_UGE: 5186 Pred = ICmpInst::ICMP_ULE; 5187 std::swap(LHS, RHS); 5188 case ICmpInst::ICMP_ULE: { 5189 ConstantRange LHSRange = getUnsignedRange(LHS); 5190 ConstantRange RHSRange = getUnsignedRange(RHS); 5191 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 5192 return true; 5193 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 5194 return false; 5195 break; 5196 } 5197 case ICmpInst::ICMP_NE: { 5198 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 5199 return true; 5200 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 5201 return true; 5202 5203 const SCEV *Diff = getMinusSCEV(LHS, RHS); 5204 if (isKnownNonZero(Diff)) 5205 return true; 5206 break; 5207 } 5208 case ICmpInst::ICMP_EQ: 5209 // The check at the top of the function catches the case where 5210 // the values are known to be equal. 5211 break; 5212 } 5213 return false; 5214} 5215 5216/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 5217/// protected by a conditional between LHS and RHS. This is used to 5218/// to eliminate casts. 5219bool 5220ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 5221 ICmpInst::Predicate Pred, 5222 const SCEV *LHS, const SCEV *RHS) { 5223 // Interpret a null as meaning no loop, where there is obviously no guard 5224 // (interprocedural conditions notwithstanding). 5225 if (!L) return true; 5226 5227 BasicBlock *Latch = L->getLoopLatch(); 5228 if (!Latch) 5229 return false; 5230 5231 BranchInst *LoopContinuePredicate = 5232 dyn_cast<BranchInst>(Latch->getTerminator()); 5233 if (!LoopContinuePredicate || 5234 LoopContinuePredicate->isUnconditional()) 5235 return false; 5236 5237 return isImpliedCond(Pred, LHS, RHS, 5238 LoopContinuePredicate->getCondition(), 5239 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 5240} 5241 5242/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected 5243/// by a conditional between LHS and RHS. This is used to help avoid max 5244/// expressions in loop trip counts, and to eliminate casts. 5245bool 5246ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 5247 ICmpInst::Predicate Pred, 5248 const SCEV *LHS, const SCEV *RHS) { 5249 // Interpret a null as meaning no loop, where there is obviously no guard 5250 // (interprocedural conditions notwithstanding). 5251 if (!L) return false; 5252 5253 // Starting at the loop predecessor, climb up the predecessor chain, as long 5254 // as there are predecessors that can be found that have unique successors 5255 // leading to the original header. 5256 for (std::pair<BasicBlock *, BasicBlock *> 5257 Pair(L->getLoopPredecessor(), L->getHeader()); 5258 Pair.first; 5259 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 5260 5261 BranchInst *LoopEntryPredicate = 5262 dyn_cast<BranchInst>(Pair.first->getTerminator()); 5263 if (!LoopEntryPredicate || 5264 LoopEntryPredicate->isUnconditional()) 5265 continue; 5266 5267 if (isImpliedCond(Pred, LHS, RHS, 5268 LoopEntryPredicate->getCondition(), 5269 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 5270 return true; 5271 } 5272 5273 return false; 5274} 5275 5276/// isImpliedCond - Test whether the condition described by Pred, LHS, 5277/// and RHS is true whenever the given Cond value evaluates to true. 5278bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, 5279 const SCEV *LHS, const SCEV *RHS, 5280 Value *FoundCondValue, 5281 bool Inverse) { 5282 // Recursively handle And and Or conditions. 5283 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) { 5284 if (BO->getOpcode() == Instruction::And) { 5285 if (!Inverse) 5286 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5287 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5288 } else if (BO->getOpcode() == Instruction::Or) { 5289 if (Inverse) 5290 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5291 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5292 } 5293 } 5294 5295 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue); 5296 if (!ICI) return false; 5297 5298 // Bail if the ICmp's operands' types are wider than the needed type 5299 // before attempting to call getSCEV on them. This avoids infinite 5300 // recursion, since the analysis of widening casts can require loop 5301 // exit condition information for overflow checking, which would 5302 // lead back here. 5303 if (getTypeSizeInBits(LHS->getType()) < 5304 getTypeSizeInBits(ICI->getOperand(0)->getType())) 5305 return false; 5306 5307 // Now that we found a conditional branch that dominates the loop, check to 5308 // see if it is the comparison we are looking for. 5309 ICmpInst::Predicate FoundPred; 5310 if (Inverse) 5311 FoundPred = ICI->getInversePredicate(); 5312 else 5313 FoundPred = ICI->getPredicate(); 5314 5315 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 5316 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 5317 5318 // Balance the types. The case where FoundLHS' type is wider than 5319 // LHS' type is checked for above. 5320 if (getTypeSizeInBits(LHS->getType()) > 5321 getTypeSizeInBits(FoundLHS->getType())) { 5322 if (CmpInst::isSigned(Pred)) { 5323 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 5324 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 5325 } else { 5326 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 5327 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 5328 } 5329 } 5330 5331 // Canonicalize the query to match the way instcombine will have 5332 // canonicalized the comparison. 5333 if (SimplifyICmpOperands(Pred, LHS, RHS)) 5334 if (LHS == RHS) 5335 return CmpInst::isTrueWhenEqual(Pred); 5336 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 5337 if (FoundLHS == FoundRHS) 5338 return CmpInst::isFalseWhenEqual(Pred); 5339 5340 // Check to see if we can make the LHS or RHS match. 5341 if (LHS == FoundRHS || RHS == FoundLHS) { 5342 if (isa<SCEVConstant>(RHS)) { 5343 std::swap(FoundLHS, FoundRHS); 5344 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 5345 } else { 5346 std::swap(LHS, RHS); 5347 Pred = ICmpInst::getSwappedPredicate(Pred); 5348 } 5349 } 5350 5351 // Check whether the found predicate is the same as the desired predicate. 5352 if (FoundPred == Pred) 5353 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 5354 5355 // Check whether swapping the found predicate makes it the same as the 5356 // desired predicate. 5357 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 5358 if (isa<SCEVConstant>(RHS)) 5359 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 5360 else 5361 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 5362 RHS, LHS, FoundLHS, FoundRHS); 5363 } 5364 5365 // Check whether the actual condition is beyond sufficient. 5366 if (FoundPred == ICmpInst::ICMP_EQ) 5367 if (ICmpInst::isTrueWhenEqual(Pred)) 5368 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 5369 return true; 5370 if (Pred == ICmpInst::ICMP_NE) 5371 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 5372 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 5373 return true; 5374 5375 // Otherwise assume the worst. 5376 return false; 5377} 5378 5379/// isImpliedCondOperands - Test whether the condition described by Pred, 5380/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 5381/// and FoundRHS is true. 5382bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 5383 const SCEV *LHS, const SCEV *RHS, 5384 const SCEV *FoundLHS, 5385 const SCEV *FoundRHS) { 5386 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 5387 FoundLHS, FoundRHS) || 5388 // ~x < ~y --> x > y 5389 isImpliedCondOperandsHelper(Pred, LHS, RHS, 5390 getNotSCEV(FoundRHS), 5391 getNotSCEV(FoundLHS)); 5392} 5393 5394/// isImpliedCondOperandsHelper - Test whether the condition described by 5395/// Pred, LHS, and RHS is true whenever the condition described by Pred, 5396/// FoundLHS, and FoundRHS is true. 5397bool 5398ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 5399 const SCEV *LHS, const SCEV *RHS, 5400 const SCEV *FoundLHS, 5401 const SCEV *FoundRHS) { 5402 switch (Pred) { 5403 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5404 case ICmpInst::ICMP_EQ: 5405 case ICmpInst::ICMP_NE: 5406 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 5407 return true; 5408 break; 5409 case ICmpInst::ICMP_SLT: 5410 case ICmpInst::ICMP_SLE: 5411 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 5412 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 5413 return true; 5414 break; 5415 case ICmpInst::ICMP_SGT: 5416 case ICmpInst::ICMP_SGE: 5417 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 5418 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 5419 return true; 5420 break; 5421 case ICmpInst::ICMP_ULT: 5422 case ICmpInst::ICMP_ULE: 5423 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 5424 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 5425 return true; 5426 break; 5427 case ICmpInst::ICMP_UGT: 5428 case ICmpInst::ICMP_UGE: 5429 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 5430 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 5431 return true; 5432 break; 5433 } 5434 5435 return false; 5436} 5437 5438/// getBECount - Subtract the end and start values and divide by the step, 5439/// rounding up, to get the number of times the backedge is executed. Return 5440/// CouldNotCompute if an intermediate computation overflows. 5441const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 5442 const SCEV *End, 5443 const SCEV *Step, 5444 bool NoWrap) { 5445 assert(!isKnownNegative(Step) && 5446 "This code doesn't handle negative strides yet!"); 5447 5448 const Type *Ty = Start->getType(); 5449 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1); 5450 const SCEV *Diff = getMinusSCEV(End, Start); 5451 const SCEV *RoundUp = getAddExpr(Step, NegOne); 5452 5453 // Add an adjustment to the difference between End and Start so that 5454 // the division will effectively round up. 5455 const SCEV *Add = getAddExpr(Diff, RoundUp); 5456 5457 if (!NoWrap) { 5458 // Check Add for unsigned overflow. 5459 // TODO: More sophisticated things could be done here. 5460 const Type *WideTy = IntegerType::get(getContext(), 5461 getTypeSizeInBits(Ty) + 1); 5462 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5463 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5464 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5465 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5466 return getCouldNotCompute(); 5467 } 5468 5469 return getUDivExpr(Add, Step); 5470} 5471 5472/// HowManyLessThans - Return the number of times a backedge containing the 5473/// specified less-than comparison will execute. If not computable, return 5474/// CouldNotCompute. 5475ScalarEvolution::BackedgeTakenInfo 5476ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5477 const Loop *L, bool isSigned) { 5478 // Only handle: "ADDREC < LoopInvariant". 5479 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 5480 5481 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5482 if (!AddRec || AddRec->getLoop() != L) 5483 return getCouldNotCompute(); 5484 5485 // Check to see if we have a flag which makes analysis easy. 5486 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() : 5487 AddRec->hasNoUnsignedWrap(); 5488 5489 if (AddRec->isAffine()) { 5490 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5491 const SCEV *Step = AddRec->getStepRecurrence(*this); 5492 5493 if (Step->isZero()) 5494 return getCouldNotCompute(); 5495 if (Step->isOne()) { 5496 // With unit stride, the iteration never steps past the limit value. 5497 } else if (isKnownPositive(Step)) { 5498 // Test whether a positive iteration can step past the limit 5499 // value and past the maximum value for its type in a single step. 5500 // Note that it's not sufficient to check NoWrap here, because even 5501 // though the value after a wrap is undefined, it's not undefined 5502 // behavior, so if wrap does occur, the loop could either terminate or 5503 // loop infinitely, but in either case, the loop is guaranteed to 5504 // iterate at least until the iteration where the wrapping occurs. 5505 const SCEV *One = getConstant(Step->getType(), 1); 5506 if (isSigned) { 5507 APInt Max = APInt::getSignedMaxValue(BitWidth); 5508 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 5509 .slt(getSignedRange(RHS).getSignedMax())) 5510 return getCouldNotCompute(); 5511 } else { 5512 APInt Max = APInt::getMaxValue(BitWidth); 5513 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 5514 .ult(getUnsignedRange(RHS).getUnsignedMax())) 5515 return getCouldNotCompute(); 5516 } 5517 } else 5518 // TODO: Handle negative strides here and below. 5519 return getCouldNotCompute(); 5520 5521 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 5522 // m. So, we count the number of iterations in which {n,+,s} < m is true. 5523 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 5524 // treat m-n as signed nor unsigned due to overflow possibility. 5525 5526 // First, we get the value of the LHS in the first iteration: n 5527 const SCEV *Start = AddRec->getOperand(0); 5528 5529 // Determine the minimum constant start value. 5530 const SCEV *MinStart = getConstant(isSigned ? 5531 getSignedRange(Start).getSignedMin() : 5532 getUnsignedRange(Start).getUnsignedMin()); 5533 5534 // If we know that the condition is true in order to enter the loop, 5535 // then we know that it will run exactly (m-n)/s times. Otherwise, we 5536 // only know that it will execute (max(m,n)-n)/s times. In both cases, 5537 // the division must round up. 5538 const SCEV *End = RHS; 5539 if (!isLoopEntryGuardedByCond(L, 5540 isSigned ? ICmpInst::ICMP_SLT : 5541 ICmpInst::ICMP_ULT, 5542 getMinusSCEV(Start, Step), RHS)) 5543 End = isSigned ? getSMaxExpr(RHS, Start) 5544 : getUMaxExpr(RHS, Start); 5545 5546 // Determine the maximum constant end value. 5547 const SCEV *MaxEnd = getConstant(isSigned ? 5548 getSignedRange(End).getSignedMax() : 5549 getUnsignedRange(End).getUnsignedMax()); 5550 5551 // If MaxEnd is within a step of the maximum integer value in its type, 5552 // adjust it down to the minimum value which would produce the same effect. 5553 // This allows the subsequent ceiling division of (N+(step-1))/step to 5554 // compute the correct value. 5555 const SCEV *StepMinusOne = getMinusSCEV(Step, 5556 getConstant(Step->getType(), 1)); 5557 MaxEnd = isSigned ? 5558 getSMinExpr(MaxEnd, 5559 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 5560 StepMinusOne)) : 5561 getUMinExpr(MaxEnd, 5562 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 5563 StepMinusOne)); 5564 5565 // Finally, we subtract these two values and divide, rounding up, to get 5566 // the number of times the backedge is executed. 5567 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 5568 5569 // The maximum backedge count is similar, except using the minimum start 5570 // value and the maximum end value. 5571 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap); 5572 5573 return BackedgeTakenInfo(BECount, MaxBECount); 5574 } 5575 5576 return getCouldNotCompute(); 5577} 5578 5579/// getNumIterationsInRange - Return the number of iterations of this loop that 5580/// produce values in the specified constant range. Another way of looking at 5581/// this is that it returns the first iteration number where the value is not in 5582/// the condition, thus computing the exit count. If the iteration count can't 5583/// be computed, an instance of SCEVCouldNotCompute is returned. 5584const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 5585 ScalarEvolution &SE) const { 5586 if (Range.isFullSet()) // Infinite loop. 5587 return SE.getCouldNotCompute(); 5588 5589 // If the start is a non-zero constant, shift the range to simplify things. 5590 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 5591 if (!SC->getValue()->isZero()) { 5592 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 5593 Operands[0] = SE.getConstant(SC->getType(), 0); 5594 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 5595 if (const SCEVAddRecExpr *ShiftedAddRec = 5596 dyn_cast<SCEVAddRecExpr>(Shifted)) 5597 return ShiftedAddRec->getNumIterationsInRange( 5598 Range.subtract(SC->getValue()->getValue()), SE); 5599 // This is strange and shouldn't happen. 5600 return SE.getCouldNotCompute(); 5601 } 5602 5603 // The only time we can solve this is when we have all constant indices. 5604 // Otherwise, we cannot determine the overflow conditions. 5605 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 5606 if (!isa<SCEVConstant>(getOperand(i))) 5607 return SE.getCouldNotCompute(); 5608 5609 5610 // Okay at this point we know that all elements of the chrec are constants and 5611 // that the start element is zero. 5612 5613 // First check to see if the range contains zero. If not, the first 5614 // iteration exits. 5615 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 5616 if (!Range.contains(APInt(BitWidth, 0))) 5617 return SE.getConstant(getType(), 0); 5618 5619 if (isAffine()) { 5620 // If this is an affine expression then we have this situation: 5621 // Solve {0,+,A} in Range === Ax in Range 5622 5623 // We know that zero is in the range. If A is positive then we know that 5624 // the upper value of the range must be the first possible exit value. 5625 // If A is negative then the lower of the range is the last possible loop 5626 // value. Also note that we already checked for a full range. 5627 APInt One(BitWidth,1); 5628 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 5629 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 5630 5631 // The exit value should be (End+A)/A. 5632 APInt ExitVal = (End + A).udiv(A); 5633 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 5634 5635 // Evaluate at the exit value. If we really did fall out of the valid 5636 // range, then we computed our trip count, otherwise wrap around or other 5637 // things must have happened. 5638 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 5639 if (Range.contains(Val->getValue())) 5640 return SE.getCouldNotCompute(); // Something strange happened 5641 5642 // Ensure that the previous value is in the range. This is a sanity check. 5643 assert(Range.contains( 5644 EvaluateConstantChrecAtConstant(this, 5645 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 5646 "Linear scev computation is off in a bad way!"); 5647 return SE.getConstant(ExitValue); 5648 } else if (isQuadratic()) { 5649 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 5650 // quadratic equation to solve it. To do this, we must frame our problem in 5651 // terms of figuring out when zero is crossed, instead of when 5652 // Range.getUpper() is crossed. 5653 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 5654 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 5655 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 5656 5657 // Next, solve the constructed addrec 5658 std::pair<const SCEV *,const SCEV *> Roots = 5659 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 5660 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5661 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5662 if (R1) { 5663 // Pick the smallest positive root value. 5664 if (ConstantInt *CB = 5665 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 5666 R1->getValue(), R2->getValue()))) { 5667 if (CB->getZExtValue() == false) 5668 std::swap(R1, R2); // R1 is the minimum root now. 5669 5670 // Make sure the root is not off by one. The returned iteration should 5671 // not be in the range, but the previous one should be. When solving 5672 // for "X*X < 5", for example, we should not return a root of 2. 5673 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 5674 R1->getValue(), 5675 SE); 5676 if (Range.contains(R1Val->getValue())) { 5677 // The next iteration must be out of the range... 5678 ConstantInt *NextVal = 5679 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 5680 5681 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5682 if (!Range.contains(R1Val->getValue())) 5683 return SE.getConstant(NextVal); 5684 return SE.getCouldNotCompute(); // Something strange happened 5685 } 5686 5687 // If R1 was not in the range, then it is a good return value. Make 5688 // sure that R1-1 WAS in the range though, just in case. 5689 ConstantInt *NextVal = 5690 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 5691 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5692 if (Range.contains(R1Val->getValue())) 5693 return R1; 5694 return SE.getCouldNotCompute(); // Something strange happened 5695 } 5696 } 5697 } 5698 5699 return SE.getCouldNotCompute(); 5700} 5701 5702 5703 5704//===----------------------------------------------------------------------===// 5705// SCEVCallbackVH Class Implementation 5706//===----------------------------------------------------------------------===// 5707 5708void ScalarEvolution::SCEVCallbackVH::deleted() { 5709 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5710 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 5711 SE->ConstantEvolutionLoopExitValue.erase(PN); 5712 SE->Scalars.erase(getValPtr()); 5713 // this now dangles! 5714} 5715 5716void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 5717 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5718 5719 // Forget all the expressions associated with users of the old value, 5720 // so that future queries will recompute the expressions using the new 5721 // value. 5722 Value *Old = getValPtr(); 5723 SmallVector<User *, 16> Worklist; 5724 SmallPtrSet<User *, 8> Visited; 5725 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 5726 UI != UE; ++UI) 5727 Worklist.push_back(*UI); 5728 while (!Worklist.empty()) { 5729 User *U = Worklist.pop_back_val(); 5730 // Deleting the Old value will cause this to dangle. Postpone 5731 // that until everything else is done. 5732 if (U == Old) 5733 continue; 5734 if (!Visited.insert(U)) 5735 continue; 5736 if (PHINode *PN = dyn_cast<PHINode>(U)) 5737 SE->ConstantEvolutionLoopExitValue.erase(PN); 5738 SE->Scalars.erase(U); 5739 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 5740 UI != UE; ++UI) 5741 Worklist.push_back(*UI); 5742 } 5743 // Delete the Old value. 5744 if (PHINode *PN = dyn_cast<PHINode>(Old)) 5745 SE->ConstantEvolutionLoopExitValue.erase(PN); 5746 SE->Scalars.erase(Old); 5747 // this now dangles! 5748} 5749 5750ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 5751 : CallbackVH(V), SE(se) {} 5752 5753//===----------------------------------------------------------------------===// 5754// ScalarEvolution Class Implementation 5755//===----------------------------------------------------------------------===// 5756 5757ScalarEvolution::ScalarEvolution() 5758 : FunctionPass(ID), FirstUnknown(0) { 5759} 5760 5761bool ScalarEvolution::runOnFunction(Function &F) { 5762 this->F = &F; 5763 LI = &getAnalysis<LoopInfo>(); 5764 TD = getAnalysisIfAvailable<TargetData>(); 5765 DT = &getAnalysis<DominatorTree>(); 5766 return false; 5767} 5768 5769void ScalarEvolution::releaseMemory() { 5770 // Iterate through all the SCEVUnknown instances and call their 5771 // destructors, so that they release their references to their values. 5772 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next) 5773 U->~SCEVUnknown(); 5774 FirstUnknown = 0; 5775 5776 Scalars.clear(); 5777 BackedgeTakenCounts.clear(); 5778 ConstantEvolutionLoopExitValue.clear(); 5779 ValuesAtScopes.clear(); 5780 UniqueSCEVs.clear(); 5781 SCEVAllocator.Reset(); 5782} 5783 5784void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 5785 AU.setPreservesAll(); 5786 AU.addRequiredTransitive<LoopInfo>(); 5787 AU.addRequiredTransitive<DominatorTree>(); 5788} 5789 5790bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 5791 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 5792} 5793 5794static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 5795 const Loop *L) { 5796 // Print all inner loops first 5797 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 5798 PrintLoopInfo(OS, SE, *I); 5799 5800 OS << "Loop "; 5801 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5802 OS << ": "; 5803 5804 SmallVector<BasicBlock *, 8> ExitBlocks; 5805 L->getExitBlocks(ExitBlocks); 5806 if (ExitBlocks.size() != 1) 5807 OS << "<multiple exits> "; 5808 5809 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 5810 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 5811 } else { 5812 OS << "Unpredictable backedge-taken count. "; 5813 } 5814 5815 OS << "\n" 5816 "Loop "; 5817 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5818 OS << ": "; 5819 5820 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 5821 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 5822 } else { 5823 OS << "Unpredictable max backedge-taken count. "; 5824 } 5825 5826 OS << "\n"; 5827} 5828 5829void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 5830 // ScalarEvolution's implementation of the print method is to print 5831 // out SCEV values of all instructions that are interesting. Doing 5832 // this potentially causes it to create new SCEV objects though, 5833 // which technically conflicts with the const qualifier. This isn't 5834 // observable from outside the class though, so casting away the 5835 // const isn't dangerous. 5836 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 5837 5838 OS << "Classifying expressions for: "; 5839 WriteAsOperand(OS, F, /*PrintType=*/false); 5840 OS << "\n"; 5841 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 5842 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { 5843 OS << *I << '\n'; 5844 OS << " --> "; 5845 const SCEV *SV = SE.getSCEV(&*I); 5846 SV->print(OS); 5847 5848 const Loop *L = LI->getLoopFor((*I).getParent()); 5849 5850 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 5851 if (AtUse != SV) { 5852 OS << " --> "; 5853 AtUse->print(OS); 5854 } 5855 5856 if (L) { 5857 OS << "\t\t" "Exits: "; 5858 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 5859 if (!ExitValue->isLoopInvariant(L)) { 5860 OS << "<<Unknown>>"; 5861 } else { 5862 OS << *ExitValue; 5863 } 5864 } 5865 5866 OS << "\n"; 5867 } 5868 5869 OS << "Determining loop execution counts for: "; 5870 WriteAsOperand(OS, F, /*PrintType=*/false); 5871 OS << "\n"; 5872 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 5873 PrintLoopInfo(OS, &SE, *I); 5874} 5875 5876